LMFDB - Embedded newform 29.18.a.a.1.10

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			1.10
Root			$19.4887$ 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)

$f(q)$	$=$	$q+19.4887 q^{2} -18855.2 q^{3} -130692. q^{4} -785915. q^{5} -367464. q^{6} -8.64265e6 q^{7} -5.10144e6 q^{8} +2.26380e8 q^{9} +O(q^{10})$	\(q+19.4887 q^{2} -18855.2 q^{3} -130692. q^{4} -785915. q^{5} -367464. q^{6} -8.64265e6 q^{7} -5.10144e6 q^{8} +2.26380e8 q^{9} -1.53164e7 q^{10} -8.67841e8 q^{11} +2.46423e9 q^{12} +4.14273e9 q^{13} -1.68434e8 q^{14} +1.48186e10 q^{15} +1.70307e10 q^{16} -3.84409e10 q^{17} +4.41185e9 q^{18} +8.62054e10 q^{19} +1.02713e11 q^{20} +1.62959e11 q^{21} -1.69131e10 q^{22} +5.59760e11 q^{23} +9.61889e10 q^{24} -1.45277e11 q^{25} +8.07364e10 q^{26} -1.83348e12 q^{27} +1.12953e12 q^{28} -5.00246e11 q^{29} +2.88795e11 q^{30} -3.37095e12 q^{31} +1.00056e12 q^{32} +1.63634e13 q^{33} -7.49162e11 q^{34} +6.79239e12 q^{35} -2.95861e13 q^{36} -4.16834e13 q^{37} +1.68003e12 q^{38} -7.81122e13 q^{39} +4.00930e12 q^{40} +8.28584e13 q^{41} +3.17586e12 q^{42} +1.08052e13 q^{43} +1.13420e14 q^{44} -1.77915e14 q^{45} +1.09090e13 q^{46} +1.87066e14 q^{47} -3.21117e14 q^{48} -1.57935e14 q^{49} -2.83127e12 q^{50} +7.24812e14 q^{51} -5.41422e14 q^{52} +2.83703e14 q^{53} -3.57321e13 q^{54} +6.82049e14 q^{55} +4.40900e13 q^{56} -1.62542e15 q^{57} -9.74915e12 q^{58} -1.01085e15 q^{59} -1.93668e15 q^{60} +2.66633e15 q^{61} -6.56954e13 q^{62} -1.95652e15 q^{63} -2.21274e15 q^{64} -3.25583e15 q^{65} +3.18900e14 q^{66} -1.02765e15 q^{67} +5.02392e15 q^{68} -1.05544e16 q^{69} +1.32375e14 q^{70} -5.46326e15 q^{71} -1.15486e15 q^{72} -1.00064e15 q^{73} -8.12356e14 q^{74} +2.73924e15 q^{75} -1.12664e16 q^{76} +7.50045e15 q^{77} -1.52230e15 q^{78} +1.18992e15 q^{79} -1.33847e16 q^{80} +5.33594e15 q^{81} +1.61480e15 q^{82} +4.53110e15 q^{83} -2.12975e16 q^{84} +3.02113e16 q^{85} +2.10579e14 q^{86} +9.43227e15 q^{87} +4.42724e15 q^{88} +4.86568e16 q^{89} -3.46734e15 q^{90} -3.58042e16 q^{91} -7.31563e16 q^{92} +6.35601e16 q^{93} +3.64568e15 q^{94} -6.77501e16 q^{95} -1.88658e16 q^{96} +8.15622e16 q^{97} -3.07795e15 q^{98} -1.96462e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	19.4887	0.0538304	0.0269152	−	0.999638i	$-0.491432\pi$
$2$	19.4887	0.0538304	0.0269152	+	0.999638i	$0.491432\pi$
$3$	−18855.2	−1.65921	−0.829605	−	0.558351i	$-0.811434\pi$
$3$	−18855.2	−1.65921	−0.829605	+	0.558351i	$0.811434\pi$
$4$	−130692.	−0.997102
$5$	−785915.	−0.899768	−0.449884	−	0.893087i	$-0.648535\pi$
$5$	−785915.	−0.899768	−0.449884	+	0.893087i	$0.648535\pi$
$6$	−367464.	−0.0893159
$7$	−8.64265e6	−0.566648	−0.283324	−	0.959024i	$-0.591437\pi$
$7$	−8.64265e6	−0.566648	−0.283324	+	0.959024i	$0.591437\pi$
$8$	−5.10144e6	−0.107505
$9$	2.26380e8	1.75298
$10$	−1.53164e7	−0.0484349
$11$	−8.67841e8	−1.22068	−0.610341	−	0.792139i	$-0.708967\pi$
$11$	−8.67841e8	−1.22068	−0.610341	+	0.792139i	$0.708967\pi$
$12$	2.46423e9	1.65440
$13$	4.14273e9	1.40854	0.704268	−	0.709934i	$-0.251275\pi$
$13$	4.14273e9	1.40854	0.704268	+	0.709934i	$0.251275\pi$
$14$	−1.68434e8	−0.0305029
$15$	1.48186e10	1.49290
$16$	1.70307e10	0.991315
$17$	−3.84409e10	−1.33653	−0.668263	−	0.743925i	$-0.732962\pi$
$17$	−3.84409e10	−1.33653	−0.668263	+	0.743925i	$0.732962\pi$
$18$	4.41185e9	0.0943635
$19$	8.62054e10	1.16447	0.582236	−	0.813020i	$-0.302178\pi$
$19$	8.62054e10	1.16447	0.582236	+	0.813020i	$0.302178\pi$
$20$	1.02713e11	0.897160
$21$	1.62959e11	0.940189
$22$	−1.69131e10	−0.0657098
$23$	5.59760e11	1.49044	0.745222	−	0.666817i	$-0.232344\pi$
$23$	5.59760e11	1.49044	0.745222	+	0.666817i	$0.232344\pi$
$24$	9.61889e10	0.178373
$25$	−1.45277e11	−0.190418
$26$	8.07364e10	0.0758221
$27$	−1.83348e12	−1.24935
$28$	1.12953e12	0.565006
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	2.88795e11	0.0803636
$31$	−3.37095e12	−0.709869	−0.354935	−	0.934891i	$-0.615497\pi$
$31$	−3.37095e12	−0.709869	−0.354935	+	0.934891i	$0.615497\pi$
$32$	1.00056e12	0.160868
$33$	1.63634e13	2.02537
$34$	−7.49162e11	−0.0719458
$35$	6.79239e12	0.509852
$36$	−2.95861e13	−1.74790
$37$	−4.16834e13	−1.95096	−0.975481	−	0.220083i	$-0.929367\pi$
$37$	−4.16834e13	−1.95096	−0.975481	+	0.220083i	$0.929367\pi$
$38$	1.68003e12	0.0626840
$39$	−7.81122e13	−2.33706
$40$	4.00930e12	0.0967294
$41$	8.28584e13	1.62059	0.810296	−	0.586021i	$-0.199306\pi$
$41$	8.28584e13	1.62059	0.810296	+	0.586021i	$0.199306\pi$
$42$	3.17586e12	0.0506107
$43$	1.08052e13	0.140978	0.0704889	−	0.997513i	$-0.477544\pi$
$43$	1.08052e13	0.140978	0.0704889	+	0.997513i	$0.477544\pi$
$44$	1.13420e14	1.21714
$45$	−1.77915e14	−1.57727
$46$	1.09090e13	0.0802312
$47$	1.87066e14	1.14594	0.572972	−	0.819575i	$-0.305790\pi$
$47$	1.87066e14	1.14594	0.572972	+	0.819575i	$0.305790\pi$
$48$	−3.21117e14	−1.64480
$49$	−1.57935e14	−0.678910
$50$	−2.83127e12	−0.0102503
$51$	7.24812e14	2.21758
$52$	−5.41422e14	−1.40446
$53$	2.83703e14	0.625921	0.312960	−	0.949766i	$-0.398679\pi$
$53$	2.83703e14	0.625921	0.312960	+	0.949766i	$0.398679\pi$
$54$	−3.57321e13	−0.0672530
$55$	6.82049e14	1.09833
$56$	4.40900e13	0.0609174
$57$	−1.62542e15	−1.93210
$58$	−9.74915e12	−0.00999605
$59$	−1.01085e15	−0.896279	−0.448139	−	0.893964i	$-0.647913\pi$
$59$	−1.01085e15	−0.896279	−0.448139	+	0.893964i	$0.647913\pi$
$60$	−1.93668e15	−1.48858
$61$	2.66633e15	1.78078	0.890391	−	0.455197i	$-0.150431\pi$
$61$	2.66633e15	1.78078	0.890391	+	0.455197i	$0.150431\pi$
$62$	−6.56954e13	−0.0382125
$63$	−1.95652e15	−0.993322
$64$	−2.21274e15	−0.982656
$65$	−3.25583e15	−1.26736
$66$	3.18900e14	0.109026
$67$	−1.02765e15	−0.309180	−0.154590	−	0.987979i	$-0.549406\pi$
$67$	−1.02765e15	−0.309180	−0.154590	+	0.987979i	$0.549406\pi$
$68$	5.02392e15	1.33265
$69$	−1.05544e16	−2.47296
$70$	1.32375e14	0.0274455
$71$	−5.46326e15	−1.00405	−0.502025	−	0.864853i	$-0.667412\pi$
$71$	−5.46326e15	−1.00405	−0.502025	+	0.864853i	$0.667412\pi$
$72$	−1.15486e15	−0.188454
$73$	−1.00064e15	−0.145223	−0.0726115	−	0.997360i	$-0.523133\pi$
$73$	−1.00064e15	−0.145223	−0.0726115	+	0.997360i	$0.523133\pi$
