LMFDB - Embedded newform 570.6.a.n.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:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6167x^{2} - 254912x - 2938616 $ x^4 - x^3 - 6167x^2 - 254912x - 2938616
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-27.2566$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -227.941 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -227.941 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -373.778 q^{11} -144.000 q^{12} +97.5091 q^{13} -911.763 q^{14} +225.000 q^{15} +256.000 q^{16} -798.890 q^{17} +324.000 q^{18} -361.000 q^{19} -400.000 q^{20} +2051.47 q^{21} -1495.11 q^{22} -3296.74 q^{23} -576.000 q^{24} +625.000 q^{25} +390.036 q^{26} -729.000 q^{27} -3647.05 q^{28} +3195.65 q^{29} +900.000 q^{30} -7647.70 q^{31} +1024.00 q^{32} +3364.00 q^{33} -3195.56 q^{34} +5698.52 q^{35} +1296.00 q^{36} +878.798 q^{37} -1444.00 q^{38} -877.582 q^{39} -1600.00 q^{40} +12469.6 q^{41} +8205.87 q^{42} -11940.2 q^{43} -5980.45 q^{44} -2025.00 q^{45} -13187.0 q^{46} +2883.69 q^{47} -2304.00 q^{48} +35150.0 q^{49} +2500.00 q^{50} +7190.01 q^{51} +1560.15 q^{52} +3876.32 q^{53} -2916.00 q^{54} +9344.45 q^{55} -14588.2 q^{56} +3249.00 q^{57} +12782.6 q^{58} +564.898 q^{59} +3600.00 q^{60} +5089.40 q^{61} -30590.8 q^{62} -18463.2 q^{63} +4096.00 q^{64} -2437.73 q^{65} +13456.0 q^{66} +34356.7 q^{67} -12782.2 q^{68} +29670.6 q^{69} +22794.1 q^{70} -26349.0 q^{71} +5184.00 q^{72} +6264.88 q^{73} +3515.19 q^{74} -5625.00 q^{75} -5776.00 q^{76} +85199.2 q^{77} -3510.33 q^{78} +81260.8 q^{79} -6400.00 q^{80} +6561.00 q^{81} +49878.2 q^{82} +28765.4 q^{83} +32823.5 q^{84} +19972.3 q^{85} -47760.9 q^{86} -28760.8 q^{87} -23921.8 q^{88} +996.626 q^{89} -8100.00 q^{90} -22226.3 q^{91} -52747.8 q^{92} +68829.3 q^{93} +11534.8 q^{94} +9025.00 q^{95} -9216.00 q^{96} +11057.0 q^{97} +140600. q^{98} -30276.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 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 + 10 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9} - 400 q^{10} + 102 q^{11} - 576 q^{12} - 122 q^{13} + 40 q^{14} + 900 q^{15} + 1024 q^{16} - 336 q^{17} + 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 90 q^{21} + 408 q^{22} - 396 q^{23} - 2304 q^{24} + 2500 q^{25} - 488 q^{26} - 2916 q^{27} + 160 q^{28} - 70 q^{29} + 3600 q^{30} - 10728 q^{31} + 4096 q^{32} - 918 q^{33} - 1344 q^{34} - 250 q^{35} + 5184 q^{36} + 10610 q^{37} - 5776 q^{38} + 1098 q^{39} - 6400 q^{40} - 3662 q^{41} - 360 q^{42} + 550 q^{43} + 1632 q^{44} - 8100 q^{45} - 1584 q^{46} + 9700 q^{47} - 9216 q^{48} + 42432 q^{49} + 10000 q^{50} + 3024 q^{51} - 1952 q^{52} + 14028 q^{53} - 11664 q^{54} - 2550 q^{55} + 640 q^{56} + 12996 q^{57} - 280 q^{58} + 22092 q^{59} + 14400 q^{60} + 20140 q^{61} - 42912 q^{62} + 810 q^{63} + 16384 q^{64} + 3050 q^{65} - 3672 q^{66} + 36624 q^{67} - 5376 q^{68} + 3564 q^{69} - 1000 q^{70} + 42236 q^{71} + 20736 q^{72} + 38560 q^{73} + 42440 q^{74} - 22500 q^{75} - 23104 q^{76} + 120840 q^{77} + 4392 q^{78} + 190160 q^{79} - 25600 q^{80} + 26244 q^{81} - 14648 q^{82} + 118456 q^{83} - 1440 q^{84} + 8400 q^{85} + 2200 q^{86} + 630 q^{87} + 6528 q^{88} + 247890 q^{89} - 32400 q^{90} + 229880 q^{91} - 6336 q^{92} + 96552 q^{93} + 38800 q^{94} + 36100 q^{95} - 36864 q^{96} - 153602 q^{97} + 169728 q^{98} + 8262 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9 - 400 * q^10 + 102 * q^11 - 576 * q^12 - 122 * q^13 + 40 * q^14 + 900 * q^15 + 1024 * q^16 - 336 * q^17 + 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 90 * q^21 + 408 * q^22 - 396 * q^23 - 2304 * q^24 + 2500 * q^25 - 488 * q^26 - 2916 * q^27 + 160 * q^28 - 70 * q^29 + 3600 * q^30 - 10728 * q^31 + 4096 * q^32 - 918 * q^33 - 1344 * q^34 - 250 * q^35 + 5184 * q^36 + 10610 * q^37 - 5776 * q^38 + 1098 * q^39 - 6400 * q^40 - 3662 * q^41 - 360 * q^42 + 550 * q^43 + 1632 * q^44 - 8100 * q^45 - 1584 * q^46 + 9700 * q^47 - 9216 * q^48 + 42432 * q^49 + 10000 * q^50 + 3024 * q^51 - 1952 * q^52 + 14028 * q^53 - 11664 * q^54 - 2550 * q^55 + 640 * q^56 + 12996 * q^57 - 280 * q^58 + 22092 * q^59 + 14400 * q^60 + 20140 * q^61 - 42912 * q^62 + 810 * q^63 + 16384 * q^64 + 3050 * q^65 - 3672 * q^66 + 36624 * q^67 - 5376 * q^68 + 3564 * q^69 - 1000 * q^70 + 42236 * q^71 + 20736 * q^72 + 38560 * q^73 + 42440 * q^74 - 22500 * q^75 - 23104 * q^76 + 120840 * q^77 + 4392 * q^78 + 190160 * q^79 - 25600 * q^80 + 26244 * q^81 - 14648 * q^82 + 118456 * q^83 - 1440 * q^84 + 8400 * q^85 + 2200 * q^86 + 630 * q^87 + 6528 * q^88 + 247890 * q^89 - 32400 * q^90 + 229880 * q^91 - 6336 * q^92 + 96552 * q^93 + 38800 * q^94 + 36100 * q^95 - 36864 * q^96 - 153602 * q^97 + 169728 * q^98 + 8262 * 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
$7$	−227.941	−1.75823	−0.879117	−	0.476606i	$-0.841867\pi$
$7$	−227.941	−1.75823	−0.879117	+	0.476606i	$0.841867\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−373.778	−0.931391	−0.465695	−	0.884945i	$-0.654196\pi$
$11$	−373.778	−0.931391	−0.465695	+	0.884945i	$0.654196\pi$
$12$	−144.000	−0.288675
$13$	97.5091	0.160025	0.0800123	−	0.996794i	$-0.474504\pi$
$13$	97.5091	0.160025	0.0800123	+	0.996794i	$0.474504\pi$
$14$	−911.763	−1.24326
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−798.890	−0.670447	−0.335224	−	0.942139i	$-0.608812\pi$
$17$	−798.890	−0.670447	−0.335224	+	0.942139i	$0.608812\pi$
$18$	324.000	0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−400.000	−0.223607
$21$	2051.47	1.01512
$22$	−1495.11	−0.658593
$23$	−3296.74	−1.29947	−0.649733	−	0.760162i	$-0.725119\pi$
$23$	−3296.74	−1.29947	−0.649733	+	0.760162i	$0.725119\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	390.036	0.113154
$27$	−729.000	−0.192450
$28$	−3647.05	−0.879117
$29$	3195.65	0.705609	0.352804	−	0.935697i	$-0.385228\pi$
$29$	3195.65	0.705609	0.352804	+	0.935697i	$0.385228\pi$
$30$	900.000	0.182574
$31$	−7647.70	−1.42931	−0.714655	−	0.699477i	$-0.753416\pi$
$31$	−7647.70	−1.42931	−0.714655	+	0.699477i	$0.753416\pi$
$32$	1024.00	0.176777
$33$	3364.00	0.537739
$34$	−3195.56	−0.474078
$35$	5698.52	0.786306
$36$	1296.00	0.166667
$37$	878.798	0.105532	0.0527661	−	0.998607i	$-0.483196\pi$
$37$	878.798	0.105532	0.0527661	+	0.998607i	$0.483196\pi$
$38$	−1444.00	−0.162221
$39$	−877.582	−0.0923902
$40$	−1600.00	−0.158114
