LMFDB - Embedded newform 570.8.a.a.1.3

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} - 2x^{3} - 4122x^{2} - 49773x + 620550 $ x^4 - 2x^3 - 4122x^2 - 49773*x + 620550
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-21.7209$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +206.862 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +206.862 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} -4759.55 q^{11} -1728.00 q^{12} -4400.24 q^{13} +1654.89 q^{14} -3375.00 q^{15} +4096.00 q^{16} +15564.3 q^{17} +5832.00 q^{18} +6859.00 q^{19} +8000.00 q^{20} -5585.27 q^{21} -38076.4 q^{22} +38699.4 q^{23} -13824.0 q^{24} +15625.0 q^{25} -35201.9 q^{26} -19683.0 q^{27} +13239.2 q^{28} -44138.0 q^{29} -27000.0 q^{30} -135145. q^{31} +32768.0 q^{32} +128508. q^{33} +124515. q^{34} +25857.7 q^{35} +46656.0 q^{36} +137545. q^{37} +54872.0 q^{38} +118806. q^{39} +64000.0 q^{40} -159925. q^{41} -44682.2 q^{42} -455779. q^{43} -304611. q^{44} +91125.0 q^{45} +309595. q^{46} -84818.4 q^{47} -110592. q^{48} -780751. q^{49} +125000. q^{50} -420237. q^{51} -281615. q^{52} +76846.2 q^{53} -157464. q^{54} -594944. q^{55} +105913. q^{56} -185193. q^{57} -353104. q^{58} +819764. q^{59} -216000. q^{60} -3.35140e6 q^{61} -1.08116e6 q^{62} +150802. q^{63} +262144. q^{64} -550030. q^{65} +1.02806e6 q^{66} +1.01099e6 q^{67} +996116. q^{68} -1.04488e6 q^{69} +206862. q^{70} -1.87052e6 q^{71} +373248. q^{72} +4.30803e6 q^{73} +1.10036e6 q^{74} -421875. q^{75} +438976. q^{76} -984570. q^{77} +950452. q^{78} +8.30117e6 q^{79} +512000. q^{80} +531441. q^{81} -1.27940e6 q^{82} -1.77982e6 q^{83} -357457. q^{84} +1.94554e6 q^{85} -3.64623e6 q^{86} +1.19173e6 q^{87} -2.43689e6 q^{88} -5.36350e6 q^{89} +729000. q^{90} -910242. q^{91} +2.47676e6 q^{92} +3.64893e6 q^{93} -678548. q^{94} +857375. q^{95} -884736. q^{96} -5.60450e6 q^{97} -6.24601e6 q^{98} -3.46971e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 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 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 2912 q^{11} - 6912 q^{12} - 3696 q^{13} - 11968 q^{14} - 13500 q^{15} + 16384 q^{16} + 16 q^{17} + 23328 q^{18} + 27436 q^{19} + 32000 q^{20} + 40392 q^{21} - 23296 q^{22} - 73016 q^{23} - 55296 q^{24} + 62500 q^{25} - 29568 q^{26} - 78732 q^{27} - 95744 q^{28} - 137784 q^{29} - 108000 q^{30} + 198072 q^{31} + 131072 q^{32} + 78624 q^{33} + 128 q^{34} - 187000 q^{35} + 186624 q^{36} + 207256 q^{37} + 219488 q^{38} + 99792 q^{39} + 256000 q^{40} - 504056 q^{41} + 323136 q^{42} - 250368 q^{43} - 186368 q^{44} + 364500 q^{45} - 584128 q^{46} - 1000376 q^{47} - 442368 q^{48} - 940908 q^{49} + 500000 q^{50} - 432 q^{51} - 236544 q^{52} - 2178688 q^{53} - 629856 q^{54} - 364000 q^{55} - 765952 q^{56} - 740772 q^{57} - 1102272 q^{58} + 327976 q^{59} - 864000 q^{60} + 572936 q^{61} + 1584576 q^{62} - 1090584 q^{63} + 1048576 q^{64} - 462000 q^{65} + 628992 q^{66} + 2017152 q^{67} + 1024 q^{68} + 1971432 q^{69} - 1496000 q^{70} + 2828960 q^{71} + 1492992 q^{72} - 132392 q^{73} + 1658048 q^{74} - 1687500 q^{75} + 1755904 q^{76} - 2304704 q^{77} + 798336 q^{78} + 3418408 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 4032448 q^{82} - 3201760 q^{83} + 2585088 q^{84} + 2000 q^{85} - 2002944 q^{86} + 3720168 q^{87} - 1490944 q^{88} - 1389392 q^{89} + 2916000 q^{90} - 7865280 q^{91} - 4673024 q^{92} - 5347944 q^{93} - 8003008 q^{94} + 3429500 q^{95} - 3538944 q^{96} - 21061144 q^{97} - 7527264 q^{98} - 2122848 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 2912 * q^11 - 6912 * q^12 - 3696 * q^13 - 11968 * q^14 - 13500 * q^15 + 16384 * q^16 + 16 * q^17 + 23328 * q^18 + 27436 * q^19 + 32000 * q^20 + 40392 * q^21 - 23296 * q^22 - 73016 * q^23 - 55296 * q^24 + 62500 * q^25 - 29568 * q^26 - 78732 * q^27 - 95744 * q^28 - 137784 * q^29 - 108000 * q^30 + 198072 * q^31 + 131072 * q^32 + 78624 * q^33 + 128 * q^34 - 187000 * q^35 + 186624 * q^36 + 207256 * q^37 + 219488 * q^38 + 99792 * q^39 + 256000 * q^40 - 504056 * q^41 + 323136 * q^42 - 250368 * q^43 - 186368 * q^44 + 364500 * q^45 - 584128 * q^46 - 1000376 * q^47 - 442368 * q^48 - 940908 * q^49 + 500000 * q^50 - 432 * q^51 - 236544 * q^52 - 2178688 * q^53 - 629856 * q^54 - 364000 * q^55 - 765952 * q^56 - 740772 * q^57 - 1102272 * q^58 + 327976 * q^59 - 864000 * q^60 + 572936 * q^61 + 1584576 * q^62 - 1090584 * q^63 + 1048576 * q^64 - 462000 * q^65 + 628992 * q^66 + 2017152 * q^67 + 1024 * q^68 + 1971432 * q^69 - 1496000 * q^70 + 2828960 * q^71 + 1492992 * q^72 - 132392 * q^73 + 1658048 * q^74 - 1687500 * q^75 + 1755904 * q^76 - 2304704 * q^77 + 798336 * q^78 + 3418408 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 4032448 * q^82 - 3201760 * q^83 + 2585088 * q^84 + 2000 * q^85 - 2002944 * q^86 + 3720168 * q^87 - 1490944 * q^88 - 1389392 * q^89 + 2916000 * q^90 - 7865280 * q^91 - 4673024 * q^92 - 5347944 * q^93 - 8003008 * q^94 + 3429500 * q^95 - 3538944 * q^96 - 21061144 * q^97 - 7527264 * q^98 - 2122848 * 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
$7$	206.862	0.227949	0.113974	−	0.993484i	$-0.463642\pi$
$7$	206.862	0.227949	0.113974	+	0.993484i	$0.463642\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	1000.00	0.316228
$11$	−4759.55	−1.07818	−0.539091	−	0.842248i	$-0.681232\pi$
$11$	−4759.55	−1.07818	−0.539091	+	0.842248i	$0.681232\pi$
$12$	−1728.00	−0.288675
$13$	−4400.24	−0.555488	−0.277744	−	0.960655i	$-0.589587\pi$
$13$	−4400.24	−0.555488	−0.277744	+	0.960655i	$0.589587\pi$
$14$	1654.89	0.161184
$15$	−3375.00	−0.258199
$16$	4096.00	0.250000
$17$	15564.3	0.768349	0.384175	−	0.923260i	$-0.374486\pi$
$17$	15564.3	0.768349	0.384175	+	0.923260i	$0.374486\pi$
$18$	5832.00	0.235702
$19$	6859.00	0.229416
$19$	6859.00	0.229416
$20$	8000.00	0.223607
$21$	−5585.27	−0.131606
$22$	−38076.4	−0.762389
$23$	38699.4	0.663219	0.331609	−	0.943417i	$-0.392408\pi$
$23$	38699.4	0.663219	0.331609	+	0.943417i	$0.392408\pi$
$24$	−13824.0	−0.204124
$25$	15625.0	0.200000
$26$	−35201.9	−0.392789
$27$	−19683.0	−0.192450
$28$	13239.2	0.113974
$29$	−44138.0	−0.336062	−0.168031	−	0.985782i	$-0.553741\pi$
$29$	−44138.0	−0.336062	−0.168031	+	0.985782i	$0.553741\pi$
$30$	−27000.0	−0.182574
$31$	−135145.	−0.814771	−0.407385	−	0.913256i	$-0.633559\pi$
$31$	−135145.	−0.814771	−0.407385	+	0.913256i	$0.633559\pi$
$32$	32768.0	0.176777
$33$	128508.	0.622488
$34$	124515.	0.543305
$35$	25857.7	0.101942
$36$	46656.0	0.166667
$37$	137545.	0.446416	0.223208	−	0.974771i	$-0.428347\pi$
$37$	137545.	0.446416	0.223208	+	0.974771i	$0.428347\pi$
