LMFDB - Embedded newform 15.14.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [15,14,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, 14); 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, 14, names="a")

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	15.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,131] 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:	$16.0846393428$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{3121}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 780 $ x^2 - x - 780
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$28.4330$ 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)

$f(q)$	$=$	\(q-18.2989 q^{2} +729.000 q^{3} -7857.15 q^{4} -15625.0 q^{5} -13339.9 q^{6} +112047. q^{7} +293681. q^{8} +531441. q^{9} +285920. q^{10} +143727. q^{11} -5.72786e6 q^{12} +627845. q^{13} -2.05033e6 q^{14} -1.13906e7 q^{15} +5.89918e7 q^{16} +7.51428e7 q^{17} -9.72477e6 q^{18} +3.68418e8 q^{19} +1.22768e8 q^{20} +8.16820e7 q^{21} -2.63004e6 q^{22} +2.64060e8 q^{23} +2.14094e8 q^{24} +2.44141e8 q^{25} -1.14888e7 q^{26} +3.87420e8 q^{27} -8.80367e8 q^{28} +5.37538e9 q^{29} +2.08436e8 q^{30} -1.57044e9 q^{31} -3.48532e9 q^{32} +1.04777e8 q^{33} -1.37503e9 q^{34} -1.75073e9 q^{35} -4.17561e9 q^{36} -1.85013e10 q^{37} -6.74163e9 q^{38} +4.57699e8 q^{39} -4.58877e9 q^{40} -8.47428e9 q^{41} -1.49469e9 q^{42} +6.20298e9 q^{43} -1.12928e9 q^{44} -8.30377e9 q^{45} -4.83201e9 q^{46} +3.77183e9 q^{47} +4.30050e10 q^{48} -8.43346e10 q^{49} -4.46750e9 q^{50} +5.47791e10 q^{51} -4.93307e9 q^{52} +2.30272e11 q^{53} -7.08936e9 q^{54} -2.24573e9 q^{55} +3.29060e10 q^{56} +2.68577e11 q^{57} -9.83633e10 q^{58} +4.11830e11 q^{59} +8.94979e10 q^{60} -4.06580e11 q^{61} +2.87372e10 q^{62} +5.95462e10 q^{63} -4.19483e11 q^{64} -9.81007e9 q^{65} -1.91730e9 q^{66} +2.96486e11 q^{67} -5.90409e11 q^{68} +1.92500e11 q^{69} +3.20364e10 q^{70} -3.97640e11 q^{71} +1.56074e11 q^{72} -1.37728e12 q^{73} +3.38553e11 q^{74} +1.77979e11 q^{75} -2.89472e12 q^{76} +1.61041e10 q^{77} -8.37537e9 q^{78} -4.66466e11 q^{79} -9.21746e11 q^{80} +2.82430e11 q^{81} +1.55070e11 q^{82} +4.77278e12 q^{83} -6.41788e11 q^{84} -1.17411e12 q^{85} -1.13508e11 q^{86} +3.91865e12 q^{87} +4.22098e10 q^{88} +6.88111e12 q^{89} +1.51949e11 q^{90} +7.03479e10 q^{91} -2.07476e12 q^{92} -1.14485e12 q^{93} -6.90203e10 q^{94} -5.75653e12 q^{95} -2.54080e12 q^{96} +1.38827e13 q^{97} +1.54323e12 q^{98} +7.63823e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 131 q^{2} + 1458 q^{3} + 6241 q^{4} - 31250 q^{5} + 95499 q^{6} + 496272 q^{7} + 1175463 q^{8} + 1062882 q^{9} - 2046875 q^{10} + 6245888 q^{11} + 4549689 q^{12} + 1761164 q^{13} + 55314084 q^{14}+ \cdots + 3319320964608 q^{99}+O(q^{100}) $ 2 * q + 131 * q^2 + 1458 * q^3 + 6241 * q^4 - 31250 * q^5 + 95499 * q^6 + 496272 * q^7 + 1175463 * q^8 + 1062882 * q^9 - 2046875 * q^10 + 6245888 * q^11 + 4549689 * q^12 + 1761164 * q^13 + 55314084 * q^14 - 22781250 * q^15 + 75148705 * q^16 + 48151604 * q^17 + 69618771 * q^18 + 38475344 * q^19 - 97515625 * q^20 + 361782288 * q^21 + 908415728 * q^22 + 734264616 * q^23 + 856912527 * q^24 + 488281250 * q^25 + 157714454 * q^26 + 774840978 * q^27 + 4536499884 * q^28 + 1126474708 * q^29 - 1492171875 * q^30 + 6100104312 * q^31 - 8296660073 * q^32 + 4553252352 * q^33 - 5404788238 * q^34 - 7754250000 * q^35 + 3316723281 * q^36 - 46819674548 * q^37 - 56001723484 * q^38 + 1283888556 * q^39 - 18366609375 * q^40 - 29607909788 * q^41 + 40323967236 * q^42 - 63189768520 * q^43 + 84899911888 * q^44 - 16607531250 * q^45 + 65368954992 * q^46 + 105004415960 * q^47 + 54783405945 * q^48 - 33594444590 * q^49 + 31982421875 * q^50 + 35102519316 * q^51 + 11044638034 * q^52 + 48425833796 * q^53 + 50752084059 * q^54 - 97592000000 * q^55 + 371708899380 * q^56 + 28048525776 * q^57 - 732719858498 * q^58 + 722768180096 * q^59 - 71088890625 * q^60 - 229984402180 * q^61 + 1173940563384 * q^62 + 263739287952 * q^63 - 1270168541071 * q^64 - 27518187500 * q^65 + 662235065712 * q^66 + 359062188984 * q^67 - 970935017018 * q^68 + 535278905064 * q^69 - 864282562500 * q^70 + 736545668224 * q^71 + 624689232183 * q^72 - 1494470740204 * q^73 - 3889351112906 * q^74 + 355957031250 * q^75 - 7546301154644 * q^76 + 2360709208704 * q^77 + 114973836966 * q^78 + 3526348590120 * q^79 - 1174198515625 * q^80 + 564859072962 * q^81 - 3000156702386 * q^82 + 5631050986968 * q^83 + 3307108415436 * q^84 - 752368812500 * q^85 - 10473766954252 * q^86 + 821200062132 * q^87 + 5422984137648 * q^88 + 5913121459764 * q^89 - 1087793296875 * q^90 + 505797926592 * q^91 + 4554248300592 * q^92 + 4446976043448 * q^93 + 15044889696176 * q^94 - 601177250000 * q^95 - 6048265193217 * q^96 + 16383233322244 * q^97 + 9118668656251 * q^98 + 3319320964608 * 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 $

$2$	−18.2989	−0.202176	−0.101088	−	0.994877i	$-0.532232\pi$
$2$	−18.2989	−0.202176	−0.101088	+	0.994877i	$0.532232\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−7857.15	−0.959125
$5$	−15625.0	−0.447214
$5$	−15625.0	−0.447214
$6$	−13339.9	−0.116726
$7$	112047.	0.359966	0.179983	−	0.983670i	$-0.442396\pi$
$7$	112047.	0.359966	0.179983	+	0.983670i	$0.442396\pi$
$8$	293681.	0.396088
$9$	531441.	0.333333
$10$	285920.	0.0904158
$11$	143727.	0.0244616	0.0122308	−	0.999925i	$-0.496107\pi$
$11$	143727.	0.0244616	0.0122308	+	0.999925i	$0.496107\pi$
$12$	−5.72786e6	−0.553751
$13$	627845.	0.0360762	0.0180381	−	0.999837i	$-0.494258\pi$
$13$	627845.	0.0360762	0.0180381	+	0.999837i	$0.494258\pi$
$14$	−2.05033e6	−0.0727764
$15$	−1.13906e7	−0.258199
$16$	5.89918e7	0.879046
$17$	7.51428e7	0.755039	0.377520	−	0.926002i	$-0.376777\pi$
$17$	7.51428e7	0.755039	0.377520	+	0.926002i	$0.376777\pi$
$18$	−9.72477e6	−0.0673919
$19$	3.68418e8	1.79656	0.898282	−	0.439420i	$-0.144816\pi$
$19$	3.68418e8	1.79656	0.898282	+	0.439420i	$0.144816\pi$
$20$	1.22768e8	0.428934
$21$	8.16820e7	0.207827
$22$	−2.63004e6	−0.00494555
$23$	2.64060e8	0.371939	0.185970	−	0.982555i	$-0.440457\pi$
$23$	2.64060e8	0.371939	0.185970	+	0.982555i	$0.440457\pi$
$24$	2.14094e8	0.228681
$25$	2.44141e8	0.200000
$26$	−1.14888e7	−0.00729373
$27$	3.87420e8	0.192450
$28$	−8.80367e8	−0.345252
$29$	5.37538e9	1.67812	0.839058	−	0.544042i	$-0.183107\pi$
$29$	5.37538e9	1.67812	0.839058	+	0.544042i	$0.183107\pi$
$30$	2.08436e8	0.0522016
$31$	−1.57044e9	−0.317812	−0.158906	−	0.987294i	$-0.550797\pi$
$31$	−1.57044e9	−0.317812	−0.158906	+	0.987294i	$0.550797\pi$
$32$	−3.48532e9	−0.573809
$33$	1.04777e8	0.0141229
$34$	−1.37503e9	−0.152651
$35$	−1.75073e9	−0.160982
$36$	−4.17561e9	−0.319708
$37$	−1.85013e10	−1.18547	−0.592735	−	0.805397i	$-0.701952\pi$
