LMFDB - Embedded newform 15.8.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [15,8,Mod(1,15)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("15.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	15.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,7] 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:	$4.68577538226$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{601}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 150 $ x^2 - x - 150
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-11.7577$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+15.7577 q^{2} +27.0000 q^{3} +120.304 q^{4} +125.000 q^{5} +425.457 q^{6} -34.4284 q^{7} -121.278 q^{8} +729.000 q^{9} +1969.71 q^{10} -3963.55 q^{11} +3248.20 q^{12} +5606.30 q^{13} -542.511 q^{14} +3375.00 q^{15} -17309.9 q^{16} -19906.7 q^{17} +11487.3 q^{18} -49993.7 q^{19} +15037.9 q^{20} -929.568 q^{21} -62456.2 q^{22} +109762. q^{23} -3274.50 q^{24} +15625.0 q^{25} +88342.2 q^{26} +19683.0 q^{27} -4141.86 q^{28} +192477. q^{29} +53182.1 q^{30} +125541. q^{31} -257240. q^{32} -107016. q^{33} -313683. q^{34} -4303.55 q^{35} +87701.3 q^{36} -74353.6 q^{37} -787784. q^{38} +151370. q^{39} -15159.7 q^{40} +577802. q^{41} -14647.8 q^{42} +264291. q^{43} -476829. q^{44} +91125.0 q^{45} +1.72959e6 q^{46} -306207. q^{47} -467368. q^{48} -822358. q^{49} +246213. q^{50} -537481. q^{51} +674458. q^{52} -446219. q^{53} +310158. q^{54} -495444. q^{55} +4175.41 q^{56} -1.34983e6 q^{57} +3.03299e6 q^{58} +1.97951e6 q^{59} +406024. q^{60} -1.27494e6 q^{61} +1.97824e6 q^{62} -25098.3 q^{63} -1.83783e6 q^{64} +700788. q^{65} -1.68632e6 q^{66} -4.12943e6 q^{67} -2.39485e6 q^{68} +2.96357e6 q^{69} -67813.9 q^{70} -2.81187e6 q^{71} -88411.6 q^{72} +4.01991e6 q^{73} -1.17164e6 q^{74} +421875. q^{75} -6.01442e6 q^{76} +136459. q^{77} +2.38524e6 q^{78} -1.32785e6 q^{79} -2.16374e6 q^{80} +531441. q^{81} +9.10480e6 q^{82} -1.91033e6 q^{83} -111830. q^{84} -2.48834e6 q^{85} +4.16460e6 q^{86} +5.19689e6 q^{87} +480691. q^{88} +8.00695e6 q^{89} +1.43592e6 q^{90} -193016. q^{91} +1.32047e7 q^{92} +3.38962e6 q^{93} -4.82511e6 q^{94} -6.24922e6 q^{95} -6.94548e6 q^{96} -3.89241e6 q^{97} -1.29584e7 q^{98} -2.88943e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 7 q^{2} + 54 q^{3} + 69 q^{4} + 250 q^{5} + 189 q^{6} + 1304 q^{7} + 1449 q^{8} + 1458 q^{9} + 875 q^{10} + 3448 q^{11} + 1863 q^{12} - 8988 q^{13} - 12264 q^{14} + 6750 q^{15} - 24495 q^{16} - 5492 q^{17}+ \cdots + 2513592 q^{99}+O(q^{100}) $ 2 * q + 7 * q^2 + 54 * q^3 + 69 * q^4 + 250 * q^5 + 189 * q^6 + 1304 * q^7 + 1449 * q^8 + 1458 * q^9 + 875 * q^10 + 3448 * q^11 + 1863 * q^12 - 8988 * q^13 - 12264 * q^14 + 6750 * q^15 - 24495 * q^16 - 5492 * q^17 + 5103 * q^18 - 49584 * q^19 + 8625 * q^20 + 35208 * q^21 - 127364 * q^22 + 91848 * q^23 + 39123 * q^24 + 31250 * q^25 + 216154 * q^26 + 39366 * q^27 - 72808 * q^28 + 181772 * q^29 + 23625 * q^30 + 304232 * q^31 - 395311 * q^32 + 93096 * q^33 - 439922 * q^34 + 163000 * q^35 + 50301 * q^36 - 502316 * q^37 - 791372 * q^38 - 242676 * q^39 + 181125 * q^40 + 631172 * q^41 - 331128 * q^42 + 353640 * q^43 - 857068 * q^44 + 182250 * q^45 + 1886472 * q^46 - 467480 * q^47 - 661365 * q^48 + 145490 * q^49 + 109375 * q^50 - 148284 * q^51 + 1423198 * q^52 - 568052 * q^53 + 137781 * q^54 + 431000 * q^55 + 2105880 * q^56 - 1338768 * q^57 + 3126746 * q^58 + 287224 * q^59 + 232875 * q^60 - 2514180 * q^61 + 413328 * q^62 + 950616 * q^63 + 291041 * q^64 - 1123500 * q^65 - 3438828 * q^66 - 5073832 * q^67 - 3134374 * q^68 + 2479896 * q^69 - 1533000 * q^70 - 3748816 * q^71 + 1056321 * q^72 - 1477212 * q^73 + 2576306 * q^74 + 843750 * q^75 - 6035444 * q^76 + 10056288 * q^77 + 5836158 * q^78 - 4627720 * q^79 - 3061875 * q^80 + 1062882 * q^81 + 8637398 * q^82 - 6072936 * q^83 - 1965816 * q^84 - 686500 * q^85 + 3382108 * q^86 + 4907844 * q^87 + 12118884 * q^88 + 16516356 * q^89 + 637875 * q^90 - 19726448 * q^91 + 14123784 * q^92 + 8214264 * q^93 - 3412736 * q^94 - 6198000 * q^95 - 10673397 * q^96 + 2723428 * q^97 - 21434497 * q^98 + 2513592 * 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 $

$2$	15.7577	1.39279	0.696396	−	0.717657i	$-0.254786\pi$
$2$	15.7577	1.39279	0.696396	+	0.717657i	$0.254786\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	120.304	0.939872
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	425.457	0.804129
$7$	−34.4284	−0.0379380	−0.0189690	−	0.999820i	$-0.506038\pi$
$7$	−34.4284	−0.0379380	−0.0189690	+	0.999820i	$0.506038\pi$
$8$	−121.278	−0.0837465
$9$	729.000	0.333333
$10$	1969.71	0.622876
$11$	−3963.55	−0.897863	−0.448931	−	0.893566i	$-0.648195\pi$
$11$	−3963.55	−0.897863	−0.448931	+	0.893566i	$0.648195\pi$
$12$	3248.20	0.542635
$13$	5606.30	0.707742	0.353871	−	0.935294i	$-0.384865\pi$
$13$	5606.30	0.707742	0.353871	+	0.935294i	$0.384865\pi$
$14$	−542.511	−0.0528397
$15$	3375.00	0.258199
$16$	−17309.9	−1.05651
$17$	−19906.7	−0.982717	−0.491358	−	0.870958i	$-0.663499\pi$
$17$	−19906.7	−0.982717	−0.491358	+	0.870958i	$0.663499\pi$
$18$	11487.3	0.464264
$19$	−49993.7	−1.67216	−0.836080	−	0.548607i	$-0.815158\pi$
$19$	−49993.7	−1.67216	−0.836080	+	0.548607i	$0.815158\pi$
$20$	15037.9	0.420323
$21$	−929.568	−0.0219035
$22$	−62456.2	−1.25054
$23$	109762.	1.88107	0.940533	−	0.339703i	$-0.110326\pi$
$23$	109762.	1.88107	0.940533	+	0.339703i	$0.110326\pi$
$24$	−3274.50	−0.0483511
$25$	15625.0	0.200000
$26$	88342.2	0.985738
$27$	19683.0	0.192450
$28$	−4141.86	−0.0356568
$29$	192477.	1.46550	0.732752	−	0.680496i	$-0.238236\pi$
$29$	192477.	1.46550	0.732752	+	0.680496i	$0.238236\pi$
$30$	53182.1	0.359618
$31$	125541.	0.756870	0.378435	−	0.925628i	$-0.376462\pi$
$31$	125541.	0.756870	0.378435	+	0.925628i	$0.376462\pi$
$32$	−257240.	−1.38776
$33$	−107016.	−0.518381
$34$	−313683.	−1.36872
$35$	−4303.55	−0.0169664
$36$	87701.3	0.313291
$37$	−74353.6	−0.241322	−0.120661	−	0.992694i	$-0.538501\pi$
$37$	−74353.6	−0.241322	−0.120661	+	0.992694i	$0.538501\pi$
$38$	−787784.	−2.32897
$39$	151370.	0.408615
$40$	−15159.7	−0.0374526
$41$	577802.	1.30929	0.654644	−	0.755937i	$-0.272818\pi$
$41$	577802.	1.30929	0.654644	+	0.755937i	$0.272818\pi$
$42$	−14647.8	−0.0305070
$43$	264291.	0.506923	0.253462	−	0.967345i	$-0.418431\pi$
$43$	264291.	0.506923	0.253462	+	0.967345i	$0.418431\pi$
$44$	−476829.	−0.843876
$45$	91125.0	0.149071
$46$	1.72959e6	2.61993
