LMFDB - Embedded newform 570.6.a.k.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:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 26355x^{2} - 7203x + 128450070 $ x^4 - x^3 - 26355x^2 - 7203x + 128450070
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-80.8568$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +94.6269 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +94.6269 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -613.114 q^{11} +144.000 q^{12} -983.389 q^{13} -378.507 q^{14} -225.000 q^{15} +256.000 q^{16} -1418.72 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} +851.642 q^{21} +2452.46 q^{22} +517.954 q^{23} -576.000 q^{24} +625.000 q^{25} +3933.55 q^{26} +729.000 q^{27} +1514.03 q^{28} +3308.73 q^{29} +900.000 q^{30} +1286.62 q^{31} -1024.00 q^{32} -5518.03 q^{33} +5674.90 q^{34} -2365.67 q^{35} +1296.00 q^{36} +5560.25 q^{37} +1444.00 q^{38} -8850.50 q^{39} +1600.00 q^{40} +8443.04 q^{41} -3406.57 q^{42} +23850.1 q^{43} -9809.83 q^{44} -2025.00 q^{45} -2071.82 q^{46} -14363.8 q^{47} +2304.00 q^{48} -7852.76 q^{49} -2500.00 q^{50} -12768.5 q^{51} -15734.2 q^{52} -16913.3 q^{53} -2916.00 q^{54} +15327.9 q^{55} -6056.12 q^{56} -3249.00 q^{57} -13234.9 q^{58} +14310.4 q^{59} -3600.00 q^{60} +42281.9 q^{61} -5146.48 q^{62} +7664.78 q^{63} +4096.00 q^{64} +24584.7 q^{65} +22072.1 q^{66} +20705.8 q^{67} -22699.6 q^{68} +4661.59 q^{69} +9462.69 q^{70} +37.7768 q^{71} -5184.00 q^{72} +30975.2 q^{73} -22241.0 q^{74} +5625.00 q^{75} -5776.00 q^{76} -58017.1 q^{77} +35402.0 q^{78} -64612.5 q^{79} -6400.00 q^{80} +6561.00 q^{81} -33772.2 q^{82} +100570. q^{83} +13626.3 q^{84} +35468.1 q^{85} -95400.6 q^{86} +29778.5 q^{87} +39239.3 q^{88} +48895.8 q^{89} +8100.00 q^{90} -93055.0 q^{91} +8287.27 q^{92} +11579.6 q^{93} +57455.4 q^{94} +9025.00 q^{95} -9216.00 q^{96} +92291.9 q^{97} +31411.0 q^{98} -49662.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 472 q^{11} + 576 q^{12} - 482 q^{13} - 104 q^{14} - 900 q^{15} + 1024 q^{16} + 1816 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} + 234 q^{21} + 1888 q^{22} - 418 q^{23} - 2304 q^{24} + 2500 q^{25} + 1928 q^{26} + 2916 q^{27} + 416 q^{28} - 10396 q^{29} + 3600 q^{30} + 528 q^{31} - 4096 q^{32} - 4248 q^{33} - 7264 q^{34} - 650 q^{35} + 5184 q^{36} + 5774 q^{37} + 5776 q^{38} - 4338 q^{39} + 6400 q^{40} + 9620 q^{41} - 936 q^{42} + 21098 q^{43} - 7552 q^{44} - 8100 q^{45} + 1672 q^{46} - 18858 q^{47} + 9216 q^{48} + 2148 q^{49} - 10000 q^{50} + 16344 q^{51} - 7712 q^{52} + 822 q^{53} - 11664 q^{54} + 11800 q^{55} - 1664 q^{56} - 12996 q^{57} + 41584 q^{58} + 28672 q^{59} - 14400 q^{60} + 77748 q^{61} - 2112 q^{62} + 2106 q^{63} + 16384 q^{64} + 12050 q^{65} + 16992 q^{66} + 82400 q^{67} + 29056 q^{68} - 3762 q^{69} + 2600 q^{70} + 928 q^{71} - 20736 q^{72} + 121100 q^{73} - 23096 q^{74} + 22500 q^{75} - 23104 q^{76} - 120220 q^{77} + 17352 q^{78} + 144284 q^{79} - 25600 q^{80} + 26244 q^{81} - 38480 q^{82} - 6082 q^{83} + 3744 q^{84} - 45400 q^{85} - 84392 q^{86} - 93564 q^{87} + 30208 q^{88} + 43260 q^{89} + 32400 q^{90} + 135148 q^{91} - 6688 q^{92} + 4752 q^{93} + 75432 q^{94} + 36100 q^{95} - 36864 q^{96} - 6862 q^{97} - 8592 q^{98} - 38232 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 - 472 * q^11 + 576 * q^12 - 482 * q^13 - 104 * q^14 - 900 * q^15 + 1024 * q^16 + 1816 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 + 234 * q^21 + 1888 * q^22 - 418 * q^23 - 2304 * q^24 + 2500 * q^25 + 1928 * q^26 + 2916 * q^27 + 416 * q^28 - 10396 * q^29 + 3600 * q^30 + 528 * q^31 - 4096 * q^32 - 4248 * q^33 - 7264 * q^34 - 650 * q^35 + 5184 * q^36 + 5774 * q^37 + 5776 * q^38 - 4338 * q^39 + 6400 * q^40 + 9620 * q^41 - 936 * q^42 + 21098 * q^43 - 7552 * q^44 - 8100 * q^45 + 1672 * q^46 - 18858 * q^47 + 9216 * q^48 + 2148 * q^49 - 10000 * q^50 + 16344 * q^51 - 7712 * q^52 + 822 * q^53 - 11664 * q^54 + 11800 * q^55 - 1664 * q^56 - 12996 * q^57 + 41584 * q^58 + 28672 * q^59 - 14400 * q^60 + 77748 * q^61 - 2112 * q^62 + 2106 * q^63 + 16384 * q^64 + 12050 * q^65 + 16992 * q^66 + 82400 * q^67 + 29056 * q^68 - 3762 * q^69 + 2600 * q^70 + 928 * q^71 - 20736 * q^72 + 121100 * q^73 - 23096 * q^74 + 22500 * q^75 - 23104 * q^76 - 120220 * q^77 + 17352 * q^78 + 144284 * q^79 - 25600 * q^80 + 26244 * q^81 - 38480 * q^82 - 6082 * q^83 + 3744 * q^84 - 45400 * q^85 - 84392 * q^86 - 93564 * q^87 + 30208 * q^88 + 43260 * q^89 + 32400 * q^90 + 135148 * q^91 - 6688 * q^92 + 4752 * q^93 + 75432 * q^94 + 36100 * q^95 - 36864 * q^96 - 6862 * q^97 - 8592 * q^98 - 38232 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−36.0000	−0.408248
$7$	94.6269	0.729910	0.364955	−	0.931025i	$-0.381084\pi$
$7$	94.6269	0.729910	0.364955	+	0.931025i	$0.381084\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	−613.114	−1.52778	−0.763888	−	0.645349i	$-0.776712\pi$
$11$	−613.114	−1.52778	−0.763888	+	0.645349i	$0.776712\pi$
$12$	144.000	0.288675
$13$	−983.389	−1.61386	−0.806932	−	0.590645i	$-0.798873\pi$
$13$	−983.389	−1.61386	−0.806932	+	0.590645i	$0.798873\pi$
$14$	−378.507	−0.516124
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	−1418.72	−1.19063	−0.595313	−	0.803494i	$-0.702972\pi$
$17$	−1418.72	−1.19063	−0.595313	+	0.803494i	$0.702972\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−400.000	−0.223607
$21$	851.642	0.421414
$22$	2452.46	1.08030
$23$	517.954	0.204161	0.102080	−	0.994776i	$-0.467450\pi$
$23$	517.954	0.204161	0.102080	+	0.994776i	$0.467450\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	3933.55	1.14117
$27$	729.000	0.192450
$28$	1514.03	0.364955
$29$	3308.73	0.730577	0.365288	−	0.930894i	$-0.380970\pi$
$29$	3308.73	0.730577	0.365288	+	0.930894i	$0.380970\pi$
$30$	900.000	0.182574
$31$	1286.62	0.240462	0.120231	−	0.992746i	$-0.461637\pi$
$31$	1286.62	0.240462	0.120231	+	0.992746i	$0.461637\pi$
$32$	−1024.00	−0.176777
$33$	−5518.03	−0.882062
$34$	5674.90	0.841900
$35$	−2365.67	−0.326426
$36$	1296.00	0.166667
$37$	5560.25	0.667713	0.333856	−	0.942624i	$-0.391650\pi$
$37$	5560.25	0.667713	0.333856	+	0.942624i	$0.391650\pi$
$38$	1444.00	0.162221
$39$	−8850.50	−0.931764
$40$	1600.00	0.158114
$41$	8443.04	0.784403	0.392202	−	0.919879i	$-0.371714\pi$
$41$	8443.04	0.784403	0.392202	+	0.919879i	$0.371714\pi$
$42$	−3406.57	−0.297985
