LMFDB - Embedded newform 7935.2.a.bl.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.51193$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51193 q^{2} +1.00000 q^{3} +4.30981 q^{4} -1.00000 q^{5} -2.51193 q^{6} -1.59040 q^{7} -5.80210 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.51193 q^{2} +1.00000 q^{3} +4.30981 q^{4} -1.00000 q^{5} -2.51193 q^{6} -1.59040 q^{7} -5.80210 q^{8} +1.00000 q^{9} +2.51193 q^{10} +2.49319 q^{11} +4.30981 q^{12} +1.40233 q^{13} +3.99499 q^{14} -1.00000 q^{15} +5.95487 q^{16} +2.09645 q^{17} -2.51193 q^{18} -5.17976 q^{19} -4.30981 q^{20} -1.59040 q^{21} -6.26273 q^{22} -5.80210 q^{24} +1.00000 q^{25} -3.52255 q^{26} +1.00000 q^{27} -6.85434 q^{28} -2.01654 q^{29} +2.51193 q^{30} -7.30184 q^{31} -3.35403 q^{32} +2.49319 q^{33} -5.26616 q^{34} +1.59040 q^{35} +4.30981 q^{36} +8.26969 q^{37} +13.0112 q^{38} +1.40233 q^{39} +5.80210 q^{40} -2.25746 q^{41} +3.99499 q^{42} -10.9125 q^{43} +10.7452 q^{44} -1.00000 q^{45} -12.5057 q^{47} +5.95487 q^{48} -4.47062 q^{49} -2.51193 q^{50} +2.09645 q^{51} +6.04377 q^{52} +7.90270 q^{53} -2.51193 q^{54} -2.49319 q^{55} +9.22768 q^{56} -5.17976 q^{57} +5.06541 q^{58} +7.58239 q^{59} -4.30981 q^{60} +6.12986 q^{61} +18.3417 q^{62} -1.59040 q^{63} -3.48462 q^{64} -1.40233 q^{65} -6.26273 q^{66} +8.02397 q^{67} +9.03533 q^{68} -3.99499 q^{70} -2.75199 q^{71} -5.80210 q^{72} +13.7613 q^{73} -20.7729 q^{74} +1.00000 q^{75} -22.3238 q^{76} -3.96518 q^{77} -3.52255 q^{78} +9.84104 q^{79} -5.95487 q^{80} +1.00000 q^{81} +5.67060 q^{82} +12.2109 q^{83} -6.85434 q^{84} -2.09645 q^{85} +27.4115 q^{86} -2.01654 q^{87} -14.4657 q^{88} +9.96197 q^{89} +2.51193 q^{90} -2.23027 q^{91} -7.30184 q^{93} +31.4136 q^{94} +5.17976 q^{95} -3.35403 q^{96} -2.31390 q^{97} +11.2299 q^{98} +2.49319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * 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 $

$2$	−2.51193	−1.77621	−0.888103	−	0.459645i	$-0.847977\pi$
$2$	−2.51193	−1.77621	−0.888103	+	0.459645i	$0.847977\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.30981	2.15491
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.51193	−1.02549
$7$	−1.59040	−0.601116	−0.300558	−	0.953764i	$-0.597173\pi$
$7$	−1.59040	−0.601116	−0.300558	+	0.953764i	$0.597173\pi$
$8$	−5.80210	−2.05135
$9$	1.00000	0.333333
$10$	2.51193	0.794343
$11$	2.49319	0.751725	0.375863	−	0.926675i	$-0.377346\pi$
$11$	2.49319	0.751725	0.375863	+	0.926675i	$0.377346\pi$
$12$	4.30981	1.24414
$13$	1.40233	0.388936	0.194468	−	0.980909i	$-0.437702\pi$
$13$	1.40233	0.388936	0.194468	+	0.980909i	$0.437702\pi$
$14$	3.99499	1.06771
$15$	−1.00000	−0.258199
$16$	5.95487	1.48872
$17$	2.09645	0.508465	0.254232	−	0.967143i	$-0.418177\pi$
$17$	2.09645	0.508465	0.254232	+	0.967143i	$0.418177\pi$
$18$	−2.51193	−0.592069
$19$	−5.17976	−1.18832	−0.594159	−	0.804348i	$-0.702515\pi$
$19$	−5.17976	−1.18832	−0.594159	+	0.804348i	$0.702515\pi$
$20$	−4.30981	−0.963704
$21$	−1.59040	−0.347055
$22$	−6.26273	−1.33522
$23$	0	0
$23$	0	0
$24$	−5.80210	−1.18435
$25$	1.00000	0.200000
$26$	−3.52255	−0.690830
$27$	1.00000	0.192450
$28$	−6.85434	−1.29535
$29$	−2.01654	−0.374461	−0.187231	−	0.982316i	$-0.559951\pi$
$29$	−2.01654	−0.374461	−0.187231	+	0.982316i	$0.559951\pi$
$30$	2.51193	0.458614
$31$	−7.30184	−1.31145	−0.655725	−	0.755000i	$-0.727637\pi$
$31$	−7.30184	−1.31145	−0.655725	+	0.755000i	$0.727637\pi$
$32$	−3.35403	−0.592915
$33$	2.49319	0.434009
$34$	−5.26616	−0.903138
$35$	1.59040	0.268827
$36$	4.30981	0.718302
$37$	8.26969	1.35953	0.679765	−	0.733430i	$-0.262082\pi$
$37$	8.26969	1.35953	0.679765	+	0.733430i	$0.262082\pi$
$38$	13.0112	2.11070
$39$	1.40233	0.224552
$40$	5.80210	0.917393
$41$	−2.25746	−0.352556	−0.176278	−	0.984340i	$-0.556406\pi$
$41$	−2.25746	−0.352556	−0.176278	+	0.984340i	$0.556406\pi$
$42$	3.99499	0.616440
$43$	−10.9125	−1.66414	−0.832070	−	0.554670i	$-0.812844\pi$
$43$	−10.9125	−1.66414	−0.832070	+	0.554670i	$0.812844\pi$
$44$	10.7452	1.61990
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−12.5057	−1.82415	−0.912075	−	0.410023i	$-0.865521\pi$
$47$	−12.5057	−1.82415	−0.912075	+	0.410023i	$0.865521\pi$
$48$	5.95487	0.859511
$49$	−4.47062	−0.638659
$50$	−2.51193	−0.355241
$51$	2.09645	0.293562
$52$	6.04377	0.838120
$53$	7.90270	1.08552	0.542760	−	0.839888i	$-0.317379\pi$
$53$	7.90270	1.08552	0.542760	+	0.839888i	$0.317379\pi$
$54$	−2.51193	−0.341831
$55$	−2.49319	−0.336182
$56$	9.22768	1.23310
$57$	−5.17976	−0.686076
$58$	5.06541	0.665120
$59$	7.58239	0.987143	0.493571	−	0.869705i	$-0.335691\pi$
$59$	7.58239	0.987143	0.493571	+	0.869705i	$0.335691\pi$
$60$	−4.30981	−0.556395
$61$	6.12986	0.784849	0.392424	−	0.919784i	$-0.371636\pi$
$61$	6.12986	0.784849	0.392424	+	0.919784i	$0.371636\pi$
$62$	18.3417	2.32940
$63$	−1.59040	−0.200372
$64$	−3.48462	−0.435578
$65$	−1.40233	−0.173937
$66$	−6.26273	−0.770889
$67$	8.02397	0.980284	0.490142	−	0.871643i	$-0.336945\pi$
$67$	8.02397	0.980284	0.490142	+	0.871643i	$0.336945\pi$
$68$	9.03533	1.09569
$69$	0	0
$70$	−3.99499	−0.477493
$71$	−2.75199	−0.326601	−0.163301	−	0.986576i	$-0.552214\pi$
$71$	−2.75199	−0.326601	−0.163301	+	0.986576i	$0.552214\pi$
$72$	−5.80210	−0.683784
$73$	13.7613	1.61063	0.805317	−	0.592844i	$-0.201995\pi$
$73$	13.7613	1.61063	0.805317	+	0.592844i	$0.201995\pi$
$74$	−20.7729	−2.41480
$75$	1.00000	0.115470
$76$	−22.3238	−2.56072
$77$	−3.96518	−0.451874