$47$	−306207.	−0.430203	−0.215101	−	0.976592i	$-0.569008\pi$
$47$	−306207.	−0.430203	−0.215101	+	0.976592i	$0.569008\pi$
$48$	−467368.	−0.609978
$49$	−822358.	−0.998561
$50$	246213.	0.278559
$51$	−537481.	−0.567372
$52$	674458.	0.665186
$53$	−446219.	−0.411702	−0.205851	−	0.978583i	$-0.565996\pi$
$53$	−446219.	−0.411702	−0.205851	+	0.978583i	$0.565996\pi$
$54$	310158.	0.268043
$55$	−495444.	−0.401536
$56$	4175.41	0.00317717
$57$	−1.34983e6	−0.965422
$58$	3.03299e6	2.04114
$59$	1.97951e6	1.25481	0.627403	−	0.778695i	$-0.284118\pi$
$59$	1.97951e6	1.25481	0.627403	+	0.778695i	$0.284118\pi$
$60$	406024.	0.242674
$61$	−1.27494e6	−0.719175	−0.359587	−	0.933111i	$-0.617083\pi$
$61$	−1.27494e6	−0.719175	−0.359587	+	0.933111i	$0.617083\pi$
$62$	1.97824e6	1.05416
$63$	−25098.3	−0.0126460
$64$	−1.83783e6	−0.876345
$65$	700788.	0.316512
$66$	−1.68632e6	−0.721998
$67$	−4.12943e6	−1.67737	−0.838684	−	0.544619i	$-0.816674\pi$
$67$	−4.12943e6	−1.67737	−0.838684	+	0.544619i	$0.816674\pi$
$68$	−2.39485e6	−0.923627
$69$	2.96357e6	1.08603
$70$	−67813.9	−0.0236306
$71$	−2.81187e6	−0.932377	−0.466188	−	0.884685i	$-0.654373\pi$
$71$	−2.81187e6	−0.932377	−0.466188	+	0.884685i	$0.654373\pi$
$72$	−88411.6	−0.0279155
$73$	4.01991e6	1.20945	0.604723	−	0.796436i	$-0.293284\pi$
$73$	4.01991e6	1.20945	0.604723	+	0.796436i	$0.293284\pi$
$74$	−1.17164e6	−0.336111
$75$	421875.	0.115470
$76$	−6.01442e6	−1.57162
$77$	136459.	0.0340631
$78$	2.38524e6	0.569116
$79$	−1.32785e6	−0.303009	−0.151505	−	0.988457i	$-0.548412\pi$
$79$	−1.32785e6	−0.303009	−0.151505	+	0.988457i	$0.548412\pi$
$80$	−2.16374e6	−0.472487
$81$	531441.	0.111111
$82$	9.10480e6	1.82357
$83$	−1.91033e6	−0.366721	−0.183361	−	0.983046i	$-0.558698\pi$
$83$	−1.91033e6	−0.366721	−0.183361	+	0.983046i	$0.558698\pi$
$84$	−111830.	−0.0205865
$85$	−2.48834e6	−0.439484
$86$	4.16460e6	0.706039
$87$	5.19689e6	0.846109
$88$	480691.	0.0751929
$89$	8.00695e6	1.20393	0.601966	−	0.798522i	$-0.294384\pi$
$89$	8.00695e6	1.20393	0.601966	+	0.798522i	$0.294384\pi$
$90$	1.43592e6	0.207625
$91$	−193016.	−0.0268503
$92$	1.32047e7	1.76796
$93$	3.38962e6	0.436979
$94$	−4.82511e6	−0.599183
$95$	−6.24922e6	−0.747813
$96$	−6.94548e6	−0.801222
$97$	−3.89241e6	−0.433029	−0.216515	−	0.976279i	$-0.569469\pi$
$97$	−3.89241e6	−0.433029	−0.216515	+	0.976279i	$0.569469\pi$
$98$	−1.29584e7	−1.39079
$99$	−2.88943e6	−0.299288
$100$	1.87974e6	0.187974
$101$	1.07779e7	1.04090	0.520450	−	0.853892i	$-0.325764\pi$
$101$	1.07779e7	1.04090	0.520450	+	0.853892i	$0.325764\pi$
$102$	−8.46944e6	−0.790231
$103$	−1.93103e7	−1.74124	−0.870622	−	0.491952i	$-0.836283\pi$
$103$	−1.93103e7	−1.74124	−0.870622	+	0.491952i	$0.836283\pi$
$104$	−679921.	−0.0592709
$105$	−116196.	−0.00979554
$106$	−7.03137e6	−0.573415
$107$	−6.90473e6	−0.544883	−0.272442	−	0.962172i	$-0.587831\pi$
$107$	−6.90473e6	−0.544883	−0.272442	+	0.962172i	$0.587831\pi$
$108$	2.36793e6	0.180878
$109$	2.39533e7	1.77163	0.885814	−	0.464040i	$-0.153601\pi$
$109$	2.39533e7	1.77163	0.885814	+	0.464040i	$0.153601\pi$
$110$	−7.80703e6	−0.559257
$111$	−2.00755e6	−0.139327
$112$	595953.	0.0400820
$113$	−9.56587e6	−0.623663	−0.311831	−	0.950137i	$-0.600942\pi$
$113$	−9.56587e6	−0.623663	−0.311831	+	0.950137i	$0.600942\pi$
$114$	−2.12702e7	−1.34463
$115$	1.37202e7	0.841238
$116$	2.31557e7	1.37738
$117$	4.08700e6	0.235914
$118$	3.11925e7	1.74768
$119$	685357.	0.0372823
$120$	−409313.	−0.0216233
$121$	−3.77744e6	−0.193843
$122$	−2.00900e7	−1.00166
$123$	1.56006e7	0.755918
$124$	1.51031e7	0.711360
$125$	1.95312e6	0.0894427
$126$	−395491.	−0.0176132
$127$	−1.19412e7	−0.517290	−0.258645	−	0.965972i	$-0.583276\pi$
$127$	−1.19412e7	−0.517290	−0.258645	+	0.965972i	$0.583276\pi$
$128$	3.96685e6	0.167190
$129$	7.13585e6	0.292672
$130$	1.10428e7	0.440835
$131$	−1.60064e6	−0.0622077	−0.0311039	−	0.999516i	$-0.509902\pi$
$131$	−1.60064e6	−0.0622077	−0.0311039	+	0.999516i	$0.509902\pi$
$132$	−1.28744e7	−0.487212
$133$	1.72121e6	0.0634384
$134$	−6.50701e7	−2.33623
$135$	2.46038e6	0.0860663
$136$	2.41424e6	0.0822991
$137$	2.88030e7	0.957008	0.478504	−	0.878085i	$-0.341179\pi$
$137$	2.88030e7	0.957008	0.478504	+	0.878085i	$0.341179\pi$
$138$	4.66989e7	1.51262
$139$	−2.14740e6	−0.0678204	−0.0339102	−	0.999425i	$-0.510796\pi$
$139$	−2.14740e6	−0.0678204	−0.0339102	+	0.999425i	$0.510796\pi$
$140$	−517733.	−0.0159462
$141$	−8.26760e6	−0.248378
$142$	−4.43085e7	−1.29861
$143$	−2.22209e7	−0.635455
$144$	−1.26189e7	−0.352171
$145$	2.40597e7	0.655393
$146$	6.33444e7	1.68451
$147$	−2.22037e7	−0.576519
$148$	−8.94501e6	−0.226811
$149$	4.96813e6	0.123038	0.0615192	−	0.998106i	$-0.480405\pi$
$149$	4.96813e6	0.123038	0.0615192	+	0.998106i	$0.480405\pi$
$150$	6.64776e6	0.160826
$151$	−2.10485e7	−0.497511	−0.248756	−	0.968566i	$-0.580022\pi$
$151$	−2.10485e7	−0.497511	−0.248756	+	0.968566i	$0.580022\pi$
$152$	6.06313e6	0.140038
$153$	−1.45120e7	−0.327572
$154$	2.15027e6	0.0474428
$155$	1.56927e7	0.338482
$156$	1.82104e7	0.384046
$157$	−2.61392e7	−0.539069	−0.269534	−	0.962991i	$-0.586870\pi$
$157$	−2.61392e7	−0.539069	−0.269534	+	0.962991i	$0.586870\pi$
$158$	−2.09239e7	−0.422029
$159$	−1.20479e7	−0.237696
$160$	−3.21550e7	−0.620624
$161$	−3.77893e6	−0.0713638
$162$	8.37426e6	0.154755
$163$	−1.01817e8	−1.84147	−0.920733	−	0.390194i	$-0.872408\pi$
$163$	−1.01817e8	−1.84147	−0.920733	+	0.390194i	$0.872408\pi$
$164$	6.95116e7	1.23056
$165$	−1.33770e7	−0.231827
$166$	−3.01024e7	−0.510766
$167$	6.14576e7	1.02110	0.510550	−	0.859848i	$-0.329442\pi$
$167$	6.14576e7	1.02110	0.510550	+	0.859848i	$0.329442\pi$
$168$	112736.	0.00183434
$169$	−3.13179e7	−0.499101
$170$	−3.92104e7	−0.612110
$171$	−3.64454e7	−0.557387
$172$	3.17951e7	0.476443
$173$	−2.74394e7	−0.402914	−0.201457	−	0.979497i	$-0.564568\pi$
$173$	−2.74394e7	−0.402914	−0.201457	+	0.979497i	$0.564568\pi$
$174$	8.18908e7	1.17845
$175$	−537944.	−0.00758760
$176$	6.86087e7	0.948604
$177$	5.34469e7	0.724462
$178$	1.26171e8	1.67683
$179$	4.05126e7	0.527964	0.263982	−	0.964528i	$-0.414964\pi$
$179$	4.05126e7	0.527964	0.263982	+	0.964528i	$0.414964\pi$
$180$	1.09627e7	0.140108
$181$	9.66189e7	1.21112	0.605560	−	0.795800i	$-0.292949\pi$
$181$	9.66189e7	1.21112	0.605560	+	0.795800i	$0.292949\pi$
$182$	−3.04148e6	−0.0373969
$183$	−3.44233e7	−0.415216
$184$	−1.33117e7	−0.157533
$185$	−9.29421e6	−0.107922
$186$	5.34124e7	0.608621
$187$	7.89012e7	0.882345
