LMFDB - Embedded newform 570.6.a.l.1.1

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:	$1$
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} - 1748x^{2} - 8028x + 111960 $ x^4 - 1748x^2 - 8028x + 111960
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			1.1
Root			$6.07644$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -100.821 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -100.821 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +338.382 q^{11} +144.000 q^{12} -137.790 q^{13} +403.284 q^{14} +225.000 q^{15} +256.000 q^{16} -1220.16 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} -907.390 q^{21} -1353.53 q^{22} +297.045 q^{23} -576.000 q^{24} +625.000 q^{25} +551.162 q^{26} +729.000 q^{27} -1613.14 q^{28} -2034.38 q^{29} -900.000 q^{30} +6503.94 q^{31} -1024.00 q^{32} +3045.43 q^{33} +4880.64 q^{34} -2520.53 q^{35} +1296.00 q^{36} +12553.4 q^{37} +1444.00 q^{38} -1240.11 q^{39} -1600.00 q^{40} -9227.60 q^{41} +3629.56 q^{42} -19580.3 q^{43} +5414.10 q^{44} +2025.00 q^{45} -1188.18 q^{46} -17723.5 q^{47} +2304.00 q^{48} -6642.11 q^{49} -2500.00 q^{50} -10981.4 q^{51} -2204.65 q^{52} -33694.1 q^{53} -2916.00 q^{54} +8459.54 q^{55} +6452.55 q^{56} -3249.00 q^{57} +8137.52 q^{58} +44727.7 q^{59} +3600.00 q^{60} -12956.9 q^{61} -26015.8 q^{62} -8166.51 q^{63} +4096.00 q^{64} -3444.76 q^{65} -12181.7 q^{66} -45706.9 q^{67} -19522.5 q^{68} +2673.41 q^{69} +10082.1 q^{70} +23097.6 q^{71} -5184.00 q^{72} -21273.9 q^{73} -50213.4 q^{74} +5625.00 q^{75} -5776.00 q^{76} -34116.0 q^{77} +4960.46 q^{78} +54876.9 q^{79} +6400.00 q^{80} +6561.00 q^{81} +36910.4 q^{82} +91994.1 q^{83} -14518.2 q^{84} -30504.0 q^{85} +78321.3 q^{86} -18309.4 q^{87} -21656.4 q^{88} -20172.5 q^{89} -8100.00 q^{90} +13892.2 q^{91} +4752.73 q^{92} +58535.5 q^{93} +70894.0 q^{94} -9025.00 q^{95} -9216.00 q^{96} +67255.2 q^{97} +26568.4 q^{98} +27408.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 336 q^{11} + 576 q^{12} - 734 q^{13} + 104 q^{14} + 900 q^{15} + 1024 q^{16} + 480 q^{17} - 1296 q^{18} - 1444 q^{19} + 1600 q^{20} - 234 q^{21} + 1344 q^{22} - 1962 q^{23} - 2304 q^{24} + 2500 q^{25} + 2936 q^{26} + 2916 q^{27} - 416 q^{28} - 8720 q^{29} - 3600 q^{30} - 240 q^{31} - 4096 q^{32} - 3024 q^{33} - 1920 q^{34} - 650 q^{35} + 5184 q^{36} - 14626 q^{37} + 5776 q^{38} - 6606 q^{39} - 6400 q^{40} - 11092 q^{41} + 936 q^{42} - 16778 q^{43} - 5376 q^{44} + 8100 q^{45} + 7848 q^{46} - 34810 q^{47} + 9216 q^{48} - 34032 q^{49} - 10000 q^{50} + 4320 q^{51} - 11744 q^{52} - 18186 q^{53} - 11664 q^{54} - 8400 q^{55} + 1664 q^{56} - 12996 q^{57} + 34880 q^{58} - 38700 q^{59} + 14400 q^{60} - 12080 q^{61} + 960 q^{62} - 2106 q^{63} + 16384 q^{64} - 18350 q^{65} + 12096 q^{66} - 84216 q^{67} + 7680 q^{68} - 17658 q^{69} + 2600 q^{70} + 3592 q^{71} - 20736 q^{72} - 41180 q^{73} + 58504 q^{74} + 22500 q^{75} - 23104 q^{76} - 6696 q^{77} + 26424 q^{78} + 15272 q^{79} + 25600 q^{80} + 26244 q^{81} + 44368 q^{82} + 133106 q^{83} - 3744 q^{84} + 12000 q^{85} + 67112 q^{86} - 78480 q^{87} + 21504 q^{88} + 133704 q^{89} - 32400 q^{90} - 86656 q^{91} - 31392 q^{92} - 2160 q^{93} + 139240 q^{94} - 36100 q^{95} - 36864 q^{96} - 161594 q^{97} + 136128 q^{98} - 27216 q^{99}+O(q^{100}) \) 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 - 336 * q^11 + 576 * q^12 - 734 * q^13 + 104 * q^14 + 900 * q^15 + 1024 * q^16 + 480 * q^17 - 1296 * q^18 - 1444 * q^19 + 1600 * q^20 - 234 * q^21 + 1344 * q^22 - 1962 * q^23 - 2304 * q^24 + 2500 * q^25 + 2936 * q^26 + 2916 * q^27 - 416 * q^28 - 8720 * q^29 - 3600 * q^30 - 240 * q^31 - 4096 * q^32 - 3024 * q^33 - 1920 * q^34 - 650 * q^35 + 5184 * q^36 - 14626 * q^37 + 5776 * q^38 - 6606 * q^39 - 6400 * q^40 - 11092 * q^41 + 936 * q^42 - 16778 * q^43 - 5376 * q^44 + 8100 * q^45 + 7848 * q^46 - 34810 * q^47 + 9216 * q^48 - 34032 * q^49 - 10000 * q^50 + 4320 * q^51 - 11744 * q^52 - 18186 * q^53 - 11664 * q^54 - 8400 * q^55 + 1664 * q^56 - 12996 * q^57 + 34880 * q^58 - 38700 * q^59 + 14400 * q^60 - 12080 * q^61 + 960 * q^62 - 2106 * q^63 + 16384 * q^64 - 18350 * q^65 + 12096 * q^66 - 84216 * q^67 + 7680 * q^68 - 17658 * q^69 + 2600 * q^70 + 3592 * q^71 - 20736 * q^72 - 41180 * q^73 + 58504 * q^74 + 22500 * q^75 - 23104 * q^76 - 6696 * q^77 + 26424 * q^78 + 15272 * q^79 + 25600 * q^80 + 26244 * q^81 + 44368 * q^82 + 133106 * q^83 - 3744 * q^84 + 12000 * q^85 + 67112 * q^86 - 78480 * q^87 + 21504 * q^88 + 133704 * q^89 - 32400 * q^90 - 86656 * q^91 - 31392 * q^92 - 2160 * q^93 + 139240 * q^94 - 36100 * q^95 - 36864 * q^96 - 161594 * q^97 + 136128 * q^98 - 27216 * 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
$7$	−100.821	−0.777690	−0.388845	−	0.921303i	$-0.627126\pi$
$7$	−100.821	−0.777690	−0.388845	+	0.921303i	$0.627126\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	338.382	0.843189	0.421594	−	0.906784i	$-0.361471\pi$
$11$	338.382	0.843189	0.421594	+	0.906784i	$0.361471\pi$
$12$	144.000	0.288675
$13$	−137.790	−0.226131	−0.113066	−	0.993588i	$-0.536067\pi$
$13$	−137.790	−0.226131	−0.113066	+	0.993588i	$0.536067\pi$
$14$	403.284	0.549910
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−1220.16	−1.02399	−0.511993	−	0.858989i	$-0.671093\pi$
$17$	−1220.16	−1.02399	−0.511993	+	0.858989i	$0.671093\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	400.000	0.223607
$21$	−907.390	−0.448999
$22$	−1353.53	−0.596225
$23$	297.045	0.117086	0.0585428	−	0.998285i	$-0.481355\pi$
$23$	297.045	0.117086	0.0585428	+	0.998285i	$0.481355\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	551.162	0.159899
$27$	729.000	0.192450
$28$	−1613.14	−0.388845
$29$	−2034.38	−0.449197	−0.224599	−	0.974451i	$-0.572107\pi$
$29$	−2034.38	−0.449197	−0.224599	+	0.974451i	$0.572107\pi$
$30$	−900.000	−0.182574
$31$	6503.94	1.21555	0.607774	−	0.794110i	$-0.292063\pi$
$31$	6503.94	1.21555	0.607774	+	0.794110i	$0.292063\pi$
$32$	−1024.00	−0.176777
$33$	3045.43	0.486815
$34$	4880.64	0.724068
$35$	−2520.53	−0.347793
$36$	1296.00	0.166667
$37$	12553.4	1.50749	0.753747	−	0.657165i	$-0.228245\pi$
$37$	12553.4	1.50749	0.753747	+	0.657165i	$0.228245\pi$
$38$	1444.00	0.162221
$39$	−1240.11	−0.130557
$40$	−1600.00	−0.158114
$41$	−9227.60	−0.857293	−0.428646	−	0.903472i	$-0.641009\pi$
$41$	−9227.60	−0.857293	−0.428646	+	0.903472i	$0.641009\pi$
