LMFDB - Embedded newform 570.8.a.c.1.4

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			1.4
Root			$-54.0924$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} +617.139 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} +617.139 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} -3899.34 q^{11} +1728.00 q^{12} -4970.13 q^{13} +4937.11 q^{14} +3375.00 q^{15} +4096.00 q^{16} -30312.4 q^{17} +5832.00 q^{18} -6859.00 q^{19} +8000.00 q^{20} +16662.7 q^{21} -31194.7 q^{22} +24239.7 q^{23} +13824.0 q^{24} +15625.0 q^{25} -39761.0 q^{26} +19683.0 q^{27} +39496.9 q^{28} -111451. q^{29} +27000.0 q^{30} -135412. q^{31} +32768.0 q^{32} -105282. q^{33} -242499. q^{34} +77142.3 q^{35} +46656.0 q^{36} +80372.0 q^{37} -54872.0 q^{38} -134193. q^{39} +64000.0 q^{40} -511416. q^{41} +133302. q^{42} -828701. q^{43} -249558. q^{44} +91125.0 q^{45} +193918. q^{46} -514925. q^{47} +110592. q^{48} -442683. q^{49} +125000. q^{50} -818436. q^{51} -318088. q^{52} +546977. q^{53} +157464. q^{54} -487417. q^{55} +315975. q^{56} -185193. q^{57} -891606. q^{58} +20228.9 q^{59} +216000. q^{60} -1.58093e6 q^{61} -1.08330e6 q^{62} +449894. q^{63} +262144. q^{64} -621266. q^{65} -842257. q^{66} +1.93405e6 q^{67} -1.94000e6 q^{68} +654472. q^{69} +617139. q^{70} +555676. q^{71} +373248. q^{72} -2.03651e6 q^{73} +642976. q^{74} +421875. q^{75} -438976. q^{76} -2.40643e6 q^{77} -1.07355e6 q^{78} +712815. q^{79} +512000. q^{80} +531441. q^{81} -4.09132e6 q^{82} +2.94412e6 q^{83} +1.06642e6 q^{84} -3.78905e6 q^{85} -6.62961e6 q^{86} -3.00917e6 q^{87} -1.99646e6 q^{88} +1.06933e7 q^{89} +729000. q^{90} -3.06726e6 q^{91} +1.55134e6 q^{92} -3.65613e6 q^{93} -4.11940e6 q^{94} -857375. q^{95} +884736. q^{96} +3.72622e6 q^{97} -3.54146e6 q^{98} -2.84262e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	617.139	0.680048	0.340024	−	0.940417i	$-0.389565\pi$
$7$	617.139	0.680048	0.340024	+	0.940417i	$0.389565\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1000.00	0.316228
$11$	−3899.34	−0.883317	−0.441658	−	0.897183i	$-0.645610\pi$
$11$	−3899.34	−0.883317	−0.441658	+	0.897183i	$0.645610\pi$
$12$	1728.00	0.288675
$13$	−4970.13	−0.627431	−0.313715	−	0.949517i	$-0.601574\pi$
$13$	−4970.13	−0.627431	−0.313715	+	0.949517i	$0.601574\pi$
$14$	4937.11	0.480867
$15$	3375.00	0.258199
$16$	4096.00	0.250000
$17$	−30312.4	−1.49641	−0.748203	−	0.663470i	$-0.769083\pi$
$17$	−30312.4	−1.49641	−0.748203	+	0.663470i	$0.769083\pi$
$18$	5832.00	0.235702
$19$	−6859.00	−0.229416
$19$	−6859.00	−0.229416
$20$	8000.00	0.223607
$21$	16662.7	0.392626
$22$	−31194.7	−0.624599
$23$	24239.7	0.415413	0.207706	−	0.978191i	$-0.433400\pi$
$23$	24239.7	0.415413	0.207706	+	0.978191i	$0.433400\pi$
$24$	13824.0	0.204124
$25$	15625.0	0.200000
$26$	−39761.0	−0.443660
$27$	19683.0	0.192450
$28$	39496.9	0.340024
$29$	−111451.	−0.848574	−0.424287	−	0.905528i	$-0.639475\pi$
$29$	−111451.	−0.848574	−0.424287	+	0.905528i	$0.639475\pi$
$30$	27000.0	0.182574
$31$	−135412.	−0.816379	−0.408190	−	0.912897i	$-0.633840\pi$
$31$	−135412.	−0.816379	−0.408190	+	0.912897i	$0.633840\pi$
$32$	32768.0	0.176777
$33$	−105282.	−0.509983
$34$	−242499.	−1.05812
$35$	77142.3	0.304127
$36$	46656.0	0.166667
$37$	80372.0	0.260855	0.130427	−	0.991458i	$-0.458365\pi$
$37$	80372.0	0.260855	0.130427	+	0.991458i	$0.458365\pi$
$38$	−54872.0	−0.162221
$39$	−134193.	−0.362247
$40$	64000.0	0.158114
$41$	−511416.	−1.15886	−0.579429	−	0.815023i	$-0.696724\pi$
$41$	−511416.	−1.15886	−0.579429	+	0.815023i	$0.696724\pi$
$42$	133302.	0.277628
$43$	−828701.	−1.58949	−0.794746	−	0.606942i	$-0.792396\pi$
$43$	−828701.	−1.58949	−0.794746	+	0.606942i	$0.792396\pi$
$44$	−249558.	−0.441658
$45$	91125.0	0.149071
$46$	193918.	0.293741
$47$	−514925.	−0.723439	−0.361719	−	0.932287i	$-0.617810\pi$
$47$	−514925.	−0.723439	−0.361719	+	0.932287i	$0.617810\pi$
$48$	110592.	0.144338
$49$	−442683.	−0.537535
$50$	125000.	0.141421
$51$	−818436.	−0.863950
$52$	−318088.	−0.313715
$53$	546977.	0.504665	0.252333	−	0.967641i	$-0.418802\pi$
$53$	546977.	0.504665	0.252333	+	0.967641i	$0.418802\pi$
$54$	157464.	0.136083
$55$	−487417.	−0.395031
$56$	315975.	0.240433
$57$	−185193.	−0.132453
$58$	−891606.	−0.600033
$59$	20228.9	0.0128230	0.00641151	−	0.999979i	$-0.497959\pi$
$59$	20228.9	0.0128230	0.00641151	+	0.999979i	$0.497959\pi$
$60$	216000.	0.129099
$61$	−1.58093e6	−0.891783	−0.445891	−	0.895087i	$-0.647113\pi$
$61$	−1.58093e6	−0.891783	−0.445891	+	0.895087i	$0.647113\pi$
$62$	−1.08330e6	−0.577267
$63$	449894.	0.226683
$64$	262144.	0.125000
$65$	−621266.	−0.280595
$66$	−842257.	−0.360612
$67$	1.93405e6	0.785607	0.392804	−	0.919622i	$-0.371505\pi$
$67$	1.93405e6	0.785607	0.392804	+	0.919622i	$0.371505\pi$
$68$	−1.94000e6	−0.748203
$69$	654472.	0.239839
$70$	617139.	0.215050
$71$	555676.	0.184254	0.0921270	−	0.995747i	$-0.470633\pi$
$71$	555676.	0.184254	0.0921270	+	0.995747i	$0.470633\pi$
$72$	373248.	0.117851
$73$	−2.03651e6	−0.612712	−0.306356	−	0.951917i	$-0.599110\pi$
$73$	−2.03651e6	−0.612712	−0.306356	+	0.951917i	$0.599110\pi$
$74$	642976.	0.184452
$75$	421875.	0.115470
$76$	−438976.	−0.114708
$77$	−2.40643e6	−0.600698
$78$	−1.07355e6	−0.256147
$79$	712815.	0.162661	0.0813303	−	0.996687i	$-0.474083\pi$
$79$	712815.	0.162661	0.0813303	+	0.996687i	$0.474083\pi$
$80$	512000.	0.111803
$81$	531441.	0.111111
$82$	−4.09132e6	−0.819437
$83$	2.94412e6	0.565174	0.282587	−	0.959242i	$-0.408807\pi$
$83$	2.94412e6	0.565174	0.282587	+	0.959242i	$0.408807\pi$
$84$	1.06642e6	0.196313
$85$	−3.78905e6	−0.669213
$86$	−6.62961e6	−1.12394
$87$	−3.00917e6	−0.489925
$88$	−1.99646e6	−0.312300
$89$	1.06933e7	1.60786	0.803930	−	0.594724i	$-0.202739\pi$
$89$	1.06933e7	1.60786	0.803930	+	0.594724i	$0.202739\pi$
$90$	729000.	0.105409
