LMFDB - Embedded newform 125.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(1,125)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("125.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 11 $ x^4 - 7*x^2 + 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.14896$ of defining polynomial
Character	$\chi$	$=$	125.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.32813 q^{2} -2.14896 q^{3} -0.236068 q^{4} +2.85410 q^{6} +3.47709 q^{7} +2.96979 q^{8} +1.61803 q^{9} +O(q^{10})$	\(q-1.32813 q^{2} -2.14896 q^{3} -0.236068 q^{4} +2.85410 q^{6} +3.47709 q^{7} +2.96979 q^{8} +1.61803 q^{9} +2.00000 q^{11} +0.507301 q^{12} +2.65626 q^{13} -4.61803 q^{14} -3.47214 q^{16} -4.29792 q^{17} -2.14896 q^{18} +7.23607 q^{19} -7.47214 q^{21} -2.65626 q^{22} +0.820830 q^{23} -6.38197 q^{24} -3.52786 q^{26} +2.96979 q^{27} -0.820830 q^{28} +0.854102 q^{29} +2.00000 q^{31} -1.32813 q^{32} -4.29792 q^{33} +5.70820 q^{34} -0.381966 q^{36} +1.64166 q^{37} -9.61045 q^{38} -5.70820 q^{39} -6.09017 q^{41} +9.92398 q^{42} +3.79062 q^{43} -0.472136 q^{44} -1.09017 q^{46} +0.507301 q^{47} +7.46149 q^{48} +5.09017 q^{49} +9.23607 q^{51} -0.627058 q^{52} +8.59584 q^{53} -3.94427 q^{54} +10.3262 q^{56} -15.5500 q^{57} -1.13436 q^{58} -4.47214 q^{59} +5.09017 q^{61} -2.65626 q^{62} +5.62605 q^{63} +8.70820 q^{64} +5.70820 q^{66} -4.29792 q^{67} +1.01460 q^{68} -1.76393 q^{69} +8.18034 q^{71} +4.80522 q^{72} -16.5646 q^{73} -2.18034 q^{74} -1.70820 q^{76} +6.95418 q^{77} +7.58124 q^{78} +2.76393 q^{79} -11.2361 q^{81} +8.08854 q^{82} -5.11875 q^{83} +1.76393 q^{84} -5.03444 q^{86} -1.83543 q^{87} +5.93958 q^{88} -8.61803 q^{89} +9.23607 q^{91} -0.193772 q^{92} -4.29792 q^{93} -0.673762 q^{94} +2.85410 q^{96} +11.2521 q^{97} -6.76041 q^{98} +3.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 - 2 * q^6 + 2 * q^9	$ 4 q + 8 q^{4} - 2 q^{6} + 2 q^{9} + 8 q^{11} - 14 q^{14} + 4 q^{16} + 20 q^{19} - 12 q^{21} - 30 q^{24} - 32 q^{26} - 10 q^{29} + 8 q^{31} - 4 q^{34} - 6 q^{36} + 4 q^{39} - 2 q^{41} + 16 q^{44} + 18 q^{46} - 2 q^{49} + 28 q^{51} + 20 q^{54} + 10 q^{56} - 2 q^{61} + 8 q^{64} - 4 q^{66} - 16 q^{69} - 12 q^{71} + 36 q^{74} + 20 q^{76} + 20 q^{79} - 36 q^{81} + 16 q^{84} + 38 q^{86} - 30 q^{89} + 28 q^{91} - 34 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 - 2 * q^6 + 2 * q^9 + 8 * q^11 - 14 * q^14 + 4 * q^16 + 20 * q^19 - 12 * q^21 - 30 * q^24 - 32 * q^26 - 10 * q^29 + 8 * q^31 - 4 * q^34 - 6 * q^36 + 4 * q^39 - 2 * q^41 + 16 * q^44 + 18 * q^46 - 2 * q^49 + 28 * q^51 + 20 * q^54 + 10 * q^56 - 2 * q^61 + 8 * q^64 - 4 * q^66 - 16 * q^69 - 12 * q^71 + 36 * q^74 + 20 * q^76 + 20 * q^79 - 36 * q^81 + 16 * q^84 + 38 * q^86 - 30 * q^89 + 28 * q^91 - 34 * q^94 - 2 * q^96 + 4 * 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 $

$2$	−1.32813	−0.939130	−0.469565	−	0.882898i	$-0.655589\pi$
$2$	−1.32813	−0.939130	−0.469565	+	0.882898i	$0.655589\pi$
$3$	−2.14896	−1.24070	−0.620352	−	0.784324i	$-0.713010\pi$
$3$	−2.14896	−1.24070	−0.620352	+	0.784324i	$0.713010\pi$
$4$	−0.236068	−0.118034
$5$	0	0
$5$	0	0
$6$	2.85410	1.16518
$7$	3.47709	1.31422	0.657109	−	0.753796i	$-0.271779\pi$
$7$	3.47709	1.31422	0.657109	+	0.753796i	$0.271779\pi$
$8$	2.96979	1.04998
$9$	1.61803	0.539345
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0.507301	0.146445
$13$	2.65626	0.736715	0.368357	−	0.929684i	$-0.379920\pi$
$13$	2.65626	0.736715	0.368357	+	0.929684i	$0.379920\pi$
$14$	−4.61803	−1.23422
$15$	0	0
$16$	−3.47214	−0.868034
$17$	−4.29792	−1.04240	−0.521200	−	0.853435i	$-0.674515\pi$
$17$	−4.29792	−1.04240	−0.521200	+	0.853435i	$0.674515\pi$
$18$	−2.14896	−0.506515
$19$	7.23607	1.66007	0.830034	−	0.557713i	$-0.188321\pi$
$19$	7.23607	1.66007	0.830034	+	0.557713i	$0.188321\pi$
$20$	0	0
$21$	−7.47214	−1.63055
$22$	−2.65626	−0.566317
$23$	0.820830	0.171155	0.0855775	−	0.996332i	$-0.472726\pi$
$23$	0.820830	0.171155	0.0855775	+	0.996332i	$0.472726\pi$
$24$	−6.38197	−1.30271
$25$	0	0
$26$	−3.52786	−0.691871
$27$	2.96979	0.571537
$28$	−0.820830	−0.155122
$29$	0.854102	0.158603	0.0793014	−	0.996851i	$-0.474731\pi$
$29$	0.854102	0.158603	0.0793014	+	0.996851i	$0.474731\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.32813	−0.234783
$33$	−4.29792	−0.748172
$34$	5.70820	0.978949
$35$	0	0
$36$	−0.381966	−0.0636610
$37$	1.64166	0.269887	0.134944	−	0.990853i	$-0.456915\pi$
$37$	1.64166	0.269887	0.134944	+	0.990853i	$0.456915\pi$
$38$	−9.61045	−1.55902
$39$	−5.70820	−0.914044
$40$	0	0
$41$	−6.09017	−0.951125	−0.475562	−	0.879682i	$-0.657755\pi$
$41$	−6.09017	−0.951125	−0.475562	+	0.879682i	$0.657755\pi$
$42$	9.92398	1.53130
$43$	3.79062	0.578064	0.289032	−	0.957319i	$-0.406667\pi$
$43$	3.79062	0.578064	0.289032	+	0.957319i	$0.406667\pi$
$44$	−0.472136	−0.0711772
$45$	0	0
$46$	−1.09017	−0.160737
$47$	0.507301	0.0739974	0.0369987	−	0.999315i	$-0.488220\pi$
$47$	0.507301	0.0739974	0.0369987	+	0.999315i	$0.488220\pi$
$48$	7.46149	1.07697
$49$	5.09017	0.727167
$50$	0	0
$51$	9.23607	1.29331
$52$	−0.627058	−0.0869574
$53$	8.59584	1.18073	0.590365	−	0.807136i	$-0.298984\pi$
$53$	8.59584	1.18073	0.590365	+	0.807136i	$0.298984\pi$
$54$	−3.94427	−0.536747
$55$	0	0
$56$	10.3262	1.37990
$57$	−15.5500	−2.05965
$58$	−1.13436	−0.148949
$59$	−4.47214	−0.582223	−0.291111	−	0.956689i	$-0.594025\pi$
$59$	−4.47214	−0.582223	−0.291111	+	0.956689i	$0.594025\pi$
$60$	0	0
$61$	5.09017	0.651729	0.325865	−	0.945416i	$-0.394345\pi$
$61$	5.09017	0.651729	0.325865	+	0.945416i	$0.394345\pi$
$62$	−2.65626	−0.337346
$63$	5.62605	0.708816
$64$	8.70820	1.08853
