LMFDB - Embedded newform 29.18.a.a.1.12

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			1.12
Root			$229.733$ 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)

$f(q)$	$=$	$q+229.733 q^{2} +12724.1 q^{3} -78294.6 q^{4} +93032.9 q^{5} +2.92314e6 q^{6} +1.03405e7 q^{7} -4.80985e7 q^{8} +3.27614e7 q^{9} +O(q^{10})$	\(q+229.733 q^{2} +12724.1 q^{3} -78294.6 q^{4} +93032.9 q^{5} +2.92314e6 q^{6} +1.03405e7 q^{7} -4.80985e7 q^{8} +3.27614e7 q^{9} +2.13728e7 q^{10} -7.26440e8 q^{11} -9.96224e8 q^{12} +8.27625e8 q^{13} +2.37557e9 q^{14} +1.18376e9 q^{15} -7.87608e8 q^{16} -2.20001e10 q^{17} +7.52638e9 q^{18} +3.65200e10 q^{19} -7.28397e9 q^{20} +1.31574e11 q^{21} -1.66888e11 q^{22} -4.80402e11 q^{23} -6.12008e11 q^{24} -7.54284e11 q^{25} +1.90133e11 q^{26} -1.22633e12 q^{27} -8.09608e11 q^{28} -5.00246e11 q^{29} +2.71948e11 q^{30} +2.08806e12 q^{31} +6.12343e12 q^{32} -9.24326e12 q^{33} -5.05415e12 q^{34} +9.62010e11 q^{35} -2.56504e12 q^{36} -2.08044e12 q^{37} +8.38986e12 q^{38} +1.05307e13 q^{39} -4.47474e12 q^{40} -7.30075e12 q^{41} +3.02268e13 q^{42} -2.95160e13 q^{43} +5.68763e13 q^{44} +3.04789e12 q^{45} -1.10364e14 q^{46} -1.79214e14 q^{47} -1.00216e13 q^{48} -1.25704e14 q^{49} -1.73284e14 q^{50} -2.79930e14 q^{51} -6.47985e13 q^{52} +4.29943e14 q^{53} -2.81729e14 q^{54} -6.75828e13 q^{55} -4.97364e14 q^{56} +4.64682e14 q^{57} -1.14923e14 q^{58} +7.94352e14 q^{59} -9.26816e13 q^{60} -1.58847e15 q^{61} +4.79697e14 q^{62} +3.38770e14 q^{63} +1.50999e15 q^{64} +7.69963e13 q^{65} -2.12349e15 q^{66} -4.15430e15 q^{67} +1.72248e15 q^{68} -6.11266e15 q^{69} +2.21006e14 q^{70} +2.33260e15 q^{71} -1.57577e15 q^{72} -4.97582e15 q^{73} -4.77946e14 q^{74} -9.59755e15 q^{75} -2.85932e15 q^{76} -7.51178e15 q^{77} +2.41926e15 q^{78} -2.38364e16 q^{79} -7.32734e13 q^{80} -1.98347e16 q^{81} -1.67723e15 q^{82} +4.82130e15 q^{83} -1.03015e16 q^{84} -2.04673e15 q^{85} -6.78082e15 q^{86} -6.36516e15 q^{87} +3.49407e16 q^{88} +8.92339e15 q^{89} +7.00201e14 q^{90} +8.55809e15 q^{91} +3.76128e16 q^{92} +2.65686e16 q^{93} -4.11715e16 q^{94} +3.39756e15 q^{95} +7.79148e16 q^{96} +1.11839e17 q^{97} -2.88784e16 q^{98} -2.37992e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	229.733	0.634555	0.317277	−	0.948333i	$-0.397231\pi$
$2$	229.733	0.634555	0.317277	+	0.948333i	$0.397231\pi$
$3$	12724.1	1.11968	0.559841	−	0.828600i	$-0.310862\pi$
$3$	12724.1	1.11968	0.559841	+	0.828600i	$0.310862\pi$
$4$	−78294.6	−0.597340
$5$	93032.9	0.106510	0.0532551	−	0.998581i	$-0.483040\pi$
$5$	93032.9	0.106510	0.0532551	+	0.998581i	$0.483040\pi$
$6$	2.92314e6	0.710500
$7$	1.03405e7	0.677969	0.338984	−	0.940792i	$-0.389917\pi$
$7$	1.03405e7	0.677969	0.338984	+	0.940792i	$0.389917\pi$
$8$	−4.80985e7	−1.01360
$9$	3.27614e7	0.253689
$10$	2.13728e7	0.0675866
$11$	−7.26440e8	−1.02179	−0.510895	−	0.859643i	$-0.670686\pi$
$11$	−7.26440e8	−1.02179	−0.510895	+	0.859643i	$0.670686\pi$
$12$	−9.96224e8	−0.668831
$13$	8.27625e8	0.281394	0.140697	−	0.990053i	$-0.455066\pi$
$13$	8.27625e8	0.281394	0.140697	+	0.990053i	$0.455066\pi$
$14$	2.37557e9	0.430208
$15$	1.18376e9	0.119258
$16$	−7.87608e8	−0.0458448
$17$	−2.20001e10	−0.764906	−0.382453	−	0.923975i	$-0.624921\pi$
$17$	−2.20001e10	−0.764906	−0.382453	+	0.923975i	$0.624921\pi$
$18$	7.52638e9	0.160979
$19$	3.65200e10	0.493316	0.246658	−	0.969103i	$-0.420668\pi$
$19$	3.65200e10	0.493316	0.246658	+	0.969103i	$0.420668\pi$
$20$	−7.28397e9	−0.0636228
$21$	1.31574e11	0.759110
$22$	−1.66888e11	−0.648382
$23$	−4.80402e11	−1.27914	−0.639570	−	0.768733i	$-0.720888\pi$
$23$	−4.80402e11	−1.27914	−0.639570	+	0.768733i	$0.720888\pi$
$24$	−6.12008e11	−1.13491
$25$	−7.54284e11	−0.988656
$26$	1.90133e11	0.178560
$27$	−1.22633e12	−0.835632
$28$	−8.09608e11	−0.404978
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	2.71948e11	0.0756755
$31$	2.08806e12	0.439712	0.219856	−	0.975532i	$-0.429441\pi$
$31$	2.08806e12	0.439712	0.219856	+	0.975532i	$0.429441\pi$
$32$	6.12343e12	0.984509
$33$	−9.24326e12	−1.14408
$34$	−5.05415e12	−0.485375
$35$	9.62010e11	0.0722106
$36$	−2.56504e12	−0.151538
$37$	−2.08044e12	−0.0973733	−0.0486867	−	0.998814i	$-0.515504\pi$
$37$	−2.08044e12	−0.0973733	−0.0486867	+	0.998814i	$0.515504\pi$
$38$	8.38986e12	0.313036
$39$	1.05307e13	0.315072
$40$	−4.47474e12	−0.107959
$41$	−7.30075e12	−0.142792	−0.0713962	−	0.997448i	$-0.522745\pi$
$41$	−7.30075e12	−0.142792	−0.0713962	+	0.997448i	$0.522745\pi$
$42$	3.02268e13	0.481697
$43$	−2.95160e13	−0.385102	−0.192551	−	0.981287i	$-0.561676\pi$
$43$	−2.95160e13	−0.385102	−0.192551	+	0.981287i	$0.561676\pi$
$44$	5.68763e13	0.610356
$45$	3.04789e12	0.0270204
$46$	−1.10364e14	−0.811684
$47$	−1.79214e14	−1.09785	−0.548923	−	0.835873i	$-0.684962\pi$
$47$	−1.79214e14	−1.09785	−0.548923	+	0.835873i	$0.684962\pi$
$48$	−1.00216e13	−0.0513316
$49$	−1.25704e14	−0.540358
$50$	−1.73284e14	−0.627356
$51$	−2.79930e14	−0.856452
$52$	−6.47985e13	−0.168088
$53$	4.29943e14	0.948562	0.474281	−	0.880374i	$-0.342708\pi$
$53$	4.29943e14	0.948562	0.474281	+	0.880374i	$0.342708\pi$
$54$	−2.81729e14	−0.530254
$55$	−6.75828e13	−0.108831
$56$	−4.97364e14	−0.687189
$57$	4.64682e14	0.552357
$58$	−1.14923e14	−0.117834
$59$	7.94352e14	0.704321	0.352161	−	0.935940i	$-0.385447\pi$
$59$	7.94352e14	0.704321	0.352161	+	0.935940i	$0.385447\pi$
$60$	−9.26816e13	−0.0712374
$61$	−1.58847e15	−1.06090	−0.530452	−	0.847715i	$-0.677978\pi$
$61$	−1.58847e15	−1.06090	−0.530452	+	0.847715i	$0.677978\pi$
$62$	4.79697e14	0.279021
$63$	3.38770e14	0.171993
$64$	1.50999e15	0.670570
$65$	7.69963e13	0.0299714
$66$	−2.12349e15	−0.725982
$67$	−4.15430e15	−1.24986	−0.624932	−	0.780680i	$-0.714873\pi$
$67$	−4.15430e15	−1.24986	−0.624932	+	0.780680i	$0.714873\pi$
$68$	1.72248e15	0.456909
$69$	−6.11266e15	−1.43223
$70$	2.21006e14	0.0458216
$71$	2.33260e15	0.428691	0.214346	−	0.976758i	$-0.431238\pi$
$71$	2.33260e15	0.428691	0.214346	+	0.976758i	$0.431238\pi$
$72$	−1.57577e15	−0.257139
$73$	−4.97582e15	−0.722138	−0.361069	−	0.932539i	$-0.617588\pi$
$73$	−4.97582e15	−0.722138	−0.361069	+	0.932539i	$0.617588\pi$
