LMFDB - Embedded newform 363.8.a.o.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,8,Mod(1,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.1"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	363.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,-23] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$113.395764251$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 1289 x^{12} + 2366 x^{11} + 623758 x^{10} - 908404 x^{9} - 141535137 x^{8} + \cdots - 20874968128476 $ x^14 - 2x^13 - 1289x^12 + 2366x^11 + 623758x^10 - 908404x^9 - 141535137x^8 + 122490614x^7 + 15472711238x^6 - 831247148x^5 - 774565663469x^4 - 859523952378x^3 + 14942261922049x^2 + 32570153376222*x - 20874968128476
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.521602$ of defining polynomial
Character	$\chi$	$=$	363.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.13964 q^{2} +27.0000 q^{3} -118.143 q^{4} -324.899 q^{5} -84.7702 q^{6} -1656.56 q^{7} +772.799 q^{8} +729.000 q^{9} +1020.07 q^{10} -3189.85 q^{12} -5927.67 q^{13} +5200.99 q^{14} -8772.28 q^{15} +12696.0 q^{16} +29281.2 q^{17} -2288.79 q^{18} +32428.8 q^{19} +38384.5 q^{20} -44727.1 q^{21} +10937.0 q^{23} +20865.6 q^{24} +27434.6 q^{25} +18610.7 q^{26} +19683.0 q^{27} +195710. q^{28} -100071. q^{29} +27541.8 q^{30} +214819. q^{31} -138779. q^{32} -91932.4 q^{34} +538215. q^{35} -86126.0 q^{36} +85292.3 q^{37} -101815. q^{38} -160047. q^{39} -251082. q^{40} +347842. q^{41} +140427. q^{42} +492042. q^{43} -236852. q^{45} -34338.3 q^{46} -953784. q^{47} +342791. q^{48} +1.92064e6 q^{49} -86134.6 q^{50} +790593. q^{51} +700311. q^{52} -633416. q^{53} -61797.5 q^{54} -1.28019e6 q^{56} +875576. q^{57} +314187. q^{58} +56983.5 q^{59} +1.03638e6 q^{60} -1.82908e6 q^{61} -674454. q^{62} -1.20763e6 q^{63} -1.18937e6 q^{64} +1.92590e6 q^{65} -1.57940e6 q^{67} -3.45936e6 q^{68} +295300. q^{69} -1.68980e6 q^{70} -1.98445e6 q^{71} +563370. q^{72} -4.30211e6 q^{73} -267787. q^{74} +740733. q^{75} -3.83122e6 q^{76} +502490. q^{78} +1.14039e6 q^{79} -4.12491e6 q^{80} +531441. q^{81} -1.09210e6 q^{82} -5.57570e6 q^{83} +5.28418e6 q^{84} -9.51345e6 q^{85} -1.54483e6 q^{86} -2.70192e6 q^{87} +1.21091e7 q^{89} +743628. q^{90} +9.81953e6 q^{91} -1.29213e6 q^{92} +5.80012e6 q^{93} +2.99454e6 q^{94} -1.05361e7 q^{95} -3.74703e6 q^{96} +1.72401e7 q^{97} -6.03012e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 23 q^{2} + 378 q^{3} + 845 q^{4} + 69 q^{5} - 621 q^{6} - 3278 q^{7} - 4602 q^{8} + 10206 q^{9} - 5320 q^{10} + 22815 q^{12} - 32188 q^{13} - 7794 q^{14} + 1863 q^{15} + 86137 q^{16} - 42917 q^{17}+ \cdots + 70266089 q^{98}+O(q^{100}) $ 14 * q - 23 * q^2 + 378 * q^3 + 845 * q^4 + 69 * q^5 - 621 * q^6 - 3278 * q^7 - 4602 * q^8 + 10206 * q^9 - 5320 * q^10 + 22815 * q^12 - 32188 * q^13 - 7794 * q^14 + 1863 * q^15 + 86137 * q^16 - 42917 * q^17 - 16767 * q^18 - 50419 * q^19 + 54475 * q^20 - 88506 * q^21 - 83492 * q^23 - 124254 * q^24 + 336991 * q^25 + 234897 * q^26 + 275562 * q^27 - 697184 * q^28 - 227028 * q^29 - 143640 * q^30 - 36481 * q^31 - 151749 * q^32 - 614562 * q^34 + 258783 * q^35 + 616005 * q^36 + 634524 * q^37 - 662891 * q^38 - 869076 * q^39 - 1585604 * q^40 - 1286544 * q^41 - 210438 * q^42 - 2632644 * q^43 + 50301 * q^45 - 1290627 * q^46 - 1692245 * q^47 + 2325699 * q^48 + 842030 * q^49 - 7870914 * q^50 - 1158759 * q^51 - 6419781 * q^52 + 1211317 * q^53 - 452709 * q^54 - 9100953 * q^56 - 1361313 * q^57 - 6265711 * q^58 + 2551943 * q^59 + 1470825 * q^60 - 10221163 * q^61 - 5723657 * q^62 - 2389662 * q^63 + 6349332 * q^64 - 7684087 * q^65 - 3570631 * q^67 - 13112925 * q^68 - 2254284 * q^69 + 3559265 * q^70 + 4528437 * q^71 - 3354858 * q^72 - 13052276 * q^73 - 4896205 * q^74 + 9098757 * q^75 - 9845214 * q^76 + 6342219 * q^78 - 14911090 * q^79 - 9395382 * q^80 + 7440174 * q^81 + 17478001 * q^82 - 7068900 * q^83 - 18823968 * q^84 - 24423120 * q^85 + 12792479 * q^86 - 6129756 * q^87 + 4800832 * q^89 - 3878280 * q^90 - 15295476 * q^91 - 3195753 * q^92 - 984987 * q^93 + 43320002 * q^94 - 7614177 * q^95 - 4097223 * q^96 - 11578773 * q^97 + 70266089 * q^98

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 $

$2$	−3.13964	−0.277507	−0.138754	−	0.990327i	$-0.544310\pi$
$2$	−3.13964	−0.277507	−0.138754	+	0.990327i	$0.544310\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−118.143	−0.922990
$5$	−324.899	−1.16240	−0.581198	−	0.813762i	$-0.697416\pi$
$5$	−324.899	−1.16240	−0.581198	+	0.813762i	$0.697416\pi$
$6$	−84.7702	−0.160219
$7$	−1656.56	−1.82542	−0.912712	−	0.408604i	$-0.866016\pi$
$7$	−1656.56	−1.82542	−0.912712	+	0.408604i	$0.866016\pi$
$8$	772.799	0.533644
$9$	729.000	0.333333
$10$	1020.07	0.322573
$11$	0	0
$11$	0	0
$12$	−3189.85	−0.532888
$13$	−5927.67	−0.748311	−0.374156	−	0.927366i	$-0.622067\pi$
$13$	−5927.67	−0.748311	−0.374156	+	0.927366i	$0.622067\pi$
$14$	5200.99	0.506568
$15$	−8772.28	−0.671109
$16$	12696.0	0.774900
$17$	29281.2	1.44550	0.722750	−	0.691110i	$-0.242878\pi$
$17$	29281.2	1.44550	0.722750	+	0.691110i	$0.242878\pi$
$18$	−2288.79	−0.0925024
$19$	32428.8	1.08466	0.542329	−	0.840166i	$-0.317543\pi$
$19$	32428.8	1.08466	0.542329	+	0.840166i	$0.317543\pi$
$20$	38384.5	1.07288
$21$	−44727.1	−1.05391
$22$	0	0
$23$	10937.0	0.187435	0.0937177	−	0.995599i	$-0.470125\pi$
$23$	10937.0	0.187435	0.0937177	+	0.995599i	$0.470125\pi$
$24$	20865.6	0.308099
$25$	27434.6	0.351163
$26$	18610.7	0.207662
$27$	19683.0	0.192450
$28$	195710.	1.68485
$29$	−100071.	−0.761932	−0.380966	−	0.924589i	$-0.624408\pi$
$29$	−100071.	−0.761932	−0.380966	+	0.924589i	$0.624408\pi$
$30$	27541.8	0.186238
$31$	214819.	1.29511	0.647556	−	0.762018i	$-0.275791\pi$
$31$	214819.	1.29511	0.647556	+	0.762018i	$0.275791\pi$
$32$	−138779.	−0.748684
$33$	0	0
$34$	−91932.4	−0.401137
$35$	538215.	2.12186
$36$	−86126.0	−0.307663
$37$	85292.3	0.276824	0.138412	−	0.990375i	$-0.455800\pi$
$37$	85292.3	0.276824	0.138412	+	0.990375i	$0.455800\pi$
$38$	−101815.	−0.301000
$39$	−160047.	−0.432038
$40$	−251082.	−0.620305
$41$	347842.	0.788203	0.394102	−	0.919067i	$-0.371056\pi$
$41$	347842.	0.788203	0.394102	+	0.919067i	$0.371056\pi$
