LMFDB - Embedded newform 570.6.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$91.4187772934$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 12189x^{2} - 95210x + 4841400 $ x^4 - 12189x^2 - 95210x + 4841400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-104.052$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +42.1343 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +42.1343 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -210.758 q^{11} -144.000 q^{12} -674.620 q^{13} -168.537 q^{14} +225.000 q^{15} +256.000 q^{16} -1996.35 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} -379.209 q^{21} +843.032 q^{22} +2914.64 q^{23} +576.000 q^{24} +625.000 q^{25} +2698.48 q^{26} -729.000 q^{27} +674.149 q^{28} +7863.10 q^{29} -900.000 q^{30} -8458.62 q^{31} -1024.00 q^{32} +1896.82 q^{33} +7985.38 q^{34} -1053.36 q^{35} +1296.00 q^{36} -8801.15 q^{37} -1444.00 q^{38} +6071.58 q^{39} +1600.00 q^{40} +717.020 q^{41} +1516.84 q^{42} -11462.2 q^{43} -3372.13 q^{44} -2025.00 q^{45} -11658.6 q^{46} -6461.06 q^{47} -2304.00 q^{48} -15031.7 q^{49} -2500.00 q^{50} +17967.1 q^{51} -10793.9 q^{52} +7494.65 q^{53} +2916.00 q^{54} +5268.95 q^{55} -2696.60 q^{56} -3249.00 q^{57} -31452.4 q^{58} -32213.5 q^{59} +3600.00 q^{60} +7348.69 q^{61} +33834.5 q^{62} +3412.88 q^{63} +4096.00 q^{64} +16865.5 q^{65} -7587.29 q^{66} -10250.8 q^{67} -31941.5 q^{68} -26231.8 q^{69} +4213.43 q^{70} +28256.7 q^{71} -5184.00 q^{72} +37170.4 q^{73} +35204.6 q^{74} -5625.00 q^{75} +5776.00 q^{76} -8880.15 q^{77} -24286.3 q^{78} -7304.46 q^{79} -6400.00 q^{80} +6561.00 q^{81} -2868.08 q^{82} -94295.6 q^{83} -6067.34 q^{84} +49908.7 q^{85} +45848.9 q^{86} -70767.9 q^{87} +13488.5 q^{88} -57710.2 q^{89} +8100.00 q^{90} -28424.7 q^{91} +46634.3 q^{92} +76127.6 q^{93} +25844.2 q^{94} -9025.00 q^{95} +9216.00 q^{96} -151919. q^{97} +60126.8 q^{98} -17071.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 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 - 88 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} + 940 q^{11} - 576 q^{12} - 34 q^{13} + 352 q^{14} + 900 q^{15} + 1024 q^{16} - 138 q^{17} - 1296 q^{18} + 1444 q^{19} - 1600 q^{20} + 792 q^{21} - 3760 q^{22} + 486 q^{23} + 2304 q^{24} + 2500 q^{25} + 136 q^{26} - 2916 q^{27} - 1408 q^{28} + 3296 q^{29} - 3600 q^{30} - 6686 q^{31} - 4096 q^{32} - 8460 q^{33} + 552 q^{34} + 2200 q^{35} + 5184 q^{36} - 14218 q^{37} - 5776 q^{38} + 306 q^{39} + 6400 q^{40} + 1342 q^{41} - 3168 q^{42} - 26330 q^{43} + 15040 q^{44} - 8100 q^{45} - 1944 q^{46} - 7010 q^{47} - 9216 q^{48} + 192 q^{49} - 10000 q^{50} + 1242 q^{51} - 544 q^{52} - 22782 q^{53} + 11664 q^{54} - 23500 q^{55} + 5632 q^{56} - 12996 q^{57} - 13184 q^{58} - 13358 q^{59} + 14400 q^{60} + 16008 q^{61} + 26744 q^{62} - 7128 q^{63} + 16384 q^{64} + 850 q^{65} + 33840 q^{66} - 22696 q^{67} - 2208 q^{68} - 4374 q^{69} - 8800 q^{70} + 52584 q^{71} - 20736 q^{72} - 101048 q^{73} + 56872 q^{74} - 22500 q^{75} + 23104 q^{76} - 103772 q^{77} - 1224 q^{78} - 113090 q^{79} - 25600 q^{80} + 26244 q^{81} - 5368 q^{82} - 65384 q^{83} + 12672 q^{84} + 3450 q^{85} + 105320 q^{86} - 29664 q^{87} - 60160 q^{88} + 97354 q^{89} + 32400 q^{90} - 125600 q^{91} + 7776 q^{92} + 60174 q^{93} + 28040 q^{94} - 36100 q^{95} + 36864 q^{96} - 198934 q^{97} - 768 q^{98} + 76140 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 + 940 * q^11 - 576 * q^12 - 34 * q^13 + 352 * q^14 + 900 * q^15 + 1024 * q^16 - 138 * q^17 - 1296 * q^18 + 1444 * q^19 - 1600 * q^20 + 792 * q^21 - 3760 * q^22 + 486 * q^23 + 2304 * q^24 + 2500 * q^25 + 136 * q^26 - 2916 * q^27 - 1408 * q^28 + 3296 * q^29 - 3600 * q^30 - 6686 * q^31 - 4096 * q^32 - 8460 * q^33 + 552 * q^34 + 2200 * q^35 + 5184 * q^36 - 14218 * q^37 - 5776 * q^38 + 306 * q^39 + 6400 * q^40 + 1342 * q^41 - 3168 * q^42 - 26330 * q^43 + 15040 * q^44 - 8100 * q^45 - 1944 * q^46 - 7010 * q^47 - 9216 * q^48 + 192 * q^49 - 10000 * q^50 + 1242 * q^51 - 544 * q^52 - 22782 * q^53 + 11664 * q^54 - 23500 * q^55 + 5632 * q^56 - 12996 * q^57 - 13184 * q^58 - 13358 * q^59 + 14400 * q^60 + 16008 * q^61 + 26744 * q^62 - 7128 * q^63 + 16384 * q^64 + 850 * q^65 + 33840 * q^66 - 22696 * q^67 - 2208 * q^68 - 4374 * q^69 - 8800 * q^70 + 52584 * q^71 - 20736 * q^72 - 101048 * q^73 + 56872 * q^74 - 22500 * q^75 + 23104 * q^76 - 103772 * q^77 - 1224 * q^78 - 113090 * q^79 - 25600 * q^80 + 26244 * q^81 - 5368 * q^82 - 65384 * q^83 + 12672 * q^84 + 3450 * q^85 + 105320 * q^86 - 29664 * q^87 - 60160 * q^88 + 97354 * q^89 + 32400 * q^90 - 125600 * q^91 + 7776 * q^92 + 60174 * q^93 + 28040 * q^94 - 36100 * q^95 + 36864 * q^96 - 198934 * q^97 - 768 * q^98 + 76140 * 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
$7$	42.1343	0.325006	0.162503	−	0.986708i	$-0.448043\pi$
$7$	42.1343	0.325006	0.162503	+	0.986708i	$0.448043\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	−210.758	−0.525173	−0.262587	−	0.964908i	$-0.584576\pi$
$11$	−210.758	−0.525173	−0.262587	+	0.964908i	$0.584576\pi$
$12$	−144.000	−0.288675
$13$	−674.620	−1.10714	−0.553568	−	0.832804i	$-0.686734\pi$
$13$	−674.620	−1.10714	−0.553568	+	0.832804i	$0.686734\pi$
$14$	−168.537	−0.229814
$15$	225.000	0.258199
$16$	256.000	0.250000
$17$	−1996.35	−1.67538	−0.837690	−	0.546145i	$-0.816095\pi$
$17$	−1996.35	−1.67538	−0.837690	+	0.546145i	$0.816095\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	−379.209	−0.187642
$22$	843.032	0.371353
$23$	2914.64	1.14886	0.574428	−	0.818555i	$-0.305225\pi$
$23$	2914.64	1.14886	0.574428	+	0.818555i	$0.305225\pi$
$24$	576.000	0.204124
$25$	625.000	0.200000
$26$	2698.48	0.782863
$27$	−729.000	−0.192450
$28$	674.149	0.162503
$29$	7863.10	1.73620	0.868098	−	0.496393i	$-0.165343\pi$
$29$	7863.10	1.73620	0.868098	+	0.496393i	$0.165343\pi$
$30$	−900.000	−0.182574
$31$	−8458.62	−1.58087	−0.790434	−	0.612548i	$-0.790145\pi$
$31$	−8458.62	−1.58087	−0.790434	+	0.612548i	$0.790145\pi$
$32$	−1024.00	−0.176777
$33$	1896.82	0.303209
$34$	7985.38	1.18467
$35$	−1053.36	−0.145347
$36$	1296.00	0.166667
$37$	−8801.15	−1.05690	−0.528451	−	0.848964i	$-0.677227\pi$
$37$	−8801.15	−1.05690	−0.528451	+	0.848964i	$0.677227\pi$
$38$	−1444.00	−0.162221
$39$	6071.58	0.639205
$40$	1600.00	0.158114
$41$	717.020	0.0666149	0.0333075	−	0.999445i	$-0.489396\pi$