$41$	12469.6	1.15849	0.579244	−	0.815154i	$-0.303348\pi$
$41$	12469.6	1.15849	0.579244	+	0.815154i	$0.303348\pi$
$42$	8205.87	0.717796
$43$	−11940.2	−0.984785	−0.492393	−	0.870373i	$-0.663878\pi$
$43$	−11940.2	−0.984785	−0.492393	+	0.870373i	$0.663878\pi$
$44$	−5980.45	−0.465695
$45$	−2025.00	−0.149071
$46$	−13187.0	−0.918861
$47$	2883.69	0.190416	0.0952081	−	0.995457i	$-0.469648\pi$
$47$	2883.69	0.190416	0.0952081	+	0.995457i	$0.469648\pi$
$48$	−2304.00	−0.144338
$49$	35150.0	2.09139
$50$	2500.00	0.141421
$51$	7190.01	0.387083
$52$	1560.15	0.0800123
$53$	3876.32	0.189553	0.0947764	−	0.995499i	$-0.469786\pi$
$53$	3876.32	0.189553	0.0947764	+	0.995499i	$0.469786\pi$
$54$	−2916.00	−0.136083
$55$	9344.45	0.416531
$56$	−14588.2	−0.621630
$57$	3249.00	0.132453
$58$	12782.6	0.498941
$59$	564.898	0.0211271	0.0105635	−	0.999944i	$-0.496637\pi$
$59$	564.898	0.0211271	0.0105635	+	0.999944i	$0.496637\pi$
$60$	3600.00	0.129099
$61$	5089.40	0.175123	0.0875613	−	0.996159i	$-0.472093\pi$
$61$	5089.40	0.175123	0.0875613	+	0.996159i	$0.472093\pi$
$62$	−30590.8	−1.01067
$63$	−18463.2	−0.586078
$64$	4096.00	0.125000
$65$	−2437.73	−0.0715652
$66$	13456.0	0.380239
$67$	34356.7	0.935027	0.467513	−	0.883986i	$-0.345150\pi$
$67$	34356.7	0.935027	0.467513	+	0.883986i	$0.345150\pi$
$68$	−12782.2	−0.335224
$69$	29670.6	0.750247
$70$	22794.1	0.556003
$71$	−26349.0	−0.620324	−0.310162	−	0.950684i	$-0.600383\pi$
$71$	−26349.0	−0.620324	−0.310162	+	0.950684i	$0.600383\pi$
$72$	5184.00	0.117851
$73$	6264.88	0.137596	0.0687979	−	0.997631i	$-0.478084\pi$
$73$	6264.88	0.137596	0.0687979	+	0.997631i	$0.478084\pi$
$74$	3515.19	0.0746225
$75$	−5625.00	−0.115470
$76$	−5776.00	−0.114708
$77$	85199.2	1.63760
$78$	−3510.33	−0.0653298
$79$	81260.8	1.46492	0.732459	−	0.680811i	$-0.238372\pi$
$79$	81260.8	1.46492	0.732459	+	0.680811i	$0.238372\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	49878.2	0.819174
$83$	28765.4	0.458327	0.229163	−	0.973388i	$-0.426401\pi$
$83$	28765.4	0.458327	0.229163	+	0.973388i	$0.426401\pi$
$84$	32823.5	0.507559
$85$	19972.3	0.299833
$86$	−47760.9	−0.696348
$87$	−28760.8	−0.407383
$88$	−23921.8	−0.329296
$89$	996.626	0.0133370	0.00666848	−	0.999978i	$-0.497877\pi$
$89$	996.626	0.0133370	0.00666848	+	0.999978i	$0.497877\pi$
$90$	−8100.00	−0.105409
$91$	−22226.3	−0.281361
$92$	−52747.8	−0.649733
$93$	68829.3	0.825213
$94$	11534.8	0.134645
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	11057.0	0.119318	0.0596592	−	0.998219i	$-0.480999\pi$
$97$	11057.0	0.119318	0.0596592	+	0.998219i	$0.480999\pi$
$98$	140600.	1.47883
$99$	−30276.0	−0.310464
$100$	10000.0	0.100000
$101$	−29200.8	−0.284833	−0.142417	−	0.989807i	$-0.545487\pi$
$101$	−29200.8	−0.284833	−0.142417	+	0.989807i	$0.545487\pi$
$102$	28760.0	0.273709
$103$	79534.3	0.738689	0.369344	−	0.929293i	$-0.379582\pi$
$103$	79534.3	0.738689	0.369344	+	0.929293i	$0.379582\pi$
$104$	6240.58	0.0565772
$105$	−51286.7	−0.453974
$106$	15505.3	0.134034
$107$	−87959.1	−0.742714	−0.371357	−	0.928490i	$-0.621107\pi$
$107$	−87959.1	−0.742714	−0.371357	+	0.928490i	$0.621107\pi$
$108$	−11664.0	−0.0962250
$109$	32972.5	0.265819	0.132910	−	0.991128i	$-0.457568\pi$
$109$	32972.5	0.265819	0.132910	+	0.991128i	$0.457568\pi$
$110$	37377.8	0.294532
$111$	−7909.18	−0.0609290
$112$	−58352.8	−0.439559
$113$	−35685.4	−0.262903	−0.131451	−	0.991323i	$-0.541964\pi$
$113$	−35685.4	−0.262903	−0.131451	+	0.991323i	$0.541964\pi$
$114$	12996.0	0.0936586
$115$	82418.5	0.581139
$116$	51130.4	0.352804
$117$	7898.24	0.0533415
$118$	2259.59	0.0149391
$119$	182100.	1.17880
$120$	14400.0	0.0912871
$121$	−21341.0	−0.132511
$122$	20357.6	0.123830
$123$	−112226.	−0.668853
$124$	−122363.	−0.714655
$125$	−15625.0	−0.0894427
$126$	−73852.8	−0.414420
$127$	−113763.	−0.625883	−0.312942	−	0.949772i	$-0.601314\pi$
$127$	−113763.	−0.625883	−0.312942	+	0.949772i	$0.601314\pi$
$128$	16384.0	0.0883883
$129$	107462.	0.568566
$130$	−9750.91	−0.0506042
$131$	−133863.	−0.681526	−0.340763	−	0.940149i	$-0.610685\pi$
$131$	−133863.	−0.681526	−0.340763	+	0.940149i	$0.610685\pi$
$132$	53824.0	0.268869
$133$	82286.6	0.403367
$134$	137427.	0.661164
$135$	18225.0	0.0860663
$136$	−51129.0	−0.237039
$137$	−4251.81	−0.0193541	−0.00967703	−	0.999953i	$-0.503080\pi$
$137$	−4251.81	−0.0193541	−0.00967703	+	0.999953i	$0.503080\pi$
$138$	118683.	0.530505
$139$	168666.	0.740443	0.370221	−	0.928944i	$-0.379282\pi$
$139$	168666.	0.740443	0.370221	+	0.928944i	$0.379282\pi$
$140$	91176.3	0.393153
$141$	−25953.2	−0.109937
$142$	−105396.	−0.438635
$143$	−36446.7	−0.149045
$144$	20736.0	0.0833333
$145$	−79891.2	−0.315558
$146$	25059.5	0.0972950
$147$	−316350.	−1.20746
$148$	14060.8	0.0527661
$149$	496944.	1.83376	0.916879	−	0.399165i	$-0.130700\pi$
$149$	496944.	1.83376	0.916879	+	0.399165i	$0.130700\pi$
$150$	−22500.0	−0.0816497
$151$	242134.	0.864197	0.432099	−	0.901826i	$-0.357773\pi$
$151$	242134.	0.864197	0.432099	+	0.901826i	$0.357773\pi$
$152$	−23104.0	−0.0811107
$153$	−64710.1	−0.223482
$154$	340797.	1.15796
$155$	191192.	0.639207
$156$	−14041.3	−0.0461951
$157$	309325.	1.00154	0.500768	−	0.865582i	$-0.333051\pi$
$157$	309325.	1.00154	0.500768	+	0.865582i	$0.333051\pi$
$158$	325043.	1.03585
$159$	−34886.9	−0.109438
$160$	−25600.0	−0.0790569
$161$	751461.	2.28477
$162$	26244.0	0.0785674
$163$	−42108.3	−0.124136	−0.0620681	−	0.998072i	$-0.519770\pi$
$163$	−42108.3	−0.124136	−0.0620681	+	0.998072i	$0.519770\pi$
$164$	199513.	0.579244
$165$	−84100.0	−0.240484
$166$	115062.	0.324086
$167$	−332698.	−0.923122	−0.461561	−	0.887108i	$-0.652710\pi$
$167$	−332698.	−0.923122	−0.461561	+	0.887108i	$0.652710\pi$
$168$	131294.	0.358898
$169$	−361785.	−0.974392
$170$	79889.0	0.212014
$171$	−29241.0	−0.0764719
$172$	−191044.	−0.492393
$173$	−97559.6	−0.247830	−0.123915	−	0.992293i	$-0.539545\pi$
$173$	−97559.6	−0.247830	−0.123915	+	0.992293i	$0.539545\pi$
$174$	−115043.	−0.288063
$175$	−142463.	−0.351647
$176$	−95687.2	−0.232848
$177$	−5084.08	−0.0121977
$178$	3986.50	0.00943066
$179$	510318.	1.19044	0.595221	−	0.803562i	$-0.297064\pi$
$179$	510318.	1.19044	0.595221	+	0.803562i	$0.297064\pi$
$180$	−32400.0	−0.0745356
$181$	636567.	1.44427	0.722134	−	0.691753i	$-0.243161\pi$
$181$	636567.	1.44427	0.722134	+	0.691753i	$0.243161\pi$
$182$	−88905.2	−0.198952
$183$	−45804.6	−0.101107
