LMFDB - Embedded newform 931.2.a.o.1.3

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 $ x^7 - 3x^6 - 6x^5 + 18x^4 + 4x^3 - 12*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.00704$ 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)

$f(q)$	$=$	$q-0.812652 q^{2} -0.415454 q^{3} -1.33960 q^{4} +2.67449 q^{5} +0.337619 q^{6} +2.71393 q^{8} -2.82740 q^{9} +O(q^{10})$	\(q-0.812652 q^{2} -0.415454 q^{3} -1.33960 q^{4} +2.67449 q^{5} +0.337619 q^{6} +2.71393 q^{8} -2.82740 q^{9} -2.17343 q^{10} -0.776233 q^{11} +0.556541 q^{12} +3.59863 q^{13} -1.11113 q^{15} +0.473713 q^{16} -0.325508 q^{17} +2.29769 q^{18} -1.00000 q^{19} -3.58274 q^{20} +0.630807 q^{22} +7.39803 q^{23} -1.12751 q^{24} +2.15291 q^{25} -2.92444 q^{26} +2.42102 q^{27} -3.12522 q^{29} +0.902960 q^{30} -2.63844 q^{31} -5.81282 q^{32} +0.322489 q^{33} +0.264525 q^{34} +3.78757 q^{36} +5.87329 q^{37} +0.812652 q^{38} -1.49507 q^{39} +7.25838 q^{40} -1.62530 q^{41} +6.67371 q^{43} +1.03984 q^{44} -7.56185 q^{45} -6.01202 q^{46} +2.04904 q^{47} -0.196806 q^{48} -1.74956 q^{50} +0.135234 q^{51} -4.82072 q^{52} +8.92812 q^{53} -1.96744 q^{54} -2.07603 q^{55} +0.415454 q^{57} +2.53971 q^{58} -8.72385 q^{59} +1.48846 q^{60} +7.04965 q^{61} +2.14413 q^{62} +3.77638 q^{64} +9.62452 q^{65} -0.262071 q^{66} +12.5731 q^{67} +0.436050 q^{68} -3.07354 q^{69} +14.3336 q^{71} -7.67336 q^{72} +13.8947 q^{73} -4.77294 q^{74} -0.894433 q^{75} +1.33960 q^{76} +1.21497 q^{78} -3.88509 q^{79} +1.26694 q^{80} +7.47637 q^{81} +1.32081 q^{82} -8.81575 q^{83} -0.870569 q^{85} -5.42340 q^{86} +1.29838 q^{87} -2.10664 q^{88} +5.40154 q^{89} +6.14515 q^{90} -9.91037 q^{92} +1.09615 q^{93} -1.66516 q^{94} -2.67449 q^{95} +2.41496 q^{96} +16.5714 q^{97} +2.19472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9	$ 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} + 22 q^{12} - 6 q^{13} + 2 q^{15} + 24 q^{16} - 19 q^{17} - 12 q^{18} - 7 q^{19} + 8 q^{20} - 6 q^{22} - q^{23} - 20 q^{24} - 3 q^{25} - 12 q^{26} + 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} + 14 q^{33} - 6 q^{34} + 46 q^{36} + 8 q^{37} - 2 q^{38} + 16 q^{39} + 10 q^{40} + 4 q^{41} + 4 q^{43} + 26 q^{44} - 14 q^{45} - 16 q^{46} - 5 q^{47} + 28 q^{48} + 16 q^{50} - 4 q^{51} - 42 q^{52} + 20 q^{53} + 24 q^{54} + 30 q^{55} - 2 q^{57} + 16 q^{59} - 44 q^{60} - 5 q^{61} - 24 q^{62} + 32 q^{64} + 26 q^{65} - 68 q^{66} - 4 q^{67} - 22 q^{68} + 36 q^{69} + 12 q^{71} - 3 q^{73} - 4 q^{74} - 18 q^{75} - 10 q^{76} - 14 q^{78} - 20 q^{79} + 4 q^{80} + 27 q^{81} + 48 q^{82} + 11 q^{83} + 26 q^{85} + 36 q^{86} + 