LMFDB - Embedded newform 29.18.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$53.1344053299$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 1610997 x^{16} - 28978880 x^{15} + 1054878119348 x^{14} + 33471007935200 x^{13} + \cdots - 13\!\cdots\!24 $ x^18 - 1610997x^16 - 28978880x^15 + 1054878119348x^14 + 33471007935200x^13 - 361118629330503872x^12 - 14867597249727884800x^11 + 69075461759211999549440x^10 + 3136429534292709271797760x^9 - 7293684107327839501793427456x^8 - 310705174164268019482139033600x^7 + 392089226833876108917621043232768x^6 + 11987811702756552456984769970831360x^5 - 8875073388959894229615422940880306176x^4 - 110123126416280653106554268008725872640x^3 + 38261887665727248243207924189998746697728x^2 - 570869901591701973911550639846099485982720x - 1366002559879573583573099965753694433050624
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{14}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-87.1238$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-87.1238 q^{2} +11891.8 q^{3} -123481. q^{4} -509857. q^{5} -1.03606e6 q^{6} -8.46695e6 q^{7} +2.21777e7 q^{8} +1.22759e7 q^{9} +O(q^{10})$	\(q-87.1238 q^{2} +11891.8 q^{3} -123481. q^{4} -509857. q^{5} -1.03606e6 q^{6} -8.46695e6 q^{7} +2.21777e7 q^{8} +1.22759e7 q^{9} +4.44206e7 q^{10} +1.21078e9 q^{11} -1.46842e9 q^{12} +3.67163e9 q^{13} +7.37673e8 q^{14} -6.06314e9 q^{15} +1.42528e10 q^{16} +1.11921e9 q^{17} -1.06952e9 q^{18} -4.26592e10 q^{19} +6.29578e10 q^{20} -1.00688e11 q^{21} -1.05488e11 q^{22} -2.90166e11 q^{23} +2.63733e11 q^{24} -5.02986e11 q^{25} -3.19886e11 q^{26} -1.38973e12 q^{27} +1.04551e12 q^{28} -5.00246e11 q^{29} +5.28243e11 q^{30} -2.87066e12 q^{31} -4.14862e12 q^{32} +1.43985e13 q^{33} -9.75100e10 q^{34} +4.31693e12 q^{35} -1.51585e12 q^{36} +1.86092e13 q^{37} +3.71663e12 q^{38} +4.36625e13 q^{39} -1.13074e13 q^{40} +3.22243e13 q^{41} +8.77229e12 q^{42} -1.08005e14 q^{43} -1.49509e14 q^{44} -6.25896e12 q^{45} +2.52804e13 q^{46} -1.67051e13 q^{47} +1.69492e14 q^{48} -1.60941e14 q^{49} +4.38220e13 q^{50} +1.33095e13 q^{51} -4.53379e14 q^{52} -8.32006e14 q^{53} +1.21079e14 q^{54} -6.17326e14 q^{55} -1.87777e14 q^{56} -5.07296e14 q^{57} +4.35833e13 q^{58} -1.16503e15 q^{59} +7.48685e14 q^{60} +2.79761e15 q^{61} +2.50103e14 q^{62} -1.03940e14 q^{63} -1.50669e15 q^{64} -1.87201e15 q^{65} -1.25445e15 q^{66} +9.97995e14 q^{67} -1.38202e14 q^{68} -3.45061e15 q^{69} -3.76107e14 q^{70} -6.23742e15 q^{71} +2.72251e14 q^{72} +2.78645e15 q^{73} -1.62131e15 q^{74} -5.98143e15 q^{75} +5.26761e15 q^{76} -1.02516e16 q^{77} -3.80404e15 q^{78} -1.59177e16 q^{79} -7.26687e15 q^{80} -1.81118e16 q^{81} -2.80750e15 q^{82} -2.95290e15 q^{83} +1.24331e16 q^{84} -5.70638e14 q^{85} +9.40982e15 q^{86} -5.94886e15 q^{87} +2.68523e16 q^{88} +3.77141e16 q^{89} +5.45304e14 q^{90} -3.10875e16 q^{91} +3.58302e16 q^{92} -3.41375e16 q^{93} +1.45541e15 q^{94} +2.17501e16 q^{95} -4.93348e16 q^{96} -1.78066e16 q^{97} +1.40218e16 q^{98} +1.48635e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) $ 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−87.1238	−0.240648	−0.120324	−	0.992735i	$-0.538393\pi$
$2$	−87.1238	−0.240648	−0.120324	+	0.992735i	$0.538393\pi$
$3$	11891.8	1.04645	0.523225	−	0.852194i	$-0.324729\pi$
$3$	11891.8	1.04645	0.523225	+	0.852194i	$0.324729\pi$
$4$	−123481.	−0.942089
$5$	−509857.	−0.583718	−0.291859	−	0.956461i	$-0.594274\pi$
$5$	−509857.	−0.583718	−0.291859	+	0.956461i	$0.594274\pi$
$6$	−1.03606e6	−0.251826
$7$	−8.46695e6	−0.555129	−0.277564	−	0.960707i	$-0.589527\pi$
$7$	−8.46695e6	−0.555129	−0.277564	+	0.960707i	$0.589527\pi$
$8$	2.21777e7	0.467359
$9$	1.22759e7	0.0950589
$10$	4.44206e7	0.140470
$11$	1.21078e9	1.70305	0.851527	−	0.524310i	$-0.175677\pi$
$11$	1.21078e9	1.70305	0.851527	+	0.524310i	$0.175677\pi$
$12$	−1.46842e9	−0.985849
$13$	3.67163e9	1.24836	0.624181	−	0.781279i	$-0.285433\pi$
$13$	3.67163e9	1.24836	0.624181	+	0.781279i	$0.285433\pi$
$14$	7.37673e8	0.133590
$15$	−6.06314e9	−0.610832
$16$	1.42528e10	0.829620
$17$	1.11921e9	0.0389132	0.0194566	−	0.999811i	$-0.493806\pi$
$17$	1.11921e9	0.0389132	0.0194566	+	0.999811i	$0.493806\pi$
$18$	−1.06952e9	−0.0228757
$19$	−4.26592e10	−0.576244	−0.288122	−	0.957594i	$-0.593031\pi$
$19$	−4.26592e10	−0.576244	−0.288122	+	0.957594i	$0.593031\pi$
$20$	6.29578e10	0.549914
$21$	−1.00688e11	−0.580915
$22$	−1.05488e11	−0.409836
$23$	−2.90166e11	−0.772610	−0.386305	−	0.922371i	$-0.626249\pi$
$23$	−2.90166e11	−0.772610	−0.386305	+	0.922371i	$0.626249\pi$
$24$	2.63733e11	0.489068
$25$	−5.02986e11	−0.659273
$26$	−3.19886e11	−0.300416
$27$	−1.38973e12	−0.946976
$28$	1.04551e12	0.522981
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	5.28243e11	0.146995
$31$	−2.87066e12	−0.604516	−0.302258	−	0.953226i	$-0.597740\pi$
$31$	−2.87066e12	−0.604516	−0.302258	+	0.953226i	$0.597740\pi$
$32$	−4.14862e12	−0.667005
$33$	1.43985e13	1.78216
$34$	−9.75100e10	−0.00936436
$35$	4.31693e12	0.324039
$36$	−1.51585e12	−0.0895539
$37$	1.86092e13	0.870991	0.435495	−	0.900191i	$-0.356573\pi$
$37$	1.86092e13	0.870991	0.435495	+	0.900191i	$0.356573\pi$
$38$	3.71663e12	0.138672
$39$	4.36625e13	1.30635
$40$	−1.13074e13	−0.272806
$41$	3.22243e13	0.630262	0.315131	−	0.949048i	$-0.397952\pi$
$41$	3.22243e13	0.630262	0.315131	+	0.949048i	$0.397952\pi$
$42$	8.77229e12	0.139796
$43$	−1.08005e14	−1.40917	−0.704584	−	0.709620i	$-0.748866\pi$
$43$	−1.08005e14	−1.40917	−0.704584	+	0.709620i	$0.748866\pi$
$44$	−1.49509e14	−1.60443
$45$	−6.25896e12	−0.0554876
$46$	2.52804e13	0.185927
$47$	−1.67051e13	−0.102333	−0.0511666	−	0.998690i	$-0.516294\pi$
$47$	−1.67051e13	−0.102333	−0.0511666	+	0.998690i	$0.516294\pi$
$48$	1.69492e14	0.868156
$49$	−1.60941e14	−0.691832
$50$	4.38220e13	0.158653
$51$	1.33095e13	0.0407207
$52$	−4.53379e14	−1.17607
$53$	−8.32006e14	−1.83561	−0.917807	−	0.397027i	$-0.870042\pi$
$53$	−8.32006e14	−1.83561	−0.917807	+	0.397027i	$0.870042\pi$
$54$	1.21079e14	0.227888
$55$	−6.17326e14	−0.994104
$56$	−1.87777e14	−0.259445
$57$	−5.07296e14	−0.603011
$58$	4.35833e13	0.0446871
$59$	−1.16503e15	−1.03299	−0.516494	−	0.856291i	$-0.672763\pi$
