LMFDB - Embedded newform 325.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, 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("325.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.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:	$2.59513806569$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67513 q^{2} +0.481194 q^{3} +5.15633 q^{4} -1.28726 q^{6} -0.806063 q^{7} -8.44358 q^{8} -2.76845 q^{9} +O(q^{10})$	\(q-2.67513 q^{2} +0.481194 q^{3} +5.15633 q^{4} -1.28726 q^{6} -0.806063 q^{7} -8.44358 q^{8} -2.76845 q^{9} -3.67513 q^{11} +2.48119 q^{12} +1.00000 q^{13} +2.15633 q^{14} +12.2750 q^{16} +1.35026 q^{17} +7.40597 q^{18} -1.67513 q^{19} -0.387873 q^{21} +9.83146 q^{22} -6.48119 q^{23} -4.06300 q^{24} -2.67513 q^{26} -2.77575 q^{27} -4.15633 q^{28} +2.41819 q^{29} -5.28726 q^{31} -15.9502 q^{32} -1.76845 q^{33} -3.61213 q^{34} -14.2750 q^{36} -3.76845 q^{37} +4.48119 q^{38} +0.481194 q^{39} -8.31265 q^{41} +1.03761 q^{42} +6.79384 q^{43} -18.9502 q^{44} +17.3380 q^{46} -3.19394 q^{47} +5.90668 q^{48} -6.35026 q^{49} +0.649738 q^{51} +5.15633 q^{52} -5.73813 q^{53} +7.42548 q^{54} +6.80606 q^{56} -0.806063 q^{57} -6.46898 q^{58} +5.98778 q^{59} -1.76845 q^{61} +14.1441 q^{62} +2.23155 q^{63} +18.1187 q^{64} +4.73084 q^{66} -9.89446 q^{67} +6.96239 q^{68} -3.11871 q^{69} +8.56230 q^{71} +23.3757 q^{72} +11.7685 q^{73} +10.0811 q^{74} -8.63752 q^{76} +2.96239 q^{77} -1.28726 q^{78} -2.26187 q^{79} +6.96968 q^{81} +22.2374 q^{82} -3.84367 q^{83} -2.00000 q^{84} -18.1744 q^{86} +1.16362 q^{87} +31.0313 q^{88} +2.77575 q^{89} -0.806063 q^{91} -33.4191 q^{92} -2.54420 q^{93} +8.54420 q^{94} -7.67513 q^{96} +1.87399 q^{97} +16.9878 q^{98} +10.1744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 4 q^{3} + 5 q^{4} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 4 * q^3 + 5 * q^4 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 4 q^{3} + 5 q^{4} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} + 2 q^{12} + 3 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} - 5 q^{18} - 2 q^{21} + 14 q^{22} - 14 q^{23} - 8 q^{24} - 3 q^{26} - 10 q^{27} - 2 q^{28} + 6 q^{29} - 10 q^{31} - 11 q^{32} + 6 q^{33} - 10 q^{34} - 11 q^{36} + 8 q^{38} - 4 q^{39} - 4 q^{41} + 14 q^{42} - 6 q^{43} - 20 q^{44} + 16 q^{46} - 10 q^{47} + 24 q^{48} - 9 q^{49} + 12 q^{51} + 5 q^{52} - 8 q^{53} + 34 q^{54} + 20 q^{56} - 2 q^{57} + 12 q^{58} - 8 q^{59} + 6 q^{61} + 6 q^{62} + 18 q^{63} + 33 q^{64} - 8 q^{66} - 10 q^{67} + 10 q^{68} + 12 q^{69} - 12 q^{71} + 45 q^{72} + 24 q^{73} - 2 q^{74} - 10 q^{76} - 2 q^{77} + 2 q^{78} - 16 q^{79} + 23 q^{81} + 24 q^{82} - 22 q^{83} - 6 q^{84} - 16 q^{86} + 6 q^{87} + 24 q^{88} + 10 q^{89} - 2 q^{91} - 32 q^{92} + 2 q^{93} + 16 q^{94} - 18 q^{96} + 14 q^{97} + 25 q^{98} - 8 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 4 * q^3 + 5 * q^4 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 + 2 * q^12 + 3 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 - 5 * q^18 - 2 * q^21 + 14 * q^22 - 14 * q^23 - 8 * q^24 - 3 * q^26 - 10 * q^27 - 2 * q^28 + 6 * q^29 - 10 * q^31 - 11 * q^32 + 6 * q^33 - 10 * q^34 - 11 * q^36 + 8 * q^38 - 4 * q^39 - 4 * q^41 + 14 * q^42 - 6 * q^43 - 20 * q^44 + 16 * q^46 - 10 * q^47 + 24 * q^48 - 9 * q^49 + 12 * q^51 + 5 * q^52 - 8 * q^53 + 34 * q^54 + 20 * q^56 - 2 * q^57 + 12 * q^58 - 8 * q^59 + 6 * q^61 + 6 * q^62 + 18 * q^63 + 33 * q^64 - 8 * q^66 - 10 * q^67 + 10 * q^68 + 12 * q^69 - 12 * q^71 + 45 * q^72 + 24 * q^73 - 2 * q^74 - 10 * q^76 - 2 * q^77 + 2 * q^78 - 16 * q^79 + 23 * q^81 + 24 * q^82 - 22 * q^83 - 6 * q^84 - 16 * q^86 + 6 * q^87 + 24 * q^88 + 10 * q^89 - 2 * q^91 - 32 * q^92 + 2 * q^93 + 16 * q^94 - 18 * q^96 + 14 * q^97 + 25 * q^98 - 8 * 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 $

$2$	−2.67513	−1.89160	−0.945802	−	0.324745i	$-0.894721\pi$
$2$	−2.67513	−1.89160	−0.945802	+	0.324745i	$0.894721\pi$
$3$	0.481194	0.277818	0.138909	−	0.990305i	$-0.455641\pi$
$3$	0.481194	0.277818	0.138909	+	0.990305i	$0.455641\pi$
$4$	5.15633	2.57816
$5$	0	0
$5$	0	0
$6$	−1.28726	−0.525521
$7$	−0.806063	−0.304663	−0.152332	−	0.988329i	$-0.548678\pi$
$7$	−0.806063	−0.304663	−0.152332	+	0.988329i	$0.548678\pi$
$8$	−8.44358	−2.98526
$9$	−2.76845	−0.922817
$10$	0	0
$11$	−3.67513	−1.10809	−0.554047	−	0.832486i	$-0.686917\pi$
$11$	−3.67513	−1.10809	−0.554047	+	0.832486i	$0.686917\pi$
$12$	2.48119	0.716259
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.15633	0.576302
$15$	0	0
$16$	12.2750	3.06876
$17$	1.35026	0.327487	0.163743	−	0.986503i	$-0.447643\pi$
$17$	1.35026	0.327487	0.163743	+	0.986503i	$0.447643\pi$
$18$	7.40597	1.74560
$19$	−1.67513	−0.384301	−0.192151	−	0.981365i	$-0.561546\pi$
$19$	−1.67513	−0.384301	−0.192151	+	0.981365i	$0.561546\pi$
$20$	0	0
$21$	−0.387873	−0.0846409
$22$	9.83146	2.09607
$23$	−6.48119	−1.35142	−0.675711	−	0.737166i	$-0.736163\pi$
$23$	−6.48119	−1.35142	−0.675711	+	0.737166i	$0.736163\pi$
$24$	−4.06300	−0.829357
$25$	0	0
$26$	−2.67513	−0.524636
$27$	−2.77575	−0.534193
$28$	−4.15633	−0.785472
$29$	2.41819	0.449047	0.224523	−	0.974469i	$-0.427917\pi$
$29$	2.41819	0.449047	0.224523	+	0.974469i	$0.427917\pi$
$30$	0	0
$31$	−5.28726	−0.949620	−0.474810	−	0.880088i	$-0.657483\pi$
$31$	−5.28726	−0.949620	−0.474810	+	0.880088i	$0.657483\pi$
$32$	−15.9502	−2.81962
$33$	−1.76845	−0.307848
$34$	−3.61213	−0.619475
$35$	0	0
$36$	−14.2750	−2.37917
$37$	−3.76845	−0.619530	−0.309765	−	0.950813i	$-0.600250\pi$
$37$	−3.76845	−0.619530	−0.309765	+	0.950813i	$0.600250\pi$
$38$	4.48119	0.726946
$39$	0.481194	0.0770528
$40$	0	0
$41$	−8.31265	−1.29822	−0.649109	−	0.760695i	$-0.724858\pi$
$41$	−8.31265	−1.29822	−0.649109	+	0.760695i	$0.724858\pi$
$42$	1.03761	0.160107
$43$	6.79384	1.03605	0.518026	−	0.855365i	$-0.326667\pi$
$43$	6.79384	1.03605	0.518026	+	0.855365i	$0.326667\pi$
$44$	−18.9502	−2.85685
$45$	0	0
