LMFDB - Embedded newform 29.12.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,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, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
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:	$22.2819522362$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 23517 x^{12} - 42196 x^{11} + 214206700 x^{10} + 532863376 x^{9} - 951901011680 x^{8} + \cdots + 30\!\cdots\!04 $ x^14 - 23517x^12 - 42196x^11 + 214206700x^10 + 532863376x^9 - 951901011680x^8 - 1439668569088x^7 + 2125122050961664x^6 - 3617975849298944x^5 - 2179155305696991232x^4 + 15507015861824716800x^3 + 709645914927917694976x^2 - 9478460460037847384064x + 30797548279705794248704
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$51.1787$ 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)

$f(q)$	$=$	$q+51.1787 q^{2} -728.829 q^{3} +571.255 q^{4} -4173.93 q^{5} -37300.5 q^{6} -8856.29 q^{7} -75577.8 q^{8} +354044. q^{9} +O(q^{10})$	\(q+51.1787 q^{2} -728.829 q^{3} +571.255 q^{4} -4173.93 q^{5} -37300.5 q^{6} -8856.29 q^{7} -75577.8 q^{8} +354044. q^{9} -213616. q^{10} +87808.9 q^{11} -416347. q^{12} -559497. q^{13} -453253. q^{14} +3.04208e6 q^{15} -5.03790e6 q^{16} +9.36587e6 q^{17} +1.81195e7 q^{18} +1.25961e7 q^{19} -2.38438e6 q^{20} +6.45472e6 q^{21} +4.49394e6 q^{22} +2.73784e7 q^{23} +5.50833e7 q^{24} -3.14064e7 q^{25} -2.86343e7 q^{26} -1.28928e8 q^{27} -5.05920e6 q^{28} -2.05111e7 q^{29} +1.55690e8 q^{30} -1.62155e8 q^{31} -1.03050e8 q^{32} -6.39976e7 q^{33} +4.79333e8 q^{34} +3.69656e7 q^{35} +2.02250e8 q^{36} +4.12147e8 q^{37} +6.44652e8 q^{38} +4.07778e8 q^{39} +3.15457e8 q^{40} -5.54011e8 q^{41} +3.30344e8 q^{42} +3.97893e8 q^{43} +5.01613e7 q^{44} -1.47776e9 q^{45} +1.40119e9 q^{46} +1.66457e9 q^{47} +3.67177e9 q^{48} -1.89889e9 q^{49} -1.60734e9 q^{50} -6.82611e9 q^{51} -3.19616e8 q^{52} -1.50567e9 q^{53} -6.59835e9 q^{54} -3.66508e8 q^{55} +6.69339e8 q^{56} -9.18040e9 q^{57} -1.04973e9 q^{58} +7.33972e9 q^{59} +1.73781e9 q^{60} +1.05983e10 q^{61} -8.29886e9 q^{62} -3.13552e9 q^{63} +5.04368e9 q^{64} +2.33530e9 q^{65} -3.27531e9 q^{66} +4.18440e9 q^{67} +5.35030e9 q^{68} -1.99542e10 q^{69} +1.89185e9 q^{70} -9.18372e9 q^{71} -2.67579e10 q^{72} -1.04450e10 q^{73} +2.10931e10 q^{74} +2.28899e10 q^{75} +7.19559e9 q^{76} -7.77661e8 q^{77} +2.08695e10 q^{78} +3.36970e10 q^{79} +2.10279e10 q^{80} +3.12484e10 q^{81} -2.83536e10 q^{82} -1.15113e10 q^{83} +3.68729e9 q^{84} -3.90925e10 q^{85} +2.03636e10 q^{86} +1.49491e10 q^{87} -6.63640e9 q^{88} +5.67342e10 q^{89} -7.56296e10 q^{90} +4.95507e9 q^{91} +1.56400e10 q^{92} +1.18183e11 q^{93} +8.51904e10 q^{94} -5.25753e10 q^{95} +7.51056e10 q^{96} -7.68751e10 q^{97} -9.71828e10 q^{98} +3.10882e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) $ 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * 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 $

$2$	51.1787	1.13090	0.565450	−	0.824783i	$-0.308703\pi$
$2$	51.1787	1.13090	0.565450	+	0.824783i	$0.308703\pi$
$3$	−728.829	−1.73164	−0.865822	−	0.500352i	$-0.833204\pi$
$3$	−728.829	−1.73164	−0.865822	+	0.500352i	$0.833204\pi$
$4$	571.255	0.278933
$5$	−4173.93	−0.597325	−0.298662	−	0.954359i	$-0.596540\pi$
$5$	−4173.93	−0.597325	−0.298662	+	0.954359i	$0.596540\pi$
$6$	−37300.5	−1.95831
$7$	−8856.29	−0.199165	−0.0995824	−	0.995029i	$-0.531751\pi$
$7$	−8856.29	−0.199165	−0.0995824	+	0.995029i	$0.531751\pi$
$8$	−75577.8	−0.815454
$9$	354044.	1.99859
$10$	−213616.	−0.675514
$11$	87808.9	0.164391	0.0821956	−	0.996616i	$-0.473807\pi$
$11$	87808.9	0.164391	0.0821956	+	0.996616i	$0.473807\pi$
$12$	−416347.	−0.483013
$13$	−559497.	−0.417936	−0.208968	−	0.977923i	$-0.567010\pi$
$13$	−559497.	−0.417936	−0.208968	+	0.977923i	$0.567010\pi$
$14$	−453253.	−0.225235
$15$	3.04208e6	1.03435
$16$	−5.03790e6	−1.20113
$17$	9.36587e6	1.59985	0.799924	−	0.600101i	$-0.204873\pi$
$17$	9.36587e6	1.59985	0.799924	+	0.600101i	$0.204873\pi$
$18$	1.81195e7	2.26020
$19$	1.25961e7	1.16706	0.583528	−	0.812093i	$-0.301672\pi$
$19$	1.25961e7	1.16706	0.583528	+	0.812093i	$0.301672\pi$
$20$	−2.38438e6	−0.166614
$21$	6.45472e6	0.344883
$22$	4.49394e6	0.185910
$23$	2.73784e7	0.886962	0.443481	−	0.896284i	$-0.353743\pi$
$23$	2.73784e7	0.886962	0.443481	+	0.896284i	$0.353743\pi$
$24$	5.50833e7	1.41208
$25$	−3.14064e7	−0.643203
$26$	−2.86343e7	−0.472643
$27$	−1.28928e8	−1.72920
$28$	−5.05920e6	−0.0555537
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	1.55690e8	1.16975
$31$	−1.62155e8	−1.01728	−0.508640	−	0.860980i	$-0.669851\pi$
$31$	−1.62155e8	−1.01728	−0.508640	+	0.860980i	$0.669851\pi$
$32$	−1.03050e8	−0.542902
$33$	−6.39976e7	−0.284667
$34$	4.79333e8	1.80927
$35$	3.69656e7	0.118966
$36$	2.02250e8	0.557473
$37$	4.12147e8	0.977107	0.488554	−	0.872534i	$-0.337525\pi$
$37$	4.12147e8	0.977107	0.488554	+	0.872534i	$0.337525\pi$
$38$	6.44652e8	1.31982
$39$	4.07778e8	0.723716
$40$	3.15457e8	0.487091
$41$	−5.54011e8	−0.746805	−0.373403	−	0.927669i	$-0.621809\pi$
$41$	−5.54011e8	−0.746805	−0.373403	+	0.927669i	$0.621809\pi$
$42$	3.30344e8	0.390028
$43$	3.97893e8	0.412753	0.206376	−	0.978473i	$-0.433833\pi$
$43$	3.97893e8	0.412753	0.206376	+	0.978473i	$0.433833\pi$
$44$	5.01613e7	0.0458542
$45$	−1.47776e9	−1.19381
$46$	1.40119e9	1.00306
$47$	1.66457e9	1.05868	0.529338	−	0.848411i	$-0.322440\pi$
$47$	1.66457e9	1.05868	0.529338	+	0.848411i	$0.322440\pi$
$48$	3.67177e9	2.07993
$49$	−1.89889e9	−0.960333
$50$	−1.60734e9	−0.727398
$51$	−6.82611e9	−2.77037
$52$	−3.19616e8	−0.116576
$53$	−1.50567e9	−0.494553	−0.247276	−	0.968945i	$-0.579536\pi$
$53$	−1.50567e9	−0.494553	−0.247276	+	0.968945i	$0.579536\pi$
$54$	−6.59835e9	−1.95555
$55$	−3.66508e8	−0.0981949
$56$	6.69339e8	0.162410
$57$	−9.18040e9	−2.02092
$58$	−1.04973e9	−0.210003
$59$	7.33972e9	1.33657	0.668287	−	0.743903i	$-0.267028\pi$
$59$	7.33972e9	1.33657	0.668287	+	0.743903i	$0.267028\pi$
$60$	1.73781e9	0.288516
$61$	1.05983e10	1.60666	0.803330	−	0.595534i	$-0.203060\pi$
$61$	1.05983e10	1.60666	0.803330	+	0.595534i	$0.203060\pi$
$62$	−8.29886e9	−1.15044
$63$	−3.13552e9	−0.398049
