LMFDB - Embedded newform 338.10.a.k.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,10,Mod(1,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	338.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-96,81,1536,-1693] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$174.082112623$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 10375x^{4} - 44865x^{3} + 25702990x^{2} + 68900300x - 16723086000 $ x^6 - 3x^5 - 10375x^4 - 44865x^3 + 25702990x^2 + 68900300*x - 16723086000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 13 $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-75.8221$ of defining polynomial
Character	$\chi$	$=$	338.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-16.0000 q^{2} +242.466 q^{3} +256.000 q^{4} +2071.64 q^{5} -3879.46 q^{6} -323.249 q^{7} -4096.00 q^{8} +39107.0 q^{9} -33146.3 q^{10} -88320.7 q^{11} +62071.4 q^{12} +5171.98 q^{14} +502304. q^{15} +65536.0 q^{16} -452044. q^{17} -625712. q^{18} -649714. q^{19} +530341. q^{20} -78377.0 q^{21} +1.41313e6 q^{22} -1.58223e6 q^{23} -993143. q^{24} +2.33858e6 q^{25} +4.70966e6 q^{27} -82751.7 q^{28} +2.92672e6 q^{29} -8.03686e6 q^{30} -1.27453e6 q^{31} -1.04858e6 q^{32} -2.14148e7 q^{33} +7.23270e6 q^{34} -669656. q^{35} +1.00114e7 q^{36} -8.01993e6 q^{37} +1.03954e7 q^{38} -8.48545e6 q^{40} -4.82644e6 q^{41} +1.25403e6 q^{42} +2.82958e7 q^{43} -2.26101e7 q^{44} +8.10157e7 q^{45} +2.53157e7 q^{46} -1.19241e7 q^{47} +1.58903e7 q^{48} -4.02491e7 q^{49} -3.74173e7 q^{50} -1.09605e8 q^{51} -3.78650e6 q^{53} -7.53546e7 q^{54} -1.82969e8 q^{55} +1.32403e6 q^{56} -1.57534e8 q^{57} -4.68275e7 q^{58} -2.26572e7 q^{59} +1.28590e8 q^{60} +2.05910e7 q^{61} +2.03925e7 q^{62} -1.26413e7 q^{63} +1.67772e7 q^{64} +3.42637e8 q^{66} -1.62784e8 q^{67} -1.15723e8 q^{68} -3.83638e8 q^{69} +1.07145e7 q^{70} +3.82791e7 q^{71} -1.60182e8 q^{72} -3.92315e8 q^{73} +1.28319e8 q^{74} +5.67028e8 q^{75} -1.66327e8 q^{76} +2.85496e7 q^{77} -1.33317e8 q^{79} +1.35767e8 q^{80} +3.72193e8 q^{81} +7.72231e7 q^{82} +5.40870e8 q^{83} -2.00645e7 q^{84} -9.36473e8 q^{85} -4.52732e8 q^{86} +7.09631e8 q^{87} +3.61762e8 q^{88} -8.59345e8 q^{89} -1.29625e9 q^{90} -4.05052e8 q^{92} -3.09031e8 q^{93} +1.90786e8 q^{94} -1.34598e9 q^{95} -2.54244e8 q^{96} -7.32952e8 q^{97} +6.43986e8 q^{98} -3.45396e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 96 q^{2} + 81 q^{3} + 1536 q^{4} - 1693 q^{5} - 1296 q^{6} - 473 q^{7} - 24576 q^{8} + 69813 q^{9} + 27088 q^{10} - 14011 q^{11} + 20736 q^{12} + 7568 q^{14} + 294780 q^{15} + 393216 q^{16} - 173558 q^{17}+ \cdots + 881769510 q^{99}+O(q^{100}) $ 6 * q - 96 * q^2 + 81 * q^3 + 1536 * q^4 - 1693 * q^5 - 1296 * q^6 - 473 * q^7 - 24576 * q^8 + 69813 * q^9 + 27088 * q^10 - 14011 * q^11 + 20736 * q^12 + 7568 * q^14 + 294780 * q^15 + 393216 * q^16 - 173558 * q^17 - 1117008 * q^18 - 322367 * q^19 - 433408 * q^20 - 2256885 * q^21 + 224176 * q^22 - 1644771 * q^23 - 331776 * q^24 + 2687569 * q^25 - 922995 * q^27 - 121088 * q^28 + 10801236 * q^29 - 4716480 * q^30 - 10435122 * q^31 - 6291456 * q^32 - 26201763 * q^33 + 2776928 * q^34 + 2168950 * q^35 + 17872128 * q^36 + 15710464 * q^37 + 5157872 * q^38 + 6934528 * q^40 + 1525478 * q^41 + 36110160 * q^42 + 50959661 * q^43 - 3586816 * q^44 - 18619731 * q^45 + 26316336 * q^46 - 68156998 * q^47 + 5308416 * q^48 + 162536361 * q^49 - 43001104 * q^50 - 84678981 * q^51 + 72278209 * q^53 + 14767920 * q^54 - 353372330 * q^55 + 1937408 * q^56 - 17951025 * q^57 - 172819776 * q^58 + 5665291 * q^59 + 75463680 * q^60 - 353387956 * q^61 + 166961952 * q^62 + 224088894 * q^63 + 100663296 * q^64 + 419228208 * q^66 - 371115369 * q^67 - 44430848 * q^68 + 280317279 * q^69 - 34703200 * q^70 - 156688763 * q^71 - 285954048 * q^72 - 466401663 * q^73 - 251367424 * q^74 + 1149481845 * q^75 - 82525952 * q^76 + 312460333 * q^77 + 162543480 * q^79 - 110952448 * q^80 + 295496586 * q^81 - 24407648 * q^82 + 435114576 * q^83 - 577762560 * q^84 - 2307296767 * q^85 - 815354576 * q^86 - 617376057 * q^87 + 57389056 * q^88 - 163315063 * q^89 + 297915696 * q^90 - 421061376 * q^92 - 2056270836 * q^93 + 1090511968 * q^94 - 537110948 * q^95 - 84934656 * q^96 + 1500514705 * q^97 - 2600581776 * q^98 + 881769510 * q^99

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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	242.466	1.72825	0.864124	−	0.503279i	$-0.167873\pi$
$3$	242.466	1.72825	0.864124	+	0.503279i	$0.167873\pi$
$4$	256.000	0.500000
$5$	2071.64	1.48235	0.741174	−	0.671313i	$-0.234269\pi$
$5$	2071.64	1.48235	0.741174	+	0.671313i	$0.234269\pi$
$6$	−3879.46	−1.22206
$7$	−323.249	−0.0508857	−0.0254429	−	0.999676i	$-0.508100\pi$
$7$	−323.249	−0.0508857	−0.0254429	+	0.999676i	$0.508100\pi$
$8$	−4096.00	−0.353553
$9$	39107.0	1.98684
$10$	−33146.3	−1.04818
$11$	−88320.7	−1.81884	−0.909422	−	0.415875i	$-0.863476\pi$
$11$	−88320.7	−1.81884	−0.909422	+	0.415875i	$0.863476\pi$
$12$	62071.4	0.864124
$13$	0	0
$13$	0	0
$14$	5171.98	0.0359816
$15$	502304.	2.56186
$16$	65536.0	0.250000
$17$	−452044.	−1.31268	−0.656342	−	0.754463i	$-0.727897\pi$
$17$	−452044.	−1.31268	−0.656342	+	0.754463i	$0.727897\pi$
$18$	−625712.	−1.40491
$19$	−649714.	−1.14375	−0.571875	−	0.820341i	$-0.693784\pi$
$19$	−649714.	−1.14375	−0.571875	+	0.820341i	$0.693784\pi$
$20$	530341.	0.741174
$21$	−78377.0	−0.0879431
$22$	1.41313e6	1.28612
$23$	−1.58223e6	−1.17895	−0.589475	−	0.807787i	$-0.700665\pi$
$23$	−1.58223e6	−1.17895	−0.589475	+	0.807787i	$0.700665\pi$
$24$	−993143.	−0.611028
$25$	2.33858e6	1.19735
$26$	0	0
$27$	4.70966e6	1.70550
$28$	−82751.7	−0.0254429
$29$	2.92672e6	0.768404	0.384202	−	0.923249i	$-0.374477\pi$
$29$	2.92672e6	0.768404	0.384202	+	0.923249i	$0.374477\pi$
$30$	−8.03686e6	−1.81151
$31$	−1.27453e6	−0.247869	−0.123935	−	0.992290i	$-0.539551\pi$
$31$	−1.27453e6	−0.247869	−0.123935	+	0.992290i	$0.539551\pi$
$32$	−1.04858e6	−0.176777
$33$	−2.14148e7	−3.14341
$34$	7.23270e6	0.928208
$35$	−669656.	−0.0754303
$36$	1.00114e7	0.993420
$37$	−8.01993e6	−0.703498	−0.351749	−	0.936094i	$-0.614413\pi$
$37$	−8.01993e6	−0.703498	−0.351749	+	0.936094i	$0.614413\pi$
$38$	1.03954e7	0.808754
$39$	0	0
$40$	−8.48545e6	−0.524089
$41$	−4.82644e6	−0.266747	−0.133374	−	0.991066i	$-0.542581\pi$
$41$	−4.82644e6	−0.266747	−0.133374	+	0.991066i	$0.542581\pi$