$74$	−4.77946e14	−0.0617887
$75$	−9.59755e15	−1.10698
$76$	−2.85932e15	−0.294677
$77$	−7.51178e15	−0.692742
$78$	2.41926e15	0.199931
$79$	−2.38364e16	−1.76771	−0.883853	−	0.467765i	$-0.845060\pi$
$79$	−2.38364e16	−1.76771	−0.883853	+	0.467765i	$0.845060\pi$
$80$	−7.32734e13	−0.00488294
$81$	−1.98347e16	−1.18933
$82$	−1.67723e15	−0.0906096
$83$	4.82130e15	0.234963	0.117482	−	0.993075i	$-0.462518\pi$
$83$	4.82130e15	0.234963	0.117482	+	0.993075i	$0.462518\pi$
$84$	−1.03015e16	−0.453447
$85$	−2.04673e15	−0.0814703
$86$	−6.78082e15	−0.244368
$87$	−6.36516e15	−0.207920
$88$	3.49407e16	1.03569
$89$	8.92339e15	0.240279	0.120139	−	0.992757i	$-0.461666\pi$
$89$	8.92339e15	0.240279	0.120139	+	0.992757i	$0.461666\pi$
$90$	7.00201e14	0.0171460
$91$	8.55809e15	0.190777
$92$	3.76128e16	0.764081
$93$	2.65686e16	0.492338
$94$	−4.11715e16	−0.696643
$95$	3.39756e15	0.0525432
$96$	7.79148e16	1.10234
$97$	1.11839e17	1.44889	0.724443	−	0.689335i	$-0.242097\pi$
$97$	1.11839e17	1.44889	0.724443	+	0.689335i	$0.242097\pi$
$98$	−2.88784e16	−0.342887
$99$	−2.37992e16	−0.259217
$100$	5.90564e16	0.590564
$101$	6.92387e16	0.636234	0.318117	−	0.948051i	$-0.396949\pi$
$101$	6.92387e16	0.636234	0.318117	+	0.948051i	$0.396949\pi$
$102$	−6.43093e16	−0.543466
$103$	−1.37085e17	−1.06629	−0.533143	−	0.846025i	$-0.678989\pi$
$103$	−1.37085e17	−1.06629	−0.533143	+	0.846025i	$0.678989\pi$
$104$	−3.98075e16	−0.285221
$105$	1.22407e16	0.0808530
$106$	9.87722e16	0.601914
$107$	1.89336e17	1.06530	0.532649	−	0.846337i	$-0.321197\pi$
$107$	1.89336e17	1.06530	0.532649	+	0.846337i	$0.321197\pi$
$108$	9.60149e16	0.499156
$109$	1.89742e17	0.912089	0.456045	−	0.889957i	$-0.349266\pi$
$109$	1.89742e17	0.912089	0.456045	+	0.889957i	$0.349266\pi$
$110$	−1.55260e16	−0.0690594
$111$	−2.64716e16	−0.109027
$112$	−8.14429e15	−0.0310814
$113$	7.35418e16	0.260236	0.130118	−	0.991499i	$-0.458464\pi$
$113$	7.35418e16	0.260236	0.130118	+	0.991499i	$0.458464\pi$
$114$	1.06753e17	0.350501
$115$	−4.46932e16	−0.136242
$116$	3.91666e16	0.110923
$117$	2.71141e16	0.0713865
$118$	1.82489e17	0.446930
$119$	−2.27492e17	−0.518582
$120$	−5.69369e16	−0.120880
$121$	2.22678e16	0.0440556
$122$	−3.64926e17	−0.673202
$123$	−9.28952e16	−0.159882
$124$	−1.63484e17	−0.262658
$125$	−1.41152e17	−0.211812
$126$	7.78269e16	0.109139
$127$	2.05297e17	0.269185	0.134592	−	0.990901i	$-0.457028\pi$
$127$	2.05297e17	0.269185	0.134592	+	0.990901i	$0.457028\pi$
$128$	−4.55715e17	−0.558996
$129$	−3.75563e17	−0.431192
$130$	1.76886e16	0.0190185
$131$	1.67087e18	1.68320	0.841601	−	0.540099i	$-0.181613\pi$
$131$	1.67087e18	1.68320	0.841601	+	0.540099i	$0.181613\pi$
$132$	7.23697e17	0.683405
$133$	3.77636e17	0.334453
$134$	−9.54383e17	−0.793107
$135$	−1.14089e17	−0.0890034
$136$	1.05817e18	0.775309
$137$	1.65338e18	1.13828	0.569140	−	0.822241i	$-0.307276\pi$
$137$	1.65338e18	1.13828	0.569140	+	0.822241i	$0.307276\pi$
$138$	−1.40428e18	−0.908829
$139$	1.36839e18	0.832886	0.416443	−	0.909162i	$-0.363277\pi$
$139$	1.36839e18	0.832886	0.416443	+	0.909162i	$0.363277\pi$
$140$	−7.53202e16	−0.0431343
$141$	−2.28033e18	−1.22924
$142$	5.35876e17	0.272028
$143$	−6.01220e17	−0.287526
$144$	−2.58031e16	−0.0116303
$145$	−4.65394e16	−0.0197785
$146$	−1.14311e18	−0.458236
$147$	−1.59946e18	−0.605030
$148$	1.62887e17	0.0581650
$149$	−2.66860e18	−0.899912	−0.449956	−	0.893051i	$-0.648560\pi$
$149$	−2.66860e18	−0.899912	−0.449956	+	0.893051i	$0.648560\pi$
$150$	−2.20488e18	−0.702440
$151$	1.97227e18	0.593831	0.296915	−	0.954904i	$-0.404042\pi$
$151$	1.97227e18	0.593831	0.296915	+	0.954904i	$0.404042\pi$
$152$	−1.75656e18	−0.500025
$153$	−7.20752e17	−0.194048
$154$	−1.72571e18	−0.439583
$155$	1.94258e17	0.0468339
$156$	−8.24500e17	−0.188205
$157$	6.67699e17	0.144356	0.0721778	−	0.997392i	$-0.477005\pi$
$157$	6.67699e17	0.144356	0.0721778	+	0.997392i	$0.477005\pi$
$158$	−5.47601e18	−1.12171
$159$	5.47061e18	1.06209
$160$	5.69680e17	0.104860
$161$	−4.96761e18	−0.867217
$162$	−4.55669e18	−0.754696
$163$	2.71449e18	0.426672	0.213336	−	0.976979i	$-0.431567\pi$
$163$	2.71449e18	0.426672	0.213336	+	0.976979i	$0.431567\pi$
$164$	5.71609e17	0.0852956
$165$	−8.59927e17	−0.121856
$166$	1.10761e18	0.149097
$167$	−1.92925e18	−0.246773	−0.123386	−	0.992359i	$-0.539375\pi$
$167$	−1.92925e18	−0.246773	−0.123386	+	0.992359i	$0.539375\pi$
$168$	−6.32849e18	−0.769434
$169$	−7.96545e18	−0.920817
$170$	−4.70202e17	−0.0516974
$171$	1.19644e18	0.125149
$172$	2.31094e18	0.230037
$173$	1.46824e19	1.39125	0.695626	−	0.718404i	$-0.255127\pi$
$173$	1.46824e19	1.39125	0.695626	+	0.718404i	$0.255127\pi$
$174$	−1.46229e18	−0.131937
$175$	−7.79971e18	−0.670278
$176$	5.72150e17	0.0468438
$177$	1.01074e19	0.788616
$178$	2.05000e18	0.152470
$179$	1.47610e19	1.04680	0.523401	−	0.852087i	$-0.324663\pi$
$179$	1.47610e19	1.04680	0.523401	+	0.852087i	$0.324663\pi$
$180$	−2.38633e17	−0.0161404
$181$	−8.73630e18	−0.563715	−0.281857	−	0.959456i	$-0.590951\pi$
$181$	−8.73630e18	−0.563715	−0.281857	+	0.959456i	$0.590951\pi$
$182$	1.96608e18	0.121058
$183$	−2.02118e19	−1.18788
$184$	2.31066e19	1.29654
$185$	−1.93549e17	−0.0103713
$186$	6.10369e18	0.312415
$187$	1.59817e19	0.781573
$188$	1.40315e19	0.655787
$189$	−1.26809e19	−0.566532
$190$	7.80533e17	0.0333415
$191$	−1.93400e19	−0.790084	−0.395042	−	0.918663i	$-0.629270\pi$
$191$	−1.93400e19	−0.790084	−0.395042	+	0.918663i	$0.629270\pi$
$192$	1.92132e19	0.750825
$193$	−5.51792e18	−0.206318	−0.103159	−	0.994665i	$-0.532895\pi$
$193$	−5.51792e18	−0.206318	−0.103159	+	0.994665i	$0.532895\pi$
$194$	2.56932e19	0.919398
$195$	9.79706e17	0.0335584
$196$	9.84192e18	0.322778
$197$	3.36243e19	1.05606	0.528032	−	0.849225i	$-0.322930\pi$
$197$	3.36243e19	1.05606	0.528032	+	0.849225i	$0.322930\pi$
$198$	−5.46747e18	−0.164487
$199$	1.59692e18	0.0460290	0.0230145	−	0.999735i	$-0.492674\pi$
$199$	1.59692e18	0.0460290	0.0230145	+	0.999735i	$0.492674\pi$
$200$	3.62799e19	1.00210
$201$	−5.28596e19	−1.39945
$202$	1.59064e19	0.403726
$203$	−5.17282e18	−0.125896
$204$	2.19170e19	0.511593
