LMFDB - Embedded newform 15.18.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [15,18,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, 18); 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, 18, names="a")

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	15.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-253] 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:	$27.4833131017$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 182396x + 3921120 $ x^3 - x^2 - 182396*x + 3921120
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$21.5502$ 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)

$f(q)$	$=$	\(q-105.550 q^{2} +6561.00 q^{3} -119931. q^{4} -390625. q^{5} -692515. q^{6} -2.39385e7 q^{7} +2.64934e7 q^{8} +4.30467e7 q^{9} +4.12305e7 q^{10} -5.09412e8 q^{11} -7.86868e8 q^{12} +4.71682e9 q^{13} +2.52671e9 q^{14} -2.56289e9 q^{15} +1.29232e10 q^{16} -4.44993e10 q^{17} -4.54359e9 q^{18} -4.25101e10 q^{19} +4.68481e10 q^{20} -1.57060e11 q^{21} +5.37686e10 q^{22} +4.70013e11 q^{23} +1.73823e11 q^{24} +1.52588e11 q^{25} -4.97862e11 q^{26} +2.82430e11 q^{27} +2.87097e12 q^{28} +3.15724e12 q^{29} +2.70514e11 q^{30} +3.46790e12 q^{31} -4.83660e12 q^{32} -3.34226e12 q^{33} +4.69691e12 q^{34} +9.35098e12 q^{35} -5.16264e12 q^{36} +3.18740e13 q^{37} +4.48695e12 q^{38} +3.09471e13 q^{39} -1.03490e13 q^{40} +8.13537e13 q^{41} +1.65778e13 q^{42} -1.24496e14 q^{43} +6.10944e13 q^{44} -1.68151e13 q^{45} -4.96099e13 q^{46} -7.05130e13 q^{47} +8.47893e13 q^{48} +3.40421e14 q^{49} -1.61057e13 q^{50} -2.91960e14 q^{51} -5.65694e14 q^{52} +2.51778e14 q^{53} -2.98105e13 q^{54} +1.98989e14 q^{55} -6.34213e14 q^{56} -2.78909e14 q^{57} -3.33247e14 q^{58} -6.39615e14 q^{59} +3.07370e14 q^{60} -4.96148e13 q^{61} -3.66037e14 q^{62} -1.03047e15 q^{63} -1.18337e15 q^{64} -1.84251e15 q^{65} +3.52776e14 q^{66} -2.75976e15 q^{67} +5.33686e15 q^{68} +3.08375e15 q^{69} -9.86997e14 q^{70} +2.50612e15 q^{71} +1.14046e15 q^{72} +8.85474e14 q^{73} -3.36430e15 q^{74} +1.00113e15 q^{75} +5.09829e15 q^{76} +1.21946e16 q^{77} -3.26647e15 q^{78} -6.85544e13 q^{79} -5.04814e15 q^{80} +1.85302e15 q^{81} -8.58690e15 q^{82} +3.38359e16 q^{83} +1.88364e16 q^{84} +1.73826e16 q^{85} +1.31405e16 q^{86} +2.07146e16 q^{87} -1.34961e16 q^{88} -3.37871e16 q^{89} +1.77484e15 q^{90} -1.12914e17 q^{91} -5.63692e16 q^{92} +2.27529e16 q^{93} +7.44266e15 q^{94} +1.66055e16 q^{95} -3.17329e16 q^{96} +6.48330e16 q^{97} -3.59315e16 q^{98} -2.19285e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 253 q^{2} + 19683 q^{3} - 7087 q^{4} - 1171875 q^{5} - 1659933 q^{6} - 4332484 q^{7} - 16188513 q^{8} + 129140163 q^{9} + 98828125 q^{10} + 943563680 q^{11} - 46497807 q^{12} + 4257013150 q^{13} + 1847483988 q^{14}+ \cdots + 40\!\cdots\!80 q^{99}+O(q^{100}) $ 3 * q - 253 * q^2 + 19683 * q^3 - 7087 * q^4 - 1171875 * q^5 - 1659933 * q^6 - 4332484 * q^7 - 16188513 * q^8 + 129140163 * q^9 + 98828125 * q^10 + 943563680 * q^11 - 46497807 * q^12 + 4257013150 * q^13 + 1847483988 * q^14 - 7688671875 * q^15 - 21943871359 * q^16 + 3063169514 * q^17 - 10890820413 * q^18 - 78122492996 * q^19 + 2768359375 * q^20 - 28425427524 * q^21 + 183716401088 * q^22 + 234308204088 * q^23 - 106212833793 * q^24 + 457763671875 * q^25 + 2665740430886 * q^26 + 847288609443 * q^27 + 3864204264572 * q^28 + 5775268588078 * q^29 + 648411328125 * q^30 + 5565463149104 * q^31 + 4307021228191 * q^32 + 6190721304480 * q^33 + 21993554360306 * q^34 + 1692376562500 * q^35 - 305072111727 * q^36 + 31751809399326 * q^37 + 29204227700564 * q^38 + 27930263277150 * q^39 + 6323637890625 * q^40 + 167461457288254 * q^41 + 12121342445268 * q^42 + 150679282040884 * q^43 + 108118677568192 * q^44 - 50445376171875 * q^45 - 194531605879776 * q^46 - 72221896199032 * q^47 - 143973739986399 * q^48 + 68970332513947 * q^49 - 38604736328125 * q^50 + 20097455181354 * q^51 - 1053111710992926 * q^52 + 76290818594558 * q^53 - 71454672729693 * q^54 - 368579562500000 * q^55 - 1101493182837180 * q^56 - 512561676546756 * q^57 - 962781990480722 * q^58 + 465601947196256 * q^59 + 18163205859375 * q^60 - 2317809676510478 * q^61 - 4124018088183048 * q^62 - 186499229984964 * q^63 - 663491579542719 * q^64 - 1662895761718750 * q^65 + 1205363307538368 * q^66 - 6392459657973196 * q^67 + 4953005408361574 * q^68 + 1537296127021368 * q^69 - 721673432812500 * q^70 + 6465608483990656 * q^71 - 696862402515873 * q^72 + 5113761577485238 * q^73 + 10473343628804518 * q^74 + 3003387451171875 * q^75 - 168461495772804 * q^76 + 26936973780565632 * q^77 + 17489922967043046 * q^78 + 8740508940658880 * q^79 + 8571824749609375 * q^80 + 5559060566555523 * q^81 + 13452036217723822 * q^82 + 38179195227158436 * q^83 + 25353044179856892 * q^84 - 1196550591406250 * q^85 - 14457556252388620 * q^86 + 37891537206379758 * q^87 - 59624030208270528 * q^88 - 17217755358726426 * q^89 + 4254226723828125 * q^90 - 110835261613033256 * q^91 - 45737184508628544 * q^92 + 36515003721271344 * q^93 - 200721746528137120 * q^94 + 30516598826562500 * q^95 + 28258366278161151 * q^96 - 94917192725726586 * q^97 - 896231490630245 * q^98 + 40617322478693280 * 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 $

$2$	−105.550	−0.291544	−0.145772	−	0.989318i	$-0.546567\pi$
$2$	−105.550	−0.291544	−0.145772	+	0.989318i	$0.546567\pi$
$3$	6561.00	0.577350
$3$	6561.00	0.577350
$4$	−119931.	−0.915002
$5$	−390625.	−0.447214
$5$	−390625.	−0.447214
$6$	−692515.	−0.168323
$7$	−2.39385e7	−1.56951	−0.784754	−	0.619807i	$-0.787211\pi$
$7$	−2.39385e7	−1.56951	−0.784754	+	0.619807i	$0.787211\pi$
$8$	2.64934e7	0.558307
$9$	4.30467e7	0.333333
$10$	4.12305e7	0.130382
$11$	−5.09412e8	−0.716526	−0.358263	−	0.933621i	$-0.616631\pi$
$11$	−5.09412e8	−0.716526	−0.358263	+	0.933621i	$0.616631\pi$
$12$	−7.86868e8	−0.528277
$13$	4.71682e9	1.60373	0.801865	−	0.597506i	$-0.203841\pi$
$13$	4.71682e9	1.60373	0.801865	+	0.597506i	$0.203841\pi$
$14$	2.52671e9	0.457580
$15$	−2.56289e9	−0.258199
$16$	1.29232e10	0.752231
$17$	−4.44993e10	−1.54717	−0.773584	−	0.633693i	$-0.781538\pi$
$17$	−4.44993e10	−1.54717	−0.773584	+	0.633693i	$0.781538\pi$
$18$	−4.54359e9	−0.0971813
$19$	−4.25101e10	−0.574231	−0.287116	−	0.957896i	$-0.592696\pi$
$19$	−4.25101e10	−0.574231	−0.287116	+	0.957896i	$0.592696\pi$
$20$	4.68481e10	0.409201
$21$	−1.57060e11	−0.906156
$22$	5.37686e10	0.208899
$23$	4.70013e11	1.25148	0.625739	−	0.780033i	$-0.284798\pi$
$23$	4.70013e11	1.25148	0.625739	+	0.780033i	$0.284798\pi$
$24$	1.73823e11	0.322339
$25$	1.52588e11	0.200000
$26$	−4.97862e11	−0.467558
$27$	2.82430e11	0.192450
$28$	2.87097e12	1.43610
$29$	3.15724e12	1.17199	0.585996	−	0.810314i	$-0.300704\pi$
$29$	3.15724e12	1.17199	0.585996	+	0.810314i	$0.300704\pi$
