LMFDB - Embedded newform 338.8.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,8,Mod(1,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, 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("338.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	338.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:	$105.586138614$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6981x^{2} - 35424x + 7188480 $ x^4 - 6981x^2 - 35424x + 7188480
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-39.9844$ of defining polynomial
Character	$\chi$	$=$	338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -39.9844 q^{3} +64.0000 q^{4} -323.700 q^{5} +319.875 q^{6} +568.591 q^{7} -512.000 q^{8} -588.246 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -39.9844 q^{3} +64.0000 q^{4} -323.700 q^{5} +319.875 q^{6} +568.591 q^{7} -512.000 q^{8} -588.246 q^{9} +2589.60 q^{10} -238.225 q^{11} -2559.00 q^{12} -4548.73 q^{14} +12943.0 q^{15} +4096.00 q^{16} +20466.6 q^{17} +4705.97 q^{18} -9642.32 q^{19} -20716.8 q^{20} -22734.8 q^{21} +1905.80 q^{22} -78264.6 q^{23} +20472.0 q^{24} +26657.0 q^{25} +110967. q^{27} +36389.8 q^{28} -138865. q^{29} -103544. q^{30} +160571. q^{31} -32768.0 q^{32} +9525.29 q^{33} -163733. q^{34} -184053. q^{35} -37647.7 q^{36} -152955. q^{37} +77138.6 q^{38} +165735. q^{40} +185436. q^{41} +181878. q^{42} +85009.0 q^{43} -15246.4 q^{44} +190415. q^{45} +626117. q^{46} -1.20335e6 q^{47} -163776. q^{48} -500247. q^{49} -213256. q^{50} -818346. q^{51} -665967. q^{53} -887733. q^{54} +77113.6 q^{55} -291119. q^{56} +385543. q^{57} +1.11092e6 q^{58} -2.48619e6 q^{59} +828351. q^{60} -3.04600e6 q^{61} -1.28456e6 q^{62} -334471. q^{63} +262144. q^{64} -76202.4 q^{66} -387876. q^{67} +1.30986e6 q^{68} +3.12937e6 q^{69} +1.47243e6 q^{70} +3.68031e6 q^{71} +301182. q^{72} +1.57546e6 q^{73} +1.22364e6 q^{74} -1.06586e6 q^{75} -617108. q^{76} -135453. q^{77} +2.29576e6 q^{79} -1.32588e6 q^{80} -3.15044e6 q^{81} -1.48349e6 q^{82} -7.93544e6 q^{83} -1.45503e6 q^{84} -6.62505e6 q^{85} -680072. q^{86} +5.55242e6 q^{87} +121971. q^{88} +8.15082e6 q^{89} -1.52332e6 q^{90} -5.00893e6 q^{92} -6.42032e6 q^{93} +9.62678e6 q^{94} +3.12122e6 q^{95} +1.31021e6 q^{96} -1.33959e6 q^{97} +4.00198e6 q^{98} +140135. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} + 256 q^{4} + 278 q^{5} + 548 q^{7} - 2048 q^{8} + 5214 q^{9}+O(q^{10}) $ 4 * q - 32 * q^2 + 256 * q^4 + 278 * q^5 + 548 * q^7 - 2048 * q^8 + 5214 * q^9	\( 4 q - 32 q^{2} + 256 q^{4} + 278 q^{5} + 548 q^{7} - 2048 q^{8} + 5214 q^{9} - 2224 q^{10} + 7392 q^{11} - 4384 q^{14} - 15528 q^{15} + 16384 q^{16} - 28316 q^{17} - 41712 q^{18} + 99888 q^{19} + 17792 q^{20} + 91074 q^{21} - 59136 q^{22} + 33388 q^{23} + 86878 q^{25} + 106272 q^{27} + 35072 q^{28} - 93140 q^{29} + 124224 q^{30} + 311160 q^{31} - 131072 q^{32} - 238638 q^{33} + 226528 q^{34} - 141544 q^{35} + 333696 q^{36} + 9636 q^{37} - 799104 q^{38} - 142336 q^{40} - 82892 q^{41} - 728592 q^{42} + 569264 q^{43} + 473088 q^{44} + 2303394 q^{45} - 267104 q^{46} - 574200 q^{47} + 717798 q^{49} - 695024 q^{50} - 2729928 q^{51} + 1235350 q^{53} - 850176 q^{54} + 1092512 q^{55} - 280576 q^{56} + 3528462 q^{57} + 745120 q^{58} - 231504 q^{59} - 993792 q^{60} - 685684 q^{61} - 2489280 q^{62} + 5951712 q^{63} + 1048576 q^{64} + 1909104 q^{66} - 3271056 q^{67} - 1812224 q^{68} - 5600034 q^{69} + 1132352 q^{70} + 175012 q^{71} - 2669568 q^{72} + 7137890 q^{73} - 77088 q^{74} - 22200960 q^{75} + 6392832 q^{76} - 13915206 q^{77} - 7053952 q^{79} + 1138688 q^{80} - 3758004 q^{81} + 663136 q^{82} + 657288 q^{83} + 5828736 q^{84} - 11814998 q^{85} - 4554112 q^{86} + 7182900 q^{87} - 3784704 q^{88} + 11452234 q^{89} - 18427152 q^{90} + 2136832 q^{92} - 2984688 q^{93} + 4593600 q^{94} + 23334088 q^{95} + 428002 q^{97} - 5742384 q^{98} - 10357656 q^{99}+O(q^{100}) \) 4 * q - 32 * q^2 + 256 * q^4 + 278 * q^5 + 548 * q^7 - 2048 * q^8 + 5214 * q^9 - 2224 * q^10 + 7392 * q^11 - 4384 * q^14 - 15528 * q^15 + 16384 * q^16 - 28316 * q^17 - 41712 * q^18 + 99888 * q^19 + 17792 * q^20 + 91074 * q^21 - 59136 * q^22 + 33388 * q^23 + 86878 * q^25 + 106272 * q^27 + 35072 * q^28 - 93140 * q^29 + 124224 * q^30 + 311160 * q^31 - 131072 * q^32 - 238638 * q^33 + 226528 * q^34 - 141544 * q^35 + 333696 * q^36 + 9636 * q^37 - 799104 * q^38 - 142336 * q^40 - 82892 * q^41 - 728592 * q^42 + 569264 * q^43 + 473088 * q^44 + 2303394 * q^45 - 267104 * q^46 - 574200 * q^47 + 717798 * q^49 - 695024 * q^50 - 2729928 * q^51 + 1235350 * q^53 - 850176 * q^54 + 1092512 * q^55 - 280576 * q^56 + 3528462 * q^57 + 745120 * q^58 - 231504 * q^59 - 993792 * q^60 - 685684 * q^61 - 2489280 * q^62 + 5951712 * q^63 + 1048576 * q^64 + 1909104 * q^66 - 3271056 * q^67 - 1812224 * q^68 - 5600034 * q^69 + 1132352 * q^70 + 175012 * q^71 - 2669568 * q^72 + 7137890 * q^73 - 77088 * q^74 - 22200960 * q^75 + 6392832 * q^76 - 13915206 * q^77 - 7053952 * q^79 + 1138688 * q^80 - 3758004 * q^81 + 663136 * q^82 + 657288 * q^83 + 5828736 * q^84 - 11814998 * q^85 - 4554112 * q^86 + 7182900 * q^87 - 3784704 * q^88 + 11452234 * q^89 - 18427152 * q^90 + 2136832 * q^92 - 2984688 * q^93 + 4593600 * q^94 + 23334088 * q^95 + 428002 * q^97 - 5742384 * q^98 - 10357656 * 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
$3$	−39.9844	−0.855001	−0.427500	−	0.904015i	$-0.640606\pi$
$3$	−39.9844	−0.855001	−0.427500	+	0.904015i	$0.640606\pi$
$4$	64.0000	0.500000
$5$	−323.700	−1.15811	−0.579053	−	0.815290i	$-0.696578\pi$
$5$	−323.700	−1.15811	−0.579053	+	0.815290i	$0.696578\pi$
$6$	319.875	0.604577
$7$	568.591	0.626552	0.313276	−	0.949662i	$-0.398574\pi$
$7$	568.591	0.626552	0.313276	+	0.949662i	$0.398574\pi$
$8$	−512.000	−0.353553
$9$	−588.246	−0.268974
$10$	2589.60	0.818905
$11$	−238.225	−0.0539651	−0.0269826	−	0.999636i	$-0.508590\pi$
$11$	−238.225	−0.0539651	−0.0269826	+	0.999636i	$0.508590\pi$
$12$	−2559.00	−0.427500
$13$	0	0
$13$	0	0
$14$	−4548.73	−0.443039
$15$	12943.0	0.990181
$16$	4096.00	0.250000
$17$	20466.6	1.01036	0.505178	−	0.863015i	$-0.331427\pi$
$17$	20466.6	1.01036	0.505178	+	0.863015i	$0.331427\pi$
$18$	4705.97	0.190193
$19$	−9642.32	−0.322511	−0.161255	−	0.986913i	$-0.551554\pi$
$19$	−9642.32	−0.322511	−0.161255	+	0.986913i	$0.551554\pi$
$20$	−20716.8	−0.579053
$21$	−22734.8	−0.535702
$22$	1905.80	0.0381591
$23$	−78264.6	−1.34128	−0.670638	−	0.741785i	$-0.733979\pi$
$23$	−78264.6	−1.34128	−0.670638	+	0.741785i	$0.733979\pi$
$24$	20472.0	0.302288
$25$	26657.0	0.341210