$46$	17.3380	2.55635
$47$	−3.19394	−0.465884	−0.232942	−	0.972491i	$-0.574835\pi$
$47$	−3.19394	−0.465884	−0.232942	+	0.972491i	$0.574835\pi$
$48$	5.90668	0.852556
$49$	−6.35026	−0.907180
$50$	0	0
$51$	0.649738	0.0909816
$52$	5.15633	0.715054
$53$	−5.73813	−0.788193	−0.394097	−	0.919069i	$-0.628943\pi$
$53$	−5.73813	−0.788193	−0.394097	+	0.919069i	$0.628943\pi$
$54$	7.42548	1.01048
$55$	0	0
$56$	6.80606	0.909498
$57$	−0.806063	−0.106766
$58$	−6.46898	−0.849418
$59$	5.98778	0.779543	0.389771	−	0.920912i	$-0.372554\pi$
$59$	5.98778	0.779543	0.389771	+	0.920912i	$0.372554\pi$
$60$	0	0
$61$	−1.76845	−0.226427	−0.113214	−	0.993571i	$-0.536114\pi$
$61$	−1.76845	−0.226427	−0.113214	+	0.993571i	$0.536114\pi$
$62$	14.1441	1.79630
$63$	2.23155	0.281149
$64$	18.1187	2.26484
$65$	0	0
$66$	4.73084	0.582326
$67$	−9.89446	−1.20880	−0.604400	−	0.796681i	$-0.706587\pi$
$67$	−9.89446	−1.20880	−0.604400	+	0.796681i	$0.706587\pi$
$68$	6.96239	0.844314
$69$	−3.11871	−0.375449
$70$	0	0
$71$	8.56230	1.01616	0.508079	−	0.861311i	$-0.330356\pi$
$71$	8.56230	1.01616	0.508079	+	0.861311i	$0.330356\pi$
$72$	23.3757	2.75485
$73$	11.7685	1.37739	0.688697	−	0.725050i	$-0.258183\pi$
$73$	11.7685	1.37739	0.688697	+	0.725050i	$0.258183\pi$
$74$	10.0811	1.17190
$75$	0	0
$76$	−8.63752	−0.990791
$77$	2.96239	0.337596
$78$	−1.28726	−0.145753
$79$	−2.26187	−0.254480	−0.127240	−	0.991872i	$-0.540612\pi$
$79$	−2.26187	−0.254480	−0.127240	+	0.991872i	$0.540612\pi$
$80$	0	0
$81$	6.96968	0.774409
$82$	22.2374	2.45571
$83$	−3.84367	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$83$	−3.84367	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−18.1744	−1.95980
$87$	1.16362	0.124753
$88$	31.0313	3.30794
$89$	2.77575	0.294229	0.147114	−	0.989120i	$-0.453001\pi$
$89$	2.77575	0.294229	0.147114	+	0.989120i	$0.453001\pi$
$90$	0	0
$91$	−0.806063	−0.0844984
$92$	−33.4191	−3.48419
$93$	−2.54420	−0.263821
$94$	8.54420	0.881267
$95$	0	0
$96$	−7.67513	−0.783340
$97$	1.87399	0.190275	0.0951375	−	0.995464i	$-0.469671\pi$
$97$	1.87399	0.190275	0.0951375	+	0.995464i	$0.469671\pi$
$98$	16.9878	1.71603
$99$	10.1744	1.02257
$100$	0	0
$101$	10.4993	1.04472	0.522359	−	0.852725i	$-0.325052\pi$
$101$	10.4993	1.04472	0.522359	+	0.852725i	$0.325052\pi$
$102$	−1.73813	−0.172101
$103$	−15.3684	−1.51429	−0.757145	−	0.653247i	$-0.773406\pi$
$103$	−15.3684	−1.51429	−0.757145	+	0.653247i	$0.773406\pi$
$104$	−8.44358	−0.827961
$105$	0	0
$106$	15.3503	1.49095
$107$	−11.1309	−1.07607	−0.538034	−	0.842923i	$-0.680833\pi$
$107$	−11.1309	−1.07607	−0.538034	+	0.842923i	$0.680833\pi$
$108$	−14.3127	−1.37724
$109$	9.58769	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$109$	9.58769	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$110$	0	0
$111$	−1.81336	−0.172116
$112$	−9.89446	−0.934939
$113$	−0.574515	−0.0540459	−0.0270229	−	0.999635i	$-0.508603\pi$
$113$	−0.574515	−0.0540459	−0.0270229	+	0.999635i	$0.508603\pi$
$114$	2.15633	0.201958
$115$	0	0
$116$	12.4690	1.15772
$117$	−2.76845	−0.255943
$118$	−16.0181	−1.47459
$119$	−1.08840	−0.0997732
$120$	0	0
$121$	2.50659	0.227872
$122$	4.73084	0.428310
$123$	−4.00000	−0.360668
$124$	−27.2628	−2.44827
$125$	0	0
$126$	−5.96968	−0.531822
$127$	4.29455	0.381080	0.190540	−	0.981679i	$-0.438976\pi$
$127$	4.29455	0.381080	0.190540	+	0.981679i	$0.438976\pi$
$128$	−16.5696	−1.46456
$129$	3.26916	0.287833
$130$	0	0
$131$	−0.836381	−0.0730749	−0.0365375	−	0.999332i	$-0.511633\pi$
$131$	−0.836381	−0.0730749	−0.0365375	+	0.999332i	$0.511633\pi$
$132$	−9.11871	−0.793682
$133$	1.35026	0.117083
$134$	26.4690	2.28657
$135$	0	0
$136$	−11.4010	−0.977632
$137$	14.9380	1.27624	0.638118	−	0.769939i	$-0.279713\pi$
$137$	14.9380	1.27624	0.638118	+	0.769939i	$0.279713\pi$
$138$	8.34297	0.710201
$139$	−8.43866	−0.715758	−0.357879	−	0.933768i	$-0.616500\pi$
$139$	−8.43866	−0.715758	−0.357879	+	0.933768i	$0.616500\pi$
$140$	0	0
$141$	−1.53690	−0.129431
$142$	−22.9053	−1.92217
$143$	−3.67513	−0.307330
$144$	−33.9829	−2.83190
$145$	0	0
$146$	−31.4821	−2.60548
$147$	−3.05571	−0.252031
$148$	−19.4314	−1.59725
$149$	−11.3503	−0.929850	−0.464925	−	0.885350i	$-0.653919\pi$
$149$	−11.3503	−0.929850	−0.464925	+	0.885350i	$0.653919\pi$
$150$	0	0
$151$	13.9878	1.13831	0.569155	−	0.822230i	$-0.307271\pi$
$151$	13.9878	1.13831	0.569155	+	0.822230i	$0.307271\pi$
$152$	14.1441	1.14724
$153$	−3.73813	−0.302210
$154$	−7.92478	−0.638597
$155$	0	0
$156$	2.48119	0.198655
$157$	−2.77575	−0.221529	−0.110764	−	0.993847i	$-0.535330\pi$
$157$	−2.77575	−0.221529	−0.110764	+	0.993847i	$0.535330\pi$
$158$	6.05079	0.481375
$159$	−2.76116	−0.218974
$160$	0	0
$161$	5.22425	0.411729
$162$	−18.6448	−1.46487
$163$	−2.23155	−0.174788	−0.0873942	−	0.996174i	$-0.527854\pi$
$163$	−2.23155	−0.174788	−0.0873942	+	0.996174i	$0.527854\pi$
$164$	−42.8627	−3.34702
$165$	0	0
$166$	10.2823	0.798064
$167$	15.6932	1.21438	0.607189	−	0.794557i	$-0.292297\pi$
$167$	15.6932	1.21438	0.607189	+	0.794557i	$0.292297\pi$
$168$	3.27504	0.252675
$169$	1.00000	0.0769231
$170$	0	0
$171$	4.63752	0.354640
$172$	35.0313	2.67111
$173$	25.5877	1.94540	0.972698	−	0.232075i	$-0.0745513\pi$
$173$	25.5877	1.94540	0.972698	+	0.232075i	$0.0745513\pi$
$174$	−3.11283	−0.235983
$175$	0	0
$176$	−45.1124	−3.40047
$177$	2.88129	0.216571
$178$	−7.42548	−0.556564
$179$	12.1260	0.906340	0.453170	−	0.891424i	$-0.350293\pi$
$179$	12.1260	0.906340	0.453170	+	0.891424i	$0.350293\pi$
$180$	0	0
$181$	−2.73084	−0.202982	−0.101491	−	0.994836i	$-0.532361\pi$
$181$	−2.73084	−0.202982	−0.101491	+	0.994836i	$0.532361\pi$
$182$	2.15633	0.159837
$183$	−0.850969	−0.0629054
$184$	54.7245	4.03434
$185$	0	0
$186$	6.80606	0.499045
$187$	−4.96239	−0.362886
$188$	−16.4690	−1.20112
$189$	2.23743	0.162749
$190$	0	0
$191$	20.6253	1.49239	0.746197	−	0.665725i	$-0.231878\pi$
$191$	20.6253	1.49239	0.746197	+	0.665725i	$0.231878\pi$
$192$	8.71862	0.629212
