LMFDB - Embedded newform 29.18.a.a.1.18

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			1.18
Root			$692.544$ 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)

$f(q)$	$=$	$q+692.544 q^{2} +5331.24 q^{3} +348545. q^{4} -1.21070e6 q^{5} +3.69212e6 q^{6} -2.86223e7 q^{7} +1.50609e8 q^{8} -1.00718e8 q^{9} +O(q^{10})$	\(q+692.544 q^{2} +5331.24 q^{3} +348545. q^{4} -1.21070e6 q^{5} +3.69212e6 q^{6} -2.86223e7 q^{7} +1.50609e8 q^{8} -1.00718e8 q^{9} -8.38462e8 q^{10} +1.87910e8 q^{11} +1.85817e9 q^{12} +3.53173e9 q^{13} -1.98222e10 q^{14} -6.45453e9 q^{15} +5.86191e10 q^{16} -4.36391e10 q^{17} -6.97516e10 q^{18} -9.77131e10 q^{19} -4.21983e11 q^{20} -1.52592e11 q^{21} +1.30136e11 q^{22} -1.67653e11 q^{23} +8.02934e11 q^{24} +7.02854e11 q^{25} +2.44588e12 q^{26} -1.22543e12 q^{27} -9.97615e12 q^{28} -5.00246e11 q^{29} -4.47004e12 q^{30} +2.46570e12 q^{31} +2.08556e13 q^{32} +1.00180e12 q^{33} -3.02220e13 q^{34} +3.46530e13 q^{35} -3.51047e13 q^{36} -1.73990e13 q^{37} -6.76706e13 q^{38} +1.88285e13 q^{39} -1.82343e14 q^{40} +1.45166e13 q^{41} -1.05677e14 q^{42} +6.38072e12 q^{43} +6.54952e13 q^{44} +1.21939e14 q^{45} -1.16107e14 q^{46} -1.24961e14 q^{47} +3.12512e14 q^{48} +5.86605e14 q^{49} +4.86757e14 q^{50} -2.32651e14 q^{51} +1.23097e15 q^{52} +7.68735e14 q^{53} -8.48663e14 q^{54} -2.27503e14 q^{55} -4.31078e15 q^{56} -5.20932e14 q^{57} -3.46442e14 q^{58} +1.01816e15 q^{59} -2.24969e15 q^{60} -9.81919e14 q^{61} +1.70761e15 q^{62} +2.88278e15 q^{63} +6.76009e15 q^{64} -4.27587e15 q^{65} +6.93787e14 q^{66} -5.56495e14 q^{67} -1.52102e16 q^{68} -8.93800e14 q^{69} +2.39987e16 q^{70} -4.08709e15 q^{71} -1.51691e16 q^{72} +7.05546e15 q^{73} -1.20496e16 q^{74} +3.74708e15 q^{75} -3.40574e16 q^{76} -5.37843e15 q^{77} +1.30396e16 q^{78} -8.93888e15 q^{79} -7.09701e16 q^{80} +6.47369e15 q^{81} +1.00534e16 q^{82} +1.10130e16 q^{83} -5.31852e16 q^{84} +5.28339e16 q^{85} +4.41893e15 q^{86} -2.66693e15 q^{87} +2.83011e16 q^{88} -1.54789e16 q^{89} +8.44483e16 q^{90} -1.01086e17 q^{91} -5.84347e16 q^{92} +1.31453e16 q^{93} -8.65407e16 q^{94} +1.18301e17 q^{95} +1.11186e17 q^{96} -5.99778e16 q^{97} +4.06250e17 q^{98} -1.89260e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	692.544	1.91290	0.956450	−	0.291897i	$-0.0942864\pi$
$2$	692.544	1.91290	0.956450	+	0.291897i	$0.0942864\pi$
$3$	5331.24	0.469135	0.234567	−	0.972100i	$-0.424633\pi$
$3$	5331.24	0.469135	0.234567	+	0.972100i	$0.424633\pi$
$4$	348545.	2.65918
$5$	−1.21070e6	−1.38609	−0.693045	−	0.720894i	$-0.743731\pi$
$5$	−1.21070e6	−1.38609	−0.693045	+	0.720894i	$0.743731\pi$
$6$	3.69212e6	0.897407
$7$	−2.86223e7	−1.87660	−0.938299	−	0.345826i	$-0.887599\pi$
$7$	−2.86223e7	−1.87660	−0.938299	+	0.345826i	$0.887599\pi$
$8$	1.50609e8	3.17385
$9$	−1.00718e8	−0.779913
$10$	−8.38462e8	−2.65145
$11$	1.87910e8	0.264310	0.132155	−	0.991229i	$-0.457810\pi$
$11$	1.87910e8	0.264310	0.132155	+	0.991229i	$0.457810\pi$
$12$	1.85817e9	1.24752
$13$	3.53173e9	1.20080	0.600398	−	0.799701i	$-0.295009\pi$
$13$	3.53173e9	1.20080	0.600398	+	0.799701i	$0.295009\pi$
$14$	−1.98222e10	−3.58974
$15$	−6.45453e9	−0.650263
$16$	5.86191e10	3.41208
$17$	−4.36391e10	−1.51726	−0.758631	−	0.651521i	$-0.774131\pi$
$17$	−4.36391e10	−1.51726	−0.758631	+	0.651521i	$0.774131\pi$
$18$	−6.97516e10	−1.49189
$19$	−9.77131e10	−1.31992	−0.659959	−	0.751302i	$-0.729426\pi$
$19$	−9.77131e10	−1.31992	−0.659959	+	0.751302i	$0.729426\pi$
$20$	−4.21983e11	−3.68587
$21$	−1.52592e11	−0.880377
$22$	1.30136e11	0.505598
$23$	−1.67653e11	−0.446402	−0.223201	−	0.974772i	$-0.571651\pi$
$23$	−1.67653e11	−0.446402	−0.223201	+	0.974772i	$0.571651\pi$
$24$	8.02934e11	1.48896
$25$	7.02854e11	0.921245
$26$	2.44588e12	2.29700
$27$	−1.22543e12	−0.835019
$28$	−9.97615e12	−4.99022
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	−4.47004e12	−1.24389
$31$	2.46570e12	0.519238	0.259619	−	0.965711i	$-0.416403\pi$
$31$	2.46570e12	0.519238	0.259619	+	0.965711i	$0.416403\pi$
$32$	2.08556e13	3.35311
$33$	1.00180e12	0.123997
$34$	−3.02220e13	−2.90237
$35$	3.46530e13	2.60113
$36$	−3.51047e13	−2.07393
$37$	−1.73990e13	−0.814347	−0.407173	−	0.913351i	$-0.633486\pi$
$37$	−1.73990e13	−0.814347	−0.407173	+	0.913351i	$0.633486\pi$
$38$	−6.76706e13	−2.52487
$39$	1.88285e13	0.563335
$40$	−1.82343e14	−4.39925
$41$	1.45166e13	0.283924	0.141962	−	0.989872i	$-0.454659\pi$
$41$	1.45166e13	0.283924	0.141962	+	0.989872i	$0.454659\pi$
$42$	−1.05677e14	−1.68407
$43$	6.38072e12	0.0832507	0.0416253	−	0.999133i	$-0.486746\pi$
$43$	6.38072e12	0.0832507	0.0416253	+	0.999133i	$0.486746\pi$
$44$	6.54952e13	0.702848
$45$	1.21939e14	1.08103
$46$	−1.16107e14	−0.853922
$47$	−1.24961e14	−0.765494	−0.382747	−	0.923853i	$-0.625022\pi$
$47$	−1.24961e14	−0.765494	−0.382747	+	0.923853i	$0.625022\pi$
$48$	3.12512e14	1.60072
$49$	5.86605e14	2.52162
$50$	4.86757e14	1.76225
$51$	−2.32651e14	−0.711800
$52$	1.23097e15	3.19314
$53$	7.68735e14	1.69602	0.848012	−	0.529977i	$-0.177799\pi$
$53$	7.68735e14	1.69602	0.848012	+	0.529977i	$0.177799\pi$
$54$	−8.48663e14	−1.59731
$55$	−2.27503e14	−0.366357
$56$	−4.31078e15	−5.95604
$57$	−5.20932e14	−0.619219
$58$	−3.46442e14	−0.355217
$59$	1.01816e15	0.902767	0.451384	−	0.892330i	$-0.350931\pi$
$59$	1.01816e15	0.902767	0.451384	+	0.892330i	$0.350931\pi$
$60$	−2.24969e15	−1.72917
$61$	−9.81919e14	−0.655801	−0.327901	−	0.944712i	$-0.606341\pi$
$61$	−9.81919e14	−0.655801	−0.327901	+	0.944712i	$0.606341\pi$
$62$	1.70761e15	0.993251
$63$	2.88278e15	1.46358
$64$	6.76009e15	3.00208
$65$	−4.27587e15	−1.66441
$66$	6.93787e14	0.237193
$67$	−5.56495e14	−0.167427	−0.0837135	−	0.996490i	$-0.526678\pi$
$67$	−5.56495e14	−0.167427	−0.0837135	+	0.996490i	$0.526678\pi$
$68$	−1.52102e16	−4.03468
$69$	−8.93800e14	−0.209422
$70$	2.39987e16	4.97570
$71$	−4.08709e15	−0.751136	−0.375568	−	0.926795i	$-0.622552\pi$
$71$	−4.08709e15	−0.751136	−0.375568	+	0.926795i	$0.622552\pi$
$72$	−1.51691e16	−2.47533
$73$	7.05546e15	1.02396	0.511978	−	0.858999i	$-0.328913\pi$
