LMFDB - Embedded newform 29.16.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,16,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, 16, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 16 $
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:	$41.3811164790$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 381613 x^{14} - 3733354 x^{13} + 57580338072 x^{12} + 1053633121552 x^{11} + \cdots + 56\!\cdots\!24 $ x^16 - 381613x^14 - 3733354x^13 + 57580338072x^12 + 1053633121552x^11 - 4368708806733008x^10 - 112027323561555872x^9 + 175073374072500887552x^8 + 5628322450139411218432x^7 - 3559766404200168515698688x^6 - 136592485261791822734163968x^5 + 31960388770880055093699280896x^4 + 1389289310261686682407697121280x^3 - 81097743966968601971743751405568x^2 - 3651876483524920831899376851877888x + 5681589407398948985967076414849024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{7}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-328.024$ 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)

$f(q)$	$=$	$q+320.024 q^{2} -2709.91 q^{3} +69647.1 q^{4} +57494.2 q^{5} -867237. q^{6} -3.02383e6 q^{7} +1.18022e7 q^{8} -7.00527e6 q^{9} +O(q^{10})$	\(q+320.024 q^{2} -2709.91 q^{3} +69647.1 q^{4} +57494.2 q^{5} -867237. q^{6} -3.02383e6 q^{7} +1.18022e7 q^{8} -7.00527e6 q^{9} +1.83995e7 q^{10} +7.24868e7 q^{11} -1.88738e8 q^{12} -3.69601e8 q^{13} -9.67696e8 q^{14} -1.55804e8 q^{15} +1.49478e9 q^{16} -1.67654e8 q^{17} -2.24185e9 q^{18} -4.86389e9 q^{19} +4.00430e9 q^{20} +8.19432e9 q^{21} +2.31975e10 q^{22} +1.40185e10 q^{23} -3.19829e10 q^{24} -2.72120e10 q^{25} -1.18281e11 q^{26} +5.78680e10 q^{27} -2.10601e11 q^{28} +1.72499e10 q^{29} -4.98611e10 q^{30} -2.48764e11 q^{31} +9.16312e10 q^{32} -1.96433e11 q^{33} -5.36533e10 q^{34} -1.73853e11 q^{35} -4.87897e11 q^{36} +5.41177e11 q^{37} -1.55656e12 q^{38} +1.00159e12 q^{39} +6.78557e11 q^{40} -1.06393e12 q^{41} +2.62237e12 q^{42} -6.53277e11 q^{43} +5.04849e12 q^{44} -4.02762e11 q^{45} +4.48624e12 q^{46} +3.74526e11 q^{47} -4.05073e12 q^{48} +4.39597e12 q^{49} -8.70848e12 q^{50} +4.54328e11 q^{51} -2.57417e13 q^{52} -1.31034e13 q^{53} +1.85191e13 q^{54} +4.16757e12 q^{55} -3.56878e13 q^{56} +1.31807e13 q^{57} +5.52037e12 q^{58} -1.64063e13 q^{59} -1.08513e13 q^{60} +2.76134e13 q^{61} -7.96105e13 q^{62} +2.11827e13 q^{63} -1.96568e13 q^{64} -2.12499e13 q^{65} -6.28632e13 q^{66} +6.77889e13 q^{67} -1.16766e13 q^{68} -3.79888e13 q^{69} -5.56369e13 q^{70} +7.57736e13 q^{71} -8.26775e13 q^{72} +6.78408e13 q^{73} +1.73189e14 q^{74} +7.37422e13 q^{75} -3.38756e14 q^{76} -2.19187e14 q^{77} +3.20532e14 q^{78} +1.40666e14 q^{79} +8.59412e13 q^{80} -5.62994e13 q^{81} -3.40482e14 q^{82} +2.18621e14 q^{83} +5.70710e14 q^{84} -9.63914e12 q^{85} -2.09064e14 q^{86} -4.67457e13 q^{87} +8.55502e14 q^{88} -2.10743e14 q^{89} -1.28893e14 q^{90} +1.11761e15 q^{91} +9.76345e14 q^{92} +6.74130e14 q^{93} +1.19857e14 q^{94} -2.79645e14 q^{95} -2.48313e14 q^{96} +1.22074e14 q^{97} +1.40681e15 q^{98} -5.07789e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) $ 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * 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 $

$2$	320.024	1.76790	0.883949	−	0.467584i	$-0.154875\pi$
$2$	320.024	1.76790	0.883949	+	0.467584i	$0.154875\pi$
$3$	−2709.91	−0.715396	−0.357698	−	0.933837i	$-0.616438\pi$
$3$	−2709.91	−0.715396	−0.357698	+	0.933837i	$0.616438\pi$
$4$	69647.1	2.12546
$5$	57494.2	0.329116	0.164558	−	0.986367i	$-0.447380\pi$
$5$	57494.2	0.329116	0.164558	+	0.986367i	$0.447380\pi$
$6$	−867237.	−1.26475
$7$	−3.02383e6	−1.38778	−0.693892	−	0.720079i	$-0.744105\pi$
$7$	−3.02383e6	−1.38778	−0.693892	+	0.720079i	$0.744105\pi$
$8$	1.18022e7	1.98970
$9$	−7.00527e6	−0.488209
$10$	1.83995e7	0.581843
$11$	7.24868e7	1.12154	0.560768	−	0.827973i	$-0.310506\pi$
$11$	7.24868e7	1.12154	0.560768	+	0.827973i	$0.310506\pi$
$12$	−1.88738e8	−1.52055
$13$	−3.69601e8	−1.63365	−0.816824	−	0.576888i	$-0.804267\pi$
$13$	−3.69601e8	−1.63365	−0.816824	+	0.576888i	$0.804267\pi$
$14$	−9.67696e8	−2.45346
$15$	−1.55804e8	−0.235448
$16$	1.49478e9	1.39212
$17$	−1.67654e8	−0.0990940	−0.0495470	−	0.998772i	$-0.515778\pi$
$17$	−1.67654e8	−0.0990940	−0.0495470	+	0.998772i	$0.515778\pi$
$18$	−2.24185e9	−0.863104
$19$	−4.86389e9	−1.24834	−0.624168	−	0.781290i	$-0.714562\pi$
$19$	−4.86389e9	−1.24834	−0.624168	+	0.781290i	$0.714562\pi$
$20$	4.00430e9	0.699523
$21$	8.19432e9	0.992814
$22$	2.31975e10	1.98276
$23$	1.40185e10	0.858502	0.429251	−	0.903185i	$-0.358777\pi$
$23$	1.40185e10	0.858502	0.429251	+	0.903185i	$0.358777\pi$
$24$	−3.19829e10	−1.42342
$25$	−2.72120e10	−0.891683
$26$	−1.18281e11	−2.88812
$27$	5.78680e10	1.06466
$28$	−2.10601e11	−2.94968
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	−4.98611e10	−0.416248
$31$	−2.48764e11	−1.62396	−0.811980	−	0.583685i	$-0.801610\pi$
$31$	−2.48764e11	−1.62396	−0.811980	+	0.583685i	$0.801610\pi$
$32$	9.16312e10	0.471431
$33$	−1.96433e11	−0.802342
$34$	−5.36533e10	−0.175188
$35$	−1.73853e11	−0.456742
$36$	−4.87897e11	−1.03767
$37$	5.41177e11	0.937187	0.468594	−	0.883414i	$-0.344761\pi$
$37$	5.41177e11	0.937187	0.468594	+	0.883414i	$0.344761\pi$
$38$	−1.55656e12	−2.20693
$39$	1.00159e12	1.16870
$40$	6.78557e11	0.654842
$41$	−1.06393e12	−0.853165	−0.426582	−	0.904449i	$-0.640283\pi$
$41$	−1.06393e12	−0.853165	−0.426582	+	0.904449i	$0.640283\pi$
$42$	2.62237e12	1.75519
$43$	−6.53277e11	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$43$	−6.53277e11	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$44$	5.04849e12	2.38378
$45$	−4.02762e11	−0.160677
$46$	4.48624e12	1.51774
$47$	3.74526e11	0.107832	0.0539160	−	0.998545i	$-0.482830\pi$
$47$	3.74526e11	0.107832	0.0539160	+	0.998545i	$0.482830\pi$
$48$	−4.05073e12	−0.995919
$49$	4.39597e12	0.925943
$50$	−8.70848e12	−1.57640
$51$	4.54328e11	0.0708914
$52$	−2.57417e13	−3.47225
$53$	−1.31034e13	−1.53220	−0.766099	−	0.642722i	$-0.777805\pi$
$53$	−1.31034e13	−1.53220	−0.766099	+	0.642722i	$0.777805\pi$
$54$	1.85191e13	1.88221
$55$	4.16757e12	0.369116
$56$	−3.56878e13	−2.76127
$57$	1.31807e13	0.893054
$58$	5.52037e12	0.328290
$59$	−1.64063e13	−0.858262	−0.429131	−	0.903242i	$-0.641180\pi$
$59$	−1.64063e13	−0.858262	−0.429131	+	0.903242i	$0.641180\pi$
$60$	−1.08513e13	−0.500436
$61$	2.76134e13	1.12498	0.562492	−	0.826803i	$-0.309843\pi$
$61$	2.76134e13	1.12498	0.562492	+	0.826803i	$0.309843\pi$
$62$	−7.96105e13	−2.87100
$63$	2.11827e13	0.677529
$64$	−1.96568e13	−0.558681
$65$	−2.12499e13	−0.537659
$66$	−6.28632e13	−1.41846
$67$	6.77889e13	1.36646	0.683231	−	0.730202i	$-0.260574\pi$
