LMFDB - Embedded newform 570.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,8,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, 8, names="a")

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
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:	$178.059464526$
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} - 2087x^{2} + 44517x - 205110 $ x^4 - x^3 - 2087x^2 + 44517x - 205110
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$6.63333$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} -1226.02 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} -1226.02 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} -4664.78 q^{11} +1728.00 q^{12} +9141.59 q^{13} -9808.17 q^{14} +3375.00 q^{15} +4096.00 q^{16} -5655.69 q^{17} +5832.00 q^{18} -6859.00 q^{19} +8000.00 q^{20} -33102.6 q^{21} -37318.3 q^{22} +28546.1 q^{23} +13824.0 q^{24} +15625.0 q^{25} +73132.7 q^{26} +19683.0 q^{27} -78465.3 q^{28} -91499.2 q^{29} +27000.0 q^{30} +257718. q^{31} +32768.0 q^{32} -125949. q^{33} -45245.5 q^{34} -153253. q^{35} +46656.0 q^{36} -349283. q^{37} -54872.0 q^{38} +246823. q^{39} +64000.0 q^{40} +16623.6 q^{41} -264821. q^{42} -873064. q^{43} -298546. q^{44} +91125.0 q^{45} +228369. q^{46} +927779. q^{47} +110592. q^{48} +679585. q^{49} +125000. q^{50} -152704. q^{51} +585062. q^{52} -101382. q^{53} +157464. q^{54} -583098. q^{55} -627723. q^{56} -185193. q^{57} -731993. q^{58} -985529. q^{59} +216000. q^{60} -756404. q^{61} +2.06174e6 q^{62} -893769. q^{63} +262144. q^{64} +1.14270e6 q^{65} -1.00759e6 q^{66} -4.75212e6 q^{67} -361964. q^{68} +770744. q^{69} -1.22602e6 q^{70} -4.47915e6 q^{71} +373248. q^{72} -3.53609e6 q^{73} -2.79427e6 q^{74} +421875. q^{75} -438976. q^{76} +5.71912e6 q^{77} +1.97458e6 q^{78} -1.32434e6 q^{79} +512000. q^{80} +531441. q^{81} +132989. q^{82} -71365.3 q^{83} -2.11856e6 q^{84} -706962. q^{85} -6.98451e6 q^{86} -2.47048e6 q^{87} -2.38837e6 q^{88} -3.73761e6 q^{89} +729000. q^{90} -1.12078e7 q^{91} +1.82695e6 q^{92} +6.95839e6 q^{93} +7.42223e6 q^{94} -857375. q^{95} +884736. q^{96} -5.37895e6 q^{97} +5.43668e6 q^{98} -3.40063e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 500 q^{5} + 864 q^{6} - 1316 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 500 * q^5 + 864 * q^6 - 1316 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 500 q^{5} + 864 q^{6} - 1316 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 6570 q^{11} + 6912 q^{12} - 17578 q^{13} - 10528 q^{14} + 13500 q^{15} + 16384 q^{16} - 28466 q^{17} + 23328 q^{18} - 27436 q^{19} + 32000 q^{20} - 35532 q^{21} - 52560 q^{22} - 32136 q^{23} + 55296 q^{24} + 62500 q^{25} - 140624 q^{26} + 78732 q^{27} - 84224 q^{28} - 159122 q^{29} + 108000 q^{30} - 67974 q^{31} + 131072 q^{32} - 177390 q^{33} - 227728 q^{34} - 164500 q^{35} + 186624 q^{36} - 823702 q^{37} - 219488 q^{38} - 474606 q^{39} + 256000 q^{40} - 781924 q^{41} - 284256 q^{42} - 1115638 q^{43} - 420480 q^{44} + 364500 q^{45} - 257088 q^{46} - 209160 q^{47} + 442368 q^{48} - 1159308 q^{49} + 500000 q^{50} - 768582 q^{51} - 1124992 q^{52} - 848424 q^{53} + 629856 q^{54} - 821250 q^{55} - 673792 q^{56} - 740772 q^{57} - 1272976 q^{58} - 3677830 q^{59} + 864000 q^{60} - 1161072 q^{61} - 543792 q^{62} - 959364 q^{63} + 1048576 q^{64} - 2197250 q^{65} - 1419120 q^{66} - 6154740 q^{67} - 1821824 q^{68} - 867672 q^{69} - 1316000 q^{70} - 4456224 q^{71} + 1492992 q^{72} + 1057792 q^{73} - 6589616 q^{74} + 1687500 q^{75} - 1755904 q^{76} + 2402388 q^{77} - 3796848 q^{78} + 2910090 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 6255392 q^{82} - 1767198 q^{83} - 2274048 q^{84} - 3558250 q^{85} - 8925104 q^{86} - 4296294 q^{87} - 3363840 q^{88} - 3677360 q^{89} + 2916000 q^{90} - 6727732 q^{91} - 2056704 q^{92} - 1835298 q^{93} - 1673280 q^{94} - 3429500 q^{95} + 3538944 q^{96} - 10419094 q^{97} - 9274464 q^{98} - 4789530 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 500 * q^5 + 864 * q^6 - 1316 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 6570 * q^11 + 6912 * q^12 - 17578 * q^13 - 10528 * q^14 + 13500 * q^15 + 16384 * q^16 - 28466 * q^17 + 23328 * q^18 - 27436 * q^19 + 32000 * q^20 - 35532 * q^21 - 52560 * q^22 - 32136 * q^23 + 55296 * q^24 + 62500 * q^25 - 140624 * q^26 + 78732 * q^27 - 84224 * q^28 - 159122 * q^29 + 108000 * q^30 - 67974 * q^31 + 131072 * q^32 - 177390 * q^33 - 227728 * q^34 - 164500 * q^35 + 186624 * q^36 - 823702 * q^37 - 219488 * q^38 - 474606 * q^39 + 256000 * q^40 - 781924 * q^41 - 284256 * q^42 - 1115638 * q^43 - 420480 * q^44 + 364500 * q^45 - 257088 * q^46 - 209160 * q^47 + 442368 * q^48 - 1159308 * q^49 + 500000 * q^50 - 768582 * q^51 - 1124992 * q^52 - 848424 * q^53 + 629856 * q^54 - 821250 * q^55 - 673792 * q^56 - 740772 * q^57 - 1272976 * q^58 - 3677830 * q^59 + 864000 * q^60 - 1161072 * q^61 - 543792 * q^62 - 959364 * q^63 + 1048576 * q^64 - 2197250 * q^65 - 1419120 * q^66 - 6154740 * q^67 - 1821824 * q^68 - 867672 * q^69 - 1316000 * q^70 - 4456224 * q^71 + 1492992 * q^72 + 1057792 * q^73 - 6589616 * q^74 + 1687500 * q^75 - 1755904 * q^76 + 2402388 * q^77 - 3796848 * q^78 + 2910090 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 6255392 * q^82 - 1767198 * q^83 - 2274048 * q^84 - 3558250 * q^85 - 8925104 * q^86 - 4296294 * q^87 - 3363840 * q^88 - 3677360 * q^89 + 2916000 * q^90 - 6727732 * q^91 - 2056704 * q^92 - 1835298 * q^93 - 1673280 * q^94 - 3429500 * q^95 + 3538944 * q^96 - 10419094 * q^97 - 9274464 * q^98 - 4789530 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	216.000	0.408248
$7$	−1226.02	−1.35100	−0.675499	−	0.737361i	$-0.736072\pi$
$7$	−1226.02	−1.35100	−0.675499	+	0.737361i	$0.736072\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1000.00	0.316228
$11$	−4664.78	−1.05671	−0.528357	−	0.849022i	$-0.677192\pi$
$11$	−4664.78	−1.05671	−0.528357	+	0.849022i	$0.677192\pi$
$12$	1728.00	0.288675
$13$	9141.59	1.15404	0.577019	−	0.816731i	$-0.304216\pi$
$13$	9141.59	1.15404	0.577019	+	0.816731i	$0.304216\pi$
$14$	−9808.17	−0.955300
$15$	3375.00	0.258199
$16$	4096.00	0.250000
$17$	−5655.69	−0.279199	−0.139600	−	0.990208i	$-0.544582\pi$
$17$	−5655.69	−0.279199	−0.139600	+	0.990208i	$0.544582\pi$
$18$	5832.00	0.235702
$19$	−6859.00	−0.229416
$19$	−6859.00	−0.229416
$20$	8000.00	0.223607
$21$	−33102.6	−0.779999
$22$	−37318.3	−0.747209
$23$	28546.1	0.489214	0.244607	−	0.969622i	$-0.421341\pi$
$23$	28546.1	0.489214	0.244607	+	0.969622i	$0.421341\pi$
$24$	13824.0	0.204124
$25$	15625.0	0.200000
$26$	73132.7	0.816028
$27$	19683.0	0.192450
$28$	−78465.3	−0.675499
$29$	−91499.2	−0.696665	−0.348333	−	0.937371i	$-0.613252\pi$
