LMFDB - Embedded newform 29.18.a.a.1.15

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			1.15
Root			$516.149$ 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)

$f(q)$	$=$	$q+516.149 q^{2} -14037.1 q^{3} +135338. q^{4} -336022. q^{5} -7.24525e6 q^{6} +1.38849e7 q^{7} +2.20183e6 q^{8} +6.79008e7 q^{9} +O(q^{10})$	\(q+516.149 q^{2} -14037.1 q^{3} +135338. q^{4} -336022. q^{5} -7.24525e6 q^{6} +1.38849e7 q^{7} +2.20183e6 q^{8} +6.79008e7 q^{9} -1.73438e8 q^{10} +9.23603e8 q^{11} -1.89976e9 q^{12} +3.11943e9 q^{13} +7.16668e9 q^{14} +4.71678e9 q^{15} -1.66025e10 q^{16} -4.14683e10 q^{17} +3.50469e10 q^{18} -3.78088e10 q^{19} -4.54765e10 q^{20} -1.94904e11 q^{21} +4.76717e11 q^{22} -1.06606e10 q^{23} -3.09074e10 q^{24} -6.50029e11 q^{25} +1.61009e12 q^{26} +8.59625e11 q^{27} +1.87915e12 q^{28} -5.00246e11 q^{29} +2.43456e12 q^{30} -6.68857e12 q^{31} -8.85798e12 q^{32} -1.29647e13 q^{33} -2.14038e13 q^{34} -4.66564e12 q^{35} +9.18954e12 q^{36} -6.29929e12 q^{37} -1.95150e13 q^{38} -4.37878e13 q^{39} -7.39865e11 q^{40} -6.57292e13 q^{41} -1.00600e14 q^{42} +8.76426e13 q^{43} +1.24999e14 q^{44} -2.28162e13 q^{45} -5.50247e12 q^{46} -1.05239e14 q^{47} +2.33052e14 q^{48} -3.98399e13 q^{49} -3.35512e14 q^{50} +5.82095e14 q^{51} +4.22177e14 q^{52} -4.84773e14 q^{53} +4.43695e14 q^{54} -3.10351e14 q^{55} +3.05723e13 q^{56} +5.30726e14 q^{57} -2.58202e14 q^{58} +1.02980e15 q^{59} +6.38360e14 q^{60} -2.52259e14 q^{61} -3.45230e15 q^{62} +9.42796e14 q^{63} -2.39591e15 q^{64} -1.04820e15 q^{65} -6.69174e15 q^{66} -4.51387e15 q^{67} -5.61223e15 q^{68} +1.49644e14 q^{69} -2.40816e15 q^{70} +4.69441e15 q^{71} +1.49506e14 q^{72} +1.67124e15 q^{73} -3.25137e15 q^{74} +9.12453e15 q^{75} -5.11696e15 q^{76} +1.28241e16 q^{77} -2.26010e16 q^{78} +7.18372e15 q^{79} +5.57882e15 q^{80} -2.08354e16 q^{81} -3.39261e16 q^{82} -3.72278e16 q^{83} -2.63779e16 q^{84} +1.39343e16 q^{85} +4.52366e16 q^{86} +7.02202e15 q^{87} +2.03362e15 q^{88} -3.65166e16 q^{89} -1.17765e16 q^{90} +4.33130e16 q^{91} -1.44279e15 q^{92} +9.38883e16 q^{93} -5.43190e16 q^{94} +1.27046e16 q^{95} +1.24341e17 q^{96} -9.68948e16 q^{97} -2.05633e16 q^{98} +6.27134e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	516.149	1.42567	0.712837	−	0.701330i	$-0.247410\pi$
$2$	516.149	1.42567	0.712837	+	0.701330i	$0.247410\pi$
$3$	−14037.1	−1.23523	−0.617615	−	0.786481i	$-0.711901\pi$
$3$	−14037.1	−1.23523	−0.617615	+	0.786481i	$0.711901\pi$
$4$	135338.	1.03255
$5$	−336022.	−0.384701	−0.192350	−	0.981326i	$-0.561611\pi$
$5$	−336022.	−0.384701	−0.192350	+	0.981326i	$0.561611\pi$
$6$	−7.24525e6	−1.76103
$7$	1.38849e7	0.910353	0.455176	−	0.890401i	$-0.349576\pi$
$7$	1.38849e7	0.910353	0.455176	+	0.890401i	$0.349576\pi$
$8$	2.20183e6	0.0464002
$9$	6.79008e7	0.525791
$10$	−1.73438e8	−0.548458
$11$	9.23603e8	1.29912	0.649558	−	0.760312i	$-0.274954\pi$
$11$	9.23603e8	1.29912	0.649558	+	0.760312i	$0.274954\pi$
$12$	−1.89976e9	−1.27543
$13$	3.11943e9	1.06061	0.530306	−	0.847806i	$-0.322077\pi$
$13$	3.11943e9	1.06061	0.530306	+	0.847806i	$0.322077\pi$
$14$	7.16668e9	1.29787
$15$	4.71678e9	0.475193
$16$	−1.66025e10	−0.966395
$17$	−4.14683e10	−1.44178	−0.720892	−	0.693048i	$-0.756268\pi$
$17$	−4.14683e10	−1.44178	−0.720892	+	0.693048i	$0.756268\pi$
$18$	3.50469e10	0.749607
$19$	−3.78088e10	−0.510725	−0.255362	−	0.966845i	$-0.582195\pi$
$19$	−3.78088e10	−0.510725	−0.255362	+	0.966845i	$0.582195\pi$
$20$	−4.54765e10	−0.397221
$21$	−1.94904e11	−1.12449
$22$	4.76717e11	1.85211
$23$	−1.06606e10	−0.0283854	−0.0141927	−	0.999899i	$-0.504518\pi$
$23$	−1.06606e10	−0.0283854	−0.0141927	+	0.999899i	$0.504518\pi$
$24$	−3.09074e10	−0.0573149
$25$	−6.50029e11	−0.852005
$26$	1.61009e12	1.51209
$27$	8.59625e11	0.585757
$28$	1.87915e12	0.939981
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	2.43456e12	0.677471
$31$	−6.68857e12	−1.40851	−0.704253	−	0.709949i	$-0.748718\pi$
$31$	−6.68857e12	−1.40851	−0.704253	+	0.709949i	$0.748718\pi$
$32$	−8.85798e12	−1.42416
$33$	−1.29647e13	−1.60470
$34$	−2.14038e13	−2.05551
$35$	−4.66564e12	−0.350213
$36$	9.18954e12	0.542904
$37$	−6.29929e12	−0.294834	−0.147417	−	0.989074i	$-0.547096\pi$
$37$	−6.29929e12	−0.294834	−0.147417	+	0.989074i	$0.547096\pi$
$38$	−1.95150e13	−0.728127
$39$	−4.37878e13	−1.31010
$40$	−7.39865e11	−0.0178502
$41$	−6.57292e13	−1.28557	−0.642785	−	0.766047i	$-0.722221\pi$
$41$	−6.57292e13	−1.28557	−0.642785	+	0.766047i	$0.722221\pi$
$42$	−1.00600e14	−1.60316
$43$	8.76426e13	1.14349	0.571746	−	0.820430i	$-0.306266\pi$
$43$	8.76426e13	1.14349	0.571746	+	0.820430i	$0.306266\pi$
$44$	1.24999e14	1.34140
$45$	−2.28162e13	−0.202272
$46$	−5.50247e12	−0.0404684
$47$	−1.05239e14	−0.644681	−0.322340	−	0.946624i	$-0.604470\pi$
$47$	−1.05239e14	−0.644681	−0.322340	+	0.946624i	$0.604470\pi$
$48$	2.33052e14	1.19372
$49$	−3.98399e13	−0.171258
$50$	−3.35512e14	−1.21468
$51$	5.82095e14	1.78093
$52$	4.22177e14	1.09513
$53$	−4.84773e14	−1.06953	−0.534766	−	0.845000i	$-0.679600\pi$
$53$	−4.84773e14	−1.06953	−0.534766	+	0.845000i	$0.679600\pi$
$54$	4.43695e14	0.835098
$55$	−3.10351e14	−0.499770
$56$	3.05723e13	0.0422405
$57$	5.30726e14	0.630862
$58$	−2.58202e14	−0.264741
$59$	1.02980e15	0.913087	0.456543	−	0.889701i	$-0.349087\pi$
$59$	1.02980e15	0.913087	0.456543	+	0.889701i	$0.349087\pi$
$60$	6.38360e14	0.490659
$61$	−2.52259e14	−0.168478	−0.0842389	−	0.996446i	$-0.526846\pi$
$61$	−2.52259e14	−0.168478	−0.0842389	+	0.996446i	$0.526846\pi$
$62$	−3.45230e15	−2.00807
$63$	9.42796e14	0.478655
$64$	−2.39591e15	−1.06400
$65$	−1.04820e15	−0.408018
$66$	−6.69174e15	−2.28779
$67$	−4.51387e15	−1.35804	−0.679022	−	0.734118i	$-0.737596\pi$
$67$	−4.51387e15	−1.35804	−0.679022	+	0.734118i	$0.737596\pi$
$68$	−5.61223e15	−1.48871
$69$	1.49644e14	0.0350625
$70$	−2.40816e15	−0.499290
$71$	4.69441e15	0.862749	0.431375	−	0.902173i	$-0.358029\pi$
$71$	4.69441e15	0.862749	0.431375	+	0.902173i	$0.358029\pi$
$72$	1.49506e14	0.0243968
$73$	1.67124e15	0.242547	0.121273	−	0.992619i	$-0.461302\pi$