$42$	1.25403e6	0.0621852
$43$	2.82958e7	1.26216	0.631079	−	0.775719i	$-0.282613\pi$
$43$	2.82958e7	1.26216	0.631079	+	0.775719i	$0.282613\pi$
$44$	−2.26101e7	−0.909422
$45$	8.10157e7	2.94519
$46$	2.53157e7	0.833643
$47$	−1.19241e7	−0.356440	−0.178220	−	0.983991i	$-0.557034\pi$
$47$	−1.19241e7	−0.356440	−0.178220	+	0.983991i	$0.557034\pi$
$48$	1.58903e7	0.432062
$49$	−4.02491e7	−0.997411
$50$	−3.74173e7	−0.846657
$51$	−1.09605e8	−2.26864
$52$	0	0
$53$	−3.78650e6	−0.0659168	−0.0329584	−	0.999457i	$-0.510493\pi$
$53$	−3.78650e6	−0.0659168	−0.0329584	+	0.999457i	$0.510493\pi$
$54$	−7.53546e7	−1.20597
$55$	−1.82969e8	−2.69616
$56$	1.32403e6	0.0179908
$57$	−1.57534e8	−1.97668
$58$	−4.68275e7	−0.543344
$59$	−2.26572e7	−0.243429	−0.121714	−	0.992565i	$-0.538839\pi$
$59$	−2.26572e7	−0.243429	−0.121714	+	0.992565i	$0.538839\pi$
$60$	1.28590e8	1.28093
$61$	2.05910e7	0.190411	0.0952056	−	0.995458i	$-0.469649\pi$
$61$	2.05910e7	0.190411	0.0952056	+	0.995458i	$0.469649\pi$
$62$	2.03925e7	0.175270
$63$	−1.26413e7	−0.101102
$64$	1.67772e7	0.125000
$65$	0	0
$66$	3.42637e8	2.22273
$67$	−1.62784e8	−0.986905	−0.493452	−	0.869773i	$-0.664265\pi$
$67$	−1.62784e8	−0.986905	−0.493452	+	0.869773i	$0.664265\pi$
$68$	−1.15723e8	−0.656342
$69$	−3.83638e8	−2.03752
$70$	1.07145e7	0.0533373
$71$	3.82791e7	0.178772	0.0893860	−	0.995997i	$-0.471510\pi$
$71$	3.82791e7	0.178772	0.0893860	+	0.995997i	$0.471510\pi$
$72$	−1.60182e8	−0.702454
$73$	−3.92315e8	−1.61690	−0.808448	−	0.588567i	$-0.799692\pi$
$73$	−3.92315e8	−1.61690	−0.808448	+	0.588567i	$0.799692\pi$
$74$	1.28319e8	0.497448
$75$	5.67028e8	2.06932
$76$	−1.66327e8	−0.571875
$77$	2.85496e7	0.0925532
$78$	0	0
$79$	−1.33317e8	−0.385092	−0.192546	−	0.981288i	$-0.561675\pi$
$79$	−1.33317e8	−0.385092	−0.192546	+	0.981288i	$0.561675\pi$
$80$	1.35767e8	0.370587
$81$	3.72193e8	0.960694
$82$	7.72231e7	0.188619
$83$	5.40870e8	1.25096	0.625478	−	0.780242i	$-0.284904\pi$
$83$	5.40870e8	1.25096	0.625478	+	0.780242i	$0.284904\pi$
$84$	−2.00645e7	−0.0439716
$85$	−9.36473e8	−1.94585
$86$	−4.52732e8	−0.892480
$87$	7.09631e8	1.32799
$88$	3.61762e8	0.643058
$89$	−8.59345e8	−1.45182	−0.725909	−	0.687791i	$-0.758581\pi$
$89$	−8.59345e8	−1.45182	−0.725909	+	0.687791i	$0.758581\pi$
$90$	−1.29625e9	−2.08256
$91$	0	0
$92$	−4.05052e8	−0.589475
$93$	−3.09031e8	−0.428379
$94$	1.90786e8	0.252041
$95$	−1.34598e9	−1.69544
$96$	−2.54244e8	−0.305514
$97$	−7.32952e8	−0.840626	−0.420313	−	0.907379i	$-0.638080\pi$
$97$	−7.32952e8	−0.840626	−0.420313	+	0.907379i	$0.638080\pi$
$98$	6.43986e8	0.705276
$99$	−3.45396e9	−3.61375
$100$	5.98677e8	0.598677
$101$	1.97094e8	0.188464	0.0942319	−	0.995550i	$-0.469960\pi$
$101$	1.97094e8	0.188464	0.0942319	+	0.995550i	$0.469960\pi$
$102$	1.75369e9	1.60417
$103$	−5.00520e7	−0.0438181	−0.0219091	−	0.999760i	$-0.506974\pi$
$103$	−5.00520e7	−0.0438181	−0.0219091	+	0.999760i	$0.506974\pi$
$104$	0	0
$105$	−1.62369e8	−0.130362
$106$	6.05839e7	0.0466102
$107$	−3.62618e8	−0.267437	−0.133719	−	0.991019i	$-0.542692\pi$
$107$	−3.62618e8	−0.267437	−0.133719	+	0.991019i	$0.542692\pi$
$108$	1.20567e9	0.852752
$109$	−3.93006e8	−0.266673	−0.133337	−	0.991071i	$-0.542569\pi$
$109$	−3.93006e8	−0.266673	−0.133337	+	0.991071i	$0.542569\pi$
$110$	2.92750e9	1.90647
$111$	−1.94456e9	−1.21582
$112$	−2.11844e7	−0.0127214
$113$	5.62974e7	0.0324814	0.0162407	−	0.999868i	$-0.494830\pi$
$113$	5.62974e7	0.0324814	0.0162407	+	0.999868i	$0.494830\pi$
$114$	2.52054e9	1.39773
$115$	−3.27782e9	−1.74761
$116$	7.49239e8	0.384202
$117$	0	0
$118$	3.62515e8	0.172130
$119$	1.46123e8	0.0667969
$120$	−2.05744e9	−0.905756
$121$	5.44260e9	2.30819
$122$	−3.29455e8	−0.134641
$123$	−1.17025e9	−0.461005
$124$	−3.26280e8	−0.123935
$125$	7.98529e8	0.292547
$126$	2.02261e8	0.0714897
$127$	2.62698e9	0.896064	0.448032	−	0.894017i	$-0.352125\pi$
$127$	2.62698e9	0.896064	0.448032	+	0.894017i	$0.352125\pi$
$128$	−2.68435e8	−0.0883883
$129$	6.86078e9	2.18132
$130$	0	0
$131$	5.16288e9	1.53169	0.765846	−	0.643024i	$-0.222320\pi$
$131$	5.16288e9	1.53169	0.765846	+	0.643024i	$0.222320\pi$
$132$	−5.48219e9	−1.57171
$133$	2.10019e8	0.0582006
$134$	2.60454e9	0.697847
$135$	9.75674e9	2.52815
$136$	1.85157e9	0.464104
$137$	3.62647e9	0.879511	0.439755	−	0.898118i	$-0.355065\pi$
$137$	3.62647e9	0.879511	0.439755	+	0.898118i	$0.355065\pi$
$138$	6.13821e9	1.44074
$139$	8.48644e8	0.192823	0.0964116	−	0.995342i	$-0.469264\pi$
$139$	8.48644e8	0.192823	0.0964116	+	0.995342i	$0.469264\pi$
$140$	−1.71432e8	−0.0377151
$141$	−2.89120e9	−0.616016
$142$	−6.12466e8	−0.126411
$143$	0	0
$144$	2.56291e9	0.496710
$145$	6.06311e9	1.13904
$146$	6.27704e9	1.14332
$147$	−9.75906e9	−1.72377
$148$	−2.05310e9	−0.351749
$149$	6.87641e9	1.14294	0.571470	−	0.820623i	$-0.306373\pi$
$149$	6.87641e9	1.14294	0.571470	+	0.820623i	$0.306373\pi$
$150$	−9.07244e9	−1.46323
$151$	7.47346e9	1.16984	0.584919	−	0.811092i	$-0.301126\pi$
$151$	7.47346e9	1.16984	0.584919	+	0.811092i	$0.301126\pi$
$152$	2.66123e9	0.404377
$153$	−1.76781e10	−2.60809
$154$	−4.56793e8	−0.0654450
$155$	−2.64037e9	−0.367428
$156$	0	0
$157$	−6.66627e9	−0.875657	−0.437829	−	0.899058i	$-0.644252\pi$
$157$	−6.66627e9	−0.875657	−0.437829	+	0.899058i	$0.644252\pi$
$158$	2.13308e9	0.272302
$159$	−9.18098e8	−0.113921
$160$	−2.17228e9	−0.262044
$161$	5.11455e8	0.0599917
$162$	−5.95508e9	−0.679313
$163$	−1.48829e10	−1.65136	−0.825682	−	0.564136i	$-0.809210\pi$
$163$	−1.48829e10	−1.65136	−0.825682	+	0.564136i	$0.809210\pi$
$164$	−1.23557e9	−0.133374
$165$	−4.43638e10	−4.65963
$166$	−8.65393e9	−0.884559
$167$	9.86588e9	0.981548	0.490774	−	0.871287i	$-0.336714\pi$
$167$	9.86588e9	0.981548	0.490774	+	0.871287i	$0.336714\pi$
$168$	3.21032e8	0.0310926
$169$	0	0
$170$	1.49836e10	1.37593
$171$	−2.54084e10	−2.27245
$172$	7.24372e9	0.631079
$173$	2.03269e10	1.72530	0.862648	−	0.505806i	$-0.168805\pi$
$173$	2.03269e10	1.72530	0.862648	+	0.505806i	$0.168805\pi$
$174$	−1.13541e10	−0.939033
$175$	−7.55944e8	−0.0609282
$176$	−5.78819e9	−0.454711
$177$	−5.49361e9	−0.420705
$178$	1.37495e10	1.02659
$179$	−9.13339e9	−0.664957	−0.332478	−	0.943111i	$-0.607885\pi$
$179$	−9.13339e9	−0.664957	−0.332478	+	0.943111i	$0.607885\pi$
$180$	2.07400e10	1.47259
$181$	2.57653e10	1.78436	0.892180	−	0.451681i	$-0.149175\pi$
