LMFDB - Embedded newform 5929.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 847)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.381966 q^{2} +1.61803 q^{3} -1.85410 q^{4} -1.00000 q^{5} -0.618034 q^{6} +1.47214 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-0.381966 q^{2} +1.61803 q^{3} -1.85410 q^{4} -1.00000 q^{5} -0.618034 q^{6} +1.47214 q^{8} -0.381966 q^{9} +0.381966 q^{10} -3.00000 q^{12} +1.23607 q^{13} -1.61803 q^{15} +3.14590 q^{16} -3.09017 q^{17} +0.145898 q^{18} +1.76393 q^{19} +1.85410 q^{20} +5.09017 q^{23} +2.38197 q^{24} -4.00000 q^{25} -0.472136 q^{26} -5.47214 q^{27} -4.61803 q^{29} +0.618034 q^{30} +4.23607 q^{31} -4.14590 q^{32} +1.18034 q^{34} +0.708204 q^{36} +6.47214 q^{37} -0.673762 q^{38} +2.00000 q^{39} -1.47214 q^{40} +11.1803 q^{41} -12.5623 q^{43} +0.381966 q^{45} -1.94427 q^{46} +6.61803 q^{47} +5.09017 q^{48} +1.52786 q^{50} -5.00000 q^{51} -2.29180 q^{52} -2.38197 q^{53} +2.09017 q^{54} +2.85410 q^{57} +1.76393 q^{58} -11.0902 q^{59} +3.00000 q^{60} +7.61803 q^{61} -1.61803 q^{62} -4.70820 q^{64} -1.23607 q^{65} -8.32624 q^{67} +5.72949 q^{68} +8.23607 q^{69} -16.0902 q^{71} -0.562306 q^{72} +14.2361 q^{73} -2.47214 q^{74} -6.47214 q^{75} -3.27051 q^{76} -0.763932 q^{78} +6.38197 q^{79} -3.14590 q^{80} -7.70820 q^{81} -4.27051 q^{82} -2.70820 q^{83} +3.09017 q^{85} +4.79837 q^{86} -7.47214 q^{87} -6.85410 q^{89} -0.145898 q^{90} -9.43769 q^{92} +6.85410 q^{93} -2.52786 q^{94} -1.76393 q^{95} -6.70820 q^{96} -7.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} + q^{6} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 + q^6 - 6 * q^8 - 3 * q^9	$ 2 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} + q^{6} - 6 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{12} - 2 q^{13} - q^{15} + 13 q^{16} + 5 q^{17} + 7 q^{18} + 8 q^{19} - 3 q^{20} - q^{23} + 7 q^{24} - 8 q^{25} + 8 q^{26} - 2 q^{27} - 7 q^{29} - q^{30} + 4 q^{31} - 15 q^{32} - 20 q^{34} - 12 q^{36} + 4 q^{37} - 17 q^{38} + 4 q^{39} + 6 q^{40} - 5 q^{43} + 3 q^{45} + 14 q^{46} + 11 q^{47} - q^{48} + 12 q^{50} - 10 q^{51} - 18 q^{52} - 7 q^{53} - 7 q^{54} - q^{57} + 8 q^{58} - 11 q^{59} + 6 q^{60} + 13 q^{61} - q^{62} + 4 q^{64} + 2 q^{65} - q^{67} + 45 q^{68} + 12 q^{69} - 21 q^{71} + 19 q^{72} + 24 q^{73} + 4 q^{74} - 4 q^{75} + 27 q^{76} - 6 q^{78} + 15 q^{79} - 13 q^{80} - 2 q^{81} + 25 q^{82} + 8 q^{83} - 5 q^{85} - 15 q^{86} - 6 q^{87} - 7 q^{89} - 7 q^{90} - 39 q^{92} + 7 q^{93} - 14 q^{94} - 8 q^{95} - 14 q^{97}+O(q^{100}) $ 2 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 + q^6 - 6 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^12 - 2 * q^13 - q^15 + 13 * q^16 + 5 * q^17 + 7 * q^18 + 8 * q^19 - 3 * q^20 - q^23 + 7 * q^24 - 8 * q^25 + 8 * q^26 - 2 * q^27 - 7 * q^29 - q^30 + 4 * q^31 - 15 * q^32 - 20 * q^34 - 12 * q^36 + 4 * q^37 - 17 * q^38 + 4 * q^39 + 6 * q^40 - 5 * q^43 + 3 * q^45 + 14 * q^46 + 11 * q^47 - q^48 + 12 * q^50 - 10 * q^51 - 18 * q^52 - 7 * q^53 - 7 * q^54 - q^57 + 8 * q^58 - 11 * q^59 + 6 * q^60 + 13 * q^61 - q^62 + 4 * q^64 + 2 * q^65 - q^67 + 45 * q^68 + 12 * q^69 - 21 * q^71 + 19 * q^72 + 24 * q^73 + 4 * q^74 - 4 * q^75 + 27 * q^76 - 6 * q^78 + 15 * q^79 - 13 * q^80 - 2 * q^81 + 25 * q^82 + 8 * q^83 - 5 * q^85 - 15 * q^86 - 6 * q^87 - 7 * q^89 - 7 * q^90 - 39 * q^92 + 7 * q^93 - 14 * q^94 - 8 * q^95 - 14 * q^97

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 $

$2$	−0.381966	−0.270091	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966	−0.270091	−0.135045	+	0.990839i	$0.543118\pi$
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	−1.85410	−0.927051
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−0.618034	−0.252311
$7$	0	0
$7$	0	0
$8$	1.47214	0.520479
$9$	−0.381966	−0.127322
$10$	0.381966	0.120788
$11$	0	0
$11$	0	0
$12$	−3.00000	−0.866025
$13$	1.23607	0.342824	0.171412	−	0.985199i	$-0.445167\pi$
$13$	1.23607	0.342824	0.171412	+	0.985199i	$0.445167\pi$
$14$	0	0
$15$	−1.61803	−0.417775
$16$	3.14590	0.786475
$17$	−3.09017	−0.749476	−0.374738	−	0.927131i	$-0.622267\pi$
$17$	−3.09017	−0.749476	−0.374738	+	0.927131i	$0.622267\pi$
$18$	0.145898	0.0343885
$19$	1.76393	0.404674	0.202337	−	0.979316i	$-0.435146\pi$
$19$	1.76393	0.404674	0.202337	+	0.979316i	$0.435146\pi$
$20$	1.85410	0.414590
$21$	0	0
$22$	0	0
$23$	5.09017	1.06137	0.530687	−	0.847568i	$-0.321934\pi$
$23$	5.09017	1.06137	0.530687	+	0.847568i	$0.321934\pi$
$24$	2.38197	0.486217
$25$	−4.00000	−0.800000
$26$	−0.472136	−0.0925935
$27$	−5.47214	−1.05311
$28$	0	0
$29$	−4.61803	−0.857547	−0.428774	−	0.903412i	$-0.641054\pi$
$29$	−4.61803	−0.857547	−0.428774	+	0.903412i	$0.641054\pi$
$30$	0.618034	0.112837
$31$	4.23607	0.760820	0.380410	−	0.924818i	$-0.375783\pi$
$31$	4.23607	0.760820	0.380410	+	0.924818i	$0.375783\pi$
$32$	−4.14590	−0.732898
$33$	0	0
$34$	1.18034	0.202427
$35$	0	0
$36$	0.708204	0.118034
$37$	6.47214	1.06401	0.532006	−	0.846740i	$-0.321438\pi$
$37$	6.47214	1.06401	0.532006	+	0.846740i	$0.321438\pi$
$38$	−0.673762	−0.109299
$39$	2.00000	0.320256
$40$	−1.47214	−0.232765
$41$	11.1803	1.74608	0.873038	−	0.487652i	$-0.162147\pi$
$41$	11.1803	1.74608	0.873038	+	0.487652i	$0.162147\pi$
$42$	0	0
$43$	−12.5623	−1.91573	−0.957867	−	0.287213i	$-0.907271\pi$
$43$	−12.5623	−1.91573	−0.957867	+	0.287213i	$0.907271\pi$
$44$	0	0
$45$	0.381966	0.0569401
$46$	−1.94427	−0.286667
$47$	6.61803	0.965339	0.482670	−	0.875802i	$-0.339667\pi$
$47$	6.61803	0.965339	0.482670	+	0.875802i	$0.339667\pi$
$48$	5.09017	0.734703
$49$	0	0
$50$	1.52786	0.216073
$51$	−5.00000	−0.700140
$52$	−2.29180	−0.317815