$67$	6.77889e13	1.36646	0.683231	+	0.730202i	$0.260574\pi$
$68$	−1.16766e13	−0.210620
$69$	−3.79888e13	−0.614169
$70$	−5.56369e13	−0.807473
$71$	7.57736e13	0.988736	0.494368	−	0.869253i	$-0.335400\pi$
$71$	7.57736e13	0.988736	0.494368	+	0.869253i	$0.335400\pi$
$72$	−8.26775e13	−0.971389
$73$	6.78408e13	0.718736	0.359368	−	0.933196i	$-0.382992\pi$
$73$	6.78408e13	0.718736	0.359368	+	0.933196i	$0.382992\pi$
$74$	1.73189e14	1.65685
$75$	7.37422e13	0.637906
$76$	−3.38756e14	−2.65329
$77$	−2.19187e14	−1.55645
$78$	3.20532e14	2.06615
$79$	1.40666e14	0.824113	0.412056	−	0.911158i	$-0.364811\pi$
$79$	1.40666e14	0.824113	0.412056	+	0.911158i	$0.364811\pi$
$80$	8.59412e13	0.458170
$81$	−5.62994e13	−0.273443
$82$	−3.40482e14	−1.50831
$83$	2.18621e14	0.884314	0.442157	−	0.896938i	$-0.354213\pi$
$83$	2.18621e14	0.884314	0.442157	+	0.896938i	$0.354213\pi$
$84$	5.70710e14	2.11019
$85$	−9.63914e12	−0.0326134
$86$	−2.09064e14	−0.647949
$87$	−4.67457e13	−0.132846
$88$	8.55502e14	2.23152
$89$	−2.10743e14	−0.505042	−0.252521	−	0.967591i	$-0.581260\pi$
$89$	−2.10743e14	−0.505042	−0.252521	+	0.967591i	$0.581260\pi$
$90$	−1.28893e14	−0.284061
$91$	1.11761e15	2.26715
$92$	9.76345e14	1.82471
$93$	6.74130e14	1.16177
$94$	1.19857e14	0.190636
$95$	−2.79645e14	−0.410847
$96$	−2.48313e14	−0.337260
$97$	1.22074e14	0.153403	0.0767017	−	0.997054i	$-0.475561\pi$
$97$	1.22074e14	0.153403	0.0767017	+	0.997054i	$0.475561\pi$
$98$	1.40681e15	1.63697
$99$	−5.07789e14	−0.547545
$100$	−1.89524e15	−1.89524
$101$	2.95770e14	0.274501	0.137251	−	0.990536i	$-0.456173\pi$
$101$	2.95770e14	0.274501	0.137251	+	0.990536i	$0.456173\pi$
$102$	1.45396e14	0.125329
$103$	−1.95803e15	−1.56870	−0.784350	−	0.620319i	$-0.787003\pi$
$103$	−1.95803e15	−1.56870	−0.784350	+	0.620319i	$0.787003\pi$
$104$	−4.36210e15	−3.25047
$105$	4.71126e14	0.326751
$106$	−4.19340e15	−2.70877
$107$	−1.08404e15	−0.652632	−0.326316	−	0.945261i	$-0.605807\pi$
$107$	−1.08404e15	−0.652632	−0.326316	+	0.945261i	$0.605807\pi$
$108$	4.03034e15	2.26289
$109$	2.77012e15	1.45144	0.725720	−	0.687990i	$-0.241507\pi$
$109$	2.77012e15	1.45144	0.725720	+	0.687990i	$0.241507\pi$
$110$	1.33372e15	0.652559
$111$	−1.46654e15	−0.670459
$112$	−4.51996e15	−1.93197
$113$	3.91491e15	1.56543	0.782715	−	0.622380i	$-0.213834\pi$
$113$	3.91491e15	1.56543	0.782715	+	0.622380i	$0.213834\pi$
$114$	4.21814e15	1.57883
$115$	8.05980e14	0.282547
$116$	1.20140e15	0.394688
$117$	2.58916e15	0.797562
$118$	−5.25040e15	−1.51732
$119$	5.06957e14	0.137521
$120$	−1.83883e15	−0.468471
$121$	1.07708e15	0.257845
$122$	8.83695e15	1.98886
$123$	2.88315e15	0.610350
$124$	−1.73257e16	−3.45167
$125$	−3.31912e15	−0.622583
$126$	6.77897e15	1.19780
$127$	−6.57717e15	−1.09524	−0.547622	−	0.836726i	$-0.684467\pi$
$127$	−6.57717e15	−1.09524	−0.547622	+	0.836726i	$0.684467\pi$
$128$	−9.29322e15	−1.45912
$129$	1.77032e15	0.262198
$130$	−6.80048e15	−0.950527
$131$	1.32917e16	1.75406	0.877032	−	0.480432i	$-0.159520\pi$
$131$	1.32917e16	1.75406	0.877032	+	0.480432i	$0.159520\pi$
$132$	−1.36810e16	−1.70535
$133$	1.47076e16	1.73242
$134$	2.16940e16	2.41576
$135$	3.32707e15	0.350396
$136$	−1.97868e15	−0.197167
$137$	−5.12443e15	−0.483327	−0.241664	−	0.970360i	$-0.577693\pi$
$137$	−5.12443e15	−0.483327	−0.241664	+	0.970360i	$0.577693\pi$
$138$	−1.21573e16	−1.08579
$139$	−1.06683e16	−0.902575	−0.451288	−	0.892379i	$-0.649035\pi$
$139$	−1.06683e16	−0.902575	−0.451288	+	0.892379i	$0.649035\pi$
$140$	−1.21083e16	−0.970787
$141$	−1.01493e15	−0.0771426
$142$	2.42493e16	1.74798
$143$	−2.67912e16	−1.83220
$144$	−1.04713e16	−0.679647
$145$	9.91768e14	0.0611153
$146$	2.17106e16	1.27065
$147$	−1.19127e16	−0.662416
$148$	3.76914e16	1.99195
$149$	−8.93337e15	−0.448868	−0.224434	−	0.974489i	$-0.572053\pi$
$149$	−8.93337e15	−0.448868	−0.224434	+	0.974489i	$0.572053\pi$
$150$	2.35992e16	1.12775
$151$	−1.44538e16	−0.657137	−0.328569	−	0.944480i	$-0.606566\pi$
$151$	−1.44538e16	−0.657137	−0.328569	+	0.944480i	$0.606566\pi$
$152$	−5.74045e16	−2.48381
$153$	1.17446e15	0.0483786
$154$	−7.01452e16	−2.75164
$155$	−1.43025e16	−0.534471
$156$	6.97577e16	2.48403
$157$	1.24747e16	0.423432	0.211716	−	0.977331i	$-0.432095\pi$
$157$	1.24747e16	0.423432	0.211716	+	0.977331i	$0.432095\pi$
$158$	4.50165e16	1.45695
$159$	3.55091e16	1.09613
$160$	5.26826e15	0.155156
$161$	−4.23894e16	−1.19142
$162$	−1.80171e16	−0.483418
$163$	−3.43143e16	−0.879161	−0.439580	−	0.898203i	$-0.644873\pi$
$163$	−3.43143e16	−0.879161	−0.439580	+	0.898203i	$0.644873\pi$
$164$	−7.40994e16	−1.81337
$165$	−1.12938e16	−0.264064
$166$	6.99639e16	1.56338
$167$	−1.59613e16	−0.340954	−0.170477	−	0.985362i	$-0.554531\pi$
$167$	−1.59613e16	−0.340954	−0.170477	+	0.985362i	$0.554531\pi$
$168$	9.67108e16	1.97540
$169$	8.54192e16	1.66880
$170$	−3.08475e15	−0.0576572
$171$	3.40728e16	0.609449
$172$	−4.54988e16	−0.778999
$173$	−2.89903e16	−0.475233	−0.237616	−	0.971359i	$-0.576366\pi$
$173$	−2.89903e16	−0.475233	−0.237616	+	0.971359i	$0.576366\pi$
$174$	−1.49597e16	−0.234857
$175$	8.22844e16	1.23746
$176$	1.08352e17	1.56132
$177$	4.44596e16	0.613997
$178$	−6.74427e16	−0.892863
$179$	−1.34540e17	−1.70786	−0.853932	−	0.520385i	$-0.825788\pi$
$179$	−1.34540e17	−1.70786	−0.853932	+	0.520385i	$0.825788\pi$
$180$	−2.80512e16	−0.341514
$181$	−5.47318e15	−0.0639221	−0.0319610	−	0.999489i	$-0.510175\pi$
$181$	−5.47318e15	−0.0639221	−0.0319610	+	0.999489i	$0.510175\pi$
$182$	3.57662e17	4.00809
$183$	−7.48300e16	−0.804809
$184$	1.65448e17	1.70816
$185$	3.11145e16	0.308443
$186$	2.15738e17	2.05390
$187$	−1.21527e16	−0.111138
$188$	2.60846e16	0.229193
$189$	−1.74983e17	−1.47752
$190$	−8.94931e16	−0.726336
$191$	−2.33991e16	−0.182578	−0.0912891	−	0.995824i	$-0.529099\pi$
$191$	−2.33991e16	−0.182578	−0.0912891	+	0.995824i	$0.529099\pi$
$192$	5.32684e16	0.399678
$193$	−7.47560e16	−0.539469	−0.269734	−	0.962935i	$-0.586936\pi$
$193$	−7.47560e16	−0.539469	−0.269734	+	0.962935i	$0.586936\pi$
$194$	3.90666e16	0.271202
$195$	5.75855e16	0.384639
$196$	3.06167e17	1.96806
$197$	−2.72973e17	−1.68897	−0.844486	−	0.535577i	$-0.820094\pi$
$197$	−2.72973e17	−1.68897	−0.844486	+	0.535577i	$0.820094\pi$
$198$	−1.62505e17	−0.968003
$199$	−1.50419e17	−0.862788	−0.431394	−	0.902164i	$-0.641978\pi$
$199$	−1.50419e17	−0.862788	−0.431394	+	0.902164i	$0.641978\pi$
$200$	−3.21161e17	−1.77418
$201$	−1.83702e17	−0.977561
$202$	9.46535e16	0.485290
$203$	−5.21607e16	−0.257705
$204$	3.16426e16	0.150677
$205$	−6.11696e16	−0.280790
$206$	−6.26615e17	−2.77330
$207$	−9.82031e16	−0.419129
$208$	−5.52473e17	−2.27424
$209$	−3.52567e17	−1.40005
$210$	1.50771e17	0.577662
