LMFDB - Embedded newform 29.18.a.a.1.4

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			1.4
Root			$-483.296$ 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)

$f(q)$	$=$	$q-483.296 q^{2} +19868.0 q^{3} +102503. q^{4} -300011. q^{5} -9.60214e6 q^{6} -1.05230e7 q^{7} +1.38073e7 q^{8} +2.65598e8 q^{9} +O(q^{10})$	\(q-483.296 q^{2} +19868.0 q^{3} +102503. q^{4} -300011. q^{5} -9.60214e6 q^{6} -1.05230e7 q^{7} +1.38073e7 q^{8} +2.65598e8 q^{9} +1.44994e8 q^{10} -3.33645e8 q^{11} +2.03653e9 q^{12} +2.39045e9 q^{13} +5.08572e9 q^{14} -5.96063e9 q^{15} -2.01083e10 q^{16} -3.71058e10 q^{17} -1.28363e11 q^{18} -5.58824e9 q^{19} -3.07520e10 q^{20} -2.09071e11 q^{21} +1.61249e11 q^{22} +2.74159e11 q^{23} +2.74324e11 q^{24} -6.72933e11 q^{25} -1.15530e12 q^{26} +2.71115e12 q^{27} -1.07864e12 q^{28} -5.00246e11 q^{29} +2.88075e12 q^{30} +1.59488e12 q^{31} +7.90850e12 q^{32} -6.62887e12 q^{33} +1.79331e13 q^{34} +3.15702e12 q^{35} +2.72246e13 q^{36} -2.65515e13 q^{37} +2.70077e12 q^{38} +4.74936e13 q^{39} -4.14234e12 q^{40} +5.75464e12 q^{41} +1.01043e14 q^{42} +9.28847e13 q^{43} -3.41996e13 q^{44} -7.96824e13 q^{45} -1.32500e14 q^{46} -3.14738e13 q^{47} -3.99512e14 q^{48} -1.21897e14 q^{49} +3.25226e14 q^{50} -7.37219e14 q^{51} +2.45028e14 q^{52} -5.46152e14 q^{53} -1.31029e15 q^{54} +1.00097e14 q^{55} -1.45294e14 q^{56} -1.11027e14 q^{57} +2.41767e14 q^{58} +1.21679e15 q^{59} -6.10982e14 q^{60} -2.14080e15 q^{61} -7.70801e14 q^{62} -2.79489e15 q^{63} -1.18651e15 q^{64} -7.17162e14 q^{65} +3.20370e15 q^{66} +5.99624e14 q^{67} -3.80345e15 q^{68} +5.44700e15 q^{69} -1.52577e15 q^{70} -1.60583e15 q^{71} +3.66719e15 q^{72} -6.06470e14 q^{73} +1.28322e16 q^{74} -1.33698e16 q^{75} -5.72811e14 q^{76} +3.51095e15 q^{77} -2.29534e16 q^{78} +3.90894e15 q^{79} +6.03271e15 q^{80} +1.95658e16 q^{81} -2.78119e15 q^{82} -3.77326e16 q^{83} -2.14304e16 q^{84} +1.11321e16 q^{85} -4.48908e16 q^{86} -9.93891e15 q^{87} -4.60674e15 q^{88} -5.40993e16 q^{89} +3.85102e16 q^{90} -2.51547e16 q^{91} +2.81021e16 q^{92} +3.16872e16 q^{93} +1.52112e16 q^{94} +1.67653e15 q^{95} +1.57126e17 q^{96} +2.26579e16 q^{97} +5.89123e16 q^{98} -8.86155e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−483.296	−1.33493	−0.667465	−	0.744642i	$-0.732620\pi$
$2$	−483.296	−1.33493	−0.667465	+	0.744642i	$0.732620\pi$
$3$	19868.0	1.74833	0.874166	−	0.485627i	$-0.161409\pi$
$3$	19868.0	1.74833	0.874166	+	0.485627i	$0.161409\pi$
$4$	102503.	0.782036
$5$	−300011.	−0.343473	−0.171736	−	0.985143i	$-0.554938\pi$
$5$	−300011.	−0.343473	−0.171736	+	0.985143i	$0.554938\pi$
$6$	−9.60214e6	−2.33390
$7$	−1.05230e7	−0.689932	−0.344966	−	0.938615i	$-0.612110\pi$
$7$	−1.05230e7	−0.689932	−0.344966	+	0.938615i	$0.612110\pi$
$8$	1.38073e7	0.290967
$9$	2.65598e8	2.05667
$10$	1.44994e8	0.458512
$11$	−3.33645e8	−0.469296	−0.234648	−	0.972080i	$-0.575394\pi$
$11$	−3.33645e8	−0.469296	−0.234648	+	0.972080i	$0.575394\pi$
$12$	2.03653e9	1.36726
$13$	2.39045e9	0.812758	0.406379	−	0.913705i	$-0.366791\pi$
$13$	2.39045e9	0.812758	0.406379	+	0.913705i	$0.366791\pi$
$14$	5.08572e9	0.921010
$15$	−5.96063e9	−0.600504
$16$	−2.01083e10	−1.17046
$17$	−3.71058e10	−1.29011	−0.645054	−	0.764137i	$-0.723165\pi$
$17$	−3.71058e10	−1.29011	−0.645054	+	0.764137i	$0.723165\pi$
$18$	−1.28363e11	−2.74550
$19$	−5.58824e9	−0.0754865	−0.0377433	−	0.999287i	$-0.512017\pi$
$19$	−5.58824e9	−0.0754865	−0.0377433	+	0.999287i	$0.512017\pi$
$20$	−3.07520e10	−0.268608
$21$	−2.09071e11	−1.20623
$22$	1.61249e11	0.626477
$23$	2.74159e11	0.729989	0.364995	−	0.931010i	$-0.381071\pi$
$23$	2.74159e11	0.729989	0.364995	+	0.931010i	$0.381071\pi$
$24$	2.74324e11	0.508707
$25$	−6.72933e11	−0.882027
$26$	−1.15530e12	−1.08497
$27$	2.71115e12	1.84740
$28$	−1.07864e12	−0.539551
$29$	−5.00246e11	−0.185695
$29$	−5.00246e11	−0.185695
$30$	2.88075e12	0.801631
$31$	1.59488e12	0.335857	0.167929	−	0.985799i	$-0.446292\pi$
$31$	1.59488e12	0.335857	0.167929	+	0.985799i	$0.446292\pi$
$32$	7.90850e12	1.27151
$33$	−6.62887e12	−0.820485
$34$	1.79331e13	1.72220
$35$	3.15702e12	0.236973
$36$	2.72246e13	1.60839
$37$	−2.65515e13	−1.24272	−0.621362	−	0.783524i	$-0.713420\pi$
$37$	−2.65515e13	−1.24272	−0.621362	+	0.783524i	$0.713420\pi$
$38$	2.70077e12	0.100769
$39$	4.74936e13	1.42097
$40$	−4.14234e12	−0.0999392
$41$	5.75464e12	0.112553	0.0562763	−	0.998415i	$-0.482077\pi$
$41$	5.75464e12	0.112553	0.0562763	+	0.998415i	$0.482077\pi$
$42$	1.01043e14	1.61023
$43$	9.28847e13	1.21189	0.605944	−	0.795507i	$-0.292796\pi$
$43$	9.28847e13	1.21189	0.605944	+	0.795507i	$0.292796\pi$
$44$	−3.41996e13	−0.367006
$45$	−7.96824e13	−0.706409
$46$	−1.32500e14	−0.974484
$47$	−3.14738e13	−0.192805	−0.0964023	−	0.995342i	$-0.530734\pi$
$47$	−3.14738e13	−0.192805	−0.0964023	+	0.995342i	$0.530734\pi$
$48$	−3.99512e14	−2.04635
$49$	−1.21897e14	−0.523994
$50$	3.25226e14	1.17744
$51$	−7.37219e14	−2.25554
$52$	2.45028e14	0.635606
$53$	−5.46152e14	−1.20495	−0.602474	−	0.798138i	$-0.705818\pi$
$53$	−5.46152e14	−1.20495	−0.602474	+	0.798138i	$0.705818\pi$
$54$	−1.31029e15	−2.46615
$55$	1.00097e14	0.161190
$56$	−1.45294e14	−0.200747
$57$	−1.11027e14	−0.131976
$58$	2.41767e14	0.247890
$59$	1.21679e15	1.07888	0.539442	−	0.842023i	$-0.318635\pi$
$59$	1.21679e15	1.07888	0.539442	+	0.842023i	$0.318635\pi$
$60$	−6.10982e14	−0.469616
$61$	−2.14080e15	−1.42979	−0.714895	−	0.699232i	$-0.753525\pi$
$61$	−2.14080e15	−1.42979	−0.714895	+	0.699232i	$0.753525\pi$
$62$	−7.70801e14	−0.448346
$63$	−2.79489e15	−1.41896
$64$	−1.18651e15	−0.526918
$65$	−7.17162e14	−0.279160
$66$	3.20370e15	1.09529
$67$	5.99624e14	0.180403	0.0902014	−	0.995924i	$-0.471249\pi$
$67$	5.99624e14	0.180403	0.0902014	+	0.995924i	$0.471249\pi$
$68$	−3.80345e15	−1.00891
$69$	5.44700e15	1.27626
$70$	−1.52577e15	−0.316342
$71$	−1.60583e15	−0.295124	−0.147562	−	0.989053i	$-0.547143\pi$
$71$	−1.60583e15	−0.295124	−0.147562	+	0.989053i	$0.547143\pi$
$72$	3.66719e15	0.598422
$73$	−6.06470e14	−0.0880167	−0.0440083	−	0.999031i	$-0.514013\pi$
$73$	−6.06470e14	−0.0880167	−0.0440083	+	0.999031i	$0.514013\pi$
$74$	1.28322e16	1.65895
$75$	−1.33698e16	−1.54208
$76$	−5.72811e14	−0.0590331
$77$	3.51095e15	0.323782
$78$	−2.29534e16	−1.89690
$79$	3.90894e15	0.289887	0.144943	−	0.989440i	$-0.453700\pi$
$79$	3.90894e15	0.289887	0.144943	+	0.989440i	$0.453700\pi$
$80$	6.03271e15	0.402020
$81$	1.95658e16	1.17321
$82$	−2.78119e15	−0.150250
$83$	−3.77326e16	−1.83888	−0.919440	−	0.393231i	$-0.871357\pi$
