LMFDB - Embedded newform 5929.2.a.bm.1.4

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
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			1.4
Root			$-0.276564$ 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)

$f(q)$	$=$	$q+1.27656 q^{2} +2.57603 q^{3} -0.370384 q^{4} +4.09144 q^{5} +3.28847 q^{6} -3.02595 q^{8} +3.63595 q^{9} +O(q^{10})$	\(q+1.27656 q^{2} +2.57603 q^{3} -0.370384 q^{4} +4.09144 q^{5} +3.28847 q^{6} -3.02595 q^{8} +3.63595 q^{9} +5.22298 q^{10} -0.954122 q^{12} +4.39091 q^{13} +10.5397 q^{15} -3.12205 q^{16} -4.19146 q^{17} +4.64152 q^{18} +1.24880 q^{19} -1.51540 q^{20} +4.97180 q^{23} -7.79494 q^{24} +11.7399 q^{25} +5.60527 q^{26} +1.63823 q^{27} -1.93542 q^{29} +13.4546 q^{30} +1.56278 q^{31} +2.06640 q^{32} -5.35067 q^{34} -1.34670 q^{36} -0.716296 q^{37} +1.59417 q^{38} +11.3111 q^{39} -12.3805 q^{40} -4.80626 q^{41} +1.35362 q^{43} +14.8763 q^{45} +6.34682 q^{46} +10.4662 q^{47} -8.04250 q^{48} +14.9867 q^{50} -10.7973 q^{51} -1.62632 q^{52} -3.97180 q^{53} +2.09131 q^{54} +3.21695 q^{57} -2.47069 q^{58} -13.7588 q^{59} -3.90373 q^{60} +11.7271 q^{61} +1.99499 q^{62} +8.88199 q^{64} +17.9651 q^{65} +7.59274 q^{67} +1.55245 q^{68} +12.8075 q^{69} +0.218316 q^{71} -11.0022 q^{72} -10.9714 q^{73} -0.914398 q^{74} +30.2423 q^{75} -0.462535 q^{76} +14.4394 q^{78} -4.56248 q^{79} -12.7737 q^{80} -6.68771 q^{81} -6.13550 q^{82} -2.45458 q^{83} -17.1491 q^{85} +1.72798 q^{86} -4.98571 q^{87} -4.20456 q^{89} +18.9905 q^{90} -1.84148 q^{92} +4.02578 q^{93} +13.3608 q^{94} +5.10938 q^{95} +5.32312 q^{96} +10.9249 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9	$ 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9} + 8 q^{10} + 14 q^{12} - 4 q^{13} + 2 q^{15} + 8 q^{16} - 22 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{23} + 20 q^{24} + 4 q^{25} - 6 q^{26} + 2 q^{27} + 12 q^{29} + 20 q^{30} + 2 q^{31} + 8 q^{32} - 24 q^{34} + 18 q^{36} + 14 q^{37} + 22 q^{38} + 20 q^{39} - 18 q^{40} - 26 q^{41} - 4 q^{43} + 36 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 4 q^{50} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 32 q^{54} + 20 q^{57} - 2 q^{58} + 4 q^{59} + 24 q^{60} + 8 q^{61} - 20 q^{62} + 26 q^{64} + 24 q^{65} + 6 q^{67} - 12 q^{68} + 14 q^{69} + 22 q^{71} + 16 q^{72} - 14 q^{73} + 44 q^{74} + 20 q^{75} + 30 q^{76} + 32 q^{78} - 28 q^{79} + 4 q^{80} - 6 q^{81} + 4 q^{82} - 22 q^{83} - 24 q^{85} - 30 q^{86} - 22 q^{87} + 22 q^{90} + 10 q^{92} - 50 q^{93} + 38 q^{94} - 24 q^{95} + 62 q^{96} + 4 q^{97}+O(q^{100}) $ 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9 + 8 * q^10 + 14 * q^12 - 4 * q^13 + 2 * q^15 + 8 * q^16 - 22 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^23 + 20 * q^24 + 4 * q^25 - 6 * q^26 + 2 * q^27 + 12 * q^29 + 20 * q^30 + 2 * q^31 + 8 * q^32 - 24 * q^34 + 18 * q^36 + 14 * q^37 + 22 * q^38 + 20 * q^39 - 18 * q^40 - 26 * q^41 - 4 * q^43 + 36 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 4 * q^50 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 32 * q^54 + 20 * q^57 - 2 * q^58 + 4 * q^59 + 24 * q^60 + 8 * q^61 - 20 * q^62 + 26 * q^64 + 24 * q^65 + 6 * q^67 - 12 * q^68 + 14 * q^69 + 22 * q^71 + 16 * q^72 - 14 * q^73 + 44 * q^74 + 20 * q^75 + 30 * q^76 + 32 * q^78 - 28 * q^79 + 4 * q^80 - 6 * q^81 + 4 * q^82 - 22 * q^83 - 24 * q^85 - 30 * q^86 - 22 * q^87 + 22 * q^90 + 10 * q^92 - 50 * q^93 + 38 * q^94 - 24 * q^95 + 62 * q^96 + 4 * 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 $

$2$	1.27656	0.902667	0.451334	−	0.892355i	$-0.350948\pi$
$2$	1.27656	0.902667	0.451334	+	0.892355i	$0.350948\pi$
$3$	2.57603	1.48727	0.743637	−	0.668584i	$-0.233099\pi$
$3$	2.57603	1.48727	0.743637	+	0.668584i	$0.233099\pi$
$4$	−0.370384	−0.185192
$5$	4.09144	1.82975	0.914873	−	0.403741i	$-0.132290\pi$
$5$	4.09144	1.82975	0.914873	+	0.403741i	$0.132290\pi$
$6$	3.28847	1.34251
$7$	0	0
$7$	0	0
$8$	−3.02595	−1.06983
$9$	3.63595	1.21198
$10$	5.22298	1.65165
$11$	0	0
$11$	0	0
$12$	−0.954122	−0.275431
$13$	4.39091	1.21782	0.608909	−	0.793240i	$-0.291607\pi$
$13$	4.39091	1.21782	0.608909	+	0.793240i	$0.291607\pi$
$14$	0	0
$15$	10.5397	2.72133
$16$	−3.12205	−0.780512
$17$	−4.19146	−1.01658	−0.508289	−	0.861186i	$-0.669722\pi$
$17$	−4.19146	−1.01658	−0.508289	+	0.861186i	$0.669722\pi$
$18$	4.64152	1.09402
$19$	1.24880	0.286494	0.143247	−	0.989687i	$-0.454246\pi$
$19$	1.24880	0.286494	0.143247	+	0.989687i	$0.454246\pi$
$20$	−1.51540	−0.338855
$21$	0	0
$22$	0	0
$23$	4.97180	1.03669	0.518346	−	0.855171i	$-0.326548\pi$
$23$	4.97180	1.03669	0.518346	+	0.855171i	$0.326548\pi$
$24$	−7.79494	−1.59114
$25$	11.7399	2.34797
$26$	5.60527	1.09928
$27$	1.63823	0.315278
$28$	0	0
$29$	−1.93542	−0.359399	−0.179699	−	0.983722i	$-0.557512\pi$
$29$	−1.93542	−0.359399	−0.179699	+	0.983722i	$0.557512\pi$
$30$	13.4546	2.45646
$31$	1.56278	0.280684	0.140342	−	0.990103i	$-0.455180\pi$
$31$	1.56278	0.280684	0.140342	+	0.990103i	$0.455180\pi$
$32$	2.06640	0.365292
$33$	0	0
$34$	−5.35067	−0.917632
$35$	0	0
$36$	−1.34670	−0.224450
$37$	−0.716296	−0.117758	−0.0588792	−	0.998265i	$-0.518753\pi$
$37$	−0.716296	−0.117758	−0.0588792	+	0.998265i	$0.518753\pi$
$38$	1.59417	0.258609
$39$	11.3111	1.81123
$40$	−12.3805	−1.95752
$41$	−4.80626	−0.750611	−0.375306	−	0.926901i	$-0.622462\pi$
$41$	−4.80626	−0.750611	−0.375306	+	0.926901i	$0.622462\pi$
$42$	0	0
$43$	1.35362	0.206424	0.103212	−	0.994659i	$-0.467088\pi$
$43$	1.35362	0.206424	0.103212	+	0.994659i	$0.467088\pi$
$44$	0	0
$45$	14.8763	2.21762
$46$	6.34682	0.935788
$47$	10.4662	1.52665	0.763327	−	0.646013i	$-0.223565\pi$