$37$	−1.85013e10	−1.18547	−0.592735	+	0.805397i	$0.701952\pi$
$38$	−6.74163e9	−0.363222
$39$	4.57699e8	0.0208286
$40$	−4.58877e9	−0.177136
$41$	−8.47428e9	−0.278617	−0.139309	−	0.990249i	$-0.544488\pi$
$41$	−8.47428e9	−0.278617	−0.139309	+	0.990249i	$0.544488\pi$
$42$	−1.49469e9	−0.0420175
$43$	6.20298e9	0.149643	0.0748214	−	0.997197i	$-0.476161\pi$
$43$	6.20298e9	0.149643	0.0748214	+	0.997197i	$0.476161\pi$
$44$	−1.12928e9	−0.0234617
$45$	−8.30377e9	−0.149071
$46$	−4.83201e9	−0.0751972
$47$	3.77183e9	0.0510407	0.0255203	−	0.999674i	$-0.491876\pi$
$47$	3.77183e9	0.0510407	0.0255203	+	0.999674i	$0.491876\pi$
$48$	4.30050e10	0.507517
$49$	−8.43346e10	−0.870424
$50$	−4.46750e9	−0.0404352
$51$	5.47791e10	0.435922
$52$	−4.93307e9	−0.0346016
$53$	2.30272e11	1.42708	0.713540	−	0.700614i	$-0.247091\pi$
$53$	2.30272e11	1.42708	0.713540	+	0.700614i	$0.247091\pi$
$54$	−7.08936e9	−0.0389088
$55$	−2.24573e9	−0.0109396
$56$	3.29060e10	0.142578
$57$	2.68577e11	1.03725
$58$	−9.83633e10	−0.339275
$59$	4.11830e11	1.27110	0.635551	−	0.772059i	$-0.280773\pi$
$59$	4.11830e11	1.27110	0.635551	+	0.772059i	$0.280773\pi$
$60$	8.94979e10	0.247645
$61$	−4.06580e11	−1.01042	−0.505210	−	0.862996i	$-0.668585\pi$
$61$	−4.06580e11	−1.01042	−0.505210	+	0.862996i	$0.668585\pi$
$62$	2.87372e10	0.0642538
$63$	5.95462e10	0.119989
$64$	−4.19483e11	−0.763035
$65$	−9.81007e9	−0.0161338
$66$	−1.91730e9	−0.00285531
$67$	2.96486e11	0.400423	0.200211	−	0.979753i	$-0.435837\pi$
$67$	2.96486e11	0.400423	0.200211	+	0.979753i	$0.435837\pi$
$68$	−5.90409e11	−0.724177
$69$	1.92500e11	0.214739
$70$	3.20364e10	0.0325466
$71$	−3.97640e11	−0.368393	−0.184196	−	0.982889i	$-0.558968\pi$
$71$	−3.97640e11	−0.368393	−0.184196	+	0.982889i	$0.558968\pi$
$72$	1.56074e11	0.132029
$73$	−1.37728e12	−1.06518	−0.532591	−	0.846373i	$-0.678781\pi$
$73$	−1.37728e12	−1.06518	−0.532591	+	0.846373i	$0.678781\pi$
$74$	3.38553e11	0.239673
$75$	1.77979e11	0.115470
$76$	−2.89472e12	−1.72313
$77$	1.61041e10	0.00880535
$78$	−8.37537e9	−0.00421104
$79$	−4.66466e11	−0.215896	−0.107948	−	0.994157i	$-0.534428\pi$
$79$	−4.66466e11	−0.215896	−0.107948	+	0.994157i	$0.534428\pi$
$80$	−9.21746e11	−0.393121
$81$	2.82430e11	0.111111
$82$	1.55070e11	0.0563297
$83$	4.77278e12	1.60237	0.801186	−	0.598415i	$-0.204203\pi$
$83$	4.77278e12	1.60237	0.801186	+	0.598415i	$0.204203\pi$
$84$	−6.41788e11	−0.199332
$85$	−1.17411e12	−0.337664
$86$	−1.13508e11	−0.0302541
$87$	3.91865e12	0.968861
$88$	4.22098e10	0.00968894
$89$	6.88111e12	1.46765	0.733827	−	0.679336i	$-0.237732\pi$
$89$	6.88111e12	1.46765	0.733827	+	0.679336i	$0.237732\pi$
$90$	1.51949e11	0.0301386
$91$	7.03479e10	0.0129862
$92$	−2.07476e12	−0.356736
$93$	−1.14485e12	−0.183489
$94$	−6.90203e10	−0.0103192
$95$	−5.75653e12	−0.803448
$96$	−2.54080e12	−0.331289
$97$	1.38827e13	1.69223	0.846113	−	0.533004i	$-0.178937\pi$
$97$	1.38827e13	1.69223	0.846113	+	0.533004i	$0.178937\pi$
$98$	1.54323e12	0.175979
$99$	7.63823e10	0.00815387
$100$	−1.91825e12	−0.191825
$101$	−1.02752e13	−0.963162	−0.481581	−	0.876402i	$-0.659937\pi$
$101$	−1.02752e13	−0.963162	−0.481581	+	0.876402i	$0.659937\pi$
$102$	−1.00240e12	−0.0881329
$103$	1.05918e13	0.874036	0.437018	−	0.899453i	$-0.356035\pi$
$103$	1.05918e13	0.874036	0.437018	+	0.899453i	$0.356035\pi$
$104$	1.84386e11	0.0142893
$105$	−1.27628e12	−0.0929428
$106$	−4.21372e12	−0.288521
$107$	1.26172e13	0.812774	0.406387	−	0.913701i	$-0.366789\pi$
$107$	1.26172e13	0.812774	0.406387	+	0.913701i	$0.366789\pi$
$108$	−3.04402e12	−0.184584
$109$	1.49988e13	0.856612	0.428306	−	0.903634i	$-0.359110\pi$
$109$	1.49988e13	0.856612	0.428306	+	0.903634i	$0.359110\pi$
$110$	4.10943e10	0.00221172
$111$	−1.34874e13	−0.684432
$112$	6.60983e12	0.316427
$113$	−3.11837e13	−1.40902	−0.704512	−	0.709693i	$-0.748834\pi$
$113$	−3.11837e13	−1.40902	−0.704512	+	0.709693i	$0.748834\pi$
$114$	−4.91465e12	−0.209706
$115$	−4.12594e12	−0.166336
$116$	−4.22352e13	−1.60952
$117$	3.33662e11	0.0120254
$118$	−7.53603e12	−0.256986
$119$	8.41950e12	0.271789
$120$	−3.34521e12	−0.102269
$121$	−3.45021e13	−0.999402
$122$	7.43996e12	0.204283
$123$	−6.17775e12	−0.160860
$124$	1.23392e13	0.304821
$125$	−3.81470e12	−0.0894427
$126$	−1.08963e12	−0.0242588
$127$	6.92694e13	1.46493	0.732466	−	0.680804i	$-0.238369\pi$
$127$	6.92694e13	1.46493	0.732466	+	0.680804i	$0.238369\pi$
$128$	3.62278e13	0.728077
$129$	4.52198e12	0.0863963
$130$	1.79513e11	0.00326185
$131$	−3.60740e13	−0.623636	−0.311818	−	0.950142i	$-0.600938\pi$
$131$	−3.60740e13	−0.623636	−0.311818	+	0.950142i	$0.600938\pi$
$132$	−8.23247e11	−0.0135456
$133$	4.12800e13	0.646702
$134$	−5.42537e12	−0.0809558
$135$	−6.05345e12	−0.0860663
$136$	2.20680e13	0.299062
$137$	8.46431e13	1.09372	0.546862	−	0.837223i	$-0.315822\pi$
$137$	8.46431e13	1.09372	0.546862	+	0.837223i	$0.315822\pi$
$138$	−3.52253e12	−0.0434151
$139$	1.23811e13	0.145600	0.0728002	−	0.997347i	$-0.476806\pi$
$139$	1.23811e13	0.145600	0.0728002	+	0.997347i	$0.476806\pi$
$140$	1.37557e13	0.154402
$141$	2.74967e12	0.0294683
$142$	7.27637e12	0.0744801
$143$	9.02380e10	0.000882481 0
$144$	3.13506e13	0.293015
$145$	−8.39903e13	−0.750476
$146$	2.52027e13	0.215354
$147$	−6.14799e13	−0.502540
$148$	1.45367e14	1.13701
$149$	−1.01554e14	−0.760303	−0.380152	−	0.924924i	$-0.624128\pi$
$149$	−1.01554e14	−0.760303	−0.380152	+	0.924924i	$0.624128\pi$
$150$	−3.25681e12	−0.0233453
$151$	−6.26055e13	−0.429796	−0.214898	−	0.976636i	$-0.568942\pi$
$151$	−6.26055e13	−0.429796	−0.214898	+	0.976636i	$0.568942\pi$
$152$	1.08198e14	0.711597
$153$	3.99340e13	0.251680
$154$	−2.94687e11	−0.00178023
$155$	2.45381e13	0.142130
$156$	−3.59621e12	−0.0199772
$157$	−3.46935e14	−1.84885	−0.924423	−	0.381368i	$-0.875453\pi$
$157$	−3.46935e14	−1.84885	−0.924423	+	0.381368i	$0.875453\pi$
$158$	8.53580e12	0.0436489
$159$	1.67868e14	0.823925
$160$	5.44581e13	0.256615
$161$	2.95871e13	0.133886
$162$	−5.16814e12	−0.0224640
$163$	−4.29452e14	−1.79347	−0.896736	−	0.442565i	$-0.854069\pi$
$163$	−4.29452e14	−1.79347	−0.896736	+	0.442565i	$0.854069\pi$
$164$	6.65837e13	0.267229
$165$	−1.63714e12	−0.00631596
$166$	−8.73364e13	−0.323961
$167$	−3.09663e14	−1.10467	−0.552334	−	0.833623i	$-0.686263\pi$
$167$	−3.09663e14	−1.10467	−0.552334	+	0.833623i	$0.686263\pi$
$168$	2.39885e13	0.0823175
$169$	−3.02481e14	−0.998699
$170$	2.14848e13	0.0682675
$171$	1.95793e14	0.598855
$172$	−4.87378e13	−0.143526
$173$	4.50613e13	0.127792	0.0638960	−	0.997957i	$-0.479647\pi$
$173$	4.50613e13	0.127792	0.0638960	+	0.997957i	$0.479647\pi$
$174$	−7.17069e13	−0.195880
$175$	2.73551e13	0.0719932
$176$	8.47869e12	0.0215029
$177$	3.00224e14	0.733871
$178$	−1.25917e14	−0.296724
$179$	1.74245e14	0.395926	0.197963	−	0.980209i	$-0.436567\pi$
