LMFDB - Embedded newform 354.8.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
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} - x^{7} - 103558 x^{6} + 5805883 x^{5} + 2559087821 x^{4} - 196601024266 x^{3} + \cdots - 22\!\cdots\!40 $ x^8 - x^7 - 103558x^6 + 5805883x^5 + 2559087821x^4 - 196601024266x^3 - 17055507548256x^2 + 1662873307981032x - 22179668074797840
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{7}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-299.356$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +319.148 q^{5} -216.000 q^{6} +134.129 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +319.148 q^{5} -216.000 q^{6} +134.129 q^{7} +512.000 q^{8} +729.000 q^{9} +2553.18 q^{10} +2917.38 q^{11} -1728.00 q^{12} -10343.7 q^{13} +1073.03 q^{14} -8616.99 q^{15} +4096.00 q^{16} -9122.15 q^{17} +5832.00 q^{18} -32743.7 q^{19} +20425.4 q^{20} -3621.49 q^{21} +23339.0 q^{22} -86624.7 q^{23} -13824.0 q^{24} +23730.2 q^{25} -82749.2 q^{26} -19683.0 q^{27} +8584.26 q^{28} +14441.0 q^{29} -68935.9 q^{30} -97822.8 q^{31} +32768.0 q^{32} -78769.2 q^{33} -72977.2 q^{34} +42807.0 q^{35} +46656.0 q^{36} -120168. q^{37} -261950. q^{38} +279279. q^{39} +163404. q^{40} +417584. q^{41} -28971.9 q^{42} -328583. q^{43} +186712. q^{44} +232659. q^{45} -692998. q^{46} +1.14848e6 q^{47} -110592. q^{48} -805552. q^{49} +189842. q^{50} +246298. q^{51} -661994. q^{52} -1.09975e6 q^{53} -157464. q^{54} +931074. q^{55} +68674.1 q^{56} +884080. q^{57} +115528. q^{58} -205379. q^{59} -551487. q^{60} -592942. q^{61} -782582. q^{62} +97780.1 q^{63} +262144. q^{64} -3.30115e6 q^{65} -630154. q^{66} +115861. q^{67} -583817. q^{68} +2.33887e6 q^{69} +342456. q^{70} -968201. q^{71} +373248. q^{72} -3.88489e6 q^{73} -961346. q^{74} -640716. q^{75} -2.09560e6 q^{76} +391305. q^{77} +2.23423e6 q^{78} -838845. q^{79} +1.30723e6 q^{80} +531441. q^{81} +3.34068e6 q^{82} +6.55543e6 q^{83} -231775. q^{84} -2.91131e6 q^{85} -2.62866e6 q^{86} -389908. q^{87} +1.49370e6 q^{88} +6.86199e6 q^{89} +1.86127e6 q^{90} -1.38739e6 q^{91} -5.54398e6 q^{92} +2.64122e6 q^{93} +9.18784e6 q^{94} -1.04501e7 q^{95} -884736. q^{96} +6.68861e6 q^{97} -6.44442e6 q^{98} +2.12677e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{2} - 216 q^{3} + 512 q^{4} - 592 q^{5} - 1728 q^{6} - 340 q^{7} + 4096 q^{8} + 5832 q^{9}+O(q^{10}) $ 8 * q + 64 * q^2 - 216 * q^3 + 512 * q^4 - 592 * q^5 - 1728 * q^6 - 340 * q^7 + 4096 * q^8 + 5832 * q^9	\( 8 q + 64 q^{2} - 216 q^{3} + 512 q^{4} - 592 q^{5} - 1728 q^{6} - 340 q^{7} + 4096 q^{8} + 5832 q^{9} - 4736 q^{10} - 2852 q^{11} - 13824 q^{12} + 1142 q^{13} - 2720 q^{14} + 15984 q^{15} + 32768 q^{16} - 22528 q^{17} + 46656 q^{18} - 33528 q^{19} - 37888 q^{20} + 9180 q^{21} - 22816 q^{22} + 41330 q^{23} - 110592 q^{24} + 209004 q^{25} + 9136 q^{26} - 157464 q^{27} - 21760 q^{28} - 48334 q^{29} + 127872 q^{30} + 217552 q^{31} + 262144 q^{32} + 77004 q^{33} - 180224 q^{34} - 171714 q^{35} + 373248 q^{36} - 77966 q^{37} - 268224 q^{38} - 30834 q^{39} - 303104 q^{40} - 446410 q^{41} + 73440 q^{42} - 470890 q^{43} - 182528 q^{44} - 431568 q^{45} + 330640 q^{46} + 1876568 q^{47} - 884736 q^{48} + 1667480 q^{49} + 1672032 q^{50} + 608256 q^{51} + 73088 q^{52} - 1155672 q^{53} - 1259712 q^{54} + 112064 q^{55} - 174080 q^{56} + 905256 q^{57} - 386672 q^{58} - 1643032 q^{59} + 1022976 q^{60} - 9094962 q^{61} + 1740416 q^{62} - 247860 q^{63} + 2097152 q^{64} - 6726234 q^{65} + 616032 q^{66} - 8552352 q^{67} - 1441792 q^{68} - 1115910 q^{69} - 1373712 q^{70} - 5829156 q^{71} + 2985984 q^{72} - 7639392 q^{73} - 623728 q^{74} - 5643108 q^{75} - 2145792 q^{76} - 17178270 q^{77} - 246672 q^{78} - 12614888 q^{79} - 2424832 q^{80} + 4251528 q^{81} - 3571280 q^{82} - 19145486 q^{83} + 587520 q^{84} - 20127842 q^{85} - 3767120 q^{86} + 1305018 q^{87} - 1460224 q^{88} - 16050066 q^{89} - 3452544 q^{90} - 20086856 q^{91} + 2645120 q^{92} - 5873904 q^{93} + 15012544 q^{94} - 8130136 q^{95} - 7077888 q^{96} - 1961876 q^{97} + 13339840 q^{98} - 2079108 q^{99}+O(q^{100}) \) 8 * q + 64 * q^2 - 216 * q^3 + 512 * q^4 - 592 * q^5 - 1728 * q^6 - 340 * q^7 + 4096 * q^8 + 5832 * q^9 - 4736 * q^10 - 2852 * q^11 - 13824 * q^12 + 1142 * q^13 - 2720 * q^14 + 15984 * q^15 + 32768 * q^16 - 22528 * q^17 + 46656 * q^18 - 33528 * q^19 - 37888 * q^20 + 9180 * q^21 - 22816 * q^22 + 41330 * q^23 - 110592 * q^24 + 209004 * q^25 + 9136 * q^26 - 157464 * q^27 - 21760 * q^28 - 48334 * q^29 + 127872 * q^30 + 217552 * q^31 + 262144 * q^32 + 77004 * q^33 - 180224 * q^34 - 171714 * q^35 + 373248 * q^36 - 77966 * q^37 - 268224 * q^38 - 30834 * q^39 - 303104 * q^40 - 446410 * q^41 + 73440 * q^42 - 470890 * q^43 - 182528 * q^44 - 431568 * q^45 + 330640 * q^46 + 1876568 * q^47 - 884736 * q^48 + 1667480 * q^49 + 1672032 * q^50 + 608256 * q^51 + 73088 * q^52 - 1155672 * q^53 - 1259712 * q^54 + 112064 * q^55 - 174080 * q^56 + 905256 * q^57 - 386672 * q^58 - 1643032 * q^59 + 1022976 * q^60 - 9094962 * q^61 + 1740416 * q^62 - 247860 * q^63 + 2097152 * q^64 - 6726234 * q^65 + 616032 * q^66 - 8552352 * q^67 - 1441792 * q^68 - 1115910 * q^69 - 1373712 * q^70 - 5829156 * q^71 + 2985984 * q^72 - 7639392 * q^73 - 623728 * q^74 - 5643108 * q^75 - 2145792 * q^76 - 17178270 * q^77 - 246672 * q^78 - 12614888 * q^79 - 2424832 * q^80 + 4251528 * q^81 - 3571280 * q^82 - 19145486 * q^83 + 587520 * q^84 - 20127842 * q^85 - 3767120 * q^86 + 1305018 * q^87 - 1460224 * q^88 - 16050066 * q^89 - 3452544 * q^90 - 20086856 * q^91 + 2645120 * q^92 - 5873904 * q^93 + 15012544 * q^94 - 8130136 * q^95 - 7077888 * q^96 - 1961876 * q^97 + 13339840 * q^98 - 2079108 * 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
$5$	319.148	1.14182	0.570909	−	0.821014i	$-0.306591\pi$
$5$	319.148	1.14182	0.570909	+	0.821014i	$0.306591\pi$
$6$	−216.000	−0.408248
$7$	134.129	0.147802	0.0739009	−	0.997266i	$-0.476455\pi$
$7$	134.129	0.147802	0.0739009	+	0.997266i	$0.476455\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2553.18	0.807387
$11$	2917.38	0.660873	0.330437	−	0.943828i	$-0.392804\pi$
$11$	2917.38	0.660873	0.330437	+	0.943828i	$0.392804\pi$
$12$	−1728.00	−0.288675
$13$	−10343.7	−1.30579	−0.652893	−	0.757450i	$-0.726445\pi$
$13$	−10343.7	−1.30579	−0.652893	+	0.757450i	$0.726445\pi$
$14$	1073.03	0.104512
$15$	−8616.99	−0.659229
$16$	4096.00	0.250000
$17$	−9122.15	−0.450325	−0.225162	−	0.974321i	$-0.572291\pi$
$17$	−9122.15	−0.450325	−0.225162	+	0.974321i	$0.572291\pi$
$18$	5832.00	0.235702
$19$	−32743.7	−1.09519	−0.547596	−	0.836743i	$-0.684457\pi$
$19$	−32743.7	−1.09519	−0.547596	+	0.836743i	$0.684457\pi$
$20$	20425.4	0.570909
$21$	−3621.49	−0.0853334
$22$	23339.0	0.467308
