LMFDB - Embedded newform 570.6.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2696x^{2} + 13833x + 894635 $ x^4 - x^3 - 2696x^2 + 13833x + 894635
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$44.4607$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +53.8996 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +53.8996 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +137.824 q^{11} -144.000 q^{12} +121.743 q^{13} -215.598 q^{14} +225.000 q^{15} +256.000 q^{16} -1682.47 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -485.096 q^{21} -551.295 q^{22} +2915.75 q^{23} +576.000 q^{24} +625.000 q^{25} -486.970 q^{26} -729.000 q^{27} +862.394 q^{28} -7935.40 q^{29} -900.000 q^{30} +4745.53 q^{31} -1024.00 q^{32} -1240.41 q^{33} +6729.89 q^{34} -1347.49 q^{35} +1296.00 q^{36} -7300.69 q^{37} +1444.00 q^{38} -1095.68 q^{39} +1600.00 q^{40} +3813.41 q^{41} +1940.39 q^{42} +19360.9 q^{43} +2205.18 q^{44} -2025.00 q^{45} -11663.0 q^{46} +28117.9 q^{47} -2304.00 q^{48} -13901.8 q^{49} -2500.00 q^{50} +15142.2 q^{51} +1947.88 q^{52} -5284.18 q^{53} +2916.00 q^{54} -3445.60 q^{55} -3449.57 q^{56} +3249.00 q^{57} +31741.6 q^{58} -17547.2 q^{59} +3600.00 q^{60} +21622.1 q^{61} -18982.1 q^{62} +4365.87 q^{63} +4096.00 q^{64} -3043.56 q^{65} +4961.66 q^{66} -12374.8 q^{67} -26919.6 q^{68} -26241.8 q^{69} +5389.96 q^{70} -43271.2 q^{71} -5184.00 q^{72} +9339.19 q^{73} +29202.8 q^{74} -5625.00 q^{75} -5776.00 q^{76} +7428.65 q^{77} +4382.73 q^{78} +96543.7 q^{79} -6400.00 q^{80} +6561.00 q^{81} -15253.6 q^{82} +25220.6 q^{83} -7761.54 q^{84} +42061.8 q^{85} -77443.5 q^{86} +71418.6 q^{87} -8820.73 q^{88} +27191.0 q^{89} +8100.00 q^{90} +6561.88 q^{91} +46652.1 q^{92} -42709.8 q^{93} -112471. q^{94} +9025.00 q^{95} +9216.00 q^{96} +119760. q^{97} +55607.3 q^{98} +11163.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 460 q^{11} - 576 q^{12} + 296 q^{13} - 432 q^{14} + 900 q^{15} + 1024 q^{16} - 412 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 972 q^{21} + 1840 q^{22} - 768 q^{23} + 2304 q^{24} + 2500 q^{25} - 1184 q^{26} - 2916 q^{27} + 1728 q^{28} - 1828 q^{29} - 3600 q^{30} + 3856 q^{31} - 4096 q^{32} + 4140 q^{33} + 1648 q^{34} - 2700 q^{35} + 5184 q^{36} + 11456 q^{37} + 5776 q^{38} - 2664 q^{39} + 6400 q^{40} - 12904 q^{41} + 3888 q^{42} + 15096 q^{43} - 7360 q^{44} - 8100 q^{45} + 3072 q^{46} + 17040 q^{47} - 9216 q^{48} + 33708 q^{49} - 10000 q^{50} + 3708 q^{51} + 4736 q^{52} + 16728 q^{53} + 11664 q^{54} + 11500 q^{55} - 6912 q^{56} + 12996 q^{57} + 7312 q^{58} - 19760 q^{59} + 14400 q^{60} + 47168 q^{61} - 15424 q^{62} + 8748 q^{63} + 16384 q^{64} - 7400 q^{65} - 16560 q^{66} + 104580 q^{67} - 6592 q^{68} + 6912 q^{69} + 10800 q^{70} - 36764 q^{71} - 20736 q^{72} + 74356 q^{73} - 45824 q^{74} - 22500 q^{75} - 23104 q^{76} + 75356 q^{77} + 10656 q^{78} + 80920 q^{79} - 25600 q^{80} + 26244 q^{81} + 51616 q^{82} + 19416 q^{83} - 15552 q^{84} + 10300 q^{85} - 60384 q^{86} + 16452 q^{87} + 29440 q^{88} - 4760 q^{89} + 32400 q^{90} + 32288 q^{91} - 12288 q^{92} - 34704 q^{93} - 68160 q^{94} + 36100 q^{95} + 36864 q^{96} + 139572 q^{97} - 134832 q^{98} - 37260 q^{99}+O(q^{100}) \) 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 - 460 * q^11 - 576 * q^12 + 296 * q^13 - 432 * q^14 + 900 * q^15 + 1024 * q^16 - 412 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 972 * q^21 + 1840 * q^22 - 768 * q^23 + 2304 * q^24 + 2500 * q^25 - 1184 * q^26 - 2916 * q^27 + 1728 * q^28 - 1828 * q^29 - 3600 * q^30 + 3856 * q^31 - 4096 * q^32 + 4140 * q^33 + 1648 * q^34 - 2700 * q^35 + 5184 * q^36 + 11456 * q^37 + 5776 * q^38 - 2664 * q^39 + 6400 * q^40 - 12904 * q^41 + 3888 * q^42 + 15096 * q^43 - 7360 * q^44 - 8100 * q^45 + 3072 * q^46 + 17040 * q^47 - 9216 * q^48 + 33708 * q^49 - 10000 * q^50 + 3708 * q^51 + 4736 * q^52 + 16728 * q^53 + 11664 * q^54 + 11500 * q^55 - 6912 * q^56 + 12996 * q^57 + 7312 * q^58 - 19760 * q^59 + 14400 * q^60 + 47168 * q^61 - 15424 * q^62 + 8748 * q^63 + 16384 * q^64 - 7400 * q^65 - 16560 * q^66 + 104580 * q^67 - 6592 * q^68 + 6912 * q^69 + 10800 * q^70 - 36764 * q^71 - 20736 * q^72 + 74356 * q^73 - 45824 * q^74 - 22500 * q^75 - 23104 * q^76 + 75356 * q^77 + 10656 * q^78 + 80920 * q^79 - 25600 * q^80 + 26244 * q^81 + 51616 * q^82 + 19416 * q^83 - 15552 * q^84 + 10300 * q^85 - 60384 * q^86 + 16452 * q^87 + 29440 * q^88 - 4760 * q^89 + 32400 * q^90 + 32288 * q^91 - 12288 * q^92 - 34704 * q^93 - 68160 * q^94 + 36100 * q^95 + 36864 * q^96 + 139572 * q^97 - 134832 * q^98 - 37260 * 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
$7$	53.8996	0.415758	0.207879	−	0.978155i	$-0.433344\pi$
$7$	53.8996	0.415758	0.207879	+	0.978155i	$0.433344\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	137.824	0.343434	0.171717	−	0.985146i	$-0.445069\pi$
$11$	137.824	0.343434	0.171717	+	0.985146i	$0.445069\pi$
$12$	−144.000	−0.288675
$13$	121.743	0.199795	0.0998974	−	0.994998i	$-0.468149\pi$
$13$	121.743	0.199795	0.0998974	+	0.994998i	$0.468149\pi$
$14$	−215.598	−0.293985
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−1682.47	−1.41197	−0.705985	−	0.708227i	$-0.749495\pi$
$17$	−1682.47	−1.41197	−0.705985	+	0.708227i	$0.749495\pi$
$18$	−324.000	−0.235702
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	−400.000	−0.223607
$21$	−485.096	−0.240038
$22$	−551.295	−0.242844
$23$	2915.75	1.14929	0.574647	−	0.818401i	$-0.305139\pi$
$23$	2915.75	1.14929	0.574647	+	0.818401i	$0.305139\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	−486.970	−0.141276
$27$	−729.000	−0.192450
$28$	862.394	0.207879
$29$	−7935.40	−1.75216	−0.876081	−	0.482165i	$-0.839851\pi$
$29$	−7935.40	−1.75216	−0.876081	+	0.482165i	$0.839851\pi$
$30$	−900.000	−0.182574
$31$	4745.53	0.886912	0.443456	−	0.896296i	$-0.353752\pi$
$31$	4745.53	0.886912	0.443456	+	0.896296i	$0.353752\pi$
$32$	−1024.00	−0.176777
$33$	−1240.41	−0.198281
$34$	6729.89	0.998414
$35$	−1347.49	−0.185933
$36$	1296.00	0.166667
$37$	−7300.69	−0.876718	−0.438359	−	0.898800i	$-0.644440\pi$
$37$	−7300.69	−0.876718	−0.438359	+	0.898800i	$0.644440\pi$
$38$	1444.00	0.162221
$39$	−1095.68	−0.115352
$40$	1600.00	0.158114
$41$	3813.41	0.354286	0.177143	−	0.984185i	$-0.443315\pi$
$41$	3813.41	0.354286	0.177143	+	0.984185i	$0.443315\pi$
$42$	1940.39	0.169732
