LMFDB - Embedded newform 529.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,8,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	529.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:	$165.251678481$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 832x^{6} - 1059x^{5} + 203052x^{4} + 678328x^{3} - 13424272x^{2} - 73308944x - 37372224 $ x^8 - 832x^6 - 1059x^5 + 203052x^4 + 678328x^3 - 13424272x^2 - 73308944x - 37372224
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-21.3077$ of defining polynomial
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-21.3077 q^{2} +86.9475 q^{3} +326.017 q^{4} +188.239 q^{5} -1852.65 q^{6} -639.155 q^{7} -4219.28 q^{8} +5372.88 q^{9} +O(q^{10})$	\(q-21.3077 q^{2} +86.9475 q^{3} +326.017 q^{4} +188.239 q^{5} -1852.65 q^{6} -639.155 q^{7} -4219.28 q^{8} +5372.88 q^{9} -4010.94 q^{10} +1629.29 q^{11} +28346.4 q^{12} +1138.20 q^{13} +13618.9 q^{14} +16366.9 q^{15} +48172.8 q^{16} -28713.3 q^{17} -114483. q^{18} -43387.0 q^{19} +61369.1 q^{20} -55573.0 q^{21} -34716.4 q^{22} -366856. q^{24} -42691.1 q^{25} -24252.3 q^{26} +277004. q^{27} -208375. q^{28} +62583.1 q^{29} -348741. q^{30} +22533.6 q^{31} -486383. q^{32} +141663. q^{33} +611814. q^{34} -120314. q^{35} +1.75165e6 q^{36} +277384. q^{37} +924475. q^{38} +98963.5 q^{39} -794233. q^{40} -130110. q^{41} +1.18413e6 q^{42} -585763. q^{43} +531177. q^{44} +1.01138e6 q^{45} -99374.3 q^{47} +4.18851e6 q^{48} -415024. q^{49} +909647. q^{50} -2.49655e6 q^{51} +371072. q^{52} +636910. q^{53} -5.90231e6 q^{54} +306696. q^{55} +2.69677e6 q^{56} -3.77239e6 q^{57} -1.33350e6 q^{58} -808062. q^{59} +5.33589e6 q^{60} +2.40412e6 q^{61} -480138. q^{62} -3.43410e6 q^{63} +4.19757e6 q^{64} +214253. q^{65} -3.01851e6 q^{66} +2.05060e6 q^{67} -9.36103e6 q^{68} +2.56361e6 q^{70} -3.83810e6 q^{71} -2.26697e7 q^{72} -2.78541e6 q^{73} -5.91041e6 q^{74} -3.71188e6 q^{75} -1.41449e7 q^{76} -1.04137e6 q^{77} -2.10868e6 q^{78} -7.20890e6 q^{79} +9.06801e6 q^{80} +1.23343e7 q^{81} +2.77235e6 q^{82} +498585. q^{83} -1.81177e7 q^{84} -5.40497e6 q^{85} +1.24813e7 q^{86} +5.44145e6 q^{87} -6.87443e6 q^{88} +1.37216e6 q^{89} -2.15503e7 q^{90} -727485. q^{91} +1.95924e6 q^{93} +2.11743e6 q^{94} -8.16712e6 q^{95} -4.22898e7 q^{96} -6.57645e6 q^{97} +8.84319e6 q^{98} +8.75398e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 40 q^{3} + 640 q^{4} - 444 q^{5} - 1745 q^{6} - 1446 q^{7} + 3177 q^{8} + 13878 q^{9}+O(q^{10}) $ 8 * q + 40 * q^3 + 640 * q^4 - 444 * q^5 - 1745 * q^6 - 1446 * q^7 + 3177 * q^8 + 13878 * q^9	\( 8 q + 40 q^{3} + 640 q^{4} - 444 q^{5} - 1745 q^{6} - 1446 q^{7} + 3177 q^{8} + 13878 q^{9} - 19502 q^{10} - 7588 q^{11} + 22733 q^{12} + 19862 q^{13} - 17544 q^{14} + 12770 q^{15} + 64336 q^{16} - 42070 q^{17} - 59129 q^{18} - 1050 q^{19} - 3364 q^{20} + 7698 q^{21} + 128220 q^{22} - 621188 q^{24} + 49496 q^{25} - 371761 q^{26} - 69500 q^{27} - 143050 q^{28} - 102578 q^{29} + 671470 q^{30} + 304172 q^{31} - 612824 q^{32} - 747242 q^{33} + 524530 q^{34} + 531048 q^{35} + 1868983 q^{36} - 286472 q^{37} + 762932 q^{38} + 1032828 q^{39} - 2105286 q^{40} + 1324414 q^{41} + 1886168 q^{42} - 2052578 q^{43} + 867298 q^{44} - 2087442 q^{45} + 675556 q^{47} + 1411151 q^{48} - 55404 q^{49} + 1458528 q^{50} - 2775482 q^{51} - 1695409 q^{52} - 203654 q^{53} - 9897559 q^{54} - 1024444 q^{55} + 5766846 q^{56} - 3908648 q^{57} - 5039991 q^{58} - 748892 q^{59} + 18153300 q^{60} - 61822 q^{61} - 4939277 q^{62} - 1411632 q^{63} + 2702267 q^{64} + 1571618 q^{65} - 3791866 q^{66} - 3235604 q^{67} - 4914980 q^{68} + 10871764 q^{70} - 4951664 q^{71} - 7940241 q^{72} + 11019370 q^{73} - 356954 q^{74} - 13607220 q^{75} - 21973240 q^{76} - 5284888 q^{77} - 1506779 q^{78} - 4202464 q^{79} - 8785886 q^{80} + 10294096 q^{81} + 32636759 q^{82} - 518568 q^{83} - 7629190 q^{84} + 9854220 q^{85} + 14681386 q^{86} + 4862532 q^{87} - 20589740 q^{88} - 4203864 q^{89} - 49021076 q^{90} - 2488406 q^{91} - 23367842 q^{93} + 12314327 q^{94} - 44485300 q^{95} - 45317009 q^{96} - 18621134 q^{97} + 35756 q^{98} + 64729930 q^{99}+O(q^{100}) \) 8 * q + 40 * q^3 + 640 * q^4 - 444 * q^5 - 1745 * q^6 - 1446 * q^7 + 3177 * q^8 + 13878 * q^9 - 19502 * q^10 - 7588 * q^11 + 22733 * q^12 + 19862 * q^13 - 17544 * q^14 + 12770 * q^15 + 64336 * q^16 - 42070 * q^17 - 59129 * q^18 - 1050 * q^19 - 3364 * q^20 + 7698 * q^21 + 128220 * q^22 - 621188 * q^24 + 49496 * q^25 - 371761 * q^26 - 69500 * q^27 - 143050 * q^28 - 102578 * q^29 + 671470 * q^30 + 304172 * q^31 - 612824 * q^32 - 747242 * q^33 + 524530 * q^34 + 531048 * q^35 + 1868983 * q^36 - 286472 * q^37 + 762932 * q^38 + 1032828 * q^39 - 2105286 * q^40 + 1324414 * q^41 + 1886168 * q^42 - 2052578 * q^43 + 867298 * q^44 - 2087442 * q^45 + 675556 * q^47 + 1411151 * q^48 - 55404 * q^49 + 1458528 * q^50 - 2775482 * q^51 - 1695409 * q^52 - 203654 * q^53 - 9897559 * q^54 - 1024444 * q^55 + 5766846 * q^56 - 3908648 * q^57 - 5039991 * q^58 - 748892 * q^59 + 18153300 * q^60 - 61822 * q^61 - 4939277 * q^62 - 1411632 * q^63 + 2702267 * q^64 + 1571618 * q^65 - 3791866 * q^66 - 3235604 * q^67 - 4914980 * q^68 + 10871764 * q^70 - 4951664 * q^71 - 7940241 * q^72 + 11019370 * q^73 - 356954 * q^74 - 13607220 * q^75 - 21973240 * q^76 - 5284888 * q^77 - 1506779 * q^78 - 4202464 * q^79 - 8785886 * q^80 + 10294096 * q^81 + 32636759 * q^82 - 518568 * q^83 - 7629190 * q^84 + 9854220 * q^85 + 14681386 * q^86 + 4862532 * q^87 - 20589740 * q^88 - 4203864 * q^89 - 49021076 * q^90 - 2488406 * q^91 - 23367842 * q^93 + 12314327 * q^94 - 44485300 * q^95 - 45317009 * q^96 - 18621134 * q^97 + 35756 * q^98 + 64729930 * 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 $

$2$	−21.3077	−1.88335	−0.941675	−	0.336524i	$-0.890749\pi$
$2$	−21.3077	−1.88335	−0.941675	+	0.336524i	$0.890749\pi$
$3$	86.9475	1.85923	0.929615	−	0.368533i	$-0.120140\pi$
$3$	86.9475	1.85923	0.929615	+	0.368533i	$0.120140\pi$
$4$	326.017	2.54701
$5$	188.239	0.673464	0.336732	−	0.941600i	$-0.390678\pi$
$5$	188.239	0.673464	0.336732	+	0.941600i	$0.390678\pi$
$6$	−1852.65	−3.50158
$7$	−639.155	−0.704309	−0.352154	−	0.935942i	$-0.614551\pi$
$7$	−639.155	−0.704309	−0.352154	+	0.935942i	$0.614551\pi$
$8$	−4219.28	−2.91355
$9$	5372.88	2.45673
$10$	−4010.94	−1.26837
$11$	1629.29	0.369083	0.184542	−	0.982825i	$-0.440920\pi$
$11$	1629.29	0.369083	0.184542	+	0.982825i	$0.440920\pi$
$12$	28346.4	4.73547
$13$	1138.20	0.143687	0.0718433	−	0.997416i	$-0.477112\pi$
$13$	1138.20	0.143687	0.0718433	+	0.997416i	$0.477112\pi$
$14$	13618.9	1.32646
$15$	16366.9	1.25212
$16$	48172.8	2.94024
$17$	−28713.3	−1.41746	−0.708732	−	0.705477i	$-0.750733\pi$