$30$	2.70514e11	0.0752763
$31$	3.46790e12	0.730285	0.365142	−	0.930952i	$-0.381020\pi$
$31$	3.46790e12	0.730285	0.365142	+	0.930952i	$0.381020\pi$
$32$	−4.83660e12	−0.777616
$33$	−3.34226e12	−0.413686
$34$	4.69691e12	0.451068
$35$	9.35098e12	0.701905
$36$	−5.16264e12	−0.305001
$37$	3.18740e13	1.49184	0.745919	−	0.666037i	$-0.232011\pi$
$37$	3.18740e13	1.49184	0.745919	+	0.666037i	$0.232011\pi$
$38$	4.48695e12	0.167414
$39$	3.09471e13	0.925914
$40$	−1.03490e13	−0.249683
$41$	8.13537e13	1.59116	0.795581	−	0.605847i	$-0.207166\pi$
$41$	8.13537e13	1.59116	0.795581	+	0.605847i	$0.207166\pi$
$42$	1.65778e13	0.264184
$43$	−1.24496e14	−1.62432	−0.812161	−	0.583433i	$-0.801709\pi$
$43$	−1.24496e14	−1.62432	−0.812161	+	0.583433i	$0.801709\pi$
$44$	6.10944e13	0.655623
$45$	−1.68151e13	−0.149071
$46$	−4.96099e13	−0.364861
$47$	−7.05130e13	−0.431954	−0.215977	−	0.976398i	$-0.569294\pi$
$47$	−7.05130e13	−0.431954	−0.215977	+	0.976398i	$0.569294\pi$
$48$	8.47893e13	0.434301
$49$	3.40421e14	1.46336
$50$	−1.61057e13	−0.0583088
$51$	−2.91960e14	−0.893258
$52$	−5.65694e14	−1.46742
$53$	2.51778e14	0.555485	0.277743	−	0.960656i	$-0.410414\pi$
$53$	2.51778e14	0.555485	0.277743	+	0.960656i	$0.410414\pi$
$54$	−2.98105e13	−0.0561076
$55$	1.98989e14	0.320440
$56$	−6.34213e14	−0.876268
$57$	−2.78909e14	−0.331533
$58$	−3.33247e14	−0.341687
$59$	−6.39615e14	−0.567122	−0.283561	−	0.958954i	$-0.591516\pi$
$59$	−6.39615e14	−0.567122	−0.283561	+	0.958954i	$0.591516\pi$
$60$	3.07370e14	0.236253
$61$	−4.96148e13	−0.0331366	−0.0165683	−	0.999863i	$-0.505274\pi$
$61$	−4.96148e13	−0.0331366	−0.0165683	+	0.999863i	$0.505274\pi$
$62$	−3.66037e14	−0.212910
$63$	−1.03047e15	−0.523169
$64$	−1.18337e15	−0.525522
$65$	−1.84251e15	−0.717210
$66$	3.52776e14	0.120608
$67$	−2.75976e15	−0.830300	−0.415150	−	0.909753i	$-0.636271\pi$
$67$	−2.75976e15	−0.830300	−0.415150	+	0.909753i	$0.636271\pi$
$68$	5.33686e15	1.41566
$69$	3.08375e15	0.722541
$70$	−9.86997e14	−0.204636
$71$	2.50612e15	0.460582	0.230291	−	0.973122i	$-0.426032\pi$
$71$	2.50612e15	0.460582	0.230291	+	0.973122i	$0.426032\pi$
$72$	1.14046e15	0.186102
$73$	8.85474e14	0.128508	0.0642542	−	0.997934i	$-0.479533\pi$
$73$	8.85474e14	0.128508	0.0642542	+	0.997934i	$0.479533\pi$
$74$	−3.36430e15	−0.434936
$75$	1.00113e15	0.115470
$76$	5.09829e15	0.525423
$77$	1.21946e16	1.12459
$78$	−3.26647e15	−0.269944
$79$	−6.85544e13	−0.00508400	−0.00254200	−	0.999997i	$-0.500809\pi$
$79$	−6.85544e13	−0.00508400	−0.00254200	+	0.999997i	$0.500809\pi$
$80$	−5.04814e15	−0.336408
$81$	1.85302e15	0.111111
$82$	−8.58690e15	−0.463894
$83$	3.38359e16	1.64897	0.824487	−	0.565881i	$-0.191464\pi$
$83$	3.38359e16	1.64897	0.824487	+	0.565881i	$0.191464\pi$
$84$	1.88364e16	0.829135
$85$	1.73826e16	0.691915
$86$	1.31405e16	0.473561
$87$	2.07146e16	0.676650
$88$	−1.34961e16	−0.400041
$89$	−3.37871e16	−0.909778	−0.454889	−	0.890548i	$-0.650321\pi$
$89$	−3.37871e16	−0.909778	−0.454889	+	0.890548i	$0.650321\pi$
$90$	1.77484e15	0.0434608
$91$	−1.12914e17	−2.51707
$92$	−5.63692e16	−1.14510
$93$	2.27529e16	0.421630
$94$	7.44266e15	0.125934
$95$	1.66055e16	0.256804
$96$	−3.17329e16	−0.448957
$97$	6.48330e16	0.839917	0.419958	−	0.907543i	$-0.362045\pi$
$97$	6.48330e16	0.839917	0.419958	+	0.907543i	$0.362045\pi$
$98$	−3.59315e16	−0.426632
$99$	−2.19285e16	−0.238842
$100$	−1.83000e16	−0.183000
$101$	2.50991e16	0.230636	0.115318	−	0.993329i	$-0.463211\pi$
$101$	2.50991e16	0.230636	0.115318	+	0.993329i	$0.463211\pi$
$102$	3.08164e16	0.260424
$103$	−1.88107e17	−1.46315	−0.731575	−	0.681760i	$-0.761215\pi$
$103$	−1.88107e17	−1.46315	−0.731575	+	0.681760i	$0.761215\pi$
$104$	1.24965e17	0.895374
$105$	6.13517e16	0.405245
$106$	−2.65752e16	−0.161948
$107$	1.04046e17	0.585414	0.292707	−	0.956202i	$-0.405444\pi$
$107$	1.04046e17	0.585414	0.292707	+	0.956202i	$0.405444\pi$
$108$	−3.38721e16	−0.176092
$109$	−3.25424e17	−1.56431	−0.782157	−	0.623082i	$-0.785880\pi$
$109$	−3.25424e17	−1.56431	−0.782157	+	0.623082i	$0.785880\pi$
$110$	−2.10033e16	−0.0934223
$111$	2.09125e17	0.861313
$112$	−3.09363e17	−1.18063
$113$	1.16099e17	0.410829	0.205415	−	0.978675i	$-0.434146\pi$
$113$	1.16099e17	0.410829	0.205415	+	0.978675i	$0.434146\pi$
$114$	2.94389e16	0.0966563
$115$	−1.83599e17	−0.559678
$116$	−3.78651e17	−1.07237
$117$	2.03044e17	0.534577
$118$	6.75115e16	0.165341
$119$	1.06525e18	2.42829
$120$	−6.78998e16	−0.144154
$121$	−2.45946e17	−0.486591
$122$	5.23685e15	0.00966077
$123$	5.33762e17	0.918658
$124$	−4.15909e17	−0.668212
$125$	−5.96046e16	−0.0894427
$126$	1.08767e17	0.152527
$127$	1.11976e18	1.46823	0.734116	−	0.679024i	$-0.237597\pi$
$127$	1.11976e18	1.46823	0.734116	+	0.679024i	$0.237597\pi$
$128$	7.58847e17	0.930828
$129$	−8.16816e17	−0.937803
$130$	1.94477e17	0.209098
$131$	3.59952e17	0.362609	0.181304	−	0.983427i	$-0.441968\pi$
$131$	3.59952e17	0.362609	0.181304	+	0.983427i	$0.441968\pi$
$132$	4.00841e17	0.378524
$133$	1.01763e18	0.901260
$134$	2.91293e17	0.242069
$135$	−1.10324e17	−0.0860663
$136$	−1.17894e18	−0.863795
$137$	−9.75314e17	−0.671459	−0.335730	−	0.941958i	$-0.608983\pi$
$137$	−9.75314e17	−0.671459	−0.335730	+	0.941958i	$0.608983\pi$
$138$	−3.25491e17	−0.210652
$139$	6.02829e17	0.366917	0.183459	−	0.983027i	$-0.441271\pi$
$139$	6.02829e17	0.366917	0.183459	+	0.983027i	$0.441271\pi$
$140$	−1.12147e18	−0.642245
$141$	−4.62636e17	−0.249389
$142$	−2.64522e17	−0.134280
$143$	−2.40281e18	−1.14911
$144$	5.56303e17	0.250744
$145$	−1.23330e18	−0.524131
$146$	−9.34620e16	−0.0374659
$147$	2.23350e18	0.844869
$148$	−3.82268e18	−1.36504
$149$	4.51405e18	1.52224	0.761120	−	0.648612i	$-0.224650\pi$
$149$	4.51405e18	1.52224	0.761120	+	0.648612i	$0.224650\pi$
$150$	−1.05669e17	−0.0336646
$151$	−5.57256e17	−0.167784	−0.0838921	−	0.996475i	$-0.526735\pi$
$151$	−5.57256e17	−0.167784	−0.0838921	+	0.996475i	$0.526735\pi$
$152$	−1.12624e18	−0.320597
$153$	−1.91555e18	−0.515723
$154$	−1.28714e18	−0.327868
$155$	−1.35465e18	−0.326593
$156$	−3.71152e18	−0.847213
$157$	5.67610e18	1.22716	0.613582	−	0.789631i	$-0.289728\pi$
$157$	5.67610e18	1.22716	0.613582	+	0.789631i	$0.289728\pi$
$158$	7.23593e15	0.00148221
$159$	1.65191e18	0.320709
$160$	1.88930e18	0.347760
$161$	−1.12514e19	−1.96420
$162$	−1.95587e17	−0.0323938
$163$	4.52801e18	0.711726	0.355863	−	0.934538i	$-0.384187\pi$
$163$	4.52801e18	0.711726	0.355863	+	0.934538i	$0.384187\pi$
$164$	−9.75684e18	−1.45592
$165$	1.30557e18	0.185006
$166$	−3.57138e18	−0.480748
$167$	9.90189e18	1.26657	0.633283	−	0.773920i	$-0.281707\pi$
$167$	9.90189e18	1.26657	0.633283	+	0.773920i	$0.281707\pi$
$168$	−4.16107e18	−0.505913
$169$	1.35980e19	1.57195
$170$	−1.83473e18	−0.201724
$171$	−1.82992e18	−0.191410
$172$	1.49309e19	1.48626
$173$	1.49801e19	1.41946	0.709729	−	0.704475i	$-0.248817\pi$