$42$	3629.56	0.317490
$43$	−19580.3	−1.61491	−0.807456	−	0.589928i	$-0.799156\pi$
$43$	−19580.3	−1.61491	−0.807456	+	0.589928i	$0.799156\pi$
$44$	5414.10	0.421594
$45$	2025.00	0.149071
$46$	−1188.18	−0.0827920
$47$	−17723.5	−1.17032	−0.585160	−	0.810918i	$-0.698968\pi$
$47$	−17723.5	−1.17032	−0.585160	+	0.810918i	$0.698968\pi$
$48$	2304.00	0.144338
$49$	−6642.11	−0.395199
$50$	−2500.00	−0.141421
$51$	−10981.4	−0.591199
$52$	−2204.65	−0.113066
$53$	−33694.1	−1.64765	−0.823824	−	0.566845i	$-0.808164\pi$
$53$	−33694.1	−1.64765	−0.823824	+	0.566845i	$0.808164\pi$
$54$	−2916.00	−0.136083
$55$	8459.54	0.377086
$56$	6452.55	0.274955
$57$	−3249.00	−0.132453
$58$	8137.52	0.317630
$59$	44727.7	1.67281	0.836405	−	0.548111i	$-0.184653\pi$
$59$	44727.7	1.67281	0.836405	+	0.548111i	$0.184653\pi$
$60$	3600.00	0.129099
$61$	−12956.9	−0.445837	−0.222919	−	0.974837i	$-0.571558\pi$
$61$	−12956.9	−0.445837	−0.222919	+	0.974837i	$0.571558\pi$
$62$	−26015.8	−0.859523
$63$	−8166.51	−0.259230
$64$	4096.00	0.125000
$65$	−3444.76	−0.101129
$66$	−12181.7	−0.344230
$67$	−45706.9	−1.24393	−0.621964	−	0.783046i	$-0.713665\pi$
$67$	−45706.9	−1.24393	−0.621964	+	0.783046i	$0.713665\pi$
$68$	−19522.5	−0.511993
$69$	2673.41	0.0675994
$70$	10082.1	0.245927
$71$	23097.6	0.543777	0.271888	−	0.962329i	$-0.412352\pi$
$71$	23097.6	0.543777	0.271888	+	0.962329i	$0.412352\pi$
$72$	−5184.00	−0.117851
$73$	−21273.9	−0.467241	−0.233620	−	0.972328i	$-0.575057\pi$
$73$	−21273.9	−0.467241	−0.233620	+	0.972328i	$0.575057\pi$
$74$	−50213.4	−1.06596
$75$	5625.00	0.115470
$76$	−5776.00	−0.114708
$77$	−34116.0	−0.655739
$78$	4960.46	0.0923177
$79$	54876.9	0.989285	0.494643	−	0.869096i	$-0.335299\pi$
$79$	54876.9	0.989285	0.494643	+	0.869096i	$0.335299\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	36910.4	0.606198
$83$	91994.1	1.46577	0.732883	−	0.680355i	$-0.238174\pi$
$83$	91994.1	1.46577	0.732883	+	0.680355i	$0.238174\pi$
$84$	−14518.2	−0.224500
$85$	−30504.0	−0.457941
$86$	78321.3	1.14192
$87$	−18309.4	−0.259344
$88$	−21656.4	−0.298112
$89$	−20172.5	−0.269952	−0.134976	−	0.990849i	$-0.543096\pi$
$89$	−20172.5	−0.269952	−0.134976	+	0.990849i	$0.543096\pi$
$90$	−8100.00	−0.105409
$91$	13892.2	0.175860
$92$	4752.73	0.0585428
$93$	58535.5	0.701797
$94$	70894.0	0.827542
$95$	−9025.00	−0.102598
$96$	−9216.00	−0.102062
$97$	67255.2	0.725766	0.362883	−	0.931835i	$-0.381792\pi$
$97$	67255.2	0.725766	0.362883	+	0.931835i	$0.381792\pi$
$98$	26568.4	0.279448
$99$	27408.9	0.281063
$100$	10000.0	0.100000
$101$	−115359.	−1.12525	−0.562625	−	0.826712i	$-0.690208\pi$
$101$	−115359.	−1.12525	−0.562625	+	0.826712i	$0.690208\pi$
$102$	43925.7	0.418041
$103$	−69993.2	−0.650074	−0.325037	−	0.945701i	$-0.605377\pi$
$103$	−69993.2	−0.650074	−0.325037	+	0.945701i	$0.605377\pi$
$104$	8818.59	0.0799495
$105$	−22684.7	−0.200799
$106$	134777.	1.16506
$107$	−15323.2	−0.129387	−0.0646935	−	0.997905i	$-0.520607\pi$
$107$	−15323.2	−0.129387	−0.0646935	+	0.997905i	$0.520607\pi$
$108$	11664.0	0.0962250
$109$	−70034.8	−0.564609	−0.282304	−	0.959325i	$-0.591099\pi$
$109$	−70034.8	−0.564609	−0.282304	+	0.959325i	$0.591099\pi$
$110$	−33838.2	−0.266640
$111$	112980.	0.870352
$112$	−25810.2	−0.194422
$113$	124238.	0.915291	0.457646	−	0.889135i	$-0.348693\pi$
$113$	124238.	0.915291	0.457646	+	0.889135i	$0.348693\pi$
$114$	12996.0	0.0936586
$115$	7426.14	0.0523623
$116$	−32550.1	−0.224599
$117$	−11161.0	−0.0753771
$118$	−178911.	−1.18286
$119$	123018.	0.796344
$120$	−14400.0	−0.0912871
$121$	−46549.0	−0.289032
$122$	51827.6	0.315255
$123$	−83048.4	−0.494958
$124$	104063.	0.607774
$125$	15625.0	0.0894427
$126$	32666.0	0.183303
$127$	−235364.	−1.29488	−0.647442	−	0.762115i	$-0.724161\pi$
$127$	−235364.	−1.29488	−0.647442	+	0.762115i	$0.724161\pi$
$128$	−16384.0	−0.0883883
$129$	−176223.	−0.932370
$130$	13779.0	0.0715090
$131$	−159118.	−0.810104	−0.405052	−	0.914294i	$-0.632747\pi$
$131$	−159118.	−0.810104	−0.405052	+	0.914294i	$0.632747\pi$
$132$	48726.9	0.243408
$133$	36396.4	0.178414
$134$	182828.	0.879589
$135$	18225.0	0.0860663
$136$	78090.2	0.362034
$137$	130703.	0.594953	0.297477	−	0.954729i	$-0.403855\pi$
$137$	130703.	0.594953	0.297477	+	0.954729i	$0.403855\pi$
$138$	−10693.6	−0.0478000
$139$	−219459.	−0.963421	−0.481710	−	0.876331i	$-0.659984\pi$
$139$	−219459.	−0.963421	−0.481710	+	0.876331i	$0.659984\pi$
$140$	−40328.4	−0.173897
$141$	−159512.	−0.675685
$142$	−92390.3	−0.384508
$143$	−46625.7	−0.190671
$144$	20736.0	0.0833333
$145$	−50859.5	−0.200887
$146$	85095.7	0.330389
$147$	−59779.0	−0.228168
$148$	200854.	0.753747
$149$	377552.	1.39319	0.696596	−	0.717464i	$-0.254697\pi$
$149$	377552.	1.39319	0.696596	+	0.717464i	$0.254697\pi$
$150$	−22500.0	−0.0816497
$151$	−529583.	−1.89013	−0.945066	−	0.326881i	$-0.894002\pi$
$151$	−529583.	−1.89013	−0.945066	+	0.326881i	$0.894002\pi$
$152$	23104.0	0.0811107
$153$	−98832.9	−0.341329
$154$	136464.	0.463678
$155$	162599.	0.543610
$156$	−19841.8	−0.0652785
$157$	−117051.	−0.378989	−0.189494	−	0.981882i	$-0.560685\pi$
$157$	−117051.	−0.378989	−0.189494	+	0.981882i	$0.560685\pi$
$158$	−219507.	−0.699530
$159$	−303247.	−0.951270
$160$	−25600.0	−0.0790569
$161$	−29948.5	−0.0910562
$162$	−26244.0	−0.0785674
$163$	−114646.	−0.337978	−0.168989	−	0.985618i	$-0.554050\pi$
$163$	−114646.	−0.337978	−0.168989	+	0.985618i	$0.554050\pi$
$164$	−147642.	−0.428646
$165$	76135.8	0.217710
$166$	−367976.	−1.03645
$167$	−332091.	−0.921437	−0.460718	−	0.887546i	$-0.652408\pi$
$167$	−332091.	−0.921437	−0.460718	+	0.887546i	$0.652408\pi$
$168$	58072.9	0.158745
$169$	−352307.	−0.948865
$170$	122016.	0.323813
$171$	−29241.0	−0.0764719
$172$	−313285.	−0.807456
$173$	−649253.	−1.64930	−0.824649	−	0.565645i	$-0.808627\pi$
$173$	−649253.	−1.64930	−0.824649	+	0.565645i	$0.808627\pi$
$174$	73237.7	0.183384
$175$	−63013.2	−0.155538
$176$	86625.7	0.210797
$177$	402550.	0.965798
$178$	80690.2	0.190885
$179$	158489.	0.369714	0.184857	−	0.982765i	$-0.440818\pi$
$179$	158489.	0.369714	0.184857	+	0.982765i	$0.440818\pi$
$180$	32400.0	0.0745356
$181$	−330469.	−0.749781	−0.374891	−	0.927069i	$-0.622320\pi$
$181$	−330469.	−0.749781	−0.374891	+	0.927069i	$0.622320\pi$
$182$	−55568.7	−0.124352
$183$	−116612.	−0.257404
$184$	−19010.9	−0.0413960
$185$	313834.	0.674172
$186$	−234142.	−0.496246