$17$	−28713.3	−1.41746	−0.708732	+	0.705477i	$0.750733\pi$
$18$	−114483.	−4.62689
$19$	−43387.0	−1.45118	−0.725591	−	0.688127i	$-0.758433\pi$
$19$	−43387.0	−1.45118	−0.725591	+	0.688127i	$0.758433\pi$
$20$	61369.1	1.71532
$21$	−55573.0	−1.30947
$22$	−34716.4	−0.695113
$23$	0	0
$23$	0	0
$24$	−366856.	−5.41697
$25$	−42691.1	−0.546446
$26$	−24252.3	−0.270612
$27$	277004.	2.70840
$28$	−208375.	−1.79388
$29$	62583.1	0.476502	0.238251	−	0.971204i	$-0.423426\pi$
$29$	62583.1	0.476502	0.238251	+	0.971204i	$0.423426\pi$
$30$	−348741.	−2.35819
$31$	22533.6	0.135851	0.0679257	−	0.997690i	$-0.478362\pi$
$31$	22533.6	0.135851	0.0679257	+	0.997690i	$0.478362\pi$
$32$	−486383.	−2.62394
$33$	141663.	0.686211
$34$	611814.	2.66958
$35$	−120314.	−0.474327
$36$	1.75165e6	6.25732
$37$	277384.	0.900276	0.450138	−	0.892959i	$-0.351375\pi$
$37$	277384.	0.900276	0.450138	+	0.892959i	$0.351375\pi$
$38$	924475.	2.73308
$39$	98963.5	0.267146
$40$	−794233.	−1.96218
$41$	−130110.	−0.294828	−0.147414	−	0.989075i	$-0.547095\pi$
$41$	−130110.	−0.294828	−0.147414	+	0.989075i	$0.547095\pi$
$42$	1.18413e6	2.46619
$43$	−585763.	−1.12352	−0.561762	−	0.827299i	$-0.689876\pi$
$43$	−585763.	−1.12352	−0.561762	+	0.827299i	$0.689876\pi$
$44$	531177.	0.940058
$45$	1.01138e6	1.65452
$46$	0	0
$47$	−99374.3	−0.139615	−0.0698074	−	0.997560i	$-0.522238\pi$
$47$	−99374.3	−0.139615	−0.0698074	+	0.997560i	$0.522238\pi$
$48$	4.18851e6	5.46657
$49$	−415024.	−0.503949
$50$	909647.	1.02915
$51$	−2.49655e6	−2.63539
$52$	371072.	0.365971
$53$	636910.	0.587641	0.293821	−	0.955861i	$-0.405073\pi$
$53$	636910.	0.587641	0.293821	+	0.955861i	$0.405073\pi$
$54$	−5.90231e6	−5.10087
$55$	306696.	0.248564
$56$	2.69677e6	2.05204
$57$	−3.77239e6	−2.69808
$58$	−1.33350e6	−0.897419
$59$	−808062.	−0.512227	−0.256114	−	0.966647i	$-0.582442\pi$
$59$	−808062.	−0.512227	−0.256114	+	0.966647i	$0.582442\pi$
$60$	5.33589e6	3.18917
$61$	2.40412e6	1.35613	0.678066	−	0.735001i	$-0.262818\pi$
$61$	2.40412e6	1.35613	0.678066	+	0.735001i	$0.262818\pi$
$62$	−480138.	−0.255856
$63$	−3.43410e6	−1.73030
$64$	4.19757e6	2.00156
$65$	214253.	0.0967678
$66$	−3.01851e6	−1.29237
$67$	2.05060e6	0.832949	0.416474	−	0.909147i	$-0.363266\pi$
$67$	2.05060e6	0.832949	0.416474	+	0.909147i	$0.363266\pi$
$68$	−9.36103e6	−3.61029
$69$	0	0
$70$	2.56361e6	0.893324
$71$	−3.83810e6	−1.27266	−0.636329	−	0.771417i	$-0.719548\pi$
$71$	−3.83810e6	−1.27266	−0.636329	+	0.771417i	$0.719548\pi$
$72$	−2.26697e7	−7.15783
$73$	−2.78541e6	−0.838029	−0.419015	−	0.907979i	$-0.637624\pi$
$73$	−2.78541e6	−0.838029	−0.419015	+	0.907979i	$0.637624\pi$
$74$	−5.91041e6	−1.69553
$75$	−3.71188e6	−1.01597
$76$	−1.41449e7	−3.69617
$77$	−1.04137e6	−0.259949
$78$	−2.10868e6	−0.503130
$79$	−7.20890e6	−1.64503	−0.822516	−	0.568742i	$-0.807430\pi$
$79$	−7.20890e6	−1.64503	−0.822516	+	0.568742i	$0.807430\pi$
$80$	9.06801e6	1.98014
$81$	1.23343e7	2.57881
$82$	2.77235e6	0.555264
$83$	498585.	0.0957120	0.0478560	−	0.998854i	$-0.484761\pi$
$83$	498585.	0.0957120	0.0478560	+	0.998854i	$0.484761\pi$
$84$	−1.81177e7	−3.33523
$85$	−5.40497e6	−0.954612
$86$	1.24813e7	2.11599
$87$	5.44145e6	0.885926
$88$	−6.87443e6	−1.07534
$89$	1.37216e6	0.206320	0.103160	−	0.994665i	$-0.467105\pi$
$89$	1.37216e6	0.206320	0.103160	+	0.994665i	$0.467105\pi$
$90$	−2.15503e7	−3.11604
$91$	−727485.	−0.101200
$92$	0	0
$93$	1.95924e6	0.252579
$94$	2.11743e6	0.262944
$95$	−8.16712e6	−0.977319
$96$	−4.22898e7	−4.87850
$97$	−6.57645e6	−0.731628	−0.365814	−	0.930688i	$-0.619209\pi$
$97$	−6.57645e6	−0.731628	−0.365814	+	0.930688i	$0.619209\pi$
$98$	8.84319e6	0.949112
$99$	8.75398e6	0.906739
$100$	−1.39180e7	−1.39180
$101$	−2.24529e6	−0.216844	−0.108422	−	0.994105i	$-0.534580\pi$
$101$	−2.24529e6	−0.216844	−0.108422	+	0.994105i	$0.534580\pi$
$102$	5.31957e7	4.96336
$103$	−2.14203e6	−0.193150	−0.0965751	−	0.995326i	$-0.530789\pi$
$103$	−2.14203e6	−0.193150	−0.0965751	+	0.995326i	$0.530789\pi$
$104$	−4.80237e6	−0.418639
$105$	−1.04610e7	−0.881883
$106$	−1.35711e7	−1.10673
$107$	−1.72640e7	−1.36238	−0.681189	−	0.732107i	$-0.738537\pi$
$107$	−1.72640e7	−1.36238	−0.681189	+	0.732107i	$0.738537\pi$
$108$	9.03080e7	6.89832
$109$	2.52636e7	1.86854	0.934269	−	0.356569i	$-0.116053\pi$
$109$	2.52636e7	1.86854	0.934269	+	0.356569i	$0.116053\pi$
$110$	−6.53498e6	−0.468134
$111$	2.41179e7	1.67382
$112$	−3.07899e7	−2.07083
$113$	−3.18384e6	−0.207576	−0.103788	−	0.994599i	$-0.533096\pi$
$113$	−3.18384e6	−0.207576	−0.103788	+	0.994599i	$0.533096\pi$
$114$	8.03808e7	5.08143
$115$	0	0
$116$	2.04032e7	1.21365
$117$	6.11540e6	0.353000
$118$	1.72179e7	0.964703
$119$	1.83523e7	0.998333
$120$	−6.90566e7	−3.64813
$121$	−1.68326e7	−0.863778
$122$	−5.12263e7	−2.55407
$123$	−1.13128e7	−0.548153
$124$	7.34632e6	0.346014
$125$	−2.27423e7	−1.04148
$126$	7.31727e7	3.25876
$127$	−2.02393e7	−0.876763	−0.438381	−	0.898789i	$-0.644448\pi$
$127$	−2.02393e7	−0.876763	−0.438381	+	0.898789i	$0.644448\pi$
$128$	−2.71834e7	−1.14570
$129$	−5.09307e7	−2.08889
$130$	−4.56524e6	−0.182248
$131$	−4.46018e7	−1.73342	−0.866708	−	0.498816i	$-0.833768\pi$
$131$	−4.46018e7	−1.73342	−0.866708	+	0.498816i	$0.833768\pi$
$132$	4.61845e7	1.74778
$133$	2.77310e7	1.02208
$134$	−4.36934e7	−1.56873
$135$	5.21430e7	1.82401
$136$	1.21149e8	4.12986
$137$	−2.84803e7	−0.946287	−0.473144	−	0.880985i	$-0.656881\pi$
$137$	−2.84803e7	−0.946287	−0.473144	+	0.880985i	$0.656881\pi$
$138$	0	0
$139$	−4.10033e7	−1.29499	−0.647495	−	0.762070i	$-0.724183\pi$
$139$	−4.10033e7	−1.29499	−0.647495	+	0.762070i	$0.724183\pi$
$140$	−3.92244e7	−1.20811
$141$	−8.64035e6	−0.259576
$142$	8.17810e7	2.39686
$143$	1.85446e6	0.0530323
$144$	2.58827e8	7.22338
$145$	1.17806e7	0.320907
$146$	5.93506e7	1.57830
$147$	−3.60853e7	−0.936957
$148$	9.04319e7	2.29301
$149$	1.46291e6	0.0362297	0.0181148	−	0.999836i	$-0.494234\pi$
$149$	1.46291e6	0.0362297	0.0181148	+	0.999836i	$0.494234\pi$
$150$	7.90916e7	1.91342
$151$	−1.38217e7	−0.326694	−0.163347	−	0.986569i	$-0.552229\pi$
$151$	−1.38217e7	−0.326694	−0.163347	+	0.986569i	$0.552229\pi$
$152$	1.83062e8	4.22810
$153$	−1.54273e8	−3.48233
$154$	2.21892e7	0.489574
$155$	4.24170e6	0.0914911
$156$	3.22638e7	0.680423
$157$	−2.49008e7	−0.513528	−0.256764	−	0.966474i	$-0.582656\pi$
$157$	−2.49008e7	−0.513528	−0.256764	+	0.966474i	$0.582656\pi$
$158$	1.53605e8	3.09817
$159$	5.53777e7	1.09256
$160$	−9.15563e7	−1.76713
$161$	0	0
$162$	−2.62816e8	−4.85679
$163$	8.38251e7	1.51606	0.758032	−	0.652218i	$-0.226161\pi$
$163$	8.38251e7	1.51606	0.758032	+	0.652218i	$0.226161\pi$
$164$	−4.24182e7	−0.750929
$165$	2.66665e7	0.462138
$166$	−1.06237e7	−0.180259