$188$	−3.68378e7	−0.404335
$189$	−677655.	−0.00730117
$190$	−9.84730e7	−1.04155
$191$	−1.42378e8	−1.47852	−0.739260	−	0.673420i	$-0.764825\pi$
$191$	−1.42378e8	−1.47852	−0.739260	+	0.673420i	$0.764825\pi$
$192$	−4.96214e7	−0.505958
$193$	1.27527e8	1.27688	0.638441	−	0.769671i	$-0.279580\pi$
$193$	1.27527e8	1.27688	0.638441	+	0.769671i	$0.279580\pi$
$194$	−6.13352e7	−0.603120
$195$	1.89213e7	0.182738
$196$	−9.89326e7	−0.938519
$197$	−1.23507e8	−1.15096	−0.575479	−	0.817816i	$-0.695184\pi$
$197$	−1.23507e8	−1.15096	−0.575479	+	0.817816i	$0.695184\pi$
$198$	−4.55306e7	−0.416846
$199$	−7.46881e7	−0.671839	−0.335920	−	0.941891i	$-0.609047\pi$
$199$	−7.46881e7	−0.671839	−0.335920	+	0.941891i	$0.609047\pi$
$200$	−1.89497e6	−0.0167493
$201$	−1.11495e8	−0.968429
$202$	1.69834e8	1.44976
$203$	−6.62670e6	−0.0555982
$204$	−6.46609e7	−0.533256
$205$	7.22252e7	0.585532
$206$	−3.04286e8	−2.42519
$207$	8.00164e7	0.627022
$208$	−9.70446e7	−0.747739
$209$	1.98153e8	1.50137
$210$	−1.83098e6	−0.0136432
$211$	1.24482e8	0.912257	0.456128	−	0.889914i	$-0.349236\pi$
$211$	1.24482e8	0.912257	0.456128	+	0.889914i	$0.349236\pi$
$212$	−5.36818e7	−0.386947
$213$	−7.59206e7	−0.538308
$214$	−1.08802e8	−0.758910
$215$	3.30363e7	0.226703
$216$	−2.38711e6	−0.0161170
$217$	−4.32219e6	−0.0287141
$218$	3.77448e8	2.46751
$219$	1.08538e8	0.698274
$220$	−5.96036e7	−0.377393
$221$	−1.11603e8	−0.695510
$222$	−3.16342e7	−0.194054
$223$	2.17519e8	1.31350	0.656749	−	0.754109i	$-0.271931\pi$
$223$	2.17519e8	1.31350	0.656749	+	0.754109i	$0.271931\pi$
$224$	8.85637e6	0.0526487
$225$	1.13906e7	0.0666667
$226$	−1.50736e8	−0.868633
$227$	1.39021e8	0.788840	0.394420	−	0.918930i	$-0.370946\pi$
$227$	1.39021e8	0.788840	0.394420	+	0.918930i	$0.370946\pi$
$228$	−1.62389e8	−0.907373
$229$	1.06507e8	0.586076	0.293038	−	0.956101i	$-0.405334\pi$
$229$	1.06507e8	0.586076	0.293038	+	0.956101i	$0.405334\pi$
$230$	2.16199e8	1.17167
$231$	3.68439e6	0.0196663
$232$	−2.33433e7	−0.122731
$233$	−3.55655e7	−0.184197	−0.0920986	−	0.995750i	$-0.529358\pi$
$233$	−3.55655e7	−0.184197	−0.0920986	+	0.995750i	$0.529358\pi$
$234$	6.44015e7	0.328579
$235$	−3.82759e7	−0.192392
$236$	2.38143e8	1.17936
$237$	−3.58521e7	−0.174942
$238$	1.07996e7	0.0519265
$239$	−8.12794e7	−0.385113	−0.192556	−	0.981286i	$-0.561678\pi$
$239$	−8.12794e7	−0.385113	−0.192556	+	0.981286i	$0.561678\pi$
$240$	−5.84209e7	−0.272790
$241$	1.78776e8	0.822717	0.411359	−	0.911474i	$-0.365054\pi$
$241$	1.78776e8	0.822717	0.411359	+	0.911474i	$0.365054\pi$
$242$	−5.95236e7	−0.269983
$243$	1.43489e7	0.0641500
$244$	−1.53379e8	−0.675932
$245$	−1.02795e8	−0.446570
$246$	2.45830e8	1.05284
$247$	−2.80280e8	−1.18346
$248$	−1.52254e7	−0.0633852
$249$	−5.15790e7	−0.211726
$250$	3.07767e7	0.124575
$251$	−3.53343e7	−0.141039	−0.0705195	−	0.997510i	$-0.522466\pi$
$251$	−3.53343e7	−0.141039	−0.0705195	+	0.997510i	$0.522466\pi$
$252$	−3.01942e6	−0.0118856
$253$	−4.35047e8	−1.68894
$254$	−1.88165e8	−0.720477
$255$	−6.71851e7	−0.253736
$256$	2.97750e8	1.10921
$257$	−4.18029e8	−1.53617	−0.768087	−	0.640345i	$-0.778791\pi$
$257$	−4.18029e8	−1.53617	−0.768087	+	0.640345i	$0.778791\pi$
$258$	1.12444e8	0.407632
$259$	2.55988e6	0.00915525
$260$	8.43073e7	0.297480
$261$	1.40316e8	0.488501
$262$	−2.52223e7	−0.0866425
$263$	2.02813e8	0.687466	0.343733	−	0.939067i	$-0.388308\pi$
$263$	2.02813e8	0.687466	0.343733	+	0.939067i	$0.388308\pi$
$264$	1.29787e7	0.0434126
$265$	−5.57774e7	−0.184119
$266$	2.71222e7	0.0883565
$267$	2.16188e8	0.695090
$268$	−4.96785e8	−1.57651
$269$	−2.88920e8	−0.904993	−0.452496	−	0.891766i	$-0.649466\pi$
$269$	−2.88920e8	−0.904993	−0.452496	+	0.891766i	$0.649466\pi$
$270$	3.87697e7	0.119873
$271$	3.61648e8	1.10381	0.551904	−	0.833908i	$-0.313902\pi$
$271$	3.61648e8	1.10381	0.551904	+	0.833908i	$0.313902\pi$
$272$	3.44583e8	1.03825
$273$	−5.21144e6	−0.0155020
$274$	4.53867e8	1.33291
$275$	−6.19305e7	−0.179573
$276$	3.56528e8	1.02073
$277$	−3.16424e8	−0.894522	−0.447261	−	0.894404i	$-0.647600\pi$
$277$	−3.16424e8	−0.894522	−0.447261	+	0.894404i	$0.647600\pi$
$278$	−3.38379e7	−0.0944597
$279$	9.15197e7	0.252290
$280$	521926.	0.00142088
$281$	−3.81619e7	−0.102603	−0.0513013	−	0.998683i	$-0.516337\pi$
$281$	−3.81619e7	−0.102603	−0.0513013	+	0.998683i	$0.516337\pi$
$282$	−1.30278e8	−0.345938
$283$	−5.36394e8	−1.40680	−0.703398	−	0.710796i	$-0.748335\pi$
$283$	−5.36394e8	−1.40680	−0.703398	+	0.710796i	$0.748335\pi$
$284$	−3.38278e8	−0.876314
$285$	−1.68729e8	−0.431750
$286$	−3.50149e8	−0.885057
$287$	−1.98928e7	−0.0496718
$288$	−1.87528e8	−0.462586
$289$	−1.40615e7	−0.0342681
$290$	3.79124e8	0.912827
$291$	−1.05095e8	−0.250009
$292$	4.83610e8	1.13672
$293$	5.38585e8	1.25088	0.625442	−	0.780270i	$-0.284919\pi$
$293$	5.38585e8	1.25088	0.625442	+	0.780270i	$0.284919\pi$
$294$	−3.49877e8	−0.802972
$295$	2.47439e8	0.561166
$296$	9.01745e6	0.0202098
$297$	−7.80146e7	−0.172794
$298$	7.82860e7	0.171367
$299$	6.15358e8	1.33131
$300$	5.07531e7	0.108527
$301$	−9.09911e6	−0.0192316
$302$	−3.31676e8	−0.692930
$303$	2.91003e8	0.600964
$304$	8.65387e8	1.76666
$305$	−1.59367e8	−0.321625
$306$	−2.28675e8	−0.456240
$307$	6.10303e7	0.120382	0.0601910	−	0.998187i	$-0.480829\pi$
$307$	6.10303e7	0.120382	0.0601910	+	0.998187i	$0.480829\pi$
$308$	1.64165e7	0.0320149
$309$	−5.21379e8	−1.00531
$310$	2.47280e8	0.471436
$311$	5.75355e8	1.08461	0.542306	−	0.840181i	$-0.317551\pi$
$311$	5.75355e8	1.08461	0.542306	+	0.840181i	$0.317551\pi$
$312$	−1.83579e7	−0.0342201
$313$	7.32396e8	1.35002	0.675011	−	0.737807i	$-0.264139\pi$
$313$	7.32396e8	1.35002	0.675011	+	0.737807i	$0.264139\pi$
$314$	−4.11893e8	−0.750811
$315$	−3.13729e6	−0.00565546
$316$	−1.59746e8	−0.284790
$317$	−1.67850e7	−0.0295947	−0.0147973	−	0.999891i	$-0.504710\pi$
$317$	−1.67850e7	−0.0295947	−0.0147973	+	0.999891i	$0.504710\pi$
$318$	−1.89847e8	−0.331061
$319$	−7.62894e8	−1.31582
$320$	−2.29729e8	−0.391913
$321$	−1.86428e8	−0.314589
$322$	−5.95470e7	−0.0993950
$323$	9.95211e8	1.64326
$324$	6.39342e7	0.104430
$325$	8.75985e7	0.141548
$326$	−1.60440e9	−2.56478
$327$	6.46739e8	1.02285
$328$	−7.00746e7	−0.109648
$329$	1.05422e7	0.0163210
$330$	−2.10790e8	−0.322887
$331$	−1.08406e9	−1.64306	−0.821532	−	0.570163i	$-0.806880\pi$
$331$	−1.08406e9	−1.64306	−0.821532	+	0.570163i	$0.806880\pi$
$332$	−2.29820e8	−0.344671
$333$	−5.42038e7	−0.0804405
$334$	9.68427e8	1.42218
$335$	−5.16179e8	−0.750142