$73$	1.67124e15	0.242547	0.121273	+	0.992619i	$0.461302\pi$
$74$	−3.25137e15	−0.420337
$75$	9.12453e15	1.05242
$76$	−5.11696e15	−0.527347
$77$	1.28241e16	1.18265
$78$	−2.26010e16	−1.86777
$79$	7.18372e15	0.532745	0.266372	−	0.963870i	$-0.414175\pi$
$79$	7.18372e15	0.532745	0.266372	+	0.963870i	$0.414175\pi$
$80$	5.57882e15	0.371773
$81$	−2.08354e16	−1.24933
$82$	−3.39261e16	−1.83280
$83$	−3.72278e16	−1.81428	−0.907138	−	0.420833i	$-0.861738\pi$
$83$	−3.72278e16	−1.81428	−0.907138	+	0.420833i	$0.861738\pi$
$84$	−2.63779e16	−1.16109
$85$	1.39343e16	0.554655
$86$	4.52366e16	1.63025
$87$	7.02202e15	0.229376
$88$	2.03362e15	0.0602792
$89$	−3.65166e16	−0.983275	−0.491637	−	0.870800i	$-0.663601\pi$
$89$	−3.65166e16	−0.983275	−0.491637	+	0.870800i	$0.663601\pi$
$90$	−1.17765e16	−0.288374
$91$	4.33130e16	0.965531
$92$	−1.44279e15	−0.0293093
$93$	9.38883e16	1.73983
$94$	−5.43190e16	−0.919104
$95$	1.27046e16	0.196476
$96$	1.24341e17	1.75917
$97$	−9.68948e16	−1.25528	−0.627640	−	0.778504i	$-0.715979\pi$
$97$	−9.68948e16	−1.25528	−0.627640	+	0.778504i	$0.715979\pi$
$98$	−2.05633e16	−0.244158
$99$	6.27134e16	0.683063
$100$	−8.79735e16	−0.879735
$101$	1.85502e17	1.70458	0.852290	−	0.523069i	$-0.175213\pi$
$101$	1.85502e17	1.70458	0.852290	+	0.523069i	$0.175213\pi$
$102$	3.00448e17	2.53903
$103$	−2.06573e16	−0.160679	−0.0803393	−	0.996768i	$-0.525600\pi$
$103$	−2.06573e16	−0.160679	−0.0803393	+	0.996768i	$0.525600\pi$
$104$	6.86847e15	0.0492126
$105$	6.54921e16	0.432593
$106$	−2.50215e17	−1.52480
$107$	2.38623e17	1.34261	0.671305	−	0.741181i	$-0.265734\pi$
$107$	2.38623e17	1.34261	0.671305	+	0.741181i	$0.265734\pi$
$108$	1.16340e17	0.604821
$109$	−4.19841e16	−0.201818	−0.100909	−	0.994896i	$-0.532175\pi$
$109$	−4.19841e16	−0.201818	−0.100909	+	0.994896i	$0.532175\pi$
$110$	−1.60187e17	−0.712510
$111$	8.84239e16	0.364187
$112$	−2.30525e17	−0.879760
$113$	−1.23383e17	−0.436603	−0.218302	−	0.975881i	$-0.570052\pi$
$113$	−1.23383e17	−0.436603	−0.218302	+	0.975881i	$0.570052\pi$
$114$	2.73934e17	0.899403
$115$	3.58220e15	0.0109199
$116$	−6.77023e16	−0.191739
$117$	2.11812e17	0.557661
$118$	5.31532e17	1.30176
$119$	−5.75783e17	−1.31253
$120$	1.03856e16	0.0220491
$121$	3.47596e17	0.687700
$122$	−1.30203e17	−0.240194
$123$	9.22649e17	1.58797
$124$	−9.05217e17	−1.45435
$125$	4.74788e17	0.712468
$126$	4.86623e17	0.682406
$127$	2.24541e17	0.294418	0.147209	−	0.989105i	$-0.452971\pi$
$127$	2.24541e17	0.294418	0.147209	+	0.989105i	$0.452971\pi$
$128$	−7.56144e16	−0.0927512
$129$	−1.23025e18	−1.41248
$130$	−5.41026e17	−0.581701
$131$	1.16045e18	1.16902	0.584510	−	0.811387i	$-0.301287\pi$
$131$	1.16045e18	1.16902	0.584510	+	0.811387i	$0.301287\pi$
$132$	−1.75462e18	−1.65693
$133$	−5.24971e17	−0.464939
$134$	−2.32983e18	−1.93613
$135$	−2.88853e17	−0.225341
$136$	−9.13062e16	−0.0668990
$137$	1.54639e18	1.06462	0.532310	−	0.846550i	$-0.321324\pi$
$137$	1.54639e18	1.06462	0.532310	+	0.846550i	$0.321324\pi$
$138$	7.72388e16	0.0499877
$139$	−6.23175e17	−0.379301	−0.189651	−	0.981852i	$-0.560736\pi$
$139$	−6.23175e17	−0.379301	−0.189651	+	0.981852i	$0.560736\pi$
$140$	−6.31437e17	−0.361611
$141$	1.47725e18	0.796328
$142$	2.42301e18	1.23000
$143$	2.88112e18	1.37786
$144$	−1.12732e18	−0.508122
$145$	1.68094e17	0.0714371
$146$	8.62611e17	0.345793
$147$	5.59237e17	0.211543
$148$	−8.52533e17	−0.304429
$149$	−4.82002e18	−1.62542	−0.812710	−	0.582668i	$-0.802009\pi$
$149$	−4.82002e18	−1.62542	−0.812710	+	0.582668i	$0.802009\pi$
$150$	4.70962e18	1.50041
$151$	−5.16236e18	−1.55433	−0.777166	−	0.629295i	$-0.783344\pi$
$151$	−5.16236e18	−1.55433	−0.777166	+	0.629295i	$0.783344\pi$
$152$	−8.32486e16	−0.0236977
$153$	−2.81573e18	−0.758077
$154$	6.61917e18	1.68608
$155$	2.24751e18	0.541853
$156$	−5.92615e18	−1.35274
$157$	−2.50188e18	−0.540903	−0.270451	−	0.962734i	$-0.587173\pi$
$157$	−2.50188e18	−0.540903	−0.270451	+	0.962734i	$0.587173\pi$
$158$	3.70787e18	0.759520
$159$	6.80482e18	1.32112
$160$	2.97648e18	0.547877
$161$	−1.48022e17	−0.0258408
$162$	−1.07542e19	−1.78114
$163$	−1.20213e18	−0.188955	−0.0944774	−	0.995527i	$-0.530118\pi$
$163$	−1.20213e18	−0.188955	−0.0944774	+	0.995527i	$0.530118\pi$
$164$	−8.89565e18	−1.32741
$165$	4.35644e18	0.617331
$166$	−1.92151e19	−2.58657
$167$	−6.33243e18	−0.809992	−0.404996	−	0.914319i	$-0.632727\pi$
$167$	−6.33243e18	−0.809992	−0.404996	+	0.914319i	$0.632727\pi$
$168$	−4.29147e17	−0.0521767
$169$	1.08042e18	0.124899
$170$	7.19215e18	0.790757
$171$	−2.56724e18	−0.268534
$172$	1.18614e19	1.18071
$173$	4.61797e18	0.437582	0.218791	−	0.975772i	$-0.429789\pi$
$173$	4.61797e18	0.437582	0.218791	+	0.975772i	$0.429789\pi$
$174$	3.62441e18	0.327016
$175$	−9.02559e18	−0.775625
$176$	−1.53342e19	−1.25546
$177$	−1.44555e19	−1.12787
$178$	−1.88480e19	−1.40183
$179$	1.70184e19	1.20689	0.603444	−	0.797406i	$-0.293795\pi$
$179$	1.70184e19	1.20689	0.603444	+	0.797406i	$0.293795\pi$
$180$	−3.08789e18	−0.208855
$181$	−9.10644e18	−0.587599	−0.293799	−	0.955867i	$-0.594920\pi$
$181$	−9.10644e18	−0.587599	−0.293799	+	0.955867i	$0.594920\pi$
$182$	2.23560e19	1.37653
$183$	3.54099e18	0.208109
$184$	−2.34729e16	−0.00131709
$185$	2.11670e18	0.113423
$186$	4.84604e19	2.48043
$187$	−3.83002e19	−1.87304
$188$	−1.42428e19	−0.665662
$189$	1.19358e19	0.533245
$190$	6.55746e18	0.280111
$191$	2.59077e19	1.05839	0.529195	−	0.848500i	$-0.322494\pi$
$191$	2.59077e19	1.05839	0.529195	+	0.848500i	$0.322494\pi$
$192$	3.36317e19	1.31428
$193$	9.47430e18	0.354250	0.177125	−	0.984188i	$-0.443320\pi$
$193$	9.47430e18	0.354250	0.177125	+	0.984188i	$0.443320\pi$
$194$	−5.00122e19	−1.78962
$195$	1.47137e19	0.503996
$196$	−5.39185e18	−0.176832
$197$	2.02734e19	0.636742	0.318371	−	0.947966i	$-0.396864\pi$
$197$	2.02734e19	0.636742	0.318371	+	0.947966i	$0.396864\pi$
$198$	3.23694e19	0.973825
$199$	2.07578e19	0.598317	0.299158	−	0.954203i	$-0.403294\pi$
$199$	2.07578e19	0.598317	0.299158	+	0.954203i	$0.403294\pi$
$200$	−1.43126e18	−0.0395332
$201$	6.33618e19	1.67749
$202$	9.57468e19	2.43018