$179$	1.74245e14	0.395926	0.197963	+	0.980209i	$0.436567\pi$
$180$	6.52439e13	0.142978
$181$	6.89956e14	1.45851	0.729257	−	0.684240i	$-0.239866\pi$
$181$	6.89956e14	1.45851	0.729257	+	0.684240i	$0.239866\pi$
$182$	−1.28729e12	−0.00262549
$183$	−2.96397e14	−0.583367
$184$	7.75496e13	0.147321
$185$	2.89083e14	0.530158
$186$	2.09494e13	0.0370970
$187$	1.08000e13	0.0184695
$188$	−2.96359e13	−0.0489544
$189$	4.34092e13	0.0692755
$190$	1.05338e14	0.162438
$191$	7.52391e14	1.12131	0.560656	−	0.828049i	$-0.310549\pi$
$191$	7.52391e14	1.12131	0.560656	+	0.828049i	$0.310549\pi$
$192$	−3.05803e14	−0.440539
$193$	4.18449e14	0.582801	0.291400	−	0.956601i	$-0.405879\pi$
$193$	4.18449e14	0.582801	0.291400	+	0.956601i	$0.405879\pi$
$194$	−2.54038e14	−0.342127
$195$	−7.15154e12	−0.00931483
$196$	6.62629e14	0.834846
$197$	−5.04365e14	−0.614772	−0.307386	−	0.951585i	$-0.599454\pi$
$197$	−5.04365e14	−0.614772	−0.307386	+	0.951585i	$0.599454\pi$
$198$	−1.39771e12	−0.00164852
$199$	−1.01359e15	−1.15696	−0.578479	−	0.815697i	$-0.696354\pi$
$199$	−1.01359e15	−1.15696	−0.578479	+	0.815697i	$0.696354\pi$
$200$	7.16995e13	0.0792175
$201$	2.16139e14	0.231184
$202$	1.88024e14	0.194728
$203$	6.02293e14	0.604065
$204$	−4.30408e14	−0.418104
$205$	1.32411e14	0.124601
$206$	−1.93819e14	−0.176709
$207$	1.40333e14	0.123980
$208$	3.70377e13	0.0317126
$209$	5.29515e13	0.0439468
$210$	2.33545e13	0.0187908
$211$	6.68511e14	0.521522	0.260761	−	0.965403i	$-0.416027\pi$
$211$	6.68511e14	0.521522	0.260761	+	0.965403i	$0.416027\pi$
$212$	−1.80928e15	−1.36875
$213$	−2.89880e14	−0.212692
$214$	−2.30881e14	−0.164323
$215$	−9.69216e13	−0.0669223
$216$	1.13778e14	0.0762271
$217$	−1.75962e14	−0.114401
$218$	−2.74461e14	−0.173186
$219$	−1.00404e15	−0.614983
$220$	1.76450e13	0.0104924
$221$	4.71780e13	0.0272389
$222$	2.46805e14	0.138376
$223$	−6.64343e14	−0.361752	−0.180876	−	0.983506i	$-0.557893\pi$
$223$	−6.64343e14	−0.361752	−0.180876	+	0.983506i	$0.557893\pi$
$224$	−3.90518e14	−0.206552
$225$	1.29746e14	0.0666667
$226$	5.70627e14	0.284870
$227$	−2.74872e15	−1.33341	−0.666703	−	0.745324i	$-0.732295\pi$
$227$	−2.74872e15	−1.33341	−0.666703	+	0.745324i	$0.732295\pi$
$228$	−2.11025e15	−0.994849
$229$	1.93108e15	0.884851	0.442426	−	0.896805i	$-0.354118\pi$
$229$	1.93108e15	0.884851	0.442426	+	0.896805i	$0.354118\pi$
$230$	7.55001e13	0.0336292
$231$	1.17399e13	0.00508377
$232$	1.57865e15	0.664681
$233$	3.04503e15	1.24674	0.623372	−	0.781925i	$-0.285762\pi$
$233$	3.04503e15	1.24674	0.623372	+	0.781925i	$0.285762\pi$
$234$	−6.10564e12	−0.00243124
$235$	−5.89349e13	−0.0228261
$236$	−3.23581e15	−1.21914
$237$	−3.40054e14	−0.124647
$238$	−1.54067e14	−0.0549491
$239$	1.63875e15	0.568756	0.284378	−	0.958712i	$-0.408213\pi$
$239$	1.63875e15	0.568756	0.284378	+	0.958712i	$0.408213\pi$
$240$	−6.71953e14	−0.226969
$241$	−2.33624e14	−0.0768081	−0.0384041	−	0.999262i	$-0.512227\pi$
$241$	−2.33624e14	−0.0768081	−0.0384041	+	0.999262i	$0.512227\pi$
$242$	6.31348e14	0.202055
$243$	2.05891e14	0.0641500
$244$	3.19456e15	0.969120
$245$	1.31773e15	0.389266
$246$	1.13046e14	0.0325219
$247$	2.31309e14	0.0648131
$248$	−4.61208e14	−0.125881
$249$	3.47935e15	0.925130
$250$	6.98046e13	0.0180832
$251$	−3.58149e15	−0.904033	−0.452016	−	0.892010i	$-0.649295\pi$
$251$	−3.58149e15	−0.904033	−0.452016	+	0.892010i	$0.649295\pi$
$252$	−4.67863e14	−0.115084
$253$	3.79525e13	0.00909824
$254$	−1.26755e15	−0.296174
$255$	−8.55924e14	−0.194950
$256$	2.77348e15	0.615836
$257$	7.60591e15	1.64659	0.823296	−	0.567612i	$-0.192133\pi$
$257$	7.60591e15	1.64659	0.823296	+	0.567612i	$0.192133\pi$
$258$	−8.27470e13	−0.0174672
$259$	−2.07301e15	−0.426729
$260$	7.70792e13	0.0154743
$261$	2.85670e15	0.559372
$262$	6.60113e14	0.126084
$263$	7.86154e15	1.46486	0.732428	−	0.680844i	$-0.238387\pi$
$263$	7.86154e15	1.46486	0.732428	+	0.680844i	$0.238387\pi$
$264$	3.07710e13	0.00559391
$265$	−3.59800e15	−0.638210
$266$	−7.55378e14	−0.130748
$267$	5.01633e15	0.847350
$268$	−2.32954e15	−0.384055
$269$	−6.04452e15	−0.972685	−0.486343	−	0.873768i	$-0.661669\pi$
$269$	−6.04452e15	−0.972685	−0.486343	+	0.873768i	$0.661669\pi$
$270$	1.10771e14	0.0174005
$271$	−1.14219e16	−1.75162	−0.875809	−	0.482658i	$-0.839672\pi$
$271$	−1.14219e16	−1.75162	−0.875809	+	0.482658i	$0.839672\pi$
$272$	4.43281e15	0.663714
$273$	5.12836e13	0.00749758
$274$	−1.54887e15	−0.221125
$275$	3.50895e13	0.00489232
$276$	−1.51250e15	−0.205962
$277$	−1.65973e15	−0.220760	−0.110380	−	0.993889i	$-0.535207\pi$
$277$	−1.65973e15	−0.220760	−0.110380	+	0.993889i	$0.535207\pi$
$278$	−2.26560e14	−0.0294369
$279$	−8.34595e14	−0.105937
$280$	−5.14156e14	−0.0637629
$281$	−1.28234e16	−1.55386	−0.776930	−	0.629587i	$-0.783224\pi$
$281$	−1.28234e16	−1.55386	−0.776930	+	0.629587i	$0.783224\pi$
$282$	−5.03158e13	−0.00595779
$283$	−1.55354e16	−1.79767	−0.898837	−	0.438283i	$-0.855587\pi$
$283$	−1.55354e16	−1.79767	−0.898837	+	0.438283i	$0.855587\pi$
$284$	3.12432e15	0.353335
$285$	−4.19651e15	−0.463871
$286$	−1.65125e12	−0.000178416 0
$287$	−9.49515e14	−0.100293
$288$	−1.85224e15	−0.191270
$289$	−4.25813e15	−0.429916
$290$	1.53693e15	0.151728
$291$	1.01205e16	0.977007
$292$	1.08215e16	1.02164
$293$	1.56366e16	1.44378	0.721891	−	0.692007i	$-0.243273\pi$
$293$	1.56366e16	1.44378	0.721891	+	0.692007i	$0.243273\pi$
$294$	1.12501e15	0.101601
$295$	−6.43485e15	−0.568454
$296$	−5.43348e15	−0.469550
$297$	5.56827e13	0.00470764
$298$	1.85833e15	0.153715
$299$	1.65789e14	0.0134182
$300$	−1.39840e15	−0.110750
$301$	6.95024e14	0.0538663
$302$	1.14561e15	0.0868944
$303$	−7.49059e15	−0.556082
$304$	2.17336e16	1.57926
$305$	6.35282e15	0.451874
$306$	−7.30747e14	−0.0508836
$307$	−4.73925e15	−0.323080	−0.161540	−	0.986866i	$-0.551646\pi$
$307$	−4.73925e15	−0.323080	−0.161540	+	0.986866i	$0.551646\pi$
$308$	−1.26532e14	−0.00844543
$309$	7.72145e15	0.504625
$310$	−4.49019e14	−0.0287352
$311$	−2.24003e16	−1.40382	−0.701911	−	0.712265i	$-0.747670\pi$
$311$	−2.24003e16	−1.40382	−0.701911	+	0.712265i	$0.747670\pi$
$312$	1.34418e14	0.00824995
$313$	−2.48799e15	−0.149558	−0.0747791	−	0.997200i	$-0.523825\pi$
$313$	−2.48799e15	−0.149558	−0.0747791	+	0.997200i	$0.523825\pi$
$314$	6.34852e15	0.373792
$315$	−9.30409e14	−0.0536606
$316$	3.66510e15	0.207071
$317$	−7.02646e14	−0.0388912	−0.0194456	−	0.999811i	$-0.506190\pi$
$317$	−7.02646e14	−0.0388912	−0.0194456	+	0.999811i	$0.506190\pi$
$318$	−3.07180e15	−0.166578
$319$	7.72585e14	0.0410494
$320$	6.55442e15	0.341240
$321$	9.19797e15	0.469255
$322$	−5.41410e14	−0.0270684
$323$	2.76840e16	1.35648
$324$	−2.21909e15	−0.106569
$325$	1.53282e14	0.00721523
$326$	7.85848e15	0.362597
$327$	1.09341e16	0.494565