$26$	0	0
$27$	110967.	1.08497
$28$	36389.8	0.313276
$29$	−138865.	−1.05730	−0.528650	−	0.848840i	$-0.677302\pi$
$29$	−138865.	−1.05730	−0.528650	+	0.848840i	$0.677302\pi$
$30$	−103544.	−0.700164
$31$	160571.	0.968055	0.484027	−	0.875053i	$-0.339174\pi$
$31$	160571.	0.968055	0.484027	+	0.875053i	$0.339174\pi$
$32$	−32768.0	−0.176777
$33$	9525.29	0.0461402
$34$	−163733.	−0.714430
$35$	−184053.	−0.725614
$36$	−37647.7	−0.134487
$37$	−152955.	−0.496430	−0.248215	−	0.968705i	$-0.579844\pi$
$37$	−152955.	−0.496430	−0.248215	+	0.968705i	$0.579844\pi$
$38$	77138.6	0.228049
$39$	0	0
$40$	165735.	0.409452
$41$	185436.	0.420195	0.210097	−	0.977680i	$-0.432622\pi$
$41$	185436.	0.420195	0.210097	+	0.977680i	$0.432622\pi$
$42$	181878.	0.378799
$43$	85009.0	0.163052	0.0815259	−	0.996671i	$-0.474021\pi$
$43$	85009.0	0.163052	0.0815259	+	0.996671i	$0.474021\pi$
$44$	−15246.4	−0.0269826
$45$	190415.	0.311500
$46$	626117.	0.948425
$47$	−1.20335e6	−1.69063	−0.845315	−	0.534268i	$-0.820587\pi$
$47$	−1.20335e6	−1.69063	−0.845315	+	0.534268i	$0.820587\pi$
$48$	−163776.	−0.213750
$49$	−500247.	−0.607433
$50$	−213256.	−0.241272
$51$	−818346.	−0.863856
$52$	0	0
$53$	−665967.	−0.614451	−0.307225	−	0.951637i	$-0.599401\pi$
$53$	−665967.	−0.614451	−0.307225	+	0.951637i	$0.599401\pi$
$54$	−887733.	−0.767192
$55$	77113.6	0.0624973
$56$	−291119.	−0.221520
$57$	385543.	0.275747
$58$	1.11092e6	0.747624
$59$	−2.48619e6	−1.57598	−0.787992	−	0.615686i	$-0.788879\pi$
$59$	−2.48619e6	−1.57598	−0.787992	+	0.615686i	$0.788879\pi$
$60$	828351.	0.495091
$61$	−3.04600e6	−1.71821	−0.859104	−	0.511801i	$-0.828978\pi$
$61$	−3.04600e6	−1.71821	−0.859104	+	0.511801i	$0.828978\pi$
$62$	−1.28456e6	−0.684518
$63$	−334471.	−0.168526
$64$	262144.	0.125000
$65$	0	0
$66$	−76202.4	−0.0326261
$67$	−387876.	−0.157554	−0.0787772	−	0.996892i	$-0.525102\pi$
$67$	−387876.	−0.157554	−0.0787772	+	0.996892i	$0.525102\pi$
$68$	1.30986e6	0.505178
$69$	3.12937e6	1.14679
$70$	1.47243e6	0.513086
$71$	3.68031e6	1.22034	0.610170	−	0.792271i	$-0.291101\pi$
$71$	3.68031e6	1.22034	0.610170	+	0.792271i	$0.291101\pi$
$72$	301182.	0.0950966
$73$	1.57546e6	0.473998	0.236999	−	0.971510i	$-0.423836\pi$
$73$	1.57546e6	0.473998	0.236999	+	0.971510i	$0.423836\pi$
$74$	1.22364e6	0.351029
$75$	−1.06586e6	−0.291734
$76$	−617108.	−0.161255
$77$	−135453.	−0.0338120
$78$	0	0
$79$	2.29576e6	0.523880	0.261940	−	0.965084i	$-0.415638\pi$
$79$	2.29576e6	0.523880	0.261940	+	0.965084i	$0.415638\pi$
$80$	−1.32588e6	−0.289527
$81$	−3.15044e6	−0.658679
$82$	−1.48349e6	−0.297122
$83$	−7.93544e6	−1.52334	−0.761672	−	0.647963i	$-0.775621\pi$
$83$	−7.93544e6	−1.52334	−0.761672	+	0.647963i	$0.775621\pi$
$84$	−1.45503e6	−0.267851
$85$	−6.62505e6	−1.17010
$86$	−680072.	−0.115295
$87$	5.55242e6	0.903993
$88$	121971.	0.0190796
$89$	8.15082e6	1.22556	0.612782	−	0.790252i	$-0.290050\pi$
$89$	8.15082e6	1.22556	0.612782	+	0.790252i	$0.290050\pi$
$90$	−1.52332e6	−0.220264
$91$	0	0
$92$	−5.00893e6	−0.670638
$93$	−6.42032e6	−0.827687
$94$	9.62678e6	1.19546
$95$	3.12122e6	0.373501
$96$	1.31021e6	0.151144
$97$	−1.33959e6	−0.149029	−0.0745145	−	0.997220i	$-0.523741\pi$
$97$	−1.33959e6	−0.149029	−0.0745145	+	0.997220i	$0.523741\pi$
$98$	4.00198e6	0.429520
$99$	140135.	0.0145152
$100$	1.70605e6	0.170605
$101$	−1.92768e7	−1.86170	−0.930852	−	0.365396i	$-0.880934\pi$
$101$	−1.92768e7	−1.86170	−0.930852	+	0.365396i	$0.880934\pi$
$102$	6.54677e6	0.610838
$103$	−1.54295e7	−1.39130	−0.695652	−	0.718379i	$-0.744884\pi$
$103$	−1.54295e7	−1.39130	−0.695652	+	0.718379i	$0.744884\pi$
$104$	0	0
$105$	7.35926e6	0.620400
$106$	5.32773e6	0.434482
$107$	−1.04249e7	−0.822673	−0.411337	−	0.911483i	$-0.634938\pi$
$107$	−1.04249e7	−0.822673	−0.411337	+	0.911483i	$0.634938\pi$
$108$	7.10186e6	0.542487
$109$	1.55544e7	1.15043	0.575216	−	0.818001i	$-0.304918\pi$
$109$	1.55544e7	1.15043	0.575216	+	0.818001i	$0.304918\pi$
$110$	−616909.	−0.0441923
$111$	6.11583e6	0.424448
$112$	2.32895e6	0.156638
$113$	−936077.	−0.0610291	−0.0305145	−	0.999534i	$-0.509715\pi$
$113$	−936077.	−0.0610291	−0.0305145	+	0.999534i	$0.509715\pi$
$114$	−3.08434e6	−0.194982
$115$	2.53343e7	1.55334
$116$	−8.88733e6	−0.528650
$117$	0	0
$118$	1.98895e7	1.11439
$119$	1.16371e7	0.633041
$120$	−6.62680e6	−0.350082
$121$	−1.94304e7	−0.997088
$122$	2.43680e7	1.21496
$123$	−7.41455e6	−0.359267
$124$	1.02765e7	0.484027
$125$	1.66602e7	0.762949
$126$	2.67577e6	0.119166
$127$	−8.47172e6	−0.366994	−0.183497	−	0.983020i	$-0.558742\pi$
$127$	−8.47172e6	−0.366994	−0.183497	+	0.983020i	$0.558742\pi$
$128$	−2.09715e6	−0.0883883
$129$	−3.39904e6	−0.139409
$130$	0	0
$131$	1.17131e7	0.455219	0.227610	−	0.973752i	$-0.426909\pi$
$131$	1.17131e7	0.455219	0.227610	+	0.973752i	$0.426909\pi$
$132$	609619.	0.0230701
$133$	−5.48254e6	−0.202070
$134$	3.10301e6	0.111408
$135$	−3.59199e7	−1.25651
$136$	−1.04789e7	−0.357215
$137$	3.74992e7	1.24595	0.622975	−	0.782242i	$-0.285924\pi$
$137$	3.74992e7	1.24595	0.622975	+	0.782242i	$0.285924\pi$
$138$	−2.50349e7	−0.810904
$139$	−2.81058e7	−0.887656	−0.443828	−	0.896112i	$-0.646380\pi$
$139$	−2.81058e7	−0.887656	−0.443828	+	0.896112i	$0.646380\pi$
$140$	−1.17794e7	−0.362807
$141$	4.81152e7	1.44549
$142$	−2.94425e7	−0.862910
$143$	0	0
$144$	−2.40945e6	−0.0672435
$145$	4.49505e7	1.22447
$146$	−1.26036e7	−0.335167
$147$	2.00021e7	0.519355
$148$	−9.78913e6	−0.248215
$149$	4.59009e7	1.13676	0.568381	−	0.822766i	$-0.307570\pi$
$149$	4.59009e7	1.13676	0.568381	+	0.822766i	$0.307570\pi$
$150$	8.52692e6	0.206287
$151$	4.77305e7	1.12818	0.564088	−	0.825714i	$-0.309228\pi$
$151$	4.77305e7	1.12818	0.564088	+	0.825714i	$0.309228\pi$
$152$	4.93687e6	0.114025
$153$	−1.20394e7	−0.271759
$154$	1.08362e6	0.0239087
$155$	−5.19768e7	−1.12111
$156$	0	0
$157$	7.12033e7	1.46842	0.734212	−	0.678921i	$-0.237552\pi$
$157$	7.12033e7	1.46842	0.734212	+	0.678921i	$0.237552\pi$
$158$	−1.83661e7	−0.370439
$159$	2.66283e7	0.525356
$160$	1.06070e7	0.204726
$161$	−4.45006e7	−0.840379
$162$	2.52035e7	0.465757
$163$	6.22061e7	1.12506	0.562531	−	0.826776i	$-0.309828\pi$
$163$	6.22061e7	1.12506	0.562531	+	0.826776i	$0.309828\pi$
$164$	1.18679e7	0.210097
$165$	−3.08334e6	−0.0534353
$166$	6.34835e7	1.07717
$167$	2.24576e7	0.373127	0.186563	−	0.982443i	$-0.440265\pi$
$167$	2.24576e7	0.373127	0.186563	+	0.982443i	$0.440265\pi$
$168$	1.16402e7	0.189399
$169$	0	0
$170$	5.30004e7	0.827386
$171$	5.67205e6	0.0867469
$172$	5.44058e6	0.0815259
$173$	8.61689e7	1.26529	0.632643	−	0.774443i	$-0.281970\pi$
