LMFDB - Embedded newform 570.6.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.a (trivial)

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:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 26355x^{2} - 7203x + 128450070 $ x^4 - x^3 - 26355x^2 - 7203x + 128450070
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-140.053$ of defining polynomial
Character	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -34.2967 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -34.2967 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +148.750 q^{11} +144.000 q^{12} +1140.54 q^{13} +137.187 q^{14} -225.000 q^{15} +256.000 q^{16} +1864.37 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -308.670 q^{21} -595.000 q^{22} +356.293 q^{23} -576.000 q^{24} +625.000 q^{25} -4562.17 q^{26} +729.000 q^{27} -548.747 q^{28} -5821.97 q^{29} +900.000 q^{30} -10419.4 q^{31} -1024.00 q^{32} +1338.75 q^{33} -7457.50 q^{34} +857.417 q^{35} +1296.00 q^{36} +6390.89 q^{37} +1444.00 q^{38} +10264.9 q^{39} +1600.00 q^{40} +3876.23 q^{41} +1234.68 q^{42} +23107.7 q^{43} +2380.00 q^{44} -2025.00 q^{45} -1425.17 q^{46} -24172.3 q^{47} +2304.00 q^{48} -15630.7 q^{49} -2500.00 q^{50} +16779.4 q^{51} +18248.7 q^{52} -24781.8 q^{53} -2916.00 q^{54} -3718.75 q^{55} +2194.99 q^{56} -3249.00 q^{57} +23287.9 q^{58} +29282.3 q^{59} -3600.00 q^{60} +559.719 q^{61} +41677.7 q^{62} -2778.03 q^{63} +4096.00 q^{64} -28513.6 q^{65} -5355.00 q^{66} +34672.3 q^{67} +29830.0 q^{68} +3206.64 q^{69} -3429.67 q^{70} +63980.4 q^{71} -5184.00 q^{72} +15833.5 q^{73} -25563.6 q^{74} +5625.00 q^{75} -5776.00 q^{76} -5101.63 q^{77} -41059.6 q^{78} +72369.2 q^{79} -6400.00 q^{80} +6561.00 q^{81} -15504.9 q^{82} -70180.7 q^{83} -4938.72 q^{84} -46609.3 q^{85} -92431.0 q^{86} -52397.7 q^{87} -9520.01 q^{88} +72450.1 q^{89} +8100.00 q^{90} -39116.8 q^{91} +5700.69 q^{92} -93774.8 q^{93} +96689.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +7227.34 q^{97} +62523.0 q^{98} +12048.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 472 q^{11} + 576 q^{12} - 482 q^{13} - 104 q^{14} - 900 q^{15} + 1024 q^{16} + 1816 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} + 234 q^{21} + 1888 q^{22} - 418 q^{23} - 2304 q^{24} + 2500 q^{25} + 1928 q^{26} + 2916 q^{27} + 416 q^{28} - 10396 q^{29} + 3600 q^{30} + 528 q^{31} - 4096 q^{32} - 4248 q^{33} - 7264 q^{34} - 650 q^{35} + 5184 q^{36} + 5774 q^{37} + 5776 q^{38} - 4338 q^{39} + 6400 q^{40} + 9620 q^{41} - 936 q^{42} + 21098 q^{43} - 7552 q^{44} - 8100 q^{45} + 1672 q^{46} - 18858 q^{47} + 9216 q^{48} + 2148 q^{49} - 10000 q^{50} + 16344 q^{51} - 7712 q^{52} + 822 q^{53} - 11664 q^{54} + 11800 q^{55} - 1664 q^{56} - 12996 q^{57} + 41584 q^{58} + 28672 q^{59} - 14400 q^{60} + 77748 q^{61} - 2112 q^{62} + 2106 q^{63} + 16384 q^{64} + 12050 q^{65} + 16992 q^{66} + 82400 q^{67} + 29056 q^{68} - 3762 q^{69} + 2600 q^{70} + 928 q^{71} - 20736 q^{72} + 121100 q^{73} - 23096 q^{74} + 22500 q^{75} - 23104 q^{76} - 120220 q^{77} + 17352 q^{78} + 144284 q^{79} - 25600 q^{80} + 26244 q^{81} - 38480 q^{82} - 6082 q^{83} + 3744 q^{84} - 45400 q^{85} - 84392 q^{86} - 93564 q^{87} + 30208 q^{88} + 43260 q^{89} + 32400 q^{90} + 135148 q^{91} - 6688 q^{92} + 4752 q^{93} + 75432 q^{94} + 36100 q^{95} - 36864 q^{96} - 6862 q^{97} - 8592 q^{98} - 38232 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 - 472 * q^11 + 576 * q^12 - 482 * q^13 - 104 * q^14 - 900 * q^15 + 1024 * q^16 + 1816 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 + 234 * q^21 + 1888 * q^22 - 418 * q^23 - 2304 * q^24 + 2500 * q^25 + 1928 * q^26 + 2916 * q^27 + 416 * q^28 - 10396 * q^29 + 3600 * q^30 + 528 * q^31 - 4096 * q^32 - 4248 * q^33 - 7264 * q^34 - 650 * q^35 + 5184 * q^36 + 5774 * q^37 + 5776 * q^38 - 4338 * q^39 + 6400 * q^40 + 9620 * q^41 - 936 * q^42 + 21098 * q^43 - 7552 * q^44 - 8100 * q^45 + 1672 * q^46 - 18858 * q^47 + 9216 * q^48 + 2148 * q^49 - 10000 * q^50 + 16344 * q^51 - 7712 * q^52 + 822 * q^53 - 11664 * q^54 + 11800 * q^55 - 1664 * q^56 - 12996 * q^57 + 41584 * q^58 + 28672 * q^59 - 14400 * q^60 + 77748 * q^61 - 2112 * q^62 + 2106 * q^63 + 16384 * q^64 + 12050 * q^65 + 16992 * q^66 + 82400 * q^67 + 29056 * q^68 - 3762 * q^69 + 2600 * q^70 + 928 * q^71 - 20736 * q^72 + 121100 * q^73 - 23096 * q^74 + 22500 * q^75 - 23104 * q^76 - 120220 * q^77 + 17352 * q^78 + 144284 * q^79 - 25600 * q^80 + 26244 * q^81 - 38480 * q^82 - 6082 * q^83 + 3744 * q^84 - 45400 * q^85 - 84392 * q^86 - 93564 * q^87 + 30208 * q^88 + 43260 * q^89 + 32400 * q^90 + 135148 * q^91 - 6688 * q^92 + 4752 * q^93 + 75432 * q^94 + 36100 * q^95 - 36864 * q^96 - 6862 * q^97 - 8592 * q^98 - 38232 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−36.0000	−0.408248
$7$	−34.2967	−0.264549	−0.132275	−	0.991213i	$-0.542228\pi$
$7$	−34.2967	−0.264549	−0.132275	+	0.991213i	$0.542228\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	148.750	0.370660	0.185330	−	0.982676i	$-0.440665\pi$
$11$	148.750	0.370660	0.185330	+	0.982676i	$0.440665\pi$
$12$	144.000	0.288675
$13$	1140.54	1.87177	0.935887	−	0.352300i	$-0.114600\pi$
$13$	1140.54	1.87177	0.935887	+	0.352300i	$0.114600\pi$
$14$	137.187	0.187065
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	1864.37	1.56463	0.782313	−	0.622885i	$-0.214040\pi$
$17$	1864.37	1.56463	0.782313	+	0.622885i	$0.214040\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−400.000	−0.223607
$21$	−308.670	−0.152738
$22$	−595.000	−0.262096
$23$	356.293	0.140439	0.0702196	−	0.997532i	$-0.477630\pi$
$23$	356.293	0.140439	0.0702196	+	0.997532i	$0.477630\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−4562.17	−1.32354
$27$	729.000	0.192450
$28$	−548.747	−0.132275
$29$	−5821.97	−1.28551	−0.642754	−	0.766072i	$-0.722208\pi$
$29$	−5821.97	−1.28551	−0.642754	+	0.766072i	$0.722208\pi$
$30$	900.000	0.182574
$31$	−10419.4	−1.94733	−0.973665	−	0.227983i	$-0.926787\pi$
$31$	−10419.4	−1.94733	−0.973665	+	0.227983i	$0.926787\pi$
$32$	−1024.00	−0.176777
$33$	1338.75	0.214001
$34$	−7457.50	−1.10636
$35$	857.417	0.118310
$36$	1296.00	0.166667
$37$	6390.89	0.767462	0.383731	−	0.923445i	$-0.374639\pi$
$37$	6390.89	0.767462	0.383731	+	0.923445i	$0.374639\pi$
$38$	1444.00	0.162221
$39$	10264.9	1.08067
$40$	1600.00	0.158114
