LMFDB - Embedded newform 570.6.a.l.1.3

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			1.3
Root			$-38.2281$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.1064 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.1064 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +31.8722 q^{11} +144.000 q^{12} +149.931 q^{13} +136.426 q^{14} +225.000 q^{15} +256.000 q^{16} -915.453 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} -306.957 q^{21} -127.489 q^{22} -2354.30 q^{23} -576.000 q^{24} +625.000 q^{25} -599.724 q^{26} +729.000 q^{27} -545.702 q^{28} +7726.26 q^{29} -900.000 q^{30} -2288.97 q^{31} -1024.00 q^{32} +286.850 q^{33} +3661.81 q^{34} -852.660 q^{35} +1296.00 q^{36} -12623.5 q^{37} +1444.00 q^{38} +1349.38 q^{39} -1600.00 q^{40} +4219.60 q^{41} +1227.83 q^{42} +2698.26 q^{43} +509.955 q^{44} +2025.00 q^{45} +9417.19 q^{46} -23938.1 q^{47} +2304.00 q^{48} -15643.8 q^{49} -2500.00 q^{50} -8239.08 q^{51} +2398.89 q^{52} +11944.5 q^{53} -2916.00 q^{54} +796.805 q^{55} +2182.81 q^{56} -3249.00 q^{57} -30905.0 q^{58} -52867.6 q^{59} +3600.00 q^{60} -20386.5 q^{61} +9155.88 q^{62} -2762.62 q^{63} +4096.00 q^{64} +3748.27 q^{65} -1147.40 q^{66} +60223.7 q^{67} -14647.2 q^{68} -21188.7 q^{69} +3410.64 q^{70} -2912.51 q^{71} -5184.00 q^{72} +27640.1 q^{73} +50494.0 q^{74} +5625.00 q^{75} -5776.00 q^{76} -1087.05 q^{77} -5397.51 q^{78} +26610.9 q^{79} +6400.00 q^{80} +6561.00 q^{81} -16878.4 q^{82} -67400.5 q^{83} -4911.32 q^{84} -22886.3 q^{85} -10793.0 q^{86} +69536.3 q^{87} -2039.82 q^{88} +90174.9 q^{89} -8100.00 q^{90} -5113.60 q^{91} -37668.7 q^{92} -20600.7 q^{93} +95752.2 q^{94} -9025.00 q^{95} -9216.00 q^{96} -142174. q^{97} +62575.0 q^{98} +2581.65 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−34.1064	−0.263082	−0.131541	−	0.991311i	$-0.541992\pi$
$7$	−34.1064	−0.263082	−0.131541	+	0.991311i	$0.541992\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	31.8722	0.0794201	0.0397100	−	0.999211i	$-0.487357\pi$
$11$	31.8722	0.0794201	0.0397100	+	0.999211i	$0.487357\pi$
$12$	144.000	0.288675
$13$	149.931	0.246055	0.123028	−	0.992403i	$-0.460740\pi$
$13$	149.931	0.246055	0.123028	+	0.992403i	$0.460740\pi$
$14$	136.426	0.186027
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−915.453	−0.768270	−0.384135	−	0.923277i	$-0.625500\pi$
$17$	−915.453	−0.768270	−0.384135	+	0.923277i	$0.625500\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	400.000	0.223607
$21$	−306.957	−0.151890
$22$	−127.489	−0.0561585
$23$	−2354.30	−0.927986	−0.463993	−	0.885839i	$-0.653584\pi$
$23$	−2354.30	−0.927986	−0.463993	+	0.885839i	$0.653584\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	−599.724	−0.173987
$27$	729.000	0.192450
$28$	−545.702	−0.131541
$29$	7726.26	1.70598	0.852990	−	0.521926i	$-0.174786\pi$
$29$	7726.26	1.70598	0.852990	+	0.521926i	$0.174786\pi$
$30$	−900.000	−0.182574
$31$	−2288.97	−0.427795	−0.213898	−	0.976856i	$-0.568616\pi$
$31$	−2288.97	−0.427795	−0.213898	+	0.976856i	$0.568616\pi$
$32$	−1024.00	−0.176777
$33$	286.850	0.0458532
$34$	3661.81	0.543249
$35$	−852.660	−0.117654
$36$	1296.00	0.166667
$37$	−12623.5	−1.51592	−0.757959	−	0.652302i	$-0.773803\pi$
$37$	−12623.5	−1.51592	−0.757959	+	0.652302i	$0.773803\pi$
$38$	1444.00	0.162221
$39$	1349.38	0.142060
$40$	−1600.00	−0.158114
$41$	4219.60	0.392023	0.196012	−	0.980602i	$-0.437201\pi$
$41$	4219.60	0.392023	0.196012	+	0.980602i	$0.437201\pi$
$42$	1227.83	0.107403
$43$	2698.26	0.222542	0.111271	−	0.993790i	$-0.464508\pi$
$43$	2698.26	0.222542	0.111271	+	0.993790i	$0.464508\pi$
$44$	509.955	0.0397100
$45$	2025.00	0.149071
$46$	9417.19	0.656185
$47$	−23938.1	−1.58068	−0.790340	−	0.612668i	$-0.790096\pi$
$47$	−23938.1	−1.58068	−0.790340	+	0.612668i	$0.790096\pi$
$48$	2304.00	0.144338
$49$	−15643.8	−0.930788
$50$	−2500.00	−0.141421
$51$	−8239.08	−0.443561
$52$	2398.89	0.123028
$53$	11944.5	0.584087	0.292043	−	0.956405i	$-0.405665\pi$
$53$	11944.5	0.584087	0.292043	+	0.956405i	$0.405665\pi$
$54$	−2916.00	−0.136083
$55$	796.805	0.0355177
$56$	2182.81	0.0930134
$57$	−3249.00	−0.132453
$58$	−30905.0	−1.20631
$59$	−52867.6	−1.97724	−0.988620	−	0.150437i	$-0.951932\pi$
$59$	−52867.6	−1.97724	−0.988620	+	0.150437i	$0.951932\pi$
$60$	3600.00	0.129099
$61$	−20386.5	−0.701486	−0.350743	−	0.936472i	$-0.614071\pi$
$61$	−20386.5	−0.701486	−0.350743	+	0.936472i	$0.614071\pi$
$62$	9155.88	0.302497
$63$	−2762.62	−0.0876939
$64$	4096.00	0.125000
$65$	3748.27	0.110039
$66$	−1147.40	−0.0324231
$67$	60223.7	1.63901	0.819503	−	0.573075i	$-0.194249\pi$
$67$	60223.7	1.63901	0.819503	+	0.573075i	$0.194249\pi$
$68$	−14647.2	−0.384135
$69$	−21188.7	−0.535773
$70$	3410.64	0.0831937
$71$	−2912.51	−0.0685681	−0.0342840	−	0.999412i	$-0.510915\pi$
$71$	−2912.51	−0.0685681	−0.0342840	+	0.999412i	$0.510915\pi$
$72$	−5184.00	−0.117851
$73$	27640.1	0.607061	0.303531	−	0.952822i	$-0.401835\pi$
$73$	27640.1	0.607061	0.303531	+	0.952822i	$0.401835\pi$
$74$	50494.0	1.07192
$75$	5625.00	0.115470
$76$	−5776.00	−0.114708
$77$	−1087.05	−0.0208940
$78$	−5397.51	−0.100452
$79$	26610.9	0.479725	0.239862	−	0.970807i	$-0.422898\pi$
$79$	26610.9	0.479725	0.239862	+	0.970807i	$0.422898\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	−16878.4	−0.277202
$83$	−67400.5	−1.07391	−0.536955	−	0.843611i	$-0.680425\pi$
$83$	−67400.5	−1.07391	−0.536955	+	0.843611i	$0.680425\pi$
$84$	−4911.32	−0.0759451
$85$	−22886.3	−0.343581
$86$	−10793.0	−0.157361
$87$	69536.3	0.984949
$88$	−2039.82	−0.0280792
$89$	90174.9	1.20673	0.603366	−	0.797465i	$-0.293826\pi$
$89$	90174.9	1.20673	0.603366	+	0.797465i	$0.293826\pi$
$90$	−8100.00	−0.105409
