LMFDB - Embedded newform 931.2.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 57x^6 - 98x^5 - 93x^4 + 152x^3 + 39x^2 - 58*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.31483$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.31483 q^{2} -3.01444 q^{3} -0.271216 q^{4} +4.02523 q^{5} +3.96349 q^{6} +2.98627 q^{8} +6.08688 q^{9} +O(q^{10})$	\(q-1.31483 q^{2} -3.01444 q^{3} -0.271216 q^{4} +4.02523 q^{5} +3.96349 q^{6} +2.98627 q^{8} +6.08688 q^{9} -5.29250 q^{10} +1.61490 q^{11} +0.817567 q^{12} +5.21945 q^{13} -12.1338 q^{15} -3.38401 q^{16} +2.70633 q^{17} -8.00322 q^{18} +1.00000 q^{19} -1.09171 q^{20} -2.12332 q^{22} -2.88811 q^{23} -9.00194 q^{24} +11.2025 q^{25} -6.86270 q^{26} -9.30522 q^{27} -6.81005 q^{29} +15.9540 q^{30} +0.440553 q^{31} -1.52313 q^{32} -4.86803 q^{33} -3.55837 q^{34} -1.65086 q^{36} -6.68583 q^{37} -1.31483 q^{38} -15.7338 q^{39} +12.0204 q^{40} +4.42729 q^{41} +8.88620 q^{43} -0.437987 q^{44} +24.5011 q^{45} +3.79738 q^{46} +0.655937 q^{47} +10.2009 q^{48} -14.7294 q^{50} -8.15807 q^{51} -1.41560 q^{52} -4.75749 q^{53} +12.2348 q^{54} +6.50034 q^{55} -3.01444 q^{57} +8.95407 q^{58} +11.1446 q^{59} +3.29089 q^{60} +10.5050 q^{61} -0.579254 q^{62} +8.77068 q^{64} +21.0095 q^{65} +6.40064 q^{66} -11.8711 q^{67} -0.734000 q^{68} +8.70605 q^{69} -3.63982 q^{71} +18.1771 q^{72} -6.49287 q^{73} +8.79074 q^{74} -33.7692 q^{75} -0.271216 q^{76} +20.6872 q^{78} +8.78112 q^{79} -13.6214 q^{80} +9.78945 q^{81} -5.82115 q^{82} +0.609081 q^{83} +10.8936 q^{85} -11.6839 q^{86} +20.5285 q^{87} +4.82252 q^{88} +11.4165 q^{89} -32.2148 q^{90} +0.783303 q^{92} -1.32802 q^{93} -0.862447 q^{94} +4.02523 q^{95} +4.59140 q^{96} -6.91655 q^{97} +9.82970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.31483	−0.929727	−0.464863	−	0.885382i	$-0.653897\pi$
$2$	−1.31483	−0.929727	−0.464863	+	0.885382i	$0.653897\pi$
$3$	−3.01444	−1.74039	−0.870195	−	0.492707i	$-0.836007\pi$
$3$	−3.01444	−1.74039	−0.870195	+	0.492707i	$0.836007\pi$
$4$	−0.271216	−0.135608
$5$	4.02523	1.80014	0.900069	−	0.435748i	$-0.143516\pi$
$5$	4.02523	1.80014	0.900069	+	0.435748i	$0.143516\pi$
$6$	3.96349	1.61809
$7$	0	0
$7$	0	0
$8$	2.98627	1.05581
$9$	6.08688	2.02896
$10$	−5.29250	−1.67364
$11$	1.61490	0.486911	0.243455	−	0.969912i	$-0.421719\pi$
$11$	1.61490	0.486911	0.243455	+	0.969912i	$0.421719\pi$
$12$	0.817567	0.236011
$13$	5.21945	1.44762	0.723808	−	0.690002i	$-0.242390\pi$
$13$	5.21945	1.44762	0.723808	+	0.690002i	$0.242390\pi$
$14$	0	0
$15$	−12.1338	−3.13294
$16$	−3.38401	−0.846002
$17$	2.70633	0.656381	0.328190	−	0.944612i	$-0.393561\pi$
$17$	2.70633	0.656381	0.328190	+	0.944612i	$0.393561\pi$
$18$	−8.00322	−1.88638
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.09171	−0.244113
$21$	0	0
$22$	−2.12332	−0.452694
$23$	−2.88811	−0.602212	−0.301106	−	0.953591i	$-0.597356\pi$
$23$	−2.88811	−0.602212	−0.301106	+	0.953591i	$0.597356\pi$
$24$	−9.00194	−1.83751
$25$	11.2025	2.24050
$26$	−6.86270	−1.34589
$27$	−9.30522	−1.79079
$28$	0	0
$29$	−6.81005	−1.26459	−0.632297	−	0.774726i	$-0.717888\pi$
$29$	−6.81005	−1.26459	−0.632297	+	0.774726i	$0.717888\pi$
$30$	15.9540	2.91278
$31$	0.440553	0.0791257	0.0395629	−	0.999217i	$-0.487403\pi$
$31$	0.440553	0.0791257	0.0395629	+	0.999217i	$0.487403\pi$
$32$	−1.52313	−0.269254
$33$	−4.86803	−0.847415
$34$	−3.55837	−0.610255
$35$	0	0
$36$	−1.65086	−0.275143
$37$	−6.68583	−1.09914	−0.549572	−	0.835447i	$-0.685209\pi$
$37$	−6.68583	−1.09914	−0.549572	+	0.835447i	$0.685209\pi$
$38$	−1.31483	−0.213294
$39$	−15.7338	−2.51942
$40$	12.0204	1.90059
$41$	4.42729	0.691427	0.345714	−	0.938340i	$-0.387637\pi$
$41$	4.42729	0.691427	0.345714	+	0.938340i	$0.387637\pi$
$42$	0	0
$43$	8.88620	1.35513	0.677567	−	0.735461i	$-0.263035\pi$
$43$	8.88620	1.35513	0.677567	+	0.735461i	$0.263035\pi$
$44$	−0.437987	−0.0660291
$45$	24.5011	3.65241
$46$	3.79738	0.559893
$47$	0.655937	0.0956782	0.0478391	−	0.998855i	$-0.484767\pi$
$47$	0.655937	0.0956782	0.0478391	+	0.998855i	$0.484767\pi$
$48$	10.2009	1.47237
$49$	0	0
$50$	−14.7294	−2.08305
$51$	−8.15807	−1.14236
$52$	−1.41560	−0.196309
$53$	−4.75749	−0.653491	−0.326746	−	0.945112i	$-0.605952\pi$
$53$	−4.75749	−0.653491	−0.326746	+	0.945112i	$0.605952\pi$
$54$	12.2348	1.66495
$55$	6.50034	0.876506
$56$	0	0
$57$	−3.01444	−0.399273
$58$	8.95407	1.17573
$59$	11.1446	1.45090	0.725450	−	0.688275i	$-0.241632\pi$
$59$	11.1446	1.45090	0.725450	+	0.688275i	$0.241632\pi$
$60$	3.29089	0.424853
$61$	10.5050	1.34503	0.672514	−	0.740084i	$-0.265214\pi$
$61$	10.5050	1.34503	0.672514	+	0.740084i	$0.265214\pi$
$62$	−0.579254	−0.0735653
$63$	0	0
$64$	8.77068	1.09634
$65$	21.0095	2.60591
$66$	6.40064	0.787864
$67$	−11.8711	−1.45029	−0.725145	−	0.688596i	$-0.758227\pi$
$67$	−11.8711	−1.45029	−0.725145	+	0.688596i	$0.758227\pi$
$68$	−0.734000	−0.0890106
$69$	8.70605	1.04808
$70$	0	0
$71$	−3.63982	−0.431967	−0.215983	−	0.976397i	$-0.569296\pi$
$71$	−3.63982	−0.431967	−0.215983	+	0.976397i	$0.569296\pi$
$72$	18.1771	2.14219
$73$	−6.49287	−0.759932	−0.379966	−	0.925000i	$-0.624064\pi$
$73$	−6.49287	−0.759932	−0.379966	+	0.925000i	$0.624064\pi$
$74$	8.79074	1.02190
$75$	−33.7692	−3.89934
$76$	−0.271216	−0.0311107
$77$	0	0
$78$	20.6872	2.34237
