LMFDB - Embedded newform 6223.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6223,2,Mod(1,6223)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6223, 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("6223.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6223 = 7^{2} \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6223.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:	$49.6909051778$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 22 x^{13} + 186 x^{11} - 763 x^{9} - 7 x^{8} + 1588 x^{7} + 64 x^{6} - 1625 x^{5} - 185 x^{4} + \cdots - 13 $ x^15 - 22x^13 + 186x^11 - 763x^9 - 7x^8 + 1588x^7 + 64x^6 - 1625x^5 - 185x^4 + 726x^3 + 145x^2 - 83*x - 13
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 889)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.371530$ of defining polynomial
Character	$\chi$	$=$	6223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.371530 q^{2} +1.28062 q^{3} -1.86197 q^{4} -0.962757 q^{5} -0.475791 q^{6} +1.43484 q^{8} -1.36000 q^{9} +O(q^{10})$	\(q-0.371530 q^{2} +1.28062 q^{3} -1.86197 q^{4} -0.962757 q^{5} -0.475791 q^{6} +1.43484 q^{8} -1.36000 q^{9} +0.357693 q^{10} +2.23995 q^{11} -2.38448 q^{12} +2.04029 q^{13} -1.23293 q^{15} +3.19084 q^{16} +0.799638 q^{17} +0.505282 q^{18} +2.50191 q^{19} +1.79262 q^{20} -0.832211 q^{22} -8.29860 q^{23} +1.83749 q^{24} -4.07310 q^{25} -0.758029 q^{26} -5.58352 q^{27} +6.47749 q^{29} +0.458071 q^{30} -10.5031 q^{31} -4.05517 q^{32} +2.86854 q^{33} -0.297090 q^{34} +2.53228 q^{36} +9.86098 q^{37} -0.929535 q^{38} +2.61284 q^{39} -1.38140 q^{40} -2.88332 q^{41} +11.3200 q^{43} -4.17072 q^{44} +1.30935 q^{45} +3.08318 q^{46} -3.43218 q^{47} +4.08627 q^{48} +1.51328 q^{50} +1.02404 q^{51} -3.79894 q^{52} -7.22108 q^{53} +2.07445 q^{54} -2.15653 q^{55} +3.20400 q^{57} -2.40658 q^{58} +0.159877 q^{59} +2.29567 q^{60} -4.11951 q^{61} +3.90221 q^{62} -4.87507 q^{64} -1.96430 q^{65} -1.06575 q^{66} +4.73560 q^{67} -1.48890 q^{68} -10.6274 q^{69} +7.88815 q^{71} -1.95138 q^{72} +10.3947 q^{73} -3.66365 q^{74} -5.21611 q^{75} -4.65847 q^{76} -0.970750 q^{78} -0.578921 q^{79} -3.07201 q^{80} -3.07039 q^{81} +1.07124 q^{82} -12.2666 q^{83} -0.769857 q^{85} -4.20574 q^{86} +8.29523 q^{87} +3.21397 q^{88} -16.0202 q^{89} -0.486464 q^{90} +15.4517 q^{92} -13.4505 q^{93} +1.27516 q^{94} -2.40873 q^{95} -5.19315 q^{96} -1.74914 q^{97} -3.04634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 4 q^{3} + 14 q^{4} - 7 q^{5} - 8 q^{6} + 9 q^{9}+O(q^{10}) $ 15 * q - 4 * q^3 + 14 * q^4 - 7 * q^5 - 8 * q^6 + 9 * q^9	$ 15 q - 4 q^{3} + 14 q^{4} - 7 q^{5} - 8 q^{6} + 9 q^{9} - 10 q^{10} + 14 q^{11} - 10 q^{12} - 6 q^{13} + 6 q^{15} + 20 q^{16} - 10 q^{17} + q^{18} - 13 q^{19} - 8 q^{20} - 11 q^{22} + 15 q^{23} - 34 q^{24} - 22 q^{26} - 22 q^{27} + 16 q^{29} + 7 q^{30} - 22 q^{31} - 14 q^{33} + 15 q^{34} + 20 q^{36} - 14 q^{37} + 6 q^{38} + 29 q^{39} - 22 q^{40} - 19 q^{41} - q^{43} + 25 q^{44} + 8 q^{45} - 28 q^{46} - 49 q^{47} + 14 q^{48} + 24 q^{50} - 8 q^{51} + 17 q^{52} - 28 q^{53} - 13 q^{54} - 39 q^{55} - 12 q^{57} - 10 q^{58} - 43 q^{59} - 60 q^{60} - 27 q^{61} - 14 q^{62} + 18 q^{64} - 8 q^{65} + 36 q^{66} + 3 q^{67} - 13 q^{68} + 17 q^{69} + 55 q^{71} - 21 q^{72} + 3 q^{73} - 12 q^{74} - 8 q^{75} + 20 q^{76} - 6 q^{78} + 18 q^{79} - 29 q^{80} - 17 q^{81} - 14 q^{82} - 17 q^{83} + 7 q^{85} + 4 q^{86} - 35 q^{87} - 114 q^{88} - 36 q^{89} + 39 q^{90} + 45 q^{92} + 15 q^{93} + 15 q^{94} + 59 q^{95} - 85 q^{96} + 2 q^{97} + 35 q^{99}+O(q^{100}) $ 15 * q - 4 * q^3 + 14 * q^4 - 7 * q^5 - 8 * q^6 + 9 * q^9 - 10 * q^10 + 14 * q^11 - 10 * q^12 - 6 * q^13 + 6 * q^15 + 20 * q^16 - 10 * q^17 + q^18 - 13 * q^19 - 8 * q^20 - 11 * q^22 + 15 * q^23 - 34 * q^24 - 22 * q^26 - 22 * q^27 + 16 * q^29 + 7 * q^30 - 22 * q^31 - 14 * q^33 + 15 * q^34 + 20 * q^36 - 14 * q^37 + 6 * q^38 + 29 * q^39 - 22 * q^40 - 19 * q^41 - q^43 + 25 * q^44 + 8 * q^45 - 28 * q^46 - 49 * q^47 + 14 * q^48 + 24 * q^50 - 8 * q^51 + 17 * q^52 - 28 * q^53 - 13 * q^54 - 39 * q^55 - 12 * q^57 - 10 * q^58 - 43 * q^59 - 60 * q^60 - 27 * q^61 - 14 * q^62 + 18 * q^64 - 8 * q^65 + 36 * q^66 + 3 * q^67 - 13 * q^68 + 17 * q^69 + 55 * q^71 - 21 * q^72 + 3 * q^73 - 12 * q^74 - 8 * q^75 + 20 * q^76 - 6 * q^78 + 18 * q^79 - 29 * q^80 - 17 * q^81 - 14 * q^82 - 17 * q^83 + 7 * q^85 + 4 * q^86 - 35 * q^87 - 114 * q^88 - 36 * q^89 + 39 * q^90 + 45 * q^92 + 15 * q^93 + 15 * q^94 + 59 * q^95 - 85 * q^96 + 2 * q^97 + 35 * 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 $

$2$	−0.371530	−0.262712	−0.131356	−	0.991335i	$-0.541933\pi$
$2$	−0.371530	−0.262712	−0.131356	+	0.991335i	$0.541933\pi$
$3$	1.28062	0.739369	0.369684	−	0.929157i	$-0.379466\pi$
$3$	1.28062	0.739369	0.369684	+	0.929157i	$0.379466\pi$
$4$	−1.86197	−0.930983
$5$	−0.962757	−0.430558	−0.215279	−	0.976553i	$-0.569066\pi$
$5$	−0.962757	−0.430558	−0.215279	+	0.976553i	$0.569066\pi$
$6$	−0.475791	−0.194241
$7$	0	0
$7$	0	0
$8$	1.43484	0.507292
$9$	−1.36000	−0.453334
$10$	0.357693	0.113113
$11$	2.23995	0.675372	0.337686	−	0.941259i	$-0.390356\pi$
$11$	2.23995	0.675372	0.337686	+	0.941259i	$0.390356\pi$
$12$	−2.38448	−0.688339
$13$	2.04029	0.565874	0.282937	−	0.959139i	$-0.408691\pi$
$13$	2.04029	0.565874	0.282937	+	0.959139i	$0.408691\pi$
$14$	0	0
$15$	−1.23293	−0.318341
$16$	3.19084	0.797711
$17$	0.799638	0.193941	0.0969704	−	0.995287i	$-0.469085\pi$
$17$	0.799638	0.193941	0.0969704	+	0.995287i	$0.469085\pi$
$18$	0.505282	0.119096
$19$	2.50191	0.573977	0.286989	−	0.957934i	$-0.407346\pi$
$19$	2.50191	0.573977	0.286989	+	0.957934i	$0.407346\pi$
$20$	1.79262	0.400842
$21$	0	0
$22$	−0.832211	−0.177428
$23$	−8.29860	−1.73038	−0.865189	−	0.501446i	$-0.832802\pi$
$23$	−8.29860	−1.73038	−0.865189	+	0.501446i	$0.832802\pi$
$24$	1.83749	0.375075
$25$	−4.07310	−0.814620
$26$	−0.758029	−0.148662
$27$	−5.58352	−1.07455