$41$	3876.23	0.360122	0.180061	−	0.983655i	$-0.442370\pi$
$41$	3876.23	0.360122	0.180061	+	0.983655i	$0.442370\pi$
$42$	1234.68	0.108002
$43$	23107.7	1.90584	0.952920	−	0.303223i	$-0.0980626\pi$
$43$	23107.7	1.90584	0.952920	+	0.303223i	$0.0980626\pi$
$44$	2380.00	0.185330
$45$	−2025.00	−0.149071
$46$	−1425.17	−0.0993055
$47$	−24172.3	−1.59615	−0.798075	−	0.602558i	$-0.794148\pi$
$47$	−24172.3	−1.59615	−0.798075	+	0.602558i	$0.794148\pi$
$48$	2304.00	0.144338
$49$	−15630.7	−0.930014
$50$	−2500.00	−0.141421
$51$	16779.4	0.903338
$52$	18248.7	0.935887
$53$	−24781.8	−1.21184	−0.605918	−	0.795527i	$-0.707194\pi$
$53$	−24781.8	−1.21184	−0.605918	+	0.795527i	$0.707194\pi$
$54$	−2916.00	−0.136083
$55$	−3718.75	−0.165764
$56$	2194.99	0.0935323
$57$	−3249.00	−0.132453
$58$	23287.9	0.908992
$59$	29282.3	1.09515	0.547576	−	0.836756i	$-0.315551\pi$
$59$	29282.3	1.09515	0.547576	+	0.836756i	$0.315551\pi$
$60$	−3600.00	−0.129099
$61$	559.719	0.0192595	0.00962976	−	0.999954i	$-0.496935\pi$
$61$	559.719	0.0192595	0.00962976	+	0.999954i	$0.496935\pi$
$62$	41677.7	1.37697
$63$	−2778.03	−0.0881831
$64$	4096.00	0.125000
$65$	−28513.6	−0.837083
$66$	−5355.00	−0.151321
$67$	34672.3	0.943618	0.471809	−	0.881701i	$-0.343601\pi$
$67$	34672.3	0.943618	0.471809	+	0.881701i	$0.343601\pi$
$68$	29830.0	0.782313
$69$	3206.64	0.0810826
$70$	−3429.67	−0.0836579
$71$	63980.4	1.50626	0.753132	−	0.657869i	$-0.228542\pi$
$71$	63980.4	1.50626	0.753132	+	0.657869i	$0.228542\pi$
$72$	−5184.00	−0.117851
$73$	15833.5	0.347752	0.173876	−	0.984768i	$-0.444371\pi$
$73$	15833.5	0.347752	0.173876	+	0.984768i	$0.444371\pi$
$74$	−25563.6	−0.542678
$75$	5625.00	0.115470
$76$	−5776.00	−0.114708
$77$	−5101.63	−0.0980578
$78$	−41059.6	−0.764149
$79$	72369.2	1.30463	0.652313	−	0.757950i	$-0.273799\pi$
$79$	72369.2	1.30463	0.652313	+	0.757950i	$0.273799\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−15504.9	−0.254645
$83$	−70180.7	−1.11821	−0.559104	−	0.829098i	$-0.688855\pi$
$83$	−70180.7	−1.11821	−0.559104	+	0.829098i	$0.688855\pi$
$84$	−4938.72	−0.0763688
$85$	−46609.3	−0.699722
$86$	−92431.0	−1.34763
$87$	−52397.7	−0.742189
$88$	−9520.01	−0.131048
$89$	72450.1	0.969536	0.484768	−	0.874643i	$-0.338904\pi$
$89$	72450.1	0.969536	0.484768	+	0.874643i	$0.338904\pi$
$90$	8100.00	0.105409
$91$	−39116.8	−0.495177
$92$	5700.69	0.0702196
$93$	−93774.8	−1.12429
$94$	96689.3	1.12865
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	7227.34	0.0779919	0.0389959	−	0.999239i	$-0.487584\pi$
$97$	7227.34	0.0779919	0.0389959	+	0.999239i	$0.487584\pi$
$98$	62523.0	0.657619
$99$	12048.8	0.123553
$100$	10000.0	0.100000
$101$	−57122.3	−0.557189	−0.278594	−	0.960409i	$-0.589869\pi$
$101$	−57122.3	−0.557189	−0.278594	+	0.960409i	$0.589869\pi$
$102$	−67117.5	−0.638756
$103$	158486.	1.47197	0.735985	−	0.676998i	$-0.236719\pi$
$103$	158486.	1.47197	0.735985	+	0.676998i	$0.236719\pi$
$104$	−72994.8	−0.661772
$105$	7716.75	0.0683064
$106$	99127.3	0.856897
$107$	21702.8	0.183255	0.0916276	−	0.995793i	$-0.470793\pi$
$107$	21702.8	0.183255	0.0916276	+	0.995793i	$0.470793\pi$
$108$	11664.0	0.0962250
$109$	−39796.2	−0.320831	−0.160415	−	0.987050i	$-0.551283\pi$
$109$	−39796.2	−0.320831	−0.160415	+	0.987050i	$0.551283\pi$
$110$	14875.0	0.117213
$111$	57518.0	0.443095
$112$	−8779.95	−0.0661374
$113$	10111.2	0.0744913	0.0372456	−	0.999306i	$-0.488142\pi$
$113$	10111.2	0.0744913	0.0372456	+	0.999306i	$0.488142\pi$
$114$	12996.0	0.0936586
$115$	−8907.33	−0.0628063
$116$	−93151.5	−0.642754
$117$	92384.0	0.623925
$118$	−117129.	−0.774390
$119$	−63941.8	−0.413921
$120$	14400.0	0.0912871
$121$	−138924.	−0.862611
$122$	−2238.88	−0.0136185
$123$	34886.0	0.207917
$124$	−166711.	−0.973665
$125$	−15625.0	−0.0894427
$126$	11112.1	0.0623549
$127$	−202642.	−1.11486	−0.557431	−	0.830224i	$-0.688213\pi$
$127$	−202642.	−1.11486	−0.557431	+	0.830224i	$0.688213\pi$
$128$	−16384.0	−0.0883883
$129$	207970.	1.10034
$130$	114054.	0.591907
$131$	91463.8	0.465662	0.232831	−	0.972517i	$-0.425201\pi$
$131$	91463.8	0.465662	0.232831	+	0.972517i	$0.425201\pi$
$132$	21420.0	0.107000
$133$	12381.1	0.0606918
$134$	−138689.	−0.667239
$135$	−18225.0	−0.0860663
$136$	−119320.	−0.553179
$137$	288820.	1.31470	0.657348	−	0.753587i	$-0.271678\pi$
$137$	288820.	1.31470	0.657348	+	0.753587i	$0.271678\pi$
$138$	−12826.6	−0.0573340
$139$	386148.	1.69518	0.847592	−	0.530649i	$-0.178052\pi$
$139$	386148.	1.69518	0.847592	+	0.530649i	$0.178052\pi$
$140$	13718.7	0.0591550
$141$	−217551.	−0.921537
$142$	−255922.	−1.06509
$143$	169656.	0.693792
$144$	20736.0	0.0833333
$145$	145549.	0.574897
$146$	−63334.0	−0.245898
$147$	−140677.	−0.536944
$148$	102254.	0.383731
$149$	−8960.62	−0.0330653	−0.0165326	−	0.999863i	$-0.505263\pi$
$149$	−8960.62	−0.0330653	−0.0165326	+	0.999863i	$0.505263\pi$
$150$	−22500.0	−0.0816497
$151$	404681.	1.44434	0.722172	−	0.691714i	$-0.243144\pi$
$151$	404681.	1.44434	0.722172	+	0.691714i	$0.243144\pi$
$152$	23104.0	0.0811107
$153$	151014.	0.521542
$154$	20406.5	0.0693374
$155$	260486.	0.870873
$156$	164238.	0.540335
$157$	−426481.	−1.38086	−0.690431	−	0.723398i	$-0.742579\pi$
$157$	−426481.	−1.38086	−0.690431	+	0.723398i	$0.742579\pi$
$158$	−289477.	−0.922510
$159$	−223037.	−0.699654
$160$	25600.0	0.0790569
$161$	−12219.7	−0.0371531
$162$	−26244.0	−0.0785674
$163$	510951.	1.50630	0.753148	−	0.657851i	$-0.228534\pi$
$163$	510951.	1.50630	0.753148	+	0.657851i	$0.228534\pi$
$164$	62019.6	0.180061
$165$	−33468.8	−0.0957040
$166$	280723.	0.790692
$167$	−398804.	−1.10654	−0.553271	−	0.833001i	$-0.686621\pi$
$167$	−398804.	−1.10654	−0.553271	+	0.833001i	$0.686621\pi$
$168$	19754.9	0.0540009
$169$	929547.	2.50354
$170$	186437.	0.494778
$171$	−29241.0	−0.0764719
$172$	369724.	0.952920
$173$	−619744.	−1.57434	−0.787168	−	0.616739i	$-0.788453\pi$
$173$	−619744.	−1.57434	−0.787168	+	0.616739i	$0.788453\pi$
$174$	209591.	0.524807
$175$	−21435.4	−0.0529099
$176$	38080.0	0.0926650
$177$	263540.	0.632286
$178$	−289800.	−0.685565
$179$	21840.6	0.0509487	0.0254743	−	0.999675i	$-0.491890\pi$
$179$	21840.6	0.0509487	0.0254743	+	0.999675i	$0.491890\pi$
$180$	−32400.0	−0.0745356
$181$	22711.9	0.0515297	0.0257649	−	0.999668i	$-0.491798\pi$
$181$	22711.9	0.0515297	0.0257649	+	0.999668i	$0.491798\pi$
$182$	156467.	0.350143
$183$	5037.47	0.0111195
$184$	−22802.8	−0.0496527