$79$	8.78112	0.987953	0.493977	−	0.869475i	$-0.335543\pi$
$79$	8.78112	0.987953	0.493977	+	0.869475i	$0.335543\pi$
$80$	−13.6214	−1.52292
$81$	9.78945	1.08772
$82$	−5.82115	−0.642838
$83$	0.609081	0.0668553	0.0334277	−	0.999441i	$-0.489358\pi$
$83$	0.609081	0.0668553	0.0334277	+	0.999441i	$0.489358\pi$
$84$	0	0
$85$	10.8936	1.18158
$86$	−11.6839	−1.25990
$87$	20.5285	2.20089
$88$	4.82252	0.514083
$89$	11.4165	1.21014	0.605072	−	0.796171i	$-0.293145\pi$
$89$	11.4165	1.21014	0.605072	+	0.796171i	$0.293145\pi$
$90$	−32.2148	−3.39574
$91$	0	0
$92$	0.783303	0.0816649
$93$	−1.32802	−0.137710
$94$	−0.862447	−0.0889546
$95$	4.02523	0.412980
$96$	4.59140	0.468608
$97$	−6.91655	−0.702269	−0.351134	−	0.936325i	$-0.614204\pi$
$97$	−6.91655	−0.702269	−0.351134	+	0.936325i	$0.614204\pi$
$98$	0	0
$99$	9.82970	0.987922
$100$	−3.03829	−0.303829
$101$	0.0670634	0.00667306	0.00333653	−	0.999994i	$-0.498938\pi$
$101$	0.0670634	0.00667306	0.00333653	+	0.999994i	$0.498938\pi$
$102$	10.7265	1.06208
$103$	−11.5525	−1.13830	−0.569149	−	0.822234i	$-0.692727\pi$
$103$	−11.5525	−1.13830	−0.569149	+	0.822234i	$0.692727\pi$
$104$	15.5867	1.52840
$105$	0	0
$106$	6.25530	0.607568
$107$	−13.3790	−1.29339	−0.646697	−	0.762747i	$-0.723850\pi$
$107$	−13.3790	−1.29339	−0.646697	+	0.762747i	$0.723850\pi$
$108$	2.52373	0.242846
$109$	17.8212	1.70696	0.853481	−	0.521124i	$-0.174487\pi$
$109$	17.8212	1.70696	0.853481	+	0.521124i	$0.174487\pi$
$110$	−8.54686	−0.814911
$111$	20.1541	1.91294
$112$	0	0
$113$	5.43115	0.510919	0.255460	−	0.966820i	$-0.417773\pi$
$113$	5.43115	0.510919	0.255460	+	0.966820i	$0.417773\pi$
$114$	3.96349	0.371215
$115$	−11.6253	−1.08407
$116$	1.84700	0.171489
$117$	31.7702	2.93715
$118$	−14.6532	−1.34894
$119$	0	0
$120$	−36.2349	−3.30778
$121$	−8.39210	−0.762918
$122$	−13.8123	−1.25051
$123$	−13.3458	−1.20335
$124$	−0.119485	−0.0107301
$125$	24.9664	2.23306
$126$	0	0
$127$	6.09351	0.540711	0.270356	−	0.962761i	$-0.412859\pi$
$127$	6.09351	0.540711	0.270356	+	0.962761i	$0.412859\pi$
$128$	−8.48571	−0.750038
$129$	−26.7870	−2.35846
$130$	−27.6240	−2.42278
$131$	8.54360	0.746457	0.373229	−	0.927739i	$-0.378251\pi$
$131$	8.54360	0.746457	0.373229	+	0.927739i	$0.378251\pi$
$132$	1.32029	0.114916
$133$	0	0
$134$	15.6086	1.34837
$135$	−37.4557	−3.22367
$136$	8.08182	0.693010
$137$	1.87908	0.160540	0.0802702	−	0.996773i	$-0.474422\pi$
$137$	1.87908	0.160540	0.0802702	+	0.996773i	$0.474422\pi$
$138$	−11.4470	−0.974433
$139$	−8.66413	−0.734882	−0.367441	−	0.930047i	$-0.619766\pi$
$139$	−8.66413	−0.734882	−0.367441	+	0.930047i	$0.619766\pi$
$140$	0	0
$141$	−1.97729	−0.166518
$142$	4.78575	0.401611
$143$	8.42889	0.704860
$144$	−20.5980	−1.71650
$145$	−27.4120	−2.27644
$146$	8.53703	0.706529
$147$	0	0
$148$	1.81331	0.149053
$149$	2.29567	0.188069	0.0940344	−	0.995569i	$-0.470024\pi$
$149$	2.29567	0.188069	0.0940344	+	0.995569i	$0.470024\pi$
$150$	44.4009	3.62532
$151$	−3.19706	−0.260173	−0.130087	−	0.991503i	$-0.541526\pi$
$151$	−3.19706	−0.260173	−0.130087	+	0.991503i	$0.541526\pi$
$152$	2.98627	0.242218
$153$	16.4731	1.33177
$154$	0	0
$155$	1.77333	0.142437
$156$	4.26725	0.341654
$157$	−12.4884	−0.996687	−0.498343	−	0.866980i	$-0.666058\pi$
$157$	−12.4884	−0.996687	−0.498343	+	0.866980i	$0.666058\pi$
$158$	−11.5457	−0.918527
$159$	14.3412	1.13733
$160$	−6.13096	−0.484695
$161$	0	0
$162$	−12.8715	−1.01128
$163$	−14.1958	−1.11190	−0.555952	−	0.831214i	$-0.687646\pi$
$163$	−14.1958	−1.11190	−0.555952	+	0.831214i	$0.687646\pi$
$164$	−1.20075	−0.0937632
$165$	−19.5949	−1.52546
$166$	−0.800839	−0.0621572
$167$	0.193288	0.0149570	0.00747852	−	0.999972i	$-0.497619\pi$
$167$	0.193288	0.0149570	0.00747852	+	0.999972i	$0.497619\pi$
$168$	0	0
$169$	14.2427	1.09559
$170$	−14.3232	−1.09854
$171$	6.08688	0.465475
$172$	−2.41008	−0.183767
$173$	−17.7970	−1.35308	−0.676540	−	0.736406i	$-0.736521\pi$
$173$	−17.7970	−1.35308	−0.676540	+	0.736406i	$0.736521\pi$
$174$	−26.9916	−2.04622
$175$	0	0
$176$	−5.46484	−0.411927
$177$	−33.5947	−2.52513
$178$	−15.0107	−1.12510
$179$	15.2728	1.14154	0.570772	−	0.821109i	$-0.306644\pi$
$179$	15.2728	1.14154	0.570772	+	0.821109i	$0.306644\pi$
$180$	−6.64509	−0.495296
$181$	−7.40779	−0.550617	−0.275308	−	0.961356i	$-0.588780\pi$
$181$	−7.40779	−0.550617	−0.275308	+	0.961356i	$0.588780\pi$
$182$	0	0
$183$	−31.6668	−2.34087
$184$	−8.62467	−0.635819
$185$	−26.9120	−1.97861
$186$	1.74613	0.128032
$187$	4.37045	0.319599
$188$	−0.177901	−0.0129748
$189$	0	0
$190$	−5.29250	−0.383958
$191$	15.7629	1.14056	0.570282	−	0.821449i	$-0.306834\pi$
$191$	15.7629	1.14056	0.570282	+	0.821449i	$0.306834\pi$
$192$	−26.4387	−1.90805
$193$	12.3796	0.891100	0.445550	−	0.895257i	$-0.353008\pi$
$193$	12.3796	0.891100	0.445550	+	0.895257i	$0.353008\pi$
$194$	9.09410	0.652918
$195$	−63.3320	−4.53530
$196$	0	0
$197$	12.5826	0.896475	0.448238	−	0.893914i	$-0.352052\pi$
$197$	12.5826	0.896475	0.448238	+	0.893914i	$0.352052\pi$
$198$	−12.9244	−0.918497
$199$	0.806681	0.0571841	0.0285921	−	0.999591i	$-0.490898\pi$
$199$	0.806681	0.0571841	0.0285921	+	0.999591i	$0.490898\pi$
$200$	33.4536	2.36553
$201$	35.7849	2.52407
$202$	−0.0881771	−0.00620412
$203$	0	0
$204$	2.21260	0.154913
$205$	17.8209	1.24466
$206$	15.1895	1.05831
$207$	−17.5796	−1.22186
$208$	−17.6627	−1.22469