$41$	717.020	0.0666149	0.0333075	+	0.999445i	$0.489396\pi$
$42$	1516.84	0.132683
$43$	−11462.2	−0.945362	−0.472681	−	0.881234i	$-0.656714\pi$
$43$	−11462.2	−0.945362	−0.472681	+	0.881234i	$0.656714\pi$
$44$	−3372.13	−0.262587
$45$	−2025.00	−0.149071
$46$	−11658.6	−0.812364
$47$	−6461.06	−0.426638	−0.213319	−	0.976983i	$-0.568427\pi$
$47$	−6461.06	−0.426638	−0.213319	+	0.976983i	$0.568427\pi$
$48$	−2304.00	−0.144338
$49$	−15031.7	−0.894371
$50$	−2500.00	−0.141421
$51$	17967.1	0.967282
$52$	−10793.9	−0.553568
$53$	7494.65	0.366489	0.183245	−	0.983067i	$-0.441340\pi$
$53$	7494.65	0.366489	0.183245	+	0.983067i	$0.441340\pi$
$54$	2916.00	0.136083
$55$	5268.95	0.234865
$56$	−2696.60	−0.114907
$57$	−3249.00	−0.132453
$58$	−31452.4	−1.22768
$59$	−32213.5	−1.20478	−0.602389	−	0.798202i	$-0.705785\pi$
$59$	−32213.5	−1.20478	−0.602389	+	0.798202i	$0.705785\pi$
$60$	3600.00	0.129099
$61$	7348.69	0.252863	0.126432	−	0.991975i	$-0.459648\pi$
$61$	7348.69	0.252863	0.126432	+	0.991975i	$0.459648\pi$
$62$	33834.5	1.11784
$63$	3412.88	0.108335
$64$	4096.00	0.125000
$65$	16865.5	0.495126
$66$	−7587.29	−0.214401
$67$	−10250.8	−0.278980	−0.139490	−	0.990223i	$-0.544546\pi$
$67$	−10250.8	−0.278980	−0.139490	+	0.990223i	$0.544546\pi$
$68$	−31941.5	−0.837690
$69$	−26231.8	−0.663292
$70$	4213.43	0.102776
$71$	28256.7	0.665236	0.332618	−	0.943062i	$-0.392068\pi$
$71$	28256.7	0.665236	0.332618	+	0.943062i	$0.392068\pi$
$72$	−5184.00	−0.117851
$73$	37170.4	0.816375	0.408188	−	0.912898i	$-0.366161\pi$
$73$	37170.4	0.816375	0.408188	+	0.912898i	$0.366161\pi$
$74$	35204.6	0.747343
$75$	−5625.00	−0.115470
$76$	5776.00	0.114708
$77$	−8880.15	−0.170684
$78$	−24286.3	−0.451986
$79$	−7304.46	−0.131680	−0.0658401	−	0.997830i	$-0.520973\pi$
$79$	−7304.46	−0.131680	−0.0658401	+	0.997830i	$0.520973\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	−2868.08	−0.0471039
$83$	−94295.6	−1.50244	−0.751219	−	0.660053i	$-0.770534\pi$
$83$	−94295.6	−1.50244	−0.751219	+	0.660053i	$0.770534\pi$
$84$	−6067.34	−0.0938211
$85$	49908.7	0.749253
$86$	45848.9	0.668472
$87$	−70767.9	−1.00239
$88$	13488.5	0.185677
$89$	−57710.2	−0.772284	−0.386142	−	0.922439i	$-0.626193\pi$
$89$	−57710.2	−0.772284	−0.386142	+	0.922439i	$0.626193\pi$
$90$	8100.00	0.105409
$91$	−28424.7	−0.359825
$92$	46634.3	0.574428
$93$	76127.6	0.912714
$94$	25844.2	0.301678
$95$	−9025.00	−0.102598
$96$	9216.00	0.102062
$97$	−151919.	−1.63939	−0.819695	−	0.572800i	$-0.805857\pi$
$97$	−151919.	−1.63939	−0.819695	+	0.572800i	$0.805857\pi$
$98$	60126.8	0.632416
$99$	−17071.4	−0.175058
$100$	10000.0	0.100000
$101$	71256.4	0.695057	0.347528	−	0.937669i	$-0.387021\pi$
$101$	71256.4	0.695057	0.347528	+	0.937669i	$0.387021\pi$
$102$	−71868.5	−0.683971
$103$	−71251.3	−0.661759	−0.330879	−	0.943673i	$-0.607345\pi$
$103$	−71251.3	−0.661759	−0.330879	+	0.943673i	$0.607345\pi$
$104$	43175.7	0.391432
$105$	9480.22	0.0839161
$106$	−29978.6	−0.259147
$107$	77968.5	0.658355	0.329177	−	0.944268i	$-0.393229\pi$
$107$	77968.5	0.658355	0.329177	+	0.944268i	$0.393229\pi$
$108$	−11664.0	−0.0962250
$109$	185434.	1.49494	0.747468	−	0.664297i	$-0.231269\pi$
$109$	185434.	1.49494	0.747468	+	0.664297i	$0.231269\pi$
$110$	−21075.8	−0.166074
$111$	79210.3	0.610203
$112$	10786.4	0.0812514
$113$	224770.	1.65593	0.827965	−	0.560780i	$-0.189499\pi$
$113$	224770.	1.65593	0.827965	+	0.560780i	$0.189499\pi$
$114$	12996.0	0.0936586
$115$	−72866.0	−0.513784
$116$	125810.	0.868098
$117$	−54644.2	−0.369045
$118$	128854.	0.851907
$119$	−84114.7	−0.544508
$120$	−14400.0	−0.0912871
$121$	−116632.	−0.724193
$122$	−29394.8	−0.178801
$123$	−6453.18	−0.0384602
$124$	−135338.	−0.790434
$125$	−15625.0	−0.0894427
$126$	−13651.5	−0.0766046
$127$	−167574.	−0.921930	−0.460965	−	0.887418i	$-0.652497\pi$
$127$	−167574.	−0.921930	−0.460965	+	0.887418i	$0.652497\pi$
$128$	−16384.0	−0.0883883
$129$	103160.	0.545805
$130$	−67462.0	−0.350107
$131$	12110.8	0.0616588	0.0308294	−	0.999525i	$-0.490185\pi$
$131$	12110.8	0.0616588	0.0308294	+	0.999525i	$0.490185\pi$
$132$	30349.2	0.151604
$133$	15210.5	0.0745614
$134$	41003.4	0.197268
$135$	18225.0	0.0860663
$136$	127766.	0.592337
$137$	312481.	1.42240	0.711200	−	0.702990i	$-0.248152\pi$
$137$	312481.	1.42240	0.711200	+	0.702990i	$0.248152\pi$
$138$	104927.	0.469018
$139$	−22038.4	−0.0967483	−0.0483741	−	0.998829i	$-0.515404\pi$
$139$	−22038.4	−0.0967483	−0.0483741	+	0.998829i	$0.515404\pi$
$140$	−16853.7	−0.0726735
$141$	58149.5	0.246319
$142$	−113027.	−0.470393
$143$	142182.	0.581438
$144$	20736.0	0.0833333
$145$	−196577.	−0.776450
$146$	−148681.	−0.577264
$147$	135285.	0.516365
$148$	−140818.	−0.528451
$149$	143488.	0.529481	0.264741	−	0.964320i	$-0.414714\pi$
$149$	143488.	0.529481	0.264741	+	0.964320i	$0.414714\pi$
$150$	22500.0	0.0816497
$151$	60288.0	0.215173	0.107587	−	0.994196i	$-0.465688\pi$
$151$	60288.0	0.215173	0.107587	+	0.994196i	$0.465688\pi$
$152$	−23104.0	−0.0811107
$153$	−161704.	−0.558460
$154$	35520.6	0.120692
$155$	211466.	0.706985
$156$	97145.3	0.319603
$157$	268382.	0.868968	0.434484	−	0.900680i	$-0.356931\pi$
$157$	268382.	0.868968	0.434484	+	0.900680i	$0.356931\pi$
$158$	29217.8	0.0931119
$159$	−67451.8	−0.211593
$160$	25600.0	0.0790569
$161$	122806.	0.373385
$162$	−26244.0	−0.0785674
$163$	578510.	1.70546	0.852730	−	0.522351i	$-0.174945\pi$
$163$	578510.	1.70546	0.852730	+	0.522351i	$0.174945\pi$
$164$	11472.3	0.0333075
$165$	−47420.6	−0.135599
$166$	377183.	1.06238
$167$	526620.	1.46119	0.730593	−	0.682813i	$-0.239243\pi$
$167$	526620.	1.46119	0.730593	+	0.682813i	$0.239243\pi$
$168$	24269.4	0.0663415
$169$	83819.3	0.225750
$170$	−199635.	−0.529802
$171$	29241.0	0.0764719
$172$	−183396.	−0.472681
$173$	−719527.	−1.82781	−0.913907	−	0.405924i	$-0.866950\pi$
$173$	−719527.	−1.82781	−0.913907	+	0.405924i	$0.866950\pi$
$174$	283071.	0.708799
$175$	26334.0	0.0650011
$176$	−53954.1	−0.131293
$177$	289921.	0.695579
$178$	230841.	0.546088
$179$	81155.9	0.189316	0.0946580	−	0.995510i	$-0.469824\pi$
$179$	81155.9	0.189316	0.0946580	+	0.995510i	$0.469824\pi$
$180$	−32400.0	−0.0745356
$181$	395071.	0.896351	0.448176	−	0.893946i	$-0.352074\pi$
$181$	395071.	0.896351	0.448176	+	0.893946i	$0.352074\pi$
$182$	113699.	0.254435
$183$	−66138.2	−0.145991
$184$	−186537.	−0.406182
$185$	220029.	0.472661