$38$	54872.0	0.162221
$39$	118806.	0.320711
$40$	64000.0	0.158114
$41$	−159925.	−0.362388	−0.181194	−	0.983447i	$-0.557996\pi$
$41$	−159925.	−0.362388	−0.181194	+	0.983447i	$0.557996\pi$
$42$	−44682.2	−0.0930597
$43$	−455779.	−0.874208	−0.437104	−	0.899411i	$-0.643996\pi$
$43$	−455779.	−0.874208	−0.437104	+	0.899411i	$0.643996\pi$
$44$	−304611.	−0.539091
$45$	91125.0	0.149071
$46$	309595.	0.468966
$47$	−84818.4	−0.119165	−0.0595824	−	0.998223i	$-0.518977\pi$
$47$	−84818.4	−0.119165	−0.0595824	+	0.998223i	$0.518977\pi$
$48$	−110592.	−0.144338
$49$	−780751.	−0.948039
$50$	125000.	0.141421
$51$	−420237.	−0.443607
$52$	−281615.	−0.277744
$53$	76846.2	0.0709017	0.0354509	−	0.999371i	$-0.488713\pi$
$53$	76846.2	0.0709017	0.0354509	+	0.999371i	$0.488713\pi$
$54$	−157464.	−0.136083
$55$	−594944.	−0.482177
$56$	105913.	0.0805921
$57$	−185193.	−0.132453
$58$	−353104.	−0.237632
$59$	819764.	0.519645	0.259823	−	0.965656i	$-0.416336\pi$
$59$	819764.	0.519645	0.259823	+	0.965656i	$0.416336\pi$
$60$	−216000.	−0.129099
$61$	−3.35140e6	−1.89048	−0.945238	−	0.326381i	$-0.894171\pi$
$61$	−3.35140e6	−1.89048	−0.945238	+	0.326381i	$0.894171\pi$
$62$	−1.08116e6	−0.576130
$63$	150802.	0.0759829
$64$	262144.	0.125000
$65$	−550030.	−0.248422
$66$	1.02806e6	0.440166
$67$	1.01099e6	0.410661	0.205331	−	0.978693i	$-0.434173\pi$
$67$	1.01099e6	0.410661	0.205331	+	0.978693i	$0.434173\pi$
$68$	996116.	0.384175
$69$	−1.04488e6	−0.382909
$70$	206862.	0.0720837
$71$	−1.87052e6	−0.620239	−0.310119	−	0.950698i	$-0.600369\pi$
$71$	−1.87052e6	−0.620239	−0.310119	+	0.950698i	$0.600369\pi$
$72$	373248.	0.117851
$73$	4.30803e6	1.29613	0.648065	−	0.761585i	$-0.275578\pi$
$73$	4.30803e6	1.29613	0.648065	+	0.761585i	$0.275578\pi$
$74$	1.10036e6	0.315664
$75$	−421875.	−0.115470
$76$	438976.	0.114708
$77$	−984570.	−0.245770
$78$	950452.	0.226777
$79$	8.30117e6	1.89428	0.947140	−	0.320820i	$-0.103958\pi$
$79$	8.30117e6	1.89428	0.947140	+	0.320820i	$0.103958\pi$
$80$	512000.	0.111803
$81$	531441.	0.111111
$82$	−1.27940e6	−0.256247
$83$	−1.77982e6	−0.341666	−0.170833	−	0.985300i	$-0.554646\pi$
$83$	−1.77982e6	−0.341666	−0.170833	+	0.985300i	$0.554646\pi$
$84$	−357457.	−0.0658031
$85$	1.94554e6	0.343616
$86$	−3.64623e6	−0.618159
$87$	1.19173e6	0.194026
$88$	−2.43689e6	−0.381195
$89$	−5.36350e6	−0.806460	−0.403230	−	0.915099i	$-0.632113\pi$
$89$	−5.36350e6	−0.806460	−0.403230	+	0.915099i	$0.632113\pi$
$90$	729000.	0.105409
$91$	−910242.	−0.126623
$92$	2.47676e6	0.331609
$93$	3.64893e6	0.470408
$94$	−678548.	−0.0842622
$95$	857375.	0.102598
$96$	−884736.	−0.102062
$97$	−5.60450e6	−0.623499	−0.311750	−	0.950164i	$-0.600915\pi$
$97$	−5.60450e6	−0.623499	−0.311750	+	0.950164i	$0.600915\pi$
$98$	−6.24601e6	−0.670365
$99$	−3.46971e6	−0.359394
$100$	1.00000e6	0.100000
$101$	1.70403e7	1.64570	0.822852	−	0.568255i	$-0.192381\pi$
$101$	1.70403e7	1.64570	0.822852	+	0.568255i	$0.192381\pi$
$102$	−3.36189e6	−0.313677
$103$	4.90262e6	0.442077	0.221038	−	0.975265i	$-0.429055\pi$
$103$	4.90262e6	0.442077	0.221038	+	0.975265i	$0.429055\pi$
$104$	−2.25292e6	−0.196395
$105$	−698159.	−0.0588561
$106$	614769.	0.0501351
$107$	6.77709e6	0.534811	0.267405	−	0.963584i	$-0.413834\pi$
$107$	6.77709e6	0.534811	0.267405	+	0.963584i	$0.413834\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.44505e7	−1.06879	−0.534394	−	0.845236i	$-0.679460\pi$
$109$	−1.44505e7	−1.06879	−0.534394	+	0.845236i	$0.679460\pi$
$110$	−4.75955e6	−0.340951
$111$	−3.71372e6	−0.257738
$112$	847306.	0.0569872
$113$	−1.17413e7	−0.765494	−0.382747	−	0.923853i	$-0.625022\pi$
$113$	−1.17413e7	−0.765494	−0.382747	+	0.923853i	$0.625022\pi$
$114$	−1.48154e6	−0.0936586
$115$	4.83742e6	0.296600
$116$	−2.82483e6	−0.168031
$117$	−3.20778e6	−0.185163
$118$	6.55811e6	0.367445
$119$	3.21966e6	0.175144
$120$	−1.72800e6	−0.0912871
$121$	3.16618e6	0.162475
$122$	−2.68112e7	−1.33677
$123$	4.31798e6	0.209225
$124$	−8.64931e6	−0.407385
$125$	1.95312e6	0.0894427
$126$	1.20642e6	0.0537280
$127$	−2.56381e7	−1.11064	−0.555320	−	0.831637i	$-0.687404\pi$
$127$	−2.56381e7	−1.11064	−0.555320	+	0.831637i	$0.687404\pi$
$128$	2.09715e6	0.0883883
$129$	1.23060e7	0.504724
$130$	−4.40024e6	−0.175661
$131$	−3.44013e7	−1.33698	−0.668491	−	0.743720i	$-0.733060\pi$
$131$	−3.44013e7	−1.33698	−0.668491	+	0.743720i	$0.733060\pi$
$132$	8.22451e6	0.311244
$133$	1.41887e6	0.0522950
$134$	8.08790e6	0.290381
$135$	−2.46038e6	−0.0860663
$136$	7.96893e6	0.271653
$137$	−4.05482e7	−1.34725	−0.673627	−	0.739072i	$-0.735264\pi$
$137$	−4.05482e7	−1.34725	−0.673627	+	0.739072i	$0.735264\pi$
$138$	−8.35907e6	−0.270758
$139$	−8.63603e6	−0.272749	−0.136374	−	0.990657i	$-0.543545\pi$
$139$	−8.63603e6	−0.272749	−0.136374	+	0.990657i	$0.543545\pi$
$140$	1.65489e6	0.0509709
$141$	2.29010e6	0.0687998
$142$	−1.49642e7	−0.438575
$143$	2.09432e7	0.598917
$144$	2.98598e6	0.0833333
$145$	−5.51725e6	−0.150292
$146$	3.44643e7	0.916503
$147$	2.10803e7	0.547351
$148$	8.80290e6	0.223208
$149$	−9.41371e6	−0.233136	−0.116568	−	0.993183i	$-0.537189\pi$
$149$	−9.41371e6	−0.233136	−0.116568	+	0.993183i	$0.537189\pi$
$150$	−3.37500e6	−0.0816497
$151$	−7.35199e7	−1.73774	−0.868871	−	0.495038i	$-0.835154\pi$
$151$	−7.35199e7	−1.73774	−0.868871	+	0.495038i	$0.835154\pi$
$152$	3.51181e6	0.0811107
$153$	1.13464e7	0.256116
$154$	−7.87656e6	−0.173786
$155$	−1.68932e7	−0.364377
$156$	7.60362e6	0.160356
$157$	5.40802e7	1.11530	0.557648	−	0.830078i	$-0.311704\pi$
$157$	5.40802e7	1.11530	0.557648	+	0.830078i	$0.311704\pi$
$158$	6.64093e7	1.33946
$159$	−2.07485e6	−0.0409351
$160$	4.09600e6	0.0790569
$161$	8.00543e6	0.151180
$162$	4.25153e6	0.0785674
$163$	5.11902e7	0.925828	0.462914	−	0.886403i	$-0.346804\pi$
$163$	5.11902e7	0.925828	0.462914	+	0.886403i	$0.346804\pi$
$164$	−1.02352e7	−0.181194
$165$	1.60635e7	0.278385
$166$	−1.42385e7	−0.241595
$167$	−3.77401e7	−0.627040	−0.313520	−	0.949582i	$-0.601508\pi$
$167$	−3.77401e7	−0.627040	−0.313520	+	0.949582i	$0.601508\pi$
$168$	−2.85966e6	−0.0465298
$169$	−4.33864e7	−0.691433
$170$	1.55643e7	0.242973
$171$	5.00021e6	0.0764719
$172$	−2.91699e7	−0.437104
$173$	−7.19275e7	−1.05617	−0.528085	−	0.849192i	$-0.677090\pi$
$173$	−7.19275e7	−1.05617	−0.528085	+	0.849192i	$0.677090\pi$
$174$	9.53381e6	0.137197
$175$	3.23222e6	0.0455898
$176$	−1.94951e7	−0.269545
$177$	−2.21336e7	−0.300017
$178$	−4.29080e7	−0.570254
$179$	1.05740e8	1.37801	0.689007	−	0.724755i	$-0.258047\pi$
$179$	1.05740e8	1.37801	0.689007	+	0.724755i	$0.258047\pi$
$180$	5.83200e6	0.0745356
$181$	−1.03786e8	−1.30096	−0.650482	−	0.759522i	$-0.725433\pi$
