LMFDB - Embedded newform 570.6.a.p.1.5

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 17192x^{3} + 62959x^{2} + 59534416x + 102975568 $ x^5 - 2x^4 - 17192x^3 + 62959x^2 + 59534416x + 102975568
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-114.056$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +234.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +234.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -283.098 q^{11} +144.000 q^{12} +571.355 q^{13} +936.450 q^{14} -225.000 q^{15} +256.000 q^{16} -1142.32 q^{17} +324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +2107.01 q^{21} -1132.39 q^{22} +1768.01 q^{23} +576.000 q^{24} +625.000 q^{25} +2285.42 q^{26} +729.000 q^{27} +3745.80 q^{28} +7209.70 q^{29} -900.000 q^{30} -129.589 q^{31} +1024.00 q^{32} -2547.88 q^{33} -4569.26 q^{34} -5852.81 q^{35} +1296.00 q^{36} +15714.0 q^{37} +1444.00 q^{38} +5142.20 q^{39} -1600.00 q^{40} -8237.99 q^{41} +8428.05 q^{42} -8954.16 q^{43} -4529.57 q^{44} -2025.00 q^{45} +7072.05 q^{46} -21087.3 q^{47} +2304.00 q^{48} +38001.7 q^{49} +2500.00 q^{50} -10280.8 q^{51} +9141.68 q^{52} -11168.8 q^{53} +2916.00 q^{54} +7077.46 q^{55} +14983.2 q^{56} +3249.00 q^{57} +28838.8 q^{58} +11757.0 q^{59} -3600.00 q^{60} -31990.1 q^{61} -518.357 q^{62} +18963.1 q^{63} +4096.00 q^{64} -14283.9 q^{65} -10191.5 q^{66} +4874.34 q^{67} -18277.1 q^{68} +15912.1 q^{69} -23411.2 q^{70} +20472.7 q^{71} +5184.00 q^{72} +49702.4 q^{73} +62856.0 q^{74} +5625.00 q^{75} +5776.00 q^{76} -66276.8 q^{77} +20568.8 q^{78} -76760.6 q^{79} -6400.00 q^{80} +6561.00 q^{81} -32952.0 q^{82} +68211.6 q^{83} +33712.2 q^{84} +28557.9 q^{85} -35816.6 q^{86} +64887.3 q^{87} -18118.3 q^{88} -142988. q^{89} -8100.00 q^{90} +133761. q^{91} +28288.2 q^{92} -1166.30 q^{93} -84349.1 q^{94} -9025.00 q^{95} +9216.00 q^{96} +169788. q^{97} +152007. q^{98} -22931.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9} - 500 q^{10} - 312 q^{11} + 720 q^{12} + 1038 q^{13} + 104 q^{14} - 1125 q^{15} + 1280 q^{16} + 756 q^{17} + 1620 q^{18} + 1805 q^{19} - 2000 q^{20} + 234 q^{21} - 1248 q^{22} + 2880 q^{23} + 2880 q^{24} + 3125 q^{25} + 4152 q^{26} + 3645 q^{27} + 416 q^{28} + 7130 q^{29} - 4500 q^{30} + 9786 q^{31} + 5120 q^{32} - 2808 q^{33} + 3024 q^{34} - 650 q^{35} + 6480 q^{36} + 19942 q^{37} + 7220 q^{38} + 9342 q^{39} - 8000 q^{40} + 1444 q^{41} + 936 q^{42} + 14624 q^{43} - 4992 q^{44} - 10125 q^{45} + 11520 q^{46} + 9536 q^{47} + 11520 q^{48} + 53649 q^{49} + 12500 q^{50} + 6804 q^{51} + 16608 q^{52} + 59994 q^{53} + 14580 q^{54} + 7800 q^{55} + 1664 q^{56} + 16245 q^{57} + 28520 q^{58} + 48498 q^{59} - 18000 q^{60} + 14930 q^{61} + 39144 q^{62} + 2106 q^{63} + 20480 q^{64} - 25950 q^{65} - 11232 q^{66} + 60296 q^{67} + 12096 q^{68} + 25920 q^{69} - 2600 q^{70} + 11356 q^{71} + 25920 q^{72} + 110130 q^{73} + 79768 q^{74} + 28125 q^{75} + 28880 q^{76} + 126476 q^{77} + 37368 q^{78} + 117706 q^{79} - 32000 q^{80} + 32805 q^{81} + 5776 q^{82} + 132722 q^{83} + 3744 q^{84} - 18900 q^{85} + 58496 q^{86} + 64170 q^{87} - 19968 q^{88} + 116608 q^{89} - 40500 q^{90} + 45052 q^{91} + 46080 q^{92} + 88074 q^{93} + 38144 q^{94} - 45125 q^{95} + 46080 q^{96} + 264146 q^{97} + 214596 q^{98} - 25272 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9 - 500 * q^10 - 312 * q^11 + 720 * q^12 + 1038 * q^13 + 104 * q^14 - 1125 * q^15 + 1280 * q^16 + 756 * q^17 + 1620 * q^18 + 1805 * q^19 - 2000 * q^20 + 234 * q^21 - 1248 * q^22 + 2880 * q^23 + 2880 * q^24 + 3125 * q^25 + 4152 * q^26 + 3645 * q^27 + 416 * q^28 + 7130 * q^29 - 4500 * q^30 + 9786 * q^31 + 5120 * q^32 - 2808 * q^33 + 3024 * q^34 - 650 * q^35 + 6480 * q^36 + 19942 * q^37 + 7220 * q^38 + 9342 * q^39 - 8000 * q^40 + 1444 * q^41 + 936 * q^42 + 14624 * q^43 - 4992 * q^44 - 10125 * q^45 + 11520 * q^46 + 9536 * q^47 + 11520 * q^48 + 53649 * q^49 + 12500 * q^50 + 6804 * q^51 + 16608 * q^52 + 59994 * q^53 + 14580 * q^54 + 7800 * q^55 + 1664 * q^56 + 16245 * q^57 + 28520 * q^58 + 48498 * q^59 - 18000 * q^60 + 14930 * q^61 + 39144 * q^62 + 2106 * q^63 + 20480 * q^64 - 25950 * q^65 - 11232 * q^66 + 60296 * q^67 + 12096 * q^68 + 25920 * q^69 - 2600 * q^70 + 11356 * q^71 + 25920 * q^72 + 110130 * q^73 + 79768 * q^74 + 28125 * q^75 + 28880 * q^76 + 126476 * q^77 + 37368 * q^78 + 117706 * q^79 - 32000 * q^80 + 32805 * q^81 + 5776 * q^82 + 132722 * q^83 + 3744 * q^84 - 18900 * q^85 + 58496 * q^86 + 64170 * q^87 - 19968 * q^88 + 116608 * q^89 - 40500 * q^90 + 45052 * q^91 + 46080 * q^92 + 88074 * q^93 + 38144 * q^94 - 45125 * q^95 + 46080 * q^96 + 264146 * q^97 + 214596 * q^98 - 25272 * 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
$7$	234.112	1.80584	0.902920	−	0.429808i	$-0.141419\pi$
$7$	234.112	1.80584	0.902920	+	0.429808i	$0.141419\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−283.098	−0.705432	−0.352716	−	0.935730i	$-0.614742\pi$
$11$	−283.098	−0.705432	−0.352716	+	0.935730i	$0.614742\pi$
$12$	144.000	0.288675
$13$	571.355	0.937665	0.468832	−	0.883287i	$-0.344675\pi$
$13$	571.355	0.937665	0.468832	+	0.883287i	$0.344675\pi$
$14$	936.450	1.27692
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	−1142.32	−0.958659	−0.479329	−	0.877635i	$-0.659120\pi$
$17$	−1142.32	−0.958659	−0.479329	+	0.877635i	$0.659120\pi$
$18$	324.000	0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	2107.01	1.04260
$22$	−1132.39	−0.498816
$23$	1768.01	0.696892	0.348446	−	0.937329i	$-0.386709\pi$
$23$	1768.01	0.696892	0.348446	+	0.937329i	$0.386709\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	2285.42	0.663029
$27$	729.000	0.192450
$28$	3745.80	0.902920
$29$	7209.70	1.59192	0.795962	−	0.605347i	$-0.206966\pi$
$29$	7209.70	1.59192	0.795962	+	0.605347i	$0.206966\pi$
$30$	−900.000	−0.182574
$31$	−129.589	−0.0242195	−0.0121097	−	0.999927i	$-0.503855\pi$
$31$	−129.589	−0.0242195	−0.0121097	+	0.999927i	$0.503855\pi$
$32$	1024.00	0.176777
$33$	−2547.88	−0.407282
$34$	−4569.26	−0.677874
$35$	−5852.81	−0.807597
$36$	1296.00	0.166667
$37$	15714.0	1.88705	0.943523	−	0.331306i	$-0.107489\pi$
$37$	15714.0	1.88705	0.943523	+	0.331306i	$0.107489\pi$
$38$	1444.00	0.162221
$39$	5142.20	0.541361
$40$	−1600.00	−0.158114
$41$	−8237.99	−0.765353	−0.382676	−	0.923883i	$-0.624998\pi$
$41$	−8237.99	−0.765353	−0.382676	+	0.923883i	$0.624998\pi$
