LMFDB - Embedded newform 294.8.a.y.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,8,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	294.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:	$91.8411974923$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 22015x - 14370 $ x^3 - 22015*x - 14370
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.652749$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.808 q^{5} +216.000 q^{6} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.808 q^{5} +216.000 q^{6} +512.000 q^{8} +729.000 q^{9} +2470.47 q^{10} +6483.16 q^{11} +1728.00 q^{12} +993.626 q^{13} +8337.82 q^{15} +4096.00 q^{16} +30919.5 q^{17} +5832.00 q^{18} -15589.3 q^{19} +19763.7 q^{20} +51865.2 q^{22} -81102.6 q^{23} +13824.0 q^{24} +17237.5 q^{25} +7949.01 q^{26} +19683.0 q^{27} -34651.6 q^{29} +66702.6 q^{30} +160512. q^{31} +32768.0 q^{32} +175045. q^{33} +247356. q^{34} +46656.0 q^{36} -11084.6 q^{37} -124714. q^{38} +26827.9 q^{39} +158110. q^{40} -459665. q^{41} +455951. q^{43} +414922. q^{44} +225121. q^{45} -648821. q^{46} +299994. q^{47} +110592. q^{48} +137900. q^{50} +834825. q^{51} +63592.0 q^{52} +1.89797e6 q^{53} +157464. q^{54} +2.00205e6 q^{55} -420911. q^{57} -277213. q^{58} -2.96267e6 q^{59} +533621. q^{60} -2.38371e6 q^{61} +1.28409e6 q^{62} +262144. q^{64} +306840. q^{65} +1.40036e6 q^{66} +4.53392e6 q^{67} +1.97885e6 q^{68} -2.18977e6 q^{69} -4.00697e6 q^{71} +373248. q^{72} -3.47310e6 q^{73} -88676.9 q^{74} +465413. q^{75} -997714. q^{76} +214623. q^{78} -692868. q^{79} +1.26488e6 q^{80} +531441. q^{81} -3.67732e6 q^{82} +2.65827e6 q^{83} +9.54818e6 q^{85} +3.64761e6 q^{86} -935594. q^{87} +3.31938e6 q^{88} -1.37358e6 q^{89} +1.80097e6 q^{90} -5.19057e6 q^{92} +4.33381e6 q^{93} +2.39996e6 q^{94} -4.81410e6 q^{95} +884736. q^{96} +299539. q^{97} +4.72622e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 70 q^{5} + 648 q^{6} + 1536 q^{8} + 2187 q^{9}+O(q^{10}) $ 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 70 * q^5 + 648 * q^6 + 1536 * q^8 + 2187 * q^9	\( 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 70 q^{5} + 648 q^{6} + 1536 q^{8} + 2187 q^{9} - 560 q^{10} + 2428 q^{11} + 5184 q^{12} - 1919 q^{13} - 1890 q^{15} + 12288 q^{16} + 24508 q^{17} + 17496 q^{18} - 1353 q^{19} - 4480 q^{20} + 19424 q^{22} + 96628 q^{23} + 41472 q^{24} + 135175 q^{25} - 15352 q^{26} + 59049 q^{27} - 114112 q^{29} - 15120 q^{30} + 221395 q^{31} + 98304 q^{32} + 65556 q^{33} + 196064 q^{34} + 139968 q^{36} + 249987 q^{37} - 10824 q^{38} - 51813 q^{39} - 35840 q^{40} + 610926 q^{41} + 600243 q^{43} + 155392 q^{44} - 51030 q^{45} + 773024 q^{46} - 123114 q^{47} + 331776 q^{48} + 1081400 q^{50} + 661716 q^{51} - 122816 q^{52} + 3004752 q^{53} + 472392 q^{54} + 2246360 q^{55} - 36531 q^{57} - 912896 q^{58} - 2852938 q^{59} - 120960 q^{60} + 665386 q^{61} + 1771160 q^{62} + 786432 q^{64} + 5835930 q^{65} + 524448 q^{66} + 10545857 q^{67} + 1568512 q^{68} + 2608956 q^{69} - 1019762 q^{71} + 1119744 q^{72} - 6858031 q^{73} + 1999896 q^{74} + 3649725 q^{75} - 86592 q^{76} - 414504 q^{78} + 1723021 q^{79} - 286720 q^{80} + 1594323 q^{81} + 4887408 q^{82} + 2635804 q^{83} + 737060 q^{85} + 4801944 q^{86} - 3081024 q^{87} + 1243136 q^{88} - 976224 q^{89} - 408240 q^{90} + 6184192 q^{92} + 5977665 q^{93} - 984912 q^{94} + 11136310 q^{95} + 2654208 q^{96} - 8485792 q^{97} + 1770012 q^{99}+O(q^{100}) \) 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 70 * q^5 + 648 * q^6 + 1536 * q^8 + 2187 * q^9 - 560 * q^10 + 2428 * q^11 + 5184 * q^12 - 1919 * q^13 - 1890 * q^15 + 12288 * q^16 + 24508 * q^17 + 17496 * q^18 - 1353 * q^19 - 4480 * q^20 + 19424 * q^22 + 96628 * q^23 + 41472 * q^24 + 135175 * q^25 - 15352 * q^26 + 59049 * q^27 - 114112 * q^29 - 15120 * q^30 + 221395 * q^31 + 98304 * q^32 + 65556 * q^33 + 196064 * q^34 + 139968 * q^36 + 249987 * q^37 - 10824 * q^38 - 51813 * q^39 - 35840 * q^40 + 610926 * q^41 + 600243 * q^43 + 155392 * q^44 - 51030 * q^45 + 773024 * q^46 - 123114 * q^47 + 331776 * q^48 + 1081400 * q^50 + 661716 * q^51 - 122816 * q^52 + 3004752 * q^53 + 472392 * q^54 + 2246360 * q^55 - 36531 * q^57 - 912896 * q^58 - 2852938 * q^59 - 120960 * q^60 + 665386 * q^61 + 1771160 * q^62 + 786432 * q^64 + 5835930 * q^65 + 524448 * q^66 + 10545857 * q^67 + 1568512 * q^68 + 2608956 * q^69 - 1019762 * q^71 + 1119744 * q^72 - 6858031 * q^73 + 1999896 * q^74 + 3649725 * q^75 - 86592 * q^76 - 414504 * q^78 + 1723021 * q^79 - 286720 * q^80 + 1594323 * q^81 + 4887408 * q^82 + 2635804 * q^83 + 737060 * q^85 + 4801944 * q^86 - 3081024 * q^87 + 1243136 * q^88 - 976224 * q^89 - 408240 * q^90 + 6184192 * q^92 + 5977665 * q^93 - 984912 * q^94 + 11136310 * q^95 + 2654208 * q^96 - 8485792 * q^97 + 1770012 * 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
$5$	308.808	1.10483	0.552413	−	0.833571i	$-0.313707\pi$
$5$	308.808	1.10483	0.552413	+	0.833571i	$0.313707\pi$
$6$	216.000	0.408248
$7$	0	0
$7$	0	0
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2470.47	0.781230
$11$	6483.16	1.46863	0.734314	−	0.678810i	$-0.237504\pi$
$11$	6483.16	1.46863	0.734314	+	0.678810i	$0.237504\pi$
$12$	1728.00	0.288675
$13$	993.626	0.125436	0.0627178	−	0.998031i	$-0.480023\pi$
$13$	993.626	0.125436	0.0627178	+	0.998031i	$0.480023\pi$
$14$	0	0
$15$	8337.82	0.637872
$16$	4096.00	0.250000
$17$	30919.5	1.52637	0.763186	−	0.646178i	$-0.223634\pi$
$17$	30919.5	1.52637	0.763186	+	0.646178i	$0.223634\pi$
$18$	5832.00	0.235702
$19$	−15589.3	−0.521421	−0.260710	−	0.965417i	$-0.583957\pi$
$19$	−15589.3	−0.521421	−0.260710	+	0.965417i	$0.583957\pi$
$20$	19763.7	0.552413
$21$	0	0
$22$	51865.2	1.03848
$23$	−81102.6	−1.38991	−0.694956	−	0.719052i	$-0.744576\pi$
$23$	−81102.6	−1.38991	−0.694956	+	0.719052i	$0.744576\pi$
$24$	13824.0	0.204124
$25$	17237.5	0.220640
$26$	7949.01	0.0886964
$27$	19683.0	0.192450
$28$	0	0
$29$	−34651.6	−0.263834	−0.131917	−	0.991261i	$-0.542113\pi$
$29$	−34651.6	−0.263834	−0.131917	+	0.991261i	$0.542113\pi$
$30$	66702.6	0.451043
$31$	160512.	0.967699	0.483850	−	0.875151i	$-0.339238\pi$
$31$	160512.	0.967699	0.483850	+	0.875151i	$0.339238\pi$
$32$	32768.0	0.176777
$33$	175045.	0.847913
$34$	247356.	1.07931
$35$	0	0