$74$	−8.12356e14	−0.105021
$75$	2.73924e15	0.315944
$76$	−1.12664e16	−1.16110
$77$	7.50045e15	0.691697
$78$	−1.52230e15	−0.125805
$79$	1.18992e15	0.0882445	0.0441222	−	0.999026i	$-0.485951\pi$
$79$	1.18992e15	0.0882445	0.0441222	+	0.999026i	$0.485951\pi$
$80$	−1.33847e16	−0.891953
$81$	5.33594e15	0.319955
$82$	1.61480e15	0.0872371
$83$	4.53110e15	0.220821	0.110410	−	0.993886i	$-0.464784\pi$
$83$	4.53110e15	0.220821	0.110410	+	0.993886i	$0.464784\pi$
$84$	−2.12975e16	−0.937464
$85$	3.02113e16	1.20256
$86$	2.10579e14	0.00758890
$87$	9.43227e15	0.308108
$88$	4.42724e15	0.131229
$89$	4.86568e16	1.31017	0.655086	−	0.755554i	$-0.272632\pi$
$89$	4.86568e16	1.31017	0.655086	+	0.755554i	$0.272632\pi$
$90$	−3.46734e15	−0.0849053
$91$	−3.58042e16	−0.798145
$92$	−7.31563e16	−1.48612
$93$	6.35601e16	1.17782
$94$	3.64568e15	0.0616867
$95$	−6.77501e16	−1.04775
$96$	−1.88658e16	−0.266913
$97$	8.15622e16	1.05665	0.528323	−	0.849044i	$-0.322821\pi$
$97$	8.15622e16	1.05665	0.528323	+	0.849044i	$0.322821\pi$
$98$	−3.07795e15	−0.0365460
$99$	−1.96462e17	−2.13983
$100$	1.89866e16	0.189866
$101$	5.29431e16	0.486494	0.243247	−	0.969964i	$-0.421787\pi$
$101$	5.29431e16	0.486494	0.243247	+	0.969964i	$0.421787\pi$
$102$	1.41256e16	0.119373
$103$	−3.67280e16	−0.285680	−0.142840	−	0.989746i	$-0.545623\pi$
$103$	−3.67280e16	−0.285680	−0.142840	+	0.989746i	$0.545623\pi$
$104$	−2.11339e16	−0.151424
$105$	−1.28072e17	−0.845951
$106$	5.52900e15	0.0336936
$107$	9.05806e15	0.0509651	0.0254826	−	0.999675i	$-0.491888\pi$
$107$	9.05806e15	0.0509651	0.0254826	+	0.999675i	$0.491888\pi$
$108$	2.39621e17	1.24573
$109$	2.79368e17	1.34292	0.671461	−	0.741040i	$-0.265667\pi$
$109$	2.79368e17	1.34292	0.671461	+	0.741040i	$0.265667\pi$
$110$	1.32922e16	0.0591235
$111$	7.85951e17	3.23706
$112$	−1.47190e17	−0.561727
$113$	3.52052e17	1.24578	0.622888	−	0.782311i	$-0.285959\pi$
$113$	3.52052e17	1.24578	0.622888	+	0.782311i	$0.285959\pi$
$114$	−3.16774e16	−0.104006
$115$	−4.39924e17	−1.34105
$116$	6.53783e16	0.185157
$117$	9.37831e17	2.46913
$118$	−1.97001e16	−0.0482471
$119$	3.32231e17	0.757340
$120$	−7.55963e16	−0.160494
$121$	2.47701e17	0.490063
$122$	5.19633e16	0.0958602
$123$	−1.56231e18	−2.68890
$124$	4.40557e17	0.707812
$125$	7.13781e17	1.07110
$126$	−3.81300e16	−0.0534709
$127$	1.84091e17	0.241379	0.120690	−	0.992690i	$-0.461489\pi$
$127$	1.84091e17	0.241379	0.120690	+	0.992690i	$0.461489\pi$
$128$	−1.74269e17	−0.213764
$129$	−2.03735e17	−0.233912
$130$	−6.34519e16	−0.0682223
$131$	−4.17053e17	−0.420132	−0.210066	−	0.977687i	$-0.567368\pi$
$131$	−4.17053e17	−0.420132	−0.210066	+	0.977687i	$0.567368\pi$
$132$	−2.13856e18	−2.01950
$133$	−7.45043e17	−0.659846
$134$	−2.00276e16	−0.0166433
$135$	1.44096e18	1.12412
$136$	1.96104e17	0.143683
$137$	2.61601e17	0.180100	0.0900501	−	0.995937i	$-0.471297\pi$
$137$	2.61601e17	0.180100	0.0900501	+	0.995937i	$0.471297\pi$
$138$	−2.05692e17	−0.133120
$139$	−2.69059e18	−1.63765	−0.818825	−	0.574043i	$-0.805374\pi$
$139$	−2.69059e18	−1.63765	−0.818825	+	0.574043i	$0.805374\pi$
$140$	−8.87712e17	−0.508374
$141$	−3.52718e18	−1.90136
$142$	−1.06472e17	−0.0540484
$143$	−3.59523e18	−1.71937
$144$	3.85540e18	1.73775
$145$	3.93151e17	0.167083
$146$	−1.95012e16	−0.00781741
$147$	2.97790e18	1.12645
$148$	5.44770e18	1.94531
$149$	2.77734e18	0.936584	0.468292	−	0.883574i	$-0.344870\pi$
$149$	2.77734e18	0.936584	0.468292	+	0.883574i	$0.344870\pi$
$150$	5.33842e16	0.0170074
$151$	3.60591e18	1.08570	0.542851	−	0.839829i	$-0.317345\pi$
$151$	3.60591e18	1.08570	0.542851	+	0.839829i	$0.317345\pi$
$152$	−4.39772e17	−0.125186
$153$	−8.70224e18	−2.34290
$154$	1.46174e17	0.0372343
$155$	2.64928e18	0.638717
$156$	1.02087e19	2.33029
$157$	−5.68384e18	−1.22884	−0.614419	−	0.788980i	$-0.710609\pi$
$157$	−5.68384e18	−1.22884	−0.614419	+	0.788980i	$0.710609\pi$
$158$	2.31900e16	0.00475023
$159$	−5.34929e18	−1.03853
$160$	−7.86356e17	−0.144744
$161$	−4.83781e18	−0.844557
$162$	1.03991e17	0.0172233
$163$	−9.54094e18	−1.49967	−0.749836	−	0.661623i	$-0.769868\pi$
$163$	−9.54094e18	−1.49967	−0.749836	+	0.661623i	$0.769868\pi$
$164$	−1.08289e19	−1.61590
$165$	−1.28602e19	−1.82236
$166$	8.83051e16	0.0118869
$167$	−4.46897e18	−0.571633	−0.285816	−	0.958284i	$-0.592265\pi$
$167$	−4.46897e18	−0.571633	−0.285816	+	0.958284i	$0.592265\pi$
$168$	−8.31327e17	−0.101075
$169$	8.51180e18	0.983975
$170$	5.88778e17	0.0647345
$171$	1.95152e19	2.04129
$172$	−1.41216e18	−0.140569
$173$	−4.07963e18	−0.386571	−0.193286	−	0.981143i	$-0.561914\pi$
$173$	−4.07963e18	−0.386571	−0.193286	+	0.981143i	$0.561914\pi$
$174$	1.83822e17	0.0165856
$175$	1.25558e18	0.107900
$176$	−1.47799e19	−1.21008
$177$	1.90598e19	1.48712
$178$	9.48256e17	0.0705271
$179$	8.85043e18	0.627644	0.313822	−	0.949482i	$-0.398390\pi$
$179$	8.85043e18	0.627644	0.313822	+	0.949482i	$0.398390\pi$
$180$	2.32521e19	1.57270
$181$	−1.55397e19	−1.00271	−0.501353	−	0.865243i	$-0.667164\pi$
$181$	−1.55397e19	−1.00271	−0.501353	+	0.865243i	$0.667164\pi$
$182$	−6.97776e17	−0.0429645
$183$	−5.02743e19	−2.95469
$184$	−2.85558e18	−0.160230
$185$	3.27596e19	1.75541
$186$	1.23870e18	0.0634026
$187$	3.33606e19	1.63147
$188$	−2.44481e19	−1.14262
$189$	1.58461e19	0.707942
$190$	−1.32036e18	−0.0564010
$191$	−1.55573e19	−0.635551	−0.317776	−	0.948166i	$-0.602936\pi$
$191$	−1.55573e19	−0.635551	−0.317776	+	0.948166i	$0.602936\pi$
$192$	4.17218e19	1.63043
$193$	2.06300e19	0.771369	0.385684	−	0.922631i	$-0.373965\pi$
$193$	2.06300e19	0.771369	0.385684	+	0.922631i	$0.373965\pi$
$194$	1.58954e18	0.0568796
$195$	6.13895e19	2.10281
$196$	2.06409e19	0.676942
$197$	8.02125e18	0.251930	0.125965	−	0.992035i	$-0.459797\pi$
$197$	8.02125e18	0.251930	0.125965	+	0.992035i	$0.459797\pi$
$198$	−3.82878e18	−0.115188
$199$	−2.03187e19	−0.585659	−0.292830	−	0.956165i	$-0.594597\pi$
$199$	−2.03187e19	−0.585659	−0.292830	+	0.956165i	$0.594597\pi$
$200$	7.41124e17	0.0204709
$201$	1.93767e19	0.512994
$202$	1.03179e18	0.0261882
$203$	4.32345e18	0.105224
$204$	−9.47273e19	−2.21115
