LMFDB - Embedded newform 507.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.80194 q^{2} +1.00000 q^{3} +1.24698 q^{4} +1.44504 q^{5} +1.80194 q^{6} +3.44504 q^{7} -1.35690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.80194 q^{2} +1.00000 q^{3} +1.24698 q^{4} +1.44504 q^{5} +1.80194 q^{6} +3.44504 q^{7} -1.35690 q^{8} +1.00000 q^{9} +2.60388 q^{10} -5.18598 q^{11} +1.24698 q^{12} +6.20775 q^{14} +1.44504 q^{15} -4.93900 q^{16} -0.753020 q^{17} +1.80194 q^{18} +7.96077 q^{19} +1.80194 q^{20} +3.44504 q^{21} -9.34481 q^{22} -2.82908 q^{23} -1.35690 q^{24} -2.91185 q^{25} +1.00000 q^{27} +4.29590 q^{28} -3.91185 q^{29} +2.60388 q^{30} -4.89977 q^{31} -6.18598 q^{32} -5.18598 q^{33} -1.35690 q^{34} +4.97823 q^{35} +1.24698 q^{36} +6.24698 q^{37} +14.3448 q^{38} -1.96077 q^{40} +1.80194 q^{41} +6.20775 q^{42} -7.09783 q^{43} -6.46681 q^{44} +1.44504 q^{45} -5.09783 q^{46} +10.5526 q^{47} -4.93900 q^{48} +4.86831 q^{49} -5.24698 q^{50} -0.753020 q^{51} -3.08815 q^{53} +1.80194 q^{54} -7.49396 q^{55} -4.67456 q^{56} +7.96077 q^{57} -7.04892 q^{58} +1.87800 q^{59} +1.80194 q^{60} +3.34481 q^{61} -8.82908 q^{62} +3.44504 q^{63} -1.26875 q^{64} -9.34481 q^{66} -4.54288 q^{67} -0.939001 q^{68} -2.82908 q^{69} +8.97046 q^{70} -9.11960 q^{71} -1.35690 q^{72} +2.95108 q^{73} +11.2567 q^{74} -2.91185 q^{75} +9.92692 q^{76} -17.8659 q^{77} -9.43296 q^{79} -7.13706 q^{80} +1.00000 q^{81} +3.24698 q^{82} -6.46681 q^{83} +4.29590 q^{84} -1.08815 q^{85} -12.7899 q^{86} -3.91185 q^{87} +7.03684 q^{88} +1.15883 q^{89} +2.60388 q^{90} -3.52781 q^{92} -4.89977 q^{93} +19.0151 q^{94} +11.5036 q^{95} -6.18598 q^{96} +8.65817 q^{97} +8.77240 q^{98} -5.18598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + q^{6} + 10 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + q^6 + 10 * q^7 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + q^{6} + 10 q^{7} + 3 q^{9} - q^{10} - q^{11} - q^{12} + q^{14} + 4 q^{15} - 5 q^{16} - 7 q^{17} + q^{18} + 11 q^{19} + q^{20} + 10 q^{21} - 5 q^{22} + 2 q^{23} - 5 q^{25} + 3 q^{27} - q^{28} - 8 q^{29} - q^{30} + 8 q^{31} - 4 q^{32} - q^{33} + 18 q^{35} - q^{36} + 14 q^{37} + 20 q^{38} + 7 q^{40} + q^{41} + q^{42} - 3 q^{43} - 16 q^{44} + 4 q^{45} + 3 q^{46} - 9 q^{47} - 5 q^{48} + 17 q^{49} - 11 q^{50} - 7 q^{51} - 13 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 11 q^{57} - 12 q^{58} - 14 q^{59} + q^{60} - 13 q^{61} - 16 q^{62} + 10 q^{63} + 4 q^{64} - 5 q^{66} + 5 q^{67} + 7 q^{68} + 2 q^{69} - 8 q^{70} - 6 q^{71} + 18 q^{73} + 7 q^{74} - 5 q^{75} + q^{76} - 15 q^{77} - 9 q^{79} - 16 q^{80} + 3 q^{81} + 5 q^{82} - 16 q^{83} - q^{84} - 7 q^{85} - 15 q^{86} - 8 q^{87} - 7 q^{88} - 5 q^{89} - q^{90} - 17 q^{92} + 8 q^{93} + 32 q^{94} + 3 q^{95} - 4 q^{96} + 5 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + q^6 + 10 * q^7 + 3 * q^9 - q^10 - q^11 - q^12 + q^14 + 4 * q^15 - 5 * q^16 - 7 * q^17 + q^18 + 11 * q^19 + q^20 + 10 * q^21 - 5 * q^22 + 2 * q^23 - 5 * q^25 + 3 * q^27 - q^28 - 8 * q^29 - q^30 + 8 * q^31 - 4 * q^32 - q^33 + 18 * q^35 - q^36 + 14 * q^37 + 20 * q^38 + 7 * q^40 + q^41 + q^42 - 3 * q^43 - 16 * q^44 + 4 * q^45 + 3 * q^46 - 9 * q^47 - 5 * q^48 + 17 * q^49 - 11 * q^50 - 7 * q^51 - 13 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 11 * q^57 - 12 * q^58 - 14 * q^59 + q^60 - 13 * q^61 - 16 * q^62 + 10 * q^63 + 4 * q^64 - 5 * q^66 + 5 * q^67 + 7 * q^68 + 2 * q^69 - 8 * q^70 - 6 * q^71 + 18 * q^73 + 7 * q^74 - 5 * q^75 + q^76 - 15 * q^77 - 9 * q^79 - 16 * q^80 + 3 * q^81 + 5 * q^82 - 16 * q^83 - q^84 - 7 * q^85 - 15 * q^86 - 8 * q^87 - 7 * q^88 - 5 * q^89 - q^90 - 17 * q^92 + 8 * q^93 + 32 * q^94 + 3 * q^95 - 4 * q^96 + 5 * q^97 - 13 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.80194	1.27416	0.637081	−	0.770797i	$-0.280142\pi$
$2$	1.80194	1.27416	0.637081	+	0.770797i	$0.280142\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.24698	0.623490
$5$	1.44504	0.646242	0.323121	−	0.946358i	$-0.395268\pi$
$5$	1.44504	0.646242	0.323121	+	0.946358i	$0.395268\pi$
$6$	1.80194	0.735638
$7$	3.44504	1.30210	0.651052	−	0.759033i	$-0.274328\pi$
$7$	3.44504	1.30210	0.651052	+	0.759033i	$0.274328\pi$
$8$	−1.35690	−0.479735
$9$	1.00000	0.333333
$10$	2.60388	0.823418
$11$	−5.18598	−1.56363	−0.781816	−	0.623509i	$-0.785706\pi$
$11$	−5.18598	−1.56363	−0.781816	+	0.623509i	$0.785706\pi$
$12$	1.24698	0.359972
$13$	0	0
$13$	0	0
$14$	6.20775	1.65909
$15$	1.44504	0.373108
$16$	−4.93900	−1.23475
$17$	−0.753020	−0.182634	−0.0913171	−	0.995822i	$-0.529108\pi$
$17$	−0.753020	−0.182634	−0.0913171	+	0.995822i	$0.529108\pi$
$18$	1.80194	0.424721
$19$	7.96077	1.82633	0.913163	−	0.407594i	$-0.133632\pi$
$19$	7.96077	1.82633	0.913163	+	0.407594i	$0.133632\pi$
$20$	1.80194	0.402926
$21$	3.44504	0.751770
$22$	−9.34481	−1.99232
$23$	−2.82908	−0.589905	−0.294952	−	0.955512i	$-0.595304\pi$
$23$	−2.82908	−0.589905	−0.294952	+	0.955512i	$0.595304\pi$
$24$	−1.35690	−0.276975
$25$	−2.91185	−0.582371
$26$	0	0
$27$	1.00000	0.192450
$28$	4.29590	0.811848
$29$	−3.91185	−0.726413	−0.363207	−	0.931709i	$-0.618318\pi$
$29$	−3.91185	−0.726413	−0.363207	+	0.931709i	$0.618318\pi$
$30$	2.60388	0.475400
$31$	−4.89977	−0.880025	−0.440013	−	0.897992i	$-0.645026\pi$
$31$	−4.89977	−0.880025	−0.440013	+	0.897992i	$0.645026\pi$
$32$	−6.18598	−1.09354
$33$	−5.18598	−0.902763
$34$	−1.35690	−0.232706
$35$	4.97823	0.841474
$36$	1.24698	0.207830
$37$	6.24698	1.02700	0.513499	−	0.858090i	$-0.328349\pi$
$37$	6.24698	1.02700	0.513499	+	0.858090i	$0.328349\pi$
$38$	14.3448	2.32704
$39$	0	0
$40$	−1.96077	−0.310025
$41$	1.80194	0.281415	0.140708	−	0.990051i	$-0.455062\pi$
$41$	1.80194	0.281415	0.140708	+	0.990051i	$0.455062\pi$
$42$	6.20775	0.957877
$43$	−7.09783	−1.08241	−0.541205	−	0.840891i	$-0.682032\pi$
$43$	−7.09783	−1.08241	−0.541205	+	0.840891i	$0.682032\pi$
$44$	−6.46681	−0.974909
$45$	1.44504	0.215414
$46$	−5.09783	−0.751635
$47$	10.5526	1.53925	0.769625	−	0.638496i	$-0.220443\pi$