$187$	−412879.	−0.863414
$188$	−283576.	−0.585160
$189$	−73498.6	−0.149666
$190$	36100.0	0.0725476
$191$	−592285.	−1.17475	−0.587377	−	0.809313i	$-0.699839\pi$
$191$	−592285.	−1.17475	−0.587377	+	0.809313i	$0.699839\pi$
$192$	36864.0	0.0721688
$193$	646179.	1.24870	0.624352	−	0.781143i	$-0.285363\pi$
$193$	646179.	1.24870	0.624352	+	0.781143i	$0.285363\pi$
$194$	−269021.	−0.513194
$195$	−31002.8	−0.0583869
$196$	−106274.	−0.197599
$197$	−501438.	−0.920559	−0.460280	−	0.887774i	$-0.652251\pi$
$197$	−501438.	−0.920559	−0.460280	+	0.887774i	$0.652251\pi$
$198$	−109636.	−0.198742
$199$	859557.	1.53866	0.769329	−	0.638853i	$-0.220591\pi$
$199$	859557.	1.53866	0.769329	+	0.638853i	$0.220591\pi$
$200$	−40000.0	−0.0707107
$201$	−411362.	−0.718182
$202$	461437.	0.795672
$203$	205108.	0.349336
$204$	−175703.	−0.295599
$205$	−230690.	−0.383393
$206$	279973.	0.459671
$207$	24060.7	0.0390285
$208$	−35274.4	−0.0565328
$209$	−122156.	−0.193441
$210$	90739.0	0.141986
$211$	−700851.	−1.08373	−0.541863	−	0.840467i	$-0.682281\pi$
$211$	−700851.	−1.08373	−0.541863	+	0.840467i	$0.682281\pi$
$212$	−539106.	−0.823824
$213$	207878.	0.313950
$214$	61292.9	0.0914904
$215$	−489508.	−0.722211
$216$	−46656.0	−0.0680414
$217$	−655734.	−0.945320
$218$	280139.	0.399239
$219$	−191465.	−0.269762
$220$	135353.	0.188543
$221$	168126.	0.231555
$222$	−451921.	−0.615432
$223$	−993828.	−1.33829	−0.669143	−	0.743133i	$-0.733339\pi$
$223$	−993828.	−1.33829	−0.669143	+	0.743133i	$0.733339\pi$
$224$	103241.	0.137477
$225$	50625.0	0.0666667
$226$	−496953.	−0.647209
$227$	476033.	0.613158	0.306579	−	0.951845i	$-0.400816\pi$
$227$	476033.	0.613158	0.306579	+	0.951845i	$0.400816\pi$
$228$	−51984.0	−0.0662266
$229$	−410551.	−0.517343	−0.258671	−	0.965965i	$-0.583285\pi$
$229$	−410551.	−0.517343	−0.258671	+	0.965965i	$0.583285\pi$
$230$	−29704.5	−0.0370257
$231$	−307044.	−0.378591
$232$	130200.	0.158815
$233$	294030.	0.354815	0.177408	−	0.984137i	$-0.443229\pi$
$233$	294030.	0.354815	0.177408	+	0.984137i	$0.443229\pi$
$234$	44644.1	0.0532997
$235$	−443088.	−0.523383
$236$	715644.	0.836405
$237$	493892.	0.571164
$238$	−492071.	−0.563100
$239$	1.53612e6	1.73952	0.869760	−	0.493475i	$-0.164274\pi$
$239$	1.53612e6	1.73952	0.869760	+	0.493475i	$0.164274\pi$
$240$	57600.0	0.0645497
$241$	−768986.	−0.852856	−0.426428	−	0.904522i	$-0.640228\pi$
$241$	−768986.	−0.852856	−0.426428	+	0.904522i	$0.640228\pi$
$242$	186196.	0.204377
$243$	59049.0	0.0641500
$244$	−207310.	−0.222919
$245$	−166053.	−0.176738
$246$	332194.	0.349988
$247$	49742.3	0.0518781
$248$	−416252.	−0.429761
$249$	827947.	0.846260
$250$	−62500.0	−0.0632456
$251$	153024.	0.153312	0.0766559	−	0.997058i	$-0.475576\pi$
$251$	153024.	0.153312	0.0766559	+	0.997058i	$0.475576\pi$
$252$	−130664.	−0.129615
$253$	100515.	0.0987253
$254$	941456.	0.915621
$255$	−274536.	−0.264392
$256$	65536.0	0.0625000
$257$	−236006.	−0.222890	−0.111445	−	0.993771i	$-0.535548\pi$
$257$	−236006.	−0.222890	−0.111445	+	0.993771i	$0.535548\pi$
$258$	704892.	0.659285
$259$	−1.26564e6	−1.17236
$260$	−55116.2	−0.0505645
$261$	−164785.	−0.149732
$262$	636471.	0.572830
$263$	−2.06206e6	−1.83828	−0.919138	−	0.393935i	$-0.871114\pi$
$263$	−2.06206e6	−1.83828	−0.919138	+	0.393935i	$0.871114\pi$
$264$	−194908.	−0.172115
$265$	−842353.	−0.736851
$266$	−145586.	−0.126158
$267$	−181553.	−0.155857
$268$	−731311.	−0.621964
$269$	−830816.	−0.700042	−0.350021	−	0.936742i	$-0.613826\pi$
$269$	−830816.	−0.700042	−0.350021	+	0.936742i	$0.613826\pi$
$270$	−72900.0	−0.0608581
$271$	483146.	0.399627	0.199814	−	0.979834i	$-0.435966\pi$
$271$	483146.	0.399627	0.199814	+	0.979834i	$0.435966\pi$
$272$	−312361.	−0.255997
$273$	125030.	0.101533
$274$	−522810.	−0.420695
$275$	211488.	0.168638
$276$	42774.6	0.0337997
$277$	−97843.5	−0.0766183	−0.0383091	−	0.999266i	$-0.512197\pi$
$277$	−97843.5	−0.0766183	−0.0383091	+	0.999266i	$0.512197\pi$
$278$	877835.	0.681241
$279$	526819.	0.405183
$280$	161314.	0.122964
$281$	−539960.	−0.407939	−0.203970	−	0.978977i	$-0.565384\pi$
$281$	−539960.	−0.407939	−0.203970	+	0.978977i	$0.565384\pi$
$282$	638046.	0.477781
$283$	−1.85058e6	−1.37354	−0.686771	−	0.726874i	$-0.740972\pi$
$283$	−1.85058e6	−1.37354	−0.686771	+	0.726874i	$0.740972\pi$
$284$	369561.	0.271888
$285$	−81225.0	−0.0592349
$286$	186503.	0.134825
$287$	930337.	0.666708
$288$	−82944.0	−0.0589256
$289$	68931.8	0.0485484
$290$	203438.	0.142049
$291$	605297.	0.419021
$292$	−340383.	−0.233620
$293$	1.83792e6	1.25071	0.625355	−	0.780341i	$-0.284954\pi$
$293$	1.83792e6	1.25071	0.625355	+	0.780341i	$0.284954\pi$
$294$	239116.	0.161339
$295$	1.11819e6	0.748104
$296$	−803415.	−0.532979
$297$	246680.	0.162272
$298$	−1.51021e6	−0.985135
$299$	−40930.0	−0.0264767
$300$	90000.0	0.0577350
$301$	1.97411e6	1.25590
$302$	2.11833e6	1.33652
$303$	−1.03823e6	−0.649663
$304$	−92416.0	−0.0573539
$305$	−323922.	−0.199384
$306$	395332.	0.241356
$307$	−2.44293e6	−1.47933	−0.739666	−	0.672974i	$-0.765017\pi$
$307$	−2.44293e6	−1.47933	−0.739666	+	0.672974i	$0.765017\pi$
$308$	−545856.	−0.327870
$309$	−629938.	−0.375320
$310$	−650394.	−0.384390
$311$	−1.34454e6	−0.788267	−0.394133	−	0.919053i	$-0.628955\pi$
$311$	−1.34454e6	−0.788267	−0.394133	+	0.919053i	$0.628955\pi$
$312$	79367.3	0.0461589
$313$	−15680.7	−0.00904703	−0.00452351	−	0.999990i	$-0.501440\pi$
$313$	−15680.7	−0.00904703	−0.00452351	+	0.999990i	$0.501440\pi$
$314$	468204.	0.267985
$315$	−204163.	−0.115931
$316$	878030.	0.494643
$317$	−1.14266e6	−0.638658	−0.319329	−	0.947644i	$-0.603457\pi$
$317$	−1.14266e6	−0.638658	−0.319329	+	0.947644i	$0.603457\pi$
$318$	1.21299e6	0.672650
$319$	−688397.	−0.378758
$320$	102400.	0.0559017
$321$	−137909.	−0.0747016
$322$	119794.	0.0643865
$323$	440478.	0.234919
$324$	104976.	0.0555556
$325$	−86119.0	−0.0452263
$326$	458582.	0.238986
$327$	−630313.	−0.325977
$328$	590567.	0.303099
$329$	1.78690e6	0.910146
$330$	−304543.	−0.153945
$331$	−2.99850e6	−1.50430	−0.752150	−	0.658992i	$-0.770983\pi$
$331$	−2.99850e6	−1.50430	−0.752150	+	0.658992i	$0.770983\pi$
$332$	1.47191e6	0.732883
$333$	1.01682e6	0.502498
$334$	1.32836e6	0.651554
$335$	−1.14267e6	−0.556301
$336$	−232292.	−0.112250
$337$	−471652.	−0.226228	−0.113114	−	0.993582i	$-0.536083\pi$
$337$	−471652.	−0.226228	−0.113114	+	0.993582i	$0.536083\pi$