$78$	−3.52255	−0.398851
$79$	9.84104	1.10720	0.553602	−	0.832781i	$-0.313253\pi$
$79$	9.84104	1.10720	0.553602	+	0.832781i	$0.313253\pi$
$80$	−5.95487	−0.665774
$81$	1.00000	0.111111
$82$	5.67060	0.626213
$83$	12.2109	1.34032	0.670162	−	0.742215i	$-0.266225\pi$
$83$	12.2109	1.34032	0.670162	+	0.742215i	$0.266225\pi$
$84$	−6.85434	−0.747870
$85$	−2.09645	−0.227392
$86$	27.4115	2.95586
$87$	−2.01654	−0.216195
$88$	−14.4657	−1.54205
$89$	9.96197	1.05597	0.527983	−	0.849255i	$-0.322948\pi$
$89$	9.96197	1.05597	0.527983	+	0.849255i	$0.322948\pi$
$90$	2.51193	0.264781
$91$	−2.23027	−0.233796
$92$	0	0
$93$	−7.30184	−0.757166
$94$	31.4136	3.24007
$95$	5.17976	0.531432
$96$	−3.35403	−0.342320
$97$	−2.31390	−0.234941	−0.117471	−	0.993076i	$-0.537479\pi$
$97$	−2.31390	−0.234941	−0.117471	+	0.993076i	$0.537479\pi$
$98$	11.2299	1.13439
$99$	2.49319	0.250575
$100$	4.30981	0.430981
$101$	14.3075	1.42365	0.711826	−	0.702356i	$-0.247869\pi$
$101$	14.3075	1.42365	0.711826	+	0.702356i	$0.247869\pi$
$102$	−5.26616	−0.521427
$103$	−19.4553	−1.91699	−0.958495	−	0.285111i	$-0.907970\pi$
$103$	−19.4553	−1.91699	−0.958495	+	0.285111i	$0.907970\pi$
$104$	−8.13644	−0.797844
$105$	1.59040	0.155208
$106$	−19.8511	−1.92811
$107$	7.93087	0.766706	0.383353	−	0.923602i	$-0.374769\pi$
$107$	7.93087	0.766706	0.383353	+	0.923602i	$0.374769\pi$
$108$	4.30981	0.414712
$109$	−7.57930	−0.725966	−0.362983	−	0.931796i	$-0.618242\pi$
$109$	−7.57930	−0.725966	−0.362983	+	0.931796i	$0.618242\pi$
$110$	6.26273	0.597128
$111$	8.26969	0.784924
$112$	−9.47064	−0.894892
$113$	4.44244	0.417909	0.208955	−	0.977925i	$-0.432994\pi$
$113$	4.44244	0.417909	0.208955	+	0.977925i	$0.432994\pi$
$114$	13.0112	1.21861
$115$	0	0
$116$	−8.69089	−0.806929
$117$	1.40233	0.129645
$118$	−19.0465	−1.75337
$119$	−3.33421	−0.305646
$120$	5.80210	0.529657
$121$	−4.78400	−0.434909
$122$	−15.3978	−1.39405
$123$	−2.25746	−0.203549
$124$	−31.4696	−2.82605
$125$	−1.00000	−0.0894427
$126$	3.99499	0.355902
$127$	−8.30606	−0.737043	−0.368522	−	0.929619i	$-0.620136\pi$
$127$	−8.30606	−0.737043	−0.368522	+	0.929619i	$0.620136\pi$
$128$	15.4612	1.36659
$129$	−10.9125	−0.960792
$130$	3.52255	0.308948
$131$	−13.5566	−1.18445	−0.592224	−	0.805773i	$-0.701750\pi$
$131$	−13.5566	−1.18445	−0.592224	+	0.805773i	$0.701750\pi$
$132$	10.7452	0.935248
$133$	8.23791	0.714317
$134$	−20.1557	−1.74119
$135$	−1.00000	−0.0860663
$136$	−12.1638	−1.04304
$137$	11.9583	1.02167	0.510834	−	0.859679i	$-0.329337\pi$
$137$	11.9583	1.02167	0.510834	+	0.859679i	$0.329337\pi$
$138$	0	0
$139$	−4.87443	−0.413444	−0.206722	−	0.978400i	$-0.566280\pi$
$139$	−4.87443	−0.413444	−0.206722	+	0.978400i	$0.566280\pi$
$140$	6.85434	0.579298
$141$	−12.5057	−1.05317
$142$	6.91282	0.580111
$143$	3.49627	0.292373
$144$	5.95487	0.496239
$145$	2.01654	0.167464
$146$	−34.5674	−2.86082
$147$	−4.47062	−0.368730
$148$	35.6408	2.92966
$149$	3.20063	0.262206	0.131103	−	0.991369i	$-0.458148\pi$
$149$	3.20063	0.262206	0.131103	+	0.991369i	$0.458148\pi$
$150$	−2.51193	−0.205099
$151$	−19.8355	−1.61419	−0.807094	−	0.590423i	$-0.798961\pi$
$151$	−19.8355	−1.61419	−0.807094	+	0.590423i	$0.798961\pi$
$152$	30.0535	2.43766
$153$	2.09645	0.169488
$154$	9.96027	0.802621
$155$	7.30184	0.586498
$156$	6.04377	0.483889
$157$	5.66003	0.451719	0.225860	−	0.974160i	$-0.427481\pi$
$157$	5.66003	0.451719	0.225860	+	0.974160i	$0.427481\pi$
$158$	−24.7201	−1.96662
$159$	7.90270	0.626725
$160$	3.35403	0.265160
$161$	0	0
$162$	−2.51193	−0.197356
$163$	7.14466	0.559613	0.279806	−	0.960056i	$-0.409730\pi$
$163$	7.14466	0.559613	0.279806	+	0.960056i	$0.409730\pi$
$164$	−9.72924	−0.759726
$165$	−2.49319	−0.194095
$166$	−30.6731	−2.38069
$167$	16.3797	1.26750	0.633748	−	0.773539i	$-0.281515\pi$
$167$	16.3797	1.26750	0.633748	+	0.773539i	$0.281515\pi$
$168$	9.22768	0.711931
$169$	−11.0335	−0.848729
$170$	5.26616	0.403896
$171$	−5.17976	−0.396106
$172$	−47.0308	−3.58607
$173$	2.96989	0.225796	0.112898	−	0.993607i	$-0.463987\pi$
$173$	2.96989	0.225796	0.112898	+	0.993607i	$0.463987\pi$
$174$	5.06541	0.384007
$175$	−1.59040	−0.120223
$176$	14.8466	1.11911
$177$	7.58239	0.569927
$178$	−25.0238	−1.87561
$179$	0.463001	0.0346063	0.0173032	−	0.999850i	$-0.494492\pi$
$179$	0.463001	0.0346063	0.0173032	+	0.999850i	$0.494492\pi$
$180$	−4.30981	−0.321235
$181$	2.86024	0.212600	0.106300	−	0.994334i	$-0.466100\pi$
$181$	2.86024	0.212600	0.106300	+	0.994334i	$0.466100\pi$
$182$	5.60228	0.415269
$183$	6.12986	0.453133
$184$	0	0
$185$	−8.26969	−0.608000
$186$	18.3417	1.34488
$187$	5.22686	0.382226
$188$	−53.8974	−3.93087
$189$	−1.59040	−0.115685
$190$	−13.0112	−0.943933
$191$	−12.5011	−0.904549	−0.452275	−	0.891879i	$-0.649387\pi$
$191$	−12.5011	−0.904549	−0.452275	+	0.891879i	$0.649387\pi$
$192$	−3.48462	−0.251481
$193$	20.3079	1.46180	0.730898	−	0.682487i	$-0.239101\pi$
$193$	20.3079	1.46180	0.730898	+	0.682487i	$0.239101\pi$
$194$	5.81237	0.417304
$195$	−1.40233	−0.100423
$196$	−19.2675	−1.37625
$197$	−10.5907	−0.754556	−0.377278	−	0.926100i	$-0.623140\pi$
$197$	−10.5907	−0.754556	−0.377278	+	0.926100i	$0.623140\pi$
$198$	−6.26273	−0.445073
$199$	−13.6327	−0.966398	−0.483199	−	0.875510i	$-0.660525\pi$
$199$	−13.6327	−0.966398	−0.483199	+	0.875510i	$0.660525\pi$
$200$	−5.80210	−0.410270
$201$	8.02397	0.565967
$202$	−35.9396	−2.52870
$203$	3.20711	0.225095
$204$	9.03533	0.632599
$205$	2.25746	0.157668