$23$	−86624.7	−1.48455	−0.742274	−	0.670096i	$-0.766253\pi$
$23$	−86624.7	−1.48455	−0.742274	+	0.670096i	$0.766253\pi$
$24$	−13824.0	−0.204124
$25$	23730.2	0.303747
$26$	−82749.2	−0.923331
$27$	−19683.0	−0.192450
$28$	8584.26	0.0739009
$29$	14441.0	0.109952	0.0549762	−	0.998488i	$-0.482492\pi$
$29$	14441.0	0.109952	0.0549762	+	0.998488i	$0.482492\pi$
$30$	−68935.9	−0.466145
$31$	−97822.8	−0.589758	−0.294879	−	0.955535i	$-0.595279\pi$
$31$	−97822.8	−0.589758	−0.294879	+	0.955535i	$0.595279\pi$
$32$	32768.0	0.176777
$33$	−78769.2	−0.381555
$34$	−72977.2	−0.318428
$35$	42807.0	0.168763
$36$	46656.0	0.166667
$37$	−120168.	−0.390017	−0.195009	−	0.980802i	$-0.562473\pi$
$37$	−120168.	−0.390017	−0.195009	+	0.980802i	$0.562473\pi$
$38$	−261950.	−0.774417
$39$	279279.	0.753896
$40$	163404.	0.403693
$41$	417584.	0.946239	0.473119	−	0.880998i	$-0.343128\pi$
$41$	417584.	0.946239	0.473119	+	0.880998i	$0.343128\pi$
$42$	−28971.9	−0.0603399
$43$	−328583.	−0.630239	−0.315120	−	0.949052i	$-0.602045\pi$
$43$	−328583.	−0.630239	−0.315120	+	0.949052i	$0.602045\pi$
$44$	186712.	0.330437
$45$	232659.	0.380606
$46$	−692998.	−1.04973
$47$	1.14848e6	1.61354	0.806772	−	0.590863i	$-0.201212\pi$
$47$	1.14848e6	1.61354	0.806772	+	0.590863i	$0.201212\pi$
$48$	−110592.	−0.144338
$49$	−805552.	−0.978155
$50$	189842.	0.214781
$51$	246298.	0.259995
$52$	−661994.	−0.652893
$53$	−1.09975e6	−1.01468	−0.507338	−	0.861747i	$-0.669370\pi$
$53$	−1.09975e6	−1.01468	−0.507338	+	0.861747i	$0.669370\pi$
$54$	−157464.	−0.136083
$55$	931074.	0.754597
$56$	68674.1	0.0522559
$57$	884080.	0.632309
$58$	115528.	0.0777481
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	−551487.	−0.329614
$61$	−592942.	−0.334471	−0.167235	−	0.985917i	$-0.553484\pi$
$61$	−592942.	−0.334471	−0.167235	+	0.985917i	$0.553484\pi$
$62$	−782582.	−0.417022
$63$	97780.1	0.0492673
$64$	262144.	0.125000
$65$	−3.30115e6	−1.49097
$66$	−630154.	−0.269800
$67$	115861.	0.0470625	0.0235312	−	0.999723i	$-0.492509\pi$
$67$	115861.	0.0470625	0.0235312	+	0.999723i	$0.492509\pi$
$68$	−583817.	−0.225162
$69$	2.33887e6	0.857105
$70$	342456.	0.119333
$71$	−968201.	−0.321042	−0.160521	−	0.987032i	$-0.551317\pi$
$71$	−968201.	−0.321042	−0.160521	+	0.987032i	$0.551317\pi$
$72$	373248.	0.117851
$73$	−3.88489e6	−1.16882	−0.584412	−	0.811457i	$-0.698675\pi$
$73$	−3.88489e6	−1.16882	−0.584412	+	0.811457i	$0.698675\pi$
$74$	−961346.	−0.275784
$75$	−640716.	−0.175368
$76$	−2.09560e6	−0.547596
$77$	391305.	0.0976783
$78$	2.23423e6	0.533085
$79$	−838845.	−0.191420	−0.0957099	−	0.995409i	$-0.530512\pi$
$79$	−838845.	−0.191420	−0.0957099	+	0.995409i	$0.530512\pi$
$80$	1.30723e6	0.285454
$81$	531441.	0.111111
$82$	3.34068e6	0.669092
$83$	6.55543e6	1.25843	0.629213	−	0.777233i	$-0.283377\pi$
$83$	6.55543e6	1.25843	0.629213	+	0.777233i	$0.283377\pi$
$84$	−231775.	−0.0426667
$85$	−2.91131e6	−0.514189
$86$	−2.62866e6	−0.445646
$87$	−389908.	−0.0634811
$88$	1.49370e6	0.233654
$89$	6.86199e6	1.03178	0.515888	−	0.856656i	$-0.327462\pi$
$89$	6.86199e6	1.03178	0.515888	+	0.856656i	$0.327462\pi$
$90$	1.86127e6	0.269129
$91$	−1.38739e6	−0.192998
$92$	−5.54398e6	−0.742274
$93$	2.64122e6	0.340497
$94$	9.18784e6	1.14095
$95$	−1.04501e7	−1.25051
$96$	−884736.	−0.102062
$97$	6.68861e6	0.744106	0.372053	−	0.928212i	$-0.378654\pi$
$97$	6.68861e6	0.744106	0.372053	+	0.928212i	$0.378654\pi$
$98$	−6.44442e6	−0.691660
$99$	2.12677e6	0.220291
$100$	1.51873e6	0.151873
$101$	630861.	0.0609269	0.0304634	−	0.999536i	$-0.490302\pi$
$101$	630861.	0.0609269	0.0304634	+	0.999536i	$0.490302\pi$
$102$	1.97038e6	0.183844
$103$	−1.05376e7	−0.950194	−0.475097	−	0.879933i	$-0.657587\pi$
$103$	−1.05376e7	−0.950194	−0.475097	+	0.879933i	$0.657587\pi$
$104$	−5.29595e6	−0.461665
$105$	−1.15579e6	−0.0974352
$106$	−8.79797e6	−0.717484
$107$	8.36822e6	0.660374	0.330187	−	0.943916i	$-0.392888\pi$
$107$	8.36822e6	0.660374	0.330187	+	0.943916i	$0.392888\pi$
$108$	−1.25971e6	−0.0962250
$109$	−1.38816e7	−1.02671	−0.513355	−	0.858176i	$-0.671598\pi$
$109$	−1.38816e7	−1.02671	−0.513355	+	0.858176i	$0.671598\pi$
$110$	7.44859e6	0.533580
$111$	3.24454e6	0.225177
$112$	549393.	0.0369505
$113$	−2.27659e6	−0.148426	−0.0742129	−	0.997242i	$-0.523644\pi$
$113$	−2.27659e6	−0.148426	−0.0742129	+	0.997242i	$0.523644\pi$
$114$	7.07264e6	0.447110
$115$	−2.76461e7	−1.69508
$116$	924225.	0.0549762
$117$	−7.54052e6	−0.435262
$118$	−1.64303e6	−0.0920575
$119$	−1.22355e6	−0.0665589
$120$	−4.41190e6	−0.233072
$121$	−1.09761e7	−0.563246
$122$	−4.74354e6	−0.236506
$123$	−1.12748e7	−0.546311
$124$	−6.26066e6	−0.294879
$125$	−1.73600e7	−0.794994
$126$	782241.	0.0348372
$127$	−1.95434e7	−0.846619	−0.423309	−	0.905985i	$-0.639132\pi$
$127$	−1.95434e7	−0.846619	−0.423309	+	0.905985i	$0.639132\pi$
$128$	2.09715e6	0.0883883
$129$	8.87174e6	0.363869
$130$	−2.64092e7	−1.05428
$131$	−3.49073e7	−1.35665	−0.678323	−	0.734764i	$-0.737293\pi$
$131$	−3.49073e7	−1.35665	−0.678323	+	0.734764i	$0.737293\pi$
$132$	−5.04123e6	−0.190778
$133$	−4.39188e6	−0.161871
$134$	926887.	0.0332782
$135$	−6.28178e6	−0.219743
$136$	−4.67054e6	−0.159214
$137$	1.88810e7	0.627341	0.313671	−	0.949532i	$-0.398441\pi$
$137$	1.88810e7	0.627341	0.313671	+	0.949532i	$0.398441\pi$
$138$	1.87109e7	0.606064
$139$	−2.01690e7	−0.636989	−0.318495	−	0.947925i	$-0.603177\pi$
$139$	−2.01690e7	−0.636989	−0.318495	+	0.947925i	$0.603177\pi$
$140$	2.73965e6	0.0843814
$141$	−3.10090e7	−0.931580
$142$	−7.74561e6	−0.227011
$143$	−3.01764e7	−0.862960
$144$	2.98598e6	0.0833333
$145$	4.60882e6	0.125546
$146$	−3.10792e7	−0.826484
$147$	2.17499e7	0.564738
$148$	−7.69077e6	−0.195009
$149$	−5.44713e6	−0.134901	−0.0674507	−	0.997723i	$-0.521487\pi$
$149$	−5.44713e6	−0.134901	−0.0674507	+	0.997723i	$0.521487\pi$
$150$	−5.12573e6	−0.124004
$151$	−3.35678e7	−0.793420	−0.396710	−	0.917944i	$-0.629848\pi$
$151$	−3.35678e7	−0.793420	−0.396710	+	0.917944i	$0.629848\pi$
$152$	−1.67648e7	−0.387209
$153$	−6.65005e6	−0.150108
$154$	3.13044e6	0.0690690
$155$	−3.12199e7	−0.673396
$156$	1.78738e7	0.376948
$157$	−1.87403e7	−0.386481	−0.193241	−	0.981151i	$-0.561900\pi$
$157$	−1.87403e7	−0.386481	−0.193241	+	0.981151i	$0.561900\pi$
$158$	−6.71076e6	−0.135354
$159$	2.96932e7	0.585823
$160$	1.04578e7	0.201847
$161$	−1.16189e7	−0.219419
$162$	4.25153e6	0.0785674
$163$	1.24638e7	0.225421	0.112711	−	0.993628i	$-0.464047\pi$
$163$	1.24638e7	0.225421	0.112711	+	0.993628i	$0.464047\pi$
$164$	2.67254e7	0.473119
$165$	−2.51390e7	−0.435667
$166$	5.24434e7	0.889842
$167$	5.38299e7	0.894367	0.447184	−	0.894442i	$-0.352427\pi$
$167$	5.38299e7	0.894367	0.447184	+	0.894442i	$0.352427\pi$
$168$	−1.85420e6	−0.0301699
$169$	4.42427e7	0.705079