$43$	23850.1	1.96707	0.983535	−	0.180716i	$-0.0578416\pi$
$43$	23850.1	1.96707	0.983535	+	0.180716i	$0.0578416\pi$
$44$	−9809.83	−0.763888
$45$	−2025.00	−0.149071
$46$	−2071.82	−0.144363
$47$	−14363.8	−0.948475	−0.474238	−	0.880397i	$-0.657276\pi$
$47$	−14363.8	−0.948475	−0.474238	+	0.880397i	$0.657276\pi$
$48$	2304.00	0.144338
$49$	−7852.76	−0.467231
$50$	−2500.00	−0.141421
$51$	−12768.5	−0.687409
$52$	−15734.2	−0.806932
$53$	−16913.3	−0.827063	−0.413531	−	0.910490i	$-0.635705\pi$
$53$	−16913.3	−0.827063	−0.413531	+	0.910490i	$0.635705\pi$
$54$	−2916.00	−0.136083
$55$	15327.9	0.683242
$56$	−6056.12	−0.258062
$57$	−3249.00	−0.132453
$58$	−13234.9	−0.516596
$59$	14310.4	0.535209	0.267604	−	0.963529i	$-0.413768\pi$
$59$	14310.4	0.535209	0.267604	+	0.963529i	$0.413768\pi$
$60$	−3600.00	−0.129099
$61$	42281.9	1.45489	0.727445	−	0.686166i	$-0.240708\pi$
$61$	42281.9	1.45489	0.727445	+	0.686166i	$0.240708\pi$
$62$	−5146.48	−0.170032
$63$	7664.78	0.243303
$64$	4096.00	0.125000
$65$	24584.7	0.721742
$66$	22072.1	0.623712
$67$	20705.8	0.563514	0.281757	−	0.959486i	$-0.409083\pi$
$67$	20705.8	0.563514	0.281757	+	0.959486i	$0.409083\pi$
$68$	−22699.6	−0.595313
$69$	4661.59	0.117872
$70$	9462.69	0.230818
$71$	37.7768	0.000889362 0	0.000444681	−	1.00000i	$-0.499858\pi$
$71$	37.7768	0.000889362 0	0.000444681		1.00000i	$0.499858\pi$
$72$	−5184.00	−0.117851
$73$	30975.2	0.680310	0.340155	−	0.940369i	$-0.389520\pi$
$73$	30975.2	0.680310	0.340155	+	0.940369i	$0.389520\pi$
$74$	−22241.0	−0.472144
$75$	5625.00	0.115470
$76$	−5776.00	−0.114708
$77$	−58017.1	−1.11514
$78$	35402.0	0.658857
$79$	−64612.5	−1.16479	−0.582396	−	0.812905i	$-0.697885\pi$
$79$	−64612.5	−1.16479	−0.582396	+	0.812905i	$0.697885\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−33772.2	−0.554657
$83$	100570.	1.60241	0.801204	−	0.598391i	$-0.204193\pi$
$83$	100570.	1.60241	0.801204	+	0.598391i	$0.204193\pi$
$84$	13626.3	0.210707
$85$	35468.1	0.532464
$86$	−95400.6	−1.39093
$87$	29778.5	0.421799
$88$	39239.3	0.540150
$89$	48895.8	0.654329	0.327165	−	0.944967i	$-0.393907\pi$
$89$	48895.8	0.654329	0.327165	+	0.944967i	$0.393907\pi$
$90$	8100.00	0.105409
$91$	−93055.0	−1.17798
$92$	8287.27	0.102080
$93$	11579.6	0.138831
$94$	57455.4	0.670673
$95$	9025.00	0.102598
$96$	−9216.00	−0.102062
$97$	92291.9	0.995943	0.497971	−	0.867193i	$-0.334078\pi$
$97$	92291.9	0.995943	0.497971	+	0.867193i	$0.334078\pi$
$98$	31411.0	0.330382
$99$	−49662.3	−0.509259
$100$	10000.0	0.100000
$101$	−16865.5	−0.164511	−0.0822556	−	0.996611i	$-0.526212\pi$
$101$	−16865.5	−0.164511	−0.0822556	+	0.996611i	$0.526212\pi$
$102$	51074.1	0.486071
$103$	80870.7	0.751101	0.375550	−	0.926802i	$-0.377454\pi$
$103$	80870.7	0.751101	0.375550	+	0.926802i	$0.377454\pi$
$104$	62936.9	0.570587
$105$	−21291.0	−0.188462
$106$	67653.2	0.584822
$107$	−200516.	−1.69313	−0.846566	−	0.532284i	$-0.821334\pi$
$107$	−200516.	−1.69313	−0.846566	+	0.532284i	$0.821334\pi$
$108$	11664.0	0.0962250
$109$	−115645.	−0.932310	−0.466155	−	0.884703i	$-0.654361\pi$
$109$	−115645.	−0.932310	−0.466155	+	0.884703i	$0.654361\pi$
$110$	−61311.4	−0.483125
$111$	50042.2	0.385504
$112$	24224.5	0.182478
$113$	−24053.7	−0.177209	−0.0886046	−	0.996067i	$-0.528241\pi$
$113$	−24053.7	−0.177209	−0.0886046	+	0.996067i	$0.528241\pi$
$114$	12996.0	0.0936586
$115$	−12948.9	−0.0913034
$116$	52939.6	0.365288
$117$	−79654.5	−0.537954
$118$	−57241.8	−0.378450
$119$	−134249.	−0.869050
$120$	14400.0	0.0912871
$121$	214858.	1.33410
$122$	−169128.	−1.02876
$123$	75987.4	0.452875
$124$	20585.9	0.120231
$125$	−15625.0	−0.0894427
$126$	−30659.1	−0.172041
$127$	15990.8	0.0879756	0.0439878	−	0.999032i	$-0.485994\pi$
$127$	15990.8	0.0879756	0.0439878	+	0.999032i	$0.485994\pi$
$128$	−16384.0	−0.0883883
$129$	214651.	1.13569
$130$	−98338.9	−0.510348
$131$	−17110.3	−0.0871121	−0.0435560	−	0.999051i	$-0.513869\pi$
$131$	−17110.3	−0.0871121	−0.0435560	+	0.999051i	$0.513869\pi$
$132$	−88288.5	−0.441031
$133$	−34160.3	−0.167453
$134$	−82823.1	−0.398465
$135$	−18225.0	−0.0860663
$136$	90798.3	0.420950
$137$	−123786.	−0.563471	−0.281735	−	0.959492i	$-0.590910\pi$
$137$	−123786.	−0.563471	−0.281735	+	0.959492i	$0.590910\pi$
$138$	−18646.4	−0.0833482
$139$	−86142.9	−0.378166	−0.189083	−	0.981961i	$-0.560552\pi$
$139$	−86142.9	−0.378166	−0.189083	+	0.981961i	$0.560552\pi$
$140$	−37850.7	−0.163213
$141$	−129275.	−0.547602
$142$	−151.107	−0.000628874 0
$143$	602930.	2.46562
$144$	20736.0	0.0833333
$145$	−82718.1	−0.326724
$146$	−123901.	−0.481052
$147$	−70674.8	−0.269756
$148$	88964.0	0.333856
$149$	−15526.0	−0.0572919	−0.0286459	−	0.999590i	$-0.509120\pi$
$149$	−15526.0	−0.0572919	−0.0286459	+	0.999590i	$0.509120\pi$
$150$	−22500.0	−0.0816497
$151$	2995.97	0.0106929	0.00534645	−	0.999986i	$-0.498298\pi$
$151$	2995.97	0.0106929	0.00534645	+	0.999986i	$0.498298\pi$
$152$	23104.0	0.0811107
$153$	−114917.	−0.396876
$154$	232068.	0.788523
$155$	−32165.5	−0.107538
$156$	−141608.	−0.465882
$157$	365967.	1.18493	0.592466	−	0.805596i	$-0.298155\pi$
$157$	365967.	1.18493	0.592466	+	0.805596i	$0.298155\pi$
$158$	258450.	0.823633
$159$	−152220.	−0.477505
$160$	25600.0	0.0790569
$161$	49012.4	0.149019
$162$	−26244.0	−0.0785674
$163$	−436835.	−1.28780	−0.643901	−	0.765109i	$-0.722685\pi$
$163$	−436835.	−1.28780	−0.643901	+	0.765109i	$0.722685\pi$
$164$	135089.	0.392202
$165$	137951.	0.394470
$166$	−402280.	−1.13307
$167$	313346.	0.869428	0.434714	−	0.900569i	$-0.356849\pi$
$167$	313346.	0.869428	0.434714	+	0.900569i	$0.356849\pi$
$168$	−54505.1	−0.148992
$169$	595760.	1.60456
$170$	−141872.	−0.376509
$171$	−29241.0	−0.0764719
$172$	381602.	0.983535
$173$	86867.9	0.220670	0.110335	−	0.993894i	$-0.464808\pi$
$173$	86867.9	0.220670	0.110335	+	0.993894i	$0.464808\pi$
$174$	−119114.	−0.298257
$175$	59141.8	0.145982
$176$	−156957.	−0.381944
$177$	128794.	0.309003
$178$	−195583.	−0.462680
$179$	577947.	1.34820	0.674101	−	0.738639i	$-0.264531\pi$
$179$	577947.	1.34820	0.674101	+	0.738639i	$0.264531\pi$
$180$	−32400.0	−0.0745356
$181$	570827.	1.29512	0.647558	−	0.762017i	$-0.275791\pi$
$181$	570827.	1.29512	0.647558	+	0.762017i	$0.275791\pi$
$182$	372220.	0.832954
$183$	380537.	0.839981
$184$	−33149.1	−0.0721817
$185$	−139006.	−0.298610
$186$	−46318.3	−0.0981681
$187$	869840.	1.81901