$29$	−91499.2	−0.696665	−0.348333	+	0.937371i	$0.613252\pi$
$30$	27000.0	0.182574
$31$	257718.	1.55374	0.776871	−	0.629660i	$-0.216806\pi$
$31$	257718.	1.55374	0.776871	+	0.629660i	$0.216806\pi$
$32$	32768.0	0.176777
$33$	−125949.	−0.610094
$34$	−45245.5	−0.197424
$35$	−153253.	−0.604185
$36$	46656.0	0.166667
$37$	−349283.	−1.13363	−0.566815	−	0.823845i	$-0.691825\pi$
$37$	−349283.	−1.13363	−0.566815	+	0.823845i	$0.691825\pi$
$38$	−54872.0	−0.162221
$39$	246823.	0.666284
$40$	64000.0	0.158114
$41$	16623.6	0.0376689	0.0188344	−	0.999823i	$-0.494004\pi$
$41$	16623.6	0.0376689	0.0188344	+	0.999823i	$0.494004\pi$
$42$	−264821.	−0.551543
$43$	−873064.	−1.67458	−0.837291	−	0.546757i	$-0.815862\pi$
$43$	−873064.	−1.67458	−0.837291	+	0.546757i	$0.815862\pi$
$44$	−298546.	−0.528357
$45$	91125.0	0.149071
$46$	228369.	0.345927
$47$	927779.	1.30347	0.651737	−	0.758445i	$-0.274041\pi$
$47$	927779.	1.30347	0.651737	+	0.758445i	$0.274041\pi$
$48$	110592.	0.144338
$49$	679585.	0.825196
$50$	125000.	0.141421
$51$	−152704.	−0.161196
$52$	585062.	0.577019
$53$	−101382.	−0.0935399	−0.0467700	−	0.998906i	$-0.514893\pi$
$53$	−101382.	−0.0935399	−0.0467700	+	0.998906i	$0.514893\pi$
$54$	157464.	0.136083
$55$	−583098.	−0.472577
$56$	−627723.	−0.477650
$57$	−185193.	−0.132453
$58$	−731993.	−0.492617
$59$	−985529.	−0.624723	−0.312361	−	0.949963i	$-0.601120\pi$
$59$	−985529.	−0.624723	−0.312361	+	0.949963i	$0.601120\pi$
$60$	216000.	0.129099
$61$	−756404.	−0.426677	−0.213339	−	0.976978i	$-0.568434\pi$
$61$	−756404.	−0.426677	−0.213339	+	0.976978i	$0.568434\pi$
$62$	2.06174e6	1.09866
$63$	−893769.	−0.450333
$64$	262144.	0.125000
$65$	1.14270e6	0.516101
$66$	−1.00759e6	−0.431401
$67$	−4.75212e6	−1.93030	−0.965151	−	0.261693i	$-0.915719\pi$
$67$	−4.75212e6	−1.93030	−0.965151	+	0.261693i	$0.915719\pi$
$68$	−361964.	−0.139600
$69$	770744.	0.282448
$70$	−1.22602e6	−0.427223
$71$	−4.47915e6	−1.48522	−0.742612	−	0.669722i	$-0.766413\pi$
$71$	−4.47915e6	−1.48522	−0.742612	+	0.669722i	$0.766413\pi$
$72$	373248.	0.117851
$73$	−3.53609e6	−1.06388	−0.531941	−	0.846781i	$-0.678537\pi$
$73$	−3.53609e6	−1.06388	−0.531941	+	0.846781i	$0.678537\pi$
$74$	−2.79427e6	−0.801598
$75$	421875.	0.115470
$76$	−438976.	−0.114708
$77$	5.71912e6	1.42762
$78$	1.97458e6	0.471134
$79$	−1.32434e6	−0.302206	−0.151103	−	0.988518i	$-0.548283\pi$
$79$	−1.32434e6	−0.302206	−0.151103	+	0.988518i	$0.548283\pi$
$80$	512000.	0.111803
$81$	531441.	0.111111
$82$	132989.	0.0266359
$83$	−71365.3	−0.0136998	−0.00684989	−	0.999977i	$-0.502180\pi$
$83$	−71365.3	−0.0136998	−0.00684989	+	0.999977i	$0.502180\pi$
$84$	−2.11856e6	−0.390000
$85$	−706962.	−0.124862
$86$	−6.98451e6	−1.18411
$87$	−2.47048e6	−0.402220
$88$	−2.38837e6	−0.373605
$89$	−3.73761e6	−0.561990	−0.280995	−	0.959709i	$-0.590664\pi$
$89$	−3.73761e6	−0.561990	−0.280995	+	0.959709i	$0.590664\pi$
$90$	729000.	0.105409
$91$	−1.12078e7	−1.55910
$92$	1.82695e6	0.244607
$93$	6.95839e6	0.897054
$94$	7.42223e6	0.921695
$95$	−857375.	−0.102598
$96$	884736.	0.102062
$97$	−5.37895e6	−0.598406	−0.299203	−	0.954189i	$-0.596721\pi$
$97$	−5.37895e6	−0.598406	−0.299203	+	0.954189i	$0.596721\pi$
$98$	5.43668e6	0.583502
$99$	−3.40063e6	−0.352238
$100$	1.00000e6	0.100000
$101$	−1.36707e7	−1.32028	−0.660139	−	0.751143i	$-0.729503\pi$
$101$	−1.36707e7	−1.32028	−0.660139	+	0.751143i	$0.729503\pi$
$102$	−1.22163e6	−0.113983
$103$	252601.	0.0227775	0.0113887	−	0.999935i	$-0.496375\pi$
$103$	252601.	0.0227775	0.0113887	+	0.999935i	$0.496375\pi$
$104$	4.68049e6	0.408014
$105$	−4.13782e6	−0.348826
$106$	−811059.	−0.0661427
$107$	656153.	0.0517800	0.0258900	−	0.999665i	$-0.491758\pi$
$107$	656153.	0.0517800	0.0258900	+	0.999665i	$0.491758\pi$
$108$	1.25971e6	0.0962250
$109$	−8.93726e6	−0.661016	−0.330508	−	0.943803i	$-0.607220\pi$
$109$	−8.93726e6	−0.661016	−0.330508	+	0.943803i	$0.607220\pi$
$110$	−4.66478e6	−0.334162
$111$	−9.43065e6	−0.654502
$112$	−5.02178e6	−0.337750
$113$	−4.69004e6	−0.305775	−0.152887	−	0.988244i	$-0.548857\pi$
$113$	−4.69004e6	−0.305775	−0.152887	+	0.988244i	$0.548857\pi$
$114$	−1.48154e6	−0.0936586
$115$	3.56826e6	0.218783
$116$	−5.85595e6	−0.348333
$117$	6.66422e6	0.384679
$118$	−7.88423e6	−0.441746
$119$	6.93400e6	0.377198
$120$	1.72800e6	0.0912871
$121$	2.27305e6	0.116643
$122$	−6.05123e6	−0.301706
$123$	448838.	0.0217481
$124$	1.64940e7	0.776871
$125$	1.95312e6	0.0894427
$126$	−7.15015e6	−0.318433
$127$	3.91285e7	1.69504	0.847521	−	0.530762i	$-0.178094\pi$
$127$	3.91285e7	1.69504	0.847521	+	0.530762i	$0.178094\pi$
$128$	2.09715e6	0.0883883
$129$	−2.35727e7	−0.966821
$130$	9.14159e6	0.364939
$131$	−3.14409e7	−1.22193	−0.610963	−	0.791659i	$-0.709218\pi$
$131$	−3.14409e7	−1.22193	−0.610963	+	0.791659i	$0.709218\pi$
$132$	−8.06075e6	−0.305047
$133$	8.40928e6	0.309940
$134$	−3.80169e7	−1.36493
$135$	2.46038e6	0.0860663
$136$	−2.89571e6	−0.0987119
$137$	−4.41045e7	−1.46542	−0.732709	−	0.680543i	$-0.761744\pi$
$137$	−4.41045e7	−1.46542	−0.732709	+	0.680543i	$0.761744\pi$
$138$	6.16595e6	0.199721
$139$	4.26450e7	1.34684	0.673421	−	0.739260i	$-0.264824\pi$
$139$	4.26450e7	1.34684	0.673421	+	0.739260i	$0.264824\pi$
$140$	−9.80817e6	−0.302092
$141$	2.50500e7	0.752561
$142$	−3.58332e7	−1.05021
$143$	−4.26436e7	−1.21949
$144$	2.98598e6	0.0833333
$145$	−1.14374e7	−0.311558
$146$	−2.82887e7	−0.752278
$147$	1.83488e7	0.476427
$148$	−2.23541e7	−0.566815
$149$	8.55796e6	0.211943	0.105971	−	0.994369i	$-0.466205\pi$
$149$	8.55796e6	0.211943	0.105971	+	0.994369i	$0.466205\pi$
$150$	3.37500e6	0.0816497
$151$	4.01350e7	0.948645	0.474322	−	0.880351i	$-0.342693\pi$
$151$	4.01350e7	0.948645	0.474322	+	0.880351i	$0.342693\pi$
$152$	−3.51181e6	−0.0811107
$153$	−4.12300e6	−0.0930665
$154$	4.57530e7	1.00948
$155$	3.22148e7	0.694855
$156$	1.57967e7	0.333142
$157$	6.26893e7	1.29284	0.646419	−	0.762982i	$-0.276266\pi$
$157$	6.26893e7	1.29284	0.646419	+	0.762982i	$0.276266\pi$
$158$	−1.05947e7	−0.213692
$159$	−2.73733e6	−0.0540053
$160$	4.09600e6	0.0790569
$161$	−3.49981e7	−0.660928
$162$	4.25153e6	0.0785674
$163$	4.59226e7	0.830557	0.415279	−	0.909694i	$-0.363684\pi$
$163$	4.59226e7	0.830557	0.415279	+	0.909694i	$0.363684\pi$
$164$	1.06391e6	0.0188344
$165$	−1.57436e7	−0.272842
$166$	−570922.	−0.00968721
$167$	2.20343e7	0.366093	0.183046	−	0.983104i	$-0.441404\pi$
$167$	2.20343e7	0.366093	0.183046	+	0.983104i	$0.441404\pi$
$168$	−1.69485e7	−0.275771
$169$	2.08202e7	0.331803
$170$	−5.65569e6	−0.0882906
$171$	−5.00021e6	−0.0764719
$172$	−5.58761e7	−0.837291
$173$	−6.47515e7	−0.950799	−0.475400	−	0.879770i	$-0.657696\pi$
$173$	−6.47515e7	−0.950799	−0.475400	+	0.879770i	$0.657696\pi$