$173$	8.61689e7	1.26529	0.632643	+	0.774443i	$0.281970\pi$
$174$	−4.44194e7	−0.639219
$175$	1.51569e7	0.213785
$176$	−975770.	−0.0134913
$177$	9.94087e7	1.34747
$178$	−6.52066e7	−0.866605
$179$	−7.11140e7	−0.926764	−0.463382	−	0.886159i	$-0.653364\pi$
$179$	−7.11140e7	−0.926764	−0.463382	+	0.886159i	$0.653364\pi$
$180$	1.21866e7	0.155750
$181$	1.39420e8	1.74763	0.873817	−	0.486254i	$-0.161637\pi$
$181$	1.39420e8	1.74763	0.873817	+	0.486254i	$0.161637\pi$
$182$	0	0
$183$	1.21793e8	1.46907
$184$	4.00715e7	0.474212
$185$	4.95117e7	0.574919
$186$	5.13626e7	0.585263
$187$	−4.87566e6	−0.0545240
$188$	−7.70143e7	−0.845315
$189$	6.30946e7	0.679792
$190$	−2.49698e7	−0.264105
$191$	−8.58028e7	−0.891015	−0.445507	−	0.895278i	$-0.646977\pi$
$191$	−8.58028e7	−0.891015	−0.445507	+	0.895278i	$0.646977\pi$
$192$	−1.04817e7	−0.106875
$193$	2.35447e7	0.235745	0.117872	−	0.993029i	$-0.462393\pi$
$193$	2.35447e7	0.235745	0.117872	+	0.993029i	$0.462393\pi$
$194$	1.07167e7	0.105379
$195$	0	0
$196$	−3.20158e7	−0.303716
$197$	7.14744e7	0.666068	0.333034	−	0.942915i	$-0.391928\pi$
$197$	7.14744e7	0.666068	0.333034	+	0.942915i	$0.391928\pi$
$198$	−1.12108e6	−0.0102638
$199$	2.15604e8	1.93941	0.969706	−	0.244273i	$-0.0785493\pi$
$199$	2.15604e8	1.93941	0.969706	+	0.244273i	$0.0785493\pi$
$200$	−1.36484e7	−0.120636
$201$	1.55090e7	0.134709
$202$	1.54215e8	1.31642
$203$	−7.89572e7	−0.662454
$204$	−5.23741e7	−0.431928
$205$	−6.00257e7	−0.486630
$206$	1.23436e8	0.983800
$207$	4.60388e7	0.360768
$208$	0	0
$209$	2.29704e6	0.0174043
$210$	−5.88741e7	−0.438689
$211$	8.93956e7	0.655130	0.327565	−	0.944829i	$-0.393772\pi$
$211$	8.93956e7	0.655130	0.327565	+	0.944829i	$0.393772\pi$
$212$	−4.26219e7	−0.307225
$213$	−1.47155e8	−1.04339
$214$	8.33990e7	0.581718
$215$	−2.75175e7	−0.188831
$216$	−5.68149e7	−0.383596
$217$	9.12990e7	0.606537
$218$	−1.24435e8	−0.813479
$219$	−6.29937e7	−0.405268
$220$	4.93527e6	0.0312487
$221$	0	0
$222$	−4.89266e7	−0.300130
$223$	1.07527e8	0.649310	0.324655	−	0.945832i	$-0.394752\pi$
$223$	1.07527e8	0.649310	0.324655	+	0.945832i	$0.394752\pi$
$224$	−1.86316e7	−0.110760
$225$	−1.56809e7	−0.0917764
$226$	7.48861e6	0.0431541
$227$	−2.15079e8	−1.22041	−0.610207	−	0.792242i	$-0.708914\pi$
$227$	−2.15079e8	−1.22041	−0.610207	+	0.792242i	$0.708914\pi$
$228$	2.46747e7	0.137873
$229$	−3.12216e8	−1.71803	−0.859016	−	0.511949i	$-0.828924\pi$
$229$	−3.12216e8	−1.71803	−0.859016	+	0.511949i	$0.828924\pi$
$230$	−2.02674e8	−1.09838
$231$	5.41600e6	0.0289092
$232$	7.10986e7	0.373812
$233$	−2.62733e8	−1.36072	−0.680360	−	0.732878i	$-0.738177\pi$
$233$	−2.62733e8	−1.36072	−0.680360	+	0.732878i	$0.738177\pi$
$234$	0	0
$235$	3.89524e8	1.95793
$236$	−1.59116e8	−0.787992
$237$	−9.17947e7	−0.447918
$238$	−9.30971e7	−0.447628
$239$	−8.68087e7	−0.411311	−0.205656	−	0.978624i	$-0.565933\pi$
$239$	−8.68087e7	−0.411311	−0.205656	+	0.978624i	$0.565933\pi$
$240$	5.30144e7	0.247545
$241$	2.12576e8	0.978260	0.489130	−	0.872211i	$-0.337314\pi$
$241$	2.12576e8	0.978260	0.489130	+	0.872211i	$0.337314\pi$
$242$	1.55443e8	0.705048
$243$	−1.16715e8	−0.521802
$244$	−1.94944e8	−0.859104
$245$	1.61930e8	0.703471
$246$	5.93164e7	0.254040
$247$	0	0
$248$	−8.22121e7	−0.342259
$249$	3.17294e8	1.30246
$250$	−1.33282e8	−0.539487
$251$	−1.19237e8	−0.475941	−0.237970	−	0.971272i	$-0.576482\pi$
$251$	−1.19237e8	−0.475941	−0.237970	+	0.971272i	$0.576482\pi$
$252$	−2.14062e7	−0.0842630
$253$	1.86446e7	0.0723821
$254$	6.77738e7	0.259504
$255$	2.64899e8	1.00044
$256$	1.67772e7	0.0625000
$257$	−3.44584e8	−1.26628	−0.633139	−	0.774038i	$-0.718234\pi$
$257$	−3.44584e8	−1.26628	−0.633139	+	0.774038i	$0.718234\pi$
$258$	2.71923e7	0.0985773
$259$	−8.69690e7	−0.311039
$260$	0	0
$261$	8.16865e7	0.284386
$262$	−9.37044e7	−0.321889
$263$	3.03650e7	0.102927	0.0514634	−	0.998675i	$-0.483611\pi$
$263$	3.03650e7	0.102927	0.0514634	+	0.998675i	$0.483611\pi$
$264$	−4.87695e6	−0.0163130
$265$	2.15574e8	0.711599
$266$	4.38603e7	0.142885
$267$	−3.25906e8	−1.04786
$268$	−2.48240e7	−0.0787772
$269$	5.05780e8	1.58427	0.792134	−	0.610348i	$-0.208970\pi$
$269$	5.05780e8	1.58427	0.792134	+	0.610348i	$0.208970\pi$
$270$	2.87360e8	0.888490
$271$	−3.64220e8	−1.11166	−0.555829	−	0.831297i	$-0.687599\pi$
$271$	−3.64220e8	−1.11166	−0.555829	+	0.831297i	$0.687599\pi$
$272$	8.38312e7	0.252589
$273$	0	0
$274$	−2.99994e8	−0.881020
$275$	−6.35037e6	−0.0184134
$276$	2.00279e8	0.573396
$277$	−1.16752e8	−0.330055	−0.165027	−	0.986289i	$-0.552771\pi$
$277$	−1.16752e8	−0.330055	−0.165027	+	0.986289i	$0.552771\pi$
$278$	2.24847e8	0.627668
$279$	−9.44549e7	−0.260381
$280$	9.42353e7	0.256543
$281$	3.12559e8	0.840349	0.420174	−	0.907443i	$-0.361969\pi$
$281$	3.12559e8	0.840349	0.420174	+	0.907443i	$0.361969\pi$
$282$	−3.84921e8	−1.02212
$283$	2.11275e8	0.554109	0.277054	−	0.960854i	$-0.410642\pi$
$283$	2.11275e8	0.554109	0.277054	+	0.960854i	$0.410642\pi$
$284$	2.35540e8	0.610170
$285$	−1.24800e8	−0.319344
$286$	0	0
$287$	1.05437e8	0.263274
$288$	1.92756e7	0.0475483
$289$	8.54345e6	0.0208205
$290$	−3.59604e8	−0.865828
$291$	5.35627e7	0.127420
$292$	1.00829e8	0.236999
$293$	−6.99504e8	−1.62463	−0.812313	−	0.583221i	$-0.801792\pi$
$293$	−6.99504e8	−1.62463	−0.812313	+	0.583221i	$0.801792\pi$
$294$	−1.60017e8	−0.367240
$295$	8.04780e8	1.82516
$296$	7.83131e7	0.175515
$297$	−2.64350e7	−0.0585507
$298$	−3.67207e8	−0.803812
$299$	0	0
$300$	−6.82153e7	−0.145867
$301$	4.83354e7	0.102160
$302$	−3.81844e8	−0.797741
$303$	7.70773e8	1.59176
$304$	−3.94949e7	−0.0806276
$305$	9.85992e8	1.98987
$306$	9.63152e7	0.192163
$307$	4.84159e8	0.955001	0.477500	−	0.878632i	$-0.341543\pi$
$307$	4.84159e8	0.955001	0.477500	+	0.878632i	$0.341543\pi$
$308$	−8.66898e6	−0.0169060
$309$	6.16940e8	1.18957
$310$	4.15814e8	0.792745
$311$	−5.82462e8	−1.09801	−0.549005	−	0.835819i	$-0.684993\pi$
$311$	−5.82462e8	−1.09801	−0.549005	+	0.835819i	$0.684993\pi$
$312$	0	0
$313$	−6.04523e8	−1.11431	−0.557157	−	0.830407i	$-0.688108\pi$
$313$	−6.04523e8	−1.11431	−0.557157	+	0.830407i	$0.688108\pi$
$314$	−5.69626e8	−1.03833
$315$	1.08269e8	0.195171
$316$	1.46929e8	0.261940
$317$	9.32561e8	1.64426	0.822129	−	0.569301i	$-0.192786\pi$
$317$	9.32561e8	1.64426	0.822129	+	0.569301i	$0.192786\pi$
$318$	−2.13026e8	−0.371483
$319$	3.30810e7	0.0570573
$320$	−8.48561e7	−0.144763
$321$	4.16832e8	0.703386
$322$	3.56005e8	0.594237
$323$	−1.97346e8	−0.325851
$324$	−2.01628e8	−0.329340
$325$	0	0
$326$	−4.97649e8	−0.795539
$327$	−6.21935e8	−0.983621
$328$	−9.49432e7	−0.148561
$329$	−6.84213e8	−1.05927