$328$	−2.48874e15	−0.110357
$329$	4.22621e14	0.0183729
$330$	2.99578e13	0.00127693
$331$	2.99883e16	1.25334	0.626672	−	0.779283i	$-0.284417\pi$
$331$	2.99883e16	1.25334	0.626672	+	0.779283i	$0.284417\pi$
$332$	−3.75004e16	−1.53688
$333$	−9.83234e15	−0.395157
$334$	5.66648e15	0.223337
$335$	−4.63260e15	−0.179074
$336$	4.81856e15	0.182689
$337$	2.60291e16	0.967975	0.483987	−	0.875075i	$-0.339188\pi$
$337$	2.60291e16	0.967975	0.483987	+	0.875075i	$0.339188\pi$
$338$	5.53506e15	0.201913
$339$	−2.27329e16	−0.813500
$340$	9.22513e15	0.323862
$341$	−2.25714e14	−0.00777419
$342$	−3.58278e15	−0.121074
$343$	−2.03055e16	−0.673289
$344$	1.82170e15	0.0592717
$345$	−3.00781e15	−0.0960344
$346$	−8.24570e14	−0.0258365
$347$	−5.96465e16	−1.83419	−0.917093	−	0.398674i	$-0.869470\pi$
$347$	−5.96465e16	−1.83419	−0.917093	+	0.398674i	$0.869470\pi$
$348$	−3.07894e16	−0.929259
$349$	−2.72283e16	−0.806595	−0.403298	−	0.915069i	$-0.632136\pi$
$349$	−2.72283e16	−0.806595	−0.403298	+	0.915069i	$0.632136\pi$
$350$	−5.00568e14	−0.0145553
$351$	2.43240e14	0.00694286
$352$	−5.00933e14	−0.0140363
$353$	5.67802e16	1.56193	0.780964	−	0.624576i	$-0.214728\pi$
$353$	5.67802e16	1.56193	0.780964	+	0.624576i	$0.214728\pi$
$354$	−5.49376e15	−0.148371
$355$	6.21313e15	0.164750
$356$	−5.40659e16	−1.40766
$357$	6.13782e15	0.156917
$358$	−3.18848e15	−0.0800467
$359$	−7.02312e16	−1.73147	−0.865737	−	0.500499i	$-0.833150\pi$
$359$	−7.02312e16	−1.73147	−0.865737	+	0.500499i	$0.833150\pi$
$360$	−2.43866e15	−0.0590453
$361$	9.36790e16	2.22764
$362$	−1.26254e16	−0.294876
$363$	−2.51520e16	−0.577005
$364$	−5.52734e14	−0.0124554
$365$	2.15200e16	0.476364
$366$	5.42373e15	0.117943
$367$	−2.11880e16	−0.452649	−0.226324	−	0.974052i	$-0.572671\pi$
$367$	−2.11880e16	−0.452649	−0.226324	+	0.974052i	$0.572671\pi$
$368$	1.55774e16	0.326952
$369$	−4.50358e15	−0.0928724
$370$	−5.28988e15	−0.107185
$371$	2.58012e16	0.513700
$372$	8.99526e15	0.175989
$373$	2.26994e16	0.436421	0.218211	−	0.975902i	$-0.429978\pi$
$373$	2.26994e16	0.436421	0.218211	+	0.975902i	$0.429978\pi$
$374$	−1.97628e14	−0.00373408
$375$	−2.78091e15	−0.0516398
$376$	1.10772e15	0.0202166
$377$	3.37490e15	0.0605400
$378$	−7.94338e14	−0.0140058
$379$	−3.61052e16	−0.625770	−0.312885	−	0.949791i	$-0.601296\pi$
$379$	−3.61052e16	−0.625770	−0.312885	+	0.949791i	$0.601296\pi$
$380$	4.52300e16	0.770607
$381$	5.04974e16	0.845779
$382$	−1.37679e16	−0.226702
$383$	2.14417e16	0.347110	0.173555	−	0.984824i	$-0.444475\pi$
$383$	2.14417e16	0.347110	0.173555	+	0.984824i	$0.444475\pi$
$384$	2.64101e16	0.420355
$385$	−2.51626e14	−0.00393787
$386$	−7.65714e15	−0.117828
$387$	3.29652e15	0.0498809
$388$	−1.09079e17	−1.62306
$389$	6.52962e16	0.955466	0.477733	−	0.878505i	$-0.341459\pi$
$389$	6.52962e16	0.955466	0.477733	+	0.878505i	$0.341459\pi$
$390$	1.30865e14	0.00188323
$391$	1.98422e16	0.280829
$392$	−2.47675e16	−0.344764
$393$	−2.62980e16	−0.360056
$394$	9.22930e15	0.124292
$395$	7.28854e15	0.0965515
$396$	−6.00147e14	−0.00782058
$397$	3.27384e16	0.419680	0.209840	−	0.977736i	$-0.432706\pi$
$397$	3.27384e16	0.419680	0.209840	+	0.977736i	$0.432706\pi$
$398$	1.85476e16	0.233909
$399$	3.00931e16	0.373374
$400$	1.44023e16	0.175809
$401$	3.67179e16	0.441001	0.220501	−	0.975387i	$-0.429231\pi$
$401$	3.67179e16	0.441001	0.220501	+	0.975387i	$0.429231\pi$
$402$	−3.95509e15	−0.0467398
$403$	−9.85991e14	−0.0114654
$404$	8.07334e16	0.923793
$405$	−4.41296e15	−0.0496904
$406$	−1.10213e16	−0.122127
$407$	−2.65913e15	−0.0289985
$408$	1.60876e16	0.172663
$409$	2.37728e14	0.00251119	0.00125559	−	0.999999i	$-0.499600\pi$
$409$	2.37728e14	0.00251119	0.00125559	+	0.999999i	$0.499600\pi$
$410$	−2.42297e15	−0.0251914
$411$	6.17048e16	0.631462
$412$	−8.32217e16	−0.838310
$413$	4.61442e16	0.457553
$414$	−2.56793e15	−0.0250657
$415$	−7.45746e16	−0.716603
$416$	−2.18824e15	−0.0207008
$417$	9.02581e15	0.0840624
$418$	−9.68953e14	−0.00888499
$419$	−1.07748e17	−0.972785	−0.486392	−	0.873741i	$-0.661687\pi$
$419$	−1.07748e17	−0.972785	−0.486392	+	0.873741i	$0.661687\pi$
$420$	1.00279e16	0.0891438
$421$	−4.46846e15	−0.0391133	−0.0195566	−	0.999809i	$-0.506225\pi$
$421$	−4.46846e15	−0.0391133	−0.0195566	+	0.999809i	$0.506225\pi$
$422$	−1.22330e16	−0.105439
$423$	2.00451e15	0.0170136
$424$	6.76266e16	0.565249
$425$	1.83454e16	0.151008
$426$	5.30447e15	0.0430011
$427$	−4.55559e16	−0.363717
$428$	−9.91356e16	−0.779552
$429$	6.57835e13	0.000509501 0
$430$	1.77356e15	0.0135301
$431$	−2.38034e17	−1.78869	−0.894347	−	0.447373i	$-0.852360\pi$
$431$	−2.38034e17	−1.78869	−0.894347	+	0.447373i	$0.852360\pi$
$432$	2.28546e16	0.169172
$433$	1.52333e16	0.111077	0.0555384	−	0.998457i	$-0.482312\pi$
$433$	1.52333e16	0.111077	0.0555384	+	0.998457i	$0.482312\pi$
$434$	3.21991e15	0.0231292
$435$	−6.12289e16	−0.433288
$436$	−1.17848e17	−0.821598
$437$	9.72846e16	0.668213
$438$	1.83727e16	0.124335
$439$	−1.46731e17	−0.978370	−0.489185	−	0.872180i	$-0.662706\pi$
$439$	−1.46731e17	−0.978370	−0.489185	+	0.872180i	$0.662706\pi$
$440$	−6.59529e14	−0.00433303
$441$	−4.48188e16	−0.290141
$442$	−8.63304e14	−0.00550705
$443$	1.80890e17	1.13708	0.568540	−	0.822656i	$-0.307508\pi$
$443$	1.80890e17	1.13708	0.568540	+	0.822656i	$0.307508\pi$
$444$	1.05973e17	0.656455
$445$	−1.07517e17	−0.656355
$446$	1.21567e16	0.0731375
$447$	−7.40330e16	−0.438961
$448$	−4.70017e16	−0.274667
$449$	−2.86599e17	−1.65072	−0.825360	−	0.564607i	$-0.809028\pi$
$449$	−2.86599e17	−1.65072	−0.825360	+	0.564607i	$0.809028\pi$
$450$	−2.37421e15	−0.0134784
$451$	−1.21798e15	−0.00681542
$452$	2.45015e17	1.35143
$453$	−4.56394e16	−0.248143
$454$	5.02984e16	0.269582
$455$	−1.09919e15	−0.00580760
$456$	7.88760e16	0.410841
$457$	2.00560e17	1.02989	0.514943	−	0.857224i	$-0.327813\pi$
$457$	2.00560e17	1.02989	0.514943	+	0.857224i	$0.327813\pi$
$458$	−3.53366e16	−0.178895
$459$	2.91119e16	0.145307
$460$	3.24182e16	0.159537
$461$	−7.03451e16	−0.341332	−0.170666	−	0.985329i	$-0.554592\pi$
$461$	−7.03451e16	−0.341332	−0.170666	+	0.985329i	$0.554592\pi$
$462$	−2.14827e14	−0.00102782
$463$	1.71885e17	0.810891	0.405446	−	0.914119i	$-0.367116\pi$
$463$	1.71885e17	0.810891	0.405446	+	0.914119i	$0.367116\pi$
$464$	3.17103e17	1.47514
$465$	1.78883e16	0.0820586
$466$	−5.57205e16	−0.252062
$467$	5.37684e16	0.239865	0.119933	−	0.992782i	$-0.461732\pi$
$467$	5.37684e16	0.239865	0.119933	+	0.992782i	$0.461732\pi$
$468$	−2.62164e15	−0.0115339
$469$	3.32203e16	0.144139
$470$	1.07844e15	0.00461488
$471$	−2.52916e17	−1.06743
$472$	1.20947e17	0.503467
$473$	8.91535e14	0.00366050
$474$	6.22260e15	0.0252007
$475$	8.99458e16	0.359313
$476$	−6.61533e16	−0.260679
$477$	1.22376e17	0.475693
$478$	−2.99872e16	−0.114989