$47$	10.4662	1.52665	0.763327	+	0.646013i	$0.223565\pi$
$48$	−8.04250	−1.16083
$49$	0	0
$50$	14.9867	2.11944
$51$	−10.7973	−1.51193
$52$	−1.62632	−0.225530
$53$	−3.97180	−0.545569	−0.272784	−	0.962075i	$-0.587945\pi$
$53$	−3.97180	−0.545569	−0.272784	+	0.962075i	$0.587945\pi$
$54$	2.09131	0.284591
$55$	0	0
$56$	0	0
$57$	3.21695	0.426095
$58$	−2.47069	−0.324417
$59$	−13.7588	−1.79125	−0.895624	−	0.444811i	$-0.853271\pi$
$59$	−13.7588	−1.79125	−0.895624	+	0.444811i	$0.853271\pi$
$60$	−3.90373	−0.503970
$61$	11.7271	1.50151	0.750753	−	0.660583i	$-0.229691\pi$
$61$	11.7271	1.50151	0.750753	+	0.660583i	$0.229691\pi$
$62$	1.99499	0.253364
$63$	0	0
$64$	8.88199	1.11025
$65$	17.9651	2.22830
$66$	0	0
$67$	7.59274	0.927600	0.463800	−	0.885940i	$-0.346486\pi$
$67$	7.59274	0.927600	0.463800	+	0.885940i	$0.346486\pi$
$68$	1.55245	0.188262
$69$	12.8075	1.54185
$70$	0	0
$71$	0.218316	0.0259094	0.0129547	−	0.999916i	$-0.495876\pi$
$71$	0.218316	0.0259094	0.0129547	+	0.999916i	$0.495876\pi$
$72$	−11.0022	−1.29662
$73$	−10.9714	−1.28411	−0.642054	−	0.766659i	$-0.721918\pi$
$73$	−10.9714	−1.28411	−0.642054	+	0.766659i	$0.721918\pi$
$74$	−0.914398	−0.106297
$75$	30.2423	3.49208
$76$	−0.462535	−0.0530564
$77$	0	0
$78$	14.4394	1.63494
$79$	−4.56248	−0.513319	−0.256659	−	0.966502i	$-0.582622\pi$
$79$	−4.56248	−0.513319	−0.256659	+	0.966502i	$0.582622\pi$
$80$	−12.7737	−1.42814
$81$	−6.68771	−0.743079
$82$	−6.13550	−0.677552
$83$	−2.45458	−0.269425	−0.134712	−	0.990885i	$-0.543011\pi$
$83$	−2.45458	−0.269425	−0.134712	+	0.990885i	$0.543011\pi$
$84$	0	0
$85$	−17.1491	−1.86008
$86$	1.72798	0.186333
$87$	−4.98571	−0.534524
$88$	0	0
$89$	−4.20456	−0.445683	−0.222841	−	0.974855i	$-0.571533\pi$
$89$	−4.20456	−0.445683	−0.222841	+	0.974855i	$0.571533\pi$
$90$	18.9905	2.00178
$91$	0	0
$92$	−1.84148	−0.191987
$93$	4.02578	0.417454
$94$	13.3608	1.37806
$95$	5.10938	0.524211
$96$	5.32312	0.543289
$97$	10.9249	1.10925	0.554627	−	0.832099i	$-0.312861\pi$
$97$	10.9249	1.10925	0.554627	+	0.832099i	$0.312861\pi$
$98$	0	0
$99$	0	0
$100$	−4.34826	−0.434826
$101$	−7.36579	−0.732924	−0.366462	−	0.930433i	$-0.619431\pi$
$101$	−7.36579	−0.732924	−0.366462	+	0.930433i	$0.619431\pi$
$102$	−13.7835	−1.36477
$103$	0.153886	0.0151629	0.00758143	−	0.999971i	$-0.497587\pi$
$103$	0.153886	0.0151629	0.00758143	+	0.999971i	$0.497587\pi$
$104$	−13.2867	−1.30286
$105$	0	0
$106$	−5.07026	−0.492467
$107$	7.94617	0.768185	0.384092	−	0.923295i	$-0.374514\pi$
$107$	7.94617	0.768185	0.384092	+	0.923295i	$0.374514\pi$
$108$	−0.606775	−0.0583869
$109$	−4.91440	−0.470714	−0.235357	−	0.971909i	$-0.575626\pi$
$109$	−4.91440	−0.470714	−0.235357	+	0.971909i	$0.575626\pi$
$110$	0	0
$111$	−1.84520	−0.175139
$112$	0	0
$113$	3.04208	0.286175	0.143088	−	0.989710i	$-0.454297\pi$
$113$	3.04208	0.286175	0.143088	+	0.989710i	$0.454297\pi$
$114$	4.10664	0.384622
$115$	20.3418	1.89688
$116$	0.716849	0.0665578
$117$	15.9651	1.47598
$118$	−17.5640	−1.61690
$119$	0	0
$120$	−31.8925	−2.91138
$121$	0	0
$122$	14.9704	1.35536
$123$	−12.3811	−1.11636
$124$	−0.578830	−0.0519804
$125$	27.5757	2.46645
$126$	0	0
$127$	−10.7954	−0.957932	−0.478966	−	0.877833i	$-0.658988\pi$
$127$	−10.7954	−0.957932	−0.478966	+	0.877833i	$0.658988\pi$
$128$	7.20562	0.636893
$129$	3.48696	0.307010
$130$	22.9336	2.01141
$131$	8.70429	0.760497	0.380249	−	0.924884i	$-0.375838\pi$
$131$	8.70429	0.760497	0.380249	+	0.924884i	$0.375838\pi$
$132$	0	0
$133$	0	0
$134$	9.69261	0.837314
$135$	6.70272	0.576878
$136$	12.6831	1.08757
$137$	11.9977	1.02503	0.512516	−	0.858677i	$-0.328713\pi$
$137$	11.9977	1.02503	0.512516	+	0.858677i	$0.328713\pi$
$138$	16.3496	1.39177
$139$	−8.18967	−0.694639	−0.347319	−	0.937747i	$-0.612908\pi$
$139$	−8.18967	−0.694639	−0.347319	+	0.937747i	$0.612908\pi$
$140$	0	0
$141$	26.9613	2.27055
$142$	0.278695	0.0233875
$143$	0	0
$144$	−11.3516	−0.945968
$145$	−7.91865	−0.657608
$146$	−14.0057	−1.15912
$147$	0	0
$148$	0.265305	0.0218079
$149$	12.0816	0.989766	0.494883	−	0.868960i	$-0.335211\pi$
$149$	12.0816	0.989766	0.494883	+	0.868960i	$0.335211\pi$
$150$	38.6062	3.15218
$151$	−6.94850	−0.565461	−0.282730	−	0.959199i	$-0.591240\pi$
$151$	−6.94850	−0.565461	−0.282730	+	0.959199i	$0.591240\pi$
$152$	−3.77880	−0.306501
$153$	−15.2399	−1.23208
$154$	0	0
$155$	6.39402	0.513580
$156$	−4.18946	−0.335425
$157$	−10.4930	−0.837436	−0.418718	−	0.908116i	$-0.637520\pi$
$157$	−10.4930	−0.837436	−0.418718	+	0.908116i	$0.637520\pi$
$158$	−5.82429	−0.463356
$159$	−10.2315	−0.811410
$160$	8.45455	0.668391
$161$	0	0
$162$	−8.53730	−0.670753
$163$	−7.81743	−0.612309	−0.306154	−	0.951982i	$-0.599042\pi$
$163$	−7.81743	−0.612309	−0.306154	+	0.951982i	$0.599042\pi$
$164$	1.78016	0.139007
$165$	0	0
$166$	−3.13342	−0.243201
$167$	−21.3503	−1.65214	−0.826068	−	0.563571i	$-0.809427\pi$
$167$	−21.3503	−1.65214	−0.826068	+	0.563571i	$0.809427\pi$
$168$	0	0
$169$	6.28007	0.483082
$170$	−21.8919	−1.67903
$171$	4.54057	0.347226
$172$	−0.501358	−0.0382282
$173$	−19.4384	−1.47787	−0.738936	−	0.673776i	$-0.764671\pi$
$173$	−19.4384	−1.47787	−0.738936	+	0.673776i	$0.764671\pi$
$174$	−6.36458	−0.482497
$175$	0	0
$176$	0	0
$177$	−35.4432	−2.66408
$178$	−5.36740	−0.402303
$179$	17.9964	1.34511	0.672557	−	0.740045i	$-0.265196\pi$
$179$	17.9964	1.34511	0.672557	+	0.740045i	$0.265196\pi$
$180$	−5.50993	−0.410686
$181$	−15.1575	−1.12665	−0.563326	−	0.826235i	$-0.690478\pi$
$181$	−15.1575	−1.12665	−0.563326	+	0.826235i	$0.690478\pi$
$182$	0	0
$183$	30.2095	2.23315
$184$	−15.0444	−1.10909
$185$	−2.93068	−0.215468
$186$	5.13916	0.376822
$187$	0	0
$188$	−3.87652	−0.282724
$189$	0	0