$59$	−1.16503e15	−1.03299	−0.516494	+	0.856291i	$0.672763\pi$
$60$	7.48685e14	0.575458
$61$	2.79761e15	1.86846	0.934230	−	0.356672i	$-0.116089\pi$
$61$	2.79761e15	1.86846	0.934230	+	0.356672i	$0.116089\pi$
$62$	2.50103e14	0.145475
$63$	−1.03940e14	−0.0527699
$64$	−1.50669e15	−0.669107
$65$	−1.87201e15	−0.728692
$66$	−1.25445e15	−0.428873
$67$	9.97995e14	0.300257	0.150128	−	0.988667i	$-0.452031\pi$
$67$	9.97995e14	0.300257	0.150128	+	0.988667i	$0.452031\pi$
$68$	−1.38202e14	−0.0366597
$69$	−3.45061e15	−0.808498
$70$	−3.76107e14	−0.0779792
$71$	−6.23742e15	−1.14633	−0.573164	−	0.819440i	$-0.694284\pi$
$71$	−6.23742e15	−1.14633	−0.573164	+	0.819440i	$0.694284\pi$
$72$	2.72251e14	0.0444266
$73$	2.78645e15	0.404396	0.202198	−	0.979345i	$-0.435192\pi$
$73$	2.78645e15	0.404396	0.202198	+	0.979345i	$0.435192\pi$
$74$	−1.62131e15	−0.209602
$75$	−5.98143e15	−0.689897
$76$	5.26761e15	0.542873
$77$	−1.02516e16	−0.945415
$78$	−3.80404e15	−0.314370
$79$	−1.59177e16	−1.18045	−0.590227	−	0.807238i	$-0.700962\pi$
$79$	−1.59177e16	−1.18045	−0.590227	+	0.807238i	$0.700962\pi$
$80$	−7.26687e15	−0.484264
$81$	−1.81118e16	−1.08602
$82$	−2.80750e15	−0.151671
$83$	−2.95290e15	−0.143908	−0.0719541	−	0.997408i	$-0.522924\pi$
$83$	−2.95290e15	−0.143908	−0.0719541	+	0.997408i	$0.522924\pi$
$84$	1.24331e16	0.547273
$85$	−5.70638e14	−0.0227143
$86$	9.40982e15	0.339113
$87$	−5.94886e15	−0.194321
$88$	2.68523e16	0.795938
$89$	3.77141e16	1.01552	0.507760	−	0.861499i	$-0.330474\pi$
$89$	3.77141e16	1.01552	0.507760	+	0.861499i	$0.330474\pi$
$90$	5.45304e14	0.0133530
$91$	−3.10875e16	−0.693002
$92$	3.58302e16	0.727867
$93$	−3.41375e16	−0.632596
$94$	1.45541e15	0.0246262
$95$	2.17501e16	0.336364
$96$	−4.93348e16	−0.697988
$97$	−1.78066e16	−0.230686	−0.115343	−	0.993326i	$-0.536797\pi$
$97$	−1.78066e16	−0.230686	−0.115343	+	0.993326i	$0.536797\pi$
$98$	1.40218e16	0.166488
$99$	1.48635e16	0.161891
$100$	6.21094e16	0.621094
$101$	−4.42857e16	−0.406941	−0.203471	−	0.979081i	$-0.565222\pi$
$101$	−4.42857e16	−0.406941	−0.203471	+	0.979081i	$0.565222\pi$
$102$	−1.15957e15	−0.00979934
$103$	1.57647e17	1.22622	0.613110	−	0.789997i	$-0.289918\pi$
$103$	1.57647e17	1.22622	0.613110	+	0.789997i	$0.289918\pi$
$104$	8.14282e16	0.583434
$105$	5.13363e16	0.339091
$106$	7.24875e16	0.441736
$107$	−6.80736e16	−0.383016	−0.191508	−	0.981491i	$-0.561338\pi$
$107$	−6.80736e16	−0.383016	−0.191508	+	0.981491i	$0.561338\pi$
$108$	1.71606e17	0.892136
$109$	−3.44265e17	−1.65488	−0.827442	−	0.561551i	$-0.810205\pi$
$109$	−3.44265e17	−1.65488	−0.827442	+	0.561551i	$0.810205\pi$
$110$	5.37838e16	0.239229
$111$	2.21298e17	0.911449
$112$	−1.20677e17	−0.460546
$113$	−4.35422e16	−0.154079	−0.0770395	−	0.997028i	$-0.524547\pi$
$113$	−4.35422e16	−0.154079	−0.0770395	+	0.997028i	$0.524547\pi$
$114$	4.41976e16	0.145113
$115$	1.47943e17	0.450986
$116$	6.17712e16	0.174941
$117$	4.50727e16	0.118668
$118$	1.01502e17	0.248586
$119$	−9.47632e15	−0.0216018
$120$	−1.34466e17	−0.285478
$121$	9.60549e17	1.90040
$122$	−2.43738e17	−0.449640
$123$	3.83207e17	0.659538
$124$	3.54473e17	0.569507
$125$	6.45440e17	0.968548
$126$	9.05561e15	0.0126990
$127$	−2.81169e17	−0.368668	−0.184334	−	0.982864i	$-0.559013\pi$
$127$	−2.81169e17	−0.368668	−0.184334	+	0.982864i	$0.559013\pi$
$128$	6.75037e17	0.828024
$129$	−1.28438e18	−1.47463
$130$	1.63096e17	0.175358
$131$	−5.62542e17	−0.566695	−0.283347	−	0.959017i	$-0.591445\pi$
$131$	−5.62542e17	−0.566695	−0.283347	+	0.959017i	$0.591445\pi$
$132$	−1.77794e18	−1.67896
$133$	3.61193e17	0.319890
$134$	−8.69491e16	−0.0722560
$135$	7.08564e17	0.552767
$136$	2.48215e16	0.0181864
$137$	−7.14175e17	−0.491677	−0.245838	−	0.969311i	$-0.579063\pi$
$137$	−7.14175e17	−0.491677	−0.245838	+	0.969311i	$0.579063\pi$
$138$	3.00630e17	0.194563
$139$	−7.21945e17	−0.439419	−0.219709	−	0.975565i	$-0.570511\pi$
$139$	−7.21945e17	−0.439419	−0.219709	+	0.975565i	$0.570511\pi$
$140$	−5.33061e17	−0.305273
$141$	−1.98654e17	−0.107087
$142$	5.43428e17	0.275861
$143$	4.44555e18	2.12603
$144$	1.74966e17	0.0788628
$145$	2.55054e17	0.108394
$146$	−2.42766e17	−0.0973169
$147$	−1.91389e18	−0.723968
$148$	−2.29789e18	−0.820551
$149$	−5.41923e18	−1.82749	−0.913743	−	0.406293i	$-0.866821\pi$
$149$	−5.41923e18	−1.82749	−0.913743	+	0.406293i	$0.866821\pi$
$150$	5.21125e17	0.166022
$151$	−4.70994e18	−1.41811	−0.709057	−	0.705151i	$-0.750879\pi$
$151$	−4.70994e18	−1.41811	−0.709057	+	0.705151i	$0.750879\pi$
$152$	−9.46080e17	−0.269313
$153$	1.37394e16	0.00369904
$154$	8.93162e17	0.227512
$155$	1.46363e18	0.352867
$156$	−5.39151e18	−1.23070
$157$	7.04524e18	1.52317	0.761585	−	0.648065i	$-0.224421\pi$
$157$	7.04524e18	1.52317	0.761585	+	0.648065i	$0.224421\pi$
$158$	1.38681e18	0.284073
$159$	−9.89409e18	−1.92088
$160$	2.11520e18	0.389343
$161$	2.45682e18	0.428898
$162$	1.57797e18	0.261349
$163$	−6.16319e18	−0.968748	−0.484374	−	0.874861i	$-0.660953\pi$
$163$	−6.16319e18	−0.968748	−0.484374	+	0.874861i	$0.660953\pi$
$164$	−3.97911e18	−0.593762
$165$	−7.34115e18	−1.04028
$166$	2.57268e17	0.0346312
$167$	−9.51858e18	−1.21754	−0.608769	−	0.793348i	$-0.708336\pi$
$167$	−9.51858e18	−1.21754	−0.608769	+	0.793348i	$0.708336\pi$
$168$	−2.23302e18	−0.271496
$169$	4.83048e18	0.558410
$170$	4.97161e16	0.00546615
$171$	−5.23680e17	−0.0547772
$172$	1.33366e19	1.32756
$173$	1.19337e19	1.13079	0.565396	−	0.824819i	$-0.308723\pi$
$173$	1.19337e19	1.13079	0.565396	+	0.824819i	$0.308723\pi$
$174$	5.18287e17	0.0467629
$175$	4.25876e18	0.365982
$176$	1.72570e19	1.41289
$177$	−1.38544e19	−1.08097
$178$	−3.28579e18	−0.244382
$179$	8.58468e18	0.608798	0.304399	−	0.952545i	$-0.401544\pi$
$179$	8.58468e18	0.608798	0.304399	+	0.952545i	$0.401544\pi$
$180$	7.72866e17	0.0522742
$181$	2.16686e19	1.39818	0.699090	−	0.715033i	$-0.253588\pi$
$181$	2.16686e19	1.39818	0.699090	+	0.715033i	$0.253588\pi$
$182$	2.70846e18	0.166769
$183$	3.32688e19	1.95525
$184$	−6.43521e18	−0.361086
$185$	−9.48804e18	−0.508413
$186$	2.97418e18	0.152233
$187$	1.35512e18	0.0662713
$188$	2.06276e18	0.0964069
$189$	1.17668e19	0.525694
$190$	−1.89495e18	−0.0809452
$191$	−3.75300e19	−1.53319	−0.766594	−	0.642132i	$-0.778050\pi$