$83$	−3.77326e16	−1.83888	−0.919440	+	0.393231i	$0.871357\pi$
$84$	−2.14304e16	−0.943315
$85$	1.11321e16	0.443117
$86$	−4.48908e16	−1.61778
$87$	−9.93891e15	−0.324657
$88$	−4.60674e15	−0.136550
$89$	−5.40993e16	−1.45672	−0.728360	−	0.685194i	$-0.759717\pi$
$89$	−5.40993e16	−1.45672	−0.728360	+	0.685194i	$0.759717\pi$
$90$	3.85102e16	0.943005
$91$	−2.51547e16	−0.560748
$92$	2.81021e16	0.570878
$93$	3.16872e16	0.587190
$94$	1.52112e16	0.257381
$95$	1.67653e15	0.0259276
$96$	1.57126e17	2.22302
$97$	2.26579e16	0.293535	0.146768	−	0.989171i	$-0.453113\pi$
$97$	2.26579e16	0.293535	0.146768	+	0.989171i	$0.453113\pi$
$98$	5.89123e16	0.699495
$99$	−8.86155e16	−0.965185
$100$	−6.89776e16	−0.689776
$101$	−1.24143e17	−1.14075	−0.570377	−	0.821383i	$-0.693203\pi$
$101$	−1.24143e17	−1.14075	−0.570377	+	0.821383i	$0.693203\pi$
$102$	3.56295e17	3.01098
$103$	−1.23746e17	−0.962534	−0.481267	−	0.876574i	$-0.659823\pi$
$103$	−1.23746e17	−0.962534	−0.481267	+	0.876574i	$0.659823\pi$
$104$	3.30057e16	0.236486
$105$	6.27237e16	0.414307
$106$	2.63953e17	1.60852
$107$	−3.03818e17	−1.70943	−0.854716	−	0.519096i	$-0.826269\pi$
$107$	−3.03818e17	−1.70943	−0.854716	+	0.519096i	$0.826269\pi$
$108$	2.77901e17	1.44474
$109$	−3.30583e17	−1.58911	−0.794557	−	0.607190i	$-0.792297\pi$
$109$	−3.30583e17	−1.58911	−0.794557	+	0.607190i	$0.792297\pi$
$110$	−4.83766e16	−0.215178
$111$	−5.27526e17	−2.17270
$112$	2.11599e17	0.807535
$113$	3.47835e17	1.23085	0.615426	−	0.788195i	$-0.288984\pi$
$113$	3.47835e17	1.23085	0.615426	+	0.788195i	$0.288984\pi$
$114$	5.36590e16	0.176178
$115$	−8.22508e16	−0.250731
$116$	−5.12767e16	−0.145220
$117$	6.34900e17	1.67157
$118$	−5.88071e17	−1.44023
$119$	3.90464e17	0.890086
$120$	−8.23001e16	−0.174727
$121$	−3.94128e17	−0.779761
$122$	1.03464e18	1.90867
$123$	1.14333e17	0.196779
$124$	1.63480e17	0.262652
$125$	4.30777e17	0.646425
$126$	1.35076e18	1.89421
$127$	7.26696e16	0.0952843	0.0476421	−	0.998864i	$-0.484829\pi$
$127$	7.26696e16	0.0952843	0.0476421	+	0.998864i	$0.484829\pi$
$128$	−4.63146e17	−0.568111
$129$	1.84544e18	2.11878
$130$	3.46601e17	0.372659
$131$	1.05479e18	1.06257	0.531287	−	0.847192i	$-0.321709\pi$
$131$	1.05479e18	1.06257	0.531287	+	0.847192i	$0.321709\pi$
$132$	−6.79479e17	−0.641649
$133$	5.88050e16	0.0520806
$134$	−2.89796e17	−0.240825
$135$	−8.13376e17	−0.634533
$136$	−5.12331e17	−0.375379
$137$	−1.31173e18	−0.903066	−0.451533	−	0.892254i	$-0.649123\pi$
$137$	−1.31173e18	−0.903066	−0.451533	+	0.892254i	$0.649123\pi$
$138$	−2.63252e18	−1.70372
$139$	−1.02425e18	−0.623419	−0.311709	−	0.950177i	$-0.600902\pi$
$139$	−1.02425e18	−0.623419	−0.311709	+	0.950177i	$0.600902\pi$
$140$	3.23604e17	0.185321
$141$	−6.25323e17	−0.337087
$142$	7.76093e17	0.393970
$143$	−7.97562e17	−0.381424
$144$	−5.34072e18	−2.40724
$145$	1.50079e17	0.0637813
$146$	2.93104e17	0.117496
$147$	−2.42185e18	−0.916116
$148$	−2.72161e18	−0.971855
$149$	4.52829e18	1.52704	0.763521	−	0.645784i	$-0.223469\pi$
$149$	4.52829e18	1.52704	0.763521	+	0.645784i	$0.223469\pi$
$150$	6.46159e18	2.05856
$151$	−9.02907e17	−0.271856	−0.135928	−	0.990719i	$-0.543402\pi$
$151$	−9.02907e17	−0.271856	−0.135928	+	0.990719i	$0.543402\pi$
$152$	−7.71585e16	−0.0219641
$153$	−9.85523e18	−2.65332
$154$	−1.69683e18	−0.432226
$155$	−4.78483e17	−0.115358
$156$	4.86823e18	1.11125
$157$	−5.03432e18	−1.08841	−0.544206	−	0.838951i	$-0.683169\pi$
$157$	−5.03432e18	−1.08841	−0.544206	+	0.838951i	$0.683169\pi$
$158$	−1.88917e18	−0.386978
$159$	−1.08510e19	−2.10665
$160$	−2.37264e18	−0.436728
$161$	−2.88498e18	−0.503643
$162$	−9.45609e18	−1.56615
$163$	−2.18412e18	−0.343306	−0.171653	−	0.985157i	$-0.554911\pi$
$163$	−2.18412e18	−0.343306	−0.171653	+	0.985157i	$0.554911\pi$
$164$	5.89868e17	0.0880201
$165$	1.98873e18	0.281814
$166$	1.82360e19	2.45477
$167$	1.47149e19	1.88220	0.941101	−	0.338126i	$-0.109793\pi$
$167$	1.47149e19	1.88220	0.941101	+	0.338126i	$0.109793\pi$
$168$	−2.88671e18	−0.350973
$169$	−2.93616e18	−0.339424
$170$	−5.38012e18	−0.591529
$171$	−1.48423e18	−0.155251
$172$	9.52096e18	0.947740
$173$	1.83712e19	1.74079	0.870396	−	0.492353i	$-0.163863\pi$
$173$	1.83712e19	1.74079	0.870396	+	0.492353i	$0.163863\pi$
$174$	4.80343e18	0.433394
$175$	7.08127e18	0.608538
$176$	6.70903e18	0.549290
$177$	2.41753e19	1.88625
$178$	2.61460e19	1.94462
$179$	1.61952e19	1.14851	0.574257	−	0.818675i	$-0.305291\pi$
$179$	1.61952e19	1.14851	0.574257	+	0.818675i	$0.305291\pi$
$180$	−8.16768e18	−0.552437
$181$	−1.14805e19	−0.740785	−0.370393	−	0.928875i	$-0.620777\pi$
$181$	−1.14805e19	−0.740785	−0.370393	+	0.928875i	$0.620777\pi$
$182$	1.21572e19	0.748559
$183$	−4.25334e19	−2.49975
$184$	3.78540e18	0.212403
$185$	7.96575e18	0.426842
$186$	−1.53143e19	−0.783857
$187$	1.23802e19	0.605442
$188$	−3.22616e18	−0.150780
$189$	−2.85295e19	−1.27458
$190$	−8.10262e17	−0.0346114
$191$	9.26399e18	0.378455	0.189228	−	0.981933i	$-0.439402\pi$
$191$	9.26399e18	0.378455	0.189228	+	0.981933i	$0.439402\pi$
$192$	−2.35737e19	−0.921228
$193$	−4.50794e19	−1.68555	−0.842773	−	0.538269i	$-0.819079\pi$
$193$	−4.50794e19	−1.68555	−0.842773	+	0.538269i	$0.819079\pi$
$194$	−1.09505e19	−0.391849
$195$	−1.42486e19	−0.488065
$196$	−1.24948e19	−0.409782
$197$	−1.13290e19	−0.355820	−0.177910	−	0.984047i	$-0.556934\pi$
$197$	−1.13290e19	−0.355820	−0.177910	+	0.984047i	$0.556934\pi$
$198$	4.28275e19	1.28845
$199$	1.89210e19	0.545373	0.272686	−	0.962103i	$-0.412088\pi$
$199$	1.89210e19	0.545373	0.272686	+	0.962103i	$0.412088\pi$
$200$	−9.29138e18	−0.256641
$201$	1.19133e19	0.315404
$202$	5.99980e19	1.52282
$203$	5.26409e18	0.128117
$204$	−7.55671e19	−1.76391
$205$	−1.72646e18	−0.0386587
$206$	5.98061e19	1.28492
$207$	7.28162e19	1.50134
$208$	−4.80679e19	−0.951298
$209$	1.86449e18	0.0354255
$210$	−3.03141e19	−0.553071
$211$	1.94470e19	0.340763	0.170381	−	0.985378i	$-0.445500\pi$
$211$	1.94470e19	0.340763	0.170381	+	0.985378i	$0.445500\pi$
$212$	−5.59822e19	−0.942313
$213$	−3.19047e19	−0.515975
$214$	1.46834e20	2.28197
$215$	−2.78664e19	−0.416250
$216$	3.74337e19	0.537534
$217$	−1.67830e19	−0.231719
$218$	1.59769e20	2.12135
$219$	−1.20494e19	−0.153882
$220$	1.02603e19	0.126057
$221$	−8.86996e19	−1.04855
$222$	2.54951e20	2.90039
$223$	−1.76267e19	−0.193010	−0.0965048	−	0.995333i	$-0.530766\pi$
$223$	−1.76267e19	−0.193010	−0.0965048	+	0.995333i	$0.530766\pi$
$224$	−8.32211e19	−0.877254
$225$	−1.78730e20	−1.81403
$226$	−1.68107e20	−1.64310