$53$	−2.38197	−0.327188	−0.163594	−	0.986528i	$-0.552309\pi$
$53$	−2.38197	−0.327188	−0.163594	+	0.986528i	$0.552309\pi$
$54$	2.09017	0.284436
$55$	0	0
$56$	0	0
$57$	2.85410	0.378035
$58$	1.76393	0.231616
$59$	−11.0902	−1.44382	−0.721909	−	0.691988i	$-0.756735\pi$
$59$	−11.0902	−1.44382	−0.721909	+	0.691988i	$0.756735\pi$
$60$	3.00000	0.387298
$61$	7.61803	0.975389	0.487695	−	0.873014i	$-0.337838\pi$
$61$	7.61803	0.975389	0.487695	+	0.873014i	$0.337838\pi$
$62$	−1.61803	−0.205491
$63$	0	0
$64$	−4.70820	−0.588525
$65$	−1.23607	−0.153315
$66$	0	0
$67$	−8.32624	−1.01721	−0.508606	−	0.860999i	$-0.669839\pi$
$67$	−8.32624	−1.01721	−0.508606	+	0.860999i	$0.669839\pi$
$68$	5.72949	0.694803
$69$	8.23607	0.991506
$70$	0	0
$71$	−16.0902	−1.90955	−0.954776	−	0.297326i	$-0.903905\pi$
$71$	−16.0902	−1.90955	−0.954776	+	0.297326i	$0.903905\pi$
$72$	−0.562306	−0.0662684
$73$	14.2361	1.66621	0.833103	−	0.553118i	$-0.186562\pi$
$73$	14.2361	1.66621	0.833103	+	0.553118i	$0.186562\pi$
$74$	−2.47214	−0.287380
$75$	−6.47214	−0.747338
$76$	−3.27051	−0.375153
$77$	0	0
$78$	−0.763932	−0.0864983
$79$	6.38197	0.718027	0.359014	−	0.933332i	$-0.383113\pi$
$79$	6.38197	0.718027	0.359014	+	0.933332i	$0.383113\pi$
$80$	−3.14590	−0.351722
$81$	−7.70820	−0.856467
$82$	−4.27051	−0.471599
$83$	−2.70820	−0.297264	−0.148632	−	0.988893i	$-0.547487\pi$
$83$	−2.70820	−0.297264	−0.148632	+	0.988893i	$0.547487\pi$
$84$	0	0
$85$	3.09017	0.335176
$86$	4.79837	0.517422
$87$	−7.47214	−0.801097
$88$	0	0
$89$	−6.85410	−0.726533	−0.363267	−	0.931685i	$-0.618339\pi$
$89$	−6.85410	−0.726533	−0.363267	+	0.931685i	$0.618339\pi$
$90$	−0.145898	−0.0153790
$91$	0	0
$92$	−9.43769	−0.983948
$93$	6.85410	0.710737
$94$	−2.52786	−0.260729
$95$	−1.76393	−0.180976
$96$	−6.70820	−0.684653
$97$	−7.00000	−0.710742	−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000	−0.710742	−0.355371	+	0.934725i	$0.615646\pi$
$98$	0	0
$99$	0	0
$100$	7.41641	0.741641
$101$	14.7984	1.47249	0.736247	−	0.676713i	$-0.236596\pi$
$101$	14.7984	1.47249	0.736247	+	0.676713i	$0.236596\pi$
$102$	1.90983	0.189101
$103$	−8.85410	−0.872421	−0.436210	−	0.899845i	$-0.643680\pi$
$103$	−8.85410	−0.872421	−0.436210	+	0.899845i	$0.643680\pi$
$104$	1.81966	0.178432
$105$	0	0
$106$	0.909830	0.0883705
$107$	2.70820	0.261812	0.130906	−	0.991395i	$-0.458211\pi$
$107$	2.70820	0.261812	0.130906	+	0.991395i	$0.458211\pi$
$108$	10.1459	0.976289
$109$	−1.52786	−0.146343	−0.0731714	−	0.997319i	$-0.523312\pi$
$109$	−1.52786	−0.146343	−0.0731714	+	0.997319i	$0.523312\pi$
$110$	0	0
$111$	10.4721	0.993971
$112$	0	0
$113$	0.145898	0.0137249	0.00686247	−	0.999976i	$-0.497816\pi$
$113$	0.145898	0.0137249	0.00686247	+	0.999976i	$0.497816\pi$
$114$	−1.09017	−0.102104
$115$	−5.09017	−0.474661
$116$	8.56231	0.794990
$117$	−0.472136	−0.0436490
$118$	4.23607	0.389962
$119$	0	0
$120$	−2.38197	−0.217443
$121$	0	0
$122$	−2.90983	−0.263444
$123$	18.0902	1.63114
$124$	−7.85410	−0.705319
$125$	9.00000	0.804984
$126$	0	0
$127$	2.94427	0.261262	0.130631	−	0.991431i	$-0.458300\pi$
$127$	2.94427	0.261262	0.130631	+	0.991431i	$0.458300\pi$
$128$	10.0902	0.891853
$129$	−20.3262	−1.78963
$130$	0.472136	0.0414091
$131$	−18.9443	−1.65517	−0.827584	−	0.561341i	$-0.810285\pi$
$131$	−18.9443	−1.65517	−0.827584	+	0.561341i	$0.810285\pi$
$132$	0	0
$133$	0	0
$134$	3.18034	0.274740
$135$	5.47214	0.470966
$136$	−4.54915	−0.390086
$137$	−15.3262	−1.30941	−0.654704	−	0.755885i	$-0.727207\pi$
$137$	−15.3262	−1.30941	−0.654704	+	0.755885i	$0.727207\pi$
$138$	−3.14590	−0.267797
$139$	−11.9443	−1.01310	−0.506550	−	0.862211i	$-0.669079\pi$
$139$	−11.9443	−1.01310	−0.506550	+	0.862211i	$0.669079\pi$
$140$	0	0
$141$	10.7082	0.901793
$142$	6.14590	0.515752
$143$	0	0
$144$	−1.20163	−0.100136
$145$	4.61803	0.383507
$146$	−5.43769	−0.450027
$147$	0	0
$148$	−12.0000	−0.986394
$149$	−8.85410	−0.725356	−0.362678	−	0.931914i	$-0.618138\pi$
$149$	−8.85410	−0.725356	−0.362678	+	0.931914i	$0.618138\pi$
$150$	2.47214	0.201849
$151$	0.0557281	0.00453509	0.00226754	−	0.999997i	$-0.499278\pi$
$151$	0.0557281	0.00453509	0.00226754	+	0.999997i	$0.499278\pi$
$152$	2.59675	0.210624
$153$	1.18034	0.0954248
$154$	0	0
$155$	−4.23607	−0.340249
$156$	−3.70820	−0.296894
$157$	−19.8885	−1.58728	−0.793639	−	0.608389i	$-0.791816\pi$
$157$	−19.8885	−1.58728	−0.793639	+	0.608389i	$0.791816\pi$
$158$	−2.43769	−0.193933
$159$	−3.85410	−0.305650
$160$	4.14590	0.327762
$161$	0	0
$162$	2.94427	0.231324
$163$	−8.70820	−0.682079	−0.341040	−	0.940049i	$-0.610779\pi$
$163$	−8.70820	−0.682079	−0.341040	+	0.940049i	$0.610779\pi$
$164$	−20.7295	−1.61870
$165$	0	0
$166$	1.03444	0.0802883
$167$	−6.47214	−0.500829	−0.250414	−	0.968139i	$-0.580567\pi$
$167$	−6.47214	−0.500829	−0.250414	+	0.968139i	$0.580567\pi$
$168$	0	0
$169$	−11.4721	−0.882472
$170$	−1.18034	−0.0905279
$171$	−0.673762	−0.0515239
$172$	23.2918	1.77598
$173$	15.3820	1.16947	0.584735	−	0.811225i	$-0.301199\pi$
$173$	15.3820	1.16947	0.584735	+	0.811225i	$0.301199\pi$
$174$	2.85410	0.216369
$175$	0	0
$176$	0	0
$177$	−17.9443	−1.34877
$178$	2.61803	0.196230
$179$	−3.76393	−0.281329	−0.140665	−	0.990057i	$-0.544924\pi$
$179$	−3.76393	−0.281329	−0.140665	+	0.990057i	$0.544924\pi$
$180$	−0.708204	−0.0527864
$181$	7.41641	0.551257	0.275629	−	0.961264i	$-0.411114\pi$
$181$	7.41641	0.551257	0.275629	+	0.961264i	$0.411114\pi$
$182$	0	0
$183$	12.3262	0.911182
$184$	7.49342	0.552422
$185$	−6.47214	−0.475841
$186$	−2.61803	−0.191964
$187$	0	0
$188$	−12.2705	−0.894919
$189$	0	0
$190$	0.673762	0.0488798
$191$	15.7639	1.14064	0.570319	−	0.821423i	$-0.306820\pi$