$170$	−2.32905e7	−0.363586
$171$	−2.38702e7	−0.365064
$172$	−2.10293e7	−0.315120
$173$	777614.	0.0114183	0.00570916	−	0.999984i	$-0.498183\pi$
$173$	777614.	0.0114183	0.00570916	+	0.999984i	$0.498183\pi$
$174$	−3.11926e6	−0.0448879
$175$	3.18291e6	0.0448943
$176$	1.19496e7	0.165218
$177$	5.54523e6	0.0751646
$178$	5.48959e7	0.729576
$179$	−1.44464e8	−1.88267	−0.941336	−	0.337470i	$-0.890429\pi$
$179$	−1.44464e8	−1.88267	−0.941336	+	0.337470i	$0.890429\pi$
$180$	1.48902e7	0.190303
$181$	−4.03624e7	−0.505944	−0.252972	−	0.967474i	$-0.581408\pi$
$181$	−4.03624e7	−0.505944	−0.252972	+	0.967474i	$0.581408\pi$
$182$	−1.10991e7	−0.136470
$183$	1.60094e7	0.193107
$184$	−4.43519e7	−0.524867
$185$	−3.83514e7	−0.445329
$186$	2.11297e7	0.240768
$187$	−2.66128e7	−0.297608
$188$	7.35027e7	0.806772
$189$	−2.64006e6	−0.0284445
$190$	−8.36006e7	−0.884243
$191$	1.39579e8	1.44945	0.724724	−	0.689039i	$-0.241967\pi$
$191$	1.39579e8	1.44945	0.724724	+	0.689039i	$0.241967\pi$
$192$	−7.07789e6	−0.0721688
$193$	−1.83138e8	−1.83370	−0.916849	−	0.399233i	$-0.869276\pi$
$193$	−1.83138e8	−1.83370	−0.916849	+	0.399233i	$0.869276\pi$
$194$	5.35089e7	0.526162
$195$	8.91311e7	0.860812
$196$	−5.15554e7	−0.489077
$197$	8.56358e7	0.798038	0.399019	−	0.916943i	$-0.369351\pi$
$197$	8.56358e7	0.798038	0.399019	+	0.916943i	$0.369351\pi$
$198$	1.70141e7	0.155769
$199$	6.24126e6	0.0561418	0.0280709	−	0.999606i	$-0.491064\pi$
$199$	6.24126e6	0.0561418	0.0280709	+	0.999606i	$0.491064\pi$
$200$	1.21499e7	0.107391
$201$	−3.12824e6	−0.0271715
$202$	5.04689e6	0.0430818
$203$	1.93696e6	0.0162512
$204$	1.57631e7	0.129998
$205$	1.33271e8	1.08043
$206$	−8.43010e7	−0.671889
$207$	−6.31494e7	−0.494850
$208$	−4.23676e7	−0.326447
$209$	−9.55257e7	−0.723783
$210$	−9.24631e6	−0.0688971
$211$	6.27202e7	0.459641	0.229821	−	0.973233i	$-0.426186\pi$
$211$	6.27202e7	0.459641	0.229821	+	0.973233i	$0.426186\pi$
$212$	−7.03838e7	−0.507338
$213$	2.61414e7	0.185353
$214$	6.69457e7	0.466955
$215$	−1.04866e8	−0.719618
$216$	−1.00777e7	−0.0680414
$217$	−1.31209e7	−0.0871674
$218$	−1.11053e8	−0.725994
$219$	1.04892e8	0.674821
$220$	5.95888e7	0.377298
$221$	9.43564e7	0.588028
$222$	2.59564e7	0.159224
$223$	7.41061e7	0.447494	0.223747	−	0.974647i	$-0.428171\pi$
$223$	7.41061e7	0.447494	0.223747	+	0.974647i	$0.428171\pi$
$224$	4.39514e6	0.0261279
$225$	1.72993e7	0.101249
$226$	−1.82127e7	−0.104953
$227$	1.73592e8	0.985009	0.492505	−	0.870310i	$-0.336081\pi$
$227$	1.73592e8	0.985009	0.492505	+	0.870310i	$0.336081\pi$
$228$	5.65811e7	0.316155
$229$	2.10444e7	0.115801	0.0579006	−	0.998322i	$-0.481559\pi$
$229$	2.10444e7	0.115801	0.0579006	+	0.998322i	$0.481559\pi$
$230$	−2.21169e8	−1.19860
$231$	−1.05652e7	−0.0563946
$232$	7.39380e6	0.0388741
$233$	7.90948e6	0.0409640	0.0204820	−	0.999790i	$-0.493480\pi$
$233$	7.90948e6	0.0409640	0.0204820	+	0.999790i	$0.493480\pi$
$234$	−6.03242e7	−0.307777
$235$	3.66535e8	1.84237
$236$	−1.31443e7	−0.0650945
$237$	2.26488e7	0.110516
$238$	−9.78837e6	−0.0470642
$239$	2.40543e8	1.13973	0.569864	−	0.821739i	$-0.306996\pi$
$239$	2.40543e8	1.13973	0.569864	+	0.821739i	$0.306996\pi$
$240$	−3.52952e7	−0.164807
$241$	5.06740e7	0.233198	0.116599	−	0.993179i	$-0.462801\pi$
$241$	5.06740e7	0.233198	0.116599	+	0.993179i	$0.462801\pi$
$242$	−8.78086e7	−0.398275
$243$	−1.43489e7	−0.0641500
$244$	−3.79483e7	−0.167235
$245$	−2.57090e8	−1.11687
$246$	−9.01982e7	−0.386300
$247$	3.38690e8	1.43009
$248$	−5.00853e7	−0.208511
$249$	−1.76997e8	−0.726553
$250$	−1.38880e8	−0.562146
$251$	−1.14512e8	−0.457083	−0.228541	−	0.973534i	$-0.573396\pi$
$251$	−1.14512e8	−0.457083	−0.228541	+	0.973534i	$0.573396\pi$
$252$	6.25793e6	0.0246336
$253$	−2.52717e8	−0.981099
$254$	−1.56347e8	−0.598650
$255$	7.86054e7	0.296867
$256$	1.67772e7	0.0625000
$257$	−3.64177e8	−1.33828	−0.669139	−	0.743137i	$-0.733337\pi$
$257$	−3.64177e8	−1.33828	−0.669139	+	0.743137i	$0.733337\pi$
$258$	7.09739e7	0.257294
$259$	−1.61181e7	−0.0576453
$260$	−2.11274e8	−0.745485
$261$	1.05275e7	0.0366508
$262$	−2.79258e8	−0.959294
$263$	5.67871e8	1.92489	0.962443	−	0.271485i	$-0.0875148\pi$
$263$	5.67871e8	1.92489	0.962443	+	0.271485i	$0.0875148\pi$
$264$	−4.03298e7	−0.134900
$265$	−3.50982e8	−1.15857
$266$	−3.51351e7	−0.114460
$267$	−1.85274e8	−0.595696
$268$	7.41509e6	0.0235312
$269$	1.62135e7	0.0507858	0.0253929	−	0.999678i	$-0.491916\pi$
$269$	1.62135e7	0.0507858	0.0253929	+	0.999678i	$0.491916\pi$
$270$	−5.02543e7	−0.155382
$271$	−3.79912e8	−1.15955	−0.579777	−	0.814775i	$-0.696860\pi$
$271$	−3.79912e8	−1.15955	−0.579777	+	0.814775i	$0.696860\pi$
$272$	−3.73643e7	−0.112581
$273$	3.74594e7	0.111427
$274$	1.51048e8	0.443597
$275$	6.92300e7	0.200738
$276$	1.49688e8	0.428552
$277$	1.24053e8	0.350694	0.175347	−	0.984507i	$-0.443895\pi$
$277$	1.24053e8	0.350694	0.175347	+	0.984507i	$0.443895\pi$
$278$	−1.61352e8	−0.450419
$279$	−7.13128e7	−0.196586
$280$	2.19172e7	0.0596666
$281$	−1.26772e8	−0.340840	−0.170420	−	0.985371i	$-0.554512\pi$
$281$	−1.26772e8	−0.340840	−0.170420	+	0.985371i	$0.554512\pi$
$282$	−2.48072e8	−0.658727
$283$	−2.43240e8	−0.637943	−0.318972	−	0.947764i	$-0.603337\pi$
$283$	−2.43240e8	−0.637943	−0.318972	+	0.947764i	$0.603337\pi$
$284$	−6.19649e7	−0.160521
$285$	2.82152e8	0.721982
$286$	−2.41411e8	−0.610205
$287$	5.60102e7	0.139856
$288$	2.38879e7	0.0589256
$289$	−3.27125e8	−0.797208
$290$	3.68705e7	0.0887742
$291$	−1.80592e8	−0.429610
$292$	−2.48633e8	−0.584412
$293$	6.19586e8	1.43901	0.719507	−	0.694485i	$-0.244368\pi$
$293$	6.19586e8	1.43901	0.719507	+	0.694485i	$0.244368\pi$
$294$	1.73999e8	0.399330
$295$	−6.55462e7	−0.148652
$296$	−6.15262e7	−0.137892
$297$	−5.74227e7	−0.127185
$298$	−4.35771e7	−0.0953896
$299$	8.96016e8	1.93850
$300$	−4.10058e7	−0.0876841
$301$	−4.40725e7	−0.0931506
$302$	−2.68542e8	−0.561033
$303$	−1.70332e7	−0.0351761
$304$	−1.34118e8	−0.273798
$305$	−1.89236e8	−0.381904
$306$	−5.32004e7	−0.106143
$307$	9.81142e7	0.193530	0.0967648	−	0.995307i	$-0.469151\pi$
$307$	9.81142e7	0.193530	0.0967648	+	0.995307i	$0.469151\pi$
$308$	2.50435e7	0.0488392
$309$	2.84516e8	0.548595
$310$	−2.49759e8	−0.476163
$311$	−8.04142e8	−1.51590	−0.757951	−	0.652311i	$-0.773799\pi$
$311$	−8.04142e8	−1.51590	−0.757951	+	0.652311i	$0.773799\pi$
$312$	1.42991e8	0.266543
$313$	−1.80847e8	−0.333354	−0.166677	−	0.986012i	$-0.553304\pi$
$313$	−1.80847e8	−0.333354	−0.166677	+	0.986012i	$0.553304\pi$
$314$	−1.49923e8	−0.273283
$315$	3.12063e7	0.0562542
$316$	−5.36861e7	−0.0957099
$317$	2.56434e8	0.452135	0.226068	−	0.974112i	$-0.427413\pi$
$317$	2.56434e8	0.452135	0.226068	+	0.974112i	$0.427413\pi$
$318$	2.37545e8	0.414239
$319$	4.21299e7	0.0726647
$320$	8.36626e7	0.142727
$321$	−2.25942e8	−0.381267