$42$	8428.05	0.737231
$43$	−8954.16	−0.738506	−0.369253	−	0.929329i	$-0.620386\pi$
$43$	−8954.16	−0.738506	−0.369253	+	0.929329i	$0.620386\pi$
$44$	−4529.57	−0.352716
$45$	−2025.00	−0.149071
$46$	7072.05	0.492777
$47$	−21087.3	−1.39244	−0.696219	−	0.717829i	$-0.745136\pi$
$47$	−21087.3	−1.39244	−0.696219	+	0.717829i	$0.745136\pi$
$48$	2304.00	0.144338
$49$	38001.7	2.26106
$50$	2500.00	0.141421
$51$	−10280.8	−0.553482
$52$	9141.68	0.468832
$53$	−11168.8	−0.546157	−0.273078	−	0.961992i	$-0.588042\pi$
$53$	−11168.8	−0.546157	−0.273078	+	0.961992i	$0.588042\pi$
$54$	2916.00	0.136083
$55$	7077.46	0.315479
$56$	14983.2	0.638461
$57$	3249.00	0.132453
$58$	28838.8	1.12566
$59$	11757.0	0.439711	0.219855	−	0.975532i	$-0.429441\pi$
$59$	11757.0	0.439711	0.219855	+	0.975532i	$0.429441\pi$
$60$	−3600.00	−0.129099
$61$	−31990.1	−1.10076	−0.550378	−	0.834915i	$-0.685517\pi$
$61$	−31990.1	−1.10076	−0.550378	+	0.834915i	$0.685517\pi$
$62$	−518.357	−0.0171258
$63$	18963.1	0.601947
$64$	4096.00	0.125000
$65$	−14283.9	−0.419336
$66$	−10191.5	−0.287992
$67$	4874.34	0.132657	0.0663283	−	0.997798i	$-0.478872\pi$
$67$	4874.34	0.132657	0.0663283	+	0.997798i	$0.478872\pi$
$68$	−18277.1	−0.479329
$69$	15912.1	0.402351
$70$	−23411.2	−0.571057
$71$	20472.7	0.481981	0.240991	−	0.970527i	$-0.422528\pi$
$71$	20472.7	0.481981	0.240991	+	0.970527i	$0.422528\pi$
$72$	5184.00	0.117851
$73$	49702.4	1.09162	0.545808	−	0.837910i	$-0.316223\pi$
$73$	49702.4	1.09162	0.545808	+	0.837910i	$0.316223\pi$
$74$	62856.0	1.33434
$75$	5625.00	0.115470
$76$	5776.00	0.114708
$77$	−66276.8	−1.27390
$78$	20568.8	0.382800
$79$	−76760.6	−1.38379	−0.691896	−	0.721997i	$-0.743224\pi$
$79$	−76760.6	−1.38379	−0.691896	+	0.721997i	$0.743224\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−32952.0	−0.541186
$83$	68211.6	1.08683	0.543417	−	0.839463i	$-0.317130\pi$
$83$	68211.6	1.08683	0.543417	+	0.839463i	$0.317130\pi$
$84$	33712.2	0.521301
$85$	28557.9	0.428725
$86$	−35816.6	−0.522202
$87$	64887.3	0.919098
$88$	−18118.3	−0.249408
$89$	−142988.	−1.91348	−0.956739	−	0.290949i	$-0.906029\pi$
$89$	−142988.	−1.91348	−0.956739	+	0.290949i	$0.906029\pi$
$90$	−8100.00	−0.105409
$91$	133761.	1.69327
$92$	28288.2	0.348446
$93$	−1166.30	−0.0139831
$94$	−84349.1	−0.984603
$95$	−9025.00	−0.102598
$96$	9216.00	0.102062
$97$	169788.	1.83223	0.916113	−	0.400921i	$-0.131310\pi$
$97$	169788.	1.83223	0.916113	+	0.400921i	$0.131310\pi$
$98$	152007.	1.59881
$99$	−22931.0	−0.235144
$100$	10000.0	0.100000
$101$	31246.0	0.304784	0.152392	−	0.988320i	$-0.451302\pi$
$101$	31246.0	0.304784	0.152392	+	0.988320i	$0.451302\pi$
$102$	−41123.4	−0.391371
$103$	198331.	1.84204	0.921018	−	0.389520i	$-0.127359\pi$
$103$	198331.	1.84204	0.921018	+	0.389520i	$0.127359\pi$
$104$	36566.7	0.331515
$105$	−52675.3	−0.466266
$106$	−44675.2	−0.386191
$107$	−9698.79	−0.0818951	−0.0409476	−	0.999161i	$-0.513038\pi$
$107$	−9698.79	−0.0818951	−0.0409476	+	0.999161i	$0.513038\pi$
$108$	11664.0	0.0962250
$109$	222392.	1.79289	0.896444	−	0.443157i	$-0.146141\pi$
$109$	222392.	1.79289	0.896444	+	0.443157i	$0.146141\pi$
$110$	28309.8	0.223077
$111$	141426.	1.08949
$112$	59932.8	0.451460
$113$	265327.	1.95472	0.977360	−	0.211582i	$-0.0678615\pi$
$113$	265327.	1.95472	0.977360	+	0.211582i	$0.0678615\pi$
$114$	12996.0	0.0936586
$115$	−44200.3	−0.311660
$116$	115355.	0.795962
$117$	46279.8	0.312555
$118$	47028.1	0.310922
$119$	−267430.	−1.73118
$120$	−14400.0	−0.0912871
$121$	−80906.4	−0.502365
$122$	−127960.	−0.778353
$123$	−74141.9	−0.441876
$124$	−2073.43	−0.0121097
$125$	−15625.0	−0.0894427
$126$	75852.4	0.425641
$127$	197536.	1.08677	0.543383	−	0.839485i	$-0.317143\pi$
$127$	197536.	1.08677	0.543383	+	0.839485i	$0.317143\pi$
$128$	16384.0	0.0883883
$129$	−80587.5	−0.426376
$130$	−57135.5	−0.296516
$131$	55683.9	0.283499	0.141749	−	0.989903i	$-0.454727\pi$
$131$	55683.9	0.283499	0.141749	+	0.989903i	$0.454727\pi$
$132$	−40766.1	−0.203641
$133$	84514.6	0.414288
$134$	19497.4	0.0938023
$135$	−18225.0	−0.0860663
$136$	−73108.2	−0.338937
$137$	24033.4	0.109399	0.0546995	−	0.998503i	$-0.482580\pi$
$137$	24033.4	0.109399	0.0546995	+	0.998503i	$0.482580\pi$
$138$	63648.4	0.284505
$139$	68586.4	0.301093	0.150547	−	0.988603i	$-0.451897\pi$
$139$	68586.4	0.301093	0.150547	+	0.988603i	$0.451897\pi$
$140$	−93645.0	−0.403798
$141$	−189786.	−0.803925
$142$	81891.0	0.340812
$143$	−161750.	−0.661459
$144$	20736.0	0.0833333
$145$	−180243.	−0.711930
$146$	198810.	0.771889
$147$	342015.	1.30542
$148$	251424.	0.943523
$149$	−131987.	−0.487039	−0.243520	−	0.969896i	$-0.578302\pi$
$149$	−131987.	−0.487039	−0.243520	+	0.969896i	$0.578302\pi$
$150$	22500.0	0.0816497
$151$	−285329.	−1.01837	−0.509183	−	0.860658i	$-0.670052\pi$
$151$	−285329.	−1.01837	−0.509183	+	0.860658i	$0.670052\pi$
$152$	23104.0	0.0811107
$153$	−92527.6	−0.319553
$154$	−265107.	−0.900782
$155$	3239.73	0.0108313
$156$	82275.1	0.270681
$157$	−381246.	−1.23440	−0.617200	−	0.786806i	$-0.711733\pi$
$157$	−381246.	−1.23440	−0.617200	+	0.786806i	$0.711733\pi$
$158$	−307043.	−0.978489
$159$	−100519.	−0.315324
$160$	−25600.0	−0.0790569
$161$	413914.	1.25848
$162$	26244.0	0.0785674
$163$	−230330.	−0.679019	−0.339510	−	0.940603i	$-0.610261\pi$
$163$	−230330.	−0.679019	−0.339510	+	0.940603i	$0.610261\pi$
$164$	−131808.	−0.382676
$165$	63697.1	0.182142
$166$	272846.	0.768507
$167$	−522204.	−1.44893	−0.724467	−	0.689309i	$-0.757914\pi$
$167$	−522204.	−1.44893	−0.724467	+	0.689309i	$0.757914\pi$
$168$	134849.	0.368616
$169$	−44846.5	−0.120785
$170$	114232.	0.303154
$171$	29241.0	0.0764719
$172$	−143267.	−0.369253
$173$	−381929.	−0.970214	−0.485107	−	0.874455i	$-0.661219\pi$
$173$	−381929.	−0.970214	−0.485107	+	0.874455i	$0.661219\pi$
$174$	259549.	0.649900
$175$	146320.	0.361168
$176$	−72473.1	−0.176358
$177$	105813.	0.253867
$178$	−571950.	−1.35303
$179$	499003.	1.16405	0.582024	−	0.813172i	$-0.302261\pi$
$179$	499003.	1.16405	0.582024	+	0.813172i	$0.302261\pi$
$180$	−32400.0	−0.0745356
$181$	−548791.	−1.24512	−0.622559	−	0.782573i	$-0.713907\pi$
$181$	−548791.	−1.24512	−0.622559	+	0.782573i	$0.713907\pi$
$182$	535045.	1.19733
$183$	−287911.	−0.635522
$184$	113153.	0.246389
$185$	−392850.	−0.843913
$186$	−4665.21	−0.00988756
$187$	323388.	0.676269
$188$	−337397.	−0.696219
$189$	170668.	0.347534
$190$	−36100.0	−0.0725476