$91$	−3.06726e6	−0.426683
$92$	1.55134e6	0.207706
$93$	−3.65613e6	−0.471337
$94$	−4.11940e6	−0.511548
$95$	−857375.	−0.102598
$96$	884736.	0.102062
$97$	3.72622e6	0.414541	0.207271	−	0.978284i	$-0.433542\pi$
$97$	3.72622e6	0.414541	0.207271	+	0.978284i	$0.433542\pi$
$98$	−3.54146e6	−0.380094
$99$	−2.84262e6	−0.294439
$100$	1.00000e6	0.100000
$101$	2.30207e6	0.222328	0.111164	−	0.993802i	$-0.464542\pi$
$101$	2.30207e6	0.222328	0.111164	+	0.993802i	$0.464542\pi$
$102$	−6.54748e6	−0.610905
$103$	−6.09959e6	−0.550010	−0.275005	−	0.961443i	$-0.588680\pi$
$103$	−6.09959e6	−0.550010	−0.275005	+	0.961443i	$0.588680\pi$
$104$	−2.54470e6	−0.221830
$105$	2.08284e6	0.175588
$106$	4.37582e6	0.356852
$107$	−7.37181e6	−0.581743	−0.290871	−	0.956762i	$-0.593945\pi$
$107$	−7.37181e6	−0.581743	−0.290871	+	0.956762i	$0.593945\pi$
$108$	1.25971e6	0.0962250
$109$	2.38555e7	1.76439	0.882196	−	0.470882i	$-0.156064\pi$
$109$	2.38555e7	1.76439	0.882196	+	0.470882i	$0.156064\pi$
$110$	−3.89934e6	−0.279329
$111$	2.17004e6	0.150605
$112$	2.52780e6	0.170012
$113$	1.50684e7	0.982410	0.491205	−	0.871044i	$-0.336557\pi$
$113$	1.50684e7	0.982410	0.491205	+	0.871044i	$0.336557\pi$
$114$	−1.48154e6	−0.0936586
$115$	3.02996e6	0.185778
$116$	−7.13285e6	−0.424287
$117$	−3.62322e6	−0.209144
$118$	161831.	0.00906725
$119$	−1.87070e7	−1.01763
$120$	1.72800e6	0.0912871
$121$	−4.28234e6	−0.219752
$122$	−1.26475e7	−0.630586
$123$	−1.38082e7	−0.669067
$124$	−8.66638e6	−0.408190
$125$	1.95312e6	0.0894427
$126$	3.59915e6	0.160289
$127$	−3.51742e7	−1.52374	−0.761871	−	0.647729i	$-0.775719\pi$
$127$	−3.51742e7	−1.52374	−0.761871	+	0.647729i	$0.775719\pi$
$128$	2.09715e6	0.0883883
$129$	−2.23749e7	−0.917694
$130$	−4.97013e6	−0.198411
$131$	1.21096e7	0.470630	0.235315	−	0.971919i	$-0.424388\pi$
$131$	1.21096e7	0.470630	0.235315	+	0.971919i	$0.424388\pi$
$132$	−6.73805e6	−0.254992
$133$	−4.23295e6	−0.156014
$134$	1.54724e7	0.555508
$135$	2.46038e6	0.0860663
$136$	−1.55200e7	−0.529059
$137$	2.39599e6	0.0796091	0.0398045	−	0.999207i	$-0.487326\pi$
$137$	2.39599e6	0.0796091	0.0398045	+	0.999207i	$0.487326\pi$
$138$	5.23578e6	0.169592
$139$	−3.62795e7	−1.14580	−0.572901	−	0.819625i	$-0.694182\pi$
$139$	−3.62795e7	−1.14580	−0.572901	+	0.819625i	$0.694182\pi$
$140$	4.93711e6	0.152063
$141$	−1.39030e7	−0.417678
$142$	4.44541e6	0.130287
$143$	1.93802e7	0.554220
$144$	2.98598e6	0.0833333
$145$	−1.39313e7	−0.379494
$146$	−1.62921e7	−0.433253
$147$	−1.19524e7	−0.310346
$148$	5.14381e6	0.130427
$149$	−5.26977e7	−1.30509	−0.652544	−	0.757751i	$-0.726298\pi$
$149$	−5.26977e7	−1.30509	−0.652544	+	0.757751i	$0.726298\pi$
$150$	3.37500e6	0.0816497
$151$	3.44151e7	0.813448	0.406724	−	0.913551i	$-0.366671\pi$
$151$	3.44151e7	0.813448	0.406724	+	0.913551i	$0.366671\pi$
$152$	−3.51181e6	−0.0811107
$153$	−2.20978e7	−0.498802
$154$	−1.92515e7	−0.424757
$155$	−1.69265e7	−0.365096
$156$	−8.58838e6	−0.181124
$157$	1.05722e7	0.218030	0.109015	−	0.994040i	$-0.465230\pi$
$157$	1.05722e7	0.218030	0.109015	+	0.994040i	$0.465230\pi$
$158$	5.70252e6	0.115018
$159$	1.47684e7	0.291369
$160$	4.09600e6	0.0790569
$161$	1.49593e7	0.282501
$162$	4.25153e6	0.0785674
$163$	3.92791e7	0.710404	0.355202	−	0.934790i	$-0.384412\pi$
$163$	3.92791e7	0.710404	0.355202	+	0.934790i	$0.384412\pi$
$164$	−3.27306e7	−0.579429
$165$	−1.31603e7	−0.228071
$166$	2.35529e7	0.399638
$167$	−2.14163e7	−0.355825	−0.177912	−	0.984046i	$-0.556934\pi$
$167$	−2.14163e7	−0.355825	−0.177912	+	0.984046i	$0.556934\pi$
$168$	8.53132e6	0.138814
$169$	−3.80464e7	−0.606331
$170$	−3.03124e7	−0.473205
$171$	−5.00021e6	−0.0764719
$172$	−5.30369e7	−0.794746
$173$	1.22025e8	1.79179	0.895897	−	0.444261i	$-0.146534\pi$
$173$	1.22025e8	1.79179	0.895897	+	0.444261i	$0.146534\pi$
$174$	−2.40734e7	−0.346429
$175$	9.64279e6	0.136010
$176$	−1.59717e7	−0.220829
$177$	546181.	0.00740338
$178$	8.55467e7	1.13693
$179$	−5.57624e7	−0.726701	−0.363350	−	0.931653i	$-0.618367\pi$
$179$	−5.57624e7	−0.726701	−0.363350	+	0.931653i	$0.618367\pi$
$180$	5.83200e6	0.0745356
$181$	−1.10873e8	−1.38979	−0.694896	−	0.719110i	$-0.744550\pi$
$181$	−1.10873e8	−1.38979	−0.694896	+	0.719110i	$0.744550\pi$
$182$	−2.45381e7	−0.301710
$183$	−4.26852e7	−0.514871
$184$	1.24107e7	0.146871
$185$	1.00465e7	0.116658
$186$	−2.92490e7	−0.333285
$187$	1.18198e8	1.32180
$188$	−3.29552e7	−0.361719
$189$	1.21471e7	0.130875
$190$	−6.85900e6	−0.0725476
$191$	−9.58547e6	−0.0995398	−0.0497699	−	0.998761i	$-0.515849\pi$
$191$	−9.58547e6	−0.0995398	−0.0497699	+	0.998761i	$0.515849\pi$
$192$	7.07789e6	0.0721688
$193$	−3.86980e7	−0.387470	−0.193735	−	0.981054i	$-0.562060\pi$
$193$	−3.86980e7	−0.387470	−0.193735	+	0.981054i	$0.562060\pi$
$194$	2.98098e7	0.293125
$195$	−1.67742e7	−0.162002
$196$	−2.83317e7	−0.268767
$197$	2.75631e7	0.256860	0.128430	−	0.991719i	$-0.459006\pi$
$197$	2.75631e7	0.256860	0.128430	+	0.991719i	$0.459006\pi$
$198$	−2.27409e7	−0.208200
$199$	1.72448e8	1.55122	0.775609	−	0.631214i	$-0.217443\pi$
$199$	1.72448e8	1.55122	0.775609	+	0.631214i	$0.217443\pi$
$200$	8.00000e6	0.0707107
$201$	5.22193e7	0.453571
$202$	1.84165e7	0.157209
$203$	−6.87805e7	−0.577071
$204$	−5.23799e7	−0.431975
$205$	−6.39269e7	−0.518257
$206$	−4.87967e7	−0.388916
$207$	1.76707e7	0.138471
$208$	−2.03576e7	−0.156858
$209$	2.67456e7	0.202647
$210$	1.66627e7	0.124159
$211$	−2.17057e8	−1.59069	−0.795343	−	0.606159i	$-0.792709\pi$
$211$	−2.17057e8	−1.59069	−0.795343	+	0.606159i	$0.792709\pi$
$212$	3.50065e7	0.252333
$213$	1.50032e7	0.106379
$214$	−5.89745e7	−0.411354
$215$	−1.03588e8	−0.710843
$216$	1.00777e7	0.0680414
$217$	−8.35681e7	−0.555177
$218$	1.90844e8	1.24761
$219$	−5.49858e7	−0.353750
$220$	−3.11947e7	−0.197516
$221$	1.50657e8	0.938891
$222$	1.73603e7	0.106493