$205$	−6.51196e19	−1.45816
$206$	−7.15780e17	−0.0153783
$207$	1.26719e20	2.61272
$208$	7.05535e19	1.39630
$209$	−7.48126e19	−1.42145
$210$	−2.49596e18	−0.0455379
$211$	1.67728e18	0.0293904	0.0146952	−	0.999892i	$-0.495322\pi$
$211$	1.67728e18	0.0293904	0.0146952	+	0.999892i	$0.495322\pi$
$212$	−3.70778e19	−0.624107
$213$	1.03011e20	1.66593
$214$	1.76530e17	0.00274347
$215$	−8.49197e18	−0.126847
$216$	9.35338e18	0.134311
$217$	2.91340e19	0.402246
$218$	5.44451e18	0.0722901
$219$	1.88674e19	0.240955
$220$	−8.91385e19	−1.09515
$221$	−1.59250e20	−1.88255
$222$	1.53172e19	0.174252
$223$	−5.12104e19	−0.560747	−0.280373	−	0.959891i	$-0.590458\pi$
$223$	−5.12104e19	−0.560747	−0.280373	+	0.959891i	$0.590458\pi$
$224$	−8.64750e18	−0.0911554
$225$	−3.28879e19	−0.333799
$226$	6.86103e18	0.0670607
$227$	−9.62999e19	−0.906580	−0.453290	−	0.891363i	$-0.649750\pi$
$227$	−9.62999e19	−0.906580	−0.453290	+	0.891363i	$0.649750\pi$
$228$	2.12430e20	1.92650
$229$	−1.05633e20	−0.922995	−0.461497	−	0.887142i	$-0.652688\pi$
$229$	−1.05633e20	−0.922995	−0.461497	+	0.887142i	$0.652688\pi$
$230$	−8.57354e18	−0.0721894
$231$	−1.41423e20	−1.14767
$232$	2.55198e18	0.0199631
$233$	8.12542e19	0.612802	0.306401	−	0.951902i	$-0.400875\pi$
$233$	8.12542e19	0.612802	0.306401	+	0.951902i	$0.400875\pi$
$234$	1.82771e19	0.132914
$235$	−1.47018e20	−1.03108
$236$	1.32110e20	0.893682
$237$	−2.24362e19	−0.146416
$238$	6.47475e18	0.0407679
$239$	−2.44589e20	−1.48612	−0.743061	−	0.669224i	$-0.766627\pi$
$239$	−2.44589e20	−1.48612	−0.743061	+	0.669224i	$0.766627\pi$
$240$	2.52371e20	1.47994
$241$	−2.96073e20	−1.67592	−0.837962	−	0.545729i	$-0.816253\pi$
$241$	−2.96073e20	−1.67592	−0.837962	+	0.545729i	$0.816253\pi$
$242$	4.82737e18	0.0263803
$243$	1.36165e20	0.718477
$244$	−3.48469e20	−1.77562
$245$	1.24124e20	0.610861
$246$	−3.04475e19	−0.144745
$247$	3.57126e20	1.64020
$248$	1.71967e19	0.0763143
$249$	−8.54349e19	−0.366388
$250$	1.39107e19	0.0576577
$251$	3.82864e20	1.53397	0.766987	−	0.641663i	$-0.221755\pi$
$251$	3.82864e20	1.53397	0.766987	+	0.641663i	$0.221755\pi$
$252$	2.55702e20	0.990444
$253$	−4.85783e20	−1.81936
$254$	3.58769e18	0.0129935
$255$	−5.69641e20	−1.99531
$256$	2.86632e20	0.971149
$257$	−3.75495e20	−1.23076	−0.615380	−	0.788231i	$-0.710997\pi$
$257$	−3.75495e20	−1.23076	−0.615380	+	0.788231i	$0.710997\pi$
$258$	−3.97052e18	−0.0125916
$259$	3.60255e20	1.10551
$260$	4.25512e20	1.26368
$261$	−1.13246e20	−0.325520
$262$	−8.12782e18	−0.0226159
$263$	1.04955e20	0.282734	0.141367	−	0.989957i	$-0.454850\pi$
$263$	1.04955e20	0.282734	0.141367	+	0.989957i	$0.454850\pi$
$264$	−8.34767e19	−0.217737
$265$	−2.22967e20	−0.563183
$266$	−1.45199e19	−0.0355198
$267$	−9.17435e20	−2.17385
$268$	1.34306e20	0.308284
$269$	5.15457e20	1.14630	0.573150	−	0.819451i	$-0.305721\pi$
$269$	5.15457e20	1.14630	0.573150	+	0.819451i	$0.305721\pi$
$270$	2.80824e19	0.0605121
$271$	−7.16586e20	−1.49634	−0.748168	−	0.663509i	$-0.769066\pi$
$271$	−7.16586e20	−1.49634	−0.748168	+	0.663509i	$0.769066\pi$
$272$	−6.54674e20	−1.32492
$273$	6.75096e20	1.32429
$274$	5.09826e18	0.00969487
$275$	1.26078e20	0.232440
$276$	1.37938e21	2.46579
$277$	−5.03082e20	−0.872089	−0.436045	−	0.899925i	$-0.643621\pi$
$277$	−5.03082e20	−0.872089	−0.436045	+	0.899925i	$0.643621\pi$
$278$	−5.24360e19	−0.0881554
$279$	−7.63116e20	−1.24439
$280$	−3.46509e19	−0.0548115
$281$	6.80781e19	0.104473	0.0522364	−	0.998635i	$-0.483365\pi$
$281$	6.80781e19	0.104473	0.0522364	+	0.998635i	$0.483365\pi$
$282$	−6.87401e19	−0.102351
$283$	2.36431e20	0.341602	0.170801	−	0.985306i	$-0.445365\pi$
$283$	2.36431e20	0.341602	0.170801	+	0.985306i	$0.445365\pi$
$284$	7.14005e20	1.00114
$285$	1.27744e21	1.73844
$286$	−7.00663e19	−0.0925546
$287$	−7.16116e20	−0.918306
$288$	2.26507e20	0.281998
$289$	6.50461e20	0.786303
$290$	7.66200e18	0.00899413
$291$	−1.53787e21	−1.75320
$292$	1.30776e20	0.144802
$293$	9.81753e20	1.05591	0.527956	−	0.849272i	$-0.322959\pi$
$293$	9.81753e20	1.05591	0.527956	+	0.849272i	$0.322959\pi$
$294$	5.80355e19	0.0606375
$295$	7.94439e20	0.806443
$296$	2.12646e20	0.209738
$297$	1.59117e21	1.52506
$298$	5.41268e19	0.0504167
$299$	2.31894e21	2.09934
$300$	−3.57997e20	−0.315028
$301$	−9.33856e19	−0.0798849
$302$	7.02744e19	0.0584438
$303$	−9.98255e20	−0.807196
$304$	1.46814e21	1.15436
$305$	−2.09551e21	−1.60229
$306$	−1.69595e20	−0.126119
$307$	−1.39865e21	−1.01166	−0.505829	−	0.862634i	$-0.668813\pi$
$307$	−1.39865e21	−1.01166	−0.505829	+	0.862634i	$0.668813\pi$
$308$	−9.80250e20	−0.689693
$309$	6.92515e20	0.474004
$310$	5.16310e19	0.0343824
$311$	1.57233e21	1.01878	0.509389	−	0.860536i	$-0.329871\pi$
$311$	1.57233e21	1.01878	0.509389	+	0.860536i	$0.329871\pi$
$312$	3.98485e20	0.251245
$313$	1.42767e21	0.875995	0.437997	−	0.898976i	$-0.355688\pi$
$313$	1.42767e21	0.875995	0.437997	+	0.898976i	$0.355688\pi$
$314$	−1.10770e20	−0.0661488
$315$	1.53766e21	0.893759
$316$	−1.55513e20	−0.0879887
$317$	−7.25852e20	−0.399801	−0.199901	−	0.979816i	$-0.564062\pi$
$317$	−7.25852e20	−0.399801	−0.199901	+	0.979816i	$0.564062\pi$
$318$	−1.04251e20	−0.0559047
$319$	4.34134e20	0.226675
$320$	1.73903e21	0.884162
$321$	−1.70792e20	−0.0845619
$322$	−9.42826e19	−0.0454629
$323$	−3.31381e21	−1.55635
$324$	−6.97366e20	−0.319028
$325$	−6.01845e20	−0.268211
$326$	−1.85940e20	−0.0807280
$327$	−5.26755e21	−2.22819
$328$	−4.22697e20	−0.174221
$329$	−1.61675e21	−0.649348
$330$	−2.50628e20	−0.0980984
$331$	−3.70574e20	−0.141363	−0.0706816	−	0.997499i	$-0.522517\pi$
$331$	−3.70574e20	−0.141363	−0.0706816	+	0.997499i	$0.522517\pi$
$332$	−5.92179e20	−0.220181
$333$	−9.43629e21	−3.41999
$334$	−8.70943e19	−0.0307712
$335$	8.07648e20	0.278190
$336$	2.77530e21	0.932023
$337$	5.35150e21	1.75235	0.876176	−	0.481991i	$-0.160086\pi$
$337$	5.35150e21	1.75235	0.876176	+	0.481991i	$0.160086\pi$
$338$	1.65884e20	0.0529678
$339$	−6.63803e21	−2.06701
$340$	−3.94838e21	−1.19908
$341$	2.92545e21	0.866524
$342$	3.80325e20	0.109884
$343$	3.37552e21	0.951351
$344$	−5.51221e19	−0.0151558
$345$	8.29487e21	2.22509
$346$	−7.95067e19	−0.0208093