$64$	5.04368e9	0.587161
$65$	2.33530e9	0.249643
$66$	−3.27531e9	−0.321930
$67$	4.18440e9	0.378636	0.189318	−	0.981916i	$-0.439372\pi$
$67$	4.18440e9	0.378636	0.189318	+	0.981916i	$0.439372\pi$
$68$	5.35030e9	0.446251
$69$	−1.99542e10	−1.53590
$70$	1.89185e9	0.134539
$71$	−9.18372e9	−0.604084	−0.302042	−	0.953295i	$-0.597668\pi$
$71$	−9.18372e9	−0.604084	−0.302042	+	0.953295i	$0.597668\pi$
$72$	−2.67579e10	−1.62976
$73$	−1.04450e10	−0.589704	−0.294852	−	0.955543i	$-0.595270\pi$
$73$	−1.04450e10	−0.589704	−0.294852	+	0.955543i	$0.595270\pi$
$74$	2.10931e10	1.10501
$75$	2.28899e10	1.11380
$76$	7.19559e9	0.325530
$77$	−7.77661e8	−0.0327410
$78$	2.08695e10	0.818450
$79$	3.36970e10	1.23209	0.616045	−	0.787711i	$-0.288734\pi$
$79$	3.36970e10	1.23209	0.616045	+	0.787711i	$0.288734\pi$
$80$	2.10279e10	0.717464
$81$	3.12484e10	0.995774
$82$	−2.83536e10	−0.844562
$83$	−1.15113e10	−0.320771	−0.160386	−	0.987054i	$-0.551274\pi$
$83$	−1.15113e10	−0.320771	−0.160386	+	0.987054i	$0.551274\pi$
$84$	3.68729e9	0.0961992
$85$	−3.90925e10	−0.955629
$86$	2.03636e10	0.466782
$87$	1.49491e10	0.321558
$88$	−6.63640e9	−0.134053
$89$	5.67342e10	1.07696	0.538480	−	0.842638i	$-0.318999\pi$
$89$	5.67342e10	1.07696	0.538480	+	0.842638i	$0.318999\pi$
$90$	−7.56296e10	−1.35008
$91$	4.95507e9	0.0832381
$92$	1.56400e10	0.247403
$93$	1.18183e11	1.76157
$94$	8.51904e10	1.19726
$95$	−5.25753e10	−0.697111
$96$	7.51056e10	0.940114
$97$	−7.68751e10	−0.908952	−0.454476	−	0.890759i	$-0.650173\pi$
$97$	−7.68751e10	−0.908952	−0.454476	+	0.890759i	$0.650173\pi$
$98$	−9.71828e10	−1.08604
$99$	3.10882e10	0.328551
$100$	−1.79411e10	−0.179411
$101$	9.64483e10	0.913118	0.456559	−	0.889693i	$-0.349082\pi$
$101$	9.64483e10	0.913118	0.456559	+	0.889693i	$0.349082\pi$
$102$	−3.49351e11	−3.13301
$103$	1.12577e11	0.956851	0.478426	−	0.878128i	$-0.341208\pi$
$103$	1.12577e11	0.956851	0.478426	+	0.878128i	$0.341208\pi$
$104$	4.22856e10	0.340807
$105$	−2.69416e10	−0.206007
$106$	−7.70582e10	−0.559290
$107$	4.12125e10	0.284065	0.142033	−	0.989862i	$-0.454636\pi$
$107$	4.12125e10	0.284065	0.142033	+	0.989862i	$0.454636\pi$
$108$	−7.36507e10	−0.482332
$109$	2.25597e11	1.40439	0.702193	−	0.711986i	$-0.252204\pi$
$109$	2.25597e11	1.40439	0.702193	+	0.711986i	$0.252204\pi$
$110$	−1.87574e10	−0.111049
$111$	−3.00384e11	−1.69200
$112$	4.46171e10	0.239223
$113$	2.77777e11	1.41829	0.709145	−	0.705063i	$-0.249081\pi$
$113$	2.77777e11	1.41829	0.709145	+	0.705063i	$0.249081\pi$
$114$	−4.69841e11	−2.28546
$115$	−1.14276e11	−0.529804
$116$	−1.17171e10	−0.0517966
$117$	−1.98087e11	−0.835283
$118$	3.75637e11	1.51153
$119$	−8.29469e10	−0.318634
$120$	−2.29914e11	−0.843468
$121$	−2.77601e11	−0.972976
$122$	5.42409e11	1.81697
$123$	4.03779e11	1.29320
$124$	−9.26317e10	−0.283753
$125$	3.34894e11	0.981526
$126$	−1.60472e11	−0.450153
$127$	−6.14224e11	−1.64970	−0.824852	−	0.565348i	$-0.808742\pi$
$127$	−6.14224e11	−1.64970	−0.824852	+	0.565348i	$0.808742\pi$
$128$	4.69174e11	1.20692
$129$	−2.89996e11	−0.714741
$130$	1.19518e11	0.282322
$131$	7.55209e11	1.71031	0.855156	−	0.518371i	$-0.173461\pi$
$131$	7.55209e11	1.71031	0.855156	+	0.518371i	$0.173461\pi$
$132$	−3.65590e10	−0.0794031
$133$	−1.11555e11	−0.232436
$134$	2.14152e11	0.428199
$135$	5.38136e11	1.03290
$136$	−7.07852e11	−1.30460
$137$	−5.22448e11	−0.924869	−0.462435	−	0.886653i	$-0.653024\pi$
$137$	−5.22448e11	−0.924869	−0.462435	+	0.886653i	$0.653024\pi$
$138$	−1.02123e12	−1.73695
$139$	8.87253e11	1.45033	0.725164	−	0.688577i	$-0.241764\pi$
$139$	8.87253e11	1.45033	0.725164	+	0.688577i	$0.241764\pi$
$140$	2.11168e10	0.0331836
$141$	−1.21319e12	−1.83325
$142$	−4.70010e11	−0.683158
$143$	−4.91288e10	−0.0687050
$144$	−1.78364e12	−2.40057
$145$	8.56122e10	0.110920
$146$	−5.34563e11	−0.666896
$147$	1.38397e12	1.66296
$148$	2.35441e11	0.272548
$149$	−6.85161e11	−0.764308	−0.382154	−	0.924099i	$-0.624818\pi$
$149$	−6.85161e11	−0.764308	−0.382154	+	0.924099i	$0.624818\pi$
$150$	1.17147e12	1.25959
$151$	1.29616e12	1.34364	0.671822	−	0.740712i	$-0.265512\pi$
$151$	1.29616e12	1.34364	0.671822	+	0.740712i	$0.265512\pi$
$152$	−9.51986e11	−0.951680
$153$	3.31593e12	3.19744
$154$	−3.97996e10	−0.0370267
$155$	6.76823e11	0.607646
$156$	2.32945e11	0.201868
$157$	−4.06291e10	−0.0339930	−0.0169965	−	0.999856i	$-0.505410\pi$
$157$	−4.06291e10	−0.0339930	−0.0169965	+	0.999856i	$0.505410\pi$
$158$	1.72457e12	1.39337
$159$	1.09738e12	0.856390
$160$	4.30123e11	0.324289
$161$	−2.42471e11	−0.176652
$162$	1.59925e12	1.12612
$163$	−1.81384e12	−1.23471	−0.617357	−	0.786683i	$-0.711797\pi$
$163$	−1.81384e12	−1.23471	−0.617357	+	0.786683i	$0.711797\pi$
$164$	−3.16482e11	−0.208309
$165$	2.67122e11	0.170039
$166$	−5.89134e11	−0.362760
$167$	1.74869e12	1.04177	0.520885	−	0.853627i	$-0.325602\pi$
$167$	1.74869e12	1.04177	0.520885	+	0.853627i	$0.325602\pi$
$168$	−4.87834e11	−0.281236
$169$	−1.47912e12	−0.825330
$170$	−2.00070e12	−1.08072
$171$	4.45958e12	2.33247
$172$	2.27299e11	0.115130
$173$	−1.71540e12	−0.841614	−0.420807	−	0.907150i	$-0.638253\pi$
$173$	−1.71540e12	−0.841614	−0.420807	+	0.907150i	$0.638253\pi$
$174$	7.65076e11	0.363650
$175$	2.78144e11	0.128103
$176$	−4.42372e11	−0.197455
$177$	−5.34940e12	−2.31447
$178$	2.90358e12	1.21793
$179$	1.75879e12	0.715356	0.357678	−	0.933845i	$-0.383569\pi$
$179$	1.75879e12	0.715356	0.357678	+	0.933845i	$0.383569\pi$
$180$	−8.44177e11	−0.332993
$181$	−1.50642e12	−0.576386	−0.288193	−	0.957572i	$-0.593054\pi$
$181$	−1.50642e12	−0.576386	−0.288193	+	0.957572i	$0.593054\pi$
$182$	2.53594e11	0.0941339
$183$	−7.72438e12	−2.78216
$184$	−2.06920e12	−0.723276
$185$	−1.72027e12	−0.583650
$186$	6.04845e12	1.99215
$187$	8.22406e11	0.263001
$188$	9.50893e11	0.295300
$189$	1.14182e12	0.344397
$190$	−2.69073e12	−0.788362
$191$	−5.24720e12	−1.49363	−0.746817	−	0.665030i	$-0.768419\pi$
$191$	−5.24720e12	−1.49363	−0.746817	+	0.665030i	$0.768419\pi$
$192$	−3.67598e12	−1.01675
$193$	−4.42273e12	−1.18884	−0.594422	−	0.804153i	$-0.702619\pi$
$193$	−4.42273e12	−1.18884	−0.594422	+	0.804153i	$0.702619\pi$
$194$	−3.93436e12	−1.02793