$211$	2.71970e17	1.00555	0.502774	−	0.864418i	$-0.332313\pi$
$211$	2.71970e17	1.00555	0.502774	+	0.864418i	$0.332313\pi$
$212$	−9.12614e17	−3.25663
$213$	−2.05340e17	−0.707337
$214$	−3.46919e17	−1.15379
$215$	−3.75596e16	−0.120624
$216$	6.82969e17	2.11835
$217$	7.52221e17	2.25371
$218$	8.86502e17	2.56600
$219$	−1.83843e17	−0.514181
$220$	2.90259e17	0.784541
$221$	6.19652e16	0.161885
$222$	−4.69328e17	−1.18530
$223$	−7.84534e17	−1.91569	−0.957845	−	0.287284i	$-0.907248\pi$
$223$	−7.84534e17	−1.91569	−0.957845	+	0.287284i	$0.907248\pi$
$224$	−2.77077e17	−0.654244
$225$	1.90627e17	0.435328
$226$	1.25286e18	2.76752
$227$	−2.92703e17	−0.625508	−0.312754	−	0.949834i	$-0.601252\pi$
$227$	−2.92703e17	−0.625508	−0.312754	+	0.949834i	$0.601252\pi$
$228$	9.17999e17	1.89815
$229$	3.66693e17	0.733731	0.366865	−	0.930274i	$-0.380431\pi$
$229$	3.66693e17	0.733731	0.366865	+	0.930274i	$0.380431\pi$
$230$	2.57933e17	0.499514
$231$	5.93979e17	1.11348
$232$	2.03586e17	0.369478
$233$	−2.23900e17	−0.393445	−0.196723	−	0.980459i	$-0.563030\pi$
$233$	−2.23900e17	−0.393445	−0.196723	+	0.980459i	$0.563030\pi$
$234$	8.28591e17	1.41001
$235$	2.15331e16	0.0354893
$236$	−1.14265e18	−1.82420
$237$	−3.81193e17	−0.589567
$238$	1.62238e17	0.243123
$239$	1.66888e16	0.0242348	0.0121174	−	0.999927i	$-0.496143\pi$
$239$	1.66888e16	0.0242348	0.0121174	+	0.999927i	$0.496143\pi$
$240$	−2.32893e17	−0.327773
$241$	−1.63462e17	−0.222992	−0.111496	−	0.993765i	$-0.535564\pi$
$241$	−1.63462e17	−0.222992	−0.111496	+	0.993765i	$0.535564\pi$
$242$	3.44692e17	0.455843
$243$	−6.77776e17	−0.869039
$244$	1.92319e18	2.39111
$245$	2.52743e17	0.304743
$246$	9.22677e17	1.07904
$247$	1.79770e18	2.03934
$248$	−2.93596e18	−3.23119
$249$	−5.92444e17	−0.632634
$250$	−1.06220e18	−1.10066
$251$	−5.99920e17	−0.603309	−0.301655	−	0.953417i	$-0.597539\pi$
$251$	−5.99920e17	−0.603309	−0.301655	+	0.953417i	$0.597539\pi$
$252$	1.47532e18	1.44006
$253$	1.01615e18	0.962842
$254$	−2.10485e18	−1.93628
$255$	2.61212e16	0.0233315
$256$	−2.32994e18	−2.02090
$257$	7.88683e17	0.664360	0.332180	−	0.943216i	$-0.392216\pi$
$257$	7.88683e17	0.664360	0.332180	+	0.943216i	$0.392216\pi$
$258$	5.66546e17	0.463540
$259$	−1.63643e18	−1.30061
$260$	−1.48000e18	−1.14277
$261$	−1.20840e17	−0.0906582
$262$	4.25365e18	3.10101
$263$	2.04623e18	1.44973	0.724864	−	0.688892i	$-0.241903\pi$
$263$	2.04623e18	1.44973	0.724864	+	0.688892i	$0.241903\pi$
$264$	−2.31834e18	−1.59642
$265$	−7.53370e17	−0.504271
$266$	4.70677e18	3.06274
$267$	5.71095e17	0.361305
$268$	4.72130e18	2.90436
$269$	1.76471e18	1.05568	0.527838	−	0.849345i	$-0.323003\pi$
$269$	1.76471e18	1.05568	0.527838	+	0.849345i	$0.323003\pi$
$270$	1.06474e18	0.619464
$271$	−2.48183e18	−1.40444	−0.702219	−	0.711961i	$-0.747807\pi$
$271$	−2.48183e18	−1.40444	−0.702219	+	0.711961i	$0.747807\pi$
$272$	−2.50606e17	−0.137951
$273$	−3.02863e18	−1.62191
$274$	−1.63994e18	−0.854473
$275$	−1.97251e18	−1.00005
$276$	−2.64581e18	−1.30539
$277$	3.85945e18	1.85322	0.926611	−	0.376022i	$-0.122708\pi$
$277$	3.85945e18	1.85322	0.926611	+	0.376022i	$0.122708\pi$
$278$	−3.41410e18	−1.59566
$279$	1.74266e18	0.792833
$280$	−2.05184e18	−0.908779
$281$	−3.09987e18	−1.33674	−0.668369	−	0.743830i	$-0.733007\pi$
$281$	−3.09987e18	−1.33674	−0.668369	+	0.743830i	$0.733007\pi$
$282$	−3.24803e17	−0.136380
$283$	−2.13630e18	−0.873504	−0.436752	−	0.899582i	$-0.643871\pi$
$283$	−2.13630e18	−0.873504	−0.436752	+	0.899582i	$0.643871\pi$
$284$	5.27741e18	2.10152
$285$	7.57815e17	0.293918
$286$	−8.57381e18	−3.23913
$287$	3.21713e18	1.18401
$288$	−6.41901e17	−0.230157
$289$	−2.83432e18	−0.990180
$290$	3.17389e17	0.108046
$291$	−3.30810e17	−0.109744
$292$	4.72491e18	1.52765
$293$	5.09825e18	1.60662	0.803311	−	0.595560i	$-0.203070\pi$
$293$	5.09825e18	1.60662	0.803311	+	0.595560i	$0.203070\pi$
$294$	−3.81235e18	−1.17108
$295$	−9.43266e17	−0.282468
$296$	6.38707e18	1.86472
$297$	4.19466e18	1.19405
$298$	−2.85889e18	−0.793552
$299$	−5.18124e18	−1.40249
$300$	5.13593e18	1.35584
$301$	1.97540e18	0.508634
$302$	−4.62557e18	−1.16175
$303$	−8.01512e17	−0.196377
$304$	−7.27045e18	−1.73784
$305$	1.58761e18	0.370250
$306$	3.75856e17	0.0855284
$307$	7.69216e18	1.70809	0.854045	−	0.520200i	$-0.174142\pi$
$307$	7.69216e18	1.70809	0.854045	+	0.520200i	$0.174142\pi$
$308$	−1.52658e19	−3.30817
$309$	5.30609e18	1.12224
$310$	−4.57714e18	−0.944891
$311$	−7.55997e18	−1.52341	−0.761705	−	0.647924i	$-0.775638\pi$
$311$	−7.55997e18	−1.52341	−0.761705	+	0.647924i	$0.775638\pi$
$312$	1.18209e19	2.32537
$313$	−5.71045e18	−1.09670	−0.548350	−	0.836249i	$-0.684744\pi$
$313$	−5.71045e18	−1.09670	−0.548350	+	0.836249i	$0.684744\pi$
$314$	3.99221e18	0.748585
$315$	1.21788e18	0.222986
$316$	9.79699e18	1.75162
$317$	−2.09776e18	−0.366278	−0.183139	−	0.983087i	$-0.558626\pi$
$317$	−2.09776e18	−0.366278	−0.183139	+	0.983087i	$0.558626\pi$
$318$	1.13638e19	1.93784
$319$	1.25039e18	0.208264
$320$	−1.13015e18	−0.183871
$321$	2.93766e18	0.466890
$322$	−1.35656e19	−2.10630
$323$	8.15451e17	0.123703
$324$	−3.92109e18	−0.581191
$325$	1.00576e19	1.45669
$326$	−1.09814e19	−1.55427
$327$	−7.50678e18	−1.03835
$328$	−1.25567e19	−1.69754
$329$	−1.13250e18	−0.149648
$330$	−3.61427e18	−0.466838
$331$	−3.70947e18	−0.468384	−0.234192	−	0.972190i	$-0.575244\pi$
$331$	−3.70947e18	−0.468384	−0.234192	+	0.972190i	$0.575244\pi$
$332$	1.52263e19	1.87957
$333$	−3.79109e18	−0.457543
$334$	−5.10800e18	−0.602771
$335$	3.89747e18	0.449724
$336$	1.22487e19	1.38212
$337$	−2.64988e18	−0.292417	−0.146208	−	0.989254i	$-0.546707\pi$
$337$	−2.64988e18	−0.292417	−0.146208	+	0.989254i	$0.546707\pi$
$338$	2.73362e19	2.95027
$339$	−1.06091e19	−1.11990
$340$	−6.71338e17	−0.0693185
$341$	−1.80321e19	−1.82133
$342$	1.09041e19	1.07744
$343$	1.06315e18	0.102775
$344$	−7.71009e18	−0.729241
$345$	−2.18414e18	−0.202133
$346$	−9.27757e18	−0.840163
$347$	−1.40658e19	−1.24650	−0.623252	−	0.782021i	$-0.714189\pi$
$347$	−1.40658e19	−1.24650	−0.623252	+	0.782021i	$0.714189\pi$
$348$	−3.25570e18	−0.282358
$349$	−6.73903e17	−0.0572014	−0.0286007	−	0.999591i	$-0.509105\pi$
$349$	−6.73903e17	−0.0572014	−0.0286007	+	0.999591i	$0.509105\pi$
$350$	2.63329e19	2.18771
$351$	−2.13881e19	−1.73928
$352$	6.64205e18	0.528727
$353$	2.54849e17	0.0198597	0.00992984	−	0.999951i	$-0.496839\pi$
$353$	2.54849e17	0.0198597	0.00992984	+	0.999951i	$0.496839\pi$
$354$	1.42281e19	1.08548
$355$	4.35654e18	0.325409
$356$	−1.46776e19	−1.07345
$357$	−1.37381e18	−0.0983819
$358$	−4.30559e19	−3.01933
$359$	8.90848e18	0.611780	0.305890	−	0.952067i	$-0.401046\pi$
$359$	8.90848e18	0.611780	0.305890	+	0.952067i	$0.401046\pi$