$184$	−210991.	−0.459431
$185$	−21970.0	−0.0471954
$186$	275317.	0.583513
$187$	298607.	0.624449
$188$	46139.0	0.0952081
$189$	166169.	0.338372
$190$	36100.0	0.0725476
$191$	874909.	1.73532	0.867660	−	0.497159i	$-0.165623\pi$
$191$	874909.	1.73532	0.867660	+	0.497159i	$0.165623\pi$
$192$	−36864.0	−0.0721688
$193$	−153050.	−0.295761	−0.147881	−	0.989005i	$-0.547245\pi$
$193$	−153050.	−0.295761	−0.147881	+	0.989005i	$0.547245\pi$
$194$	44228.0	0.0843709
$195$	21939.5	0.0413182
$196$	562399.	1.04569
$197$	649077.	1.19160	0.595800	−	0.803133i	$-0.296835\pi$
$197$	649077.	1.19160	0.595800	+	0.803133i	$0.296835\pi$
$198$	−121104.	−0.219531
$199$	−13359.3	−0.0239140	−0.0119570	−	0.999929i	$-0.503806\pi$
$199$	−13359.3	−0.0239140	−0.0119570	+	0.999929i	$0.503806\pi$
$200$	40000.0	0.0707107
$201$	−309210.	−0.539838
$202$	−116803.	−0.201408
$203$	−728418.	−1.24063
$204$	115040.	0.193542
$205$	−311739.	−0.518091
$206$	318137.	0.522332
$207$	−267036.	−0.433155
$208$	24962.3	0.0400061
$209$	134934.	0.213676
$210$	−205147.	−0.321008
$211$	−916971.	−1.41791	−0.708956	−	0.705253i	$-0.750834\pi$
$211$	−916971.	−1.41791	−0.708956	+	0.705253i	$0.750834\pi$
$212$	62021.2	0.0947764
$213$	237141.	0.358144
$214$	−351836.	−0.525178
$215$	298506.	0.440409
$216$	−46656.0	−0.0680414
$217$	1.74322e6	2.51306
$218$	131890.	0.187962
$219$	−56383.9	−0.0794410
$220$	149511.	0.208265
$221$	−77899.0	−0.107288
$222$	−31636.7	−0.0430833
$223$	−767378.	−1.03335	−0.516675	−	0.856182i	$-0.672830\pi$
$223$	−767378.	−1.03335	−0.516675	+	0.856182i	$0.672830\pi$
$224$	−233411.	−0.310815
$225$	50625.0	0.0666667
$226$	−142742.	−0.185900
$227$	−334127.	−0.430375	−0.215188	−	0.976573i	$-0.569036\pi$
$227$	−334127.	−0.430375	−0.215188	+	0.976573i	$0.569036\pi$
$228$	51984.0	0.0662266
$229$	−622496.	−0.784419	−0.392209	−	0.919876i	$-0.628289\pi$
$229$	−622496.	−0.784419	−0.392209	+	0.919876i	$0.628289\pi$
$230$	329674.	0.410927
$231$	−766793.	−0.945471
$232$	204521.	0.249470
$233$	−190988.	−0.230471	−0.115236	−	0.993338i	$-0.536762\pi$
$233$	−190988.	−0.230471	−0.115236	+	0.993338i	$0.536762\pi$
$234$	31592.9	0.0377182
$235$	−72092.2	−0.0851567
$236$	9038.36	0.0105635
$237$	−731348.	−0.845771
$238$	728398.	0.833540
$239$	−1.01790e6	−1.15268	−0.576342	−	0.817209i	$-0.695520\pi$
$239$	−1.01790e6	−1.15268	−0.576342	+	0.817209i	$0.695520\pi$
$240$	57600.0	0.0645497
$241$	−16891.4	−0.0187337	−0.00936683	−	0.999956i	$-0.502982\pi$
$241$	−16891.4	−0.0187337	−0.00936683	+	0.999956i	$0.502982\pi$
$242$	−85364.2	−0.0936995
$243$	−59049.0	−0.0641500
$244$	81430.5	0.0875613
$245$	−878749.	−0.935297
$246$	−448904.	−0.472950
$247$	−35200.8	−0.0367122
$248$	−489453.	−0.505337
$249$	−258889.	−0.264615
$250$	−62500.0	−0.0632456
$251$	693518.	0.694821	0.347411	−	0.937713i	$-0.387061\pi$
$251$	693518.	0.694821	0.347411	+	0.937713i	$0.387061\pi$
$252$	−295411.	−0.293039
$253$	1.23225e6	1.21031
$254$	−455054.	−0.442566
$255$	−179750.	−0.173109
$256$	65536.0	0.0625000
$257$	−1.28272e6	−1.21143	−0.605717	−	0.795680i	$-0.707114\pi$
$257$	−1.28272e6	−1.21143	−0.605717	+	0.795680i	$0.707114\pi$
$258$	429848.	0.402037
$259$	−200314.	−0.185550
$260$	−39003.6	−0.0357826
$261$	258847.	0.235203
$262$	−535452.	−0.481912
$263$	−669317.	−0.596681	−0.298341	−	0.954459i	$-0.596433\pi$
$263$	−669317.	−0.596681	−0.298341	+	0.954459i	$0.596433\pi$
$264$	215296.	0.190119
$265$	−96908.1	−0.0847706
$266$	329146.	0.285223
$267$	−8969.63	−0.00770010
$268$	549707.	0.467513
$269$	−775990.	−0.653846	−0.326923	−	0.945051i	$-0.606012\pi$
$269$	−775990.	−0.653846	−0.326923	+	0.945051i	$0.606012\pi$
$270$	72900.0	0.0608581
$271$	−1.45318e6	−1.20198	−0.600989	−	0.799257i	$-0.705226\pi$
$271$	−1.45318e6	−1.20198	−0.600989	+	0.799257i	$0.705226\pi$
$272$	−204516.	−0.167612
$273$	200037.	0.162444
$274$	−17007.2	−0.0136854
$275$	−233611.	−0.186278
$276$	474730.	0.375124
$277$	1.39958e6	1.09597	0.547985	−	0.836488i	$-0.315395\pi$
$277$	1.39958e6	1.09597	0.547985	+	0.836488i	$0.315395\pi$
$278$	674666.	0.523572
$279$	−619463.	−0.476437
$280$	364705.	0.278001
$281$	1.04629e6	0.790469	0.395235	−	0.918580i	$-0.370663\pi$
$281$	1.04629e6	0.790469	0.395235	+	0.918580i	$0.370663\pi$
$282$	−103813.	−0.0777371
$283$	2.30735e6	1.71257	0.856283	−	0.516507i	$-0.172768\pi$
$283$	2.30735e6	1.71257	0.856283	+	0.516507i	$0.172768\pi$
$284$	−421584.	−0.310162
$285$	−81225.0	−0.0592349
$286$	−145787.	−0.105391
$287$	−2.84232e6	−2.03689
$288$	82944.0	0.0589256
$289$	−781632.	−0.550500
$290$	−319565.	−0.223133
$291$	−99512.9	−0.0688885
$292$	100238.	0.0687979
$293$	137002.	0.0932306	0.0466153	−	0.998913i	$-0.485157\pi$
$293$	137002.	0.0932306	0.0466153	+	0.998913i	$0.485157\pi$
$294$	−1.26540e6	−0.853806
$295$	−14122.4	−0.00944832
$296$	56243.1	0.0373113
$297$	272484.	0.179246
$298$	1.98778e6	1.29666
$299$	−321462.	−0.207947
$300$	−90000.0	−0.0577350
$301$	2.72166e6	1.73148
$302$	968535.	0.611080
$303$	262807.	0.164449
$304$	−92416.0	−0.0573539
$305$	−127235.	−0.0783172
$306$	−258840.	−0.158026
$307$	712439.	0.431421	0.215711	−	0.976457i	$-0.430793\pi$
$307$	712439.	0.431421	0.215711	+	0.976457i	$0.430793\pi$
$308$	1.36319e6	0.818802
$309$	−715809.	−0.426482
$310$	764770.	0.451988
$311$	1.62428e6	0.952268	0.476134	−	0.879373i	$-0.342038\pi$
$311$	1.62428e6	0.952268	0.476134	+	0.879373i	$0.342038\pi$
$312$	−56165.2	−0.0326649
$313$	−3.37279e6	−1.94594	−0.972968	−	0.230941i	$-0.925820\pi$
$313$	−3.37279e6	−1.94594	−0.972968	+	0.230941i	$0.925820\pi$
$314$	1.23730e6	0.708192
$315$	461580.	0.262102
$316$	1.30017e6	0.732459
$317$	−1.70220e6	−0.951399	−0.475699	−	0.879608i	$-0.657805\pi$
$317$	−1.70220e6	−0.951399	−0.475699	+	0.879608i	$0.657805\pi$
$318$	−139548.	−0.0773846
$319$	−1.19446e6	−0.657197
$320$	−102400.	−0.0559017
$321$	791632.	0.428806
$322$	3.00584e6	1.61557
$323$	288399.	0.153811
$324$	104976.	0.0555556
$325$	60943.2	0.0320049
$326$	−168433.	−0.0877776
$327$	−296753.	−0.153471
$328$	798051.	0.409587
$329$	−657310.	−0.334796
$330$	−336400.	−0.170048
$331$	3.37219e6	1.69177	0.845886	−	0.533364i	$-0.179072\pi$
$331$	3.37219e6	1.69177	0.845886	+	0.533364i	$0.179072\pi$
$332$	460246.	0.229163
$333$	71182.7	0.0351774
$334$	−1.33079e6	−0.652746
$335$	−858917.	−0.418157
$336$	525175.	0.253779
$337$	−4.09299e6	−1.96320	−0.981602	−	0.190937i	$-0.938847\pi$
