LMFDB - Embedded newform 570.6.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 25872x^{2} - 1407374x - 6356280 $ x^4 - 25872x^2 - 1407374x - 6356280
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.97007$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -177.358 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -177.358 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -464.803 q^{11} -144.000 q^{12} +535.413 q^{13} +709.432 q^{14} -225.000 q^{15} +256.000 q^{16} +173.676 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1596.22 q^{21} +1859.21 q^{22} +2051.32 q^{23} +576.000 q^{24} +625.000 q^{25} -2141.65 q^{26} -729.000 q^{27} -2837.73 q^{28} +6005.28 q^{29} +900.000 q^{30} -7404.30 q^{31} -1024.00 q^{32} +4183.23 q^{33} -694.704 q^{34} -4433.95 q^{35} +1296.00 q^{36} -1709.29 q^{37} -1444.00 q^{38} -4818.72 q^{39} -1600.00 q^{40} -731.943 q^{41} -6384.89 q^{42} +24127.7 q^{43} -7436.85 q^{44} +2025.00 q^{45} -8205.27 q^{46} -22819.3 q^{47} -2304.00 q^{48} +14648.8 q^{49} -2500.00 q^{50} -1563.08 q^{51} +8566.61 q^{52} -5428.32 q^{53} +2916.00 q^{54} -11620.1 q^{55} +11350.9 q^{56} -3249.00 q^{57} -24021.1 q^{58} +16791.6 q^{59} -3600.00 q^{60} +51053.5 q^{61} +29617.2 q^{62} -14366.0 q^{63} +4096.00 q^{64} +13385.3 q^{65} -16732.9 q^{66} -59420.7 q^{67} +2778.82 q^{68} -18461.9 q^{69} +17735.8 q^{70} +5792.90 q^{71} -5184.00 q^{72} -56301.8 q^{73} +6837.17 q^{74} -5625.00 q^{75} +5776.00 q^{76} +82436.5 q^{77} +19274.9 q^{78} +71932.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} +2927.77 q^{82} +83624.9 q^{83} +25539.5 q^{84} +4341.90 q^{85} -96510.7 q^{86} -54047.5 q^{87} +29747.4 q^{88} +125338. q^{89} -8100.00 q^{90} -94959.7 q^{91} +32821.1 q^{92} +66638.7 q^{93} +91277.1 q^{94} +9025.00 q^{95} +9216.00 q^{96} +19704.2 q^{97} -58595.4 q^{98} -37649.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 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 - 108 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 246 q^{11} - 576 q^{12} + 640 q^{13} + 432 q^{14} - 900 q^{15} + 1024 q^{16} - 612 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 972 q^{21} + 984 q^{22} - 1242 q^{23} + 2304 q^{24} + 2500 q^{25} - 2560 q^{26} - 2916 q^{27} - 1728 q^{28} - 6230 q^{29} + 3600 q^{30} - 11360 q^{31} - 4096 q^{32} + 2214 q^{33} + 2448 q^{34} - 2700 q^{35} + 5184 q^{36} - 4792 q^{37} - 5776 q^{38} - 5760 q^{39} - 6400 q^{40} + 9170 q^{41} - 3888 q^{42} - 11412 q^{43} - 3936 q^{44} + 8100 q^{45} + 4968 q^{46} - 29858 q^{47} - 9216 q^{48} + 31092 q^{49} - 10000 q^{50} + 5508 q^{51} + 10240 q^{52} + 27498 q^{53} + 11664 q^{54} - 6150 q^{55} + 6912 q^{56} - 12996 q^{57} + 24920 q^{58} + 54984 q^{59} - 14400 q^{60} + 20868 q^{61} + 45440 q^{62} - 8748 q^{63} + 16384 q^{64} + 16000 q^{65} - 8856 q^{66} - 20244 q^{67} - 9792 q^{68} + 11178 q^{69} + 10800 q^{70} + 86864 q^{71} - 20736 q^{72} - 3728 q^{73} + 19168 q^{74} - 22500 q^{75} + 23104 q^{76} + 18796 q^{77} + 23040 q^{78} + 164192 q^{79} + 25600 q^{80} + 26244 q^{81} - 36680 q^{82} - 60506 q^{83} + 15552 q^{84} - 15300 q^{85} + 45648 q^{86} + 56070 q^{87} + 15744 q^{88} + 113798 q^{89} - 32400 q^{90} + 159528 q^{91} - 19872 q^{92} + 102240 q^{93} + 119432 q^{94} + 36100 q^{95} + 36864 q^{96} + 79440 q^{97} - 124368 q^{98} - 19926 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 246 * q^11 - 576 * q^12 + 640 * q^13 + 432 * q^14 - 900 * q^15 + 1024 * q^16 - 612 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 972 * q^21 + 984 * q^22 - 1242 * q^23 + 2304 * q^24 + 2500 * q^25 - 2560 * q^26 - 2916 * q^27 - 1728 * q^28 - 6230 * q^29 + 3600 * q^30 - 11360 * q^31 - 4096 * q^32 + 2214 * q^33 + 2448 * q^34 - 2700 * q^35 + 5184 * q^36 - 4792 * q^37 - 5776 * q^38 - 5760 * q^39 - 6400 * q^40 + 9170 * q^41 - 3888 * q^42 - 11412 * q^43 - 3936 * q^44 + 8100 * q^45 + 4968 * q^46 - 29858 * q^47 - 9216 * q^48 + 31092 * q^49 - 10000 * q^50 + 5508 * q^51 + 10240 * q^52 + 27498 * q^53 + 11664 * q^54 - 6150 * q^55 + 6912 * q^56 - 12996 * q^57 + 24920 * q^58 + 54984 * q^59 - 14400 * q^60 + 20868 * q^61 + 45440 * q^62 - 8748 * q^63 + 16384 * q^64 + 16000 * q^65 - 8856 * q^66 - 20244 * q^67 - 9792 * q^68 + 11178 * q^69 + 10800 * q^70 + 86864 * q^71 - 20736 * q^72 - 3728 * q^73 + 19168 * q^74 - 22500 * q^75 + 23104 * q^76 + 18796 * q^77 + 23040 * q^78 + 164192 * q^79 + 25600 * q^80 + 26244 * q^81 - 36680 * q^82 - 60506 * q^83 + 15552 * q^84 - 15300 * q^85 + 45648 * q^86 + 56070 * q^87 + 15744 * q^88 + 113798 * q^89 - 32400 * q^90 + 159528 * q^91 - 19872 * q^92 + 102240 * q^93 + 119432 * q^94 + 36100 * q^95 + 36864 * q^96 + 79440 * q^97 - 124368 * q^98 - 19926 * 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
$7$	−177.358	−1.36806	−0.684031	−	0.729453i	$-0.739775\pi$
$7$	−177.358	−1.36806	−0.684031	+	0.729453i	$0.739775\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−100.000	−0.316228
$11$	−464.803	−1.15821	−0.579105	−	0.815253i	$-0.696598\pi$
$11$	−464.803	−1.15821	−0.579105	+	0.815253i	$0.696598\pi$
$12$	−144.000	−0.288675
$13$	535.413	0.878680	0.439340	−	0.898321i	$-0.355212\pi$
$13$	535.413	0.878680	0.439340	+	0.898321i	$0.355212\pi$
$14$	709.432	0.967365
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	173.676	0.145753	0.0728765	−	0.997341i	$-0.476782\pi$
$17$	173.676	0.145753	0.0728765	+	0.997341i	$0.476782\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	400.000	0.223607
$21$	1596.22	0.789851
$22$	1859.21	0.818978
$23$	2051.32	0.808562	0.404281	−	0.914635i	$-0.367522\pi$
$23$	2051.32	0.808562	0.404281	+	0.914635i	$0.367522\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	−2141.65	−0.621320
$27$	−729.000	−0.192450
$28$	−2837.73	−0.684031
$29$	6005.28	1.32598	0.662992	−	0.748627i	$-0.269287\pi$
$29$	6005.28	1.32598	0.662992	+	0.748627i	$0.269287\pi$
$30$	900.000	0.182574
$31$	−7404.30	−1.38382	−0.691911	−	0.721983i	$-0.743231\pi$
$31$	−7404.30	−1.38382	−0.691911	+	0.721983i	$0.743231\pi$
$32$	−1024.00	−0.176777
$33$	4183.23	0.668693
$34$	−694.704	−0.103063
$35$	−4433.95	−0.611816
$36$	1296.00	0.166667
$37$	−1709.29	−0.205264	−0.102632	−	0.994719i	$-0.532726\pi$
$37$	−1709.29	−0.205264	−0.102632	+	0.994719i	$0.532726\pi$
$38$	−1444.00	−0.162221
$39$	−4818.72	−0.507306
$40$	−1600.00	−0.158114
$41$	−731.943	−0.0680013	−0.0340007	−	0.999422i	$-0.510825\pi$