$338$	1.40923e6	0.670949
$339$	1.11814e6	0.528444
$340$	−488064.	−0.228970
$341$	2.20081e6	1.02494
$342$	116964.	0.0540738
$343$	2.36416e6	1.08503
$344$	1.25314e6	0.570958
$345$	66835.2	0.0302314
$346$	2.59701e6	1.16623
$347$	3.94833e6	1.76031	0.880155	−	0.474686i	$-0.157438\pi$
$347$	3.94833e6	1.76031	0.880155	+	0.474686i	$0.157438\pi$
$348$	−292951.	−0.129672
$349$	1.67138e6	0.734534	0.367267	−	0.930116i	$-0.380294\pi$
$349$	1.67138e6	0.734534	0.367267	+	0.930116i	$0.380294\pi$
$350$	252053.	0.109982
$351$	−100449.	−0.0435190
$352$	−346503.	−0.149056
$353$	−2.75199e6	−1.17547	−0.587733	−	0.809055i	$-0.699980\pi$
$353$	−2.75199e6	−1.17547	−0.587733	+	0.809055i	$0.699980\pi$
$354$	−1.61020e6	−0.682922
$355$	577439.	0.243184
$356$	−322761.	−0.134976
$357$	1.10716e6	0.459769
$358$	−633955.	−0.261427
$359$	−2.57834e6	−1.05586	−0.527928	−	0.849289i	$-0.677031\pi$
$359$	−2.57834e6	−1.05586	−0.527928	+	0.849289i	$0.677031\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	1.32188e6	0.530175
$363$	−418941.	−0.166873
$364$	222275.	0.0879300
$365$	−531848.	−0.208956
$366$	466448.	0.182012
$367$	1.06607e6	0.413163	0.206582	−	0.978429i	$-0.433766\pi$
$367$	1.06607e6	0.413163	0.206582	+	0.978429i	$0.433766\pi$
$368$	76043.6	0.0292714
$369$	−747436.	−0.285764
$370$	−1.25534e6	−0.476711
$371$	3.39708e6	1.28136
$372$	936567.	0.350899
$373$	906366.	0.337312	0.168656	−	0.985675i	$-0.446057\pi$
$373$	906366.	0.337312	0.168656	+	0.985675i	$0.446057\pi$
$374$	1.65152e6	0.610526
$375$	140625.	0.0516398
$376$	1.13430e6	0.413771
$377$	280318.	0.101578
$378$	293994.	0.105830
$379$	2.63998e6	0.944068	0.472034	−	0.881580i	$-0.343520\pi$
$379$	2.63998e6	0.944068	0.472034	+	0.881580i	$0.343520\pi$
$380$	−144400.	−0.0512989
$381$	−2.11828e6	−0.747601
$382$	2.36914e6	0.830677
$383$	3.26776e6	1.13829	0.569145	−	0.822237i	$-0.307274\pi$
$383$	3.26776e6	1.13829	0.569145	+	0.822237i	$0.307274\pi$
$384$	−147456.	−0.0510310
$385$	−852900.	−0.293256
$386$	−2.58472e6	−0.882967
$387$	−1.58601e6	−0.538304
$388$	1.07608e6	0.362883
$389$	345348.	0.115713	0.0578566	−	0.998325i	$-0.481573\pi$
$389$	345348.	0.115713	0.0578566	+	0.998325i	$0.481573\pi$
$390$	124011.	0.0412857
$391$	−362443.	−0.119894
$392$	425095.	0.139724
$393$	−1.43206e6	−0.467714
$394$	2.00575e6	0.650934
$395$	1.37192e6	0.442422
$396$	438542.	0.140531
$397$	−2.18911e6	−0.697095	−0.348548	−	0.937291i	$-0.613325\pi$
$397$	−2.18911e6	−0.697095	−0.348548	+	0.937291i	$0.613325\pi$
$398$	−3.43823e6	−1.08800
$399$	327568.	0.103008
$400$	160000.	0.0500000
$401$	1.39504e6	0.433238	0.216619	−	0.976256i	$-0.430497\pi$
$401$	1.39504e6	0.433238	0.216619	+	0.976256i	$0.430497\pi$
$402$	1.64545e6	0.507831
$403$	−896181.	−0.274874
$404$	−1.84575e6	−0.562625
$405$	164025.	0.0496904
$406$	−820434.	−0.247018
$407$	4.24782e6	1.27110
$408$	702812.	0.209020
$409$	−728709.	−0.215400	−0.107700	−	0.994183i	$-0.534349\pi$
$409$	−728709.	−0.215400	−0.107700	+	0.994183i	$0.534349\pi$
$410$	922760.	0.271100
$411$	1.17632e6	0.343496
$412$	−1.11989e6	−0.325037
$413$	−4.50950e6	−1.30093
$414$	−96242.7	−0.0275973
$415$	2.29985e6	0.655510
$416$	141097.	0.0399747
$417$	−1.97513e6	−0.556231
$418$	488623.	0.136783
$419$	5.11992e6	1.42472	0.712358	−	0.701816i	$-0.247627\pi$
$419$	5.11992e6	1.42472	0.712358	+	0.701816i	$0.247627\pi$
$420$	−362956.	−0.100399
$421$	5.45327e6	1.49952	0.749760	−	0.661710i	$-0.230169\pi$
$421$	5.45327e6	1.49952	0.749760	+	0.661710i	$0.230169\pi$
$422$	2.80341e6	0.766311
$423$	−1.43560e6	−0.390107
$424$	2.15642e6	0.582532
$425$	−762600.	−0.204797
$426$	−831513.	−0.221996
$427$	1.30633e6	0.346723
$428$	−245172.	−0.0646935
$429$	−419632.	−0.110084
$430$	1.95803e6	0.510680
$431$	888167.	0.230304	0.115152	−	0.993348i	$-0.463265\pi$
$431$	888167.	0.230304	0.115152	+	0.993348i	$0.463265\pi$
$432$	186624.	0.0481125
$433$	−1.76624e6	−0.452720	−0.226360	−	0.974044i	$-0.572683\pi$
$433$	−1.76624e6	−0.452720	−0.226360	+	0.974044i	$0.572683\pi$
$434$	2.62294e6	0.668442
$435$	−457736.	−0.115982
$436$	−1.12056e6	−0.282304
$437$	−107233.	−0.0268613
$438$	765862.	0.190750
$439$	6.99040e6	1.73118	0.865588	−	0.500758i	$-0.166945\pi$
$439$	6.99040e6	1.73118	0.865588	+	0.500758i	$0.166945\pi$
$440$	−541410.	−0.133320
$441$	−538011.	−0.131733
$442$	−672505.	−0.163734
$443$	−3.50456e6	−0.848445	−0.424223	−	0.905558i	$-0.639453\pi$
$443$	−3.50456e6	−0.848445	−0.424223	+	0.905558i	$0.639453\pi$
$444$	1.80768e6	0.435176
$445$	−504314.	−0.120726
$446$	3.97531e6	0.946311
$447$	3.39797e6	0.804359
$448$	−412963.	−0.0972112
$449$	7.69628e6	1.80163	0.900814	−	0.434205i	$-0.142971\pi$
$449$	7.69628e6	1.80163	0.900814	+	0.434205i	$0.142971\pi$
$450$	−202500.	−0.0471405
$451$	−3.12245e6	−0.722860
$452$	1.98781e6	0.457646
$453$	−4.76625e6	−1.09127
$454$	−1.90413e6	−0.433568
$455$	347305.	0.0786470
$456$	207936.	0.0468293
$457$	3.18915e6	0.714307	0.357153	−	0.934046i	$-0.383747\pi$
$457$	3.18915e6	0.714307	0.357153	+	0.934046i	$0.383747\pi$
$458$	1.64220e6	0.365817
$459$	−889496.	−0.197066
$460$	118818.	0.0261811
$461$	7.03406e6	1.54154	0.770768	−	0.637116i	$-0.219873\pi$
$461$	7.03406e6	1.54154	0.770768	+	0.637116i	$0.219873\pi$
$462$	1.22818e6	0.267704
$463$	1.17619e6	0.254991	0.127495	−	0.991839i	$-0.459306\pi$
$463$	1.17619e6	0.254991	0.127495	+	0.991839i	$0.459306\pi$
$464$	−520801.	−0.112299
$465$	1.46339e6	0.313853
$466$	−1.17612e6	−0.250892
$467$	6.31003e6	1.33887	0.669437	−	0.742869i	$-0.266536\pi$
$467$	6.31003e6	1.33887	0.669437	+	0.742869i	$0.266536\pi$
$468$	−178576.	−0.0376886
$469$	4.60822e6	0.967389
$470$	1.77235e6	0.370088
$471$	−1.05346e6	−0.218809
$472$	−2.86257e6	−0.591428
$473$	−6.62562e6	−1.36168
$474$	−1.97557e6	−0.403874
$475$	−225625.	−0.0458831
$476$	1.96828e6	0.398172
$477$	−2.72922e6	−0.549216
$478$	−6.14447e6	−1.23003
$479$	−1.56170e6	−0.310999	−0.155499	−	0.987836i	$-0.549699\pi$
$479$	−1.56170e6	−0.310999	−0.155499	+	0.987836i	$0.549699\pi$
$480$	−230400.	−0.0456435
$481$	−1.72973e6	−0.340891
$482$	3.07594e6	0.603060
$483$	−269536.	−0.0525713
$484$	−744783.	−0.144516
$485$	1.68138e6	0.324572
$486$	−236196.	−0.0453609
$487$	−8.46796e6	−1.61792	−0.808958	−	0.587866i	$-0.799968\pi$
$487$	−8.46796e6	−1.61792	−0.808958	+	0.587866i	$0.799968\pi$
$488$	829241.	0.157627
$489$	−1.03181e6	−0.195132
$490$	664211.	0.124973
