LMFDB - Embedded newform 29.18.a.a.1.13

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			1.13
Root			$235.511$ 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)

$f(q)$	$=$	$q+235.511 q^{2} -19946.7 q^{3} -75606.8 q^{4} +778691. q^{5} -4.69767e6 q^{6} -1.72672e7 q^{7} -4.86750e7 q^{8} +2.68732e8 q^{9} +O(q^{10})$	\(q+235.511 q^{2} -19946.7 q^{3} -75606.8 q^{4} +778691. q^{5} -4.69767e6 q^{6} -1.72672e7 q^{7} -4.86750e7 q^{8} +2.68732e8 q^{9} +1.83390e8 q^{10} +1.17600e9 q^{11} +1.50811e9 q^{12} -1.07629e9 q^{13} -4.06661e9 q^{14} -1.55323e10 q^{15} -1.55355e9 q^{16} +4.32819e10 q^{17} +6.32892e10 q^{18} -5.95569e10 q^{19} -5.88743e10 q^{20} +3.44424e11 q^{21} +2.76960e11 q^{22} +2.99832e11 q^{23} +9.70908e11 q^{24} -1.56580e11 q^{25} -2.53478e11 q^{26} -2.78440e12 q^{27} +1.30552e12 q^{28} -5.00246e11 q^{29} -3.65803e12 q^{30} +1.91301e12 q^{31} +6.01406e12 q^{32} -2.34573e13 q^{33} +1.01934e13 q^{34} -1.34458e13 q^{35} -2.03180e13 q^{36} +3.89515e12 q^{37} -1.40263e13 q^{38} +2.14685e13 q^{39} -3.79028e13 q^{40} -4.62222e13 q^{41} +8.11156e13 q^{42} -1.07893e14 q^{43} -8.89134e13 q^{44} +2.09259e14 q^{45} +7.06136e13 q^{46} -9.39944e13 q^{47} +3.09883e13 q^{48} +6.55259e13 q^{49} -3.68762e13 q^{50} -8.63333e14 q^{51} +8.13749e13 q^{52} +5.88108e14 q^{53} -6.55755e14 q^{54} +9.15739e14 q^{55} +8.40482e14 q^{56} +1.18797e15 q^{57} -1.17813e14 q^{58} -1.38353e15 q^{59} +1.17435e15 q^{60} -1.80522e15 q^{61} +4.50534e14 q^{62} -4.64025e15 q^{63} +1.62000e15 q^{64} -8.38098e14 q^{65} -5.52444e15 q^{66} -4.26355e15 q^{67} -3.27241e15 q^{68} -5.98067e15 q^{69} -3.16663e15 q^{70} +4.78140e15 q^{71} -1.30805e16 q^{72} +1.29021e16 q^{73} +9.17348e14 q^{74} +3.12326e15 q^{75} +4.50291e15 q^{76} -2.03062e16 q^{77} +5.05606e15 q^{78} -1.04276e16 q^{79} -1.20974e15 q^{80} +2.08356e16 q^{81} -1.08858e16 q^{82} +1.77422e16 q^{83} -2.60408e16 q^{84} +3.37032e16 q^{85} -2.54099e16 q^{86} +9.97828e15 q^{87} -5.72417e16 q^{88} +3.94668e16 q^{89} +4.92827e16 q^{90} +1.85845e16 q^{91} -2.26693e16 q^{92} -3.81583e16 q^{93} -2.21367e16 q^{94} -4.63764e16 q^{95} -1.19961e17 q^{96} +2.19647e16 q^{97} +1.54320e16 q^{98} +3.16028e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	235.511	0.650512	0.325256	−	0.945626i	$-0.394549\pi$
$2$	235.511	0.650512	0.325256	+	0.945626i	$0.394549\pi$
$3$	−19946.7	−1.75526	−0.877629	−	0.479340i	$-0.840876\pi$
$3$	−19946.7	−1.75526	−0.877629	+	0.479340i	$0.840876\pi$
$4$	−75606.8	−0.576834
$5$	778691.	0.891497	0.445749	−	0.895158i	$-0.352938\pi$
$5$	778691.	0.891497	0.445749	+	0.895158i	$0.352938\pi$
$6$	−4.69767e6	−1.14182
$7$	−1.72672e7	−1.13211	−0.566055	−	0.824367i	$-0.691531\pi$
$7$	−1.72672e7	−1.13211	−0.566055	+	0.824367i	$0.691531\pi$
$8$	−4.86750e7	−1.02575
$9$	2.68732e8	2.08093
$10$	1.83390e8	0.579930
$11$	1.17600e9	1.65413	0.827063	−	0.562109i	$-0.190010\pi$
$11$	1.17600e9	1.65413	0.827063	+	0.562109i	$0.190010\pi$
$12$	1.50811e9	1.01249
$13$	−1.07629e9	−0.365941	−0.182971	−	0.983118i	$-0.558571\pi$
$13$	−1.07629e9	−0.365941	−0.182971	+	0.983118i	$0.558571\pi$
$14$	−4.06661e9	−0.736452
$15$	−1.55323e10	−1.56481
$16$	−1.55355e9	−0.0904287
$17$	4.32819e10	1.50484	0.752421	−	0.658683i	$-0.228886\pi$
$17$	4.32819e10	1.50484	0.752421	+	0.658683i	$0.228886\pi$
$18$	6.32892e10	1.35367
$19$	−5.95569e10	−0.804501	−0.402251	−	0.915530i	$-0.631772\pi$
$19$	−5.95569e10	−0.804501	−0.402251	+	0.915530i	$0.631772\pi$
$20$	−5.88743e10	−0.514246
$21$	3.44424e11	1.98715
$22$	2.76960e11	1.07603
$23$	2.99832e11	0.798347	0.399173	−	0.916875i	$-0.369297\pi$
$23$	2.99832e11	0.798347	0.399173	+	0.916875i	$0.369297\pi$
$24$	9.70908e11	1.80046
$25$	−1.56580e11	−0.205233
$26$	−2.53478e11	−0.238049
$27$	−2.78440e12	−1.89732
$28$	1.30552e12	0.653040
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	−3.65803e12	−1.01793
$31$	1.91301e12	0.402850	0.201425	−	0.979504i	$-0.435443\pi$
$31$	1.91301e12	0.402850	0.201425	+	0.979504i	$0.435443\pi$
$32$	6.01406e12	0.966925
$33$	−2.34573e13	−2.90342
$34$	1.01934e13	0.978918
$35$	−1.34458e13	−1.00927
$36$	−2.03180e13	−1.20035
$37$	3.89515e12	0.182309	0.0911547	−	0.995837i	$-0.470944\pi$
$37$	3.89515e12	0.182309	0.0911547	+	0.995837i	$0.470944\pi$
$38$	−1.40263e13	−0.523338
$39$	2.14685e13	0.642321
$40$	−3.79028e13	−0.914453
$41$	−4.62222e13	−0.904041	−0.452021	−	0.892007i	$-0.649297\pi$
$41$	−4.62222e13	−0.904041	−0.452021	+	0.892007i	$0.649297\pi$
$42$	8.11156e13	1.29266
$43$	−1.07893e14	−1.40770	−0.703851	−	0.710347i	$-0.748538\pi$
$43$	−1.07893e14	−1.40770	−0.703851	+	0.710347i	$0.748538\pi$
$44$	−8.89134e13	−0.954156
$45$	2.09259e14	1.85515
$46$	7.06136e13	0.519334
$47$	−9.39944e13	−0.575798	−0.287899	−	0.957661i	$-0.592957\pi$
$47$	−9.39944e13	−0.575798	−0.287899	+	0.957661i	$0.592957\pi$
$48$	3.09883e13	0.158726
$49$	6.55259e13	0.281674
$50$	−3.68762e13	−0.133506
$51$	−8.63333e14	−2.64139
$52$	8.13749e13	0.211087
$53$	5.88108e14	1.29752	0.648758	−	0.760995i	$-0.275289\pi$
$53$	5.88108e14	1.29752	0.648758	+	0.760995i	$0.275289\pi$
$54$	−6.55755e14	−1.23423
$55$	9.15739e14	1.47465
$56$	8.40482e14	1.16126
$57$	1.18797e15	1.41211
$58$	−1.17813e14	−0.120797
$59$	−1.38353e15	−1.22673	−0.613363	−	0.789801i	$-0.710184\pi$
$59$	−1.38353e15	−1.22673	−0.613363	+	0.789801i	$0.710184\pi$
$60$	1.17435e15	0.902634
$61$	−1.80522e15	−1.20566	−0.602832	−	0.797868i	$-0.705961\pi$
$61$	−1.80522e15	−1.20566	−0.602832	+	0.797868i	$0.705961\pi$
$62$	4.50534e14	0.262059
$63$	−4.64025e15	−2.35584
$64$	1.62000e15	0.719425
$65$	−8.38098e14	−0.326236
$66$	−5.52444e15	−1.88871
$67$	−4.26355e15	−1.28273	−0.641366	−	0.767235i	$-0.721632\pi$
$67$	−4.26355e15	−1.28273	−0.641366	+	0.767235i	$0.721632\pi$
$68$	−3.27241e15	−0.868044
$69$	−5.98067e15	−1.40131
$70$	−3.16663e15	−0.656545
$71$	4.78140e15	0.878737	0.439368	−	0.898307i	$-0.355202\pi$
$71$	4.78140e15	0.878737	0.439368	+	0.898307i	$0.355202\pi$
$72$	−1.30805e16	−2.13452
$73$	1.29021e16	1.87248	0.936238	−	0.351366i	$-0.114283\pi$