$41$	−731.943	−0.0680013	−0.0340007	+	0.999422i	$0.510825\pi$
$42$	−6384.89	−0.558509
$43$	24127.7	1.98996	0.994980	−	0.100070i	$-0.0319068\pi$
$43$	24127.7	1.98996	0.994980	+	0.100070i	$0.0319068\pi$
$44$	−7436.85	−0.579105
$45$	2025.00	0.149071
$46$	−8205.27	−0.571739
$47$	−22819.3	−1.50681	−0.753403	−	0.657560i	$-0.771589\pi$
$47$	−22819.3	−1.50681	−0.753403	+	0.657560i	$0.771589\pi$
$48$	−2304.00	−0.144338
$49$	14648.8	0.871592
$50$	−2500.00	−0.141421
$51$	−1563.08	−0.0841505
$52$	8566.61	0.439340
$53$	−5428.32	−0.265446	−0.132723	−	0.991153i	$-0.542372\pi$
$53$	−5428.32	−0.265446	−0.132723	+	0.991153i	$0.542372\pi$
$54$	2916.00	0.136083
$55$	−11620.1	−0.517967
$56$	11350.9	0.483683
$57$	−3249.00	−0.132453
$58$	−24021.1	−0.937612
$59$	16791.6	0.628003	0.314001	−	0.949423i	$-0.398330\pi$
$59$	16791.6	0.628003	0.314001	+	0.949423i	$0.398330\pi$
$60$	−3600.00	−0.129099
$61$	51053.5	1.75671	0.878357	−	0.478005i	$-0.158640\pi$
$61$	51053.5	1.75671	0.878357	+	0.478005i	$0.158640\pi$
$62$	29617.2	0.978509
$63$	−14366.0	−0.456020
$64$	4096.00	0.125000
$65$	13385.3	0.392957
$66$	−16732.9	−0.472837
$67$	−59420.7	−1.61715	−0.808576	−	0.588391i	$-0.799762\pi$
$67$	−59420.7	−1.61715	−0.808576	+	0.588391i	$0.799762\pi$
$68$	2778.82	0.0728765
$69$	−18461.9	−0.466823
$70$	17735.8	0.432619
$71$	5792.90	0.136380	0.0681900	−	0.997672i	$-0.478278\pi$
$71$	5792.90	0.136380	0.0681900	+	0.997672i	$0.478278\pi$
$72$	−5184.00	−0.117851
$73$	−56301.8	−1.23656	−0.618280	−	0.785958i	$-0.712170\pi$
$73$	−56301.8	−1.23656	−0.618280	+	0.785958i	$0.712170\pi$
$74$	6837.17	0.145143
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	82436.5	1.58450
$78$	19274.9	0.358719
$79$	71932.4	1.29675	0.648376	−	0.761321i	$-0.275449\pi$
$79$	71932.4	1.29675	0.648376	+	0.761321i	$0.275449\pi$
$80$	6400.00	0.111803
$81$	6561.00	0.111111
$82$	2927.77	0.0480842
$83$	83624.9	1.33242	0.666209	−	0.745766i	$-0.267916\pi$
$83$	83624.9	1.33242	0.666209	+	0.745766i	$0.267916\pi$
$84$	25539.5	0.394925
$85$	4341.90	0.0651827
$86$	−96510.7	−1.40711
$87$	−54047.5	−0.765557
$88$	29747.4	0.409489
$89$	125338.	1.67729	0.838647	−	0.544675i	$-0.183347\pi$
$89$	125338.	1.67729	0.838647	+	0.544675i	$0.183347\pi$
$90$	−8100.00	−0.105409
$91$	−94959.7	−1.20209
$92$	32821.1	0.404281
$93$	66638.7	0.798950
$94$	91277.1	1.06547
$95$	9025.00	0.102598
$96$	9216.00	0.102062
$97$	19704.2	0.212633	0.106316	−	0.994332i	$-0.466094\pi$
$97$	19704.2	0.212633	0.106316	+	0.994332i	$0.466094\pi$
$98$	−58595.4	−0.616308
$99$	−37649.1	−0.386070
$100$	10000.0	0.100000
$101$	−70891.2	−0.691495	−0.345747	−	0.938328i	$-0.612375\pi$
$101$	−70891.2	−0.691495	−0.345747	+	0.938328i	$0.612375\pi$
$102$	6252.34	0.0595034
$103$	−11519.4	−0.106989	−0.0534944	−	0.998568i	$-0.517036\pi$
$103$	−11519.4	−0.106989	−0.0534944	+	0.998568i	$0.517036\pi$
$104$	−34266.4	−0.310660
$105$	39905.5	0.353232
$106$	21713.3	0.187698
$107$	−24983.5	−0.210957	−0.105479	−	0.994422i	$-0.533637\pi$
$107$	−24983.5	−0.210957	−0.105479	+	0.994422i	$0.533637\pi$
$108$	−11664.0	−0.0962250
$109$	84410.5	0.680504	0.340252	−	0.940334i	$-0.389488\pi$
$109$	84410.5	0.680504	0.340252	+	0.940334i	$0.389488\pi$
$110$	46480.3	0.366258
$111$	15383.6	0.118509
$112$	−45403.6	−0.342015
$113$	−204453.	−1.50625	−0.753126	−	0.657877i	$-0.771455\pi$
$113$	−204453.	−1.50625	−0.753126	+	0.657877i	$0.771455\pi$
$114$	12996.0	0.0936586
$115$	51282.9	0.361600
$116$	96084.4	0.662992
$117$	43368.5	0.292893
$118$	−67166.3	−0.444065
$119$	−30802.8	−0.199399
$120$	14400.0	0.0912871
$121$	54991.1	0.341451
$122$	−204214.	−1.24218
$123$	6587.48	0.0392606
$124$	−118469.	−0.691911
$125$	15625.0	0.0894427
$126$	57464.0	0.322455
$127$	−330032.	−1.81571	−0.907857	−	0.419280i	$-0.862282\pi$
$127$	−330032.	−1.81571	−0.907857	+	0.419280i	$0.862282\pi$
$128$	−16384.0	−0.0883883
$129$	−217149.	−1.14890
$130$	−53541.3	−0.277863
$131$	−234542.	−1.19411	−0.597053	−	0.802202i	$-0.703662\pi$
$131$	−234542.	−1.19411	−0.597053	+	0.802202i	$0.703662\pi$
$132$	66931.7	0.334347
$133$	−64026.2	−0.313855
$134$	237683.	1.14350
$135$	−18225.0	−0.0860663
$136$	−11115.3	−0.0515315
$137$	−221612.	−1.00877	−0.504385	−	0.863479i	$-0.668281\pi$
$137$	−221612.	−1.00877	−0.504385	+	0.863479i	$0.668281\pi$
$138$	73847.4	0.330094
$139$	−85413.0	−0.374962	−0.187481	−	0.982268i	$-0.560032\pi$
$139$	−85413.0	−0.374962	−0.187481	+	0.982268i	$0.560032\pi$
$140$	−70943.2	−0.305908
$141$	205373.	0.869954
$142$	−23171.6	−0.0964352
$143$	−248862.	−1.01770
$144$	20736.0	0.0833333
$145$	150132.	0.592998
$146$	225207.	0.874380
$147$	−131840.	−0.503214
$148$	−27348.7	−0.102632
$149$	456176.	1.68332	0.841661	−	0.540007i	$-0.181578\pi$
$149$	456176.	1.68332	0.841661	+	0.540007i	$0.181578\pi$
$150$	22500.0	0.0816497
$151$	8751.42	0.0312346	0.0156173	−	0.999878i	$-0.495029\pi$
$151$	8751.42	0.0312346	0.0156173	+	0.999878i	$0.495029\pi$
$152$	−23104.0	−0.0811107
$153$	14067.8	0.0485843
$154$	−329746.	−1.12041
$155$	−185108.	−0.618864
$156$	−77099.5	−0.253653
$157$	−86034.8	−0.278564	−0.139282	−	0.990253i	$-0.544479\pi$
$157$	−86034.8	−0.278564	−0.139282	+	0.990253i	$0.544479\pi$
$158$	−287730.	−0.916942
$159$	48854.9	0.153255
$160$	−25600.0	−0.0790569
$161$	−363817.	−1.10616
$162$	−26244.0	−0.0785674
$163$	281927.	0.831127	0.415563	−	0.909564i	$-0.363584\pi$
$163$	281927.	0.831127	0.415563	+	0.909564i	$0.363584\pi$
$164$	−11711.1	−0.0340007
$165$	104581.	0.299049
$166$	−334499.	−0.942161
$167$	−467561.	−1.29732	−0.648660	−	0.761078i	$-0.724670\pi$
$167$	−467561.	−1.29732	−0.648660	+	0.761078i	$0.724670\pi$
$168$	−102158.	−0.279254
$169$	−84625.9	−0.227922
$170$	−17367.6	−0.0460911
$171$	29241.0	0.0764719
$172$	386043.	0.994980
$173$	−518177.	−1.31632	−0.658162	−	0.752876i	$-0.728666\pi$
$173$	−518177.	−1.31632	−0.658162	+	0.752876i	$0.728666\pi$
$174$	216190.	0.541330
$175$	−110849.	−0.273612
$176$	−118990.	−0.289553
$177$	−151124.	−0.362577
$178$	−501354.	−1.18603
$179$	−740069.	−1.72639	−0.863196	−	0.504869i	$-0.831541\pi$
$179$	−740069.	−1.72639	−0.863196	+	0.504869i	$0.831541\pi$
$180$	32400.0	0.0745356
$181$	797442.	1.80927	0.904633	−	0.426190i	$-0.140145\pi$
$181$	797442.	1.80927	0.904633	+	0.426190i	$0.140145\pi$
$182$	379839.	0.850004
$183$	−459482.	−1.01424
$184$	−131284.	−0.285870
$185$	−42732.3	−0.0917968