$479$	1.45707e17	0.551188	0.275594	−	0.961274i	$-0.411125\pi$
$479$	1.45707e17	0.551188	0.275594	+	0.961274i	$0.411125\pi$
$480$	3.97000e16	0.148157
$481$	−1.16159e16	−0.0427672
$482$	4.27506e15	0.0155287
$483$	2.15690e16	0.0772989
$484$	2.71088e17	0.958551
$485$	−2.16917e17	−0.756786
$486$	−3.76757e15	−0.0129696
$487$	2.20545e17	0.749132	0.374566	−	0.927200i	$-0.377792\pi$
$487$	2.20545e17	0.749132	0.374566	+	0.927200i	$0.377792\pi$
$488$	−1.19405e17	−0.400215
$489$	−3.13070e17	−1.03546
$490$	−2.41129e16	−0.0787001
$491$	−2.43820e16	−0.0785309	−0.0392654	−	0.999229i	$-0.512502\pi$
$491$	−2.43820e16	−0.0785309	−0.0392654	+	0.999229i	$0.512502\pi$
$492$	4.85395e16	0.154285
$493$	4.03921e17	1.26704
$494$	−4.23270e15	−0.0131036
$495$	−1.19347e15	−0.00364652
$496$	−9.26429e16	−0.279371
$497$	−4.45543e16	−0.132609
$498$	−6.36682e16	−0.187039
$499$	2.54719e17	0.738599	0.369299	−	0.929311i	$-0.379598\pi$
$499$	2.54719e17	0.738599	0.369299	+	0.929311i	$0.379598\pi$
$500$	2.99727e16	0.0857867
$501$	−2.25744e17	−0.637781
$502$	6.55371e16	0.182774
$503$	−3.72489e17	−1.02547	−0.512733	−	0.858548i	$-0.671367\pi$
$503$	−3.72489e17	−1.02547	−0.512733	+	0.858548i	$0.671367\pi$
$504$	1.74876e16	0.0475260
$505$	1.60549e17	0.430739
$506$	−6.94488e14	−0.00183944
$507$	−2.20509e17	−0.576599
$508$	−5.44260e17	−1.40505
$509$	−1.62073e17	−0.413091	−0.206546	−	0.978437i	$-0.566222\pi$
$509$	−1.62073e17	−0.413091	−0.206546	+	0.978437i	$0.566222\pi$
$510$	1.56624e16	0.0394142
$511$	−1.54320e17	−0.383429
$512$	−3.47530e17	−0.852584
$513$	1.42733e17	0.345749
$514$	−1.39180e17	−0.332901
$515$	−1.65498e17	−0.390881
$516$	−3.55298e16	−0.0828648
$517$	5.42113e14	0.00124854
$518$	3.79337e16	0.0862743
$519$	3.28497e16	0.0737808
$520$	−2.88103e15	−0.00639038
$521$	1.71142e17	0.374896	0.187448	−	0.982275i	$-0.439978\pi$
$521$	1.71142e17	0.374896	0.187448	+	0.982275i	$0.439978\pi$
$522$	−5.22743e16	−0.113092
$523$	4.86625e17	1.03976	0.519880	−	0.854239i	$-0.325977\pi$
$523$	4.86625e17	1.03976	0.519880	+	0.854239i	$0.325977\pi$
$524$	2.83439e17	0.598145
$525$	1.99419e16	0.0415653
$526$	−1.43857e17	−0.296159
$527$	−1.18007e17	−0.239960
$528$	6.18096e15	0.0124147
$529$	−4.34308e17	−0.861661
$530$	6.58394e16	0.129031
$531$	2.18863e17	0.423700
$532$	−3.24343e17	−0.620268
$533$	−5.32053e15	−0.0100514
$534$	−9.17932e16	−0.171314
$535$	−1.97144e17	−0.363484
$536$	8.70725e16	0.158602
$537$	1.27024e17	0.228588
$538$	1.10608e17	0.196653
$539$	−1.21211e16	−0.0212920
$540$	4.75628e16	0.0825483
$541$	2.80840e17	0.481589	0.240795	−	0.970576i	$-0.422592\pi$
$541$	2.80840e17	0.481589	0.240795	+	0.970576i	$0.422592\pi$
$542$	2.09009e17	0.354135
$543$	5.02978e17	0.842073
$544$	−2.61897e17	−0.433249
$545$	−2.34356e17	−0.383089
$546$	−9.38432e14	−0.00151583
$547$	−6.77006e17	−1.08062	−0.540312	−	0.841464i	$-0.681694\pi$
$547$	−6.77006e17	−1.08062	−0.540312	+	0.841464i	$0.681694\pi$
$548$	−6.65054e17	−1.04902
$549$	−2.16073e17	−0.336807
$550$	−6.42099e14	−0.000989109 0
$551$	1.98039e18	3.01484
$552$	5.65336e16	0.0850556
$553$	−5.22660e16	−0.0777152
$554$	3.03713e16	0.0446323
$555$	2.10741e17	0.306087
$556$	−9.72800e16	−0.139649
$557$	−4.76254e17	−0.675740	−0.337870	−	0.941193i	$-0.609706\pi$
$557$	−4.76254e17	−0.675740	−0.337870	+	0.941193i	$0.609706\pi$
$558$	1.52721e16	0.0214179
$559$	3.89451e15	0.00539854
$560$	−1.03279e17	−0.141510
$561$	7.87322e15	0.0106634
$562$	2.34654e17	0.314153
$563$	−1.40153e17	−0.185480	−0.0927400	−	0.995690i	$-0.529563\pi$
$563$	−1.40153e17	−0.185480	−0.0927400	+	0.995690i	$0.529563\pi$
$564$	−2.16045e16	−0.0282638
$565$	4.87246e17	0.630134
$566$	2.84280e17	0.363446
$567$	3.16453e16	0.0399962
$568$	−1.16780e17	−0.145916
$569$	4.19192e17	0.517825	0.258912	−	0.965901i	$-0.416636\pi$
$569$	4.19192e17	0.517825	0.258912	+	0.965901i	$0.416636\pi$
$570$	7.67914e16	0.0937835
$571$	4.21896e17	0.509414	0.254707	−	0.967018i	$-0.418021\pi$
$571$	4.21896e17	0.509414	0.254707	+	0.967018i	$0.418021\pi$
$572$	−7.09014e14	−0.000846410 0
$573$	5.48493e17	0.647390
$574$	1.73750e16	0.0202768
$575$	6.44679e16	0.0743879
$576$	−2.22930e17	−0.254345
$577$	−2.42814e17	−0.273924	−0.136962	−	0.990576i	$-0.543734\pi$
$577$	−2.42814e17	−0.273924	−0.136962	+	0.990576i	$0.543734\pi$
$578$	7.79190e16	0.0869185
$579$	3.05049e17	0.336480
$580$	6.59924e17	0.719801
$581$	5.34774e17	0.576800
$582$	−1.85194e17	−0.197527
$583$	3.30963e16	0.0349087
$584$	−4.04481e17	−0.421905
$585$	−5.21347e15	−0.00537792
$586$	−2.86131e17	−0.291898
$587$	1.71527e18	1.73055	0.865274	−	0.501299i	$-0.167144\pi$
$587$	1.71527e18	1.73055	0.865274	+	0.501299i	$0.167144\pi$
$588$	4.83057e17	0.481998
$589$	−5.78578e17	−0.570969
$590$	1.17750e17	0.114928
$591$	−3.67682e17	−0.354939
$592$	−1.09142e18	−1.04208
$593$	−1.76024e18	−1.66232	−0.831161	−	0.556031i	$-0.812324\pi$
$593$	−1.76024e18	−1.66232	−0.831161	+	0.556031i	$0.812324\pi$
$594$	−1.01893e15	−0.000951771 0
$595$	−1.31555e17	−0.121548
$596$	7.97926e17	0.729226
$597$	−7.38908e17	−0.667970
$598$	−3.03375e15	−0.00271283
$599$	−1.01218e18	−0.895328	−0.447664	−	0.894202i	$-0.647744\pi$
$599$	−1.01218e18	−0.895328	−0.447664	+	0.894202i	$0.647744\pi$
$600$	5.22690e16	0.0457363
$601$	−1.00124e18	−0.866669	−0.433335	−	0.901233i	$-0.642663\pi$
$601$	−1.00124e18	−0.866669	−0.433335	+	0.901233i	$0.642663\pi$
$602$	−1.27181e16	−0.0108905
$603$	1.57565e17	0.133474
$604$	4.91901e17	0.412228
$605$	5.39095e17	0.446946
$606$	1.37069e17	0.112426
$607$	−1.81791e18	−1.47518	−0.737590	−	0.675249i	$-0.764036\pi$
$607$	−1.81791e18	−1.47518	−0.737590	+	0.675249i	$0.764036\pi$
$608$	−1.28405e18	−1.03089
$609$	4.39072e17	0.348757
$610$	−1.16249e17	−0.0913580
$611$	2.36812e15	0.00184135
$612$	−3.13767e17	−0.241392
$613$	−1.45199e18	−1.10527	−0.552637	−	0.833422i	$-0.686378\pi$
$613$	−1.45199e18	−1.10527	−0.552637	+	0.833422i	$0.686378\pi$
$614$	8.67229e16	0.0653190
$615$	9.65274e16	0.0719386
$616$	4.72947e15	0.00348769
$617$	7.36777e17	0.537629	0.268814	−	0.963192i	$-0.413368\pi$
$617$	7.36777e17	0.537629	0.268814	+	0.963192i	$0.413368\pi$
$618$	−1.41294e17	−0.102023
$619$	3.78289e16	0.0270293	0.0135147	−	0.999909i	$-0.495698\pi$
$619$	3.78289e16	0.0270293	0.0135147	+	0.999909i	$0.495698\pi$
$620$	−1.92800e17	−0.136320
$621$	1.02302e17	0.0715798
$622$	4.09901e17	0.283819
$623$	7.71006e17	0.528306
$624$	2.70004e16	0.0183093
$625$	5.96046e16	0.0400000
$626$	4.55273e16	0.0302370
$627$	3.86017e16	0.0253727
$628$	2.72592e18	1.77327
$629$	−1.39024e18	−0.895077
$630$	1.70254e16	0.0108489
$631$	1.18325e18	0.746253	0.373127	−	0.927780i	$-0.378286\pi$
$631$	1.18325e18	0.746253	0.373127	+	0.927780i	$0.378286\pi$
$632$	−1.36992e17	−0.0855137
$633$	4.87344e17	0.301101
$634$	1.28576e16	0.00786286