$227$	8.39919e19	0.790711	0.395355	−	0.918528i	$-0.370621\pi$
$227$	8.39919e19	0.790711	0.395355	+	0.918528i	$0.370621\pi$
$228$	−1.13806e19	−0.103210
$229$	1.76637e19	0.154341	0.0771704	−	0.997018i	$-0.475411\pi$
$229$	1.76637e19	0.154341	0.0771704	+	0.997018i	$0.475411\pi$
$230$	3.97515e19	0.334709
$231$	6.97556e19	0.566079
$232$	−6.90705e18	−0.0540312
$233$	2.60305e19	0.196317	0.0981584	−	0.995171i	$-0.468705\pi$
$233$	2.60305e19	0.196317	0.0981584	+	0.995171i	$0.468705\pi$
$234$	−3.06844e20	−2.23143
$235$	9.44249e18	0.0662231
$236$	1.24725e20	0.843725
$237$	7.76628e19	0.506818
$238$	−1.88710e20	−1.18820
$239$	−1.83193e20	−1.11308	−0.556540	−	0.830821i	$-0.687872\pi$
$239$	−1.83193e20	−1.11308	−0.556540	+	0.830821i	$0.687872\pi$
$240$	1.19858e20	0.702864
$241$	2.24968e20	1.27343	0.636716	−	0.771098i	$-0.280292\pi$
$241$	2.24968e20	1.27343	0.636716	+	0.771098i	$0.280292\pi$
$242$	1.90480e20	1.04093
$243$	3.86160e19	0.203757
$244$	−2.19438e20	−1.11815
$245$	3.65704e19	0.179978
$246$	−5.52568e19	−0.262686
$247$	−1.33584e19	−0.0613523
$248$	2.20210e19	0.0977234
$249$	−7.49673e20	−3.21497
$250$	−2.08193e20	−0.862931
$251$	2.41892e20	0.969159	0.484579	−	0.874747i	$-0.338973\pi$
$251$	2.41892e20	0.969159	0.484579	+	0.874747i	$0.338973\pi$
$252$	−2.86485e20	−1.10968
$253$	−9.14719e19	−0.342581
$254$	−3.51209e19	−0.127198
$255$	2.21174e20	0.774715
$256$	3.79355e20	1.28531
$257$	3.65608e20	1.19835	0.599176	−	0.800617i	$-0.295495\pi$
$257$	3.65608e20	1.19835	0.599176	+	0.800617i	$0.295495\pi$
$258$	−8.91892e20	−2.82843
$259$	2.79402e20	0.857395
$260$	−7.35112e19	−0.218313
$261$	−1.32865e20	−0.381913
$262$	−5.09775e20	−1.41846
$263$	−3.32508e20	−0.895734	−0.447867	−	0.894100i	$-0.647816\pi$
$263$	−3.32508e20	−0.895734	−0.447867	+	0.894100i	$0.647816\pi$
$264$	−9.15267e19	−0.238734
$265$	1.63852e20	0.413867
$266$	−2.84202e19	−0.0695239
$267$	−1.07485e21	−2.54683
$268$	6.14633e19	0.141081
$269$	−6.81391e19	−0.151531	−0.0757656	−	0.997126i	$-0.524140\pi$
$269$	−6.81391e19	−0.151531	−0.0757656	+	0.997126i	$0.524140\pi$
$270$	3.93101e20	0.847056
$271$	6.15028e20	1.28427	0.642135	−	0.766592i	$-0.278049\pi$
$271$	6.15028e20	1.28427	0.642135	+	0.766592i	$0.278049\pi$
$272$	7.46134e20	1.51001
$273$	−4.99775e20	−0.980374
$274$	6.33954e20	1.20553
$275$	2.24521e20	0.413931
$276$	5.58334e20	0.998084
$277$	−3.10395e20	−0.538068	−0.269034	−	0.963131i	$-0.586704\pi$
$277$	−3.10395e20	−0.538068	−0.269034	+	0.963131i	$0.586704\pi$
$278$	4.95016e20	0.832220
$279$	4.23599e20	0.690747
$280$	4.35899e19	0.0689513
$281$	1.28540e21	1.97259	0.986293	−	0.165004i	$-0.0527636\pi$
$281$	1.28540e21	1.97259	0.986293	+	0.165004i	$0.0527636\pi$
$282$	3.02216e20	0.449987
$283$	−5.30349e20	−0.766261	−0.383131	−	0.923694i	$-0.625154\pi$
$283$	−5.30349e20	−0.766261	−0.383131	+	0.923694i	$0.625154\pi$
$284$	−1.64603e20	−0.230797
$285$	3.33094e19	0.0453300
$286$	3.85459e20	0.509174
$287$	−6.05561e19	−0.0776536
$288$	2.10048e21	2.61507
$289$	5.49600e20	0.664377
$290$	−7.25328e19	−0.0851435
$291$	4.50168e20	0.513197
$292$	−6.21650e19	−0.0688322
$293$	−8.63321e20	−0.928533	−0.464267	−	0.885695i	$-0.653682\pi$
$293$	−8.63321e20	−0.928533	−0.464267	+	0.885695i	$0.653682\pi$
$294$	1.17047e21	1.22295
$295$	−3.65051e20	−0.370567
$296$	−3.66605e20	−0.361592
$297$	−9.04562e20	−0.866979
$298$	−2.18850e21	−2.03849
$299$	6.55365e20	0.593305
$300$	−1.37045e21	−1.20596
$301$	−9.77426e20	−0.836120
$302$	4.36371e20	0.362908
$303$	−2.46648e21	−1.99442
$304$	1.12370e20	0.0883536
$305$	6.42263e20	0.491093
$306$	4.76299e21	3.54199
$307$	7.48147e20	0.541141	0.270571	−	0.962700i	$-0.412788\pi$
$307$	7.48147e20	0.541141	0.270571	+	0.962700i	$0.412788\pi$
$308$	3.59882e20	0.253209
$309$	−2.45860e21	−1.68283
$310$	2.31249e20	0.153995
$311$	−4.35748e20	−0.282340	−0.141170	−	0.989985i	$-0.545086\pi$
$311$	−4.35748e20	−0.282340	−0.141170	+	0.989985i	$0.545086\pi$
$312$	6.55758e20	0.413456
$313$	−2.98877e21	−1.83386	−0.916930	−	0.399048i	$-0.869341\pi$
$313$	−2.98877e21	−1.83386	−0.916930	+	0.399048i	$0.869341\pi$
$314$	2.43307e21	1.45295
$315$	8.38498e20	0.487374
$316$	4.00678e20	0.226702
$317$	3.16053e21	1.74083	0.870416	−	0.492317i	$-0.163850\pi$
$317$	3.16053e21	1.74083	0.870416	+	0.492317i	$0.163850\pi$
$318$	5.24422e21	2.81223
$319$	1.66905e20	0.0871461
$320$	3.55967e20	0.180982
$321$	−6.03627e21	−2.98866
$322$	1.39430e21	0.672327
$323$	2.07356e20	0.0973857
$324$	2.00556e21	0.917492
$325$	−1.60861e21	−0.716875
$326$	1.05558e21	0.458289
$327$	−6.56803e21	−2.77830
$328$	7.94560e19	0.0327491
$329$	3.31199e20	0.133022
$330$	−9.61147e20	−0.376202
$331$	−1.35128e21	−0.515476	−0.257738	−	0.966215i	$-0.582977\pi$
$331$	−1.35128e21	−0.515476	−0.257738	+	0.966215i	$0.582977\pi$
$332$	−3.86771e21	−1.43807
$333$	−7.05204e21	−2.55587
$334$	−7.11163e21	−2.51261
$335$	−1.79894e20	−0.0619634
$336$	4.20406e21	1.41184
$337$	−5.59047e20	−0.183060	−0.0915301	−	0.995802i	$-0.529176\pi$
$337$	−5.59047e20	−0.183060	−0.0915301	+	0.995802i	$0.529176\pi$
$338$	1.41903e21	0.453107
$339$	6.91079e21	2.15194
$340$	1.14108e21	0.346533
$341$	−5.32125e20	−0.157617
$342$	7.17321e20	0.207249
$343$	3.73069e21	1.05145
$344$	1.28249e21	0.352619
$345$	−1.63416e21	−0.438362
$346$	−8.87875e21	−2.32383
$347$	1.65092e21	0.421623	0.210812	−	0.977527i	$-0.432389\pi$
$347$	1.65092e21	0.421623	0.210812	+	0.977527i	$0.432389\pi$
$348$	−1.01877e21	−0.253893
$349$	7.35940e21	1.78989	0.894944	−	0.446178i	$-0.147215\pi$
$349$	7.35940e21	1.78989	0.894944	+	0.446178i	$0.147215\pi$
$350$	−3.42235e21	−0.812355
$351$	6.48088e21	1.50149
$352$	−2.63863e21	−0.596714
$353$	−8.51349e21	−1.87942	−0.939708	−	0.341979i	$-0.888903\pi$
$353$	−8.51349e21	−1.87942	−0.939708	+	0.341979i	$0.888903\pi$
$354$	−1.16838e22	−2.51801
$355$	4.81768e20	0.101367
$356$	−5.54534e21	−1.13921
$357$	7.75775e21	1.55617
$358$	−7.82709e21	−1.53319
$359$	9.23849e21	1.76725	0.883626	−	0.468194i	$-0.155095\pi$
$359$	9.23849e21	1.76725	0.883626	+	0.468194i	$0.155095\pi$
$360$	−1.10020e21	−0.205542
$361$	−5.44916e21	−0.994302
$362$	5.54847e21	0.988896
$363$	−7.83055e21	−1.36328
$364$	−2.57843e21	−0.438525
$365$	1.81948e20	0.0302313
$366$	2.05562e22	3.33698
$367$	−1.01182e21	−0.160488	−0.0802442	−	0.996775i	$-0.525570\pi$
$367$	−1.01182e21	−0.160488	−0.0802442	+	0.996775i	$0.525570\pi$
$368$	−5.51287e21	−0.854420
$369$	1.52842e21	0.231483
$370$	−3.84981e21	−0.569803
$371$	5.74716e21	0.831333
$372$	3.24803e21	0.459204