$190$	6.52245	0.473188
$191$	−23.7574	−1.71903	−0.859513	−	0.511115i	$-0.829233\pi$
$191$	−23.7574	−1.71903	−0.859513	+	0.511115i	$0.829233\pi$
$192$	22.8803	1.65124
$193$	14.0582	1.01193	0.505965	−	0.862554i	$-0.331137\pi$
$193$	14.0582	1.01193	0.505965	+	0.862554i	$0.331137\pi$
$194$	13.9463	1.00129
$195$	46.2788	3.31409
$196$	0	0
$197$	18.0665	1.28718	0.643591	−	0.765369i	$-0.277444\pi$
$197$	18.0665	1.28718	0.643591	+	0.765369i	$0.277444\pi$
$198$	0	0
$199$	−1.54374	−0.109433	−0.0547163	−	0.998502i	$-0.517425\pi$
$199$	−1.54374	−0.109433	−0.0547163	+	0.998502i	$0.517425\pi$
$200$	−35.5242	−2.51194
$201$	19.5591	1.37960
$202$	−9.40291	−0.661586
$203$	0	0
$204$	3.99917	0.279998
$205$	−19.6645	−1.37343
$206$	0.196446	0.0136870
$207$	18.0772	1.25645
$208$	−13.7086	−0.950522
$209$	0	0
$210$	0	0
$211$	−22.0836	−1.52030	−0.760149	−	0.649749i	$-0.774874\pi$
$211$	−22.0836	−1.52030	−0.760149	+	0.649749i	$0.774874\pi$
$212$	1.47109	0.101035
$213$	0.562390	0.0385343
$214$	10.1438	0.693415
$215$	5.53824	0.377704
$216$	−4.95720	−0.337295
$217$	0	0
$218$	−6.27354	−0.424898
$219$	−28.2628	−1.90982
$220$	0	0
$221$	−18.4043	−1.23801
$222$	−2.35552	−0.158092
$223$	8.57414	0.574167	0.287083	−	0.957906i	$-0.407314\pi$
$223$	8.57414	0.574167	0.287083	+	0.957906i	$0.407314\pi$
$224$	0	0
$225$	42.6856	2.84570
$226$	3.88342	0.258321
$227$	26.5709	1.76357	0.881786	−	0.471650i	$-0.156341\pi$
$227$	26.5709	1.76357	0.881786	+	0.471650i	$0.156341\pi$
$228$	−1.19151	−0.0789094
$229$	−11.4113	−0.754081	−0.377040	−	0.926197i	$-0.623058\pi$
$229$	−11.4113	−0.754081	−0.377040	+	0.926197i	$0.623058\pi$
$230$	25.9676	1.71225
$231$	0	0
$232$	5.85648	0.384497
$233$	26.6130	1.74348	0.871738	−	0.489972i	$-0.162993\pi$
$233$	26.6130	1.74348	0.871738	+	0.489972i	$0.162993\pi$
$234$	20.3805	1.33232
$235$	42.8218	2.79339
$236$	5.09606	0.331725
$237$	−11.7531	−0.763445
$238$	0	0
$239$	−7.51280	−0.485963	−0.242981	−	0.970031i	$-0.578125\pi$
$239$	−7.51280	−0.485963	−0.242981	+	0.970031i	$0.578125\pi$
$240$	−32.9054	−2.12403
$241$	−27.4388	−1.76749	−0.883744	−	0.467971i	$-0.844985\pi$
$241$	−27.4388	−1.76749	−0.883744	+	0.467971i	$0.844985\pi$
$242$	0	0
$243$	−22.1425	−1.42044
$244$	−4.34355	−0.278067
$245$	0	0
$246$	−15.8052	−1.00771
$247$	5.48336	0.348898
$248$	−4.72889	−0.300285
$249$	−6.32307	−0.400708
$250$	35.2022	2.22638
$251$	−1.92514	−0.121514	−0.0607568	−	0.998153i	$-0.519351\pi$
$251$	−1.92514	−0.121514	−0.0607568	+	0.998153i	$0.519351\pi$
$252$	0	0
$253$	0	0
$254$	−13.7810	−0.864694
$255$	−44.1767	−2.76645
$256$	−8.56553	−0.535346
$257$	−10.1604	−0.633791	−0.316895	−	0.948460i	$-0.602640\pi$
$257$	−10.1604	−0.633791	−0.316895	+	0.948460i	$0.602640\pi$
$258$	4.45133	0.277128
$259$	0	0
$260$	−6.65400	−0.412663
$261$	−7.03709	−0.435585
$262$	11.1116	0.686476
$263$	−4.38774	−0.270560	−0.135280	−	0.990807i	$-0.543193\pi$
$263$	−4.38774	−0.270560	−0.135280	+	0.990807i	$0.543193\pi$
$264$	0	0
$265$	−16.2504	−0.998253
$266$	0	0
$267$	−10.8311	−0.662853
$268$	−2.81223	−0.171784
$269$	−0.625379	−0.0381300	−0.0190650	−	0.999818i	$-0.506069\pi$
$269$	−0.625379	−0.0381300	−0.0190650	+	0.999818i	$0.506069\pi$
$270$	8.55645	0.520729
$271$	11.9375	0.725151	0.362575	−	0.931954i	$-0.381898\pi$
$271$	11.9375	0.725151	0.362575	+	0.931954i	$0.381898\pi$
$272$	13.0859	0.793452
$273$	0	0
$274$	15.3158	0.925263
$275$	0	0
$276$	−4.74371	−0.285538
$277$	28.5571	1.71583	0.857915	−	0.513792i	$-0.171760\pi$
$277$	28.5571	1.71583	0.857915	+	0.513792i	$0.171760\pi$
$278$	−10.4546	−0.627028
$279$	5.68220	0.340184
$280$	0	0
$281$	14.6981	0.876814	0.438407	−	0.898777i	$-0.355543\pi$
$281$	14.6981	0.876814	0.438407	+	0.898777i	$0.355543\pi$
$282$	34.4178	2.04955
$283$	−22.5396	−1.33984	−0.669921	−	0.742433i	$-0.733672\pi$
$283$	−22.5396	−1.33984	−0.669921	+	0.742433i	$0.733672\pi$
$284$	−0.0808609	−0.00479821
$285$	13.1619	0.779646
$286$	0	0
$287$	0	0
$288$	7.51333	0.442727
$289$	0.568350	0.0334323
$290$	−10.1087	−0.593601
$291$	28.1429	1.64976
$292$	4.06364	0.237807
$293$	−16.8280	−0.983105	−0.491553	−	0.870848i	$-0.663570\pi$
$293$	−16.8280	−0.983105	−0.491553	+	0.870848i	$0.663570\pi$
$294$	0	0
$295$	−56.2934	−3.27753
$296$	2.16747	0.125982
$297$	0	0
$298$	15.4230	0.893429
$299$	21.8307	1.26250
$300$	−11.2013	−0.646705
$301$	0	0
$302$	−8.87021	−0.510423
$303$	−18.9745	−1.09006
$304$	−3.89881	−0.223612
$305$	47.9808	2.74738
$306$	−19.4548	−1.11216
$307$	−0.238354	−0.0136036	−0.00680179	−	0.999977i	$-0.502165\pi$
$307$	−0.238354	−0.0136036	−0.00680179	+	0.999977i	$0.502165\pi$
$308$	0	0
$309$	0.396416	0.0225513
$310$	8.16238	0.463592
$311$	0.656523	0.0372280	0.0186140	−	0.999827i	$-0.494075\pi$
$311$	0.656523	0.0372280	0.0186140	+	0.999827i	$0.494075\pi$
$312$	−34.2269	−1.93772
$313$	7.45262	0.421247	0.210624	−	0.977567i	$-0.432451\pi$
$313$	7.45262	0.421247	0.210624	+	0.977567i	$0.432451\pi$
$314$	−13.3950	−0.755926
$315$	0	0
$316$	1.68987	0.0950625
$317$	17.4412	0.979595	0.489797	−	0.871836i	$-0.337071\pi$
$317$	17.4412	0.979595	0.489797	+	0.871836i	$0.337071\pi$
$318$	−13.0612	−0.732433
$319$	0	0
$320$	36.3401	2.03147
$321$	20.4696	1.14250
$322$	0	0
$323$	−5.23429	−0.291244
$324$	2.47702	0.137612
$325$	51.5486	2.85940
$326$	−9.97946	−0.552711
$327$	−12.6597	−0.700081
$328$	14.5435	0.803030
$329$	0	0
$330$	0	0
$331$	−28.6146	−1.57280	−0.786399	−	0.617719i	$-0.788057\pi$
$331$	−28.6146	−1.57280	−0.786399	+	0.617719i	$0.788057\pi$
$332$	0.909136	0.0498953
$333$	−2.60442	−0.142721
$334$	−27.2550	−1.49133
$335$	31.0652	1.69727
$336$	0	0
$337$	1.73053	0.0942679	0.0471339	−	0.998889i	$-0.484991\pi$