$43$	19360.9	1.59681	0.798406	−	0.602119i	$-0.205677\pi$
$43$	19360.9	1.59681	0.798406	+	0.602119i	$0.205677\pi$
$44$	2205.18	0.171717
$45$	−2025.00	−0.149071
$46$	−11663.0	−0.812674
$47$	28117.9	1.85668	0.928341	−	0.371729i	$-0.121235\pi$
$47$	28117.9	1.85668	0.928341	+	0.371729i	$0.121235\pi$
$48$	−2304.00	−0.144338
$49$	−13901.8	−0.827145
$50$	−2500.00	−0.141421
$51$	15142.2	0.815201
$52$	1947.88	0.0998974
$53$	−5284.18	−0.258397	−0.129199	−	0.991619i	$-0.541240\pi$
$53$	−5284.18	−0.258397	−0.129199	+	0.991619i	$0.541240\pi$
$54$	2916.00	0.136083
$55$	−3445.60	−0.153588
$56$	−3449.57	−0.146993
$57$	3249.00	0.132453
$58$	31741.6	1.23897
$59$	−17547.2	−0.656262	−0.328131	−	0.944632i	$-0.606419\pi$
$59$	−17547.2	−0.656262	−0.328131	+	0.944632i	$0.606419\pi$
$60$	3600.00	0.129099
$61$	21622.1	0.744001	0.372000	−	0.928233i	$-0.378672\pi$
$61$	21622.1	0.744001	0.372000	+	0.928233i	$0.378672\pi$
$62$	−18982.1	−0.627142
$63$	4365.87	0.138586
$64$	4096.00	0.125000
$65$	−3043.56	−0.0893509
$66$	4961.66	0.140206
$67$	−12374.8	−0.336783	−0.168392	−	0.985720i	$-0.553857\pi$
$67$	−12374.8	−0.336783	−0.168392	+	0.985720i	$0.553857\pi$
$68$	−26919.6	−0.705985
$69$	−26241.8	−0.663546
$70$	5389.96	0.131474
$71$	−43271.2	−1.01872	−0.509358	−	0.860555i	$-0.670117\pi$
$71$	−43271.2	−1.01872	−0.509358	+	0.860555i	$0.670117\pi$
$72$	−5184.00	−0.117851
$73$	9339.19	0.205117	0.102559	−	0.994727i	$-0.467297\pi$
$73$	9339.19	0.205117	0.102559	+	0.994727i	$0.467297\pi$
$74$	29202.8	0.619933
$75$	−5625.00	−0.115470
$76$	−5776.00	−0.114708
$77$	7428.65	0.142785
$78$	4382.73	0.0815659
$79$	96543.7	1.74043	0.870214	−	0.492673i	$-0.163980\pi$
$79$	96543.7	1.74043	0.870214	+	0.492673i	$0.163980\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−15253.6	−0.250518
$83$	25220.6	0.401846	0.200923	−	0.979607i	$-0.435606\pi$
$83$	25220.6	0.401846	0.200923	+	0.979607i	$0.435606\pi$
$84$	−7761.54	−0.120019
$85$	42061.8	0.631452
$86$	−77443.5	−1.12912
$87$	71418.6	1.01161
$88$	−8820.73	−0.121422
$89$	27191.0	0.363873	0.181936	−	0.983310i	$-0.441763\pi$
$89$	27191.0	0.363873	0.181936	+	0.983310i	$0.441763\pi$
$90$	8100.00	0.105409
$91$	6561.88	0.0830662
$92$	46652.1	0.574647
$93$	−42709.8	−0.512059
$94$	−112471.	−1.31287
$95$	9025.00	0.102598
$96$	9216.00	0.102062
$97$	119760.	1.29235	0.646177	−	0.763187i	$-0.276367\pi$
$97$	119760.	1.29235	0.646177	+	0.763187i	$0.276367\pi$
$98$	55607.3	0.584880
$99$	11163.7	0.114478
$100$	10000.0	0.100000
$101$	−46475.9	−0.453340	−0.226670	−	0.973972i	$-0.572784\pi$
$101$	−46475.9	−0.453340	−0.226670	+	0.973972i	$0.572784\pi$
$102$	−60569.0	−0.576434
$103$	−141512.	−1.31432	−0.657160	−	0.753751i	$-0.728243\pi$
$103$	−141512.	−1.31432	−0.657160	+	0.753751i	$0.728243\pi$
$104$	−7791.52	−0.0706381
$105$	12127.4	0.107348
$106$	21136.7	0.182714
$107$	4716.62	0.0398264	0.0199132	−	0.999802i	$-0.493661\pi$
$107$	4716.62	0.0398264	0.0199132	+	0.999802i	$0.493661\pi$
$108$	−11664.0	−0.0962250
$109$	−54152.0	−0.436565	−0.218282	−	0.975886i	$-0.570045\pi$
$109$	−54152.0	−0.436565	−0.218282	+	0.975886i	$0.570045\pi$
$110$	13782.4	0.108603
$111$	65706.2	0.506173
$112$	13798.3	0.103939
$113$	122125.	0.899723	0.449861	−	0.893098i	$-0.351473\pi$
$113$	122125.	0.899723	0.449861	+	0.893098i	$0.351473\pi$
$114$	−12996.0	−0.0936586
$115$	−72893.9	−0.513980
$116$	−126966.	−0.876081
$117$	9861.15	0.0665983
$118$	70188.7	0.464047
$119$	−90684.6	−0.587038
$120$	−14400.0	−0.0912871
$121$	−142056.	−0.882053
$122$	−86488.4	−0.526088
$123$	−34320.7	−0.204547
$124$	75928.5	0.443456
$125$	−15625.0	−0.0894427
$126$	−17463.5	−0.0979951
$127$	4664.23	0.0256608	0.0128304	−	0.999918i	$-0.495916\pi$
$127$	4664.23	0.0256608	0.0128304	+	0.999918i	$0.495916\pi$
$128$	−16384.0	−0.0883883
$129$	−174248.	−0.921920
$130$	12174.3	0.0631806
$131$	−352988.	−1.79714	−0.898570	−	0.438831i	$-0.855393\pi$
$131$	−352988.	−1.79714	−0.898570	+	0.438831i	$0.855393\pi$
$132$	−19846.6	−0.0991407
$133$	−19457.8	−0.0953814
$134$	49499.1	0.238142
$135$	18225.0	0.0860663
$136$	107678.	0.499207
$137$	−352202.	−1.60321	−0.801604	−	0.597855i	$-0.796020\pi$
$137$	−352202.	−1.60321	−0.801604	+	0.597855i	$0.796020\pi$
$138$	104967.	0.469198
$139$	274159.	1.20355	0.601777	−	0.798664i	$-0.294459\pi$
$139$	274159.	1.20355	0.601777	+	0.798664i	$0.294459\pi$
$140$	−21559.8	−0.0929663
$141$	−253061.	−1.07196
$142$	173085.	0.720341
$143$	16779.0	0.0686162
$144$	20736.0	0.0833333
$145$	198385.	0.783590
$146$	−37356.8	−0.145040
$147$	125116.	0.477553
$148$	−116811.	−0.438359
$149$	106435.	0.392751	0.196375	−	0.980529i	$-0.437083\pi$
$149$	106435.	0.392751	0.196375	+	0.980529i	$0.437083\pi$
$150$	22500.0	0.0816497
$151$	210268.	0.750466	0.375233	−	0.926931i	$-0.377563\pi$
$151$	210268.	0.750466	0.375233	+	0.926931i	$0.377563\pi$
$152$	23104.0	0.0811107
$153$	−136280.	−0.470657
$154$	−29714.6	−0.100964
$155$	−118638.	−0.396639
$156$	−17530.9	−0.0576758
$157$	−80915.2	−0.261988	−0.130994	−	0.991383i	$-0.541817\pi$
$157$	−80915.2	−0.261988	−0.130994	+	0.991383i	$0.541817\pi$
$158$	−386175.	−1.23067
$159$	47557.6	0.149186
$160$	25600.0	0.0790569
$161$	157158.	0.477828
$162$	−26244.0	−0.0785674
$163$	−378773.	−1.11663	−0.558315	−	0.829629i	$-0.688552\pi$
$163$	−378773.	−1.11663	−0.558315	+	0.829629i	$0.688552\pi$
$164$	61014.5	0.177143
$165$	31010.4	0.0886742
$166$	−100882.	−0.284148
$167$	−505883.	−1.40365	−0.701825	−	0.712349i	$-0.747631\pi$
$167$	−505883.	−1.40365	−0.701825	+	0.712349i	$0.747631\pi$
$168$	31046.2	0.0848662
$169$	−356472.	−0.960082
$170$	−168247.	−0.446504
$171$	−29241.0	−0.0764719
$172$	309774.	0.798406
$173$	−430633.	−1.09394	−0.546968	−	0.837153i	$-0.684218\pi$
$173$	−430633.	−1.09394	−0.546968	+	0.837153i	$0.684218\pi$
$174$	−285675.	−0.715317
$175$	33687.3	0.0831516
$176$	35282.9	0.0858584
$177$	157925.	0.378893
$178$	−108764.	−0.257297
$179$	−212623.	−0.495996	−0.247998	−	0.968761i	$-0.579773\pi$
$179$	−212623.	−0.495996	−0.247998	+	0.968761i	$0.579773\pi$
$180$	−32400.0	−0.0745356
$181$	−675316.	−1.53218	−0.766091	−	0.642732i	$-0.777801\pi$
$181$	−675316.	−1.53218	−0.766091	+	0.642732i	$0.777801\pi$
$182$	−26247.5	−0.0587367
$183$	−194599.	−0.429549
$184$	−186608.	−0.406337
$185$	182517.	0.392080
$186$	170839.	0.362080
$187$	−231885.	−0.484918
$188$	449886.	0.928341