$193$	21.7889	1.56840	0.784200	−	0.620508i	$-0.213073\pi$
$193$	21.7889	1.56840	0.784200	+	0.620508i	$0.213073\pi$
$194$	−5.01317	−0.359925
$195$	0	0
$196$	−32.7440	−2.33886
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−27.2179	−1.93429
$199$	−16.7513	−1.18747	−0.593734	−	0.804661i	$-0.702347\pi$
$199$	−16.7513	−1.18747	−0.593734	+	0.804661i	$0.702347\pi$
$200$	0	0
$201$	−4.76116	−0.335826
$202$	−28.0870	−1.97619
$203$	−1.94921	−0.136808
$204$	3.35026	0.234565
$205$	0	0
$206$	41.1124	2.86443
$207$	17.9429	1.24712
$208$	12.2750	0.851121
$209$	6.15633	0.425842
$210$	0	0
$211$	−4.90175	−0.337451	−0.168725	−	0.985663i	$-0.553965\pi$
$211$	−4.90175	−0.337451	−0.168725	+	0.985663i	$0.553965\pi$
$212$	−29.5877	−2.03209
$213$	4.12013	0.282307
$214$	29.7767	2.03549
$215$	0	0
$216$	23.4372	1.59470
$217$	4.26187	0.289314
$218$	−25.6483	−1.73712
$219$	5.66291	0.382664
$220$	0	0
$221$	1.35026	0.0908284
$222$	4.85097	0.325576
$223$	−24.9076	−1.66794	−0.833969	−	0.551811i	$-0.813937\pi$
$223$	−24.9076	−1.66794	−0.833969	+	0.551811i	$0.813937\pi$
$224$	12.8568	0.859034
$225$	0	0
$226$	1.53690	0.102233
$227$	−9.95509	−0.660743	−0.330371	−	0.943851i	$-0.607174\pi$
$227$	−9.95509	−0.660743	−0.330371	+	0.943851i	$0.607174\pi$
$228$	−4.15633	−0.275259
$229$	5.35026	0.353555	0.176778	−	0.984251i	$-0.443433\pi$
$229$	5.35026	0.353555	0.176778	+	0.984251i	$0.443433\pi$
$230$	0	0
$231$	1.42548	0.0937900
$232$	−20.4182	−1.34052
$233$	10.7612	0.704987	0.352493	−	0.935814i	$-0.385334\pi$
$233$	10.7612	0.704987	0.352493	+	0.935814i	$0.385334\pi$
$234$	7.40597	0.484144
$235$	0	0
$236$	30.8749	2.00979
$237$	−1.08840	−0.0706990
$238$	2.91160	0.188731
$239$	−11.8618	−0.767274	−0.383637	−	0.923484i	$-0.625329\pi$
$239$	−11.8618	−0.767274	−0.383637	+	0.923484i	$0.625329\pi$
$240$	0	0
$241$	−28.6253	−1.84392	−0.921959	−	0.387288i	$-0.873412\pi$
$241$	−28.6253	−1.84392	−0.921959	+	0.387288i	$0.873412\pi$
$242$	−6.70545	−0.431043
$243$	11.6810	0.749337
$244$	−9.11871	−0.583766
$245$	0	0
$246$	10.7005	0.682240
$247$	−1.67513	−0.106586
$248$	44.6434	2.83486
$249$	−1.84955	−0.117211
$250$	0	0
$251$	−19.3865	−1.22366	−0.611831	−	0.790988i	$-0.709567\pi$
$251$	−19.3865	−1.22366	−0.611831	+	0.790988i	$0.709567\pi$
$252$	11.5066	0.724847
$253$	23.8192	1.49750
$254$	−11.4885	−0.720852
$255$	0	0
$256$	8.08840	0.505525
$257$	−22.8627	−1.42614	−0.713069	−	0.701094i	$-0.752695\pi$
$257$	−22.8627	−1.42614	−0.713069	+	0.701094i	$0.752695\pi$
$258$	−8.74543	−0.544467
$259$	3.03761	0.188748
$260$	0	0
$261$	−6.69464	−0.414388
$262$	2.23743	0.138229
$263$	−21.8822	−1.34932	−0.674658	−	0.738130i	$-0.735709\pi$
$263$	−21.8822	−1.34932	−0.674658	+	0.738130i	$0.735709\pi$
$264$	14.9321	0.919005
$265$	0	0
$266$	−3.61213	−0.221474
$267$	1.33567	0.0817419
$268$	−51.0191	−3.11648
$269$	22.7513	1.38717	0.693586	−	0.720374i	$-0.256030\pi$
$269$	22.7513	1.38717	0.693586	+	0.720374i	$0.256030\pi$
$270$	0	0
$271$	0.123638	0.00751049	0.00375525	−	0.999993i	$-0.498805\pi$
$271$	0.123638	0.00751049	0.00375525	+	0.999993i	$0.498805\pi$
$272$	16.5745	1.00498
$273$	−0.387873	−0.0234751
$274$	−39.9610	−2.41413
$275$	0	0
$276$	−16.0811	−0.967969
$277$	15.3503	0.922308	0.461154	−	0.887320i	$-0.347436\pi$
$277$	15.3503	0.922308	0.461154	+	0.887320i	$0.347436\pi$
$278$	22.5745	1.35393
$279$	14.6375	0.876325
$280$	0	0
$281$	13.9248	0.830683	0.415341	−	0.909666i	$-0.363662\pi$
$281$	13.9248	0.830683	0.415341	+	0.909666i	$0.363662\pi$
$282$	4.11142	0.244831
$283$	−20.3815	−1.21156	−0.605778	−	0.795634i	$-0.707138\pi$
$283$	−20.3815	−1.21156	−0.605778	+	0.795634i	$0.707138\pi$
$284$	44.1500	2.61982
$285$	0	0
$286$	9.83146	0.581346
$287$	6.70052	0.395519
$288$	44.1573	2.60199
$289$	−15.1768	−0.892753
$290$	0	0
$291$	0.901754	0.0528618
$292$	60.6820	3.55114
$293$	−5.38058	−0.314337	−0.157168	−	0.987572i	$-0.550237\pi$
$293$	−5.38058	−0.314337	−0.157168	+	0.987572i	$0.550237\pi$
$294$	8.17442	0.476742
$295$	0	0
$296$	31.8192	1.84946
$297$	10.2012	0.591935
$298$	30.3634	1.75891
$299$	−6.48119	−0.374817
$300$	0	0
$301$	−5.47627	−0.315647
$302$	−37.4191	−2.15323
$303$	5.05220	0.290241
$304$	−20.5623	−1.17933
$305$	0	0
$306$	10.0000	0.571662
$307$	19.1695	1.09406	0.547031	−	0.837113i	$-0.315758\pi$
$307$	19.1695	1.09406	0.547031	+	0.837113i	$0.315758\pi$
$308$	15.2750	0.870376
$309$	−7.39517	−0.420696
$310$	0	0
$311$	−25.2506	−1.43183	−0.715915	−	0.698187i	$-0.753990\pi$
$311$	−25.2506	−1.43183	−0.715915	+	0.698187i	$0.753990\pi$
$312$	−4.06300	−0.230022
$313$	−2.81194	−0.158940	−0.0794702	−	0.996837i	$-0.525323\pi$
$313$	−2.81194	−0.158940	−0.0794702	+	0.996837i	$0.525323\pi$
$314$	7.42548	0.419044
$315$	0	0
$316$	−11.6629	−0.656090
$317$	23.7685	1.33497	0.667485	−	0.744624i	$-0.267371\pi$
$317$	23.7685	1.33497	0.667485	+	0.744624i	$0.267371\pi$
$318$	7.38646	0.414212
$319$	−8.88717	−0.497586
$320$	0	0
$321$	−5.35614	−0.298951
$322$	−13.9756	−0.778828
$323$	−2.26187	−0.125854
$324$	35.9380	1.99655
$325$	0	0
$326$	5.96968	0.330630
$327$	4.61354	0.255129
$328$	70.1886	3.87551
$329$	2.57452	0.141938
$330$	0	0
$331$	−11.8011	−0.648649	−0.324325	−	0.945946i	$-0.605137\pi$
$331$	−11.8011	−0.648649	−0.324325	+	0.945946i	$0.605137\pi$
$332$	−19.8192	−1.08772
$333$	10.4328	0.571713
$334$	−41.9814	−2.29712
$335$	0	0
$336$	−4.76116	−0.259742
$337$	−16.1114	−0.877645	−0.438822	−	0.898574i	$-0.644604\pi$
$337$	−16.1114	−0.877645	−0.438822	+	0.898574i	$0.644604\pi$
$338$	−2.67513	−0.145508
$339$	−0.276454	−0.0150149
$340$	0	0
$341$	19.4314	1.05227
$342$	−12.4060	−0.670838
$343$	10.7612	0.581048
$344$	−57.3644	−3.09288
$345$	0	0
$346$	−68.4504	−3.67992
$347$	−27.4944	−1.47598	−0.737988	−	0.674814i	$-0.764224\pi$
$347$	−27.4944	−1.47598	−0.737988	+	0.674814i	$0.764224\pi$
$348$	6.00000	0.321634
$349$	−17.6023	−0.942228	−0.471114	−	0.882072i	$-0.656148\pi$
$349$	−17.6023	−0.942228	−0.471114	+	0.882072i	$0.656148\pi$