$73$	1.29021e16	1.87248	0.936238	+	0.351366i	$0.114283\pi$
$74$	9.17348e14	0.118594
$75$	3.12326e15	0.360236
$76$	4.50291e15	0.464064
$77$	−2.03062e16	−1.87265
$78$	5.05606e15	0.417838
$79$	−1.04276e16	−0.773308	−0.386654	−	0.922225i	$-0.626369\pi$
$79$	−1.04276e16	−0.773308	−0.386654	+	0.922225i	$0.626369\pi$
$80$	−1.20974e15	−0.0806170
$81$	2.08356e16	1.24935
$82$	−1.08858e16	−0.588090
$83$	1.77422e16	0.864658	0.432329	−	0.901716i	$-0.357692\pi$
$83$	1.77422e16	0.864658	0.432329	+	0.901716i	$0.357692\pi$
$84$	−2.60408e16	−1.14625
$85$	3.37032e16	1.34156
$86$	−2.54099e16	−0.915728
$87$	9.97828e15	0.325943
$88$	−5.72417e16	−1.69672
$89$	3.94668e16	1.06271	0.531357	−	0.847148i	$-0.321682\pi$
$89$	3.94668e16	1.06271	0.531357	+	0.847148i	$0.321682\pi$
$90$	4.92827e16	1.20679
$91$	1.85845e16	0.414286
$92$	−2.26693e16	−0.460514
$93$	−3.81583e16	−0.707105
$94$	−2.21367e16	−0.374564
$95$	−4.63764e16	−0.717211
$96$	−1.19961e17	−1.69720
$97$	2.19647e16	0.284555	0.142277	−	0.989827i	$-0.454557\pi$
$97$	2.19647e16	0.284555	0.142277	+	0.989827i	$0.454557\pi$
$98$	1.54320e16	0.183232
$99$	3.16028e17	3.44212
$100$	1.18385e16	0.118385
$101$	−1.58193e17	−1.45363	−0.726816	−	0.686832i	$-0.759001\pi$
$101$	−1.58193e17	−1.45363	−0.726816	+	0.686832i	$0.759001\pi$
$102$	−2.03324e17	−1.71825
$103$	−8.93648e16	−0.695105	−0.347552	−	0.937661i	$-0.612987\pi$
$103$	−8.93648e16	−0.695105	−0.347552	+	0.937661i	$0.612987\pi$
$104$	5.23885e16	0.375364
$105$	2.68200e17	1.77154
$106$	1.38506e17	0.844050
$107$	1.38880e17	0.781406	0.390703	−	0.920517i	$-0.372232\pi$
$107$	1.38880e17	0.781406	0.390703	+	0.920517i	$0.372232\pi$
$108$	2.10519e17	1.09444
$109$	2.65523e17	1.27637	0.638186	−	0.769882i	$-0.279685\pi$
$109$	2.65523e17	1.27637	0.638186	+	0.769882i	$0.279685\pi$
$110$	2.15666e17	0.959277
$111$	−7.76954e16	−0.320000
$112$	2.68255e16	0.102375
$113$	−2.38287e17	−0.843204	−0.421602	−	0.906781i	$-0.638532\pi$
$113$	−2.38287e17	−0.843204	−0.421602	+	0.906781i	$0.638532\pi$
$114$	2.79779e17	0.918593
$115$	2.33477e17	0.711724
$116$	3.78220e16	0.107115
$117$	−2.89234e17	−0.761499
$118$	−3.25837e17	−0.798000
$119$	−7.47358e17	−1.70365
$120$	7.56037e17	1.60510
$121$	8.77523e17	1.73613
$122$	−4.25148e17	−0.784299
$123$	9.21983e17	1.58683
$124$	−1.44637e17	−0.232377
$125$	−7.16021e17	−1.07446
$126$	−1.09283e18	−1.53251
$127$	5.28804e17	0.693367	0.346684	−	0.937982i	$-0.387308\pi$
$127$	5.28804e17	0.693367	0.346684	+	0.937982i	$0.387308\pi$
$128$	−4.06747e17	−0.498930
$129$	2.15211e18	2.47088
$130$	−1.97381e17	−0.212220
$131$	−1.63593e18	−1.64800	−0.824001	−	0.566588i	$-0.808263\pi$
$131$	−1.63593e18	−1.64800	−0.824001	+	0.566588i	$0.808263\pi$
$132$	1.77353e18	1.67479
$133$	1.02838e18	0.910784
$134$	−1.00411e18	−0.834433
$135$	−2.16819e18	−1.69145
$136$	−2.10675e18	−1.54359
$137$	−1.37527e18	−0.946814	−0.473407	−	0.880844i	$-0.656976\pi$
$137$	−1.37527e18	−0.946814	−0.473407	+	0.880844i	$0.656976\pi$
$138$	−1.40851e18	−0.911566
$139$	−1.99714e18	−1.21558	−0.607789	−	0.794098i	$-0.707943\pi$
$139$	−1.99714e18	−1.21558	−0.607789	+	0.794098i	$0.707943\pi$
$140$	1.01659e18	0.582183
$141$	1.87488e18	1.01067
$142$	1.12607e18	0.571629
$143$	−1.26572e18	−0.605313
$144$	−4.17489e17	−0.188176
$145$	−3.89537e17	−0.165547
$146$	3.03858e18	1.21807
$147$	−1.30703e18	−0.494410
$148$	−2.94499e17	−0.105162
$149$	2.88652e18	0.973398	0.486699	−	0.873570i	$-0.338201\pi$
$149$	2.88652e18	0.973398	0.486699	+	0.873570i	$0.338201\pi$
$150$	7.35561e17	0.234338
$151$	−3.21267e18	−0.967301	−0.483650	−	0.875261i	$-0.660689\pi$
$151$	−3.21267e18	−0.967301	−0.483650	+	0.875261i	$0.660689\pi$
$152$	2.89894e18	0.825217
$153$	1.16312e19	3.13147
$154$	−4.78232e18	−1.21818
$155$	1.48964e18	0.359139
$156$	−1.62316e18	−0.370513
$157$	2.54641e18	0.550531	0.275265	−	0.961368i	$-0.411234\pi$
$157$	2.54641e18	0.550531	0.275265	+	0.961368i	$0.411234\pi$
$158$	−2.45580e18	−0.503046
$159$	−1.17308e19	−2.27747
$160$	4.68309e18	0.862011
$161$	−5.17726e18	−0.903817
$162$	4.90700e18	0.812715
$163$	−1.81952e18	−0.285997	−0.142999	−	0.989723i	$-0.545674\pi$
$163$	−1.81952e18	−0.285997	−0.142999	+	0.989723i	$0.545674\pi$
$164$	3.49471e18	0.521482
$165$	−1.82660e19	−2.58839
$166$	4.17848e18	0.562471
$167$	−1.95624e18	−0.250226	−0.125113	−	0.992142i	$-0.539929\pi$
$167$	−1.95624e18	−0.250226	−0.125113	+	0.992142i	$0.539929\pi$
$168$	−1.67649e19	−2.03831
$169$	−7.49201e18	−0.866087
$170$	7.93747e18	0.872702
$171$	−1.60048e19	−1.67411
$172$	8.15743e18	0.812011
$173$	−7.52793e18	−0.713319	−0.356659	−	0.934234i	$-0.616084\pi$
$173$	−7.52793e18	−0.713319	−0.356659	+	0.934234i	$0.616084\pi$
$174$	2.34999e18	0.212030
$175$	2.70370e18	0.232346
$176$	−1.82698e18	−0.149581
$177$	2.75970e19	2.15322
$178$	9.29485e18	0.691309
$179$	−1.45319e19	−1.03055	−0.515277	−	0.857024i	$-0.672311\pi$
$179$	−1.45319e19	−1.03055	−0.515277	+	0.857024i	$0.672311\pi$
$180$	−1.58214e19	−1.07011
$181$	−1.29394e19	−0.834923	−0.417461	−	0.908695i	$-0.637080\pi$
$181$	−1.29394e19	−0.834923	−0.417461	+	0.908695i	$0.637080\pi$
$182$	4.37686e18	0.269498
$183$	3.60082e19	2.11625
$184$	−1.45943e19	−0.818904
$185$	3.03311e18	0.162528
$186$	−8.98668e18	−0.459980
$187$	5.08994e19	2.48920
$188$	7.10662e18	0.332140
$189$	4.80788e19	2.14797
$190$	−1.09221e19	−0.466554
$191$	−4.75079e19	−1.94081	−0.970403	−	0.241491i	$-0.922363\pi$
$191$	−4.75079e19	−1.94081	−0.970403	+	0.241491i	$0.922363\pi$
$192$	−3.23137e19	−1.26278
$193$	5.71277e18	0.213604	0.106802	−	0.994280i	$-0.465939\pi$
$193$	5.71277e18	0.213604	0.106802	+	0.994280i	$0.465939\pi$
$194$	5.17292e18	0.185106
$195$	1.67173e19	0.572628
$196$	−4.95420e18	−0.162479
$197$	2.99391e19	0.940319	0.470159	−	0.882581i	$-0.344196\pi$
$197$	2.99391e19	0.940319	0.470159	+	0.882581i	$0.344196\pi$
$198$	7.44280e19	2.23914
$199$	4.00199e18	0.115352	0.0576759	−	0.998335i	$-0.481631\pi$
$199$	4.00199e18	0.115352	0.0576759	+	0.998335i	$0.481631\pi$
$200$	7.62154e18	0.210517
$201$	8.50440e19	2.25153
$202$	−3.72560e19	−0.945606