$191$	15.7639	1.14064	0.570319	+	0.821423i	$0.306820\pi$
$192$	−7.61803	−0.549784
$193$	−15.3262	−1.10321	−0.551603	−	0.834107i	$-0.685984\pi$
$193$	−15.3262	−1.10321	−0.551603	+	0.834107i	$0.685984\pi$
$194$	2.67376	0.191965
$195$	−2.00000	−0.143223
$196$	0	0
$197$	−4.29180	−0.305778	−0.152889	−	0.988243i	$-0.548858\pi$
$197$	−4.29180	−0.305778	−0.152889	+	0.988243i	$0.548858\pi$
$198$	0	0
$199$	8.23607	0.583839	0.291920	−	0.956443i	$-0.405706\pi$
$199$	8.23607	0.583839	0.291920	+	0.956443i	$0.405706\pi$
$200$	−5.88854	−0.416383
$201$	−13.4721	−0.950251
$202$	−5.65248	−0.397707
$203$	0	0
$204$	9.27051	0.649066
$205$	−11.1803	−0.780869
$206$	3.38197	0.235633
$207$	−1.94427	−0.135136
$208$	3.88854	0.269622
$209$	0	0
$210$	0	0
$211$	15.6180	1.07519	0.537595	−	0.843203i	$-0.319333\pi$
$211$	15.6180	1.07519	0.537595	+	0.843203i	$0.319333\pi$
$212$	4.41641	0.303320
$213$	−26.0344	−1.78385
$214$	−1.03444	−0.0707130
$215$	12.5623	0.856742
$216$	−8.05573	−0.548123
$217$	0	0
$218$	0.583592	0.0395258
$219$	23.0344	1.55652
$220$	0	0
$221$	−3.81966	−0.256938
$222$	−4.00000	−0.268462
$223$	−2.03444	−0.136236	−0.0681182	−	0.997677i	$-0.521699\pi$
$223$	−2.03444	−0.136236	−0.0681182	+	0.997677i	$0.521699\pi$
$224$	0	0
$225$	1.52786	0.101858
$226$	−0.0557281	−0.00370698
$227$	16.0344	1.06424	0.532122	−	0.846668i	$-0.321395\pi$
$227$	16.0344	1.06424	0.532122	+	0.846668i	$0.321395\pi$
$228$	−5.29180	−0.350458
$229$	−6.76393	−0.446973	−0.223487	−	0.974707i	$-0.571744\pi$
$229$	−6.76393	−0.446973	−0.223487	+	0.974707i	$0.571744\pi$
$230$	1.94427	0.128201
$231$	0	0
$232$	−6.79837	−0.446335
$233$	−29.4164	−1.92713	−0.963566	−	0.267469i	$-0.913813\pi$
$233$	−29.4164	−1.92713	−0.963566	+	0.267469i	$0.913813\pi$
$234$	0.180340	0.0117892
$235$	−6.61803	−0.431713
$236$	20.5623	1.33849
$237$	10.3262	0.670761
$238$	0	0
$239$	−17.0902	−1.10547	−0.552736	−	0.833357i	$-0.686416\pi$
$239$	−17.0902	−1.10547	−0.552736	+	0.833357i	$0.686416\pi$
$240$	−5.09017	−0.328569
$241$	−16.2705	−1.04808	−0.524038	−	0.851695i	$-0.675575\pi$
$241$	−16.2705	−1.04808	−0.524038	+	0.851695i	$0.675575\pi$
$242$	0	0
$243$	3.94427	0.253025
$244$	−14.1246	−0.904236
$245$	0	0
$246$	−6.90983	−0.440555
$247$	2.18034	0.138732
$248$	6.23607	0.395991
$249$	−4.38197	−0.277696
$250$	−3.43769	−0.217419
$251$	−23.0000	−1.45175	−0.725874	−	0.687828i	$-0.758564\pi$
$251$	−23.0000	−1.45175	−0.725874	+	0.687828i	$0.758564\pi$
$252$	0	0
$253$	0	0
$254$	−1.12461	−0.0705644
$255$	5.00000	0.313112
$256$	5.56231	0.347644
$257$	8.56231	0.534102	0.267051	−	0.963682i	$-0.413951\pi$
$257$	8.56231	0.534102	0.267051	+	0.963682i	$0.413951\pi$
$258$	7.76393	0.483361
$259$	0	0
$260$	2.29180	0.142131
$261$	1.76393	0.109185
$262$	7.23607	0.447046
$263$	−17.1246	−1.05595	−0.527974	−	0.849260i	$-0.677048\pi$
$263$	−17.1246	−1.05595	−0.527974	+	0.849260i	$0.677048\pi$
$264$	0	0
$265$	2.38197	0.146323
$266$	0	0
$267$	−11.0902	−0.678707
$268$	15.4377	0.943007
$269$	−16.8541	−1.02761	−0.513806	−	0.857906i	$-0.671765\pi$
$269$	−16.8541	−1.02761	−0.513806	+	0.857906i	$0.671765\pi$
$270$	−2.09017	−0.127204
$271$	4.79837	0.291480	0.145740	−	0.989323i	$-0.453444\pi$
$271$	4.79837	0.291480	0.145740	+	0.989323i	$0.453444\pi$
$272$	−9.72136	−0.589444
$273$	0	0
$274$	5.85410	0.353659
$275$	0	0
$276$	−15.2705	−0.919177
$277$	23.0344	1.38401	0.692003	−	0.721895i	$-0.256729\pi$
$277$	23.0344	1.38401	0.692003	+	0.721895i	$0.256729\pi$
$278$	4.56231	0.273629
$279$	−1.61803	−0.0968692
$280$	0	0
$281$	−25.1803	−1.50213	−0.751067	−	0.660226i	$-0.770460\pi$
$281$	−25.1803	−1.50213	−0.751067	+	0.660226i	$0.770460\pi$
$282$	−4.09017	−0.243566
$283$	−11.9443	−0.710013	−0.355007	−	0.934864i	$-0.615521\pi$
$283$	−11.9443	−0.710013	−0.355007	+	0.934864i	$0.615521\pi$
$284$	29.8328	1.77025
$285$	−2.85410	−0.169062
$286$	0	0
$287$	0	0
$288$	1.58359	0.0933141
$289$	−7.45085	−0.438285
$290$	−1.76393	−0.103582
$291$	−11.3262	−0.663956
$292$	−26.3951	−1.54466
$293$	11.0000	0.642627	0.321313	−	0.946973i	$-0.395876\pi$
$293$	11.0000	0.642627	0.321313	+	0.946973i	$0.395876\pi$
$294$	0	0
$295$	11.0902	0.645695
$296$	9.52786	0.553796
$297$	0	0
$298$	3.38197	0.195912
$299$	6.29180	0.363864
$300$	12.0000	0.692820
$301$	0	0
$302$	−0.0212862	−0.00122489
$303$	23.9443	1.37556
$304$	5.54915	0.318266
$305$	−7.61803	−0.436207
$306$	−0.450850	−0.0257734
$307$	23.1803	1.32297	0.661486	−	0.749958i	$-0.269926\pi$
$307$	23.1803	1.32297	0.661486	+	0.749958i	$0.269926\pi$
$308$	0	0
$309$	−14.3262	−0.814991
$310$	1.61803	0.0918982
$311$	−9.00000	−0.510343	−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000	−0.510343	−0.255172	+	0.966896i	$0.582132\pi$
$312$	2.94427	0.166687
$313$	−18.3262	−1.03586	−0.517930	−	0.855423i	$-0.673297\pi$
$313$	−18.3262	−1.03586	−0.517930	+	0.855423i	$0.673297\pi$
$314$	7.59675	0.428709
$315$	0	0
$316$	−11.8328	−0.665648
$317$	−4.43769	−0.249246	−0.124623	−	0.992204i	$-0.539772\pi$
$317$	−4.43769	−0.249246	−0.124623	+	0.992204i	$0.539772\pi$
$318$	1.47214	0.0825533
$319$	0	0
$320$	4.70820	0.263197
$321$	4.38197	0.244577
$322$	0	0
$323$	−5.45085	−0.303293
$324$	14.2918	0.793989
$325$	−4.94427	−0.274259
$326$	3.32624	0.184223
$327$	−2.47214	−0.136709
$328$	16.4590	0.908795
$329$	0	0
$330$	0	0
$331$	6.18034	0.339702	0.169851	−	0.985470i	$-0.445671\pi$
$331$	6.18034	0.339702	0.169851	+	0.985470i	$0.445671\pi$
$332$	5.02129	0.275579
$333$	−2.47214	−0.135472
$334$	2.47214	0.135269
$335$	8.32624	0.454911
$336$	0	0
$337$	25.9443	1.41327	0.706637	−	0.707576i	$-0.250211\pi$
$337$	25.9443	1.41327	0.706637	+	0.707576i	$0.250211\pi$
$338$	4.38197	0.238348