$330$	2.46667e7	0.0377844
$331$	−6.83657e8	−1.03619	−0.518096	−	0.855322i	$-0.673359\pi$
$331$	−6.83657e8	−1.03619	−0.518096	+	0.855322i	$0.673359\pi$
$332$	−5.07868e8	−0.761672
$333$	8.99753e7	0.133527
$334$	−1.79661e8	−0.263840
$335$	1.25556e8	0.182465
$336$	−9.31217e7	−0.133926
$337$	1.36368e9	1.94092	0.970459	−	0.241264i	$-0.0775621\pi$
$337$	1.36368e9	1.94092	0.970459	+	0.241264i	$0.0775621\pi$
$338$	0	0
$339$	3.74285e7	0.0521799
$340$	−4.24003e8	−0.585050
$341$	−3.82519e7	−0.0522412
$342$	−4.53764e7	−0.0613393
$343$	−7.52695e8	−1.00714
$344$	−4.35246e7	−0.0576475
$345$	−1.01298e9	−1.32811
$346$	−6.89351e8	−0.894693
$347$	−1.81419e8	−0.233093	−0.116547	−	0.993185i	$-0.537182\pi$
$347$	−1.81419e8	−0.233093	−0.116547	+	0.993185i	$0.537182\pi$
$348$	3.55355e8	0.451996
$349$	−4.46973e8	−0.562849	−0.281425	−	0.959583i	$-0.590807\pi$
$349$	−4.46973e8	−0.562849	−0.281425	+	0.959583i	$0.590807\pi$
$350$	−1.21255e8	−0.151169
$351$	0	0
$352$	7.80616e6	0.00953978
$353$	1.21232e8	0.146691	0.0733456	−	0.997307i	$-0.476632\pi$
$353$	1.21232e8	0.146691	0.0733456	+	0.997307i	$0.476632\pi$
$354$	−7.95270e8	−0.952803
$355$	−1.19132e9	−1.41328
$356$	5.21653e8	0.612782
$357$	−4.65304e8	−0.541250
$358$	5.68912e8	0.655321
$359$	−1.84724e8	−0.210714	−0.105357	−	0.994434i	$-0.533599\pi$
$359$	−1.84724e8	−0.210714	−0.105357	+	0.994434i	$0.533599\pi$
$360$	−9.74927e7	−0.110132
$361$	−8.00897e8	−0.895987
$362$	−1.11536e9	−1.23576
$363$	7.76914e8	0.852511
$364$	0	0
$365$	−5.09976e8	−0.548940
$366$	−9.74341e8	−1.03879
$367$	8.90694e8	0.940583	0.470292	−	0.882511i	$-0.344149\pi$
$367$	8.90694e8	0.940583	0.470292	+	0.882511i	$0.344149\pi$
$368$	−3.20572e8	−0.335319
$369$	−1.09082e8	−0.113021
$370$	−3.96093e8	−0.406529
$371$	−3.78663e8	−0.384985
$372$	−4.10901e8	−0.413844
$373$	4.42654e8	0.441655	0.220828	−	0.975313i	$-0.429124\pi$
$373$	4.42654e8	0.441655	0.220828	+	0.975313i	$0.429124\pi$
$374$	3.90053e7	0.0385543
$375$	−6.66149e8	−0.652322
$376$	6.16114e8	0.597728
$377$	0	0
$378$	−5.04757e8	−0.480686
$379$	1.48711e9	1.40315	0.701576	−	0.712595i	$-0.252480\pi$
$379$	1.48711e9	1.40315	0.701576	+	0.712595i	$0.252480\pi$
$380$	1.99758e8	0.186751
$381$	3.38737e8	0.313780
$382$	6.86423e8	0.630042
$383$	8.93538e8	0.812676	0.406338	−	0.913723i	$-0.366806\pi$
$383$	8.93538e8	0.812676	0.406338	+	0.913723i	$0.366806\pi$
$384$	8.38534e7	0.0755721
$385$	4.38461e7	0.0391578
$386$	−1.88357e8	−0.166697
$387$	−5.00062e7	−0.0438567
$388$	−8.57337e7	−0.0745145
$389$	−5.98070e8	−0.515143	−0.257572	−	0.966259i	$-0.582922\pi$
$389$	−5.98070e8	−0.515143	−0.257572	+	0.966259i	$0.582922\pi$
$390$	0	0
$391$	−1.60181e9	−1.35517
$392$	2.56126e8	0.214760
$393$	−4.68340e8	−0.389213
$394$	−5.71795e8	−0.470981
$395$	−7.43139e8	−0.606709
$396$	8.96863e6	0.00725760
$397$	−2.04211e9	−1.63800	−0.818999	−	0.573795i	$-0.805471\pi$
$397$	−2.04211e9	−1.63800	−0.818999	+	0.573795i	$0.805471\pi$
$398$	−1.72483e9	−1.37137
$399$	2.19216e8	0.172770
$400$	1.09187e8	0.0853024
$401$	−1.62581e9	−1.25911	−0.629555	−	0.776956i	$-0.716763\pi$
$401$	−1.62581e9	−1.25911	−0.629555	+	0.776956i	$0.716763\pi$
$402$	−1.24072e8	−0.0952538
$403$	0	0
$404$	−1.23372e9	−0.930852
$405$	1.01980e9	0.762820
$406$	6.31657e8	0.468425
$407$	3.64378e7	0.0267899
$408$	4.18993e8	0.305419
$409$	−7.07238e7	−0.0511133	−0.0255567	−	0.999673i	$-0.508136\pi$
$409$	−7.07238e7	−0.0511133	−0.0255567	+	0.999673i	$0.508136\pi$
$410$	4.80206e8	0.344099
$411$	−1.49939e9	−1.06529
$412$	−9.87488e8	−0.695652
$413$	−1.41362e9	−0.987436
$414$	−3.68311e8	−0.255101
$415$	2.56871e9	1.76419
$416$	0	0
$417$	1.12380e9	0.758947
$418$	−1.83763e7	−0.0123067
$419$	1.51778e9	1.00800	0.504000	−	0.863704i	$-0.331861\pi$
$419$	1.51778e9	1.00800	0.504000	+	0.863704i	$0.331861\pi$
$420$	4.70993e8	0.310200
$421$	−6.23005e8	−0.406916	−0.203458	−	0.979084i	$-0.565218\pi$
$421$	−6.23005e8	−0.406916	−0.203458	+	0.979084i	$0.565218\pi$
$422$	−7.15164e8	−0.463247
$423$	7.07864e8	0.454735
$424$	3.40975e8	0.217241
$425$	5.45578e8	0.344743
$426$	1.17724e9	0.737789
$427$	−1.73193e9	−1.07655
$428$	−6.67192e8	−0.411337
$429$	0	0
$430$	2.20140e8	0.133524
$431$	−7.98630e8	−0.480480	−0.240240	−	0.970714i	$-0.577226\pi$
$431$	−7.98630e8	−0.480480	−0.240240	+	0.970714i	$0.577226\pi$
$432$	4.54519e8	0.271243
$433$	−1.06522e9	−0.630568	−0.315284	−	0.948997i	$-0.602100\pi$
$433$	−1.06522e9	−0.630568	−0.315284	+	0.948997i	$0.602100\pi$
$434$	−7.30392e8	−0.428886
$435$	−1.79732e9	−1.04692
$436$	9.95483e8	0.575216
$437$	7.54652e8	0.432575
$438$	5.03950e8	0.286568
$439$	2.79260e9	1.57537	0.787685	−	0.616079i	$-0.211280\pi$
$439$	2.79260e9	1.57537	0.787685	+	0.616079i	$0.211280\pi$
$440$	−3.94822e7	−0.0220961
$441$	2.94268e8	0.163383
$442$	0	0
$443$	1.37114e9	0.749323	0.374661	−	0.927162i	$-0.377759\pi$
$443$	1.37114e9	0.749323	0.374661	+	0.927162i	$0.377759\pi$
$444$	3.91413e8	0.212224
$445$	−2.63842e9	−1.41933
$446$	−8.60220e8	−0.459132
$447$	−1.83532e9	−0.971932
$448$	1.49053e8	0.0783190
$449$	−8.60372e8	−0.448564	−0.224282	−	0.974524i	$-0.572004\pi$
$449$	−8.60372e8	−0.448564	−0.224282	+	0.974524i	$0.572004\pi$
$450$	1.25447e8	0.0648957
$451$	−4.41755e7	−0.0226759
$452$	−5.99089e7	−0.0305145
$453$	−1.90848e9	−0.964592
$454$	1.72063e9	0.862963
$455$	0	0
$456$	−1.97398e8	−0.0974912
$457$	−8.06859e8	−0.395449	−0.197725	−	0.980258i	$-0.563355\pi$
$457$	−8.06859e8	−0.395449	−0.197725	+	0.980258i	$0.563355\pi$
$458$	2.49773e9	1.21483
$459$	2.27111e9	1.09621
$460$	1.62139e9	0.776670
$461$	−1.50889e8	−0.0717308	−0.0358654	−	0.999357i	$-0.511419\pi$
$461$	−1.50889e8	−0.0717308	−0.0358654	+	0.999357i	$0.511419\pi$
$462$	−4.33280e7	−0.0204419
$463$	2.52574e9	1.18265	0.591324	−	0.806434i	$-0.298605\pi$
$463$	2.52574e9	1.18265	0.591324	+	0.806434i	$0.298605\pi$
$464$	−5.68789e8	−0.264325
$465$	2.07826e9	0.958550
$466$	2.10186e9	0.962175
$467$	2.68879e9	1.22165	0.610827	−	0.791764i	$-0.290837\pi$
$467$	2.68879e9	1.22165	0.610827	+	0.791764i	$0.290837\pi$
$468$	0	0
$469$	−2.20543e8	−0.0987161
$470$	−3.11619e9	−1.38447
$471$	−2.84702e9	−1.25550
$472$	1.27293e9	0.557194
$473$	−2.02513e7	−0.00879911
$474$	7.34358e8	0.316726
$475$	−2.57035e8	−0.110044
$476$	7.44777e8	0.316520
$477$	3.91752e8	0.165271
$478$	6.94469e8	0.290841
$479$	2.62585e8	0.109168	0.0545841	−	0.998509i	$-0.482617\pi$
$479$	2.62585e8	0.109168	0.0545841	+	0.998509i	$0.482617\pi$
$480$	−4.24115e8	−0.175041
$481$	0	0
$482$	−1.70061e9	−0.691734
$483$	1.77933e9	0.718524
$484$	−1.24355e9	−0.498544