$491$	−3.52356e6	−0.659595	−0.329798	−	0.944052i	$-0.606981\pi$
$491$	−3.52356e6	−0.659595	−0.329798	+	0.944052i	$0.606981\pi$
$492$	−1.32877e6	−0.247479
$493$	2.48227e6	0.459972
$494$	−198969.	−0.0366833
$495$	685223.	0.125695
$496$	1.66501e6	0.303887
$497$	−2.32872e6	−0.422889
$498$	−3.31179e6	−0.598396
$499$	−2.48461e6	−0.446691	−0.223345	−	0.974739i	$-0.571698\pi$
$499$	−2.48461e6	−0.446691	−0.223345	+	0.974739i	$0.571698\pi$
$500$	250000.	0.0447214
$501$	−2.98882e6	−0.531992
$502$	−612096.	−0.108408
$503$	6.40608e6	1.12894	0.564472	−	0.825452i	$-0.309080\pi$
$503$	6.40608e6	1.12894	0.564472	+	0.825452i	$0.309080\pi$
$504$	522657.	0.0916516
$505$	−2.88398e6	−0.503227
$506$	−402059.	−0.0698093
$507$	−3.17076e6	−0.547827
$508$	−3.76582e6	−0.647442
$509$	8.82942e6	1.51056	0.755280	−	0.655403i	$-0.227501\pi$
$509$	8.82942e6	1.51056	0.755280	+	0.655403i	$0.227501\pi$
$510$	1.09814e6	0.186954
$511$	2.14486e6	0.363368
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	944024.	0.157607
$515$	−1.74983e6	−0.290722
$516$	−2.81957e6	−0.466185
$517$	−5.99731e6	−0.986802
$518$	5.06257e6	0.828985
$519$	−5.84328e6	−0.952222
$520$	220465.	0.0357545
$521$	−8.72524e6	−1.40826	−0.704130	−	0.710071i	$-0.748663\pi$
$521$	−8.72524e6	−1.40826	−0.704130	+	0.710071i	$0.748663\pi$
$522$	659139.	0.105877
$523$	−7.82647e6	−1.25116	−0.625578	−	0.780161i	$-0.715137\pi$
$523$	−7.82647e6	−1.25116	−0.625578	+	0.780161i	$0.715137\pi$
$524$	−2.54589e6	−0.405052
$525$	−567119.	−0.0897999
$526$	8.24822e6	1.29986
$527$	−7.93584e6	−1.24471
$528$	779631.	0.121704
$529$	−6.34811e6	−0.986291
$530$	3.36941e6	0.521032
$531$	3.62295e6	0.557604
$532$	582343.	0.0892071
$533$	1.27148e6	0.193861
$534$	726212.	0.110207
$535$	−383080.	−0.0578636
$536$	2.92524e6	0.439795
$537$	1.42640e6	0.213455
$538$	3.32326e6	0.495004
$539$	−2.24757e6	−0.333227
$540$	291600.	0.0430331
$541$	3.49228e6	0.512998	0.256499	−	0.966545i	$-0.417431\pi$
$541$	3.49228e6	0.512998	0.256499	+	0.966545i	$0.417431\pi$
$542$	−1.93258e6	−0.282579
$543$	−2.97422e6	−0.432886
$544$	1.24944e6	0.181017
$545$	−1.75087e6	−0.252501
$546$	−500119.	−0.0717945
$547$	8.09970e6	1.15745	0.578723	−	0.815524i	$-0.303551\pi$
$547$	8.09970e6	1.15745	0.578723	+	0.815524i	$0.303551\pi$
$548$	2.09124e6	0.297477
$549$	−1.04951e6	−0.148612
$550$	−845954.	−0.119245
$551$	734411.	0.103053
$552$	−171098.	−0.0239000
$553$	−5.53275e6	−0.769357
$554$	391374.	0.0541773
$555$	2.82450e6	0.389233
$556$	−3.51134e6	−0.481710
$557$	1.19227e7	1.62831	0.814153	−	0.580650i	$-0.197202\pi$
$557$	1.19227e7	1.62831	0.814153	+	0.580650i	$0.197202\pi$
$558$	−2.10728e6	−0.286508
$559$	2.69798e6	0.365182
$560$	−645255.	−0.0869483
$561$	−3.71591e6	−0.498492
$562$	2.15984e6	0.288457
$563$	−3.95187e6	−0.525451	−0.262725	−	0.964871i	$-0.584621\pi$
$563$	−3.95187e6	−0.525451	−0.262725	+	0.964871i	$0.584621\pi$
$564$	−2.55218e6	−0.337843
$565$	3.10596e6	0.409331
$566$	7.40232e6	0.971241
$567$	−661487.	−0.0864100
$568$	−1.47824e6	−0.192254
$569$	−3.57739e6	−0.463219	−0.231609	−	0.972809i	$-0.574399\pi$
$569$	−3.57739e6	−0.463219	−0.231609	+	0.972809i	$0.574399\pi$
$570$	324900.	0.0418854
$571$	5.66709e6	0.727394	0.363697	−	0.931517i	$-0.381514\pi$
$571$	5.66709e6	0.727394	0.363697	+	0.931517i	$0.381514\pi$
$572$	−746012.	−0.0953357
$573$	−5.33056e6	−0.678245
$574$	−3.72135e6	−0.471434
$575$	185653.	0.0234171
$576$	331776.	0.0416667
$577$	−1.20109e6	−0.150189	−0.0750943	−	0.997176i	$-0.523926\pi$
$577$	−1.20109e6	−0.150189	−0.0750943	+	0.997176i	$0.523926\pi$
$578$	−275727.	−0.0343289
$579$	5.81561e6	0.720939
$580$	−813752.	−0.100444
$581$	−9.27494e6	−1.13991
$582$	−2.42119e6	−0.296293
$583$	−1.14015e7	−1.38928
$584$	1.36153e6	0.165195
$585$	−279026.	−0.0337097
$586$	−7.35166e6	−0.884385
$587$	9.55646e6	1.14473	0.572363	−	0.820000i	$-0.306027\pi$
$587$	9.55646e6	1.14473	0.572363	+	0.820000i	$0.306027\pi$
$588$	−956463.	−0.114084
$589$	−2.34792e6	−0.278866
$590$	−4.47277e6	−0.528989
$591$	−4.51294e6	−0.531485
$592$	3.21366e6	0.376873
$593$	3.52251e6	0.411354	0.205677	−	0.978620i	$-0.434060\pi$
$593$	3.52251e6	0.411354	0.205677	+	0.978620i	$0.434060\pi$
$594$	−986720.	−0.114743
$595$	3.07544e6	0.356136
$596$	6.04083e6	0.696596
$597$	7.73601e6	0.888345
$598$	163720.	0.0187219
$599$	1.14904e7	1.30848	0.654242	−	0.756286i	$-0.272988\pi$
$599$	1.14904e7	1.30848	0.654242	+	0.756286i	$0.272988\pi$
$600$	−360000.	−0.0408248
$601$	−6.47200e6	−0.730891	−0.365445	−	0.930833i	$-0.619083\pi$
$601$	−6.47200e6	−0.730891	−0.365445	+	0.930833i	$0.619083\pi$
$602$	−7.89644e6	−0.888056
$603$	−3.70226e6	−0.414642
$604$	−8.47333e6	−0.945066
$605$	−1.16372e6	−0.129259
$606$	4.15293e6	0.459381
$607$	−7.84651e6	−0.864380	−0.432190	−	0.901783i	$-0.642259\pi$
$607$	−7.84651e6	−0.864380	−0.432190	+	0.901783i	$0.642259\pi$
$608$	369664.	0.0405554
$609$	1.84598e6	0.201689
$610$	1.29569e6	0.140986
$611$	2.44213e6	0.264646
$612$	−1.58133e6	−0.170664
$613$	−3.00780e6	−0.323294	−0.161647	−	0.986849i	$-0.551681\pi$
$613$	−3.00780e6	−0.323294	−0.161647	+	0.986849i	$0.551681\pi$
$614$	9.77174e6	1.04605
$615$	−2.07621e6	−0.221352
$616$	2.18342e6	0.231839
$617$	−8.31323e6	−0.879138	−0.439569	−	0.898209i	$-0.644869\pi$
$617$	−8.31323e6	−0.879138	−0.439569	+	0.898209i	$0.644869\pi$
$618$	2.51975e6	0.265391
$619$	1.50290e7	1.57654	0.788268	−	0.615333i	$-0.210978\pi$
$619$	1.50290e7	1.57654	0.788268	+	0.615333i	$0.210978\pi$
$620$	2.60158e6	0.271805
$621$	216546.	0.0225331
$622$	5.37816e6	0.557389
$623$	2.03382e6	0.209938
$624$	−317469.	−0.0326392
$625$	390625.	0.0400000
$626$	62723.0	0.00639721
$627$	−1.09940e6	−0.111683
$628$	−1.87282e6	−0.189494
$629$	−1.53171e7	−1.54365
$630$	816651.	0.0819757
$631$	−6.53004e6	−0.652894	−0.326447	−	0.945216i	$-0.605851\pi$
$631$	−6.53004e6	−0.652894	−0.326447	+	0.945216i	$0.605851\pi$
$632$	−3.51212e6	−0.349765
$633$	−6.30766e6	−0.625690
$634$	4.57063e6	0.451599
$635$	−5.88410e6	−0.579089
$636$	−4.85196e6	−0.475635
$637$	915219.	0.0893668
$638$	2.75359e6	0.267822
$639$	1.87090e6	0.181259
$640$	−409600.	−0.0395285
$641$	1.75398e7	1.68609	0.843044	−	0.537845i	$-0.180761\pi$
$641$	1.75398e7	1.68609	0.843044	+	0.537845i	$0.180761\pi$
$642$	551636.	0.0528220
$643$	4.16655e6	0.397419	0.198710	−	0.980058i	$-0.436325\pi$
$643$	4.16655e6	0.397419	0.198710	+	0.980058i	$0.436325\pi$