$181$	2.57653e10	1.78436	0.892180	+	0.451681i	$0.149175\pi$
$182$	0	0
$183$	4.99262e9	0.329078
$184$	6.48083e9	0.416822
$185$	−1.66144e10	−1.04283
$186$	4.94449e9	0.302910
$187$	3.99248e10	2.38757
$188$	−3.05258e9	−0.178220
$189$	−1.52239e9	−0.0867858
$190$	2.15356e10	1.19885
$191$	−1.48931e10	−0.809720	−0.404860	−	0.914379i	$-0.632680\pi$
$191$	−1.48931e10	−0.809720	−0.404860	+	0.914379i	$0.632680\pi$
$192$	4.06791e9	0.216031
$193$	−3.54691e9	−0.184010	−0.0920051	−	0.995759i	$-0.529328\pi$
$193$	−3.54691e9	−0.184010	−0.0920051	+	0.995759i	$0.529328\pi$
$194$	1.17272e10	0.594412
$195$	0	0
$196$	−1.03038e10	−0.498705
$197$	−1.73630e10	−0.821348	−0.410674	−	0.911782i	$-0.634707\pi$
$197$	−1.73630e10	−0.821348	−0.410674	+	0.911782i	$0.634707\pi$
$198$	5.52633e10	2.55531
$199$	3.76276e9	0.170086	0.0850429	−	0.996377i	$-0.472897\pi$
$199$	3.76276e9	0.170086	0.0850429	+	0.996377i	$0.472897\pi$
$200$	−9.57883e9	−0.423329
$201$	−3.94697e10	−1.70562
$202$	−3.15351e9	−0.133264
$203$	−9.46058e8	−0.0391008
$204$	−2.80590e10	−1.13432
$205$	−9.99867e9	−0.395412
$206$	8.00832e8	0.0309841
$207$	−6.18763e10	−2.34238
$208$	0	0
$209$	5.73832e10	2.08030
$210$	2.59791e9	0.0921800
$211$	−4.32571e10	−1.50240	−0.751201	−	0.660074i	$-0.770525\pi$
$211$	−4.32571e10	−1.50240	−0.751201	+	0.660074i	$0.770525\pi$
$212$	−9.69343e8	−0.0329584
$213$	9.28140e9	0.308962
$214$	5.80188e9	0.189107
$215$	5.86188e10	1.87096
$216$	−1.92908e10	−0.602987
$217$	4.11990e8	0.0126130
$218$	6.28809e9	0.188567
$219$	−9.51233e10	−2.79440
$220$	−4.68401e10	−1.34808
$221$	0	0
$222$	3.11130e10	0.859713
$223$	3.28691e10	0.890053	0.445027	−	0.895517i	$-0.353194\pi$
$223$	3.28691e10	0.890053	0.445027	+	0.895517i	$0.353194\pi$
$224$	3.38951e8	0.00899541
$225$	9.14549e10	2.37895
$226$	−9.00758e8	−0.0229678
$227$	−6.91613e10	−1.72881	−0.864404	−	0.502798i	$-0.832304\pi$
$227$	−6.91613e10	−1.72881	−0.864404	+	0.502798i	$0.832304\pi$
$228$	−4.03287e10	−0.988342
$229$	3.37155e10	0.810158	0.405079	−	0.914282i	$-0.367244\pi$
$229$	3.37155e10	0.810158	0.405079	+	0.914282i	$0.367244\pi$
$230$	5.24452e10	1.23575
$231$	6.92231e9	0.159955
$232$	−1.19878e10	−0.271672
$233$	−1.18954e10	−0.264410	−0.132205	−	0.991222i	$-0.542206\pi$
$233$	−1.18954e10	−0.264410	−0.132205	+	0.991222i	$0.542206\pi$
$234$	0	0
$235$	−2.47025e10	−0.528368
$236$	−5.80024e9	−0.121714
$237$	−3.23250e10	−0.665535
$238$	−2.33796e9	−0.0472325
$239$	−1.57903e10	−0.313040	−0.156520	−	0.987675i	$-0.550028\pi$
$239$	−1.57903e10	−0.313040	−0.156520	+	0.987675i	$0.550028\pi$
$240$	3.29190e10	0.640466
$241$	−2.20834e10	−0.421687	−0.210843	−	0.977520i	$-0.567621\pi$
$241$	−2.20834e10	−0.421687	−0.210843	+	0.977520i	$0.567621\pi$
$242$	−8.70816e10	−1.63214
$243$	−2.45608e9	−0.0451871
$244$	5.27129e9	0.0952056
$245$	−8.33818e10	−1.47851
$246$	1.87240e10	0.325980
$247$	0	0
$248$	5.22047e9	0.0876350
$249$	1.31143e11	2.16196
$250$	−1.27765e10	−0.206862
$251$	−6.29786e10	−1.00152	−0.500762	−	0.865585i	$-0.666947\pi$
$251$	−6.29786e10	−1.00152	−0.500762	+	0.865585i	$0.666947\pi$
$252$	−3.23617e9	−0.0505509
$253$	1.39744e11	2.14432
$254$	−4.20316e10	−0.633613
$255$	−2.27063e11	−3.36292
$256$	4.29497e9	0.0625000
$257$	−3.54456e10	−0.506832	−0.253416	−	0.967357i	$-0.581554\pi$
$257$	−3.54456e10	−0.506832	−0.253416	+	0.967357i	$0.581554\pi$
$258$	−1.09772e11	−1.54243
$259$	2.59243e9	0.0357980
$260$	0	0
$261$	1.14455e11	1.52670
$262$	−8.26062e10	−1.08307
$263$	6.47320e10	0.834292	0.417146	−	0.908840i	$-0.363030\pi$
$263$	6.47320e10	0.834292	0.417146	+	0.908840i	$0.363030\pi$
$264$	8.77150e10	1.11136
$265$	−7.84427e9	−0.0977116
$266$	−3.36031e9	−0.0411540
$267$	−2.08362e11	−2.50910
$268$	−4.16727e10	−0.493452
$269$	1.09719e11	1.27760	0.638800	−	0.769373i	$-0.279431\pi$
$269$	1.09719e11	1.27760	0.638800	+	0.769373i	$0.279431\pi$
$270$	−1.56108e11	−1.78767
$271$	−8.64910e10	−0.974112	−0.487056	−	0.873371i	$-0.661929\pi$
$271$	−8.64910e10	−0.974112	−0.487056	+	0.873371i	$0.661929\pi$
$272$	−2.96251e10	−0.328171
$273$	0	0
$274$	−5.80235e10	−0.621908
$275$	−2.06545e11	−2.17780
$276$	−9.82114e10	−1.01876
$277$	−7.77431e10	−0.793419	−0.396710	−	0.917944i	$-0.629848\pi$
$277$	−7.77431e10	−0.793419	−0.396710	+	0.917944i	$0.629848\pi$
$278$	−1.35783e10	−0.136347
$279$	−4.98430e10	−0.492476
$280$	2.74291e9	0.0266686
$281$	9.42110e10	0.901411	0.450706	−	0.892673i	$-0.351172\pi$
$281$	9.42110e10	0.901411	0.450706	+	0.892673i	$0.351172\pi$
$282$	4.62592e10	0.435589
$283$	−1.77969e11	−1.64932	−0.824661	−	0.565627i	$-0.808634\pi$
$283$	−1.77969e11	−1.64932	−0.824661	+	0.565627i	$0.808634\pi$
$284$	9.79946e9	0.0893860
$285$	−3.26354e11	−2.93013
$286$	0	0
$287$	1.56014e9	0.0135736
$288$	−4.10066e10	−0.351227
$289$	8.57557e10	0.723140
$290$	−9.70098e10	−0.805424
$291$	−1.77716e11	−1.45281
$292$	−1.00433e11	−0.808448
$293$	6.82054e10	0.540648	0.270324	−	0.962769i	$-0.412869\pi$
$293$	6.82054e10	0.540648	0.270324	+	0.962769i	$0.412869\pi$
$294$	1.56145e11	1.21889
$295$	−4.69376e10	−0.360846
$296$	3.28496e10	0.248724
$297$	−4.15961e11	−3.10205
$298$	−1.10023e11	−0.808181
$299$	0	0
$300$	1.45159e11	1.03466
$301$	−9.14658e9	−0.0642258
$302$	−1.19575e11	−0.827200
$303$	4.77888e10	0.325712
$304$	−4.25797e10	−0.285938
$305$	4.26571e10	0.282256
$306$	2.82849e11	1.84420
$307$	1.38459e11	0.889605	0.444803	−	0.895629i	$-0.353274\pi$
$307$	1.38459e11	0.889605	0.444803	+	0.895629i	$0.353274\pi$
$308$	7.30869e9	0.0462766
$309$	−1.21359e10	−0.0757286
$310$	4.22459e10	0.259811
$311$	−2.41824e11	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$311$	−2.41824e11	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$312$	0	0
$313$	2.23726e11	1.31755	0.658776	−	0.752339i	$-0.271075\pi$
$313$	2.23726e11	1.31755	0.658776	+	0.752339i	$0.271075\pi$
$314$	1.06660e11	0.619183
$315$	−2.61882e10	−0.149868
$316$	−3.41293e10	−0.192546
$317$	6.73120e10	0.374391	0.187196	−	0.982323i	$-0.440060\pi$
$317$	6.73120e10	0.374391	0.187196	+	0.982323i	$0.440060\pi$
$318$	1.46896e10	0.0805540
$319$	−2.58490e11	−1.39761
$320$	3.47564e10	0.185293
$321$	−8.79226e10	−0.462198
$322$	−8.18328e9	−0.0424205
$323$	2.93699e11	1.50138
$324$	9.52813e10	0.480347
$325$	0	0
$326$	2.38126e11	1.16769
$327$	−9.52907e10	−0.460878
$328$	1.97691e10	0.0943094
$329$	3.85446e9	0.0181377
$330$	7.09822e11	3.29486