$189$	−39292.8	−0.0800126
$190$	−36100.0	−0.0725476
$191$	−499269.	−0.990264	−0.495132	−	0.868818i	$-0.664880\pi$
$191$	−499269.	−0.990264	−0.495132	+	0.868818i	$0.664880\pi$
$192$	−36864.0	−0.0721688
$193$	196074.	0.378903	0.189451	−	0.981890i	$-0.439329\pi$
$193$	196074.	0.378903	0.189451	+	0.981890i	$0.439329\pi$
$194$	−479039.	−0.913833
$195$	27392.1	0.0515868
$196$	−222429.	−0.413573
$197$	370392.	0.679980	0.339990	−	0.940429i	$-0.389576\pi$
$197$	370392.	0.679980	0.339990	+	0.940429i	$0.389576\pi$
$198$	−44654.9	−0.0809481
$199$	−618794.	−1.10768	−0.553839	−	0.832624i	$-0.686838\pi$
$199$	−618794.	−1.10768	−0.553839	+	0.832624i	$0.686838\pi$
$200$	−40000.0	−0.0707107
$201$	111373.	0.194442
$202$	185903.	0.320560
$203$	−427715.	−0.728475
$204$	242276.	0.407601
$205$	−95335.2	−0.158441
$206$	566049.	0.929365
$207$	236176.	0.383098
$208$	31166.1	0.0499487
$209$	−49754.4	−0.0787891
$210$	−48509.6	−0.0759067
$211$	−62599.0	−0.0967968	−0.0483984	−	0.998828i	$-0.515412\pi$
$211$	−62599.0	−0.0967968	−0.0483984	+	0.998828i	$0.515412\pi$
$212$	−84546.8	−0.129199
$213$	389441.	0.588156
$214$	−18866.5	−0.0281615
$215$	−484022.	−0.714116
$216$	46656.0	0.0680414
$217$	255782.	0.368741
$218$	216608.	0.308698
$219$	−84052.7	−0.118424
$220$	−55129.5	−0.0767941
$221$	−204828.	−0.282104
$222$	−262825.	−0.357918
$223$	1.14948e6	1.54789	0.773946	−	0.633251i	$-0.218280\pi$
$223$	1.14948e6	1.54789	0.773946	+	0.633251i	$0.218280\pi$
$224$	−55193.2	−0.0734963
$225$	50625.0	0.0666667
$226$	−488500.	−0.636200
$227$	−558920.	−0.719921	−0.359960	−	0.932968i	$-0.617210\pi$
$227$	−558920.	−0.719921	−0.359960	+	0.932968i	$0.617210\pi$
$228$	51984.0	0.0662266
$229$	−1.57296e6	−1.98211	−0.991057	−	0.133440i	$-0.957398\pi$
$229$	−1.57296e6	−1.98211	−0.991057	+	0.133440i	$0.957398\pi$
$230$	291575.	0.363439
$231$	−66857.9	−0.0824371
$232$	507866.	0.619483
$233$	−383408.	−0.462670	−0.231335	−	0.972874i	$-0.574309\pi$
$233$	−383408.	−0.462670	−0.231335	+	0.972874i	$0.574309\pi$
$234$	−39444.6	−0.0470921
$235$	−702947.	−0.830334
$236$	−280755.	−0.328131
$237$	−868893.	−1.00484
$238$	362738.	0.415098
$239$	−317773.	−0.359850	−0.179925	−	0.983680i	$-0.557586\pi$
$239$	−317773.	−0.359850	−0.179925	+	0.983680i	$0.557586\pi$
$240$	57600.0	0.0645497
$241$	−1.30913e6	−1.45191	−0.725955	−	0.687742i	$-0.758602\pi$
$241$	−1.30913e6	−1.45191	−0.725955	+	0.687742i	$0.758602\pi$
$242$	568222.	0.623706
$243$	−59049.0	−0.0641500
$244$	345954.	0.372000
$245$	347546.	0.369911
$246$	137283.	0.144637
$247$	−43949.1	−0.0458361
$248$	−303714.	−0.313571
$249$	−226985.	−0.232006
$250$	62500.0	0.0632456
$251$	−584074.	−0.585172	−0.292586	−	0.956239i	$-0.594516\pi$
$251$	−584074.	−0.585172	−0.292586	+	0.956239i	$0.594516\pi$
$252$	69853.9	0.0692930
$253$	401861.	0.394706
$254$	−18656.9	−0.0181450
$255$	−378556.	−0.364569
$256$	65536.0	0.0625000
$257$	−538075.	−0.508171	−0.254085	−	0.967182i	$-0.581774\pi$
$257$	−538075.	−0.508171	−0.254085	+	0.967182i	$0.581774\pi$
$258$	696991.	0.651896
$259$	−393504.	−0.364502
$260$	−48697.0	−0.0446755
$261$	−642768.	−0.584054
$262$	1.41195e6	1.27077
$263$	320542.	0.285757	0.142878	−	0.989740i	$-0.454364\pi$
$263$	320542.	0.285757	0.142878	+	0.989740i	$0.454364\pi$
$264$	79386.5	0.0701031
$265$	132104.	0.115559
$266$	77831.0	0.0674448
$267$	−244719.	−0.210082
$268$	−197996.	−0.168392
$269$	−786706.	−0.662875	−0.331437	−	0.943477i	$-0.607534\pi$
$269$	−786706.	−0.662875	−0.331437	+	0.943477i	$0.607534\pi$
$270$	−72900.0	−0.0608581
$271$	1.21805e6	1.00750	0.503748	−	0.863851i	$-0.331954\pi$
$271$	1.21805e6	1.00750	0.503748	+	0.863851i	$0.331954\pi$
$272$	−430713.	−0.352993
$273$	−59056.9	−0.0479583
$274$	1.40881e6	1.13364
$275$	86139.9	0.0686867
$276$	−419869.	−0.331773
$277$	−673677.	−0.527537	−0.263768	−	0.964586i	$-0.584965\pi$
$277$	−673677.	−0.527537	−0.263768	+	0.964586i	$0.584965\pi$
$278$	−1.09664e6	−0.851042
$279$	384388.	0.295637
$280$	86239.4	0.0657371
$281$	246097.	0.185927	0.0929633	−	0.995670i	$-0.470366\pi$
$281$	246097.	0.185927	0.0929633	+	0.995670i	$0.470366\pi$
$282$	1.01224e6	0.757988
$283$	2.46217e6	1.82748	0.913739	−	0.406301i	$-0.133182\pi$
$283$	2.46217e6	1.82748	0.913739	+	0.406301i	$0.133182\pi$
$284$	−692340.	−0.509358
$285$	−81225.0	−0.0592349
$286$	−67116.1	−0.0485190
$287$	205541.	0.147297
$288$	−82944.0	−0.0589256
$289$	1.41086e6	0.993660
$290$	−793540.	−0.554082
$291$	−1.07784e6	−0.746141
$292$	149427.	0.102559
$293$	−1.50307e6	−1.02285	−0.511423	−	0.859329i	$-0.670882\pi$
$293$	−1.50307e6	−1.02285	−0.511423	+	0.859329i	$0.670882\pi$
$294$	−500466.	−0.337681
$295$	438679.	0.293489
$296$	467244.	0.309967
$297$	−100474.	−0.0660938
$298$	−425738.	−0.277717
$299$	354971.	0.229623
$300$	−90000.0	−0.0577350
$301$	1.04354e6	0.663887
$302$	−841072.	−0.530660
$303$	418283.	0.261736
$304$	−92416.0	−0.0573539
$305$	−540552.	−0.332727
$306$	545121.	0.332805
$307$	−1.22912e6	−0.744302	−0.372151	−	0.928172i	$-0.621380\pi$
$307$	−1.22912e6	−0.744302	−0.372151	+	0.928172i	$0.621380\pi$
$308$	118858.	0.0713926
$309$	1.27361e6	0.758823
$310$	474553.	0.280466
$311$	−2.22112e6	−1.30218	−0.651090	−	0.759001i	$-0.725688\pi$
$311$	−2.22112e6	−1.30218	−0.651090	+	0.759001i	$0.725688\pi$
$312$	70123.7	0.0407829
$313$	2.16477e6	1.24897	0.624485	−	0.781037i	$-0.285309\pi$
$313$	2.16477e6	1.24897	0.624485	+	0.781037i	$0.285309\pi$
$314$	323661.	0.185253
$315$	−109147.	−0.0619775
$316$	1.54470e6	0.870214
$317$	2.05697e6	1.14969	0.574844	−	0.818263i	$-0.305063\pi$
$317$	2.05697e6	1.14969	0.574844	+	0.818263i	$0.305063\pi$
$318$	−190230.	−0.105490
$319$	−1.09369e6	−0.601751
$320$	−102400.	−0.0559017
$321$	−42449.6	−0.0229938
$322$	−628632.	−0.337876
$323$	607372.	0.323928
$324$	104976.	0.0555556
$325$	76089.1	0.0399590
$326$	1.51509e6	0.789577
$327$	487368.	0.252051
$328$	−244058.	−0.125259
$329$	1.51554e6	0.771931
$330$	−124041.	−0.0627021
$331$	3.09668e6	1.55355	0.776776	−	0.629776i	$-0.216854\pi$
$331$	3.09668e6	1.55355	0.776776	+	0.629776i	$0.216854\pi$
$332$	403529.	0.200923
$333$	−591356.	−0.292239
$334$	2.02353e6	0.992531
$335$	309370.	0.150614
$336$	−124185.	−0.0600095
$337$	−672599.	−0.322613	−0.161306	−	0.986904i	$-0.551571\pi$
$337$	−672599.	−0.322613	−0.161306	+	0.986904i	$0.551571\pi$
$338$	1.42589e6	0.678881
$339$	−1.09913e6	−0.519455