$195$	−1.70204e12	−0.432293
$196$	−1.08475e12	−0.267869
$197$	−4.36997e12	−1.04933	−0.524667	−	0.851307i	$-0.675810\pi$
$197$	−4.36997e12	−1.04933	−0.524667	+	0.851307i	$0.675810\pi$
$198$	1.59105e12	0.371558
$199$	−2.20695e11	−0.0501304	−0.0250652	−	0.999686i	$-0.507979\pi$
$199$	−2.20695e11	−0.0501304	−0.0250652	+	0.999686i	$0.507979\pi$
$200$	2.37363e12	0.524503
$201$	−3.04971e12	−0.655663
$202$	4.93609e12	1.03264
$203$	1.81653e11	0.0369840
$204$	−3.89945e12	−0.772748
$205$	2.31241e12	0.446085
$206$	5.76153e12	1.08210
$207$	9.69317e12	1.77267
$208$	2.81869e12	0.501995
$209$	1.10605e12	0.191854
$210$	−1.37883e12	−0.232973
$211$	4.09579e12	0.674193	0.337097	−	0.941470i	$-0.390555\pi$
$211$	4.09579e12	0.674193	0.337097	+	0.941470i	$0.390555\pi$
$212$	−8.60122e11	−0.137947
$213$	6.69336e12	1.04606
$214$	2.10920e12	0.321249
$215$	−1.66078e12	−0.246547
$216$	9.74409e12	1.41009
$217$	1.43609e12	0.202606
$218$	1.15457e13	1.58822
$219$	7.61264e12	1.02116
$220$	−2.09370e11	−0.0273898
$221$	−5.24018e12	−0.668634
$222$	−1.53733e13	−1.91348
$223$	−4.81881e12	−0.585144	−0.292572	−	0.956243i	$-0.594511\pi$
$223$	−4.81881e12	−0.585144	−0.292572	+	0.956243i	$0.594511\pi$
$224$	9.12638e11	0.108127
$225$	−1.11193e13	−1.28550
$226$	1.42163e13	1.60394
$227$	6.59572e12	0.726307	0.363153	−	0.931729i	$-0.381700\pi$
$227$	6.59572e12	0.726307	0.363153	+	0.931729i	$0.381700\pi$
$228$	−5.24435e12	−0.563703
$229$	1.15555e13	1.21254	0.606268	−	0.795261i	$-0.292666\pi$
$229$	1.15555e13	1.21254	0.606268	+	0.795261i	$0.292666\pi$
$230$	−5.84847e12	−0.599155
$231$	5.66782e11	0.0566957
$232$	1.55019e12	0.151426
$233$	2.94321e12	0.280778	0.140389	−	0.990096i	$-0.455165\pi$
$233$	2.94321e12	0.280778	0.140389	+	0.990096i	$0.455165\pi$
$234$	−1.01378e13	−0.944620
$235$	−6.94780e12	−0.632374
$236$	4.19285e12	0.372815
$237$	−2.45594e13	−2.13354
$238$	−4.24511e12	−0.360343
$239$	−7.67013e12	−0.636230	−0.318115	−	0.948052i	$-0.603050\pi$
$239$	−7.67013e12	−0.636230	−0.318115	+	0.948052i	$0.603050\pi$
$240$	−1.53257e13	−1.24239
$241$	2.36605e13	1.87469	0.937346	−	0.348399i	$-0.113275\pi$
$241$	2.36605e13	1.87469	0.937346	+	0.348399i	$0.113275\pi$
$242$	−1.42073e13	−1.10034
$243$	6.44243e10	0.00487770
$244$	6.05436e12	0.448151
$245$	7.92585e12	0.573631
$246$	2.06649e13	1.46248
$247$	−7.04749e12	−0.487754
$248$	1.22553e13	0.829544
$249$	8.38978e12	0.555461
$250$	1.71394e13	1.11001
$251$	2.11603e13	1.34065	0.670325	−	0.742068i	$-0.266155\pi$
$251$	2.11603e13	1.34065	0.670325	+	0.742068i	$0.266155\pi$
$252$	−1.79118e12	−0.111029
$253$	2.40407e12	0.145809
$254$	−3.14351e13	−1.86565
$255$	2.84917e13	1.65481
$256$	1.36823e13	0.777747
$257$	−3.00938e13	−1.67434	−0.837172	−	0.546940i	$-0.815793\pi$
$257$	−3.00938e13	−1.67434	−0.837172	+	0.546940i	$0.815793\pi$
$258$	−1.48416e13	−0.808300
$259$	−3.65009e12	−0.194605
$260$	1.33405e12	0.0696338
$261$	−7.26186e12	−0.371129
$262$	3.86506e13	1.93419
$263$	−2.99305e13	−1.46675	−0.733376	−	0.679823i	$-0.762057\pi$
$263$	−2.99305e13	−1.46675	−0.733376	+	0.679823i	$0.762057\pi$
$264$	4.83680e12	0.232133
$265$	6.28457e12	0.295409
$266$	−5.70922e12	−0.262862
$267$	−4.13495e13	−1.86491
$268$	2.39036e12	0.105614
$269$	−3.70918e13	−1.60561	−0.802806	−	0.596240i	$-0.796661\pi$
$269$	−3.70918e13	−1.60561	−0.802806	+	0.596240i	$0.796661\pi$
$270$	2.75411e13	1.16810
$271$	4.49528e13	1.86821	0.934105	−	0.357000i	$-0.116200\pi$
$271$	4.49528e13	1.86821	0.934105	+	0.357000i	$0.116200\pi$
$272$	−4.71843e13	−1.92163
$273$	−3.61140e12	−0.144139
$274$	−2.67382e13	−1.04593
$275$	−2.75776e12	−0.105737
$276$	−1.13989e13	−0.428414
$277$	3.43515e13	1.26563	0.632816	−	0.774302i	$-0.281899\pi$
$277$	3.43515e13	1.26563	0.632816	+	0.774302i	$0.281899\pi$
$278$	4.54084e13	1.64017
$279$	−5.74099e13	−2.03312
$280$	−2.79378e12	−0.0970114
$281$	2.84688e13	0.969359	0.484679	−	0.874692i	$-0.338936\pi$
$281$	2.84688e13	0.969359	0.484679	+	0.874692i	$0.338936\pi$
$282$	−6.20892e13	−2.07322
$283$	−2.08503e13	−0.682790	−0.341395	−	0.939920i	$-0.610899\pi$
$283$	−2.08503e13	−0.682790	−0.341395	+	0.939920i	$0.610899\pi$
$284$	−5.24624e12	−0.168499
$285$	3.83184e13	1.20715
$286$	−2.51435e12	−0.0776984
$287$	4.90649e12	0.148737
$288$	−3.64842e13	−1.08504
$289$	5.34476e13	1.55952
$290$	4.38152e12	0.125440
$291$	5.60288e13	1.57398
$292$	−5.96678e12	−0.164488
$293$	−6.21975e13	−1.68268	−0.841339	−	0.540509i	$-0.818232\pi$
$293$	−6.21975e13	−1.68268	−0.841339	+	0.540509i	$0.818232\pi$
$294$	7.08296e13	1.88064
$295$	−3.06355e13	−0.798369
$296$	−3.11491e13	−0.796786
$297$	−1.13210e13	−0.284266
$298$	−3.50656e13	−0.864355
$299$	−1.53181e13	−0.370693
$300$	1.30760e13	0.310675
$301$	−3.52386e12	−0.0822059
$302$	6.63356e13	1.51953
$303$	−7.02943e13	−1.58120
$304$	−6.34579e13	−1.40178
$305$	−4.42368e13	−0.959697
$306$	1.69705e14	3.61599
$307$	5.66594e13	1.18580	0.592899	−	0.805277i	$-0.297983\pi$
$307$	5.66594e13	1.18580	0.592899	+	0.805277i	$0.297983\pi$
$308$	−4.44243e11	−0.00913254
$309$	−8.20492e13	−1.65693
$310$	3.46389e13	0.687186
$311$	−5.55766e12	−0.108320	−0.0541601	−	0.998532i	$-0.517248\pi$
$311$	−5.55766e12	−0.108320	−0.0541601	+	0.998532i	$0.517248\pi$
$312$	−3.08190e13	−0.590157
$313$	5.08683e13	0.957092	0.478546	−	0.878063i	$-0.341164\pi$
$313$	5.08683e13	0.957092	0.478546	+	0.878063i	$0.341164\pi$
$314$	−2.07934e12	−0.0384426
$315$	1.30875e13	0.237765
$316$	1.92496e13	0.343671
$317$	3.58702e13	0.629372	0.314686	−	0.949196i	$-0.398101\pi$
$317$	3.58702e13	0.629372	0.314686	+	0.949196i	$0.398101\pi$
$318$	5.61622e13	0.968490
$319$	−1.80106e12	−0.0305267
$320$	−2.10520e13	−0.350726
$321$	−3.00369e13	−0.491900
$322$	−1.24093e13	−0.199775
$323$	1.17973e14	1.86711
$324$	1.78508e13	0.277754
$325$	1.75718e13	0.268818
$326$	−9.28298e13	−1.39634
$327$	−1.64421e14	−2.43190
$328$	4.18710e13	0.608985
$329$	−1.47419e13	−0.210851
$330$	1.36709e13	0.192297
$331$	4.44597e13	0.615053	0.307527	−	0.951539i	$-0.400499\pi$
$331$	4.44597e13	0.615053	0.307527	+	0.951539i	$0.400499\pi$
$332$	−6.57590e12	−0.0894737
$333$	1.45918e14	1.95284
$334$	8.94956e13	1.17814