$188$	−229821.	−0.474238
$189$	68983.0	0.140471
$190$	−36100.0	−0.0725476
$191$	210943.	0.418390	0.209195	−	0.977874i	$-0.432916\pi$
$191$	210943.	0.418390	0.209195	+	0.977874i	$0.432916\pi$
$192$	36864.0	0.0721688
$193$	−418042.	−0.807842	−0.403921	−	0.914794i	$-0.632353\pi$
$193$	−418042.	−0.807842	−0.403921	+	0.914794i	$0.632353\pi$
$194$	−369168.	−0.704238
$195$	221262.	0.416698
$196$	−125644.	−0.233616
$197$	921835.	1.69234	0.846170	−	0.532913i	$-0.178903\pi$
$197$	921835.	1.69234	0.846170	+	0.532913i	$0.178903\pi$
$198$	198649.	0.360100
$199$	720466.	1.28968	0.644838	−	0.764319i	$-0.276925\pi$
$199$	720466.	1.28968	0.644838	+	0.764319i	$0.276925\pi$
$200$	−40000.0	−0.0707107
$201$	186352.	0.325345
$202$	67462.0	0.116327
$203$	313094.	0.533255
$204$	−204296.	−0.343704
$205$	−211076.	−0.350796
$206$	−323483.	−0.531108
$207$	41954.3	0.0680535
$208$	−251747.	−0.403466
$209$	221334.	0.350496
$210$	85164.2	0.133263
$211$	561945.	0.868936	0.434468	−	0.900687i	$-0.356936\pi$
$211$	561945.	0.868936	0.434468	+	0.900687i	$0.356936\pi$
$212$	−270613.	−0.413531
$213$	339.991	0.000513474 0
$214$	802066.	1.19722
$215$	−596254.	−0.879701
$216$	−46656.0	−0.0680414
$217$	121749.	0.175515
$218$	462580.	0.659242
$219$	278777.	0.392777
$220$	245246.	0.341621
$221$	1.39516e6	1.92151
$222$	−200169.	−0.272593
$223$	121273.	0.163305	0.0816527	−	0.996661i	$-0.473980\pi$
$223$	121273.	0.163305	0.0816527	+	0.996661i	$0.473980\pi$
$224$	−96897.9	−0.129031
$225$	50625.0	0.0666667
$226$	96214.9	0.125306
$227$	−678530.	−0.873985	−0.436993	−	0.899465i	$-0.643956\pi$
$227$	−678530.	−0.873985	−0.436993	+	0.899465i	$0.643956\pi$
$228$	−51984.0	−0.0662266
$229$	212100.	0.267271	0.133635	−	0.991031i	$-0.457335\pi$
$229$	212100.	0.267271	0.133635	+	0.991031i	$0.457335\pi$
$230$	51795.4	0.0645613
$231$	−522154.	−0.643826
$232$	−211758.	−0.258298
$233$	−719902.	−0.868728	−0.434364	−	0.900738i	$-0.643027\pi$
$233$	−719902.	−0.868728	−0.434364	+	0.900738i	$0.643027\pi$
$234$	318618.	0.380391
$235$	359096.	0.424171
$236$	228967.	0.267604
$237$	−581512.	−0.672493
$238$	536998.	0.614511
$239$	239724.	0.271466	0.135733	−	0.990745i	$-0.456661\pi$
$239$	239724.	0.271466	0.135733	+	0.990745i	$0.456661\pi$
$240$	−57600.0	−0.0645497
$241$	1.13435e6	1.25807	0.629036	−	0.777376i	$-0.283450\pi$
$241$	1.13435e6	1.25807	0.629036	+	0.777376i	$0.283450\pi$
$242$	−859433.	−0.943351
$243$	59049.0	0.0641500
$244$	676511.	0.727445
$245$	196319.	0.208952
$246$	−303950.	−0.320231
$247$	355003.	0.370246
$248$	−82343.6	−0.0850160
$249$	905130.	0.925151
$250$	62500.0	0.0632456
$251$	−1.52013e6	−1.52299	−0.761493	−	0.648173i	$-0.775533\pi$
$251$	−1.52013e6	−1.52299	−0.761493	+	0.648173i	$0.775533\pi$
$252$	122636.	0.121652
$253$	−317565.	−0.311912
$254$	−63963.4	−0.0622081
$255$	319213.	0.307418
$256$	65536.0	0.0625000
$257$	642217.	0.606526	0.303263	−	0.952907i	$-0.401924\pi$
$257$	642217.	0.606526	0.303263	+	0.952907i	$0.401924\pi$
$258$	−858605.	−0.803053
$259$	526149.	0.487370
$260$	393355.	0.360871
$261$	268007.	0.243526
$262$	68441.0	0.0615975
$263$	−229857.	−0.204912	−0.102456	−	0.994738i	$-0.532670\pi$
$263$	−229857.	−0.204912	−0.102456	+	0.994738i	$0.532670\pi$
$264$	353154.	0.311856
$265$	422832.	0.369874
$266$	136641.	0.118407
$267$	440062.	0.377777
$268$	331293.	0.281757
$269$	783628.	0.660282	0.330141	−	0.943932i	$-0.392904\pi$
$269$	783628.	0.660282	0.330141	+	0.943932i	$0.392904\pi$
$270$	72900.0	0.0608581
$271$	966852.	0.799718	0.399859	−	0.916577i	$-0.369059\pi$
$271$	966852.	0.799718	0.399859	+	0.916577i	$0.369059\pi$
$272$	−363193.	−0.297657
$273$	−837495.	−0.680104
$274$	495146.	0.398434
$275$	−383196.	−0.305555
$276$	74585.4	0.0589361
$277$	121779.	0.0953617	0.0476808	−	0.998863i	$-0.484817\pi$
$277$	121779.	0.0953617	0.0476808	+	0.998863i	$0.484817\pi$
$278$	344572.	0.267404
$279$	104216.	0.0801539
$280$	151403.	0.115409
$281$	−1.47565e6	−1.11486	−0.557428	−	0.830226i	$-0.688212\pi$
$281$	−1.47565e6	−1.11486	−0.557428	+	0.830226i	$0.688212\pi$
$282$	517098.	0.387213
$283$	−744205.	−0.552365	−0.276183	−	0.961105i	$-0.589069\pi$
$283$	−744205.	−0.552365	−0.276183	+	0.961105i	$0.589069\pi$
$284$	604.428	0.000444681 0
$285$	81225.0	0.0592349
$286$	−2.41172e6	−1.74346
$287$	798939.	0.572544
$288$	−82944.0	−0.0589256
$289$	592921.	0.417592
$290$	330873.	0.231029
$291$	830627.	0.575008
$292$	495603.	0.340155
$293$	122599.	0.0834289	0.0417145	−	0.999130i	$-0.486718\pi$
$293$	122599.	0.0834289	0.0417145	+	0.999130i	$0.486718\pi$
$294$	282699.	0.190746
$295$	−357761.	−0.239353
$296$	−355856.	−0.236072
$297$	−446960.	−0.294021
$298$	62103.9	0.0405115
$299$	−509351.	−0.329487
$300$	90000.0	0.0577350
$301$	2.25686e6	1.43578
$302$	−11983.9	−0.00756102
$303$	−151789.	−0.0949806
$304$	−92416.0	−0.0573539
$305$	−1.05705e6	−0.650646
$306$	459667.	0.280633
$307$	−2.36136e6	−1.42994	−0.714968	−	0.699157i	$-0.753559\pi$
$307$	−2.36136e6	−1.42994	−0.714968	+	0.699157i	$0.753559\pi$
$308$	−928273.	−0.557570
$309$	727836.	0.433648
$310$	128662.	0.0760407
$311$	−2.31762e6	−1.35875	−0.679377	−	0.733789i	$-0.737750\pi$
$311$	−2.31762e6	−1.35875	−0.679377	+	0.733789i	$0.737750\pi$
$312$	566432.	0.329428
$313$	−558773.	−0.322385	−0.161192	−	0.986923i	$-0.551534\pi$
$313$	−558773.	−0.322385	−0.161192	+	0.986923i	$0.551534\pi$
$314$	−1.46387e6	−0.837873
$315$	−191619.	−0.108809
$316$	−1.03380e6	−0.582396
$317$	−1.36549e6	−0.763201	−0.381601	−	0.924327i	$-0.624627\pi$
$317$	−1.36549e6	−0.763201	−0.381601	+	0.924327i	$0.624627\pi$
$318$	608879.	0.337647
$319$	−2.02863e6	−1.11616
$320$	−102400.	−0.0559017
$321$	−1.80465e6	−0.977530
$322$	−196050.	−0.105372
$323$	512159.	0.273148
$324$	104976.	0.0555556
$325$	−614618.	−0.322773
$326$	1.74734e6	0.910613
$327$	−1.04080e6	−0.538269
$328$	−540355.	−0.277328
$329$	−1.35921e6	−0.692302
$330$	−551803.	−0.278933
$331$	−2.09707e6	−1.05207	−0.526033	−	0.850464i	$-0.676321\pi$
$331$	−2.09707e6	−1.05207	−0.526033	+	0.850464i	$0.676321\pi$
$332$	1.60912e6	0.801204
$333$	450380.	0.222571
$334$	−1.25339e6	−0.614778
$335$	−517645.	−0.252011
$336$	218020.	0.105353
$337$	1.99343e6	0.956152	0.478076	−	0.878319i	$-0.341334\pi$
$337$	1.99343e6	0.956152	0.478076	+	0.878319i	$0.341334\pi$
$338$	−2.38304e6	−1.13459
$339$	−216484.	−0.102312
$340$	567490.	0.266232
