LMFDB - Embedded newform 29.16.a.a.1.3

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			1.3
Root			$281.475$ 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)

$f(q)$	$=$	$q-289.475 q^{2} +4726.56 q^{3} +51028.0 q^{4} +42761.9 q^{5} -1.36822e6 q^{6} +3.84346e6 q^{7} -5.28581e6 q^{8} +7.99150e6 q^{9} +O(q^{10})$	\(q-289.475 q^{2} +4726.56 q^{3} +51028.0 q^{4} +42761.9 q^{5} -1.36822e6 q^{6} +3.84346e6 q^{7} -5.28581e6 q^{8} +7.99150e6 q^{9} -1.23785e7 q^{10} -9.93047e7 q^{11} +2.41187e8 q^{12} -2.12186e8 q^{13} -1.11259e9 q^{14} +2.02117e8 q^{15} -1.41973e8 q^{16} -1.04195e9 q^{17} -2.31334e9 q^{18} -7.23234e9 q^{19} +2.18205e9 q^{20} +1.81664e10 q^{21} +2.87463e10 q^{22} +2.50164e10 q^{23} -2.49837e10 q^{24} -2.86890e10 q^{25} +6.14227e10 q^{26} -3.00487e10 q^{27} +1.96124e11 q^{28} +1.72499e10 q^{29} -5.85078e10 q^{30} -6.48340e10 q^{31} +2.14303e11 q^{32} -4.69370e11 q^{33} +3.01618e11 q^{34} +1.64354e11 q^{35} +4.07790e11 q^{36} -6.94616e11 q^{37} +2.09358e12 q^{38} -1.00291e12 q^{39} -2.26031e11 q^{40} +1.24986e12 q^{41} -5.25872e12 q^{42} -2.69349e12 q^{43} -5.06732e12 q^{44} +3.41731e11 q^{45} -7.24164e12 q^{46} -2.08007e12 q^{47} -6.71047e11 q^{48} +1.00247e13 q^{49} +8.30476e12 q^{50} -4.92483e12 q^{51} -1.08274e13 q^{52} -3.67599e12 q^{53} +8.69835e12 q^{54} -4.24646e12 q^{55} -2.03158e13 q^{56} -3.41841e13 q^{57} -4.99341e12 q^{58} +2.50869e13 q^{59} +1.03136e13 q^{60} -1.69406e12 q^{61} +1.87678e13 q^{62} +3.07150e13 q^{63} -5.73833e13 q^{64} -9.07348e12 q^{65} +1.35871e14 q^{66} -1.14676e13 q^{67} -5.31685e13 q^{68} +1.18242e14 q^{69} -4.75763e13 q^{70} -7.22982e13 q^{71} -4.22415e13 q^{72} +2.46900e13 q^{73} +2.01074e14 q^{74} -1.35600e14 q^{75} -3.69051e14 q^{76} -3.81674e14 q^{77} +2.90318e14 q^{78} -6.45470e13 q^{79} -6.07105e12 q^{80} -2.56696e14 q^{81} -3.61803e14 q^{82} +9.53772e13 q^{83} +9.26993e14 q^{84} -4.45556e13 q^{85} +7.79700e14 q^{86} +8.15326e13 q^{87} +5.24906e14 q^{88} -3.92599e13 q^{89} -9.89228e13 q^{90} -8.15531e14 q^{91} +1.27654e15 q^{92} -3.06442e14 q^{93} +6.02130e14 q^{94} -3.09268e14 q^{95} +1.01292e15 q^{96} +7.04551e14 q^{97} -2.90189e15 q^{98} -7.93594e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−289.475	−1.59914	−0.799570	−	0.600573i	$-0.794939\pi$
$2$	−289.475	−1.59914	−0.799570	+	0.600573i	$0.794939\pi$
$3$	4726.56	1.24777	0.623887	−	0.781514i	$-0.285552\pi$
$3$	4726.56	1.24777	0.623887	+	0.781514i	$0.285552\pi$
$4$	51028.0	1.55725
$5$	42761.9	0.244783	0.122392	−	0.992482i	$-0.460944\pi$
$5$	42761.9	0.244783	0.122392	+	0.992482i	$0.460944\pi$
$6$	−1.36822e6	−1.99537
$7$	3.84346e6	1.76395	0.881977	−	0.471292i	$-0.156212\pi$
$7$	3.84346e6	1.76395	0.881977	+	0.471292i	$0.156212\pi$
$8$	−5.28581e6	−0.891120
$9$	7.99150e6	0.556941
$10$	−1.23785e7	−0.391443
$11$	−9.93047e7	−1.53647	−0.768236	−	0.640166i	$-0.778865\pi$
$11$	−9.93047e7	−1.53647	−0.768236	+	0.640166i	$0.778865\pi$
$12$	2.41187e8	1.94310
$13$	−2.12186e8	−0.937869	−0.468935	−	0.883233i	$-0.655362\pi$
$13$	−2.12186e8	−0.937869	−0.468935	+	0.883233i	$0.655362\pi$
$14$	−1.11259e9	−2.82081
$15$	2.02117e8	0.305434
$16$	−1.41973e8	−0.132223
$17$	−1.04195e9	−0.615856	−0.307928	−	0.951410i	$-0.599636\pi$
$17$	−1.04195e9	−0.615856	−0.307928	+	0.951410i	$0.599636\pi$
$18$	−2.31334e9	−0.890628
$19$	−7.23234e9	−1.85621	−0.928104	−	0.372321i	$-0.878562\pi$
$19$	−7.23234e9	−1.85621	−0.928104	+	0.372321i	$0.878562\pi$
$20$	2.18205e9	0.381189
$21$	1.81664e10	2.20102
$22$	2.87463e10	2.45704
$23$	2.50164e10	1.53203	0.766014	−	0.642824i	$-0.222237\pi$
$23$	2.50164e10	1.53203	0.766014	+	0.642824i	$0.222237\pi$
$24$	−2.49837e10	−1.11192
$25$	−2.86890e10	−0.940081
$26$	6.14227e10	1.49978
$27$	−3.00487e10	−0.552837
$28$	1.96124e11	2.74692
$29$	1.72499e10	0.185695
$29$	1.72499e10	0.185695
$30$	−5.85078e10	−0.488432
$31$	−6.48340e10	−0.423243	−0.211621	−	0.977352i	$-0.567874\pi$
$31$	−6.48340e10	−0.423243	−0.211621	+	0.977352i	$0.567874\pi$
$32$	2.14303e11	1.10256
$33$	−4.69370e11	−1.91717
$34$	3.01618e11	0.984840
$35$	1.64354e11	0.431787
$36$	4.07790e11	0.867297
$37$	−6.94616e11	−1.20291	−0.601453	−	0.798908i	$-0.705411\pi$
$37$	−6.94616e11	−1.20291	−0.601453	+	0.798908i	$0.705411\pi$
$38$	2.09358e12	2.96834
$39$	−1.00291e12	−1.17025
$40$	−2.26031e11	−0.218131
$41$	1.24986e12	1.00226	0.501131	−	0.865371i	$-0.332917\pi$
$41$	1.24986e12	1.00226	0.501131	+	0.865371i	$0.332917\pi$
$42$	−5.25872e12	−3.51974
$43$	−2.69349e12	−1.51113	−0.755566	−	0.655073i	$-0.772638\pi$
$43$	−2.69349e12	−1.51113	−0.755566	+	0.655073i	$0.772638\pi$
$44$	−5.06732e12	−2.39267
$45$	3.41731e11	0.136330
$46$	−7.24164e12	−2.44993
$47$	−2.08007e12	−0.598887	−0.299443	−	0.954114i	$-0.596801\pi$
$47$	−2.08007e12	−0.598887	−0.299443	+	0.954114i	$0.596801\pi$
$48$	−6.71047e11	−0.164985
$49$	1.00247e13	2.11154
$50$	8.30476e12	1.50332
$51$	−4.92483e12	−0.768450
$52$	−1.08274e13	−1.46050
$53$	−3.67599e12	−0.429838	−0.214919	−	0.976632i	$-0.568949\pi$
$53$	−3.67599e12	−0.429838	−0.214919	+	0.976632i	$0.568949\pi$
$54$	8.69835e12	0.884064
$55$	−4.24646e12	−0.376103
$56$	−2.03158e13	−1.57190
$57$	−3.41841e13	−2.31613
$58$	−4.99341e12	−0.296953
$59$	2.50869e13	1.31237	0.656185	−	0.754600i	$-0.272169\pi$
$59$	2.50869e13	1.31237	0.656185	+	0.754600i	$0.272169\pi$
$60$	1.03136e13	0.475637
$61$	−1.69406e12	−0.0690168	−0.0345084	−	0.999404i	$-0.510987\pi$
$61$	−1.69406e12	−0.0690168	−0.0345084	+	0.999404i	$0.510987\pi$
$62$	1.87678e13	0.676825
$63$	3.07150e13	0.982420
$64$	−5.73833e13	−1.63093
$65$	−9.07348e12	−0.229575
$66$	1.35871e14	3.06583
$67$	−1.14676e13	−0.231159	−0.115580	−	0.993298i	$-0.536873\pi$
$67$	−1.14676e13	−0.231159	−0.115580	+	0.993298i	$0.536873\pi$
$68$	−5.31685e13	−0.959042
$69$	1.18242e14	1.91163
$70$	−4.75763e13	−0.690487
$71$	−7.22982e13	−0.943387	−0.471693	−	0.881763i	$-0.656357\pi$
$71$	−7.22982e13	−0.943387	−0.471693	+	0.881763i	$0.656357\pi$
$72$	−4.22415e13	−0.496302
$73$	2.46900e13	0.261578	0.130789	−	0.991410i	$-0.458249\pi$