$337$	1.73053	0.0942679	0.0471339	+	0.998889i	$0.484991\pi$
$338$	8.01691	0.436062
$339$	7.83651	0.425621
$340$	6.35176	0.344472
$341$	0	0
$342$	5.79633	0.313430
$343$	0	0
$344$	−4.09597	−0.220840
$345$	52.4012	2.82119
$346$	−24.8143	−1.33403
$347$	2.73009	0.146559	0.0732796	−	0.997311i	$-0.476653\pi$
$347$	2.73009	0.146559	0.0732796	+	0.997311i	$0.476653\pi$
$348$	1.84663	0.0989896
$349$	−30.9063	−1.65437	−0.827187	−	0.561927i	$-0.810060\pi$
$349$	−30.9063	−1.65437	−0.827187	+	0.561927i	$0.810060\pi$
$350$	0	0
$351$	7.19332	0.383951
$352$	0	0
$353$	23.9543	1.27496	0.637480	−	0.770467i	$-0.279977\pi$
$353$	23.9543	1.27496	0.637480	+	0.770467i	$0.279977\pi$
$354$	−45.2456	−2.40478
$355$	0.893227	0.0474076
$356$	1.55730	0.0825369
$357$	0	0
$358$	22.9736	1.21419
$359$	−1.51611	−0.0800170	−0.0400085	−	0.999199i	$-0.512739\pi$
$359$	−1.51611	−0.0800170	−0.0400085	+	0.999199i	$0.512739\pi$
$360$	−45.0148	−2.37249
$361$	−17.4405	−0.917921
$362$	−19.3496	−1.01699
$363$	0	0
$364$	0	0
$365$	−44.8889	−2.34959
$366$	38.5644	2.01579
$367$	−8.72207	−0.455288	−0.227644	−	0.973744i	$-0.573102\pi$
$367$	−8.72207	−0.455288	−0.227644	+	0.973744i	$0.573102\pi$
$368$	−15.5222	−0.809151
$369$	−17.4753	−0.909729
$370$	−3.74120	−0.194496
$371$	0	0
$372$	−1.49108	−0.0773091
$373$	−36.8111	−1.90601	−0.953004	−	0.302957i	$-0.902026\pi$
$373$	−36.8111	−1.90601	−0.953004	+	0.302957i	$0.902026\pi$
$374$	0	0
$375$	71.0360	3.66828
$376$	−31.6702	−1.63327
$377$	−8.49825	−0.437682
$378$	0	0
$379$	2.59838	0.133470	0.0667349	−	0.997771i	$-0.478742\pi$
$379$	2.59838	0.133470	0.0667349	+	0.997771i	$0.478742\pi$
$380$	−1.89243	−0.0970798
$381$	−27.8092	−1.42471
$382$	−30.3278	−1.55171
$383$	−19.2392	−0.983078	−0.491539	−	0.870856i	$-0.663565\pi$
$383$	−19.2392	−0.983078	−0.491539	+	0.870856i	$0.663565\pi$
$384$	18.5619	0.947235
$385$	0	0
$386$	17.9462	0.913435
$387$	4.92168	0.250183
$388$	−4.04640	−0.205425
$389$	−28.3331	−1.43654	−0.718272	−	0.695762i	$-0.755067\pi$
$389$	−28.3331	−1.43654	−0.718272	+	0.695762i	$0.755067\pi$
$390$	59.0778	2.99152
$391$	−20.8391	−1.05388
$392$	0	0
$393$	22.4225	1.13107
$394$	23.0630	1.16190
$395$	−18.6671	−0.939243
$396$	0	0
$397$	10.3666	0.520287	0.260143	−	0.965570i	$-0.416230\pi$
$397$	10.3666	0.520287	0.260143	+	0.965570i	$0.416230\pi$
$398$	−1.97068	−0.0987812
$399$	0	0
$400$	−36.6524	−1.83262
$401$	−12.7878	−0.638592	−0.319296	−	0.947655i	$-0.603446\pi$
$401$	−12.7878	−0.638592	−0.319296	+	0.947655i	$0.603446\pi$
$402$	24.9685	1.24532
$403$	6.86203	0.341822
$404$	2.72817	0.135732
$405$	−27.3624	−1.35965
$406$	0	0
$407$	0	0
$408$	32.6722	1.61752
$409$	32.0217	1.58337	0.791686	−	0.610928i	$-0.209203\pi$
$409$	32.0217	1.58337	0.791686	+	0.610928i	$0.209203\pi$
$410$	−25.1030	−1.23975
$411$	30.9065	1.52450
$412$	−0.0569970	−0.00280804
$413$	0	0
$414$	23.0767	1.13416
$415$	−10.0427	−0.492979
$416$	9.07338	0.444859
$417$	−21.0969	−1.03312
$418$	0	0
$419$	20.0934	0.981629	0.490815	−	0.871264i	$-0.336699\pi$
$419$	20.0934	0.981629	0.490815	+	0.871264i	$0.336699\pi$
$420$	0	0
$421$	−22.4243	−1.09289	−0.546446	−	0.837494i	$-0.684020\pi$
$421$	−22.4243	−1.09289	−0.546446	+	0.837494i	$0.684020\pi$
$422$	−28.1911	−1.37232
$423$	38.0546	1.85028
$424$	12.0185	0.583668
$425$	−49.2072	−2.38690
$426$	0.717927	0.0347837
$427$	0	0
$428$	−2.94313	−0.142262
$429$	0	0
$430$	7.06991	0.340941
$431$	12.0856	0.582144	0.291072	−	0.956701i	$-0.405988\pi$
$431$	12.0856	0.582144	0.291072	+	0.956701i	$0.405988\pi$
$432$	−5.11463	−0.246078
$433$	0.302453	0.0145350	0.00726749	−	0.999974i	$-0.497687\pi$
$433$	0.302453	0.0145350	0.00726749	+	0.999974i	$0.497687\pi$
$434$	0	0
$435$	−20.3987	−0.978044
$436$	1.82022	0.0871725
$437$	6.20878	0.297006
$438$	−36.0792	−1.72393
$439$	3.52592	0.168283	0.0841416	−	0.996454i	$-0.473185\pi$
$439$	3.52592	0.168283	0.0841416	+	0.996454i	$0.473185\pi$
$440$	0	0
$441$	0	0
$442$	−23.4943	−1.11751
$443$	−21.8443	−1.03786	−0.518928	−	0.854818i	$-0.673669\pi$
$443$	−21.8443	−1.03786	−0.518928	+	0.854818i	$0.673669\pi$
$444$	0.683434	0.0324343
$445$	−17.2027	−0.815487
$446$	10.9454	0.518281
$447$	31.1227	1.47205
$448$	0	0
$449$	9.30172	0.438975	0.219488	−	0.975615i	$-0.429561\pi$
$449$	9.30172	0.438975	0.219488	+	0.975615i	$0.429561\pi$
$450$	54.4908	2.56872
$451$	0	0
$452$	−1.12674	−0.0529974
$453$	−17.8996	−0.840995
$454$	33.9194	1.59192
$455$	0	0
$456$	−9.73431	−0.455851
$457$	−11.3165	−0.529365	−0.264683	−	0.964336i	$-0.585267\pi$
$457$	−11.3165	−0.529365	−0.264683	+	0.964336i	$0.585267\pi$
$458$	−14.5673	−0.680684
$459$	−6.86658	−0.320505
$460$	−7.53429	−0.351288
$461$	0.678821	0.0316158	0.0158079	−	0.999875i	$-0.494968\pi$
$461$	0.678821	0.0316158	0.0158079	+	0.999875i	$0.494968\pi$
$462$	0	0
$463$	−13.4936	−0.627103	−0.313551	−	0.949571i	$-0.601519\pi$
$463$	−13.4936	−0.627103	−0.313551	+	0.949571i	$0.601519\pi$
$464$	6.04247	0.280515
$465$	16.4712	0.763835
$466$	33.9732	1.57378
$467$	−29.6568	−1.37235	−0.686176	−	0.727435i	$-0.740712\pi$
$467$	−29.6568	−1.37235	−0.686176	+	0.727435i	$0.740712\pi$
$468$	−5.91323	−0.273339
$469$	0	0
$470$	54.6648	2.52150
$471$	−27.0304	−1.24550
$472$	41.6335	1.91634
$473$	0	0
$474$	−15.0036	−0.689137
$475$	14.6607	0.672680
$476$	0	0
$477$	−14.4413	−0.661220
$478$	−9.59057	−0.438662
$479$	−4.70136	−0.214811	−0.107405	−	0.994215i	$-0.534254\pi$
$479$	−4.70136	−0.214811	−0.107405	+	0.994215i	$0.534254\pi$
$480$	21.7792	0.994080
$481$	−3.14519	−0.143408
$482$	−35.0274	−1.59545
$483$	0	0
$484$	0	0
$485$	44.6985	2.02965
$486$	−28.2663	−1.28218
$487$	32.3738	1.46700	0.733498	−	0.679692i	$-0.237886\pi$