$42$	140427.	0.292467
$43$	492042.	0.943762	0.471881	−	0.881662i	$-0.343575\pi$
$43$	492042.	0.943762	0.471881	+	0.881662i	$0.343575\pi$
$44$	0	0
$45$	−236852.	−0.387465
$46$	−34338.3	−0.0520147
$47$	−953784.	−1.34001	−0.670004	−	0.742357i	$-0.733708\pi$
$47$	−953784.	−1.34001	−0.670004	+	0.742357i	$0.733708\pi$
$48$	342791.	0.447389
$49$	1.92064e6	2.33217
$50$	−86134.6	−0.0974502
$51$	790593.	0.834560
$52$	700311.	0.690683
$53$	−633416.	−0.584418	−0.292209	−	0.956354i	$-0.594390\pi$
$53$	−633416.	−0.584418	−0.292209	+	0.956354i	$0.594390\pi$
$54$	−61797.5	−0.0534063
$55$	0	0
$56$	−1.28019e6	−0.974126
$57$	875576.	0.626227
$58$	314187.	0.211442
$59$	56983.5	0.0361216	0.0180608	−	0.999837i	$-0.494251\pi$
$59$	56983.5	0.0361216	0.0180608	+	0.999837i	$0.494251\pi$
$60$	1.03638e6	0.619427
$61$	−1.82908e6	−1.03176	−0.515878	−	0.856662i	$-0.672534\pi$
$61$	−1.82908e6	−1.03176	−0.515878	+	0.856662i	$0.672534\pi$
$62$	−674454.	−0.359403
$63$	−1.20763e6	−0.608475
$64$	−1.18937e6	−0.567134
$65$	1.92590e6	0.869833
$66$	0	0
$67$	−1.57940e6	−0.641550	−0.320775	−	0.947155i	$-0.603943\pi$
$67$	−1.57940e6	−0.641550	−0.320775	+	0.947155i	$0.603943\pi$
$68$	−3.45936e6	−1.33418
$69$	295300.	0.108216
$70$	−1.68980e6	−0.588833
$71$	−1.98445e6	−0.658017	−0.329008	−	0.944327i	$-0.606714\pi$
$71$	−1.98445e6	−0.658017	−0.329008	+	0.944327i	$0.606714\pi$
$72$	563370.	0.177881
$73$	−4.30211e6	−1.29435	−0.647175	−	0.762342i	$-0.724050\pi$
$73$	−4.30211e6	−1.29435	−0.647175	+	0.762342i	$0.724050\pi$
$74$	−267787.	−0.0768207
$75$	740733.	0.202744
$76$	−3.83122e6	−1.00113
$77$	0	0
$78$	502490.	0.119894
$79$	1.14039e6	0.260231	0.130115	−	0.991499i	$-0.458465\pi$
$79$	1.14039e6	0.260231	0.130115	+	0.991499i	$0.458465\pi$
$80$	−4.12491e6	−0.900740
$81$	531441.	0.111111
$82$	−1.09210e6	−0.218732
$83$	−5.57570e6	−1.07035	−0.535175	−	0.844741i	$-0.679754\pi$
$83$	−5.57570e6	−1.07035	−0.535175	+	0.844741i	$0.679754\pi$
$84$	5.28418e6	0.972747
$85$	−9.51345e6	−1.68024
$86$	−1.54483e6	−0.261901
$87$	−2.70192e6	−0.439901
$88$	0	0
$89$	1.21091e7	1.82073	0.910364	−	0.413808i	$-0.135801\pi$
$89$	1.21091e7	1.82073	0.910364	+	0.413808i	$0.135801\pi$
$90$	743628.	0.107524
$91$	9.81953e6	1.36598
$92$	−1.29213e6	−0.173001
$93$	5.80012e6	0.747733
$94$	2.99454e6	0.371862
$95$	−1.05361e7	−1.26080
$96$	−3.74703e6	−0.432253
$97$	1.72401e7	1.91796	0.958978	−	0.283481i	$-0.0914894\pi$
$97$	1.72401e7	1.91796	0.958978	+	0.283481i	$0.0914894\pi$
$98$	−6.03012e6	−0.647195
$99$	0	0
$100$	−3.24119e6	−0.324119
$101$	−4.19794e6	−0.405426	−0.202713	−	0.979238i	$-0.564976\pi$
$101$	−4.19794e6	−0.405426	−0.202713	+	0.979238i	$0.564976\pi$
$102$	−2.48217e6	−0.231596
$103$	2.13658e7	1.92659	0.963294	−	0.268448i	$-0.0865106\pi$
$103$	2.13658e7	1.92659	0.963294	+	0.268448i	$0.0865106\pi$
$104$	−4.58089e6	−0.399331
$105$	1.45318e7	1.22506
$106$	1.98870e6	0.162180
$107$	−2.87275e6	−0.226702	−0.113351	−	0.993555i	$-0.536158\pi$
$107$	−2.87275e6	−0.226702	−0.113351	+	0.993555i	$0.536158\pi$
$108$	−2.32540e6	−0.177629
$109$	−2.68209e6	−0.198372	−0.0991862	−	0.995069i	$-0.531624\pi$
$109$	−2.68209e6	−0.198372	−0.0991862	+	0.995069i	$0.531624\pi$
$110$	0	0
$111$	2.30289e6	0.159824
$112$	−2.10316e7	−1.41452
$113$	4.83750e6	0.315389	0.157695	−	0.987488i	$-0.449594\pi$
$113$	4.83750e6	0.315389	0.157695	+	0.987488i	$0.449594\pi$
$114$	−2.74899e6	−0.173783
$115$	−3.55343e6	−0.217874
$116$	1.18227e7	0.703255
$117$	−4.32127e6	−0.249437
$118$	−178908.	−0.0100240
$119$	−4.85061e7	−2.63865
$120$	−6.77921e6	−0.358133
$121$	0	0
$122$	5.74263e6	0.286320
$123$	9.39173e6	0.455069
$124$	−2.53793e7	−1.19537
$125$	1.64693e7	0.754206
$126$	3.79152e6	0.168856
$127$	−4.52009e6	−0.195809	−0.0979047	−	0.995196i	$-0.531214\pi$
$127$	−4.52009e6	−0.195809	−0.0979047	+	0.995196i	$0.531214\pi$
$128$	2.14979e7	0.906068
$129$	1.32851e7	0.544881
$130$	−6.04661e6	−0.241385
$131$	2.18807e7	0.850376	0.425188	−	0.905105i	$-0.360208\pi$
$131$	2.18807e7	0.850376	0.425188	+	0.905105i	$0.360208\pi$
$132$	0	0
$133$	−5.37201e7	−1.97996
$134$	4.95874e6	0.178035
$135$	−6.39499e6	−0.223703
$136$	2.26285e7	0.771382
$137$	3.47636e7	1.15505	0.577527	−	0.816372i	$-0.304018\pi$
$137$	3.47636e7	1.15505	0.577527	+	0.816372i	$0.304018\pi$
$138$	−927133.	−0.0300307
$139$	−5.00383e7	−1.58034	−0.790170	−	0.612887i	$-0.790008\pi$
$139$	−5.00383e7	−1.58034	−0.790170	+	0.612887i	$0.790008\pi$
$140$	−6.35861e7	−1.95846
$141$	−2.57522e7	−0.773654
$142$	6.23046e6	0.182604
$143$	0	0
$144$	9.25535e6	0.258300
$145$	3.25131e7	0.885666
$146$	1.35071e7	0.359191
$147$	5.18574e7	1.34648
$148$	−1.00767e7	−0.255506
$149$	−1.76156e7	−0.436260	−0.218130	−	0.975920i	$-0.569996\pi$
$149$	−1.76156e7	−0.436260	−0.218130	+	0.975920i	$0.569996\pi$
$150$	−2.32563e6	−0.0562629
$151$	−2.40503e6	−0.0568462	−0.0284231	−	0.999596i	$-0.509049\pi$
$151$	−2.40503e6	−0.0568462	−0.0284231	+	0.999596i	$0.509049\pi$
$152$	2.50609e7	0.578821
$153$	2.13460e7	0.481833
$154$	0	0
$155$	−6.97946e7	−1.50543
$156$	1.89084e7	0.398766
$157$	−5.56315e6	−0.114729	−0.0573643	−	0.998353i	$-0.518270\pi$
$157$	−5.56315e6	−0.114729	−0.0573643	+	0.998353i	$0.518270\pi$
$158$	−3.58041e6	−0.0722159
$159$	−1.71022e7	−0.337414
$160$	4.50892e7	0.870267
$161$	−1.81178e7	−0.342149
$162$	−1.66853e6	−0.0308341
$163$	−4.30131e7	−0.777936	−0.388968	−	0.921251i	$-0.627168\pi$
$163$	−4.30131e7	−0.777936	−0.388968	+	0.921251i	$0.627168\pi$
$164$	−4.10950e7	−0.727503
$165$	0	0
$166$	1.75057e7	0.297030
$167$	4.37764e7	0.727332	0.363666	−	0.931529i	$-0.381525\pi$
$167$	4.37764e7	0.727332	0.363666	+	0.931529i	$0.381525\pi$
$168$	−3.45650e7	−0.562412
$169$	−2.76113e7	−0.440031
$170$	2.98688e7	0.466279
$171$	2.36406e7	0.361553
$172$	−5.81312e7	−0.871083
$173$	−1.03503e8	−1.51982	−0.759910	−	0.650028i	$-0.774757\pi$
$173$	−1.03503e8	−1.51982	−0.759910	+	0.650028i	$0.774757\pi$
$174$	8.48305e6	0.122076
$175$	−4.54470e7	−0.641020
$176$	0	0
$177$	1.53856e6	0.0208548
$178$	−3.80180e7	−0.505265
$179$	1.38743e8	1.80812	0.904059	−	0.427407i	$-0.140573\pi$
$179$	1.38743e8	1.80812	0.904059	+	0.427407i	$0.140573\pi$
$180$	2.79823e7	0.357626
$181$	5.31818e7	0.666635	0.333318	−	0.942815i	$-0.391832\pi$