$73$	7.05546e15	1.02396	0.511978	+	0.858999i	$0.328913\pi$
$74$	−1.20496e16	−1.55776
$75$	3.74708e15	0.432188
$76$	−3.40574e16	−3.50991
$77$	−5.37843e15	−0.496003
$78$	1.30396e16	1.07760
$79$	−8.93888e15	−0.662907	−0.331454	−	0.943472i	$-0.607539\pi$
$79$	−8.93888e15	−0.662907	−0.331454	+	0.943472i	$0.607539\pi$
$80$	−7.09701e16	−4.72945
$81$	6.47369e15	0.388177
$82$	1.00534e16	0.543118
$83$	1.10130e16	0.536711	0.268355	−	0.963320i	$-0.413520\pi$
$83$	1.10130e16	0.536711	0.268355	+	0.963320i	$0.413520\pi$
$84$	−5.31852e16	−2.34108
$85$	5.28339e16	2.10306
$86$	4.41893e15	0.159250
$87$	−2.66693e15	−0.0871161
$88$	2.83011e16	0.838880
$89$	−1.54789e16	−0.416797	−0.208398	−	0.978044i	$-0.566825\pi$
$89$	−1.54789e16	−0.416797	−0.208398	+	0.978044i	$0.566825\pi$
$90$	8.44483e16	2.06790
$91$	−1.01086e17	−2.25341
$92$	−5.84347e16	−1.18706
$93$	1.31453e16	0.243593
$94$	−8.65407e16	−1.46431
$95$	1.18301e17	1.82952
$96$	1.11186e17	1.57306
$97$	−5.99778e16	−0.777018	−0.388509	−	0.921445i	$-0.627010\pi$
$97$	−5.99778e16	−0.777018	−0.388509	+	0.921445i	$0.627010\pi$
$98$	4.06250e17	4.82360
$99$	−1.89260e16	−0.206138
$100$	2.44976e17	2.44976
$101$	−1.27316e17	−1.16991	−0.584956	−	0.811065i	$-0.698888\pi$
$101$	−1.27316e17	−1.16991	−0.584956	+	0.811065i	$0.698888\pi$
$102$	−1.61121e17	−1.36160
$103$	−2.10485e17	−1.63721	−0.818607	−	0.574353i	$-0.805254\pi$
$103$	−2.10485e17	−1.63721	−0.818607	+	0.574353i	$0.805254\pi$
$104$	5.31912e17	3.81115
$105$	1.84743e17	1.22028
$106$	5.32383e17	3.24432
$107$	1.24745e17	0.701878	0.350939	−	0.936398i	$-0.385862\pi$
$107$	1.24745e17	0.701878	0.350939	+	0.936398i	$0.385862\pi$
$108$	−4.27117e17	−2.22047
$109$	3.52223e17	1.69314	0.846568	−	0.532280i	$-0.178665\pi$
$109$	3.52223e17	1.69314	0.846568	+	0.532280i	$0.178665\pi$
$110$	−1.57556e17	−0.700804
$111$	−9.27582e16	−0.382038
$112$	−1.67781e18	−6.40310
$113$	1.08445e17	0.383744	0.191872	−	0.981420i	$-0.438544\pi$
$113$	1.08445e17	0.383744	0.191872	+	0.981420i	$0.438544\pi$
$114$	−3.60768e17	−1.18450
$115$	2.02978e17	0.618753
$116$	−1.74358e17	−0.493798
$117$	−3.55709e17	−0.936516
$118$	7.05123e17	1.72690
$119$	1.24905e18	2.84729
$120$	−9.72112e17	−2.06384
$121$	−4.70137e17	−0.930140
$122$	−6.80022e17	−1.25448
$123$	7.73914e16	0.133199
$124$	8.59408e17	1.38075
$125$	7.27456e16	0.109162
$126$	1.99645e18	2.79969
$127$	−3.59575e17	−0.471475	−0.235737	−	0.971817i	$-0.575750\pi$
$127$	−3.59575e17	−0.471475	−0.235737	+	0.971817i	$0.575750\pi$
$128$	1.94807e18	2.38958
$129$	3.40171e16	0.0390558
$130$	−2.96122e18	−3.18385
$131$	−1.26158e18	−1.27089	−0.635445	−	0.772146i	$-0.719184\pi$
$131$	−1.26158e18	−1.27089	−0.635445	+	0.772146i	$0.719184\pi$
$132$	3.49170e17	0.329730
$133$	2.79677e18	2.47695
$134$	−3.85397e17	−0.320271
$135$	1.48363e18	1.15741
$136$	−6.57246e18	−4.81557
$137$	−5.96340e17	−0.410553	−0.205276	−	0.978704i	$-0.565809\pi$
$137$	−5.96340e17	−0.410553	−0.205276	+	0.978704i	$0.565809\pi$
$138$	−6.18996e17	−0.400604
$139$	−9.14798e16	−0.0556800	−0.0278400	−	0.999612i	$-0.508863\pi$
$139$	−9.14798e16	−0.0556800	−0.0278400	+	0.999612i	$0.508863\pi$
$140$	1.20781e19	6.91689
$141$	−6.66195e17	−0.359120
$142$	−2.83049e18	−1.43685
$143$	6.63649e17	0.317382
$144$	−5.90400e18	−2.66112
$145$	6.05648e17	0.257390
$146$	4.88622e18	1.95873
$147$	3.12733e18	1.18298
$148$	−6.06433e18	−2.16550
$149$	3.82602e17	0.129022	0.0645110	−	0.997917i	$-0.479451\pi$
$149$	3.82602e17	0.129022	0.0645110	+	0.997917i	$0.479451\pi$
$150$	2.59502e18	0.826732
$151$	2.68003e18	0.806931	0.403465	−	0.914995i	$-0.367806\pi$
$151$	2.68003e18	0.806931	0.403465	+	0.914995i	$0.367806\pi$
$152$	−1.47165e19	−4.18923
$153$	4.39525e18	1.18333
$154$	−3.72479e18	−0.948803
$155$	−2.98523e18	−0.719711
$156$	6.56257e18	1.49801
$157$	3.04280e18	0.657849	0.328925	−	0.944356i	$-0.393314\pi$
$157$	3.04280e18	0.657849	0.328925	+	0.944356i	$0.393314\pi$
$158$	−6.19056e18	−1.26807
$159$	4.09831e18	0.795664
$160$	−2.52499e19	−4.64771
$161$	4.79862e18	0.837716
$162$	4.48331e18	0.742543
$163$	6.81347e17	0.107096	0.0535481	−	0.998565i	$-0.482947\pi$
$163$	6.81347e17	0.107096	0.0535481	+	0.998565i	$0.482947\pi$
$164$	5.05968e18	0.755006
$165$	−1.21287e18	−0.171871
$166$	7.62696e18	1.02667
$167$	−1.00785e19	−1.28915	−0.644577	−	0.764540i	$-0.722966\pi$
$167$	−1.00785e19	−1.28915	−0.644577	+	0.764540i	$0.722966\pi$
$168$	−2.29818e19	−2.79419
$169$	3.82271e18	0.441911
$170$	3.65898e19	4.02294
$171$	9.84147e18	1.02942
$172$	2.22397e18	0.221379
$173$	−1.14654e19	−1.08642	−0.543209	−	0.839597i	$-0.682791\pi$
$173$	−1.14654e19	−1.08642	−0.543209	+	0.839597i	$0.682791\pi$
$174$	−1.84697e18	−0.166644
$175$	−2.01173e19	−1.72880
$176$	1.10151e19	0.901845
$177$	5.42808e18	0.423519
$178$	−1.07198e19	−0.797290
$179$	−1.59020e19	−1.12772	−0.563859	−	0.825871i	$-0.690684\pi$
$179$	−1.59020e19	−1.12772	−0.563859	+	0.825871i	$0.690684\pi$
$180$	4.25013e19	2.87466
$181$	−1.95856e19	−1.26377	−0.631886	−	0.775062i	$-0.717719\pi$
$181$	−1.95856e19	−1.26377	−0.631886	+	0.775062i	$0.717719\pi$
$182$	−7.00066e19	−4.31055
$183$	−5.23485e18	−0.307659
$184$	−2.52502e19	−1.41681
$185$	2.10650e19	1.12876
$186$	9.10367e18	0.465968
$187$	−8.20025e18	−0.401027
$188$	−4.35544e19	−2.03559
$189$	3.50746e19	1.56699
$190$	8.19287e19	3.49970
$191$	3.38346e19	1.38222	0.691110	−	0.722750i	$-0.257122\pi$
$191$	3.38346e19	1.38222	0.691110	+	0.722750i	$0.257122\pi$
$192$	3.60397e19	1.40838
$193$	−2.11072e19	−0.789212	−0.394606	−	0.918851i	$-0.629119\pi$
$193$	−2.11072e19	−0.789212	−0.394606	+	0.918851i	$0.629119\pi$
$194$	−4.15373e19	−1.48636
$195$	−2.27957e19	−0.780833
$196$	2.04458e20	6.70544
$197$	4.14291e18	0.130119	0.0650597	−	0.997881i	$-0.479276\pi$
$197$	4.14291e18	0.130119	0.0650597	+	0.997881i	$0.479276\pi$
$198$	−1.31071e19	−0.394322
$199$	−1.70002e19	−0.490007	−0.245003	−	0.969522i	$-0.578789\pi$
$199$	−1.70002e19	−0.490007	−0.245003	+	0.969522i	$0.578789\pi$
$200$	1.05856e20	2.92390
$201$	−2.96681e18	−0.0785458