$360$	−4.75347e18	−0.319700
$361$	8.47628e18	0.558343
$362$	−1.75155e18	−0.113008
$363$	−2.91880e18	−0.184461
$364$	7.78383e19	4.81874
$365$	3.90045e18	0.236548
$366$	−2.39474e19	−1.42282
$367$	2.15271e19	1.25311	0.626555	−	0.779377i	$-0.284464\pi$
$367$	2.15271e19	1.25311	0.626555	+	0.779377i	$0.284464\pi$
$368$	2.09545e19	1.19514
$369$	7.45310e18	0.416523
$370$	9.95738e18	0.545296
$371$	3.96224e19	2.12636
$372$	4.69512e19	2.46931
$373$	3.17421e19	1.63613	0.818067	−	0.575123i	$-0.195046\pi$
$373$	3.17421e19	1.63613	0.818067	+	0.575123i	$0.195046\pi$
$374$	−3.88915e18	−0.196480
$375$	8.99452e18	0.445393
$376$	4.42022e18	0.214553
$377$	−6.37558e18	−0.303361
$378$	−5.59986e19	−2.61210
$379$	2.52302e18	0.115379	0.0576896	−	0.998335i	$-0.481627\pi$
$379$	2.52302e18	0.115379	0.0576896	+	0.998335i	$0.481627\pi$
$380$	−1.94765e19	−0.873240
$381$	1.78236e19	0.783533
$382$	−7.48826e18	−0.322780
$383$	4.82610e18	0.203988	0.101994	−	0.994785i	$-0.467478\pi$
$383$	4.82610e18	0.203988	0.101994	+	0.994785i	$0.467478\pi$
$384$	2.51838e19	1.04385
$385$	−1.26020e19	−0.512253
$386$	−2.39237e19	−0.953726
$387$	4.57638e18	0.178933
$388$	8.50210e18	0.326053
$389$	−3.59548e19	−1.35249	−0.676247	−	0.736675i	$-0.736395\pi$
$389$	−3.59548e19	−1.35249	−0.676247	+	0.736675i	$0.736395\pi$
$390$	1.84287e19	0.680003
$391$	−2.35025e18	−0.0850724
$392$	5.18821e19	1.84235
$393$	−3.60194e19	−1.25485
$394$	−8.73577e19	−2.98593
$395$	8.08749e18	0.271229
$396$	−3.53660e19	−1.16378
$397$	−2.27791e18	−0.0735542	−0.0367771	−	0.999323i	$-0.511709\pi$
$397$	−2.27791e18	−0.0735542	−0.0367771	+	0.999323i	$0.511709\pi$
$398$	−4.81376e19	−1.52532
$399$	−3.98562e19	−1.23937
$400$	−4.06760e19	−1.24133
$401$	5.26225e19	1.57612	0.788060	−	0.615599i	$-0.211086\pi$
$401$	5.26225e19	1.57612	0.788060	+	0.615599i	$0.211086\pi$
$402$	−5.87890e19	−1.72823
$403$	9.19436e19	2.65298
$404$	2.05995e19	0.583441
$405$	−3.23689e18	−0.0899943
$406$	−1.66926e19	−0.455596
$407$	3.92282e19	1.05109
$408$	5.36207e18	0.141053
$409$	−6.26595e19	−1.61831	−0.809155	−	0.587595i	$-0.800075\pi$
$409$	−6.26595e19	−1.61831	−0.809155	+	0.587595i	$0.800075\pi$
$410$	−1.95757e19	−0.496408
$411$	1.38868e19	0.345770
$412$	−1.36371e20	−3.33421
$413$	4.96098e19	1.19108
$414$	−3.14273e19	−0.740977
$415$	1.25694e19	0.291042
$416$	−3.38670e19	−0.770152
$417$	2.89101e19	0.645698
$418$	−1.12830e20	−2.47515
$419$	5.99220e19	1.29116	0.645581	−	0.763692i	$-0.276615\pi$
$419$	5.99220e19	1.29116	0.645581	+	0.763692i	$0.276615\pi$
$420$	3.28125e19	0.694497
$421$	6.28850e19	1.30747	0.653734	−	0.756724i	$-0.273201\pi$
$421$	6.28850e19	1.30747	0.653734	+	0.756724i	$0.273201\pi$
$422$	8.70368e19	1.77770
$423$	−2.62366e18	−0.0526446
$424$	−1.54649e20	−3.04861
$425$	4.56220e18	0.0883604
$426$	−6.57136e19	−1.25050
$427$	−8.34982e19	−1.56123
$428$	−7.55004e19	−1.38714
$429$	7.26019e19	1.31074
$430$	−1.20200e19	−0.213250
$431$	−7.11167e19	−1.23992	−0.619958	−	0.784635i	$-0.712850\pi$
$431$	−7.11167e19	−1.23992	−0.619958	+	0.784635i	$0.712850\pi$
$432$	8.65000e19	1.48214
$433$	8.23689e19	1.38709	0.693544	−	0.720414i	$-0.256048\pi$
$433$	8.23689e19	1.38709	0.693544	+	0.720414i	$0.256048\pi$
$434$	2.40728e20	3.98432
$435$	−2.68761e18	−0.0437216
$436$	1.92931e20	3.08498
$437$	−6.81842e19	−1.07170
$438$	−5.88340e19	−0.909018
$439$	−1.23409e20	−1.87441	−0.937203	−	0.348784i	$-0.886595\pi$
$439$	−1.23409e20	−1.87441	−0.937203	+	0.348784i	$0.886595\pi$
$440$	4.91864e19	0.734429
$441$	−3.07950e19	−0.452054
$442$	1.98303e19	0.286195
$443$	−1.56266e19	−0.221736	−0.110868	−	0.993835i	$-0.535363\pi$
$443$	−1.56266e19	−0.221736	−0.110868	+	0.993835i	$0.535363\pi$
$444$	−1.02140e20	−1.42504
$445$	−1.21165e19	−0.166218
$446$	−2.51069e20	−3.38674
$447$	2.42087e19	0.321118
$448$	5.94389e19	0.775328
$449$	−2.43822e19	−0.312770	−0.156385	−	0.987696i	$-0.549984\pi$
$449$	−2.43822e19	−0.312770	−0.156385	+	0.987696i	$0.549984\pi$
$450$	6.10052e19	0.769615
$451$	−7.71206e19	−0.956856
$452$	2.72662e20	3.32726
$453$	3.91687e19	0.470113
$454$	−9.36718e19	−1.10583
$455$	6.42561e19	0.746155
$456$	1.55561e20	1.77691
$457$	−4.43056e19	−0.497837	−0.248918	−	0.968524i	$-0.580075\pi$
$457$	−4.43056e19	−0.497837	−0.248918	+	0.968524i	$0.580075\pi$
$458$	1.17350e20	1.29716
$459$	−9.70181e18	−0.105501
$460$	5.61342e19	0.600542
$461$	1.22897e20	1.29355	0.646777	−	0.762679i	$-0.276116\pi$
$461$	1.22897e20	1.29355	0.646777	+	0.762679i	$0.276116\pi$
$462$	1.90087e20	1.96851
$463$	−3.54742e19	−0.361456	−0.180728	−	0.983533i	$-0.557845\pi$
$463$	−3.54742e19	−0.361456	−0.180728	+	0.983533i	$0.557845\pi$
$464$	2.57848e19	0.258511
$465$	3.87586e19	0.382359
$466$	−7.16532e19	−0.695571
$467$	1.58210e20	1.51132	0.755660	−	0.654964i	$-0.227316\pi$
$467$	1.58210e20	1.51132	0.755660	+	0.654964i	$0.227316\pi$
$468$	1.80327e20	1.69519
$469$	−2.04982e20	−1.89635
$470$	6.89109e18	0.0627414
$471$	−3.38055e19	−0.302922
$472$	−1.93630e20	−1.70768
$473$	−4.73539e19	−0.411053
$474$	−1.21991e20	−1.04229
$475$	1.32356e20	1.11312
$476$	3.53081e19	0.292295
$477$	9.17928e19	0.748033
$478$	5.34080e18	0.0428447
$479$	−6.09511e19	−0.481354	−0.240677	−	0.970605i	$-0.577370\pi$
$479$	−6.09511e19	−0.481354	−0.240677	+	0.970605i	$0.577370\pi$
$480$	−1.42765e19	−0.110998
$481$	−2.00020e20	−1.53103
$482$	−5.23118e19	−0.394228
$483$	1.14872e20	0.852333
$484$	7.50156e19	0.548039
$485$	7.01855e18	0.0504875
$486$	−2.16904e20	−1.53637
$487$	7.02646e19	0.490083	0.245041	−	0.969513i	$-0.421198\pi$
$487$	7.02646e19	0.490083	0.245041	+	0.969513i	$0.421198\pi$
$488$	3.25899e20	2.23838
$489$	9.29888e19	0.628948
$490$	8.08837e19	0.538754
$491$	−1.94527e20	−1.27605	−0.638027	−	0.770014i	$-0.720249\pi$
$491$	−1.94527e20	−1.27605	−0.638027	+	0.770014i	$0.720249\pi$
$492$	2.00803e20	1.29728
$493$	−2.89201e18	−0.0184013
$494$	5.75306e20	3.60535
$495$	−2.91949e19	−0.180206
$496$	−3.71848e20	−2.26075
$497$	−2.29126e20	−1.37215
$498$	−1.89596e20	−1.11843
$499$	−9.54759e19	−0.554804	−0.277402	−	0.960754i	$-0.589473\pi$
$499$	−9.54759e19	−0.554804	−0.277402	+	0.960754i	$0.589473\pi$
$500$	−2.31167e20	−1.32328
$501$	4.32538e19	0.243917
$502$	−1.91988e20	−1.06659
$503$	−1.94514e20	−1.06461	−0.532305	−	0.846553i	$-0.678674\pi$
$503$	−1.94514e20	−1.06461	−0.532305	+	0.846553i	$0.678674\pi$
$504$	2.50002e20	1.34808
$505$	1.70051e19	0.0903427
$506$	3.25193e20	1.70221
$507$	−2.31479e20	−1.19385
$508$	−4.58081e20	−2.32790
$509$	−7.49415e19	−0.375266	−0.187633	−	0.982239i	$-0.560082\pi$
$509$	−7.49415e19	−0.375266	−0.187633	+	0.982239i	$0.560082\pi$
$510$	8.35941e18	0.0412477
$511$	−2.05139e20	−0.997450
$512$	−4.41114e20	−2.11362