$337$	−4.09299e6	−1.96320	−0.981602	+	0.190937i	$0.938847\pi$
$338$	−1.44714e6	−0.688999
$339$	321169.	0.151787
$340$	319556.	0.149917
$341$	2.85854e6	1.33125
$342$	−116964.	−0.0540738
$343$	−4.18111e6	−1.91892
$344$	−764175.	−0.348174
$345$	−741766.	−0.335521
$346$	−390238.	−0.175243
$347$	−173181.	−0.0772105	−0.0386053	−	0.999255i	$-0.512291\pi$
$347$	−173181.	−0.0772105	−0.0386053	+	0.999255i	$0.512291\pi$
$348$	−460173.	−0.203692
$349$	−4.44023e6	−1.95138	−0.975691	−	0.219151i	$-0.929671\pi$
$349$	−4.44023e6	−1.95138	−0.975691	+	0.219151i	$0.929671\pi$
$350$	−569852.	−0.248652
$351$	−71084.1	−0.0307967
$352$	−382749.	−0.164648
$353$	2.96513e6	1.26650	0.633252	−	0.773945i	$-0.281720\pi$
$353$	2.96513e6	1.26650	0.633252	+	0.773945i	$0.281720\pi$
$354$	−20336.3	−0.00862510
$355$	658725.	0.277417
$356$	15946.0	0.00666848
$357$	−1.63890e6	−0.680583
$358$	2.04127e6	0.841770
$359$	2.86844e6	1.17466	0.587328	−	0.809349i	$-0.300180\pi$
$359$	2.86844e6	1.17466	0.587328	+	0.809349i	$0.300180\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	2.54627e6	1.02125
$363$	192069.	0.0765053
$364$	−355621.	−0.140680
$365$	−156622.	−0.0615347
$366$	−183219.	−0.0714935
$367$	2.25741e6	0.874874	0.437437	−	0.899249i	$-0.355886\pi$
$367$	2.25741e6	0.874874	0.437437	+	0.899249i	$0.355886\pi$
$368$	−843965.	−0.324867
$369$	1.01003e6	0.386162
$370$	−87879.8	−0.0333722
$371$	−883572.	−0.333278
$372$	1.10127e6	0.412606
$373$	556979.	0.207284	0.103642	−	0.994615i	$-0.466950\pi$
$373$	556979.	0.207284	0.103642	+	0.994615i	$0.466950\pi$
$374$	1.19443e6	0.441552
$375$	140625.	0.0516398
$376$	184556.	0.0673223
$377$	311605.	0.112915
$378$	664675.	0.239265
$379$	−1.76197e6	−0.630087	−0.315043	−	0.949077i	$-0.602019\pi$
$379$	−1.76197e6	−0.630087	−0.315043	+	0.949077i	$0.602019\pi$
$380$	144400.	0.0512989
$381$	1.02387e6	0.361354
$382$	3.49964e6	1.22706
$383$	−809254.	−0.281895	−0.140948	−	0.990017i	$-0.545015\pi$
$383$	−809254.	−0.281895	−0.140948	+	0.990017i	$0.545015\pi$
$384$	−147456.	−0.0510310
$385$	−2.12998e6	−0.732359
$386$	−612202.	−0.209135
$387$	−967158.	−0.328262
$388$	176912.	0.0596592
$389$	−3.59275e6	−1.20380	−0.601898	−	0.798573i	$-0.705589\pi$
$389$	−3.59275e6	−1.20380	−0.601898	+	0.798573i	$0.705589\pi$
$390$	87758.2	0.0292164
$391$	2.63373e6	0.871224
$392$	2.24960e6	0.739417
$393$	1.20477e6	0.393479
$394$	2.59631e6	0.842589
$395$	−2.03152e6	−0.655132
$396$	−484416.	−0.155232
$397$	−5.39144e6	−1.71684	−0.858418	−	0.512951i	$-0.828552\pi$
$397$	−5.39144e6	−1.71684	−0.858418	+	0.512951i	$0.828552\pi$
$398$	−53437.2	−0.0169097
$399$	−740579.	−0.232884
$400$	160000.	0.0500000
$401$	−2.54067e6	−0.789019	−0.394509	−	0.918892i	$-0.629085\pi$
$401$	−2.54067e6	−0.789019	−0.394509	+	0.918892i	$0.629085\pi$
$402$	−1.23684e6	−0.381723
$403$	−745720.	−0.228725
$404$	−467212.	−0.142417
$405$	−164025.	−0.0496904
$406$	−2.91367e6	−0.877254
$407$	−328475.	−0.0982917
$408$	460161.	0.136855
$409$	−1.95357e6	−0.577459	−0.288730	−	0.957411i	$-0.593233\pi$
$409$	−1.95357e6	−0.577459	−0.288730	+	0.957411i	$0.593233\pi$
$410$	−1.24696e6	−0.366346
$411$	38266.3	0.0111741
$412$	1.27255e6	0.369344
$413$	−128763.	−0.0371464
$414$	−1.06814e6	−0.306287
$415$	−719135.	−0.204970
$416$	99849.3	0.0282886
$417$	−1.51800e6	−0.427495
$418$	539735.	0.151092
$419$	−974272.	−0.271110	−0.135555	−	0.990770i	$-0.543282\pi$
$419$	−974272.	−0.271110	−0.135555	+	0.990770i	$0.543282\pi$
$420$	−820587.	−0.226987
$421$	−2.89976e6	−0.797363	−0.398682	−	0.917089i	$-0.630532\pi$
$421$	−2.89976e6	−0.797363	−0.398682	+	0.917089i	$0.630532\pi$
$422$	−3.66788e6	−1.00262
$423$	233579.	0.0634721
$424$	248085.	0.0670170
$425$	−499306.	−0.134089
$426$	948564.	0.253246
$427$	−1.16008e6	−0.307907
$428$	−1.40735e6	−0.371357
$429$	328021.	0.0860514
$430$	1.19402e6	0.311416
$431$	2.82869e6	0.733487	0.366744	−	0.930322i	$-0.380473\pi$
$431$	2.82869e6	0.733487	0.366744	+	0.930322i	$0.380473\pi$
$432$	−186624.	−0.0481125
$433$	−5.60941e6	−1.43780	−0.718898	−	0.695116i	$-0.755353\pi$
$433$	−5.60941e6	−1.43780	−0.718898	+	0.695116i	$0.755353\pi$
$434$	6.97289e6	1.77700
$435$	719021.	0.182187
$436$	527561.	0.132910
$437$	1.19012e6	0.298118
$438$	−225536.	−0.0561733
$439$	−475714.	−0.117811	−0.0589053	−	0.998264i	$-0.518761\pi$
$439$	−475714.	−0.117811	−0.0589053	+	0.998264i	$0.518761\pi$
$440$	598045.	0.147266
$441$	2.84715e6	0.697129
$442$	−311596.	−0.0758641
$443$	7.67456e6	1.85799	0.928997	−	0.370087i	$-0.120672\pi$
$443$	7.67456e6	1.85799	0.928997	+	0.370087i	$0.120672\pi$
$444$	−126547.	−0.0304645
$445$	−24915.6	−0.00596447
$446$	−3.06951e6	−0.730689
$447$	−4.47250e6	−1.05872
$448$	−933645.	−0.219779
$449$	6.06434e6	1.41961	0.709803	−	0.704400i	$-0.248784\pi$
$449$	6.06434e6	1.41961	0.709803	+	0.704400i	$0.248784\pi$
$450$	202500.	0.0471405
$451$	−4.66084e6	−1.07900
$452$	−570967.	−0.131451
$453$	−2.17920e6	−0.498944
$454$	−1.33651e6	−0.304321
$455$	555657.	0.125828
$456$	207936.	0.0468293
$457$	8.82965e6	1.97767	0.988833	−	0.149028i	$-0.0476144\pi$
$457$	8.82965e6	1.97767	0.988833	+	0.149028i	$0.0476144\pi$
$458$	−2.48998e6	−0.554668
$459$	582391.	0.129028
$460$	1.31870e6	0.290569
$461$	7.04975e6	1.54497	0.772487	−	0.635030i	$-0.219012\pi$
$461$	7.04975e6	1.54497	0.772487	+	0.635030i	$0.219012\pi$
$462$	−3.06717e6	−0.668549
$463$	505010.	0.109483	0.0547416	−	0.998501i	$-0.482566\pi$
$463$	505010.	0.109483	0.0547416	+	0.998501i	$0.482566\pi$
$464$	818086.	0.176402
$465$	−1.72073e6	−0.369046
$466$	−763952.	−0.162968
$467$	−903646.	−0.191737	−0.0958685	−	0.995394i	$-0.530563\pi$
$467$	−903646.	−0.191737	−0.0958685	+	0.995394i	$0.530563\pi$
$468$	126372.	0.0266708
$469$	−7.83128e6	−1.64400
$470$	−288369.	−0.0602149
$471$	−2.78393e6	−0.578237
$472$	36153.5	0.00746956
$473$	4.46299e6	0.917220
$474$	−2.92539e6	−0.598051
$475$	−225625.	−0.0458831
$476$	2.91359e6	0.589402
$477$	313982.	0.0631843
$478$	−4.07160e6	−0.815070
$479$	3.78344e6	0.753438	0.376719	−	0.926327i	$-0.377052\pi$
$479$	3.78344e6	0.753438	0.376719	+	0.926327i	$0.377052\pi$
$480$	230400.	0.0456435
$481$	85690.8	0.0168877
$482$	−67565.5	−0.0132467
$483$	−6.76315e6	−1.31911
$484$	−341457.	−0.0662555
$485$	−276425.	−0.0533608
$486$	−236196.	−0.0453609
$487$	2.40831e6	0.460141	0.230070	−	0.973174i	$-0.426104\pi$
$487$	2.40831e6	0.460141	0.230070	+	0.973174i	$0.426104\pi$