$191$	272842.	0.541163	0.270581	−	0.962697i	$-0.412784\pi$
$191$	272842.	0.541163	0.270581	+	0.962697i	$0.412784\pi$
$192$	36864.0	0.0721688
$193$	915835.	1.76980	0.884900	−	0.465782i	$-0.154227\pi$
$193$	915835.	1.76980	0.884900	+	0.465782i	$0.154227\pi$
$194$	679154.	1.29558
$195$	−128555.	−0.242104
$196$	608027.	1.13053
$197$	575821.	1.05711	0.528557	−	0.848898i	$-0.322733\pi$
$197$	575821.	1.05711	0.528557	+	0.848898i	$0.322733\pi$
$198$	−91723.8	−0.166272
$199$	−531296.	−0.951050	−0.475525	−	0.879702i	$-0.657742\pi$
$199$	−531296.	−0.951050	−0.475525	+	0.879702i	$0.657742\pi$
$200$	40000.0	0.0707107
$201$	43869.0	0.0765893
$202$	124984.	0.215515
$203$	1.68788e6	2.87476
$204$	−164494.	−0.276741
$205$	205950.	0.342276
$206$	793325.	1.30252
$207$	143209.	0.232297
$208$	146267.	0.234416
$209$	−102198.	−0.161837
$210$	−210701.	−0.329700
$211$	598246.	0.925068	0.462534	−	0.886601i	$-0.346940\pi$
$211$	598246.	0.925068	0.462534	+	0.886601i	$0.346940\pi$
$212$	−178701.	−0.273078
$213$	184255.	0.278272
$214$	−38795.1	−0.0579086
$215$	223854.	0.330270
$216$	46656.0	0.0680414
$217$	−30338.5	−0.0437365
$218$	889569.	1.26776
$219$	447321.	0.630245
$220$	113239.	0.157739
$221$	−652668.	−0.898901
$222$	565704.	0.770383
$223$	−510688.	−0.687691	−0.343846	−	0.939026i	$-0.611730\pi$
$223$	−510688.	−0.687691	−0.343846	+	0.939026i	$0.611730\pi$
$224$	239731.	0.319231
$225$	50625.0	0.0666667
$226$	1.06131e6	1.38220
$227$	494611.	0.637087	0.318544	−	0.947908i	$-0.396806\pi$
$227$	494611.	0.637087	0.318544	+	0.947908i	$0.396806\pi$
$228$	51984.0	0.0662266
$229$	−1.17338e6	−1.47859	−0.739296	−	0.673380i	$-0.764842\pi$
$229$	−1.17338e6	−1.47859	−0.739296	+	0.673380i	$0.764842\pi$
$230$	−176801.	−0.220377
$231$	−596491.	−0.735486
$232$	461421.	0.562830
$233$	−865392.	−1.04429	−0.522147	−	0.852855i	$-0.674869\pi$
$233$	−865392.	−1.04429	−0.522147	+	0.852855i	$0.674869\pi$
$234$	185119.	0.221010
$235$	527182.	0.622717
$236$	188112.	0.219855
$237$	−690846.	−0.798933
$238$	−1.06972e6	−1.22413
$239$	−849937.	−0.962481	−0.481240	−	0.876589i	$-0.659814\pi$
$239$	−849937.	−0.962481	−0.481240	+	0.876589i	$0.659814\pi$
$240$	−57600.0	−0.0645497
$241$	−690965.	−0.766326	−0.383163	−	0.923681i	$-0.625165\pi$
$241$	−690965.	−0.766326	−0.383163	+	0.923681i	$0.625165\pi$
$242$	−323626.	−0.355226
$243$	59049.0	0.0641500
$244$	−511842.	−0.550378
$245$	−950041.	−1.01118
$246$	−296568.	−0.312454
$247$	206259.	0.215115
$248$	−8293.71	−0.00856288
$249$	613904.	0.627484
$250$	−62500.0	−0.0632456
$251$	−563557.	−0.564616	−0.282308	−	0.959324i	$-0.591100\pi$
$251$	−563557.	−0.564616	−0.282308	+	0.959324i	$0.591100\pi$
$252$	303410.	0.300973
$253$	−500521.	−0.491610
$254$	790142.	0.768460
$255$	257021.	0.247525
$256$	65536.0	0.0625000
$257$	−334332.	−0.315751	−0.157875	−	0.987459i	$-0.550464\pi$
$257$	−334332.	−0.315751	−0.157875	+	0.987459i	$0.550464\pi$
$258$	−322350.	−0.301494
$259$	3.67884e6	3.40771
$260$	−228542.	−0.209668
$261$	583986.	0.530641
$262$	222735.	0.200464
$263$	1.49791e6	1.33535	0.667677	−	0.744451i	$-0.267289\pi$
$263$	1.49791e6	1.33535	0.667677	+	0.744451i	$0.267289\pi$
$264$	−163065.	−0.143996
$265$	279220.	0.244249
$266$	338058.	0.292946
$267$	−1.28689e6	−1.10475
$268$	77989.4	0.0663283
$269$	891462.	0.751142	0.375571	−	0.926794i	$-0.377447\pi$
$269$	891462.	0.751142	0.375571	+	0.926794i	$0.377447\pi$
$270$	−72900.0	−0.0608581
$271$	−1.46591e6	−1.21251	−0.606255	−	0.795270i	$-0.707329\pi$
$271$	−1.46591e6	−1.21251	−0.606255	+	0.795270i	$0.707329\pi$
$272$	−292433.	−0.239665
$273$	1.20385e6	0.977612
$274$	96133.4	0.0773567
$275$	−176936.	−0.141086
$276$	254594.	0.201175
$277$	−723090.	−0.566230	−0.283115	−	0.959086i	$-0.591368\pi$
$277$	−723090.	−0.566230	−0.283115	+	0.959086i	$0.591368\pi$
$278$	274346.	0.212905
$279$	−10496.7	−0.00807316
$280$	−374580.	−0.285529
$281$	−2.13148e6	−1.61034	−0.805168	−	0.593047i	$-0.797925\pi$
$281$	−2.13148e6	−1.61034	−0.805168	+	0.593047i	$0.797925\pi$
$282$	−759142.	−0.568461
$283$	−1.85710e6	−1.37838	−0.689189	−	0.724582i	$-0.742033\pi$
$283$	−1.85710e6	−1.37838	−0.689189	+	0.724582i	$0.742033\pi$
$284$	327564.	0.240991
$285$	−81225.0	−0.0592349
$286$	−646998.	−0.467722
$287$	−1.92862e6	−1.38210
$288$	82944.0	0.0589256
$289$	−114971.	−0.0809737
$290$	−720970.	−0.503410
$291$	1.52810e6	1.05784
$292$	795238.	0.545808
$293$	1.25357e6	0.853063	0.426531	−	0.904473i	$-0.359735\pi$
$293$	1.25357e6	0.853063	0.426531	+	0.904473i	$0.359735\pi$
$294$	1.36806e6	0.923074
$295$	−293925.	−0.196645
$296$	1.00570e6	0.667172
$297$	−206379.	−0.135761
$298$	−527946.	−0.344389
$299$	1.01016e6	0.653451
$300$	90000.0	0.0577350
$301$	−2.09628e6	−1.33362
$302$	−1.14132e6	−0.720093
$303$	281214.	0.175967
$304$	92416.0	0.0573539
$305$	799753.	0.492273
$306$	−370110.	−0.225958
$307$	1.56287e6	0.946402	0.473201	−	0.880954i	$-0.343098\pi$
$307$	1.56287e6	0.946402	0.473201	+	0.880954i	$0.343098\pi$
$308$	−1.06043e6	−0.636949
$309$	1.78498e6	1.06350
$310$	12958.9	0.00765887
$311$	1.07300e6	0.629067	0.314534	−	0.949246i	$-0.398152\pi$
$311$	1.07300e6	0.629067	0.314534	+	0.949246i	$0.398152\pi$
$312$	329100.	0.191400
$313$	−990403.	−0.571414	−0.285707	−	0.958317i	$-0.592228\pi$
$313$	−990403.	−0.571414	−0.285707	+	0.958317i	$0.592228\pi$
$314$	−1.52498e6	−0.872853
$315$	−474078.	−0.269199
$316$	−1.22817e6	−0.691896
$317$	−41136.6	−0.0229922	−0.0114961	−	0.999934i	$-0.503659\pi$
$317$	−41136.6	−0.0229922	−0.0114961	+	0.999934i	$0.503659\pi$
$318$	−402077.	−0.222968
$319$	−2.04105e6	−1.12299
$320$	−102400.	−0.0559017
$321$	−87289.1	−0.0472822
$322$	1.65565e6	0.889877
$323$	−412376.	−0.219931
$324$	104976.	0.0555556
$325$	357097.	0.187533
$326$	−921321.	−0.480139
$327$	2.00153e6	1.03512
$328$	−527231.	−0.270593
$329$	−4.93680e6	−2.51452
$330$	254788.	0.128794
$331$	1.06784e6	0.535718	0.267859	−	0.963458i	$-0.413684\pi$
$331$	1.06784e6	0.535718	0.267859	+	0.963458i	$0.413684\pi$
$332$	1.09139e6	0.543417
$333$	1.27283e6	0.629015
$334$	−2.08881e6	−1.02455
$335$	−121858.	−0.0593258
$336$	539395.	0.260651
$337$	1.01772e6	0.488152	0.244076	−	0.969756i	$-0.421515\pi$
$337$	1.01772e6	0.488152	0.244076	+	0.969756i	$0.421515\pi$
$338$	−179386.	−0.0854076
$339$	2.38794e6	1.12856
$340$	456926.	0.214363
$341$	36686.5	0.0170852
$342$	116964.	0.0540738
$343$	4.96193e6	2.27728