$205$	−6.79210e17	−0.0152088
$206$	−3.14930e19	−0.676617
$207$	−1.57386e19	−0.324503
$208$	−6.51844e17	−0.0129005
$209$	−2.65296e19	−0.504065
$210$	2.81209e18	0.0513057
$211$	4.22470e19	0.740279	0.370140	−	0.928976i	$-0.379310\pi$
$211$	4.22470e19	0.740279	0.370140	+	0.928976i	$0.379310\pi$
$212$	−3.36622e19	−0.566614
$213$	2.96801e19	0.479998
$214$	4.34968e19	0.675990
$215$	−2.74596e18	−0.0410173
$216$	5.89846e19	0.846996
$217$	2.15917e19	0.298111
$218$	4.35900e19	0.578771
$219$	−6.33126e19	−0.808565
$220$	5.29136e18	0.0650092
$221$	−1.82078e19	−0.215240
$222$	−6.08141e18	−0.0691837
$223$	−4.22544e18	−0.0462680	−0.0231340	−	0.999732i	$-0.507364\pi$
$223$	−4.22544e18	−0.0462680	−0.0231340	+	0.999732i	$0.507364\pi$
$224$	6.33195e19	0.667466
$225$	−2.47114e19	−0.250811
$226$	1.68950e19	0.165134
$227$	3.67578e19	0.346043	0.173021	−	0.984918i	$-0.444647\pi$
$227$	3.67578e19	0.346043	0.173021	+	0.984918i	$0.444647\pi$
$228$	−3.63821e19	−0.329945
$229$	−2.92669e19	−0.255726	−0.127863	−	0.991792i	$-0.540812\pi$
$229$	−2.92669e19	−0.255726	−0.127863	+	0.991792i	$0.540812\pi$
$230$	−1.02675e19	−0.0864527
$231$	−9.55803e19	−0.775651
$232$	2.40611e19	0.188221
$233$	−2.04761e19	−0.154427	−0.0772133	−	0.997015i	$-0.524602\pi$
$233$	−2.04761e19	−0.154427	−0.0772133	+	0.997015i	$0.524602\pi$
$234$	6.22902e18	0.0452986
$235$	−1.66728e19	−0.116932
$236$	−6.21934e19	−0.420719
$237$	−3.03295e20	−1.97927
$238$	−5.22626e19	−0.329069
$239$	−1.49389e20	−0.907689	−0.453844	−	0.891081i	$-0.649948\pi$
$239$	−1.49389e20	−0.907689	−0.453844	+	0.891081i	$0.649948\pi$
$240$	−9.32335e17	−0.00546734
$241$	−2.36643e20	−1.33952	−0.669759	−	0.742578i	$-0.733603\pi$
$241$	−2.36643e20	−1.33952	−0.669759	+	0.742578i	$0.733603\pi$
$242$	5.11565e18	0.0279557
$243$	−9.40093e19	−0.496041
$244$	1.24369e20	0.633721
$245$	−1.16946e19	−0.0575537
$246$	−2.13411e19	−0.101454
$247$	3.02248e19	0.138816
$248$	−1.00432e20	−0.445692
$249$	6.13465e19	0.263084
$250$	−3.24273e19	−0.134406
$251$	−3.80775e20	−1.52560	−0.762802	−	0.646632i	$-0.776177\pi$
$251$	−3.80775e20	−1.52560	−0.762802	+	0.646632i	$0.776177\pi$
$252$	−2.65239e19	−0.102738
$253$	3.48983e20	1.30701
$254$	4.71635e19	0.170812
$255$	−2.60427e19	−0.0912209
$256$	−3.02610e20	−1.02528
$257$	7.76753e19	0.254596	0.127298	−	0.991865i	$-0.459370\pi$
$257$	7.76753e19	0.254596	0.127298	+	0.991865i	$0.459370\pi$
$258$	−8.62795e19	−0.273615
$259$	−2.15128e19	−0.0660161
$260$	−6.02839e18	−0.0179031
$261$	−1.63888e19	−0.0471088
$262$	3.83855e20	1.06808
$263$	6.67228e19	0.179742	0.0898711	−	0.995953i	$-0.471354\pi$
$263$	6.67228e19	0.179742	0.0898711	+	0.995953i	$0.471354\pi$
$264$	4.44587e20	1.15964
$265$	3.99988e19	0.101032
$266$	8.67556e19	0.212229
$267$	1.13542e20	0.269036
$268$	3.25259e20	0.746593
$269$	8.11664e20	1.80502	0.902510	−	0.430669i	$-0.141722\pi$
$269$	8.11664e20	1.80502	0.902510	+	0.430669i	$0.141722\pi$
$270$	−2.62100e19	−0.0564775
$271$	−4.19069e20	−0.875077	−0.437538	−	0.899200i	$-0.644150\pi$
$271$	−4.19069e20	−0.875077	−0.437538	+	0.899200i	$0.644150\pi$
$272$	1.73274e19	0.0350670
$273$	1.08894e20	0.213609
$274$	3.79838e20	0.722301
$275$	5.47942e20	1.01020
$276$	4.78588e20	0.855528
$277$	−8.47731e20	−1.46954	−0.734768	−	0.678319i	$-0.762709\pi$
$277$	−8.47731e20	−1.46954	−0.734768	+	0.678319i	$0.762709\pi$
$278$	3.14366e20	0.528512
$279$	6.84077e19	0.111550
$280$	−4.62712e19	−0.0731927
$281$	−1.05133e21	−1.61337	−0.806684	−	0.590983i	$-0.798740\pi$
$281$	−1.05133e21	−1.61337	−0.806684	+	0.590983i	$0.798740\pi$
$282$	−5.23869e20	−0.780019
$283$	3.65657e20	0.528310	0.264155	−	0.964480i	$-0.414907\pi$
$283$	3.65657e20	0.528310	0.264155	+	0.964480i	$0.414907\pi$
$284$	−1.82630e20	−0.256074
$285$	4.32307e19	0.0588317
$286$	−1.38120e20	−0.182451
$287$	−7.54937e19	−0.0968088
$288$	2.00612e20	0.249759
$289$	−3.43238e20	−0.414919
$290$	−1.06916e19	−0.0125505
$291$	1.42305e21	1.62229
$292$	3.89580e20	0.431362
$293$	−9.28876e20	−0.999040	−0.499520	−	0.866302i	$-0.666490\pi$
$293$	−9.28876e20	−0.999040	−0.499520	+	0.866302i	$0.666490\pi$
$294$	−3.67450e20	−0.383924
$295$	7.39008e19	0.0750174
$296$	1.00066e20	0.0986976
$297$	8.90854e20	0.853840
$298$	−6.13066e20	−0.571044
$299$	−3.97593e20	−0.359942
$300$	7.51436e20	0.661244
$301$	−3.05212e20	−0.261087
$302$	4.53097e20	0.376818
$303$	8.80996e20	0.712380
$304$	−2.87634e19	−0.0226160
$305$	−1.47780e20	−0.112997
$306$	−1.65581e20	−0.123134
$307$	−5.91724e20	−0.427999	−0.214000	−	0.976834i	$-0.568649\pi$
$307$	−5.91724e20	−0.427999	−0.214000	+	0.976834i	$0.568649\pi$
$308$	5.88131e20	0.413803
$309$	−1.74428e21	−1.19390
$310$	4.46276e19	0.0297187
$311$	−8.06888e20	−0.522817	−0.261409	−	0.965228i	$-0.584187\pi$
$311$	−8.06888e20	−0.522817	−0.261409	+	0.965228i	$0.584187\pi$
$312$	−5.06513e20	−0.319357
$313$	1.54376e21	0.947223	0.473611	−	0.880734i	$-0.342950\pi$
$313$	1.54376e21	0.947223	0.473611	+	0.880734i	$0.342950\pi$
$314$	1.53393e20	0.0916015
$315$	3.15168e19	0.0183190
$316$	1.86626e21	1.05592
$317$	−2.83485e21	−1.56144	−0.780722	−	0.624879i	$-0.785148\pi$
$317$	−2.83485e21	−1.56144	−0.780722	+	0.624879i	$0.785148\pi$
$318$	1.25678e21	0.673953
$319$	3.63399e20	0.189742
$320$	1.40479e20	0.0714226
$321$	2.40912e21	1.19279
$322$	−1.14123e21	−0.550297
$323$	−8.03442e20	−0.377340
$324$	1.55295e21	0.710435
$325$	−6.24265e20	−0.278202
$326$	6.23610e20	0.270747
$327$	2.41428e21	1.02125
$328$	3.51155e20	0.144734
$329$	−1.85317e21	−0.744305
$330$	−1.97554e20	−0.0773245
$331$	1.87670e21	0.715907	0.357954	−	0.933739i	$-0.383475\pi$
$331$	1.87670e21	0.715907	0.357954	+	0.933739i	$0.383475\pi$
$332$	−3.77482e20	−0.140353
$333$	−6.81580e19	−0.0247025
$334$	−4.43212e20	−0.156591
$335$	−3.86487e20	−0.133123
$336$	−1.03628e20	−0.0348012
$337$	−9.28557e20	−0.304057	−0.152028	−	0.988376i	$-0.548581\pi$
$337$	−9.28557e20	−0.304057	−0.152028	+	0.988376i	$0.548581\pi$
$338$	−1.82993e21	−0.584309
$339$	9.35750e20	0.291382
$340$	1.60248e20	0.0486655
$341$	−1.51685e21	−0.449294
$342$	2.74863e20	0.0794136
$343$	−3.70537e21	−1.04431
$344$	1.41968e21	0.390340