$373$	1.12008e21	0.154783	0.0773913	−	0.997001i	$-0.475341\pi$
$373$	1.12008e21	0.154783	0.0773913	+	0.997001i	$0.475341\pi$
$374$	−5.98328e21	−0.808222
$375$	8.55870e21	1.13017
$376$	−4.34568e20	−0.0560998
$377$	−1.19581e21	−0.150925
$378$	1.37882e22	1.70148
$379$	−1.16495e22	−1.40564	−0.702818	−	0.711370i	$-0.748075\pi$
$379$	−1.16495e22	−1.40564	−0.702818	+	0.711370i	$0.748075\pi$
$380$	1.71850e20	0.0202763
$381$	1.44380e21	0.166589
$382$	−4.47725e21	−0.505211
$383$	1.22320e22	1.34992	0.674961	−	0.737853i	$-0.264160\pi$
$383$	1.22320e22	1.34992	0.674961	+	0.737853i	$0.264160\pi$
$384$	−9.20179e21	−0.993246
$385$	−1.05332e21	−0.111210
$386$	2.17867e22	2.25009
$387$	2.46700e22	2.49245
$388$	2.32250e21	0.229555
$389$	−7.44259e21	−0.719702	−0.359851	−	0.933010i	$-0.617172\pi$
$389$	−7.44259e21	−0.719702	−0.359851	+	0.933010i	$0.617172\pi$
$390$	6.88629e21	0.651532
$391$	−1.01729e22	−0.941764
$392$	−1.68307e21	−0.152465
$393$	2.09565e22	1.85773
$394$	5.47527e21	0.474994
$395$	−1.17272e21	−0.0995682
$396$	−9.08335e21	−0.754809
$397$	−4.16905e21	−0.339092	−0.169546	−	0.985522i	$-0.554230\pi$
$397$	−4.16905e21	−0.339092	−0.169546	+	0.985522i	$0.554230\pi$
$398$	−9.14446e21	−0.728034
$399$	1.16834e21	0.0910541
$400$	1.35315e22	1.03237
$401$	1.17444e22	0.877212	0.438606	−	0.898680i	$-0.355472\pi$
$401$	1.17444e22	0.877212	0.438606	+	0.898680i	$0.355472\pi$
$402$	−5.75767e21	−0.421042
$403$	3.81249e21	0.272971
$404$	−1.27251e22	−0.892110
$405$	−5.86997e21	−0.402966
$406$	−2.54411e21	−0.171027
$407$	8.85878e21	0.583205
$408$	−1.01790e22	−0.656287
$409$	1.53113e22	0.966864	0.483432	−	0.875382i	$-0.339390\pi$
$409$	1.53113e22	0.966864	0.483432	+	0.875382i	$0.339390\pi$
$410$	8.34389e20	0.0516066
$411$	−2.60615e22	−1.57886
$412$	−1.26844e22	−0.752736
$413$	−1.28043e22	−0.744356
$414$	−3.51918e22	−2.00419
$415$	1.13202e22	0.631605
$416$	1.89049e22	1.03343
$417$	−2.03498e22	−1.08994
$418$	−9.01100e20	−0.0472906
$419$	−1.02234e22	−0.525745	−0.262873	−	0.964831i	$-0.584670\pi$
$419$	−1.02234e22	−0.525745	−0.262873	+	0.964831i	$0.584670\pi$
$420$	6.42936e21	0.324003
$421$	2.67783e21	0.132247	0.0661235	−	0.997811i	$-0.478937\pi$
$421$	2.67783e21	0.132247	0.0661235	+	0.997811i	$0.478937\pi$
$422$	−9.39867e21	−0.454894
$423$	−8.35939e21	−0.396535
$424$	−7.54088e21	−0.350600
$425$	2.49697e22	1.13791
$426$	1.54194e22	0.688790
$427$	2.25276e22	0.986457
$428$	−3.11423e22	−1.33684
$429$	−1.58460e22	−0.666856
$430$	1.34677e22	0.555665
$431$	3.09230e22	1.25091	0.625453	−	0.780262i	$-0.284914\pi$
$431$	3.09230e22	1.25091	0.625453	+	0.780262i	$0.284914\pi$
$432$	−5.45166e22	−2.16231
$433$	−1.33504e22	−0.519216	−0.259608	−	0.965714i	$-0.583593\pi$
$433$	−1.33504e22	−0.519216	−0.259608	+	0.965714i	$0.583593\pi$
$434$	8.11114e21	0.309328
$435$	2.98178e21	0.111511
$436$	−3.38857e22	−1.24274
$437$	−1.53207e21	−0.0551043
$438$	5.82341e21	0.205422
$439$	4.49435e22	1.55496	0.777478	−	0.628910i	$-0.216499\pi$
$439$	4.49435e22	1.55496	0.777478	+	0.628910i	$0.216499\pi$
$440$	1.38207e21	0.0469011
$441$	−3.23756e22	−1.07768
$442$	4.28682e22	1.39973
$443$	3.45696e22	1.10729	0.553647	−	0.832752i	$-0.313236\pi$
$443$	3.45696e22	1.10729	0.553647	+	0.832752i	$0.313236\pi$
$444$	−5.40730e22	−1.69912
$445$	1.62304e22	0.500344
$446$	8.51890e21	0.257654
$447$	8.99681e22	2.66978
$448$	1.24857e22	0.363537
$449$	2.85633e22	0.816046	0.408023	−	0.912972i	$-0.366218\pi$
$449$	2.85633e22	0.816046	0.408023	+	0.912972i	$0.366218\pi$
$450$	8.63794e22	2.42161
$451$	−1.92001e21	−0.0528205
$452$	3.56541e22	0.962570
$453$	−1.79390e22	−0.475294
$454$	−4.05929e22	−1.05554
$455$	7.54669e21	0.192602
$456$	−1.53299e21	−0.0384005
$457$	5.77530e22	1.42000	0.709998	−	0.704204i	$-0.248696\pi$
$457$	5.77530e22	1.42000	0.709998	+	0.704204i	$0.248696\pi$
$458$	−8.53681e21	−0.206034
$459$	−1.00599e23	−2.38335
$460$	−8.43095e21	−0.196081
$461$	−4.65144e22	−1.06201	−0.531006	−	0.847368i	$-0.678186\pi$
$461$	−4.65144e22	−1.06201	−0.531006	+	0.847368i	$0.678186\pi$
$462$	−3.37126e22	−0.755675
$463$	4.08660e22	0.899340	0.449670	−	0.893195i	$-0.351542\pi$
$463$	4.08660e22	0.899340	0.449670	+	0.893195i	$0.351542\pi$
$464$	1.00591e22	0.217348
$465$	−9.50651e21	−0.201684
$466$	−1.25804e22	−0.262069
$467$	−7.35170e22	−1.50382	−0.751908	−	0.659269i	$-0.770866\pi$
$467$	−7.35170e22	−1.50382	−0.751908	+	0.659269i	$0.770866\pi$
$468$	6.50791e22	1.30723
$469$	−6.30985e21	−0.124466
$470$	−4.56352e21	−0.0884032
$471$	−1.00022e23	−1.90291
$472$	1.68006e22	0.313920
$473$	−3.09905e22	−0.568734
$474$	−3.75341e22	−0.676567
$475$	3.76051e21	0.0665811
$476$	4.00237e22	0.696079
$477$	−1.45057e23	−2.47818
$478$	8.85364e22	1.48588
$479$	−1.40645e22	−0.231886	−0.115943	−	0.993256i	$-0.536989\pi$
$479$	−1.40645e22	−0.231886	−0.115943	+	0.993256i	$0.536989\pi$
$480$	−4.71396e22	−0.763546
$481$	−6.34701e22	−1.01003
$482$	−1.08726e23	−1.69994
$483$	−5.73188e22	−0.880535
$484$	−4.03993e22	−0.609801
$485$	−6.79763e21	−0.100821
$486$	−1.86629e22	−0.272002
$487$	−2.07478e22	−0.297150	−0.148575	−	0.988901i	$-0.547469\pi$
$487$	−2.07478e22	−0.297150	−0.148575	+	0.988901i	$0.547469\pi$
$488$	−2.95586e22	−0.416021
$489$	−4.33941e22	−0.600213
$490$	−1.76743e22	−0.240257
$491$	−2.47141e22	−0.330181	−0.165090	−	0.986278i	$-0.552792\pi$
$491$	−2.47141e22	−0.330181	−0.165090	+	0.986278i	$0.552792\pi$
$492$	1.17195e22	0.153888
$493$	1.85620e22	0.239567
$494$	6.45607e21	0.0819010
$495$	2.65856e22	0.331515
$496$	−3.20704e22	−0.393106
$497$	1.68982e22	0.203615
$498$	3.62314e23	4.29176
$499$	−7.15008e22	−0.832638	−0.416319	−	0.909219i	$-0.636680\pi$
$499$	−7.15008e22	−0.832638	−0.416319	+	0.909219i	$0.636680\pi$
$500$	4.41560e22	0.505527
$501$	2.92355e23	3.29071
$502$	−1.16905e23	−1.29376
$503$	1.80252e23	1.96134	0.980669	−	0.195676i	$-0.0626901\pi$
$503$	1.80252e23	1.96134	0.980669	+	0.195676i	$0.0626901\pi$
$504$	−3.85899e22	−0.412870
$505$	3.72444e22	0.391818
$506$	4.42080e22	0.457321
$507$	−5.83356e22	−0.593425
$508$	7.44885e21	0.0745157
$509$	−1.36071e22	−0.133864	−0.0669321	−	0.997758i	$-0.521321\pi$
$509$	−1.36071e22	−0.133864	−0.0669321	+	0.997758i	$0.521321\pi$
$510$	−1.06892e23	−1.03419
$511$	6.38188e21	0.0607255
$512$	−1.22635e23	−1.14768
$513$	−1.51506e22	−0.139454
$514$	−1.76697e23	−1.59972
$515$	3.71253e22	0.330604
$516$	1.89163e23	1.65696
$517$	1.05011e22	0.0904825
$518$	−1.35034e23	−1.14456
$519$	3.65000e23	3.04348
$520$	−9.90207e21	−0.0812264
$521$	−1.97298e23	−1.59222	−0.796110	−	0.605152i	$-0.793112\pi$