$28$	0	0
$29$	6.47749	1.20284	0.601420	−	0.798933i	$-0.294602\pi$
$29$	6.47749	1.20284	0.601420	+	0.798933i	$0.294602\pi$
$30$	0.458071	0.0836319
$31$	−10.5031	−1.88641	−0.943203	−	0.332216i	$-0.892204\pi$
$31$	−10.5031	−1.88641	−0.943203	+	0.332216i	$0.892204\pi$
$32$	−4.05517	−0.716860
$33$	2.86854	0.499348
$34$	−0.297090	−0.0509505
$35$	0	0
$36$	2.53228	0.422046
$37$	9.86098	1.62114	0.810568	−	0.585645i	$-0.199159\pi$
$37$	9.86098	1.62114	0.810568	+	0.585645i	$0.199159\pi$
$38$	−0.929535	−0.150790
$39$	2.61284	0.418389
$40$	−1.38140	−0.218418
$41$	−2.88332	−0.450299	−0.225150	−	0.974324i	$-0.572287\pi$
$41$	−2.88332	−0.450299	−0.225150	+	0.974324i	$0.572287\pi$
$42$	0	0
$43$	11.3200	1.72629	0.863145	−	0.504956i	$-0.168491\pi$
$43$	11.3200	1.72629	0.863145	+	0.504956i	$0.168491\pi$
$44$	−4.17072	−0.628759
$45$	1.30935	0.195187
$46$	3.08318	0.454590
$47$	−3.43218	−0.500635	−0.250317	−	0.968164i	$-0.580535\pi$
$47$	−3.43218	−0.500635	−0.250317	+	0.968164i	$0.580535\pi$
$48$	4.08627	0.589803
$49$	0	0
$50$	1.51328	0.214010
$51$	1.02404	0.143394
$52$	−3.79894	−0.526819
$53$	−7.22108	−0.991892	−0.495946	−	0.868353i	$-0.665179\pi$
$53$	−7.22108	−0.991892	−0.495946	+	0.868353i	$0.665179\pi$
$54$	2.07445	0.282297
$55$	−2.15653	−0.290786
$56$	0	0
$57$	3.20400	0.424381
$58$	−2.40658	−0.316000
$59$	0.159877	0.0208142	0.0104071	−	0.999946i	$-0.496687\pi$
$59$	0.159877	0.0208142	0.0104071	+	0.999946i	$0.496687\pi$
$60$	2.29567	0.296370
$61$	−4.11951	−0.527449	−0.263725	−	0.964598i	$-0.584951\pi$
$61$	−4.11951	−0.527449	−0.263725	+	0.964598i	$0.584951\pi$
$62$	3.90221	0.495581
$63$	0	0
$64$	−4.87507	−0.609384
$65$	−1.96430	−0.243641
$66$	−1.06575	−0.131185
$67$	4.73560	0.578546	0.289273	−	0.957247i	$-0.406587\pi$
$67$	4.73560	0.578546	0.289273	+	0.957247i	$0.406587\pi$
$68$	−1.48890	−0.180555
$69$	−10.6274	−1.27939
$70$	0	0
$71$	7.88815	0.936152	0.468076	−	0.883688i	$-0.344947\pi$
$71$	7.88815	0.936152	0.468076	+	0.883688i	$0.344947\pi$
$72$	−1.95138	−0.229973
$73$	10.3947	1.21660	0.608302	−	0.793705i	$-0.291851\pi$
$73$	10.3947	1.21660	0.608302	+	0.793705i	$0.291851\pi$
$74$	−3.66365	−0.425891
$75$	−5.21611	−0.602304
$76$	−4.65847	−0.534363
$77$	0	0
$78$	−0.970750	−0.109916
$79$	−0.578921	−0.0651337	−0.0325668	−	0.999470i	$-0.510368\pi$
$79$	−0.578921	−0.0651337	−0.0325668	+	0.999470i	$0.510368\pi$
$80$	−3.07201	−0.343461
$81$	−3.07039	−0.341154
$82$	1.07124	0.118299
$83$	−12.2666	−1.34643	−0.673216	−	0.739445i	$-0.735088\pi$
$83$	−12.2666	−1.34643	−0.673216	+	0.739445i	$0.735088\pi$
$84$	0	0
$85$	−0.769857	−0.0835027
$86$	−4.20574	−0.453516
$87$	8.29523	0.889342
$88$	3.21397	0.342610
$89$	−16.0202	−1.69813	−0.849066	−	0.528286i	$-0.822835\pi$
$89$	−16.0202	−1.69813	−0.849066	+	0.528286i	$0.822835\pi$
$90$	−0.486464	−0.0512778
$91$	0	0
$92$	15.4517	1.61095
$93$	−13.4505	−1.39475
$94$	1.27516	0.131523
$95$	−2.40873	−0.247130
$96$	−5.19315	−0.530023
$97$	−1.74914	−0.177598	−0.0887989	−	0.996050i	$-0.528303\pi$
$97$	−1.74914	−0.177598	−0.0887989	+	0.996050i	$0.528303\pi$
$98$	0	0
$99$	−3.04634	−0.306169
$100$	7.58397	0.758397
$101$	4.42131	0.439937	0.219969	−	0.975507i	$-0.429405\pi$
$101$	4.42131	0.439937	0.219969	+	0.975507i	$0.429405\pi$
$102$	−0.380460	−0.0376712
$103$	6.98895	0.688642	0.344321	−	0.938852i	$-0.388109\pi$
$103$	6.98895	0.688642	0.344321	+	0.938852i	$0.388109\pi$
$104$	2.92748	0.287063
$105$	0	0
$106$	2.68285	0.260581
$107$	8.70072	0.841130	0.420565	−	0.907262i	$-0.361832\pi$
$107$	8.70072	0.841130	0.420565	+	0.907262i	$0.361832\pi$
$108$	10.3963	1.00039
$109$	−0.782092	−0.0749108	−0.0374554	−	0.999298i	$-0.511925\pi$
$109$	−0.782092	−0.0749108	−0.0374554	+	0.999298i	$0.511925\pi$
$110$	0.801216	0.0763930
$111$	12.6282	1.19862
$112$	0	0
$113$	10.9872	1.03358	0.516792	−	0.856111i	$-0.327126\pi$
$113$	10.9872	1.03358	0.516792	+	0.856111i	$0.327126\pi$
$114$	−1.19038	−0.111490
$115$	7.98953	0.745028
$116$	−12.0609	−1.11982
$117$	−2.77480	−0.256530
$118$	−0.0593990	−0.00546812
$119$	0	0
$120$	−1.76905	−0.161492
$121$	−5.98261	−0.543873
$122$	1.53052	0.138567
$123$	−3.69245	−0.332937
$124$	19.5563	1.75621
$125$	8.73519	0.781299
$126$	0	0
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	9.92158	0.876952
$129$	14.4967	1.27636
$130$	0.729797	0.0640074
$131$	−1.99888	−0.174643	−0.0873215	−	0.996180i	$-0.527831\pi$
$131$	−1.99888	−0.174643	−0.0873215	+	0.996180i	$0.527831\pi$
$132$	−5.34112	−0.464885
$133$	0	0
$134$	−1.75942	−0.151991
$135$	5.37557	0.462656
$136$	1.14735	0.0983845
$137$	−12.8751	−1.10000	−0.549998	−	0.835166i	$-0.685372\pi$
$137$	−12.8751	−1.10000	−0.549998	+	0.835166i	$0.685372\pi$
$138$	3.94840	0.336110
$139$	−14.8863	−1.26264	−0.631318	−	0.775524i	$-0.717486\pi$
$139$	−14.8863	−1.26264	−0.631318	+	0.775524i	$0.717486\pi$
$140$	0	0
$141$	−4.39533	−0.370153
$142$	−2.93069	−0.245938
$143$	4.57015	0.382175
$144$	−4.33956	−0.361630
$145$	−6.23624	−0.517892
$146$	−3.86194	−0.319616
$147$	0	0
$148$	−18.3608	−1.50925
$149$	−4.78549	−0.392042	−0.196021	−	0.980600i	$-0.562802\pi$
$149$	−4.78549	−0.392042	−0.196021	+	0.980600i	$0.562802\pi$
$150$	1.93794	0.158232
$151$	10.4867	0.853397	0.426699	−	0.904394i	$-0.359677\pi$
$151$	10.4867	0.853397	0.426699	+	0.904394i	$0.359677\pi$
$152$	3.58983	0.291174
$153$	−1.08751	−0.0879199
$154$	0	0
$155$	10.1119	0.812207
$156$	−4.86502	−0.389513
$157$	−12.3137	−0.982739	−0.491369	−	0.870951i	$-0.663503\pi$
$157$	−12.3137	−0.982739	−0.491369	+	0.870951i	$0.663503\pi$
$158$	0.215087	0.0171114
$159$	−9.24749	−0.733373
$160$	3.90414	0.308650
$161$	0	0
$162$	1.14074	0.0896251
$163$	−17.6316	−1.38101	−0.690506	−	0.723327i	$-0.742612\pi$
$163$	−17.6316	−1.38101	−0.690506	+	0.723327i	$0.742612\pi$
$164$	5.36865	0.419221
$165$	−2.76170	−0.214998
$166$	4.55741	0.353724
$167$	19.9214	1.54157	0.770783	−	0.637097i	$-0.219865\pi$