$513$	−2.81463e20	−1.32905
$514$	2.52397e20	1.17452
$515$	−1.12575e20	−0.516284
$516$	1.23298e20	0.557293
$517$	2.71482e19	0.120938
$518$	−5.23695e20	−2.29935
$519$	7.85611e19	0.339979
$520$	−2.50796e20	−1.06978
$521$	−8.21636e19	−0.345459	−0.172729	−	0.984969i	$-0.555259\pi$
$521$	−8.21636e19	−0.345459	−0.172729	+	0.984969i	$0.555259\pi$
$522$	−3.86717e19	−0.160274
$523$	−1.69193e20	−0.691224	−0.345612	−	0.938378i	$-0.612329\pi$
$523$	−1.69193e20	−0.691224	−0.345612	+	0.938378i	$0.612329\pi$
$524$	9.25728e20	3.72820
$525$	−2.22984e20	−0.885275
$526$	6.54842e20	2.56297
$527$	4.17064e19	0.160925
$528$	−2.93624e20	−1.11696
$529$	−7.01180e19	−0.262974
$530$	−2.41096e20	−0.891499
$531$	1.14930e20	0.419012
$532$	1.02434e21	3.68219
$533$	3.93229e20	1.39377
$534$	1.82764e20	0.638750
$535$	−6.23262e19	−0.214792
$536$	8.00057e20	2.71885
$537$	3.64591e20	1.22180
$538$	5.64748e20	1.86633
$539$	3.18650e20	1.03848
$540$	2.31721e20	0.744753
$541$	−2.39468e20	−0.759046	−0.379523	−	0.925182i	$-0.623912\pi$
$541$	−2.39468e20	−0.759046	−0.379523	+	0.925182i	$0.623912\pi$
$542$	−7.94245e20	−2.48290
$543$	1.48319e19	0.0457296
$544$	−1.53623e19	−0.0467160
$545$	1.59266e20	0.477692
$546$	−9.69233e20	−2.86737
$547$	4.56044e20	1.33077	0.665383	−	0.746502i	$-0.268268\pi$
$547$	4.56044e20	1.33077	0.665383	+	0.746502i	$0.268268\pi$
$548$	−3.56902e20	−1.02729
$549$	−1.93439e20	−0.549228
$550$	−6.31250e20	−1.76799
$551$	−8.39015e19	−0.231810
$552$	−4.48351e20	−1.22201
$553$	−4.25350e20	−1.14369
$554$	1.23512e21	3.27631
$555$	−8.43177e19	−0.220659
$556$	−7.43015e20	−1.91839
$557$	−2.87268e20	−0.731769	−0.365884	−	0.930660i	$-0.619233\pi$
$557$	−2.87268e20	−0.731769	−0.365884	+	0.930660i	$0.619233\pi$
$558$	5.57693e20	1.40165
$559$	2.41452e20	0.598745
$560$	−2.59871e20	−0.635841
$561$	3.29328e19	0.0795073
$562$	−9.92032e20	−2.36322
$563$	3.29412e19	0.0774330	0.0387165	−	0.999250i	$-0.487673\pi$
$563$	3.29412e19	0.0774330	0.0387165	+	0.999250i	$0.487673\pi$
$564$	−7.06872e19	−0.163964
$565$	2.25085e20	0.515208
$566$	−6.83668e20	−1.54427
$567$	1.70240e20	0.379479
$568$	8.94294e20	1.96729
$569$	−3.70088e20	−0.803457	−0.401728	−	0.915759i	$-0.631590\pi$
$569$	−3.70088e20	−0.803457	−0.401728	+	0.915759i	$0.631590\pi$
$570$	2.42519e20	0.519618
$571$	6.48804e19	0.137196	0.0685982	−	0.997644i	$-0.478147\pi$
$571$	6.48804e19	0.137196	0.0685982	+	0.997644i	$0.478147\pi$
$572$	−1.86593e21	−3.89426
$573$	6.34096e19	0.130616
$574$	1.02956e21	2.09320
$575$	−3.81470e20	−0.765512
$576$	1.37701e20	0.272753
$577$	6.92712e20	1.35436	0.677180	−	0.735818i	$-0.263202\pi$
$577$	6.92712e20	1.35436	0.677180	+	0.735818i	$0.263202\pi$
$578$	−9.07048e20	−1.75054
$579$	2.02582e20	0.385934
$580$	6.90738e19	0.129898
$581$	−6.61072e20	−1.22724
$582$	−1.05867e20	−0.194016
$583$	−9.49823e20	−1.71842
$584$	8.00669e20	1.43007
$585$	1.48861e20	0.262490
$586$	1.63156e21	2.84034
$587$	−8.27288e20	−1.42191	−0.710953	−	0.703239i	$-0.751736\pi$
$587$	−8.27288e20	−1.42191	−0.710953	+	0.703239i	$0.751736\pi$
$588$	−8.29686e20	−1.40794
$589$	1.20996e21	2.02725
$590$	−3.01867e20	−0.499374
$591$	7.39733e20	1.20828
$592$	8.08941e20	1.30468
$593$	−1.04653e21	−1.66664	−0.833321	−	0.552789i	$-0.813563\pi$
$593$	−1.04653e21	−1.66664	−0.833321	+	0.552789i	$0.813563\pi$
$594$	1.34239e21	2.11096
$595$	2.91471e19	0.0452604
$596$	−6.22183e20	−0.954051
$597$	4.07622e20	0.617235
$598$	−1.65812e21	−2.47946
$599$	1.18926e21	1.75621	0.878103	−	0.478472i	$-0.158809\pi$
$599$	1.18926e21	1.75621	0.878103	+	0.478472i	$0.158809\pi$
$600$	8.70319e20	1.26924
$601$	−2.80139e20	−0.403473	−0.201737	−	0.979440i	$-0.564658\pi$
$601$	−2.80139e20	−0.403473	−0.201737	+	0.979440i	$0.564658\pi$
$602$	6.32174e20	0.899213
$603$	−4.74879e20	−0.667119
$604$	−1.00667e21	−1.39672
$605$	6.19260e19	0.0848609
$606$	−2.56503e20	−0.347174
$607$	4.02004e20	0.537422	0.268711	−	0.963221i	$-0.413402\pi$
$607$	4.02004e20	0.537422	0.268711	+	0.963221i	$0.413402\pi$
$608$	−4.45684e20	−0.588505
$609$	1.41351e20	0.184361
$610$	5.08073e20	0.654565
$611$	−1.38425e20	−0.176160
$612$	8.17979e19	0.102827
$613$	9.23563e20	1.14687	0.573433	−	0.819252i	$-0.305611\pi$
$613$	9.23563e20	1.14687	0.573433	+	0.819252i	$0.305611\pi$
$614$	2.46167e21	3.01973
$615$	1.65765e20	0.200876
$616$	−2.58689e21	−3.09687
$617$	1.37246e21	1.62316	0.811579	−	0.584243i	$-0.198608\pi$
$617$	1.37246e21	1.62316	0.811579	+	0.584243i	$0.198608\pi$
$618$	1.69807e21	1.98401
$619$	1.03911e20	0.119945	0.0599726	−	0.998200i	$-0.480899\pi$
$619$	1.03911e20	0.119945	0.0599726	+	0.998200i	$0.480899\pi$
$620$	−9.96128e20	−1.13600
$621$	8.11220e20	0.914012
$622$	−2.41937e21	−2.69323
$623$	6.37250e20	0.700890
$624$	1.49715e21	1.62698
$625$	6.39614e20	0.686781
$626$	−1.82748e21	−1.93885
$627$	9.55428e20	1.00159
$628$	8.68829e20	0.899989
$629$	−9.07305e19	−0.0928696
$630$	3.89752e20	0.394216
$631$	1.89176e19	0.0189080	0.00945400	−	0.999955i	$-0.496991\pi$
$631$	1.89176e19	0.0189080	0.00945400	+	0.999955i	$0.496991\pi$
$632$	1.66017e21	1.63974
$633$	−7.37016e20	−0.719364
$634$	−6.71332e20	−0.647542
$635$	−3.78149e20	−0.360462
$636$	2.47311e21	2.32978
$637$	−1.62476e21	−1.51266
$638$	4.00154e20	0.368190
$639$	−5.30814e20	−0.482710
$640$	−5.34306e20	−0.480220
$641$	1.80906e21	1.60701	0.803505	−	0.595298i	$-0.202966\pi$
$641$	1.80906e21	1.60701	0.803505	+	0.595298i	$0.202966\pi$
$642$	9.40122e20	0.825413
$643$	7.87543e20	0.683427	0.341713	−	0.939804i	$-0.388993\pi$
$643$	7.87543e20	0.683427	0.341713	+	0.939804i	$0.388993\pi$
$644$	−2.95230e21	−2.53231
$645$	1.01783e20	0.0862937
$646$	2.60963e20	0.218693
$647$	−1.99599e21	−1.65339	−0.826695	−	0.562650i	$-0.809782\pi$
$647$	−1.99599e21	−1.65339	−0.826695	+	0.562650i	$0.809782\pi$
$648$	−6.64456e20	−0.544068
$649$	−1.18924e21	−0.962573
$650$	3.21867e21	2.57529
$651$	−2.03845e21	−1.61229
$652$	−2.38989e21	−1.86862
$653$	5.04577e20	0.390013	0.195006	−	0.980802i	$-0.437527\pi$
$653$	5.04577e20	0.390013	0.195006	+	0.980802i	$0.437527\pi$
$654$	−2.40235e21	−1.83570
$655$	7.64195e20	0.577291
$656$	−1.59034e21	−1.18771
$657$	−4.75243e20	−0.350894
$658$	−3.62427e20	−0.264562
$659$	−8.43742e20	−0.608932	−0.304466	−	0.952523i	$-0.598478\pi$
$659$	−8.43742e20	−0.608932	−0.304466	+	0.952523i	$0.598478\pi$
$660$	−7.86577e20	−0.561257
$661$	−2.80462e20	−0.197863	−0.0989313	−	0.995094i	$-0.531542\pi$
$661$	−2.80462e20	−0.197863	−0.0989313	+	0.995094i	$0.531542\pi$
$662$	−1.18712e21	−0.828054
$663$	−1.67920e20	−0.115812
$664$	2.58021e21	1.75952
$665$	8.45599e20	0.570167
$666$	−1.21324e21	−0.808890
$667$	2.41817e20	0.159420
$668$	−1.11166e21	−0.724684
$669$	2.12602e21	1.37048