$173$	1.49801e19	1.41946	0.709729	+	0.704475i	$0.248817\pi$
$174$	−2.18643e18	−0.197273
$175$	−3.65272e18	−0.313902
$176$	−6.58326e18	−0.538993
$177$	−4.19652e18	−0.327428
$178$	3.56623e18	0.265240
$179$	4.67407e18	0.331470	0.165735	−	0.986170i	$-0.447000\pi$
$179$	4.67407e18	0.331470	0.165735	+	0.986170i	$0.447000\pi$
$180$	2.01666e18	0.136400
$181$	1.00176e17	0.00646394	0.00323197	−	0.999995i	$-0.498971\pi$
$181$	1.00176e17	0.00646394	0.00323197	+	0.999995i	$0.498971\pi$
$182$	1.19181e19	0.733835
$183$	−3.25523e17	−0.0191314
$184$	1.24523e19	0.698709
$185$	−1.24508e19	−0.667170
$186$	−2.40157e18	−0.122924
$187$	2.26685e19	1.10859
$188$	8.45671e18	0.395239
$189$	−6.76094e18	−0.302052
$190$	−1.75272e18	−0.0748696
$191$	−1.79795e19	−0.734503	−0.367252	−	0.930122i	$-0.619701\pi$
$191$	−1.79795e19	−0.734503	−0.367252	+	0.930122i	$0.619701\pi$
$192$	−7.76409e18	−0.303410
$193$	1.20664e19	0.451171	0.225585	−	0.974223i	$-0.427571\pi$
$193$	1.20664e19	0.451171	0.225585	+	0.974223i	$0.427571\pi$
$194$	−6.84313e18	−0.244873
$195$	−1.20887e19	−0.414081
$196$	−4.08271e19	−1.33897
$197$	1.55077e19	0.487062	0.243531	−	0.969893i	$-0.421694\pi$
$197$	1.55077e19	0.487062	0.243531	+	0.969893i	$0.421694\pi$
$198$	2.31456e18	0.0696329
$199$	−1.56769e19	−0.451865	−0.225932	−	0.974143i	$-0.572543\pi$
$199$	−1.56769e19	−0.451865	−0.225932	+	0.974143i	$0.572543\pi$
$200$	4.04258e18	0.111661
$201$	−1.81068e19	−0.479374
$202$	−2.64922e18	−0.0672405
$203$	−7.55796e19	−1.83945
$204$	3.50151e19	0.817333
$205$	−3.17788e19	−0.711590
$206$	1.98548e19	0.426573
$207$	2.02325e19	0.417159
$208$	6.09566e19	1.20638
$209$	2.16552e19	0.411451
$210$	−6.47569e18	−0.118147
$211$	−4.67993e19	−0.820046	−0.410023	−	0.912075i	$-0.634479\pi$
$211$	−4.67993e19	−0.820046	−0.410023	+	0.912075i	$0.634479\pi$
$212$	−3.01960e19	−0.508270
$213$	1.64427e19	0.265917
$214$	−1.09821e19	−0.170674
$215$	4.86311e19	0.726419
$216$	7.48253e18	0.107446
$217$	−8.30163e19	−1.14619
$218$	3.43485e19	0.456066
$219$	5.80960e18	0.0741944
$220$	−2.38650e19	−0.293203
$221$	−2.09895e20	−2.48124
$222$	−2.20732e19	−0.251111
$223$	−1.70487e19	−0.186681	−0.0933407	−	0.995634i	$-0.529755\pi$
$223$	−1.70487e19	−0.186681	−0.0933407	+	0.995634i	$0.529755\pi$
$224$	1.15781e20	1.22047
$225$	6.56841e18	0.0666667
$226$	−1.22543e19	−0.119775
$227$	2.03225e20	1.91318	0.956592	−	0.291429i	$-0.0941307\pi$
$227$	2.03225e20	1.91318	0.956592	+	0.291429i	$0.0941307\pi$
$228$	3.34499e19	0.303353
$229$	1.73884e19	0.151935	0.0759677	−	0.997110i	$-0.475795\pi$
$229$	1.73884e19	0.151935	0.0759677	+	0.997110i	$0.475795\pi$
$230$	1.93789e19	0.163171
$231$	8.00086e19	0.649284
$232$	8.36461e19	0.654331
$233$	−7.22288e19	−0.544735	−0.272368	−	0.962193i	$-0.587807\pi$
$233$	−7.22288e19	−0.544735	−0.272368	+	0.962193i	$0.587807\pi$
$234$	−2.14313e19	−0.155853
$235$	2.75441e19	0.193176
$236$	7.67098e19	0.518918
$237$	−4.49786e17	−0.00293525
$238$	−1.12437e20	−0.707954
$239$	−4.28634e19	−0.260438	−0.130219	−	0.991485i	$-0.541568\pi$
$239$	−4.28634e19	−0.260438	−0.130219	+	0.991485i	$0.541568\pi$
$240$	−3.31208e19	−0.194225
$241$	2.14062e20	1.21170	0.605848	−	0.795580i	$-0.292834\pi$
$241$	2.14062e20	1.21170	0.605848	+	0.795580i	$0.292834\pi$
$242$	2.59596e19	0.141863
$243$	1.21577e19	0.0641500
$244$	5.95036e18	0.0303201
$245$	−1.32977e20	−0.654432
$246$	−5.63386e19	−0.267829
$247$	−2.00513e20	−0.920912
$248$	9.18766e19	0.407723
$249$	2.21997e20	0.952035
$250$	6.29128e18	0.0260765
$251$	4.02872e20	1.61414	0.807068	−	0.590458i	$-0.201053\pi$
$251$	4.02872e20	1.61414	0.807068	+	0.590458i	$0.201053\pi$
$252$	1.23586e20	0.478701
$253$	−2.39430e20	−0.896716
$254$	−1.18191e20	−0.428054
$255$	1.14047e20	0.399477
$256$	7.50103e19	0.254145
$257$	7.39189e19	0.242283	0.121142	−	0.992635i	$-0.461344\pi$
$257$	7.39189e19	0.242283	0.121142	+	0.992635i	$0.461344\pi$
$258$	8.62150e19	0.273411
$259$	−7.63015e20	−2.34145
$260$	2.20974e20	0.656248
$261$	1.35909e20	0.390664
$262$	−3.79930e19	−0.105716
$263$	1.87464e20	0.505004	0.252502	−	0.967596i	$-0.418747\pi$
$263$	1.87464e20	0.505004	0.252502	+	0.967596i	$0.418747\pi$
$264$	−8.85478e19	−0.230964
$265$	−9.83507e19	−0.248420
$266$	−1.07411e20	−0.262757
$267$	−2.21677e20	−0.525261
$268$	3.30981e20	0.759726
$269$	−4.94362e20	−1.09939	−0.549694	−	0.835366i	$-0.685256\pi$
$269$	−4.94362e20	−1.09939	−0.549694	+	0.835366i	$0.685256\pi$
$270$	1.16447e19	0.0250921
$271$	−2.66243e20	−0.555954	−0.277977	−	0.960588i	$-0.589664\pi$
$271$	−2.66243e20	−0.555954	−0.277977	+	0.960588i	$0.589664\pi$
$272$	−5.75075e20	−1.16383
$273$	−7.40827e20	−1.45323
$274$	1.02945e20	0.195760
$275$	−7.77302e19	−0.143305
$276$	−3.69838e20	−0.661127
$277$	7.36150e19	0.127611	0.0638055	−	0.997962i	$-0.479676\pi$
$277$	7.36150e19	0.127611	0.0638055	+	0.997962i	$0.479676\pi$
$278$	−6.36287e19	−0.106973
$279$	1.49282e20	0.243428
$280$	2.47739e20	0.391879
$281$	7.23193e20	1.10982	0.554908	−	0.831912i	$-0.312754\pi$
$281$	7.23193e20	1.10982	0.554908	+	0.831912i	$0.312754\pi$
$282$	4.88313e19	0.0727078
$283$	2.78845e20	0.402883	0.201441	−	0.979501i	$-0.435437\pi$
$283$	2.78845e20	0.402883	0.201441	+	0.979501i	$0.435437\pi$
$284$	−3.00562e20	−0.421433
$285$	1.08949e20	0.148266
$286$	2.53617e20	0.335017
$287$	−1.94749e21	−2.49734
$288$	−2.08200e20	−0.259205
$289$	1.15295e21	1.39373
$290$	1.30175e20	0.152807
$291$	4.25369e20	0.484926
$292$	−1.06196e20	−0.117586
$293$	3.59066e20	0.386188	0.193094	−	0.981180i	$-0.438148\pi$
$293$	3.59066e20	0.386188	0.193094	+	0.981180i	$0.438148\pi$
$294$	−2.35747e20	−0.246316
$295$	2.49850e20	0.253625
$296$	8.44451e20	0.832904
$297$	−1.43873e20	−0.137895
$298$	−4.76459e20	−0.443800
$299$	2.21697e21	2.00703
$300$	−1.20067e20	−0.105655
$301$	2.98024e21	2.54939
$302$	5.88185e19	0.0489165
$303$	1.64675e20	0.133158
$304$	−5.49368e20	−0.431955
$305$	1.93808e19	0.0148191
$306$	2.02187e20	0.150356
$307$	−3.57691e20	−0.258721	−0.129361	−	0.991598i	$-0.541292\pi$
$307$	−3.57691e20	−0.258721	−0.129361	+	0.991598i	$0.541292\pi$
$308$	−1.46251e21	−1.02900
$309$	−1.23417e21	−0.844751
$310$	1.42983e20	0.0952163
$311$	−2.19139e21	−1.41989	−0.709947	−	0.704255i	$-0.751281\pi$
$311$	−2.19139e21	−1.41989	−0.709947	+	0.704255i	$0.751281\pi$
$312$	8.19894e20	0.516944
$313$	1.02616e21	0.629637	0.314818	−	0.949152i	$-0.398056\pi$
$313$	1.02616e21	0.629637	0.314818	+	0.949152i	$0.398056\pi$
$314$	−5.99113e20	−0.357772
$315$	4.02529e20	0.233968
$316$	8.22181e18	0.00465187
$317$	8.06555e19	0.0444253	0.0222126	−	0.999753i	$-0.492929\pi$
$317$	8.06555e19	0.0444253	0.0222126	+	0.999753i	$0.492929\pi$
$318$	−1.74360e20	−0.0935009
$319$	−1.60834e21	−0.839762
$320$	4.62254e20	0.235021
$321$	6.82645e20	0.337989
$322$	1.18759e21	0.572652
$323$	1.89167e21	0.888432