$336$	1.60907e7	0.0231413
$337$	7.36350e7	0.104804	0.0524022	−	0.998626i	$-0.483312\pi$
$337$	7.36350e7	0.104804	0.0524022	+	0.998626i	$0.483312\pi$
$338$	−4.93496e8	−0.695145
$339$	−2.58278e8	−0.360072
$340$	−2.99356e8	−0.413059
$341$	−4.97590e8	−0.679565
$342$	−5.74294e8	−0.776324
$343$	5.66658e7	0.0758214
$344$	−3.20526e7	−0.0424530
$345$	3.70446e8	0.485689
$346$	−4.32380e8	−0.561176
$347$	−2.99713e8	−0.385082	−0.192541	−	0.981289i	$-0.561673\pi$
$347$	−2.99713e8	−0.385082	−0.192541	+	0.981289i	$0.561673\pi$
$348$	6.25204e8	0.795233
$349$	−4.00569e8	−0.504415	−0.252208	−	0.967673i	$-0.581157\pi$
$349$	−4.00569e8	−0.504415	−0.252208	+	0.967673i	$0.581157\pi$
$350$	−8.47674e6	−0.0105679
$351$	1.10349e8	0.136205
$352$	1.01958e9	1.24602
$353$	−5.93100e8	−0.717657	−0.358828	−	0.933404i	$-0.616824\pi$
$353$	−5.93100e8	−0.717657	−0.358828	+	0.933404i	$0.616824\pi$
$354$	8.42197e8	1.00903
$355$	−3.51484e8	−0.416972
$356$	9.63264e8	1.13154
$357$	1.85046e7	0.0215249
$358$	6.38383e8	0.735344
$359$	8.77947e8	1.00147	0.500735	−	0.865601i	$-0.333063\pi$
$359$	8.77947e8	1.00147	0.500735	+	0.865601i	$0.333063\pi$
$360$	−1.10514e7	−0.0124842
$361$	1.60550e9	1.79612
$362$	1.52249e9	1.68684
$363$	−1.01991e8	−0.111915
$364$	−2.32205e7	−0.0252358
$365$	5.02489e8	0.540881
$366$	−5.42430e8	−0.578309
$367$	4.65347e8	0.491412	0.245706	−	0.969344i	$-0.420980\pi$
$367$	4.65347e8	0.491412	0.245706	+	0.969344i	$0.420980\pi$
$368$	−1.89997e9	−1.98737
$369$	4.21217e8	0.436429
$370$	−1.46455e8	−0.150313
$371$	1.53626e7	0.0156191
$372$	4.07783e8	0.410704
$373$	−2.88096e8	−0.287446	−0.143723	−	0.989618i	$-0.545907\pi$
$373$	−2.88096e8	−0.287446	−0.143723	+	0.989618i	$0.545907\pi$
$374$	1.24330e9	1.22892
$375$	5.27344e7	0.0516398
$376$	3.71362e7	0.0360280
$377$	1.07909e9	1.03720
$378$	−1.06782e7	−0.0101690
$379$	−8.21572e8	−0.775190	−0.387595	−	0.921830i	$-0.626694\pi$
$379$	−8.21572e8	−0.775190	−0.387595	+	0.921830i	$0.626694\pi$
$380$	−7.51803e8	−0.702848
$381$	−3.22412e8	−0.298657
$382$	−2.24355e9	−2.05927
$383$	−6.41573e8	−0.583513	−0.291757	−	0.956493i	$-0.594240\pi$
$383$	−6.41573e8	−0.583513	−0.291757	+	0.956493i	$0.594240\pi$
$384$	1.07105e8	0.0965273
$385$	1.70574e7	0.0152335
$386$	2.00952e9	1.77843
$387$	1.92668e8	0.168974
$388$	−4.68270e8	−0.406992
$389$	−1.25481e9	−1.08082	−0.540411	−	0.841401i	$-0.681731\pi$
$389$	−1.25481e9	−1.08082	−0.540411	+	0.841401i	$0.681731\pi$
$390$	2.98155e8	0.254516
$391$	−2.18500e9	−1.84855
$392$	9.97338e7	0.0836260
$393$	−4.32173e7	−0.0359157
$394$	−1.94618e9	−1.60305
$395$	−1.65982e8	−0.135510
$396$	−3.47608e8	−0.281292
$397$	1.29837e9	1.04144	0.520718	−	0.853729i	$-0.325664\pi$
$397$	1.29837e9	1.04144	0.520718	+	0.853729i	$0.325664\pi$
$398$	−1.17691e9	−0.935733
$399$	4.64726e7	0.0366262
$400$	−2.70467e8	−0.211303
$401$	2.16310e9	1.67522	0.837610	−	0.546268i	$-0.183952\pi$
$401$	2.16310e9	1.67522	0.837610	+	0.546268i	$0.183952\pi$
$402$	−1.75689e9	−1.34882
$403$	7.03823e8	0.535668
$404$	1.29662e9	0.978313
$405$	6.64301e7	0.0496904
$406$	−1.04421e8	−0.0774368
$407$	2.94704e8	0.216674
$408$	6.51846e7	0.0475154
$409$	−1.26448e9	−0.913864	−0.456932	−	0.889502i	$-0.651052\pi$
$409$	−1.26448e9	−0.913864	−0.456932	+	0.889502i	$0.651052\pi$
$410$	1.13810e9	0.815524
$411$	7.77680e8	0.552529
$412$	−2.32310e9	−1.63655
$413$	−6.81516e7	−0.0476048
$414$	1.26087e9	0.873312
$415$	−2.38792e8	−0.164003
$416$	−1.44217e9	−0.982174
$417$	−5.79797e7	−0.0391561
$418$	3.12242e9	2.09110
$419$	−1.84627e9	−1.22616	−0.613080	−	0.790021i	$-0.710070\pi$
$419$	−1.84627e9	−1.22616	−0.613080	+	0.790021i	$0.710070\pi$
$420$	−1.39788e7	−0.00920655
$421$	2.24531e9	1.46652	0.733262	−	0.679947i	$-0.237997\pi$
$421$	2.24531e9	1.46652	0.733262	+	0.679947i	$0.237997\pi$
$422$	1.96154e9	1.27058
$423$	−2.23225e8	−0.143401
$424$	5.41165e7	0.0344786
$425$	−3.11042e8	−0.196543
$426$	−1.19633e9	−0.749752
$427$	4.38941e7	0.0272840
$428$	−8.30664e8	−0.512120
$429$	−5.99963e8	−0.366880
$430$	5.20575e8	0.315750
$431$	−1.63983e9	−0.986568	−0.493284	−	0.869868i	$-0.664204\pi$
$431$	−1.63983e9	−0.986568	−0.493284	+	0.869868i	$0.664204\pi$
$432$	−3.40711e8	−0.203326
$433$	2.53503e9	1.50063	0.750317	−	0.661078i	$-0.229901\pi$
$433$	2.53503e9	1.50063	0.750317	+	0.661078i	$0.229901\pi$
$434$	−6.81076e7	−0.0399928
$435$	6.49611e8	0.378391
$436$	2.88167e9	1.66510
$437$	−5.48740e9	−3.14544
$438$	1.71030e9	0.972551
$439$	1.74546e8	0.0984655	0.0492327	−	0.998787i	$-0.484322\pi$
$439$	1.74546e8	0.0984655	0.0492327	+	0.998787i	$0.484322\pi$
$440$	6.00864e7	0.0336273
$441$	−5.99499e8	−0.332854
$442$	−1.75860e9	−0.968701
$443$	−1.13523e9	−0.620400	−0.310200	−	0.950671i	$-0.600396\pi$
$443$	−1.13523e9	−0.620400	−0.310200	+	0.950671i	$0.600396\pi$
$444$	−2.41515e8	−0.130950
$445$	1.00087e9	0.538415
$446$	3.42758e9	1.82943
$447$	1.34139e8	0.0710363
$448$	6.32736e7	0.0332468
$449$	2.28121e9	1.18933	0.594665	−	0.803973i	$-0.297285\pi$
$449$	2.28121e9	1.18933	0.594665	+	0.803973i	$0.297285\pi$
$450$	1.79489e8	0.0928528
$451$	−2.29015e9	−1.17556
$452$	−1.15081e9	−0.586163
$453$	−5.68311e8	−0.287238
$454$	2.19064e9	1.09869
$455$	−2.41270e7	−0.0120078
$456$	1.63705e8	0.0808507
$457$	2.93541e9	1.43867	0.719335	−	0.694663i	$-0.244447\pi$
$457$	2.93541e9	1.43867	0.719335	+	0.694663i	$0.244447\pi$
$458$	1.67830e9	0.816282
$459$	−3.91824e8	−0.189124
$460$	1.65059e9	0.790656
$461$	−6.32918e8	−0.300881	−0.150440	−	0.988619i	$-0.548069\pi$
$461$	−6.32918e8	−0.300881	−0.150440	+	0.988619i	$0.548069\pi$
$462$	5.80573e7	0.0273911
$463$	−1.41260e9	−0.661431	−0.330716	−	0.943730i	$-0.607290\pi$
$463$	−1.41260e9	−0.661431	−0.330716	+	0.943730i	$0.607290\pi$
$464$	−3.33177e9	−1.54832
$465$	4.23702e8	0.195423
$466$	−5.60429e8	−0.256549
$467$	−3.77542e8	−0.171536	−0.0857682	−	0.996315i	$-0.527334\pi$
$467$	−3.77542e8	−0.171536	−0.0857682	+	0.996315i	$0.527334\pi$
$468$	4.91680e8	0.221729
$469$	1.42170e8	0.0636359
$470$	−6.03138e8	−0.267963
$471$	−7.05760e8	−0.311232
$472$	−2.40071e8	−0.105086
$473$	−1.04753e9	−0.455147
$474$	−5.64944e8	−0.243658
$475$	−7.81152e8	−0.334432
$476$	8.24509e7	0.0350406
$477$	−3.25294e8	−0.137234
$478$	−1.28077e9	−0.536382
$479$	4.30550e9	1.78999	0.894993	−	0.446080i	$-0.147180\pi$
$479$	4.30550e9	1.78999	0.894993	+	0.446080i	$0.147180\pi$
$480$	−8.68185e8	−0.358317
$481$	−4.16849e8	−0.170793
$482$	2.81710e9	1.14587
$483$	−1.02031e8	−0.0412019