$65$	0	0
$66$	5.70820	0.702631
$67$	−4.29792	−0.525075	−0.262537	−	0.964922i	$-0.584559\pi$
$67$	−4.29792	−0.525075	−0.262537	+	0.964922i	$0.584559\pi$
$68$	1.01460	0.123039
$69$	−1.76393	−0.212352
$70$	0	0
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	4.80522	0.566301
$73$	−16.5646	−1.93874	−0.969372	−	0.245598i	$-0.921016\pi$
$73$	−16.5646	−1.93874	−0.969372	+	0.245598i	$0.921016\pi$
$74$	−2.18034	−0.253459
$75$	0	0
$76$	−1.70820	−0.195944
$77$	6.95418	0.792503
$78$	7.58124	0.858407
$79$	2.76393	0.310967	0.155483	−	0.987839i	$-0.450307\pi$
$79$	2.76393	0.310967	0.155483	+	0.987839i	$0.450307\pi$
$80$	0	0
$81$	−11.2361	−1.24845
$82$	8.08854	0.893230
$83$	−5.11875	−0.561856	−0.280928	−	0.959729i	$-0.590642\pi$
$83$	−5.11875	−0.561856	−0.280928	+	0.959729i	$0.590642\pi$
$84$	1.76393	0.192461
$85$	0	0
$86$	−5.03444	−0.542878
$87$	−1.83543	−0.196779
$88$	5.93958	0.633162
$89$	−8.61803	−0.913510	−0.456755	−	0.889593i	$-0.650988\pi$
$89$	−8.61803	−0.913510	−0.456755	+	0.889593i	$0.650988\pi$
$90$	0	0
$91$	9.23607	0.968203
$92$	−0.193772	−0.0202021
$93$	−4.29792	−0.445674
$94$	−0.673762	−0.0694933
$95$	0	0
$96$	2.85410	0.291296
$97$	11.2521	1.14248	0.571239	−	0.820784i	$-0.306463\pi$
$97$	11.2521	1.14248	0.571239	+	0.820784i	$0.306463\pi$
$98$	−6.76041	−0.682905
$99$	3.23607	0.325237
$100$	0	0
$101$	−11.0902	−1.10351	−0.551757	−	0.834005i	$-0.686042\pi$
$101$	−11.0902	−1.10351	−0.551757	+	0.834005i	$0.686042\pi$
$102$	−12.2667	−1.21459
$103$	−12.8938	−1.27046	−0.635230	−	0.772323i	$-0.719095\pi$
$103$	−12.8938	−1.27046	−0.635230	+	0.772323i	$0.719095\pi$
$104$	7.88854	0.773535
$105$	0	0
$106$	−11.4164	−1.10886
$107$	10.1177	0.978120	0.489060	−	0.872250i	$-0.337340\pi$
$107$	10.1177	0.978120	0.489060	+	0.872250i	$0.337340\pi$
$108$	−0.701073	−0.0674607
$109$	−12.5623	−1.20325	−0.601625	−	0.798778i	$-0.705480\pi$
$109$	−12.5623	−1.20325	−0.601625	+	0.798778i	$0.705480\pi$
$110$	0	0
$111$	−3.52786	−0.334850
$112$	−12.0729	−1.14079
$113$	2.65626	0.249880	0.124940	−	0.992164i	$-0.460126\pi$
$113$	2.65626	0.249880	0.124940	+	0.992164i	$0.460126\pi$
$114$	20.6525	1.93428
$115$	0	0
$116$	−0.201626	−0.0187205
$117$	4.29792	0.397343
$118$	5.93958	0.546783
$119$	−14.9443	−1.36994
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−6.76041	−0.612059
$123$	13.0875	1.18006
$124$	−0.472136	−0.0423991
$125$	0	0
$126$	−7.47214	−0.665671
$127$	−18.7136	−1.66056	−0.830281	−	0.557344i	$-0.811820\pi$
$127$	−18.7136	−1.66056	−0.830281	+	0.557344i	$0.811820\pi$
$128$	−8.90937	−0.787485
$129$	−8.14590	−0.717206
$130$	0	0
$131$	−14.1803	−1.23894	−0.619471	−	0.785020i	$-0.712653\pi$
$131$	−14.1803	−1.23894	−0.619471	+	0.785020i	$0.712653\pi$
$132$	1.01460	0.0883098
$133$	25.1605	2.18169
$134$	5.70820	0.493114
$135$	0	0
$136$	−12.7639	−1.09450
$137$	14.9230	1.27496	0.637478	−	0.770469i	$-0.279978\pi$
$137$	14.9230	1.27496	0.637478	+	0.770469i	$0.279978\pi$
$138$	2.34273	0.199427
$139$	8.29180	0.703301	0.351650	−	0.936131i	$-0.385621\pi$
$139$	8.29180	0.703301	0.351650	+	0.936131i	$0.385621\pi$
$140$	0	0
$141$	−1.09017	−0.0918089
$142$	−10.8646	−0.911734
$143$	5.31252	0.444256
$144$	−5.61803	−0.468169
$145$	0	0
$146$	22.0000	1.82073
$147$	−10.9386	−0.902199
$148$	−0.387543	−0.0318559
$149$	19.2705	1.57870	0.789351	−	0.613942i	$-0.210417\pi$
$149$	19.2705	1.57870	0.789351	+	0.613942i	$0.210417\pi$
$150$	0	0
$151$	18.1803	1.47950	0.739748	−	0.672885i	$-0.234945\pi$
$151$	18.1803	1.47950	0.739748	+	0.672885i	$0.234945\pi$
$152$	21.4896	1.74304
$153$	−6.95418	−0.562212
$154$	−9.23607	−0.744264
$155$	0	0
$156$	1.34752	0.107888
$157$	7.58124	0.605049	0.302525	−	0.953142i	$-0.402171\pi$
$157$	7.58124	0.605049	0.302525	+	0.953142i	$0.402171\pi$
$158$	−3.67086	−0.292038
$159$	−18.4721	−1.46494
$160$	0	0
$161$	2.85410	0.224935
$162$	14.9230	1.17246
$163$	−14.7292	−1.15368	−0.576840	−	0.816857i	$-0.695714\pi$
$163$	−14.7292	−1.15368	−0.576840	+	0.816857i	$0.695714\pi$
$164$	1.43769	0.112265
$165$	0	0
$166$	6.79837	0.527656
$167$	6.44688	0.498875	0.249437	−	0.968391i	$-0.419754\pi$
$167$	6.44688	0.498875	0.249437	+	0.968391i	$0.419754\pi$
$168$	−22.1907	−1.71205
$169$	−5.94427	−0.457252
$170$	0	0
$171$	11.7082	0.895349
$172$	−0.894844	−0.0682312
$173$	18.2063	1.38420	0.692099	−	0.721802i	$-0.256686\pi$
$173$	18.2063	1.38420	0.692099	+	0.721802i	$0.256686\pi$
$174$	2.43769	0.184801
$175$	0	0
$176$	−6.94427	−0.523444
$177$	9.61045	0.722365
$178$	11.4459	0.857905
$179$	18.9443	1.41596	0.707981	−	0.706232i	$-0.249606\pi$
$179$	18.9443	1.41596	0.707981	+	0.706232i	$0.249606\pi$
$180$	0	0
$181$	0.0901699	0.00670228	0.00335114	−	0.999994i	$-0.498933\pi$
$181$	0.0901699	0.00670228	0.00335114	+	0.999994i	$0.498933\pi$
$182$	−12.2667	−0.909269
$183$	−10.9386	−0.808603
$184$	2.43769	0.179709
$185$	0	0
$186$	5.70820	0.418546
$187$	−8.59584	−0.628590
$188$	−0.119757	−0.00873421
$189$	10.3262	0.751123
$190$	0	0
$191$	8.18034	0.591909	0.295954	−	0.955202i	$-0.404362\pi$
$191$	8.18034	0.591909	0.295954	+	0.955202i	$0.404362\pi$
$192$	−18.7136	−1.35054
$193$	−6.95418	−0.500573	−0.250287	−	0.968172i	$-0.580525\pi$
$193$	−6.95418	−0.500573	−0.250287	+	0.968172i	$0.580525\pi$
$194$	−14.9443	−1.07294
$195$	0	0
$196$	−1.20163	−0.0858304
$197$	−23.5188	−1.67565	−0.837823	−	0.545942i	$-0.816172\pi$
$197$	−23.5188	−1.67565	−0.837823	+	0.545942i	$0.816172\pi$
$198$	−4.29792	−0.305440
$199$	−16.1803	−1.14699	−0.573497	−	0.819208i	$-0.694414\pi$
$199$	−16.1803	−1.14699	−0.573497	+	0.819208i	$0.694414\pi$
$200$	0	0
$201$	9.23607	0.651462
$202$	14.7292	1.03634