$331$	−1.30577e10	−0.0597918	−0.0298959	−	0.999553i	$-0.509518\pi$
$331$	−1.30577e10	−0.0597918	−0.0298959	+	0.999553i	$0.509518\pi$
$332$	1.38463e11	0.625478
$333$	−3.13635e11	−1.39774
$334$	−1.57854e11	−0.694059
$335$	−3.37231e11	−1.46294
$336$	−5.13652e9	−0.0219858
$337$	9.86243e10	0.416533	0.208266	−	0.978072i	$-0.433218\pi$
$337$	9.86243e10	0.416533	0.208266	+	0.978072i	$0.433218\pi$
$338$	0	0
$339$	1.36502e10	0.0561360
$340$	−2.39737e11	−0.972927
$341$	1.12567e11	0.450835
$342$	4.06534e11	1.60686
$343$	2.60547e10	0.101640
$344$	−1.15899e11	−0.446240
$345$	−7.94762e11	−3.02031
$346$	−3.25230e11	−1.21997
$347$	−2.70738e11	−1.00246	−0.501229	−	0.865315i	$-0.667119\pi$
$347$	−2.70738e11	−1.00246	−0.501229	+	0.865315i	$0.667119\pi$
$348$	1.81665e11	0.663996
$349$	4.49289e11	1.62111	0.810553	−	0.585665i	$-0.199167\pi$
$349$	4.49289e11	1.62111	0.810553	+	0.585665i	$0.199167\pi$
$350$	1.20951e10	0.0430827
$351$	0	0
$352$	9.26110e10	0.321529
$353$	3.91119e11	1.34067	0.670337	−	0.742057i	$-0.266150\pi$
$353$	3.91119e11	1.34067	0.670337	+	0.742057i	$0.266150\pi$
$354$	8.78977e10	0.297484
$355$	7.93007e10	0.265002
$356$	−2.19992e11	−0.725909
$357$	3.54298e10	0.115442
$358$	1.46134e11	0.470195
$359$	4.82667e11	1.53364	0.766818	−	0.641865i	$-0.221839\pi$
$359$	4.82667e11	1.53364	0.766818	+	0.641865i	$0.221839\pi$
$360$	−3.31840e11	−1.04128
$361$	9.94411e10	0.308165
$362$	−4.12245e11	−1.26173
$363$	1.31965e12	3.98913
$364$	0	0
$365$	−8.12737e11	−2.39680
$366$	−7.98819e10	−0.232693
$367$	8.75496e9	0.0251917	0.0125958	−	0.999921i	$-0.495991\pi$
$367$	8.75496e9	0.0251917	0.0125958	+	0.999921i	$0.495991\pi$
$368$	−1.03693e11	−0.294737
$369$	−1.88748e11	−0.529984
$370$	2.65831e11	0.737391
$371$	1.22398e9	0.00335422
$372$	−7.91119e10	−0.214190
$373$	−2.44379e11	−0.653693	−0.326846	−	0.945077i	$-0.605986\pi$
$373$	−2.44379e11	−0.653693	−0.326846	+	0.945077i	$0.605986\pi$
$374$	−6.38797e11	−1.68827
$375$	1.93617e11	0.505594
$376$	4.88412e10	0.126021
$377$	0	0
$378$	2.43583e10	0.0613668
$379$	−9.92531e10	−0.247097	−0.123549	−	0.992339i	$-0.539427\pi$
$379$	−9.92531e10	−0.247097	−0.123549	+	0.992339i	$0.539427\pi$
$380$	−3.44570e11	−0.847718
$381$	6.36953e11	1.54862
$382$	2.38289e11	0.572558
$383$	−6.77313e11	−1.60840	−0.804202	−	0.594357i	$-0.797407\pi$
$383$	−6.77313e11	−1.60840	−0.804202	+	0.594357i	$0.797407\pi$
$384$	−6.50866e10	−0.152757
$385$	5.91445e10	0.137196
$386$	5.67505e10	0.130115
$387$	1.10656e12	2.50770
$388$	−1.87636e11	−0.420313
$389$	−8.14332e11	−1.80314	−0.901568	−	0.432637i	$-0.857583\pi$
$389$	−8.14332e11	−1.80314	−0.901568	+	0.432637i	$0.857583\pi$
$390$	0	0
$391$	7.15238e11	1.54759
$392$	1.64860e11	0.352638
$393$	1.25183e12	2.64714
$394$	2.77808e11	0.580781
$395$	−2.76186e11	−0.570841
$396$	−8.84213e11	−1.80688
$397$	5.08779e11	1.02795	0.513975	−	0.857805i	$-0.328173\pi$
$397$	5.08779e11	1.02795	0.513975	+	0.857805i	$0.328173\pi$
$398$	−6.02042e10	−0.120269
$399$	5.09227e10	0.100585
$400$	1.53261e11	0.299338
$401$	−5.16372e11	−0.997271	−0.498635	−	0.866812i	$-0.666165\pi$
$401$	−5.16372e11	−0.997271	−0.498635	+	0.866812i	$0.666165\pi$
$402$	6.31515e11	1.20605
$403$	0	0
$404$	5.04562e10	0.0942319
$405$	7.71050e11	1.42408
$406$	1.51369e10	0.0276484
$407$	7.08326e11	1.27955
$408$	4.48944e11	0.802087
$409$	2.62291e11	0.463478	0.231739	−	0.972778i	$-0.425558\pi$
$409$	2.62291e11	0.463478	0.231739	+	0.972778i	$0.425558\pi$
$410$	1.59979e11	0.279599
$411$	8.79296e11	1.52001
$412$	−1.28133e10	−0.0219091
$413$	7.32391e9	0.0123870
$414$	9.90022e11	1.65632
$415$	1.12049e12	1.85435
$416$	0	0
$417$	2.05768e11	0.333246
$418$	−9.18132e11	−1.47100
$419$	−3.20332e10	−0.0507736	−0.0253868	−	0.999678i	$-0.508082\pi$
$419$	−3.20332e10	−0.0507736	−0.0253868	+	0.999678i	$0.508082\pi$
$420$	−4.15665e10	−0.0651811
$421$	2.73798e10	0.0424777	0.0212389	−	0.999774i	$-0.493239\pi$
$421$	2.73798e10	0.0424777	0.0212389	+	0.999774i	$0.493239\pi$
$422$	6.92113e11	1.06236
$423$	−4.66317e11	−0.708189
$424$	1.55095e10	0.0233051
$425$	−1.05714e12	−1.57175
$426$	−1.48502e11	−0.218469
$427$	−6.65601e9	−0.00968921
$428$	−9.28301e10	−0.133719
$429$	0	0
$430$	−9.37900e11	−1.32297
$431$	3.23502e11	0.451574	0.225787	−	0.974177i	$-0.427505\pi$
$431$	3.23502e11	0.451574	0.225787	+	0.974177i	$0.427505\pi$
$432$	3.08652e11	0.426376
$433$	−8.59258e11	−1.17470	−0.587351	−	0.809332i	$-0.699829\pi$
$433$	−8.59258e11	−1.17470	−0.587351	+	0.809332i	$0.699829\pi$
$434$	−6.59184e9	−0.00891873
$435$	1.47010e12	1.96855
$436$	−1.00609e11	−0.133337
$437$	1.02800e12	1.34842
$438$	1.52197e12	1.97594
$439$	7.18588e11	0.923400	0.461700	−	0.887036i	$-0.347240\pi$
$439$	7.18588e11	0.923400	0.461700	+	0.887036i	$0.347240\pi$
$440$	7.49441e11	0.953236
$441$	−1.57402e12	−1.98170
$442$	0	0
$443$	2.12241e11	0.261826	0.130913	−	0.991394i	$-0.458209\pi$
$443$	2.12241e11	0.261826	0.130913	+	0.991394i	$0.458209\pi$
$444$	−4.97808e11	−0.607909
$445$	−1.78026e12	−2.15210
$446$	−5.25906e11	−0.629363
$447$	1.66730e12	1.97528
$448$	−5.42322e9	−0.00636071
$449$	8.97769e11	1.04245	0.521226	−	0.853419i	$-0.325475\pi$
$449$	8.97769e11	1.04245	0.521226	+	0.853419i	$0.325475\pi$
$450$	−1.46328e12	−1.68217
$451$	4.26275e11	0.485172
$452$	1.44121e10	0.0162407
$453$	1.81206e12	2.02177
$454$	1.10658e12	1.22245
$455$	0	0
$456$	6.45259e11	0.698863
$457$	−1.14101e12	−1.22367	−0.611837	−	0.790984i	$-0.709569\pi$
$457$	−1.14101e12	−1.22367	−0.611837	+	0.790984i	$0.709569\pi$
$458$	−5.39448e11	−0.572868
$459$	−2.12897e12	−2.23879
$460$	−8.39123e11	−0.873806
$461$	7.89279e11	0.813910	0.406955	−	0.913448i	$-0.366591\pi$
$461$	7.89279e11	0.813910	0.406955	+	0.913448i	$0.366591\pi$
$462$	−1.10757e11	−0.113105
$463$	7.23863e11	0.732052	0.366026	−	0.930605i	$-0.380718\pi$
$463$	7.23863e11	0.732052	0.366026	+	0.930605i	$0.380718\pi$
$464$	1.91805e11	0.192101
$465$	−6.40201e11	−0.635007
$466$	1.90327e11	0.186966
$467$	−6.62553e11	−0.644607	−0.322303	−	0.946636i	$-0.604457\pi$
$467$	−6.62553e11	−0.644607	−0.322303	+	0.946636i	$0.604457\pi$
$468$	0	0
$469$	5.26198e10	0.0502193
$470$	3.95241e11	0.373612
$471$	−1.61635e12	−1.51335
$472$	9.28039e10	0.0860651
$473$	−2.49910e12	−2.29567
$474$	5.17200e11	0.470604
$475$	−1.51941e12	−1.36947
$476$	3.74074e10	0.0333984
$477$	−1.48078e11	−0.130966
$478$	2.52645e11	0.221353