$185$	−159772.	−0.343220
$186$	375099.	0.794994
$187$	277326.	0.579944
$188$	−386757.	−0.798075
$189$	−25002.3	−0.0509126
$190$	−36100.0	−0.0725476
$191$	153640.	0.304734	0.152367	−	0.988324i	$-0.451310\pi$
$191$	153640.	0.304734	0.152367	+	0.988324i	$0.451310\pi$
$192$	36864.0	0.0721688
$193$	875318.	1.69150	0.845751	−	0.533578i	$-0.179153\pi$
$193$	875318.	1.69150	0.845751	+	0.533578i	$0.179153\pi$
$194$	−28909.4	−0.0551486
$195$	−256622.	−0.483290
$196$	−250092.	−0.465007
$197$	820414.	1.50615	0.753074	−	0.657936i	$-0.228570\pi$
$197$	820414.	1.50615	0.753074	+	0.657936i	$0.228570\pi$
$198$	−48195.0	−0.0873654
$199$	683129.	1.22284	0.611421	−	0.791306i	$-0.290598\pi$
$199$	683129.	1.22284	0.611421	+	0.791306i	$0.290598\pi$
$200$	−40000.0	−0.0707107
$201$	312051.	0.544798
$202$	228489.	0.393992
$203$	199674.	0.340081
$204$	268470.	0.451669
$205$	−96905.7	−0.161051
$206$	−633946.	−1.04084
$207$	28859.8	0.0468130
$208$	291979.	0.467944
$209$	−53698.8	−0.0850352
$210$	−30867.0	−0.0482999
$211$	−211031.	−0.326318	−0.163159	−	0.986600i	$-0.552168\pi$
$211$	−211031.	−0.326318	−0.163159	+	0.986600i	$0.552168\pi$
$212$	−396509.	−0.605918
$213$	575824.	0.869642
$214$	−86811.2	−0.129581
$215$	−577693.	−0.852317
$216$	−46656.0	−0.0680414
$217$	357352.	0.515165
$218$	159185.	0.226861
$219$	142502.	0.200775
$220$	−59500.0	−0.0828821
$221$	2.12640e6	2.92863
$222$	−230072.	−0.313315
$223$	1.09637e6	1.47637	0.738184	−	0.674599i	$-0.235683\pi$
$223$	1.09637e6	1.47637	0.738184	+	0.674599i	$0.235683\pi$
$224$	35119.8	0.0467662
$225$	50625.0	0.0666667
$226$	−40444.7	−0.0526733
$227$	−957257.	−1.23300	−0.616501	−	0.787354i	$-0.711451\pi$
$227$	−957257.	−1.23300	−0.616501	+	0.787354i	$0.711451\pi$
$228$	−51984.0	−0.0662266
$229$	531154.	0.669317	0.334659	−	0.942339i	$-0.391379\pi$
$229$	531154.	0.669317	0.334659	+	0.942339i	$0.391379\pi$
$230$	35629.3	0.0444108
$231$	−45914.7	−0.0566137
$232$	372606.	0.454496
$233$	−18960.6	−0.0228803	−0.0114402	−	0.999935i	$-0.503642\pi$
$233$	−18960.6	−0.0228803	−0.0114402	+	0.999935i	$0.503642\pi$
$234$	−369536.	−0.441181
$235$	604308.	0.713820
$236$	468516.	0.547576
$237$	651323.	0.753226
$238$	255767.	0.292686
$239$	465206.	0.526805	0.263403	−	0.964686i	$-0.415155\pi$
$239$	465206.	0.526805	0.263403	+	0.964686i	$0.415155\pi$
$240$	−57600.0	−0.0645497
$241$	−1.41287e6	−1.56697	−0.783484	−	0.621412i	$-0.786559\pi$
$241$	−1.41287e6	−1.56697	−0.783484	+	0.621412i	$0.786559\pi$
$242$	555698.	0.609958
$243$	59049.0	0.0641500
$244$	8955.50	0.00962976
$245$	390768.	0.415915
$246$	−139544.	−0.147019
$247$	−411736.	−0.429415
$248$	666843.	0.688485
$249$	−631626.	−0.645598
$250$	62500.0	0.0632456
$251$	752819.	0.754234	0.377117	−	0.926166i	$-0.376915\pi$
$251$	752819.	0.754234	0.377117	+	0.926166i	$0.376915\pi$
$252$	−44448.5	−0.0440916
$253$	52998.7	0.0520551
$254$	810569.	0.788326
$255$	−419484.	−0.403985
$256$	65536.0	0.0625000
$257$	1.28310e6	1.21179	0.605895	−	0.795545i	$-0.292815\pi$
$257$	1.28310e6	1.21179	0.605895	+	0.795545i	$0.292815\pi$
$258$	−831879.	−0.778056
$259$	−219186.	−0.203032
$260$	−456217.	−0.418542
$261$	−471580.	−0.428503
$262$	−365855.	−0.329273
$263$	−926179.	−0.825669	−0.412834	−	0.910806i	$-0.635461\pi$
$263$	−926179.	−0.825669	−0.412834	+	0.910806i	$0.635461\pi$
$264$	−85680.1	−0.0756606
$265$	619546.	0.541949
$266$	−49524.4	−0.0429156
$267$	652051.	0.559762
$268$	554757.	0.471809
$269$	388774.	0.327579	0.163790	−	0.986495i	$-0.447628\pi$
$269$	388774.	0.327579	0.163790	+	0.986495i	$0.447628\pi$
$270$	72900.0	0.0608581
$271$	−332637.	−0.275136	−0.137568	−	0.990492i	$-0.543929\pi$
$271$	−332637.	−0.275136	−0.137568	+	0.990492i	$0.543929\pi$
$272$	477280.	0.391157
$273$	−352052.	−0.285890
$274$	−1.15528e6	−0.929631
$275$	92968.8	0.0741320
$276$	51306.2	0.0405413
$277$	1.13035e6	0.885146	0.442573	−	0.896733i	$-0.354066\pi$
$277$	1.13035e6	0.885146	0.442573	+	0.896733i	$0.354066\pi$
$278$	−1.54459e6	−1.19868
$279$	−843974.	−0.649110
$280$	−54874.7	−0.0418289
$281$	−2.39691e6	−1.81087	−0.905434	−	0.424488i	$-0.860454\pi$
$281$	−2.39691e6	−1.81087	−0.905434	+	0.424488i	$0.860454\pi$
$282$	870203.	0.651625
$283$	−496875.	−0.368791	−0.184396	−	0.982852i	$-0.559033\pi$
$283$	−496875.	−0.368791	−0.184396	+	0.982852i	$0.559033\pi$
$284$	1.02369e6	0.753132
$285$	81225.0	0.0592349
$286$	−678624.	−0.490585
$287$	−132942.	−0.0952700
$288$	−82944.0	−0.0589256
$289$	2.05603e6	1.44806
$290$	−582197.	−0.406514
$291$	65046.1	0.0450286
$292$	253336.	0.173876
$293$	−443119.	−0.301544	−0.150772	−	0.988569i	$-0.548176\pi$
$293$	−443119.	−0.301544	−0.150772	+	0.988569i	$0.548176\pi$
$294$	562707.	0.379676
$295$	−732056.	−0.489767
$296$	−409017.	−0.271339
$297$	108439.	0.0713335
$298$	35842.5	0.0233807
$299$	406368.	0.262870
$300$	90000.0	0.0577350
$301$	−792518.	−0.504189
$302$	−1.61872e6	−1.02130
$303$	−514101.	−0.321693
$304$	−92416.0	−0.0573539
$305$	−13993.0	−0.00861312
$306$	−604057.	−0.368786
$307$	2.01345e6	1.21926	0.609629	−	0.792687i	$-0.291319\pi$
$307$	2.01345e6	1.21926	0.609629	+	0.792687i	$0.291319\pi$
$308$	−81626.1	−0.0490289
$309$	1.42638e6	0.849843
$310$	−1.04194e6	−0.615800
$311$	−2.84464e6	−1.66773	−0.833867	−	0.551966i	$-0.813878\pi$
$311$	−2.84464e6	−1.66773	−0.833867	+	0.551966i	$0.813878\pi$
$312$	−656953.	−0.382074
$313$	83906.4	0.0484099	0.0242049	−	0.999707i	$-0.492295\pi$
$313$	83906.4	0.0484099	0.0242049	+	0.999707i	$0.492295\pi$
$314$	1.70592e6	0.976417
$315$	69450.7	0.0394367
$316$	1.15791e6	0.652313
$317$	1.68748e6	0.943173	0.471586	−	0.881820i	$-0.343682\pi$
$317$	1.68748e6	0.943173	0.471586	+	0.881820i	$0.343682\pi$
$318$	892146.	0.494730
$319$	−866019.	−0.476487
$320$	−102400.	−0.0559017
$321$	195325.	0.105802
$322$	48878.7	0.0262712
$323$	−673039.	−0.358950
$324$	104976.	0.0555556
$325$	712840.	0.374355
$326$	−2.04380e6	−1.06511
$327$	−358166.	−0.185232
$328$	−248079.	−0.127322
$329$	829030.	0.422260
$330$	133875.	0.0676729
$331$	−375316.	−0.188290	−0.0941449	−	0.995559i	$-0.530012\pi$
$331$	−375316.	−0.188290	−0.0941449	+	0.995559i	$0.530012\pi$
$332$	−1.12289e6	−0.559104
$333$	517662.	0.255821
$334$	1.59522e6	0.782444
$335$	−866808.	−0.421999
$336$	−79019.5	−0.0381844
$337$	−2.48793e6	−1.19334	−0.596669	−	0.802488i	$-0.703509\pi$