$670$	1.24728e21	0.795067
$671$	2.00161e21	1.26171
$672$	7.50855e20	0.468044
$673$	−1.95228e21	−1.20346	−0.601728	−	0.798701i	$-0.705521\pi$
$673$	−1.95228e21	−1.20346	−0.601728	+	0.798701i	$0.705521\pi$
$674$	−8.48025e20	−0.516963
$675$	−1.57470e21	−0.949337
$676$	5.94920e21	3.54698
$677$	2.03645e21	1.20076	0.600382	−	0.799713i	$-0.295015\pi$
$677$	2.03645e21	1.20076	0.600382	+	0.799713i	$0.295015\pi$
$678$	−3.39515e21	−1.97987
$679$	−3.69131e20	−0.212891
$680$	−1.13763e20	−0.0648909
$681$	7.93199e20	0.447485
$682$	−5.77071e21	−3.21993
$683$	−4.89870e19	−0.0270349	−0.0135175	−	0.999909i	$-0.504303\pi$
$683$	−4.89870e19	−0.0270349	−0.0135175	+	0.999909i	$0.504303\pi$
$684$	2.37307e21	1.29536
$685$	−2.94625e20	−0.159071
$686$	3.40232e20	0.181696
$687$	−9.93708e20	−0.524908
$688$	−9.76506e20	−0.510225
$689$	4.84303e21	2.50307
$690$	−6.98976e20	−0.357350
$691$	−2.50968e21	−1.26921	−0.634605	−	0.772837i	$-0.718837\pi$
$691$	−2.50968e21	−1.26921	−0.634605	+	0.772837i	$0.718837\pi$
$692$	−2.01909e21	−1.01009
$693$	1.53547e21	0.759873
$694$	−4.50139e21	−2.20369
$695$	−6.13364e20	−0.297052
$696$	−5.51701e20	−0.264323
$697$	1.78372e20	0.0845435
$698$	−2.15665e20	−0.101126
$699$	6.06750e20	0.281469
$700$	5.73087e21	2.63018
$701$	1.27935e21	0.580904	0.290452	−	0.956889i	$-0.406194\pi$
$701$	1.27935e21	0.580904	0.290452	+	0.956889i	$0.406194\pi$
$702$	−6.84469e21	−3.07486
$703$	−2.63222e21	−1.16992
$704$	−1.42486e21	−0.626581
$705$	−5.83528e19	−0.0253889
$706$	8.15576e19	0.0351099
$707$	−8.94358e20	−0.380948
$708$	3.09648e21	1.30503
$709$	1.13333e21	0.472618	0.236309	−	0.971678i	$-0.424062\pi$
$709$	1.13333e21	0.472618	0.236309	+	0.971678i	$0.424062\pi$
$710$	1.39420e21	0.575289
$711$	−9.85405e20	−0.402339
$712$	−2.48723e21	−1.00488
$713$	−3.48729e21	−1.39417
$714$	−4.39652e20	−0.173929
$715$	−1.54034e21	−0.603005
$716$	−9.37031e21	−3.63000
$717$	−4.52251e19	−0.0173375
$718$	2.85092e21	1.08156
$719$	−8.34392e20	−0.313259	−0.156629	−	0.987657i	$-0.550063\pi$
$719$	−8.34392e20	−0.313259	−0.156629	+	0.987657i	$0.550063\pi$
$720$	−6.02041e20	−0.223683
$721$	5.92074e21	2.17702
$722$	2.71261e21	0.987093
$723$	4.42969e20	0.159528
$724$	−3.81191e20	−0.135864
$725$	−4.69404e20	−0.165581
$726$	−9.34085e20	−0.326108
$727$	−1.08579e21	−0.375178	−0.187589	−	0.982248i	$-0.560067\pi$
$727$	−1.08579e21	−0.375178	−0.187589	+	0.982248i	$0.560067\pi$
$728$	1.31902e22	4.51094
$729$	2.64455e21	0.895149
$730$	1.24824e21	0.418192
$731$	1.09525e20	0.0363188
$732$	−5.21169e21	−1.71059
$733$	−2.85161e21	−0.926426	−0.463213	−	0.886247i	$-0.653304\pi$
$733$	−2.85161e21	−0.926426	−0.463213	+	0.886247i	$0.653304\pi$
$734$	6.88917e21	2.21537
$735$	−6.84912e20	−0.218012
$736$	1.28453e21	0.404725
$737$	4.91380e21	1.53254
$738$	2.38517e21	0.736370
$739$	2.17508e21	0.664725	0.332362	−	0.943152i	$-0.392154\pi$
$739$	2.17508e21	0.664725	0.332362	+	0.943152i	$0.392154\pi$
$740$	2.16704e21	0.655584
$741$	−4.87161e21	−1.45894
$742$	1.26801e22	3.75919
$743$	−1.29739e21	−0.380763	−0.190381	−	0.981710i	$-0.560972\pi$
$743$	−1.29739e21	−0.380763	−0.190381	+	0.981710i	$0.560972\pi$
$744$	7.95621e21	2.31158
$745$	−5.13617e20	−0.147730
$746$	1.01582e22	2.89252
$747$	−1.53150e21	−0.431730
$748$	−8.46400e20	−0.236218
$749$	3.27796e21	0.905711
$750$	2.87846e21	0.787409
$751$	−3.99677e21	−1.08245	−0.541227	−	0.840877i	$-0.682040\pi$
$751$	−3.99677e21	−1.08245	−0.541227	+	0.840877i	$0.682040\pi$
$752$	5.59834e20	0.150116
$753$	1.62573e21	0.431605
$754$	−2.04033e21	−0.536310
$755$	−8.31012e20	−0.216274
$756$	−1.21870e22	−3.14040
$757$	6.02816e21	1.53803	0.769016	−	0.639229i	$-0.220746\pi$
$757$	6.02816e21	1.53803	0.769016	+	0.639229i	$0.220746\pi$
$758$	8.07427e20	0.203979
$759$	−2.75369e21	−0.688813
$760$	−3.30043e21	−0.817463
$761$	−5.21472e21	−1.27893	−0.639464	−	0.768821i	$-0.720844\pi$
$761$	−5.21472e21	−1.27893	−0.639464	+	0.768821i	$0.720844\pi$
$762$	5.70396e21	1.38521
$763$	−8.37635e21	−2.01429
$764$	−1.62968e21	−0.388063
$765$	6.75247e19	0.0159222
$766$	1.54446e21	0.360630
$767$	6.06378e21	1.40210
$768$	6.31393e21	1.44574
$769$	−2.12559e21	−0.481984	−0.240992	−	0.970527i	$-0.577473\pi$
$769$	−2.12559e21	−0.481984	−0.240992	+	0.970527i	$0.577473\pi$
$770$	−4.03294e21	−0.905610
$771$	−2.13726e21	−0.475281
$772$	−5.20654e21	−1.14662
$773$	−7.66603e21	−1.67195	−0.835977	−	0.548765i	$-0.815098\pi$
$773$	−7.66603e21	−1.67195	−0.835977	+	0.548765i	$0.815098\pi$
$774$	1.46455e21	0.316335
$775$	6.76938e21	1.44806
$776$	1.44074e21	0.305227
$777$	4.43457e21	0.930453
$778$	−1.15064e22	−2.39107
$779$	5.17482e21	1.06504
$780$	4.01066e21	0.817536
$781$	5.49258e21	1.10890
$782$	−7.52136e20	−0.150399
$783$	9.98216e20	0.197702
$784$	6.57101e21	1.28903
$785$	7.17225e20	0.139358
$786$	−1.15270e22	−2.21845
$787$	7.71046e21	1.46984	0.734920	−	0.678154i	$-0.237220\pi$
$787$	7.71046e21	1.46984	0.734920	+	0.678154i	$0.237220\pi$
$788$	−1.90118e22	−3.58984
$789$	−5.54511e21	−1.03713
$790$	2.58819e21	0.479504
$791$	−1.18380e22	−2.17248
$792$	−5.99302e21	−1.08945
$793$	−1.02060e22	−1.83783
$794$	−7.28985e20	−0.130036
$795$	2.04157e21	0.360753
$796$	−1.04762e22	−1.83382
$797$	−4.19663e21	−0.727719	−0.363859	−	0.931454i	$-0.618541\pi$
$797$	−4.19663e21	−0.727719	−0.363859	+	0.931454i	$0.618541\pi$
$798$	−1.27549e22	−2.19107
$799$	−6.27908e19	−0.0106855
$800$	−2.49347e21	−0.420367
$801$	1.47631e21	0.246566
$802$	1.68405e22	2.78642
$803$	4.91756e21	0.806089
$804$	−1.27943e22	−2.07777
$805$	−2.43715e21	−0.392114
$806$	2.94241e22	4.69019
$807$	−4.78221e21	−0.755226
$808$	3.49073e21	0.546175
$809$	1.03184e21	0.159956	0.0799779	−	0.996797i	$-0.474515\pi$
$809$	1.03184e21	0.159956	0.0799779	+	0.996797i	$0.474515\pi$
$810$	−1.03588e21	−0.159101
$811$	8.00945e20	0.121884	0.0609420	−	0.998141i	$-0.480590\pi$
$811$	8.00945e20	0.121884	0.0609420	+	0.998141i	$0.480590\pi$
$812$	−3.63284e21	−0.547742
$813$	6.72555e21	1.00473
$814$	1.25539e22	1.85822
$815$	−1.97287e21	−0.289346
$816$	6.79121e20	0.0986895
$817$	3.17747e21	0.457526
$818$	−2.00525e22	−2.86101
$819$	−7.82916e21	−1.10684
$820$	−4.26029e21	−0.596809
$821$	9.54685e21	1.32521	0.662607	−	0.748967i	$-0.269450\pi$
$821$	9.54685e21	1.32521	0.662607	+	0.748967i	$0.269450\pi$
$822$	4.44410e21	0.611286
$823$	8.26893e21	1.12707	0.563534	−	0.826093i	$-0.309441\pi$
$823$	8.26893e21	1.12707	0.563534	+	0.826093i	$0.309441\pi$
$824$	−2.31090e22	−3.12124
$825$	5.34533e21	0.715435
$826$	1.58763e22	2.10571
$827$	6.84297e21	0.899401	0.449701	−	0.893179i	$-0.351531\pi$
$827$	6.84297e21	0.899401	0.449701	+	0.893179i	$0.351531\pi$
$828$	−6.83956e21	−0.890842