$347$	−1.00040e20	−0.0255490	−0.0127745	−	0.999918i	$-0.504066\pi$
$347$	−1.00040e20	−0.0255490	−0.0127745	+	0.999918i	$0.504066\pi$
$348$	−1.23272e21	−0.307215
$349$	5.96784e21	1.45145	0.725723	−	0.687987i	$-0.241505\pi$
$349$	5.96784e21	1.45145	0.725723	+	0.687987i	$0.241505\pi$
$350$	2.44696e19	0.00580830
$351$	−7.59561e21	−1.75975
$352$	−8.68328e20	−0.196368
$353$	1.28562e21	0.283811	0.141905	−	0.989880i	$-0.454677\pi$
$353$	1.28562e21	0.283811	0.141905	+	0.989880i	$0.454677\pi$
$354$	3.71450e20	0.0800520
$355$	4.29365e21	0.903412
$356$	−6.35906e21	−1.30638
$357$	−6.26430e21	−1.25659
$358$	1.72483e20	0.0337864
$359$	−4.59597e21	−0.879173	−0.439587	−	0.898200i	$-0.644875\pi$
$359$	−4.59597e21	−0.879173	−0.439587	+	0.898200i	$0.644875\pi$
$360$	9.07624e20	0.169564
$361$	1.95099e21	0.355995
$362$	−3.02848e20	−0.0539761
$363$	−4.67046e21	−0.813118
$364$	4.67932e21	0.795832
$365$	7.86421e20	0.130667
$366$	−9.79781e20	−0.159052
$367$	−2.58887e21	−0.410629	−0.205314	−	0.978696i	$-0.565822\pi$
$367$	−2.58887e21	−0.410629	−0.205314	+	0.978696i	$0.565822\pi$
$368$	9.53309e21	1.47750
$369$	1.87575e22	2.84086
$370$	6.38442e20	0.0944946
$371$	−2.45195e21	−0.354677
$372$	−8.30681e21	−1.17441
$373$	4.09666e21	0.566115	0.283057	−	0.959103i	$-0.408651\pi$
$373$	4.09666e21	0.566115	0.283057	+	0.959103i	$0.408651\pi$
$374$	6.50154e20	0.0878228
$375$	−1.34585e22	−1.77718
$376$	−9.54307e20	−0.123195
$377$	−2.07239e21	−0.261559
$378$	3.08820e20	0.0381088
$379$	3.95807e21	0.477584	0.238792	−	0.971071i	$-0.423249\pi$
$379$	3.95807e21	0.477584	0.238792	+	0.971071i	$0.423249\pi$
$380$	8.85441e21	1.04472
$381$	−3.47107e21	−0.400499
$382$	−3.03191e20	−0.0342120
$383$	1.39722e22	1.54197	0.770985	−	0.636853i	$-0.219764\pi$
$383$	1.39722e22	1.54197	0.770985	+	0.636853i	$0.219764\pi$
$384$	3.28588e21	0.354680
$385$	−5.89471e21	−0.622367
$386$	4.02052e20	0.0415231
$387$	2.44608e21	0.247131
$388$	−1.06595e22	−1.05358
$389$	−1.63212e22	−1.57826	−0.789132	−	0.614224i	$-0.789469\pi$
$389$	−1.63212e22	−1.57826	−0.789132	+	0.614224i	$0.789469\pi$
$390$	1.19640e21	0.113195
$391$	−2.15177e22	−1.99202
$392$	8.05697e20	0.0729861
$393$	7.86364e21	0.697087
$394$	1.56324e20	0.0135615
$395$	−9.35176e20	−0.0793995
$396$	2.56760e22	2.13363
$397$	−9.90803e20	−0.0805875	−0.0402938	−	0.999188i	$-0.512829\pi$
$397$	−9.90803e20	−0.0805875	−0.0402938	+	0.999188i	$0.512829\pi$
$398$	−3.95985e20	−0.0315263
$399$	1.40480e22	1.09482
$400$	−2.47417e21	−0.188764
$401$	−2.98533e21	−0.222980	−0.111490	−	0.993766i	$-0.535562\pi$
$401$	−2.98533e21	−0.222980	−0.111490	+	0.993766i	$0.535562\pi$
$402$	3.77625e20	0.0276147
$403$	−1.39649e22	−0.999877
$404$	−6.91925e21	−0.485084
$405$	−4.19360e21	−0.287885
$406$	8.42584e19	0.00566425
$407$	3.61746e22	2.38150
$408$	−3.69759e21	−0.238400
$409$	1.65249e21	0.104350	0.0521749	−	0.998638i	$-0.483385\pi$
$409$	1.65249e21	0.104350	0.0521749	+	0.998638i	$0.483385\pi$
$410$	−1.26910e21	−0.0784931
$411$	−4.93255e21	−0.298824
$412$	4.80006e21	0.284853
$413$	8.73639e21	0.507875
$414$	2.46958e21	0.140644
$415$	−3.56106e21	−0.198687
$416$	4.14506e21	0.226588
$417$	5.07316e22	2.71721
$418$	−1.45800e21	−0.0765172
$419$	−2.85949e22	−1.47051	−0.735257	−	0.677788i	$-0.762939\pi$
$419$	−2.85949e22	−1.47051	−0.735257	+	0.677788i	$0.762939\pi$
$420$	1.67380e22	0.843500
$421$	1.51584e22	0.748609	0.374305	−	0.927306i	$-0.377881\pi$
$421$	1.51584e22	0.748609	0.374305	+	0.927306i	$0.377881\pi$
$422$	3.26880e19	0.00158210
$423$	4.23480e22	2.00882
$424$	−1.44730e21	−0.0672895
$425$	5.58459e21	0.254499
$426$	2.00755e21	0.0896777
$427$	−2.30442e22	−1.00908
$428$	−1.18382e21	−0.0508175
$429$	6.77889e22	2.85280
$430$	−1.65497e20	−0.00682824
$431$	−3.55571e22	−1.43837	−0.719183	−	0.694821i	$-0.755483\pi$
$431$	−3.55571e22	−1.43837	−0.719183	+	0.694821i	$0.755483\pi$
$432$	−3.12254e22	−1.23850
$433$	2.14410e22	0.833867	0.416934	−	0.908937i	$-0.363105\pi$
$433$	2.14410e22	0.833867	0.416934	+	0.908937i	$0.363105\pi$
$434$	5.67783e20	0.0216531
$435$	−7.41296e21	−0.277225
$436$	−3.65112e22	−1.33903
$437$	4.82544e22	1.73558
$438$	3.67700e20	0.0129707
$439$	−2.13072e22	−0.737188	−0.368594	−	0.929591i	$-0.620161\pi$
$439$	−2.13072e22	−0.737188	−0.368594	+	0.929591i	$0.620161\pi$
$440$	−3.47943e21	−0.118076
$441$	−3.57533e22	−1.19011
$442$	−3.10358e21	−0.101338
$443$	−2.64440e21	−0.0847024	−0.0423512	−	0.999103i	$-0.513485\pi$
$443$	−2.64440e21	−0.0847024	−0.0423512	+	0.999103i	$0.513485\pi$
$444$	−1.02718e23	−3.22768
$445$	−3.82401e22	−1.17885
$446$	−9.98023e20	−0.0301852
$447$	−5.23675e22	−1.55399
$448$	1.91240e22	0.556820
$449$	3.66791e22	1.04791	0.523955	−	0.851746i	$-0.324456\pi$
$449$	3.66791e22	1.04791	0.523955	+	0.851746i	$0.324456\pi$
$450$	−6.40942e20	−0.0179685
$451$	−7.19079e22	−1.97823
$452$	−4.60105e22	−1.24217
$453$	−6.79903e22	−1.80141
$454$	−1.87676e21	−0.0488015
$455$	2.81390e22	0.718145
$456$	8.29200e21	0.207710
$457$	2.39001e21	0.0587642	0.0293821	−	0.999568i	$-0.490646\pi$
$457$	2.39001e21	0.0587642	0.0293821	+	0.999568i	$0.490646\pi$
$458$	−2.05865e21	−0.0496852
$459$	7.04805e22	1.66979
$460$	5.74946e22	1.33717
$461$	2.47250e22	0.564520	0.282260	−	0.959338i	$-0.408916\pi$
$461$	2.47250e22	0.564520	0.282260	+	0.959338i	$0.408916\pi$
$462$	−2.75614e21	−0.0617796
$463$	3.13719e22	0.690402	0.345201	−	0.938529i	$-0.387811\pi$
$463$	3.13719e22	0.690402	0.345201	+	0.938529i	$0.387811\pi$
$464$	−8.51953e21	−0.184083
$465$	−4.99528e22	−1.05977
$466$	1.58354e21	0.0329874
$467$	−4.29573e22	−0.878706	−0.439353	−	0.898315i	$-0.644792\pi$
$467$	−4.29573e22	−0.878706	−0.439353	+	0.898315i	$0.644792\pi$
$468$	−1.22567e23	−2.46198
$469$	8.88165e21	0.175196
$470$	−2.86519e21	−0.0555037
$471$	1.07170e23	2.03890
$472$	5.15677e21	0.0963543
$473$	−9.37720e21	−0.172089
$474$	−4.37253e20	−0.00788164
$475$	−1.25237e22	−0.221736
$476$	−4.34200e22	−0.755146
$477$	6.42247e22	1.09723
$478$	−4.76671e21	−0.0799985
$479$	1.17283e23	1.93368	0.966839	−	0.255388i	$-0.0822032\pi$
$479$	1.17283e23	1.93368	0.966839	+	0.255388i	$0.0822032\pi$