$335$	−1.74654e13	−0.226169
$336$	−3.25182e13	−0.414249
$337$	−5.68333e12	−0.0712260	−0.0356130	−	0.999366i	$-0.511338\pi$
$337$	−5.68333e12	−0.0712260	−0.0356130	+	0.999366i	$0.511338\pi$
$338$	−7.56995e13	−0.933365
$339$	−2.02452e14	−2.45597
$340$	−2.23318e13	−0.266557
$341$	−1.42386e13	−0.167232
$342$	2.28235e14	2.63778
$343$	3.43289e13	0.390430
$344$	−3.00719e13	−0.336581
$345$	8.32873e13	0.917432
$346$	−8.77921e13	−0.951781
$347$	−5.92324e13	−0.632044	−0.316022	−	0.948752i	$-0.602347\pi$
$347$	−5.92324e13	−0.632044	−0.316022	+	0.948752i	$0.602347\pi$
$348$	8.53976e12	0.0896932
$349$	3.25654e12	0.0336679	0.0168340	−	0.999858i	$-0.494641\pi$
$349$	3.25654e12	0.0336679	0.0168340	+	0.999858i	$0.494641\pi$
$350$	1.42351e13	0.144872
$351$	7.21348e13	0.722696
$352$	−9.04868e12	−0.0892484
$353$	1.57195e14	1.52643	0.763216	−	0.646143i	$-0.223619\pi$
$353$	1.57195e14	1.52643	0.763216	+	0.646143i	$0.223619\pi$
$354$	−2.73775e14	−2.61743
$355$	3.83322e13	0.360834
$356$	3.24097e13	0.300400
$357$	6.04541e13	0.551760
$358$	9.00124e13	0.808995
$359$	1.01249e14	0.896129	0.448065	−	0.894001i	$-0.352113\pi$
$359$	1.01249e14	0.896129	0.448065	+	0.894001i	$0.352113\pi$
$360$	1.11686e14	0.973495
$361$	4.21716e13	0.362018
$362$	−7.70965e13	−0.651835
$363$	2.02324e14	1.68485
$364$	2.83061e12	0.0232179
$365$	4.35969e13	0.352245
$366$	−3.95323e14	−3.14635
$367$	2.20548e14	1.72918	0.864589	−	0.502480i	$-0.167579\pi$
$367$	2.20548e14	1.72918	0.864589	+	0.502480i	$0.167579\pi$
$368$	−1.37930e14	−1.06536
$369$	−1.96145e14	−1.49256
$370$	−8.80412e13	−0.660050
$371$	1.33347e13	0.0984976
$372$	6.75126e13	0.491359
$373$	−4.59003e13	−0.329167	−0.164584	−	0.986363i	$-0.552628\pi$
$373$	−4.59003e13	−0.329167	−0.164584	+	0.986363i	$0.552628\pi$
$374$	4.20896e13	0.297428
$375$	−2.44080e14	−1.69965
$376$	−1.25804e14	−0.863302
$377$	1.14759e13	0.0776087
$378$	5.84370e13	0.389478
$379$	−2.04271e14	−1.34181	−0.670906	−	0.741543i	$-0.734094\pi$
$379$	−2.04271e14	−1.34181	−0.670906	+	0.741543i	$0.734094\pi$
$380$	−3.00339e13	−0.194447
$381$	4.47664e14	2.85670
$382$	−2.68545e14	−1.68915
$383$	1.71297e14	1.06208	0.531040	−	0.847347i	$-0.321802\pi$
$383$	1.71297e14	1.06208	0.531040	+	0.847347i	$0.321802\pi$
$384$	−3.41948e14	−2.08996
$385$	3.24591e12	0.0195570
$386$	−2.26349e14	−1.34446
$387$	1.40872e14	0.824924
$388$	−4.39153e13	−0.253537
$389$	1.51514e14	0.862442	0.431221	−	0.902246i	$-0.358083\pi$
$389$	1.51514e14	0.862442	0.431221	+	0.902246i	$0.358083\pi$
$390$	−8.71080e13	−0.488880
$391$	2.56422e14	1.41900
$392$	1.43514e14	0.783108
$393$	−5.50418e14	−2.96165
$394$	−2.23649e14	−1.18669
$395$	−1.40649e14	−0.735958
$396$	1.77593e13	0.0916437
$397$	−3.34084e14	−1.70023	−0.850116	−	0.526596i	$-0.823468\pi$
$397$	−3.34084e14	−1.70023	−0.850116	+	0.526596i	$0.823468\pi$
$398$	−1.12949e13	−0.0566924
$399$	8.13043e13	0.402497
$400$	1.58222e14	0.772570
$401$	−2.69916e14	−1.29998	−0.649988	−	0.759945i	$-0.725226\pi$
$401$	−2.69916e14	−1.29998	−0.649988	+	0.759945i	$0.725226\pi$
$402$	−1.56080e14	−0.741489
$403$	9.07251e13	0.425157
$404$	5.50966e13	0.254699
$405$	−1.30429e14	−0.594800
$406$	9.29674e12	0.0418252
$407$	3.61901e13	0.160628
$408$	5.15903e14	2.25911
$409$	3.78654e13	0.163593	0.0817965	−	0.996649i	$-0.473934\pi$
$409$	3.78654e13	0.163593	0.0817965	+	0.996649i	$0.473934\pi$
$410$	1.18346e14	0.504478
$411$	3.80775e14	1.60154
$412$	6.43101e13	0.266898
$413$	−6.50027e13	−0.266199
$414$	4.96083e14	2.00472
$415$	4.80475e13	0.191605
$416$	5.76560e13	0.226898
$417$	−6.46655e14	−2.51145
$418$	5.66061e13	0.216967
$419$	2.94673e14	1.11471	0.557356	−	0.830273i	$-0.311816\pi$
$419$	2.94673e14	1.11471	0.557356	+	0.830273i	$0.311816\pi$
$420$	−1.53905e13	−0.0574622
$421$	−4.37175e13	−0.161103	−0.0805514	−	0.996750i	$-0.525668\pi$
$421$	−4.37175e13	−0.161103	−0.0805514	+	0.996750i	$0.525668\pi$
$422$	2.09617e14	0.762445
$423$	5.89331e14	2.11586
$424$	1.13795e14	0.403285
$425$	−2.94148e14	−1.02903
$426$	3.42557e14	1.18299
$427$	−9.38620e13	−0.319990
$428$	2.35429e13	0.0792353
$429$	3.58065e13	0.118973
$430$	−8.49965e13	−0.278820
$431$	−1.18644e14	−0.384256	−0.192128	−	0.981370i	$-0.561539\pi$
$431$	−1.18644e14	−0.384256	−0.192128	+	0.981370i	$0.561539\pi$
$432$	6.49526e14	2.07700
$433$	−1.04303e14	−0.329317	−0.164658	−	0.986351i	$-0.552652\pi$
$433$	−1.04303e14	−0.329317	−0.164658	+	0.986351i	$0.552652\pi$
$434$	7.34971e13	0.229127
$435$	−6.23966e13	−0.192075
$436$	1.28873e14	0.391730
$437$	3.44861e14	1.03513
$438$	3.89605e14	1.15483
$439$	1.11165e14	0.325397	0.162699	−	0.986676i	$-0.447980\pi$
$439$	1.11165e14	0.325397	0.162699	+	0.986676i	$0.447980\pi$
$440$	2.76999e13	0.0800734
$441$	−6.72292e14	−1.91931
$442$	−2.68185e14	−0.756158
$443$	2.56546e14	0.714405	0.357202	−	0.934027i	$-0.383731\pi$
$443$	2.56546e14	0.714405	0.357202	+	0.934027i	$0.383731\pi$
$444$	−1.71596e14	−0.471955
$445$	−2.36805e14	−0.643295
$446$	−2.46620e14	−0.661739
$447$	4.99365e14	1.32351
$448$	−4.46683e13	−0.116942
$449$	4.48715e14	1.16042	0.580210	−	0.814467i	$-0.302970\pi$
$449$	4.48715e14	1.16042	0.580210	+	0.814467i	$0.302970\pi$
$450$	−5.69069e14	−1.45377
$451$	−4.86471e13	−0.122768
$452$	1.58682e14	0.395608
$453$	−9.44676e14	−2.32671
$454$	3.37560e14	0.821380
$455$	−2.06821e13	−0.0497202
$456$	6.93835e14	1.64797
$457$	7.18782e14	1.68678	0.843390	−	0.537302i	$-0.180557\pi$
$457$	7.18782e14	1.68678	0.843390	+	0.537302i	$0.180557\pi$
$458$	5.91396e14	1.37126
$459$	−1.20752e15	−2.76646
$460$	−6.52805e13	−0.147780
$461$	−2.64494e13	−0.0591644	−0.0295822	−	0.999562i	$-0.509418\pi$
$461$	−2.64494e13	−0.0591644	−0.0295822	+	0.999562i	$0.509418\pi$
$462$	2.90071e13	0.0641171
$463$	−2.87582e14	−0.628155	−0.314077	−	0.949397i	$-0.601695\pi$
$463$	−2.87582e14	−0.628155	−0.314077	+	0.949397i	$0.601695\pi$
$464$	1.03333e14	0.223044
$465$	−4.93288e14	−1.05223
$466$	1.50629e14	0.317532
$467$	−3.95083e14	−0.823087	−0.411544	−	0.911390i	$-0.635010\pi$
$467$	−3.95083e14	−0.823087	−0.411544	+	0.911390i	$0.635010\pi$
$468$	−1.13158e14	−0.232988
$469$	−3.70583e13	−0.0754110
$470$	−3.55579e14	−0.715151