$167$	19.9214	1.54157	0.770783	+	0.637097i	$0.219865\pi$
$168$	0	0
$169$	−8.83723	−0.679787
$170$	0.286025	0.0219371
$171$	−3.40260	−0.260203
$172$	−21.0775	−1.60715
$173$	−13.8449	−1.05261	−0.526304	−	0.850297i	$-0.676423\pi$
$173$	−13.8449	−1.05261	−0.526304	+	0.850297i	$0.676423\pi$
$174$	−3.08193	−0.233640
$175$	0	0
$176$	7.14735	0.538751
$177$	0.204742	0.0153893
$178$	5.95197	0.446119
$179$	6.38959	0.477581	0.238790	−	0.971071i	$-0.423249\pi$
$179$	6.38959	0.477581	0.238790	+	0.971071i	$0.423249\pi$
$180$	−2.43797	−0.181715
$181$	11.4802	0.853315	0.426658	−	0.904413i	$-0.359691\pi$
$181$	11.4802	0.853315	0.426658	+	0.904413i	$0.359691\pi$
$182$	0	0
$183$	−5.27554	−0.389979
$184$	−11.9071	−0.877806
$185$	−9.49373	−0.697993
$186$	4.99726	0.366417
$187$	1.79115	0.130982
$188$	6.39059	0.466082
$189$	0	0
$190$	0.894916	0.0649240
$191$	−25.4901	−1.84440	−0.922200	−	0.386714i	$-0.873610\pi$
$191$	−25.4901	−1.84440	−0.922200	+	0.386714i	$0.873610\pi$
$192$	−6.24313	−0.450559
$193$	−25.4887	−1.83472	−0.917359	−	0.398060i	$-0.869683\pi$
$193$	−25.4887	−1.83472	−0.917359	+	0.398060i	$0.869683\pi$
$194$	0.649857	0.0466570
$195$	−2.51553	−0.180141
$196$	0	0
$197$	−6.40843	−0.456581	−0.228291	−	0.973593i	$-0.573314\pi$
$197$	−6.40843	−0.456581	−0.228291	+	0.973593i	$0.573314\pi$
$198$	1.13181	0.0804341
$199$	−11.4734	−0.813330	−0.406665	−	0.913577i	$-0.633308\pi$
$199$	−11.4734	−0.813330	−0.406665	+	0.913577i	$0.633308\pi$
$200$	−5.84424	−0.413250
$201$	6.06452	0.427758
$202$	−1.64265	−0.115577
$203$	0	0
$204$	−1.90672	−0.133497
$205$	2.77594	0.193880
$206$	−2.59661	−0.180914
$207$	11.2861	0.784439
$208$	6.51024	0.451404
$209$	5.60416	0.387648
$210$	0	0
$211$	−8.05556	−0.554568	−0.277284	−	0.960788i	$-0.589434\pi$
$211$	−8.05556	−0.554568	−0.277284	+	0.960788i	$0.589434\pi$
$212$	13.4454	0.923434
$213$	10.1018	0.692161
$214$	−3.23258	−0.220975
$215$	−10.8984	−0.743268
$216$	−8.01145	−0.545110
$217$	0	0
$218$	0.290571	0.0196799
$219$	13.3117	0.899519
$220$	4.01538	0.270717
$221$	1.63149	0.109746
$222$	−4.69176	−0.314891
$223$	−24.6646	−1.65166	−0.825831	−	0.563918i	$-0.809293\pi$
$223$	−24.6646	−1.65166	−0.825831	+	0.563918i	$0.809293\pi$
$224$	0	0
$225$	5.53943	0.369295
$226$	−4.08206	−0.271535
$227$	−23.6543	−1.56999	−0.784994	−	0.619503i	$-0.787334\pi$
$227$	−23.6543	−1.56999	−0.784994	+	0.619503i	$0.787334\pi$
$228$	−5.96574	−0.395091
$229$	−14.3925	−0.951081	−0.475540	−	0.879694i	$-0.657747\pi$
$229$	−14.3925	−0.951081	−0.475540	+	0.879694i	$0.657747\pi$
$230$	−2.96835	−0.195727
$231$	0	0
$232$	9.29414	0.610190
$233$	−7.83240	−0.513117	−0.256559	−	0.966529i	$-0.582589\pi$
$233$	−7.83240	−0.513117	−0.256559	+	0.966529i	$0.582589\pi$
$234$	1.03092	0.0673934
$235$	3.30435	0.215552
$236$	−0.297685	−0.0193776
$237$	−0.741380	−0.0481578
$238$	0	0
$239$	−0.0880954	−0.00569842	−0.00284921	−	0.999996i	$-0.500907\pi$
$239$	−0.0880954	−0.00569842	−0.00284921	+	0.999996i	$0.500907\pi$
$240$	−3.93409	−0.253944
$241$	−0.813298	−0.0523891	−0.0261946	−	0.999657i	$-0.508339\pi$
$241$	−0.813298	−0.0523891	−0.0261946	+	0.999657i	$0.508339\pi$
$242$	2.22272	0.142882
$243$	12.8186	0.822311
$244$	7.67038	0.491046
$245$	0	0
$246$	1.37186	0.0874665
$247$	5.10461	0.324799
$248$	−15.0702	−0.956958
$249$	−15.7089	−0.995510
$250$	−3.24539	−0.205256
$251$	−14.0214	−0.885022	−0.442511	−	0.896763i	$-0.645912\pi$
$251$	−14.0214	−0.885022	−0.442511	+	0.896763i	$0.645912\pi$
$252$	0	0
$253$	−18.5885	−1.16865
$254$	−0.371530	−0.0233119
$255$	−0.985897	−0.0617393
$256$	6.06397	0.378998
$257$	−28.8464	−1.79939	−0.899694	−	0.436520i	$-0.856211\pi$
$257$	−28.8464	−1.79939	−0.899694	+	0.436520i	$0.856211\pi$
$258$	−5.38597	−0.335316
$259$	0	0
$260$	3.65746	0.226826
$261$	−8.80940	−0.545288
$262$	0.742645	0.0458807
$263$	23.2853	1.43583	0.717917	−	0.696128i	$-0.245096\pi$
$263$	23.2853	1.43583	0.717917	+	0.696128i	$0.245096\pi$
$264$	4.11589	0.253315
$265$	6.95214	0.427067
$266$	0	0
$267$	−20.5158	−1.25555
$268$	−8.81752	−0.538616
$269$	−0.297508	−0.0181394	−0.00906970	−	0.999959i	$-0.502887\pi$
$269$	−0.297508	−0.0181394	−0.00906970	+	0.999959i	$0.502887\pi$
$270$	−1.99719	−0.121545
$271$	−12.8826	−0.782562	−0.391281	−	0.920271i	$-0.627968\pi$
$271$	−12.8826	−0.782562	−0.391281	+	0.920271i	$0.627968\pi$
$272$	2.55152	0.154709
$273$	0	0
$274$	4.78350	0.288982
$275$	−9.12356	−0.550171
$276$	19.7878	1.19109
$277$	−8.65365	−0.519947	−0.259974	−	0.965616i	$-0.583714\pi$
$277$	−8.65365	−0.519947	−0.259974	+	0.965616i	$0.583714\pi$
$278$	5.53070	0.331709
$279$	14.2842	0.855172
$280$	0	0
$281$	−11.5710	−0.690269	−0.345134	−	0.938553i	$-0.612167\pi$
$281$	−11.5710	−0.690269	−0.345134	+	0.938553i	$0.612167\pi$
$282$	1.63300	0.0972436
$283$	−3.14963	−0.187226	−0.0936130	−	0.995609i	$-0.529842\pi$
$283$	−3.14963	−0.187226	−0.0936130	+	0.995609i	$0.529842\pi$
$284$	−14.6875	−0.871541
$285$	−3.08468	−0.182720
$286$	−1.69795	−0.100402
$287$	0	0
$288$	5.51504	0.324977
$289$	−16.3606	−0.962387
$290$	2.31695	0.136056
$291$	−2.23998	−0.131310
$292$	−19.3545	−1.13264
$293$	−22.8850	−1.33696	−0.668479	−	0.743731i	$-0.733054\pi$
$293$	−22.8850	−1.33696	−0.668479	+	0.743731i	$0.733054\pi$
$294$	0	0
$295$	−0.153922	−0.00896170
$296$	14.1489	0.822388
$297$	−12.5068	−0.725720
$298$	1.77795	0.102994
$299$	−16.9315	−0.979176
$300$	9.71221	0.560735
$301$	0	0
$302$	−3.89613	−0.224197
$303$	5.66204	0.325276
$304$	7.98320	0.457868
$305$	3.96608	0.227097
$306$	0.404043	0.0230976
$307$	24.5670	1.40211	0.701057	−	0.713105i	$-0.252712\pi$
$307$	24.5670	1.40211	0.701057	+	0.713105i	$0.252712\pi$
$308$	0	0
$309$	8.95022	0.509160
$310$	−3.75688	−0.213376
$311$	−9.09371	−0.515657	−0.257829	−	0.966191i	$-0.583007\pi$
$311$	−9.09371	−0.515657	−0.257829	+	0.966191i	$0.583007\pi$
$312$	3.74900	0.212245
$313$	18.9742	1.07248	0.536242	−	0.844064i	$-0.319843\pi$
$313$	18.9742	1.07248	0.536242	+	0.844064i	$0.319843\pi$