$167$	3.89864e7	0.647747	0.323873	−	0.946100i	$-0.395015\pi$
$167$	3.89864e7	0.647747	0.323873	+	0.946100i	$0.395015\pi$
$168$	2.34478e8	3.81522
$169$	−6.14530e7	−0.979354
$170$	1.15167e8	1.79787
$171$	−2.33113e8	−3.56517
$172$	−1.90969e8	−2.86162
$173$	9.35688e7	1.37395	0.686973	−	0.726683i	$-0.258939\pi$
$173$	9.35688e7	1.37395	0.686973	+	0.726683i	$0.258939\pi$
$174$	−1.15945e8	−1.66851
$175$	2.72862e7	0.384867
$176$	7.84876e7	1.08519
$177$	−7.02590e7	−0.952348
$178$	−2.92376e7	−0.388572
$179$	3.65707e7	0.476592	0.238296	−	0.971193i	$-0.423411\pi$
$179$	3.65707e7	0.476592	0.238296	+	0.971193i	$0.423411\pi$
$180$	3.29729e8	4.21408
$181$	−8.44628e6	−0.105874	−0.0529372	−	0.998598i	$-0.516858\pi$
$181$	−8.44628e6	−0.105874	−0.0529372	+	0.998598i	$0.516858\pi$
$182$	1.55010e7	0.190594
$183$	2.09033e8	2.52136
$184$	0	0
$185$	5.22145e7	0.606304
$186$	−4.17468e7	−0.475694
$187$	−4.67824e7	−0.523163
$188$	−3.23977e7	−0.355600
$189$	−1.77049e8	−1.90755
$190$	1.74022e8	1.84063
$191$	−1.13851e8	−1.18228	−0.591138	−	0.806570i	$-0.701321\pi$
$191$	−1.13851e8	−1.18228	−0.591138	+	0.806570i	$0.701321\pi$
$192$	3.64969e8	3.72136
$193$	1.22314e8	1.22469	0.612345	−	0.790591i	$-0.290226\pi$
$193$	1.22314e8	1.22469	0.612345	+	0.790591i	$0.290226\pi$
$194$	1.40129e8	1.37791
$195$	1.86288e7	0.179913
$196$	−1.35305e8	−1.28356
$197$	−1.16456e8	−1.08525	−0.542623	−	0.839976i	$-0.682569\pi$
$197$	−1.16456e8	−1.08525	−0.542623	+	0.839976i	$0.682569\pi$
$198$	−1.86527e8	−1.70771
$199$	1.76140e8	1.58443	0.792216	−	0.610241i	$-0.208928\pi$
$199$	1.76140e8	1.58443	0.792216	+	0.610241i	$0.208928\pi$
$200$	1.80125e8	1.59210
$201$	1.78294e8	1.54864
$202$	4.78418e7	0.408393
$203$	−4.00003e7	−0.335604
$204$	−8.13918e8	−6.71236
$205$	−2.44919e7	−0.198556
$206$	4.56416e7	0.363769
$207$	0	0
$208$	5.48302e7	0.422472
$209$	−7.06900e7	−0.535607
$210$	2.22900e8	1.66089
$211$	1.86839e8	1.36924	0.684620	−	0.728901i	$-0.259968\pi$
$211$	1.86839e8	1.36924	0.684620	+	0.728901i	$0.259968\pi$
$212$	2.07643e8	1.49673
$213$	−3.33713e8	−2.36616
$214$	3.67855e8	2.56584
$215$	−1.10263e8	−0.756654
$216$	−1.16876e9	−7.89108
$217$	−1.44024e7	−0.0956813
$218$	−5.38308e8	−3.51911
$219$	−2.42185e8	−1.55809
$220$	9.99881e7	0.633095
$221$	−3.26814e7	−0.203671
$222$	−5.13896e8	−3.15239
$223$	−1.16234e8	−0.701884	−0.350942	−	0.936397i	$-0.614139\pi$
$223$	−1.16234e8	−0.701884	−0.350942	+	0.936397i	$0.614139\pi$
$224$	3.10874e8	1.84806
$225$	−2.29374e8	−1.34247
$226$	6.78402e7	0.390938
$227$	1.60833e8	0.912609	0.456304	−	0.889824i	$-0.349173\pi$
$227$	1.60833e8	0.912609	0.456304	+	0.889824i	$0.349173\pi$
$228$	−1.22986e9	−6.87202
$229$	1.58215e8	0.870610	0.435305	−	0.900283i	$-0.356641\pi$
$229$	1.58215e8	0.870610	0.435305	+	0.900283i	$0.356641\pi$
$230$	0	0
$231$	−9.05446e7	−0.483304
$232$	−2.64056e8	−1.38831
$233$	6.74565e7	0.349364	0.174682	−	0.984625i	$-0.444110\pi$
$233$	6.74565e7	0.349364	0.174682	+	0.984625i	$0.444110\pi$
$234$	−1.30305e8	−0.664822
$235$	−1.87061e7	−0.0940256
$236$	−2.63442e8	−1.30465
$237$	−6.26796e8	−3.05849
$238$	−3.91044e8	−1.88021
$239$	1.29369e8	0.612968	0.306484	−	0.951876i	$-0.400847\pi$
$239$	1.29369e8	0.612968	0.306484	+	0.951876i	$0.400847\pi$
$240$	7.88441e8	3.68154
$241$	−4.84417e7	−0.222925	−0.111463	−	0.993769i	$-0.535554\pi$
$241$	−4.84417e7	−0.222925	−0.111463	+	0.993769i	$0.535554\pi$
$242$	3.58663e8	1.62680
$243$	4.66633e8	2.08619
$244$	7.83784e8	3.45408
$245$	−7.81236e7	−0.339392
$246$	2.41049e8	1.03236
$247$	−4.93830e7	−0.208515
$248$	−9.50754e7	−0.395810
$249$	4.33508e7	0.177951
$250$	4.84585e8	1.96146
$251$	−3.23668e8	−1.29194	−0.645968	−	0.763364i	$-0.723546\pi$
$251$	−3.23668e8	−1.29194	−0.645968	+	0.763364i	$0.723546\pi$
$252$	−1.11958e9	−4.40708
$253$	0	0
$254$	4.31252e8	1.65125
$255$	−4.69949e8	−1.77484
$256$	4.19262e7	0.156187
$257$	3.44328e7	0.126534	0.0632670	−	0.997997i	$-0.479848\pi$
$257$	3.44328e7	0.126534	0.0632670	+	0.997997i	$0.479848\pi$
$258$	1.08521e9	3.93411
$259$	−1.77292e8	−0.634072
$260$	6.98502e7	0.246468
$261$	3.36251e8	1.17064
$262$	9.50360e8	3.26463
$263$	7.34996e7	0.249138	0.124569	−	0.992211i	$-0.460245\pi$
$263$	7.34996e7	0.249138	0.124569	+	0.992211i	$0.460245\pi$
$264$	−5.97715e8	−1.99931
$265$	1.19891e8	0.395756
$266$	−5.90883e8	−1.92493
$267$	1.19306e8	0.383595
$268$	6.68529e8	2.12153
$269$	−3.31972e8	−1.03984	−0.519922	−	0.854213i	$-0.674039\pi$
$269$	−3.31972e8	−1.03984	−0.519922	+	0.854213i	$0.674039\pi$
$270$	−1.11105e9	−3.43525
$271$	−6.60070e7	−0.201464	−0.100732	−	0.994914i	$-0.532118\pi$
$271$	−6.60070e7	−0.201464	−0.100732	+	0.994914i	$0.532118\pi$
$272$	−1.38320e9	−4.16768
$273$	−6.32531e7	−0.188153
$274$	6.06849e8	1.78219
$275$	−6.95562e7	−0.201684
$276$	0	0
$277$	−5.05242e8	−1.42830	−0.714151	−	0.699991i	$-0.753187\pi$
$277$	−5.05242e8	−1.42830	−0.714151	+	0.699991i	$0.753187\pi$
$278$	8.73684e8	2.43892
$279$	1.21070e8	0.333751
$280$	5.07638e8	1.38198
$281$	−6.11069e8	−1.64293	−0.821463	−	0.570262i	$-0.806842\pi$
$281$	−6.11069e8	−1.64293	−0.821463	+	0.570262i	$0.806842\pi$
$282$	1.84106e8	0.488872
$283$	−1.33286e8	−0.349567	−0.174784	−	0.984607i	$-0.555923\pi$
$283$	−1.33286e8	−0.349567	−0.174784	+	0.984607i	$0.555923\pi$
$284$	−1.25128e9	−3.24147
$285$	−7.10111e8	−1.81706
$286$	−3.95141e7	−0.0998784
$287$	8.31608e7	0.207650
$288$	−2.61328e9	−6.44632
$289$	4.14116e8	1.00921
$290$	−2.51017e8	−0.604380
$291$	−5.71806e8	−1.36026
$292$	−9.08091e8	−2.13447
$293$	4.33046e8	1.00577	0.502884	−	0.864354i	$-0.332272\pi$
$293$	4.33046e8	1.00577	0.502884	+	0.864354i	$0.332272\pi$
$294$	7.68893e8	1.76462
$295$	−1.52109e8	−0.344967
$296$	−1.17036e9	−2.62300
$297$	4.51321e8	0.999626
$298$	−3.11711e7	−0.0682332
$299$	0	0
$300$	−1.21014e9	−2.58768
$301$	3.74394e8	0.791308
$302$	2.94508e8	0.615280
$303$	−1.95222e8	−0.403162
$304$	−2.09007e9	−4.26681
$305$	4.52550e8	0.913307
$306$	3.28720e9	6.55845
$307$	9.27048e8	1.82860	0.914298	−	0.405042i	$-0.132743\pi$
$307$	9.27048e8	1.82860	0.914298	+	0.405042i	$0.132743\pi$
$308$	−3.39504e8	−0.662091
$309$	−1.86244e8	−0.359110
$310$	−9.03807e7	−0.172310
$311$	−9.34538e8	−1.76172	−0.880858	−	0.473381i	$-0.843033\pi$
$311$	−9.34538e8	−1.76172	−0.880858	+	0.473381i	$0.843033\pi$
$312$	−4.17555e8	−0.778345
$313$	7.84627e7	0.144630	0.0723149	−	0.997382i	$-0.476961\pi$
$313$	7.84627e7	0.144630	0.0723149	+	0.997382i	$0.476961\pi$
$314$	5.30578e8	0.967154
$315$	−6.46432e8	−1.16530
$316$	−2.35022e9	−4.18991
$317$	1.46811e8	0.258851	0.129426	−	0.991589i	$-0.458687\pi$
$317$	1.46811e8	0.258851	0.129426	+	0.991589i	$0.458687\pi$
$318$	−1.17997e9	−2.05767
$319$	1.01966e8	0.175869
$320$	7.90147e8	1.34798