$206$	48.8705	3.40497
$207$	0	0
$208$	8.35067	0.579015
$209$	−12.9141	−0.893289
$210$	−3.99499	−0.275681
$211$	−27.5053	−1.89354	−0.946770	−	0.321911i	$-0.895675\pi$
$211$	−27.5053	−1.89354	−0.946770	+	0.321911i	$0.895675\pi$
$212$	34.0592	2.33919
$213$	−2.75199	−0.188563
$214$	−19.9218	−1.36183
$215$	10.9125	0.744226
$216$	−5.80210	−0.394783
$217$	11.6129	0.788333
$218$	19.0387	1.28946
$219$	13.7613	0.929900
$220$	−10.7452	−0.724440
$221$	2.93992	0.197760
$222$	−20.7729	−1.39419
$223$	−2.52033	−0.168774	−0.0843869	−	0.996433i	$-0.526893\pi$
$223$	−2.52033	−0.168774	−0.0843869	+	0.996433i	$0.526893\pi$
$224$	5.33427	0.356411
$225$	1.00000	0.0666667
$226$	−11.1591	−0.742293
$227$	21.6973	1.44010	0.720051	−	0.693921i	$-0.244118\pi$
$227$	21.6973	1.44010	0.720051	+	0.693921i	$0.244118\pi$
$228$	−22.3238	−1.47843
$229$	20.8353	1.37683	0.688417	−	0.725316i	$-0.258306\pi$
$229$	20.8353	1.37683	0.688417	+	0.725316i	$0.258306\pi$
$230$	0	0
$231$	−3.96518	−0.260890
$232$	11.7001	0.768152
$233$	17.5274	1.14826	0.574129	−	0.818765i	$-0.305341\pi$
$233$	17.5274	1.14826	0.574129	+	0.818765i	$0.305341\pi$
$234$	−3.52255	−0.230277
$235$	12.5057	0.815785
$236$	32.6787	2.12720
$237$	9.84104	0.639245
$238$	8.37531	0.542891
$239$	4.77525	0.308885	0.154443	−	0.988002i	$-0.450642\pi$
$239$	4.77525	0.308885	0.154443	+	0.988002i	$0.450642\pi$
$240$	−5.95487	−0.384385
$241$	11.5456	0.743714	0.371857	−	0.928290i	$-0.378721\pi$
$241$	11.5456	0.743714	0.371857	+	0.928290i	$0.378721\pi$
$242$	12.0171	0.772489
$243$	1.00000	0.0641500
$244$	26.4186	1.69128
$245$	4.47062	0.285617
$246$	5.67060	0.361544
$247$	−7.26372	−0.462179
$248$	42.3660	2.69024
$249$	12.2109	0.773837
$250$	2.51193	0.158869
$251$	−5.80115	−0.366165	−0.183083	−	0.983098i	$-0.558608\pi$
$251$	−5.80115	−0.366165	−0.183083	+	0.983098i	$0.558608\pi$
$252$	−6.85434	−0.431783
$253$	0	0
$254$	20.8643	1.30914
$255$	−2.09645	−0.131285
$256$	−31.8683	−1.99177
$257$	5.24140	0.326950	0.163475	−	0.986548i	$-0.447730\pi$
$257$	5.24140	0.326950	0.163475	+	0.986548i	$0.447730\pi$
$258$	27.4115	1.70656
$259$	−13.1522	−0.817235
$260$	−6.04377	−0.374819
$261$	−2.01654	−0.124820
$262$	34.0533	2.10382
$263$	14.3576	0.885330	0.442665	−	0.896687i	$-0.354033\pi$
$263$	14.3576	0.885330	0.442665	+	0.896687i	$0.354033\pi$
$264$	−14.4657	−0.890305
$265$	−7.90270	−0.485459
$266$	−20.6931	−1.26877
$267$	9.96197	0.609663
$268$	34.5818	2.11242
$269$	30.5797	1.86448	0.932239	−	0.361844i	$-0.117853\pi$
$269$	30.5797	1.86448	0.932239	+	0.361844i	$0.117853\pi$
$270$	2.51193	0.152871
$271$	−18.3742	−1.11615	−0.558076	−	0.829790i	$-0.688460\pi$
$271$	−18.3742	−1.11615	−0.558076	+	0.829790i	$0.688460\pi$
$272$	12.4841	0.756960
$273$	−2.23027	−0.134982
$274$	−30.0385	−1.81469
$275$	2.49319	0.150345
$276$	0	0
$277$	17.8523	1.07264	0.536319	−	0.844015i	$-0.319814\pi$
$277$	17.8523	1.07264	0.536319	+	0.844015i	$0.319814\pi$
$278$	12.2442	0.734361
$279$	−7.30184	−0.437150
$280$	−9.22768	−0.551460
$281$	22.4601	1.33986	0.669929	−	0.742425i	$-0.266325\pi$
$281$	22.4601	1.33986	0.669929	+	0.742425i	$0.266325\pi$
$282$	31.4136	1.87065
$283$	26.7107	1.58779	0.793894	−	0.608057i	$-0.208051\pi$
$283$	26.7107	1.58779	0.793894	+	0.608057i	$0.208051\pi$
$284$	−11.8606	−0.703795
$285$	5.17976	0.306822
$286$	−8.78240	−0.519314
$287$	3.59028	0.211927
$288$	−3.35403	−0.197638
$289$	−12.6049	−0.741463
$290$	−5.06541	−0.297451
$291$	−2.31390	−0.135643
$292$	59.3085	3.47077
$293$	−25.5734	−1.49401	−0.747007	−	0.664816i	$-0.768510\pi$
$293$	−25.5734	−1.49401	−0.747007	+	0.664816i	$0.768510\pi$
$294$	11.2299	0.654941
$295$	−7.58239	−0.441464
$296$	−47.9816	−2.78887
$297$	2.49319	0.144670
$298$	−8.03977	−0.465731
$299$	0	0
$300$	4.30981	0.248827
$301$	17.3553	1.00034
$302$	49.8254	2.86713
$303$	14.3075	0.821946
$304$	−30.8448	−1.76907
$305$	−6.12986	−0.350995
$306$	−5.26616	−0.301046
$307$	17.1284	0.977570	0.488785	−	0.872404i	$-0.337440\pi$
$307$	17.1284	0.977570	0.488785	+	0.872404i	$0.337440\pi$
$308$	−17.0892	−0.973747
$309$	−19.4553	−1.10677
$310$	−18.3417	−1.04174
$311$	−14.8742	−0.843439	−0.421720	−	0.906726i	$-0.638573\pi$
$311$	−14.8742	−0.843439	−0.421720	+	0.906726i	$0.638573\pi$
$312$	−8.13644	−0.460635
$313$	−16.5098	−0.933189	−0.466595	−	0.884471i	$-0.654519\pi$
$313$	−16.5098	−0.933189	−0.466595	+	0.884471i	$0.654519\pi$
$314$	−14.2176	−0.802347
$315$	1.59040	0.0896091
$316$	42.4131	2.38592
$317$	−11.5824	−0.650535	−0.325267	−	0.945622i	$-0.605454\pi$
$317$	−11.5824	−0.650535	−0.325267	+	0.945622i	$0.605454\pi$
$318$	−19.8511	−1.11319
$319$	−5.02761	−0.281492
$320$	3.48462	0.194796
$321$	7.93087	0.442658
$322$	0	0
$323$	−10.8591	−0.604218
$324$	4.30981	0.239434
$325$	1.40233	0.0777871
$326$	−17.9469	−0.993987
$327$	−7.57930	−0.419136
$328$	13.0980	0.723217
$329$	19.8892	1.09653
$330$	6.26273	0.344752
$331$	25.5809	1.40605	0.703026	−	0.711164i	$-0.251832\pi$
$331$	25.5809	1.40605	0.703026	+	0.711164i	$0.251832\pi$
$332$	52.6269	2.88827
$333$	8.26969	0.453176
$334$	−41.1447	−2.25134
$335$	−8.02397	−0.438396
$336$	−9.47064	−0.516666
$337$	−10.6899	−0.582318	−0.291159	−	0.956675i	$-0.594041\pi$
$337$	−10.6899	−0.582318	−0.291159	+	0.956675i	$0.594041\pi$
$338$	27.7154	1.50752
$339$	4.44244	0.241280
$340$	−9.03533	−0.490009
$341$	−18.2049	−0.985849
$342$	13.0112	0.703566
$343$	18.2429	0.985025
$344$	63.3154	3.41374
$345$	0	0
$346$	−7.46016	−0.401061