$202$	−8.81722e19	−2.23792
$203$	1.43182e19	0.348475
$204$	−8.10891e19	−1.89281
$205$	−1.75752e19	−0.393544
$206$	−1.45770e20	−3.13183
$207$	1.68857e19	0.348154
$208$	2.07027e20	4.09721
$209$	−1.83613e19	−0.348867
$210$	1.27943e20	2.33427
$211$	−4.49788e19	−0.788147	−0.394073	−	0.919079i	$-0.628934\pi$
$211$	−4.49788e19	−0.788147	−0.394073	+	0.919079i	$0.628934\pi$
$212$	2.67939e20	4.51004
$213$	−2.17893e19	−0.352384
$214$	8.63915e19	1.34262
$215$	−7.72513e18	−0.115393
$216$	−1.84561e20	−2.65023
$217$	−7.05741e19	−0.974401
$218$	2.43929e20	3.23880
$219$	3.76144e19	0.480373
$220$	−7.92950e19	−0.974211
$221$	−1.54122e20	−1.82192
$222$	−6.42391e19	−0.730801
$223$	1.13550e19	0.124335	0.0621677	−	0.998066i	$-0.480199\pi$
$223$	1.13550e19	0.124335	0.0621677	+	0.998066i	$0.480199\pi$
$224$	−5.96935e20	−6.29244
$225$	−7.07901e19	−0.718490
$226$	7.51027e19	0.734064
$227$	−1.12513e20	−1.05921	−0.529604	−	0.848245i	$-0.677659\pi$
$227$	−1.12513e20	−1.05921	−0.529604	+	0.848245i	$0.677659\pi$
$228$	−1.81568e20	−1.64662
$229$	−1.44943e20	−1.26647	−0.633237	−	0.773958i	$-0.718274\pi$
$229$	−1.44943e20	−1.26647	−0.633237	+	0.773958i	$0.718274\pi$
$230$	1.40571e20	1.18361
$231$	−2.86737e19	−0.232692
$232$	−7.53418e19	−0.589370
$233$	−1.01961e20	−0.768971	−0.384486	−	0.923131i	$-0.625621\pi$
$233$	−1.01961e20	−0.768971	−0.384486	+	0.923131i	$0.625621\pi$
$234$	−2.46344e20	−1.79146
$235$	1.51290e20	1.06104
$236$	3.54876e20	2.40063
$237$	−4.76553e19	−0.310993
$238$	8.65023e20	5.44658
$239$	−2.59237e19	−0.157513	−0.0787563	−	0.996894i	$-0.525095\pi$
$239$	−2.59237e19	−0.157513	−0.0787563	+	0.996894i	$0.525095\pi$
$240$	−3.78358e20	−2.21875
$241$	−2.09900e19	−0.118814	−0.0594071	−	0.998234i	$-0.518921\pi$
$241$	−2.09900e19	−0.118814	−0.0594071	+	0.998234i	$0.518921\pi$
$242$	−3.25590e20	−1.77927
$243$	1.92765e20	1.01713
$244$	−3.42243e20	−1.74390
$245$	−7.10202e20	−3.49519
$246$	5.35969e19	0.254795
$247$	−3.45096e20	−1.58495
$248$	3.71358e20	1.64799
$249$	5.87127e19	0.251790
$250$	5.03795e19	0.208816
$251$	4.81720e20	1.93005	0.965025	−	0.262159i	$-0.0844346\pi$
$251$	4.81720e20	1.93005	0.965025	+	0.262159i	$0.0844346\pi$
$252$	1.00478e21	3.89193
$253$	−3.15038e19	−0.117988
$254$	−2.49022e20	−0.901883
$255$	2.81670e20	0.986618
$256$	4.63067e20	1.56893
$257$	−3.69060e18	−0.0120967	−0.00604834	−	0.999982i	$-0.501925\pi$
$257$	−3.69060e18	−0.0120967	−0.00604834	+	0.999982i	$0.501925\pi$
$258$	2.35583e19	0.0747098
$259$	4.97999e20	1.52820
$260$	−1.49033e21	−4.42598
$261$	5.03838e19	0.144826
$262$	−8.73698e20	−2.43109
$263$	3.72803e20	1.00428	0.502140	−	0.864786i	$-0.332546\pi$
$263$	3.72803e20	1.00428	0.502140	+	0.864786i	$0.332546\pi$
$264$	1.50880e20	0.393548
$265$	−9.30708e20	−2.35084
$266$	1.93689e21	4.73817
$267$	−8.25215e19	−0.195534
$268$	−1.93963e20	−0.445220
$269$	6.27699e20	1.39591	0.697954	−	0.716142i	$-0.254094\pi$
$269$	6.27699e20	1.39591	0.697954	+	0.716142i	$0.254094\pi$
$270$	1.02748e21	2.21401
$271$	−3.51051e20	−0.733047	−0.366523	−	0.930409i	$-0.619452\pi$
$271$	−3.51051e20	−0.733047	−0.366523	+	0.930409i	$0.619452\pi$
$272$	−2.55809e21	−5.17701
$273$	−5.38915e20	−1.05715
$274$	−4.12991e20	−0.785347
$275$	1.32074e20	0.243494
$276$	−3.11529e20	−0.556893
$277$	6.90633e20	1.19721	0.598603	−	0.801046i	$-0.295723\pi$
$277$	6.90633e20	1.19721	0.598603	+	0.801046i	$0.295723\pi$
$278$	−6.33537e19	−0.106510
$279$	−2.48341e20	−0.404961
$280$	5.21906e21	8.25561
$281$	−1.02395e21	−1.57136	−0.785678	−	0.618636i	$-0.787686\pi$
$281$	−1.02395e21	−1.57136	−0.785678	+	0.618636i	$0.787686\pi$
$282$	−4.61369e20	−0.686960
$283$	5.49495e20	0.793924	0.396962	−	0.917835i	$-0.370064\pi$
$283$	5.49495e20	0.793924	0.396962	+	0.917835i	$0.370064\pi$
$284$	−1.42453e21	−1.99741
$285$	6.30692e20	0.858293
$286$	4.59606e20	0.607120
$287$	−4.15498e20	−0.532811
$288$	−2.10054e21	−2.61513
$289$	1.07713e21	1.30208
$290$	4.19438e20	0.492362
$291$	−3.19756e20	−0.364526
$292$	2.45914e21	2.72289
$293$	−1.60424e20	−0.172542	−0.0862708	−	0.996272i	$-0.527495\pi$
$293$	−1.60424e20	−0.172542	−0.0862708	+	0.996272i	$0.527495\pi$
$294$	2.16581e21	2.26292
$295$	−1.23269e21	−1.25132
$296$	−2.62045e21	−2.58462
$297$	−2.30271e20	−0.220703
$298$	2.64969e20	0.246806
$299$	−5.92107e20	−0.536037
$300$	1.30603e21	1.14927
$301$	−1.82631e20	−0.156228
$302$	1.85604e21	1.54358
$303$	−6.78755e20	−0.548846
$304$	−5.72785e21	−4.50366
$305$	1.18881e21	0.908999
$306$	3.04390e21	2.26359
$307$	1.96045e21	1.41801	0.709006	−	0.705202i	$-0.249144\pi$
$307$	1.96045e21	1.41801	0.709006	+	0.705202i	$0.249144\pi$
$308$	−1.87462e21	−1.31896
$309$	−1.12215e21	−0.768074
$310$	−2.06740e21	−1.37673
$311$	−6.31045e20	−0.408881	−0.204440	−	0.978879i	$-0.565537\pi$
$311$	−6.31045e20	−0.408881	−0.204440	+	0.978879i	$0.565537\pi$
$312$	2.83575e21	1.78794
$313$	−1.70837e21	−1.04823	−0.524114	−	0.851648i	$-0.675603\pi$
$313$	−1.70837e21	−1.04823	−0.524114	+	0.851648i	$0.675603\pi$
$314$	2.10727e21	1.25840
$315$	−3.49018e21	−2.02866
$316$	−3.11560e21	−1.76279
$317$	−2.10066e21	−1.15705	−0.578526	−	0.815664i	$-0.696372\pi$
$317$	−2.10066e21	−1.15705	−0.578526	+	0.815664i	$0.696372\pi$
$318$	2.83826e21	1.52202
$319$	−9.40015e19	−0.0490811
$320$	−8.18444e21	−4.16116
$321$	6.65046e20	0.329275
$322$	3.32326e21	1.60247
$323$	4.26411e21	2.00266
$324$	2.25637e21	1.03223
$325$	2.48229e21	1.10623
$326$	4.71862e20	0.204864
$327$	1.87778e21	0.794309
$328$	2.18633e21	0.901133
$329$	3.57666e21	1.43652
$330$	−8.39967e20	−0.328771
$331$	1.58109e21	0.603140	0.301570	−	0.953444i	$-0.402489\pi$
$331$	1.58109e21	0.603140	0.301570	+	0.953444i	$0.402489\pi$
$332$	3.83851e21	1.42721
$333$	1.75239e21	0.635120
$334$	−6.97978e21	−2.46602
$335$	6.73749e20	0.232069
$336$	−8.94482e21	−3.00391
$337$	−2.22590e21	−0.728874	−0.364437	−	0.931228i	$-0.618739\pi$
$337$	−2.22590e21	−0.728874	−0.364437	+	0.931228i	$0.618739\pi$
$338$	2.64740e21	0.845332
$339$	5.78145e20	0.180028
$340$	1.84150e22	5.59243
$341$	4.63332e20	0.137240