$223$	5.20130e7	0.314084	0.157042	−	0.987592i	$-0.449804\pi$
$223$	5.20130e7	0.314084	0.157042	+	0.987592i	$0.449804\pi$
$224$	2.02224e7	0.120217
$225$	1.13906e7	0.0666667
$226$	1.20547e8	0.694669
$227$	−2.01058e8	−1.14086	−0.570428	−	0.821348i	$-0.693223\pi$
$227$	−2.01058e8	−1.14086	−0.570428	+	0.821348i	$0.693223\pi$
$228$	−1.18524e7	−0.0662266
$229$	−2.50710e8	−1.37958	−0.689790	−	0.724010i	$-0.742297\pi$
$229$	−2.50710e8	−1.37958	−0.689790	+	0.724010i	$0.742297\pi$
$230$	2.42397e7	0.131365
$231$	−6.49737e7	−0.346813
$232$	−5.70628e7	−0.300016
$233$	−3.51661e8	−1.82129	−0.910645	−	0.413190i	$-0.864415\pi$
$233$	−3.51661e8	−1.82129	−0.910645	+	0.413190i	$0.864415\pi$
$234$	−2.89858e7	−0.147887
$235$	−6.43657e7	−0.323532
$236$	1.29465e6	0.00641151
$237$	1.92460e7	0.0939121
$238$	−1.49656e8	−0.719572
$239$	1.19631e8	0.566826	0.283413	−	0.958998i	$-0.408533\pi$
$239$	1.19631e8	0.566826	0.283413	+	0.958998i	$0.408533\pi$
$240$	1.38240e7	0.0645497
$241$	2.13046e8	0.980425	0.490212	−	0.871603i	$-0.336919\pi$
$241$	2.13046e8	0.980425	0.490212	+	0.871603i	$0.336919\pi$
$242$	−3.42587e7	−0.155388
$243$	1.43489e7	0.0641500
$244$	−1.01180e8	−0.445891
$245$	−5.53354e7	−0.240393
$246$	−1.10466e8	−0.473102
$247$	3.40901e7	0.143942
$248$	−6.93311e7	−0.288634
$249$	7.94912e7	0.326303
$250$	1.56250e7	0.0632456
$251$	−2.38887e8	−0.953531	−0.476765	−	0.879031i	$-0.658191\pi$
$251$	−2.38887e8	−0.953531	−0.476765	+	0.879031i	$0.658191\pi$
$252$	2.87932e7	0.113341
$253$	−9.45188e7	−0.366941
$254$	−2.81394e8	−1.07745
$255$	−1.02304e8	−0.386370
$256$	1.67772e7	0.0625000
$257$	−4.60534e7	−0.169237	−0.0846187	−	0.996413i	$-0.526967\pi$
$257$	−4.60534e7	−0.169237	−0.0846187	+	0.996413i	$0.526967\pi$
$258$	−1.78999e8	−0.648907
$259$	4.96007e7	0.177394
$260$	−3.97610e7	−0.140298
$261$	−8.12476e7	−0.282858
$262$	9.68767e7	0.332786
$263$	3.53267e8	1.19745	0.598726	−	0.800954i	$-0.295674\pi$
$263$	3.53267e8	1.19745	0.598726	+	0.800954i	$0.295674\pi$
$264$	−5.39044e7	−0.180306
$265$	6.83721e7	0.225693
$266$	−3.38636e7	−0.110318
$267$	2.88720e8	0.928298
$268$	1.23779e8	0.392804
$269$	4.31453e8	1.35145	0.675726	−	0.737153i	$-0.263830\pi$
$269$	4.31453e8	1.35145	0.675726	+	0.737153i	$0.263830\pi$
$270$	1.96830e7	0.0608581
$271$	2.73481e8	0.834707	0.417353	−	0.908744i	$-0.362958\pi$
$271$	2.73481e8	0.834707	0.417353	+	0.908744i	$0.362958\pi$
$272$	−1.24160e8	−0.374102
$273$	−8.28159e7	−0.246345
$274$	1.91679e7	0.0562921
$275$	−6.09271e7	−0.176663
$276$	4.18862e7	0.119919
$277$	1.99480e8	0.563924	0.281962	−	0.959426i	$-0.409015\pi$
$277$	1.99480e8	0.563924	0.281962	+	0.959426i	$0.409015\pi$
$278$	−2.90236e8	−0.810204
$279$	−9.87155e7	−0.272126
$280$	3.94969e7	0.107525
$281$	−1.44168e8	−0.387612	−0.193806	−	0.981040i	$-0.562083\pi$
$281$	−1.44168e8	−0.387612	−0.193806	+	0.981040i	$0.562083\pi$
$282$	−1.11224e8	−0.295343
$283$	−2.66542e8	−0.699057	−0.349528	−	0.936926i	$-0.613658\pi$
$283$	−2.66542e8	−0.699057	−0.349528	+	0.936926i	$0.613658\pi$
$284$	3.55632e7	0.0921270
$285$	−2.31491e7	−0.0592349
$286$	1.55042e8	0.391893
$287$	−3.15614e8	−0.788079
$288$	2.38879e7	0.0589256
$289$	5.08505e8	1.23923
$290$	−1.11451e8	−0.268343
$291$	1.00608e8	0.239335
$292$	−1.30337e8	−0.306356
$293$	2.37563e8	0.551751	0.275875	−	0.961193i	$-0.411032\pi$
$293$	2.37563e8	0.551751	0.275875	+	0.961193i	$0.411032\pi$
$294$	−9.56195e7	−0.219448
$295$	2.52861e6	0.00573463
$296$	4.11505e7	0.0922261
$297$	−7.67507e7	−0.169994
$298$	−4.21582e8	−0.922837
$299$	−1.20474e8	−0.260643
$300$	2.70000e7	0.0577350
$301$	−5.11424e8	−1.08093
$302$	2.75321e8	0.575194
$303$	6.21558e7	0.128361
$304$	−2.80945e7	−0.0573539
$305$	−1.97617e8	−0.398817
$306$	−1.76782e8	−0.352706
$307$	6.83552e8	1.34830	0.674151	−	0.738593i	$-0.264510\pi$
$307$	6.83552e8	1.34830	0.674151	+	0.738593i	$0.264510\pi$
$308$	−1.54012e8	−0.300349
$309$	−1.64689e8	−0.317548
$310$	−1.35412e8	−0.258162
$311$	−1.59619e8	−0.300900	−0.150450	−	0.988618i	$-0.548072\pi$
$311$	−1.59619e8	−0.300900	−0.150450	+	0.988618i	$0.548072\pi$
$312$	−6.87070e7	−0.128074
$313$	−8.70033e8	−1.60373	−0.801864	−	0.597507i	$-0.796158\pi$
$313$	−8.70033e8	−1.60373	−0.801864	+	0.597507i	$0.796158\pi$
$314$	8.45776e7	0.154171
$315$	5.62368e7	0.101376
$316$	4.56202e7	0.0813303
$317$	−5.96120e8	−1.05106	−0.525528	−	0.850776i	$-0.676132\pi$
$317$	−5.96120e8	−1.05106	−0.525528	+	0.850776i	$0.676132\pi$
$318$	1.18147e8	0.206029
$319$	4.34584e8	0.749560
$320$	3.27680e7	0.0559017
$321$	−1.99039e8	−0.335869
$322$	1.19674e8	0.199758
$323$	2.07913e8	0.343299
$324$	3.40122e7	0.0555556
$325$	−7.76582e7	−0.125486
$326$	3.14233e8	0.502331
$327$	6.44098e8	1.01867
$328$	−2.61845e8	−0.409718
$329$	−3.17780e8	−0.491973
$330$	−1.05282e8	−0.161271
$331$	−1.05032e9	−1.59192	−0.795962	−	0.605346i	$-0.793035\pi$
$331$	−1.05032e9	−1.59192	−0.795962	+	0.605346i	$0.793035\pi$
$332$	1.88424e8	0.282587
$333$	5.85912e7	0.0869516
$334$	−1.71330e8	−0.251606
$335$	2.41756e8	0.351334
$336$	6.82506e7	0.0981565
$337$	−2.63958e8	−0.375690	−0.187845	−	0.982199i	$-0.560150\pi$
$337$	−2.63958e8	−0.375690	−0.187845	+	0.982199i	$0.560150\pi$
$338$	−3.04371e8	−0.428741
$339$	4.06847e8	0.567195
$340$	−2.42499e8	−0.334607
$341$	5.28018e8	0.721121
$342$	−4.00017e7	−0.0540738
$343$	−7.81437e8	−1.04560
$344$	−4.24295e8	−0.561970
$345$	8.18090e7	0.107259
$346$	9.76202e8	1.26699
$347$	−5.36070e8	−0.688761	−0.344380	−	0.938830i	$-0.611911\pi$
$347$	−5.36070e8	−0.688761	−0.344380	+	0.938830i	$0.611911\pi$
$348$	−1.92587e8	−0.244962
$349$	−6.21040e8	−0.782043	−0.391022	−	0.920382i	$-0.627878\pi$
$349$	−6.21040e8	−0.782043	−0.391022	+	0.920382i	$0.627878\pi$
$350$	7.71423e7	0.0961733
$351$	−9.78270e7	−0.120749
$352$	−1.27773e8	−0.156150
$353$	1.14350e9	1.38365	0.691825	−	0.722065i	$-0.256807\pi$