$479$	−2.25076e12	−1.95353	−0.976763	−	0.214320i	$-0.931246\pi$
$479$	−2.25076e12	−1.95353	−0.976763	+	0.214320i	$0.931246\pi$
$480$	−5.26704e11	−0.452878
$481$	0	0
$482$	3.53335e11	0.298178
$483$	1.24011e11	0.103680
$484$	1.39331e12	1.15410
$485$	−1.51842e12	−1.24610
$486$	3.92973e10	0.0319521
$487$	−4.78992e11	−0.385876	−0.192938	−	0.981211i	$-0.561802\pi$
$487$	−4.78992e11	−0.385876	−0.192938	+	0.981211i	$0.561802\pi$
$488$	−8.43406e10	−0.0673205
$489$	−3.60860e12	−2.85397
$490$	1.33411e12	1.04546
$491$	−1.43609e10	−0.0111510	−0.00557551	−	0.999984i	$-0.501775\pi$
$491$	−1.43609e10	−0.0111510	−0.00557551	+	0.999984i	$0.501775\pi$
$492$	−2.99584e11	−0.230503
$493$	−1.32300e12	−1.00867
$494$	0	0
$495$	−7.15537e12	−5.35684
$496$	−8.35276e10	−0.0619673
$497$	−1.23737e10	−0.00909694
$498$	−2.09829e12	−1.52874
$499$	−1.19092e11	−0.0859862	−0.0429931	−	0.999075i	$-0.513689\pi$
$499$	−1.19092e11	−0.0859862	−0.0429931	+	0.999075i	$0.513689\pi$
$500$	2.04424e11	0.146274
$501$	2.39214e12	1.69636
$502$	1.00766e12	0.708184
$503$	1.92943e12	1.34392	0.671960	−	0.740587i	$-0.265453\pi$
$503$	1.92943e12	1.34392	0.671960	+	0.740587i	$0.265453\pi$
$504$	5.17787e10	0.0357449
$505$	4.08309e11	0.279369
$506$	−2.23590e12	−1.51627
$507$	0	0
$508$	6.72506e11	0.448032
$509$	2.58236e12	1.70525	0.852624	−	0.522525i	$-0.175010\pi$
$509$	2.58236e12	1.70525	0.852624	+	0.522525i	$0.175010\pi$
$510$	3.63301e12	2.37794
$511$	1.26815e11	0.0822769
$512$	−6.87195e10	−0.0441942
$513$	−3.05994e12	−1.95067
$514$	5.67130e11	0.358384
$515$	−1.03690e11	−0.0649537
$516$	1.75636e12	1.09066
$517$	1.05315e12	0.648308
$518$	−4.14789e10	−0.0253130
$519$	4.92859e12	2.98174
$520$	0	0
$521$	−2.01270e12	−1.19676	−0.598382	−	0.801211i	$-0.704189\pi$
$521$	−2.01270e12	−1.19676	−0.598382	+	0.801211i	$0.704189\pi$
$522$	−1.83128e12	−1.07954
$523$	−2.41278e12	−1.41013	−0.705067	−	0.709141i	$-0.749083\pi$
$523$	−2.41278e12	−1.41013	−0.705067	+	0.709141i	$0.749083\pi$
$524$	1.32170e12	0.765846
$525$	−1.83291e11	−0.105299
$526$	−1.03571e12	−0.589933
$527$	5.76143e11	0.325374
$528$	−1.40344e12	−0.785853
$529$	7.02308e11	0.389922
$530$	1.25508e11	0.0690925
$531$	−8.86054e11	−0.483654
$532$	5.37650e10	0.0291003
$533$	0	0
$534$	3.33380e12	1.77420
$535$	−7.51214e11	−0.396435
$536$	6.66763e11	0.348923
$537$	−2.21454e12	−1.14921
$538$	−1.75550e12	−0.903400
$539$	3.55483e12	1.81413
$540$	2.49773e12	1.26408
$541$	1.72399e12	0.865260	0.432630	−	0.901572i	$-0.357586\pi$
$541$	1.72399e12	0.865260	0.432630	+	0.901572i	$0.357586\pi$
$542$	1.38386e12	0.688801
$543$	6.24723e12	3.08381
$544$	4.74002e11	0.232052
$545$	−8.14168e11	−0.395303
$546$	0	0
$547$	1.89229e12	0.903741	0.451870	−	0.892084i	$-0.350757\pi$
$547$	1.89229e12	0.903741	0.451870	+	0.892084i	$0.350757\pi$
$548$	9.28375e11	0.439755
$549$	8.05250e11	0.378317
$550$	3.30472e12	1.53994
$551$	−1.90153e12	−0.878863
$552$	1.57138e12	0.720371
$553$	4.30947e10	0.0195957
$554$	1.24389e12	0.561032
$555$	−4.02844e12	−1.80226
$556$	2.17253e11	0.0964116
$557$	−2.08244e11	−0.0916694	−0.0458347	−	0.998949i	$-0.514595\pi$
$557$	−2.08244e11	−0.0916694	−0.0458347	+	0.998949i	$0.514595\pi$
$558$	7.97488e11	0.348233
$559$	0	0
$560$	−4.38866e10	−0.0188576
$561$	9.68043e12	4.12631
$562$	−1.50738e12	−0.637394
$563$	1.52235e12	0.638597	0.319299	−	0.947654i	$-0.396553\pi$
$563$	1.52235e12	0.638597	0.319299	+	0.947654i	$0.396553\pi$
$564$	−7.40147e11	−0.308008
$565$	1.16628e11	0.0481488
$566$	2.84751e12	1.16625
$567$	−1.20311e11	−0.0488856
$568$	−1.56791e11	−0.0632054
$569$	−2.49853e12	−0.999261	−0.499631	−	0.866239i	$-0.666531\pi$
$569$	−2.49853e12	−0.999261	−0.499631	+	0.866239i	$0.666531\pi$
$570$	5.22167e12	2.07192
$571$	−1.73010e12	−0.681098	−0.340549	−	0.940227i	$-0.610613\pi$
$571$	−1.73010e12	−0.681098	−0.340549	+	0.940227i	$0.610613\pi$
$572$	0	0
$573$	−3.61108e12	−1.39940
$574$	−2.49623e10	−0.00959800
$575$	−3.70018e12	−1.41162
$576$	6.56106e11	0.248355
$577$	3.24966e12	1.22052	0.610262	−	0.792199i	$-0.291064\pi$
$577$	3.24966e12	1.22052	0.610262	+	0.792199i	$0.291064\pi$
$578$	−1.37209e12	−0.511337
$579$	−8.60006e11	−0.318015
$580$	1.55216e12	0.569521
$581$	−1.74836e11	−0.0636557
$582$	2.84346e12	1.02729
$583$	3.34426e11	0.119892
$584$	1.60692e12	0.571659
$585$	0	0
$586$	−1.09129e12	−0.382296
$587$	−2.11024e12	−0.733603	−0.366802	−	0.930299i	$-0.619547\pi$
$587$	−2.11024e12	−0.733603	−0.366802	+	0.930299i	$0.619547\pi$
$588$	−2.49832e12	−0.861886
$589$	8.28080e11	0.283500
$590$	7.51002e11	0.255157
$591$	−4.20995e12	−1.41949
$592$	−5.25594e11	−0.175874
$593$	2.79941e11	0.0929651	0.0464826	−	0.998919i	$-0.485199\pi$
$593$	2.79941e11	0.0929651	0.0464826	+	0.998919i	$0.485199\pi$
$594$	6.65537e12	2.19348
$595$	3.02714e11	0.0990162
$596$	1.76036e12	0.571470
$597$	9.12344e11	0.293951
$598$	0	0
$599$	−5.96835e11	−0.189423	−0.0947117	−	0.995505i	$-0.530193\pi$
$599$	−5.96835e11	−0.189423	−0.0947117	+	0.995505i	$0.530193\pi$
$600$	−2.32255e12	−0.731617
$601$	2.18920e11	0.0684465	0.0342232	−	0.999414i	$-0.489104\pi$
$601$	2.18920e11	0.0684465	0.0342232	+	0.999414i	$0.489104\pi$
$602$	1.46345e11	0.0454145
$603$	−6.36599e12	−1.96082
$604$	1.91321e12	0.584919
$605$	1.12751e13	3.42154
$606$	−7.64621e11	−0.230313
$607$	−4.54396e12	−1.35858	−0.679290	−	0.733870i	$-0.737712\pi$
$607$	−4.54396e12	−1.35858	−0.679290	+	0.733870i	$0.737712\pi$
$608$	6.81275e11	0.202188
$609$	−2.29387e11	−0.0675758
$610$	−6.82514e11	−0.199585
$611$	0	0
$612$	−4.52558e12	−1.30405
$613$	1.88769e12	0.539955	0.269978	−	0.962867i	$-0.412984\pi$
$613$	1.88769e12	0.539955	0.269978	+	0.962867i	$0.412984\pi$
$614$	−2.21534e12	−0.629046
$615$	−2.42434e12	−0.683370
$616$	−1.16939e11	−0.0327225
$617$	−4.37252e12	−1.21464	−0.607322	−	0.794456i	$-0.707756\pi$
$617$	−4.37252e12	−1.21464	−0.607322	+	0.794456i	$0.707756\pi$
$618$	1.94175e11	0.0535482
$619$	3.63885e11	0.0996221	0.0498111	−	0.998759i	$-0.484138\pi$
$619$	3.63885e11	0.0996221	0.0498111	+	0.998759i	$0.484138\pi$
$620$	−6.75935e11	−0.183714
$621$	−7.45178e12	−2.01070
$622$	3.86918e12	1.03648
$623$	2.77782e11	0.0738768
$624$	0	0
$625$	−2.91327e12	−0.763697
$626$	−3.57962e12	−0.931650
$627$	1.39135e13	3.59528
$628$	−1.70656e12	−0.437829
$629$	3.62536e12	0.923470
$630$	4.19012e11	0.105973
$631$	−5.15487e12	−1.29445	−0.647225	−	0.762299i	$-0.724071\pi$