$324$	−2.22235e20	−0.101667
$325$	7.19730e20	0.320746
$326$	−4.77933e20	−0.207499
$327$	−2.13510e21	−0.903157
$328$	2.15534e21	0.888357
$329$	1.68798e21	0.677955
$330$	−1.37803e20	−0.0539374
$331$	1.60438e21	0.612025	0.306012	−	0.952028i	$-0.401005\pi$
$331$	1.60438e21	0.612025	0.306012	+	0.952028i	$0.401005\pi$
$332$	−4.05798e21	−1.50881
$333$	1.37207e21	0.497279
$334$	−1.04515e21	−0.369260
$335$	1.07803e21	0.371321
$336$	−2.02973e21	−0.681639
$337$	−1.51531e21	−0.496190	−0.248095	−	0.968736i	$-0.579805\pi$
$337$	−1.51531e21	−0.496190	−0.248095	+	0.968736i	$0.579805\pi$
$338$	−1.43527e21	−0.458292
$339$	7.61725e20	0.237192
$340$	−2.08471e21	−0.633104
$341$	−1.76659e21	−0.523268
$342$	1.93149e20	0.0558045
$343$	−2.58034e21	−0.727240
$344$	−3.29832e21	−0.906871
$345$	−1.20459e21	−0.323130
$346$	−1.58115e21	−0.413834
$347$	4.99855e21	1.27657	0.638283	−	0.769801i	$-0.279645\pi$
$347$	4.99855e21	1.27657	0.638283	+	0.769801i	$0.279645\pi$
$348$	−2.48433e21	−0.619136
$349$	−7.23627e21	−1.75994	−0.879971	−	0.475027i	$-0.842438\pi$
$349$	−7.23627e21	−1.75994	−0.879971	+	0.475027i	$0.842438\pi$
$350$	3.85546e20	0.0915161
$351$	1.33217e21	0.308638
$352$	2.46382e21	0.557182
$353$	3.25282e20	0.0718083	0.0359041	−	0.999355i	$-0.488569\pi$
$353$	3.25282e20	0.0718083	0.0359041	+	0.999355i	$0.488569\pi$
$354$	4.42943e20	0.0954597
$355$	−9.78955e20	−0.205978
$356$	4.05212e21	0.832449
$357$	6.98909e21	1.40198
$358$	−4.93348e20	−0.0966380
$359$	−1.95689e21	−0.374338	−0.187169	−	0.982328i	$-0.559931\pi$
$359$	−1.95689e21	−0.374338	−0.187169	+	0.982328i	$0.559931\pi$
$360$	−4.45490e20	−0.0832275
$361$	−3.67328e21	−0.670259
$362$	−1.05736e19	−0.00188452
$363$	−1.61365e21	−0.280933
$364$	1.35419e22	2.30312
$365$	−3.45888e20	−0.0574707
$366$	3.43590e19	0.00557765
$367$	−2.21711e21	−0.351662	−0.175831	−	0.984420i	$-0.556261\pi$
$367$	−2.21711e21	−0.351662	−0.175831	+	0.984420i	$0.556261\pi$
$368$	6.07409e21	0.941401
$369$	3.50201e21	0.530388
$370$	1.31418e21	0.194509
$371$	−6.02718e21	−0.871838
$372$	−2.72878e21	−0.385792
$373$	−1.07577e22	−1.48660	−0.743298	−	0.668961i	$-0.766739\pi$
$373$	−1.07577e22	−1.48660	−0.743298	+	0.668961i	$0.766739\pi$
$374$	−2.39267e21	−0.323201
$375$	−3.91066e20	−0.0516398
$376$	−1.86813e21	−0.241163
$377$	1.48921e22	1.87956
$378$	7.13618e20	0.0880614
$379$	7.81839e21	0.943374	0.471687	−	0.881766i	$-0.343645\pi$
$379$	7.81839e21	0.943374	0.471687	+	0.881766i	$0.343645\pi$
$380$	−1.99152e21	−0.234976
$381$	7.34677e21	0.847684
$382$	1.89774e21	0.214140
$383$	9.49308e21	1.04765	0.523827	−	0.851825i	$-0.324504\pi$
$383$	9.49308e21	1.04765	0.523827	+	0.851825i	$0.324504\pi$
$384$	4.97880e21	0.537414
$385$	−4.76350e21	−0.502933
$386$	−1.27361e21	−0.131536
$387$	−5.35913e21	−0.541441
$388$	−7.77549e21	−0.768526
$389$	7.30323e21	0.706225	0.353113	−	0.935581i	$-0.385123\pi$
$389$	7.30323e21	0.706225	0.353113	+	0.935581i	$0.385123\pi$
$390$	1.27596e21	0.120723
$391$	−2.09153e22	−1.93625
$392$	9.01892e21	0.817002
$393$	2.36164e21	0.209352
$394$	−1.63684e21	−0.142000
$395$	2.67791e19	0.00227363
$396$	2.62991e21	0.218541
$397$	−6.92001e21	−0.562843	−0.281422	−	0.959584i	$-0.590806\pi$
$397$	−6.92001e21	−0.562843	−0.281422	+	0.959584i	$0.590806\pi$
$398$	1.65470e21	0.131738
$399$	6.67666e21	0.520343
$400$	1.97193e21	0.150446
$401$	−1.52720e22	−1.14070	−0.570348	−	0.821403i	$-0.693192\pi$
$401$	−1.52720e22	−1.14070	−0.570348	+	0.821403i	$0.693192\pi$
$402$	1.91117e21	0.139759
$403$	1.63575e22	1.17118
$404$	−3.01017e21	−0.211032
$405$	−7.23836e20	−0.0496904
$406$	7.97743e21	0.536280
$407$	−1.62370e22	−1.06894
$408$	−7.73502e21	−0.498712
$409$	2.22167e21	0.140292	0.0701458	−	0.997537i	$-0.477654\pi$
$409$	2.22167e21	0.140292	0.0701458	+	0.997537i	$0.477654\pi$
$410$	3.35426e21	0.207460
$411$	−6.39903e21	−0.387667
$412$	2.25599e22	1.33879
$413$	1.53114e22	0.890103
$414$	−2.13555e21	−0.121620
$415$	−1.32171e22	−0.737443
$416$	−2.28134e22	−1.24709
$417$	3.95516e21	0.211840
$418$	−2.28571e21	−0.119956
$419$	−1.64936e22	−0.848198	−0.424099	−	0.905616i	$-0.639409\pi$
$419$	−1.64936e22	−0.848198	−0.424099	+	0.905616i	$0.639409\pi$
$420$	−7.35799e21	−0.370800
$421$	6.48638e21	0.320335	0.160168	−	0.987090i	$-0.448797\pi$
$421$	6.48638e21	0.320335	0.160168	+	0.987090i	$0.448797\pi$
$422$	4.93967e21	0.239079
$423$	−3.03535e21	−0.143985
$424$	6.67045e21	0.310131
$425$	−6.79006e21	−0.309434
$426$	−1.73553e21	−0.0775265
$427$	1.18770e21	0.0520082
$428$	−1.24784e22	−0.535655
$429$	−1.57648e22	−0.663441
$430$	−5.13302e21	−0.211783
$431$	−2.94810e22	−1.19257	−0.596286	−	0.802772i	$-0.703358\pi$
$431$	−2.94810e22	−1.19257	−0.596286	+	0.802772i	$0.703358\pi$
$432$	3.64990e21	0.144767
$433$	−4.61864e22	−1.79625	−0.898125	−	0.439741i	$-0.855070\pi$
$433$	−4.61864e22	−1.79625	−0.898125	+	0.439741i	$0.855070\pi$
$434$	8.76239e21	0.334164
$435$	−8.09166e21	−0.302607
$436$	3.90284e22	1.43135
$437$	−1.99803e22	−0.718638
$438$	−6.13204e20	−0.0216309
$439$	−5.08029e21	−0.175768	−0.0878840	−	0.996131i	$-0.528010\pi$
$439$	−5.08029e21	−0.175768	−0.0878840	+	0.996131i	$0.528010\pi$
$440$	5.27191e21	0.178904
$441$	1.46540e22	0.487785
$442$	2.21545e22	0.723390
$443$	4.56719e22	1.46291	0.731454	−	0.681890i	$-0.238842\pi$
$443$	4.56719e22	1.46291	0.731454	+	0.681890i	$0.238842\pi$
$444$	−2.50806e22	−0.788103
$445$	1.31981e22	0.406865
$446$	1.79950e21	0.0544258
$447$	2.96167e22	0.878865
$448$	2.83281e22	0.824811
$449$	9.26468e21	0.264689	0.132345	−	0.991204i	$-0.457749\pi$
$449$	9.26468e21	0.264689	0.132345	+	0.991204i	$0.457749\pi$
$450$	−6.93297e20	−0.0194363
$451$	−4.14426e22	−1.14011
$452$	−1.39239e22	−0.375910
$453$	−3.65616e21	−0.0968703
$454$	−2.14504e22	−0.557777
$455$	4.41069e22	1.12567
$456$	−7.38925e21	−0.185097
$457$	2.45492e22	0.603601	0.301801	−	0.953371i	$-0.402412\pi$
$457$	2.45492e22	0.603601	0.301801	+	0.953371i	$0.402412\pi$
$458$	−1.83535e21	−0.0442958
$459$	−1.25679e22	−0.297753
$460$	2.20192e22	0.512106
$461$	4.22070e22	0.963667	0.481834	−	0.876263i	$-0.339971\pi$
$461$	4.22070e22	0.963667	0.481834	+	0.876263i	$0.339971\pi$
$462$	−8.44492e21	−0.189295
$463$	2.72110e22	0.598832	0.299416	−	0.954123i	$-0.403208\pi$
$463$	2.72110e22	0.598832	0.299416	+	0.954123i	$0.403208\pi$
$464$	4.08017e22	0.881608
$465$	−8.88785e21	−0.188559
$466$	7.62377e21	0.158814
$467$	−4.73325e22	−0.968202	−0.484101	−	0.875012i	$-0.660853\pi$
$467$	−4.73325e22	−0.968202	−0.484101	+	0.875012i	$0.660853\pi$
$468$	−2.43513e22	−0.489139
$469$	6.60644e22	1.30316
$470$	−2.90729e21	−0.0563192
$471$	3.72409e22	0.708504
$472$	−1.69456e22	−0.316628
$473$	6.34196e22	1.16387
$474$	4.74749e19	0.000855753 0
$475$	−6.48653e21	−0.114846
$476$	−1.27756e23	−2.22189
$477$	1.08382e22	0.185162
$478$	4.52424e21	0.0759292