$635$	−1.08233e18	−0.655137
$636$	−1.31897e18	−0.790247
$637$	−5.29490e16	−0.0314016
$638$	−1.41374e16	−0.00829920
$639$	−2.11322e17	−0.122798
$640$	−5.66059e17	−0.325606
$641$	2.00244e17	0.114020	0.0570102	−	0.998374i	$-0.481843\pi$
$641$	2.00244e17	0.114020	0.0570102	+	0.998374i	$0.481843\pi$
$642$	−1.68312e17	−0.0948721
$643$	2.12199e18	1.18406	0.592028	−	0.805917i	$-0.298327\pi$
$643$	2.12199e18	1.18406	0.592028	+	0.805917i	$0.298327\pi$
$644$	−2.32470e17	−0.128413
$645$	−7.06559e16	−0.0386376
$646$	−5.06586e17	−0.274247
$647$	−1.12704e18	−0.604032	−0.302016	−	0.953303i	$-0.597660\pi$
$647$	−1.12704e18	−0.604032	−0.302016	+	0.953303i	$0.597660\pi$
$648$	8.29443e16	0.0440097
$649$	5.91910e16	0.0310932
$650$	−2.80489e15	−0.00145875
$651$	−1.28277e17	−0.0660497
$652$	3.37427e18	1.72016
$653$	−2.48373e18	−1.25363	−0.626813	−	0.779169i	$-0.715641\pi$
$653$	−2.48373e18	−1.25363	−0.626813	+	0.779169i	$0.715641\pi$
$654$	−2.00082e17	−0.0999891
$655$	5.63656e17	0.278898
$656$	−4.99913e17	−0.244917
$657$	−7.31943e17	−0.355060
$658$	−7.73349e15	−0.00371456
$659$	3.56057e18	1.69342	0.846709	−	0.532056i	$-0.178580\pi$
$659$	3.56057e18	1.69342	0.846709	+	0.532056i	$0.178580\pi$
$660$	1.28632e16	0.00605779
$661$	−1.25090e18	−0.583329	−0.291664	−	0.956521i	$-0.594209\pi$
$661$	−1.25090e18	−0.583329	−0.291664	+	0.956521i	$0.594209\pi$
$662$	−5.48752e17	−0.253396
$663$	3.43928e16	0.0157264
$664$	1.40167e18	0.634680
$665$	−6.45000e17	−0.289214
$666$	1.79921e17	0.0798911
$667$	1.41942e18	0.624158
$668$	2.43307e18	1.05952
$669$	−4.84306e17	−0.208858
$670$	8.47713e16	0.0362045
$671$	−5.84364e16	−0.0247165
$672$	−2.84688e17	−0.119253
$673$	2.74283e18	1.13789	0.568946	−	0.822375i	$-0.307352\pi$
$673$	2.74283e18	1.13789	0.568946	+	0.822375i	$0.307352\pi$
$674$	−4.76302e17	−0.195701
$675$	9.45851e16	0.0384900
$676$	2.37664e18	0.957877
$677$	4.19537e18	1.67473	0.837364	−	0.546646i	$-0.184095\pi$
$677$	4.19537e18	1.67473	0.837364	+	0.546646i	$0.184095\pi$
$678$	4.15987e17	0.164470
$679$	1.55551e18	0.609144
$680$	−3.44813e17	−0.133744
$681$	−2.00382e18	−0.769842
$682$	4.13031e15	0.00157175
$683$	−2.74346e18	−1.03410	−0.517052	−	0.855954i	$-0.672971\pi$
$683$	−2.74346e18	−1.03410	−0.517052	+	0.855954i	$0.672971\pi$
$684$	−1.53837e18	−0.574376
$685$	−1.32255e18	−0.489128
$686$	3.71567e17	0.136123
$687$	1.40776e18	0.510869
$688$	3.65925e17	0.131543
$689$	1.44575e17	0.0514836
$690$	5.50396e16	0.0194158
$691$	−5.46424e18	−1.90951	−0.954756	−	0.297390i	$-0.903884\pi$
$691$	−5.46424e18	−1.90951	−0.954756	+	0.297390i	$0.903884\pi$
$692$	−3.54053e17	−0.122569
$693$	8.55838e15	0.00293512
$694$	1.09146e18	0.370828
$695$	−1.93454e17	−0.0651144
$696$	1.15083e18	0.383754
$697$	−6.36782e17	−0.210367
$698$	4.98248e17	0.163074
$699$	2.21982e18	0.719808
$700$	−2.14933e17	−0.0690505
$701$	−5.09836e18	−1.62279	−0.811397	−	0.584495i	$-0.801293\pi$
$701$	−5.09836e18	−1.62279	−0.811397	+	0.584495i	$0.801293\pi$
$702$	−4.45101e15	−0.00140368
$703$	−6.81621e18	−2.12977
$704$	−6.02909e16	−0.0186651
$705$	−4.29635e16	−0.0131786
$706$	−1.03901e18	−0.315784
$707$	−1.15130e18	−0.346706
$708$	−2.35891e18	−0.703874
$709$	−2.21731e18	−0.655580	−0.327790	−	0.944751i	$-0.606304\pi$
$709$	−2.21731e18	−0.655580	−0.327790	+	0.944751i	$0.606304\pi$
$710$	−1.13693e17	−0.0333085
$711$	−2.47899e17	−0.0719653
$712$	2.02085e18	0.581320
$713$	−4.14691e17	−0.118207
$714$	−1.12315e17	−0.0317249
$715$	−1.40997e15	−0.000394658 0
$716$	−1.36907e18	−0.379743
$717$	1.19465e18	0.328371
$718$	1.28515e18	0.350062
$719$	5.05135e18	1.36355	0.681773	−	0.731563i	$-0.261209\pi$
$719$	5.05135e18	1.36355	0.681773	+	0.731563i	$0.261209\pi$
$720$	−4.89854e17	−0.131040
$721$	1.18678e18	0.314623
$722$	−1.71422e18	−0.450375
$723$	−1.70312e17	−0.0443452
$724$	−5.42109e18	−1.39890
$725$	1.31235e18	0.335623
$726$	4.60253e17	0.116656
$727$	2.06443e18	0.518594	0.259297	−	0.965798i	$-0.416509\pi$
$727$	2.06443e18	0.518594	0.259297	+	0.965798i	$0.416509\pi$
$728$	2.06599e16	0.00514367
$729$	1.50095e17	0.0370370
$730$	−3.93792e17	−0.0963092
$731$	4.66110e17	0.112986
$732$	2.32884e18	0.559522
$733$	−2.95043e18	−0.702603	−0.351301	−	0.936262i	$-0.614261\pi$
$733$	−2.95043e18	−0.702603	−0.351301	+	0.936262i	$0.614261\pi$
$734$	3.87717e17	0.0915147
$735$	9.60623e17	0.224743
$736$	−9.20335e17	−0.213422
$737$	4.26130e16	0.00979498
$738$	8.24104e16	0.0187766
$739$	−1.77031e18	−0.399816	−0.199908	−	0.979815i	$-0.564064\pi$
$739$	−1.77031e18	−0.399816	−0.199908	+	0.979815i	$0.564064\pi$
$740$	−2.27137e18	−0.508488
$741$	1.68625e17	0.0374199
$742$	−4.72133e17	−0.103858
$743$	8.75773e18	1.90970	0.954848	−	0.297094i	$-0.0960174\pi$
$743$	8.75773e18	1.90970	0.954848	+	0.297094i	$0.0960174\pi$
$744$	−3.36221e17	−0.0726776
$745$	1.58678e18	0.340018
$746$	−4.15372e17	−0.0882339
$747$	2.53645e18	0.534124
$748$	−8.48575e16	−0.0177145
$749$	1.41372e18	0.292571
$750$	5.08876e16	0.0104403
$751$	3.32951e18	0.677205	0.338602	−	0.940930i	$-0.390046\pi$
$751$	3.32951e18	0.677205	0.338602	+	0.940930i	$0.390046\pi$
$752$	2.22507e17	0.0448671
$753$	−2.61090e18	−0.521944
$754$	−6.17569e16	−0.0122397
$755$	9.78211e17	0.192211
$756$	−3.41072e17	−0.0664439
$757$	1.11835e17	0.0216001	0.0108000	−	0.999942i	$-0.496562\pi$
$757$	1.11835e17	0.0216001	0.0108000	+	0.999942i	$0.496562\pi$
$758$	6.60685e17	0.126516
$759$	2.76674e16	0.00525287
$760$	−1.69059e18	−0.318236
$761$	1.10635e18	0.206486	0.103243	−	0.994656i	$-0.467078\pi$
$761$	1.10635e18	0.206486	0.103243	+	0.994656i	$0.467078\pi$
$762$	−9.24045e17	−0.170996
$763$	1.68057e18	0.308351
$764$	−5.91165e18	−1.07548
$765$	−6.23968e17	−0.112555
$766$	−3.92359e17	−0.0701773
$767$	2.58565e17	0.0458565
$768$	2.02186e18	0.355553
$769$	7.10729e18	1.23932	0.619659	−	0.784871i	$-0.287271\pi$
$769$	7.10729e18	1.23932	0.619659	+	0.784871i	$0.287271\pi$
$770$	4.60448e15	0.000796142 0
$771$	5.54471e18	0.950661
$772$	−3.28782e18	−0.558979
$773$	4.57751e18	0.771724	0.385862	−	0.922556i	$-0.373904\pi$
$773$	4.57751e18	0.771724	0.385862	+	0.922556i	$0.373904\pi$
$774$	−6.03226e16	−0.0100847
$775$	−3.83408e17	−0.0635623
$776$	4.07709e18	0.670270
$777$	−1.51122e18	−0.246372
$778$	−1.19485e18	−0.193172
$779$	−3.12208e18	−0.500554
$780$	5.61908e16	0.00893408
$781$	−5.71515e16	−0.00901148
$782$	−3.63091e17	−0.0567768
$783$	2.08253e18	0.322954
$784$	−4.97504e18	−0.765143
$785$	5.42086e18	0.826829
$786$	4.81223e17	0.0727947
$787$	−8.42386e18	−1.26379	−0.631896	−	0.775053i	$-0.717723\pi$
$787$	−8.42386e18	−1.26379	−0.631896	+	0.775053i	$0.717723\pi$
$788$	3.96287e18	0.589643
$789$	5.73106e18	0.845736
$790$	−1.33372e17	−0.0195204
$791$	−3.49403e18	−0.507201
$792$	2.24320e16	0.00322965
$793$	−2.55269e17	−0.0364521