$47$	10.5526	1.53925	0.769625	+	0.638496i	$0.220443\pi$
$48$	−4.93900	−0.712883
$49$	4.86831	0.695473
$50$	−5.24698	−0.742035
$51$	−0.753020	−0.105444
$52$	0	0
$53$	−3.08815	−0.424189	−0.212095	−	0.977249i	$-0.568029\pi$
$53$	−3.08815	−0.424189	−0.212095	+	0.977249i	$0.568029\pi$
$54$	1.80194	0.245213
$55$	−7.49396	−1.01049
$56$	−4.67456	−0.624665
$57$	7.96077	1.05443
$58$	−7.04892	−0.925568
$59$	1.87800	0.244495	0.122248	−	0.992500i	$-0.460990\pi$
$59$	1.87800	0.244495	0.122248	+	0.992500i	$0.460990\pi$
$60$	1.80194	0.232629
$61$	3.34481	0.428260	0.214130	−	0.976805i	$-0.431308\pi$
$61$	3.34481	0.428260	0.214130	+	0.976805i	$0.431308\pi$
$62$	−8.82908	−1.12129
$63$	3.44504	0.434034
$64$	−1.26875	−0.158594
$65$	0	0
$66$	−9.34481	−1.15027
$67$	−4.54288	−0.555001	−0.277500	−	0.960726i	$-0.589506\pi$
$67$	−4.54288	−0.555001	−0.277500	+	0.960726i	$0.589506\pi$
$68$	−0.939001	−0.113871
$69$	−2.82908	−0.340582
$70$	8.97046	1.07218
$71$	−9.11960	−1.08230	−0.541149	−	0.840927i	$-0.682011\pi$
$71$	−9.11960	−1.08230	−0.541149	+	0.840927i	$0.682011\pi$
$72$	−1.35690	−0.159912
$73$	2.95108	0.345398	0.172699	−	0.984975i	$-0.444751\pi$
$73$	2.95108	0.345398	0.172699	+	0.984975i	$0.444751\pi$
$74$	11.2567	1.30856
$75$	−2.91185	−0.336232
$76$	9.92692	1.13870
$77$	−17.8659	−2.03601
$78$	0	0
$79$	−9.43296	−1.06129	−0.530645	−	0.847594i	$-0.678050\pi$
$79$	−9.43296	−1.06129	−0.530645	+	0.847594i	$0.678050\pi$
$80$	−7.13706	−0.797948
$81$	1.00000	0.111111
$82$	3.24698	0.358569
$83$	−6.46681	−0.709825	−0.354912	−	0.934900i	$-0.615489\pi$
$83$	−6.46681	−0.709825	−0.354912	+	0.934900i	$0.615489\pi$
$84$	4.29590	0.468721
$85$	−1.08815	−0.118026
$86$	−12.7899	−1.37917
$87$	−3.91185	−0.419395
$88$	7.03684	0.750129
$89$	1.15883	0.122836	0.0614181	−	0.998112i	$-0.480438\pi$
$89$	1.15883	0.122836	0.0614181	+	0.998112i	$0.480438\pi$
$90$	2.60388	0.274473
$91$	0	0
$92$	−3.52781	−0.367800
$93$	−4.89977	−0.508083
$94$	19.0151	1.96125
$95$	11.5036	1.18025
$96$	−6.18598	−0.631354
$97$	8.65817	0.879104	0.439552	−	0.898217i	$-0.355137\pi$
$97$	8.65817	0.879104	0.439552	+	0.898217i	$0.355137\pi$
$98$	8.77240	0.886146
$99$	−5.18598	−0.521211
$100$	−3.63102	−0.363102
$101$	−8.47650	−0.843443	−0.421722	−	0.906725i	$-0.638574\pi$
$101$	−8.47650	−0.843443	−0.421722	+	0.906725i	$0.638574\pi$
$102$	−1.35690	−0.134353
$103$	5.64742	0.556456	0.278228	−	0.960515i	$-0.410253\pi$
$103$	5.64742	0.556456	0.278228	+	0.960515i	$0.410253\pi$
$104$	0	0
$105$	4.97823	0.485825
$106$	−5.56465	−0.540486
$107$	−6.73556	−0.651151	−0.325576	−	0.945516i	$-0.605558\pi$
$107$	−6.73556	−0.651151	−0.325576	+	0.945516i	$0.605558\pi$
$108$	1.24698	0.119991
$109$	−2.07606	−0.198851	−0.0994255	−	0.995045i	$-0.531700\pi$
$109$	−2.07606	−0.198851	−0.0994255	+	0.995045i	$0.531700\pi$
$110$	−13.5036	−1.28752
$111$	6.24698	0.592937
$112$	−17.0151	−1.60777
$113$	6.16852	0.580286	0.290143	−	0.956983i	$-0.406297\pi$
$113$	6.16852	0.580286	0.290143	+	0.956983i	$0.406297\pi$
$114$	14.3448	1.34351
$115$	−4.08815	−0.381222
$116$	−4.87800	−0.452911
$117$	0	0
$118$	3.38404	0.311526
$119$	−2.59419	−0.237809
$120$	−1.96077	−0.178993
$121$	15.8944	1.44495
$122$	6.02715	0.545672
$123$	1.80194	0.162475
$124$	−6.10992	−0.548687
$125$	−11.4330	−1.02260
$126$	6.20775	0.553030
$127$	−14.2620	−1.26555	−0.632776	−	0.774335i	$-0.718085\pi$
$127$	−14.2620	−1.26555	−0.632776	+	0.774335i	$0.718085\pi$
$128$	10.0858	0.891463
$129$	−7.09783	−0.624929
$130$	0	0
$131$	22.6015	1.97470	0.987350	−	0.158554i	$-0.0506831\pi$
$131$	22.6015	1.97470	0.987350	+	0.158554i	$0.0506831\pi$
$132$	−6.46681	−0.562864
$133$	27.4252	2.37807
$134$	−8.18598	−0.707161
$135$	1.44504	0.124369
$136$	1.02177	0.0876161
$137$	−13.6353	−1.16495	−0.582473	−	0.812850i	$-0.697915\pi$
$137$	−13.6353	−1.16495	−0.582473	+	0.812850i	$0.697915\pi$
$138$	−5.09783	−0.433957
$139$	17.6015	1.49294	0.746469	−	0.665420i	$-0.231748\pi$
$139$	17.6015	1.49294	0.746469	+	0.665420i	$0.231748\pi$
$140$	6.20775	0.524651
$141$	10.5526	0.888686
$142$	−16.4330	−1.37902
$143$	0	0
$144$	−4.93900	−0.411583
$145$	−5.65279	−0.469439
$146$	5.31767	0.440093
$147$	4.86831	0.401532
$148$	7.78986	0.640322
$149$	12.7385	1.04358	0.521791	−	0.853073i	$-0.325264\pi$
$149$	12.7385	1.04358	0.521791	+	0.853073i	$0.325264\pi$
$150$	−5.24698	−0.428414
$151$	15.6407	1.27282	0.636412	−	0.771350i	$-0.280418\pi$
$151$	15.6407	1.27282	0.636412	+	0.771350i	$0.280418\pi$
$152$	−10.8019	−0.876153
$153$	−0.753020	−0.0608781
$154$	−32.1933	−2.59421
$155$	−7.08038	−0.568710
$156$	0	0
$157$	−0.823708	−0.0657391	−0.0328695	−	0.999460i	$-0.510465\pi$
$157$	−0.823708	−0.0657391	−0.0328695	+	0.999460i	$0.510465\pi$
$158$	−16.9976	−1.35226
$159$	−3.08815	−0.244906
$160$	−8.93900	−0.706690
$161$	−9.74632	−0.768117
$162$	1.80194	0.141574
$163$	6.26875	0.491006	0.245503	−	0.969396i	$-0.421047\pi$
$163$	6.26875	0.491006	0.245503	+	0.969396i	$0.421047\pi$
$164$	2.24698	0.175460
$165$	−7.49396	−0.583404
$166$	−11.6528	−0.904432
$167$	−7.45042	−0.576531	−0.288265	−	0.957551i	$-0.593079\pi$
$167$	−7.45042	−0.576531	−0.288265	+	0.957551i	$0.593079\pi$
$168$	−4.67456	−0.360650
$169$	0	0
$170$	−1.96077	−0.150384
$171$	7.96077	0.608775
$172$	−8.85086	−0.674871
$173$	−2.00969	−0.152794	−0.0763969	−	0.997077i	$-0.524342\pi$
$173$	−2.00969	−0.152794	−0.0763969	+	0.997077i	$0.524342\pi$
$174$	−7.04892	−0.534377
$175$	−10.0315	−0.758307
$176$	25.6136	1.93070
$177$	1.87800	0.141159
$178$	2.08815	0.156513
$179$	20.0368	1.49762	0.748812	−	0.662783i	$-0.230625\pi$
$179$	20.0368	1.49762	0.748812	+	0.662783i	$0.230625\pi$
$180$	1.80194	0.134309
$181$	24.1226	1.79302	0.896509	−	0.443026i	$-0.146095\pi$
$181$	24.1226	1.79302	0.896509	+	0.443026i	$0.146095\pi$
$182$	0	0
$183$	3.34481	0.247256
$184$	3.83877	0.282998
$185$	9.02715	0.663689
$186$	−8.82908	−0.647380
$187$	3.90515	0.285573
$188$	13.1588	0.959707
$189$	3.44504	0.250590
$190$	20.7289	1.50383
$191$	−7.08038	−0.512318	−0.256159	−	0.966635i	$-0.582457\pi$