$203$	2.96979	0.208438
$204$	−2.18034	−0.152654
$205$	0	0
$206$	17.1246	1.19313
$207$	1.32813	0.0923115
$208$	−9.22290	−0.639493
$209$	14.4721	1.00106
$210$	0	0
$211$	5.81966	0.400642	0.200321	−	0.979730i	$-0.435802\pi$
$211$	5.81966	0.400642	0.200321	+	0.979730i	$0.435802\pi$
$212$	−2.02920	−0.139366
$213$	−17.5792	−1.20451
$214$	−13.4377	−0.918582
$215$	0	0
$216$	8.81966	0.600102
$217$	6.95418	0.472081
$218$	16.6844	1.13001
$219$	35.5967	2.40541
$220$	0	0
$221$	−11.4164	−0.767951
$222$	4.68547	0.314468
$223$	7.46149	0.499658	0.249829	−	0.968290i	$-0.419626\pi$
$223$	7.46149	0.499658	0.249829	+	0.968290i	$0.419626\pi$
$224$	−4.61803	−0.308555
$225$	0	0
$226$	−3.52786	−0.234670
$227$	−12.0729	−0.801309	−0.400654	−	0.916229i	$-0.631217\pi$
$227$	−12.0729	−0.801309	−0.400654	+	0.916229i	$0.631217\pi$
$228$	3.67086	0.243109
$229$	−20.3262	−1.34320	−0.671598	−	0.740916i	$-0.734392\pi$
$229$	−20.3262	−1.34320	−0.671598	+	0.740916i	$0.734392\pi$
$230$	0	0
$231$	−14.9443	−0.983261
$232$	2.53650	0.166530
$233$	−1.01460	−0.0664688	−0.0332344	−	0.999448i	$-0.510581\pi$
$233$	−1.01460	−0.0664688	−0.0332344	+	0.999448i	$0.510581\pi$
$234$	−5.70820	−0.373157
$235$	0	0
$236$	1.05573	0.0687220
$237$	−5.93958	−0.385817
$238$	19.8480	1.28655
$239$	−11.7082	−0.757341	−0.378670	−	0.925532i	$-0.623619\pi$
$239$	−11.7082	−0.757341	−0.378670	+	0.925532i	$0.623619\pi$
$240$	0	0
$241$	−1.09017	−0.0702240	−0.0351120	−	0.999383i	$-0.511179\pi$
$241$	−1.09017	−0.0702240	−0.0351120	+	0.999383i	$0.511179\pi$
$242$	9.29692	0.597628
$243$	15.2365	0.977422
$244$	−1.20163	−0.0769262
$245$	0	0
$246$	−17.3820	−1.10823
$247$	19.2209	1.22300
$248$	5.93958	0.377164
$249$	11.0000	0.697097
$250$	0	0
$251$	−20.3607	−1.28515	−0.642577	−	0.766221i	$-0.722135\pi$
$251$	−20.3607	−1.28515	−0.642577	+	0.766221i	$0.722135\pi$
$252$	−1.32813	−0.0836644
$253$	1.64166	0.103210
$254$	24.8541	1.55949
$255$	0	0
$256$	−5.58359	−0.348975
$257$	−13.9084	−0.867580	−0.433790	−	0.901014i	$-0.642824\pi$
$257$	−13.9084	−0.867580	−0.433790	+	0.901014i	$0.642824\pi$
$258$	10.8188	0.673550
$259$	5.70820	0.354691
$260$	0	0
$261$	1.38197	0.0855415
$262$	18.8333	1.16353
$263$	0.119757	0.00738456	0.00369228	−	0.999993i	$-0.498825\pi$
$263$	0.119757	0.00738456	0.00369228	+	0.999993i	$0.498825\pi$
$264$	−12.7639	−0.785566
$265$	0	0
$266$	−33.4164	−2.04889
$267$	18.5198	1.13339
$268$	1.01460	0.0619767
$269$	1.05573	0.0643689	0.0321844	−	0.999482i	$-0.489754\pi$
$269$	1.05573	0.0643689	0.0321844	+	0.999482i	$0.489754\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	14.9230	0.904838
$273$	−19.8480	−1.20125
$274$	−19.8197	−1.19735
$275$	0	0
$276$	0.416408	0.0250648
$277$	−16.1771	−0.971987	−0.485993	−	0.873962i	$-0.661542\pi$
$277$	−16.1771	−0.971987	−0.485993	+	0.873962i	$0.661542\pi$
$278$	−11.0126	−0.660491
$279$	3.23607	0.193738
$280$	0	0
$281$	31.2705	1.86544	0.932721	−	0.360599i	$-0.117428\pi$
$281$	31.2705	1.86544	0.932721	+	0.360599i	$0.117428\pi$
$282$	1.44789	0.0862205
$283$	−1.01460	−0.0603118	−0.0301559	−	0.999545i	$-0.509600\pi$
$283$	−1.01460	−0.0603118	−0.0301559	+	0.999545i	$0.509600\pi$
$284$	−1.93112	−0.114591
$285$	0	0
$286$	−7.05573	−0.417214
$287$	−21.1761	−1.24998
$288$	−2.14896	−0.126629
$289$	1.47214	0.0865962
$290$	0	0
$291$	−24.1803	−1.41748
$292$	3.91038	0.228838
$293$	−28.4438	−1.66170	−0.830852	−	0.556493i	$-0.812147\pi$
$293$	−28.4438	−1.66170	−0.830852	+	0.556493i	$0.812147\pi$
$294$	14.5279	0.847282
$295$	0	0
$296$	4.87539	0.283376
$297$	5.93958	0.344650
$298$	−25.5938	−1.48261
$299$	2.18034	0.126092
$300$	0	0
$301$	13.1803	0.759702
$302$	−24.1459	−1.38944
$303$	23.8323	1.36913
$304$	−25.1246	−1.44100
$305$	0	0
$306$	9.23607	0.527991
$307$	−9.80422	−0.559556	−0.279778	−	0.960065i	$-0.590261\pi$
$307$	−9.80422	−0.559556	−0.279778	+	0.960065i	$0.590261\pi$
$308$	−1.64166	−0.0935423
$309$	27.7082	1.57626
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	−16.9522	−0.959728
$313$	15.9376	0.900845	0.450422	−	0.892816i	$-0.351273\pi$
$313$	15.9376	0.900845	0.450422	+	0.892816i	$0.351273\pi$
$314$	−10.0689	−0.568220
$315$	0	0
$316$	−0.652476	−0.0367046
$317$	−17.5792	−0.987348	−0.493674	−	0.869647i	$-0.664346\pi$
$317$	−17.5792	−0.987348	−0.493674	+	0.869647i	$0.664346\pi$
$318$	24.5334	1.37577
$319$	1.70820	0.0956411
$320$	0	0
$321$	−21.7426	−1.21356
$322$	−3.79062	−0.211243
$323$	−31.1001	−1.73045
$324$	2.65248	0.147360
$325$	0	0
$326$	19.5623	1.08346
$327$	26.9959	1.49288
$328$	−18.0865	−0.998662
$329$	1.76393	0.0972487
$330$	0	0
$331$	5.81966	0.319877	0.159939	−	0.987127i	$-0.448870\pi$
$331$	5.81966	0.319877	0.159939	+	0.987127i	$0.448870\pi$
$332$	1.20837	0.0663181
$333$	2.65626	0.145562
$334$	−8.56231	−0.468509
$335$	0	0
$336$	25.9443	1.41538
$337$	1.64166	0.0894269	0.0447135	−	0.999000i	$-0.485763\pi$
$337$	1.64166	0.0894269	0.0447135	+	0.999000i	$0.485763\pi$
$338$	7.89477	0.429419
$339$	−5.70820	−0.310027
$340$	0	0
$341$	4.00000	0.216612
$342$	−15.5500	−0.840849
$343$	−6.64066	−0.358562
$344$	11.2574	0.606956
$345$	0	0
$346$	−24.1803	−1.29994
$347$	28.6376	1.53735	0.768673	−	0.639642i	$-0.220918\pi$
$347$	28.6376	1.53735	0.768673	+	0.639642i	$0.220918\pi$
$348$	0.433287	0.0232266
$349$	−9.27051	−0.496239	−0.248120	−	0.968729i	$-0.579813\pi$
$349$	−9.27051	−0.496239	−0.248120	+	0.968729i	$0.579813\pi$
$350$	0	0
$351$	7.88854	0.421059
$352$	−2.65626	−0.141579
$353$	21.8772	1.16440	0.582202	−	0.813044i	$-0.302191\pi$
$353$	21.8772	1.16440	0.582202	+	0.813044i	$0.302191\pi$
$354$	−12.7639	−0.678395
$355$	0	0
$356$	2.03444	0.107825
$357$	32.1147	1.69969