$342$	6.81565e21	1.96918
$343$	−1.01316e22	−2.85546
$344$	9.60996e20	0.264225
$345$	1.08212e21	0.290278
$346$	−7.94029e21	−2.07821
$347$	4.33893e21	1.10811	0.554054	−	0.832481i	$-0.313080\pi$
$347$	4.33893e21	1.10811	0.554054	+	0.832481i	$0.313080\pi$
$348$	−9.29545e20	−0.231658
$349$	−2.18374e21	−0.531110	−0.265555	−	0.964096i	$-0.585555\pi$
$349$	−2.18374e21	−0.531110	−0.265555	+	0.964096i	$0.585555\pi$
$350$	−1.39321e22	−3.30703
$351$	−4.32789e21	−1.00269
$352$	3.91898e21	0.886259
$353$	−3.47144e21	−0.766346	−0.383173	−	0.923677i	$-0.625169\pi$
$353$	−3.47144e21	−0.766346	−0.383173	+	0.923677i	$0.625169\pi$
$354$	3.75918e21	0.810150
$355$	4.94824e21	1.04114
$356$	−5.39508e21	−1.10834
$357$	6.65899e21	1.33576
$358$	−1.10128e22	−2.15721
$359$	−1.75255e21	−0.335248	−0.167624	−	0.985851i	$-0.553610\pi$
$359$	−1.75255e21	−0.335248	−0.167624	+	0.985851i	$0.553610\pi$
$360$	1.83652e22	3.43103
$361$	4.06746e21	0.742184
$362$	−1.35639e22	−2.41747
$363$	−2.50641e21	−0.436361
$364$	−3.52331e22	−5.99223
$365$	−8.54205e21	−1.41929
$366$	−3.62536e21	−0.588521
$367$	−7.13436e21	−1.13160	−0.565801	−	0.824542i	$-0.691433\pi$
$367$	−7.13436e21	−1.13160	−0.565801	+	0.824542i	$0.691433\pi$
$368$	−9.82769e21	−1.52316
$369$	−1.46208e21	−0.221436
$370$	1.45884e22	2.15920
$371$	−2.20030e22	−3.18275
$372$	4.58171e21	0.647758
$373$	1.34759e22	1.86223	0.931115	−	0.364727i	$-0.118838\pi$
$373$	1.34759e22	1.86223	0.931115	+	0.364727i	$0.118838\pi$
$374$	−5.67903e21	−0.767124
$375$	3.87824e20	0.0512117
$376$	−1.88202e22	−2.42957
$377$	−1.76674e21	−0.222982
$378$	2.42907e22	2.99750
$379$	−3.46196e21	−0.417723	−0.208862	−	0.977945i	$-0.566976\pi$
$379$	−3.46196e21	−0.417723	−0.208862	+	0.977945i	$0.566976\pi$
$380$	4.12332e22	4.86504
$381$	−1.91698e21	−0.221185
$382$	2.34319e22	2.64405
$383$	−2.91323e21	−0.321503	−0.160751	−	0.986995i	$-0.551392\pi$
$383$	−2.91323e21	−0.321503	−0.160751	+	0.986995i	$0.551392\pi$
$384$	1.03856e22	1.12103
$385$	6.51166e21	0.687504
$386$	−1.46177e22	−1.50968
$387$	−6.42654e20	−0.0649283
$388$	−2.09049e22	−2.06623
$389$	1.03535e22	1.00119	0.500596	−	0.865681i	$-0.333114\pi$
$389$	1.03535e22	1.00119	0.500596	+	0.865681i	$0.333114\pi$
$390$	−1.57870e22	−1.49365
$391$	7.31625e21	0.677308
$392$	8.83482e22	8.00324
$393$	−6.72578e21	−0.596219
$394$	2.86914e21	0.248906
$395$	1.08223e22	0.918849
$396$	−6.59655e21	−0.548160
$397$	1.91830e22	1.56026	0.780131	−	0.625616i	$-0.215152\pi$
$397$	1.91830e22	1.56026	0.780131	+	0.625616i	$0.215152\pi$
$398$	−1.17734e22	−0.937334
$399$	1.49103e22	1.16203
$400$	4.12006e22	3.14336
$401$	−5.66654e21	−0.423244	−0.211622	−	0.977352i	$-0.567875\pi$
$401$	−5.66654e21	−0.423244	−0.211622	+	0.977352i	$0.567875\pi$
$402$	−2.05464e21	−0.150250
$403$	8.70821e21	0.623499
$404$	−4.43755e22	−3.11101
$405$	−7.83770e21	−0.538048
$406$	9.91598e21	0.666598
$407$	−3.26945e21	−0.215240
$408$	−3.50394e22	−2.25915
$409$	−2.61500e21	−0.165129	−0.0825646	−	0.996586i	$-0.526311\pi$
$409$	−2.61500e21	−0.165129	−0.0825646	+	0.996586i	$0.526311\pi$
$410$	−1.21716e22	−0.752810
$411$	−3.17923e21	−0.192605
$412$	−7.33636e22	−4.35366
$413$	−2.91422e22	−1.69413
$414$	1.16941e22	0.665984
$415$	−1.33334e22	−0.743929
$416$	7.36564e22	4.02640
$417$	−4.87700e20	−0.0261214
$418$	−1.27160e22	−0.667348
$419$	−2.36877e22	−1.21816	−0.609080	−	0.793109i	$-0.708461\pi$
$419$	−2.36877e22	−1.21816	−0.609080	+	0.793109i	$0.708461\pi$
$420$	6.43913e22	3.24495
$421$	−8.65022e21	−0.427198	−0.213599	−	0.976921i	$-0.568519\pi$
$421$	−8.65022e21	−0.427198	−0.213599	+	0.976921i	$0.568519\pi$
$422$	−3.11498e22	−1.50765
$423$	1.25858e22	0.597018
$424$	1.15779e23	5.38293
$425$	−3.06719e22	−1.39777
$426$	−1.50900e22	−0.674075
$427$	2.81048e22	1.23067
$428$	4.34793e22	1.86642
$429$	3.53807e21	0.148895
$430$	−5.34999e21	−0.220735
$431$	−1.12853e22	−0.456518	−0.228259	−	0.973600i	$-0.573303\pi$
$431$	−1.12853e22	−0.456518	−0.228259	+	0.973600i	$0.573303\pi$
$432$	−7.18335e22	−2.84915
$433$	2.82398e21	0.109828	0.0549142	−	0.998491i	$-0.482511\pi$
$433$	2.82398e21	0.109828	0.0549142	+	0.998491i	$0.482511\pi$
$434$	−4.88757e22	−1.86393
$435$	3.22885e21	0.120751
$436$	1.22765e23	4.50236
$437$	1.63819e22	0.589214
$438$	2.60496e22	0.918906
$439$	2.83523e22	0.980933	0.490466	−	0.871460i	$-0.336826\pi$
$439$	2.83523e22	0.980933	0.490466	+	0.871460i	$0.336826\pi$
$440$	−3.42641e22	−1.16276
$441$	−5.90817e22	−1.96664
$442$	−1.06736e23	−3.48515
$443$	2.98888e22	0.957363	0.478682	−	0.877989i	$-0.341115\pi$
$443$	2.98888e22	0.957363	0.478682	+	0.877989i	$0.341115\pi$
$444$	−3.23304e22	−1.01591
$445$	1.87403e22	0.577717
$446$	7.86381e21	0.237841
$447$	2.03974e21	0.0605287
$448$	−1.93489e23	−5.63370
$449$	−2.92246e22	−0.834939	−0.417470	−	0.908691i	$-0.637083\pi$
$449$	−2.92246e22	−0.834939	−0.417470	+	0.908691i	$0.637083\pi$
$450$	−4.90252e22	−1.37440
$451$	2.72782e21	0.0750438
$452$	3.77978e22	1.02045
$453$	1.42879e22	0.378559
$454$	−7.79199e22	−2.02616
$455$	1.22385e23	3.12343
$456$	−7.84571e22	−1.96531
$457$	1.32298e22	0.325285	0.162643	−	0.986685i	$-0.447998\pi$
$457$	1.32298e22	0.325285	0.162643	+	0.986685i	$0.447998\pi$
$458$	−1.00379e23	−2.42264
$459$	5.34767e22	1.26694
$460$	7.07469e22	1.64538
$461$	4.47870e22	1.02257	0.511286	−	0.859410i	$-0.329169\pi$
$461$	4.47870e22	1.02257	0.511286	+	0.859410i	$0.329169\pi$
$462$	−1.98578e22	−0.445116
$463$	2.70002e22	0.594195	0.297098	−	0.954847i	$-0.403981\pi$
$463$	2.70002e22	0.594195	0.297098	+	0.954847i	$0.403981\pi$
$464$	−2.93240e22	−0.633607
$465$	−1.59150e22	−0.337641
$466$	−7.06127e22	−1.47096
$467$	1.05678e22	0.216169	0.108084	−	0.994142i	$-0.465528\pi$
$467$	1.05678e22	0.216169	0.108084	+	0.994142i	$0.465528\pi$
$468$	−1.23981e23	−2.49037
$469$	1.59282e22	0.314193
$470$	1.04775e23	2.02967
$471$	1.62219e22	0.308620
$472$	1.53345e23	2.86525
$473$	1.19900e21	0.0220040
$474$	−3.30034e22	−0.594898
$475$	−6.86780e22	−1.21597
$476$	4.35350e23	7.57146
$477$	−7.74255e22	−1.32275
$478$	−1.79533e22	−0.301306