$479$	−3.54183e22	−0.583950	−0.291975	−	0.956426i	$-0.594312\pi$
$479$	−3.54183e22	−0.583950	−0.291975	+	0.956426i	$0.594312\pi$
$480$	1.23957e22	0.200779
$481$	1.50344e23	2.39251
$482$	−2.25942e22	−0.353263
$483$	−7.38204e22	−1.13403
$484$	2.94966e22	0.445232
$485$	−2.53254e22	−0.375622
$486$	−1.28324e21	−0.0187025
$487$	−2.32584e22	−0.333107	−0.166553	−	0.986032i	$-0.553264\pi$
$487$	−2.32584e22	−0.333107	−0.166553	+	0.986032i	$0.553264\pi$
$488$	−1.31447e21	−0.0185004
$489$	2.97083e22	0.410915
$490$	1.40357e22	0.190796
$491$	2.08629e22	0.278728	0.139364	−	0.990241i	$-0.455494\pi$
$491$	2.08629e22	0.278728	0.139364	+	0.990241i	$0.455494\pi$
$492$	−6.40147e22	−0.840574
$493$	−1.40495e23	−1.81327
$494$	2.11642e22	0.268486
$495$	8.56583e21	0.106813
$496$	4.48165e22	0.549343
$497$	−5.99929e22	−0.722887
$498$	−2.34318e22	−0.277560
$499$	−1.49399e23	−1.73978	−0.869890	−	0.493246i	$-0.835810\pi$
$499$	−1.49399e23	−1.73978	−0.869890	+	0.493246i	$0.835810\pi$
$500$	7.14845e21	0.0818403
$501$	6.49663e22	0.731252
$502$	−4.25232e22	−0.470592
$503$	1.02620e23	1.11662	0.558309	−	0.829633i	$-0.311450\pi$
$503$	1.02620e23	1.11662	0.558309	+	0.829633i	$0.311450\pi$
$504$	−2.73008e22	−0.292089
$505$	−9.80435e21	−0.103144
$506$	2.52719e22	0.261432
$507$	8.92165e22	0.907565
$508$	−1.34295e23	−1.34344
$509$	−1.41389e23	−1.39096	−0.695481	−	0.718545i	$-0.744809\pi$
$509$	−1.41389e23	−1.39096	−0.695481	+	0.718545i	$0.744809\pi$
$510$	−1.20377e22	−0.116465
$511$	−2.11969e22	−0.201695
$512$	−1.07381e23	−1.00492
$513$	−1.20061e22	−0.110511
$514$	−7.80215e21	−0.0706362
$515$	7.34794e22	0.654341
$516$	9.79617e22	0.858092
$517$	3.59202e22	0.309506
$518$	8.05364e22	0.682636
$519$	9.82844e22	0.819524
$520$	−4.88144e22	−0.400423
$521$	1.43662e23	1.15937	0.579685	−	0.814841i	$-0.303176\pi$
$521$	1.43662e23	1.15937	0.579685	+	0.814841i	$0.303176\pi$
$522$	−1.43452e22	−0.113896
$523$	−1.08226e23	−0.845412	−0.422706	−	0.906267i	$-0.638920\pi$
$523$	−1.08226e23	−0.845412	−0.422706	+	0.906267i	$0.638920\pi$
$524$	−4.31694e22	−0.331788
$525$	−2.39655e22	−0.181231
$526$	−1.97869e22	−0.147231
$527$	−1.54319e23	−1.12987
$528$	−4.31927e22	−0.311188
$529$	7.98621e22	0.566197
$530$	1.03809e22	0.0724255
$531$	−2.75333e22	−0.189041
$532$	−1.22045e23	−0.824655
$533$	3.83731e23	2.55179
$534$	2.33981e22	0.153137
$535$	−4.06429e22	−0.261805
$536$	−7.31154e22	−0.463562
$537$	3.06665e22	0.191374
$538$	5.21800e22	0.320520
$539$	−1.73415e23	−1.04853
$540$	1.32313e22	0.0787508
$541$	1.33856e23	0.784265	0.392132	−	0.919909i	$-0.371738\pi$
$541$	1.33856e23	0.784265	0.392132	+	0.919909i	$0.371738\pi$
$542$	2.81019e22	0.162085
$543$	6.57257e20	0.00373196
$544$	2.15225e23	1.20310
$545$	1.27119e23	0.699582
$546$	7.81944e22	0.423680
$547$	−6.84817e22	−0.365327	−0.182664	−	0.983175i	$-0.558472\pi$
$547$	−6.84817e22	−0.365327	−0.182664	+	0.983175i	$0.558472\pi$
$548$	1.16971e23	0.614387
$549$	−2.13576e21	−0.0110455
$550$	8.20443e21	0.0417797
$551$	−1.34215e23	−0.672994
$552$	8.16992e22	0.403400
$553$	1.64109e21	0.00797937
$554$	−7.77007e21	−0.0372042
$555$	−8.16895e22	−0.385191
$556$	−7.22980e22	−0.335730
$557$	2.95445e23	1.35116	0.675580	−	0.737286i	$-0.263893\pi$
$557$	2.95445e23	1.35116	0.675580	+	0.737286i	$0.263893\pi$
$558$	−1.57567e22	−0.0709700
$559$	−5.87224e23	−2.60497
$560$	1.20845e23	0.527995
$561$	1.48728e23	0.640042
$562$	−7.63332e22	−0.323560
$563$	−4.12155e23	−1.72084	−0.860418	−	0.509590i	$-0.829797\pi$
$563$	−4.12155e23	−1.72084	−0.860418	+	0.509590i	$0.829797\pi$
$564$	5.54845e22	0.228191
$565$	−4.53512e22	−0.183728
$566$	−2.94322e22	−0.117458
$567$	−4.43585e22	−0.174390
$568$	6.63958e22	0.257146
$569$	5.03050e23	1.91936	0.959681	−	0.281092i	$-0.0906966\pi$
$569$	5.03050e23	1.91936	0.959681	+	0.281092i	$0.0906966\pi$
$570$	−1.14996e22	−0.0432260
$571$	5.27359e23	1.95299	0.976493	−	0.215547i	$-0.0691536\pi$
$571$	5.27359e23	1.95299	0.976493	+	0.215547i	$0.0691536\pi$
$572$	2.88172e23	1.05144
$573$	−1.17963e23	−0.424066
$574$	2.05557e23	0.728085
$575$	7.17183e22	0.250296
$576$	−5.09402e22	−0.175174
$577$	2.31429e23	0.784192	0.392096	−	0.919924i	$-0.371750\pi$
$577$	2.31429e23	0.784192	0.392096	+	0.919924i	$0.371750\pi$
$578$	−1.21694e23	−0.406334
$579$	7.91677e22	0.260484
$580$	1.47911e23	0.479581
$581$	−8.09980e23	−2.58808
$582$	−4.48978e22	−0.141377
$583$	−1.28259e23	−0.398019
$584$	2.34593e22	0.0717472
$585$	−7.93140e22	−0.239070
$586$	−3.78994e22	−0.112591
$587$	−1.67583e23	−0.490688	−0.245344	−	0.969436i	$-0.578901\pi$
$587$	−1.67583e23	−0.490688	−0.245344	+	0.969436i	$0.578901\pi$
$588$	−2.67867e23	−0.773057
$589$	−1.47421e23	−0.419352
$590$	−2.63717e22	−0.0739428
$591$	1.01746e23	0.281206
$592$	4.11915e23	1.12221
$593$	4.62003e23	1.24074	0.620369	−	0.784310i	$-0.286983\pi$
$593$	4.62003e23	1.24074	0.620369	+	0.784310i	$0.286983\pi$
$594$	1.51858e22	0.0402026
$595$	−4.16112e23	−1.08597
$596$	−5.41375e23	−1.39285
$597$	−1.02856e23	−0.260884
$598$	−2.34001e23	−0.585138
$599$	6.81228e21	0.0167944	0.00839720	−	0.999965i	$-0.497327\pi$
$599$	6.81228e21	0.0167944	0.00839720	+	0.999965i	$0.497327\pi$
$600$	2.65233e22	0.0644678
$601$	−7.15068e23	−1.71362	−0.856809	−	0.515633i	$-0.827557\pi$
$601$	−7.15068e23	−1.71362	−0.856809	+	0.515633i	$0.827557\pi$
$602$	−3.14565e23	−0.743258
$603$	−1.18798e23	−0.276767
$604$	6.68324e22	0.153523
$605$	9.60726e22	0.217610
$606$	−1.73815e22	−0.0388213
$607$	−2.99308e23	−0.659195	−0.329597	−	0.944122i	$-0.606913\pi$
$607$	−2.99308e23	−0.659195	−0.329597	+	0.944122i	$0.606913\pi$
$608$	2.05604e23	0.446531
$609$	−4.95877e23	−1.06201
$610$	−2.04565e21	−0.00432043
$611$	−3.32597e23	−0.692737
$612$	2.29734e23	0.471888
$613$	7.66386e23	1.55251	0.776253	−	0.630421i	$-0.217118\pi$
$613$	7.66386e23	1.55251	0.776253	+	0.630421i	$0.217118\pi$
$614$	3.77544e22	0.0754286
$615$	−2.08501e23	−0.410836
$616$	3.23076e23	0.627868
$617$	−1.04769e23	−0.200820	−0.100410	−	0.994946i	$-0.532016\pi$
$617$	−1.04769e23	−0.200820	−0.100410	+	0.994946i	$0.532016\pi$
$618$	1.30267e23	0.246282
$619$	7.62993e23	1.42282	0.711410	−	0.702777i	$-0.248057\pi$
$619$	7.62993e23	1.42282	0.711410	+	0.702777i	$0.248057\pi$
$620$	1.62465e23	0.298834
$621$	1.32746e23	0.240847
$622$	2.31301e23	0.413961
$623$	8.08812e23	1.42790
$624$	3.99936e23	0.696501
$625$	2.32831e22	0.0400000
$626$	−1.08312e23	−0.183567
$627$	1.42080e23	0.237552
$628$	−6.80741e23	−1.12286
$629$	−1.41837e24	−2.30813
$630$	−4.24870e22	−0.0682121
$631$	2.67118e22	0.0423110	0.0211555	−	0.999776i	$-0.493265\pi$
$631$	2.67118e22	0.0423110	0.0211555	+	0.999776i	$0.493265\pi$
$632$	−1.81624e21	−0.00283843
$633$	−3.07050e23	−0.473454
$634$	−8.51320e21	−0.0129519
$635$	−4.37408e23	−0.656613
$636$	−1.98116e23	−0.293450
$637$	1.60571e24	2.34683