$358$	−25.1605	−1.32977
$359$	7.88854	0.416341	0.208171	−	0.978093i	$-0.433249\pi$
$359$	7.88854	0.416341	0.208171	+	0.978093i	$0.433249\pi$
$360$	0	0
$361$	33.3607	1.75583
$362$	−0.119757	−0.00629431
$363$	15.0427	0.789538
$364$	−2.18034	−0.114281
$365$	0	0
$366$	14.5279	0.759384
$367$	13.0875	0.683164	0.341582	−	0.939852i	$-0.389037\pi$
$367$	13.0875	0.683164	0.341582	+	0.939852i	$0.389037\pi$
$368$	−2.85003	−0.148568
$369$	−9.85410	−0.512984
$370$	0	0
$371$	29.8885	1.55174
$372$	1.01460	0.0526047
$373$	31.4876	1.63037	0.815183	−	0.579203i	$-0.196636\pi$
$373$	31.4876	1.63037	0.815183	+	0.579203i	$0.196636\pi$
$374$	11.4164	0.590328
$375$	0	0
$376$	1.50658	0.0776958
$377$	2.26872	0.116845
$378$	−13.7146	−0.705403
$379$	28.9443	1.48677	0.743384	−	0.668865i	$-0.233220\pi$
$379$	28.9443	1.48677	0.743384	+	0.668865i	$0.233220\pi$
$380$	0	0
$381$	40.2148	2.06027
$382$	−10.8646	−0.555879
$383$	1.52190	0.0777656	0.0388828	−	0.999244i	$-0.487620\pi$
$383$	1.52190	0.0777656	0.0388828	+	0.999244i	$0.487620\pi$
$384$	19.1459	0.977035
$385$	0	0
$386$	9.23607	0.470103
$387$	6.13335	0.311776
$388$	−2.65626	−0.134851
$389$	−23.6180	−1.19748	−0.598741	−	0.800943i	$-0.704332\pi$
$389$	−23.6180	−1.19748	−0.598741	+	0.800943i	$0.704332\pi$
$390$	0	0
$391$	−3.52786	−0.178412
$392$	15.1167	0.763511
$393$	30.4730	1.53716
$394$	31.2361	1.57365
$395$	0	0
$396$	−0.763932	−0.0383890
$397$	−31.7271	−1.59234	−0.796169	−	0.605074i	$-0.793143\pi$
$397$	−31.7271	−1.59234	−0.796169	+	0.605074i	$0.793143\pi$
$398$	21.4896	1.07718
$399$	−54.0689	−2.70683
$400$	0	0
$401$	−37.2705	−1.86120	−0.930600	−	0.366037i	$-0.880714\pi$
$401$	−37.2705	−1.86120	−0.930600	+	0.366037i	$0.880714\pi$
$402$	−12.2667	−0.611808
$403$	5.31252	0.264636
$404$	2.61803	0.130252
$405$	0	0
$406$	−3.94427	−0.195751
$407$	3.28332	0.162748
$408$	27.4292	1.35795
$409$	−13.7426	−0.679530	−0.339765	−	0.940510i	$-0.610348\pi$
$409$	−13.7426	−0.679530	−0.339765	+	0.940510i	$0.610348\pi$
$410$	0	0
$411$	−32.0689	−1.58184
$412$	3.04381	0.149958
$413$	−15.5500	−0.765167
$414$	−1.76393	−0.0866925
$415$	0	0
$416$	−3.52786	−0.172968
$417$	−17.8187	−0.872588
$418$	−19.2209	−0.940125
$419$	3.41641	0.166902	0.0834512	−	0.996512i	$-0.473406\pi$
$419$	3.41641	0.166902	0.0834512	+	0.996512i	$0.473406\pi$
$420$	0	0
$421$	10.0902	0.491765	0.245882	−	0.969300i	$-0.420922\pi$
$421$	10.0902	0.491765	0.245882	+	0.969300i	$0.420922\pi$
$422$	−7.72927	−0.376255
$423$	0.820830	0.0399101
$424$	25.5279	1.23974
$425$	0	0
$426$	23.3475	1.13119
$427$	17.6990	0.856514
$428$	−2.38848	−0.115451
$429$	−11.4164	−0.551189
$430$	0	0
$431$	−14.1803	−0.683043	−0.341521	−	0.939874i	$-0.610942\pi$
$431$	−14.1803	−0.683043	−0.341521	+	0.939874i	$0.610942\pi$
$432$	−10.3115	−0.496113
$433$	−14.2959	−0.687018	−0.343509	−	0.939149i	$-0.611616\pi$
$433$	−14.2959	−0.687018	−0.343509	+	0.939149i	$0.611616\pi$
$434$	−9.23607	−0.443345
$435$	0	0
$436$	2.96556	0.142024
$437$	5.93958	0.284129
$438$	−47.2771	−2.25899
$439$	10.6525	0.508415	0.254207	−	0.967150i	$-0.418185\pi$
$439$	10.6525	0.508415	0.254207	+	0.967150i	$0.418185\pi$
$440$	0	0
$441$	8.23607	0.392194
$442$	15.1625	0.721206
$443$	−24.3396	−1.15641	−0.578206	−	0.815891i	$-0.696247\pi$
$443$	−24.3396	−1.15641	−0.578206	+	0.815891i	$0.696247\pi$
$444$	0.832816	0.0395237
$445$	0	0
$446$	−9.90983	−0.469244
$447$	−41.4116	−1.95870
$448$	30.2792	1.43056
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	0	0
$451$	−12.1803	−0.573550
$452$	−0.627058	−0.0294943
$453$	−39.0688	−1.83561
$454$	16.0344	0.752534
$455$	0	0
$456$	−46.1803	−2.16259
$457$	−13.9084	−0.650606	−0.325303	−	0.945610i	$-0.605466\pi$
$457$	−13.9084	−0.650606	−0.325303	+	0.945610i	$0.605466\pi$
$458$	26.9959	1.26144
$459$	−12.7639	−0.595769
$460$	0	0
$461$	21.2705	0.990666	0.495333	−	0.868703i	$-0.335046\pi$
$461$	21.2705	0.990666	0.495333	+	0.868703i	$0.335046\pi$
$462$	19.8480	0.923410
$463$	−22.9375	−1.06600	−0.532998	−	0.846116i	$-0.678935\pi$
$463$	−22.9375	−1.06600	−0.532998	+	0.846116i	$0.678935\pi$
$464$	−2.96556	−0.137673
$465$	0	0
$466$	1.34752	0.0624229
$467$	−21.6834	−1.00339	−0.501694	−	0.865045i	$-0.667290\pi$
$467$	−21.6834	−1.00339	−0.501694	+	0.865045i	$0.667290\pi$
$468$	−1.01460	−0.0469000
$469$	−14.9443	−0.690062
$470$	0	0
$471$	−16.2918	−0.750686
$472$	−13.2813	−0.611322
$473$	7.58124	0.348586
$474$	7.88854	0.362333
$475$	0	0
$476$	3.52786	0.161699
$477$	13.9084	0.636820
$478$	15.5500	0.711242
$479$	−29.5967	−1.35231	−0.676155	−	0.736759i	$-0.736355\pi$
$479$	−29.5967	−1.35231	−0.676155	+	0.736759i	$0.736355\pi$
$480$	0	0
$481$	4.36068	0.198830
$482$	1.44789	0.0659495
$483$	−6.13335	−0.279077
$484$	1.65248	0.0751125
$485$	0	0
$486$	−20.2361	−0.917927
$487$	25.6678	1.16312	0.581559	−	0.813504i	$-0.302443\pi$
$487$	25.6678	1.16312	0.581559	+	0.813504i	$0.302443\pi$
$488$	15.1167	0.684303
$489$	31.6525	1.43137
$490$	0	0
$491$	−11.8197	−0.533414	−0.266707	−	0.963778i	$-0.585936\pi$
$491$	−11.8197	−0.533414	−0.266707	+	0.963778i	$0.585936\pi$
$492$	−3.08955	−0.139288
$493$	−3.67086	−0.165327
$494$	−25.5279	−1.14855
$495$	0	0
$496$	−6.94427	−0.311807
$497$	28.4438	1.27588
$498$	−14.6094	−0.654665
$499$	16.1803	0.724331	0.362166	−	0.932114i	$-0.382037\pi$
$499$	16.1803	0.724331	0.362166	+	0.932114i	$0.382037\pi$
$500$	0	0
$501$	−13.8541	−0.618956
$502$	27.0417	1.20693
$503$	−8.78962	−0.391910	−0.195955	−	0.980613i	$-0.562781\pi$
$503$	−8.78962	−0.391910	−0.195955	+	0.980613i	$0.562781\pi$
$504$	16.7082	0.744243
$505$	0	0
$506$	−2.18034	−0.0969279
$507$	12.7740	0.567314