$186$	−266555.	−0.564943
$187$	−80725.2	−0.168813
$188$	−365108.	−0.753403
$189$	129294.	0.263284
$190$	−36100.0	−0.0725476
$191$	−677830.	−1.34443	−0.672214	−	0.740357i	$-0.734656\pi$
$191$	−677830.	−1.34443	−0.672214	+	0.740357i	$0.734656\pi$
$192$	−36864.0	−0.0721688
$193$	−599323.	−1.15816	−0.579079	−	0.815271i	$-0.696588\pi$
$193$	−599323.	−1.15816	−0.579079	+	0.815271i	$0.696588\pi$
$194$	−78816.9	−0.150354
$195$	−120468.	−0.226874
$196$	234381.	0.435796
$197$	−913469.	−1.67698	−0.838490	−	0.544916i	$-0.816561\pi$
$197$	−913469.	−1.67698	−0.838490	+	0.544916i	$0.816561\pi$
$198$	150596.	0.272993
$199$	−777236.	−1.39130	−0.695650	−	0.718381i	$-0.744883\pi$
$199$	−777236.	−1.39130	−0.695650	+	0.718381i	$0.744883\pi$
$200$	−40000.0	−0.0707107
$201$	534787.	0.933664
$202$	283565.	0.488961
$203$	−1.06508e6	−1.81403
$204$	−25009.3	−0.0420753
$205$	−18298.6	−0.0304111
$206$	46077.8	0.0756525
$207$	166157.	0.269521
$208$	137066.	0.219670
$209$	−167794.	−0.265712
$210$	−159622.	−0.249773
$211$	438515.	0.678076	0.339038	−	0.940773i	$-0.389898\pi$
$211$	438515.	0.678076	0.339038	+	0.940773i	$0.389898\pi$
$212$	−86853.1	−0.132723
$213$	−52136.1	−0.0787390
$214$	99934.1	0.149169
$215$	603192.	0.889937
$216$	46656.0	0.0680414
$217$	1.31321e6	1.89315
$218$	−337642.	−0.481189
$219$	506716.	0.713928
$220$	−185921.	−0.258984
$221$	92988.4	0.128070
$222$	−61534.6	−0.0837986
$223$	253681.	0.341607	0.170803	−	0.985305i	$-0.445364\pi$
$223$	253681.	0.341607	0.170803	+	0.985305i	$0.445364\pi$
$224$	181615.	0.241841
$225$	50625.0	0.0666667
$226$	817812.	1.06508
$227$	−436025.	−0.561625	−0.280813	−	0.959763i	$-0.590604\pi$
$227$	−436025.	−0.561625	−0.280813	+	0.959763i	$0.590604\pi$
$228$	−51984.0	−0.0662266
$229$	1.00535e6	1.26685	0.633427	−	0.773802i	$-0.281647\pi$
$229$	1.00535e6	1.26685	0.633427	+	0.773802i	$0.281647\pi$
$230$	−205132.	−0.255690
$231$	−741929.	−0.914813
$232$	−384338.	−0.468806
$233$	1.26085e6	1.52151	0.760755	−	0.649039i	$-0.224829\pi$
$233$	1.26085e6	1.52151	0.760755	+	0.649039i	$0.224829\pi$
$234$	−173474.	−0.207107
$235$	−570482.	−0.673864
$236$	268665.	0.314001
$237$	−647391.	−0.748680
$238$	123211.	0.140996
$239$	−783233.	−0.886944	−0.443472	−	0.896288i	$-0.646253\pi$
$239$	−783233.	−0.886944	−0.443472	+	0.896288i	$0.646253\pi$
$240$	−57600.0	−0.0645497
$241$	683254.	0.757773	0.378887	−	0.925443i	$-0.376307\pi$
$241$	683254.	0.757773	0.378887	+	0.925443i	$0.376307\pi$
$242$	−219964.	−0.241443
$243$	−59049.0	−0.0641500
$244$	816857.	0.878357
$245$	366221.	0.389788
$246$	−26349.9	−0.0277614
$247$	193284.	0.201583
$248$	473875.	0.489255
$249$	−752624.	−0.769271
$250$	−62500.0	−0.0632456
$251$	−159091.	−0.159390	−0.0796952	−	0.996819i	$-0.525395\pi$
$251$	−159091.	−0.159390	−0.0796952	+	0.996819i	$0.525395\pi$
$252$	−229856.	−0.228010
$253$	−953459.	−0.936485
$254$	1.32013e6	1.28390
$255$	−39077.1	−0.0376333
$256$	65536.0	0.0625000
$257$	−1.38427e6	−1.30734	−0.653670	−	0.756780i	$-0.726771\pi$
$257$	−1.38427e6	−1.30734	−0.653670	+	0.756780i	$0.726771\pi$
$258$	868597.	0.812398
$259$	303157.	0.280813
$260$	214165.	0.196479
$261$	486427.	0.441994
$262$	938170.	0.844361
$263$	538976.	0.480486	0.240243	−	0.970713i	$-0.422773\pi$
$263$	538976.	0.480486	0.240243	+	0.970713i	$0.422773\pi$
$264$	−267727.	−0.236419
$265$	−135708.	−0.118711
$266$	256105.	0.221929
$267$	−1.12805e6	−0.968386
$268$	−950732.	−0.808576
$269$	−302609.	−0.254977	−0.127489	−	0.991840i	$-0.540692\pi$
$269$	−302609.	−0.254977	−0.127489	+	0.991840i	$0.540692\pi$
$270$	72900.0	0.0608581
$271$	806768.	0.667306	0.333653	−	0.942696i	$-0.391719\pi$
$271$	806768.	0.667306	0.333653	+	0.942696i	$0.391719\pi$
$272$	44461.1	0.0364383
$273$	854638.	0.694026
$274$	886449.	0.713308
$275$	−290502.	−0.231642
$276$	−295390.	−0.233412
$277$	−1.52143e6	−1.19139	−0.595694	−	0.803211i	$-0.703123\pi$
$277$	−1.52143e6	−1.19139	−0.595694	+	0.803211i	$0.703123\pi$
$278$	341652.	0.265138
$279$	−599749.	−0.461274
$280$	283773.	0.216309
$281$	−2.17452e6	−1.64285	−0.821425	−	0.570316i	$-0.806821\pi$
$281$	−2.17452e6	−1.64285	−0.821425	+	0.570316i	$0.806821\pi$
$282$	−821494.	−0.615151
$283$	1.21558e6	0.902230	0.451115	−	0.892466i	$-0.351026\pi$
$283$	1.21558e6	0.902230	0.451115	+	0.892466i	$0.351026\pi$
$284$	92686.5	0.0681900
$285$	−81225.0	−0.0592349
$286$	995447.	0.719620
$287$	129816.	0.0930300
$288$	−82944.0	−0.0589256
$289$	−1.38969e6	−0.978756
$290$	−600528.	−0.419313
$291$	−177338.	−0.122764
$292$	−900829.	−0.618280
$293$	−649268.	−0.441830	−0.220915	−	0.975293i	$-0.570904\pi$
$293$	−649268.	−0.441830	−0.220915	+	0.975293i	$0.570904\pi$
$294$	527358.	0.355826
$295$	419789.	0.280851
$296$	109395.	0.0725717
$297$	338842.	0.222898
$298$	−1.82471e6	−1.19029
$299$	1.09830e6	0.710467
$300$	−90000.0	−0.0577350
$301$	−4.27924e6	−2.72239
$302$	−35005.7	−0.0220862
$303$	638021.	0.399235
$304$	92416.0	0.0573539
$305$	1.27634e6	0.785627
$306$	−56271.0	−0.0343543
$307$	2.24128e6	1.35722	0.678610	−	0.734499i	$-0.262583\pi$
$307$	2.24128e6	1.35722	0.678610	+	0.734499i	$0.262583\pi$
$308$	1.31898e6	0.792251
$309$	103675.	0.0617700
$310$	740430.	0.437603
$311$	−2.11332e6	−1.23898	−0.619490	−	0.785005i	$-0.712661\pi$
$311$	−2.11332e6	−1.23898	−0.619490	+	0.785005i	$0.712661\pi$
$312$	308398.	0.179360
$313$	−135006.	−0.0778920	−0.0389460	−	0.999241i	$-0.512400\pi$
$313$	−135006.	−0.0778920	−0.0389460	+	0.999241i	$0.512400\pi$
$314$	344139.	0.196974
$315$	−359150.	−0.203939
$316$	1.15092e6	0.648376
$317$	−2.91526e6	−1.62941	−0.814704	−	0.579877i	$-0.803101\pi$
$317$	−2.91526e6	−1.62941	−0.814704	+	0.579877i	$0.803101\pi$
$318$	−195420.	−0.108368
$319$	−2.79127e6	−1.53577
$320$	102400.	0.0559017
$321$	224852.	0.121796
$322$	1.45527e6	0.782175
$323$	62697.0	0.0334380
$324$	104976.	0.0555556
$325$	334633.	0.175736
$326$	−1.12771e6	−0.587695
$327$	−759695.	−0.392889
$328$	46844.3	0.0240421
$329$	4.04718e6	2.06140
$330$	−418323.	−0.211459
$331$	−1.07282e6	−0.538214	−0.269107	−	0.963110i	$-0.586729\pi$
$331$	−1.07282e6	−0.538214	−0.269107	+	0.963110i	$0.586729\pi$
$332$	1.33800e6	0.666209
$333$	−138453.	−0.0684213
$334$	1.87024e6	0.917344
$335$	−1.48552e6	−0.723213
$336$	408633.	0.197463
$337$	2.79253e6	1.33944	0.669720	−	0.742613i	$-0.266414\pi$
$337$	2.79253e6	1.33944	0.669720	+	0.742613i	$0.266414\pi$