$337$	−2.48793e6	−1.19334	−0.596669	+	0.802488i	$0.703509\pi$
$338$	−3.71819e6	−1.77027
$339$	91000.5	0.0430075
$340$	−745750.	−0.349861
$341$	−1.54989e6	−0.721797
$342$	116964.	0.0540738
$343$	1.11251e6	0.510584
$344$	−1.47890e6	−0.673816
$345$	−80166.0	−0.0362612
$346$	2.47898e6	1.11322
$347$	−498265.	−0.222145	−0.111073	−	0.993812i	$-0.535429\pi$
$347$	−498265.	−0.222145	−0.111073	+	0.993812i	$0.535429\pi$
$348$	−838364.	−0.371094
$349$	133574.	0.0587028	0.0293514	−	0.999569i	$-0.490656\pi$
$349$	133574.	0.0587028	0.0293514	+	0.999569i	$0.490656\pi$
$350$	85741.7	0.0374129
$351$	831456.	0.360223
$352$	−152320.	−0.0655240
$353$	281870.	0.120396	0.0601980	−	0.998186i	$-0.480827\pi$
$353$	281870.	0.120396	0.0601980	+	0.998186i	$0.480827\pi$
$354$	−1.05416e6	−0.447094
$355$	−1.59951e6	−0.673622
$356$	1.15920e6	0.484768
$357$	−575476.	−0.238977
$358$	−87362.6	−0.0360262
$359$	4.17309e6	1.70892	0.854460	−	0.519518i	$-0.173888\pi$
$359$	4.17309e6	1.70892	0.854460	+	0.519518i	$0.173888\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−90847.8	−0.0364370
$363$	−1.25032e6	−0.498029
$364$	−625870.	−0.247588
$365$	−395838.	−0.155520
$366$	−20149.9	−0.00786267
$367$	2.84118e6	1.10112	0.550558	−	0.834797i	$-0.314415\pi$
$367$	2.84118e6	1.10112	0.550558	+	0.834797i	$0.314415\pi$
$368$	91211.1	0.0351098
$369$	313974.	0.120041
$370$	639089.	0.242693
$371$	849934.	0.320590
$372$	−1.50040e6	−0.562146
$373$	−4.86188e6	−1.80939	−0.904695	−	0.426060i	$-0.859901\pi$
$373$	−4.86188e6	−1.80939	−0.904695	+	0.426060i	$0.859901\pi$
$374$	−1.10930e6	−0.410083
$375$	−140625.	−0.0516398
$376$	1.54703e6	0.564324
$377$	−6.64021e6	−2.40618
$378$	100009.	0.0360006
$379$	1.89991e6	0.679415	0.339708	−	0.940531i	$-0.389672\pi$
$379$	1.89991e6	0.679415	0.339708	+	0.940531i	$0.389672\pi$
$380$	144400.	0.0512989
$381$	−1.82378e6	−0.643665
$382$	−614559.	−0.215479
$383$	−3.09421e6	−1.07784	−0.538919	−	0.842358i	$-0.681167\pi$
$383$	−3.09421e6	−1.07784	−0.538919	+	0.842358i	$0.681167\pi$
$384$	−147456.	−0.0510310
$385$	127541.	0.0438528
$386$	−3.50127e6	−1.19607
$387$	1.87173e6	0.635280
$388$	115637.	0.0389959
$389$	−3.22237e6	−1.07970	−0.539848	−	0.841763i	$-0.681518\pi$
$389$	−3.22237e6	−1.07970	−0.539848	+	0.841763i	$0.681518\pi$
$390$	1.02649e6	0.341738
$391$	664264.	0.219735
$392$	1.00037e6	0.328809
$393$	823174.	0.268850
$394$	−3.28166e6	−1.06501
$395$	−1.80923e6	−0.583446
$396$	192780.	0.0617766
$397$	−1.92728e6	−0.613717	−0.306859	−	0.951755i	$-0.599278\pi$
$397$	−1.92728e6	−0.613717	−0.306859	+	0.951755i	$0.599278\pi$
$398$	−2.73252e6	−0.864680
$399$	111430.	0.0350404
$400$	160000.	0.0500000
$401$	480845.	0.149329	0.0746644	−	0.997209i	$-0.476211\pi$
$401$	480845.	0.149329	0.0746644	+	0.997209i	$0.476211\pi$
$402$	−1.24820e6	−0.385230
$403$	−1.18838e7	−3.64496
$404$	−913957.	−0.278594
$405$	−164025.	−0.0496904
$406$	−798697.	−0.240473
$407$	950646.	0.284467
$408$	−1.07388e6	−0.319378
$409$	−3.36840e6	−0.995668	−0.497834	−	0.867272i	$-0.665871\pi$
$409$	−3.36840e6	−0.995668	−0.497834	+	0.867272i	$0.665871\pi$
$410$	387623.	0.113881
$411$	2.59938e6	0.759040
$412$	2.53578e6	0.735985
$413$	−1.00428e6	−0.289722
$414$	−115439.	−0.0331018
$415$	1.75452e6	0.500078
$416$	−1.16792e6	−0.330886
$417$	3.47533e6	0.978715
$418$	214795.	0.0601290
$419$	−1.72677e6	−0.480507	−0.240254	−	0.970710i	$-0.577231\pi$
$419$	−1.72677e6	−0.480507	−0.240254	+	0.970710i	$0.577231\pi$
$420$	123468.	0.0341532
$421$	6.88025e6	1.89190	0.945951	−	0.324309i	$-0.105132\pi$
$421$	6.88025e6	1.89190	0.945951	+	0.324309i	$0.105132\pi$
$422$	844125.	0.230741
$423$	−1.95796e6	−0.532050
$424$	1.58604e6	0.428449
$425$	1.16523e6	0.312925
$426$	−2.30330e6	−0.614930
$427$	−19196.5	−0.00509509
$428$	347245.	0.0916276
$429$	1.52690e6	0.400561
$430$	2.31077e6	0.602679
$431$	6.57589e6	1.70514	0.852572	−	0.522610i	$-0.175041\pi$
$431$	6.57589e6	1.70514	0.852572	+	0.522610i	$0.175041\pi$
$432$	186624.	0.0481125
$433$	6.40443e6	1.64158	0.820788	−	0.571233i	$-0.193535\pi$
$433$	6.40443e6	1.64158	0.820788	+	0.571233i	$0.193535\pi$
$434$	−1.42941e6	−0.364277
$435$	1.30994e6	0.331917
$436$	−636740.	−0.160415
$437$	−128622.	−0.0322189
$438$	−570006.	−0.141969
$439$	4.61471e6	1.14283	0.571417	−	0.820660i	$-0.306394\pi$
$439$	4.61471e6	1.14283	0.571417	+	0.820660i	$0.306394\pi$
$440$	238000.	0.0586065
$441$	−1.26609e6	−0.310005
$442$	−8.50560e6	−2.07085
$443$	709966.	0.171881	0.0859405	−	0.996300i	$-0.472610\pi$
$443$	709966.	0.171881	0.0859405	+	0.996300i	$0.472610\pi$
$444$	920288.	0.221547
$445$	−1.81125e6	−0.433590
$446$	−4.38548e6	−1.04395
$447$	−80645.5	−0.0190902
$448$	−140479.	−0.0330687
$449$	−7.60136e6	−1.77941	−0.889704	−	0.456539i	$-0.849089\pi$
$449$	−7.60136e6	−1.77941	−0.889704	+	0.456539i	$0.849089\pi$
$450$	−202500.	−0.0471405
$451$	576589.	0.133483
$452$	161779.	0.0372456
$453$	3.64213e6	0.833892
$454$	3.82903e6	0.871865
$455$	977921.	0.221450
$456$	207936.	0.0468293
$457$	5.76215e6	1.29061	0.645304	−	0.763926i	$-0.276731\pi$
$457$	5.76215e6	1.29061	0.645304	+	0.763926i	$0.276731\pi$
$458$	−2.12462e6	−0.473279
$459$	1.35913e6	0.301113
$460$	−142517.	−0.0314031
$461$	−1.22229e6	−0.267870	−0.133935	−	0.990990i	$-0.542761\pi$
$461$	−1.22229e6	−0.267870	−0.133935	+	0.990990i	$0.542761\pi$
$462$	183659.	0.0400319
$463$	−1.41076e6	−0.305844	−0.152922	−	0.988238i	$-0.548868\pi$
$463$	−1.41076e6	−0.305844	−0.152922	+	0.988238i	$0.548868\pi$
$464$	−1.49042e6	−0.321377
$465$	2.34437e6	0.502798
$466$	75842.3	0.0161788
$467$	−7.26181e6	−1.54082	−0.770411	−	0.637547i	$-0.779949\pi$
$467$	−7.26181e6	−1.54082	−0.770411	+	0.637547i	$0.779949\pi$
$468$	1.47814e6	0.311962
$469$	−1.18915e6	−0.249634
$470$	−2.41723e6	−0.504747
$471$	−3.83833e6	−0.797241
$472$	−1.87406e6	−0.387195
$473$	3.43728e6	0.706418
$474$	−2.60529e6	−0.532611
$475$	−225625.	−0.0458831
$476$	−1.02307e6	−0.206961
$477$	−2.00733e6	−0.403945
$478$	−1.86082e6	−0.372508
$479$	2.58287e6	0.514355	0.257178	−	0.966364i	$-0.417207\pi$
$479$	2.58287e6	0.514355	0.257178	+	0.966364i	$0.417207\pi$
$480$	230400.	0.0456435
$481$	7.28909e6	1.43652
$482$	5.65149e6	1.10801
$483$	−109977.	−0.0214503
$484$	−2.22279e6	−0.431306
$485$	−180684.	−0.0348790
$486$	−236196.	−0.0453609
$487$	5.60709e6	1.07131	0.535655	−	0.844437i	$-0.320065\pi$
$487$	5.60709e6	1.07131	0.535655	+	0.844437i	$0.320065\pi$