$339$	0.236068	0.0128215
$340$	−5.72949	−0.310725
$341$	0	0
$342$	0.257354	0.0139161
$343$	0	0
$344$	−18.4934	−0.997099
$345$	−8.23607	−0.443415
$346$	−5.87539	−0.315863
$347$	2.34752	0.126022	0.0630108	−	0.998013i	$-0.479930\pi$
$347$	2.34752	0.126022	0.0630108	+	0.998013i	$0.479930\pi$
$348$	13.8541	0.742658
$349$	−32.7984	−1.75566	−0.877828	−	0.478975i	$-0.841008\pi$
$349$	−32.7984	−1.75566	−0.877828	+	0.478975i	$0.841008\pi$
$350$	0	0
$351$	−6.76393	−0.361032
$352$	0	0
$353$	−24.0902	−1.28219	−0.641095	−	0.767461i	$-0.721520\pi$
$353$	−24.0902	−1.28219	−0.641095	+	0.767461i	$0.721520\pi$
$354$	6.85410	0.364291
$355$	16.0902	0.853978
$356$	12.7082	0.673533
$357$	0	0
$358$	1.43769	0.0759845
$359$	−15.6180	−0.824288	−0.412144	−	0.911119i	$-0.635220\pi$
$359$	−15.6180	−0.824288	−0.412144	+	0.911119i	$0.635220\pi$
$360$	0.562306	0.0296361
$361$	−15.8885	−0.836239
$362$	−2.83282	−0.148889
$363$	0	0
$364$	0	0
$365$	−14.2361	−0.745150
$366$	−4.70820	−0.246102
$367$	−32.8328	−1.71386	−0.856930	−	0.515434i	$-0.827631\pi$
$367$	−32.8328	−1.71386	−0.856930	+	0.515434i	$0.827631\pi$
$368$	16.0132	0.834743
$369$	−4.27051	−0.222314
$370$	2.47214	0.128520
$371$	0	0
$372$	−12.7082	−0.658890
$373$	−15.4377	−0.799334	−0.399667	−	0.916661i	$-0.630874\pi$
$373$	−15.4377	−0.799334	−0.399667	+	0.916661i	$0.630874\pi$
$374$	0	0
$375$	14.5623	0.751994
$376$	9.74265	0.502439
$377$	−5.70820	−0.293987
$378$	0	0
$379$	32.0689	1.64727	0.823634	−	0.567122i	$-0.191943\pi$
$379$	32.0689	1.64727	0.823634	+	0.567122i	$0.191943\pi$
$380$	3.27051	0.167774
$381$	4.76393	0.244064
$382$	−6.02129	−0.308076
$383$	34.5967	1.76781	0.883906	−	0.467665i	$-0.154905\pi$
$383$	34.5967	1.76781	0.883906	+	0.467665i	$0.154905\pi$
$384$	16.3262	0.833145
$385$	0	0
$386$	5.85410	0.297966
$387$	4.79837	0.243915
$388$	12.9787	0.658894
$389$	−34.1803	−1.73301	−0.866506	−	0.499167i	$-0.833640\pi$
$389$	−34.1803	−1.73301	−0.866506	+	0.499167i	$0.833640\pi$
$390$	0.763932	0.0386832
$391$	−15.7295	−0.795475
$392$	0	0
$393$	−30.6525	−1.54621
$394$	1.63932	0.0825878
$395$	−6.38197	−0.321112
$396$	0	0
$397$	0.819660	0.0411376	0.0205688	−	0.999788i	$-0.493452\pi$
$397$	0.819660	0.0411376	0.0205688	+	0.999788i	$0.493452\pi$
$398$	−3.14590	−0.157690
$399$	0	0
$400$	−12.5836	−0.629180
$401$	−17.5279	−0.875300	−0.437650	−	0.899145i	$-0.644189\pi$
$401$	−17.5279	−0.875300	−0.437650	+	0.899145i	$0.644189\pi$
$402$	5.14590	0.256654
$403$	5.23607	0.260827
$404$	−27.4377	−1.36508
$405$	7.70820	0.383024
$406$	0	0
$407$	0	0
$408$	−7.36068	−0.364408
$409$	17.7082	0.875614	0.437807	−	0.899069i	$-0.355755\pi$
$409$	17.7082	0.875614	0.437807	+	0.899069i	$0.355755\pi$
$410$	4.27051	0.210905
$411$	−24.7984	−1.22321
$412$	16.4164	0.808778
$413$	0	0
$414$	0.742646	0.0364990
$415$	2.70820	0.132941
$416$	−5.12461	−0.251255
$417$	−19.3262	−0.946410
$418$	0	0
$419$	−29.8885	−1.46015	−0.730075	−	0.683367i	$-0.760515\pi$
$419$	−29.8885	−1.46015	−0.730075	+	0.683367i	$0.760515\pi$
$420$	0	0
$421$	0.763932	0.0372318	0.0186159	−	0.999827i	$-0.494074\pi$
$421$	0.763932	0.0372318	0.0186159	+	0.999827i	$0.494074\pi$
$422$	−5.96556	−0.290399
$423$	−2.52786	−0.122909
$424$	−3.50658	−0.170294
$425$	12.3607	0.599581
$426$	9.94427	0.481802
$427$	0	0
$428$	−5.02129	−0.242713
$429$	0	0
$430$	−4.79837	−0.231398
$431$	−13.8541	−0.667329	−0.333664	−	0.942692i	$-0.608285\pi$
$431$	−13.8541	−0.667329	−0.333664	+	0.942692i	$0.608285\pi$
$432$	−17.2148	−0.828247
$433$	8.96556	0.430857	0.215429	−	0.976520i	$-0.430885\pi$
$433$	8.96556	0.430857	0.215429	+	0.976520i	$0.430885\pi$
$434$	0	0
$435$	7.47214	0.358261
$436$	2.83282	0.135667
$437$	8.97871	0.429510
$438$	−8.79837	−0.420403
$439$	−3.38197	−0.161412	−0.0807062	−	0.996738i	$-0.525718\pi$
$439$	−3.38197	−0.161412	−0.0807062	+	0.996738i	$0.525718\pi$
$440$	0	0
$441$	0	0
$442$	1.45898	0.0693966
$443$	3.09017	0.146818	0.0734092	−	0.997302i	$-0.476612\pi$
$443$	3.09017	0.146818	0.0734092	+	0.997302i	$0.476612\pi$
$444$	−19.4164	−0.921462
$445$	6.85410	0.324916
$446$	0.777088	0.0367962
$447$	−14.3262	−0.677608
$448$	0	0
$449$	12.3262	0.581711	0.290856	−	0.956767i	$-0.406060\pi$
$449$	12.3262	0.581711	0.290856	+	0.956767i	$0.406060\pi$
$450$	−0.583592	−0.0275108
$451$	0	0
$452$	−0.270510	−0.0127237
$453$	0.0901699	0.00423655
$454$	−6.12461	−0.287442
$455$	0	0
$456$	4.20163	0.196759
$457$	−0.145898	−0.00682482	−0.00341241	−	0.999994i	$-0.501086\pi$
$457$	−0.145898	−0.00682482	−0.00341241	+	0.999994i	$0.501086\pi$
$458$	2.58359	0.120723
$459$	16.9098	0.789283
$460$	9.43769	0.440035
$461$	18.5066	0.861937	0.430969	−	0.902367i	$-0.358172\pi$
$461$	18.5066	0.861937	0.430969	+	0.902367i	$0.358172\pi$
$462$	0	0
$463$	22.2361	1.03340	0.516699	−	0.856167i	$-0.327161\pi$
$463$	22.2361	1.03340	0.516699	+	0.856167i	$0.327161\pi$
$464$	−14.5279	−0.674439
$465$	−6.85410	−0.317851
$466$	11.2361	0.520501
$467$	4.50658	0.208540	0.104270	−	0.994549i	$-0.466749\pi$
$467$	4.50658	0.208540	0.104270	+	0.994549i	$0.466749\pi$
$468$	0.875388	0.0404648
$469$	0	0
$470$	2.52786	0.116602
$471$	−32.1803	−1.48279
$472$	−16.3262	−0.751476
$473$	0	0
$474$	−3.94427	−0.181166
$475$	−7.05573	−0.323739
$476$	0	0
$477$	0.909830	0.0416583
$478$	6.52786	0.298578
$479$	−21.7639	−0.994419	−0.497210	−	0.867630i	$-0.665642\pi$
$479$	−21.7639	−0.994419	−0.497210	+	0.867630i	$0.665642\pi$
$480$	6.70820	0.306186
$481$	8.00000	0.364769
$482$	6.21478	0.283076
$483$	0	0
$484$	0	0
$485$	7.00000	0.317854
$486$	−1.50658	−0.0683398
$487$	−32.5967	−1.47710	−0.738550	−	0.674199i	$-0.764489\pi$
$487$	−32.5967	−1.47710	−0.738550	+	0.674199i	$0.764489\pi$