$521$	−1.97298e23	−1.59222	−0.796110	+	0.605152i	$0.793112\pi$
$522$	6.42129e22	0.509827
$523$	−1.69196e23	−1.32168	−0.660840	−	0.750527i	$-0.729800\pi$
$523$	−1.69196e23	−1.32168	−0.660840	+	0.750527i	$0.729800\pi$
$524$	1.08119e23	0.830970
$525$	1.40691e23	1.06393
$526$	1.60700e23	1.19574
$527$	−5.91795e22	−0.433292
$528$	1.33295e23	0.960342
$529$	−6.58867e22	−0.467116
$530$	−7.91888e22	−0.552483
$531$	3.23178e23	2.21890
$532$	6.02769e21	0.0407289
$533$	1.37562e22	0.0914780
$534$	5.19468e23	3.39984
$535$	9.11488e22	0.587143
$536$	8.27919e21	0.0524913
$537$	3.21767e23	2.00799
$538$	3.29313e22	0.202283
$539$	4.06703e22	0.245908
$540$	−8.33734e22	−0.496227
$541$	2.64343e23	1.54879	0.774393	−	0.632705i	$-0.218055\pi$
$541$	2.64343e23	1.54879	0.774393	+	0.632705i	$0.218055\pi$
$542$	−2.97241e23	−1.71441
$543$	−2.28095e23	−1.29514
$544$	−2.93451e23	−1.64038
$545$	9.91785e22	0.545817
$546$	2.41539e23	1.30873
$547$	−2.16373e23	−1.15428	−0.577140	−	0.816645i	$-0.695831\pi$
$547$	−2.16373e23	−1.15428	−0.577140	+	0.816645i	$0.695831\pi$
$548$	−1.34456e23	−0.706230
$549$	−5.68592e23	−2.94060
$550$	−1.08510e23	−0.552569
$551$	2.79550e21	0.0140175
$552$	7.52084e22	0.371351
$553$	−4.11337e22	−0.200002
$554$	1.50013e23	0.718282
$555$	1.58264e23	0.746261
$556$	−1.04989e23	−0.487536
$557$	1.92378e23	0.879803	0.439902	−	0.898046i	$-0.355013\pi$
$557$	1.92378e23	0.879803	0.439902	+	0.898046i	$0.355013\pi$
$558$	−2.04723e23	−0.922098
$559$	2.22036e23	0.984972
$560$	−6.34822e22	−0.277366
$561$	2.45969e23	1.05851
$562$	−6.21231e23	−2.63326
$563$	7.69399e22	0.321241	0.160620	−	0.987016i	$-0.448651\pi$
$563$	7.69399e22	0.321241	0.160620	+	0.987016i	$0.448651\pi$
$564$	−6.40974e22	−0.263614
$565$	−1.04354e23	−0.422764
$566$	2.56315e23	1.02290
$567$	−2.05891e23	−0.809435
$568$	−2.21722e22	−0.0858713
$569$	3.70381e22	0.141317	0.0706585	−	0.997501i	$-0.477490\pi$
$569$	3.70381e22	0.141317	0.0706585	+	0.997501i	$0.477490\pi$
$570$	−1.60983e22	−0.0605123
$571$	−3.94973e23	−1.46272	−0.731359	−	0.681992i	$-0.761114\pi$
$571$	−3.94973e23	−1.46272	−0.731359	+	0.681992i	$0.761114\pi$
$572$	−8.17525e22	−0.298287
$573$	1.84057e23	0.661666
$574$	2.92665e22	0.103662
$575$	−1.84491e23	−0.643870
$576$	−3.15136e23	−1.08369
$577$	−1.84408e23	−0.624864	−0.312432	−	0.949940i	$-0.601144\pi$
$577$	−1.84408e23	−0.624864	−0.312432	+	0.949940i	$0.601144\pi$
$578$	−2.65619e23	−0.886896
$579$	−8.95638e23	−2.94690
$580$	1.53836e22	0.0498792
$581$	3.97060e23	1.26870
$582$	−2.17564e23	−0.685082
$583$	1.82221e23	0.565478
$584$	−8.37371e21	−0.0256100
$585$	−1.90477e23	−0.574140
$586$	4.17239e23	1.23953
$587$	−2.41072e23	−0.705868	−0.352934	−	0.935648i	$-0.614816\pi$
$587$	−2.41072e23	−0.705868	−0.352934	+	0.935648i	$0.614816\pi$
$588$	−2.48247e23	−0.716435
$589$	−8.91260e21	−0.0253527
$590$	1.76428e23	0.494681
$591$	−2.25085e23	−0.622091
$592$	5.33905e23	1.45455
$593$	−2.14784e23	−0.576816	−0.288408	−	0.957508i	$-0.593126\pi$
$593$	−2.14784e23	−0.576816	−0.288408	+	0.957508i	$0.593126\pi$
$594$	4.37171e23	1.15736
$595$	−1.17144e23	−0.305720
$596$	4.64163e23	1.19420
$597$	3.75923e23	0.953493
$598$	−3.16735e23	−0.792020
$599$	−5.21308e23	−1.28519	−0.642594	−	0.766207i	$-0.722142\pi$
$599$	−5.21308e23	−1.28519	−0.642594	+	0.766207i	$0.722142\pi$
$600$	−1.84601e23	−0.448693
$601$	3.89846e23	0.934244	0.467122	−	0.884193i	$-0.345291\pi$
$601$	3.89846e23	0.934244	0.467122	+	0.884193i	$0.345291\pi$
$602$	4.72386e23	1.11616
$603$	1.59259e23	0.371028
$604$	−9.25506e22	−0.212601
$605$	1.18243e23	0.267827
$606$	1.19204e24	2.66240
$607$	−6.08218e23	−1.33954	−0.669769	−	0.742569i	$-0.733607\pi$
$607$	−6.08218e23	−1.33954	−0.669769	+	0.742569i	$0.733607\pi$
$608$	−4.41946e22	−0.0959818
$609$	1.04587e23	0.223991
$610$	−3.10403e23	−0.655575
$611$	−7.52366e22	−0.156704
$612$	−1.01019e24	−2.07499
$613$	2.14767e23	0.435065	0.217532	−	0.976053i	$-0.430199\pi$
$613$	2.14767e23	0.435065	0.217532	+	0.976053i	$0.430199\pi$
$614$	−3.61576e23	−0.722385
$615$	−3.43013e22	−0.0675883
$616$	4.84767e22	0.0942100
$617$	−5.92651e23	−1.13599	−0.567996	−	0.823032i	$-0.692281\pi$
$617$	−5.92651e23	−1.13599	−0.567996	+	0.823032i	$0.692281\pi$
$618$	1.18823e24	2.24646
$619$	−9.41696e23	−1.75606	−0.878032	−	0.478602i	$-0.841144\pi$
$619$	−9.41696e23	−1.75606	−0.878032	+	0.478602i	$0.841144\pi$
$620$	−4.90459e22	−0.0902139
$621$	7.43288e23	1.34859
$622$	2.10595e23	0.376904
$623$	5.69287e23	1.00504
$624$	−9.55014e23	−1.66319
$625$	3.84169e23	0.659997
$626$	1.44446e24	2.44807
$627$	3.70437e22	0.0619356
$628$	−5.16033e23	−0.851177
$629$	9.85215e23	1.60325
$630$	−4.05243e23	−0.650610
$631$	−8.19677e23	−1.29835	−0.649177	−	0.760637i	$-0.724887\pi$
$631$	−8.19677e23	−1.29835	−0.649177	+	0.760637i	$0.724887\pi$
$632$	5.39718e22	0.0843475
$633$	3.86374e23	0.595767
$634$	−1.52747e24	−2.32389
$635$	−2.18017e22	−0.0327275
$636$	−1.11226e24	−1.64748
$637$	−2.91389e23	−0.425881
$638$	−8.06644e22	−0.116334
$639$	−4.26506e23	−0.606972
$640$	1.38949e23	0.195130
$641$	−6.49742e23	−0.900425	−0.450212	−	0.892922i	$-0.648652\pi$
$641$	−6.49742e23	−0.900425	−0.450212	+	0.892922i	$0.648652\pi$
$642$	2.91730e24	3.98964
$643$	7.70131e23	1.03937	0.519687	−	0.854357i	$-0.326049\pi$
$643$	7.70131e23	1.03937	0.519687	+	0.854357i	$0.326049\pi$
$644$	−2.95719e23	−0.393867
$645$	−5.53651e23	−0.727744
$646$	−1.00214e23	−0.130003
$647$	2.53577e23	0.324656	0.162328	−	0.986737i	$-0.448100\pi$
$647$	2.53577e23	0.324656	0.162328	+	0.986737i	$0.448100\pi$
$648$	2.70151e23	0.341365
$649$	−4.05977e23	−0.506316
$650$	7.77436e23	0.956977
$651$	−3.33444e23	−0.405121
$652$	−2.23879e23	−0.268478
$653$	2.05600e23	0.243367	0.121684	−	0.992569i	$-0.461171\pi$
$653$	2.05600e23	0.243367	0.121684	+	0.992569i	$0.461171\pi$
$654$	3.17430e24	3.70883
$655$	−3.16448e23	−0.364965
$656$	−1.15716e23	−0.131738
$657$	−1.61077e23	−0.181021
$658$	−1.60067e23	−0.177575
$659$	4.75471e23	0.520713	0.260356	−	0.965513i	$-0.416160\pi$
$659$	4.75471e23	0.520713	0.260356	+	0.965513i	$0.416160\pi$
$660$	2.03851e23	0.220389
$661$	1.28500e24	1.37148	0.685741	−	0.727845i	$-0.259478\pi$
$661$	1.28500e24	1.37148	0.685741	+	0.727845i	$0.259478\pi$
$662$	6.53070e23	0.688124
$663$	−1.76229e24	−1.83321
$664$	−5.20985e23	−0.535053
$665$	−1.76422e22	−0.0178882
$666$	3.40822e24	3.41190
$667$	−1.37147e23	−0.135556
$668$	1.50832e24	1.47195
$669$	−3.50207e23	−0.337445
$670$	8.69420e22	0.0827168
$671$	7.14266e23	0.670994