$191$	−7.08038	−0.512318	−0.256159	+	0.966635i	$0.582457\pi$
$192$	−1.26875	−0.0915641
$193$	9.76809	0.703122	0.351561	−	0.936165i	$-0.385651\pi$
$193$	9.76809	0.703122	0.351561	+	0.936165i	$0.385651\pi$
$194$	15.6015	1.12012
$195$	0	0
$196$	6.07069	0.433621
$197$	23.4112	1.66798	0.833989	−	0.551781i	$-0.186052\pi$
$197$	23.4112	1.66798	0.833989	+	0.551781i	$0.186052\pi$
$198$	−9.34481	−0.664107
$199$	4.02475	0.285307	0.142654	−	0.989773i	$-0.454437\pi$
$199$	4.02475	0.285307	0.142654	+	0.989773i	$0.454437\pi$
$200$	3.95108	0.279384
$201$	−4.54288	−0.320430
$202$	−15.2741	−1.07468
$203$	−13.4765	−0.945865
$204$	−0.939001	−0.0657432
$205$	2.60388	0.181863
$206$	10.1763	0.709016
$207$	−2.82908	−0.196635
$208$	0	0
$209$	−41.2844	−2.85570
$210$	8.97046	0.619021
$211$	−3.91185	−0.269303	−0.134652	−	0.990893i	$-0.542992\pi$
$211$	−3.91185	−0.269303	−0.134652	+	0.990893i	$0.542992\pi$
$212$	−3.85086	−0.264478
$213$	−9.11960	−0.624865
$214$	−12.1371	−0.829673
$215$	−10.2567	−0.699499
$216$	−1.35690	−0.0923251
$217$	−16.8799	−1.14588
$218$	−3.74094	−0.253368
$219$	2.95108	0.199416
$220$	−9.34481	−0.630027
$221$	0	0
$222$	11.2567	0.755498
$223$	7.44935	0.498846	0.249423	−	0.968395i	$-0.419759\pi$
$223$	7.44935	0.498846	0.249423	+	0.968395i	$0.419759\pi$
$224$	−21.3110	−1.42390
$225$	−2.91185	−0.194124
$226$	11.1153	0.739378
$227$	−21.2500	−1.41041	−0.705205	−	0.709004i	$-0.749145\pi$
$227$	−21.2500	−1.41041	−0.705205	+	0.709004i	$0.749145\pi$
$228$	9.92692	0.657426
$229$	9.29590	0.614290	0.307145	−	0.951663i	$-0.400626\pi$
$229$	9.29590	0.614290	0.307145	+	0.951663i	$0.400626\pi$
$230$	−7.36658	−0.485738
$231$	−17.8659	−1.17549
$232$	5.30798	0.348486
$233$	16.2107	1.06200	0.531000	−	0.847372i	$-0.321816\pi$
$233$	16.2107	1.06200	0.531000	+	0.847372i	$0.321816\pi$
$234$	0	0
$235$	15.2489	0.994728
$236$	2.34183	0.152440
$237$	−9.43296	−0.612737
$238$	−4.67456	−0.303007
$239$	−13.5090	−0.873826	−0.436913	−	0.899504i	$-0.643928\pi$
$239$	−13.5090	−0.873826	−0.436913	+	0.899504i	$0.643928\pi$
$240$	−7.13706	−0.460695
$241$	6.26875	0.403806	0.201903	−	0.979406i	$-0.435287\pi$
$241$	6.26875	0.403806	0.201903	+	0.979406i	$0.435287\pi$
$242$	28.6407	1.84109
$243$	1.00000	0.0641500
$244$	4.17092	0.267015
$245$	7.03492	0.449444
$246$	3.24698	0.207020
$247$	0	0
$248$	6.64848	0.422179
$249$	−6.46681	−0.409818
$250$	−20.6015	−1.30295
$251$	−0.753020	−0.0475302	−0.0237651	−	0.999718i	$-0.507565\pi$
$251$	−0.753020	−0.0475302	−0.0237651	+	0.999718i	$0.507565\pi$
$252$	4.29590	0.270616
$253$	14.6716	0.922394
$254$	−25.6993	−1.61252
$255$	−1.08815	−0.0681423
$256$	20.7114	1.29446
$257$	19.7265	1.23050	0.615252	−	0.788331i	$-0.289054\pi$
$257$	19.7265	1.23050	0.615252	+	0.788331i	$0.289054\pi$
$258$	−12.7899	−0.796262
$259$	21.5211	1.33726
$260$	0	0
$261$	−3.91185	−0.242138
$262$	40.7265	2.51609
$263$	−17.6093	−1.08583	−0.542917	−	0.839787i	$-0.682680\pi$
$263$	−17.6093	−1.08583	−0.542917	+	0.839787i	$0.682680\pi$
$264$	7.03684	0.433087
$265$	−4.46250	−0.274129
$266$	49.4185	3.03004
$267$	1.15883	0.0709195
$268$	−5.66487	−0.346037
$269$	−16.3870	−0.999135	−0.499567	−	0.866275i	$-0.666508\pi$
$269$	−16.3870	−0.999135	−0.499567	+	0.866275i	$0.666508\pi$
$270$	2.60388	0.158467
$271$	−0.795233	−0.0483070	−0.0241535	−	0.999708i	$-0.507689\pi$
$271$	−0.795233	−0.0483070	−0.0241535	+	0.999708i	$0.507689\pi$
$272$	3.71917	0.225508
$273$	0	0
$274$	−24.5700	−1.48433
$275$	15.1008	0.910614
$276$	−3.52781	−0.212349
$277$	−4.83340	−0.290411	−0.145205	−	0.989402i	$-0.546384\pi$
$277$	−4.83340	−0.290411	−0.145205	+	0.989402i	$0.546384\pi$
$278$	31.7168	1.90225
$279$	−4.89977	−0.293342
$280$	−6.75494	−0.403685
$281$	18.7748	1.12001	0.560005	−	0.828489i	$-0.310799\pi$
$281$	18.7748	1.12001	0.560005	+	0.828489i	$0.310799\pi$
$282$	19.0151	1.13233
$283$	−7.91723	−0.470631	−0.235315	−	0.971919i	$-0.575612\pi$
$283$	−7.91723	−0.470631	−0.235315	+	0.971919i	$0.575612\pi$
$284$	−11.3720	−0.674802
$285$	11.5036	0.681417
$286$	0	0
$287$	6.20775	0.366432
$288$	−6.18598	−0.364512
$289$	−16.4330	−0.966645
$290$	−10.1860	−0.598141
$291$	8.65817	0.507551
$292$	3.67994	0.215352
$293$	6.57912	0.384356	0.192178	−	0.981360i	$-0.438445\pi$
$293$	6.57912	0.384356	0.192178	+	0.981360i	$0.438445\pi$
$294$	8.77240	0.511617
$295$	2.71379	0.158003
$296$	−8.47650	−0.492687
$297$	−5.18598	−0.300921
$298$	22.9541	1.32969
$299$	0	0
$300$	−3.63102	−0.209637
$301$	−24.4523	−1.40941
$302$	28.1836	1.62178
$303$	−8.47650	−0.486962
$304$	−39.3183	−2.25506
$305$	4.83340	0.276759
$306$	−1.35690	−0.0775686
$307$	−24.8649	−1.41911	−0.709556	−	0.704649i	$-0.751105\pi$
$307$	−24.8649	−1.41911	−0.709556	+	0.704649i	$0.751105\pi$
$308$	−22.2784	−1.26943
$309$	5.64742	0.321270
$310$	−12.7584	−0.724628
$311$	−17.0804	−0.968539	−0.484270	−	0.874919i	$-0.660915\pi$
$311$	−17.0804	−0.968539	−0.484270	+	0.874919i	$0.660915\pi$
$312$	0	0
$313$	15.6974	0.887269	0.443635	−	0.896208i	$-0.353689\pi$
$313$	15.6974	0.887269	0.443635	+	0.896208i	$0.353689\pi$
$314$	−1.48427	−0.0837622
$315$	4.97823	0.280491
$316$	−11.7627	−0.661704
$317$	32.7821	1.84123	0.920613	−	0.390477i	$-0.127690\pi$
$317$	32.7821	1.84123	0.920613	+	0.390477i	$0.127690\pi$
$318$	−5.56465	−0.312050
$319$	20.2868	1.13584
$320$	−1.83340	−0.102490
$321$	−6.73556	−0.375942
$322$	−17.5623	−0.978706
$323$	−5.99462	−0.333550
$324$	1.24698	0.0692766
$325$	0	0
$326$	11.2959	0.625622
$327$	−2.07606	−0.114807
$328$	−2.44504	−0.135005
$329$	36.3540	2.00426
$330$	−13.5036	−0.743351
$331$	−29.1618	−1.60288	−0.801439	−	0.598076i	$-0.795932\pi$
$331$	−29.1618	−1.60288	−0.801439	+	0.598076i	$0.795932\pi$
$332$	−8.06398	−0.442569
$333$	6.24698	0.342332
$334$	−13.4252	−0.734594
$335$	−6.56465	−0.358665
$336$	−17.0151	−0.928248
$337$	−33.2911	−1.81348	−0.906741	−	0.421688i	$-0.861438\pi$
$337$	−33.2911	−1.81348	−0.906741	+	0.421688i	$0.861438\pi$
$338$	0	0
$339$	6.16852	0.335028
$340$	−1.35690	−0.0735880
$341$	25.4101	1.37604
$342$	14.3448	0.775679
$343$	−7.34375	−0.396525