$353$	1.14350e9	1.38365	0.691825	+	0.722065i	$0.256807\pi$
$354$	4.36945e6	0.00523498
$355$	6.94595e7	0.0824009
$356$	6.84373e8	0.803930
$357$	−5.05088e8	−0.587528
$358$	−4.46099e8	−0.513855
$359$	−1.02998e9	−1.17489	−0.587444	−	0.809265i	$-0.699866\pi$
$359$	−1.02998e9	−1.17489	−0.587444	+	0.809265i	$0.699866\pi$
$360$	4.66560e7	0.0527046
$361$	4.70459e7	0.0526316
$362$	−8.86982e8	−0.982732
$363$	−1.15623e8	−0.126874
$364$	−1.96304e8	−0.213341
$365$	−2.54564e8	−0.274013
$366$	−3.41482e8	−0.364069
$367$	−4.12106e8	−0.435189	−0.217594	−	0.976039i	$-0.569821\pi$
$367$	−4.12106e8	−0.435189	−0.217594	+	0.976039i	$0.569821\pi$
$368$	9.92858e7	0.103853
$369$	−3.72822e8	−0.386286
$370$	8.03720e7	0.0824895
$371$	3.37561e8	0.343197
$372$	−2.33992e8	−0.235668
$373$	4.10195e8	0.409269	0.204635	−	0.978838i	$-0.434399\pi$
$373$	4.10195e8	0.409269	0.204635	+	0.978838i	$0.434399\pi$
$374$	9.45587e8	0.934654
$375$	5.27344e7	0.0516398
$376$	−2.63642e8	−0.255774
$377$	5.53924e8	0.532421
$378$	9.71771e7	0.0925428
$379$	7.81318e8	0.737209	0.368604	−	0.929586i	$-0.379836\pi$
$379$	7.81318e8	0.737209	0.368604	+	0.929586i	$0.379836\pi$
$380$	−5.48720e7	−0.0512989
$381$	−9.49704e8	−0.879733
$382$	−7.66838e7	−0.0703852
$383$	1.40717e9	1.27983	0.639913	−	0.768447i	$-0.278970\pi$
$383$	1.40717e9	1.27983	0.639913	+	0.768447i	$0.278970\pi$
$384$	5.66231e7	0.0510310
$385$	−3.00804e8	−0.268640
$386$	−3.09584e8	−0.273983
$387$	−6.04123e8	−0.529831
$388$	2.38478e8	0.207271
$389$	−9.11166e8	−0.784827	−0.392413	−	0.919789i	$-0.628360\pi$
$389$	−9.11166e8	−0.784827	−0.392413	+	0.919789i	$0.628360\pi$
$390$	−1.34193e8	−0.114553
$391$	−7.34764e8	−0.621626
$392$	−2.26654e8	−0.190047
$393$	3.26959e8	0.271719
$394$	2.20505e8	0.181627
$395$	8.91019e7	0.0727440
$396$	−1.81927e8	−0.147219
$397$	1.23062e9	0.987091	0.493545	−	0.869720i	$-0.335701\pi$
$397$	1.23062e9	0.987091	0.493545	+	0.869720i	$0.335701\pi$
$398$	1.37959e9	1.09688
$399$	−1.14290e8	−0.0900746
$400$	6.40000e7	0.0500000
$401$	−3.29019e7	−0.0254809	−0.0127405	−	0.999919i	$-0.504056\pi$
$401$	−3.29019e7	−0.0254809	−0.0127405	+	0.999919i	$0.504056\pi$
$402$	4.17754e8	0.320723
$403$	6.73016e8	0.512221
$404$	1.47332e8	0.111164
$405$	6.64301e7	0.0496904
$406$	−5.50244e8	−0.408051
$407$	−3.13397e8	−0.230417
$408$	−4.19039e8	−0.305453
$409$	8.09372e8	0.584947	0.292474	−	0.956274i	$-0.405522\pi$
$409$	8.09372e8	0.584947	0.292474	+	0.956274i	$0.405522\pi$
$410$	−5.11416e8	−0.366463
$411$	6.46917e7	0.0459623
$412$	−3.90374e8	−0.275005
$413$	1.24840e7	0.00872028
$414$	1.41366e8	0.0979137
$415$	3.68015e8	0.252753
$416$	−1.62861e8	−0.110915
$417$	−9.79546e8	−0.661529
$418$	2.13964e8	0.143293
$419$	1.69058e9	1.12276	0.561378	−	0.827560i	$-0.310271\pi$
$419$	1.69058e9	1.12276	0.561378	+	0.827560i	$0.310271\pi$
$420$	1.33302e8	0.0877938
$421$	1.93291e9	1.26248	0.631239	−	0.775589i	$-0.282547\pi$
$421$	1.93291e9	1.26248	0.631239	+	0.775589i	$0.282547\pi$
$422$	−1.73645e9	−1.12479
$423$	−3.75381e8	−0.241146
$424$	2.80052e8	0.178426
$425$	−4.73632e8	−0.299281
$426$	1.20026e8	0.0752214
$427$	−9.75655e8	−0.606455
$428$	−4.71796e8	−0.290871
$429$	5.23265e8	0.319979
$430$	−8.28701e8	−0.502642
$431$	−1.03164e9	−0.620665	−0.310333	−	0.950628i	$-0.600440\pi$
$431$	−1.03164e9	−0.620665	−0.310333	+	0.950628i	$0.600440\pi$
$432$	8.06216e7	0.0481125
$433$	−1.67696e8	−0.0992693	−0.0496347	−	0.998767i	$-0.515806\pi$
$433$	−1.67696e8	−0.0992693	−0.0496347	+	0.998767i	$0.515806\pi$
$434$	−6.68545e8	−0.392570
$435$	−3.76146e8	−0.219101
$436$	1.52675e9	0.882196
$437$	−1.66260e8	−0.0953022
$438$	−4.39886e8	−0.250139
$439$	−1.24889e9	−0.704526	−0.352263	−	0.935901i	$-0.614588\pi$
$439$	−1.24889e9	−0.704526	−0.352263	+	0.935901i	$0.614588\pi$
$440$	−2.49558e8	−0.139665
$441$	−3.22716e8	−0.179178
$442$	1.20525e9	0.663896
$443$	−1.49377e9	−0.816340	−0.408170	−	0.912906i	$-0.633833\pi$
$443$	−1.49377e9	−0.816340	−0.408170	+	0.912906i	$0.633833\pi$
$444$	1.38883e8	0.0753023
$445$	1.33667e9	0.719057
$446$	4.16104e8	0.222091
$447$	−1.42284e9	−0.753493
$448$	1.61779e8	0.0850060
$449$	−2.86865e9	−1.49560	−0.747799	−	0.663925i	$-0.768889\pi$
$449$	−2.86865e9	−1.49560	−0.747799	+	0.663925i	$0.768889\pi$
$450$	9.11250e7	0.0471405
$451$	1.99418e9	1.02364
$452$	9.64378e8	0.491205
$453$	9.29208e8	0.469644
$454$	−1.60846e9	−0.806707
$455$	−3.83407e8	−0.190818
$456$	−9.48188e7	−0.0468293
$457$	2.70676e9	1.32661	0.663306	−	0.748349i	$-0.269153\pi$
$457$	2.70676e9	1.32661	0.663306	+	0.748349i	$0.269153\pi$
$458$	−2.00568e9	−0.975510
$459$	−5.96639e8	−0.287983
$460$	1.93918e8	0.0928891
$461$	−2.74743e9	−1.30609	−0.653046	−	0.757318i	$-0.726509\pi$
$461$	−2.74743e9	−1.30609	−0.653046	+	0.757318i	$0.726509\pi$
$462$	−5.19789e8	−0.245234
$463$	1.06477e9	0.498567	0.249284	−	0.968431i	$-0.419805\pi$
$463$	1.06477e9	0.498567	0.249284	+	0.968431i	$0.419805\pi$
$464$	−4.56502e8	−0.212144
$465$	−4.57016e8	−0.210788
$466$	−2.81329e9	−1.28785
$467$	−8.23306e8	−0.374070	−0.187035	−	0.982353i	$-0.559888\pi$
$467$	−8.23306e8	−0.374070	−0.187035	+	0.982353i	$0.559888\pi$
$468$	−2.31886e8	−0.104572
$469$	1.19358e9	0.534251
$470$	−5.14925e8	−0.228771
$471$	2.85450e8	0.125880
$472$	1.03572e7	0.00453363
$473$	3.23139e9	1.40402
$474$	1.53968e8	0.0664059
$475$	−1.07172e8	−0.0458831
$476$	−1.19725e9	−0.508814
$477$	3.98746e8	0.168222
$478$	9.57046e8	0.400807
$479$	5.94152e8	0.247015	0.123507	−	0.992344i	$-0.460586\pi$
$479$	5.94152e8	0.247015	0.123507	+	0.992344i	$0.460586\pi$
$480$	1.10592e8	0.0456435
$481$	−3.99459e8	−0.163668
$482$	1.70437e9	0.693265
$483$	4.03900e8	0.163102
$484$	−2.74070e8	−0.109876
$485$	4.65778e8	0.185388
$486$	1.14791e8	0.0453609
$487$	9.50680e8	0.372978	0.186489	−	0.982457i	$-0.440289\pi$
