LMFDB - Embedded newform 29.18.a.a.1.6

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			1.6
Root			$-315.569$ 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)

$f(q)$	$=$	$q-315.569 q^{2} -7907.47 q^{3} -31488.2 q^{4} -995824. q^{5} +2.49535e6 q^{6} -2.13865e7 q^{7} +5.12990e7 q^{8} -6.66120e7 q^{9} +O(q^{10})$	\(q-315.569 q^{2} -7907.47 q^{3} -31488.2 q^{4} -995824. q^{5} +2.49535e6 q^{6} -2.13865e7 q^{7} +5.12990e7 q^{8} -6.66120e7 q^{9} +3.14251e8 q^{10} +5.11611e8 q^{11} +2.48992e8 q^{12} -1.37593e9 q^{13} +6.74891e9 q^{14} +7.87445e9 q^{15} -1.20611e10 q^{16} -6.75675e9 q^{17} +2.10207e10 q^{18} +6.41492e10 q^{19} +3.13567e10 q^{20} +1.69113e11 q^{21} -1.61448e11 q^{22} +1.22098e11 q^{23} -4.05645e11 q^{24} +2.28726e11 q^{25} +4.34201e11 q^{26} +1.54791e12 q^{27} +6.73421e11 q^{28} -5.00246e11 q^{29} -2.48493e12 q^{30} +8.62034e12 q^{31} -2.91773e12 q^{32} -4.04555e12 q^{33} +2.13222e12 q^{34} +2.12972e13 q^{35} +2.09749e12 q^{36} +2.36569e13 q^{37} -2.02435e13 q^{38} +1.08801e13 q^{39} -5.10847e13 q^{40} -6.41281e13 q^{41} -5.33669e13 q^{42} +3.79160e13 q^{43} -1.61097e13 q^{44} +6.63338e13 q^{45} -3.85302e13 q^{46} +4.19389e13 q^{47} +9.53732e13 q^{48} +2.24751e14 q^{49} -7.21788e13 q^{50} +5.34288e13 q^{51} +4.33256e13 q^{52} -1.40307e14 q^{53} -4.88471e14 q^{54} -5.09474e14 q^{55} -1.09710e15 q^{56} -5.07258e14 q^{57} +1.57862e14 q^{58} -1.63023e15 q^{59} -2.47952e14 q^{60} -2.76607e15 q^{61} -2.72031e15 q^{62} +1.42460e15 q^{63} +2.50162e15 q^{64} +1.37019e15 q^{65} +1.27665e15 q^{66} -1.19230e14 q^{67} +2.12758e14 q^{68} -9.65484e14 q^{69} -6.72073e15 q^{70} +4.36790e15 q^{71} -3.41713e15 q^{72} -4.32865e15 q^{73} -7.46539e15 q^{74} -1.80864e15 q^{75} -2.01994e15 q^{76} -1.09415e16 q^{77} -3.43344e15 q^{78} +2.94592e15 q^{79} +1.20108e16 q^{80} -3.63774e15 q^{81} +2.02368e16 q^{82} +1.59845e16 q^{83} -5.32506e15 q^{84} +6.72853e15 q^{85} -1.19651e16 q^{86} +3.95569e15 q^{87} +2.62451e16 q^{88} -4.76949e16 q^{89} -2.09329e16 q^{90} +2.94263e16 q^{91} -3.84463e15 q^{92} -6.81651e16 q^{93} -1.32346e16 q^{94} -6.38813e16 q^{95} +2.30719e16 q^{96} +7.89071e16 q^{97} -7.09245e16 q^{98} -3.40794e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−315.569	−0.871645	−0.435822	−	0.900033i	$-0.643542\pi$
$2$	−315.569	−0.871645	−0.435822	+	0.900033i	$0.643542\pi$
$3$	−7907.47	−0.695836	−0.347918	−	0.937525i	$-0.613111\pi$
$3$	−7907.47	−0.695836	−0.347918	+	0.937525i	$0.613111\pi$
$4$	−31488.2	−0.240236
$5$	−995824.	−1.14009	−0.570043	−	0.821615i	$-0.693073\pi$
$5$	−995824.	−1.14009	−0.570043	+	0.821615i	$0.693073\pi$
$6$	2.49535e6	0.606522
$7$	−2.13865e7	−1.40219	−0.701094	−	0.713069i	$-0.747305\pi$
$7$	−2.13865e7	−1.40219	−0.701094	+	0.713069i	$0.747305\pi$
$8$	5.12990e7	1.08104
$9$	−6.66120e7	−0.515812
$10$	3.14251e8	0.993750
$11$	5.11611e8	0.719617	0.359809	−	0.933026i	$-0.382842\pi$
$11$	5.11611e8	0.719617	0.359809	+	0.933026i	$0.382842\pi$
$12$	2.48992e8	0.167165
$13$	−1.37593e9	−0.467819	−0.233910	−	0.972258i	$-0.575152\pi$
$13$	−1.37593e9	−0.467819	−0.233910	+	0.972258i	$0.575152\pi$
$14$	6.74891e9	1.22221
$15$	7.87445e9	0.793313
$16$	−1.20611e10	−0.702051
$17$	−6.75675e9	−0.234921	−0.117460	−	0.993078i	$-0.537475\pi$
$17$	−6.75675e9	−0.234921	−0.117460	+	0.993078i	$0.537475\pi$
$18$	2.10207e10	0.449604
$19$	6.41492e10	0.866534	0.433267	−	0.901266i	$-0.357361\pi$
$19$	6.41492e10	0.866534	0.433267	+	0.901266i	$0.357361\pi$
$20$	3.13567e10	0.273889
$21$	1.69113e11	0.975693
$22$	−1.61448e11	−0.627251
$23$	1.22098e11	0.325103	0.162551	−	0.986700i	$-0.448028\pi$
$23$	1.22098e11	0.325103	0.162551	+	0.986700i	$0.448028\pi$
$24$	−4.05645e11	−0.752230
$25$	2.28726e11	0.299796
$26$	4.34201e11	0.407772
$27$	1.54791e12	1.05476
$28$	6.73421e11	0.336855
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	−2.48493e12	−0.691487
$31$	8.62034e12	1.81531	0.907654	−	0.419720i	$-0.137872\pi$
$31$	8.62034e12	1.81531	0.907654	+	0.419720i	$0.137872\pi$
$32$	−2.91773e12	−0.469106
$33$	−4.04555e12	−0.500736
$34$	2.13222e12	0.204768
$35$	2.12972e13	1.59861
$36$	2.09749e12	0.123916
$37$	2.36569e13	1.10724	0.553622	−	0.832768i	$-0.313245\pi$
$37$	2.36569e13	1.10724	0.553622	+	0.832768i	$0.313245\pi$
$38$	−2.02435e13	−0.755310
$39$	1.08801e13	0.325526
$40$	−5.10847e13	−1.23248
$41$	−6.41281e13	−1.25425	−0.627127	−	0.778917i	$-0.715769\pi$
$41$	−6.41281e13	−1.25425	−0.627127	+	0.778917i	$0.715769\pi$
$42$	−5.33669e13	−0.850458
$43$	3.79160e13	0.494698	0.247349	−	0.968926i	$-0.420441\pi$
$43$	3.79160e13	0.494698	0.247349	+	0.968926i	$0.420441\pi$
$44$	−1.61097e13	−0.172878
$45$	6.63338e13	0.588070
$46$	−3.85302e13	−0.283374
$47$	4.19389e13	0.256912	0.128456	−	0.991715i	$-0.458998\pi$
$47$	4.19389e13	0.256912	0.128456	+	0.991715i	$0.458998\pi$
$48$	9.53732e13	0.488513
$49$	2.24751e14	0.966129
$50$	−7.21788e13	−0.261315
$51$	5.34288e13	0.163467
$52$	4.33256e13	0.112387
$53$	−1.40307e14	−0.309552	−0.154776	−	0.987950i	$-0.549466\pi$
$53$	−1.40307e14	−0.309552	−0.154776	+	0.987950i	$0.549466\pi$
$54$	−4.88471e14	−0.919373
$55$	−5.09474e14	−0.820426
$56$	−1.09710e15	−1.51583
$57$	−5.07258e14	−0.602966
$58$	1.57862e14	0.161860
$59$	−1.63023e15	−1.44546	−0.722732	−	0.691129i	$-0.757114\pi$
$59$	−1.63023e15	−1.44546	−0.722732	+	0.691129i	$0.757114\pi$
$60$	−2.47952e14	−0.190582
$61$	−2.76607e15	−1.84740	−0.923698	−	0.383120i	$-0.874849\pi$
$61$	−2.76607e15	−1.84740	−0.923698	+	0.383120i	$0.874849\pi$
$62$	−2.72031e15	−1.58230
$63$	1.42460e15	0.723265
$64$	2.50162e15	1.11094
$65$	1.37019e15	0.533354
$66$	1.27665e15	0.436464
$67$	−1.19230e14	−0.0358716	−0.0179358	−	0.999839i	$-0.505709\pi$
$67$	−1.19230e14	−0.0358716	−0.0179358	+	0.999839i	$0.505709\pi$
$68$	2.12758e14	0.0564364
$69$	−9.65484e14	−0.226218
$70$	−6.72073e15	−1.39342
$71$	4.36790e15	0.802743	0.401371	−	0.915915i	$-0.368534\pi$
$71$	4.36790e15	0.802743	0.401371	+	0.915915i	$0.368534\pi$
$72$	−3.41713e15	−0.557616
$73$	−4.32865e15	−0.628214	−0.314107	−	0.949388i	$-0.601705\pi$