$344$	9.63102	0.519270
$345$	−4.08815	−0.220098
$346$	−3.62133	−0.194684
$347$	−0.873690	−0.0469022	−0.0234511	−	0.999725i	$-0.507465\pi$
$347$	−0.873690	−0.0469022	−0.0234511	+	0.999725i	$0.507465\pi$
$348$	−4.87800	−0.261488
$349$	−3.23191	−0.173000	−0.0865002	−	0.996252i	$-0.527568\pi$
$349$	−3.23191	−0.173000	−0.0865002	+	0.996252i	$0.527568\pi$
$350$	−18.0761	−0.966206
$351$	0	0
$352$	32.0804	1.70989
$353$	8.14675	0.433608	0.216804	−	0.976215i	$-0.430437\pi$
$353$	8.14675	0.433608	0.216804	+	0.976215i	$0.430437\pi$
$354$	3.38404	0.179860
$355$	−13.1782	−0.699427
$356$	1.44504	0.0765871
$357$	−2.59419	−0.137299
$358$	36.1051	1.90822
$359$	2.64071	0.139371	0.0696857	−	0.997569i	$-0.477800\pi$
$359$	2.64071	0.139371	0.0696857	+	0.997569i	$0.477800\pi$
$360$	−1.96077	−0.103342
$361$	44.3739	2.33547
$362$	43.4674	2.28460
$363$	15.8944	0.834239
$364$	0	0
$365$	4.26444	0.223211
$366$	6.02715	0.315044
$367$	−2.90408	−0.151592	−0.0757960	−	0.997123i	$-0.524150\pi$
$367$	−2.90408	−0.151592	−0.0757960	+	0.997123i	$0.524150\pi$
$368$	13.9729	0.728385
$369$	1.80194	0.0938051
$370$	16.2664	0.845648
$371$	−10.6388	−0.552339
$372$	−6.10992	−0.316784
$373$	−8.39852	−0.434859	−0.217429	−	0.976076i	$-0.569767\pi$
$373$	−8.39852	−0.434859	−0.217429	+	0.976076i	$0.569767\pi$
$374$	7.03684	0.363866
$375$	−11.4330	−0.590396
$376$	−14.3187	−0.738432
$377$	0	0
$378$	6.20775	0.319292
$379$	15.7482	0.808932	0.404466	−	0.914553i	$-0.367457\pi$
$379$	15.7482	0.808932	0.404466	+	0.914553i	$0.367457\pi$
$380$	14.3448	0.735873
$381$	−14.2620	−0.730667
$382$	−12.7584	−0.652776
$383$	12.7385	0.650909	0.325455	−	0.945558i	$-0.394483\pi$
$383$	12.7385	0.650909	0.325455	+	0.945558i	$0.394483\pi$
$384$	10.0858	0.514686
$385$	−25.8170	−1.31576
$386$	17.6015	0.895892
$387$	−7.09783	−0.360803
$388$	10.7966	0.548112
$389$	−0.310371	−0.0157365	−0.00786823	−	0.999969i	$-0.502505\pi$
$389$	−0.310371	−0.0157365	−0.00786823	+	0.999969i	$0.502505\pi$
$390$	0	0
$391$	2.13036	0.107737
$392$	−6.60579	−0.333643
$393$	22.6015	1.14009
$394$	42.1855	2.12528
$395$	−13.6310	−0.685851
$396$	−6.46681	−0.324970
$397$	1.49098	0.0748299	0.0374150	−	0.999300i	$-0.488088\pi$
$397$	1.49098	0.0748299	0.0374150	+	0.999300i	$0.488088\pi$
$398$	7.25236	0.363528
$399$	27.4252	1.37298
$400$	14.3817	0.719083
$401$	−23.8334	−1.19018	−0.595092	−	0.803658i	$-0.702884\pi$
$401$	−23.8334	−1.19018	−0.595092	+	0.803658i	$0.702884\pi$
$402$	−8.18598	−0.408280
$403$	0	0
$404$	−10.5700	−0.525878
$405$	1.44504	0.0718047
$406$	−24.2838	−1.20519
$407$	−32.3967	−1.60585
$408$	1.02177	0.0505852
$409$	4.26742	0.211010	0.105505	−	0.994419i	$-0.466354\pi$
$409$	4.26742	0.211010	0.105505	+	0.994419i	$0.466354\pi$
$410$	4.69202	0.231722
$411$	−13.6353	−0.672581
$412$	7.04221	0.346945
$413$	6.46980	0.318358
$414$	−5.09783	−0.250545
$415$	−9.34481	−0.458719
$416$	0	0
$417$	17.6015	0.861948
$418$	−74.3919	−3.63863
$419$	29.6896	1.45043	0.725217	−	0.688521i	$-0.241740\pi$
$419$	29.6896	1.45043	0.725217	+	0.688521i	$0.241740\pi$
$420$	6.20775	0.302907
$421$	29.3991	1.43282	0.716412	−	0.697677i	$-0.245783\pi$
$421$	29.3991	1.43282	0.716412	+	0.697677i	$0.245783\pi$
$422$	−7.04892	−0.343136
$423$	10.5526	0.513083
$424$	4.19029	0.203499
$425$	2.19269	0.106361
$426$	−16.4330	−0.796180
$427$	11.5230	0.557638
$428$	−8.39911	−0.405986
$429$	0	0
$430$	−18.4819	−0.891275
$431$	−33.0562	−1.59226	−0.796131	−	0.605124i	$-0.793123\pi$
$431$	−33.0562	−1.59226	−0.796131	+	0.605124i	$0.793123\pi$
$432$	−4.93900	−0.237628
$433$	−29.2664	−1.40645	−0.703226	−	0.710967i	$-0.748258\pi$
$433$	−29.2664	−1.40645	−0.703226	+	0.710967i	$0.748258\pi$
$434$	−30.4166	−1.46004
$435$	−5.65279	−0.271031
$436$	−2.58881	−0.123982
$437$	−22.5217	−1.07736
$438$	5.31767	0.254088
$439$	−2.13169	−0.101740	−0.0508699	−	0.998705i	$-0.516199\pi$
$439$	−2.13169	−0.101740	−0.0508699	+	0.998705i	$0.516199\pi$
$440$	10.1685	0.484765
$441$	4.86831	0.231824
$442$	0	0
$443$	−22.9922	−1.09239	−0.546197	−	0.837657i	$-0.683925\pi$
$443$	−22.9922	−1.09239	−0.546197	+	0.837657i	$0.683925\pi$
$444$	7.78986	0.369690
$445$	1.67456	0.0793819
$446$	13.4233	0.635610
$447$	12.7385	0.602513
$448$	−4.37090	−0.206505
$449$	−12.9379	−0.610579	−0.305289	−	0.952260i	$-0.598753\pi$
$449$	−12.9379	−0.610579	−0.305289	+	0.952260i	$0.598753\pi$
$450$	−5.24698	−0.247345
$451$	−9.34481	−0.440030
$452$	7.69202	0.361802
$453$	15.6407	0.734865
$454$	−38.2911	−1.79709
$455$	0	0
$456$	−10.8019	−0.505847
$457$	−4.85325	−0.227025	−0.113513	−	0.993537i	$-0.536210\pi$
$457$	−4.85325	−0.227025	−0.113513	+	0.993537i	$0.536210\pi$
$458$	16.7506	0.782705
$459$	−0.753020	−0.0351480
$460$	−5.09783	−0.237688
$461$	18.8345	0.877208	0.438604	−	0.898680i	$-0.355473\pi$
$461$	18.8345	0.877208	0.438604	+	0.898680i	$0.355473\pi$
$462$	−32.1933	−1.49777
$463$	−22.8767	−1.06317	−0.531585	−	0.847005i	$-0.678403\pi$
$463$	−22.8767	−1.06317	−0.531585	+	0.847005i	$0.678403\pi$
$464$	19.3207	0.896939
$465$	−7.08038	−0.328345
$466$	29.2107	1.35316
$467$	13.0000	0.601568	0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000	0.601568	0.300784	+	0.953692i	$0.402752\pi$
$468$	0	0
$469$	−15.6504	−0.722668
$470$	27.4776	1.26745
$471$	−0.823708	−0.0379545
$472$	−2.54825	−0.117293
$473$	36.8092	1.69249
$474$	−16.9976	−0.780726
$475$	−23.1806	−1.06360
$476$	−3.23490	−0.148271
$477$	−3.08815	−0.141396
$478$	−24.3424	−1.11340
$479$	−38.0901	−1.74038	−0.870190	−	0.492717i	$-0.836004\pi$
$479$	−38.0901	−1.74038	−0.870190	+	0.492717i	$0.836004\pi$
$480$	−8.93900	−0.408008
$481$	0	0
$482$	11.2959	0.514514
$483$	−9.74632	−0.443473
$484$	19.8200	0.900909
$485$	12.5114	0.568114
$486$	1.80194	0.0817376
$487$	−21.2500	−0.962928	−0.481464	−	0.876466i	$-0.659895\pi$
$487$	−21.2500	−0.962928	−0.481464	+	0.876466i	$0.659895\pi$
$488$	−4.53856	−0.205451
$489$	6.26875	0.283483
$490$	12.6765	0.572665
$491$	−6.35019	−0.286580	−0.143290	−	0.989681i	$-0.545768\pi$
$491$	−6.35019	−0.286580	−0.143290	+	0.989681i	$0.545768\pi$