$174$	−1.97638e7	−0.284412
$175$	−1.91566e7	−0.270200
$176$	−1.91070e7	−0.264178
$177$	−2.66093e7	−0.360684
$178$	−2.99008e7	−0.397387
$179$	5.05932e7	0.659335	0.329668	−	0.944097i	$-0.393063\pi$
$179$	5.05932e7	0.659335	0.329668	+	0.944097i	$0.393063\pi$
$180$	5.83200e6	0.0745356
$181$	−1.39134e8	−1.74405	−0.872026	−	0.489459i	$-0.837194\pi$
$181$	−1.39134e8	−1.74405	−0.872026	+	0.489459i	$0.837194\pi$
$182$	−8.96623e7	−1.10245
$183$	−2.04229e7	−0.246342
$184$	1.46156e7	0.172963
$185$	−4.36604e7	−0.506975
$186$	5.56671e7	0.634313
$187$	2.63826e7	0.295034
$188$	5.93779e7	0.651737
$189$	−2.41318e7	−0.260000
$190$	−6.85900e6	−0.0725476
$191$	6.61827e7	0.687270	0.343635	−	0.939103i	$-0.388342\pi$
$191$	6.61827e7	0.687270	0.343635	+	0.939103i	$0.388342\pi$
$192$	7.07789e6	0.0721688
$193$	−5.81508e7	−0.582244	−0.291122	−	0.956686i	$-0.594029\pi$
$193$	−5.81508e7	−0.582244	−0.291122	+	0.956686i	$0.594029\pi$
$194$	−4.30316e7	−0.423137
$195$	3.08529e7	0.297971
$196$	4.34934e7	0.412598
$197$	1.32939e8	1.23885	0.619426	−	0.785055i	$-0.287366\pi$
$197$	1.32939e8	1.23885	0.619426	+	0.785055i	$0.287366\pi$
$198$	−2.72050e7	−0.249070
$199$	−7.83654e7	−0.704918	−0.352459	−	0.935827i	$-0.614654\pi$
$199$	−7.83654e7	−0.704918	−0.352459	+	0.935827i	$0.614654\pi$
$200$	8.00000e6	0.0707107
$201$	−1.28307e8	−1.11446
$202$	−1.09365e8	−0.933578
$203$	1.12180e8	0.941194
$204$	−9.77304e6	−0.0805979
$205$	2.07795e6	0.0168460
$206$	2.02081e6	0.0161061
$207$	2.08101e7	0.163071
$208$	3.74440e7	0.288509
$209$	3.19958e7	0.242427
$210$	−3.31026e7	−0.246657
$211$	5.07664e7	0.372039	0.186019	−	0.982546i	$-0.440441\pi$
$211$	5.07664e7	0.372039	0.186019	+	0.982546i	$0.440441\pi$
$212$	−6.48847e6	−0.0467700
$213$	−1.20937e8	−0.857494
$214$	5.24922e6	0.0366140
$215$	−1.09133e8	−0.748896
$216$	1.00777e7	0.0680414
$217$	−3.15968e8	−2.09910
$218$	−7.14981e7	−0.467409
$219$	−9.54745e7	−0.614233
$220$	−3.73183e7	−0.236288
$221$	−5.17020e7	−0.322207
$222$	−7.54452e7	−0.462803
$223$	−1.46701e8	−0.885861	−0.442930	−	0.896556i	$-0.646061\pi$
$223$	−1.46701e8	−0.885861	−0.442930	+	0.896556i	$0.646061\pi$
$224$	−4.01743e7	−0.238825
$225$	1.13906e7	0.0666667
$226$	−3.75203e7	−0.216215
$227$	−5.87583e7	−0.333410	−0.166705	−	0.986007i	$-0.553313\pi$
$227$	−5.87583e7	−0.333410	−0.166705	+	0.986007i	$0.553313\pi$
$228$	−1.18524e7	−0.0662266
$229$	3.04392e8	1.67498	0.837488	−	0.546456i	$-0.184024\pi$
$229$	3.04392e8	1.67498	0.837488	+	0.546456i	$0.184024\pi$
$230$	2.85461e7	0.154703
$231$	1.54416e8	0.824236
$232$	−4.68476e7	−0.246308
$233$	−2.17333e8	−1.12559	−0.562793	−	0.826598i	$-0.690273\pi$
$233$	−2.17333e8	−1.12559	−0.562793	+	0.826598i	$0.690273\pi$
$234$	5.33138e7	0.272009
$235$	1.15972e8	0.582931
$236$	−6.30739e7	−0.312361
$237$	−3.57571e7	−0.174479
$238$	5.54720e7	0.266719
$239$	2.48827e8	1.17897	0.589487	−	0.807778i	$-0.299330\pi$
$239$	2.48827e8	1.17897	0.589487	+	0.807778i	$0.299330\pi$
$240$	1.38240e7	0.0645497
$241$	−3.68119e8	−1.69406	−0.847030	−	0.531544i	$-0.821612\pi$
$241$	−3.68119e8	−1.69406	−0.847030	+	0.531544i	$0.821612\pi$
$242$	1.81844e7	0.0824793
$243$	1.43489e7	0.0641500
$244$	−4.84099e7	−0.213339
$245$	8.49481e7	0.369039
$246$	3.59071e6	0.0153783
$247$	−6.27022e7	−0.264754
$248$	1.31952e8	0.549331
$249$	−1.92686e6	−0.00790957
$250$	1.56250e7	0.0632456
$251$	−1.97259e8	−0.787370	−0.393685	−	0.919245i	$-0.628800\pi$
$251$	−1.97259e8	−0.787370	−0.393685	+	0.919245i	$0.628800\pi$
$252$	−5.72012e7	−0.225166
$253$	−1.33161e8	−0.516959
$254$	3.13028e8	1.19858
$255$	−1.90880e7	−0.0720890
$256$	1.67772e7	0.0625000
$257$	−2.06192e8	−0.757713	−0.378857	−	0.925455i	$-0.623683\pi$
$257$	−2.06192e8	−0.757713	−0.378857	+	0.925455i	$0.623683\pi$
$258$	−1.88582e8	−0.683646
$259$	4.28229e8	1.53153
$260$	7.31327e7	0.258051
$261$	−6.67029e7	−0.232222
$262$	−2.51527e8	−0.864032
$263$	−1.32978e8	−0.450749	−0.225375	−	0.974272i	$-0.572361\pi$
$263$	−1.32978e8	−0.450749	−0.225375	+	0.974272i	$0.572361\pi$
$264$	−6.44860e7	−0.215701
$265$	−1.26728e7	−0.0418323
$266$	6.72742e7	0.219161
$267$	−1.00915e8	−0.324465
$268$	−3.04136e8	−0.965151
$269$	1.76304e8	0.552241	0.276120	−	0.961123i	$-0.410951\pi$
$269$	1.76304e8	0.552241	0.276120	+	0.961123i	$0.410951\pi$
$270$	1.96830e7	0.0608581
$271$	−2.81735e8	−0.859902	−0.429951	−	0.902852i	$-0.641469\pi$
$271$	−2.81735e8	−0.859902	−0.429951	+	0.902852i	$0.641469\pi$
$272$	−2.31657e7	−0.0697999
$273$	−3.02610e8	−0.900149
$274$	−3.52836e8	−1.03621
$275$	−7.28873e7	−0.211343
$276$	4.93276e7	0.141224
$277$	3.32412e8	0.939718	0.469859	−	0.882742i	$-0.344305\pi$
$277$	3.32412e8	0.939718	0.469859	+	0.882742i	$0.344305\pi$
$278$	3.41160e8	0.952360
$279$	1.87877e8	0.517914
$280$	−7.84653e7	−0.213612
$281$	3.64016e8	0.978698	0.489349	−	0.872088i	$-0.337234\pi$
$281$	3.64016e8	0.978698	0.489349	+	0.872088i	$0.337234\pi$
$282$	2.00400e8	0.532141
$283$	4.69965e8	1.23257	0.616287	−	0.787522i	$-0.288636\pi$
$283$	4.69965e8	1.23257	0.616287	+	0.787522i	$0.288636\pi$
$284$	−2.86666e8	−0.742612
$285$	−2.31491e7	−0.0592349
$286$	−3.41148e8	−0.862308
$287$	−2.03809e7	−0.0508906
$288$	2.38879e7	0.0589256
$289$	−3.78352e8	−0.922048
$290$	−9.14992e7	−0.220305
$291$	−1.45232e8	−0.345490
$292$	−2.26310e8	−0.531941
$293$	−7.25312e8	−1.68457	−0.842284	−	0.539035i	$-0.818789\pi$
$293$	−7.25312e8	−1.68457	−0.842284	+	0.539035i	$0.818789\pi$
$294$	1.46790e8	0.336885
$295$	−1.23191e8	−0.279385
$296$	−1.78833e8	−0.400799
$297$	−9.18170e7	−0.203365
$298$	6.84636e7	0.149866
$299$	2.60957e8	0.564572
$300$	2.70000e7	0.0577350
$301$	1.07040e9	2.26236
$302$	3.21080e8	0.670793
$303$	−3.69109e8	−0.762263
$304$	−2.80945e7	−0.0573539
$305$	−9.45505e7	−0.190816
$306$	−3.29840e7	−0.0658079
$307$	1.97615e8	0.389795	0.194898	−	0.980824i	$-0.437563\pi$
$307$	1.97615e8	0.389795	0.194898	+	0.980824i	$0.437563\pi$
$308$	3.66024e8	0.713809
$309$	6.82023e6	0.0131506
$310$	2.57718e8	0.491337
$311$	8.09420e8	1.52585	0.762927	−	0.646485i	$-0.223762\pi$
$311$	8.09420e8	1.52585	0.762927	+	0.646485i	$0.223762\pi$
$312$	1.26373e8	0.235567
$313$	−3.54187e8	−0.652870	−0.326435	−	0.945220i	$-0.605847\pi$
$313$	−3.54187e8	−0.652870	−0.326435	+	0.945220i	$0.605847\pi$
$314$	5.01514e8	0.914175
$315$	−1.11721e8	−0.201395
$316$	−8.47576e7	−0.151103
$317$	1.06264e9	1.87361	0.936803	−	0.349857i	$-0.113770\pi$
$317$	1.06264e9	1.87361	0.936803	+	0.349857i	$0.113770\pi$
$318$	−2.18986e7	−0.0381875
$319$	4.26824e8	0.736176
$320$	3.27680e7	0.0559017
$321$	1.77161e7	0.0298952
$322$	−2.79985e8	−0.467346
$323$	3.87924e7	0.0640527
$324$	3.40122e7	0.0555556
$325$	1.42837e8	0.230808
$326$	3.67381e8	0.587293