$73$	−4.32865e15	−0.628214	−0.314107	+	0.949388i	$0.601705\pi$
$74$	−7.46539e15	−0.965123
$75$	−1.80864e15	−0.208609
$76$	−2.01994e15	−0.208173
$77$	−1.09415e16	−1.00904
$78$	−3.43344e15	−0.283743
$79$	2.94592e15	0.218470	0.109235	−	0.994016i	$-0.465160\pi$
$79$	2.94592e15	0.218470	0.109235	+	0.994016i	$0.465160\pi$
$80$	1.20108e16	0.800399
$81$	−3.63774e15	−0.218127
$82$	2.02368e16	1.09326
$83$	1.59845e16	0.778998	0.389499	−	0.921027i	$-0.372648\pi$
$83$	1.59845e16	0.778998	0.389499	+	0.921027i	$0.372648\pi$
$84$	−5.32506e15	−0.234396
$85$	6.72853e15	0.267830
$86$	−1.19651e16	−0.431201
$87$	3.95569e15	0.129214
$88$	2.62451e16	0.777939
$89$	−4.76949e16	−1.28427	−0.642136	−	0.766591i	$-0.721951\pi$
$89$	−4.76949e16	−1.28427	−0.642136	+	0.766591i	$0.721951\pi$
$90$	−2.09329e16	−0.512588
$91$	2.94263e16	0.655970
$92$	−3.84463e15	−0.0781013
$93$	−6.81651e16	−1.26316
$94$	−1.32346e16	−0.223936
$95$	−6.38813e16	−0.987924
$96$	2.30719e16	0.326421
$97$	7.89071e16	1.02225	0.511124	−	0.859507i	$-0.329229\pi$
$97$	7.89071e16	1.02225	0.511124	+	0.859507i	$0.329229\pi$
$98$	−7.09245e16	−0.842121
$99$	−3.40794e16	−0.371187
$100$	−7.20216e15	−0.0720216
$101$	1.49136e17	1.37041	0.685204	−	0.728351i	$-0.259713\pi$
$101$	1.49136e17	1.37041	0.685204	+	0.728351i	$0.259713\pi$
$102$	−1.68605e16	−0.142485
$103$	1.33117e16	0.103542	0.0517712	−	0.998659i	$-0.483513\pi$
$103$	1.33117e16	0.103542	0.0517712	+	0.998659i	$0.483513\pi$
$104$	−7.05838e16	−0.505734
$105$	−1.68407e17	−1.11237
$106$	4.42764e16	0.269819
$107$	2.72657e17	1.53410	0.767052	−	0.641585i	$-0.221723\pi$
$107$	2.72657e17	1.53410	0.767052	+	0.641585i	$0.221723\pi$
$108$	−4.87407e16	−0.253390
$109$	1.72394e17	0.828698	0.414349	−	0.910118i	$-0.364009\pi$
$109$	1.72394e17	0.828698	0.414349	+	0.910118i	$0.364009\pi$
$110$	1.60774e17	0.715120
$111$	−1.87066e17	−0.770461
$112$	2.57946e17	0.984407
$113$	2.40002e17	0.849276	0.424638	−	0.905363i	$-0.360401\pi$
$113$	2.40002e17	0.849276	0.424638	+	0.905363i	$0.360401\pi$
$114$	1.60075e17	0.525572
$115$	−1.21588e17	−0.370645
$116$	1.57518e16	0.0446106
$117$	9.16535e16	0.241307
$118$	5.14451e17	1.25993
$119$	1.44503e17	0.329403
$120$	4.03951e17	0.857607
$121$	−2.43702e17	−0.482151
$122$	8.72887e17	1.61027
$123$	5.07091e17	0.872756
$124$	−2.71439e17	−0.436102
$125$	5.31983e17	0.798293
$126$	−4.49559e17	−0.630430
$127$	−6.65758e17	−0.872941	−0.436471	−	0.899719i	$-0.643772\pi$
$127$	−6.65758e17	−0.872941	−0.436471	+	0.899719i	$0.643772\pi$
$128$	−4.07002e17	−0.499243
$129$	−2.99820e17	−0.344229
$130$	−4.32388e17	−0.464895
$131$	1.39611e18	1.40641	0.703207	−	0.710985i	$-0.251751\pi$
$131$	1.39611e18	1.40641	0.703207	+	0.710985i	$0.251751\pi$
$132$	1.27387e17	0.120295
$133$	−1.37193e18	−1.21504
$134$	3.76254e16	0.0312673
$135$	−1.54144e18	−1.20251
$136$	−3.46614e17	−0.253960
$137$	4.58730e16	0.0315815	0.0157907	−	0.999875i	$-0.494973\pi$
$137$	4.58730e16	0.0315815	0.0157907	+	0.999875i	$0.494973\pi$
$138$	3.04677e17	0.197182
$139$	−1.34481e18	−0.818534	−0.409267	−	0.912415i	$-0.634215\pi$
$139$	−1.34481e18	−0.818534	−0.409267	+	0.912415i	$0.634215\pi$
$140$	−6.70609e17	−0.384044
$141$	−3.31631e17	−0.178769
$142$	−1.37837e18	−0.699706
$143$	−7.03941e17	−0.336651
$144$	8.03417e17	0.362126
$145$	4.98157e17	0.211709
$146$	1.36599e18	0.547579
$147$	−1.77721e18	−0.672268
$148$	−7.44913e17	−0.266000
$149$	−2.59099e17	−0.0873741	−0.0436870	−	0.999045i	$-0.513910\pi$
$149$	−2.59099e17	−0.0873741	−0.0436870	+	0.999045i	$0.513910\pi$
$150$	5.70752e17	0.181833
$151$	−1.93546e18	−0.582747	−0.291374	−	0.956609i	$-0.594112\pi$
$151$	−1.93546e18	−0.582747	−0.291374	+	0.956609i	$0.594112\pi$
$152$	3.29079e18	0.936763
$153$	4.50080e17	0.121175
$154$	3.45281e18	0.879523
$155$	−8.58434e18	−2.06961
$156$	−3.42596e17	−0.0782029
$157$	−8.04298e18	−1.73888	−0.869441	−	0.494037i	$-0.835521\pi$
$157$	−8.04298e18	−1.73888	−0.869441	+	0.494037i	$0.835521\pi$
$158$	−9.29642e17	−0.190428
$159$	1.10947e18	0.215397
$160$	2.90555e18	0.534821
$161$	−2.61124e18	−0.455855
$162$	1.14796e18	0.190129
$163$	9.78002e17	0.153725	0.0768626	−	0.997042i	$-0.475510\pi$
$163$	9.78002e17	0.153725	0.0768626	+	0.997042i	$0.475510\pi$
$164$	2.01928e18	0.301317
$165$	4.02865e18	0.570882
$166$	−5.04423e18	−0.679009
$167$	−5.00993e18	−0.640828	−0.320414	−	0.947278i	$-0.603822\pi$
$167$	−5.00993e18	−0.640828	−0.320414	+	0.947278i	$0.603822\pi$
$168$	8.67532e18	1.05477
$169$	−6.75723e18	−0.781145
$170$	−2.12332e18	−0.233453
$171$	−4.27311e18	−0.446969
$172$	−1.19391e18	−0.118844
$173$	6.12749e18	0.580618	0.290309	−	0.956933i	$-0.406242\pi$
$173$	6.12749e18	0.580618	0.290309	+	0.956933i	$0.406242\pi$
$174$	−1.24829e18	−0.112628
$175$	−4.89164e18	−0.420370
$176$	−6.17061e18	−0.505208
$177$	1.28910e19	1.00581
$178$	1.50510e19	1.11943
$179$	7.42368e18	0.526464	0.263232	−	0.964733i	$-0.415212\pi$
$179$	7.42368e18	0.526464	0.263232	+	0.964733i	$0.415212\pi$
$180$	−2.08873e18	−0.141275
$181$	2.52476e19	1.62911	0.814557	−	0.580083i	$-0.196980\pi$
$181$	2.52476e19	1.62911	0.814557	+	0.580083i	$0.196980\pi$
$182$	−9.28604e18	−0.571773
$183$	2.18727e19	1.28549
$184$	6.26348e18	0.351451
$185$	−2.35581e19	−1.26235
$186$	2.15108e19	1.10102
$187$	−3.45682e18	−0.169053
$188$	−1.32058e18	−0.0617195
$189$	−3.31043e19	−1.47897
$190$	2.01590e19	0.861118
$191$	8.67816e18	0.354522	0.177261	−	0.984164i	$-0.443276\pi$
$191$	8.67816e18	0.354522	0.177261	+	0.984164i	$0.443276\pi$
$192$	−1.97815e19	−0.773036
$193$	4.64291e19	1.73601	0.868007	−	0.496551i	$-0.165401\pi$
$193$	4.64291e19	1.73601	0.868007	+	0.496551i	$0.165401\pi$
$194$	−2.49006e19	−0.891037
$195$	−1.08347e19	−0.371127
$196$	−7.07700e18	−0.232099
$197$	−5.76051e17	−0.0180925	−0.00904624	−	0.999959i	$-0.502880\pi$
$197$	−5.76051e17	−0.0180925	−0.00904624	+	0.999959i	$0.502880\pi$
$198$	1.07544e19	0.323543
$199$	3.17059e18	0.0913880	0.0456940	−	0.998955i	$-0.485450\pi$
$199$	3.17059e18	0.0913880	0.0456940	+	0.998955i	$0.485450\pi$
$200$	1.17334e19	0.324093
$201$	9.42810e17	0.0249608
$202$	−4.70626e19	−1.19451