$186$	−304510.	−0.645386
$187$	420746.	0.879865
$188$	−103377.	−0.213319
$189$	−30715.9	−0.0625474
$190$	36100.0	0.0725476
$191$	882496.	1.75037	0.875184	−	0.483790i	$-0.160740\pi$
$191$	882496.	1.75037	0.875184	+	0.483790i	$0.160740\pi$
$192$	−36864.0	−0.0721688
$193$	315735.	0.610140	0.305070	−	0.952330i	$-0.401320\pi$
$193$	315735.	0.610140	0.305070	+	0.952330i	$0.401320\pi$
$194$	607675.	1.15922
$195$	−151790.	−0.285861
$196$	−240507.	−0.447186
$197$	−462680.	−0.849406	−0.424703	−	0.905333i	$-0.639622\pi$
$197$	−462680.	−0.849406	−0.424703	+	0.905333i	$0.639622\pi$
$198$	68285.6	0.123784
$199$	985520.	1.76414	0.882069	−	0.471119i	$-0.156150\pi$
$199$	985520.	1.76414	0.882069	+	0.471119i	$0.156150\pi$
$200$	−40000.0	−0.0707107
$201$	92257.6	0.161069
$202$	−285025.	−0.491479
$203$	331306.	0.564274
$204$	287474.	0.483641
$205$	−17925.5	−0.0297911
$206$	285005.	0.467934
$207$	236086.	0.382952
$208$	−172703.	−0.276784
$209$	−76083.6	−0.120483
$210$	−37920.9	−0.0593377
$211$	−349548.	−0.540506	−0.270253	−	0.962789i	$-0.587107\pi$
$211$	−349548.	−0.540506	−0.270253	+	0.962789i	$0.587107\pi$
$212$	119914.	0.183245
$213$	−254310.	−0.384074
$214$	−311874.	−0.465527
$215$	286556.	0.422779
$216$	46656.0	0.0680414
$217$	−356398.	−0.513791
$218$	−741736.	−1.05708
$219$	−334533.	−0.471334
$220$	84303.2	0.117432
$221$	1.34678e6	1.85487
$222$	−316841.	−0.431479
$223$	276536.	0.372383	0.186192	−	0.982513i	$-0.440385\pi$
$223$	276536.	0.372383	0.186192	+	0.982513i	$0.440385\pi$
$224$	−43145.6	−0.0574534
$225$	50625.0	0.0666667
$226$	−899079.	−1.17092
$227$	528814.	0.681143	0.340571	−	0.940219i	$-0.389379\pi$
$227$	528814.	0.681143	0.340571	+	0.940219i	$0.389379\pi$
$228$	−51984.0	−0.0662266
$229$	−104956.	−0.132256	−0.0661282	−	0.997811i	$-0.521065\pi$
$229$	−104956.	−0.132256	−0.0661282	+	0.997811i	$0.521065\pi$
$230$	291464.	0.363300
$231$	79921.3	0.0985446
$232$	−503238.	−0.613838
$233$	−881192.	−1.06336	−0.531681	−	0.846945i	$-0.678439\pi$
$233$	−881192.	−1.06336	−0.531681	+	0.846945i	$0.678439\pi$
$234$	218577.	0.260954
$235$	161526.	0.190798
$236$	−515415.	−0.602389
$237$	65740.1	0.0760256
$238$	336459.	0.385026
$239$	1.24460e6	1.40940	0.704701	−	0.709505i	$-0.251081\pi$
$239$	1.24460e6	1.40940	0.704701	+	0.709505i	$0.251081\pi$
$240$	57600.0	0.0645497
$241$	708069.	0.785295	0.392647	−	0.919689i	$-0.371559\pi$
$241$	708069.	0.785295	0.392647	+	0.919689i	$0.371559\pi$
$242$	466528.	0.512082
$243$	−59049.0	−0.0641500
$244$	117579.	0.126432
$245$	375792.	0.399975
$246$	25812.7	0.0271954
$247$	−243538.	−0.253994
$248$	541352.	0.558921
$249$	848661.	0.867433
$250$	62500.0	0.0632456
$251$	308105.	0.308684	0.154342	−	0.988017i	$-0.450674\pi$
$251$	308105.	0.308684	0.154342	+	0.988017i	$0.450674\pi$
$252$	54606.1	0.0541676
$253$	−614284.	−0.603348
$254$	670297.	0.651903
$255$	−449178.	−0.432581
$256$	65536.0	0.0625000
$257$	−1.61211e6	−1.52252	−0.761259	−	0.648448i	$-0.775418\pi$
$257$	−1.61211e6	−1.52252	−0.761259	+	0.648448i	$0.775418\pi$
$258$	−412640.	−0.385942
$259$	−370830.	−0.343499
$260$	269848.	0.247563
$261$	636911.	0.578732
$262$	−48443.3	−0.0435994
$263$	460120.	0.410187	0.205094	−	0.978742i	$-0.434250\pi$
$263$	460120.	0.410187	0.205094	+	0.978742i	$0.434250\pi$
$264$	−121397.	−0.107200
$265$	−187366.	−0.163899
$266$	−60842.0	−0.0527229
$267$	519392.	0.445879
$268$	−164014.	−0.139490
$269$	1.76187e6	1.48455	0.742274	−	0.670096i	$-0.233747\pi$
$269$	1.76187e6	1.48455	0.742274	+	0.670096i	$0.233747\pi$
$270$	−72900.0	−0.0608581
$271$	219007.	0.181148	0.0905741	−	0.995890i	$-0.471130\pi$
$271$	219007.	0.181148	0.0905741	+	0.995890i	$0.471130\pi$
$272$	−511065.	−0.418845
$273$	255822.	0.207745
$274$	−1.24992e6	−1.00579
$275$	−131724.	−0.105035
$276$	−419708.	−0.331646
$277$	−812005.	−0.635857	−0.317928	−	0.948115i	$-0.602987\pi$
$277$	−812005.	−0.635857	−0.317928	+	0.948115i	$0.602987\pi$
$278$	88153.6	0.0684114
$279$	−685148.	−0.526956
$280$	67414.9	0.0513879
$281$	537890.	0.406376	0.203188	−	0.979140i	$-0.434870\pi$
$281$	537890.	0.406376	0.203188	+	0.979140i	$0.434870\pi$
$282$	−232598.	−0.174174
$283$	−992700.	−0.736804	−0.368402	−	0.929667i	$-0.620095\pi$
$283$	−992700.	−0.736804	−0.368402	+	0.929667i	$0.620095\pi$
$284$	452107.	0.332618
$285$	81225.0	0.0592349
$286$	−568726.	−0.411139
$287$	30211.2	0.0216502
$288$	−82944.0	−0.0589256
$289$	2.56554e6	1.80690
$290$	786310.	0.549033
$291$	1.36727e6	0.946502
$292$	594726.	0.408188
$293$	1.48491e6	1.01049	0.505245	−	0.862976i	$-0.331402\pi$
$293$	1.48491e6	1.01049	0.505245	+	0.862976i	$0.331402\pi$
$294$	−541141.	−0.365126
$295$	805336.	0.538793
$296$	563273.	0.373671
$297$	153643.	0.101070
$298$	−573953.	−0.374400
$299$	−1.96628e6	−1.27194
$300$	−90000.0	−0.0577350
$301$	−482954.	−0.307248
$302$	−241152.	−0.152150
$303$	−641307.	−0.401291
$304$	92416.0	0.0573539
$305$	−183717.	−0.113084
$306$	646816.	0.394891
$307$	−103155.	−0.0624663	−0.0312332	−	0.999512i	$-0.509943\pi$
$307$	−103155.	−0.0624663	−0.0312332	+	0.999512i	$0.509943\pi$
$308$	−142082.	−0.0853421
$309$	641262.	0.382067
$310$	−845862.	−0.499914
$311$	−1.84732e6	−1.08303	−0.541515	−	0.840691i	$-0.682149\pi$
$311$	−1.84732e6	−1.08303	−0.541515	+	0.840691i	$0.682149\pi$
$312$	−388581.	−0.225993
$313$	−1.96273e6	−1.13240	−0.566200	−	0.824268i	$-0.691587\pi$
$313$	−1.96273e6	−1.13240	−0.566200	+	0.824268i	$0.691587\pi$
$314$	−1.07353e6	−0.614453
$315$	−85322.0	−0.0484490
$316$	−116871.	−0.0658401
$317$	1.09872e6	0.614101	0.307051	−	0.951693i	$-0.400658\pi$
$317$	1.09872e6	0.614101	0.307051	+	0.951693i	$0.400658\pi$
$318$	269807.	0.149619
$319$	−1.65721e6	−0.911803
$320$	−102400.	−0.0559017
$321$	−701717.	−0.380101
$322$	−491226.	−0.264023
$323$	−720681.	−0.384359
$324$	104976.	0.0555556
$325$	−421638.	−0.221427
$326$	−2.31404e6	−1.20594
$327$	−1.66890e6	−0.863102
$328$	−45889.3	−0.0235519
$329$	−272232.	−0.138660
$330$	189682.	0.0958830
$331$	−945619.	−0.474402	−0.237201	−	0.971461i	$-0.576230\pi$
$331$	−945619.	−0.474402	−0.237201	+	0.971461i	$0.576230\pi$
$332$	−1.50873e6	−0.751219
$333$	−712893.	−0.352301
$334$	−2.10648e6	−1.03322
$335$	256271.	0.124764
$336$	−97077.5	−0.0469105
$337$	−1.16967e6	−0.561033	−0.280516	−	0.959849i	$-0.590506\pi$
$337$	−1.16967e6	−0.561033	−0.280516	+	0.959849i	$0.590506\pi$
$338$	−335277.	−0.159629