$203$	−6.94587e18	−0.169048
$204$	7.87796e19	1.83890
$205$	2.20865e19	0.494559
$206$	−1.06623e19	−0.229075
$207$	−7.23864e17	−0.0149248
$208$	−5.17904e19	−1.02497
$209$	−3.49203e19	−0.663490
$210$	3.38037e19	0.616737
$211$	5.35352e19	0.938076	0.469038	−	0.883178i	$-0.344601\pi$
$211$	5.35352e19	0.938076	0.469038	+	0.883178i	$0.344601\pi$
$212$	−6.56082e19	−1.10434
$213$	−6.58960e19	−1.06569
$214$	1.23165e20	1.91412
$215$	−2.94498e19	−0.439902
$216$	1.89275e18	0.0271792
$217$	−9.28702e19	−1.28224
$218$	−2.16701e19	−0.287727
$219$	−2.34595e19	−0.299601
$220$	−4.20023e19	−0.516036
$221$	−1.29357e20	−1.52917
$222$	4.56399e19	0.519212
$223$	−1.04666e19	−0.114608	−0.0573039	−	0.998357i	$-0.518250\pi$
$223$	−1.04666e19	−0.114608	−0.0573039	+	0.998357i	$0.518250\pi$
$224$	−1.22992e20	−1.29649
$225$	−4.41374e19	−0.447977
$226$	−6.36838e19	−0.622454
$227$	−4.22359e19	−0.397614	−0.198807	−	0.980039i	$-0.563707\pi$
$227$	−4.22359e19	−0.397614	−0.198807	+	0.980039i	$0.563707\pi$
$228$	7.18274e19	0.651394
$229$	−1.25099e20	−1.09308	−0.546540	−	0.837433i	$-0.684056\pi$
$229$	−1.25099e20	−1.09308	−0.546540	+	0.837433i	$0.684056\pi$
$230$	1.84895e18	0.0155682
$231$	−1.80014e20	−1.46085
$232$	−1.10146e18	−0.00861630
$233$	−2.04113e20	−1.53938	−0.769691	−	0.638417i	$-0.779590\pi$
$233$	−2.04113e20	−1.53938	−0.769691	+	0.638417i	$0.779590\pi$
$234$	1.09326e20	0.795042
$235$	3.53626e19	0.248009
$236$	1.39371e20	0.942804
$237$	−1.00839e20	−0.658062
$238$	−2.97190e20	−1.87124
$239$	−3.36970e19	−0.204743	−0.102371	−	0.994746i	$-0.532643\pi$
$239$	−3.36970e19	−0.204743	−0.102371	+	0.994746i	$0.532643\pi$
$240$	−7.83106e19	−0.459224
$241$	2.57672e19	0.145855	0.0729276	−	0.997337i	$-0.476766\pi$
$241$	2.57672e19	0.145855	0.0729276	+	0.997337i	$0.476766\pi$
$242$	1.79411e20	0.980436
$243$	1.81457e20	0.957458
$244$	−3.41402e19	−0.173961
$245$	1.33871e19	0.0658831
$246$	4.76224e20	2.26393
$247$	−1.17942e20	−0.541681
$248$	−1.47271e19	−0.0653550
$249$	5.22571e20	2.24105
$250$	2.45062e20	1.01575
$251$	−4.86627e20	−1.94971	−0.974854	−	0.222843i	$-0.928466\pi$
$251$	−4.86627e20	−1.94971	−0.974854	+	0.222843i	$0.928466\pi$
$252$	1.27596e20	0.494234
$253$	−9.84618e18	−0.0368760
$254$	1.15897e20	0.419744
$255$	−1.95597e20	−0.685126
$256$	2.75009e20	0.931766
$257$	2.04630e19	0.0670716	0.0335358	−	0.999438i	$-0.489323\pi$
$257$	2.04630e19	0.0670716	0.0335358	+	0.999438i	$0.489323\pi$
$258$	−6.34993e20	−2.01373
$259$	−8.74651e19	−0.268403
$260$	−1.41861e20	−0.421298
$261$	−3.39671e19	−0.0976370
$262$	5.98967e20	1.66664
$263$	−6.44913e20	−1.73731	−0.868655	−	0.495417i	$-0.835015\pi$
$263$	−6.44913e20	−1.73731	−0.868655	+	0.495417i	$0.835015\pi$
$264$	−2.85462e19	−0.0744586
$265$	1.62895e20	0.411450
$266$	−2.70963e20	−0.662852
$267$	5.12588e20	1.21457
$268$	−6.10898e20	−1.40224
$269$	−4.64402e20	−1.03276	−0.516381	−	0.856359i	$-0.672721\pi$
$269$	−4.64402e20	−1.03276	−0.516381	+	0.856359i	$0.672721\pi$
$270$	−1.49091e20	−0.321263
$271$	7.75662e20	1.61970	0.809848	−	0.586640i	$-0.199550\pi$
$271$	7.75662e20	1.61970	0.809848	+	0.586640i	$0.199550\pi$
$272$	6.88478e20	1.39333
$273$	−6.07990e20	−1.19265
$274$	7.98168e20	1.51780
$275$	−6.00369e20	−1.10685
$276$	2.02526e19	0.0362037
$277$	5.21418e20	0.903875	0.451937	−	0.892050i	$-0.350733\pi$
$277$	5.21418e20	0.903875	0.451937	+	0.892050i	$0.350733\pi$
$278$	−3.21651e20	−0.540760
$279$	−4.54159e20	−0.740580
$280$	−1.02730e19	−0.0162500
$281$	6.48003e19	0.0994427	0.0497214	−	0.998763i	$-0.484167\pi$
$281$	6.48003e19	0.0994427	0.0497214	+	0.998763i	$0.484167\pi$
$282$	7.62482e20	1.13530
$283$	−5.68561e20	−0.821471	−0.410736	−	0.911755i	$-0.634728\pi$
$283$	−5.68561e20	−0.821471	−0.410736	+	0.911755i	$0.634728\pi$
$284$	6.35331e20	0.890829
$285$	−1.78336e20	−0.242693
$286$	1.48709e21	1.96438
$287$	−9.12644e20	−1.17032
$288$	−6.01464e20	−0.748813
$289$	8.92377e20	1.07874
$290$	8.67615e19	0.101846
$291$	1.36012e21	1.55056
$292$	2.26183e20	0.250441
$293$	1.33483e21	1.43565	0.717827	−	0.696221i	$-0.245137\pi$
$293$	1.33483e21	1.43565	0.717827	+	0.696221i	$0.245137\pi$
$294$	2.88650e20	0.301591
$295$	−3.46036e20	−0.351265
$296$	−1.38700e19	−0.0136803
$297$	7.93953e20	0.760965
$298$	−2.48785e21	−2.31732
$299$	−3.32550e19	−0.0301060
$300$	1.23490e21	1.08667
$301$	1.21691e21	1.04098
$302$	−2.66455e21	−2.21597
$303$	−2.60392e21	−2.10555
$304$	6.27721e20	0.493562
$305$	8.47645e19	0.0648135
$306$	−1.45333e21	−1.08077
$307$	−1.80419e21	−1.30499	−0.652495	−	0.757793i	$-0.726278\pi$
$307$	−1.80419e21	−1.30499	−0.652495	+	0.757793i	$0.726278\pi$
$308$	1.73559e21	1.22114
$309$	2.89970e20	0.198475
$310$	1.16005e21	0.772506
$311$	−3.24498e20	−0.210256	−0.105128	−	0.994459i	$-0.533525\pi$
$311$	−3.24498e20	−0.210256	−0.105128	+	0.994459i	$0.533525\pi$
$312$	−9.64135e19	−0.0607888
$313$	1.27852e21	0.784479	0.392239	−	0.919863i	$-0.371700\pi$
$313$	1.27852e21	0.784479	0.392239	+	0.919863i	$0.371700\pi$
$314$	−1.29134e21	−0.771151
$315$	−3.16800e20	−0.184139
$316$	9.72230e20	0.550084
$317$	3.00882e21	1.65727	0.828633	−	0.559792i	$-0.189119\pi$
$317$	3.00882e21	1.65727	0.828633	+	0.559792i	$0.189119\pi$
$318$	3.51230e21	1.88348
$319$	−4.62029e20	−0.241240
$320$	8.05079e20	0.409321
$321$	−3.34958e21	−1.65843
$322$	−7.64012e19	−0.0368405
$323$	1.56786e21	0.736354
$324$	−2.81982e21	−1.29000
$325$	−2.02772e21	−0.903648
$326$	−6.20480e20	−0.269388
$327$	5.89337e20	0.249292
$328$	−1.44725e20	−0.0596506
$329$	−1.46123e21	−0.586887
$330$	2.24857e21	0.880113
$331$	2.19172e21	0.836079	0.418039	−	0.908429i	$-0.362717\pi$
$331$	2.19172e21	0.836079	0.418039	+	0.908429i	$0.362717\pi$
$332$	−5.03833e21	−1.87332
$333$	−4.27727e20	−0.155021
$334$	−3.26848e21	−1.15478
$335$	1.51676e21	0.522440
$336$	3.23590e21	1.08670
$337$	2.42912e21	0.795418	0.397709	−	0.917512i	$-0.369805\pi$
$337$	2.42912e21	0.795418	0.397709	+	0.917512i	$0.369805\pi$
$338$	5.57660e20	0.178065
$339$	1.73194e21	0.539305
$340$	1.88583e21	0.572707
$341$	−6.17759e21	−1.82981
$342$	−1.32508e21	−0.382843