$314$	4.57491	0.258177
$315$	0	0
$316$	1.07793	0.0606383
$317$	3.92505	0.220453	0.110226	−	0.993907i	$-0.464842\pi$
$317$	3.92505	0.220453	0.110226	+	0.993907i	$0.464842\pi$
$318$	3.43572	0.192666
$319$	14.5093	0.812363
$320$	4.69351	0.262375
$321$	11.1424	0.621905
$322$	0	0
$323$	2.00062	0.111318
$324$	5.71695	0.317608
$325$	−8.31029	−0.460972
$326$	6.55066	0.362808
$327$	−1.00157	−0.0553867
$328$	−4.13710	−0.228433
$329$	0	0
$330$	1.02606	0.0564826
$331$	25.3846	1.39526	0.697631	−	0.716457i	$-0.254237\pi$
$331$	25.3846	1.39526	0.697631	+	0.716457i	$0.254237\pi$
$332$	22.8400	1.25351
$333$	−13.4110	−0.734916
$334$	−7.40142	−0.404988
$335$	−4.55923	−0.249097
$336$	0	0
$337$	17.2922	0.941966	0.470983	−	0.882142i	$-0.343899\pi$
$337$	17.2922	0.941966	0.470983	+	0.882142i	$0.343899\pi$
$338$	3.28330	0.178588
$339$	14.0704	0.764200
$340$	1.43345	0.0777396
$341$	−23.5264	−1.27403
$342$	1.26417	0.0683585
$343$	0	0
$344$	16.2424	0.875732
$345$	10.2316	0.550850
$346$	5.14380	0.276532
$347$	−10.3398	−0.555071	−0.277536	−	0.960715i	$-0.589518\pi$
$347$	−10.3398	−0.555071	−0.277536	+	0.960715i	$0.589518\pi$
$348$	−15.4454	−0.827961
$349$	−0.152153	−0.00814458	−0.00407229	−	0.999992i	$-0.501296\pi$
$349$	−0.152153	−0.00814458	−0.00407229	+	0.999992i	$0.501296\pi$
$350$	0	0
$351$	−11.3920	−0.608059
$352$	−9.08339	−0.484147
$353$	2.54555	0.135486	0.0677430	−	0.997703i	$-0.478420\pi$
$353$	2.54555	0.135486	0.0677430	+	0.997703i	$0.478420\pi$
$354$	−0.0760678	−0.00404296
$355$	−7.59437	−0.403067
$356$	29.8290	1.58093
$357$	0	0
$358$	−2.37393	−0.125466
$359$	15.0752	0.795641	0.397820	−	0.917463i	$-0.369767\pi$
$359$	15.0752	0.795641	0.397820	+	0.917463i	$0.369767\pi$
$360$	1.87871	0.0990165
$361$	−12.7405	−0.670550
$362$	−4.26524	−0.224176
$363$	−7.66147	−0.402123
$364$	0	0
$365$	−10.0075	−0.523819
$366$	1.96002	0.102452
$367$	14.6778	0.766177	0.383089	−	0.923712i	$-0.374860\pi$
$367$	14.6778	0.766177	0.383089	+	0.923712i	$0.374860\pi$
$368$	−26.4796	−1.38034
$369$	3.92133	0.204136
$370$	3.52721	0.183371
$371$	0	0
$372$	25.0443	1.29849
$373$	−33.7919	−1.74968	−0.874839	−	0.484413i	$-0.839033\pi$
$373$	−33.7919	−1.74968	−0.874839	+	0.484413i	$0.839033\pi$
$374$	−0.665467	−0.0344105
$375$	11.1865	0.577668
$376$	−4.92462	−0.253968
$377$	13.2159	0.680655
$378$	0	0
$379$	25.4294	1.30622	0.653109	−	0.757264i	$-0.273464\pi$
$379$	25.4294	1.30622	0.653109	+	0.757264i	$0.273464\pi$
$380$	4.48497	0.230074
$381$	1.28062	0.0656084
$382$	9.47035	0.484545
$383$	−34.9848	−1.78764	−0.893819	−	0.448428i	$-0.851984\pi$
$383$	−34.9848	−1.78764	−0.893819	+	0.448428i	$0.851984\pi$
$384$	12.7058	0.648391
$385$	0	0
$386$	9.46983	0.482002
$387$	−15.3953	−0.782586
$388$	3.25683	0.165340
$389$	−15.4747	−0.784598	−0.392299	−	0.919838i	$-0.628320\pi$
$389$	−15.4747	−0.784598	−0.392299	+	0.919838i	$0.628320\pi$
$390$	0.934596	0.0473251
$391$	−6.63588	−0.335591
$392$	0	0
$393$	−2.55981	−0.129126
$394$	2.38092	0.119949
$395$	0.557360	0.0280438
$396$	5.67218	0.285038
$397$	31.5489	1.58339	0.791696	−	0.610915i	$-0.209198\pi$
$397$	31.5489	1.58339	0.791696	+	0.610915i	$0.209198\pi$
$398$	4.26273	0.213671
$399$	0	0
$400$	−12.9966	−0.649831
$401$	34.6823	1.73195	0.865976	−	0.500086i	$-0.166698\pi$
$401$	34.6823	1.73195	0.865976	+	0.500086i	$0.166698\pi$
$402$	−2.25315	−0.112377
$403$	−21.4293	−1.06747
$404$	−8.23233	−0.409574
$405$	2.95603	0.146887
$406$	0	0
$407$	22.0881	1.09487
$408$	1.46932	0.0727424
$409$	−13.8039	−0.682558	−0.341279	−	0.939962i	$-0.610860\pi$
$409$	−13.8039	−0.682558	−0.341279	+	0.939962i	$0.610860\pi$
$410$	−1.03135	−0.0509345
$411$	−16.4882	−0.813302
$412$	−13.0132	−0.641114
$413$	0	0
$414$	−4.19314	−0.206081
$415$	11.8097	0.579717
$416$	−8.27371	−0.405652
$417$	−19.0637	−0.933553
$418$	−2.08212	−0.101840
$419$	−37.2761	−1.82106	−0.910530	−	0.413444i	$-0.864326\pi$
$419$	−37.2761	−1.82106	−0.910530	+	0.413444i	$0.864326\pi$
$420$	0	0
$421$	20.8228	1.01484	0.507421	−	0.861698i	$-0.330599\pi$
$421$	20.8228	1.01484	0.507421	+	0.861698i	$0.330599\pi$
$422$	2.99288	0.145691
$423$	4.66777	0.226955
$424$	−10.3611	−0.503178
$425$	−3.25701	−0.157988
$426$	−3.75311	−0.181839
$427$	0	0
$428$	−16.2004	−0.783078
$429$	5.85264	0.282568
$430$	4.04910	0.195265
$431$	24.7451	1.19193	0.595965	−	0.803011i	$-0.296770\pi$
$431$	24.7451	1.19193	0.595965	+	0.803011i	$0.296770\pi$
$432$	−17.8162	−0.857180
$433$	8.74097	0.420064	0.210032	−	0.977694i	$-0.432643\pi$
$433$	8.74097	0.420064	0.210032	+	0.977694i	$0.432643\pi$
$434$	0	0
$435$	−7.98628	−0.382913
$436$	1.45623	0.0697406
$437$	−20.7623	−0.993197
$438$	−4.94569	−0.236314
$439$	−36.0908	−1.72252	−0.861261	−	0.508163i	$-0.830325\pi$
$439$	−36.0908	−1.72252	−0.861261	+	0.508163i	$0.830325\pi$
$440$	−3.09427	−0.147514
$441$	0	0
$442$	−0.606148	−0.0288315
$443$	−19.0167	−0.903511	−0.451756	−	0.892142i	$-0.649202\pi$
$443$	−19.0167	−0.903511	−0.451756	+	0.892142i	$0.649202\pi$
$444$	−23.5133	−1.11589
$445$	15.4235	0.731144
$446$	9.16363	0.433911
$447$	−6.12841	−0.289864
$448$	0	0
$449$	−23.5936	−1.11345	−0.556725	−	0.830697i	$-0.687942\pi$
$449$	−23.5936	−1.11345	−0.556725	+	0.830697i	$0.687942\pi$
$450$	−2.05806	−0.0970181
$451$	−6.45851	−0.304119
$452$	−20.4577	−0.962249
$453$	13.4295	0.630975
$454$	8.78828	0.412454
$455$	0	0
$456$	4.59722	0.215285
$457$	22.2933	1.04284	0.521419	−	0.853301i	$-0.325403\pi$
$457$	22.2933	1.04284	0.521419	+	0.853301i	$0.325403\pi$
$458$	5.34724	0.249860
$459$	−4.46480	−0.208399
$460$	−14.8762	−0.693608
$461$	25.9230	1.20736	0.603678	−	0.797228i	$-0.293701\pi$
$461$	25.9230	1.20736	0.603678	+	0.797228i	$0.293701\pi$
$462$	0	0
$463$	−7.59191	−0.352826	−0.176413	−	0.984316i	$-0.556449\pi$
$463$	−7.59191	−0.352826	−0.176413	+	0.984316i	$0.556449\pi$
$464$	20.6687	0.959518
$465$	12.9495	0.600520
$466$	2.90997	0.134802
$467$	10.3505	0.478965	0.239483	−	0.970901i	$-0.423022\pi$