$484$	−4.54440e8	−0.182187
$485$	−4.86551e8	−0.193656
$486$	2.26105e8	0.0893477
$487$	8.36858e8	0.328322	0.164161	−	0.986434i	$-0.447508\pi$
$487$	8.36858e8	0.328322	0.164161	+	0.986434i	$0.447508\pi$
$488$	1.54622e8	0.0602284
$489$	−2.74906e9	−1.06317
$490$	−1.61980e9	−0.621979
$491$	3.30420e9	1.25974	0.629870	−	0.776700i	$-0.283108\pi$
$491$	3.30420e9	1.25974	0.629870	+	0.776700i	$0.283108\pi$
$492$	1.87681e9	0.710466
$493$	−3.83159e9	−1.44017
$494$	−4.41656e9	−1.64831
$495$	−3.61178e8	−0.133845
$496$	−2.17311e9	−0.799643
$497$	9.68084e7	0.0353725
$498$	−8.12764e8	−0.294891
$499$	3.42619e9	1.23441	0.617205	−	0.786802i	$-0.288265\pi$
$499$	3.42619e9	1.23441	0.617205	+	0.786802i	$0.288265\pi$
$500$	2.34968e8	0.0840647
$501$	1.65935e9	0.589532
$502$	−5.56786e8	−0.196438
$503$	2.20556e9	0.772734	0.386367	−	0.922345i	$-0.373730\pi$
$503$	2.20556e9	0.772734	0.386367	+	0.922345i	$0.373730\pi$
$504$	3.04387e6	0.00105906
$505$	1.34724e9	0.465505
$506$	−6.85531e9	−2.35234
$507$	−8.45583e8	−0.288156
$508$	−1.43656e9	−0.486186
$509$	1.55340e9	0.522122	0.261061	−	0.965322i	$-0.415928\pi$
$509$	1.55340e9	0.522122	0.261061	+	0.965322i	$0.415928\pi$
$510$	−1.05868e9	−0.353402
$511$	−1.38399e8	−0.0458839
$512$	4.18409e9	1.37770
$513$	−9.84027e8	−0.321807
$514$	−6.58715e9	−2.13957
$515$	−2.41379e9	−0.778708
$516$	8.58468e8	0.275074
$517$	1.21367e9	0.386263
$518$	4.03377e7	0.0127514
$519$	−7.40863e8	−0.232623
$520$	−8.49901e7	−0.0265068
$521$	5.82978e9	1.80601	0.903005	−	0.429629i	$-0.141356\pi$
$521$	5.82978e9	1.80601	0.903005	+	0.429629i	$0.141356\pi$
$522$	2.21105e9	0.680381
$523$	−1.98399e9	−0.606433	−0.303216	−	0.952922i	$-0.598060\pi$
$523$	−1.98399e9	−0.606433	−0.303216	+	0.952922i	$0.598060\pi$
$524$	−1.92563e8	−0.0584673
$525$	−1.45245e7	−0.00438070
$526$	3.19586e9	0.957498
$527$	−2.49912e9	−0.743788
$528$	1.85243e9	0.547677
$529$	8.64284e9	2.53841
$530$	−8.78921e8	−0.256439
$531$	1.44307e9	0.418269
$532$	2.07067e8	0.0596239
$533$	3.23933e9	0.926638
$534$	3.40661e9	0.968117
$535$	−8.63091e8	−0.243679
$536$	5.00809e8	0.140474
$537$	1.09384e9	0.304820
$538$	−4.55271e9	−1.26047
$539$	3.25946e9	0.896570
$540$	2.95992e8	0.0808913
$541$	−7.16394e9	−1.94519	−0.972594	−	0.232511i	$-0.925306\pi$
$541$	−7.16394e9	−1.94519	−0.972594	+	0.232511i	$0.925306\pi$
$542$	5.69872e9	1.53737
$543$	2.60871e9	0.699240
$544$	5.12080e9	1.36377
$545$	2.99416e9	0.792296
$546$	−8.21200e7	−0.0215911
$547$	1.97289e9	0.515403	0.257702	−	0.966225i	$-0.417035\pi$
$547$	1.97289e9	0.515403	0.257702	+	0.966225i	$0.417035\pi$
$548$	3.46510e9	0.899464
$549$	−9.29429e8	−0.239725
$550$	−9.75879e8	−0.250107
$551$	−9.62266e9	−2.45056
$552$	−3.59416e8	−0.0909515
$553$	4.57160e7	0.0114956
$554$	−4.98611e9	−1.24588
$555$	−2.50944e8	−0.0623090
$556$	−2.58339e8	−0.0637424
$557$	−6.01464e9	−1.47474	−0.737372	−	0.675487i	$-0.763933\pi$
$557$	−6.01464e9	−1.47474	−0.737372	+	0.675487i	$0.763933\pi$
$558$	1.44214e9	0.351388
$559$	1.48169e9	0.358771
$560$	7.44941e7	0.0179252
$561$	2.13033e9	0.509422
$562$	−6.01342e8	−0.142904
$563$	1.43964e9	0.339996	0.169998	−	0.985444i	$-0.445624\pi$
$563$	1.43964e9	0.339996	0.169998	+	0.985444i	$0.445624\pi$
$564$	−9.94621e8	−0.233443
$565$	−1.19573e9	−0.278910
$566$	−8.45231e9	−1.95938
$567$	−1.82967e7	−0.00421533
$568$	3.41018e8	0.0780833
$569$	−4.34990e9	−0.989889	−0.494944	−	0.868925i	$-0.664812\pi$
$569$	−4.34990e9	−0.989889	−0.494944	+	0.868925i	$0.664812\pi$
$570$	−2.65877e9	−0.601338
$571$	−3.91778e9	−0.880671	−0.440336	−	0.897833i	$-0.645141\pi$
$571$	−3.91778e9	−0.880671	−0.440336	+	0.897833i	$0.645141\pi$
$572$	−2.67325e9	−0.597246
$573$	−3.84422e9	−0.853624
$574$	−3.13464e8	−0.0691825
$575$	1.71503e9	0.376213
$576$	−1.33978e9	−0.292115
$577$	−5.57477e9	−1.20812	−0.604062	−	0.796938i	$-0.706452\pi$
$577$	−5.57477e9	−1.20812	−0.604062	+	0.796938i	$0.706452\pi$
$578$	−2.21577e8	−0.0477284
$579$	3.44322e9	0.737209
$580$	2.89446e9	0.615985
$581$	6.57698e7	0.0139127
$582$	−1.65605e9	−0.348211
$583$	1.76861e9	0.369652
$584$	−4.87526e8	−0.101287
$585$	5.10874e8	0.105504
$586$	8.48683e9	1.74222
$587$	3.96579e9	0.809275	0.404638	−	0.914477i	$-0.367398\pi$
$587$	3.96579e9	0.809275	0.404638	+	0.914477i	$0.367398\pi$
$588$	−2.67118e9	−0.541854
$589$	−6.27628e9	−1.26561
$590$	3.89906e9	0.781588
$591$	−3.33469e9	−0.664506
$592$	1.28705e9	0.254959
$593$	1.59443e9	0.313988	0.156994	−	0.987600i	$-0.449820\pi$
$593$	1.59443e9	0.313988	0.156994	+	0.987600i	$0.449820\pi$
$594$	−1.22933e9	−0.240666
$595$	8.56696e7	0.0166731
$596$	5.97683e8	0.115640
$597$	−2.01658e9	−0.387887
$598$	9.69660e9	1.85424
$599$	1.99503e9	0.379276	0.189638	−	0.981854i	$-0.439269\pi$
$599$	1.99503e9	0.379276	0.189638	+	0.981854i	$0.439269\pi$
$600$	−5.11641e7	−0.00967021
$601$	5.69444e9	1.07002	0.535008	−	0.844847i	$-0.320308\pi$
$601$	5.69444e9	1.07002	0.535008	+	0.844847i	$0.320308\pi$
$602$	−1.43381e8	−0.0267857
$603$	−3.01035e9	−0.559123
$604$	−2.53221e9	−0.467597
$605$	−4.72180e8	−0.0866890
$606$	4.58553e9	0.837019
$607$	1.61948e9	0.293910	0.146955	−	0.989143i	$-0.453053\pi$
$607$	1.61948e9	0.293910	0.146955	+	0.989143i	$0.453053\pi$
$608$	1.28604e10	2.32055
$609$	−1.78921e8	−0.0320997
$610$	−2.51125e9	−0.447956
$611$	−1.71669e9	−0.304472
$612$	−1.74584e9	−0.307876
$613$	−8.66201e8	−0.151882	−0.0759412	−	0.997112i	$-0.524196\pi$
$613$	−8.66201e8	−0.151882	−0.0759412	+	0.997112i	$0.524196\pi$
$614$	9.61694e8	0.167667
$615$	1.95008e9	0.338057
$616$	−1.65494e7	−0.00285267
$617$	−8.93265e9	−1.53102	−0.765512	−	0.643421i	$-0.777514\pi$
$617$	−8.93265e9	−1.53102	−0.765512	+	0.643421i	$0.777514\pi$
$618$	−8.21571e9	−1.40019
$619$	−3.70947e9	−0.628630	−0.314315	−	0.949319i	$-0.601775\pi$
$619$	−3.70947e9	−0.628630	−0.314315	+	0.949319i	$0.601775\pi$
$620$	1.88788e9	0.318130
$621$	2.16044e9	0.362011
$622$	9.06625e9	1.51064
$623$	−2.75667e8	−0.0456747
$624$	−2.62020e9	−0.431707
$625$	2.44141e8	0.0400000
$626$	1.15408e10	1.88030
$627$	5.35012e9	0.866817
$628$	−3.14464e9	−0.506656
$629$	1.48014e9	0.237151
$630$	−4.94363e7	−0.00787688
$631$	1.11559e9	0.176767	0.0883834	−	0.996087i	$-0.471830\pi$
$631$	1.11559e9	0.176767	0.0883834	+	0.996087i	$0.471830\pi$
$632$	1.61039e8	0.0253760
$633$	3.36101e9	0.526692
$634$	−2.64492e8	−0.0412192
$635$	−1.49265e9	−0.231339
$636$	−1.44941e9	−0.223404
$637$	−4.61039e9	−0.706723
$638$	−1.20214e10	−1.83267
$639$	−2.04986e9	−0.310792