$485$	4.33626e8	0.172591
$486$	9.33723e8	0.368970
$487$	2.26544e9	0.888796	0.444398	−	0.895830i	$-0.353418\pi$
$487$	2.26544e9	0.888796	0.444398	+	0.895830i	$0.353418\pi$
$488$	1.55955e9	0.607478
$489$	−2.48728e9	−0.961929
$490$	−1.29544e9	−0.497429
$491$	2.76777e9	1.05523	0.527613	−	0.849485i	$-0.323087\pi$
$491$	2.76777e9	1.05523	0.527613	+	0.849485i	$0.323087\pi$
$492$	−4.74531e8	−0.179633
$493$	−2.84209e9	−1.06825
$494$	0	0
$495$	−4.53617e7	−0.0168101
$496$	6.57697e8	0.242014
$497$	2.09259e9	0.764606
$498$	−2.53835e9	−0.920978
$499$	1.33804e9	0.482078	0.241039	−	0.970515i	$-0.422512\pi$
$499$	1.33804e9	0.482078	0.241039	+	0.970515i	$0.422512\pi$
$500$	1.06625e9	0.381475
$501$	−8.97956e8	−0.319024
$502$	9.53896e8	0.336541
$503$	4.40806e8	0.154440	0.0772199	−	0.997014i	$-0.475396\pi$
$503$	4.40806e8	0.154440	0.0772199	+	0.997014i	$0.475396\pi$
$504$	1.71249e8	0.0595830
$505$	6.23992e9	2.15605
$506$	−1.49157e8	−0.0511819
$507$	0	0
$508$	−5.42190e8	−0.183497
$509$	−3.24570e8	−0.109093	−0.0545464	−	0.998511i	$-0.517371\pi$
$509$	−3.24570e8	−0.109093	−0.0545464	+	0.998511i	$0.517371\pi$
$510$	−2.11919e9	−0.707415
$511$	8.95791e8	0.296984
$512$	−1.34218e8	−0.0441942
$513$	−1.06998e9	−0.349915
$514$	2.75667e9	0.895394
$515$	4.99454e9	1.61128
$516$	−2.17538e8	−0.0697047
$517$	2.86668e8	0.0912351
$518$	6.95752e8	0.219938
$519$	−3.44541e9	−1.08182
$520$	0	0
$521$	1.45685e9	0.451320	0.225660	−	0.974206i	$-0.427546\pi$
$521$	1.45685e9	0.451320	0.225660	+	0.974206i	$0.427546\pi$
$522$	−6.53492e8	−0.201091
$523$	1.89197e9	0.578306	0.289153	−	0.957283i	$-0.406626\pi$
$523$	1.89197e9	0.578306	0.289153	+	0.957283i	$0.406626\pi$
$524$	7.49636e8	0.227610
$525$	−6.06041e8	−0.182787
$526$	−2.42920e8	−0.0727803
$527$	3.28633e9	0.978081
$528$	3.90156e7	0.0115351
$529$	2.72052e9	0.799020
$530$	−1.72459e9	−0.503176
$531$	1.46249e9	0.423898
$532$	−3.50883e8	−0.101035
$533$	0	0
$534$	2.60725e9	0.740948
$535$	3.37454e9	0.952743
$536$	1.98592e8	0.0557039
$537$	2.84345e9	0.792384
$538$	−4.04624e9	−1.12025
$539$	1.19171e8	0.0327802
$540$	−2.29888e9	−0.628257
$541$	−1.32498e9	−0.359765	−0.179883	−	0.983688i	$-0.557572\pi$
$541$	−1.32498e9	−0.359765	−0.179883	+	0.983688i	$0.557572\pi$
$542$	2.91376e9	0.786061
$543$	−5.57464e9	−1.49423
$544$	−6.70650e8	−0.178608
$545$	−5.03497e9	−1.33232
$546$	0	0
$547$	1.87811e9	0.490643	0.245321	−	0.969442i	$-0.421107\pi$
$547$	1.87811e9	0.490643	0.245321	+	0.969442i	$0.421107\pi$
$548$	2.39995e9	0.622975
$549$	1.79180e9	0.462153
$550$	5.08029e7	0.0130203
$551$	1.33898e9	0.340991
$552$	−1.60223e9	−0.405452
$553$	1.30535e9	0.328238
$554$	9.34018e8	0.233384
$555$	−1.97970e9	−0.491556
$556$	−1.79877e9	−0.443828
$557$	−1.45013e8	−0.0355560	−0.0177780	−	0.999842i	$-0.505659\pi$
$557$	−1.45013e8	−0.0355560	−0.0177780	+	0.999842i	$0.505659\pi$
$558$	7.55639e8	0.184117
$559$	0	0
$560$	−7.53882e8	−0.181403
$561$	1.94950e8	0.0466181
$562$	−2.50047e9	−0.594216
$563$	−4.80100e9	−1.13384	−0.566921	−	0.823772i	$-0.691865\pi$
$563$	−4.80100e9	−1.13384	−0.566921	+	0.823772i	$0.691865\pi$
$564$	3.07937e9	0.722745
$565$	3.03009e8	0.0706782
$566$	−1.69020e9	−0.391814
$567$	−1.79131e9	−0.412697
$568$	−1.88432e9	−0.431455
$569$	−6.37330e9	−1.45035	−0.725173	−	0.688567i	$-0.758240\pi$
$569$	−6.37330e9	−1.45035	−0.725173	+	0.688567i	$0.758240\pi$
$570$	9.98403e8	0.225810
$571$	3.01445e9	0.677613	0.338807	−	0.940856i	$-0.389977\pi$
$571$	3.01445e9	0.677613	0.338807	+	0.940856i	$0.389977\pi$
$572$	0	0
$573$	3.43078e9	0.761818
$574$	−8.43498e8	−0.186163
$575$	−2.08630e9	−0.457656
$576$	−1.54205e8	−0.0336217
$577$	5.46768e9	1.18492	0.592458	−	0.805601i	$-0.298158\pi$
$577$	5.46768e9	1.18492	0.592458	+	0.805601i	$0.298158\pi$
$578$	−6.83476e7	−0.0147223
$579$	−9.41421e8	−0.201562
$580$	2.87683e9	0.612233
$581$	−4.51202e9	−0.954454
$582$	−4.28502e8	−0.0900994
$583$	1.58650e8	0.0331589
$584$	−8.06634e8	−0.167584
$585$	0	0
$586$	5.59603e9	1.14878
$587$	4.11829e9	0.840395	0.420197	−	0.907433i	$-0.361961\pi$
$587$	4.11829e9	0.840395	0.420197	+	0.907433i	$0.361961\pi$
$588$	1.28013e9	0.259678
$589$	−1.54827e9	−0.312208
$590$	−6.43824e9	−1.29058
$591$	−2.85786e9	−0.569489
$592$	−6.26505e8	−0.124108
$593$	6.94912e8	0.136848	0.0684240	−	0.997656i	$-0.478203\pi$
$593$	6.94912e8	0.136848	0.0684240	+	0.997656i	$0.478203\pi$
$594$	2.11480e8	0.0414016
$595$	−3.76695e9	−0.733128
$596$	2.93766e9	0.568381
$597$	−8.62079e9	−1.65820
$598$	0	0
$599$	5.53945e9	1.05311	0.526554	−	0.850142i	$-0.323484\pi$
$599$	5.53945e9	1.05311	0.526554	+	0.850142i	$0.323484\pi$
$600$	5.45723e8	0.103144
$601$	1.86929e9	0.351250	0.175625	−	0.984457i	$-0.443805\pi$
$601$	1.86929e9	0.351250	0.175625	+	0.984457i	$0.443805\pi$
$602$	−3.86683e8	−0.0722383
$603$	2.28166e8	0.0423780
$604$	3.05476e9	0.564088
$605$	6.28964e9	1.15473
$606$	−6.16618e9	−1.12554
$607$	7.85549e9	1.42565	0.712825	−	0.701342i	$-0.247415\pi$
$607$	7.85549e9	1.42565	0.712825	+	0.701342i	$0.247415\pi$
$608$	3.15960e8	0.0570124
$609$	3.15706e9	0.566398
$610$	−7.88794e9	−1.40705
$611$	0	0
$612$	−7.70521e8	−0.135880
$613$	−1.11128e10	−1.94855	−0.974277	−	0.225356i	$-0.927646\pi$
$613$	−1.11128e10	−1.94855	−0.974277	+	0.225356i	$0.927646\pi$
$614$	−3.87327e9	−0.675287
$615$	2.40009e9	0.416069
$616$	6.93518e7	0.0119543
$617$	2.98964e9	0.512414	0.256207	−	0.966622i	$-0.417527\pi$
$617$	2.98964e9	0.512414	0.256207	+	0.966622i	$0.417527\pi$
$618$	−4.93552e9	−0.841150
$619$	−4.26716e9	−0.723138	−0.361569	−	0.932345i	$-0.617759\pi$
$619$	−4.26716e9	−0.723138	−0.361569	+	0.932345i	$0.617759\pi$
$620$	−3.32651e9	−0.560555
$621$	−8.68476e9	−1.45525
$622$	4.65969e9	0.776410
$623$	4.63449e9	0.767880
$624$	0	0
$625$	−7.47550e9	−1.22479
$626$	4.83618e9	0.787939
$627$	−9.18459e7	−0.0148807
$628$	4.55701e9	0.734212
$629$	−3.13047e9	−0.501572
$630$	−8.66148e8	−0.138007
$631$	7.15079e9	1.13306	0.566528	−	0.824042i	$-0.308286\pi$
$631$	7.15079e9	1.13306	0.566528	+	0.824042i	$0.308286\pi$
$632$	−1.17543e9	−0.185220
$633$	−3.57443e9	−0.560136
$634$	−7.46049e9	−1.16267
$635$	2.74230e9	0.425018
$636$	1.70421e9	0.262678
$637$	0	0
$638$	−2.64648e8	−0.0403456
$639$	−2.16493e9	−0.328239
$640$	6.78849e8	0.102363
$641$	3.08822e9	0.463133	0.231566	−	0.972819i	$-0.425615\pi$
$641$	3.08822e9	0.463133	0.231566	+	0.972819i	$0.425615\pi$
$642$	−3.33466e9	−0.497369
$643$	6.17325e9	0.915747	0.457873	−	0.889017i	$-0.348611\pi$
$643$	6.17325e9	0.915747	0.457873	+	0.889017i	$0.348611\pi$
$644$	−2.84804e9	−0.420189
$645$	1.10027e9	0.161451
$646$	1.57876e9	0.230411