$350$	0	0
$351$	−2.77575	−0.148158
$352$	58.6190	3.12440
$353$	−15.7685	−0.839270	−0.419635	−	0.907693i	$-0.637842\pi$
$353$	−15.7685	−0.839270	−0.419635	+	0.907693i	$0.637842\pi$
$354$	−7.70782	−0.409666
$355$	0	0
$356$	14.3127	0.758569
$357$	−0.523730	−0.0277187
$358$	−32.4387	−1.71444
$359$	−14.8242	−0.782389	−0.391195	−	0.920308i	$-0.627938\pi$
$359$	−14.8242	−0.782389	−0.391195	+	0.920308i	$0.627938\pi$
$360$	0	0
$361$	−16.1939	−0.852312
$362$	7.30536	0.383961
$363$	1.20616	0.0633067
$364$	−4.15633	−0.217851
$365$	0	0
$366$	2.27645	0.118992
$367$	27.0313	1.41102	0.705510	−	0.708700i	$-0.250718\pi$
$367$	27.0313	1.41102	0.705510	+	0.708700i	$0.250718\pi$
$368$	−79.5569	−4.14719
$369$	23.0132	1.19802
$370$	0	0
$371$	4.62530	0.240134
$372$	−13.1187	−0.680174
$373$	−12.9525	−0.670657	−0.335329	−	0.942101i	$-0.608847\pi$
$373$	−12.9525	−0.670657	−0.335329	+	0.942101i	$0.608847\pi$
$374$	13.2750	0.686436
$375$	0	0
$376$	26.9683	1.39078
$377$	2.41819	0.124543
$378$	−5.98541	−0.307856
$379$	−30.2858	−1.55568	−0.777840	−	0.628463i	$-0.783684\pi$
$379$	−30.2858	−1.55568	−0.777840	+	0.628463i	$0.783684\pi$
$380$	0	0
$381$	2.06651	0.105871
$382$	−55.1754	−2.82302
$383$	21.0943	1.07787	0.538934	−	0.842348i	$-0.318827\pi$
$383$	21.0943	1.07787	0.538934	+	0.842348i	$0.318827\pi$
$384$	−7.97319	−0.406880
$385$	0	0
$386$	−58.2882	−2.96679
$387$	−18.8084	−0.956086
$388$	9.66291	0.490560
$389$	−6.77575	−0.343544	−0.171772	−	0.985137i	$-0.554949\pi$
$389$	−6.77575	−0.343544	−0.171772	+	0.985137i	$0.554949\pi$
$390$	0	0
$391$	−8.75131	−0.442573
$392$	53.6190	2.70817
$393$	−0.402462	−0.0203015
$394$	5.35026	0.269542
$395$	0	0
$396$	52.4626	2.63635
$397$	−10.4690	−0.525423	−0.262711	−	0.964874i	$-0.584617\pi$
$397$	−10.4690	−0.525423	−0.262711	+	0.964874i	$0.584617\pi$
$398$	44.8119	2.24622
$399$	0.649738	0.0325276
$400$	0	0
$401$	5.01317	0.250346	0.125173	−	0.992135i	$-0.460051\pi$
$401$	5.01317	0.250346	0.125173	+	0.992135i	$0.460051\pi$
$402$	12.7367	0.635250
$403$	−5.28726	−0.263377
$404$	54.1378	2.69345
$405$	0	0
$406$	5.21440	0.258787
$407$	13.8496	0.686497
$408$	−5.48612	−0.271603
$409$	−14.3879	−0.711435	−0.355717	−	0.934594i	$-0.615763\pi$
$409$	−14.3879	−0.711435	−0.355717	+	0.934594i	$0.615763\pi$
$410$	0	0
$411$	7.18806	0.354561
$412$	−79.2443	−3.90408
$413$	−4.82653	−0.237498
$414$	−47.9995	−2.35905
$415$	0	0
$416$	−15.9502	−0.782021
$417$	−4.06063	−0.198850
$418$	−16.4690	−0.805524
$419$	17.4617	0.853059	0.426529	−	0.904474i	$-0.359736\pi$
$419$	17.4617	0.853059	0.426529	+	0.904474i	$0.359736\pi$
$420$	0	0
$421$	2.88717	0.140712	0.0703559	−	0.997522i	$-0.477586\pi$
$421$	2.88717	0.140712	0.0703559	+	0.997522i	$0.477586\pi$
$422$	13.1128	0.638323
$423$	8.84226	0.429925
$424$	48.4504	2.35296
$425$	0	0
$426$	−11.0219	−0.534012
$427$	1.42548	0.0689840
$428$	−57.3947	−2.77428
$429$	−1.76845	−0.0853817
$430$	0	0
$431$	0.889535	0.0428474	0.0214237	−	0.999770i	$-0.493180\pi$
$431$	0.889535	0.0428474	0.0214237	+	0.999770i	$0.493180\pi$
$432$	−34.0724	−1.63931
$433$	25.2506	1.21347	0.606733	−	0.794906i	$-0.292480\pi$
$433$	25.2506	1.21347	0.606733	+	0.794906i	$0.292480\pi$
$434$	−11.4010	−0.547268
$435$	0	0
$436$	49.4372	2.36761
$437$	10.8568	0.519354
$438$	−15.1490	−0.723849
$439$	28.8119	1.37512	0.687560	−	0.726128i	$-0.258682\pi$
$439$	28.8119	1.37512	0.687560	+	0.726128i	$0.258682\pi$
$440$	0	0
$441$	17.5804	0.837162
$442$	−3.61213	−0.171811
$443$	−36.9805	−1.75700	−0.878498	−	0.477746i	$-0.841454\pi$
$443$	−36.9805	−1.75700	−0.878498	+	0.477746i	$0.841454\pi$
$444$	−9.35026	−0.443744
$445$	0	0
$446$	66.6312	3.15508
$447$	−5.46168	−0.258329
$448$	−14.6048	−0.690013
$449$	−12.6859	−0.598686	−0.299343	−	0.954146i	$-0.596768\pi$
$449$	−12.6859	−0.598686	−0.299343	+	0.954146i	$0.596768\pi$
$450$	0	0
$451$	30.5501	1.43855
$452$	−2.96239	−0.139339
$453$	6.73084	0.316242
$454$	26.6312	1.24986
$455$	0	0
$456$	6.80606	0.318723
$457$	25.0494	1.17176	0.585880	−	0.810398i	$-0.300749\pi$
$457$	25.0494	1.17176	0.585880	+	0.810398i	$0.300749\pi$
$458$	−14.3127	−0.668786
$459$	−3.74798	−0.174941
$460$	0	0
$461$	−36.8872	−1.71801	−0.859003	−	0.511970i	$-0.828916\pi$
$461$	−36.8872	−1.71801	−0.859003	+	0.511970i	$0.828916\pi$
$462$	−3.81336	−0.177413
$463$	39.0191	1.81337	0.906685	−	0.421809i	$-0.138605\pi$
$463$	39.0191	1.81337	0.906685	+	0.421809i	$0.138605\pi$
$464$	29.6834	1.37802
$465$	0	0
$466$	−28.7875	−1.33356
$467$	−32.7694	−1.51639	−0.758194	−	0.652029i	$-0.773918\pi$
$467$	−32.7694	−1.51639	−0.758194	+	0.652029i	$0.773918\pi$
$468$	−14.2750	−0.659864
$469$	7.97556	0.368277
$470$	0	0
$471$	−1.33567	−0.0615446
$472$	−50.5583	−2.32714
$473$	−24.9683	−1.14804
$474$	2.91160	0.133734
$475$	0	0
$476$	−5.61213	−0.257231
$477$	15.8858	0.727359
$478$	31.7318	1.45138
$479$	16.8749	0.771036	0.385518	−	0.922700i	$-0.374023\pi$
$479$	16.8749	0.771036	0.385518	+	0.922700i	$0.374023\pi$
$480$	0	0
$481$	−3.76845	−0.171827
$482$	76.5764	3.48796
$483$	2.51388	0.114386
$484$	12.9248	0.587490
$485$	0	0
$486$	−31.2482	−1.41745
$487$	9.24472	0.418918	0.209459	−	0.977817i	$-0.432830\pi$
$487$	9.24472	0.418918	0.209459	+	0.977817i	$0.432830\pi$
$488$	14.9321	0.675943
$489$	−1.07381	−0.0485593
$490$	0	0
$491$	−25.7499	−1.16208	−0.581038	−	0.813876i	$-0.697353\pi$
$491$	−25.7499	−1.16208	−0.581038	+	0.813876i	$0.697353\pi$
$492$	−20.6253	−0.929860
$493$	3.26519	0.147057
$494$	4.48119	0.201618
$495$	0	0
$496$	−64.9013	−2.91415
$497$	−6.90175	−0.309586
$498$	4.94780	0.221716
$499$	−27.7015	−1.24009	−0.620044	−	0.784567i	$-0.712885\pi$
$499$	−27.7015	−1.24009	−0.620044	+	0.784567i	$0.712885\pi$
$500$	0	0
$501$	7.55149	0.337376
$502$	51.8613	2.31468
$503$	−2.35519	−0.105013	−0.0525063	−	0.998621i	$-0.516721\pi$
$503$	−2.35519	−0.105013	−0.0525063	+	0.998621i	$0.516721\pi$
$504$	−18.8423	−0.839301
$505$	0	0
$506$	−63.7196	−2.83268