$480$	1.48269e22	0.240160
$481$	−1.72683e23	−2.74800
$482$	−5.77008e21	−0.0902157
$483$	9.12181e22	1.40130
$484$	−3.23726e22	−0.488643
$485$	−6.41009e22	−0.950735
$486$	2.65368e21	0.0386759
$487$	−7.07916e22	−1.01388	−0.506939	−	0.861982i	$-0.669223\pi$
$487$	−7.07916e22	−1.01388	−0.506939	+	0.861982i	$0.669223\pi$
$488$	−1.36021e22	−0.191443
$489$	1.79897e23	2.48827
$490$	2.41900e21	0.0328829
$491$	1.04343e23	1.39402	0.697009	−	0.717062i	$-0.254514\pi$
$491$	1.04343e23	1.39402	0.697009	+	0.717062i	$0.254514\pi$
$492$	2.04182e23	2.68111
$493$	1.92299e22	0.248187
$494$	6.95991e21	0.0882927
$495$	1.54402e23	1.92535
$496$	−5.74096e22	−0.703704
$497$	4.72170e22	0.568943
$498$	−1.66501e21	−0.0197228
$499$	−1.07405e23	−1.25075	−0.625373	−	0.780326i	$-0.715053\pi$
$499$	−1.07405e23	−1.25075	−0.625373	+	0.780326i	$0.715053\pi$
$500$	−9.32856e22	−1.06800
$501$	8.42634e22	0.948459
$502$	7.46152e21	0.0825744
$503$	−2.30240e22	−0.250527	−0.125263	−	0.992124i	$-0.539978\pi$
$503$	−2.30240e22	−0.250527	−0.125263	+	0.992124i	$0.539978\pi$
$504$	9.98108e21	0.106787
$505$	−4.16088e22	−0.437732
$506$	−9.46727e21	−0.0979367
$507$	−1.60492e23	−1.63262
$508$	−2.40592e22	−0.240680
$509$	−1.30026e23	−1.27917	−0.639584	−	0.768721i	$-0.720893\pi$
$509$	−1.30026e23	−1.27917	−0.639584	+	0.768721i	$0.720893\pi$
$510$	−1.11015e22	−0.107408
$511$	8.64821e21	0.0822903
$512$	2.84279e22	0.266042
$513$	−1.58056e23	−1.45483
$514$	−7.31791e21	−0.0662523
$515$	2.88650e22	0.257046
$516$	2.66265e22	0.233234
$517$	−1.62344e23	−1.39883
$518$	7.02090e21	0.0595100
$519$	7.69225e22	0.641403
$520$	1.66094e22	0.136247
$521$	−1.40296e23	−1.13221	−0.566104	−	0.824334i	$-0.691550\pi$
$521$	−1.40296e23	−1.13221	−0.566104	+	0.824334i	$0.691550\pi$
$522$	−2.20701e21	−0.0175229
$523$	1.22013e23	0.953105	0.476553	−	0.879146i	$-0.341886\pi$
$523$	1.22013e23	0.953105	0.476553	+	0.879146i	$0.341886\pi$
$524$	5.45056e22	0.418914
$525$	−2.36743e22	−0.179029
$526$	2.04543e21	0.0152197
$527$	1.29582e23	0.948759
$528$	2.78679e23	2.00778
$529$	1.72282e23	1.22142
$530$	−4.34533e21	−0.0303164
$531$	−2.28835e23	−1.57116
$532$	9.73713e22	0.657934
$533$	3.43260e23	2.28266
$534$	−1.78796e22	−0.117019
$535$	−7.11887e21	−0.0458568
$536$	5.24251e21	0.0332383
$537$	−1.66877e23	−1.04139
$538$	1.00456e22	0.0617058
$539$	1.37063e23	0.828733
$540$	−1.88322e23	−1.12087
$541$	−8.56150e22	−0.501618	−0.250809	−	0.968037i	$-0.580697\pi$
$541$	−8.56150e22	−0.501618	−0.250809	+	0.968037i	$0.580697\pi$
$542$	−1.39653e22	−0.0805484
$543$	2.93004e23	1.66370
$544$	−3.84625e22	−0.215004
$545$	−2.19559e23	−1.20832
$546$	1.31567e22	0.0712871
$547$	2.78919e23	1.48794	0.743971	−	0.668212i	$-0.232940\pi$
$547$	2.78919e23	1.48794	0.743971	+	0.668212i	$0.232940\pi$
$548$	−3.41892e22	−0.179578
$549$	6.03604e23	3.12167
$550$	2.45709e21	0.0125123
$551$	−4.31240e22	−0.216237
$552$	5.38427e22	0.265855
$553$	−1.02841e22	−0.0500036
$554$	−9.80441e21	−0.0469449
$555$	−6.17691e23	−2.91260
$556$	3.51639e23	1.63290
$557$	−1.69610e23	−0.775678	−0.387839	−	0.921727i	$-0.626778\pi$
$557$	−1.69610e23	−0.775678	−0.387839	+	0.921727i	$0.626778\pi$
$558$	−1.48721e22	−0.0669857
$559$	4.47630e22	0.198573
$560$	1.15679e23	0.505424
$561$	−6.29022e23	−2.70696
$562$	1.32675e21	0.00562382
$563$	−3.29493e23	−1.37570	−0.687852	−	0.725851i	$-0.741446\pi$
$563$	−3.29493e23	−1.37570	−0.687852	+	0.725851i	$0.741446\pi$
$564$	4.60975e23	1.89585
$565$	−2.76683e23	−1.12091
$566$	4.60773e21	0.0183886
$567$	−4.61167e22	−0.181302
$568$	2.78705e22	0.107940
$569$	1.05677e23	0.403206	0.201603	−	0.979467i	$-0.435385\pi$
$569$	1.05677e23	0.403206	0.201603	+	0.979467i	$0.435385\pi$
$570$	2.48957e22	0.0935812
$571$	−1.32465e22	−0.0490563	−0.0245281	−	0.999699i	$-0.507808\pi$
$571$	−1.32465e22	−0.0490563	−0.0245281	+	0.999699i	$0.507808\pi$
$572$	4.69869e23	1.71439
$573$	2.93337e23	1.05451
$574$	−1.39562e22	−0.0494328
$575$	−8.13205e22	−0.283807
$576$	−5.00921e23	−1.72257
$577$	4.02544e23	1.36402	0.682008	−	0.731345i	$-0.261107\pi$
$577$	4.02544e23	1.36402	0.682008	+	0.731345i	$0.261107\pi$
$578$	1.26766e22	0.0423270
$579$	−3.88984e23	−1.27986
$580$	−5.13818e22	−0.166599
$581$	−3.91607e22	−0.125128
$582$	−2.99712e22	−0.0943753
$583$	−2.46209e23	−0.764050
$584$	5.10473e21	0.0156122
$585$	−7.37055e23	−2.22165
$586$	1.91331e22	0.0568402
$587$	4.56104e23	1.33549	0.667745	−	0.744390i	$-0.267260\pi$
$587$	4.56104e23	1.33549	0.667745	+	0.744390i	$0.267260\pi$
$588$	−3.89189e23	−1.12319
$589$	−2.90594e23	−0.826623
$590$	1.54826e22	0.0434111
$591$	−1.51243e23	−0.418004
$592$	−7.09897e23	−1.93402
$593$	3.60874e23	0.969149	0.484575	−	0.874750i	$-0.338974\pi$
$593$	3.60874e23	0.969149	0.484575	+	0.874750i	$0.338974\pi$
$594$	3.10098e22	0.0820945
$595$	−2.61105e23	−0.681430
$596$	−3.62977e23	−0.933870
$597$	3.83114e23	0.971732
$598$	4.51930e22	0.113009
$599$	4.64168e23	1.14432	0.572160	−	0.820142i	$-0.306106\pi$
$599$	4.64168e23	1.14432	0.572160	+	0.820142i	$0.306106\pi$
$600$	−1.39741e22	−0.0339655
$601$	−8.15409e22	−0.195408	−0.0977040	−	0.995216i	$-0.531150\pi$
$601$	−8.15409e22	−0.195408	−0.0977040	+	0.995216i	$0.531150\pi$
$602$	−1.81996e21	−0.00430023
$603$	−2.32640e23	−0.541985
$604$	−4.71264e23	−1.08256
$605$	−1.94672e23	−0.440943
$606$	−1.94547e22	−0.0434517
$607$	−6.31110e22	−0.138996	−0.0694978	−	0.997582i	$-0.522140\pi$
$607$	−6.31110e22	−0.138996	−0.0694978	+	0.997582i	$0.522140\pi$
$608$	8.62538e22	0.187326
$609$	−8.15198e22	−0.174589
$610$	−4.08387e22	−0.0862519
$611$	7.74965e23	1.61411
$612$	1.13732e24	2.33611
$613$	−4.91922e23	−0.996511	−0.498256	−	0.867030i	$-0.666026\pi$
$613$	−4.91922e23	−0.996511	−0.498256	+	0.867030i	$0.666026\pi$
$614$	−2.72579e22	−0.0544579
$615$	1.22785e24	2.41939
$616$	−3.82631e22	−0.0743608
$617$	3.00531e23	0.576056	0.288028	−	0.957622i	$-0.407000\pi$
$617$	3.00531e23	0.576056	0.288028	+	0.957622i	$0.407000\pi$
$618$	1.34962e22	0.0255158
$619$	−8.49651e23	−1.58442	−0.792210	−	0.610249i	$-0.791069\pi$
$619$	−8.49651e23	−1.58442	−0.792210	+	0.610249i	$0.791069\pi$