$209$	1.61490	0.111705
$210$	0	0
$211$	−4.01368	−0.276313	−0.138157	−	0.990410i	$-0.544118\pi$
$211$	−4.01368	−0.276313	−0.138157	+	0.990410i	$0.544118\pi$
$212$	1.29031	0.0886188
$213$	10.9720	0.751791
$214$	17.5911	1.20250
$215$	35.7690	2.43943
$216$	−27.7879	−1.89073
$217$	0	0
$218$	−23.4319	−1.58701
$219$	19.5724	1.32258
$220$	−1.76300	−0.118861
$221$	14.1255	0.950187
$222$	−26.4992	−1.77851
$223$	25.4284	1.70281	0.851407	−	0.524505i	$-0.175750\pi$
$223$	25.4284	1.70281	0.851407	+	0.524505i	$0.175750\pi$
$224$	0	0
$225$	68.1881	4.54587
$226$	−7.14104	−0.475015
$227$	21.2387	1.40966	0.704832	−	0.709375i	$-0.251023\pi$
$227$	21.2387	1.40966	0.704832	+	0.709375i	$0.251023\pi$
$228$	0.817567	0.0541447
$229$	−9.41348	−0.622060	−0.311030	−	0.950400i	$-0.600674\pi$
$229$	−9.41348	−0.622060	−0.311030	+	0.950400i	$0.600674\pi$
$230$	15.2853	1.00788
$231$	0	0
$232$	−20.3366	−1.33517
$233$	13.0170	0.852770	0.426385	−	0.904542i	$-0.359787\pi$
$233$	13.0170	0.852770	0.426385	+	0.904542i	$0.359787\pi$
$234$	−41.7724	−2.73075
$235$	2.64030	0.172234
$236$	−3.02259	−0.196754
$237$	−26.4702	−1.71942
$238$	0	0
$239$	12.1280	0.784497	0.392248	−	0.919859i	$-0.371697\pi$
$239$	12.1280	0.784497	0.392248	+	0.919859i	$0.371697\pi$
$240$	41.0610	2.65048
$241$	−9.76645	−0.629113	−0.314556	−	0.949239i	$-0.601856\pi$
$241$	−9.76645	−0.629113	−0.314556	+	0.949239i	$0.601856\pi$
$242$	11.0342	0.709305
$243$	−1.59408	−0.102260
$244$	−2.84913	−0.182397
$245$	0	0
$246$	17.5475	1.11879
$247$	5.21945	0.332106
$248$	1.31561	0.0835413
$249$	−1.83604	−0.116354
$250$	−32.8266	−2.07614
$251$	−1.99555	−0.125958	−0.0629789	−	0.998015i	$-0.520060\pi$
$251$	−1.99555	−0.125958	−0.0629789	+	0.998015i	$0.520060\pi$
$252$	0	0
$253$	−4.66401	−0.293224
$254$	−8.01194	−0.502714
$255$	−32.8381	−2.05640
$256$	−6.38408	−0.399005
$257$	−2.42885	−0.151507	−0.0757537	−	0.997127i	$-0.524136\pi$
$257$	−2.42885	−0.151507	−0.0757537	+	0.997127i	$0.524136\pi$
$258$	35.2204	2.19272
$259$	0	0
$260$	−5.69812	−0.353382
$261$	−41.4519	−2.56581
$262$	−11.2334	−0.694001
$263$	1.81948	0.112194	0.0560971	−	0.998425i	$-0.482134\pi$
$263$	1.81948	0.112194	0.0560971	+	0.998425i	$0.482134\pi$
$264$	−14.5372	−0.894705
$265$	−19.1500	−1.17637
$266$	0	0
$267$	−34.4143	−2.10612
$268$	3.21965	0.196671
$269$	25.6076	1.56132	0.780662	−	0.624954i	$-0.214882\pi$
$269$	25.6076	1.56132	0.780662	+	0.624954i	$0.214882\pi$
$270$	49.2479	2.99713
$271$	13.2977	0.807775	0.403888	−	0.914809i	$-0.367659\pi$
$271$	13.2977	0.807775	0.403888	+	0.914809i	$0.367659\pi$
$272$	−9.15824	−0.555300
$273$	0	0
$274$	−2.47067	−0.149259
$275$	18.0909	1.09092
$276$	−2.36122	−0.142129
$277$	−7.01712	−0.421618	−0.210809	−	0.977527i	$-0.567610\pi$
$277$	−7.01712	−0.421618	−0.210809	+	0.977527i	$0.567610\pi$
$278$	11.3919	0.683240
$279$	2.68159	0.160543
$280$	0	0
$281$	−23.8630	−1.42354	−0.711772	−	0.702410i	$-0.752107\pi$
$281$	−23.8630	−1.42354	−0.711772	+	0.702410i	$0.752107\pi$
$282$	2.59980	0.154816
$283$	31.9668	1.90023	0.950115	−	0.311899i	$-0.100965\pi$
$283$	31.9668	1.90023	0.950115	+	0.311899i	$0.100965\pi$
$284$	0.987178	0.0585783
$285$	−12.1338	−0.718746
$286$	−11.0826	−0.655327
$287$	0	0
$288$	−9.27112	−0.546306
$289$	−9.67579	−0.569164
$290$	36.0422	2.11647
$291$	20.8496	1.22222
$292$	1.76097	0.103053
$293$	−10.4989	−0.613355	−0.306677	−	0.951814i	$-0.599217\pi$
$293$	−10.4989	−0.613355	−0.306677	+	0.951814i	$0.599217\pi$
$294$	0	0
$295$	44.8594	2.61182
$296$	−19.9657	−1.16048
$297$	−15.0270	−0.871955
$298$	−3.01842	−0.174853
$299$	−15.0744	−0.871772
$300$	9.15877	0.528782
$301$	0	0
$302$	4.20360	0.241890
$303$	−0.202159	−0.0116137
$304$	−3.38401	−0.194086
$305$	42.2851	2.42124
$306$	−21.6593	−1.23818
$307$	11.5671	0.660168	0.330084	−	0.943952i	$-0.392923\pi$
$307$	11.5671	0.660168	0.330084	+	0.943952i	$0.392923\pi$
$308$	0	0
$309$	34.8243	1.98108
$310$	−2.33163	−0.132428
$311$	−18.8327	−1.06790	−0.533952	−	0.845515i	$-0.679294\pi$
$311$	−18.8327	−1.06790	−0.533952	+	0.845515i	$0.679294\pi$
$312$	−46.9852	−2.66001
$313$	−5.03403	−0.284540	−0.142270	−	0.989828i	$-0.545440\pi$
$313$	−5.03403	−0.284540	−0.142270	+	0.989828i	$0.545440\pi$
$314$	16.4202	0.926646
$315$	0	0
$316$	−2.38158	−0.133975
$317$	18.5536	1.04207	0.521036	−	0.853535i	$-0.325546\pi$
$317$	18.5536	1.04207	0.521036	+	0.853535i	$0.325546\pi$
$318$	−18.8563	−1.05741
$319$	−10.9975	−0.615744
$320$	35.3040	1.97355
$321$	40.3301	2.25101
$322$	0	0
$323$	2.70633	0.150584
$324$	−2.65506	−0.147503
$325$	58.4708	3.24338
$326$	18.6652	1.03377
$327$	−53.7211	−2.97078
$328$	13.2211	0.730012
$329$	0	0
$330$	25.7640	1.41826
$331$	−7.96438	−0.437762	−0.218881	−	0.975752i	$-0.570241\pi$
$331$	−7.96438	−0.437762	−0.218881	+	0.975752i	$0.570241\pi$
$332$	−0.165193	−0.00906613
$333$	−40.6958	−2.23012
$334$	−0.254141	−0.0139060
$335$	−47.7841	−2.61072
$336$	0	0
$337$	−8.38621	−0.456826	−0.228413	−	0.973564i	$-0.573354\pi$
$337$	−8.38621	−0.456826	−0.228413	+	0.973564i	$0.573354\pi$
$338$	−18.7267	−1.01860
$339$	−16.3719	−0.889199
$340$	−2.95452	−0.160231
$341$	0.711449	0.0385271
$342$	−8.00322	−0.432765
$343$	0	0
$344$	26.5366	1.43076
$345$	35.0438	1.88670
$346$	23.4001	1.25799
$347$	−12.8792	−0.691390	−0.345695	−	0.938347i	$-0.612357\pi$