$203$	8.63786e18	0.210228
$204$	6.52738e19	1.52364
$205$	−3.59928e19	−0.805950
$206$	−2.10464e19	−0.452174
$207$	8.05745e19	1.66131
$208$	1.67208e18	0.0330916
$209$	−7.00388e19	−1.33075
$210$	6.31640e19	1.15241
$211$	2.94921e19	0.516780	0.258390	−	0.966041i	$-0.416808\pi$
$211$	2.94921e19	0.516780	0.258390	+	0.966041i	$0.416808\pi$
$212$	−4.44650e19	−0.748451
$213$	−9.53732e19	−1.54241
$214$	3.27077e19	0.508314
$215$	−8.40152e19	−1.25496
$216$	1.35531e20	1.94617
$217$	−3.30323e19	−0.456070
$218$	6.25335e19	0.830296
$219$	−2.57355e20	−3.28668
$220$	−6.92360e19	−0.850628
$221$	−4.65840e19	−0.550683
$222$	−1.82981e19	−0.208164
$223$	−9.09795e19	−0.996213	−0.498106	−	0.867116i	$-0.665971\pi$
$223$	−9.09795e19	−0.996213	−0.498106	+	0.867116i	$0.665971\pi$
$224$	−1.03846e20	−1.09467
$225$	−4.20780e19	−0.427075
$226$	−5.61190e19	−0.548515
$227$	1.83903e20	1.73128	0.865641	−	0.500664i	$-0.166911\pi$
$227$	1.83903e20	1.73128	0.865641	+	0.500664i	$0.166911\pi$
$228$	−8.98183e19	−0.814551
$229$	−5.41115e19	−0.472812	−0.236406	−	0.971654i	$-0.575969\pi$
$229$	−5.41115e19	−0.472812	−0.236406	+	0.971654i	$0.575969\pi$
$230$	5.49862e19	0.462985
$231$	4.05042e20	3.28699
$232$	2.43495e19	0.190477
$233$	−2.28051e20	−1.71991	−0.859957	−	0.510367i	$-0.829509\pi$
$233$	−2.28051e20	−1.71991	−0.859957	+	0.510367i	$0.829509\pi$
$234$	−6.81176e19	−0.495364
$235$	−7.31926e19	−0.513323
$236$	1.04604e20	0.707617
$237$	2.07996e20	1.35736
$238$	−1.76011e20	−1.10824
$239$	−2.83766e20	−1.72416	−0.862081	−	0.506771i	$-0.830839\pi$
$239$	−2.83766e20	−1.72416	−0.862081	+	0.506771i	$0.830839\pi$
$240$	2.41303e19	0.141504
$241$	−1.32125e20	−0.747893	−0.373947	−	0.927450i	$-0.621996\pi$
$241$	−1.32125e20	−0.747893	−0.373947	+	0.927450i	$0.621996\pi$
$242$	2.06666e20	1.12938
$243$	−5.60238e19	−0.295610
$244$	1.36487e20	0.695467
$245$	5.10244e19	0.251111
$246$	2.17137e20	1.03225
$247$	6.41006e19	0.294400
$248$	−9.31158e19	−0.413223
$249$	−3.53899e20	−1.51770
$250$	−1.68631e20	−0.698950
$251$	−3.72040e20	−1.49061	−0.745303	−	0.666726i	$-0.767695\pi$
$251$	−3.72040e20	−1.49061	−0.745303	+	0.666726i	$0.767695\pi$
$252$	3.50834e20	1.35893
$253$	3.52602e20	1.32057
$254$	1.24539e20	0.451044
$255$	−6.72269e20	−2.35479
$256$	−3.08130e20	−1.04398
$257$	3.16781e20	1.03831	0.519155	−	0.854680i	$-0.326247\pi$
$257$	3.16781e20	1.03831	0.519155	+	0.854680i	$0.326247\pi$
$258$	5.06845e20	1.60734
$259$	−6.72583e19	−0.206394
$260$	6.33659e19	0.188184
$261$	−1.34432e20	−0.386419
$262$	−3.85278e20	−1.07205
$263$	−6.49458e20	−1.74955	−0.874776	−	0.484527i	$-0.838992\pi$
$263$	−6.49458e20	−1.74955	−0.874776	+	0.484527i	$0.838992\pi$
$264$	1.14179e21	2.97818
$265$	4.57955e20	1.15673
$266$	2.42195e20	0.592476
$267$	−7.87233e20	−1.86534
$268$	3.22354e20	0.739923
$269$	1.36603e20	0.303785	0.151892	−	0.988397i	$-0.451463\pi$
$269$	1.36603e20	0.303785	0.151892	+	0.988397i	$0.451463\pi$
$270$	−5.10631e20	−1.10031
$271$	−3.80311e20	−0.794144	−0.397072	−	0.917787i	$-0.629974\pi$
$271$	−3.80311e20	−0.794144	−0.397072	+	0.917787i	$0.629974\pi$
$272$	−6.72408e19	−0.136081
$273$	−3.70701e20	−0.727179
$274$	−3.23892e20	−0.615914
$275$	−1.84138e20	−0.339481
$276$	4.52179e20	0.808320
$277$	9.68058e20	1.67812	0.839061	−	0.544037i	$-0.183105\pi$
$277$	9.68058e20	1.67812	0.839061	+	0.544037i	$0.183105\pi$
$278$	−4.70348e20	−0.790749
$279$	5.14087e20	0.838303
$280$	6.54476e20	1.03526
$281$	4.90913e20	0.753358	0.376679	−	0.926344i	$-0.377066\pi$
$281$	4.90913e20	0.753358	0.376679	+	0.926344i	$0.377066\pi$
$282$	4.41554e20	0.657456
$283$	−7.78095e20	−1.12421	−0.562106	−	0.827065i	$-0.690009\pi$
$283$	−7.78095e20	−1.12421	−0.562106	+	0.827065i	$0.690009\pi$
$284$	−3.61506e20	−0.506885
$285$	9.25058e20	1.25889
$286$	−2.98089e20	−0.393763
$287$	7.98129e20	1.02347
$288$	1.61617e21	2.01210
$289$	1.04608e21	1.26455
$290$	−9.17401e19	−0.107690
$291$	−4.38124e20	−0.499467
$292$	−9.75487e20	−1.08011
$293$	−1.60829e21	−1.72977	−0.864886	−	0.501969i	$-0.832609\pi$
$293$	−1.60829e21	−1.72977	−0.864886	+	0.501969i	$0.832609\pi$
$294$	−3.07819e20	−0.321620
$295$	−1.07734e21	−1.09362
$296$	−1.89596e20	−0.187004
$297$	−3.27445e21	−3.13840
$298$	6.79805e20	0.633208
$299$	−3.22707e20	−0.292148
$300$	−2.36140e20	−0.207796
$301$	1.86301e21	1.59367
$302$	−7.56617e20	−0.629241
$303$	3.15543e21	2.55150
$304$	9.25249e19	0.0727500
$305$	−1.40571e21	−1.07485
$306$	2.73928e21	2.03706
$307$	1.77172e21	1.28150	0.640750	−	0.767749i	$-0.278623\pi$
$307$	1.77172e21	1.28150	0.640750	+	0.767749i	$0.278623\pi$
$308$	1.53529e21	1.08021
$309$	1.78254e21	1.22009
$310$	3.50827e20	0.233624
$311$	2.57293e21	1.66711	0.833556	−	0.552434i	$-0.186301\pi$
$311$	2.57293e21	1.66711	0.833556	+	0.552434i	$0.186301\pi$
$312$	−1.04498e21	−0.658861
$313$	2.57753e21	1.58153	0.790763	−	0.612122i	$-0.209684\pi$
$313$	2.57753e21	1.58153	0.790763	+	0.612122i	$0.209684\pi$
$314$	5.99707e20	0.358127
$315$	−3.61332e21	−2.10023
$316$	7.88394e20	0.446070
$317$	6.60712e20	0.363922	0.181961	−	0.983306i	$-0.441755\pi$
$317$	6.60712e20	0.363922	0.181961	+	0.983306i	$0.441755\pi$
$318$	−2.76274e21	−1.48153
$319$	−5.88289e20	−0.307164
$320$	1.26148e21	0.641365
$321$	−2.77020e21	−1.37157
$322$	−1.21930e21	−0.587944
$323$	−2.57774e21	−1.21065
$324$	−1.57531e21	−0.720665
$325$	1.68526e20	0.0751030
$326$	−4.28516e20	−0.186045
$327$	−5.29632e21	−2.24036
$328$	2.24987e21	0.927320
$329$	1.62302e21	0.651867
$330$	−4.30183e21	−1.68378
$331$	−5.79021e20	−0.220880	−0.110440	−	0.993883i	$-0.535226\pi$
$331$	−5.79021e20	−0.220880	−0.110440	+	0.993883i	$0.535226\pi$
$332$	−1.34143e21	−0.498764
$333$	1.04675e21	0.379373
$334$	−4.60716e20	−0.162775
$335$	−3.31999e21	−1.14355
$336$	−5.35082e20	−0.179695
$337$	2.21420e21	0.725042	0.362521	−	0.931976i	$-0.381916\pi$
$337$	2.21420e21	0.725042	0.362521	+	0.931976i	$0.381916\pi$
$338$	−1.76445e21	−0.563400
$339$	4.75304e21	1.48004
$340$	−2.54819e21	−0.773859
$341$	2.24970e21	0.666364
$342$	−3.76931e21	−1.08903
$343$	2.88543e21	0.813224