$638$	1.69760e23	0.244827
$639$	1.07880e23	0.153527
$640$	−2.96425e23	−0.416279
$641$	−7.71926e23	−1.06975	−0.534875	−	0.844931i	$-0.679641\pi$
$641$	−7.71926e23	−1.06975	−0.534875	+	0.844931i	$0.679641\pi$
$642$	−7.20533e22	−0.0985386
$643$	5.74619e23	0.775509	0.387754	−	0.921763i	$-0.373251\pi$
$643$	5.74619e23	0.775509	0.387754	+	0.921763i	$0.373251\pi$
$644$	1.34939e24	1.79725
$645$	3.19069e23	0.419398
$646$	−1.99666e23	−0.259017
$647$	−6.99931e23	−0.896125	−0.448063	−	0.894002i	$-0.647886\pi$
$647$	−6.99931e23	−0.896125	−0.448063	+	0.894002i	$0.647886\pi$
$648$	4.90929e22	0.0620341
$649$	3.25828e23	0.406358
$650$	−7.59676e22	−0.0935115
$651$	−5.44670e23	−0.661752
$652$	−5.43050e23	−0.651231
$653$	1.29872e24	1.53728	0.768640	−	0.639682i	$-0.220934\pi$
$653$	1.29872e24	1.53728	0.768640	+	0.639682i	$0.220934\pi$
$654$	2.25361e23	0.263310
$655$	−1.40606e23	−0.162164
$656$	1.05135e24	1.19692
$657$	3.81168e22	0.0428362
$658$	−1.78166e23	−0.197654
$659$	−4.10190e23	−0.449220	−0.224610	−	0.974449i	$-0.572111\pi$
$659$	−4.10190e23	−0.449220	−0.224610	+	0.974449i	$0.572111\pi$
$660$	−1.56578e23	−0.169281
$661$	1.61344e24	1.72202	0.861012	−	0.508584i	$-0.169831\pi$
$661$	1.61344e24	1.72202	0.861012	+	0.508584i	$0.169831\pi$
$662$	−1.69342e23	−0.178432
$663$	−1.37712e24	−1.43254
$664$	8.96428e23	0.920634
$665$	−3.97511e23	−0.403056
$666$	−1.44822e23	−0.144979
$667$	1.48394e24	1.46672
$668$	−1.18754e24	−1.15891
$669$	−1.11857e23	−0.107781
$670$	−1.13786e23	−0.108257
$671$	2.52744e22	0.0237432
$672$	7.59638e23	0.704641
$673$	−3.46816e23	−0.317666	−0.158833	−	0.987305i	$-0.550773\pi$
$673$	−3.46816e23	−0.317666	−0.158833	+	0.987305i	$0.550773\pi$
$674$	1.59942e23	0.144661
$675$	4.30953e22	0.0384900
$676$	−1.63083e24	−1.43834
$677$	2.06445e24	1.79805	0.899024	−	0.437899i	$-0.144277\pi$
$677$	2.06445e24	1.79805	0.899024	+	0.437899i	$0.144277\pi$
$678$	−8.04002e22	−0.0691520
$679$	−1.55200e24	−1.31826
$680$	4.60523e23	0.386301
$681$	1.33336e24	1.10458
$682$	1.86464e23	0.152556
$683$	1.79202e22	0.0144799	0.00723997	−	0.999974i	$-0.497695\pi$
$683$	1.79202e22	0.0144799	0.00723997	+	0.999974i	$0.497695\pi$
$684$	2.19465e23	0.175141
$685$	3.80982e23	0.300286
$686$	2.72356e23	0.212022
$687$	1.14086e23	0.0877199
$688$	−1.60889e24	−1.22187
$689$	1.18759e24	0.890848
$690$	1.27145e23	0.0942066
$691$	−1.82328e24	−1.33441	−0.667207	−	0.744873i	$-0.732510\pi$
$691$	−1.82328e24	−1.33441	−0.667207	+	0.744873i	$0.732510\pi$
$692$	−1.79658e24	−1.29881
$693$	5.24936e23	0.374864
$694$	−5.27598e23	−0.372175
$695$	−2.35480e23	−0.164090
$696$	5.48802e23	0.377778
$697$	−3.62019e24	−2.46180
$698$	7.63789e23	0.513101
$699$	−4.73893e23	−0.314503
$700$	4.38076e23	0.287221
$701$	−2.61207e24	−1.69193	−0.845965	−	0.533239i	$-0.820975\pi$
$701$	−2.61207e24	−1.69193	−0.845965	+	0.533239i	$0.820975\pi$
$702$	−1.40611e23	−0.0899815
$703$	−1.35497e24	−0.856660
$704$	6.02824e23	0.376550
$705$	1.80717e23	0.111530
$706$	−3.43335e22	−0.0209353
$707$	−6.00835e23	−0.361985
$708$	5.03293e23	0.299598
$709$	−1.84759e24	−1.08671	−0.543353	−	0.839504i	$-0.682845\pi$
$709$	−1.84759e24	−1.08671	−0.543353	+	0.839504i	$0.682845\pi$
$710$	1.03329e23	0.0600518
$711$	−2.95104e21	−0.00169467
$712$	−8.95136e23	−0.507936
$713$	1.62996e24	0.913935
$714$	−7.37699e23	−0.408738
$715$	9.38597e23	0.513899
$716$	−5.60566e23	−0.303296
$717$	−2.81227e23	−0.150364
$718$	2.06550e23	0.109136
$719$	−9.54585e23	−0.498447	−0.249224	−	0.968446i	$-0.580175\pi$
$719$	−9.54585e23	−0.498447	−0.249224	+	0.968446i	$0.580175\pi$
$720$	−2.17306e23	−0.112136
$721$	4.50300e24	2.29643
$722$	3.87715e23	0.195410
$723$	1.40446e24	0.699573
$724$	−1.20143e22	−0.00591452
$725$	4.81756e23	0.234398
$726$	1.70321e23	0.0819044
$727$	3.28829e23	0.156289	0.0781443	−	0.996942i	$-0.475101\pi$
$727$	3.28829e23	0.156289	0.0781443	+	0.996942i	$0.475101\pi$
$728$	−2.99147e24	−1.40530
$729$	7.97664e22	0.0370370
$730$	3.65086e22	0.0167552
$731$	5.53997e24	2.51310
$732$	3.90403e22	0.0175053
$733$	1.68096e24	0.745031	0.372515	−	0.928026i	$-0.378495\pi$
$733$	1.68096e24	0.745031	0.372515	+	0.928026i	$0.378495\pi$
$734$	2.34016e23	0.102525
$735$	−8.72462e23	−0.377837
$736$	−2.27326e24	−0.973169
$737$	1.40585e24	0.594931
$738$	−3.69638e23	−0.154631
$739$	1.71501e24	0.709231	0.354616	−	0.935012i	$-0.384612\pi$
$739$	1.71501e24	0.709231	0.354616	+	0.935012i	$0.384612\pi$
$740$	1.49324e24	0.610462
$741$	−1.31556e24	−0.531689
$742$	6.36170e23	0.254179
$743$	−1.92121e24	−0.758873	−0.379436	−	0.925218i	$-0.623882\pi$
$743$	−1.92121e24	−0.758873	−0.379436	+	0.925218i	$0.623882\pi$
$744$	6.02802e23	0.235399
$745$	−1.76330e24	−0.680766
$746$	1.13547e24	0.433408
$747$	1.45652e24	0.549658
$748$	−2.71866e24	−1.01436
$749$	−2.49070e24	−0.918812
$750$	4.12771e22	0.0150553
$751$	3.66527e24	1.32180	0.660902	−	0.750472i	$-0.270174\pi$
$751$	3.66527e24	1.32180	0.660902	+	0.750472i	$0.270174\pi$
$752$	−9.11256e23	−0.324929
$753$	2.64324e24	0.931922
$754$	−1.57187e24	−0.547974
$755$	2.17678e23	0.0750354
$756$	8.10847e23	0.276378
$757$	−2.09505e24	−0.706121	−0.353061	−	0.935600i	$-0.614859\pi$
$757$	−2.09505e24	−0.706121	−0.353061	+	0.935600i	$0.614859\pi$
$758$	−8.25233e23	−0.275035
$759$	−1.57090e24	−0.517719
$760$	4.39937e23	0.143376
$761$	3.96049e24	1.27638	0.638189	−	0.769880i	$-0.279684\pi$
$761$	3.96049e24	1.27638	0.638189	+	0.769880i	$0.279684\pi$
$762$	−7.75453e23	−0.247137
$763$	7.79015e24	2.45520
$764$	2.15630e24	0.672072
$765$	7.48262e23	0.230638
$766$	−1.00200e24	−0.305437
$767$	−3.01695e24	−0.909511
$768$	4.92142e23	0.146731
$769$	−1.03312e24	−0.304632	−0.152316	−	0.988332i	$-0.548673\pi$
$769$	−1.03312e24	−0.304632	−0.152316	+	0.988332i	$0.548673\pi$
$770$	5.02789e23	0.146627
$771$	4.84982e23	0.139882
$772$	−1.44714e24	−0.412822
$773$	5.97296e23	0.168525	0.0842624	−	0.996444i	$-0.473147\pi$
$773$	5.97296e23	0.168525	0.0842624	+	0.996444i	$0.473147\pi$
$774$	5.65657e23	0.157854
$775$	5.29160e23	0.146057
$776$	1.71765e24	0.468932
$777$	−5.00614e24	−1.35184
$778$	−7.70857e23	−0.205896
$779$	−3.45836e24	−0.913695
$780$	1.44981e24	0.378885
$781$	−1.27665e24	−0.330019
$782$	2.20761e24	0.564501
$783$	8.91698e23	0.225550
$784$	4.39934e24	1.10078
$785$	−2.21723e24	−0.548805
$786$	−2.49272e23	−0.0610354
$787$	−4.68780e24	−1.13549	−0.567746	−	0.823204i	$-0.692184\pi$
$787$	−4.68780e24	−1.13549	−0.567746	+	0.823204i	$0.692184\pi$
$788$	−1.85986e24	−0.445663
$789$	1.22995e24	0.291564
$790$	−2.82654e21	−0.000662864 0
$791$	−2.77923e24	−0.644800
$792$	−5.80962e23	−0.133347
$793$	−2.34024e23	−0.0531421
$794$	7.30408e23	0.164093
$795$	−6.45279e23	−0.143426
$796$	1.88015e24	0.413457
$797$	−4.23199e24	−0.920764	−0.460382	−	0.887721i	$-0.652288\pi$
$797$	−4.23199e24	−0.920764	−0.460382	+	0.887721i	$0.652288\pi$