$347$	−12.8792	−0.691390	−0.345695	+	0.938347i	$0.612357\pi$
$348$	−5.56767	−0.298458
$349$	−6.10735	−0.326919	−0.163460	−	0.986550i	$-0.552265\pi$
$349$	−6.10735	−0.326919	−0.163460	+	0.986550i	$0.552265\pi$
$350$	0	0
$351$	−48.5682	−2.59238
$352$	−2.45971	−0.131103
$353$	11.8104	0.628606	0.314303	−	0.949323i	$-0.398229\pi$
$353$	11.8104	0.628606	0.314303	+	0.949323i	$0.398229\pi$
$354$	44.1714	2.34768
$355$	−14.6511	−0.777600
$356$	−3.09633	−0.164105
$357$	0	0
$358$	−20.0812	−1.06132
$359$	19.8856	1.04952	0.524762	−	0.851249i	$-0.324154\pi$
$359$	19.8856	1.04952	0.524762	+	0.851249i	$0.324154\pi$
$360$	73.1668	3.85623
$361$	1.00000	0.0526316
$362$	9.74000	0.511923
$363$	25.2975	1.32778
$364$	0	0
$365$	−26.1353	−1.36798
$366$	41.6365	2.17637
$367$	−12.1539	−0.634430	−0.317215	−	0.948354i	$-0.602748\pi$
$367$	−12.1539	−0.634430	−0.317215	+	0.948354i	$0.602748\pi$
$368$	9.77339	0.509473
$369$	26.9484	1.40288
$370$	35.3848	1.83957
$371$	0	0
$372$	0.360182	0.0186746
$373$	21.4558	1.11094	0.555471	−	0.831536i	$-0.312538\pi$
$373$	21.4558	1.11094	0.555471	+	0.831536i	$0.312538\pi$
$374$	−5.74641	−0.297140
$375$	−75.2598	−3.88640
$376$	1.95880	0.101018
$377$	−35.5447	−1.83065
$378$	0	0
$379$	−0.558193	−0.0286725	−0.0143362	−	0.999897i	$-0.504564\pi$
$379$	−0.558193	−0.0286725	−0.0143362	+	0.999897i	$0.504564\pi$
$380$	−1.09171	−0.0560035
$381$	−18.3685	−0.941049
$382$	−20.7256	−1.06041
$383$	16.9350	0.865336	0.432668	−	0.901553i	$-0.357572\pi$
$383$	16.9350	0.865336	0.432668	+	0.901553i	$0.357572\pi$
$384$	25.5797	1.30536
$385$	0	0
$386$	−16.2770	−0.828479
$387$	54.0892	2.74951
$388$	1.87588	0.0952334
$389$	−6.24045	−0.316404	−0.158202	−	0.987407i	$-0.550570\pi$
$389$	−6.24045	−0.316404	−0.158202	+	0.987407i	$0.550570\pi$
$390$	83.2709	4.21659
$391$	−7.81617	−0.395281
$392$	0	0
$393$	−25.7542	−1.29913
$394$	−16.5440	−0.833477
$395$	35.3460	1.77845
$396$	−2.66598	−0.133970
$397$	−33.3701	−1.67480	−0.837400	−	0.546591i	$-0.815925\pi$
$397$	−33.3701	−1.67480	−0.837400	+	0.546591i	$0.815925\pi$
$398$	−1.06065	−0.0531656
$399$	0	0
$400$	−37.9093	−1.89546
$401$	−31.6007	−1.57806	−0.789031	−	0.614354i	$-0.789417\pi$
$401$	−31.6007	−1.57806	−0.789031	+	0.614354i	$0.789417\pi$
$402$	−47.0511	−2.34670
$403$	2.29945	0.114544
$404$	−0.0181887	−0.000904921 0
$405$	39.4048	1.95804
$406$	0	0
$407$	−10.7969	−0.535185
$408$	−24.3622	−1.20611
$409$	−22.8822	−1.13145	−0.565727	−	0.824593i	$-0.691404\pi$
$409$	−22.8822	−1.13145	−0.565727	+	0.824593i	$0.691404\pi$
$410$	−23.4315	−1.15720
$411$	−5.66437	−0.279403
$412$	3.13322	0.154363
$413$	0	0
$414$	23.1142	1.13600
$415$	2.45169	0.120349
$416$	−7.94992	−0.389777
$417$	26.1175	1.27898
$418$	−2.12332	−0.103855
$419$	−35.8409	−1.75094	−0.875471	−	0.483271i	$-0.839449\pi$
$419$	−35.8409	−1.75094	−0.875471	+	0.483271i	$0.839449\pi$
$420$	0	0
$421$	20.4928	0.998758	0.499379	−	0.866384i	$-0.333562\pi$
$421$	20.4928	0.998758	0.499379	+	0.866384i	$0.333562\pi$
$422$	5.27731	0.256896
$423$	3.99261	0.194127
$424$	−14.2071	−0.689960
$425$	30.3176	1.47062
$426$	−14.4264	−0.698960
$427$	0	0
$428$	3.62859	0.175395
$429$	−25.4084	−1.22673
$430$	−47.0302	−2.26800
$431$	−18.4643	−0.889396	−0.444698	−	0.895681i	$-0.646689\pi$
$431$	−18.4643	−0.889396	−0.444698	+	0.895681i	$0.646689\pi$
$432$	31.4890	1.51501
$433$	−10.9024	−0.523934	−0.261967	−	0.965077i	$-0.584371\pi$
$433$	−10.9024	−0.523934	−0.261967	+	0.965077i	$0.584371\pi$
$434$	0	0
$435$	82.6320	3.96190
$436$	−4.83340	−0.231478
$437$	−2.88811	−0.138157
$438$	−25.7344	−1.22964
$439$	11.9913	0.572316	0.286158	−	0.958182i	$-0.407622\pi$
$439$	11.9913	0.572316	0.286158	+	0.958182i	$0.407622\pi$
$440$	19.4118	0.925420
$441$	0	0
$442$	−18.5727	−0.883414
$443$	5.12656	0.243570	0.121785	−	0.992556i	$-0.461138\pi$
$443$	5.12656	0.243570	0.121785	+	0.992556i	$0.461138\pi$
$444$	−5.46611	−0.259410
$445$	45.9539	2.17842
$446$	−33.4341	−1.58315
$447$	−6.92018	−0.327313
$448$	0	0
$449$	−8.35649	−0.394367	−0.197184	−	0.980367i	$-0.563179\pi$
$449$	−8.35649	−0.394367	−0.197184	+	0.980367i	$0.563179\pi$
$450$	−89.6559	−4.22642
$451$	7.14964	0.336663
$452$	−1.47302	−0.0692848
$453$	9.63736	0.452803
$454$	−27.9253	−1.31060
$455$	0	0
$456$	−9.00194	−0.421555
$457$	−13.5750	−0.635013	−0.317507	−	0.948256i	$-0.602846\pi$
$457$	−13.5750	−0.635013	−0.317507	+	0.948256i	$0.602846\pi$
$458$	12.3771	0.578346
$459$	−25.1830	−1.17544
$460$	3.15297	0.147008
$461$	37.0681	1.72643	0.863216	−	0.504835i	$-0.168447\pi$
$461$	37.0681	1.72643	0.863216	+	0.504835i	$0.168447\pi$
$462$	0	0
$463$	10.6201	0.493556	0.246778	−	0.969072i	$-0.420628\pi$
$463$	10.6201	0.493556	0.246778	+	0.969072i	$0.420628\pi$
$464$	23.0453	1.06985
$465$	−5.34560	−0.247896
$466$	−17.1151	−0.792843
$467$	−9.65297	−0.446686	−0.223343	−	0.974740i	$-0.571697\pi$
$467$	−9.65297	−0.446686	−0.223343	+	0.974740i	$0.571697\pi$
$468$	−8.61659	−0.398302
$469$	0	0
$470$	−3.47155	−0.160131
$471$	37.6457	1.73462
$472$	33.2807	1.53187
$473$	14.3503	0.659829
$474$	34.8039	1.59860
$475$	11.2025	0.514005
$476$	0	0
$477$	−28.9583	−1.32591
$478$	−15.9463	−0.729367
$479$	5.14848	0.235240	0.117620	−	0.993059i	$-0.462474\pi$
$479$	5.14848	0.235240	0.117620	+	0.993059i	$0.462474\pi$
$480$	18.4814	0.843558
$481$	−34.8964	−1.59114