$181$	−1.03786e8	−1.30096	−0.650482	+	0.759522i	$0.725433\pi$
$182$	−7.28193e6	−0.0895358
$183$	9.04877e7	1.09147
$184$	1.98141e7	0.234483
$185$	1.71932e7	0.199643
$186$	2.91914e7	0.332629
$187$	−7.40792e7	−0.828420
$188$	−5.42838e6	−0.0595824
$189$	−4.07166e6	−0.0438688
$190$	6.85900e6	0.0725476
$191$	−9.31968e7	−0.967797	−0.483898	−	0.875124i	$-0.660780\pi$
$191$	−9.31968e7	−0.967797	−0.483898	+	0.875124i	$0.660780\pi$
$192$	−7.07789e6	−0.0721688
$193$	−8.30000e7	−0.831051	−0.415525	−	0.909582i	$-0.636402\pi$
$193$	−8.30000e7	−0.831051	−0.415525	+	0.909582i	$0.636402\pi$
$194$	−4.48360e7	−0.440880
$195$	1.48508e7	0.143426
$196$	−4.99681e7	−0.474020
$197$	−1.99572e8	−1.85981	−0.929905	−	0.367799i	$-0.880112\pi$
$197$	−1.99572e8	−1.85981	−0.929905	+	0.367799i	$0.880112\pi$
$198$	−2.77577e7	−0.254130
$199$	−9.87743e7	−0.888502	−0.444251	−	0.895902i	$-0.646530\pi$
$199$	−9.87743e7	−0.888502	−0.444251	+	0.895902i	$0.646530\pi$
$200$	8.00000e6	0.0707107
$201$	−2.72967e7	−0.237095
$202$	1.36322e8	1.16369
$203$	−9.13047e6	−0.0766050
$204$	−2.68951e7	−0.221803
$205$	−1.99906e7	−0.162065
$206$	3.92209e7	0.312595
$207$	2.82119e7	0.221073
$208$	−1.80234e7	−0.138872
$209$	−3.26458e7	−0.247352
$210$	−5.58527e6	−0.0416176
$211$	−1.15091e8	−0.843440	−0.421720	−	0.906726i	$-0.638573\pi$
$211$	−1.15091e8	−0.843440	−0.421720	+	0.906726i	$0.638573\pi$
$212$	4.91816e6	0.0354509
$213$	5.05041e7	0.358095
$214$	5.42168e7	0.378168
$215$	−5.69724e7	−0.390958
$216$	−1.00777e7	−0.0680414
$217$	−2.79564e7	−0.185726
$218$	−1.15604e8	−0.755747
$219$	−1.16317e8	−0.748322
$220$	−3.80764e7	−0.241089
$221$	−6.84867e7	−0.426809
$222$	−2.97098e7	−0.182249
$223$	−2.99317e7	−0.180744	−0.0903720	−	0.995908i	$-0.528806\pi$
$223$	−2.99317e7	−0.180744	−0.0903720	+	0.995908i	$0.528806\pi$
$224$	6.77845e6	0.0402960
$225$	1.13906e7	0.0666667
$226$	−9.39304e7	−0.541286
$227$	1.49092e8	0.845985	0.422992	−	0.906133i	$-0.360980\pi$
$227$	1.49092e8	0.845985	0.422992	+	0.906133i	$0.360980\pi$
$228$	−1.18524e7	−0.0662266
$229$	−1.98793e7	−0.109390	−0.0546948	−	0.998503i	$-0.517419\pi$
$229$	−1.98793e7	−0.109390	−0.0546948	+	0.998503i	$0.517419\pi$
$230$	3.86994e7	0.209728
$231$	2.65834e7	0.141895
$232$	−2.25987e7	−0.118816
$233$	−2.38916e8	−1.23737	−0.618684	−	0.785640i	$-0.712334\pi$
$233$	−2.38916e8	−1.23737	−0.618684	+	0.785640i	$0.712334\pi$
$234$	−2.56622e7	−0.130930
$235$	−1.06023e7	−0.0532921
$236$	5.24649e7	0.259823
$237$	−2.24131e8	−1.09366
$238$	2.57573e7	0.123846
$239$	5.31139e7	0.251661	0.125830	−	0.992052i	$-0.459841\pi$
$239$	5.31139e7	0.251661	0.125830	+	0.992052i	$0.459841\pi$
$240$	−1.38240e7	−0.0645497
$241$	1.05694e8	0.486395	0.243198	−	0.969977i	$-0.421804\pi$
$241$	1.05694e8	0.486395	0.243198	+	0.969977i	$0.421804\pi$
$242$	2.53294e7	0.114887
$243$	−1.43489e7	−0.0641500
$244$	−2.14489e8	−0.945238
$245$	−9.75939e7	−0.423976
$246$	3.45438e7	0.147944
$247$	−3.01812e7	−0.127438
$248$	−6.91945e7	−0.288065
$249$	4.80551e7	0.197261
$250$	1.56250e7	0.0632456
$251$	−3.73051e8	−1.48905	−0.744526	−	0.667594i	$-0.767324\pi$
$251$	−3.73051e8	−1.48905	−0.744526	+	0.667594i	$0.767324\pi$
$252$	9.65135e6	0.0379915
$253$	−1.84192e8	−0.715070
$254$	−2.05105e8	−0.785342
$255$	−5.25296e7	−0.198387
$256$	1.67772e7	0.0625000
$257$	−2.63207e8	−0.967235	−0.483617	−	0.875280i	$-0.660677\pi$
$257$	−2.63207e8	−0.967235	−0.483617	+	0.875280i	$0.660677\pi$
$258$	9.84483e7	0.356894
$259$	2.84529e7	0.101760
$260$	−3.52019e7	−0.124211
$261$	−3.21766e7	−0.112021
$262$	−2.75211e8	−0.945390
$263$	8.66354e7	0.293664	0.146832	−	0.989161i	$-0.453092\pi$
$263$	8.66354e7	0.293664	0.146832	+	0.989161i	$0.453092\pi$
$264$	6.57961e7	0.220083
$265$	9.60577e6	0.0317082
$266$	1.13509e7	0.0369782
$267$	1.44814e8	0.465610
$268$	6.47032e7	0.205331
$269$	4.47057e8	1.40033	0.700164	−	0.713982i	$-0.253110\pi$
$269$	4.47057e8	1.40033	0.700164	+	0.713982i	$0.253110\pi$
$270$	−1.96830e7	−0.0608581
$271$	1.51318e8	0.461848	0.230924	−	0.972972i	$-0.425825\pi$
$271$	1.51318e8	0.461848	0.230924	+	0.972972i	$0.425825\pi$
$272$	6.37514e7	0.192087
$273$	2.45765e7	0.0731057
$274$	−3.24385e8	−0.952652
$275$	−7.43680e7	−0.215636
$276$	−6.68726e7	−0.191455
$277$	−1.93832e8	−0.547956	−0.273978	−	0.961736i	$-0.588340\pi$
$277$	−1.93832e8	−0.547956	−0.273978	+	0.961736i	$0.588340\pi$
$278$	−6.90883e7	−0.192862
$279$	−9.85210e7	−0.271590
$280$	1.32392e7	0.0360419
$281$	−1.20191e8	−0.323146	−0.161573	−	0.986861i	$-0.551657\pi$
$281$	−1.20191e8	−0.323146	−0.161573	+	0.986861i	$0.551657\pi$
$282$	1.83208e7	0.0486488
$283$	3.47711e8	0.911940	0.455970	−	0.889995i	$-0.349292\pi$
$283$	3.47711e8	0.911940	0.455970	+	0.889995i	$0.349292\pi$
$284$	−1.19714e8	−0.310119
$285$	−2.31491e7	−0.0592349
$286$	1.67545e8	0.423498
$287$	−3.30824e7	−0.0826058
$288$	2.38879e7	0.0589256
$289$	−1.68091e8	−0.409639
$290$	−4.41380e7	−0.106272
$291$	1.51321e8	0.359977
$292$	2.75714e8	0.648065
$293$	4.72827e8	1.09816	0.549079	−	0.835770i	$-0.314978\pi$
$293$	4.72827e8	1.09816	0.549079	+	0.835770i	$0.314978\pi$
$294$	1.68642e8	0.387035
$295$	1.02470e8	0.232392
$296$	7.04232e7	0.157832
$297$	9.36823e7	0.207496
$298$	−7.53097e7	−0.164852
$299$	−1.70287e8	−0.368410
$300$	−2.70000e7	−0.0577350
$301$	−9.42833e7	−0.199275
$302$	−5.88159e8	−1.22877
$303$	−4.60087e8	−0.950148
$304$	2.80945e7	0.0573539
$305$	−4.18925e8	−0.845447
$306$	9.07711e7	0.181102
$307$	−5.24168e8	−1.03392	−0.516959	−	0.856010i	$-0.672936\pi$
$307$	−5.24168e8	−1.03392	−0.516959	+	0.856010i	$0.672936\pi$
$308$	−6.30125e7	−0.122885
$309$	−1.32371e8	−0.255233
$310$	−1.35145e8	−0.257653
$311$	3.84447e8	0.724728	0.362364	−	0.932037i	$-0.381970\pi$
$311$	3.84447e8	0.724728	0.362364	+	0.932037i	$0.381970\pi$
$312$	6.08289e7	0.113389
$313$	5.87950e8	1.08376	0.541882	−	0.840454i	$-0.317712\pi$
$313$	5.87950e8	1.08376	0.541882	+	0.840454i	$0.317712\pi$
$314$	4.32642e8	0.788633
$315$	1.88503e7	0.0339806
$316$	5.31275e8	0.947140
$317$	1.74116e8	0.306996	0.153498	−	0.988149i	$-0.450946\pi$
$317$	1.74116e8	0.306996	0.153498	+	0.988149i	$0.450946\pi$
$318$	−1.65988e7	−0.0289455
$319$	2.10077e8	0.362336
$320$	3.27680e7	0.0559017
$321$	−1.82982e8	−0.308773
$322$	6.40434e7	0.106900
$323$	1.06756e8	0.176271
$324$	3.40122e7	0.0555556
$325$	−6.87538e7	−0.111098
$326$	4.09522e8	0.654659
$327$	3.90164e8	0.617065
$328$	−8.18817e7	−0.128123
$329$	−1.75457e7	−0.0271635
$330$	1.28508e8	0.196848
$331$	1.35303e8	0.205073	0.102536	−	0.994729i	$-0.467304\pi$
$331$	1.35303e8	0.205073	0.102536	+	0.994729i	$0.467304\pi$
$332$	−1.13908e8	−0.170833
$333$	1.00271e8	0.148805