$341$	−788845.	−0.367372
$342$	116964.	0.0540738
$343$	−2.33348e6	−1.07095
$344$	−1.52641e6	−0.695464
$345$	−116540.	−0.0527140
$346$	−347472.	−0.156038
$347$	2.46044e6	1.09695	0.548477	−	0.836166i	$-0.315208\pi$
$347$	2.46044e6	1.09695	0.548477	+	0.836166i	$0.315208\pi$
$348$	476456.	0.210899
$349$	4.02725e6	1.76989	0.884943	−	0.465699i	$-0.154197\pi$
$349$	4.02725e6	1.76989	0.884943	+	0.465699i	$0.154197\pi$
$350$	−236567.	−0.103225
$351$	−716890.	−0.310588
$352$	627829.	0.270075
$353$	−624915.	−0.266922	−0.133461	−	0.991054i	$-0.542609\pi$
$353$	−624915.	−0.266922	−0.133461	+	0.991054i	$0.542609\pi$
$354$	−515176.	−0.218498
$355$	−944.419	−0.000397735 0
$356$	782332.	0.327165
$357$	−1.20824e6	−0.501746
$358$	−2.31179e6	−0.953323
$359$	3.80986e6	1.56017	0.780087	−	0.625671i	$-0.215175\pi$
$359$	3.80986e6	1.56017	0.780087	+	0.625671i	$0.215175\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−2.28331e6	−0.915785
$363$	1.93372e6	0.770243
$364$	−1.48888e6	−0.588988
$365$	−774380.	−0.304244
$366$	−1.52215e6	−0.593956
$367$	1.24404e6	0.482137	0.241068	−	0.970508i	$-0.422502\pi$
$367$	1.24404e6	0.482137	0.241068	+	0.970508i	$0.422502\pi$
$368$	132596.	0.0510402
$369$	683886.	0.261468
$370$	556025.	0.211149
$371$	−1.60045e6	−0.603682
$372$	185273.	0.0694153
$373$	3.30542e6	1.23014	0.615069	−	0.788473i	$-0.289128\pi$
$373$	3.30542e6	1.23014	0.615069	+	0.788473i	$0.289128\pi$
$374$	−3.47936e6	−1.28624
$375$	−140625.	−0.0516398
$376$	919286.	0.335337
$377$	−3.25376e6	−1.17905
$378$	−275932.	−0.0993282
$379$	166417.	0.0595114	0.0297557	−	0.999557i	$-0.490527\pi$
$379$	166417.	0.0595114	0.0297557	+	0.999557i	$0.490527\pi$
$380$	144400.	0.0512989
$381$	143918.	0.0507927
$382$	−843770.	−0.295846
$383$	−3.24313e6	−1.12971	−0.564855	−	0.825190i	$-0.691068\pi$
$383$	−3.24313e6	−1.12971	−0.564855	+	0.825190i	$0.691068\pi$
$384$	−147456.	−0.0510310
$385$	1.45043e6	0.498705
$386$	1.67217e6	0.571231
$387$	1.93186e6	0.655690
$388$	1.47667e6	0.497971
$389$	2.36343e6	0.791898	0.395949	−	0.918272i	$-0.370416\pi$
$389$	2.36343e6	0.791898	0.395949	+	0.918272i	$0.370416\pi$
$390$	−885050.	−0.294650
$391$	−734834.	−0.243079
$392$	502576.	0.165191
$393$	−153992.	−0.0502942
$394$	−3.68734e6	−1.19667
$395$	1.61531e6	0.520911
$396$	−794596.	−0.254629
$397$	−4.68658e6	−1.49238	−0.746190	−	0.665733i	$-0.768119\pi$
$397$	−4.68658e6	−1.49238	−0.746190	+	0.665733i	$0.768119\pi$
$398$	−2.88186e6	−0.911939
$399$	−307443.	−0.0966789
$400$	160000.	0.0500000
$401$	−1.51865e6	−0.471626	−0.235813	−	0.971799i	$-0.575775\pi$
$401$	−1.51865e6	−0.471626	−0.235813	+	0.971799i	$0.575775\pi$
$402$	−745408.	−0.230054
$403$	−1.26525e6	−0.388072
$404$	−269848.	−0.0822556
$405$	−164025.	−0.0496904
$406$	−1.25238e6	−0.377068
$407$	−3.40907e6	−1.02012
$408$	817185.	0.243036
$409$	5.38381e6	1.59141	0.795704	−	0.605686i	$-0.207101\pi$
$409$	5.38381e6	1.59141	0.795704	+	0.605686i	$0.207101\pi$
$410$	844304.	0.248050
$411$	−1.11408e6	−0.325320
$412$	1.29393e6	0.375550
$413$	1.35415e6	0.390654
$414$	−167817.	−0.0481211
$415$	−2.51425e6	−0.716619
$416$	1.00699e6	0.285293
$417$	−775287.	−0.218334
$418$	−885337.	−0.247838
$419$	−3.99972e6	−1.11300	−0.556499	−	0.830849i	$-0.687856\pi$
$419$	−3.99972e6	−1.11300	−0.556499	+	0.830849i	$0.687856\pi$
$420$	−340657.	−0.0942310
$421$	4.80526e6	1.32133	0.660666	−	0.750680i	$-0.270274\pi$
$421$	4.80526e6	1.32133	0.660666	+	0.750680i	$0.270274\pi$
$422$	−2.24778e6	−0.614431
$423$	−1.16347e6	−0.316158
$424$	1.08245e6	0.292411
$425$	−886702.	−0.238125
$426$	−1359.96	−0.000363081 0
$427$	4.00100e6	1.06194
$428$	−3.20826e6	−0.846566
$429$	5.42637e6	1.42353
$430$	2.38501e6	0.622042
$431$	−2.77677e6	−0.720023	−0.360012	−	0.932948i	$-0.617227\pi$
$431$	−2.77677e6	−0.720023	−0.360012	+	0.932948i	$0.617227\pi$
$432$	186624.	0.0481125
$433$	−1.83502e6	−0.470349	−0.235174	−	0.971953i	$-0.575566\pi$
$433$	−1.83502e6	−0.470349	−0.235174	+	0.971953i	$0.575566\pi$
$434$	−486995.	−0.124108
$435$	−744463.	−0.188634
$436$	−1.85032e6	−0.466155
$437$	−186982.	−0.0468377
$438$	−1.11511e6	−0.277735
$439$	−1.23249e6	−0.305227	−0.152614	−	0.988286i	$-0.548769\pi$
$439$	−1.23249e6	−0.305227	−0.152614	+	0.988286i	$0.548769\pi$
$440$	−980983.	−0.241563
$441$	−636073.	−0.155744
$442$	−5.58063e6	−1.35871
$443$	−1.44347e6	−0.349461	−0.174730	−	0.984616i	$-0.555905\pi$
$443$	−1.44347e6	−0.349461	−0.174730	+	0.984616i	$0.555905\pi$
$444$	800676.	0.192752
$445$	−1.22239e6	−0.292625
$446$	−485090.	−0.115474
$447$	−139734.	−0.0330775
$448$	387592.	0.0912388
$449$	6.78670e6	1.58870	0.794352	−	0.607458i	$-0.207811\pi$
$449$	6.78670e6	1.58870	0.794352	+	0.607458i	$0.207811\pi$
$450$	−202500.	−0.0471405
$451$	−5.17655e6	−1.19839
$452$	−384860.	−0.0886046
$453$	26963.8	0.00617355
$454$	2.71412e6	0.618001
$455$	2.32637e6	0.526806
$456$	207936.	0.0468293
$457$	5.70240e6	1.27723	0.638613	−	0.769528i	$-0.279509\pi$
$457$	5.70240e6	1.27723	0.638613	+	0.769528i	$0.279509\pi$
$458$	−848399.	−0.188989
$459$	−1.03425e6	−0.229136
$460$	−207182.	−0.0456517
$461$	−3.10351e6	−0.680143	−0.340072	−	0.940400i	$-0.610451\pi$
$461$	−3.10351e6	−0.680143	−0.340072	+	0.940400i	$0.610451\pi$
$462$	2.08862e6	0.455254
$463$	−2.39485e6	−0.519189	−0.259594	−	0.965718i	$-0.583589\pi$
$463$	−2.39485e6	−0.519189	−0.259594	+	0.965718i	$0.583589\pi$
$464$	847034.	0.182644
$465$	−289489.	−0.0620869
$466$	2.87961e6	0.614283
$467$	7.82454e6	1.66022	0.830112	−	0.557597i	$-0.188276\pi$
$467$	7.82454e6	1.66022	0.830112	+	0.557597i	$0.188276\pi$
$468$	−1.27447e6	−0.268977
$469$	1.95932e6	0.411315
$470$	−1.43638e6	−0.299934
$471$	3.29371e6	0.684120
$472$	−915868.	−0.189225
$473$	−1.46229e7	−3.00524
$474$	2.32605e6	0.475524
$475$	−225625.	−0.0458831
$476$	−2.14799e6	−0.434525
$477$	−1.36998e6	−0.275688
$478$	−958894.	−0.191956
$479$	317612.	0.0632496	0.0316248	−	0.999500i	$-0.489932\pi$
$479$	317612.	0.0632496	0.0316248	+	0.999500i	$0.489932\pi$
$480$	230400.	0.0456435
$481$	−5.46788e6	−1.07760
$482$	−4.53741e6	−0.889592
$483$	441112.	0.0860361
$484$	3.43773e6	0.667050
$485$	−2.30730e6	−0.445399
$486$	−236196.	−0.0453609
$487$	2.12267e6	0.405565	0.202783	−	0.979224i	$-0.435002\pi$
$487$	2.12267e6	0.405565	0.202783	+	0.979224i	$0.435002\pi$
$488$	−2.70604e6	−0.514381
$489$	−3.93152e6	−0.743513
$490$	−785276.	−0.147752