$322$	−9.29512e7	−0.155153
$323$	2.98693e8	0.493192
$324$	3.40122e7	0.0555556
$325$	−2.45457e8	−0.396629
$326$	9.97106e7	0.159397
$327$	3.74804e8	0.592772
$328$	2.13803e8	0.334546
$329$	1.54045e8	0.238485
$330$	−2.01112e8	−0.308063
$331$	7.23950e8	1.09726	0.548632	−	0.836064i	$-0.315149\pi$
$331$	7.23950e8	1.09726	0.548632	+	0.836064i	$0.315149\pi$
$332$	4.19548e8	0.629213
$333$	−8.76027e7	−0.130006
$334$	4.30639e8	0.632413
$335$	3.69767e7	0.0537368
$336$	−1.48336e7	−0.0213334
$337$	5.14260e8	0.731945	0.365972	−	0.930626i	$-0.380736\pi$
$337$	5.14260e8	0.731945	0.365972	+	0.930626i	$0.380736\pi$
$338$	3.53942e8	0.498566
$339$	6.14678e7	0.0856937
$340$	−1.86324e8	−0.257094
$341$	−2.85386e8	−0.389756
$342$	−1.90961e8	−0.258139
$343$	−2.18509e8	−0.292375
$344$	−1.68234e8	−0.222823
$345$	7.46444e8	0.978657
$346$	6.22091e6	0.00807398
$347$	1.80074e8	0.231365	0.115683	−	0.993286i	$-0.463094\pi$
$347$	1.80074e8	0.231365	0.115683	+	0.993286i	$0.463094\pi$
$348$	−2.49541e7	−0.0317405
$349$	−9.22057e8	−1.16110	−0.580549	−	0.814226i	$-0.697162\pi$
$349$	−9.22057e8	−1.16110	−0.580549	+	0.814226i	$0.697162\pi$
$350$	2.54633e7	0.0317451
$351$	2.03594e8	0.251299
$352$	9.55966e7	0.116827
$353$	7.10394e8	0.859584	0.429792	−	0.902928i	$-0.358587\pi$
$353$	7.10394e8	0.859584	0.429792	+	0.902928i	$0.358587\pi$
$354$	4.43619e7	0.0531494
$355$	−3.08999e8	−0.366571
$356$	4.39168e8	0.515888
$357$	3.30357e7	0.0384278
$358$	−1.15571e9	−1.33125
$359$	1.68759e8	0.192503	0.0962514	−	0.995357i	$-0.469315\pi$
$359$	1.68759e8	0.192503	0.0962514	+	0.995357i	$0.469315\pi$
$360$	1.19121e8	0.134564
$361$	1.78278e8	0.199445
$362$	−3.22900e8	−0.357756
$363$	2.96354e8	0.325190
$364$	−8.87927e7	−0.0964989
$365$	−1.23985e9	−1.33458
$366$	1.28076e8	0.136547
$367$	1.63146e9	1.72284	0.861419	−	0.507895i	$-0.169576\pi$
$367$	1.63146e9	1.72284	0.861419	+	0.507895i	$0.169576\pi$
$368$	−3.54815e8	−0.371137
$369$	3.04419e8	0.315413
$370$	−3.06811e8	−0.314895
$371$	−1.47508e8	−0.149971
$372$	1.69038e8	0.170249
$373$	1.08661e9	1.08416	0.542078	−	0.840328i	$-0.317638\pi$
$373$	1.08661e9	1.08416	0.542078	+	0.840328i	$0.317638\pi$
$374$	−2.12902e8	−0.210440
$375$	4.68719e8	0.458990
$376$	5.88022e8	0.570474
$377$	−1.49373e8	−0.143574
$378$	−2.11205e7	−0.0201133
$379$	−3.15599e8	−0.297782	−0.148891	−	0.988854i	$-0.547570\pi$
$379$	−3.15599e8	−0.297782	−0.148891	+	0.988854i	$0.547570\pi$
$380$	−6.68805e8	−0.625254
$381$	5.27673e8	0.488796
$382$	1.11663e9	1.02491
$383$	7.06697e8	0.642743	0.321372	−	0.946953i	$-0.395856\pi$
$383$	7.06697e8	0.642743	0.321372	+	0.946953i	$0.395856\pi$
$384$	−5.66231e7	−0.0510310
$385$	1.24884e8	0.111531
$386$	−1.46510e9	−1.29662
$387$	−2.39537e8	−0.210080
$388$	4.28071e8	0.372053
$389$	3.95928e8	0.341030	0.170515	−	0.985355i	$-0.445457\pi$
$389$	3.95928e8	0.341030	0.170515	+	0.985355i	$0.445457\pi$
$390$	7.13049e8	0.608686
$391$	7.90204e8	0.668529
$392$	−4.12443e8	−0.345830
$393$	9.42497e8	0.783260
$394$	6.85086e8	0.564298
$395$	−2.67715e8	−0.218566
$396$	1.36113e8	0.110146
$397$	−1.69179e9	−1.35700	−0.678500	−	0.734601i	$-0.737369\pi$
$397$	−1.69179e9	−1.35700	−0.678500	+	0.734601i	$0.737369\pi$
$398$	4.99300e7	0.0396982
$399$	1.18581e8	0.0934565
$400$	9.71990e7	0.0759367
$401$	−1.31847e9	−1.02110	−0.510548	−	0.859849i	$-0.670557\pi$
$401$	−1.31847e9	−1.02110	−0.510548	+	0.859849i	$0.670557\pi$
$402$	−2.50259e7	−0.0192132
$403$	1.01185e9	0.770099
$404$	4.03751e7	0.0304634
$405$	1.69608e8	0.126869
$406$	1.54957e7	0.0114913
$407$	−3.50576e8	−0.257752
$408$	1.26105e8	0.0919222
$409$	7.65102e8	0.552952	0.276476	−	0.961021i	$-0.410833\pi$
$409$	7.65102e8	0.552952	0.276476	+	0.961021i	$0.410833\pi$
$410$	1.06617e9	0.763981
$411$	−5.09788e8	−0.362196
$412$	−6.74408e8	−0.475097
$413$	−2.75473e7	−0.0192422
$414$	−5.05195e8	−0.349911
$415$	2.09215e9	1.43689
$416$	−3.38941e8	−0.230833
$417$	5.44562e8	0.367766
$418$	−7.64206e8	−0.511792
$419$	−2.00535e9	−1.33180	−0.665902	−	0.746039i	$-0.731953\pi$
$419$	−2.00535e9	−1.33180	−0.665902	+	0.746039i	$0.731953\pi$
$420$	−7.39705e7	−0.0487176
$421$	1.17061e9	0.764582	0.382291	−	0.924042i	$-0.375135\pi$
$421$	1.17061e9	0.764582	0.382291	+	0.924042i	$0.375135\pi$
$422$	5.01762e8	0.325016
$423$	8.37242e8	0.537848
$424$	−5.63070e8	−0.358742
$425$	−2.16471e8	−0.136785
$426$	2.09131e8	0.131065
$427$	−7.95308e7	−0.0494354
$428$	5.35566e8	0.330187
$429$	8.14761e8	0.498230
$430$	−8.38932e8	−0.508847
$431$	2.19094e9	1.31814	0.659069	−	0.752083i	$-0.270951\pi$
$431$	2.19094e9	1.31814	0.659069	+	0.752083i	$0.270951\pi$
$432$	−8.06216e7	−0.0481125
$433$	−2.07257e9	−1.22688	−0.613438	−	0.789743i	$-0.710214\pi$
$433$	−2.07257e9	−1.22688	−0.613438	+	0.789743i	$0.710214\pi$
$434$	−1.04967e8	−0.0616367
$435$	−1.24438e8	−0.0724838
$436$	−8.88425e8	−0.513355
$437$	2.83641e9	1.62587
$438$	8.39137e8	0.477170
$439$	−7.57095e8	−0.427095	−0.213547	−	0.976933i	$-0.568502\pi$
$439$	−7.57095e8	−0.427095	−0.213547	+	0.976933i	$0.568502\pi$
$440$	4.76710e8	0.266790
$441$	−5.87248e8	−0.326052
$442$	7.54851e8	0.415799
$443$	1.63901e9	0.895710	0.447855	−	0.894106i	$-0.352188\pi$
$443$	1.63901e9	0.895710	0.447855	+	0.894106i	$0.352188\pi$
$444$	2.07651e8	0.112588
$445$	2.18999e9	1.17810
$446$	5.92849e8	0.316426
$447$	1.47073e8	0.0778853
$448$	3.51611e7	0.0184752
$449$	−4.36670e8	−0.227663	−0.113831	−	0.993500i	$-0.536312\pi$
$449$	−4.36670e8	−0.227663	−0.113831	+	0.993500i	$0.536312\pi$
$450$	1.38395e8	0.0715938
$451$	1.21825e9	0.625344
$452$	−1.45701e8	−0.0742129
$453$	9.06330e8	0.458081
$454$	1.38874e9	0.696507
$455$	−4.42781e8	−0.220368
$456$	4.52649e8	0.223555
$457$	2.88443e9	1.41369	0.706844	−	0.707369i	$-0.250118\pi$
$457$	2.88443e9	1.41369	0.706844	+	0.707369i	$0.250118\pi$
$458$	1.68356e8	0.0818839
$459$	1.79551e8	0.0866651
$460$	−1.76935e9	−0.847542
$461$	−2.73090e9	−1.29823	−0.649117	−	0.760688i	$-0.724862\pi$
$461$	−2.73090e9	−1.29823	−0.649117	+	0.760688i	$0.724862\pi$
$462$	−8.45219e7	−0.0398770
$463$	1.90108e9	0.890158	0.445079	−	0.895491i	$-0.353176\pi$
$463$	1.90108e9	0.890158	0.445079	+	0.895491i	$0.353176\pi$
$464$	5.91504e7	0.0274881
$465$	8.42938e8	0.388786
$466$	6.32758e7	0.0289659
$467$	2.16043e9	0.981594	0.490797	−	0.871274i	$-0.336706\pi$
$467$	2.16043e9	0.981594	0.490797	+	0.871274i	$0.336706\pi$
$468$	−4.82594e8	−0.217631
$469$	1.55403e7	0.00695592
$470$	2.93228e9	1.30275
$471$	5.05989e8	0.223135
$472$	−1.05154e8	−0.0460287
$473$	−9.58601e8	−0.416508
$474$	1.81190e8	0.0781468
$475$	−7.77015e8	−0.332661
$476$	−7.83069e7	−0.0332794
$477$	−8.01715e8	−0.338225
$478$	1.92435e9	0.805909
$479$	−2.39817e9	−0.997022	−0.498511	−	0.866883i	$-0.666120\pi$
$479$	−2.39817e9	−0.997022	−0.498511	+	0.866883i	$0.666120\pi$