$508$	4.41768	0.196003
$509$	15.5279	0.688260	0.344130	−	0.938922i	$-0.388174\pi$
$509$	15.5279	0.688260	0.344130	+	0.938922i	$0.388174\pi$
$510$	0	0
$511$	−57.5967	−2.54793
$512$	25.2345	1.11522
$513$	21.4896	0.948790
$514$	18.4721	0.814771
$515$	0	0
$516$	1.92299	0.0846547
$517$	1.01460	0.0446221
$518$	−7.58124	−0.333101
$519$	−39.1246	−1.71738
$520$	0	0
$521$	23.9098	1.04751	0.523754	−	0.851869i	$-0.324531\pi$
$521$	23.9098	1.04751	0.523754	+	0.851869i	$0.324531\pi$
$522$	−1.83543	−0.0803347
$523$	15.6698	0.685192	0.342596	−	0.939483i	$-0.388694\pi$
$523$	15.6698	0.685192	0.342596	+	0.939483i	$0.388694\pi$
$524$	3.34752	0.146237
$525$	0	0
$526$	−0.159054	−0.00693507
$527$	−8.59584	−0.374441
$528$	14.9230	0.649439
$529$	−22.3262	−0.970706
$530$	0	0
$531$	−7.23607	−0.314019
$532$	−5.93958	−0.257514
$533$	−16.1771	−0.700707
$534$	−24.5967	−1.06441
$535$	0	0
$536$	−12.7639	−0.551318
$537$	−40.7105	−1.75679
$538$	−1.40215	−0.0604508
$539$	10.1803	0.438498
$540$	0	0
$541$	0.0901699	0.00387671	0.00193835	−	0.999998i	$-0.499383\pi$
$541$	0.0901699	0.00387671	0.00193835	+	0.999998i	$0.499383\pi$
$542$	10.6250	0.456385
$543$	−0.193772	−0.00831554
$544$	5.70820	0.244737
$545$	0	0
$546$	26.3607	1.12813
$547$	−14.3417	−0.613205	−0.306602	−	0.951838i	$-0.599192\pi$
$547$	−14.3417	−0.613205	−0.306602	+	0.951838i	$0.599192\pi$
$548$	−3.52284	−0.150488
$549$	8.23607	0.351507
$550$	0	0
$551$	6.18034	0.263291
$552$	−5.23851	−0.222966
$553$	9.61045	0.408678
$554$	21.4853	0.912823
$555$	0	0
$556$	−1.95743	−0.0830134
$557$	34.1439	1.44672	0.723361	−	0.690470i	$-0.242596\pi$
$557$	34.1439	1.44672	0.723361	+	0.690470i	$0.242596\pi$
$558$	−4.29792	−0.181946
$559$	10.0689	0.425868
$560$	0	0
$561$	18.4721	0.779894
$562$	−41.5313	−1.75189
$563$	37.4272	1.57737	0.788684	−	0.614799i	$-0.210763\pi$
$563$	37.4272	1.57737	0.788684	+	0.614799i	$0.210763\pi$
$564$	0.257354	0.0108366
$565$	0	0
$566$	1.34752	0.0566407
$567$	−39.0688	−1.64074
$568$	24.2939	1.01935
$569$	−23.2148	−0.973214	−0.486607	−	0.873621i	$-0.661766\pi$
$569$	−23.2148	−0.973214	−0.486607	+	0.873621i	$0.661766\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	−1.25412	−0.0524373
$573$	−17.5792	−0.734383
$574$	28.1246	1.17390
$575$	0	0
$576$	14.0902	0.587090
$577$	−21.2501	−0.884653	−0.442327	−	0.896854i	$-0.645847\pi$
$577$	−21.2501	−0.884653	−0.442327	+	0.896854i	$0.645847\pi$
$578$	−1.95519	−0.0813252
$579$	14.9443	0.621063
$580$	0	0
$581$	−17.7984	−0.738401
$582$	32.1147	1.33120
$583$	17.1917	0.712007
$584$	−49.1935	−2.03564
$585$	0	0
$586$	37.7771	1.56056
$587$	−11.6397	−0.480420	−0.240210	−	0.970721i	$-0.577216\pi$
$587$	−11.6397	−0.480420	−0.240210	+	0.970721i	$0.577216\pi$
$588$	2.58225	0.106490
$589$	14.4721	0.596314
$590$	0	0
$591$	50.5410	2.07898
$592$	−5.70007	−0.234271
$593$	36.0250	1.47937	0.739686	−	0.672953i	$-0.234974\pi$
$593$	36.0250	1.47937	0.739686	+	0.672953i	$0.234974\pi$
$594$	−7.88854	−0.323671
$595$	0	0
$596$	−4.54915	−0.186340
$597$	34.7709	1.42308
$598$	−2.89578	−0.118417
$599$	−38.5410	−1.57474	−0.787372	−	0.616479i	$-0.788559\pi$
$599$	−38.5410	−1.57474	−0.787372	+	0.616479i	$0.788559\pi$
$600$	0	0
$601$	6.27051	0.255779	0.127890	−	0.991788i	$-0.459180\pi$
$601$	6.27051	0.255779	0.127890	+	0.991788i	$0.459180\pi$
$602$	−17.5052	−0.713459
$603$	−6.95418	−0.283196
$604$	−4.29180	−0.174631
$605$	0	0
$606$	−31.6525	−1.28579
$607$	−35.3980	−1.43676	−0.718380	−	0.695651i	$-0.755116\pi$
$607$	−35.3980	−1.43676	−0.718380	+	0.695651i	$0.755116\pi$
$608$	−9.61045	−0.389755
$609$	−6.38197	−0.258610
$610$	0	0
$611$	1.34752	0.0545150
$612$	1.64166	0.0663602
$613$	−10.6250	−0.429142	−0.214571	−	0.976708i	$-0.568835\pi$
$613$	−10.6250	−0.429142	−0.214571	+	0.976708i	$0.568835\pi$
$614$	13.0213	0.525496
$615$	0	0
$616$	20.6525	0.832112
$617$	38.6813	1.55725	0.778625	−	0.627489i	$-0.215917\pi$
$617$	38.6813	1.55725	0.778625	+	0.627489i	$0.215917\pi$
$618$	−36.8001	−1.48032
$619$	39.5967	1.59153	0.795764	−	0.605607i	$-0.207070\pi$
$619$	39.5967	1.59153	0.795764	+	0.605607i	$0.207070\pi$
$620$	0	0
$621$	2.43769	0.0978213
$622$	23.9064	0.958558
$623$	−29.9657	−1.20055
$624$	19.8197	0.793421
$625$	0	0
$626$	−21.1672	−0.846011
$627$	−31.1001	−1.24202
$628$	−1.78969	−0.0714164
$629$	−7.05573	−0.281330
$630$	0	0
$631$	−10.3607	−0.412452	−0.206226	−	0.978504i	$-0.566118\pi$
$631$	−10.3607	−0.412452	−0.206226	+	0.978504i	$0.566118\pi$
$632$	8.20830	0.326509
$633$	−12.5062	−0.497078
$634$	23.3475	0.927249
$635$	0	0
$636$	4.36068	0.172912
$637$	13.5208	0.535715
$638$	−2.26872	−0.0898194
$639$	13.2361	0.523611
$640$	0	0
$641$	26.2705	1.03762	0.518811	−	0.854889i	$-0.326375\pi$
$641$	26.2705	1.03762	0.518811	+	0.854889i	$0.326375\pi$
$642$	28.8771	1.13969
$643$	2.22298	0.0876656	0.0438328	−	0.999039i	$-0.486043\pi$
$643$	2.22298	0.0876656	0.0438328	+	0.999039i	$0.486043\pi$
$644$	−0.673762	−0.0265499
$645$	0	0
$646$	41.3050	1.62512
$647$	19.4604	0.765068	0.382534	−	0.923942i	$-0.375052\pi$
$647$	19.4604	0.765068	0.382534	+	0.923942i	$0.375052\pi$
$648$	−33.3688	−1.31085
$649$	−8.94427	−0.351093
$650$	0	0
$651$	−14.9443	−0.585712
$652$	3.47709	0.136173
$653$	−26.1751	−1.02431	−0.512155	−	0.858893i	$-0.671153\pi$
$653$	−26.1751	−1.02431	−0.512155	+	0.858893i	$0.671153\pi$
$654$	−35.8541	−1.40201
$655$	0	0
$656$	21.1459	0.825609
$657$	−26.8021	−1.04565
$658$	−2.34273	−0.0913292
$659$	−10.6525	−0.414962	−0.207481	−	0.978239i	$-0.566526\pi$
$659$	−10.6525	−0.414962	−0.207481	+	0.978239i	$0.566526\pi$
$660$	0	0
$661$	−22.2705	−0.866222	−0.433111	−	0.901340i	$-0.642584\pi$