$479$	−5.13246e22	−0.846202	−0.423101	−	0.906083i	$-0.639058\pi$
$479$	−5.13246e22	−0.846202	−0.423101	+	0.906083i	$0.639058\pi$
$480$	−1.34613e23	−2.18040
$481$	−6.14486e22	−0.977865
$482$	−1.45365e22	−0.227280
$483$	2.55826e22	0.393002
$484$	−1.63864e23	−2.47342
$485$	7.26151e22	1.07702
$486$	1.33498e23	1.94566
$487$	9.35507e22	1.33983	0.669917	−	0.742436i	$-0.266330\pi$
$487$	9.35507e22	1.33983	0.669917	+	0.742436i	$0.266330\pi$
$488$	−1.47886e23	−2.08142
$489$	3.63242e21	0.0502425
$490$	−4.91846e23	−6.68594
$491$	9.22771e22	1.23282	0.616412	−	0.787424i	$-0.288586\pi$
$491$	9.22771e22	1.23282	0.616412	+	0.787424i	$0.288586\pi$
$492$	2.69744e22	0.354199
$493$	2.18303e22	0.281748
$494$	−2.38994e23	−3.03185
$495$	2.29137e22	0.285726
$496$	1.44537e23	1.77168
$497$	1.16982e23	1.40958
$498$	4.06611e22	0.481648
$499$	−5.12198e22	−0.596462	−0.298231	−	0.954494i	$-0.596397\pi$
$499$	−5.12198e22	−0.596462	−0.298231	+	0.954494i	$0.596397\pi$
$500$	2.53551e22	0.290282
$501$	−5.37307e22	−0.604786
$502$	3.33612e23	3.69199
$503$	8.68951e22	0.945513	0.472756	−	0.881193i	$-0.343259\pi$
$503$	8.68951e22	0.945513	0.472756	+	0.881193i	$0.343259\pi$
$504$	4.34174e23	4.64520
$505$	1.54142e23	1.62160
$506$	−2.18178e22	−0.225700
$507$	2.03798e22	0.207316
$508$	−1.25328e23	−1.25374
$509$	9.32555e22	0.917431	0.458715	−	0.888583i	$-0.348310\pi$
$509$	9.32555e22	0.917431	0.458715	+	0.888583i	$0.348310\pi$
$510$	1.95069e23	1.88730
$511$	−2.01944e23	−1.92155
$512$	6.53565e22	0.611637
$513$	1.19740e23	1.10216
$514$	−2.55590e21	−0.0231397
$515$	2.54835e23	2.26933
$516$	1.18565e22	0.103857
$517$	−2.34814e22	−0.202327
$518$	3.44886e23	2.92330
$519$	−6.11248e22	−0.509677
$520$	−6.43985e23	−5.28260
$521$	1.25624e22	0.101380	0.0506901	−	0.998714i	$-0.483858\pi$
$521$	1.25624e22	0.101380	0.0506901	+	0.998714i	$0.483858\pi$
$522$	3.48930e22	0.277038
$523$	−2.28074e23	−1.78161	−0.890803	−	0.454389i	$-0.849858\pi$
$523$	−2.28074e23	−1.78161	−0.890803	+	0.454389i	$0.849858\pi$
$524$	−4.39716e23	−3.37953
$525$	−1.07250e23	−0.811042
$526$	2.58182e23	1.92109
$527$	−1.07601e23	−0.787820
$528$	5.87243e22	0.423087
$529$	−1.12942e23	−0.800726
$530$	−6.44556e23	−4.49692
$531$	−1.02548e23	−0.704080
$532$	9.74800e23	6.58668
$533$	5.12687e22	0.340935
$534$	−5.71498e22	−0.374036
$535$	−1.51029e23	−0.972866
$536$	−8.38134e22	−0.531389
$537$	−8.47772e22	−0.529051
$538$	4.34709e23	2.67023
$539$	1.10229e23	0.666488
$540$	5.17110e23	3.07777
$541$	−1.06925e23	−0.626475	−0.313238	−	0.949675i	$-0.601414\pi$
$541$	−1.06925e23	−0.626475	−0.313238	+	0.949675i	$0.601414\pi$
$542$	−2.43118e23	−1.40224
$543$	−1.04415e23	−0.592879
$544$	−9.10120e23	−5.08754
$545$	−4.26436e23	−2.34684
$546$	−3.73222e23	−2.02223
$547$	−5.99143e22	−0.319623	−0.159812	−	0.987148i	$-0.551089\pi$
$547$	−5.99143e22	−0.319623	−0.159812	+	0.987148i	$0.551089\pi$
$548$	−2.07851e23	−1.09174
$549$	9.88970e22	0.511468
$550$	9.14667e22	0.465779
$551$	4.88806e22	0.245103
$552$	−1.34615e23	−0.664676
$553$	2.55851e23	1.24401
$554$	4.78293e23	2.29014
$555$	1.12302e23	0.529539
$556$	−3.18848e22	−0.148063
$557$	2.23993e23	1.02439	0.512195	−	0.858869i	$-0.328832\pi$
$557$	2.23993e23	1.02439	0.512195	+	0.858869i	$0.328832\pi$
$558$	−1.71987e23	−0.774649
$559$	2.25350e22	0.0999671
$560$	2.03133e24	8.87527
$561$	−4.37175e22	−0.188136
$562$	−7.09129e23	−3.00585
$563$	−2.48713e23	−1.03843	−0.519214	−	0.854644i	$-0.673775\pi$
$563$	−2.48713e23	−1.03843	−0.519214	+	0.854644i	$0.673775\pi$
$564$	−2.32199e23	−0.954965
$565$	−1.31294e23	−0.531904
$566$	3.80549e23	1.51870
$567$	−1.85292e23	−0.728451
$568$	−6.15554e23	−2.38400
$569$	3.59174e23	1.37041	0.685206	−	0.728349i	$-0.259712\pi$
$569$	3.59174e23	1.37041	0.685206	+	0.728349i	$0.259712\pi$
$570$	4.36781e23	1.64183
$571$	8.41265e22	0.311549	0.155774	−	0.987793i	$-0.450213\pi$
$571$	8.41265e22	0.311549	0.155774	+	0.987793i	$0.450213\pi$
$572$	2.31311e23	0.843977
$573$	1.80380e23	0.648447
$574$	−2.87751e23	−1.01921
$575$	−1.17836e23	−0.411245
$576$	−6.80863e23	−2.34136
$577$	−3.32241e23	−1.12579	−0.562896	−	0.826528i	$-0.690313\pi$
$577$	−3.32241e23	−1.12579	−0.562896	+	0.826528i	$0.690313\pi$
$578$	7.45962e23	2.49075
$579$	−1.12528e23	−0.370246
$580$	2.11095e23	0.684449
$581$	−3.15216e23	−1.00719
$582$	−2.21445e23	−0.697301
$583$	1.44453e23	0.448276
$584$	1.06262e24	3.24989
$585$	4.30657e23	1.29810
$586$	−1.11100e23	−0.330055
$587$	4.95967e23	1.45221	0.726104	−	0.687585i	$-0.241329\pi$
$587$	4.95967e23	1.45221	0.726104	+	0.687585i	$0.241329\pi$
$588$	1.09001e24	3.14576
$589$	−2.40932e23	−0.685352
$590$	−8.53693e23	−2.39364
$591$	2.20868e22	0.0610435
$592$	−1.01991e24	−2.77862
$593$	−6.80185e23	−1.82668	−0.913339	−	0.407199i	$-0.866505\pi$
$593$	−6.80185e23	−1.82668	−0.913339	+	0.407199i	$0.866505\pi$
$594$	−1.59473e23	−0.422184
$595$	−1.51223e24	−3.94660
$596$	1.33354e23	0.343093
$597$	−9.06320e22	−0.229879
$598$	−4.10060e23	−1.02539
$599$	−3.73292e23	−0.920281	−0.460140	−	0.887846i	$-0.652201\pi$
$599$	−3.73292e23	−0.920281	−0.460140	+	0.887846i	$0.652201\pi$
$600$	5.64345e23	1.37170
$601$	6.68434e23	1.60186	0.800931	−	0.598756i	$-0.204338\pi$
$601$	6.68434e23	1.60186	0.800931	+	0.598756i	$0.204338\pi$
$602$	−1.26480e23	−0.298848
$603$	5.60491e22	0.130579
$604$	9.34112e23	2.14578
$605$	5.69194e23	1.28926
$606$	−4.70067e23	−1.04989
$607$	−2.49571e23	−0.549655	−0.274828	−	0.961494i	$-0.588621\pi$
$607$	−2.49571e23	−0.549655	−0.274828	+	0.961494i	$0.588621\pi$
$608$	−2.03786e24	−4.42583
$609$	7.63337e22	0.163482
$610$	8.23302e23	1.73882
$611$	−4.41328e23	−0.919202
$612$	1.53194e24	3.14670
$613$	7.82314e23	1.58477	0.792387	−	0.610019i	$-0.208838\pi$
$613$	7.82314e23	1.58477	0.792387	+	0.610019i	$0.208838\pi$
$614$	1.35770e24	2.71252
$615$	−9.36977e22	−0.184625
$616$	−8.10041e23	−1.57424
$617$	−7.74160e23	−1.48391	−0.741954	−	0.670451i	$-0.766101\pi$
$617$	−7.74160e23	−1.48391	−0.741954	+	0.670451i	$0.766101\pi$
$618$	−7.77136e23	−1.46925