$344$	5.25169e21	1.44395
$345$	−4.65709e21	−1.24926
$346$	−1.77291e21	−0.464023
$347$	−8.61128e20	−0.219921	−0.109961	−	0.993936i	$-0.535072\pi$
$347$	−8.61128e20	−0.219921	−0.109961	+	0.993936i	$0.535072\pi$
$348$	−7.54426e20	−0.188015
$349$	−3.22448e21	−0.784231	−0.392116	−	0.919916i	$-0.628257\pi$
$349$	−3.22448e21	−0.784231	−0.392116	+	0.919916i	$0.628257\pi$
$350$	6.36750e20	0.151144
$351$	2.99682e21	0.694306
$352$	7.07252e21	1.59942
$353$	−4.67884e21	−1.03289	−0.516444	−	0.856321i	$-0.672745\pi$
$353$	−4.67884e21	−1.03289	−0.516444	+	0.856321i	$0.672745\pi$
$354$	6.49938e21	1.40070
$355$	3.72323e21	0.783392
$356$	−2.98396e21	−0.613010
$357$	1.49073e22	2.99034
$358$	−3.42241e21	−0.670388
$359$	1.83991e21	0.351961	0.175981	−	0.984394i	$-0.443690\pi$
$359$	1.83991e21	0.351961	0.175981	+	0.984394i	$0.443690\pi$
$360$	−1.01857e22	−1.90291
$361$	−1.93336e21	−0.352778
$362$	−3.04736e21	−0.543127
$363$	−1.75037e22	−3.04736
$364$	−1.40512e21	−0.238974
$365$	1.00468e22	1.66931
$366$	8.48031e21	1.37665
$367$	−2.68412e20	−0.0425736	−0.0212868	−	0.999773i	$-0.506776\pi$
$367$	−2.68412e20	−0.0425736	−0.0212868	+	0.999773i	$0.506776\pi$
$368$	−4.65805e20	−0.0721935
$369$	−1.24214e22	−1.88125
$370$	7.14330e20	0.105727
$371$	−1.01550e22	−1.46893
$372$	2.88503e21	0.407882
$373$	−6.09640e21	−0.842458	−0.421229	−	0.906954i	$-0.638401\pi$
$373$	−6.09640e21	−0.842458	−0.421229	+	0.906954i	$0.638401\pi$
$374$	1.19874e22	1.61925
$375$	1.42823e22	1.88596
$376$	4.57518e21	0.590625
$377$	5.38411e20	0.0679536
$378$	1.13231e22	1.39728
$379$	−2.23884e21	−0.270140	−0.135070	−	0.990836i	$-0.543126\pi$
$379$	−2.23884e21	−0.270140	−0.135070	+	0.990836i	$0.543126\pi$
$380$	3.50637e21	0.413711
$381$	−1.05479e22	−1.21704
$382$	−1.11886e22	−1.26252
$383$	−4.54910e21	−0.502038	−0.251019	−	0.967982i	$-0.580766\pi$
$383$	−4.54910e21	−0.502038	−0.251019	+	0.967982i	$0.580766\pi$
$384$	8.11327e21	0.875751
$385$	−1.58122e22	−1.66947
$386$	1.34542e21	0.138952
$387$	−2.89943e22	−2.92933
$388$	−1.66068e21	−0.164141
$389$	1.78285e21	0.172403	0.0862013	−	0.996278i	$-0.472527\pi$
$389$	1.78285e21	0.172403	0.0862013	+	0.996278i	$0.472527\pi$
$390$	3.93710e21	0.372501
$391$	1.29773e22	1.20139
$392$	−3.18948e21	−0.288927
$393$	3.26314e22	2.89267
$394$	7.05096e21	0.611689
$395$	−8.11985e21	−0.689402
$396$	−2.38939e22	−1.98553
$397$	5.04507e21	0.410344	0.205172	−	0.978726i	$-0.434225\pi$
$397$	5.04507e21	0.410344	0.205172	+	0.978726i	$0.434225\pi$
$398$	9.42510e20	0.0750378
$399$	−2.05129e22	−1.59866
$400$	2.43255e20	0.0185589
$401$	−2.20790e21	−0.164912	−0.0824558	−	0.996595i	$-0.526276\pi$
$401$	−2.20790e21	−0.164912	−0.0824558	+	0.996595i	$0.526276\pi$
$402$	2.00288e22	1.46465
$403$	−2.05896e21	−0.147419
$404$	1.19604e22	0.838505
$405$	1.62245e22	1.11379
$406$	2.03431e21	0.136756
$407$	4.58068e21	0.301563
$408$	4.20228e22	2.70940
$409$	1.03741e21	0.0655093	0.0327546	−	0.999463i	$-0.489572\pi$
$409$	1.03741e21	0.0655093	0.0327546	+	0.999463i	$0.489572\pi$
$410$	−8.47669e21	−0.524281
$411$	2.74322e22	1.66190
$412$	6.75659e21	0.400960
$413$	2.38898e22	1.38879
$414$	1.89761e22	1.08070
$415$	1.38157e22	0.770840
$416$	−6.47288e21	−0.353838
$417$	3.98364e22	2.13365
$418$	−1.64949e22	−0.865667
$419$	2.57171e21	0.132252	0.0661260	−	0.997811i	$-0.478936\pi$
$419$	2.57171e21	0.132252	0.0661260	+	0.997811i	$0.478936\pi$
$420$	−2.02777e22	−1.02188
$421$	−1.51851e22	−0.749929	−0.374964	−	0.927039i	$-0.622345\pi$
$421$	−1.51851e22	−0.749929	−0.374964	+	0.927039i	$0.622345\pi$
$422$	6.94571e21	0.336171
$423$	−2.52593e22	−1.19820
$424$	−2.86262e22	−1.33093
$425$	−6.77708e21	−0.308842
$426$	−2.24614e22	−1.00336
$427$	3.11711e22	1.36494
$428$	−1.05003e22	−0.450742
$429$	2.52469e22	1.06248
$430$	−1.97865e22	−0.816369
$431$	1.61217e22	0.652159	0.326080	−	0.945342i	$-0.394272\pi$
$431$	1.61217e22	0.652159	0.326080	+	0.945342i	$0.394272\pi$
$432$	4.32571e21	0.171572
$433$	1.33784e22	0.520304	0.260152	−	0.965568i	$-0.416227\pi$
$433$	1.33784e22	0.520304	0.260152	+	0.965568i	$0.416227\pi$
$434$	−7.77947e21	−0.296679
$435$	7.77000e21	0.290578
$436$	−2.00754e22	−0.736255
$437$	−1.78571e22	−0.642271
$438$	−6.06098e22	−2.13803
$439$	−2.74725e22	−0.950495	−0.475247	−	0.879852i	$-0.657641\pi$
$439$	−2.74725e22	−0.950495	−0.475247	+	0.879852i	$0.657641\pi$
$440$	−4.45736e22	−1.51262
$441$	1.76089e22	0.586144
$442$	−1.09710e22	−0.358226
$443$	2.36854e22	0.758664	0.379332	−	0.925261i	$-0.376154\pi$
$443$	2.36854e22	0.758664	0.379332	+	0.925261i	$0.376154\pi$
$444$	5.87430e21	0.184587
$445$	3.07324e22	0.947407
$446$	−2.14266e22	−0.648048
$447$	−5.75766e22	−1.70857
$448$	−2.79729e22	−0.814468
$449$	3.82802e22	1.09366	0.546828	−	0.837245i	$-0.315835\pi$
$449$	3.82802e22	1.09366	0.546828	+	0.837245i	$0.315835\pi$
$450$	−9.90982e21	−0.277817
$451$	−5.43573e22	−1.49540
$452$	1.80161e22	0.486389
$453$	6.40822e22	1.69786
$454$	4.33110e22	1.12622
$455$	1.44716e22	0.369335
$456$	−5.78243e22	−1.44847
$457$	−3.13779e22	−0.771499	−0.385750	−	0.922603i	$-0.626057\pi$
$457$	−3.13779e22	−0.771499	−0.385750	+	0.922603i	$0.626057\pi$
$458$	−1.27438e22	−0.307570
$459$	−1.20514e23	−2.85516
$460$	−1.76524e22	−0.410547
$461$	−5.72641e22	−1.30745	−0.653724	−	0.756733i	$-0.726794\pi$
$461$	−5.72641e22	−1.30745	−0.653724	+	0.756733i	$0.726794\pi$
$462$	9.53917e22	2.13823
$463$	3.37162e21	0.0741994	0.0370997	−	0.999312i	$-0.488188\pi$
$463$	3.37162e21	0.0741994	0.0370997	+	0.999312i	$0.488188\pi$
$464$	7.77160e20	0.0167922
$465$	−2.97135e22	−0.630382
$466$	−5.37084e22	−1.11882
$467$	1.63940e22	0.335345	0.167673	−	0.985843i	$-0.446375\pi$
$467$	1.63940e22	0.335345	0.167673	+	0.985843i	$0.446375\pi$
$468$	2.18680e22	0.439258
$469$	7.36197e22	1.45219
$470$	−1.72376e22	−0.333923
$471$	−5.07926e22	−0.966324
$472$	6.73435e22	1.25831
$473$	−1.26882e23	−2.32852
$474$	4.89852e22	0.882976
$475$	9.32542e21	0.165110
$476$	5.65053e22	0.982721
$477$	1.58044e23	2.70004
$478$	−6.68299e22	−1.12159
$479$	2.55512e22	0.421270	0.210635	−	0.977565i	$-0.432447\pi$