$344$	−573066.	−0.261101
$345$	−397803.	−0.179937
$346$	−1.52772e6	−0.686045
$347$	−1.57764e6	−0.703372	−0.351686	−	0.936118i	$-0.614391\pi$
$347$	−1.57764e6	−0.703372	−0.351686	+	0.936118i	$0.614391\pi$
$348$	1.03820e6	0.459549
$349$	−2.96825e6	−1.30448	−0.652238	−	0.758014i	$-0.726170\pi$
$349$	−2.96825e6	−1.30448	−0.652238	+	0.758014i	$0.726170\pi$
$350$	585281.	0.255384
$351$	416518.	0.180454
$352$	−289893.	−0.124704
$353$	−2.32608e6	−0.993547	−0.496774	−	0.867880i	$-0.665482\pi$
$353$	−2.32608e6	−0.993547	−0.496774	+	0.867880i	$0.665482\pi$
$354$	423253.	0.179511
$355$	−511818.	−0.215549
$356$	−2.28780e6	−0.956739
$357$	−2.40687e6	−0.999500
$358$	1.99601e6	0.823106
$359$	3.06115e6	1.25357	0.626786	−	0.779192i	$-0.284370\pi$
$359$	3.06115e6	1.25357	0.626786	+	0.779192i	$0.284370\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−2.19516e6	−0.880431
$363$	−728158.	−0.290041
$364$	2.14018e6	0.846637
$365$	−1.24256e6	−0.488186
$366$	−1.15164e6	−0.449382
$367$	1.75698e6	0.680928	0.340464	−	0.940257i	$-0.389416\pi$
$367$	1.75698e6	0.680928	0.340464	+	0.940257i	$0.389416\pi$
$368$	452611.	0.174223
$369$	−667277.	−0.255118
$370$	−1.57140e6	−0.596736
$371$	−2.61476e6	−0.986272
$372$	−18660.9	−0.00699156
$373$	−5.06079e6	−1.88342	−0.941709	−	0.336430i	$-0.890781\pi$
$373$	−5.06079e6	−1.88342	−0.941709	+	0.336430i	$0.890781\pi$
$374$	1.29355e6	0.478194
$375$	−140625.	−0.0516398
$376$	−1.34959e6	−0.492301
$377$	4.11930e6	1.49269
$378$	682672.	0.245744
$379$	−4.06610e6	−1.45405	−0.727025	−	0.686611i	$-0.759098\pi$
$379$	−4.06610e6	−1.45405	−0.727025	+	0.686611i	$0.759098\pi$
$380$	−144400.	−0.0512989
$381$	1.77782e6	0.627445
$382$	1.09137e6	0.382660
$383$	−3.72164e6	−1.29640	−0.648198	−	0.761472i	$-0.724477\pi$
$383$	−3.72164e6	−1.29640	−0.648198	+	0.761472i	$0.724477\pi$
$384$	147456.	0.0510310
$385$	1.65692e6	0.569705
$386$	3.66334e6	1.25144
$387$	−725287.	−0.246169
$388$	2.71662e6	0.916113
$389$	−4.13441e6	−1.38529	−0.692643	−	0.721280i	$-0.743554\pi$
$389$	−4.13441e6	−1.38529	−0.692643	+	0.721280i	$0.743554\pi$
$390$	−514220.	−0.171193
$391$	−2.01963e6	−0.668082
$392$	2.43211e6	0.799406
$393$	501155.	0.163678
$394$	2.30328e6	0.747492
$395$	1.91902e6	0.618851
$396$	−366895.	−0.117572
$397$	1.95608e6	0.622887	0.311444	−	0.950265i	$-0.399187\pi$
$397$	1.95608e6	0.622887	0.311444	+	0.950265i	$0.399187\pi$
$398$	−2.12518e6	−0.672494
$399$	760631.	0.239189
$400$	160000.	0.0500000
$401$	1.11500e6	0.346268	0.173134	−	0.984898i	$-0.444611\pi$
$401$	1.11500e6	0.346268	0.173134	+	0.984898i	$0.444611\pi$
$402$	175476.	0.0541568
$403$	−74041.5	−0.0227098
$404$	499937.	0.152392
$405$	−164025.	−0.0496904
$406$	6.75152e6	2.03276
$407$	−4.44861e6	−1.33118
$408$	−657974.	−0.195685
$409$	−5.58844e6	−1.65189	−0.825947	−	0.563747i	$-0.809359\pi$
$409$	−5.58844e6	−1.65189	−0.825947	+	0.563747i	$0.809359\pi$
$410$	823799.	0.242026
$411$	216300.	0.0631615
$412$	3.17330e6	0.921018
$413$	2.75246e6	0.794048
$414$	572836.	0.164259
$415$	−1.70529e6	−0.486047
$416$	585068.	0.165757
$417$	617278.	0.173836
$418$	−408794.	−0.114436
$419$	625361.	0.174019	0.0870093	−	0.996208i	$-0.472269\pi$
$419$	625361.	0.174019	0.0870093	+	0.996208i	$0.472269\pi$
$420$	−842805.	−0.233133
$421$	2.09648e6	0.576482	0.288241	−	0.957558i	$-0.406930\pi$
$421$	2.09648e6	0.576482	0.288241	+	0.957558i	$0.406930\pi$
$422$	2.39298e6	0.654122
$423$	−1.70807e6	−0.464146
$424$	−714804.	−0.193096
$425$	−713948.	−0.191732
$426$	737019.	0.196768
$427$	−7.48929e6	−1.98779
$428$	−155181.	−0.0409476
$429$	−1.45575e6	−0.381894
$430$	895416.	0.233536
$431$	−3.00809e6	−0.780005	−0.390002	−	0.920814i	$-0.627526\pi$
$431$	−3.00809e6	−0.780005	−0.390002	+	0.920814i	$0.627526\pi$
$432$	186624.	0.0481125
$433$	3.39918e6	0.871274	0.435637	−	0.900123i	$-0.356523\pi$
$433$	3.39918e6	0.871274	0.435637	+	0.900123i	$0.356523\pi$
$434$	−121354.	−0.0309264
$435$	−1.62218e6	−0.411033
$436$	3.55827e6	0.896444
$437$	638252.	0.159878
$438$	1.78929e6	0.445651
$439$	3.11626e6	0.771742	0.385871	−	0.922553i	$-0.373901\pi$
$439$	3.11626e6	0.771742	0.385871	+	0.922553i	$0.373901\pi$
$440$	452957.	0.111539
$441$	3.07813e6	0.753687
$442$	−2.61067e6	−0.635619
$443$	−2.57473e6	−0.623335	−0.311668	−	0.950191i	$-0.600888\pi$
$443$	−2.57473e6	−0.623335	−0.311668	+	0.950191i	$0.600888\pi$
$444$	2.26282e6	0.544743
$445$	3.57469e6	0.855733
$446$	−2.04275e6	−0.486271
$447$	−1.18788e6	−0.281192
$448$	958925.	0.225730
$449$	−7.62758e6	−1.78554	−0.892772	−	0.450508i	$-0.851243\pi$
$449$	−7.62758e6	−1.78554	−0.892772	+	0.450508i	$0.851243\pi$
$450$	202500.	0.0471405
$451$	2.33216e6	0.539905
$452$	4.24523e6	0.977360
$453$	−2.56796e6	−0.587954
$454$	1.97844e6	0.450489
$455$	−3.34403e6	−0.757255
$456$	207936.	0.0468293
$457$	7.40800e6	1.65925	0.829623	−	0.558324i	$-0.188556\pi$
$457$	7.40800e6	1.65925	0.829623	+	0.558324i	$0.188556\pi$
$458$	−4.69350e6	−1.04552
$459$	−832748.	−0.184494
$460$	−707205.	−0.155830
$461$	−2.19717e6	−0.481516	−0.240758	−	0.970585i	$-0.577396\pi$
$461$	−2.19717e6	−0.481516	−0.240758	+	0.970585i	$0.577396\pi$
$462$	−2.38597e6	−0.520067
$463$	−2.51119e6	−0.544412	−0.272206	−	0.962239i	$-0.587753\pi$
$463$	−2.51119e6	−0.544412	−0.272206	+	0.962239i	$0.587753\pi$
$464$	1.84568e6	0.397981
$465$	29157.6	0.00625344
$466$	−3.46157e6	−0.738428
$467$	−5.89562e6	−1.25094	−0.625471	−	0.780247i	$-0.715093\pi$
$467$	−5.89562e6	−1.25094	−0.625471	+	0.780247i	$0.715093\pi$
$468$	740476.	0.156277
$469$	1.14114e6	0.239557
$470$	2.10873e6	0.440328
$471$	−3.43121e6	−0.712681
$472$	752449.	0.155461
$473$	2.53491e6	0.520966
$474$	−2.76338e6	−0.564931
$475$	225625.	0.0458831
$476$	−4.27889e6	−0.865592
$477$	−904674.	−0.182052
$478$	−3.39975e6	−0.680577
$479$	3.48186e6	0.693382	0.346691	−	0.937979i	$-0.387305\pi$
$479$	3.48186e6	0.693382	0.346691	+	0.937979i	$0.387305\pi$
$480$	−230400.	−0.0456435
$481$	8.97828e6	1.76942
$482$	−2.76386e6	−0.541874
$483$	3.72522e6	0.726582
$484$	−1.29450e6	−0.251183
$485$	−4.24471e6	−0.819396
$486$	236196.	0.0453609
$487$	−2.24389e6	−0.428724	−0.214362	−	0.976754i	$-0.568767\pi$
$487$	−2.24389e6	−0.428724	−0.214362	+	0.976754i	$0.568767\pi$
$488$	−2.04737e6	−0.389176
$489$	−2.07297e6	−0.392032
$490$	−3.80017e6	−0.715010
$491$	−8.67841e6	−1.62456	−0.812281	−	0.583266i	$-0.801774\pi$