$321$	−1.50106e9	−2.53297
$322$	0	0
$323$	1.24578e9	2.05700
$324$	4.02121e9	6.56824
$325$	−4.85909e7	−0.0785169
$326$	−1.78612e9	−2.85528
$327$	2.19661e9	3.47404
$328$	5.48972e8	0.858998
$329$	6.35156e7	0.0983320
$330$	−5.68201e8	−0.870368
$331$	−5.09422e8	−0.772111	−0.386055	−	0.922476i	$-0.626163\pi$
$331$	−5.09422e8	−0.772111	−0.386055	+	0.922476i	$0.626163\pi$
$332$	1.62547e8	0.243779
$333$	1.49035e9	2.21174
$334$	−8.30709e8	−1.21993
$335$	3.86002e8	0.560961
$336$	−2.67711e9	−3.85016
$337$	1.03024e9	1.46633	0.733166	−	0.680050i	$-0.238042\pi$
$337$	1.03024e9	1.46633	0.733166	+	0.680050i	$0.238042\pi$
$338$	1.30942e9	1.84447
$339$	−2.76827e8	−0.385931
$340$	−1.76211e9	−2.43140
$341$	3.67138e7	0.0501405
$342$	4.96709e9	6.71445
$343$	7.91636e8	1.05924
$344$	2.47150e9	3.27345
$345$	0	0
$346$	−1.99373e9	−2.58762
$347$	−1.22094e9	−1.56871	−0.784354	−	0.620313i	$-0.787006\pi$
$347$	−1.22094e9	−1.56871	−0.784354	+	0.620313i	$0.787006\pi$
$348$	1.77400e9	2.25646
$349$	1.05987e9	1.33464	0.667320	−	0.744771i	$-0.267441\pi$
$349$	1.05987e9	1.33464	0.667320	+	0.744771i	$0.267441\pi$
$350$	−5.81406e8	−0.724838
$351$	3.15286e8	0.389161
$352$	−7.92460e8	−0.968452
$353$	8.39230e8	1.01548	0.507738	−	0.861512i	$-0.330482\pi$
$353$	8.39230e8	1.01548	0.507738	+	0.861512i	$0.330482\pi$
$354$	1.49706e9	1.79360
$355$	−7.22480e8	−0.857090
$356$	4.47348e8	0.525497
$357$	1.59569e9	1.85613
$358$	−7.79236e8	−0.897590
$359$	−7.38651e8	−0.842576	−0.421288	−	0.906927i	$-0.638422\pi$
$359$	−7.38651e8	−0.842576	−0.421288	+	0.906927i	$0.638422\pi$
$360$	−4.26731e9	−4.82054
$361$	9.88556e8	1.10593
$362$	1.79971e8	0.199398
$363$	−1.46355e9	−1.60596
$364$	−2.37172e8	−0.257756
$365$	−5.24323e8	−0.564383
$366$	−4.45400e9	−4.74861
$367$	−1.62094e9	−1.71174	−0.855868	−	0.517194i	$-0.826976\pi$
$367$	−1.62094e9	−1.71174	−0.855868	+	0.517194i	$0.826976\pi$
$368$	0	0
$369$	−6.99067e8	−0.724314
$370$	−1.11257e9	−1.14188
$371$	−4.07084e8	−0.413881
$372$	6.38745e8	0.643320
$373$	−1.09809e9	−1.09562	−0.547808	−	0.836604i	$-0.684537\pi$
$373$	−1.09809e9	−1.09562	−0.547808	+	0.836604i	$0.684537\pi$
$374$	9.96824e8	0.985298
$375$	−1.97739e9	−1.93634
$376$	4.19288e8	0.406775
$377$	7.12320e7	0.0684669
$378$	3.77249e9	3.59259
$379$	−9.27372e7	−0.0875018	−0.0437509	−	0.999042i	$-0.513931\pi$
$379$	−9.27372e7	−0.0875018	−0.0437509	+	0.999042i	$0.513931\pi$
$380$	−2.66262e9	−2.48924
$381$	−1.75976e9	−1.63010
$382$	2.42589e9	2.22664
$383$	8.14572e8	0.740856	0.370428	−	0.928861i	$-0.379211\pi$
$383$	8.14572e8	0.740856	0.370428	+	0.928861i	$0.379211\pi$
$384$	−2.36353e9	−2.13011
$385$	−1.96027e8	−0.175066
$386$	−2.60623e9	−2.30652
$387$	−3.14723e9	−2.76020
$388$	−2.14403e9	−1.86346
$389$	1.35871e9	1.17032	0.585159	−	0.810919i	$-0.301032\pi$
$389$	1.35871e9	1.17032	0.585159	+	0.810919i	$0.301032\pi$
$390$	−3.96936e8	−0.338840
$391$	0	0
$392$	1.75110e9	1.46828
$393$	−3.87802e9	−3.22282
$394$	2.48140e9	2.04390
$395$	−1.35700e9	−1.10787
$396$	2.85395e9	2.30947
$397$	2.07777e9	1.66660	0.833300	−	0.552821i	$-0.186449\pi$
$397$	2.07777e9	1.66660	0.833300	+	0.552821i	$0.186449\pi$
$398$	−3.75314e9	−2.98404
$399$	2.41114e9	1.90028
$400$	−2.05655e9	−1.60668
$401$	9.70183e8	0.751361	0.375680	−	0.926749i	$-0.377409\pi$
$401$	9.70183e8	0.751361	0.375680	+	0.926749i	$0.377409\pi$
$402$	−3.79904e9	−2.91664
$403$	2.56477e7	0.0195200
$404$	−7.32001e8	−0.552303
$405$	2.32181e9	1.73673
$406$	8.52314e8	0.632060
$407$	4.51940e8	0.332277
$408$	1.05337e10	7.67836
$409$	−4.43084e7	−0.0320224	−0.0160112	−	0.999872i	$-0.505097\pi$
$409$	−4.43084e7	−0.0320224	−0.0160112	+	0.999872i	$0.505097\pi$
$410$	5.21865e8	0.373951
$411$	−2.47629e9	−1.75936
$412$	−6.98338e8	−0.491955
$413$	5.16477e8	0.360766
$414$	0	0
$415$	9.38532e7	0.0644586
$416$	−5.53600e8	−0.377025
$417$	−3.56513e9	−2.40768
$418$	1.50624e9	1.00873
$419$	−7.38219e8	−0.490271	−0.245135	−	0.969489i	$-0.578832\pi$
$419$	−7.38219e8	−0.490271	−0.245135	+	0.969489i	$0.578832\pi$
$420$	−3.41046e9	−2.24616
$421$	−1.11608e8	−0.0728967	−0.0364483	−	0.999336i	$-0.511604\pi$
$421$	−1.11608e8	−0.0728967	−0.0364483	+	0.999336i	$0.511604\pi$
$422$	−3.98111e9	−2.57876
$423$	−5.33926e8	−0.342996
$424$	−2.68730e9	−1.71213
$425$	1.22580e9	0.774567
$426$	7.11065e9	4.45632
$427$	−1.53661e9	−0.955136
$428$	−5.62835e9	−3.46999
$429$	1.61240e8	0.0985992
$430$	2.34946e9	1.42504
$431$	−1.89063e9	−1.13746	−0.568730	−	0.822524i	$-0.692565\pi$
$431$	−1.89063e9	−1.13746	−0.568730	+	0.822524i	$0.692565\pi$
$432$	1.33441e10	7.96334
$433$	7.97013e8	0.471800	0.235900	−	0.971777i	$-0.424196\pi$
$433$	7.97013e8	0.471800	0.235900	+	0.971777i	$0.424196\pi$
$434$	3.06883e8	0.180201
$435$	1.02429e9	0.596639
$436$	8.23635e9	4.75918
$437$	0	0
$438$	5.16039e9	2.93443
$439$	3.82327e8	0.215679	0.107840	−	0.994168i	$-0.465607\pi$
$439$	3.82327e8	0.215679	0.107840	+	0.994168i	$0.465607\pi$
$440$	−1.29404e9	−0.724206
$441$	−2.22987e9	−1.23807
$442$	6.96366e8	0.383583
$443$	−2.31678e9	−1.26611	−0.633056	−	0.774106i	$-0.718200\pi$
$443$	−2.31678e9	−1.26611	−0.633056	+	0.774106i	$0.718200\pi$
$444$	7.86283e9	4.26323
$445$	2.58294e8	0.138949
$446$	2.47667e9	1.32189
$447$	1.27196e8	0.0673593
$448$	−2.68290e9	−1.40972
$449$	4.47596e8	0.233358	0.116679	−	0.993170i	$-0.462775\pi$
$449$	4.47596e8	0.233358	0.116679	+	0.993170i	$0.462775\pi$
$450$	4.88742e9	2.52834
$451$	−2.11988e8	−0.108816
$452$	−1.03799e9	−0.528697
$453$	−1.20176e9	−0.607399
$454$	−3.42698e9	−1.71876
$455$	−1.36941e8	−0.0681544
$456$	1.59168e10	7.86100
$457$	−2.31021e9	−1.13226	−0.566128	−	0.824317i	$-0.691559\pi$
$457$	−2.31021e9	−1.13226	−0.566128	+	0.824317i	$0.691559\pi$
$458$	−3.37119e9	−1.63966
$459$	−7.95371e9	−3.83906
$460$	0	0
$461$	−1.90114e9	−0.903777	−0.451888	−	0.892075i	$-0.649249\pi$
$461$	−1.90114e9	−0.903777	−0.451888	+	0.892075i	$0.649249\pi$
$462$	1.92929e9	0.910231
$463$	8.12980e8	0.380668	0.190334	−	0.981719i	$-0.439043\pi$
$463$	8.12980e8	0.380668	0.190334	+	0.981719i	$0.439043\pi$
$464$	3.01481e9	1.40103
$465$	3.68805e8	0.170103
$466$	−1.43734e9	−0.657975
$467$	2.31278e9	1.05081	0.525406	−	0.850852i	$-0.323914\pi$
$467$	2.31278e9	1.05081	0.525406	+	0.850852i	$0.323914\pi$
$468$	1.99372e9	0.899092
$469$	−1.31065e9	−0.586653
$470$	3.98584e8	0.177083
$471$	−2.16506e9	−0.954767
$472$	3.40944e9	1.49240
$473$	−9.54379e8	−0.414674
$474$	1.33556e10	5.76021
$475$	1.85224e9	0.792992
$476$	5.98315e9	2.54276
$477$	3.42204e9	1.44368
$478$	−2.75655e9	−1.15443
$479$	−2.05808e9	−0.855634	−0.427817	−	0.903865i	$-0.640717\pi$
$479$	−2.05808e9	−0.855634	−0.427817	+	0.903865i	$0.640717\pi$
$480$	−7.96060e9	−3.28550
$481$	3.15718e8	0.129358