$480$	−2.82361e8	−0.116536
$481$	1.24298e9	0.509280
$482$	4.05392e8	0.164896
$483$	3.13710e8	0.126682
$484$	−7.02469e8	−0.281623
$485$	2.13465e9	0.849633
$486$	−1.14791e8	−0.0453609
$487$	2.94508e9	1.15544	0.577718	−	0.816236i	$-0.303943\pi$
$487$	2.94508e9	1.15544	0.577718	+	0.816236i	$0.303943\pi$
$488$	−3.03586e8	−0.118253
$489$	−3.36523e8	−0.130147
$490$	−2.05672e9	−0.789749
$491$	−2.47730e9	−0.944481	−0.472241	−	0.881470i	$-0.656555\pi$
$491$	−2.47730e9	−0.944481	−0.472241	+	0.881470i	$0.656555\pi$
$492$	−7.21586e8	−0.273156
$493$	−1.31733e8	−0.0495143
$494$	2.70952e9	1.01122
$495$	6.78753e8	0.251532
$496$	−4.00682e8	−0.147440
$497$	−1.29864e8	−0.0474506
$498$	−1.41597e9	−0.513750
$499$	2.09171e9	0.753617	0.376808	−	0.926291i	$-0.377022\pi$
$499$	2.09171e9	0.753617	0.376808	+	0.926291i	$0.377022\pi$
$500$	−1.11104e9	−0.397497
$501$	−1.45341e9	−0.516363
$502$	−9.16100e8	−0.323206
$503$	−2.28640e9	−0.801058	−0.400529	−	0.916284i	$-0.631174\pi$
$503$	−2.28640e9	−0.801058	−0.400529	+	0.916284i	$0.631174\pi$
$504$	5.00634e7	0.0174186
$505$	2.01338e8	0.0695673
$506$	−2.02174e9	−0.693742
$507$	−1.19455e9	−0.407078
$508$	−1.25078e9	−0.423309
$509$	−1.86659e9	−0.627389	−0.313695	−	0.949524i	$-0.601567\pi$
$509$	−1.86659e9	−0.627389	−0.313695	+	0.949524i	$0.601567\pi$
$510$	6.28843e8	0.209917
$511$	−5.21077e8	−0.172754
$512$	1.34218e8	0.0441942
$513$	6.44494e8	0.210770
$514$	−2.91341e9	−0.946305
$515$	−3.36306e9	−1.08495
$516$	5.67791e8	0.181934
$517$	3.35055e9	1.06635
$518$	−1.28945e8	−0.0407614
$519$	−2.09956e7	−0.00659238
$520$	−1.69019e9	−0.527138
$521$	5.27830e9	1.63517	0.817583	−	0.575811i	$-0.195314\pi$
$521$	5.27830e9	1.63517	0.817583	+	0.575811i	$0.195314\pi$
$522$	8.42200e7	0.0259160
$523$	4.76478e9	1.45642	0.728210	−	0.685354i	$-0.240352\pi$
$523$	4.76478e9	1.45642	0.728210	+	0.685354i	$0.240352\pi$
$524$	−2.23407e9	−0.678323
$525$	−8.59387e7	−0.0259198
$526$	4.54297e9	1.36110
$527$	8.92354e8	0.265583
$528$	−3.22639e8	−0.0953889
$529$	4.09902e9	1.20388
$530$	−2.80785e9	−0.819235
$531$	−1.49721e8	−0.0433963
$532$	−2.81081e8	−0.0809357
$533$	−4.31935e9	−1.23559
$534$	−1.48219e9	−0.421221
$535$	2.67070e9	0.754026
$536$	5.93208e7	0.0166391
$537$	3.90053e9	1.08696
$538$	1.29708e8	0.0359110
$539$	−2.35010e9	−0.646436
$540$	−4.02034e8	−0.109871
$541$	−2.56129e9	−0.695454	−0.347727	−	0.937596i	$-0.613046\pi$
$541$	−2.56129e9	−0.695454	−0.347727	+	0.937596i	$0.613046\pi$
$542$	−3.03930e9	−0.819928
$543$	1.08979e9	0.292107
$544$	−2.98915e8	−0.0796069
$545$	−4.43029e9	−1.17232
$546$	2.99675e8	0.0787910
$547$	1.83572e9	0.479568	0.239784	−	0.970826i	$-0.422923\pi$
$547$	1.83572e9	0.479568	0.239784	+	0.970826i	$0.422923\pi$
$548$	1.20839e9	0.313671
$549$	−4.32255e8	−0.111490
$550$	5.53840e8	0.141943
$551$	−4.72852e8	−0.120419
$552$	1.19750e9	0.303032
$553$	−1.12514e8	−0.0282922
$554$	9.92423e8	0.247978
$555$	1.03549e9	0.257111
$556$	−1.29081e9	−0.318495
$557$	−2.68214e9	−0.657641	−0.328820	−	0.944392i	$-0.606651\pi$
$557$	−2.68214e9	−0.657641	−0.328820	+	0.944392i	$0.606651\pi$
$558$	−5.70503e8	−0.139007
$559$	3.39875e9	0.822958
$560$	1.75337e8	0.0421907
$561$	7.18544e8	0.171824
$562$	−1.01418e9	−0.241010
$563$	−7.19760e9	−1.69984	−0.849921	−	0.526910i	$-0.823350\pi$
$563$	−7.19760e9	−1.69984	−0.849921	+	0.526910i	$0.823350\pi$
$564$	−1.98457e9	−0.465790
$565$	−7.26567e8	−0.169475
$566$	−1.94592e9	−0.451094
$567$	7.12817e7	0.0164224
$568$	−4.95719e8	−0.113505
$569$	−8.54848e9	−1.94534	−0.972671	−	0.232189i	$-0.925411\pi$
$569$	−8.54848e9	−1.94534	−0.972671	+	0.232189i	$0.925411\pi$
$570$	2.25722e9	0.510518
$571$	7.25047e9	1.62982	0.814911	−	0.579587i	$-0.196786\pi$
$571$	7.25047e9	1.62982	0.814911	+	0.579587i	$0.196786\pi$
$572$	−1.93129e9	−0.431480
$573$	−3.76863e9	−0.836839
$574$	4.48082e8	0.0988930
$575$	−2.05562e9	−0.450927
$576$	1.91103e8	0.0416667
$577$	−5.68024e9	−1.23098	−0.615490	−	0.788145i	$-0.711042\pi$
$577$	−5.68024e9	−1.23098	−0.615490	+	0.788145i	$0.711042\pi$
$578$	−2.61700e9	−0.563711
$579$	4.94473e9	1.05869
$580$	2.94964e8	0.0627728
$581$	8.79274e8	0.185998
$582$	−1.44474e9	−0.303780
$583$	−3.20838e9	−0.670572
$584$	−1.98907e9	−0.413242
$585$	−2.40654e9	−0.496990
$586$	4.95669e9	1.01754
$587$	2.80625e9	0.572655	0.286327	−	0.958132i	$-0.407566\pi$
$587$	2.80625e9	0.572655	0.286327	+	0.958132i	$0.407566\pi$
$588$	1.39199e9	0.282369
$589$	3.20308e9	0.645899
$590$	−5.24370e8	−0.105113
$591$	−2.31217e9	−0.460747
$592$	−4.92209e8	−0.0975043
$593$	−9.23383e9	−1.81840	−0.909202	−	0.416355i	$-0.863307\pi$
$593$	−9.23383e9	−1.81840	−0.909202	+	0.416355i	$0.863307\pi$
$594$	−4.59382e8	−0.0899335
$595$	−3.90492e8	−0.0759980
$596$	−3.48617e8	−0.0674507
$597$	−1.68514e8	−0.0324135
$598$	7.16813e9	1.37073
$599$	−2.65856e9	−0.505420	−0.252710	−	0.967542i	$-0.581322\pi$
$599$	−2.65856e9	−0.505420	−0.252710	+	0.967542i	$0.581322\pi$
$600$	−3.28047e8	−0.0620021
$601$	−7.40132e8	−0.139075	−0.0695374	−	0.997579i	$-0.522152\pi$
$601$	−7.40132e8	−0.139075	−0.0695374	+	0.997579i	$0.522152\pi$
$602$	−3.52580e8	−0.0658674
$603$	8.44626e7	0.0156875
$604$	−2.14834e9	−0.396710
$605$	−3.50299e9	−0.643124
$606$	−1.36266e8	−0.0248733
$607$	−5.21369e9	−0.946204	−0.473102	−	0.881008i	$-0.656866\pi$
$607$	−5.21369e9	−0.946204	−0.473102	+	0.881008i	$0.656866\pi$
$608$	−1.07295e9	−0.193604
$609$	−5.22980e7	−0.00938262
$610$	−1.51389e9	−0.270047
$611$	−1.18795e10	−2.10695
$612$	−4.25603e8	−0.0750541
$613$	−4.36241e9	−0.764919	−0.382459	−	0.923972i	$-0.624923\pi$
$613$	−4.36241e9	−0.764919	−0.382459	+	0.923972i	$0.624923\pi$
$614$	7.84914e8	0.136846
$615$	−3.59832e9	−0.623788
$616$	2.00348e8	0.0345345
$617$	−2.10920e9	−0.361510	−0.180755	−	0.983528i	$-0.557854\pi$
$617$	−2.10920e9	−0.361510	−0.180755	+	0.983528i	$0.557854\pi$
$618$	2.27613e9	0.387915
$619$	−6.07418e9	−1.02937	−0.514684	−	0.857380i	$-0.672091\pi$
$619$	−6.07418e9	−1.02937	−0.514684	+	0.857380i	$0.672091\pi$
$620$	−1.99807e9	−0.336698
$621$	1.70503e9	0.285702
$622$	−6.43313e9	−1.07190
$623$	9.20393e8	0.152498
$624$	1.14393e9	0.188474
$625$	−7.39432e9	−1.21148
$626$	−1.44677e9	−0.235717
$627$	2.57919e9	0.417876
$628$	−1.19938e9	−0.193241
$629$	1.09619e9	0.175634
$630$	2.49650e8	0.0397778
$631$	2.61613e9	0.414531	0.207266	−	0.978285i	$-0.433544\pi$
$631$	2.61613e9	0.414531	0.207266	+	0.978285i	$0.433544\pi$
$632$	−4.29489e8	−0.0676771
$633$	−1.69345e9	−0.265374
$634$	2.05147e9	0.319708
$635$	−6.23724e9	−0.966684
$636$	1.90036e9	0.292912
$637$	8.33236e9	1.27726
$638$	3.37039e8	0.0513817
$639$	−7.05819e8	−0.107014
$640$	6.69301e8	0.100923
$641$	6.44130e9	0.965985	0.482992	−	0.875625i	$-0.339550\pi$
$641$	6.44130e9	0.965985	0.482992	+	0.875625i	$0.339550\pi$