$487$	32.3738	1.46700	0.733498	+	0.679692i	$0.237886\pi$
$488$	−35.4857	−1.60636
$489$	−20.1380	−0.910671
$490$	0	0
$491$	−6.85594	−0.309404	−0.154702	−	0.987961i	$-0.549442\pi$
$491$	−6.85594	−0.309404	−0.154702	+	0.987961i	$0.549442\pi$
$492$	4.58576	0.206742
$493$	8.11224	0.365357
$494$	6.99986	0.314939
$495$	0	0
$496$	−4.87908	−0.219077
$497$	0	0
$498$	−8.07181	−0.361706
$499$	10.9670	0.490952	0.245476	−	0.969403i	$-0.421056\pi$
$499$	10.9670	0.490952	0.245476	+	0.969403i	$0.421056\pi$
$500$	−10.2136	−0.456766
$501$	−54.9991	−2.45718
$502$	−2.45756	−0.109686
$503$	26.9334	1.20090	0.600451	−	0.799662i	$-0.294988\pi$
$503$	26.9334	1.20090	0.600451	+	0.799662i	$0.294988\pi$
$504$	0	0
$505$	−30.1367	−1.34106
$506$	0	0
$507$	16.1777	0.718475
$508$	3.99843	0.177402
$509$	−30.3958	−1.34727	−0.673635	−	0.739064i	$-0.735268\pi$
$509$	−30.3958	−1.34727	−0.673635	+	0.739064i	$0.735268\pi$
$510$	−56.3944	−2.49718
$511$	0	0
$512$	−25.3457	−1.12013
$513$	2.04582	0.0903252
$514$	−12.9705	−0.572102
$515$	0.629616	0.0277442
$516$	−1.29151	−0.0568558
$517$	0	0
$518$	0	0
$519$	−50.0739	−2.19800
$520$	−54.3615	−2.38391
$521$	0.935426	0.0409818	0.0204909	−	0.999790i	$-0.493477\pi$
$521$	0.935426	0.0409818	0.0204909	+	0.999790i	$0.493477\pi$
$522$	−8.98330	−0.393188
$523$	−26.1853	−1.14500	−0.572502	−	0.819903i	$-0.694027\pi$
$523$	−26.1853	−1.14500	−0.572502	+	0.819903i	$0.694027\pi$
$524$	−3.22393	−0.140838
$525$	0	0
$526$	−5.60124	−0.244226
$527$	−6.55034	−0.285337
$528$	0	0
$529$	1.71881	0.0747307
$530$	−20.7446	−0.901090
$531$	−50.0265	−2.17096
$532$	0	0
$533$	−21.1038	−0.914109
$534$	−13.8266	−0.598335
$535$	32.5112	1.40558
$536$	−22.9752	−0.992378
$537$	46.3594	2.00055
$538$	−0.798336	−0.0344187
$539$	0	0
$540$	−2.48258	−0.106833
$541$	26.7566	1.15035	0.575177	−	0.818029i	$-0.304933\pi$
$541$	26.7566	1.15035	0.575177	+	0.818029i	$0.304933\pi$
$542$	15.2390	0.654570
$543$	−39.0464	−1.67564
$544$	−8.66124	−0.371348
$545$	−20.1070	−0.861287
$546$	0	0
$547$	46.4581	1.98641	0.993203	−	0.116397i	$-0.0371345\pi$
$547$	46.4581	1.98641	0.993203	+	0.116397i	$0.0371345\pi$
$548$	−4.44376	−0.189828
$549$	42.6393	1.81980
$550$	0	0
$551$	−2.41695	−0.102966
$552$	−38.7549	−1.64952
$553$	0	0
$554$	36.4550	1.54882
$555$	−7.54953	−0.320460
$556$	3.03332	0.128642
$557$	35.0974	1.48712	0.743562	−	0.668667i	$-0.233135\pi$
$557$	35.0974	1.48712	0.743562	+	0.668667i	$0.233135\pi$
$558$	7.25369	0.307073
$559$	5.94360	0.251388
$560$	0	0
$561$	0	0
$562$	18.7630	0.791471
$563$	8.94791	0.377109	0.188555	−	0.982063i	$-0.439620\pi$
$563$	8.94791	0.377109	0.188555	+	0.982063i	$0.439620\pi$
$564$	−9.98604	−0.420488
$565$	12.4465	0.523628
$566$	−28.7733	−1.20943
$567$	0	0
$568$	−0.660614	−0.0277187
$569$	19.4256	0.814365	0.407183	−	0.913347i	$-0.366511\pi$
$569$	19.4256	0.814365	0.407183	+	0.913347i	$0.366511\pi$
$570$	16.8021	0.703761
$571$	16.0171	0.670295	0.335148	−	0.942166i	$-0.391214\pi$
$571$	16.0171	0.670295	0.335148	+	0.942166i	$0.391214\pi$
$572$	0	0
$573$	−61.1999	−2.55666
$574$	0	0
$575$	58.3683	2.43412
$576$	32.2945	1.34560
$577$	32.9192	1.37044	0.685222	−	0.728335i	$-0.259705\pi$
$577$	32.9192	1.37044	0.685222	+	0.728335i	$0.259705\pi$
$578$	0.725535	0.0301783
$579$	36.2143	1.50502
$580$	2.93294	0.121784
$581$	0	0
$582$	35.9262	1.48919
$583$	0	0
$584$	33.1990	1.37378
$585$	65.3203	2.70066
$586$	−21.4821	−0.887417
$587$	−27.4372	−1.13246	−0.566228	−	0.824249i	$-0.691598\pi$
$587$	−27.4372	−1.13246	−0.566228	+	0.824249i	$0.691598\pi$
$588$	0	0
$589$	1.95160	0.0804142
$590$	−71.8622	−2.95852
$591$	46.5398	1.91439
$592$	2.23631	0.0919118
$593$	−14.6132	−0.600092	−0.300046	−	0.953925i	$-0.597002\pi$
$593$	−14.6132	−0.600092	−0.300046	+	0.953925i	$0.597002\pi$
$594$	0	0
$595$	0	0
$596$	−4.47485	−0.183297
$597$	−3.97672	−0.162756
$598$	27.8683	1.13962
$599$	25.2765	1.03277	0.516384	−	0.856357i	$-0.327278\pi$
$599$	25.2765	1.03277	0.516384	+	0.856357i	$0.327278\pi$
$600$	−91.5115	−3.73594
$601$	9.30098	0.379395	0.189697	−	0.981843i	$-0.439249\pi$
$601$	9.30098	0.379395	0.189697	+	0.981843i	$0.439249\pi$
$602$	0	0
$603$	27.6068	1.12424
$604$	2.57361	0.104719
$605$	0	0
$606$	−24.2222	−0.983960
$607$	2.12671	0.0863207	0.0431603	−	0.999068i	$-0.486257\pi$
$607$	2.12671	0.0863207	0.0431603	+	0.999068i	$0.486257\pi$
$608$	2.58052	0.104654
$609$	0	0
$610$	61.2506	2.47997
$611$	45.9561	1.85919
$612$	5.64463	0.228171
$613$	−40.9448	−1.65374	−0.826872	−	0.562390i	$-0.809882\pi$
$613$	−40.9448	−1.65374	−0.826872	+	0.562390i	$0.809882\pi$
$614$	−0.304274	−0.0122795
$615$	−50.6564	−2.04266
$616$	0	0
$617$	−7.53813	−0.303474	−0.151737	−	0.988421i	$-0.548487\pi$
$617$	−7.53813	−0.303474	−0.151737	+	0.988421i	$0.548487\pi$
$618$	0.506051	0.0203563
$619$	19.5055	0.783994	0.391997	−	0.919967i	$-0.371784\pi$
$619$	19.5055	0.783994	0.391997	+	0.919967i	$0.371784\pi$
$620$	−2.36824	−0.0951110
$621$	8.14496	0.326846
$622$	0.838094	0.0336045
$623$	0	0
$624$	−35.3139	−1.41369
$625$	54.1250	2.16500
$626$	9.51375	0.380246
$627$	0	0
$628$	3.88645	0.155086
$629$	3.00233	0.119711
$630$	0	0
$631$	−10.6654	−0.424582	−0.212291	−	0.977207i	$-0.568092\pi$
$631$	−10.6654	−0.424582	−0.212291	+	0.977207i	$0.568092\pi$
$632$	13.8058	0.549166
$633$	−56.8881	−2.26110
$634$	22.2648	0.884248
$635$	−44.1685	−1.75277
$636$	3.78958	0.150267
$637$	0	0
$638$	0	0
$639$	0.793787	0.0314017
$640$	29.4814	1.16535
$641$	0.448349	0.0177087	0.00885436	−	0.999961i	$-0.497182\pi$
$641$	0.448349	0.0177087	0.00885436	+	0.999961i	$0.497182\pi$
$642$	26.1307	1.03130
$643$	31.6440	1.24792	0.623958	−	0.781458i	$-0.285524\pi$