$347$	−18.2573	−0.980104	−0.490052	−	0.871693i	$-0.663022\pi$
$347$	−18.2573	−0.980104	−0.490052	+	0.871693i	$0.663022\pi$
$348$	−8.69089	−0.465881
$349$	37.2949	1.99635	0.998175	−	0.0603921i	$-0.0192351\pi$
$349$	37.2949	1.99635	0.998175	+	0.0603921i	$0.0192351\pi$
$350$	3.99499	0.213541
$351$	1.40233	0.0748507
$352$	−8.36225	−0.445709
$353$	3.62599	0.192992	0.0964959	−	0.995333i	$-0.469237\pi$
$353$	3.62599	0.192992	0.0964959	+	0.995333i	$0.469237\pi$
$354$	−19.0465	−1.01231
$355$	2.75199	0.146061
$356$	42.9342	2.27551
$357$	−3.33421	−0.176465
$358$	−1.16303	−0.0614679
$359$	17.9340	0.946520	0.473260	−	0.880923i	$-0.343077\pi$
$359$	17.9340	0.946520	0.473260	+	0.880923i	$0.343077\pi$
$360$	5.80210	0.305798
$361$	7.82991	0.412100
$362$	−7.18474	−0.377622
$363$	−4.78400	−0.251095
$364$	−9.61204	−0.503808
$365$	−13.7613	−0.720297
$366$	−15.3978	−0.804857
$367$	−18.8008	−0.981394	−0.490697	−	0.871330i	$-0.663258\pi$
$367$	−18.8008	−0.981394	−0.490697	+	0.871330i	$0.663258\pi$
$368$	0	0
$369$	−2.25746	−0.117519
$370$	20.7729	1.07993
$371$	−12.5685	−0.652523
$372$	−31.4696	−1.63162
$373$	−23.7794	−1.23125	−0.615626	−	0.788038i	$-0.711097\pi$
$373$	−23.7794	−1.23125	−0.615626	+	0.788038i	$0.711097\pi$
$374$	−13.1295	−0.678912
$375$	−1.00000	−0.0516398
$376$	72.5596	3.74198
$377$	−2.82784	−0.145641
$378$	3.99499	0.205480
$379$	8.13824	0.418033	0.209017	−	0.977912i	$-0.432974\pi$
$379$	8.13824	0.418033	0.209017	+	0.977912i	$0.432974\pi$
$380$	22.3238	1.14519
$381$	−8.30606	−0.425532
$382$	31.4020	1.60667
$383$	−28.4537	−1.45392	−0.726959	−	0.686681i	$-0.759067\pi$
$383$	−28.4537	−1.45392	−0.726959	+	0.686681i	$0.759067\pi$
$384$	15.4612	0.789001
$385$	3.96518	0.202084
$386$	−51.0122	−2.59645
$387$	−10.9125	−0.554714
$388$	−9.97249	−0.506277
$389$	22.9759	1.16492	0.582461	−	0.812859i	$-0.302090\pi$
$389$	22.9759	1.16492	0.582461	+	0.812859i	$0.302090\pi$
$390$	3.52255	0.178371
$391$	0	0
$392$	25.9390	1.31012
$393$	−13.5566	−0.683841
$394$	26.6031	1.34025
$395$	−9.84104	−0.495157
$396$	10.7452	0.539966
$397$	4.23489	0.212543	0.106271	−	0.994337i	$-0.466109\pi$
$397$	4.23489	0.212543	0.106271	+	0.994337i	$0.466109\pi$
$398$	34.2445	1.71652
$399$	8.23791	0.412411
$400$	5.95487	0.297743
$401$	−8.12304	−0.405645	−0.202823	−	0.979216i	$-0.565011\pi$
$401$	−8.12304	−0.405645	−0.202823	+	0.979216i	$0.565011\pi$
$402$	−20.1557	−1.00527
$403$	−10.2396	−0.510069
$404$	61.6628	3.06784
$405$	−1.00000	−0.0496904
$406$	−8.05604	−0.399815
$407$	20.6179	1.02199
$408$	−12.1638	−0.602200
$409$	22.4568	1.11042	0.555210	−	0.831710i	$-0.312638\pi$
$409$	22.4568	1.11042	0.555210	+	0.831710i	$0.312638\pi$
$410$	−5.67060	−0.280051
$411$	11.9583	0.589860
$412$	−83.8488	−4.13093
$413$	−12.0591	−0.593388
$414$	0	0
$415$	−12.2109	−0.599411
$416$	−4.70345	−0.230606
$417$	−4.87443	−0.238702
$418$	32.4394	1.58666
$419$	15.3947	0.752083	0.376041	−	0.926603i	$-0.377285\pi$
$419$	15.3947	0.752083	0.376041	+	0.926603i	$0.377285\pi$
$420$	6.85434	0.334458
$421$	21.7095	1.05806	0.529028	−	0.848604i	$-0.322557\pi$
$421$	21.7095	1.05806	0.529028	+	0.848604i	$0.322557\pi$
$422$	69.0914	3.36332
$423$	−12.5057	−0.608050
$424$	−45.8523	−2.22678
$425$	2.09645	0.101693
$426$	6.91282	0.334927
$427$	−9.74896	−0.471785
$428$	34.1806	1.65218
$429$	3.49627	0.168801
$430$	−27.4115	−1.32190
$431$	−7.14844	−0.344328	−0.172164	−	0.985068i	$-0.555076\pi$
$431$	−7.14844	−0.344328	−0.172164	+	0.985068i	$0.555076\pi$
$432$	5.95487	0.286504
$433$	−21.3319	−1.02514	−0.512572	−	0.858644i	$-0.671307\pi$
$433$	−21.3319	−1.02514	−0.512572	+	0.858644i	$0.671307\pi$
$434$	−29.1708	−1.40024
$435$	2.01654	0.0966855
$436$	−32.6654	−1.56439
$437$	0	0
$438$	−34.5674	−1.65169
$439$	−2.58730	−0.123485	−0.0617425	−	0.998092i	$-0.519666\pi$
$439$	−2.58730	−0.123485	−0.0617425	+	0.998092i	$0.519666\pi$
$440$	14.4657	0.689627
$441$	−4.47062	−0.212886
$442$	−7.38487	−0.351263
$443$	−29.0527	−1.38034	−0.690169	−	0.723649i	$-0.742464\pi$
$443$	−29.0527	−1.38034	−0.690169	+	0.723649i	$0.742464\pi$
$444$	35.6408	1.69144
$445$	−9.96197	−0.472243
$446$	6.33090	0.299777
$447$	3.20063	0.151384
$448$	5.54195	0.261833
$449$	−31.5842	−1.49055	−0.745275	−	0.666757i	$-0.767682\pi$
$449$	−31.5842	−1.49055	−0.745275	+	0.666757i	$0.767682\pi$
$450$	−2.51193	−0.118414
$451$	−5.62828	−0.265025
$452$	19.1461	0.900556
$453$	−19.8355	−0.931952
$454$	−54.5023	−2.55792
$455$	2.23027	0.104557
$456$	30.0535	1.40738
$457$	33.4905	1.56662	0.783311	−	0.621631i	$-0.213529\pi$
$457$	33.4905	1.56662	0.783311	+	0.621631i	$0.213529\pi$
$458$	−52.3368	−2.44554
$459$	2.09645	0.0978541
$460$	0	0
$461$	4.72711	0.220163	0.110082	−	0.993923i	$-0.464889\pi$
$461$	4.72711	0.220163	0.110082	+	0.993923i	$0.464889\pi$
$462$	9.96027	0.463394
$463$	−4.93792	−0.229485	−0.114742	−	0.993395i	$-0.536604\pi$
$463$	−4.93792	−0.229485	−0.114742	+	0.993395i	$0.536604\pi$
$464$	−12.0082	−0.557467
$465$	7.30184	0.338615
$466$	−44.0276	−2.03954
$467$	−11.0984	−0.513570	−0.256785	−	0.966468i	$-0.582663\pi$
$467$	−11.0984	−0.513570	−0.256785	+	0.966468i	$0.582663\pi$
$468$	6.04377	0.279373
$469$	−12.7613	−0.589264
$470$	−31.4136	−1.44900
$471$	5.66003	0.260800
$472$	−43.9938	−2.02498
$473$	−27.2069	−1.25098
$474$	−24.7201	−1.13543
$475$	−5.17976	−0.237664
$476$	−14.3698	−0.658640
$477$	7.90270	0.361840
$478$	−11.9951	−0.548644
$479$	−2.56279	−0.117097	−0.0585485	−	0.998285i	$-0.518647\pi$