$203$	1.06985e19	0.260380
$204$	−1.68238e18	−0.0392705
$205$	6.38603e19	1.42996
$206$	−4.20077e18	−0.0902522
$207$	−8.13317e18	−0.167692
$208$	1.65953e19	0.328433
$209$	3.28194e19	0.623573
$210$	5.31440e19	0.969595
$211$	5.34809e19	0.937125	0.468562	−	0.883430i	$-0.344772\pi$
$211$	5.34809e19	0.937125	0.468562	+	0.883430i	$0.344772\pi$
$212$	4.41800e18	0.0743654
$213$	−3.45390e19	−0.558578
$214$	−8.60421e19	−1.33719
$215$	−3.77577e19	−0.563999
$216$	7.94059e19	1.14024
$217$	−1.84359e20	−2.54540
$218$	−5.44021e19	−0.722330
$219$	3.42287e19	0.437134
$220$	1.60424e19	0.197096
$221$	9.29682e18	0.109901
$222$	5.90324e19	0.671568
$223$	4.77547e19	0.522907	0.261453	−	0.965216i	$-0.415798\pi$
$223$	4.77547e19	0.522907	0.261453	+	0.965216i	$0.415798\pi$
$224$	6.24000e19	0.657774
$225$	−1.52359e19	−0.154638
$226$	−7.57373e19	−0.740266
$227$	1.06755e20	1.00501	0.502505	−	0.864574i	$-0.332412\pi$
$227$	1.06755e20	1.00501	0.502505	+	0.864574i	$0.332412\pi$
$228$	1.59726e19	0.144854
$229$	−1.26344e20	−1.10396	−0.551978	−	0.833859i	$-0.686127\pi$
$229$	−1.26344e20	−1.10396	−0.551978	+	0.833859i	$0.686127\pi$
$230$	3.83693e19	0.323071
$231$	8.65200e19	0.702126
$232$	−2.56621e19	−0.200745
$233$	−1.61809e20	−1.22033	−0.610166	−	0.792273i	$-0.708897\pi$
$233$	−1.61809e20	−1.22033	−0.610166	+	0.792273i	$0.708897\pi$
$234$	−2.89230e19	−0.210334
$235$	−4.17638e19	−0.292902
$236$	5.13330e19	0.347252
$237$	−2.32948e19	−0.152019
$238$	−4.56007e19	−0.287122
$239$	−1.37926e20	−0.838036	−0.419018	−	0.907978i	$-0.637626\pi$
$239$	−1.37926e20	−0.838036	−0.419018	+	0.907978i	$0.637626\pi$
$240$	−9.49749e19	−0.556946
$241$	2.01305e20	1.13949	0.569744	−	0.821822i	$-0.307042\pi$
$241$	2.01305e20	1.13949	0.569744	+	0.821822i	$0.307042\pi$
$242$	7.69047e19	0.420264
$243$	−1.71131e20	−0.902977
$244$	8.70986e19	0.443811
$245$	−2.23813e20	−1.10147
$246$	−1.60022e20	−0.760733
$247$	−8.82649e19	−0.405382
$248$	4.42215e20	1.96243
$249$	−1.26397e20	−0.542055
$250$	−1.67877e20	−0.695828
$251$	4.43763e20	1.77797	0.888986	−	0.457935i	$-0.151411\pi$
$251$	4.43763e20	1.77797	0.888986	+	0.457935i	$0.151411\pi$
$252$	−4.48579e19	−0.173754
$253$	6.24664e19	0.233950
$254$	2.10093e20	0.760894
$255$	−5.32057e19	−0.186366
$256$	−1.99456e20	−0.675782
$257$	−4.08550e20	−1.33910	−0.669550	−	0.742767i	$-0.733513\pi$
$257$	−4.08550e20	−1.33910	−0.669550	+	0.742767i	$0.733513\pi$
$258$	9.46138e19	0.300045
$259$	−5.05938e20	−1.55256
$260$	−4.31446e19	−0.128131
$261$	3.33224e19	0.0957838
$262$	−4.40569e20	−1.22589
$263$	1.16766e20	0.314553	0.157276	−	0.987555i	$-0.449729\pi$
$263$	1.16766e20	0.314553	0.157276	+	0.987555i	$0.449729\pi$
$264$	−2.07532e20	−0.541318
$265$	1.39721e20	0.352915
$266$	4.32938e20	1.05909
$267$	3.77146e20	0.893643
$268$	3.75434e18	0.00861763
$269$	−6.22672e20	−1.38473	−0.692365	−	0.721548i	$-0.743431\pi$
$269$	−6.22672e20	−1.38473	−0.692365	+	0.721548i	$0.743431\pi$
$270$	4.86431e20	1.04816
$271$	−8.41395e20	−1.75696	−0.878478	−	0.477782i	$-0.841441\pi$
$271$	−8.41395e20	−1.75696	−0.878478	+	0.477782i	$0.841441\pi$
$272$	8.14941e19	0.164927
$273$	−2.32688e20	−0.456448
$274$	−1.44761e19	−0.0275278
$275$	1.17019e20	0.215738
$276$	3.04013e19	0.0543457
$277$	−6.92049e19	−0.119966	−0.0599831	−	0.998199i	$-0.519105\pi$
$277$	−6.92049e19	−0.119966	−0.0599831	+	0.998199i	$0.519105\pi$
$278$	4.24382e20	0.713470
$279$	−5.74218e20	−0.936357
$280$	1.09252e21	1.72817
$281$	−6.44501e20	−0.989054	−0.494527	−	0.869162i	$-0.664659\pi$
$281$	−6.44501e20	−0.989054	−0.494527	+	0.869162i	$0.664659\pi$
$282$	1.04652e20	0.155823
$283$	9.78929e20	1.41438	0.707191	−	0.707023i	$-0.249962\pi$
$283$	9.78929e20	1.41438	0.707191	+	0.707023i	$0.249962\pi$
$284$	−1.37537e20	−0.192847
$285$	5.05140e20	0.687433
$286$	2.22142e20	0.293440
$287$	1.37147e21	1.75870
$288$	1.94356e20	0.241970
$289$	−7.81587e20	−0.944812
$290$	−1.57203e20	−0.184535
$291$	−6.23956e20	−0.711317
$292$	1.36301e20	0.150919
$293$	8.03510e20	0.864205	0.432103	−	0.901824i	$-0.357772\pi$
$293$	8.03510e20	0.864205	0.432103	+	0.901824i	$0.357772\pi$
$294$	5.60834e20	0.585979
$295$	1.62342e21	1.64795
$296$	1.21357e21	1.19698
$297$	7.91925e20	0.759021
$298$	8.17637e19	0.0761591
$299$	−1.67998e20	−0.152089
$300$	5.69509e19	0.0501153
$301$	−8.10890e20	−0.693660
$302$	6.10771e20	0.507948
$303$	−1.17929e21	−0.953580
$304$	−7.73713e20	−0.608351
$305$	2.75452e21	2.10619
$306$	−1.42031e20	−0.105622
$307$	−2.20273e21	−1.59326	−0.796628	−	0.604470i	$-0.793385\pi$
$307$	−2.20273e21	−1.59326	−0.796628	+	0.604470i	$0.793385\pi$
$308$	3.44529e20	0.242407
$309$	−1.05262e20	−0.0720486
$310$	2.70895e21	1.80396
$311$	−1.92782e21	−1.24912	−0.624559	−	0.780978i	$-0.714721\pi$
$311$	−1.92782e21	−1.24912	−0.624559	+	0.780978i	$0.714721\pi$
$312$	5.58140e20	0.351908
$313$	3.57479e20	0.219343	0.109671	−	0.993968i	$-0.465020\pi$
$313$	3.57479e20	0.219343	0.109671	+	0.993968i	$0.465020\pi$
$314$	2.53812e21	1.51569
$315$	−1.41865e21	−0.824584
$316$	−9.27617e19	−0.0524842
$317$	−8.20244e20	−0.451793	−0.225896	−	0.974151i	$-0.572531\pi$
$317$	−8.20244e20	−0.451793	−0.225896	+	0.974151i	$0.572531\pi$
$318$	−3.50115e20	−0.187750
$319$	−2.55931e20	−0.133630
$320$	−2.49118e21	−1.26657
$321$	−2.15603e21	−1.06749
$322$	8.24026e20	0.397344
$323$	−4.33440e20	−0.203567
$324$	1.14546e20	0.0524018
$325$	−3.14711e20	−0.140250
$326$	−3.08627e20	−0.133994
$327$	−1.36320e21	−0.576638
$328$	−3.28971e21	−1.35591
$329$	−8.96925e20	−0.360239
$330$	−1.27132e21	−0.497606
$331$	−3.55022e21	−1.35431	−0.677154	−	0.735841i	$-0.736787\pi$
$331$	−3.55022e21	−1.35431	−0.677154	+	0.735841i	$0.736787\pi$
$332$	−5.03324e20	−0.187143
$333$	−1.57583e21	−0.571129
$334$	1.58098e21	0.558575
$335$	1.18732e20	0.0408967
$336$	−2.03970e21	−0.684986
$337$	1.94450e21	0.636727	0.318364	−	0.947969i	$-0.396867\pi$
$337$	1.94450e21	0.636727	0.318364	+	0.947969i	$0.396867\pi$
$338$	2.13237e21	0.680881
$339$	−1.89781e21	−0.590957
$340$	−2.11869e20	−0.0643423
$341$	4.41026e21	1.30633
$342$	1.34846e21	0.389598