$334$	−3.01921e8	−0.443385
$335$	1.26373e8	0.183653
$336$	−2.28773e7	−0.0329016
$337$	6.48003e8	0.922300	0.461150	−	0.887322i	$-0.347437\pi$
$337$	6.48003e8	0.922300	0.461150	+	0.887322i	$0.347437\pi$
$338$	−3.47091e8	−0.488917
$339$	3.17015e8	0.441958
$340$	1.24515e8	0.171808
$341$	6.43232e8	0.878471
$342$	4.00017e7	0.0540738
$343$	−3.31867e8	−0.444053
$344$	−2.33359e8	−0.309079
$345$	−1.30610e8	−0.171242
$346$	−5.75420e8	−0.746824
$347$	2.97258e8	0.381928	0.190964	−	0.981597i	$-0.438839\pi$
$347$	2.97258e8	0.381928	0.190964	+	0.981597i	$0.438839\pi$
$348$	7.62705e7	0.0970128
$349$	−1.30821e9	−1.64736	−0.823678	−	0.567058i	$-0.808082\pi$
$349$	−1.30821e9	−1.64736	−0.823678	+	0.567058i	$0.808082\pi$
$350$	2.58577e7	0.0322368
$351$	8.66099e7	0.106904
$352$	−1.55961e8	−0.190597
$353$	−1.38083e9	−1.67082	−0.835411	−	0.549626i	$-0.814770\pi$
$353$	−1.38083e9	−1.67082	−0.835411	+	0.549626i	$0.814770\pi$
$354$	−1.77069e8	−0.212144
$355$	−2.33815e8	−0.277379
$356$	−3.43264e8	−0.403230
$357$	−8.69309e7	−0.101120
$358$	8.45919e8	0.974402
$359$	−4.49561e7	−0.0512812	−0.0256406	−	0.999671i	$-0.508163\pi$
$359$	−4.49561e7	−0.0512812	−0.0256406	+	0.999671i	$0.508163\pi$
$360$	4.66560e7	0.0527046
$361$	4.70459e7	0.0526316
$362$	−8.30290e8	−0.919920
$363$	−8.54867e7	−0.0938049
$364$	−5.82555e7	−0.0633114
$365$	5.38504e8	0.579647
$366$	7.23902e8	0.771784
$367$	2.85156e7	0.0301128	0.0150564	−	0.999887i	$-0.495207\pi$
$367$	2.85156e7	0.0301128	0.0150564	+	0.999887i	$0.495207\pi$
$368$	1.58513e8	0.165805
$369$	−1.16585e8	−0.120796
$370$	1.37545e8	0.141169
$371$	1.58965e7	0.0161620
$372$	2.33531e8	0.235204
$373$	1.45520e9	1.45192	0.725961	−	0.687736i	$-0.241395\pi$
$373$	1.45520e9	1.45192	0.725961	+	0.687736i	$0.241395\pi$
$374$	−5.92634e8	−0.585781
$375$	−5.27344e7	−0.0516398
$376$	−4.34270e7	−0.0421311
$377$	1.94218e8	0.186679
$378$	−3.25733e7	−0.0310199
$379$	5.12940e6	0.00483982	0.00241991	−	0.999997i	$-0.499230\pi$
$379$	5.12940e6	0.00483982	0.00241991	+	0.999997i	$0.499230\pi$
$380$	5.48720e7	0.0512989
$381$	6.92230e8	0.641229
$382$	−7.45574e8	−0.684336
$383$	−1.02289e9	−0.930321	−0.465161	−	0.885226i	$-0.654003\pi$
$383$	−1.02289e9	−0.930321	−0.465161	+	0.885226i	$0.654003\pi$
$384$	−5.66231e7	−0.0510310
$385$	−1.23071e8	−0.109912
$386$	−6.64000e8	−0.587642
$387$	−3.32263e8	−0.291403
$388$	−3.58688e8	−0.311750
$389$	1.14619e9	0.987262	0.493631	−	0.869671i	$-0.335669\pi$
$389$	1.14619e9	0.987262	0.493631	+	0.869671i	$0.335669\pi$
$390$	1.18806e8	0.101418
$391$	6.02330e8	0.509584
$392$	−3.99745e8	−0.335183
$393$	9.28836e8	0.771907
$394$	−1.59658e9	−1.31508
$395$	1.03765e9	0.847148
$396$	−2.22062e8	−0.179697
$397$	−2.44382e9	−1.96021	−0.980105	−	0.198478i	$-0.936400\pi$
$397$	−2.44382e9	−1.96021	−0.980105	+	0.198478i	$0.936400\pi$
$398$	−7.90194e8	−0.628266
$399$	−3.83094e7	−0.0301926
$400$	6.40000e7	0.0500000
$401$	1.32316e9	1.02473	0.512364	−	0.858768i	$-0.328770\pi$
$401$	1.32316e9	1.02473	0.512364	+	0.858768i	$0.328770\pi$
$402$	−2.18373e8	−0.167652
$403$	5.94672e8	0.452595
$404$	1.09058e9	0.822852
$405$	6.64301e7	0.0496904
$406$	−7.30438e7	−0.0541679
$407$	−6.54654e8	−0.481318
$408$	−2.15161e8	−0.156839
$409$	−2.67709e8	−0.193478	−0.0967390	−	0.995310i	$-0.530841\pi$
$409$	−2.67709e8	−0.193478	−0.0967390	+	0.995310i	$0.530841\pi$
$410$	−1.59925e8	−0.114597
$411$	1.09480e9	0.777837
$412$	3.13767e8	0.221038
$413$	1.69578e8	0.118452
$414$	2.25695e8	0.156322
$415$	−2.22477e8	−0.152798
$416$	−1.44187e8	−0.0981973
$417$	2.33173e8	0.157471
$418$	−2.61166e8	−0.174904
$419$	−7.90101e7	−0.0524727	−0.0262364	−	0.999656i	$-0.508352\pi$
$419$	−7.90101e7	−0.0524727	−0.0262364	+	0.999656i	$0.508352\pi$
$420$	−4.46822e7	−0.0294281
$421$	−4.68482e7	−0.0305989	−0.0152995	−	0.999883i	$-0.504870\pi$
$421$	−4.68482e7	−0.0305989	−0.0152995	+	0.999883i	$0.504870\pi$
$422$	−9.20731e8	−0.596402
$423$	−6.18326e7	−0.0397216
$424$	3.93452e7	0.0250675
$425$	2.43192e8	0.153670
$426$	4.04033e8	0.253211
$427$	−6.93276e8	−0.430932
$428$	4.33734e8	0.267405
$429$	−5.65466e8	−0.345785
$430$	−4.55779e8	−0.276449
$431$	−1.24607e9	−0.749675	−0.374838	−	0.927090i	$-0.622302\pi$
$431$	−1.24607e9	−0.749675	−0.374838	+	0.927090i	$0.622302\pi$
$432$	−8.06216e7	−0.0481125
$433$	−2.37190e9	−1.40407	−0.702036	−	0.712141i	$-0.747726\pi$
$433$	−2.37190e9	−1.40407	−0.702036	+	0.712141i	$0.747726\pi$
$434$	−2.23651e8	−0.131328
$435$	1.48966e8	0.0867709
$436$	−9.24834e8	−0.534394
$437$	2.65439e8	0.152153
$438$	−9.30535e8	−0.529143
$439$	2.34409e9	1.32236	0.661179	−	0.750229i	$-0.270057\pi$
$439$	2.34409e9	1.32236	0.661179	+	0.750229i	$0.270057\pi$
$440$	−3.04611e8	−0.170475
$441$	−5.69168e8	−0.316013
$442$	−5.47894e8	−0.301799
$443$	8.56836e8	0.468257	0.234129	−	0.972206i	$-0.424776\pi$
$443$	8.56836e8	0.468257	0.234129	+	0.972206i	$0.424776\pi$
$444$	−2.37678e8	−0.128869
$445$	−6.70437e8	−0.360660
$446$	−2.39453e8	−0.127805
$447$	2.54170e8	0.134601
$448$	5.42276e7	0.0284936
$449$	2.19478e9	1.14427	0.572136	−	0.820159i	$-0.306115\pi$
$449$	2.19478e9	1.14427	0.572136	+	0.820159i	$0.306115\pi$
$450$	9.11250e7	0.0471405
$451$	7.61172e8	0.390720
$452$	−7.51443e8	−0.382747
$453$	1.98504e9	1.00329
$454$	1.19273e9	0.598201
$455$	−1.13780e8	−0.0566274
$456$	−9.48188e7	−0.0468293
$457$	−2.93559e9	−1.43876	−0.719382	−	0.694615i	$-0.755575\pi$
$457$	−2.93559e9	−1.43876	−0.719382	+	0.694615i	$0.755575\pi$
$458$	−1.59034e8	−0.0773502
$459$	−3.06352e8	−0.147869
$460$	3.09595e8	0.148300
$461$	1.22481e9	0.582259	0.291129	−	0.956684i	$-0.405969\pi$
$461$	1.22481e9	0.582259	0.291129	+	0.956684i	$0.405969\pi$
$462$	2.12667e8	0.100335
$463$	−1.86735e9	−0.874362	−0.437181	−	0.899374i	$-0.644023\pi$
$463$	−1.86735e9	−0.874362	−0.437181	+	0.899374i	$0.644023\pi$
$464$	−1.80789e8	−0.0840156
$465$	4.56116e8	0.210373
$466$	−1.91133e9	−0.874951
$467$	1.86953e9	0.849422	0.424711	−	0.905329i	$-0.360376\pi$
$467$	1.86953e9	0.849422	0.424711	+	0.905329i	$0.360376\pi$
$468$	−2.05298e8	−0.0925813
$469$	2.09135e8	0.0936097
$470$	−8.48184e7	−0.0376832
$471$	−1.46017e9	−0.643916
$472$	4.19719e8	0.183722
$473$	2.16931e9	0.942555
$474$	−1.79305e9	−0.773337
$475$	1.07172e8	0.0458831
$476$	2.06058e8	0.0875722
$477$	5.60209e7	0.0236339
$478$	4.24911e8	0.177951
$479$	−4.47751e9	−1.86150	−0.930748	−	0.365661i	$-0.880843\pi$
$479$	−4.47751e9	−1.86150	−0.930748	+	0.365661i	$0.880843\pi$
$480$	−1.10592e8	−0.0456435
$481$	−6.05233e8	−0.247979
$482$	8.45549e8	0.343933
$483$	−2.16147e8	−0.0872837
$484$	2.02635e8	0.0812374
$485$	−7.00562e8	−0.278837
$486$	−1.14791e8	−0.0453609