$619$	−5.84028e23	−1.08909	−0.544544	−	0.838732i	$-0.683297\pi$
$619$	−5.84028e23	−1.08909	−0.544544	+	0.838732i	$0.683297\pi$
$620$	−1.04049e24	−1.91384
$621$	2.05447e23	0.372754
$622$	−4.37026e23	−0.782148
$623$	4.43041e23	0.782159
$624$	1.10371e24	1.92214
$625$	−6.24308e23	−1.07255
$626$	−1.18312e24	−2.00515
$627$	−9.78885e22	−0.163666
$628$	1.06055e24	1.74934
$629$	7.59277e23	1.23558
$630$	−2.41710e24	−3.88061
$631$	−1.27153e23	−0.201409	−0.100704	−	0.994916i	$-0.532110\pi$
$631$	−1.27153e23	−0.201409	−0.100704	+	0.994916i	$0.532110\pi$
$632$	−1.34628e24	−2.10397
$633$	−2.39793e23	−0.369747
$634$	−1.45480e24	−2.21332
$635$	4.35338e23	0.653506
$636$	1.42844e24	2.11582
$637$	2.07173e24	3.02795
$638$	−6.51001e22	−0.0938871
$639$	4.11644e23	0.585821
$640$	−2.35853e24	−3.31217
$641$	−1.38119e24	−1.91408	−0.957041	−	0.289954i	$-0.906360\pi$
$641$	−1.38119e24	−1.91408	−0.957041	+	0.289954i	$0.906360\pi$
$642$	4.60574e23	0.629871
$643$	−3.70339e23	−0.499812	−0.249906	−	0.968270i	$-0.580400\pi$
$643$	−3.70339e23	−0.499812	−0.249906	+	0.968270i	$0.580400\pi$
$644$	1.67254e24	2.22764
$645$	−4.11845e22	−0.0541348
$646$	2.95308e24	3.83089
$647$	−1.13657e24	−1.45516	−0.727578	−	0.686025i	$-0.759354\pi$
$647$	−1.13657e24	−1.45516	−0.727578	+	0.686025i	$0.759354\pi$
$648$	9.74998e23	1.23202
$649$	1.91324e23	0.238610
$650$	1.71910e24	2.11610
$651$	−3.76247e23	−0.457125
$652$	2.37480e23	0.284788
$653$	6.52707e23	0.772602	0.386301	−	0.922373i	$-0.373753\pi$
$653$	6.52707e23	0.772602	0.386301	+	0.922373i	$0.373753\pi$
$654$	1.30045e24	1.51943
$655$	1.52739e24	1.76157
$656$	8.50949e23	0.968771
$657$	−7.10613e23	−0.798596
$658$	2.47699e24	2.74793
$659$	3.47853e23	0.380952	0.190476	−	0.981692i	$-0.438997\pi$
$659$	3.47853e23	0.380952	0.190476	+	0.981692i	$0.438997\pi$
$660$	−4.22740e23	−0.457036
$661$	−7.87787e23	−0.840807	−0.420404	−	0.907337i	$-0.638112\pi$
$661$	−7.87787e23	−0.840807	−0.420404	+	0.907337i	$0.638112\pi$
$662$	1.09497e24	1.15375
$663$	−8.21660e23	−0.854726
$664$	1.65865e24	1.70344
$665$	−3.38605e24	−3.43328
$666$	1.21361e24	1.21492
$667$	8.38680e22	0.0828947
$668$	−3.51280e24	−3.42810
$669$	6.05361e22	0.0583300
$670$	4.66600e23	0.443925
$671$	−1.84513e23	−0.173335
$672$	−3.18240e24	−2.95200
$673$	−1.43571e24	−1.31504	−0.657520	−	0.753437i	$-0.728395\pi$
$673$	−1.43571e24	−1.31504	−0.657520	+	0.753437i	$0.728395\pi$
$674$	−1.54154e24	−1.39426
$675$	−8.61298e23	−0.769256
$676$	1.33239e24	1.17512
$677$	−4.49928e23	−0.391867	−0.195934	−	0.980617i	$-0.562774\pi$
$677$	−4.49928e23	−0.391867	−0.195934	+	0.980617i	$0.562774\pi$
$678$	4.00391e23	0.344375
$679$	1.71670e24	1.45815
$680$	7.95727e24	6.67481
$681$	−5.99831e23	−0.496911
$682$	3.20877e23	0.262526
$683$	1.89091e24	1.52790	0.763951	−	0.645274i	$-0.223257\pi$
$683$	1.89091e24	1.52790	0.763951	+	0.645274i	$0.223257\pi$
$684$	3.43019e24	2.73742
$685$	7.21989e23	0.569063
$686$	−7.01655e24	−5.46221
$687$	−7.72727e23	−0.594147
$688$	3.74032e23	0.284058
$689$	2.71497e24	2.03658
$690$	7.49418e23	0.555273
$691$	8.37734e23	0.613116	0.306558	−	0.951852i	$-0.400823\pi$
$691$	8.37734e23	0.613116	0.306558	+	0.951852i	$0.400823\pi$
$692$	−3.99620e24	−2.88899
$693$	5.41705e23	0.386839
$694$	3.00490e24	2.11970
$695$	1.10755e23	0.0771775
$696$	−4.01665e23	−0.276494
$697$	−6.33492e23	−0.430787
$698$	−1.51234e24	−1.01596
$699$	−5.43580e23	−0.360751
$700$	−7.01177e24	−4.59721
$701$	1.84498e24	1.19506	0.597530	−	0.801847i	$-0.296149\pi$
$701$	1.84498e24	1.19506	0.597530	+	0.801847i	$0.296149\pi$
$702$	−2.99725e24	−1.91804
$703$	1.70011e24	1.07487
$704$	1.27029e24	0.793480
$705$	8.06562e23	0.497772
$706$	−2.40412e24	−1.46594
$707$	3.64409e24	2.19545
$708$	1.89193e24	1.12622
$709$	1.80381e24	1.06096	0.530478	−	0.847699i	$-0.322012\pi$
$709$	1.80381e24	1.06096	0.530478	+	0.847699i	$0.322012\pi$
$710$	3.42687e24	1.99160
$711$	9.00306e23	0.517010
$712$	−2.33126e24	−1.32285
$713$	−4.13384e23	−0.231789
$714$	4.61164e24	2.55518
$715$	−8.03480e23	−0.439920
$716$	−5.54255e24	−2.99881
$717$	−1.38206e23	−0.0738947
$718$	−1.21372e24	−0.641297
$719$	−1.49991e23	−0.0783192	−0.0391596	−	0.999233i	$-0.512468\pi$
$719$	−1.49991e23	−0.0783192	−0.0391596	+	0.999233i	$0.512468\pi$
$720$	7.14797e24	3.68856
$721$	6.02458e24	3.07239
$722$	2.81689e24	1.41972
$723$	−1.11903e23	−0.0557399
$724$	−6.82645e24	−3.36060
$725$	−3.51600e23	−0.171071
$726$	−1.73580e24	−0.834715
$727$	1.11078e24	0.527942	0.263971	−	0.964531i	$-0.414968\pi$
$727$	1.11078e24	0.527942	0.263971	+	0.964531i	$0.414968\pi$
$728$	−1.52245e25	−7.15199
$729$	1.91662e23	0.0889922
$730$	−5.91574e24	−2.71497
$731$	−2.78449e23	−0.126313
$732$	−1.82458e24	−0.818122
$733$	2.81616e24	1.24817	0.624085	−	0.781357i	$-0.285472\pi$
$733$	2.81616e24	1.24817	0.624085	+	0.781357i	$0.285472\pi$
$734$	−4.94086e24	−2.16464
$735$	−3.78626e24	−1.63971
$736$	−3.49651e24	−1.49683
$737$	−1.04571e23	−0.0442526
$738$	−1.01256e24	−0.423585
$739$	−2.69598e24	−1.11491	−0.557455	−	0.830207i	$-0.688222\pi$
$739$	−2.69598e24	−1.11491	−0.557455	+	0.830207i	$0.688222\pi$
$740$	7.34208e24	3.00158
$741$	−1.83979e24	−0.743556
$742$	−1.52380e25	−6.08829
$743$	2.14872e24	0.848741	0.424371	−	0.905489i	$-0.360495\pi$
$743$	2.14872e24	0.848741	0.424371	+	0.905489i	$0.360495\pi$
$744$	1.97980e24	0.773127
$745$	−4.63216e23	−0.178836
$746$	9.33266e24	3.56226
$747$	−1.10920e24	−0.418588
$748$	−2.85815e24	−1.06640
$749$	−3.57049e24	−1.31714
$750$	2.68585e23	0.0979628
$751$	3.89371e24	1.40418	0.702092	−	0.712086i	$-0.252249\pi$
$751$	3.89371e24	1.40418	0.702092	+	0.712086i	$0.252249\pi$
$752$	−7.32508e24	−2.61193
$753$	2.56817e24	0.905453
$754$	−1.22354e24	−0.426543
$755$	−3.24472e24	−1.11848
$756$	1.22251e25	4.16693
$757$	4.80857e24	1.62069	0.810347	−	0.585950i	$-0.199278\pi$
$757$	4.80857e24	1.62069	0.810347	+	0.585950i	$0.199278\pi$
$758$	−2.39756e24	−0.799062
$759$	−1.67954e23	−0.0553524
$760$	1.78173e25	5.80664
$761$	2.78114e24	0.896301	0.448150	−	0.893958i	$-0.352083\pi$