$343$	−3.78323e21	−1.06626
$344$	1.92974e20	0.0530583
$345$	−5.02838e19	−0.0134886
$346$	2.38356e21	0.623849
$347$	7.18872e21	1.83591	0.917954	−	0.396687i	$-0.129840\pi$
$347$	7.18872e21	1.83591	0.917954	+	0.396687i	$0.129840\pi$
$348$	9.50346e20	0.236842
$349$	−4.03283e20	−0.0980830	−0.0490415	−	0.998797i	$-0.515617\pi$
$349$	−4.03283e20	−0.0980830	−0.0490415	+	0.998797i	$0.515617\pi$
$350$	−4.65855e21	−1.10579
$351$	2.68154e21	0.621261
$352$	−8.18126e21	−1.85015
$353$	3.67101e20	0.0810403	0.0405202	−	0.999179i	$-0.487098\pi$
$353$	3.67101e20	0.0810403	0.0405202	+	0.999179i	$0.487098\pi$
$354$	−7.46118e21	−1.60798
$355$	−1.57742e21	−0.331900
$356$	−4.94208e21	−1.01528
$357$	8.08234e21	1.62128
$358$	8.78401e21	1.72063
$359$	3.60904e21	0.690381	0.345191	−	0.938533i	$-0.387814\pi$
$359$	3.60904e21	0.690381	0.345191	+	0.938533i	$0.387814\pi$
$360$	−5.02374e19	−0.00938546
$361$	−4.05088e21	−0.739160
$362$	−4.70028e21	−0.837724
$363$	−4.87925e21	−0.849467
$364$	5.86189e21	0.996956
$365$	−5.61575e20	−0.0933079
$366$	1.82768e21	0.296695
$367$	−8.08060e21	−1.28169	−0.640843	−	0.767672i	$-0.721415\pi$
$367$	−8.08060e21	−1.28169	−0.640843	+	0.767672i	$0.721415\pi$
$368$	1.76993e20	0.0274315
$369$	−4.46306e21	−0.675941
$370$	1.09253e21	0.161704
$371$	−6.73103e21	−0.973651
$372$	1.27066e22	1.79645
$373$	4.68821e21	0.647861	0.323931	−	0.946081i	$-0.394996\pi$
$373$	4.68821e21	0.647861	0.323931	+	0.946081i	$0.394996\pi$
$374$	−1.97686e22	−2.67035
$375$	−6.66467e21	−0.880061
$376$	−2.31719e20	−0.0299133
$377$	−1.56048e21	−0.196951
$378$	6.16066e21	0.760234
$379$	−2.25267e21	−0.271810	−0.135905	−	0.990722i	$-0.543394\pi$
$379$	−2.25267e21	−0.271810	−0.135905	+	0.990722i	$0.543394\pi$
$380$	1.71941e21	0.202871
$381$	−3.15191e21	−0.363674
$382$	1.33723e22	1.50892
$383$	−1.50972e22	−1.66612	−0.833061	−	0.553181i	$-0.813414\pi$
$383$	−1.50972e22	−1.66612	−0.833061	+	0.553181i	$0.813414\pi$
$384$	1.06141e21	0.114569
$385$	−4.30920e21	−0.454967
$386$	4.89015e21	0.505045
$387$	5.95100e21	0.601238
$388$	−1.31135e22	−1.29614
$389$	8.83729e21	0.854570	0.427285	−	0.904117i	$-0.359470\pi$
$389$	8.83729e21	0.854570	0.427285	+	0.904117i	$0.359470\pi$
$390$	7.59445e21	0.718534
$391$	4.42077e20	0.0409257
$392$	−8.77208e19	−0.00794641
$393$	−1.62894e22	−1.44401
$394$	1.04641e22	0.907787
$395$	−2.41389e21	−0.204947
$396$	8.48749e21	0.705294
$397$	2.13787e22	1.73885	0.869425	−	0.494064i	$-0.164489\pi$
$397$	2.13787e22	1.73885	0.869425	+	0.494064i	$0.164489\pi$
$398$	1.07141e22	0.853005
$399$	7.36909e21	0.574307
$400$	1.07921e22	0.823374
$401$	1.75807e22	1.31313	0.656565	−	0.754269i	$-0.272009\pi$
$401$	1.75807e22	1.31313	0.656565	+	0.754269i	$0.272009\pi$
$402$	3.27041e22	2.39156
$403$	−2.08645e22	−1.49388
$404$	2.51055e22	1.76006
$405$	7.00115e21	0.480620
$406$	−3.58511e21	−0.241008
$407$	−5.81805e21	−0.383023
$408$	1.28168e21	0.0826356
$409$	3.76504e21	0.237750	0.118875	−	0.992909i	$-0.462071\pi$
$409$	3.76504e21	0.237750	0.118875	+	0.992909i	$0.462071\pi$
$410$	1.13999e22	0.705080
$411$	−2.17069e22	−1.31505
$412$	−2.79572e21	−0.165908
$413$	1.42987e22	0.831231
$414$	−3.73622e20	−0.0212779
$415$	1.25094e22	0.697953
$416$	−2.76318e22	−1.51049
$417$	8.74758e21	0.468524
$418$	−1.80241e22	−0.945921
$419$	−8.81300e21	−0.453215	−0.226608	−	0.973986i	$-0.572764\pi$
$419$	−8.81300e21	−0.453215	−0.226608	+	0.973986i	$0.572764\pi$
$420$	8.86356e21	0.446673
$421$	1.20256e22	0.593892	0.296946	−	0.954894i	$-0.404032\pi$
$421$	1.20256e22	0.593892	0.296946	+	0.954894i	$0.404032\pi$
$422$	2.76321e22	1.33739
$423$	−7.14580e21	−0.338967
$424$	−1.06739e21	−0.0496265
$425$	2.69556e22	1.22841
$426$	−3.40121e22	−1.51933
$427$	−3.50259e21	−0.153374
$428$	3.22947e22	1.38631
$429$	−4.04426e22	−1.70197
$430$	−1.52005e22	−0.627157
$431$	−1.09708e22	−0.443795	−0.221898	−	0.975070i	$-0.571225\pi$
$431$	−1.09708e22	−0.443795	−0.221898	+	0.975070i	$0.571225\pi$
$432$	−1.42720e22	−0.566072
$433$	3.18105e22	1.23715	0.618576	−	0.785725i	$-0.287710\pi$
$433$	3.18105e22	1.23715	0.618576	+	0.785725i	$0.287710\pi$
$434$	−4.79349e22	−1.82805
$435$	−2.35955e21	−0.0882412
$436$	−5.68205e21	−0.208386
$437$	4.03065e20	0.0144971
$438$	−1.21086e22	−0.427133
$439$	2.50012e22	0.864992	0.432496	−	0.901636i	$-0.357633\pi$
$439$	2.50012e22	0.864992	0.432496	+	0.901636i	$0.357633\pi$
$440$	−6.83342e20	−0.0231894
$441$	−2.70516e21	−0.0900460
$442$	−6.67677e22	−2.18010
$443$	2.30077e22	0.736955	0.368477	−	0.929637i	$-0.379879\pi$
$443$	2.30077e22	0.736955	0.368477	+	0.929637i	$0.379879\pi$
$444$	1.19671e22	0.376040
$445$	1.22704e22	0.378266
$446$	−5.40232e21	−0.163393
$447$	6.76593e22	2.00777
$448$	−3.32670e22	−0.968614
$449$	−4.08798e22	−1.16793	−0.583963	−	0.811780i	$-0.698499\pi$
$449$	−4.08798e22	−1.16793	−0.583963	+	0.811780i	$0.698499\pi$
$450$	−2.27815e22	−0.638669
$451$	−6.07077e22	−1.67010
$452$	−1.66983e22	−0.450813
$453$	7.24647e22	1.91996
$454$	−2.18000e22	−0.566869
$455$	−1.45541e22	−0.371440
$456$	1.16857e21	0.0292721
$457$	4.53655e22	1.11542	0.557709	−	0.830036i	$-0.311680\pi$
$457$	4.53655e22	1.11542	0.557709	+	0.830036i	$0.311680\pi$
$458$	−6.45697e22	−1.55838
$459$	−3.56472e22	−0.844534
$460$	4.84808e20	0.0112753
$461$	4.02535e22	0.919065	0.459532	−	0.888161i	$-0.348017\pi$
$461$	4.02535e22	0.919065	0.459532	+	0.888161i	$0.348017\pi$
$462$	−9.29141e22	−2.08269
$463$	−7.05141e22	−1.55181	−0.775903	−	0.630852i	$-0.782705\pi$
$463$	−7.05141e22	−1.55181	−0.775903	+	0.630852i	$0.782705\pi$
$464$	8.30536e21	0.179455
$465$	−3.15485e22	−0.669313
$466$	−1.05353e23	−2.19466
$467$	9.52372e22	1.94811	0.974055	−	0.226314i	$-0.0726674\pi$
$467$	9.52372e22	1.94811	0.974055	+	0.226314i	$0.0726674\pi$
$468$	2.86661e22	0.575810
$469$	−6.26747e22	−1.23630
$470$	1.82524e22	0.353580
$471$	3.51192e22	0.668139
$472$	2.26745e21	0.0423674
$473$	8.09470e22	1.48553
$474$	−5.20479e22	−0.938182
$475$	2.45768e22	0.435140
$476$	−7.79253e22	−1.35525
$477$	−3.29165e22	−0.562350
$478$	−1.73927e22	−0.291897
$479$	6.70259e22	1.10507	0.552536	−	0.833489i	$-0.313660\pi$