$643$	31.6440	1.24792	0.623958	+	0.781458i	$0.285524\pi$
$644$	0	0
$645$	14.2667	0.561750
$646$	−6.68191	−0.262896
$647$	30.1242	1.18430	0.592152	−	0.805826i	$-0.298279\pi$
$647$	30.1242	1.18430	0.592152	+	0.805826i	$0.298279\pi$
$648$	20.2367	0.794972
$649$	0	0
$650$	65.8051	2.58109
$651$	0	0
$652$	2.89545	0.113395
$653$	34.6110	1.35443	0.677217	−	0.735784i	$-0.263186\pi$
$653$	34.6110	1.35443	0.677217	+	0.735784i	$0.263186\pi$
$654$	−16.1609	−0.631940
$655$	35.6131	1.39152
$656$	15.0054	0.585861
$657$	−39.8916	−1.55632
$658$	0	0
$659$	−20.2587	−0.789167	−0.394584	−	0.918860i	$-0.629111\pi$
$659$	−20.2587	−0.789167	−0.394584	+	0.918860i	$0.629111\pi$
$660$	0	0
$661$	−40.6737	−1.58202	−0.791012	−	0.611801i	$-0.790445\pi$
$661$	−40.6737	−1.58202	−0.791012	+	0.611801i	$0.790445\pi$
$662$	−36.5283	−1.41971
$663$	−47.4102	−1.84126
$664$	7.42742	0.288240
$665$	0	0
$666$	−3.32471	−0.128830
$667$	−9.62253	−0.372586
$668$	7.90781	0.305962
$669$	22.0873	0.853943
$670$	39.6567	1.53207
$671$	0	0
$672$	0	0
$673$	24.7484	0.953980	0.476990	−	0.878909i	$-0.341728\pi$
$673$	24.7484	0.953980	0.476990	+	0.878909i	$0.341728\pi$
$674$	2.20913	0.0850925
$675$	19.2326	0.740263
$676$	−2.32604	−0.0894630
$677$	11.3821	0.437452	0.218726	−	0.975786i	$-0.429810\pi$
$677$	11.3821	0.437452	0.218726	+	0.975786i	$0.429810\pi$
$678$	10.0038	0.384194
$679$	0	0
$680$	51.8923	1.98998
$681$	68.4475	2.62291
$682$	0	0
$683$	−0.212700	−0.00813875	−0.00406938	−	0.999992i	$-0.501295\pi$
$683$	−0.212700	−0.00813875	−0.00406938	+	0.999992i	$0.501295\pi$
$684$	−1.68176	−0.0643035
$685$	49.0878	1.87555
$686$	0	0
$687$	−29.3959	−1.12152
$688$	−4.22605	−0.161117
$689$	−17.4398	−0.664404
$690$	66.8935	2.54659
$691$	−36.3804	−1.38398	−0.691988	−	0.721909i	$-0.743265\pi$
$691$	−36.3804	−1.38398	−0.691988	+	0.721909i	$0.743265\pi$
$692$	7.19966	0.273690
$693$	0	0
$694$	3.48514	0.132294
$695$	−33.5075	−1.27101
$696$	15.0865	0.571852
$697$	20.1452	0.763056
$698$	−39.4538	−1.49335
$699$	68.5560	2.59303
$700$	0	0
$701$	−18.7394	−0.707779	−0.353889	−	0.935287i	$-0.615141\pi$
$701$	−18.7394	−0.707779	−0.353889	+	0.935287i	$0.615141\pi$
$702$	9.18273	0.346580
$703$	−0.894509	−0.0337371
$704$	0	0
$705$	110.310	4.15453
$706$	30.5792	1.15086
$707$	0	0
$708$	13.1276	0.493366
$709$	−12.7596	−0.479195	−0.239598	−	0.970872i	$-0.577015\pi$
$709$	−12.7596	−0.479195	−0.239598	+	0.970872i	$0.577015\pi$
$710$	1.14026	0.0427933
$711$	−16.5889	−0.622134
$712$	12.7228	0.476807
$713$	7.76984	0.290983
$714$	0	0
$715$	0	0
$716$	−6.66558	−0.249105
$717$	−19.3532	−0.722759
$718$	−1.93541	−0.0722287
$719$	17.1228	0.638571	0.319286	−	0.947658i	$-0.396557\pi$
$719$	17.1228	0.638571	0.319286	+	0.947658i	$0.396557\pi$
$720$	−46.4444	−1.73088
$721$	0	0
$722$	−22.2639	−0.828577
$723$	−70.6832	−2.62874
$724$	5.61411	0.208647
$725$	−22.7216	−0.843858
$726$	0	0
$727$	8.65786	0.321102	0.160551	−	0.987028i	$-0.448673\pi$
$727$	8.65786	0.321102	0.160551	+	0.987028i	$0.448673\pi$
$728$	0	0
$729$	−36.9766	−1.36950
$730$	−57.3036	−2.12090
$731$	−5.67363	−0.209847
$732$	−11.1891	−0.413562
$733$	−28.0866	−1.03740	−0.518702	−	0.854955i	$-0.673584\pi$
$733$	−28.0866	−1.03740	−0.518702	+	0.854955i	$0.673584\pi$
$734$	−11.1343	−0.410974
$735$	0	0
$736$	10.2737	0.378695
$737$	0	0
$738$	−22.3084	−0.821182
$739$	−33.8965	−1.24690	−0.623451	−	0.781862i	$-0.714270\pi$
$739$	−33.8965	−1.24690	−0.623451	+	0.781862i	$0.714270\pi$
$740$	1.08548	0.0399030
$741$	14.1253	0.518906
$742$	0	0
$743$	−5.65321	−0.207396	−0.103698	−	0.994609i	$-0.533068\pi$
$743$	−5.65321	−0.207396	−0.103698	+	0.994609i	$0.533068\pi$
$744$	−12.1818	−0.446606
$745$	49.4313	1.81102
$746$	−46.9918	−1.72049
$747$	−8.92472	−0.326538
$748$	0	0
$749$	0	0
$750$	90.6820	3.31124
$751$	44.3409	1.61802	0.809012	−	0.587792i	$-0.200003\pi$
$751$	44.3409	1.61802	0.809012	+	0.587792i	$0.200003\pi$
$752$	−32.6760	−1.19157
$753$	−4.95922	−0.180724
$754$	−10.8486	−0.395081
$755$	−28.4294	−1.03465
$756$	0	0
$757$	−21.3781	−0.777001	−0.388500	−	0.921449i	$-0.627007\pi$
$757$	−21.3781	−0.777001	−0.388500	+	0.921449i	$0.627007\pi$
$758$	3.31700	0.120479
$759$	0	0
$760$	−15.4607	−0.560819
$761$	4.58574	0.166233	0.0831164	−	0.996540i	$-0.473513\pi$
$761$	4.58574	0.166233	0.0831164	+	0.996540i	$0.473513\pi$
$762$	−35.5002	−1.28604
$763$	0	0
$764$	8.79936	0.318350
$765$	−62.3533	−2.25439
$766$	−24.5601	−0.887392
$767$	−60.4138	−2.18142
$768$	−22.0651	−0.796206
$769$	−12.8223	−0.462385	−0.231193	−	0.972908i	$-0.574263\pi$
$769$	−12.8223	−0.462385	−0.231193	+	0.972908i	$0.574263\pi$
$770$	0	0
$771$	−26.1736	−0.942621
$772$	−5.20692	−0.187401
$773$	−54.0639	−1.94454	−0.972272	−	0.233855i	$-0.924866\pi$
$773$	−54.0639	−1.94454	−0.972272	+	0.233855i	$0.924866\pi$
$774$	6.28284	0.225832
$775$	18.3468	0.659038
$776$	−33.0581	−1.18672
$777$	0	0
$778$	−36.1690	−1.29672
$779$	−6.00205	−0.215046
$780$	−17.1409	−0.613743
$781$	0	0
$782$	−26.6025	−0.951302
$783$	−3.17067	−0.113310
$784$	0	0
$785$	−42.9316	−1.53229
$786$	28.6238	1.02098
$787$	43.8514	1.56314	0.781568	−	0.623821i	$-0.214420\pi$
$787$	43.8514	1.56314	0.781568	+	0.623821i	$0.214420\pi$
$788$	−6.69153	−0.238376
$789$	−11.3030	−0.402397
$790$	−23.8297	−0.847824
$791$	0	0
$792$	0	0
$793$	51.4928	1.82856
$794$	13.2337	0.469646
$795$	−41.8615	−1.48468
$796$	0.571776	0.0202660
$797$	35.7697	1.26703	0.633514	−	0.773731i	$-0.281612\pi$
$797$	35.7697	1.26703	0.633514	+	0.773731i	$0.281612\pi$
$798$	0	0
$799$	−43.8687	−1.55196
$800$	24.2593	0.857694
$801$	−15.2876	−0.540160
$802$	−16.3244	−0.576436
$803$	0	0
$804$	−7.24440	−0.255490
$805$	0	0