$479$	−2.56279	−0.117097	−0.0585485	+	0.998285i	$0.518647\pi$
$480$	3.35403	0.153090
$481$	11.5968	0.528769
$482$	−29.0017	−1.32099
$483$	0	0
$484$	−20.6182	−0.937189
$485$	2.31390	0.105069
$486$	−2.51193	−0.113944
$487$	33.6436	1.52454	0.762269	−	0.647260i	$-0.224085\pi$
$487$	33.6436	1.52454	0.762269	+	0.647260i	$0.224085\pi$
$488$	−35.5661	−1.61000
$489$	7.14466	0.323093
$490$	−11.2299	−0.507315
$491$	4.74608	0.214187	0.107094	−	0.994249i	$-0.465846\pi$
$491$	4.74608	0.214187	0.107094	+	0.994249i	$0.465846\pi$
$492$	−9.72924	−0.438628
$493$	−4.22758	−0.190400
$494$	18.2460	0.820926
$495$	−2.49319	−0.112061
$496$	−43.4815	−1.95238
$497$	4.37678	0.196325
$498$	−30.6731	−1.37449
$499$	13.8374	0.619446	0.309723	−	0.950827i	$-0.399764\pi$
$499$	13.8374	0.619446	0.309723	+	0.950827i	$0.399764\pi$
$500$	−4.30981	−0.192741
$501$	16.3797	0.731790
$502$	14.5721	0.650385
$503$	−28.7933	−1.28383	−0.641915	−	0.766776i	$-0.721860\pi$
$503$	−28.7933	−1.28383	−0.641915	+	0.766776i	$0.721860\pi$
$504$	9.22768	0.411034
$505$	−14.3075	−0.636676
$506$	0	0
$507$	−11.0335	−0.490014
$508$	−35.7976	−1.58826
$509$	−5.24738	−0.232586	−0.116293	−	0.993215i	$-0.537101\pi$
$509$	−5.24738	−0.232586	−0.116293	+	0.993215i	$0.537101\pi$
$510$	5.26616	0.233189
$511$	−21.8860	−0.968178
$512$	49.1286	2.17120
$513$	−5.17976	−0.228692
$514$	−13.1661	−0.580730
$515$	19.4553	0.857304
$516$	−47.0308	−2.07042
$517$	−31.1792	−1.37126
$518$	33.0373	1.45158
$519$	2.96989	0.130364
$520$	8.13644	0.356807
$521$	−12.6498	−0.554199	−0.277099	−	0.960841i	$-0.589373\pi$
$521$	−12.6498	−0.554199	−0.277099	+	0.960841i	$0.589373\pi$
$522$	5.06541	0.221707
$523$	30.5481	1.33578	0.667888	−	0.744262i	$-0.267199\pi$
$523$	30.5481	1.33578	0.667888	+	0.744262i	$0.267199\pi$
$524$	−58.4265	−2.55237
$525$	−1.59040	−0.0694109
$526$	−36.0654	−1.57253
$527$	−15.3080	−0.666826
$528$	14.8466	0.646116
$529$	0	0
$530$	19.8511	0.862275
$531$	7.58239	0.329048
$532$	35.5039	1.53929
$533$	−3.16570	−0.137122
$534$	−25.0238	−1.08289
$535$	−7.93087	−0.342881
$536$	−46.5559	−2.01091
$537$	0.463001	0.0199800
$538$	−76.8142	−3.31170
$539$	−11.1461	−0.480096
$540$	−4.30981	−0.185465
$541$	8.34871	0.358939	0.179470	−	0.983764i	$-0.442562\pi$
$541$	8.34871	0.358939	0.179470	+	0.983764i	$0.442562\pi$
$542$	46.1547	1.98251
$543$	2.86024	0.122745
$544$	−7.03158	−0.301477
$545$	7.57930	0.324662
$546$	5.60228	0.239756
$547$	22.6661	0.969133	0.484566	−	0.874754i	$-0.338977\pi$
$547$	22.6661	0.969133	0.484566	+	0.874754i	$0.338977\pi$
$548$	51.5381	2.20160
$549$	6.12986	0.261616
$550$	−6.26273	−0.267044
$551$	10.4452	0.444979
$552$	0	0
$553$	−15.6512	−0.665558
$554$	−44.8437	−1.90523
$555$	−8.26969	−0.351029
$556$	−21.0079	−0.890933
$557$	33.5592	1.42195	0.710974	−	0.703218i	$-0.248254\pi$
$557$	33.5592	1.42195	0.710974	+	0.703218i	$0.248254\pi$
$558$	18.3417	0.776468
$559$	−15.3029	−0.647244
$560$	9.47064	0.400208
$561$	5.22686	0.220678
$562$	−56.4183	−2.37986
$563$	17.0809	0.719874	0.359937	−	0.932977i	$-0.382798\pi$
$563$	17.0809	0.719874	0.359937	+	0.932977i	$0.382798\pi$
$564$	−53.8974	−2.26949
$565$	−4.44244	−0.186895
$566$	−67.0956	−2.82024
$567$	−1.59040	−0.0667907
$568$	15.9673	0.669974
$569$	7.08542	0.297036	0.148518	−	0.988910i	$-0.452550\pi$
$569$	7.08542	0.297036	0.148518	+	0.988910i	$0.452550\pi$
$570$	−13.0112	−0.544980
$571$	−30.1941	−1.26358	−0.631792	−	0.775138i	$-0.717681\pi$
$571$	−30.1941	−1.26358	−0.631792	+	0.775138i	$0.717681\pi$
$572$	15.0683	0.630036
$573$	−12.5011	−0.522242
$574$	−9.01854	−0.376427
$575$	0	0
$576$	−3.48462	−0.145193
$577$	12.8111	0.533332	0.266666	−	0.963789i	$-0.414078\pi$
$577$	12.8111	0.533332	0.266666	+	0.963789i	$0.414078\pi$
$578$	31.6626	1.31699
$579$	20.3079	0.843968
$580$	8.69089	0.360870
$581$	−19.4203	−0.805691
$582$	5.81237	0.240931
$583$	19.7029	0.816012
$584$	−79.8442	−3.30398
$585$	−1.40233	−0.0579791
$586$	64.2387	2.65368
$587$	42.1029	1.73777	0.868887	−	0.495011i	$-0.164836\pi$
$587$	42.1029	1.73777	0.868887	+	0.495011i	$0.164836\pi$
$588$	−19.2675	−0.794579
$589$	37.8218	1.55842
$590$	19.0465	0.784130
$591$	−10.5907	−0.435643
$592$	49.2449	2.02395
$593$	−21.0955	−0.866288	−0.433144	−	0.901325i	$-0.642596\pi$
$593$	−21.0955	−0.866288	−0.433144	+	0.901325i	$0.642596\pi$
$594$	−6.26273	−0.256963
$595$	3.33421	0.136689
$596$	13.7941	0.565029
$597$	−13.6327	−0.557950
$598$	0	0
$599$	37.7727	1.54335	0.771674	−	0.636018i	$-0.219420\pi$
$599$	37.7727	1.54335	0.771674	+	0.636018i	$0.219420\pi$
$600$	−5.80210	−0.236870
$601$	−18.5173	−0.755337	−0.377669	−	0.925941i	$-0.623274\pi$
$601$	−18.5173	−0.755337	−0.377669	+	0.925941i	$0.623274\pi$
$602$	−43.5953	−1.77681
$603$	8.02397	0.326761
$604$	−85.4872	−3.47843
$605$	4.78400	0.194497
$606$	−35.9396	−1.45994
$607$	33.6704	1.36664	0.683320	−	0.730119i	$-0.260535\pi$
$607$	33.6704	1.36664	0.683320	+	0.730119i	$0.260535\pi$
$608$	17.3731	0.704572
$609$	3.20711	0.129959
$610$	15.3978	0.623439
$611$	−17.5371	−0.709477
$612$	9.03533	0.365231
$613$	32.4906	1.31228	0.656142	−	0.754638i	$-0.272187\pi$
$613$	32.4906	1.31228	0.656142	+	0.754638i	$0.272187\pi$
$614$	−43.0254	−1.73637
$615$	2.25746	0.0910297
$616$	23.0064	0.926953
$617$	−5.09269	−0.205024	−0.102512	−	0.994732i	$-0.532688\pi$
$617$	−5.09269	−0.205024	−0.102512	+	0.994732i	$0.532688\pi$
$618$	48.8705	1.96586
$619$	−4.08724	−0.164280	−0.0821401	−	0.996621i	$-0.526175\pi$