$491$	7.61911e6	1.42627	0.713133	−	0.701029i	$-0.247276\pi$
$491$	7.61911e6	1.42627	0.713133	+	0.701029i	$0.247276\pi$
$492$	1.21580e6	0.226438
$493$	−4.69417e6	−0.869844
$494$	−1.42001e6	−0.261803
$495$	1.24156e6	0.227747
$496$	329375.	0.0601154
$497$	3574.70	0.000649154 0
$498$	−3.62052e6	−0.654180
$499$	−1.11962e6	−0.201289	−0.100644	−	0.994922i	$-0.532090\pi$
$499$	−1.11962e6	−0.201289	−0.100644	+	0.994922i	$0.532090\pi$
$500$	−250000.	−0.0447214
$501$	2.82012e6	0.501964
$502$	6.08051e6	1.07691
$503$	−9.34148e6	−1.64625	−0.823125	−	0.567860i	$-0.807771\pi$
$503$	−9.34148e6	−1.64625	−0.823125	+	0.567860i	$0.807771\pi$
$504$	−490546.	−0.0860207
$505$	421637.	0.0735717
$506$	1.27026e6	0.220555
$507$	5.36184e6	0.926390
$508$	255853.	0.0439878
$509$	3.60261e6	0.616343	0.308172	−	0.951331i	$-0.400283\pi$
$509$	3.60261e6	0.616343	0.308172	+	0.951331i	$0.400283\pi$
$510$	−1.27685e6	−0.217378
$511$	2.93109e6	0.496565
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	−2.56887e6	−0.428878
$515$	−2.02177e6	−0.335902
$516$	3.43442e6	0.567844
$517$	8.80668e6	1.44906
$518$	−2.10459e6	−0.344623
$519$	781811.	0.127404
$520$	−1.57342e6	−0.255174
$521$	−7.78592e6	−1.25665	−0.628327	−	0.777950i	$-0.716260\pi$
$521$	−7.78592e6	−1.25665	−0.628327	+	0.777950i	$0.716260\pi$
$522$	−1.07203e6	−0.172199
$523$	1.13511e7	1.81461	0.907304	−	0.420475i	$-0.138137\pi$
$523$	1.13511e7	1.81461	0.907304	+	0.420475i	$0.138137\pi$
$524$	−273764.	−0.0435560
$525$	532276.	0.0842828
$526$	919428.	0.144895
$527$	−1.82536e6	−0.286300
$528$	−1.41262e6	−0.220516
$529$	−6.16807e6	−0.958318
$530$	−1.69133e6	−0.261540
$531$	1.15915e6	0.178403
$532$	−546565.	−0.0837264
$533$	−8.30279e6	−1.26592
$534$	−1.76025e6	−0.267129
$535$	5.01291e6	0.757191
$536$	−1.32517e6	−0.199232
$537$	5.20152e6	0.778385
$538$	−3.13451e6	−0.466890
$539$	4.81464e6	0.713825
$540$	−291600.	−0.0430331
$541$	6.97868e6	1.02513	0.512566	−	0.858648i	$-0.328695\pi$
$541$	6.97868e6	1.02513	0.512566	+	0.858648i	$0.328695\pi$
$542$	−3.86741e6	−0.565486
$543$	5.13745e6	0.747735
$544$	1.45277e6	0.210475
$545$	2.89112e6	0.416942
$546$	3.34998e6	0.480906
$547$	−6.40187e6	−0.914826	−0.457413	−	0.889254i	$-0.651224\pi$
$547$	−6.40187e6	−0.914826	−0.457413	+	0.889254i	$0.651224\pi$
$548$	−1.98058e6	−0.281735
$549$	3.42483e6	0.484963
$550$	1.53279e6	0.216060
$551$	−1.19445e6	−0.167606
$552$	−298342.	−0.0416741
$553$	−6.11407e6	−0.850194
$554$	−487117.	−0.0674309
$555$	−1.25106e6	−0.172403
$556$	−1.37829e6	−0.189083
$557$	−1.37919e7	−1.88358	−0.941791	−	0.336199i	$-0.890859\pi$
$557$	−1.37919e7	−1.88358	−0.941791	+	0.336199i	$0.890859\pi$
$558$	−416865.	−0.0566774
$559$	−2.34540e7	−3.17458
$560$	−605612.	−0.0816064
$561$	7.82856e6	1.05021
$562$	5.90261e6	0.788322
$563$	1.05556e6	0.140350	0.0701749	−	0.997535i	$-0.477644\pi$
$563$	1.05556e6	0.140350	0.0701749	+	0.997535i	$0.477644\pi$
$564$	−2.06839e6	−0.273801
$565$	601343.	0.0792503
$566$	2.97682e6	0.390581
$567$	620847.	0.0811011
$568$	−2417.71	−0.000314437 0
$569$	−1.24916e6	−0.161747	−0.0808736	−	0.996724i	$-0.525771\pi$
$569$	−1.24916e6	−0.161747	−0.0808736	+	0.996724i	$0.525771\pi$
$570$	−324900.	−0.0418854
$571$	1.16283e7	1.49255	0.746273	−	0.665640i	$-0.231841\pi$
$571$	1.16283e7	1.49255	0.746273	+	0.665640i	$0.231841\pi$
$572$	9.64687e6	1.23281
$573$	1.89848e6	0.241557
$574$	−3.19575e6	−0.404850
$575$	323722.	0.0408321
$576$	331776.	0.0416667
$577$	−6.27747e6	−0.784956	−0.392478	−	0.919761i	$-0.628382\pi$
$577$	−6.27747e6	−0.784956	−0.392478	+	0.919761i	$0.628382\pi$
$578$	−2.37168e6	−0.295282
$579$	−3.76238e6	−0.466408
$580$	−1.32349e6	−0.163362
$581$	9.51662e6	1.16961
$582$	−3.32251e6	−0.406592
$583$	1.03698e7	1.26357
$584$	−1.98241e6	−0.240526
$585$	1.99136e6	0.240581
$586$	−490395.	−0.0589932
$587$	7.88932e6	0.945027	0.472513	−	0.881323i	$-0.343347\pi$
$587$	7.88932e6	0.945027	0.472513	+	0.881323i	$0.343347\pi$
$588$	−1.13080e6	−0.134878
$589$	−464470.	−0.0551657
$590$	1.43104e6	0.169248
$591$	8.29651e6	0.977073
$592$	1.42342e6	0.166928
$593$	8.29668e6	0.968874	0.484437	−	0.874826i	$-0.339024\pi$
$593$	8.29668e6	0.968874	0.484437	+	0.874826i	$0.339024\pi$
$594$	1.78784e6	0.207904
$595$	3.35623e6	0.388651
$596$	−248415.	−0.0286459
$597$	6.48419e6	0.744595
$598$	2.03740e6	0.232983
$599$	1.16906e7	1.33128	0.665638	−	0.746274i	$-0.268159\pi$
$599$	1.16906e7	1.33128	0.665638	+	0.746274i	$0.268159\pi$
$600$	−360000.	−0.0408248
$601$	−8.58241e6	−0.969221	−0.484611	−	0.874730i	$-0.661039\pi$
$601$	−8.58241e6	−0.969221	−0.484611	+	0.874730i	$0.661039\pi$
$602$	−9.02746e6	−1.01525
$603$	1.67717e6	0.187838
$604$	47935.6	0.00534645
$605$	−5.37146e6	−0.596628
$606$	607158.	0.0671615
$607$	−5.59550e6	−0.616406	−0.308203	−	0.951321i	$-0.599728\pi$
$607$	−5.59550e6	−0.616406	−0.308203	+	0.951321i	$0.599728\pi$
$608$	369664.	0.0405554
$609$	2.81785e6	0.307875
$610$	4.22819e6	0.460076
$611$	1.41252e7	1.53071
$612$	−1.83867e6	−0.198438
$613$	−1.22426e7	−1.31589	−0.657947	−	0.753064i	$-0.728575\pi$
$613$	−1.22426e7	−1.31589	−0.657947	+	0.753064i	$0.728575\pi$
$614$	9.44545e6	1.01112
$615$	−1.89968e6	−0.202532
$616$	3.71309e6	0.394261
$617$	6.16362e6	0.651813	0.325907	−	0.945402i	$-0.394331\pi$
$617$	6.16362e6	0.651813	0.325907	+	0.945402i	$0.394331\pi$
$618$	−2.91135e6	−0.306636
$619$	1.03768e6	0.108852	0.0544260	−	0.998518i	$-0.482667\pi$
$619$	1.03768e6	0.108852	0.0544260	+	0.998518i	$0.482667\pi$
$620$	−514648.	−0.0537689
$621$	377589.	0.0392907
$622$	9.27047e6	0.960784
$623$	4.62685e6	0.477601
$624$	−2.26573e6	−0.232941
$625$	390625.	0.0400000
$626$	2.23509e6	0.227961
$627$	1.99201e6	0.202359
$628$	5.85548e6	0.592466
$629$	−7.88846e6	−0.794997
$630$	766478.	0.0769393
$631$	1.02819e7	1.02802	0.514008	−	0.857785i	$-0.328160\pi$
$631$	1.02819e7	1.02802	0.514008	+	0.857785i	$0.328160\pi$
$632$	4.13520e6	0.411816
$633$	5.05751e6	0.501680
$634$	5.46194e6	0.539665
$635$	−399771.	−0.0393439
$636$	−2.43551e6	−0.238753
$637$	7.72231e6	0.754048
$638$	8.11451e6	0.789243
$639$	3059.92	0.000296454 0
$640$	409600.	0.0395285
$641$	4.63984e6	0.446023	0.223012	−	0.974816i	$-0.428411\pi$
$641$	4.63984e6	0.446023	0.223012	+	0.974816i	$0.428411\pi$
$642$	7.21859e6	0.691218
$643$	−1.41813e7	−1.35266	−0.676332	−	0.736597i	$-0.736431\pi$