$492$	2.24698	0.101302
$493$	2.94571	0.132668
$494$	0	0
$495$	−7.49396	−0.336828
$496$	24.2000	1.08661
$497$	−31.4174	−1.40926
$498$	−11.6528	−0.522174
$499$	−4.65087	−0.208202	−0.104101	−	0.994567i	$-0.533196\pi$
$499$	−4.65087	−0.208202	−0.104101	+	0.994567i	$0.533196\pi$
$500$	−14.2567	−0.637578
$501$	−7.45042	−0.332860
$502$	−1.35690	−0.0605612
$503$	15.4752	0.690004	0.345002	−	0.938602i	$-0.387878\pi$
$503$	15.4752	0.690004	0.345002	+	0.938602i	$0.387878\pi$
$504$	−4.67456	−0.208222
$505$	−12.2489	−0.545069
$506$	26.4373	1.17528
$507$	0	0
$508$	−17.7845	−0.789059
$509$	−20.5047	−0.908855	−0.454428	−	0.890784i	$-0.650156\pi$
$509$	−20.5047	−0.908855	−0.454428	+	0.890784i	$0.650156\pi$
$510$	−1.96077	−0.0868244
$511$	10.1666	0.449744
$512$	17.1491	0.757892
$513$	7.96077	0.351477
$514$	35.5459	1.56786
$515$	8.16075	0.359606
$516$	−8.85086	−0.389637
$517$	−54.7254	−2.40682
$518$	38.7797	1.70388
$519$	−2.00969	−0.0882155
$520$	0	0
$521$	−42.0267	−1.84122	−0.920611	−	0.390481i	$-0.872309\pi$
$521$	−42.0267	−1.84122	−0.920611	+	0.390481i	$0.872309\pi$
$522$	−7.04892	−0.308523
$523$	−29.9885	−1.31131	−0.655653	−	0.755062i	$-0.727607\pi$
$523$	−29.9885	−1.31131	−0.655653	+	0.755062i	$0.727607\pi$
$524$	28.1836	1.23121
$525$	−10.0315	−0.437809
$526$	−31.7308	−1.38353
$527$	3.68963	0.160723
$528$	25.6136	1.11469
$529$	−14.9963	−0.652012
$530$	−8.04115	−0.349285
$531$	1.87800	0.0814984
$532$	34.1987	1.48270
$533$	0	0
$534$	2.08815	0.0903629
$535$	−9.73317	−0.420802
$536$	6.16421	0.266253
$537$	20.0368	0.864653
$538$	−29.5284	−1.27306
$539$	−25.2470	−1.08746
$540$	1.80194	0.0775431
$541$	36.3803	1.56411	0.782056	−	0.623208i	$-0.214171\pi$
$541$	36.3803	1.56411	0.782056	+	0.623208i	$0.214171\pi$
$542$	−1.43296	−0.0615509
$543$	24.1226	1.03520
$544$	4.65817	0.199717
$545$	−3.00000	−0.128506
$546$	0	0
$547$	−25.8159	−1.10381	−0.551905	−	0.833907i	$-0.686099\pi$
$547$	−25.8159	−1.10381	−0.551905	+	0.833907i	$0.686099\pi$
$548$	−17.0030	−0.726331
$549$	3.34481	0.142753
$550$	27.2107	1.16027
$551$	−31.1414	−1.32667
$552$	3.83877	0.163389
$553$	−32.4969	−1.38191
$554$	−8.70948	−0.370030
$555$	9.02715	0.383181
$556$	21.9487	0.930832
$557$	17.9903	0.762274	0.381137	−	0.924519i	$-0.375533\pi$
$557$	17.9903	0.762274	0.381137	+	0.924519i	$0.375533\pi$
$558$	−8.82908	−0.373765
$559$	0	0
$560$	−24.5875	−1.03901
$561$	3.90515	0.164876
$562$	33.8310	1.42707
$563$	−39.1323	−1.64923	−0.824614	−	0.565695i	$-0.808608\pi$
$563$	−39.1323	−1.64923	−0.824614	+	0.565695i	$0.808608\pi$
$564$	13.1588	0.554087
$565$	8.91377	0.375005
$566$	−14.2664	−0.599660
$567$	3.44504	0.144678
$568$	12.3744	0.519216
$569$	30.6002	1.28283	0.641413	−	0.767196i	$-0.278349\pi$
$569$	30.6002	1.28283	0.641413	+	0.767196i	$0.278349\pi$
$570$	20.7289	0.868236
$571$	−2.96184	−0.123949	−0.0619745	−	0.998078i	$-0.519740\pi$
$571$	−2.96184	−0.123949	−0.0619745	+	0.998078i	$0.519740\pi$
$572$	0	0
$573$	−7.08038	−0.295787
$574$	11.1860	0.466894
$575$	8.23788	0.343543
$576$	−1.26875	−0.0528646
$577$	−0.819396	−0.0341119	−0.0170560	−	0.999855i	$-0.505429\pi$
$577$	−0.819396	−0.0341119	−0.0170560	+	0.999855i	$0.505429\pi$
$578$	−29.6112	−1.23166
$579$	9.76809	0.405948
$580$	−7.04892	−0.292690
$581$	−22.2784	−0.924265
$582$	15.6015	0.646702
$583$	16.0151	0.663276
$584$	−4.00431	−0.165700
$585$	0	0
$586$	11.8552	0.489732
$587$	−31.7995	−1.31251	−0.656254	−	0.754540i	$-0.727860\pi$
$587$	−31.7995	−1.31251	−0.656254	+	0.754540i	$0.727860\pi$
$588$	6.07069	0.250351
$589$	−39.0060	−1.60721
$590$	4.89008	0.201322
$591$	23.4112	0.963008
$592$	−30.8538	−1.26808
$593$	−4.26337	−0.175076	−0.0875379	−	0.996161i	$-0.527900\pi$
$593$	−4.26337	−0.175076	−0.0875379	+	0.996161i	$0.527900\pi$
$594$	−9.34481	−0.383422
$595$	−3.74871	−0.153682
$596$	15.8847	0.650663
$597$	4.02475	0.164722
$598$	0	0
$599$	24.7278	1.01035	0.505175	−	0.863017i	$-0.331428\pi$
$599$	24.7278	1.01035	0.505175	+	0.863017i	$0.331428\pi$
$600$	3.95108	0.161302
$601$	6.82371	0.278345	0.139172	−	0.990268i	$-0.455556\pi$
$601$	6.82371	0.278345	0.139172	+	0.990268i	$0.455556\pi$
$602$	−44.0616	−1.79582
$603$	−4.54288	−0.185000
$604$	19.5036	0.793592
$605$	22.9681	0.933785
$606$	−15.2741	−0.620469
$607$	31.9963	1.29869	0.649344	−	0.760494i	$-0.275043\pi$
$607$	31.9963	1.29869	0.649344	+	0.760494i	$0.275043\pi$
$608$	−49.2452	−1.99716
$609$	−13.4765	−0.546095
$610$	8.70948	0.352637
$611$	0	0
$612$	−0.939001	−0.0379569
$613$	33.5875	1.35659	0.678293	−	0.734792i	$-0.262720\pi$
$613$	33.5875	1.35659	0.678293	+	0.734792i	$0.262720\pi$
$614$	−44.8049	−1.80818
$615$	2.60388	0.104998
$616$	24.2422	0.976746
$617$	−26.5870	−1.07035	−0.535176	−	0.844740i	$-0.679755\pi$
$617$	−26.5870	−1.07035	−0.535176	+	0.844740i	$0.679755\pi$
$618$	10.1763	0.409350
$619$	−9.17928	−0.368946	−0.184473	−	0.982838i	$-0.559058\pi$
$619$	−9.17928	−0.368946	−0.184473	+	0.982838i	$0.559058\pi$
$620$	−8.82908	−0.354585
$621$	−2.82908	−0.113527
$622$	−30.7778	−1.23408
$623$	3.99223	0.159945
$624$	0	0
$625$	−1.96184	−0.0784735
$626$	28.2857	1.13053
$627$	−41.2844	−1.64874
$628$	−1.02715	−0.0409876
$629$	−4.70410	−0.187565
$630$	8.97046	0.357392
$631$	17.0043	0.676931	0.338465	−	0.940979i	$-0.390092\pi$
$631$	17.0043	0.676931	0.338465	+	0.940979i	$0.390092\pi$
$632$	12.7995	0.509139
$633$	−3.91185	−0.155482
$634$	59.0713	2.34602
$635$	−20.6093	−0.817853
$636$	−3.85086	−0.152696
$637$	0	0
$638$	36.5555	1.44725
$639$	−9.11960	−0.360766
$640$	14.5743	0.576101
$641$	−21.6649	−0.855711	−0.427856	−	0.903847i	$-0.640731\pi$
$641$	−21.6649	−0.855711	−0.427856	+	0.903847i	$0.640731\pi$
$642$	−12.1371	−0.479012
$643$	9.35557	0.368948	0.184474	−	0.982837i	$-0.440942\pi$
$643$	9.35557	0.368948	0.184474	+	0.982837i	$0.440942\pi$
$644$	−12.1535	−0.478913
$645$	−10.2567	−0.403856
$646$	−10.8019	−0.424997
$647$	−0.702775	−0.0276289	−0.0138145	−	0.999905i	$-0.504397\pi$
$647$	−0.702775	−0.0276289	−0.0138145	+	0.999905i	$0.504397\pi$
$648$	−1.35690	−0.0533039