$488$	11.2148	0.507669
$489$	−14.0902	−0.637180
$490$	0	0
$491$	22.1459	0.999430	0.499715	−	0.866190i	$-0.333438\pi$
$491$	22.1459	0.999430	0.499715	+	0.866190i	$0.333438\pi$
$492$	−33.5410	−1.51215
$493$	14.2705	0.642711
$494$	−0.832816	−0.0374702
$495$	0	0
$496$	13.3262	0.598366
$497$	0	0
$498$	1.67376	0.0750031
$499$	−10.0902	−0.451698	−0.225849	−	0.974162i	$-0.572516\pi$
$499$	−10.0902	−0.451698	−0.225849	+	0.974162i	$0.572516\pi$
$500$	−16.6869	−0.746262
$501$	−10.4721	−0.467861
$502$	8.78522	0.392103
$503$	34.8328	1.55312	0.776559	−	0.630044i	$-0.216963\pi$
$503$	34.8328	1.55312	0.776559	+	0.630044i	$0.216963\pi$
$504$	0	0
$505$	−14.7984	−0.658519
$506$	0	0
$507$	−18.5623	−0.824381
$508$	−5.45898	−0.242203
$509$	10.7426	0.476159	0.238080	−	0.971246i	$-0.423482\pi$
$509$	10.7426	0.476159	0.238080	+	0.971246i	$0.423482\pi$
$510$	−1.90983	−0.0845687
$511$	0	0
$512$	−22.3050	−0.985749
$513$	−9.65248	−0.426167
$514$	−3.27051	−0.144256
$515$	8.85410	0.390158
$516$	37.6869	1.65907
$517$	0	0
$518$	0	0
$519$	24.8885	1.09249
$520$	−1.81966	−0.0797974
$521$	12.2361	0.536072	0.268036	−	0.963409i	$-0.413625\pi$
$521$	12.2361	0.536072	0.268036	+	0.963409i	$0.413625\pi$
$522$	−0.673762	−0.0294898
$523$	−16.5623	−0.724219	−0.362110	−	0.932136i	$-0.617943\pi$
$523$	−16.5623	−0.724219	−0.362110	+	0.932136i	$0.617943\pi$
$524$	35.1246	1.53443
$525$	0	0
$526$	6.54102	0.285202
$527$	−13.0902	−0.570217
$528$	0	0
$529$	2.90983	0.126514
$530$	−0.909830	−0.0395205
$531$	4.23607	0.183830
$532$	0	0
$533$	13.8197	0.598596
$534$	4.23607	0.183313
$535$	−2.70820	−0.117086
$536$	−12.2574	−0.529437
$537$	−6.09017	−0.262810
$538$	6.43769	0.277549
$539$	0	0
$540$	−10.1459	−0.436610
$541$	0.708204	0.0304481	0.0152240	−	0.999884i	$-0.495154\pi$
$541$	0.708204	0.0304481	0.0152240	+	0.999884i	$0.495154\pi$
$542$	−1.83282	−0.0787262
$543$	12.0000	0.514969
$544$	12.8115	0.549290
$545$	1.52786	0.0654465
$546$	0	0
$547$	−1.72949	−0.0739477	−0.0369738	−	0.999316i	$-0.511772\pi$
$547$	−1.72949	−0.0739477	−0.0369738	+	0.999316i	$0.511772\pi$
$548$	28.4164	1.21389
$549$	−2.90983	−0.124189
$550$	0	0
$551$	−8.14590	−0.347027
$552$	12.1246	0.516058
$553$	0	0
$554$	−8.79837	−0.373807
$555$	−10.4721	−0.444517
$556$	22.1459	0.939195
$557$	−9.76393	−0.413711	−0.206856	−	0.978371i	$-0.566323\pi$
$557$	−9.76393	−0.413711	−0.206856	+	0.978371i	$0.566323\pi$
$558$	0.618034	0.0261635
$559$	−15.5279	−0.656759
$560$	0	0
$561$	0	0
$562$	9.61803	0.405712
$563$	31.9787	1.34774	0.673871	−	0.738849i	$-0.264630\pi$
$563$	31.9787	1.34774	0.673871	+	0.738849i	$0.264630\pi$
$564$	−19.8541	−0.836009
$565$	−0.145898	−0.00613798
$566$	4.56231	0.191768
$567$	0	0
$568$	−23.6869	−0.993881
$569$	37.3050	1.56390	0.781952	−	0.623338i	$-0.214224\pi$
$569$	37.3050	1.56390	0.781952	+	0.623338i	$0.214224\pi$
$570$	1.09017	0.0456622
$571$	34.3050	1.43562	0.717809	−	0.696240i	$-0.245145\pi$
$571$	34.3050	1.43562	0.717809	+	0.696240i	$0.245145\pi$
$572$	0	0
$573$	25.5066	1.06555
$574$	0	0
$575$	−20.3607	−0.849099
$576$	1.79837	0.0749322
$577$	−9.65248	−0.401838	−0.200919	−	0.979608i	$-0.564393\pi$
$577$	−9.65248	−0.401838	−0.200919	+	0.979608i	$0.564393\pi$
$578$	2.84597	0.118377
$579$	−24.7984	−1.03059
$580$	−8.56231	−0.355530
$581$	0	0
$582$	4.32624	0.179328
$583$	0	0
$584$	20.9574	0.867225
$585$	0.472136	0.0195204
$586$	−4.20163	−0.173568
$587$	−1.00000	−0.0412744	−0.0206372	−	0.999787i	$-0.506569\pi$
$587$	−1.00000	−0.0412744	−0.0206372	+	0.999787i	$0.506569\pi$
$588$	0	0
$589$	7.47214	0.307884
$590$	−4.23607	−0.174396
$591$	−6.94427	−0.285649
$592$	20.3607	0.836819
$593$	−11.1246	−0.456833	−0.228417	−	0.973564i	$-0.573355\pi$
$593$	−11.1246	−0.456833	−0.228417	+	0.973564i	$0.573355\pi$
$594$	0	0
$595$	0	0
$596$	16.4164	0.672442
$597$	13.3262	0.545407
$598$	−2.40325	−0.0982763
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	−9.52786	−0.388973
$601$	−13.7082	−0.559169	−0.279585	−	0.960121i	$-0.590197\pi$
$601$	−13.7082	−0.559169	−0.279585	+	0.960121i	$0.590197\pi$
$602$	0	0
$603$	3.18034	0.129513
$604$	−0.103326	−0.00420426
$605$	0	0
$606$	−9.14590	−0.371527
$607$	−20.2016	−0.819959	−0.409979	−	0.912095i	$-0.634464\pi$
$607$	−20.2016	−0.819959	−0.409979	+	0.912095i	$0.634464\pi$
$608$	−7.31308	−0.296585
$609$	0	0
$610$	2.90983	0.117816
$611$	8.18034	0.330941
$612$	−2.18847	−0.0884637
$613$	−0.888544	−0.0358879	−0.0179440	−	0.999839i	$-0.505712\pi$
$613$	−0.888544	−0.0358879	−0.0179440	+	0.999839i	$0.505712\pi$
$614$	−8.85410	−0.357322
$615$	−18.0902	−0.729466
$616$	0	0
$617$	9.41641	0.379090	0.189545	−	0.981872i	$-0.439299\pi$
$617$	9.41641	0.379090	0.189545	+	0.981872i	$0.439299\pi$
$618$	5.47214	0.220122
$619$	39.7082	1.59601	0.798004	−	0.602653i	$-0.205889\pi$
$619$	39.7082	1.59601	0.798004	+	0.602653i	$0.205889\pi$
$620$	7.85410	0.315428
$621$	−27.8541	−1.11775
$622$	3.43769	0.137839
$623$	0	0
$624$	6.29180	0.251873
$625$	11.0000	0.440000
$626$	7.00000	0.279776
$627$	0	0
$628$	36.8754	1.47149
$629$	−20.0000	−0.797452
$630$	0	0
$631$	17.8328	0.709913	0.354957	−	0.934883i	$-0.384496\pi$
$631$	17.8328	0.709913	0.354957	+	0.934883i	$0.384496\pi$
$632$	9.39512	0.373718
$633$	25.2705	1.00441
$634$	1.69505	0.0673190
$635$	−2.94427	−0.116840
$636$	7.14590	0.283353
$637$	0	0
$638$	0	0
$639$	6.14590	0.243128
$640$	−10.0902	−0.398849
$641$	31.6525	1.25020	0.625099	−	0.780546i	$-0.285059\pi$
$641$	31.6525	1.25020	0.625099	+	0.780546i	$0.285059\pi$
$642$	−1.67376	−0.0660581
$643$	−1.58359	−0.0624508	−0.0312254	−	0.999512i	$-0.509941\pi$
$643$	−1.58359	−0.0624508	−0.0312254	+	0.999512i	$0.509941\pi$