$798$	−7.04723e23	−0.151703
$799$	3.13778e24	0.668306
$800$	−7.38006e23	−0.155523
$801$	−1.45442e24	−0.303259
$802$	1.61197e24	0.332563
$803$	−4.51072e23	−0.0920796
$804$	2.17157e24	0.438628
$805$	4.39508e24	0.878419
$806$	−1.72653e24	−0.341450
$807$	−3.24351e24	−0.634732
$808$	6.64962e23	0.128766
$809$	−6.89799e24	−1.32178	−0.660891	−	0.750482i	$-0.729821\pi$
$809$	−6.89799e24	−1.32178	−0.660891	+	0.750482i	$0.729821\pi$
$810$	7.64010e22	0.0144869
$811$	−5.76842e24	−1.08238	−0.541190	−	0.840900i	$-0.682026\pi$
$811$	−5.76842e24	−1.08238	−0.541190	+	0.840900i	$0.682026\pi$
$812$	9.06434e24	1.68310
$813$	−1.74682e24	−0.320980
$814$	1.71382e24	0.311643
$815$	−1.76876e24	−0.318294
$816$	−3.77307e24	−0.671937
$817$	5.29232e24	0.932737
$818$	−2.34498e23	−0.0409012
$819$	−4.86056e24	−0.839022
$820$	3.81127e24	0.651106
$821$	4.82230e24	0.815338	0.407669	−	0.913130i	$-0.366342\pi$
$821$	4.82230e24	0.815338	0.407669	+	0.913130i	$0.366342\pi$
$822$	6.75419e23	0.113022
$823$	−4.94083e24	−0.818278	−0.409139	−	0.912472i	$-0.634171\pi$
$823$	−4.94083e24	−0.818278	−0.409139	+	0.912472i	$0.634171\pi$
$824$	−4.98361e24	−0.816888
$825$	−5.09988e23	−0.0827373
$826$	−1.61612e24	−0.259504
$827$	3.01636e24	0.479386	0.239693	−	0.970849i	$-0.422953\pi$
$827$	3.01636e24	0.479386	0.239693	+	0.970849i	$0.422953\pi$
$828$	−2.42651e24	−0.381702
$829$	9.18768e23	0.143051	0.0715257	−	0.997439i	$-0.477213\pi$
$829$	9.18768e23	0.143051	0.0715257	+	0.997439i	$0.477213\pi$
$830$	1.39507e24	0.214997
$831$	4.82988e23	0.0736763
$832$	−5.58175e24	−0.842795
$833$	−1.51485e25	−2.26406
$834$	−4.17468e23	−0.0617606
$835$	−3.86792e24	−0.566426
$836$	−2.59713e24	−0.376479
$837$	9.79437e23	0.140543
$838$	1.74091e24	0.247287
$839$	7.98403e24	1.12265	0.561326	−	0.827595i	$-0.310291\pi$
$839$	7.98403e24	1.12265	0.561326	+	0.827595i	$0.310291\pi$
$840$	1.62542e24	0.226251
$841$	2.71101e24	0.373564
$842$	−6.84639e23	−0.0933918
$843$	4.74487e24	0.640752
$844$	5.61269e24	0.750344
$845$	−5.31172e24	−0.702997
$846$	3.20382e23	0.0419779
$847$	5.88758e24	0.763708
$848$	3.25378e24	0.417853
$849$	1.82950e24	0.232604
$850$	7.16692e23	0.0902135
$851$	1.49812e25	1.86700
$852$	−1.97199e24	−0.243315
$853$	5.88324e24	0.718704	0.359352	−	0.933202i	$-0.382998\pi$
$853$	5.88324e24	0.718704	0.359352	+	0.933202i	$0.382998\pi$
$854$	−1.25362e23	−0.0151627
$855$	7.14813e23	0.0856013
$856$	2.75653e24	0.326841
$857$	1.15530e25	1.35630	0.678152	−	0.734922i	$-0.262781\pi$
$857$	1.15530e25	1.35630	0.678152	+	0.734922i	$0.262781\pi$
$858$	1.66398e24	0.193422
$859$	−8.55025e24	−0.984095	−0.492047	−	0.870568i	$-0.663751\pi$
$859$	−8.55025e24	−0.984095	−0.492047	+	0.870568i	$0.663751\pi$
$860$	−5.83239e24	−0.664675
$861$	−1.27775e25	−1.44184
$862$	3.11172e24	0.347687
$863$	−7.97738e24	−0.882610	−0.441305	−	0.897357i	$-0.645484\pi$
$863$	−7.97738e24	−0.882610	−0.441305	+	0.897357i	$0.645484\pi$
$864$	−1.36600e24	−0.149652
$865$	−5.85160e24	−0.634801
$866$	4.87498e24	0.523685
$867$	7.56451e24	0.804671
$868$	9.95624e24	1.04876
$869$	3.49225e22	0.00364281
$870$	8.54076e23	0.0882232
$871$	−1.30173e25	−1.33158
$872$	−8.62159e24	−0.873367
$873$	2.79085e24	0.279972
$874$	2.10892e24	0.209514
$875$	1.42685e24	0.140381
$876$	−6.96752e23	−0.0678880
$877$	1.63184e25	1.57464	0.787321	−	0.616543i	$-0.211467\pi$
$877$	1.63184e25	1.57464	0.787321	+	0.616543i	$0.211467\pi$
$878$	5.36225e23	0.0512441
$879$	2.35583e24	0.222966
$880$	2.57158e24	0.241045
$881$	−3.38146e24	−0.313913	−0.156956	−	0.987606i	$-0.550168\pi$
$881$	−3.38146e24	−0.313913	−0.156956	+	0.987606i	$0.550168\pi$
$882$	−1.54673e24	−0.142211
$883$	1.13867e25	1.03689	0.518443	−	0.855112i	$-0.326512\pi$
$883$	1.13867e25	1.03689	0.518443	+	0.855112i	$0.326512\pi$
$884$	2.51730e25	2.27034
$885$	1.63926e24	0.146430
$886$	−4.82068e24	−0.426502
$887$	4.89146e24	0.428635	0.214317	−	0.976764i	$-0.431247\pi$
$887$	4.89146e24	0.428635	0.214317	+	0.976764i	$0.431247\pi$
$888$	5.54044e24	0.480877
$889$	−2.68055e25	−2.30440
$890$	−1.39306e24	−0.118619
$891$	−9.43952e23	−0.0796140
$892$	2.04467e24	0.170814
$893$	2.99752e24	0.248041
$894$	−3.12604e24	−0.256228
$895$	−1.82581e24	−0.148238
$896$	−1.81657e25	−1.46094
$897$	1.45455e25	1.15876
$898$	−9.77889e23	−0.0771686
$899$	1.09490e25	0.855887
$900$	−7.87757e23	−0.0610001
$901$	−1.12039e25	−0.859429
$902$	4.37427e24	0.332392
$903$	1.95533e25	1.47189
$904$	3.07586e24	0.229369
$905$	−3.91314e22	−0.00289076
$906$	3.85908e23	0.0282419
$907$	−2.47170e25	−1.79198	−0.895990	−	0.444074i	$-0.853533\pi$
$907$	−2.47170e25	−1.79198	−0.895990	+	0.444074i	$0.853533\pi$
$908$	−2.43730e25	−1.75057
$909$	1.08044e24	0.0768786
$910$	−4.65549e24	−0.328181
$911$	7.05356e24	0.492609	0.246304	−	0.969193i	$-0.420784\pi$
$911$	7.05356e24	0.492609	0.246304	+	0.969193i	$0.420784\pi$
$912$	−3.60440e24	−0.249389
$913$	−1.72364e25	−1.18153
$914$	−2.59118e24	−0.175976
$915$	1.27157e23	0.00855583
$916$	−2.08542e24	−0.139021
$917$	−8.61670e24	−0.569117
$918$	1.32655e24	0.0868080
$919$	5.70217e24	0.369707	0.184854	−	0.982766i	$-0.440819\pi$
$919$	5.70217e24	0.369707	0.184854	+	0.982766i	$0.440819\pi$
$920$	−4.86416e24	−0.312472
$921$	−2.34681e24	−0.149373
$922$	−4.45496e24	−0.280951
$923$	1.18209e25	0.738649
$924$	−9.59552e24	−0.594096
$925$	4.86358e24	0.298368
$926$	−2.87212e24	−0.174586
$927$	−8.09740e24	−0.487717
$928$	−1.52703e25	−0.911359
$929$	1.10885e25	0.655752	0.327876	−	0.944721i	$-0.393667\pi$
$929$	1.10885e25	0.655752	0.327876	+	0.944721i	$0.393667\pi$
$930$	9.38114e23	0.0549731
$931$	−1.44713e25	−0.840304
$932$	8.66249e24	0.498434
$933$	−1.43777e25	−0.819776
$934$	4.99595e24	0.282273
$935$	−8.85489e24	−0.495775
$936$	5.37933e24	0.298458
$937$	−6.37448e24	−0.350476	−0.175238	−	0.984526i	$-0.556069\pi$
$937$	−6.37448e24	−0.350476	−0.175238	+	0.984526i	$0.556069\pi$
$938$	−6.97311e24	−0.379929
$939$	6.73266e24	0.363521
$940$	−3.30340e24	−0.176756
$941$	6.53698e24	0.346630	0.173315	−	0.984866i	$-0.444552\pi$
$941$	6.53698e24	0.346630	0.173315	+	0.984866i	$0.444552\pi$
$942$	−3.93078e24	−0.206560
$943$	3.82373e25	1.99130
$944$	−8.26590e24	−0.426607
$945$	2.64099e24	0.135082
$946$	−6.69395e24	−0.339319
$947$	1.40620e25	0.706434	0.353217	−	0.935541i	$-0.385088\pi$
$947$	1.40620e25	0.706434	0.353217	+	0.935541i	$0.385088\pi$
$948$	5.39433e22	0.00268576
$949$	4.17663e24	0.206093
$950$	6.84654e23	0.0334827
$951$	5.29181e23	0.0256490
$952$	2.82220e25	1.35573
$953$	−3.29795e25	−1.57020	−0.785098	−	0.619371i	$-0.787388\pi$
$953$	−3.29795e25	−1.57020	−0.785098	+	0.619371i	$0.787388\pi$
$954$	−1.14397e24	−0.0539828
$955$	7.02324e24	0.328480
$956$	5.14066e24	0.238302
$957$	−1.05523e25	−0.484837
$958$	3.73840e24	0.170247
$959$	2.33475e25	1.05386