$339$	−2.02293e6	−0.956051
$340$	798538.	0.374627
$341$	1.78272e6	0.830229
$342$	−116964.	−0.0540738
$343$	−1.34150e6	−0.615682
$344$	733583.	0.334236
$345$	655794.	0.296633
$346$	2.87811e6	1.29246
$347$	1.19758e6	0.533926	0.266963	−	0.963707i	$-0.413980\pi$
$347$	1.19758e6	0.533926	0.266963	+	0.963707i	$0.413980\pi$
$348$	−1.13229e6	−0.501196
$349$	−313078.	−0.137590	−0.0687952	−	0.997631i	$-0.521916\pi$
$349$	−313078.	−0.137590	−0.0687952	+	0.997631i	$0.521916\pi$
$350$	−105336.	−0.0459628
$351$	491798.	0.213068
$352$	215816.	0.0928384
$353$	2.31376e6	0.988282	0.494141	−	0.869382i	$-0.335483\pi$
$353$	2.31376e6	0.988282	0.494141	+	0.869382i	$0.335483\pi$
$354$	−1.15968e6	−0.491849
$355$	−706418.	−0.297503
$356$	−923363.	−0.386142
$357$	757032.	0.314372
$358$	−324623.	−0.133867
$359$	1.47275e6	0.603104	0.301552	−	0.953450i	$-0.402495\pi$
$359$	1.47275e6	0.603104	0.301552	+	0.953450i	$0.402495\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−1.58028e6	−0.633816
$363$	1.04969e6	0.418113
$364$	−454795.	−0.179913
$365$	−929259.	−0.365094
$366$	264553.	0.103231
$367$	1.99818e6	0.774408	0.387204	−	0.921994i	$-0.373441\pi$
$367$	1.99818e6	0.774408	0.387204	+	0.921994i	$0.373441\pi$
$368$	746148.	0.287214
$369$	58078.6	0.0222050
$370$	−880115.	−0.334222
$371$	315782.	0.119111
$372$	1.21804e6	0.456357
$373$	−4.08612e6	−1.52068	−0.760342	−	0.649523i	$-0.774969\pi$
$373$	−4.08612e6	−1.52068	−0.760342	+	0.649523i	$0.774969\pi$
$374$	−1.68298e6	−0.622158
$375$	140625.	0.0516398
$376$	413508.	0.150839
$377$	−5.30460e6	−1.92220
$378$	122864.	0.0442277
$379$	4.69794e6	1.68000	0.840000	−	0.542587i	$-0.182555\pi$
$379$	4.69794e6	1.68000	0.840000	+	0.542587i	$0.182555\pi$
$380$	−144400.	−0.0512989
$381$	1.50817e6	0.532277
$382$	−3.52998e6	−1.23770
$383$	970394.	0.338027	0.169013	−	0.985614i	$-0.445942\pi$
$383$	970394.	0.338027	0.169013	+	0.985614i	$0.445942\pi$
$384$	147456.	0.0510310
$385$	222004.	0.0763323
$386$	−1.26294e6	−0.431434
$387$	−928441.	−0.315121
$388$	−2.43070e6	−0.819695
$389$	4.51520e6	1.51288	0.756438	−	0.654065i	$-0.226938\pi$
$389$	4.51520e6	1.51288	0.756438	+	0.654065i	$0.226938\pi$
$390$	607158.	0.202134
$391$	−5.81863e6	−1.92477
$392$	962029.	0.316208
$393$	−108997.	−0.0355987
$394$	1.85072e6	0.600621
$395$	182611.	0.0588892
$396$	−273142.	−0.0875288
$397$	5.34819e6	1.70306	0.851531	−	0.524305i	$-0.175675\pi$
$397$	5.34819e6	1.70306	0.851531	+	0.524305i	$0.175675\pi$
$398$	−3.94208e6	−1.24743
$399$	−136894.	−0.0430481
$400$	160000.	0.0500000
$401$	1.64514e6	0.510907	0.255453	−	0.966821i	$-0.417775\pi$
$401$	1.64514e6	0.510907	0.255453	+	0.966821i	$0.417775\pi$
$402$	−369030.	−0.113893
$403$	5.70636e6	1.75023
$404$	1.14010e6	0.347528
$405$	−164025.	−0.0496904
$406$	−1.32523e6	−0.399002
$407$	1.85491e6	0.555057
$408$	−1.14990e6	−0.341986
$409$	368225.	0.108844	0.0544221	−	0.998518i	$-0.482668\pi$
$409$	368225.	0.108844	0.0544221	+	0.998518i	$0.482668\pi$
$410$	71702.0	0.0210655
$411$	−2.81233e6	−0.821223
$412$	−1.14002e6	−0.330879
$413$	−1.35729e6	−0.391560
$414$	−944344.	−0.270788
$415$	2.35739e6	0.671910
$416$	690811.	0.195716
$417$	198346.	0.0558577
$418$	304335.	0.0851943
$419$	1.01367e6	0.282073	0.141036	−	0.990004i	$-0.454957\pi$
$419$	1.01367e6	0.282073	0.141036	+	0.990004i	$0.454957\pi$
$420$	151684.	0.0419581
$421$	−5.53535e6	−1.52209	−0.761044	−	0.648700i	$-0.775313\pi$
$421$	−5.53535e6	−1.52209	−0.761044	+	0.648700i	$0.775313\pi$
$422$	1.39819e6	0.382196
$423$	−523346.	−0.142213
$424$	−479657.	−0.129574
$425$	−1.24772e6	−0.335076
$426$	1.01724e6	0.271581
$427$	309632.	0.0821820
$428$	1.24750e6	0.329177
$429$	−1.27963e6	−0.335693
$430$	−1.14622e6	−0.298950
$431$	1.29691e6	0.336292	0.168146	−	0.985762i	$-0.446222\pi$
$431$	1.29691e6	0.336292	0.168146	+	0.985762i	$0.446222\pi$
$432$	−186624.	−0.0481125
$433$	−6.89054e6	−1.76617	−0.883087	−	0.469210i	$-0.844539\pi$
$433$	−6.89054e6	−1.76617	−0.883087	+	0.469210i	$0.844539\pi$
$434$	1.42559e6	0.363305
$435$	1.76920e6	0.448284
$436$	2.96694e6	0.747468
$437$	1.05219e6	0.263566
$438$	1.33813e6	0.333284
$439$	−146297.	−0.0362304	−0.0181152	−	0.999836i	$-0.505767\pi$
$439$	−146297.	−0.0362304	−0.0181152	+	0.999836i	$0.505767\pi$
$440$	−337213.	−0.0830371
$441$	−1.21757e6	−0.298124
$442$	−5.38710e6	−1.31159
$443$	−828057.	−0.200471	−0.100235	−	0.994964i	$-0.531960\pi$
$443$	−828057.	−0.200471	−0.100235	+	0.994964i	$0.531960\pi$
$444$	1.26737e6	0.305101
$445$	1.44275e6	0.345376
$446$	−1.10615e6	−0.263315
$447$	−1.29139e6	−0.305696
$448$	172582.	0.0406257
$449$	−595290.	−0.139352	−0.0696759	−	0.997570i	$-0.522197\pi$
$449$	−595290.	−0.139352	−0.0696759	+	0.997570i	$0.522197\pi$
$450$	−202500.	−0.0471405
$451$	−151118.	−0.0349844
$452$	3.59632e6	0.827965
$453$	−542592.	−0.124230
$454$	−2.11526e6	−0.481641
$455$	710617.	0.160919
$456$	207936.	0.0468293
$457$	−5.83354e6	−1.30660	−0.653299	−	0.757100i	$-0.726615\pi$
$457$	−5.83354e6	−1.30660	−0.653299	+	0.757100i	$0.726615\pi$
$458$	419822.	0.0935194
$459$	1.45534e6	0.322427
$460$	−1.16586e6	−0.256892
$461$	1.90531e6	0.417556	0.208778	−	0.977963i	$-0.433051\pi$
$461$	1.90531e6	0.417556	0.208778	+	0.977963i	$0.433051\pi$
$462$	−319685.	−0.0696816
$463$	3.17108e6	0.687471	0.343735	−	0.939067i	$-0.388308\pi$
$463$	3.17108e6	0.687471	0.343735	+	0.939067i	$0.388308\pi$
$464$	2.01295e6	0.434049
$465$	−1.90319e6	−0.408178
$466$	3.52477e6	0.751910
$467$	−667129.	−0.141553	−0.0707763	−	0.997492i	$-0.522548\pi$
$467$	−667129.	−0.141553	−0.0707763	+	0.997492i	$0.522548\pi$
$468$	−874308.	−0.184523
$469$	−431913.	−0.0906700
$470$	−646106.	−0.134915
$471$	−2.41544e6	−0.501699
$472$	2.06166e6	0.425954
$473$	2.41576e6	0.496479
$474$	−262961.	−0.0537582
$475$	225625.	0.0458831
$476$	−1.34584e6	−0.272254
$477$	607066.	0.122163
$478$	−4.97840e6	−0.996597
$479$	−960007.	−0.191177	−0.0955885	−	0.995421i	$-0.530473\pi$
$479$	−960007.	−0.191177	−0.0955885	+	0.995421i	$0.530473\pi$
$480$	−230400.	−0.0456435
$481$	5.93743e6	1.17013
$482$	−2.83227e6	−0.555287
$483$	−1.10526e6	−0.215574
$484$	−1.86611e6	−0.362097
$485$	3.79797e6	0.733157
$486$	236196.	0.0453609
$487$	−7.75364e6	−1.48144	−0.740719	−	0.671815i	$-0.765515\pi$
$487$	−7.75364e6	−1.48144	−0.740719	+	0.671815i	$0.765515\pi$
$488$	−470316.	−0.0894006
$489$	−5.20659e6	−0.984648