$345$	−5.68678e20	−0.152547
$346$	3.37304e21	0.882826
$347$	−7.21325e21	−1.84217	−0.921086	−	0.389359i	$-0.872697\pi$
$347$	−7.21325e21	−1.84217	−0.921086	+	0.389359i	$0.872697\pi$
$348$	4.98358e20	0.124199
$349$	−4.69225e21	−1.14121	−0.570604	−	0.821225i	$-0.693291\pi$
$349$	−4.69225e21	−1.14121	−0.570604	+	0.821225i	$0.693291\pi$
$350$	−1.79185e21	−0.425328
$351$	−1.01494e21	−0.235142
$352$	−4.44830e21	−1.00596
$353$	−2.11595e21	−0.467112	−0.233556	−	0.972343i	$-0.575036\pi$
$353$	−2.11595e21	−0.467112	−0.233556	+	0.972343i	$0.575036\pi$
$354$	2.32200e21	0.500420
$355$	2.17009e20	0.0456600
$356$	−6.98653e20	−0.143528
$357$	−2.89463e21	−0.580648
$358$	3.39109e21	0.664253
$359$	−3.24100e20	−0.0619978	−0.0309989	−	0.999519i	$-0.509869\pi$
$359$	−3.24100e20	−0.0619978	−0.0309989	+	0.999519i	$0.509869\pi$
$360$	−1.46599e20	−0.0273879
$361$	−4.14668e21	−0.756640
$362$	−2.00702e21	−0.357708
$363$	2.83336e20	0.0493283
$364$	−6.70052e20	−0.113958
$365$	−4.62915e20	−0.0769151
$366$	−4.64333e21	−0.753773
$367$	8.63792e21	1.37008	0.685042	−	0.728503i	$-0.259784\pi$
$367$	8.63792e21	1.37008	0.685042	+	0.728503i	$0.259784\pi$
$368$	3.78368e20	0.0586419
$369$	−2.39183e20	−0.0362248
$370$	−4.44647e19	−0.00658113
$371$	4.44584e21	0.643095
$372$	−2.08017e21	−0.294093
$373$	−5.05868e21	−0.699056	−0.349528	−	0.936926i	$-0.613658\pi$
$373$	−5.05868e21	−0.699056	−0.349528	+	0.936926i	$0.613658\pi$
$374$	3.67153e21	0.495951
$375$	−1.79602e21	−0.237162
$376$	8.61995e21	1.11278
$377$	−4.14016e20	−0.0522536
$378$	−2.91323e21	−0.359496
$379$	9.37765e21	1.13152	0.565758	−	0.824571i	$-0.308584\pi$
$379$	9.37765e21	1.13152	0.565758	+	0.824571i	$0.308584\pi$
$380$	−2.66010e20	−0.0313861
$381$	2.61221e21	0.301401
$382$	−4.44305e21	−0.501351
$383$	1.43697e22	1.58583	0.792917	−	0.609330i	$-0.208562\pi$
$383$	1.43697e22	1.58583	0.792917	+	0.609330i	$0.208562\pi$
$384$	−5.79854e21	−0.625897
$385$	−6.98842e20	−0.0737841
$386$	−1.26765e21	−0.130920
$387$	−9.66986e20	−0.0976960
$388$	−8.75640e21	−0.865478
$389$	−1.45535e21	−0.140733	−0.0703663	−	0.997521i	$-0.522417\pi$
$389$	−1.45535e21	−0.140733	−0.0703663	+	0.997521i	$0.522417\pi$
$390$	2.25071e20	0.0212947
$391$	1.05689e22	0.978421
$392$	6.04616e21	0.547707
$393$	2.12602e22	1.88465
$394$	7.72462e21	0.670130
$395$	−2.21757e21	−0.188279
$396$	1.86335e21	0.154840
$397$	−6.68339e21	−0.543598	−0.271799	−	0.962354i	$-0.587619\pi$
$397$	−6.68339e21	−0.543598	−0.271799	+	0.962354i	$0.587619\pi$
$398$	3.66866e20	0.0292079
$399$	4.80506e21	0.374481
$400$	5.94080e20	0.0453247
$401$	9.84549e21	0.735377	0.367688	−	0.929949i	$-0.380149\pi$
$401$	9.84549e21	0.735377	0.367688	+	0.929949i	$0.380149\pi$
$402$	−1.21436e22	−0.888028
$403$	1.72813e21	0.123732
$404$	−5.42101e21	−0.380048
$405$	−1.84528e21	−0.126676
$406$	−1.18837e21	−0.0798877
$407$	1.51131e21	0.0994951
$408$	1.34642e22	0.868099
$409$	−1.58484e22	−1.00078	−0.500389	−	0.865800i	$-0.666810\pi$
$409$	−1.58484e22	−1.00078	−0.500389	+	0.865800i	$0.666810\pi$
$410$	−1.56037e20	−0.00965085
$411$	2.10378e22	1.27451
$412$	1.07330e22	0.636935
$413$	8.21402e21	0.477508
$414$	−3.61569e21	−0.205915
$415$	4.48539e20	0.0250260
$416$	5.06790e21	0.277035
$417$	1.74115e22	0.932568
$418$	−6.09473e21	−0.319857
$419$	1.11973e22	0.575828	0.287914	−	0.957656i	$-0.407038\pi$
$419$	1.11973e22	0.575828	0.287914	+	0.957656i	$0.407038\pi$
$420$	−9.58378e20	−0.0482967
$421$	−1.00797e22	−0.497792	−0.248896	−	0.968530i	$-0.580068\pi$
$421$	−1.00797e22	−0.497792	−0.248896	+	0.968530i	$0.580068\pi$
$422$	9.70556e21	0.469748
$423$	−5.87131e21	−0.278511
$424$	−2.06796e22	−0.961462
$425$	1.65943e22	0.756228
$426$	6.81852e21	0.304585
$427$	−1.64257e22	−0.719260
$428$	−1.48240e22	−0.636345
$429$	−7.64995e21	−0.321938
$430$	−6.30839e20	−0.0260278
$431$	−2.31740e22	−0.937442	−0.468721	−	0.883346i	$-0.655285\pi$
$431$	−2.31740e22	−0.937442	−0.468721	+	0.883346i	$0.655285\pi$
$432$	9.65866e20	0.0383094
$433$	−2.13204e22	−0.829180	−0.414590	−	0.910008i	$-0.636075\pi$
$433$	−2.13204e22	−0.829180	−0.414590	+	0.910008i	$0.636075\pi$
$434$	4.96032e21	0.189168
$435$	−5.92169e20	−0.0221456
$436$	−1.48557e22	−0.544828
$437$	−1.75443e22	−0.631020
$438$	−1.45450e22	−0.513079
$439$	3.95516e22	1.36841	0.684204	−	0.729291i	$-0.260150\pi$
$439$	3.95516e22	1.36841	0.684204	+	0.729291i	$0.260150\pi$
$440$	3.25063e21	0.110311
$441$	−4.11823e21	−0.137083
$442$	−4.18294e21	−0.136582
$443$	−7.17524e21	−0.229829	−0.114914	−	0.993375i	$-0.536659\pi$
$443$	−7.17524e21	−0.229829	−0.114914	+	0.993375i	$0.536659\pi$
$444$	2.07258e21	0.0651263
$445$	8.30169e20	0.0255921
$446$	−9.70725e20	−0.0293596
$447$	−3.39554e22	−1.00762
$448$	1.56141e22	0.454625
$449$	−1.33120e22	−0.380320	−0.190160	−	0.981753i	$-0.560901\pi$
$449$	−1.33120e22	−0.380320	−0.190160	+	0.981753i	$0.560901\pi$
$450$	−5.67703e21	−0.159153
$451$	5.30356e21	0.145904
$452$	−5.75792e21	−0.155449
$453$	2.50953e22	0.664902
$454$	8.44450e21	0.219583
$455$	7.96184e20	0.0203197
$456$	−2.23505e22	−0.559869
$457$	−3.02477e22	−0.743712	−0.371856	−	0.928290i	$-0.621278\pi$
$457$	−3.02477e22	−0.743712	−0.371856	+	0.928290i	$0.621278\pi$
$458$	−6.72358e21	−0.162272
$459$	2.69793e22	0.639180
$460$	3.49923e21	0.0813825
$461$	3.38719e22	0.773360	0.386680	−	0.922214i	$-0.373622\pi$
$461$	3.38719e22	0.773360	0.386680	+	0.922214i	$0.373622\pi$
$462$	−2.19580e22	−0.492193
$463$	−4.39885e22	−0.968057	−0.484028	−	0.875052i	$-0.660827\pi$
$463$	−4.39885e22	−0.968057	−0.484028	+	0.875052i	$0.660827\pi$
$464$	3.93998e20	0.00851317
$465$	2.47175e21	0.0524390
$466$	−4.70405e21	−0.0979922
$467$	1.57316e22	0.321795	0.160898	−	0.986971i	$-0.448561\pi$
$467$	1.57316e22	0.321795	0.160898	+	0.986971i	$0.448561\pi$
$468$	−2.12289e21	−0.0426420
$469$	−4.29577e22	−0.847368
$470$	−3.83031e21	−0.0741997
$471$	8.49583e21	0.161632
$472$	−3.82071e22	−0.713900
$473$	2.14416e22	0.393494
$474$	−6.96771e22	−1.25596
$475$	−2.75464e22	−0.487719
$476$	1.78114e22	0.309770
$477$	1.40855e22	0.240639
$478$	−3.43197e22	−0.575978
$479$	6.16080e22	1.01575	0.507873	−	0.861432i	$-0.330432\pi$