$640$	4.95856e8	0.0747697
$641$	4.96276e8	0.0744252	0.0372126	−	0.999307i	$-0.488152\pi$
$641$	4.96276e8	0.0744252	0.0372126	+	0.999307i	$0.488152\pi$
$642$	−2.93766e9	−0.438157
$643$	−8.93408e8	−0.132529	−0.0662646	−	0.997802i	$-0.521108\pi$
$643$	−8.93408e8	−0.132529	−0.0662646	+	0.997802i	$0.521108\pi$
$644$	−4.54619e8	−0.0670728
$645$	8.91981e8	0.130887
$646$	1.56822e10	2.28872
$647$	3.05033e9	0.442774	0.221387	−	0.975186i	$-0.428942\pi$
$647$	3.05033e9	0.442774	0.221387	+	0.975186i	$0.428942\pi$
$648$	−6.44520e7	−0.00930517
$649$	−7.84590e9	−1.12664
$650$	1.38035e9	0.197148
$651$	−1.16699e8	−0.0165781
$652$	−1.22489e10	−1.73074
$653$	−1.29545e10	−1.82064	−0.910319	−	0.413908i	$-0.864164\pi$
$653$	−1.29545e10	−1.82064	−0.910319	+	0.413908i	$0.864164\pi$
$654$	1.01911e10	1.42462
$655$	−2.00080e8	−0.0278201
$656$	−1.00017e10	−1.38328
$657$	2.93052e9	0.403149
$658$	1.66121e8	0.0227318
$659$	8.43740e9	1.14844	0.574222	−	0.818700i	$-0.305305\pi$
$659$	8.43740e9	1.14844	0.574222	+	0.818700i	$0.305305\pi$
$660$	−1.60930e9	−0.217888
$661$	7.97949e9	1.07466	0.537328	−	0.843373i	$-0.319434\pi$
$661$	7.97949e9	1.07466	0.537328	+	0.843373i	$0.319434\pi$
$662$	−1.70822e10	−2.28845
$663$	−3.01328e9	−0.401553
$664$	2.31681e8	0.0307116
$665$	2.15151e8	0.0283705
$666$	−8.54125e8	−0.112037
$667$	2.11267e10	2.75671
$668$	7.39357e9	0.959702
$669$	5.87301e9	0.758349
$670$	−8.13376e9	−1.04479
$671$	5.05328e9	0.645720
$672$	2.39122e8	0.0303967
$673$	−4.53364e9	−0.573317	−0.286658	−	0.958033i	$-0.592544\pi$
$673$	−4.53364e9	−0.573317	−0.286658	+	0.958033i	$0.592544\pi$
$674$	1.16032e9	0.145971
$675$	3.07547e8	0.0384900
$676$	−3.76765e9	−0.469091
$677$	1.06085e9	0.131400	0.0656998	−	0.997839i	$-0.479072\pi$
$677$	1.06085e9	0.131400	0.0656998	+	0.997839i	$0.479072\pi$
$678$	−4.06986e9	−0.501505
$679$	1.34009e8	0.0164282
$680$	3.01781e8	0.0368053
$681$	3.75356e9	0.455437
$682$	−7.84084e9	−0.946493
$683$	1.53865e9	0.184785	0.0923924	−	0.995723i	$-0.470549\pi$
$683$	1.53865e9	0.184785	0.0923924	+	0.995723i	$0.470549\pi$
$684$	−4.38451e9	−0.523872
$685$	3.60037e9	0.427987
$686$	8.92920e8	0.105603
$687$	2.87569e9	0.338371
$688$	−4.57485e9	−0.535571
$689$	−2.50164e9	−0.291379
$690$	5.83736e9	0.676464
$691$	−5.67788e9	−0.654656	−0.327328	−	0.944911i	$-0.606148\pi$
$691$	−5.67788e9	−0.654656	−0.327328	+	0.944911i	$0.606148\pi$
$692$	−3.30105e9	−0.378688
$693$	9.94785e7	0.0113544
$694$	−4.72278e9	−0.536339
$695$	−2.68424e8	−0.0303302
$696$	−6.30268e8	−0.0708586
$697$	−1.15021e10	−1.28666
$698$	−6.31202e9	−0.702546
$699$	−9.60269e8	−0.106346
$700$	−6.47166e7	−0.00713136
$701$	3.43469e9	0.376595	0.188298	−	0.982112i	$-0.439703\pi$
$701$	3.43469e9	0.376595	0.188298	+	0.982112i	$0.439703\pi$
$702$	1.73884e9	0.189705
$703$	3.71722e9	0.403528
$704$	7.28433e9	0.786837
$705$	−1.03345e9	−0.111078
$706$	−9.34587e9	−0.999547
$707$	−3.71066e8	−0.0394897
$708$	6.42985e9	0.680902
$709$	−1.79411e10	−1.89055	−0.945273	−	0.326281i	$-0.894204\pi$
$709$	−1.79411e10	−1.89055	−0.945273	+	0.326281i	$0.894204\pi$
$710$	−5.53856e9	−0.580755
$711$	−9.68006e8	−0.101003
$712$	−9.71065e8	−0.100825
$713$	1.37797e10	1.42372
$714$	2.91590e8	0.0299798
$715$	−2.77761e9	−0.284184
$716$	4.87381e9	0.496218
$717$	−2.19455e9	−0.222345
$718$	1.38344e10	1.39484
$719$	−5.25757e9	−0.527514	−0.263757	−	0.964589i	$-0.584962\pi$
$719$	−5.25757e9	−0.527514	−0.263757	+	0.964589i	$0.584962\pi$
$720$	−1.57737e9	−0.157496
$721$	6.64825e8	0.0660593
$722$	2.52989e10	2.50162
$723$	4.82696e9	0.474996
$724$	1.16236e10	1.13830
$725$	3.00746e9	0.293101
$726$	−1.60714e9	−0.155874
$727$	7.82419e9	0.755212	0.377606	−	0.925966i	$-0.376747\pi$
$727$	7.82419e9	0.755212	0.377606	+	0.925966i	$0.376747\pi$
$728$	2.34086e7	0.00224862
$729$	3.87420e8	0.0370370
$730$	7.91805e9	0.753335
$731$	−5.26116e9	−0.498162
$732$	−4.14125e9	−0.390249
$733$	4.35449e9	0.408388	0.204194	−	0.978930i	$-0.434543\pi$
$733$	4.35449e9	0.408388	0.204194	+	0.978930i	$0.434543\pi$
$734$	7.33278e9	0.684435
$735$	−2.77546e9	−0.257827
$736$	−2.82351e10	−2.61046
$737$	1.63672e10	1.50605
$738$	6.63740e9	0.607856
$739$	4.46423e9	0.406903	0.203452	−	0.979085i	$-0.434784\pi$
$739$	4.46423e9	0.406903	0.203452	+	0.979085i	$0.434784\pi$
$740$	−1.11813e9	−0.101433
$741$	−7.56756e9	−0.683270
$742$	2.42079e8	0.0217542
$743$	1.19060e9	0.106489	0.0532447	−	0.998581i	$-0.483044\pi$
$743$	1.19060e9	0.106489	0.0532447	+	0.998581i	$0.483044\pi$
$744$	−4.11086e8	−0.0365955
$745$	6.21016e8	0.0550245
$746$	−4.53971e9	−0.400352
$747$	−1.39263e9	−0.122240
$748$	9.49210e9	0.829291
$749$	2.37719e8	0.0206718
$750$	8.30970e8	0.0719235
$751$	−1.78291e9	−0.153599	−0.0767997	−	0.997047i	$-0.524470\pi$
$751$	−1.78291e9	−0.153599	−0.0767997	+	0.997047i	$0.524470\pi$
$752$	5.30042e9	0.454515
$753$	−9.54027e8	−0.0814289
$754$	1.70039e10	1.44460
$755$	−2.63107e9	−0.222494
$756$	−8.15243e7	−0.00686216
$757$	−5.28551e9	−0.442844	−0.221422	−	0.975178i	$-0.571070\pi$
$757$	−5.28551e9	−0.442844	−0.221422	+	0.975178i	$0.571070\pi$
$758$	−1.29460e10	−1.07968
$759$	−1.17463e10	−0.975109
$760$	7.57892e8	0.0626267
$761$	−6.71171e9	−0.552061	−0.276030	−	0.961149i	$-0.589019\pi$
$761$	−6.71171e9	−0.552061	−0.276030	+	0.961149i	$0.589019\pi$
$762$	−5.08045e9	−0.415968
$763$	−8.24675e8	−0.0672120
$764$	−1.71286e10	−1.38962
$765$	−1.81400e9	−0.146495
$766$	−1.01097e10	−0.812713
$767$	1.10978e10	0.888079
$768$	8.03926e9	0.640401
$769$	1.25190e10	0.992725	0.496363	−	0.868115i	$-0.334669\pi$
$769$	1.25190e10	0.992725	0.496363	+	0.868115i	$0.334669\pi$
$770$	2.68784e8	0.0212171
$771$	−1.12868e10	−0.886911
$772$	1.53419e10	1.20011
$773$	1.89490e9	0.147556	0.0737781	−	0.997275i	$-0.476494\pi$
$773$	1.89490e9	0.147556	0.0737781	+	0.997275i	$0.476494\pi$
$774$	3.03599e9	0.235346
$775$	1.96158e9	0.151374
$776$	4.72063e8	0.0362647
$777$	6.91168e7	0.00528579
$778$	−1.97729e10	−1.50536
$779$	−2.88865e10	−2.18934
$780$	2.27630e9	0.171750
$781$	1.11450e10	0.837146
$782$	−3.44304e10	−2.57465
$783$	3.78853e9	0.282036
$784$	1.42349e10	1.05499
$785$	−3.26741e9	−0.241079
$786$	−6.81003e8	−0.0500231
$787$	−2.12095e10	−1.55103	−0.775513	−	0.631331i	$-0.782509\pi$
$787$	−2.12095e10	−1.55103	−0.775513	+	0.631331i	$0.782509\pi$
$788$	−1.48583e10	−1.08175
$789$	5.47596e9	0.396909
$790$	−2.61548e9	−0.188737
$791$	3.29338e8	0.0236605
$792$	3.50424e8	0.0250643
$793$	−7.14769e9	−0.508990