$36$	46656.0	0.166667
$37$	−11084.6	−0.0359761	−0.0179881	−	0.999838i	$-0.505726\pi$
$37$	−11084.6	−0.0359761	−0.0179881	+	0.999838i	$0.505726\pi$
$38$	−124714.	−0.368700
$39$	26827.9	0.0724203
$40$	158110.	0.390615
$41$	−459665.	−1.04159	−0.520796	−	0.853681i	$-0.674365\pi$
$41$	−459665.	−1.04159	−0.520796	+	0.853681i	$0.674365\pi$
$42$	0	0
$43$	455951.	0.874538	0.437269	−	0.899331i	$-0.355946\pi$
$43$	455951.	0.874538	0.437269	+	0.899331i	$0.355946\pi$
$44$	414922.	0.734314
$45$	225121.	0.368275
$46$	−648821.	−0.982817
$47$	299994.	0.421474	0.210737	−	0.977543i	$-0.432414\pi$
$47$	299994.	0.421474	0.210737	+	0.977543i	$0.432414\pi$
$48$	110592.	0.144338
$49$	0	0
$50$	137900.	0.156016
$51$	834825.	0.881252
$52$	63592.0	0.0627178
$53$	1.89797e6	1.75115	0.875577	−	0.483078i	$-0.160481\pi$
$53$	1.89797e6	1.75115	0.875577	+	0.483078i	$0.160481\pi$
$54$	157464.	0.136083
$55$	2.00205e6	1.62258
$56$	0	0
$57$	−420911.	−0.301042
$58$	−277213.	−0.186559
$59$	−2.96267e6	−1.87802	−0.939011	−	0.343887i	$-0.888256\pi$
$59$	−2.96267e6	−1.87802	−0.939011	+	0.343887i	$0.888256\pi$
$60$	533621.	0.318936
$61$	−2.38371e6	−1.34462	−0.672309	−	0.740271i	$-0.734697\pi$
$61$	−2.38371e6	−1.34462	−0.672309	+	0.740271i	$0.734697\pi$
$62$	1.28409e6	0.684267
$63$	0	0
$64$	262144.	0.125000
$65$	306840.	0.138585
$66$	1.40036e6	0.599565
$67$	4.53392e6	1.84167	0.920835	−	0.389953i	$-0.127509\pi$
$67$	4.53392e6	1.84167	0.920835	+	0.389953i	$0.127509\pi$
$68$	1.97885e6	0.763186
$69$	−2.18977e6	−0.802466
$70$	0	0
$71$	−4.00697e6	−1.32866	−0.664328	−	0.747441i	$-0.731282\pi$
$71$	−4.00697e6	−1.32866	−0.664328	+	0.747441i	$0.731282\pi$
$72$	373248.	0.117851
$73$	−3.47310e6	−1.04493	−0.522465	−	0.852661i	$-0.674988\pi$
$73$	−3.47310e6	−1.04493	−0.522465	+	0.852661i	$0.674988\pi$
$74$	−88676.9	−0.0254390
$75$	465413.	0.127387
$76$	−997714.	−0.260710
$77$	0	0
$78$	214623.	0.0512089
$79$	−692868.	−0.158109	−0.0790543	−	0.996870i	$-0.525190\pi$
$79$	−692868.	−0.158109	−0.0790543	+	0.996870i	$0.525190\pi$
$80$	1.26488e6	0.276206
$81$	531441.	0.111111
$82$	−3.67732e6	−0.736517
$83$	2.65827e6	0.510301	0.255151	−	0.966901i	$-0.417875\pi$
$83$	2.65827e6	0.510301	0.255151	+	0.966901i	$0.417875\pi$
$84$	0	0
$85$	9.54818e6	1.68638
$86$	3.64761e6	0.618392
$87$	−935594.	−0.152325
$88$	3.31938e6	0.519239
$89$	−1.37358e6	−0.206533	−0.103267	−	0.994654i	$-0.532929\pi$
$89$	−1.37358e6	−0.206533	−0.103267	+	0.994654i	$0.532929\pi$
$90$	1.80097e6	0.260410
$91$	0	0
$92$	−5.19057e6	−0.694956
$93$	4.33381e6	0.558701
$94$	2.39996e6	0.298027
$95$	−4.81410e6	−0.576079
$96$	884736.	0.102062
$97$	299539.	0.0333236	0.0166618	−	0.999861i	$-0.494696\pi$
$97$	299539.	0.0333236	0.0166618	+	0.999861i	$0.494696\pi$
$98$	0	0
$99$	4.72622e6	0.489543
$100$	1.10320e6	0.110320
$101$	1.41961e6	0.137102	0.0685509	−	0.997648i	$-0.478162\pi$
$101$	1.41961e6	0.137102	0.0685509	+	0.997648i	$0.478162\pi$
$102$	6.67860e6	0.623139
$103$	1.87186e7	1.68788	0.843942	−	0.536435i	$-0.180229\pi$
$103$	1.87186e7	1.68788	0.843942	+	0.536435i	$0.180229\pi$
$104$	508736.	0.0443482
$105$	0	0
$106$	1.51838e7	1.23825
$107$	4.20594e6	0.331909	0.165955	−	0.986133i	$-0.446929\pi$
$107$	4.20594e6	0.331909	0.165955	+	0.986133i	$0.446929\pi$
$108$	1.25971e6	0.0962250
$109$	1.09047e7	0.806531	0.403265	−	0.915083i	$-0.367875\pi$
$109$	1.09047e7	0.806531	0.403265	+	0.915083i	$0.367875\pi$
$110$	1.60164e7	1.14734
$111$	−299284.	−0.0207708
$112$	0	0
$113$	7.18622e6	0.468517	0.234259	−	0.972174i	$-0.424734\pi$
$113$	7.18622e6	0.468517	0.234259	+	0.972174i	$0.424734\pi$
$114$	−3.36728e6	−0.212869
$115$	−2.50452e7	−1.53561
$116$	−2.21770e6	−0.131917
$117$	724353.	0.0418119
$118$	−2.37013e7	−1.32796
$119$	0	0
$120$	4.26897e6	0.225522
$121$	2.25441e7	1.15687
$122$	−1.90697e7	−0.950788
$123$	−1.24110e7	−0.601364
$124$	1.02727e7	0.483850
$125$	−1.88026e7	−0.861057
$126$	0	0
$127$	−1.62113e7	−0.702270	−0.351135	−	0.936325i	$-0.614204\pi$
$127$	−1.62113e7	−0.702270	−0.351135	+	0.936325i	$0.614204\pi$
$128$	2.09715e6	0.0883883
$129$	1.23107e7	0.504915
$130$	2.45472e6	0.0979941
$131$	6.75469e6	0.262516	0.131258	−	0.991348i	$-0.458098\pi$
$131$	6.75469e6	0.262516	0.131258	+	0.991348i	$0.458098\pi$
$132$	1.12029e7	0.423957
$133$	0	0
$134$	3.62713e7	1.30226
$135$	6.07827e6	0.212624
$136$	1.58308e7	0.539654
$137$	5.52773e7	1.83664	0.918322	−	0.395833i	$-0.129544\pi$
$137$	5.52773e7	1.83664	0.918322	+	0.395833i	$0.129544\pi$
$138$	−1.75182e7	−0.567429
$139$	−3.26212e7	−1.03026	−0.515132	−	0.857111i	$-0.672257\pi$
$139$	−3.26212e7	−1.03026	−0.515132	+	0.857111i	$0.672257\pi$
$140$	0	0
$141$	8.09985e6	0.243338
$142$	−3.20558e7	−0.939501
$143$	6.44183e6	0.184218
$144$	2.98598e6	0.0833333
$145$	−1.07007e7	−0.291491
$146$	−2.77848e7	−0.738877
$147$	0	0
$148$	−709415.	−0.0179881
$149$	−6.42596e7	−1.59143	−0.795713	−	0.605674i	$-0.792904\pi$
$149$	−6.42596e7	−1.59143	−0.795713	+	0.605674i	$0.792904\pi$
$150$	3.72331e6	0.0900761
$151$	6.22531e7	1.47144	0.735719	−	0.677287i	$-0.236844\pi$
$151$	6.22531e7	1.47144	0.735719	+	0.677287i	$0.236844\pi$
$152$	−7.98171e6	−0.184350
$153$	2.25403e7	0.508791
$154$	0	0
$155$	4.95673e7	1.06914
$156$	1.71699e6	0.0362102
$157$	1.77979e7	0.367045	0.183522	−	0.983016i	$-0.441250\pi$
$157$	1.77979e7	0.367045	0.183522	+	0.983016i	$0.441250\pi$
$158$	−5.54294e6	−0.111800
$159$	5.12453e7	1.01103
$160$	1.01190e7	0.195307
$161$	0	0
$162$	4.25153e6	0.0785674
$163$	3.84337e7	0.695114	0.347557	−	0.937659i	$-0.387011\pi$
$163$	3.84337e7	0.695114	0.347557	+	0.937659i	$0.387011\pi$
$164$	−2.94186e7	−0.520796
$165$	5.40554e7	0.936797
$166$	2.12662e7	0.360837
$167$	−5.42631e7	−0.901566	−0.450783	−	0.892634i	$-0.648855\pi$
$167$	−5.42631e7	−0.901566	−0.450783	+	0.892634i	$0.648855\pi$
$168$	0	0
$169$	−6.17612e7	−0.984266
$170$	7.63855e7	1.19245
$171$	−1.13646e7	−0.173807
$172$	2.91809e7	0.437269
$173$	1.71106e7	0.251249	0.125624	−	0.992078i	$-0.459907\pi$
$173$	1.71106e7	0.251249	0.125624	+	0.992078i	$0.459907\pi$
$174$	−7.48475e6	−0.107710
$175$	0	0
$176$	2.65550e7	0.367157
$177$	−7.99920e7	−1.08428
$178$	−1.09887e7	−0.146041
$179$	−6.40238e7	−0.834365	−0.417182	−	0.908823i	$-0.636982\pi$
$179$	−6.40238e7	−0.834365	−0.417182	+	0.908823i	$0.636982\pi$