$479$	2.55512e22	0.421270	0.210635	+	0.977565i	$0.432447\pi$
$480$	−9.34123e22	−1.51305
$481$	−4.19231e21	−0.0667145
$482$	−3.11168e22	−0.486514
$483$	1.03269e23	1.58643
$484$	−6.63467e22	−1.00146
$485$	1.71037e22	0.253680
$486$	−1.31942e22	−0.192298
$487$	−5.53989e22	−0.793424	−0.396712	−	0.917943i	$-0.629849\pi$
$487$	−5.53989e22	−0.793424	−0.396712	+	0.917943i	$0.629849\pi$
$488$	8.78690e22	1.23671
$489$	3.62934e22	0.501999
$490$	1.20168e22	0.163351
$491$	6.02848e22	0.805407	0.402703	−	0.915331i	$-0.368071\pi$
$491$	6.02848e22	0.805407	0.402703	+	0.915331i	$0.368071\pi$
$492$	−6.97081e22	−0.915335
$493$	−2.16516e22	−0.279442
$494$	1.50964e22	0.191511
$495$	2.46088e23	3.06864
$496$	−2.97196e21	−0.0364292
$497$	−8.25614e22	−0.994827
$498$	−8.33471e22	−0.987281
$499$	1.11315e23	1.29628	0.648139	−	0.761522i	$-0.275548\pi$
$499$	1.11315e23	1.29628	0.648139	+	0.761522i	$0.275548\pi$
$500$	5.41361e22	0.619786
$501$	3.90207e22	0.439212
$502$	−8.76193e22	−0.969657
$503$	1.56214e23	1.69978	0.849890	−	0.526960i	$-0.176668\pi$
$503$	1.56214e23	1.69978	0.849890	+	0.526960i	$0.176668\pi$
$504$	2.25864e23	2.41651
$505$	−1.23183e23	−1.29591
$506$	8.30415e22	0.859045
$507$	1.49441e23	1.52021
$508$	−3.99812e22	−0.399958
$509$	−1.47117e23	−1.44731	−0.723654	−	0.690163i	$-0.757539\pi$
$509$	−1.47117e23	−1.44731	−0.723654	+	0.690163i	$0.757539\pi$
$510$	−1.58327e23	−1.53182
$511$	−2.22783e23	−2.11985
$512$	−1.92547e22	−0.180195
$513$	1.65830e23	1.52639
$514$	7.46052e22	0.675433
$515$	−6.95876e22	−0.619684
$516$	−1.62714e23	−1.42529
$517$	−1.10537e23	−0.952443
$518$	−1.58400e22	−0.134262
$519$	1.50158e23	1.25206
$520$	4.07945e22	0.334636
$521$	8.41832e22	0.679368	0.339684	−	0.940540i	$-0.389680\pi$
$521$	8.41832e22	0.679368	0.339684	+	0.940540i	$0.389680\pi$
$522$	−3.16602e22	−0.251371
$523$	−2.39260e23	−1.86898	−0.934492	−	0.355985i	$-0.884146\pi$
$523$	−2.39260e23	−1.86898	−0.934492	+	0.355985i	$0.884146\pi$
$524$	1.23687e23	0.950624
$525$	−5.39300e22	−0.407827
$526$	−1.52954e23	−1.13811
$527$	8.27988e22	0.606225
$528$	3.64422e22	0.262552
$529$	−5.11507e22	−0.362642
$530$	1.07853e23	0.752468
$531$	−3.71799e23	−2.55273
$532$	−7.77526e22	−0.525371
$533$	4.97486e22	0.330826
$534$	−1.85402e23	−1.21343
$535$	1.08144e23	0.696622
$536$	2.07529e23	1.31576
$537$	2.89863e23	1.80889
$538$	3.21715e22	0.197616
$539$	7.70583e22	0.465924
$540$	1.63930e23	0.975686
$541$	−1.90963e23	−1.11885	−0.559426	−	0.828880i	$-0.688978\pi$
$541$	−1.90963e23	−1.11885	−0.559426	+	0.828880i	$0.688978\pi$
$542$	−8.95672e22	−0.516601
$543$	2.58099e23	1.46550
$544$	2.60300e23	1.45507
$545$	2.06760e23	1.13788
$546$	−8.73040e22	−0.473039
$547$	−1.41110e23	−0.752774	−0.376387	−	0.926463i	$-0.622834\pi$
$547$	−1.41110e23	−0.752774	−0.376387	+	0.926463i	$0.622834\pi$
$548$	1.03980e23	0.546154
$549$	−4.85120e23	−2.50890
$550$	−4.33664e22	−0.220836
$551$	2.97931e22	0.149392
$552$	2.91109e23	1.43739
$553$	1.80055e23	0.875470
$554$	2.27988e23	1.09164
$555$	−6.05007e22	−0.285279
$556$	1.50997e23	0.701187
$557$	1.94784e23	0.890810	0.445405	−	0.895329i	$-0.353060\pi$
$557$	1.94784e23	0.890810	0.445405	+	0.895329i	$0.353060\pi$
$558$	1.21073e23	0.545326
$559$	1.16124e23	0.515136
$560$	2.08888e22	0.0912673
$561$	−1.01528e24	−4.36919
$562$	1.15615e23	0.490068
$563$	−1.69266e23	−0.706723	−0.353361	−	0.935487i	$-0.614961\pi$
$563$	−1.69266e23	−0.706723	−0.353361	+	0.935487i	$0.614961\pi$
$564$	−1.41754e23	−0.582991
$565$	−1.85552e23	−0.751714
$566$	−1.83250e23	−0.731313
$567$	−3.59772e23	−1.41440
$568$	−2.32735e23	−0.901364
$569$	3.11008e23	1.18664	0.593318	−	0.804968i	$-0.297818\pi$
$569$	3.11008e23	1.18664	0.593318	+	0.804968i	$0.297818\pi$
$570$	2.17861e23	0.818923
$571$	7.44215e22	0.275608	0.137804	−	0.990460i	$-0.455996\pi$
$571$	7.44215e22	0.275608	0.137804	+	0.990460i	$0.455996\pi$
$572$	9.56967e22	0.349165
$573$	9.47627e23	3.40662
$574$	1.87968e23	0.665783
$575$	−4.69477e22	−0.163847
$576$	4.35346e23	1.49707
$577$	−2.74482e23	−0.930079	−0.465040	−	0.885290i	$-0.653960\pi$
$577$	−2.74482e23	−0.930079	−0.465040	+	0.885290i	$0.653960\pi$
$578$	2.46364e23	0.822604
$579$	−1.13951e23	−0.374930
$580$	2.94517e22	0.0954931
$581$	−3.06359e23	−0.978888
$582$	−1.03183e23	−0.324910
$583$	6.91614e23	2.14625
$584$	−6.28010e23	−1.92069
$585$	−2.25224e23	−0.678874
$586$	−3.78769e23	−1.12524
$587$	−6.16868e22	−0.180621	−0.0903106	−	0.995914i	$-0.528786\pi$
$587$	−6.16868e22	−0.180621	−0.0903106	+	0.995914i	$0.528786\pi$
$588$	9.88202e22	0.285193
$589$	−1.13933e23	−0.324093
$590$	−2.53726e23	−0.711415
$591$	−5.97186e23	−1.65050
$592$	−6.05132e21	−0.0164860
$593$	−4.94389e23	−1.32771	−0.663856	−	0.747860i	$-0.731081\pi$
$593$	−4.94389e23	−1.32771	−0.663856	+	0.747860i	$0.731081\pi$
$594$	−7.71167e23	−2.04157
$595$	−5.81961e23	−1.51880
$596$	−2.18240e23	−0.561489
$597$	−7.98266e22	−0.202472
$598$	−7.60008e22	−0.190046
$599$	3.64186e23	0.897832	0.448916	−	0.893574i	$-0.351810\pi$
$599$	3.64186e23	0.897832	0.448916	+	0.893574i	$0.351810\pi$
$600$	−1.52025e23	−0.369512
$601$	5.23131e23	1.25365	0.626826	−	0.779159i	$-0.284354\pi$
$601$	5.23131e23	1.25365	0.626826	+	0.779159i	$0.284354\pi$
$602$	4.38758e23	1.03670
$603$	−1.14575e24	−2.66928
$604$	2.42899e23	0.557972
$605$	6.83319e23	1.54776
$606$	7.43136e23	1.65978
$607$	6.04371e23	1.33107	0.665533	−	0.746368i	$-0.268204\pi$
$607$	6.04371e23	1.33107	0.665533	+	0.746368i	$0.268204\pi$
$608$	−3.58179e23	−0.777892
$609$	−1.72297e23	−0.369004
$610$	−3.31059e23	−0.699200
$611$	1.01165e23	0.210708
$612$	−8.79400e23	−1.80634
$613$	−7.19761e23	−1.45806	−0.729028	−	0.684484i	$-0.760028\pi$
$613$	−7.19761e23	−1.45806	−0.729028	+	0.684484i	$0.760028\pi$
$614$	4.17259e23	0.833632
$615$	7.17939e23	1.41465
$616$	9.88405e23	1.92087
$617$	−5.24480e23	−1.00532	−0.502661	−	0.864484i	$-0.667646\pi$
$617$	−5.24480e23	−1.00532	−0.502661	+	0.864484i	$0.667646\pi$
$618$	4.19806e23	0.793682
$619$	1.30453e23	0.243267	0.121634	−	0.992575i	$-0.461187\pi$