$794$	−5.99075e17	−0.0848492
$795$	−2.62294e18	−0.368471
$796$	7.96393e18	1.10967
$797$	−4.95824e18	−0.685249	−0.342625	−	0.939472i	$-0.611316\pi$
$797$	−4.95824e18	−0.685249	−0.342625	+	0.939472i	$0.611316\pi$
$798$	−5.50670e17	−0.0754871
$799$	2.83426e17	0.0385377
$800$	−8.50908e17	−0.114762
$801$	3.65691e18	0.489218
$802$	−6.71897e17	−0.0891598
$803$	−1.97952e17	−0.0260560
$804$	−1.69823e18	−0.221734
$805$	−4.62298e17	−0.0598755
$806$	1.80425e16	0.00231803
$807$	−4.40646e18	−0.561580
$808$	−3.01762e18	−0.381497
$809$	−2.91720e18	−0.365848	−0.182924	−	0.983127i	$-0.558556\pi$
$809$	−2.91720e18	−0.365848	−0.182924	+	0.983127i	$0.558556\pi$
$810$	8.07522e16	0.0100462
$811$	2.27898e18	0.281258	0.140629	−	0.990062i	$-0.455088\pi$
$811$	2.27898e18	0.281258	0.140629	+	0.990062i	$0.455088\pi$
$812$	−4.73231e18	−0.579374
$813$	−8.32659e18	−1.01130
$814$	4.86590e16	0.00586280
$815$	6.71018e18	0.802065
$816$	3.23152e18	0.383195
$817$	2.28529e18	0.268843
$818$	−4.35016e15	−0.000507702 0
$819$	3.73857e16	0.00432873
$820$	−1.04037e18	−0.119508
$821$	−9.35907e18	−1.06660	−0.533301	−	0.845926i	$-0.679049\pi$
$821$	−9.35907e18	−1.06660	−0.533301	+	0.845926i	$0.679049\pi$
$822$	−1.12913e18	−0.127666
$823$	−1.20581e19	−1.35264	−0.676319	−	0.736609i	$-0.736426\pi$
$823$	−1.20581e19	−1.35264	−0.676319	+	0.736609i	$0.736426\pi$
$824$	3.11063e18	0.346195
$825$	2.55803e16	0.00282458
$826$	−8.44386e17	−0.0925062
$827$	−7.53213e18	−0.818714	−0.409357	−	0.912374i	$-0.634247\pi$
$827$	−7.53213e18	−0.818714	−0.409357	+	0.912374i	$0.634247\pi$
$828$	−1.10261e18	−0.118912
$829$	1.09464e19	1.17130	0.585649	−	0.810565i	$-0.300840\pi$
$829$	1.09464e19	1.17130	0.585649	+	0.810565i	$0.300840\pi$
$830$	1.36463e18	0.144880
$831$	−1.20995e18	−0.127456
$832$	−2.63370e17	−0.0275274
$833$	−6.33714e18	−0.657205
$834$	−1.65162e17	−0.0169954
$835$	4.83848e18	0.494023
$836$	−4.16048e17	−0.0421505
$837$	−6.08420e17	−0.0611629
$838$	1.97166e18	0.196674
$839$	−1.38440e19	−1.37028	−0.685139	−	0.728413i	$-0.740258\pi$
$839$	−1.38440e19	−1.37028	−0.685139	+	0.728413i	$0.740258\pi$
$840$	−3.74820e17	−0.0368135
$841$	1.86341e19	1.81607
$842$	8.17677e16	0.00790775
$843$	−9.34826e18	−0.897122
$844$	−5.25259e18	−0.500204
$845$	4.72626e18	0.446632
$846$	−3.66802e16	−0.00343973
$847$	−3.86584e18	−0.359751
$848$	1.35842e19	1.25447
$849$	−1.13253e19	−1.03789
$850$	−3.35700e17	−0.0305301
$851$	−4.88546e18	−0.440923
$852$	2.27763e18	0.203998
$853$	1.10709e19	0.984039	0.492020	−	0.870584i	$-0.336259\pi$
$853$	1.10709e19	0.984039	0.492020	+	0.870584i	$0.336259\pi$
$854$	8.33622e17	0.0735348
$855$	−3.05926e18	−0.267816
$856$	3.70545e18	0.321930
$857$	−3.38629e18	−0.291977	−0.145989	−	0.989286i	$-0.546636\pi$
$857$	−3.38629e18	−0.291977	−0.145989	+	0.989286i	$0.546636\pi$
$858$	−1.20376e15	−0.000103009 0
$859$	5.43237e18	0.461354	0.230677	−	0.973030i	$-0.425906\pi$
$859$	5.43237e18	0.461354	0.230677	+	0.973030i	$0.425906\pi$
$860$	7.61528e17	0.0641868
$861$	−6.92196e17	−0.0579040
$862$	4.35575e18	0.361631
$863$	1.86531e18	0.153703	0.0768513	−	0.997043i	$-0.475513\pi$
$863$	1.86531e18	0.153703	0.0768513	+	0.997043i	$0.475513\pi$
$864$	−1.35028e18	−0.110430
$865$	−7.04082e17	−0.0571503
$866$	−2.78752e17	−0.0224570
$867$	−3.10418e18	−0.248212
$868$	1.38256e18	0.109725
$869$	−6.70437e16	−0.00528116
$870$	1.12042e18	0.0876003
$871$	1.86147e17	0.0144457
$872$	4.40487e18	0.339294
$873$	7.37784e18	0.564075
$874$	−1.78020e18	−0.135097
$875$	−4.27424e17	−0.0321963
$876$	7.88887e18	0.589845
$877$	1.78738e19	1.32654	0.663269	−	0.748381i	$-0.269169\pi$
$877$	1.78738e19	1.32654	0.663269	+	0.748381i	$0.269169\pi$
$878$	2.68501e18	0.197803
$879$	1.13991e19	0.833568
$880$	−1.32480e17	−0.00961638
$881$	3.72462e18	0.268372	0.134186	−	0.990956i	$-0.457158\pi$
$881$	3.72462e18	0.268372	0.134186	+	0.990956i	$0.457158\pi$
$882$	8.20134e17	0.0586596
$883$	−1.78621e19	−1.26820	−0.634102	−	0.773250i	$-0.718630\pi$
$883$	−1.78621e19	−1.26820	−0.634102	+	0.773250i	$0.718630\pi$
$884$	−3.70685e17	−0.0261255
$885$	−4.69100e18	−0.328197
$886$	−3.31009e18	−0.229890
$887$	1.20818e19	0.832967	0.416483	−	0.909143i	$-0.363262\pi$
$887$	1.20818e19	0.832967	0.416483	+	0.909143i	$0.363262\pi$
$888$	−3.96101e18	−0.271095
$889$	7.76141e18	0.527326
$890$	1.96745e18	0.132699
$891$	4.05927e16	0.00271796
$892$	5.21985e18	0.346965
$893$	1.38961e18	0.0916978
$894$	1.35472e18	0.0887474
$895$	−2.72257e18	−0.177064
$896$	4.05920e18	0.262083
$897$	1.20860e17	0.00774697
$898$	5.24444e18	0.333736
$899$	−8.44170e18	−0.533325
$900$	−1.01944e18	−0.0639417
$901$	1.73033e19	1.07750
$902$	2.22877e16	0.00137791
$903$	5.06672e17	0.0310997
$904$	−9.15808e18	−0.558097
$905$	−1.07806e19	−0.652267
$906$	8.35150e17	0.0501685
$907$	−1.97495e19	−1.17790	−0.588951	−	0.808168i	$-0.700459\pi$
$907$	−1.97495e19	−1.17790	−0.588951	+	0.808168i	$0.700459\pi$
$908$	2.15971e19	1.27890
$909$	−5.46064e18	−0.321054
$910$	2.01139e16	0.00117416
$911$	−2.11213e19	−1.22420	−0.612100	−	0.790781i	$-0.709675\pi$
$911$	−2.11213e19	−1.22420	−0.612100	+	0.790781i	$0.709675\pi$
$912$	1.58438e19	0.911787
$913$	6.85975e17	0.0391966
$914$	−3.67002e18	−0.208218
$915$	4.63120e18	0.260890
$916$	−1.51728e19	−0.848683
$917$	−4.04197e18	−0.224488
$918$	−5.32714e17	−0.0293776
$919$	−2.23735e18	−0.122513	−0.0612566	−	0.998122i	$-0.519511\pi$
$919$	−2.23735e18	−0.122513	−0.0612566	+	0.998122i	$0.519511\pi$
$920$	−1.21171e18	−0.0658838
$921$	−3.45491e18	−0.186530
$922$	1.28723e18	0.0690092
$923$	−2.49656e17	−0.0132902
$924$	−9.22421e16	−0.00487597
$925$	−4.51691e18	−0.237094
$926$	−3.14531e18	−0.163943
$927$	5.62894e18	0.291345
$928$	−1.87349e19	−0.962919
$929$	2.69207e19	1.37399	0.686996	−	0.726662i	$-0.258929\pi$
$929$	2.69207e19	1.37399	0.686996	+	0.726662i	$0.258929\pi$
$930$	−3.27335e17	−0.0165903
$931$	−3.10704e19	−1.56377
$932$	−2.39252e19	−1.19578
$933$	−1.63298e19	−0.810497
$934$	−9.83900e17	−0.0484949
$935$	−1.68750e17	−0.00825980
$936$	9.79904e16	0.00476311
$937$	1.74551e19	0.842588	0.421294	−	0.906924i	$-0.361576\pi$
$937$	1.74551e19	0.842588	0.421294	+	0.906924i	$0.361576\pi$
$938$	−6.07894e17	−0.0291413
$939$	−1.81374e18	−0.0863474
$940$	4.63060e17	0.0218931
$941$	−2.30287e19	−1.08128	−0.540638	−	0.841255i	$-0.681817\pi$
$941$	−2.30287e19	−1.08128	−0.540638	+	0.841255i	$0.681817\pi$
$942$	4.62807e18	0.215809
$943$	−2.23772e18	−0.103629
$944$	2.42946e19	1.11736
$945$	−6.78268e17	−0.0309809
$946$	−1.63141e16	−0.000740065 0
$947$	−2.31518e18	−0.104306	−0.0521532	−	0.998639i	$-0.516608\pi$
$947$	−2.31518e18	−0.104306	−0.0521532	+	0.998639i	$0.516608\pi$
$948$	2.67186e18	0.119553
$949$	−8.64718e17	−0.0384277
$950$	−1.64591e18	−0.0726443