$181$	5.31818e7	0.666635	0.333318	+	0.942815i	$0.391832\pi$
$182$	−3.08298e7	−0.379071
$183$	−4.93851e7	−0.595685
$184$	8.45211e6	0.100024
$185$	−2.77114e7	−0.321779
$186$	−1.82103e7	−0.207501
$187$	0	0
$188$	1.12683e8	1.23681
$189$	−3.26060e7	−0.351303
$190$	3.30795e7	0.349881
$191$	−4.41707e7	−0.458688	−0.229344	−	0.973345i	$-0.573658\pi$
$191$	−4.41707e7	−0.458688	−0.229344	+	0.973345i	$0.573658\pi$
$192$	−3.21129e7	−0.327435
$193$	7.06171e7	0.707065	0.353533	−	0.935422i	$-0.384980\pi$
$193$	7.06171e7	0.707065	0.353533	+	0.935422i	$0.384980\pi$
$194$	−5.41276e7	−0.532247
$195$	5.19992e7	0.502198
$196$	−2.26910e8	−2.15257
$197$	−1.37664e8	−1.28289	−0.641444	−	0.767170i	$-0.721664\pi$
$197$	−1.37664e8	−1.28289	−0.641444	+	0.767170i	$0.721664\pi$
$198$	0	0
$199$	2.12879e7	0.191491	0.0957453	−	0.995406i	$-0.469477\pi$
$199$	2.12879e7	0.191491	0.0957453	+	0.995406i	$0.469477\pi$
$200$	2.12014e7	0.187396
$201$	−4.26438e7	−0.370399
$202$	1.31800e7	0.112509
$203$	1.65774e8	1.39085
$204$	−9.34028e7	−0.770290
$205$	−1.13014e8	−0.916204
$206$	−6.70809e7	−0.534642
$207$	7.97309e6	0.0624785
$208$	−7.52574e7	−0.579866
$209$	0	0
$210$	−4.56246e7	−0.339963
$211$	4.06828e7	0.298141	0.149071	−	0.988827i	$-0.452372\pi$
$211$	4.06828e7	0.298141	0.149071	+	0.988827i	$0.452372\pi$
$212$	7.48335e7	0.539412
$213$	−5.35803e7	−0.379906
$214$	9.01940e6	0.0629114
$215$	−1.59864e8	−1.09702
$216$	1.52110e7	0.102700
$217$	−3.55861e8	−2.36413
$218$	8.42080e6	0.0550498
$219$	−1.16157e8	−0.747293
$220$	0	0
$221$	−1.73569e8	−1.08168
$222$	−7.23025e6	−0.0443525
$223$	−2.50596e8	−1.51324	−0.756618	−	0.653857i	$-0.773150\pi$
$223$	−2.50596e8	−1.51324	−0.756618	+	0.653857i	$0.773150\pi$
$224$	2.29895e8	1.36667
$225$	1.99998e7	0.117054
$226$	−1.51880e7	−0.0875228
$227$	−9.36400e7	−0.531338	−0.265669	−	0.964064i	$-0.585593\pi$
$227$	−9.36400e7	−0.531338	−0.265669	+	0.964064i	$0.585593\pi$
$228$	−1.03443e8	−0.578001
$229$	6.85914e7	0.377438	0.188719	−	0.982031i	$-0.439566\pi$
$229$	6.85914e7	0.377438	0.188719	+	0.982031i	$0.439566\pi$
$230$	1.11565e7	0.0604616
$231$	0	0
$232$	−7.73349e7	−0.406600
$233$	−1.30274e8	−0.674702	−0.337351	−	0.941379i	$-0.609531\pi$
$233$	−1.30274e8	−0.674702	−0.337351	+	0.941379i	$0.609531\pi$
$234$	1.35672e7	0.0692206
$235$	3.09884e8	1.55762
$236$	−6.73219e6	−0.0333399
$237$	3.07905e7	0.150244
$238$	1.52291e8	0.732244
$239$	8.85655e7	0.419635	0.209818	−	0.977741i	$-0.432713\pi$
$239$	8.85655e7	0.419635	0.209818	+	0.977741i	$0.432713\pi$
$240$	−1.11373e8	−0.520042
$241$	−1.80384e8	−0.830114	−0.415057	−	0.909796i	$-0.636238\pi$
$241$	−1.80384e8	−0.830114	−0.415057	+	0.909796i	$0.636238\pi$
$242$	0	0
$243$	1.43489e7	0.0641500
$244$	2.16092e8	0.952301
$245$	−6.24016e8	−2.71091
$246$	−2.94866e7	−0.126285
$247$	−1.92227e8	−0.811661
$248$	1.66012e8	0.691128
$249$	−1.50544e8	−0.617967
$250$	−5.17076e7	−0.209298
$251$	−4.17529e8	−1.66659	−0.833295	−	0.552828i	$-0.813549\pi$
$251$	−4.17529e8	−1.66659	−0.833295	+	0.552828i	$0.813549\pi$
$252$	1.42673e8	0.561616
$253$	0	0
$254$	1.41914e7	0.0543385
$255$	−2.56863e8	−0.970088
$256$	8.47435e7	0.315694
$257$	−2.84477e7	−0.104540	−0.0522699	−	0.998633i	$-0.516646\pi$
$257$	−2.84477e7	−0.104540	−0.0522699	+	0.998633i	$0.516646\pi$
$258$	−4.17105e7	−0.151209
$259$	−1.41292e8	−0.505321
$260$	−2.27530e8	−0.802847
$261$	−7.29519e7	−0.253977
$262$	−6.86974e7	−0.235986
$263$	1.35098e8	0.457935	0.228968	−	0.973434i	$-0.426465\pi$
$263$	1.35098e8	0.457935	0.228968	+	0.973434i	$0.426465\pi$
$264$	0	0
$265$	2.05797e8	0.679325
$266$	1.68662e8	0.549453
$267$	3.26944e8	1.05120
$268$	1.86595e8	0.592144
$269$	−2.04317e8	−0.639987	−0.319993	−	0.947420i	$-0.603681\pi$
$269$	−2.04317e8	−0.639987	−0.319993	+	0.947420i	$0.603681\pi$
$270$	2.00780e7	0.0620792
$271$	1.25605e8	0.383366	0.191683	−	0.981457i	$-0.438605\pi$
$271$	1.25605e8	0.383366	0.191683	+	0.981457i	$0.438605\pi$
$272$	3.71753e8	1.12012
$273$	2.65127e8	0.788652
$274$	−1.09145e8	−0.320536
$275$	0	0
$276$	−3.48875e7	−0.0998822
$277$	1.12648e8	0.318452	0.159226	−	0.987242i	$-0.449100\pi$
$277$	1.12648e8	0.318452	0.159226	+	0.987242i	$0.449100\pi$
$278$	1.57102e8	0.438556
$279$	1.56603e8	0.431704
$280$	4.15932e8	1.13232
$281$	4.80961e8	1.29312	0.646558	−	0.762865i	$-0.276208\pi$
$281$	4.80961e8	1.29312	0.646558	+	0.762865i	$0.276208\pi$
$282$	8.08525e7	0.214695
$283$	−1.53397e8	−0.402313	−0.201157	−	0.979559i	$-0.564470\pi$
$283$	−1.53397e8	−0.402313	−0.201157	+	0.979559i	$0.564470\pi$
$284$	2.34449e8	0.607343
$285$	−2.84474e8	−0.727924
$286$	0	0
$287$	−5.76220e8	−1.43881
$288$	−1.01170e8	−0.249561
$289$	4.47051e8	1.08947
$290$	−1.02079e8	−0.245779
$291$	4.65482e8	1.10733
$292$	5.08263e8	1.19467
$293$	−5.12204e8	−1.18961	−0.594807	−	0.803869i	$-0.702772\pi$
$293$	−5.12204e8	−1.18961	−0.594807	+	0.803869i	$0.702772\pi$
$294$	−1.62813e8	−0.373658
$295$	−1.85139e7	−0.0419876
$296$	6.59138e7	0.147725
$297$	0	0
$298$	5.53065e7	0.121065
$299$	−6.48310e7	−0.140260
$300$	−8.75122e7	−0.187130
$301$	−8.15096e8	−1.72277
$302$	7.55092e6	0.0157752
$303$	−1.13344e8	−0.234073
$304$	4.11714e8	0.840501
$305$	5.94266e8	1.19931
$306$	−6.70187e7	−0.133712
$307$	−1.33560e8	−0.263447	−0.131724	−	0.991286i	$-0.542051\pi$
$307$	−1.33560e8	−0.263447	−0.131724	+	0.991286i	$0.542051\pi$
$308$	0	0
$309$	5.76877e8	1.11232
$310$	2.19130e8	0.417768
$311$	−1.21509e8	−0.229059	−0.114529	−	0.993420i	$-0.536536\pi$
$311$	−1.21509e8	−0.229059	−0.114529	+	0.993420i	$0.536536\pi$
$312$	−1.23684e8	−0.230554
$313$	−8.28300e8	−1.52680	−0.763400	−	0.645925i	$-0.776472\pi$
$313$	−8.28300e8	−1.52680	−0.763400	+	0.645925i	$0.776472\pi$
$314$	1.74663e7	0.0318380
$315$	3.92359e8	0.707288
$316$	−1.34729e8	−0.240190
$317$	5.04412e8	0.889360	0.444680	−	0.895689i	$-0.353317\pi$
$317$	5.04412e8	0.889360	0.444680	+	0.895689i	$0.353317\pi$
$318$	5.36948e7	0.0936348
$319$	0	0
$320$	3.86425e8	0.659234
$321$	−7.75643e7	−0.130886
$322$	5.68834e7	0.0949489
$323$	9.49554e8	1.56787
$324$	−6.27859e7	−0.102554
$325$	−1.62623e8	−0.262779
$326$	1.35045e8	0.215883
$327$	−7.24165e7	−0.114530
$328$	2.68812e8	0.420620