$642$	−1.80753e9	−0.269596
$643$	6.42061e9	0.952441	0.476220	−	0.879326i	$-0.342006\pi$
$643$	6.42061e9	0.952441	0.476220	+	0.879326i	$0.342006\pi$
$644$	−7.43609e8	−0.109710
$645$	2.83140e9	0.415472
$646$	2.38954e9	0.348739
$647$	5.79769e9	0.841570	0.420785	−	0.907160i	$-0.361755\pi$
$647$	5.79769e9	0.841570	0.420785	+	0.907160i	$0.361755\pi$
$648$	2.72098e8	0.0392837
$649$	−5.99168e8	−0.0860384
$650$	−1.96366e9	−0.280459
$651$	3.54264e8	0.0503261
$652$	7.97685e8	0.112711
$653$	−5.29082e9	−0.743578	−0.371789	−	0.928317i	$-0.621256\pi$
$653$	−5.29082e9	−0.743578	−0.371789	+	0.928317i	$0.621256\pi$
$654$	2.99843e9	0.419153
$655$	−1.11406e10	−1.54904
$656$	1.71043e9	0.236560
$657$	−2.83209e9	−0.389608
$658$	1.23236e9	0.168634
$659$	6.58899e9	0.896850	0.448425	−	0.893820i	$-0.351985\pi$
$659$	6.58899e9	0.896850	0.448425	+	0.893820i	$0.351985\pi$
$660$	−1.60890e9	−0.217833
$661$	3.86916e9	0.521089	0.260545	−	0.965462i	$-0.416098\pi$
$661$	3.86916e9	0.521089	0.260545	+	0.965462i	$0.416098\pi$
$662$	5.79160e9	0.775882
$663$	−2.54762e9	−0.339498
$664$	3.35638e9	0.444921
$665$	−1.40166e9	−0.184828
$666$	−7.00822e8	−0.0919280
$667$	−1.25095e9	−0.163230
$668$	3.44511e9	0.447184
$669$	−2.00086e9	−0.258361
$670$	2.95814e8	0.0379976
$671$	−1.72984e9	−0.221043
$672$	−1.18669e8	−0.0150850
$673$	−4.55131e9	−0.575550	−0.287775	−	0.957698i	$-0.592916\pi$
$673$	−4.55131e9	−0.575550	−0.287775	+	0.957698i	$0.592916\pi$
$674$	4.11408e9	0.517563
$675$	−4.67082e8	−0.0584561
$676$	2.83153e9	0.352540
$677$	3.14550e9	0.389609	0.194805	−	0.980842i	$-0.437593\pi$
$677$	3.14550e9	0.389609	0.194805	+	0.980842i	$0.437593\pi$
$678$	4.91742e8	0.0605946
$679$	8.97137e8	0.109980
$680$	−1.49059e9	−0.181793
$681$	−4.68700e9	−0.568695
$682$	−2.28309e9	−0.275599
$683$	−1.39868e10	−1.67976	−0.839879	−	0.542774i	$-0.817374\pi$
$683$	−1.39868e10	−1.67976	−0.839879	+	0.542774i	$0.817374\pi$
$684$	−1.52769e9	−0.182532
$685$	6.02584e9	0.716309
$686$	−1.74807e9	−0.206740
$687$	−5.68200e8	−0.0668579
$688$	−1.34588e9	−0.157560
$689$	1.13754e10	1.32495
$690$	5.97155e9	0.692015
$691$	−3.62313e9	−0.417745	−0.208872	−	0.977943i	$-0.566979\pi$
$691$	−3.62313e9	−0.417745	−0.208872	+	0.977943i	$0.566979\pi$
$692$	4.97673e7	0.00570916
$693$	2.85262e8	0.0325594
$694$	1.44059e9	0.163600
$695$	−6.43688e9	−0.727325
$696$	−1.99633e8	−0.0224439
$697$	−3.80927e9	−0.426115
$698$	−7.37645e9	−0.821020
$699$	−2.13556e8	−0.0236506
$700$	2.03706e8	0.0224472
$701$	2.11707e9	0.232126	0.116063	−	0.993242i	$-0.462973\pi$
$701$	2.11707e9	0.232126	0.116063	+	0.993242i	$0.462973\pi$
$702$	1.62875e9	0.177695
$703$	3.93475e9	0.427144
$704$	7.64773e8	0.0826092
$705$	−9.89644e9	−1.06369
$706$	5.68316e9	0.607817
$707$	8.46168e7	0.00900510
$708$	3.54895e8	0.0375823
$709$	6.94371e9	0.731694	0.365847	−	0.930675i	$-0.380779\pi$
$709$	6.94371e9	0.731694	0.365847	+	0.930675i	$0.380779\pi$
$710$	−2.47199e9	−0.259205
$711$	−6.11518e8	−0.0638066
$712$	3.51334e9	0.364788
$713$	8.47387e9	0.875525
$714$	2.64286e8	0.0271725
$715$	−9.63071e9	−0.985342
$716$	−9.24571e9	−0.941336
$717$	−6.49467e9	−0.658022
$718$	1.35007e9	0.136120
$719$	2.10736e9	0.211441	0.105720	−	0.994396i	$-0.466285\pi$
$719$	2.10736e9	0.211441	0.105720	+	0.994396i	$0.466285\pi$
$720$	9.52970e8	0.0951514
$721$	−1.41340e9	−0.140440
$722$	1.42622e9	0.141029
$723$	−1.36820e9	−0.134637
$724$	−2.58320e9	−0.252972
$725$	3.42689e8	0.0333977
$726$	2.37083e9	0.229944
$727$	1.52446e10	1.47145	0.735725	−	0.677281i	$-0.236842\pi$
$727$	1.52446e10	1.47145	0.735725	+	0.677281i	$0.236842\pi$
$728$	−7.10341e8	−0.0682350
$729$	3.87420e8	0.0370370
$730$	−9.91884e9	−0.943693
$731$	2.99738e9	0.283812
$732$	1.02460e9	0.0965534
$733$	−8.80231e9	−0.825530	−0.412765	−	0.910838i	$-0.635437\pi$
$733$	−8.80231e9	−0.825530	−0.412765	+	0.910838i	$0.635437\pi$
$734$	1.30517e10	1.21823
$735$	6.94143e9	0.644827
$736$	−2.83852e9	−0.262434
$737$	3.38010e8	0.0311023
$738$	2.43535e9	0.223031
$739$	1.46818e10	1.33820	0.669102	−	0.743170i	$-0.266679\pi$
$739$	1.46818e10	1.33820	0.669102	+	0.743170i	$0.266679\pi$
$740$	−2.45449e9	−0.222664
$741$	−9.14462e9	−0.825661
$742$	−1.18006e9	−0.106045
$743$	1.31756e9	0.117845	0.0589224	−	0.998263i	$-0.481234\pi$
$743$	1.31756e9	0.117845	0.0589224	+	0.998263i	$0.481234\pi$
$744$	1.35230e9	0.120384
$745$	−1.73844e9	−0.154033
$746$	8.69286e9	0.766614
$747$	4.77891e9	0.419476
$748$	−1.70322e9	−0.148804
$749$	1.12242e9	0.0976045
$750$	3.74975e9	0.324555
$751$	−6.26370e9	−0.539624	−0.269812	−	0.962913i	$-0.586962\pi$
$751$	−6.26370e9	−0.539624	−0.269812	+	0.962913i	$0.586962\pi$
$752$	4.70417e9	0.403386
$753$	3.09184e9	0.263897
$754$	−1.19498e9	−0.101522
$755$	−1.07131e10	−0.905941
$756$	−1.68964e8	−0.0142222
$757$	8.13983e9	0.681993	0.340997	−	0.940065i	$-0.389236\pi$
$757$	8.13983e9	0.681993	0.340997	+	0.940065i	$0.389236\pi$
$758$	−2.52479e9	−0.210564
$759$	6.82336e9	0.566438
$760$	−5.35044e9	−0.442122
$761$	−8.43213e9	−0.693571	−0.346786	−	0.937944i	$-0.612727\pi$
$761$	−8.43213e9	−0.693571	−0.346786	+	0.937944i	$0.612727\pi$
$762$	4.22138e9	0.345631
$763$	−1.86193e9	−0.151750
$764$	8.93304e9	0.724724
$765$	−2.12235e9	−0.171396
$766$	5.65358e9	0.454488
$767$	2.12437e9	0.169999
$768$	−4.52985e8	−0.0360844
$769$	−1.10963e10	−0.879902	−0.439951	−	0.898022i	$-0.645004\pi$
$769$	−1.10963e10	−0.879902	−0.439951	+	0.898022i	$0.645004\pi$
$770$	9.99073e8	0.0788642
$771$	9.83277e9	0.772655
$772$	−1.17208e10	−0.916849
$773$	−8.97205e9	−0.698656	−0.349328	−	0.937000i	$-0.613590\pi$
$773$	−8.97205e9	−0.698656	−0.349328	+	0.937000i	$0.613590\pi$
$774$	−1.91630e9	−0.148549
$775$	−2.32136e9	−0.179137
$776$	3.42457e9	0.263081
$777$	4.35188e8	0.0332815
$778$	3.16743e9	0.241145
$779$	−1.36733e10	−1.03631
$780$	5.70439e9	0.430406
$781$	−2.82461e9	−0.212168
$782$	6.32163e9	0.472721
$783$	−2.84243e8	−0.0211604
$784$	−3.29954e9	−0.244539
$785$	−5.98093e9	−0.441291
$786$	7.53998e9	0.553849
$787$	−7.29218e9	−0.533268	−0.266634	−	0.963798i	$-0.585912\pi$
$787$	−7.29218e9	−0.533268	−0.266634	+	0.963798i	$0.585912\pi$
$788$	5.48069e9	0.399019
$789$	−1.53325e10	−1.11133
$790$	−2.14172e9	−0.154550
$791$	−3.05356e8	−0.0219376
$792$	1.08891e9	0.0778847
$793$	6.13319e9	0.436747
$794$	−1.35343e10	−0.959543
$795$	9.47650e9	0.668903
$796$	3.99440e8	0.0280709
$797$	−6.90636e9	−0.483220	−0.241610	−	0.970373i	$-0.577675\pi$
$797$	−6.90636e9	−0.483220	−0.241610	+	0.970373i	$0.577675\pi$
$798$	9.48647e8	0.0660837
$799$	−1.04766e10	−0.726619
$800$	7.77592e8	0.0536954
$801$	5.00239e9	0.343925
$802$	−1.05478e10	−0.722024
$803$	−1.13337e10	−0.772445
$804$	−2.00208e8	−0.0135858
$805$	−3.70814e9	−0.250536
$806$	8.09476e9	0.544542