$338$	338504.	0.161165
$339$	1.84008e6	0.869634
$340$	69470.4	0.0325914
$341$	3.44154e6	1.60276
$342$	−116964.	−0.0540738
$343$	382767.	0.175671
$344$	−1.54417e6	−0.703557
$345$	−461546.	−0.208770
$346$	2.07271e6	0.930782
$347$	551516.	0.245886	0.122943	−	0.992414i	$-0.460767\pi$
$347$	551516.	0.245886	0.122943	+	0.992414i	$0.460767\pi$
$348$	−864760.	−0.382778
$349$	−3.04968e6	−1.34027	−0.670133	−	0.742241i	$-0.733763\pi$
$349$	−3.04968e6	−1.34027	−0.670133	+	0.742241i	$0.733763\pi$
$350$	443395.	0.193473
$351$	−390316.	−0.169102
$352$	475959.	0.204745
$353$	−2.24249e6	−0.957842	−0.478921	−	0.877858i	$-0.658972\pi$
$353$	−2.24249e6	−0.957842	−0.478921	+	0.877858i	$0.658972\pi$
$354$	604497.	0.256381
$355$	144823.	0.0609910
$356$	2.00541e6	0.838647
$357$	277225.	0.115123
$358$	2.96027e6	1.22074
$359$	−3.29132e6	−1.34782	−0.673912	−	0.738811i	$-0.735387\pi$
$359$	−3.29132e6	−1.34782	−0.673912	+	0.738811i	$0.735387\pi$
$360$	−129600.	−0.0527046
$361$	130321.	0.0526316
$362$	−3.18977e6	−1.27934
$363$	−494920.	−0.197137
$364$	−1.51936e6	−0.601044
$365$	−1.40755e6	−0.553006
$366$	1.83793e6	0.717176
$367$	280146.	0.108572	0.0542862	−	0.998525i	$-0.482712\pi$
$367$	280146.	0.108572	0.0542862	+	0.998525i	$0.482712\pi$
$368$	525137.	0.202140
$369$	−59287.4	−0.0226671
$370$	170929.	0.0649101
$371$	962756.	0.363146
$372$	1.06622e6	0.399475
$373$	2.44113e6	0.908488	0.454244	−	0.890877i	$-0.349909\pi$
$373$	2.44113e6	0.908488	0.454244	+	0.890877i	$0.349909\pi$
$374$	322901.	0.119369
$375$	−140625.	−0.0516398
$376$	1.46043e6	0.532736
$377$	3.21530e6	1.16511
$378$	−517176.	−0.186170
$379$	1.08801e6	0.389078	0.194539	−	0.980895i	$-0.437679\pi$
$379$	1.08801e6	0.389078	0.194539	+	0.980895i	$0.437679\pi$
$380$	144400.	0.0512989
$381$	2.97029e6	1.04830
$382$	2.71132e6	0.950654
$383$	351536.	0.122454	0.0612270	−	0.998124i	$-0.480499\pi$
$383$	351536.	0.122454	0.0612270	+	0.998124i	$0.480499\pi$
$384$	147456.	0.0510310
$385$	2.06091e6	0.708611
$386$	2.39729e6	0.818942
$387$	1.95434e6	0.663320
$388$	315268.	0.106316
$389$	2.45203e6	0.821582	0.410791	−	0.911729i	$-0.365253\pi$
$389$	2.45203e6	0.821582	0.410791	+	0.911729i	$0.365253\pi$
$390$	481872.	0.160424
$391$	356265.	0.117850
$392$	−937526.	−0.308154
$393$	2.11088e6	0.689418
$394$	3.65387e6	1.18580
$395$	1.79831e6	0.579925
$396$	−602385.	−0.193035
$397$	3.67908e6	1.17156	0.585778	−	0.810472i	$-0.300789\pi$
$397$	3.67908e6	1.17156	0.585778	+	0.810472i	$0.300789\pi$
$398$	3.10895e6	0.983797
$399$	576236.	0.181204
$400$	160000.	0.0500000
$401$	−4.33449e6	−1.34610	−0.673049	−	0.739598i	$-0.735016\pi$
$401$	−4.33449e6	−1.34610	−0.673049	+	0.739598i	$0.735016\pi$
$402$	−2.13915e6	−0.660200
$403$	−3.96436e6	−1.21594
$404$	−1.13426e6	−0.345747
$405$	164025.	0.0496904
$406$	4.26033e6	1.28271
$407$	794485.	0.237739
$408$	100037.	0.0297517
$409$	−1.34530e6	−0.397658	−0.198829	−	0.980034i	$-0.563714\pi$
$409$	−1.34530e6	−0.397658	−0.198829	+	0.980034i	$0.563714\pi$
$410$	73194.3	0.0215039
$411$	1.99451e6	0.582414
$412$	−184311.	−0.0534944
$413$	−2.97812e6	−0.859146
$414$	−664627.	−0.190580
$415$	2.09062e6	0.595875
$416$	−548263.	−0.155330
$417$	768717.	0.216484
$418$	671176.	0.187887
$419$	3.05787e6	0.850911	0.425455	−	0.904979i	$-0.360114\pi$
$419$	3.05787e6	0.850911	0.425455	+	0.904979i	$0.360114\pi$
$420$	638489.	0.176616
$421$	−3.38663e6	−0.931243	−0.465621	−	0.884984i	$-0.654169\pi$
$421$	−3.38663e6	−0.931243	−0.465621	+	0.884984i	$0.654169\pi$
$422$	−1.75406e6	−0.479472
$423$	−1.84836e6	−0.502268
$424$	347413.	0.0938492
$425$	108548.	0.0291506
$426$	208545.	0.0556769
$427$	−9.05475e6	−2.40329
$428$	−399737.	−0.105479
$429$	2.23976e6	0.587567
$430$	−2.41277e6	−0.629281
$431$	3.91738e6	1.01579	0.507893	−	0.861420i	$-0.330425\pi$
$431$	3.91738e6	1.01579	0.507893	+	0.861420i	$0.330425\pi$
$432$	−186624.	−0.0481125
$433$	−724664.	−0.185745	−0.0928724	−	0.995678i	$-0.529605\pi$
$433$	−724664.	−0.185745	−0.0928724	+	0.995678i	$0.529605\pi$
$434$	−5.25285e6	−1.33866
$435$	−1.35119e6	−0.342367
$436$	1.35057e6	0.340252
$437$	740525.	0.185497
$438$	−2.02687e6	−0.504823
$439$	524470.	0.129885	0.0649426	−	0.997889i	$-0.479314\pi$
$439$	524470.	0.129885	0.0649426	+	0.997889i	$0.479314\pi$
$440$	743685.	0.183129
$441$	1.18656e6	0.290531
$442$	−371954.	−0.0905593
$443$	−4.67976e6	−1.13296	−0.566480	−	0.824076i	$-0.691695\pi$
$443$	−4.67976e6	−1.13296	−0.566480	+	0.824076i	$0.691695\pi$
$444$	246138.	0.0592545
$445$	3.13346e6	0.750109
$446$	−1.01473e6	−0.241552
$447$	−4.10559e6	−0.971866
$448$	−726458.	−0.171008
$449$	5.36687e6	1.25634	0.628168	−	0.778078i	$-0.283805\pi$
$449$	5.36687e6	1.25634	0.628168	+	0.778078i	$0.283805\pi$
$450$	−202500.	−0.0471405
$451$	340209.	0.0787598
$452$	−3.27125e6	−0.753126
$453$	−78762.8	−0.0180333
$454$	1.74410e6	0.397129
$455$	−2.37399e6	−0.537590
$456$	207936.	0.0468293
$457$	3.69159e6	0.826842	0.413421	−	0.910540i	$-0.364334\pi$
$457$	3.69159e6	0.826842	0.413421	+	0.910540i	$0.364334\pi$
$458$	−4.02138e6	−0.895802
$459$	−126610.	−0.0280502
$460$	820527.	0.180800
$461$	−4.24028e6	−0.929272	−0.464636	−	0.885502i	$-0.653815\pi$
$461$	−4.24028e6	−0.929272	−0.464636	+	0.885502i	$0.653815\pi$
$462$	2.96772e6	0.646871
$463$	2.98697e6	0.647557	0.323779	−	0.946133i	$-0.395047\pi$
$463$	2.98697e6	0.647557	0.323779	+	0.946133i	$0.395047\pi$
$464$	1.53735e6	0.331496
$465$	1.66597e6	0.357301
$466$	−5.04341e6	−1.07587
$467$	3.91149e6	0.829947	0.414974	−	0.909833i	$-0.363791\pi$
$467$	3.91149e6	0.829947	0.414974	+	0.909833i	$0.363791\pi$
$468$	693895.	0.146447
$469$	1.05387e7	2.21236
$470$	2.28193e6	0.476494
$471$	774313.	0.160829
$472$	−1.07466e6	−0.222032
$473$	−1.12146e7	−2.30479
$474$	2.58957e6	0.529397
$475$	225625.	0.0458831
$476$	−492845.	−0.0996995
$477$	−439694.	−0.0884819
$478$	3.13293e6	0.627164
$479$	−4.07717e6	−0.811933	−0.405966	−	0.913888i	$-0.633065\pi$
$479$	−4.07717e6	−0.811933	−0.405966	+	0.913888i	$0.633065\pi$
$480$	230400.	0.0456435
$481$	−915178.	−0.180361
$482$	−2.73301e6	−0.535827
$483$	3.27436e6	0.638643
$484$	879857.	0.170726
$485$	492606.	0.0950923
$486$	236196.	0.0453609
$487$	4.37454e6	0.835815	0.417907	−	0.908490i	$-0.362764\pi$
$487$	4.37454e6	0.835815	0.417907	+	0.908490i	$0.362764\pi$
$488$	−3.26743e6	−0.621092
$489$	−2.53734e6	−0.479851
$490$	−1.46488e6	−0.275621