$479$	6.70259e22	1.10507	0.552536	+	0.833489i	$0.313660\pi$
$480$	−4.17812e22	−0.676753
$481$	−1.96502e22	−0.312704
$482$	1.32997e22	0.207942
$483$	2.07780e21	0.0319193
$484$	4.70429e22	0.710082
$485$	3.25588e22	0.482907
$486$	9.36587e22	1.36502
$487$	1.12205e23	1.60700	0.803500	−	0.595305i	$-0.202969\pi$
$487$	1.12205e23	1.60700	0.803500	+	0.595305i	$0.202969\pi$
$488$	−5.55432e20	−0.00781740
$489$	1.68745e22	0.233402
$490$	6.90973e21	0.0939278
$491$	−5.89344e22	−0.787364	−0.393682	−	0.919247i	$-0.628799\pi$
$491$	−5.89344e22	−0.787364	−0.393682	+	0.919247i	$0.628799\pi$
$492$	1.24869e23	1.63966
$493$	2.07444e22	0.267733
$494$	−6.08755e22	−0.772260
$495$	−2.10731e22	−0.262775
$496$	1.11047e23	1.36117
$497$	6.51814e22	0.785406
$498$	2.69725e23	3.19500
$499$	8.25049e22	0.960782	0.480391	−	0.877054i	$-0.340495\pi$
$499$	8.25049e22	0.960782	0.480391	+	0.877054i	$0.340495\pi$
$500$	6.42569e22	0.735656
$501$	8.88892e22	1.00053
$502$	−2.51172e23	−2.77965
$503$	2.78400e22	0.302929	0.151465	−	0.988463i	$-0.451601\pi$
$503$	2.78400e22	0.302929	0.151465	+	0.988463i	$0.451601\pi$
$504$	2.07588e21	0.0222097
$505$	−6.23329e22	−0.655753
$506$	−5.08210e21	−0.0525731
$507$	−1.51661e22	−0.154278
$508$	3.03889e22	0.304000
$509$	−3.62283e22	−0.356407	−0.178204	−	0.983994i	$-0.557029\pi$
$509$	−3.62283e22	−0.356407	−0.178204	+	0.983994i	$0.557029\pi$
$510$	−1.00957e23	−0.976766
$511$	2.32051e22	0.220803
$512$	1.51856e23	1.42115
$513$	−3.25014e22	−0.299160
$514$	1.05620e22	0.0956222
$515$	6.94132e21	0.0618131
$516$	−1.66499e23	−1.45845
$517$	−9.71990e22	−0.837514
$518$	−4.51450e22	−0.382654
$519$	−6.48231e22	−0.540514
$520$	−2.30796e21	−0.0189321
$521$	−1.75240e23	−1.41421	−0.707103	−	0.707110i	$-0.749998\pi$
$521$	−1.75240e23	−1.41421	−0.707103	+	0.707110i	$0.749998\pi$
$522$	−1.75321e22	−0.139198
$523$	−1.99588e23	−1.55909	−0.779544	−	0.626348i	$-0.784549\pi$
$523$	−1.99588e23	−1.55909	−0.779544	+	0.626348i	$0.784549\pi$
$524$	1.57053e23	1.20707
$525$	1.26693e23	0.958075
$526$	−3.32871e23	−2.47684
$527$	2.77363e23	2.03076
$528$	2.15247e23	1.55078
$529$	−1.40936e23	−0.999194
$530$	8.40779e22	0.586593
$531$	6.99244e22	0.480093
$532$	−7.10485e22	−0.480071
$533$	−2.05038e23	−1.36349
$534$	2.64572e23	1.73158
$535$	−8.01826e22	−0.516503
$536$	−9.93880e21	−0.0630135
$537$	−2.38889e23	−1.49078
$538$	−2.39701e23	−1.47238
$539$	−3.67962e22	−0.222484
$540$	−3.90928e22	−0.232675
$541$	−5.50197e20	−0.00322360	−0.00161180	−	0.999999i	$-0.500513\pi$
$541$	−5.50197e20	−0.00322360	−0.00161180	+	0.999999i	$0.500513\pi$
$542$	4.00357e23	2.30916
$543$	1.27828e23	0.725819
$544$	3.67325e23	2.05334
$545$	1.41076e22	0.0776395
$546$	−3.13813e23	−1.70033
$547$	8.86601e22	0.472973	0.236486	−	0.971635i	$-0.424004\pi$
$547$	8.86601e22	0.472973	0.236486	+	0.971635i	$0.424004\pi$
$548$	2.09285e23	1.09927
$549$	−1.71286e22	−0.0885841
$550$	−3.09880e23	−1.57801
$551$	1.89137e22	0.0948392
$552$	3.29492e20	0.00162691
$553$	9.97453e22	0.484986
$554$	2.69130e23	1.28863
$555$	−2.97124e22	−0.140103
$556$	−8.43392e22	−0.391646
$557$	−2.60101e23	−1.18952	−0.594761	−	0.803902i	$-0.702753\pi$
$557$	−2.60101e23	−1.18952	−0.594761	+	0.803902i	$0.702753\pi$
$558$	−2.34414e23	−1.05583
$559$	2.73395e23	1.21280
$560$	7.74614e22	0.338444
$561$	5.37625e23	2.31364
$562$	3.34466e22	0.141773
$563$	8.69568e22	0.363063	0.181532	−	0.983385i	$-0.441895\pi$
$563$	8.69568e22	0.363063	0.181532	+	0.983385i	$0.441895\pi$
$564$	1.99928e23	0.822246
$565$	4.14593e22	0.167961
$566$	−2.93462e23	−1.17115
$567$	−2.89297e23	−1.13734
$568$	1.03363e22	0.0400317
$569$	3.65363e23	1.39403	0.697013	−	0.717059i	$-0.254512\pi$
$569$	3.65363e23	1.39403	0.697013	+	0.717059i	$0.254512\pi$
$570$	−9.20478e22	−0.346001
$571$	−3.86232e23	−1.43035	−0.715173	−	0.698947i	$-0.753652\pi$
$571$	−3.86232e23	−1.43035	−0.715173	+	0.698947i	$0.753652\pi$
$572$	3.89924e23	1.42270
$573$	−3.63670e23	−1.30735
$574$	−4.71060e23	−1.66850
$575$	6.92971e21	0.0241846
$576$	−1.62684e23	−0.559441
$577$	−2.29995e23	−0.779335	−0.389668	−	0.920956i	$-0.627410\pi$
$577$	−2.29995e23	−0.779335	−0.389668	+	0.920956i	$0.627410\pi$
$578$	4.60600e23	1.53793
$579$	−1.32992e23	−0.437580
$580$	2.27495e22	0.0737621
$581$	−5.16904e23	−1.65163
$582$	7.02027e23	2.21059
$583$	−4.47738e23	−1.38945
$584$	3.67980e21	0.0112542
$585$	−7.11734e22	−0.214532
$586$	6.88969e23	2.04677
$587$	5.92659e23	1.73533	0.867663	−	0.497152i	$-0.165621\pi$
$587$	5.92659e23	1.73533	0.867663	+	0.497152i	$0.165621\pi$
$588$	7.56860e22	0.218428
$589$	2.52887e23	0.719359
$590$	−1.78606e23	−0.500789
$591$	−2.84580e23	−0.786523
$592$	1.04584e23	0.284926
$593$	−6.07009e23	−1.63016	−0.815080	−	0.579348i	$-0.803307\pi$
$593$	−6.07009e23	−1.63016	−0.815080	+	0.579348i	$0.803307\pi$
$594$	4.09798e23	1.08489
$595$	1.93476e23	0.504932
$596$	−6.52332e23	−1.67832
$597$	−2.91381e23	−0.739058
$598$	−1.71646e22	−0.0429213
$599$	6.07307e23	1.49720	0.748600	−	0.663022i	$-0.230726\pi$
$599$	6.07307e23	1.49720	0.748600	+	0.663022i	$0.230726\pi$
$600$	2.00907e22	0.0488326
$601$	8.94735e22	0.214418	0.107209	−	0.994237i	$-0.465809\pi$
$601$	8.94735e22	0.214418	0.107209	+	0.994237i	$0.465809\pi$
$602$	6.28107e23	1.48410
$603$	−3.06495e23	−0.714047
$604$	−6.98663e23	−1.60492
$605$	−1.16800e23	−0.264559
$606$	−1.34401e24	−3.00182
$607$	−6.70135e23	−1.47591	−0.737953	−	0.674852i	$-0.764207\pi$
$607$	−6.70135e23	−1.47591	−0.737953	+	0.674852i	$0.764207\pi$
$608$	3.34909e23	0.727356
$609$	9.75001e22	0.208813
$610$	4.37511e22	0.0924029
$611$	−3.28285e23	−0.683756
$612$	−3.81075e23	−0.782750
$613$	−5.22474e23	−1.05840	−0.529201	−	0.848496i	$-0.677508\pi$
$613$	−5.22474e23	−1.05840	−0.529201	+	0.848496i	$0.677508\pi$
$614$	−9.31233e23	−1.86049
$615$	−3.10030e23	−0.610894
$616$	2.82366e22	0.0548753
$617$	9.69650e23	1.85862	0.929311	−	0.369299i	$-0.120402\pi$
$617$	9.69650e23	1.85862	0.929311	+	0.369299i	$0.120402\pi$
$618$	1.49668e23	0.282960
$619$	−6.20297e23	−1.15672	−0.578362	−	0.815781i	$-0.696308\pi$