$91$	−5113.60	−0.0647326
$92$	−37668.7	−0.463993
$93$	−20600.7	−0.246988
$94$	95752.2	1.11771
$95$	−9025.00	−0.102598
$96$	−9216.00	−0.102062
$97$	−142174.	−1.53423	−0.767114	−	0.641511i	$-0.778308\pi$
$97$	−142174.	−1.53423	−0.767114	+	0.641511i	$0.778308\pi$
$98$	62575.0	0.658167
$99$	2581.65	0.0264734
$100$	10000.0	0.100000
$101$	90923.0	0.886891	0.443446	−	0.896301i	$-0.353756\pi$
$101$	90923.0	0.886891	0.443446	+	0.896301i	$0.353756\pi$
$102$	32956.3	0.313645
$103$	27767.1	0.257892	0.128946	−	0.991652i	$-0.458841\pi$
$103$	27767.1	0.257892	0.128946	+	0.991652i	$0.458841\pi$
$104$	−9595.58	−0.0869937
$105$	−7673.94	−0.0679274
$106$	−47777.9	−0.413012
$107$	−25276.8	−0.213433	−0.106717	−	0.994289i	$-0.534034\pi$
$107$	−25276.8	−0.213433	−0.106717	+	0.994289i	$0.534034\pi$
$108$	11664.0	0.0962250
$109$	18627.6	0.150172	0.0750861	−	0.997177i	$-0.476077\pi$
$109$	18627.6	0.150172	0.0750861	+	0.997177i	$0.476077\pi$
$110$	−3187.22	−0.0251148
$111$	−113612.	−0.875216
$112$	−8731.23	−0.0657704
$113$	26316.7	0.193881	0.0969404	−	0.995290i	$-0.469094\pi$
$113$	26316.7	0.193881	0.0969404	+	0.995290i	$0.469094\pi$
$114$	12996.0	0.0936586
$115$	−58857.4	−0.415008
$116$	123620.	0.852990
$117$	12144.4	0.0820184
$118$	211470.	1.39812
$119$	31222.8	0.202118
$120$	−14400.0	−0.0912871
$121$	−160035.	−0.993692
$122$	81546.2	0.496025
$123$	37976.4	0.226335
$124$	−36623.5	−0.213898
$125$	15625.0	0.0894427
$126$	11050.5	0.0620089
$127$	−146357.	−0.805202	−0.402601	−	0.915376i	$-0.631894\pi$
$127$	−146357.	−0.805202	−0.402601	+	0.915376i	$0.631894\pi$
$128$	−16384.0	−0.0883883
$129$	24284.3	0.128485
$130$	−14993.1	−0.0778095
$131$	190779.	0.971299	0.485650	−	0.874154i	$-0.338583\pi$
$131$	190779.	0.971299	0.485650	+	0.874154i	$0.338583\pi$
$132$	4589.60	0.0229266
$133$	12312.4	0.0603551
$134$	−240895.	−1.15895
$135$	18225.0	0.0860663
$136$	58589.0	0.271624
$137$	−347454.	−1.58160	−0.790799	−	0.612076i	$-0.790335\pi$
$137$	−347454.	−1.58160	−0.790799	+	0.612076i	$0.790335\pi$
$138$	84754.7	0.378849
$139$	−108960.	−0.478334	−0.239167	−	0.970978i	$-0.576874\pi$
$139$	−108960.	−0.478334	−0.239167	+	0.970978i	$0.576874\pi$
$140$	−13642.6	−0.0588268
$141$	−215442.	−0.912607
$142$	11650.1	0.0484850
$143$	4778.63	0.0195417
$144$	20736.0	0.0833333
$145$	193156.	0.762938
$146$	−110560.	−0.429257
$147$	−140794.	−0.537391
$148$	−201976.	−0.757959
$149$	137095.	0.505890	0.252945	−	0.967481i	$-0.418601\pi$
$149$	137095.	0.505890	0.252945	+	0.967481i	$0.418601\pi$
$150$	−22500.0	−0.0816497
$151$	−288866.	−1.03099	−0.515495	−	0.856893i	$-0.672392\pi$
$151$	−288866.	−1.03099	−0.515495	+	0.856893i	$0.672392\pi$
$152$	23104.0	0.0811107
$153$	−74151.7	−0.256090
$154$	4348.18	0.0147743
$155$	−57224.3	−0.191316
$156$	21590.1	0.0710301
$157$	30764.1	0.0996081	0.0498041	−	0.998759i	$-0.484140\pi$
$157$	30764.1	0.0996081	0.0498041	+	0.998759i	$0.484140\pi$
$158$	−106444.	−0.339217
$159$	107500.	0.337223
$160$	−25600.0	−0.0790569
$161$	80296.5	0.244136
$162$	−26244.0	−0.0785674
$163$	−124833.	−0.368009	−0.184005	−	0.982925i	$-0.558906\pi$
$163$	−124833.	−0.368009	−0.184005	+	0.982925i	$0.558906\pi$
$164$	67513.6	0.196012
$165$	7171.24	0.0205062
$166$	269602.	0.759369
$167$	101944.	0.282859	0.141429	−	0.989948i	$-0.454830\pi$
$167$	101944.	0.282859	0.141429	+	0.989948i	$0.454830\pi$
$168$	19645.3	0.0537013
$169$	−348814.	−0.939457
$170$	91545.3	0.242948
$171$	−29241.0	−0.0764719
$172$	43172.1	0.111271
$173$	187595.	0.476548	0.238274	−	0.971198i	$-0.423418\pi$
$173$	187595.	0.476548	0.238274	+	0.971198i	$0.423418\pi$
$174$	−278145.	−0.696464
$175$	−21316.5	−0.0526163
$176$	8159.28	0.0198550
$177$	−475808.	−1.14156
$178$	−360700.	−0.853288
$179$	177581.	0.414252	0.207126	−	0.978314i	$-0.433589\pi$
$179$	177581.	0.414252	0.207126	+	0.978314i	$0.433589\pi$
$180$	32400.0	0.0745356
$181$	−673638.	−1.52838	−0.764188	−	0.644994i	$-0.776860\pi$
$181$	−673638.	−1.52838	−0.764188	+	0.644994i	$0.776860\pi$
$182$	20454.4	0.0457729
$183$	−183479.	−0.405003
$184$	150675.	0.328093
$185$	−315588.	−0.677939
$186$	82403.0	0.174647
$187$	−29177.5	−0.0610160
$188$	−383009.	−0.790340
$189$	−24863.6	−0.0506301
$190$	36100.0	0.0725476
$191$	−959796.	−1.90369	−0.951843	−	0.306585i	$-0.900814\pi$
$191$	−959796.	−1.90369	−0.951843	+	0.306585i	$0.900814\pi$
$192$	36864.0	0.0721688
$193$	−447537.	−0.864840	−0.432420	−	0.901672i	$-0.642340\pi$
$193$	−447537.	−0.864840	−0.432420	+	0.901672i	$0.642340\pi$
$194$	568695.	1.08486
$195$	33734.5	0.0635312
$196$	−250300.	−0.465394
$197$	70806.9	0.129990	0.0649951	−	0.997886i	$-0.479297\pi$
$197$	70806.9	0.129990	0.0649951	+	0.997886i	$0.479297\pi$
$198$	−10326.6	−0.0187195
$199$	−864193.	−1.54696	−0.773478	−	0.633823i	$-0.781485\pi$
$199$	−864193.	−1.54696	−0.773478	+	0.633823i	$0.781485\pi$
$200$	−40000.0	−0.0707107
$201$	542014.	0.946281
$202$	−363692.	−0.627127
$203$	−263515.	−0.448812
$204$	−131825.	−0.221780
$205$	105490.	0.175318
$206$	−111069.	−0.182357
$207$	−190698.	−0.309329
$208$	38382.3	0.0615138
$209$	−11505.9	−0.0182202
$210$	30695.7	0.0480319
$211$	−418770.	−0.647545	−0.323772	−	0.946135i	$-0.604951\pi$
$211$	−418770.	−0.647545	−0.323772	+	0.946135i	$0.604951\pi$
$212$	191112.	0.292043
$213$	−26212.6	−0.0395878
$214$	101107.	0.150920
$215$	67456.5	0.0995239
$216$	−46656.0	−0.0680414
$217$	78068.5	0.112545
$218$	−74510.2	−0.106188
$219$	248761.	0.350487
$220$	12748.9	0.0177589
$221$	−137255.	−0.189037
$222$	454446.	0.618871
$223$	−1.02581e6	−1.38135	−0.690675	−	0.723165i	$-0.742686\pi$
$223$	−1.02581e6	−1.38135	−0.690675	+	0.723165i	$0.742686\pi$
$224$	34924.9	0.0465067