$491$	−8.67841e6	−1.62456	−0.812281	+	0.583266i	$0.801774\pi$
$492$	−1.18627e6	−0.220938
$493$	−8.23576e6	−1.52611
$494$	825037.	0.152109
$495$	573274.	0.105160
$496$	−33174.8	−0.00605487
$497$	4.79292e6	0.870381
$498$	2.45562e6	0.443698
$499$	−8.66566e6	−1.55794	−0.778969	−	0.627063i	$-0.784257\pi$
$499$	−8.66566e6	−1.55794	−0.778969	+	0.627063i	$0.784257\pi$
$500$	−250000.	−0.0447214
$501$	−4.69983e6	−0.836543
$502$	−2.25423e6	−0.399244
$503$	−1.76699e6	−0.311396	−0.155698	−	0.987805i	$-0.549763\pi$
$503$	−1.76699e6	−0.311396	−0.155698	+	0.987805i	$0.549763\pi$
$504$	1.21364e6	0.212820
$505$	−781151.	−0.136303
$506$	−2.00208e6	−0.347621
$507$	−403618.	−0.0697350
$508$	3.16057e6	0.543383
$509$	−7.99519e6	−1.36784	−0.683918	−	0.729559i	$-0.739725\pi$
$509$	−7.99519e6	−1.36784	−0.683918	+	0.729559i	$0.739725\pi$
$510$	1.02808e6	0.175026
$511$	1.16359e7	1.97129
$512$	262144.	0.0441942
$513$	263169.	0.0441511
$514$	−1.33733e6	−0.223270
$515$	−4.95828e6	−0.823783
$516$	−1.28940e6	−0.213188
$517$	5.96977e6	0.982271
$518$	1.47154e7	2.40961
$519$	−3.43736e6	−0.560154
$520$	−914168.	−0.148258
$521$	2.89810e6	0.467756	0.233878	−	0.972266i	$-0.424858\pi$
$521$	2.89810e6	0.467756	0.233878	+	0.972266i	$0.424858\pi$
$522$	2.33594e6	0.375220
$523$	−3.76904e6	−0.602527	−0.301263	−	0.953541i	$-0.597408\pi$
$523$	−3.76904e6	−0.602527	−0.301263	+	0.953541i	$0.597408\pi$
$524$	890942.	0.141749
$525$	1.31688e6	0.208521
$526$	5.99164e6	0.944238
$527$	148032.	0.0232182
$528$	−652258.	−0.101820
$529$	−3.31048e6	−0.514341
$530$	1.11688e6	0.172710
$531$	952318.	0.146570
$532$	1.35223e6	0.207144
$533$	−4.70682e6	−0.717644
$534$	−5.14755e6	−0.781174
$535$	242470.	0.0366246
$536$	311958.	0.0469012
$537$	4.49103e6	0.672063
$538$	3.56585e6	0.531137
$539$	−1.07582e7	−1.59503
$540$	−291600.	−0.0430331
$541$	−3.98244e6	−0.585000	−0.292500	−	0.956265i	$-0.594487\pi$
$541$	−3.98244e6	−0.585000	−0.292500	+	0.956265i	$0.594487\pi$
$542$	−5.86365e6	−0.857374
$543$	−4.93912e6	−0.718869
$544$	−1.16973e6	−0.169468
$545$	−5.55980e6	−0.801804
$546$	4.81541e6	0.691276
$547$	−487271.	−0.0696309	−0.0348154	−	0.999394i	$-0.511084\pi$
$547$	−487271.	−0.0696309	−0.0348154	+	0.999394i	$0.511084\pi$
$548$	384534.	0.0546995
$549$	−2.59120e6	−0.366919
$550$	−707746.	−0.0997632
$551$	2.60270e6	0.365212
$552$	1.01838e6	0.142253
$553$	−1.79706e7	−2.49891
$554$	−2.89236e6	−0.400385
$555$	−3.53565e6	−0.487233
$556$	1.09738e6	0.150547
$557$	9.99109e6	1.36450	0.682252	−	0.731117i	$-0.261001\pi$
$557$	9.99109e6	1.36450	0.682252	+	0.731117i	$0.261001\pi$
$558$	−41986.9	−0.00570859
$559$	−5.11601e6	−0.692471
$560$	−1.49832e6	−0.201899
$561$	2.91049e6	0.390444
$562$	−8.52594e6	−1.13868
$563$	6.40920e6	0.852182	0.426091	−	0.904680i	$-0.359890\pi$
$563$	6.40920e6	0.852182	0.426091	+	0.904680i	$0.359890\pi$
$564$	−3.03657e6	−0.401962
$565$	−6.63316e6	−0.874178
$566$	−7.42838e6	−0.974660
$567$	1.53601e6	0.200649
$568$	1.31026e6	0.170406
$569$	1.24836e7	1.61644	0.808219	−	0.588882i	$-0.200432\pi$
$569$	1.24836e7	1.61644	0.808219	+	0.588882i	$0.200432\pi$
$570$	−324900.	−0.0418854
$571$	1.41584e7	1.81729	0.908646	−	0.417568i	$-0.137117\pi$
$571$	1.41584e7	1.81729	0.908646	+	0.417568i	$0.137117\pi$
$572$	−2.58799e6	−0.330730
$573$	2.45558e6	0.312440
$574$	−7.71446e6	−0.977296
$575$	1.10501e6	0.139378
$576$	331776.	0.0416667
$577$	−5.00466e6	−0.625799	−0.312900	−	0.949786i	$-0.601300\pi$
$577$	−5.00466e6	−0.625799	−0.312900	+	0.949786i	$0.601300\pi$
$578$	−459884.	−0.0572570
$579$	8.24251e6	1.02179
$580$	−2.88388e6	−0.355965
$581$	1.59692e7	1.96265
$582$	6.11238e6	0.748003
$583$	3.16187e6	0.385277
$584$	3.18095e6	0.385945
$585$	−1.15699e6	−0.139779
$586$	5.01430e6	0.603207
$587$	2.76487e6	0.331191	0.165596	−	0.986194i	$-0.447045\pi$
$587$	2.76487e6	0.331191	0.165596	+	0.986194i	$0.447045\pi$
$588$	5.47224e6	0.652712
$589$	−46781.7	−0.00555633
$590$	−1.17570e6	−0.139049
$591$	5.18239e6	0.610325
$592$	4.02279e6	0.471762
$593$	−4.00352e6	−0.467526	−0.233763	−	0.972294i	$-0.575104\pi$
$593$	−4.00352e6	−0.467526	−0.233763	+	0.972294i	$0.575104\pi$
$594$	−825514.	−0.0959972
$595$	6.68576e6	0.774209
$596$	−2.11178e6	−0.243520
$597$	−4.78166e6	−0.549089
$598$	4.04065e6	0.462060
$599$	−1.64308e7	−1.87107	−0.935536	−	0.353232i	$-0.885083\pi$
$599$	−1.64308e7	−1.87107	−0.935536	+	0.353232i	$0.885083\pi$
$600$	360000.	0.0408248
$601$	6.82746e6	0.771033	0.385517	−	0.922701i	$-0.374023\pi$
$601$	6.82746e6	0.771033	0.385517	+	0.922701i	$0.374023\pi$
$602$	−8.38512e6	−0.943014
$603$	394821.	0.0442188
$604$	−4.56527e6	−0.509183
$605$	2.02266e6	0.224664
$606$	1.12486e6	0.124427
$607$	1.06184e7	1.16974	0.584868	−	0.811128i	$-0.301146\pi$
$607$	1.06184e7	1.16974	0.584868	+	0.811128i	$0.301146\pi$
$608$	369664.	0.0405554
$609$	1.51909e7	1.65974
$610$	3.19901e6	0.348090
$611$	−1.20483e7	−1.30564
$612$	−1.48044e6	−0.159776
$613$	1.10450e7	1.18718	0.593588	−	0.804769i	$-0.297711\pi$
$613$	1.10450e7	1.18718	0.593588	+	0.804769i	$0.297711\pi$
$614$	6.25146e6	0.669207
$615$	1.85355e6	0.197613
$616$	−4.24172e6	−0.450391
$617$	3.49853e6	0.369975	0.184988	−	0.982741i	$-0.440775\pi$
$617$	3.49853e6	0.369975	0.184988	+	0.982741i	$0.440775\pi$
$618$	7.13992e6	0.752008
$619$	5.12272e6	0.537371	0.268685	−	0.963228i	$-0.413411\pi$
$619$	5.12272e6	0.537371	0.268685	+	0.963228i	$0.413411\pi$
$620$	51835.7	0.00541564
$621$	1.28888e6	0.134117
$622$	4.29198e6	0.444818
$623$	−3.34752e7	−3.45544
$624$	1.31640e6	0.135340
$625$	390625.	0.0400000
$626$	−3.96161e6	−0.404051
$627$	−919786.	−0.0934368
$628$	−6.09993e6	−0.617200
$629$	−1.79504e7	−1.80903
$630$	−1.89631e6	−0.190352
$631$	−1.74594e6	−0.174564	−0.0872822	−	0.996184i	$-0.527818\pi$
$631$	−1.74594e6	−0.174564	−0.0872822	+	0.996184i	$0.527818\pi$
$632$	−4.91268e6	−0.489244
$633$	5.38422e6	0.534088
$634$	−164546.	−0.0162579
$635$	−4.93839e6	−0.486017
$636$	−1.60831e6	−0.157662
$637$	2.17124e7	2.12012
$638$	−8.16421e6	−0.794077
$639$	1.65829e6	0.160660
$640$	−409600.	−0.0395285
$641$	1.01597e7	0.976642	0.488321	−	0.872664i	$-0.337610\pi$
$641$	1.01597e7	0.976642	0.488321	+	0.872664i	$0.337610\pi$
$642$	−349156.	−0.0334335
$643$	8.09227e6	0.771868	0.385934	−	0.922526i	$-0.373879\pi$
$643$	8.09227e6	0.771868	0.385934	+	0.922526i	$0.373879\pi$
$644$	6.62262e6	0.629238
$645$	2.01469e6	0.190681
$646$	−1.64950e6	−0.155515