$487$	−3.39583e8	−0.133228	−0.0666138	−	0.997779i	$-0.521220\pi$
$487$	−3.39583e8	−0.133228	−0.0666138	+	0.997779i	$0.521220\pi$
$488$	−1.71591e9	−0.668384
$489$	−1.38214e9	−0.534527
$490$	−7.80751e8	−0.299796
$491$	1.94382e9	0.741090	0.370545	−	0.928815i	$-0.379171\pi$
$491$	1.94382e9	0.741090	0.370545	+	0.928815i	$0.379171\pi$
$492$	2.76351e8	0.104612
$493$	−6.86978e8	−0.258213
$494$	−2.41450e8	−0.0901120
$495$	−4.33714e8	−0.160726
$496$	−5.53556e8	−0.203693
$497$	−3.86940e8	−0.141383
$498$	3.84441e8	0.139485
$499$	2.10946e9	0.760010	0.380005	−	0.924984i	$-0.375922\pi$
$499$	2.10946e9	0.760010	0.380005	+	0.924984i	$0.375922\pi$
$500$	1.25000e8	0.0447214
$501$	1.01898e9	0.362022
$502$	−2.98440e9	−1.05292
$503$	−1.79602e9	−0.629252	−0.314626	−	0.949216i	$-0.601879\pi$
$503$	−1.79602e9	−0.629252	−0.314626	+	0.949216i	$0.601879\pi$
$504$	7.72108e7	0.0268640
$505$	2.13003e9	0.735981
$506$	−1.47353e9	−0.505631
$507$	1.17143e9	0.399199
$508$	−1.64084e9	−0.555320
$509$	−3.43630e9	−1.15499	−0.577496	−	0.816393i	$-0.695970\pi$
$509$	−3.43630e9	−1.15499	−0.577496	+	0.816393i	$0.695970\pi$
$510$	−4.20237e8	−0.140281
$511$	8.91167e8	0.295451
$512$	1.34218e8	0.0441942
$513$	−1.35006e8	−0.0441511
$514$	−2.10566e9	−0.683938
$515$	6.12827e8	0.197703
$516$	7.87586e8	0.252362
$517$	4.03698e8	0.128481
$518$	2.27623e8	0.0719552
$519$	1.94204e9	0.609779
$520$	−2.81615e8	−0.0878304
$521$	7.64671e7	0.0236888	0.0118444	−	0.999930i	$-0.496230\pi$
$521$	7.64671e7	0.0236888	0.0118444	+	0.999930i	$0.496230\pi$
$522$	−2.57413e8	−0.0792106
$523$	2.55749e9	0.781731	0.390865	−	0.920448i	$-0.372176\pi$
$523$	2.55749e9	0.781731	0.390865	+	0.920448i	$0.372176\pi$
$524$	−2.20169e9	−0.668491
$525$	−8.72698e7	−0.0263213
$526$	6.93083e8	0.207651
$527$	−2.10345e9	−0.626029
$528$	5.26369e8	0.155622
$529$	−1.90718e9	−0.560141
$530$	7.68462e7	0.0224211
$531$	5.97608e8	0.173215
$532$	9.08074e7	0.0261475
$533$	7.03709e8	0.201302
$534$	1.15852e9	0.329236
$535$	8.47137e8	0.239175
$536$	5.17625e8	0.145191
$537$	−2.85498e9	−0.795596
$538$	3.57646e9	0.990182
$539$	3.71603e9	1.02216
$540$	−1.57464e8	−0.0430331
$541$	−2.25165e8	−0.0611379	−0.0305689	−	0.999533i	$-0.509732\pi$
$541$	−2.25165e8	−0.0611379	−0.0305689	+	0.999533i	$0.509732\pi$
$542$	1.21055e9	0.326576
$543$	2.80223e9	0.751112
$544$	5.10011e8	0.135826
$545$	−1.80632e9	−0.477976
$546$	1.96612e8	0.0516935
$547$	3.44718e9	0.900551	0.450275	−	0.892890i	$-0.351326\pi$
$547$	3.44718e9	0.900551	0.450275	+	0.892890i	$0.351326\pi$
$548$	−2.59508e9	−0.673627
$549$	−2.44317e9	−0.630159
$550$	−5.94944e8	−0.152478
$551$	−3.02743e8	−0.0770980
$552$	−5.34980e8	−0.135379
$553$	1.71719e9	0.431799
$554$	−1.55065e9	−0.387464
$555$	−4.64216e8	−0.115264
$556$	−5.52706e8	−0.136374
$557$	−3.37891e9	−0.828483	−0.414241	−	0.910167i	$-0.635953\pi$
$557$	−3.37891e9	−0.828483	−0.414241	+	0.910167i	$0.635953\pi$
$558$	−7.88168e8	−0.192043
$559$	2.00554e9	0.485612
$560$	1.05913e8	0.0254854
$561$	2.00014e9	0.478289
$562$	−9.61525e8	−0.228499
$563$	2.10759e9	0.497745	0.248873	−	0.968536i	$-0.419940\pi$
$563$	2.10759e9	0.497745	0.248873	+	0.968536i	$0.419940\pi$
$564$	1.46566e8	0.0343999
$565$	−1.46766e9	−0.342339
$566$	2.78169e9	0.644839
$567$	1.09935e8	0.0253276
$568$	−9.57708e8	−0.219288
$569$	4.41050e9	1.00368	0.501840	−	0.864960i	$-0.332657\pi$
$569$	4.41050e9	1.00368	0.501840	+	0.864960i	$0.332657\pi$
$570$	−1.85193e8	−0.0418854
$571$	4.94406e9	1.11137	0.555683	−	0.831394i	$-0.312457\pi$
$571$	4.94406e9	1.11137	0.555683	+	0.831394i	$0.312457\pi$
$572$	1.34036e9	0.299458
$573$	2.51631e9	0.558758
$574$	−2.64659e8	−0.0584111
$575$	6.04678e8	0.132644
$576$	1.91103e8	0.0416667
$577$	9.44836e8	0.204758	0.102379	−	0.994745i	$-0.467355\pi$
$577$	9.44836e8	0.204758	0.102379	+	0.994745i	$0.467355\pi$
$578$	−1.34473e9	−0.289659
$579$	2.24100e9	0.479807
$580$	−3.53104e8	−0.0751458
$581$	−3.68176e8	−0.0778824
$582$	1.21057e9	0.254542
$583$	−3.65754e8	−0.0764449
$584$	2.20571e9	0.458251
$585$	−4.00972e8	−0.0828073
$586$	3.78261e9	0.776516
$587$	−3.67002e9	−0.748919	−0.374459	−	0.927243i	$-0.622172\pi$
$587$	−3.67002e9	−0.748919	−0.374459	+	0.927243i	$0.622172\pi$
$588$	1.34914e9	0.273675
$589$	−9.26963e8	−0.186921
$590$	8.19764e8	0.164326
$591$	5.38846e9	1.07376
$592$	5.63386e8	0.111604
$593$	−2.74952e9	−0.541458	−0.270729	−	0.962656i	$-0.587265\pi$
$593$	−2.74952e9	−0.541458	−0.270729	+	0.962656i	$0.587265\pi$
$594$	7.49458e8	0.146722
$595$	4.02458e8	0.0783269
$596$	−6.02478e8	−0.116568
$597$	2.66691e9	0.512977
$598$	−1.36229e9	−0.260505
$599$	−6.51031e9	−1.23768	−0.618839	−	0.785517i	$-0.712397\pi$
$599$	−6.51031e9	−1.23768	−0.618839	+	0.785517i	$0.712397\pi$
$600$	−2.16000e8	−0.0408248
$601$	4.32572e9	0.812827	0.406413	−	0.913689i	$-0.366779\pi$
$601$	4.32572e9	0.812827	0.406413	+	0.913689i	$0.366779\pi$
$602$	−7.54266e8	−0.140908
$603$	7.37010e8	0.136887
$604$	−4.70527e9	−0.868871
$605$	3.95772e8	0.0726610
$606$	−3.68070e9	−0.671856
$607$	2.42214e9	0.439582	0.219791	−	0.975547i	$-0.429463\pi$
$607$	2.42214e9	0.439582	0.219791	+	0.975547i	$0.429463\pi$
$608$	2.24756e8	0.0405554
$609$	2.46523e8	0.0442279
$610$	−3.35140e9	−0.597821
$611$	3.73222e8	0.0661946
$612$	7.26169e8	0.128058
$613$	4.99809e9	0.876381	0.438190	−	0.898882i	$-0.355620\pi$
$613$	4.99809e9	0.876381	0.438190	+	0.898882i	$0.355620\pi$
$614$	−4.19334e9	−0.731091
$615$	5.39747e8	0.0935681
$616$	−5.04100e8	−0.0868928
$617$	4.85821e9	0.832680	0.416340	−	0.909209i	$-0.363313\pi$
$617$	4.85821e9	0.832680	0.416340	+	0.909209i	$0.363313\pi$
$618$	−1.05897e9	−0.180477
$619$	−3.22430e9	−0.546410	−0.273205	−	0.961956i	$-0.588084\pi$
$619$	−3.22430e9	−0.546410	−0.273205	+	0.961956i	$0.588084\pi$
$620$	−1.08116e9	−0.182188
$621$	−7.61720e8	−0.127636
$622$	3.07557e9	0.512460
$623$	−1.10950e9	−0.183832
$624$	4.86631e8	0.0801778
$625$	2.44141e8	0.0400000
$626$	4.70360e9	0.766338
$627$	8.81436e8	0.142809
$628$	3.46114e9	0.557648
$629$	2.14080e9	0.343004
$630$	1.50802e8	0.0240279
$631$	−3.33117e8	−0.0527829	−0.0263915	−	0.999652i	$-0.508402\pi$
$631$	−3.33117e8	−0.0527829	−0.0263915	+	0.999652i	$0.508402\pi$
$632$	4.25020e9	0.669729
$633$	3.10747e9	0.486960
$634$	1.39293e9	0.217079
$635$	−3.20477e9	−0.496694
$636$	−1.32790e8	−0.0204676
$637$	3.43549e9	0.526624
$638$	1.68062e9	0.256210
$639$	−1.36361e9	−0.206746
$640$	2.62144e8	0.0395285
$641$	5.35301e9	0.802777	0.401388	−	0.915908i	$-0.368528\pi$
$641$	5.35301e9	0.802777	0.401388	+	0.915908i	$0.368528\pi$
$642$	−1.46385e9	−0.218336
$643$	3.59195e9	0.532834	0.266417	−	0.963858i	$-0.414160\pi$