$467$	10.3505	0.478965	0.239483	+	0.970901i	$0.423022\pi$
$468$	5.16657	0.238825
$469$	0	0
$470$	−1.22767	−0.0566280
$471$	−15.7692	−0.726606
$472$	0.229397	0.0105588
$473$	25.3564	1.16589
$474$	0.275445	0.0126516
$475$	−10.1905	−0.467573
$476$	0	0
$477$	9.82069	0.449658
$478$	0.0327301	0.00149704
$479$	27.3615	1.25018	0.625090	−	0.780553i	$-0.285062\pi$
$479$	27.3615	1.25018	0.625090	+	0.780553i	$0.285062\pi$
$480$	4.99974	0.228206
$481$	20.1192	0.917358
$482$	0.302165	0.0137632
$483$	0	0
$484$	11.1394	0.506337
$485$	1.68399	0.0764661
$486$	−4.76248	−0.216031
$487$	−29.1382	−1.32038	−0.660190	−	0.751099i	$-0.729524\pi$
$487$	−29.1382	−1.32038	−0.660190	+	0.751099i	$0.729524\pi$
$488$	−5.91083	−0.267571
$489$	−22.5794	−1.02108
$490$	0	0
$491$	6.21945	0.280680	0.140340	−	0.990103i	$-0.455180\pi$
$491$	6.21945	0.280680	0.140340	+	0.990103i	$0.455180\pi$
$492$	6.87522	0.309959
$493$	5.17965	0.233279
$494$	−1.89652	−0.0853284
$495$	2.93289	0.131823
$496$	−33.5137	−1.50481
$497$	0	0
$498$	5.83633	0.261532
$499$	−37.8076	−1.69250	−0.846250	−	0.532785i	$-0.821145\pi$
$499$	−37.8076	−1.69250	−0.846250	+	0.532785i	$0.821145\pi$
$500$	−16.2646	−0.727376
$501$	25.5119	1.13979
$502$	5.20937	0.232505
$503$	−6.79017	−0.302759	−0.151379	−	0.988476i	$-0.548372\pi$
$503$	−6.79017	−0.302759	−0.151379	+	0.988476i	$0.548372\pi$
$504$	0	0
$505$	−4.25665	−0.189418
$506$	6.90619	0.307017
$507$	−11.3172	−0.502613
$508$	−1.86197	−0.0826113
$509$	11.2643	0.499283	0.249641	−	0.968338i	$-0.419687\pi$
$509$	11.2643	0.499283	0.249641	+	0.968338i	$0.419687\pi$
$510$	0.366291	0.0162196
$511$	0	0
$512$	−22.0961	−0.976519
$513$	−13.9695	−0.616767
$514$	10.7173	0.472720
$515$	−6.72866	−0.296500
$516$	−26.9924	−1.18827
$517$	−7.68792	−0.338114
$518$	0	0
$519$	−17.7301	−0.778265
$520$	−2.81845	−0.123597
$521$	−38.3857	−1.68171	−0.840854	−	0.541261i	$-0.817947\pi$
$521$	−38.3857	−1.68171	−0.840854	+	0.541261i	$0.817947\pi$
$522$	3.27296	0.143254
$523$	−26.0041	−1.13708	−0.568541	−	0.822655i	$-0.692492\pi$
$523$	−26.0041	−1.13708	−0.568541	+	0.822655i	$0.692492\pi$
$524$	3.72184	0.162590
$525$	0	0
$526$	−8.65120	−0.377210
$527$	−8.39865	−0.365851
$528$	9.15306	0.398336
$529$	45.8668	1.99421
$530$	−2.58293	−0.112195
$531$	−0.217433	−0.00943577
$532$	0	0
$533$	−5.88281	−0.254813
$534$	7.62224	0.329846
$535$	−8.37668	−0.362155
$536$	6.79481	0.293491
$537$	8.18267	0.353108
$538$	0.110533	0.00476543
$539$	0	0
$540$	−10.0091	−0.430724
$541$	−0.870121	−0.0374094	−0.0187047	−	0.999825i	$-0.505954\pi$
$541$	−0.870121	−0.0374094	−0.0187047	+	0.999825i	$0.505954\pi$
$542$	4.78628	0.205588
$543$	14.7018	0.630914
$544$	−3.24267	−0.139028
$545$	0.752964	0.0322534
$546$	0	0
$547$	−11.6591	−0.498506	−0.249253	−	0.968438i	$-0.580185\pi$
$547$	−11.6591	−0.498506	−0.249253	+	0.968438i	$0.580185\pi$
$548$	23.9730	1.02408
$549$	5.60254	0.239111
$550$	3.38968	0.144536
$551$	16.2061	0.690402
$552$	−15.2486	−0.649022
$553$	0	0
$554$	3.21509	0.136596
$555$	−12.1579	−0.516074
$556$	27.7177	1.17549
$557$	35.7970	1.51677	0.758384	−	0.651808i	$-0.225989\pi$
$557$	35.7970	1.51677	0.758384	+	0.651808i	$0.225989\pi$
$558$	−5.30701	−0.224664
$559$	23.0961	0.976862
$560$	0	0
$561$	2.29379	0.0968440
$562$	4.29898	0.181342
$563$	6.54472	0.275827	0.137913	−	0.990444i	$-0.455960\pi$
$563$	6.54472	0.275827	0.137913	+	0.990444i	$0.455960\pi$
$564$	8.18395	0.344606
$565$	−10.5780	−0.445018
$566$	1.17018	0.0491865
$567$	0	0
$568$	11.3182	0.474902
$569$	14.3441	0.601334	0.300667	−	0.953729i	$-0.402791\pi$
$569$	14.3441	0.601334	0.300667	+	0.953729i	$0.402791\pi$
$570$	1.14605	0.0480028
$571$	16.6278	0.695852	0.347926	−	0.937522i	$-0.386886\pi$
$571$	16.6278	0.695852	0.347926	+	0.937522i	$0.386886\pi$
$572$	−8.50946	−0.355798
$573$	−32.6432	−1.36369
$574$	0	0
$575$	33.8010	1.40960
$576$	6.63011	0.276255
$577$	7.14531	0.297463	0.148732	−	0.988878i	$-0.452481\pi$
$577$	7.14531	0.297463	0.148732	+	0.988878i	$0.452481\pi$
$578$	6.07845	0.252830
$579$	−32.6415	−1.35653
$580$	11.6117	0.482148
$581$	0	0
$582$	0.832222	0.0344967
$583$	−16.1749	−0.669895
$584$	14.9147	0.617173
$585$	2.67145	0.110451
$586$	8.50248	0.351234
$587$	−39.7703	−1.64150	−0.820749	−	0.571289i	$-0.806444\pi$
$587$	−39.7703	−1.64150	−0.820749	+	0.571289i	$0.806444\pi$
$588$	0	0
$589$	−26.2777	−1.08275
$590$	0.0571868	0.00235434
$591$	−8.20678	−0.337582
$592$	31.4649	1.29320
$593$	32.1878	1.32179	0.660897	−	0.750477i	$-0.270176\pi$
$593$	32.1878	1.32179	0.660897	+	0.750477i	$0.270176\pi$
$594$	4.64667	0.190655
$595$	0	0
$596$	8.91041	0.364985
$597$	−14.6931	−0.601350
$598$	6.29058	0.257241
$599$	22.3764	0.914274	0.457137	−	0.889396i	$-0.348875\pi$
$599$	22.3764	0.914274	0.457137	+	0.889396i	$0.348875\pi$
$600$	−7.48427	−0.305544
$601$	−43.3598	−1.76868	−0.884342	−	0.466840i	$-0.845392\pi$
$601$	−43.3598	−1.76868	−0.884342	+	0.466840i	$0.845392\pi$
$602$	0	0
$603$	−6.44043	−0.262274
$604$	−19.5259	−0.794498
$605$	5.75979	0.234169
$606$	−2.10362	−0.0854537
$607$	18.1854	0.738124	0.369062	−	0.929405i	$-0.379679\pi$
$607$	18.1854	0.738124	0.369062	+	0.929405i	$0.379679\pi$
$608$	−10.1457	−0.411461
$609$	0	0
$610$	−1.47352	−0.0596611
$611$	−7.00263	−0.283296
$612$	2.02490	0.0818519
$613$	−19.8064	−0.799972	−0.399986	−	0.916521i	$-0.630985\pi$
$613$	−19.8064	−0.799972	−0.399986	+	0.916521i	$0.630985\pi$
$614$	−9.12739	−0.368352
$615$	3.55493	0.143349
$616$	0	0
$617$	−25.5426	−1.02831	−0.514154	−	0.857698i	$-0.671894\pi$
$617$	−25.5426	−1.02831	−0.514154	+	0.857698i	$0.671894\pi$
$618$	−3.32528	−0.133762
$619$	39.7581	1.59801	0.799007	−	0.601321i	$-0.205359\pi$
$619$	39.7581	1.59801	0.799007	+	0.601321i	$0.205359\pi$
$620$	−18.8280	−0.756151
$621$	46.3354	1.85938
$622$	3.37859	0.135469
$623$	0	0
$624$	8.33717	0.333754
$625$	11.9556	0.478226
$626$	−7.04948	−0.281754
$627$	7.17682	0.286615