$620$	−3.46240e23	−0.636866
$621$	−1.02631e24	−1.86208
$622$	3.06426e22	0.0548412
$623$	−4.20523e23	−0.742406
$624$	−1.33030e24	−2.31676
$625$	−4.50133e23	−0.773323
$626$	2.78234e22	0.0471551
$627$	1.41061e24	2.35848
$628$	7.42833e23	1.22528
$629$	1.60235e24	2.60751
$630$	2.99670e22	0.0481114
$631$	−1.93048e23	−0.305785	−0.152893	−	0.988243i	$-0.548859\pi$
$631$	−1.93048e23	−0.305785	−0.152893	+	0.988243i	$0.548859\pi$
$632$	−6.07031e21	−0.00948670
$633$	−3.16255e22	−0.0487648
$634$	−1.41459e22	−0.0215215
$635$	−1.44680e23	−0.217185
$636$	6.99111e23	1.03552
$637$	−6.54283e23	−0.956269
$638$	8.46071e21	0.0122020
$639$	−1.23677e24	−1.76008
$640$	1.36961e23	0.192338
$641$	5.24529e23	0.726903	0.363451	−	0.931613i	$-0.381598\pi$
$641$	5.24529e23	0.726903	0.363451	+	0.931613i	$0.381598\pi$
$642$	−3.32851e21	−0.00455200
$643$	−2.31290e23	−0.312150	−0.156075	−	0.987745i	$-0.549884\pi$
$643$	−2.31290e23	−0.312150	−0.156075	+	0.987745i	$0.549884\pi$
$644$	6.32264e23	0.842110
$645$	1.60118e23	0.210466
$646$	−6.45819e22	−0.0837788
$647$	7.94058e23	1.01664	0.508318	−	0.861169i	$-0.330267\pi$
$647$	7.94058e23	1.01664	0.508318	+	0.861169i	$0.330267\pi$
$648$	−2.72210e22	−0.0343967
$649$	8.77254e23	1.09407
$650$	−1.17292e22	−0.0144379
$651$	−5.49328e23	−0.667411
$652$	1.24693e24	1.49533
$653$	−1.36083e24	−1.61080	−0.805398	−	0.592734i	$-0.798048\pi$
$653$	−1.36083e24	−1.61080	−0.805398	+	0.592734i	$0.798048\pi$
$654$	−1.02658e23	−0.119944
$655$	3.27768e23	0.378021
$656$	1.41113e24	1.60652
$657$	−2.26526e23	−0.254573
$658$	−3.15083e22	−0.0349546
$659$	−7.29550e23	−0.798968	−0.399484	−	0.916740i	$-0.630811\pi$
$659$	−7.29550e23	−0.798968	−0.399484	+	0.916740i	$0.630811\pi$
$660$	1.68073e24	1.81708
$661$	−1.20400e24	−1.28503	−0.642515	−	0.766273i	$-0.722109\pi$
$661$	−1.20400e24	−1.28503	−0.642515	+	0.766273i	$0.722109\pi$
$662$	−7.22199e21	−0.00760964
$663$	3.00270e24	3.12354
$664$	−2.31151e22	−0.0237393
$665$	5.85540e23	0.593708
$666$	−1.83901e23	−0.184100
$667$	−2.80018e23	−0.276768
$668$	5.84059e23	0.569976
$669$	9.65584e23	0.930397
$670$	1.57400e22	0.0149751
$671$	−2.31395e24	−2.17377
$672$	1.63051e23	0.151246
$673$	−8.62749e23	−0.790235	−0.395118	−	0.918630i	$-0.629296\pi$
$673$	−8.62749e23	−0.790235	−0.395118	+	0.918630i	$0.629296\pi$
$674$	1.04294e23	0.0943298
$675$	2.66363e23	0.237899
$676$	−1.11243e24	−0.981124
$677$	−1.43773e24	−1.25220	−0.626099	−	0.779743i	$-0.715349\pi$
$677$	−1.43773e24	−1.25220	−0.626099	+	0.779743i	$0.715349\pi$
$678$	−1.29366e23	−0.111268
$679$	−7.04913e23	−0.598746
$680$	−1.54121e23	−0.129281
$681$	1.81576e24	1.50421
$682$	5.70132e22	0.0466453
$683$	6.24758e22	0.0504819	0.0252409	−	0.999681i	$-0.491965\pi$
$683$	6.24758e22	0.0504819	0.0252409	+	0.999681i	$0.491965\pi$
$684$	−2.55048e24	−2.03538
$685$	−2.05596e23	−0.162048
$686$	6.57845e22	0.0512116
$687$	1.99174e24	1.53144
$688$	1.84020e23	0.139754
$689$	1.17531e24	0.881632
$690$	1.61656e23	0.119777
$691$	−2.01108e24	−1.47186	−0.735930	−	0.677058i	$-0.763255\pi$
$691$	−2.01108e24	−1.47186	−0.735930	+	0.677058i	$0.763255\pi$
$692$	5.33176e23	0.385451
$693$	1.69795e24	1.21253
$694$	−1.94965e21	−0.00137531
$695$	2.11457e24	1.47350
$696$	−4.81181e22	−0.0331230
$697$	−3.18515e24	−2.16596
$698$	1.16305e23	0.0781319
$699$	−1.53207e24	−1.01677
$700$	−1.64095e23	−0.107587
$701$	−1.31601e24	−0.852425	−0.426212	−	0.904623i	$-0.640152\pi$
$701$	−1.31601e24	−0.852425	−0.426212	+	0.904623i	$0.640152\pi$
$702$	−1.48028e23	−0.0947283
$703$	−3.59334e24	−2.27184
$704$	1.92031e24	1.19951
$705$	2.77206e24	1.71079
$706$	2.50551e22	0.0152776
$707$	−4.57569e23	−0.275671
$708$	−2.49096e24	−1.48281
$709$	7.01345e23	0.412514	0.206257	−	0.978498i	$-0.433872\pi$
$709$	7.01345e23	0.412514	0.206257	+	0.978498i	$0.433872\pi$
$710$	8.36777e22	0.0486310
$711$	2.69374e23	0.154691
$712$	−2.48220e23	−0.140850
$713$	−1.88693e24	−1.05802
$714$	−1.22083e23	−0.0676426
$715$	2.82555e24	1.54704
$716$	−1.15668e24	−0.625826
$717$	4.61178e24	2.46579
$718$	−8.95694e22	−0.0473262
$719$	−8.89271e23	−0.464343	−0.232171	−	0.972675i	$-0.574583\pi$
$719$	−8.89271e23	−0.464343	−0.232171	+	0.972675i	$0.574583\pi$
$720$	−3.03002e24	−1.56358
$721$	3.17427e23	0.161880
$722$	3.80222e22	0.0191633
$723$	5.58253e24	2.78071
$724$	2.03091e24	0.999801
$725$	7.26745e22	0.0353597
$726$	−9.10212e22	−0.0437705
$727$	−9.59968e23	−0.456262	−0.228131	−	0.973630i	$-0.573261\pi$
$727$	−9.59968e23	−0.456262	−0.228131	+	0.973630i	$0.573261\pi$
$728$	1.82653e23	0.0858044
$729$	−3.25651e24	−1.51206
$730$	1.53263e22	0.00703385
$731$	−4.15362e23	−0.188421
$732$	6.57046e24	2.94613
$733$	2.57462e24	1.14112	0.570558	−	0.821257i	$-0.306727\pi$
$733$	2.57462e24	1.14112	0.570558	+	0.821257i	$0.306727\pi$
$734$	−5.04537e22	−0.0221043
$735$	−2.34038e24	−1.01355
$736$	5.60075e23	0.239764
$737$	8.91840e23	0.377410
$738$	3.65558e23	0.152925
$739$	−2.94397e24	−1.21746	−0.608731	−	0.793377i	$-0.708321\pi$
$739$	−2.94397e24	−1.21746	−0.608731	+	0.793377i	$0.708321\pi$
$740$	−4.28143e24	−1.75033
$741$	−6.73369e24	−2.72144
$742$	−4.77852e22	−0.0190924
$743$	−1.10562e24	−0.436719	−0.218359	−	0.975868i	$-0.570070\pi$
$743$	−1.10562e24	−0.436719	−0.218359	+	0.975868i	$0.570070\pi$
$744$	−3.24248e23	−0.126622
$745$	−2.18276e24	−0.842708
$746$	7.98385e22	0.0304742
$747$	1.02575e24	0.387094
$748$	−4.35997e24	−1.62675
$749$	−7.82857e22	−0.0288793
$750$	−2.62289e23	−0.0956663
$751$	−5.32694e24	−1.92105	−0.960523	−	0.278199i	$-0.910263\pi$
$751$	−5.32694e24	−1.92105	−0.960523	+	0.278199i	$0.910263\pi$
$752$	3.18586e24	1.13599
$753$	−7.21899e24	−2.54518
$754$	−4.03881e22	−0.0140798
$755$	−2.83394e24	−0.976880
$756$	−2.07096e24	−0.705890
$757$	5.68982e24	1.91771	0.958857	−	0.283890i	$-0.0916251\pi$
$757$	5.68982e24	1.91771	0.958857	+	0.283890i	$0.0916251\pi$
$758$	7.71375e22	0.0257085
$759$	9.15956e24	3.01870
$760$	3.45623e23	0.112639
$761$	−2.00377e24	−0.645770	−0.322885	−	0.946438i	$-0.604653\pi$
$761$	−2.00377e24	−0.645770	−0.322885	+	0.946438i	$0.604653\pi$
$762$	−6.76467e22	−0.0215590
$763$	−2.41448e24	−0.760965