$643$	3.59195e9	0.532834	0.266417	+	0.963858i	$0.414160\pi$
$644$	5.12347e8	0.0755899
$645$	1.53825e9	0.225720
$646$	8.54045e8	0.124643
$647$	8.07758e9	1.17251	0.586254	−	0.810127i	$-0.300602\pi$
$647$	8.07758e9	1.17251	0.586254	+	0.810127i	$0.300602\pi$
$648$	2.72098e8	0.0392837
$649$	−3.90171e9	−0.560272
$650$	−5.50030e8	−0.0785579
$651$	7.54824e8	0.107229
$652$	3.27617e9	0.462914
$653$	7.62872e9	1.07215	0.536075	−	0.844170i	$-0.319906\pi$
$653$	7.62872e9	1.07215	0.536075	+	0.844170i	$0.319906\pi$
$654$	3.12132e9	0.436331
$655$	−4.30017e9	−0.597917
$656$	−6.55053e8	−0.0905969
$657$	3.14055e9	0.432044
$658$	−1.40366e8	−0.0192075
$659$	−7.79965e9	−1.06164	−0.530819	−	0.847485i	$-0.678115\pi$
$659$	−7.79965e9	−1.06164	−0.530819	+	0.847485i	$0.678115\pi$
$660$	1.02806e9	0.139193
$661$	8.75949e9	1.17971	0.589853	−	0.807511i	$-0.299186\pi$
$661$	8.75949e9	1.17971	0.589853	+	0.807511i	$0.299186\pi$
$662$	1.08242e9	0.145008
$663$	1.84914e9	0.246418
$664$	−9.11267e8	−0.120797
$665$	1.77358e8	0.0233870
$666$	8.02164e8	0.105221
$667$	−1.70811e9	−0.222883
$668$	−2.41537e9	−0.313520
$669$	8.08155e8	0.104353
$670$	1.01099e9	0.129863
$671$	1.59511e10	2.03828
$672$	−1.83018e8	−0.0232649
$673$	−6.97171e9	−0.881631	−0.440815	−	0.897598i	$-0.645311\pi$
$673$	−6.97171e9	−0.881631	−0.440815	+	0.897598i	$0.645311\pi$
$674$	5.18402e9	0.652165
$675$	−3.07547e8	−0.0384900
$676$	−2.77673e9	−0.345717
$677$	−5.15536e8	−0.0638556	−0.0319278	−	0.999490i	$-0.510165\pi$
$677$	−5.15536e8	−0.0638556	−0.0319278	+	0.999490i	$0.510165\pi$
$678$	2.53612e9	0.312512
$679$	−1.15936e9	−0.142126
$680$	9.96116e8	0.121487
$681$	−4.02547e9	−0.488429
$682$	5.14586e9	0.621173
$683$	−7.68537e9	−0.922980	−0.461490	−	0.887145i	$-0.652685\pi$
$683$	−7.68537e9	−0.922980	−0.461490	+	0.887145i	$0.652685\pi$
$684$	3.20014e8	0.0382360
$685$	−5.06852e9	−0.602510
$686$	−2.65494e9	−0.313993
$687$	5.36740e8	0.0631562
$688$	−1.86687e9	−0.218552
$689$	−3.38142e8	−0.0393851
$690$	−1.04488e9	−0.121087
$691$	1.42973e10	1.64847	0.824233	−	0.566251i	$-0.191607\pi$
$691$	1.42973e10	1.64847	0.824233	+	0.566251i	$0.191607\pi$
$692$	−4.60336e9	−0.528085
$693$	−7.17751e8	−0.0819234
$694$	2.37807e9	0.270064
$695$	−1.07950e9	−0.121977
$696$	6.10164e8	0.0685984
$697$	−2.48913e9	−0.278440
$698$	−1.04657e10	−1.16486
$699$	6.45072e9	0.714395
$700$	2.06862e8	0.0227949
$701$	−2.31241e9	−0.253543	−0.126771	−	0.991932i	$-0.540461\pi$
$701$	−2.31241e9	−0.253543	−0.126771	+	0.991932i	$0.540461\pi$
$702$	6.92879e8	0.0755923
$703$	9.43424e8	0.102415
$704$	−1.24769e9	−0.134773
$705$	2.86262e8	0.0307682
$706$	−1.10467e10	−1.18145
$707$	3.52498e9	0.375136
$708$	−1.41655e9	−0.150009
$709$	4.95543e9	0.522179	0.261090	−	0.965315i	$-0.415918\pi$
$709$	4.95543e9	0.522179	0.261090	+	0.965315i	$0.415918\pi$
$710$	−1.87052e9	−0.196137
$711$	6.05155e9	0.631427
$712$	−2.74611e9	−0.285127
$713$	−5.23005e9	−0.540371
$714$	−6.95447e8	−0.0715024
$715$	2.61790e9	0.267844
$716$	6.76735e9	0.689007
$717$	−1.43407e9	−0.145296
$718$	−3.59649e8	−0.0362612
$719$	−5.76278e8	−0.0578204	−0.0289102	−	0.999582i	$-0.509204\pi$
$719$	−5.76278e8	−0.0578204	−0.0289102	+	0.999582i	$0.509204\pi$
$720$	3.73248e8	0.0372678
$721$	1.01416e9	0.100771
$722$	3.76367e8	0.0372161
$723$	−2.85373e9	−0.280820
$724$	−6.64232e9	−0.650482
$725$	−6.89656e8	−0.0672125
$726$	−6.83894e8	−0.0663301
$727$	1.58205e10	1.52703	0.763517	−	0.645788i	$-0.223471\pi$
$727$	1.58205e10	1.52703	0.763517	+	0.645788i	$0.223471\pi$
$728$	−4.66044e8	−0.0447679
$729$	3.87420e8	0.0370370
$730$	4.30803e9	0.409873
$731$	−7.09389e9	−0.671697
$732$	5.79121e9	0.545734
$733$	9.97214e9	0.935243	0.467622	−	0.883929i	$-0.345111\pi$
$733$	9.97214e9	0.935243	0.467622	+	0.883929i	$0.345111\pi$
$734$	2.28125e8	0.0212930
$735$	2.63504e9	0.244783
$736$	1.26810e9	0.117242
$737$	−4.81185e9	−0.442767
$738$	−9.32684e8	−0.0854156
$739$	1.38681e10	1.26405	0.632023	−	0.774950i	$-0.282225\pi$
$739$	1.38681e10	1.26405	0.632023	+	0.774950i	$0.282225\pi$
$740$	1.10036e9	0.0998217
$741$	8.14894e8	0.0735762
$742$	1.27172e8	0.0114282
$743$	1.94879e10	1.74303	0.871515	−	0.490368i	$-0.163138\pi$
$743$	1.94879e10	1.74303	0.871515	+	0.490368i	$0.163138\pi$
$744$	1.86825e9	0.166314
$745$	−1.17671e9	−0.104262
$746$	1.16416e10	1.02666
$747$	−1.29749e9	−0.113889
$748$	−4.74107e9	−0.414210
$749$	1.40192e9	0.121909
$750$	−4.21875e8	−0.0365148
$751$	1.83916e10	1.58446	0.792229	−	0.610224i	$-0.208920\pi$
$751$	1.83916e10	1.58446	0.792229	+	0.610224i	$0.208920\pi$
$752$	−3.47416e8	−0.0297912
$753$	1.00724e10	0.859704
$754$	1.55374e9	0.132002
$755$	−9.18998e9	−0.777142
$756$	−2.60586e8	−0.0219344
$757$	4.10747e9	0.344143	0.172072	−	0.985084i	$-0.444954\pi$
$757$	4.10747e9	0.344143	0.172072	+	0.985084i	$0.444954\pi$
$758$	4.10352e7	0.00342227
$759$	4.97318e9	0.412846
$760$	4.38976e8	0.0362738
$761$	−1.47492e10	−1.21317	−0.606587	−	0.795017i	$-0.707462\pi$
$761$	−1.47492e10	−1.21317	−0.606587	+	0.795017i	$0.707462\pi$
$762$	5.53784e9	0.453417
$763$	−2.98926e9	−0.243629
$764$	−5.96460e9	−0.483898
$765$	1.41830e9	0.114539
$766$	−8.18311e9	−0.657836
$767$	−3.60716e9	−0.288657
$768$	−4.52985e8	−0.0360844
$769$	−5.32547e9	−0.422295	−0.211147	−	0.977454i	$-0.567720\pi$
$769$	−5.32547e9	−0.422295	−0.211147	+	0.977454i	$0.567720\pi$
$770$	−9.84570e8	−0.0777193
$771$	7.10659e9	0.558433
$772$	−5.31200e9	−0.415525
$773$	1.61135e10	1.25476	0.627381	−	0.778713i	$-0.284127\pi$
$773$	1.61135e10	1.25476	0.627381	+	0.778713i	$0.284127\pi$
$774$	−2.65810e9	−0.206053
$775$	−2.11165e9	−0.162954
$776$	−2.86950e9	−0.220440
$777$	−7.68228e8	−0.0587512
$778$	9.16951e9	0.698100
$779$	−1.09693e9	−0.0831374
$780$	9.50452e8	0.0717132
$781$	8.90286e9	0.668730
$782$	4.81864e9	0.360330
$783$	8.68768e8	0.0646752
$784$	−3.19796e9	−0.237010
$785$	6.76003e9	0.498775
$786$	7.43069e9	0.545821
$787$	2.35231e10	1.72022	0.860109	−	0.510111i	$-0.170396\pi$
$787$	2.35231e10	1.72022	0.860109	+	0.510111i	$0.170396\pi$
$788$	−1.27726e10	−0.929905
$789$	−2.33915e9	−0.169547
$790$	8.30117e9	0.599024
$791$	−2.42883e9	−0.174493
$792$	−1.77649e9	−0.127065
$793$	1.47469e10	1.05014
$794$	−1.95506e10	−1.38608
$795$	−2.59356e8	−0.0183067
$796$	−6.32156e9	−0.444251
$797$	−7.94400e9	−0.555821	−0.277911	−	0.960607i	$-0.589642\pi$
$797$	−7.94400e9	−0.555821	−0.277911	+	0.960607i	$0.589642\pi$
$798$	−3.06475e8	−0.0213494
$799$	−1.32014e9	−0.0915602
$800$	5.12000e8	0.0353553
$801$	−3.90999e9	−0.268820
$802$	1.05853e10	0.724592
$803$	−2.05043e10	−1.39746
$804$	−1.74699e9	−0.118548
$805$	1.00068e9	0.0676097
$806$	4.75738e9	0.320033