$343$	1.68512e20	0.0474931
$344$	1.94505e21	0.534791
$345$	9.61452e20	0.257908
$346$	−1.93365e21	−0.506093
$347$	−4.84060e21	−1.23623	−0.618114	−	0.786089i	$-0.712103\pi$
$347$	−4.84060e21	−1.23623	−0.618114	+	0.786089i	$0.712103\pi$
$348$	−1.24557e20	−0.0310417
$349$	1.59208e21	0.387212	0.193606	−	0.981079i	$-0.437982\pi$
$349$	1.59208e21	0.387212	0.193606	+	0.981079i	$0.437982\pi$
$350$	1.54365e21	0.366413
$351$	−2.12981e21	−0.493436
$352$	−1.49274e21	−0.337577
$353$	6.08838e21	1.34405	0.672027	−	0.740526i	$-0.265424\pi$
$353$	6.08838e21	1.34405	0.672027	+	0.740526i	$0.265424\pi$
$354$	−4.06801e21	−0.876706
$355$	−4.34966e21	−0.915196
$356$	1.50182e21	0.308528
$357$	−1.14265e21	−0.229211
$358$	−2.34268e21	−0.458889
$359$	−2.58700e21	−0.494874	−0.247437	−	0.968904i	$-0.579588\pi$
$359$	−2.58700e21	−0.494874	−0.247437	+	0.968904i	$0.579588\pi$
$360$	3.40286e21	0.635730
$361$	−1.36526e21	−0.249118
$362$	−7.96735e21	−1.42001
$363$	1.92707e21	0.335498
$364$	−9.26581e20	−0.157587
$365$	4.31057e21	0.716218
$366$	−6.90233e21	−1.12049
$367$	6.02033e21	0.954902	0.477451	−	0.878658i	$-0.341561\pi$
$367$	6.02033e21	0.954902	0.477451	+	0.878658i	$0.341561\pi$
$368$	−1.47264e21	−0.228239
$369$	4.27170e21	0.646959
$370$	7.43421e21	1.10032
$371$	3.00066e21	0.434049
$372$	2.14640e21	0.303455
$373$	6.17726e20	0.0853632	0.0426816	−	0.999089i	$-0.486410\pi$
$373$	6.17726e20	0.0853632	0.0426816	+	0.999089i	$0.486410\pi$
$374$	1.09087e21	0.147354
$375$	−4.20664e21	−0.555481
$376$	2.15142e21	0.277734
$377$	6.88305e20	0.0868719
$378$	1.04467e22	1.28913
$379$	4.08422e21	0.492806	0.246403	−	0.969167i	$-0.420751\pi$
$379$	4.08422e21	0.492806	0.246403	+	0.969167i	$0.420751\pi$
$380$	2.01151e21	0.237335
$381$	5.26447e21	0.607424
$382$	−2.73856e21	−0.309018
$383$	−9.15618e21	−1.01047	−0.505236	−	0.862981i	$-0.668595\pi$
$383$	−9.15618e21	−1.01047	−0.505236	+	0.862981i	$0.668595\pi$
$384$	3.21836e21	0.347392
$385$	1.08959e22	1.15039
$386$	−1.46516e22	−1.51319
$387$	−2.52566e21	−0.255171
$388$	−2.48464e21	−0.245580
$389$	2.04002e22	1.97271	0.986353	−	0.164647i	$-0.0526485\pi$
$389$	2.04002e22	1.97271	0.986353	+	0.164647i	$0.0526485\pi$
$390$	3.41910e21	0.323491
$391$	−8.24983e20	−0.0763734
$392$	1.15295e22	1.04443
$393$	−1.10397e22	−0.978634
$394$	1.81784e20	0.0157702
$395$	−2.93362e21	−0.249074
$396$	1.07310e21	0.0891724
$397$	−1.95388e22	−1.58920	−0.794600	−	0.607133i	$-0.792319\pi$
$397$	−1.95388e22	−1.58920	−0.794600	+	0.607133i	$0.792319\pi$
$398$	−1.00054e21	−0.0796579
$399$	1.08485e22	0.845472
$400$	−2.75870e21	−0.210472
$401$	−6.18980e21	−0.462327	−0.231164	−	0.972915i	$-0.574253\pi$
$401$	−6.18980e21	−0.462327	−0.231164	+	0.972915i	$0.574253\pi$
$402$	−2.97522e20	−0.0217569
$403$	−1.18610e22	−0.849236
$404$	−4.69601e21	−0.329221
$405$	3.62255e21	0.248683
$406$	−3.37612e21	−0.226959
$407$	1.21031e22	0.796792
$408$	2.74084e21	0.176715
$409$	−3.10347e21	−0.195975	−0.0979873	−	0.995188i	$-0.531240\pi$
$409$	−3.10347e21	−0.195975	−0.0979873	+	0.995188i	$0.531240\pi$
$410$	−2.01523e22	−1.24641
$411$	−3.62740e20	−0.0219755
$412$	−4.19162e20	−0.0248746
$413$	3.48649e22	2.02681
$414$	2.56658e21	0.146168
$415$	−1.59178e22	−0.888124
$416$	4.01460e21	0.219457
$417$	1.06341e22	0.569565
$418$	−1.03568e22	−0.543534
$419$	1.60292e22	0.824315	0.412158	−	0.911113i	$-0.364775\pi$
$419$	1.60292e22	0.824315	0.412158	+	0.911113i	$0.364775\pi$
$420$	5.30282e21	0.267232
$421$	3.96177e21	0.195655	0.0978277	−	0.995203i	$-0.468811\pi$
$421$	3.96177e21	0.195655	0.0978277	+	0.995203i	$0.468811\pi$
$422$	−1.68769e22	−0.816840
$423$	−2.79363e21	−0.132518
$424$	−7.19758e21	−0.334639
$425$	−1.54544e21	−0.0704283
$426$	1.08995e22	0.486881
$427$	5.91566e22	2.59040
$428$	−8.58547e21	−0.368546
$429$	5.56639e21	0.234254
$430$	1.19151e22	0.491606
$431$	4.04092e22	1.63465	0.817323	−	0.576180i	$-0.195457\pi$
$431$	4.04092e22	1.63465	0.817323	+	0.576180i	$0.195457\pi$
$432$	−1.86695e22	−0.740493
$433$	−2.66739e22	−1.03738	−0.518692	−	0.854961i	$-0.673581\pi$
$433$	−2.66739e22	−1.03738	−0.518692	+	0.854961i	$0.673581\pi$
$434$	5.81779e22	2.21868
$435$	−3.93917e21	−0.147315
$436$	−5.42836e21	−0.199083
$437$	7.83247e21	0.281713
$438$	−1.08015e22	−0.381026
$439$	−2.82215e22	−0.976410	−0.488205	−	0.872729i	$-0.662348\pi$
$439$	−2.82215e22	−0.976410	−0.488205	+	0.872729i	$0.662348\pi$
$440$	−2.61355e22	−0.886917
$441$	−1.49711e22	−0.498341
$442$	−2.93379e21	−0.0957942
$443$	−2.15646e22	−0.690731	−0.345366	−	0.938468i	$-0.612245\pi$
$443$	−2.15646e22	−0.690731	−0.345366	+	0.938468i	$0.612245\pi$
$444$	5.89038e21	0.185092
$445$	4.74957e22	1.46418
$446$	−1.50699e22	−0.455789
$447$	2.04882e21	0.0607981
$448$	−5.35010e22	−1.55775
$449$	−5.02081e22	−1.43443	−0.717217	−	0.696850i	$-0.754584\pi$
$449$	−5.02081e22	−1.43443	−0.717217	+	0.696850i	$0.754584\pi$
$450$	4.80798e21	0.134789
$451$	−3.28086e22	−0.902583
$452$	−7.55723e21	−0.204026
$453$	1.53046e22	0.405497
$454$	−3.36887e22	−0.876011
$455$	−2.93034e22	−0.747863
$456$	−2.60218e22	−0.651833
$457$	−2.23352e22	−0.549163	−0.274582	−	0.961564i	$-0.588539\pi$
$457$	−2.23352e22	−0.549163	−0.274582	+	0.961564i	$0.588539\pi$
$458$	3.98701e22	0.962257
$459$	−1.04588e22	−0.247785
$460$	3.82858e21	0.0890422
$461$	−6.00965e22	−1.37212	−0.686058	−	0.727547i	$-0.740660\pi$
$461$	−6.00965e22	−1.37212	−0.686058	+	0.727547i	$0.740660\pi$
$462$	−2.73030e22	−0.612004
$463$	−3.87177e22	−0.852061	−0.426031	−	0.904709i	$-0.640088\pi$
$463$	−3.87177e22	−0.852061	−0.426031	+	0.904709i	$0.640088\pi$
$464$	6.03355e21	0.130368
$465$	6.78805e22	1.44011
$466$	5.10620e22	1.06370
$467$	7.80405e22	1.59634	0.798172	−	0.602429i	$-0.205800\pi$
$467$	7.80405e22	1.59634	0.798172	+	0.602429i	$0.205800\pi$
$468$	−2.88600e21	−0.0579705
$469$	2.54992e21	0.0502987
$470$	1.31793e22	0.255307
$471$	6.35997e22	1.20998
$472$	−8.36292e22	−1.56261
$473$	1.93982e22	0.355994
$474$	7.35112e21	0.132507
$475$	1.46726e22	0.259783
$476$	−4.55014e21	−0.0791344
$477$	9.34610e21	0.159670
$478$	4.35250e22	0.730469