$619$	1.30453e23	0.243267	0.121634	+	0.992575i	$0.461187\pi$
$620$	−1.12627e23	−0.207164
$621$	−8.34852e23	−1.51472
$622$	6.05953e23	1.08448
$623$	−6.81481e23	−1.20311
$624$	−3.33524e22	−0.0580843
$625$	−4.38098e23	−0.752647
$626$	6.07035e23	1.02880
$627$	1.39705e24	2.33580
$628$	−1.92526e23	−0.317565
$629$	1.68589e23	0.274347
$630$	−8.50975e23	−1.36622
$631$	−2.38798e22	−0.0378252	−0.0189126	−	0.999821i	$-0.506020\pi$
$631$	−2.38798e22	−0.0378252	−0.0189126	+	0.999821i	$0.506020\pi$
$632$	5.07562e23	0.793220
$633$	−5.88272e23	−0.907082
$634$	1.55605e23	0.236736
$635$	4.11775e23	0.618135
$636$	8.86931e23	1.31372
$637$	−7.05250e22	−0.103076
$638$	−1.38548e23	−0.199814
$639$	1.28491e24	1.82859
$640$	−3.16730e23	−0.444795
$641$	8.65450e22	0.119936	0.0599679	−	0.998200i	$-0.480900\pi$
$641$	8.65450e22	0.119936	0.0599679	+	0.998200i	$0.480900\pi$
$642$	−6.52411e23	−0.892223
$643$	−9.25999e23	−1.24973	−0.624867	−	0.780731i	$-0.714847\pi$
$643$	−9.25999e23	−1.24973	−0.624867	+	0.780731i	$0.714847\pi$
$644$	3.91436e23	0.521352
$645$	1.67583e24	2.20278
$646$	−6.07085e23	−0.787540
$647$	3.23089e23	0.413653	0.206826	−	0.978378i	$-0.433687\pi$
$647$	3.23089e23	0.413653	0.206826	+	0.978378i	$0.433687\pi$
$648$	−1.01417e24	−1.28152
$649$	−1.62703e24	−2.02916
$650$	3.96896e22	0.0488554
$651$	6.58887e23	0.800521
$652$	1.37568e23	0.164973
$653$	−6.28781e23	−0.744282	−0.372141	−	0.928176i	$-0.621376\pi$
$653$	−6.28781e23	−0.744282	−0.372141	+	0.928176i	$0.621376\pi$
$654$	−1.24734e24	−1.45738
$655$	−1.27388e24	−1.46919
$656$	7.18087e22	0.0817513
$657$	3.46721e24	3.89650
$658$	3.82239e23	0.424048
$659$	9.25389e23	1.01344	0.506721	−	0.862110i	$-0.330858\pi$
$659$	9.25389e23	1.01344	0.506721	+	0.862110i	$0.330858\pi$
$660$	1.38103e24	1.49307
$661$	−1.44194e23	−0.153898	−0.0769491	−	0.997035i	$-0.524518\pi$
$661$	−1.44194e23	−0.153898	−0.0769491	+	0.997035i	$0.524518\pi$
$662$	−1.36365e23	−0.143685
$663$	9.29198e23	0.966592
$664$	−8.63604e23	−0.886923
$665$	8.00791e23	0.811962
$666$	2.46521e23	0.246787
$667$	−1.49990e23	−0.148249
$668$	1.47905e23	0.144339
$669$	1.81474e24	1.74861
$670$	−7.81893e23	−0.743895
$671$	−2.12293e24	−1.99432
$672$	2.07139e24	1.92142
$673$	−8.81034e23	−0.806983	−0.403492	−	0.914983i	$-0.632204\pi$
$673$	−8.81034e23	−0.806983	−0.403492	+	0.914983i	$0.632204\pi$
$674$	5.21468e23	0.471649
$675$	4.35981e23	0.389391
$676$	5.66447e23	0.499588
$677$	4.96302e23	0.432257	0.216129	−	0.976365i	$-0.430657\pi$
$677$	4.96302e23	0.432257	0.216129	+	0.976365i	$0.430657\pi$
$678$	1.11939e24	0.962785
$679$	−3.79269e23	−0.322147
$680$	−1.64051e24	−1.37611
$681$	−3.66826e24	−3.03885
$682$	5.29827e23	0.433478
$683$	2.17565e24	1.75798	0.878988	−	0.476845i	$-0.158220\pi$
$683$	2.17565e24	1.75798	0.878988	+	0.476845i	$0.158220\pi$
$684$	1.21007e24	0.965685
$685$	−1.07091e24	−0.844082
$686$	6.79549e23	0.529012
$687$	1.07935e24	0.829907
$688$	1.67617e23	0.127297
$689$	−6.32976e23	−0.474814
$690$	−1.09679e24	−0.812659
$691$	−2.37141e23	−0.173558	−0.0867789	−	0.996228i	$-0.527657\pi$
$691$	−2.37141e23	−0.173558	−0.0867789	+	0.996228i	$0.527657\pi$
$692$	5.69162e23	0.411466
$693$	−5.45692e24	−3.89686
$694$	−2.02805e23	−0.143061
$695$	−1.55516e24	−1.08369
$696$	−4.85693e23	−0.334336
$697$	−2.00059e24	−1.36044
$698$	−7.59400e23	−0.510152
$699$	4.54887e24	3.01889
$700$	−2.04418e23	−0.134025
$701$	1.08975e24	0.705869	0.352934	−	0.935648i	$-0.385184\pi$
$701$	1.08975e24	0.705869	0.352934	+	0.935648i	$0.385184\pi$
$702$	7.05784e23	0.451654
$703$	−2.31983e23	−0.146668
$704$	1.90512e24	1.19002
$705$	1.45995e24	0.901014
$706$	−1.10192e24	−0.671907
$707$	2.73155e24	1.64567
$708$	−2.08652e24	−1.24205
$709$	−1.04251e24	−0.613179	−0.306589	−	0.951842i	$-0.599188\pi$
$709$	−1.04251e24	−0.613179	−0.306589	+	0.951842i	$0.599188\pi$
$710$	8.76860e23	0.509606
$711$	−2.80222e24	−1.60920
$712$	−1.92105e24	−1.09008
$713$	5.73582e23	0.321614
$714$	3.51084e24	1.94525
$715$	−9.85601e23	−0.539635
$716$	1.09871e24	0.594458
$717$	5.66020e24	3.02635
$718$	4.33319e23	0.228955
$719$	−3.32463e24	−1.73599	−0.867997	−	0.496569i	$-0.834593\pi$
$719$	−3.32463e24	−1.73599	−0.867997	+	0.496569i	$0.834593\pi$
$720$	−3.25095e23	−0.167758
$721$	1.54308e24	0.786935
$722$	−4.55327e23	−0.229486
$723$	2.63546e24	1.31275
$724$	9.78306e23	0.481612
$725$	7.83286e22	0.0381107
$726$	−4.12231e24	−1.98235
$727$	2.02664e24	0.963241	0.481620	−	0.876380i	$-0.340048\pi$
$727$	2.02664e24	0.963241	0.481620	+	0.876380i	$0.340048\pi$
$728$	−9.04603e23	−0.424954
$729$	−1.57322e24	−0.730474
$730$	2.36612e24	1.08590
$731$	−4.66981e24	−2.11837
$732$	−2.72246e24	−1.22073
$733$	−1.25213e24	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$733$	−1.25213e24	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$734$	−6.32139e22	−0.0276946
$735$	−1.01777e24	−0.440765
$736$	1.80321e24	0.771941
$737$	−5.01393e24	−2.12180
$738$	−2.92537e24	−1.22378
$739$	3.95948e23	0.163742	0.0818711	−	0.996643i	$-0.473910\pi$
$739$	3.95948e23	0.163742	0.0818711	+	0.996643i	$0.473910\pi$
$740$	−2.29324e23	−0.0937519
$741$	−1.27860e24	−0.516748
$742$	−2.39161e24	−0.955557
$743$	−3.30249e24	−1.30448	−0.652239	−	0.758013i	$-0.726170\pi$
$743$	−3.30249e24	−1.30448	−0.652239	+	0.758013i	$0.726170\pi$
$744$	1.85736e24	0.725313
$745$	2.24770e24	0.867782
$746$	−1.43577e24	−0.548029
$747$	4.76790e24	1.79929
$748$	−3.84834e24	−1.43585
$749$	−2.39807e24	−0.884638
$750$	3.36363e24	1.22684
$751$	−2.02824e24	−0.731441	−0.365721	−	0.930725i	$-0.619177\pi$
$751$	−2.02824e24	−0.731441	−0.365721	+	0.930725i	$0.619177\pi$
$752$	1.46025e23	0.0520687
$753$	7.42098e24	2.61640
$754$	1.26801e23	0.0442046
$755$	−2.50167e24	−0.862346
$756$	−3.63508e24	−1.23902
$757$	−2.14857e23	−0.0724159	−0.0362080	−	0.999344i	$-0.511528\pi$
$757$	−2.14857e23	−0.0724159	−0.0362080	+	0.999344i	$0.511528\pi$
$758$	−5.27270e23	−0.175729
$759$	−7.03326e24	−2.31794
$760$	2.25737e24	0.735679
$761$	7.68917e23	0.247805	0.123902	−	0.992294i	$-0.460459\pi$