$628$	22.9276	0.914913
$629$	7.88522	0.314404
$630$	0	0
$631$	22.0695	0.878571	0.439286	−	0.898347i	$-0.355232\pi$
$631$	22.0695	0.878571	0.439286	+	0.898347i	$0.355232\pi$
$632$	−0.830657	−0.0330418
$633$	−10.3161	−0.410030
$634$	−1.45828	−0.0579155
$635$	−0.962757	−0.0382058
$636$	17.2185	0.682758
$637$	0	0
$638$	−5.39064	−0.213417
$639$	−10.7279	−0.424390
$640$	−9.55206	−0.377578
$641$	12.9160	0.510150	0.255075	−	0.966921i	$-0.417900\pi$
$641$	12.9160	0.510150	0.255075	+	0.966921i	$0.417900\pi$
$642$	−4.13972	−0.163382
$643$	28.7773	1.13487	0.567433	−	0.823420i	$-0.307937\pi$
$643$	28.7773	1.13487	0.567433	+	0.823420i	$0.307937\pi$
$644$	0	0
$645$	−13.9568	−0.549549
$646$	−0.743291	−0.0292444
$647$	2.20023	0.0865000	0.0432500	−	0.999064i	$-0.486229\pi$
$647$	2.20023	0.0865000	0.0432500	+	0.999064i	$0.486229\pi$
$648$	−4.40550	−0.173065
$649$	0.358116	0.0140573
$650$	3.08753	0.121103
$651$	0	0
$652$	32.8294	1.28570
$653$	2.10650	0.0824338	0.0412169	−	0.999150i	$-0.486877\pi$
$653$	2.10650	0.0824338	0.0412169	+	0.999150i	$0.486877\pi$
$654$	0.372112	0.0145507
$655$	1.92443	0.0751939
$656$	−9.20024	−0.359209
$657$	−14.1368	−0.551528
$658$	0	0
$659$	−26.4209	−1.02921	−0.514606	−	0.857427i	$-0.672062\pi$
$659$	−26.4209	−1.02921	−0.514606	+	0.857427i	$0.672062\pi$
$660$	5.14220	0.200160
$661$	18.4078	0.715979	0.357990	−	0.933726i	$-0.383462\pi$
$661$	18.4078	0.715979	0.357990	+	0.933726i	$0.383462\pi$
$662$	−9.43114	−0.366552
$663$	2.08933	0.0811427
$664$	−17.6006	−0.683034
$665$	0	0
$666$	4.98258	0.193071
$667$	−53.7541	−2.08137
$668$	−37.0930	−1.43517
$669$	−31.5860	−1.22119
$670$	1.69389	0.0654408
$671$	−9.22751	−0.356224
$672$	0	0
$673$	10.3119	0.397494	0.198747	−	0.980051i	$-0.436313\pi$
$673$	10.3119	0.397494	0.198747	+	0.980051i	$0.436313\pi$
$674$	−6.42458	−0.247466
$675$	22.7422	0.875350
$676$	16.4546	0.632870
$677$	34.5701	1.32864	0.664319	−	0.747449i	$-0.268722\pi$
$677$	34.5701	1.32864	0.664319	+	0.747449i	$0.268722\pi$
$678$	−5.22759	−0.200764
$679$	0	0
$680$	−1.10462	−0.0423602
$681$	−30.2922	−1.16080
$682$	8.74077	0.334701
$683$	−0.116721	−0.00446622	−0.00223311	−	0.999998i	$-0.500711\pi$
$683$	−0.116721	−0.00446622	−0.00223311	+	0.999998i	$0.500711\pi$
$684$	6.33553	0.242245
$685$	12.3956	0.473612
$686$	0	0
$687$	−18.4313	−0.703199
$688$	36.1205	1.37708
$689$	−14.7331	−0.561285
$690$	−3.80135	−0.144715
$691$	14.1475	0.538196	0.269098	−	0.963113i	$-0.413275\pi$
$691$	14.1475	0.538196	0.269098	+	0.963113i	$0.413275\pi$
$692$	25.7787	0.979959
$693$	0	0
$694$	3.84156	0.145824
$695$	14.3318	0.543638
$696$	11.9023	0.451155
$697$	−2.30561	−0.0873314
$698$	0.0565296	0.00213968
$699$	−10.0304	−0.379383
$700$	0	0
$701$	36.8024	1.39001	0.695003	−	0.719006i	$-0.255403\pi$
$701$	36.8024	1.39001	0.695003	+	0.719006i	$0.255403\pi$
$702$	4.23247	0.159744
$703$	24.6713	0.930495
$704$	−10.9199	−0.411561
$705$	4.23163	0.159372
$706$	−0.945749	−0.0355937
$707$	0	0
$708$	−0.381222	−0.0143272
$709$	−6.19475	−0.232649	−0.116324	−	0.993211i	$-0.537111\pi$
$709$	−6.19475	−0.232649	−0.116324	+	0.993211i	$0.537111\pi$
$710$	2.82154	0.105891
$711$	0.787333	0.0295273
$712$	−22.9863	−0.861448
$713$	87.1608	3.26420
$714$	0	0
$715$	−4.39994	−0.164548
$716$	−11.8972	−0.444619
$717$	−0.112817	−0.00421323
$718$	−5.60091	−0.209024
$719$	−1.26188	−0.0470601	−0.0235301	−	0.999723i	$-0.507491\pi$
$719$	−1.26188	−0.0470601	−0.0235301	+	0.999723i	$0.507491\pi$
$720$	4.17794	0.155703
$721$	0	0
$722$	4.73347	0.176161
$723$	−1.04153	−0.0387349
$724$	−21.3757	−0.794422
$725$	−26.3835	−0.979857
$726$	2.84647	0.105642
$727$	46.2728	1.71616	0.858081	−	0.513515i	$-0.171657\pi$
$727$	46.2728	1.71616	0.858081	+	0.513515i	$0.171657\pi$
$728$	0	0
$729$	25.6269	0.949145
$730$	3.71810	0.137613
$731$	9.05194	0.334798
$732$	9.82288	0.363064
$733$	15.7574	0.582012	0.291006	−	0.956721i	$-0.406010\pi$
$733$	15.7574	0.582012	0.291006	+	0.956721i	$0.406010\pi$
$734$	−5.45327	−0.201284
$735$	0	0
$736$	33.6522	1.24044
$737$	10.6075	0.390733
$738$	−1.45689	−0.0536289
$739$	−34.1894	−1.25768	−0.628838	−	0.777536i	$-0.716469\pi$
$739$	−34.1894	−1.25768	−0.628838	+	0.777536i	$0.716469\pi$
$740$	17.6770	0.649819
$741$	6.53709	0.240146
$742$	0	0
$743$	−17.5917	−0.645377	−0.322688	−	0.946505i	$-0.604587\pi$
$743$	−17.5917	−0.645377	−0.322688	+	0.946505i	$0.604587\pi$
$744$	−19.2992	−0.707545
$745$	4.60726	0.168797
$746$	12.5547	0.459661
$747$	16.6826	0.610384
$748$	−3.33506	−0.121942
$749$	0	0
$750$	−4.15612	−0.151760
$751$	14.7177	0.537056	0.268528	−	0.963272i	$-0.413463\pi$
$751$	14.7177	0.537056	0.268528	+	0.963272i	$0.413463\pi$
$752$	−10.9515	−0.399362
$753$	−17.9561	−0.654357
$754$	−4.91012	−0.178816
$755$	−10.0962	−0.367437
$756$	0	0
$757$	7.11827	0.258718	0.129359	−	0.991598i	$-0.458708\pi$
$757$	7.11827	0.258718	0.129359	+	0.991598i	$0.458708\pi$
$758$	−9.44778	−0.343159
$759$	−23.8049	−0.864062
$760$	−3.45613	−0.125367
$761$	−40.3710	−1.46345	−0.731724	−	0.681601i	$-0.761284\pi$
$761$	−40.3710	−1.46345	−0.731724	+	0.681601i	$0.761284\pi$
$762$	−0.475791	−0.0172361
$763$	0	0
$764$	47.4617	1.71710
$765$	1.04701	0.0378546
$766$	12.9979	0.469633
$767$	0.326194	0.0117782
$768$	7.76567	0.280220
$769$	4.88708	0.176233	0.0881163	−	0.996110i	$-0.471915\pi$
$769$	4.88708	0.176233	0.0881163	+	0.996110i	$0.471915\pi$
$770$	0	0
$771$	−36.9414	−1.33041
$772$	47.4591	1.70809
$773$	−36.7332	−1.32120	−0.660601	−	0.750737i	$-0.729698\pi$
$773$	−36.7332	−1.32120	−0.660601	+	0.750737i	$0.729698\pi$
$774$	5.71981	0.205595
$775$	42.7800	1.53670
$776$	−2.50972	−0.0900939
$777$	0	0
$778$	5.74932	0.206123
$779$	−7.21381	−0.258462
$780$	4.68383	0.167708
$781$	17.6691	0.632250
$782$	2.46543	0.0881636
$783$	−36.1672	−1.29251
$784$	0	0
$785$	11.8551	0.423126
$786$	0.951048	0.0339228
$787$	−43.1960	−1.53977	−0.769886	−	0.638182i	$-0.779687\pi$
$787$	−43.1960	−1.53977	−0.769886	+	0.638182i	$0.779687\pi$