$488$	325722.	0.0619152
$489$	378975.	0.0716701
$490$	−3.51500e6	−0.661355
$491$	3.18189e6	0.595636	0.297818	−	0.954623i	$-0.403741\pi$
$491$	3.18189e6	0.595636	0.297818	+	0.954623i	$0.403741\pi$
$492$	−1.79562e6	−0.334426
$493$	−2.55297e6	−0.473073
$494$	−140803.	−0.0259594
$495$	756900.	0.138844
$496$	−1.95781e6	−0.357328
$497$	6.00601e6	1.09067
$498$	−1.03555e6	−0.187111
$499$	−6.24921e6	−1.12350	−0.561751	−	0.827306i	$-0.689872\pi$
$499$	−6.24921e6	−1.12350	−0.561751	+	0.827306i	$0.689872\pi$
$500$	−250000.	−0.0447214
$501$	2.99428e6	0.532965
$502$	2.77407e6	0.491313
$503$	−900937.	−0.158772	−0.0793861	−	0.996844i	$-0.525296\pi$
$503$	−900937.	−0.158772	−0.0793861	+	0.996844i	$0.525296\pi$
$504$	−1.18164e6	−0.207210
$505$	730019.	0.127381
$506$	4.92899e6	0.855819
$507$	3.25606e6	0.562566
$508$	−1.82021e6	−0.312942
$509$	6.15819e6	1.05356	0.526779	−	0.850002i	$-0.323400\pi$
$509$	6.15819e6	1.05356	0.526779	+	0.850002i	$0.323400\pi$
$510$	−719001.	−0.122406
$511$	−1.42802e6	−0.241926
$512$	262144.	0.0441942
$513$	263169.	0.0441511
$514$	−5.13089e6	−0.856613
$515$	−1.98836e6	−0.330352
$516$	1.71939e6	0.284283
$517$	−1.07786e6	−0.177352
$518$	−801256.	−0.131204
$519$	878036.	0.143085
$520$	−156015.	−0.0253021
$521$	−4.77227e6	−0.770249	−0.385124	−	0.922865i	$-0.625841\pi$
$521$	−4.77227e6	−0.770249	−0.385124	+	0.922865i	$0.625841\pi$
$522$	1.03539e6	0.166314
$523$	−9.61791e6	−1.53754	−0.768770	−	0.639525i	$-0.779131\pi$
$523$	−9.61791e6	−1.53754	−0.768770	+	0.639525i	$0.779131\pi$
$524$	−2.14181e6	−0.340763
$525$	1.28217e6	0.203023
$526$	−2.67727e6	−0.421917
$527$	6.10967e6	0.958277
$528$	861184.	0.134435
$529$	4.43214e6	0.688612
$530$	−387632.	−0.0599419
$531$	45756.7	0.00704236
$532$	1.31659e6	0.201683
$533$	1.21589e6	0.185386
$534$	−35878.5	−0.00544479
$535$	2.19898e6	0.332152
$536$	2.19883e6	0.330582
$537$	−4.59286e6	−0.687302
$538$	−3.10396e6	−0.462339
$539$	−1.31383e7	−1.94790
$540$	291600.	0.0430331
$541$	−1.20576e7	−1.77120	−0.885602	−	0.464445i	$-0.846254\pi$
$541$	−1.20576e7	−1.77120	−0.885602	+	0.464445i	$0.846254\pi$
$542$	−5.81272e6	−0.849927
$543$	−5.72910e6	−0.833849
$544$	−818063.	−0.118519
$545$	−824314.	−0.118878
$546$	800146.	0.114865
$547$	−3.94255e6	−0.563390	−0.281695	−	0.959504i	$-0.590897\pi$
$547$	−3.94255e6	−0.563390	−0.281695	+	0.959504i	$0.590897\pi$
$548$	−68028.9	−0.00967703
$549$	412242.	0.0583742
$550$	−934445.	−0.131719
$551$	−1.15363e6	−0.161878
$552$	1.89892e6	0.265252
$553$	−1.85227e7	−2.57567
$554$	5.59833e6	0.774968
$555$	197730.	0.0272483
$556$	2.69866e6	0.370221
$557$	−771728.	−0.105396	−0.0526982	−	0.998610i	$-0.516782\pi$
$557$	−771728.	−0.105396	−0.0526982	+	0.998610i	$0.516782\pi$
$558$	−2.47785e6	−0.336892
$559$	−1.16428e6	−0.157590
$560$	1.45882e6	0.196577
$561$	−2.68747e6	−0.360526
$562$	4.18515e6	0.558946
$563$	−8.65557e6	−1.15087	−0.575433	−	0.817849i	$-0.695166\pi$
$563$	−8.65557e6	−1.15087	−0.575433	+	0.817849i	$0.695166\pi$
$564$	−415251.	−0.0549684
$565$	892136.	0.117574
$566$	9.22940e6	1.21097
$567$	−1.49552e6	−0.195359
$568$	−1.68634e6	−0.219317
$569$	−7.40352e6	−0.958645	−0.479322	−	0.877639i	$-0.659118\pi$
$569$	−7.40352e6	−0.958645	−0.479322	+	0.877639i	$0.659118\pi$
$570$	−324900.	−0.0418854
$571$	−2.11647e6	−0.271658	−0.135829	−	0.990732i	$-0.543370\pi$
$571$	−2.11647e6	−0.271658	−0.135829	+	0.990732i	$0.543370\pi$
$572$	−583148.	−0.0745227
$573$	−7.87418e6	−1.00189
$574$	−1.13693e7	−1.44030
$575$	−2.06046e6	−0.259893
$576$	331776.	0.0416667
$577$	6.44043e6	0.805332	0.402666	−	0.915347i	$-0.368084\pi$
$577$	6.44043e6	0.805332	0.402666	+	0.915347i	$0.368084\pi$
$578$	−3.12653e6	−0.389262
$579$	1.37745e6	0.170758
$580$	−1.27826e6	−0.157779
$581$	−6.55680e6	−0.805846
$582$	−398052.	−0.0487115
$583$	−1.44888e6	−0.176548
$584$	400952.	0.0486475
$585$	−197456.	−0.0238551
$586$	548009.	0.0659240
$587$	−5.10143e6	−0.611078	−0.305539	−	0.952180i	$-0.598837\pi$
$587$	−5.10143e6	−0.611078	−0.305539	+	0.952180i	$0.598837\pi$
$588$	−5.06159e6	−0.603732
$589$	2.76082e6	0.327906
$590$	−56489.8	−0.00668097
$591$	−5.84169e6	−0.687971
$592$	224972.	0.0263830
$593$	1.21359e7	1.41721	0.708606	−	0.705604i	$-0.249324\pi$
$593$	1.21359e7	1.41721	0.708606	+	0.705604i	$0.249324\pi$
$594$	1.08994e6	0.126746
$595$	−4.55249e6	−0.527177
$596$	7.95111e6	0.916879
$597$	120234.	0.0138067
$598$	−1.28585e6	−0.147040
$599$	−1.48624e6	−0.169247	−0.0846237	−	0.996413i	$-0.526969\pi$
$599$	−1.48624e6	−0.169247	−0.0846237	+	0.996413i	$0.526969\pi$
$600$	−360000.	−0.0408248
$601$	−1.51395e6	−0.170972	−0.0854862	−	0.996339i	$-0.527244\pi$
$601$	−1.51395e6	−0.170972	−0.0854862	+	0.996339i	$0.527244\pi$
$602$	1.08867e7	1.22434
$603$	2.78289e6	0.311676
$604$	3.87414e6	0.432099
$605$	533526.	0.0592608
$606$	1.05123e6	0.116283
$607$	−2.64835e6	−0.291745	−0.145872	−	0.989303i	$-0.546599\pi$
$607$	−2.64835e6	−0.291745	−0.145872	+	0.989303i	$0.546599\pi$
$608$	−369664.	−0.0405554
$609$	6.55576e6	0.716275
$610$	−508940.	−0.0553786
$611$	281186.	0.0304713
$612$	−1.03536e6	−0.111741
$613$	5.52718e6	0.594090	0.297045	−	0.954863i	$-0.403999\pi$
$613$	5.52718e6	0.594090	0.297045	+	0.954863i	$0.403999\pi$
$614$	2.84975e6	0.305061
$615$	2.80565e6	0.299120
$616$	5.45275e6	0.578980
$617$	−889351.	−0.0940503	−0.0470252	−	0.998894i	$-0.514974\pi$
$617$	−889351.	−0.0940503	−0.0470252	+	0.998894i	$0.514974\pi$
$618$	−2.86324e6	−0.301568
$619$	2.96270e6	0.310786	0.155393	−	0.987853i	$-0.450336\pi$
$619$	2.96270e6	0.310786	0.155393	+	0.987853i	$0.450336\pi$
$620$	3.05908e6	0.319603
$621$	2.40332e6	0.250082
$622$	6.49711e6	0.673355
$623$	−227172.	−0.0234495
$624$	−224661.	−0.0230976
$625$	390625.	0.0400000
$626$	−1.34912e7	−1.37598
$627$	−1.21440e6	−0.123366
$628$	4.94920e6	0.500768
$629$	−702063.	−0.0707538
$630$	1.84632e6	0.185334
$631$	1.12731e7	1.12712	0.563559	−	0.826076i	$-0.309432\pi$
$631$	1.12731e7	1.12712	0.563559	+	0.826076i	$0.309432\pi$
$632$	5.20069e6	0.517927
$633$	8.25274e6	0.818632
$634$	−6.80880e6	−0.672740
$635$	2.84409e6	0.279904
$636$	−558190.	−0.0547192
$637$	3.42744e6	0.334674
$638$	−4.77785e6	−0.464709
$639$	−2.13427e6	−0.206775
$640$	−409600.	−0.0395285
$641$	1.74248e7	1.67503	0.837516	−	0.546413i	$-0.184007\pi$
$641$	1.74248e7	1.67503	0.837516	+	0.546413i	$0.184007\pi$
$642$	3.16653e6	0.303212