$644$	−479175.	−0.0455281
$645$	−4.40557e6	−0.416968
$646$	−1.76191e6	−0.166113
$647$	−1.02441e7	−0.962083	−0.481042	−	0.876698i	$-0.659741\pi$
$647$	−1.02441e7	−0.962083	−0.481042	+	0.876698i	$0.659741\pi$
$648$	−419904.	−0.0392837
$649$	1.51350e7	1.41050
$650$	344476.	0.0319798
$651$	−5.90161e6	−0.545780
$652$	−1.83433e6	−0.168989
$653$	3.65399e6	0.335339	0.167670	−	0.985843i	$-0.446376\pi$
$653$	3.65399e6	0.335339	0.167670	+	0.985843i	$0.446376\pi$
$654$	2.52125e6	0.230501
$655$	−3.97795e6	−0.362289
$656$	−2.36227e6	−0.214323
$657$	−1.72319e6	−0.155747
$658$	−7.14761e6	−0.643571
$659$	−1.47252e7	−1.32083	−0.660415	−	0.750901i	$-0.729620\pi$
$659$	−1.47252e7	−1.32083	−0.660415	+	0.750901i	$0.729620\pi$
$660$	1.21817e6	0.108855
$661$	1.47490e7	1.31299	0.656493	−	0.754332i	$-0.272039\pi$
$661$	1.47490e7	1.31299	0.656493	+	0.754332i	$0.272039\pi$
$662$	1.19940e7	1.06370
$663$	1.51314e6	0.133689
$664$	−5.88762e6	−0.518227
$665$	909910.	0.0797893
$666$	−4.06729e6	−0.355320
$667$	−604303.	−0.0525945
$668$	−5.31345e6	−0.460718
$669$	−8.94445e6	−0.772660
$670$	4.57069e6	0.393364
$671$	−4.38437e6	−0.375925
$672$	929167.	0.0793726
$673$	−1.38705e7	−1.18047	−0.590235	−	0.807232i	$-0.700965\pi$
$673$	−1.38705e7	−1.18047	−0.590235	+	0.807232i	$0.700965\pi$
$674$	1.88661e6	0.159968
$675$	455625.	0.0384900
$676$	−5.63691e6	−0.474432
$677$	−1.49893e6	−0.125693	−0.0628463	−	0.998023i	$-0.520018\pi$
$677$	−1.49893e6	−0.125693	−0.0628463	+	0.998023i	$0.520018\pi$
$678$	−4.47258e6	−0.373666
$679$	−6.78074e6	−0.564421
$680$	1.95225e6	0.161906
$681$	4.28430e6	0.354007
$682$	−8.80325e6	−0.724740
$683$	−1.98115e7	−1.62505	−0.812523	−	0.582929i	$-0.801907\pi$
$683$	−1.98115e7	−1.62505	−0.812523	+	0.582929i	$0.801907\pi$
$684$	−467856.	−0.0382360
$685$	3.26756e6	0.266071
$686$	−9.45666e6	−0.767233
$687$	−3.69496e6	−0.298688
$688$	−5.01256e6	−0.403728
$689$	4.64273e6	0.372585
$690$	−267341.	−0.0213768
$691$	6.08875e6	0.485102	0.242551	−	0.970139i	$-0.422016\pi$
$691$	6.08875e6	0.485102	0.242551	+	0.970139i	$0.422016\pi$
$692$	−1.03881e7	−0.824649
$693$	−2.76340e6	−0.218580
$694$	−1.57933e7	−1.24473
$695$	−5.48647e6	−0.430855
$696$	1.17180e6	0.0916920
$697$	1.12591e7	0.877856
$698$	−6.68552e6	−0.519394
$699$	2.64627e6	0.204853
$700$	−1.00821e6	−0.0777690
$701$	2.41176e7	1.85370	0.926850	−	0.375433i	$-0.122506\pi$
$701$	2.41176e7	1.85370	0.926850	+	0.375433i	$0.122506\pi$
$702$	401797.	0.0307726
$703$	−4.53176e6	−0.345843
$704$	1.38601e6	0.105399
$705$	−3.98779e6	−0.302176
$706$	1.10080e7	0.831180
$707$	1.16306e7	0.875095
$708$	6.44079e6	0.482899
$709$	−1.88765e7	−1.41028	−0.705140	−	0.709068i	$-0.749116\pi$
$709$	−1.88765e7	−1.41028	−0.705140	+	0.709068i	$0.749116\pi$
$710$	−2.30976e6	−0.171957
$711$	4.44503e6	0.329762
$712$	1.29104e6	0.0954423
$713$	1.93197e6	0.142323
$714$	−4.42864e6	−0.325106
$715$	−1.16564e6	−0.0852709
$716$	2.53582e6	0.184857
$717$	1.38250e7	1.00431
$718$	1.03134e7	0.746603
$719$	1.22218e7	0.881687	0.440844	−	0.897584i	$-0.354679\pi$
$719$	1.22218e7	0.881687	0.440844	+	0.897584i	$0.354679\pi$
$720$	518400.	0.0372678
$721$	7.05679e6	0.505556
$722$	−521284.	−0.0372161
$723$	−6.92087e6	−0.492397
$724$	−5.28751e6	−0.374891
$725$	−1.27149e6	−0.0898395
$726$	1.67576e6	0.117997
$727$	1.57095e7	1.10237	0.551184	−	0.834383i	$-0.314176\pi$
$727$	1.57095e7	1.10237	0.551184	+	0.834383i	$0.314176\pi$
$728$	−889100.	−0.0621759
$729$	531441.	0.0370370
$730$	2.12739e6	0.147754
$731$	2.38911e7	1.65365
$732$	−1.86579e6	−0.128702
$733$	−2.41007e7	−1.65680	−0.828400	−	0.560136i	$-0.810749\pi$
$733$	−2.41007e7	−1.65680	−0.828400	+	0.560136i	$0.810749\pi$
$734$	−4.26429e6	−0.292151
$735$	−1.49447e6	−0.102040
$736$	−304175.	−0.0206980
$737$	−1.54664e7	−1.04887
$738$	2.98974e6	0.202066
$739$	−2.51694e7	−1.69536	−0.847678	−	0.530510i	$-0.822000\pi$
$739$	−2.51694e7	−1.69536	−0.847678	+	0.530510i	$0.822000\pi$
$740$	5.02134e6	0.337086
$741$	447681.	0.0299518
$742$	−1.35883e7	−0.906058
$743$	1.28943e7	0.856890	0.428445	−	0.903568i	$-0.359062\pi$
$743$	1.28943e7	0.856890	0.428445	+	0.903568i	$0.359062\pi$
$744$	−3.74627e6	−0.248123
$745$	9.43879e6	0.623054
$746$	−3.62547e6	−0.238516
$747$	7.45152e6	0.488589
$748$	−6.60607e6	−0.431707
$749$	1.54490e6	0.100623
$750$	−562500.	−0.0365148
$751$	1.94823e7	1.26049	0.630247	−	0.776394i	$-0.282953\pi$
$751$	1.94823e7	1.26049	0.630247	+	0.776394i	$0.282953\pi$
$752$	−4.53722e6	−0.292580
$753$	1.37722e6	0.0885146
$754$	−1.12127e6	−0.0718262
$755$	−1.32396e7	−0.845292
$756$	−1.17598e6	−0.0748332
$757$	1.59354e7	1.01070	0.505352	−	0.862913i	$-0.331363\pi$
$757$	1.59354e7	1.01070	0.505352	+	0.862913i	$0.331363\pi$
$758$	−1.05599e7	−0.667557
$759$	904632.	0.0569991
$760$	577600.	0.0362738
$761$	3.36602e6	0.210695	0.105348	−	0.994435i	$-0.466404\pi$
$761$	3.36602e6	0.210695	0.105348	+	0.994435i	$0.466404\pi$
$762$	8.47310e6	0.528634
$763$	7.06098e6	0.439090
$764$	−9.47655e6	−0.587377
$765$	−2.47082e6	−0.152647
$766$	−1.30710e7	−0.804892
$767$	−6.16305e6	−0.378275
$768$	589824.	0.0360844
$769$	1.70140e7	1.03750	0.518752	−	0.854925i	$-0.326397\pi$
$769$	1.70140e7	1.03750	0.518752	+	0.854925i	$0.326397\pi$
$770$	3.41160e6	0.207363
$771$	−2.12405e6	−0.128686
$772$	1.03389e7	0.624352
$773$	1.40266e7	0.844315	0.422157	−	0.906523i	$-0.361273\pi$
$773$	1.40266e7	0.844315	0.422157	+	0.906523i	$0.361273\pi$
$774$	6.34403e6	0.380638
$775$	4.06496e6	0.243110
$776$	−4.30433e6	−0.256597
$777$	−1.13908e7	−0.676863
$778$	−1.38139e6	−0.0818216
$779$	3.33116e6	0.196676
$780$	−496046.	−0.0291934
$781$	7.81579e6	0.458506
$782$	1.44977e6	0.0847779
$783$	−1.48306e6	−0.0864481
$784$	−1.70038e6	−0.0987997
$785$	−2.92628e6	−0.169489
$786$	5.72824e6	0.330723
$787$	−3.56203e6	−0.205003	−0.102502	−	0.994733i	$-0.532685\pi$
$787$	−3.56203e6	−0.205003	−0.102502	+	0.994733i	$0.532685\pi$
$788$	−8.02301e6	−0.460280
$789$	−1.85585e7	−1.06133
$790$	−5.48769e6	−0.312839
$791$	−1.25258e7	−0.711812
$792$	−1.75417e6	−0.0993708
$793$	1.78534e6	0.100818
$794$	8.75645e6	0.492921
$795$	−7.58118e6	−0.425421
$796$	1.37529e7	0.769329
$797$	2.31981e7	1.29362	0.646810	−	0.762651i	$-0.276103\pi$
$797$	2.31981e7	1.29362	0.646810	+	0.762651i	$0.276103\pi$
$798$	−1.31027e6	−0.0728373
$799$	2.16255e7	1.19839
$800$	−640000.	−0.0353553
$801$	−1.63398e6	−0.0899838