$487$	9.50680e8	0.372978	0.186489	+	0.982457i	$0.440289\pi$
$488$	−8.09438e8	−0.315293
$489$	1.06054e9	0.410152
$490$	−4.42683e8	−0.169983
$491$	1.00970e9	0.384952	0.192476	−	0.981302i	$-0.438348\pi$
$491$	1.00970e9	0.384952	0.192476	+	0.981302i	$0.438348\pi$
$492$	−8.83726e8	−0.334534
$493$	3.37834e9	1.26981
$494$	2.72721e8	0.101783
$495$	−3.55327e8	−0.131677
$496$	−5.54649e8	−0.204095
$497$	3.42929e8	0.125302
$498$	6.35929e8	0.230731
$499$	−1.16136e9	−0.418423	−0.209211	−	0.977870i	$-0.567090\pi$
$499$	−1.16136e9	−0.418423	−0.209211	+	0.977870i	$0.567090\pi$
$500$	1.25000e8	0.0447214
$501$	−5.78239e8	−0.205435
$502$	−1.91110e9	−0.674248
$503$	−1.84999e8	−0.0648158	−0.0324079	−	0.999475i	$-0.510318\pi$
$503$	−1.84999e8	−0.0648158	−0.0324079	+	0.999475i	$0.510318\pi$
$504$	2.30346e8	0.0801444
$505$	2.87759e8	0.0994279
$506$	−7.56150e8	−0.259466
$507$	−1.02725e9	−0.350065
$508$	−2.25115e9	−0.761871
$509$	1.19774e9	0.402579	0.201290	−	0.979532i	$-0.435487\pi$
$509$	1.19774e9	0.402579	0.201290	+	0.979532i	$0.435487\pi$
$510$	−8.18436e8	−0.273205
$511$	−1.25681e9	−0.416674
$512$	1.34218e8	0.0441942
$513$	−1.35006e8	−0.0441511
$514$	−3.68428e8	−0.119669
$515$	−7.62449e8	−0.245972
$516$	−1.43200e9	−0.458847
$517$	2.00787e9	0.639025
$518$	3.96805e8	0.125436
$519$	3.29468e9	1.03449
$520$	−3.18088e8	−0.0992055
$521$	1.15136e9	0.356680	0.178340	−	0.983969i	$-0.442927\pi$
$521$	1.15136e9	0.356680	0.178340	+	0.983969i	$0.442927\pi$
$522$	−6.49981e8	−0.200011
$523$	−1.31591e9	−0.402227	−0.201113	−	0.979568i	$-0.564456\pi$
$523$	−1.31591e9	−0.402227	−0.201113	+	0.979568i	$0.564456\pi$
$524$	7.75014e8	0.235315
$525$	2.60355e8	0.0785252
$526$	2.82614e9	0.846727
$527$	4.10467e9	1.22164
$528$	−4.31235e8	−0.127496
$529$	−2.81726e9	−0.827432
$530$	5.46977e8	0.159589
$531$	1.47469e7	0.00427434
$532$	−2.70909e8	−0.0780069
$533$	2.54180e9	0.727103
$534$	2.30976e9	0.656406
$535$	−9.21476e8	−0.260163
$536$	9.90233e8	0.277754
$537$	−1.50558e9	−0.419561
$538$	3.45162e9	0.955621
$539$	1.72617e9	0.474813
$540$	1.57464e8	0.0430331
$541$	−4.60448e9	−1.25023	−0.625115	−	0.780532i	$-0.714948\pi$
$541$	−4.60448e9	−1.25023	−0.625115	+	0.780532i	$0.714948\pi$
$542$	2.18784e9	0.590227
$543$	−2.99356e9	−0.802397
$544$	−9.93278e8	−0.264530
$545$	2.98193e9	0.789060
$546$	−6.62527e8	−0.174193
$547$	−1.97338e8	−0.0515532	−0.0257766	−	0.999668i	$-0.508206\pi$
$547$	−1.97338e8	−0.0515532	−0.0257766	+	0.999668i	$0.508206\pi$
$548$	1.53343e8	0.0398045
$549$	−1.15250e9	−0.297261
$550$	−4.87417e8	−0.124920
$551$	7.64440e8	0.194676
$552$	3.35090e8	0.0847958
$553$	4.39906e8	0.110617
$554$	1.59584e9	0.398754
$555$	2.71255e8	0.0673524
$556$	−2.32189e9	−0.572901
$557$	1.13888e9	0.279245	0.139622	−	0.990205i	$-0.455411\pi$
$557$	1.13888e9	0.279245	0.139622	+	0.990205i	$0.455411\pi$
$558$	−7.89724e8	−0.192422
$559$	4.11875e9	0.997296
$560$	3.15975e8	0.0760317
$561$	3.19136e9	0.763142
$562$	−1.15335e9	−0.274083
$563$	−5.72180e9	−1.35130	−0.675652	−	0.737221i	$-0.736138\pi$
$563$	−5.72180e9	−1.35130	−0.675652	+	0.737221i	$0.736138\pi$
$564$	−8.89791e8	−0.208839
$565$	1.88355e9	0.439347
$566$	−2.13233e9	−0.494308
$567$	3.27973e8	0.0755609
$568$	2.84506e8	0.0651437
$569$	−5.71793e9	−1.30120	−0.650602	−	0.759419i	$-0.725484\pi$
$569$	−5.71793e9	−1.30120	−0.650602	+	0.759419i	$0.725484\pi$
$570$	−1.85193e8	−0.0418854
$571$	−1.89431e9	−0.425818	−0.212909	−	0.977072i	$-0.568294\pi$
$571$	−1.89431e9	−0.425818	−0.212909	+	0.977072i	$0.568294\pi$
$572$	1.24033e9	0.277110
$573$	−2.58808e8	−0.0574693
$574$	−2.52491e9	−0.557256
$575$	3.78745e8	0.0830826
$576$	1.91103e8	0.0416667
$577$	2.21556e9	0.480140	0.240070	−	0.970756i	$-0.422830\pi$
$577$	2.21556e9	0.480140	0.240070	+	0.970756i	$0.422830\pi$
$578$	4.06804e9	0.876269
$579$	−1.04485e9	−0.223706
$580$	−8.91606e8	−0.189747
$581$	1.81693e9	0.384345
$582$	8.04864e8	0.169236
$583$	−2.13285e9	−0.445779
$584$	−1.04269e9	−0.216627
$585$	−4.52903e8	−0.0935318
$586$	1.90051e9	0.390147
$587$	4.62738e9	0.944281	0.472141	−	0.881523i	$-0.343481\pi$
$587$	4.62738e9	0.944281	0.472141	+	0.881523i	$0.343481\pi$
$588$	−7.64956e8	−0.155173
$589$	9.28793e8	0.187290
$590$	2.02289e7	0.00405500
$591$	7.44203e8	0.148298
$592$	3.29204e8	0.0652137
$593$	6.14225e9	1.20958	0.604792	−	0.796384i	$-0.293256\pi$
$593$	6.14225e9	1.20958	0.604792	+	0.796384i	$0.293256\pi$
$594$	−6.14005e8	−0.120204
$595$	−2.33837e9	−0.455097
$596$	−3.37265e9	−0.652544
$597$	4.65610e9	0.895596
$598$	−9.63795e8	−0.184302
$599$	−5.34698e8	−0.101652	−0.0508259	−	0.998708i	$-0.516185\pi$
$599$	−5.34698e8	−0.101652	−0.0508259	+	0.998708i	$0.516185\pi$
$600$	2.16000e8	0.0408248
$601$	1.36037e9	0.255620	0.127810	−	0.991799i	$-0.459205\pi$
$601$	1.36037e9	0.255620	0.127810	+	0.991799i	$0.459205\pi$
$602$	−4.09139e9	−0.764334
$603$	1.40992e9	0.261869
$604$	2.20257e9	0.406724
$605$	−5.35293e8	−0.0982760
$606$	4.97247e8	0.0907649
$607$	−5.54565e9	−1.00645	−0.503225	−	0.864155i	$-0.667853\pi$
$607$	−5.54565e9	−1.00645	−0.503225	+	0.864155i	$0.667853\pi$
$608$	−2.24756e8	−0.0405554
$609$	−1.85707e9	−0.333172
$610$	−1.58093e9	−0.282006
$611$	2.55924e9	0.453908
$612$	−1.41426e9	−0.249401
$613$	7.38465e9	1.29485	0.647423	−	0.762131i	$-0.275847\pi$
$613$	7.38465e9	1.29485	0.647423	+	0.762131i	$0.275847\pi$
$614$	5.46842e9	0.953394
$615$	−1.72603e9	−0.299216
$616$	−1.23209e9	−0.212379
$617$	5.89706e9	1.01074	0.505368	−	0.862904i	$-0.331357\pi$
$617$	5.89706e9	1.01074	0.505368	+	0.862904i	$0.331357\pi$
$618$	−1.31751e9	−0.224541
$619$	7.54341e9	1.27835	0.639176	−	0.769061i	$-0.279276\pi$
$619$	7.54341e9	1.27835	0.639176	+	0.769061i	$0.279276\pi$
$620$	−1.08330e9	−0.182548
$621$	4.77110e8	0.0799462
$622$	−1.27695e9	−0.212769
$623$	6.59927e9	1.09342
$624$	−5.49656e8	−0.0905618
$625$	2.44141e8	0.0400000