$647$	3.79521e9	0.550897	0.275449	−	0.961316i	$-0.411174\pi$
$647$	3.79521e9	0.550897	0.275449	+	0.961316i	$0.411174\pi$
$648$	1.61303e9	0.232878
$649$	5.92272e8	0.0850481
$650$	0	0
$651$	−3.65054e9	−0.518589
$652$	3.98119e9	0.562531
$653$	1.06721e10	1.49988	0.749938	−	0.661508i	$-0.230083\pi$
$653$	1.06721e10	1.49988	0.749938	+	0.661508i	$0.230083\pi$
$654$	4.97548e9	0.695525
$655$	−3.79152e9	−0.527192
$656$	7.59546e8	0.105049
$657$	−9.26755e8	−0.127493
$658$	5.47371e9	0.749015
$659$	−1.22821e10	−1.67176	−0.835880	−	0.548912i	$-0.815042\pi$
$659$	−1.22821e10	−1.67176	−0.835880	+	0.548912i	$0.815042\pi$
$660$	−1.97334e8	−0.0267176
$661$	7.27345e9	0.979570	0.489785	−	0.871843i	$-0.337075\pi$
$661$	7.27345e9	0.979570	0.489785	+	0.871843i	$0.337075\pi$
$662$	5.46926e9	0.732699
$663$	0	0
$664$	4.06295e9	0.538583
$665$	1.77470e9	0.234018
$666$	−7.19802e8	−0.0944177
$667$	1.08682e10	1.41813
$668$	1.43729e9	0.186563
$669$	−4.29942e9	−0.555161
$670$	−1.00444e9	−0.129022
$671$	7.25634e8	0.0927233
$672$	7.44974e8	0.0946997
$673$	−4.86569e8	−0.0615307	−0.0307654	−	0.999527i	$-0.509794\pi$
$673$	−4.86569e8	−0.0615307	−0.0307654	+	0.999527i	$0.509794\pi$
$674$	−1.09094e10	−1.37244
$675$	2.95804e9	0.370203
$676$	0	0
$677$	4.31885e9	0.534944	0.267472	−	0.963566i	$-0.413812\pi$
$677$	4.31885e9	0.534944	0.267472	+	0.963566i	$0.413812\pi$
$678$	−2.99428e8	−0.0368968
$679$	−7.61679e8	−0.0933744
$680$	3.39203e9	0.413693
$681$	8.59980e9	1.04345
$682$	3.06015e8	0.0369401
$683$	7.78033e9	0.934384	0.467192	−	0.884156i	$-0.345266\pi$
$683$	7.78033e9	0.934384	0.467192	+	0.884156i	$0.345266\pi$
$684$	3.63011e8	0.0433734
$685$	−1.21385e10	−1.44294
$686$	6.02156e9	0.712156
$687$	1.24838e10	1.46892
$688$	3.48197e8	0.0407629
$689$	0	0
$690$	8.10382e9	0.939113
$691$	−1.52753e10	−1.76123	−0.880614	−	0.473834i	$-0.842870\pi$
$691$	−1.52753e10	−1.76123	−0.880614	+	0.473834i	$0.842870\pi$
$692$	5.51481e9	0.632643
$693$	7.96795e7	0.00909453
$694$	1.45135e9	0.164822
$695$	9.09787e9	1.02800
$696$	−2.84284e9	−0.319610
$697$	3.79525e9	0.424546
$698$	3.57578e9	0.397994
$699$	1.05052e10	1.16342
$700$	9.70044e8	0.106893
$701$	−1.39687e9	−0.153159	−0.0765794	−	0.997063i	$-0.524400\pi$
$701$	−1.39687e9	−0.153159	−0.0765794	+	0.997063i	$0.524400\pi$
$702$	0	0
$703$	1.47484e9	0.160104
$704$	−6.24493e7	−0.00674564
$705$	−1.55749e10	−1.67403
$706$	−9.69853e8	−0.103726
$707$	−1.09606e10	−1.16645
$708$	6.36216e9	0.673734
$709$	−1.39372e9	−0.146863	−0.0734315	−	0.997300i	$-0.523395\pi$
$709$	−1.39372e9	−0.146863	−0.0734315	+	0.997300i	$0.523395\pi$
$710$	9.53055e9	0.999341
$711$	−1.35047e9	−0.140910
$712$	−4.17322e9	−0.433303
$713$	−1.25670e10	−1.29843
$714$	3.72243e9	0.382722
$715$	0	0
$716$	−4.55129e9	−0.463382
$717$	3.47099e9	0.351671
$718$	1.47780e9	0.148997
$719$	−8.13847e9	−0.816566	−0.408283	−	0.912855i	$-0.633872\pi$
$719$	−8.13847e9	−0.816566	−0.408283	+	0.912855i	$0.633872\pi$
$720$	7.79942e8	0.0778750
$721$	−8.77308e9	−0.871724
$722$	6.40718e9	0.633558
$723$	−8.49972e9	−0.836413
$724$	8.92289e9	0.873817
$725$	−3.70171e9	−0.360761
$726$	−6.21531e9	−0.602816
$727$	−9.98246e9	−0.963534	−0.481767	−	0.876299i	$-0.660005\pi$
$727$	−9.98246e9	−0.963534	−0.481767	+	0.876299i	$0.660005\pi$
$728$	0	0
$729$	1.15568e10	1.10482
$730$	4.07981e9	0.388159
$731$	1.73985e9	0.164740
$732$	7.79473e9	0.734534
$733$	6.61890e9	0.620758	0.310379	−	0.950613i	$-0.399544\pi$
$733$	6.61890e9	0.620758	0.310379	+	0.950613i	$0.399544\pi$
$734$	−7.12555e9	−0.665093
$735$	−6.47468e9	−0.601469
$736$	2.56457e9	0.237106
$737$	9.24017e7	0.00850245
$738$	8.72655e8	0.0799182
$739$	−4.04220e9	−0.368436	−0.184218	−	0.982885i	$-0.558975\pi$
$739$	−4.04220e9	−0.368436	−0.184218	+	0.982885i	$0.558975\pi$
$740$	3.16875e9	0.287459
$741$	0	0
$742$	3.02930e9	0.272226
$743$	1.02577e10	0.917461	0.458730	−	0.888576i	$-0.348304\pi$
$743$	1.02577e10	0.917461	0.458730	+	0.888576i	$0.348304\pi$
$744$	3.28720e9	0.292632
$745$	−1.48582e10	−1.31649
$746$	−3.54123e9	−0.312297
$747$	4.66799e9	0.409740
$748$	−3.12042e8	−0.0272620
$749$	−5.92749e9	−0.515448
$750$	5.32919e9	0.461261
$751$	1.65159e10	1.42286	0.711431	−	0.702756i	$-0.248048\pi$
$751$	1.65159e10	1.42286	0.711431	+	0.702756i	$0.248048\pi$
$752$	−4.92891e9	−0.422658
$753$	4.76762e9	0.406930
$754$	0	0
$755$	−1.54504e10	−1.30655
$756$	4.03806e9	0.339896
$757$	3.47806e9	0.291408	0.145704	−	0.989328i	$-0.453455\pi$
$757$	3.47806e9	0.291408	0.145704	+	0.989328i	$0.453455\pi$
$758$	−1.18968e10	−0.992178
$759$	−7.45493e8	−0.0618867
$760$	−1.59807e9	−0.132053
$761$	1.49264e10	1.22775	0.613873	−	0.789404i	$-0.289611\pi$
$761$	1.49264e10	1.22775	0.613873	+	0.789404i	$0.289611\pi$
$762$	−2.70990e9	−0.221876
$763$	8.84411e9	0.720806
$764$	−5.49138e9	−0.445507
$765$	3.89716e9	0.314726
$766$	−7.14831e9	−0.574649
$767$	0	0
$768$	−6.70827e8	−0.0534375
$769$	9.17109e9	0.727242	0.363621	−	0.931547i	$-0.381540\pi$
$769$	9.17109e9	0.727242	0.363621	+	0.931547i	$0.381540\pi$
$770$	−3.50769e8	−0.0276888
$771$	1.37780e10	1.08267
$772$	1.50686e9	0.117872
$773$	−5.28554e8	−0.0411587	−0.0205793	−	0.999788i	$-0.506551\pi$
$773$	−5.28554e8	−0.0411587	−0.0205793	+	0.999788i	$0.506551\pi$
$774$	4.00050e8	0.0310113
$775$	4.28033e9	0.330310
$776$	6.85870e8	0.0526897
$777$	3.47741e9	0.265939
$778$	4.78456e9	0.364261
$779$	−1.78803e9	−0.135517
$780$	0	0
$781$	−8.76743e8	−0.0658557
$782$	1.28145e10	0.958247
$783$	−1.54093e10	−1.14714
$784$	−2.04901e9	−0.151858
$785$	−2.30485e10	−1.70059
$786$	3.74672e9	0.275215
$787$	−4.23714e9	−0.309857	−0.154928	−	0.987926i	$-0.549515\pi$
$787$	−4.23714e9	−0.309857	−0.154928	+	0.987926i	$0.549515\pi$
$788$	4.57436e9	0.333034
$789$	−1.21413e9	−0.0880025
$790$	5.94511e9	0.429008
$791$	−5.32245e8	−0.0382379
$792$	−7.17491e7	−0.00513190
$793$	0	0
$794$	1.63369e10	1.15824
$795$	−8.61959e9	−0.608418
$796$	1.37986e10	0.969706
$797$	−8.78818e9	−0.614886	−0.307443	−	0.951566i	$-0.599473\pi$
$797$	−8.78818e9	−0.614886	−0.307443	+	0.951566i	$0.599473\pi$
$798$	−1.75373e9	−0.122167
$799$	−2.46285e10	−1.70814
$800$	−8.73496e8	−0.0603179
$801$	−4.79469e9	−0.329645
$802$	1.30065e10	0.890325
$803$	−3.75313e8	−0.0255793
$804$	9.92575e8	0.0673546
$805$	1.44049e10	0.973248
$806$	0	0
$807$	−2.02233e10	−1.35455
$808$	9.86973e9	0.658212
$809$	−1.41351e10	−0.938597	−0.469299	−	0.883039i	$-0.655493\pi$
$809$	−1.41351e10	−0.938597	−0.469299	+	0.883039i	$0.655493\pi$
$810$	−8.15840e9	−0.539395
$811$	2.03802e10	1.34164	0.670818	−	0.741622i	$-0.265943\pi$