$73$	2.46900e13	0.261578	0.130789	+	0.991410i	$0.458249\pi$
$74$	2.01074e14	1.92362
$75$	−1.35600e14	−1.17301
$76$	−3.69051e14	−2.89058
$77$	−3.81674e14	−2.71027
$78$	2.90318e14	1.87139
$79$	−6.45470e13	−0.378158	−0.189079	−	0.981962i	$-0.560550\pi$
$79$	−6.45470e13	−0.378158	−0.189079	+	0.981962i	$0.560550\pi$
$80$	−6.07105e12	−0.0323660
$81$	−2.56696e14	−1.24676
$82$	−3.61803e14	−1.60276
$83$	9.53772e13	0.385797	0.192899	−	0.981219i	$-0.438211\pi$
$83$	9.53772e13	0.385797	0.192899	+	0.981219i	$0.438211\pi$
$84$	9.26993e14	3.42753
$85$	−4.45556e13	−0.150751
$86$	7.79700e14	2.41651
$87$	8.15326e13	0.231706
$88$	5.24906e14	1.36918
$89$	−3.92599e13	−0.0940857	−0.0470429	−	0.998893i	$-0.514980\pi$
$89$	−3.92599e13	−0.0940857	−0.0470429	+	0.998893i	$0.514980\pi$
$90$	−9.89228e13	−0.218011
$91$	−8.15531e14	−1.65436
$92$	1.27654e15	2.38575
$93$	−3.06442e14	−0.528112
$94$	6.02130e14	0.957704
$95$	−3.09268e14	−0.454368
$96$	1.01292e15	1.37575
$97$	7.04551e14	0.885369	0.442685	−	0.896677i	$-0.354026\pi$
$97$	7.04551e14	0.885369	0.442685	+	0.896677i	$0.354026\pi$
$98$	−2.90189e15	−3.37664
$99$	−7.93594e14	−0.855725
$100$	−1.46394e15	−1.46394
$101$	8.30706e13	0.0770969	0.0385485	−	0.999257i	$-0.487727\pi$
$101$	8.30706e13	0.0770969	0.0385485	+	0.999257i	$0.487727\pi$
$102$	1.42562e15	1.22886
$103$	8.75577e14	0.701480	0.350740	−	0.936473i	$-0.385930\pi$
$103$	8.75577e14	0.701480	0.350740	+	0.936473i	$0.385930\pi$
$104$	1.12158e15	0.835755
$105$	7.76828e14	0.538772
$106$	1.06411e15	0.687372
$107$	1.67891e15	1.01076	0.505381	−	0.862896i	$-0.331352\pi$
$107$	1.67891e15	1.01076	0.505381	+	0.862896i	$0.331352\pi$
$108$	−1.53332e15	−0.860906
$109$	1.97512e15	1.03489	0.517445	−	0.855717i	$-0.326883\pi$
$109$	1.97512e15	1.03489	0.517445	+	0.855717i	$0.326883\pi$
$110$	1.22924e15	0.601441
$111$	−3.28315e15	−1.50096
$112$	−5.45670e14	−0.233236
$113$	−3.18445e15	−1.27335	−0.636673	−	0.771134i	$-0.719690\pi$
$113$	−3.18445e15	−1.27335	−0.636673	+	0.771134i	$0.719690\pi$
$114$	9.89545e15	3.70382
$115$	1.06975e15	0.375015
$116$	8.80226e14	0.289174
$117$	−1.69569e15	−0.522338
$118$	−7.26203e15	−2.09866
$119$	−4.00469e15	−1.08634
$120$	−1.06835e15	−0.272179
$121$	5.68418e15	1.36075
$122$	4.90388e14	0.110367
$123$	5.90753e15	1.25060
$124$	−3.30834e15	−0.659095
$125$	−2.53178e15	−0.474899
$126$	−8.89125e15	−1.57103
$127$	−8.79047e15	−1.46381	−0.731904	−	0.681408i	$-0.761368\pi$
$127$	−8.79047e15	−1.46381	−0.731904	+	0.681408i	$0.761368\pi$
$128$	9.58876e15	1.50552
$129$	−1.27310e16	−1.88555
$130$	2.62655e15	0.367122
$131$	9.41506e15	1.24248	0.621238	−	0.783622i	$-0.286630\pi$
$131$	9.41506e15	1.24248	0.621238	+	0.783622i	$0.286630\pi$
$132$	−2.39510e16	−2.98551
$133$	−2.77972e16	−3.27427
$134$	3.31958e15	0.369656
$135$	−1.28494e15	−0.135325
$136$	5.50754e15	0.548802
$137$	−2.98067e15	−0.281132	−0.140566	−	0.990071i	$-0.544892\pi$
$137$	−2.98067e15	−0.281132	−0.140566	+	0.990071i	$0.544892\pi$
$138$	−3.42281e16	−3.05696
$139$	1.81243e16	1.53338	0.766692	−	0.642015i	$-0.221901\pi$
$139$	1.81243e16	1.53338	0.766692	+	0.642015i	$0.221901\pi$
$140$	8.38663e15	0.672399
$141$	−9.83160e15	−0.747276
$142$	2.09285e16	1.50861
$143$	2.10711e16	1.44101
$144$	−1.13458e15	−0.0736405
$145$	7.37637e14	0.0454551
$146$	−7.14716e15	−0.418299
$147$	4.73822e16	2.63472
$148$	−3.54448e16	−1.87323
$149$	−2.78496e16	−1.39934	−0.699668	−	0.714468i	$-0.746669\pi$
$149$	−2.78496e16	−1.39934	−0.699668	+	0.714468i	$0.746669\pi$
$150$	3.92530e16	1.87581
$151$	−2.92586e16	−1.33023	−0.665114	−	0.746742i	$-0.731617\pi$
$151$	−2.92586e16	−1.33023	−0.665114	+	0.746742i	$0.731617\pi$
$152$	3.82287e16	1.65410
$153$	−8.32673e15	−0.342996
$154$	1.10485e17	4.33410
$155$	−2.77242e15	−0.103603
$156$	−5.11766e16	−1.82237
$157$	4.50330e15	0.152856	0.0764281	−	0.997075i	$-0.475648\pi$
$157$	4.50330e15	0.152856	0.0764281	+	0.997075i	$0.475648\pi$
$158$	1.86848e16	0.604727
$159$	−1.73748e16	−0.536341
$160$	9.16400e15	0.269889
$161$	9.61498e16	2.70243
$162$	7.43073e16	1.99374
$163$	−2.49151e16	−0.638346	−0.319173	−	0.947697i	$-0.603405\pi$
$163$	−2.49151e16	−0.638346	−0.319173	+	0.947697i	$0.603405\pi$
$164$	6.37776e16	1.56077
$165$	−2.00711e16	−0.469291
$166$	−2.76093e16	−0.616944
$167$	3.27533e16	0.699650	0.349825	−	0.936815i	$-0.386241\pi$
$167$	3.27533e16	0.699650	0.349825	+	0.936815i	$0.386241\pi$
$168$	−9.60240e16	−1.96137
$169$	−6.16283e15	−0.120401
$170$	1.28978e16	0.241072
$171$	−5.77972e16	−1.03380
$172$	−1.37443e17	−2.35321
$173$	−3.54743e16	−0.581524	−0.290762	−	0.956795i	$-0.593909\pi$
$173$	−3.54743e16	−0.581524	−0.290762	+	0.956795i	$0.593909\pi$
$174$	−2.36017e16	−0.370530
$175$	−1.10265e17	−1.65826
$176$	1.40986e16	0.203157
$177$	1.18575e17	1.63754
$178$	1.13648e16	0.150456
$179$	−6.23197e16	−0.791094	−0.395547	−	0.918446i	$-0.629445\pi$
$179$	−6.23197e16	−0.791094	−0.395547	+	0.918446i	$0.629445\pi$
$180$	1.74379e16	0.212300
$181$	−4.41992e15	−0.0516208	−0.0258104	−	0.999667i	$-0.508217\pi$
$181$	−4.41992e15	−0.0516208	−0.0258104	+	0.999667i	$0.508217\pi$
$182$	2.36076e17	2.64555
$183$	−8.00707e15	−0.0861174
$184$	−1.32232e17	−1.36522
$185$	−2.97031e16	−0.294451
$186$	8.87073e16	0.844525
$187$	1.03470e17	0.946246
$188$	−1.06142e17	−0.932616
$189$	−1.15491e17	−0.975180
$190$	8.95255e16	0.726599
$191$	−1.28449e16	−0.100226	−0.0501131	−	0.998744i	$-0.515958\pi$
$191$	−1.28449e16	−0.100226	−0.0501131	+	0.998744i	$0.515958\pi$
$192$	−2.71226e17	−2.03503
$193$	1.27484e17	0.919972	0.459986	−	0.887926i	$-0.347854\pi$
$193$	1.27484e17	0.919972	0.459986	+	0.887926i	$0.347854\pi$
$194$	−2.03950e17	−1.41583
$195$	−4.28864e16	−0.286457
$196$	5.11538e17	3.28819
$197$	−1.93748e17	−1.19878	−0.599392	−	0.800456i	$-0.704591\pi$
$197$	−1.93748e17	−1.19878	−0.599392	+	0.800456i	$0.704591\pi$
$198$	2.29726e17	1.36842
$199$	1.00519e17	0.576566	0.288283	−	0.957545i	$-0.406916\pi$
$199$	1.00519e17	0.576566	0.288283	+	0.957545i	$0.406916\pi$
$200$	1.51645e17	0.837726
$201$	−5.42023e16	−0.288434
$202$	−2.40469e16	−0.123289
$203$	6.62993e16	0.327558