$479$	6.16080e22	1.01575	0.507873	+	0.861432i	$0.330432\pi$
$480$	7.24864e21	0.117410
$481$	−1.72182e21	−0.0274003
$482$	−5.43648e22	−0.849998
$483$	−6.32082e22	−0.971008
$484$	−1.74345e21	−0.0263162
$485$	1.04047e22	0.154321
$486$	−2.15971e22	−0.314765
$487$	7.16791e22	1.02659	0.513294	−	0.858213i	$-0.328425\pi$
$487$	7.16791e22	1.02659	0.513294	+	0.858213i	$0.328425\pi$
$488$	7.64032e22	1.07533
$489$	3.45393e22	0.477737
$490$	−2.68664e21	−0.0365210
$491$	1.13697e23	1.51900	0.759500	−	0.650508i	$-0.225444\pi$
$491$	1.13697e23	1.51900	0.759500	+	0.650508i	$0.225444\pi$
$492$	7.27319e21	0.0955040
$493$	1.10054e22	0.142039
$494$	6.94366e21	0.0880865
$495$	−2.21411e21	−0.0276092
$496$	−1.64457e21	−0.0201585
$497$	2.41204e22	0.290639
$498$	1.40933e22	0.166942
$499$	−7.22784e22	−0.841694	−0.420847	−	0.907132i	$-0.638267\pi$
$499$	−7.22784e22	−0.841694	−0.420847	+	0.907132i	$0.638267\pi$
$500$	1.10514e22	0.126524
$501$	−2.45478e22	−0.276307
$502$	−8.74768e22	−0.968080
$503$	−1.06422e22	−0.115799	−0.0578996	−	0.998322i	$-0.518440\pi$
$503$	−1.06422e22	−0.115799	−0.0578996	+	0.998322i	$0.518440\pi$
$504$	−1.62943e22	−0.174332
$505$	6.44147e21	0.0677655
$506$	8.01731e22	0.829371
$507$	−1.01353e23	−1.03102
$508$	−1.60736e22	−0.160795
$509$	1.10578e23	1.08785	0.543925	−	0.839134i	$-0.316938\pi$
$509$	1.10578e23	1.08785	0.543925	+	0.839134i	$0.316938\pi$
$510$	−5.98288e21	−0.0578847
$511$	−5.14527e22	−0.489587
$512$	−9.78823e21	−0.0916029
$513$	−4.47855e22	−0.412230
$514$	1.78446e22	0.161555
$515$	−1.27534e22	−0.113570
$516$	2.94046e22	0.257568
$517$	1.30189e23	1.12177
$518$	−4.94222e21	−0.0418908
$519$	1.86820e23	1.55776
$520$	−3.70341e21	−0.0303790
$521$	2.39034e23	1.92903	0.964517	−	0.264021i	$-0.0850487\pi$
$521$	2.39034e23	1.92903	0.964517	+	0.264021i	$0.0850487\pi$
$522$	−3.76505e21	−0.0298931
$523$	1.48163e23	1.15738	0.578690	−	0.815547i	$-0.303564\pi$
$523$	1.48163e23	1.15738	0.578690	+	0.815547i	$0.303564\pi$
$524$	−1.30820e23	−1.00544
$525$	−9.92439e22	−0.750498
$526$	1.53285e22	0.114056
$527$	−4.59374e22	−0.336338
$528$	7.28006e21	0.0524502
$529$	8.97358e22	0.636199
$530$	9.18906e21	0.0641101
$531$	2.60241e22	0.178678
$532$	−2.95669e22	−0.199782
$533$	−6.04229e21	−0.0401809
$534$	2.60843e22	0.170718
$535$	1.76145e22	0.113465
$536$	1.99816e23	1.26686
$537$	1.87820e23	1.17209
$538$	1.86466e23	1.14538
$539$	9.13162e22	0.552133
$540$	8.93254e21	0.0531653
$541$	−2.09915e23	−1.22989	−0.614947	−	0.788569i	$-0.710822\pi$
$541$	−2.09915e23	−1.22989	−0.614947	+	0.788569i	$0.710822\pi$
$542$	−9.62741e22	−0.555284
$543$	−1.11161e23	−0.631181
$544$	−1.34716e23	−0.753057
$545$	1.76522e22	0.0971469
$546$	2.50165e22	0.135547
$547$	−3.41881e23	−1.82382	−0.911911	−	0.410388i	$-0.865393\pi$
$547$	−3.41881e23	−1.82382	−0.911911	+	0.410388i	$0.865393\pi$
$548$	−1.29451e23	−0.679940
$549$	−5.20406e22	−0.269139
$550$	1.25881e23	0.641027
$551$	−1.82690e22	−0.0916064
$552$	2.94010e23	1.45171
$553$	−2.46481e23	−1.19845
$554$	−1.94752e23	−0.932501
$555$	−2.46273e21	−0.0116125
$556$	−1.07138e23	−0.497516
$557$	−2.09089e23	−0.956228	−0.478114	−	0.878298i	$-0.658679\pi$
$557$	−2.09089e23	−0.956228	−0.478114	+	0.878298i	$0.658679\pi$
$558$	1.57155e22	0.0707846
$559$	−2.44282e22	−0.108366
$560$	−7.57687e20	−0.00331048
$561$	2.03352e23	0.875114
$562$	−2.41525e23	−1.02377
$563$	1.05722e23	0.441413	0.220706	−	0.975340i	$-0.429164\pi$
$563$	1.05722e23	0.441413	0.220706	+	0.975340i	$0.429164\pi$
$564$	1.78538e23	0.734273
$565$	6.84180e21	0.0277178
$566$	8.40035e22	0.335242
$567$	−2.05101e23	−0.806329
$568$	−1.12195e23	−0.434521
$569$	3.48917e22	0.133128	0.0665638	−	0.997782i	$-0.478796\pi$
$569$	3.48917e22	0.133128	0.0665638	+	0.997782i	$0.478796\pi$
$570$	9.93154e21	0.0373319
$571$	−2.52923e22	−0.0936659	−0.0468329	−	0.998903i	$-0.514913\pi$
$571$	−2.52923e22	−0.0936659	−0.0468329	+	0.998903i	$0.514913\pi$
$572$	4.70722e22	0.171751
$573$	−2.46083e23	−0.884643
$574$	−1.73434e22	−0.0614305
$575$	3.62360e23	1.26463
$576$	4.94693e22	0.170116
$577$	−1.08332e23	−0.367081	−0.183541	−	0.983012i	$-0.558756\pi$
$577$	−1.08332e23	−0.367081	−0.183541	+	0.983012i	$0.558756\pi$
$578$	−7.88532e22	−0.263289
$579$	−7.02103e22	−0.231011
$580$	3.64378e21	0.0118145
$581$	4.98548e22	0.159298
$582$	3.26922e23	1.02943
$583$	−3.12327e23	−0.969231
$584$	2.39329e23	0.731959
$585$	2.52251e21	0.00760339
$586$	−2.13394e23	−0.633946
$587$	−4.69915e23	−1.37593	−0.687963	−	0.725745i	$-0.741495\pi$
$587$	−4.69915e23	−1.37593	−0.687963	+	0.725745i	$0.741495\pi$
$588$	1.25229e23	0.361408
$589$	7.62559e22	0.216917
$590$	1.69775e22	0.0476027
$591$	4.27837e23	1.18246
$592$	1.63857e21	0.00446406
$593$	−1.02674e23	−0.275737	−0.137868	−	0.990451i	$-0.544025\pi$
$593$	−1.02674e23	−0.275737	−0.137868	+	0.990451i	$0.544025\pi$
$594$	2.04659e23	0.541809
$595$	−2.11643e22	−0.0552343
$596$	2.08937e23	0.537554
$597$	2.03193e22	0.0515379
$598$	−9.13403e22	−0.228403
$599$	−3.97247e23	−0.979338	−0.489669	−	0.871908i	$-0.662882\pi$
$599$	−3.97247e23	−0.979338	−0.489669	+	0.871908i	$0.662882\pi$
$600$	4.61628e23	1.12204
$601$	−2.33403e22	−0.0559338	−0.0279669	−	0.999609i	$-0.508903\pi$
$601$	−2.33403e22	−0.0559338	−0.0279669	+	0.999609i	$0.508903\pi$
$602$	−7.01173e22	−0.165674
$603$	−1.36101e23	−0.317076
$604$	−1.54418e23	−0.354719
$605$	2.07164e21	0.00469237
$606$	2.02394e23	0.452044
$607$	−8.22713e23	−1.81194	−0.905971	−	0.423339i	$-0.860858\pi$
$607$	−8.22713e23	−1.81194	−0.905971	+	0.423339i	$0.860858\pi$
$608$	2.23627e23	0.485674
$609$	−6.58192e22	−0.140963
$610$	−3.39501e22	−0.0717030
$611$	−1.48322e23	−0.308927
$612$	5.64310e22	0.115913
$613$	−4.88325e23	−0.989224	−0.494612	−	0.869114i	$-0.664690\pi$
$613$	−4.88325e23	−0.989224	−0.494612	+	0.869114i	$0.664690\pi$
$614$	−1.35939e23	−0.271589
$615$	−8.64231e21	−0.0170291
$616$	3.61305e23	0.702163
$617$	−7.75198e23	−1.48590	−0.742948	−	0.669349i	$-0.766573\pi$
$617$	−7.75198e23	−1.48590	−0.742948	+	0.669349i	$0.766573\pi$
$618$	−4.00719e23	−0.757596
$619$	3.73621e23	0.696723	0.348362	−	0.937360i	$-0.386738\pi$