$644$	0	0
$645$	20.3262	0.800345
$646$	2.08204	0.0819167
$647$	−6.18034	−0.242974	−0.121487	−	0.992593i	$-0.538766\pi$
$647$	−6.18034	−0.242974	−0.121487	+	0.992593i	$0.538766\pi$
$648$	−11.3475	−0.445773
$649$	0	0
$650$	1.88854	0.0740748
$651$	0	0
$652$	16.1459	0.632322
$653$	18.2361	0.713632	0.356816	−	0.934175i	$-0.383862\pi$
$653$	18.2361	0.713632	0.356816	+	0.934175i	$0.383862\pi$
$654$	0.944272	0.0369240
$655$	18.9443	0.740214
$656$	35.1722	1.37324
$657$	−5.43769	−0.212145
$658$	0	0
$659$	31.4721	1.22598	0.612990	−	0.790091i	$-0.289967\pi$
$659$	31.4721	1.22598	0.612990	+	0.790091i	$0.289967\pi$
$660$	0	0
$661$	34.5623	1.34432	0.672159	−	0.740407i	$-0.265367\pi$
$661$	34.5623	1.34432	0.672159	+	0.740407i	$0.265367\pi$
$662$	−2.36068	−0.0917504
$663$	−6.18034	−0.240025
$664$	−3.98684	−0.154720
$665$	0	0
$666$	0.944272	0.0365898
$667$	−23.5066	−0.910178
$668$	12.0000	0.464294
$669$	−3.29180	−0.127268
$670$	−3.18034	−0.122867
$671$	0	0
$672$	0	0
$673$	−6.58359	−0.253779	−0.126889	−	0.991917i	$-0.540499\pi$
$673$	−6.58359	−0.253779	−0.126889	+	0.991917i	$0.540499\pi$
$674$	−9.90983	−0.381712
$675$	21.8885	0.842490
$676$	21.2705	0.818097
$677$	36.2705	1.39399	0.696994	−	0.717077i	$-0.254520\pi$
$677$	36.2705	1.39399	0.696994	+	0.717077i	$0.254520\pi$
$678$	−0.0901699	−0.00346296
$679$	0	0
$680$	4.54915	0.174452
$681$	25.9443	0.994187
$682$	0	0
$683$	0.493422	0.0188803	0.00944014	−	0.999955i	$-0.496995\pi$
$683$	0.493422	0.0188803	0.00944014	+	0.999955i	$0.496995\pi$
$684$	1.24922	0.0477653
$685$	15.3262	0.585585
$686$	0	0
$687$	−10.9443	−0.417550
$688$	−39.5197	−1.50668
$689$	−2.94427	−0.112168
$690$	3.14590	0.119762
$691$	−18.5410	−0.705334	−0.352667	−	0.935749i	$-0.614725\pi$
$691$	−18.5410	−0.705334	−0.352667	+	0.935749i	$0.614725\pi$
$692$	−28.5197	−1.08416
$693$	0	0
$694$	−0.896674	−0.0340373
$695$	11.9443	0.453072
$696$	−11.0000	−0.416954
$697$	−34.5492	−1.30864
$698$	12.5279	0.474187
$699$	−47.5967	−1.80027
$700$	0	0
$701$	18.5066	0.698984	0.349492	−	0.936939i	$-0.386354\pi$
$701$	18.5066	0.698984	0.349492	+	0.936939i	$0.386354\pi$
$702$	2.58359	0.0975114
$703$	11.4164	0.430578
$704$	0	0
$705$	−10.7082	−0.403294
$706$	9.20163	0.346308
$707$	0	0
$708$	33.2705	1.25038
$709$	−7.03444	−0.264184	−0.132092	−	0.991237i	$-0.542169\pi$
$709$	−7.03444	−0.264184	−0.132092	+	0.991237i	$0.542169\pi$
$710$	−6.14590	−0.230651
$711$	−2.43769	−0.0914207
$712$	−10.0902	−0.378145
$713$	21.5623	0.807515
$714$	0	0
$715$	0	0
$716$	6.97871	0.260807
$717$	−27.6525	−1.03270
$718$	5.96556	0.222633
$719$	2.88854	0.107725	0.0538623	−	0.998548i	$-0.482847\pi$
$719$	2.88854	0.107725	0.0538623	+	0.998548i	$0.482847\pi$
$720$	1.20163	0.0447820
$721$	0	0
$722$	6.06888	0.225860
$723$	−26.3262	−0.979083
$724$	−13.7508	−0.511044
$725$	18.4721	0.686038
$726$	0	0
$727$	12.4508	0.461776	0.230888	−	0.972980i	$-0.425837\pi$
$727$	12.4508	0.461776	0.230888	+	0.972980i	$0.425837\pi$
$728$	0	0
$729$	29.5066	1.09284
$730$	5.43769	0.201258
$731$	38.8197	1.43580
$732$	−22.8541	−0.844712
$733$	−52.9443	−1.95554	−0.977771	−	0.209677i	$-0.932759\pi$
$733$	−52.9443	−1.95554	−0.977771	+	0.209677i	$0.932759\pi$
$734$	12.5410	0.462897
$735$	0	0
$736$	−21.1033	−0.777879
$737$	0	0
$738$	1.63119	0.0600449
$739$	−11.3820	−0.418692	−0.209346	−	0.977842i	$-0.567134\pi$
$739$	−11.3820	−0.418692	−0.209346	+	0.977842i	$0.567134\pi$
$740$	12.0000	0.441129
$741$	3.52786	0.129599
$742$	0	0
$743$	−14.9098	−0.546989	−0.273494	−	0.961874i	$-0.588179\pi$
$743$	−14.9098	−0.546989	−0.273494	+	0.961874i	$0.588179\pi$
$744$	10.0902	0.369924
$745$	8.85410	0.324389
$746$	5.89667	0.215893
$747$	1.03444	0.0378482
$748$	0	0
$749$	0	0
$750$	−5.56231	−0.203107
$751$	41.3050	1.50724	0.753620	−	0.657311i	$-0.228306\pi$
$751$	41.3050	1.50724	0.753620	+	0.657311i	$0.228306\pi$
$752$	20.8197	0.759215
$753$	−37.2148	−1.35618
$754$	2.18034	0.0794033
$755$	−0.0557281	−0.00202815
$756$	0	0
$757$	−14.7639	−0.536604	−0.268302	−	0.963335i	$-0.586463\pi$
$757$	−14.7639	−0.536604	−0.268302	+	0.963335i	$0.586463\pi$
$758$	−12.2492	−0.444912
$759$	0	0
$760$	−2.59675	−0.0941939
$761$	−15.3050	−0.554804	−0.277402	−	0.960754i	$-0.589473\pi$
$761$	−15.3050	−0.554804	−0.277402	+	0.960754i	$0.589473\pi$
$762$	−1.81966	−0.0659193
$763$	0	0
$764$	−29.2279	−1.05743
$765$	−1.18034	−0.0426753
$766$	−13.2148	−0.477469
$767$	−13.7082	−0.494975
$768$	9.00000	0.324760
$769$	−48.5623	−1.75120	−0.875601	−	0.483035i	$-0.839534\pi$
$769$	−48.5623	−1.75120	−0.875601	+	0.483035i	$0.839534\pi$
$770$	0	0
$771$	13.8541	0.498943
$772$	28.4164	1.02273
$773$	−40.2361	−1.44719	−0.723595	−	0.690224i	$-0.757512\pi$
$773$	−40.2361	−1.44719	−0.723595	+	0.690224i	$0.757512\pi$
$774$	−1.83282	−0.0658792
$775$	−16.9443	−0.608656
$776$	−10.3050	−0.369926
$777$	0	0
$778$	13.0557	0.468071
$779$	19.7214	0.706591
$780$	3.70820	0.132775
$781$	0	0
$782$	6.00813	0.214850
$783$	25.2705	0.903094
$784$	0	0
$785$	19.8885	0.709853
$786$	11.7082	0.417618
$787$	−20.5623	−0.732967	−0.366484	−	0.930425i	$-0.619438\pi$
$787$	−20.5623	−0.732967	−0.366484	+	0.930425i	$0.619438\pi$
$788$	7.95743	0.283472
$789$	−27.7082	−0.986438
$790$	2.43769	0.0867293
$791$	0	0
$792$	0	0
$793$	9.41641	0.334386
$794$	−0.313082	−0.0111109
$795$	3.85410	0.136691
$796$	−15.2705	−0.541249
$797$	−32.2361	−1.14186	−0.570930	−	0.820999i	$-0.693417\pi$
$797$	−32.2361	−1.14186	−0.570930	+	0.820999i	$0.693417\pi$
$798$	0	0
$799$	−20.4508	−0.723499
$800$	16.5836	0.586319
$801$	2.61803	0.0925037
$802$	6.69505	0.236410
$803$	0	0
$804$	24.9787	0.880931