$180$	1.44078e7	0.184138
$181$	6.60928e6	0.0828475	0.0414237	−	0.999142i	$-0.486811\pi$
$181$	6.60928e6	0.0828475	0.0414237	+	0.999142i	$0.486811\pi$
$182$	0	0
$183$	−6.43601e7	−0.776315
$184$	−4.15245e7	−0.491408
$185$	−3.42302e6	−0.0397474
$186$	3.46705e7	0.395062
$187$	2.00456e8	2.24167
$188$	1.91996e7	0.210737
$189$	0	0
$190$	−3.85128e7	−0.407350
$191$	2.26170e7	0.234865	0.117432	−	0.993081i	$-0.462534\pi$
$191$	2.26170e7	0.234865	0.117432	+	0.993081i	$0.462534\pi$
$192$	7.07789e6	0.0721688
$193$	1.60034e7	0.160236	0.0801182	−	0.996785i	$-0.474470\pi$
$193$	1.60034e7	0.160236	0.0801182	+	0.996785i	$0.474470\pi$
$194$	2.39631e6	0.0235634
$195$	8.28468e6	0.0800119
$196$	0	0
$197$	−1.29465e7	−0.120648	−0.0603242	−	0.998179i	$-0.519213\pi$
$197$	−1.29465e7	−0.120648	−0.0603242	+	0.998179i	$0.519213\pi$
$198$	3.78098e7	0.346159
$199$	−2.02812e8	−1.82435	−0.912173	−	0.409806i	$-0.865597\pi$
$199$	−2.02812e8	−1.82435	−0.912173	+	0.409806i	$0.865597\pi$
$200$	8.82562e6	0.0780082
$201$	1.22416e8	1.06329
$202$	1.13569e7	0.0969457
$203$	0	0
$204$	5.34288e7	0.440626
$205$	−1.41948e8	−1.15078
$206$	1.49749e8	1.19351
$207$	−5.91238e7	−0.463304
$208$	4.06989e6	0.0313589
$209$	−1.01068e8	−0.765774
$210$	0	0
$211$	2.54584e8	1.86570	0.932851	−	0.360262i	$-0.117313\pi$
$211$	2.54584e8	1.86570	0.932851	+	0.360262i	$0.117313\pi$
$212$	1.21470e8	0.875577
$213$	−1.08188e8	−0.767100
$214$	3.36475e7	0.234695
$215$	1.40802e8	0.966213
$216$	1.00777e7	0.0680414
$217$	0	0
$218$	8.72376e7	0.570303
$219$	−9.37737e7	−0.603291
$220$	1.28131e8	0.811290
$221$	3.07224e7	0.191462
$222$	−2.39428e6	−0.0146872
$223$	1.97491e8	1.19256	0.596280	−	0.802777i	$-0.296645\pi$
$223$	1.97491e8	1.19256	0.596280	+	0.802777i	$0.296645\pi$
$224$	0	0
$225$	1.25662e7	0.0735468
$226$	5.74897e7	0.331292
$227$	6.19026e7	0.351251	0.175626	−	0.984457i	$-0.443805\pi$
$227$	6.19026e7	0.351251	0.175626	+	0.984457i	$0.443805\pi$
$228$	−2.69383e7	−0.150521
$229$	−3.10406e8	−1.70807	−0.854035	−	0.520215i	$-0.825852\pi$
$229$	−3.10406e8	−1.70807	−0.854035	+	0.520215i	$0.825852\pi$
$230$	−2.00361e8	−1.08584
$231$	0	0
$232$	−1.77416e7	−0.0932794
$233$	1.23511e8	0.639676	0.319838	−	0.947472i	$-0.396371\pi$
$233$	1.23511e8	0.639676	0.319838	+	0.947472i	$0.396371\pi$
$234$	5.79483e6	0.0295655
$235$	9.26408e7	0.465655
$236$	−1.89611e8	−0.939011
$237$	−1.87074e7	−0.0912841
$238$	0	0
$239$	1.86771e8	0.884944	0.442472	−	0.896782i	$-0.354102\pi$
$239$	1.86771e8	0.884944	0.442472	+	0.896782i	$0.354102\pi$
$240$	3.41517e7	0.159468
$241$	−1.09315e8	−0.503060	−0.251530	−	0.967849i	$-0.580934\pi$
$241$	−1.09315e8	−0.503060	−0.251530	+	0.967849i	$0.580934\pi$
$242$	1.80353e8	0.818031
$243$	1.43489e7	0.0641500
$244$	−1.52557e8	−0.672309
$245$	0	0
$246$	−9.92876e7	−0.425228
$247$	−1.54899e7	−0.0654048
$248$	8.21819e7	0.342133
$249$	7.17734e7	0.294622
$250$	−1.50420e8	−0.608859
$251$	−1.32241e8	−0.527846	−0.263923	−	0.964544i	$-0.585016\pi$
$251$	−1.32241e8	−0.527846	−0.263923	+	0.964544i	$0.585016\pi$
$252$	0	0
$253$	−5.25801e8	−2.04127
$254$	−1.29690e8	−0.496580
$255$	2.57801e8	0.973630
$256$	1.67772e7	0.0625000
$257$	−1.24448e8	−0.457323	−0.228662	−	0.973506i	$-0.573435\pi$
$257$	−1.24448e8	−0.457323	−0.228662	+	0.973506i	$0.573435\pi$
$258$	9.84855e7	0.357029
$259$	0	0
$260$	1.96377e7	0.0692923
$261$	−2.52610e7	−0.0879446
$262$	5.40375e7	0.185627
$263$	−4.86242e8	−1.64819	−0.824095	−	0.566452i	$-0.808316\pi$
$263$	−4.86242e8	−1.64819	−0.824095	+	0.566452i	$0.808316\pi$
$264$	8.96231e7	0.299783
$265$	5.86110e8	1.93472
$266$	0	0
$267$	−3.70867e7	−0.119242
$268$	2.90171e8	0.920835
$269$	−5.81470e8	−1.82135	−0.910676	−	0.413120i	$-0.864439\pi$
$269$	−5.81470e8	−1.82135	−0.910676	+	0.413120i	$0.864439\pi$
$270$	4.86262e7	0.150348
$271$	−2.41838e8	−0.738127	−0.369064	−	0.929404i	$-0.620322\pi$
$271$	−2.41838e8	−0.738127	−0.369064	+	0.929404i	$0.620322\pi$
$272$	1.26646e8	0.381593
$273$	0	0
$274$	4.42219e8	1.29870
$275$	1.11754e8	0.324039
$276$	−1.40145e8	−0.401233
$277$	2.47532e8	0.699764	0.349882	−	0.936794i	$-0.386222\pi$
$277$	2.47532e8	0.699764	0.349882	+	0.936794i	$0.386222\pi$
$278$	−2.60970e8	−0.728507
$279$	1.17013e8	0.322566
$280$	0	0
$281$	−3.68601e8	−0.991026	−0.495513	−	0.868601i	$-0.665020\pi$
$281$	−3.68601e8	−0.991026	−0.495513	+	0.868601i	$0.665020\pi$
$282$	6.47988e7	0.172066
$283$	1.66154e8	0.435771	0.217885	−	0.975974i	$-0.430084\pi$
$283$	1.66154e8	0.435771	0.217885	+	0.975974i	$0.430084\pi$
$284$	−2.56446e8	−0.664328
$285$	−1.29981e8	−0.332600
$286$	5.15346e7	0.130262
$287$	0	0
$288$	2.38879e7	0.0589256
$289$	5.45674e8	1.32981
$290$	−8.56056e7	−0.206115
$291$	8.08755e6	0.0192394
$292$	−2.22278e8	−0.522465
$293$	−2.64915e7	−0.0615276	−0.0307638	−	0.999527i	$-0.509794\pi$
$293$	−2.64915e7	−0.0615276	−0.0307638	+	0.999527i	$0.509794\pi$
$294$	0	0
$295$	−9.14896e8	−2.07489
$296$	−5.67532e6	−0.0127195
$297$	1.27608e8	0.282638
$298$	−5.14077e8	−1.12531
$299$	−8.05857e7	−0.174345
$300$	2.97865e7	0.0636934
$301$	0	0
$302$	4.98025e8	1.04046
$303$	3.83294e7	0.0791558
$304$	−6.38537e7	−0.130355
$305$	−7.36109e8	−1.48557
$306$	1.80322e8	0.359769
$307$	−7.09759e8	−1.39999	−0.699997	−	0.714146i	$-0.746815\pi$
$307$	−7.09759e8	−1.39999	−0.699997	+	0.714146i	$0.746815\pi$
$308$	0	0
$309$	5.05401e8	0.974500
$310$	3.96538e8	0.755996
$311$	4.23291e7	0.0797953	0.0398977	−	0.999204i	$-0.487297\pi$
$311$	4.23291e7	0.0797953	0.0398977	+	0.999204i	$0.487297\pi$
$312$	1.37359e7	0.0256045
$313$	−8.10096e6	−0.0149325	−0.00746623	−	0.999972i	$-0.502377\pi$
$313$	−8.10096e6	−0.0149325	−0.00746623	+	0.999972i	$0.502377\pi$
$314$	1.42383e8	0.259540
$315$	0	0
$316$	−4.43435e7	−0.0790543
$317$	−4.74883e8	−0.837295	−0.418648	−	0.908149i	$-0.637496\pi$
$317$	−4.74883e8	−0.837295	−0.418648	+	0.908149i	$0.637496\pi$
$318$	4.09962e8	0.714906
$319$	−2.24652e8	−0.387474
$320$	8.09522e7	0.138103
$321$	1.13560e8	0.191628
$322$	0	0
$323$	−4.82012e8	−0.795883
$324$	3.40122e7	0.0555556
$325$	1.71277e7	0.0276762
$326$	3.07470e8	0.491520
$327$	2.94427e8	0.465651
$328$	−2.35348e8	−0.368259
$329$	0	0
$330$	4.32443e8	0.662415
$331$	−9.10035e8	−1.37931	−0.689653	−	0.724140i	$-0.742237\pi$
$331$	−9.10035e8	−1.37931	−0.689653	+	0.724140i	$0.742237\pi$