$647$	5.95543e6	0.559310	0.279655	−	0.960101i	$-0.409780\pi$
$647$	5.95543e6	0.559310	0.279655	+	0.960101i	$0.409780\pi$
$648$	419904.	0.0392837
$649$	−3.32839e6	−0.310186
$650$	1.42839e6	0.132606
$651$	−273046.	−0.0252513
$652$	−3.68528e6	−0.339510
$653$	1.10559e7	1.01464	0.507320	−	0.861758i	$-0.330636\pi$
$653$	1.10559e7	1.01464	0.507320	+	0.861758i	$0.330636\pi$
$654$	8.00612e6	0.731944
$655$	−1.39210e6	−0.126784
$656$	−2.10892e6	−0.191338
$657$	4.02589e6	0.363872
$658$	−1.97472e7	−1.77804
$659$	−2.14926e7	−1.92786	−0.963930	−	0.266157i	$-0.914246\pi$
$659$	−2.14926e7	−1.92786	−0.963930	+	0.266157i	$0.914246\pi$
$660$	1.01915e6	0.0910709
$661$	1.26763e7	1.12847	0.564233	−	0.825616i	$-0.309172\pi$
$661$	1.26763e7	1.12847	0.564233	+	0.825616i	$0.309172\pi$
$662$	4.27136e6	0.378810
$663$	−5.87401e6	−0.518980
$664$	4.36554e6	0.384254
$665$	−2.11287e6	−0.185275
$666$	5.09134e6	0.444781
$667$	1.27468e7	1.10940
$668$	−8.35526e6	−0.724467
$669$	−4.59619e6	−0.397039
$670$	−487434.	−0.0419497
$671$	9.05635e6	0.776510
$672$	2.15758e6	0.184308
$673$	−3.07273e6	−0.261509	−0.130754	−	0.991415i	$-0.541740\pi$
$673$	−3.07273e6	−0.261509	−0.130754	+	0.991415i	$0.541740\pi$
$674$	4.07090e6	0.345176
$675$	455625.	0.0384900
$676$	−717543.	−0.0603923
$677$	−6.81228e6	−0.571243	−0.285621	−	0.958343i	$-0.592200\pi$
$677$	−6.81228e6	−0.571243	−0.285621	+	0.958343i	$0.592200\pi$
$678$	9.55176e6	0.798011
$679$	3.97496e7	3.30871
$680$	1.82771e6	0.151577
$681$	4.45150e6	0.367822
$682$	146746.	0.0120811
$683$	499763.	0.0409933	0.0204966	−	0.999790i	$-0.493475\pi$
$683$	499763.	0.0409933	0.0204966	+	0.999790i	$0.493475\pi$
$684$	467856.	0.0382360
$685$	−600834.	−0.0489247
$686$	1.98477e7	1.61028
$687$	−1.05604e7	−0.853666
$688$	−2.29227e6	−0.184626
$689$	−6.38136e6	−0.512112
$690$	−1.59121e6	−0.127235
$691$	8.19600e6	0.652990	0.326495	−	0.945199i	$-0.394132\pi$
$691$	8.19600e6	0.652990	0.326495	+	0.945199i	$0.394132\pi$
$692$	−6.11087e6	−0.485107
$693$	−5.36842e6	−0.424633
$694$	−6.31057e6	−0.497359
$695$	−1.71466e6	−0.134653
$696$	4.15279e6	0.324950
$697$	9.41039e6	0.733712
$698$	−1.18730e7	−0.922404
$699$	−7.78853e6	−0.602924
$700$	2.34112e6	0.180584
$701$	−2.20076e7	−1.69152	−0.845759	−	0.533565i	$-0.820852\pi$
$701$	−2.20076e7	−1.69152	−0.845759	+	0.533565i	$0.820852\pi$
$702$	1.66607e6	0.127600
$703$	5.67276e6	0.432918
$704$	−1.15957e6	−0.0881791
$705$	4.74464e6	0.359526
$706$	−9.30434e6	−0.702544
$707$	7.31509e6	0.550391
$708$	1.69301e6	0.126934
$709$	−4.08432e6	−0.305144	−0.152572	−	0.988292i	$-0.548756\pi$
$709$	−4.08432e6	−0.305144	−0.152572	+	0.988292i	$0.548756\pi$
$710$	−2.04727e6	−0.152416
$711$	−6.21761e6	−0.461264
$712$	−9.15120e6	−0.676516
$713$	−229115.	−0.0168784
$714$	−9.62750e6	−0.706753
$715$	4.04374e6	0.295814
$716$	7.98405e6	0.582024
$717$	−7.64944e6	−0.555689
$718$	1.22446e7	0.886409
$719$	5.82067e6	0.419905	0.209952	−	0.977712i	$-0.432669\pi$
$719$	5.82067e6	0.419905	0.209952	+	0.977712i	$0.432669\pi$
$720$	−518400.	−0.0372678
$721$	4.64318e7	3.32642
$722$	521284.	0.0372161
$723$	−6.21869e6	−0.442439
$724$	−8.78065e6	−0.622559
$725$	4.50606e6	0.318385
$726$	−2.91263e6	−0.205090
$727$	−6.10262e6	−0.428233	−0.214117	−	0.976808i	$-0.568687\pi$
$727$	−6.10262e6	−0.428233	−0.214117	+	0.976808i	$0.568687\pi$
$728$	8.56073e6	0.598663
$729$	531441.	0.0370370
$730$	−4.97024e6	−0.345199
$731$	1.02285e7	0.707975
$732$	−4.60658e6	−0.317761
$733$	−9.95650e6	−0.684458	−0.342229	−	0.939617i	$-0.611182\pi$
$733$	−9.95650e6	−0.684458	−0.342229	+	0.939617i	$0.611182\pi$
$734$	7.02792e6	0.481489
$735$	−8.55037e6	−0.583804
$736$	1.81044e6	0.123194
$737$	−1.37992e6	−0.0935802
$738$	−2.66911e6	−0.180395
$739$	9.66325e6	0.650897	0.325448	−	0.945560i	$-0.394485\pi$
$739$	9.66325e6	0.650897	0.325448	+	0.945560i	$0.394485\pi$
$740$	−6.28560e6	−0.421956
$741$	1.85633e6	0.124197
$742$	−1.04590e7	−0.697400
$743$	−1.08116e7	−0.718485	−0.359242	−	0.933244i	$-0.616965\pi$
$743$	−1.08116e7	−0.718485	−0.359242	+	0.933244i	$0.616965\pi$
$744$	−74643.4	−0.00494378
$745$	3.29966e6	0.217811
$746$	−2.02432e7	−1.33178
$747$	5.52514e6	0.362278
$748$	5.17420e6	0.338134
$749$	−2.27061e6	−0.147890
$750$	−562500.	−0.0365148
$751$	457934.	0.0296280	0.0148140	−	0.999890i	$-0.495284\pi$
$751$	457934.	0.0296280	0.0148140	+	0.999890i	$0.495284\pi$
$752$	−5.39834e6	−0.348110
$753$	−5.07201e6	−0.325981
$754$	1.64772e7	1.05549
$755$	7.13323e6	0.455427
$756$	2.73069e6	0.173767
$757$	−2.06665e7	−1.31077	−0.655385	−	0.755295i	$-0.727494\pi$
$757$	−2.06665e7	−1.31077	−0.655385	+	0.755295i	$0.727494\pi$
$758$	−1.62644e7	−1.02817
$759$	−4.50469e6	−0.283831
$760$	−577600.	−0.0362738
$761$	4.17562e6	0.261372	0.130686	−	0.991424i	$-0.458282\pi$
$761$	4.17562e6	0.261372	0.130686	+	0.991424i	$0.458282\pi$
$762$	7.11128e6	0.443670
$763$	5.20648e7	3.23767
$764$	4.36547e6	0.270581
$765$	2.31319e6	0.142908
$766$	−1.48866e7	−0.916691
$767$	6.71743e6	0.412301
$768$	589824.	0.0360844
$769$	1.44867e7	0.883395	0.441698	−	0.897164i	$-0.354376\pi$
$769$	1.44867e7	0.883395	0.441698	+	0.897164i	$0.354376\pi$
$770$	6.62768e6	0.402842
$771$	−3.00898e6	−0.182299
$772$	1.46534e7	0.884900
$773$	−1.11556e7	−0.671496	−0.335748	−	0.941952i	$-0.608989\pi$
$773$	−1.11556e7	−0.671496	−0.335748	+	0.941952i	$0.608989\pi$
$774$	−2.90115e6	−0.174067
$775$	−80993.3	−0.00484390
$776$	1.08665e7	0.647789
$777$	3.31096e7	1.96744
$778$	−1.65376e7	−0.979546
$779$	−2.97391e6	−0.175584
$780$	−2.05688e6	−0.121052
$781$	−5.79580e6	−0.340005
$782$	−8.07851e6	−0.472405
$783$	5.25587e6	0.306366
$784$	9.72842e6	0.565265
$785$	9.53115e6	0.552041
$786$	2.00462e6	0.115738
$787$	−1.60944e7	−0.926269	−0.463134	−	0.886288i	$-0.653275\pi$
$787$	−1.60944e7	−0.926269	−0.463134	+	0.886288i	$0.653275\pi$
$788$	9.21313e6	0.528557
$789$	1.34812e7	0.770967
$790$	7.67606e6	0.437594
$791$	6.21163e7	3.52991
$792$	−1.46758e6	−0.0831360
$793$	−1.82777e7	−1.03214
$794$	7.82431e6	0.440448
$795$	2.51298e6	0.141017
$796$	−8.50073e6	−0.475525
$797$	2.39160e6	0.133365	0.0666827	−	0.997774i	$-0.478758\pi$
$797$	2.39160e6	0.133365	0.0666827	+	0.997774i	$0.478758\pi$
$798$	3.04253e6	0.169132
$799$	2.40883e7	1.33487
$800$	640000.	0.0353553
$801$	−1.15820e7	−0.637826
$802$	4.45998e6	0.244848
$803$	−1.40707e7	−0.770062
$804$	701905.	0.0382946
$805$	−1.03478e7	−0.562808