$491$	8.45256e6	1.58228	0.791142	−	0.611632i	$-0.209487\pi$
$491$	8.45256e6	1.58228	0.791142	+	0.611632i	$0.209487\pi$
$492$	105400.	0.0196303
$493$	1.04297e6	0.193266
$494$	−773136.	−0.142541
$495$	−941227.	−0.172656
$496$	−1.89550e6	−0.345955
$497$	−1.02742e6	−0.186576
$498$	3.01049e6	0.543957
$499$	462733.	0.0831916	0.0415958	−	0.999135i	$-0.486756\pi$
$499$	462733.	0.0831916	0.0415958	+	0.999135i	$0.486756\pi$
$500$	250000.	0.0447214
$501$	4.20805e6	0.749008
$502$	636365.	0.112706
$503$	−4.52443e6	−0.797341	−0.398671	−	0.917094i	$-0.630528\pi$
$503$	−4.52443e6	−0.797341	−0.398671	+	0.917094i	$0.630528\pi$
$504$	919424.	0.161228
$505$	−1.77228e6	−0.309246
$506$	3.81383e6	0.662195
$507$	761633.	0.131591
$508$	−5.28052e6	−0.907857
$509$	−3.31915e6	−0.567848	−0.283924	−	0.958847i	$-0.591636\pi$
$509$	−3.31915e6	−0.567848	−0.283924	+	0.958847i	$0.591636\pi$
$510$	156308.	0.0266107
$511$	9.98557e6	1.69169
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	5.53708e6	0.924428
$515$	−287986.	−0.0478468
$516$	−3.47439e6	−0.574452
$517$	1.06065e7	1.74520
$518$	−1.21263e6	−0.198565
$519$	4.66360e6	0.759981
$520$	−856661.	−0.138931
$521$	1.17275e7	1.89282	0.946412	−	0.322962i	$-0.104679\pi$
$521$	1.17275e7	1.89282	0.946412	+	0.322962i	$0.104679\pi$
$522$	−1.94571e6	−0.312537
$523$	−1.06231e7	−1.69823	−0.849115	−	0.528208i	$-0.822864\pi$
$523$	−1.06231e7	−1.69823	−0.849115	+	0.528208i	$0.822864\pi$
$524$	−3.75268e6	−0.597053
$525$	997638.	0.157970
$526$	−2.15591e6	−0.339755
$527$	−1.28595e6	−0.201696
$528$	1.07091e6	0.167173
$529$	−2.22844e6	−0.346228
$530$	542832.	0.0839413
$531$	1.36012e6	0.209334
$532$	−1.02442e6	−0.156927
$533$	−391892.	−0.0597514
$534$	4.51218e6	0.684752
$535$	−624588.	−0.0943429
$536$	3.80293e6	0.571750
$537$	6.66062e6	0.996733
$538$	1.21044e6	0.180296
$539$	−6.80883e6	−1.00949
$540$	−291600.	−0.0430331
$541$	3.79848e6	0.557977	0.278989	−	0.960294i	$-0.410001\pi$
$541$	3.79848e6	0.557977	0.278989	+	0.960294i	$0.410001\pi$
$542$	−3.22707e6	−0.471857
$543$	−7.17698e6	−1.04458
$544$	−177844.	−0.0257657
$545$	2.11026e6	0.304330
$546$	−3.41855e6	−0.490750
$547$	4.14052e6	0.591680	0.295840	−	0.955238i	$-0.404401\pi$
$547$	4.14052e6	0.591680	0.295840	+	0.955238i	$0.404401\pi$
$548$	−3.54579e6	−0.504385
$549$	4.13534e6	0.585572
$550$	1.16201e6	0.163796
$551$	2.16790e6	0.304201
$552$	1.18156e6	0.165047
$553$	−1.27578e7	−1.77404
$554$	6.08573e6	0.842439
$555$	384591.	0.0529989
$556$	−1.36661e6	−0.187481
$557$	−1.49034e6	−0.203539	−0.101769	−	0.994808i	$-0.532450\pi$
$557$	−1.49034e6	−0.203539	−0.101769	+	0.994808i	$0.532450\pi$
$558$	2.39899e6	0.326170
$559$	1.29183e7	1.74854
$560$	−1.13509e6	−0.152954
$561$	726527.	0.0974640
$562$	8.69809e6	1.16167
$563$	206889.	0.0275085	0.0137542	−	0.999905i	$-0.495622\pi$
$563$	206889.	0.0275085	0.0137542	+	0.999905i	$0.495622\pi$
$564$	3.28597e6	0.434977
$565$	−5.11132e6	−0.673616
$566$	−4.86232e6	−0.637973
$567$	−1.16365e6	−0.152007
$568$	−370746.	−0.0482176
$569$	−882672.	−0.114293	−0.0571464	−	0.998366i	$-0.518200\pi$
$569$	−882672.	−0.114293	−0.0571464	+	0.998366i	$0.518200\pi$
$570$	324900.	0.0418854
$571$	−7.73644e6	−0.993004	−0.496502	−	0.868036i	$-0.665382\pi$
$571$	−7.73644e6	−0.993004	−0.496502	+	0.868036i	$0.665382\pi$
$572$	−3.98179e6	−0.508848
$573$	6.10047e6	0.776206
$574$	−519263.	−0.0657821
$575$	1.28207e6	0.161712
$576$	331776.	0.0416667
$577$	−1.12065e7	−1.40130	−0.700651	−	0.713504i	$-0.747107\pi$
$577$	−1.12065e7	−1.40130	−0.700651	+	0.713504i	$0.747107\pi$
$578$	5.55877e6	0.692085
$579$	5.39391e6	0.668663
$580$	2.40211e6	0.296499
$581$	−1.48315e7	−1.82283
$582$	709352.	0.0868070
$583$	2.52310e6	0.307442
$584$	3.60332e6	0.437190
$585$	1.08421e6	0.130986
$586$	2.59707e6	0.312421
$587$	3.40837e6	0.408274	0.204137	−	0.978942i	$-0.434561\pi$
$587$	3.40837e6	0.408274	0.204137	+	0.978942i	$0.434561\pi$
$588$	−2.10943e6	−0.251607
$589$	−2.67295e6	−0.317470
$590$	−1.67916e6	−0.198592
$591$	8.22122e6	0.968205
$592$	−437579.	−0.0513159
$593$	−9.87756e6	−1.15349	−0.576744	−	0.816925i	$-0.695677\pi$
$593$	−9.87756e6	−1.15349	−0.576744	+	0.816925i	$0.695677\pi$
$594$	−1.35537e6	−0.157612
$595$	−770070.	−0.0891740
$596$	7.29882e6	0.841661
$597$	6.99513e6	0.803267
$598$	−4.39321e6	−0.502376
$599$	2.77791e6	0.316338	0.158169	−	0.987412i	$-0.449441\pi$
$599$	2.77791e6	0.316338	0.158169	+	0.987412i	$0.449441\pi$
$600$	360000.	0.0408248
$601$	−1.59740e7	−1.80396	−0.901982	−	0.431774i	$-0.857888\pi$
$601$	−1.59740e7	−1.80396	−0.901982	+	0.431774i	$0.857888\pi$
$602$	1.71169e7	1.92502
$603$	−4.81308e6	−0.539051
$604$	140023.	0.0156173
$605$	1.37478e6	0.152702
$606$	−2.55208e6	−0.282302
$607$	7.53030e6	0.829546	0.414773	−	0.909925i	$-0.363861\pi$
$607$	7.53030e6	0.829546	0.414773	+	0.909925i	$0.363861\pi$
$608$	−369664.	−0.0405554
$609$	9.58575e6	1.04733
$610$	−5.10535e6	−0.555522
$611$	−1.22177e7	−1.32400
$612$	225084.	0.0242922
$613$	−1.49828e7	−1.61043	−0.805216	−	0.592982i	$-0.797951\pi$
$613$	−1.49828e7	−1.61043	−0.805216	+	0.592982i	$0.797951\pi$
$614$	−8.96512e6	−0.959699
$615$	164687.	0.0175579
$616$	−5.27594e6	−0.560206
$617$	−436190.	−0.0461278	−0.0230639	−	0.999734i	$-0.507342\pi$
$617$	−436190.	−0.0461278	−0.0230639	+	0.999734i	$0.507342\pi$
$618$	−414700.	−0.0436780
$619$	−1.31886e7	−1.38348	−0.691738	−	0.722149i	$-0.743155\pi$
$619$	−1.31886e7	−1.38348	−0.691738	+	0.722149i	$0.743155\pi$
$620$	−2.96172e6	−0.309432
$621$	−1.49541e6	−0.155608
$622$	8.45328e6	0.876091
$623$	−2.22298e7	−2.29464
$624$	−1.23359e6	−0.126826
$625$	390625.	0.0400000
$626$	540025.	0.0550780
$627$	1.51015e6	0.153409
$628$	−1.37656e6	−0.139282
$629$	−296863.	−0.0299178
$630$	1.43660e6	0.144206
$631$	3.98839e6	0.398772	0.199386	−	0.979921i	$-0.436105\pi$
$631$	3.98839e6	0.398772	0.199386	+	0.979921i	$0.436105\pi$
$632$	−4.60367e6	−0.458471
$633$	−3.94664e6	−0.391487
$634$	1.16611e7	1.15217
$635$	−8.25081e6	−0.812012
$636$	781678.	0.0766276
$637$	7.84318e6	0.765850
$638$	1.11651e7	1.08595
$639$	469225.	0.0454600
$640$	−409600.	−0.0395285
$641$	1.58226e7	1.52101	0.760507	−	0.649330i	$-0.224951\pi$
$641$	1.58226e7	1.52101	0.760507	+	0.649330i	$0.224951\pi$
$642$	−899407.	−0.0861229
$643$	5.61190e6	0.535282	0.267641	−	0.963519i	$-0.413756\pi$
$643$	5.61190e6	0.535282	0.267641	+	0.963519i	$0.413756\pi$
$644$	−5.82108e6	−0.553081