$490$	−1.50317e6	−0.282825
$491$	5.73211e6	1.07303	0.536514	−	0.843892i	$-0.319741\pi$
$491$	5.73211e6	1.07303	0.536514	+	0.843892i	$0.319741\pi$
$492$	−103251.	−0.0192301
$493$	−1.56975e7	−2.90879
$494$	974151.	0.179601
$495$	426785.	0.0782882
$496$	−2.16541e6	−0.395217
$497$	1.19058e6	0.216205
$498$	−3.39464e6	−0.613367
$499$	−4.65684e6	−0.837221	−0.418610	−	0.908166i	$-0.637483\pi$
$499$	−4.65684e6	−0.837221	−0.418610	+	0.908166i	$0.637483\pi$
$500$	−250000.	−0.0447214
$501$	−4.73958e6	−0.843617
$502$	−1.23242e6	−0.218273
$503$	−9.48419e6	−1.67140	−0.835700	−	0.549186i	$-0.814938\pi$
$503$	−9.48419e6	−1.67140	−0.835700	+	0.549186i	$0.814938\pi$
$504$	−218424.	−0.0383023
$505$	−1.78141e6	−0.310839
$506$	2.45714e6	0.426632
$507$	−754373.	−0.130337
$508$	−2.68119e6	−0.460965
$509$	−3.53012e6	−0.603941	−0.301971	−	0.953317i	$-0.597644\pi$
$509$	−3.53012e6	−0.603941	−0.301971	+	0.953317i	$0.597644\pi$
$510$	1.79671e6	0.305881
$511$	1.56615e6	0.265327
$512$	−262144.	−0.0441942
$513$	−263169.	−0.0441511
$514$	6.44845e6	1.07658
$515$	1.78128e6	0.295948
$516$	1.65056e6	0.272903
$517$	1.36172e6	0.224059
$518$	1.48332e6	0.242891
$519$	6.47575e6	1.05529
$520$	−1.07939e6	−0.175054
$521$	862947.	0.139280	0.0696402	−	0.997572i	$-0.477815\pi$
$521$	862947.	0.139280	0.0696402	+	0.997572i	$0.477815\pi$
$522$	−2.54764e6	−0.409225
$523$	−1.68744e6	−0.269758	−0.134879	−	0.990862i	$-0.543065\pi$
$523$	−1.68744e6	−0.269758	−0.134879	+	0.990862i	$0.543065\pi$
$524$	193773.	0.0308294
$525$	−237006.	−0.0375284
$526$	−1.84048e6	−0.290046
$527$	1.68863e7	2.64855
$528$	485586.	0.0758022
$529$	2.05879e6	0.319870
$530$	749465.	0.115894
$531$	−2.60929e6	−0.401593
$532$	243368.	0.0372807
$533$	−483716.	−0.0737518
$534$	−2.07757e6	−0.315284
$535$	−1.94921e6	−0.294425
$536$	656054.	0.0986342
$537$	−730403.	−0.109302
$538$	−7.04750e6	−1.04973
$539$	3.16805e6	0.469700
$540$	291600.	0.0430331
$541$	6.74968e6	0.991494	0.495747	−	0.868467i	$-0.334894\pi$
$541$	6.74968e6	0.991494	0.495747	+	0.868467i	$0.334894\pi$
$542$	−876026.	−0.128091
$543$	−3.55564e6	−0.517509
$544$	2.04426e6	0.296168
$545$	−4.63585e6	−0.668556
$546$	−1.02329e6	−0.146898
$547$	1.12662e7	1.60994	0.804968	−	0.593318i	$-0.202182\pi$
$547$	1.12662e7	1.60994	0.804968	+	0.593318i	$0.202182\pi$
$548$	4.99969e6	0.711200
$549$	595244.	0.0842877
$550$	526895.	0.0742707
$551$	2.83858e6	0.398311
$552$	1.67883e6	0.234509
$553$	−307769.	−0.0427968
$554$	3.24802e6	0.449619
$555$	−1.98026e6	−0.272891
$556$	−352615.	−0.0483741
$557$	8.62465e6	1.17789	0.588944	−	0.808174i	$-0.299544\pi$
$557$	8.62465e6	1.17789	0.588944	+	0.808174i	$0.299544\pi$
$558$	2.74059e6	0.372614
$559$	7.73265e6	1.04664
$560$	−269660.	−0.0363367
$561$	−3.78671e6	−0.507990
$562$	−2.15156e6	−0.287351
$563$	−1.46836e7	−1.95237	−0.976184	−	0.216945i	$-0.930391\pi$
$563$	−1.46836e7	−1.95237	−0.976184	+	0.216945i	$0.930391\pi$
$564$	930392.	0.123160
$565$	−5.61924e6	−0.740554
$566$	3.97080e6	0.520999
$567$	276443.	0.0361117
$568$	−1.80843e6	−0.235196
$569$	−9.50758e6	−1.23109	−0.615545	−	0.788102i	$-0.711064\pi$
$569$	−9.50758e6	−1.23109	−0.615545	+	0.788102i	$0.711064\pi$
$570$	−324900.	−0.0418854
$571$	1.01310e6	0.130035	0.0650177	−	0.997884i	$-0.479290\pi$
$571$	1.01310e6	0.130035	0.0650177	+	0.997884i	$0.479290\pi$
$572$	2.27491e6	0.290719
$573$	−7.94246e6	−1.01058
$574$	−120845.	−0.0153090
$575$	1.82165e6	0.229771
$576$	331776.	0.0416667
$577$	8.07864e6	1.01018	0.505090	−	0.863067i	$-0.331459\pi$
$577$	8.07864e6	1.01018	0.505090	+	0.863067i	$0.331459\pi$
$578$	−1.02622e7	−1.27767
$579$	−2.84161e6	−0.352264
$580$	−3.14524e6	−0.388225
$581$	−3.97308e6	−0.488301
$582$	−5.46908e6	−0.669278
$583$	−1.57956e6	−0.192470
$584$	−2.37890e6	−0.288632
$585$	1.36611e6	0.165042
$586$	−5.93965e6	−0.714524
$587$	8.79577e6	1.05361	0.526803	−	0.849987i	$-0.323390\pi$
$587$	8.79577e6	1.05361	0.526803	+	0.849987i	$0.323390\pi$
$588$	2.16456e6	0.258183
$589$	−3.05356e6	−0.362676
$590$	−3.22135e6	−0.380984
$591$	4.16412e6	0.490405
$592$	−2.25309e6	−0.264226
$593$	−5.79734e6	−0.677006	−0.338503	−	0.940965i	$-0.609920\pi$
$593$	−5.79734e6	−0.677006	−0.338503	+	0.940965i	$0.609920\pi$
$594$	−614570.	−0.0714670
$595$	2.10287e6	0.243512
$596$	2.29581e6	0.264741
$597$	−8.86968e6	−1.01853
$598$	7.86510e6	0.899397
$599$	−1.53091e7	−1.74334	−0.871670	−	0.490093i	$-0.836963\pi$
$599$	−1.53091e7	−1.74334	−0.871670	+	0.490093i	$0.836963\pi$
$600$	360000.	0.0408248
$601$	5.77032e6	0.651649	0.325824	−	0.945430i	$-0.394358\pi$
$601$	5.77032e6	0.651649	0.325824	+	0.945430i	$0.394358\pi$
$602$	1.93181e6	0.217257
$603$	−830318.	−0.0929933
$604$	964607.	0.107587
$605$	2.91580e6	0.323869
$606$	2.56523e6	0.283756
$607$	5.92237e6	0.652415	0.326208	−	0.945298i	$-0.394229\pi$
$607$	5.92237e6	0.652415	0.326208	+	0.945298i	$0.394229\pi$
$608$	−369664.	−0.0405554
$609$	−2.98176e6	−0.325783
$610$	734869.	0.0799624
$611$	4.35876e6	0.472346
$612$	−2.58726e6	−0.279230
$613$	1.00960e7	1.08517	0.542583	−	0.840002i	$-0.317446\pi$
$613$	1.00960e7	1.08517	0.542583	+	0.840002i	$0.317446\pi$
$614$	412622.	0.0441704
$615$	161330.	0.0171999
$616$	568330.	0.0603460
$617$	−8.99298e6	−0.951022	−0.475511	−	0.879710i	$-0.657737\pi$
$617$	−8.99298e6	−0.951022	−0.475511	+	0.879710i	$0.657737\pi$
$618$	−2.56505e6	−0.270162
$619$	−7.72814e6	−0.810678	−0.405339	−	0.914166i	$-0.632847\pi$
$619$	−7.72814e6	−0.810678	−0.405339	+	0.914166i	$0.632847\pi$
$620$	3.38345e6	0.353493
$621$	−2.12477e6	−0.221097
$622$	7.38927e6	0.765818
$623$	−2.43158e6	−0.250997
$624$	1.55432e6	0.159801
$625$	390625.	0.0400000
$626$	7.85093e6	0.800728
$627$	684753.	0.0695609
$628$	4.29411e6	0.434484
$629$	1.75701e7	1.77071
$630$	341288.	0.0342586
$631$	−3.74241e6	−0.374178	−0.187089	−	0.982343i	$-0.559905\pi$
$631$	−3.74241e6	−0.374178	−0.187089	+	0.982343i	$0.559905\pi$
$632$	467485.	0.0465560
$633$	3.14593e6	0.312061
$634$	−4.39489e6	−0.434235
$635$	4.18936e6	0.412300
$636$	−1.07923e6	−0.105796
$637$	1.01407e7	0.990190
$638$	6.62884e6	0.644742
$639$	2.28879e6	0.221745
$640$	409600.	0.0395285
$641$	1.45395e7	1.39767	0.698833	−	0.715285i	$-0.253703\pi$
$641$	1.45395e7	1.39767	0.698833	+	0.715285i	$0.253703\pi$
$642$	2.80687e6	0.268772
$643$	1.77387e7	1.69198	0.845990	−	0.533199i	$-0.179010\pi$