$332$	1.70130e8	0.255151
$333$	−8.08068e6	−0.0119920
$334$	−4.34105e8	−0.637503
$335$	1.40011e9	2.03472
$336$	0	0
$337$	−1.34422e9	−1.91323	−0.956614	−	0.291359i	$-0.905893\pi$
$337$	−1.34422e9	−1.91323	−0.956614	+	0.291359i	$0.905893\pi$
$338$	−4.94090e8	−0.695981
$339$	1.94028e8	0.270499
$340$	6.11084e8	0.843188
$341$	1.04062e9	1.42119
$342$	−9.09167e7	−0.122900
$343$	0	0
$344$	2.33447e8	0.309196
$345$	−6.76219e8	−0.886586
$346$	1.36885e8	0.177660
$347$	−4.76825e8	−0.612641	−0.306320	−	0.951928i	$-0.599098\pi$
$347$	−4.76825e8	−0.612641	−0.306320	+	0.951928i	$0.599098\pi$
$348$	−5.98780e7	−0.0761623
$349$	9.67291e8	1.21806	0.609029	−	0.793148i	$-0.291559\pi$
$349$	9.67291e8	1.21806	0.609029	+	0.793148i	$0.291559\pi$
$350$	0	0
$351$	1.95575e7	0.0241401
$352$	2.12440e8	0.259619
$353$	6.82965e8	0.826394	0.413197	−	0.910642i	$-0.364412\pi$
$353$	6.82965e8	0.826394	0.413197	+	0.910642i	$0.364412\pi$
$354$	−6.39936e8	−0.766699
$355$	−1.23739e9	−1.46793
$356$	−8.79093e7	−0.103267
$357$	0	0
$358$	−5.12191e8	−0.589985
$359$	−1.12680e9	−1.28534	−0.642668	−	0.766145i	$-0.722172\pi$
$359$	−1.12680e9	−1.28534	−0.642668	+	0.766145i	$0.722172\pi$
$360$	1.15262e8	0.130205
$361$	−6.50846e8	−0.728120
$362$	5.28743e7	0.0585820
$363$	6.08692e8	0.667920
$364$	0	0
$365$	−1.07252e9	−1.15447
$366$	−5.14881e8	−0.548938
$367$	−1.02430e9	−1.08168	−0.540838	−	0.841126i	$-0.681893\pi$
$367$	−1.02430e9	−1.08168	−0.540838	+	0.841126i	$0.681893\pi$
$368$	−3.32196e8	−0.347478
$369$	−3.35096e8	−0.347197
$370$	−2.73842e7	−0.0281056
$371$	0	0
$372$	2.77364e8	0.279351
$373$	−7.01164e8	−0.699582	−0.349791	−	0.936828i	$-0.613747\pi$
$373$	−7.01164e8	−0.699582	−0.349791	+	0.936828i	$0.613747\pi$
$374$	1.60365e9	1.58510
$375$	−5.07669e8	−0.497131
$376$	1.53597e8	0.149014
$377$	−3.44307e7	−0.0330942
$378$	0	0
$379$	3.40034e8	0.320838	0.160419	−	0.987049i	$-0.448715\pi$
$379$	3.40034e8	0.320838	0.160419	+	0.987049i	$0.448715\pi$
$380$	−3.08102e8	−0.288040
$381$	−4.37705e8	−0.405456
$382$	1.80936e8	0.166074
$383$	−8.59927e8	−0.782107	−0.391053	−	0.920368i	$-0.627889\pi$
$383$	−8.59927e8	−0.782107	−0.391053	+	0.920368i	$0.627889\pi$
$384$	5.66231e7	0.0510310
$385$	0	0
$386$	1.28027e8	0.113304
$387$	3.32389e8	0.291513
$388$	1.91705e7	0.0166618
$389$	1.93050e7	0.0166282	0.00831410	−	0.999965i	$-0.497354\pi$
$389$	1.93050e7	0.0166282	0.00831410	+	0.999965i	$0.497354\pi$
$390$	6.62774e7	0.0565769
$391$	−2.50765e9	−2.12152
$392$	0	0
$393$	1.82377e8	0.151564
$394$	−1.03572e8	−0.0853114
$395$	−2.13963e8	−0.174683
$396$	3.02478e8	0.244771
$397$	−6.53361e8	−0.524066	−0.262033	−	0.965059i	$-0.584393\pi$
$397$	−6.53361e8	−0.524066	−0.262033	+	0.965059i	$0.584393\pi$
$398$	−1.62249e9	−1.29001
$399$	0	0
$400$	7.06049e7	0.0551601
$401$	1.73105e9	1.34062	0.670309	−	0.742082i	$-0.266161\pi$
$401$	1.73105e9	1.34062	0.670309	+	0.742082i	$0.266161\pi$
$402$	9.79326e8	0.751858
$403$	1.59488e8	0.121384
$404$	9.08549e7	0.0685509
$405$	1.64113e8	0.122758
$406$	0	0
$407$	−7.18633e7	−0.0528356
$408$	4.27431e8	0.311570
$409$	−1.79673e9	−1.29852	−0.649262	−	0.760564i	$-0.724922\pi$
$409$	−1.79673e9	−1.29852	−0.649262	+	0.760564i	$0.724922\pi$
$410$	−1.13559e9	−0.813723
$411$	1.49249e9	1.06039
$412$	1.19799e9	0.843942
$413$	0	0
$414$	−4.72990e8	−0.327606
$415$	8.20897e8	0.563794
$416$	3.25591e7	0.0221741
$417$	−8.80774e8	−0.594824
$418$	−8.08542e8	−0.541484
$419$	1.18733e9	0.788536	0.394268	−	0.918995i	$-0.370998\pi$
$419$	1.18733e9	0.788536	0.394268	+	0.918995i	$0.370998\pi$
$420$	0	0
$421$	−3.66435e8	−0.239337	−0.119669	−	0.992814i	$-0.538183\pi$
$421$	−3.66435e8	−0.239337	−0.119669	+	0.992814i	$0.538183\pi$
$422$	2.03667e9	1.31925
$423$	2.18696e8	0.140491
$424$	9.71762e8	0.619127
$425$	5.32975e8	0.336779
$426$	−8.65507e8	−0.542421
$427$	0	0
$428$	2.69180e8	0.165955
$429$	1.73929e8	0.106359
$430$	1.12641e9	0.683216
$431$	−6.53441e7	−0.0393130	−0.0196565	−	0.999807i	$-0.506257\pi$
$431$	−6.53441e7	−0.0393130	−0.0196565	+	0.999807i	$0.506257\pi$
$432$	8.06216e7	0.0481125
$433$	−1.55564e9	−0.920874	−0.460437	−	0.887692i	$-0.652307\pi$
$433$	−1.55564e9	−0.920874	−0.460437	+	0.887692i	$0.652307\pi$
$434$	0	0
$435$	−2.88919e8	−0.168292
$436$	6.97901e8	0.403265
$437$	1.26433e9	0.724729
$438$	−7.50190e8	−0.426591
$439$	−2.67260e9	−1.50768	−0.753839	−	0.657060i	$-0.771800\pi$
$439$	−2.67260e9	−1.50768	−0.753839	+	0.657060i	$0.771800\pi$
$440$	1.02505e9	0.573668
$441$	0	0
$442$	2.45779e8	0.135384
$443$	−2.34634e9	−1.28227	−0.641133	−	0.767430i	$-0.721535\pi$
$443$	−2.34634e9	−1.28227	−0.641133	+	0.767430i	$0.721535\pi$
$444$	−1.91542e7	−0.0103854
$445$	−4.24173e8	−0.228183
$446$	1.57993e9	0.843267
$447$	−1.73501e9	−0.918810
$448$	0	0
$449$	2.07584e9	1.08226	0.541129	−	0.840940i	$-0.317997\pi$
$449$	2.07584e9	1.08226	0.541129	+	0.840940i	$0.317997\pi$
$450$	1.00529e8	0.0520054
$451$	−2.98008e9	−1.52971
$452$	4.59918e8	0.234259
$453$	1.68083e9	0.849535
$454$	4.95220e8	0.248372
$455$	0	0
$456$	−2.15506e8	−0.106435
$457$	−1.67014e9	−0.818554	−0.409277	−	0.912410i	$-0.634219\pi$
$457$	−1.67014e9	−0.818554	−0.409277	+	0.912410i	$0.634219\pi$
$458$	−2.48325e9	−1.20779
$459$	6.08588e8	0.293751
$460$	−1.60289e9	−0.767806
$461$	−1.80273e8	−0.0856995	−0.0428498	−	0.999082i	$-0.513644\pi$
$461$	−1.80273e8	−0.0856995	−0.0428498	+	0.999082i	$0.513644\pi$
$462$	0	0
$463$	−2.76184e9	−1.29320	−0.646598	−	0.762831i	$-0.723809\pi$
$463$	−2.76184e9	−1.29320	−0.646598	+	0.762831i	$0.723809\pi$
$464$	−1.41933e8	−0.0659585
$465$	1.33832e9	0.617268
$466$	9.88089e8	0.452319
$467$	2.45133e9	1.11376	0.556880	−	0.830593i	$-0.311998\pi$
$467$	2.45133e9	1.11376	0.556880	+	0.830593i	$0.311998\pi$
$468$	4.63586e7	0.0209059
$469$	0	0
$470$	7.41126e8	0.329268
$471$	4.80542e8	0.211913
$472$	−1.51688e9	−0.663981
$473$	2.95600e9	1.28437
$474$	−1.49659e8	−0.0645476
$475$	−2.68721e8	−0.115047
$476$	0	0
$477$	1.38362e9	0.583718
$478$	1.49417e9	0.625750
$479$	3.43106e9	1.42644	0.713220	−	0.700940i	$-0.247236\pi$
$479$	3.43106e9	1.42644	0.713220	+	0.700940i	$0.247236\pi$
$480$	2.73214e8	0.112761
$481$	−1.10140e7	−0.00451269
$482$	−8.74520e8	−0.355717
$483$	0	0
$484$	1.44282e9	0.578435
$485$	9.25001e7	0.0368168
$486$	1.14791e8	0.0453609