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	−27.2705	−0.959967
$808$	21.7852	0.766401
$809$	32.5066	1.14287	0.571435	−	0.820647i	$-0.306387\pi$
$809$	32.5066	1.14287	0.571435	+	0.820647i	$0.306387\pi$
$810$	−2.94427	−0.103451
$811$	−1.16718	−0.0409854	−0.0204927	−	0.999790i	$-0.506523\pi$
$811$	−1.16718	−0.0409854	−0.0204927	+	0.999790i	$0.506523\pi$
$812$	0	0
$813$	7.76393	0.272293
$814$	0	0
$815$	8.70820	0.305035
$816$	−15.7295	−0.550642
$817$	−22.1591	−0.775247
$818$	−6.76393	−0.236495
$819$	0	0
$820$	20.7295	0.723905
$821$	56.6656	1.97764	0.988822	−	0.149100i	$-0.0476377\pi$
$821$	56.6656	1.97764	0.988822	+	0.149100i	$0.0476377\pi$
$822$	9.47214	0.330379
$823$	−31.8885	−1.11156	−0.555782	−	0.831328i	$-0.687581\pi$
$823$	−31.8885	−1.11156	−0.555782	+	0.831328i	$0.687581\pi$
$824$	−13.0344	−0.454076
$825$	0	0
$826$	0	0
$827$	−19.5967	−0.681446	−0.340723	−	0.940164i	$-0.610672\pi$
$827$	−19.5967	−0.681446	−0.340723	+	0.940164i	$0.610672\pi$
$828$	3.60488	0.125278
$829$	47.9787	1.66637	0.833185	−	0.552995i	$-0.186515\pi$
$829$	47.9787	1.66637	0.833185	+	0.552995i	$0.186515\pi$
$830$	−1.03444	−0.0359060
$831$	37.2705	1.29290
$832$	−5.81966	−0.201760
$833$	0	0
$834$	7.38197	0.255617
$835$	6.47214	0.223978
$836$	0	0
$837$	−23.1803	−0.801230
$838$	11.4164	0.394373
$839$	−30.5967	−1.05632	−0.528159	−	0.849146i	$-0.677117\pi$
$839$	−30.5967	−1.05632	−0.528159	+	0.849146i	$0.677117\pi$
$840$	0	0
$841$	−7.67376	−0.264612
$842$	−0.291796	−0.0100560
$843$	−40.7426	−1.40325
$844$	−28.9574	−0.996756
$845$	11.4721	0.394653
$846$	0.965558	0.0331966
$847$	0	0
$848$	−7.49342	−0.257325
$849$	−19.3262	−0.663275
$850$	−4.72136	−0.161941
$851$	32.9443	1.12932
$852$	48.2705	1.65372
$853$	34.9098	1.19529	0.597645	−	0.801761i	$-0.296103\pi$
$853$	34.9098	1.19529	0.597645	+	0.801761i	$0.296103\pi$
$854$	0	0
$855$	0.673762	0.0230422
$856$	3.98684	0.136268
$857$	15.0902	0.515470	0.257735	−	0.966216i	$-0.417024\pi$
$857$	15.0902	0.515470	0.257735	+	0.966216i	$0.417024\pi$
$858$	0	0
$859$	−21.5623	−0.735696	−0.367848	−	0.929886i	$-0.619905\pi$
$859$	−21.5623	−0.735696	−0.367848	+	0.929886i	$0.619905\pi$
$860$	−23.2918	−0.794244
$861$	0	0
$862$	5.29180	0.180239
$863$	−47.9443	−1.63204	−0.816021	−	0.578022i	$-0.803825\pi$
$863$	−47.9443	−1.63204	−0.816021	+	0.578022i	$0.803825\pi$
$864$	22.6869	0.771825
$865$	−15.3820	−0.523003
$866$	−3.42454	−0.116371
$867$	−12.0557	−0.409434
$868$	0	0
$869$	0	0
$870$	−2.85410	−0.0967631
$871$	−10.2918	−0.348724
$872$	−2.24922	−0.0761683
$873$	2.67376	0.0904931
$874$	−3.42956	−0.116007
$875$	0	0
$876$	−42.7082	−1.44298
$877$	13.0000	0.438979	0.219489	−	0.975615i	$-0.429561\pi$
$877$	13.0000	0.438979	0.219489	+	0.975615i	$0.429561\pi$
$878$	1.29180	0.0435960
$879$	17.7984	0.600324
$880$	0	0
$881$	−14.1459	−0.476587	−0.238294	−	0.971193i	$-0.576588\pi$
$881$	−14.1459	−0.476587	−0.238294	+	0.971193i	$0.576588\pi$
$882$	0	0
$883$	31.6312	1.06447	0.532237	−	0.846595i	$-0.321351\pi$
$883$	31.6312	1.06447	0.532237	+	0.846595i	$0.321351\pi$
$884$	7.08204	0.238195
$885$	17.9443	0.603190
$886$	−1.18034	−0.0396543
$887$	−57.2148	−1.92108	−0.960542	−	0.278134i	$-0.910284\pi$
$887$	−57.2148	−1.92108	−0.960542	+	0.278134i	$0.910284\pi$
$888$	15.4164	0.517341
$889$	0	0
$890$	−2.61803	−0.0877567
$891$	0	0
$892$	3.77206	0.126298
$893$	11.6738	0.390648
$894$	5.47214	0.183016
$895$	3.76393	0.125814
$896$	0	0
$897$	10.1803	0.339912
$898$	−4.70820	−0.157115
$899$	−19.5623	−0.652439
$900$	−2.83282	−0.0944272
$901$	7.36068	0.245220
$902$	0	0
$903$	0	0
$904$	0.214782	0.00714353
$905$	−7.41641	−0.246530
$906$	−0.0344419	−0.00114425
$907$	−15.7639	−0.523433	−0.261716	−	0.965145i	$-0.584289\pi$
$907$	−15.7639	−0.523433	−0.261716	+	0.965145i	$0.584289\pi$
$908$	−29.7295	−0.986608
$909$	−5.65248	−0.187481
$910$	0	0
$911$	−45.1803	−1.49689	−0.748446	−	0.663196i	$-0.769200\pi$
$911$	−45.1803	−1.49689	−0.748446	+	0.663196i	$0.769200\pi$
$912$	8.97871	0.297315
$913$	0	0
$914$	0.0557281	0.00184332
$915$	−12.3262	−0.407493
$916$	12.5410	0.414367
$917$	0	0
$918$	−6.45898	−0.213178
$919$	−14.8885	−0.491128	−0.245564	−	0.969380i	$-0.578973\pi$
$919$	−14.8885	−0.491128	−0.245564	+	0.969380i	$0.578973\pi$
$920$	−7.49342	−0.247051
$921$	37.5066	1.23588
$922$	−7.06888	−0.232801
$923$	−19.8885	−0.654639
$924$	0	0
$925$	−25.8885	−0.851210
$926$	−8.49342	−0.279111
$927$	3.38197	0.111078
$928$	19.1459	0.628495
$929$	−24.0000	−0.787414	−0.393707	−	0.919236i	$-0.628808\pi$
$929$	−24.0000	−0.787414	−0.393707	+	0.919236i	$0.628808\pi$
$930$	2.61803	0.0858487
$931$	0	0
$932$	54.5410	1.78655
$933$	−14.5623	−0.476748
$934$	−1.72136	−0.0563246
$935$	0	0
$936$	−0.695048	−0.0227184
$937$	51.7214	1.68966	0.844832	−	0.535032i	$-0.179701\pi$
$937$	51.7214	1.68966	0.844832	+	0.535032i	$0.179701\pi$
$938$	0	0
$939$	−29.6525	−0.967672
$940$	12.2705	0.400220
$941$	−27.0689	−0.882420	−0.441210	−	0.897404i	$-0.645451\pi$
$941$	−27.0689	−0.882420	−0.441210	+	0.897404i	$0.645451\pi$
$942$	12.2918	0.400488
$943$	56.9098	1.85324
$944$	−34.8885	−1.13553
$945$	0	0
$946$	0	0
$947$	6.29180	0.204456	0.102228	−	0.994761i	$-0.467403\pi$
$947$	6.29180	0.204456	0.102228	+	0.994761i	$0.467403\pi$
$948$	−19.1459	−0.621830
$949$	17.5967	0.571215
$950$	2.69505	0.0874389
$951$	−7.18034	−0.232838
$952$	0	0
$953$	−6.23607	−0.202006	−0.101003	−	0.994886i	$-0.532205\pi$
$953$	−6.23607	−0.202006	−0.101003	+	0.994886i	$0.532205\pi$
$954$	−0.347524	−0.0112515
$955$	−15.7639	−0.510109
$956$	31.6869	1.02483
$957$	0	0
$958$	8.31308	0.268583
$959$	0	0
$960$	7.61803	0.245871
$961$	−13.0557	−0.421153
$962$	−3.05573	−0.0985206