$643$	1.77387e7	1.69198	0.845990	+	0.533199i	$0.179010\pi$
$644$	1.96490e6	0.186692
$645$	−2.57900e6	−0.244091
$646$	2.88272e6	0.271783
$647$	−697833.	−0.0655377	−0.0327688	−	0.999463i	$-0.510433\pi$
$647$	−697833.	−0.0655377	−0.0327688	+	0.999463i	$0.510433\pi$
$648$	−419904.	−0.0392837
$649$	6.78924e6	0.632717
$650$	1.68655e6	0.156573
$651$	3.20759e6	0.296637
$652$	9.25616e6	0.852730
$653$	1.21909e7	1.11880	0.559399	−	0.828898i	$-0.311032\pi$
$653$	1.21909e7	1.11880	0.559399	+	0.828898i	$0.311032\pi$
$654$	6.67562e6	0.610305
$655$	−302770.	−0.0275747
$656$	183557.	0.0166537
$657$	3.01080e6	0.272125
$658$	1.08893e6	0.0980472
$659$	2.75765e6	0.247358	0.123679	−	0.992322i	$-0.460531\pi$
$659$	2.75765e6	0.247358	0.123679	+	0.992322i	$0.460531\pi$
$660$	−758729.	−0.0677995
$661$	−1.45968e7	−1.29943	−0.649716	−	0.760177i	$-0.725112\pi$
$661$	−1.45968e7	−1.29943	−0.649716	+	0.760177i	$0.725112\pi$
$662$	3.78248e6	0.335453
$663$	−1.21210e7	−1.07091
$664$	6.03492e6	0.531192
$665$	−380262.	−0.0333449
$666$	2.85157e6	0.249114
$667$	2.29181e7	1.99464
$668$	8.42591e6	0.730593
$669$	−2.48883e6	−0.214996
$670$	−1.02508e6	−0.0882211
$671$	−1.54880e6	−0.132797
$672$	388310.	0.0331708
$673$	−1.07005e7	−0.910677	−0.455339	−	0.890318i	$-0.650482\pi$
$673$	−1.07005e7	−0.910677	−0.455339	+	0.890318i	$0.650482\pi$
$674$	4.67867e6	0.396710
$675$	−455625.	−0.0384900
$676$	1.34111e6	0.112875
$677$	1.43643e7	1.20452	0.602259	−	0.798301i	$-0.294268\pi$
$677$	1.43643e7	1.20452	0.602259	+	0.798301i	$0.294268\pi$
$678$	8.09171e6	0.676030
$679$	−6.40100e6	−0.532811
$680$	−3.19415e6	−0.264901
$681$	−4.75932e6	−0.393258
$682$	−7.13089e6	−0.587060
$683$	2.26535e7	1.85816	0.929081	−	0.369877i	$-0.120600\pi$
$683$	2.26535e7	1.85816	0.929081	+	0.369877i	$0.120600\pi$
$684$	467856.	0.0382360
$685$	−7.81201e6	−0.636116
$686$	5.36601e6	0.435353
$687$	944600.	0.0763583
$688$	−2.93433e6	−0.236341
$689$	−5.05604e6	−0.405754
$690$	−2.62318e6	−0.209751
$691$	2.27355e7	1.81138	0.905691	−	0.423938i	$-0.139353\pi$
$691$	2.27355e7	1.81138	0.905691	+	0.423938i	$0.139353\pi$
$692$	−1.15124e7	−0.913907
$693$	−719292.	−0.0568947
$694$	−4.79032e6	−0.377543
$695$	550960.	0.0432672
$696$	4.52914e6	0.354399
$697$	−1.43142e6	−0.111605
$698$	1.25231e6	0.0972912
$699$	7.93073e6	0.613932
$700$	421343.	0.0325006
$701$	−8.41277e6	−0.646613	−0.323306	−	0.946294i	$-0.604794\pi$
$701$	−8.41277e6	−0.646613	−0.323306	+	0.946294i	$0.604794\pi$
$702$	−1.96719e6	−0.150662
$703$	−3.17721e6	−0.242470
$704$	−863265.	−0.0656466
$705$	−1.45374e6	−0.110157
$706$	−9.25502e6	−0.698821
$707$	3.00234e6	0.225897
$708$	4.63874e6	0.347790
$709$	6.70103e6	0.500640	0.250320	−	0.968163i	$-0.419464\pi$
$709$	6.70103e6	0.500640	0.250320	+	0.968163i	$0.419464\pi$
$710$	2.82567e6	0.210366
$711$	−591661.	−0.0438934
$712$	3.69345e6	0.273044
$713$	−2.46539e7	−1.81619
$714$	−3.02813e6	−0.222295
$715$	−3.55454e6	−0.260027
$716$	1.29849e6	0.0946580
$717$	−1.12014e7	−0.813718
$718$	−5.89099e6	−0.426459
$719$	1.19095e7	0.859153	0.429577	−	0.903030i	$-0.358663\pi$
$719$	1.19095e7	0.859153	0.429577	+	0.903030i	$0.358663\pi$
$720$	−518400.	−0.0372678
$721$	−3.00213e6	−0.215075
$722$	−521284.	−0.0372161
$723$	−6.37262e6	−0.453390
$724$	6.32113e6	0.448176
$725$	4.91444e6	0.347239
$726$	−4.19875e6	−0.295651
$727$	−1.67973e7	−1.17870	−0.589351	−	0.807877i	$-0.700617\pi$
$727$	−1.67973e7	−1.17870	−0.589351	+	0.807877i	$0.700617\pi$
$728$	1.81918e6	0.127218
$729$	531441.	0.0370370
$730$	3.71704e6	0.258160
$731$	2.28826e7	1.58384
$732$	−1.05821e6	−0.0729953
$733$	−9.75964e6	−0.670925	−0.335462	−	0.942054i	$-0.608893\pi$
$733$	−9.75964e6	−0.670925	−0.335462	+	0.942054i	$0.608893\pi$
$734$	−7.99273e6	−0.547589
$735$	−3.38213e6	−0.230926
$736$	−2.98459e6	−0.203091
$737$	2.16045e6	0.146513
$738$	−232314.	−0.0157013
$739$	1.33048e7	0.896185	0.448093	−	0.893987i	$-0.352103\pi$
$739$	1.33048e7	0.896185	0.448093	+	0.893987i	$0.352103\pi$
$740$	3.52046e6	0.236331
$741$	2.19184e6	0.146644
$742$	−1.26313e6	−0.0842243
$743$	−9.23873e6	−0.613960	−0.306980	−	0.951716i	$-0.599319\pi$
$743$	−9.23873e6	−0.613960	−0.306980	+	0.951716i	$0.599319\pi$
$744$	−4.87217e6	−0.322693
$745$	−3.58721e6	−0.236791
$746$	1.63445e7	1.07529
$747$	−7.63795e6	−0.500812
$748$	6.73194e6	0.439932
$749$	3.28515e6	0.213969
$750$	−562500.	−0.0365148
$751$	3.55337e6	0.229901	0.114950	−	0.993371i	$-0.463329\pi$
$751$	3.55337e6	0.229901	0.114950	+	0.993371i	$0.463329\pi$
$752$	−1.65403e6	−0.106659
$753$	−2.77294e6	−0.178219
$754$	2.12184e7	1.35920
$755$	−1.50720e6	−0.0962284
$756$	−491455.	−0.0312737
$757$	−7.04959e6	−0.447120	−0.223560	−	0.974690i	$-0.571768\pi$
$757$	−7.04959e6	−0.447120	−0.223560	+	0.974690i	$0.571768\pi$
$758$	−1.87917e7	−1.18794
$759$	5.52856e6	0.348343
$760$	577600.	0.0362738
$761$	−1.95250e7	−1.22216	−0.611081	−	0.791568i	$-0.709265\pi$
$761$	−1.95250e7	−1.22216	−0.611081	+	0.791568i	$0.709265\pi$
$762$	−6.03267e6	−0.376376
$763$	7.81313e6	0.485863
$764$	1.41199e7	0.875184
$765$	4.04260e6	0.249751
$766$	−3.88158e6	−0.239021
$767$	2.17318e7	1.33385
$768$	−589824.	−0.0360844
$769$	2.03020e7	1.23801	0.619004	−	0.785388i	$-0.287537\pi$
$769$	2.03020e7	1.23801	0.619004	+	0.785388i	$0.287537\pi$
$770$	−888015.	−0.0539751
$771$	1.45090e7	0.879026
$772$	5.05176e6	0.305070
$773$	−3.15938e7	−1.90175	−0.950873	−	0.309581i	$-0.899811\pi$
$773$	−3.15938e7	−1.90175	−0.950873	+	0.309581i	$0.899811\pi$
$774$	3.71376e6	0.222824
$775$	−5.28664e6	−0.316173
$776$	9.72280e6	0.579612
$777$	3.33747e6	0.198319
$778$	−1.80608e7	−1.06977
$779$	258844.	0.0152825
$780$	−2.42863e6	−0.142931
$781$	−5.95533e6	−0.349364
$782$	2.32745e7	1.36102
$783$	−5.73220e6	−0.334131
$784$	−3.84811e6	−0.223593
$785$	−6.70954e6	−0.388614
$786$	435989.	0.0251721
$787$	2.27199e7	1.30758	0.653792	−	0.756674i	$-0.273177\pi$
$787$	2.27199e7	1.30758	0.653792	+	0.756674i	$0.273177\pi$
$788$	−7.40288e6	−0.424703
$789$	−4.14108e6	−0.236822
$790$	−730446.	−0.0416409
$791$	9.47052e6	0.538186
$792$	1.09257e6	0.0618922
$793$	−4.95758e6	−0.279954
$794$	−2.13927e7	−1.20425
$795$	1.68630e6	0.0946272
$796$	1.57683e7	0.882069
$797$	2.21510e7	1.23523	0.617616	−	0.786480i	$-0.288099\pi$
$797$	2.21510e7	1.23523	0.617616	+	0.786480i	$0.288099\pi$
$798$	547578.	0.0304396
$799$	1.28985e7	0.714780
$800$	−640000.	−0.0353553