$951$	−5.12229e17	−0.0224538
$952$	2.47265e18	0.107652
$953$	1.88776e19	0.816288	0.408144	−	0.912917i	$-0.366176\pi$
$953$	1.88776e19	0.816288	0.408144	+	0.912917i	$0.366176\pi$
$954$	−2.23934e18	−0.0961737
$955$	−1.17561e19	−0.501466
$956$	−1.28759e19	−0.545508
$957$	5.63215e17	0.0236999
$958$	−2.66627e18	−0.111437
$959$	9.48398e18	0.393704
$960$	4.77817e18	0.197015
$961$	−2.19513e19	−0.898996
$962$	2.12558e17	0.00864650
$963$	6.70532e18	0.270925
$964$	1.83562e18	0.0736686
$965$	−6.53827e18	−0.260636
$966$	−3.94688e17	−0.0156280
$967$	3.58183e18	0.140875	0.0704374	−	0.997516i	$-0.477561\pi$
$967$	3.58183e18	0.140875	0.0704374	+	0.997516i	$0.477561\pi$
$968$	−1.01326e19	−0.395851
$969$	2.01816e19	0.783162
$970$	3.96934e18	0.153004
$971$	3.44871e19	1.32048	0.660240	−	0.751055i	$-0.270455\pi$
$971$	3.44871e19	1.32048	0.660240	+	0.751055i	$0.270455\pi$
$972$	−1.61772e18	−0.0615279
$973$	1.38726e18	0.0524112
$974$	−4.03572e18	−0.151456
$975$	1.11743e17	0.00416572
$976$	−2.39849e19	−0.888206
$977$	1.61246e19	0.593162	0.296581	−	0.955008i	$-0.404154\pi$
$977$	1.61246e19	0.593162	0.296581	+	0.955008i	$0.404154\pi$
$978$	5.72883e18	0.209345
$979$	9.89000e17	0.0359012
$980$	−1.03536e19	−0.373354
$981$	7.97098e18	0.285537
$982$	4.46164e17	0.0158770
$983$	−1.25333e19	−0.443065	−0.221532	−	0.975153i	$-0.571106\pi$
$983$	−1.25333e19	−0.443065	−0.221532	+	0.975153i	$0.571106\pi$
$984$	−1.81429e18	−0.0637146
$985$	7.88070e18	0.274934
$986$	−7.39130e18	−0.256166
$987$	3.08091e17	0.0106076
$988$	−1.81743e18	−0.0621639
$989$	1.63796e18	0.0556581
$990$	2.18392e16	0.000737238 0
$991$	−5.10124e18	−0.171079	−0.0855396	−	0.996335i	$-0.527261\pi$
$991$	−5.10124e18	−0.171079	−0.0855396	+	0.996335i	$0.527261\pi$
$992$	5.47348e18	0.182363
$993$	2.18615e19	0.723618
$994$	8.15292e17	0.0268103
$995$	1.58374e19	0.517407
$996$	−2.73378e19	−0.887315
$997$	2.50551e18	0.0807939	0.0403969	−	0.999184i	$-0.487138\pi$
$997$	2.50551e18	0.0807939	0.0403969	+	0.999184i	$0.487138\pi$
$998$	−4.66108e18	−0.149327
$999$	−7.16778e18	−0.228144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.14.a.c.1.1	✓	2
3.2	odd	2		45.14.a.b.1.2		2
5.2	odd	4		75.14.b.e.49.2		4
5.3	odd	4		75.14.b.e.49.3		4
5.4	even	2		75.14.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.14.a.c.1.1	✓	2	1.1	even	1	trivial
45.14.a.b.1.2		2	3.2	odd	2
75.14.a.c.1.2		2	5.4	even	2
75.14.b.e.49.2		4	5.2	odd	4
75.14.b.e.49.3		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q-18.2989 q^{2} +729.000 q^{3} -7857.15 q^{4} -15625.0 q^{5} -13339.9 q^{6} +112047. q^{7} +293681. q^{8} +531441. q^{9} +285920. q^{10} +143727. q^{11} -5.72786e6 q^{12} +627845. q^{13} -2.05033e6 q^{14} -1.13906e7 q^{15} +5.89918e7 q^{16} +7.51428e7 q^{17} -9.72477e6 q^{18} +3.68418e8 q^{19} +1.22768e8 q^{20} +8.16820e7 q^{21} -2.63004e6 q^{22} +2.64060e8 q^{23} +2.14094e8 q^{24} +2.44141e8 q^{25} -1.14888e7 q^{26} +3.87420e8 q^{27} -8.80367e8 q^{28} +5.37538e9 q^{29} +2.08436e8 q^{30} -1.57044e9 q^{31} -3.48532e9 q^{32} +1.04777e8 q^{33} -1.37503e9 q^{34} -1.75073e9 q^{35} -4.17561e9 q^{36} -1.85013e10 q^{37} -6.74163e9 q^{38} +4.57699e8 q^{39} -4.58877e9 q^{40} -8.47428e9 q^{41} -1.49469e9 q^{42} +6.20298e9 q^{43} -1.12928e9 q^{44} -8.30377e9 q^{45} -4.83201e9 q^{46} +3.77183e9 q^{47} +4.30050e10 q^{48} -8.43346e10 q^{49} -4.46750e9 q^{50} +5.47791e10 q^{51} -4.93307e9 q^{52} +2.30272e11 q^{53} -7.08936e9 q^{54} -2.24573e9 q^{55} +3.29060e10 q^{56} +2.68577e11 q^{57} -9.83633e10 q^{58} +4.11830e11 q^{59} +8.94979e10 q^{60} -4.06580e11 q^{61} +2.87372e10 q^{62} +5.95462e10 q^{63} -4.19483e11 q^{64} -9.81007e9 q^{65} -1.91730e9 q^{66} +2.96486e11 q^{67} -5.90409e11 q^{68} +1.92500e11 q^{69} +3.20364e10 q^{70} -3.97640e11 q^{71} +1.56074e11 q^{72} -1.37728e12 q^{73} +3.38553e11 q^{74} +1.77979e11 q^{75} -2.89472e12 q^{76} +1.61041e10 q^{77} -8.37537e9 q^{78} -4.66466e11 q^{79} -9.21746e11 q^{80} +2.82430e11 q^{81} +1.55070e11 q^{82} +4.77278e12 q^{83} -6.41788e11 q^{84} -1.17411e12 q^{85} -1.13508e11 q^{86} +3.91865e12 q^{87} +4.22098e10 q^{88} +6.88111e12 q^{89} +1.51949e11 q^{90} +7.03479e10 q^{91} -2.07476e12 q^{92} -1.14485e12 q^{93} -6.90203e10 q^{94} -5.75653e12 q^{95} -2.54080e12 q^{96} +1.38827e13 q^{97} +1.54323e12 q^{98} +7.63823e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 131 q^{2} + 1458 q^{3} + 6241 q^{4} - 31250 q^{5} + 95499 q^{6} + 496272 q^{7} + 1175463 q^{8} + 1062882 q^{9} - 2046875 q^{10} + 6245888 q^{11} + 4549689 q^{12} + 1761164 q^{13} + 55314084 q^{14}+ \cdots + 3319320964608 q^{99}+O(q^{100}) \) 2 * q + 131 * q^2 + 1458 * q^3 + 6241 * q^4 - 31250 * q^5 + 95499 * q^6 + 496272 * q^7 + 1175463 * q^8 + 1062882 * q^9 - 2046875 * q^10 + 6245888 * q^11 + 4549689 * q^12 + 1761164 * q^13 + 55314084 * q^14 - 22781250 * q^15 + 75148705 * q^16 + 48151604 * q^17 + 69618771 * q^18 + 38475344 * q^19 - 97515625 * q^20 + 361782288 * q^21 + 908415728 * q^22 + 734264616 * q^23 + 856912527 * q^24 + 488281250 * q^25 + 157714454 * q^26 + 774840978 * q^27 + 4536499884 * q^28 + 1126474708 * q^29 - 1492171875 * q^30 + 6100104312 * q^31 - 8296660073 * q^32 + 4553252352 * q^33 - 5404788238 * q^34 - 7754250000 * q^35 + 3316723281 * q^36 - 46819674548 * q^37 - 56001723484 * q^38 + 1283888556 * q^39 - 18366609375 * q^40 - 29607909788 * q^41 + 40323967236 * q^42 - 63189768520 * q^43 + 84899911888 * q^44 - 16607531250 * q^45 + 65368954992 * q^46 + 105004415960 * q^47 + 54783405945 * q^48 - 33594444590 * q^49 + 31982421875 * q^50 + 35102519316 * q^51 + 11044638034 * q^52 + 48425833796 * q^53 + 50752084059 * q^54 - 97592000000 * q^55 + 371708899380 * q^56 + 28048525776 * q^57 - 732719858498 * q^58 + 722768180096 * q^59 - 71088890625 * q^60 - 229984402180 * q^61 + 1173940563384 * q^62 + 263739287952 * q^63 - 1270168541071 * q^64 - 27518187500 * q^65 + 662235065712 * q^66 + 359062188984 * q^67 - 970935017018 * q^68 + 535278905064 * q^69 - 864282562500 * q^70 + 736545668224 * q^71 + 624689232183 * q^72 - 1494470740204 * q^73 - 3889351112906 * q^74 + 355957031250 * q^75 - 7546301154644 * q^76 + 2360709208704 * q^77 + 114973836966 * q^78 + 3526348590120 * q^79 - 1174198515625 * q^80 + 564859072962 * q^81 - 3000156702386 * q^82 + 5631050986968 * q^83 + 3307108415436 * q^84 - 752368812500 * q^85 - 10473766954252 * q^86 + 821200062132 * q^87 + 5422984137648 * q^88 + 5913121459764 * q^89 - 1087793296875 * q^90 + 505797926592 * q^91 + 4554248300592 * q^92 + 4446976043448 * q^93 + 15044889696176 * q^94 - 601177250000 * q^95 - 6048265193217 * q^96 + 16383233322244 * q^97 + 9118668656251 * q^98 + 3319320964608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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