$631$	−5.15487e12	−1.29445	−0.647225	+	0.762299i	$0.724071\pi$
$632$	5.46068e11	0.136151
$633$	−1.04884e13	−2.59652
$634$	−1.07699e12	−0.264734
$635$	5.44216e12	1.32828
$636$	−2.35033e11	−0.0569603
$637$	0	0
$638$	4.13583e12	0.988258
$639$	1.49698e12	0.355191
$640$	−5.56103e11	−0.131022
$641$	−4.21103e12	−0.985206	−0.492603	−	0.870254i	$-0.663955\pi$
$641$	−4.21103e12	−0.985206	−0.492603	+	0.870254i	$0.663955\pi$
$642$	1.40676e12	0.326823
$643$	−2.64608e12	−0.610454	−0.305227	−	0.952280i	$-0.598732\pi$
$643$	−2.64608e12	−0.610454	−0.305227	+	0.952280i	$0.598732\pi$
$644$	1.30932e11	0.0299958
$645$	1.42131e13	3.23347
$646$	−4.69919e12	−1.06164
$647$	−1.64583e12	−0.369246	−0.184623	−	0.982809i	$-0.559106\pi$
$647$	−1.64583e12	−0.369246	−0.184623	+	0.982809i	$0.559106\pi$
$648$	−1.52450e12	−0.339657
$649$	2.00110e12	0.442759
$650$	0	0
$651$	9.98938e10	0.0217984
$652$	−3.81002e12	−0.825682
$653$	−1.34152e12	−0.288727	−0.144363	−	0.989525i	$-0.546113\pi$
$653$	−1.34152e12	−0.288727	−0.144363	+	0.989525i	$0.546113\pi$
$654$	1.52465e12	0.325890
$655$	1.06957e13	2.27050
$656$	−3.16306e11	−0.0666868
$657$	−1.53423e13	−3.21252
$658$	−6.16714e10	−0.0128253
$659$	2.87415e12	0.593643	0.296822	−	0.954933i	$-0.404073\pi$
$659$	2.87415e12	0.593643	0.296822	+	0.954933i	$0.404073\pi$
$660$	−1.13571e13	−2.32982
$661$	−5.83418e12	−1.18870	−0.594351	−	0.804206i	$-0.702591\pi$
$661$	−5.83418e12	−1.18870	−0.594351	+	0.804206i	$0.702591\pi$
$662$	2.08923e11	0.0422792
$663$	0	0
$664$	−2.21541e12	−0.442279
$665$	4.35085e11	0.0862734
$666$	5.01816e12	0.988350
$667$	−4.63075e12	−0.905910
$668$	2.52566e12	0.490774
$669$	7.96965e12	1.53823
$670$	5.39569e12	1.03445
$671$	−1.81861e12	−0.346328
$672$	8.21842e10	0.0155463
$673$	3.05453e12	0.573953	0.286976	−	0.957938i	$-0.407350\pi$
$673$	3.05453e12	0.573953	0.286976	+	0.957938i	$0.407350\pi$
$674$	−1.57799e12	−0.294533
$675$	1.10139e13	2.04209
$676$	0	0
$677$	3.54962e12	0.649431	0.324715	−	0.945812i	$-0.394731\pi$
$677$	3.54962e12	0.649431	0.324715	+	0.945812i	$0.394731\pi$
$678$	−2.18404e11	−0.0396941
$679$	2.36926e11	0.0427758
$680$	3.83580e12	0.687963
$681$	−1.67693e13	−2.98781
$682$	−1.80108e12	−0.318789
$683$	−2.11804e12	−0.372427	−0.186214	−	0.982509i	$-0.559622\pi$
$683$	−2.11804e12	−0.372427	−0.186214	+	0.982509i	$0.559622\pi$
$684$	−6.50454e12	−1.13622
$685$	7.51275e12	1.30374
$686$	−4.16876e11	−0.0718701
$687$	8.17488e12	1.40015
$688$	1.85439e12	0.315539
$689$	0	0
$690$	1.27162e13	2.13568
$691$	−4.53146e12	−0.756113	−0.378056	−	0.925783i	$-0.623407\pi$
$691$	−4.53146e12	−0.756113	−0.378056	+	0.925783i	$0.623407\pi$
$692$	5.20368e12	0.862648
$693$	1.11649e12	0.183888
$694$	4.33180e12	0.708845
$695$	1.75809e12	0.285831
$696$	−2.90665e12	−0.469516
$697$	2.18176e12	0.350155
$698$	−7.18863e12	−1.14630
$699$	−2.88424e12	−0.456966
$700$	−1.93522e11	−0.0304641
$701$	−8.76423e12	−1.37083	−0.685413	−	0.728154i	$-0.740378\pi$
$701$	−8.76423e12	−1.37083	−0.685413	+	0.728154i	$0.740378\pi$
$702$	0	0
$703$	5.21066e12	0.804626
$704$	−1.48178e12	−0.227355
$705$	−5.98954e12	−0.913150
$706$	−6.25791e12	−0.947999
$707$	−6.37105e10	−0.00959012
$708$	−1.40636e12	−0.210353
$709$	1.22926e13	1.82699	0.913493	−	0.406855i	$-0.133375\pi$
$709$	1.22926e13	1.82699	0.913493	+	0.406855i	$0.133375\pi$
$710$	−1.26881e12	−0.187385
$711$	−5.21364e12	−0.765117
$712$	3.51988e12	0.513295
$713$	2.01660e12	0.292225
$714$	−5.66877e11	−0.0816295
$715$	0	0
$716$	−2.33815e12	−0.332478
$717$	−3.82861e12	−0.541010
$718$	−7.72267e12	−1.08444
$719$	1.36942e13	1.91098	0.955492	−	0.295018i	$-0.0953257\pi$
$719$	1.36942e13	1.91098	0.955492	+	0.295018i	$0.0953257\pi$
$720$	5.30945e12	0.736297
$721$	1.61792e10	0.00222972
$722$	−1.59106e12	−0.217906
$723$	−5.35449e12	−0.728779
$724$	6.59593e12	0.892180
$725$	6.84437e12	0.920052
$726$	−2.11144e13	−2.82074
$727$	−6.80422e12	−0.903386	−0.451693	−	0.892173i	$-0.649180\pi$
$727$	−6.80422e12	−0.903386	−0.451693	+	0.892173i	$0.649180\pi$
$728$	0	0
$729$	−7.92138e12	−1.03879
$730$	1.30038e13	1.69480
$731$	−1.27909e13	−1.65681
$732$	1.27811e12	0.164539
$733$	−1.07488e13	−1.37529	−0.687644	−	0.726048i	$-0.741355\pi$
$733$	−1.07488e13	−1.37529	−0.687644	+	0.726048i	$0.741355\pi$
$734$	−1.40079e11	−0.0178132
$735$	−2.02173e13	−2.55523
$736$	1.65909e12	0.208411
$737$	1.43772e13	1.79503
$738$	3.01996e12	0.374755
$739$	2.67055e12	0.329382	0.164691	−	0.986345i	$-0.447337\pi$
$739$	2.67055e12	0.329382	0.164691	+	0.986345i	$0.447337\pi$
$740$	−4.25329e12	−0.521414
$741$	0	0
$742$	−1.95837e10	−0.00237179
$743$	−1.70018e12	−0.204666	−0.102333	−	0.994750i	$-0.532631\pi$
$743$	−1.70018e12	−0.204666	−0.102333	+	0.994750i	$0.532631\pi$
$744$	1.26579e12	0.151455
$745$	1.42455e13	1.69424
$746$	3.91006e12	0.462231
$747$	2.11518e13	2.48545
$748$	1.02208e13	1.19378
$749$	1.17216e11	0.0136087
$750$	−3.09787e12	−0.357509
$751$	7.55427e12	0.866588	0.433294	−	0.901253i	$-0.357351\pi$
$751$	7.55427e12	0.866588	0.433294	+	0.901253i	$0.357351\pi$
$752$	−7.81460e11	−0.0891100
$753$	−1.52702e13	−1.73088
$754$	0	0
$755$	1.54823e13	1.73411
$756$	−3.89733e11	−0.0433929
$757$	−5.47470e12	−0.605939	−0.302970	−	0.953000i	$-0.597978\pi$
$757$	−5.47470e12	−0.605939	−0.302970	+	0.953000i	$0.597978\pi$
$758$	1.58805e12	0.174724
$759$	3.38832e13	3.70592
$760$	5.51312e12	0.599427
$761$	−2.70489e12	−0.292361	−0.146180	−	0.989258i	$-0.546698\pi$
$761$	−2.70489e12	−0.292361	−0.146180	+	0.989258i	$0.546698\pi$
$762$	−1.01913e13	−1.09504
$763$	1.27039e11	0.0135699
$764$	−3.81263e12	−0.404860
$765$	−3.66226e13	−3.86610
$766$	1.08370e13	1.13731
$767$	0	0
$768$	1.04139e12	0.108015
$769$	−1.13975e13	−1.17528	−0.587640	−	0.809123i	$-0.699943\pi$
$769$	−1.13975e13	−1.17528	−0.587640	+	0.809123i	$0.699943\pi$
$770$	−9.46312e11	−0.0970122
$771$	−8.59438e12	−0.875931
$772$	−9.08008e11	−0.0920051
$773$	4.56053e12	0.459417	0.229709	−	0.973259i	$-0.426223\pi$
$773$	4.56053e12	0.459417	0.229709	+	0.973259i	$0.426223\pi$
$774$	−1.77050e13	−1.77322
$775$	−2.98059e12	−0.296787
$776$	3.00217e12	0.297206
$777$	6.28578e11	0.0618678
$778$	1.30293e13	1.27501
$779$	3.13581e12	0.305092
$780$	0	0
$781$	−3.38084e12	−0.325158
$782$	−1.14438e13	−1.09431
$783$	1.37838e13	1.31052
$784$	−2.63777e12	−0.249353
$785$	−1.38101e13	−1.29803