$340$	672989.	0.315726
$341$	654048.	0.304595
$342$	116964.	0.0540738
$343$	−1.65519e6	−0.759650
$344$	−1.23910e6	−0.564558
$345$	656045.	0.296747
$346$	1.72253e6	0.773530
$347$	1.35102e6	0.602334	0.301167	−	0.953571i	$-0.402624\pi$
$347$	1.35102e6	0.602334	0.301167	+	0.953571i	$0.402624\pi$
$348$	1.14270e6	0.505805
$349$	−4.25648e6	−1.87063	−0.935313	−	0.353821i	$-0.884882\pi$
$349$	−4.25648e6	−1.87063	−0.935313	+	0.353821i	$0.884882\pi$
$350$	−134749.	−0.0587970
$351$	−88750.3	−0.0384505
$352$	−141132.	−0.0607110
$353$	2.85917e6	1.22125	0.610623	−	0.791921i	$-0.290919\pi$
$353$	2.85917e6	1.22125	0.610623	+	0.791921i	$0.290919\pi$
$354$	−631698.	−0.267918
$355$	1.08178e6	0.455584
$356$	435056.	0.181936
$357$	816161.	0.338926
$358$	850492.	0.350722
$359$	−2.57491e6	−1.05445	−0.527226	−	0.849725i	$-0.676768\pi$
$359$	−2.57491e6	−1.05445	−0.527226	+	0.849725i	$0.676768\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	2.70126e6	1.08342
$363$	1.27850e6	0.509254
$364$	104990.	0.0415331
$365$	−233480.	−0.0917312
$366$	778396.	0.303737
$367$	1.96392e6	0.761129	0.380565	−	0.924754i	$-0.375730\pi$
$367$	1.96392e6	0.761129	0.380565	+	0.924754i	$0.375730\pi$
$368$	746433.	0.287324
$369$	308886.	0.118095
$370$	−730069.	−0.277242
$371$	−284815.	−0.107431
$372$	−683357.	−0.256030
$373$	−281558.	−0.104784	−0.0523921	−	0.998627i	$-0.516685\pi$
$373$	−281558.	−0.104784	−0.0523921	+	0.998627i	$0.516685\pi$
$374$	927539.	0.342889
$375$	140625.	0.0516398
$376$	−1.79954e6	−0.656437
$377$	−966077.	−0.350073
$378$	157171.	0.0565775
$379$	−1.77889e6	−0.636138	−0.318069	−	0.948068i	$-0.603034\pi$
$379$	−1.77889e6	−0.636138	−0.318069	+	0.948068i	$0.603034\pi$
$380$	144400.	0.0512989
$381$	−41978.1	−0.0148153
$382$	1.99707e6	0.700222
$383$	−4.32645e6	−1.50707	−0.753537	−	0.657406i	$-0.771654\pi$
$383$	−4.32645e6	−1.50707	−0.753537	+	0.657406i	$0.771654\pi$
$384$	147456.	0.0510310
$385$	−185716.	−0.0638555
$386$	−784298.	−0.267925
$387$	1.56823e6	0.532271
$388$	1.91616e6	0.646177
$389$	−2.81212e6	−0.942237	−0.471119	−	0.882070i	$-0.656150\pi$
$389$	−2.81212e6	−0.942237	−0.471119	+	0.882070i	$0.656150\pi$
$390$	−109568.	−0.0364774
$391$	−4.90568e6	−1.62277
$392$	889717.	0.292440
$393$	3.17689e6	1.03758
$394$	−1.48157e6	−0.480818
$395$	−2.41359e6	−0.778343
$396$	178620.	0.0572389
$397$	5.04595e6	1.60682	0.803408	−	0.595428i	$-0.203018\pi$
$397$	5.04595e6	1.60682	0.803408	+	0.595428i	$0.203018\pi$
$398$	2.47518e6	0.783247
$399$	175120.	0.0550685
$400$	160000.	0.0500000
$401$	−5.90706e6	−1.83447	−0.917235	−	0.398347i	$-0.869584\pi$
$401$	−5.90706e6	−1.83447	−0.917235	+	0.398347i	$0.869584\pi$
$402$	−445492.	−0.137491
$403$	577733.	0.177200
$404$	−743614.	−0.226670
$405$	−164025.	−0.0496904
$406$	1.71086e6	0.515110
$407$	−1.00621e6	−0.301094
$408$	−969104.	−0.288217
$409$	4.41096e6	1.30384	0.651921	−	0.758287i	$-0.273963\pi$
$409$	4.41096e6	1.30384	0.651921	+	0.758287i	$0.273963\pi$
$410$	381341.	0.112035
$411$	3.16981e6	0.925613
$412$	−2.26420e6	−0.657160
$413$	−945786.	−0.272846
$414$	−944704.	−0.270891
$415$	−630514.	−0.179711
$416$	−124664.	−0.0353191
$417$	−2.46743e6	−0.694873
$418$	199018.	0.0557123
$419$	5.36398e6	1.49263	0.746315	−	0.665593i	$-0.231821\pi$
$419$	5.36398e6	1.49263	0.746315	+	0.665593i	$0.231821\pi$
$420$	194039.	0.0536741
$421$	2.81350e6	0.773646	0.386823	−	0.922154i	$-0.373572\pi$
$421$	2.81350e6	0.773646	0.386823	+	0.922154i	$0.373572\pi$
$422$	250396.	0.0684457
$423$	2.27755e6	0.618894
$424$	338187.	0.0913572
$425$	−1.05155e6	−0.282394
$426$	−1.55776e6	−0.415889
$427$	1.16542e6	0.309324
$428$	75465.9	0.0199132
$429$	−151011.	−0.0396156
$430$	1.93609e6	0.504956
$431$	−3.66733e6	−0.950949	−0.475475	−	0.879729i	$-0.657724\pi$
$431$	−3.66733e6	−0.950949	−0.475475	+	0.879729i	$0.657724\pi$
$432$	−186624.	−0.0481125
$433$	−3.19336e6	−0.818519	−0.409259	−	0.912418i	$-0.634213\pi$
$433$	−3.19336e6	−0.818519	−0.409259	+	0.912418i	$0.634213\pi$
$434$	−1.02313e6	−0.260739
$435$	−1.78547e6	−0.452406
$436$	−866432.	−0.218282
$437$	−1.05259e6	−0.263666
$438$	336211.	0.0837387
$439$	4.84345e6	1.19948	0.599741	−	0.800194i	$-0.295270\pi$
$439$	4.84345e6	1.19948	0.599741	+	0.800194i	$0.295270\pi$
$440$	220518.	0.0543016
$441$	−1.12605e6	−0.275715
$442$	819314.	0.199478
$443$	3.82748e6	0.926624	0.463312	−	0.886195i	$-0.346661\pi$
$443$	3.82748e6	0.926624	0.463312	+	0.886195i	$0.346661\pi$
$444$	1.05130e6	0.253087
$445$	−679774.	−0.162729
$446$	−4.59794e6	−1.09453
$447$	−957912.	−0.226755
$448$	220773.	0.0519697
$449$	−4.55005e6	−1.06512	−0.532562	−	0.846391i	$-0.678771\pi$
$449$	−4.55005e6	−1.06512	−0.532562	+	0.846391i	$0.678771\pi$
$450$	−202500.	−0.0471405
$451$	525579.	0.121674
$452$	1.95400e6	0.449861
$453$	−1.89241e6	−0.433282
$454$	2.23568e6	0.509061
$455$	−164047.	−0.0371484
$456$	−207936.	−0.0468293
$457$	3.90722e6	0.875139	0.437570	−	0.899185i	$-0.355839\pi$
$457$	3.90722e6	0.875139	0.437570	+	0.899185i	$0.355839\pi$
$458$	6.29183e6	1.40157
$459$	1.22652e6	0.271734
$460$	−1.16630e6	−0.256990
$461$	5.26269e6	1.15333	0.576667	−	0.816979i	$-0.304353\pi$
$461$	5.26269e6	1.15333	0.576667	+	0.816979i	$0.304353\pi$
$462$	267431.	0.0582918
$463$	7.16926e6	1.55425	0.777127	−	0.629344i	$-0.216676\pi$
$463$	7.16926e6	1.55425	0.777127	+	0.629344i	$0.216676\pi$
$464$	−2.03146e6	−0.438040
$465$	1.06774e6	0.229000
$466$	1.53363e6	0.327157
$467$	−6.62872e6	−1.40649	−0.703246	−	0.710947i	$-0.748267\pi$
$467$	−6.62872e6	−1.40649	−0.703246	+	0.710947i	$0.748267\pi$
$468$	157778.	0.0332991
$469$	−666996.	−0.140020
$470$	2.81179e6	0.587135
$471$	728237.	0.151259
$472$	1.12302e6	0.232024
$473$	2.66839e6	0.548399
$474$	3.47557e6	0.710527
$475$	−225625.	−0.0458831
$476$	−1.45095e6	−0.293519
$477$	−428018.	−0.0861324
$478$	1.27109e6	0.254453
$479$	58865.9	0.0117226	0.00586131	−	0.999983i	$-0.498134\pi$
$479$	58865.9	0.0117226	0.00586131	+	0.999983i	$0.498134\pi$
$480$	−230400.	−0.0456435
$481$	−888805.	−0.175164
$482$	5.23651e6	1.02666
$483$	−1.41442e6	−0.275874
$484$	−2.27289e6	−0.441027
$485$	−2.99400e6	−0.577959
$486$	236196.	0.0453609
$487$	−9.46054e6	−1.80756	−0.903782	−	0.427994i	$-0.859221\pi$
$487$	−9.46054e6	−1.80756	−0.903782	+	0.427994i	$0.859221\pi$
$488$	−1.38381e6	−0.263044
$489$	3.40895e6	0.644687
$490$	−1.39018e6	−0.261566