$479$	−2.64287e22	−0.435737	−0.217868	−	0.975978i	$-0.569910\pi$
$479$	−2.64287e22	−0.435737	−0.217868	+	0.975978i	$0.569910\pi$
$480$	−2.29755e22	−0.372148
$481$	−3.25503e22	−0.517990
$482$	−6.35257e22	−0.993229
$483$	2.06483e22	0.317200
$484$	7.67372e21	0.115830
$485$	−7.85775e22	−1.16545
$486$	5.40038e22	0.787075
$487$	1.17859e23	1.68798	0.843990	−	0.536359i	$-0.180201\pi$
$487$	1.17859e23	1.68798	0.843990	+	0.536359i	$0.180201\pi$
$488$	−1.41897e23	−1.99712
$489$	−7.73352e21	−0.106968
$490$	7.06283e22	0.960091
$491$	1.48201e22	0.197997	0.0989987	−	0.995088i	$-0.468436\pi$
$491$	1.48201e22	0.197997	0.0989987	+	0.995088i	$0.468436\pi$
$492$	−1.59674e22	−0.209667
$493$	3.38004e21	0.0436237
$494$	2.78537e22	0.353349
$495$	3.39371e22	0.423185
$496$	−1.03971e23	−1.27444
$497$	−9.34139e22	−1.12560
$498$	3.98871e22	0.472479
$499$	−5.26975e22	−0.613671	−0.306835	−	0.951763i	$-0.599270\pi$
$499$	−5.26975e22	−0.613671	−0.306835	+	0.951763i	$0.599270\pi$
$500$	−1.67512e22	−0.191778
$501$	3.96159e22	0.445912
$502$	−1.40038e23	−1.54976
$503$	−3.83785e22	−0.417600	−0.208800	−	0.977958i	$-0.566956\pi$
$503$	−3.83785e22	−0.417600	−0.208800	+	0.977958i	$0.566956\pi$
$504$	7.30803e22	0.781881
$505$	−1.48513e23	−1.56238
$506$	−1.97125e22	−0.203921
$507$	5.34326e22	0.543549
$508$	2.09635e22	0.209712
$509$	7.58745e21	0.0746440	0.0373220	−	0.999303i	$-0.488117\pi$
$509$	7.58745e21	0.0746440	0.0373220	+	0.999303i	$0.488117\pi$
$510$	1.67901e22	0.162445
$511$	9.25745e22	0.880874
$512$	1.16289e23	1.08828
$513$	9.92969e22	0.913983
$514$	1.28926e23	1.16722
$515$	−1.32561e22	−0.118047
$516$	9.44078e21	0.0826961
$517$	2.14564e22	0.184879
$518$	1.59658e23	1.35328
$519$	−4.84530e22	−0.404015
$520$	7.02891e22	0.576580
$521$	1.63978e23	1.32332	0.661658	−	0.749806i	$-0.269853\pi$
$521$	1.63978e23	1.32332	0.661658	+	0.749806i	$0.269853\pi$
$522$	−1.05155e22	−0.0834895
$523$	6.80859e22	0.531854	0.265927	−	0.963993i	$-0.414322\pi$
$523$	6.80859e22	0.531854	0.265927	+	0.963993i	$0.414322\pi$
$524$	−4.39609e22	−0.337871
$525$	3.86806e22	0.292509
$526$	−3.68478e22	−0.274178
$527$	−5.82455e22	−0.426454
$528$	4.87939e22	0.351542
$529$	−1.26142e23	−0.894308
$530$	−4.40915e22	−0.307617
$531$	1.08593e23	0.745587
$532$	4.31995e22	0.291897
$533$	8.82359e22	0.586764
$534$	−1.19016e23	−0.778939
$535$	−2.71518e23	−1.74901
$536$	−6.11639e21	−0.0387788
$537$	−5.87025e22	−0.366333
$538$	1.96496e23	1.20699
$539$	1.14985e23	0.695243
$540$	4.85372e22	0.288887
$541$	9.06476e22	0.531104	0.265552	−	0.964097i	$-0.414446\pi$
$541$	9.06476e22	0.531104	0.265552	+	0.964097i	$0.414446\pi$
$542$	2.65518e23	1.53144
$543$	−1.99644e23	−1.13360
$544$	1.97144e22	0.110203
$545$	−1.71674e23	−0.944787
$546$	7.34291e22	0.397860
$547$	−3.17897e21	−0.0169588	−0.00847939	−	0.999964i	$-0.502699\pi$
$547$	−3.17897e21	−0.0169588	−0.00847939	+	0.999964i	$0.502699\pi$
$548$	−1.44446e21	−0.00758700
$549$	1.84254e23	0.952909
$550$	−3.69275e22	−0.188047
$551$	−3.20904e22	−0.160911
$552$	−4.95283e22	−0.244552
$553$	−6.30029e22	−0.306335
$554$	2.18389e22	0.104568
$555$	1.86285e23	0.878391
$556$	4.23457e22	0.196641
$557$	3.98889e23	1.82425	0.912123	−	0.409917i	$-0.134442\pi$
$557$	3.98889e23	1.82425	0.912123	+	0.409917i	$0.134442\pi$
$558$	1.81206e23	0.816170
$559$	−5.21698e22	−0.231429
$560$	−2.56868e23	−1.12231
$561$	2.73347e22	0.117633
$562$	2.03385e23	0.862104
$563$	−3.64283e22	−0.152096	−0.0760479	−	0.997104i	$-0.524230\pi$
$563$	−3.64283e22	−0.152096	−0.0760479	+	0.997104i	$0.524230\pi$
$564$	1.04424e22	0.0429467
$565$	−2.39000e23	−0.968247
$566$	−3.08920e23	−1.23284
$567$	7.77984e22	0.305854
$568$	2.24069e23	0.867801
$569$	−1.41386e23	−0.539451	−0.269725	−	0.962937i	$-0.586933\pi$
$569$	−1.41386e23	−0.539451	−0.269725	+	0.962937i	$0.586933\pi$
$570$	−1.59407e23	−0.599197
$571$	−4.43634e23	−1.64293	−0.821463	−	0.570262i	$-0.806841\pi$
$571$	−4.43634e23	−1.64293	−0.821463	+	0.570262i	$0.806841\pi$
$572$	2.21658e22	0.0808756
$573$	−6.86223e22	−0.246690
$574$	−4.32795e23	−1.53296
$575$	2.79269e22	0.0974644
$576$	−1.66638e23	−0.573038
$577$	−1.05383e23	−0.357088	−0.178544	−	0.983932i	$-0.557139\pi$
$577$	−1.05383e23	−0.357088	−0.178544	+	0.983932i	$0.557139\pi$
$578$	2.46645e23	0.823540
$579$	−3.67137e23	−1.20798
$580$	−1.56861e22	−0.0508600
$581$	−3.41853e23	−1.09230
$582$	1.96901e23	0.620016
$583$	−7.17823e22	−0.222759
$584$	−2.22055e23	−0.679128
$585$	−9.12708e22	−0.275110
$586$	−2.53563e23	−0.753280
$587$	−1.99309e23	−0.583585	−0.291792	−	0.956482i	$-0.594252\pi$
$587$	−1.99309e23	−0.583585	−0.291792	+	0.956482i	$0.594252\pi$
$588$	5.59612e22	0.161503
$589$	5.52988e23	1.57303
$590$	−5.12302e23	−1.43643
$591$	4.55511e21	0.0125894
$592$	−2.85329e23	−0.777342
$593$	3.92789e23	1.05486	0.527429	−	0.849599i	$-0.323156\pi$
$593$	3.92789e23	1.05486	0.527429	+	0.849599i	$0.323156\pi$
$594$	−2.49907e23	−0.661597
$595$	−1.43900e23	−0.375548
$596$	8.15856e21	0.0209904
$597$	−2.50714e22	−0.0635911
$598$	5.30149e22	0.132568
$599$	2.94313e23	0.725572	0.362786	−	0.931872i	$-0.381826\pi$
$599$	2.94313e23	0.725572	0.362786	+	0.931872i	$0.381826\pi$
$600$	−9.27816e22	−0.225515
$601$	−3.15686e23	−0.756522	−0.378261	−	0.925699i	$-0.623478\pi$
$601$	−3.15686e23	−0.756522	−0.378261	+	0.925699i	$0.623478\pi$
$602$	2.55892e23	0.604625
$603$	7.94216e21	0.0185030
$604$	6.09441e22	0.139997
$605$	2.42684e23	0.549693
$606$	3.72147e23	0.831183
$607$	8.10555e23	1.78517	0.892583	−	0.450883i	$-0.148891\pi$
$607$	8.10555e23	1.78517	0.892583	+	0.450883i	$0.148891\pi$
$608$	−1.87170e23	−0.406496
$609$	−8.45982e22	−0.181182
$610$	−8.69242e23	−1.83585
$611$	−5.77050e22	−0.120189
$612$	−1.41722e22	−0.0291106
$613$	1.27884e23	0.259060	0.129530	−	0.991575i	$-0.458653\pi$
$613$	1.27884e23	0.259060	0.129530	+	0.991575i	$0.458653\pi$
$614$	6.95114e23	1.38875
$615$	−5.04974e23	−0.995017
$616$	−5.61290e23	−1.09082
$617$	−6.97757e22	−0.133746	−0.0668730	−	0.997761i	$-0.521302\pi$
$617$	−6.97757e22	−0.133746	−0.0668730	+	0.997761i	$0.521302\pi$
$618$	3.32175e22	0.0628008