$191$	−3.75300e19	−1.53319	−0.766594	+	0.642132i	$0.778050\pi$
$192$	−1.79174e19	−0.700187
$193$	4.82432e18	0.180384	0.0901922	−	0.995924i	$-0.471252\pi$
$193$	4.82432e18	0.180384	0.0901922	+	0.995924i	$0.471252\pi$
$194$	1.55138e18	0.0555141
$195$	−2.22616e19	−0.762540
$196$	1.98733e19	0.651767
$197$	−2.01589e19	−0.633147	−0.316573	−	0.948568i	$-0.602532\pi$
$197$	−2.01589e19	−0.633147	−0.316573	+	0.948568i	$0.602532\pi$
$198$	−1.29496e18	−0.0389586
$199$	4.43335e19	1.27785	0.638927	−	0.769268i	$-0.279379\pi$
$199$	4.43335e19	1.27785	0.638927	+	0.769268i	$0.279379\pi$
$200$	−1.11550e19	−0.308117
$201$	1.18680e19	0.314204
$202$	3.85834e18	0.0979295
$203$	4.23556e18	0.103085
$204$	−1.64348e18	−0.0383625
$205$	−1.64298e19	−0.367895
$206$	−1.37348e19	−0.295087
$207$	−3.56206e18	−0.0734435
$208$	5.23309e19	1.03567
$209$	−5.16510e19	−0.981376
$210$	−4.47261e18	−0.0816013
$211$	2.60142e19	0.455838	0.227919	−	0.973680i	$-0.426808\pi$
$211$	2.60142e19	0.455838	0.227919	+	0.973680i	$0.426808\pi$
$212$	1.02737e20	1.72931
$213$	−7.41745e19	−1.19958
$214$	5.93083e18	0.0921719
$215$	5.50672e19	0.822557
$216$	−3.08210e19	−0.442578
$217$	2.43058e19	0.335584
$218$	2.99937e19	0.398244
$219$	3.31360e19	0.423180
$220$	7.62283e19	0.936534
$221$	4.10934e18	0.0485777
$222$	−1.92803e19	−0.219338
$223$	−8.69820e19	−0.952441	−0.476221	−	0.879326i	$-0.657994\pi$
$223$	−8.69820e19	−0.952441	−0.476221	+	0.879326i	$0.657994\pi$
$224$	3.51262e19	0.370274
$225$	−6.17461e18	−0.0626698
$226$	3.79356e18	0.0370787
$227$	6.09365e19	0.573664	0.286832	−	0.957981i	$-0.407398\pi$
$227$	6.09365e19	0.573664	0.286832	+	0.957981i	$0.407398\pi$
$228$	6.26417e19	0.568090
$229$	−9.37138e19	−0.818846	−0.409423	−	0.912345i	$-0.634270\pi$
$229$	−9.37138e19	−0.818846	−0.409423	+	0.912345i	$0.634270\pi$
$230$	−1.28894e19	−0.108529
$231$	−1.21911e20	−0.989330
$232$	−1.10943e19	−0.0867864
$233$	−1.28515e20	−0.969235	−0.484618	−	0.874726i	$-0.661041\pi$
$233$	−1.28515e20	−0.969235	−0.484618	+	0.874726i	$0.661041\pi$
$234$	−3.92690e18	−0.0285572
$235$	8.51719e18	0.0597337
$236$	1.43860e20	0.973167
$237$	−1.89290e20	−1.23529
$238$	8.25612e17	0.00519843
$239$	1.72588e20	1.04864	0.524322	−	0.851520i	$-0.324319\pi$
$239$	1.72588e20	1.04864	0.524322	+	0.851520i	$0.324319\pi$
$240$	−8.64165e19	−0.506758
$241$	−2.53190e20	−1.43318	−0.716592	−	0.697493i	$-0.754299\pi$
$241$	−2.53190e20	−1.43318	−0.716592	+	0.697493i	$0.754299\pi$
$242$	−8.36867e19	−0.457326
$243$	−3.59126e19	−0.189493
$244$	−3.45453e20	−1.76025
$245$	8.20570e19	0.403835
$246$	−3.33864e19	−0.158716
$247$	−1.56629e20	−0.719362
$248$	−6.36645e19	−0.282526
$249$	−3.51155e19	−0.150593
$250$	−5.62332e19	−0.233079
$251$	3.40975e20	1.36614	0.683070	−	0.730353i	$-0.260644\pi$
$251$	3.40975e20	1.36614	0.683070	+	0.730353i	$0.260644\pi$
$252$	1.28346e19	0.0497140
$253$	−3.51328e20	−1.31580
$254$	2.44965e19	0.0887191
$255$	−6.78594e18	−0.0237694
$256$	1.38674e20	0.469845
$257$	−2.70336e20	−0.886078	−0.443039	−	0.896502i	$-0.646100\pi$
$257$	−2.70336e20	−0.886078	−0.443039	+	0.896502i	$0.646100\pi$
$258$	1.11900e20	0.354865
$259$	−1.57563e20	−0.483512
$260$	2.31158e20	0.686492
$261$	−6.14099e18	−0.0176520
$262$	4.90108e19	0.136374
$263$	−7.41502e19	−0.199751	−0.0998754	−	0.995000i	$-0.531844\pi$
$263$	−7.41502e19	−0.199751	−0.0998754	+	0.995000i	$0.531844\pi$
$264$	3.19324e20	0.832910
$265$	4.24204e20	1.07148
$266$	−3.14685e19	−0.0769807
$267$	4.48490e20	1.06269
$268$	−1.23234e20	−0.282868
$269$	−3.11096e20	−0.691830	−0.345915	−	0.938266i	$-0.612431\pi$
$269$	−3.11096e20	−0.691830	−0.345915	+	0.938266i	$0.612431\pi$
$270$	−6.17328e19	−0.133022
$271$	5.18576e19	0.108286	0.0541431	−	0.998533i	$-0.482757\pi$
$271$	5.18576e19	0.108286	0.0541431	+	0.998533i	$0.482757\pi$
$272$	1.59519e19	0.0322831
$273$	−3.69688e20	−0.725193
$274$	6.22216e19	0.118321
$275$	−6.09007e20	−1.12278
$276$	4.26087e20	0.761677
$277$	1.00188e21	1.73676	0.868378	−	0.495903i	$-0.165163\pi$
$277$	1.00188e21	1.73676	0.868378	+	0.495903i	$0.165163\pi$
$278$	6.28986e19	0.105745
$279$	−3.52400e19	−0.0574646
$280$	9.57394e19	0.151442
$281$	9.94108e20	1.52556	0.762781	−	0.646657i	$-0.223833\pi$
$281$	9.94108e20	1.52556	0.762781	+	0.646657i	$0.223833\pi$
$282$	1.73075e19	0.0257701
$283$	2.79721e20	0.404148	0.202074	−	0.979370i	$-0.435232\pi$
$283$	2.79721e20	0.404148	0.202074	+	0.979370i	$0.435232\pi$
$284$	7.70206e20	1.07994
$285$	2.58648e20	0.351988
$286$	−3.87313e20	−0.511624
$287$	−2.72842e20	−0.349876
$288$	−5.09282e19	−0.0634048
$289$	−8.25988e20	−0.998486
$290$	−2.22213e19	−0.0260847
$291$	−2.11754e20	−0.241402
$292$	−3.44075e20	−0.380977
$293$	4.68917e20	0.504337	0.252169	−	0.967683i	$-0.418856\pi$
$293$	4.68917e20	0.504337	0.252169	+	0.967683i	$0.418856\pi$
$294$	1.66745e20	0.174221
$295$	5.93999e20	0.602974
$296$	4.12709e20	0.407066
$297$	−1.68266e21	−1.61275
$298$	4.72143e20	0.439780
$299$	−1.06538e21	−0.964498
$300$	7.38596e20	0.649944
$301$	9.14475e20	0.782270
$302$	4.10348e20	0.341266
$303$	−5.26639e20	−0.425844
$304$	−6.08011e20	−0.478064
$305$	−1.42638e21	−1.09065
$306$	−1.19702e18	−0.000890166 0
$307$	4.75074e19	0.0343625	0.0171813	−	0.999852i	$-0.494531\pi$
$307$	4.75074e19	0.0343625	0.0171813	+	0.999852i	$0.494531\pi$
$308$	1.26589e21	0.890665
$309$	1.87471e21	1.28318
$310$	−1.27517e20	−0.0849165
$311$	2.09781e21	1.35926	0.679632	−	0.733553i	$-0.262140\pi$
$311$	2.09781e21	1.35926	0.679632	+	0.733553i	$0.262140\pi$
$312$	9.68332e20	0.610535
$313$	−1.45587e21	−0.893299	−0.446649	−	0.894709i	$-0.647383\pi$
$313$	−1.45587e21	−0.893299	−0.446649	+	0.894709i	$0.647383\pi$
$314$	−6.13807e20	−0.366547
$315$	5.29943e19	0.0308028
$316$	1.96553e21	1.11209
$317$	−1.41923e21	−0.781714	−0.390857	−	0.920451i	$-0.627821\pi$
$317$	−1.41923e21	−0.781714	−0.390857	+	0.920451i	$0.627821\pi$
$318$	8.62010e20	0.462255
$319$	−6.05690e20	−0.316249
$320$	7.68198e20	0.390570
$321$	−8.09521e20	−0.400807
$322$	−2.14048e20	−0.103213
$323$	−4.77446e19	−0.0224235
$324$	2.23647e21	1.02313
$325$	−1.84678e21	−0.823012
$326$	5.36960e20	0.233127
$327$	−4.09395e21	−1.73176
$328$	7.14660e20	0.294559
$329$	1.41441e20	0.0568081