$802$	−5.58018e6	−0.306346
$803$	−7.19871e6	−0.393972
$804$	−6.58180e6	−0.359091
$805$	−748711.	−0.0407216
$806$	3.58472e6	0.194365
$807$	−7.47734e6	−0.404169
$808$	7.38299e6	0.397836
$809$	−1.04705e7	−0.562464	−0.281232	−	0.959640i	$-0.590743\pi$
$809$	−1.04705e7	−0.562464	−0.281232	+	0.959640i	$0.590743\pi$
$810$	−656100.	−0.0351364
$811$	−1.07335e7	−0.573043	−0.286522	−	0.958074i	$-0.592499\pi$
$811$	−1.07335e7	−0.573043	−0.286522	+	0.958074i	$0.592499\pi$
$812$	3.28173e6	0.174668
$813$	4.34831e6	0.230725
$814$	−1.69913e7	−0.898805
$815$	−2.86614e6	−0.151148
$816$	−2.81125e6	−0.147800
$817$	7.06850e6	0.370486
$818$	2.91484e6	0.152311
$819$	1.12527e6	0.0586200
$820$	−3.69104e6	−0.191697
$821$	7.54581e6	0.390704	0.195352	−	0.980733i	$-0.437415\pi$
$821$	7.54581e6	0.390704	0.195352	+	0.980733i	$0.437415\pi$
$822$	−4.70529e6	−0.242889
$823$	−9.61785e6	−0.494969	−0.247485	−	0.968892i	$-0.579604\pi$
$823$	−9.61785e6	−0.494969	−0.247485	+	0.968892i	$0.579604\pi$
$824$	4.47956e6	0.229836
$825$	1.90340e6	0.0973631
$826$	1.80380e7	0.919895
$827$	−4.08891e6	−0.207895	−0.103947	−	0.994583i	$-0.533147\pi$
$827$	−4.08891e6	−0.207895	−0.103947	+	0.994583i	$0.533147\pi$
$828$	384971.	0.0195143
$829$	1.54474e7	0.780675	0.390337	−	0.920672i	$-0.372358\pi$
$829$	1.54474e7	0.780675	0.390337	+	0.920672i	$0.372358\pi$
$830$	−9.19941e6	−0.463516
$831$	−880591.	−0.0442356
$832$	−564390.	−0.0282664
$833$	8.10443e6	0.404678
$834$	7.90052e6	0.393315
$835$	−8.30227e6	−0.412079
$836$	−1.95449e6	−0.0967204
$837$	4.74137e6	0.233932
$838$	−2.04797e7	−1.00743
$839$	1.46511e7	0.718563	0.359282	−	0.933229i	$-0.383022\pi$
$839$	1.46511e7	0.718563	0.359282	+	0.933229i	$0.383022\pi$
$840$	1.45182e6	0.0709930
$841$	−1.63724e7	−0.798222
$842$	−2.18131e7	−1.06032
$843$	−4.85964e6	−0.235524
$844$	−1.12136e7	−0.541863
$845$	−8.80767e6	−0.424345
$846$	5.74242e6	0.275847
$847$	4.69312e6	0.224777
$848$	−8.62570e6	−0.411912
$849$	−1.66552e7	−0.793015
$850$	3.05040e6	0.144814
$851$	3.72892e6	0.176506
$852$	3.32605e6	0.156975
$853$	−6.15499e6	−0.289637	−0.144819	−	0.989458i	$-0.546260\pi$
$853$	−6.15499e6	−0.289637	−0.144819	+	0.989458i	$0.546260\pi$
$854$	−5.22531e6	−0.245170
$855$	−731025.	−0.0341993
$856$	980686.	0.0457452
$857$	−1.15139e7	−0.535515	−0.267757	−	0.963486i	$-0.586283\pi$
$857$	−1.15139e7	−0.535515	−0.267757	+	0.963486i	$0.586283\pi$
$858$	1.67853e6	0.0778413
$859$	3.53585e7	1.63497	0.817486	−	0.575948i	$-0.195367\pi$
$859$	3.53585e7	1.63497	0.817486	+	0.575948i	$0.195367\pi$
$860$	−7.83213e6	−0.361105
$861$	8.37303e6	0.384924
$862$	−3.55267e6	−0.162849
$863$	−1.15368e7	−0.527299	−0.263649	−	0.964619i	$-0.584926\pi$
$863$	−1.15368e7	−0.527299	−0.263649	+	0.964619i	$0.584926\pi$
$864$	−746496.	−0.0340207
$865$	−1.62313e7	−0.737588
$866$	7.06495e6	0.320121
$867$	620386.	0.0280294
$868$	−1.04918e7	−0.472660
$869$	1.85693e7	0.834154
$870$	1.83094e6	0.0820118
$871$	6.29798e6	0.281291
$872$	4.48223e6	0.199619
$873$	5.44767e6	0.241922
$874$	428934.	0.0189938
$875$	−1.57533e6	−0.0695587
$876$	−3.06345e6	−0.134881
$877$	2.97218e7	1.30490	0.652448	−	0.757834i	$-0.273742\pi$
$877$	2.97218e7	1.30490	0.652448	+	0.757834i	$0.273742\pi$
$878$	−2.79616e7	−1.22413
$879$	1.65412e7	0.722098
$880$	2.16564e6	0.0942714
$881$	1.70271e6	0.0739094	0.0369547	−	0.999317i	$-0.488234\pi$
$881$	1.70271e6	0.0739094	0.0369547	+	0.999317i	$0.488234\pi$
$882$	2.15204e6	0.0931493
$883$	−2.83047e7	−1.22168	−0.610840	−	0.791754i	$-0.709168\pi$
$883$	−2.83047e7	−1.22168	−0.610840	+	0.791754i	$0.709168\pi$
$884$	2.69002e6	0.115778
$885$	1.00637e7	0.431918
$886$	1.40182e7	0.599941
$887$	−3.27007e7	−1.39556	−0.697779	−	0.716313i	$-0.745828\pi$
$887$	−3.27007e7	−1.39556	−0.697779	+	0.716313i	$0.745828\pi$
$888$	−7.23073e6	−0.307716
$889$	2.37297e7	1.00702
$890$	2.01725e6	0.0853662
$891$	2.22012e6	0.0936877
$892$	−1.59012e7	−0.669143
$893$	6.39818e6	0.268490
$894$	−1.35919e7	−0.568768
$895$	3.96222e6	0.165341
$896$	1.65185e6	0.0687387
$897$	−368370.	−0.0152863
$898$	−3.07851e7	−1.27394
$899$	−1.32315e7	−0.546021
$900$	810000.	0.0333333
$901$	4.11122e7	1.68717
$902$	1.24898e7	0.511139
$903$	1.77670e7	0.725094
$904$	−7.95125e6	−0.323604
$905$	−8.26173e6	−0.335312
$906$	1.90650e7	0.771643
$907$	−2.62799e7	−1.06073	−0.530367	−	0.847768i	$-0.677946\pi$
$907$	−2.62799e7	−1.06073	−0.530367	+	0.847768i	$0.677946\pi$
$908$	7.61653e6	0.306579
$909$	−9.34410e6	−0.375083
$910$	−1.38922e6	−0.0556118
$911$	−1.48067e6	−0.0591100	−0.0295550	−	0.999563i	$-0.509409\pi$
$911$	−1.48067e6	−0.0591100	−0.0295550	+	0.999563i	$0.509409\pi$
$912$	−831744.	−0.0331133
$913$	3.11291e7	1.23592
$914$	−1.27566e7	−0.505091
$915$	−2.91530e6	−0.115115
$916$	−6.56882e6	−0.258671
$917$	1.60424e7	0.630009
$918$	3.55798e6	0.139347
$919$	−1.59092e7	−0.621382	−0.310691	−	0.950511i	$-0.600560\pi$
$919$	−1.59092e7	−0.621382	−0.310691	+	0.950511i	$0.600560\pi$
$920$	−475273.	−0.0185129
$921$	−2.19864e7	−0.854093
$922$	−2.81362e7	−1.09003
$923$	−3.18263e6	−0.122965
$924$	−4.91270e6	−0.189296
$925$	7.84584e6	0.301499
$926$	−4.70476e6	−0.180306
$927$	−5.66945e6	−0.216691
$928$	2.08321e6	0.0794076
$929$	−7.61502e6	−0.289489	−0.144744	−	0.989469i	$-0.546236\pi$
$929$	−7.61502e6	−0.289489	−0.144744	+	0.989469i	$0.546236\pi$
$930$	−5.85355e6	−0.221928
$931$	2.39780e6	0.0906648
$932$	4.70449e6	0.177408
$933$	−1.21009e7	−0.455106
$934$	−2.52401e7	−0.946726
$935$	−1.03220e7	−0.386131
$936$	714306.	0.0266498
$937$	3.29643e7	1.22658	0.613289	−	0.789859i	$-0.289846\pi$
$937$	3.29643e7	1.22658	0.613289	+	0.789859i	$0.289846\pi$
$938$	−1.84329e7	−0.684047
$939$	−141127.	−0.00522330
$940$	−7.08940e6	−0.261692
$941$	2.49710e7	0.919308	0.459654	−	0.888098i	$-0.347973\pi$
$941$	2.49710e7	0.919308	0.459654	+	0.888098i	$0.347973\pi$
$942$	4.21384e6	0.154721
$943$	−2.74102e6	−0.100377
$944$	1.14503e7	0.418203
$945$	−1.83746e6	−0.0669329
$946$	2.65025e7	0.962850
$947$	−3.96522e7	−1.43679	−0.718394	−	0.695636i	$-0.755123\pi$
$947$	−3.96522e7	−1.43679	−0.718394	+	0.695636i	$0.755123\pi$
$948$	7.90227e6	0.285582
$949$	2.93134e6	0.105658
$950$	902500.	0.0324443
$951$	−1.02839e7	−0.368729
$952$	−7.87314e6	−0.281550
$953$	2.61305e7	0.931999	0.466000	−	0.884785i	$-0.345695\pi$
$953$	2.61305e7	0.931999	0.466000	+	0.884785i	$0.345695\pi$
$954$	1.09169e7	0.388355