$649$	−9.73928	−0.382300
$650$	0	0
$651$	−16.8799	−0.661576
$652$	7.81700	0.306137
$653$	−37.3411	−1.46127	−0.730635	−	0.682768i	$-0.760776\pi$
$653$	−37.3411	−1.46127	−0.730635	+	0.682768i	$0.760776\pi$
$654$	−3.74094	−0.146282
$655$	32.6601	1.27614
$656$	−8.89977	−0.347478
$657$	2.95108	0.115133
$658$	65.5077	2.55376
$659$	−0.735562	−0.0286534	−0.0143267	−	0.999897i	$-0.504560\pi$
$659$	−0.735562	−0.0286534	−0.0143267	+	0.999897i	$0.504560\pi$
$660$	−9.34481	−0.363746
$661$	13.8485	0.538643	0.269321	−	0.963050i	$-0.413201\pi$
$661$	13.8485	0.538643	0.269321	+	0.963050i	$0.413201\pi$
$662$	−52.5478	−2.04233
$663$	0	0
$664$	8.77479	0.340528
$665$	39.6305	1.53681
$666$	11.2567	0.436187
$667$	11.0670	0.428515
$668$	−9.29052	−0.359461
$669$	7.44935	0.288009
$670$	−11.8291	−0.456997
$671$	−17.3461	−0.669640
$672$	−21.3110	−0.822088
$673$	−6.35019	−0.244782	−0.122391	−	0.992482i	$-0.539056\pi$
$673$	−6.35019	−0.244782	−0.122391	+	0.992482i	$0.539056\pi$
$674$	−59.9885	−2.31067
$675$	−2.91185	−0.112077
$676$	0	0
$677$	33.7241	1.29612	0.648061	−	0.761589i	$-0.275580\pi$
$677$	33.7241	1.29612	0.648061	+	0.761589i	$0.275580\pi$
$678$	11.1153	0.426880
$679$	29.8278	1.14468
$680$	1.47650	0.0566212
$681$	−21.2500	−0.814300
$682$	45.7875	1.75329
$683$	19.2687	0.737298	0.368649	−	0.929569i	$-0.379820\pi$
$683$	19.2687	0.737298	0.368649	+	0.929569i	$0.379820\pi$
$684$	9.92692	0.379565
$685$	−19.7036	−0.752837
$686$	−13.2330	−0.505237
$687$	9.29590	0.354661
$688$	35.0562	1.33651
$689$	0	0
$690$	−7.36658	−0.280441
$691$	−39.4010	−1.49889	−0.749443	−	0.662069i	$-0.769679\pi$
$691$	−39.4010	−1.49889	−0.749443	+	0.662069i	$0.769679\pi$
$692$	−2.50604	−0.0952654
$693$	−17.8659	−0.678670
$694$	−1.57434	−0.0597610
$695$	25.4349	0.964800
$696$	5.30798	0.201198
$697$	−1.35690	−0.0513961
$698$	−5.82371	−0.220431
$699$	16.2107	0.613146
$700$	−12.5090	−0.472797
$701$	18.3985	0.694902	0.347451	−	0.937698i	$-0.387047\pi$
$701$	18.3985	0.694902	0.347451	+	0.937698i	$0.387047\pi$
$702$	0	0
$703$	49.7308	1.87563
$704$	6.57971	0.247982
$705$	15.2489	0.574307
$706$	14.6799	0.552487
$707$	−29.2019	−1.09825
$708$	2.34183	0.0880114
$709$	−38.4553	−1.44422	−0.722110	−	0.691778i	$-0.756828\pi$
$709$	−38.4553	−1.44422	−0.722110	+	0.691778i	$0.756828\pi$
$710$	−23.7463	−0.891183
$711$	−9.43296	−0.353764
$712$	−1.57242	−0.0589288
$713$	13.8619	0.519131
$714$	−4.67456	−0.174941
$715$	0	0
$716$	24.9855	0.933753
$717$	−13.5090	−0.504504
$718$	4.75840	0.177582
$719$	48.4999	1.80874	0.904371	−	0.426747i	$-0.140341\pi$
$719$	48.4999	1.80874	0.904371	+	0.426747i	$0.140341\pi$
$720$	−7.13706	−0.265983
$721$	19.4556	0.724564
$722$	79.9590	2.97576
$723$	6.26875	0.233137
$724$	30.0804	1.11793
$725$	11.3907	0.423042
$726$	28.6407	1.06296
$727$	19.0344	0.705948	0.352974	−	0.935633i	$-0.385170\pi$
$727$	19.0344	0.705948	0.352974	+	0.935633i	$0.385170\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	7.68425	0.284407
$731$	5.34481	0.197685
$732$	4.17092	0.154161
$733$	24.6213	0.909410	0.454705	−	0.890642i	$-0.349745\pi$
$733$	24.6213	0.909410	0.454705	+	0.890642i	$0.349745\pi$
$734$	−5.23298	−0.193153
$735$	7.03492	0.259487
$736$	17.5007	0.645083
$737$	23.5593	0.867817
$738$	3.24698	0.119523
$739$	−44.5115	−1.63738	−0.818692	−	0.574233i	$-0.805300\pi$
$739$	−44.5115	−1.63738	−0.818692	+	0.574233i	$0.805300\pi$
$740$	11.2567	0.413803
$741$	0	0
$742$	−19.1704	−0.703769
$743$	10.4112	0.381950	0.190975	−	0.981595i	$-0.438835\pi$
$743$	10.4112	0.381950	0.190975	+	0.981595i	$0.438835\pi$
$744$	6.64848	0.243745
$745$	18.4077	0.674407
$746$	−15.1336	−0.554081
$747$	−6.46681	−0.236608
$748$	4.86964	0.178052
$749$	−23.2043	−0.847866
$750$	−20.6015	−0.752260
$751$	1.69979	0.0620263	0.0310131	−	0.999519i	$-0.490127\pi$
$751$	1.69979	0.0620263	0.0310131	+	0.999519i	$0.490127\pi$
$752$	−52.1191	−1.90059
$753$	−0.753020	−0.0274416
$754$	0	0
$755$	22.6015	0.822552
$756$	4.29590	0.156240
$757$	27.4252	0.996786	0.498393	−	0.866951i	$-0.333924\pi$
$757$	27.4252	0.996786	0.498393	+	0.866951i	$0.333924\pi$
$758$	28.3773	1.03071
$759$	14.6716	0.532545
$760$	−15.6093	−0.566207
$761$	−5.02608	−0.182195	−0.0910977	−	0.995842i	$-0.529038\pi$
$761$	−5.02608	−0.182195	−0.0910977	+	0.995842i	$0.529038\pi$
$762$	−25.6993	−0.930988
$763$	−7.15213	−0.258924
$764$	−8.82908	−0.319425
$765$	−1.08815	−0.0393420
$766$	22.9541	0.829364
$767$	0	0
$768$	20.7114	0.747358
$769$	42.4456	1.53063	0.765314	−	0.643657i	$-0.222584\pi$
$769$	42.4456	1.53063	0.765314	+	0.643657i	$0.222584\pi$
$770$	−46.5206	−1.67649
$771$	19.7265	0.710431
$772$	12.1806	0.438390
$773$	26.3593	0.948078	0.474039	−	0.880504i	$-0.342796\pi$
$773$	26.3593	0.948078	0.474039	+	0.880504i	$0.342796\pi$
$774$	−12.7899	−0.459722
$775$	14.2674	0.512501
$776$	−11.7482	−0.421737
$777$	21.5211	0.772065
$778$	−0.559270	−0.0200508
$779$	14.3448	0.513956
$780$	0	0
$781$	47.2941	1.69232
$782$	3.83877	0.137274
$783$	−3.91185	−0.139798
$784$	−24.0446	−0.858736
$785$	−1.19029	−0.0424834
$786$	40.7265	1.45266
$787$	17.1424	0.611062	0.305531	−	0.952182i	$-0.401166\pi$
$787$	17.1424	0.611062	0.305531	+	0.952182i	$0.401166\pi$
$788$	29.1933	1.03997
$789$	−17.6093	−0.626906
$790$	−24.5623	−0.873886
$791$	21.2508	0.755592
$792$	7.03684	0.250043
$793$	0	0
$794$	2.68664	0.0953455
$795$	−4.46250	−0.158269
$796$	5.01879	0.177886
$797$	30.1629	1.06842	0.534212	−	0.845351i	$-0.320608\pi$
$797$	30.1629	1.06842	0.534212	+	0.845351i	$0.320608\pi$
$798$	49.4185	1.74940
$799$	−7.94630	−0.281120
$800$	18.0127	0.636844
$801$	1.15883	0.0409454
$802$	−42.9463	−1.51649
$803$	−15.3043	−0.540076
$804$	−5.66487	−0.199785
$805$	−14.0838	−0.496390
$806$	0	0
$807$	−16.3870	−0.576851
$808$	11.5017	0.404629
$809$	−29.8504	−1.04948	−0.524742	−	0.851261i	$-0.675838\pi$
$809$	−29.8504	−1.04948	−0.524742	+	0.851261i	$0.675838\pi$
$810$	2.60388	0.0914909
$811$	47.7362	1.67624	0.838122	−	0.545484i	$-0.183654\pi$
$811$	47.7362	1.67624	0.838122	+	0.545484i	$0.183654\pi$