$330$	6.39588e20	0.250341
$331$	−2.25352e21	−0.859652	−0.429826	−	0.902912i	$-0.641425\pi$
$331$	−2.25352e21	−0.859652	−0.429826	+	0.902912i	$0.641425\pi$
$332$	3.64629e20	0.135574
$333$	2.28445e20	0.0827954
$334$	8.29295e20	0.292997
$335$	−5.08834e20	−0.175265
$336$	−1.43508e21	−0.481939
$337$	−4.48100e21	−1.46731	−0.733653	−	0.679525i	$-0.762186\pi$
$337$	−4.48100e21	−1.46731	−0.733653	+	0.679525i	$0.762186\pi$
$338$	−4.20849e20	−0.134380
$339$	−5.17797e20	−0.161236
$340$	7.04632e19	0.0213989
$341$	−3.47575e21	−1.02952
$342$	4.56250e19	0.0131820
$343$	3.33235e21	0.939185
$344$	−2.39530e21	−0.658588
$345$	1.75932e21	0.471935
$346$	−1.03971e21	−0.272123
$347$	5.55926e21	1.41977	0.709883	−	0.704320i	$-0.248748\pi$
$347$	5.55926e21	1.41977	0.709883	+	0.704320i	$0.248748\pi$
$348$	7.34573e20	0.183068
$349$	−1.37198e21	−0.333681	−0.166840	−	0.985984i	$-0.553356\pi$
$349$	−1.37198e21	−0.333681	−0.166840	+	0.985984i	$0.553356\pi$
$350$	−3.71039e20	−0.0880726
$351$	−5.10259e21	−1.18217
$352$	−5.02308e21	−1.13595
$353$	−3.29098e21	−0.726508	−0.363254	−	0.931690i	$-0.618334\pi$
$353$	−3.29098e21	−0.726508	−0.363254	+	0.931690i	$0.618334\pi$
$354$	1.20705e21	0.260133
$355$	3.18019e21	0.669133
$356$	−4.65699e21	−0.956709
$357$	−1.12691e20	−0.0226052
$358$	−7.47930e20	−0.146506
$359$	−6.67590e21	−1.27705	−0.638524	−	0.769602i	$-0.720455\pi$
$359$	−6.67590e21	−1.27705	−0.638524	+	0.769602i	$0.720455\pi$
$360$	−1.38809e20	−0.0259326
$361$	−3.66058e21	−0.667942
$362$	−1.88785e21	−0.336469
$363$	1.14227e22	1.98867
$364$	3.83874e21	0.652870
$365$	−1.42069e21	−0.236053
$366$	−2.89850e21	−0.470526
$367$	−1.26512e21	−0.200665	−0.100332	−	0.994954i	$-0.531991\pi$
$367$	−1.26512e21	−0.200665	−0.100332	+	0.994954i	$0.531991\pi$
$368$	−4.13567e21	−0.640973
$369$	3.95583e20	0.0599120
$370$	8.26634e20	0.122348
$371$	7.04455e21	1.01900
$372$	4.21534e21	0.595961
$373$	7.65052e21	1.05722	0.528611	−	0.848864i	$-0.322713\pi$
$373$	7.65052e21	1.05722	0.528611	+	0.848864i	$0.322713\pi$
$374$	−1.18063e20	−0.0159480
$375$	7.67548e21	1.01354
$376$	−3.70479e20	−0.0478263
$377$	−1.83672e21	−0.231815
$378$	−1.02517e21	−0.126507
$379$	5.93877e21	0.716578	0.358289	−	0.933611i	$-0.383360\pi$
$379$	5.93877e21	0.716578	0.358289	+	0.933611i	$0.383360\pi$
$380$	−2.68573e21	−0.316885
$381$	−3.34362e21	−0.385793
$382$	3.26976e21	0.368958
$383$	−7.37496e21	−0.813898	−0.406949	−	0.913451i	$-0.633407\pi$
$383$	−7.37496e21	−0.813898	−0.406949	+	0.913451i	$0.633407\pi$
$384$	8.02744e21	0.866486
$385$	5.22687e21	0.551856
$386$	−4.20313e20	−0.0434091
$387$	−1.32586e21	−0.133954
$388$	2.19879e21	0.217327
$389$	1.44343e22	1.39581	0.697904	−	0.716192i	$-0.254116\pi$
$389$	1.44343e22	1.39581	0.697904	+	0.716192i	$0.254116\pi$
$390$	1.93952e21	0.183503
$391$	−3.24758e20	−0.0300647
$392$	−3.56930e21	−0.323334
$393$	−6.68967e21	−0.593018
$394$	1.75632e21	0.152365
$395$	8.11572e21	0.689052
$396$	−1.83536e21	−0.152515
$397$	−6.71950e21	−0.546535	−0.273267	−	0.961938i	$-0.588104\pi$
$397$	−6.71950e21	−0.546535	−0.273267	+	0.961938i	$0.588104\pi$
$398$	−3.86250e21	−0.307512
$399$	4.29525e21	0.334749
$400$	−7.16893e21	−0.546946
$401$	1.52024e22	1.13549	0.567747	−	0.823203i	$-0.307815\pi$
$401$	1.52024e22	1.13549	0.567747	+	0.823203i	$0.307815\pi$
$402$	−1.03399e21	−0.0756124
$403$	−1.05400e22	−0.754655
$404$	5.46846e21	0.383375
$405$	9.23442e21	0.633931
$406$	−3.69018e20	−0.0248071
$407$	2.25317e22	1.48335
$408$	2.95173e20	0.0190312
$409$	−6.59661e21	−0.416556	−0.208278	−	0.978070i	$-0.566786\pi$
$409$	−6.59661e21	−0.416556	−0.208278	+	0.978070i	$0.566786\pi$
$410$	1.43142e21	0.0885331
$411$	−8.49286e21	−0.514515
$412$	−1.94665e22	−1.15521
$413$	9.86427e21	0.573442
$414$	3.10340e20	0.0176740
$415$	1.50556e21	0.0840018
$416$	−1.52322e22	−0.832664
$417$	−8.58526e21	−0.459830
$418$	4.50003e21	0.236166
$419$	1.94856e22	1.00206	0.501031	−	0.865429i	$-0.332954\pi$
$419$	1.94856e22	1.00206	0.501031	+	0.865429i	$0.332954\pi$
$420$	−6.33908e21	−0.319453
$421$	1.38890e22	0.685920	0.342960	−	0.939350i	$-0.388570\pi$
$421$	1.38890e22	0.685920	0.342960	+	0.939350i	$0.388570\pi$
$422$	−2.26646e21	−0.109696
$423$	−2.05070e20	−0.00972767
$424$	−1.84519e22	−0.857891
$425$	−5.62948e20	−0.0256544
$426$	6.46236e21	0.288675
$427$	−2.36872e22	−1.03724
$428$	8.40583e21	0.360835
$429$	5.28658e22	2.22479
$430$	−4.79766e21	−0.197946
$431$	1.46282e22	0.591745	0.295873	−	0.955227i	$-0.404390\pi$
$431$	1.46282e22	0.591745	0.295873	+	0.955227i	$0.404390\pi$
$432$	−1.98075e22	−0.785630
$433$	−3.91853e22	−1.52397	−0.761985	−	0.647595i	$-0.775775\pi$
$433$	−3.91853e22	−1.52397	−0.761985	+	0.647595i	$0.775775\pi$
$434$	−2.11761e21	−0.0807575
$435$	3.03306e21	0.113429
$436$	4.25104e22	1.55905
$437$	1.23782e22	0.445212
$438$	−2.88693e21	−0.101837
$439$	−4.12726e20	−0.0142795	−0.00713976	−	0.999975i	$-0.502273\pi$
$439$	−4.12726e20	−0.0142795	−0.00713976	+	0.999975i	$0.502273\pi$
$440$	−1.36908e22	−0.464603
$441$	−1.97570e21	−0.0657648
$442$	−3.58021e20	−0.0116901
$443$	1.82450e22	0.584404	0.292202	−	0.956357i	$-0.405612\pi$
$443$	1.82450e22	0.584404	0.292202	+	0.956357i	$0.405612\pi$
$444$	−2.73262e22	−0.858666
$445$	−1.92288e22	−0.592777
$446$	7.57820e21	0.229203
$447$	−6.44446e22	−1.91237
$448$	1.27571e22	0.371440
$449$	−2.01226e22	−0.574897	−0.287449	−	0.957796i	$-0.592807\pi$
$449$	−2.01226e22	−0.574897	−0.287449	+	0.957796i	$0.592807\pi$
$450$	5.37955e20	0.0150813
$451$	3.90167e22	1.07337
$452$	5.37665e21	0.145156
$453$	−5.60099e22	−1.48399
$454$	−5.30902e21	−0.138051
$455$	1.58502e22	0.404518
$456$	−1.12506e22	−0.281823
$457$	−5.37889e22	−1.32253	−0.661264	−	0.750153i	$-0.729980\pi$
$457$	−5.37889e22	−1.32253	−0.661264	+	0.750153i	$0.729980\pi$
$458$	8.16470e21	0.197053
$459$	−1.55540e21	−0.0368498
$460$	−1.82682e22	−0.424869
$461$	6.00087e22	1.37011	0.685056	−	0.728490i	$-0.259778\pi$
$461$	6.00087e22	1.37011	0.685056	+	0.728490i	$0.259778\pi$
$462$	1.06213e22	0.238080
$463$	1.18819e22	0.261486	0.130743	−	0.991416i	$-0.458264\pi$
$463$	1.18819e22	0.261486	0.130743	+	0.991416i	$0.458264\pi$
$464$	−7.12989e21	−0.154057
$465$	1.74052e22	0.369258
$466$	1.11967e22	0.233244