$643$	−1.41813e7	−1.35266	−0.676332	+	0.736597i	$0.736431\pi$
$644$	784198.	0.0745094
$645$	−5.36628e6	−0.507895
$646$	−2.04864e6	−0.193145
$647$	−7.60555e6	−0.714282	−0.357141	−	0.934050i	$-0.616248\pi$
$647$	−7.60555e6	−0.714282	−0.357141	+	0.934050i	$0.616248\pi$
$648$	−419904.	−0.0392837
$649$	−8.77394e6	−0.817679
$650$	2.45847e6	0.228235
$651$	1.09574e6	0.101334
$652$	−6.98937e6	−0.643901
$653$	−1.93820e7	−1.77875	−0.889376	−	0.457177i	$-0.848861\pi$
$653$	−1.93820e7	−1.77875	−0.889376	+	0.457177i	$0.848861\pi$
$654$	4.16322e6	0.380614
$655$	427756.	0.0389577
$656$	2.16142e6	0.196101
$657$	2.50899e6	0.226770
$658$	5.43682e6	0.489531
$659$	−1.52426e6	−0.136725	−0.0683623	−	0.997661i	$-0.521777\pi$
$659$	−1.52426e6	−0.136725	−0.0683623	+	0.997661i	$0.521777\pi$
$660$	2.20721e6	0.197235
$661$	4.95206e6	0.440841	0.220421	−	0.975405i	$-0.429257\pi$
$661$	4.95206e6	0.440841	0.220421	+	0.975405i	$0.429257\pi$
$662$	8.38828e6	0.743923
$663$	1.25564e7	1.10938
$664$	−6.43648e6	−0.566537
$665$	854007.	0.0748872
$666$	−1.80152e6	−0.157381
$667$	1.71377e6	0.149155
$668$	5.01354e6	0.434714
$669$	1.09145e6	0.0942844
$670$	2.07058e6	0.178199
$671$	−2.59236e7	−2.22275
$672$	−872081.	−0.0744961
$673$	−1.19068e7	−1.01335	−0.506674	−	0.862138i	$-0.669125\pi$
$673$	−1.19068e7	−1.01335	−0.506674	+	0.862138i	$0.669125\pi$
$674$	−7.97373e6	−0.676101
$675$	455625.	0.0384900
$676$	9.53216e6	0.802278
$677$	−1.09393e7	−0.917316	−0.458658	−	0.888613i	$-0.651670\pi$
$677$	−1.09393e7	−0.917316	−0.458658	+	0.888613i	$0.651670\pi$
$678$	865934.	0.0723453
$679$	8.73330e6	0.726949
$680$	−2.26996e6	−0.188255
$681$	−6.10677e6	−0.504596
$682$	3.15538e6	0.259771
$683$	2.25582e7	1.85035	0.925173	−	0.379546i	$-0.123920\pi$
$683$	2.25582e7	1.85035	0.925173	+	0.379546i	$0.123920\pi$
$684$	−467856.	−0.0382360
$685$	3.09466e6	0.251992
$686$	9.33390e6	0.757274
$687$	1.90890e6	0.154309
$688$	6.10564e6	0.491768
$689$	1.66323e7	1.33477
$690$	466159.	0.0372745
$691$	1.92705e7	1.53531	0.767657	−	0.640861i	$-0.221423\pi$
$691$	1.92705e7	1.53531	0.767657	+	0.640861i	$0.221423\pi$
$692$	1.38989e6	0.110335
$693$	−4.69938e6	−0.371713
$694$	−9.84175e6	−0.775664
$695$	2.15357e6	0.169121
$696$	−1.90583e6	−0.149128
$697$	−1.19783e7	−0.933931
$698$	−1.61090e7	−1.25150
$699$	−6.47912e6	−0.501560
$700$	946269.	0.0729910
$701$	3.93645e6	0.302559	0.151280	−	0.988491i	$-0.451661\pi$
$701$	3.93645e6	0.302559	0.151280	+	0.988491i	$0.451661\pi$
$702$	2.86756e6	0.219619
$703$	−2.00725e6	−0.153184
$704$	−2.51132e6	−0.190972
$705$	3.23186e6	0.244895
$706$	2.49966e6	0.188742
$707$	−1.59593e6	−0.120078
$708$	2.06070e6	0.154501
$709$	1.86732e7	1.39509	0.697546	−	0.716540i	$-0.254275\pi$
$709$	1.86732e7	1.39509	0.697546	+	0.716540i	$0.254275\pi$
$710$	3777.68	0.000281241 0
$711$	−5.23361e6	−0.388264
$712$	−3.12933e6	−0.231340
$713$	666410.	0.0490928
$714$	4.83298e6	0.354788
$715$	−1.50732e7	−1.10266
$716$	9.24715e6	0.674101
$717$	2.15751e6	0.156731
$718$	−1.52395e7	−1.10321
$719$	−1.00226e7	−0.723034	−0.361517	−	0.932366i	$-0.617741\pi$
$719$	−1.00226e7	−0.723034	−0.361517	+	0.932366i	$0.617741\pi$
$720$	−518400.	−0.0372678
$721$	7.65254e6	0.548236
$722$	−521284.	−0.0372161
$723$	1.02092e7	0.726348
$724$	9.13324e6	0.647558
$725$	2.06795e6	0.146115
$726$	−7.73490e6	−0.544644
$727$	−1.12364e7	−0.788479	−0.394239	−	0.919008i	$-0.628992\pi$
$727$	−1.12364e7	−0.788479	−0.394239	+	0.919008i	$0.628992\pi$
$728$	5.95552e6	0.416477
$729$	531441.	0.0370370
$730$	3.09752e6	0.215133
$731$	−3.38368e7	−2.34205
$732$	6.08860e6	0.419990
$733$	−1.41728e7	−0.974309	−0.487155	−	0.873316i	$-0.661965\pi$
$733$	−1.41728e7	−0.974309	−0.487155	+	0.873316i	$0.661965\pi$
$734$	−4.97617e6	−0.340922
$735$	1.76687e6	0.120639
$736$	−530385.	−0.0360908
$737$	−1.26950e7	−0.860923
$738$	−2.73555e6	−0.184886
$739$	1.54330e7	1.03953	0.519767	−	0.854308i	$-0.326019\pi$
$739$	1.54330e7	1.03953	0.519767	+	0.854308i	$0.326019\pi$
$740$	−2.22410e6	−0.149305
$741$	3.19503e6	0.213761
$742$	6.40181e6	0.426867
$743$	−2.07933e6	−0.138182	−0.0690908	−	0.997610i	$-0.522010\pi$
$743$	−2.07933e6	−0.138182	−0.0690908	+	0.997610i	$0.522010\pi$
$744$	−741093.	−0.0490840
$745$	388149.	0.0256217
$746$	−1.32217e7	−0.869840
$747$	8.14617e6	0.534136
$748$	1.39174e7	0.909506
$749$	−1.89742e7	−1.23583
$750$	562500.	0.0365148
$751$	−1.90164e7	−1.23035	−0.615175	−	0.788391i	$-0.710915\pi$
$751$	−1.90164e7	−1.23035	−0.615175	+	0.788391i	$0.710915\pi$
$752$	−3.67714e6	−0.237119
$753$	−1.36812e7	−0.879297
$754$	1.30151e7	0.833715
$755$	−74899.3	−0.00478201
$756$	1.10373e6	0.0702356
$757$	−1.37514e6	−0.0872182	−0.0436091	−	0.999049i	$-0.513886\pi$
$757$	−1.37514e6	−0.0872182	−0.0436091	+	0.999049i	$0.513886\pi$
$758$	−665669.	−0.0420809
$759$	−2.85809e6	−0.180082
$760$	−577600.	−0.0362738
$761$	1.05023e7	0.657390	0.328695	−	0.944436i	$-0.393391\pi$
$761$	1.05023e7	0.657390	0.328695	+	0.944436i	$0.393391\pi$
$762$	−575670.	−0.0359159
$763$	−1.09431e7	−0.680502
$764$	3.37508e6	0.209195
$765$	2.87292e6	0.177488
$766$	1.29725e7	0.798826
$767$	−1.40727e7	−0.863753
$768$	589824.	0.0360844
$769$	−4.99693e6	−0.304711	−0.152355	−	0.988326i	$-0.548686\pi$
$769$	−4.99693e6	−0.304711	−0.152355	+	0.988326i	$0.548686\pi$
$770$	−5.80171e6	−0.352638
$771$	5.77996e6	0.350178
$772$	−6.68867e6	−0.403921
$773$	−3.43234e6	−0.206606	−0.103303	−	0.994650i	$-0.532941\pi$
$773$	−3.43234e6	−0.206606	−0.103303	+	0.994650i	$0.532941\pi$
$774$	−7.72745e6	−0.463643
$775$	804137.	0.0480923
$776$	−5.90668e6	−0.352119
$777$	4.73534e6	0.281383
$778$	−9.45374e6	−0.559957
$779$	−3.04794e6	−0.179954
$780$	3.54020e6	0.208349
$781$	−23161.5	−0.00135875
$782$	2.93934e6	0.171883
$783$	2.41206e6	0.140600
$784$	−2.01031e6	−0.116808
$785$	−9.14918e6	−0.529917
$786$	615969.	0.0355633
$787$	1.76794e7	1.01749	0.508746	−	0.860917i	$-0.330109\pi$
$787$	1.76794e7	1.01749	0.508746	+	0.860917i	$0.330109\pi$
$788$	1.47494e7	0.846170
$789$	−2.06871e6	−0.118306
$790$	−6.46125e6	−0.368340
$791$	−2.27613e6	−0.129347
$792$	3.17838e6	0.180050
$793$	−4.15796e7	−2.34799
$794$	1.87463e7	1.05527
$795$	3.80549e6	0.213547
$796$	1.15275e7	0.644838
$797$	2.92233e7	1.62961	0.814804	−	0.579737i	$-0.196845\pi$
$797$	2.92233e7	1.62961	0.814804	+	0.579737i	$0.196845\pi$
$798$	1.22977e6	0.0683623
$799$	2.03783e7	1.12928
$800$	−640000.	−0.0353553