$812$	−16.8049	−0.589737
$813$	−0.795233	−0.0278900
$814$	−58.3769	−2.04611
$815$	9.05861	0.317309
$816$	3.71917	0.130197
$817$	−56.5042	−1.97683
$818$	7.68963	0.268862
$819$	0	0
$820$	3.24698	0.113389
$821$	−17.9299	−0.625758	−0.312879	−	0.949793i	$-0.601293\pi$
$821$	−17.9299	−0.625758	−0.312879	+	0.949793i	$0.601293\pi$
$822$	−24.5700	−0.856978
$823$	54.3196	1.89346	0.946731	−	0.322026i	$-0.104364\pi$
$823$	54.3196	1.89346	0.946731	+	0.322026i	$0.104364\pi$
$824$	−7.66296	−0.266952
$825$	15.1008	0.525743
$826$	11.6582	0.405640
$827$	49.1041	1.70752	0.853758	−	0.520670i	$-0.174318\pi$
$827$	49.1041	1.70752	0.853758	+	0.520670i	$0.174318\pi$
$828$	−3.52781	−0.122600
$829$	−7.35796	−0.255553	−0.127776	−	0.991803i	$-0.540784\pi$
$829$	−7.35796	−0.255553	−0.127776	+	0.991803i	$0.540784\pi$
$830$	−16.8388	−0.584482
$831$	−4.83340	−0.167669
$832$	0	0
$833$	−3.66594	−0.127017
$834$	31.7168	1.09826
$835$	−10.7662	−0.372579
$836$	−51.4808	−1.78050
$837$	−4.89977	−0.169361
$838$	53.4989	1.84809
$839$	−36.5013	−1.26016	−0.630082	−	0.776529i	$-0.716979\pi$
$839$	−36.5013	−1.26016	−0.630082	+	0.776529i	$0.716979\pi$
$840$	−6.75494	−0.233068
$841$	−13.6974	−0.472324
$842$	52.9754	1.82565
$843$	18.7748	0.646638
$844$	−4.87800	−0.167908
$845$	0	0
$846$	19.0151	0.653751
$847$	54.7569	1.88147
$848$	15.2524	0.523768
$849$	−7.91723	−0.271719
$850$	3.95108	0.135521
$851$	−17.6732	−0.605831
$852$	−11.3720	−0.389597
$853$	−9.73855	−0.333441	−0.166721	−	0.986004i	$-0.553318\pi$
$853$	−9.73855	−0.333441	−0.166721	+	0.986004i	$0.553318\pi$
$854$	20.7638	0.710522
$855$	11.5036	0.393416
$856$	9.13946	0.312380
$857$	−15.2030	−0.519323	−0.259662	−	0.965700i	$-0.583611\pi$
$857$	−15.2030	−0.519323	−0.259662	+	0.965700i	$0.583611\pi$
$858$	0	0
$859$	−31.9885	−1.09143	−0.545717	−	0.837970i	$-0.683743\pi$
$859$	−31.9885	−1.09143	−0.545717	+	0.837970i	$0.683743\pi$
$860$	−12.7899	−0.436130
$861$	6.20775	0.211560
$862$	−59.5652	−2.02880
$863$	−35.2905	−1.20130	−0.600652	−	0.799511i	$-0.705092\pi$
$863$	−35.2905	−1.20130	−0.600652	+	0.799511i	$0.705092\pi$
$864$	−6.18598	−0.210451
$865$	−2.90408	−0.0987418
$866$	−52.7362	−1.79205
$867$	−16.4330	−0.558093
$868$	−21.0489	−0.714447
$869$	48.9191	1.65947
$870$	−10.1860	−0.345337
$871$	0	0
$872$	2.81700	0.0953958
$873$	8.65817	0.293035
$874$	−40.5827	−1.37273
$875$	−39.3870	−1.33152
$876$	3.67994	0.124334
$877$	−15.3263	−0.517532	−0.258766	−	0.965940i	$-0.583316\pi$
$877$	−15.3263	−0.517532	−0.258766	+	0.965940i	$0.583316\pi$
$878$	−3.84117	−0.129633
$879$	6.57912	0.221908
$880$	37.0127	1.24770
$881$	−36.4306	−1.22738	−0.613689	−	0.789548i	$-0.710315\pi$
$881$	−36.4306	−1.22738	−0.613689	+	0.789548i	$0.710315\pi$
$882$	8.77240	0.295382
$883$	−37.6819	−1.26810	−0.634048	−	0.773294i	$-0.718608\pi$
$883$	−37.6819	−1.26810	−0.634048	+	0.773294i	$0.718608\pi$
$884$	0	0
$885$	2.71379	0.0912231
$886$	−41.4306	−1.39189
$887$	4.24890	0.142664	0.0713320	−	0.997453i	$-0.477275\pi$
$887$	4.24890	0.142664	0.0713320	+	0.997453i	$0.477275\pi$
$888$	−8.47650	−0.284453
$889$	−49.1333	−1.64788
$890$	3.01746	0.101145
$891$	−5.18598	−0.173737
$892$	9.28919	0.311025
$893$	84.0066	2.81117
$894$	22.9541	0.767699
$895$	28.9541	0.967828
$896$	34.7458	1.16078
$897$	0	0
$898$	−23.3134	−0.777977
$899$	19.1672	0.639262
$900$	−3.63102	−0.121034
$901$	2.32544	0.0774715
$902$	−16.8388	−0.560670
$903$	−24.4523	−0.813723
$904$	−8.37004	−0.278383
$905$	34.8582	1.15872
$906$	28.1836	0.936337
$907$	−12.6183	−0.418985	−0.209493	−	0.977810i	$-0.567181\pi$
$907$	−12.6183	−0.418985	−0.209493	+	0.977810i	$0.567181\pi$
$908$	−26.4983	−0.879376
$909$	−8.47650	−0.281148
$910$	0	0
$911$	6.77777	0.224558	0.112279	−	0.993677i	$-0.464185\pi$
$911$	6.77777	0.224558	0.112279	+	0.993677i	$0.464185\pi$
$912$	−39.3183	−1.30196
$913$	33.5368	1.10990
$914$	−8.74525	−0.289267
$915$	4.83340	0.159787
$916$	11.5918	0.383004
$917$	77.8631	2.57126
$918$	−1.35690	−0.0447842
$919$	−20.4674	−0.675157	−0.337579	−	0.941297i	$-0.609608\pi$
$919$	−20.4674	−0.675157	−0.337579	+	0.941297i	$0.609608\pi$
$920$	5.54719	0.182885
$921$	−24.8649	−0.819325
$922$	33.9385	1.11771
$923$	0	0
$924$	−22.2784	−0.732907
$925$	−18.1903	−0.598093
$926$	−41.2223	−1.35465
$927$	5.64742	0.185485
$928$	24.1987	0.794360
$929$	−4.65220	−0.152634	−0.0763169	−	0.997084i	$-0.524316\pi$
$929$	−4.65220	−0.152634	−0.0763169	+	0.997084i	$0.524316\pi$
$930$	−12.7584	−0.418364
$931$	38.7555	1.27016
$932$	20.2145	0.662147
$933$	−17.0804	−0.559186
$934$	23.4252	0.766496
$935$	5.64310	0.184549
$936$	0	0
$937$	−41.8544	−1.36732	−0.683662	−	0.729798i	$-0.739614\pi$
$937$	−41.8544	−1.36732	−0.683662	+	0.729798i	$0.739614\pi$
$938$	−28.2010	−0.920797
$939$	15.6974	0.512265
$940$	19.0151	0.620203
$941$	30.3454	0.989232	0.494616	−	0.869112i	$-0.335309\pi$
$941$	30.3454	0.989232	0.494616	+	0.869112i	$0.335309\pi$
$942$	−1.48427	−0.0483601
$943$	−5.09783	−0.166008
$944$	−9.27545	−0.301890
$945$	4.97823	0.161942
$946$	66.3279	2.15651
$947$	12.0325	0.391004	0.195502	−	0.980703i	$-0.437366\pi$
$947$	12.0325	0.391004	0.195502	+	0.980703i	$0.437366\pi$
$948$	−11.7627	−0.382035
$949$	0	0
$950$	−41.7700	−1.35520
$951$	32.7821	1.06303
$952$	3.52004	0.114085
$953$	22.9825	0.744478	0.372239	−	0.928137i	$-0.378590\pi$
$953$	22.9825	0.744478	0.372239	+	0.928137i	$0.378590\pi$
$954$	−5.56465	−0.180162
$955$	−10.2314	−0.331082
$956$	−16.8455	−0.544822
$957$	20.2868	0.655779
$958$	−68.6359	−2.21753
$959$	−46.9743	−1.51688
$960$	−1.83340	−0.0591726
$961$	−6.99223	−0.225556
$962$	0	0
$963$	−6.73556	−0.217050
$964$	7.81700	0.251769
$965$	14.1153	0.454387
$966$	−17.5623	−0.565056
$967$	−38.8883	−1.25056	−0.625281	−	0.780399i	$-0.715016\pi$
$967$	−38.8883	−1.25056	−0.625281	+	0.780399i	$0.715016\pi$
$968$	−21.5670	−0.693191
$969$	−5.99462	−0.192575
$970$	22.5448	0.723870
$971$	−57.5133	−1.84569	−0.922845	−	0.385171i	$-0.874143\pi$
$971$	−57.5133	−1.84569	−0.922845	+	0.385171i	$0.874143\pi$
$972$	1.24698	0.0399969