$507$	0.481194	0.0213706
$508$	22.1441	0.982486
$509$	21.5125	0.953523	0.476762	−	0.879033i	$-0.341810\pi$
$509$	21.5125	0.953523	0.476762	+	0.879033i	$0.341810\pi$
$510$	0	0
$511$	−9.48612	−0.419641
$512$	11.5017	0.508306
$513$	4.64974	0.205291
$514$	61.1608	2.69769
$515$	0	0
$516$	16.8568	0.742081
$517$	11.7381	0.516243
$518$	−8.12601	−0.357036
$519$	12.3127	0.540465
$520$	0	0
$521$	37.7440	1.65360	0.826798	−	0.562499i	$-0.190160\pi$
$521$	37.7440	1.65360	0.826798	+	0.562499i	$0.190160\pi$
$522$	17.9090	0.783858
$523$	−23.7416	−1.03815	−0.519075	−	0.854729i	$-0.673723\pi$
$523$	−23.7416	−1.03815	−0.519075	+	0.854729i	$0.673723\pi$
$524$	−4.31265	−0.188399
$525$	0	0
$526$	58.5379	2.55237
$527$	−7.13918	−0.310988
$528$	−21.7078	−0.944712
$529$	19.0059	0.826343
$530$	0	0
$531$	−16.5769	−0.719376
$532$	6.96239	0.301858
$533$	−8.31265	−0.360061
$534$	−3.57310	−0.154623
$535$	0	0
$536$	83.5447	3.60858
$537$	5.83497	0.251797
$538$	−60.8627	−2.62398
$539$	23.3380	1.00524
$540$	0	0
$541$	13.0376	0.560531	0.280265	−	0.959923i	$-0.409578\pi$
$541$	13.0376	0.560531	0.280265	+	0.959923i	$0.409578\pi$
$542$	−0.330749	−0.0142069
$543$	−1.31406	−0.0563919
$544$	−21.5369	−0.923387
$545$	0	0
$546$	1.03761	0.0444057
$547$	−8.43041	−0.360458	−0.180229	−	0.983625i	$-0.557684\pi$
$547$	−8.43041	−0.360458	−0.180229	+	0.983625i	$0.557684\pi$
$548$	77.0249	3.29034
$549$	4.89587	0.208951
$550$	0	0
$551$	−4.05079	−0.172569
$552$	26.3331	1.12081
$553$	1.82321	0.0775306
$554$	−41.0640	−1.74464
$555$	0	0
$556$	−43.5125	−1.84534
$557$	−13.6932	−0.580201	−0.290100	−	0.956996i	$-0.593689\pi$
$557$	−13.6932	−0.580201	−0.290100	+	0.956996i	$0.593689\pi$
$558$	−39.1573	−1.65766
$559$	6.79384	0.287349
$560$	0	0
$561$	−2.38787	−0.100816
$562$	−37.2506	−1.57132
$563$	8.86907	0.373787	0.186893	−	0.982380i	$-0.440158\pi$
$563$	8.86907	0.373787	0.186893	+	0.982380i	$0.440158\pi$
$564$	−7.92478	−0.333693
$565$	0	0
$566$	54.5233	2.29178
$567$	−5.61801	−0.235934
$568$	−72.2965	−3.03349
$569$	−32.7816	−1.37428	−0.687139	−	0.726526i	$-0.741134\pi$
$569$	−32.7816	−1.37428	−0.687139	+	0.726526i	$0.741134\pi$
$570$	0	0
$571$	40.2882	1.68601	0.843005	−	0.537906i	$-0.180785\pi$
$571$	40.2882	1.68601	0.843005	+	0.537906i	$0.180785\pi$
$572$	−18.9502	−0.792346
$573$	9.92478	0.414614
$574$	−17.9248	−0.748166
$575$	0	0
$576$	−50.1608	−2.09003
$577$	−28.8568	−1.20133	−0.600663	−	0.799502i	$-0.705097\pi$
$577$	−28.8568	−1.20133	−0.600663	+	0.799502i	$0.705097\pi$
$578$	40.5999	1.68873
$579$	10.4847	0.435729
$580$	0	0
$581$	3.09825	0.128537
$582$	−2.41231	−0.0999935
$583$	21.0884	0.873392
$584$	−99.3679	−4.11187
$585$	0	0
$586$	14.3938	0.594600
$587$	−41.6786	−1.72026	−0.860131	−	0.510074i	$-0.829618\pi$
$587$	−41.6786	−1.72026	−0.860131	+	0.510074i	$0.829618\pi$
$588$	−15.7562	−0.649776
$589$	8.85685	0.364940
$590$	0	0
$591$	−0.962389	−0.0395874
$592$	−46.2579	−1.90119
$593$	−22.4993	−0.923935	−0.461968	−	0.886897i	$-0.652856\pi$
$593$	−22.4993	−0.923935	−0.461968	+	0.886897i	$0.652856\pi$
$594$	−27.2896	−1.11971
$595$	0	0
$596$	−58.5256	−2.39730
$597$	−8.06063	−0.329900
$598$	17.3380	0.709005
$599$	4.15045	0.169583	0.0847913	−	0.996399i	$-0.472978\pi$
$599$	4.15045	0.169583	0.0847913	+	0.996399i	$0.472978\pi$
$600$	0	0
$601$	27.9248	1.13908	0.569538	−	0.821965i	$-0.307122\pi$
$601$	27.9248	1.13908	0.569538	+	0.821965i	$0.307122\pi$
$602$	14.6497	0.597079
$603$	27.3923	1.11550
$604$	72.1255	2.93475
$605$	0	0
$606$	−13.5153	−0.549021
$607$	−8.19489	−0.332620	−0.166310	−	0.986073i	$-0.553185\pi$
$607$	−8.19489	−0.332620	−0.166310	+	0.986073i	$0.553185\pi$
$608$	26.7186	1.08358
$609$	−0.937951	−0.0380077
$610$	0	0
$611$	−3.19394	−0.129213
$612$	−19.2750	−0.779147
$613$	−33.1392	−1.33848	−0.669239	−	0.743047i	$-0.733380\pi$
$613$	−33.1392	−1.33848	−0.669239	+	0.743047i	$0.733380\pi$
$614$	−51.2809	−2.06953
$615$	0	0
$616$	−25.0132	−1.00781
$617$	29.0132	1.16803	0.584013	−	0.811744i	$-0.301482\pi$
$617$	29.0132	1.16803	0.584013	+	0.811744i	$0.301482\pi$
$618$	19.7830	0.795791
$619$	12.2134	0.490900	0.245450	−	0.969409i	$-0.421064\pi$
$619$	12.2134	0.490900	0.245450	+	0.969409i	$0.421064\pi$
$620$	0	0
$621$	17.9902	0.721920
$622$	67.5487	2.70845
$623$	−2.23743	−0.0896406
$624$	5.90668	0.236456
$625$	0	0
$626$	7.52232	0.300652
$627$	2.96239	0.118306
$628$	−14.3127	−0.571137
$629$	−5.08840	−0.202888
$630$	0	0
$631$	−1.22188	−0.0486424	−0.0243212	−	0.999704i	$-0.507742\pi$
$631$	−1.22188	−0.0486424	−0.0243212	+	0.999704i	$0.507742\pi$
$632$	19.0982	0.759687
$633$	−2.35870	−0.0937498
$634$	−63.5837	−2.52523
$635$	0	0
$636$	−14.2374	−0.564551
$637$	−6.35026	−0.251607
$638$	23.7743	0.941235
$639$	−23.7043	−0.937728
$640$	0	0
$641$	−22.1016	−0.872960	−0.436480	−	0.899714i	$-0.643775\pi$
$641$	−22.1016	−0.872960	−0.436480	+	0.899714i	$0.643775\pi$
$642$	14.3284	0.565496
$643$	−11.6688	−0.460172	−0.230086	−	0.973170i	$-0.573901\pi$
$643$	−11.6688	−0.460172	−0.230086	+	0.973170i	$0.573901\pi$
$644$	26.9380	1.06150
$645$	0	0
$646$	6.05079	0.238065
$647$	−11.9575	−0.470096	−0.235048	−	0.971984i	$-0.575525\pi$
$647$	−11.9575	−0.470096	−0.235048	+	0.971984i	$0.575525\pi$
$648$	−58.8491	−2.31181
$649$	−22.0059	−0.863806
$650$	0	0
$651$	2.05079	0.0803766
$652$	−11.5066	−0.450633
$653$	10.9986	0.430408	0.215204	−	0.976569i	$-0.430958\pi$
$653$	10.9986	0.430408	0.215204	+	0.976569i	$0.430958\pi$
$654$	−12.3418	−0.482604
$655$	0	0
$656$	−102.038	−3.98392
$657$	−32.5804	−1.27108
$658$	−6.88717	−0.268490
$659$	−2.63989	−0.102835	−0.0514177	−	0.998677i	$-0.516374\pi$
$659$	−2.63989	−0.102835	−0.0514177	+	0.998677i	$0.516374\pi$
$660$	0	0
$661$	18.3028	0.711896	0.355948	−	0.934506i	$-0.384158\pi$
$661$	18.3028	0.711896	0.355948	+	0.934506i	$0.384158\pi$
$662$	31.5696	1.22699
$663$	0.649738	0.0252337
$664$	32.4544	1.25947
$665$	0	0
$666$	−27.9090	−1.08145
$667$	−15.6728	−0.606852