$619$	−4.65056e23	−0.867231	−0.433616	−	0.901098i	$-0.642762\pi$
$619$	−4.65056e23	−0.867231	−0.433616	+	0.901098i	$0.642762\pi$
$620$	2.70305e23	0.497193
$621$	1.88996e23	0.342904
$622$	6.08361e23	1.08879
$623$	1.02003e24	1.80079
$624$	−1.31227e23	−0.228536
$625$	−7.04265e23	−1.20992
$626$	−1.12809e23	−0.191189
$627$	−2.59519e23	−0.433905
$628$	2.53259e23	0.417742
$629$	−1.59844e23	−0.260115
$630$	4.47681e23	0.718744
$631$	−7.75153e22	−0.122783	−0.0613915	−	0.998114i	$-0.519554\pi$
$631$	−7.75153e22	−0.122783	−0.0613915	+	0.998114i	$0.519554\pi$
$632$	1.51123e23	0.236175
$633$	−4.22898e23	−0.652086
$634$	2.58844e23	0.393803
$635$	6.62978e23	0.995228
$636$	−3.49352e22	−0.0517461
$637$	−3.09242e23	−0.451974
$638$	8.07640e22	0.116478
$639$	−2.90954e23	−0.414064
$640$	4.05303e23	0.569180
$641$	5.85561e23	0.811482	0.405741	−	0.913988i	$-0.367014\pi$
$641$	5.85561e23	0.811482	0.405741	+	0.913988i	$0.367014\pi$
$642$	6.80376e23	0.930468
$643$	−6.65442e23	−0.898084	−0.449042	−	0.893511i	$-0.648235\pi$
$643$	−6.65442e23	−0.898084	−0.449042	+	0.893511i	$0.648235\pi$
$644$	8.22231e22	0.109513
$645$	2.98568e23	0.392451
$646$	1.36780e23	0.177438
$647$	8.21816e23	1.05218	0.526088	−	0.850430i	$-0.323658\pi$
$647$	8.21816e23	1.05218	0.526088	+	0.850430i	$0.323658\pi$
$648$	−1.86612e23	−0.235805
$649$	−8.34044e23	−1.04018
$650$	9.93131e22	0.122248
$651$	1.45781e24	1.77118
$652$	−3.07955e22	−0.0369303
$653$	−7.80377e22	−0.0923724	−0.0461862	−	0.998933i	$-0.514707\pi$
$653$	−7.80377e22	−0.0923724	−0.0461862	+	0.998933i	$0.514707\pi$
$654$	4.30183e23	0.502624
$655$	−1.39028e24	−1.60343
$656$	7.73459e23	0.880551
$657$	2.88340e23	0.324040
$658$	2.83042e23	0.314001
$659$	1.19207e24	1.30550	0.652750	−	0.757573i	$-0.273615\pi$
$659$	1.19207e24	1.30550	0.652750	+	0.757573i	$0.273615\pi$
$660$	−1.26855e23	−0.137146
$661$	−1.53508e24	−1.63840	−0.819198	−	0.573510i	$-0.805581\pi$
$661$	−1.53508e24	−1.63840	−0.819198	+	0.573510i	$0.805581\pi$
$662$	1.12034e24	1.18048
$663$	−7.35143e22	−0.0764728
$664$	8.19990e23	0.842132
$665$	1.36620e24	1.38525
$666$	4.97285e23	0.497822
$667$	−6.10789e22	−0.0603701
$668$	1.57754e23	0.153950
$669$	−3.77619e23	−0.363858
$670$	−3.74682e22	−0.0356474
$671$	−1.41515e24	−1.32942
$672$	−4.93427e23	−0.457703
$673$	4.93850e21	0.00452342	0.00226171	−	0.999997i	$-0.499280\pi$
$673$	4.93850e21	0.00452342	0.00226171	+	0.999997i	$0.499280\pi$
$674$	−6.13624e23	−0.555000
$675$	3.54046e23	0.316212
$676$	2.12773e23	0.187659
$677$	−9.66209e23	−0.841525	−0.420763	−	0.907171i	$-0.638238\pi$
$677$	−9.66209e23	−0.841525	−0.420763	+	0.907171i	$0.638238\pi$
$678$	5.98891e23	0.515104
$679$	−1.68754e24	−1.43338
$680$	3.45167e23	0.289536
$681$	−8.44166e23	−0.699322
$682$	−1.39174e24	−1.13865
$683$	−1.71586e24	−1.38646	−0.693228	−	0.720718i	$-0.743812\pi$
$683$	−1.71586e24	−1.38646	−0.693228	+	0.720718i	$0.743812\pi$
$684$	1.34552e23	0.107378
$685$	−4.56815e22	−0.0360056
$686$	−5.31772e22	−0.0413971
$687$	9.99059e23	0.768172
$688$	−4.57310e23	−0.347304
$689$	1.93052e23	0.144814
$690$	−3.03405e23	−0.224804
$691$	−2.64232e24	−1.93385	−0.966924	−	0.255066i	$-0.917903\pi$
$691$	−2.64232e24	−1.93385	−0.966924	+	0.255066i	$0.917903\pi$
$692$	−1.92943e23	−0.139485
$693$	7.28839e23	0.520474
$694$	1.52754e24	1.07755
$695$	1.33920e24	0.933199
$696$	2.02923e23	0.139686
$697$	4.33297e23	0.294651
$698$	−5.02412e23	−0.337512
$699$	1.27950e24	0.849152
$700$	1.54029e23	0.100988
$701$	1.38637e24	0.898002	0.449001	−	0.893531i	$-0.351780\pi$
$701$	1.38637e24	0.898002	0.449001	+	0.893531i	$0.351780\pi$
$702$	6.72102e23	0.430101
$703$	1.51757e24	0.959465
$704$	1.27986e24	0.799455
$705$	3.30246e23	0.203812
$706$	−1.92130e24	−1.17154
$707$	−3.18949e24	−1.92157
$708$	−4.05914e23	−0.241631
$709$	−1.20551e24	−0.709052	−0.354526	−	0.935046i	$-0.615358\pi$
$709$	−1.20551e24	−0.709052	−0.354526	+	0.935046i	$0.615358\pi$
$710$	1.37262e24	0.797725
$711$	−1.96234e23	−0.112689
$712$	−2.44670e24	−1.38835
$713$	1.05252e24	0.590161
$714$	3.60586e23	0.199790
$715$	7.01001e23	0.383811
$716$	−2.33758e23	−0.126475
$717$	1.09064e24	0.583136
$718$	8.16379e23	0.431354
$719$	5.41870e23	0.282943	0.141472	−	0.989942i	$-0.454817\pi$
$719$	5.41870e23	0.282943	0.141472	+	0.989942i	$0.454817\pi$
$720$	−8.00062e23	−0.412855
$721$	−2.84691e23	−0.145186
$722$	4.30835e23	0.217142
$723$	−1.59182e24	−0.792898
$724$	−7.94999e23	−0.391371
$725$	−1.14419e23	−0.0556707
$726$	−6.08122e23	−0.292435
$727$	7.86250e23	0.373696	0.186848	−	0.982389i	$-0.440173\pi$
$727$	7.86250e23	0.373696	0.186848	+	0.982389i	$0.440173\pi$
$728$	1.50954e24	0.709133
$729$	1.82300e24	0.846451
$730$	−1.36028e24	−0.624288
$731$	−2.56189e23	−0.116215
$732$	−6.88730e23	−0.308820
$733$	3.43379e24	1.52191	0.760956	−	0.648804i	$-0.224730\pi$
$733$	3.43379e24	1.52191	0.760956	+	0.648804i	$0.224730\pi$
$734$	−1.89983e24	−0.832335
$735$	1.76979e24	0.766443
$736$	−3.56248e23	−0.152508
$737$	−6.09994e22	−0.0258138
$738$	−1.34802e24	−0.563918
$739$	2.43966e24	1.00891	0.504454	−	0.863439i	$-0.331694\pi$
$739$	2.43966e24	1.00891	0.504454	+	0.863439i	$0.331694\pi$
$740$	7.41802e23	0.303262
$741$	6.97953e23	0.282079
$742$	−9.46917e23	−0.378337
$743$	−1.12421e24	−0.444059	−0.222030	−	0.975040i	$-0.571268\pi$
$743$	−1.12421e24	−0.444059	−0.222030	+	0.975040i	$0.571268\pi$
$744$	−3.49680e24	−1.36553
$745$	2.58017e23	0.0996140
$746$	−1.94935e23	−0.0744064
$747$	−1.06476e24	−0.401816
$748$	1.08849e23	0.0406126
$749$	−5.83118e24	−2.15110
$750$	1.32749e24	0.484182
$751$	2.18172e24	0.786792	0.393396	−	0.919369i	$-0.371300\pi$
$751$	2.18172e24	0.786792	0.393396	+	0.919369i	$0.371300\pi$
$752$	−5.05831e23	−0.180366
$753$	−3.50905e24	−1.23718
$754$	−2.17208e23	−0.0757214
$755$	1.92738e24	0.664382
$756$	1.04239e24	0.355301
$757$	−4.36313e23	−0.147056	−0.0735280	−	0.997293i	$-0.523426\pi$
$757$	−4.36313e23	−0.147056	−0.0735280	+	0.997293i	$0.523426\pi$
$758$	−1.28885e24	−0.429551
$759$	−4.93952e23	−0.162791
$760$	−3.27705e24	−1.06799
$761$	−2.03386e24	−0.655468	−0.327734	−	0.944770i	$-0.606285\pi$