$807$	−1.20705e10	−0.808480
$808$	8.72462e9	0.581844
$809$	−1.14827e10	−0.762471	−0.381236	−	0.924478i	$-0.624501\pi$
$809$	−1.14827e10	−0.762471	−0.381236	+	0.924478i	$0.624501\pi$
$810$	5.31441e8	0.0351364
$811$	−2.98307e9	−0.196377	−0.0981883	−	0.995168i	$-0.531305\pi$
$811$	−2.98307e9	−0.196377	−0.0981883	+	0.995168i	$0.531305\pi$
$812$	−5.84350e8	−0.0383025
$813$	−4.08559e9	−0.266648
$814$	−5.23724e9	−0.340343
$815$	6.39877e9	0.414043
$816$	−1.72129e9	−0.110902
$817$	−3.12619e9	−0.200557
$818$	−2.14167e9	−0.136810
$819$	−6.63566e8	−0.0422076
$820$	−1.27940e9	−0.0810323
$821$	2.47488e10	1.56082	0.780411	−	0.625266i	$-0.215010\pi$
$821$	2.47488e10	1.56082	0.780411	+	0.625266i	$0.215010\pi$
$822$	8.75841e9	0.550014
$823$	−1.29801e10	−0.811668	−0.405834	−	0.913947i	$-0.633019\pi$
$823$	−1.29801e10	−0.811668	−0.405834	+	0.913947i	$0.633019\pi$
$824$	2.51014e9	0.156298
$825$	2.00794e9	0.124498
$826$	1.35662e9	0.0837585
$827$	1.63430e10	1.00476	0.502381	−	0.864646i	$-0.332458\pi$
$827$	1.63430e10	1.00476	0.502381	+	0.864646i	$0.332458\pi$
$828$	1.80556e9	0.110536
$829$	2.58055e10	1.57316	0.786579	−	0.617490i	$-0.211850\pi$
$829$	2.58055e10	1.57316	0.786579	+	0.617490i	$0.211850\pi$
$830$	−1.77982e9	−0.108044
$831$	5.23346e9	0.316363
$832$	−1.15350e9	−0.0694360
$833$	−1.21519e10	−0.728426
$834$	1.86538e9	0.111349
$835$	−4.71751e9	−0.280421
$836$	−2.08933e9	−0.123676
$837$	2.66007e9	0.156803
$838$	−6.32081e8	−0.0371038
$839$	−6.76897e9	−0.395690	−0.197845	−	0.980233i	$-0.563394\pi$
$839$	−6.76897e9	−0.395690	−0.197845	+	0.980233i	$0.563394\pi$
$840$	−3.57457e8	−0.0208088
$841$	−1.53017e10	−0.887062
$842$	−3.74786e8	−0.0216367
$843$	3.24515e9	0.186568
$844$	−7.36585e9	−0.421720
$845$	−5.42330e9	−0.309218
$846$	−4.94661e8	−0.0280874
$847$	6.54961e8	0.0370359
$848$	3.14762e8	0.0177254
$849$	−9.38820e9	−0.526509
$850$	1.94554e9	0.108661
$851$	5.32292e9	0.296072
$852$	3.23227e9	0.179048
$853$	−2.17274e10	−1.19863	−0.599317	−	0.800512i	$-0.704561\pi$
$853$	−2.17274e10	−1.19863	−0.599317	+	0.800512i	$0.704561\pi$
$854$	−5.54621e9	−0.304715
$855$	6.25026e8	0.0341993
$856$	3.46987e9	0.189084
$857$	−1.72647e10	−0.936970	−0.468485	−	0.883471i	$-0.655200\pi$
$857$	−1.72647e10	−0.936970	−0.468485	+	0.883471i	$0.655200\pi$
$858$	−4.52373e9	−0.244507
$859$	2.88521e10	1.55311	0.776554	−	0.630051i	$-0.216966\pi$
$859$	2.88521e10	1.55311	0.776554	+	0.630051i	$0.216966\pi$
$860$	−3.64623e9	−0.195479
$861$	8.93225e8	0.0476925
$862$	−9.96859e9	−0.530101
$863$	3.79538e9	0.201010	0.100505	−	0.994937i	$-0.467954\pi$
$863$	3.79538e9	0.201010	0.100505	+	0.994937i	$0.467954\pi$
$864$	−6.44973e8	−0.0340207
$865$	−8.99093e9	−0.472333
$866$	−1.89752e10	−0.992829
$867$	4.53845e9	0.236505
$868$	−1.78921e9	−0.0928630
$869$	−3.95098e10	−2.04238
$870$	1.19173e9	0.0613563
$871$	−4.44859e9	−0.228117
$872$	−7.39867e9	−0.377873
$873$	−4.08568e9	−0.207833
$874$	2.12351e9	0.107588
$875$	4.04027e8	0.0203884
$876$	−7.44428e9	−0.374161
$877$	−2.28605e9	−0.114443	−0.0572213	−	0.998362i	$-0.518224\pi$
$877$	−2.28605e9	−0.114443	−0.0572213	+	0.998362i	$0.518224\pi$
$878$	1.87527e10	0.935048
$879$	−1.27663e10	−0.634022
$880$	−2.43689e9	−0.120544
$881$	−4.06251e9	−0.200161	−0.100080	−	0.994979i	$-0.531910\pi$
$881$	−4.06251e9	−0.200161	−0.100080	+	0.994979i	$0.531910\pi$
$882$	−4.55334e9	−0.223455
$883$	1.07134e10	0.523679	0.261840	−	0.965111i	$-0.415671\pi$
$883$	1.07134e10	0.523679	0.261840	+	0.965111i	$0.415671\pi$
$884$	−4.38315e9	−0.213404
$885$	−2.76670e9	−0.134172
$886$	6.85469e9	0.331108
$887$	−3.68605e10	−1.77349	−0.886745	−	0.462259i	$-0.847039\pi$
$887$	−3.68605e10	−1.77349	−0.886745	+	0.462259i	$0.847039\pi$
$888$	−1.90143e9	−0.0911243
$889$	−5.30355e9	−0.253169
$890$	−5.36350e9	−0.255025
$891$	−2.52942e9	−0.119798
$892$	−1.91563e9	−0.0903720
$893$	−5.81770e8	−0.0273383
$894$	2.03336e9	0.0951773
$895$	1.32175e10	0.616266
$896$	4.33821e8	0.0201480
$897$	4.59774e9	0.212702
$898$	1.75583e10	0.809123
$899$	5.96505e9	0.273814
$900$	7.29000e8	0.0333333
$901$	1.19606e9	0.0544773
$902$	6.08938e9	0.276280
$903$	2.54565e9	0.115051
$904$	−6.01155e9	−0.270643
$905$	−1.29733e10	−0.581808
$906$	1.58803e10	0.709430
$907$	1.92263e10	0.855597	0.427798	−	0.903874i	$-0.359289\pi$
$907$	1.92263e10	0.855597	0.427798	+	0.903874i	$0.359289\pi$
$908$	9.54186e9	0.422992
$909$	1.24224e10	0.548568
$910$	−9.10242e8	−0.0400416
$911$	−2.04778e10	−0.897366	−0.448683	−	0.893691i	$-0.648107\pi$
$911$	−2.04778e10	−0.897366	−0.448683	+	0.893691i	$0.648107\pi$
$912$	−7.58551e8	−0.0331133
$913$	8.47114e9	0.368378
$914$	−2.34848e10	−1.01736
$915$	1.13110e10	0.488119
$916$	−1.27227e9	−0.0546948
$917$	−7.11632e9	−0.304764
$918$	−2.45082e9	−0.104559
$919$	−2.68137e10	−1.13960	−0.569801	−	0.821783i	$-0.692980\pi$
$919$	−2.68137e10	−1.13960	−0.569801	+	0.821783i	$0.692980\pi$
$920$	2.47676e9	0.104864
$921$	1.41525e10	0.596933
$922$	9.79849e9	0.411719
$923$	8.23075e9	0.344535
$924$	1.70134e9	0.0709477
$925$	2.14915e9	0.0892832
$926$	−1.49388e10	−0.618267
$927$	3.57401e9	0.147359
$928$	−1.44631e9	−0.0594080
$929$	−2.85833e10	−1.16965	−0.584827	−	0.811158i	$-0.698837\pi$
$929$	−2.85833e10	−1.16965	−0.584827	+	0.811158i	$0.698837\pi$
$930$	3.64893e9	0.148756
$931$	−5.35517e9	−0.217495
$932$	−1.52906e10	−0.618684
$933$	−1.03801e10	−0.418422
$934$	1.49562e10	0.600632
$935$	−9.25990e9	−0.370481
$936$	−1.64238e9	−0.0654649
$937$	4.64965e10	1.84643	0.923213	−	0.384288i	$-0.125553\pi$
$937$	4.64965e10	1.84643	0.923213	+	0.384288i	$0.125553\pi$
$938$	1.67308e9	0.0661921
$939$	−1.58746e10	−0.625712
$940$	−6.78548e8	−0.0266460
$941$	−4.13029e10	−1.61591	−0.807955	−	0.589244i	$-0.799426\pi$
$941$	−4.13029e10	−1.61591	−0.807955	+	0.589244i	$0.799426\pi$
$942$	−1.16813e10	−0.455317
$943$	−6.18901e9	−0.240342
$944$	3.35775e9	0.129911
$945$	−5.08958e8	−0.0196187
$946$	1.73544e10	0.666487
$947$	−3.91284e10	−1.49716	−0.748578	−	0.663047i	$-0.769263\pi$
$947$	−3.91284e10	−1.49716	−0.748578	+	0.663047i	$0.769263\pi$
$948$	−1.43444e10	−0.546832
$949$	−1.89564e10	−0.719985
$950$	8.57375e8	0.0324443
$951$	−4.70114e9	−0.177244
$952$	1.64847e9	0.0619229
$953$	−1.91770e10	−0.717720	−0.358860	−	0.933391i	$-0.616834\pi$
$953$	−1.91770e10	−0.717720	−0.358860	+	0.933391i	$0.616834\pi$
$954$	4.48167e8	0.0167117
$955$	−1.16496e10	−0.432812
$956$	3.39929e9	0.125830
$957$	−5.67208e9	−0.209195
$958$	−3.58201e10	−1.31628
$959$	−8.38787e9	−0.307105
$960$	−8.84736e8	−0.0322749
$961$	−9.24832e9	−0.336148
$962$	−4.84186e9	−0.175347
$963$	4.94050e9	0.178270
$964$	6.76439e9	0.243198
$965$	−1.03750e10	−0.371657