$661$	−22.2705	−0.866222	−0.433111	+	0.901340i	$0.642584\pi$
$662$	−7.72927	−0.300407
$663$	24.5334	0.952799
$664$	−15.2016	−0.589938
$665$	0	0
$666$	−3.52786	−0.136702
$667$	0.701073	0.0271456
$668$	−1.52190	−0.0588842
$669$	−16.0344	−0.619927
$670$	0	0
$671$	10.1803	0.393008
$672$	9.92398	0.382826
$673$	−16.5646	−0.638520	−0.319260	−	0.947667i	$-0.603434\pi$
$673$	−16.5646	−0.638520	−0.319260	+	0.947667i	$0.603434\pi$
$674$	−2.18034	−0.0839836
$675$	0	0
$676$	1.40325	0.0539712
$677$	5.31252	0.204177	0.102088	−	0.994775i	$-0.467448\pi$
$677$	5.31252	0.204177	0.102088	+	0.994775i	$0.467448\pi$
$678$	7.58124	0.291156
$679$	39.1246	1.50146
$680$	0	0
$681$	25.9443	0.994187
$682$	−5.31252	−0.203427
$683$	36.2928	1.38871	0.694353	−	0.719634i	$-0.255691\pi$
$683$	36.2928	1.38871	0.694353	+	0.719634i	$0.255691\pi$
$684$	−2.76393	−0.105682
$685$	0	0
$686$	8.81966	0.336736
$687$	43.6803	1.66651
$688$	−13.1616	−0.501779
$689$	22.8328	0.869861
$690$	0	0
$691$	−14.1803	−0.539446	−0.269723	−	0.962938i	$-0.586932\pi$
$691$	−14.1803	−0.539446	−0.269723	+	0.962938i	$0.586932\pi$
$692$	−4.29792	−0.163382
$693$	11.2521	0.427432
$694$	−38.0344	−1.44377
$695$	0	0
$696$	−5.45085	−0.206614
$697$	26.1751	0.991452
$698$	12.3125	0.466033
$699$	2.18034	0.0824680
$700$	0	0
$701$	22.0000	0.830929	0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000	0.830929	0.415464	+	0.909610i	$0.363619\pi$
$702$	−10.4770	−0.395430
$703$	11.8792	0.448031
$704$	17.4164	0.656406
$705$	0	0
$706$	−29.0557	−1.09353
$707$	−38.5615	−1.45026
$708$	−2.26872	−0.0852637
$709$	20.9787	0.787872	0.393936	−	0.919138i	$-0.371113\pi$
$709$	20.9787	0.787872	0.393936	+	0.919138i	$0.371113\pi$
$710$	0	0
$711$	4.47214	0.167718
$712$	−25.5938	−0.959167
$713$	1.64166	0.0614807
$714$	−42.6525	−1.59623
$715$	0	0
$716$	−4.47214	−0.167132
$717$	25.1605	0.939635
$718$	−10.4770	−0.390999
$719$	17.2361	0.642797	0.321398	−	0.946944i	$-0.395847\pi$
$719$	17.2361	0.642797	0.321398	+	0.946944i	$0.395847\pi$
$720$	0	0
$721$	−44.8328	−1.66966
$722$	−44.3074	−1.64895
$723$	2.34273	0.0871272
$724$	−0.0212862	−0.000791097 0
$725$	0	0
$726$	−19.9787	−0.741480
$727$	37.5469	1.39254	0.696269	−	0.717780i	$-0.254842\pi$
$727$	37.5469	1.39254	0.696269	+	0.717780i	$0.254842\pi$
$728$	27.4292	1.01659
$729$	0.965558	0.0357614
$730$	0	0
$731$	−16.2918	−0.602574
$732$	2.58225	0.0954426
$733$	−9.22290	−0.340656	−0.170328	−	0.985387i	$-0.554483\pi$
$733$	−9.22290	−0.340656	−0.170328	+	0.985387i	$0.554483\pi$
$734$	−17.3820	−0.641580
$735$	0	0
$736$	−1.09017	−0.0401842
$737$	−8.59584	−0.316632
$738$	13.0875	0.481759
$739$	28.2918	1.04073	0.520365	−	0.853944i	$-0.325796\pi$
$739$	28.2918	1.04073	0.520365	+	0.853944i	$0.325796\pi$
$740$	0	0
$741$	−41.3050	−1.51738
$742$	−39.6959	−1.45728
$743$	6.32713	0.232120	0.116060	−	0.993242i	$-0.462974\pi$
$743$	6.32713	0.232120	0.116060	+	0.993242i	$0.462974\pi$
$744$	−12.7639	−0.467948
$745$	0	0
$746$	−41.8197	−1.53113
$747$	−8.28232	−0.303034
$748$	2.02920	0.0741950
$749$	35.1803	1.28546
$750$	0	0
$751$	−14.1803	−0.517448	−0.258724	−	0.965951i	$-0.583302\pi$
$751$	−14.1803	−0.517448	−0.258724	+	0.965951i	$0.583302\pi$
$752$	−1.76142	−0.0642323
$753$	43.7543	1.59450
$754$	−3.01316	−0.109733
$755$	0	0
$756$	−2.43769	−0.0886581
$757$	−0.627058	−0.0227908	−0.0113954	−	0.999935i	$-0.503627\pi$
$757$	−0.627058	−0.0227908	−0.0113954	+	0.999935i	$0.503627\pi$
$758$	−38.4418	−1.39627
$759$	−3.52786	−0.128053
$760$	0	0
$761$	−37.2705	−1.35105	−0.675527	−	0.737335i	$-0.736084\pi$
$761$	−37.2705	−1.35105	−0.675527	+	0.737335i	$0.736084\pi$
$762$	−53.4105	−1.93486
$763$	−43.6803	−1.58133
$764$	−1.93112	−0.0698653
$765$	0	0
$766$	−2.02129	−0.0730320
$767$	−11.8792	−0.428932
$768$	11.9989	0.432974
$769$	−8.49342	−0.306281	−0.153140	−	0.988204i	$-0.548939\pi$
$769$	−8.49342	−0.306281	−0.153140	+	0.988204i	$0.548939\pi$
$770$	0	0
$771$	29.8885	1.07641
$772$	1.64166	0.0590846
$773$	−3.28332	−0.118093	−0.0590464	−	0.998255i	$-0.518806\pi$
$773$	−3.28332	−0.118093	−0.0590464	+	0.998255i	$0.518806\pi$
$774$	−8.14590	−0.292798
$775$	0	0
$776$	33.4164	1.19958
$777$	−12.2667	−0.440066
$778$	31.3678	1.12459
$779$	−44.0689	−1.57893
$780$	0	0
$781$	16.3607	0.585431
$782$	4.68547	0.167552
$783$	2.53650	0.0906473
$784$	−17.6738	−0.631206
$785$	0	0
$786$	−40.4721	−1.44359
$787$	47.1574	1.68098	0.840490	−	0.541828i	$-0.182267\pi$
$787$	47.1574	1.68098	0.840490	+	0.541828i	$0.182267\pi$
$788$	5.55204	0.197783
$789$	−0.257354	−0.00916205
$790$	0	0
$791$	9.23607	0.328397
$792$	9.61045	0.341492
$793$	13.5208	0.480139
$794$	42.1378	1.49541
$795$	0	0
$796$	3.81966	0.135384
$797$	−31.7271	−1.12383	−0.561916	−	0.827194i	$-0.689936\pi$
$797$	−31.7271	−1.12383	−0.561916	+	0.827194i	$0.689936\pi$
$798$	71.8106	2.54207
$799$	−2.18034	−0.0771349
$800$	0	0
$801$	−13.9443	−0.492697
$802$	49.5001	1.74791
$803$	−33.1293	−1.16911
$804$	−2.18034	−0.0768947
$805$	0	0
$806$	−7.05573	−0.248527
$807$	−2.26872	−0.0798627
$808$	−32.9355	−1.15867
$809$	54.7984	1.92661	0.963304	−	0.268412i	$-0.0864990\pi$
$809$	54.7984	1.92661	0.963304	+	0.268412i	$0.0864990\pi$
$810$	0	0
$811$	22.0000	0.772524	0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000	0.772524	0.386262	+	0.922389i	$0.373766\pi$
$812$	−0.701073	−0.0246028
$813$	17.1917	0.602939
$814$	−4.36068	−0.152842
$815$	0	0
$816$	−32.0689	−1.12264
$817$	27.4292	0.959626
$818$	18.2520	0.638167
$819$	14.9443	0.522195
$820$	0	0
$821$	−27.2705	−0.951747	−0.475874	−	0.879514i	$-0.657868\pi$
$821$	−27.2705	−0.951747	−0.475874	+	0.879514i	$0.657868\pi$
$822$	42.5917	1.48556