$645$	−5.42873e6	−0.513806
$646$	−250788.	−0.0236443
$647$	−1.53830e7	−1.44471	−0.722353	−	0.691525i	$-0.756939\pi$
$647$	−1.53830e7	−1.44471	−0.722353	+	0.691525i	$0.756939\pi$
$648$	−419904.	−0.0392837
$649$	−7.80478e6	−0.727359
$650$	−1.33853e6	−0.124264
$651$	−1.18189e7	−1.09301
$652$	4.51083e6	0.415563
$653$	1.30815e6	0.120053	0.0600265	−	0.998197i	$-0.480881\pi$
$653$	1.30815e6	0.120053	0.0600265	+	0.998197i	$0.480881\pi$
$654$	3.03878e6	0.277814
$655$	−5.86356e6	−0.534021
$656$	−187377.	−0.0170003
$657$	−4.56045e6	−0.412187
$658$	−1.61887e7	−1.45763
$659$	1.79181e7	1.60723	0.803615	−	0.595149i	$-0.202907\pi$
$659$	1.79181e7	1.60723	0.803615	+	0.595149i	$0.202907\pi$
$660$	1.67329e6	0.149524
$661$	1.24925e7	1.11210	0.556051	−	0.831148i	$-0.312316\pi$
$661$	1.24925e7	1.11210	0.556051	+	0.831148i	$0.312316\pi$
$662$	4.29126e6	0.380575
$663$	−836895.	−0.0739414
$664$	−5.35199e6	−0.471081
$665$	−1.60066e6	−0.140360
$666$	553811.	0.0483811
$667$	1.23187e7	1.07214
$668$	−7.48098e6	−0.648660
$669$	−2.28313e6	−0.197227
$670$	5.94207e6	0.511389
$671$	−2.37298e7	−2.03465
$672$	−1.63453e6	−0.139627
$673$	1.18467e7	1.00823	0.504116	−	0.863636i	$-0.331818\pi$
$673$	1.18467e7	1.00823	0.504116	+	0.863636i	$0.331818\pi$
$674$	−1.11701e7	−0.947127
$675$	−455625.	−0.0384900
$676$	−1.35401e6	−0.113961
$677$	5.95235e6	0.499134	0.249567	−	0.968358i	$-0.419712\pi$
$677$	5.95235e6	0.499134	0.249567	+	0.968358i	$0.419712\pi$
$678$	−7.36031e6	−0.614924
$679$	−3.49470e6	−0.290895
$680$	−277882.	−0.0230456
$681$	3.92423e6	0.324255
$682$	−1.37662e7	−1.13332
$683$	−9.89319e6	−0.811493	−0.405746	−	0.913986i	$-0.632988\pi$
$683$	−9.89319e6	−0.811493	−0.405746	+	0.913986i	$0.632988\pi$
$684$	467856.	0.0382360
$685$	−5.54030e6	−0.451136
$686$	−1.53107e6	−0.124218
$687$	−9.04811e6	−0.731419
$688$	6.17669e6	0.497490
$689$	−2.90639e6	−0.233242
$690$	1.84619e6	0.147622
$691$	−1.31393e7	−1.04683	−0.523415	−	0.852078i	$-0.675342\pi$
$691$	−1.31393e7	−1.04683	−0.523415	+	0.852078i	$0.675342\pi$
$692$	−8.29084e6	−0.658162
$693$	6.67736e6	0.528168
$694$	−2.20606e6	−0.173868
$695$	−2.13533e6	−0.167688
$696$	3.45904e6	0.270665
$697$	−127121.	−0.00991140
$698$	1.21987e7	0.947711
$699$	−1.13477e7	−0.878444
$700$	−1.77358e6	−0.136806
$701$	2.64964e6	0.203654	0.101827	−	0.994802i	$-0.467531\pi$
$701$	2.64964e6	0.203654	0.101827	+	0.994802i	$0.467531\pi$
$702$	1.56126e6	0.119573
$703$	−617055.	−0.0470907
$704$	−1.90383e6	−0.144776
$705$	5.13434e6	0.389055
$706$	8.96996e6	0.677297
$707$	1.25731e7	0.946007
$708$	−2.41799e6	−0.181289
$709$	2.06464e6	0.154251	0.0771257	−	0.997021i	$-0.475426\pi$
$709$	2.06464e6	0.154251	0.0771257	+	0.997021i	$0.475426\pi$
$710$	−579290.	−0.0431271
$711$	5.82652e6	0.432250
$712$	−8.02166e6	−0.593013
$713$	−1.51886e7	−1.11890
$714$	−1.10890e6	−0.0814043
$715$	−6.22154e6	−0.455127
$716$	−1.18411e7	−0.863196
$717$	7.04909e6	0.512077
$718$	1.31653e7	0.953056
$719$	−1.64668e7	−1.18792	−0.593960	−	0.804494i	$-0.702436\pi$
$719$	−1.64668e7	−1.18792	−0.593960	+	0.804494i	$0.702436\pi$
$720$	518400.	0.0372678
$721$	2.04306e6	0.146367
$722$	−521284.	−0.0372161
$723$	−6.14928e6	−0.437501
$724$	1.27591e7	0.904633
$725$	3.75330e6	0.265197
$726$	1.97968e6	0.139397
$727$	−1.12187e7	−0.787236	−0.393618	−	0.919274i	$-0.628777\pi$
$727$	−1.12187e7	−0.787236	−0.393618	+	0.919274i	$0.628777\pi$
$728$	6.07742e6	0.425002
$729$	531441.	0.0370370
$730$	5.63018e6	0.391035
$731$	4.19040e6	0.290043
$732$	−7.35171e6	−0.507120
$733$	−2.06322e7	−1.41836	−0.709180	−	0.705028i	$-0.750935\pi$
$733$	−2.06322e7	−1.41836	−0.709180	+	0.705028i	$0.750935\pi$
$734$	−1.12058e6	−0.0767722
$735$	−3.29599e6	−0.225044
$736$	−2.10055e6	−0.142935
$737$	2.76190e7	1.87300
$738$	237149.	0.0160281
$739$	2.05403e7	1.38356	0.691778	−	0.722111i	$-0.256828\pi$
$739$	2.05403e7	1.38356	0.691778	+	0.722111i	$0.256828\pi$
$740$	−683717.	−0.0458984
$741$	−1.73956e6	−0.116384
$742$	−3.85102e6	−0.256783
$743$	−1.03955e7	−0.690833	−0.345416	−	0.938449i	$-0.612262\pi$
$743$	−1.03955e7	−0.690833	−0.345416	+	0.938449i	$0.612262\pi$
$744$	−4.26488e6	−0.282471
$745$	1.14044e7	0.752804
$746$	−9.76453e6	−0.642398
$747$	6.77361e6	0.444139
$748$	−1.29160e6	−0.0844063
$749$	4.43103e6	0.288602
$750$	562500.	0.0365148
$751$	6.76123e6	0.437447	0.218724	−	0.975787i	$-0.429811\pi$
$751$	6.76123e6	0.437447	0.218724	+	0.975787i	$0.429811\pi$
$752$	−5.84173e6	−0.376701
$753$	1.43182e6	0.0920241
$754$	−1.28612e7	−0.823860
$755$	218786.	0.0139685
$756$	2.06870e6	0.131642
$757$	−1.29976e7	−0.824373	−0.412187	−	0.911099i	$-0.635235\pi$
$757$	−1.29976e7	−0.824373	−0.412187	+	0.911099i	$0.635235\pi$
$758$	−4.35206e6	−0.275120
$759$	8.58113e6	0.540680
$760$	−577600.	−0.0362738
$761$	−1.17498e7	−0.735479	−0.367739	−	0.929929i	$-0.619868\pi$
$761$	−1.17498e7	−0.735479	−0.367739	+	0.929929i	$0.619868\pi$
$762$	−1.18812e7	−0.741262
$763$	−1.49709e7	−0.930971
$764$	−1.08453e7	−0.672214
$765$	351694.	0.0217276
$766$	−1.40615e6	−0.0865881
$767$	8.99043e6	0.551813
$768$	−589824.	−0.0360844
$769$	−2.24427e7	−1.36855	−0.684273	−	0.729226i	$-0.739880\pi$
$769$	−2.24427e7	−1.36855	−0.684273	+	0.729226i	$0.739880\pi$
$770$	−8.24365e6	−0.501064
$771$	1.24584e7	0.754793
$772$	−9.58918e6	−0.579079
$773$	1.07423e7	0.646620	0.323310	−	0.946293i	$-0.395204\pi$
$773$	1.07423e7	0.646620	0.323310	+	0.946293i	$0.395204\pi$
$774$	−7.81737e6	−0.469038
$775$	−4.62769e6	−0.276764
$776$	−1.26107e6	−0.0751770
$777$	−2.72841e6	−0.162128
$778$	−9.80810e6	−0.580946
$779$	−264231.	−0.0156006
$780$	−1.92749e6	−0.113437
$781$	−2.69256e6	−0.157957
$782$	−1.42506e6	−0.0833327
$783$	−4.37785e6	−0.255186
$784$	3.75010e6	0.217898
$785$	−2.15087e6	−0.124578
$786$	−8.44353e6	−0.487492
$787$	−1.26423e7	−0.727593	−0.363797	−	0.931478i	$-0.618520\pi$
$787$	−1.26423e7	−0.727593	−0.363797	+	0.931478i	$0.618520\pi$
$788$	−1.46155e7	−0.838490
$789$	−4.85079e6	−0.277408
$790$	−7.19324e6	−0.410069
$791$	3.62614e7	2.06064
$792$	2.40954e6	0.136496
$793$	2.73347e7	1.54359
$794$	−1.47163e7	−0.828415
$795$	1.22137e6	0.0685378
$796$	−1.24358e7	−0.695650
$797$	1.20769e7	0.673456	0.336728	−	0.941602i	$-0.390680\pi$
$797$	1.20769e7	0.673456	0.336728	+	0.941602i	$0.390680\pi$
$798$	−2.30494e6	−0.128131
$799$	−3.96316e6	−0.219621
$800$	−640000.	−0.0353553
$801$	1.01524e7	0.559098