$761$	−2.03386e24	−0.655468	−0.327734	+	0.944770i	$0.606285\pi$
$762$	−1.66130e24	−0.529458
$763$	−3.68690e24	−1.16199
$764$	−2.73259e23	−0.0851690
$765$	−4.48201e23	−0.138150
$766$	2.88941e24	0.880773
$767$	2.24309e24	0.676216
$768$	1.57719e24	0.470234
$769$	−3.84100e24	−1.13258	−0.566291	−	0.824205i	$-0.691622\pi$
$769$	−3.84100e24	−1.13258	−0.566291	+	0.824205i	$0.691622\pi$
$770$	−3.43840e24	−1.00273
$771$	3.23060e24	0.931795
$772$	−1.46197e24	−0.417053
$773$	4.16257e24	1.17445	0.587227	−	0.809422i	$-0.300220\pi$
$773$	4.16257e24	1.17445	0.587227	+	0.809422i	$0.300220\pi$
$774$	7.97020e23	0.222419
$775$	1.97170e24	0.544221
$776$	4.04785e24	1.10510
$777$	4.00069e24	1.08033
$778$	−6.43766e24	−1.71950
$779$	−4.11377e24	−1.08685
$780$	3.41165e23	0.0891580
$781$	2.23466e24	0.577668
$782$	2.60339e23	0.0665705
$783$	−7.74334e23	−0.195863
$784$	−2.71076e24	−0.678272
$785$	8.00940e24	1.98248
$786$	3.48379e24	0.853021
$787$	−5.59878e24	−1.35615	−0.678076	−	0.734992i	$-0.737186\pi$
$787$	−5.59878e24	−1.35615	−0.678076	+	0.734992i	$0.737186\pi$
$788$	1.81388e22	0.00434646
$789$	−9.23326e23	−0.218877
$790$	9.25760e23	0.217104
$791$	−5.13280e24	−1.19084
$792$	−1.74824e24	−0.401270
$793$	3.80593e24	0.864248
$794$	6.16584e24	1.38522
$795$	−1.10484e24	−0.245571
$796$	−9.98362e22	−0.0219547
$797$	4.49297e24	0.977547	0.488774	−	0.872411i	$-0.337444\pi$
$797$	4.49297e24	0.977547	0.488774	+	0.872411i	$0.337444\pi$
$798$	−3.42344e24	−0.736951
$799$	−2.83370e23	−0.0603541
$800$	−6.67361e23	−0.140636
$801$	3.17705e24	0.662442
$802$	1.95331e24	0.402985
$803$	−2.21458e24	−0.452074
$804$	−2.96874e22	−0.00599646
$805$	2.60033e24	0.519714
$806$	3.74296e24	0.740232
$807$	4.92376e24	0.963545
$808$	7.65051e24	1.48147
$809$	−8.27335e24	−1.58533	−0.792663	−	0.609660i	$-0.791306\pi$
$809$	−8.27335e24	−1.58533	−0.792663	+	0.609660i	$0.791306\pi$
$810$	−1.14316e24	−0.216763
$811$	−1.41755e23	−0.0265987	−0.0132994	−	0.999912i	$-0.504233\pi$
$811$	−1.41755e23	−0.0265987	−0.0132994	+	0.999912i	$0.504233\pi$
$812$	−3.36877e23	−0.0625525
$813$	6.65331e24	1.22255
$814$	−3.81937e24	−0.694520
$815$	−9.73918e23	−0.175260
$816$	−6.44413e23	−0.114762
$817$	2.43228e24	0.428673
$818$	9.79360e23	0.170820
$819$	−1.96015e24	−0.338357
$820$	−2.01084e24	−0.343527
$821$	7.24646e24	1.22521	0.612603	−	0.790391i	$-0.290122\pi$
$821$	7.24646e24	1.22521	0.612603	+	0.790391i	$0.290122\pi$
$822$	1.14469e23	0.0191549
$823$	9.54778e24	1.58126	0.790631	−	0.612293i	$-0.209753\pi$
$823$	9.54778e24	1.58126	0.790631	+	0.612293i	$0.209753\pi$
$824$	6.82878e23	0.111934
$825$	−9.25322e23	−0.150119
$826$	−1.10023e25	−1.76666
$827$	−2.52417e24	−0.401163	−0.200582	−	0.979677i	$-0.564283\pi$
$827$	−2.52417e24	−0.401163	−0.200582	+	0.979677i	$0.564283\pi$
$828$	2.56099e23	0.0402856
$829$	1.13224e25	1.76288	0.881442	−	0.472293i	$-0.156574\pi$
$829$	1.13224e25	1.76288	0.881442	+	0.472293i	$0.156574\pi$
$830$	5.02316e24	0.774129
$831$	5.47236e23	0.0834768
$832$	−3.44206e24	−0.519721
$833$	−1.51859e24	−0.226964
$834$	−3.35579e24	−0.496459
$835$	4.98901e24	0.730599
$836$	−1.03342e24	−0.149805
$837$	1.33435e25	1.91471
$838$	−5.05833e24	−0.718510
$839$	−5.80093e24	−0.815683	−0.407841	−	0.913053i	$-0.633718\pi$
$839$	−5.80093e24	−0.815683	−0.407841	+	0.913053i	$0.633718\pi$
$840$	−8.63910e24	−1.20253
$841$	2.50246e23	0.0344828
$842$	−1.25021e24	−0.170542
$843$	5.09638e24	0.688220
$844$	−1.68401e24	−0.225131
$845$	6.72901e24	0.890572
$846$	8.81584e23	0.115509
$847$	5.21192e24	0.676066
$848$	1.69226e24	0.217321
$849$	−7.74086e24	−0.984178
$850$	4.87694e23	0.0613884
$851$	2.88845e24	0.359968
$852$	1.08757e24	0.134190
$853$	1.01659e25	1.24188	0.620941	−	0.783857i	$-0.286750\pi$
$853$	1.01659e25	1.24188	0.620941	+	0.783857i	$0.286750\pi$
$854$	−1.86680e25	−2.25790
$855$	4.25526e24	0.509583
$856$	1.39870e25	1.65843
$857$	−5.53683e24	−0.650016	−0.325008	−	0.945711i	$-0.605367\pi$
$857$	−5.53683e24	−0.650016	−0.325008	+	0.945711i	$0.605367\pi$
$858$	−1.75658e24	−0.204186
$859$	−1.42220e25	−1.63688	−0.818442	−	0.574590i	$-0.805162\pi$
$859$	−1.42220e25	−1.63688	−0.818442	+	0.574590i	$0.805162\pi$
$860$	1.18892e24	0.135493
$861$	−1.08449e25	−1.22377
$862$	−1.27519e25	−1.42483
$863$	1.16678e25	1.29091	0.645454	−	0.763799i	$-0.276668\pi$
$863$	1.16678e25	1.29091	0.645454	+	0.763799i	$0.276668\pi$
$864$	−4.51637e24	−0.494792
$865$	−6.10190e24	−0.661955
$866$	8.41746e24	0.904230
$867$	6.18038e24	0.657435
$868$	5.80512e24	0.611496
$869$	1.50717e24	0.157215
$870$	1.24308e24	0.128406
$871$	1.64053e23	0.0167814
$872$	8.84362e24	0.895859
$873$	−5.25616e24	−0.527287
$874$	−2.47168e24	−0.245553
$875$	−1.13772e25	−1.11936
$876$	−1.07780e24	−0.105015
$877$	−8.90782e24	−0.859557	−0.429779	−	0.902934i	$-0.641408\pi$
$877$	−8.90782e24	−0.859557	−0.429779	+	0.902934i	$0.641408\pi$
$878$	8.90584e24	0.851083
$879$	−6.35374e24	−0.601345
$880$	6.14484e24	0.575981
$881$	−1.13232e25	−1.05117	−0.525586	−	0.850740i	$-0.676154\pi$
$881$	−1.13232e25	−1.05117	−0.525586	+	0.850740i	$0.676154\pi$
$882$	4.72442e24	0.434376
$883$	−1.32064e25	−1.20259	−0.601295	−	0.799027i	$-0.705348\pi$
$883$	−1.32064e25	−1.20259	−0.601295	+	0.799027i	$0.705348\pi$
$884$	−2.92740e23	−0.0264020
$885$	−1.28372e25	−1.14671
$886$	6.80511e24	0.602072
$887$	−1.25886e25	−1.10313	−0.551566	−	0.834131i	$-0.685969\pi$
$887$	−1.25886e25	−1.10313	−0.551566	+	0.834131i	$0.685969\pi$
$888$	−9.59631e24	−0.832903
$889$	1.42382e25	1.22403
$890$	−1.49882e25	−1.27624
$891$	−1.86110e24	−0.156968
$892$	−1.50371e24	−0.125621
$893$	2.69035e24	0.222623
$894$	−6.46544e23	−0.0529943
$895$	−7.39268e24	−0.600214
$896$	8.70435e24	0.700032
$897$	1.32844e24	0.105829
$898$	1.58441e25	1.25032
$899$	−4.31230e24	−0.337094
$900$	4.79751e23	0.0371496
$901$	9.48016e23	0.0727202
$902$	1.03534e25	0.786732
$903$	6.41209e24	0.482674
$904$	1.23119e25	0.918105
$905$	−2.51421e25	−1.85733
$906$	−4.82966e24	−0.353449
$907$	−2.63490e25	−1.91030	−0.955150	−	0.296121i	$-0.904307\pi$