$643$	1.15288e6	0.109966	0.0549830	−	0.998487i	$-0.482490\pi$
$643$	1.15288e6	0.109966	0.0549830	+	0.998487i	$0.482490\pi$
$644$	1.20234e7	1.14238
$645$	−2.68655e6	−0.254270
$646$	1.15360e6	0.108761
$647$	9.30356e6	0.873753	0.436876	−	0.899522i	$-0.356085\pi$
$647$	9.30356e6	0.873753	0.436876	+	0.899522i	$0.356085\pi$
$648$	419904.	0.0392837
$649$	−211146.	−0.0196776
$650$	243773.	0.0226309
$651$	−1.56890e7	−1.45092
$652$	−673733.	−0.0620681
$653$	2.51585e6	0.230888	0.115444	−	0.993314i	$-0.463171\pi$
$653$	2.51585e6	0.230888	0.115444	+	0.993314i	$0.463171\pi$
$654$	−1.18701e6	−0.108520
$655$	3.34658e6	0.304788
$656$	3.19221e6	0.289622
$657$	507455.	0.0458653
$658$	−2.62924e6	−0.236737
$659$	2.77734e6	0.249124	0.124562	−	0.992212i	$-0.460247\pi$
$659$	2.77734e6	0.249124	0.124562	+	0.992212i	$0.460247\pi$
$660$	−1.34560e6	−0.120242
$661$	5.21058e6	0.463855	0.231928	−	0.972733i	$-0.425497\pi$
$661$	5.21058e6	0.463855	0.231928	+	0.972733i	$0.425497\pi$
$662$	1.34888e7	1.19626
$663$	701091.	0.0619428
$664$	1.84099e6	0.162043
$665$	−2.05716e6	−0.180391
$666$	284731.	0.0248742
$667$	−1.05352e7	−0.916914
$668$	−5.32317e6	−0.461561
$669$	6.90641e6	0.596605
$670$	−3.43567e6	−0.295681
$671$	−1.90231e6	−0.163108
$672$	2.10070e6	0.179449
$673$	9.15065e6	0.778779	0.389390	−	0.921073i	$-0.372686\pi$
$673$	9.15065e6	0.778779	0.389390	+	0.921073i	$0.372686\pi$
$674$	−1.63719e7	−1.38820
$675$	−455625.	−0.0384900
$676$	−5.78856e6	−0.487196
$677$	1.15325e7	0.967057	0.483528	−	0.875329i	$-0.339355\pi$
$677$	1.15325e7	0.967057	0.483528	+	0.875329i	$0.339355\pi$
$678$	1.28468e6	0.107330
$679$	−2.52034e6	−0.209790
$680$	1.27822e6	0.106007
$681$	3.00715e6	0.248477
$682$	1.14342e7	0.941333
$683$	1.39768e7	1.14645	0.573226	−	0.819398i	$-0.305692\pi$
$683$	1.39768e7	1.14645	0.573226	+	0.819398i	$0.305692\pi$
$684$	−467856.	−0.0382360
$685$	106295.	0.00865540
$686$	−1.67244e7	−1.35688
$687$	5.60247e6	0.452884
$688$	−3.05670e6	−0.246196
$689$	377977.	0.0303331
$690$	−2.96706e6	−0.237249
$691$	1.48600e7	1.18392	0.591962	−	0.805966i	$-0.298354\pi$
$691$	1.48600e7	1.18392	0.591962	+	0.805966i	$0.298354\pi$
$692$	−1.56095e6	−0.123915
$693$	6.90114e6	0.545868
$694$	−692724.	−0.0545961
$695$	−4.21666e6	−0.331136
$696$	−1.84069e6	−0.144032
$697$	−9.96180e6	−0.776705
$698$	−1.77609e7	−1.37984
$699$	1.71889e6	0.133063
$700$	−2.27941e6	−0.175823
$701$	2.19369e7	1.68609	0.843044	−	0.537845i	$-0.180761\pi$
$701$	2.19369e7	1.68609	0.843044	+	0.537845i	$0.180761\pi$
$702$	−284337.	−0.0217766
$703$	−317246.	−0.0242107
$704$	−1.53099e6	−0.116424
$705$	648830.	0.0491652
$706$	1.18605e7	0.895554
$707$	6.65604e6	0.500804
$708$	−81345.3	−0.00609887
$709$	2.23862e7	1.67249	0.836246	−	0.548355i	$-0.184746\pi$
$709$	2.23862e7	1.67249	0.836246	+	0.548355i	$0.184746\pi$
$710$	2.63490e6	0.196164
$711$	6.58213e6	0.488306
$712$	63784.1	0.00471533
$713$	2.52125e7	1.85734
$714$	−6.55558e6	−0.481245
$715$	911169.	0.0666551
$716$	8.16509e6	0.595221
$717$	9.16109e6	0.665502
$718$	1.14738e7	0.830607
$719$	−1.59564e6	−0.115110	−0.0575551	−	0.998342i	$-0.518330\pi$
$719$	−1.59564e6	−0.115110	−0.0575551	+	0.998342i	$0.518330\pi$
$720$	−518400.	−0.0372678
$721$	−1.81291e7	−1.29879
$722$	521284.	0.0372161
$723$	152022.	0.0108159
$724$	1.01851e7	0.722134
$725$	1.99728e6	0.141122
$726$	768278.	0.0540974
$727$	6.29332e6	0.441615	0.220807	−	0.975317i	$-0.429131\pi$
$727$	6.29332e6	0.441615	0.220807	+	0.975317i	$0.429131\pi$
$728$	−1.42248e6	−0.0994760
$729$	531441.	0.0370370
$730$	−626488.	−0.0435116
$731$	9.53893e6	0.660247
$732$	−732874.	−0.0505536
$733$	1.15682e7	0.795254	0.397627	−	0.917547i	$-0.369834\pi$
$733$	1.15682e7	0.795254	0.397627	+	0.917547i	$0.369834\pi$
$734$	9.02965e6	0.618630
$735$	7.90874e6	0.539994
$736$	−3.37586e6	−0.229715
$737$	−1.28418e7	−0.870875
$738$	4.04014e6	0.273058
$739$	3.63321e6	0.244726	0.122363	−	0.992485i	$-0.460953\pi$
$739$	3.63321e6	0.244726	0.122363	+	0.992485i	$0.460953\pi$
$740$	−351519.	−0.0235977
$741$	316807.	0.0211958
$742$	−3.53429e6	−0.235663
$743$	−1.08981e7	−0.724234	−0.362117	−	0.932133i	$-0.617946\pi$
$743$	−1.08981e7	−0.724234	−0.362117	+	0.932133i	$0.617946\pi$
$744$	4.40507e6	0.291757
$745$	−1.24236e7	−0.820082
$746$	2.22792e6	0.146572
$747$	2.33000e6	0.152776
$748$	4.77772e6	0.312224
$749$	2.00495e7	1.30586
$750$	562500.	0.0365148
$751$	1.65115e7	1.06828	0.534141	−	0.845395i	$-0.320635\pi$
$751$	1.65115e7	1.06828	0.534141	+	0.845395i	$0.320635\pi$
$752$	738224.	0.0476040
$753$	−6.24166e6	−0.401155
$754$	1.24642e6	0.0798428
$755$	−6.05334e6	−0.386481
$756$	2.65870e6	0.169186
$757$	2.82409e6	0.179118	0.0895590	−	0.995982i	$-0.471454\pi$
$757$	2.82409e6	0.179118	0.0895590	+	0.995982i	$0.471454\pi$
$758$	−7.04788e6	−0.445538
$759$	−1.10902e7	−0.698773
$760$	577600.	0.0362738
$761$	1.81214e7	1.13430	0.567152	−	0.823613i	$-0.308045\pi$
$761$	1.81214e7	1.13430	0.567152	+	0.823613i	$0.308045\pi$
$762$	4.09548e6	0.255516
$763$	−7.51578e6	−0.467372
$764$	1.39985e7	0.867660
$765$	1.61775e6	0.0999444
$766$	−3.23701e6	−0.199330
$767$	55082.7	0.00338085
$768$	−589824.	−0.0360844
$769$	−6.57303e6	−0.400820	−0.200410	−	0.979712i	$-0.564227\pi$
$769$	−6.57303e6	−0.400820	−0.200410	+	0.979712i	$0.564227\pi$
$770$	−8.51992e6	−0.517856
$771$	1.15445e7	0.699422
$772$	−2.44881e6	−0.147881
$773$	2.20924e7	1.32982	0.664911	−	0.746922i	$-0.268469\pi$
$773$	2.20924e7	1.32982	0.664911	+	0.746922i	$0.268469\pi$
$774$	−3.86863e6	−0.232116
$775$	−4.77981e6	−0.285862
$776$	707647.	0.0421854
$777$	1.80283e6	0.107128
$778$	−1.43710e7	−0.851212
$779$	−4.50151e6	−0.265775
$780$	351033.	0.0206591
$781$	9.84867e6	0.577764
$782$	1.05349e7	0.616048
$783$	−2.32963e6	−0.135794
$784$	8.99839e6	0.522847
$785$	−7.73313e6	−0.447900
$786$	4.81907e6	0.278232
$787$	2.34794e7	1.35129	0.675646	−	0.737226i	$-0.263865\pi$
$787$	2.34794e7	1.35129	0.675646	+	0.737226i	$0.263865\pi$
$788$	1.03852e7	0.595800
$789$	6.02385e6	0.344494
$790$	−8.12608e6	−0.463248
$791$	8.13416e6	0.462244
$792$	−1.93766e6	−0.109765
$793$	496263.	0.0280239
$794$	−2.15658e7	−1.21399
$795$	872173.	0.0489423
$796$	−213749.	−0.0119570
$797$	−1.84388e7	−1.02822	−0.514112	−	0.857723i	$-0.671878\pi$
$797$	−1.84388e7	−1.02822	−0.514112	+	0.857723i	$0.671878\pi$
$798$	−2.96232e6	−0.164674
$799$	−2.30375e6	−0.127664