$626$	−6.96026e9	−1.13401
$627$	7.22130e8	0.116998
$628$	6.76621e8	0.109015
$629$	−2.43627e9	−0.390345
$630$	4.49894e8	0.0716834
$631$	8.19812e9	1.29901	0.649504	−	0.760358i	$-0.274977\pi$
$631$	8.19812e9	1.29901	0.649504	+	0.760358i	$0.274977\pi$
$632$	3.64961e8	0.0575092
$633$	−5.86053e9	−0.918384
$634$	−4.76896e9	−0.743209
$635$	−4.39678e9	−0.681438
$636$	9.45176e8	0.145684
$637$	2.20019e9	0.337266
$638$	3.47667e9	0.530019
$639$	4.05088e8	0.0614180
$640$	2.62144e8	0.0395285
$641$	−9.39397e8	−0.140879	−0.0704395	−	0.997516i	$-0.522440\pi$
$641$	−9.39397e8	−0.140879	−0.0704395	+	0.997516i	$0.522440\pi$
$642$	−1.59231e9	−0.237495
$643$	2.12166e9	0.314729	0.157364	−	0.987541i	$-0.449700\pi$
$643$	2.12166e9	0.314729	0.157364	+	0.987541i	$0.449700\pi$
$644$	9.57393e8	0.141250
$645$	−2.79687e9	−0.410405
$646$	1.66330e9	0.242749
$647$	1.30389e10	1.89267	0.946334	−	0.323190i	$-0.104755\pi$
$647$	1.30389e10	1.89267	0.946334	+	0.323190i	$0.104755\pi$
$648$	2.72098e8	0.0392837
$649$	−7.88794e7	−0.0113268
$650$	−6.21266e8	−0.0887321
$651$	−2.25634e9	−0.320532
$652$	2.51386e9	0.355202
$653$	7.62830e9	1.07209	0.536046	−	0.844189i	$-0.319918\pi$
$653$	7.62830e9	1.07209	0.536046	+	0.844189i	$0.319918\pi$
$654$	5.15278e9	0.720310
$655$	1.51370e9	0.210472
$656$	−2.09476e9	−0.289715
$657$	−1.48462e9	−0.204237
$658$	−2.54224e9	−0.347878
$659$	8.42652e9	1.14696	0.573481	−	0.819219i	$-0.305593\pi$
$659$	8.42652e9	1.14696	0.573481	+	0.819219i	$0.305593\pi$
$660$	−8.42257e8	−0.114036
$661$	1.14011e10	1.53547	0.767735	−	0.640767i	$-0.221384\pi$
$661$	1.14011e10	1.53547	0.767735	+	0.640767i	$0.221384\pi$
$662$	−8.40254e9	−1.12566
$663$	4.06773e9	0.542069
$664$	1.50739e9	0.199819
$665$	−5.29119e8	−0.0697715
$666$	4.68729e8	0.0614840
$667$	−2.70153e9	−0.352509
$668$	−1.37064e9	−0.177912
$669$	1.40435e9	0.181336
$670$	1.93405e9	0.248431
$671$	6.16459e9	0.787727
$672$	5.46005e8	0.0694071
$673$	−1.05006e10	−1.32789	−0.663946	−	0.747781i	$-0.731119\pi$
$673$	−1.05006e10	−1.32789	−0.663946	+	0.747781i	$0.731119\pi$
$674$	−2.11166e9	−0.265653
$675$	3.07547e8	0.0384900
$676$	−2.43497e9	−0.303165
$677$	1.18985e10	1.47377	0.736886	−	0.676017i	$-0.236295\pi$
$677$	1.18985e10	1.47377	0.736886	+	0.676017i	$0.236295\pi$
$678$	3.25477e9	0.401067
$679$	2.29960e9	0.281908
$680$	−1.94000e9	−0.236603
$681$	−5.42856e9	−0.658673
$682$	4.22414e9	0.509910
$683$	−5.15003e8	−0.0618496	−0.0309248	−	0.999522i	$-0.509845\pi$
$683$	−5.15003e8	−0.0618496	−0.0309248	+	0.999522i	$0.509845\pi$
$684$	−3.20014e8	−0.0382360
$685$	2.99498e8	0.0356023
$686$	−6.25150e9	−0.739349
$687$	−6.76916e9	−0.796501
$688$	−3.39436e9	−0.397373
$689$	−2.71854e9	−0.316642
$690$	6.54472e8	0.0758437
$691$	3.67190e9	0.423368	0.211684	−	0.977338i	$-0.432105\pi$
$691$	3.67190e9	0.423368	0.211684	+	0.977338i	$0.432105\pi$
$692$	7.80961e9	0.895897
$693$	−1.75429e9	−0.200233
$694$	−4.28856e9	−0.487027
$695$	−4.53494e9	−0.512418
$696$	−1.54069e9	−0.173214
$697$	1.55022e10	1.73412
$698$	−4.96832e9	−0.552988
$699$	−9.49486e9	−1.05152
$700$	6.17139e8	0.0680048
$701$	5.94285e9	0.651601	0.325800	−	0.945439i	$-0.394366\pi$
$701$	5.94285e9	0.651601	0.325800	+	0.945439i	$0.394366\pi$
$702$	−7.82616e8	−0.0853825
$703$	−5.51271e8	−0.0598442
$704$	−1.02219e9	−0.110415
$705$	−1.73787e9	−0.186791
$706$	9.14803e9	0.978388
$707$	1.42070e9	0.151193
$708$	3.49556e7	0.00370169
$709$	4.94540e9	0.521122	0.260561	−	0.965457i	$-0.416093\pi$
$709$	4.94540e9	0.521122	0.260561	+	0.965457i	$0.416093\pi$
$710$	5.55676e8	0.0582663
$711$	5.19642e8	0.0542202
$712$	5.47499e9	0.568464
$713$	−3.28235e9	−0.339134
$714$	−4.04071e9	−0.415445
$715$	2.42252e9	0.247855
$716$	−3.56879e9	−0.363350
$717$	3.23003e9	0.327257
$718$	−8.23980e9	−0.830771
$719$	5.85264e9	0.587220	0.293610	−	0.955925i	$-0.405143\pi$
$719$	5.85264e9	0.587220	0.293610	+	0.955925i	$0.405143\pi$
$720$	3.73248e8	0.0372678
$721$	−3.76429e9	−0.374033
$722$	3.76367e8	0.0372161
$723$	5.75225e9	0.566048
$724$	−7.09586e9	−0.694896
$725$	−1.74142e9	−0.169715
$726$	−9.24986e8	−0.0897133
$727$	−4.76651e9	−0.460076	−0.230038	−	0.973182i	$-0.573885\pi$
$727$	−4.76651e9	−0.460076	−0.230038	+	0.973182i	$0.573885\pi$
$728$	−1.57044e9	−0.150855
$729$	3.87420e8	0.0370370
$730$	−2.03651e9	−0.193757
$731$	2.51199e10	2.37853
$732$	−2.73185e9	−0.257436
$733$	6.90084e9	0.647199	0.323600	−	0.946194i	$-0.395107\pi$
$733$	6.90084e9	0.647199	0.323600	+	0.946194i	$0.395107\pi$
$734$	−3.29685e9	−0.307725
$735$	−1.49405e9	−0.138791
$736$	7.94287e8	0.0734353
$737$	−7.54151e9	−0.693940
$738$	−2.98258e9	−0.273146
$739$	−1.43630e10	−1.30915	−0.654577	−	0.755995i	$-0.727153\pi$
$739$	−1.43630e10	−1.30915	−0.654577	+	0.755995i	$0.727153\pi$
$740$	6.42976e8	0.0583289
$741$	9.20433e8	0.0831052
$742$	2.70048e9	0.242677
$743$	1.06577e10	0.953240	0.476620	−	0.879109i	$-0.341862\pi$
$743$	1.06577e10	0.953240	0.476620	+	0.879109i	$0.341862\pi$
$744$	−1.87194e9	−0.166643
$745$	−6.58721e9	−0.583653
$746$	3.28156e9	0.289397
$747$	2.14626e9	0.188391
$748$	7.56470e9	0.660900
$749$	−4.54943e9	−0.395613
$750$	4.21875e8	0.0365148
$751$	2.86094e9	0.246473	0.123236	−	0.992377i	$-0.460673\pi$
$751$	2.86094e9	0.246473	0.123236	+	0.992377i	$0.460673\pi$
$752$	−2.10913e9	−0.180860
$753$	−6.44995e9	−0.550521
$754$	4.43139e9	0.376479
$755$	4.30189e9	0.363785
$756$	7.77417e8	0.0654377
$757$	−7.22882e8	−0.0605664	−0.0302832	−	0.999541i	$-0.509641\pi$
$757$	−7.22882e8	−0.0605664	−0.0302832	+	0.999541i	$0.509641\pi$
$758$	6.25054e9	0.521285
$759$	−2.55201e9	−0.211854
$760$	−4.38976e8	−0.0362738
$761$	1.61196e10	1.32589	0.662946	−	0.748668i	$-0.269306\pi$
$761$	1.61196e10	1.32589	0.662946	+	0.748668i	$0.269306\pi$
$762$	−7.59763e9	−0.622065
$763$	1.47221e10	1.19987
$764$	−6.13470e8	−0.0497699