$619$	−4.08724	−0.164280	−0.0821401	+	0.996621i	$0.526175\pi$
$620$	31.4696	1.26385
$621$	0	0
$622$	37.3630	1.49812
$623$	−15.8436	−0.634759
$624$	8.35067	0.334294
$625$	1.00000	0.0400000
$626$	41.4715	1.65754
$627$	−12.9141	−0.515740
$628$	24.3937	0.973413
$629$	17.3370	0.691273
$630$	−3.99499	−0.159164
$631$	−3.17685	−0.126468	−0.0632342	−	0.997999i	$-0.520142\pi$
$631$	−3.17685	−0.126468	−0.0632342	+	0.997999i	$0.520142\pi$
$632$	−57.0987	−2.27127
$633$	−27.5053	−1.09324
$634$	29.0943	1.15548
$635$	8.30606	0.329616
$636$	34.0592	1.35053
$637$	−6.26927	−0.248397
$638$	12.6290	0.499988
$639$	−2.75199	−0.108867
$640$	−15.4612	−0.611158
$641$	−14.8001	−0.584570	−0.292285	−	0.956331i	$-0.594416\pi$
$641$	−14.8001	−0.584570	−0.292285	+	0.956331i	$0.594416\pi$
$642$	−19.9218	−0.786252
$643$	9.25155	0.364845	0.182423	−	0.983220i	$-0.441606\pi$
$643$	9.25155	0.364845	0.182423	+	0.983220i	$0.441606\pi$
$644$	0	0
$645$	10.9125	0.429679
$646$	27.2774	1.07322
$647$	46.1539	1.81450	0.907249	−	0.420593i	$-0.138178\pi$
$647$	46.1539	1.81450	0.907249	+	0.420593i	$0.138178\pi$
$648$	−5.80210	−0.227928
$649$	18.9043	0.742060
$650$	−3.52255	−0.138166
$651$	11.6129	0.455145
$652$	30.7921	1.20591
$653$	19.1596	0.749773	0.374886	−	0.927071i	$-0.377682\pi$
$653$	19.1596	0.749773	0.374886	+	0.927071i	$0.377682\pi$
$654$	19.0387	0.744473
$655$	13.5566	0.529701
$656$	−13.4429	−0.524857
$657$	13.7613	0.536878
$658$	−49.9603	−1.94766
$659$	17.3741	0.676798	0.338399	−	0.941003i	$-0.390115\pi$
$659$	17.3741	0.676798	0.338399	+	0.941003i	$0.390115\pi$
$660$	−10.7452	−0.418256
$661$	2.92030	0.113586	0.0567932	−	0.998386i	$-0.481912\pi$
$661$	2.92030	0.113586	0.0567932	+	0.998386i	$0.481912\pi$
$662$	−64.2575	−2.49744
$663$	2.93992	0.114177
$664$	−70.8491	−2.74948
$665$	−8.23791	−0.319452
$666$	−20.7729	−0.804934
$667$	0	0
$668$	70.5933	2.73134
$669$	−2.52033	−0.0974416
$670$	20.1557	0.778682
$671$	15.2829	0.589990
$672$	5.33427	0.205774
$673$	29.7703	1.14756	0.573780	−	0.819009i	$-0.305476\pi$
$673$	29.7703	1.14756	0.573780	+	0.819009i	$0.305476\pi$
$674$	26.8524	1.03432
$675$	1.00000	0.0384900
$676$	−47.5522	−1.82893
$677$	10.5140	0.404087	0.202044	−	0.979377i	$-0.435242\pi$
$677$	10.5140	0.404087	0.202044	+	0.979377i	$0.435242\pi$
$678$	−11.1591	−0.428563
$679$	3.68004	0.141227
$680$	12.1638	0.466462
$681$	21.6973	0.831444
$682$	45.7295	1.75107
$683$	38.1823	1.46101	0.730503	−	0.682910i	$-0.239286\pi$
$683$	38.1823	1.46101	0.730503	+	0.682910i	$0.239286\pi$
$684$	−22.3238	−0.853572
$685$	−11.9583	−0.456904
$686$	−45.8250	−1.74961
$687$	20.8353	0.794915
$688$	−64.9825	−2.47743
$689$	11.0822	0.422197
$690$	0	0
$691$	−1.68562	−0.0641242	−0.0320621	−	0.999486i	$-0.510207\pi$
$691$	−1.68562	−0.0641242	−0.0320621	+	0.999486i	$0.510207\pi$
$692$	12.7997	0.486570
$693$	−3.96518	−0.150625
$694$	45.8612	1.74087
$695$	4.87443	0.184898
$696$	11.7001	0.443493
$697$	−4.73267	−0.179263
$698$	−93.6823	−3.54593
$699$	17.5274	0.662947
$700$	−6.85434	−0.259070
$701$	41.7892	1.57836	0.789179	−	0.614163i	$-0.210506\pi$
$701$	41.7892	1.57836	0.789179	+	0.614163i	$0.210506\pi$
$702$	−3.52255	−0.132950
$703$	−42.8350	−1.61555
$704$	−8.68782	−0.327435
$705$	12.5057	0.470994
$706$	−9.10824	−0.342793
$707$	−22.7547	−0.855780
$708$	32.6787	1.22814
$709$	24.1022	0.905176	0.452588	−	0.891720i	$-0.350501\pi$
$709$	24.1022	0.905176	0.452588	+	0.891720i	$0.350501\pi$
$710$	−6.91282	−0.259434
$711$	9.84104	0.369068
$712$	−57.8003	−2.16616
$713$	0	0
$714$	8.37531	0.313438
$715$	−3.49627	−0.130753
$716$	1.99545	0.0745734
$717$	4.77525	0.178335
$718$	−45.0490	−1.68121
$719$	9.76431	0.364147	0.182074	−	0.983285i	$-0.441719\pi$
$719$	9.76431	0.364147	0.182074	+	0.983285i	$0.441719\pi$
$720$	−5.95487	−0.221925
$721$	30.9418	1.15233
$722$	−19.6682	−0.731975
$723$	11.5456	0.429384
$724$	12.3271	0.458134
$725$	−2.01654	−0.0748923
$726$	12.0171	0.445997
$727$	21.9714	0.814875	0.407437	−	0.913233i	$-0.366422\pi$
$727$	21.9714	0.814875	0.407437	+	0.913233i	$0.366422\pi$
$728$	12.9402	0.479597
$729$	1.00000	0.0370370
$730$	34.5674	1.27940
$731$	−22.8776	−0.846157
$732$	26.4186	0.976458
$733$	−3.26771	−0.120696	−0.0603478	−	0.998177i	$-0.519221\pi$
$733$	−3.26771	−0.120696	−0.0603478	+	0.998177i	$0.519221\pi$
$734$	47.2264	1.74316
$735$	4.47062	0.164901
$736$	0	0
$737$	20.0053	0.736904
$738$	5.67060	0.208738
$739$	−23.7749	−0.874575	−0.437287	−	0.899322i	$-0.644061\pi$
$739$	−23.7749	−0.874575	−0.437287	+	0.899322i	$0.644061\pi$
$740$	−35.6408	−1.31018
$741$	−7.26372	−0.266839
$742$	31.5712	1.15902
$743$	−9.08839	−0.333421	−0.166710	−	0.986006i	$-0.553314\pi$
$743$	−9.08839	−0.333421	−0.166710	+	0.986006i	$0.553314\pi$
$744$	42.3660	1.55321
$745$	−3.20063	−0.117262
$746$	59.7324	2.18696
$747$	12.2109	0.446775
$748$	22.5268	0.823661
$749$	−12.6133	−0.460880
$750$	2.51193	0.0917229
$751$	−10.6977	−0.390364	−0.195182	−	0.980767i	$-0.562530\pi$
$751$	−10.6977	−0.390364	−0.195182	+	0.980767i	$0.562530\pi$
$752$	−74.4701	−2.71564
$753$	−5.80115	−0.211406
$754$	7.10336	0.258689
$755$	19.8355	0.721887
$756$	−6.85434	−0.249290
$757$	5.56719	0.202343	0.101171	−	0.994869i	$-0.467741\pi$
$757$	5.56719	0.202343	0.101171	+	0.994869i	$0.467741\pi$
$758$	−20.4427	−0.742513
$759$	0	0
$760$	−30.0535	−1.09015
$761$	−40.7621	−1.47763	−0.738813	−	0.673911i	$-0.764613\pi$
$761$	−40.7621	−1.47763	−0.738813	+	0.673911i	$0.764613\pi$