$806$	−296166.	−0.0160582
$807$	8.02315e6	0.433672
$808$	1.99975e6	0.107757
$809$	2.16246e6	0.116166	0.0580828	−	0.998312i	$-0.481501\pi$
$809$	2.16246e6	0.116166	0.0580828	+	0.998312i	$0.481501\pi$
$810$	−656100.	−0.0351364
$811$	−2.68791e7	−1.43504	−0.717518	−	0.696540i	$-0.754722\pi$
$811$	−2.68791e7	−1.43504	−0.717518	+	0.696540i	$0.754722\pi$
$812$	2.70061e7	1.43738
$813$	−1.31932e7	−0.700043
$814$	−1.77944e7	−0.941289
$815$	5.75826e6	0.303667
$816$	−2.63190e6	−0.138370
$817$	−3.23245e6	−0.169425
$818$	−2.23538e7	−1.16807
$819$	1.08347e7	0.564425
$820$	3.29520e6	0.171138
$821$	1.36035e7	0.704357	0.352178	−	0.935933i	$-0.385441\pi$
$821$	1.36035e7	0.704357	0.352178	+	0.935933i	$0.385441\pi$
$822$	865201.	0.0446619
$823$	8.41923e6	0.433284	0.216642	−	0.976251i	$-0.430490\pi$
$823$	8.41923e6	0.433284	0.216642	+	0.976251i	$0.430490\pi$
$824$	1.26932e7	0.651258
$825$	−1.59243e6	−0.0814563
$826$	1.10099e7	0.561476
$827$	−1.99839e7	−1.01605	−0.508027	−	0.861341i	$-0.669625\pi$
$827$	−1.99839e7	−1.01605	−0.508027	+	0.861341i	$0.669625\pi$
$828$	2.29134e6	0.116149
$829$	1.69559e7	0.856909	0.428455	−	0.903563i	$-0.359058\pi$
$829$	1.69559e7	0.856909	0.428455	+	0.903563i	$0.359058\pi$
$830$	−6.82116e6	−0.343687
$831$	−6.50781e6	−0.326913
$832$	2.34027e6	0.117208
$833$	−4.34099e7	−2.16759
$834$	2.46911e6	0.122921
$835$	1.30551e7	0.647983
$836$	−1.63518e6	−0.0809187
$837$	−94470.6	−0.00466104
$838$	2.50144e6	0.123050
$839$	2.63071e7	1.29023	0.645116	−	0.764085i	$-0.276809\pi$
$839$	2.63071e7	1.29023	0.645116	+	0.764085i	$0.276809\pi$
$840$	−3.37122e6	−0.164850
$841$	3.14686e7	1.53422
$842$	8.38592e6	0.407634
$843$	−1.91834e7	−0.929728
$844$	9.57194e6	0.462534
$845$	1.12116e6	0.0540165
$846$	−6.83228e6	−0.328201
$847$	−1.89412e7	−0.907191
$848$	−2.85922e6	−0.136539
$849$	−1.67139e7	−0.795807
$850$	−2.85579e6	−0.135575
$851$	2.77826e7	1.31507
$852$	2.94807e6	0.139136
$853$	−1.19395e7	−0.561842	−0.280921	−	0.959731i	$-0.590640\pi$
$853$	−1.19395e7	−0.561842	−0.280921	+	0.959731i	$0.590640\pi$
$854$	−2.99572e7	−1.40558
$855$	−731025.	−0.0341993
$856$	−620722.	−0.0289543
$857$	2.70584e7	1.25849	0.629244	−	0.777207i	$-0.283364\pi$
$857$	2.70584e7	1.25849	0.629244	+	0.777207i	$0.283364\pi$
$858$	−5.82299e6	−0.270040
$859$	1.49195e7	0.689876	0.344938	−	0.938625i	$-0.387900\pi$
$859$	1.49195e7	0.689876	0.344938	+	0.938625i	$0.387900\pi$
$860$	3.58166e6	0.165135
$861$	−1.73575e7	−0.797959
$862$	−1.20323e7	−0.551546
$863$	120341.	0.00550032	0.00275016	−	0.999996i	$-0.499125\pi$
$863$	120341.	0.00550032	0.00275016	+	0.999996i	$0.499125\pi$
$864$	746496.	0.0340207
$865$	9.54823e6	0.433893
$866$	1.35967e7	0.616084
$867$	−1.03474e6	−0.0467502
$868$	−485415.	−0.0218683
$869$	2.17308e7	0.976172
$870$	−6.48873e6	−0.290644
$871$	2.78498e6	0.124387
$872$	1.42331e7	0.633882
$873$	1.37529e7	0.610742
$874$	2.55301e6	0.113051
$875$	−3.65801e6	−0.161519
$876$	7.15714e6	0.315123
$877$	−2.10316e7	−0.923366	−0.461683	−	0.887045i	$-0.652754\pi$
$877$	−2.10316e7	−0.923366	−0.461683	+	0.887045i	$0.652754\pi$
$878$	1.24650e7	0.545704
$879$	1.12822e7	0.492516
$880$	1.81183e6	0.0788697
$881$	1.30856e7	0.568008	0.284004	−	0.958823i	$-0.408337\pi$
$881$	1.30856e7	0.568008	0.284004	+	0.958823i	$0.408337\pi$
$882$	1.23125e7	0.532937
$883$	−4.12188e7	−1.77907	−0.889536	−	0.456865i	$-0.848972\pi$
$883$	−4.12188e7	−1.77907	−0.889536	+	0.456865i	$0.848972\pi$
$884$	−1.04427e7	−0.449450
$885$	−2.64533e6	−0.113533
$886$	−1.02989e7	−0.440765
$887$	3.80575e6	0.162417	0.0812084	−	0.996697i	$-0.474122\pi$
$887$	3.80575e6	0.162417	0.0812084	+	0.996697i	$0.474122\pi$
$888$	9.05127e6	0.385192
$889$	4.62455e7	1.96253
$890$	1.42988e7	0.605095
$891$	−1.85741e6	−0.0783814
$892$	−8.17101e6	−0.343846
$893$	−7.61251e6	−0.319447
$894$	−4.75152e6	−0.198833
$895$	−1.24751e7	−0.520578
$896$	3.83570e6	0.159615
$897$	9.09146e6	0.377270
$898$	−3.05103e7	−1.26257
$899$	−934300.	−0.0385556
$900$	810000.	0.0333333
$901$	1.27583e7	0.523578
$902$	9.32864e6	0.381770
$903$	−1.88665e7	−0.769968
$904$	1.69809e7	0.691098
$905$	1.37198e7	0.556834
$906$	−1.02718e7	−0.415746
$907$	−2.10475e7	−0.849538	−0.424769	−	0.905302i	$-0.639645\pi$
$907$	−2.10475e7	−0.849538	−0.424769	+	0.905302i	$0.639645\pi$
$908$	7.91377e6	0.318544
$909$	2.53093e6	0.101595
$910$	−1.33761e7	−0.535460
$911$	3.04476e7	1.21551	0.607753	−	0.794126i	$-0.292071\pi$
$911$	3.04476e7	1.21551	0.607753	+	0.794126i	$0.292071\pi$
$912$	831744.	0.0331133
$913$	−1.93106e7	−0.766688
$914$	2.96320e7	1.17326
$915$	7.19778e6	0.284214
$916$	−1.87740e7	−0.739296
$917$	1.30363e7	0.511954
$918$	−3.33099e6	−0.130457
$919$	−1.48226e7	−0.578944	−0.289472	−	0.957186i	$-0.593480\pi$
$919$	−1.48226e7	−0.578944	−0.289472	+	0.957186i	$0.593480\pi$
$920$	−2.82882e6	−0.110188
$921$	1.40658e7	0.546406
$922$	−8.78866e6	−0.340483
$923$	1.16972e7	0.451937
$924$	−9.54386e6	−0.367743
$925$	9.82125e6	0.377409
$926$	−1.00448e7	−0.384957
$927$	1.60648e7	0.614012
$928$	7.38273e6	0.281415
$929$	−1.52808e7	−0.580909	−0.290455	−	0.956889i	$-0.593806\pi$
$929$	−1.52808e7	−0.580909	−0.290455	+	0.956889i	$0.593806\pi$
$930$	116630.	0.00442185
$931$	1.37186e7	0.518723
$932$	−1.38463e7	−0.522147
$933$	9.65696e6	0.363192
$934$	−2.35825e7	−0.884549
$935$	−8.08469e6	−0.302437
$936$	2.96190e6	0.110505
$937$	1.66763e6	0.0620512	0.0310256	−	0.999519i	$-0.490123\pi$
$937$	1.66763e6	0.0620512	0.0310256	+	0.999519i	$0.490123\pi$
$938$	4.56457e6	0.169392
$939$	−8.91363e6	−0.329906
$940$	8.43491e6	0.311359
$941$	1.00868e7	0.371345	0.185673	−	0.982612i	$-0.440554\pi$
$941$	1.00868e7	0.371345	0.185673	+	0.982612i	$0.440554\pi$
$942$	−1.37249e7	−0.503942
$943$	−1.45649e7	−0.533368
$944$	3.00980e6	0.109928
$945$	−4.26670e6	−0.155422
$946$	1.01396e7	0.368378
$947$	−1.70197e7	−0.616704	−0.308352	−	0.951272i	$-0.599777\pi$
$947$	−1.70197e7	−0.616704	−0.308352	+	0.951272i	$0.599777\pi$
$948$	−1.10535e7	−0.399466
$949$	2.83977e7	1.02357
$950$	902500.	0.0324443
$951$	−370229.	−0.0132745
$952$	−1.71155e7	−0.612066
$953$	−2.22871e7	−0.794917	−0.397458	−	0.917620i	$-0.630108\pi$
$953$	−2.22871e7	−0.794917	−0.397458	+	0.917620i	$0.630108\pi$
$954$	−3.61869e6	−0.128730
$955$	−6.82105e6	−0.242015
$956$	−1.35990e7	−0.481240
$957$	−1.83695e7	−0.648361
$958$	1.39274e7	0.490295
$959$	5.62651e6	0.197557
$960$	−921600.	−0.0322749