$204$	−2.51304e17	−1.19667
$205$	5.34462e16	0.245337
$206$	−2.53458e17	−1.12176
$207$	1.99919e17	0.853250
$208$	3.01248e16	0.124008
$209$	7.18205e17	2.85201
$210$	−2.24873e17	−0.861572
$211$	−2.96633e17	−1.09673	−0.548366	−	0.836238i	$-0.684750\pi$
$211$	−2.96633e17	−1.09673	−0.548366	+	0.836238i	$0.684750\pi$
$212$	−1.87578e17	−0.669366
$213$	−3.41722e17	−1.17713
$214$	−4.86003e17	−1.61635
$215$	−1.15179e17	−0.369900
$216$	1.58832e17	0.492645
$217$	−2.49187e17	−0.746582
$218$	−5.71747e17	−1.65493
$219$	1.16699e17	0.326390
$220$	−2.16688e17	−0.585686
$221$	2.21087e17	0.577593
$222$	9.50390e17	2.40024
$223$	−1.39271e17	−0.340074	−0.170037	−	0.985438i	$-0.554389\pi$
$223$	−1.39271e17	−0.340074	−0.170037	+	0.985438i	$0.554389\pi$
$224$	8.23666e17	1.94487
$225$	−2.29268e17	−0.523570
$226$	9.21821e17	2.03626
$227$	2.08249e17	0.445031	0.222515	−	0.974929i	$-0.428573\pi$
$227$	2.08249e17	0.445031	0.222515	+	0.974929i	$0.428573\pi$
$228$	−1.74434e18	−3.60679
$229$	5.29988e17	1.06047	0.530237	−	0.847849i	$-0.322103\pi$
$229$	5.29988e17	1.06047	0.530237	+	0.847849i	$0.322103\pi$
$230$	−3.09666e17	−0.599701
$231$	−1.80401e18	−3.38180
$232$	−9.11795e16	−0.165477
$233$	−5.85047e17	−1.02807	−0.514033	−	0.857770i	$-0.671849\pi$
$233$	−5.85047e17	−1.02807	−0.514033	+	0.857770i	$0.671849\pi$
$234$	4.90860e17	0.835292
$235$	−8.89478e16	−0.146597
$236$	1.28013e18	2.04369
$237$	−3.05086e17	−0.471856
$238$	1.15926e18	1.73721
$239$	8.52412e17	1.23784	0.618921	−	0.785453i	$-0.287570\pi$
$239$	8.52412e17	1.23784	0.618921	+	0.785453i	$0.287570\pi$
$240$	−2.86952e16	−0.0403854
$241$	−1.06101e18	−1.44742	−0.723708	−	0.690106i	$-0.757564\pi$
$241$	−1.06101e18	−1.44742	−0.723708	+	0.690106i	$0.757564\pi$
$242$	−1.64543e18	−2.17603
$243$	−7.82126e17	−1.00284
$244$	−8.64443e16	−0.107476
$245$	4.28673e17	0.516869
$246$	−1.71008e18	−1.99988
$247$	1.53460e18	1.74088
$248$	3.42700e17	0.377160
$249$	4.50806e17	0.481388
$250$	7.32889e17	0.759431
$251$	8.30299e17	0.834990	0.417495	−	0.908679i	$-0.362908\pi$
$251$	8.30299e17	0.834990	0.417495	+	0.908679i	$0.362908\pi$
$252$	1.56733e18	1.52987
$253$	−2.48425e18	−2.35392
$254$	2.54462e18	2.34083
$255$	−2.10595e17	−0.188104
$256$	−8.95374e17	−0.776613
$257$	9.06280e17	0.763421	0.381711	−	0.924282i	$-0.375335\pi$
$257$	9.06280e17	0.763421	0.381711	+	0.924282i	$0.375335\pi$
$258$	3.68530e18	3.01526
$259$	−2.66973e18	−2.12187
$260$	−4.63001e17	−0.357505
$261$	1.37852e17	0.103421
$262$	−2.72543e18	−1.98689
$263$	9.91691e17	0.702600	0.351300	−	0.936263i	$-0.385740\pi$
$263$	9.91691e17	0.702600	0.351300	+	0.936263i	$0.385740\pi$
$264$	2.48100e18	1.70843
$265$	−1.57192e17	−0.105217
$266$	8.04661e18	5.23601
$267$	−1.85564e17	−0.117398
$268$	−5.85168e17	−0.359972
$269$	−7.15605e17	−0.428086	−0.214043	−	0.976824i	$-0.568663\pi$
$269$	−7.15605e17	−0.428086	−0.214043	+	0.976824i	$0.568663\pi$
$270$	3.71958e17	0.216404
$271$	2.29064e18	1.29625	0.648123	−	0.761536i	$-0.275554\pi$
$271$	2.29064e18	1.29625	0.648123	+	0.761536i	$0.275554\pi$
$272$	1.47929e17	0.0814304
$273$	−3.85466e18	−2.06427
$274$	8.62831e17	0.449569
$275$	2.84895e18	1.44441
$276$	6.03364e18	2.97688
$277$	−3.76730e18	−1.80897	−0.904486	−	0.426504i	$-0.859745\pi$
$277$	−3.76730e18	−1.80897	−0.904486	+	0.426504i	$0.859745\pi$
$278$	−5.24655e18	−2.45210
$279$	−5.18121e17	−0.235722
$280$	−8.68742e17	−0.384774
$281$	−2.53289e18	−1.09224	−0.546120	−	0.837707i	$-0.683896\pi$
$281$	−2.53289e18	−1.09224	−0.546120	+	0.837707i	$0.683896\pi$
$282$	2.84601e18	1.19500
$283$	−3.30122e18	−1.34982	−0.674911	−	0.737899i	$-0.735818\pi$
$283$	−3.30122e18	−1.34982	−0.674911	+	0.737899i	$0.735818\pi$
$284$	−3.68923e18	−1.46909
$285$	−1.46178e18	−0.566949
$286$	−6.09957e18	−2.30438
$287$	4.80378e18	1.76795
$288$	1.71260e18	0.614063
$289$	−1.77677e18	−0.620721
$290$	−2.13528e17	−0.0726891
$291$	3.33011e18	1.10474
$292$	1.25988e18	0.407342
$293$	−1.33446e18	−0.420533	−0.210266	−	0.977644i	$-0.567433\pi$
$293$	−1.33446e18	−0.420533	−0.210266	+	0.977644i	$0.567433\pi$
$294$	−1.37160e19	−4.21329
$295$	1.07276e18	0.321246
$296$	3.67161e18	1.07193
$297$	2.98398e18	0.849419
$298$	8.06178e18	2.23774
$299$	−5.30815e18	−1.43684
$300$	−6.91941e18	−1.82667
$301$	−1.03523e19	−2.66557
$302$	8.46963e18	2.12722
$303$	3.92638e17	0.0961996
$304$	1.02680e18	0.245433
$305$	−7.24411e16	−0.0168941
$306$	2.41038e18	0.548498
$307$	1.81526e18	0.403090	0.201545	−	0.979479i	$-0.435404\pi$
$307$	1.81526e18	0.403090	0.201545	+	0.979479i	$0.435404\pi$
$308$	−1.94761e19	−4.22056
$309$	4.13847e18	0.875289
$310$	8.02547e17	0.165675
$311$	2.63807e18	0.531599	0.265800	−	0.964028i	$-0.414364\pi$
$311$	2.63807e18	0.531599	0.265800	+	0.964028i	$0.414364\pi$
$312$	5.30120e18	1.04283
$313$	5.91236e18	1.13548	0.567738	−	0.823209i	$-0.307819\pi$
$313$	5.91236e18	1.13548	0.567738	+	0.823209i	$0.307819\pi$
$314$	−1.30359e18	−0.244439
$315$	1.31343e18	0.240480
$316$	−3.29370e18	−0.588886
$317$	1.81007e18	0.316047	0.158024	−	0.987435i	$-0.449488\pi$
$317$	1.81007e18	0.316047	0.158024	+	0.987435i	$0.449488\pi$
$318$	5.02957e18	0.857685
$319$	−1.71299e18	−0.285316
$320$	−2.45382e18	−0.399224
$321$	7.93547e18	1.26120
$322$	−2.78330e19	−4.32156
$323$	7.53572e18	1.14316
$324$	−1.30987e19	−1.94151
$325$	6.08742e18	0.881673
$326$	7.21231e18	1.02080
$327$	9.33551e18	1.29131
$328$	−6.60650e18	−0.893136
$329$	−7.99469e18	−1.05641
$330$	5.81010e18	0.750463
$331$	4.42127e17	0.0558260	0.0279130	−	0.999610i	$-0.491114\pi$
$331$	4.42127e17	0.0558260	0.0279130	+	0.999610i	$0.491114\pi$
$332$	4.86690e18	0.600782
$333$	−5.55102e18	−0.669948
$334$	−9.48126e18	−1.11884
$335$	−4.90375e17	−0.0565839
$336$	−2.57914e18	−0.291025
$337$	1.52009e19	1.67744	0.838719	−	0.544565i	$-0.183305\pi$
$337$	1.52009e19	1.67744	0.838719	+	0.544565i	$0.183305\pi$
$338$	1.78399e18	0.192538
$339$	−1.50515e19	−1.58885
$340$	−2.27358e18	−0.234757
$341$	6.43832e18	0.650301
$342$	1.67309e19	1.65319
$343$	2.02823e19	1.96070
$344$	1.42373e19	1.34660
$345$	5.05624e18	0.467934