$672$	−1.65344e24	−1.53373
$673$	−1.67748e24	−1.53649	−0.768243	−	0.640158i	$-0.778869\pi$
$673$	−1.67748e24	−1.53649	−0.768243	+	0.640158i	$0.778869\pi$
$674$	2.70185e23	0.244373
$675$	−1.82442e24	−1.62946
$676$	−3.00965e23	−0.265441
$677$	−1.54349e23	−0.134431	−0.0672157	−	0.997738i	$-0.521412\pi$
$677$	−1.54349e23	−0.134431	−0.0672157	+	0.997738i	$0.521412\pi$
$678$	−3.33995e24	−2.87269
$679$	−2.38429e23	−0.202519
$680$	1.53705e23	0.128932
$681$	1.66875e24	1.38243
$682$	2.57174e23	0.210407
$683$	1.85540e24	1.49921	0.749603	−	0.661887i	$-0.230244\pi$
$683$	1.85540e24	1.49921	0.749603	+	0.661887i	$0.230244\pi$
$684$	−1.52138e23	−0.121411
$685$	3.93533e23	0.310178
$686$	−1.80303e24	−1.40361
$687$	3.50943e23	0.269839
$688$	−1.86775e24	−1.41846
$689$	−1.30555e24	−0.979332
$690$	7.89784e23	0.585182
$691$	−2.75614e22	−0.0201715	−0.0100857	−	0.999949i	$-0.503210\pi$
$691$	−2.75614e22	−0.0201715	−0.0100857	+	0.999949i	$0.503210\pi$
$692$	1.88311e24	1.36136
$693$	9.32501e23	0.665912
$694$	−7.97881e23	−0.562837
$695$	3.07286e23	0.214127
$696$	−1.37229e23	−0.0944645
$697$	−2.13530e23	−0.145205
$698$	−3.55677e24	−2.38937
$699$	5.17175e23	0.343227
$700$	7.25851e23	0.475899
$701$	−5.28699e23	−0.342457	−0.171228	−	0.985231i	$-0.554774\pi$
$701$	−5.28699e23	−0.342457	−0.171228	+	0.985231i	$0.554774\pi$
$702$	−3.13218e24	−2.00439
$703$	1.48376e23	0.0938089
$704$	3.95874e23	0.247280
$705$	1.87604e23	0.115780
$706$	4.11454e24	2.50889
$707$	1.30636e24	0.787042
$708$	2.47804e24	1.47511
$709$	−3.39444e23	−0.199653	−0.0998263	−	0.995005i	$-0.531829\pi$
$709$	−3.39444e23	−0.199653	−0.0998263	+	0.995005i	$0.531829\pi$
$710$	−2.32836e23	−0.135318
$711$	1.03821e24	0.596200
$712$	−7.46965e23	−0.423858
$713$	4.37253e23	0.245172
$714$	−3.74929e24	−2.07737
$715$	2.39277e23	0.131009
$716$	1.66006e24	0.898180
$717$	−3.63968e24	−1.94604
$718$	−4.46493e24	−2.35916
$719$	2.86419e24	1.49557	0.747783	−	0.663943i	$-0.231118\pi$
$719$	2.86419e24	1.49557	0.747783	+	0.663943i	$0.231118\pi$
$720$	1.60228e24	0.826820
$721$	1.30218e24	0.664083
$722$	2.63356e24	1.32732
$723$	4.46967e24	2.22638
$724$	−1.17678e24	−0.579320
$725$	3.36632e23	0.163788
$726$	3.78447e24	1.81988
$727$	−1.30072e24	−0.618216	−0.309108	−	0.951027i	$-0.600030\pi$
$727$	−1.30072e24	−0.618216	−0.309108	+	0.951027i	$0.600030\pi$
$728$	−3.47319e23	−0.163159
$729$	−1.75951e24	−0.816975
$730$	−8.79346e22	−0.0403567
$731$	−3.44656e24	−1.56347
$732$	−4.35980e24	−1.95489
$733$	−4.23988e24	−1.87919	−0.939593	−	0.342295i	$-0.888796\pi$
$733$	−4.23988e24	−1.87919	−0.939593	+	0.342295i	$0.888796\pi$
$734$	4.89011e23	0.214241
$735$	7.26582e23	0.314661
$736$	2.16819e24	0.928188
$737$	−2.00062e23	−0.0846623
$738$	−7.38680e23	−0.309013
$739$	−1.19578e24	−0.494510	−0.247255	−	0.968950i	$-0.579529\pi$
$739$	−1.19578e24	−0.494510	−0.247255	+	0.968950i	$0.579529\pi$
$740$	8.16513e23	0.333805
$741$	−2.65405e23	−0.107264
$742$	−2.77758e24	−1.10977
$743$	8.73902e23	0.345190	0.172595	−	0.984993i	$-0.444785\pi$
$743$	8.73902e23	0.345190	0.172595	+	0.984993i	$0.444785\pi$
$744$	4.37515e23	0.170853
$745$	−1.35854e24	−0.524497
$746$	−5.41328e23	−0.206624
$747$	−1.00217e25	−3.78196
$748$	1.26900e24	0.473477
$749$	3.19708e24	1.17939
$750$	−4.13638e24	−1.50869
$751$	−7.38808e22	−0.0266435	−0.0133218	−	0.999911i	$-0.504241\pi$
$751$	−7.38808e22	−0.0266435	−0.0133218	+	0.999911i	$0.504241\pi$
$752$	6.32884e23	0.225669
$753$	4.80592e24	1.69441
$754$	5.77933e23	0.201475
$755$	2.70882e23	0.0933751
$756$	−2.92435e24	−0.996769
$757$	3.16508e24	1.06677	0.533383	−	0.845874i	$-0.320920\pi$
$757$	3.16508e24	1.06677	0.533383	+	0.845874i	$0.320920\pi$
$758$	5.63014e24	1.87642
$759$	−1.81737e24	−0.598945
$760$	2.31484e22	0.00754406
$761$	−3.36254e24	−1.08367	−0.541835	−	0.840485i	$-0.682270\pi$
$761$	−3.36254e24	−1.08367	−0.541835	+	0.840485i	$0.682270\pi$
$762$	−6.97783e23	−0.222384
$763$	3.47872e24	1.09638
$764$	9.49587e23	0.295966
$765$	2.95668e24	0.911343
$766$	−5.91169e24	−1.80205
$767$	2.90868e24	0.876872
$768$	7.53704e24	2.24714
$769$	3.45866e24	1.01984	0.509922	−	0.860221i	$-0.329674\pi$
$769$	3.45866e24	1.01984	0.509922	+	0.860221i	$0.329674\pi$
$770$	5.09067e23	0.148458
$771$	7.26392e24	2.09512
$772$	−4.62077e24	−1.31816
$773$	3.92947e24	1.10868	0.554342	−	0.832289i	$-0.312970\pi$
$773$	3.92947e24	1.10868	0.554342	+	0.832289i	$0.312970\pi$
$774$	−1.19229e25	−3.32724
$775$	−1.07325e24	−0.296235
$776$	3.12845e23	0.0854091
$777$	5.55116e24	1.49901
$778$	3.59697e24	0.960750
$779$	−3.21583e22	−0.00849620
$780$	−1.46052e24	−0.381684
$781$	5.35778e23	0.138500
$782$	4.91652e24	1.25719
$783$	−1.35624e24	−0.343054
$784$	2.45114e24	0.613312
$785$	1.51035e24	0.373840
$786$	−1.01282e25	−2.47994
$787$	6.06056e24	1.46801	0.734003	−	0.679147i	$-0.237650\pi$
$787$	6.06056e24	1.46801	0.734003	+	0.679147i	$0.237650\pi$
$788$	−1.16126e24	−0.278264
$789$	−6.60629e24	−1.56604
$790$	5.66773e23	0.132916
$791$	−3.66026e24	−0.849204
$792$	−1.22354e24	−0.280837
$793$	−5.11747e24	−1.16207
$794$	2.01488e24	0.452664
$795$	3.25541e24	0.723577
$796$	1.93946e24	0.426501
$797$	−4.49531e24	−0.978057	−0.489028	−	0.872268i	$-0.662649\pi$
$797$	−4.49531e24	−0.978057	−0.489028	+	0.872268i	$0.662649\pi$
$798$	−5.64654e23	−0.121551
$799$	1.16786e24	0.248739
$800$	−5.32189e24	−1.12150
$801$	−1.43687e25	−2.99599
$802$	−5.67603e24	−1.17102
$803$	2.02346e23	0.0413059
$804$	1.22115e24	0.246657
$805$	8.65525e23	0.172988
$806$	−1.84256e24	−0.364397
$807$	−1.35379e24	−0.264927
$808$	−1.71408e24	−0.331922
$809$	2.90929e24	0.557474	0.278737	−	0.960367i	$-0.410084\pi$
$809$	2.90929e24	0.557474	0.278737	+	0.960367i	$0.410084\pi$
$810$	2.83693e24	0.537931
$811$	−3.36765e24	−0.631902	−0.315951	−	0.948775i	$-0.602324\pi$
$811$	−3.36765e24	−0.631902	−0.315951	+	0.948775i	$0.602324\pi$
$812$	5.39585e23	0.100192
$813$	1.22194e25	2.24533
$814$	−4.28141e24	−0.778538
$815$	6.55260e23	0.117916
$816$	1.48242e25	2.64001
$817$	−5.19062e23	−0.0914812
$818$	−7.39991e24	−1.29069
$819$	−6.68105e24	−1.15327
$820$	−1.76967e23	−0.0302325
$821$	−2.74451e24	−0.464032	−0.232016	−	0.972712i	$-0.574532\pi$
$821$	−2.74451e24	−0.464032	−0.232016	+	0.972712i	$0.574532\pi$
$822$	1.25954e25	2.10767
$823$	1.10777e25	1.83464	0.917318	−	0.398156i	$-0.130350\pi$
$823$	1.10777e25	1.83464	0.917318	+	0.398156i	$0.130350\pi$
$824$	−1.70860e24	−0.280066
$825$	4.46078e24	0.723690
$826$	6.18827e24	0.993663
$827$	3.30322e24	0.524977	0.262489	−	0.964935i	$-0.415457\pi$