$329$	1.58000e9	2.44608
$330$	0	0
$331$	3.62665e8	0.549676	0.274838	−	0.961490i	$-0.411376\pi$
$331$	3.62665e8	0.549676	0.274838	+	0.961490i	$0.411376\pi$
$332$	6.58728e8	0.987922
$333$	6.21781e7	0.0922747
$334$	−1.37442e8	−0.201840
$335$	5.13146e8	0.745735
$336$	−5.67853e8	−0.816674
$337$	−2.46084e8	−0.350251	−0.175125	−	0.984546i	$-0.556033\pi$
$337$	−2.46084e8	−0.350251	−0.175125	+	0.984546i	$0.556033\pi$
$338$	8.66893e7	0.122112
$339$	1.30613e8	0.182090
$340$	1.12394e9	1.55085
$341$	0	0
$342$	−7.42228e7	−0.100333
$343$	−1.81741e9	−2.43178
$344$	3.80249e8	0.503633
$345$	−9.59426e7	−0.125790
$346$	3.24962e8	0.421761
$347$	−1.31921e9	−1.69496	−0.847480	−	0.530828i	$-0.821881\pi$
$347$	−1.31921e9	−1.69496	−0.847480	+	0.530828i	$0.821881\pi$
$348$	3.19212e8	0.406025
$349$	−5.11888e7	−0.0644594	−0.0322297	−	0.999480i	$-0.510261\pi$
$349$	−5.11888e7	−0.0644594	−0.0322297	+	0.999480i	$0.510261\pi$
$350$	1.42687e8	0.177888
$351$	−1.16674e8	−0.144013
$352$	0	0
$353$	−6.46661e8	−0.782465	−0.391233	−	0.920292i	$-0.627951\pi$
$353$	−6.46661e8	−0.782465	−0.391233	+	0.920292i	$0.627951\pi$
$354$	−4.83050e6	−0.00578737
$355$	6.44748e8	0.764875
$356$	−1.43060e9	−1.68051
$357$	−1.30966e9	−1.52342
$358$	−4.35604e8	−0.501766
$359$	1.43435e9	1.63616	0.818080	−	0.575104i	$-0.195038\pi$
$359$	1.43435e9	1.63616	0.818080	+	0.575104i	$0.195038\pi$
$360$	−1.83039e8	−0.206768
$361$	1.57753e8	0.176482
$362$	−1.66972e8	−0.184996
$363$	0	0
$364$	−1.16011e9	−1.26079
$365$	1.39775e9	1.50455
$366$	1.55051e8	0.165307
$367$	−6.32780e8	−0.668223	−0.334112	−	0.942533i	$-0.608436\pi$
$367$	−6.32780e8	−0.668223	−0.334112	+	0.942533i	$0.608436\pi$
$368$	1.38856e8	0.145244
$369$	2.53577e8	0.262734
$370$	8.70038e7	0.0892960
$371$	1.04929e9	1.06681
$372$	−6.85242e8	−0.690150
$373$	1.73311e8	0.172920	0.0864599	−	0.996255i	$-0.472445\pi$
$373$	1.73311e8	0.172920	0.0864599	+	0.996255i	$0.472445\pi$
$374$	0	0
$375$	4.44671e8	0.435441
$376$	−7.37083e8	−0.715087
$377$	5.93189e8	0.570162
$378$	1.02371e8	0.0974891
$379$	1.23599e8	0.116621	0.0583105	−	0.998298i	$-0.481429\pi$
$379$	1.23599e8	0.116621	0.0583105	+	0.998298i	$0.481429\pi$
$380$	1.24476e9	1.16371
$381$	−1.22042e8	−0.113051
$382$	1.38680e8	0.127289
$383$	1.42530e8	0.129632	0.0648159	−	0.997897i	$-0.479354\pi$
$383$	1.42530e8	0.129632	0.0648159	+	0.997897i	$0.479354\pi$
$384$	5.80443e8	0.523119
$385$	0	0
$386$	−2.21712e8	−0.196216
$387$	3.58699e8	0.314587
$388$	−2.03679e9	−1.77025
$389$	−6.64554e8	−0.572409	−0.286205	−	0.958168i	$-0.592394\pi$
$389$	−6.64554e8	−0.572409	−0.286205	+	0.958168i	$0.592394\pi$
$390$	−1.63259e8	−0.139364
$391$	3.20249e8	0.270938
$392$	1.48427e9	1.24455
$393$	5.90778e8	0.490965
$394$	4.32215e8	0.356011
$395$	−3.70512e8	−0.302491
$396$	0	0
$397$	3.05049e8	0.244683	0.122341	−	0.992488i	$-0.460960\pi$
$397$	3.05049e8	0.244683	0.122341	+	0.992488i	$0.460960\pi$
$398$	−6.68363e7	−0.0531400
$399$	−1.45044e9	−1.14313
$400$	3.48308e8	0.272116
$401$	1.66426e9	1.28889	0.644447	−	0.764649i	$-0.277088\pi$
$401$	1.66426e9	1.28889	0.644447	+	0.764649i	$0.277088\pi$
$402$	1.33886e8	0.102788
$403$	−1.27338e9	−0.969147
$404$	4.95956e8	0.374204
$405$	−1.72665e8	−0.129155
$406$	−5.20469e8	−0.385971
$407$	0	0
$408$	6.10969e8	0.445357
$409$	−7.97481e8	−0.576353	−0.288177	−	0.957577i	$-0.593049\pi$
$409$	−7.97481e8	−0.576353	−0.288177	+	0.957577i	$0.593049\pi$
$410$	3.54821e8	0.254253
$411$	9.38616e8	0.666871
$412$	−2.52421e9	−1.77822
$413$	−9.43966e7	−0.0659373
$414$	−2.50326e7	−0.0173382
$415$	1.81154e9	1.24417
$416$	8.22635e8	0.560248
$417$	−1.35103e9	−0.912410
$418$	0	0
$419$	1.70754e9	1.13402	0.567010	−	0.823711i	$-0.308100\pi$
$419$	1.70754e9	1.13402	0.567010	+	0.823711i	$0.308100\pi$
$420$	−1.71683e9	−1.13072
$421$	4.33041e7	0.0282840	0.0141420	−	0.999900i	$-0.495498\pi$
$421$	4.33041e7	0.0282840	0.0141420	+	0.999900i	$0.495498\pi$
$422$	−1.27729e8	−0.0827363
$423$	−6.95309e8	−0.446670
$424$	−4.89503e8	−0.311871
$425$	8.03318e8	0.507605
$426$	1.68223e8	0.105427
$427$	3.02997e9	1.88339
$428$	3.39395e8	0.209243
$429$	0	0
$430$	5.01915e8	0.304432
$431$	1.95369e9	1.17540	0.587698	−	0.809080i	$-0.300034\pi$
$431$	1.95369e9	1.17540	0.587698	+	0.809080i	$0.300034\pi$
$432$	2.49895e8	0.149130
$433$	−6.94306e7	−0.0411002	−0.0205501	−	0.999789i	$-0.506542\pi$
$433$	−6.94306e7	−0.0411002	−0.0205501	+	0.999789i	$0.506542\pi$
$434$	1.11727e9	0.656063
$435$	8.77853e8	0.511339
$436$	3.16870e8	0.183096
$437$	3.54674e8	0.203303
$438$	3.64691e8	0.207379
$439$	−2.35341e9	−1.32761	−0.663806	−	0.747904i	$-0.731060\pi$
$439$	−2.35341e9	−1.32761	−0.663806	+	0.747904i	$0.731060\pi$
$440$	0	0
$441$	1.40015e9	0.777391
$442$	5.44945e8	0.300175
$443$	−1.38310e9	−0.755857	−0.377928	−	0.925835i	$-0.623363\pi$
$443$	−1.38310e9	−0.755857	−0.377928	+	0.925835i	$0.623363\pi$
$444$	−2.72070e8	−0.147516
$445$	−3.93422e9	−2.11641
$446$	7.86780e8	0.419934
$447$	−4.75621e8	−0.251875
$448$	1.97026e9	1.03526
$449$	2.72720e9	1.42186	0.710928	−	0.703265i	$-0.248275\pi$
$449$	2.72720e9	1.42186	0.710928	+	0.703265i	$0.248275\pi$
$450$	−6.27921e7	−0.0324834
$451$	0	0
$452$	−5.71516e8	−0.291101
$453$	−6.49358e7	−0.0328202
$454$	2.93995e8	0.147450
$455$	−3.19036e9	−1.58781
$456$	6.76644e8	0.334182
$457$	−1.56713e9	−0.768065	−0.384033	−	0.923320i	$-0.625465\pi$
$457$	−1.56713e9	−0.768065	−0.384033	+	0.923320i	$0.625465\pi$
$458$	−2.15352e8	−0.104742
$459$	5.76342e8	0.278187
$460$	4.19812e8	0.201095
$461$	2.51125e9	1.19381	0.596907	−	0.802311i	$-0.296396\pi$
$461$	2.51125e9	1.19381	0.596907	+	0.802311i	$0.296396\pi$
$462$	0	0
$463$	2.26078e9	1.05858	0.529292	−	0.848440i	$-0.322458\pi$
$463$	2.26078e9	1.05858	0.529292	+	0.848440i	$0.322458\pi$
$464$	−1.27050e9	−0.590421
$465$	−1.88446e9	−0.869161
$466$	4.09013e8	0.187235
$467$	2.60651e9	1.18427	0.592135	−	0.805839i	$-0.298285\pi$
$467$	2.60651e9	1.18427	0.592135	+	0.805839i	$0.298285\pi$
$468$	5.10526e8	0.230228
$469$	2.61637e9	1.17110
$470$	−9.72923e8	−0.432251
$471$	−1.50205e8	−0.0662386
$472$	4.40368e7	0.0192761
$473$	0	0
$474$	−9.66710e7	−0.0416939
$475$	8.89669e8	0.380891
$476$	5.73064e9	2.43545
$477$	−4.61760e8	−0.194806