$807$	−4.37763e8	−0.0293212
$808$	3.23001e8	0.0215409
$809$	3.14663e9	0.208942	0.104471	−	0.994528i	$-0.466685\pi$
$809$	3.14663e9	0.208942	0.104471	+	0.994528i	$0.466685\pi$
$810$	1.35687e9	0.0897096
$811$	7.96292e9	0.524203	0.262101	−	0.965040i	$-0.415584\pi$
$811$	7.96292e9	0.524203	0.262101	+	0.965040i	$0.415584\pi$
$812$	1.23966e8	0.00812559
$813$	1.02576e10	0.669469
$814$	−2.80461e9	−0.182258
$815$	3.97780e9	0.257390
$816$	1.00884e9	0.0649988
$817$	1.07590e10	0.690233
$818$	6.12081e9	0.390996
$819$	−1.01140e9	−0.0643326
$820$	8.52935e9	0.540216
$821$	3.29660e9	0.207905	0.103952	−	0.994582i	$-0.466851\pi$
$821$	3.29660e9	0.207905	0.103952	+	0.994582i	$0.466851\pi$
$822$	−4.07830e9	−0.256111
$823$	−1.24257e10	−0.776999	−0.388500	−	0.921449i	$-0.627007\pi$
$823$	−1.24257e10	−0.776999	−0.388500	+	0.921449i	$0.627007\pi$
$824$	−5.39526e9	−0.335944
$825$	−1.86921e9	−0.115896
$826$	−2.20378e8	−0.0136063
$827$	4.41350e9	0.271340	0.135670	−	0.990754i	$-0.456681\pi$
$827$	4.41350e9	0.271340	0.135670	+	0.990754i	$0.456681\pi$
$828$	−4.04156e9	−0.247425
$829$	8.72723e9	0.532029	0.266015	−	0.963969i	$-0.414293\pi$
$829$	8.72723e9	0.532029	0.266015	+	0.963969i	$0.414293\pi$
$830$	1.67372e10	1.01604
$831$	−3.34943e9	−0.202473
$832$	−2.71153e9	−0.163223
$833$	7.34837e9	0.440487
$834$	4.35650e9	0.260050
$835$	1.71797e10	1.02120
$836$	−6.11365e9	−0.361892
$837$	1.92545e9	0.113499
$838$	−1.60428e10	−0.941727
$839$	−2.17827e10	−1.27334	−0.636671	−	0.771136i	$-0.719689\pi$
$839$	−2.17827e10	−1.27334	−0.636671	+	0.771136i	$0.719689\pi$
$840$	−5.91764e8	−0.0344485
$841$	−1.70413e10	−0.987910
$842$	9.36486e9	0.540641
$843$	3.42284e9	0.196784
$844$	4.01410e9	0.229821
$845$	1.41200e10	0.805072
$846$	6.69794e9	0.380316
$847$	−1.47221e9	−0.0832489
$848$	−4.50456e9	−0.253669
$849$	6.56747e9	0.368317
$850$	−1.73176e9	−0.0967214
$851$	1.04095e10	0.579000
$852$	1.67305e9	0.0926767
$853$	1.58424e10	0.873975	0.436988	−	0.899467i	$-0.356045\pi$
$853$	1.58424e10	0.873975	0.436988	+	0.899467i	$0.356045\pi$
$854$	−6.36247e8	−0.0349561
$855$	−7.61810e9	−0.416836
$856$	4.28453e9	0.233477
$857$	2.86266e10	1.55359	0.776795	−	0.629754i	$-0.216844\pi$
$857$	2.86266e10	1.55359	0.776795	+	0.629754i	$0.216844\pi$
$858$	6.51809e9	0.352302
$859$	−2.17783e10	−1.17233	−0.586164	−	0.810193i	$-0.699362\pi$
$859$	−2.17783e10	−1.17233	−0.586164	+	0.810193i	$0.699362\pi$
$860$	−6.71146e9	−0.359809
$861$	−1.51228e9	−0.0807458
$862$	1.75275e10	0.932064
$863$	2.85634e10	1.51277	0.756384	−	0.654128i	$-0.226964\pi$
$863$	2.85634e10	1.51277	0.756384	+	0.654128i	$0.226964\pi$
$864$	−6.44973e8	−0.0340207
$865$	2.48174e8	0.0130376
$866$	−1.65805e10	−0.867533
$867$	8.83238e9	0.460268
$868$	−8.39737e8	−0.0435837
$869$	−2.44723e9	−0.126504
$870$	−9.95505e8	−0.0512538
$871$	−1.19842e9	−0.0614536
$872$	−7.10740e9	−0.362997
$873$	4.87600e9	0.248035
$874$	2.26913e10	1.14966
$875$	−2.32848e9	−0.117502
$876$	6.71310e9	0.337410
$877$	−2.74548e10	−1.37442	−0.687211	−	0.726458i	$-0.741165\pi$
$877$	−2.74548e10	−1.37442	−0.687211	+	0.726458i	$0.741165\pi$
$878$	−6.05676e9	−0.302002
$879$	−1.67288e10	−0.830816
$880$	3.81368e9	0.188649
$881$	1.02452e10	0.504782	0.252391	−	0.967625i	$-0.418783\pi$
$881$	1.02452e10	0.504782	0.252391	+	0.967625i	$0.418783\pi$
$882$	−4.69798e9	−0.230553
$883$	3.23693e10	1.58223	0.791116	−	0.611666i	$-0.209500\pi$
$883$	3.23693e10	1.58223	0.791116	+	0.611666i	$0.209500\pi$
$884$	6.03881e9	0.294014
$885$	1.76975e9	0.0858242
$886$	1.31120e10	0.633363
$887$	−9.60511e9	−0.462136	−0.231068	−	0.972938i	$-0.574222\pi$
$887$	−9.60511e9	−0.462136	−0.231068	+	0.972938i	$0.574222\pi$
$888$	1.66121e9	0.0796120
$889$	−2.62134e9	−0.125132
$890$	1.75199e10	0.833042
$891$	1.55041e9	0.0734304
$892$	4.74279e9	0.223747
$893$	−3.76055e10	−1.76714
$894$	1.17658e9	0.0550732
$895$	−4.61054e10	−2.14967
$896$	2.81289e8	0.0130640
$897$	−2.41924e10	−1.11920
$898$	−3.49336e9	−0.160982
$899$	−1.41266e9	−0.0648454
$900$	1.10716e9	0.0506245
$901$	1.00321e10	0.456933
$902$	9.74601e9	0.442185
$903$	1.18996e9	0.0537805
$904$	−1.16561e9	−0.0524764
$905$	−1.28816e10	−0.577696
$906$	7.25064e9	0.323912
$907$	1.72814e10	0.769049	0.384524	−	0.923115i	$-0.374365\pi$
$907$	1.72814e10	0.769049	0.384524	+	0.923115i	$0.374365\pi$
$908$	1.11099e10	0.492505
$909$	4.59898e8	0.0203090
$910$	−3.54225e9	−0.155824
$911$	6.29595e9	0.275897	0.137949	−	0.990439i	$-0.455949\pi$
$911$	6.29595e9	0.275897	0.137949	+	0.990439i	$0.455949\pi$
$912$	3.62119e9	0.158077
$913$	1.91247e10	0.831661
$914$	2.30755e10	0.999629
$915$	5.10938e9	0.220493
$916$	1.34684e9	0.0579006
$917$	−4.68208e9	−0.200515
$918$	1.43641e9	0.0612814
$919$	1.91283e10	0.812967	0.406484	−	0.913658i	$-0.366755\pi$
$919$	1.91283e10	0.812967	0.406484	+	0.913658i	$0.366755\pi$
$920$	−1.41548e10	−0.599302
$921$	−2.64908e9	−0.111734
$922$	−2.18472e10	−0.917990
$923$	1.00147e10	0.419212
$924$	−6.76176e8	−0.0281973
$925$	−2.85162e9	−0.118467
$926$	1.52087e10	0.629437
$927$	−7.68193e9	−0.316731
$928$	4.73203e8	0.0194370
$929$	1.91374e10	0.783120	0.391560	−	0.920153i	$-0.371936\pi$
$929$	1.91374e10	0.783120	0.391560	+	0.920153i	$0.371936\pi$
$930$	6.74350e9	0.274913
$931$	2.63768e10	1.07127
$932$	5.06207e8	0.0204820
$933$	2.17118e10	0.875206
$934$	1.72835e10	0.694092
$935$	−8.49340e9	−0.339814
$936$	−3.86075e9	−0.153888
$937$	1.89347e10	0.751917	0.375959	−	0.926636i	$-0.377313\pi$
$937$	1.89347e10	0.751917	0.375959	+	0.926636i	$0.377313\pi$
$938$	1.24323e8	0.00491858
$939$	4.88286e9	0.192462
$940$	2.34582e10	0.921187
$941$	2.68365e10	1.04994	0.524968	−	0.851122i	$-0.324077\pi$
$941$	2.68365e10	1.04994	0.524968	+	0.851122i	$0.324077\pi$
$942$	4.04791e9	0.157780
$943$	−3.61731e10	−1.40474
$944$	−8.41232e8	−0.0325472
$945$	−8.42570e8	−0.0324784
$946$	−7.66881e9	−0.294516
$947$	−2.07924e10	−0.795573	−0.397786	−	0.917478i	$-0.630221\pi$
$947$	−2.07924e10	−0.795573	−0.397786	+	0.917478i	$0.630221\pi$
$948$	1.44952e9	0.0552581
$949$	4.01840e10	1.52624
$950$	−6.21612e9	−0.235227
$951$	−6.92372e9	−0.261040
$952$	−6.26455e8	−0.0235321
$953$	2.94329e10	1.10156	0.550781	−	0.834650i	$-0.314330\pi$
$953$	2.94329e10	1.10156	0.550781	+	0.834650i	$0.314330\pi$
$954$	−6.41372e9	−0.239161
$955$	4.45462e10	1.65500
$956$	1.53948e10	0.569864
$957$	−1.13751e9	−0.0419530
$958$	−1.91853e10	−0.705001
$959$	2.53250e9	0.0927222
$960$	−2.25889e9	−0.0824036
$961$	−1.79433e10	−0.652185
$962$	9.94384e9	0.360115
$963$	6.10043e9	0.220125
$964$	3.24314e9	0.116599
$965$	−5.84481e10	−2.09375
$966$	2.50968e9	0.0895775
$967$	3.07634e10	1.09406	0.547031	−	0.837113i	$-0.315758\pi$
$967$	3.07634e10	1.09406	0.547031	+	0.837113i	$0.315758\pi$
$968$	−5.61975e9	−0.199138
$969$	−8.06471e9	−0.284745