$491$	5.67252e6	1.06187	0.530936	−	0.847412i	$-0.321840\pi$
$491$	5.67252e6	1.06187	0.530936	+	0.847412i	$0.321840\pi$
$492$	−549131.	−0.102273
$493$	1.33511e7	2.47400
$494$	175796.	0.0324110
$495$	−279093.	−0.0511961
$496$	1.21486e6	0.221728
$497$	−2.33230e6	−0.423539
$498$	907941.	0.164053
$499$	−9.98280e6	−1.79474	−0.897368	−	0.441282i	$-0.854524\pi$
$499$	−9.98280e6	−1.79474	−0.897368	+	0.441282i	$0.854524\pi$
$500$	−250000.	−0.0447214
$501$	4.55295e6	0.810398
$502$	2.33630e6	0.413779
$503$	−242940.	−0.0428133	−0.0214067	−	0.999771i	$-0.506814\pi$
$503$	−242940.	−0.0428133	−0.0214067	+	0.999771i	$0.506814\pi$
$504$	−279416.	−0.0489975
$505$	1.16190e6	0.202740
$506$	−1.60744e6	−0.279100
$507$	3.20825e6	0.554304
$508$	74627.7	0.0128304
$509$	2.35453e6	0.402818	0.201409	−	0.979507i	$-0.435448\pi$
$509$	2.35453e6	0.402818	0.201409	+	0.979507i	$0.435448\pi$
$510$	1.51422e6	0.257789
$511$	503379.	0.0852791
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	2.15230e6	0.359331
$515$	3.53781e6	0.587782
$516$	−2.78797e6	−0.460960
$517$	3.87531e6	0.637647
$518$	1.57402e6	0.257742
$519$	3.87570e6	0.631585
$520$	194788.	0.0315903
$521$	−3.09311e6	−0.499230	−0.249615	−	0.968345i	$-0.580304\pi$
$521$	−3.09311e6	−0.499230	−0.249615	+	0.968345i	$0.580304\pi$
$522$	2.57107e6	0.412988
$523$	−2.49646e6	−0.399089	−0.199544	−	0.979889i	$-0.563946\pi$
$523$	−2.49646e6	−0.399089	−0.199544	+	0.979889i	$0.563946\pi$
$524$	−5.64781e6	−0.898570
$525$	−303185.	−0.0480076
$526$	−1.28217e6	−0.202060
$527$	−7.98422e6	−1.25229
$528$	−317546.	−0.0495704
$529$	2.06528e6	0.320878
$530$	−528418.	−0.0817123
$531$	−1.42132e6	−0.218754
$532$	−311324.	−0.0476907
$533$	464254.	0.0707844
$534$	978875.	0.148551
$535$	−117915.	−0.0178109
$536$	791986.	0.119071
$537$	1.91361e6	0.286363
$538$	3.14682e6	0.468723
$539$	−1.91600e6	−0.284069
$540$	291600.	0.0430331
$541$	4.37052e6	0.642007	0.321003	−	0.947078i	$-0.395980\pi$
$541$	4.37052e6	0.642007	0.321003	+	0.947078i	$0.395980\pi$
$542$	−4.87221e6	−0.712407
$543$	6.07784e6	0.884606
$544$	1.72285e6	0.249603
$545$	1.35380e6	0.195238
$546$	236228.	0.0339117
$547$	−6.23499e6	−0.890980	−0.445490	−	0.895287i	$-0.646970\pi$
$547$	−6.23499e6	−0.890980	−0.445490	+	0.895287i	$0.646970\pi$
$548$	−5.63523e6	−0.801604
$549$	1.75139e6	0.248000
$550$	−344560.	−0.0485688
$551$	2.86468e6	0.401973
$552$	1.67947e6	0.234599
$553$	5.20367e6	0.723597
$554$	2.69471e6	0.373025
$555$	−1.64266e6	−0.226368
$556$	4.38655e6	0.601777
$557$	−2.20103e6	−0.300599	−0.150299	−	0.988641i	$-0.548024\pi$
$557$	−2.20103e6	−0.300599	−0.150299	+	0.988641i	$0.548024\pi$
$558$	−1.53755e6	−0.209047
$559$	2.35704e6	0.319035
$560$	−344957.	−0.0464831
$561$	2.08696e6	0.279968
$562$	−984390.	−0.131470
$563$	4.50252e6	0.598667	0.299333	−	0.954149i	$-0.403236\pi$
$563$	4.50252e6	0.598667	0.299333	+	0.954149i	$0.403236\pi$
$564$	−4.04897e6	−0.535978
$565$	−3.05313e6	−0.402368
$566$	−9.84869e6	−1.29222
$567$	353635.	0.0461953
$568$	2.76936e6	0.360171
$569$	−1.96946e6	−0.255015	−0.127508	−	0.991838i	$-0.540698\pi$
$569$	−1.96946e6	−0.255015	−0.127508	+	0.991838i	$0.540698\pi$
$570$	324900.	0.0418854
$571$	−6.98166e6	−0.896124	−0.448062	−	0.894002i	$-0.647886\pi$
$571$	−6.98166e6	−0.896124	−0.448062	+	0.894002i	$0.647886\pi$
$572$	268465.	0.0343081
$573$	4.49342e6	0.571729
$574$	−822165.	−0.104155
$575$	1.82235e6	0.229859
$576$	331776.	0.0416667
$577$	9.73499e6	1.21729	0.608647	−	0.793441i	$-0.291712\pi$
$577$	9.73499e6	1.21729	0.608647	+	0.793441i	$0.291712\pi$
$578$	−5.64342e6	−0.702624
$579$	−1.76467e6	−0.218760
$580$	3.17416e6	0.391795
$581$	1.35938e6	0.167071
$582$	4.31135e6	0.527602
$583$	−728286.	−0.0887422
$584$	−597708.	−0.0725199
$585$	−246529.	−0.0297836
$586$	6.01228e6	0.723262
$587$	−7.02206e6	−0.841142	−0.420571	−	0.907260i	$-0.638170\pi$
$587$	−7.02206e6	−0.841142	−0.420571	+	0.907260i	$0.638170\pi$
$588$	2.00186e6	0.238776
$589$	−1.71314e6	−0.203472
$590$	−1.75472e6	−0.207528
$591$	−3.33353e6	−0.392587
$592$	−1.86898e6	−0.219179
$593$	1.11700e7	1.30442	0.652209	−	0.758039i	$-0.273842\pi$
$593$	1.11700e7	1.30442	0.652209	+	0.758039i	$0.273842\pi$
$594$	401894.	0.0467354
$595$	2.26711e6	0.262531
$596$	1.70295e6	0.196375
$597$	5.56915e6	0.639518
$598$	−1.41989e6	−0.162368
$599$	−1.30059e7	−1.48106	−0.740531	−	0.672023i	$-0.765426\pi$
$599$	−1.30059e7	−1.48106	−0.740531	+	0.672023i	$0.765426\pi$
$600$	360000.	0.0408248
$601$	−1.44799e7	−1.63524	−0.817618	−	0.575761i	$-0.804706\pi$
$601$	−1.44799e7	−1.63524	−0.817618	+	0.575761i	$0.804706\pi$
$602$	−4.17417e6	−0.469439
$603$	−1.00236e6	−0.112261
$604$	3.36429e6	0.375233
$605$	3.55139e6	0.394466
$606$	−1.67313e6	−0.185075
$607$	−1.30604e7	−1.43875	−0.719375	−	0.694622i	$-0.755572\pi$
$607$	−1.30604e7	−1.43875	−0.719375	+	0.694622i	$0.755572\pi$
$608$	369664.	0.0405554
$609$	3.84944e6	0.420585
$610$	2.16221e6	0.235274
$611$	3.42314e6	0.370956
$612$	−2.18048e6	−0.235328
$613$	−1.34776e7	−1.44864	−0.724320	−	0.689464i	$-0.757846\pi$
$613$	−1.34776e7	−1.44864	−0.724320	+	0.689464i	$0.757846\pi$
$614$	4.91649e6	0.526301
$615$	858017.	0.0914762
$616$	−475434.	−0.0504822
$617$	−1.15779e6	−0.122438	−0.0612192	−	0.998124i	$-0.519499\pi$
$617$	−1.15779e6	−0.122438	−0.0612192	+	0.998124i	$0.519499\pi$
$618$	−5.09444e6	−0.536569
$619$	−5.82236e6	−0.610763	−0.305381	−	0.952230i	$-0.598784\pi$
$619$	−5.82236e6	−0.610763	−0.305381	+	0.952230i	$0.598784\pi$
$620$	−1.89821e6	−0.198320
$621$	−2.12559e6	−0.221182
$622$	8.88447e6	0.920780
$623$	1.46558e6	0.151283
$624$	−280495.	−0.0288379
$625$	390625.	0.0400000
$626$	−8.65910e6	−0.883155
$627$	447790.	0.0454889
$628$	−1.29464e6	−0.130994
$629$	1.22832e7	1.23790
$630$	436587.	0.0438247
$631$	−1.40805e6	−0.140781	−0.0703907	−	0.997519i	$-0.522425\pi$
$631$	−1.40805e6	−0.140781	−0.0703907	+	0.997519i	$0.522425\pi$
$632$	−6.17880e6	−0.615334
$633$	563391.	0.0558857
$634$	−8.22788e6	−0.812952
$635$	−116606.	−0.0114759
$636$	760921.	0.0745928
$637$	−1.69244e6	−0.165259
$638$	4.37475e6	0.425502
$639$	−3.50497e6	−0.339572
$640$	409600.	0.0395285
$641$	−6.81024e6	−0.654662	−0.327331	−	0.944910i	$-0.606149\pi$
$641$	−6.81024e6	−0.654662	−0.327331	+	0.944910i	$0.606149\pi$
$642$	169798.	0.0162591
$643$	1.17675e7	1.12242	0.561210	−	0.827674i	$-0.310336\pi$
$643$	1.17675e7	1.12242	0.561210	+	0.827674i	$0.310336\pi$