$960$	3.03285e24	0.135689
$961$	−1.05238e25	−0.466684
$962$	−1.58688e25	−0.697520
$963$	4.47884e24	0.195138
$964$	−2.56727e25	−1.10871
$965$	−4.71344e24	−0.201770
$966$	7.79176e24	0.330621
$967$	−7.72859e24	−0.325069	−0.162534	−	0.986703i	$-0.551967\pi$
$967$	−7.72859e24	−0.325069	−0.162534	+	0.986703i	$0.551967\pi$
$968$	−6.51595e24	−0.271667
$969$	1.24113e25	0.512937
$970$	2.67310e24	0.109510
$971$	6.48625e24	0.263409	0.131704	−	0.991289i	$-0.457955\pi$
$971$	6.48625e24	0.263409	0.131704	+	0.991289i	$0.457955\pi$
$972$	−1.45808e24	−0.0586974
$973$	−1.44308e25	−0.575880
$974$	2.45493e24	0.0971153
$975$	4.72215e24	0.185183
$976$	−6.41184e23	−0.0249264
$977$	3.48651e25	1.34365	0.671826	−	0.740709i	$-0.265510\pi$
$977$	3.48651e25	1.34365	0.671826	+	0.740709i	$0.265510\pi$
$978$	−3.13572e24	−0.119800
$979$	1.72116e25	0.651880
$980$	1.59481e25	0.598807
$981$	−1.40084e25	−0.521438
$982$	−2.20208e24	−0.0812616
$983$	3.69470e25	1.35168	0.675840	−	0.737048i	$-0.263781\pi$
$983$	3.69470e25	1.35168	0.675840	+	0.737048i	$0.263781\pi$
$984$	1.41412e25	0.512893
$985$	−6.05770e24	−0.217821
$986$	1.48293e25	0.528647
$987$	1.10748e25	0.391418
$988$	2.40477e25	0.842636
$989$	−5.85146e25	−2.03280
$990$	−9.04125e23	−0.0311408
$991$	4.08576e25	1.39523	0.697616	−	0.716472i	$-0.254244\pi$
$991$	4.08576e25	1.39523	0.697616	+	0.716472i	$0.254244\pi$
$992$	−1.67728e25	−0.567881
$993$	1.05263e25	0.353353
$994$	6.33226e24	0.210753
$995$	6.12378e24	0.202080
$996$	−2.66244e25	−0.871114
$997$	−4.40879e25	−1.43024	−0.715122	−	0.699000i	$-0.753629\pi$
$997$	−4.40879e25	−1.43024	−0.715122	+	0.699000i	$0.753629\pi$
$998$	1.57691e25	0.507222
$999$	9.00216e24	0.287104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.18.a.c.1.2	✓	3
3.2	odd	2		45.18.a.d.1.2		3
5.2	odd	4		75.18.b.e.49.3		6
5.3	odd	4		75.18.b.e.49.4		6
5.4	even	2		75.18.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.18.a.c.1.2	✓	3	1.1	even	1	trivial
45.18.a.d.1.2		3	3.2	odd	2
75.18.a.d.1.2		3	5.4	even	2
75.18.b.e.49.3		6	5.2	odd	4
75.18.b.e.49.4		6	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:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q-105.550 q^{2} +6561.00 q^{3} -119931. q^{4} -390625. q^{5} -692515. q^{6} -2.39385e7 q^{7} +2.64934e7 q^{8} +4.30467e7 q^{9} +4.12305e7 q^{10} -5.09412e8 q^{11} -7.86868e8 q^{12} +4.71682e9 q^{13} +2.52671e9 q^{14} -2.56289e9 q^{15} +1.29232e10 q^{16} -4.44993e10 q^{17} -4.54359e9 q^{18} -4.25101e10 q^{19} +4.68481e10 q^{20} -1.57060e11 q^{21} +5.37686e10 q^{22} +4.70013e11 q^{23} +1.73823e11 q^{24} +1.52588e11 q^{25} -4.97862e11 q^{26} +2.82430e11 q^{27} +2.87097e12 q^{28} +3.15724e12 q^{29} +2.70514e11 q^{30} +3.46790e12 q^{31} -4.83660e12 q^{32} -3.34226e12 q^{33} +4.69691e12 q^{34} +9.35098e12 q^{35} -5.16264e12 q^{36} +3.18740e13 q^{37} +4.48695e12 q^{38} +3.09471e13 q^{39} -1.03490e13 q^{40} +8.13537e13 q^{41} +1.65778e13 q^{42} -1.24496e14 q^{43} +6.10944e13 q^{44} -1.68151e13 q^{45} -4.96099e13 q^{46} -7.05130e13 q^{47} +8.47893e13 q^{48} +3.40421e14 q^{49} -1.61057e13 q^{50} -2.91960e14 q^{51} -5.65694e14 q^{52} +2.51778e14 q^{53} -2.98105e13 q^{54} +1.98989e14 q^{55} -6.34213e14 q^{56} -2.78909e14 q^{57} -3.33247e14 q^{58} -6.39615e14 q^{59} +3.07370e14 q^{60} -4.96148e13 q^{61} -3.66037e14 q^{62} -1.03047e15 q^{63} -1.18337e15 q^{64} -1.84251e15 q^{65} +3.52776e14 q^{66} -2.75976e15 q^{67} +5.33686e15 q^{68} +3.08375e15 q^{69} -9.86997e14 q^{70} +2.50612e15 q^{71} +1.14046e15 q^{72} +8.85474e14 q^{73} -3.36430e15 q^{74} +1.00113e15 q^{75} +5.09829e15 q^{76} +1.21946e16 q^{77} -3.26647e15 q^{78} -6.85544e13 q^{79} -5.04814e15 q^{80} +1.85302e15 q^{81} -8.58690e15 q^{82} +3.38359e16 q^{83} +1.88364e16 q^{84} +1.73826e16 q^{85} +1.31405e16 q^{86} +2.07146e16 q^{87} -1.34961e16 q^{88} -3.37871e16 q^{89} +1.77484e15 q^{90} -1.12914e17 q^{91} -5.63692e16 q^{92} +2.27529e16 q^{93} +7.44266e15 q^{94} +1.66055e16 q^{95} -3.17329e16 q^{96} +6.48330e16 q^{97} -3.59315e16 q^{98} -2.19285e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 253 q^{2} + 19683 q^{3} - 7087 q^{4} - 1171875 q^{5} - 1659933 q^{6} - 4332484 q^{7} - 16188513 q^{8} + 129140163 q^{9} + 98828125 q^{10} + 943563680 q^{11} - 46497807 q^{12} + 4257013150 q^{13} + 1847483988 q^{14}+ \cdots + 40\!\cdots\!80 q^{99}+O(q^{100}) \) 3 * q - 253 * q^2 + 19683 * q^3 - 7087 * q^4 - 1171875 * q^5 - 1659933 * q^6 - 4332484 * q^7 - 16188513 * q^8 + 129140163 * q^9 + 98828125 * q^10 + 943563680 * q^11 - 46497807 * q^12 + 4257013150 * q^13 + 1847483988 * q^14 - 7688671875 * q^15 - 21943871359 * q^16 + 3063169514 * q^17 - 10890820413 * q^18 - 78122492996 * q^19 + 2768359375 * q^20 - 28425427524 * q^21 + 183716401088 * q^22 + 234308204088 * q^23 - 106212833793 * q^24 + 457763671875 * q^25 + 2665740430886 * q^26 + 847288609443 * q^27 + 3864204264572 * q^28 + 5775268588078 * q^29 + 648411328125 * q^30 + 5565463149104 * q^31 + 4307021228191 * q^32 + 6190721304480 * q^33 + 21993554360306 * q^34 + 1692376562500 * q^35 - 305072111727 * q^36 + 31751809399326 * q^37 + 29204227700564 * q^38 + 27930263277150 * q^39 + 6323637890625 * q^40 + 167461457288254 * q^41 + 12121342445268 * q^42 + 150679282040884 * q^43 + 108118677568192 * q^44 - 50445376171875 * q^45 - 194531605879776 * q^46 - 72221896199032 * q^47 - 143973739986399 * q^48 + 68970332513947 * q^49 - 38604736328125 * q^50 + 20097455181354 * q^51 - 1053111710992926 * q^52 + 76290818594558 * q^53 - 71454672729693 * q^54 - 368579562500000 * q^55 - 1101493182837180 * q^56 - 512561676546756 * q^57 - 962781990480722 * q^58 + 465601947196256 * q^59 + 18163205859375 * q^60 - 2317809676510478 * q^61 - 4124018088183048 * q^62 - 186499229984964 * q^63 - 663491579542719 * q^64 - 1662895761718750 * q^65 + 1205363307538368 * q^66 - 6392459657973196 * q^67 + 4953005408361574 * q^68 + 1537296127021368 * q^69 - 721673432812500 * q^70 + 6465608483990656 * q^71 - 696862402515873 * q^72 + 5113761577485238 * q^73 + 10473343628804518 * q^74 + 3003387451171875 * q^75 - 168461495772804 * q^76 + 26936973780565632 * q^77 + 17489922967043046 * q^78 + 8740508940658880 * q^79 + 8571824749609375 * q^80 + 5559060566555523 * q^81 + 13452036217723822 * q^82 + 38179195227158436 * q^83 + 25353044179856892 * q^84 - 1196550591406250 * q^85 - 14457556252388620 * q^86 + 37891537206379758 * q^87 - 59624030208270528 * q^88 - 17217755358726426 * q^89 + 4254226723828125 * q^90 - 110835261613033256 * q^91 - 45737184508628544 * q^92 + 36515003721271344 * q^93 - 200721746528137120 * q^94 + 30516598826562500 * q^95 + 28258366278161151 * q^96 - 94917192725726586 * q^97 - 896231490630245 * q^98 + 40617322478693280 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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