$966$	−1.72917e9	−0.0617189
$967$	3.42399e10	1.21770	0.608849	−	0.793286i	$-0.291632\pi$
$967$	3.42399e10	1.21770	0.608849	+	0.793286i	$0.291632\pi$
$968$	1.62108e9	0.0574435
$969$	−2.88240e9	−0.101770
$970$	−5.60450e9	−0.197168
$971$	−6.42267e9	−0.225138	−0.112569	−	0.993644i	$-0.535908\pi$
$971$	−6.42267e9	−0.225138	−0.112569	+	0.993644i	$0.535908\pi$
$972$	−9.18330e8	−0.0320750
$973$	−1.78647e9	−0.0621727
$974$	−2.71666e9	−0.0942061
$975$	1.85635e9	0.0641422
$976$	−1.37273e10	−0.472619
$977$	2.38602e10	0.818545	0.409272	−	0.912412i	$-0.365783\pi$
$977$	2.38602e10	0.818545	0.409272	+	0.912412i	$0.365783\pi$
$978$	−1.10571e10	−0.377968
$979$	2.55278e10	0.869510
$980$	−6.24601e9	−0.211988
$981$	−1.05344e10	−0.356262
$982$	1.55506e10	0.524030
$983$	−2.08936e10	−0.701577	−0.350788	−	0.936455i	$-0.614086\pi$
$983$	−2.08936e10	−0.701577	−0.350788	+	0.936455i	$0.614086\pi$
$984$	2.21081e9	0.0739721
$985$	−2.49466e10	−0.831733
$986$	−5.49582e9	−0.182584
$987$	4.73734e8	0.0156828
$988$	−1.93160e9	−0.0637188
$989$	−1.76384e10	−0.579791
$990$	−3.46971e9	−0.113650
$991$	3.63659e10	1.18696	0.593480	−	0.804849i	$-0.297754\pi$
$991$	3.63659e10	1.18696	0.593480	+	0.804849i	$0.297754\pi$
$992$	−4.42845e9	−0.144033
$993$	−3.65317e9	−0.118399
$994$	−3.09552e9	−0.0999727
$995$	−1.23468e10	−0.397350
$996$	3.07553e9	0.0986306
$997$	5.24744e9	0.167693	0.0838464	−	0.996479i	$-0.473279\pi$
$997$	5.24744e9	0.167693	0.0838464	+	0.996479i	$0.473279\pi$
$998$	1.68757e10	0.537408
$999$	−2.70731e9	−0.0859128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.8.a.a.1.3	✓	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +206.862 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +125.000 q^{5} -216.000 q^{6} +206.862 q^{7} +512.000 q^{8} +729.000 q^{9} +1000.00 q^{10} -4759.55 q^{11} -1728.00 q^{12} -4400.24 q^{13} +1654.89 q^{14} -3375.00 q^{15} +4096.00 q^{16} +15564.3 q^{17} +5832.00 q^{18} +6859.00 q^{19} +8000.00 q^{20} -5585.27 q^{21} -38076.4 q^{22} +38699.4 q^{23} -13824.0 q^{24} +15625.0 q^{25} -35201.9 q^{26} -19683.0 q^{27} +13239.2 q^{28} -44138.0 q^{29} -27000.0 q^{30} -135145. q^{31} +32768.0 q^{32} +128508. q^{33} +124515. q^{34} +25857.7 q^{35} +46656.0 q^{36} +137545. q^{37} +54872.0 q^{38} +118806. q^{39} +64000.0 q^{40} -159925. q^{41} -44682.2 q^{42} -455779. q^{43} -304611. q^{44} +91125.0 q^{45} +309595. q^{46} -84818.4 q^{47} -110592. q^{48} -780751. q^{49} +125000. q^{50} -420237. q^{51} -281615. q^{52} +76846.2 q^{53} -157464. q^{54} -594944. q^{55} +105913. q^{56} -185193. q^{57} -353104. q^{58} +819764. q^{59} -216000. q^{60} -3.35140e6 q^{61} -1.08116e6 q^{62} +150802. q^{63} +262144. q^{64} -550030. q^{65} +1.02806e6 q^{66} +1.01099e6 q^{67} +996116. q^{68} -1.04488e6 q^{69} +206862. q^{70} -1.87052e6 q^{71} +373248. q^{72} +4.30803e6 q^{73} +1.10036e6 q^{74} -421875. q^{75} +438976. q^{76} -984570. q^{77} +950452. q^{78} +8.30117e6 q^{79} +512000. q^{80} +531441. q^{81} -1.27940e6 q^{82} -1.77982e6 q^{83} -357457. q^{84} +1.94554e6 q^{85} -3.64623e6 q^{86} +1.19173e6 q^{87} -2.43689e6 q^{88} -5.36350e6 q^{89} +729000. q^{90} -910242. q^{91} +2.47676e6 q^{92} +3.64893e6 q^{93} -678548. q^{94} +857375. q^{95} -884736. q^{96} -5.60450e6 q^{97} -6.24601e6 q^{98} -3.46971e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} - 108 q^{3} + 256 q^{4} + 500 q^{5} - 864 q^{6} - 1496 q^{7} + 2048 q^{8} + 2916 q^{9} + 4000 q^{10} - 2912 q^{11} - 6912 q^{12} - 3696 q^{13} - 11968 q^{14} - 13500 q^{15} + 16384 q^{16} + 16 q^{17} + 23328 q^{18} + 27436 q^{19} + 32000 q^{20} + 40392 q^{21} - 23296 q^{22} - 73016 q^{23} - 55296 q^{24} + 62500 q^{25} - 29568 q^{26} - 78732 q^{27} - 95744 q^{28} - 137784 q^{29} - 108000 q^{30} + 198072 q^{31} + 131072 q^{32} + 78624 q^{33} + 128 q^{34} - 187000 q^{35} + 186624 q^{36} + 207256 q^{37} + 219488 q^{38} + 99792 q^{39} + 256000 q^{40} - 504056 q^{41} + 323136 q^{42} - 250368 q^{43} - 186368 q^{44} + 364500 q^{45} - 584128 q^{46} - 1000376 q^{47} - 442368 q^{48} - 940908 q^{49} + 500000 q^{50} - 432 q^{51} - 236544 q^{52} - 2178688 q^{53} - 629856 q^{54} - 364000 q^{55} - 765952 q^{56} - 740772 q^{57} - 1102272 q^{58} + 327976 q^{59} - 864000 q^{60} + 572936 q^{61} + 1584576 q^{62} - 1090584 q^{63} + 1048576 q^{64} - 462000 q^{65} + 628992 q^{66} + 2017152 q^{67} + 1024 q^{68} + 1971432 q^{69} - 1496000 q^{70} + 2828960 q^{71} + 1492992 q^{72} - 132392 q^{73} + 1658048 q^{74} - 1687500 q^{75} + 1755904 q^{76} - 2304704 q^{77} + 798336 q^{78} + 3418408 q^{79} + 2048000 q^{80} + 2125764 q^{81} - 4032448 q^{82} - 3201760 q^{83} + 2585088 q^{84} + 2000 q^{85} - 2002944 q^{86} + 3720168 q^{87} - 1490944 q^{88} - 1389392 q^{89} + 2916000 q^{90} - 7865280 q^{91} - 4673024 q^{92} - 5347944 q^{93} - 8003008 q^{94} + 3429500 q^{95} - 3538944 q^{96} - 21061144 q^{97} - 7527264 q^{98} - 2122848 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 108 * q^3 + 256 * q^4 + 500 * q^5 - 864 * q^6 - 1496 * q^7 + 2048 * q^8 + 2916 * q^9 + 4000 * q^10 - 2912 * q^11 - 6912 * q^12 - 3696 * q^13 - 11968 * q^14 - 13500 * q^15 + 16384 * q^16 + 16 * q^17 + 23328 * q^18 + 27436 * q^19 + 32000 * q^20 + 40392 * q^21 - 23296 * q^22 - 73016 * q^23 - 55296 * q^24 + 62500 * q^25 - 29568 * q^26 - 78732 * q^27 - 95744 * q^28 - 137784 * q^29 - 108000 * q^30 + 198072 * q^31 + 131072 * q^32 + 78624 * q^33 + 128 * q^34 - 187000 * q^35 + 186624 * q^36 + 207256 * q^37 + 219488 * q^38 + 99792 * q^39 + 256000 * q^40 - 504056 * q^41 + 323136 * q^42 - 250368 * q^43 - 186368 * q^44 + 364500 * q^45 - 584128 * q^46 - 1000376 * q^47 - 442368 * q^48 - 940908 * q^49 + 500000 * q^50 - 432 * q^51 - 236544 * q^52 - 2178688 * q^53 - 629856 * q^54 - 364000 * q^55 - 765952 * q^56 - 740772 * q^57 - 1102272 * q^58 + 327976 * q^59 - 864000 * q^60 + 572936 * q^61 + 1584576 * q^62 - 1090584 * q^63 + 1048576 * q^64 - 462000 * q^65 + 628992 * q^66 + 2017152 * q^67 + 1024 * q^68 + 1971432 * q^69 - 1496000 * q^70 + 2828960 * q^71 + 1492992 * q^72 - 132392 * q^73 + 1658048 * q^74 - 1687500 * q^75 + 1755904 * q^76 - 2304704 * q^77 + 798336 * q^78 + 3418408 * q^79 + 2048000 * q^80 + 2125764 * q^81 - 4032448 * q^82 - 3201760 * q^83 + 2585088 * q^84 + 2000 * q^85 - 2002944 * q^86 + 3720168 * q^87 - 1490944 * q^88 - 1389392 * q^89 + 2916000 * q^90 - 7865280 * q^91 - 4673024 * q^92 - 5347944 * q^93 - 8003008 * q^94 + 3429500 * q^95 - 3538944 * q^96 - 21061144 * q^97 - 7527264 * q^98 - 2122848 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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