$794$	2.04593e10	1.45050
$795$	−1.50599e9	−0.106301
$796$	−8.98524e9	−0.631443
$797$	5.56395e9	0.389295	0.194647	−	0.980873i	$-0.437644\pi$
$797$	5.56395e9	0.389295	0.194647	+	0.980873i	$0.437644\pi$
$798$	7.32298e8	0.0510127
$799$	6.09558e9	0.422767
$800$	−4.01937e9	−0.277551
$801$	5.83706e9	0.401311
$802$	3.40854e10	2.33323
$803$	−1.59331e10	−1.08592
$804$	−1.34132e10	−0.910199
$805$	−4.72366e8	−0.0319149
$806$	1.10906e10	0.746075
$807$	−7.80085e9	−0.522498
$808$	−1.30712e9	−0.0871718
$809$	6.34040e9	0.421014	0.210507	−	0.977592i	$-0.432488\pi$
$809$	6.34040e9	0.421014	0.210507	+	0.977592i	$0.432488\pi$
$810$	1.04678e9	0.0692084
$811$	1.06272e10	0.699597	0.349798	−	0.936825i	$-0.386250\pi$
$811$	1.06272e10	0.699597	0.349798	+	0.936825i	$0.386250\pi$
$812$	−7.97215e8	−0.0522552
$813$	9.76449e9	0.637283
$814$	4.64385e9	0.301782
$815$	−1.27271e10	−0.823528
$816$	9.30375e9	0.599436
$817$	−1.32129e10	−0.847657
$818$	−1.99253e10	−1.27282
$819$	−1.40709e8	−0.00895010
$820$	8.68895e9	0.550324
$821$	2.17793e10	1.37355	0.686773	−	0.726872i	$-0.259027\pi$
$821$	2.17793e10	1.37355	0.686773	+	0.726872i	$0.259027\pi$
$822$	1.22544e10	0.769558
$823$	2.93033e10	1.83239	0.916194	−	0.400734i	$-0.131245\pi$
$823$	2.93033e10	1.83239	0.916194	+	0.400734i	$0.131245\pi$
$824$	2.34192e9	0.145823
$825$	−1.67212e9	−0.103676
$826$	−1.07391e9	−0.0663036
$827$	1.35378e10	0.832301	0.416150	−	0.909296i	$-0.363379\pi$
$827$	1.35378e10	0.832301	0.416150	+	0.909296i	$0.363379\pi$
$828$	9.62626e9	0.589320
$829$	−5.06434e9	−0.308732	−0.154366	−	0.988014i	$-0.549334\pi$
$829$	−5.06434e9	−0.308732	−0.154366	+	0.988014i	$0.549334\pi$
$830$	−3.76280e9	−0.228422
$831$	−8.54346e9	−0.516452
$832$	−1.03034e10	−0.620226
$833$	1.63704e10	0.981302
$834$	−9.13624e8	−0.0545364
$835$	7.68220e9	0.456649
$836$	2.38385e10	1.41110
$837$	2.47103e9	0.145660
$838$	−2.90929e10	−1.70779
$839$	−7.42054e9	−0.433779	−0.216890	−	0.976196i	$-0.569591\pi$
$839$	−7.42054e9	−0.433779	−0.216890	+	0.976196i	$0.569591\pi$
$840$	1.40920e7	0.000820343 0
$841$	1.97977e10	1.14770
$842$	3.53808e10	2.04256
$843$	−1.03037e9	−0.0592376
$844$	1.49756e10	0.857404
$845$	−3.91473e9	−0.223205
$846$	−3.51750e9	−0.199728
$847$	1.30051e8	0.00735399
$848$	7.72401e9	0.434968
$849$	−1.44826e10	−0.812214
$850$	−4.90130e9	−0.273744
$851$	−8.16119e9	−0.453942
$852$	−9.13351e9	−0.505940
$853$	−5.19233e9	−0.286444	−0.143222	−	0.989691i	$-0.545746\pi$
$853$	−5.19233e9	−0.286444	−0.143222	+	0.989691i	$0.545746\pi$
$854$	6.91668e8	0.0380010
$855$	−4.55568e9	−0.249271
$856$	8.37391e8	0.0456321
$857$	−3.38094e10	−1.83486	−0.917432	−	0.397892i	$-0.869742\pi$
$857$	−3.38094e10	−1.83486	−0.917432	+	0.397892i	$0.869742\pi$
$858$	−9.45401e9	−0.510988
$859$	1.19130e10	0.641277	0.320639	−	0.947202i	$-0.396103\pi$
$859$	1.19130e10	0.641277	0.320639	+	0.947202i	$0.396103\pi$
$860$	3.97439e9	0.213072
$861$	−5.37106e8	−0.0286780
$862$	−2.58398e10	−1.37408
$863$	−1.42156e10	−0.752882	−0.376441	−	0.926441i	$-0.622852\pi$
$863$	−1.42156e10	−0.752882	−0.376441	+	0.926441i	$0.622852\pi$
$864$	−5.06325e9	−0.267074
$865$	−3.42992e9	−0.180189
$866$	3.99461e10	2.09007
$867$	−3.79661e8	−0.0197847
$868$	−5.19975e8	−0.0269876
$869$	5.26302e9	0.272061
$870$	1.02363e10	0.527021
$871$	−2.31508e10	−1.18714
$872$	−2.90501e9	−0.148368
$873$	−2.83756e9	−0.144343
$874$	−8.64686e10	−4.38095
$875$	−6.72430e7	−0.00339328
$876$	1.30575e10	0.656288
$877$	−2.34323e9	−0.117305	−0.0586525	−	0.998278i	$-0.518680\pi$
$877$	−2.34323e9	−0.117305	−0.0586525	+	0.998278i	$0.518680\pi$
$878$	2.75043e9	0.137142
$879$	1.45418e10	0.722198
$880$	8.57609e9	0.424228
$881$	1.08237e9	0.0533288	0.0266644	−	0.999644i	$-0.491511\pi$
$881$	1.08237e9	0.0533288	0.0266644	+	0.999644i	$0.491511\pi$
$882$	−9.44669e9	−0.463596
$883$	−1.55829e10	−0.761705	−0.380852	−	0.924636i	$-0.624369\pi$
$883$	−1.55829e10	−0.761705	−0.380852	+	0.924636i	$0.624369\pi$
$884$	−1.34262e10	−0.653690
$885$	6.68086e9	0.323989
$886$	−1.78886e10	−0.864088
$887$	−1.48785e10	−0.715858	−0.357929	−	0.933749i	$-0.616517\pi$
$887$	−1.48785e10	−0.715858	−0.357929	+	0.933749i	$0.616517\pi$
$888$	2.43471e8	0.0116682
$889$	4.11116e8	0.0196249
$890$	1.57713e10	0.749900
$891$	−2.10639e9	−0.0997625
$892$	2.61683e10	1.23452
$893$	1.53084e10	0.719368
$894$	2.11372e9	0.0989388
$895$	5.06407e9	0.236113
$896$	−1.36572e8	−0.00634286
$897$	1.66147e10	0.768632
$898$	3.59465e10	1.65649
$899$	2.41639e10	1.10919
$900$	1.37033e9	0.0626581
$901$	8.88276e9	0.404586
$902$	−3.60873e10	−1.63731
$903$	−2.45676e8	−0.0111034
$904$	1.16013e9	0.0522296
$905$	1.20774e10	0.541629
$906$	−8.95524e9	−0.400063
$907$	−3.01866e10	−1.34335	−0.671673	−	0.740848i	$-0.734424\pi$
$907$	−3.01866e10	−1.34335	−0.671673	+	0.740848i	$0.734424\pi$
$908$	1.67247e10	0.741408
$909$	7.85709e9	0.346967
$910$	−3.80185e8	−0.0167244
$911$	−3.12329e10	−1.36867	−0.684334	−	0.729168i	$-0.739907\pi$
$911$	−3.12329e10	−1.36867	−0.684334	+	0.729168i	$0.739907\pi$
$912$	2.33654e10	1.01998
$913$	7.57170e9	0.329265
$914$	4.62551e10	2.00377
$915$	−4.30291e9	−0.185690
$916$	1.28132e10	0.550836
$917$	5.51076e7	0.00236004
$918$	−6.17422e9	−0.263410
$919$	−1.27737e10	−0.542891	−0.271446	−	0.962454i	$-0.587502\pi$
$919$	−1.27737e10	−0.542891	−0.271446	+	0.962454i	$0.587502\pi$
$920$	−1.66396e9	−0.0704508
$921$	1.64782e9	0.0695025
$922$	−9.97330e9	−0.419064
$923$	−1.57642e10	−0.659882
$924$	4.43245e8	0.0184838
$925$	−1.16178e9	−0.0482643
$926$	−2.22592e10	−0.921237
$927$	−1.40772e10	−0.580415
$928$	−4.95129e10	−2.03376
$929$	−3.36628e10	−1.37751	−0.688755	−	0.724994i	$-0.741843\pi$
$929$	−3.36628e10	−1.37751	−0.688755	+	0.724994i	$0.741843\pi$
$930$	6.67655e9	0.272184
$931$	4.11127e10	1.66975
$932$	−4.27866e9	−0.173122
$933$	1.55346e10	0.626201
$934$	−5.94917e9	−0.238915
$935$	9.86266e9	0.394596
$936$	−4.95662e8	−0.0197570
$937$	3.94639e9	0.156715	0.0783577	−	0.996925i	$-0.475032\pi$
$937$	3.94639e9	0.156715	0.0783577	+	0.996925i	$0.475032\pi$
$938$	2.24026e9	0.0886317
$939$	1.97747e10	0.779436
$940$	−4.60473e9	−0.180824
$941$	−1.71604e10	−0.671373	−0.335686	−	0.941974i	$-0.608968\pi$
$941$	−1.71604e10	−0.671373	−0.335686	+	0.941974i	$0.608968\pi$
$942$	−1.11211e10	−0.433481
$943$	6.34206e10	2.46286
$944$	−3.42652e10	−1.32572
$945$	−8.47069e7	−0.00326518
$946$	−1.65066e10	−0.633926
$947$	2.96234e10	1.13347	0.566735	−	0.823900i	$-0.308206\pi$