$827$	3.30322e24	0.524977	0.262489	+	0.964935i	$0.415457\pi$
$828$	7.46388e24	1.17410
$829$	9.19970e24	1.43239	0.716193	−	0.697902i	$-0.245883\pi$
$829$	9.19970e24	1.43239	0.716193	+	0.697902i	$0.245883\pi$
$830$	−5.47101e24	−0.843147
$831$	−6.16694e24	−0.940721
$832$	−2.83630e24	−0.428257
$833$	4.52308e24	0.676008
$834$	9.83498e24	1.45500
$835$	−4.41462e24	−0.646485
$836$	1.91116e23	0.0277040
$837$	4.32398e24	0.620464
$838$	4.94092e24	0.701832
$839$	−1.09643e25	−1.54172	−0.770860	−	0.637005i	$-0.780173\pi$
$839$	−1.09643e25	−1.54172	−0.770860	+	0.637005i	$0.780173\pi$
$840$	8.66044e23	0.120550
$841$	2.50246e23	0.0344828
$842$	−1.29419e24	−0.176540
$843$	2.55384e25	3.44874
$844$	1.99338e24	0.266489
$845$	8.80879e23	0.116583
$846$	4.04006e24	0.529346
$847$	4.14741e24	0.537982
$848$	1.09822e25	1.41034
$849$	−1.05370e25	−1.33968
$850$	−1.20678e25	−1.51903
$851$	−7.27935e24	−0.907175
$852$	−3.27033e24	−0.403511
$853$	1.14862e25	1.40317	0.701585	−	0.712586i	$-0.252476\pi$
$853$	1.14862e25	1.40317	0.701585	+	0.712586i	$0.252476\pi$
$854$	−1.08875e25	−1.31685
$855$	4.45284e23	0.0533243
$856$	−4.19491e24	−0.497388
$857$	2.31803e24	0.272134	0.136067	−	0.990700i	$-0.456554\pi$
$857$	2.31803e24	0.272134	0.136067	+	0.990700i	$0.456554\pi$
$858$	7.65830e24	0.890206
$859$	1.32318e24	0.152292	0.0761458	−	0.997097i	$-0.475739\pi$
$859$	1.32318e24	0.152292	0.0761458	+	0.997097i	$0.475739\pi$
$860$	−2.85639e24	−0.325523
$861$	−1.20313e24	−0.135764
$862$	−1.49450e25	−1.66987
$863$	3.81911e24	0.422543	0.211271	−	0.977427i	$-0.432240\pi$
$863$	3.81911e24	0.422543	0.211271	+	0.977427i	$0.432240\pi$
$864$	2.14411e25	2.34899
$865$	−5.51158e24	−0.597914
$866$	6.45221e24	0.693117
$867$	1.09195e25	1.16155
$868$	−1.72030e24	−0.181212
$869$	−1.30420e24	−0.136043
$870$	−1.44108e24	−0.148859
$871$	1.43337e24	0.146624
$872$	−4.56445e24	−0.462380
$873$	6.01791e24	0.603704
$874$	7.40442e23	0.0735604
$875$	−4.53307e24	−0.445989
$876$	−1.23510e24	−0.120342
$877$	−1.62063e25	−1.56382	−0.781911	−	0.623390i	$-0.785755\pi$
$877$	−1.62063e25	−1.56382	−0.781911	+	0.623390i	$0.785755\pi$
$878$	−2.17210e25	−2.07576
$879$	−1.71525e25	−1.62338
$880$	−2.01278e24	−0.188666
$881$	−1.61631e25	−1.50048	−0.750240	−	0.661165i	$-0.770062\pi$
$881$	−1.61631e25	−1.50048	−0.750240	+	0.661165i	$0.770062\pi$
$882$	1.56470e25	1.43863
$883$	5.94276e24	0.541155	0.270578	−	0.962698i	$-0.412785\pi$
$883$	5.94276e24	0.541155	0.270578	+	0.962698i	$0.412785\pi$
$884$	−9.09197e24	−0.820000
$885$	−7.25285e24	−0.647874
$886$	−1.67073e25	−1.47816
$887$	2.29096e24	0.200755	0.100377	−	0.994949i	$-0.467995\pi$
$887$	2.29096e24	0.200755	0.100377	+	0.994949i	$0.467995\pi$
$888$	−7.28371e24	−0.632183
$889$	−7.64702e23	−0.0657397
$890$	−7.84407e24	−0.667923
$891$	−6.52805e24	−0.550583
$892$	−1.80679e24	−0.150940
$893$	1.75883e23	0.0145542
$894$	−4.34812e25	−3.56396
$895$	−4.85875e24	−0.394483
$896$	4.87368e24	0.391958
$897$	1.30208e25	1.03729
$898$	−1.38045e25	−1.08936
$899$	−7.97835e23	−0.0623671
$900$	−1.83203e25	−1.41864
$901$	2.02654e25	1.55451
$902$	9.27931e23	0.0705116
$903$	−1.94195e25	−1.46182
$904$	4.80265e24	0.358137
$905$	3.44427e24	0.254439
$906$	8.66983e24	0.634484
$907$	2.34214e25	1.69805	0.849026	−	0.528351i	$-0.177190\pi$
$907$	2.34214e25	1.69805	0.849026	+	0.528351i	$0.177190\pi$
$908$	8.60942e24	0.618364
$909$	−3.29723e25	−2.34615
$910$	−3.64729e24	−0.257109
$911$	−1.57508e25	−1.10001	−0.550004	−	0.835162i	$-0.685374\pi$
$911$	−1.57508e25	−1.10001	−0.550004	+	0.835162i	$0.685374\pi$
$912$	2.23257e24	0.154472
$913$	1.25893e25	0.862978
$914$	−2.79118e25	−1.89559
$915$	1.27605e25	0.858595
$916$	1.81058e24	0.120700
$917$	−1.10995e25	−0.733103
$918$	4.86193e25	3.18160
$919$	−9.58900e24	−0.621715	−0.310858	−	0.950456i	$-0.600616\pi$
$919$	−9.58900e24	−0.621715	−0.310858	+	0.950456i	$0.600616\pi$
$920$	−1.13566e24	−0.0729545
$921$	1.48642e25	0.946095
$922$	2.24802e25	1.41771
$923$	−3.83867e24	−0.239864
$924$	7.15015e24	0.442694
$925$	1.78674e25	1.09612
$926$	−1.97504e25	−1.20056
$927$	−3.28668e25	−1.97961
$928$	−3.95620e24	−0.236113
$929$	−2.17835e24	−0.128823	−0.0644115	−	0.997923i	$-0.520517\pi$
$929$	−2.17835e24	−0.128823	−0.0644115	+	0.997923i	$0.520517\pi$
$930$	4.59446e24	0.269234
$931$	6.81190e23	0.0395545
$932$	2.66820e24	0.153527
$933$	−8.65746e24	−0.493624
$934$	3.55305e25	2.00749
$935$	−3.71418e24	−0.207953
$936$	8.76625e24	0.486373
$937$	1.96898e25	1.08257	0.541283	−	0.840840i	$-0.317939\pi$
$937$	1.96898e25	1.08257	0.541283	+	0.840840i	$0.317939\pi$
$938$	3.04952e24	0.166153
$939$	−5.93810e25	−3.20620
$940$	9.67883e23	0.0517888
$941$	−1.10073e25	−0.583674	−0.291837	−	0.956468i	$-0.594266\pi$
$941$	−1.10073e25	−0.583674	−0.291837	+	0.956468i	$0.594266\pi$
$942$	4.83402e25	2.54025
$943$	1.57769e24	0.0821621
$944$	−2.44676e25	−1.26279
$945$	8.55915e24	0.437784
$946$	1.49776e25	0.759220
$947$	3.05310e25	1.53379	0.766896	−	0.641771i	$-0.221800\pi$
$947$	3.05310e25	1.53379	0.766896	+	0.641771i	$0.221800\pi$
$948$	7.96067e24	0.396350
$949$	−1.44974e24	−0.0715363
$950$	−1.81744e24	−0.0888811
$951$	6.27936e25	3.04355
$952$	5.39126e24	0.258986
$953$	−2.21873e25	−1.05637	−0.528184	−	0.849130i	$-0.677127\pi$
$953$	−2.21873e25	−1.05637	−0.528184	+	0.849130i	$0.677127\pi$
$954$	7.01054e25	3.30819
$955$	−2.77930e24	−0.129989
$956$	−1.87778e25	−0.870469
$957$	3.31607e24	0.152360
$958$	6.79734e24	0.309551
$959$	1.38033e25	0.623054
$960$	7.07236e24	0.316416
$961$	−2.00065e25	−0.887200
$962$	3.06749e25	1.34832
$963$	−8.06936e25	−3.51573
$964$	2.30599e25	0.995869
$965$	1.35243e25	0.578939
$966$	2.77020e25	1.17545
$967$	2.79398e25	1.17516	0.587581	−	0.809165i	$-0.300080\pi$
$967$	2.79398e25	1.17516	0.587581	+	0.809165i	$0.300080\pi$
$968$	−5.44184e24	−0.226885
$969$	4.11976e24	0.170263
$970$	3.28527e24	0.134589
$971$	−3.49302e25	−1.41853	−0.709264	−	0.704943i	$-0.750973\pi$
$971$	−3.49302e25	−1.41853	−0.709264	+	0.704943i	$0.750973\pi$
$972$	3.95825e24	0.159346
$973$	1.07782e25	0.430117
$974$	1.00273e25	0.396674
$975$	−3.19600e25	−1.25334
$976$	4.30478e25	1.67351
$977$	3.10933e25	1.19829	0.599146	−	0.800640i	$-0.295507\pi$
$977$	3.10933e25	1.19829	0.599146	+	0.800640i	$0.295507\pi$
$978$	2.09722e25	0.801242
$979$	1.80499e25	0.683633
$980$	3.74858e24	0.140749
$981$	−8.78022e25	−3.26828
$982$	1.19442e25	0.440768
$983$	2.95496e24	0.108105	0.0540526	−	0.998538i	$-0.482786\pi$
$983$	2.95496e24	0.108105	0.0540526	+	0.998538i	$0.482786\pi$