$764$	2.03322e24	0.633710
$765$	6.83922e24	2.10807
$766$	2.72300e23	0.0830048
$767$	−4.18766e24	−1.26244
$768$	−5.40452e24	−1.61134
$769$	5.67344e24	1.67291	0.836455	−	0.548036i	$-0.184624\pi$
$769$	5.67344e24	1.67291	0.836455	+	0.548036i	$0.184624\pi$
$770$	−1.14880e23	−0.0335022
$771$	7.08006e24	2.04209
$772$	−2.69618e24	−0.769134
$773$	−2.77759e24	−0.783686	−0.391843	−	0.920032i	$-0.628162\pi$
$773$	−2.77759e24	−0.783686	−0.391843	+	0.920032i	$0.628162\pi$
$774$	4.76709e22	0.0133032
$775$	4.89723e23	0.135172
$776$	−4.16085e23	−0.113594
$777$	−6.79270e24	−1.83427
$778$	−3.18078e23	−0.0849585
$779$	7.14284e24	1.88713
$780$	−8.02313e24	−2.09672
$781$	4.74124e24	1.22563
$782$	−4.19351e23	−0.107231
$783$	9.17191e23	0.231998
$784$	−2.68974e24	−0.673014
$785$	4.46701e24	1.10567
$786$	1.53252e23	0.0375245
$787$	−2.82408e24	−0.684057	−0.342029	−	0.939690i	$-0.611114\pi$
$787$	−2.82408e24	−0.684057	−0.342029	+	0.939690i	$0.611114\pi$
$788$	−1.04831e24	−0.251199
$789$	−1.97895e24	−0.469115
$790$	−1.82253e22	−0.00427411
$791$	−3.04266e24	−0.705917
$792$	1.00224e24	0.230042
$793$	1.10459e25	2.50830
$794$	−1.93094e22	−0.00433806
$795$	4.20409e24	0.934440
$796$	2.65550e24	0.583962
$797$	3.11696e24	0.678165	0.339083	−	0.940757i	$-0.389883\pi$
$797$	3.11696e24	0.678165	0.339083	+	0.940757i	$0.389883\pi$
$798$	2.73776e23	0.0589348
$799$	−7.19099e24	−1.53159
$800$	−1.45359e23	−0.0306321
$801$	1.10149e25	2.29670
$802$	−5.81803e22	−0.0120031
$803$	8.68400e23	0.177271
$804$	−2.53238e24	−0.511507
$805$	3.80211e24	0.759905
$806$	−2.72158e23	−0.0538238
$807$	−9.71907e24	−1.90195
$808$	−2.70086e23	−0.0523005
$809$	3.12323e24	0.598468	0.299234	−	0.954180i	$-0.403269\pi$
$809$	3.12323e24	0.598468	0.299234	+	0.954180i	$0.403269\pi$
$810$	−8.17277e22	−0.0154970
$811$	−7.42465e23	−0.139315	−0.0696576	−	0.997571i	$-0.522191\pi$
$811$	−7.42465e23	−0.139315	−0.0696576	+	0.997571i	$0.522191\pi$
$812$	−5.65042e23	−0.104919
$813$	1.35114e25	2.48274
$814$	7.04995e23	0.128197
$815$	7.49837e24	1.34936
$816$	1.23440e25	2.19832
$817$	9.31467e23	0.164165
$818$	3.22050e22	0.00561720
$819$	−8.10534e24	−1.39913
$820$	8.51063e24	1.45393
$821$	−1.28823e23	−0.0217809	−0.0108905	−	0.999941i	$-0.503467\pi$
$821$	−1.28823e23	−0.0217809	−0.0108905	+	0.999941i	$0.503467\pi$
$822$	−9.61288e22	−0.0160858
$823$	8.56178e24	1.41796	0.708982	−	0.705226i	$-0.249155\pi$
$823$	8.56178e24	1.41796	0.708982	+	0.705226i	$0.249155\pi$
$824$	1.87366e23	0.0307120
$825$	−2.37723e24	−0.385666
$826$	1.70261e23	0.0273391
$827$	−3.61352e24	−0.574292	−0.287146	−	0.957887i	$-0.592707\pi$
$827$	−3.61352e24	−0.574292	−0.287146	+	0.957887i	$0.592707\pi$
$828$	−1.65611e25	−2.60514
$829$	−1.17676e25	−1.83221	−0.916105	−	0.400938i	$-0.868684\pi$
$829$	−1.17676e25	−1.83221	−0.916105	+	0.400938i	$0.868684\pi$
$830$	−6.94003e22	−0.0106954
$831$	9.48574e24	1.44698
$832$	−9.16680e24	−1.38411
$833$	6.07117e24	0.907381
$834$	9.88693e23	0.146268
$835$	3.51223e24	0.514337
$836$	9.77742e24	1.41733
$837$	6.18057e24	0.886874
$838$	−5.57277e23	−0.0791584
$839$	−5.73391e24	−0.806259	−0.403129	−	0.915143i	$-0.632078\pi$
$839$	−5.73391e24	−0.806259	−0.403129	+	0.915143i	$0.632078\pi$
$840$	6.53352e23	0.0909438
$841$	2.50246e23	0.0344828
$842$	2.95417e23	0.0402979
$843$	−1.28363e24	−0.173342
$844$	−2.19208e23	−0.0293052
$845$	−6.68955e24	−0.885349
$846$	8.25308e23	0.108135
$847$	−2.14079e24	−0.277694
$848$	4.83166e24	0.620485
$849$	−4.45797e24	−0.566789
$850$	1.08836e23	0.0136998
$851$	−2.33327e25	−2.90780
$852$	−1.34627e25	−1.66110
$853$	−1.17903e25	−1.44031	−0.720156	−	0.693813i	$-0.755930\pi$
$853$	−1.17903e25	−1.44031	−0.720156	+	0.693813i	$0.755930\pi$
$854$	−4.49101e23	−0.0543190
$855$	−1.53373e25	−1.83669
$856$	−4.62092e22	−0.00547900
$857$	1.09653e25	1.28731	0.643654	−	0.765317i	$-0.277418\pi$
$857$	1.09653e25	1.28731	0.643654	+	0.765317i	$0.277418\pi$
$858$	1.32112e24	0.153568
$859$	4.09625e24	0.471460	0.235730	−	0.971819i	$-0.424252\pi$
$859$	4.09625e24	0.471460	0.235730	+	0.971819i	$0.424252\pi$
$860$	1.10983e24	0.126480
$861$	1.35025e25	1.52366
$862$	−6.92961e23	−0.0774278
$863$	8.76772e24	0.970052	0.485026	−	0.874500i	$-0.338810\pi$
$863$	8.76772e24	0.970052	0.485026	+	0.874500i	$0.338810\pi$
$864$	−1.83451e24	−0.200980
$865$	3.20624e24	0.347824
$866$	4.17856e23	0.0448874
$867$	−1.22646e25	−1.30464
$868$	−3.80758e24	−0.401080
$869$	−1.03266e24	−0.107718
$870$	−1.44469e23	−0.0149231
$871$	−4.25729e24	−0.435491
$872$	−1.42518e24	−0.144371
$873$	1.84640e25	1.85228
$874$	9.40415e23	0.0934269
$875$	−6.16896e24	−0.606937
$876$	−2.46582e24	−0.240257
$877$	9.20364e24	0.888102	0.444051	−	0.896001i	$-0.353541\pi$
$877$	9.20364e24	0.888102	0.444051	+	0.896001i	$0.353541\pi$
$878$	−4.15250e23	−0.0396831
$879$	−1.85112e25	−1.75198
$880$	1.16158e25	1.08879
$881$	7.51021e24	0.697199	0.348600	−	0.937272i	$-0.386657\pi$
$881$	7.51021e24	0.697199	0.348600	+	0.937272i	$0.386657\pi$
$882$	−6.96786e23	−0.0640643
$883$	−2.44824e24	−0.222940	−0.111470	−	0.993768i	$-0.535556\pi$
$883$	−2.44824e24	−0.222940	−0.111470	+	0.993768i	$0.535556\pi$
$884$	2.08128e25	1.87709
$885$	−1.49793e25	−1.33806
$886$	−5.15359e22	−0.00455956
$887$	−2.99182e24	−0.262171	−0.131086	−	0.991371i	$-0.541846\pi$
$887$	−2.99182e24	−0.262171	−0.131086	+	0.991371i	$0.541846\pi$
$888$	−4.00948e24	−0.347999
$889$	−1.59103e24	−0.136777
$890$	−7.45249e23	−0.0634580
$891$	−4.63075e24	−0.390563
$892$	6.69280e24	0.559122
$893$	1.61261e25	1.33442
$894$	−1.02057e24	−0.0836518
$895$	−6.95569e24	−0.564734
$896$	1.50615e24	0.121129
$897$	−4.37241e25	−3.48325
$898$	7.14827e23	0.0564094
$899$	1.68631e24	0.131819
$900$	4.29819e24	0.332831
$901$	−1.09058e25	−0.836560
$902$	−1.40139e24	−0.106489
$903$	1.76081e24	0.132546
$904$	−1.79597e24	−0.133927
$905$	1.22129e25	0.902203
$906$	−1.32504e24	−0.0969705
$907$	−4.41603e24	−0.320162	−0.160081	−	0.987104i	$-0.551176\pi$
$907$	−4.41603e24	−0.320162	−0.160081	+	0.987104i	$0.551176\pi$
$908$	1.25856e25	0.903953
$909$	1.19853e25	0.852814
$910$	5.48393e23	0.0386580