$482$	12.8412	0.584903
$483$	0	0
$484$	2.27607	0.103458
$485$	−27.8407	−1.26418
$486$	2.09595	0.0950742
$487$	−41.3799	−1.87510	−0.937551	−	0.347847i	$-0.886913\pi$
$487$	−41.3799	−1.87510	−0.937551	+	0.347847i	$0.886913\pi$
$488$	31.3708	1.42009
$489$	42.7926	1.93515
$490$	0	0
$491$	0.425814	0.0192167	0.00960837	−	0.999954i	$-0.496942\pi$
$491$	0.425814	0.0192167	0.00960837	+	0.999954i	$0.496942\pi$
$492$	3.61961	0.163185
$493$	−18.4302	−0.830055
$494$	−6.86270	−0.308768
$495$	39.5668	1.77840
$496$	−1.49084	−0.0669405
$497$	0	0
$498$	2.41409	0.108178
$499$	−36.7654	−1.64584	−0.822922	−	0.568154i	$-0.807658\pi$
$499$	−36.7654	−1.64584	−0.822922	+	0.568154i	$0.807658\pi$
$500$	−6.77129	−0.302821
$501$	−0.582655	−0.0260311
$502$	2.62381	0.117106
$503$	−7.98940	−0.356230	−0.178115	−	0.984010i	$-0.557000\pi$
$503$	−7.98940	−0.356230	−0.178115	+	0.984010i	$0.557000\pi$
$504$	0	0
$505$	0.269946	0.0120124
$506$	6.13239	0.272618
$507$	−42.9338	−1.90676
$508$	−1.65266	−0.0733249
$509$	39.7557	1.76214	0.881070	−	0.472987i	$-0.156824\pi$
$509$	39.7557	1.76214	0.881070	+	0.472987i	$0.156824\pi$
$510$	43.1766	1.91189
$511$	0	0
$512$	25.3654	1.12100
$513$	−9.30522	−0.410836
$514$	3.19353	0.140861
$515$	−46.5013	−2.04909
$516$	7.26506	0.319827
$517$	1.05927	0.0465868
$518$	0	0
$519$	53.6480	2.35489
$520$	62.7400	2.75133
$521$	19.6450	0.860664	0.430332	−	0.902671i	$-0.358396\pi$
$521$	19.6450	0.860664	0.430332	+	0.902671i	$0.358396\pi$
$522$	54.5023	2.38550
$523$	−3.20781	−0.140268	−0.0701338	−	0.997538i	$-0.522343\pi$
$523$	−3.20781	−0.140268	−0.0701338	+	0.997538i	$0.522343\pi$
$524$	−2.31716	−0.101226
$525$	0	0
$526$	−2.39231	−0.104310
$527$	1.19228	0.0519366
$528$	16.4734	0.716915
$529$	−14.6588	−0.637340
$530$	25.1790	1.09371
$531$	67.8356	2.94382
$532$	0	0
$533$	23.1081	1.00092
$534$	45.2490	1.95812
$535$	−53.8534	−2.32829
$536$	−35.4504	−1.53122
$537$	−46.0391	−1.98673
$538$	−33.6697	−1.45160
$539$	0	0
$540$	10.1586	0.437156
$541$	−17.8218	−0.766220	−0.383110	−	0.923703i	$-0.625147\pi$
$541$	−17.8218	−0.766220	−0.383110	+	0.923703i	$0.625147\pi$
$542$	−17.4842	−0.751010
$543$	22.3304	0.958288
$544$	−4.12210	−0.176733
$545$	71.7345	3.07277
$546$	0	0
$547$	5.56646	0.238005	0.119002	−	0.992894i	$-0.462030\pi$
$547$	5.56646	0.238005	0.119002	+	0.992894i	$0.462030\pi$
$548$	−0.509636	−0.0217706
$549$	63.9427	2.72901
$550$	−23.7865	−1.01426
$551$	−6.81005	−0.290118
$552$	25.9986	1.10657
$553$	0	0
$554$	9.22633	0.391989
$555$	81.1247	3.44355
$556$	2.34985	0.0996560
$557$	−12.0788	−0.511795	−0.255897	−	0.966704i	$-0.582371\pi$
$557$	−12.0788	−0.511795	−0.255897	+	0.966704i	$0.582371\pi$
$558$	−3.52585	−0.149261
$559$	46.3811	1.96171
$560$	0	0
$561$	−13.1745	−0.556227
$562$	31.3758	1.32351
$563$	17.9554	0.756730	0.378365	−	0.925656i	$-0.376486\pi$
$563$	17.9554	0.756730	0.378365	+	0.925656i	$0.376486\pi$
$564$	0.536272	0.0225811
$565$	21.8616	0.919725
$566$	−42.0310	−1.76670
$567$	0	0
$568$	−10.8695	−0.456073
$569$	23.2302	0.973860	0.486930	−	0.873441i	$-0.338117\pi$
$569$	23.2302	0.973860	0.486930	+	0.873441i	$0.338117\pi$
$570$	15.9540	0.668238
$571$	−2.60448	−0.108994	−0.0544970	−	0.998514i	$-0.517356\pi$
$571$	−2.60448	−0.108994	−0.0544970	+	0.998514i	$0.517356\pi$
$572$	−2.28605	−0.0955847
$573$	−47.5164	−1.98503
$574$	0	0
$575$	−32.3540	−1.34925
$576$	53.3861	2.22442
$577$	35.5104	1.47832	0.739159	−	0.673531i	$-0.235223\pi$
$577$	35.5104	1.47832	0.739159	+	0.673531i	$0.235223\pi$
$578$	12.7220	0.529167
$579$	−37.3175	−1.55086
$580$	7.43459	0.308704
$581$	0	0
$582$	−27.4137	−1.13633
$583$	−7.68287	−0.318192
$584$	−19.3894	−0.802341
$585$	127.882	5.28728
$586$	13.8043	0.570252
$587$	13.2781	0.548047	0.274024	−	0.961723i	$-0.411645\pi$
$587$	13.2781	0.548047	0.274024	+	0.961723i	$0.411645\pi$
$588$	0	0
$589$	0.440553	0.0181527
$590$	−58.9826	−2.42828
$591$	−37.9296	−1.56022
$592$	22.6249	0.929878
$593$	−31.7766	−1.30491	−0.652455	−	0.757827i	$-0.726261\pi$
$593$	−31.7766	−1.30491	−0.652455	+	0.757827i	$0.726261\pi$
$594$	19.7580	0.810680
$595$	0	0
$596$	−0.622624	−0.0255037
$597$	−2.43170	−0.0995227
$598$	19.8202	0.810510
$599$	−15.6980	−0.641405	−0.320702	−	0.947180i	$-0.603919\pi$
$599$	−15.6980	−0.641405	−0.320702	+	0.947180i	$0.603919\pi$
$600$	−100.844	−4.11694
$601$	−8.25276	−0.336637	−0.168319	−	0.985733i	$-0.553834\pi$
$601$	−8.25276	−0.336637	−0.168319	+	0.985733i	$0.553834\pi$
$602$	0	0
$603$	−72.2582	−2.94258
$604$	0.867095	0.0352816
$605$	−33.7801	−1.37336
$606$	0.265805	0.0107976
$607$	−10.5423	−0.427899	−0.213949	−	0.976845i	$-0.568633\pi$
$607$	−10.5423	−0.427899	−0.213949	+	0.976845i	$0.568633\pi$
$608$	−1.52313	−0.0617712
$609$	0	0
$610$	−55.5978	−2.25109
$611$	3.42363	0.138505
$612$	−4.46777	−0.180599
$613$	10.5497	0.426100	0.213050	−	0.977041i	$-0.431660\pi$
$613$	10.5497	0.426100	0.213050	+	0.977041i	$0.431660\pi$
$614$	−15.2088	−0.613776
$615$	−53.7201	−2.16620
$616$	0	0
$617$	−31.8232	−1.28116	−0.640578	−	0.767893i	$-0.721305\pi$
$617$	−31.8232	−1.28116	−0.640578	+	0.767893i	$0.721305\pi$
$618$	−45.7881	−1.84187
$619$	48.2962	1.94119	0.970595	−	0.240720i	$-0.0773834\pi$
$619$	48.2962	1.94119	0.970595	+	0.240720i	$0.0773834\pi$
$620$	−0.480956	−0.0193156
$621$	26.8745	1.07844