$961$	−2.86124e7	−0.999413
$962$	3.59131e7	1.25117
$963$	−785602.	−0.0272984
$964$	−1.10554e7	−0.383163
$965$	−2.28959e7	−0.791478
$966$	1.49009e7	0.513771
$967$	−1.28269e7	−0.441118	−0.220559	−	0.975374i	$-0.570788\pi$
$967$	−1.28269e7	−0.441118	−0.220559	+	0.975374i	$0.570788\pi$
$968$	−5.17801e6	−0.177613
$969$	−3.71138e6	−0.126977
$970$	−1.69788e7	−0.579400
$971$	−2.42355e7	−0.824905	−0.412453	−	0.910979i	$-0.635328\pi$
$971$	−2.42355e7	−0.824905	−0.412453	+	0.910979i	$0.635328\pi$
$972$	944784.	0.0320750
$973$	1.60569e7	0.543727
$974$	−8.97554e6	−0.303154
$975$	3.21387e6	0.108272
$976$	−8.18947e6	−0.275189
$977$	4.09752e7	1.37336	0.686681	−	0.726959i	$-0.259067\pi$
$977$	4.09752e7	1.37336	0.686681	+	0.726959i	$0.259067\pi$
$978$	−8.29189e6	−0.277208
$979$	4.04795e7	1.34983
$980$	−1.52007e7	−0.505589
$981$	1.80138e7	0.597629
$982$	−3.47136e7	−1.14874
$983$	2.92008e7	0.963853	0.481927	−	0.876212i	$-0.339937\pi$
$983$	2.92008e7	0.963853	0.481927	+	0.876212i	$0.339937\pi$
$984$	−4.74508e6	−0.156227
$985$	−1.43955e7	−0.472756
$986$	−3.29430e7	−1.07912
$987$	−4.44312e7	−1.45176
$988$	3.30015e6	0.107558
$989$	−1.58311e7	−0.514659
$990$	2.29310e6	0.0743591
$991$	5.92788e6	0.191741	0.0958705	−	0.995394i	$-0.469437\pi$
$991$	5.92788e6	0.191741	0.0958705	+	0.995394i	$0.469437\pi$
$992$	−132699.	−0.00428144
$993$	9.61057e6	0.309297
$994$	1.91717e7	0.615453
$995$	1.32824e7	0.425323
$996$	9.82247e6	0.313742
$997$	−1.04533e7	−0.333054	−0.166527	−	0.986037i	$-0.553255\pi$
$997$	−1.04533e7	−0.333054	−0.166527	+	0.986037i	$0.553255\pi$
$998$	−3.46626e7	−1.10163
$999$	1.14555e7	0.363162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.p.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.p.1.5	✓	5	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +234.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +234.112 q^{7} +64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -283.098 q^{11} +144.000 q^{12} +571.355 q^{13} +936.450 q^{14} -225.000 q^{15} +256.000 q^{16} -1142.32 q^{17} +324.000 q^{18} +361.000 q^{19} -400.000 q^{20} +2107.01 q^{21} -1132.39 q^{22} +1768.01 q^{23} +576.000 q^{24} +625.000 q^{25} +2285.42 q^{26} +729.000 q^{27} +3745.80 q^{28} +7209.70 q^{29} -900.000 q^{30} -129.589 q^{31} +1024.00 q^{32} -2547.88 q^{33} -4569.26 q^{34} -5852.81 q^{35} +1296.00 q^{36} +15714.0 q^{37} +1444.00 q^{38} +5142.20 q^{39} -1600.00 q^{40} -8237.99 q^{41} +8428.05 q^{42} -8954.16 q^{43} -4529.57 q^{44} -2025.00 q^{45} +7072.05 q^{46} -21087.3 q^{47} +2304.00 q^{48} +38001.7 q^{49} +2500.00 q^{50} -10280.8 q^{51} +9141.68 q^{52} -11168.8 q^{53} +2916.00 q^{54} +7077.46 q^{55} +14983.2 q^{56} +3249.00 q^{57} +28838.8 q^{58} +11757.0 q^{59} -3600.00 q^{60} -31990.1 q^{61} -518.357 q^{62} +18963.1 q^{63} +4096.00 q^{64} -14283.9 q^{65} -10191.5 q^{66} +4874.34 q^{67} -18277.1 q^{68} +15912.1 q^{69} -23411.2 q^{70} +20472.7 q^{71} +5184.00 q^{72} +49702.4 q^{73} +62856.0 q^{74} +5625.00 q^{75} +5776.00 q^{76} -66276.8 q^{77} +20568.8 q^{78} -76760.6 q^{79} -6400.00 q^{80} +6561.00 q^{81} -32952.0 q^{82} +68211.6 q^{83} +33712.2 q^{84} +28557.9 q^{85} -35816.6 q^{86} +64887.3 q^{87} -18118.3 q^{88} -142988. q^{89} -8100.00 q^{90} +133761. q^{91} +28288.2 q^{92} -1166.30 q^{93} -84349.1 q^{94} -9025.00 q^{95} +9216.00 q^{96} +169788. q^{97} +152007. q^{98} -22931.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9	\( 5 q + 20 q^{2} + 45 q^{3} + 80 q^{4} - 125 q^{5} + 180 q^{6} + 26 q^{7} + 320 q^{8} + 405 q^{9} - 500 q^{10} - 312 q^{11} + 720 q^{12} + 1038 q^{13} + 104 q^{14} - 1125 q^{15} + 1280 q^{16} + 756 q^{17} + 1620 q^{18} + 1805 q^{19} - 2000 q^{20} + 234 q^{21} - 1248 q^{22} + 2880 q^{23} + 2880 q^{24} + 3125 q^{25} + 4152 q^{26} + 3645 q^{27} + 416 q^{28} + 7130 q^{29} - 4500 q^{30} + 9786 q^{31} + 5120 q^{32} - 2808 q^{33} + 3024 q^{34} - 650 q^{35} + 6480 q^{36} + 19942 q^{37} + 7220 q^{38} + 9342 q^{39} - 8000 q^{40} + 1444 q^{41} + 936 q^{42} + 14624 q^{43} - 4992 q^{44} - 10125 q^{45} + 11520 q^{46} + 9536 q^{47} + 11520 q^{48} + 53649 q^{49} + 12500 q^{50} + 6804 q^{51} + 16608 q^{52} + 59994 q^{53} + 14580 q^{54} + 7800 q^{55} + 1664 q^{56} + 16245 q^{57} + 28520 q^{58} + 48498 q^{59} - 18000 q^{60} + 14930 q^{61} + 39144 q^{62} + 2106 q^{63} + 20480 q^{64} - 25950 q^{65} - 11232 q^{66} + 60296 q^{67} + 12096 q^{68} + 25920 q^{69} - 2600 q^{70} + 11356 q^{71} + 25920 q^{72} + 110130 q^{73} + 79768 q^{74} + 28125 q^{75} + 28880 q^{76} + 126476 q^{77} + 37368 q^{78} + 117706 q^{79} - 32000 q^{80} + 32805 q^{81} + 5776 q^{82} + 132722 q^{83} + 3744 q^{84} - 18900 q^{85} + 58496 q^{86} + 64170 q^{87} - 19968 q^{88} + 116608 q^{89} - 40500 q^{90} + 45052 q^{91} + 46080 q^{92} + 88074 q^{93} + 38144 q^{94} - 45125 q^{95} + 46080 q^{96} + 264146 q^{97} + 214596 q^{98} - 25272 q^{99}+O(q^{100}) \) 5 * q + 20 * q^2 + 45 * q^3 + 80 * q^4 - 125 * q^5 + 180 * q^6 + 26 * q^7 + 320 * q^8 + 405 * q^9 - 500 * q^10 - 312 * q^11 + 720 * q^12 + 1038 * q^13 + 104 * q^14 - 1125 * q^15 + 1280 * q^16 + 756 * q^17 + 1620 * q^18 + 1805 * q^19 - 2000 * q^20 + 234 * q^21 - 1248 * q^22 + 2880 * q^23 + 2880 * q^24 + 3125 * q^25 + 4152 * q^26 + 3645 * q^27 + 416 * q^28 + 7130 * q^29 - 4500 * q^30 + 9786 * q^31 + 5120 * q^32 - 2808 * q^33 + 3024 * q^34 - 650 * q^35 + 6480 * q^36 + 19942 * q^37 + 7220 * q^38 + 9342 * q^39 - 8000 * q^40 + 1444 * q^41 + 936 * q^42 + 14624 * q^43 - 4992 * q^44 - 10125 * q^45 + 11520 * q^46 + 9536 * q^47 + 11520 * q^48 + 53649 * q^49 + 12500 * q^50 + 6804 * q^51 + 16608 * q^52 + 59994 * q^53 + 14580 * q^54 + 7800 * q^55 + 1664 * q^56 + 16245 * q^57 + 28520 * q^58 + 48498 * q^59 - 18000 * q^60 + 14930 * q^61 + 39144 * q^62 + 2106 * q^63 + 20480 * q^64 - 25950 * q^65 - 11232 * q^66 + 60296 * q^67 + 12096 * q^68 + 25920 * q^69 - 2600 * q^70 + 11356 * q^71 + 25920 * q^72 + 110130 * q^73 + 79768 * q^74 + 28125 * q^75 + 28880 * q^76 + 126476 * q^77 + 37368 * q^78 + 117706 * q^79 - 32000 * q^80 + 32805 * q^81 + 5776 * q^82 + 132722 * q^83 + 3744 * q^84 - 18900 * q^85 + 58496 * q^86 + 64170 * q^87 - 19968 * q^88 + 116608 * q^89 - 40500 * q^90 + 45052 * q^91 + 46080 * q^92 + 88074 * q^93 + 38144 * q^94 - 45125 * q^95 + 46080 * q^96 + 264146 * q^97 + 214596 * q^98 - 25272 * q^99

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