$225$	50625.0	0.0666667
$226$	−105267.	−0.137094
$227$	−782919.	−1.00844	−0.504222	−	0.863574i	$-0.668221\pi$
$227$	−782919.	−1.00844	−0.504222	+	0.863574i	$0.668221\pi$
$228$	−51984.0	−0.0662266
$229$	879635.	1.10844	0.554222	−	0.832369i	$-0.313016\pi$
$229$	879635.	1.10844	0.554222	+	0.832369i	$0.313016\pi$
$230$	235430.	0.293455
$231$	−9783.41	−0.0120631
$232$	−494480.	−0.603155
$233$	112744.	0.136051	0.0680257	−	0.997684i	$-0.478330\pi$
$233$	112744.	0.136051	0.0680257	+	0.997684i	$0.478330\pi$
$234$	−48577.6	−0.0579958
$235$	−598451.	−0.706902
$236$	−845881.	−0.988620
$237$	239498.	0.276969
$238$	−124891.	−0.142919
$239$	99236.2	0.112376	0.0561882	−	0.998420i	$-0.482105\pi$
$239$	99236.2	0.112376	0.0561882	+	0.998420i	$0.482105\pi$
$240$	57600.0	0.0645497
$241$	−107560.	−0.119291	−0.0596456	−	0.998220i	$-0.518997\pi$
$241$	−107560.	−0.119291	−0.0596456	+	0.998220i	$0.518997\pi$
$242$	640141.	0.702647
$243$	59049.0	0.0641500
$244$	−326185.	−0.350743
$245$	−391094.	−0.416261
$246$	−151906.	−0.160043
$247$	−54125.1	−0.0564490
$248$	146494.	0.151248
$249$	−606604.	−0.620022
$250$	−62500.0	−0.0632456
$251$	310433.	0.311016	0.155508	−	0.987835i	$-0.450299\pi$
$251$	310433.	0.311016	0.155508	+	0.987835i	$0.450299\pi$
$252$	−44201.9	−0.0438469
$253$	−75036.6	−0.0737007
$254$	585429.	0.569364
$255$	−205977.	−0.198366
$256$	65536.0	0.0625000
$257$	285738.	0.269858	0.134929	−	0.990855i	$-0.456919\pi$
$257$	285738.	0.269858	0.134929	+	0.990855i	$0.456919\pi$
$258$	−97137.3	−0.0908525
$259$	430542.	0.398810
$260$	59972.4	0.0550196
$261$	625827.	0.568660
$262$	−763117.	−0.686812
$263$	1.18199e6	1.05372	0.526860	−	0.849952i	$-0.323369\pi$
$263$	1.18199e6	1.05372	0.526860	+	0.849952i	$0.323369\pi$
$264$	−18358.4	−0.0162116
$265$	298612.	0.261211
$266$	−49249.6	−0.0426775
$267$	811574.	0.696707
$268$	963580.	0.819503
$269$	1.21848e6	1.02669	0.513344	−	0.858183i	$-0.328406\pi$
$269$	1.21848e6	1.02669	0.513344	+	0.858183i	$0.328406\pi$
$270$	−72900.0	−0.0608581
$271$	−2.03262e6	−1.68126	−0.840628	−	0.541613i	$-0.817814\pi$
$271$	−2.03262e6	−1.68126	−0.840628	+	0.541613i	$0.817814\pi$
$272$	−234356.	−0.192067
$273$	−46022.4	−0.0373734
$274$	1.38982e6	1.11836
$275$	19920.1	0.0158840
$276$	−339019.	−0.267887
$277$	−2.02586e6	−1.58639	−0.793196	−	0.608967i	$-0.791584\pi$
$277$	−2.02586e6	−1.58639	−0.793196	+	0.608967i	$0.791584\pi$
$278$	435841.	0.338233
$279$	−185407.	−0.142598
$280$	54570.2	0.0415969
$281$	−703127.	−0.531212	−0.265606	−	0.964082i	$-0.585572\pi$
$281$	−703127.	−0.531212	−0.265606	+	0.964082i	$0.585572\pi$
$282$	861770.	0.645310
$283$	−2.47935e6	−1.84023	−0.920115	−	0.391649i	$-0.871905\pi$
$283$	−2.47935e6	−1.84023	−0.920115	+	0.391649i	$0.871905\pi$
$284$	−46600.2	−0.0342840
$285$	−81225.0	−0.0592349
$286$	−19114.5	−0.0138181
$287$	−143915.	−0.103134
$288$	−82944.0	−0.0589256
$289$	−581803.	−0.409762
$290$	−772626.	−0.539479
$291$	−1.27956e6	−0.885787
$292$	442242.	0.303531
$293$	−2.81648e6	−1.91663	−0.958314	−	0.285718i	$-0.907768\pi$
$293$	−2.81648e6	−1.91663	−0.958314	+	0.285718i	$0.907768\pi$
$294$	563175.	0.379993
$295$	−1.32169e6	−0.884248
$296$	807904.	0.535958
$297$	23234.8	0.0152844
$298$	−548381.	−0.357718
$299$	−352982.	−0.228336
$300$	90000.0	0.0577350
$301$	−92027.8	−0.0585468
$302$	1.15546e6	0.729019
$303$	818307.	0.512047
$304$	−92416.0	−0.0573539
$305$	−509664.	−0.313714
$306$	296607.	0.181083
$307$	2.31303e6	1.40067	0.700333	−	0.713816i	$-0.253035\pi$
$307$	2.31303e6	1.40067	0.700333	+	0.713816i	$0.253035\pi$
$308$	−17392.7	−0.0104470
$309$	249904.	0.148894
$310$	228897.	0.135281
$311$	2.61499e6	1.53310	0.766549	−	0.642186i	$-0.221972\pi$
$311$	2.61499e6	1.53310	0.766549	+	0.642186i	$0.221972\pi$
$312$	−86360.2	−0.0502258
$313$	3.35313e6	1.93459	0.967296	−	0.253649i	$-0.0816308\pi$
$313$	3.35313e6	1.93459	0.967296	+	0.253649i	$0.0816308\pi$
$314$	−123056.	−0.0704336
$315$	−69065.4	−0.0392179
$316$	425775.	0.239862
$317$	1.20646e6	0.674320	0.337160	−	0.941447i	$-0.390534\pi$
$317$	1.20646e6	0.674320	0.337160	+	0.941447i	$0.390534\pi$
$318$	−430001.	−0.238452
$319$	246253.	0.135489
$320$	102400.	0.0559017
$321$	−227491.	−0.123226
$322$	−321186.	−0.172630
$323$	330478.	0.176253
$324$	104976.	0.0555556
$325$	93706.8	0.0492111
$326$	499330.	0.260222
$327$	167648.	0.0867020
$328$	−270054.	−0.138601
$329$	816440.	0.415848
$330$	−28685.0	−0.0145001
$331$	1.34627e6	0.675403	0.337701	−	0.941253i	$-0.390351\pi$
$331$	1.34627e6	0.675403	0.337701	+	0.941253i	$0.390351\pi$
$332$	−1.07841e6	−0.536955
$333$	−1.02250e6	−0.505306
$334$	−407775.	−0.200011
$335$	1.50559e6	0.732986
$336$	−78581.1	−0.0379726
$337$	−4.11904e6	−1.97570	−0.987850	−	0.155409i	$-0.950331\pi$
$337$	−4.11904e6	−1.97570	−0.987850	+	0.155409i	$0.950331\pi$
$338$	1.39525e6	0.664296
$339$	236850.	0.111937
$340$	−366181.	−0.171790
$341$	−72954.5	−0.0339755
$342$	116964.	0.0540738
$343$	1.10678e6	0.507955
$344$	−172689.	−0.0786806
$345$	−529717.	−0.239605
$346$	−750381.	−0.336970
$347$	4.06552e6	1.81256	0.906281	−	0.422676i	$-0.138909\pi$
$347$	4.06552e6	1.81256	0.906281	+	0.422676i	$0.138909\pi$
$348$	1.11258e6	0.492474
$349$	−1.68169e6	−0.739065	−0.369532	−	0.929218i	$-0.620482\pi$
$349$	−1.68169e6	−0.739065	−0.369532	+	0.929218i	$0.620482\pi$
$350$	85266.0	0.0372054
$351$	109300.	0.0473534
$352$	−32637.1	−0.0140396
$353$	−483067.	−0.206334	−0.103167	−	0.994664i	$-0.532898\pi$
$353$	−483067.	−0.206334	−0.103167	+	0.994664i	$0.532898\pi$
$354$	1.90323e6	0.807205
$355$	−72812.8	−0.0306646
$356$	1.44280e6	0.603366
$357$	281005.	0.116693
$358$	−710325.	−0.292920