$970$	1.70772e10	0.600781
$971$	1.82869e10	0.641020	0.320510	−	0.947245i	$-0.396146\pi$
$971$	1.82869e10	0.641020	0.320510	+	0.947245i	$0.396146\pi$
$972$	−9.18330e8	−0.0320750
$973$	−2.70525e9	−0.0941482
$974$	2.35607e10	0.817017
$975$	6.62734e9	0.228994
$976$	−2.42869e9	−0.0836177
$977$	−7.33555e9	−0.251653	−0.125826	−	0.992052i	$-0.540158\pi$
$977$	−7.33555e9	−0.251653	−0.125826	+	0.992052i	$0.540158\pi$
$978$	−2.69219e9	−0.0920278
$979$	2.00190e10	0.681873
$980$	−1.64538e10	−0.558437
$981$	−1.01197e10	−0.342237
$982$	−1.98184e10	−0.667849
$983$	2.08551e10	0.700285	0.350142	−	0.936696i	$-0.386133\pi$
$983$	2.08551e10	0.700285	0.350142	+	0.936696i	$0.386133\pi$
$984$	−5.77269e9	−0.193150
$985$	2.73305e10	0.911214
$986$	−1.05387e9	−0.0350119
$987$	−4.15920e9	−0.137689
$988$	2.16761e10	0.715043
$989$	2.84634e10	0.935621
$990$	5.43003e9	0.177860
$991$	5.03707e10	1.64407	0.822034	−	0.569438i	$-0.192839\pi$
$991$	5.03707e10	1.64407	0.822034	+	0.569438i	$0.192839\pi$
$992$	−3.20546e9	−0.104256
$993$	−1.95467e10	−0.633505
$994$	−1.03891e9	−0.0335526
$995$	1.99188e9	0.0641037
$996$	−1.13278e10	−0.363276
$997$	−5.54924e10	−1.77337	−0.886687	−	0.462371i	$-0.846999\pi$
$997$	−5.54924e10	−1.77337	−0.886687	+	0.462371i	$0.846999\pi$
$998$	1.67337e10	0.532887
$999$	2.36527e9	0.0750589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.d.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.d.1.8	✓	8	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +319.148 q^{5} -216.000 q^{6} +134.129 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} +319.148 q^{5} -216.000 q^{6} +134.129 q^{7} +512.000 q^{8} +729.000 q^{9} +2553.18 q^{10} +2917.38 q^{11} -1728.00 q^{12} -10343.7 q^{13} +1073.03 q^{14} -8616.99 q^{15} +4096.00 q^{16} -9122.15 q^{17} +5832.00 q^{18} -32743.7 q^{19} +20425.4 q^{20} -3621.49 q^{21} +23339.0 q^{22} -86624.7 q^{23} -13824.0 q^{24} +23730.2 q^{25} -82749.2 q^{26} -19683.0 q^{27} +8584.26 q^{28} +14441.0 q^{29} -68935.9 q^{30} -97822.8 q^{31} +32768.0 q^{32} -78769.2 q^{33} -72977.2 q^{34} +42807.0 q^{35} +46656.0 q^{36} -120168. q^{37} -261950. q^{38} +279279. q^{39} +163404. q^{40} +417584. q^{41} -28971.9 q^{42} -328583. q^{43} +186712. q^{44} +232659. q^{45} -692998. q^{46} +1.14848e6 q^{47} -110592. q^{48} -805552. q^{49} +189842. q^{50} +246298. q^{51} -661994. q^{52} -1.09975e6 q^{53} -157464. q^{54} +931074. q^{55} +68674.1 q^{56} +884080. q^{57} +115528. q^{58} -205379. q^{59} -551487. q^{60} -592942. q^{61} -782582. q^{62} +97780.1 q^{63} +262144. q^{64} -3.30115e6 q^{65} -630154. q^{66} +115861. q^{67} -583817. q^{68} +2.33887e6 q^{69} +342456. q^{70} -968201. q^{71} +373248. q^{72} -3.88489e6 q^{73} -961346. q^{74} -640716. q^{75} -2.09560e6 q^{76} +391305. q^{77} +2.23423e6 q^{78} -838845. q^{79} +1.30723e6 q^{80} +531441. q^{81} +3.34068e6 q^{82} +6.55543e6 q^{83} -231775. q^{84} -2.91131e6 q^{85} -2.62866e6 q^{86} -389908. q^{87} +1.49370e6 q^{88} +6.86199e6 q^{89} +1.86127e6 q^{90} -1.38739e6 q^{91} -5.54398e6 q^{92} +2.64122e6 q^{93} +9.18784e6 q^{94} -1.04501e7 q^{95} -884736. q^{96} +6.68861e6 q^{97} -6.44442e6 q^{98} +2.12677e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{2} - 216 q^{3} + 512 q^{4} - 592 q^{5} - 1728 q^{6} - 340 q^{7} + 4096 q^{8} + 5832 q^{9}+O(q^{10}) \) 8 * q + 64 * q^2 - 216 * q^3 + 512 * q^4 - 592 * q^5 - 1728 * q^6 - 340 * q^7 + 4096 * q^8 + 5832 * q^9	\( 8 q + 64 q^{2} - 216 q^{3} + 512 q^{4} - 592 q^{5} - 1728 q^{6} - 340 q^{7} + 4096 q^{8} + 5832 q^{9} - 4736 q^{10} - 2852 q^{11} - 13824 q^{12} + 1142 q^{13} - 2720 q^{14} + 15984 q^{15} + 32768 q^{16} - 22528 q^{17} + 46656 q^{18} - 33528 q^{19} - 37888 q^{20} + 9180 q^{21} - 22816 q^{22} + 41330 q^{23} - 110592 q^{24} + 209004 q^{25} + 9136 q^{26} - 157464 q^{27} - 21760 q^{28} - 48334 q^{29} + 127872 q^{30} + 217552 q^{31} + 262144 q^{32} + 77004 q^{33} - 180224 q^{34} - 171714 q^{35} + 373248 q^{36} - 77966 q^{37} - 268224 q^{38} - 30834 q^{39} - 303104 q^{40} - 446410 q^{41} + 73440 q^{42} - 470890 q^{43} - 182528 q^{44} - 431568 q^{45} + 330640 q^{46} + 1876568 q^{47} - 884736 q^{48} + 1667480 q^{49} + 1672032 q^{50} + 608256 q^{51} + 73088 q^{52} - 1155672 q^{53} - 1259712 q^{54} + 112064 q^{55} - 174080 q^{56} + 905256 q^{57} - 386672 q^{58} - 1643032 q^{59} + 1022976 q^{60} - 9094962 q^{61} + 1740416 q^{62} - 247860 q^{63} + 2097152 q^{64} - 6726234 q^{65} + 616032 q^{66} - 8552352 q^{67} - 1441792 q^{68} - 1115910 q^{69} - 1373712 q^{70} - 5829156 q^{71} + 2985984 q^{72} - 7639392 q^{73} - 623728 q^{74} - 5643108 q^{75} - 2145792 q^{76} - 17178270 q^{77} - 246672 q^{78} - 12614888 q^{79} - 2424832 q^{80} + 4251528 q^{81} - 3571280 q^{82} - 19145486 q^{83} + 587520 q^{84} - 20127842 q^{85} - 3767120 q^{86} + 1305018 q^{87} - 1460224 q^{88} - 16050066 q^{89} - 3452544 q^{90} - 20086856 q^{91} + 2645120 q^{92} - 5873904 q^{93} + 15012544 q^{94} - 8130136 q^{95} - 7077888 q^{96} - 1961876 q^{97} + 13339840 q^{98} - 2079108 q^{99}+O(q^{100}) \) 8 * q + 64 * q^2 - 216 * q^3 + 512 * q^4 - 592 * q^5 - 1728 * q^6 - 340 * q^7 + 4096 * q^8 + 5832 * q^9 - 4736 * q^10 - 2852 * q^11 - 13824 * q^12 + 1142 * q^13 - 2720 * q^14 + 15984 * q^15 + 32768 * q^16 - 22528 * q^17 + 46656 * q^18 - 33528 * q^19 - 37888 * q^20 + 9180 * q^21 - 22816 * q^22 + 41330 * q^23 - 110592 * q^24 + 209004 * q^25 + 9136 * q^26 - 157464 * q^27 - 21760 * q^28 - 48334 * q^29 + 127872 * q^30 + 217552 * q^31 + 262144 * q^32 + 77004 * q^33 - 180224 * q^34 - 171714 * q^35 + 373248 * q^36 - 77966 * q^37 - 268224 * q^38 - 30834 * q^39 - 303104 * q^40 - 446410 * q^41 + 73440 * q^42 - 470890 * q^43 - 182528 * q^44 - 431568 * q^45 + 330640 * q^46 + 1876568 * q^47 - 884736 * q^48 + 1667480 * q^49 + 1672032 * q^50 + 608256 * q^51 + 73088 * q^52 - 1155672 * q^53 - 1259712 * q^54 + 112064 * q^55 - 174080 * q^56 + 905256 * q^57 - 386672 * q^58 - 1643032 * q^59 + 1022976 * q^60 - 9094962 * q^61 + 1740416 * q^62 - 247860 * q^63 + 2097152 * q^64 - 6726234 * q^65 + 616032 * q^66 - 8552352 * q^67 - 1441792 * q^68 - 1115910 * q^69 - 1373712 * q^70 - 5829156 * q^71 + 2985984 * q^72 - 7639392 * q^73 - 623728 * q^74 - 5643108 * q^75 - 2145792 * q^76 - 17178270 * q^77 - 246672 * q^78 - 12614888 * q^79 - 2424832 * q^80 + 4251528 * q^81 - 3571280 * q^82 - 19145486 * q^83 + 587520 * q^84 - 20127842 * q^85 - 3767120 * q^86 + 1305018 * q^87 - 1460224 * q^88 - 16050066 * q^89 - 3452544 * q^90 - 20086856 * q^91 + 2645120 * q^92 - 5873904 * q^93 + 15012544 * q^94 - 8130136 * q^95 - 7077888 * q^96 - 1961876 * q^97 + 13339840 * q^98 - 2079108 * q^99

Introduction

L-functions

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