$761$	7.68917e23	0.247805	0.123902	+	0.992294i	$0.460459\pi$
$762$	−2.48415e24	−0.791698
$763$	−4.58484e24	−1.44499
$764$	3.59192e24	1.11952
$765$	9.05714e24	2.79170
$766$	−1.07136e24	−0.326582
$767$	1.48908e24	0.448909
$768$	6.14619e24	1.83246
$769$	2.61133e24	0.769996	0.384998	−	0.922917i	$-0.374202\pi$
$769$	2.61133e24	0.769996	0.384998	+	0.922917i	$0.374202\pi$
$770$	−3.72395e24	−1.08601
$771$	−6.31874e24	−1.82250
$772$	−4.31924e23	−0.123214
$773$	3.94911e24	1.11423	0.557113	−	0.830437i	$-0.311909\pi$
$773$	3.94911e24	1.11423	0.557113	+	0.830437i	$0.311909\pi$
$774$	−6.82846e24	−1.90557
$775$	−2.99539e23	−0.0826778
$776$	−1.06913e24	−0.291882
$777$	1.34158e24	0.362275
$778$	4.19881e23	0.112150
$779$	2.75285e24	0.727302
$780$	−1.26394e24	−0.330311
$781$	5.62291e24	1.45354
$782$	3.05629e24	0.781516
$783$	1.39289e24	0.352323
$784$	−1.01798e23	−0.0254714
$785$	1.98287e24	0.490797
$786$	7.68504e24	1.88172
$787$	1.10266e24	0.267090	0.133545	−	0.991043i	$-0.457364\pi$
$787$	1.10266e24	0.267090	0.133545	+	0.991043i	$0.457364\pi$
$788$	−2.26360e24	−0.542408
$789$	1.29546e25	3.07092
$790$	−1.91231e24	−0.448464
$791$	4.11454e24	0.954600
$792$	−1.53827e25	−3.53076
$793$	1.94294e24	0.441202
$794$	1.18817e24	0.266934
$795$	−9.13470e24	−2.03036
$796$	−3.02577e23	−0.0665389
$797$	−6.59070e24	−1.43396	−0.716978	−	0.697096i	$-0.754475\pi$
$797$	−6.59070e24	−1.43396	−0.716978	+	0.697096i	$0.754475\pi$
$798$	−4.83099e24	−1.03995
$799$	−4.06826e24	−0.866485
$800$	−9.41681e23	−0.198444
$801$	1.06060e25	2.21144
$802$	−5.19983e23	−0.107277
$803$	1.51728e25	3.09731
$804$	−6.42990e24	−1.29876
$805$	−4.03149e24	−0.805750
$806$	−4.84906e23	−0.0958980
$807$	−2.72478e24	−0.533221
$808$	7.70003e24	1.49106
$809$	2.58316e24	0.494981	0.247491	−	0.968890i	$-0.420394\pi$
$809$	2.58316e24	0.494981	0.247491	+	0.968890i	$0.420394\pi$
$810$	3.82103e24	0.724533
$811$	−3.92832e24	−0.737105	−0.368553	−	0.929607i	$-0.620147\pi$
$811$	−3.92832e24	−0.737105	−0.368553	+	0.929607i	$0.620147\pi$
$812$	−6.53081e23	−0.121266
$813$	7.58595e24	1.39393
$814$	1.07880e24	0.196170
$815$	−1.41684e24	−0.254966
$816$	1.34123e24	0.238857
$817$	6.42577e24	1.13250
$818$	2.44321e23	0.0426146
$819$	4.99426e24	0.862101
$820$	2.72130e24	0.464900
$821$	1.09354e25	1.84892	0.924460	−	0.381279i	$-0.124516\pi$
$821$	1.09354e25	1.84892	0.924460	+	0.381279i	$0.124516\pi$
$822$	6.46058e24	1.08109
$823$	2.95956e24	0.490149	0.245075	−	0.969504i	$-0.421188\pi$
$823$	2.95956e24	0.490149	0.245075	+	0.969504i	$0.421188\pi$
$824$	4.34984e24	0.713004
$825$	3.67295e24	0.595876
$826$	5.62629e24	0.903424
$827$	2.77446e23	0.0440941	0.0220471	−	0.999757i	$-0.492982\pi$
$827$	2.77446e23	0.0440941	0.0220471	+	0.999757i	$0.492982\pi$
$828$	−6.09198e24	−0.958297
$829$	−4.78418e24	−0.744894	−0.372447	−	0.928054i	$-0.621481\pi$
$829$	−4.78418e24	−0.744894	−0.372447	+	0.928054i	$0.621481\pi$
$830$	3.25375e24	0.501441
$831$	−1.93096e25	−2.94554
$832$	−1.74359e24	−0.263267
$833$	2.83609e24	0.423874
$834$	9.38190e24	1.38797
$835$	−1.52331e24	−0.223076
$836$	5.29541e24	0.767620
$837$	−5.32658e24	−0.764332
$838$	6.05664e23	0.0860315
$839$	−6.38891e24	−0.898360	−0.449180	−	0.893441i	$-0.648284\pi$
$839$	−6.38891e24	−0.898360	−0.449180	+	0.893441i	$0.648284\pi$
$840$	−1.30546e25	−1.81715
$841$	2.50246e23	0.0344828
$842$	−3.57625e24	−0.487838
$843$	−9.79212e24	−1.32234
$844$	−2.22981e24	−0.298096
$845$	−5.83396e24	−0.772114
$846$	−5.94883e24	−0.779442
$847$	−1.51524e25	−1.96549
$848$	−9.13658e23	−0.117333
$849$	1.55205e25	1.97328
$850$	−1.59608e24	−0.200906
$851$	1.16789e24	0.145546
$852$	7.21086e24	0.889715
$853$	6.33170e24	0.773488	0.386744	−	0.922187i	$-0.373600\pi$
$853$	6.33170e24	0.773488	0.386744	+	0.922187i	$0.373600\pi$
$854$	7.34112e24	0.887913
$855$	−1.24628e25	−1.49247
$856$	−6.75998e24	−0.801527
$857$	−1.03611e25	−1.21638	−0.608190	−	0.793792i	$-0.708104\pi$
$857$	−1.03611e25	−1.21638	−0.608190	+	0.793792i	$0.708104\pi$
$858$	5.94591e24	0.691157
$859$	7.30022e24	0.840223	0.420111	−	0.907473i	$-0.361991\pi$
$859$	7.30022e24	0.840223	0.420111	+	0.907473i	$0.361991\pi$
$860$	6.35212e24	0.723905
$861$	−1.59201e25	−1.79646
$862$	3.79683e24	0.424238
$863$	−7.53914e24	−0.834123	−0.417062	−	0.908878i	$-0.636940\pi$
$863$	−7.53914e24	−0.834123	−0.417062	+	0.908878i	$0.636940\pi$
$864$	−1.67455e25	−1.83456
$865$	−5.86193e24	−0.635922
$866$	3.15076e24	0.338464
$867$	−2.08660e25	−2.21961
$868$	2.49747e24	0.263077
$869$	−1.22628e25	−1.27915
$870$	1.82992e24	0.189024
$871$	4.58883e24	0.469404
$872$	−1.29244e25	−1.30924
$873$	5.90262e24	0.592139
$874$	−4.20553e24	−0.417805
$875$	1.23637e25	1.21641
$876$	1.94578e25	1.89587
$877$	−1.45008e25	−1.39925	−0.699625	−	0.714511i	$-0.746649\pi$
$877$	−1.45008e25	−1.39925	−0.699625	+	0.714511i	$0.746649\pi$
$878$	−6.47006e24	−0.618308
$879$	3.20801e25	3.03620
$880$	−1.42265e24	−0.133351
$881$	−1.15220e25	−1.06963	−0.534814	−	0.844970i	$-0.679618\pi$
$881$	−1.15220e25	−1.06963	−0.534814	+	0.844970i	$0.679618\pi$
$882$	4.14708e24	0.381294
$883$	−2.03017e24	−0.184870	−0.0924348	−	0.995719i	$-0.529465\pi$
$883$	−2.03017e24	−0.184870	−0.0924348	+	0.995719i	$0.529465\pi$
$884$	3.52206e24	0.317653
$885$	2.14895e25	1.91959
$886$	5.57816e24	0.493520
$887$	5.57024e24	0.488116	0.244058	−	0.969761i	$-0.421521\pi$
$887$	5.57024e24	0.488116	0.244058	+	0.969761i	$0.421521\pi$
$888$	3.78183e24	0.328240
$889$	−9.13097e24	−0.784968
$890$	7.23781e24	0.616300
$891$	2.45026e25	2.06658
$892$	6.87866e24	0.574649
$893$	5.59802e24	0.463230
$894$	−1.35599e25	−1.11144
$895$	−1.13158e25	−0.918736
$896$	7.02338e24	0.564844
$897$	6.43694e24	0.512795
$898$	9.01539e24	0.711436
$899$	−9.56976e23	−0.0748073
$900$	3.18139e24	0.246351
$901$	2.54545e25	1.95255
$902$	−1.28017e25	−0.972775
$903$	−3.71609e25	−2.79731
$904$	1.15986e25	0.864917
$905$	−1.00758e25	−0.744331
$906$	1.50920e25	1.10448
$907$	1.39704e25	1.01285	0.506427	−	0.862283i	$-0.330966\pi$
$907$	1.39704e25	1.01285	0.506427	+	0.862283i	$0.330966\pi$
$908$	−1.39043e25	−0.998663