$622$	24.7618	0.992858
$623$	0	0
$624$	53.2432	2.13143
$625$	44.4831	1.77932
$626$	6.61891	0.264545
$627$	−4.86803	−0.194410
$628$	3.38707	0.135159
$629$	−18.0940	−0.721457
$630$	0	0
$631$	4.94230	0.196750	0.0983750	−	0.995149i	$-0.468636\pi$
$631$	4.94230	0.196750	0.0983750	+	0.995149i	$0.468636\pi$
$632$	26.2228	1.04309
$633$	12.0990	0.480893
$634$	−24.3948	−0.968842
$635$	24.5278	0.973355
$636$	−3.88956	−0.154231
$637$	0	0
$638$	14.4599	0.572474
$639$	−22.1551	−0.876443
$640$	−34.1569	−1.35017
$641$	38.0533	1.50302	0.751508	−	0.659724i	$-0.229327\pi$
$641$	38.0533	1.50302	0.751508	+	0.659724i	$0.229327\pi$
$642$	−53.0274	−2.09282
$643$	−12.8821	−0.508019	−0.254009	−	0.967202i	$-0.581749\pi$
$643$	−12.8821	−0.508019	−0.254009	+	0.967202i	$0.581749\pi$
$644$	0	0
$645$	−107.824	−4.24555
$646$	−3.55837	−0.140002
$647$	−24.9667	−0.981543	−0.490772	−	0.871288i	$-0.663285\pi$
$647$	−24.9667	−0.981543	−0.490772	+	0.871288i	$0.663285\pi$
$648$	29.2339	1.14842
$649$	17.9974	0.706458
$650$	−76.8793	−3.01545
$651$	0	0
$652$	3.85015	0.150783
$653$	−35.0795	−1.37277	−0.686383	−	0.727240i	$-0.740803\pi$
$653$	−35.0795	−1.37277	−0.686383	+	0.727240i	$0.740803\pi$
$654$	70.6342	2.76201
$655$	34.3899	1.34373
$656$	−14.9820	−0.584949
$657$	−39.5213	−1.54187
$658$	0	0
$659$	−25.9992	−1.01278	−0.506392	−	0.862303i	$-0.669021\pi$
$659$	−25.9992	−1.01278	−0.506392	+	0.862303i	$0.669021\pi$
$660$	5.31446	0.206865
$661$	34.5021	1.34198	0.670988	−	0.741468i	$-0.265870\pi$
$661$	34.5021	1.34198	0.670988	+	0.741468i	$0.265870\pi$
$662$	10.4718	0.406999
$663$	−42.5807	−1.65370
$664$	1.81888	0.0705862
$665$	0	0
$666$	53.5082	2.07340
$667$	19.6682	0.761554
$668$	−0.0524227	−0.00202830
$669$	−76.6526	−2.96356
$670$	62.8280	2.42726
$671$	16.9645	0.654908
$672$	0	0
$673$	−14.0570	−0.541858	−0.270929	−	0.962599i	$-0.587331\pi$
$673$	−14.0570	−0.541858	−0.270929	+	0.962599i	$0.587331\pi$
$674$	11.0265	0.424723
$675$	−104.242	−4.01226
$676$	−3.86285	−0.148571
$677$	2.58630	0.0993997	0.0496999	−	0.998764i	$-0.484174\pi$
$677$	2.58630	0.0993997	0.0496999	+	0.998764i	$0.484174\pi$
$678$	21.5263	0.826712
$679$	0	0
$680$	32.5312	1.24751
$681$	−64.0229	−2.45336
$682$	−0.935437	−0.0358197
$683$	43.6180	1.66900	0.834498	−	0.551012i	$-0.185758\pi$
$683$	43.6180	1.66900	0.834498	+	0.551012i	$0.185758\pi$
$684$	−1.65086	−0.0631222
$685$	7.56372	0.288995
$686$	0	0
$687$	28.3764	1.08263
$688$	−30.0710	−1.14645
$689$	−24.8315	−0.946004
$690$	−46.0768	−1.75411
$691$	−8.52917	−0.324465	−0.162232	−	0.986753i	$-0.551869\pi$
$691$	−8.52917	−0.324465	−0.162232	+	0.986753i	$0.551869\pi$
$692$	4.82683	0.183489
$693$	0	0
$694$	16.9340	0.642804
$695$	−34.8751	−1.32289
$696$	61.3037	2.32371
$697$	11.9817	0.453840
$698$	8.03014	0.303945
$699$	−39.2389	−1.48415
$700$	0	0
$701$	−36.6789	−1.38534	−0.692671	−	0.721254i	$-0.743566\pi$
$701$	−36.6789	−1.38534	−0.692671	+	0.721254i	$0.743566\pi$
$702$	63.8590	2.41020
$703$	−6.68583	−0.252161
$704$	14.1638	0.533817
$705$	−7.95903	−0.299754
$706$	−15.5287	−0.584431
$707$	0	0
$708$	9.11143	0.342428
$709$	25.2002	0.946415	0.473208	−	0.880951i	$-0.343096\pi$
$709$	25.2002	0.946415	0.473208	+	0.880951i	$0.343096\pi$
$710$	19.2637	0.722955
$711$	53.4496	2.00452
$712$	34.0926	1.27768
$713$	−1.27237	−0.0476505
$714$	0	0
$715$	33.9282	1.26884
$716$	−4.14224	−0.154803
$717$	−36.5593	−1.36533
$718$	−26.1463	−0.975771
$719$	6.45827	0.240853	0.120426	−	0.992722i	$-0.461574\pi$
$719$	6.45827	0.240853	0.120426	+	0.992722i	$0.461574\pi$
$720$	−82.9119	−3.08994
$721$	0	0
$722$	−1.31483	−0.0489330
$723$	29.4404	1.09490
$724$	2.00911	0.0746681
$725$	−76.2894	−2.83332
$726$	−33.2620	−1.23447
$727$	−37.8391	−1.40338	−0.701688	−	0.712485i	$-0.747570\pi$
$727$	−37.8391	−1.40338	−0.701688	+	0.712485i	$0.747570\pi$
$728$	0	0
$729$	−24.5631	−0.909743
$730$	34.3635	1.27185
$731$	24.0490	0.889483
$732$	8.58854	0.317442
$733$	3.75562	0.138717	0.0693584	−	0.997592i	$-0.477905\pi$
$733$	3.75562	0.138717	0.0693584	+	0.997592i	$0.477905\pi$
$734$	15.9804	0.589846
$735$	0	0
$736$	4.39897	0.162148
$737$	−19.1707	−0.706162
$738$	−35.4326	−1.30429
$739$	−44.6922	−1.64403	−0.822015	−	0.569466i	$-0.807150\pi$
$739$	−44.6922	−1.64403	−0.822015	+	0.569466i	$0.807150\pi$
$740$	7.29897	0.268316
$741$	−15.7338	−0.577994
$742$	0	0
$743$	28.4487	1.04368	0.521841	−	0.853042i	$-0.325245\pi$
$743$	28.4487	1.04368	0.521841	+	0.853042i	$0.325245\pi$
$744$	−3.96583	−0.145395
$745$	9.24061	0.338550
$746$	−28.2108	−1.03287
$747$	3.70740	0.135647
$748$	−1.18534	−0.0433402
$749$	0	0
$750$	98.9540	3.61329
$751$	−45.3886	−1.65625	−0.828126	−	0.560541i	$-0.810593\pi$
$751$	−45.3886	−1.65625	−0.828126	+	0.560541i	$0.810593\pi$
$752$	−2.21970	−0.0809440
$753$	6.01546	0.219216
$754$	46.7354	1.70200
$755$	−12.8689	−0.468347
$756$	0	0
$757$	−23.7118	−0.861820	−0.430910	−	0.902395i	$-0.641807\pi$
$757$	−23.7118	−0.861820	−0.430910	+	0.902395i	$0.641807\pi$
$758$	0.733930	0.0266576
$759$	14.0594	0.510324
$760$	12.0204	0.436026
$761$	−42.0135	−1.52299	−0.761494	−	0.648172i	$-0.775534\pi$
$761$	−42.0135	−1.52299	−0.761494	+	0.648172i	$0.775534\pi$
$762$	24.1515	0.874918
$763$	0	0
$764$	−4.27515	−0.154670
$765$	66.3080	2.39737
$766$	−22.2666	−0.804526
$767$	58.1685	2.10034
$768$	19.2445	0.694425