$801$	−4.67452e6	−0.257428
$802$	−6.58055e6	−0.361265
$803$	−7.83395e6	−0.428738
$804$	1.47612e6	0.0805345
$805$	−3.07016e6	−0.166983
$806$	−2.28254e7	−1.23760
$807$	−1.58569e7	−0.857104
$808$	−4.56041e6	−0.245740
$809$	−856575.	−0.0460145	−0.0230072	−	0.999735i	$-0.507324\pi$
$809$	−856575.	−0.0460145	−0.0230072	+	0.999735i	$0.507324\pi$
$810$	656100.	0.0351364
$811$	−2.41826e7	−1.29107	−0.645536	−	0.763730i	$-0.723366\pi$
$811$	−2.41826e7	−1.29107	−0.645536	+	0.763730i	$0.723366\pi$
$812$	5.30090e6	0.282137
$813$	−1.97106e6	−0.104586
$814$	−7.41965e6	−0.392484
$815$	−1.44627e7	−0.762705
$816$	4.59958e6	0.241820
$817$	−4.13787e6	−0.216881
$818$	−1.47290e6	−0.0769645
$819$	−2.30240e6	−0.119942
$820$	−286808.	−0.0148956
$821$	−2.37506e7	−1.22975	−0.614875	−	0.788625i	$-0.710793\pi$
$821$	−2.37506e7	−1.22975	−0.614875	+	0.788625i	$0.710793\pi$
$822$	1.12493e7	0.580692
$823$	−1.16602e7	−0.600077	−0.300038	−	0.953927i	$-0.596999\pi$
$823$	−1.16602e7	−0.600077	−0.300038	+	0.953927i	$0.596999\pi$
$824$	4.56008e6	0.233967
$825$	1.18551e6	0.0606418
$826$	5.42917e6	0.276875
$827$	1.08538e7	0.551848	0.275924	−	0.961180i	$-0.411016\pi$
$827$	1.08538e7	0.551848	0.275924	+	0.961180i	$0.411016\pi$
$828$	3.77738e6	0.191476
$829$	5.41419e6	0.273619	0.136810	−	0.990597i	$-0.456315\pi$
$829$	5.41419e6	0.273619	0.136810	+	0.990597i	$0.456315\pi$
$830$	−9.42956e6	−0.475112
$831$	7.30805e6	0.367112
$832$	−2.76324e6	−0.138392
$833$	3.00085e7	1.49841
$834$	−793383.	−0.0394973
$835$	−1.31655e7	−0.653463
$836$	−1.21734e6	−0.0602415
$837$	6.16634e6	0.304238
$838$	−4.05468e6	−0.199456
$839$	3.29355e7	1.61532	0.807660	−	0.589648i	$-0.200734\pi$
$839$	3.29355e7	1.61532	0.807660	+	0.589648i	$0.200734\pi$
$840$	−606734.	−0.0296688
$841$	4.13171e7	2.01437
$842$	2.21414e7	1.07628
$843$	−4.84101e6	−0.234621
$844$	−5.59277e6	−0.270253
$845$	−2.09548e6	−0.100958
$846$	2.09338e6	0.100559
$847$	−4.91421e6	−0.235367
$848$	1.91863e6	0.0916223
$849$	8.93430e6	0.425394
$850$	4.99087e6	0.236935
$851$	−2.56522e7	−1.21423
$852$	−4.06897e6	−0.192037
$853$	2.54608e7	1.19812	0.599059	−	0.800705i	$-0.295541\pi$
$853$	2.54608e7	1.19812	0.599059	+	0.800705i	$0.295541\pi$
$854$	−1.23853e6	−0.0581114
$855$	−731025.	−0.0341993
$856$	−4.98999e6	−0.232763
$857$	−3.36988e7	−1.56734	−0.783669	−	0.621178i	$-0.786654\pi$
$857$	−3.36988e7	−1.56734	−0.783669	+	0.621178i	$0.786654\pi$
$858$	5.11854e6	0.237371
$859$	−7.66604e6	−0.354477	−0.177239	−	0.984168i	$-0.556716\pi$
$859$	−7.66604e6	−0.354477	−0.177239	+	0.984168i	$0.556716\pi$
$860$	4.58489e6	0.211389
$861$	−271900.	−0.0124998
$862$	−5.18764e6	−0.237794
$863$	−1.84147e7	−0.841662	−0.420831	−	0.907139i	$-0.638262\pi$
$863$	−1.84147e7	−0.841662	−0.420831	+	0.907139i	$0.638262\pi$
$864$	746496.	0.0340207
$865$	1.79882e7	0.817423
$866$	2.75621e7	1.24887
$867$	−2.30899e7	−1.04321
$868$	−5.70237e6	−0.256895
$869$	1.53947e6	0.0691549
$870$	−7.07679e6	−0.316984
$871$	6.91543e6	0.308868
$872$	−1.18678e7	−0.528540
$873$	−1.23054e7	−0.546463
$874$	−4.20874e6	−0.186369
$875$	−658349.	−0.0290694
$876$	−5.35253e6	−0.235667
$877$	2.92849e7	1.28571	0.642857	−	0.765987i	$-0.277749\pi$
$877$	2.92849e7	1.28571	0.642857	+	0.765987i	$0.277749\pi$
$878$	585187.	0.0256188
$879$	−1.33642e7	−0.583406
$880$	1.34885e6	0.0587161
$881$	−1.17884e6	−0.0511699	−0.0255849	−	0.999673i	$-0.508145\pi$
$881$	−1.17884e6	−0.0511699	−0.0255849	+	0.999673i	$0.508145\pi$
$882$	4.87027e6	0.210805
$883$	−8.64064e6	−0.372944	−0.186472	−	0.982460i	$-0.559705\pi$
$883$	−8.64064e6	−0.372944	−0.186472	+	0.982460i	$0.559705\pi$
$884$	2.15484e7	0.927437
$885$	−7.24803e6	−0.311073
$886$	3.31223e6	0.141754
$887$	2.42978e7	1.03695	0.518475	−	0.855093i	$-0.326500\pi$
$887$	2.42978e7	1.03695	0.518475	+	0.855093i	$0.326500\pi$
$888$	−5.06946e6	−0.215739
$889$	−7.06063e6	−0.299633
$890$	−5.77102e6	−0.244218
$891$	−1.38278e6	−0.0583526
$892$	4.42458e6	0.186192
$893$	−2.33244e6	−0.0978774
$894$	5.16558e6	0.216160
$895$	−2.02890e6	−0.0846647
$896$	−690329.	−0.0287267
$897$	1.76965e7	0.734355
$898$	2.38116e6	0.0985366
$899$	−6.65110e7	−2.74469
$900$	810000.	0.0333333
$901$	−1.49619e7	−0.614009
$902$	604471.	0.0247377
$903$	4.34658e6	0.177390
$904$	−1.43853e7	−0.585459
$905$	−9.87676e6	−0.400860
$906$	2.17037e6	0.0878441
$907$	−1.76213e7	−0.711247	−0.355624	−	0.934629i	$-0.615732\pi$
$907$	−1.76213e7	−0.711247	−0.355624	+	0.934629i	$0.615732\pi$
$908$	8.46102e6	0.340571
$909$	5.77177e6	0.231686
$910$	−2.84247e6	−0.113787
$911$	3.91841e6	0.156428	0.0782140	−	0.996937i	$-0.475078\pi$
$911$	3.91841e6	0.156428	0.0782140	+	0.996937i	$0.475078\pi$
$912$	−831744.	−0.0331133
$913$	1.98736e7	0.789040
$914$	2.33342e7	0.923904
$915$	1.65346e6	0.0652890
$916$	−1.67929e6	−0.0661282
$917$	510281.	0.0200395
$918$	−5.82135e6	−0.227990
$919$	−3.27348e7	−1.27856	−0.639280	−	0.768974i	$-0.720768\pi$
$919$	−3.27348e7	−1.27856	−0.639280	+	0.768974i	$0.720768\pi$
$920$	4.66343e6	0.181650
$921$	928399.	0.0360650
$922$	−7.62126e6	−0.295256
$923$	−1.90625e7	−0.736507
$924$	1.27874e6	0.0492723
$925$	−5.50072e6	−0.211380
$926$	−1.26843e7	−0.486115
$927$	−5.77136e6	−0.220586
$928$	−8.05181e6	−0.306919
$929$	−3.89116e7	−1.47924	−0.739622	−	0.673023i	$-0.764996\pi$
$929$	−3.89116e7	−1.47924	−0.739622	+	0.673023i	$0.764996\pi$
$930$	7.61276e6	0.288626
$931$	−5.42644e6	−0.205183
$932$	−1.40991e7	−0.531681
$933$	1.66258e7	0.625287
$934$	2.66852e6	0.100093
$935$	−1.05186e7	−0.393488
$936$	3.49723e6	0.130477
$937$	−3.76135e7	−1.39957	−0.699785	−	0.714354i	$-0.746721\pi$
$937$	−3.76135e7	−1.39957	−0.699785	+	0.714354i	$0.746721\pi$
$938$	1.72765e6	0.0641134
$939$	1.76646e7	0.653792
$940$	2.58442e6	0.0953991
$941$	1.01083e7	0.372137	0.186068	−	0.982537i	$-0.440425\pi$
$941$	1.01083e7	0.372137	0.186068	+	0.982537i	$0.440425\pi$
$942$	9.66174e6	0.354755
$943$	2.08986e6	0.0765310
$944$	−8.24664e6	−0.301195
$945$	767898.	0.0279720
$946$	−9.66303e6	−0.351063
$947$	−313348.	−0.0113541	−0.00567705	−	0.999984i	$-0.501807\pi$
$947$	−313348.	−0.0113541	−0.00567705	+	0.999984i	$0.501807\pi$
$948$	1.05184e6	0.0380128
$949$	−2.50759e7	−0.903838
$950$	−902500.	−0.0324443
$951$	−9.88851e6	−0.354552
$952$	5.38334e6	0.192513
$953$	−5.17010e7	−1.84402	−0.922012	−	0.387160i	$-0.873456\pi$
$953$	−5.17010e7	−1.84402	−0.922012	+	0.387160i	$0.873456\pi$