$471$	2.96117e13	0.0588637
$472$	−5.54720e14	−1.08992
$473$	3.49386e13	0.0678529
$474$	−1.25692e15	−2.41282
$475$	−3.95598e14	−0.750654
$476$	−4.73838e13	−0.0888775
$477$	−5.33074e14	−0.988409
$478$	−3.92547e14	−0.719513
$479$	−8.44436e14	−1.53010	−0.765052	−	0.643968i	$-0.777287\pi$
$479$	−8.44436e14	−1.53010	−0.765052	+	0.643968i	$0.777287\pi$
$480$	−3.13486e14	−0.561553
$481$	−2.30595e14	−0.408368
$482$	1.21091e15	2.12009
$483$	1.76720e14	0.305898
$484$	−1.58581e14	−0.271395
$485$	3.20871e14	0.542939
$486$	3.29715e12	0.00551619
$487$	6.39006e14	1.05705	0.528525	−	0.848918i	$-0.322745\pi$
$487$	6.39006e14	1.05705	0.528525	+	0.848918i	$0.322745\pi$
$488$	−8.01000e14	−1.31016
$489$	1.32198e15	2.13809
$490$	4.05634e14	0.648719
$491$	8.53081e14	1.34909	0.674546	−	0.738232i	$-0.264339\pi$
$491$	8.53081e14	1.34909	0.674546	+	0.738232i	$0.264339\pi$
$492$	2.30661e14	0.360717
$493$	−1.92105e14	−0.297084
$494$	−3.60681e14	−0.551601
$495$	−1.29760e14	−0.196251
$496$	8.16919e14	1.22188
$497$	8.13337e13	0.120312
$498$	4.29377e14	0.628171
$499$	6.90483e14	0.999080	0.499540	−	0.866291i	$-0.333502\pi$
$499$	6.90483e14	0.999080	0.499540	+	0.866291i	$0.333502\pi$
$500$	1.91310e14	0.273780
$501$	−1.27449e15	−1.80398
$502$	1.08295e15	1.51614
$503$	5.65264e14	0.782757	0.391379	−	0.920230i	$-0.371998\pi$
$503$	5.65264e14	0.782757	0.391379	+	0.920230i	$0.371998\pi$
$504$	2.36976e14	0.324591
$505$	−4.02569e14	−0.545428
$506$	1.23037e14	0.164895
$507$	1.07803e15	1.42918
$508$	−3.50878e14	−0.460157
$509$	−3.98188e14	−0.516583	−0.258291	−	0.966067i	$-0.583159\pi$
$509$	−3.98188e14	−0.516583	−0.258291	+	0.966067i	$0.583159\pi$
$510$	1.45817e15	1.87142
$511$	9.25043e13	0.117448
$512$	−2.60629e14	−0.327370
$513$	−1.62399e15	−2.01808
$514$	−1.54016e15	−1.89351
$515$	−4.69888e14	−0.571551
$516$	−1.65662e14	−0.199365
$517$	1.46164e14	0.174037
$518$	−1.86807e14	−0.220079
$519$	1.25024e15	1.45738
$520$	−1.76497e14	−0.203573
$521$	−5.18751e14	−0.592041	−0.296021	−	0.955182i	$-0.595660\pi$
$521$	−5.18751e14	−0.592041	−0.296021	+	0.955182i	$0.595660\pi$
$522$	−3.71652e14	−0.419709
$523$	−3.12541e14	−0.349259	−0.174629	−	0.984634i	$-0.555873\pi$
$523$	−3.12541e14	−0.349259	−0.174629	+	0.984634i	$0.555873\pi$
$524$	4.31417e14	0.477063
$525$	−2.02720e14	−0.221830
$526$	−1.53180e15	−1.65875
$527$	−1.51872e15	−1.62749
$528$	3.22414e14	0.341922
$529$	−2.03233e14	−0.213299
$530$	3.21636e14	0.334077
$531$	2.59858e15	2.67127
$532$	−6.37262e13	−0.0648342
$533$	3.09968e14	0.312117
$534$	−2.11621e15	−2.10903
$535$	−1.72018e14	−0.169679
$536$	−3.16248e14	−0.308760
$537$	−1.28186e15	−1.23874
$538$	−1.89831e15	−1.81579
$539$	−1.66740e14	−0.157870
$540$	3.07413e14	0.288109
$541$	7.88985e14	0.731954	0.365977	−	0.930624i	$-0.380735\pi$
$541$	7.88985e14	0.731954	0.365977	+	0.930624i	$0.380735\pi$
$542$	2.30062e15	2.11276
$543$	1.09792e15	0.998095
$544$	−9.65150e14	−0.868562
$545$	−9.41625e14	−0.838875
$546$	−1.84827e14	−0.163006
$547$	1.97410e15	1.72361	0.861804	−	0.507242i	$-0.169335\pi$
$547$	1.97410e15	1.72361	0.861804	+	0.507242i	$0.169335\pi$
$548$	−2.98451e14	−0.257977
$549$	3.75228e15	3.21105
$550$	−1.41138e14	−0.119578
$551$	−2.58361e14	−0.216717
$552$	1.50809e15	1.25246
$553$	−2.98431e14	−0.245389
$554$	1.75806e15	1.43130
$555$	1.25378e15	1.01067
$556$	5.06848e14	0.404544
$557$	−2.96366e14	−0.234220	−0.117110	−	0.993119i	$-0.537363\pi$
$557$	−2.96366e14	−0.234220	−0.117110	+	0.993119i	$0.537363\pi$
$558$	−2.93816e15	−2.29926
$559$	−2.22620e14	−0.172504
$560$	−1.86229e14	−0.142894
$561$	−5.99393e14	−0.455424
$562$	1.45700e15	1.09625
$563$	−2.54707e15	−1.89777	−0.948887	−	0.315617i	$-0.897788\pi$
$563$	−2.54707e15	−1.89777	−0.948887	+	0.315617i	$0.897788\pi$
$564$	−6.93038e14	−0.511355
$565$	−1.15942e15	−0.847179
$566$	−1.06709e15	−0.772167
$567$	−2.76745e14	−0.198323
$568$	6.94085e14	0.492603
$569$	−1.67547e15	−1.17766	−0.588829	−	0.808257i	$-0.700411\pi$
$569$	−1.67547e15	−1.17766	−0.588829	+	0.808257i	$0.700411\pi$
$570$	1.96108e15	1.36516
$571$	−8.04995e14	−0.555002	−0.277501	−	0.960725i	$-0.589506\pi$
$571$	−8.04995e14	−0.555002	−0.277501	+	0.960725i	$0.589506\pi$
$572$	−2.80651e13	−0.0191641
$573$	3.82431e15	2.58644
$574$	2.51107e14	0.168207
$575$	−8.59857e14	−0.570497
$576$	1.78569e15	1.17350
$577$	−1.10330e15	−0.718169	−0.359084	−	0.933305i	$-0.616911\pi$
$577$	−1.10330e15	−0.718169	−0.359084	+	0.933305i	$0.616911\pi$
$578$	2.73538e15	1.76366
$579$	3.22341e15	2.05866
$580$	4.89064e13	0.0309394
$581$	1.01948e14	0.0638863
$582$	2.86748e15	1.78001
$583$	−1.32211e14	−0.0813002
$584$	7.89413e14	0.480877
$585$	8.26801e14	0.498935
$586$	−3.18318e15	−1.90294
$587$	−1.50726e15	−0.892644	−0.446322	−	0.894872i	$-0.647266\pi$
$587$	−1.50726e15	−0.892644	−0.446322	+	0.894872i	$0.647266\pi$
$588$	7.90599e14	0.463853
$589$	−2.04252e15	−1.18722
$590$	−1.56788e15	−0.902875
$591$	3.18496e15	1.81707
$592$	−2.07635e15	−1.17363
$593$	3.61709e14	0.202562	0.101281	−	0.994858i	$-0.467706\pi$
$593$	3.61709e14	0.202562	0.101281	+	0.994858i	$0.467706\pi$
$594$	−5.79394e14	−0.321476
$595$	3.46215e14	0.190328
$596$	−3.91402e14	−0.213191
$597$	1.60849e14	0.0868079
$598$	−7.83962e14	−0.419216
$599$	−8.39054e14	−0.444573	−0.222286	−	0.974981i	$-0.571352\pi$
$599$	−8.39054e14	−0.444573	−0.222286	+	0.974981i	$0.571352\pi$
$600$	−1.72997e15	−0.908252
$601$	1.03676e15	0.539346	0.269673	−	0.962952i	$-0.413084\pi$
$601$	1.03676e15	0.539346	0.269673	+	0.962952i	$0.413084\pi$
$602$	−1.80346e14	−0.0929665
$603$	1.48146e15	0.756738
$604$	7.40436e14	0.374787
$605$	1.15869e15	0.581182
$606$	−3.59757e15	−1.78817
$607$	8.64270e14	0.425708	0.212854	−	0.977084i	$-0.431724\pi$
$607$	8.64270e14	0.425708	0.212854	+	0.977084i	$0.431724\pi$
$608$	−1.29802e15	−0.633597
$609$	−1.32394e14	−0.0640431
$610$	−2.26398e15	−1.08532
$611$	−9.31321e14	−0.442459
$612$	1.89424e15	0.891873
$613$	4.82427e14	0.225112	0.112556	−	0.993645i	$-0.464096\pi$
$613$	4.82427e14	0.225112	0.112556	+	0.993645i	$0.464096\pi$
$614$	2.89975e15	1.34102
$615$	−1.68535e15	−0.772461
$616$	5.87739e13	0.0266987