$823$	18.2063	0.634631	0.317316	−	0.948320i	$-0.397219\pi$
$823$	18.2063	0.634631	0.317316	+	0.948320i	$0.397219\pi$
$824$	−38.2918	−1.33396
$825$	0	0
$826$	20.6525	0.718592
$827$	26.8021	0.932002	0.466001	−	0.884784i	$-0.345694\pi$
$827$	26.8021	0.932002	0.466001	+	0.884784i	$0.345694\pi$
$828$	−0.313529	−0.0108959
$829$	10.8541	0.376979	0.188489	−	0.982075i	$-0.439641\pi$
$829$	10.8541	0.376979	0.188489	+	0.982075i	$0.439641\pi$
$830$	0	0
$831$	34.7639	1.20595
$832$	23.1313	0.801933
$833$	−21.8772	−0.757998
$834$	23.6656	0.819474
$835$	0	0
$836$	−3.41641	−0.118159
$837$	5.93958	0.205302
$838$	−4.53744	−0.156743
$839$	−31.7082	−1.09469	−0.547344	−	0.836907i	$-0.684361\pi$
$839$	−31.7082	−1.09469	−0.547344	+	0.836907i	$0.684361\pi$
$840$	0	0
$841$	−28.2705	−0.974845
$842$	−13.4011	−0.461831
$843$	−67.1991	−2.31446
$844$	−1.37384	−0.0472894
$845$	0	0
$846$	−1.09017	−0.0374808
$847$	−24.3396	−0.836320
$848$	−29.8459	−1.02491
$849$	2.18034	0.0748291
$850$	0	0
$851$	1.34752	0.0461925
$852$	4.14989	0.142173
$853$	−34.3834	−1.17726	−0.588632	−	0.808401i	$-0.700333\pi$
$853$	−34.3834	−1.17726	−0.588632	+	0.808401i	$0.700333\pi$
$854$	−23.5066	−0.804379
$855$	0	0
$856$	30.0476	1.02701
$857$	−0.627058	−0.0214199	−0.0107100	−	0.999943i	$-0.503409\pi$
$857$	−0.627058	−0.0214199	−0.0107100	+	0.999943i	$0.503409\pi$
$858$	15.1625	0.517639
$859$	−26.8328	−0.915524	−0.457762	−	0.889075i	$-0.651349\pi$
$859$	−26.8328	−0.915524	−0.457762	+	0.889075i	$0.651349\pi$
$860$	0	0
$861$	45.5066	1.55086
$862$	18.8333	0.641466
$863$	−49.5001	−1.68500	−0.842502	−	0.538693i	$-0.818918\pi$
$863$	−49.5001	−1.68500	−0.842502	+	0.538693i	$0.818918\pi$
$864$	−3.94427	−0.134187
$865$	0	0
$866$	18.9868	0.645199
$867$	−3.16356	−0.107440
$868$	−1.64166	−0.0557216
$869$	5.52786	0.187520
$870$	0	0
$871$	−11.4164	−0.386830
$872$	−37.3074	−1.26339
$873$	18.2063	0.616190
$874$	−7.88854	−0.266834
$875$	0	0
$876$	−8.40325	−0.283920
$877$	−29.4584	−0.994739	−0.497370	−	0.867539i	$-0.665701\pi$
$877$	−29.4584	−0.994739	−0.497370	+	0.867539i	$0.665701\pi$
$878$	−14.1479	−0.477468
$879$	61.1246	2.06168
$880$	0	0
$881$	−13.4508	−0.453171	−0.226585	−	0.973991i	$-0.572756\pi$
$881$	−13.4508	−0.453171	−0.226585	+	0.973991i	$0.572756\pi$
$882$	−10.9386	−0.368321
$883$	37.8605	1.27411	0.637053	−	0.770820i	$-0.280153\pi$
$883$	37.8605	1.27411	0.637053	+	0.770820i	$0.280153\pi$
$884$	2.69505	0.0906443
$885$	0	0
$886$	32.3262	1.08602
$887$	−10.6708	−0.358290	−0.179145	−	0.983823i	$-0.557333\pi$
$887$	−10.6708	−0.358290	−0.179145	+	0.983823i	$0.557333\pi$
$888$	−10.4770	−0.351586
$889$	−65.0689	−2.18234
$890$	0	0
$891$	−22.4721	−0.752845
$892$	−1.76142	−0.0589766
$893$	3.67086	0.122841
$894$	55.0000	1.83948
$895$	0	0
$896$	−30.9787	−1.03493
$897$	−4.68547	−0.156443
$898$	−13.2813	−0.443203
$899$	1.70820	0.0569718
$900$	0	0
$901$	−36.9443	−1.23079
$902$	16.1771	0.538638
$903$	−28.3240	−0.942565
$904$	7.88854	0.262369
$905$	0	0
$906$	51.8885	1.72388
$907$	11.6854	0.388007	0.194004	−	0.981001i	$-0.437853\pi$
$907$	11.6854	0.388007	0.194004	+	0.981001i	$0.437853\pi$
$908$	2.85003	0.0945817
$909$	−17.9443	−0.595174
$910$	0	0
$911$	46.7214	1.54795	0.773974	−	0.633218i	$-0.218266\pi$
$911$	46.7214	1.54795	0.773974	+	0.633218i	$0.218266\pi$
$912$	53.9918	1.78785
$913$	−10.2375	−0.338812
$914$	18.4721	0.611004
$915$	0	0
$916$	4.79837	0.158543
$917$	−49.3063	−1.62824
$918$	16.9522	0.559505
$919$	−12.7639	−0.421043	−0.210522	−	0.977589i	$-0.567516\pi$
$919$	−12.7639	−0.421043	−0.210522	+	0.977589i	$0.567516\pi$
$920$	0	0
$921$	21.0689	0.694243
$922$	−28.2500	−0.930365
$923$	21.7291	0.715223
$924$	3.52786	0.116058
$925$	0	0
$926$	30.4640	1.00111
$927$	−20.8626	−0.685216
$928$	−1.13436	−0.0372372
$929$	−17.9656	−0.589431	−0.294715	−	0.955585i	$-0.595225\pi$
$929$	−17.9656	−0.589431	−0.294715	+	0.955585i	$0.595225\pi$
$930$	0	0
$931$	36.8328	1.20715
$932$	0.239515	0.00784557
$933$	38.6813	1.26637
$934$	28.7984	0.942312
$935$	0	0
$936$	12.7639	0.417202
$937$	−6.56664	−0.214523	−0.107261	−	0.994231i	$-0.534208\pi$
$937$	−6.56664	−0.214523	−0.107261	+	0.994231i	$0.534208\pi$
$938$	19.8480	0.648059
$939$	−34.2492	−1.11768
$940$	0	0
$941$	54.3607	1.77211	0.886054	−	0.463583i	$-0.153436\pi$
$941$	54.3607	1.77211	0.886054	+	0.463583i	$0.153436\pi$
$942$	21.6376	0.704992
$943$	−4.99899	−0.162790
$944$	15.5279	0.505389
$945$	0	0
$946$	−10.0689	−0.327368
$947$	8.71560	0.283219	0.141610	−	0.989923i	$-0.454772\pi$
$947$	8.71560	0.283219	0.141610	+	0.989923i	$0.454772\pi$
$948$	1.40215	0.0455396
$949$	−44.0000	−1.42830
$950$	0	0
$951$	37.7771	1.22501
$952$	−44.3814	−1.43841
$953$	8.59584	0.278447	0.139223	−	0.990261i	$-0.455539\pi$
$953$	8.59584	0.278447	0.139223	+	0.990261i	$0.455539\pi$
$954$	−18.4721	−0.598057
$955$	0	0
$956$	2.76393	0.0893920
$957$	−3.67086	−0.118662
$958$	39.3084	1.27000
$959$	51.8885	1.67557
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−5.79155	−0.186727
$963$	16.3709	0.527544
$964$	0.257354	0.00828882
$965$	0	0
$966$	8.14590	0.262090
$967$	6.44688	0.207318	0.103659	−	0.994613i	$-0.466945\pi$
$967$	6.44688	0.207318	0.103659	+	0.994613i	$0.466945\pi$
$968$	−20.7885	−0.668169
$969$	66.8328	2.14698
$970$	0	0
$971$	−1.81966	−0.0583957	−0.0291978	−	0.999574i	$-0.509295\pi$
$971$	−1.81966	−0.0583957	−0.0291978	+	0.999574i	$0.509295\pi$
$972$	−3.59685	−0.115369
$973$	28.8313	0.924290
$974$	−34.0902	−1.09232
$975$	0	0
$976$	−17.6738	−0.565723
$977$	−16.1771	−0.517551	−0.258775	−	0.965938i	$-0.583319\pi$
$977$	−16.1771	−0.517551	−0.258775	+	0.965938i	$0.583319\pi$