$359$	65764.0	0.0269310	0.0134655	−	0.999909i	$-0.495714\pi$
$359$	65764.0	0.0269310	0.0134655	+	0.999909i	$0.495714\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	2.69455e6	1.08072
$363$	−1.44032e6	−0.573709
$364$	−81817.6	−0.0323663
$365$	691002.	0.271486
$366$	733916.	0.286380
$367$	1.90927e6	0.739948	0.369974	−	0.929042i	$-0.379367\pi$
$367$	1.90927e6	0.739948	0.369974	+	0.929042i	$0.379367\pi$
$368$	−602700.	−0.231997
$369$	341788.	0.130674
$370$	1.26235e6	0.479375
$371$	−407383.	−0.153662
$372$	−329612.	−0.123494
$373$	−2.86806e6	−1.06737	−0.533687	−	0.845682i	$-0.679194\pi$
$373$	−2.86806e6	−1.06737	−0.533687	+	0.845682i	$0.679194\pi$
$374$	116710.	0.0431448
$375$	140625.	0.0516398
$376$	1.53204e6	0.558855
$377$	1.15840e6	0.419766
$378$	99454.2	0.0358009
$379$	919638.	0.328866	0.164433	−	0.986388i	$-0.447421\pi$
$379$	919638.	0.328866	0.164433	+	0.986388i	$0.447421\pi$
$380$	−144400.	−0.0512989
$381$	−1.31721e6	−0.464883
$382$	3.83918e6	1.34611
$383$	−4.50769e6	−1.57021	−0.785104	−	0.619364i	$-0.787391\pi$
$383$	−4.50769e6	−1.57021	−0.785104	+	0.619364i	$0.787391\pi$
$384$	−147456.	−0.0510310
$385$	−27176.1	−0.00934406
$386$	1.79015e6	0.611535
$387$	218559.	0.0741807
$388$	−2.27478e6	−0.767114
$389$	5.57054e6	1.86648	0.933240	−	0.359254i	$-0.116969\pi$
$389$	5.57054e6	1.86648	0.933240	+	0.359254i	$0.116969\pi$
$390$	−134938.	−0.0449234
$391$	2.15525e6	0.712944
$392$	1.00120e6	0.329083
$393$	1.71701e6	0.560780
$394$	−283228.	−0.0919169
$395$	665273.	0.214539
$396$	41306.4	0.0132367
$397$	−1.16290e6	−0.370312	−0.185156	−	0.982709i	$-0.559279\pi$
$397$	−1.16290e6	−0.370312	−0.185156	+	0.982709i	$0.559279\pi$
$398$	3.45677e6	1.09386
$399$	110812.	0.0348460
$400$	160000.	0.0500000
$401$	−2.35244e6	−0.730563	−0.365281	−	0.930897i	$-0.619027\pi$
$401$	−2.35244e6	−0.730563	−0.365281	+	0.930897i	$0.619027\pi$
$402$	−2.16805e6	−0.669122
$403$	−343187.	−0.105261
$404$	1.45477e6	0.443446
$405$	164025.	0.0496904
$406$	1.05406e6	0.317358
$407$	−402339.	−0.120394
$408$	527301.	0.156822
$409$	5.44543e6	1.60962	0.804811	−	0.593531i	$-0.202266\pi$
$409$	5.44543e6	1.60962	0.804811	+	0.593531i	$0.202266\pi$
$410$	−421960.	−0.123969
$411$	−3.12709e6	−0.913136
$412$	444274.	0.128946
$413$	1.80312e6	0.520175
$414$	762792.	0.218728
$415$	−1.68501e6	−0.480267
$416$	−153529.	−0.0434968
$417$	−980642.	−0.276166
$418$	46023.4	0.0128836
$419$	4.12834e6	1.14879	0.574395	−	0.818578i	$-0.305237\pi$
$419$	4.12834e6	1.14879	0.574395	+	0.818578i	$0.305237\pi$
$420$	−122783.	−0.0339637
$421$	5.15670e6	1.41797	0.708984	−	0.705224i	$-0.249154\pi$
$421$	5.15670e6	1.41797	0.708984	+	0.705224i	$0.249154\pi$
$422$	1.67508e6	0.457883
$423$	−1.93898e6	−0.526894
$424$	−764446.	−0.206506
$425$	−572158.	−0.153654
$426$	104850.	0.0279928
$427$	695311.	0.184548
$428$	−404428.	−0.106717
$429$	43007.6	0.0112824
$430$	−269826.	−0.0703740
$431$	−1.43854e6	−0.373017	−0.186509	−	0.982453i	$-0.559717\pi$
$431$	−1.43854e6	−0.373017	−0.186509	+	0.982453i	$0.559717\pi$
$432$	186624.	0.0481125
$433$	4.26997e6	1.09447	0.547237	−	0.836978i	$-0.315680\pi$
$433$	4.26997e6	1.09447	0.547237	+	0.836978i	$0.315680\pi$
$434$	−312274.	−0.0795814
$435$	1.73841e6	0.440482
$436$	298041.	0.0750861
$437$	849901.	0.212895
$438$	−995043.	−0.247832
$439$	5.38398e6	1.33334	0.666672	−	0.745351i	$-0.267718\pi$
$439$	5.38398e6	1.33334	0.666672	+	0.745351i	$0.267718\pi$
$440$	−50995.5	−0.0125574
$441$	−1.26714e6	−0.310263
$442$	549019.	0.133669
$443$	1.83295e6	0.443752	0.221876	−	0.975075i	$-0.428782\pi$
$443$	1.83295e6	0.443752	0.221876	+	0.975075i	$0.428782\pi$
$444$	−1.81779e6	−0.437608
$445$	2.25437e6	0.539667
$446$	4.10323e6	0.976762
$447$	1.23386e6	0.292076
$448$	−139700.	−0.0328852
$449$	−5.33052e6	−1.24783	−0.623913	−	0.781494i	$-0.714458\pi$
$449$	−5.33052e6	−1.24783	−0.623913	+	0.781494i	$0.714458\pi$
$450$	−202500.	−0.0471405
$451$	134488.	0.0311345
$452$	421067.	0.0969404
$453$	−2.59979e6	−0.595242
$454$	3.13168e6	0.713078
$455$	−127840.	−0.0289493
$456$	207936.	0.0468293
$457$	560697.	0.125585	0.0627925	−	0.998027i	$-0.479999\pi$
$457$	560697.	0.125585	0.0627925	+	0.998027i	$0.479999\pi$
$458$	−3.51854e6	−0.783788
$459$	−667365.	−0.147854
$460$	−941719.	−0.207504
$461$	3.92602e6	0.860399	0.430200	−	0.902734i	$-0.358443\pi$
$461$	3.92602e6	0.860399	0.430200	+	0.902734i	$0.358443\pi$
$462$	39133.6	0.00852992
$463$	−6.79474e6	−1.47306	−0.736529	−	0.676406i	$-0.763537\pi$
$463$	−6.79474e6	−1.47306	−0.736529	+	0.676406i	$0.763537\pi$
$464$	1.97792e6	0.426495
$465$	−515018.	−0.110456
$466$	−450975.	−0.0962028
$467$	−1.43475e6	−0.304427	−0.152213	−	0.988348i	$-0.548640\pi$
$467$	−1.43475e6	−0.304427	−0.152213	+	0.988348i	$0.548640\pi$
$468$	194310.	0.0410092
$469$	−2.05401e6	−0.431193
$470$	2.39381e6	0.499855
$471$	276877.	0.0575088
$472$	3.38352e6	0.699060
$473$	85999.4	0.0176743
$474$	−957993.	−0.195847
$475$	−225625.	−0.0458831
$476$	499565.	0.101059
$477$	967502.	0.194696
$478$	−396945.	−0.0794622
$479$	7.30911e6	1.45555	0.727773	−	0.685818i	$-0.240556\pi$
$479$	7.30911e6	1.45555	0.727773	+	0.685818i	$0.240556\pi$
$480$	−230400.	−0.0456435
$481$	−1.89265e6	−0.373000
$482$	430240.	0.0843516
$483$	722669.	0.140952
$484$	−2.56056e6	−0.496846
$485$	−3.55434e6	−0.686128
$486$	−236196.	−0.0453609
$487$	−3.60156e6	−0.688126	−0.344063	−	0.938947i	$-0.611803\pi$
$487$	−3.60156e6	−0.688126	−0.344063	+	0.938947i	$0.611803\pi$
$488$	1.30474e6	0.248013
$489$	−1.12349e6	−0.212470
$490$	1.56438e6	0.294341
$491$	7.80138e6	1.46039	0.730193	−	0.683241i	$-0.239430\pi$
$491$	7.80138e6	1.46039	0.730193	+	0.683241i	$0.239430\pi$
$492$	607623.	0.113167