$769$	−13.8751	−0.500348	−0.250174	−	0.968201i	$-0.580488\pi$
$769$	−13.8751	−0.500348	−0.250174	+	0.968201i	$0.580488\pi$
$770$	0	0
$771$	7.32163	0.263682
$772$	−3.35754	−0.120840
$773$	22.7374	0.817807	0.408904	−	0.912578i	$-0.365911\pi$
$773$	22.7374	0.817807	0.408904	+	0.912578i	$0.365911\pi$
$774$	−71.1183	−2.55629
$775$	4.93529	0.177281
$776$	−20.6547	−0.741459
$777$	0	0
$778$	8.20515	0.294169
$779$	4.42729	0.158624
$780$	17.1767	0.615023
$781$	−5.87794	−0.210329
$782$	10.2770	0.367503
$783$	63.3690	2.26462
$784$	0	0
$785$	−50.2689	−1.79417
$786$	33.8624	1.20783
$787$	−41.8083	−1.49030	−0.745152	−	0.666895i	$-0.767623\pi$
$787$	−41.8083	−1.49030	−0.745152	+	0.666895i	$0.767623\pi$
$788$	−3.41262	−0.121569
$789$	−5.48473	−0.195262
$790$	−46.4741	−1.65347
$791$	0	0
$792$	29.3541	1.04305
$793$	54.8304	1.94708
$794$	43.8761	1.55711
$795$	57.7266	2.04735
$796$	−0.218785	−0.00775463
$797$	−3.43467	−0.121662	−0.0608310	−	0.998148i	$-0.519375\pi$
$797$	−3.43467	−0.121662	−0.0608310	+	0.998148i	$0.519375\pi$
$798$	0	0
$799$	1.77518	0.0628014
$800$	−17.0629	−0.603263
$801$	69.4906	2.45533
$802$	41.5496	1.46717
$803$	−10.4853	−0.370019
$804$	−9.70545	−0.342285
$805$	0	0
$806$	−3.02339	−0.106494
$807$	−77.1927	−2.71731
$808$	0.200269	0.00704545
$809$	38.2871	1.34610	0.673052	−	0.739595i	$-0.264983\pi$
$809$	38.2871	1.34610	0.673052	+	0.739595i	$0.264983\pi$
$810$	−51.8107	−1.82044
$811$	−35.4750	−1.24570	−0.622848	−	0.782343i	$-0.714024\pi$
$811$	−35.4750	−1.24570	−0.622848	+	0.782343i	$0.714024\pi$
$812$	0	0
$813$	−40.0851	−1.40584
$814$	14.1962	0.497575
$815$	−57.1415	−2.00158
$816$	27.6070	0.966438
$817$	8.88620	0.310889
$818$	30.0863	1.05194
$819$	0	0
$820$	−4.83331	−0.168787
$821$	−8.01294	−0.279653	−0.139827	−	0.990176i	$-0.544655\pi$
$821$	−8.01294	−0.279653	−0.139827	+	0.990176i	$0.544655\pi$
$822$	7.44770	0.259768
$823$	−30.1673	−1.05157	−0.525783	−	0.850619i	$-0.676228\pi$
$823$	−30.1673	−1.05157	−0.525783	+	0.850619i	$0.676228\pi$
$824$	−34.4988	−1.20182
$825$	−54.5340	−1.89863
$826$	0	0
$827$	30.4531	1.05896	0.529479	−	0.848323i	$-0.322388\pi$
$827$	30.4531	1.05896	0.529479	+	0.848323i	$0.322388\pi$
$828$	4.76787	0.165695
$829$	6.26242	0.217503	0.108751	−	0.994069i	$-0.465315\pi$
$829$	6.26242	0.217503	0.108751	+	0.994069i	$0.465315\pi$
$830$	−3.22356	−0.111891
$831$	21.1527	0.733780
$832$	45.7782	1.58707
$833$	0	0
$834$	−34.3402	−1.18910
$835$	0.778027	0.0269247
$836$	−0.437987	−0.0151481
$837$	−4.09945	−0.141698
$838$	47.1247	1.62790
$839$	−6.86060	−0.236854	−0.118427	−	0.992963i	$-0.537785\pi$
$839$	−6.86060	−0.236854	−0.118427	+	0.992963i	$0.537785\pi$
$840$	0	0
$841$	17.3768	0.599199
$842$	−26.9446	−0.928572
$843$	71.9336	2.47752
$844$	1.08858	0.0374703
$845$	57.3301	1.97222
$846$	−5.24961	−0.180485
$847$	0	0
$848$	16.0994	0.552855
$849$	−96.3622	−3.30714
$850$	−39.8625	−1.36727
$851$	19.3094	0.661918
$852$	−2.97579	−0.101949
$853$	−26.9735	−0.923557	−0.461778	−	0.886995i	$-0.652788\pi$
$853$	−26.9735	−0.923557	−0.461778	+	0.886995i	$0.652788\pi$
$854$	0	0
$855$	24.5011	0.837919
$856$	−39.9532	−1.36557
$857$	−5.06697	−0.173084	−0.0865422	−	0.996248i	$-0.527582\pi$
$857$	−5.06697	−0.173084	−0.0865422	+	0.996248i	$0.527582\pi$
$858$	33.4078	1.14052
$859$	34.4157	1.17425	0.587125	−	0.809497i	$-0.300260\pi$
$859$	34.4157	1.17425	0.587125	+	0.809497i	$0.300260\pi$
$860$	−9.70114	−0.330806
$861$	0	0
$862$	24.2775	0.826895
$863$	−37.7836	−1.28617	−0.643084	−	0.765795i	$-0.722345\pi$
$863$	−37.7836	−1.28617	−0.643084	+	0.765795i	$0.722345\pi$
$864$	14.1731	0.482178
$865$	−71.6370	−2.43573
$866$	14.3348	0.487115
$867$	29.1671	0.990568
$868$	0	0
$869$	14.1806	0.481045
$870$	−108.647	−3.68349
$871$	−61.9609	−2.09946
$872$	53.2189	1.80222
$873$	−42.1002	−1.42488
$874$	3.79738	0.128448
$875$	0	0
$876$	−5.30835	−0.179353
$877$	−6.94742	−0.234598	−0.117299	−	0.993097i	$-0.537424\pi$
$877$	−6.94742	−0.234598	−0.117299	+	0.993097i	$0.537424\pi$
$878$	−15.7666	−0.532097
$879$	31.6485	1.06748
$880$	−21.9972	−0.741526
$881$	55.8959	1.88318	0.941591	−	0.336758i	$-0.109331\pi$
$881$	55.8959	1.88318	0.941591	+	0.336758i	$0.109331\pi$
$882$	0	0
$883$	42.1647	1.41895	0.709477	−	0.704729i	$-0.248931\pi$
$883$	42.1647	1.41895	0.709477	+	0.704729i	$0.248931\pi$
$884$	−3.83108	−0.128853
$885$	−135.226	−4.54558
$886$	−6.74057	−0.226454
$887$	−44.7081	−1.50115	−0.750575	−	0.660786i	$-0.770223\pi$
$887$	−44.7081	−1.50115	−0.750575	+	0.660786i	$0.770223\pi$
$888$	60.1854	2.01969
$889$	0	0
$890$	−60.4217	−2.02534
$891$	15.8090	0.529621
$892$	−6.89661	−0.230916
$893$	0.655937	0.0219501
$894$	9.09887	0.304312
$895$	61.4766	2.05494
$896$	0	0
$897$	45.4408	1.51722
$898$	10.9874	0.366654
$899$	−3.00019	−0.100062
$900$	−18.4937	−0.616458
$901$	−12.8753	−0.428939
$902$	−9.40057	−0.313005
$903$	0	0
$904$	16.2189	0.539431
$905$	−29.8181	−0.991186
$906$	−12.6715	−0.420983
$907$	20.3975	0.677287	0.338643	−	0.940915i	$-0.390032\pi$
$907$	20.3975	0.677287	0.338643	+	0.940915i	$0.390032\pi$
$908$	−5.76029	−0.191162
$909$	0.408207	0.0135394
$910$	0	0
$911$	−42.3351	−1.40262	−0.701312	−	0.712854i	$-0.747402\pi$
$911$	−42.3351	−1.40262	−0.701312	+	0.712854i	$0.747402\pi$
$912$	10.2009	0.337786
$913$	0.983605	0.0325526
$914$	17.8489	0.590389