$668$	80.9194	3.13087
$669$	−11.9854	−0.463383
$670$	0	0
$671$	6.49929	0.250902
$672$	6.18664	0.238655
$673$	−6.71037	−0.258666	−0.129333	−	0.991601i	$-0.541284\pi$
$673$	−6.71037	−0.258666	−0.129333	+	0.991601i	$0.541284\pi$
$674$	43.1002	1.66016
$675$	0	0
$676$	5.15633	0.198320
$677$	1.57593	0.0605679	0.0302840	−	0.999541i	$-0.490359\pi$
$677$	1.57593	0.0605679	0.0302840	+	0.999541i	$0.490359\pi$
$678$	0.739549	0.0284022
$679$	−1.51056	−0.0579698
$680$	0	0
$681$	−4.79033	−0.183566
$682$	−51.9814	−1.99047
$683$	−15.1939	−0.581380	−0.290690	−	0.956817i	$-0.593885\pi$
$683$	−15.1939	−0.581380	−0.290690	+	0.956817i	$0.593885\pi$
$684$	23.9126	0.914320
$685$	0	0
$686$	−28.7875	−1.09911
$687$	2.57452	0.0982239
$688$	83.3947	3.17939
$689$	−5.73813	−0.218606
$690$	0	0
$691$	−18.7127	−0.711866	−0.355933	−	0.934511i	$-0.615837\pi$
$691$	−18.7127	−0.711866	−0.355933	+	0.934511i	$0.615837\pi$
$692$	131.938	5.01555
$693$	−8.20123	−0.311539
$694$	73.5510	2.79196
$695$	0	0
$696$	−9.82512	−0.372420
$697$	−11.2243	−0.425149
$698$	47.0884	1.78232
$699$	5.17821	0.195858
$700$	0	0
$701$	24.3028	0.917904	0.458952	−	0.888461i	$-0.348225\pi$
$701$	24.3028	0.917904	0.458952	+	0.888461i	$0.348225\pi$
$702$	7.42548	0.280257
$703$	6.31265	0.238086
$704$	−66.5886	−2.50965
$705$	0	0
$706$	42.1827	1.58757
$707$	−8.46310	−0.318287
$708$	14.8568	0.558355
$709$	−9.66291	−0.362898	−0.181449	−	0.983400i	$-0.558079\pi$
$709$	−9.66291	−0.362898	−0.181449	+	0.983400i	$0.558079\pi$
$710$	0	0
$711$	6.26187	0.234838
$712$	−23.4372	−0.878348
$713$	34.2677	1.28334
$714$	1.40105	0.0524329
$715$	0	0
$716$	62.5256	2.33669
$717$	−5.70782	−0.213162
$718$	39.6566	1.47997
$719$	28.4142	1.05967	0.529836	−	0.848100i	$-0.322254\pi$
$719$	28.4142	1.05967	0.529836	+	0.848100i	$0.322254\pi$
$720$	0	0
$721$	12.3879	0.461349
$722$	43.3209	1.61224
$723$	−13.7743	−0.512273
$724$	−14.0811	−0.523320
$725$	0	0
$726$	−3.22662	−0.119751
$727$	34.8545	1.29268	0.646341	−	0.763049i	$-0.276299\pi$
$727$	34.8545	1.29268	0.646341	+	0.763049i	$0.276299\pi$
$728$	6.80606	0.252249
$729$	−15.2882	−0.566230
$730$	0	0
$731$	9.17347	0.339293
$732$	−4.38787	−0.162180
$733$	−6.25202	−0.230923	−0.115462	−	0.993312i	$-0.536835\pi$
$733$	−6.25202	−0.230923	−0.115462	+	0.993312i	$0.536835\pi$
$734$	−72.3122	−2.66909
$735$	0	0
$736$	103.376	3.81050
$737$	36.3634	1.33946
$738$	−61.5633	−2.26617
$739$	−32.0846	−1.18025	−0.590126	−	0.807311i	$-0.700922\pi$
$739$	−32.0846	−1.18025	−0.590126	+	0.807311i	$0.700922\pi$
$740$	0	0
$741$	−0.806063	−0.0296115
$742$	−12.3733	−0.454238
$743$	30.5442	1.12056	0.560279	−	0.828304i	$-0.310694\pi$
$743$	30.5442	1.12056	0.560279	+	0.828304i	$0.310694\pi$
$744$	21.4821	0.787574
$745$	0	0
$746$	34.6497	1.26862
$747$	10.6410	0.389335
$748$	−25.5877	−0.935579
$749$	8.97224	0.327838
$750$	0	0
$751$	28.1622	1.02765	0.513827	−	0.857894i	$-0.328227\pi$
$751$	28.1622	1.02765	0.513827	+	0.857894i	$0.328227\pi$
$752$	−39.2057	−1.42968
$753$	−9.32865	−0.339955
$754$	−6.46898	−0.235586
$755$	0	0
$756$	11.5369	0.419593
$757$	−35.4109	−1.28703	−0.643515	−	0.765433i	$-0.722525\pi$
$757$	−35.4109	−1.28703	−0.643515	+	0.765433i	$0.722525\pi$
$758$	81.0186	2.94273
$759$	11.4617	0.416033
$760$	0	0
$761$	−19.2388	−0.697407	−0.348704	−	0.937233i	$-0.613378\pi$
$761$	−19.2388	−0.697407	−0.348704	+	0.937233i	$0.613378\pi$
$762$	−5.52820	−0.200265
$763$	−7.72829	−0.279783
$764$	106.351	3.84764
$765$	0	0
$766$	−56.4299	−2.03890
$767$	5.98778	0.216206
$768$	3.89209	0.140444
$769$	48.9643	1.76570	0.882849	−	0.469657i	$-0.155622\pi$
$769$	48.9643	1.76570	0.882849	+	0.469657i	$0.155622\pi$
$770$	0	0
$771$	−11.0014	−0.396206
$772$	112.351	4.04359
$773$	−46.1681	−1.66055	−0.830275	−	0.557354i	$-0.811817\pi$
$773$	−46.1681	−1.66055	−0.830275	+	0.557354i	$0.811817\pi$
$774$	50.3150	1.80854
$775$	0	0
$776$	−15.8232	−0.568020
$777$	1.46168	0.0524375
$778$	18.1260	0.649849
$779$	13.9248	0.498907
$780$	0	0
$781$	−31.4676	−1.12600
$782$	23.4109	0.837172
$783$	−6.71228	−0.239877
$784$	−77.9497	−2.78392
$785$	0	0
$786$	1.07664	0.0384024
$787$	22.6458	0.807234	0.403617	−	0.914928i	$-0.367753\pi$
$787$	22.6458	0.807234	0.403617	+	0.914928i	$0.367753\pi$
$788$	−10.3127	−0.367373
$789$	−10.5296	−0.374864
$790$	0	0
$791$	0.463096	0.0164658
$792$	−85.9086	−3.05263
$793$	−1.76845	−0.0627996
$794$	28.0059	0.993891
$795$	0	0
$796$	−86.3752	−3.06149
$797$	−8.23743	−0.291785	−0.145892	−	0.989300i	$-0.546605\pi$
$797$	−8.23743	−0.291785	−0.145892	+	0.989300i	$0.546605\pi$
$798$	−1.73813	−0.0615293
$799$	−4.31265	−0.152571
$800$	0	0
$801$	−7.68452	−0.271519
$802$	−13.4109	−0.473555
$803$	−43.2506	−1.52628
$804$	−24.5501	−0.865814
$805$	0	0
$806$	14.1441	0.498205
$807$	10.9478	0.385381
$808$	−88.6516	−3.11875
$809$	44.1319	1.55159	0.775797	−	0.630982i	$-0.217348\pi$
$809$	44.1319	1.55159	0.775797	+	0.630982i	$0.217348\pi$
$810$	0	0
$811$	22.6883	0.796694	0.398347	−	0.917235i	$-0.369584\pi$
$811$	22.6883	0.796694	0.398347	+	0.917235i	$0.369584\pi$
$812$	−10.0508	−0.352713
$813$	0.0594941	0.00208655
$814$	−37.0494	−1.29858
$815$	0	0
$816$	7.97556	0.279201
$817$	−11.3806	−0.398156
$818$	38.4894	1.34575
$819$	2.23155	0.0779766
$820$	0	0
$821$	−50.2736	−1.75456	−0.877281	−	0.479978i	$-0.840645\pi$
$821$	−50.2736	−1.75456	−0.877281	+	0.479978i	$0.840645\pi$
$822$	−19.2290	−0.670688
$823$	−5.13093	−0.178853	−0.0894265	−	0.995993i	$-0.528503\pi$
$823$	−5.13093	−0.178853	−0.0894265	+	0.995993i	$0.528503\pi$
$824$	129.764	4.52054
$825$	0	0
$826$	12.9116	0.449252
$827$	−18.6946	−0.650076	−0.325038	−	0.945701i	$-0.605377\pi$
$827$	−18.6946	−0.650076	−0.325038	+	0.945701i	$0.605377\pi$
$828$	92.5193	3.21527
$829$	−3.44121	−0.119518	−0.0597591	−	0.998213i	$-0.519033\pi$
$829$	−3.44121	−0.119518	−0.0597591	+	0.998213i	$0.519033\pi$
$830$	0	0
$831$	7.38646	0.256233
$832$	18.1187	0.628153
$833$	−8.57452	−0.297089