$467$	−5.33892e22	−1.09209	−0.546047	−	0.837755i	$-0.683868\pi$
$467$	−5.33892e22	−1.09209	−0.546047	+	0.837755i	$0.683868\pi$
$468$	−5.56564e21	−0.111796
$469$	−8.44998e21	−0.166681
$470$	−7.42049e20	−0.0143748
$471$	8.37809e22	1.59392
$472$	−2.58377e22	−0.482777
$473$	−1.30771e23	−2.39989
$474$	1.64917e22	0.297269
$475$	2.14569e22	0.379902
$476$	1.17015e21	0.0203508
$477$	−1.02136e22	−0.174491
$478$	−1.50365e22	−0.252354
$479$	2.89523e22	0.477344	0.238672	−	0.971100i	$-0.423288\pi$
$479$	2.89523e22	0.477344	0.238672	+	0.971100i	$0.423288\pi$
$480$	2.51537e22	0.407428
$481$	6.83263e22	1.08731
$482$	2.20589e22	0.344892
$483$	2.92162e22	0.448821
$484$	−1.18610e23	−1.79034
$485$	9.07883e21	0.134656
$486$	3.12884e21	0.0456010
$487$	−2.64061e22	−0.378188	−0.189094	−	0.981959i	$-0.560555\pi$
$487$	−2.64061e22	−0.378188	−0.189094	+	0.981959i	$0.560555\pi$
$488$	6.20444e22	0.873241
$489$	−7.32917e22	−1.01375
$490$	−7.14911e21	−0.0971819
$491$	−1.09311e23	−1.46039	−0.730196	−	0.683238i	$-0.760571\pi$
$491$	−1.09311e23	−1.46039	−0.730196	+	0.683238i	$0.760571\pi$
$492$	−4.73189e22	−0.621343
$493$	−5.59882e20	−0.00722599
$494$	1.36461e22	0.173113
$495$	−7.57825e21	−0.0944984
$496$	−4.09149e22	−0.501518
$497$	5.28120e22	0.636360
$498$	3.05939e21	0.0362398
$499$	9.52325e22	1.10900	0.554499	−	0.832185i	$-0.312910\pi$
$499$	9.52325e22	1.10900	0.554499	+	0.832185i	$0.312910\pi$
$500$	−7.96999e22	−0.912458
$501$	−1.13194e23	−1.27409
$502$	−2.97070e22	−0.328759
$503$	1.55505e23	1.69206	0.846032	−	0.533133i	$-0.178985\pi$
$503$	1.55505e23	1.69206	0.846032	+	0.533133i	$0.178985\pi$
$504$	−2.30514e21	−0.0246625
$505$	2.25794e22	0.237539
$506$	3.06091e22	0.316643
$507$	5.74433e22	0.584348
$508$	3.47192e22	0.347318
$509$	6.64642e22	0.653863	0.326931	−	0.945048i	$-0.393985\pi$
$509$	6.64642e22	0.653863	0.326931	+	0.945048i	$0.393985\pi$
$510$	5.91216e20	0.00572005
$511$	−2.35927e22	−0.224492
$512$	−1.00560e23	−0.941091
$513$	5.92848e22	0.545690
$514$	2.35527e22	0.213233
$515$	−8.03773e22	−0.715767
$516$	1.58597e23	1.38923
$517$	−2.02262e22	−0.174279
$518$	1.37275e22	0.116356
$519$	1.41914e23	1.18332
$520$	−4.15167e22	−0.340561
$521$	1.46467e23	1.18200	0.591001	−	0.806671i	$-0.298733\pi$
$521$	1.46467e23	1.18200	0.591001	+	0.806671i	$0.298733\pi$
$522$	5.35026e20	0.00424791
$523$	−2.07548e21	−0.0162127	−0.00810634	−	0.999967i	$-0.502580\pi$
$523$	−2.07548e21	−0.0162127	−0.00810634	+	0.999967i	$0.502580\pi$
$524$	6.94635e22	0.533877
$525$	5.06445e22	0.382982
$526$	6.46024e21	0.0480695
$527$	−3.21288e21	−0.0235236
$528$	2.05218e23	1.47852
$529$	−5.68536e22	−0.403074
$530$	−3.69582e22	−0.257849
$531$	−1.43018e22	−0.0981948
$532$	−4.46006e22	−0.301365
$533$	1.18316e23	0.786795
$534$	−3.90741e22	−0.255734
$535$	3.47078e22	0.223573
$536$	2.21332e22	0.140328
$537$	1.02088e23	0.637077
$538$	2.71038e22	0.166487
$539$	−1.94865e23	−1.17823
$540$	−8.74945e22	−0.520756
$541$	1.01863e23	0.596813	0.298407	−	0.954439i	$-0.403545\pi$
$541$	1.01863e23	0.596813	0.298407	+	0.954439i	$0.403545\pi$
$542$	−4.51803e21	−0.0260588
$543$	2.57680e23	1.46313
$544$	−4.64319e21	−0.0259553
$545$	1.75526e23	0.965986
$546$	3.22086e22	0.174516
$547$	−3.10603e23	−1.65697	−0.828483	−	0.560014i	$-0.810796\pi$
$547$	−3.10603e23	−1.65697	−0.828483	+	0.560014i	$0.810796\pi$
$548$	8.81873e22	0.463203
$549$	3.43432e22	0.177614
$550$	5.30589e22	0.270194
$551$	2.13401e22	0.107006
$552$	−7.65265e22	−0.377859
$553$	1.34774e23	0.655304
$554$	−8.72878e22	−0.417946
$555$	−1.12830e23	−0.532029
$556$	8.91468e22	0.413971
$557$	−1.39937e23	−0.639974	−0.319987	−	0.947422i	$-0.603679\pi$
$557$	−1.39937e23	−0.639974	−0.319987	+	0.947422i	$0.603679\pi$
$558$	3.07024e21	0.0138287
$559$	−3.96556e23	−1.75915
$560$	6.15282e22	0.268829
$561$	1.61149e22	0.0693496
$562$	−8.66104e22	−0.367123
$563$	−2.79221e22	−0.116581	−0.0582904	−	0.998300i	$-0.518565\pi$
$563$	−2.79221e22	−0.116581	−0.0582904	+	0.998300i	$0.518565\pi$
$564$	2.45301e22	0.100885
$565$	2.22003e22	0.0899387
$566$	−2.43704e22	−0.0972573
$567$	1.53352e23	0.602883
$568$	−1.38331e23	−0.535747
$569$	−4.52802e23	−1.72764	−0.863821	−	0.503799i	$-0.831935\pi$
$569$	−4.52802e23	−1.72764	−0.863821	+	0.503799i	$0.831935\pi$
$570$	−2.25344e22	−0.0847052
$571$	−2.03048e22	−0.0751953	−0.0375977	−	0.999293i	$-0.511971\pi$
$571$	−2.03048e22	−0.0751953	−0.0375977	+	0.999293i	$0.511971\pi$
$572$	−5.48943e23	−2.00291
$573$	−4.46301e23	−1.60440
$574$	2.37710e22	0.0841970
$575$	1.45949e23	0.509361
$576$	−1.84961e22	−0.0636045
$577$	3.29301e23	1.11583	0.557916	−	0.829898i	$-0.311601\pi$
$577$	3.29301e23	1.11583	0.557916	+	0.829898i	$0.311601\pi$
$578$	7.19631e22	0.240283
$579$	5.73701e22	0.188763
$580$	−3.14944e22	−0.102116
$581$	2.50021e22	0.0798876
$582$	1.84488e22	0.0580928
$583$	−1.00738e24	−3.12615
$584$	6.17969e22	0.188998
$585$	−2.29806e22	−0.0692686
$586$	−4.08538e22	−0.121368
$587$	4.23320e22	0.123950	0.0619748	−	0.998078i	$-0.480260\pi$
$587$	4.23320e22	0.123950	0.0619748	+	0.998078i	$0.480260\pi$
$588$	2.36330e23	0.682042
$589$	1.22460e23	0.348349
$590$	−5.17514e22	−0.145104
$591$	−2.39727e23	−0.662557
$592$	2.65233e23	0.722591
$593$	4.22926e23	1.13579	0.567897	−	0.823099i	$-0.307757\pi$
$593$	4.22926e23	1.13579	0.567897	+	0.823099i	$0.307757\pi$
$594$	1.46600e23	0.388105
$595$	4.83156e21	0.0126094
$596$	6.69174e23	1.72165
$597$	5.27207e23	1.33721
$598$	9.28203e22	0.232104
$599$	5.02655e22	0.123920	0.0619601	−	0.998079i	$-0.480265\pi$
$599$	5.02655e22	0.123920	0.0619601	+	0.998079i	$0.480265\pi$
$600$	−1.32654e23	−0.322430
$601$	−7.08089e23	−1.69690	−0.848448	−	0.529279i	$-0.822462\pi$
$601$	−7.08089e23	−1.69690	−0.848448	+	0.529279i	$0.822462\pi$
$602$	−7.96725e22	−0.188251
$603$	1.22513e22	0.0285421
$604$	5.81590e23	1.33599
$605$	−4.89743e23	−1.10930
$606$	4.58828e22	0.102478
$607$	−8.09046e23	−1.78184	−0.890922	−	0.454157i	$-0.849940\pi$
$607$	−8.09046e23	−1.78184	−0.890922	+	0.454157i	$0.849940\pi$
$608$	1.76977e23	0.384358
$609$	5.03687e22	0.107873
$610$	1.24272e23	0.262463
$611$	−6.13349e22	−0.127749
$612$	−1.69656e21	−0.00348483
$613$	2.51284e23	0.509038	0.254519	−	0.967068i	$-0.418083\pi$