$644$	2.51453e6	0.238914
$645$	4.35620e6	0.412295
$646$	−2.42949e6	−0.229052
$647$	−1.66768e7	−1.56621	−0.783106	−	0.621888i	$-0.786366\pi$
$647$	−1.66768e7	−1.56621	−0.783106	+	0.621888i	$0.786366\pi$
$648$	−419904.	−0.0392837
$649$	−2.41842e6	−0.225382
$650$	−304356.	−0.0282552
$651$	−2.30204e6	−0.212893
$652$	−6.06036e6	−0.558315
$653$	798441.	0.0732757	0.0366378	−	0.999329i	$-0.488335\pi$
$653$	798441.	0.0732757	0.0366378	+	0.999329i	$0.488335\pi$
$654$	−1.94947e6	−0.178227
$655$	8.82470e6	0.803705
$656$	976233.	0.0885714
$657$	756474.	0.0683724
$658$	−6.06217e6	−0.545837
$659$	−1.71609e7	−1.53931	−0.769655	−	0.638460i	$-0.779572\pi$
$659$	−1.71609e7	−1.53931	−0.769655	+	0.638460i	$0.779572\pi$
$660$	496166.	0.0443371
$661$	5.15051e6	0.458508	0.229254	−	0.973367i	$-0.426371\pi$
$661$	5.15051e6	0.458508	0.229254	+	0.973367i	$0.426371\pi$
$662$	−1.23867e7	−1.09853
$663$	1.84346e6	0.162873
$664$	−1.61412e6	−0.142074
$665$	486444.	0.0426559
$666$	2.36542e6	0.206644
$667$	−2.31377e7	−2.01375
$668$	−8.09413e6	−0.701825
$669$	−1.03454e7	−0.893676
$670$	−1.23748e6	−0.106500
$671$	2.98004e6	0.255515
$672$	496739.	0.0424331
$673$	−1.53735e7	−1.30839	−0.654193	−	0.756328i	$-0.726992\pi$
$673$	−1.53735e7	−1.30839	−0.654193	+	0.756328i	$0.726992\pi$
$674$	2.69040e6	0.228122
$675$	−455625.	−0.0384900
$676$	−5.70355e6	−0.480041
$677$	−2.02918e7	−1.70156	−0.850782	−	0.525518i	$-0.823871\pi$
$677$	−2.02918e7	−1.70156	−0.850782	+	0.525518i	$0.823871\pi$
$678$	4.39650e6	0.367310
$679$	6.45501e6	0.537307
$680$	−2.69196e6	−0.223252
$681$	5.03028e6	0.415646
$682$	−2.61619e6	−0.215381
$683$	−5.88954e6	−0.483092	−0.241546	−	0.970389i	$-0.577654\pi$
$683$	−5.88954e6	−0.483092	−0.241546	+	0.970389i	$0.577654\pi$
$684$	−467856.	−0.0382360
$685$	8.80504e6	0.716977
$686$	6.62078e6	0.537154
$687$	1.41566e7	1.14437
$688$	4.95638e6	0.399203
$689$	−643309.	−0.0516264
$690$	−2.62418e6	−0.209832
$691$	4.05114e6	0.322762	0.161381	−	0.986892i	$-0.448405\pi$
$691$	4.05114e6	0.322762	0.161381	+	0.986892i	$0.448405\pi$
$692$	−6.89013e6	−0.546968
$693$	601721.	0.0475951
$694$	−5.40407e6	−0.425915
$695$	−6.85398e6	−0.538246
$696$	−4.57079e6	−0.357658
$697$	−6.41595e6	−0.500241
$698$	1.70259e7	1.32273
$699$	3.45067e6	0.267123
$700$	538996.	0.0415758
$701$	−9.46762e6	−0.727689	−0.363844	−	0.931460i	$-0.618536\pi$
$701$	−9.46762e6	−0.727689	−0.363844	+	0.931460i	$0.618536\pi$
$702$	355001.	0.0271886
$703$	2.63555e6	0.201133
$704$	564527.	0.0429292
$705$	6.32652e6	0.479393
$706$	−1.14367e7	−0.863552
$707$	−2.50503e6	−0.188480
$708$	2.52679e6	0.189446
$709$	−1.01721e7	−0.759971	−0.379985	−	0.924992i	$-0.624071\pi$
$709$	−1.01721e7	−0.759971	−0.379985	+	0.924992i	$0.624071\pi$
$710$	−4.32712e6	−0.322146
$711$	7.82004e6	0.580143
$712$	−1.74022e6	−0.128649
$713$	1.38368e7	1.01932
$714$	−3.26465e6	−0.239657
$715$	−419476.	−0.0306861
$716$	−3.40197e6	−0.247998
$717$	2.85995e6	0.207760
$718$	1.02997e7	0.745610
$719$	2.09519e7	1.51147	0.755736	−	0.654876i	$-0.227279\pi$
$719$	2.09519e7	1.51147	0.755736	+	0.654876i	$0.227279\pi$
$720$	−518400.	−0.0372678
$721$	−7.62746e6	−0.546439
$722$	−521284.	−0.0372161
$723$	1.17822e7	0.838260
$724$	−1.08051e7	−0.766091
$725$	−4.95963e6	−0.350432
$726$	−5.11400e6	−0.360097
$727$	−6.38429e6	−0.447999	−0.223999	−	0.974589i	$-0.571911\pi$
$727$	−6.38429e6	−0.447999	−0.223999	+	0.974589i	$0.571911\pi$
$728$	−419960.	−0.0293684
$729$	531441.	0.0370370
$730$	933919.	0.0648638
$731$	−3.25741e7	−2.25465
$732$	−3.11358e6	−0.214774
$733$	3.31675e6	0.228010	0.114005	−	0.993480i	$-0.463632\pi$
$733$	3.31675e6	0.228010	0.114005	+	0.993480i	$0.463632\pi$
$734$	−7.85568e6	−0.538200
$735$	−3.12791e6	−0.213568
$736$	−2.98573e6	−0.203169
$737$	−1.70554e6	−0.115663
$738$	−1.23554e6	−0.0835059
$739$	2.06970e7	1.39411	0.697055	−	0.717017i	$-0.254493\pi$
$739$	2.06970e7	1.39411	0.697055	+	0.717017i	$0.254493\pi$
$740$	2.92028e6	0.196040
$741$	395542.	0.0264635
$742$	1.13926e6	0.0759649
$743$	−429578.	−0.0285476	−0.0142738	−	0.999898i	$-0.504544\pi$
$743$	−429578.	−0.0285476	−0.0142738	+	0.999898i	$0.504544\pi$
$744$	2.73343e6	0.181040
$745$	−2.66087e6	−0.175644
$746$	1.12623e6	0.0740936
$747$	2.04287e6	0.133949
$748$	−3.71016e6	−0.242459
$749$	254224.	0.0165582
$750$	−562500.	−0.0365148
$751$	1.31135e7	0.848434	0.424217	−	0.905561i	$-0.360549\pi$
$751$	1.31135e7	0.848434	0.424217	+	0.905561i	$0.360549\pi$
$752$	7.19817e6	0.464171
$753$	5.25667e6	0.337849
$754$	3.86431e6	0.247539
$755$	−5.25670e6	−0.335619
$756$	−628685.	−0.0400063
$757$	−8.63134e6	−0.547442	−0.273721	−	0.961809i	$-0.588255\pi$
$757$	−8.63134e6	−0.547442	−0.273721	+	0.961809i	$0.588255\pi$
$758$	7.11557e6	0.449818
$759$	−3.61675e6	−0.227884
$760$	−577600.	−0.0362738
$761$	3.32766e6	0.208294	0.104147	−	0.994562i	$-0.466789\pi$
$761$	3.32766e6	0.208294	0.104147	+	0.994562i	$0.466789\pi$
$762$	167912.	0.0104760
$763$	−2.91877e6	−0.181505
$764$	−7.98830e6	−0.495132
$765$	3.40701e6	0.210484
$766$	1.73058e7	1.06566
$767$	−2.13624e6	−0.131118
$768$	−589824.	−0.0360844
$769$	−2.21676e6	−0.135177	−0.0675886	−	0.997713i	$-0.521531\pi$
$769$	−2.21676e6	−0.135177	−0.0675886	+	0.997713i	$0.521531\pi$
$770$	742865.	0.0451526
$771$	4.84267e6	0.293393
$772$	3.13719e6	0.189451
$773$	2.32932e7	1.40210	0.701052	−	0.713110i	$-0.252714\pi$
$773$	2.32932e7	1.40210	0.701052	+	0.713110i	$0.252714\pi$
$774$	−6.27292e6	−0.376372
$775$	2.96596e6	0.177382
$776$	−7.66463e6	−0.456916
$777$	3.54154e6	0.210445
$778$	1.12485e7	0.666262
$779$	−1.37664e6	−0.0812787
$780$	438273.	0.0257934
$781$	−5.96381e6	−0.349861
$782$	1.96227e7	1.14747
$783$	5.78491e6	0.337204
$784$	−3.55887e6	−0.206786
$785$	2.02288e6	0.117164
$786$	−1.27076e7	−0.733679
$787$	−3.33148e7	−1.91735	−0.958673	−	0.284512i	$-0.908168\pi$
$787$	−3.33148e7	−1.91735	−0.958673	+	0.284512i	$0.908168\pi$
$788$	5.92627e6	0.339990
$789$	−2.88488e6	−0.164982
$790$	9.65437e6	0.550372
$791$	6.58249e6	0.374067
$792$	−714479.	−0.0404740
$793$	2.63233e6	0.148647
$794$	−2.01838e7	−1.13619
$795$	−1.18894e6	−0.0667178
$796$	−9.90071e6	−0.553839
$797$	2.73232e7	1.52365	0.761826	−	0.647782i	$-0.224303\pi$
$797$	2.73232e7	1.52365	0.761826	+	0.647782i	$0.224303\pi$
$798$	−700479.	−0.0389393
$799$	−4.73075e7	−2.62158
$800$	−640000.	−0.0353553
$801$	2.20247e6	0.121291