$487$	1.89939e9	0.745182	0.372591	−	0.927996i	$-0.378470\pi$
$487$	1.89939e9	0.745182	0.372591	+	0.927996i	$0.378470\pi$
$488$	−1.22046e9	−0.475394
$489$	1.03771e9	0.401324
$490$	0	0
$491$	5.21957e9	1.98998	0.994991	−	0.0999634i	$-0.0318726\pi$
$491$	5.21957e9	1.98998	0.994991	+	0.0999634i	$0.0318726\pi$
$492$	−7.94301e8	−0.300682
$493$	−1.07141e9	−0.402709
$494$	−1.23919e8	−0.0462482
$495$	1.45950e9	0.540860
$496$	6.57455e8	0.241925
$497$	0	0
$498$	5.74187e8	0.208330
$499$	1.71816e9	0.619029	0.309514	−	0.950895i	$-0.399834\pi$
$499$	1.71816e9	0.619029	0.309514	+	0.950895i	$0.399834\pi$
$500$	−1.20336e9	−0.430528
$501$	−1.46510e9	−0.520519
$502$	−1.05793e9	−0.373243
$503$	−1.00189e9	−0.351020	−0.175510	−	0.984478i	$-0.556157\pi$
$503$	−1.00189e9	−0.351020	−0.175510	+	0.984478i	$0.556157\pi$
$504$	0	0
$505$	4.38386e8	0.151474
$506$	−4.20641e9	−1.44339
$507$	−1.66755e9	−0.568266
$508$	−1.03752e9	−0.351135
$509$	3.94187e9	1.32492	0.662461	−	0.749097i	$-0.269512\pi$
$509$	3.94187e9	1.32492	0.662461	+	0.749097i	$0.269512\pi$
$510$	2.06241e9	0.688460
$511$	0	0
$512$	1.34218e8	0.0441942
$513$	−3.06844e8	−0.100347
$514$	−9.95587e8	−0.323376
$515$	5.78045e9	1.86482
$516$	7.87884e8	0.252457
$517$	1.94491e9	0.618989
$518$	0	0
$519$	4.61986e8	0.145059
$520$	1.57102e8	0.0489971
$521$	3.80175e9	1.17775	0.588873	−	0.808225i	$-0.299572\pi$
$521$	3.80175e9	1.17775	0.588873	+	0.808225i	$0.299572\pi$
$522$	−2.02088e8	−0.0621862
$523$	−1.78525e9	−0.545687	−0.272843	−	0.962058i	$-0.587964\pi$
$523$	−1.78525e9	−0.545687	−0.272843	+	0.962058i	$0.587964\pi$
$524$	4.32300e8	0.131258
$525$	0	0
$526$	−3.88993e9	−1.16545
$527$	4.96293e9	1.47707
$528$	7.16985e8	0.211978
$529$	3.17281e9	0.931857
$530$	4.68888e9	1.36805
$531$	−2.15978e9	−0.626007
$532$	0	0
$533$	−4.56735e8	−0.130653
$534$	−2.96694e8	−0.0843168
$535$	1.29883e9	0.366702
$536$	2.32136e9	0.651128
$537$	−1.72864e9	−0.481721
$538$	−4.65176e9	−1.28789
$539$	0	0
$540$	3.89009e8	0.106312
$541$	3.90163e9	1.05939	0.529695	−	0.848188i	$-0.322307\pi$
$541$	3.90163e9	1.05939	0.529695	+	0.848188i	$0.322307\pi$
$542$	−1.93470e9	−0.521935
$543$	1.78451e8	0.0478320
$544$	1.01317e9	0.269827
$545$	3.36746e9	0.891076
$546$	0	0
$547$	1.55347e9	0.405833	0.202917	−	0.979196i	$-0.434958\pi$
$547$	1.55347e9	0.405833	0.202917	+	0.979196i	$0.434958\pi$
$548$	3.53775e9	0.918322
$549$	−1.73772e9	−0.448206
$550$	8.94029e8	0.229130
$551$	5.40194e8	0.137568
$552$	−1.12116e9	−0.283715
$553$	0	0
$554$	1.98025e9	0.494808
$555$	−9.24215e7	−0.0229481
$556$	−2.08776e9	−0.515132
$557$	−2.15437e9	−0.528234	−0.264117	−	0.964491i	$-0.585081\pi$
$557$	−2.15437e9	−0.528234	−0.264117	+	0.964491i	$0.585081\pi$
$558$	9.36103e8	0.228089
$559$	4.53045e8	0.109698
$560$	0	0
$561$	5.41230e9	1.29423
$562$	−2.94881e9	−0.700761
$563$	−4.31625e9	−1.01936	−0.509679	−	0.860365i	$-0.670236\pi$
$563$	−4.31625e9	−1.01936	−0.509679	+	0.860365i	$0.670236\pi$
$564$	5.18390e8	0.121669
$565$	2.21916e9	0.517630
$566$	1.32923e9	0.308136
$567$	0	0
$568$	−2.05157e9	−0.469751
$569$	−2.58635e9	−0.588565	−0.294282	−	0.955718i	$-0.595081\pi$
$569$	−2.58635e9	−0.588565	−0.294282	+	0.955718i	$0.595081\pi$
$570$	−1.03985e9	−0.235183
$571$	3.73419e9	0.839402	0.419701	−	0.907663i	$-0.362135\pi$
$571$	3.73419e9	0.839402	0.419701	+	0.907663i	$0.362135\pi$
$572$	4.12277e8	0.0921092
$573$	6.10658e8	0.135599
$574$	0	0
$575$	−1.39801e9	−0.306671
$576$	1.91103e8	0.0416667
$577$	−4.46603e9	−0.967846	−0.483923	−	0.875111i	$-0.660789\pi$
$577$	−4.46603e9	−0.967846	−0.483923	+	0.875111i	$0.660789\pi$
$578$	4.36539e9	0.940320
$579$	4.32091e8	0.0925126
$580$	−6.84845e8	−0.145745
$581$	0	0
$582$	6.47004e7	0.0136043
$583$	1.23049e10	2.57180
$584$	−1.77823e9	−0.369439
$585$	2.23686e8	0.0461949
$586$	−2.11932e8	−0.0435066
$587$	7.59680e9	1.55023	0.775117	−	0.631818i	$-0.217691\pi$
$587$	7.59680e9	1.55023	0.775117	+	0.631818i	$0.217691\pi$
$588$	0	0
$589$	−2.50226e9	−0.504579
$590$	−7.31917e9	−1.46717
$591$	−3.49557e8	−0.0696564
$592$	−4.54026e7	−0.00899403
$593$	7.56585e9	1.48993	0.744965	−	0.667103i	$-0.232466\pi$
$593$	7.56585e9	1.48993	0.744965	+	0.667103i	$0.232466\pi$
$594$	1.02086e9	0.199855
$595$	0	0
$596$	−4.11262e9	−0.795713
$597$	−5.47591e9	−1.05329
$598$	−6.44685e8	−0.123280
$599$	−5.13555e9	−0.976321	−0.488161	−	0.872754i	$-0.662332\pi$
$599$	−5.13555e9	−0.976321	−0.488161	+	0.872754i	$0.662332\pi$
$600$	2.38292e8	0.0450380
$601$	−5.69082e9	−1.06934	−0.534668	−	0.845062i	$-0.679563\pi$
$601$	−5.69082e9	−1.06934	−0.534668	+	0.845062i	$0.679563\pi$
$602$	0	0
$603$	3.30522e9	0.613890
$604$	3.98420e9	0.735719
$605$	6.96181e9	1.27814
$606$	3.06635e8	0.0559716
$607$	2.87845e9	0.522394	0.261197	−	0.965286i	$-0.415883\pi$
$607$	2.87845e9	0.522394	0.261197	+	0.965286i	$0.415883\pi$
$608$	−5.10830e8	−0.0921751
$609$	0	0
$610$	−5.88887e9	−1.05046
$611$	2.98082e8	0.0528679
$612$	1.44258e9	0.254395
$613$	8.73479e9	1.53158	0.765792	−	0.643088i	$-0.222347\pi$
$613$	8.73479e9	1.53158	0.765792	+	0.643088i	$0.222347\pi$
$614$	−5.67807e9	−0.989946
$615$	−3.83260e9	−0.664402
$616$	0	0
$617$	−2.09281e9	−0.358701	−0.179350	−	0.983785i	$-0.557400\pi$
$617$	−2.09281e9	−0.358701	−0.179350	+	0.983785i	$0.557400\pi$
$618$	4.04321e9	0.689075
$619$	2.71508e9	0.460113	0.230057	−	0.973177i	$-0.426109\pi$
$619$	2.71508e9	0.460113	0.230057	+	0.973177i	$0.426109\pi$
$620$	3.17231e9	0.534570
$621$	−1.59634e9	−0.267489
$622$	3.38633e8	0.0564238
$623$	0	0
$624$	1.09887e8	0.0181051
$625$	−7.15307e9	−1.17196
$626$	−6.48077e7	−0.0105588
$627$	−2.72883e9	−0.442120
$628$	1.13906e9	0.183522
$629$	−3.42730e8	−0.0549130
$630$	0	0
$631$	5.11357e9	0.810254	0.405127	−	0.914260i	$-0.367227\pi$
$631$	5.11357e9	0.810254	0.405127	+	0.914260i	$0.367227\pi$
$632$	−3.54748e8	−0.0558999
$633$	6.87377e9	1.07716
$634$	−3.79906e9	−0.592057
$635$	−5.00618e9	−0.775887
$636$	3.27970e9	0.505515
$637$	0	0
$638$	−1.79721e9	−0.273986
$639$	−2.92108e9	−0.442885
$640$	6.47618e8	0.0976537
$641$	−3.98014e9	−0.596892	−0.298446	−	0.954427i	$-0.596468\pi$
$641$	−3.98014e9	−0.596892	−0.298446	+	0.954427i	$0.596468\pi$
$642$	9.08482e8	0.135501
$643$	−1.15835e10	−1.71830	−0.859152	−	0.511721i	$-0.829008\pi$
$643$	−1.15835e10	−1.71830	−0.859152	+	0.511721i	$0.829008\pi$
$644$	0	0