$834$	10.8627	0.376146
$835$	0	0
$836$	31.7440	1.09789
$837$	14.6761	0.507280
$838$	−46.7123	−1.61365
$839$	−52.6248	−1.81681	−0.908406	−	0.418090i	$-0.862700\pi$
$839$	−52.6248	−1.81681	−0.908406	+	0.418090i	$0.862700\pi$
$840$	0	0
$841$	−23.1524	−0.798357
$842$	−7.72355	−0.266171
$843$	6.70052	0.230778
$844$	−25.2750	−0.870003
$845$	0	0
$846$	−23.6542	−0.813248
$847$	−2.02047	−0.0694241
$848$	−70.4358	−2.41878
$849$	−9.80748	−0.336592
$850$	0	0
$851$	24.4241	0.837246
$852$	21.2447	0.727832
$853$	6.31853	0.216342	0.108171	−	0.994132i	$-0.465501\pi$
$853$	6.31853	0.216342	0.108171	+	0.994132i	$0.465501\pi$
$854$	−3.81336	−0.130490
$855$	0	0
$856$	93.9850	3.21234
$857$	0.775746	0.0264990	0.0132495	−	0.999912i	$-0.495782\pi$
$857$	0.775746	0.0264990	0.0132495	+	0.999912i	$0.495782\pi$
$858$	4.73084	0.161508
$859$	3.24869	0.110844	0.0554220	−	0.998463i	$-0.482350\pi$
$859$	3.24869	0.110844	0.0554220	+	0.998463i	$0.482350\pi$
$860$	0	0
$861$	3.22425	0.109882
$862$	−2.37962	−0.0810503
$863$	19.9208	0.678112	0.339056	−	0.940766i	$-0.389892\pi$
$863$	19.9208	0.678112	0.339056	+	0.940766i	$0.389892\pi$
$864$	44.2736	1.50622
$865$	0	0
$866$	−67.5487	−2.29540
$867$	−7.30299	−0.248022
$868$	21.9756	0.745899
$869$	8.31265	0.281987
$870$	0	0
$871$	−9.89446	−0.335261
$872$	−80.9544	−2.74146
$873$	−5.18806	−0.175589
$874$	−29.0435	−0.982411
$875$	0	0
$876$	29.1998	0.986570
$877$	−22.1378	−0.747539	−0.373770	−	0.927522i	$-0.621935\pi$
$877$	−22.1378	−0.747539	−0.373770	+	0.927522i	$0.621935\pi$
$878$	−77.0757	−2.60118
$879$	−2.58910	−0.0873283
$880$	0	0
$881$	2.23155	0.0751828	0.0375914	−	0.999293i	$-0.488031\pi$
$881$	2.23155	0.0751828	0.0375914	+	0.999293i	$0.488031\pi$
$882$	−47.0299	−1.58358
$883$	4.30440	0.144855	0.0724273	−	0.997374i	$-0.476925\pi$
$883$	4.30440	0.144855	0.0724273	+	0.997374i	$0.476925\pi$
$884$	6.96239	0.234170
$885$	0	0
$886$	98.9276	3.32354
$887$	−15.9330	−0.534979	−0.267489	−	0.963561i	$-0.586194\pi$
$887$	−15.9330	−0.534979	−0.267489	+	0.963561i	$0.586194\pi$
$888$	15.3112	0.513811
$889$	−3.46168	−0.116101
$890$	0	0
$891$	−25.6145	−0.858118
$892$	−128.432	−4.30022
$893$	5.35026	0.179040
$894$	14.6107	0.488655
$895$	0	0
$896$	13.3561	0.446197
$897$	−3.11871	−0.104131
$898$	33.9365	1.13248
$899$	−12.7856	−0.426423
$900$	0	0
$901$	−7.74798	−0.258123
$902$	−81.7255	−2.72116
$903$	−2.63515	−0.0876923
$904$	4.85097	0.161341
$905$	0	0
$906$	−18.0059	−0.598205
$907$	51.9086	1.72360	0.861798	−	0.507251i	$-0.169338\pi$
$907$	51.9086	1.72360	0.861798	+	0.507251i	$0.169338\pi$
$908$	−51.3317	−1.70350
$909$	−29.0668	−0.964085
$910$	0	0
$911$	−9.67750	−0.320630	−0.160315	−	0.987066i	$-0.551251\pi$
$911$	−9.67750	−0.320630	−0.160315	+	0.987066i	$0.551251\pi$
$912$	−9.89446	−0.327638
$913$	14.1260	0.467503
$914$	−67.0103	−2.21651
$915$	0	0
$916$	27.5877	0.911523
$917$	0.674176	0.0222632
$918$	10.0263	0.330919
$919$	13.5515	0.447022	0.223511	−	0.974701i	$-0.428248\pi$
$919$	13.5515	0.447022	0.223511	+	0.974701i	$0.428248\pi$
$920$	0	0
$921$	9.22425	0.303949
$922$	98.6780	3.24979
$923$	8.56230	0.281831
$924$	7.35026	0.241806
$925$	0	0
$926$	−104.381	−3.43017
$927$	42.5466	1.39741
$928$	−38.5705	−1.26614
$929$	−9.44992	−0.310042	−0.155021	−	0.987911i	$-0.549545\pi$
$929$	−9.44992	−0.310042	−0.155021	+	0.987911i	$0.549545\pi$
$930$	0	0
$931$	10.6375	0.348631
$932$	55.4880	1.81757
$933$	−12.1504	−0.397788
$934$	87.6625	2.86840
$935$	0	0
$936$	23.3757	0.764057
$937$	−16.0409	−0.524035	−0.262017	−	0.965063i	$-0.584388\pi$
$937$	−16.0409	−0.524035	−0.262017	+	0.965063i	$0.584388\pi$
$938$	−21.3357	−0.696634
$939$	−1.35309	−0.0441565
$940$	0	0
$941$	−21.6747	−0.706574	−0.353287	−	0.935515i	$-0.614936\pi$
$941$	−21.6747	−0.706574	−0.353287	+	0.935515i	$0.614936\pi$
$942$	3.57310	0.116418
$943$	53.8759	1.75444
$944$	73.5002	2.39223
$945$	0	0
$946$	66.7934	2.17164
$947$	4.63118	0.150493	0.0752466	−	0.997165i	$-0.476026\pi$
$947$	4.63118	0.150493	0.0752466	+	0.997165i	$0.476026\pi$
$948$	−5.61213	−0.182273
$949$	11.7685	0.382020
$950$	0	0
$951$	11.4372	0.370878
$952$	9.18997	0.297849
$953$	−26.2981	−0.851878	−0.425939	−	0.904752i	$-0.640056\pi$
$953$	−26.2981	−0.851878	−0.425939	+	0.904752i	$0.640056\pi$
$954$	−42.4965	−1.37587
$955$	0	0
$956$	−61.1632	−1.97816
$957$	−4.27645	−0.138238
$958$	−45.1427	−1.45849
$959$	−12.0409	−0.388822
$960$	0	0
$961$	−3.04491	−0.0982228
$962$	10.0811	0.325028
$963$	30.8155	0.993014
$964$	−147.601	−4.75392
$965$	0	0
$966$	−6.72496	−0.216372
$967$	11.9405	0.383981	0.191990	−	0.981397i	$-0.438506\pi$
$967$	11.9405	0.383981	0.191990	+	0.981397i	$0.438506\pi$
$968$	−21.1646	−0.680255
$969$	−1.08840	−0.0349643
$970$	0	0
$971$	30.1524	0.967635	0.483818	−	0.875169i	$-0.339250\pi$
$971$	30.1524	0.967635	0.483818	+	0.875169i	$0.339250\pi$
$972$	60.2311	1.93191
$973$	6.80209	0.218065
$974$	−24.7308	−0.792427
$975$	0	0
$976$	−21.7078	−0.694850
$977$	−26.9321	−0.861633	−0.430817	−	0.902439i	$-0.641774\pi$
$977$	−26.9321	−0.861633	−0.430817	+	0.902439i	$0.641774\pi$
$978$	2.87258	0.0918549
$979$	−10.2012	−0.326033
$980$	0	0
$981$	−26.5431	−0.847455
$982$	68.8843	2.19819
$983$	20.5902	0.656727	0.328363	−	0.944551i	$-0.393503\pi$
$983$	20.5902	0.656727	0.328363	+	0.944551i	$0.393503\pi$
$984$	33.7743	1.07669
$985$	0	0
$986$	−8.73481	−0.278173
$987$	1.23884	0.0394328
$988$	−8.63752	−0.274796
$989$	−44.0322	−1.40014
$990$	0	0
$991$	−48.1378	−1.52915	−0.764573	−	0.644537i	$-0.777050\pi$
$991$	−48.1378	−1.52915	−0.764573	+	0.644537i	$0.777050\pi$
$992$	84.3327	2.67756
$993$	−5.67864	−0.180206
$994$	18.4631	0.585614
$995$	0	0
$996$	−9.53690	−0.302188
$997$	−33.4255	−1.05860	−0.529298	−	0.848436i	$-0.677545\pi$
$997$	−33.4255	−1.05860	−0.529298	+	0.848436i	$0.677545\pi$
$998$	74.1051	2.34576
$999$	10.4603	0.330948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.a.j.1.1		3
3.2	odd	2		2925.2.a.bj.1.3		3