$619$	−6.20297e23	−1.15672	−0.578362	+	0.815781i	$0.696308\pi$
$620$	3.04173e23	0.559489
$621$	−9.16414e21	−0.0166270
$622$	−1.67489e23	−0.299757
$623$	−5.07029e23	−0.895127
$624$	7.26989e23	1.26607
$625$	3.36393e23	0.577919
$626$	6.59908e23	1.11841
$627$	4.90181e23	0.819562
$628$	−3.38599e23	−0.558507
$629$	2.61221e23	0.425086
$630$	−1.63516e23	−0.262522
$631$	3.42700e23	0.542831	0.271416	−	0.962462i	$-0.412508\pi$
$631$	3.42700e23	0.542831	0.271416	+	0.962462i	$0.412508\pi$
$632$	1.58174e22	0.0247195
$633$	−7.51480e23	−1.15874
$634$	1.55300e24	2.36272
$635$	−7.54508e22	−0.113263
$636$	9.20951e23	1.36411
$637$	−1.24278e23	−0.181639
$638$	−2.38476e23	−0.343929
$639$	3.18754e23	0.453626
$640$	2.54081e22	0.0356814
$641$	9.02601e22	0.125084	0.0625421	−	0.998042i	$-0.480079\pi$
$641$	9.02601e22	0.125084	0.0625421	+	0.998042i	$0.480079\pi$
$642$	−1.72888e24	−2.36438
$643$	−1.96066e22	−0.0264612	−0.0132306	−	0.999912i	$-0.504212\pi$
$643$	−1.96066e22	−0.0264612	−0.0132306	+	0.999912i	$0.504212\pi$
$644$	−2.00329e22	−0.0266818
$645$	4.13391e23	0.543380
$646$	8.09252e23	1.04980
$647$	1.44965e23	0.185600	0.0928000	−	0.995685i	$-0.470418\pi$
$647$	1.44965e23	0.185600	0.0928000	+	0.995685i	$0.470418\pi$
$648$	−4.58761e22	−0.0579694
$649$	9.51129e23	1.18620
$650$	−1.04661e24	−1.28831
$651$	1.30363e24	1.58386
$652$	−1.62694e23	−0.195104
$653$	−9.28369e23	−1.09890	−0.549451	−	0.835526i	$-0.685163\pi$
$653$	−9.28369e23	−1.09890	−0.549451	+	0.835526i	$0.685163\pi$
$654$	3.04186e23	0.355409
$655$	−3.89938e23	−0.449722
$656$	1.09127e24	1.24237
$657$	1.13479e23	0.127529
$658$	−7.54214e23	−0.836709
$659$	4.89538e23	0.536118	0.268059	−	0.963403i	$-0.413618\pi$
$659$	4.89538e23	0.536118	0.268059	+	0.963403i	$0.413618\pi$
$660$	5.89591e23	0.637423
$661$	−7.40641e23	−0.790488	−0.395244	−	0.918576i	$-0.629340\pi$
$661$	−7.40641e23	−0.790488	−0.395244	+	0.918576i	$0.629340\pi$
$662$	1.13125e24	1.19198
$663$	1.81581e24	1.88888
$664$	−8.19694e22	−0.0841827
$665$	1.76402e23	0.178862
$666$	−2.20771e23	−0.221009
$667$	5.33293e21	0.00527104
$668$	−8.57018e23	−0.836354
$669$	1.46921e23	0.141567
$670$	7.82875e23	0.744829
$671$	−2.32987e23	−0.218872
$672$	1.72646e24	1.60146
$673$	1.46659e24	1.34332	0.671660	−	0.740860i	$-0.265582\pi$
$673$	1.46659e24	1.34332	0.671660	+	0.740860i	$0.265582\pi$
$674$	1.25379e24	1.13401
$675$	−5.58781e23	−0.499068
$676$	1.46222e23	0.128964
$677$	−1.59152e24	−1.38614	−0.693070	−	0.720870i	$-0.743742\pi$
$677$	−1.59152e24	−1.38614	−0.693070	+	0.720870i	$0.743742\pi$
$678$	8.93937e23	0.768873
$679$	−1.34538e24	−1.14275
$680$	3.06809e22	0.0257361
$681$	5.92871e23	0.491145
$682$	−3.18856e24	−2.60872
$683$	−1.84692e24	−1.49235	−0.746177	−	0.665748i	$-0.768113\pi$
$683$	−1.84692e24	−1.49235	−0.746177	+	0.665748i	$0.768113\pi$
$684$	−3.47445e23	−0.277274
$685$	−5.19622e23	−0.409560
$686$	−1.95271e24	−1.52014
$687$	1.75603e24	1.35021
$688$	−1.45509e24	−1.10507
$689$	−1.51222e24	−1.13436
$690$	−2.59540e22	−0.0192303
$691$	−3.60170e23	−0.263599	−0.131800	−	0.991276i	$-0.542076\pi$
$691$	−3.60170e23	−0.263599	−0.131800	+	0.991276i	$0.542076\pi$
$692$	6.24987e23	0.451824
$693$	8.70769e23	0.621828
$694$	3.71045e24	2.61741
$695$	2.09401e23	0.145917
$696$	1.54613e22	0.0106431
$697$	2.72568e24	1.85351
$698$	−2.08154e23	−0.139834
$699$	2.86517e24	1.90149
$700$	−1.22150e24	−0.800869
$701$	−1.80037e24	−1.16616	−0.583081	−	0.812414i	$-0.698153\pi$
$701$	−1.80037e24	−1.16616	−0.583081	+	0.812414i	$0.698153\pi$
$702$	1.38407e24	0.885715
$703$	2.38168e23	0.150579
$704$	−2.21287e24	−1.38226
$705$	−4.96389e23	−0.306348
$706$	1.89479e23	0.115537
$707$	2.57568e24	1.55177
$708$	−1.95637e24	−1.16458
$709$	−1.24117e23	−0.0730027	−0.0365013	−	0.999334i	$-0.511621\pi$
$709$	−1.24117e23	−0.0730027	−0.0365013	+	0.999334i	$0.511621\pi$
$710$	−8.14186e23	−0.473181
$711$	4.87780e23	0.280112
$712$	−8.04034e22	−0.0456241
$713$	7.13043e22	0.0399811
$714$	4.17169e24	2.31141
$715$	−9.68118e23	−0.530063
$716$	2.30323e24	1.24617
$717$	4.73009e23	0.252904
$718$	1.86280e24	0.984259
$719$	−1.34718e24	−0.703446	−0.351723	−	0.936104i	$-0.614404\pi$
$719$	−1.34718e24	−0.703446	−0.351723	+	0.936104i	$0.614404\pi$
$720$	3.78806e23	0.195475
$721$	−2.86825e23	−0.146274
$722$	−2.09086e24	−1.05380
$723$	−3.61697e23	−0.180165
$724$	−1.23245e24	−0.606723
$725$	3.25174e23	0.158213
$726$	−2.51842e24	−1.21106
$727$	−3.13123e24	−1.48824	−0.744120	−	0.668046i	$-0.767131\pi$
$727$	−3.13123e24	−1.48824	−0.744120	+	0.668046i	$0.767131\pi$
$728$	9.53680e22	0.0448008
$729$	1.43554e23	0.0666546
$730$	−2.89856e23	−0.133027
$731$	−3.63439e24	−1.64867
$732$	4.79230e23	0.214882
$733$	2.67197e23	0.118426	0.0592131	−	0.998245i	$-0.481141\pi$
$733$	2.67197e23	0.118426	0.0592131	+	0.998245i	$0.481141\pi$
$734$	−4.17079e24	−1.82727
$735$	−1.87916e23	−0.0813808
$736$	9.44315e22	0.0404255
$737$	−4.16903e24	−1.76425
$738$	−2.30360e24	−0.963671
$739$	−3.71335e24	−1.53564	−0.767818	−	0.640669i	$-0.778657\pi$
$739$	−3.71335e24	−1.53564	−0.767818	+	0.640669i	$0.778657\pi$
$740$	2.86470e23	0.117114
$741$	1.65556e24	0.669100
$742$	−3.47422e24	−1.38811
$743$	9.57958e23	0.378392	0.189196	−	0.981939i	$-0.439412\pi$
$743$	9.57958e23	0.378392	0.189196	+	0.981939i	$0.439412\pi$
$744$	2.06726e23	0.0807284
$745$	1.61963e24	0.625300
$746$	2.41982e24	0.923639
$747$	−2.52779e24	−0.953930
$748$	−5.18347e24	−1.93400
$749$	3.31326e24	1.22225
$750$	−3.43996e24	−1.25468
$751$	−2.38922e24	−0.861620	−0.430810	−	0.902443i	$-0.641772\pi$
$751$	−2.38922e24	−0.861620	−0.430810	+	0.902443i	$0.641772\pi$
$752$	1.74723e24	0.623016
$753$	6.83085e24	2.40834
$754$	−8.05442e23	−0.280788
$755$	1.73467e24	0.597953
$756$	1.61537e24	0.550600
$757$	−3.36288e24	−1.13343	−0.566717	−	0.823913i	$-0.691787\pi$
$757$	−3.36288e24	−1.13343	−0.566717	+	0.823913i	$0.691787\pi$
$758$	−1.16272e24	−0.387512
$759$	1.38212e23	0.0455503
$760$	2.79734e22	0.00911652
$761$	3.88764e23	0.125290	0.0626451	−	0.998036i	$-0.480046\pi$
$761$	3.88764e23	0.125290	0.0626451	+	0.998036i	$0.480046\pi$