$955$	−1.48071e7	−0.525366
$956$	2.45779e7	0.869760
$957$	−6.19557e6	−0.218676
$958$	6.24679e6	0.219909
$959$	−1.31776e7	−0.462689
$960$	921600.	0.0322749
$961$	1.36721e7	0.477558
$962$	6.91893e6	0.241047
$963$	−1.24118e6	−0.0431290
$964$	−1.23038e7	−0.426428
$965$	1.61545e7	0.558437
$966$	1.07814e6	0.0371736
$967$	−2.76525e7	−0.950975	−0.475487	−	0.879723i	$-0.657728\pi$
$967$	−2.76525e7	−0.950975	−0.475487	+	0.879723i	$0.657728\pi$
$968$	2.97913e6	0.102188
$969$	3.96430e6	0.135630
$970$	−6.72552e6	−0.229507
$971$	−4.29175e7	−1.46078	−0.730392	−	0.683028i	$-0.760663\pi$
$971$	−4.29175e7	−1.46078	−0.730392	+	0.683028i	$0.760663\pi$
$972$	944784.	0.0320750
$973$	2.21261e7	0.749242
$974$	3.38718e7	1.14404
$975$	−775071.	−0.0261114
$976$	−3.31697e6	−0.111459
$977$	−8.19028e6	−0.274513	−0.137256	−	0.990536i	$-0.543828\pi$
$977$	−8.19028e6	−0.274513	−0.137256	+	0.990536i	$0.543828\pi$
$978$	4.12724e6	0.137979
$979$	−6.82602e6	−0.227620
$980$	−2.65684e6	−0.0883692
$981$	−5.67282e6	−0.188203
$982$	1.40942e7	0.466404
$983$	4.61603e7	1.52365	0.761824	−	0.647784i	$-0.224304\pi$
$983$	4.61603e7	1.52365	0.761824	+	0.647784i	$0.224304\pi$
$984$	5.31510e6	0.174994
$985$	−1.25360e7	−0.411687
$986$	−9.92907e6	−0.325249
$987$	1.60821e7	0.525473
$988$	795878.	0.0259390
$989$	−5.81625e6	−0.189083
$990$	−2.74089e6	−0.0888799
$991$	2.83610e7	0.917355	0.458677	−	0.888603i	$-0.348323\pi$
$991$	2.83610e7	0.917355	0.458677	+	0.888603i	$0.348323\pi$
$992$	−6.66004e6	−0.214881
$993$	−2.69865e7	−0.868508
$994$	9.31489e6	0.299028
$995$	2.14889e7	0.688109
$996$	1.32471e7	0.423130
$997$	3.07177e7	0.978702	0.489351	−	0.872087i	$-0.337234\pi$
$997$	3.07177e7	0.978702	0.489351	+	0.872087i	$0.337234\pi$
$998$	9.93845e6	0.315858
$999$	9.15139e6	0.290117

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.l.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -100.821 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -100.821 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +338.382 q^{11} +144.000 q^{12} -137.790 q^{13} +403.284 q^{14} +225.000 q^{15} +256.000 q^{16} -1220.16 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} -907.390 q^{21} -1353.53 q^{22} +297.045 q^{23} -576.000 q^{24} +625.000 q^{25} +551.162 q^{26} +729.000 q^{27} -1613.14 q^{28} -2034.38 q^{29} -900.000 q^{30} +6503.94 q^{31} -1024.00 q^{32} +3045.43 q^{33} +4880.64 q^{34} -2520.53 q^{35} +1296.00 q^{36} +12553.4 q^{37} +1444.00 q^{38} -1240.11 q^{39} -1600.00 q^{40} -9227.60 q^{41} +3629.56 q^{42} -19580.3 q^{43} +5414.10 q^{44} +2025.00 q^{45} -1188.18 q^{46} -17723.5 q^{47} +2304.00 q^{48} -6642.11 q^{49} -2500.00 q^{50} -10981.4 q^{51} -2204.65 q^{52} -33694.1 q^{53} -2916.00 q^{54} +8459.54 q^{55} +6452.55 q^{56} -3249.00 q^{57} +8137.52 q^{58} +44727.7 q^{59} +3600.00 q^{60} -12956.9 q^{61} -26015.8 q^{62} -8166.51 q^{63} +4096.00 q^{64} -3444.76 q^{65} -12181.7 q^{66} -45706.9 q^{67} -19522.5 q^{68} +2673.41 q^{69} +10082.1 q^{70} +23097.6 q^{71} -5184.00 q^{72} -21273.9 q^{73} -50213.4 q^{74} +5625.00 q^{75} -5776.00 q^{76} -34116.0 q^{77} +4960.46 q^{78} +54876.9 q^{79} +6400.00 q^{80} +6561.00 q^{81} +36910.4 q^{82} +91994.1 q^{83} -14518.2 q^{84} -30504.0 q^{85} +78321.3 q^{86} -18309.4 q^{87} -21656.4 q^{88} -20172.5 q^{89} -8100.00 q^{90} +13892.2 q^{91} +4752.73 q^{92} +58535.5 q^{93} +70894.0 q^{94} -9025.00 q^{95} -9216.00 q^{96} +67255.2 q^{97} +26568.4 q^{98} +27408.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 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	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 336 q^{11} + 576 q^{12} - 734 q^{13} + 104 q^{14} + 900 q^{15} + 1024 q^{16} + 480 q^{17} - 1296 q^{18} - 1444 q^{19} + 1600 q^{20} - 234 q^{21} + 1344 q^{22} - 1962 q^{23} - 2304 q^{24} + 2500 q^{25} + 2936 q^{26} + 2916 q^{27} - 416 q^{28} - 8720 q^{29} - 3600 q^{30} - 240 q^{31} - 4096 q^{32} - 3024 q^{33} - 1920 q^{34} - 650 q^{35} + 5184 q^{36} - 14626 q^{37} + 5776 q^{38} - 6606 q^{39} - 6400 q^{40} - 11092 q^{41} + 936 q^{42} - 16778 q^{43} - 5376 q^{44} + 8100 q^{45} + 7848 q^{46} - 34810 q^{47} + 9216 q^{48} - 34032 q^{49} - 10000 q^{50} + 4320 q^{51} - 11744 q^{52} - 18186 q^{53} - 11664 q^{54} - 8400 q^{55} + 1664 q^{56} - 12996 q^{57} + 34880 q^{58} - 38700 q^{59} + 14400 q^{60} - 12080 q^{61} + 960 q^{62} - 2106 q^{63} + 16384 q^{64} - 18350 q^{65} + 12096 q^{66} - 84216 q^{67} + 7680 q^{68} - 17658 q^{69} + 2600 q^{70} + 3592 q^{71} - 20736 q^{72} - 41180 q^{73} + 58504 q^{74} + 22500 q^{75} - 23104 q^{76} - 6696 q^{77} + 26424 q^{78} + 15272 q^{79} + 25600 q^{80} + 26244 q^{81} + 44368 q^{82} + 133106 q^{83} - 3744 q^{84} + 12000 q^{85} + 67112 q^{86} - 78480 q^{87} + 21504 q^{88} + 133704 q^{89} - 32400 q^{90} - 86656 q^{91} - 31392 q^{92} - 2160 q^{93} + 139240 q^{94} - 36100 q^{95} - 36864 q^{96} - 161594 q^{97} + 136128 q^{98} - 27216 q^{99}+O(q^{100}) \) 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 - 336 * q^11 + 576 * q^12 - 734 * q^13 + 104 * q^14 + 900 * q^15 + 1024 * q^16 + 480 * q^17 - 1296 * q^18 - 1444 * q^19 + 1600 * q^20 - 234 * q^21 + 1344 * q^22 - 1962 * q^23 - 2304 * q^24 + 2500 * q^25 + 2936 * q^26 + 2916 * q^27 - 416 * q^28 - 8720 * q^29 - 3600 * q^30 - 240 * q^31 - 4096 * q^32 - 3024 * q^33 - 1920 * q^34 - 650 * q^35 + 5184 * q^36 - 14626 * q^37 + 5776 * q^38 - 6606 * q^39 - 6400 * q^40 - 11092 * q^41 + 936 * q^42 - 16778 * q^43 - 5376 * q^44 + 8100 * q^45 + 7848 * q^46 - 34810 * q^47 + 9216 * q^48 - 34032 * q^49 - 10000 * q^50 + 4320 * q^51 - 11744 * q^52 - 18186 * q^53 - 11664 * q^54 - 8400 * q^55 + 1664 * q^56 - 12996 * q^57 + 34880 * q^58 - 38700 * q^59 + 14400 * q^60 - 12080 * q^61 + 960 * q^62 - 2106 * q^63 + 16384 * q^64 - 18350 * q^65 + 12096 * q^66 - 84216 * q^67 + 7680 * q^68 - 17658 * q^69 + 2600 * q^70 + 3592 * q^71 - 20736 * q^72 - 41180 * q^73 + 58504 * q^74 + 22500 * q^75 - 23104 * q^76 - 6696 * q^77 + 26424 * q^78 + 15272 * q^79 + 25600 * q^80 + 26244 * q^81 + 44368 * q^82 + 133106 * q^83 - 3744 * q^84 + 12000 * q^85 + 67112 * q^86 - 78480 * q^87 + 21504 * q^88 + 133704 * q^89 - 32400 * q^90 - 86656 * q^91 - 31392 * q^92 - 2160 * q^93 + 139240 * q^94 - 36100 * q^95 - 36864 * q^96 - 161594 * q^97 + 136128 * q^98 - 27216 * q^99

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