$800$	640000.	0.0353553
$801$	80726.7	0.00444566
$802$	−1.01627e7	−0.557920
$803$	−2.34167e6	−0.128156
$804$	−4.94736e6	−0.269919
$805$	−1.87865e7	−1.02178
$806$	−2.98288e6	−0.161733
$807$	6.98391e6	0.377498
$808$	−1.86885e6	−0.100704
$809$	2.43145e7	1.30615	0.653075	−	0.757293i	$-0.273479\pi$
$809$	2.43145e7	1.30615	0.653075	+	0.757293i	$0.273479\pi$
$810$	−656100.	−0.0351364
$811$	−3.17591e7	−1.69557	−0.847786	−	0.530338i	$-0.822065\pi$
$811$	−3.17591e7	−1.69557	−0.847786	+	0.530338i	$0.822065\pi$
$812$	−1.16547e7	−0.620313
$813$	1.30786e7	0.693962
$814$	−1.31390e6	−0.0695027
$815$	1.05271e6	0.0555154
$816$	1.84064e6	0.0967708
$817$	4.31042e6	0.225925
$818$	−7.81429e6	−0.408325
$819$	−1.80033e6	−0.0937869
$820$	−4.98782e6	−0.259046
$821$	3.60484e7	1.86650	0.933250	−	0.359228i	$-0.116960\pi$
$821$	3.60484e7	1.86650	0.933250	+	0.359228i	$0.116960\pi$
$822$	153065.	0.00790126
$823$	1.87207e7	0.963436	0.481718	−	0.876326i	$-0.340013\pi$
$823$	1.87207e7	0.963436	0.481718	+	0.876326i	$0.340013\pi$
$824$	5.09020e6	0.261166
$825$	2.10250e6	0.107548
$826$	−515053.	−0.0262665
$827$	−5.40602e6	−0.274861	−0.137431	−	0.990511i	$-0.543884\pi$
$827$	−5.40602e6	−0.274861	−0.137431	+	0.990511i	$0.543884\pi$
$828$	−4.27257e6	−0.216578
$829$	2.53619e7	1.28172	0.640862	−	0.767656i	$-0.278577\pi$
$829$	2.53619e7	1.28172	0.640862	+	0.767656i	$0.278577\pi$
$830$	−2.87654e6	−0.144936
$831$	−1.25962e7	−0.632759
$832$	399397.	0.0200031
$833$	−2.80810e7	−1.40217
$834$	−6.07199e6	−0.302285
$835$	8.31745e6	0.412833
$836$	2.15894e6	0.106838
$837$	5.57517e6	0.275071
$838$	−3.89709e6	−0.191704
$839$	2.89798e7	1.42131	0.710657	−	0.703539i	$-0.248398\pi$
$839$	2.89798e7	1.42131	0.710657	+	0.703539i	$0.248398\pi$
$840$	−3.28235e6	−0.160504
$841$	−1.02990e7	−0.502117
$842$	−1.15990e7	−0.563821
$843$	−9.41658e6	−0.456378
$844$	−1.46715e7	−0.708956
$845$	9.04462e6	0.435761
$846$	934315.	0.0448815
$847$	4.86449e6	0.232986
$848$	992339.	0.0473882
$849$	−2.07661e7	−0.988750
$850$	−1.99723e6	−0.0948156
$851$	−2.89717e6	−0.137135
$852$	3.79426e6	0.179072
$853$	−1.21655e7	−0.572478	−0.286239	−	0.958158i	$-0.592405\pi$
$853$	−1.21655e7	−0.572478	−0.286239	+	0.958158i	$0.592405\pi$
$854$	−4.64033e6	−0.217723
$855$	731025.	0.0341993
$856$	−5.62938e6	−0.262589
$857$	−4.53734e6	−0.211032	−0.105516	−	0.994418i	$-0.533649\pi$
$857$	−4.53734e6	−0.211032	−0.105516	+	0.994418i	$0.533649\pi$
$858$	1.31208e6	0.0608475
$859$	1.94035e6	0.0897216	0.0448608	−	0.998993i	$-0.485716\pi$
$859$	1.94035e6	0.0897216	0.0448608	+	0.998993i	$0.485716\pi$
$860$	4.77609e6	0.220205
$861$	2.55809e7	1.17600
$862$	1.13148e7	0.518654
$863$	−1.58443e7	−0.724180	−0.362090	−	0.932143i	$-0.617937\pi$
$863$	−1.58443e7	−0.724180	−0.362090	+	0.932143i	$0.617937\pi$
$864$	−746496.	−0.0340207
$865$	2.43899e6	0.110833
$866$	−2.24376e7	−1.01667
$867$	7.03468e6	0.317831
$868$	2.78915e7	1.25653
$869$	−3.03735e7	−1.36441
$870$	2.87608e6	0.128826
$871$	3.35009e6	0.149627
$872$	2.11024e6	0.0939812
$873$	895616.	0.0397728
$874$	4.76049e6	0.210801
$875$	3.56157e6	0.157261
$876$	−902142.	−0.0397205
$877$	−2.73427e7	−1.20045	−0.600223	−	0.799833i	$-0.704921\pi$
$877$	−2.73427e7	−1.20045	−0.600223	+	0.799833i	$0.704921\pi$
$878$	−1.90285e6	−0.0833046
$879$	−1.23302e6	−0.0538267
$880$	2.39218e6	0.104133
$881$	1.66113e7	0.721049	0.360524	−	0.932750i	$-0.382598\pi$
$881$	1.66113e7	0.721049	0.360524	+	0.932750i	$0.382598\pi$
$882$	1.13886e7	0.492945
$883$	−4.04894e7	−1.74759	−0.873795	−	0.486295i	$-0.838348\pi$
$883$	−4.04894e7	−1.74759	−0.873795	+	0.486295i	$0.838348\pi$
$884$	−1.24638e6	−0.0536440
$885$	127102.	0.00545499
$886$	3.06983e7	1.31380
$887$	3.80297e7	1.62298	0.811492	−	0.584364i	$-0.198656\pi$
$887$	3.80297e7	1.62298	0.811492	+	0.584364i	$0.198656\pi$
$888$	−506188.	−0.0215417
$889$	2.59313e7	1.10045
$890$	−99662.6	−0.00421752
$891$	−2.45236e6	−0.103488
$892$	−1.22781e7	−0.516675
$893$	−1.04101e6	−0.0436845
$894$	−1.78900e7	−0.748629
$895$	−1.27580e7	−0.532382
$896$	−3.73458e6	−0.155407
$897$	2.89316e6	0.120058
$898$	2.42574e7	1.00381
$899$	−2.44393e7	−1.00853
$900$	810000.	0.0333333
$901$	−3.09676e6	−0.127085
$902$	−1.86434e7	−0.762971
$903$	−2.44950e7	−0.999672
$904$	−2.28387e6	−0.0929501
$905$	−1.59142e7	−0.645896
$906$	−8.71681e6	−0.352807
$907$	2.26185e7	0.912948	0.456474	−	0.889737i	$-0.349112\pi$
$907$	2.26185e7	0.912948	0.456474	+	0.889737i	$0.349112\pi$
$908$	−5.34604e6	−0.215188
$909$	−2.36526e6	−0.0949444
$910$	2.22263e6	0.0889741
$911$	8.62105e6	0.344163	0.172082	−	0.985083i	$-0.444951\pi$
$911$	8.62105e6	0.344163	0.172082	+	0.985083i	$0.444951\pi$
$912$	831744.	0.0331133
$913$	−1.07519e7	−0.426881
$914$	3.53186e7	1.39842
$915$	1.14512e6	0.0452165
$916$	−9.95994e6	−0.392209
$917$	3.05128e7	1.19828
$918$	2.32956e6	0.0912363
$919$	−2.61840e7	−1.02270	−0.511348	−	0.859374i	$-0.670854\pi$
$919$	−2.61840e7	−1.02270	−0.511348	+	0.859374i	$0.670854\pi$
$920$	5.27478e6	0.205464
$921$	−6.41195e6	−0.249081
$922$	2.81990e7	1.09246
$923$	−2.56927e6	−0.0992670
$924$	−1.22687e7	−0.472735
$925$	549249.	0.0211064
$926$	2.02004e6	0.0774163
$927$	6.44228e6	0.246230
$928$	3.27234e6	0.124735
$929$	−2.61411e7	−0.993768	−0.496884	−	0.867817i	$-0.665523\pi$
$929$	−2.61411e7	−0.993768	−0.496884	+	0.867817i	$0.665523\pi$
$930$	−6.88293e6	−0.260955
$931$	−1.26891e7	−0.479797
$932$	−3.05581e6	−0.115236
$933$	−1.46185e7	−0.549792
$934$	−3.61458e6	−0.135579
$935$	−7.46519e6	−0.279262
$936$	505487.	0.0188591
$937$	−2.48946e7	−0.926311	−0.463156	−	0.886277i	$-0.653283\pi$
$937$	−2.48946e7	−0.926311	−0.463156	+	0.886277i	$0.653283\pi$
$938$	−3.13251e7	−1.16248
$939$	3.03551e7	1.12349
$940$	−1.15348e6	−0.0425784
$941$	4.59582e7	1.69195	0.845977	−	0.533220i	$-0.179018\pi$
$941$	4.59582e7	1.69195	0.845977	+	0.533220i	$0.179018\pi$
$942$	−1.11357e7	−0.408875
$943$	−4.11089e7	−1.50541
$944$	144614.	0.00528177
$945$	−4.15422e6	−0.151325
$946$	1.78520e7	0.648572
$947$	−3.85344e7	−1.39628	−0.698142	−	0.715959i	$-0.745990\pi$
$947$	−3.85344e7	−1.39628	−0.698142	+	0.715959i	$0.745990\pi$
$948$	−1.17016e7	−0.422886
$949$	610882.	0.0220187
$950$	−902500.	−0.0324443
$951$	1.53198e7	0.549290
$952$	1.16544e7	0.416770
$953$	1.97231e7	0.703466	0.351733	−	0.936100i	$-0.385592\pi$
$953$	1.97231e7	0.703466	0.351733	+	0.936100i	$0.385592\pi$
$954$	1.25593e6	0.0446780