$762$	−1.62686e24	−0.518480
$763$	−5.82946e23	−0.183726
$764$	3.50630e24	1.09284
$765$	9.46146e23	0.291633
$766$	−7.79241e24	−2.37535
$767$	3.21240e24	0.968431
$768$	−3.86033e24	−1.15094
$769$	2.09395e24	0.617436	0.308718	−	0.951154i	$-0.400100\pi$
$769$	2.09395e24	0.617436	0.308718	+	0.951154i	$0.400100\pi$
$770$	−2.22419e24	−0.648635
$771$	−2.87242e23	−0.0828487
$772$	1.28223e24	0.365779
$773$	6.75555e24	1.90605	0.953026	−	0.302889i	$-0.0979510\pi$
$773$	6.75555e24	1.90605	0.953026	+	0.302889i	$0.0979510\pi$
$774$	3.07160e24	0.857170
$775$	4.34776e24	1.20006
$776$	−2.13346e23	−0.0582452
$777$	1.22776e24	0.331539
$778$	4.56136e24	1.21834
$779$	2.48514e24	0.656572
$780$	1.99132e24	0.520399
$781$	4.33577e24	1.12081
$782$	2.28178e23	0.0583467
$783$	−4.30025e23	−0.108772
$784$	6.61443e23	0.165503
$785$	8.40687e23	0.208086
$786$	−8.40777e24	−2.05868
$787$	−7.73206e24	−1.87288	−0.936440	−	0.350829i	$-0.885900\pi$
$787$	−7.73206e24	−1.87288	−0.936440	+	0.350829i	$0.885900\pi$
$788$	2.74376e24	0.657466
$789$	9.05273e24	2.14598
$790$	−1.24593e24	−0.292188
$791$	−1.71315e24	−0.397463
$792$	1.38084e23	0.0316943
$793$	−7.86903e23	−0.178690
$794$	1.10346e25	2.47903
$795$	−2.28657e24	−0.508235
$796$	2.80932e24	0.617790
$797$	−4.44530e24	−0.967175	−0.483587	−	0.875296i	$-0.660666\pi$
$797$	−4.44530e24	−0.967175	−0.483587	+	0.875296i	$0.660666\pi$
$798$	3.80355e24	0.818774
$799$	4.36408e24	0.929490
$800$	5.75794e24	1.21340
$801$	−2.47950e24	−0.516997
$802$	9.07424e24	1.87210
$803$	1.54357e24	0.315096
$804$	8.57526e24	1.73209
$805$	4.97385e22	0.00994095
$806$	−1.07692e25	−2.12979
$807$	6.51887e24	1.27570
$808$	4.08445e23	0.0790928
$809$	−1.34191e24	−0.257134	−0.128567	−	0.991701i	$-0.541038\pi$
$809$	−1.34191e24	−0.257134	−0.128567	+	0.991701i	$0.541038\pi$
$810$	3.61364e24	0.685207
$811$	5.73577e24	1.07625	0.538127	−	0.842864i	$-0.319132\pi$
$811$	5.73577e24	1.07625	0.538127	+	0.842864i	$0.319132\pi$
$812$	−9.40040e23	−0.174550
$813$	−1.08881e25	−2.00070
$814$	−3.00298e24	−0.546066
$815$	4.03943e23	0.0726910
$816$	−9.66426e24	−1.72108
$817$	−3.31366e24	−0.584010
$818$	1.94332e24	0.338954
$819$	2.94098e24	0.507668
$820$	2.98913e24	0.510655
$821$	−4.81584e24	−0.814246	−0.407123	−	0.913373i	$-0.633468\pi$
$821$	−4.81584e24	−0.814246	−0.407123	+	0.913373i	$0.633468\pi$
$822$	−1.12040e25	−1.87483
$823$	−6.74979e24	−1.11787	−0.558935	−	0.829211i	$-0.688790\pi$
$823$	−6.74979e24	−1.11787	−0.558935	+	0.829211i	$0.688790\pi$
$824$	−4.54840e22	−0.00745551
$825$	8.42745e24	1.36722
$826$	7.38027e24	1.18506
$827$	−4.27964e23	−0.0680159	−0.0340080	−	0.999422i	$-0.510827\pi$
$827$	−4.27964e23	−0.0680159	−0.0340080	+	0.999422i	$0.510827\pi$
$828$	−9.79662e22	−0.0154106
$829$	−9.37249e24	−1.45929	−0.729645	−	0.683826i	$-0.760315\pi$
$829$	−9.37249e24	−1.45929	−0.729645	+	0.683826i	$0.760315\pi$
$830$	6.45669e24	0.995053
$831$	−7.31922e24	−1.11649
$832$	−7.47388e24	−1.12849
$833$	1.65209e24	0.246917
$834$	4.51506e24	0.667962
$835$	2.12784e24	0.311604
$836$	−4.72604e24	−0.685084
$837$	−5.74967e24	−0.825042
$838$	−4.54882e24	−0.646137
$839$	−5.66299e24	−0.796286	−0.398143	−	0.917323i	$-0.630345\pi$
$839$	−5.66299e24	−0.796286	−0.398143	+	0.917323i	$0.630345\pi$
$840$	1.44203e23	0.0200724
$841$	2.50246e23	0.0344828
$842$	6.20698e24	0.846697
$843$	−9.09609e23	−0.122835
$844$	7.24534e24	0.968607
$845$	−3.63047e23	−0.0480486
$846$	−3.68830e24	−0.483257
$847$	4.82634e24	0.626050
$848$	8.04847e24	1.03359
$849$	7.98096e24	1.01471
$850$	1.39131e25	1.75131
$851$	6.71543e22	0.00836898
$852$	−8.91822e24	−1.10038
$853$	5.37185e23	0.0656232	0.0328116	−	0.999462i	$-0.489554\pi$
$853$	5.37185e23	0.0656232	0.0328116	+	0.999462i	$0.489554\pi$
$854$	−1.80786e24	−0.218661
$855$	8.62650e23	0.103305
$856$	5.25408e23	0.0622974
$857$	6.58671e24	0.773271	0.386635	−	0.922233i	$-0.373637\pi$
$857$	6.58671e24	0.773271	0.386635	+	0.922233i	$0.373637\pi$
$858$	−2.08744e25	−2.42645
$859$	−7.68349e24	−0.884335	−0.442168	−	0.896932i	$-0.645790\pi$
$859$	−7.68349e24	−0.884335	−0.442168	+	0.896932i	$0.645790\pi$
$860$	−3.98568e24	−0.454219
$861$	1.28109e25	1.44562
$862$	−5.66258e24	−0.632707
$863$	−1.14599e25	−1.26791	−0.633955	−	0.773370i	$-0.718570\pi$
$863$	−1.14599e25	−1.26791	−0.633955	+	0.773370i	$0.718570\pi$
$864$	−7.61455e24	−0.834213
$865$	−1.55174e24	−0.168338
$866$	1.64189e25	1.76377
$867$	−1.25264e25	−1.33249
$868$	−1.25689e25	−1.32397
$869$	6.63491e24	0.692097
$870$	−1.21788e24	−0.125803
$871$	−1.40807e25	−1.44036
$872$	−9.24421e22	−0.00936440
$873$	−6.57923e24	−0.660015
$874$	2.08041e23	0.0206682
$875$	6.59239e24	0.648597
$876$	−3.17495e24	−0.309352
$877$	1.57130e25	1.51623	0.758113	−	0.652123i	$-0.226122\pi$
$877$	1.57130e25	1.51623	0.758113	+	0.652123i	$0.226122\pi$
$878$	1.29043e25	1.23320
$879$	−1.87371e25	−1.77336
$880$	5.15261e24	0.482975
$881$	4.05407e24	0.376354	0.188177	−	0.982135i	$-0.439742\pi$
$881$	4.05407e24	0.376354	0.188177	+	0.982135i	$0.439742\pi$
$882$	−1.39626e24	−0.128376
$883$	1.54343e25	1.40547	0.702734	−	0.711452i	$-0.251962\pi$
$883$	1.54343e25	1.40547	0.702734	+	0.711452i	$0.251962\pi$
$884$	−1.75070e25	−1.57894
$885$	4.85736e24	0.433893
$886$	1.18754e25	1.05066
$887$	8.22200e24	0.720488	0.360244	−	0.932858i	$-0.382693\pi$
$887$	8.22200e24	0.720488	0.360244	+	0.932858i	$0.382693\pi$
$888$	1.94695e23	0.0168983
$889$	3.11773e24	0.268024
$890$	6.33334e24	0.539285
$891$	−1.92436e25	−1.62303
$892$	−1.41653e24	−0.118338
$893$	3.97895e24	0.329254
$894$	3.49223e25	2.86242
$895$	−5.71854e24	−0.464290
$896$	−1.04990e24	−0.0844363
$897$	4.66805e23	0.0371878
$898$	−2.11001e25	−1.66508
$899$	3.34593e24	0.261553
$900$	−5.97347e24	−0.462557
$901$	2.01027e25	1.54203
$902$	−3.13342e25	−2.38102
$903$	−1.70819e25	−1.28585
$904$	−2.71668e23	−0.0202585
$905$	3.05996e24	0.226049
$906$	3.74026e25	2.73723
$907$	1.15905e25	0.840314	0.420157	−	0.907452i	$-0.361975\pi$
$907$	1.15905e25	0.840314	0.420157	+	0.907452i	$0.361975\pi$
$908$	−5.71612e24	−0.410555
$909$	1.25957e25	0.896253