$493$	−7.07302e6	−1.31065
$494$	216500.	0.0399154
$495$	64541.2	0.0118392
$496$	−585977.	−0.106949
$497$	99335.3	0.0180390
$498$	2.42642e6	0.438422
$499$	946880.	0.170233	0.0851165	−	0.996371i	$-0.472874\pi$
$499$	946880.	0.170233	0.0851165	+	0.996371i	$0.472874\pi$
$500$	250000.	0.0447214
$501$	917494.	0.163309
$502$	−1.24173e6	−0.219922
$503$	−5.54090e6	−0.976474	−0.488237	−	0.872711i	$-0.662360\pi$
$503$	−5.54090e6	−0.976474	−0.488237	+	0.872711i	$0.662360\pi$
$504$	176807.	0.0310045
$505$	2.27308e6	0.396630
$506$	300146.	0.0521143
$507$	−3.13932e6	−0.542396
$508$	−2.34171e6	−0.402601
$509$	4.56492e6	0.780977	0.390489	−	0.920608i	$-0.372306\pi$
$509$	4.56492e6	0.780977	0.390489	+	0.920608i	$0.372306\pi$
$510$	823908.	0.140266
$511$	−942704.	−0.159707
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−1.14295e6	−0.190818
$515$	694178.	0.115333
$516$	388549.	0.0642424
$517$	−762958.	−0.125538
$518$	−1.72217e6	−0.282001
$519$	1.68836e6	0.275135
$520$	−239889.	−0.0389048
$521$	5.99857e6	0.968174	0.484087	−	0.875020i	$-0.339152\pi$
$521$	5.99857e6	0.968174	0.484087	+	0.875020i	$0.339152\pi$
$522$	−2.50331e6	−0.402104
$523$	−5273.94	−0.000843103 0	−0.000421552	−	1.00000i	$-0.500134\pi$
$523$	−5273.94	−0.000843103 0	−0.000421552		1.00000i	$0.500134\pi$
$524$	3.05247e6	0.485650
$525$	−191848.	−0.0303781
$526$	−4.72797e6	−0.745092
$527$	2.09544e6	0.328662
$528$	73433.5	0.0114633
$529$	−893629.	−0.138841
$530$	−1.19445e6	−0.184704
$531$	−4.28227e6	−0.659080
$532$	196998.	0.0301775
$533$	632649.	0.0964594
$534$	−3.24630e6	−0.492646
$535$	−631919.	−0.0954503
$536$	−3.85432e6	−0.579476
$537$	1.59823e6	0.239168
$538$	−4.87393e6	−0.725979
$539$	−498601.	−0.0739232
$540$	291600.	0.0430331
$541$	−7.25642e6	−1.06593	−0.532966	−	0.846137i	$-0.678923\pi$
$541$	−7.25642e6	−1.06593	−0.532966	+	0.846137i	$0.678923\pi$
$542$	8.13050e6	1.18883
$543$	−6.06274e6	−0.882408
$544$	937424.	0.135812
$545$	465689.	0.0671591
$546$	184090.	0.0264270
$547$	−4.30048e6	−0.614537	−0.307269	−	0.951623i	$-0.599415\pi$
$547$	−4.30048e6	−0.614537	−0.307269	+	0.951623i	$0.599415\pi$
$548$	−5.55927e6	−0.790799
$549$	−1.65131e6	−0.233829
$550$	−79680.5	−0.0112317
$551$	−2.78918e6	−0.391379
$552$	1.35607e6	0.189424
$553$	−907602.	−0.126207
$554$	8.10345e6	1.12175
$555$	−2.84029e6	−0.391408
$556$	−1.74336e6	−0.239167
$557$	687162.	0.0938471	0.0469235	−	0.998898i	$-0.485058\pi$
$557$	687162.	0.0938471	0.0469235	+	0.998898i	$0.485058\pi$
$558$	741627.	0.100832
$559$	404552.	0.0547577
$560$	−218281.	−0.0294134
$561$	−262597.	−0.0352276
$562$	2.81251e6	0.375623
$563$	5.51555e6	0.733361	0.366681	−	0.930347i	$-0.380494\pi$
$563$	5.51555e6	0.733361	0.366681	+	0.930347i	$0.380494\pi$
$564$	−3.44708e6	−0.456303
$565$	657917.	0.0867061
$566$	9.91741e6	1.30124
$567$	−223772.	−0.0292313
$568$	186401.	0.0242425
$569$	−5.32410e6	−0.689391	−0.344695	−	0.938715i	$-0.612018\pi$
$569$	−5.32410e6	−0.689391	−0.344695	+	0.938715i	$0.612018\pi$
$570$	324900.	0.0418854
$571$	4.94172e6	0.634290	0.317145	−	0.948377i	$-0.397276\pi$
$571$	4.94172e6	0.634290	0.317145	+	0.948377i	$0.397276\pi$
$572$	76458.0	0.00977086
$573$	−8.63816e6	−1.09909
$574$	575661.	0.0729268
$575$	−1.47144e6	−0.185597
$576$	331776.	0.0416667
$577$	3.57994e6	0.447647	0.223824	−	0.974630i	$-0.428146\pi$
$577$	3.57994e6	0.447647	0.223824	+	0.974630i	$0.428146\pi$
$578$	2.32721e6	0.289745
$579$	−4.02784e6	−0.499316
$580$	3.09050e6	0.381469
$581$	2.29879e6	0.282526
$582$	5.11825e6	0.626346
$583$	380696.	0.0463882
$584$	−1.76897e6	−0.214629
$585$	303610.	0.0366798
$586$	1.12659e7	1.35526
$587$	−1.04531e7	−1.25214	−0.626069	−	0.779768i	$-0.715337\pi$
$587$	−1.04531e7	−1.25214	−0.626069	+	0.779768i	$0.715337\pi$
$588$	−2.25270e6	−0.268695
$589$	826319.	0.0981430
$590$	5.28676e6	0.625258
$591$	637262.	0.0750498
$592$	−3.23162e6	−0.378980
$593$	−8.82696e6	−1.03080	−0.515400	−	0.856950i	$-0.672357\pi$
$593$	−8.82696e6	−1.03080	−0.515400	+	0.856950i	$0.672357\pi$
$594$	−92939.3	−0.0108077
$595$	780570.	0.0903898
$596$	2.19352e6	0.252945
$597$	−7.77774e6	−0.893136
$598$	1.41193e6	0.161458
$599$	−301924.	−0.0343819	−0.0171910	−	0.999852i	$-0.505472\pi$
$599$	−301924.	−0.0343819	−0.0171910	+	0.999852i	$0.505472\pi$
$600$	−360000.	−0.0408248
$601$	−929593.	−0.104980	−0.0524900	−	0.998621i	$-0.516716\pi$
$601$	−929593.	−0.104980	−0.0524900	+	0.998621i	$0.516716\pi$
$602$	368111.	0.0413988
$603$	4.87812e6	0.546335
$604$	−4.62186e6	−0.515495
$605$	−4.00088e6	−0.444393
$606$	−3.27323e6	−0.362072
$607$	1.38633e7	1.52720	0.763598	−	0.645692i	$-0.223431\pi$
$607$	1.38633e7	1.52720	0.763598	+	0.645692i	$0.223431\pi$
$608$	369664.	0.0405554
$609$	−2.37163e6	−0.259122
$610$	2.03865e6	0.221829
$611$	−3.58905e6	−0.388935
$612$	−1.18643e6	−0.128045
$613$	−5.89166e6	−0.633266	−0.316633	−	0.948548i	$-0.602552\pi$
$613$	−5.89166e6	−0.633266	−0.316633	+	0.948548i	$0.602552\pi$
$614$	−9.25210e6	−0.990420
$615$	949410.	0.101220
$616$	69570.9	0.00738713
$617$	1.30582e7	1.38093	0.690464	−	0.723367i	$-0.257406\pi$
$617$	1.30582e7	1.38093	0.690464	+	0.723367i	$0.257406\pi$
$618$	−999617.	−0.105284
$619$	−6.38767e6	−0.670063	−0.335032	−	0.942207i	$-0.608747\pi$
$619$	−6.38767e6	−0.670063	−0.335032	+	0.942207i	$0.608747\pi$
$620$	−915588.	−0.0956579
$621$	−1.71628e6	−0.178591
$622$	−1.04600e7	−1.08406
$623$	−3.07554e6	−0.317469
$624$	345441.	0.0355150
$625$	390625.	0.0400000
$626$	−1.34125e7	−1.36796
$627$	−103553.	−0.0105194
$628$	492225.	0.0498041
$629$	1.15562e7	1.16463
$630$	276262.	0.0277312
$631$	8.42759e6	0.842616	0.421308	−	0.906918i	$-0.361571\pi$