16 q^{87} - 32 q^{88} + 10 q^{89} - 32 q^{90} - 30 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{95} + 12 q^{96} + 4 q^{97} + 15 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 + 22 * q^12 - 6 * q^13 + 2 * q^15 + 24 * q^16 - 19 * q^17 - 12 * q^18 - 7 * q^19 + 8 * q^20 - 6 * q^22 - q^23 - 20 * q^24 - 3 * q^25 - 12 * q^26 + 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 + 14 * q^33 - 6 * q^34 + 46 * q^36 + 8 * q^37 - 2 * q^38 + 16 * q^39 + 10 * q^40 + 4 * q^41 + 4 * q^43 + 26 * q^44 - 14 * q^45 - 16 * q^46 - 5 * q^47 + 28 * q^48 + 16 * q^50 - 4 * q^51 - 42 * q^52 + 20 * q^53 + 24 * q^54 + 30 * q^55 - 2 * q^57 + 16 * q^59 - 44 * q^60 - 5 * q^61 - 24 * q^62 + 32 * q^64 + 26 * q^65 - 68 * q^66 - 4 * q^67 - 22 * q^68 + 36 * q^69 + 12 * q^71 - 3 * q^73 - 4 * q^74 - 18 * q^75 - 10 * q^76 - 14 * q^78 - 20 * q^79 + 4 * q^80 + 27 * q^81 + 48 * q^82 + 11 * q^83 + 26 * q^85 + 36 * q^86 + 16 * q^87 - 32 * q^88 + 10 * q^89 - 32 * q^90 - 30 * q^92 - 4 * q^93 - 16 * q^94 - 2 * q^95 + 12 * q^96 + 4 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.812652	−0.574632	−0.287316	−	0.957836i	$-0.592763\pi$
$2$	−0.812652	−0.574632	−0.287316	+	0.957836i	$0.592763\pi$
$3$	−0.415454	−0.239862	−0.119931	−	0.992782i	$-0.538267\pi$
$3$	−0.415454	−0.239862	−0.119931	+	0.992782i	$0.538267\pi$
$4$	−1.33960	−0.669798
$5$	2.67449	1.19607	0.598035	−	0.801470i	$-0.295949\pi$
$5$	2.67449	1.19607	0.598035	+	0.801470i	$0.295949\pi$
$6$	0.337619	0.137833
$7$	0	0
$7$	0	0
$8$	2.71393	0.959519
$9$	−2.82740	−0.942466
$10$	−2.17343	−0.687299
$11$	−0.776233	−0.234043	−0.117022	−	0.993129i	$-0.537335\pi$
$11$	−0.776233	−0.234043	−0.117022	+	0.993129i	$0.537335\pi$
$12$	0.556541	0.160659
$13$	3.59863	0.998082	0.499041	−	0.866578i	$-0.333686\pi$
$13$	3.59863	0.998082	0.499041	+	0.866578i	$0.333686\pi$
$14$	0	0
$15$	−1.11113	−0.286892
$16$	0.473713	0.118428
$17$	−0.325508	−0.0789473	−0.0394737	−	0.999221i	$-0.512568\pi$
$17$	−0.325508	−0.0789473	−0.0394737	+	0.999221i	$0.512568\pi$
$18$	2.29769	0.541571
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.58274	−0.801125
$21$	0	0
$22$	0.630807	0.134489
$23$	7.39803	1.54260	0.771298	−	0.636475i	$-0.219608\pi$
$23$	7.39803	1.54260	0.771298	+	0.636475i	$0.219608\pi$
$24$	−1.12751	−0.230153
$25$	2.15291	0.430581
$26$	−2.92444	−0.573529
$27$	2.42102	0.465925
$28$	0	0
$29$	−3.12522	−0.580338	−0.290169	−	0.956975i	$-0.593712\pi$
$29$	−3.12522	−0.580338	−0.290169	+	0.956975i	$0.593712\pi$
$30$	0.902960	0.164857
$31$	−2.63844	−0.473877	−0.236939	−	0.971525i	$-0.576144\pi$
$31$	−2.63844	−0.473877	−0.236939	+	0.971525i	$0.576144\pi$