$619$	3.73621e23	0.696723	0.348362	+	0.937360i	$0.386738\pi$
$620$	−1.52094e22	−0.0279757
$621$	5.89131e23	1.06889
$622$	−1.85369e23	−0.331756
$623$	9.22727e22	0.162901
$624$	−8.29410e21	−0.0144444
$625$	5.62342e23	0.966095
$626$	3.54653e23	0.601065
$627$	−3.37564e23	−0.564393
$628$	−5.22772e22	−0.0862293
$629$	4.57697e22	0.0744814
$630$	7.24046e21	0.0116244
$631$	−1.13613e24	−1.79962	−0.899809	−	0.436285i	$-0.856294\pi$
$631$	−1.13613e24	−1.79962	−0.899809	+	0.436285i	$0.856294\pi$
$632$	1.14649e24	1.79175
$633$	5.37554e23	0.828877
$634$	−6.51260e23	−0.990821
$635$	1.90993e22	0.0286709
$636$	−4.28319e23	−0.634428
$637$	−1.04036e23	−0.152054
$638$	8.34849e22	0.120402
$639$	7.64192e22	0.108754
$640$	−4.23965e22	−0.0595388
$641$	−3.42621e23	−0.474811	−0.237405	−	0.971411i	$-0.576297\pi$
$641$	−3.42621e23	−0.474811	−0.237405	+	0.971411i	$0.576297\pi$
$642$	5.53455e23	0.756894
$643$	−1.15762e24	−1.56233	−0.781163	−	0.624328i	$-0.785373\pi$
$643$	−1.15762e24	−1.56233	−0.781163	+	0.624328i	$0.785373\pi$
$644$	3.88937e23	0.518023
$645$	−3.49398e22	−0.0459264
$646$	−1.84577e23	−0.239443
$647$	−5.33662e23	−0.683250	−0.341625	−	0.939836i	$-0.610977\pi$
$647$	−5.33662e23	−0.683250	−0.341625	+	0.939836i	$0.610977\pi$
$648$	9.54018e23	1.20551
$649$	−5.77049e23	−0.719669
$650$	−1.43414e23	−0.176534
$651$	2.74733e23	0.333790
$652$	−2.12530e23	−0.254868
$653$	1.49336e24	1.76767	0.883835	−	0.467799i	$-0.154953\pi$
$653$	1.49336e24	1.76767	0.883835	+	0.467799i	$0.154953\pi$
$654$	5.54641e23	0.648039
$655$	1.55446e23	0.179278
$656$	5.75013e21	0.00654629
$657$	−1.63015e23	−0.183198
$658$	−4.25736e23	−0.472302
$659$	−9.29158e23	−1.01757	−0.508784	−	0.860894i	$-0.669905\pi$
$659$	−9.29158e23	−1.01757	−0.508784	+	0.860894i	$0.669905\pi$
$660$	6.73276e22	0.0727897
$661$	1.32196e24	1.41094	0.705468	−	0.708742i	$-0.250737\pi$
$661$	1.32196e24	1.41094	0.705468	+	0.708742i	$0.250737\pi$
$662$	4.31140e23	0.454282
$663$	−2.31677e23	−0.241000
$664$	−2.31897e23	−0.238159
$665$	3.51326e22	0.0356226
$666$	−1.56582e22	−0.0156751
$667$	2.40319e23	0.237530
$668$	1.51049e23	0.147407
$669$	−5.37647e22	−0.0518054
$670$	−8.87890e22	−0.0844740
$671$	1.15393e24	1.08402
$672$	8.05681e23	0.747350
$673$	1.93206e24	1.76967	0.884835	−	0.465904i	$-0.154271\pi$
$673$	1.93206e24	1.76967	0.884835	+	0.465904i	$0.154271\pi$
$674$	−2.13321e23	−0.192941
$675$	9.25001e23	0.826152
$676$	6.23652e23	0.550041
$677$	6.80798e23	0.592945	0.296473	−	0.955041i	$-0.404190\pi$
$677$	6.80798e23	0.592945	0.296473	+	0.955041i	$0.404190\pi$
$678$	2.14973e23	0.184898
$679$	1.15648e24	0.982300
$680$	9.84446e22	0.0825783
$681$	4.67709e23	0.387458
$682$	−3.48471e23	−0.285101
$683$	2.42421e24	1.95881	0.979407	−	0.201893i	$-0.0647095\pi$
$683$	2.42421e24	1.95881	0.979407	+	0.201893i	$0.0647095\pi$
$684$	−9.36751e22	−0.0747562
$685$	1.53819e23	0.121239
$686$	−8.51247e23	−0.662675
$687$	−3.72394e23	−0.286332
$688$	2.32470e22	0.0176549
$689$	3.55831e23	0.266920
$690$	−1.30644e23	−0.0967996
$691$	−1.94726e23	−0.142515	−0.0712575	−	0.997458i	$-0.522701\pi$
$691$	−1.94726e23	−0.142515	−0.0712575	+	0.997458i	$0.522701\pi$
$692$	−1.14955e24	−0.831050
$693$	−2.46096e23	−0.175741
$694$	−1.65712e24	−1.16896
$695$	1.27306e23	0.0887109
$696$	3.06155e23	0.210748
$697$	1.60617e23	0.109223
$698$	−1.07797e24	−0.724160
$699$	−2.60539e23	−0.172909
$700$	6.10674e23	0.400384
$701$	8.12374e23	0.526203	0.263101	−	0.964768i	$-0.415255\pi$
$701$	8.12374e23	0.526203	0.263101	+	0.964768i	$0.415255\pi$
$702$	−2.33166e23	−0.149210
$703$	−7.59775e22	−0.0480358
$704$	−1.09692e24	−0.685182
$705$	−2.12146e23	−0.130926
$706$	−4.86105e23	−0.296408
$707$	7.15965e23	0.431347
$708$	−7.91352e23	−0.471072
$709$	−2.48341e24	−1.46068	−0.730342	−	0.683082i	$-0.760639\pi$
$709$	−2.48341e24	−1.46068	−0.730342	+	0.683082i	$0.760639\pi$
$710$	4.98541e22	0.0289738
$711$	−7.80913e23	−0.448447
$712$	−4.29202e23	−0.243546
$713$	−1.00311e24	−0.562453
$714$	−6.64992e23	−0.368453
$715$	−5.59332e22	−0.0306245
$716$	−1.15570e24	−0.625297
$717$	−1.90084e24	−1.01632
$718$	−7.44566e22	−0.0393410
$719$	−1.78692e24	−0.933062	−0.466531	−	0.884505i	$-0.654496\pi$
$719$	−1.78692e24	−0.933062	−0.466531	+	0.884505i	$0.654496\pi$
$720$	−2.40054e21	−0.00123875
$721$	−1.41753e24	−0.722909
$722$	−9.52631e23	−0.480129
$723$	−3.01106e24	−1.49983
$724$	6.84004e23	0.336729
$725$	3.77328e23	0.183589
$726$	6.50918e22	0.0313015
$727$	−9.01344e23	−0.428399	−0.214199	−	0.976790i	$-0.568714\pi$
$727$	−9.01344e23	−0.428399	−0.214199	+	0.976790i	$0.568714\pi$
$728$	−4.11631e23	−0.193371
$729$	1.36528e24	0.633923
$730$	−1.06347e23	−0.0488069
$731$	6.49354e23	0.294567
$732$	1.58248e24	0.709566
$733$	1.88863e24	0.837075	0.418537	−	0.908200i	$-0.362543\pi$
$733$	1.88863e24	0.837075	0.418537	+	0.908200i	$0.362543\pi$
$734$	1.98442e24	0.869394
$735$	−1.48803e23	−0.0644419
$736$	−2.94170e24	−1.25932
$737$	3.01785e24	1.27710
$738$	−5.49483e22	−0.0229866
$739$	−1.35232e24	−0.559245	−0.279623	−	0.960110i	$-0.590209\pi$
$739$	−1.35232e24	−0.559245	−0.279623	+	0.960110i	$0.590209\pi$
$740$	1.51538e22	0.00619517
$741$	3.84583e23	0.155430
$742$	1.02136e24	0.408079
$743$	−1.18982e24	−0.469978	−0.234989	−	0.971998i	$-0.575505\pi$
$743$	−1.18982e24	−0.469978	−0.234989	+	0.971998i	$0.575505\pi$
$744$	−1.27791e24	−0.499034
$745$	−2.48267e23	−0.0958499
$746$	−1.16215e24	−0.443590
$747$	1.57952e23	0.0596075
$748$	−1.25128e24	−0.466865
$749$	1.95783e24	0.722238
$750$	−4.12606e23	−0.150493
$751$	1.13711e24	0.410074	0.205037	−	0.978754i	$-0.434268\pi$
$751$	1.13711e24	0.410074	0.205037	+	0.978754i	$0.434268\pi$
$752$	1.41151e23	0.0503305
$753$	−4.84500e24	−1.70819
$754$	−9.51134e22	−0.0331578
$755$	1.83486e23	0.0632491
$756$	9.92845e23	0.338412
$757$	−4.87000e24	−1.64140	−0.820699	−	0.571361i	$-0.806416\pi$
$757$	−4.87000e24	−1.64140	−0.820699	+	0.571361i	$0.806416\pi$
$758$	2.15436e24	0.718009
$759$	4.44048e24	1.46344
$760$	−1.63417e23	−0.0532578
$761$	−6.48907e23	−0.209128	−0.104564	−	0.994518i	$-0.533345\pi$
$761$	−6.48907e23	−0.209128	−0.104564	+	0.994518i	$0.533345\pi$