$488$	−35822.0	−0.00680927
$489$	4.59856e6	0.869660
$490$	−1.56307e6	−0.294096
$491$	1.79394e6	0.335818	0.167909	−	0.985802i	$-0.446298\pi$
$491$	1.79394e6	0.335818	0.167909	+	0.985802i	$0.446298\pi$
$492$	558177.	0.103958
$493$	−1.08543e7	−2.01134
$494$	1.64695e6	0.303642
$495$	−301219.	−0.0552547
$496$	−2.66737e6	−0.486833
$497$	−2.19431e6	−0.398481
$498$	2.52651e6	0.456506
$499$	2.70944e6	0.487112	0.243556	−	0.969887i	$-0.421686\pi$
$499$	2.70944e6	0.487112	0.243556	+	0.969887i	$0.421686\pi$
$500$	−250000.	−0.0447214
$501$	−3.58924e6	−0.638863
$502$	−3.01128e6	−0.533324
$503$	−9.67452e6	−1.70494	−0.852471	−	0.522775i	$-0.824897\pi$
$503$	−9.67452e6	−1.70494	−0.852471	+	0.522775i	$0.824897\pi$
$504$	177794.	0.0311774
$505$	1.42806e6	0.249182
$506$	−211995.	−0.0368085
$507$	8.36592e6	1.44542
$508$	−3.24228e6	−0.557431
$509$	7.81169e6	1.33644	0.668222	−	0.743962i	$-0.267056\pi$
$509$	7.81169e6	1.33644	0.668222	+	0.743962i	$0.267056\pi$
$510$	1.67794e6	0.285660
$511$	−543036.	−0.0919977
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−5.13239e6	−0.856864
$515$	−3.96216e6	−0.658285
$516$	3.32751e6	0.550168
$517$	−3.59563e6	−0.591629
$518$	876745.	0.143565
$519$	−5.57770e6	−0.908943
$520$	1.82487e6	0.295954
$521$	−427731.	−0.0690361	−0.0345180	−	0.999404i	$-0.510990\pi$
$521$	−427731.	−0.0690361	−0.0345180	+	0.999404i	$0.510990\pi$
$522$	1.88632e6	0.302997
$523$	1.04844e6	0.167606	0.0838032	−	0.996482i	$-0.473293\pi$
$523$	1.04844e6	0.167606	0.0838032	+	0.996482i	$0.473293\pi$
$524$	1.46342e6	0.232831
$525$	−192919.	−0.0305475
$526$	3.70472e6	0.583836
$527$	−1.94257e7	−3.04684
$528$	342720.	0.0535001
$529$	−6.30940e6	−0.980277
$530$	−2.47818e6	−0.383216
$531$	2.37186e6	0.365051
$532$	198098.	0.0303459
$533$	4.42101e6	0.674067
$534$	−2.60820e6	−0.395811
$535$	−542570.	−0.0819542
$536$	−2.21903e6	−0.333619
$537$	196566.	0.0294152
$538$	−1.55510e6	−0.231634
$539$	−2.32507e6	−0.344719
$540$	−291600.	−0.0430331
$541$	−4.43514e6	−0.651499	−0.325750	−	0.945456i	$-0.605617\pi$
$541$	−4.43514e6	−0.651499	−0.325750	+	0.945456i	$0.605617\pi$
$542$	1.33055e6	0.194550
$543$	204407.	0.0297507
$544$	−1.90912e6	−0.276590
$545$	994906.	0.143480
$546$	1.40821e6	0.202155
$547$	−6.31985e6	−0.903105	−0.451553	−	0.892244i	$-0.649130\pi$
$547$	−6.31985e6	−0.903105	−0.451553	+	0.892244i	$0.649130\pi$
$548$	4.62112e6	0.657348
$549$	45337.2	0.00641984
$550$	−371875.	−0.0524192
$551$	2.10173e6	0.294916
$552$	−205225.	−0.0286670
$553$	−2.48202e6	−0.345138
$554$	−4.52141e6	−0.625893
$555$	−1.43795e6	−0.198158
$556$	6.17837e6	0.847592
$557$	7.35307e6	1.00422	0.502112	−	0.864803i	$-0.332557\pi$
$557$	7.35307e6	1.00422	0.502112	+	0.864803i	$0.332557\pi$
$558$	3.37589e6	0.458990
$559$	2.63554e7	3.56730
$560$	219499.	0.0295775
$561$	2.49593e6	0.334831
$562$	9.58765e6	1.28048
$563$	−1.21188e7	−1.61134	−0.805670	−	0.592365i	$-0.798194\pi$
$563$	−1.21188e7	−1.61134	−0.805670	+	0.592365i	$0.798194\pi$
$564$	−3.48081e6	−0.460769
$565$	−252779.	−0.0333135
$566$	1.98750e6	0.260775
$567$	−225020.	−0.0293944
$568$	−4.09475e6	−0.532545
$569$	−3.22312e6	−0.417346	−0.208673	−	0.977985i	$-0.566914\pi$
$569$	−3.22312e6	−0.417346	−0.208673	+	0.977985i	$0.566914\pi$
$570$	−324900.	−0.0418854
$571$	−404549.	−0.0519255	−0.0259627	−	0.999663i	$-0.508265\pi$
$571$	−404549.	−0.0519255	−0.0259627	+	0.999663i	$0.508265\pi$
$572$	2.71450e6	0.346896
$573$	1.38276e6	0.175938
$574$	531767.	0.0673661
$575$	222683.	0.0280878
$576$	331776.	0.0416667
$577$	2.00205e6	0.250343	0.125172	−	0.992135i	$-0.460052\pi$
$577$	2.00205e6	0.250343	0.125172	+	0.992135i	$0.460052\pi$
$578$	−8.22413e6	−1.02393
$579$	7.87786e6	0.976589
$580$	2.32879e6	0.287449
$581$	2.40696e6	0.295821
$582$	−260184.	−0.0318400
$583$	−3.68630e6	−0.449179
$584$	−1.01334e6	−0.122949
$585$	−2.30960e6	−0.279028
$586$	1.77247e6	0.213224
$587$	1.26153e7	1.51114	0.755569	−	0.655069i	$-0.227361\pi$
$587$	1.26153e7	1.51114	0.755569	+	0.655069i	$0.227361\pi$
$588$	−2.25083e6	−0.268472
$589$	3.76141e6	0.446748
$590$	2.92823e6	0.346318
$591$	7.38372e6	0.869574
$592$	1.63607e6	0.191866
$593$	3.02364e6	0.353096	0.176548	−	0.984292i	$-0.443507\pi$
$593$	3.02364e6	0.353096	0.176548	+	0.984292i	$0.443507\pi$
$594$	−433755.	−0.0504404
$595$	1.59855e6	0.185111
$596$	−143370.	−0.0165326
$597$	6.14816e6	0.706008
$598$	−1.62547e6	−0.185877
$599$	1.16163e6	0.132282	0.0661412	−	0.997810i	$-0.478931\pi$
$599$	1.16163e6	0.132282	0.0661412	+	0.997810i	$0.478931\pi$
$600$	−360000.	−0.0408248
$601$	1.41403e7	1.59688	0.798441	−	0.602073i	$-0.205658\pi$
$601$	1.41403e7	1.59688	0.798441	+	0.602073i	$0.205658\pi$
$602$	3.17007e6	0.356515
$603$	2.80846e6	0.314539
$604$	6.47490e6	0.722172
$605$	3.47311e6	0.385771
$606$	2.05640e6	0.227471
$607$	1.18789e7	1.30860	0.654299	−	0.756236i	$-0.272964\pi$
$607$	1.18789e7	1.30860	0.654299	+	0.756236i	$0.272964\pi$
$608$	369664.	0.0405554
$609$	1.79707e6	0.196346
$610$	55971.9	0.00609040
$611$	−2.75696e7	−2.98763
$612$	2.41623e6	0.260771
$613$	−1.37570e6	−0.147867	−0.0739335	−	0.997263i	$-0.523555\pi$
$613$	−1.37570e6	−0.147867	−0.0739335	+	0.997263i	$0.523555\pi$
$614$	−8.05381e6	−0.862145
$615$	−872151.	−0.0929831
$616$	326504.	0.0346687
$617$	4.54793e6	0.480951	0.240475	−	0.970655i	$-0.422697\pi$
$617$	4.54793e6	0.480951	0.240475	+	0.970655i	$0.422697\pi$
$618$	−5.70551e6	−0.600929
$619$	5.48774e6	0.575661	0.287830	−	0.957681i	$-0.407066\pi$
$619$	5.48774e6	0.575661	0.287830	+	0.957681i	$0.407066\pi$
$620$	4.16777e6	0.435436
$621$	259738.	0.0270275
$622$	1.13786e7	1.17927
$623$	−2.48480e6	−0.256490
$624$	2.62781e6	0.270167
$625$	390625.	0.0400000
$626$	−335625.	−0.0342310
$627$	−483289.	−0.0490951
$628$	−6.82369e6	−0.690431
$629$	1.19150e7	1.20079
$630$	−277803.	−0.0278860
$631$	−1.28567e7	−1.28545	−0.642727	−	0.766095i	$-0.722197\pi$
$631$	−1.28567e7	−1.28545	−0.642727	+	0.766095i	$0.722197\pi$
$632$	−4.63163e6	−0.461255
$633$	−1.89928e6	−0.188400
$634$	−6.74993e6	−0.666924
$635$	5.06606e6	0.498581
$636$	−3.56858e6	−0.349827
$637$	−1.78275e7	−1.74078
$638$	3.46408e6	0.336927
$639$	5.18241e6	0.502088
$640$	409600.	0.0395285
$641$	1.09210e6	0.104982	0.0524912	−	0.998621i	$-0.483284\pi$
$641$	1.09210e6	0.104982	0.0524912	+	0.998621i	$0.483284\pi$
$642$	−781301.	−0.0748136