$32$	−5.81282	−1.02757
$33$	0.322489	0.0561381
$34$	0.264525	0.0453656
$35$	0	0
$36$	3.78757	0.631262
$37$	5.87329	0.965563	0.482782	−	0.875741i	$-0.339626\pi$
$37$	5.87329	0.965563	0.482782	+	0.875741i	$0.339626\pi$
$38$	0.812652	0.131830
$39$	−1.49507	−0.239402
$40$	7.25838	1.14765
$41$	−1.62530	−0.253830	−0.126915	−	0.991914i	$-0.540508\pi$
$41$	−1.62530	−0.253830	−0.126915	+	0.991914i	$0.540508\pi$
$42$	0	0
$43$	6.67371	1.01773	0.508865	−	0.860846i	$-0.330065\pi$
$43$	6.67371	1.01773	0.508865	+	0.860846i	$0.330065\pi$
$44$	1.03984	0.156762
$45$	−7.56185	−1.12725
$46$	−6.01202	−0.886424
$47$	2.04904	0.298884	0.149442	−	0.988771i	$-0.452252\pi$
$47$	2.04904	0.298884	0.149442	+	0.988771i	$0.452252\pi$
$48$	−0.196806	−0.0284065
$49$	0	0
$50$	−1.74956	−0.247426
$51$	0.135234	0.0189365
$52$	−4.82072	−0.668513
$53$	8.92812	1.22637	0.613186	−	0.789939i	$-0.289888\pi$
$53$	8.92812	1.22637	0.613186	+	0.789939i	$0.289888\pi$
$54$	−1.96744	−0.267735
$55$	−2.07603	−0.279932
$56$	0	0
$57$	0.415454	0.0550282
$58$	2.53971	0.333481
$59$	−8.72385	−1.13575	−0.567874	−	0.823115i	$-0.692234\pi$
$59$	−8.72385	−1.13575	−0.567874	+	0.823115i	$0.692234\pi$
$60$	1.48846	0.192160
$61$	7.04965	0.902616	0.451308	−	0.892368i	$-0.350958\pi$
$61$	7.04965	0.902616	0.451308	+	0.892368i	$0.350958\pi$
$62$	2.14413	0.272305
$63$	0	0
$64$	3.77638	0.472047
$65$	9.62452	1.19377
$66$	−0.262071	−0.0322588
$67$	12.5731	1.53605	0.768023	−	0.640423i	$-0.221241\pi$
$67$	12.5731	1.53605	0.768023	+	0.640423i	$0.221241\pi$
$68$	0.436050	0.0528788
$69$	−3.07354	−0.370011
$70$	0	0
$71$	14.3336	1.70108	0.850540	−	0.525910i	$-0.176275\pi$
$71$	14.3336	1.70108	0.850540	+	0.525910i	$0.176275\pi$
$72$	−7.67336	−0.904314
$73$	13.8947	1.62625	0.813123	−	0.582092i	$-0.197766\pi$
$73$	13.8947	1.62625	0.813123	+	0.582092i	$0.197766\pi$
$74$	−4.77294	−0.554843
$75$	−0.894433	−0.103280
$76$	1.33960	0.153662
$77$	0	0
$78$	1.21497	0.137568
$79$	−3.88509	−0.437107	−0.218553	−	0.975825i	$-0.570134\pi$
$79$	−3.88509	−0.437107	−0.218553	+	0.975825i	$0.570134\pi$
$80$	1.26694	0.141648
$81$	7.47637	0.830708
$82$	1.32081	0.145859
$83$	−8.81575	−0.967655	−0.483827	−	0.875163i	$-0.660754\pi$
$83$	−8.81575	−0.967655	−0.483827	+	0.875163i	$0.660754\pi$
$84$	0	0
$85$	−0.870569	−0.0944265
$86$	−5.42340	−0.584820
$87$	1.29838	0.139201
$88$	−2.10664	−0.224569
$89$	5.40154	0.572562	0.286281	−	0.958146i	$-0.407581\pi$
$89$	5.40154	0.572562	0.286281	+	0.958146i	$0.407581\pi$
$90$	6.14515	0.647756
$91$	0	0
$92$	−9.91037	−1.03323
$93$	1.09615	0.113665
$94$	−1.66516	−0.171748