$911$	7.37401e23	0.0514988	0.0257494	−	0.999668i	$-0.491803\pi$
$911$	7.37401e23	0.0514988	0.0257494	+	0.999668i	$0.491803\pi$
$912$	−2.76821e25	−1.91532
$913$	−3.93227e24	−0.269552
$914$	4.65782e22	0.00316330
$915$	3.95113e25	2.65854
$916$	1.38054e25	0.920320
$917$	3.60444e24	0.238067
$918$	1.37357e24	0.0898854
$919$	2.81949e24	0.182805	0.0914025	−	0.995814i	$-0.470865\pi$
$919$	2.81949e24	0.182805	0.0914025	+	0.995814i	$0.470865\pi$
$920$	2.24425e24	0.144170
$921$	2.63719e25	1.67855
$922$	4.81859e23	0.0303883
$923$	−2.26328e25	−1.41424
$924$	1.84828e25	1.14435
$925$	6.05566e24	0.371498
$926$	6.11397e23	0.0371646
$927$	−8.31447e24	−0.500792
$928$	−5.00527e23	−0.0298724
$929$	−2.66491e25	−1.57597	−0.787987	−	0.615691i	$-0.788877\pi$
$929$	−2.66491e25	−1.57597	−0.787987	+	0.615691i	$0.788877\pi$
$930$	−9.73515e23	−0.0570476
$931$	−1.36149e25	−0.790571
$932$	−1.06193e25	−0.611027
$933$	−2.96466e25	−1.69037
$934$	−8.37181e23	−0.0473011
$935$	−2.62186e25	−1.46795
$936$	−4.78429e24	−0.265444
$937$	2.40281e25	1.32109	0.660546	−	0.750786i	$-0.270325\pi$
$937$	2.40281e25	1.32109	0.660546	+	0.750786i	$0.270325\pi$
$938$	1.73092e23	0.00943087
$939$	−2.69191e25	−1.45346
$940$	1.92141e25	1.02810
$941$	−2.84838e25	−1.51038	−0.755191	−	0.655505i	$-0.772456\pi$
$941$	−2.84838e25	−1.51038	−0.755191	+	0.655505i	$0.772456\pi$
$942$	2.08860e24	0.109755
$943$	4.63808e25	2.41540
$944$	−1.72154e25	−0.888495
$945$	−1.24537e25	−0.636983
$946$	−1.82749e23	−0.00926363
$947$	−2.96161e25	−1.48783	−0.743915	−	0.668274i	$-0.767033\pi$
$947$	−2.96161e25	−1.48783	−0.743915	+	0.668274i	$0.767033\pi$
$948$	2.93224e24	0.145992
$949$	−4.14540e24	−0.204552
$950$	−2.44071e23	−0.0119362
$951$	1.36861e25	0.663355
$952$	−1.69486e24	−0.0814177
$953$	−2.13032e25	−1.01427	−0.507137	−	0.861865i	$-0.669296\pi$
$953$	−2.13032e25	−1.01427	−0.507137	+	0.861865i	$0.669296\pi$
$954$	1.25166e24	0.0590641
$955$	1.22267e25	0.571849
$956$	3.19658e25	1.48181
$957$	−8.18571e24	−0.376101
$958$	2.28570e24	0.104091
$959$	−2.26092e24	−0.102053
$960$	−3.27898e25	−1.46701
$961$	−1.11868e25	−0.496086
$962$	−3.36537e24	−0.147926
$963$	2.05056e24	0.0893408
$964$	3.86945e25	1.67107
$965$	−1.62134e25	−0.694053
$966$	1.77772e24	0.0754324
$967$	1.29168e25	0.543289	0.271645	−	0.962398i	$-0.412432\pi$
$967$	1.29168e25	0.543289	0.271645	+	0.962398i	$0.412432\pi$
$968$	−1.26363e24	−0.0526842
$969$	6.24827e25	2.58231
$970$	−1.24924e24	−0.0511785
$971$	2.16722e25	0.880117	0.440058	−	0.897969i	$-0.354958\pi$
$971$	2.16722e25	0.880117	0.440058	+	0.897969i	$0.354958\pi$
$972$	−1.77957e25	−0.716395
$973$	2.32538e25	0.927972
$974$	−1.37964e24	−0.0545775
$975$	1.13479e25	0.445018
$976$	4.54094e25	1.76532
$977$	4.15573e25	1.60156	0.800780	−	0.598959i	$-0.204419\pi$
$977$	4.15573e25	1.60156	0.800780	+	0.598959i	$0.204419\pi$
$978$	3.50595e24	0.133945
$979$	−4.22263e25	−1.59930
$980$	−1.62220e25	−0.609091
$981$	6.32432e25	2.35411
$982$	2.03350e24	0.0750406
$983$	−1.75624e25	−0.642510	−0.321255	−	0.946993i	$-0.604105\pi$
$983$	−1.75624e25	−0.642510	−0.321255	+	0.946993i	$0.604105\pi$
$984$	7.97005e24	0.289070
$985$	−6.30402e24	−0.226678
$986$	3.74766e23	0.0133600
$987$	3.04842e25	1.07740
$988$	−4.66736e25	−1.63545
$989$	6.04832e24	0.210120
$990$	3.00910e24	0.103642
$991$	2.42479e25	0.828032	0.414016	−	0.910269i	$-0.364126\pi$
$991$	2.42479e25	0.828032	0.414016	+	0.910269i	$0.364126\pi$
$992$	−3.37284e24	−0.114195
$993$	6.98726e24	0.234551
$994$	9.20197e23	0.0306265
$995$	1.59688e25	0.526957
$996$	1.11657e25	0.365326
$997$	−5.59049e25	−1.81360	−0.906799	−	0.421563i	$-0.861482\pi$
$997$	−5.59049e25	−1.81360	−0.906799	+	0.421563i	$0.861482\pi$
$998$	−2.09318e24	−0.0673281
$999$	7.64257e25	2.43743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.10	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+19.4887 q^{2} -18855.2 q^{3} -130692. q^{4} -785915. q^{5} -367464. q^{6} -8.64265e6 q^{7} -5.10144e6 q^{8} +2.26380e8 q^{9} +O(q^{10})\)	\(q+19.4887 q^{2} -18855.2 q^{3} -130692. q^{4} -785915. q^{5} -367464. q^{6} -8.64265e6 q^{7} -5.10144e6 q^{8} +2.26380e8 q^{9} -1.53164e7 q^{10} -8.67841e8 q^{11} +2.46423e9 q^{12} +4.14273e9 q^{13} -1.68434e8 q^{14} +1.48186e10 q^{15} +1.70307e10 q^{16} -3.84409e10 q^{17} +4.41185e9 q^{18} +8.62054e10 q^{19} +1.02713e11 q^{20} +1.62959e11 q^{21} -1.69131e10 q^{22} +5.59760e11 q^{23} +9.61889e10 q^{24} -1.45277e11 q^{25} +8.07364e10 q^{26} -1.83348e12 q^{27} +1.12953e12 q^{28} -5.00246e11 q^{29} +2.88795e11 q^{30} -3.37095e12 q^{31} +1.00056e12 q^{32} +1.63634e13 q^{33} -7.49162e11 q^{34} +6.79239e12 q^{35} -2.95861e13 q^{36} -4.16834e13 q^{37} +1.68003e12 q^{38} -7.81122e13 q^{39} +4.00930e12 q^{40} +8.28584e13 q^{41} +3.17586e12 q^{42} +1.08052e13 q^{43} +1.13420e14 q^{44} -1.77915e14 q^{45} +1.09090e13 q^{46} +1.87066e14 q^{47} -3.21117e14 q^{48} -1.57935e14 q^{49} -2.83127e12 q^{50} +7.24812e14 q^{51} -5.41422e14 q^{52} +2.83703e14 q^{53} -3.57321e13 q^{54} +6.82049e14 q^{55} +4.40900e13 q^{56} -1.62542e15 q^{57} -9.74915e12 q^{58} -1.01085e15 q^{59} -1.93668e15 q^{60} +2.66633e15 q^{61} -6.56954e13 q^{62} -1.95652e15 q^{63} -2.21274e15 q^{64} -3.25583e15 q^{65} +3.18900e14 q^{66} -1.02765e15 q^{67} +5.02392e15 q^{68} -1.05544e16 q^{69} +1.32375e14 q^{70} -5.46326e15 q^{71} -1.15486e15 q^{72} -1.00064e15 q^{73} -8.12356e14 q^{74} +2.73924e15 q^{75} -1.12664e16 q^{76} +7.50045e15 q^{77} -1.52230e15 q^{78} +1.18992e15 q^{79} -1.33847e16 q^{80} +5.33594e15 q^{81} +1.61480e15 q^{82} +4.53110e15 q^{83} -2.12975e16 q^{84} +3.02113e16 q^{85} +2.10579e14 q^{86} +9.43227e15 q^{87} +4.42724e15 q^{88} +4.86568e16 q^{89} -3.46734e15 q^{90} -3.58042e16 q^{91} -7.31563e16 q^{92} +6.35601e16 q^{93} +3.64568e15 q^{94} -6.77501e16 q^{95} -1.88658e16 q^{96} +8.15622e16 q^{97} -3.07795e15 q^{98} -1.96462e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 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

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Groups

Database

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