$802$	2.36282e7	1.29717
$803$	1.28716e6	0.0704441
$804$	1.78197e6	0.0972210
$805$	−3.92895e6	−0.213691
$806$	−2.31093e6	−0.125300
$807$	7.08035e6	0.382711
$808$	2.97446e6	0.160280
$809$	−1.92098e7	−1.03193	−0.515966	−	0.856609i	$-0.672567\pi$
$809$	−1.92098e7	−1.03193	−0.515966	+	0.856609i	$0.672567\pi$
$810$	656100.	0.0351364
$811$	−3.35126e7	−1.78919	−0.894595	−	0.446878i	$-0.852536\pi$
$811$	−3.35126e7	−1.78919	−0.894595	+	0.446878i	$0.852536\pi$
$812$	−6.84344e6	−0.364237
$813$	−1.09625e7	−0.581678
$814$	4.02484e6	0.212906
$815$	9.46931e6	0.499372
$816$	3.87642e6	0.203800
$817$	−6.98928e6	−0.366334
$818$	−1.76439e7	−0.921956
$819$	531512.	0.0276887
$820$	−1.52536e6	−0.0792207
$821$	−2.27808e7	−1.17953	−0.589767	−	0.807573i	$-0.700780\pi$
$821$	−2.27808e7	−1.17953	−0.589767	+	0.807573i	$0.700780\pi$
$822$	−1.26793e7	−0.654507
$823$	1.06573e6	0.0548464	0.0274232	−	0.999624i	$-0.491270\pi$
$823$	1.06573e6	0.0548464	0.0274232	+	0.999624i	$0.491270\pi$
$824$	9.05679e6	0.464682
$825$	−775259.	−0.0396563
$826$	3.78314e6	0.192931
$827$	1.60398e6	0.0815520	0.0407760	−	0.999168i	$-0.487017\pi$
$827$	1.60398e6	0.0815520	0.0407760	+	0.999168i	$0.487017\pi$
$828$	3.77882e6	0.191549
$829$	1.47136e7	0.743589	0.371794	−	0.928315i	$-0.378743\pi$
$829$	1.47136e7	0.743589	0.371794	+	0.928315i	$0.378743\pi$
$830$	2.52206e6	0.127075
$831$	6.06310e6	0.304573
$832$	498658.	0.0249743
$833$	2.33894e7	1.16790
$834$	9.86973e6	0.491349
$835$	1.26471e7	0.627732
$836$	−796071.	−0.0393945
$837$	−3.45949e6	−0.170686
$838$	−2.14559e7	−1.05545
$839$	3.57233e7	1.75205	0.876026	−	0.482263i	$-0.160185\pi$
$839$	3.57233e7	1.75205	0.876026	+	0.482263i	$0.160185\pi$
$840$	−776154.	−0.0379533
$841$	4.24595e7	2.07007
$842$	−1.12540e7	−0.547050
$843$	−2.21488e6	−0.107345
$844$	−1.00158e6	−0.0483984
$845$	8.91179e6	0.429362
$846$	−9.11019e6	−0.437624
$847$	−7.65674e6	−0.366721
$848$	−1.35275e6	−0.0645993
$849$	−2.21595e7	−1.05510
$850$	4.20618e6	0.199683
$851$	−2.12870e7	−1.00761
$852$	6.23106e6	0.294078
$853$	−9.51318e6	−0.447665	−0.223832	−	0.974628i	$-0.571857\pi$
$853$	−9.51318e6	−0.447665	−0.223832	+	0.974628i	$0.571857\pi$
$854$	−4.66169e6	−0.218725
$855$	731025.	0.0341993
$856$	−301864.	−0.0140808
$857$	1.32585e6	0.0616656	0.0308328	−	0.999525i	$-0.490184\pi$
$857$	1.32585e6	0.0616656	0.0308328	+	0.999525i	$0.490184\pi$
$858$	604045.	0.0280125
$859$	−1.00800e7	−0.466099	−0.233049	−	0.972465i	$-0.574870\pi$
$859$	−1.00800e7	−0.466099	−0.233049	+	0.972465i	$0.574870\pi$
$860$	−7.74435e6	−0.357058
$861$	−1.84987e6	−0.0850420
$862$	1.46693e7	0.672423
$863$	1.91198e7	0.873887	0.436944	−	0.899489i	$-0.356061\pi$
$863$	1.91198e7	0.873887	0.436944	+	0.899489i	$0.356061\pi$
$864$	746496.	0.0340207
$865$	1.07658e7	0.489223
$866$	1.27735e7	0.578780
$867$	−1.26977e7	−0.573690
$868$	4.09252e6	0.184370
$869$	1.33060e7	0.597722
$870$	7.14186e6	0.319899
$871$	−1.50654e6	−0.0672875
$872$	3.46573e6	0.154349
$873$	9.70054e6	0.430785
$874$	4.21035e6	0.186440
$875$	−842181.	−0.0371865
$876$	−1.34484e6	−0.0592122
$877$	2.15867e7	0.947735	0.473867	−	0.880596i	$-0.342858\pi$
$877$	2.15867e7	0.947735	0.473867	+	0.880596i	$0.342858\pi$
$878$	−1.93738e7	−0.848162
$879$	1.35276e7	0.590541
$880$	−882073.	−0.0383970
$881$	4.57781e7	1.98709	0.993546	−	0.113433i	$-0.0361846\pi$
$881$	4.57781e7	1.98709	0.993546	+	0.113433i	$0.0361846\pi$
$882$	4.50419e6	0.194960
$883$	−1.24168e6	−0.0535931	−0.0267966	−	0.999641i	$-0.508531\pi$
$883$	−1.24168e6	−0.0535931	−0.0267966	+	0.999641i	$0.508531\pi$
$884$	−3.27726e6	−0.141052
$885$	−3.94811e6	−0.169446
$886$	−1.53099e7	−0.655222
$887$	2.34585e7	1.00113	0.500567	−	0.865698i	$-0.333125\pi$
$887$	2.34585e7	1.00113	0.500567	+	0.865698i	$0.333125\pi$
$888$	−4.20520e6	−0.178959
$889$	251400.	0.0106687
$890$	2.71910e6	0.115067
$891$	904262.	0.0381593
$892$	1.83917e7	0.773946
$893$	−1.01506e7	−0.425952
$894$	3.83165e6	0.160340
$895$	5.31558e6	0.221816
$896$	−883091.	−0.0367482
$897$	−3.19474e6	−0.132573
$898$	1.82002e7	0.753157
$899$	−3.76577e7	−1.55401
$900$	810000.	0.0333333
$901$	8.89048e6	0.364849
$902$	−2.10231e6	−0.0860362
$903$	−9.39189e6	−0.383295
$904$	−7.81600e6	−0.318100
$905$	1.68829e7	0.685213
$906$	7.56965e6	0.306376
$907$	3.96914e7	1.60206	0.801028	−	0.598626i	$-0.204287\pi$
$907$	3.96914e7	1.60206	0.801028	+	0.598626i	$0.204287\pi$
$908$	−8.94271e6	−0.359960
$909$	−3.76455e6	−0.151113
$910$	656188.	0.0262679
$911$	1.58251e7	0.631757	0.315879	−	0.948800i	$-0.397701\pi$
$911$	1.58251e7	0.631757	0.315879	+	0.948800i	$0.397701\pi$
$912$	831744.	0.0331133
$913$	3.47600e6	0.138007
$914$	−1.56289e7	−0.618817
$915$	4.86497e6	0.192100
$916$	−2.51673e7	−0.991057
$917$	−1.90259e7	−0.747175
$918$	−4.90609e6	−0.192145
$919$	2.09138e7	0.816855	0.408428	−	0.912791i	$-0.366077\pi$
$919$	2.09138e7	0.816855	0.408428	+	0.912791i	$0.366077\pi$
$920$	4.66521e6	0.181719
$921$	1.10621e7	0.429723
$922$	−2.10507e7	−0.815530
$923$	−5.26795e6	−0.203534
$924$	−1.06973e6	−0.0412185
$925$	−4.56293e6	−0.175344
$926$	−2.86770e7	−1.09902
$927$	−1.14625e7	−0.438107
$928$	8.12585e6	0.309741
$929$	2.94233e7	1.11854	0.559270	−	0.828985i	$-0.311081\pi$
$929$	2.94233e7	1.11854	0.559270	+	0.828985i	$0.311081\pi$
$930$	−4.27098e6	−0.161927
$931$	5.01856e6	0.189760
$932$	−6.13453e6	−0.231335
$933$	1.99901e7	0.751814
$934$	2.65149e7	0.994540
$935$	5.79712e6	0.216862
$936$	−631113.	−0.0235460
$937$	−3.29112e7	−1.22460	−0.612301	−	0.790625i	$-0.709756\pi$
$937$	−3.29112e7	−1.22460	−0.612301	+	0.790625i	$0.709756\pi$
$938$	2.66798e6	0.0990093
$939$	−1.94830e7	−0.721093
$940$	−1.12471e7	−0.415167
$941$	−9.35784e6	−0.344510	−0.172255	−	0.985052i	$-0.555105\pi$
$941$	−9.35784e6	−0.344510	−0.172255	+	0.985052i	$0.555105\pi$
$942$	−2.91295e6	−0.106956
$943$	1.11190e7	0.407179
$944$	−4.49208e6	−0.164065
$945$	982320.	0.0357827
$946$	−1.06736e7	−0.387777
$947$	1.02869e7	0.372742	0.186371	−	0.982479i	$-0.440327\pi$
$947$	1.02869e7	0.372742	0.186371	+	0.982479i	$0.440327\pi$
$948$	−1.39023e7	−0.502418
$949$	1.13698e6	0.0409813
$950$	902500.	0.0324443
$951$	−1.85127e7	−0.663772
$952$	5.80381e6	0.207549
$953$	−1.10120e7	−0.392767	−0.196383	−	0.980527i	$-0.562920\pi$
$953$	−1.10120e7	−0.392767	−0.196383	+	0.980527i	$0.562920\pi$
$954$	1.71207e6	0.0609048
$955$	1.24817e7	0.442859