$761$	2.78114e24	0.896301	0.448150	+	0.893958i	$0.352083\pi$
$762$	−1.32759e24	−0.423105
$763$	−1.00814e25	−3.17733
$764$	1.17929e25	3.67558
$765$	−5.32133e24	−1.64020
$766$	−2.01754e24	−0.615002
$767$	3.59588e24	1.08404
$768$	2.46872e24	0.736041
$769$	−5.74822e24	−1.69496	−0.847481	−	0.530826i	$-0.821882\pi$
$769$	−5.74822e24	−1.69496	−0.847481	+	0.530826i	$0.821882\pi$
$770$	4.50961e24	1.31513
$771$	−1.96755e22	−0.00567497
$772$	−7.35680e24	−2.09866
$773$	−1.48268e24	−0.418334	−0.209167	−	0.977880i	$-0.567075\pi$
$773$	−1.48268e24	−0.418334	−0.209167	+	0.977880i	$0.567075\pi$
$774$	−4.45066e23	−0.124201
$775$	1.73303e24	0.478345
$776$	−9.03322e24	−2.46614
$777$	2.65495e24	0.716932
$778$	7.17027e24	1.91518
$779$	−1.41846e24	−0.374756
$780$	−7.94531e24	−2.07638
$781$	−7.68007e23	−0.198533
$782$	5.06682e24	1.29562
$783$	6.13016e23	0.155059
$784$	3.43862e25	8.60395
$785$	−3.68392e24	−0.911838
$786$	−4.65789e24	−1.14051
$787$	−6.70716e24	−1.62463	−0.812314	−	0.583221i	$-0.801792\pi$
$787$	−6.70716e24	−1.62463	−0.812314	+	0.583221i	$0.801792\pi$
$788$	1.44399e24	0.346012
$789$	1.98750e24	0.471143
$790$	7.49491e24	1.75767
$791$	−3.10394e24	−0.720133
$792$	−2.85043e24	−0.654253
$793$	−3.46788e24	−0.787483
$794$	1.32851e25	2.98463
$795$	−4.96182e24	−1.10286
$796$	−5.92532e24	−1.30302
$797$	4.78958e24	1.04208	0.521041	−	0.853532i	$-0.325544\pi$
$797$	4.78958e24	1.04208	0.521041	+	0.853532i	$0.325544\pi$
$798$	1.03260e25	2.22284
$799$	5.45318e24	1.16145
$800$	1.46584e25	3.08903
$801$	1.55900e24	0.325065
$802$	−3.92432e24	−0.809623
$803$	1.32580e24	0.270641
$804$	−1.03407e24	−0.208868
$805$	−5.80969e24	−1.16115
$806$	6.03081e24	1.19269
$807$	3.34641e24	0.654869
$808$	−1.91750e25	−3.71313
$809$	5.37246e24	1.02946	0.514731	−	0.857352i	$-0.327892\pi$
$809$	5.37246e24	1.02946	0.514731	+	0.857352i	$0.327892\pi$
$810$	−5.42795e24	−1.02923
$811$	3.86635e24	0.725477	0.362738	−	0.931891i	$-0.381842\pi$
$811$	3.86635e24	0.725477	0.362738	+	0.931891i	$0.381842\pi$
$812$	4.99053e24	0.926660
$813$	−1.87154e24	−0.343898
$814$	−2.26424e24	−0.411732
$815$	−8.24906e23	−0.148445
$816$	−1.36378e25	−2.42872
$817$	−6.23480e23	−0.109884
$818$	−1.81100e24	−0.315876
$819$	1.01812e25	1.75746
$820$	−6.12575e24	−1.04651
$821$	8.68968e24	1.46922	0.734610	−	0.678490i	$-0.237365\pi$
$821$	8.68968e24	1.46922	0.734610	+	0.678490i	$0.237365\pi$
$822$	−2.20176e24	−0.368433
$823$	−7.00584e24	−1.16028	−0.580138	−	0.814518i	$-0.697002\pi$
$823$	−7.00584e24	−1.16028	−0.580138	+	0.814518i	$0.697002\pi$
$824$	−3.17011e25	−5.19628
$825$	7.04116e23	0.114231
$826$	−2.01822e25	−3.24070
$827$	−7.81539e24	−1.24209	−0.621046	−	0.783774i	$-0.713292\pi$
$827$	−7.81539e24	−1.24209	−0.621046	+	0.783774i	$0.713292\pi$
$828$	5.88543e24	0.925807
$829$	2.98628e24	0.464961	0.232481	−	0.972601i	$-0.425316\pi$
$829$	2.98628e24	0.464961	0.232481	+	0.972601i	$0.425316\pi$
$830$	−9.23395e24	−1.42306
$831$	3.68193e24	0.561651
$832$	2.38748e25	3.60489
$833$	−2.55989e25	−3.82595
$834$	−3.37754e23	−0.0499676
$835$	1.22020e25	1.78688
$836$	−6.39973e24	−0.927702
$837$	−3.02155e24	−0.433574
$838$	−1.64048e25	−2.33022
$839$	1.15380e25	1.62239	0.811195	−	0.584775i	$-0.198817\pi$
$839$	1.15380e25	1.62239	0.811195	+	0.584775i	$0.198817\pi$
$840$	2.78241e25	3.87299
$841$	2.50246e23	0.0344828
$842$	−5.99066e24	−0.817188
$843$	−5.45891e24	−0.737177
$844$	−1.56771e25	−2.09583
$845$	−4.62816e24	−0.612528
$846$	8.71622e24	1.14204
$847$	1.34564e25	1.74550
$848$	4.50626e25	5.78697
$849$	2.92949e24	0.372457
$850$	−2.12417e25	−2.67379
$851$	2.91700e24	0.363526
$852$	−7.59453e24	−0.937054
$853$	7.69836e24	0.940441	0.470220	−	0.882549i	$-0.344174\pi$
$853$	7.69836e24	0.940441	0.470220	+	0.882549i	$0.344174\pi$
$854$	1.94638e25	2.35416
$855$	−1.19151e25	−1.42687
$856$	1.87878e25	2.22766
$857$	1.93069e24	0.226661	0.113330	−	0.993557i	$-0.463848\pi$
$857$	1.93069e24	0.226661	0.113330	+	0.993557i	$0.463848\pi$
$858$	2.45027e24	0.284821
$859$	−3.46906e24	−0.399273	−0.199636	−	0.979870i	$-0.563976\pi$
$859$	−3.46906e24	−0.399273	−0.199636	+	0.979870i	$0.563976\pi$
$860$	−2.69255e24	−0.306851
$861$	−2.21512e24	−0.249960
$862$	−7.81559e24	−0.873273
$863$	−1.16592e25	−1.28997	−0.644984	−	0.764196i	$-0.723136\pi$
$863$	−1.16592e25	−1.28997	−0.644984	+	0.764196i	$0.723136\pi$
$864$	−2.55571e25	−2.79991
$865$	1.38812e25	1.50587
$866$	1.95573e24	0.210091
$867$	5.74246e24	0.610851
$868$	−2.45982e25	−2.59111
$869$	−1.67971e24	−0.175213
$870$	2.23612e24	0.230984
$871$	−1.96539e24	−0.201046
$872$	5.30480e25	5.37377
$873$	6.04085e24	0.606006
$874$	1.13452e25	1.12711
$875$	−2.08214e24	−0.204853
$876$	1.31103e25	1.27740
$877$	3.28156e24	0.316653	0.158327	−	0.987387i	$-0.449390\pi$
$877$	3.28156e24	0.316653	0.158327	+	0.987387i	$0.449390\pi$
$878$	1.96352e25	1.87643
$879$	−8.55258e23	−0.0809453
$880$	−1.33360e25	−1.25004
$881$	5.35366e24	0.496999	0.248500	−	0.968632i	$-0.420063\pi$
$881$	5.35366e24	0.496999	0.248500	+	0.968632i	$0.420063\pi$
$882$	−4.09167e25	−3.76199
$883$	−3.04687e24	−0.277452	−0.138726	−	0.990331i	$-0.544301\pi$
$883$	−3.04687e24	−0.277452	−0.138726	+	0.990331i	$0.544301\pi$
$884$	−5.37183e25	−4.84483
$885$	−6.57177e24	−0.587036
$886$	2.06993e25	1.83134
$887$	−1.37863e25	−1.20808	−0.604042	−	0.796953i	$-0.706444\pi$
$887$	−1.37863e25	−1.20808	−0.604042	+	0.796953i	$0.706444\pi$
$888$	−1.39702e25	−1.21253
$889$	1.02919e25	0.884768
$890$	1.29784e25	1.10512
$891$	1.21647e24	0.102599
$892$	3.95771e24	0.330631
$893$	1.22103e25	1.01039
$894$	1.41261e24	0.115785
$895$	1.92525e25	1.56312
$896$	−5.57583e25	−4.48427
$897$	−3.15666e24	−0.251474
$898$	−2.02393e25	−1.59715
$899$	−1.23346e24	−0.0964201
$900$	−2.46735e25	−1.91060
$901$	−3.35470e25	−2.57331
$902$	1.88913e24	0.143551
$903$	−9.73648e23	−0.0732919
$904$	1.63328e25	1.21795
$905$	2.37123e25	1.75170
$906$	9.89499e24	0.724146
$907$	−7.92447e24	−0.574524	−0.287262	−	0.957852i	$-0.592745\pi$
$907$	−7.92447e24	−0.574524	−0.287262	+	0.957852i	$0.592745\pi$
$908$	−3.92157e25	−2.81663