$613$	2.51284e23	0.509038	0.254519	+	0.967068i	$0.418083\pi$
$614$	−4.13902e21	−0.00826926
$615$	−1.95381e23	−0.384984
$616$	−2.27357e23	−0.441848
$617$	7.50265e23	1.43810	0.719052	−	0.694956i	$-0.244576\pi$
$617$	7.50265e23	1.43810	0.719052	+	0.694956i	$0.244576\pi$
$618$	−1.63332e23	−0.308794
$619$	−3.42661e23	−0.638991	−0.319495	−	0.947588i	$-0.603513\pi$
$619$	−3.42661e23	−0.638991	−0.319495	+	0.947588i	$0.603513\pi$
$620$	−1.80731e23	−0.332432
$621$	4.03253e23	0.731643
$622$	−1.82769e23	−0.327104
$623$	−3.19323e23	−0.563744
$624$	6.22311e23	1.08377
$625$	5.46655e22	0.0939146
$626$	1.26841e23	0.214970
$627$	−6.14226e23	−1.02696
$628$	−8.69956e23	−1.43496
$629$	2.08277e22	0.0338930
$630$	−4.61706e21	−0.00741261
$631$	−6.00753e23	−0.951583	−0.475791	−	0.879558i	$-0.657838\pi$
$631$	−6.00753e23	−0.951583	−0.475791	+	0.879558i	$0.657838\pi$
$632$	−3.53016e23	−0.551695
$633$	3.09357e23	0.477012
$634$	1.23648e23	0.188118
$635$	1.43356e23	0.215198
$636$	1.22174e24	1.80964
$637$	−5.90917e23	−0.863657
$638$	5.27700e22	0.0761047
$639$	−7.65701e22	−0.108969
$640$	−3.44172e23	−0.483333
$641$	6.99551e23	0.969451	0.484725	−	0.874666i	$-0.338920\pi$
$641$	6.99551e23	0.969451	0.484725	+	0.874666i	$0.338920\pi$
$642$	7.05285e22	0.0964533
$643$	−1.08453e24	−1.46368	−0.731842	−	0.681475i	$-0.761339\pi$
$643$	−1.08453e24	−1.46368	−0.731842	+	0.681475i	$0.761339\pi$
$644$	−3.03372e23	−0.404060
$645$	6.54851e23	0.860765
$646$	4.15969e21	0.00539616
$647$	1.22825e24	1.57254	0.786269	−	0.617884i	$-0.212010\pi$
$647$	1.22825e24	1.57254	0.786269	+	0.617884i	$0.212010\pi$
$648$	−4.01677e23	−0.507563
$649$	−1.41060e24	−1.75924
$650$	1.60898e23	0.198056
$651$	2.89040e23	0.351172
$652$	7.61039e23	0.912646
$653$	−3.22798e23	−0.382093	−0.191046	−	0.981581i	$-0.561188\pi$
$653$	−3.22798e23	−0.382093	−0.191046	+	0.981581i	$0.561188\pi$
$654$	3.56680e23	0.416743
$655$	2.86816e23	0.330790
$656$	4.59285e23	0.522878
$657$	3.42062e22	0.0384414
$658$	−1.23229e22	−0.0136707
$659$	1.83624e23	0.201096	0.100548	−	0.994932i	$-0.467940\pi$
$659$	1.83624e23	0.201096	0.100548	+	0.994932i	$0.467940\pi$
$660$	9.06496e23	0.980037
$661$	9.64603e23	1.02952	0.514762	−	0.857333i	$-0.327880\pi$
$661$	9.64603e23	1.02952	0.514762	+	0.857333i	$0.327880\pi$
$662$	1.96335e23	0.206873
$663$	4.88676e22	0.0508342
$664$	−6.54885e22	−0.0672568
$665$	−1.84157e23	−0.186725
$666$	−1.99030e22	−0.0199245
$667$	1.45155e23	0.143470
$668$	1.17537e24	1.14703
$669$	−1.03438e24	−0.996683
$670$	4.43316e22	0.0421772
$671$	3.38730e24	3.18209
$672$	4.17715e23	0.387473
$673$	−7.70198e23	−0.705463	−0.352731	−	0.935725i	$-0.614747\pi$
$673$	−7.70198e23	−0.705463	−0.352731	+	0.935725i	$0.614747\pi$
$674$	3.90401e23	0.353104
$675$	6.99015e23	0.624316
$676$	−5.96474e23	−0.526071
$677$	6.57265e22	0.0572449	0.0286224	−	0.999590i	$-0.490888\pi$
$677$	6.57265e22	0.0572449	0.0286224	+	0.999590i	$0.490888\pi$
$678$	4.51124e22	0.0388011
$679$	1.50768e23	0.128061
$680$	−1.26554e22	−0.0106157
$681$	7.24648e23	0.600311
$682$	3.02820e23	0.247752
$683$	1.47166e24	1.18914	0.594569	−	0.804045i	$-0.297323\pi$
$683$	1.47166e24	1.18914	0.594569	+	0.804045i	$0.297323\pi$
$684$	6.46648e22	0.0516049
$685$	3.64127e23	0.287001
$686$	−2.90327e23	−0.226013
$687$	−1.11443e24	−0.856882
$688$	−1.53937e24	−1.16907
$689$	−3.05482e24	−2.29151
$690$	−1.53278e23	−0.113570
$691$	1.79824e23	0.131608	0.0658042	−	0.997833i	$-0.479039\pi$
$691$	1.79824e23	0.131608	0.0658042	+	0.997833i	$0.479039\pi$
$692$	−1.47359e24	−1.06531
$693$	−1.25848e23	−0.0898701
$694$	−4.84344e23	−0.341663
$695$	3.68089e23	0.256496
$696$	−1.31932e23	−0.0908177
$697$	3.60658e22	0.0245255
$698$	1.19532e23	0.0802994
$699$	−1.52828e24	−1.01426
$700$	−5.25877e23	−0.344787
$701$	3.41970e23	0.221506	0.110753	−	0.993848i	$-0.464674\pi$
$701$	3.41970e23	0.221506	0.110753	+	0.993848i	$0.464674\pi$
$702$	4.44556e23	0.284486
$703$	−7.93854e23	−0.501904
$704$	−1.82428e24	−1.13953
$705$	1.01285e23	0.0625083
$706$	2.86723e23	0.174833
$707$	3.74965e23	0.225905
$708$	1.71076e24	1.01837
$709$	2.32305e24	1.36636	0.683182	−	0.730249i	$-0.260596\pi$
$709$	2.32305e24	1.36636	0.683182	+	0.730249i	$0.260596\pi$
$710$	−2.77070e23	−0.161025
$711$	−1.95404e23	−0.112213
$712$	8.36409e23	0.474612
$713$	8.32969e23	0.467055
$714$	9.81806e21	0.00543990
$715$	−2.26659e24	−1.24100
$716$	−1.06005e24	−0.573542
$717$	2.05239e24	1.09735
$718$	5.81630e23	0.307319
$719$	1.36078e24	0.710547	0.355274	−	0.934762i	$-0.384388\pi$
$719$	1.36078e24	0.710547	0.355274	+	0.934762i	$0.384388\pi$
$720$	−8.92075e22	−0.0460336
$721$	−1.33479e24	−0.680711
$722$	3.18924e23	0.160739
$723$	−3.01090e24	−1.49976
$724$	−2.67567e24	−1.31721
$725$	2.51617e23	0.122424
$726$	−9.95189e23	−0.478569
$727$	−1.58459e24	−0.753136	−0.376568	−	0.926389i	$-0.622896\pi$
$727$	−1.58459e24	−0.753136	−0.376568	+	0.926389i	$0.622896\pi$
$728$	−6.89449e23	−0.323881
$729$	1.91189e24	0.887728
$730$	1.23776e23	0.0568056
$731$	−1.20881e23	−0.0548352
$732$	−4.10807e24	−1.84202
$733$	−3.25222e24	−1.44144	−0.720720	−	0.693227i	$-0.756188\pi$
$733$	−3.25222e24	−1.44144	−0.720720	+	0.693227i	$0.756188\pi$
$734$	1.10222e23	0.0482895
$735$	9.75809e23	0.422593
$736$	1.20379e24	0.515335
$737$	1.20836e24	0.511353
$738$	−3.44647e22	−0.0144177
$739$	−6.41592e23	−0.265327	−0.132664	−	0.991161i	$-0.542353\pi$
$739$	−6.41592e23	−0.265327	−0.132664	+	0.991161i	$0.542353\pi$
$740$	1.17160e24	0.478970
$741$	−1.86261e24	−0.752777
$742$	−6.13748e23	−0.245221
$743$	−4.92406e23	−0.194499	−0.0972497	−	0.995260i	$-0.531005\pi$
$743$	−4.92406e23	−0.194499	−0.0972497	+	0.995260i	$0.531005\pi$
$744$	−7.57089e23	−0.295649
$745$	2.76303e24	1.06674
$746$	−6.66542e23	−0.254418
$747$	−3.62496e22	−0.0136798
$748$	−1.67333e23	−0.0624334
$749$	5.76376e23	0.212623
$750$	−6.68717e23	−0.243905
$751$	1.80397e24	0.650562	0.325281	−	0.945617i	$-0.394541\pi$
$751$	1.80397e24	0.650562	0.325281	+	0.945617i	$0.394541\pi$
$752$	−2.38093e23	−0.0848976
$753$	4.05482e24	1.42960
$754$	1.60022e23	0.0557858
$755$	2.40139e24	0.827779
$756$	−1.45298e24	−0.495250
$757$	4.70923e24	1.58721	0.793606	−	0.608432i	$-0.208201\pi$