$482$	1.03218e9	0.419847
$483$	0	0
$484$	−5.48770e9	−2.20005
$485$	−1.23794e9	−0.492725
$486$	−9.94287e9	−3.92903
$487$	−2.99505e8	−0.117504	−0.0587520	−	0.998273i	$-0.518712\pi$
$487$	−2.99505e8	−0.117504	−0.0587520	+	0.998273i	$0.518712\pi$
$488$	−1.01437e10	−3.95117
$489$	7.28838e9	2.81871
$490$	1.66463e9	0.639193
$491$	−1.40636e9	−0.536182	−0.268091	−	0.963394i	$-0.586393\pi$
$491$	−1.40636e9	−0.536182	−0.268091	+	0.963394i	$0.586393\pi$
$492$	−3.68816e9	−1.39615
$493$	−1.79697e9	−0.675424
$494$	1.05224e9	0.392707
$495$	1.64784e9	0.610657
$496$	1.08551e9	0.399435
$497$	2.45314e9	0.896345
$498$	−9.23704e8	−0.335143
$499$	−6.52753e8	−0.235178	−0.117589	−	0.993062i	$-0.537517\pi$
$499$	−6.52753e8	−0.235178	−0.117589	+	0.993062i	$0.537517\pi$
$500$	−7.41437e9	−2.65265
$501$	3.38977e9	1.20431
$502$	6.89660e9	2.43317
$503$	4.89782e9	1.71599	0.857995	−	0.513658i	$-0.171710\pi$
$503$	4.89782e9	1.71599	0.857995	+	0.513658i	$0.171710\pi$
$504$	1.44894e10	5.04132
$505$	−4.22651e8	−0.146037
$506$	0	0
$507$	−5.34319e9	−1.82084
$508$	−6.59835e9	−2.23312
$509$	−4.40431e9	−1.48035	−0.740177	−	0.672412i	$-0.765259\pi$
$509$	−4.40431e9	−1.48035	−0.740177	+	0.672412i	$0.765259\pi$
$510$	1.00135e10	3.34265
$511$	1.78031e9	0.590231
$512$	2.58613e9	0.851540
$513$	−1.20184e10	−3.93038
$514$	−7.33684e8	−0.238308
$515$	−4.03213e8	−0.130080
$516$	−1.66043e10	−5.32042
$517$	−1.61910e8	−0.0515295
$518$	3.77767e9	1.19418
$519$	8.13557e9	2.55448
$520$	−9.03994e8	−0.281938
$521$	−4.10159e9	−1.27063	−0.635317	−	0.772251i	$-0.719131\pi$
$521$	−4.10159e9	−1.27063	−0.635317	+	0.772251i	$0.719131\pi$
$522$	−7.16473e9	−2.20472
$523$	2.81959e8	0.0861846	0.0430923	−	0.999071i	$-0.486279\pi$
$523$	2.81959e8	0.0861846	0.0430923	+	0.999071i	$0.486279\pi$
$524$	−1.45409e10	−4.41502
$525$	2.37247e9	0.715555
$526$	−1.56610e9	−0.469214
$527$	−6.47014e8	−0.192565
$528$	6.82430e9	2.01762
$529$	0	0
$530$	−2.55460e9	−0.745346
$531$	−4.34162e9	−1.25841
$532$	9.04077e9	2.60324
$533$	−1.48091e8	−0.0423628
$534$	−2.54214e9	−0.722444
$535$	−3.24976e9	−0.917513
$536$	−8.65204e9	−2.42684
$537$	3.17973e9	0.886095
$538$	7.07355e9	1.95839
$539$	−6.76194e8	−0.185999
$540$	1.69995e10	4.64577
$541$	5.49037e9	1.49077	0.745386	−	0.666634i	$-0.232265\pi$
$541$	5.49037e9	1.49077	0.745386	+	0.666634i	$0.232265\pi$
$542$	1.40646e9	0.379427
$543$	−7.34384e8	−0.196845
$544$	1.39657e10	3.71934
$545$	4.75559e9	1.25839
$546$	1.34778e9	0.354359
$547$	−1.46859e9	−0.383659	−0.191829	−	0.981428i	$-0.561442\pi$
$547$	−1.46859e9	−0.383659	−0.191829	+	0.981428i	$0.561442\pi$
$548$	−9.28507e9	−2.41020
$549$	1.29171e10	3.33166
$550$	1.48208e9	0.379842
$551$	−2.71529e9	−0.691490
$552$	0	0
$553$	4.60761e9	1.15861
$554$	1.07655e10	2.68999
$555$	4.53992e9	1.12726
$556$	−1.33678e10	−3.29835
$557$	−9.24360e8	−0.226646	−0.113323	−	0.993558i	$-0.536149\pi$
$557$	−9.24360e8	−0.226646	−0.113323	+	0.993558i	$0.536149\pi$
$558$	−2.57972e9	−0.628569
$559$	−6.66715e8	−0.161435
$560$	−5.79586e9	−1.39463
$561$	−4.06761e9	−0.972679
$562$	1.30205e10	3.09420
$563$	6.05124e9	1.42911	0.714554	−	0.699581i	$-0.246630\pi$
$563$	6.05124e9	1.42911	0.714554	+	0.699581i	$0.246630\pi$
$564$	−2.81690e9	−0.661142
$565$	−5.99323e8	−0.139795
$566$	2.84001e9	0.658357
$567$	−7.88356e9	−1.81628
$568$	1.61940e10	3.70796
$569$	2.41253e9	0.549009	0.274504	−	0.961586i	$-0.411486\pi$
$569$	2.41253e9	0.549009	0.274504	+	0.961586i	$0.411486\pi$
$570$	1.51308e10	3.42216
$571$	8.05596e8	0.181089	0.0905443	−	0.995892i	$-0.471139\pi$
$571$	8.05596e8	0.181089	0.0905443	+	0.995892i	$0.471139\pi$
$572$	6.04584e8	0.135074
$573$	−9.89905e9	−2.19812
$574$	−1.77196e9	−0.391078
$575$	0	0
$576$	2.25530e10	4.91729
$577$	−5.18931e8	−0.112459	−0.0562295	−	0.998418i	$-0.517908\pi$
$577$	−5.18931e8	−0.112459	−0.0562295	+	0.998418i	$0.517908\pi$
$578$	−8.82385e9	−1.90069
$579$	1.06349e10	2.27698
$580$	3.84067e9	0.817352
$581$	−3.18673e8	−0.0674108
$582$	1.21839e10	2.56185
$583$	1.03771e9	0.216889
$584$	1.17524e10	2.44164
$585$	1.15116e9	0.237733
$586$	−9.22720e9	−1.89421
$587$	−8.20772e9	−1.67490	−0.837450	−	0.546513i	$-0.815955\pi$
$587$	−8.20772e9	−1.67490	−0.837450	+	0.546513i	$0.815955\pi$
$588$	−1.17644e10	−2.38643
$589$	−9.77663e8	−0.197145
$590$	3.24108e9	0.649693
$591$	−1.01255e10	−2.01772
$592$	1.33624e10	2.64702
$593$	−2.50638e9	−0.493577	−0.246789	−	0.969069i	$-0.579375\pi$
$593$	−2.50638e9	−0.493577	−0.246789	+	0.969069i	$0.579375\pi$
$594$	−9.61659e9	−1.88265
$595$	3.45461e9	0.672342
$596$	4.76932e8	0.0922772
$597$	1.53150e10	2.94582
$598$	0	0
$599$	−6.57651e9	−1.25026	−0.625131	−	0.780519i	$-0.714955\pi$
$599$	−6.57651e9	−1.25026	−0.625131	+	0.780519i	$0.714955\pi$
$600$	1.56615e10	2.96008
$601$	7.94544e9	1.49299	0.746496	−	0.665390i	$-0.231735\pi$
$601$	7.94544e9	1.49299	0.746496	+	0.665390i	$0.231735\pi$
$602$	−7.97746e9	−1.49031
$603$	1.10176e10	2.04633
$604$	−4.50610e9	−0.832092
$605$	−3.16855e9	−0.581723
$606$	4.15973e9	0.759296
$607$	2.68877e9	0.487970	0.243985	−	0.969779i	$-0.421545\pi$
$607$	2.68877e9	0.487970	0.243985	+	0.969779i	$0.421545\pi$
$608$	2.11027e10	3.80781
$609$	−3.47793e9	−0.623965
$610$	−9.64278e9	−1.72008
$611$	−1.13108e8	−0.0200608
$612$	−5.02956e10	−8.86953
$613$	−8.66814e9	−1.51990	−0.759949	−	0.649983i	$-0.774776\pi$
$613$	−8.66814e9	−1.51990	−0.759949	+	0.649983i	$0.774776\pi$
$614$	−1.97532e10	−3.44389
$615$	−2.12951e9	−0.369161
$616$	4.39383e9	0.757375
$617$	−1.12347e10	−1.92559	−0.962795	−	0.270232i	$-0.912900\pi$
$617$	−1.12347e10	−1.92559	−0.962795	+	0.270232i	$0.912900\pi$
$618$	3.96843e9	0.676331
$619$	−2.76878e9	−0.469215	−0.234607	−	0.972090i	$-0.575380\pi$
$619$	−2.76878e9	−0.469215	−0.234607	+	0.972090i	$0.575380\pi$
$620$	1.38286e9	0.233028
$621$	0	0
$622$	1.99128e10	3.31793
$623$	−8.77024e8	−0.145313
$624$	4.76735e9	0.785473
$625$	−9.45748e8	−0.154951
$626$	−1.67186e9	−0.272389
$627$	−6.14632e9	−0.995816
$628$	−8.11808e9	−1.30796
$629$	−7.96462e9	−1.27611
$630$	1.37740e10	2.19466
$631$	2.81973e7	0.00446791	0.00223396	−	0.999998i	$-0.499289\pi$
$631$	2.81973e7	0.00446791	0.00223396	+	0.999998i	$0.499289\pi$
$632$	3.04164e10	4.79289
$633$	1.62452e10	2.54573
$634$	−3.12820e9	−0.487508
$635$	−3.80982e9	−0.590469
$636$	1.80541e10	2.78276
$637$	−4.72379e8	−0.0724107
$638$	−2.17266e9	−0.331222
$639$	−2.06216e10	−3.12658
$640$	−5.11698e9	−0.771585
$641$	−6.22935e9	−0.934199	−0.467100	−	0.884205i	$-0.654701\pi$
$641$	−6.22935e9	−0.934199	−0.467100	+	0.884205i	$0.654701\pi$
$642$	3.19841e10	4.77048
$643$	−9.36940e8	−0.138987	−0.0694934	−	0.997582i	$-0.522138\pi$
$643$	−9.36940e8	−0.138987	−0.0694934	+	0.997582i	$0.522138\pi$