$762$	20.8643	0.755833
$763$	12.0542	0.436390
$764$	−53.8775	−1.94922
$765$	−2.09645	−0.0757975
$766$	71.4739	2.58246
$767$	10.6330	0.383935
$768$	−31.8683	−1.14995
$769$	15.2852	0.551199	0.275600	−	0.961273i	$-0.411124\pi$
$769$	15.2852	0.551199	0.275600	+	0.961273i	$0.411124\pi$
$770$	−9.96027	−0.358943
$771$	5.24140	0.188764
$772$	87.5234	3.15003
$773$	8.24374	0.296507	0.148253	−	0.988949i	$-0.452635\pi$
$773$	8.24374	0.296507	0.148253	+	0.988949i	$0.452635\pi$
$774$	27.4115	0.985285
$775$	−7.30184	−0.262290
$776$	13.4255	0.481947
$777$	−13.1522	−0.471831
$778$	−57.7138	−2.06914
$779$	11.6931	0.418949
$780$	−6.04377	−0.216402
$781$	−6.86124	−0.245514
$782$	0	0
$783$	−2.01654	−0.0720651
$784$	−26.6219	−0.950783
$785$	−5.66003	−0.202015
$786$	34.0533	1.21464
$787$	32.1369	1.14556	0.572779	−	0.819710i	$-0.305865\pi$
$787$	32.1369	1.14556	0.572779	+	0.819710i	$0.305865\pi$
$788$	−45.6439	−1.62600
$789$	14.3576	0.511145
$790$	24.7201	0.879500
$791$	−7.06527	−0.251212
$792$	−14.4657	−0.514018
$793$	8.59608	0.305256
$794$	−10.6378	−0.377520
$795$	−7.90270	−0.280280
$796$	−58.7545	−2.08250
$797$	−38.3271	−1.35762	−0.678808	−	0.734316i	$-0.737503\pi$
$797$	−38.3271	−1.35762	−0.678808	+	0.734316i	$0.737503\pi$
$798$	−20.6931	−0.732527
$799$	−26.2177	−0.927516
$800$	−3.35403	−0.118583
$801$	9.96197	0.351989
$802$	20.4045	0.720509
$803$	34.3094	1.21075
$804$	34.5818	1.21961
$805$	0	0
$806$	25.7211	0.905988
$807$	30.5797	1.07646
$808$	−83.0137	−2.92041
$809$	3.10548	0.109183	0.0545915	−	0.998509i	$-0.482614\pi$
$809$	3.10548	0.109183	0.0545915	+	0.998509i	$0.482614\pi$
$810$	2.51193	0.0882604
$811$	40.9743	1.43880	0.719401	−	0.694595i	$-0.244417\pi$
$811$	40.9743	1.43880	0.719401	+	0.694595i	$0.244417\pi$
$812$	13.8220	0.485058
$813$	−18.3742	−0.644410
$814$	−51.7908	−1.81527
$815$	−7.14466	−0.250266
$816$	12.4841	0.437031
$817$	56.5241	1.97753
$818$	−56.4101	−1.97233
$819$	−2.23027	−0.0779318
$820$	9.72924	0.339760
$821$	−44.9576	−1.56903	−0.784515	−	0.620109i	$-0.787088\pi$
$821$	−44.9576	−1.56903	−0.784515	+	0.620109i	$0.787088\pi$
$822$	−30.0385	−1.04771
$823$	−18.4722	−0.643899	−0.321950	−	0.946757i	$-0.604338\pi$
$823$	−18.4722	−0.643899	−0.321950	+	0.946757i	$0.604338\pi$
$824$	112.882	3.93242
$825$	2.49319	0.0868017
$826$	30.2916	1.05398
$827$	29.7148	1.03328	0.516642	−	0.856202i	$-0.327182\pi$
$827$	29.7148	1.03328	0.516642	+	0.856202i	$0.327182\pi$
$828$	0	0
$829$	−19.8833	−0.690576	−0.345288	−	0.938497i	$-0.612219\pi$
$829$	−19.8833	−0.690576	−0.345288	+	0.938497i	$0.612219\pi$
$830$	30.6731	1.06468
$831$	17.8523	0.619288
$832$	−4.88658	−0.169412
$833$	−9.37244	−0.324736
$834$	12.2442	0.423984
$835$	−16.3797	−0.566842
$836$	−55.6575	−1.92495
$837$	−7.30184	−0.252389
$838$	−38.6706	−1.33585
$839$	43.2744	1.49400	0.746999	−	0.664825i	$-0.231494\pi$
$839$	43.2744	1.49400	0.746999	+	0.664825i	$0.231494\pi$
$840$	−9.22768	−0.318385
$841$	−24.9336	−0.859779
$842$	−54.5328	−1.87932
$843$	22.4601	0.773567
$844$	−118.543	−4.08040
$845$	11.0335	0.379563
$846$	31.4136	1.08002
$847$	7.60850	0.261431
$848$	47.0595	1.61603
$849$	26.7107	0.916709
$850$	−5.26616	−0.180628
$851$	0	0
$852$	−11.8606	−0.406336
$853$	−26.7741	−0.916728	−0.458364	−	0.888765i	$-0.651564\pi$
$853$	−26.7741	−0.916728	−0.458364	+	0.888765i	$0.651564\pi$
$854$	24.4887	0.837988
$855$	5.17976	0.177144
$856$	−46.0157	−1.57278
$857$	−3.59399	−0.122768	−0.0613842	−	0.998114i	$-0.519551\pi$
$857$	−3.59399	−0.122768	−0.0613842	+	0.998114i	$0.519551\pi$
$858$	−8.78240	−0.299826
$859$	−31.8519	−1.08677	−0.543387	−	0.839482i	$-0.682858\pi$
$859$	−31.8519	−1.08677	−0.543387	+	0.839482i	$0.682858\pi$
$860$	47.0308	1.60374
$861$	3.59028	0.122356
$862$	17.9564	0.611598
$863$	−19.4332	−0.661515	−0.330758	−	0.943716i	$-0.607304\pi$
$863$	−19.4332	−0.661515	−0.330758	+	0.943716i	$0.607304\pi$
$864$	−3.35403	−0.114107
$865$	−2.96989	−0.100979
$866$	53.5842	1.82087
$867$	−12.6049	−0.428084
$868$	50.0493	1.69879
$869$	24.5356	0.832313
$870$	−5.06541	−0.171733
$871$	11.2522	0.381267
$872$	43.9759	1.48921
$873$	−2.31390	−0.0783138
$874$	0	0
$875$	1.59040	0.0537655
$876$	59.3085	2.00385
$877$	−12.7159	−0.429386	−0.214693	−	0.976682i	$-0.568875\pi$
$877$	−12.7159	−0.429386	−0.214693	+	0.976682i	$0.568875\pi$
$878$	6.49912	0.219335
$879$	−25.5734	−0.862570
$880$	−14.8466	−0.500479
$881$	37.7632	1.27228	0.636138	−	0.771575i	$-0.280531\pi$
$881$	37.7632	1.27228	0.636138	+	0.771575i	$0.280531\pi$
$882$	11.2299	0.378130
$883$	−18.1681	−0.611405	−0.305703	−	0.952127i	$-0.598891\pi$
$883$	−18.1681	−0.611405	−0.305703	+	0.952127i	$0.598891\pi$
$884$	12.6705	0.426155
$885$	−7.58239	−0.254879
$886$	72.9786	2.45176
$887$	8.25567	0.277198	0.138599	−	0.990349i	$-0.455740\pi$
$887$	8.25567	0.277198	0.138599	+	0.990349i	$0.455740\pi$
$888$	−47.9816	−1.61016
$889$	13.2100	0.443049
$890$	25.0238	0.838800
$891$	2.49319	0.0835250
$892$	−10.8622	−0.363692
$893$	64.7768	2.16767
$894$	−8.03977	−0.268890
$895$	−0.463001	−0.0154764
$896$	−24.5896	−0.821480
$897$	0	0
$898$	79.3374	2.64752
$899$	14.7244	0.491087
$900$	4.30981	0.143660
$901$	16.5677	0.551949
$902$	14.1379	0.470740
$903$	17.3553	0.577548
$904$	−25.7755	−0.857279
$905$	−2.86024	−0.0950777
$906$	49.8254	1.65534
$907$	−6.59754	−0.219068	−0.109534	−	0.993983i	$-0.534936\pi$
$907$	−6.59754	−0.219068	−0.109534	+	0.993983i	$0.534936\pi$
$908$	93.5115	3.10329
$909$	14.3075	0.474551