$327$	−2.41306e8	−0.381638
$328$	8.51130e6	0.0133180
$329$	−1.13748e9	−1.76099
$330$	−1.25949e8	−0.192929
$331$	2.26602e8	0.343452	0.171726	−	0.985145i	$-0.445066\pi$
$331$	2.26602e8	0.343452	0.171726	+	0.985145i	$0.445066\pi$
$332$	−4.56738e6	−0.00684989
$333$	−2.54627e8	−0.377877
$334$	1.76274e8	0.258867
$335$	−5.94015e8	−0.863258
$336$	−1.35588e8	−0.195000
$337$	3.83591e8	0.545964	0.272982	−	0.962019i	$-0.411990\pi$
$337$	3.83591e8	0.545964	0.272982	+	0.962019i	$0.411990\pi$
$338$	1.66561e8	0.234620
$339$	−1.26631e8	−0.176539
$340$	−4.52455e7	−0.0624309
$341$	−1.20220e9	−1.64186
$342$	−4.00017e7	−0.0540738
$343$	1.76496e8	0.236160
$344$	−4.47009e8	−0.592054
$345$	9.63430e7	0.126315
$346$	−5.18012e8	−0.672317
$347$	5.75945e8	0.739993	0.369997	−	0.929033i	$-0.379359\pi$
$347$	5.75945e8	0.739993	0.369997	+	0.929033i	$0.379359\pi$
$348$	−1.58111e8	−0.201110
$349$	−1.03015e9	−1.29721	−0.648606	−	0.761124i	$-0.724648\pi$
$349$	−1.03015e9	−1.29721	−0.648606	+	0.761124i	$0.724648\pi$
$350$	−1.53253e8	−0.191060
$351$	1.79934e8	0.222095
$352$	−1.52856e8	−0.186802
$353$	−8.91753e8	−1.07903	−0.539514	−	0.841976i	$-0.681392\pi$
$353$	−8.91753e8	−1.07903	−0.539514	+	0.841976i	$0.681392\pi$
$354$	−2.12874e8	−0.255042
$355$	−5.59894e8	−0.664212
$356$	−2.39207e8	−0.280995
$357$	1.87218e8	0.217775
$358$	4.04745e8	0.466220
$359$	−1.42951e9	−1.63063	−0.815316	−	0.579017i	$-0.803437\pi$
$359$	−1.42951e9	−1.63063	−0.815316	+	0.579017i	$0.803437\pi$
$360$	4.66560e7	0.0527046
$361$	4.70459e7	0.0526316
$362$	−1.11308e9	−1.23323
$363$	6.13723e7	0.0673440
$364$	−7.17298e8	−0.779552
$365$	−4.42011e8	−0.475782
$366$	−1.63383e8	−0.174190
$367$	−1.08198e9	−1.14259	−0.571293	−	0.820746i	$-0.693558\pi$
$367$	−1.08198e9	−1.14259	−0.571293	+	0.820746i	$0.693558\pi$
$368$	1.16925e8	0.122304
$369$	1.21186e7	0.0125563
$370$	−3.49283e8	−0.358486
$371$	1.24297e8	0.126372
$372$	4.45337e8	0.448527
$373$	−1.41493e9	−1.41174	−0.705870	−	0.708341i	$-0.749444\pi$
$373$	−1.41493e9	−1.41174	−0.705870	+	0.708341i	$0.749444\pi$
$374$	2.11061e8	0.208620
$375$	5.27344e7	0.0516398
$376$	4.75023e8	0.460847
$377$	−8.36448e8	−0.803978
$378$	−1.93054e8	−0.183848
$379$	−1.51393e8	−0.142846	−0.0714232	−	0.997446i	$-0.522754\pi$
$379$	−1.51393e8	−0.142846	−0.0714232	+	0.997446i	$0.522754\pi$
$380$	−5.48720e7	−0.0512989
$381$	1.05647e9	0.978633
$382$	5.29461e8	0.485973
$383$	5.80373e8	0.527851	0.263926	−	0.964543i	$-0.414983\pi$
$383$	5.80373e8	0.527851	0.263926	+	0.964543i	$0.414983\pi$
$384$	5.66231e7	0.0510310
$385$	7.14891e8	0.638450
$386$	−4.65206e8	−0.411709
$387$	−6.36464e8	−0.558194
$388$	−3.44252e8	−0.299203
$389$	1.59614e8	0.137482	0.0687411	−	0.997635i	$-0.478102\pi$
$389$	1.59614e8	0.137482	0.0687411	+	0.997635i	$0.478102\pi$
$390$	2.46823e8	0.210698
$391$	−1.61448e8	−0.136588
$392$	3.47947e8	0.291751
$393$	−8.48904e8	−0.705480
$394$	1.06351e9	0.876000
$395$	−1.65542e8	−0.135151
$396$	−2.17640e8	−0.176119
$397$	2.30750e8	0.185087	0.0925435	−	0.995709i	$-0.470500\pi$
$397$	2.30750e8	0.185087	0.0925435	+	0.995709i	$0.470500\pi$
$398$	−6.26923e8	−0.498453
$399$	2.27051e8	0.178944
$400$	6.40000e7	0.0500000
$401$	−7.76649e8	−0.601477	−0.300739	−	0.953707i	$-0.597233\pi$
$401$	−7.76649e8	−0.601477	−0.300739	+	0.953707i	$0.597233\pi$
$402$	−1.02646e9	−0.788043
$403$	2.35595e9	1.79308
$404$	−8.74924e8	−0.660139
$405$	6.64301e7	0.0496904
$406$	8.97439e8	0.665524
$407$	1.62933e9	1.19792
$408$	−7.81843e7	−0.0569913
$409$	5.26460e8	0.380482	0.190241	−	0.981737i	$-0.439073\pi$
$409$	5.26460e8	0.380482	0.190241	+	0.981737i	$0.439073\pi$
$410$	1.66236e7	0.0119119
$411$	−1.19082e9	−0.846059
$412$	1.61665e7	0.0113887
$413$	1.20828e9	0.844000
$414$	1.66481e8	0.115309
$415$	−8.92066e6	−0.00612673
$416$	2.99552e8	0.204007
$417$	1.15142e9	0.777599
$418$	2.55966e8	0.171422
$419$	−2.31838e9	−1.53970	−0.769850	−	0.638225i	$-0.779669\pi$
$419$	−2.31838e9	−1.53970	−0.769850	+	0.638225i	$0.779669\pi$
$420$	−2.64821e8	−0.174413
$421$	−2.16319e9	−1.41288	−0.706442	−	0.707771i	$-0.749701\pi$
$421$	−2.16319e9	−1.41288	−0.706442	+	0.707771i	$0.749701\pi$
$422$	4.06131e8	0.263071
$423$	6.76351e8	0.434491
$424$	−5.19078e7	−0.0330714
$425$	−8.83702e7	−0.0558399
$426$	−9.67497e8	−0.606340
$427$	9.27368e8	0.576440
$428$	4.19938e7	0.0258900
$429$	−1.15138e9	−0.704071
$430$	−8.73064e8	−0.529550
$431$	−2.19064e8	−0.131796	−0.0658979	−	0.997826i	$-0.520991\pi$
$431$	−2.19064e8	−0.131796	−0.0658979	+	0.997826i	$0.520991\pi$
$432$	8.06216e7	0.0481125
$433$	3.08103e9	1.82384	0.911922	−	0.410363i	$-0.134598\pi$
$433$	3.08103e9	1.82384	0.911922	+	0.410363i	$0.134598\pi$
$434$	−2.52774e9	−1.48429
$435$	−3.08810e8	−0.179878
$436$	−5.71985e8	−0.330508
$437$	−1.95798e8	−0.112233
$438$	−7.63796e8	−0.434328
$439$	2.69086e9	1.51798	0.758988	−	0.651105i	$-0.225694\pi$
$439$	2.69086e9	1.51798	0.758988	+	0.651105i	$0.225694\pi$
$440$	−2.98546e8	−0.167081
$441$	4.95417e8	0.275065
$442$	−4.13616e8	−0.227835
$443$	3.73882e7	0.0204325	0.0102162	−	0.999948i	$-0.496748\pi$
$443$	3.73882e7	0.0204325	0.0102162	+	0.999948i	$0.496748\pi$
$444$	−6.03561e8	−0.327251
$445$	−4.67201e8	−0.251330
$446$	−1.17361e9	−0.626398
$447$	2.31065e8	0.122365
$448$	−3.21394e8	−0.168875
$449$	1.53922e9	0.802489	0.401244	−	0.915971i	$-0.368578\pi$
$449$	1.53922e9	0.802489	0.401244	+	0.915971i	$0.368578\pi$
$450$	9.11250e7	0.0471405
$451$	−7.75457e7	−0.0398052
$452$	−3.00162e8	−0.152887
$453$	1.08364e9	0.547700
$454$	−4.70066e8	−0.235757
$455$	−1.40097e9	−0.697252
$456$	−9.48188e7	−0.0468293
$457$	−3.29252e9	−1.61370	−0.806848	−	0.590759i	$-0.798828\pi$
$457$	−3.29252e9	−1.61370	−0.806848	+	0.590759i	$0.798828\pi$
$458$	2.43513e9	1.18439
$459$	−1.11321e8	−0.0537320
$460$	2.28369e8	0.109392
$461$	2.59005e9	1.23128	0.615638	−	0.788029i	$-0.288898\pi$
$461$	2.59005e9	1.23128	0.615638	+	0.788029i	$0.288898\pi$
$462$	1.23533e9	0.582823
$463$	2.10724e9	0.986689	0.493344	−	0.869834i	$-0.335774\pi$
$463$	2.10724e9	0.986689	0.493344	+	0.869834i	$0.335774\pi$
$464$	−3.74781e8	−0.174166
$465$	8.69799e8	0.401175
$466$	−1.73866e9	−0.795910
$467$	9.33516e8	0.424143	0.212072	−	0.977254i	$-0.431979\pi$
$467$	9.33516e8	0.424143	0.212072	+	0.977254i	$0.431979\pi$
$468$	4.26510e8	0.192340
$469$	5.82620e9	2.60784
$470$	9.27779e8	0.412194
$471$	1.69261e9	0.746421
$472$	−5.04591e8	−0.220873
$473$	4.07266e9	1.76955
$474$	−2.86057e8	−0.123375
$475$	−1.07172e8	−0.0458831
$476$	4.43776e8	0.188599
$477$	−7.39078e7	−0.0311800
$478$	1.99061e9	0.833660
$479$	9.27378e8	0.385552	0.192776	−	0.981243i	$-0.438251\pi$
$479$	9.27378e8	0.385552	0.192776	+	0.981243i	$0.438251\pi$
$480$	1.10592e8	0.0456435