$909$	−4.25114e25	−3.02491
$910$	3.40822e24	0.240257
$911$	8.39404e24	0.586226	0.293113	−	0.956078i	$-0.405309\pi$
$911$	8.39404e24	0.586226	0.293113	+	0.956078i	$0.405309\pi$
$912$	−1.84557e24	−0.127695
$913$	2.08648e25	1.43025
$914$	−7.38982e24	−0.501870
$915$	2.80393e25	1.88663
$916$	4.09120e24	0.272734
$917$	2.82479e25	1.86572
$918$	−2.83824e25	−1.85732
$919$	2.42245e25	1.57062	0.785312	−	0.619101i	$-0.212503\pi$
$919$	2.42245e25	1.57062	0.785312	+	0.619101i	$0.212503\pi$
$920$	−1.13645e25	−0.730051
$921$	−3.53400e25	−2.24936
$922$	−1.34863e25	−0.850511
$923$	−5.14618e24	−0.321566
$924$	−3.06239e25	−1.89605
$925$	−6.09902e23	−0.0374158
$926$	7.94052e23	0.0482676
$927$	−2.40152e25	−1.44647
$928$	−3.00851e24	−0.179553
$929$	−4.97693e24	−0.294325	−0.147163	−	0.989112i	$-0.547014\pi$
$929$	−4.97693e24	−0.294325	−0.147163	+	0.989112i	$0.547014\pi$
$930$	−6.99785e24	−0.410071
$931$	−3.90252e24	−0.226607
$932$	1.72422e25	0.992104
$933$	−5.13216e25	−2.92621
$934$	3.86097e24	0.218146
$935$	3.96349e25	2.21911
$936$	1.40785e25	0.781107
$937$	−1.25724e25	−0.691243	−0.345622	−	0.938374i	$-0.612332\pi$
$937$	−1.25724e25	−0.691243	−0.345622	+	0.938374i	$0.612332\pi$
$938$	1.73382e25	0.944670
$939$	−5.14133e25	−2.77599
$940$	5.53386e24	0.296102
$941$	1.11635e25	0.591954	0.295977	−	0.955195i	$-0.404355\pi$
$941$	1.11635e25	0.591954	0.295977	+	0.955195i	$0.404355\pi$
$942$	−1.19622e25	−0.628606
$943$	−1.38589e25	−0.721739
$944$	2.14939e24	0.110931
$945$	3.74385e25	1.91491
$946$	−2.98820e25	−1.51473
$947$	2.07992e24	0.104489	0.0522446	−	0.998634i	$-0.483362\pi$
$947$	2.07992e24	0.104489	0.0522446	+	0.998634i	$0.483362\pi$
$948$	−1.57259e25	−0.782969
$949$	−1.38864e25	−0.685216
$950$	2.19624e24	0.107406
$951$	−1.31791e25	−0.638778
$952$	3.63777e25	1.74751
$953$	−1.70658e25	−0.812526	−0.406263	−	0.913756i	$-0.633168\pi$
$953$	−1.70658e25	−0.812526	−0.406263	+	0.913756i	$0.633168\pi$
$954$	3.72209e25	1.75641
$955$	−3.69940e25	−1.73022
$956$	2.14546e25	0.994555
$957$	1.17344e25	0.539151
$958$	6.01759e24	0.274041
$959$	2.37472e25	1.07190
$960$	−2.51624e25	−1.12576
$961$	−1.88905e25	−0.837712
$962$	−9.87333e23	−0.0433986
$963$	3.73214e25	1.62605
$964$	9.98953e24	0.431410
$965$	4.44848e24	0.190427
$966$	2.43211e25	1.03199
$967$	−3.25340e24	−0.136840	−0.0684198	−	0.997657i	$-0.521796\pi$
$967$	−3.25340e24	−0.136840	−0.0684198	+	0.997657i	$0.521796\pi$
$968$	−4.27135e25	−1.78084
$969$	5.14175e25	2.12500
$970$	4.02811e24	0.165022
$971$	−5.58701e24	−0.226890	−0.113445	−	0.993544i	$-0.536189\pi$
$971$	−5.58701e24	−0.226890	−0.113445	+	0.993544i	$0.536189\pi$
$972$	4.23578e24	0.170518
$973$	3.44851e25	1.37617
$974$	−1.30470e25	−0.516132
$975$	−3.36154e24	−0.131825
$976$	2.80450e24	0.109027
$977$	−1.61241e25	−0.621402	−0.310701	−	0.950508i	$-0.600564\pi$
$977$	−1.61241e25	−0.621402	−0.310701	+	0.950508i	$0.600564\pi$
$978$	8.54749e24	0.326556
$979$	4.64128e25	1.75786
$980$	−3.85779e24	−0.144850
$981$	7.13546e25	2.65604
$982$	1.41977e25	0.523927
$983$	−7.09243e24	−0.259472	−0.129736	−	0.991549i	$-0.541413\pi$
$983$	−7.09243e24	−0.259472	−0.129736	+	0.991549i	$0.541413\pi$
$984$	−4.48775e25	−1.62769
$985$	2.33133e25	0.838292
$986$	−5.09919e24	−0.181780
$987$	−3.23740e25	−1.14420
$988$	−4.84644e24	−0.169820
$989$	−3.23498e25	−1.12384
$990$	5.79564e25	1.99619
$991$	1.10068e25	0.375867	0.187934	−	0.982182i	$-0.439821\pi$
$991$	1.10068e25	0.375867	0.187934	+	0.982182i	$0.439821\pi$
$992$	1.15049e25	0.389525
$993$	1.15496e25	0.387701
$994$	−1.94441e25	−0.647147
$995$	3.11631e24	0.102836
$996$	2.67572e25	0.875460
$997$	−2.52579e25	−0.819386	−0.409693	−	0.912223i	$-0.634364\pi$
$997$	−2.52579e25	−0.819386	−0.409693	+	0.912223i	$0.634364\pi$
$998$	2.62158e25	0.843244
$999$	−1.08456e25	−0.345898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.13	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+235.511 q^{2} -19946.7 q^{3} -75606.8 q^{4} +778691. q^{5} -4.69767e6 q^{6} -1.72672e7 q^{7} -4.86750e7 q^{8} +2.68732e8 q^{9} +O(q^{10})\)	\(q+235.511 q^{2} -19946.7 q^{3} -75606.8 q^{4} +778691. q^{5} -4.69767e6 q^{6} -1.72672e7 q^{7} -4.86750e7 q^{8} +2.68732e8 q^{9} +1.83390e8 q^{10} +1.17600e9 q^{11} +1.50811e9 q^{12} -1.07629e9 q^{13} -4.06661e9 q^{14} -1.55323e10 q^{15} -1.55355e9 q^{16} +4.32819e10 q^{17} +6.32892e10 q^{18} -5.95569e10 q^{19} -5.88743e10 q^{20} +3.44424e11 q^{21} +2.76960e11 q^{22} +2.99832e11 q^{23} +9.70908e11 q^{24} -1.56580e11 q^{25} -2.53478e11 q^{26} -2.78440e12 q^{27} +1.30552e12 q^{28} -5.00246e11 q^{29} -3.65803e12 q^{30} +1.91301e12 q^{31} +6.01406e12 q^{32} -2.34573e13 q^{33} +1.01934e13 q^{34} -1.34458e13 q^{35} -2.03180e13 q^{36} +3.89515e12 q^{37} -1.40263e13 q^{38} +2.14685e13 q^{39} -3.79028e13 q^{40} -4.62222e13 q^{41} +8.11156e13 q^{42} -1.07893e14 q^{43} -8.89134e13 q^{44} +2.09259e14 q^{45} +7.06136e13 q^{46} -9.39944e13 q^{47} +3.09883e13 q^{48} +6.55259e13 q^{49} -3.68762e13 q^{50} -8.63333e14 q^{51} +8.13749e13 q^{52} +5.88108e14 q^{53} -6.55755e14 q^{54} +9.15739e14 q^{55} +8.40482e14 q^{56} +1.18797e15 q^{57} -1.17813e14 q^{58} -1.38353e15 q^{59} +1.17435e15 q^{60} -1.80522e15 q^{61} +4.50534e14 q^{62} -4.64025e15 q^{63} +1.62000e15 q^{64} -8.38098e14 q^{65} -5.52444e15 q^{66} -4.26355e15 q^{67} -3.27241e15 q^{68} -5.98067e15 q^{69} -3.16663e15 q^{70} +4.78140e15 q^{71} -1.30805e16 q^{72} +1.29021e16 q^{73} +9.17348e14 q^{74} +3.12326e15 q^{75} +4.50291e15 q^{76} -2.03062e16 q^{77} +5.05606e15 q^{78} -1.04276e16 q^{79} -1.20974e15 q^{80} +2.08356e16 q^{81} -1.08858e16 q^{82} +1.77422e16 q^{83} -2.60408e16 q^{84} +3.37032e16 q^{85} -2.54099e16 q^{86} +9.97828e15 q^{87} -5.72417e16 q^{88} +3.94668e16 q^{89} +4.92827e16 q^{90} +1.85845e16 q^{91} -2.26693e16 q^{92} -3.81583e16 q^{93} -2.21367e16 q^{94} -4.63764e16 q^{95} -1.19961e17 q^{96} +2.19647e16 q^{97} +1.54320e16 q^{98} +3.16028e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

Varieties

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