$643$	1.47390e7	1.40586	0.702930	−	0.711259i	$-0.251875\pi$
$643$	1.47390e7	1.40586	0.702930	+	0.711259i	$0.251875\pi$
$644$	−195515.	−0.0185765
$645$	−5.19924e6	−0.492086
$646$	2.69216e6	0.253816
$647$	−6.54046e6	−0.614254	−0.307127	−	0.951669i	$-0.599368\pi$
$647$	−6.54046e6	−0.614254	−0.307127	+	0.951669i	$0.599368\pi$
$648$	−419904.	−0.0392837
$649$	4.35574e6	0.405929
$650$	−2.85136e6	−0.264709
$651$	3.21616e6	0.297431
$652$	8.17522e6	0.753148
$653$	−1.07827e7	−0.989568	−0.494784	−	0.869016i	$-0.664753\pi$
$653$	−1.07827e7	−0.989568	−0.494784	+	0.869016i	$0.664753\pi$
$654$	1.43266e6	0.130979
$655$	−2.28659e6	−0.208250
$656$	992314.	0.0900305
$657$	1.28251e6	0.115917
$658$	−3.31612e6	−0.298583
$659$	9.27679e6	0.832116	0.416058	−	0.909338i	$-0.363411\pi$
$659$	9.27679e6	0.832116	0.416058	+	0.909338i	$0.363411\pi$
$660$	−535500.	−0.0478520
$661$	−5.45372e6	−0.485500	−0.242750	−	0.970089i	$-0.578050\pi$
$661$	−5.45372e6	−0.485500	−0.242750	+	0.970089i	$0.578050\pi$
$662$	1.50126e6	0.133141
$663$	1.91376e7	1.69084
$664$	4.49157e6	0.395346
$665$	−309527.	−0.0271422
$666$	−2.07065e6	−0.180893
$667$	−2.07433e6	−0.180536
$668$	−6.38086e6	−0.553271
$669$	9.86733e6	0.852382
$670$	3.46723e6	0.298398
$671$	83258.3	0.00713873
$672$	316078.	0.0270005
$673$	−1.02341e7	−0.870986	−0.435493	−	0.900192i	$-0.643426\pi$
$673$	−1.02341e7	−0.870986	−0.435493	+	0.900192i	$0.643426\pi$
$674$	9.95172e6	0.843817
$675$	455625.	0.0384900
$676$	1.48727e7	1.25177
$677$	1.53143e7	1.28418	0.642090	−	0.766629i	$-0.278068\pi$
$677$	1.53143e7	1.28418	0.642090	+	0.766629i	$0.278068\pi$
$678$	−364002.	−0.0304109
$679$	−247874.	−0.0206327
$680$	2.98300e6	0.247389
$681$	−8.61532e6	−0.711875
$682$	6.19956e6	0.510388
$683$	−1.28493e7	−1.05397	−0.526986	−	0.849874i	$-0.676678\pi$
$683$	−1.28493e7	−1.05397	−0.526986	+	0.849874i	$0.676678\pi$
$684$	−467856.	−0.0382360
$685$	−7.22049e6	−0.587950
$686$	−4.45003e6	−0.361037
$687$	4.78039e6	0.386431
$688$	5.91558e6	0.476460
$689$	−2.82648e7	−2.26828
$690$	320664.	0.0256406
$691$	−555664.	−0.0442708	−0.0221354	−	0.999755i	$-0.507046\pi$
$691$	−555664.	−0.0442708	−0.0221354	+	0.999755i	$0.507046\pi$
$692$	−9.91591e6	−0.787168
$693$	−413232.	−0.0326859
$694$	1.99306e6	0.157080
$695$	−9.65370e6	−0.758109
$696$	3.35346e6	0.262403
$697$	7.22674e6	0.563456
$698$	−534296.	−0.0415091
$699$	−170645.	−0.0132099
$700$	−342967.	−0.0264549
$701$	1.18413e7	0.910132	0.455066	−	0.890458i	$-0.349616\pi$
$701$	1.18413e7	0.910132	0.455066	+	0.890458i	$0.349616\pi$
$702$	−3.32583e6	−0.254716
$703$	−2.30711e6	−0.176068
$704$	609280.	0.0463325
$705$	5.43877e6	0.412124
$706$	−1.12748e6	−0.0851328
$707$	1.95911e6	0.147404
$708$	4.21664e6	0.316143
$709$	−2.12821e7	−1.59000	−0.795002	−	0.606606i	$-0.792530\pi$
$709$	−2.12821e7	−1.59000	−0.795002	+	0.606606i	$0.792530\pi$
$710$	6.39804e6	0.476323
$711$	5.86190e6	0.434875
$712$	−4.63681e6	−0.342783
$713$	−3.71237e6	−0.273481
$714$	2.30190e6	0.168983
$715$	−4.24140e6	−0.310273
$716$	349450.	0.0254743
$717$	4.18685e6	0.304151
$718$	−1.66924e7	−1.20839
$719$	5.69123e6	0.410567	0.205284	−	0.978703i	$-0.434188\pi$
$719$	5.69123e6	0.410567	0.205284	+	0.978703i	$0.434188\pi$
$720$	−518400.	−0.0372678
$721$	−5.43556e6	−0.389409
$722$	−521284.	−0.0372161
$723$	−1.27158e7	−0.904690
$724$	363391.	0.0257649
$725$	−3.63873e6	−0.257102
$726$	5.00128e6	0.352160
$727$	−9.24730e6	−0.648902	−0.324451	−	0.945903i	$-0.605179\pi$
$727$	−9.24730e6	−0.648902	−0.324451	+	0.945903i	$0.605179\pi$
$728$	2.50348e6	0.175071
$729$	531441.	0.0370370
$730$	1.58335e6	0.109969
$731$	4.30815e7	2.98193
$732$	80599.5	0.00555974
$733$	−9.96970e6	−0.685366	−0.342683	−	0.939451i	$-0.611336\pi$
$733$	−9.96970e6	−0.685366	−0.342683	+	0.939451i	$0.611336\pi$
$734$	−1.13647e7	−0.778607
$735$	3.51692e6	0.240128
$736$	−364844.	−0.0248264
$737$	5.15751e6	0.349761
$738$	−1.25590e6	−0.0848816
$739$	−2.01922e7	−1.36011	−0.680053	−	0.733163i	$-0.738043\pi$
$739$	−2.01922e7	−1.36011	−0.680053	+	0.733163i	$0.738043\pi$
$740$	−2.55636e6	−0.171610
$741$	−3.70563e6	−0.247923
$742$	−3.39974e6	−0.226692
$743$	2.26791e7	1.50714	0.753569	−	0.657369i	$-0.228331\pi$
$743$	2.26791e7	1.50714	0.753569	+	0.657369i	$0.228331\pi$
$744$	6.00159e6	0.397497
$745$	224015.	0.0147872
$746$	1.94475e7	1.27943
$747$	−5.68464e6	−0.372736
$748$	4.43721e6	0.289972
$749$	−744333.	−0.0484800
$750$	562500.	0.0365148
$751$	8.27843e6	0.535609	0.267805	−	0.963473i	$-0.413702\pi$
$751$	8.27843e6	0.535609	0.267805	+	0.963473i	$0.413702\pi$
$752$	−6.18811e6	−0.399037
$753$	6.77537e6	0.435457
$754$	2.65609e7	1.70143
$755$	−1.01170e7	−0.645930
$756$	−400036.	−0.0254563
$757$	−9.08003e6	−0.575901	−0.287950	−	0.957645i	$-0.592974\pi$
$757$	−9.08003e6	−0.575901	−0.287950	+	0.957645i	$0.592974\pi$
$758$	−7.59965e6	−0.480419
$759$	476988.	0.0300541
$760$	−577600.	−0.0362738
$761$	1.22929e7	0.769471	0.384736	−	0.923027i	$-0.374293\pi$
$761$	1.22929e7	0.769471	0.384736	+	0.923027i	$0.374293\pi$
$762$	7.29512e6	0.455140
$763$	1.36488e6	0.0848755
$764$	2.45824e6	0.152367
$765$	−3.77536e6	−0.233241
$766$	1.23769e7	0.762147
$767$	3.33977e7	2.04988
$768$	589824.	0.0360844
$769$	−2.10319e7	−1.28252	−0.641258	−	0.767325i	$-0.721587\pi$
$769$	−2.10319e7	−1.28252	−0.641258	+	0.767325i	$0.721587\pi$
$770$	−510163.	−0.0310086
$771$	1.15479e7	0.699627
$772$	1.40051e7	0.845751
$773$	−4.14872e6	−0.249727	−0.124864	−	0.992174i	$-0.539849\pi$
$773$	−4.14872e6	−0.249727	−0.124864	+	0.992174i	$0.539849\pi$
$774$	−7.48691e6	−0.449211
$775$	−6.51214e6	−0.389466
$776$	−462550.	−0.0275743
$777$	−1.97268e6	−0.117220
$778$	1.28895e7	0.763460
$779$	−1.39932e6	−0.0826176
$780$	−4.10596e6	−0.241645
$781$	9.51709e6	0.558312
$782$	−2.65706e6	−0.155376
$783$	−4.24422e6	−0.247396
$784$	−4.00147e6	−0.232503
$785$	1.06620e7	0.617540
$786$	−3.29270e6	−0.190106
$787$	−2.45443e7	−1.41258	−0.706290	−	0.707923i	$-0.749633\pi$
$787$	−2.45443e7	−1.41258	−0.706290	+	0.707923i	$0.749633\pi$
$788$	1.31266e7	0.753074
$789$	−8.33561e6	−0.476700
$790$	7.23692e6	0.412559
$791$	−346779.	−0.0197066
$792$	−771121.	−0.0436827
$793$	638384.	0.0360495
$794$	7.70911e6	0.433963
$795$	5.57591e6	0.312895
$796$	1.09301e7	0.611421
$797$	−2.69314e7	−1.50180	−0.750902	−	0.660414i	$-0.770381\pi$
$797$	−2.69314e7	−1.50180	−0.750902	+	0.660414i	$0.770381\pi$