$829$	−3.33077e21	−0.429918	−0.214959	−	0.976623i	$-0.568962\pi$
$829$	−3.33077e21	−0.429918	−0.214959	+	0.976623i	$0.568962\pi$
$830$	4.02252e21	0.514532
$831$	−1.04588e22	−1.32579
$832$	7.26519e21	0.912688
$833$	−7.37003e20	−0.0917554
$834$	9.25192e21	1.14153
$835$	−9.17684e20	−0.112213
$836$	−2.45553e22	−2.97576
$837$	−1.43955e22	−1.72896
$838$	1.91764e22	2.28264
$839$	−1.35185e21	−0.159483	−0.0797415	−	0.996816i	$-0.525409\pi$
$839$	−1.35185e21	−0.159483	−0.0797415	+	0.996816i	$0.525409\pi$
$840$	5.56031e21	0.650136
$841$	2.97558e20	0.0344828
$842$	2.01247e22	2.31147
$843$	8.40039e21	0.956296
$844$	1.89419e22	2.13725
$845$	4.91111e21	0.549230
$846$	−8.39632e20	−0.0930703
$847$	−3.25691e21	−0.357833
$848$	−1.95867e22	−2.13301
$849$	5.78920e21	0.624901
$850$	1.46001e21	0.156212
$851$	7.58647e21	0.804577
$852$	−1.43013e22	−1.50342
$853$	−9.63995e21	−1.00452	−0.502258	−	0.864718i	$-0.667497\pi$
$853$	−9.63995e21	−1.00452	−0.502258	+	0.864718i	$0.667497\pi$
$854$	−2.67214e22	−2.76010
$855$	1.95899e21	0.200579
$856$	−1.27941e22	−1.29854
$857$	7.31336e21	0.735801	0.367901	−	0.929865i	$-0.380077\pi$
$857$	7.31336e21	0.735801	0.367901	+	0.929865i	$0.380077\pi$
$858$	2.32343e22	2.31726
$859$	−2.01857e22	−1.99570	−0.997848	−	0.0655651i	$-0.979115\pi$
$859$	−2.01857e22	−1.99570	−0.997848	+	0.0655651i	$0.979115\pi$
$860$	−2.61592e21	−0.256381
$861$	−8.71816e21	−0.847034
$862$	−2.27590e22	−2.19204
$863$	1.60602e22	1.53346	0.766728	−	0.641972i	$-0.221884\pi$
$863$	1.60602e22	1.53346	0.766728	+	0.641972i	$0.221884\pi$
$864$	5.30251e21	0.501913
$865$	−1.66677e21	−0.156407
$866$	2.63600e22	2.45223
$867$	7.68075e21	0.708371
$868$	5.23900e22	4.79016
$869$	1.01964e22	0.924273
$870$	−8.60097e20	−0.0772953
$871$	−2.50549e22	−2.23232
$872$	3.26934e22	2.88793
$873$	−8.55161e20	−0.0748930
$874$	−2.18206e22	−1.89465
$875$	1.00364e22	0.864010
$876$	−1.28041e22	−1.09287
$877$	1.54381e22	1.30646	0.653231	−	0.757159i	$-0.273413\pi$
$877$	1.54381e22	1.30646	0.653231	+	0.757159i	$0.273413\pi$
$878$	−3.94939e22	−3.31376
$879$	−1.38158e22	−1.14937
$880$	6.22960e21	0.513854
$881$	2.71627e21	0.222154	0.111077	−	0.993812i	$-0.464570\pi$
$881$	2.71627e21	0.222154	0.111077	+	0.993812i	$0.464570\pi$
$882$	−9.85511e21	−0.799185
$883$	−2.24993e21	−0.180911	−0.0904554	−	0.995901i	$-0.528832\pi$
$883$	−2.24993e21	−0.180911	−0.0904554	+	0.995901i	$0.528832\pi$
$884$	4.31569e21	0.344079
$885$	2.55617e21	0.202076
$886$	−5.00088e21	−0.392007
$887$	4.36758e21	0.339480	0.169740	−	0.985489i	$-0.445707\pi$
$887$	4.36758e21	0.339480	0.169740	+	0.985489i	$0.445707\pi$
$888$	−1.73084e22	−1.33401
$889$	1.98882e22	1.51996
$890$	−3.87756e21	−0.293856
$891$	−4.08096e21	−0.306676
$892$	−5.46405e22	−4.07173
$893$	−1.82165e21	−0.134611
$894$	7.74735e21	0.567704
$895$	−7.73526e21	−0.562085
$896$	2.81011e22	2.02495
$897$	1.40407e22	1.00334
$898$	−7.80289e21	−0.552946
$899$	−4.29116e21	−0.301562
$900$	1.32766e22	0.925272
$901$	2.19684e21	0.151832
$902$	−2.46804e22	−1.69162
$903$	−5.35316e21	−0.363875
$904$	4.62045e22	3.11473
$905$	−3.14676e20	−0.0210378
$906$	1.25349e22	0.831112
$907$	−9.72247e21	−0.639326	−0.319663	−	0.947531i	$-0.603570\pi$
$907$	−9.72247e21	−0.639326	−0.319663	+	0.947531i	$0.603570\pi$
$908$	−2.03859e22	−1.32949
$909$	−2.07195e21	−0.134014
$910$	2.05635e22	1.31913
$911$	−3.00900e21	−0.191441	−0.0957205	−	0.995408i	$-0.530515\pi$
$911$	−3.00900e21	−0.191441	−0.0957205	+	0.995408i	$0.530515\pi$
$912$	1.97023e22	1.24324
$913$	1.58471e22	0.991790
$914$	−1.41788e22	−0.880124
$915$	−4.30229e21	−0.264875
$916$	2.55391e22	1.55952
$917$	−4.01918e22	−2.43426
$918$	−3.10481e21	−0.186515
$919$	−2.77238e22	−1.65191	−0.825955	−	0.563736i	$-0.809364\pi$
$919$	−2.77238e22	−1.65191	−0.825955	+	0.563736i	$0.809364\pi$
$920$	9.51233e21	0.562183
$921$	−2.08451e22	−1.22196
$922$	3.93300e22	2.28687
$923$	−2.80060e22	−1.61525
$924$	4.13689e22	2.36665
$925$	−1.47265e22	−0.835673
$926$	−1.13526e22	−0.639017
$927$	1.37165e22	0.765854
$928$	1.58063e21	0.0875426
$929$	1.58031e22	0.868208	0.434104	−	0.900863i	$-0.357065\pi$
$929$	1.58031e22	0.868208	0.434104	+	0.900863i	$0.357065\pi$
$930$	1.24037e22	0.675971
$931$	−2.13815e22	−1.15589
$932$	−1.55940e22	−0.836253
$933$	2.04869e22	1.08984
$934$	5.06308e22	2.67186
$935$	−6.98710e20	−0.0365771
$936$	3.05577e22	1.58691
$937$	1.47124e22	0.757942	0.378971	−	0.925409i	$-0.376278\pi$
$937$	1.47124e22	0.757942	0.378971	+	0.925409i	$0.376278\pi$
$938$	−6.55990e22	−3.35256
$939$	1.54748e22	0.784574
$940$	1.49972e21	0.0754310
$941$	2.39389e22	1.19449	0.597243	−	0.802060i	$-0.296263\pi$
$941$	2.39389e22	1.19449	0.597243	+	0.802060i	$0.296263\pi$
$942$	−1.08186e22	−0.535534
$943$	−1.49146e22	−0.732444
$944$	−2.45238e22	−1.19481
$945$	−1.00605e22	−0.486274
$946$	−1.51544e22	−0.726699
$947$	2.03543e22	0.968348	0.484174	−	0.874972i	$-0.339120\pi$
$947$	2.03543e22	0.968348	0.484174	+	0.874972i	$0.339120\pi$
$948$	−2.65490e22	−1.25310
$949$	−2.50740e22	−1.17416
$950$	4.23571e22	1.96788
$951$	5.68474e21	0.262034
$952$	5.98320e21	0.273625
$953$	1.60668e22	0.729008	0.364504	−	0.931202i	$-0.381239\pi$
$953$	1.60668e22	0.729008	0.364504	+	0.931202i	$0.381239\pi$
$954$	2.93759e22	1.32245
$955$	−1.34531e21	−0.0600894
$956$	1.16232e21	0.0515102
$957$	−3.38844e21	−0.148991
$958$	−1.95058e22	−0.850985
$959$	1.54954e22	0.670754
$960$	3.06262e21	0.131540
$961$	3.84185e22	1.63725
$962$	−6.40110e22	−2.70671
$963$	7.59401e21	0.318621
$964$	−1.13847e22	−0.473962
$965$	−4.29804e21	−0.177548
$966$	3.67616e22	1.50684
$967$	−2.61938e21	−0.106537	−0.0532685	−	0.998580i	$-0.516964\pi$
$967$	−2.61938e21	−0.106537	−0.0532685	+	0.998580i	$0.516964\pi$
$968$	1.27119e22	0.513034
$969$	−2.20980e21	−0.0884963
$970$	2.24610e21	0.0892568
$971$	−2.35493e22	−0.928612	−0.464306	−	0.885675i	$-0.653696\pi$
$971$	−2.35493e22	−0.928612	−0.464306	+	0.885675i	$0.653696\pi$
$972$	−4.72051e22	−1.84711
$973$	3.22590e22	1.25258
$974$	2.24863e22	0.866416
$975$	−2.72552e22	−1.04211
$976$	4.12760e22	1.56612
$977$	−4.94505e22	−1.86192	−0.930961	−	0.365120i	$-0.881028\pi$
$977$	−4.94505e22	−1.86192	−0.930961	+	0.365120i	$0.881028\pi$
$978$	2.97586e22	1.11191
$979$	−1.52761e22	−0.566424
$980$	1.76028e22	0.647719
$981$	−1.94054e22	−0.708607
$982$	−6.22533e22	−2.25593
$983$	1.47938e22	0.532020	0.266010	−	0.963970i	$-0.414295\pi$
$983$	1.47938e22	0.532020	0.266010	+	0.963970i	$0.414295\pi$
$984$	3.40275e22	1.21441
$985$	−1.56943e22	−0.555868
$986$	−9.25512e20	−0.0325316
$987$	3.06898e21	0.107057
$988$	1.25205e23	4.33454
$989$	−9.15794e21	−0.314648
$990$	−9.34307e21	−0.318585
$991$	−4.48584e22	−1.51807	−0.759035	−	0.651050i	$-0.774329\pi$