$786$	−2.00292e13	−1.87181
$787$	−1.13068e13	−1.05064	−0.525318	−	0.850906i	$-0.676054\pi$
$787$	−1.13068e13	−1.05064	−0.525318	+	0.850906i	$0.676054\pi$
$788$	−4.44493e12	−0.410674
$789$	1.56953e13	1.44186
$790$	4.41898e12	0.403645
$791$	−1.81981e10	−0.00165284
$792$	1.41474e13	1.27765
$793$	0	0
$794$	−8.14046e12	−0.726870
$795$	−1.90197e12	−0.168870
$796$	9.63268e11	0.0850429
$797$	2.07792e13	1.82418	0.912088	−	0.409994i	$-0.134469\pi$
$797$	2.07792e13	1.82418	0.912088	+	0.409994i	$0.134469\pi$
$798$	−8.14763e11	−0.0711243
$799$	5.39023e12	0.467893
$800$	−2.45218e12	−0.211664
$801$	−3.36064e13	−2.88453
$802$	8.26195e12	0.705177
$803$	3.46496e13	2.94088
$804$	−1.01042e13	−0.852808
$805$	1.05955e12	0.0889285
$806$	0	0
$807$	2.66031e13	2.20801
$808$	−8.07299e11	−0.0666320
$809$	1.62520e13	1.33395	0.666974	−	0.745081i	$-0.267589\pi$
$809$	1.62520e13	1.33395	0.666974	+	0.745081i	$0.267589\pi$
$810$	−1.23368e13	−1.00698
$811$	−1.58175e13	−1.28394	−0.641969	−	0.766730i	$-0.721882\pi$
$811$	−1.58175e13	−1.28394	−0.641969	+	0.766730i	$0.721882\pi$
$812$	−2.42191e11	−0.0195504
$813$	−2.09712e13	−1.68351
$814$	−1.13332e13	−0.904780
$815$	−3.08320e13	−2.44790
$816$	−7.18310e12	−0.567161
$817$	−1.83842e13	−1.44359
$818$	−4.19666e12	−0.327728
$819$	0	0
$820$	−2.55966e12	−0.197706
$821$	2.02338e13	1.55430	0.777149	−	0.629317i	$-0.216665\pi$
$821$	2.02338e13	1.55430	0.777149	+	0.629317i	$0.216665\pi$
$822$	−1.40687e13	−1.07481
$823$	1.31293e13	0.997565	0.498782	−	0.866727i	$-0.333781\pi$
$823$	1.31293e13	0.997565	0.498782	+	0.866727i	$0.333781\pi$
$824$	2.05013e11	0.0154920
$825$	−5.00803e13	−3.76378
$826$	−1.17183e11	−0.00875897
$827$	6.91456e12	0.514032	0.257016	−	0.966407i	$-0.417261\pi$
$827$	6.91456e12	0.514032	0.257016	+	0.966407i	$0.417261\pi$
$828$	−1.58403e13	−1.17119
$829$	−2.56314e13	−1.88485	−0.942426	−	0.334414i	$-0.891462\pi$
$829$	−2.56314e13	−1.88485	−0.942426	+	0.334414i	$0.891462\pi$
$830$	−1.79278e13	−1.31122
$831$	−1.88501e13	−1.37122
$832$	0	0
$833$	1.81944e13	1.30929
$834$	−3.29228e12	−0.235641
$835$	2.04386e13	1.45500
$836$	1.46901e13	1.04015
$837$	−6.00261e12	−0.422742
$838$	5.12532e11	0.0359023
$839$	9.91399e12	0.690748	0.345374	−	0.938465i	$-0.387752\pi$
$839$	9.91399e12	0.690748	0.345374	+	0.938465i	$0.387752\pi$
$840$	6.65064e11	0.0460900
$841$	−5.94148e12	−0.409555
$842$	−4.38077e11	−0.0300363
$843$	2.28430e13	1.55786
$844$	−1.10738e13	−0.751201
$845$	0	0
$846$	7.46107e12	0.500765
$847$	−1.75931e12	−0.117454
$848$	−2.48152e11	−0.0164792
$849$	−4.31515e13	−2.85044
$850$	1.69143e13	1.11139
$851$	1.26894e13	0.829388
$852$	2.37604e12	0.154481
$853$	−1.42759e13	−0.923280	−0.461640	−	0.887067i	$-0.652739\pi$
$853$	−1.42759e13	−0.923280	−0.461640	+	0.887067i	$0.652739\pi$
$854$	1.06496e11	0.00685130
$855$	−5.26371e13	−3.36856
$856$	1.48528e12	0.0945534
$857$	2.99825e12	0.189869	0.0949344	−	0.995484i	$-0.469736\pi$
$857$	2.99825e12	0.189869	0.0949344	+	0.995484i	$0.469736\pi$
$858$	0	0
$859$	7.23194e12	0.453196	0.226598	−	0.973988i	$-0.427240\pi$
$859$	7.23194e12	0.453196	0.226598	+	0.973988i	$0.427240\pi$
$860$	1.50064e13	0.935478
$861$	3.78282e11	0.0234586
$862$	−5.17603e12	−0.319311
$863$	2.46804e13	1.51462	0.757311	−	0.653054i	$-0.226513\pi$
$863$	2.46804e13	1.51462	0.757311	+	0.653054i	$0.226513\pi$
$864$	−4.93844e12	−0.301493
$865$	4.21101e13	2.55749
$866$	1.37481e13	0.830640
$867$	2.07929e13	1.24977
$868$	1.05470e11	0.00630650
$869$	1.17747e13	0.700423
$870$	−2.35216e13	−1.39197
$871$	0	0
$872$	1.60975e12	0.0942833
$873$	−2.86635e13	−1.67019
$874$	−1.64480e13	−0.953480
$875$	−2.58124e11	−0.0148865
$876$	−2.43516e13	−1.39720
$877$	−8.23060e12	−0.469822	−0.234911	−	0.972017i	$-0.575480\pi$
$877$	−8.23060e12	−0.469822	−0.234911	+	0.972017i	$0.575480\pi$
$878$	−1.14974e13	−0.652942
$879$	1.65375e13	0.934373
$880$	−1.19911e13	−0.674040
$881$	1.17358e13	0.656330	0.328165	−	0.944620i	$-0.393570\pi$
$881$	1.17358e13	0.656330	0.328165	+	0.944620i	$0.393570\pi$
$882$	2.51843e13	1.40127
$883$	−1.84130e13	−1.01930	−0.509649	−	0.860382i	$-0.670225\pi$
$883$	−1.84130e13	−1.01930	−0.509649	+	0.860382i	$0.670225\pi$
$884$	0	0
$885$	−1.13808e13	−0.623632
$886$	−3.39586e12	−0.185139
$887$	−2.39771e13	−1.30059	−0.650294	−	0.759682i	$-0.725354\pi$
$887$	−2.39771e13	−1.30059	−0.650294	+	0.759682i	$0.725354\pi$
$888$	7.96493e12	0.429857
$889$	−8.49167e11	−0.0455969
$890$	2.84841e13	1.52176
$891$	−3.28723e13	−1.74735
$892$	8.41449e12	0.445027
$893$	7.74728e12	0.407678
$894$	−2.66768e13	−1.39674
$895$	−1.89211e13	−0.985697
$896$	8.67715e10	0.00449770
$897$	0	0
$898$	−1.43643e13	−0.737125
$899$	−3.73019e12	−0.190464
$900$	2.34124e13	1.18948
$901$	1.71166e12	0.0865279
$902$	−6.82040e12	−0.343068
$903$	−2.21774e12	−0.110998
$904$	−2.30594e11	−0.0114839
$905$	5.33766e13	2.64504
$906$	−2.89930e13	−1.42961
$907$	−5.21702e12	−0.255971	−0.127985	−	0.991776i	$-0.540851\pi$
$907$	−5.21702e12	−0.255971	−0.127985	+	0.991776i	$0.540851\pi$
$908$	−1.77053e13	−0.864404
$909$	7.70777e12	0.374448
$910$	0	0
$911$	−2.45077e13	−1.17888	−0.589441	−	0.807811i	$-0.700652\pi$
$911$	−2.45077e13	−1.17888	−0.589441	+	0.807811i	$0.700652\pi$
$912$	−1.03241e13	−0.494171
$913$	−4.77701e13	−2.27529
$914$	1.82561e13	0.865268
$915$	1.03429e13	0.487807
$916$	8.63117e12	0.405079
$917$	−1.66890e12	−0.0779413
$918$	3.40636e13	1.58306
$919$	−2.88261e13	−1.33311	−0.666554	−	0.745456i	$-0.732232\pi$
$919$	−2.88261e13	−1.33311	−0.666554	+	0.745456i	$0.732232\pi$
$920$	1.34260e13	0.617874
$921$	3.35716e13	1.53746
$922$	−1.26285e13	−0.575521
$923$	0	0
$924$	1.77211e12	0.0799774
$925$	−1.87553e13	−0.842336
$926$	−1.15818e13	−0.517639
$927$	−1.95738e12	−0.0870596
$928$	−3.06888e12	−0.135836
$929$	1.24962e13	0.550435	0.275218	−	0.961382i	$-0.411250\pi$
$929$	1.24962e13	0.550435	0.275218	+	0.961382i	$0.411250\pi$
$930$	1.02432e13	0.449018
$931$	2.61504e13	1.14079
$932$	−3.04522e12	−0.132205
$933$	−5.86342e13	−2.53328
$934$	1.06009e13	0.455806
$935$	8.27100e13	3.53921
$936$	0	0
$937$	4.48550e13	1.90100	0.950501	−	0.310722i	$-0.100571\pi$
$937$	4.48550e13	1.90100	0.950501	+	0.310722i	$0.100571\pi$
$938$	−8.41916e11	−0.0355104
$939$	5.42461e13	2.27706
$940$	−6.32385e12	−0.264184
$941$	2.65409e13	1.10348	0.551738	−	0.834017i	$-0.313965\pi$