$346$	1.02689e19	0.929939
$347$	8.59496e18	0.761681	0.380840	−	0.924641i	$-0.375635\pi$
$347$	8.59496e18	0.761681	0.380840	+	0.924641i	$0.375635\pi$
$348$	4.16044e18	0.360824
$349$	−1.46390e18	−0.124257	−0.0621285	−	0.998068i	$-0.519789\pi$
$349$	−1.46390e18	−0.124257	−0.0621285	+	0.998068i	$0.519789\pi$
$350$	3.19190e19	2.65179
$351$	6.37592e18	0.518489
$352$	−2.12813e19	−1.69406
$353$	−2.06973e19	−1.61289	−0.806443	−	0.591312i	$-0.798610\pi$
$353$	−2.06973e19	−1.61289	−0.806443	+	0.591312i	$0.798610\pi$
$354$	−3.43244e19	−2.61866
$355$	−3.09160e18	−0.230925
$356$	−2.00335e18	−0.146515
$357$	−1.89284e19	−1.35551
$358$	1.80400e19	1.26507
$359$	1.04670e19	0.718808	0.359404	−	0.933182i	$-0.382980\pi$
$359$	1.04670e19	0.718808	0.359404	+	0.933182i	$0.382980\pi$
$360$	−1.80633e18	−0.121486
$361$	3.71256e19	2.44551
$362$	1.27946e18	0.0825489
$363$	2.68667e19	1.69791
$364$	−4.16149e19	−2.57625
$365$	1.05579e18	0.0640298
$366$	2.31785e18	0.137714
$367$	−2.61234e18	−0.152067	−0.0760334	−	0.997105i	$-0.524226\pi$
$367$	−2.61234e18	−0.152067	−0.0760334	+	0.997105i	$0.524226\pi$
$368$	−3.55167e18	−0.202570
$369$	9.98823e18	0.558201
$370$	8.59831e18	0.470869
$371$	−1.41285e19	−0.758215
$372$	−1.56371e19	−0.822402
$373$	2.14486e19	1.10556	0.552781	−	0.833326i	$-0.313566\pi$
$373$	2.14486e19	1.10556	0.552781	+	0.833326i	$0.313566\pi$
$374$	−2.99521e19	−1.51318
$375$	−1.19666e19	−0.592567
$376$	1.09949e19	0.533680
$377$	−3.66019e18	−0.174158
$378$	3.34318e19	1.55945
$379$	1.98489e19	0.907699	0.453849	−	0.891078i	$-0.350050\pi$
$379$	1.98489e19	0.907699	0.453849	+	0.891078i	$0.350050\pi$
$380$	−1.57813e19	−0.707565
$381$	−4.15487e19	−1.82650
$382$	3.71829e18	0.160276
$383$	2.76126e19	1.16712	0.583562	−	0.812069i	$-0.301659\pi$
$383$	2.76126e19	1.16712	0.583562	+	0.812069i	$0.301659\pi$
$384$	4.53219e19	1.87855
$385$	−1.63211e19	−0.663428
$386$	−3.69034e19	−1.47116
$387$	−2.15251e19	−0.841612
$388$	3.59518e19	1.37874
$389$	−4.17634e19	−1.57099	−0.785495	−	0.618868i	$-0.787592\pi$
$389$	−4.17634e19	−1.57099	−0.785495	+	0.618868i	$0.787592\pi$
$390$	1.24146e19	0.458086
$391$	−2.60658e19	−0.943509
$392$	−5.29884e19	−1.88163
$393$	4.45009e19	1.55033
$394$	5.60853e19	1.91702
$395$	−2.76015e18	−0.0925666
$396$	−4.04955e19	−1.33258
$397$	−1.01632e19	−0.328171	−0.164086	−	0.986446i	$-0.552467\pi$
$397$	−1.01632e19	−0.328171	−0.164086	+	0.986446i	$0.552467\pi$
$398$	−2.90977e19	−0.922009
$399$	−1.31385e20	−4.08555
$400$	4.07308e18	0.124300
$401$	−3.63397e19	−1.08842	−0.544212	−	0.838948i	$-0.683171\pi$
$401$	−3.63397e19	−1.08842	−0.544212	+	0.838948i	$0.683171\pi$
$402$	1.56902e19	0.461247
$403$	1.37569e19	0.396947
$404$	4.23892e18	0.120059
$405$	−1.09768e19	−0.305185
$406$	−1.91920e19	−0.523812
$407$	6.89787e19	1.84823
$408$	2.60317e19	0.684781
$409$	4.90002e19	1.26553	0.632766	−	0.774343i	$-0.281919\pi$
$409$	4.90002e19	1.26553	0.632766	+	0.774343i	$0.281919\pi$
$410$	−1.54714e19	−0.392328
$411$	−1.40883e19	−0.350789
$412$	4.46789e19	1.09238
$413$	9.64204e19	2.31496
$414$	−5.78716e19	−1.36447
$415$	4.07851e18	0.0944366
$416$	−4.54722e19	−1.03406
$417$	8.56659e19	1.91332
$418$	−2.07903e20	−4.56077
$419$	4.44645e19	0.958095	0.479047	−	0.877789i	$-0.340982\pi$
$419$	4.44645e19	0.958095	0.479047	+	0.877789i	$0.340982\pi$
$420$	3.96400e19	0.839003
$421$	−5.14817e19	−1.07038	−0.535189	−	0.844733i	$-0.679759\pi$
$421$	−5.14817e19	−1.07038	−0.535189	+	0.844733i	$0.679759\pi$
$422$	8.58679e19	1.75383
$423$	−1.66229e19	−0.333545
$424$	1.94306e19	0.383038
$425$	2.98925e19	0.578955
$426$	9.89201e19	1.88240
$427$	−6.51105e18	−0.121742
$428$	8.56713e19	1.57401
$429$	9.95940e19	1.79806
$430$	3.33414e19	0.591522
$431$	−1.79869e19	−0.313601	−0.156801	−	0.987630i	$-0.550118\pi$
$431$	−1.79869e19	−0.313601	−0.156801	+	0.987630i	$0.550118\pi$
$432$	4.26612e18	0.0730978
$433$	−9.18408e18	−0.154659	−0.0773297	−	0.997006i	$-0.524639\pi$
$433$	−9.18408e18	−0.154659	−0.0773297	+	0.997006i	$0.524639\pi$
$434$	7.21335e19	1.19389
$435$	3.48649e18	0.0567177
$436$	1.00786e20	1.61158
$437$	−1.80927e20	−2.84376
$438$	−3.37815e19	−0.521943
$439$	−4.71428e19	−0.716030	−0.358015	−	0.933716i	$-0.616546\pi$
$439$	−4.71428e19	−0.716030	−0.358015	+	0.933716i	$0.616546\pi$
$440$	2.24459e19	0.335153
$441$	8.01120e19	1.17600
$442$	−6.39993e19	−0.923651
$443$	−9.75755e19	−1.38456	−0.692282	−	0.721627i	$-0.743394\pi$
$443$	−9.75755e19	−1.38456	−0.692282	+	0.721627i	$0.743394\pi$
$444$	−1.67532e20	−2.33736
$445$	−1.67882e18	−0.0230306
$446$	4.03154e19	0.543825
$447$	−1.31633e20	−1.74606
$448$	−2.20551e20	−2.87689
$449$	−3.88682e19	−0.498594	−0.249297	−	0.968427i	$-0.580200\pi$
$449$	−3.88682e19	−0.498594	−0.249297	+	0.968427i	$0.580200\pi$
$450$	6.63675e19	0.837262
$451$	−1.24117e20	−1.53995
$452$	−1.62496e20	−1.98292
$453$	−1.38293e20	−1.65982
$454$	−6.02831e19	−0.711667
$455$	−3.48736e19	−0.404959
$456$	1.80691e20	2.06395
$457$	−1.11442e20	−1.25221	−0.626103	−	0.779740i	$-0.715351\pi$
$457$	−1.11442e20	−1.25221	−0.626103	+	0.779740i	$0.715351\pi$
$458$	−1.53419e20	−1.69585
$459$	3.13092e19	0.340468
$460$	5.45872e19	0.583992
$461$	1.17649e20	1.23831	0.619157	−	0.785267i	$-0.287474\pi$
$461$	1.17649e20	1.23831	0.619157	+	0.785267i	$0.287474\pi$
$462$	5.22216e20	5.40798
$463$	7.25181e19	0.738906	0.369453	−	0.929249i	$-0.379545\pi$
$463$	7.25181e19	0.738906	0.369453	+	0.929249i	$0.379545\pi$
$464$	−2.44902e18	−0.0245532
$465$	−1.31040e19	−0.129273
$466$	1.69357e20	1.64402
$467$	−1.48850e20	−1.42191	−0.710955	−	0.703237i	$-0.751737\pi$
$467$	−1.48850e20	−1.42191	−0.710955	+	0.703237i	$0.751737\pi$
$468$	−8.65275e19	−0.813411
$469$	−4.40753e19	−0.407754
$470$	2.57482e19	0.234430
$471$	2.12851e19	0.190730
$472$	−1.32604e20	−1.16948
$473$	2.67477e20	2.32181
$474$	8.83147e19	0.754563
$475$	2.07489e20	1.74499
$476$	−2.04351e20	−1.69171
$477$	−2.93767e19	−0.239395
$478$	−2.46752e20	−1.97948
$479$	1.11244e20	0.878537	0.439268	−	0.898356i	$-0.355238\pi$
$479$	1.11244e20	0.878537	0.439268	+	0.898356i	$0.355238\pi$