$788$	11.9323	0.425069
$789$	29.8197	1.06161
$790$	−0.207076	−0.00736743
$791$	0	0
$792$	−4.37101	−0.155317
$793$	−8.40498	−0.298470
$794$	−11.7214	−0.415975
$795$	8.90308	0.315760
$796$	21.3631	0.757196
$797$	0.404087	0.0143135	0.00715675	−	0.999974i	$-0.497722\pi$
$797$	0.404087	0.0143135	0.00715675	+	0.999974i	$0.497722\pi$
$798$	0	0
$799$	−2.74450	−0.0970934
$800$	16.5171	0.583968
$801$	21.7874	0.769821
$802$	−12.8855	−0.455004
$803$	23.2836	0.821660
$804$	−11.2919	−0.398236
$805$	0	0
$806$	7.96162	0.280436
$807$	−0.380996	−0.0134117
$808$	6.34387	0.223176
$809$	25.1478	0.884151	0.442075	−	0.896978i	$-0.354242\pi$
$809$	25.1478	0.884151	0.442075	+	0.896978i	$0.354242\pi$
$810$	−1.09826	−0.0385888
$811$	−27.3312	−0.959730	−0.479865	−	0.877342i	$-0.659314\pi$
$811$	−27.3312	−0.959730	−0.479865	+	0.877342i	$0.659314\pi$
$812$	0	0
$813$	−16.4978	−0.578602
$814$	−8.20642	−0.287635
$815$	16.9749	0.594605
$816$	3.26754	0.114387
$817$	28.3217	0.990851
$818$	5.12856	0.179316
$819$	0	0
$820$	−5.16870	−0.180499
$821$	−32.6182	−1.13838	−0.569191	−	0.822205i	$-0.692743\pi$
$821$	−32.6182	−1.13838	−0.569191	+	0.822205i	$0.692743\pi$
$822$	6.12586	0.213664
$823$	6.13018	0.213684	0.106842	−	0.994276i	$-0.465926\pi$
$823$	6.13018	0.213684	0.106842	+	0.994276i	$0.465926\pi$
$824$	10.0280	0.349342
$825$	−11.6838	−0.406779
$826$	0	0
$827$	−28.8595	−1.00354	−0.501772	−	0.865000i	$-0.667318\pi$
$827$	−28.8595	−1.00354	−0.501772	+	0.865000i	$0.667318\pi$
$828$	−21.0144	−0.730299
$829$	−11.9148	−0.413817	−0.206909	−	0.978360i	$-0.566340\pi$
$829$	−11.9148	−0.413817	−0.206909	+	0.978360i	$0.566340\pi$
$830$	−4.38768	−0.152298
$831$	−11.0821	−0.384433
$832$	−9.94654	−0.344834
$833$	0	0
$834$	7.08274	0.245255
$835$	−19.1795	−0.663734
$836$	−10.4347	−0.360893
$837$	58.6441	2.02704
$838$	13.8492	0.478413
$839$	20.8380	0.719408	0.359704	−	0.933066i	$-0.382878\pi$
$839$	20.8380	0.719408	0.359704	+	0.933066i	$0.382878\pi$
$840$	0	0
$841$	12.9578	0.446822
$842$	−7.73631	−0.266611
$843$	−14.8181	−0.510363
$844$	14.9992	0.516293
$845$	8.50810	0.292688
$846$	−1.73422	−0.0596236
$847$	0	0
$848$	−23.0413	−0.791243
$849$	−4.03349	−0.138429
$850$	1.21008	0.0415053
$851$	−81.8324	−2.80518
$852$	−18.8091	−0.644390
$853$	−25.5733	−0.875612	−0.437806	−	0.899069i	$-0.644244\pi$
$853$	−25.5733	−0.875612	−0.437806	+	0.899069i	$0.644244\pi$
$854$	0	0
$855$	3.27588	0.112033
$856$	12.4841	0.426698
$857$	43.0081	1.46913	0.734564	−	0.678540i	$-0.237387\pi$
$857$	43.0081	1.46913	0.734564	+	0.678540i	$0.237387\pi$
$858$	−2.17443	−0.0742340
$859$	−6.28089	−0.214301	−0.107151	−	0.994243i	$-0.534173\pi$
$859$	−6.28089	−0.214301	−0.107151	+	0.994243i	$0.534173\pi$
$860$	20.2925	0.691969
$861$	0	0
$862$	−9.19356	−0.313134
$863$	36.6089	1.24618	0.623090	−	0.782150i	$-0.285877\pi$
$863$	36.6089	1.24618	0.623090	+	0.782150i	$0.285877\pi$
$864$	22.6421	0.770301
$865$	13.3293	0.453208
$866$	−3.24754	−0.110356
$867$	−20.9517	−0.711559
$868$	0	0
$869$	−1.29676	−0.0439894
$870$	2.96715	0.100596
$871$	9.66198	0.327384
$872$	−1.12217	−0.0380016
$873$	2.37883	0.0805111
$874$	7.71384	0.260925
$875$	0	0
$876$	−24.7859	−0.837437
$877$	5.89097	0.198924	0.0994620	−	0.995041i	$-0.468288\pi$
$877$	5.89097	0.198924	0.0994620	+	0.995041i	$0.468288\pi$
$878$	13.4088	0.452526
$879$	−29.3071	−0.988504
$880$	−6.88115	−0.231964
$881$	38.1587	1.28560	0.642799	−	0.766035i	$-0.277773\pi$
$881$	38.1587	1.28560	0.642799	+	0.766035i	$0.277773\pi$
$882$	0	0
$883$	−7.83747	−0.263752	−0.131876	−	0.991266i	$-0.542100\pi$
$883$	−7.83747	−0.263752	−0.131876	+	0.991266i	$0.542100\pi$
$884$	−3.03778	−0.102172
$885$	−0.197117	−0.00662600
$886$	7.06529	0.237363
$887$	−26.6447	−0.894643	−0.447321	−	0.894373i	$-0.647622\pi$
$887$	−26.6447	−0.894643	−0.447321	+	0.894373i	$0.647622\pi$
$888$	18.1194	0.608048
$889$	0	0
$890$	−5.73030	−0.192080
$891$	−6.87752	−0.230406
$892$	45.9246	1.53767
$893$	−8.58699	−0.287353
$894$	2.27689	0.0761506
$895$	−6.15162	−0.205626
$896$	0	0
$897$	−21.6829	−0.723972
$898$	8.76574	0.292516
$899$	−68.0335	−2.26904
$900$	−10.3142	−0.343807
$901$	−5.77425	−0.192368
$902$	2.39953	0.0798957
$903$	0	0
$904$	15.7648	0.524329
$905$	−11.0526	−0.367402
$906$	−4.98948	−0.165764
$907$	50.0552	1.66206	0.831028	−	0.556230i	$-0.187753\pi$
$907$	50.0552	1.66206	0.831028	+	0.556230i	$0.187753\pi$
$908$	44.0434	1.46163
$909$	−6.01300	−0.199439
$910$	0	0
$911$	11.7183	0.388244	0.194122	−	0.980977i	$-0.437814\pi$
$911$	11.7183	0.388244	0.194122	+	0.980977i	$0.437814\pi$
$912$	10.2235	0.338533
$913$	−27.4766	−0.909342
$914$	−8.28265	−0.273966
$915$	5.07906	0.167909
$916$	26.7983	0.885440
$917$	0	0
$918$	1.65881	0.0547488
$919$	−26.0943	−0.860772	−0.430386	−	0.902645i	$-0.641623\pi$
$919$	−26.0943	−0.860772	−0.430386	+	0.902645i	$0.641623\pi$
$920$	11.4637	0.377946
$921$	31.4611	1.03668
$922$	−9.63119	−0.317186
$923$	16.0941	0.529744
$924$	0	0
$925$	−40.1648	−1.32061
$926$	2.82063	0.0926915
$927$	−9.50499	−0.312185
$928$	−26.2673	−0.862267
$929$	−35.0351	−1.14947	−0.574733	−	0.818341i	$-0.694894\pi$
$929$	−35.0351	−1.14947	−0.574733	+	0.818341i	$0.694894\pi$
$930$	−4.81115	−0.157764
$931$	0	0
$932$	14.5836	0.477703
$933$	−11.6456	−0.381261
$934$	−3.84553	−0.125830
$935$	−1.72444	−0.0563953
$936$	−3.98138	−0.130135
$937$	9.47344	0.309484	0.154742	−	0.987955i	$-0.450545\pi$
$937$	9.47344	0.309484	0.154742	+	0.987955i	$0.450545\pi$
$938$	0	0
$939$	24.2988	0.792961
$940$	−6.15259	−0.200675
$941$	−10.8364	−0.353256	−0.176628	−	0.984278i	$-0.556519\pi$
$941$	−10.8364	−0.353256	−0.176628	+	0.984278i	$0.556519\pi$
$942$	5.85873	0.190888
$943$	23.9276	0.779188
$944$	0.510141	0.0166037
$945$	0	0
$946$	−9.42066	−0.306292
$947$	21.0904	0.685345	0.342672	−	0.939455i	$-0.388668\pi$
$947$	21.0904	0.685345	0.342672	+	0.939455i	$0.388668\pi$
$948$	1.38042	0.0448341