$481$	−3.19300e9	−1.30825
$482$	−2.94495e9	−1.19788
$483$	−9.44949e8	−0.381587
$484$	1.45475e8	0.0583216
$485$	−6.72368e8	−0.267615
$486$	1.14791e8	0.0453609
$487$	3.59857e7	0.0141182	0.00705909	−	0.999975i	$-0.497753\pi$
$487$	3.59857e7	0.0141182	0.00705909	+	0.999975i	$0.497753\pi$
$488$	−3.87279e8	−0.150853
$489$	1.23991e9	0.479523
$490$	6.79585e8	0.260950
$491$	−4.85651e9	−1.85157	−0.925783	−	0.378056i	$-0.876593\pi$
$491$	−4.85651e9	−1.85157	−0.925783	+	0.378056i	$0.876593\pi$
$492$	2.87256e7	0.0108741
$493$	5.17491e8	0.194509
$494$	−5.01617e8	−0.187210
$495$	−4.25079e8	−0.157526
$496$	1.05561e9	0.388436
$497$	5.49154e9	2.00653
$498$	−1.54149e7	−0.00559291
$499$	−5.20186e8	−0.187416	−0.0937080	−	0.995600i	$-0.529872\pi$
$499$	−5.20186e8	−0.187416	−0.0937080	+	0.995600i	$0.529872\pi$
$500$	1.25000e8	0.0447214
$501$	5.94926e8	0.211364
$502$	−1.57807e9	−0.556754
$503$	−4.48316e8	−0.157071	−0.0785355	−	0.996911i	$-0.525024\pi$
$503$	−4.48316e8	−0.157071	−0.0785355	+	0.996911i	$0.525024\pi$
$504$	−4.57610e8	−0.159217
$505$	−1.70884e9	−0.590446
$506$	−1.06529e9	−0.365545
$507$	5.62144e8	0.191567
$508$	2.50423e9	0.847521
$509$	−1.93635e9	−0.650837	−0.325419	−	0.945570i	$-0.605505\pi$
$509$	−1.93635e9	−0.650837	−0.325419	+	0.945570i	$0.605505\pi$
$510$	−1.52704e8	−0.0509746
$511$	4.33532e9	1.43730
$512$	1.34218e8	0.0441942
$513$	−1.35006e8	−0.0441511
$514$	−1.64953e9	−0.535784
$515$	3.15752e7	0.0101864
$516$	−1.50866e9	−0.483410
$517$	−4.32789e9	−1.37740
$518$	3.42583e9	1.08296
$519$	−1.74829e9	−0.548944
$520$	5.85062e8	0.182469
$521$	3.32620e9	1.03042	0.515212	−	0.857063i	$-0.327713\pi$
$521$	3.32620e9	1.03042	0.515212	+	0.857063i	$0.327713\pi$
$522$	−5.33623e8	−0.164206
$523$	−2.66642e9	−0.815029	−0.407515	−	0.913199i	$-0.633604\pi$
$523$	−2.66642e9	−0.815029	−0.407515	+	0.913199i	$0.633604\pi$
$524$	−2.01222e9	−0.610963
$525$	−5.17228e8	−0.156000
$526$	−1.06382e9	−0.318728
$527$	−1.45757e9	−0.433804
$528$	−5.15888e8	−0.152523
$529$	−2.58995e9	−0.760669
$530$	−1.01382e8	−0.0295799
$531$	−7.18451e8	−0.208241
$532$	5.38194e8	0.154970
$533$	1.51966e8	0.0434713
$534$	−8.07323e8	−0.229431
$535$	8.20191e7	0.0231567
$536$	−2.43308e9	−0.682465
$537$	1.36602e9	0.380667
$538$	1.41043e9	0.390493
$539$	−3.17012e9	−0.871996
$540$	1.57464e8	0.0430331
$541$	3.53887e9	0.960892	0.480446	−	0.877024i	$-0.340475\pi$
$541$	3.53887e9	0.960892	0.480446	+	0.877024i	$0.340475\pi$
$542$	−2.25388e9	−0.608042
$543$	−3.75663e9	−1.00693
$544$	−1.85326e8	−0.0493560
$545$	−1.11716e9	−0.295615
$546$	−2.42088e9	−0.636501
$547$	6.17856e9	1.61410	0.807052	−	0.590481i	$-0.201062\pi$
$547$	6.17856e9	1.61410	0.807052	+	0.590481i	$0.201062\pi$
$548$	−2.82269e9	−0.732709
$549$	−5.51419e8	−0.142226
$550$	−5.83098e8	−0.149442
$551$	6.27593e8	0.159826
$552$	3.94621e8	0.0998604
$553$	1.62367e9	0.408280
$554$	2.65930e9	0.664481
$555$	−1.17883e9	−0.292702
$556$	2.72928e9	0.673421
$557$	4.64096e8	0.113793	0.0568964	−	0.998380i	$-0.481880\pi$
$557$	4.64096e8	0.113793	0.0568964	+	0.998380i	$0.481880\pi$
$558$	1.50301e9	0.366221
$559$	−7.98120e9	−1.93253
$560$	−6.27723e8	−0.151046
$561$	7.12330e8	0.170338
$562$	2.91213e9	0.692044
$563$	6.20879e9	1.46632	0.733158	−	0.680059i	$-0.238046\pi$
$563$	6.20879e9	1.46632	0.733158	+	0.680059i	$0.238046\pi$
$564$	1.60320e9	0.376280
$565$	−5.86255e8	−0.136747
$566$	3.75972e9	0.871561
$567$	−6.51558e8	−0.150111
$568$	−2.29333e9	−0.525106
$569$	−3.12134e8	−0.0710311	−0.0355155	−	0.999369i	$-0.511307\pi$
$569$	−3.12134e8	−0.0710311	−0.0355155	+	0.999369i	$0.511307\pi$
$570$	−1.85193e8	−0.0418854
$571$	5.24046e9	1.17799	0.588997	−	0.808135i	$-0.299523\pi$
$571$	5.24046e9	1.17799	0.588997	+	0.808135i	$0.299523\pi$
$572$	−2.72919e9	−0.609744
$573$	1.78693e9	0.396796
$574$	−1.63047e8	−0.0359851
$575$	4.46033e8	0.0978429
$576$	1.91103e8	0.0416667
$577$	−6.89035e9	−1.49323	−0.746614	−	0.665257i	$-0.768322\pi$
$577$	−6.89035e9	−1.49323	−0.746614	+	0.665257i	$0.768322\pi$
$578$	−3.02681e9	−0.651986
$579$	−1.57007e9	−0.336159
$580$	−7.31993e8	−0.155779
$581$	8.74954e7	0.0185084
$582$	−1.16185e9	−0.244298
$583$	4.72927e8	0.0988449
$584$	−1.81048e9	−0.376139
$585$	8.33027e8	0.172034
$586$	−5.80250e9	−1.19117
$587$	1.37892e9	0.281388	0.140694	−	0.990053i	$-0.455067\pi$
$587$	1.37892e9	0.281388	0.140694	+	0.990053i	$0.455067\pi$
$588$	1.17432e9	0.238214
$589$	−1.76769e9	−0.356453
$590$	−9.85529e8	−0.197555
$591$	3.58934e9	0.715251
$592$	−1.43066e9	−0.283408
$593$	−3.35153e9	−0.660012	−0.330006	−	0.943979i	$-0.607051\pi$
$593$	−3.35153e9	−0.660012	−0.330006	+	0.943979i	$0.607051\pi$
$594$	−7.34536e8	−0.143800
$595$	8.66750e8	0.168688
$596$	5.47709e8	0.105971
$597$	−2.11587e9	−0.406985
$598$	2.08765e9	0.399213
$599$	6.74203e9	1.28173	0.640865	−	0.767654i	$-0.278576\pi$
$599$	6.74203e9	1.28173	0.640865	+	0.767654i	$0.278576\pi$
$600$	2.16000e8	0.0408248
$601$	4.63680e9	0.871281	0.435640	−	0.900121i	$-0.356522\pi$
$601$	4.63680e9	0.871281	0.435640	+	0.900121i	$0.356522\pi$
$602$	8.56316e9	1.59973
$603$	−3.46429e9	−0.643434
$604$	2.56864e9	0.474322
$605$	2.84131e8	0.0521645
$606$	−2.95287e9	−0.539001
$607$	−4.15246e9	−0.753607	−0.376804	−	0.926293i	$-0.622977\pi$
$607$	−4.15246e9	−0.753607	−0.376804	+	0.926293i	$0.622977\pi$
$608$	−2.24756e8	−0.0405554
$609$	3.02886e9	0.543398
$610$	−7.56404e8	−0.134927
$611$	8.48138e9	1.50426
$612$	−2.63872e8	−0.0465332
$613$	−5.87720e9	−1.03053	−0.515263	−	0.857032i	$-0.672306\pi$
$613$	−5.87720e9	−1.03053	−0.515263	+	0.857032i	$0.672306\pi$
$614$	1.58092e9	0.275627
$615$	5.61048e7	0.00972606
$616$	2.92819e9	0.504739
$617$	4.26910e9	0.731709	0.365854	−	0.930672i	$-0.380777\pi$
$617$	4.26910e9	0.731709	0.365854	+	0.930672i	$0.380777\pi$
$618$	5.45619e7	0.00929886
$619$	6.08008e9	1.03037	0.515183	−	0.857080i	$-0.327724\pi$
$619$	6.08008e9	1.03037	0.515183	+	0.857080i	$0.327724\pi$
$620$	2.06174e9	0.347427
$621$	5.61873e8	0.0941493
$622$	6.47536e9	1.07894
$623$	4.58238e9	0.759247
$624$	1.01099e9	0.166571
$625$	2.44141e8	0.0400000
$626$	−2.83349e9	−0.461649
$627$	8.63886e8	0.139965
$628$	4.01211e9	0.646419
$629$	1.97544e9	0.316509
$630$	−8.93769e8	−0.142408
$631$	−2.76268e9	−0.437751	−0.218876	−	0.975753i	$-0.570239\pi$
$631$	−2.76268e9	−0.437751	−0.218876	+	0.975753i	$0.570239\pi$
$632$	−6.78061e8	−0.106846
$633$	1.37069e9	0.214797
$634$	8.50111e9	1.32484
$635$	4.89107e9	0.758046
$636$	−1.75189e8	−0.0270027
$637$	6.21248e9	0.952308
$638$	3.41459e9	0.520555
$639$	−3.26530e9	−0.495074
$640$	2.62144e8	0.0395285
$641$	−4.56044e9	−0.683918	−0.341959	−	0.939715i	$-0.611090\pi$
$641$	−4.56044e9	−0.683918	−0.341959	+	0.939715i	$0.611090\pi$