$480$	4.33142e19	0.336761
$481$	1.47388e20	1.12817
$482$	3.07138e20	2.31462
$483$	4.54458e20	3.37202
$484$	2.90052e20	2.11902
$485$	3.01279e19	0.216723
$486$	2.26406e20	1.60367
$487$	2.43709e19	0.169983	0.0849914	−	0.996382i	$-0.472914\pi$
$487$	2.43709e19	0.169983	0.0849914	+	0.996382i	$0.472914\pi$
$488$	8.95447e18	0.0615022
$489$	−1.17763e20	−0.796512
$490$	−1.24090e20	−0.826546
$491$	−3.50344e19	−0.229818	−0.114909	−	0.993376i	$-0.536658\pi$
$491$	−3.50344e19	−0.229818	−0.114909	+	0.993376i	$0.536658\pi$
$492$	3.01449e20	1.94749
$493$	−1.79735e19	−0.114362
$494$	−4.44230e20	−2.78391
$495$	−3.39356e19	−0.209467
$496$	9.20470e18	0.0559625
$497$	−2.77875e20	−1.66409
$498$	−1.30497e20	−0.769807
$499$	−2.41953e20	−1.40597	−0.702987	−	0.711203i	$-0.748151\pi$
$499$	−2.41953e20	−1.40597	−0.702987	+	0.711203i	$0.748151\pi$
$500$	−1.29192e20	−0.739537
$501$	1.54810e20	0.873006
$502$	−2.40351e20	−1.33527
$503$	1.26232e20	0.690892	0.345446	−	0.938439i	$-0.387728\pi$
$503$	1.26232e20	0.690892	0.345446	+	0.938439i	$0.387728\pi$
$504$	−1.62354e20	−0.875454
$505$	3.55225e18	0.0188720
$506$	7.19130e20	3.76425
$507$	−2.91290e19	−0.150233
$508$	−4.48560e20	−2.27951
$509$	1.72269e20	0.862630	0.431315	−	0.902201i	$-0.358050\pi$
$509$	1.72269e20	0.862630	0.431315	+	0.902201i	$0.358050\pi$
$510$	6.09621e19	0.300804
$511$	9.48953e19	0.461411
$512$	−5.50159e19	−0.263611
$513$	2.17322e20	1.02618
$514$	−2.62346e20	−1.22082
$515$	3.74413e19	0.171710
$516$	−6.49635e20	−2.93628
$517$	2.06561e20	0.920173
$518$	7.72821e20	3.39317
$519$	−1.67672e20	−0.725611
$520$	4.79607e19	0.204579
$521$	−4.93138e18	−0.0207341	−0.0103671	−	0.999946i	$-0.503300\pi$
$521$	−4.93138e18	−0.0207341	−0.0103671	+	0.999946i	$0.503300\pi$
$522$	−3.99049e19	−0.165385
$523$	−3.17341e20	−1.29647	−0.648237	−	0.761438i	$-0.724494\pi$
$523$	−3.17341e20	−1.29647	−0.648237	+	0.761438i	$0.724494\pi$
$524$	4.80431e20	1.93485
$525$	−5.21175e20	−2.06914
$526$	−2.87070e20	−1.12356
$527$	6.75536e19	0.260657
$528$	6.66381e19	0.253494
$529$	3.59187e20	1.34711
$530$	4.55032e19	0.168257
$531$	2.00482e20	0.730913
$532$	−1.41844e21	−5.09885
$533$	−2.65203e20	−0.939991
$534$	5.37163e19	0.187735
$535$	7.17933e19	0.247417
$536$	6.06155e19	0.205991
$537$	−2.94558e20	−0.987106
$538$	2.07150e20	0.684570
$539$	−9.95495e20	−3.24432
$540$	−6.55678e19	−0.210735
$541$	7.25991e19	0.230119	0.115059	−	0.993359i	$-0.463294\pi$
$541$	7.25991e19	0.230119	0.115059	+	0.993359i	$0.463294\pi$
$542$	−6.63084e20	−2.07288
$543$	−2.08910e19	−0.0644111
$544$	−2.23293e20	−0.679021
$545$	8.44596e19	0.253323
$546$	1.11583e21	3.30105
$547$	−2.39003e20	−0.697426	−0.348713	−	0.937230i	$-0.613381\pi$
$547$	−2.39003e20	−0.697426	−0.348713	+	0.937230i	$0.613381\pi$
$548$	−1.52098e20	−0.437793
$549$	−1.35381e19	−0.0384383
$550$	−8.24702e20	−2.30981
$551$	−1.24757e20	−0.344689
$552$	−6.25004e20	−1.70349
$553$	−2.48084e20	−0.667053
$554$	1.09054e21	2.89280
$555$	−1.40393e20	−0.367409
$556$	9.24848e20	2.38786
$557$	3.12730e20	0.796628	0.398314	−	0.917249i	$-0.369595\pi$
$557$	3.12730e20	0.796628	0.398314	+	0.917249i	$0.369595\pi$
$558$	1.49983e20	0.376952
$559$	5.71522e20	1.41724
$560$	−2.33339e19	−0.0570921
$561$	4.89059e20	1.18070
$562$	7.33208e20	1.74665
$563$	−8.31724e19	−0.195509	−0.0977544	−	0.995211i	$-0.531166\pi$
$563$	−8.31724e19	−0.195509	−0.0977544	+	0.995211i	$0.531166\pi$
$564$	−5.01686e20	−1.16369
$565$	−1.36173e20	−0.311694
$566$	9.55623e20	2.15856
$567$	−9.86603e20	−2.19922
$568$	3.82154e20	0.840671
$569$	−3.19710e20	−0.694087	−0.347043	−	0.937849i	$-0.612814\pi$
$569$	−3.19710e20	−0.694087	−0.347043	+	0.937849i	$0.612814\pi$
$570$	4.23148e20	0.906632
$571$	−8.89925e19	−0.188184	−0.0940920	−	0.995564i	$-0.529995\pi$
$571$	−8.89925e19	−0.188184	−0.0940920	+	0.995564i	$0.529995\pi$
$572$	1.07522e21	2.24401
$573$	−6.07123e19	−0.125060
$574$	−1.39058e21	−2.82719
$575$	−7.17697e20	−1.44023
$576$	−4.58579e20	−0.908333
$577$	−3.76481e20	−0.736078	−0.368039	−	0.929810i	$-0.619971\pi$
$577$	−3.76481e20	−0.736078	−0.368039	+	0.929810i	$0.619971\pi$
$578$	5.14330e20	0.992621
$579$	6.02560e20	1.14792
$580$	3.76401e19	0.0707849
$581$	3.66579e20	0.680529
$582$	−9.63983e20	−1.76664
$583$	3.65043e20	0.660435
$584$	−1.30507e20	−0.233097
$585$	−7.25108e19	−0.127860
$586$	3.86294e20	0.672491
$587$	2.98425e20	0.512919	0.256460	−	0.966555i	$-0.417444\pi$
$587$	2.98425e20	0.512919	0.256460	+	0.966555i	$0.417444\pi$
$588$	2.41781e21	4.10292
$589$	4.68901e20	0.785627
$590$	−3.10538e20	−0.513717
$591$	−9.15763e20	−1.49581
$592$	9.86170e19	0.159052
$593$	9.37482e20	1.49298	0.746488	−	0.665399i	$-0.231738\pi$
$593$	9.37482e20	1.49298	0.746488	+	0.665399i	$0.231738\pi$
$594$	−8.63788e20	−1.35834
$595$	−1.71248e20	−0.265918
$596$	−1.42111e21	−2.17912
$597$	4.75108e20	0.719424
$598$	1.53658e21	2.29771
$599$	−1.03781e21	−1.53256	−0.766279	−	0.642507i	$-0.777894\pi$
$599$	−1.03781e21	−1.53256	−0.766279	+	0.642507i	$0.777894\pi$
$600$	7.16758e20	1.04529
$601$	6.99638e20	1.00766	0.503831	−	0.863802i	$-0.331923\pi$
$601$	6.99638e20	1.00766	0.503831	+	0.863802i	$0.331923\pi$
$602$	2.99675e21	4.26262
$603$	−9.16432e19	−0.128742
$604$	−1.49301e21	−2.07150
$605$	2.43066e20	0.333088
$606$	−1.13659e20	−0.153837
$607$	−7.10901e20	−0.950373	−0.475186	−	0.879885i	$-0.657619\pi$
$607$	−7.10901e20	−0.950373	−0.475186	+	0.879885i	$0.657619\pi$
$608$	−1.54991e21	−2.04659
$609$	3.13368e20	0.408719
$610$	2.09699e19	0.0270161
$611$	4.41363e20	0.561678
$612$	−4.24896e20	−0.534130
$613$	2.95544e20	0.367002	0.183501	−	0.983020i	$-0.441257\pi$
$613$	2.95544e20	0.367002	0.183501	+	0.983020i	$0.441257\pi$
$614$	−5.25474e20	−0.644597
$615$	2.52617e20	0.306125
$616$	2.01746e21	2.41518
$617$	5.96405e20	0.705346	0.352673	−	0.935747i	$-0.385273\pi$
$617$	5.96405e20	0.705346	0.352673	+	0.935747i	$0.385273\pi$
$618$	−1.19799e21	−1.39971
$619$	−3.80787e20	−0.439544	−0.219772	−	0.975551i	$-0.570531\pi$
$619$	−3.80787e20	−0.439544	−0.219772	+	0.975551i	$0.570531\pi$
$620$	−1.41471e20	−0.161335