$811$	2.03802e10	1.34164	0.670818	+	0.741622i	$0.265943\pi$
$812$	−5.05326e9	−0.331227
$813$	1.45631e10	0.950468
$814$	−2.91502e8	−0.0189433
$815$	−2.01361e10	−1.30294
$816$	−3.35194e9	−0.215964
$817$	−8.19684e8	−0.0525859
$818$	5.65791e8	0.0361426
$819$	0	0
$820$	−3.84164e9	−0.243315
$821$	−1.35670e10	−0.855622	−0.427811	−	0.903868i	$-0.640715\pi$
$821$	−1.35670e10	−0.855622	−0.427811	+	0.903868i	$0.640715\pi$
$822$	1.19951e10	0.753272
$823$	−1.39571e10	−0.872764	−0.436382	−	0.899761i	$-0.643740\pi$
$823$	−1.39571e10	−0.872764	−0.436382	+	0.899761i	$0.643740\pi$
$824$	7.89991e9	0.491900
$825$	2.53916e8	0.0157435
$826$	1.13090e10	0.698222
$827$	−3.26790e9	−0.200909	−0.100454	−	0.994942i	$-0.532030\pi$
$827$	−3.26790e9	−0.200909	−0.100454	+	0.994942i	$0.532030\pi$
$828$	2.94648e9	0.180384
$829$	1.24986e10	0.761938	0.380969	−	0.924588i	$-0.375590\pi$
$829$	1.24986e10	0.761938	0.380969	+	0.924588i	$0.375590\pi$
$830$	−2.05497e10	−1.24747
$831$	4.66827e9	0.282197
$832$	0	0
$833$	−1.02384e10	−0.613724
$834$	−8.99037e9	−0.536656
$835$	−7.26955e9	−0.432120
$836$	1.47011e8	0.00870216
$837$	1.78180e10	1.05031
$838$	−1.21423e10	−0.712764
$839$	−1.91725e10	−1.12076	−0.560378	−	0.828237i	$-0.689344\pi$
$839$	−1.91725e10	−1.12076	−0.560378	+	0.828237i	$0.689344\pi$
$840$	−3.76794e9	−0.219345
$841$	2.03349e9	0.117884
$842$	4.98404e9	0.287733
$843$	−1.24975e10	−0.718499
$844$	5.72132e9	0.327565
$845$	0	0
$846$	−5.66291e9	−0.321546
$847$	−1.10480e10	−0.624727
$848$	−2.72780e9	−0.153613
$849$	−8.44770e9	−0.473763
$850$	−4.36463e9	−0.243770
$851$	1.19710e10	0.665850
$852$	−9.41793e9	−0.521695
$853$	−8.67539e9	−0.478594	−0.239297	−	0.970946i	$-0.576917\pi$
$853$	−8.67539e9	−0.478594	−0.239297	+	0.970946i	$0.576917\pi$
$854$	1.38554e10	0.761233
$855$	−1.83605e9	−0.100462
$856$	5.33753e9	0.290859
$857$	4.53758e9	0.246258	0.123129	−	0.992391i	$-0.460707\pi$
$857$	4.53758e9	0.246258	0.123129	+	0.992391i	$0.460707\pi$
$858$	0	0
$859$	−6.82340e9	−0.367303	−0.183651	−	0.982991i	$-0.558792\pi$
$859$	−6.82340e9	−0.367303	−0.183651	+	0.982991i	$0.558792\pi$
$860$	−1.76112e9	−0.0944156
$861$	−4.21585e9	−0.225099
$862$	6.38904e9	0.339750
$863$	1.16020e10	0.614463	0.307231	−	0.951635i	$-0.400597\pi$
$863$	1.16020e10	0.614463	0.307231	+	0.951635i	$0.400597\pi$
$864$	−3.63615e9	−0.191798
$865$	−2.78929e10	−1.46534
$866$	8.52177e9	0.445879
$867$	−3.41605e8	−0.0178015
$868$	5.84314e9	0.303268
$869$	−5.46908e8	−0.0282713
$870$	1.43786e10	0.740284
$871$	0	0
$872$	−7.96386e9	−0.406739
$873$	7.88008e8	0.0400849
$874$	−6.03722e9	−0.305877
$875$	9.47286e9	0.478027
$876$	−4.03160e9	−0.202634
$877$	−1.78415e10	−0.893165	−0.446583	−	0.894742i	$-0.647359\pi$
$877$	−1.78415e10	−0.893165	−0.446583	+	0.894742i	$0.647359\pi$
$878$	−2.23408e10	−1.11395
$879$	2.79693e10	1.38906
$880$	3.15857e8	0.0156243
$881$	3.03345e9	0.149459	0.0747294	−	0.997204i	$-0.476191\pi$
$881$	3.03345e9	0.149459	0.0747294	+	0.997204i	$0.476191\pi$
$882$	−2.35414e9	−0.115530
$883$	−3.29743e9	−0.161181	−0.0805904	−	0.996747i	$-0.525681\pi$
$883$	−3.29743e9	−0.161181	−0.0805904	+	0.996747i	$0.525681\pi$
$884$	0	0
$885$	−3.21787e10	−1.56051
$886$	−1.09691e10	−0.529851
$887$	2.43031e10	1.16931	0.584654	−	0.811283i	$-0.301230\pi$
$887$	2.43031e10	1.16931	0.584654	+	0.811283i	$0.301230\pi$
$888$	−3.13130e9	−0.150065
$889$	−4.81695e9	−0.229941
$890$	2.11074e10	1.00362
$891$	7.50515e8	0.0355457
$892$	6.88176e9	0.324655
$893$	1.16031e10	0.545246
$894$	1.46826e10	0.687260
$895$	2.30196e10	1.07329
$896$	−1.19242e9	−0.0553799
$897$	0	0
$898$	6.88297e9	0.317182
$899$	−2.22976e10	−1.02352
$900$	−1.00358e9	−0.0458882
$901$	−1.36301e10	−0.620814
$902$	3.53404e8	0.0160342
$903$	−1.93266e9	−0.0873472
$904$	4.79271e8	0.0215770
$905$	−4.51304e10	−2.02395
$906$	1.52678e10	0.682069
$907$	8.88142e9	0.395236	0.197618	−	0.980279i	$-0.436679\pi$
$907$	8.88142e9	0.395236	0.197618	+	0.980279i	$0.436679\pi$
$908$	−1.37650e10	−0.610207
$909$	1.13395e10	0.500750
$910$	0	0
$911$	−1.00948e10	−0.442369	−0.221184	−	0.975232i	$-0.570992\pi$
$911$	−1.00948e10	−0.442369	−0.221184	+	0.975232i	$0.570992\pi$
$912$	1.57918e9	0.0689367
$913$	1.89042e9	0.0822074
$914$	6.45487e9	0.279625
$915$	−3.94243e10	−1.70134
$916$	−1.99818e10	−0.859016
$917$	6.65994e9	0.285219
$918$	−1.81689e10	−0.775138
$919$	2.63373e10	1.11935	0.559675	−	0.828712i	$-0.310926\pi$
$919$	2.63373e10	1.11935	0.559675	+	0.828712i	$0.310926\pi$
$920$	−1.29712e10	−0.549188
$921$	−1.93588e10	−0.816526
$922$	1.20712e9	0.0507213
$923$	0	0
$924$	3.46624e8	0.0144546
$925$	−4.07733e9	−0.169387
$926$	−2.02059e10	−0.836259
$927$	9.07634e9	0.374224
$928$	4.55031e9	0.186906
$929$	2.21833e10	0.907762	0.453881	−	0.891062i	$-0.350039\pi$
$929$	2.21833e10	0.907762	0.453881	+	0.891062i	$0.350039\pi$
$930$	−1.66261e10	−0.677797
$931$	4.82354e9	0.195903
$932$	−1.68149e10	−0.680360
$933$	2.32894e10	0.938799
$934$	−2.15103e10	−0.863839
$935$	1.57825e9	0.0631446
$936$	0	0
$937$	−1.31025e10	−0.520313	−0.260156	−	0.965566i	$-0.583774\pi$
$937$	−1.31025e10	−0.520313	−0.260156	+	0.965566i	$0.583774\pi$
$938$	1.76434e9	0.0698028
$939$	2.41715e10	0.952739
$940$	2.49296e10	0.978965
$941$	3.23092e9	0.126404	0.0632022	−	0.998001i	$-0.479869\pi$
$941$	3.23092e9	0.126404	0.0632022	+	0.998001i	$0.479869\pi$
$942$	2.27762e10	0.887774
$943$	−1.45131e10	−0.563597
$944$	−1.01834e10	−0.393996
$945$	−2.04238e10	−0.787272
$946$	1.62010e8	0.00622191
$947$	−4.41273e10	−1.68843	−0.844214	−	0.536007i	$-0.819932\pi$
$947$	−4.41273e10	−1.68843	−0.844214	+	0.536007i	$0.819932\pi$
$948$	−5.87486e9	−0.223959
$949$	0	0
$950$	2.05628e9	0.0778126
$951$	−3.72879e10	−1.40584
$952$	−5.95821e9	−0.223814
$953$	−2.04661e10	−0.765967	−0.382984	−	0.923755i	$-0.625103\pi$
$953$	−2.04661e10	−0.765967	−0.382984	+	0.923755i	$0.625103\pi$
$954$	−3.13402e9	−0.116864
$955$	2.77744e10	1.03189
$956$	−5.55575e9	−0.205656
$957$	−1.32273e9	−0.0487841
$958$	−2.10068e9	−0.0771935
$959$	2.13217e10	0.780652
$960$	3.39292e9	0.123773
$961$	−1.72972e9	−0.0628700
$962$	0	0
$963$	6.13239e9	0.221278
$964$	1.36049e10	0.489130
$965$	−7.62142e9	−0.273018
$966$	−1.42346e10	−0.508073
$967$	4.43495e10	1.57723	0.788617	−	0.614885i	$-0.210798\pi$
$967$	4.43495e10	1.57723	0.788617	+	0.614885i	$0.210798\pi$
$968$	9.94837e9	0.352524
$969$	7.89075e9	0.278603
$970$	−3.46901e9	−0.122040
$971$	−6.87519e9	−0.241000	−0.120500	−	0.992713i	$-0.538450\pi$
$971$	−6.87519e9	−0.241000	−0.120500	+	0.992713i	$0.538450\pi$
$972$	−7.46978e9	−0.260901
$973$	−1.59807e10	−0.556163