$973$	60.6378	1.94396
$974$	−38.2911	−1.22693
$975$	0	0
$976$	−16.5200	−0.528794
$977$	16.3690	0.523690	0.261845	−	0.965110i	$-0.415669\pi$
$977$	16.3690	0.523690	0.261845	+	0.965110i	$0.415669\pi$
$978$	11.2959	0.361203
$979$	−6.00969	−0.192070
$980$	8.77240	0.280224
$981$	−2.07606	−0.0662836
$982$	−11.4426	−0.365150
$983$	−15.6963	−0.500635	−0.250318	−	0.968164i	$-0.580535\pi$
$983$	−15.6963	−0.500635	−0.250318	+	0.968164i	$0.580535\pi$
$984$	−2.44504	−0.0779451
$985$	33.8301	1.07792
$986$	5.30798	0.169040
$987$	36.3540	1.15716
$988$	0	0
$989$	20.0804	0.638519
$990$	−13.5036	−0.429174
$991$	−11.2644	−0.357827	−0.178913	−	0.983865i	$-0.557258\pi$
$991$	−11.2644	−0.357827	−0.178913	+	0.983865i	$0.557258\pi$
$992$	30.3099	0.962340
$993$	−29.1618	−0.925422
$994$	−56.6122	−1.79563
$995$	5.81594	0.184378
$996$	−8.06398	−0.255517
$997$	−7.70112	−0.243897	−0.121948	−	0.992536i	$-0.538914\pi$
$997$	−7.70112	−0.243897	−0.121948	+	0.992536i	$0.538914\pi$
$998$	−8.38059	−0.265283
$999$	6.24698	0.197646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.a.k.1.3	yes	3
3.2	odd	2		1521.2.a.p.1.1		3
4.3	odd	2		8112.2.a.cf.1.2		3
13.2	odd	12		507.2.j.h.316.6		12
13.3	even	3		507.2.e.j.22.1		6
13.4	even	6		507.2.e.k.484.3		6
13.5	odd	4		507.2.b.g.337.1		6
13.6	odd	12		507.2.j.h.361.1		12
13.7	odd	12		507.2.j.h.361.6		12
13.8	odd	4		507.2.b.g.337.6		6
13.9	even	3		507.2.e.j.484.1		6
13.10	even	6		507.2.e.k.22.3		6
13.11	odd	12		507.2.j.h.316.1		12
13.12	even	2		507.2.a.j.1.1	✓	3
39.5	even	4		1521.2.b.m.1351.6		6
39.8	even	4		1521.2.b.m.1351.1		6
39.38	odd	2		1521.2.a.q.1.3		3
52.51	odd	2		8112.2.a.by.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.j.1.1	✓	3	13.12	even	2
507.2.a.k.1.3	yes	3	1.1	even	1	trivial
507.2.b.g.337.1		6	13.5	odd	4
507.2.b.g.337.6		6	13.8	odd	4
507.2.e.j.22.1		6	13.3	even	3
507.2.e.j.484.1		6	13.9	even	3
507.2.e.k.22.3		6	13.10	even	6
507.2.e.k.484.3		6	13.4	even	6
507.2.j.h.316.1		12	13.11	odd	12
507.2.j.h.316.6		12	13.2	odd	12
507.2.j.h.361.1		12	13.6	odd	12
507.2.j.h.361.6		12	13.7	odd	12
1521.2.a.p.1.1		3	3.2	odd	2
1521.2.a.q.1.3		3	39.38	odd	2
1521.2.b.m.1351.1		6	39.8	even	4
1521.2.b.m.1351.6		6	39.5	even	4
8112.2.a.by.1.2		3	52.51	odd	2
8112.2.a.cf.1.2		3	4.3	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q+1.80194 q^{2} +1.00000 q^{3} +1.24698 q^{4} +1.44504 q^{5} +1.80194 q^{6} +3.44504 q^{7} -1.35690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.80194 q^{2} +1.00000 q^{3} +1.24698 q^{4} +1.44504 q^{5} +1.80194 q^{6} +3.44504 q^{7} -1.35690 q^{8} +1.00000 q^{9} +2.60388 q^{10} -5.18598 q^{11} +1.24698 q^{12} +6.20775 q^{14} +1.44504 q^{15} -4.93900 q^{16} -0.753020 q^{17} +1.80194 q^{18} +7.96077 q^{19} +1.80194 q^{20} +3.44504 q^{21} -9.34481 q^{22} -2.82908 q^{23} -1.35690 q^{24} -2.91185 q^{25} +1.00000 q^{27} +4.29590 q^{28} -3.91185 q^{29} +2.60388 q^{30} -4.89977 q^{31} -6.18598 q^{32} -5.18598 q^{33} -1.35690 q^{34} +4.97823 q^{35} +1.24698 q^{36} +6.24698 q^{37} +14.3448 q^{38} -1.96077 q^{40} +1.80194 q^{41} +6.20775 q^{42} -7.09783 q^{43} -6.46681 q^{44} +1.44504 q^{45} -5.09783 q^{46} +10.5526 q^{47} -4.93900 q^{48} +4.86831 q^{49} -5.24698 q^{50} -0.753020 q^{51} -3.08815 q^{53} +1.80194 q^{54} -7.49396 q^{55} -4.67456 q^{56} +7.96077 q^{57} -7.04892 q^{58} +1.87800 q^{59} +1.80194 q^{60} +3.34481 q^{61} -8.82908 q^{62} +3.44504 q^{63} -1.26875 q^{64} -9.34481 q^{66} -4.54288 q^{67} -0.939001 q^{68} -2.82908 q^{69} +8.97046 q^{70} -9.11960 q^{71} -1.35690 q^{72} +2.95108 q^{73} +11.2567 q^{74} -2.91185 q^{75} +9.92692 q^{76} -17.8659 q^{77} -9.43296 q^{79} -7.13706 q^{80} +1.00000 q^{81} +3.24698 q^{82} -6.46681 q^{83} +4.29590 q^{84} -1.08815 q^{85} -12.7899 q^{86} -3.91185 q^{87} +7.03684 q^{88} +1.15883 q^{89} +2.60388 q^{90} -3.52781 q^{92} -4.89977 q^{93} +19.0151 q^{94} +11.5036 q^{95} -6.18598 q^{96} +8.65817 q^{97} +8.77240 q^{98} -5.18598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + q^{6} + 10 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + q^6 + 10 * q^7 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + q^{6} + 10 q^{7} + 3 q^{9} - q^{10} - q^{11} - q^{12} + q^{14} + 4 q^{15} - 5 q^{16} - 7 q^{17} + q^{18} + 11 q^{19} + q^{20} + 10 q^{21} - 5 q^{22} + 2 q^{23} - 5 q^{25} + 3 q^{27} - q^{28} - 8 q^{29} - q^{30} + 8 q^{31} - 4 q^{32} - q^{33} + 18 q^{35} - q^{36} + 14 q^{37} + 20 q^{38} + 7 q^{40} + q^{41} + q^{42} - 3 q^{43} - 16 q^{44} + 4 q^{45} + 3 q^{46} - 9 q^{47} - 5 q^{48} + 17 q^{49} - 11 q^{50} - 7 q^{51} - 13 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 11 q^{57} - 12 q^{58} - 14 q^{59} + q^{60} - 13 q^{61} - 16 q^{62} + 10 q^{63} + 4 q^{64} - 5 q^{66} + 5 q^{67} + 7 q^{68} + 2 q^{69} - 8 q^{70} - 6 q^{71} + 18 q^{73} + 7 q^{74} - 5 q^{75} + q^{76} - 15 q^{77} - 9 q^{79} - 16 q^{80} + 3 q^{81} + 5 q^{82} - 16 q^{83} - q^{84} - 7 q^{85} - 15 q^{86} - 8 q^{87} - 7 q^{88} - 5 q^{89} - q^{90} - 17 q^{92} + 8 q^{93} + 32 q^{94} + 3 q^{95} - 4 q^{96} + 5 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + q^6 + 10 * q^7 + 3 * q^9 - q^10 - q^11 - q^12 + q^14 + 4 * q^15 - 5 * q^16 - 7 * q^17 + q^18 + 11 * q^19 + q^20 + 10 * q^21 - 5 * q^22 + 2 * q^23 - 5 * q^25 + 3 * q^27 - q^28 - 8 * q^29 - q^30 + 8 * q^31 - 4 * q^32 - q^33 + 18 * q^35 - q^36 + 14 * q^37 + 20 * q^38 + 7 * q^40 + q^41 + q^42 - 3 * q^43 - 16 * q^44 + 4 * q^45 + 3 * q^46 - 9 * q^47 - 5 * q^48 + 17 * q^49 - 11 * q^50 - 7 * q^51 - 13 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 11 * q^57 - 12 * q^58 - 14 * q^59 + q^60 - 13 * q^61 - 16 * q^62 + 10 * q^63 + 4 * q^64 - 5 * q^66 + 5 * q^67 + 7 * q^68 + 2 * q^69 - 8 * q^70 - 6 * q^71 + 18 * q^73 + 7 * q^74 - 5 * q^75 + q^76 - 15 * q^77 - 9 * q^79 - 16 * q^80 + 3 * q^81 + 5 * q^82 - 16 * q^83 - q^84 - 7 * q^85 - 15 * q^86 - 8 * q^87 - 7 * q^88 - 5 * q^89 - q^90 - 17 * q^92 + 8 * q^93 + 32 * q^94 + 3 * q^95 - 4 * q^96 + 5 * q^97 - 13 * q^98 - q^99

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