$617$	−2.79762e15	−1.25956	−0.629782	−	0.776772i	$-0.716856\pi$
$617$	−2.79762e15	−1.25956	−0.629782	+	0.776772i	$0.716856\pi$
$618$	−4.19917e15	−1.87382
$619$	1.54534e15	0.683479	0.341740	−	0.939795i	$-0.388984\pi$
$619$	1.54534e15	0.683479	0.341740	+	0.939795i	$0.388984\pi$
$620$	3.86638e14	0.169493
$621$	−3.52984e15	−1.53374
$622$	−2.84434e14	−0.122499
$623$	−5.02455e14	−0.214493
$624$	−2.05434e15	−0.869277
$625$	1.35692e14	0.0569135
$626$	2.60337e15	1.08237
$627$	−8.06121e14	−0.332222
$628$	−2.32096e13	−0.00948177
$629$	3.86011e15	1.56322
$630$	6.69798e14	0.268888
$631$	−2.53259e15	−1.00787	−0.503934	−	0.863742i	$-0.668115\pi$
$631$	−2.53259e15	−1.00787	−0.503934	+	0.863742i	$0.668115\pi$
$632$	−2.54675e15	−1.00471
$633$	−2.98513e15	−1.16746
$634$	1.83579e15	0.711756
$635$	2.56373e15	0.985409
$636$	6.26882e14	0.238875
$637$	1.06243e15	0.401358
$638$	−9.21759e13	−0.0345226
$639$	−3.25144e15	−1.20732
$640$	−1.95830e15	−0.720925
$641$	−1.92553e15	−0.702798	−0.351399	−	0.936226i	$-0.614294\pi$
$641$	−1.92553e15	−0.702798	−0.351399	+	0.936226i	$0.614294\pi$
$642$	−1.53725e15	−0.556290
$643$	4.46405e13	0.0160165	0.00800826	−	0.999968i	$-0.497451\pi$
$643$	4.46405e13	0.0160165	0.00800826	+	0.999968i	$0.497451\pi$
$644$	−1.38513e14	−0.0492740
$645$	1.21042e15	0.426932
$646$	6.03772e15	2.11152
$647$	2.01053e14	0.0697167	0.0348584	−	0.999392i	$-0.488902\pi$
$647$	2.01053e14	0.0697167	0.0348584	+	0.999392i	$0.488902\pi$
$648$	−2.36169e15	−0.812008
$649$	6.44492e14	0.219721
$650$	8.99301e14	0.304006
$651$	−1.04666e15	−0.350842
$652$	−1.03616e15	−0.344403
$653$	2.73857e15	0.902614	0.451307	−	0.892369i	$-0.350958\pi$
$653$	2.73857e15	0.902614	0.451307	+	0.892369i	$0.350958\pi$
$654$	−8.41486e15	−2.75023
$655$	−3.15219e15	−1.02161
$656$	2.79105e15	0.897010
$657$	−3.69801e15	−1.17858
$658$	−7.54471e14	−0.238451
$659$	3.05971e15	0.958981	0.479490	−	0.877547i	$-0.340822\pi$
$659$	3.05971e15	0.958981	0.479490	+	0.877547i	$0.340822\pi$
$660$	1.52595e14	0.0474294
$661$	3.78012e15	1.16519	0.582596	−	0.812762i	$-0.302037\pi$
$661$	3.78012e15	1.16519	0.582596	+	0.812762i	$0.302037\pi$
$662$	2.27539e15	0.695564
$663$	3.81919e15	1.15784
$664$	8.70000e14	0.261574
$665$	4.65622e14	0.138840
$666$	7.46790e15	2.20846
$667$	−5.61562e14	−0.164705
$668$	9.98947e14	0.290584
$669$	3.51209e15	1.01326
$670$	−8.93856e14	−0.255774
$671$	9.30628e14	0.264121
$672$	−6.65157e14	−0.187238
$673$	5.91178e15	1.65057	0.825287	−	0.564713i	$-0.191013\pi$
$673$	5.91178e15	1.65057	0.825287	+	0.564713i	$0.191013\pi$
$674$	−2.90865e14	−0.0805494
$675$	4.04916e15	1.11223
$676$	−8.44957e14	−0.230212
$677$	−5.34933e14	−0.144565	−0.0722823	−	0.997384i	$-0.523028\pi$
$677$	−5.34933e14	−0.144565	−0.0722823	+	0.997384i	$0.523028\pi$
$678$	−1.03612e16	−2.77746
$679$	6.80828e14	0.181031
$680$	2.95453e15	0.779272
$681$	−4.80715e15	−1.25770
$682$	−7.28713e14	−0.189122
$683$	−9.35017e12	−0.00240716	−0.00120358	−	0.999999i	$-0.500383\pi$
$683$	−9.35017e12	−0.00240716	−0.00120358	+	0.999999i	$0.500383\pi$
$684$	2.54756e15	0.650602
$685$	2.18067e15	0.552447
$686$	1.75691e15	0.441536
$687$	−8.42200e15	−2.09968
$688$	−2.00455e15	−0.495770
$689$	8.42419e14	0.206691
$690$	4.26253e15	1.03752
$691$	−5.16953e15	−1.24831	−0.624155	−	0.781301i	$-0.714556\pi$
$691$	−5.16953e15	−1.24831	−0.624155	+	0.781301i	$0.714556\pi$
$692$	−9.79934e14	−0.234754
$693$	−2.75326e14	−0.0654358
$694$	−3.03144e15	−0.714778
$695$	−3.70333e15	−0.866316
$696$	−1.12982e15	−0.262216
$697$	−5.18880e15	−1.19478
$698$	1.66665e14	0.0380750
$699$	−2.14509e15	−0.486208
$700$	1.58891e14	0.0357323
$701$	3.36842e15	0.751584	0.375792	−	0.926704i	$-0.377371\pi$
$701$	3.36842e15	0.751584	0.375792	+	0.926704i	$0.377371\pi$
$702$	3.69176e15	0.817296
$703$	5.19144e15	1.14034
$704$	4.42880e14	0.0965242
$705$	5.06375e15	1.09505
$706$	8.04503e15	1.72624
$707$	−8.54174e14	−0.181861
$708$	−3.05587e15	−0.645583
$709$	4.40570e15	0.923550	0.461775	−	0.886997i	$-0.347213\pi$
$709$	4.40570e15	0.923550	0.461775	+	0.886997i	$0.347213\pi$
$710$	1.96179e15	0.408067
$711$	1.19302e16	2.46245
$712$	−4.28785e15	−0.878212
$713$	−4.43953e15	−0.902288
$714$	3.09396e15	0.623985
$715$	2.05060e14	0.0410392
$716$	1.00472e15	0.199536
$717$	5.59021e15	1.10172
$718$	5.18178e15	1.01343
$719$	5.91044e15	1.14712	0.573562	−	0.819162i	$-0.305561\pi$
$719$	5.91044e15	1.14712	0.573562	+	0.819162i	$0.305561\pi$
$720$	7.44480e15	1.43392
$721$	−9.97014e14	−0.190571
$722$	2.15829e15	0.409406
$723$	−1.72444e16	−3.24630
$724$	−8.60549e14	−0.160773
$725$	6.44181e14	0.119440
$726$	1.03547e16	1.90539
$727$	5.70858e15	1.04253	0.521266	−	0.853395i	$-0.325460\pi$
$727$	5.70858e15	1.04253	0.521266	+	0.853395i	$0.325460\pi$
$728$	−3.74494e14	−0.0678769
$729$	−5.58252e15	−1.00422
$730$	2.23123e15	0.398354
$731$	3.72662e15	0.660342
$732$	−4.41259e15	−0.776037
$733$	−5.29228e15	−0.923785	−0.461892	−	0.886936i	$-0.652829\pi$
$733$	−5.29228e15	−0.923785	−0.461892	+	0.886936i	$0.652829\pi$
$734$	1.12873e16	1.95553
$735$	−5.77659e15	−0.993324
$736$	−2.82134e15	−0.481534
$737$	3.67428e14	0.0622444
$738$	−1.00384e16	−1.68793
$739$	−1.63592e15	−0.273034	−0.136517	−	0.990638i	$-0.543591\pi$
$739$	−1.63592e15	−0.273034	−0.136517	+	0.990638i	$0.543591\pi$
$740$	−9.82714e14	−0.162799
$741$	5.13641e15	0.844617
$742$	6.82450e14	0.111391
$743$	−5.38230e15	−0.872026	−0.436013	−	0.899940i	$-0.643610\pi$
$743$	−5.38230e15	−0.872026	−0.436013	+	0.899940i	$0.643610\pi$
$744$	−8.93201e15	−1.43648
$745$	2.85982e15	0.456540
$746$	−2.34911e15	−0.372255
$747$	−4.07551e15	−0.641090
$748$	4.69804e14	0.0733597
$749$	−3.64990e14	−0.0565759
$750$	−1.24917e16	−1.92214
$751$	−3.32903e15	−0.508508	−0.254254	−	0.967138i	$-0.581830\pi$
$751$	−3.32903e15	−0.508508	−0.254254	+	0.967138i	$0.581830\pi$
$752$	−8.38593e15	−1.27161
$753$	−1.54222e16	−2.32153
$754$	5.87323e14	0.0877677
$755$	−5.41007e15	−0.802592
$756$	6.52272e14	0.0960636
$757$	−2.82555e14	−0.0413120	−0.0206560	−	0.999787i	$-0.506575\pi$
$757$	−2.82555e14	−0.0413120	−0.0206560	+	0.999787i	$0.506575\pi$
$758$	−1.04543e16	−1.51745
$759$	−1.75215e15	−0.252489