$644$	0	0
$645$	−9.58714e9	−1.40679
$646$	−2.65448e10	−3.87405
$647$	−1.71887e9	−0.249504	−0.124752	−	0.992188i	$-0.539814\pi$
$647$	−1.71887e9	−0.249504	−0.124752	+	0.992188i	$0.539814\pi$
$648$	−5.20420e10	−7.51349
$649$	−1.31657e9	−0.189054
$650$	1.03536e9	0.147875
$651$	−1.25226e9	−0.177894
$652$	2.73284e10	3.86142
$653$	1.11139e10	1.56196	0.780981	−	0.624554i	$-0.214719\pi$
$653$	1.11139e10	1.56196	0.780981	+	0.624554i	$0.214719\pi$
$654$	−4.68046e10	−6.54283
$655$	−8.39579e9	−1.16739
$656$	−6.26779e9	−0.866864
$657$	−1.49657e10	−2.05881
$658$	−1.35337e9	−0.185194
$659$	−2.55105e9	−0.347232	−0.173616	−	0.984813i	$-0.555545\pi$
$659$	−2.55105e9	−0.347232	−0.173616	+	0.984813i	$0.555545\pi$
$660$	8.69372e9	1.17707
$661$	1.34691e10	1.81399	0.906993	−	0.421146i	$-0.138372\pi$
$661$	1.34691e10	1.81399	0.906993	+	0.421146i	$0.138372\pi$
$662$	1.08546e10	1.45415
$663$	−2.84157e9	−0.378670
$664$	−2.10367e9	−0.278862
$665$	5.22006e9	0.688334
$666$	−3.17559e10	−4.16548
$667$	0	0
$668$	1.27102e10	1.64981
$669$	−1.01062e10	−1.30496
$670$	−8.22481e9	−1.05649
$671$	3.91702e9	0.500526
$672$	2.70298e10	3.43597
$673$	1.20855e9	0.152831	0.0764154	−	0.997076i	$-0.475652\pi$
$673$	1.20855e9	0.152831	0.0764154	+	0.997076i	$0.475652\pi$
$674$	−2.19519e10	−2.76162
$675$	−1.18256e10	−1.47999
$676$	−2.00347e10	−2.49442
$677$	−1.03356e10	−1.28019	−0.640097	−	0.768294i	$-0.721106\pi$
$677$	−1.03356e10	−1.28019	−0.640097	+	0.768294i	$0.721106\pi$
$678$	5.89854e9	0.726843
$679$	4.20337e9	0.515292
$680$	2.28051e10	2.78131
$681$	1.39840e10	1.69675
$682$	−7.82285e8	−0.0944321
$683$	4.58153e8	0.0550223	0.0275111	−	0.999621i	$-0.491242\pi$
$683$	4.58153e8	0.0550223	0.0275111	+	0.999621i	$0.491242\pi$
$684$	−7.59987e10	−9.08050
$685$	−5.36111e9	−0.637291
$686$	−1.68679e10	−1.99493
$687$	1.37564e10	1.61866
$688$	−2.82179e10	−3.30343
$689$	7.24929e8	0.0844362
$690$	0	0
$691$	−6.02963e9	−0.695212	−0.347606	−	0.937641i	$-0.613005\pi$
$691$	−6.02963e9	−0.695212	−0.347606	+	0.937641i	$0.613005\pi$
$692$	3.05050e10	3.49945
$693$	−5.59515e9	−0.638625
$694$	2.60155e10	2.95443
$695$	−7.71841e9	−0.872130
$696$	−2.29590e10	−2.58119
$697$	3.73590e9	0.417908
$698$	−2.25834e10	−2.51360
$699$	5.86518e9	0.649548
$700$	8.89577e9	0.980258
$701$	−9.96825e9	−1.09296	−0.546482	−	0.837471i	$-0.684033\pi$
$701$	−9.96825e9	−1.09296	−0.546482	+	0.837471i	$0.684033\pi$
$702$	−6.71800e9	−0.732926
$703$	−1.20349e10	−1.30646
$704$	6.83907e9	0.738742
$705$	−1.62645e9	−0.174815
$706$	−1.78820e10	−1.91250
$707$	1.43509e9	0.152725
$708$	−2.29056e10	−2.42564
$709$	−4.66397e9	−0.491466	−0.245733	−	0.969338i	$-0.579029\pi$
$709$	−4.66397e9	−0.491466	−0.245733	+	0.969338i	$0.579029\pi$
$710$	1.53944e10	1.61420
$711$	−3.87325e10	−4.04140
$712$	−5.78953e9	−0.601123
$713$	0	0
$714$	−3.40003e10	−3.49574
$715$	3.49081e8	0.0357154
$716$	1.19227e10	1.21388
$717$	1.12483e10	1.13965
$718$	1.57389e10	1.58686
$719$	−3.16368e9	−0.317426	−0.158713	−	0.987325i	$-0.550734\pi$
$719$	−3.16368e9	−0.317426	−0.158713	+	0.987325i	$0.550734\pi$
$720$	4.87213e10	4.86469
$721$	1.36909e9	0.136037
$722$	−2.10638e10	−2.08285
$723$	−4.21189e9	−0.414470
$724$	−2.75363e9	−0.269663
$725$	−2.67174e9	−0.260382
$726$	3.11849e10	3.02459
$727$	−5.00250e9	−0.482855	−0.241428	−	0.970419i	$-0.577616\pi$
$727$	−5.00250e9	−0.482855	−0.241428	+	0.970419i	$0.577616\pi$
$728$	3.06946e9	0.294851
$729$	1.35974e10	1.29990
$730$	1.11721e10	1.06293
$731$	1.68192e10	1.59256
$732$	6.81481e10	6.42192
$733$	3.68820e9	0.345900	0.172950	−	0.984931i	$-0.444670\pi$
$733$	3.68820e9	0.345900	0.172950	+	0.984931i	$0.444670\pi$
$734$	3.45385e10	3.22380
$735$	−6.79266e9	−0.631007
$736$	0	0
$737$	3.34102e9	0.307428
$738$	1.48955e10	1.36414
$739$	−2.90694e9	−0.264960	−0.132480	−	0.991186i	$-0.542294\pi$
$739$	−2.90694e9	−0.264960	−0.132480	+	0.991186i	$0.542294\pi$
$740$	1.70228e10	1.54426
$741$	−4.29373e9	−0.387678
$742$	8.67402e9	0.779483
$743$	1.70273e9	0.152295	0.0761473	−	0.997097i	$-0.475738\pi$
$743$	1.70273e9	0.152295	0.0761473	+	0.997097i	$0.475738\pi$
$744$	−8.26657e9	−0.735902
$745$	2.75376e8	0.0243994
$746$	2.33978e10	2.06343
$747$	2.67884e9	0.235139
$748$	−1.52518e10	−1.33250
$749$	1.10344e10	0.959535
$750$	4.21335e10	3.64681
$751$	6.10891e9	0.526289	0.263144	−	0.964756i	$-0.415240\pi$
$751$	6.10891e9	0.526289	0.263144	+	0.964756i	$0.415240\pi$
$752$	−4.78714e9	−0.410501
$753$	−2.81421e10	−2.40201
$754$	−1.51779e9	−0.128947
$755$	−2.60178e9	−0.220017
$756$	−5.77208e10	−4.85855
$757$	4.90563e9	0.411016	0.205508	−	0.978655i	$-0.434115\pi$
$757$	4.90563e9	0.411016	0.205508	+	0.978655i	$0.434115\pi$
$758$	1.97601e9	0.164796
$759$	0	0
$760$	3.44593e10	2.84747
$761$	1.56857e10	1.29020	0.645100	−	0.764098i	$-0.276816\pi$
$761$	1.56857e10	1.29020	0.645100	+	0.764098i	$0.276816\pi$
$762$	3.74963e10	3.07005
$763$	−1.61473e10	−1.31603
$764$	−3.71173e10	−3.01127
$765$	−2.90402e10	−2.34523
$766$	−1.73566e10	−1.39529
$767$	−9.19734e8	−0.0736001
$768$	3.64538e9	0.290388
$769$	8.48511e9	0.672845	0.336423	−	0.941711i	$-0.390783\pi$
$769$	8.48511e9	0.672845	0.336423	+	0.941711i	$0.390783\pi$
$770$	4.17687e9	0.329711
$771$	2.99385e9	0.235256
$772$	3.98765e10	3.11929
$773$	−1.25408e10	−0.976558	−0.488279	−	0.872688i	$-0.662375\pi$
$773$	−1.25408e10	−0.976558	−0.488279	+	0.872688i	$0.662375\pi$
$774$	6.70602e10	5.19842
$775$	−9.61982e8	−0.0742354
$776$	2.77479e10	2.13164
$777$	−1.54151e10	−1.17889
$778$	−2.89510e10	−2.20412
$779$	5.64510e9	0.427849
$780$	6.07330e9	0.458241
$781$	−6.25338e9	−0.469717
$782$	0	0
$783$	1.73358e10	1.29056
$784$	−1.99929e10	−1.48173
$785$	−4.68730e9	−0.345843
$786$	8.26315e10	6.06969
$787$	2.44401e10	1.78728	0.893639	−	0.448786i	$-0.148143\pi$
$787$	2.44401e10	1.78728	0.893639	+	0.448786i	$0.148143\pi$
$788$	−3.79665e10	−2.76413
$789$	6.39061e9	0.463204
$790$	2.89144e10	2.08651
$791$	2.03497e9	0.146198
$792$	−3.69355e10	−2.64183
$793$	2.73637e9	0.194858
$794$	−4.42725e10	−3.13879
$795$	1.04243e10	0.735800
$796$	5.74248e10	4.03556
$797$	−9.51793e7	−0.00665945	−0.00332972	−	0.999994i	$-0.501060\pi$
$797$	−9.51793e7	−0.00665945	−0.00332972	+	0.999994i	$0.501060\pi$
$798$	−5.13758e10	−3.57889
$799$	2.85337e9	0.197899
$800$	2.07642e10	1.43384
$801$	7.37246e9	0.506872
$802$	−2.06723e10	−1.41508
$803$	−4.53825e9	−0.309303
$804$	5.81270e10	3.94440
$805$	0	0
$806$	−5.46492e8	−0.0367630
$807$	−2.88642e10	−1.93331
$808$	9.47349e9	0.631786
$809$	−1.67314e10	−1.11100	−0.555498	−	0.831518i	$-0.687472\pi$
$809$	−1.67314e10	−1.11100	−0.555498	+	0.831518i	$0.687472\pi$
$810$	−4.94723e10	−3.27088
$811$	−7.07377e9	−0.465670	−0.232835	−	0.972516i	$-0.574800\pi$