$757$	4.70923e24	1.58721	0.793606	+	0.608432i	$0.208201\pi$
$758$	−5.17408e23	−0.172443
$759$	−4.17795e24	−1.37692
$760$	4.82365e23	0.157203
$761$	−1.95775e24	−0.630938	−0.315469	−	0.948936i	$-0.602162\pi$
$761$	−1.95775e24	−0.630938	−0.315469	+	0.948936i	$0.602162\pi$
$762$	2.91309e23	0.0928402
$763$	2.91488e24	0.918674
$764$	4.63426e24	1.44440
$765$	−7.00510e21	−0.00215920
$766$	6.42534e23	0.195863
$767$	−4.27757e24	−1.28954
$768$	1.64909e24	0.491669
$769$	−4.43376e23	−0.130737	−0.0653685	−	0.997861i	$-0.520822\pi$
$769$	−4.43376e23	−0.130737	−0.0653685	+	0.997861i	$0.520822\pi$
$770$	−4.55385e23	−0.132803
$771$	−3.21479e24	−0.927237
$772$	−5.95714e23	−0.169938
$773$	−1.74076e24	−0.491148	−0.245574	−	0.969378i	$-0.578976\pi$
$773$	−1.74076e24	−0.491148	−0.245574	+	0.969378i	$0.578976\pi$
$774$	1.15514e23	0.0322357
$775$	1.44390e24	0.398541
$776$	−3.94909e23	−0.107813
$777$	−1.87372e24	−0.505972
$778$	−1.25757e24	−0.335898
$779$	−1.37466e24	−0.363185
$780$	2.74890e24	0.718380
$781$	−7.55217e24	−1.95226
$782$	2.82941e22	0.00723500
$783$	6.95208e23	0.175849
$784$	−2.29386e24	−0.573958
$785$	−3.59206e24	−0.889102
$786$	5.82829e23	0.142708
$787$	4.61324e24	1.11743	0.558716	−	0.829359i	$-0.311294\pi$
$787$	4.61324e24	1.11743	0.558716	+	0.829359i	$0.311294\pi$
$788$	2.48925e24	0.596481
$789$	−8.81783e23	−0.209029
$790$	−7.07072e23	−0.165819
$791$	3.68670e23	0.0855337
$792$	3.29637e23	0.0756610
$793$	1.02718e25	2.33251
$794$	5.85428e23	0.131522
$795$	5.04457e24	1.12125
$796$	−5.47437e24	−1.20385
$797$	5.57236e24	1.21239	0.606197	−	0.795314i	$-0.292694\pi$
$797$	5.57236e24	1.21239	0.606197	+	0.795314i	$0.292694\pi$
$798$	−3.74219e23	−0.0805565
$799$	−1.86965e22	−0.00398211
$800$	2.08670e24	0.439739
$801$	4.62975e23	0.0965341
$802$	−1.32449e24	−0.273254
$803$	3.37378e24	0.688708
$804$	−1.46548e24	−0.296008
$805$	−1.25263e24	−0.250356
$806$	9.18286e23	0.181606
$807$	−3.69950e24	−0.723966
$808$	−9.82153e23	−0.190188
$809$	−6.80620e24	−1.30419	−0.652097	−	0.758135i	$-0.726111\pi$
$809$	−6.80620e24	−1.30419	−0.652097	+	0.758135i	$0.726111\pi$
$810$	−8.04537e23	−0.152554
$811$	4.02357e24	0.754978	0.377489	−	0.926014i	$-0.376788\pi$
$811$	4.02357e24	0.754978	0.377489	+	0.926014i	$0.376788\pi$
$812$	−5.23013e23	−0.0971151
$813$	6.16682e23	0.113316
$814$	−1.96305e24	−0.356964
$815$	3.14234e24	0.565476
$816$	1.89697e23	0.0337827
$817$	4.60741e24	0.812025
$818$	5.74722e23	0.100243
$819$	−3.81628e23	−0.0658760
$820$	2.02877e24	0.346590
$821$	−8.02999e23	−0.135768	−0.0678841	−	0.997693i	$-0.521625\pi$
$821$	−8.02999e23	−0.135768	−0.0678841	+	0.997693i	$0.521625\pi$
$822$	7.39930e23	0.123817
$823$	−5.51859e24	−0.913966	−0.456983	−	0.889475i	$-0.651070\pi$
$823$	−5.51859e24	−0.913966	−0.456983	+	0.889475i	$0.651070\pi$
$824$	3.49624e24	0.573085
$825$	−7.24222e24	−1.17493
$826$	−8.59412e23	−0.137997
$827$	1.83989e23	0.0292411	0.0146206	−	0.999893i	$-0.495346\pi$
$827$	1.83989e23	0.0292411	0.0146206	+	0.999893i	$0.495346\pi$
$828$	4.39848e23	0.0691902
$829$	7.00467e24	1.09062	0.545311	−	0.838234i	$-0.316412\pi$
$829$	7.00467e24	1.09062	0.545311	+	0.838234i	$0.316412\pi$
$830$	−1.31170e23	−0.0202148
$831$	1.19142e25	1.81743
$832$	−5.53203e24	−0.835288
$833$	−1.80127e23	−0.0269214
$834$	7.47980e23	0.110657
$835$	4.85311e24	0.710698
$836$	6.37794e24	0.924543
$837$	3.98945e24	0.572462
$838$	−1.69766e24	−0.241144
$839$	1.22149e25	1.71757	0.858784	−	0.512337i	$-0.171220\pi$
$839$	1.22149e25	1.71757	0.858784	+	0.512337i	$0.171220\pi$
$840$	1.13852e24	0.158477
$841$	2.50246e23	0.0344828
$842$	−1.21006e24	−0.165065
$843$	1.18218e25	1.59643
$844$	−3.21228e24	−0.429439
$845$	−2.46285e24	−0.325954
$846$	1.78665e22	0.00234094
$847$	−8.13293e24	−1.05496
$848$	−1.18584e25	−1.52286
$849$	3.32640e24	0.422921
$850$	4.90461e22	0.00617367
$851$	−5.39977e24	−0.672936
$852$	9.15917e24	1.13011
$853$	5.70078e24	0.696414	0.348207	−	0.937418i	$-0.386791\pi$
$853$	5.70078e24	0.696414	0.348207	+	0.937418i	$0.386791\pi$
$854$	2.06372e24	0.249608
$855$	2.67002e23	0.0319744
$856$	−1.50971e24	−0.179006
$857$	9.87303e24	1.15908	0.579540	−	0.814944i	$-0.303232\pi$
$857$	9.87303e24	1.15908	0.579540	+	0.814944i	$0.303232\pi$
$858$	−4.60587e24	−0.535389
$859$	−7.04326e24	−0.810647	−0.405323	−	0.914173i	$-0.632841\pi$
$859$	−7.04326e24	−0.810647	−0.405323	+	0.914173i	$0.632841\pi$
$860$	−6.79978e24	−0.774922
$861$	−3.24459e24	−0.366128
$862$	−1.27447e24	−0.142402
$863$	1.51811e24	0.167962	0.0839809	−	0.996467i	$-0.473237\pi$
$863$	1.51811e24	0.167962	0.0839809	+	0.996467i	$0.473237\pi$
$864$	5.76547e24	0.631638
$865$	−6.08447e24	−0.660064
$866$	3.41397e24	0.366740
$867$	−9.82252e24	−1.04487
$868$	−3.00131e24	−0.316150
$869$	−1.92728e25	−2.01038
$870$	−2.64252e23	−0.0272963
$871$	3.66427e24	0.374829
$872$	−7.63499e24	−0.773425
$873$	−2.18593e23	−0.0219288
$874$	−1.07844e24	−0.107139
$875$	−5.46491e24	−0.537669
$876$	−4.09168e24	−0.398673
$877$	1.74614e25	1.68493	0.842466	−	0.538750i	$-0.181103\pi$
$877$	1.74614e25	1.68493	0.842466	+	0.538750i	$0.181103\pi$
$878$	3.59583e22	0.00343633
$879$	5.57629e24	0.527764
$880$	−8.79860e24	−0.824728
$881$	−1.19036e25	−1.10505	−0.552526	−	0.833496i	$-0.686336\pi$
$881$	−1.19036e25	−1.10505	−0.552526	+	0.833496i	$0.686336\pi$
$882$	1.72131e23	0.0158261
$883$	−8.08654e24	−0.736371	−0.368185	−	0.929752i	$-0.620021\pi$
$883$	−8.08654e24	−0.736371	−0.368185	+	0.929752i	$0.620021\pi$
$884$	−5.07427e23	−0.0457645
$885$	7.06375e24	0.630983
$886$	−1.58958e24	−0.140635
$887$	−2.01706e24	−0.176753	−0.0883767	−	0.996087i	$-0.528168\pi$
$887$	−2.01706e24	−0.176753	−0.0883767	+	0.996087i	$0.528168\pi$
$888$	4.90787e24	0.425974
$889$	2.38064e24	0.204658
$890$	1.67528e24	0.142650
$891$	−2.19295e25	−1.84956
$892$	1.07407e25	0.897284
$893$	7.12624e23	0.0589689
$894$	5.61466e24	0.460208
$895$	−4.37696e24	−0.355366
$896$	−5.71551e24	−0.459660
$897$	−1.26694e25	−1.00930
$898$	1.75316e24	0.138348
$899$	1.43604e24	0.112256
$900$	7.62450e23	0.0590405
$901$	−9.31191e23	−0.0714295
$902$	−3.39928e24	−0.258304
$903$	1.08748e25	0.818607
$904$	−9.65663e23	−0.0720102
$905$	−1.10479e25	−0.816143
$906$	4.87979e24	0.357118