$621$	−7.51711e20	−0.846962
$622$	−7.63658e20	−0.850101
$623$	−1.50894e20	−0.165963
$624$	1.42387e20	0.154734
$625$	7.67255e20	0.823834
$626$	−1.71148e21	−1.81579
$627$	3.39464e21	3.55867
$628$	2.29794e20	0.238035
$629$	7.23754e20	0.740817
$630$	−3.80206e20	−0.384561
$631$	5.90416e20	0.590116	0.295058	−	0.955479i	$-0.404661\pi$
$631$	5.90416e20	0.590116	0.295058	+	0.955479i	$0.404661\pi$
$632$	3.41183e20	0.336984
$633$	−1.40205e21	−1.36847
$634$	−5.23972e20	−0.505404
$635$	−3.75897e20	−0.358315
$636$	−8.86600e20	−0.835217
$637$	−2.12709e21	−1.98035
$638$	4.95870e20	0.456260
$639$	−5.77771e20	−0.525411
$640$	4.10033e20	0.368527
$641$	1.32754e21	1.17927	0.589633	−	0.807672i	$-0.299273\pi$
$641$	1.32754e21	1.17927	0.589633	+	0.807672i	$0.299273\pi$
$642$	−2.29712e21	−2.01684
$643$	−1.53813e21	−1.33478	−0.667391	−	0.744707i	$-0.732589\pi$
$643$	−1.53813e21	−1.33478	−0.667391	+	0.744707i	$0.732589\pi$
$644$	4.90633e21	4.20836
$645$	−5.44400e20	−0.461551
$646$	−2.18140e21	−1.82807
$647$	−7.55656e19	−0.0625954	−0.0312977	−	0.999510i	$-0.509964\pi$
$647$	−7.55656e19	−0.0625954	−0.0312977	+	0.999510i	$0.509964\pi$
$648$	1.35685e21	1.11101
$649$	−2.49124e21	−2.01642
$650$	−1.76216e21	−1.40992
$651$	−1.17780e21	−0.931566
$652$	−1.27137e21	−0.994064
$653$	1.70514e21	1.31799	0.658993	−	0.752149i	$-0.270983\pi$
$653$	1.70514e21	1.31799	0.658993	+	0.752149i	$0.270983\pi$
$654$	−2.70240e21	−2.06498
$655$	4.02605e20	0.304137
$656$	−1.77446e20	−0.132522
$657$	1.97311e20	0.145683
$658$	2.31426e21	1.68935
$659$	1.19110e21	0.859624	0.429812	−	0.902918i	$-0.358580\pi$
$659$	1.19110e21	0.859624	0.429812	+	0.902918i	$0.358580\pi$
$660$	−1.02419e21	−0.730804
$661$	−1.86775e21	−1.31768	−0.658838	−	0.752285i	$-0.728952\pi$
$661$	−1.86775e21	−1.31768	−0.658838	+	0.752285i	$0.728952\pi$
$662$	−1.27985e20	−0.0892737
$663$	1.04498e21	0.720705
$664$	−5.04146e20	−0.343792
$665$	−1.18866e21	−0.801485
$666$	1.60688e21	1.07134
$667$	4.31531e20	0.284491
$668$	1.67133e21	1.08953
$669$	−6.58271e20	−0.424335
$670$	1.41952e20	0.0904855
$671$	1.68228e20	0.106042
$672$	3.89311e21	2.42676
$673$	1.52319e21	0.938947	0.469473	−	0.882947i	$-0.344444\pi$
$673$	1.52319e21	0.938947	0.469473	+	0.882947i	$0.344444\pi$
$674$	−4.40030e21	−2.68246
$675$	8.62067e20	0.519712
$676$	−3.14477e20	−0.187494
$677$	1.42963e21	0.842961	0.421481	−	0.906837i	$-0.361511\pi$
$677$	1.42963e21	0.842961	0.421481	+	0.906837i	$0.361511\pi$
$678$	4.35704e21	2.54079
$679$	2.70792e21	1.56175
$680$	2.35513e20	0.134337
$681$	9.84305e20	0.555298
$682$	−1.86373e21	−1.03992
$683$	−1.22411e21	−0.675561	−0.337780	−	0.941225i	$-0.609676\pi$
$683$	−1.22411e21	−0.675561	−0.337780	+	0.941225i	$0.609676\pi$
$684$	−2.94927e21	−1.60988
$685$	−1.27459e20	−0.0688164
$686$	−5.87123e21	−3.13544
$687$	2.50502e21	1.32323
$688$	3.82404e20	0.199807
$689$	7.79995e20	0.403132
$690$	−1.46366e21	−0.748292
$691$	1.57467e21	0.796352	0.398176	−	0.917309i	$-0.369643\pi$
$691$	1.57467e21	0.796352	0.398176	+	0.917309i	$0.369643\pi$
$692$	−1.81018e21	−0.905579
$693$	−3.05015e21	−1.50946
$694$	−2.48803e21	−1.21803
$695$	7.75031e20	0.375347
$696$	−4.30966e20	−0.206478
$697$	−1.30229e21	−0.617249
$698$	4.23763e20	0.198704
$699$	−2.76526e21	−1.28279
$700$	−5.62660e21	−2.58233
$701$	2.82681e21	1.28355	0.641774	−	0.766894i	$-0.278199\pi$
$701$	2.82681e21	1.28355	0.641774	+	0.766894i	$0.278199\pi$
$702$	−1.84567e21	−0.829137
$703$	5.02370e21	2.23284
$704$	5.69843e21	2.50588
$705$	−4.20418e20	−0.182921
$706$	5.99136e21	2.57923
$707$	3.19279e20	0.135995
$708$	6.05062e21	2.55006
$709$	−3.64709e21	−1.52090	−0.760448	−	0.649399i	$-0.775021\pi$
$709$	−3.64709e21	−1.52090	−0.760448	+	0.649399i	$0.775021\pi$
$710$	8.94943e20	0.369282
$711$	−5.15828e20	−0.210612
$712$	2.07520e20	0.0838417
$713$	−1.62192e21	−0.648420
$714$	5.47931e21	2.16765
$715$	9.01040e20	0.352735
$716$	−3.18005e21	−1.23193
$717$	4.02898e21	1.54455
$718$	−3.02993e21	−1.14947
$719$	−3.98779e21	−1.49715	−0.748575	−	0.663050i	$-0.769262\pi$
$719$	−3.98779e21	−1.49715	−0.748575	+	0.663050i	$0.769262\pi$
$720$	−4.85168e19	−0.0180260
$721$	3.36525e21	1.23738
$722$	−1.07469e22	−3.91071
$723$	−5.01495e21	−1.80605
$724$	−2.25539e20	−0.0803865
$725$	−4.94882e20	−0.174569
$726$	−7.77723e21	−2.71519
$727$	9.42833e20	0.325782	0.162891	−	0.986644i	$-0.447918\pi$
$727$	9.42833e20	0.325782	0.162891	+	0.986644i	$0.447918\pi$
$728$	4.31074e21	1.47423
$729$	−1.34563e19	−0.00455481
$730$	−3.05626e20	−0.102393
$731$	2.80648e21	0.930640
$732$	−4.08585e20	−0.134106
$733$	−5.52007e20	−0.179335	−0.0896675	−	0.995972i	$-0.528580\pi$
$733$	−5.52007e20	−0.179335	−0.0896675	+	0.995972i	$0.528580\pi$
$734$	7.56208e20	0.243176
$735$	2.02615e21	0.644936
$736$	5.36110e21	1.68916
$737$	1.13879e21	0.355170
$738$	−2.89135e21	−0.892642
$739$	1.36785e21	0.418027	0.209013	−	0.977913i	$-0.432975\pi$
$739$	1.36785e21	0.418027	0.209013	+	0.977913i	$0.432975\pi$
$740$	−1.51569e21	−0.458534
$741$	7.25340e21	2.17223
$742$	4.08986e21	1.21249
$743$	1.78723e21	0.524523	0.262261	−	0.964997i	$-0.415532\pi$
$743$	1.78723e21	0.524523	0.262261	+	0.964997i	$0.415532\pi$
$744$	1.61979e21	0.470611
$745$	−1.19090e21	−0.342534
$746$	−6.20885e21	−1.76795
$747$	7.62207e20	0.214866
$748$	5.27988e21	1.47354
$749$	6.45282e21	1.78294
$750$	3.46405e21	0.947598
$751$	−6.07827e21	−1.64619	−0.823095	−	0.567903i	$-0.807755\pi$
$751$	−6.07827e21	−1.64619	−0.823095	+	0.567903i	$0.807755\pi$
$752$	2.95315e20	0.0791866
$753$	3.92446e21	1.04188
$754$	1.05953e21	0.278503
$755$	−1.25115e21	−0.325617
$756$	−5.89327e21	−1.51860
$757$	−3.07725e21	−0.785135	−0.392567	−	0.919723i	$-0.628413\pi$
$757$	−3.07725e21	−0.785135	−0.392567	+	0.919723i	$0.628413\pi$
$758$	−5.74576e21	−1.45154
$759$	−1.17420e22	−2.93716
$760$	1.63473e21	0.404897
$761$	7.14337e21	1.75194	0.875968	−	0.482370i	$-0.160224\pi$
$761$	7.14337e21	1.75194	0.875968	+	0.482370i	$0.160224\pi$
$762$	1.20273e22	2.92083
$763$	7.59129e21	1.82550
$764$	−6.55450e20	−0.156077
$765$	−3.56066e20	−0.0839596