$978$	−42.0386	−1.34425
$979$	−17.2361	−0.550867
$980$	0	0
$981$	−20.3262	−0.648967
$982$	15.6981	0.500945
$983$	41.9646	1.33846	0.669232	−	0.743054i	$-0.266623\pi$
$983$	41.9646	1.33846	0.669232	+	0.743054i	$0.266623\pi$
$984$	38.8673	1.23904
$985$	0	0
$986$	4.87539	0.155264
$987$	−3.79062	−0.120657
$988$	−4.53744	−0.144355
$989$	3.11146	0.0989386
$990$	0	0
$991$	−0.360680	−0.0114574	−0.00572869	−	0.999984i	$-0.501824\pi$
$991$	−0.360680	−0.0114574	−0.00572869	+	0.999984i	$0.501824\pi$
$992$	−2.65626	−0.0843364
$993$	−12.5062	−0.396873
$994$	−37.7771	−1.19822
$995$	0	0
$996$	−2.59675	−0.0822811
$997$	−23.5188	−0.744848	−0.372424	−	0.928063i	$-0.621473\pi$
$997$	−23.5188	−0.744848	−0.372424	+	0.928063i	$0.621473\pi$
$998$	−21.4896	−0.680242
$999$	4.87539	0.154250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.a.c.1.2	✓	4
3.2	odd	2		1125.2.a.k.1.3		4
4.3	odd	2		2000.2.a.o.1.4		4
5.2	odd	4		125.2.b.a.124.2		4
5.3	odd	4		125.2.b.a.124.3		4
5.4	even	2	inner	125.2.a.c.1.3	yes	4
7.6	odd	2		6125.2.a.o.1.2		4
8.3	odd	2		8000.2.a.bk.1.1		4
8.5	even	2		8000.2.a.bj.1.4		4
15.2	even	4		1125.2.b.a.874.3		4
15.8	even	4		1125.2.b.a.874.2		4
15.14	odd	2		1125.2.a.k.1.2		4
20.3	even	4		2000.2.c.c.1249.4		4
20.7	even	4		2000.2.c.c.1249.1		4
20.19	odd	2		2000.2.a.o.1.1		4
25.2	odd	20		625.2.e.b.124.1		8
25.3	odd	20		625.2.e.h.249.2		8
25.4	even	10		625.2.d.k.376.1		8
25.6	even	5		625.2.d.k.251.2		8
25.8	odd	20		625.2.e.h.374.1		8
25.9	even	10		625.2.d.l.126.2		8
25.11	even	5		625.2.d.l.501.1		8
25.12	odd	20		625.2.e.b.499.2		8
25.13	odd	20		625.2.e.b.499.1		8
25.14	even	10		625.2.d.l.501.2		8
25.16	even	5		625.2.d.l.126.1		8
25.17	odd	20		625.2.e.h.374.2		8
25.19	even	10		625.2.d.k.251.1		8
25.21	even	5		625.2.d.k.376.2		8
25.22	odd	20		625.2.e.h.249.1		8
25.23	odd	20		625.2.e.b.124.2		8
35.34	odd	2		6125.2.a.o.1.3		4
40.19	odd	2		8000.2.a.bk.1.4		4
40.29	even	2		8000.2.a.bj.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.a.c.1.2	✓	4	1.1	even	1	trivial
125.2.a.c.1.3	yes	4	5.4	even	2	inner
125.2.b.a.124.2		4	5.2	odd	4
125.2.b.a.124.3		4	5.3	odd	4
625.2.d.k.251.1		8	25.19	even	10
625.2.d.k.251.2		8	25.6	even	5
625.2.d.k.376.1		8	25.4	even	10
625.2.d.k.376.2		8	25.21	even	5
625.2.d.l.126.1		8	25.16	even	5
625.2.d.l.126.2		8	25.9	even	10
625.2.d.l.501.1		8	25.11	even	5
625.2.d.l.501.2		8	25.14	even	10
625.2.e.b.124.1		8	25.2	odd	20
625.2.e.b.124.2		8	25.23	odd	20
625.2.e.b.499.1		8	25.13	odd	20
625.2.e.b.499.2		8	25.12	odd	20
625.2.e.h.249.1		8	25.22	odd	20
625.2.e.h.249.2		8	25.3	odd	20
625.2.e.h.374.1		8	25.8	odd	20
625.2.e.h.374.2		8	25.17	odd	20
1125.2.a.k.1.2		4	15.14	odd	2
1125.2.a.k.1.3		4	3.2	odd	2
1125.2.b.a.874.2		4	15.8	even	4
1125.2.b.a.874.3		4	15.2	even	4
2000.2.a.o.1.1		4	20.19	odd	2
2000.2.a.o.1.4		4	4.3	odd	2
2000.2.c.c.1249.1		4	20.7	even	4
2000.2.c.c.1249.4		4	20.3	even	4
6125.2.a.o.1.2		4	7.6	odd	2
6125.2.a.o.1.3		4	35.34	odd	2
8000.2.a.bj.1.1		4	40.29	even	2
8000.2.a.bj.1.4		4	8.5	even	2
8000.2.a.bk.1.1		4	8.3	odd	2
8000.2.a.bk.1.4		4	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.a (trivial)

\(f(q)\)	\(=\)	\(q-1.32813 q^{2} -2.14896 q^{3} -0.236068 q^{4} +2.85410 q^{6} +3.47709 q^{7} +2.96979 q^{8} +1.61803 q^{9} +O(q^{10})\)	\(q-1.32813 q^{2} -2.14896 q^{3} -0.236068 q^{4} +2.85410 q^{6} +3.47709 q^{7} +2.96979 q^{8} +1.61803 q^{9} +2.00000 q^{11} +0.507301 q^{12} +2.65626 q^{13} -4.61803 q^{14} -3.47214 q^{16} -4.29792 q^{17} -2.14896 q^{18} +7.23607 q^{19} -7.47214 q^{21} -2.65626 q^{22} +0.820830 q^{23} -6.38197 q^{24} -3.52786 q^{26} +2.96979 q^{27} -0.820830 q^{28} +0.854102 q^{29} +2.00000 q^{31} -1.32813 q^{32} -4.29792 q^{33} +5.70820 q^{34} -0.381966 q^{36} +1.64166 q^{37} -9.61045 q^{38} -5.70820 q^{39} -6.09017 q^{41} +9.92398 q^{42} +3.79062 q^{43} -0.472136 q^{44} -1.09017 q^{46} +0.507301 q^{47} +7.46149 q^{48} +5.09017 q^{49} +9.23607 q^{51} -0.627058 q^{52} +8.59584 q^{53} -3.94427 q^{54} +10.3262 q^{56} -15.5500 q^{57} -1.13436 q^{58} -4.47214 q^{59} +5.09017 q^{61} -2.65626 q^{62} +5.62605 q^{63} +8.70820 q^{64} +5.70820 q^{66} -4.29792 q^{67} +1.01460 q^{68} -1.76393 q^{69} +8.18034 q^{71} +4.80522 q^{72} -16.5646 q^{73} -2.18034 q^{74} -1.70820 q^{76} +6.95418 q^{77} +7.58124 q^{78} +2.76393 q^{79} -11.2361 q^{81} +8.08854 q^{82} -5.11875 q^{83} +1.76393 q^{84} -5.03444 q^{86} -1.83543 q^{87} +5.93958 q^{88} -8.61803 q^{89} +9.23607 q^{91} -0.193772 q^{92} -4.29792 q^{93} -0.673762 q^{94} +2.85410 q^{96} +11.2521 q^{97} -6.76041 q^{98} +3.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 - 2 * q^6 + 2 * q^9	\( 4 q + 8 q^{4} - 2 q^{6} + 2 q^{9} + 8 q^{11} - 14 q^{14} + 4 q^{16} + 20 q^{19} - 12 q^{21} - 30 q^{24} - 32 q^{26} - 10 q^{29} + 8 q^{31} - 4 q^{34} - 6 q^{36} + 4 q^{39} - 2 q^{41} + 16 q^{44} + 18 q^{46} - 2 q^{49} + 28 q^{51} + 20 q^{54} + 10 q^{56} - 2 q^{61} + 8 q^{64} - 4 q^{66} - 16 q^{69} - 12 q^{71} + 36 q^{74} + 20 q^{76} + 20 q^{79} - 36 q^{81} + 16 q^{84} + 38 q^{86} - 30 q^{89} + 28 q^{91} - 34 q^{94} - 2 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 - 2 * q^6 + 2 * q^9 + 8 * q^11 - 14 * q^14 + 4 * q^16 + 20 * q^19 - 12 * q^21 - 30 * q^24 - 32 * q^26 - 10 * q^29 + 8 * q^31 - 4 * q^34 - 6 * q^36 + 4 * q^39 - 2 * q^41 + 16 * q^44 + 18 * q^46 - 2 * q^49 + 28 * q^51 + 20 * q^54 + 10 * q^56 - 2 * q^61 + 8 * q^64 - 4 * q^66 - 16 * q^69 - 12 * q^71 + 36 * q^74 + 20 * q^76 + 20 * q^79 - 36 * q^81 + 16 * q^84 + 38 * q^86 - 30 * q^89 + 28 * q^91 - 34 * q^94 - 2 * q^96 + 4 * q^99

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