$478$	−2.78063e8	−0.116452
$479$	−3.69188e9	−1.53488	−0.767438	−	0.641123i	$-0.778469\pi$
$479$	−3.69188e9	−1.53488	−0.767438	+	0.641123i	$0.778469\pi$
$480$	1.21741e9	0.502449
$481$	−5.05585e8	−0.207151
$482$	5.66339e8	0.230363
$483$	−4.89181e8	−0.197540
$484$	0	0
$485$	−5.60129e9	−2.22942
$486$	−4.50504e7	−0.0178021
$487$	−4.57363e8	−0.179436	−0.0897180	−	0.995967i	$-0.528597\pi$
$487$	−4.57363e8	−0.179436	−0.0897180	+	0.995967i	$0.528597\pi$
$488$	−1.41351e9	−0.550590
$489$	−1.16135e9	−0.449142
$490$	1.95918e9	0.752296
$491$	−2.68320e9	−1.02298	−0.511491	−	0.859289i	$-0.670906\pi$
$491$	−2.68320e9	−1.02298	−0.511491	+	0.859289i	$0.670906\pi$
$492$	−1.10956e9	−0.420024
$493$	−2.93021e9	−1.10137
$494$	6.03523e8	0.225242
$495$	0	0
$496$	2.72734e9	1.00358
$497$	3.28737e9	1.20116
$498$	4.72653e8	0.171490
$499$	−1.86676e9	−0.672568	−0.336284	−	0.941761i	$-0.609170\pi$
$499$	−1.86676e9	−0.672568	−0.336284	+	0.941761i	$0.609170\pi$
$500$	−1.94573e9	−0.696124
$501$	1.18196e9	0.419925
$502$	1.31089e9	0.462491
$503$	4.44792e9	1.55836	0.779182	−	0.626798i	$-0.215635\pi$
$503$	4.44792e9	1.55836	0.779182	+	0.626798i	$0.215635\pi$
$504$	−9.33256e8	−0.324709
$505$	1.36391e9	0.471265
$506$	0	0
$507$	−7.45504e8	−0.254052
$508$	5.34015e8	0.180730
$509$	−6.09237e8	−0.204774	−0.102387	−	0.994745i	$-0.532648\pi$
$509$	−6.09237e8	−0.204774	−0.102387	+	0.994745i	$0.532648\pi$
$510$	8.06457e8	0.269206
$511$	7.12670e9	2.36274
$512$	−3.01779e9	−0.993675
$513$	6.38295e8	0.208742
$514$	8.93155e7	0.0290106
$515$	−6.94174e9	−2.23946
$516$	−1.56954e9	−0.502920
$517$	0	0
$518$	4.43605e8	0.140230
$519$	−2.79459e9	−0.877469
$520$	1.48833e9	0.464181
$521$	−5.17948e9	−1.60455	−0.802276	−	0.596953i	$-0.796378\pi$
$521$	−5.17948e9	−1.60455	−0.802276	+	0.596953i	$0.796378\pi$
$522$	2.29042e8	0.0704805
$523$	−3.39726e9	−1.03842	−0.519209	−	0.854647i	$-0.673773\pi$
$523$	−3.39726e9	−1.03842	−0.519209	+	0.854647i	$0.673773\pi$
$524$	−2.58504e9	−0.784889
$525$	−1.22707e9	−0.370093
$526$	−4.24159e8	−0.127080
$527$	6.29017e9	1.87208
$528$	0	0
$529$	−3.28521e9	−0.964868
$530$	−6.46126e8	−0.188518
$531$	4.15410e7	0.0120405
$532$	6.34664e9	1.82748
$533$	−2.06189e9	−0.589821
$534$	−1.02649e9	−0.291715
$535$	9.33355e8	0.263517
$536$	−1.22056e9	−0.342359
$537$	3.74607e9	1.04392
$538$	6.41480e8	0.177601
$539$	0	0
$540$	7.55522e8	0.206476
$541$	−3.43167e9	−0.931784	−0.465892	−	0.884842i	$-0.654266\pi$
$541$	−3.43167e9	−0.931784	−0.465892	+	0.884842i	$0.654266\pi$
$542$	−3.94353e8	−0.106387
$543$	1.43591e9	0.384882
$544$	−4.06362e9	−1.08222
$545$	8.71410e8	0.230587
$546$	−8.32403e8	−0.218857
$547$	−7.64825e9	−1.99805	−0.999025	−	0.0441449i	$-0.985944\pi$
$547$	−7.64825e9	−1.99805	−0.999025	+	0.0441449i	$0.985944\pi$
$548$	−4.10706e9	−1.06610
$549$	−1.33340e9	−0.343919
$550$	0	0
$551$	−3.24518e9	−0.826435
$552$	2.28207e8	0.0577487
$553$	−1.88912e9	−0.475031
$554$	−3.53673e8	−0.0883727
$555$	−7.48208e8	−0.185779
$556$	5.91166e9	1.45864
$557$	2.46388e9	0.604125	0.302062	−	0.953288i	$-0.402325\pi$
$557$	2.46388e9	0.604125	0.302062	+	0.953288i	$0.402325\pi$
$558$	−4.91677e8	−0.119801
$559$	−2.91666e9	−0.706228
$560$	6.83315e9	1.64423
$561$	0	0
$562$	−1.51004e9	−0.358849
$563$	4.80512e9	1.13481	0.567407	−	0.823437i	$-0.307946\pi$
$563$	4.80512e9	1.13481	0.567407	+	0.823437i	$0.307946\pi$
$564$	3.04243e9	0.714075
$565$	−1.57170e9	−0.366607
$566$	4.81611e8	0.111645
$567$	−8.80363e8	−0.202825
$568$	−1.53358e9	−0.351146
$569$	1.91268e9	0.435261	0.217631	−	0.976031i	$-0.430167\pi$
$569$	1.91268e9	0.435261	0.217631	+	0.976031i	$0.430167\pi$
$570$	8.93146e8	0.202004
$571$	−5.11420e9	−1.14961	−0.574806	−	0.818290i	$-0.694922\pi$
$571$	−5.11420e9	−1.14961	−0.574806	+	0.818290i	$0.694922\pi$
$572$	0	0
$573$	−1.19261e9	−0.264823
$574$	1.80912e9	0.399279
$575$	3.00053e8	0.0658203
$576$	−8.67049e8	−0.189045
$577$	7.21875e9	1.56440	0.782198	−	0.623030i	$-0.214098\pi$
$577$	7.21875e9	1.56440	0.782198	+	0.623030i	$0.214098\pi$
$578$	−1.40358e9	−0.302336
$579$	1.90666e9	0.408224
$580$	−3.84118e9	−0.817460
$581$	9.23647e9	1.95384
$582$	−1.46145e9	−0.307293
$583$	0	0
$584$	−3.32466e9	−0.690721
$585$	1.40398e9	0.289944
$586$	1.60813e9	0.330127
$587$	5.59159e9	1.14104	0.570522	−	0.821283i	$-0.306741\pi$
$587$	5.59159e9	1.14104	0.570522	+	0.821283i	$0.306741\pi$
$588$	−6.12657e9	−1.24279
$589$	6.96632e9	1.40475
$590$	5.81269e7	0.0116519
$591$	−3.71693e9	−0.740676
$592$	1.08287e9	0.214511
$593$	−6.64072e9	−1.30775	−0.653873	−	0.756604i	$-0.726857\pi$
$593$	−6.64072e9	−1.30775	−0.653873	+	0.756604i	$0.726857\pi$
$594$	0	0
$595$	1.57596e10	3.06715
$596$	2.08115e9	0.402663
$597$	5.74774e8	0.110557
$598$	2.03546e8	0.0389232
$599$	4.98631e9	0.947950	0.473975	−	0.880538i	$-0.342819\pi$
$599$	4.98631e9	0.947950	0.473975	+	0.880538i	$0.342819\pi$
$600$	5.72438e8	0.108193
$601$	1.99239e9	0.374381	0.187191	−	0.982324i	$-0.440062\pi$
$601$	1.99239e9	0.374381	0.187191	+	0.982324i	$0.440062\pi$
$602$	2.55911e9	0.478080
$603$	−1.15138e9	−0.213850
$604$	2.84137e8	0.0524685
$605$	0	0
$606$	3.55860e8	0.0649568
$607$	−1.02364e9	−0.185775	−0.0928875	−	0.995677i	$-0.529610\pi$
$607$	−1.02364e9	−0.185775	−0.0928875	+	0.995677i	$0.529610\pi$
$608$	−4.50043e9	−0.812066
$609$	4.47589e9	0.803007
$610$	−1.86578e9	−0.332817
$611$	5.65372e9	1.00274
$612$	−2.52188e9	−0.444727
$613$	1.00525e10	1.76264	0.881320	−	0.472520i	$-0.156656\pi$
$613$	1.00525e10	1.76264	0.881320	+	0.472520i	$0.156656\pi$
$614$	4.19331e8	0.0731085
$615$	−3.05137e9	−0.528970
$616$	0	0
$617$	−1.40682e9	−0.241124	−0.120562	−	0.992706i	$-0.538470\pi$
$617$	−1.40682e9	−0.241124	−0.120562	+	0.992706i	$0.538470\pi$
$618$	−1.81118e9	−0.308676
$619$	−6.83926e9	−1.15902	−0.579511	−	0.814964i	$-0.696756\pi$
$619$	−6.83926e9	−1.15902	−0.579511	+	0.814964i	$0.696756\pi$
$620$	8.24572e9	1.38950
$621$	2.15273e8	0.0360720
$622$	3.81494e8	0.0635655
$623$	−2.00594e10	−3.32360
$624$	−2.03195e9	−0.334786
$625$	−7.49419e9	−1.22785
$626$	2.60056e9	0.423698
$627$	0	0
$628$	6.57245e8	0.105893
$629$	2.49746e9	0.400149
$630$	−1.23186e9	−0.196278
$631$	1.06266e10	1.68381	0.841904	−	0.539627i	$-0.181435\pi$