$955$	−2.18727e7	−0.776058
$956$	−1.62864e7	−0.576342
$957$	1.07502e7	0.379433
$958$	1.51337e7	0.532761
$959$	969160.	0.0340290
$960$	921600.	0.0322749
$961$	2.98581e7	1.04293
$962$	342763.	0.0119414
$963$	−7.12469e6	−0.247571
$964$	−270262.	−0.00936683
$965$	3.82626e6	0.132268
$966$	−2.70526e7	−0.932752
$967$	−4.91374e7	−1.68984	−0.844921	−	0.534891i	$-0.820352\pi$
$967$	−4.91374e7	−1.68984	−0.844921	+	0.534891i	$0.820352\pi$
$968$	−1.36583e6	−0.0468497
$969$	−2.59559e6	−0.0888029
$970$	−1.10570e6	−0.0377318
$971$	4.12175e7	1.40292	0.701461	−	0.712708i	$-0.252531\pi$
$971$	4.12175e7	1.40292	0.701461	+	0.712708i	$0.252531\pi$
$972$	−944784.	−0.0320750
$973$	−3.84459e7	−1.30187
$974$	9.63325e6	0.325368
$975$	−548489.	−0.0184780
$976$	1.30289e6	0.0437807
$977$	2.80481e7	0.940085	0.470043	−	0.882644i	$-0.344238\pi$
$977$	2.80481e7	0.940085	0.470043	+	0.882644i	$0.344238\pi$
$978$	1.51590e6	0.0506784
$979$	−372517.	−0.0124219
$980$	−1.40600e7	−0.467649
$981$	2.67078e6	0.0886064
$982$	1.27275e7	0.421178
$983$	2.71681e6	0.0896757	0.0448379	−	0.998994i	$-0.485723\pi$
$983$	2.71681e6	0.0896757	0.0448379	+	0.998994i	$0.485723\pi$
$984$	−7.18246e6	−0.236475
$985$	−1.62269e7	−0.532900
$986$	−1.02119e7	−0.334513
$987$	5.91579e6	0.193295
$988$	−563213.	−0.0183561
$989$	3.93638e7	1.27969
$990$	3.02760e6	0.0981772
$991$	4.01076e7	1.29731	0.648654	−	0.761084i	$-0.275332\pi$
$991$	4.01076e7	1.29731	0.648654	+	0.761084i	$0.275332\pi$
$992$	−7.83124e6	−0.252669
$993$	−3.03497e7	−0.976745
$994$	2.40240e7	0.771223
$995$	333983.	0.0106946
$996$	−4.14222e6	−0.132307
$997$	2.34138e6	0.0745993	0.0372996	−	0.999304i	$-0.488124\pi$
$997$	2.34138e6	0.0745993	0.0372996	+	0.999304i	$0.488124\pi$
$998$	−2.49968e7	−0.794436
$999$	−640644.	−0.0203097

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.n.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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -227.941 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -227.941 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -373.778 q^{11} -144.000 q^{12} +97.5091 q^{13} -911.763 q^{14} +225.000 q^{15} +256.000 q^{16} -798.890 q^{17} +324.000 q^{18} -361.000 q^{19} -400.000 q^{20} +2051.47 q^{21} -1495.11 q^{22} -3296.74 q^{23} -576.000 q^{24} +625.000 q^{25} +390.036 q^{26} -729.000 q^{27} -3647.05 q^{28} +3195.65 q^{29} +900.000 q^{30} -7647.70 q^{31} +1024.00 q^{32} +3364.00 q^{33} -3195.56 q^{34} +5698.52 q^{35} +1296.00 q^{36} +878.798 q^{37} -1444.00 q^{38} -877.582 q^{39} -1600.00 q^{40} +12469.6 q^{41} +8205.87 q^{42} -11940.2 q^{43} -5980.45 q^{44} -2025.00 q^{45} -13187.0 q^{46} +2883.69 q^{47} -2304.00 q^{48} +35150.0 q^{49} +2500.00 q^{50} +7190.01 q^{51} +1560.15 q^{52} +3876.32 q^{53} -2916.00 q^{54} +9344.45 q^{55} -14588.2 q^{56} +3249.00 q^{57} +12782.6 q^{58} +564.898 q^{59} +3600.00 q^{60} +5089.40 q^{61} -30590.8 q^{62} -18463.2 q^{63} +4096.00 q^{64} -2437.73 q^{65} +13456.0 q^{66} +34356.7 q^{67} -12782.2 q^{68} +29670.6 q^{69} +22794.1 q^{70} -26349.0 q^{71} +5184.00 q^{72} +6264.88 q^{73} +3515.19 q^{74} -5625.00 q^{75} -5776.00 q^{76} +85199.2 q^{77} -3510.33 q^{78} +81260.8 q^{79} -6400.00 q^{80} +6561.00 q^{81} +49878.2 q^{82} +28765.4 q^{83} +32823.5 q^{84} +19972.3 q^{85} -47760.9 q^{86} -28760.8 q^{87} -23921.8 q^{88} +996.626 q^{89} -8100.00 q^{90} -22226.3 q^{91} -52747.8 q^{92} +68829.3 q^{93} +11534.8 q^{94} +9025.00 q^{95} -9216.00 q^{96} +11057.0 q^{97} +140600. q^{98} -30276.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 10 q^{7} + 256 q^{8} + 324 q^{9} - 400 q^{10} + 102 q^{11} - 576 q^{12} - 122 q^{13} + 40 q^{14} + 900 q^{15} + 1024 q^{16} - 336 q^{17} + 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 90 q^{21} + 408 q^{22} - 396 q^{23} - 2304 q^{24} + 2500 q^{25} - 488 q^{26} - 2916 q^{27} + 160 q^{28} - 70 q^{29} + 3600 q^{30} - 10728 q^{31} + 4096 q^{32} - 918 q^{33} - 1344 q^{34} - 250 q^{35} + 5184 q^{36} + 10610 q^{37} - 5776 q^{38} + 1098 q^{39} - 6400 q^{40} - 3662 q^{41} - 360 q^{42} + 550 q^{43} + 1632 q^{44} - 8100 q^{45} - 1584 q^{46} + 9700 q^{47} - 9216 q^{48} + 42432 q^{49} + 10000 q^{50} + 3024 q^{51} - 1952 q^{52} + 14028 q^{53} - 11664 q^{54} - 2550 q^{55} + 640 q^{56} + 12996 q^{57} - 280 q^{58} + 22092 q^{59} + 14400 q^{60} + 20140 q^{61} - 42912 q^{62} + 810 q^{63} + 16384 q^{64} + 3050 q^{65} - 3672 q^{66} + 36624 q^{67} - 5376 q^{68} + 3564 q^{69} - 1000 q^{70} + 42236 q^{71} + 20736 q^{72} + 38560 q^{73} + 42440 q^{74} - 22500 q^{75} - 23104 q^{76} + 120840 q^{77} + 4392 q^{78} + 190160 q^{79} - 25600 q^{80} + 26244 q^{81} - 14648 q^{82} + 118456 q^{83} - 1440 q^{84} + 8400 q^{85} + 2200 q^{86} + 630 q^{87} + 6528 q^{88} + 247890 q^{89} - 32400 q^{90} + 229880 q^{91} - 6336 q^{92} + 96552 q^{93} + 38800 q^{94} + 36100 q^{95} - 36864 q^{96} - 153602 q^{97} + 169728 q^{98} + 8262 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 10 * q^7 + 256 * q^8 + 324 * q^9 - 400 * q^10 + 102 * q^11 - 576 * q^12 - 122 * q^13 + 40 * q^14 + 900 * q^15 + 1024 * q^16 - 336 * q^17 + 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 90 * q^21 + 408 * q^22 - 396 * q^23 - 2304 * q^24 + 2500 * q^25 - 488 * q^26 - 2916 * q^27 + 160 * q^28 - 70 * q^29 + 3600 * q^30 - 10728 * q^31 + 4096 * q^32 - 918 * q^33 - 1344 * q^34 - 250 * q^35 + 5184 * q^36 + 10610 * q^37 - 5776 * q^38 + 1098 * q^39 - 6400 * q^40 - 3662 * q^41 - 360 * q^42 + 550 * q^43 + 1632 * q^44 - 8100 * q^45 - 1584 * q^46 + 9700 * q^47 - 9216 * q^48 + 42432 * q^49 + 10000 * q^50 + 3024 * q^51 - 1952 * q^52 + 14028 * q^53 - 11664 * q^54 - 2550 * q^55 + 640 * q^56 + 12996 * q^57 - 280 * q^58 + 22092 * q^59 + 14400 * q^60 + 20140 * q^61 - 42912 * q^62 + 810 * q^63 + 16384 * q^64 + 3050 * q^65 - 3672 * q^66 + 36624 * q^67 - 5376 * q^68 + 3564 * q^69 - 1000 * q^70 + 42236 * q^71 + 20736 * q^72 + 38560 * q^73 + 42440 * q^74 - 22500 * q^75 - 23104 * q^76 + 120840 * q^77 + 4392 * q^78 + 190160 * q^79 - 25600 * q^80 + 26244 * q^81 - 14648 * q^82 + 118456 * q^83 - 1440 * q^84 + 8400 * q^85 + 2200 * q^86 + 630 * q^87 + 6528 * q^88 + 247890 * q^89 - 32400 * q^90 + 229880 * q^91 - 6336 * q^92 + 96552 * q^93 + 38800 * q^94 + 36100 * q^95 - 36864 * q^96 - 153602 * q^97 + 169728 * q^98 + 8262 * q^99

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