$915$	−127.466	−4.21390
$916$	2.55309	0.0843564
$917$	0	0
$918$	33.1114	1.09284
$919$	48.4005	1.59659	0.798293	−	0.602270i	$-0.205737\pi$
$919$	48.4005	1.59659	0.798293	+	0.602270i	$0.205737\pi$
$920$	−34.7163	−1.14456
$921$	−34.8683	−1.14895
$922$	−48.7383	−1.60511
$923$	−18.9979	−0.625322
$924$	0	0
$925$	−74.8978	−2.46263
$926$	−13.9636	−0.458872
$927$	−70.3184	−2.30956
$928$	10.3726	0.340498
$929$	−58.1426	−1.90760	−0.953798	−	0.300449i	$-0.902864\pi$
$929$	−58.1426	−1.90760	−0.953798	+	0.300449i	$0.902864\pi$
$930$	7.02857	0.230476
$931$	0	0
$932$	−3.53041	−0.115643
$933$	56.7701	1.85857
$934$	12.6920	0.415296
$935$	17.5921	0.575322
$936$	94.8743	3.10106
$937$	0.198191	0.00647462	0.00323731	−	0.999995i	$-0.498970\pi$
$937$	0.198191	0.00647462	0.00323731	+	0.999995i	$0.498970\pi$
$938$	0	0
$939$	15.1748	0.495211
$940$	−0.716092	−0.0233563
$941$	11.8456	0.386157	0.193079	−	0.981183i	$-0.438153\pi$
$941$	11.8456	0.386157	0.193079	+	0.981183i	$0.438153\pi$
$942$	−49.4978	−1.61273
$943$	−12.7865	−0.416386
$944$	−37.7133	−1.22746
$945$	0	0
$946$	−18.8683	−0.613460
$947$	20.3829	0.662354	0.331177	−	0.943569i	$-0.392554\pi$
$947$	20.3829	0.662354	0.331177	+	0.943569i	$0.392554\pi$
$948$	7.17915	0.233168
$949$	−33.8892	−1.10009
$950$	−14.7294	−0.477884
$951$	−55.9287	−1.81361
$952$	0	0
$953$	25.0309	0.810831	0.405415	−	0.914133i	$-0.367127\pi$
$953$	25.0309	0.810831	0.405415	+	0.914133i	$0.367127\pi$
$954$	38.0752	1.23273
$955$	63.4493	2.05317
$956$	−3.28932	−0.106384
$957$	33.1515	1.07164
$958$	−6.76939	−0.218709
$959$	0	0
$960$	−106.422	−3.43476
$961$	−30.8059	−0.993739
$962$	45.8829	1.47932
$963$	−81.4361	−2.62424
$964$	2.64882	0.0853128
$965$	49.8305	1.60410
$966$	0	0
$967$	−55.7276	−1.79208	−0.896040	−	0.443973i	$-0.853569\pi$
$967$	−55.7276	−1.79208	−0.896040	+	0.443973i	$0.853569\pi$
$968$	−25.0611	−0.805493
$969$	−8.15807	−0.262075
$970$	36.6058	1.17534
$971$	38.0762	1.22192	0.610961	−	0.791661i	$-0.290783\pi$
$971$	38.0762	1.22192	0.610961	+	0.791661i	$0.290783\pi$
$972$	0.432341	0.0138673
$973$	0	0
$974$	54.4076	1.74333
$975$	−176.257	−5.64474
$976$	−35.5490	−1.13790
$977$	−38.7229	−1.23886	−0.619428	−	0.785053i	$-0.712635\pi$
$977$	−38.7229	−1.23886	−0.619428	+	0.785053i	$0.712635\pi$
$978$	−56.2651	−1.79916
$979$	18.4365	0.589232
$980$	0	0
$981$	108.476	3.46336
$982$	−0.559874	−0.0178663
$983$	30.0635	0.958876	0.479438	−	0.877576i	$-0.340840\pi$
$983$	30.0635	0.958876	0.479438	+	0.877576i	$0.340840\pi$
$984$	−39.8542	−1.27051
$985$	50.6480	1.61378
$986$	24.2326	0.771725
$987$	0	0
$988$	−1.41560	−0.0450363
$989$	−25.6643	−0.816078
$990$	−52.0237	−1.65342
$991$	−19.1158	−0.607233	−0.303617	−	0.952794i	$-0.598194\pi$
$991$	−19.1158	−0.607233	−0.303617	+	0.952794i	$0.598194\pi$
$992$	−0.671021	−0.0213049
$993$	24.0082	0.761877
$994$	0	0
$995$	3.24708	0.102939
$996$	0.497964	0.0157786
$997$	43.3237	1.37208	0.686038	−	0.727565i	$-0.259348\pi$
$997$	43.3237	1.37208	0.686038	+	0.727565i	$0.259348\pi$
$998$	48.3403	1.53019
$999$	62.2131	1.96834

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.q.1.4	yes	10
3.2	odd	2		8379.2.a.cs.1.7		10
7.2	even	3		931.2.f.q.704.7		20
7.3	odd	6		931.2.f.r.324.7		20
7.4	even	3		931.2.f.q.324.7		20
7.5	odd	6		931.2.f.r.704.7		20
7.6	odd	2		931.2.a.p.1.4	✓	10
21.20	even	2		8379.2.a.ct.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.4	✓	10	7.6	odd	2
931.2.a.q.1.4	yes	10	1.1	even	1	trivial
931.2.f.q.324.7		20	7.4	even	3
931.2.f.q.704.7		20	7.2	even	3
931.2.f.r.324.7		20	7.3	odd	6
931.2.f.r.704.7		20	7.5	odd	6
8379.2.a.cs.1.7		10	3.2	odd	2
8379.2.a.ct.1.7		10	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-1.31483 q^{2} -3.01444 q^{3} -0.271216 q^{4} +4.02523 q^{5} +3.96349 q^{6} +2.98627 q^{8} +6.08688 q^{9} +O(q^{10})\)	\(q-1.31483 q^{2} -3.01444 q^{3} -0.271216 q^{4} +4.02523 q^{5} +3.96349 q^{6} +2.98627 q^{8} +6.08688 q^{9} -5.29250 q^{10} +1.61490 q^{11} +0.817567 q^{12} +5.21945 q^{13} -12.1338 q^{15} -3.38401 q^{16} +2.70633 q^{17} -8.00322 q^{18} +1.00000 q^{19} -1.09171 q^{20} -2.12332 q^{22} -2.88811 q^{23} -9.00194 q^{24} +11.2025 q^{25} -6.86270 q^{26} -9.30522 q^{27} -6.81005 q^{29} +15.9540 q^{30} +0.440553 q^{31} -1.52313 q^{32} -4.86803 q^{33} -3.55837 q^{34} -1.65086 q^{36} -6.68583 q^{37} -1.31483 q^{38} -15.7338 q^{39} +12.0204 q^{40} +4.42729 q^{41} +8.88620 q^{43} -0.437987 q^{44} +24.5011 q^{45} +3.79738 q^{46} +0.655937 q^{47} +10.2009 q^{48} -14.7294 q^{50} -8.15807 q^{51} -1.41560 q^{52} -4.75749 q^{53} +12.2348 q^{54} +6.50034 q^{55} -3.01444 q^{57} +8.95407 q^{58} +11.1446 q^{59} +3.29089 q^{60} +10.5050 q^{61} -0.579254 q^{62} +8.77068 q^{64} +21.0095 q^{65} +6.40064 q^{66} -11.8711 q^{67} -0.734000 q^{68} +8.70605 q^{69} -3.63982 q^{71} +18.1771 q^{72} -6.49287 q^{73} +8.79074 q^{74} -33.7692 q^{75} -0.271216 q^{76} +20.6872 q^{78} +8.78112 q^{79} -13.6214 q^{80} +9.78945 q^{81} -5.82115 q^{82} +0.609081 q^{83} +10.8936 q^{85} -11.6839 q^{86} +20.5285 q^{87} +4.82252 q^{88} +11.4165 q^{89} -32.2148 q^{90} +0.783303 q^{92} -1.32802 q^{93} -0.862447 q^{94} +4.02523 q^{95} +4.59140 q^{96} -6.91655 q^{97} +9.82970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

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