$802$	1.73379e7	0.951835
$803$	2.61693e7	1.43220
$804$	8.55659e6	0.466832
$805$	−9.09543e6	−0.494691
$806$	1.58574e7	0.859796
$807$	2.72348e6	0.147211
$808$	4.53704e6	0.244480
$809$	−1.74362e7	−0.936657	−0.468329	−	0.883554i	$-0.655144\pi$
$809$	−1.74362e7	−0.936657	−0.468329	+	0.883554i	$0.655144\pi$
$810$	−656100.	−0.0351364
$811$	1.82230e7	0.972897	0.486448	−	0.873709i	$-0.338292\pi$
$811$	1.82230e7	0.972897	0.486448	+	0.873709i	$0.338292\pi$
$812$	−1.70413e7	−0.907013
$813$	−7.26091e6	−0.385270
$814$	−3.17794e6	−0.168107
$815$	7.04817e6	0.371691
$816$	−400150.	−0.0210376
$817$	8.71009e6	0.456528
$818$	5.38119e6	0.281187
$819$	−7.69174e6	−0.400696
$820$	−292777.	−0.0152056
$821$	3.45896e7	1.79097	0.895484	−	0.445093i	$-0.146829\pi$
$821$	3.45896e7	1.79097	0.895484	+	0.445093i	$0.146829\pi$
$822$	−7.97804e6	−0.411829
$823$	1.24813e7	0.642333	0.321166	−	0.947023i	$-0.395925\pi$
$823$	1.24813e7	0.642333	0.321166	+	0.947023i	$0.395925\pi$
$824$	737244.	0.0378263
$825$	2.61452e6	0.133739
$826$	1.19125e7	0.607508
$827$	1.56510e7	0.795752	0.397876	−	0.917439i	$-0.369747\pi$
$827$	1.56510e7	0.795752	0.397876	+	0.917439i	$0.369747\pi$
$828$	2.65851e6	0.134760
$829$	2.15080e7	1.08696	0.543479	−	0.839423i	$-0.317107\pi$
$829$	2.15080e7	1.08696	0.543479	+	0.839423i	$0.317107\pi$
$830$	−8.36249e6	−0.421347
$831$	1.36929e7	0.687849
$832$	2.19305e6	0.109835
$833$	2.54415e6	0.127037
$834$	−3.07487e6	−0.153078
$835$	−1.16890e7	−0.580179
$836$	−2.68470e6	−0.132856
$837$	5.39774e6	0.266317
$838$	−1.22315e7	−0.601685
$839$	1.95321e7	0.957950	0.478975	−	0.877828i	$-0.341008\pi$
$839$	1.95321e7	0.957950	0.478975	+	0.877828i	$0.341008\pi$
$840$	−2.55395e6	−0.124886
$841$	1.55522e7	0.758231
$842$	1.35465e7	0.658488
$843$	1.95707e7	0.948500
$844$	7.01624e6	0.339038
$845$	−2.11565e6	−0.101930
$846$	7.39344e6	0.355157
$847$	−9.75310e6	−0.467126
$848$	−1.38965e6	−0.0663614
$849$	−1.09402e7	−0.520903
$850$	−434190.	−0.0206126
$851$	−3.50630e6	−0.165968
$852$	−834178.	−0.0393695
$853$	−9.33840e6	−0.439440	−0.219720	−	0.975563i	$-0.570514\pi$
$853$	−9.33840e6	−0.439440	−0.219720	+	0.975563i	$0.570514\pi$
$854$	3.62190e7	1.69938
$855$	731025.	0.0341993
$856$	1.59895e6	0.0745846
$857$	2.01622e7	0.937749	0.468875	−	0.883265i	$-0.344660\pi$
$857$	2.01622e7	0.937749	0.468875	+	0.883265i	$0.344660\pi$
$858$	−8.95902e6	−0.415473
$859$	−3.58234e7	−1.65647	−0.828237	−	0.560379i	$-0.810656\pi$
$859$	−3.58234e7	−1.65647	−0.828237	+	0.560379i	$0.810656\pi$
$860$	9.65107e6	0.444969
$861$	−1.16834e6	−0.0537109
$862$	−1.56695e7	−0.718269
$863$	−3.67297e7	−1.67877	−0.839383	−	0.543541i	$-0.817083\pi$
$863$	−3.67297e7	−1.67877	−0.839383	+	0.543541i	$0.817083\pi$
$864$	746496.	0.0340207
$865$	−1.29544e7	−0.588678
$866$	2.89866e6	0.131341
$867$	1.25072e7	0.565085
$868$	2.10114e7	0.946576
$869$	−3.34344e7	−1.50191
$870$	5.40475e6	0.242090
$871$	−3.18146e7	−1.42096
$872$	−5.40227e6	−0.240594
$873$	1.59604e6	0.0708776
$874$	−2.96210e6	−0.131166
$875$	−2.77122e6	−0.122363
$876$	8.10746e6	0.356964
$877$	5.68096e6	0.249415	0.124708	−	0.992194i	$-0.460201\pi$
$877$	5.68096e6	0.249415	0.124708	+	0.992194i	$0.460201\pi$
$878$	−2.09788e6	−0.0918427
$879$	5.84342e6	0.255091
$880$	−2.97474e6	−0.129492
$881$	−3.73234e7	−1.62010	−0.810050	−	0.586361i	$-0.800560\pi$
$881$	−3.73234e7	−1.62010	−0.810050	+	0.586361i	$0.800560\pi$
$882$	−4.74622e6	−0.205436
$883$	2.77655e7	1.19840	0.599202	−	0.800598i	$-0.295485\pi$
$883$	2.77655e7	1.19840	0.599202	+	0.800598i	$0.295485\pi$
$884$	1.48781e6	0.0640351
$885$	−3.77810e6	−0.162150
$886$	1.87190e7	0.801123
$887$	1.11088e7	0.474085	0.237043	−	0.971499i	$-0.423822\pi$
$887$	1.11088e7	0.474085	0.237043	+	0.971499i	$0.423822\pi$
$888$	−984553.	−0.0418993
$889$	5.85339e7	2.48401
$890$	−1.25338e7	−0.530407
$891$	−3.04957e6	−0.128690
$892$	4.05890e6	0.170803
$893$	−8.23776e6	−0.345685
$894$	1.64223e7	0.687213
$895$	−1.85017e7	−0.772066
$896$	2.90583e6	0.120921
$897$	−9.88471e6	−0.410188
$898$	−2.14675e7	−0.888363
$899$	−4.44649e7	−1.83492
$900$	810000.	0.0333333
$901$	−942769.	−0.0386895
$902$	−1.36084e6	−0.0556916
$903$	3.85131e7	1.57177
$904$	1.30850e7	0.532540
$905$	1.99360e7	0.809129
$906$	315051.	0.0127515
$907$	−798853.	−0.0322440	−0.0161220	−	0.999870i	$-0.505132\pi$
$907$	−798853.	−0.0322440	−0.0161220	+	0.999870i	$0.505132\pi$
$908$	−6.97640e6	−0.280813
$909$	−5.74219e6	−0.230498
$910$	9.49597e6	0.380133
$911$	−1.70870e7	−0.682133	−0.341066	−	0.940039i	$-0.610788\pi$
$911$	−1.70870e7	−0.682133	−0.341066	+	0.940039i	$0.610788\pi$
$912$	−831744.	−0.0331133
$913$	−3.88691e7	−1.54322
$914$	−1.47663e7	−0.584666
$915$	−1.14870e7	−0.453582
$916$	1.60855e7	0.633427
$917$	4.15980e7	1.63361
$918$	506439.	0.0198345
$919$	9.93460e6	0.388027	0.194013	−	0.980999i	$-0.437850\pi$
$919$	9.93460e6	0.388027	0.194013	+	0.980999i	$0.437850\pi$
$920$	−3.28211e6	−0.127845
$921$	−2.01715e7	−0.783591
$922$	1.69611e7	0.657094
$923$	3.10160e6	0.119834
$924$	−1.18709e7	−0.457407
$925$	−1.06831e6	−0.0410528
$926$	−1.19479e7	−0.457892
$927$	−933075.	−0.0356629
$928$	−6.14940e6	−0.234403
$929$	1.68971e7	0.642353	0.321177	−	0.947019i	$-0.395922\pi$
$929$	1.68971e7	0.642353	0.321177	+	0.947019i	$0.395922\pi$
$930$	−6.66387e6	−0.252650
$931$	5.28823e6	0.199957
$932$	2.01737e7	0.760755
$933$	1.90199e7	0.715325
$934$	−1.56460e7	−0.586861
$935$	−2.01813e6	−0.0754953
$936$	−2.77558e6	−0.103553
$937$	1.89292e7	0.704342	0.352171	−	0.935936i	$-0.385444\pi$
$937$	1.89292e7	0.704342	0.352171	+	0.935936i	$0.385444\pi$
$938$	−4.21550e7	−1.56438
$939$	1.21506e6	0.0449710
$940$	−9.12771e6	−0.336932
$941$	−8.72232e6	−0.321113	−0.160557	−	0.987027i	$-0.551329\pi$
$941$	−8.72232e6	−0.321113	−0.160557	+	0.987027i	$0.551329\pi$
$942$	−3.09725e6	−0.113723
$943$	−1.50145e6	−0.0549833
$944$	4.29864e6	0.157001
$945$	3.23235e6	0.117744
$946$	4.48585e7	1.62973
$947$	−1.03850e7	−0.376298	−0.188149	−	0.982141i	$-0.560249\pi$
$947$	−1.03850e7	−0.376298	−0.188149	+	0.982141i	$0.560249\pi$
$948$	−1.03583e7	−0.374340
$949$	−3.01447e7	−1.08654
$950$	−902500.	−0.0324443
$951$	2.62374e7	0.940739
$952$	1.97138e6	0.0704982
$953$	3.97021e7	1.41606	0.708029	−	0.706183i	$-0.249585\pi$
$953$	3.97021e7	1.41606	0.708029	+	0.706183i	$0.249585\pi$
$954$	1.75878e6	0.0625662
$955$	−1.69457e7	−0.601246
$956$	−1.25317e7	−0.443472