$910$	−5.60228	−0.185714
$911$	34.1484	1.13139	0.565693	−	0.824616i	$-0.308609\pi$
$911$	34.1484	1.13139	0.565693	+	0.824616i	$0.308609\pi$
$912$	−30.8448	−1.02137
$913$	30.4442	1.00756
$914$	−84.1260	−2.78264
$915$	−6.12986	−0.202647
$916$	89.7961	2.96695
$917$	21.5605	0.711991
$918$	−5.26616	−0.173809
$919$	3.80327	0.125458	0.0627291	−	0.998031i	$-0.480020\pi$
$919$	3.80327	0.125458	0.0627291	+	0.998031i	$0.480020\pi$
$920$	0	0
$921$	17.1284	0.564400
$922$	−11.8742	−0.391055
$923$	−3.85919	−0.127027
$924$	−17.0892	−0.562193
$925$	8.26969	0.271906
$926$	12.4037	0.407612
$927$	−19.4553	−0.638996
$928$	6.76353	0.222024
$929$	−12.4054	−0.407009	−0.203505	−	0.979074i	$-0.565233\pi$
$929$	−12.4054	−0.407009	−0.203505	+	0.979074i	$0.565233\pi$
$930$	−18.3417	−0.601449
$931$	23.1567	0.758931
$932$	75.5398	2.47439
$933$	−14.8742	−0.486960
$934$	27.8783	0.912207
$935$	−5.22686	−0.170937
$936$	−8.13644	−0.265948
$937$	10.5566	0.344869	0.172435	−	0.985021i	$-0.444837\pi$
$937$	10.5566	0.344869	0.172435	+	0.985021i	$0.444837\pi$
$938$	32.0557	1.04665
$939$	−16.5098	−0.538777
$940$	53.8974	1.75794
$941$	−25.9188	−0.844928	−0.422464	−	0.906380i	$-0.638835\pi$
$941$	−25.9188	−0.844928	−0.422464	+	0.906380i	$0.638835\pi$
$942$	−14.2176	−0.463235
$943$	0	0
$944$	45.1521	1.46958
$945$	1.59040	0.0517358
$946$	68.3420	2.22199
$947$	41.3184	1.34267	0.671334	−	0.741155i	$-0.265722\pi$
$947$	41.3184	1.34267	0.671334	+	0.741155i	$0.265722\pi$
$948$	42.4131	1.37751
$949$	19.2978	0.626433
$950$	13.0112	0.422140
$951$	−11.5824	−0.375586
$952$	19.3454	0.626989
$953$	−32.9581	−1.06762	−0.533809	−	0.845605i	$-0.679240\pi$
$953$	−32.9581	−1.06762	−0.533809	+	0.845605i	$0.679240\pi$
$954$	−19.8511	−0.642702
$955$	12.5011	0.404527
$956$	20.5805	0.665619
$957$	−5.02761	−0.162519
$958$	6.43757	0.207988
$959$	−19.0186	−0.614141
$960$	3.48462	0.112466
$961$	22.3169	0.719899
$962$	−29.1304	−0.939203
$963$	7.93087	0.255569
$964$	49.7592	1.60264
$965$	−20.3079	−0.653735
$966$	0	0
$967$	−42.0973	−1.35376	−0.676880	−	0.736094i	$-0.736668\pi$
$967$	−42.0973	−1.35376	−0.676880	+	0.736094i	$0.736668\pi$
$968$	27.7573	0.892152
$969$	−10.8591	−0.348845
$970$	−5.81237	−0.186624
$971$	58.2970	1.87084	0.935419	−	0.353540i	$-0.115022\pi$
$971$	58.2970	1.87084	0.935419	+	0.353540i	$0.115022\pi$
$972$	4.30981	0.138237
$973$	7.75231	0.248528
$974$	−84.5106	−2.70789
$975$	1.40233	0.0449104
$976$	36.5025	1.16842
$977$	−21.9452	−0.702088	−0.351044	−	0.936359i	$-0.614173\pi$
$977$	−21.9452	−0.702088	−0.351044	+	0.936359i	$0.614173\pi$
$978$	−17.9469	−0.573879
$979$	24.8371	0.793796
$980$	19.2675	0.615478
$981$	−7.57930	−0.241989
$982$	−11.9218	−0.380441
$983$	−17.9205	−0.571577	−0.285788	−	0.958293i	$-0.592255\pi$
$983$	−17.9205	−0.571577	−0.285788	+	0.958293i	$0.592255\pi$
$984$	13.0980	0.417550
$985$	10.5907	0.337447
$986$	10.6194	0.338190
$987$	19.8892	0.633080
$988$	−31.3053	−0.995953
$989$	0	0
$990$	6.26273	0.199043
$991$	37.6887	1.19722	0.598611	−	0.801040i	$-0.295720\pi$
$991$	37.6887	1.19722	0.598611	+	0.801040i	$0.295720\pi$
$992$	24.4906	0.777578
$993$	25.5809	0.811784
$994$	−10.9942	−0.348714
$995$	13.6327	0.432186
$996$	52.6269	1.66755
$997$	−7.42463	−0.235140	−0.117570	−	0.993065i	$-0.537510\pi$
$997$	−7.42463	−0.235140	−0.117570	+	0.993065i	$0.537510\pi$
$998$	−34.7586	−1.10026
$999$	8.26969	0.261641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bl.1.1	✓	12
23.22	odd	2		7935.2.a.bm.1.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.1	✓	12	1.1	even	1	trivial
7935.2.a.bm.1.1	yes	12	23.22	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51193 q^{2} +1.00000 q^{3} +4.30981 q^{4} -1.00000 q^{5} -2.51193 q^{6} -1.59040 q^{7} -5.80210 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.51193 q^{2} +1.00000 q^{3} +4.30981 q^{4} -1.00000 q^{5} -2.51193 q^{6} -1.59040 q^{7} -5.80210 q^{8} +1.00000 q^{9} +2.51193 q^{10} +2.49319 q^{11} +4.30981 q^{12} +1.40233 q^{13} +3.99499 q^{14} -1.00000 q^{15} +5.95487 q^{16} +2.09645 q^{17} -2.51193 q^{18} -5.17976 q^{19} -4.30981 q^{20} -1.59040 q^{21} -6.26273 q^{22} -5.80210 q^{24} +1.00000 q^{25} -3.52255 q^{26} +1.00000 q^{27} -6.85434 q^{28} -2.01654 q^{29} +2.51193 q^{30} -7.30184 q^{31} -3.35403 q^{32} +2.49319 q^{33} -5.26616 q^{34} +1.59040 q^{35} +4.30981 q^{36} +8.26969 q^{37} +13.0112 q^{38} +1.40233 q^{39} +5.80210 q^{40} -2.25746 q^{41} +3.99499 q^{42} -10.9125 q^{43} +10.7452 q^{44} -1.00000 q^{45} -12.5057 q^{47} +5.95487 q^{48} -4.47062 q^{49} -2.51193 q^{50} +2.09645 q^{51} +6.04377 q^{52} +7.90270 q^{53} -2.51193 q^{54} -2.49319 q^{55} +9.22768 q^{56} -5.17976 q^{57} +5.06541 q^{58} +7.58239 q^{59} -4.30981 q^{60} +6.12986 q^{61} +18.3417 q^{62} -1.59040 q^{63} -3.48462 q^{64} -1.40233 q^{65} -6.26273 q^{66} +8.02397 q^{67} +9.03533 q^{68} -3.99499 q^{70} -2.75199 q^{71} -5.80210 q^{72} +13.7613 q^{73} -20.7729 q^{74} +1.00000 q^{75} -22.3238 q^{76} -3.96518 q^{77} -3.52255 q^{78} +9.84104 q^{79} -5.95487 q^{80} +1.00000 q^{81} +5.67060 q^{82} +12.2109 q^{83} -6.85434 q^{84} -2.09645 q^{85} +27.4115 q^{86} -2.01654 q^{87} -14.4657 q^{88} +9.96197 q^{89} +2.51193 q^{90} -2.23027 q^{91} -7.30184 q^{93} +31.4136 q^{94} +5.17976 q^{95} -3.35403 q^{96} -2.31390 q^{97} +11.2299 q^{98} +2.49319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Introduction

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