$645$	3.80164e9	0.557843
$646$	−3.85610e9	−0.562774
$647$	−6.28625e9	−0.912487	−0.456244	−	0.889855i	$-0.650805\pi$
$647$	−6.28625e9	−0.912487	−0.456244	+	0.889855i	$0.650805\pi$
$648$	2.72098e8	0.0392837
$649$	−1.92074e10	−2.75812
$650$	1.37021e8	0.0195700
$651$	0	0
$652$	2.45976e9	0.347557
$653$	3.39197e9	0.476712	0.238356	−	0.971178i	$-0.423391\pi$
$653$	3.39197e9	0.476712	0.238356	+	0.971178i	$0.423391\pi$
$654$	2.35541e9	0.329265
$655$	2.08590e9	0.290035
$656$	−1.88279e9	−0.260398
$657$	−2.53189e9	−0.348310
$658$	0	0
$659$	1.04865e10	1.42735	0.713676	−	0.700476i	$-0.247029\pi$
$659$	1.04865e10	1.42735	0.713676	+	0.700476i	$0.247029\pi$
$660$	3.45955e9	0.468398
$661$	6.25959e9	0.843026	0.421513	−	0.906822i	$-0.361499\pi$
$661$	6.25959e9	0.843026	0.421513	+	0.906822i	$0.361499\pi$
$662$	−7.28028e9	−0.975316
$663$	8.29504e8	0.110540
$664$	1.36104e9	0.180419
$665$	0	0
$666$	−6.46454e7	−0.00847965
$667$	2.81034e9	0.366706
$668$	−3.47284e9	−0.450783
$669$	5.33225e9	0.688525
$670$	1.12009e10	1.43877
$671$	−1.54540e10	−1.97474
$672$	0	0
$673$	5.20341e9	0.658014	0.329007	−	0.944327i	$-0.393286\pi$
$673$	5.20341e9	0.658014	0.329007	+	0.944327i	$0.393286\pi$
$674$	−1.07538e10	−1.35286
$675$	3.39286e8	0.0424623
$676$	−3.95272e9	−0.492133
$677$	−6.31906e9	−0.782694	−0.391347	−	0.920243i	$-0.627991\pi$
$677$	−6.31906e9	−0.782694	−0.391347	+	0.920243i	$0.627991\pi$
$678$	1.55222e9	0.191271
$679$	0	0
$680$	4.88867e9	0.596224
$681$	1.67137e9	0.202795
$682$	8.32497e9	1.00493
$683$	−6.54540e9	−0.786074	−0.393037	−	0.919523i	$-0.628576\pi$
$683$	−6.54540e9	−0.786074	−0.393037	+	0.919523i	$0.628576\pi$
$684$	−7.27333e8	−0.0869035
$685$	1.70701e10	2.02917
$686$	0	0
$687$	−8.38096e9	−0.986155
$688$	1.86758e9	0.218635
$689$	1.88587e9	0.219657
$690$	−5.40975e9	−0.626911
$691$	−2.70830e9	−0.312265	−0.156132	−	0.987736i	$-0.549903\pi$
$691$	−2.70830e9	−0.312265	−0.156132	+	0.987736i	$0.549903\pi$
$692$	1.09508e9	0.125624
$693$	0	0
$694$	−3.81460e9	−0.433203
$695$	−1.00737e10	−1.13826
$696$	−4.79024e8	−0.0538549
$697$	−1.42126e10	−1.58986
$698$	7.73832e9	0.861297
$699$	3.33480e9	0.369317
$700$	0	0
$701$	−8.01526e9	−0.878830	−0.439415	−	0.898284i	$-0.644814\pi$
$701$	−8.01526e9	−0.878830	−0.439415	+	0.898284i	$0.644814\pi$
$702$	1.56460e8	0.0170696
$703$	1.72801e8	0.0187587
$704$	1.69952e9	0.183579
$705$	2.50130e9	0.268846
$706$	5.46372e9	0.584349
$707$	0	0
$708$	−5.11949e9	−0.542138
$709$	−1.39871e10	−1.47389	−0.736945	−	0.675952i	$-0.763732\pi$
$709$	−1.39871e10	−1.47389	−0.736945	+	0.675952i	$0.763732\pi$
$710$	−9.89909e9	−1.03799
$711$	−5.05101e8	−0.0527029
$712$	−7.03274e8	−0.0730205
$713$	−1.30179e10	−1.34502
$714$	0	0
$715$	1.98929e9	0.203529
$716$	−4.09752e9	−0.417182
$717$	5.04281e9	0.510923
$718$	−9.01440e9	−0.908869
$719$	1.84921e10	1.85539	0.927693	−	0.373345i	$-0.121789\pi$
$719$	1.84921e10	1.85539	0.927693	+	0.373345i	$0.121789\pi$
$720$	9.22096e8	0.0920688
$721$	0	0
$722$	−5.20677e9	−0.514859
$723$	−2.95150e9	−0.290442
$724$	4.22994e8	0.0414237
$725$	−5.97308e8	−0.0582124
$726$	4.86953e9	0.472290
$727$	−6.52913e8	−0.0630210	−0.0315105	−	0.999503i	$-0.510032\pi$
$727$	−6.52913e8	−0.0630210	−0.0315105	+	0.999503i	$0.510032\pi$
$728$	0	0
$729$	3.87420e8	0.0370370
$730$	−8.58018e9	−0.816331
$731$	1.40978e10	1.33487
$732$	−4.11905e9	−0.388158
$733$	−5.99796e9	−0.562522	−0.281261	−	0.959631i	$-0.590753\pi$
$733$	−5.99796e9	−0.562522	−0.281261	+	0.959631i	$0.590753\pi$
$734$	−8.19443e9	−0.764861
$735$	0	0
$736$	−2.65757e9	−0.245704
$737$	2.93941e10	2.70473
$738$	−2.68077e9	−0.245506
$739$	3.08607e9	0.281287	0.140644	−	0.990060i	$-0.455083\pi$
$739$	3.08607e9	0.281287	0.140644	+	0.990060i	$0.455083\pi$
$740$	−2.19073e8	−0.0198737
$741$	−4.18228e8	−0.0377615
$742$	0	0
$743$	−1.65397e10	−1.47933	−0.739667	−	0.672974i	$-0.765017\pi$
$743$	−1.65397e10	−1.47933	−0.739667	+	0.672974i	$0.765017\pi$
$744$	2.21891e9	0.197531
$745$	−1.98439e10	−1.75825
$746$	−5.60931e9	−0.494679
$747$	1.93788e9	0.170100
$748$	1.28292e10	1.12084
$749$	0	0
$750$	−4.06135e9	−0.351525
$751$	−1.80372e9	−0.155392	−0.0776962	−	0.996977i	$-0.524756\pi$
$751$	−1.80372e9	−0.155392	−0.0776962	+	0.996977i	$0.524756\pi$
$752$	1.22878e9	0.105368
$753$	−3.57050e9	−0.304752
$754$	−2.75446e8	−0.0234011
$755$	1.92243e10	1.62568
$756$	0	0
$757$	−8.71019e9	−0.729780	−0.364890	−	0.931051i	$-0.618893\pi$
$757$	−8.71019e9	−0.729780	−0.364890	+	0.931051i	$0.618893\pi$
$758$	2.72028e9	0.226867
$759$	−1.41966e10	−1.17853
$760$	−2.46482e9	−0.203675
$761$	−2.28491e10	−1.87941	−0.939707	−	0.341980i	$-0.888902\pi$
$761$	−2.28491e10	−1.87941	−0.939707	+	0.341980i	$0.888902\pi$
$762$	−3.50164e9	−0.286701
$763$	0	0
$764$	1.44749e9	0.117432
$765$	6.96062e9	0.562125
$766$	−6.87942e9	−0.553033
$767$	−2.94378e9	−0.235571
$768$	4.52985e8	0.0360844
$769$	−1.04328e10	−0.827288	−0.413644	−	0.910439i	$-0.635744\pi$
$769$	−1.04328e10	−0.827288	−0.413644	+	0.910439i	$0.635744\pi$
$770$	0	0
$771$	−3.36010e9	−0.264036
$772$	1.02422e9	0.0801182
$773$	1.84483e10	1.43657	0.718286	−	0.695748i	$-0.244927\pi$
$773$	1.84483e10	1.43657	0.718286	+	0.695748i	$0.244927\pi$
$774$	2.65911e9	0.206131
$775$	2.76682e9	0.213514
$776$	1.53364e8	0.0117817
$777$	0	0
$778$	1.54440e8	0.0117579
$779$	7.16584e9	0.543108
$780$	5.30219e8	0.0400059
$781$	−2.59778e10	−1.95130
$782$	−2.00612e10	−1.50014
$783$	−6.82048e8	−0.0507749
$784$	0	0
$785$	5.49613e9	0.405521
$786$	1.45901e9	0.107172
$787$	1.74841e10	1.27859	0.639297	−	0.768960i	$-0.279225\pi$
$787$	1.74841e10	1.27859	0.639297	+	0.768960i	$0.279225\pi$
$788$	−8.28579e8	−0.0603242
$789$	−1.31285e10	−0.951583
$790$	−1.71171e9	−0.123519
$791$	0	0
$792$	2.41982e9	0.173080
$793$	−2.36851e9	−0.168663
$794$	−5.22689e9	−0.370571
$795$	1.58250e10	1.11701
$796$	−1.29799e10	−0.912173
$797$	8.77363e9	0.613869	0.306934	−	0.951731i	$-0.400697\pi$
$797$	8.77363e9	0.613869	0.306934	+	0.951731i	$0.400697\pi$
$798$	0	0
$799$	9.27567e9	0.643326
$800$	5.64839e8	0.0390041
$801$	−1.00134e9	−0.0688444
$802$	1.38484e10	0.947960
$803$	−2.25166e10	−1.53461
$804$	7.83461e9	0.531644
$805$	0	0
$806$	1.27591e9	0.0858315
$807$	−1.56997e10	−1.05156
$808$	7.26839e8	0.0484728
$809$	−2.46036e10	−1.63372	−0.816862	−	0.576833i	$-0.804289\pi$