$631$	1.06266e10	1.68381	0.841904	+	0.539627i	$0.181435\pi$
$632$	8.81291e8	0.138870
$633$	1.09843e9	0.172132
$634$	−1.58367e9	−0.246804
$635$	1.46857e9	0.227608
$636$	2.02050e9	0.311430
$637$	−1.13849e10	−1.74519
$638$	0	0
$639$	−1.44667e9	−0.219339
$640$	−6.98465e9	−1.05321
$641$	4.38990e9	0.658342	0.329171	−	0.944270i	$-0.393231\pi$
$641$	4.38990e9	0.658342	0.329171	+	0.944270i	$0.393231\pi$
$642$	2.43524e8	0.0363219
$643$	−8.47636e9	−1.25739	−0.628697	−	0.777651i	$-0.716411\pi$
$643$	−8.47636e9	−1.25739	−0.628697	+	0.777651i	$0.716411\pi$
$644$	2.14049e9	0.315800
$645$	−4.31633e9	−0.633367
$646$	−2.98125e9	−0.435096
$647$	−1.20293e9	−0.174613	−0.0873063	−	0.996182i	$-0.527826\pi$
$647$	−1.20293e9	−0.174613	−0.0873063	+	0.996182i	$0.527826\pi$
$648$	4.10697e8	0.0592937
$649$	0	0
$650$	5.10577e8	0.0729230
$651$	−9.60824e9	−1.36493
$652$	5.08168e9	0.718027
$653$	−3.30426e9	−0.464385	−0.232193	−	0.972670i	$-0.574590\pi$
$653$	−3.30426e9	−0.464385	−0.232193	+	0.972670i	$0.574590\pi$
$654$	2.27362e8	0.0317830
$655$	−7.10902e9	−0.988473
$656$	4.41618e9	0.610778
$657$	−3.13624e9	−0.431450
$658$	−4.96062e9	−0.678806
$659$	−8.72843e9	−1.18806	−0.594028	−	0.804444i	$-0.702463\pi$
$659$	−8.72843e9	−1.18806	−0.594028	+	0.804444i	$0.702463\pi$
$660$	0	0
$661$	−1.07586e10	−1.44895	−0.724473	−	0.689303i	$-0.757917\pi$
$661$	−1.07586e10	−1.44895	−0.724473	+	0.689303i	$0.757917\pi$
$662$	−1.13863e9	−0.152539
$663$	−4.68637e9	−0.624510
$664$	−4.30889e9	−0.571186
$665$	1.74536e10	2.30150
$666$	−1.95217e8	−0.0256069
$667$	−1.09448e9	−0.142813
$668$	−5.17186e9	−0.671320
$669$	−6.76609e9	−0.873668
$670$	−1.61109e9	−0.206947
$671$	0	0
$672$	6.20718e9	0.789045
$673$	−4.13126e9	−0.522432	−0.261216	−	0.965280i	$-0.584124\pi$
$673$	−4.13126e9	−0.522432	−0.261216	+	0.965280i	$0.584124\pi$
$674$	7.72614e8	0.0971971
$675$	5.39995e8	0.0675813
$676$	3.26207e9	0.406144
$677$	3.46057e9	0.428635	0.214317	−	0.976764i	$-0.431247\pi$
$677$	3.46057e9	0.428635	0.214317	+	0.976764i	$0.431247\pi$
$678$	−4.10076e8	−0.0505313
$679$	−2.85592e10	−3.50108
$680$	−7.35198e9	−0.896650
$681$	−2.52828e9	−0.306768
$682$	0	0
$683$	−1.30563e10	−1.56801	−0.784006	−	0.620753i	$-0.786827\pi$
$683$	−1.30563e10	−1.56801	−0.784006	+	0.620753i	$0.786827\pi$
$684$	−2.79296e9	−0.333709
$685$	−1.12947e10	−1.34263
$686$	5.70601e9	0.674836
$687$	1.85197e9	0.217914
$688$	6.24694e9	0.731321
$689$	3.75468e9	0.437327
$690$	3.01225e8	0.0349075
$691$	5.11420e9	0.589664	0.294832	−	0.955549i	$-0.404736\pi$
$691$	5.11420e9	0.589664	0.294832	+	0.955549i	$0.404736\pi$
$692$	1.22281e10	1.40278
$693$	0	0
$694$	4.14182e9	0.470363
$695$	1.62574e10	1.83698
$696$	−2.08804e9	−0.234751
$697$	1.01852e10	1.13935
$698$	1.60714e8	0.0178879
$699$	−3.51740e9	−0.389539
$700$	5.36923e9	0.591655
$701$	−1.07835e10	−1.18235	−0.591175	−	0.806543i	$-0.701336\pi$
$701$	−1.07835e10	−1.18235	−0.591175	+	0.806543i	$0.701336\pi$
$702$	3.66315e8	0.0399645
$703$	2.76592e9	0.300259
$704$	0	0
$705$	8.36686e9	0.899292
$706$	2.03028e9	0.217140
$707$	6.95413e9	0.740073
$708$	−1.81769e8	−0.0192488
$709$	−4.17468e9	−0.439908	−0.219954	−	0.975510i	$-0.570591\pi$
$709$	−4.17468e9	−0.439908	−0.219954	+	0.975510i	$0.570591\pi$
$710$	−2.02427e9	−0.212258
$711$	8.31344e8	0.0867435
$712$	9.35786e9	0.971620
$713$	2.34948e9	0.242750
$714$	4.11187e9	0.422762
$715$	0	0
$716$	−1.63915e10	−1.66887
$717$	2.39127e9	0.242276
$718$	−4.50335e9	−0.454046
$719$	−3.53308e9	−0.354489	−0.177244	−	0.984167i	$-0.556718\pi$
$719$	−3.53308e9	−0.354489	−0.177244	+	0.984167i	$0.556718\pi$
$720$	−3.00706e9	−0.300247
$721$	−3.53937e10	−3.51684
$722$	−4.95286e8	−0.0489751
$723$	−4.87036e9	−0.479266
$724$	−6.28304e9	−0.615297
$725$	−2.74541e9	−0.267562
$726$	0	0
$727$	3.02429e9	0.291913	0.145957	−	0.989291i	$-0.453374\pi$
$727$	3.02429e9	0.291913	0.145957	+	0.989291i	$0.453374\pi$
$728$	7.58852e9	0.728949
$729$	3.87420e8	0.0370370
$730$	−4.38844e9	−0.417522
$731$	1.44076e10	1.36421
$732$	5.83448e9	0.549811
$733$	−2.04302e10	−1.91605	−0.958027	−	0.286677i	$-0.907449\pi$
$733$	−2.04302e10	−1.91605	−0.958027	+	0.286677i	$0.907449\pi$
$734$	1.98670e9	0.185437
$735$	−1.68484e10	−1.56514
$736$	−1.51783e9	−0.140330
$737$	0	0
$738$	−7.96138e8	−0.0729107
$739$	−7.88680e9	−0.718862	−0.359431	−	0.933172i	$-0.617029\pi$
$739$	−7.88680e9	−0.718862	−0.359431	+	0.933172i	$0.617029\pi$
$740$	3.27390e9	0.296999
$741$	−5.19013e9	−0.468613
$742$	−3.29439e9	−0.296048
$743$	−5.31124e8	−0.0475045	−0.0237522	−	0.999718i	$-0.507561\pi$
$743$	−5.31124e8	−0.0475045	−0.0237522	+	0.999718i	$0.507561\pi$
$744$	4.48232e9	0.399023
$745$	5.72329e9	0.507106
$746$	−5.44133e8	−0.0479865
$747$	−4.06468e9	−0.356783
$748$	0	0
$749$	4.75888e9	0.413827
$750$	−1.39610e9	−0.120838
$751$	2.53404e9	0.218310	0.109155	−	0.994025i	$-0.465186\pi$
$751$	2.53404e9	0.218310	0.109155	+	0.994025i	$0.465186\pi$
$752$	−1.21092e10	−1.03837
$753$	−1.12733e10	−0.962207
$754$	−1.86240e9	−0.158224
$755$	7.81393e8	0.0660777
$756$	3.85217e9	0.324249
$757$	1.12293e10	0.940844	0.470422	−	0.882442i	$-0.344102\pi$
$757$	1.12293e10	0.940844	0.470422	+	0.882442i	$0.344102\pi$
$758$	−3.88055e8	−0.0323632
$759$	0	0
$760$	−8.14227e9	−0.672818
$761$	1.06239e10	0.873852	0.436926	−	0.899497i	$-0.356067\pi$
$761$	1.06239e10	0.873852	0.436926	+	0.899497i	$0.356067\pi$
$762$	3.83168e8	0.0313724
$763$	4.44304e9	0.362114
$764$	5.21844e9	0.423364
$765$	−6.93530e9	−0.560081
$766$	−4.47493e8	−0.0359738
$767$	−3.37779e8	−0.0270302
$768$	2.28807e9	0.182266
$769$	6.21266e9	0.492646	0.246323	−	0.969188i	$-0.420778\pi$
$769$	6.21266e9	0.492646	0.246323	+	0.969188i	$0.420778\pi$
$770$	0	0
$771$	−7.68089e8	−0.0603561
$772$	−8.34290e9	−0.652614
$773$	−1.75118e10	−1.36365	−0.681823	−	0.731517i	$-0.738813\pi$
$773$	−1.75118e10	−1.36365	−0.681823	+	0.731517i	$0.738813\pi$
$774$	−1.12618e9	−0.0873003
$775$	5.89347e9	0.454795
$776$	1.33231e10	1.02350
$777$	−3.81488e9	−0.291747
$778$	2.08646e9	0.158848
$779$	1.12801e10	0.854931
$780$	−6.14332e9	−0.463524
$781$	0	0
$782$	−1.00547e9	−0.0751872
$783$	−1.96970e9	−0.146634
$784$	2.43844e10	1.80720
$785$	1.80746e9	0.133360
$786$	−1.85483e9	−0.136246