$811$	−7.07377e9	−0.465670	−0.232835	+	0.972516i	$0.574800\pi$
$812$	−1.30408e10	−0.854786
$813$	−5.73915e9	−0.374568
$814$	−9.62978e9	−0.625793
$815$	1.57792e10	1.02101
$816$	−1.20266e11	−7.74867
$817$	2.54145e10	1.63044
$818$	9.44108e8	0.0603094
$819$	−3.90869e9	−0.248621
$820$	−7.98476e9	−0.505724
$821$	−1.14579e9	−0.0722607	−0.0361304	−	0.999347i	$-0.511503\pi$
$821$	−1.14579e9	−0.0722607	−0.0361304	+	0.999347i	$0.511503\pi$
$822$	5.27641e10	3.31350
$823$	1.74865e10	1.09346	0.546730	−	0.837309i	$-0.315872\pi$
$823$	1.74865e10	1.09346	0.546730	+	0.837309i	$0.315872\pi$
$824$	9.03782e9	0.562754
$825$	−6.04774e9	−0.374977
$826$	−1.10049e10	−0.679449
$827$	−4.70708e9	−0.289389	−0.144694	−	0.989476i	$-0.546220\pi$
$827$	−4.70708e9	−0.289389	−0.144694	+	0.989476i	$0.546220\pi$
$828$	0	0
$829$	−3.27355e9	−0.199562	−0.0997811	−	0.995009i	$-0.531814\pi$
$829$	−3.27355e9	−0.199562	−0.0997811	+	0.995009i	$0.531814\pi$
$830$	−1.99979e9	−0.121398
$831$	−4.39296e10	−2.65554
$832$	4.77767e9	0.287597
$833$	1.19167e10	0.714330
$834$	7.59647e10	4.53451
$835$	7.33876e9	0.436234
$836$	−2.30461e10	−1.36419
$837$	6.24189e9	0.367940
$838$	1.57297e10	0.923352
$839$	7.60099e9	0.444328	0.222164	−	0.975009i	$-0.428688\pi$
$839$	7.60099e9	0.444328	0.222164	+	0.975009i	$0.428688\pi$
$840$	4.41379e10	2.56941
$841$	−1.33332e10	−0.772946
$842$	2.37810e9	0.137290
$843$	−5.31309e10	−3.05458
$844$	6.09127e10	3.48746
$845$	−1.15679e10	−0.659560
$846$	1.13767e10	0.645982
$847$	1.07586e10	0.608366
$848$	3.06817e10	1.72780
$849$	−1.15889e10	−0.649926
$850$	−2.61190e10	−1.45878
$851$	0	0
$852$	−1.08796e11	−6.02664
$853$	1.06027e10	0.584916	0.292458	−	0.956278i	$-0.405527\pi$
$853$	1.06027e10	0.584916	0.292458	+	0.956278i	$0.405527\pi$
$854$	3.27415e10	1.79886
$855$	−4.38809e10	−2.40101
$856$	7.28415e10	3.96936
$857$	3.25969e10	1.76906	0.884532	−	0.466479i	$-0.154478\pi$
$857$	3.25969e10	1.76906	0.884532	+	0.466479i	$0.154478\pi$
$858$	−3.43566e9	−0.185697
$859$	3.28664e10	1.76920	0.884599	−	0.466353i	$-0.154432\pi$
$859$	3.28664e10	1.76920	0.884599	+	0.466353i	$0.154432\pi$
$860$	−3.59478e10	−1.92720
$861$	7.23063e9	0.386069
$862$	4.02849e10	2.14223
$863$	9.63622e9	0.510351	0.255176	−	0.966895i	$-0.417867\pi$
$863$	9.63622e9	0.510351	0.255176	+	0.966895i	$0.417867\pi$
$864$	−1.34730e11	−7.10668
$865$	1.76133e10	0.925303
$866$	−1.69825e10	−0.888564
$867$	3.60064e10	1.87635
$868$	−4.69544e9	−0.243701
$869$	−1.17454e10	−0.607154
$870$	−2.18253e10	−1.12368
$871$	2.33398e9	0.119684
$872$	−1.06594e11	−5.44409
$873$	−3.53344e10	−1.79741
$874$	0	0
$875$	1.45359e10	0.733521
$876$	−7.89563e10	−3.96846
$877$	−9.13957e8	−0.0457538	−0.0228769	−	0.999738i	$-0.507283\pi$
$877$	−9.13957e8	−0.0457538	−0.0228769	+	0.999738i	$0.507283\pi$
$878$	−8.14649e9	−0.406200
$879$	3.76523e10	1.86995
$880$	1.47744e10	0.730838
$881$	2.85437e10	1.40635	0.703176	−	0.711016i	$-0.251765\pi$
$881$	2.85437e10	1.40635	0.703176	+	0.711016i	$0.251765\pi$
$882$	4.75133e10	2.33172
$883$	6.16630e9	0.301413	0.150707	−	0.988579i	$-0.451845\pi$
$883$	6.16630e9	0.301413	0.150707	+	0.988579i	$0.451845\pi$
$884$	−1.06547e10	−0.518750
$885$	−1.32255e10	−0.641372
$886$	4.93652e10	2.38453
$887$	−4.16328e8	−0.0200310	−0.0100155	−	0.999950i	$-0.503188\pi$
$887$	−4.16328e8	−0.0200310	−0.0100155	+	0.999950i	$0.503188\pi$
$888$	−1.01760e11	−4.87676
$889$	1.29360e10	0.617512
$890$	−5.50365e9	−0.261689
$891$	2.00963e10	0.951794
$892$	−3.78942e10	−1.78770
$893$	4.31155e9	0.202606
$894$	−2.71025e9	−0.126861
$895$	6.88402e9	0.320968
$896$	1.73744e10	0.806924
$897$	0	0
$898$	−9.53722e9	−0.439496
$899$	1.41022e9	0.0647334
$900$	−7.47797e10	−3.41928
$901$	−1.82878e10	−0.832961
$902$	4.51697e9	0.204939
$903$	3.25526e10	1.47122
$904$	1.34335e10	0.604784
$905$	−1.58992e9	−0.0713026
$906$	2.56067e10	1.14395
$907$	8.01334e9	0.356605	0.178303	−	0.983976i	$-0.442939\pi$
$907$	8.01334e9	0.356605	0.178303	+	0.983976i	$0.442939\pi$
$908$	5.24343e10	2.32442
$909$	−1.20636e10	−0.532728
$910$	2.91790e9	0.128359
$911$	−1.58468e10	−0.694426	−0.347213	−	0.937786i	$-0.612872\pi$
$911$	−1.58468e10	−0.694426	−0.347213	+	0.937786i	$0.612872\pi$
$912$	−1.81727e11	−7.93299
$913$	8.12341e8	0.0353257
$914$	4.92252e10	2.13244
$915$	3.93481e10	1.69805
$916$	5.15808e10	2.21745
$917$	2.85075e10	1.22086
$918$	1.69475e11	7.23030
$919$	7.88167e9	0.334976	0.167488	−	0.985874i	$-0.446434\pi$
$919$	7.88167e9	0.334976	0.167488	+	0.985874i	$0.446434\pi$
$920$	0	0
$921$	8.06046e10	3.39978
$922$	4.05089e10	1.70213
$923$	−4.36852e9	−0.182864
$924$	−2.95191e10	−1.23098
$925$	−1.18418e10	−0.491952
$926$	−1.73227e10	−0.716931
$927$	−1.15089e10	−0.474518
$928$	−3.04394e10	−1.25031
$929$	1.82739e9	0.0747782	0.0373891	−	0.999301i	$-0.488096\pi$
$929$	1.82739e9	0.0747782	0.0373891	+	0.999301i	$0.488096\pi$
$930$	−7.85838e9	−0.320363
$931$	1.80066e10	0.731321
$932$	2.19920e10	0.889833
$933$	−8.12558e10	−3.27543
$934$	−4.92799e10	−1.97905
$935$	−8.80627e9	−0.352331
$936$	−2.58026e10	−1.02848
$937$	−1.59441e10	−0.633158	−0.316579	−	0.948566i	$-0.602534\pi$
$937$	−1.59441e10	−0.633158	−0.316579	+	0.948566i	$0.602534\pi$
$938$	2.79269e10	1.10487
$939$	6.82214e9	0.268900
$940$	−6.09851e9	−0.239484
$941$	−1.62795e10	−0.636909	−0.318455	−	0.947938i	$-0.603164\pi$
$941$	−1.62795e10	−0.636909	−0.318455	+	0.947938i	$0.603164\pi$
$942$	4.61325e10	1.79816
$943$	0	0
$944$	−3.89266e10	−1.50607
$945$	−3.33275e10	−1.28467
$946$	2.03356e10	0.780976
$947$	−1.58030e10	−0.604665	−0.302333	−	0.953203i	$-0.597765\pi$
$947$	−1.58030e10	−0.604665	−0.302333	+	0.953203i	$0.597765\pi$
$948$	−2.04346e11	−7.79000
$949$	−3.17035e9	−0.120414
$950$	−3.94668e10	−1.49348
$951$	1.27648e10	0.481264
$952$	−7.74333e10	−2.90870
$953$	−2.46781e9	−0.0923607	−0.0461804	−	0.998933i	$-0.514705\pi$
$953$	−2.46781e9	−0.0923607	−0.0461804	+	0.998933i	$0.514705\pi$
$954$	−7.29156e10	−2.71895
$955$	−2.14312e10	−0.796221
$956$	4.21765e10	1.56123
$957$	8.86571e9	0.326980
$958$	4.38529e10	1.61146
$959$	1.82033e10	0.666478
$960$	6.87013e10	2.50620
$961$	−2.70049e10	−0.981544
$962$	−6.72722e9	−0.243625
$963$	−9.27572e10	−3.34700
$964$	−1.57928e10	−0.567793
$965$	2.30243e10	0.824785
$966$	0	0
$967$	−2.14651e10	−0.763379	−0.381689	−	0.924291i	$-0.624658\pi$
$967$	−2.14651e10	−0.763379	−0.381689	+	0.924291i	$0.624658\pi$
$968$	7.10213e10	2.51666
$969$	1.08318e11	3.82443
$970$	2.63777e10	0.927974
$971$	7.97270e9	0.279472	0.139736	−	0.990189i	$-0.455375\pi$
$971$	7.97270e9	0.279472	0.139736	+	0.990189i	$0.455375\pi$
$972$	1.52130e11	5.31354
$973$	2.62074e10	0.912073
$974$	6.38175e9	0.221301
$975$	−4.22486e9	−0.145981