$642$	1.41729e8	0.0211391
$643$	−5.32233e9	−0.789521	−0.394760	−	0.918784i	$-0.629172\pi$
$643$	−5.32233e9	−0.789521	−0.394760	+	0.918784i	$0.629172\pi$
$644$	−2.23988e9	−0.330464
$645$	−2.94659e9	−0.432375
$646$	3.10339e8	0.0452921
$647$	3.18208e9	0.461897	0.230949	−	0.972966i	$-0.425817\pi$
$647$	3.18208e9	0.461897	0.230949	+	0.972966i	$0.425817\pi$
$648$	2.72098e8	0.0392837
$649$	4.59728e9	0.660153
$650$	1.14270e9	0.163206
$651$	−8.53113e9	−1.21192
$652$	2.93905e9	0.415279
$653$	9.07611e9	1.27557	0.637784	−	0.770215i	$-0.279851\pi$
$653$	9.07611e9	1.27557	0.637784	+	0.770215i	$0.279851\pi$
$654$	−1.93045e9	−0.269859
$655$	−3.93011e9	−0.546462
$656$	6.80904e7	0.00941722
$657$	−2.57781e9	−0.354627
$658$	−9.09981e9	−1.24521
$659$	5.36153e9	0.729777	0.364888	−	0.931051i	$-0.381107\pi$
$659$	5.36153e9	0.729777	0.364888	+	0.931051i	$0.381107\pi$
$660$	−1.00759e9	−0.136421
$661$	6.20884e9	0.836191	0.418096	−	0.908403i	$-0.362698\pi$
$661$	6.20884e9	0.836191	0.418096	+	0.908403i	$0.362698\pi$
$662$	1.81282e9	0.242857
$663$	−1.39595e9	−0.186026
$664$	−3.65390e7	−0.00484361
$665$	1.05116e9	0.138609
$666$	−2.03702e9	−0.267199
$667$	−2.61194e9	−0.340819
$668$	1.41019e9	0.183046
$669$	−3.96092e9	−0.511452
$670$	−4.75212e9	−0.610415
$671$	3.52846e9	0.450876
$672$	−1.08470e9	−0.137886
$673$	3.64417e9	0.460836	0.230418	−	0.973092i	$-0.425991\pi$
$673$	3.64417e9	0.460836	0.230418	+	0.973092i	$0.425991\pi$
$674$	3.06873e9	0.386055
$675$	3.07547e8	0.0384900
$676$	1.33249e9	0.165902
$677$	9.03739e9	1.11939	0.559697	−	0.828697i	$-0.310918\pi$
$677$	9.03739e9	1.11939	0.559697	+	0.828697i	$0.310918\pi$
$678$	−1.01305e9	−0.124832
$679$	6.59470e9	0.808446
$680$	−3.61964e8	−0.0441453
$681$	−1.58647e9	−0.192494
$682$	−9.61760e9	−1.16097
$683$	−4.80985e9	−0.577643	−0.288821	−	0.957383i	$-0.593263\pi$
$683$	−4.80985e9	−0.577643	−0.288821	+	0.957383i	$0.593263\pi$
$684$	−3.20014e8	−0.0382360
$685$	−5.51307e9	−0.655354
$686$	1.41197e9	0.166990
$687$	8.21857e9	0.967047
$688$	−3.57607e9	−0.418646
$689$	−9.26797e8	−0.107949
$690$	7.70744e8	0.0893179
$691$	8.74228e9	1.00798	0.503990	−	0.863710i	$-0.331865\pi$
$691$	8.74228e9	1.00798	0.503990	+	0.863710i	$0.331865\pi$
$692$	−4.14410e9	−0.475400
$693$	4.16924e9	0.475873
$694$	4.60756e9	0.523254
$695$	5.33063e9	0.602326
$696$	−1.26488e9	−0.142206
$697$	−9.40182e7	−0.0105171
$698$	−8.24120e9	−0.917268
$699$	−5.86798e9	−0.649858
$700$	−1.22602e9	−0.135100
$701$	1.06528e10	1.16803	0.584013	−	0.811744i	$-0.301482\pi$
$701$	1.06528e10	1.16803	0.584013	+	0.811744i	$0.301482\pi$
$702$	1.43947e9	0.157045
$703$	2.39573e9	0.260073
$704$	−1.22285e9	−0.132089
$705$	3.13125e9	0.336555
$706$	−7.13402e9	−0.762988
$707$	1.67605e10	1.78369
$708$	−1.70299e9	−0.180342
$709$	1.03896e10	1.09481	0.547403	−	0.836869i	$-0.315617\pi$
$709$	1.03896e10	1.09481	0.547403	+	0.836869i	$0.315617\pi$
$710$	−4.47915e9	−0.469669
$711$	−9.65442e8	−0.100735
$712$	−1.91365e9	−0.198693
$713$	7.35684e9	0.760113
$714$	1.49774e9	0.153990
$715$	−5.33044e9	−0.545371
$716$	3.23796e9	0.329668
$717$	6.71832e9	0.680681
$718$	−1.14361e10	−1.15303
$719$	7.96840e9	0.799503	0.399752	−	0.916624i	$-0.369096\pi$
$719$	7.96840e9	0.799503	0.399752	+	0.916624i	$0.369096\pi$
$720$	3.73248e8	0.0372678
$721$	−3.09694e8	−0.0307723
$722$	3.76367e8	0.0372161
$723$	−9.93922e9	−0.978066
$724$	−8.90460e9	−0.872026
$725$	−1.42967e9	−0.139333
$726$	4.90978e8	0.0476194
$727$	1.46339e10	1.41251	0.706253	−	0.707960i	$-0.250384\pi$
$727$	1.46339e10	1.41251	0.706253	+	0.707960i	$0.250384\pi$
$728$	−5.73838e9	−0.551226
$729$	3.87420e8	0.0370370
$730$	−3.53609e9	−0.336429
$731$	4.93778e9	0.467543
$732$	−1.30707e9	−0.123171
$733$	1.27362e10	1.19447	0.597234	−	0.802067i	$-0.296266\pi$
$733$	1.27362e10	1.19447	0.597234	+	0.802067i	$0.296266\pi$
$734$	−8.65586e9	−0.807930
$735$	2.29360e9	0.213065
$736$	9.35398e8	0.0864817
$737$	2.21676e10	2.03978
$738$	9.69491e7	0.00887864
$739$	−1.95071e10	−1.77802	−0.889009	−	0.457890i	$-0.848605\pi$
$739$	−1.95071e10	−1.77802	−0.889009	+	0.457890i	$0.848605\pi$
$740$	−2.79427e9	−0.253488
$741$	−1.69296e9	−0.152856
$742$	9.94376e8	0.0893587
$743$	1.07928e10	0.965326	0.482663	−	0.875806i	$-0.339670\pi$
$743$	1.07928e10	0.965326	0.482663	+	0.875806i	$0.339670\pi$
$744$	3.56270e9	0.317156
$745$	1.06974e9	0.0947836
$746$	−1.13195e10	−0.998251
$747$	−5.20253e7	−0.00456660
$748$	1.68849e9	0.147517
$749$	−8.04457e8	−0.0699547
$750$	4.21875e8	0.0365148
$751$	1.57746e10	1.35899	0.679497	−	0.733679i	$-0.262198\pi$
$751$	1.57746e10	1.35899	0.679497	+	0.733679i	$0.262198\pi$
$752$	3.80018e9	0.325868
$753$	−5.32599e9	−0.454588
$754$	−6.69158e9	−0.568498
$755$	5.01687e9	0.424247
$756$	−1.54443e9	−0.130000
$757$	−1.16114e9	−0.0972855	−0.0486427	−	0.998816i	$-0.515490\pi$
$757$	−1.16114e9	−0.0972855	−0.0486427	+	0.998816i	$0.515490\pi$
$758$	−1.21115e9	−0.101008
$759$	−3.59536e9	−0.298467
$760$	−4.38976e8	−0.0362738
$761$	−7.77889e9	−0.639840	−0.319920	−	0.947445i	$-0.603656\pi$
$761$	−7.77889e9	−0.639840	−0.319920	+	0.947445i	$0.603656\pi$
$762$	8.45176e9	0.691998
$763$	1.09573e10	0.893031
$764$	4.23569e9	0.343635
$765$	−5.15375e8	−0.0416206
$766$	4.64299e9	0.373247
$767$	−9.00930e9	−0.720954
$768$	4.52985e8	0.0360844
$769$	6.68999e9	0.530497	0.265249	−	0.964180i	$-0.414546\pi$
$769$	6.68999e9	0.530497	0.265249	+	0.964180i	$0.414546\pi$
$770$	5.71912e9	0.451452
$771$	−5.56717e9	−0.437466
$772$	−3.72165e9	−0.291122
$773$	−2.23508e10	−1.74046	−0.870230	−	0.492645i	$-0.836030\pi$
$773$	−2.23508e10	−1.74046	−0.870230	+	0.492645i	$0.836030\pi$
$774$	−5.09171e9	−0.394703
$775$	4.02685e9	0.310748
$776$	−2.75402e9	−0.211569
$777$	1.15622e10	0.884231
$778$	1.27691e9	0.0972147
$779$	−1.14022e8	−0.00864183
$780$	1.97458e9	0.148986
$781$	2.08943e10	1.56946
$782$	−1.29158e9	−0.0965826
$783$	−1.80098e9	−0.134073
$784$	2.78358e9	0.206299
$785$	7.83616e9	0.578175
$786$	−6.79123e9	−0.498849
$787$	−9.69306e9	−0.708841	−0.354421	−	0.935086i	$-0.615322\pi$
$787$	−9.69306e9	−0.708841	−0.354421	+	0.935086i	$0.615322\pi$
$788$	8.50807e9	0.619426
$789$	−3.59041e9	−0.260240
$790$	−1.32434e9	−0.0955661
$791$	5.75008e9	0.413101
$792$	−1.74112e9	−0.124535
$793$	−6.91474e9	−0.492402
$794$	1.84600e9	0.130876
$795$	−3.42166e8	−0.0241519
$796$	−5.01539e9	−0.352459
$797$	1.58293e10	1.10754	0.553769	−	0.832670i	$-0.313189\pi$
$797$	1.58293e10	1.10754	0.553769	+	0.832670i	$0.313189\pi$
$798$	1.81640e9	0.126533
$799$	−5.24723e9	−0.363929
$800$	5.12000e8	0.0353553
$801$	−2.72471e9	−0.187330
$802$	−6.21319e9	−0.425309
$803$	1.64951e10	1.12422
$804$	−8.21166e9	−0.557230
$805$	−4.37476e9	−0.295576
$806$	1.88476e10	1.26790