$760$	3.97353e15	0.568462
$761$	−7.57126e15	−1.07536	−0.537678	−	0.843150i	$-0.680698\pi$
$761$	−7.57126e15	−1.07536	−0.537678	+	0.843150i	$0.680698\pi$
$762$	2.29108e16	3.23064
$763$	−1.99795e15	−0.279704
$764$	−2.99749e15	−0.416624
$765$	−1.38405e16	−1.90991
$766$	8.76676e15	1.20110
$767$	−4.10655e15	−0.558602
$768$	−9.97203e15	−1.34678
$769$	−4.50644e15	−0.604280	−0.302140	−	0.953264i	$-0.597701\pi$
$769$	−4.50644e15	−0.604280	−0.302140	+	0.953264i	$0.597701\pi$
$770$	1.66121e14	0.0221170
$771$	2.19332e16	2.89937
$772$	−2.52651e15	−0.331608
$773$	−1.06249e16	−1.38464	−0.692322	−	0.721588i	$-0.743412\pi$
$773$	−1.06249e16	−1.38464	−0.692322	+	0.721588i	$0.743412\pi$
$774$	7.20963e15	0.932906
$775$	5.09270e15	0.654317
$776$	5.81005e15	0.741208
$777$	2.66029e15	0.336987
$778$	7.75428e15	0.975335
$779$	−6.97838e15	−0.871563
$780$	−9.72297e14	−0.120581
$781$	−8.06412e14	−0.0993061
$782$	1.31234e16	1.60475
$783$	2.64446e15	0.321105
$784$	9.56644e15	1.15348
$785$	1.69583e14	0.0203048
$786$	−2.81697e16	−3.34933
$787$	4.31875e15	0.509914	0.254957	−	0.966952i	$-0.417939\pi$
$787$	4.31875e15	0.509914	0.254957	+	0.966952i	$0.417939\pi$
$788$	−2.49637e15	−0.292694
$789$	2.18142e16	2.53989
$790$	−7.19824e15	−0.832295
$791$	−2.46007e15	−0.282473
$792$	−2.34958e15	−0.267918
$793$	−5.92974e15	−0.671480
$794$	−1.70980e16	−1.92279
$795$	−4.58038e15	−0.511543
$796$	−1.26073e14	−0.0139830
$797$	−2.55939e15	−0.281913	−0.140957	−	0.990016i	$-0.545018\pi$
$797$	−2.55939e15	−0.281913	−0.140957	+	0.990016i	$0.545018\pi$
$798$	4.16105e15	0.455184
$799$	1.55901e16	1.69372
$800$	3.23642e15	0.349197
$801$	2.00864e16	2.15240
$802$	−1.38140e16	−1.47014
$803$	−9.17167e14	−0.0969422
$804$	−1.74216e15	−0.182886
$805$	1.01206e15	0.105518
$806$	4.64319e15	0.480810
$807$	2.70336e16	2.78035
$808$	−7.28935e15	−0.744606
$809$	−8.76754e15	−0.889531	−0.444765	−	0.895647i	$-0.646713\pi$
$809$	−8.76754e15	−0.889531	−0.444765	+	0.895647i	$0.646713\pi$
$810$	−6.67518e15	−0.672659
$811$	1.37707e16	1.37830	0.689149	−	0.724620i	$-0.257985\pi$
$811$	1.37707e16	1.37830	0.689149	+	0.724620i	$0.257985\pi$
$812$	1.03770e14	0.0103161
$813$	−3.27629e16	−3.23507
$814$	1.85216e15	0.181654
$815$	7.57084e15	0.737525
$816$	3.43893e16	3.32757
$817$	5.01190e15	0.481705
$818$	1.93790e15	0.185007
$819$	1.75432e15	0.166359
$820$	1.32097e15	0.124428
$821$	−1.43759e15	−0.134508	−0.0672541	−	0.997736i	$-0.521424\pi$
$821$	−1.43759e15	−0.134508	−0.0672541	+	0.997736i	$0.521424\pi$
$822$	1.94876e16	1.81119
$823$	1.01048e16	0.932887	0.466443	−	0.884551i	$-0.345535\pi$
$823$	1.01048e16	0.932887	0.466443	+	0.884551i	$0.345535\pi$
$824$	−8.50831e15	−0.780268
$825$	2.00994e15	0.183099
$826$	−3.32675e15	−0.301044
$827$	1.32100e16	1.18747	0.593736	−	0.804660i	$-0.297652\pi$
$827$	1.32100e16	1.18747	0.593736	+	0.804660i	$0.297652\pi$
$828$	5.53727e15	0.494457
$829$	6.70050e15	0.594371	0.297185	−	0.954820i	$-0.403952\pi$
$829$	6.70050e15	0.594371	0.297185	+	0.954820i	$0.403952\pi$
$830$	2.45900e15	0.216685
$831$	−2.50364e16	−2.19162
$832$	−2.82192e15	−0.245396
$833$	−1.77848e16	−1.53639
$834$	−3.30950e16	−2.84020
$835$	−7.29891e15	−0.622275
$836$	6.31837e14	0.0535143
$837$	2.09063e16	1.75908
$838$	1.50810e16	1.26063
$839$	−1.02237e16	−0.849017	−0.424508	−	0.905424i	$-0.639553\pi$
$839$	−1.02237e16	−0.849017	−0.424508	+	0.905424i	$0.639553\pi$
$840$	2.03619e15	0.167989
$841$	4.20707e14	0.0344828
$842$	−2.23740e15	−0.182191
$843$	−2.07489e16	−1.67858
$844$	2.33974e15	0.188055
$845$	6.17376e15	0.492990
$846$	3.01612e16	2.39283
$847$	2.45852e15	0.193783
$848$	7.58542e15	0.594022
$849$	1.51963e16	1.18235
$850$	−1.50541e16	−1.16373
$851$	1.12839e16	0.866657
$852$	3.82361e15	0.291780
$853$	1.66742e16	1.26423	0.632115	−	0.774875i	$-0.282187\pi$
$853$	1.66742e16	1.26423	0.632115	+	0.774875i	$0.282187\pi$
$854$	−4.80373e15	−0.361877
$855$	−1.86140e16	−1.39324
$856$	−3.11475e15	−0.231642
$857$	−9.13512e15	−0.675025	−0.337512	−	0.941321i	$-0.609585\pi$
$857$	−9.13512e15	−0.675025	−0.337512	+	0.941321i	$0.609585\pi$
$858$	1.83253e15	0.134546
$859$	−8.83731e15	−0.644700	−0.322350	−	0.946621i	$-0.604473\pi$
$859$	−8.83731e15	−0.644700	−0.322350	+	0.946621i	$0.604473\pi$
$860$	−9.48729e14	−0.0687703
$861$	−3.57599e15	−0.257560
$862$	−6.07204e15	−0.434555
$863$	−1.60167e16	−1.13898	−0.569488	−	0.821999i	$-0.692859\pi$
$863$	−1.60167e16	−1.13898	−0.569488	+	0.821999i	$0.692859\pi$
$864$	1.32860e16	0.938789
$865$	7.15998e15	0.502717
$866$	−5.33809e15	−0.372424
$867$	−3.89541e16	−2.70053
$868$	8.20373e14	0.0565136
$869$	2.95890e15	0.202545
$870$	−3.19337e15	−0.217217
$871$	−2.34116e15	−0.158246
$872$	−1.70501e16	−1.14521
$873$	−2.72172e16	−1.81662
$874$	1.76495e16	1.17063
$875$	−2.96592e15	−0.195485
$876$	4.34876e15	0.284835
$877$	−1.63197e16	−1.06222	−0.531111	−	0.847302i	$-0.678225\pi$
$877$	−1.63197e16	−1.06222	−0.531111	+	0.847302i	$0.678225\pi$
$878$	5.68929e15	0.367992
$879$	4.53313e16	2.91380
$880$	1.84643e15	0.117945
$881$	2.65985e16	1.68845	0.844227	−	0.535986i	$-0.180060\pi$
$881$	2.65985e16	1.68845	0.844227	+	0.535986i	$0.180060\pi$
$882$	−3.44070e16	−2.17055
$883$	−1.26430e16	−0.792621	−0.396310	−	0.918117i	$-0.629710\pi$
$883$	−1.26430e16	−0.792621	−0.396310	+	0.918117i	$0.629710\pi$
$884$	−2.99348e15	−0.186504
$885$	2.23280e16	1.38249
$886$	1.31297e16	0.807920
$887$	−2.51712e16	−1.53931	−0.769653	−	0.638463i	$-0.779571\pi$
$887$	−2.51712e16	−1.53931	−0.769653	+	0.638463i	$0.779571\pi$
$888$	2.27024e16	1.37975
$889$	5.43975e15	0.328563
$890$	−1.21193e16	−0.727502
$891$	2.74389e15	0.163696
$892$	−2.75277e15	−0.163216
$893$	2.09671e16	1.23553
$894$	2.55569e16	1.49676
$895$	−7.34107e15	−0.427300
$896$	−4.15515e15	−0.240377
$897$	1.11643e16	0.641908
$898$	2.29646e16	1.31232
$899$	3.32598e15	0.188904
$900$	−6.35193e15	−0.358569
$901$	−1.41019e16	−0.791210
$902$	−2.48969e15	−0.138838
$903$	2.56829e15	0.142351
$904$	−2.09938e16	−1.15655
$905$	6.28769e15	0.344290
$906$	−4.83473e16	−2.63128
$907$	2.94262e15	0.159182	0.0795909	−	0.996828i	$-0.474639\pi$
$907$	2.94262e15	0.159182	0.0795909	+	0.996828i	$0.474639\pi$