$809$	−2.46036e10	−1.63372	−0.816862	+	0.576833i	$0.804289\pi$
$810$	1.31291e9	0.0868033
$811$	2.27226e10	1.49584	0.747921	−	0.663788i	$-0.231052\pi$
$811$	2.27226e10	1.49584	0.747921	+	0.663788i	$0.231052\pi$
$812$	0	0
$813$	−6.52961e9	−0.426158
$814$	−5.74906e8	−0.0373604
$815$	1.18687e10	0.767980
$816$	3.41944e9	0.220313
$817$	−7.10795e9	−0.456003
$818$	−1.43738e10	−0.918196
$819$	0	0
$820$	−9.08469e9	−0.575389
$821$	1.35672e10	0.855637	0.427819	−	0.903865i	$-0.359282\pi$
$821$	1.35672e10	0.855637	0.427819	+	0.903865i	$0.359282\pi$
$822$	1.19399e10	0.749807
$823$	2.41431e10	1.50971	0.754854	−	0.655893i	$-0.227708\pi$
$823$	2.41431e10	1.50971	0.754854	+	0.655893i	$0.227708\pi$
$824$	9.58391e9	0.596757
$825$	3.01735e9	0.187084
$826$	0	0
$827$	5.22827e9	0.321432	0.160716	−	0.987001i	$-0.448620\pi$
$827$	5.22827e9	0.321432	0.160716	+	0.987001i	$0.448620\pi$
$828$	−3.78392e9	−0.231652
$829$	−8.00808e9	−0.488188	−0.244094	−	0.969752i	$-0.578491\pi$
$829$	−8.00808e9	−0.488188	−0.244094	+	0.969752i	$0.578491\pi$
$830$	6.56718e9	0.398662
$831$	6.68335e9	0.404009
$832$	2.60473e8	0.0156795
$833$	0	0
$834$	−7.04619e9	−0.420604
$835$	−1.67569e10	−0.996073
$836$	−6.46833e9	−0.382887
$837$	3.15935e9	0.186234
$838$	9.49863e9	0.557579
$839$	1.13828e10	0.665397	0.332699	−	0.943033i	$-0.392041\pi$
$839$	1.13828e10	0.665397	0.332699	+	0.943033i	$0.392041\pi$
$840$	0	0
$841$	−1.60491e10	−0.930392
$842$	−2.93148e9	−0.169237
$843$	−9.95224e9	−0.572169
$844$	1.62934e10	0.932851
$845$	−1.90724e10	−1.08744
$846$	1.74957e9	0.0993424
$847$	0	0
$848$	7.77410e9	0.437789
$849$	4.48615e9	0.251592
$850$	4.26380e9	0.238139
$851$	8.98991e8	0.0500037
$852$	−6.92405e9	−0.383550
$853$	2.07865e9	0.114673	0.0573364	−	0.998355i	$-0.481739\pi$
$853$	2.07865e9	0.114673	0.0573364	+	0.998355i	$0.481739\pi$
$854$	0	0
$855$	−3.50948e9	−0.192026
$856$	2.15344e9	0.117348
$857$	1.18988e10	0.645760	0.322880	−	0.946440i	$-0.395349\pi$
$857$	1.18988e10	0.645760	0.322880	+	0.946440i	$0.395349\pi$
$858$	1.39144e9	0.0752069
$859$	2.54060e10	1.36761	0.683803	−	0.729667i	$-0.260325\pi$
$859$	2.54060e10	1.36761	0.683803	+	0.729667i	$0.260325\pi$
$860$	9.01130e9	0.483106
$861$	0	0
$862$	−5.22753e8	−0.0277985
$863$	5.99565e9	0.317540	0.158770	−	0.987316i	$-0.449247\pi$
$863$	5.99565e9	0.317540	0.158770	+	0.987316i	$0.449247\pi$
$864$	6.44973e8	0.0340207
$865$	5.28389e9	0.277586
$866$	−1.24451e10	−0.651157
$867$	1.47332e10	0.767768
$868$	0	0
$869$	−4.49197e9	−0.232203
$870$	−2.31135e9	−0.119000
$871$	4.50502e9	0.231011
$872$	5.58321e9	0.285152
$873$	2.18364e8	0.0111079
$874$	1.01147e10	0.512461
$875$	0	0
$876$	−6.00152e9	−0.301645
$877$	−8.82768e9	−0.441924	−0.220962	−	0.975282i	$-0.570920\pi$
$877$	−8.82768e9	−0.441924	−0.220962	+	0.975282i	$0.570920\pi$
$878$	−2.13808e10	−1.06609
$879$	−7.15271e8	−0.0355230
$880$	8.20040e9	0.405645
$881$	7.07937e9	0.348802	0.174401	−	0.984675i	$-0.444201\pi$
$881$	7.07937e9	0.348802	0.174401	+	0.984675i	$0.444201\pi$
$882$	0	0
$883$	3.43253e10	1.67785	0.838923	−	0.544251i	$-0.183186\pi$
$883$	3.43253e10	1.67785	0.838923	+	0.544251i	$0.183186\pi$
$884$	1.96623e9	0.0957308
$885$	−2.47022e10	−1.19794
$886$	−1.87707e10	−0.906699
$887$	1.04644e10	0.503481	0.251741	−	0.967795i	$-0.418997\pi$
$887$	1.04644e10	0.503481	0.251741	+	0.967795i	$0.418997\pi$
$888$	−1.53234e8	−0.00734360
$889$	0	0
$890$	−3.39339e9	−0.161350
$891$	3.44541e9	0.163181
$892$	1.26394e10	0.596280
$893$	−4.67670e9	−0.219765
$894$	−1.38801e10	−0.649697
$895$	−1.97711e10	−0.921828
$896$	0	0
$897$	−2.17581e9	−0.100658
$898$	1.66067e10	0.765272
$899$	−5.56198e9	−0.255312
$900$	8.04234e8	0.0367734
$901$	5.86843e10	2.67291
$902$	−2.38406e10	−1.08167
$903$	0	0
$904$	3.67934e9	0.165646
$905$	2.04100e9	0.0915320
$906$	1.34467e10	0.600712
$907$	−3.09566e10	−1.37761	−0.688806	−	0.724945i	$-0.741865\pi$
$907$	−3.09566e10	−1.37761	−0.688806	+	0.724945i	$0.741865\pi$
$908$	3.96176e9	0.175626
$909$	1.03489e9	0.0457006
$910$	0	0
$911$	1.55078e10	0.679572	0.339786	−	0.940503i	$-0.389645\pi$
$911$	1.55078e10	0.679572	0.339786	+	0.940503i	$0.389645\pi$
$912$	−1.72405e9	−0.0752606
$913$	1.72340e10	0.749443
$914$	−1.33612e10	−0.578805
$915$	−1.98749e10	−0.857693
$916$	−1.98660e10	−0.854035
$917$	0	0
$918$	4.86870e9	0.207713
$919$	3.32232e10	1.41201	0.706003	−	0.708209i	$-0.250496\pi$
$919$	3.32232e10	1.41201	0.706003	+	0.708209i	$0.250496\pi$
$920$	−1.28231e10	−0.542921
$921$	−1.91635e10	−0.808287
$922$	−1.44219e9	−0.0605987
$923$	−3.98143e9	−0.166661
$924$	0	0
$925$	−1.91071e8	−0.00793779
$926$	−2.20947e10	−0.914428
$927$	1.36458e10	0.562628
$928$	−1.13546e9	−0.0466397
$929$	3.55693e8	0.0145553	0.00727764	−	0.999974i	$-0.497683\pi$
$929$	3.55693e8	0.0145553	0.00727764	+	0.999974i	$0.497683\pi$
$930$	1.07065e10	0.436474
$931$	0	0
$932$	7.90471e9	0.319838
$933$	1.14289e9	0.0460699
$934$	1.96106e10	0.787548
$935$	6.19024e10	2.47666
$936$	3.70869e8	0.0147827
$937$	4.28321e9	0.170091	0.0850454	−	0.996377i	$-0.472896\pi$
$937$	4.28321e9	0.170091	0.0850454	+	0.996377i	$0.472896\pi$
$938$	0	0
$939$	−2.18726e8	−0.00862126
$940$	5.92901e9	0.232828
$941$	−3.30117e10	−1.29153	−0.645765	−	0.763536i	$-0.723462\pi$
$941$	−3.30117e10	−1.29153	−0.645765	+	0.763536i	$0.723462\pi$
$942$	3.84434e9	0.149845
$943$	3.72800e10	1.44772
$944$	−1.21351e10	−0.469505
$945$	0	0
$946$	2.36480e10	0.908188
$947$	7.37823e9	0.282310	0.141155	−	0.989987i	$-0.454918\pi$
$947$	7.37823e9	0.282310	0.141155	+	0.989987i	$0.454918\pi$
$948$	−1.19728e9	−0.0456420
$949$	−3.45096e9	−0.131072
$950$	−2.14977e9	−0.0813502
$951$	−1.28218e10	−0.483413
$952$	0	0
$953$	−6.89038e9	−0.257880	−0.128940	−	0.991652i	$-0.541158\pi$
$953$	−6.89038e9	−0.257880	−0.128940	+	0.991652i	$0.541158\pi$
$954$	1.10690e10	0.412751
$955$	6.98431e9	0.259485
$956$	1.19533e10	0.442472
$957$	−6.06560e9	−0.223708
$958$	2.74485e10	1.00865
$959$	0	0
$960$	2.18571e9	0.0797339
$961$	−1.74866e9	−0.0635584
$962$	−8.81116e7	−0.00319095
$963$	3.06613e9	0.110636
$964$	−6.99616e9	−0.251530
$965$	4.94198e9	0.177033
$966$	0	0
$967$	2.74855e10	0.977489	0.488744	−	0.872427i	$-0.337455\pi$
$967$	2.74855e10	0.977489	0.488744	+	0.872427i	$0.337455\pi$
$968$	1.15426e10	0.409016
$969$	−1.30143e10	−0.459503