$909$	1.28231e25	0.912429
$910$	8.47570e25	5.97481
$911$	−2.52478e24	−0.176326	−0.0881631	−	0.996106i	$-0.528100\pi$
$911$	−2.52478e24	−0.176326	−0.0881631	+	0.996106i	$0.528100\pi$
$912$	−3.05365e25	−2.11282
$913$	2.06945e24	0.141858
$914$	9.16218e24	0.622238
$915$	6.33783e24	0.426443
$916$	−5.05192e25	−3.36779
$917$	3.61093e25	2.38495
$918$	3.70349e25	2.42353
$919$	−1.98228e25	−1.28524	−0.642618	−	0.766187i	$-0.722152\pi$
$919$	−1.98228e25	−1.28524	−0.642618	+	0.766187i	$0.722152\pi$
$920$	3.05704e25	1.96383
$921$	1.04516e25	0.665239
$922$	3.10170e25	1.95608
$923$	−1.44345e25	−0.901961
$924$	−9.99405e24	−0.618771
$925$	−1.22290e25	−0.750213
$926$	1.86988e25	1.13664
$927$	2.11997e25	1.27688
$928$	−1.04329e25	−0.622657
$929$	−3.96531e24	−0.234500	−0.117250	−	0.993102i	$-0.537408\pi$
$929$	−3.96531e24	−0.234500	−0.117250	+	0.993102i	$0.537408\pi$
$930$	−1.10218e25	−0.645874
$931$	−5.73190e25	−3.32833
$932$	−3.55381e25	−2.04484
$933$	−3.36425e24	−0.191820
$934$	7.31869e24	0.413509
$935$	9.92804e24	0.555859
$936$	−5.35731e25	−2.97237
$937$	3.49400e25	1.92104	0.960521	−	0.278209i	$-0.0897407\pi$
$937$	3.49400e25	1.92104	0.960521	+	0.278209i	$0.0897407\pi$
$938$	1.10310e25	0.601020
$939$	−9.10774e24	−0.491760
$940$	5.27313e25	2.82151
$941$	−9.30551e24	−0.493433	−0.246717	−	0.969088i	$-0.579352\pi$
$941$	−9.30551e24	−0.493433	−0.246717	+	0.969088i	$0.579352\pi$
$942$	1.12344e25	0.590359
$943$	−2.43376e24	−0.126744
$944$	5.96839e25	3.08031
$945$	−4.24648e25	−2.17199
$946$	8.30362e23	0.0420914
$947$	−2.38956e24	−0.120045	−0.0600223	−	0.998197i	$-0.519117\pi$
$947$	−2.38956e24	−0.120045	−0.0600223	+	0.998197i	$0.519117\pi$
$948$	−1.66100e25	−0.826987
$949$	2.49180e25	1.22956
$950$	−4.75625e25	−2.32602
$951$	−1.11991e25	−0.542813
$952$	1.88119e26	9.03688
$953$	3.02564e25	1.44055	0.720274	−	0.693689i	$-0.244016\pi$
$953$	3.02564e25	1.44055	0.720274	+	0.693689i	$0.244016\pi$
$954$	−5.36206e25	−2.53029
$955$	−4.09635e25	−1.91588
$956$	−9.03558e24	−0.418855
$957$	−5.01144e23	−0.0230256
$958$	−3.55446e25	−1.61870
$959$	1.70686e25	0.770442
$960$	−4.36332e25	−1.95214
$961$	−1.64704e25	−0.730392
$962$	−4.25558e25	−1.87056
$963$	−1.25641e25	−0.547404
$964$	−7.31597e24	−0.315949
$965$	2.55545e25	1.09392
$966$	1.77171e25	0.751773
$967$	2.12960e24	0.0895720	0.0447860	−	0.998997i	$-0.485739\pi$
$967$	2.12960e24	0.0895720	0.0447860	+	0.998997i	$0.485739\pi$
$968$	−7.08070e25	−2.95213
$969$	2.27330e25	0.939517
$970$	5.02891e25	2.06022
$971$	1.04332e25	0.423695	0.211847	−	0.977303i	$-0.432052\pi$
$971$	1.04332e25	0.423695	0.211847	+	0.977303i	$0.432052\pi$
$972$	6.71872e25	2.70473
$973$	2.61836e24	0.104489
$974$	6.47879e25	2.56297
$975$	1.32337e25	0.518969
$976$	−5.75592e25	−2.23765
$977$	−1.93550e25	−0.745916	−0.372958	−	0.927848i	$-0.621656\pi$
$977$	−1.93550e25	−0.745916	−0.372958	+	0.927848i	$0.621656\pi$
$978$	2.51561e24	0.0961088
$979$	−2.90864e24	−0.110163
$980$	−2.47537e26	−9.29435
$981$	−3.54752e25	−1.32050
$982$	6.39059e25	2.35827
$983$	4.41117e25	1.61380	0.806898	−	0.590690i	$-0.201144\pi$
$983$	4.41117e25	1.61380	0.806898	+	0.590690i	$0.201144\pi$
$984$	1.16559e25	0.422753
$985$	−5.01582e24	−0.180357
$986$	1.51185e25	0.538956
$987$	1.90680e25	0.673923
$988$	−1.20281e26	−4.21468
$989$	−1.06975e24	−0.0371632
$990$	1.58687e25	0.546566
$991$	−2.59046e25	−0.884607	−0.442304	−	0.896865i	$-0.645839\pi$
$991$	−2.59046e25	−0.884607	−0.442304	+	0.896865i	$0.645839\pi$
$992$	5.14237e25	1.74106
$993$	8.42916e24	0.282954
$994$	8.10151e25	2.69638
$995$	2.05821e25	0.679193
$996$	2.04640e25	0.669555
$997$	−2.55254e25	−0.828063	−0.414032	−	0.910262i	$-0.635880\pi$
$997$	−2.55254e25	−0.828063	−0.414032	+	0.910262i	$0.635880\pi$
$998$	−3.54719e25	−1.14097
$999$	2.13212e25	0.679995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.18	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+692.544 q^{2} +5331.24 q^{3} +348545. q^{4} -1.21070e6 q^{5} +3.69212e6 q^{6} -2.86223e7 q^{7} +1.50609e8 q^{8} -1.00718e8 q^{9} +O(q^{10})\)	\(q+692.544 q^{2} +5331.24 q^{3} +348545. q^{4} -1.21070e6 q^{5} +3.69212e6 q^{6} -2.86223e7 q^{7} +1.50609e8 q^{8} -1.00718e8 q^{9} -8.38462e8 q^{10} +1.87910e8 q^{11} +1.85817e9 q^{12} +3.53173e9 q^{13} -1.98222e10 q^{14} -6.45453e9 q^{15} +5.86191e10 q^{16} -4.36391e10 q^{17} -6.97516e10 q^{18} -9.77131e10 q^{19} -4.21983e11 q^{20} -1.52592e11 q^{21} +1.30136e11 q^{22} -1.67653e11 q^{23} +8.02934e11 q^{24} +7.02854e11 q^{25} +2.44588e12 q^{26} -1.22543e12 q^{27} -9.97615e12 q^{28} -5.00246e11 q^{29} -4.47004e12 q^{30} +2.46570e12 q^{31} +2.08556e13 q^{32} +1.00180e12 q^{33} -3.02220e13 q^{34} +3.46530e13 q^{35} -3.51047e13 q^{36} -1.73990e13 q^{37} -6.76706e13 q^{38} +1.88285e13 q^{39} -1.82343e14 q^{40} +1.45166e13 q^{41} -1.05677e14 q^{42} +6.38072e12 q^{43} +6.54952e13 q^{44} +1.21939e14 q^{45} -1.16107e14 q^{46} -1.24961e14 q^{47} +3.12512e14 q^{48} +5.86605e14 q^{49} +4.86757e14 q^{50} -2.32651e14 q^{51} +1.23097e15 q^{52} +7.68735e14 q^{53} -8.48663e14 q^{54} -2.27503e14 q^{55} -4.31078e15 q^{56} -5.20932e14 q^{57} -3.46442e14 q^{58} +1.01816e15 q^{59} -2.24969e15 q^{60} -9.81919e14 q^{61} +1.70761e15 q^{62} +2.88278e15 q^{63} +6.76009e15 q^{64} -4.27587e15 q^{65} +6.93787e14 q^{66} -5.56495e14 q^{67} -1.52102e16 q^{68} -8.93800e14 q^{69} +2.39987e16 q^{70} -4.08709e15 q^{71} -1.51691e16 q^{72} +7.05546e15 q^{73} -1.20496e16 q^{74} +3.74708e15 q^{75} -3.40574e16 q^{76} -5.37843e15 q^{77} +1.30396e16 q^{78} -8.93888e15 q^{79} -7.09701e16 q^{80} +6.47369e15 q^{81} +1.00534e16 q^{82} +1.10130e16 q^{83} -5.31852e16 q^{84} +5.28339e16 q^{85} +4.41893e15 q^{86} -2.66693e15 q^{87} +2.83011e16 q^{88} -1.54789e16 q^{89} +8.44483e16 q^{90} -1.01086e17 q^{91} -5.84347e16 q^{92} +1.31453e16 q^{93} -8.65407e16 q^{94} +1.18301e17 q^{95} +1.11186e17 q^{96} -5.99778e16 q^{97} +4.06250e17 q^{98} -1.89260e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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