$806$	8.75982	0.308551
$807$	−1.61100	−0.0567098
$808$	22.2885	0.784107
$809$	−30.7068	−1.07959	−0.539797	−	0.841795i	$-0.681499\pi$
$809$	−30.7068	−1.07959	−0.539797	+	0.841795i	$0.681499\pi$
$810$	−34.9298	−1.22731
$811$	−17.0984	−0.600405	−0.300202	−	0.953876i	$-0.597054\pi$
$811$	−17.0984	−0.600405	−0.300202	+	0.953876i	$0.597054\pi$
$812$	0	0
$813$	30.7514	1.07850
$814$	0	0
$815$	−31.9845	−1.12037
$816$	33.7098	1.18008
$817$	1.69039	0.0591394
$818$	40.8778	1.42926
$819$	0	0
$820$	7.28342	0.254348
$821$	−12.3822	−0.432142	−0.216071	−	0.976378i	$-0.569324\pi$
$821$	−12.3822	−0.432142	−0.216071	+	0.976378i	$0.569324\pi$
$822$	39.4541	1.37612
$823$	46.1384	1.60829	0.804143	−	0.594436i	$-0.202625\pi$
$823$	46.1384	1.60829	0.804143	+	0.594436i	$0.202625\pi$
$824$	−0.465652	−0.0162217
$825$	0	0
$826$	0	0
$827$	46.7103	1.62428	0.812138	−	0.583466i	$-0.198304\pi$
$827$	46.7103	1.62428	0.812138	+	0.583466i	$0.198304\pi$
$828$	−6.69552	−0.232685
$829$	−4.02555	−0.139813	−0.0699065	−	0.997554i	$-0.522270\pi$
$829$	−4.02555	−0.139813	−0.0699065	+	0.997554i	$0.522270\pi$
$830$	−12.8202	−0.444996
$831$	73.5641	2.55191
$832$	39.0000	1.35208
$833$	0	0
$834$	−26.9315	−0.932562
$835$	−87.3534	−3.02299
$836$	0	0
$837$	2.56020	0.0884933
$838$	25.6506	0.886084
$839$	14.3021	0.493765	0.246882	−	0.969045i	$-0.420594\pi$
$839$	14.3021	0.493765	0.246882	+	0.969045i	$0.420594\pi$
$840$	0	0
$841$	−25.2541	−0.870833
$842$	−28.6260	−0.986518
$843$	37.8628	1.30406
$844$	8.17941	0.281547
$845$	25.6945	0.883918
$846$	48.5792	1.67019
$847$	0	0
$848$	12.4002	0.425823
$849$	−58.0628	−1.99271
$850$	−62.8161	−2.15457
$851$	−3.56128	−0.122079
$852$	−0.208300	−0.00713625
$853$	32.3007	1.10595	0.552977	−	0.833197i	$-0.313492\pi$
$853$	32.3007	1.10595	0.552977	+	0.833197i	$0.313492\pi$
$854$	0	0
$855$	18.5775	0.635336
$856$	−24.0447	−0.821830
$857$	−16.2318	−0.554468	−0.277234	−	0.960802i	$-0.589418\pi$
$857$	−16.2318	−0.554468	−0.277234	+	0.960802i	$0.589418\pi$
$858$	0	0
$859$	28.2893	0.965220	0.482610	−	0.875835i	$-0.339689\pi$
$859$	28.2893	0.965220	0.482610	+	0.875835i	$0.339689\pi$
$860$	−2.05127	−0.0699479
$861$	0	0
$862$	15.4281	0.525482
$863$	31.9865	1.08883	0.544417	−	0.838815i	$-0.316751\pi$
$863$	31.9865	1.08883	0.544417	+	0.838815i	$0.316751\pi$
$864$	3.38524	0.115168
$865$	−79.5309	−2.70413
$866$	0.386101	0.0131203
$867$	1.46409	0.0497230
$868$	0	0
$869$	0	0
$870$	−26.0403	−0.882848
$871$	33.3390	1.12965
$872$	14.8707	0.503586
$873$	39.7223	1.34440
$874$	7.92590	0.268098
$875$	0	0
$876$	10.4681	0.353684
$877$	45.7968	1.54645	0.773224	−	0.634133i	$-0.218643\pi$
$877$	45.7968	1.54645	0.773224	+	0.634133i	$0.218643\pi$
$878$	4.50107	0.151904
$879$	−43.3496	−1.46215
$880$	0	0
$881$	−26.7142	−0.900025	−0.450012	−	0.893022i	$-0.648580\pi$
$881$	−26.7142	−0.900025	−0.450012	+	0.893022i	$0.648580\pi$
$882$	0	0
$883$	−28.4869	−0.958662	−0.479331	−	0.877634i	$-0.659121\pi$
$883$	−28.4869	−0.958662	−0.479331	+	0.877634i	$0.659121\pi$
$884$	6.81667	0.229269
$885$	−145.014	−4.87459
$886$	−27.8857	−0.936838
$887$	23.6139	0.792879	0.396439	−	0.918061i	$-0.370246\pi$
$887$	23.6139	0.792879	0.396439	+	0.918061i	$0.370246\pi$
$888$	5.58349	0.187370
$889$	0	0
$890$	−21.9604	−0.736113
$891$	0	0
$892$	−3.17572	−0.106331
$893$	13.0702	0.437377
$894$	39.7301	1.32877
$895$	73.6312	2.46122
$896$	0	0
$897$	56.2367	1.87769
$898$	11.8742	0.396249
$899$	−3.02464	−0.100877
$900$	−15.8101	−0.527002
$901$	16.6477	0.554614
$902$	0	0
$903$	0	0
$904$	−9.20519	−0.306160
$905$	−62.0161	−2.06149
$906$	−22.8500	−0.759139
$907$	23.9434	0.795029	0.397514	−	0.917596i	$-0.369873\pi$
$907$	23.9434	0.795029	0.397514	+	0.917596i	$0.369873\pi$
$908$	−9.84143	−0.326599
$909$	−26.7817	−0.888292
$910$	0	0
$911$	18.2388	0.604280	0.302140	−	0.953264i	$-0.402299\pi$
$911$	18.2388	0.604280	0.302140	+	0.953264i	$0.402299\pi$
$912$	−10.0435	−0.332572
$913$	0	0
$914$	−14.4463	−0.477841
$915$	123.600	4.08610
$916$	4.22657	0.139650
$917$	0	0
$918$	−8.76563	−0.289309
$919$	28.4024	0.936909	0.468455	−	0.883488i	$-0.344811\pi$
$919$	28.4024	0.936909	0.468455	+	0.883488i	$0.344811\pi$
$920$	−61.5533	−2.02935
$921$	−0.614008	−0.0202323
$922$	0.866558	0.0285386
$923$	0.958607	0.0315529
$924$	0	0
$925$	−8.40922	−0.276493
$926$	−17.2255	−0.566065
$927$	0.559523	0.0183771
$928$	−3.99936	−0.131285
$929$	−3.38963	−0.111210	−0.0556051	−	0.998453i	$-0.517709\pi$
$929$	−3.38963	−0.111210	−0.0556051	+	0.998453i	$0.517709\pi$
$930$	21.0266	0.689488
$931$	0	0
$932$	−9.85704	−0.322878
$933$	1.69123	0.0553682
$934$	−37.8588	−1.23878
$935$	0	0
$936$	−48.3096	−1.57905
$937$	−45.3871	−1.48273	−0.741367	−	0.671100i	$-0.765822\pi$
$937$	−45.3871	−1.48273	−0.741367	+	0.671100i	$0.765822\pi$
$938$	0	0
$939$	19.1982	0.626510
$940$	−15.8605	−0.517313
$941$	−21.5279	−0.701789	−0.350894	−	0.936415i	$-0.614122\pi$
$941$	−21.5279	−0.701789	−0.350894	+	0.936415i	$0.614122\pi$
$942$	−34.5061	−1.12427
$943$	−23.8958	−0.778153
$944$	42.9558	1.39809
$945$	0	0
$946$	0	0
$947$	−11.2673	−0.366140	−0.183070	−	0.983100i	$-0.558603\pi$
$947$	−11.2673	−0.366140	−0.183070	+	0.983100i	$0.558603\pi$
$948$	4.35316	0.141384
$949$	−48.1745	−1.56381
$950$	18.7153	0.607206
$951$	44.9291	1.45693
$952$	0	0
$953$	−23.8696	−0.773213	−0.386607	−	0.922245i	$-0.626353\pi$
$953$	−23.8696	−0.773213	−0.386607	+	0.922245i	$0.626353\pi$
$954$	−18.4352	−0.596862
$955$	−97.2019	−3.14538
$956$	2.78262	0.0899964
$957$	0	0
$958$	−6.00159	−0.193902
$959$	0	0
$960$	93.6133	3.02136
$961$	−28.5577	−0.921217
$962$	−4.01504	−0.129450
$963$	28.8919	0.931027
$964$	10.1629	0.327325
$965$	57.5181	1.85157