$970$	7.40001e8	0.0260334
$971$	5.63592e9	0.197559	0.0987797	−	0.995109i	$-0.468506\pi$
$971$	5.63592e9	0.197559	0.0987797	+	0.995109i	$0.468506\pi$
$972$	9.18330e8	0.0320750
$973$	0	0
$974$	1.51951e10	0.526923
$975$	4.62447e8	0.0159788
$976$	−9.76367e9	−0.336154
$977$	−3.09224e10	−1.06082	−0.530411	−	0.847740i	$-0.677962\pi$
$977$	−3.09224e10	−1.06082	−0.530411	+	0.847740i	$0.677962\pi$
$978$	8.30169e9	0.283779
$979$	−8.90515e9	−0.303320
$980$	0	0
$981$	7.94953e9	0.268844
$982$	4.17565e10	1.40713
$983$	−1.10312e10	−0.370413	−0.185207	−	0.982700i	$-0.559295\pi$
$983$	−1.10312e10	−0.370413	−0.185207	+	0.982700i	$0.559295\pi$
$984$	−6.35441e9	−0.212614
$985$	−3.99800e9	−0.133296
$986$	−8.57127e9	−0.284758
$987$	0	0
$988$	−9.91354e8	−0.0327024
$989$	−3.69788e10	−1.21553
$990$	1.16760e10	0.382446
$991$	3.61339e10	1.17939	0.589695	−	0.807626i	$-0.299248\pi$
$991$	3.61339e10	1.17939	0.589695	+	0.807626i	$0.299248\pi$
$992$	5.25964e9	0.171067
$993$	−2.45710e10	−0.796342
$994$	0	0
$995$	−6.26299e10	−2.01558
$996$	4.59350e9	0.147311
$997$	2.33816e9	0.0747206	0.0373603	−	0.999302i	$-0.488105\pi$
$997$	2.33816e9	0.0747206	0.0373603	+	0.999302i	$0.488105\pi$
$998$	1.37453e10	0.437719
$999$	−2.18178e8	−0.00692361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.8.a.y.1.3		3
7.2	even	3		42.8.e.d.25.1	✓	6
7.3	odd	6		294.8.e.z.79.3		6
7.4	even	3		42.8.e.d.37.1	yes	6
7.5	odd	6		294.8.e.z.67.3		6
7.6	odd	2		294.8.a.x.1.1		3
21.2	odd	6		126.8.g.k.109.3		6
21.11	odd	6		126.8.g.k.37.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.d.25.1	✓	6	7.2	even	3
42.8.e.d.37.1	yes	6	7.4	even	3
126.8.g.k.37.3		6	21.11	odd	6
126.8.g.k.109.3		6	21.2	odd	6
294.8.a.x.1.1		3	7.6	odd	2
294.8.a.y.1.3		3	1.1	even	1	trivial
294.8.e.z.67.3		6	7.5	odd	6
294.8.e.z.79.3		6	7.3	odd	6

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.808 q^{5} +216.000 q^{6} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +308.808 q^{5} +216.000 q^{6} +512.000 q^{8} +729.000 q^{9} +2470.47 q^{10} +6483.16 q^{11} +1728.00 q^{12} +993.626 q^{13} +8337.82 q^{15} +4096.00 q^{16} +30919.5 q^{17} +5832.00 q^{18} -15589.3 q^{19} +19763.7 q^{20} +51865.2 q^{22} -81102.6 q^{23} +13824.0 q^{24} +17237.5 q^{25} +7949.01 q^{26} +19683.0 q^{27} -34651.6 q^{29} +66702.6 q^{30} +160512. q^{31} +32768.0 q^{32} +175045. q^{33} +247356. q^{34} +46656.0 q^{36} -11084.6 q^{37} -124714. q^{38} +26827.9 q^{39} +158110. q^{40} -459665. q^{41} +455951. q^{43} +414922. q^{44} +225121. q^{45} -648821. q^{46} +299994. q^{47} +110592. q^{48} +137900. q^{50} +834825. q^{51} +63592.0 q^{52} +1.89797e6 q^{53} +157464. q^{54} +2.00205e6 q^{55} -420911. q^{57} -277213. q^{58} -2.96267e6 q^{59} +533621. q^{60} -2.38371e6 q^{61} +1.28409e6 q^{62} +262144. q^{64} +306840. q^{65} +1.40036e6 q^{66} +4.53392e6 q^{67} +1.97885e6 q^{68} -2.18977e6 q^{69} -4.00697e6 q^{71} +373248. q^{72} -3.47310e6 q^{73} -88676.9 q^{74} +465413. q^{75} -997714. q^{76} +214623. q^{78} -692868. q^{79} +1.26488e6 q^{80} +531441. q^{81} -3.67732e6 q^{82} +2.65827e6 q^{83} +9.54818e6 q^{85} +3.64761e6 q^{86} -935594. q^{87} +3.31938e6 q^{88} -1.37358e6 q^{89} +1.80097e6 q^{90} -5.19057e6 q^{92} +4.33381e6 q^{93} +2.39996e6 q^{94} -4.81410e6 q^{95} +884736. q^{96} +299539. q^{97} +4.72622e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 70 q^{5} + 648 q^{6} + 1536 q^{8} + 2187 q^{9}+O(q^{10}) \) 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 70 * q^5 + 648 * q^6 + 1536 * q^8 + 2187 * q^9	\( 3 q + 24 q^{2} + 81 q^{3} + 192 q^{4} - 70 q^{5} + 648 q^{6} + 1536 q^{8} + 2187 q^{9} - 560 q^{10} + 2428 q^{11} + 5184 q^{12} - 1919 q^{13} - 1890 q^{15} + 12288 q^{16} + 24508 q^{17} + 17496 q^{18} - 1353 q^{19} - 4480 q^{20} + 19424 q^{22} + 96628 q^{23} + 41472 q^{24} + 135175 q^{25} - 15352 q^{26} + 59049 q^{27} - 114112 q^{29} - 15120 q^{30} + 221395 q^{31} + 98304 q^{32} + 65556 q^{33} + 196064 q^{34} + 139968 q^{36} + 249987 q^{37} - 10824 q^{38} - 51813 q^{39} - 35840 q^{40} + 610926 q^{41} + 600243 q^{43} + 155392 q^{44} - 51030 q^{45} + 773024 q^{46} - 123114 q^{47} + 331776 q^{48} + 1081400 q^{50} + 661716 q^{51} - 122816 q^{52} + 3004752 q^{53} + 472392 q^{54} + 2246360 q^{55} - 36531 q^{57} - 912896 q^{58} - 2852938 q^{59} - 120960 q^{60} + 665386 q^{61} + 1771160 q^{62} + 786432 q^{64} + 5835930 q^{65} + 524448 q^{66} + 10545857 q^{67} + 1568512 q^{68} + 2608956 q^{69} - 1019762 q^{71} + 1119744 q^{72} - 6858031 q^{73} + 1999896 q^{74} + 3649725 q^{75} - 86592 q^{76} - 414504 q^{78} + 1723021 q^{79} - 286720 q^{80} + 1594323 q^{81} + 4887408 q^{82} + 2635804 q^{83} + 737060 q^{85} + 4801944 q^{86} - 3081024 q^{87} + 1243136 q^{88} - 976224 q^{89} - 408240 q^{90} + 6184192 q^{92} + 5977665 q^{93} - 984912 q^{94} + 11136310 q^{95} + 2654208 q^{96} - 8485792 q^{97} + 1770012 q^{99}+O(q^{100}) \) 3 * q + 24 * q^2 + 81 * q^3 + 192 * q^4 - 70 * q^5 + 648 * q^6 + 1536 * q^8 + 2187 * q^9 - 560 * q^10 + 2428 * q^11 + 5184 * q^12 - 1919 * q^13 - 1890 * q^15 + 12288 * q^16 + 24508 * q^17 + 17496 * q^18 - 1353 * q^19 - 4480 * q^20 + 19424 * q^22 + 96628 * q^23 + 41472 * q^24 + 135175 * q^25 - 15352 * q^26 + 59049 * q^27 - 114112 * q^29 - 15120 * q^30 + 221395 * q^31 + 98304 * q^32 + 65556 * q^33 + 196064 * q^34 + 139968 * q^36 + 249987 * q^37 - 10824 * q^38 - 51813 * q^39 - 35840 * q^40 + 610926 * q^41 + 600243 * q^43 + 155392 * q^44 - 51030 * q^45 + 773024 * q^46 - 123114 * q^47 + 331776 * q^48 + 1081400 * q^50 + 661716 * q^51 - 122816 * q^52 + 3004752 * q^53 + 472392 * q^54 + 2246360 * q^55 - 36531 * q^57 - 912896 * q^58 - 2852938 * q^59 - 120960 * q^60 + 665386 * q^61 + 1771160 * q^62 + 786432 * q^64 + 5835930 * q^65 + 524448 * q^66 + 10545857 * q^67 + 1568512 * q^68 + 2608956 * q^69 - 1019762 * q^71 + 1119744 * q^72 - 6858031 * q^73 + 1999896 * q^74 + 3649725 * q^75 - 86592 * q^76 - 414504 * q^78 + 1723021 * q^79 - 286720 * q^80 + 1594323 * q^81 + 4887408 * q^82 + 2635804 * q^83 + 737060 * q^85 + 4801944 * q^86 - 3081024 * q^87 + 1243136 * q^88 - 976224 * q^89 - 408240 * q^90 + 6184192 * q^92 + 5977665 * q^93 - 984912 * q^94 + 11136310 * q^95 + 2654208 * q^96 - 8485792 * q^97 + 1770012 * q^99

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