$954$	−2.42827e6	−0.0863824
$955$	−2.20624e7	−0.782788
$956$	1.99136e7	0.704701
$957$	1.49149e7	0.526430
$958$	3.84003e6	0.135183
$959$	1.31662e7	0.462288
$960$	921600.	0.0322749
$961$	4.29191e7	1.49914
$962$	−2.37497e7	−0.827410
$963$	6.31545e6	0.219452
$964$	1.13291e7	0.392647
$965$	−7.89337e6	−0.272863
$966$	4.42103e6	0.152434
$967$	4.12743e7	1.41943	0.709714	−	0.704490i	$-0.248824\pi$
$967$	4.12743e7	1.41943	0.709714	+	0.704490i	$0.248824\pi$
$968$	7.46445e6	0.256041
$969$	6.48613e6	0.221910
$970$	−1.51919e7	−0.518421
$971$	−3.75197e6	−0.127706	−0.0638531	−	0.997959i	$-0.520339\pi$
$971$	−3.75197e6	−0.127706	−0.0638531	+	0.997959i	$0.520339\pi$
$972$	−944784.	−0.0320750
$973$	−928574.	−0.0314437
$974$	3.10146e7	1.04753
$975$	3.79474e6	0.127841
$976$	1.88127e6	0.0632158
$977$	−4.56688e7	−1.53068	−0.765338	−	0.643629i	$-0.777428\pi$
$977$	−4.56688e7	−1.53068	−0.765338	+	0.643629i	$0.777428\pi$
$978$	2.08264e7	0.696251
$979$	1.21629e7	0.405583
$980$	6.01268e6	0.199987
$981$	1.50201e7	0.498312
$982$	−2.29284e7	−0.758745
$983$	5.01976e7	1.65691	0.828455	−	0.560055i	$-0.189220\pi$
$983$	5.01976e7	1.65691	0.828455	+	0.560055i	$0.189220\pi$
$984$	413004.	0.0135977
$985$	1.15670e7	0.379866
$986$	6.27899e7	2.05682
$987$	2.45009e6	0.0800552
$988$	−3.89661e6	−0.126997
$989$	−3.34083e7	−1.08608
$990$	−1.70714e6	−0.0553581
$991$	−4.10710e7	−1.32847	−0.664235	−	0.747524i	$-0.731242\pi$
$991$	−4.10710e7	−1.32847	−0.664235	+	0.747524i	$0.731242\pi$
$992$	8.66163e6	0.279460
$993$	8.51057e6	0.273896
$994$	−4.76231e6	−0.152880
$995$	−2.46380e7	−0.788947
$996$	1.35786e7	0.433716
$997$	2.13194e6	0.0679260	0.0339630	−	0.999423i	$-0.489187\pi$
$997$	2.13194e6	0.0679260	0.0339630	+	0.999423i	$0.489187\pi$
$998$	1.86274e7	0.592004
$999$	6.41604e6	0.203401

Twists

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +42.1343 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +42.1343 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} -210.758 q^{11} -144.000 q^{12} -674.620 q^{13} -168.537 q^{14} +225.000 q^{15} +256.000 q^{16} -1996.35 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} -379.209 q^{21} +843.032 q^{22} +2914.64 q^{23} +576.000 q^{24} +625.000 q^{25} +2698.48 q^{26} -729.000 q^{27} +674.149 q^{28} +7863.10 q^{29} -900.000 q^{30} -8458.62 q^{31} -1024.00 q^{32} +1896.82 q^{33} +7985.38 q^{34} -1053.36 q^{35} +1296.00 q^{36} -8801.15 q^{37} -1444.00 q^{38} +6071.58 q^{39} +1600.00 q^{40} +717.020 q^{41} +1516.84 q^{42} -11462.2 q^{43} -3372.13 q^{44} -2025.00 q^{45} -11658.6 q^{46} -6461.06 q^{47} -2304.00 q^{48} -15031.7 q^{49} -2500.00 q^{50} +17967.1 q^{51} -10793.9 q^{52} +7494.65 q^{53} +2916.00 q^{54} +5268.95 q^{55} -2696.60 q^{56} -3249.00 q^{57} -31452.4 q^{58} -32213.5 q^{59} +3600.00 q^{60} +7348.69 q^{61} +33834.5 q^{62} +3412.88 q^{63} +4096.00 q^{64} +16865.5 q^{65} -7587.29 q^{66} -10250.8 q^{67} -31941.5 q^{68} -26231.8 q^{69} +4213.43 q^{70} +28256.7 q^{71} -5184.00 q^{72} +37170.4 q^{73} +35204.6 q^{74} -5625.00 q^{75} +5776.00 q^{76} -8880.15 q^{77} -24286.3 q^{78} -7304.46 q^{79} -6400.00 q^{80} +6561.00 q^{81} -2868.08 q^{82} -94295.6 q^{83} -6067.34 q^{84} +49908.7 q^{85} +45848.9 q^{86} -70767.9 q^{87} +13488.5 q^{88} -57710.2 q^{89} +8100.00 q^{90} -28424.7 q^{91} +46634.3 q^{92} +76127.6 q^{93} +25844.2 q^{94} -9025.00 q^{95} +9216.00 q^{96} -151919. q^{97} +60126.8 q^{98} -17071.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} - 88 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} + 940 q^{11} - 576 q^{12} - 34 q^{13} + 352 q^{14} + 900 q^{15} + 1024 q^{16} - 138 q^{17} - 1296 q^{18} + 1444 q^{19} - 1600 q^{20} + 792 q^{21} - 3760 q^{22} + 486 q^{23} + 2304 q^{24} + 2500 q^{25} + 136 q^{26} - 2916 q^{27} - 1408 q^{28} + 3296 q^{29} - 3600 q^{30} - 6686 q^{31} - 4096 q^{32} - 8460 q^{33} + 552 q^{34} + 2200 q^{35} + 5184 q^{36} - 14218 q^{37} - 5776 q^{38} + 306 q^{39} + 6400 q^{40} + 1342 q^{41} - 3168 q^{42} - 26330 q^{43} + 15040 q^{44} - 8100 q^{45} - 1944 q^{46} - 7010 q^{47} - 9216 q^{48} + 192 q^{49} - 10000 q^{50} + 1242 q^{51} - 544 q^{52} - 22782 q^{53} + 11664 q^{54} - 23500 q^{55} + 5632 q^{56} - 12996 q^{57} - 13184 q^{58} - 13358 q^{59} + 14400 q^{60} + 16008 q^{61} + 26744 q^{62} - 7128 q^{63} + 16384 q^{64} + 850 q^{65} + 33840 q^{66} - 22696 q^{67} - 2208 q^{68} - 4374 q^{69} - 8800 q^{70} + 52584 q^{71} - 20736 q^{72} - 101048 q^{73} + 56872 q^{74} - 22500 q^{75} + 23104 q^{76} - 103772 q^{77} - 1224 q^{78} - 113090 q^{79} - 25600 q^{80} + 26244 q^{81} - 5368 q^{82} - 65384 q^{83} + 12672 q^{84} + 3450 q^{85} + 105320 q^{86} - 29664 q^{87} - 60160 q^{88} + 97354 q^{89} + 32400 q^{90} - 125600 q^{91} + 7776 q^{92} + 60174 q^{93} + 28040 q^{94} - 36100 q^{95} + 36864 q^{96} - 198934 q^{97} - 768 q^{98} + 76140 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 36 * q^3 + 64 * q^4 - 100 * q^5 + 144 * q^6 - 88 * q^7 - 256 * q^8 + 324 * q^9 + 400 * q^10 + 940 * q^11 - 576 * q^12 - 34 * q^13 + 352 * q^14 + 900 * q^15 + 1024 * q^16 - 138 * q^17 - 1296 * q^18 + 1444 * q^19 - 1600 * q^20 + 792 * q^21 - 3760 * q^22 + 486 * q^23 + 2304 * q^24 + 2500 * q^25 + 136 * q^26 - 2916 * q^27 - 1408 * q^28 + 3296 * q^29 - 3600 * q^30 - 6686 * q^31 - 4096 * q^32 - 8460 * q^33 + 552 * q^34 + 2200 * q^35 + 5184 * q^36 - 14218 * q^37 - 5776 * q^38 + 306 * q^39 + 6400 * q^40 + 1342 * q^41 - 3168 * q^42 - 26330 * q^43 + 15040 * q^44 - 8100 * q^45 - 1944 * q^46 - 7010 * q^47 - 9216 * q^48 + 192 * q^49 - 10000 * q^50 + 1242 * q^51 - 544 * q^52 - 22782 * q^53 + 11664 * q^54 - 23500 * q^55 + 5632 * q^56 - 12996 * q^57 - 13184 * q^58 - 13358 * q^59 + 14400 * q^60 + 16008 * q^61 + 26744 * q^62 - 7128 * q^63 + 16384 * q^64 + 850 * q^65 + 33840 * q^66 - 22696 * q^67 - 2208 * q^68 - 4374 * q^69 - 8800 * q^70 + 52584 * q^71 - 20736 * q^72 - 101048 * q^73 + 56872 * q^74 - 22500 * q^75 + 23104 * q^76 - 103772 * q^77 - 1224 * q^78 - 113090 * q^79 - 25600 * q^80 + 26244 * q^81 - 5368 * q^82 - 65384 * q^83 + 12672 * q^84 + 3450 * q^85 + 105320 * q^86 - 29664 * q^87 - 60160 * q^88 + 97354 * q^89 + 32400 * q^90 - 125600 * q^91 + 7776 * q^92 + 60174 * q^93 + 28040 * q^94 - 36100 * q^95 + 36864 * q^96 - 198934 * q^97 - 768 * q^98 + 76140 * q^99

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