$631$	8.42759e6	0.842616	0.421308	+	0.906918i	$0.361571\pi$
$632$	−1.70310e6	−0.169608
$633$	−3.76893e6	−0.373860
$634$	−4.82585e6	−0.476816
$635$	−3.65893e6	−0.360097
$636$	1.72000e6	0.168611
$637$	−2.34548e6	−0.229025
$638$	−985011.	−0.0958053
$639$	−235914.	−0.0228560
$640$	−409600.	−0.0395285
$641$	−9.99104e6	−0.960430	−0.480215	−	0.877151i	$-0.659441\pi$
$641$	−9.99104e6	−0.960430	−0.480215	+	0.877151i	$0.659441\pi$
$642$	909964.	0.0871338
$643$	−2.00027e7	−1.90793	−0.953964	−	0.299920i	$-0.903040\pi$
$643$	−2.00027e7	−1.90793	−0.953964	+	0.299920i	$0.903040\pi$
$644$	1.28474e6	0.122068
$645$	607108.	0.0574602
$646$	−1.32191e6	−0.124630
$647$	874950.	0.0821718	0.0410859	−	0.999156i	$-0.486918\pi$
$647$	874950.	0.0821718	0.0410859	+	0.999156i	$0.486918\pi$
$648$	−419904.	−0.0392837
$649$	−1.68500e6	−0.157032
$650$	−374827.	−0.0347975
$651$	702617.	0.0649779
$652$	−1.99732e6	−0.184005
$653$	−4.14665e6	−0.380552	−0.190276	−	0.981731i	$-0.560938\pi$
$653$	−4.14665e6	−0.380552	−0.190276	+	0.981731i	$0.560938\pi$
$654$	−670592.	−0.0613075
$655$	4.76948e6	0.434378
$656$	1.08022e6	0.0980058
$657$	2.23885e6	0.202354
$658$	−3.26576e6	−0.294049
$659$	−8.70090e6	−0.780460	−0.390230	−	0.920717i	$-0.627604\pi$
$659$	−8.70090e6	−0.780460	−0.390230	+	0.920717i	$0.627604\pi$
$660$	114740.	0.0102531
$661$	1.49078e7	1.32712	0.663559	−	0.748124i	$-0.269045\pi$
$661$	1.49078e7	1.32712	0.663559	+	0.748124i	$0.269045\pi$
$662$	−5.38509e6	−0.477582
$663$	−1.23529e6	−0.109140
$664$	4.31363e6	0.379684
$665$	307810.	0.0269916
$666$	4.09002e6	0.357305
$667$	−1.81899e7	−1.58313
$668$	1.63110e6	0.141429
$669$	−9.23227e6	−0.797523
$670$	−6.02237e6	−0.518299
$671$	−649764.	−0.0557121
$672$	314324.	0.0268507
$673$	−9.57636e6	−0.815010	−0.407505	−	0.913203i	$-0.633601\pi$
$673$	−9.57636e6	−0.815010	−0.407505	+	0.913203i	$0.633601\pi$
$674$	1.64762e7	1.39703
$675$	455625.	0.0384900
$676$	−5.58102e6	−0.469728
$677$	1.49767e7	1.25587	0.627936	−	0.778265i	$-0.283900\pi$
$677$	1.49767e7	1.25587	0.627936	+	0.778265i	$0.283900\pi$
$678$	−947400.	−0.0791515
$679$	4.84903e6	0.403627
$680$	1.46472e6	0.121474
$681$	−7.04627e6	−0.582226
$682$	291818.	0.0240243
$683$	2.04298e7	1.67576	0.837881	−	0.545853i	$-0.183794\pi$
$683$	2.04298e7	1.67576	0.837881	+	0.545853i	$0.183794\pi$
$684$	−467856.	−0.0382360
$685$	−8.68635e6	−0.707312
$686$	−4.42711e6	−0.359178
$687$	7.91671e6	0.639960
$688$	690754.	0.0556356
$689$	1.79085e6	0.143718
$690$	2.11887e6	0.169426
$691$	2.21732e7	1.76658	0.883290	−	0.468826i	$-0.155323\pi$
$691$	2.21732e7	1.76658	0.883290	+	0.468826i	$0.155323\pi$
$692$	3.00152e6	0.238274
$693$	−88050.7	−0.00696465
$694$	−1.62621e7	−1.28167
$695$	−2.72401e6	−0.213917
$696$	−4.45032e6	−0.348232
$697$	−3.86285e6	−0.301180
$698$	6.72676e6	0.522598
$699$	1.01469e6	0.0785493
$700$	−341064.	−0.0263082
$701$	1.33739e7	1.02793	0.513965	−	0.857811i	$-0.328176\pi$
$701$	1.33739e7	1.02793	0.513965	+	0.857811i	$0.328176\pi$
$702$	−437199.	−0.0334839
$703$	4.55709e6	0.347775
$704$	130548.	0.00992751
$705$	−5.38606e6	−0.408130
$706$	1.93227e6	0.145900
$707$	−3.10106e6	−0.233325
$708$	−7.61293e6	−0.570780
$709$	1.55456e7	1.16143	0.580713	−	0.814108i	$-0.302774\pi$
$709$	1.55456e7	1.16143	0.580713	+	0.814108i	$0.302774\pi$
$710$	291251.	0.0216831
$711$	2.15548e6	0.159908
$712$	−5.77119e6	−0.426644
$713$	5.38892e6	0.396988
$714$	−1.12402e6	−0.0825142
$715$	119466.	0.00873933
$716$	2.84130e6	0.207126
$717$	893126.	0.0648806
$718$	−263056.	−0.0190431
$719$	5.40570e6	0.389968	0.194984	−	0.980806i	$-0.437534\pi$
$719$	5.40570e6	0.389968	0.194984	+	0.980806i	$0.437534\pi$
$720$	518400.	0.0372678
$721$	−947036.	−0.0678467
$722$	−521284.	−0.0372161
$723$	−968040.	−0.0688728
$724$	−1.07782e7	−0.764188
$725$	4.82891e6	0.341196
$726$	5.76127e6	0.405673
$727$	2.98586e6	0.209524	0.104762	−	0.994497i	$-0.466592\pi$
$727$	2.98586e6	0.209524	0.104762	+	0.994497i	$0.466592\pi$
$728$	327270.	0.0228864
$729$	531441.	0.0370370
$730$	−2.76401e6	−0.191970
$731$	−2.47013e6	−0.170972
$732$	−2.93566e6	−0.202502
$733$	4.85325e6	0.333636	0.166818	−	0.985988i	$-0.446651\pi$
$733$	4.85325e6	0.333636	0.166818	+	0.985988i	$0.446651\pi$
$734$	−7.63706e6	−0.523222
$735$	−3.51984e6	−0.240328
$736$	2.41080e6	0.164046
$737$	1.91946e6	0.130170
$738$	−1.36715e6	−0.0924008
$739$	−5.27708e6	−0.355453	−0.177727	−	0.984080i	$-0.556874\pi$
$739$	−5.27708e6	−0.355453	−0.177727	+	0.984080i	$0.556874\pi$
$740$	−5.04940e6	−0.338970
$741$	−487126.	−0.0325908
$742$	1.62953e6	0.108656
$743$	−2.36362e7	−1.57074	−0.785372	−	0.619024i	$-0.787528\pi$
$743$	−2.36362e7	−1.57074	−0.785372	+	0.619024i	$0.787528\pi$
$744$	1.31845e6	0.0873234
$745$	3.42738e6	0.226241
$746$	1.14723e7	0.754748
$747$	−5.45944e6	−0.357970
$748$	−466840.	−0.0305080
$749$	862099.	0.0561504
$750$	−562500.	−0.0365148
$751$	−1.38581e7	−0.896613	−0.448306	−	0.893880i	$-0.647973\pi$
$751$	−1.38581e7	−0.896613	−0.448306	+	0.893880i	$0.647973\pi$
$752$	−6.12814e6	−0.395170
$753$	2.79389e6	0.179565
$754$	−4.63362e6	−0.296819
$755$	−7.22165e6	−0.461072
$756$	−397817.	−0.0253150
$757$	1.88210e7	1.19372	0.596860	−	0.802345i	$-0.296415\pi$
$757$	1.88210e7	1.19372	0.596860	+	0.802345i	$0.296415\pi$
$758$	−3.67855e6	−0.232543
$759$	−675329.	−0.0425511
$760$	577600.	0.0362738
$761$	3.69012e6	0.230983	0.115491	−	0.993308i	$-0.463156\pi$
$761$	3.69012e6	0.230983	0.115491	+	0.993308i	$0.463156\pi$
$762$	5.26886e6	0.328722
$763$	−635318.	−0.0395076
$764$	−1.53567e7	−0.951843
$765$	−1.85379e6	−0.114527
$766$	1.80308e7	1.11031
$767$	−7.92648e6	−0.486510
$768$	589824.	0.0360844
$769$	3.15204e6	0.192210	0.0961051	−	0.995371i	$-0.469362\pi$