$910$	−7.51210e24	−0.529553
$911$	6.98881e24	0.488087	0.244043	−	0.969764i	$-0.421526\pi$
$911$	6.98881e24	0.488087	0.244043	+	0.969764i	$0.421526\pi$
$912$	−8.81140e24	−0.609662
$913$	−3.43837e25	−2.35695
$914$	2.34154e25	1.59022
$915$	−1.18985e24	−0.0800595
$916$	−1.69306e25	−1.12866
$917$	1.61128e25	1.06422
$918$	−1.83993e25	−1.20403
$919$	−5.84747e24	−0.379128	−0.189564	−	0.981868i	$-0.560708\pi$
$919$	−5.84747e24	−0.379128	−0.189564	+	0.981868i	$0.560708\pi$
$920$	7.88741e21	0.000506685 0
$921$	2.53257e25	1.61196
$922$	2.07768e25	1.31029
$923$	1.46439e25	0.915043
$924$	−2.43627e25	−1.50839
$925$	4.09472e24	0.251200
$926$	−3.63958e25	−2.21237
$927$	−1.40265e24	−0.0844833
$928$	4.43117e24	0.264461
$929$	5.01290e24	0.296452	0.148226	−	0.988953i	$-0.452644\pi$
$929$	5.01290e24	0.296452	0.148226	+	0.988953i	$0.452644\pi$
$930$	−1.62838e25	−0.954222
$931$	1.50630e24	0.0874658
$932$	−2.76243e25	−1.58948
$933$	4.55502e24	0.259714
$934$	4.91566e25	2.77737
$935$	1.28697e25	0.720561
$936$	4.66374e23	0.0258756
$937$	−2.07412e25	−1.14038	−0.570188	−	0.821514i	$-0.693130\pi$
$937$	−2.07412e25	−1.14038	−0.570188	+	0.821514i	$0.693130\pi$
$938$	−3.23495e25	−1.76256
$939$	−1.79468e25	−0.969011
$940$	4.78590e24	0.256081
$941$	−1.94560e25	−1.03167	−0.515836	−	0.856687i	$-0.672519\pi$
$941$	−1.94560e25	−1.03167	−0.515836	+	0.856687i	$0.672519\pi$
$942$	1.81267e25	0.952548
$943$	7.00714e23	0.0364915
$944$	−1.70973e25	−0.882402
$945$	−4.01070e24	−0.205140
$946$	4.17807e25	2.11788
$947$	−2.20262e25	−1.10653	−0.553266	−	0.833004i	$-0.686619\pi$
$947$	−2.20262e25	−1.10653	−0.553266	+	0.833004i	$0.686619\pi$
$948$	−1.36473e25	−0.679479
$949$	5.21333e24	0.257248
$950$	1.26853e25	0.620368
$951$	−4.22352e25	−2.04710
$952$	−1.26778e24	−0.0609017
$953$	−1.05496e25	−0.502278	−0.251139	−	0.967951i	$-0.580805\pi$
$953$	−1.05496e25	−0.502278	−0.251139	+	0.967951i	$0.580805\pi$
$954$	−1.69898e25	−0.801728
$955$	−8.70557e24	−0.407163
$956$	−4.56048e24	−0.211406
$957$	6.48556e24	0.297986
$958$	3.45953e25	1.57547
$959$	2.14715e25	0.969179
$960$	−1.13010e25	−0.505605
$961$	2.21869e25	0.983891
$962$	−1.01424e25	−0.445814
$963$	1.62027e25	0.705933
$964$	3.48727e24	0.150602
$965$	−3.18357e24	−0.136280
$966$	1.07245e24	0.0455065
$967$	−3.35428e25	−1.41083	−0.705415	−	0.708794i	$-0.749239\pi$
$967$	−3.35428e25	−1.41083	−0.705415	+	0.708794i	$0.749239\pi$
$968$	7.65349e23	0.0319094
$969$	−2.20083e25	−0.909567
$970$	1.68052e25	0.688468
$971$	−1.25784e25	−0.510815	−0.255407	−	0.966834i	$-0.582210\pi$
$971$	−1.25784e25	−0.510815	−0.255407	+	0.966834i	$0.582210\pi$
$972$	2.45580e25	0.988620
$973$	−8.65272e24	−0.345298
$974$	5.79145e25	2.29106
$975$	2.84633e25	1.11621
$976$	4.18813e24	0.162816
$977$	3.33733e25	1.28616	0.643081	−	0.765798i	$-0.277656\pi$
$977$	3.33733e25	1.28616	0.643081	+	0.765798i	$0.277656\pi$
$978$	8.70975e24	0.332756
$979$	−3.37268e25	−1.27739
$980$	1.81178e24	0.0680274
$981$	−2.85076e24	−0.106114
$982$	−3.04189e25	−1.12253
$983$	−1.02112e25	−0.373570	−0.186785	−	0.982401i	$-0.559807\pi$
$983$	−1.02112e25	−0.373570	−0.186785	+	0.982401i	$0.559807\pi$
$984$	2.03152e24	0.0736822
$985$	−6.81231e24	−0.244955
$986$	1.07072e25	0.381699
$987$	2.05115e25	0.724940
$988$	−1.59620e25	−0.559310
$989$	−9.34324e23	−0.0324585
$990$	−1.08768e25	−0.374631
$991$	3.91853e25	1.33813	0.669063	−	0.743206i	$-0.266696\pi$
$991$	3.91853e25	1.33813	0.669063	+	0.743206i	$0.266696\pi$
$992$	5.92472e25	2.00594
$993$	−3.07655e25	−1.03275
$994$	3.36433e25	1.11973
$995$	−6.97509e24	−0.230173
$996$	7.07237e25	2.31398
$997$	3.84939e25	1.24877	0.624385	−	0.781116i	$-0.285349\pi$
$997$	3.84939e25	1.24877	0.624385	+	0.781116i	$0.285349\pi$
$998$	4.25848e25	1.36976
$999$	−5.41503e24	−0.172701

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.15	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+516.149 q^{2} -14037.1 q^{3} +135338. q^{4} -336022. q^{5} -7.24525e6 q^{6} +1.38849e7 q^{7} +2.20183e6 q^{8} +6.79008e7 q^{9} +O(q^{10})\)	\(q+516.149 q^{2} -14037.1 q^{3} +135338. q^{4} -336022. q^{5} -7.24525e6 q^{6} +1.38849e7 q^{7} +2.20183e6 q^{8} +6.79008e7 q^{9} -1.73438e8 q^{10} +9.23603e8 q^{11} -1.89976e9 q^{12} +3.11943e9 q^{13} +7.16668e9 q^{14} +4.71678e9 q^{15} -1.66025e10 q^{16} -4.14683e10 q^{17} +3.50469e10 q^{18} -3.78088e10 q^{19} -4.54765e10 q^{20} -1.94904e11 q^{21} +4.76717e11 q^{22} -1.06606e10 q^{23} -3.09074e10 q^{24} -6.50029e11 q^{25} +1.61009e12 q^{26} +8.59625e11 q^{27} +1.87915e12 q^{28} -5.00246e11 q^{29} +2.43456e12 q^{30} -6.68857e12 q^{31} -8.85798e12 q^{32} -1.29647e13 q^{33} -2.14038e13 q^{34} -4.66564e12 q^{35} +9.18954e12 q^{36} -6.29929e12 q^{37} -1.95150e13 q^{38} -4.37878e13 q^{39} -7.39865e11 q^{40} -6.57292e13 q^{41} -1.00600e14 q^{42} +8.76426e13 q^{43} +1.24999e14 q^{44} -2.28162e13 q^{45} -5.50247e12 q^{46} -1.05239e14 q^{47} +2.33052e14 q^{48} -3.98399e13 q^{49} -3.35512e14 q^{50} +5.82095e14 q^{51} +4.22177e14 q^{52} -4.84773e14 q^{53} +4.43695e14 q^{54} -3.10351e14 q^{55} +3.05723e13 q^{56} +5.30726e14 q^{57} -2.58202e14 q^{58} +1.02980e15 q^{59} +6.38360e14 q^{60} -2.52259e14 q^{61} -3.45230e15 q^{62} +9.42796e14 q^{63} -2.39591e15 q^{64} -1.04820e15 q^{65} -6.69174e15 q^{66} -4.51387e15 q^{67} -5.61223e15 q^{68} +1.49644e14 q^{69} -2.40816e15 q^{70} +4.69441e15 q^{71} +1.49506e14 q^{72} +1.67124e15 q^{73} -3.25137e15 q^{74} +9.12453e15 q^{75} -5.11696e15 q^{76} +1.28241e16 q^{77} -2.26010e16 q^{78} +7.18372e15 q^{79} +5.57882e15 q^{80} -2.08354e16 q^{81} -3.39261e16 q^{82} -3.72278e16 q^{83} -2.63779e16 q^{84} +1.39343e16 q^{85} +4.52366e16 q^{86} +7.02202e15 q^{87} +2.03362e15 q^{88} -3.65166e16 q^{89} -1.17765e16 q^{90} +4.33130e16 q^{91} -1.44279e15 q^{92} +9.38883e16 q^{93} -5.43190e16 q^{94} +1.27046e16 q^{95} +1.24341e17 q^{96} -9.68948e16 q^{97} -2.05633e16 q^{98} +6.27134e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 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

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