$765$	−2.76222e9	−0.223071
$766$	1.12574e10	0.904974
$767$	−1.00540e8	−0.00804556
$768$	4.52985e8	0.0360844
$769$	−2.48228e10	−1.96838	−0.984189	−	0.177124i	$-0.943321\pi$
$769$	−2.48228e10	−1.96838	−0.984189	+	0.177124i	$0.943321\pi$
$770$	−2.40643e9	−0.189957
$771$	−1.24344e9	−0.0977092
$772$	−2.47667e9	−0.193735
$773$	−1.24574e10	−0.970060	−0.485030	−	0.874498i	$-0.661191\pi$
$773$	−1.24574e10	−0.970060	−0.485030	+	0.874498i	$0.661191\pi$
$774$	−4.83299e9	−0.374647
$775$	−2.11582e9	−0.163276
$776$	1.90783e9	0.146562
$777$	1.33922e9	0.102418
$778$	−7.28933e9	−0.554956
$779$	3.50780e9	0.265860
$780$	−1.07355e9	−0.0810009
$781$	−2.16677e9	−0.162755
$782$	−5.87811e9	−0.439556
$783$	−2.19368e9	−0.163308
$784$	−1.81323e9	−0.134384
$785$	1.32153e9	0.0975061
$786$	2.61567e9	0.192134
$787$	3.95767e9	0.289420	0.144710	−	0.989474i	$-0.453775\pi$
$787$	3.95767e9	0.289420	0.144710	+	0.989474i	$0.453775\pi$
$788$	1.76404e9	0.128430
$789$	9.53822e9	0.691349
$790$	7.12815e8	0.0514378
$791$	9.29929e9	0.668086
$792$	−1.45542e9	−0.104100
$793$	7.85744e9	0.559532
$794$	9.84496e9	0.697978
$795$	1.84605e9	0.130304
$796$	1.10367e10	0.775609
$797$	1.61800e10	1.13208	0.566038	−	0.824379i	$-0.308476\pi$
$797$	1.61800e10	1.13208	0.566038	+	0.824379i	$0.308476\pi$
$798$	−9.14318e8	−0.0636923
$799$	1.56086e10	1.08256
$800$	5.12000e8	0.0353553
$801$	7.79544e9	0.535953
$802$	−2.63215e8	−0.0180177
$803$	7.94104e9	0.541219
$804$	3.34204e9	0.226785
$805$	1.86991e9	0.126338
$806$	5.38413e9	0.362195
$807$	1.16492e10	0.780261
$808$	1.17866e9	0.0786047
$809$	−1.54849e10	−1.02823	−0.514114	−	0.857722i	$-0.671879\pi$
$809$	−1.54849e10	−1.02823	−0.514114	+	0.857722i	$0.671879\pi$
$810$	5.31441e8	0.0351364
$811$	−3.51012e9	−0.231073	−0.115536	−	0.993303i	$-0.536859\pi$
$811$	−3.51012e9	−0.231073	−0.115536	+	0.993303i	$0.536859\pi$
$812$	−4.40195e9	−0.288536
$813$	7.38398e9	0.481918
$814$	−2.50718e9	−0.162930
$815$	4.90989e9	0.317702
$816$	−3.35231e9	−0.215988
$817$	5.68406e9	0.364655
$818$	6.47498e9	0.413620
$819$	−2.23603e9	−0.142228
$820$	−4.09132e9	−0.259129
$821$	1.63061e10	1.02837	0.514184	−	0.857680i	$-0.328095\pi$
$821$	1.63061e10	1.02837	0.514184	+	0.857680i	$0.328095\pi$
$822$	5.17533e8	0.0325003
$823$	−2.53495e10	−1.58515	−0.792574	−	0.609776i	$-0.791259\pi$
$823$	−2.53495e10	−1.58515	−0.792574	+	0.609776i	$0.791259\pi$
$824$	−3.12299e9	−0.194458
$825$	−1.64503e9	−0.101997
$826$	9.98724e7	0.00616617
$827$	6.40564e9	0.393816	0.196908	−	0.980422i	$-0.436910\pi$
$827$	6.40564e9	0.393816	0.196908	+	0.980422i	$0.436910\pi$
$828$	1.13093e9	0.0692355
$829$	−2.66102e10	−1.62221	−0.811106	−	0.584899i	$-0.801134\pi$
$829$	−2.66102e10	−1.62221	−0.811106	+	0.584899i	$0.801134\pi$
$830$	2.94412e9	0.178724
$831$	5.38596e9	0.325581
$832$	−1.30289e9	−0.0784288
$833$	1.34188e10	0.804370
$834$	−7.83637e9	−0.467771
$835$	−2.67703e9	−0.159130
$836$	1.71172e9	0.101323
$837$	−2.66532e9	−0.157112
$838$	1.35246e10	0.793908
$839$	1.24536e10	0.727995	0.363997	−	0.931400i	$-0.381412\pi$
$839$	1.24536e10	0.727995	0.363997	+	0.931400i	$0.381412\pi$
$840$	1.06642e9	0.0620796
$841$	−4.82862e9	−0.279922
$842$	1.54633e10	0.892707
$843$	−3.89254e9	−0.223788
$844$	−1.38916e10	−0.795343
$845$	−4.75580e9	−0.271159
$846$	−3.00304e9	−0.170516
$847$	−2.64280e9	−0.149442
$848$	2.24042e9	0.126166
$849$	−7.19662e9	−0.403601
$850$	−3.78905e9	−0.211624
$851$	1.94819e9	0.108362
$852$	9.60208e8	0.0531896
$853$	1.74849e10	0.964590	0.482295	−	0.876009i	$-0.339803\pi$
$853$	1.74849e10	0.964590	0.482295	+	0.876009i	$0.339803\pi$
$854$	−7.80524e9	−0.428829
$855$	−6.25026e8	−0.0341993
$856$	−3.77437e9	−0.205677
$857$	1.42851e10	0.775263	0.387631	−	0.921814i	$-0.373293\pi$
$857$	1.42851e10	0.775263	0.387631	+	0.921814i	$0.373293\pi$
$858$	4.18612e9	0.226259
$859$	−3.03280e10	−1.63256	−0.816278	−	0.577659i	$-0.803966\pi$
$859$	−3.03280e10	−1.63256	−0.816278	+	0.577659i	$0.803966\pi$
$860$	−6.62961e9	−0.355421
$861$	−8.52159e9	−0.454998
$862$	−8.25311e9	−0.438876
$863$	2.39179e10	1.26673	0.633366	−	0.773852i	$-0.281673\pi$
$863$	2.39179e10	1.26673	0.633366	+	0.773852i	$0.281673\pi$
$864$	6.44973e8	0.0340207
$865$	1.52532e10	0.801315
$866$	−1.34157e9	−0.0701940
$867$	1.37296e10	0.715471
$868$	−5.34836e9	−0.277589
$869$	−2.77951e9	−0.143681
$870$	−3.00917e9	−0.154928
$871$	−9.61246e9	−0.492914
$872$	1.22140e10	0.623807
$873$	2.71642e9	0.138180
$874$	−1.33008e9	−0.0673889
$875$	1.20535e9	0.0608253
$876$	−3.51909e9	−0.176875
$877$	−1.17981e10	−0.590627	−0.295314	−	0.955400i	$-0.595424\pi$
$877$	−1.17981e10	−0.590627	−0.295314	+	0.955400i	$0.595424\pi$
$878$	−9.99109e9	−0.498175
$879$	6.41421e9	0.318554
$880$	−1.99646e9	−0.0987578
$881$	2.29166e9	0.112911	0.0564553	−	0.998405i	$-0.482020\pi$
$881$	2.29166e9	0.112911	0.0564553	+	0.998405i	$0.482020\pi$
$882$	−2.58173e9	−0.126698
$883$	−3.40653e10	−1.66514	−0.832568	−	0.553922i	$-0.813130\pi$
$883$	−3.40653e10	−1.66514	−0.832568	+	0.553922i	$0.813130\pi$
$884$	9.64202e9	0.469445
$885$	6.82726e7	0.00331089
$886$	−1.19502e10	−0.577239
$887$	−3.23552e9	−0.155672	−0.0778361	−	0.996966i	$-0.524801\pi$
$887$	−3.23552e9	−0.155672	−0.0778361	+	0.996966i	$0.524801\pi$
$888$	1.11106e9	0.0532467
$889$	−2.17074e10	−1.03622
$890$	1.06933e10	0.508450
$891$	−2.07227e9	−0.0981463
$892$	3.32883e9	0.157042
$893$	3.53187e9	0.165968
$894$	−1.13827e10	−0.532800
$895$	−6.97030e9	−0.324991
$896$	1.29423e9	0.0601083
$897$	−3.25281e9	−0.150482
$898$	−2.29492e10	−1.05755
$899$	1.50918e10	0.692758
$900$	7.29000e8	0.0333333
$901$	−1.65802e10	−0.755184
$902$	1.59535e10	0.723822
$903$	−1.38084e10	−0.624076
$904$	7.71502e9	0.347334
$905$	−1.38591e10	−0.621534
$906$	7.43366e9	0.332089
$907$	−8.16332e8	−0.0363280	−0.0181640	−	0.999835i	$-0.505782\pi$