$762$	6.00111e23	0.191256
$763$	1.96203e24	0.618368
$764$	1.51422e24	0.471949
$765$	−6.70537e22	−0.0206681
$766$	3.30120e24	1.00630
$767$	6.57425e23	0.198192
$768$	−3.85043e24	−1.14799
$769$	6.36490e24	1.87680	0.938400	−	0.345552i	$-0.112308\pi$
$769$	6.36490e24	1.87680	0.938400	+	0.345552i	$0.112308\pi$
$770$	−1.60547e23	−0.0468201
$771$	9.88345e23	0.285067
$772$	4.32023e23	0.123242
$773$	−3.69484e22	−0.0104249	−0.00521243	−	0.999986i	$-0.501659\pi$
$773$	−3.69484e22	−0.0104249	−0.00521243	+	0.999986i	$0.501659\pi$
$774$	−2.22149e23	−0.0619935
$775$	−1.57499e24	−0.434724
$776$	−5.37930e24	−1.46859
$777$	−2.73730e23	−0.0739170
$778$	−3.34342e23	−0.0893026
$779$	−2.66623e23	−0.0704417
$780$	−7.67056e22	−0.0200458
$781$	−1.69449e24	−0.438033
$782$	2.42802e24	0.620862
$783$	6.13467e23	0.155173
$784$	9.90053e22	0.0247726
$785$	6.21179e22	0.0153753
$786$	4.88419e24	1.19592
$787$	6.07502e22	0.0147151	0.00735754	−	0.999973i	$-0.497658\pi$
$787$	6.07502e22	0.0147151	0.00735754	+	0.999973i	$0.497658\pi$
$788$	−2.63260e24	−0.630829
$789$	8.48984e23	0.201254
$790$	−5.09449e23	−0.119473
$791$	7.60461e23	0.176432
$792$	1.14470e24	0.262742
$793$	−1.31466e24	−0.298532
$794$	−1.53540e24	−0.344943
$795$	5.08947e23	0.113123
$796$	−1.25030e23	−0.0274950
$797$	3.40409e24	0.740637	0.370318	−	0.928905i	$-0.379249\pi$
$797$	3.40409e24	0.740637	0.370318	+	0.928905i	$0.379249\pi$
$798$	1.10388e24	0.237629
$799$	3.94273e24	0.839748
$800$	−4.61880e24	−0.973340
$801$	2.92343e23	0.0609559
$802$	2.26184e24	0.466637
$803$	3.61463e24	0.737874
$804$	4.13862e24	0.835947
$805$	−4.62151e23	−0.0923675
$806$	3.97009e23	0.0785150
$807$	1.03277e25	2.02105
$808$	−3.33028e24	−0.644887
$809$	−6.50111e24	−1.24573	−0.622867	−	0.782328i	$-0.714032\pi$
$809$	−6.50111e24	−1.24573	−0.622867	+	0.782328i	$0.714032\pi$
$810$	−4.23922e23	−0.0803828
$811$	−4.30312e24	−0.807433	−0.403716	−	0.914884i	$-0.632282\pi$
$811$	−4.30312e24	−0.807433	−0.403716	+	0.914884i	$0.632282\pi$
$812$	4.05003e23	0.0752025
$813$	−5.33225e24	−0.979808
$814$	3.47199e23	0.0631351
$815$	2.52537e23	0.0454449
$816$	2.20475e23	0.0392639
$817$	−1.07792e24	−0.189977
$818$	−3.64091e24	−0.635049
$819$	2.80375e23	0.0483978
$820$	5.31785e22	0.00908485
$821$	8.45855e23	0.143014	0.0715070	−	0.997440i	$-0.477219\pi$
$821$	8.45855e23	0.143014	0.0715070	+	0.997440i	$0.477219\pi$
$822$	4.83308e24	0.808748
$823$	−5.49132e24	−0.909449	−0.454724	−	0.890632i	$-0.650262\pi$
$823$	−5.49132e24	−0.909449	−0.454724	+	0.890632i	$0.650262\pi$
$824$	6.59358e24	1.08079
$825$	6.97205e24	1.13110
$826$	1.88704e24	0.303005
$827$	7.56396e24	1.20213	0.601067	−	0.799199i	$-0.294743\pi$
$827$	7.56396e24	1.20213	0.601067	+	0.799199i	$0.294743\pi$
$828$	1.23225e24	0.193839
$829$	3.26490e24	0.508342	0.254171	−	0.967159i	$-0.418197\pi$
$829$	3.26490e24	0.508342	0.254171	+	0.967159i	$0.418197\pi$
$830$	1.03045e23	0.0158804
$831$	−1.07866e25	−1.64541
$832$	1.24970e24	0.188694
$833$	2.76549e24	0.413323
$834$	4.00001e24	0.591766
$835$	−1.79483e23	−0.0262839
$836$	2.07712e24	0.301098
$837$	−2.56065e24	−0.367437
$838$	2.57239e24	0.365395
$839$	−8.41852e22	−0.0118375	−0.00591874	−	0.999982i	$-0.501884\pi$
$839$	−8.41852e22	−0.0118375	−0.00591874	+	0.999982i	$0.501884\pi$
$840$	−5.88758e23	−0.0819526
$841$	2.50246e23	0.0344828
$842$	−2.31563e24	−0.315876
$843$	−1.33771e25	−1.80646
$844$	−3.30771e24	−0.442198
$845$	−7.41049e23	−0.0980765
$846$	−1.34884e24	−0.176730
$847$	2.30261e23	0.0298683
$848$	−3.38626e23	−0.0434866
$849$	4.65263e24	0.591539
$850$	3.81226e24	0.479868
$851$	9.99446e23	0.124554
$852$	−2.32379e24	−0.286722
$853$	5.40778e24	0.660621	0.330311	−	0.943872i	$-0.392847\pi$
$853$	5.40778e24	0.660621	0.330311	+	0.943872i	$0.392847\pi$
$854$	−3.77353e24	−0.456410
$855$	1.11309e23	0.0133296
$856$	−9.10677e24	−1.07979
$857$	−1.42595e24	−0.167404	−0.0837022	−	0.996491i	$-0.526674\pi$
$857$	−1.42595e24	−0.167404	−0.0837022	+	0.996491i	$0.526674\pi$
$858$	−1.75745e24	−0.204287
$859$	1.60064e25	1.84226	0.921129	−	0.389256i	$-0.127268\pi$
$859$	1.60064e25	1.84226	0.921129	+	0.389256i	$0.127268\pi$
$860$	2.14994e23	0.0245013
$861$	−9.60586e23	−0.108395
$862$	−5.32385e24	−0.594859
$863$	7.05353e24	0.780396	0.390198	−	0.920731i	$-0.372407\pi$
$863$	7.05353e24	0.780396	0.390198	+	0.920731i	$0.372407\pi$
$864$	−7.50933e24	−0.822687
$865$	1.36595e24	0.148183
$866$	−4.89801e24	−0.526160
$867$	−4.36738e24	−0.464578
$868$	−1.69051e24	−0.178074
$869$	1.73157e25	1.80623
$870$	−1.36041e23	−0.0140526
$871$	−3.43821e24	−0.351704
$872$	−9.12629e24	−0.924494
$873$	3.66401e24	0.367566
$874$	−4.03050e24	−0.400417
$875$	−1.45958e24	−0.143602
$876$	4.95703e24	0.482989
$877$	−7.66451e24	−0.739584	−0.369792	−	0.929115i	$-0.620571\pi$
$877$	−7.66451e24	−0.739584	−0.369792	+	0.929115i	$0.620571\pi$
$878$	9.08632e24	0.868330
$879$	−1.18191e25	−1.11861
$880$	5.32287e22	0.00498934
$881$	7.07926e24	0.657193	0.328597	−	0.944470i	$-0.393424\pi$
$881$	7.07926e24	0.657193	0.328597	+	0.944470i	$0.393424\pi$
$882$	−9.46095e23	−0.0869865
$883$	−6.05402e24	−0.551287	−0.275644	−	0.961260i	$-0.588891\pi$
$883$	−6.05402e24	−0.551287	−0.275644	+	0.961260i	$0.588891\pi$
$884$	1.42557e24	0.128572
$885$	9.40318e23	0.0839957
$886$	−1.64839e24	−0.145839
$887$	−1.70506e25	−1.49413	−0.747066	−	0.664750i	$-0.768538\pi$
$887$	−1.70506e25	−1.49413	−0.747066	+	0.664750i	$0.768538\pi$
$888$	1.27324e24	0.110510
$889$	2.12288e24	0.182499
$890$	1.90718e23	0.0162396
$891$	1.44087e25	1.21525
$892$	3.30829e23	0.0276377
$893$	−6.54491e24	−0.541584
$894$	−7.80069e24	−0.639387
$895$	1.37326e24	0.111495
$896$	−4.71234e24	−0.378982
$897$	−5.05899e24	−0.403021
$898$	−3.05821e24	−0.241334
$899$	−1.04454e24	−0.0816525
$900$	1.93477e24	0.149819
$901$	−9.45876e24	−0.725560
$902$	1.21840e24	0.0925840
$903$	−3.88353e24	−0.292335
$904$	−3.53725e24	−0.263775
$905$	−8.12763e23	−0.0600414
$906$	5.76523e24	0.421917
$907$	−7.75494e24	−0.562233	−0.281117	−	0.959674i	$-0.590705\pi$
$907$	−7.75494e24	−0.562233	−0.281117	+	0.959674i	$0.590705\pi$