$908$	3.76784e15	0.202591
$909$	3.41470e16	1.82495
$910$	−1.05848e15	−0.0562285
$911$	−1.50922e16	−0.796898	−0.398449	−	0.917190i	$-0.630451\pi$
$911$	−1.50922e16	−0.796898	−0.398449	+	0.917190i	$0.630451\pi$
$912$	4.62500e16	2.42739
$913$	−1.01080e15	−0.0527320
$914$	3.67863e16	1.90758
$915$	3.22410e16	1.66185
$916$	6.60115e15	0.338216
$917$	−6.68835e15	−0.340634
$918$	−6.17993e16	−3.12859
$919$	2.33438e16	1.17472	0.587362	−	0.809324i	$-0.300166\pi$
$919$	2.33438e16	1.17472	0.587362	+	0.809324i	$0.300166\pi$
$920$	8.63670e15	0.432031
$921$	−4.12950e16	−2.05338
$922$	−1.35364e15	−0.0669089
$923$	5.13826e15	0.252468
$924$	3.23777e14	0.0158143
$925$	−1.29440e16	−0.628478
$926$	−1.47181e16	−0.710380
$927$	3.98572e16	1.91235
$928$	2.11367e15	0.100814
$929$	2.32092e16	1.10046	0.550228	−	0.835014i	$-0.314541\pi$
$929$	2.32092e16	1.10046	0.550228	+	0.835014i	$0.314541\pi$
$930$	−2.52458e16	−1.18996
$931$	−2.39187e16	−1.12076
$932$	1.68132e15	0.0783184
$933$	4.05058e15	0.187572
$934$	−2.02198e16	−0.930829
$935$	−3.43267e15	−0.157097
$936$	1.49710e16	0.681134
$937$	2.61093e16	1.18094	0.590469	−	0.807060i	$-0.298943\pi$
$937$	2.61093e16	1.18094	0.590469	+	0.807060i	$0.298943\pi$
$938$	−1.89659e15	−0.0852822
$939$	−3.70743e16	−1.65734
$940$	−3.96896e15	−0.176390
$941$	−2.35970e16	−1.04259	−0.521295	−	0.853377i	$-0.674551\pi$
$941$	−2.35970e16	−1.04259	−0.521295	+	0.853377i	$0.674551\pi$
$942$	1.51548e15	0.0665689
$943$	−1.51679e16	−0.662388
$944$	−3.69768e16	−1.60540
$945$	−4.76589e15	−0.205717
$946$	1.78811e15	0.0767348
$947$	−4.43332e15	−0.189149	−0.0945745	−	0.995518i	$-0.530149\pi$
$947$	−4.43332e15	−0.189149	−0.0945745	+	0.995518i	$0.530149\pi$
$948$	−1.40297e16	−0.595116
$949$	5.84397e15	0.246459
$950$	−2.02462e16	−0.848914
$951$	−2.61432e16	−1.08985
$952$	6.26894e15	0.259831
$953$	−4.25137e15	−0.175194	−0.0875968	−	0.996156i	$-0.527919\pi$
$953$	−4.25137e15	−0.175194	−0.0875968	+	0.996156i	$0.527919\pi$
$954$	−2.72820e16	−1.11779
$955$	2.19015e16	0.892184
$956$	−4.38160e15	−0.177466
$957$	1.31266e15	0.0528613
$958$	−4.32171e16	−1.73039
$959$	4.62696e15	0.184201
$960$	1.53433e16	0.607333
$961$	8.85661e14	0.0348569
$962$	−1.18015e16	−0.461823
$963$	1.45911e16	0.567731
$964$	1.35162e16	0.522914
$965$	1.84602e16	0.710126
$966$	9.04429e15	0.345939
$967$	−1.88143e16	−0.715553	−0.357776	−	0.933807i	$-0.616465\pi$
$967$	−1.88143e16	−0.715553	−0.357776	+	0.933807i	$0.616465\pi$
$968$	2.09805e16	0.793417
$969$	−8.59824e16	−3.23317
$970$	1.64218e16	0.614010
$971$	−2.57026e16	−0.955588	−0.477794	−	0.878472i	$-0.658563\pi$
$971$	−2.57026e16	−0.955588	−0.477794	+	0.878472i	$0.658563\pi$
$972$	3.68027e13	0.00136055
$973$	−7.85777e15	−0.288854
$974$	3.27035e16	1.19542
$975$	−1.28068e16	−0.465496
$976$	−5.33934e16	−1.92981
$977$	3.40579e16	1.22405	0.612024	−	0.790840i	$-0.290356\pi$
$977$	3.40579e16	1.22405	0.612024	+	0.790840i	$0.290356\pi$
$978$	6.76570e16	2.41796
$979$	4.98176e15	0.177043
$980$	4.52768e15	0.160005
$981$	7.98712e16	2.80679
$982$	4.36595e16	1.52569
$983$	−2.90884e15	−0.101083	−0.0505413	−	0.998722i	$-0.516095\pi$
$983$	−2.90884e15	−0.101083	−0.0505413	+	0.998722i	$0.516095\pi$
$984$	−3.05168e16	−1.05455
$985$	1.82400e16	0.626794
$986$	−9.83166e15	−0.335973
$987$	1.07443e16	0.365119
$988$	−4.02591e15	−0.136051
$989$	1.08937e16	0.366096
$990$	−6.64095e15	−0.221941
$991$	3.04918e14	0.0101339	0.00506697	−	0.999987i	$-0.498387\pi$
$991$	3.04918e14	0.0101339	0.00506697	+	0.999987i	$0.498387\pi$
$992$	1.67100e16	0.552283
$993$	−3.24035e16	−1.06505
$994$	4.16255e15	0.136061
$995$	9.21167e14	0.0299441
$996$	4.79270e15	0.154937
$997$	−1.31510e16	−0.422800	−0.211400	−	0.977400i	$-0.567802\pi$
$997$	−1.31510e16	−0.422800	−0.211400	+	0.977400i	$0.567802\pi$
$998$	3.53380e16	1.12986
$999$	−5.31372e16	−1.68962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.11	✓	14
3.2	odd	2		261.12.a.e.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.11	✓	14	1.1	even	1	trivial
261.12.a.e.1.4		14	3.2	odd	2

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+51.1787 q^{2} -728.829 q^{3} +571.255 q^{4} -4173.93 q^{5} -37300.5 q^{6} -8856.29 q^{7} -75577.8 q^{8} +354044. q^{9} +O(q^{10})\)	\(q+51.1787 q^{2} -728.829 q^{3} +571.255 q^{4} -4173.93 q^{5} -37300.5 q^{6} -8856.29 q^{7} -75577.8 q^{8} +354044. q^{9} -213616. q^{10} +87808.9 q^{11} -416347. q^{12} -559497. q^{13} -453253. q^{14} +3.04208e6 q^{15} -5.03790e6 q^{16} +9.36587e6 q^{17} +1.81195e7 q^{18} +1.25961e7 q^{19} -2.38438e6 q^{20} +6.45472e6 q^{21} +4.49394e6 q^{22} +2.73784e7 q^{23} +5.50833e7 q^{24} -3.14064e7 q^{25} -2.86343e7 q^{26} -1.28928e8 q^{27} -5.05920e6 q^{28} -2.05111e7 q^{29} +1.55690e8 q^{30} -1.62155e8 q^{31} -1.03050e8 q^{32} -6.39976e7 q^{33} +4.79333e8 q^{34} +3.69656e7 q^{35} +2.02250e8 q^{36} +4.12147e8 q^{37} +6.44652e8 q^{38} +4.07778e8 q^{39} +3.15457e8 q^{40} -5.54011e8 q^{41} +3.30344e8 q^{42} +3.97893e8 q^{43} +5.01613e7 q^{44} -1.47776e9 q^{45} +1.40119e9 q^{46} +1.66457e9 q^{47} +3.67177e9 q^{48} -1.89889e9 q^{49} -1.60734e9 q^{50} -6.82611e9 q^{51} -3.19616e8 q^{52} -1.50567e9 q^{53} -6.59835e9 q^{54} -3.66508e8 q^{55} +6.69339e8 q^{56} -9.18040e9 q^{57} -1.04973e9 q^{58} +7.33972e9 q^{59} +1.73781e9 q^{60} +1.05983e10 q^{61} -8.29886e9 q^{62} -3.13552e9 q^{63} +5.04368e9 q^{64} +2.33530e9 q^{65} -3.27531e9 q^{66} +4.18440e9 q^{67} +5.35030e9 q^{68} -1.99542e10 q^{69} +1.89185e9 q^{70} -9.18372e9 q^{71} -2.67579e10 q^{72} -1.04450e10 q^{73} +2.10931e10 q^{74} +2.28899e10 q^{75} +7.19559e9 q^{76} -7.77661e8 q^{77} +2.08695e10 q^{78} +3.36970e10 q^{79} +2.10279e10 q^{80} +3.12484e10 q^{81} -2.83536e10 q^{82} -1.15113e10 q^{83} +3.68729e9 q^{84} -3.90925e10 q^{85} +2.03636e10 q^{86} +1.49491e10 q^{87} -6.63640e9 q^{88} +5.67342e10 q^{89} -7.56296e10 q^{90} +4.95507e9 q^{91} +1.56400e10 q^{92} +1.18183e11 q^{93} +8.51904e10 q^{94} -5.25753e10 q^{95} +7.51056e10 q^{96} -7.68751e10 q^{97} -9.71828e10 q^{98} +3.10882e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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