$907$	−2.63490e25	−1.91030	−0.955150	+	0.296121i	$0.904307\pi$
$908$	−3.36153e24	−0.241439
$909$	−9.93423e24	−0.706873
$910$	9.24726e24	0.651870
$911$	−1.67606e25	−1.17053	−0.585267	−	0.810841i	$-0.699010\pi$
$911$	−1.67606e25	−1.17053	−0.585267	+	0.810841i	$0.699010\pi$
$912$	6.11812e24	0.423313
$913$	8.17786e24	0.560580
$914$	7.04829e24	0.478675
$915$	−2.17813e25	−1.46556
$916$	3.97833e24	0.265209
$917$	−2.98579e25	−1.97206
$918$	3.30047e24	0.215980
$919$	4.41589e24	0.286310	0.143155	−	0.989700i	$-0.454275\pi$
$919$	4.41589e24	0.286310	0.143155	+	0.989700i	$0.454275\pi$
$920$	−6.23733e24	−0.400684
$921$	1.74180e25	1.10865
$922$	1.89646e25	1.19600
$923$	−6.00992e24	−0.375539
$924$	−2.72436e24	−0.168676
$925$	5.41095e24	0.331947
$926$	1.22181e25	0.742695
$927$	−8.86722e23	−0.0534084
$928$	1.45959e24	0.0871107
$929$	1.83089e25	1.08275	0.541377	−	0.840780i	$-0.317903\pi$
$929$	1.83089e25	1.08275	0.541377	+	0.840780i	$0.317903\pi$
$930$	−2.14210e25	−1.25526
$931$	1.44176e25	0.837184
$932$	5.09508e24	0.293168
$933$	1.52442e25	0.869182
$934$	−2.46272e25	−1.39145
$935$	3.44239e24	0.192735
$936$	4.70173e24	0.260863
$937$	3.00507e25	1.65222	0.826109	−	0.563510i	$-0.190549\pi$
$937$	3.00507e25	1.65222	0.826109	+	0.563510i	$0.190549\pi$
$938$	−8.04674e23	−0.0438426
$939$	−2.82675e24	−0.152627
$940$	1.31506e24	0.0703656
$941$	−2.92801e25	−1.55260	−0.776301	−	0.630362i	$-0.782906\pi$
$941$	−2.92801e25	−1.55260	−0.776301	+	0.630362i	$0.782906\pi$
$942$	−2.00701e25	−1.05467
$943$	−7.82989e24	−0.407762
$944$	1.96625e25	1.01479
$945$	3.29660e25	1.68615
$946$	−6.12148e24	−0.310300
$947$	4.62610e24	0.232402	0.116201	−	0.993226i	$-0.462928\pi$
$947$	4.62610e24	0.232402	0.116201	+	0.993226i	$0.462928\pi$
$948$	7.33511e23	0.0365204
$949$	5.95592e24	0.293891
$950$	−4.63022e24	−0.226439
$951$	6.48606e24	0.314374
$952$	7.41286e24	0.356100
$953$	3.39292e24	0.161541	0.0807707	−	0.996733i	$-0.474262\pi$
$953$	3.39292e24	0.161541	0.0807707	+	0.996733i	$0.474262\pi$
$954$	−2.94934e24	−0.139176
$955$	−8.64192e24	−0.404186
$956$	4.34302e24	0.201326
$957$	2.02377e24	0.0929843
$958$	8.34008e24	0.379808
$959$	−9.81063e23	−0.0442832
$960$	1.96989e25	0.881327
$961$	5.17602e25	2.29534
$962$	1.02719e25	0.451503
$963$	−1.81622e25	−0.791309
$964$	−6.33873e24	−0.273746
$965$	−4.62352e25	−1.97921
$966$	−6.51597e24	−0.276486
$967$	−1.83591e25	−0.772193	−0.386097	−	0.922458i	$-0.626177\pi$
$967$	−1.83591e25	−0.772193	−0.386097	+	0.922458i	$0.626177\pi$
$968$	−1.25016e25	−0.521227
$969$	3.42742e24	0.141649
$970$	2.47966e25	1.01586
$971$	−2.67760e24	−0.108738	−0.0543691	−	0.998521i	$-0.517315\pi$
$971$	−2.67760e24	−0.108738	−0.0543691	+	0.998521i	$0.517315\pi$
$972$	5.38862e24	0.216927
$973$	2.87608e25	1.14774
$974$	−3.71927e25	−1.47132
$975$	2.48857e24	0.0975912
$976$	3.33620e25	1.29697
$977$	1.64049e25	0.632222	0.316111	−	0.948722i	$-0.397623\pi$
$977$	1.64049e25	0.632222	0.316111	+	0.948722i	$0.397623\pi$
$978$	2.44046e24	0.0932377
$979$	−2.44012e25	−0.924184
$980$	7.04745e24	0.264612
$981$	−1.14835e25	−0.427452
$982$	−4.67678e24	−0.172583
$983$	2.24351e25	0.820774	0.410387	−	0.911911i	$-0.365394\pi$
$983$	2.24351e25	0.820774	0.410387	+	0.911911i	$0.365394\pi$
$984$	2.60133e25	0.943488
$985$	5.73646e23	0.0206270
$986$	−1.06664e24	−0.0380244
$987$	7.09241e24	0.250668
$988$	2.77930e24	0.0973871
$989$	4.62945e24	0.160828
$990$	−1.07095e25	−0.368867
$991$	6.96192e24	0.237740	0.118870	−	0.992910i	$-0.462073\pi$
$991$	6.96192e24	0.237740	0.118870	+	0.992910i	$0.462073\pi$
$992$	−2.51519e25	−0.851571
$993$	2.80733e25	0.942377
$994$	2.94786e25	0.981119
$995$	−3.15735e24	−0.104190
$996$	3.98002e24	0.130221
$997$	−3.04245e25	−0.986995	−0.493498	−	0.869747i	$-0.664282\pi$
$997$	−3.04245e25	−0.986995	−0.493498	+	0.869747i	$0.664282\pi$
$998$	1.66297e25	0.534903
$999$	3.66187e25	1.16787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.6	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-315.569 q^{2} -7907.47 q^{3} -31488.2 q^{4} -995824. q^{5} +2.49535e6 q^{6} -2.13865e7 q^{7} +5.12990e7 q^{8} -6.66120e7 q^{9} +O(q^{10})\)	\(q-315.569 q^{2} -7907.47 q^{3} -31488.2 q^{4} -995824. q^{5} +2.49535e6 q^{6} -2.13865e7 q^{7} +5.12990e7 q^{8} -6.66120e7 q^{9} +3.14251e8 q^{10} +5.11611e8 q^{11} +2.48992e8 q^{12} -1.37593e9 q^{13} +6.74891e9 q^{14} +7.87445e9 q^{15} -1.20611e10 q^{16} -6.75675e9 q^{17} +2.10207e10 q^{18} +6.41492e10 q^{19} +3.13567e10 q^{20} +1.69113e11 q^{21} -1.61448e11 q^{22} +1.22098e11 q^{23} -4.05645e11 q^{24} +2.28726e11 q^{25} +4.34201e11 q^{26} +1.54791e12 q^{27} +6.73421e11 q^{28} -5.00246e11 q^{29} -2.48493e12 q^{30} +8.62034e12 q^{31} -2.91773e12 q^{32} -4.04555e12 q^{33} +2.13222e12 q^{34} +2.12972e13 q^{35} +2.09749e12 q^{36} +2.36569e13 q^{37} -2.02435e13 q^{38} +1.08801e13 q^{39} -5.10847e13 q^{40} -6.41281e13 q^{41} -5.33669e13 q^{42} +3.79160e13 q^{43} -1.61097e13 q^{44} +6.63338e13 q^{45} -3.85302e13 q^{46} +4.19389e13 q^{47} +9.53732e13 q^{48} +2.24751e14 q^{49} -7.21788e13 q^{50} +5.34288e13 q^{51} +4.33256e13 q^{52} -1.40307e14 q^{53} -4.88471e14 q^{54} -5.09474e14 q^{55} -1.09710e15 q^{56} -5.07258e14 q^{57} +1.57862e14 q^{58} -1.63023e15 q^{59} -2.47952e14 q^{60} -2.76607e15 q^{61} -2.72031e15 q^{62} +1.42460e15 q^{63} +2.50162e15 q^{64} +1.37019e15 q^{65} +1.27665e15 q^{66} -1.19230e14 q^{67} +2.12758e14 q^{68} -9.65484e14 q^{69} -6.72073e15 q^{70} +4.36790e15 q^{71} -3.41713e15 q^{72} -4.32865e15 q^{73} -7.46539e15 q^{74} -1.80864e15 q^{75} -2.01994e15 q^{76} -1.09415e16 q^{77} -3.43344e15 q^{78} +2.94592e15 q^{79} +1.20108e16 q^{80} -3.63774e15 q^{81} +2.02368e16 q^{82} +1.59845e16 q^{83} -5.32506e15 q^{84} +6.72853e15 q^{85} -1.19651e16 q^{86} +3.95569e15 q^{87} +2.62451e16 q^{88} -4.76949e16 q^{89} -2.09329e16 q^{90} +2.94263e16 q^{91} -3.84463e15 q^{92} -6.81651e16 q^{93} -1.32346e16 q^{94} -6.38813e16 q^{95} +2.30719e16 q^{96} +7.89071e16 q^{97} -7.09245e16 q^{98} -3.40794e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

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