$947$	2.96234e10	1.13347	0.566735	+	0.823900i	$0.308206\pi$
$948$	−4.31313e9	−0.164423
$949$	2.25368e10	0.855976
$950$	−1.23091e10	−0.465795
$951$	−4.53194e8	−0.0170865
$952$	−8.31186e7	−0.00312226
$953$	−2.70351e9	−0.101182	−0.0505910	−	0.998719i	$-0.516111\pi$
$953$	−2.70351e9	−0.101182	−0.0505910	+	0.998719i	$0.516111\pi$
$954$	−5.12587e9	−0.191138
$955$	−1.77973e10	−0.661215
$956$	−9.77821e9	−0.361957
$957$	−2.05981e10	−0.759689
$958$	6.78446e10	2.49308
$959$	−9.91642e8	−0.0363069
$960$	−6.20267e9	−0.226271
$961$	−1.17520e10	−0.427148
$962$	−6.56856e9	−0.237880
$963$	−5.03355e9	−0.181628
$964$	2.15074e10	0.773248
$965$	1.59409e10	0.571039
$966$	−1.60777e9	−0.0573857
$967$	3.15584e10	1.12233	0.561167	−	0.827703i	$-0.310353\pi$
$967$	3.15584e10	1.12233	0.561167	+	0.827703i	$0.310353\pi$
$968$	4.58120e8	0.0162336
$969$	2.68707e10	0.948736
$970$	−7.66690e9	−0.269723
$971$	2.06410e10	0.723540	0.361770	−	0.932267i	$-0.382173\pi$
$971$	2.06410e10	0.723540	0.361770	+	0.932267i	$0.382173\pi$
$972$	1.72622e9	0.0602928
$973$	7.39315e7	0.00257297
$974$	1.31869e10	0.457285
$975$	2.36516e9	0.0817230
$976$	2.20690e10	0.759817
$977$	3.75871e10	1.28946	0.644731	−	0.764410i	$-0.276970\pi$
$977$	3.75871e10	1.28946	0.644731	+	0.764410i	$0.276970\pi$
$978$	−4.33187e10	−1.48078
$979$	−3.17359e10	−1.08097
$980$	−1.23666e10	−0.419718
$981$	1.74620e10	0.590543
$982$	5.20664e10	1.75456
$983$	−6.64465e9	−0.223118	−0.111559	−	0.993758i	$-0.535584\pi$
$983$	−6.64465e9	−0.223118	−0.111559	+	0.993758i	$0.535584\pi$
$984$	−1.89201e9	−0.0633055
$985$	−1.54384e10	−0.514724
$986$	−6.03769e10	−2.00586
$987$	2.84640e8	0.00942294
$988$	−3.37187e10	−1.11230
$989$	2.90090e10	0.953556
$990$	−5.69132e9	−0.186419
$991$	1.79433e10	0.585657	0.292829	−	0.956165i	$-0.405403\pi$
$991$	1.79433e10	0.585657	0.292829	+	0.956165i	$0.405403\pi$
$992$	−3.22943e10	−1.05035
$993$	−2.92696e10	−0.948623
$994$	1.52547e9	0.0492666
$995$	−9.33601e9	−0.300456
$996$	−6.20514e9	−0.198996
$997$	−9.85820e8	−0.0315039	−0.0157520	−	0.999876i	$-0.505014\pi$
$997$	−9.85820e8	−0.0315039	−0.0157520	+	0.999876i	$0.505014\pi$
$998$	5.39887e10	1.71928
$999$	−1.46350e9	−0.0464424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.8.a.c.1.2	✓	2
3.2	odd	2		45.8.a.i.1.1		2
4.3	odd	2		240.8.a.p.1.2		2
5.2	odd	4		75.8.b.d.49.4		4
5.3	odd	4		75.8.b.d.49.1		4
5.4	even	2		75.8.a.e.1.1		2
15.2	even	4		225.8.b.n.199.1		4
15.8	even	4		225.8.b.n.199.4		4
15.14	odd	2		225.8.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.8.a.c.1.2	✓	2	1.1	even	1	trivial
45.8.a.i.1.1		2	3.2	odd	2
75.8.a.e.1.1		2	5.4	even	2
75.8.b.d.49.1		4	5.3	odd	4
75.8.b.d.49.4		4	5.2	odd	4
225.8.a.t.1.2		2	15.14	odd	2
225.8.b.n.199.1		4	15.2	even	4
225.8.b.n.199.4		4	15.8	even	4
240.8.a.p.1.2		2	4.3	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q+15.7577 q^{2} +27.0000 q^{3} +120.304 q^{4} +125.000 q^{5} +425.457 q^{6} -34.4284 q^{7} -121.278 q^{8} +729.000 q^{9} +1969.71 q^{10} -3963.55 q^{11} +3248.20 q^{12} +5606.30 q^{13} -542.511 q^{14} +3375.00 q^{15} -17309.9 q^{16} -19906.7 q^{17} +11487.3 q^{18} -49993.7 q^{19} +15037.9 q^{20} -929.568 q^{21} -62456.2 q^{22} +109762. q^{23} -3274.50 q^{24} +15625.0 q^{25} +88342.2 q^{26} +19683.0 q^{27} -4141.86 q^{28} +192477. q^{29} +53182.1 q^{30} +125541. q^{31} -257240. q^{32} -107016. q^{33} -313683. q^{34} -4303.55 q^{35} +87701.3 q^{36} -74353.6 q^{37} -787784. q^{38} +151370. q^{39} -15159.7 q^{40} +577802. q^{41} -14647.8 q^{42} +264291. q^{43} -476829. q^{44} +91125.0 q^{45} +1.72959e6 q^{46} -306207. q^{47} -467368. q^{48} -822358. q^{49} +246213. q^{50} -537481. q^{51} +674458. q^{52} -446219. q^{53} +310158. q^{54} -495444. q^{55} +4175.41 q^{56} -1.34983e6 q^{57} +3.03299e6 q^{58} +1.97951e6 q^{59} +406024. q^{60} -1.27494e6 q^{61} +1.97824e6 q^{62} -25098.3 q^{63} -1.83783e6 q^{64} +700788. q^{65} -1.68632e6 q^{66} -4.12943e6 q^{67} -2.39485e6 q^{68} +2.96357e6 q^{69} -67813.9 q^{70} -2.81187e6 q^{71} -88411.6 q^{72} +4.01991e6 q^{73} -1.17164e6 q^{74} +421875. q^{75} -6.01442e6 q^{76} +136459. q^{77} +2.38524e6 q^{78} -1.32785e6 q^{79} -2.16374e6 q^{80} +531441. q^{81} +9.10480e6 q^{82} -1.91033e6 q^{83} -111830. q^{84} -2.48834e6 q^{85} +4.16460e6 q^{86} +5.19689e6 q^{87} +480691. q^{88} +8.00695e6 q^{89} +1.43592e6 q^{90} -193016. q^{91} +1.32047e7 q^{92} +3.38962e6 q^{93} -4.82511e6 q^{94} -6.24922e6 q^{95} -6.94548e6 q^{96} -3.89241e6 q^{97} -1.29584e7 q^{98} -2.88943e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 7 q^{2} + 54 q^{3} + 69 q^{4} + 250 q^{5} + 189 q^{6} + 1304 q^{7} + 1449 q^{8} + 1458 q^{9} + 875 q^{10} + 3448 q^{11} + 1863 q^{12} - 8988 q^{13} - 12264 q^{14} + 6750 q^{15} - 24495 q^{16} - 5492 q^{17}+ \cdots + 2513592 q^{99}+O(q^{100}) \) 2 * q + 7 * q^2 + 54 * q^3 + 69 * q^4 + 250 * q^5 + 189 * q^6 + 1304 * q^7 + 1449 * q^8 + 1458 * q^9 + 875 * q^10 + 3448 * q^11 + 1863 * q^12 - 8988 * q^13 - 12264 * q^14 + 6750 * q^15 - 24495 * q^16 - 5492 * q^17 + 5103 * q^18 - 49584 * q^19 + 8625 * q^20 + 35208 * q^21 - 127364 * q^22 + 91848 * q^23 + 39123 * q^24 + 31250 * q^25 + 216154 * q^26 + 39366 * q^27 - 72808 * q^28 + 181772 * q^29 + 23625 * q^30 + 304232 * q^31 - 395311 * q^32 + 93096 * q^33 - 439922 * q^34 + 163000 * q^35 + 50301 * q^36 - 502316 * q^37 - 791372 * q^38 - 242676 * q^39 + 181125 * q^40 + 631172 * q^41 - 331128 * q^42 + 353640 * q^43 - 857068 * q^44 + 182250 * q^45 + 1886472 * q^46 - 467480 * q^47 - 661365 * q^48 + 145490 * q^49 + 109375 * q^50 - 148284 * q^51 + 1423198 * q^52 - 568052 * q^53 + 137781 * q^54 + 431000 * q^55 + 2105880 * q^56 - 1338768 * q^57 + 3126746 * q^58 + 287224 * q^59 + 232875 * q^60 - 2514180 * q^61 + 413328 * q^62 + 950616 * q^63 + 291041 * q^64 - 1123500 * q^65 - 3438828 * q^66 - 5073832 * q^67 - 3134374 * q^68 + 2479896 * q^69 - 1533000 * q^70 - 3748816 * q^71 + 1056321 * q^72 - 1477212 * q^73 + 2576306 * q^74 + 843750 * q^75 - 6035444 * q^76 + 10056288 * q^77 + 5836158 * q^78 - 4627720 * q^79 - 3061875 * q^80 + 1062882 * q^81 + 8637398 * q^82 - 6072936 * q^83 - 1965816 * q^84 - 686500 * q^85 + 3382108 * q^86 + 4907844 * q^87 + 12118884 * q^88 + 16516356 * q^89 + 637875 * q^90 - 19726448 * q^91 + 14123784 * q^92 + 8214264 * q^93 - 3412736 * q^94 - 6198000 * q^95 - 10673397 * q^96 + 2723428 * q^97 - 21434497 * q^98 + 2513592 * q^99

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