$801$	3.96056e6	0.218110
$802$	6.07461e6	0.333490
$803$	−1.89913e7	−1.03936
$804$	2.98163e6	0.162672
$805$	−1.22531e6	−0.0666433
$806$	5.06099e6	0.274409
$807$	7.05265e6	0.381214
$808$	1.07939e6	0.0581635
$809$	2.33358e7	1.25358	0.626789	−	0.779189i	$-0.284369\pi$
$809$	2.33358e7	1.25358	0.626789	+	0.779189i	$0.284369\pi$
$810$	656100.	0.0351364
$811$	2.56264e7	1.36815	0.684077	−	0.729409i	$-0.260205\pi$
$811$	2.56264e7	1.36815	0.684077	+	0.729409i	$0.260205\pi$
$812$	5.00951e6	0.266628
$813$	8.70167e6	0.461717
$814$	1.36363e7	0.721331
$815$	1.09209e7	0.575922
$816$	−3.26874e6	−0.171852
$817$	−8.60990e6	−0.451277
$818$	−2.15352e7	−1.12530
$819$	−7.53745e6	−0.392658
$820$	−3.37722e6	−0.175398
$821$	3.39526e7	1.75799	0.878993	−	0.476834i	$-0.158216\pi$
$821$	3.39526e7	1.75799	0.878993	+	0.476834i	$0.158216\pi$
$822$	4.45631e6	0.230036
$823$	−3.55156e6	−0.182776	−0.0913882	−	0.995815i	$-0.529130\pi$
$823$	−3.55156e6	−0.182776	−0.0913882	+	0.995815i	$0.529130\pi$
$824$	−5.17572e6	−0.265554
$825$	−3.44877e6	−0.176412
$826$	−5.41661e6	−0.276234
$827$	−6.74117e6	−0.342745	−0.171373	−	0.985206i	$-0.554820\pi$
$827$	−6.74117e6	−0.342745	−0.171373	+	0.985206i	$0.554820\pi$
$828$	671269.	0.0340268
$829$	1.21627e7	0.614674	0.307337	−	0.951601i	$-0.400562\pi$
$829$	1.21627e7	0.614674	0.307337	+	0.951601i	$0.400562\pi$
$830$	1.00570e7	0.506726
$831$	1.09601e6	0.0550571
$832$	−4.02796e6	−0.201733
$833$	1.11409e7	0.556298
$834$	3.10115e6	0.154386
$835$	−7.83366e6	−0.388820
$836$	3.54135e6	0.175248
$837$	937946.	0.0462769
$838$	1.59989e7	0.787008
$839$	2.04276e7	1.00187	0.500935	−	0.865485i	$-0.332989\pi$
$839$	2.04276e7	1.00187	0.500935	+	0.865485i	$0.332989\pi$
$840$	1.36263e6	0.0666314
$841$	−9.56349e6	−0.466258
$842$	−1.92211e7	−0.934323
$843$	−1.32809e7	−0.643662
$844$	8.99112e6	0.434468
$845$	−1.48940e7	−0.717579
$846$	4.65389e6	0.223558
$847$	2.03314e7	0.973773
$848$	−4.32980e6	−0.206766
$849$	−6.69784e6	−0.318908
$850$	3.54681e6	0.168380
$851$	2.87995e6	0.136321
$852$	5439.85	0.000256737 0
$853$	3.21514e7	1.51296	0.756479	−	0.654018i	$-0.226918\pi$
$853$	3.21514e7	1.51296	0.756479	+	0.654018i	$0.226918\pi$
$854$	−1.60040e7	−0.750904
$855$	731025.	0.0341993
$856$	1.28331e7	0.598612
$857$	−2.63220e7	−1.22424	−0.612121	−	0.790764i	$-0.709683\pi$
$857$	−2.63220e7	−1.22424	−0.612121	+	0.790764i	$0.709683\pi$
$858$	−2.17055e7	−1.00659
$859$	1.21188e6	0.0560374	0.0280187	−	0.999607i	$-0.491080\pi$
$859$	1.21188e6	0.0560374	0.0280187	+	0.999607i	$0.491080\pi$
$860$	−9.54006e6	−0.439850
$861$	7.19045e6	0.330558
$862$	1.11071e7	0.509133
$863$	−5.47409e6	−0.250199	−0.125099	−	0.992144i	$-0.539925\pi$
$863$	−5.47409e6	−0.250199	−0.125099	+	0.992144i	$0.539925\pi$
$864$	−746496.	−0.0340207
$865$	−2.17170e6	−0.0986868
$866$	7.34007e6	0.332587
$867$	5.33628e6	0.241097
$868$	1.94798e6	0.0877577
$869$	3.96148e7	1.77954
$870$	2.97785e6	0.133384
$871$	−2.03618e7	−0.909435
$872$	7.40127e6	0.329621
$873$	7.47565e6	0.331981
$874$	747926.	0.0331192
$875$	−1.47854e6	−0.0652851
$876$	4.46043e6	0.196389
$877$	−2.98986e7	−1.31266	−0.656330	−	0.754474i	$-0.727892\pi$
$877$	−2.98986e7	−1.31266	−0.656330	+	0.754474i	$0.727892\pi$
$878$	4.92998e6	0.215828
$879$	1.10339e6	0.0481677
$880$	3.92393e6	0.170811
$881$	892818.	0.0387546	0.0193773	−	0.999812i	$-0.493832\pi$
$881$	892818.	0.0387546	0.0193773	+	0.999812i	$0.493832\pi$
$882$	2.54429e6	0.110127
$883$	−9.71539e6	−0.419332	−0.209666	−	0.977773i	$-0.567238\pi$
$883$	−9.71539e6	−0.419332	−0.209666	+	0.977773i	$0.567238\pi$
$884$	2.23225e7	0.960754
$885$	−3.21985e6	−0.138190
$886$	5.77388e6	0.247106
$887$	3.82580e7	1.63273	0.816364	−	0.577538i	$-0.195987\pi$
$887$	3.82580e7	1.63273	0.816364	+	0.577538i	$0.195987\pi$
$888$	−3.20270e6	−0.136296
$889$	1.51316e6	0.0642142
$890$	4.88958e6	0.206917
$891$	−4.02264e6	−0.169753
$892$	1.94036e6	0.0816527
$893$	5.18535e6	0.217595
$894$	558935.	0.0233893
$895$	−1.44487e7	−0.602934
$896$	−1.55037e6	−0.0645155
$897$	−4.58415e6	−0.190230
$898$	−2.71468e7	−1.12338
$899$	4.25707e6	0.175676
$900$	810000.	0.0333333
$901$	2.39953e7	0.984723
$902$	2.07062e7	0.847392
$903$	2.03118e7	0.828951
$904$	1.53944e6	0.0626529
$905$	−1.42707e7	−0.579193
$906$	−107855.	−0.00436536
$907$	−3.97217e7	−1.60328	−0.801641	−	0.597806i	$-0.796039\pi$
$907$	−3.97217e7	−1.60328	−0.801641	+	0.597806i	$0.796039\pi$
$908$	−1.08565e7	−0.436993
$909$	−1.36611e6	−0.0548371
$910$	−9.30550e6	−0.372508
$911$	9.37882e6	0.374414	0.187207	−	0.982320i	$-0.440056\pi$
$911$	9.37882e6	0.374414	0.187207	+	0.982320i	$0.440056\pi$
$912$	−831744.	−0.0331133
$913$	−6.16609e7	−2.44812
$914$	−2.28096e7	−0.903135
$915$	−9.51343e6	−0.375651
$916$	3.39360e6	0.133635
$917$	−1.61909e6	−0.0635840
$918$	4.13700e6	0.162024
$919$	−3.04741e7	−1.19026	−0.595131	−	0.803629i	$-0.702900\pi$
$919$	−3.04741e7	−1.19026	−0.595131	+	0.803629i	$0.702900\pi$
$920$	828727.	0.0322806
$921$	−2.12523e7	−0.825574
$922$	1.24140e7	0.480934
$923$	−37149.2	−0.00143531
$924$	−8.35446e6	−0.321913
$925$	3.47515e6	0.133543
$926$	9.57939e6	0.367122
$927$	6.55053e6	0.250367
$928$	−3.38813e6	−0.129149
$929$	−2.66683e7	−1.01381	−0.506905	−	0.862002i	$-0.669211\pi$
$929$	−2.66683e7	−1.01381	−0.506905	+	0.862002i	$0.669211\pi$
$930$	1.15796e6	0.0439021
$931$	2.83485e6	0.107190
$932$	−1.15184e7	−0.434364
$933$	−2.08586e7	−0.784477
$934$	−3.12982e7	−1.17396
$935$	−2.17460e7	−0.813487
$936$	5.09789e6	0.190196
$937$	−1.31362e7	−0.488788	−0.244394	−	0.969676i	$-0.578589\pi$
$937$	−1.31362e7	−0.488788	−0.244394	+	0.969676i	$0.578589\pi$
$938$	−7.83729e6	−0.290843
$939$	−5.02896e6	−0.186129
$940$	5.74554e6	0.212086
$941$	−2.01910e6	−0.0743333	−0.0371666	−	0.999309i	$-0.511833\pi$
$941$	−2.01910e6	−0.0743333	−0.0371666	+	0.999309i	$0.511833\pi$
$942$	−1.31748e7	−0.483746
$943$	4.37311e6	0.160144
$944$	3.66347e6	0.133802
$945$	−1.72457e6	−0.0628207
$946$	5.84915e7	2.12503
$947$	3.06998e7	1.11240	0.556200	−	0.831048i	$-0.312259\pi$
$947$	3.06998e7	1.11240	0.556200	+	0.831048i	$0.312259\pi$
$948$	−9.30419e6	−0.336247
$949$	−3.04607e7	−1.09793
$950$	902500.	0.0324443
$951$	−1.22894e7	−0.440634
$952$	8.59196e6	0.307256
$953$	4.06107e7	1.44847	0.724233	−	0.689556i	$-0.242194\pi$
$953$	4.06107e7	1.44847	0.724233	+	0.689556i	$0.242194\pi$
$954$	5.47991e6	0.194941