$798$	−445719.	−0.0247773
$799$	−4.50662e7	−2.49738
$800$	−640000.	−0.0353553
$801$	5.86846e6	0.323179
$802$	−1.92338e6	−0.105591
$803$	2.35524e6	0.128898
$804$	4.99282e6	0.272399
$805$	305492.	0.0166154
$806$	4.75352e7	2.57738
$807$	3.49897e6	0.189128
$808$	3.65583e6	0.196996
$809$	1.07394e7	0.576913	0.288456	−	0.957493i	$-0.406858\pi$
$809$	1.07394e7	0.576913	0.288456	+	0.957493i	$0.406858\pi$
$810$	656100.	0.0351364
$811$	1.37435e7	0.733747	0.366873	−	0.930271i	$-0.380428\pi$
$811$	1.37435e7	0.733747	0.366873	+	0.930271i	$0.380428\pi$
$812$	3.19479e6	0.170040
$813$	−2.99373e6	−0.158850
$814$	−3.80258e6	−0.201149
$815$	−1.27738e7	−0.673636
$816$	4.29552e6	0.225834
$817$	−8.34189e6	−0.437230
$818$	1.34736e7	0.704044
$819$	−3.16846e6	−0.165059
$820$	−1.55049e6	−0.0805257
$821$	−2.34142e7	−1.21233	−0.606165	−	0.795339i	$-0.707293\pi$
$821$	−2.34142e7	−1.21233	−0.606165	+	0.795339i	$0.707293\pi$
$822$	−1.03975e7	−0.536723
$823$	−3.26808e7	−1.68187	−0.840936	−	0.541134i	$-0.817995\pi$
$823$	−3.26808e7	−1.68187	−0.840936	+	0.541134i	$0.817995\pi$
$824$	−1.01431e7	−0.520420
$825$	836719.	0.0428001
$826$	4.01713e6	0.204864
$827$	−3.24011e6	−0.164739	−0.0823695	−	0.996602i	$-0.526249\pi$
$827$	−3.24011e6	−0.164739	−0.0823695	+	0.996602i	$0.526249\pi$
$828$	461756.	0.0234065
$829$	1.19172e7	0.602267	0.301133	−	0.953582i	$-0.402635\pi$
$829$	1.19172e7	0.602267	0.301133	+	0.953582i	$0.402635\pi$
$830$	−7.01807e6	−0.353608
$831$	1.01732e7	0.511039
$832$	4.67167e6	0.233972
$833$	−2.91415e7	−1.45512
$834$	−1.39013e7	−0.692056
$835$	9.97010e6	0.494861
$836$	−859181.	−0.0425176
$837$	−7.59576e6	−0.374764
$838$	6.90709e6	0.339770
$839$	7.70311e6	0.377800	0.188900	−	0.981996i	$-0.439508\pi$
$839$	7.70311e6	0.377800	0.188900	+	0.981996i	$0.439508\pi$
$840$	−493872.	−0.0241499
$841$	1.33842e7	0.652533
$842$	−2.75210e7	−1.33778
$843$	−2.15722e7	−1.04550
$844$	−3.37650e6	−0.163159
$845$	−2.32387e7	−1.11962
$846$	7.83183e6	0.376216
$847$	4.76464e6	0.228203
$848$	−6.34415e6	−0.302959
$849$	−4.47187e6	−0.212922
$850$	−4.66093e6	−0.221272
$851$	2.27703e6	0.107782
$852$	9.21318e6	0.434821
$853$	1.45542e7	0.684884	0.342442	−	0.939539i	$-0.388746\pi$
$853$	1.45542e7	0.684884	0.342442	+	0.939539i	$0.388746\pi$
$854$	76786.0	0.00360278
$855$	731025.	0.0341993
$856$	−1.38898e6	−0.0647905
$857$	−8.43725e6	−0.392418	−0.196209	−	0.980562i	$-0.562863\pi$
$857$	−8.43725e6	−0.392418	−0.196209	+	0.980562i	$0.562863\pi$
$858$	−6.10762e6	−0.283239
$859$	1.70266e7	0.787311	0.393655	−	0.919258i	$-0.371210\pi$
$859$	1.70266e7	0.787311	0.393655	+	0.919258i	$0.371210\pi$
$860$	−9.24310e6	−0.426159
$861$	−1.19648e6	−0.0550042
$862$	−2.63035e7	−1.20572
$863$	−2.31049e7	−1.05603	−0.528016	−	0.849235i	$-0.677064\pi$
$863$	−2.31049e7	−1.05603	−0.528016	+	0.849235i	$0.677064\pi$
$864$	−746496.	−0.0340207
$865$	1.54936e7	0.704064
$866$	−2.56177e7	−1.16077
$867$	1.85043e7	0.836036
$868$	5.71763e6	0.257583
$869$	1.07649e7	0.483572
$870$	−5.23977e6	−0.234701
$871$	3.95453e7	1.76624
$872$	2.54696e6	0.113431
$873$	585415.	0.0259973
$874$	514488.	0.0227822
$875$	535885.	0.0236620
$876$	2.28002e6	0.100387
$877$	4.19637e7	1.84236	0.921180	−	0.389138i	$-0.127227\pi$
$877$	4.19637e7	1.84236	0.921180	+	0.389138i	$0.127227\pi$
$878$	−1.84588e7	−0.808105
$879$	−3.98807e6	−0.174097
$880$	−952001.	−0.0414410
$881$	−2.74856e7	−1.19307	−0.596533	−	0.802588i	$-0.703456\pi$
$881$	−2.74856e7	−1.19307	−0.596533	+	0.802588i	$0.703456\pi$
$882$	5.06436e6	0.219206
$883$	−2.77312e7	−1.19692	−0.598462	−	0.801151i	$-0.704221\pi$
$883$	−2.77312e7	−1.19692	−0.598462	+	0.801151i	$0.704221\pi$
$884$	3.40224e7	1.46431
$885$	−6.58851e6	−0.282767
$886$	−2.83986e6	−0.121538
$887$	3.03743e6	0.129628	0.0648138	−	0.997897i	$-0.479355\pi$
$887$	3.03743e6	0.129628	0.0648138	+	0.997897i	$0.479355\pi$
$888$	−3.68115e6	−0.156658
$889$	6.94996e6	0.294936
$890$	7.24501e6	0.306594
$891$	975949.	0.0411844
$892$	1.75419e7	0.738184
$893$	8.72621e6	0.366182
$894$	322582.	0.0134988
$895$	−546016.	−0.0227849
$896$	561917.	0.0233831
$897$	3.65731e6	0.151768
$898$	3.04054e7	1.25823
$899$	6.06616e7	2.50331
$900$	810000.	0.0333333
$901$	−4.62026e7	−1.89607
$902$	−2.30636e6	−0.0943866
$903$	−7.13267e6	−0.291093
$904$	−647115.	−0.0263366
$905$	−567798.	−0.0230448
$906$	−1.45685e7	−0.589651
$907$	4.35461e6	0.175765	0.0878823	−	0.996131i	$-0.471990\pi$
$907$	4.35461e6	0.175765	0.0878823	+	0.996131i	$0.471990\pi$
$908$	−1.53161e7	−0.616501
$909$	−4.62691e6	−0.185730
$910$	−3.91168e6	−0.156589
$911$	9.94232e6	0.396910	0.198455	−	0.980110i	$-0.436408\pi$
$911$	9.94232e6	0.396910	0.198455	+	0.980110i	$0.436408\pi$
$912$	−831744.	−0.0331133
$913$	−1.04394e7	−0.414475
$914$	−2.30486e7	−0.912597
$915$	−125937.	−0.00497279
$916$	8.49847e6	0.334659
$917$	−3.13690e6	−0.123191
$918$	−5.43651e6	−0.212919
$919$	−2.07729e7	−0.811350	−0.405675	−	0.914017i	$-0.632964\pi$
$919$	−2.07729e7	−0.811350	−0.405675	+	0.914017i	$0.632964\pi$
$920$	570069.	0.0222054
$921$	1.81211e7	0.703939
$922$	4.88918e6	0.189413
$923$	7.29725e7	2.81939
$924$	−734635.	−0.0283069
$925$	3.99431e6	0.153492
$926$	5.64304e6	0.216265
$927$	1.28374e7	0.490657
$928$	5.96170e6	0.227248
$929$	−2.40385e7	−0.913837	−0.456918	−	0.889509i	$-0.651047\pi$
$929$	−2.40385e7	−0.913837	−0.456918	+	0.889509i	$0.651047\pi$
$930$	−9.37748e6	−0.355532
$931$	5.64270e6	0.213360
$932$	−303369.	−0.0114402
$933$	−2.56018e7	−0.962867
$934$	2.90472e7	1.08953
$935$	−6.93314e6	−0.259359
$936$	−5.91258e6	−0.220591
$937$	−2.84683e7	−1.05928	−0.529642	−	0.848221i	$-0.677674\pi$
$937$	−2.84683e7	−1.05928	−0.529642	+	0.848221i	$0.677674\pi$
$938$	4.75658e6	0.176518
$939$	755157.	0.0279495
$940$	9.66893e6	0.356910
$941$	1.90770e7	0.702321	0.351161	−	0.936315i	$-0.385787\pi$
$941$	1.90770e7	0.702321	0.351161	+	0.936315i	$0.385787\pi$
$942$	1.53533e7	0.563734
$943$	1.38107e6	0.0505752
$944$	7.49626e6	0.273788
$945$	625057.	0.0227688
$946$	−1.37491e7	−0.499513
$947$	1.04106e7	0.377224	0.188612	−	0.982052i	$-0.439601\pi$
$947$	1.04106e7	0.377224	0.188612	+	0.982052i	$0.439601\pi$
$948$	1.04212e7	0.376613
$949$	1.80588e7	0.650914
$950$	902500.	0.0324443
$951$	1.51873e7	0.544541
$952$	4.09228e6	0.146343
$953$	1.36160e7	0.485642	0.242821	−	0.970071i	$-0.421927\pi$
$953$	1.36160e7	0.485642	0.242821	+	0.970071i	$0.421927\pi$