4.3	odd	2		5200.2.a.cj.1.1		3
5.2	odd	4		65.2.b.a.14.1	✓	6
5.3	odd	4		65.2.b.a.14.6	yes	6
5.4	even	2		325.2.a.k.1.3		3
13.12	even	2		4225.2.a.bh.1.3		3
15.2	even	4		585.2.c.b.469.6		6
15.8	even	4		585.2.c.b.469.1		6
15.14	odd	2		2925.2.a.bf.1.1		3
20.3	even	4		1040.2.d.c.209.3		6
20.7	even	4		1040.2.d.c.209.4		6
20.19	odd	2		5200.2.a.cb.1.3		3
65.2	even	12		845.2.l.e.654.6		12
65.3	odd	12		845.2.n.f.529.1		12
65.7	even	12		845.2.l.d.699.1		12
65.8	even	4		845.2.d.a.844.2		6
65.12	odd	4		845.2.b.c.339.6		6
65.17	odd	12		845.2.n.g.484.6		12
65.18	even	4		845.2.d.b.844.6		6
65.22	odd	12		845.2.n.f.484.1		12
65.23	odd	12		845.2.n.g.529.6		12
65.28	even	12		845.2.l.d.654.1		12
65.32	even	12		845.2.l.e.699.5		12
65.33	even	12		845.2.l.e.699.6		12
65.37	even	12		845.2.l.d.654.2		12
65.38	odd	4		845.2.b.c.339.1		6
65.42	odd	12		845.2.n.f.529.6		12
65.43	odd	12		845.2.n.g.484.1		12
65.47	even	4		845.2.d.b.844.5		6
65.48	odd	12		845.2.n.f.484.6		12
65.57	even	4		845.2.d.a.844.1		6
65.58	even	12		845.2.l.d.699.2		12
65.62	odd	12		845.2.n.g.529.1		12
65.63	even	12		845.2.l.e.654.5		12
65.64	even	2		4225.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	5.2	odd	4
65.2.b.a.14.6	yes	6	5.3	odd	4
325.2.a.j.1.1		3	1.1	even	1	trivial
325.2.a.k.1.3		3	5.4	even	2
585.2.c.b.469.1		6	15.8	even	4
585.2.c.b.469.6		6	15.2	even	4
845.2.b.c.339.1		6	65.38	odd	4
845.2.b.c.339.6		6	65.12	odd	4
845.2.d.a.844.1		6	65.57	even	4
845.2.d.a.844.2		6	65.8	even	4
845.2.d.b.844.5		6	65.47	even	4
845.2.d.b.844.6		6	65.18	even	4
845.2.l.d.654.1		12	65.28	even	12
845.2.l.d.654.2		12	65.37	even	12
845.2.l.d.699.1		12	65.7	even	12
845.2.l.d.699.2		12	65.58	even	12
845.2.l.e.654.5		12	65.63	even	12
845.2.l.e.654.6		12	65.2	even	12
845.2.l.e.699.5		12	65.32	even	12
845.2.l.e.699.6		12	65.33	even	12
845.2.n.f.484.1		12	65.22	odd	12
845.2.n.f.484.6		12	65.48	odd	12
845.2.n.f.529.1		12	65.3	odd	12
845.2.n.f.529.6		12	65.42	odd	12
845.2.n.g.484.1		12	65.43	odd	12
845.2.n.g.484.6		12	65.17	odd	12
845.2.n.g.529.1		12	65.62	odd	12
845.2.n.g.529.6		12	65.23	odd	12
1040.2.d.c.209.3		6	20.3	even	4
1040.2.d.c.209.4		6	20.7	even	4
2925.2.a.bf.1.1		3	15.14	odd	2
2925.2.a.bj.1.3		3	3.2	odd	2
4225.2.a.ba.1.1		3	65.64	even	2
4225.2.a.bh.1.3		3	13.12	even	2
5200.2.a.cb.1.3		3	20.19	odd	2
5200.2.a.cj.1.1		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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67513 q^{2} +0.481194 q^{3} +5.15633 q^{4} -1.28726 q^{6} -0.806063 q^{7} -8.44358 q^{8} -2.76845 q^{9} +O(q^{10})\)	\(q-2.67513 q^{2} +0.481194 q^{3} +5.15633 q^{4} -1.28726 q^{6} -0.806063 q^{7} -8.44358 q^{8} -2.76845 q^{9} -3.67513 q^{11} +2.48119 q^{12} +1.00000 q^{13} +2.15633 q^{14} +12.2750 q^{16} +1.35026 q^{17} +7.40597 q^{18} -1.67513 q^{19} -0.387873 q^{21} +9.83146 q^{22} -6.48119 q^{23} -4.06300 q^{24} -2.67513 q^{26} -2.77575 q^{27} -4.15633 q^{28} +2.41819 q^{29} -5.28726 q^{31} -15.9502 q^{32} -1.76845 q^{33} -3.61213 q^{34} -14.2750 q^{36} -3.76845 q^{37} +4.48119 q^{38} +0.481194 q^{39} -8.31265 q^{41} +1.03761 q^{42} +6.79384 q^{43} -18.9502 q^{44} +17.3380 q^{46} -3.19394 q^{47} +5.90668 q^{48} -6.35026 q^{49} +0.649738 q^{51} +5.15633 q^{52} -5.73813 q^{53} +7.42548 q^{54} +6.80606 q^{56} -0.806063 q^{57} -6.46898 q^{58} +5.98778 q^{59} -1.76845 q^{61} +14.1441 q^{62} +2.23155 q^{63} +18.1187 q^{64} +4.73084 q^{66} -9.89446 q^{67} +6.96239 q^{68} -3.11871 q^{69} +8.56230 q^{71} +23.3757 q^{72} +11.7685 q^{73} +10.0811 q^{74} -8.63752 q^{76} +2.96239 q^{77} -1.28726 q^{78} -2.26187 q^{79} +6.96968 q^{81} +22.2374 q^{82} -3.84367 q^{83} -2.00000 q^{84} -18.1744 q^{86} +1.16362 q^{87} +31.0313 q^{88} +2.77575 q^{89} -0.806063 q^{91} -33.4191 q^{92} -2.54420 q^{93} +8.54420 q^{94} -7.67513 q^{96} +1.87399 q^{97} +16.9878 q^{98} +10.1744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 4 q^{3} + 5 q^{4} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 4 * q^3 + 5 * q^4 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 4 q^{3} + 5 q^{4} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} + 2 q^{12} + 3 q^{13} - 4 q^{14} + 5 q^{16} - 6 q^{17} - 5 q^{18} - 2 q^{21} + 14 q^{22} - 14 q^{23} - 8 q^{24} - 3 q^{26} - 10 q^{27} - 2 q^{28} + 6 q^{29} - 10 q^{31} - 11 q^{32} + 6 q^{33} - 10 q^{34} - 11 q^{36} + 8 q^{38} - 4 q^{39} - 4 q^{41} + 14 q^{42} - 6 q^{43} - 20 q^{44} + 16 q^{46} - 10 q^{47} + 24 q^{48} - 9 q^{49} + 12 q^{51} + 5 q^{52} - 8 q^{53} + 34 q^{54} + 20 q^{56} - 2 q^{57} + 12 q^{58} - 8 q^{59} + 6 q^{61} + 6 q^{62} + 18 q^{63} + 33 q^{64} - 8 q^{66} - 10 q^{67} + 10 q^{68} + 12 q^{69} - 12 q^{71} + 45 q^{72} + 24 q^{73} - 2 q^{74} - 10 q^{76} - 2 q^{77} + 2 q^{78} - 16 q^{79} + 23 q^{81} + 24 q^{82} - 22 q^{83} - 6 q^{84} - 16 q^{86} + 6 q^{87} + 24 q^{88} + 10 q^{89} - 2 q^{91} - 32 q^{92} + 2 q^{93} + 16 q^{94} - 18 q^{96} + 14 q^{97} + 25 q^{98} - 8 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 4 * q^3 + 5 * q^4 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 + 2 * q^12 + 3 * q^13 - 4 * q^14 + 5 * q^16 - 6 * q^17 - 5 * q^18 - 2 * q^21 + 14 * q^22 - 14 * q^23 - 8 * q^24 - 3 * q^26 - 10 * q^27 - 2 * q^28 + 6 * q^29 - 10 * q^31 - 11 * q^32 + 6 * q^33 - 10 * q^34 - 11 * q^36 + 8 * q^38 - 4 * q^39 - 4 * q^41 + 14 * q^42 - 6 * q^43 - 20 * q^44 + 16 * q^46 - 10 * q^47 + 24 * q^48 - 9 * q^49 + 12 * q^51 + 5 * q^52 - 8 * q^53 + 34 * q^54 + 20 * q^56 - 2 * q^57 + 12 * q^58 - 8 * q^59 + 6 * q^61 + 6 * q^62 + 18 * q^63 + 33 * q^64 - 8 * q^66 - 10 * q^67 + 10 * q^68 + 12 * q^69 - 12 * q^71 + 45 * q^72 + 24 * q^73 - 2 * q^74 - 10 * q^76 - 2 * q^77 + 2 * q^78 - 16 * q^79 + 23 * q^81 + 24 * q^82 - 22 * q^83 - 6 * q^84 - 16 * q^86 + 6 * q^87 + 24 * q^88 + 10 * q^89 - 2 * q^91 - 32 * q^92 + 2 * q^93 + 16 * q^94 - 18 * q^96 + 14 * q^97 + 25 * q^98 - 8 * q^99

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