$787$	1.35514e10	0.990997	0.495499	−	0.868609i	$-0.334985\pi$
$787$	1.35514e10	0.990997	0.495499	+	0.868609i	$0.334985\pi$
$788$	1.62640e10	1.18409
$789$	3.64765e9	0.264389
$790$	1.16327e9	0.0839434
$791$	−8.01361e9	−0.575719
$792$	0	0
$793$	1.08422e10	0.772075
$794$	−9.57743e8	−0.0679012
$795$	5.55651e9	0.392208
$796$	−2.51501e9	−0.176744
$797$	8.58457e9	0.600640	0.300320	−	0.953838i	$-0.402906\pi$
$797$	8.58457e9	0.600640	0.300320	+	0.953838i	$0.402906\pi$
$798$	4.55387e9	0.317227
$799$	−2.79280e10	−1.93698
$800$	−3.80734e9	−0.262910
$801$	8.82750e9	0.606909
$802$	−5.22519e9	−0.357677
$803$	0	0
$804$	5.03806e9	0.341875
$805$	5.88647e9	0.397712
$806$	3.99794e9	0.268945
$807$	−5.51655e9	−0.369496
$808$	−3.24416e9	−0.216353
$809$	1.96443e9	0.130441	0.0652207	−	0.997871i	$-0.479225\pi$
$809$	1.96443e9	0.130441	0.0652207	+	0.997871i	$0.479225\pi$
$810$	5.42105e8	0.0358415
$811$	2.38624e9	0.157088	0.0785438	−	0.996911i	$-0.474973\pi$
$811$	2.38624e9	0.157088	0.0785438	+	0.996911i	$0.474973\pi$
$812$	−1.95850e10	−1.28374
$813$	3.39133e9	0.221336
$814$	0	0
$815$	1.39749e10	0.904270
$816$	1.00373e10	0.646700
$817$	1.59563e10	1.02366
$818$	2.50380e9	0.159942
$819$	7.15844e9	0.455328
$820$	1.33517e10	0.845647
$821$	−4.38247e8	−0.0276387	−0.0138194	−	0.999905i	$-0.504399\pi$
$821$	−4.38247e8	−0.0276387	−0.0138194	+	0.999905i	$0.504399\pi$
$822$	−2.94691e9	−0.185061
$823$	1.49310e9	0.0933663	0.0466832	−	0.998910i	$-0.485135\pi$
$823$	1.49310e9	0.0933663	0.0466832	+	0.998910i	$0.485135\pi$
$824$	1.65115e10	1.02811
$825$	0	0
$826$	2.96371e8	0.0182981
$827$	−2.74902e9	−0.169008	−0.0845042	−	0.996423i	$-0.526931\pi$
$827$	−2.74902e9	−0.169008	−0.0845042	+	0.996423i	$0.526931\pi$
$828$	−9.41962e8	−0.0576670
$829$	−2.68318e9	−0.163572	−0.0817861	−	0.996650i	$-0.526062\pi$
$829$	−2.68318e9	−0.163572	−0.0817861	+	0.996650i	$0.526062\pi$
$830$	−5.68758e9	−0.345266
$831$	3.04149e9	0.183858
$832$	7.05017e9	0.424393
$833$	5.62388e10	3.37115
$834$	4.24176e9	0.253200
$835$	−1.42229e10	−0.845447
$836$	0	0
$837$	4.22829e9	0.249244
$838$	−5.36104e9	−0.314699
$839$	4.31552e9	0.252271	0.126135	−	0.992013i	$-0.459743\pi$
$839$	4.31552e9	0.252271	0.126135	+	0.992013i	$0.459743\pi$
$840$	1.12302e10	0.653745
$841$	−7.23563e9	−0.419460
$842$	−1.35959e8	−0.00784903
$843$	1.29859e10	0.746581
$844$	−4.80637e9	−0.275181
$845$	8.97088e9	0.511489
$846$	2.18302e9	0.123954
$847$	0	0
$848$	−8.04183e9	−0.452865
$849$	−4.14172e9	−0.232276
$850$	−2.52213e9	−0.140864
$851$	9.32844e8	0.0518866
$852$	6.33012e9	0.350649
$853$	1.97919e10	1.09186	0.545930	−	0.837831i	$-0.316177\pi$
$853$	1.97919e10	1.09186	0.545930	+	0.837831i	$0.316177\pi$
$854$	−9.51301e9	−0.522655
$855$	−7.68080e9	−0.420267
$856$	−2.22006e9	−0.120978
$857$	2.86789e9	0.155643	0.0778215	−	0.996967i	$-0.475204\pi$
$857$	2.86789e9	0.155643	0.0778215	+	0.996967i	$0.475204\pi$
$858$	0	0
$859$	−3.50044e10	−1.88428	−0.942142	−	0.335215i	$-0.891191\pi$
$859$	−3.50044e10	−1.88428	−0.942142	+	0.335215i	$0.891191\pi$
$860$	1.88868e10	1.01254
$861$	−1.55579e10	−0.830694
$862$	−6.13386e9	−0.326181
$863$	−3.23684e10	−1.71429	−0.857143	−	0.515078i	$-0.827763\pi$
$863$	−3.23684e10	−1.71429	−0.857143	+	0.515078i	$0.827763\pi$
$864$	−2.73159e9	−0.144084
$865$	3.36281e10	1.76663
$866$	2.17987e8	0.0114056
$867$	1.20704e10	0.629005
$868$	4.20423e10	2.18207
$869$	0	0
$870$	−2.75614e9	−0.141900
$871$	9.36216e9	0.480079
$872$	−2.07272e9	−0.105860
$873$	1.25680e10	0.639318
$874$	−1.11355e9	−0.0564181
$875$	−2.72823e10	−1.37674
$876$	1.37231e10	0.689744
$877$	1.36182e10	0.681741	0.340871	−	0.940110i	$-0.389278\pi$
$877$	1.36182e10	0.681741	0.340871	+	0.940110i	$0.389278\pi$
$878$	7.38885e9	0.368422
$879$	−1.38295e10	−0.686824
$880$	0	0
$881$	2.28881e10	1.12770	0.563851	−	0.825877i	$-0.309319\pi$
$881$	2.28881e10	1.12770	0.563851	+	0.825877i	$0.309319\pi$
$882$	−4.39596e9	−0.215732
$883$	−3.22248e10	−1.57517	−0.787585	−	0.616207i	$-0.788669\pi$
$883$	−3.22248e10	−1.57517	−0.787585	+	0.616207i	$0.788669\pi$
$884$	2.05060e10	0.998383
$885$	−4.99876e8	−0.0242416
$886$	4.34242e9	0.209756
$887$	1.23059e10	0.592081	0.296041	−	0.955175i	$-0.404334\pi$
$887$	1.23059e10	0.592081	0.296041	+	0.955175i	$0.404334\pi$
$888$	1.77967e9	0.0852893
$889$	7.48779e9	0.357435
$890$	1.23520e10	0.587318
$891$	0	0
$892$	2.96061e10	1.39670
$893$	−3.09300e10	−1.45345
$894$	1.49328e9	0.0698970
$895$	−4.50777e10	−2.10175
$896$	−3.56125e10	−1.65396
$897$	−1.75044e9	−0.0809791
$898$	−8.56243e9	−0.394575
$899$	−2.14972e10	−0.986787
$900$	−2.36283e9	−0.108040
$901$	−1.85472e10	−0.844776
$902$	0	0
$903$	−2.20076e10	−0.994639
$904$	3.73841e9	0.168305
$905$	−1.72787e10	−0.774893
$906$	2.03875e8	0.00910784
$907$	−5.53790e9	−0.246445	−0.123222	−	0.992379i	$-0.539323\pi$
$907$	−5.53790e9	−0.246445	−0.123222	+	0.992379i	$0.539323\pi$
$908$	1.10629e10	0.490419
$909$	−3.06030e9	−0.135142
$910$	1.00166e10	0.440630
$911$	−1.58122e10	−0.692911	−0.346456	−	0.938066i	$-0.612615\pi$
$911$	−1.58122e10	−0.692911	−0.346456	+	0.938066i	$0.612615\pi$
$912$	1.11163e10	0.485263
$913$	0	0
$914$	4.92022e9	0.213144
$915$	1.60452e10	0.692421
$916$	−8.10357e9	−0.348371
$917$	−3.62466e10	−1.55230
$918$	−1.80951e9	−0.0771988
$919$	−1.25552e10	−0.533604	−0.266802	−	0.963751i	$-0.585967\pi$
$919$	−1.25552e10	−0.533604	−0.266802	+	0.963751i	$0.585967\pi$
$920$	−2.74609e9	−0.116267
$921$	−3.60613e9	−0.152101
$922$	−7.88441e9	−0.331292
$923$	1.17632e10	0.492401
$924$	0	0
$925$	2.33996e9	0.0972103
$926$	−7.09803e9	−0.293765
$927$	1.55757e10	0.642196
$928$	1.38878e10	0.570446
$929$	−6.07012e9	−0.248394	−0.124197	−	0.992258i	$-0.539636\pi$
$929$	−6.07012e9	−0.248394	−0.124197	+	0.992258i	$0.539636\pi$
$930$	5.91650e9	0.241199
$931$	6.22841e10	2.52961
$932$	1.53909e10	0.622743
$933$	−3.28074e9	−0.132247
$934$	−8.18350e9	−0.328643
$935$	0	0
$936$	−3.33947e9	−0.133110
$937$	−4.22666e8	−0.0167845	−0.00839226	−	0.999965i	$-0.502671\pi$
$937$	−4.22666e8	−0.0167845	−0.00839226	+	0.999965i	$0.502671\pi$
$938$	−8.21445e9	−0.324989
$939$	−2.23641e10	−0.881499
$940$	−3.66105e10	−1.43767
$941$	−3.60538e10	−1.41055	−0.705274	−	0.708935i	$-0.749176\pi$