$957$	2.51214e7	0.886676
$958$	1.63087e7	0.574123
$959$	3.93047e7	1.38006
$960$	−921600.	−0.0322749
$961$	2.61946e7	0.914962
$962$	3.66071e6	0.127535
$963$	−2.02367e6	−0.0703191
$964$	1.09321e7	0.378887
$965$	−1.49831e7	−0.517944
$966$	−1.30974e7	−0.451589
$967$	−3.61663e7	−1.24376	−0.621882	−	0.783111i	$-0.713631\pi$
$967$	−3.61663e7	−1.24376	−0.621882	+	0.783111i	$0.713631\pi$
$968$	−3.51943e6	−0.120721
$969$	−564273.	−0.0193055
$970$	−1.97042e6	−0.0672404
$971$	4.93115e7	1.67842	0.839209	−	0.543809i	$-0.183018\pi$
$971$	4.93115e7	1.67842	0.839209	+	0.543809i	$0.183018\pi$
$972$	−944784.	−0.0320750
$973$	1.51487e7	0.512971
$974$	−1.74982e7	−0.591010
$975$	−3.01170e6	−0.101461
$976$	1.30697e7	0.439179
$977$	−2.54182e7	−0.851939	−0.425970	−	0.904737i	$-0.640067\pi$
$977$	−2.54182e7	−0.851939	−0.425970	+	0.904737i	$0.640067\pi$
$978$	1.01494e7	0.339306
$979$	−5.82577e7	−1.94266
$980$	5.85954e6	0.194894
$981$	6.83725e6	0.226835
$982$	−3.38103e7	−1.11884
$983$	−3.29336e7	−1.08706	−0.543532	−	0.839388i	$-0.682913\pi$
$983$	−3.29336e7	−1.08706	−0.543532	+	0.839388i	$0.682913\pi$
$984$	−421599.	−0.0138807
$985$	−2.28367e7	−0.749969
$986$	−4.17189e6	−0.136660
$987$	−3.64246e7	−1.19015
$988$	3.09255e6	0.100791
$989$	4.94935e7	1.60901
$990$	3.76491e6	0.122086
$991$	−3.13422e7	−1.01378	−0.506892	−	0.862010i	$-0.669206\pi$
$991$	−3.13422e7	−1.01378	−0.506892	+	0.862010i	$0.669206\pi$
$992$	7.58201e6	0.244627
$993$	9.65534e6	0.310738
$994$	4.10967e6	0.131929
$995$	−1.94309e7	−0.622208
$996$	−1.20420e7	−0.384636
$997$	−1.23943e7	−0.394897	−0.197448	−	0.980313i	$-0.563266\pi$
$997$	−1.23943e7	−0.394897	−0.197448	+	0.980313i	$0.563266\pi$
$998$	−1.85093e6	−0.0588253
$999$	1.24607e6	0.0395030

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.j.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -177.358 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -177.358 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -464.803 q^{11} -144.000 q^{12} +535.413 q^{13} +709.432 q^{14} -225.000 q^{15} +256.000 q^{16} +173.676 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1596.22 q^{21} +1859.21 q^{22} +2051.32 q^{23} +576.000 q^{24} +625.000 q^{25} -2141.65 q^{26} -729.000 q^{27} -2837.73 q^{28} +6005.28 q^{29} +900.000 q^{30} -7404.30 q^{31} -1024.00 q^{32} +4183.23 q^{33} -694.704 q^{34} -4433.95 q^{35} +1296.00 q^{36} -1709.29 q^{37} -1444.00 q^{38} -4818.72 q^{39} -1600.00 q^{40} -731.943 q^{41} -6384.89 q^{42} +24127.7 q^{43} -7436.85 q^{44} +2025.00 q^{45} -8205.27 q^{46} -22819.3 q^{47} -2304.00 q^{48} +14648.8 q^{49} -2500.00 q^{50} -1563.08 q^{51} +8566.61 q^{52} -5428.32 q^{53} +2916.00 q^{54} -11620.1 q^{55} +11350.9 q^{56} -3249.00 q^{57} -24021.1 q^{58} +16791.6 q^{59} -3600.00 q^{60} +51053.5 q^{61} +29617.2 q^{62} -14366.0 q^{63} +4096.00 q^{64} +13385.3 q^{65} -16732.9 q^{66} -59420.7 q^{67} +2778.82 q^{68} -18461.9 q^{69} +17735.8 q^{70} +5792.90 q^{71} -5184.00 q^{72} -56301.8 q^{73} +6837.17 q^{74} -5625.00 q^{75} +5776.00 q^{76} +82436.5 q^{77} +19274.9 q^{78} +71932.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} +2927.77 q^{82} +83624.9 q^{83} +25539.5 q^{84} +4341.90 q^{85} -96510.7 q^{86} -54047.5 q^{87} +29747.4 q^{88} +125338. q^{89} -8100.00 q^{90} -94959.7 q^{91} +32821.1 q^{92} +66638.7 q^{93} +91277.1 q^{94} +9025.00 q^{95} +9216.00 q^{96} +19704.2 q^{97} -58595.4 q^{98} -37649.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} + 100 q^{5} + 144 q^{6} - 108 q^{7} - 256 q^{8} + 324 q^{9} - 400 q^{10} - 246 q^{11} - 576 q^{12} + 640 q^{13} + 432 q^{14} - 900 q^{15} + 1024 q^{16} - 612 q^{17} - 1296 q^{18} + 1444 q^{19} + 1600 q^{20} + 972 q^{21} + 984 q^{22} - 1242 q^{23} + 2304 q^{24} + 2500 q^{25} - 2560 q^{26} - 2916 q^{27} - 1728 q^{28} - 6230 q^{29} + 3600 q^{30} - 11360 q^{31} - 4096 q^{32} + 2214 q^{33} + 2448 q^{34} - 2700 q^{35} + 5184 q^{36} - 4792 q^{37} - 5776 q^{38} - 5760 q^{39} - 6400 q^{40} + 9170 q^{41} - 3888 q^{42} - 11412 q^{43} - 3936 q^{44} + 8100 q^{45} + 4968 q^{46} - 29858 q^{47} - 9216 q^{48} + 31092 q^{49} - 10000 q^{50} + 5508 q^{51} + 10240 q^{52} + 27498 q^{53} + 11664 q^{54} - 6150 q^{55} + 6912 q^{56} - 12996 q^{57} + 24920 q^{58} + 54984 q^{59} - 14400 q^{60} + 20868 q^{61} + 45440 q^{62} - 8748 q^{63} + 16384 q^{64} + 16000 q^{65} - 8856 q^{66} - 20244 q^{67} - 9792 q^{68} + 11178 q^{69} + 10800 q^{70} + 86864 q^{71} - 20736 q^{72} - 3728 q^{73} + 19168 q^{74} - 22500 q^{75} + 23104 q^{76} + 18796 q^{77} + 23040 q^{78} + 164192 q^{79} + 25600 q^{80} + 26244 q^{81} - 36680 q^{82} - 60506 q^{83} + 15552 q^{84} - 15300 q^{85} + 45648 q^{86} + 56070 q^{87} + 15744 q^{88} + 113798 q^{89} - 32400 q^{90} + 159528 q^{91} - 19872 q^{92} + 102240 q^{93} + 119432 q^{94} + 36100 q^{95} + 36864 q^{96} + 79440 q^{97} - 124368 q^{98} - 19926 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 + 100 * q^5 + 144 * q^6 - 108 * q^7 - 256 * q^8 + 324 * q^9 - 400 * q^10 - 246 * q^11 - 576 * q^12 + 640 * q^13 + 432 * q^14 - 900 * q^15 + 1024 * q^16 - 612 * q^17 - 1296 * q^18 + 1444 * q^19 + 1600 * q^20 + 972 * q^21 + 984 * q^22 - 1242 * q^23 + 2304 * q^24 + 2500 * q^25 - 2560 * q^26 - 2916 * q^27 - 1728 * q^28 - 6230 * q^29 + 3600 * q^30 - 11360 * q^31 - 4096 * q^32 + 2214 * q^33 + 2448 * q^34 - 2700 * q^35 + 5184 * q^36 - 4792 * q^37 - 5776 * q^38 - 5760 * q^39 - 6400 * q^40 + 9170 * q^41 - 3888 * q^42 - 11412 * q^43 - 3936 * q^44 + 8100 * q^45 + 4968 * q^46 - 29858 * q^47 - 9216 * q^48 + 31092 * q^49 - 10000 * q^50 + 5508 * q^51 + 10240 * q^52 + 27498 * q^53 + 11664 * q^54 - 6150 * q^55 + 6912 * q^56 - 12996 * q^57 + 24920 * q^58 + 54984 * q^59 - 14400 * q^60 + 20868 * q^61 + 45440 * q^62 - 8748 * q^63 + 16384 * q^64 + 16000 * q^65 - 8856 * q^66 - 20244 * q^67 - 9792 * q^68 + 11178 * q^69 + 10800 * q^70 + 86864 * q^71 - 20736 * q^72 - 3728 * q^73 + 19168 * q^74 - 22500 * q^75 + 23104 * q^76 + 18796 * q^77 + 23040 * q^78 + 164192 * q^79 + 25600 * q^80 + 26244 * q^81 - 36680 * q^82 - 60506 * q^83 + 15552 * q^84 - 15300 * q^85 + 45648 * q^86 + 56070 * q^87 + 15744 * q^88 + 113798 * q^89 - 32400 * q^90 + 159528 * q^91 - 19872 * q^92 + 102240 * q^93 + 119432 * q^94 + 36100 * q^95 + 36864 * q^96 + 79440 * q^97 - 124368 * q^98 - 19926 * q^99

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