$984$	1.57863e24	0.0572563
$985$	3.39883e24	0.122214
$986$	−8.97096e24	−0.319805
$987$	6.58027e24	0.232567
$988$	−1.36928e24	−0.0479797
$989$	2.54652e25	0.884665
$990$	−1.28487e25	−0.442549
$991$	8.68124e24	0.296453	0.148226	−	0.988953i	$-0.452644\pi$
$991$	8.68124e24	0.296453	0.148226	+	0.988953i	$0.452644\pi$
$992$	1.26131e25	0.427046
$993$	−2.68473e25	−0.901224
$994$	−8.16682e24	−0.271812
$995$	−5.67652e24	−0.187321
$996$	−7.68437e25	−2.51422
$997$	−4.12471e24	−0.133809	−0.0669044	−	0.997759i	$-0.521312\pi$
$997$	−4.12471e24	−0.133809	−0.0669044	+	0.997759i	$0.521312\pi$
$998$	3.45560e25	1.11151
$999$	−7.19852e25	−2.29581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.a.1.4	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-483.296 q^{2} +19868.0 q^{3} +102503. q^{4} -300011. q^{5} -9.60214e6 q^{6} -1.05230e7 q^{7} +1.38073e7 q^{8} +2.65598e8 q^{9} +O(q^{10})\)	\(q-483.296 q^{2} +19868.0 q^{3} +102503. q^{4} -300011. q^{5} -9.60214e6 q^{6} -1.05230e7 q^{7} +1.38073e7 q^{8} +2.65598e8 q^{9} +1.44994e8 q^{10} -3.33645e8 q^{11} +2.03653e9 q^{12} +2.39045e9 q^{13} +5.08572e9 q^{14} -5.96063e9 q^{15} -2.01083e10 q^{16} -3.71058e10 q^{17} -1.28363e11 q^{18} -5.58824e9 q^{19} -3.07520e10 q^{20} -2.09071e11 q^{21} +1.61249e11 q^{22} +2.74159e11 q^{23} +2.74324e11 q^{24} -6.72933e11 q^{25} -1.15530e12 q^{26} +2.71115e12 q^{27} -1.07864e12 q^{28} -5.00246e11 q^{29} +2.88075e12 q^{30} +1.59488e12 q^{31} +7.90850e12 q^{32} -6.62887e12 q^{33} +1.79331e13 q^{34} +3.15702e12 q^{35} +2.72246e13 q^{36} -2.65515e13 q^{37} +2.70077e12 q^{38} +4.74936e13 q^{39} -4.14234e12 q^{40} +5.75464e12 q^{41} +1.01043e14 q^{42} +9.28847e13 q^{43} -3.41996e13 q^{44} -7.96824e13 q^{45} -1.32500e14 q^{46} -3.14738e13 q^{47} -3.99512e14 q^{48} -1.21897e14 q^{49} +3.25226e14 q^{50} -7.37219e14 q^{51} +2.45028e14 q^{52} -5.46152e14 q^{53} -1.31029e15 q^{54} +1.00097e14 q^{55} -1.45294e14 q^{56} -1.11027e14 q^{57} +2.41767e14 q^{58} +1.21679e15 q^{59} -6.10982e14 q^{60} -2.14080e15 q^{61} -7.70801e14 q^{62} -2.79489e15 q^{63} -1.18651e15 q^{64} -7.17162e14 q^{65} +3.20370e15 q^{66} +5.99624e14 q^{67} -3.80345e15 q^{68} +5.44700e15 q^{69} -1.52577e15 q^{70} -1.60583e15 q^{71} +3.66719e15 q^{72} -6.06470e14 q^{73} +1.28322e16 q^{74} -1.33698e16 q^{75} -5.72811e14 q^{76} +3.51095e15 q^{77} -2.29534e16 q^{78} +3.90894e15 q^{79} +6.03271e15 q^{80} +1.95658e16 q^{81} -2.78119e15 q^{82} -3.77326e16 q^{83} -2.14304e16 q^{84} +1.11321e16 q^{85} -4.48908e16 q^{86} -9.93891e15 q^{87} -4.60674e15 q^{88} -5.40993e16 q^{89} +3.85102e16 q^{90} -2.51547e16 q^{91} +2.81021e16 q^{92} +3.16872e16 q^{93} +1.52112e16 q^{94} +1.67653e15 q^{95} +1.57126e17 q^{96} +2.26579e16 q^{97} +5.89123e16 q^{98} -8.86155e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9}+O(q^{10}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9	\( 18 q - 15400 q^{3} + 862698 q^{4} - 564228 q^{5} - 6666170 q^{6} - 43925040 q^{7} + 86936640 q^{8} + 488532554 q^{9} - 1301706588 q^{10} + 414318256 q^{11} + 4613809340 q^{12} - 1708529620 q^{13} - 10178671680 q^{14} - 35937136948 q^{15} + 13408243234 q^{16} - 31137019060 q^{17} - 216144895280 q^{18} - 236294644572 q^{19} - 343491571178 q^{20} + 292681980344 q^{21} + 237072099770 q^{22} + 448660830360 q^{23} + 1331075294514 q^{24} + 3016314845934 q^{25} + 4625052436620 q^{26} - 3633286593580 q^{27} - 5255043772340 q^{28} - 9004435433298 q^{29} + 11322123726866 q^{30} + 4286667897456 q^{31} + 20489566928480 q^{32} + 12272773628920 q^{33} - 29135914295852 q^{34} - 34335586657384 q^{35} - 34363200450796 q^{36} - 33745027570060 q^{37} - 96773461186360 q^{38} - 104536576294796 q^{39} - 136020881729180 q^{40} - 62894681812676 q^{41} - 363718470035260 q^{42} + 43558449431040 q^{43} - 49608048285572 q^{44} + 133812803620916 q^{45} - 219540697042836 q^{46} - 141597817069240 q^{47} - 267256681151460 q^{48} + 453054608269810 q^{49} - 13\!\cdots\!40 q^{50}+ \cdots + 11\!\cdots\!56 q^{99}+O(q^{100}) \) 18 * q - 15400 * q^3 + 862698 * q^4 - 564228 * q^5 - 6666170 * q^6 - 43925040 * q^7 + 86936640 * q^8 + 488532554 * q^9 - 1301706588 * q^10 + 414318256 * q^11 + 4613809340 * q^12 - 1708529620 * q^13 - 10178671680 * q^14 - 35937136948 * q^15 + 13408243234 * q^16 - 31137019060 * q^17 - 216144895280 * q^18 - 236294644572 * q^19 - 343491571178 * q^20 + 292681980344 * q^21 + 237072099770 * q^22 + 448660830360 * q^23 + 1331075294514 * q^24 + 3016314845934 * q^25 + 4625052436620 * q^26 - 3633286593580 * q^27 - 5255043772340 * q^28 - 9004435433298 * q^29 + 11322123726866 * q^30 + 4286667897456 * q^31 + 20489566928480 * q^32 + 12272773628920 * q^33 - 29135914295852 * q^34 - 34335586657384 * q^35 - 34363200450796 * q^36 - 33745027570060 * q^37 - 96773461186360 * q^38 - 104536576294796 * q^39 - 136020881729180 * q^40 - 62894681812676 * q^41 - 363718470035260 * q^42 + 43558449431040 * q^43 - 49608048285572 * q^44 + 133812803620916 * q^45 - 219540697042836 * q^46 - 141597817069240 * q^47 - 267256681151460 * q^48 + 453054608269810 * q^49 - 1348659632272640 * q^50 - 1366163894523096 * q^51 - 1312273323620630 * q^52 - 485951074130100 * q^53 - 1795598060978246 * q^54 - 3426804650590972 * q^55 - 5564818824556288 * q^56 - 5205401672025040 * q^57 - 4547356113106800 * q^59 - 13819026055113000 * q^60 - 6121039899052148 * q^61 - 10199136673985490 * q^62 - 14641672030091800 * q^63 - 9962823646631806 * q^64 - 13420652091655824 * q^65 - 27721841054867288 * q^66 - 17715742779810920 * q^67 - 24471819430698220 * q^68 - 17159735572757960 * q^69 + 9006543780480744 * q^70 - 18877957007949512 * q^71 - 44531687124196680 * q^72 - 11641701802444700 * q^73 - 53655919274849056 * q^74 - 21032918050227748 * q^75 - 66122191206313032 * q^76 - 8842889451812280 * q^77 - 28799653307053650 * q^78 - 44197796400782136 * q^79 - 157325108946937442 * q^80 - 41532487375317502 * q^81 - 65440892426610260 * q^82 - 9547427423528400 * q^83 - 54796688181105048 * q^84 - 34123627920307712 * q^85 - 119642903919749046 * q^86 + 7703794759599400 * q^87 - 114332767598176050 * q^88 - 48534239108944036 * q^89 + 56810599078278752 * q^90 - 104774225723277192 * q^91 - 3343093822255980 * q^92 + 128149288210966200 * q^93 + 83032272917645478 * q^94 + 200021462885519192 * q^95 + 140361624410708610 * q^96 + 53343624485398380 * q^97 + 448366099002416160 * q^98 + 117966192294311356 * q^99

Introduction

L-functions

Modular forms

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