$908$	−2.87794e24	−0.206705
$909$	2.26835e24	0.161405
$910$	1.82910e23	0.0128939
$911$	−2.50624e25	−1.75031	−0.875157	−	0.483839i	$-0.839242\pi$
$911$	−2.50624e25	−1.75031	−0.875157	+	0.483839i	$0.839242\pi$
$912$	−3.65987e23	−0.0253227
$913$	−3.50238e24	−0.240083
$914$	−6.94891e24	−0.471926
$915$	−1.88036e24	−0.126521
$916$	2.29144e24	0.152755
$917$	1.72777e25	1.14116
$918$	6.19805e24	0.405595
$919$	2.04540e25	1.32616	0.663080	−	0.748549i	$-0.269249\pi$
$919$	2.04540e25	1.32616	0.663080	+	0.748549i	$0.269249\pi$
$920$	2.14967e24	0.138094
$921$	−7.52913e24	−0.479223
$922$	7.78150e24	0.490739
$923$	1.93052e24	0.120631
$924$	7.48341e24	0.463327
$925$	1.56924e24	0.0962687
$926$	−1.01056e25	−0.614285
$927$	−4.49110e24	−0.270505
$928$	−3.06322e24	−0.182819
$929$	1.76735e25	1.04518	0.522588	−	0.852585i	$-0.324967\pi$
$929$	1.76735e25	1.04518	0.522588	+	0.852585i	$0.324967\pi$
$930$	5.67844e23	0.0332754
$931$	−4.59070e24	−0.266567
$932$	1.60317e24	0.0922452
$933$	−1.02669e25	−0.585389
$934$	3.61408e24	0.204197
$935$	1.48683e24	0.0832456
$936$	−1.30415e24	−0.0723573
$937$	3.49574e24	0.192200	0.0960999	−	0.995372i	$-0.469363\pi$
$937$	3.49574e24	0.192200	0.0960999	+	0.995372i	$0.469363\pi$
$938$	−9.86883e24	−0.537702
$939$	1.96428e25	1.06059
$940$	1.30539e24	0.0698481
$941$	6.46098e24	0.342600	0.171300	−	0.985219i	$-0.445203\pi$
$941$	6.46098e24	0.342600	0.171300	+	0.985219i	$0.445203\pi$
$942$	1.95178e24	0.102565
$943$	3.50729e24	0.182651
$944$	−6.25638e23	−0.0322895
$945$	−1.17974e24	−0.0603415
$946$	4.92586e24	0.249693
$947$	−2.80049e25	−1.40689	−0.703444	−	0.710751i	$-0.748355\pi$
$947$	−2.80049e25	−1.40689	−0.703444	+	0.710751i	$0.748355\pi$
$948$	2.37464e25	1.18230
$949$	−4.11811e24	−0.203206
$950$	−6.32834e24	−0.309485
$951$	−3.60708e25	−1.74832
$952$	1.09420e25	0.525635
$953$	1.94809e24	0.0927511	0.0463756	−	0.998924i	$-0.485233\pi$
$953$	1.94809e24	0.0927511	0.0463756	+	0.998924i	$0.485233\pi$
$954$	3.23591e24	0.152699
$955$	−1.79926e24	−0.0841520
$956$	1.16964e25	0.542199
$957$	4.62391e24	0.212450
$958$	1.41534e25	0.644547
$959$	1.70969e25	0.771718
$960$	1.78746e24	0.0799706
$961$	−1.81901e25	−0.806653
$962$	−3.95560e23	−0.0173870
$963$	6.20290e24	0.270254
$964$	1.85278e25	0.800148
$965$	−5.13348e23	−0.0219750
$966$	−1.45210e25	−0.616158
$967$	1.95943e25	0.824146	0.412073	−	0.911151i	$-0.364805\pi$
$967$	1.95943e25	0.824146	0.412073	+	0.911151i	$0.364805\pi$
$968$	−1.07105e24	−0.0446548
$969$	−1.02230e25	−0.422501
$970$	2.39031e24	0.0979253
$971$	−2.44987e25	−0.994902	−0.497451	−	0.867492i	$-0.665730\pi$
$971$	−2.44987e25	−0.994902	−0.497451	+	0.867492i	$0.665730\pi$
$972$	7.36042e24	0.296305
$973$	1.41499e25	0.564671
$974$	1.64671e25	0.651427
$975$	−7.94318e24	−0.311498
$976$	1.25109e24	0.0486370
$977$	−4.65590e24	−0.179432	−0.0897161	−	0.995967i	$-0.528596\pi$
$977$	−4.65590e24	−0.179432	−0.0897161	+	0.995967i	$0.528596\pi$
$978$	7.93484e24	0.303150
$979$	−6.48231e24	−0.245514
$980$	9.15623e23	0.0343791
$981$	6.21620e24	0.231387
$982$	2.61201e25	0.963888
$983$	−2.74294e25	−1.00349	−0.501743	−	0.865017i	$-0.667308\pi$
$983$	−2.74294e25	−1.00349	−0.501743	+	0.865017i	$0.667308\pi$
$984$	4.46812e24	0.162056
$985$	3.12816e24	0.112482
$986$	2.52832e24	0.0901318
$987$	−2.35799e25	−0.833385
$988$	−2.36644e24	−0.0829204
$989$	1.41796e25	0.492600
$990$	−5.08654e23	−0.0175196
$991$	5.89835e24	0.201421	0.100710	−	0.994916i	$-0.467888\pi$
$991$	5.89835e24	0.201421	0.100710	+	0.994916i	$0.467888\pi$
$992$	1.27861e25	0.432900
$993$	2.38792e25	0.801589
$994$	5.54125e24	0.184427
$995$	1.48566e23	0.00490256
$996$	−4.80310e24	−0.157151
$997$	4.81262e25	1.56125	0.780626	−	0.624999i	$-0.214901\pi$
$997$	4.81262e25	1.56125	0.780626	+	0.624999i	$0.214901\pi$
$998$	−1.66048e25	−0.534101
$999$	2.55130e24	0.0813682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.12	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+229.733 q^{2} +12724.1 q^{3} -78294.6 q^{4} +93032.9 q^{5} +2.92314e6 q^{6} +1.03405e7 q^{7} -4.80985e7 q^{8} +3.27614e7 q^{9} +O(q^{10})\)	\(q+229.733 q^{2} +12724.1 q^{3} -78294.6 q^{4} +93032.9 q^{5} +2.92314e6 q^{6} +1.03405e7 q^{7} -4.80985e7 q^{8} +3.27614e7 q^{9} +2.13728e7 q^{10} -7.26440e8 q^{11} -9.96224e8 q^{12} +8.27625e8 q^{13} +2.37557e9 q^{14} +1.18376e9 q^{15} -7.87608e8 q^{16} -2.20001e10 q^{17} +7.52638e9 q^{18} +3.65200e10 q^{19} -7.28397e9 q^{20} +1.31574e11 q^{21} -1.66888e11 q^{22} -4.80402e11 q^{23} -6.12008e11 q^{24} -7.54284e11 q^{25} +1.90133e11 q^{26} -1.22633e12 q^{27} -8.09608e11 q^{28} -5.00246e11 q^{29} +2.71948e11 q^{30} +2.08806e12 q^{31} +6.12343e12 q^{32} -9.24326e12 q^{33} -5.05415e12 q^{34} +9.62010e11 q^{35} -2.56504e12 q^{36} -2.08044e12 q^{37} +8.38986e12 q^{38} +1.05307e13 q^{39} -4.47474e12 q^{40} -7.30075e12 q^{41} +3.02268e13 q^{42} -2.95160e13 q^{43} +5.68763e13 q^{44} +3.04789e12 q^{45} -1.10364e14 q^{46} -1.79214e14 q^{47} -1.00216e13 q^{48} -1.25704e14 q^{49} -1.73284e14 q^{50} -2.79930e14 q^{51} -6.47985e13 q^{52} +4.29943e14 q^{53} -2.81729e14 q^{54} -6.75828e13 q^{55} -4.97364e14 q^{56} +4.64682e14 q^{57} -1.14923e14 q^{58} +7.94352e14 q^{59} -9.26816e13 q^{60} -1.58847e15 q^{61} +4.79697e14 q^{62} +3.38770e14 q^{63} +1.50999e15 q^{64} +7.69963e13 q^{65} -2.12349e15 q^{66} -4.15430e15 q^{67} +1.72248e15 q^{68} -6.11266e15 q^{69} +2.21006e14 q^{70} +2.33260e15 q^{71} -1.57577e15 q^{72} -4.97582e15 q^{73} -4.77946e14 q^{74} -9.59755e15 q^{75} -2.85932e15 q^{76} -7.51178e15 q^{77} +2.41926e15 q^{78} -2.38364e16 q^{79} -7.32734e13 q^{80} -1.98347e16 q^{81} -1.67723e15 q^{82} +4.82130e15 q^{83} -1.03015e16 q^{84} -2.04673e15 q^{85} -6.78082e15 q^{86} -6.36516e15 q^{87} +3.49407e16 q^{88} +8.92339e15 q^{89} +7.00201e14 q^{90} +8.55809e15 q^{91} +3.76128e16 q^{92} +2.65686e16 q^{93} -4.11715e16 q^{94} +3.39756e15 q^{95} +7.79148e16 q^{96} +1.11839e17 q^{97} -2.88784e16 q^{98} -2.37992e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 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

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