$907$	−3.72297e24	−0.269916	−0.134958	−	0.990851i	$-0.543090\pi$
$907$	−3.72297e24	−0.269916	−0.134958	+	0.990851i	$0.543090\pi$
$908$	−7.52453e24	−0.540442
$909$	−5.43648e23	−0.0386834
$910$	−1.38093e24	−0.0973463
$911$	5.29320e24	0.369668	0.184834	−	0.982770i	$-0.440825\pi$
$911$	5.29320e24	0.369668	0.184834	+	0.982770i	$0.440825\pi$
$912$	−7.23037e24	−0.500270
$913$	−3.57533e24	−0.245084
$914$	4.68629e24	0.318263
$915$	−1.69623e25	−1.14131
$916$	1.15719e25	0.771425
$917$	4.76302e24	0.314589
$918$	1.35513e23	0.00886783
$919$	−1.68830e25	−1.09463	−0.547317	−	0.836925i	$-0.684351\pi$
$919$	−1.68830e25	−1.09463	−0.547317	+	0.836925i	$0.684351\pi$
$920$	3.28103e24	0.210773
$921$	5.64951e23	0.0359587
$922$	−5.22818e24	−0.329714
$923$	−2.29015e25	−1.43103
$924$	1.50538e25	0.932037
$925$	−9.36017e24	−0.574221
$926$	−1.03520e24	−0.0629259
$927$	1.93526e24	0.116563
$928$	2.07533e24	0.123860
$929$	4.53155e23	0.0267987	0.0133993	−	0.999910i	$-0.495735\pi$
$929$	4.53155e23	0.0267987	0.0133993	+	0.999910i	$0.495735\pi$
$930$	−1.51641e24	−0.0888610
$931$	6.86562e24	0.398664
$932$	1.58692e25	0.913106
$933$	2.49469e25	1.42240
$934$	4.65147e24	0.262810
$935$	−6.90919e23	−0.0386837
$936$	9.99606e23	0.0554606
$937$	2.83857e25	1.56068	0.780340	−	0.625356i	$-0.215046\pi$
$937$	2.83857e25	1.56068	0.780340	+	0.625356i	$0.215046\pi$
$938$	7.36194e23	0.0401114
$939$	−1.73130e25	−0.934793
$940$	−1.05171e24	−0.0562744
$941$	2.95047e25	1.56451	0.782256	−	0.622957i	$-0.214069\pi$
$941$	2.95047e25	1.56451	0.782256	+	0.622957i	$0.214069\pi$
$942$	−7.29931e24	−0.383574
$943$	−9.35041e24	−0.486947
$944$	−1.66049e25	−0.856988
$945$	−5.99938e24	−0.306857
$946$	1.13933e25	0.577528
$947$	−3.21196e24	−0.161360	−0.0806798	−	0.996740i	$-0.525709\pi$
$947$	−3.21196e24	−0.161360	−0.0806798	+	0.996740i	$0.525709\pi$
$948$	2.33738e25	1.16375
$949$	1.02308e25	0.504833
$950$	−1.86941e24	−0.0914226
$951$	−1.68772e25	−0.818025
$952$	−2.10162e23	−0.0100958
$953$	2.92181e25	1.39111	0.695557	−	0.718471i	$-0.255158\pi$
$953$	2.92181e25	1.39111	0.695557	+	0.718471i	$0.255158\pi$
$954$	8.89850e23	0.0419910
$955$	1.91349e25	0.894949
$956$	−2.13114e25	−0.987915
$957$	−7.20277e24	−0.330939
$958$	−2.52244e24	−0.114872
$959$	6.04688e24	0.272944
$960$	9.13530e24	0.408712
$961$	−1.43094e25	−0.634561
$962$	−5.95284e24	−0.261659
$963$	−8.35667e23	−0.0364091
$964$	3.12643e25	1.35019
$965$	−2.45971e24	−0.105294
$966$	−2.54542e24	−0.108008
$967$	−2.17775e25	−0.915975	−0.457987	−	0.888959i	$-0.651430\pi$
$967$	−2.17775e25	−0.915975	−0.457987	+	0.888959i	$0.651430\pi$
$968$	2.13027e25	0.888167
$969$	−5.67772e23	−0.0234651
$970$	−7.90981e23	−0.0324046
$971$	−3.40426e25	−1.38248	−0.691241	−	0.722624i	$-0.742936\pi$
$971$	−3.40426e25	−1.38248	−0.691241	+	0.722624i	$0.742936\pi$
$972$	4.43454e24	0.178519
$973$	6.11267e24	0.243934
$974$	2.30059e24	0.0910100
$975$	−2.19616e25	−0.861242
$976$	3.98737e25	1.55011
$977$	−1.73365e25	−0.668125	−0.334062	−	0.942551i	$-0.608420\pi$
$977$	−1.73365e25	−0.668125	−0.334062	+	0.942551i	$0.608420\pi$
$978$	6.38545e24	0.243956
$979$	4.56635e25	1.72948
$980$	−1.01325e25	−0.380448
$981$	−4.22617e24	−0.157312
$982$	9.52354e24	0.351440
$983$	3.34045e25	1.22208	0.611041	−	0.791599i	$-0.290751\pi$
$983$	3.34045e25	1.22208	0.611041	+	0.791599i	$0.290751\pi$
$984$	8.49863e24	0.308241
$985$	1.02782e25	0.369579
$986$	4.87790e22	0.00173892
$987$	1.68199e24	0.0594468
$988$	1.93407e25	0.677703
$989$	3.13395e25	1.08874
$990$	6.60245e23	0.0227408
$991$	−2.11099e25	−0.720876	−0.360438	−	0.932783i	$-0.617373\pi$
$991$	−2.11099e25	−0.720876	−0.360438	+	0.932783i	$0.617373\pi$
$992$	1.19093e25	0.403215
$993$	−2.67985e25	−0.899584
$994$	−4.60118e24	−0.153139
$995$	−2.26037e25	−0.745906
$996$	4.33611e24	0.141872
$997$	2.65907e25	0.862621	0.431311	−	0.902203i	$-0.358051\pi$
$997$	2.65907e25	0.862621	0.431311	+	0.902203i	$0.358051\pi$
$998$	−8.29701e24	−0.266878
$999$	−2.58618e25	−0.824808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.8	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.8	✓	18	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-87.1238 q^{2} +11891.8 q^{3} -123481. q^{4} -509857. q^{5} -1.03606e6 q^{6} -8.46695e6 q^{7} +2.21777e7 q^{8} +1.22759e7 q^{9} +O(q^{10})\)	\(q-87.1238 q^{2} +11891.8 q^{3} -123481. q^{4} -509857. q^{5} -1.03606e6 q^{6} -8.46695e6 q^{7} +2.21777e7 q^{8} +1.22759e7 q^{9} +4.44206e7 q^{10} +1.21078e9 q^{11} -1.46842e9 q^{12} +3.67163e9 q^{13} +7.37673e8 q^{14} -6.06314e9 q^{15} +1.42528e10 q^{16} +1.11921e9 q^{17} -1.06952e9 q^{18} -4.26592e10 q^{19} +6.29578e10 q^{20} -1.00688e11 q^{21} -1.05488e11 q^{22} -2.90166e11 q^{23} +2.63733e11 q^{24} -5.02986e11 q^{25} -3.19886e11 q^{26} -1.38973e12 q^{27} +1.04551e12 q^{28} -5.00246e11 q^{29} +5.28243e11 q^{30} -2.87066e12 q^{31} -4.14862e12 q^{32} +1.43985e13 q^{33} -9.75100e10 q^{34} +4.31693e12 q^{35} -1.51585e12 q^{36} +1.86092e13 q^{37} +3.71663e12 q^{38} +4.36625e13 q^{39} -1.13074e13 q^{40} +3.22243e13 q^{41} +8.77229e12 q^{42} -1.08005e14 q^{43} -1.49509e14 q^{44} -6.25896e12 q^{45} +2.52804e13 q^{46} -1.67051e13 q^{47} +1.69492e14 q^{48} -1.60941e14 q^{49} +4.38220e13 q^{50} +1.33095e13 q^{51} -4.53379e14 q^{52} -8.32006e14 q^{53} +1.21079e14 q^{54} -6.17326e14 q^{55} -1.87777e14 q^{56} -5.07296e14 q^{57} +4.35833e13 q^{58} -1.16503e15 q^{59} +7.48685e14 q^{60} +2.79761e15 q^{61} +2.50103e14 q^{62} -1.03940e14 q^{63} -1.50669e15 q^{64} -1.87201e15 q^{65} -1.25445e15 q^{66} +9.97995e14 q^{67} -1.38202e14 q^{68} -3.45061e15 q^{69} -3.76107e14 q^{70} -6.23742e15 q^{71} +2.72251e14 q^{72} +2.78645e15 q^{73} -1.62131e15 q^{74} -5.98143e15 q^{75} +5.26761e15 q^{76} -1.02516e16 q^{77} -3.80404e15 q^{78} -1.59177e16 q^{79} -7.26687e15 q^{80} -1.81118e16 q^{81} -2.80750e15 q^{82} -2.95290e15 q^{83} +1.24331e16 q^{84} -5.70638e14 q^{85} +9.40982e15 q^{86} -5.94886e15 q^{87} +2.68523e16 q^{88} +3.77141e16 q^{89} +5.45304e14 q^{90} -3.10875e16 q^{91} +3.58302e16 q^{92} -3.41375e16 q^{93} +1.45541e15 q^{94} +2.17501e16 q^{95} -4.93348e16 q^{96} -1.78066e16 q^{97} +1.40218e16 q^{98} +1.48635e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more