$807$	4.76020e9	0.318836
$808$	−6.99939e9	−0.466789
$809$	−7.03323e9	−0.467020	−0.233510	−	0.972354i	$-0.575021\pi$
$809$	−7.03323e9	−0.467020	−0.233510	+	0.972354i	$0.575021\pi$
$810$	5.31441e8	0.0351364
$811$	−2.22464e10	−1.46449	−0.732244	−	0.681042i	$-0.761527\pi$
$811$	−2.22464e10	−1.46449	−0.732244	+	0.681042i	$0.761527\pi$
$812$	7.17951e9	0.470597
$813$	−7.60685e9	−0.496464
$814$	1.30346e10	0.847059
$815$	5.74032e9	0.371437
$816$	−6.25474e8	−0.0402990
$817$	5.98835e9	0.384176
$818$	4.21168e9	0.269041
$819$	−8.17047e9	−0.519701
$820$	1.32989e8	0.00842301
$821$	1.45023e10	0.914611	0.457305	−	0.889310i	$-0.348815\pi$
$821$	1.45023e10	0.914611	0.457305	+	0.889310i	$0.348815\pi$
$822$	−9.52658e9	−0.598254
$823$	−1.39647e9	−0.0873237	−0.0436619	−	0.999046i	$-0.513902\pi$
$823$	−1.39647e9	−0.0873237	−0.0436619	+	0.999046i	$0.513902\pi$
$824$	1.29332e8	0.00805305
$825$	−1.96796e9	−0.122019
$826$	9.66624e9	0.596798
$827$	6.31315e9	0.388130	0.194065	−	0.980989i	$-0.437833\pi$
$827$	6.31315e9	0.388130	0.194065	+	0.980989i	$0.437833\pi$
$828$	1.33185e9	0.0815357
$829$	−2.65187e9	−0.161663	−0.0808317	−	0.996728i	$-0.525758\pi$
$829$	−2.65187e9	−0.161663	−0.0808317	+	0.996728i	$0.525758\pi$
$830$	−7.13653e7	−0.00433225
$831$	8.97512e9	0.542546
$832$	2.39641e9	0.144255
$833$	−3.84352e9	−0.230394
$834$	9.21132e9	0.549846
$835$	2.75429e9	0.163722
$836$	2.04773e9	0.121213
$837$	5.07267e9	0.299018
$838$	−1.85471e10	−1.08873
$839$	2.35103e10	1.37433	0.687165	−	0.726502i	$-0.258855\pi$
$839$	2.35103e10	1.37433	0.687165	+	0.726502i	$0.258855\pi$
$840$	−2.11856e9	−0.123329
$841$	−8.87778e9	−0.514657
$842$	−1.73055e10	−0.999060
$843$	9.82844e9	0.565051
$844$	3.24905e9	0.186019
$845$	2.60252e9	0.148387
$846$	5.41081e9	0.307232
$847$	−2.78680e9	−0.157585
$848$	−4.15262e8	−0.0233850
$849$	1.26890e10	0.711627
$850$	−7.06962e8	−0.0394848
$851$	−9.97067e9	−0.554588
$852$	−7.73998e9	−0.428747
$853$	1.25648e10	0.693160	0.346580	−	0.938020i	$-0.387343\pi$
$853$	1.25648e10	0.693160	0.346580	+	0.938020i	$0.387343\pi$
$854$	7.41894e9	0.407605
$855$	−6.25026e8	−0.0341993
$856$	3.35950e8	0.0183070
$857$	2.24742e10	1.21970	0.609848	−	0.792519i	$-0.291231\pi$
$857$	2.24742e10	1.21970	0.609848	+	0.792519i	$0.291231\pi$
$858$	−9.21101e9	−0.497854
$859$	−1.20621e10	−0.649302	−0.324651	−	0.945834i	$-0.605247\pi$
$859$	−1.20621e10	−0.649302	−0.324651	+	0.945834i	$0.605247\pi$
$860$	−6.98451e9	−0.374448
$861$	−5.50285e8	−0.0293817
$862$	−1.75252e9	−0.0931937
$863$	−3.12352e10	−1.65427	−0.827136	−	0.562001i	$-0.810032\pi$
$863$	−3.12352e10	−1.65427	−0.827136	+	0.562001i	$0.810032\pi$
$864$	6.44973e8	0.0340207
$865$	−8.09394e9	−0.425210
$866$	2.46482e10	1.28965
$867$	−1.02155e10	−0.532344
$868$	−2.02219e10	−1.04955
$869$	6.17775e9	0.319346
$870$	−2.47048e9	−0.127193
$871$	−4.34419e10	−2.22764
$872$	−4.57588e9	−0.233704
$873$	−3.92125e9	−0.199469
$874$	−1.56638e9	−0.0793610
$875$	−2.39457e9	−0.120837
$876$	−6.11037e9	−0.307116
$877$	−1.16277e10	−0.582096	−0.291048	−	0.956709i	$-0.594004\pi$
$877$	−1.16277e10	−0.582096	−0.291048	+	0.956709i	$0.594004\pi$
$878$	2.15268e10	1.07337
$879$	−1.95834e10	−0.972585
$880$	−2.38837e9	−0.118144
$881$	−6.80837e9	−0.335450	−0.167725	−	0.985834i	$-0.553642\pi$
$881$	−6.80837e9	−0.335450	−0.167725	+	0.985834i	$0.553642\pi$
$882$	3.96334e9	0.194501
$883$	−4.66300e8	−0.0227931	−0.0113965	−	0.999935i	$-0.503628\pi$
$883$	−4.66300e8	−0.0227931	−0.0113965	+	0.999935i	$0.503628\pi$
$884$	−3.30893e9	−0.161103
$885$	−3.32616e9	−0.161303
$886$	2.99105e8	0.0144480
$887$	−3.49184e10	−1.68005	−0.840025	−	0.542548i	$-0.817460\pi$
$887$	−3.49184e10	−1.68005	−0.840025	+	0.542548i	$0.817460\pi$
$888$	−4.82849e9	−0.231401
$889$	−4.79724e10	−2.29000
$890$	−3.73761e9	−0.177717
$891$	−2.47906e9	−0.117413
$892$	−9.38885e9	−0.442930
$893$	−6.36364e9	−0.299037
$894$	1.84852e9	0.0865252
$895$	6.32414e9	0.294864
$896$	−2.57115e9	−0.119413
$897$	7.04583e9	0.325956
$898$	1.23138e10	0.567445
$899$	−2.35810e10	−1.08244
$900$	7.29000e8	0.0333333
$901$	5.73388e8	0.0261163
$902$	−6.20366e8	−0.0281465
$903$	2.89007e10	1.30617
$904$	−2.40130e9	−0.108108
$905$	−1.73918e10	−0.779964
$906$	8.66915e9	0.387283
$907$	−9.65664e9	−0.429735	−0.214867	−	0.976643i	$-0.568932\pi$
$907$	−9.65664e9	−0.429735	−0.214867	+	0.976643i	$0.568932\pi$
$908$	−3.76053e9	−0.166705
$909$	−9.96593e9	−0.440093
$910$	−1.12078e10	−0.493032
$911$	5.54939e8	0.0243182	0.0121591	−	0.999926i	$-0.496130\pi$
$911$	5.54939e8	0.0243182	0.0121591	+	0.999926i	$0.496130\pi$
$912$	−7.58551e8	−0.0331133
$913$	3.32904e8	0.0144767
$914$	−2.63402e10	−1.14106
$915$	−2.55286e9	−0.110168
$916$	1.94811e10	0.837488
$917$	3.85472e10	1.65082
$918$	−8.90568e8	−0.0379942
$919$	−9.56305e9	−0.406436	−0.203218	−	0.979134i	$-0.565140\pi$
$919$	−9.56305e9	−0.406436	−0.203218	+	0.979134i	$0.565140\pi$
$920$	1.82695e9	0.0773516
$921$	5.33562e9	0.225048
$922$	2.07204e10	0.870644
$923$	−4.09466e10	−1.71400
$924$	9.88265e9	0.412118
$925$	−5.45755e9	−0.226726
$926$	1.68579e10	0.697694
$927$	1.84146e8	0.00759249
$928$	−2.99824e9	−0.123154
$929$	−2.73541e10	−1.11935	−0.559677	−	0.828711i	$-0.689075\pi$
$929$	−2.73541e10	−1.11935	−0.559677	+	0.828711i	$0.689075\pi$
$930$	6.95839e9	0.283673
$931$	−4.66127e9	−0.189313
$932$	−1.39093e10	−0.562793
$933$	2.18543e10	0.880952
$934$	7.46812e9	0.299915
$935$	3.29782e9	0.131943
$936$	3.41208e9	0.136005
$937$	−1.94603e10	−0.772787	−0.386394	−	0.922334i	$-0.626279\pi$
$937$	−1.94603e10	−0.772787	−0.386394	+	0.922334i	$0.626279\pi$
$938$	4.66096e10	1.84402
$939$	−9.56304e9	−0.376935
$940$	7.42223e9	0.291465
$941$	1.34447e10	0.526002	0.263001	−	0.964796i	$-0.415288\pi$
$941$	1.34447e10	0.526002	0.263001	+	0.964796i	$0.415288\pi$
$942$	1.35409e10	0.527799
$943$	4.74540e8	0.0184281
$944$	−4.03673e9	−0.156181
$945$	−3.01647e9	−0.116275
$946$	3.25813e10	1.25126
$947$	8.81228e9	0.337181	0.168591	−	0.985686i	$-0.446078\pi$
$947$	8.81228e9	0.337181	0.168591	+	0.985686i	$0.446078\pi$
$948$	−2.28845e9	−0.0872395
$949$	−3.23255e10	−1.22776
$950$	−8.57375e8	−0.0324443
$951$	2.86912e10	1.08173
$952$	3.55021e9	0.133360
$953$	2.10715e10	0.788623	0.394312	−	0.918977i	$-0.370983\pi$
$953$	2.10715e10	0.788623	0.394312	+	0.918977i	$0.370983\pi$
$954$	−5.91262e8	−0.0220476
$955$	8.27283e9	0.307356
$956$	1.59249e10	0.589487
$957$	1.15242e10	0.425031
$958$	7.41903e9	0.272626
$959$	5.40731e10	1.97978
$960$	8.84736e8	0.0322749
$961$	3.89060e10	1.41412
$962$	−2.55440e10	−0.925074
$963$	4.78336e8	0.0172600
$964$	−2.35596e10	−0.847030
$965$	−7.26885e9	−0.260387
$966$	−7.55959e9	−0.269823
$967$	−8.38176e9	−0.298087	−0.149043	−	0.988831i	$-0.547619\pi$