$949$	21.2081	0.688445
$950$	3.78609	0.122837
$951$	5.02652	0.162996
$952$	0	0
$953$	13.9881	0.453119	0.226559	−	0.973997i	$-0.427252\pi$
$953$	13.9881	0.453119	0.226559	+	0.973997i	$0.427252\pi$
$954$	−3.64868	−0.118130
$955$	24.5408	0.794121
$956$	0.164031	0.00530513
$957$	18.5809	0.600636
$958$	−10.1656	−0.328437
$959$	0	0
$960$	6.01062	0.193992
$961$	79.3144	2.55853
$962$	−7.47491	−0.241001
$963$	−11.8330	−0.381313
$964$	1.51433	0.0487734
$965$	24.5394	0.789952
$966$	0	0
$967$	−8.85653	−0.284807	−0.142403	−	0.989809i	$-0.545483\pi$
$967$	−8.85653	−0.284807	−0.142403	+	0.989809i	$0.545483\pi$
$968$	−8.58407	−0.275902
$969$	2.56204	0.0823047
$970$	−0.625654	−0.0200885
$971$	5.66289	0.181731	0.0908654	−	0.995863i	$-0.471037\pi$
$971$	5.66289	0.181731	0.0908654	+	0.995863i	$0.471037\pi$
$972$	−23.8677	−0.765557
$973$	0	0
$974$	10.8257	0.346879
$975$	−10.6424	−0.340828
$976$	−13.1447	−0.420752
$977$	−62.2741	−1.99232	−0.996162	−	0.0875286i	$-0.972103\pi$
$977$	−62.2741	−1.99232	−0.996162	+	0.0875286i	$0.972103\pi$
$978$	8.38894	0.268249
$979$	−35.8844	−1.14687
$980$	0	0
$981$	1.06365	0.0339596
$982$	−2.31071	−0.0737378
$983$	26.8957	0.857840	0.428920	−	0.903343i	$-0.358894\pi$
$983$	26.8957	0.857840	0.428920	+	0.903343i	$0.358894\pi$
$984$	−5.29807	−0.168896
$985$	6.16975	0.196585
$986$	−1.92440	−0.0612852
$987$	0	0
$988$	−9.50461	−0.302382
$989$	−93.9405	−2.98713
$990$	−1.08966	−0.0346316
$991$	−4.13986	−0.131507	−0.0657536	−	0.997836i	$-0.520945\pi$
$991$	−4.13986	−0.131507	−0.0657536	+	0.997836i	$0.520945\pi$
$992$	42.5917	1.35229
$993$	32.5081	1.03161
$994$	0	0
$995$	11.0461	0.350186
$996$	29.2494	0.926803
$997$	−44.9031	−1.42210	−0.711048	−	0.703143i	$-0.751779\pi$
$997$	−44.9031	−1.42210	−0.711048	+	0.703143i	$0.751779\pi$
$998$	14.0467	0.444640
$999$	−55.0590	−1.74199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.j.1.7		15
7.6	odd	2		889.2.a.b.1.7	✓	15
21.20	even	2		8001.2.a.q.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.b.1.7	✓	15	7.6	odd	2
6223.2.a.j.1.7		15	1.1	even	1	trivial
8001.2.a.q.1.9		15	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6223 = 7^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6223.a (trivial)

\(f(q)\)	\(=\)	\(q-0.371530 q^{2} +1.28062 q^{3} -1.86197 q^{4} -0.962757 q^{5} -0.475791 q^{6} +1.43484 q^{8} -1.36000 q^{9} +O(q^{10})\)	\(q-0.371530 q^{2} +1.28062 q^{3} -1.86197 q^{4} -0.962757 q^{5} -0.475791 q^{6} +1.43484 q^{8} -1.36000 q^{9} +0.357693 q^{10} +2.23995 q^{11} -2.38448 q^{12} +2.04029 q^{13} -1.23293 q^{15} +3.19084 q^{16} +0.799638 q^{17} +0.505282 q^{18} +2.50191 q^{19} +1.79262 q^{20} -0.832211 q^{22} -8.29860 q^{23} +1.83749 q^{24} -4.07310 q^{25} -0.758029 q^{26} -5.58352 q^{27} +6.47749 q^{29} +0.458071 q^{30} -10.5031 q^{31} -4.05517 q^{32} +2.86854 q^{33} -0.297090 q^{34} +2.53228 q^{36} +9.86098 q^{37} -0.929535 q^{38} +2.61284 q^{39} -1.38140 q^{40} -2.88332 q^{41} +11.3200 q^{43} -4.17072 q^{44} +1.30935 q^{45} +3.08318 q^{46} -3.43218 q^{47} +4.08627 q^{48} +1.51328 q^{50} +1.02404 q^{51} -3.79894 q^{52} -7.22108 q^{53} +2.07445 q^{54} -2.15653 q^{55} +3.20400 q^{57} -2.40658 q^{58} +0.159877 q^{59} +2.29567 q^{60} -4.11951 q^{61} +3.90221 q^{62} -4.87507 q^{64} -1.96430 q^{65} -1.06575 q^{66} +4.73560 q^{67} -1.48890 q^{68} -10.6274 q^{69} +7.88815 q^{71} -1.95138 q^{72} +10.3947 q^{73} -3.66365 q^{74} -5.21611 q^{75} -4.65847 q^{76} -0.970750 q^{78} -0.578921 q^{79} -3.07201 q^{80} -3.07039 q^{81} +1.07124 q^{82} -12.2666 q^{83} -0.769857 q^{85} -4.20574 q^{86} +8.29523 q^{87} +3.21397 q^{88} -16.0202 q^{89} -0.486464 q^{90} +15.4517 q^{92} -13.4505 q^{93} +1.27516 q^{94} -2.40873 q^{95} -5.19315 q^{96} -1.74914 q^{97} -3.04634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 4 q^{3} + 14 q^{4} - 7 q^{5} - 8 q^{6} + 9 q^{9}+O(q^{10}) \) 15 * q - 4 * q^3 + 14 * q^4 - 7 * q^5 - 8 * q^6 + 9 * q^9	\( 15 q - 4 q^{3} + 14 q^{4} - 7 q^{5} - 8 q^{6} + 9 q^{9} - 10 q^{10} + 14 q^{11} - 10 q^{12} - 6 q^{13} + 6 q^{15} + 20 q^{16} - 10 q^{17} + q^{18} - 13 q^{19} - 8 q^{20} - 11 q^{22} + 15 q^{23} - 34 q^{24} - 22 q^{26} - 22 q^{27} + 16 q^{29} + 7 q^{30} - 22 q^{31} - 14 q^{33} + 15 q^{34} + 20 q^{36} - 14 q^{37} + 6 q^{38} + 29 q^{39} - 22 q^{40} - 19 q^{41} - q^{43} + 25 q^{44} + 8 q^{45} - 28 q^{46} - 49 q^{47} + 14 q^{48} + 24 q^{50} - 8 q^{51} + 17 q^{52} - 28 q^{53} - 13 q^{54} - 39 q^{55} - 12 q^{57} - 10 q^{58} - 43 q^{59} - 60 q^{60} - 27 q^{61} - 14 q^{62} + 18 q^{64} - 8 q^{65} + 36 q^{66} + 3 q^{67} - 13 q^{68} + 17 q^{69} + 55 q^{71} - 21 q^{72} + 3 q^{73} - 12 q^{74} - 8 q^{75} + 20 q^{76} - 6 q^{78} + 18 q^{79} - 29 q^{80} - 17 q^{81} - 14 q^{82} - 17 q^{83} + 7 q^{85} + 4 q^{86} - 35 q^{87} - 114 q^{88} - 36 q^{89} + 39 q^{90} + 45 q^{92} + 15 q^{93} + 15 q^{94} + 59 q^{95} - 85 q^{96} + 2 q^{97} + 35 q^{99}+O(q^{100}) \) 15 * q - 4 * q^3 + 14 * q^4 - 7 * q^5 - 8 * q^6 + 9 * q^9 - 10 * q^10 + 14 * q^11 - 10 * q^12 - 6 * q^13 + 6 * q^15 + 20 * q^16 - 10 * q^17 + q^18 - 13 * q^19 - 8 * q^20 - 11 * q^22 + 15 * q^23 - 34 * q^24 - 22 * q^26 - 22 * q^27 + 16 * q^29 + 7 * q^30 - 22 * q^31 - 14 * q^33 + 15 * q^34 + 20 * q^36 - 14 * q^37 + 6 * q^38 + 29 * q^39 - 22 * q^40 - 19 * q^41 - q^43 + 25 * q^44 + 8 * q^45 - 28 * q^46 - 49 * q^47 + 14 * q^48 + 24 * q^50 - 8 * q^51 + 17 * q^52 - 28 * q^53 - 13 * q^54 - 39 * q^55 - 12 * q^57 - 10 * q^58 - 43 * q^59 - 60 * q^60 - 27 * q^61 - 14 * q^62 + 18 * q^64 - 8 * q^65 + 36 * q^66 + 3 * q^67 - 13 * q^68 + 17 * q^69 + 55 * q^71 - 21 * q^72 + 3 * q^73 - 12 * q^74 - 8 * q^75 + 20 * q^76 - 6 * q^78 + 18 * q^79 - 29 * q^80 - 17 * q^81 - 14 * q^82 - 17 * q^83 + 7 * q^85 + 4 * q^86 - 35 * q^87 - 114 * q^88 - 36 * q^89 + 39 * q^90 + 45 * q^92 + 15 * q^93 + 15 * q^94 + 59 * q^95 - 85 * q^96 + 2 * q^97 + 35 * q^99

Introduction

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