$956$	−5.08436e6	−0.179925
$957$	9.84319e6	0.347421
$958$	−235464.	−0.00828915
$959$	−1.89835e7	−0.666546
$960$	921600.	0.0322749
$961$	−6.10908e6	−0.213387
$962$	3.55522e6	0.123859
$963$	382046.	0.0132755
$964$	−2.09461e7	−0.725955
$965$	−4.90186e6	−0.169450
$966$	5.65769e6	0.195073
$967$	−1.85043e7	−0.636366	−0.318183	−	0.948029i	$-0.603073\pi$
$967$	−1.85043e7	−0.636366	−0.318183	+	0.948029i	$0.603073\pi$
$968$	9.09156e6	0.311853
$969$	−5.46635e6	−0.187020
$970$	1.19760e7	0.408678
$971$	4.72576e6	0.160851	0.0804255	−	0.996761i	$-0.474372\pi$
$971$	4.72576e6	0.160851	0.0804255	+	0.996761i	$0.474372\pi$
$972$	−944784.	−0.0320750
$973$	1.47771e7	0.500387
$974$	3.78422e7	1.27814
$975$	−684802.	−0.0230703
$976$	5.53526e6	0.186000
$977$	2.27688e6	0.0763140	0.0381570	−	0.999272i	$-0.487851\pi$
$977$	2.27688e6	0.0763140	0.0381570	+	0.999272i	$0.487851\pi$
$978$	−1.36358e7	−0.455863
$979$	3.74757e6	0.124966
$980$	5.56073e6	0.184955
$981$	−4.38631e6	−0.145522
$982$	−2.26901e7	−0.750857
$983$	3.13944e7	1.03626	0.518130	−	0.855302i	$-0.326628\pi$
$983$	3.13944e7	1.03626	0.518130	+	0.855302i	$0.326628\pi$
$984$	2.19652e6	0.0723183
$985$	−9.25980e6	−0.304096
$986$	−5.34044e7	−1.74938
$987$	−1.36399e7	−0.445674
$988$	−703185.	−0.0229180
$989$	5.64516e7	1.83521
$990$	1.11637e6	0.0362011
$991$	−5.51463e7	−1.78374	−0.891871	−	0.452290i	$-0.850607\pi$
$991$	−5.51463e7	−1.78374	−0.891871	+	0.452290i	$0.850607\pi$
$992$	−4.85942e6	−0.156785
$993$	−2.78701e7	−0.896944
$994$	9.32921e6	0.299488
$995$	1.54699e7	0.495369
$996$	−3.63176e6	−0.116003
$997$	−4.29716e7	−1.36913	−0.684564	−	0.728953i	$-0.740007\pi$
$997$	−4.29716e7	−1.36913	−0.684564	+	0.728953i	$0.740007\pi$
$998$	3.99312e7	1.26907
$999$	5.32220e6	0.168724

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.a.i.1.3	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +53.8996 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +53.8996 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +137.824 q^{11} -144.000 q^{12} +121.743 q^{13} -215.598 q^{14} +225.000 q^{15} +256.000 q^{16} -1682.47 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -485.096 q^{21} -551.295 q^{22} +2915.75 q^{23} +576.000 q^{24} +625.000 q^{25} -486.970 q^{26} -729.000 q^{27} +862.394 q^{28} -7935.40 q^{29} -900.000 q^{30} +4745.53 q^{31} -1024.00 q^{32} -1240.41 q^{33} +6729.89 q^{34} -1347.49 q^{35} +1296.00 q^{36} -7300.69 q^{37} +1444.00 q^{38} -1095.68 q^{39} +1600.00 q^{40} +3813.41 q^{41} +1940.39 q^{42} +19360.9 q^{43} +2205.18 q^{44} -2025.00 q^{45} -11663.0 q^{46} +28117.9 q^{47} -2304.00 q^{48} -13901.8 q^{49} -2500.00 q^{50} +15142.2 q^{51} +1947.88 q^{52} -5284.18 q^{53} +2916.00 q^{54} -3445.60 q^{55} -3449.57 q^{56} +3249.00 q^{57} +31741.6 q^{58} -17547.2 q^{59} +3600.00 q^{60} +21622.1 q^{61} -18982.1 q^{62} +4365.87 q^{63} +4096.00 q^{64} -3043.56 q^{65} +4961.66 q^{66} -12374.8 q^{67} -26919.6 q^{68} -26241.8 q^{69} +5389.96 q^{70} -43271.2 q^{71} -5184.00 q^{72} +9339.19 q^{73} +29202.8 q^{74} -5625.00 q^{75} -5776.00 q^{76} +7428.65 q^{77} +4382.73 q^{78} +96543.7 q^{79} -6400.00 q^{80} +6561.00 q^{81} -15253.6 q^{82} +25220.6 q^{83} -7761.54 q^{84} +42061.8 q^{85} -77443.5 q^{86} +71418.6 q^{87} -8820.73 q^{88} +27191.0 q^{89} +8100.00 q^{90} +6561.88 q^{91} +46652.1 q^{92} -42709.8 q^{93} -112471. q^{94} +9025.00 q^{95} +9216.00 q^{96} +119760. q^{97} +55607.3 q^{98} +11163.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 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	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 460 q^{11} - 576 q^{12} + 296 q^{13} - 432 q^{14} + 900 q^{15} + 1024 q^{16} - 412 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 972 q^{21} + 1840 q^{22} - 768 q^{23} + 2304 q^{24} + 2500 q^{25} - 1184 q^{26} - 2916 q^{27} + 1728 q^{28} - 1828 q^{29} - 3600 q^{30} + 3856 q^{31} - 4096 q^{32} + 4140 q^{33} + 1648 q^{34} - 2700 q^{35} + 5184 q^{36} + 11456 q^{37} + 5776 q^{38} - 2664 q^{39} + 6400 q^{40} - 12904 q^{41} + 3888 q^{42} + 15096 q^{43} - 7360 q^{44} - 8100 q^{45} + 3072 q^{46} + 17040 q^{47} - 9216 q^{48} + 33708 q^{49} - 10000 q^{50} + 3708 q^{51} + 4736 q^{52} + 16728 q^{53} + 11664 q^{54} + 11500 q^{55} - 6912 q^{56} + 12996 q^{57} + 7312 q^{58} - 19760 q^{59} + 14400 q^{60} + 47168 q^{61} - 15424 q^{62} + 8748 q^{63} + 16384 q^{64} - 7400 q^{65} - 16560 q^{66} + 104580 q^{67} - 6592 q^{68} + 6912 q^{69} + 10800 q^{70} - 36764 q^{71} - 20736 q^{72} + 74356 q^{73} - 45824 q^{74} - 22500 q^{75} - 23104 q^{76} + 75356 q^{77} + 10656 q^{78} + 80920 q^{79} - 25600 q^{80} + 26244 q^{81} + 51616 q^{82} + 19416 q^{83} - 15552 q^{84} + 10300 q^{85} - 60384 q^{86} + 16452 q^{87} + 29440 q^{88} - 4760 q^{89} + 32400 q^{90} + 32288 q^{91} - 12288 q^{92} - 34704 q^{93} - 68160 q^{94} + 36100 q^{95} + 36864 q^{96} + 139572 q^{97} - 134832 q^{98} - 37260 q^{99}+O(q^{100}) \) 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 - 460 * q^11 - 576 * q^12 + 296 * q^13 - 432 * q^14 + 900 * q^15 + 1024 * q^16 - 412 * q^17 - 1296 * q^18 - 1444 * q^19 - 1600 * q^20 - 972 * q^21 + 1840 * q^22 - 768 * q^23 + 2304 * q^24 + 2500 * q^25 - 1184 * q^26 - 2916 * q^27 + 1728 * q^28 - 1828 * q^29 - 3600 * q^30 + 3856 * q^31 - 4096 * q^32 + 4140 * q^33 + 1648 * q^34 - 2700 * q^35 + 5184 * q^36 + 11456 * q^37 + 5776 * q^38 - 2664 * q^39 + 6400 * q^40 - 12904 * q^41 + 3888 * q^42 + 15096 * q^43 - 7360 * q^44 - 8100 * q^45 + 3072 * q^46 + 17040 * q^47 - 9216 * q^48 + 33708 * q^49 - 10000 * q^50 + 3708 * q^51 + 4736 * q^52 + 16728 * q^53 + 11664 * q^54 + 11500 * q^55 - 6912 * q^56 + 12996 * q^57 + 7312 * q^58 - 19760 * q^59 + 14400 * q^60 + 47168 * q^61 - 15424 * q^62 + 8748 * q^63 + 16384 * q^64 - 7400 * q^65 - 16560 * q^66 + 104580 * q^67 - 6592 * q^68 + 6912 * q^69 + 10800 * q^70 - 36764 * q^71 - 20736 * q^72 + 74356 * q^73 - 45824 * q^74 - 22500 * q^75 - 23104 * q^76 + 75356 * q^77 + 10656 * q^78 + 80920 * q^79 - 25600 * q^80 + 26244 * q^81 + 51616 * q^82 + 19416 * q^83 - 15552 * q^84 + 10300 * q^85 - 60384 * q^86 + 16452 * q^87 + 29440 * q^88 - 4760 * q^89 + 32400 * q^90 + 32288 * q^91 - 12288 * q^92 - 34704 * q^93 - 68160 * q^94 + 36100 * q^95 + 36864 * q^96 + 139572 * q^97 - 134832 * q^98 - 37260 * q^99

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