$991$	−4.48584e22	−1.51807	−0.759035	+	0.651050i	$0.774329\pi$
$992$	−2.27946e22	−0.765586
$993$	1.00523e22	0.335080
$994$	−7.33258e22	−2.42582
$995$	−8.64821e21	−0.283957
$996$	−4.12620e22	−1.34464
$997$	5.76938e21	0.186602	0.0933008	−	0.995638i	$-0.470258\pi$
$997$	5.76938e21	0.186602	0.0933008	+	0.995638i	$0.470258\pi$
$998$	−3.05545e22	−0.980836
$999$	3.13168e22	0.997784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.16	✓	16	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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+320.024 q^{2} -2709.91 q^{3} +69647.1 q^{4} +57494.2 q^{5} -867237. q^{6} -3.02383e6 q^{7} +1.18022e7 q^{8} -7.00527e6 q^{9} +O(q^{10})\)	\(q+320.024 q^{2} -2709.91 q^{3} +69647.1 q^{4} +57494.2 q^{5} -867237. q^{6} -3.02383e6 q^{7} +1.18022e7 q^{8} -7.00527e6 q^{9} +1.83995e7 q^{10} +7.24868e7 q^{11} -1.88738e8 q^{12} -3.69601e8 q^{13} -9.67696e8 q^{14} -1.55804e8 q^{15} +1.49478e9 q^{16} -1.67654e8 q^{17} -2.24185e9 q^{18} -4.86389e9 q^{19} +4.00430e9 q^{20} +8.19432e9 q^{21} +2.31975e10 q^{22} +1.40185e10 q^{23} -3.19829e10 q^{24} -2.72120e10 q^{25} -1.18281e11 q^{26} +5.78680e10 q^{27} -2.10601e11 q^{28} +1.72499e10 q^{29} -4.98611e10 q^{30} -2.48764e11 q^{31} +9.16312e10 q^{32} -1.96433e11 q^{33} -5.36533e10 q^{34} -1.73853e11 q^{35} -4.87897e11 q^{36} +5.41177e11 q^{37} -1.55656e12 q^{38} +1.00159e12 q^{39} +6.78557e11 q^{40} -1.06393e12 q^{41} +2.62237e12 q^{42} -6.53277e11 q^{43} +5.04849e12 q^{44} -4.02762e11 q^{45} +4.48624e12 q^{46} +3.74526e11 q^{47} -4.05073e12 q^{48} +4.39597e12 q^{49} -8.70848e12 q^{50} +4.54328e11 q^{51} -2.57417e13 q^{52} -1.31034e13 q^{53} +1.85191e13 q^{54} +4.16757e12 q^{55} -3.56878e13 q^{56} +1.31807e13 q^{57} +5.52037e12 q^{58} -1.64063e13 q^{59} -1.08513e13 q^{60} +2.76134e13 q^{61} -7.96105e13 q^{62} +2.11827e13 q^{63} -1.96568e13 q^{64} -2.12499e13 q^{65} -6.28632e13 q^{66} +6.77889e13 q^{67} -1.16766e13 q^{68} -3.79888e13 q^{69} -5.56369e13 q^{70} +7.57736e13 q^{71} -8.26775e13 q^{72} +6.78408e13 q^{73} +1.73189e14 q^{74} +7.37422e13 q^{75} -3.38756e14 q^{76} -2.19187e14 q^{77} +3.20532e14 q^{78} +1.40666e14 q^{79} +8.59412e13 q^{80} -5.62994e13 q^{81} -3.40482e14 q^{82} +2.18621e14 q^{83} +5.70710e14 q^{84} -9.63914e12 q^{85} -2.09064e14 q^{86} -4.67457e13 q^{87} +8.55502e14 q^{88} -2.10743e14 q^{89} -1.28893e14 q^{90} +1.11761e15 q^{91} +9.76345e14 q^{92} +6.74130e14 q^{93} +1.19857e14 q^{94} -2.79645e14 q^{95} -2.48313e14 q^{96} +1.22074e14 q^{97} +1.40681e15 q^{98} -5.07789e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9} + 27111646 q^{10} - 128305158 q^{11} - 566454670 q^{12} - 500341634 q^{13} - 2456995576 q^{14} - 1005836398 q^{15} + 3638194738 q^{16} - 1889649440 q^{17} + 7114827706 q^{18} - 11903789760 q^{19} + 21125268698 q^{20} + 1845797984 q^{21} + 14207940510 q^{22} - 6296706268 q^{23} + 19916867274 q^{24} + 57929280374 q^{25} + 46861268662 q^{26} - 66882170482 q^{27} - 50278055968 q^{28} + 275998020944 q^{29} - 288715178542 q^{30} - 791595409290 q^{31} - 846144416938 q^{32} - 1192946764766 q^{33} - 1500307227904 q^{34} - 731093348200 q^{35} - 766217409340 q^{36} - 22311934700 q^{37} + 1194772372172 q^{38} - 1484120611454 q^{39} - 5651885433026 q^{40} + 871755491316 q^{41} - 5429421460912 q^{42} - 4296897329422 q^{43} - 10539797438606 q^{44} - 4399313787580 q^{45} - 20780033587764 q^{46} - 7817561912774 q^{47} - 36311476834866 q^{48} - 18565097654464 q^{49} - 33573686907474 q^{50} - 27333906159300 q^{51} - 48854284368422 q^{52} - 41630222638006 q^{53} - 88633328654882 q^{54} - 68569446879302 q^{55} - 66690562169864 q^{56} - 80322439188772 q^{57} - 2207984167552 q^{58} - 60146094578732 q^{59} - 170149488214170 q^{60} - 71628304977160 q^{61} - 95316700851110 q^{62} - 99862426093816 q^{63} - 20954801982074 q^{64} - 53095801190146 q^{65} - 84071816219318 q^{66} - 44591877980312 q^{67} + 24848392371308 q^{68} + 33786235351468 q^{69} - 254302493648008 q^{70} - 2238339487076 q^{71} - 335696824658688 q^{72} + 60304297937180 q^{73} - 4683993400652 q^{74} - 408007582551580 q^{75} - 511662725684676 q^{76} + 2082869459792 q^{77} + 134746909641474 q^{78} - 9999680374282 q^{79} + 10\!\cdots\!46 q^{80}+ \cdots + 531562034651476 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 - 3214 * q^3 + 239962 * q^4 - 82010 * q^5 - 112778 * q^6 - 3706320 * q^7 - 21137070 * q^8 + 73272578 * q^9 + 27111646 * q^10 - 128305158 * q^11 - 566454670 * q^12 - 500341634 * q^13 - 2456995576 * q^14 - 1005836398 * q^15 + 3638194738 * q^16 - 1889649440 * q^17 + 7114827706 * q^18 - 11903789760 * q^19 + 21125268698 * q^20 + 1845797984 * q^21 + 14207940510 * q^22 - 6296706268 * q^23 + 19916867274 * q^24 + 57929280374 * q^25 + 46861268662 * q^26 - 66882170482 * q^27 - 50278055968 * q^28 + 275998020944 * q^29 - 288715178542 * q^30 - 791595409290 * q^31 - 846144416938 * q^32 - 1192946764766 * q^33 - 1500307227904 * q^34 - 731093348200 * q^35 - 766217409340 * q^36 - 22311934700 * q^37 + 1194772372172 * q^38 - 1484120611454 * q^39 - 5651885433026 * q^40 + 871755491316 * q^41 - 5429421460912 * q^42 - 4296897329422 * q^43 - 10539797438606 * q^44 - 4399313787580 * q^45 - 20780033587764 * q^46 - 7817561912774 * q^47 - 36311476834866 * q^48 - 18565097654464 * q^49 - 33573686907474 * q^50 - 27333906159300 * q^51 - 48854284368422 * q^52 - 41630222638006 * q^53 - 88633328654882 * q^54 - 68569446879302 * q^55 - 66690562169864 * q^56 - 80322439188772 * q^57 - 2207984167552 * q^58 - 60146094578732 * q^59 - 170149488214170 * q^60 - 71628304977160 * q^61 - 95316700851110 * q^62 - 99862426093816 * q^63 - 20954801982074 * q^64 - 53095801190146 * q^65 - 84071816219318 * q^66 - 44591877980312 * q^67 + 24848392371308 * q^68 + 33786235351468 * q^69 - 254302493648008 * q^70 - 2238339487076 * q^71 - 335696824658688 * q^72 + 60304297937180 * q^73 - 4683993400652 * q^74 - 408007582551580 * q^75 - 511662725684676 * q^76 + 2082869459792 * q^77 + 134746909641474 * q^78 - 9999680374282 * q^79 + 1065964290115846 * q^80 + 1227860473120604 * q^81 - 482856386515020 * q^82 + 1449900899821108 * q^83 + 2256322335776952 * q^84 + 1364385639985788 * q^85 + 1206993542651814 * q^86 - 55441102457126 * q^87 + 2648043460385618 * q^88 - 162544796147532 * q^89 + 1885912570259156 * q^90 + 858443116817000 * q^91 + 2263858121857900 * q^92 + 3752667465062574 * q^93 + 3639931425958406 * q^94 - 73522560256708 * q^95 + 6634505750804190 * q^96 + 463840517939252 * q^97 + 2013726729859888 * q^98 + 531562034651476 * q^99

Introduction

L-functions

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