$769$	3.15204e6	0.192210	0.0961051	+	0.995371i	$0.469362\pi$
$770$	108705.	0.00660725
$771$	2.57164e6	0.155802
$772$	−7.16060e6	−0.432420
$773$	−158167.	−0.00952066	−0.00476033	−	0.999989i	$-0.501515\pi$
$773$	−158167.	−0.00952066	−0.00476033	+	0.999989i	$0.501515\pi$
$774$	−874236.	−0.0524537
$775$	−1.43061e6	−0.0855591
$776$	9.09912e6	0.542432
$777$	3.87488e6	0.230253
$778$	−2.22822e7	−1.31980
$779$	−1.52328e6	−0.0899363
$780$	539751.	0.0317656
$781$	−92828.2	−0.00544568
$782$	−8.62099e6	−0.504127
$783$	5.63244e6	0.328316
$784$	−4.00480e6	−0.232697
$785$	769102.	0.0445461
$786$	−6.86806e6	−0.396531
$787$	2.12157e7	1.22101	0.610507	−	0.792011i	$-0.290966\pi$
$787$	2.12157e7	1.22101	0.610507	+	0.792011i	$0.290966\pi$
$788$	1.13291e6	0.0649951
$789$	1.06379e7	0.608365
$790$	−2.66109e6	−0.151702
$791$	−897566.	−0.0510065
$792$	−165225.	−0.00935974
$793$	−3.05657e6	−0.172604
$794$	4.65162e6	0.261850
$795$	2.68751e6	0.150811
$796$	−1.38271e7	−0.773478
$797$	−1.41948e7	−0.791560	−0.395780	−	0.918345i	$-0.629526\pi$
$797$	−1.41948e7	−0.791560	−0.395780	+	0.918345i	$0.629526\pi$
$798$	−443247.	−0.0246399
$799$	2.19142e7	1.21439
$800$	−640000.	−0.0353553
$801$	7.30417e6	0.402244
$802$	9.40976e6	0.516586
$803$	880950.	0.0482128
$804$	8.67222e6	0.473140
$805$	2.00741e6	0.109181
$806$	1.37275e6	0.0744310
$807$	1.09663e7	0.592759
$808$	−5.81907e6	−0.313563
$809$	−519774.	−0.0279218	−0.0139609	−	0.999903i	$-0.504444\pi$
$809$	−519774.	−0.0279218	−0.0139609	+	0.999903i	$0.504444\pi$
$810$	−656100.	−0.0351364
$811$	4.77302e6	0.254825	0.127412	−	0.991850i	$-0.459333\pi$
$811$	4.77302e6	0.254825	0.127412	+	0.991850i	$0.459333\pi$
$812$	−4.21624e6	−0.224406
$813$	−1.82936e7	−0.970674
$814$	1.60936e6	0.0851316
$815$	−3.12081e6	−0.164579
$816$	−2.10920e6	−0.110890
$817$	−974071.	−0.0510547
$818$	−2.17817e7	−1.13818
$819$	−414202.	−0.0215775
$820$	1.68784e6	0.0876591
$821$	1.77632e7	0.919738	0.459869	−	0.887987i	$-0.347896\pi$
$821$	1.77632e7	0.919738	0.459869	+	0.887987i	$0.347896\pi$
$822$	1.25083e7	0.645685
$823$	−2.20845e7	−1.13655	−0.568275	−	0.822839i	$-0.692389\pi$
$823$	−2.20845e7	−1.13655	−0.568275	+	0.822839i	$0.692389\pi$
$824$	−1.77710e6	−0.0911786
$825$	179281.	0.00917064
$826$	−7.21248e6	−0.367820
$827$	−1.49320e7	−0.759195	−0.379598	−	0.925152i	$-0.623938\pi$
$827$	−1.49320e7	−0.759195	−0.379598	+	0.925152i	$0.623938\pi$
$828$	−3.05117e6	−0.154664
$829$	1.86878e7	0.944433	0.472217	−	0.881483i	$-0.343454\pi$
$829$	1.86878e7	0.944433	0.472217	+	0.881483i	$0.343454\pi$
$830$	6.74005e6	0.339600
$831$	−1.82328e7	−0.915904
$832$	614117.	0.0307569
$833$	1.43211e7	0.715096
$834$	3.92257e6	0.195279
$835$	2.54859e6	0.126498
$836$	−184094.	−0.00911011
$837$	−1.66866e6	−0.0823293
$838$	−1.65134e7	−0.812317
$839$	2.52104e7	1.23645	0.618224	−	0.786002i	$-0.287853\pi$
$839$	2.52104e7	1.23645	0.618224	+	0.786002i	$0.287853\pi$
$840$	491132.	0.0240160
$841$	3.91839e7	1.91037
$842$	−2.06268e7	−1.00266
$843$	−6.32814e6	−0.306695
$844$	−6.70033e6	−0.323772
$845$	−8.72034e6	−0.420138
$846$	7.75593e6	0.372570
$847$	5.45822e6	0.261422
$848$	3.05778e6	0.146022
$849$	−2.23142e7	−1.06246
$850$	2.28863e6	0.108650
$851$	2.97195e7	1.40675
$852$	−419402.	−0.0197939
$853$	−2.75534e7	−1.29659	−0.648295	−	0.761389i	$-0.724518\pi$
$853$	−2.75534e7	−1.29659	−0.648295	+	0.761389i	$0.724518\pi$
$854$	−2.78124e6	−0.130495
$855$	−731025.	−0.0341993
$856$	1.61771e6	0.0754601
$857$	−1.95715e7	−0.910272	−0.455136	−	0.890422i	$-0.650409\pi$
$857$	−1.95715e7	−0.910272	−0.455136	+	0.890422i	$0.650409\pi$
$858$	−172031.	−0.00797788
$859$	−2.99519e7	−1.38497	−0.692486	−	0.721432i	$-0.743484\pi$
$859$	−2.99519e7	−1.38497	−0.692486	+	0.721432i	$0.743484\pi$
$860$	1.07930e6	0.0497620
$861$	−1.29524e6	−0.0595445
$862$	5.75416e6	0.263763
$863$	−6.02134e6	−0.275211	−0.137606	−	0.990487i	$-0.543941\pi$
$863$	−6.02134e6	−0.275211	−0.137606	+	0.990487i	$0.543941\pi$
$864$	−746496.	−0.0340207
$865$	4.68988e6	0.213119
$866$	−1.70799e7	−0.773909
$867$	−5.23623e6	−0.236576
$868$	1.24910e6	0.0562726
$869$	848148.	0.0380998
$870$	−6.95363e6	−0.311468
$871$	9.02940e6	0.403286
$872$	−1.19216e6	−0.0530939
$873$	−1.15161e7	−0.511409
$874$	−3.39960e6	−0.150539
$875$	−532912.	−0.0235307
$876$	3.98017e6	0.175243
$877$	2.29639e7	1.00820	0.504101	−	0.863645i	$-0.331824\pi$
$877$	2.29639e7	1.00820	0.504101	+	0.863645i	$0.331824\pi$
$878$	−2.15359e7	−0.942816
$879$	−2.53483e7	−1.10657
$880$	203982.	0.00887943
$881$	1.92625e6	0.0836130	0.0418065	−	0.999126i	$-0.486689\pi$
$881$	1.92625e6	0.0836130	0.0418065	+	0.999126i	$0.486689\pi$
$882$	5.06858e6	0.219389
$883$	2.69881e7	1.16485	0.582427	−	0.812883i	$-0.302103\pi$
$883$	2.69881e7	1.16485	0.582427	+	0.812883i	$0.302103\pi$
$884$	−2.19607e6	−0.0945184
$885$	−1.18952e7	−0.510521
$886$	−7.33179e6	−0.313780
$887$	−2.30796e7	−0.984962	−0.492481	−	0.870323i	$-0.663910\pi$
$887$	−2.30796e7	−0.984962	−0.492481	+	0.870323i	$0.663910\pi$
$888$	7.27114e6	0.309435
$889$	4.99171e6	0.211834
$890$	−9.01749e6	−0.381602
$891$	209113.	0.00882445
$892$	−1.64129e7	−0.690675
$893$	8.64164e6	0.362633
$894$	−4.93542e6	−0.206529
$895$	4.43953e6	0.185259
$896$	558799.	0.0232534
$897$	−3.17684e6	−0.131830
$898$	2.13221e7	0.882346
$899$	−1.76852e7	−0.729811
$900$	810000.	0.0333333
$901$	−1.09346e7	−0.448736
$902$	−537952.	−0.0220154
$903$	−828251.	−0.0338020
$904$	−1.68427e6	−0.0685472
$905$	−1.68409e7	−0.683510
$906$	1.03992e7	0.420900
$907$	1.56301e7	0.630876	0.315438	−	0.948946i	$-0.397849\pi$
$907$	1.56301e7	0.630876	0.315438	+	0.948946i	$0.397849\pi$
$908$	−1.25267e7	−0.504222
$909$	7.36476e6	0.295630