$941$	−3.60538e10	−1.41055	−0.705274	+	0.708935i	$0.749176\pi$
$942$	4.71589e8	0.0183817
$943$	3.80435e9	0.147737
$944$	7.23460e8	0.0279906
$945$	1.05937e10	0.408353
$946$	0	0
$947$	−2.42390e10	−0.927449	−0.463724	−	0.885980i	$-0.653487\pi$
$947$	−2.42390e10	−0.927449	−0.463724	+	0.885980i	$0.653487\pi$
$948$	−3.63767e9	−0.138674
$949$	2.55015e10	0.968576
$950$	−2.79324e9	−0.105700
$951$	1.36191e10	0.513472
$952$	−3.74854e10	−1.40810
$953$	−2.06886e10	−0.774295	−0.387148	−	0.922018i	$-0.626540\pi$
$953$	−2.06886e10	−0.774295	−0.387148	+	0.922018i	$0.626540\pi$
$954$	1.44976e9	0.0540601
$955$	1.43510e10	0.533176
$956$	−1.04634e10	−0.387319
$957$	0	0
$958$	1.15912e10	0.425939
$959$	−5.75879e10	−2.10846
$960$	1.04335e10	0.380609
$961$	1.86347e10	0.677315
$962$	1.58735e9	0.0574858
$963$	−2.09424e9	−0.0755673
$964$	2.13110e10	0.766186
$965$	−2.29435e10	−0.821889
$966$	1.53585e9	0.0548187
$967$	4.91299e9	0.174724	0.0873621	−	0.996177i	$-0.472156\pi$
$967$	4.91299e9	0.174724	0.0873621	+	0.996177i	$0.472156\pi$
$968$	0	0
$969$	2.56379e10	0.905211
$970$	1.75860e10	0.618681
$971$	4.08278e10	1.43116	0.715581	−	0.698530i	$-0.246162\pi$
$971$	4.08278e10	1.43116	0.715581	+	0.698530i	$0.246162\pi$
$972$	−1.69522e9	−0.0592098
$973$	8.28914e10	2.88479
$974$	1.43595e9	0.0497948
$975$	−4.39082e9	−0.151715
$976$	−2.32219e10	−0.799508
$977$	3.23195e10	1.10875	0.554375	−	0.832267i	$-0.312957\pi$
$977$	3.23195e10	1.10875	0.554375	+	0.832267i	$0.312957\pi$
$978$	3.64623e9	0.124640
$979$	0	0
$980$	7.37229e10	2.50214
$981$	−1.95525e9	−0.0661241
$982$	8.42427e9	0.283885
$983$	−3.43228e10	−1.15251	−0.576256	−	0.817269i	$-0.695487\pi$
$983$	−3.43228e10	−1.15251	−0.576256	+	0.817269i	$0.695487\pi$
$984$	7.25791e9	0.242845
$985$	4.47270e10	1.49122
$986$	9.19978e9	0.305639
$987$	4.26600e10	1.41225
$988$	2.27102e10	0.749155
$989$	5.38147e9	0.176894
$990$	0	0
$991$	−1.89205e10	−0.617554	−0.308777	−	0.951134i	$-0.599920\pi$
$991$	−1.89205e10	−0.617554	−0.308777	+	0.951134i	$0.599920\pi$
$992$	−2.98124e10	−0.969629
$993$	9.79194e9	0.317356
$994$	−1.03211e10	−0.333330
$995$	−6.91643e9	−0.222588
$996$	1.77857e10	0.570377
$997$	−2.25462e10	−0.720511	−0.360255	−	0.932854i	$-0.617310\pi$
$997$	−2.25462e10	−0.720511	−0.360255	+	0.932854i	$0.617310\pi$
$998$	5.86094e9	0.186642
$999$	1.67881e9	0.0532748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.8.a.o.1.7		14
11.3	even	5		33.8.e.b.31.4	yes	28
11.4	even	5		33.8.e.b.16.4	✓	28
11.10	odd	2		363.8.a.r.1.8		14
33.14	odd	10		99.8.f.b.64.4		28
33.26	odd	10		99.8.f.b.82.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.16.4	✓	28	11.4	even	5
33.8.e.b.31.4	yes	28	11.3	even	5
99.8.f.b.64.4		28	33.14	odd	10
99.8.f.b.82.4		28	33.26	odd	10
363.8.a.o.1.7		14	1.1	even	1	trivial
363.8.a.r.1.8		14	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q-3.13964 q^{2} +27.0000 q^{3} -118.143 q^{4} -324.899 q^{5} -84.7702 q^{6} -1656.56 q^{7} +772.799 q^{8} +729.000 q^{9} +1020.07 q^{10} -3189.85 q^{12} -5927.67 q^{13} +5200.99 q^{14} -8772.28 q^{15} +12696.0 q^{16} +29281.2 q^{17} -2288.79 q^{18} +32428.8 q^{19} +38384.5 q^{20} -44727.1 q^{21} +10937.0 q^{23} +20865.6 q^{24} +27434.6 q^{25} +18610.7 q^{26} +19683.0 q^{27} +195710. q^{28} -100071. q^{29} +27541.8 q^{30} +214819. q^{31} -138779. q^{32} -91932.4 q^{34} +538215. q^{35} -86126.0 q^{36} +85292.3 q^{37} -101815. q^{38} -160047. q^{39} -251082. q^{40} +347842. q^{41} +140427. q^{42} +492042. q^{43} -236852. q^{45} -34338.3 q^{46} -953784. q^{47} +342791. q^{48} +1.92064e6 q^{49} -86134.6 q^{50} +790593. q^{51} +700311. q^{52} -633416. q^{53} -61797.5 q^{54} -1.28019e6 q^{56} +875576. q^{57} +314187. q^{58} +56983.5 q^{59} +1.03638e6 q^{60} -1.82908e6 q^{61} -674454. q^{62} -1.20763e6 q^{63} -1.18937e6 q^{64} +1.92590e6 q^{65} -1.57940e6 q^{67} -3.45936e6 q^{68} +295300. q^{69} -1.68980e6 q^{70} -1.98445e6 q^{71} +563370. q^{72} -4.30211e6 q^{73} -267787. q^{74} +740733. q^{75} -3.83122e6 q^{76} +502490. q^{78} +1.14039e6 q^{79} -4.12491e6 q^{80} +531441. q^{81} -1.09210e6 q^{82} -5.57570e6 q^{83} +5.28418e6 q^{84} -9.51345e6 q^{85} -1.54483e6 q^{86} -2.70192e6 q^{87} +1.21091e7 q^{89} +743628. q^{90} +9.81953e6 q^{91} -1.29213e6 q^{92} +5.80012e6 q^{93} +2.99454e6 q^{94} -1.05361e7 q^{95} -3.74703e6 q^{96} +1.72401e7 q^{97} -6.03012e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 23 q^{2} + 378 q^{3} + 845 q^{4} + 69 q^{5} - 621 q^{6} - 3278 q^{7} - 4602 q^{8} + 10206 q^{9} - 5320 q^{10} + 22815 q^{12} - 32188 q^{13} - 7794 q^{14} + 1863 q^{15} + 86137 q^{16} - 42917 q^{17}+ \cdots + 70266089 q^{98}+O(q^{100}) \) 14 * q - 23 * q^2 + 378 * q^3 + 845 * q^4 + 69 * q^5 - 621 * q^6 - 3278 * q^7 - 4602 * q^8 + 10206 * q^9 - 5320 * q^10 + 22815 * q^12 - 32188 * q^13 - 7794 * q^14 + 1863 * q^15 + 86137 * q^16 - 42917 * q^17 - 16767 * q^18 - 50419 * q^19 + 54475 * q^20 - 88506 * q^21 - 83492 * q^23 - 124254 * q^24 + 336991 * q^25 + 234897 * q^26 + 275562 * q^27 - 697184 * q^28 - 227028 * q^29 - 143640 * q^30 - 36481 * q^31 - 151749 * q^32 - 614562 * q^34 + 258783 * q^35 + 616005 * q^36 + 634524 * q^37 - 662891 * q^38 - 869076 * q^39 - 1585604 * q^40 - 1286544 * q^41 - 210438 * q^42 - 2632644 * q^43 + 50301 * q^45 - 1290627 * q^46 - 1692245 * q^47 + 2325699 * q^48 + 842030 * q^49 - 7870914 * q^50 - 1158759 * q^51 - 6419781 * q^52 + 1211317 * q^53 - 452709 * q^54 - 9100953 * q^56 - 1361313 * q^57 - 6265711 * q^58 + 2551943 * q^59 + 1470825 * q^60 - 10221163 * q^61 - 5723657 * q^62 - 2389662 * q^63 + 6349332 * q^64 - 7684087 * q^65 - 3570631 * q^67 - 13112925 * q^68 - 2254284 * q^69 + 3559265 * q^70 + 4528437 * q^71 - 3354858 * q^72 - 13052276 * q^73 - 4896205 * q^74 + 9098757 * q^75 - 9845214 * q^76 + 6342219 * q^78 - 14911090 * q^79 - 9395382 * q^80 + 7440174 * q^81 + 17478001 * q^82 - 7068900 * q^83 - 18823968 * q^84 - 24423120 * q^85 + 12792479 * q^86 - 6129756 * q^87 + 4800832 * q^89 - 3878280 * q^90 - 15295476 * q^91 - 3195753 * q^92 - 984987 * q^93 + 43320002 * q^94 - 7614177 * q^95 - 4097223 * q^96 - 11578773 * q^97 + 70266089 * q^98

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