$954$	8.02931e6	0.285632
$955$	−3.84100e6	−0.136281
$956$	7.44329e6	0.263403
$957$	−7.79417e6	−0.275100
$958$	−1.03315e7	−0.363704
$959$	−9.90555e6	−0.347802
$960$	−921600.	−0.0322749
$961$	7.99353e7	2.79209
$962$	−2.91564e7	−1.01577
$963$	1.75793e6	0.0610850
$964$	−2.26060e7	−0.783484
$965$	−2.18829e7	−0.756463
$966$	439908.	0.0151677
$967$	1.92401e7	0.661670	0.330835	−	0.943689i	$-0.392670\pi$
$967$	1.92401e7	0.661670	0.330835	+	0.943689i	$0.392670\pi$
$968$	8.89116e6	0.304979
$969$	−6.05735e6	−0.207240
$970$	722734.	0.0246632
$971$	2.73741e7	0.931732	0.465866	−	0.884855i	$-0.345743\pi$
$971$	2.73741e7	0.931732	0.465866	+	0.884855i	$0.345743\pi$
$972$	944784.	0.0320750
$973$	−1.32436e7	−0.448460
$974$	−2.24284e7	−0.757530
$975$	6.41556e6	0.216134
$976$	143288.	0.00481488
$977$	−3.27651e7	−1.09819	−0.549093	−	0.835761i	$-0.685027\pi$
$977$	−3.27651e7	−1.09819	−0.549093	+	0.835761i	$0.685027\pi$
$978$	−1.83942e7	−0.614943
$979$	1.07770e7	0.359368
$980$	6.25230e6	0.207957
$981$	−3.22349e6	−0.106944
$982$	−7.17576e6	−0.237459
$983$	−3.39811e7	−1.12164	−0.560820	−	0.827938i	$-0.689514\pi$
$983$	−3.39811e7	−1.12164	−0.560820	+	0.827938i	$0.689514\pi$
$984$	−2.23271e6	−0.0735096
$985$	−2.05103e7	−0.673569
$986$	4.34173e7	1.42223
$987$	7.46127e6	0.243792
$988$	−6.58778e6	−0.214707
$989$	8.23313e6	0.267654
$990$	1.20488e6	0.0390710
$991$	−5.88603e7	−1.90388	−0.951938	−	0.306291i	$-0.900912\pi$
$991$	−5.88603e7	−1.90388	−0.951938	+	0.306291i	$0.900912\pi$
$992$	1.06695e7	0.344243
$993$	−3.37784e6	−0.108709
$994$	8.77726e6	0.281769
$995$	−1.70782e7	−0.546871
$996$	−1.01060e7	−0.322799
$997$	−5.35191e7	−1.70518	−0.852591	−	0.522579i	$-0.824970\pi$
$997$	−5.35191e7	−1.70518	−0.852591	+	0.522579i	$0.824970\pi$
$998$	−1.08378e7	−0.344440
$999$	4.65896e6	0.147698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.k.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.k.1.2	✓	4	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -34.2967 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -34.2967 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +148.750 q^{11} +144.000 q^{12} +1140.54 q^{13} +137.187 q^{14} -225.000 q^{15} +256.000 q^{16} +1864.37 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -308.670 q^{21} -595.000 q^{22} +356.293 q^{23} -576.000 q^{24} +625.000 q^{25} -4562.17 q^{26} +729.000 q^{27} -548.747 q^{28} -5821.97 q^{29} +900.000 q^{30} -10419.4 q^{31} -1024.00 q^{32} +1338.75 q^{33} -7457.50 q^{34} +857.417 q^{35} +1296.00 q^{36} +6390.89 q^{37} +1444.00 q^{38} +10264.9 q^{39} +1600.00 q^{40} +3876.23 q^{41} +1234.68 q^{42} +23107.7 q^{43} +2380.00 q^{44} -2025.00 q^{45} -1425.17 q^{46} -24172.3 q^{47} +2304.00 q^{48} -15630.7 q^{49} -2500.00 q^{50} +16779.4 q^{51} +18248.7 q^{52} -24781.8 q^{53} -2916.00 q^{54} -3718.75 q^{55} +2194.99 q^{56} -3249.00 q^{57} +23287.9 q^{58} +29282.3 q^{59} -3600.00 q^{60} +559.719 q^{61} +41677.7 q^{62} -2778.03 q^{63} +4096.00 q^{64} -28513.6 q^{65} -5355.00 q^{66} +34672.3 q^{67} +29830.0 q^{68} +3206.64 q^{69} -3429.67 q^{70} +63980.4 q^{71} -5184.00 q^{72} +15833.5 q^{73} -25563.6 q^{74} +5625.00 q^{75} -5776.00 q^{76} -5101.63 q^{77} -41059.6 q^{78} +72369.2 q^{79} -6400.00 q^{80} +6561.00 q^{81} -15504.9 q^{82} -70180.7 q^{83} -4938.72 q^{84} -46609.3 q^{85} -92431.0 q^{86} -52397.7 q^{87} -9520.01 q^{88} +72450.1 q^{89} +8100.00 q^{90} -39116.8 q^{91} +5700.69 q^{92} -93774.8 q^{93} +96689.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +7227.34 q^{97} +62523.0 q^{98} +12048.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 472 q^{11} + 576 q^{12} - 482 q^{13} - 104 q^{14} - 900 q^{15} + 1024 q^{16} + 1816 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} + 234 q^{21} + 1888 q^{22} - 418 q^{23} - 2304 q^{24} + 2500 q^{25} + 1928 q^{26} + 2916 q^{27} + 416 q^{28} - 10396 q^{29} + 3600 q^{30} + 528 q^{31} - 4096 q^{32} - 4248 q^{33} - 7264 q^{34} - 650 q^{35} + 5184 q^{36} + 5774 q^{37} + 5776 q^{38} - 4338 q^{39} + 6400 q^{40} + 9620 q^{41} - 936 q^{42} + 21098 q^{43} - 7552 q^{44} - 8100 q^{45} + 1672 q^{46} - 18858 q^{47} + 9216 q^{48} + 2148 q^{49} - 10000 q^{50} + 16344 q^{51} - 7712 q^{52} + 822 q^{53} - 11664 q^{54} + 11800 q^{55} - 1664 q^{56} - 12996 q^{57} + 41584 q^{58} + 28672 q^{59} - 14400 q^{60} + 77748 q^{61} - 2112 q^{62} + 2106 q^{63} + 16384 q^{64} + 12050 q^{65} + 16992 q^{66} + 82400 q^{67} + 29056 q^{68} - 3762 q^{69} + 2600 q^{70} + 928 q^{71} - 20736 q^{72} + 121100 q^{73} - 23096 q^{74} + 22500 q^{75} - 23104 q^{76} - 120220 q^{77} + 17352 q^{78} + 144284 q^{79} - 25600 q^{80} + 26244 q^{81} - 38480 q^{82} - 6082 q^{83} + 3744 q^{84} - 45400 q^{85} - 84392 q^{86} - 93564 q^{87} + 30208 q^{88} + 43260 q^{89} + 32400 q^{90} + 135148 q^{91} - 6688 q^{92} + 4752 q^{93} + 75432 q^{94} + 36100 q^{95} - 36864 q^{96} - 6862 q^{97} - 8592 q^{98} - 38232 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 - 472 * q^11 + 576 * q^12 - 482 * q^13 - 104 * q^14 - 900 * q^15 + 1024 * q^16 + 1816 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 + 234 * q^21 + 1888 * q^22 - 418 * q^23 - 2304 * q^24 + 2500 * q^25 + 1928 * q^26 + 2916 * q^27 + 416 * q^28 - 10396 * q^29 + 3600 * q^30 + 528 * q^31 - 4096 * q^32 - 4248 * q^33 - 7264 * q^34 - 650 * q^35 + 5184 * q^36 + 5774 * q^37 + 5776 * q^38 - 4338 * q^39 + 6400 * q^40 + 9620 * q^41 - 936 * q^42 + 21098 * q^43 - 7552 * q^44 - 8100 * q^45 + 1672 * q^46 - 18858 * q^47 + 9216 * q^48 + 2148 * q^49 - 10000 * q^50 + 16344 * q^51 - 7712 * q^52 + 822 * q^53 - 11664 * q^54 + 11800 * q^55 - 1664 * q^56 - 12996 * q^57 + 41584 * q^58 + 28672 * q^59 - 14400 * q^60 + 77748 * q^61 - 2112 * q^62 + 2106 * q^63 + 16384 * q^64 + 12050 * q^65 + 16992 * q^66 + 82400 * q^67 + 29056 * q^68 - 3762 * q^69 + 2600 * q^70 + 928 * q^71 - 20736 * q^72 + 121100 * q^73 - 23096 * q^74 + 22500 * q^75 - 23104 * q^76 - 120220 * q^77 + 17352 * q^78 + 144284 * q^79 - 25600 * q^80 + 26244 * q^81 - 38480 * q^82 - 6082 * q^83 + 3744 * q^84 - 45400 * q^85 - 84392 * q^86 - 93564 * q^87 + 30208 * q^88 + 43260 * q^89 + 32400 * q^90 + 135148 * q^91 - 6688 * q^92 + 4752 * q^93 + 75432 * q^94 + 36100 * q^95 - 36864 * q^96 - 6862 * q^97 - 8592 * q^98 - 38232 * q^99

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