$941$	2.65409e13	1.10348	0.551738	+	0.834017i	$0.313965\pi$
$942$	2.58615e13	1.07010
$943$	7.63656e12	0.314481
$944$	−1.48486e12	−0.0608572
$945$	−3.15386e12	−0.128647
$946$	3.99856e13	1.62328
$947$	−2.62042e13	−1.05875	−0.529377	−	0.848387i	$-0.677574\pi$
$947$	−2.62042e13	−1.05875	−0.529377	+	0.848387i	$0.677574\pi$
$948$	−8.27520e12	−0.332768
$949$	0	0
$950$	2.43106e13	0.968364
$951$	1.63209e13	0.647041
$952$	−5.98518e11	−0.0236163
$953$	2.20756e13	0.866950	0.433475	−	0.901166i	$-0.357287\pi$
$953$	2.20756e13	0.866950	0.433475	+	0.901166i	$0.357287\pi$
$954$	2.36925e12	0.0926070
$955$	−3.08532e13	−1.20029
$956$	−4.04231e12	−0.156520
$957$	−6.26751e13	−2.41541
$958$	3.60122e13	1.38135
$959$	−1.17225e12	−0.0447545
$960$	8.42726e12	0.320233
$961$	−2.48152e13	−0.938561
$962$	0	0
$963$	−1.41809e13	−0.531355
$964$	−5.65336e12	−0.210843
$965$	−7.34793e12	−0.272767
$966$	−1.98417e12	−0.0733132
$967$	−1.80518e13	−0.663898	−0.331949	−	0.943297i	$-0.607706\pi$
$967$	−1.80518e13	−0.663898	−0.331949	+	0.943297i	$0.607706\pi$
$968$	−2.22929e13	−0.816070
$969$	7.12122e13	2.59476
$970$	2.42946e13	0.881126
$971$	−1.61183e13	−0.581879	−0.290940	−	0.956741i	$-0.593968\pi$
$971$	−1.61183e13	−0.581879	−0.290940	+	0.956741i	$0.593968\pi$
$972$	−6.28757e11	−0.0225936
$973$	−2.74323e11	−0.00981194
$974$	7.66387e12	0.272856
$975$	0	0
$976$	1.34945e12	0.0476028
$977$	3.09179e13	1.08564	0.542818	−	0.839850i	$-0.317357\pi$
$977$	3.09179e13	1.08564	0.542818	+	0.839850i	$0.317357\pi$
$978$	5.77376e13	2.01806
$979$	7.58979e13	2.64063
$980$	−2.13457e13	−0.739255
$981$	−1.53693e13	−0.529837
$982$	2.29774e11	0.00788496
$983$	−1.01227e13	−0.345784	−0.172892	−	0.984941i	$-0.555311\pi$
$983$	−1.01227e13	−0.345784	−0.172892	+	0.984941i	$0.555311\pi$
$984$	4.79335e12	0.162990
$985$	−3.59700e13	−1.21752
$986$	2.11681e13	0.713239
$987$	9.34577e11	0.0313464
$988$	0	0
$989$	−4.47705e13	−1.48802
$990$	1.14486e14	3.78786
$991$	7.78955e12	0.256555	0.128278	−	0.991738i	$-0.459055\pi$
$991$	7.78955e12	0.256555	0.128278	+	0.991738i	$0.459055\pi$
$992$	1.33644e12	0.0438175
$993$	−3.16606e12	−0.103335
$994$	1.97979e11	0.00643251
$995$	7.79511e12	0.252126
$996$	3.35726e13	1.08098
$997$	4.46662e12	0.143170	0.0715849	−	0.997435i	$-0.477194\pi$
$997$	4.46662e12	0.143170	0.0715849	+	0.997435i	$0.477194\pi$
$998$	1.90547e12	0.0608014
$999$	−3.77712e13	−1.19982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.k.1.6		6
13.4	even	6		26.10.c.b.3.1	✓	12
13.10	even	6		26.10.c.b.9.1	yes	12
13.12	even	2		338.10.a.l.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.c.b.3.1	✓	12	13.4	even	6
26.10.c.b.9.1	yes	12	13.10	even	6
338.10.a.k.1.6		6	1.1	even	1	trivial
338.10.a.l.1.6		6	13.12	even	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +242.466 q^{3} +256.000 q^{4} +2071.64 q^{5} -3879.46 q^{6} -323.249 q^{7} -4096.00 q^{8} +39107.0 q^{9} -33146.3 q^{10} -88320.7 q^{11} +62071.4 q^{12} +5171.98 q^{14} +502304. q^{15} +65536.0 q^{16} -452044. q^{17} -625712. q^{18} -649714. q^{19} +530341. q^{20} -78377.0 q^{21} +1.41313e6 q^{22} -1.58223e6 q^{23} -993143. q^{24} +2.33858e6 q^{25} +4.70966e6 q^{27} -82751.7 q^{28} +2.92672e6 q^{29} -8.03686e6 q^{30} -1.27453e6 q^{31} -1.04858e6 q^{32} -2.14148e7 q^{33} +7.23270e6 q^{34} -669656. q^{35} +1.00114e7 q^{36} -8.01993e6 q^{37} +1.03954e7 q^{38} -8.48545e6 q^{40} -4.82644e6 q^{41} +1.25403e6 q^{42} +2.82958e7 q^{43} -2.26101e7 q^{44} +8.10157e7 q^{45} +2.53157e7 q^{46} -1.19241e7 q^{47} +1.58903e7 q^{48} -4.02491e7 q^{49} -3.74173e7 q^{50} -1.09605e8 q^{51} -3.78650e6 q^{53} -7.53546e7 q^{54} -1.82969e8 q^{55} +1.32403e6 q^{56} -1.57534e8 q^{57} -4.68275e7 q^{58} -2.26572e7 q^{59} +1.28590e8 q^{60} +2.05910e7 q^{61} +2.03925e7 q^{62} -1.26413e7 q^{63} +1.67772e7 q^{64} +3.42637e8 q^{66} -1.62784e8 q^{67} -1.15723e8 q^{68} -3.83638e8 q^{69} +1.07145e7 q^{70} +3.82791e7 q^{71} -1.60182e8 q^{72} -3.92315e8 q^{73} +1.28319e8 q^{74} +5.67028e8 q^{75} -1.66327e8 q^{76} +2.85496e7 q^{77} -1.33317e8 q^{79} +1.35767e8 q^{80} +3.72193e8 q^{81} +7.72231e7 q^{82} +5.40870e8 q^{83} -2.00645e7 q^{84} -9.36473e8 q^{85} -4.52732e8 q^{86} +7.09631e8 q^{87} +3.61762e8 q^{88} -8.59345e8 q^{89} -1.29625e9 q^{90} -4.05052e8 q^{92} -3.09031e8 q^{93} +1.90786e8 q^{94} -1.34598e9 q^{95} -2.54244e8 q^{96} -7.32952e8 q^{97} +6.43986e8 q^{98} -3.45396e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 96 q^{2} + 81 q^{3} + 1536 q^{4} - 1693 q^{5} - 1296 q^{6} - 473 q^{7} - 24576 q^{8} + 69813 q^{9} + 27088 q^{10} - 14011 q^{11} + 20736 q^{12} + 7568 q^{14} + 294780 q^{15} + 393216 q^{16} - 173558 q^{17}+ \cdots + 881769510 q^{99}+O(q^{100}) \) 6 * q - 96 * q^2 + 81 * q^3 + 1536 * q^4 - 1693 * q^5 - 1296 * q^6 - 473 * q^7 - 24576 * q^8 + 69813 * q^9 + 27088 * q^10 - 14011 * q^11 + 20736 * q^12 + 7568 * q^14 + 294780 * q^15 + 393216 * q^16 - 173558 * q^17 - 1117008 * q^18 - 322367 * q^19 - 433408 * q^20 - 2256885 * q^21 + 224176 * q^22 - 1644771 * q^23 - 331776 * q^24 + 2687569 * q^25 - 922995 * q^27 - 121088 * q^28 + 10801236 * q^29 - 4716480 * q^30 - 10435122 * q^31 - 6291456 * q^32 - 26201763 * q^33 + 2776928 * q^34 + 2168950 * q^35 + 17872128 * q^36 + 15710464 * q^37 + 5157872 * q^38 + 6934528 * q^40 + 1525478 * q^41 + 36110160 * q^42 + 50959661 * q^43 - 3586816 * q^44 - 18619731 * q^45 + 26316336 * q^46 - 68156998 * q^47 + 5308416 * q^48 + 162536361 * q^49 - 43001104 * q^50 - 84678981 * q^51 + 72278209 * q^53 + 14767920 * q^54 - 353372330 * q^55 + 1937408 * q^56 - 17951025 * q^57 - 172819776 * q^58 + 5665291 * q^59 + 75463680 * q^60 - 353387956 * q^61 + 166961952 * q^62 + 224088894 * q^63 + 100663296 * q^64 + 419228208 * q^66 - 371115369 * q^67 - 44430848 * q^68 + 280317279 * q^69 - 34703200 * q^70 - 156688763 * q^71 - 285954048 * q^72 - 466401663 * q^73 - 251367424 * q^74 + 1149481845 * q^75 - 82525952 * q^76 + 312460333 * q^77 + 162543480 * q^79 - 110952448 * q^80 + 295496586 * q^81 - 24407648 * q^82 + 435114576 * q^83 - 577762560 * q^84 - 2307296767 * q^85 - 815354576 * q^86 - 617376057 * q^87 + 57389056 * q^88 - 163315063 * q^89 + 297915696 * q^90 - 421061376 * q^92 - 2056270836 * q^93 + 1090511968 * q^94 - 537110948 * q^95 - 84934656 * q^96 + 1500514705 * q^97 - 2600581776 * q^98 + 881769510 * q^99

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