$955$	−5.27356e6	−0.187109
$956$	3.83558e6	0.135733
$957$	−1.82576e7	−0.644414
$958$	−1.27045e6	−0.0447242
$959$	−1.17135e7	−0.411283
$960$	−921600.	−0.0322749
$961$	−2.69738e7	−0.942178
$962$	2.18715e7	0.761976
$963$	−1.62418e7	−0.564377
$964$	1.81496e7	0.629036
$965$	1.04511e7	0.361278
$966$	−1.76445e6	−0.0608367
$967$	−2.25532e7	−0.775608	−0.387804	−	0.921742i	$-0.626766\pi$
$967$	−2.25532e7	−0.775608	−0.387804	+	0.921742i	$0.626766\pi$
$968$	−1.37509e7	−0.471676
$969$	4.60943e6	0.157702
$970$	9.22919e6	0.314945
$971$	4.45749e7	1.51720	0.758598	−	0.651559i	$-0.225885\pi$
$971$	4.45749e7	1.51720	0.758598	+	0.651559i	$0.225885\pi$
$972$	944784.	0.0320750
$973$	−8.15144e6	−0.276027
$974$	−8.49069e6	−0.286778
$975$	−5.53156e6	−0.186353
$976$	1.08242e7	0.363722
$977$	4.21455e7	1.41259	0.706293	−	0.707920i	$-0.250366\pi$
$977$	4.21455e7	1.41259	0.706293	+	0.707920i	$0.250366\pi$
$978$	1.57261e7	0.525743
$979$	−2.99787e7	−0.999668
$980$	3.14110e6	0.104476
$981$	−9.36724e6	−0.310770
$982$	−3.04764e7	−1.00852
$983$	−7.47617e6	−0.246772	−0.123386	−	0.992359i	$-0.539375\pi$
$983$	−7.47617e6	−0.246772	−0.123386	+	0.992359i	$0.539375\pi$
$984$	−4.86319e6	−0.160116
$985$	−2.30459e7	−0.756837
$986$	1.87767e7	0.615073
$987$	−1.22328e7	−0.399701
$988$	5.68005e6	0.185123
$989$	1.23533e7	0.401598
$990$	−4.96623e6	−0.161042
$991$	5.19925e7	1.68173	0.840865	−	0.541245i	$-0.182047\pi$
$991$	5.19925e7	1.68173	0.840865	+	0.541245i	$0.182047\pi$
$992$	−1.31750e6	−0.0425080
$993$	−1.88736e7	−0.607411
$994$	−14298.8	−0.000459022 0
$995$	−1.80116e7	−0.576761
$996$	1.44821e7	0.462575
$997$	5.14642e7	1.63971	0.819856	−	0.572570i	$-0.194054\pi$
$997$	5.14642e7	1.63971	0.819856	+	0.572570i	$0.194054\pi$
$998$	4.47848e6	0.142333
$999$	4.05342e6	0.128501

Twists

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +94.6269 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} +94.6269 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -613.114 q^{11} +144.000 q^{12} -983.389 q^{13} -378.507 q^{14} -225.000 q^{15} +256.000 q^{16} -1418.72 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} +851.642 q^{21} +2452.46 q^{22} +517.954 q^{23} -576.000 q^{24} +625.000 q^{25} +3933.55 q^{26} +729.000 q^{27} +1514.03 q^{28} +3308.73 q^{29} +900.000 q^{30} +1286.62 q^{31} -1024.00 q^{32} -5518.03 q^{33} +5674.90 q^{34} -2365.67 q^{35} +1296.00 q^{36} +5560.25 q^{37} +1444.00 q^{38} -8850.50 q^{39} +1600.00 q^{40} +8443.04 q^{41} -3406.57 q^{42} +23850.1 q^{43} -9809.83 q^{44} -2025.00 q^{45} -2071.82 q^{46} -14363.8 q^{47} +2304.00 q^{48} -7852.76 q^{49} -2500.00 q^{50} -12768.5 q^{51} -15734.2 q^{52} -16913.3 q^{53} -2916.00 q^{54} +15327.9 q^{55} -6056.12 q^{56} -3249.00 q^{57} -13234.9 q^{58} +14310.4 q^{59} -3600.00 q^{60} +42281.9 q^{61} -5146.48 q^{62} +7664.78 q^{63} +4096.00 q^{64} +24584.7 q^{65} +22072.1 q^{66} +20705.8 q^{67} -22699.6 q^{68} +4661.59 q^{69} +9462.69 q^{70} +37.7768 q^{71} -5184.00 q^{72} +30975.2 q^{73} -22241.0 q^{74} +5625.00 q^{75} -5776.00 q^{76} -58017.1 q^{77} +35402.0 q^{78} -64612.5 q^{79} -6400.00 q^{80} +6561.00 q^{81} -33772.2 q^{82} +100570. q^{83} +13626.3 q^{84} +35468.1 q^{85} -95400.6 q^{86} +29778.5 q^{87} +39239.3 q^{88} +48895.8 q^{89} +8100.00 q^{90} -93055.0 q^{91} +8287.27 q^{92} +11579.6 q^{93} +57455.4 q^{94} +9025.00 q^{95} -9216.00 q^{96} +92291.9 q^{97} +31411.0 q^{98} -49662.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 100 q^{5} - 144 q^{6} + 26 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 472 q^{11} + 576 q^{12} - 482 q^{13} - 104 q^{14} - 900 q^{15} + 1024 q^{16} + 1816 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} + 234 q^{21} + 1888 q^{22} - 418 q^{23} - 2304 q^{24} + 2500 q^{25} + 1928 q^{26} + 2916 q^{27} + 416 q^{28} - 10396 q^{29} + 3600 q^{30} + 528 q^{31} - 4096 q^{32} - 4248 q^{33} - 7264 q^{34} - 650 q^{35} + 5184 q^{36} + 5774 q^{37} + 5776 q^{38} - 4338 q^{39} + 6400 q^{40} + 9620 q^{41} - 936 q^{42} + 21098 q^{43} - 7552 q^{44} - 8100 q^{45} + 1672 q^{46} - 18858 q^{47} + 9216 q^{48} + 2148 q^{49} - 10000 q^{50} + 16344 q^{51} - 7712 q^{52} + 822 q^{53} - 11664 q^{54} + 11800 q^{55} - 1664 q^{56} - 12996 q^{57} + 41584 q^{58} + 28672 q^{59} - 14400 q^{60} + 77748 q^{61} - 2112 q^{62} + 2106 q^{63} + 16384 q^{64} + 12050 q^{65} + 16992 q^{66} + 82400 q^{67} + 29056 q^{68} - 3762 q^{69} + 2600 q^{70} + 928 q^{71} - 20736 q^{72} + 121100 q^{73} - 23096 q^{74} + 22500 q^{75} - 23104 q^{76} - 120220 q^{77} + 17352 q^{78} + 144284 q^{79} - 25600 q^{80} + 26244 q^{81} - 38480 q^{82} - 6082 q^{83} + 3744 q^{84} - 45400 q^{85} - 84392 q^{86} - 93564 q^{87} + 30208 q^{88} + 43260 q^{89} + 32400 q^{90} + 135148 q^{91} - 6688 q^{92} + 4752 q^{93} + 75432 q^{94} + 36100 q^{95} - 36864 q^{96} - 6862 q^{97} - 8592 q^{98} - 38232 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 100 * q^5 - 144 * q^6 + 26 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 - 472 * q^11 + 576 * q^12 - 482 * q^13 - 104 * q^14 - 900 * q^15 + 1024 * q^16 + 1816 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 + 234 * q^21 + 1888 * q^22 - 418 * q^23 - 2304 * q^24 + 2500 * q^25 + 1928 * q^26 + 2916 * q^27 + 416 * q^28 - 10396 * q^29 + 3600 * q^30 + 528 * q^31 - 4096 * q^32 - 4248 * q^33 - 7264 * q^34 - 650 * q^35 + 5184 * q^36 + 5774 * q^37 + 5776 * q^38 - 4338 * q^39 + 6400 * q^40 + 9620 * q^41 - 936 * q^42 + 21098 * q^43 - 7552 * q^44 - 8100 * q^45 + 1672 * q^46 - 18858 * q^47 + 9216 * q^48 + 2148 * q^49 - 10000 * q^50 + 16344 * q^51 - 7712 * q^52 + 822 * q^53 - 11664 * q^54 + 11800 * q^55 - 1664 * q^56 - 12996 * q^57 + 41584 * q^58 + 28672 * q^59 - 14400 * q^60 + 77748 * q^61 - 2112 * q^62 + 2106 * q^63 + 16384 * q^64 + 12050 * q^65 + 16992 * q^66 + 82400 * q^67 + 29056 * q^68 - 3762 * q^69 + 2600 * q^70 + 928 * q^71 - 20736 * q^72 + 121100 * q^73 - 23096 * q^74 + 22500 * q^75 - 23104 * q^76 - 120220 * q^77 + 17352 * q^78 + 144284 * q^79 - 25600 * q^80 + 26244 * q^81 - 38480 * q^82 - 6082 * q^83 + 3744 * q^84 - 45400 * q^85 - 84392 * q^86 - 93564 * q^87 + 30208 * q^88 + 43260 * q^89 + 32400 * q^90 + 135148 * q^91 - 6688 * q^92 + 4752 * q^93 + 75432 * q^94 + 36100 * q^95 - 36864 * q^96 - 6862 * q^97 - 8592 * q^98 - 38232 * q^99

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