$766$	−7.99317e21	−1.86639
$767$	−5.32309e21	−1.23083
$768$	−4.23204e21	−0.969038
$769$	−5.04957e21	−1.14500	−0.572502	−	0.819903i	$-0.694027\pi$
$769$	−5.04957e21	−1.14500	−0.572502	+	0.819903i	$0.694027\pi$
$770$	4.72455e21	1.06091
$771$	4.28359e21	0.952577
$772$	6.50523e21	1.43263
$773$	−7.16118e21	−1.56185	−0.780923	−	0.624627i	$-0.785251\pi$
$773$	−7.16118e21	−1.56185	−0.780923	+	0.624627i	$0.785251\pi$
$774$	6.23097e21	1.34586
$775$	1.86002e21	0.397883
$776$	−3.72412e21	−0.788971
$777$	−1.26187e22	−2.64762
$778$	1.20895e22	2.51223
$779$	−9.03938e21	−1.86041
$780$	−2.18841e21	−0.446086
$781$	7.17955e21	1.44949
$782$	7.54542e21	1.50880
$783$	−5.18336e20	−0.102659
$784$	−1.42323e21	−0.279194
$785$	1.92569e20	0.0374166
$786$	−1.28819e22	−2.47920
$787$	5.54080e21	1.05624	0.528119	−	0.849170i	$-0.322897\pi$
$787$	5.54080e21	1.05624	0.528119	+	0.849170i	$0.322897\pi$
$788$	−9.88658e21	−1.86681
$789$	4.68729e21	0.876687
$790$	7.98995e20	0.148027
$791$	−1.22393e22	−2.24613
$792$	4.19478e21	0.762554
$793$	3.59456e20	0.0647287
$794$	2.94199e21	0.524792
$795$	−7.42979e20	−0.131287
$796$	5.12926e21	0.897857
$797$	−5.72484e21	−0.992718	−0.496359	−	0.868117i	$-0.665330\pi$
$797$	−5.72484e21	−0.992718	−0.496359	+	0.868117i	$0.665330\pi$
$798$	3.80328e22	6.53336
$799$	2.16733e21	0.368828
$800$	−6.14814e21	−1.03650
$801$	−3.13745e20	−0.0524002
$802$	1.05194e22	1.74054
$803$	−2.45184e21	−0.401907
$804$	−2.76583e21	−0.449164
$805$	4.11154e21	0.661509
$806$	−3.98228e21	−0.634773
$807$	−3.38235e21	−0.534155
$808$	−4.39095e20	−0.0687026
$809$	−3.00164e21	−0.465313	−0.232657	−	0.972559i	$-0.574742\pi$
$809$	−3.00164e21	−0.465313	−0.232657	+	0.972559i	$0.574742\pi$
$810$	3.17752e21	0.488034
$811$	−2.47655e20	−0.0376869	−0.0188435	−	0.999822i	$-0.505998\pi$
$811$	−2.47655e20	−0.0376869	−0.0188435	+	0.999822i	$0.505998\pi$
$812$	3.38312e21	0.510090
$813$	1.08269e22	1.61742
$814$	−1.99676e22	−2.95558
$815$	−1.06542e21	−0.156256
$816$	6.99196e20	0.101607
$817$	1.94802e22	2.80498
$818$	−1.41844e22	−2.02376
$819$	−6.51731e21	−0.921381
$820$	2.72725e21	0.382051
$821$	−4.40547e21	−0.611530	−0.305765	−	0.952107i	$-0.598912\pi$
$821$	−4.40547e21	−0.611530	−0.305765	+	0.952107i	$0.598912\pi$
$822$	4.07823e21	0.560961
$823$	5.30124e20	0.0722568	0.0361284	−	0.999347i	$-0.488497\pi$
$823$	5.30124e20	0.0722568	0.0361284	+	0.999347i	$0.488497\pi$
$824$	−4.62813e21	−0.625103
$825$	1.34658e22	1.80230
$826$	−2.79113e22	−3.70195
$827$	−8.31326e21	−1.09265	−0.546324	−	0.837574i	$-0.683973\pi$
$827$	−8.31326e21	−1.09265	−0.546324	+	0.837574i	$0.683973\pi$
$828$	1.02015e22	1.32872
$829$	−2.95251e21	−0.381095	−0.190547	−	0.981678i	$-0.561026\pi$
$829$	−2.95251e21	−0.381095	−0.190547	+	0.981678i	$0.561026\pi$
$830$	−1.18063e21	−0.151017
$831$	−1.78064e22	−2.25719
$832$	1.21760e22	1.52960
$833$	−1.04452e22	−1.30040
$834$	−2.47982e22	−3.05967
$835$	1.40059e21	0.171263
$836$	3.66485e22	4.44130
$837$	1.94818e21	0.233984
$838$	−1.28714e22	−1.53213
$839$	3.93506e20	0.0464234	0.0232117	−	0.999731i	$-0.492611\pi$
$839$	3.93506e20	0.0464234	0.0232117	+	0.999731i	$0.492611\pi$
$840$	−4.10616e21	−0.480111
$841$	2.97558e20	0.0344828
$842$	1.49027e22	1.71168
$843$	−1.19719e22	−1.36287
$844$	−1.51366e22	−1.70789
$845$	−2.63534e20	−0.0294721
$846$	4.81192e21	0.533385
$847$	2.18469e22	2.40030
$848$	5.21893e20	0.0568345
$849$	−1.56034e22	−1.68427
$850$	−8.65313e21	−0.925830
$851$	−1.73768e22	−1.84289
$852$	−1.74374e22	−1.83309
$853$	−6.76596e21	−0.705037	−0.352519	−	0.935805i	$-0.614675\pi$
$853$	−6.76596e21	−0.705037	−0.352519	+	0.935805i	$0.614675\pi$
$854$	1.88479e21	0.194683
$855$	−2.47152e21	−0.253057
$856$	−8.87439e21	−0.900710
$857$	1.70740e21	0.171782	0.0858912	−	0.996305i	$-0.472626\pi$
$857$	1.70740e21	0.171782	0.0858912	+	0.996305i	$0.472626\pi$
$858$	−2.88300e22	−2.87534
$859$	4.76445e20	0.0471046	0.0235523	−	0.999723i	$-0.492502\pi$
$859$	4.76445e20	0.0471046	0.0235523	+	0.999723i	$0.492502\pi$
$860$	−5.87734e21	−0.576026
$861$	2.27054e22	2.20600
$862$	5.20678e21	0.501493
$863$	4.24541e21	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$863$	4.24541e21	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$864$	−6.43953e21	−0.609538
$865$	−1.51695e21	−0.142347
$866$	2.65856e21	0.247322
$867$	−8.39800e21	−0.774520
$868$	−1.27155e22	−1.16261
$869$	6.40982e21	0.581029
$870$	−1.00925e21	−0.0906996
$871$	2.43327e21	0.216797
$872$	−1.04401e22	−0.922211
$873$	5.63042e21	0.493099
$874$	5.23740e22	4.54758
$875$	−9.73082e21	−0.837701
$876$	5.95492e21	0.508270
$877$	1.65114e22	1.39729	0.698646	−	0.715467i	$-0.253786\pi$
$877$	1.65114e22	1.39729	0.698646	+	0.715467i	$0.253786\pi$
$878$	1.36467e22	1.14503
$879$	−6.30743e21	−0.524730
$880$	6.02884e20	0.0497294
$881$	−9.40723e21	−0.769383	−0.384691	−	0.923045i	$-0.625692\pi$
$881$	−9.40723e21	−0.769383	−0.384691	+	0.923045i	$0.625692\pi$
$882$	−2.31905e22	−1.88059
$883$	5.51619e21	0.443541	0.221770	−	0.975099i	$-0.428816\pi$
$883$	5.51619e21	0.443541	0.221770	+	0.975099i	$0.428816\pi$
$884$	1.12816e22	0.899456
$885$	5.07047e21	0.400843
$886$	2.82457e22	2.21411
$887$	3.25143e21	0.252724	0.126362	−	0.991984i	$-0.459670\pi$
$887$	3.25143e21	0.252724	0.126362	+	0.991984i	$0.459670\pi$
$888$	1.73541e22	1.33753
$889$	−3.37858e22	−2.58209
$890$	4.85978e20	0.0368292
$891$	2.54912e22	1.91561
$892$	−7.10669e21	−0.529579
$893$	1.50438e22	1.11166
$894$	3.81045e22	2.79219
$895$	−2.66491e21	−0.193646
$896$	3.68540e22	2.65568
$897$	−2.50893e22	−1.79286
$898$	1.12514e22	0.797322
$899$	−1.11838e21	−0.0785943
$900$	−1.16991e22	−0.815330
$901$	3.83019e21	0.264719
$902$	3.59287e22	2.46259
$903$	−4.89310e22	−3.32603
$904$	1.68324e22	1.13471
$905$	−1.89004e20	−0.0126359
$906$	4.00323e22	2.65429
$907$	−8.30356e21	−0.546021	−0.273011	−	0.962011i	$-0.588019\pi$
$907$	−8.30356e21	−0.546021	−0.273011	+	0.962011i	$0.588019\pi$
$908$	1.06265e22	0.693024
$909$	6.63859e20	0.0429385
$910$	1.00950e22	0.647587
$911$	−1.03645e22	−0.659419	−0.329710	−	0.944082i	$-0.606951\pi$