$966$	0	0
$967$	20.5165	0.659765	0.329882	−	0.944022i	$-0.392991\pi$
$967$	20.5165	0.659765	0.329882	+	0.944022i	$0.392991\pi$
$968$	0	0
$969$	−13.4837	−0.433159
$970$	57.0605	1.83210
$971$	34.7645	1.11565	0.557824	−	0.829960i	$-0.311637\pi$
$971$	34.7645	1.11565	0.557824	+	0.829960i	$0.311637\pi$
$972$	8.20122	0.263054
$973$	0	0
$974$	41.3272	1.32421
$975$	132.791	4.25272
$976$	−36.6127	−1.17194
$977$	5.78294	0.185013	0.0925064	−	0.995712i	$-0.470512\pi$
$977$	5.78294	0.185013	0.0925064	+	0.995712i	$0.470512\pi$
$978$	−25.7074	−0.822032
$979$	0	0
$980$	0	0
$981$	−17.8685	−0.570498
$982$	−8.75204	−0.279289
$983$	17.2321	0.549618	0.274809	−	0.961499i	$-0.411385\pi$
$983$	17.2321	0.549618	0.274809	+	0.961499i	$0.411385\pi$
$984$	37.4645	1.19432
$985$	73.9178	2.35522
$986$	10.3558	0.329796
$987$	0	0
$988$	−2.03095	−0.0646131
$989$	6.72991	0.213999
$990$	0	0
$991$	−24.0077	−0.762630	−0.381315	−	0.924445i	$-0.624529\pi$
$991$	−24.0077	−0.762630	−0.381315	+	0.924445i	$0.624529\pi$
$992$	3.22933	0.102531
$993$	−73.7121	−2.33918
$994$	0	0
$995$	−6.31610	−0.200234
$996$	2.34197	0.0742080
$997$	−36.0335	−1.14119	−0.570596	−	0.821231i	$-0.693288\pi$
$997$	−36.0335	−1.14119	−0.570596	+	0.821231i	$0.693288\pi$
$998$	14.0001	0.443166
$999$	−1.17346	−0.0371266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bm.1.4		6
7.6	odd	2		847.2.a.n.1.4	yes	6
11.10	odd	2		5929.2.a.bj.1.3		6
21.20	even	2		7623.2.a.cp.1.3		6
77.6	even	10		847.2.f.z.729.4		24
77.13	even	10		847.2.f.z.323.4		24
77.20	odd	10		847.2.f.y.323.3		24
77.27	odd	10		847.2.f.y.729.3		24
77.41	even	10		847.2.f.z.372.3		24
77.48	odd	10		847.2.f.y.148.4		24
77.62	even	10		847.2.f.z.148.3		24
77.69	odd	10		847.2.f.y.372.4		24
77.76	even	2		847.2.a.m.1.3	✓	6
231.230	odd	2		7623.2.a.cs.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.3	✓	6	77.76	even	2
847.2.a.n.1.4	yes	6	7.6	odd	2
847.2.f.y.148.4		24	77.48	odd	10
847.2.f.y.323.3		24	77.20	odd	10
847.2.f.y.372.4		24	77.69	odd	10
847.2.f.y.729.3		24	77.27	odd	10
847.2.f.z.148.3		24	77.62	even	10
847.2.f.z.323.4		24	77.13	even	10
847.2.f.z.372.3		24	77.41	even	10
847.2.f.z.729.4		24	77.6	even	10
5929.2.a.bj.1.3		6	11.10	odd	2
5929.2.a.bm.1.4		6	1.1	even	1	trivial
7623.2.a.cp.1.3		6	21.20	even	2
7623.2.a.cs.1.4		6	231.230	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+1.27656 q^{2} +2.57603 q^{3} -0.370384 q^{4} +4.09144 q^{5} +3.28847 q^{6} -3.02595 q^{8} +3.63595 q^{9} +O(q^{10})\)	\(q+1.27656 q^{2} +2.57603 q^{3} -0.370384 q^{4} +4.09144 q^{5} +3.28847 q^{6} -3.02595 q^{8} +3.63595 q^{9} +5.22298 q^{10} -0.954122 q^{12} +4.39091 q^{13} +10.5397 q^{15} -3.12205 q^{16} -4.19146 q^{17} +4.64152 q^{18} +1.24880 q^{19} -1.51540 q^{20} +4.97180 q^{23} -7.79494 q^{24} +11.7399 q^{25} +5.60527 q^{26} +1.63823 q^{27} -1.93542 q^{29} +13.4546 q^{30} +1.56278 q^{31} +2.06640 q^{32} -5.35067 q^{34} -1.34670 q^{36} -0.716296 q^{37} +1.59417 q^{38} +11.3111 q^{39} -12.3805 q^{40} -4.80626 q^{41} +1.35362 q^{43} +14.8763 q^{45} +6.34682 q^{46} +10.4662 q^{47} -8.04250 q^{48} +14.9867 q^{50} -10.7973 q^{51} -1.62632 q^{52} -3.97180 q^{53} +2.09131 q^{54} +3.21695 q^{57} -2.47069 q^{58} -13.7588 q^{59} -3.90373 q^{60} +11.7271 q^{61} +1.99499 q^{62} +8.88199 q^{64} +17.9651 q^{65} +7.59274 q^{67} +1.55245 q^{68} +12.8075 q^{69} +0.218316 q^{71} -11.0022 q^{72} -10.9714 q^{73} -0.914398 q^{74} +30.2423 q^{75} -0.462535 q^{76} +14.4394 q^{78} -4.56248 q^{79} -12.7737 q^{80} -6.68771 q^{81} -6.13550 q^{82} -2.45458 q^{83} -17.1491 q^{85} +1.72798 q^{86} -4.98571 q^{87} -4.20456 q^{89} +18.9905 q^{90} -1.84148 q^{92} +4.02578 q^{93} +13.3608 q^{94} +5.10938 q^{95} +5.32312 q^{96} +10.9249 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9	\( 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9} + 8 q^{10} + 14 q^{12} - 4 q^{13} + 2 q^{15} + 8 q^{16} - 22 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{23} + 20 q^{24} + 4 q^{25} - 6 q^{26} + 2 q^{27} + 12 q^{29} + 20 q^{30} + 2 q^{31} + 8 q^{32} - 24 q^{34} + 18 q^{36} + 14 q^{37} + 22 q^{38} + 20 q^{39} - 18 q^{40} - 26 q^{41} - 4 q^{43} + 36 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 4 q^{50} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 32 q^{54} + 20 q^{57} - 2 q^{58} + 4 q^{59} + 24 q^{60} + 8 q^{61} - 20 q^{62} + 26 q^{64} + 24 q^{65} + 6 q^{67} - 12 q^{68} + 14 q^{69} + 22 q^{71} + 16 q^{72} - 14 q^{73} + 44 q^{74} + 20 q^{75} + 30 q^{76} + 32 q^{78} - 28 q^{79} + 4 q^{80} - 6 q^{81} + 4 q^{82} - 22 q^{83} - 24 q^{85} - 30 q^{86} - 22 q^{87} + 22 q^{90} + 10 q^{92} - 50 q^{93} + 38 q^{94} - 24 q^{95} + 62 q^{96} + 4 q^{97}+O(q^{100}) \) 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9 + 8 * q^10 + 14 * q^12 - 4 * q^13 + 2 * q^15 + 8 * q^16 - 22 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^23 + 20 * q^24 + 4 * q^25 - 6 * q^26 + 2 * q^27 + 12 * q^29 + 20 * q^30 + 2 * q^31 + 8 * q^32 - 24 * q^34 + 18 * q^36 + 14 * q^37 + 22 * q^38 + 20 * q^39 - 18 * q^40 - 26 * q^41 - 4 * q^43 + 36 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 4 * q^50 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 32 * q^54 + 20 * q^57 - 2 * q^58 + 4 * q^59 + 24 * q^60 + 8 * q^61 - 20 * q^62 + 26 * q^64 + 24 * q^65 + 6 * q^67 - 12 * q^68 + 14 * q^69 + 22 * q^71 + 16 * q^72 - 14 * q^73 + 44 * q^74 + 20 * q^75 + 30 * q^76 + 32 * q^78 - 28 * q^79 + 4 * q^80 - 6 * q^81 + 4 * q^82 - 22 * q^83 - 24 * q^85 - 30 * q^86 - 22 * q^87 + 22 * q^90 + 10 * q^92 - 50 * q^93 + 38 * q^94 - 24 * q^95 + 62 * q^96 + 4 * q^97

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