$967$	−8.38176e9	−0.298087	−0.149043	+	0.988831i	$0.547619\pi$
$968$	1.16380e9	0.0412396
$969$	1.04739e9	0.0369809
$970$	−5.37895e9	−0.189233
$971$	1.05194e10	0.368742	0.184371	−	0.982857i	$-0.440975\pi$
$971$	1.05194e10	0.368742	0.184371	+	0.982857i	$0.440975\pi$
$972$	9.18330e8	0.0320750
$973$	−5.22837e10	−1.81958
$974$	2.87886e8	0.00998306
$975$	3.85661e9	0.133257
$976$	−3.09823e9	−0.106669
$977$	1.62963e10	0.559059	0.279529	−	0.960137i	$-0.409822\pi$
$977$	1.62963e10	0.559059	0.279529	+	0.960137i	$0.409822\pi$
$978$	9.91928e9	0.339074
$979$	1.74351e10	0.593862
$980$	5.43668e9	0.184519
$981$	−6.51527e9	−0.220339
$982$	−3.88521e10	−1.30925
$983$	3.02334e9	0.101519	0.0507597	−	0.998711i	$-0.483836\pi$
$983$	3.02334e9	0.101519	0.0507597	+	0.998711i	$0.483836\pi$
$984$	2.29805e8	0.00768913
$985$	1.66173e10	0.554031
$986$	4.13993e9	0.137538
$987$	−3.07119e10	−1.01671
$988$	−4.01294e9	−0.132377
$989$	−2.49226e10	−0.819230
$990$	−3.40063e9	−0.111387
$991$	−3.28205e10	−1.07124	−0.535620	−	0.844459i	$-0.679922\pi$
$991$	−3.28205e10	−1.07124	−0.535620	+	0.844459i	$0.679922\pi$
$992$	8.44491e9	0.274665
$993$	6.11825e9	0.198292
$994$	4.39323e10	1.41883
$995$	−9.79568e9	−0.315249
$996$	−1.23319e8	−0.00395479
$997$	−4.27161e10	−1.36508	−0.682541	−	0.730848i	$-0.739125\pi$
$997$	−4.27161e10	−1.36508	−0.682541	+	0.730848i	$0.739125\pi$
$998$	−4.16149e9	−0.132523
$999$	−6.87494e9	−0.218167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.c.1.1	✓	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} -1226.02 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} -1226.02 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} -4664.78 q^{11} +1728.00 q^{12} +9141.59 q^{13} -9808.17 q^{14} +3375.00 q^{15} +4096.00 q^{16} -5655.69 q^{17} +5832.00 q^{18} -6859.00 q^{19} +8000.00 q^{20} -33102.6 q^{21} -37318.3 q^{22} +28546.1 q^{23} +13824.0 q^{24} +15625.0 q^{25} +73132.7 q^{26} +19683.0 q^{27} -78465.3 q^{28} -91499.2 q^{29} +27000.0 q^{30} +257718. q^{31} +32768.0 q^{32} -125949. q^{33} -45245.5 q^{34} -153253. q^{35} +46656.0 q^{36} -349283. q^{37} -54872.0 q^{38} +246823. q^{39} +64000.0 q^{40} +16623.6 q^{41} -264821. q^{42} -873064. q^{43} -298546. q^{44} +91125.0 q^{45} +228369. q^{46} +927779. q^{47} +110592. q^{48} +679585. q^{49} +125000. q^{50} -152704. q^{51} +585062. q^{52} -101382. q^{53} +157464. q^{54} -583098. q^{55} -627723. q^{56} -185193. q^{57} -731993. q^{58} -985529. q^{59} +216000. q^{60} -756404. q^{61} +2.06174e6 q^{62} -893769. q^{63} +262144. q^{64} +1.14270e6 q^{65} -1.00759e6 q^{66} -4.75212e6 q^{67} -361964. q^{68} +770744. q^{69} -1.22602e6 q^{70} -4.47915e6 q^{71} +373248. q^{72} -3.53609e6 q^{73} -2.79427e6 q^{74} +421875. q^{75} -438976. q^{76} +5.71912e6 q^{77} +1.97458e6 q^{78} -1.32434e6 q^{79} +512000. q^{80} +531441. q^{81} +132989. q^{82} -71365.3 q^{83} -2.11856e6 q^{84} -706962. q^{85} -6.98451e6 q^{86} -2.47048e6 q^{87} -2.38837e6 q^{88} -3.73761e6 q^{89} +729000. q^{90} -1.12078e7 q^{91} +1.82695e6 q^{92} +6.95839e6 q^{93} +7.42223e6 q^{94} -857375. q^{95} +884736. q^{96} -5.37895e6 q^{97} +5.43668e6 q^{98} -3.40063e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 500 q^{5} + 864 q^{6} - 1316 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 500 * q^5 + 864 * q^6 - 1316 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 500 q^{5} + 864 q^{6} - 1316 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 6570 q^{11} + 6912 q^{12} - 17578 q^{13} - 10528 q^{14} + 13500 q^{15} + 16384 q^{16} - 28466 q^{17} + 23328 q^{18} - 27436 q^{19} + 32000 q^{20} - 35532 q^{21} - 52560 q^{22} - 32136 q^{23} + 55296 q^{24} + 62500 q^{25} - 140624 q^{26} + 78732 q^{27} - 84224 q^{28} - 159122 q^{29} + 108000 q^{30} - 67974 q^{31} + 131072 q^{32} - 177390 q^{33} - 227728 q^{34} - 164500 q^{35} + 186624 q^{36} - 823702 q^{37} - 219488 q^{38} - 474606 q^{39} + 256000 q^{40} - 781924 q^{41} - 284256 q^{42} - 1115638 q^{43} - 420480 q^{44} + 364500 q^{45} - 257088 q^{46} - 209160 q^{47} + 442368 q^{48} - 1159308 q^{49} + 500000 q^{50} - 768582 q^{51} - 1124992 q^{52} - 848424 q^{53} + 629856 q^{54} - 821250 q^{55} - 673792 q^{56} - 740772 q^{57} - 1272976 q^{58} - 3677830 q^{59} + 864000 q^{60} - 1161072 q^{61} - 543792 q^{62} - 959364 q^{63} + 1048576 q^{64} - 2197250 q^{65} - 1419120 q^{66} - 6154740 q^{67} - 1821824 q^{68} - 867672 q^{69} - 1316000 q^{70} - 4456224 q^{71} + 1492992 q^{72} + 1057792 q^{73} - 6589616 q^{74} + 1687500 q^{75} - 1755904 q^{76} + 2402388 q^{77} - 3796848 q^{78} + 2910090 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 6255392 q^{82} - 1767198 q^{83} - 2274048 q^{84} - 3558250 q^{85} - 8925104 q^{86} - 4296294 q^{87} - 3363840 q^{88} - 3677360 q^{89} + 2916000 q^{90} - 6727732 q^{91} - 2056704 q^{92} - 1835298 q^{93} - 1673280 q^{94} - 3429500 q^{95} + 3538944 q^{96} - 10419094 q^{97} - 9274464 q^{98} - 4789530 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 500 * q^5 + 864 * q^6 - 1316 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 6570 * q^11 + 6912 * q^12 - 17578 * q^13 - 10528 * q^14 + 13500 * q^15 + 16384 * q^16 - 28466 * q^17 + 23328 * q^18 - 27436 * q^19 + 32000 * q^20 - 35532 * q^21 - 52560 * q^22 - 32136 * q^23 + 55296 * q^24 + 62500 * q^25 - 140624 * q^26 + 78732 * q^27 - 84224 * q^28 - 159122 * q^29 + 108000 * q^30 - 67974 * q^31 + 131072 * q^32 - 177390 * q^33 - 227728 * q^34 - 164500 * q^35 + 186624 * q^36 - 823702 * q^37 - 219488 * q^38 - 474606 * q^39 + 256000 * q^40 - 781924 * q^41 - 284256 * q^42 - 1115638 * q^43 - 420480 * q^44 + 364500 * q^45 - 257088 * q^46 - 209160 * q^47 + 442368 * q^48 - 1159308 * q^49 + 500000 * q^50 - 768582 * q^51 - 1124992 * q^52 - 848424 * q^53 + 629856 * q^54 - 821250 * q^55 - 673792 * q^56 - 740772 * q^57 - 1272976 * q^58 - 3677830 * q^59 + 864000 * q^60 - 1161072 * q^61 - 543792 * q^62 - 959364 * q^63 + 1048576 * q^64 - 2197250 * q^65 - 1419120 * q^66 - 6154740 * q^67 - 1821824 * q^68 - 867672 * q^69 - 1316000 * q^70 - 4456224 * q^71 + 1492992 * q^72 + 1057792 * q^73 - 6589616 * q^74 + 1687500 * q^75 - 1755904 * q^76 + 2402388 * q^77 - 3796848 * q^78 + 2910090 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 6255392 * q^82 - 1767198 * q^83 - 2274048 * q^84 - 3558250 * q^85 - 8925104 * q^86 - 4296294 * q^87 - 3363840 * q^88 - 3677360 * q^89 + 2916000 * q^90 - 6727732 * q^91 - 2056704 * q^92 - 1835298 * q^93 - 1673280 * q^94 - 3429500 * q^95 + 3538944 * q^96 - 10419094 * q^97 - 9274464 * q^98 - 4789530 * q^99

Introduction

L-functions

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