$976$	1.15813e11	3.98735
$977$	−9.53879e9	−0.327237	−0.163618	−	0.986524i	$-0.552317\pi$
$977$	−9.53879e9	−0.327237	−0.163618	+	0.986524i	$0.552317\pi$
$978$	−1.55299e11	−5.30862
$979$	2.23565e9	0.0761491
$980$	−2.54696e10	−0.864433
$981$	1.35738e11	4.59050
$982$	2.99663e10	1.00982
$983$	9.66381e9	0.324497	0.162249	−	0.986750i	$-0.448125\pi$
$983$	9.66381e9	0.324497	0.162249	+	0.986750i	$0.448125\pi$
$984$	4.77318e10	1.59707
$985$	−2.19215e10	−0.730875
$986$	3.82892e10	1.27206
$987$	5.52253e9	0.182822
$988$	−1.60997e10	−0.531090
$989$	0	0
$990$	−3.51117e10	−1.15008
$991$	2.82627e10	0.922477	0.461238	−	0.887276i	$-0.347405\pi$
$991$	2.82627e10	0.922477	0.461238	+	0.887276i	$0.347405\pi$
$992$	−1.09599e10	−0.356466
$993$	−4.42930e10	−1.43553
$994$	−5.22707e10	−1.68813
$995$	3.31565e10	1.06706
$996$	1.41331e10	0.453241
$997$	2.32367e10	0.742576	0.371288	−	0.928518i	$-0.378916\pi$
$997$	2.32367e10	0.742576	0.371288	+	0.928518i	$0.378916\pi$
$998$	1.39086e10	0.442923
$999$	7.68365e10	2.43831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.8.a.c.1.1		8
23.22	odd	2		23.8.a.b.1.1	✓	8
69.68	even	2		207.8.a.f.1.8		8
92.91	even	2		368.8.a.h.1.1		8
115.114	odd	2		575.8.a.b.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.8.a.b.1.1	✓	8	23.22	odd	2
207.8.a.f.1.8		8	69.68	even	2
368.8.a.h.1.1		8	92.91	even	2
529.8.a.c.1.1		8	1.1	even	1	trivial
575.8.a.b.1.8		8	115.114	odd	2

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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-21.3077 q^{2} +86.9475 q^{3} +326.017 q^{4} +188.239 q^{5} -1852.65 q^{6} -639.155 q^{7} -4219.28 q^{8} +5372.88 q^{9} +O(q^{10})\)	\(q-21.3077 q^{2} +86.9475 q^{3} +326.017 q^{4} +188.239 q^{5} -1852.65 q^{6} -639.155 q^{7} -4219.28 q^{8} +5372.88 q^{9} -4010.94 q^{10} +1629.29 q^{11} +28346.4 q^{12} +1138.20 q^{13} +13618.9 q^{14} +16366.9 q^{15} +48172.8 q^{16} -28713.3 q^{17} -114483. q^{18} -43387.0 q^{19} +61369.1 q^{20} -55573.0 q^{21} -34716.4 q^{22} -366856. q^{24} -42691.1 q^{25} -24252.3 q^{26} +277004. q^{27} -208375. q^{28} +62583.1 q^{29} -348741. q^{30} +22533.6 q^{31} -486383. q^{32} +141663. q^{33} +611814. q^{34} -120314. q^{35} +1.75165e6 q^{36} +277384. q^{37} +924475. q^{38} +98963.5 q^{39} -794233. q^{40} -130110. q^{41} +1.18413e6 q^{42} -585763. q^{43} +531177. q^{44} +1.01138e6 q^{45} -99374.3 q^{47} +4.18851e6 q^{48} -415024. q^{49} +909647. q^{50} -2.49655e6 q^{51} +371072. q^{52} +636910. q^{53} -5.90231e6 q^{54} +306696. q^{55} +2.69677e6 q^{56} -3.77239e6 q^{57} -1.33350e6 q^{58} -808062. q^{59} +5.33589e6 q^{60} +2.40412e6 q^{61} -480138. q^{62} -3.43410e6 q^{63} +4.19757e6 q^{64} +214253. q^{65} -3.01851e6 q^{66} +2.05060e6 q^{67} -9.36103e6 q^{68} +2.56361e6 q^{70} -3.83810e6 q^{71} -2.26697e7 q^{72} -2.78541e6 q^{73} -5.91041e6 q^{74} -3.71188e6 q^{75} -1.41449e7 q^{76} -1.04137e6 q^{77} -2.10868e6 q^{78} -7.20890e6 q^{79} +9.06801e6 q^{80} +1.23343e7 q^{81} +2.77235e6 q^{82} +498585. q^{83} -1.81177e7 q^{84} -5.40497e6 q^{85} +1.24813e7 q^{86} +5.44145e6 q^{87} -6.87443e6 q^{88} +1.37216e6 q^{89} -2.15503e7 q^{90} -727485. q^{91} +1.95924e6 q^{93} +2.11743e6 q^{94} -8.16712e6 q^{95} -4.22898e7 q^{96} -6.57645e6 q^{97} +8.84319e6 q^{98} +8.75398e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 40 q^{3} + 640 q^{4} - 444 q^{5} - 1745 q^{6} - 1446 q^{7} + 3177 q^{8} + 13878 q^{9}+O(q^{10}) \) 8 * q + 40 * q^3 + 640 * q^4 - 444 * q^5 - 1745 * q^6 - 1446 * q^7 + 3177 * q^8 + 13878 * q^9	\( 8 q + 40 q^{3} + 640 q^{4} - 444 q^{5} - 1745 q^{6} - 1446 q^{7} + 3177 q^{8} + 13878 q^{9} - 19502 q^{10} - 7588 q^{11} + 22733 q^{12} + 19862 q^{13} - 17544 q^{14} + 12770 q^{15} + 64336 q^{16} - 42070 q^{17} - 59129 q^{18} - 1050 q^{19} - 3364 q^{20} + 7698 q^{21} + 128220 q^{22} - 621188 q^{24} + 49496 q^{25} - 371761 q^{26} - 69500 q^{27} - 143050 q^{28} - 102578 q^{29} + 671470 q^{30} + 304172 q^{31} - 612824 q^{32} - 747242 q^{33} + 524530 q^{34} + 531048 q^{35} + 1868983 q^{36} - 286472 q^{37} + 762932 q^{38} + 1032828 q^{39} - 2105286 q^{40} + 1324414 q^{41} + 1886168 q^{42} - 2052578 q^{43} + 867298 q^{44} - 2087442 q^{45} + 675556 q^{47} + 1411151 q^{48} - 55404 q^{49} + 1458528 q^{50} - 2775482 q^{51} - 1695409 q^{52} - 203654 q^{53} - 9897559 q^{54} - 1024444 q^{55} + 5766846 q^{56} - 3908648 q^{57} - 5039991 q^{58} - 748892 q^{59} + 18153300 q^{60} - 61822 q^{61} - 4939277 q^{62} - 1411632 q^{63} + 2702267 q^{64} + 1571618 q^{65} - 3791866 q^{66} - 3235604 q^{67} - 4914980 q^{68} + 10871764 q^{70} - 4951664 q^{71} - 7940241 q^{72} + 11019370 q^{73} - 356954 q^{74} - 13607220 q^{75} - 21973240 q^{76} - 5284888 q^{77} - 1506779 q^{78} - 4202464 q^{79} - 8785886 q^{80} + 10294096 q^{81} + 32636759 q^{82} - 518568 q^{83} - 7629190 q^{84} + 9854220 q^{85} + 14681386 q^{86} + 4862532 q^{87} - 20589740 q^{88} - 4203864 q^{89} - 49021076 q^{90} - 2488406 q^{91} - 23367842 q^{93} + 12314327 q^{94} - 44485300 q^{95} - 45317009 q^{96} - 18621134 q^{97} + 35756 q^{98} + 64729930 q^{99}+O(q^{100}) \) 8 * q + 40 * q^3 + 640 * q^4 - 444 * q^5 - 1745 * q^6 - 1446 * q^7 + 3177 * q^8 + 13878 * q^9 - 19502 * q^10 - 7588 * q^11 + 22733 * q^12 + 19862 * q^13 - 17544 * q^14 + 12770 * q^15 + 64336 * q^16 - 42070 * q^17 - 59129 * q^18 - 1050 * q^19 - 3364 * q^20 + 7698 * q^21 + 128220 * q^22 - 621188 * q^24 + 49496 * q^25 - 371761 * q^26 - 69500 * q^27 - 143050 * q^28 - 102578 * q^29 + 671470 * q^30 + 304172 * q^31 - 612824 * q^32 - 747242 * q^33 + 524530 * q^34 + 531048 * q^35 + 1868983 * q^36 - 286472 * q^37 + 762932 * q^38 + 1032828 * q^39 - 2105286 * q^40 + 1324414 * q^41 + 1886168 * q^42 - 2052578 * q^43 + 867298 * q^44 - 2087442 * q^45 + 675556 * q^47 + 1411151 * q^48 - 55404 * q^49 + 1458528 * q^50 - 2775482 * q^51 - 1695409 * q^52 - 203654 * q^53 - 9897559 * q^54 - 1024444 * q^55 + 5766846 * q^56 - 3908648 * q^57 - 5039991 * q^58 - 748892 * q^59 + 18153300 * q^60 - 61822 * q^61 - 4939277 * q^62 - 1411632 * q^63 + 2702267 * q^64 + 1571618 * q^65 - 3791866 * q^66 - 3235604 * q^67 - 4914980 * q^68 + 10871764 * q^70 - 4951664 * q^71 - 7940241 * q^72 + 11019370 * q^73 - 356954 * q^74 - 13607220 * q^75 - 21973240 * q^76 - 5284888 * q^77 - 1506779 * q^78 - 4202464 * q^79 - 8785886 * q^80 + 10294096 * q^81 + 32636759 * q^82 - 518568 * q^83 - 7629190 * q^84 + 9854220 * q^85 + 14681386 * q^86 + 4862532 * q^87 - 20589740 * q^88 - 4203864 * q^89 - 49021076 * q^90 - 2488406 * q^91 - 23367842 * q^93 + 12314327 * q^94 - 44485300 * q^95 - 45317009 * q^96 - 18621134 * q^97 + 35756 * q^98 + 64729930 * q^99

Introduction

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