$963$	−1.03444	−0.0333344
$964$	30.1672	0.971620
$965$	15.3262	0.493369
$966$	0	0
$967$	27.4508	0.882760	0.441380	−	0.897320i	$-0.354489\pi$
$967$	27.4508	0.882760	0.441380	+	0.897320i	$0.354489\pi$
$968$	0	0
$969$	−8.81966	−0.283328
$970$	−2.67376	−0.0858493
$971$	28.2492	0.906561	0.453280	−	0.891368i	$-0.350254\pi$
$971$	28.2492	0.906561	0.453280	+	0.891368i	$0.350254\pi$
$972$	−7.31308	−0.234567
$973$	0	0
$974$	12.4508	0.398951
$975$	−8.00000	−0.256205
$976$	23.9656	0.767119
$977$	−10.8197	−0.346152	−0.173076	−	0.984909i	$-0.555371\pi$
$977$	−10.8197	−0.346152	−0.173076	+	0.984909i	$0.555371\pi$
$978$	5.38197	0.172096
$979$	0	0
$980$	0	0
$981$	0.583592	0.0186327
$982$	−8.45898	−0.269937
$983$	12.3820	0.394923	0.197462	−	0.980311i	$-0.436730\pi$
$983$	12.3820	0.394923	0.197462	+	0.980311i	$0.436730\pi$
$984$	26.6312	0.848971
$985$	4.29180	0.136748
$986$	−5.45085	−0.173590
$987$	0	0
$988$	−4.04257	−0.128611
$989$	−63.9443	−2.03331
$990$	0	0
$991$	−0.729490	−0.0231730	−0.0115865	−	0.999933i	$-0.503688\pi$
$991$	−0.729490	−0.0231730	−0.0115865	+	0.999933i	$0.503688\pi$
$992$	−17.5623	−0.557604
$993$	10.0000	0.317340
$994$	0	0
$995$	−8.23607	−0.261101
$996$	8.12461	0.257438
$997$	55.8673	1.76933	0.884667	−	0.466224i	$-0.154386\pi$
$997$	55.8673	1.76933	0.884667	+	0.466224i	$0.154386\pi$
$998$	3.85410	0.121999
$999$	−35.4164	−1.12053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.i.1.2		2
7.6	odd	2		847.2.a.d.1.2	✓	2
11.10	odd	2		5929.2.a.s.1.1		2
21.20	even	2		7623.2.a.bx.1.1		2
77.6	even	10		847.2.f.j.729.1		4
77.13	even	10		847.2.f.j.323.1		4
77.20	odd	10		847.2.f.d.323.1		4
77.27	odd	10		847.2.f.d.729.1		4
77.41	even	10		847.2.f.c.372.1		4
77.48	odd	10		847.2.f.l.148.1		4
77.62	even	10		847.2.f.c.148.1		4
77.69	odd	10		847.2.f.l.372.1		4
77.76	even	2		847.2.a.h.1.1	yes	2
231.230	odd	2		7623.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.d.1.2	✓	2	7.6	odd	2
847.2.a.h.1.1	yes	2	77.76	even	2
847.2.f.c.148.1		4	77.62	even	10
847.2.f.c.372.1		4	77.41	even	10
847.2.f.d.323.1		4	77.20	odd	10
847.2.f.d.729.1		4	77.27	odd	10
847.2.f.j.323.1		4	77.13	even	10
847.2.f.j.729.1		4	77.6	even	10
847.2.f.l.148.1		4	77.48	odd	10
847.2.f.l.372.1		4	77.69	odd	10
5929.2.a.i.1.2		2	1.1	even	1	trivial
5929.2.a.s.1.1		2	11.10	odd	2
7623.2.a.t.1.2		2	231.230	odd	2
7623.2.a.bx.1.1		2	21.20	even	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} +1.61803 q^{3} -1.85410 q^{4} -1.00000 q^{5} -0.618034 q^{6} +1.47214 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} +1.61803 q^{3} -1.85410 q^{4} -1.00000 q^{5} -0.618034 q^{6} +1.47214 q^{8} -0.381966 q^{9} +0.381966 q^{10} -3.00000 q^{12} +1.23607 q^{13} -1.61803 q^{15} +3.14590 q^{16} -3.09017 q^{17} +0.145898 q^{18} +1.76393 q^{19} +1.85410 q^{20} +5.09017 q^{23} +2.38197 q^{24} -4.00000 q^{25} -0.472136 q^{26} -5.47214 q^{27} -4.61803 q^{29} +0.618034 q^{30} +4.23607 q^{31} -4.14590 q^{32} +1.18034 q^{34} +0.708204 q^{36} +6.47214 q^{37} -0.673762 q^{38} +2.00000 q^{39} -1.47214 q^{40} +11.1803 q^{41} -12.5623 q^{43} +0.381966 q^{45} -1.94427 q^{46} +6.61803 q^{47} +5.09017 q^{48} +1.52786 q^{50} -5.00000 q^{51} -2.29180 q^{52} -2.38197 q^{53} +2.09017 q^{54} +2.85410 q^{57} +1.76393 q^{58} -11.0902 q^{59} +3.00000 q^{60} +7.61803 q^{61} -1.61803 q^{62} -4.70820 q^{64} -1.23607 q^{65} -8.32624 q^{67} +5.72949 q^{68} +8.23607 q^{69} -16.0902 q^{71} -0.562306 q^{72} +14.2361 q^{73} -2.47214 q^{74} -6.47214 q^{75} -3.27051 q^{76} -0.763932 q^{78} +6.38197 q^{79} -3.14590 q^{80} -7.70820 q^{81} -4.27051 q^{82} -2.70820 q^{83} +3.09017 q^{85} +4.79837 q^{86} -7.47214 q^{87} -6.85410 q^{89} -0.145898 q^{90} -9.43769 q^{92} +6.85410 q^{93} -2.52786 q^{94} -1.76393 q^{95} -6.70820 q^{96} -7.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} + q^{6} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 + q^6 - 6 * q^8 - 3 * q^9	\( 2 q - 3 q^{2} + q^{3} + 3 q^{4} - 2 q^{5} + q^{6} - 6 q^{8} - 3 q^{9} + 3 q^{10} - 6 q^{12} - 2 q^{13} - q^{15} + 13 q^{16} + 5 q^{17} + 7 q^{18} + 8 q^{19} - 3 q^{20} - q^{23} + 7 q^{24} - 8 q^{25} + 8 q^{26} - 2 q^{27} - 7 q^{29} - q^{30} + 4 q^{31} - 15 q^{32} - 20 q^{34} - 12 q^{36} + 4 q^{37} - 17 q^{38} + 4 q^{39} + 6 q^{40} - 5 q^{43} + 3 q^{45} + 14 q^{46} + 11 q^{47} - q^{48} + 12 q^{50} - 10 q^{51} - 18 q^{52} - 7 q^{53} - 7 q^{54} - q^{57} + 8 q^{58} - 11 q^{59} + 6 q^{60} + 13 q^{61} - q^{62} + 4 q^{64} + 2 q^{65} - q^{67} + 45 q^{68} + 12 q^{69} - 21 q^{71} + 19 q^{72} + 24 q^{73} + 4 q^{74} - 4 q^{75} + 27 q^{76} - 6 q^{78} + 15 q^{79} - 13 q^{80} - 2 q^{81} + 25 q^{82} + 8 q^{83} - 5 q^{85} - 15 q^{86} - 6 q^{87} - 7 q^{89} - 7 q^{90} - 39 q^{92} + 7 q^{93} - 14 q^{94} - 8 q^{95} - 14 q^{97}+O(q^{100}) \) 2 * q - 3 * q^2 + q^3 + 3 * q^4 - 2 * q^5 + q^6 - 6 * q^8 - 3 * q^9 + 3 * q^10 - 6 * q^12 - 2 * q^13 - q^15 + 13 * q^16 + 5 * q^17 + 7 * q^18 + 8 * q^19 - 3 * q^20 - q^23 + 7 * q^24 - 8 * q^25 + 8 * q^26 - 2 * q^27 - 7 * q^29 - q^30 + 4 * q^31 - 15 * q^32 - 20 * q^34 - 12 * q^36 + 4 * q^37 - 17 * q^38 + 4 * q^39 + 6 * q^40 - 5 * q^43 + 3 * q^45 + 14 * q^46 + 11 * q^47 - q^48 + 12 * q^50 - 10 * q^51 - 18 * q^52 - 7 * q^53 - 7 * q^54 - q^57 + 8 * q^58 - 11 * q^59 + 6 * q^60 + 13 * q^61 - q^62 + 4 * q^64 + 2 * q^65 - q^67 + 45 * q^68 + 12 * q^69 - 21 * q^71 + 19 * q^72 + 24 * q^73 + 4 * q^74 - 4 * q^75 + 27 * q^76 - 6 * q^78 + 15 * q^79 - 13 * q^80 - 2 * q^81 + 25 * q^82 + 8 * q^83 - 5 * q^85 - 15 * q^86 - 6 * q^87 - 7 * q^89 - 7 * q^90 - 39 * q^92 + 7 * q^93 - 14 * q^94 - 8 * q^95 - 14 * q^97

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