$907$	−8.16332e8	−0.0363280	−0.0181640	+	0.999835i	$0.505782\pi$
$908$	−1.28677e10	−0.570428
$909$	1.67821e9	0.0741092
$910$	−3.06726e9	−0.134929
$911$	2.35955e10	1.03399	0.516994	−	0.855989i	$-0.327051\pi$
$911$	2.35955e10	1.03399	0.516994	+	0.855989i	$0.327051\pi$
$912$	−7.58551e8	−0.0331133
$913$	−1.14801e10	−0.499227
$914$	2.16541e10	0.938056
$915$	−5.33565e9	−0.230257
$916$	−1.60454e10	−0.689790
$917$	7.47330e9	0.320051
$918$	−4.77312e9	−0.203635
$919$	−3.94356e10	−1.67604	−0.838020	−	0.545640i	$-0.816287\pi$
$919$	−3.94356e10	−1.67604	−0.838020	+	0.545640i	$0.816287\pi$
$920$	1.55134e9	0.0656825
$921$	1.84559e10	0.778443
$922$	−2.19795e10	−0.923546
$923$	−2.76178e9	−0.115607
$924$	−4.15831e9	−0.173406
$925$	1.25581e9	0.0521709
$926$	8.51819e9	0.352540
$927$	−4.44660e9	−0.183337
$928$	−3.65202e9	−0.150008
$929$	3.67740e10	1.50483	0.752413	−	0.658692i	$-0.228890\pi$
$929$	3.67740e10	1.50483	0.752413	+	0.658692i	$0.228890\pi$
$930$	−3.65613e9	−0.149050
$931$	3.03636e9	0.123319
$932$	−2.25063e10	−0.910645
$933$	−4.30971e9	−0.173725
$934$	−6.58645e9	−0.264507
$935$	1.47748e10	0.591127
$936$	−1.85509e9	−0.0739434
$937$	2.25171e10	0.894179	0.447089	−	0.894489i	$-0.352461\pi$
$937$	2.25171e10	0.894179	0.447089	+	0.894489i	$0.352461\pi$
$938$	9.54861e9	0.377772
$939$	−2.34909e10	−0.925912
$940$	−4.11940e9	−0.161766
$941$	−1.99173e10	−0.779230	−0.389615	−	0.920978i	$-0.627392\pi$
$941$	−1.99173e10	−0.779230	−0.389615	+	0.920978i	$0.627392\pi$
$942$	2.28360e9	0.0890105
$943$	−1.23966e10	−0.481405
$944$	8.28576e7	0.00320576
$945$	1.51839e9	0.0585292
$946$	2.58511e10	0.992795
$947$	6.22928e9	0.238349	0.119174	−	0.992873i	$-0.461975\pi$
$947$	6.22928e9	0.238349	0.119174	+	0.992873i	$0.461975\pi$
$948$	1.23174e9	0.0469561
$949$	1.01217e10	0.384435
$950$	−8.57375e8	−0.0324443
$951$	−1.60952e10	−0.606828
$952$	−9.57797e9	−0.359786
$953$	−3.58488e10	−1.34168	−0.670840	−	0.741602i	$-0.734066\pi$
$953$	−3.58488e10	−1.34168	−0.670840	+	0.741602i	$0.734066\pi$
$954$	3.18997e9	0.118951
$955$	−1.19818e9	−0.0445155
$956$	7.65637e9	0.283413
$957$	1.17338e10	0.432758
$958$	4.75321e9	0.174666
$959$	1.47866e9	0.0541380
$960$	8.84736e8	0.0322749
$961$	−9.17614e9	−0.333525
$962$	−3.19567e9	−0.115731
$963$	−5.37405e9	−0.193914
$964$	1.36350e10	0.490212
$965$	−4.83725e9	−0.173282
$966$	3.23120e9	0.115330
$967$	−3.86678e10	−1.37517	−0.687586	−	0.726103i	$-0.741330\pi$
$967$	−3.86678e10	−1.37517	−0.687586	+	0.726103i	$0.741330\pi$
$968$	−2.19256e9	−0.0776940
$969$	5.61365e9	0.198204
$970$	3.72622e9	0.131089
$971$	−1.32865e10	−0.465738	−0.232869	−	0.972508i	$-0.574811\pi$
$971$	−1.32865e10	−0.465738	−0.232869	+	0.972508i	$0.574811\pi$
$972$	9.18330e8	0.0320750
$973$	−2.23895e10	−0.779200
$974$	7.60544e9	0.263735
$975$	−2.09677e9	−0.0724494
$976$	−6.47550e9	−0.222946
$977$	−3.41614e10	−1.17194	−0.585969	−	0.810334i	$-0.699286\pi$
$977$	−3.41614e10	−1.17194	−0.585969	+	0.810334i	$0.699286\pi$
$978$	8.48429e9	0.290021
$979$	−4.16969e10	−1.42025
$980$	−3.54146e9	−0.120196
$981$	1.73906e10	0.588131
$982$	8.07759e9	0.272202
$983$	−4.25214e10	−1.42781	−0.713905	−	0.700243i	$-0.753075\pi$
$983$	−4.25214e10	−1.42781	−0.713905	+	0.700243i	$0.753075\pi$
$984$	−7.06981e9	−0.236551
$985$	3.44538e9	0.114871
$986$	2.70267e10	0.897892
$987$	−8.58007e9	−0.284041
$988$	2.18177e9	0.0719712
$989$	−2.00875e10	−0.660295
$990$	−2.84262e9	−0.0931097
$991$	1.65974e10	0.541729	0.270865	−	0.962617i	$-0.412690\pi$
$991$	1.65974e10	0.541729	0.270865	+	0.962617i	$0.412690\pi$
$992$	−4.43719e9	−0.144317
$993$	−2.83586e10	−0.919098
$994$	2.74343e9	0.0886016
$995$	2.15560e10	0.693726
$996$	5.08744e9	0.163152
$997$	−2.20018e10	−0.703114	−0.351557	−	0.936167i	$-0.614348\pi$
$997$	−2.20018e10	−0.703114	−0.351557	+	0.936167i	$0.614348\pi$
$998$	−9.29088e9	−0.295869
$999$	1.58196e9	0.0502015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.c.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.8.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} +617.139 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} +216.000 q^{6} +617.139 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} -3899.34 q^{11} +1728.00 q^{12} -4970.13 q^{13} +4937.11 q^{14} +3375.00 q^{15} +4096.00 q^{16} -30312.4 q^{17} +5832.00 q^{18} -6859.00 q^{19} +8000.00 q^{20} +16662.7 q^{21} -31194.7 q^{22} +24239.7 q^{23} +13824.0 q^{24} +15625.0 q^{25} -39761.0 q^{26} +19683.0 q^{27} +39496.9 q^{28} -111451. q^{29} +27000.0 q^{30} -135412. q^{31} +32768.0 q^{32} -105282. q^{33} -242499. q^{34} +77142.3 q^{35} +46656.0 q^{36} +80372.0 q^{37} -54872.0 q^{38} -134193. q^{39} +64000.0 q^{40} -511416. q^{41} +133302. q^{42} -828701. q^{43} -249558. q^{44} +91125.0 q^{45} +193918. q^{46} -514925. q^{47} +110592. q^{48} -442683. q^{49} +125000. q^{50} -818436. q^{51} -318088. q^{52} +546977. q^{53} +157464. q^{54} -487417. q^{55} +315975. q^{56} -185193. q^{57} -891606. q^{58} +20228.9 q^{59} +216000. q^{60} -1.58093e6 q^{61} -1.08330e6 q^{62} +449894. q^{63} +262144. q^{64} -621266. q^{65} -842257. q^{66} +1.93405e6 q^{67} -1.94000e6 q^{68} +654472. q^{69} +617139. q^{70} +555676. q^{71} +373248. q^{72} -2.03651e6 q^{73} +642976. q^{74} +421875. q^{75} -438976. q^{76} -2.40643e6 q^{77} -1.07355e6 q^{78} +712815. q^{79} +512000. q^{80} +531441. q^{81} -4.09132e6 q^{82} +2.94412e6 q^{83} +1.06642e6 q^{84} -3.78905e6 q^{85} -6.62961e6 q^{86} -3.00917e6 q^{87} -1.99646e6 q^{88} +1.06933e7 q^{89} +729000. q^{90} -3.06726e6 q^{91} +1.55134e6 q^{92} -3.65613e6 q^{93} -4.11940e6 q^{94} -857375. q^{95} +884736. q^{96} +3.72622e6 q^{97} -3.54146e6 q^{98} -2.84262e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 500 q^{5} + 864 q^{6} - 1316 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more