$974$	−1.81236e10	−0.628474
$975$	0	0
$976$	−1.24764e10	−0.429552
$977$	5.33603e10	1.83057	0.915286	−	0.402803i	$-0.131964\pi$
$977$	5.33603e10	1.83057	0.915286	+	0.402803i	$0.131964\pi$
$978$	1.98982e10	0.680186
$979$	−1.94173e9	−0.0661378
$980$	1.03635e10	0.351736
$981$	−9.14982e9	−0.309436
$982$	−2.21422e10	−0.746157
$983$	3.38459e10	1.13650	0.568249	−	0.822857i	$-0.307621\pi$
$983$	3.38459e10	1.13650	0.568249	+	0.822857i	$0.307621\pi$
$984$	3.79625e9	0.127020
$985$	−2.31363e10	−0.771377
$986$	2.27367e10	0.755367
$987$	2.73579e10	0.905675
$988$	0	0
$989$	−6.65320e9	−0.218697
$990$	3.62894e8	0.0118866
$991$	9.43799e9	0.308051	0.154025	−	0.988067i	$-0.450776\pi$
$991$	9.43799e9	0.308051	0.154025	+	0.988067i	$0.450776\pi$
$992$	−5.26158e9	−0.171130
$993$	2.73356e10	0.885945
$994$	−1.67408e10	−0.540658
$995$	−6.97910e10	−2.24605
$996$	2.03068e10	0.651230
$997$	−3.40792e9	−0.108907	−0.0544536	−	0.998516i	$-0.517342\pi$
$997$	−3.40792e9	−0.108907	−0.0544536	+	0.998516i	$0.517342\pi$
$998$	−1.07043e10	−0.340880
$999$	−1.69729e10	−0.538614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.8.a.i.1.2		4
13.3	even	3		26.8.c.b.9.3	yes	8
13.5	odd	4		338.8.b.h.337.6		8
13.8	odd	4		338.8.b.h.337.2		8
13.9	even	3		26.8.c.b.3.3	✓	8
13.12	even	2		338.8.a.j.1.2		4
39.29	odd	6		234.8.h.b.217.4		8
39.35	odd	6		234.8.h.b.55.4		8
52.3	odd	6		208.8.i.b.113.2		8
52.35	odd	6		208.8.i.b.81.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.c.b.3.3	✓	8	13.9	even	3
26.8.c.b.9.3	yes	8	13.3	even	3
208.8.i.b.81.2		8	52.35	odd	6
208.8.i.b.113.2		8	52.3	odd	6
234.8.h.b.55.4		8	39.35	odd	6
234.8.h.b.217.4		8	39.29	odd	6
338.8.a.i.1.2		4	1.1	even	1	trivial
338.8.a.j.1.2		4	13.12	even	2
338.8.b.h.337.2		8	13.8	odd	4
338.8.b.h.337.6		8	13.5	odd	4

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -39.9844 q^{3} +64.0000 q^{4} -323.700 q^{5} +319.875 q^{6} +568.591 q^{7} -512.000 q^{8} -588.246 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -39.9844 q^{3} +64.0000 q^{4} -323.700 q^{5} +319.875 q^{6} +568.591 q^{7} -512.000 q^{8} -588.246 q^{9} +2589.60 q^{10} -238.225 q^{11} -2559.00 q^{12} -4548.73 q^{14} +12943.0 q^{15} +4096.00 q^{16} +20466.6 q^{17} +4705.97 q^{18} -9642.32 q^{19} -20716.8 q^{20} -22734.8 q^{21} +1905.80 q^{22} -78264.6 q^{23} +20472.0 q^{24} +26657.0 q^{25} +110967. q^{27} +36389.8 q^{28} -138865. q^{29} -103544. q^{30} +160571. q^{31} -32768.0 q^{32} +9525.29 q^{33} -163733. q^{34} -184053. q^{35} -37647.7 q^{36} -152955. q^{37} +77138.6 q^{38} +165735. q^{40} +185436. q^{41} +181878. q^{42} +85009.0 q^{43} -15246.4 q^{44} +190415. q^{45} +626117. q^{46} -1.20335e6 q^{47} -163776. q^{48} -500247. q^{49} -213256. q^{50} -818346. q^{51} -665967. q^{53} -887733. q^{54} +77113.6 q^{55} -291119. q^{56} +385543. q^{57} +1.11092e6 q^{58} -2.48619e6 q^{59} +828351. q^{60} -3.04600e6 q^{61} -1.28456e6 q^{62} -334471. q^{63} +262144. q^{64} -76202.4 q^{66} -387876. q^{67} +1.30986e6 q^{68} +3.12937e6 q^{69} +1.47243e6 q^{70} +3.68031e6 q^{71} +301182. q^{72} +1.57546e6 q^{73} +1.22364e6 q^{74} -1.06586e6 q^{75} -617108. q^{76} -135453. q^{77} +2.29576e6 q^{79} -1.32588e6 q^{80} -3.15044e6 q^{81} -1.48349e6 q^{82} -7.93544e6 q^{83} -1.45503e6 q^{84} -6.62505e6 q^{85} -680072. q^{86} +5.55242e6 q^{87} +121971. q^{88} +8.15082e6 q^{89} -1.52332e6 q^{90} -5.00893e6 q^{92} -6.42032e6 q^{93} +9.62678e6 q^{94} +3.12122e6 q^{95} +1.31021e6 q^{96} -1.33959e6 q^{97} +4.00198e6 q^{98} +140135. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} + 256 q^{4} + 278 q^{5} + 548 q^{7} - 2048 q^{8} + 5214 q^{9}+O(q^{10}) \) 4 * q - 32 * q^2 + 256 * q^4 + 278 * q^5 + 548 * q^7 - 2048 * q^8 + 5214 * q^9	\( 4 q - 32 q^{2} + 256 q^{4} + 278 q^{5} + 548 q^{7} - 2048 q^{8} + 5214 q^{9} - 2224 q^{10} + 7392 q^{11} - 4384 q^{14} - 15528 q^{15} + 16384 q^{16} - 28316 q^{17} - 41712 q^{18} + 99888 q^{19} + 17792 q^{20} + 91074 q^{21} - 59136 q^{22} + 33388 q^{23} + 86878 q^{25} + 106272 q^{27} + 35072 q^{28} - 93140 q^{29} + 124224 q^{30} + 311160 q^{31} - 131072 q^{32} - 238638 q^{33} + 226528 q^{34} - 141544 q^{35} + 333696 q^{36} + 9636 q^{37} - 799104 q^{38} - 142336 q^{40} - 82892 q^{41} - 728592 q^{42} + 569264 q^{43} + 473088 q^{44} + 2303394 q^{45} - 267104 q^{46} - 574200 q^{47} + 717798 q^{49} - 695024 q^{50} - 2729928 q^{51} + 1235350 q^{53} - 850176 q^{54} + 1092512 q^{55} - 280576 q^{56} + 3528462 q^{57} + 745120 q^{58} - 231504 q^{59} - 993792 q^{60} - 685684 q^{61} - 2489280 q^{62} + 5951712 q^{63} + 1048576 q^{64} + 1909104 q^{66} - 3271056 q^{67} - 1812224 q^{68} - 5600034 q^{69} + 1132352 q^{70} + 175012 q^{71} - 2669568 q^{72} + 7137890 q^{73} - 77088 q^{74} - 22200960 q^{75} + 6392832 q^{76} - 13915206 q^{77} - 7053952 q^{79} + 1138688 q^{80} - 3758004 q^{81} + 663136 q^{82} + 657288 q^{83} + 5828736 q^{84} - 11814998 q^{85} - 4554112 q^{86} + 7182900 q^{87} - 3784704 q^{88} + 11452234 q^{89} - 18427152 q^{90} + 2136832 q^{92} - 2984688 q^{93} + 4593600 q^{94} + 23334088 q^{95} + 428002 q^{97} - 5742384 q^{98} - 10357656 q^{99}+O(q^{100}) \) 4 * q - 32 * q^2 + 256 * q^4 + 278 * q^5 + 548 * q^7 - 2048 * q^8 + 5214 * q^9 - 2224 * q^10 + 7392 * q^11 - 4384 * q^14 - 15528 * q^15 + 16384 * q^16 - 28316 * q^17 - 41712 * q^18 + 99888 * q^19 + 17792 * q^20 + 91074 * q^21 - 59136 * q^22 + 33388 * q^23 + 86878 * q^25 + 106272 * q^27 + 35072 * q^28 - 93140 * q^29 + 124224 * q^30 + 311160 * q^31 - 131072 * q^32 - 238638 * q^33 + 226528 * q^34 - 141544 * q^35 + 333696 * q^36 + 9636 * q^37 - 799104 * q^38 - 142336 * q^40 - 82892 * q^41 - 728592 * q^42 + 569264 * q^43 + 473088 * q^44 + 2303394 * q^45 - 267104 * q^46 - 574200 * q^47 + 717798 * q^49 - 695024 * q^50 - 2729928 * q^51 + 1235350 * q^53 - 850176 * q^54 + 1092512 * q^55 - 280576 * q^56 + 3528462 * q^57 + 745120 * q^58 - 231504 * q^59 - 993792 * q^60 - 685684 * q^61 - 2489280 * q^62 + 5951712 * q^63 + 1048576 * q^64 + 1909104 * q^66 - 3271056 * q^67 - 1812224 * q^68 - 5600034 * q^69 + 1132352 * q^70 + 175012 * q^71 - 2669568 * q^72 + 7137890 * q^73 - 77088 * q^74 - 22200960 * q^75 + 6392832 * q^76 - 13915206 * q^77 - 7053952 * q^79 + 1138688 * q^80 - 3758004 * q^81 + 663136 * q^82 + 657288 * q^83 + 5828736 * q^84 - 11814998 * q^85 - 4554112 * q^86 + 7182900 * q^87 - 3784704 * q^88 + 11452234 * q^89 - 18427152 * q^90 + 2136832 * q^92 - 2984688 * q^93 + 4593600 * q^94 + 23334088 * q^95 + 428002 * q^97 - 5742384 * q^98 - 10357656 * q^99

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