$911$	−1.03645e22	−0.659419	−0.329710	+	0.944082i	$0.606951\pi$
$912$	4.85323e21	0.306246
$913$	−9.47141e21	−0.592767
$914$	3.22596e22	2.00245
$915$	−3.42397e20	−0.0210801
$916$	2.70442e22	1.65142
$917$	3.61864e22	2.19167
$918$	−9.06323e21	−0.544456
$919$	−2.03801e22	−1.21434	−0.607169	−	0.794573i	$-0.707695\pi$
$919$	−2.03801e22	−1.21434	−0.607169	+	0.794573i	$0.707695\pi$
$920$	−5.65449e21	−0.334183
$921$	8.57996e21	0.502965
$922$	−3.40565e22	−1.98024
$923$	1.53407e22	0.884773
$924$	−9.20548e22	−5.26631
$925$	1.99278e22	1.13083
$926$	−2.09922e22	−1.18161
$927$	6.99718e21	0.390683
$928$	3.69670e21	0.204741
$929$	−9.82920e21	−0.540008	−0.270004	−	0.962859i	$-0.587025\pi$
$929$	−9.82920e21	−0.540008	−0.270004	+	0.962859i	$0.587025\pi$
$930$	3.79329e21	0.206726
$931$	−7.25017e22	−3.91945
$932$	−2.98537e22	−1.60096
$933$	1.24690e22	0.663316
$934$	4.30884e22	2.27383
$935$	4.42459e21	0.231625
$936$	8.96308e21	0.465466
$937$	2.94342e22	1.51637	0.758185	−	0.652039i	$-0.226086\pi$
$937$	2.94342e22	1.51637	0.758185	+	0.652039i	$0.226086\pi$
$938$	1.27587e22	0.652056
$939$	2.79451e22	1.41682
$940$	−4.53883e21	−0.228289
$941$	3.81978e22	1.90597	0.952985	−	0.303018i	$-0.0979942\pi$
$941$	3.81978e22	1.90597	0.952985	+	0.303018i	$0.0979942\pi$
$942$	−6.16152e21	−0.305004
$943$	3.12670e22	1.53549
$944$	−3.56167e21	−0.173526
$945$	−4.93861e21	−0.238708
$946$	−7.74279e22	−3.71290
$947$	2.62401e22	1.24836	0.624182	−	0.781279i	$-0.285432\pi$
$947$	2.62401e22	1.24836	0.624182	+	0.781279i	$0.285432\pi$
$948$	−1.55679e22	−0.734797
$949$	−5.23889e21	−0.245326
$950$	−6.00628e22	−2.79048
$951$	8.55543e21	0.394356
$952$	2.11680e22	0.968062
$953$	−2.17474e22	−0.986759	−0.493380	−	0.869814i	$-0.664239\pi$
$953$	−2.17474e22	−0.986759	−0.493380	+	0.869814i	$0.664239\pi$
$954$	8.50382e21	0.382826
$955$	−5.49273e20	−0.0245337
$956$	4.34968e22	1.92763
$957$	−8.09658e21	−0.356010
$958$	−3.22024e22	−1.40490
$959$	−1.14561e22	−0.495904
$960$	−1.15981e22	−0.498142
$961$	−1.92618e22	−0.820865
$962$	−4.26652e22	−1.80410
$963$	1.34170e22	0.562935
$964$	−5.41414e22	−2.25399
$965$	5.45144e21	0.225194
$966$	−1.31554e23	−5.39234
$967$	4.63342e21	0.188453	0.0942266	−	0.995551i	$-0.469962\pi$
$967$	4.63342e21	0.188453	0.0942266	+	0.995551i	$0.469962\pi$
$968$	−3.00455e22	−1.21259
$969$	3.56181e22	1.42640
$970$	−8.72129e21	−0.346571
$971$	−2.60985e22	−1.02913	−0.514566	−	0.857451i	$-0.672047\pi$
$971$	−2.60985e22	−1.02913	−0.514566	+	0.857451i	$0.672047\pi$
$972$	−3.99103e22	−1.56167
$973$	6.96602e22	2.70482
$974$	−7.05478e21	−0.271826
$975$	2.87726e22	1.10013
$976$	2.40511e20	0.00912561
$977$	1.99565e22	0.751407	0.375703	−	0.926740i	$-0.377401\pi$
$977$	1.99565e22	0.751407	0.375703	+	0.926740i	$0.377401\pi$
$978$	3.40895e22	1.27373
$979$	3.89869e21	0.144560
$980$	2.18743e22	0.804894
$981$	1.57841e22	0.576373
$982$	1.01416e22	0.367511
$983$	1.60853e22	0.578465	0.289232	−	0.957259i	$-0.406600\pi$
$983$	1.60853e22	0.578465	0.289232	+	0.957259i	$0.406600\pi$
$984$	−3.12261e22	−1.11443
$985$	−8.28503e21	−0.293442
$986$	5.20288e21	0.182880
$987$	−3.77874e22	−1.31816
$988$	7.83077e22	2.71099
$989$	−6.73816e22	−2.31510
$990$	9.82350e21	0.334967
$991$	−5.04422e22	−1.70703	−0.853515	−	0.521068i	$-0.825534\pi$
$991$	−5.04422e22	−1.70703	−0.853515	+	0.521068i	$0.825534\pi$
$992$	−1.38941e22	−0.466652
$993$	2.08974e21	0.0696583
$994$	8.04381e22	2.66112
$995$	4.29837e21	0.141134
$996$	2.30037e22	0.749641
$997$	−1.94001e22	−0.627466	−0.313733	−	0.949511i	$-0.601580\pi$
$997$	−1.94001e22	−0.627466	−0.313733	+	0.949511i	$0.601580\pi$
$998$	7.00395e22	2.24835
$999$	2.08723e22	0.665011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.a.1.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-289.475 q^{2} +4726.56 q^{3} +51028.0 q^{4} +42761.9 q^{5} -1.36822e6 q^{6} +3.84346e6 q^{7} -5.28581e6 q^{8} +7.99150e6 q^{9} +O(q^{10})\)	\(q-289.475 q^{2} +4726.56 q^{3} +51028.0 q^{4} +42761.9 q^{5} -1.36822e6 q^{6} +3.84346e6 q^{7} -5.28581e6 q^{8} +7.99150e6 q^{9} -1.23785e7 q^{10} -9.93047e7 q^{11} +2.41187e8 q^{12} -2.12186e8 q^{13} -1.11259e9 q^{14} +2.02117e8 q^{15} -1.41973e8 q^{16} -1.04195e9 q^{17} -2.31334e9 q^{18} -7.23234e9 q^{19} +2.18205e9 q^{20} +1.81664e10 q^{21} +2.87463e10 q^{22} +2.50164e10 q^{23} -2.49837e10 q^{24} -2.86890e10 q^{25} +6.14227e10 q^{26} -3.00487e10 q^{27} +1.96124e11 q^{28} +1.72499e10 q^{29} -5.85078e10 q^{30} -6.48340e10 q^{31} +2.14303e11 q^{32} -4.69370e11 q^{33} +3.01618e11 q^{34} +1.64354e11 q^{35} +4.07790e11 q^{36} -6.94616e11 q^{37} +2.09358e12 q^{38} -1.00291e12 q^{39} -2.26031e11 q^{40} +1.24986e12 q^{41} -5.25872e12 q^{42} -2.69349e12 q^{43} -5.06732e12 q^{44} +3.41731e11 q^{45} -7.24164e12 q^{46} -2.08007e12 q^{47} -6.71047e11 q^{48} +1.00247e13 q^{49} +8.30476e12 q^{50} -4.92483e12 q^{51} -1.08274e13 q^{52} -3.67599e12 q^{53} +8.69835e12 q^{54} -4.24646e12 q^{55} -2.03158e13 q^{56} -3.41841e13 q^{57} -4.99341e12 q^{58} +2.50869e13 q^{59} +1.03136e13 q^{60} -1.69406e12 q^{61} +1.87678e13 q^{62} +3.07150e13 q^{63} -5.73833e13 q^{64} -9.07348e12 q^{65} +1.35871e14 q^{66} -1.14676e13 q^{67} -5.31685e13 q^{68} +1.18242e14 q^{69} -4.75763e13 q^{70} -7.22982e13 q^{71} -4.22415e13 q^{72} +2.46900e13 q^{73} +2.01074e14 q^{74} -1.35600e14 q^{75} -3.69051e14 q^{76} -3.81674e14 q^{77} +2.90318e14 q^{78} -6.45470e13 q^{79} -6.07105e12 q^{80} -2.56696e14 q^{81} -3.61803e14 q^{82} +9.53772e13 q^{83} +9.26993e14 q^{84} -4.45556e13 q^{85} +7.79700e14 q^{86} +8.15326e13 q^{87} +5.24906e14 q^{88} -3.92599e13 q^{89} -9.89228e13 q^{90} -8.15531e14 q^{91} +1.27654e15 q^{92} -3.06442e14 q^{93} +6.02130e14 q^{94} -3.09268e14 q^{95} +1.01292e15 q^{96} +7.04551e14 q^{97} -2.90189e15 q^{98} -7.93594e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} - 3214 q^{3} + 239962 q^{4} - 82010 q^{5} - 112778 q^{6} - 3706320 q^{7} - 21137070 q^{8} + 73272578 q^{9}+O(q^{10}) \) 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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