$910$	511360.	0.0204703
$911$	1.76849e7	0.706003	0.353001	−	0.935623i	$-0.385161\pi$
$911$	1.76849e7	0.706003	0.353001	+	0.935623i	$0.385161\pi$
$912$	−831744.	−0.0331133
$913$	−2.14820e6	−0.0852899
$914$	−2.24279e6	−0.0888021
$915$	−4.58697e6	−0.181123
$916$	1.40742e7	0.554222
$917$	−6.50679e6	−0.255531
$918$	2.66946e6	0.104548
$919$	−1.45332e7	−0.567640	−0.283820	−	0.958878i	$-0.591602\pi$
$919$	−1.45332e7	−0.567640	−0.283820	+	0.958878i	$0.591602\pi$
$920$	3.76687e6	0.146728
$921$	2.08172e7	0.808675
$922$	−1.57041e7	−0.608394
$923$	−436676.	−0.0168715
$924$	−156534.	−0.00603157
$925$	−7.88969e6	−0.303184
$926$	2.71789e7	1.04161
$927$	2.24914e6	0.0859640
$928$	−7.91169e6	−0.301578
$929$	−5.41583e6	−0.205886	−0.102943	−	0.994687i	$-0.532826\pi$
$929$	−5.41583e6	−0.205886	−0.102943	+	0.994687i	$0.532826\pi$
$930$	2.06007e6	0.0781044
$931$	5.64740e6	0.213537
$932$	1.80390e6	0.0680257
$933$	2.35350e7	0.885134
$934$	5.73898e6	0.215262
$935$	−729437.	−0.0272872
$936$	−777242.	−0.0289979
$937$	3.60577e7	1.34168	0.670841	−	0.741601i	$-0.265933\pi$
$937$	3.60577e7	1.34168	0.670841	+	0.741601i	$0.265933\pi$
$938$	8.21605e6	0.304899
$939$	3.01782e7	1.11694
$940$	−9.57522e6	−0.353451
$941$	4.81040e7	1.77095	0.885477	−	0.464683i	$-0.153832\pi$
$941$	4.81040e7	1.77095	0.885477	+	0.464683i	$0.153832\pi$
$942$	−1.10751e6	−0.0406648
$943$	−9.93419e6	−0.363792
$944$	−1.35341e7	−0.494310
$945$	−621589.	−0.0226425
$946$	−343998.	−0.0124976
$947$	4.75198e7	1.72187	0.860934	−	0.508716i	$-0.169880\pi$
$947$	4.75198e7	1.72187	0.860934	+	0.508716i	$0.169880\pi$
$948$	3.83197e6	0.138485
$949$	4.14410e6	0.149371
$950$	902500.	0.0324443
$951$	1.08582e7	0.389319
$952$	−1.99826e6	−0.0714594
$953$	2.35327e6	0.0839341	0.0419671	−	0.999119i	$-0.486638\pi$
$953$	2.35327e6	0.0839341	0.0419671	+	0.999119i	$0.486638\pi$
$954$	−3.87001e6	−0.137671
$955$	−2.39949e7	−0.851354
$956$	1.58778e6	0.0561882
$957$	2.21627e6	0.0782247
$958$	−2.92364e7	−1.02923
$959$	1.18504e7	0.416089
$960$	921600.	0.0322749
$961$	−2.33898e7	−0.816991
$962$	7.57062e6	0.263751
$963$	−2.04742e6	−0.0711444
$964$	−1.72096e6	−0.0596456
$965$	−1.11884e7	−0.386768
$966$	−2.89068e6	−0.0996682
$967$	−4.51703e7	−1.55341	−0.776706	−	0.629864i	$-0.783111\pi$
$967$	−4.51703e7	−1.55341	−0.776706	+	0.629864i	$0.783111\pi$
$968$	1.02423e7	0.351323
$969$	2.97431e6	0.101760
$970$	1.42174e7	0.485165
$971$	−3.92928e7	−1.33741	−0.668706	−	0.743527i	$-0.733152\pi$
$971$	−3.92928e7	−1.33741	−0.668706	+	0.743527i	$0.733152\pi$
$972$	944784.	0.0320750
$973$	3.71624e6	0.125841
$974$	1.44062e7	0.486579
$975$	843361.	0.0284120
$976$	−5.21895e6	−0.175371
$977$	−2.43011e7	−0.814496	−0.407248	−	0.913318i	$-0.633512\pi$
$977$	−2.43011e7	−0.814496	−0.407248	+	0.913318i	$0.633512\pi$
$978$	4.49397e6	0.150239
$979$	2.87407e6	0.0958387
$980$	−6.25750e6	−0.208131
$981$	1.50883e6	0.0500574
$982$	−3.12055e7	−1.03265
$983$	−3.32344e7	−1.09699	−0.548496	−	0.836153i	$-0.684799\pi$
$983$	−3.32344e7	−1.09699	−0.548496	+	0.836153i	$0.684799\pi$
$984$	−2.43049e6	−0.0800214
$985$	1.77017e6	0.0581333
$986$	2.82921e7	0.926772
$987$	7.34796e6	0.240090
$988$	−866001.	−0.0282245
$989$	−6.35250e6	−0.206516
$990$	−258165.	−0.00837161
$991$	2.71928e7	0.879570	0.439785	−	0.898103i	$-0.355055\pi$
$991$	2.71928e7	0.879570	0.439785	+	0.898103i	$0.355055\pi$
$992$	2.34391e6	0.0756242
$993$	1.21164e7	0.389944
$994$	−397341.	−0.0127555
$995$	−2.16048e7	−0.691820
$996$	−9.70567e6	−0.310011
$997$	5.03197e6	0.160325	0.0801623	−	0.996782i	$-0.474456\pi$
$997$	5.03197e6	0.160325	0.0801623	+	0.996782i	$0.474456\pi$
$998$	−3.78752e6	−0.120373
$999$	−9.20254e6	−0.291739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.l.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.l.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.1064 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} -34.1064 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +31.8722 q^{11} +144.000 q^{12} +149.931 q^{13} +136.426 q^{14} +225.000 q^{15} +256.000 q^{16} -915.453 q^{17} -324.000 q^{18} -361.000 q^{19} +400.000 q^{20} -306.957 q^{21} -127.489 q^{22} -2354.30 q^{23} -576.000 q^{24} +625.000 q^{25} -599.724 q^{26} +729.000 q^{27} -545.702 q^{28} +7726.26 q^{29} -900.000 q^{30} -2288.97 q^{31} -1024.00 q^{32} +286.850 q^{33} +3661.81 q^{34} -852.660 q^{35} +1296.00 q^{36} -12623.5 q^{37} +1444.00 q^{38} +1349.38 q^{39} -1600.00 q^{40} +4219.60 q^{41} +1227.83 q^{42} +2698.26 q^{43} +509.955 q^{44} +2025.00 q^{45} +9417.19 q^{46} -23938.1 q^{47} +2304.00 q^{48} -15643.8 q^{49} -2500.00 q^{50} -8239.08 q^{51} +2398.89 q^{52} +11944.5 q^{53} -2916.00 q^{54} +796.805 q^{55} +2182.81 q^{56} -3249.00 q^{57} -30905.0 q^{58} -52867.6 q^{59} +3600.00 q^{60} -20386.5 q^{61} +9155.88 q^{62} -2762.62 q^{63} +4096.00 q^{64} +3748.27 q^{65} -1147.40 q^{66} +60223.7 q^{67} -14647.2 q^{68} -21188.7 q^{69} +3410.64 q^{70} -2912.51 q^{71} -5184.00 q^{72} +27640.1 q^{73} +50494.0 q^{74} +5625.00 q^{75} -5776.00 q^{76} -1087.05 q^{77} -5397.51 q^{78} +26610.9 q^{79} +6400.00 q^{80} +6561.00 q^{81} -16878.4 q^{82} -67400.5 q^{83} -4911.32 q^{84} -22886.3 q^{85} -10793.0 q^{86} +69536.3 q^{87} -2039.82 q^{88} +90174.9 q^{89} -8100.00 q^{90} -5113.60 q^{91} -37668.7 q^{92} -20600.7 q^{93} +95752.2 q^{94} -9025.00 q^{95} -9216.00 q^{96} -142174. q^{97} +62575.0 q^{98} +2581.65 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} + 100 q^{5} - 144 q^{6} - 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 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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