$95$	−2.67449	−0.274397
$96$	2.41496	0.246476
$97$	16.5714	1.68257	0.841286	−	0.540590i	$-0.181799\pi$
$97$	16.5714	1.68257	0.841286	+	0.540590i	$0.181799\pi$
$98$	0	0
$99$	2.19472	0.220578
$100$	−2.88403	−0.288403
$101$	13.4438	1.33771	0.668853	−	0.743395i	$-0.266785\pi$
$101$	13.4438	1.33771	0.668853	+	0.743395i	$0.266785\pi$
$102$	−0.109898	−0.0108815
$103$	−18.2090	−1.79419	−0.897093	−	0.441841i	$-0.854325\pi$
$103$	−18.2090	−1.79419	−0.897093	+	0.441841i	$0.854325\pi$
$104$	9.76644	0.957678
$105$	0	0
$106$	−7.25545	−0.704712
$107$	−0.654916	−0.0633131	−0.0316566	−	0.999499i	$-0.510078\pi$
$107$	−0.654916	−0.0633131	−0.0316566	+	0.999499i	$0.510078\pi$
$108$	−3.24318	−0.312076
$109$	1.40305	0.134388	0.0671938	−	0.997740i	$-0.478595\pi$
$109$	1.40305	0.134388	0.0671938	+	0.997740i	$0.478595\pi$
$110$	1.68709	0.160858
$111$	−2.44008	−0.231602
$112$	0	0
$113$	17.5009	1.64635	0.823173	−	0.567791i	$-0.192202\pi$
$113$	17.5009	1.64635	0.823173	+	0.567791i	$0.192202\pi$
$114$	−0.337619	−0.0316210
$115$	19.7860	1.84505
$116$	4.18653	0.388710
$117$	−10.1748	−0.940658
$118$	7.08946	0.652637
$119$	0	0
$120$	−3.01552	−0.275278
$121$	−10.3975	−0.945224
$122$	−5.72892	−0.518672
$123$	0.675239	0.0608842
$124$	3.53444	0.317402
$125$	−7.61453	−0.681064
$126$	0	0
$127$	−10.2896	−0.913056	−0.456528	−	0.889709i	$-0.650907\pi$
$127$	−10.2896	−0.913056	−0.456528	+	0.889709i	$0.650907\pi$
$128$	8.55677	0.756318
$129$	−2.77262	−0.244115
$130$	−7.82138	−0.685981
$131$	−20.1701	−1.76227	−0.881135	−	0.472864i	$-0.843220\pi$
$131$	−20.1701	−1.76227	−0.881135	+	0.472864i	$0.843220\pi$
$132$	−0.432005	−0.0376012
$133$	0	0
$134$	−10.2175	−0.882660
$135$	6.47499	0.557278
$136$	−0.883407	−0.0757515
$137$	−1.99649	−0.170572	−0.0852858	−	0.996357i	$-0.527180\pi$
$137$	−1.99649	−0.170572	−0.0852858	+	0.996357i	$0.527180\pi$
$138$	2.49772	0.212620
$139$	7.12404	0.604253	0.302127	−	0.953268i	$-0.402303\pi$
$139$	7.12404	0.604253	0.302127	+	0.953268i	$0.402303\pi$
$140$	0	0
$141$	−0.851283	−0.0716910
$142$	−11.6482	−0.977495
$143$	−2.79338	−0.233594
$144$	−1.33937	−0.111615
$145$	−8.35837	−0.694125
$146$	−11.2915	−0.934492
$147$	0	0
$148$	−7.86784	−0.646733
$149$	−0.216824	−0.0177629	−0.00888145	−	0.999961i	$-0.502827\pi$
$149$	−0.216824	−0.0177629	−0.00888145	+	0.999961i	$0.502827\pi$
$150$	0.726863	0.0593481
$151$	−9.02699	−0.734606	−0.367303	−	0.930101i	$-0.619719\pi$
$151$	−9.02699	−0.734606	−0.367303	+	0.930101i	$0.619719\pi$
$152$	−2.71393	−0.220129
$153$	0.920341	0.0744052
$154$	0	0
$155$	−7.05647	−0.566790
$156$	2.00279	0.160351
$157$	−23.7041	−1.89180	−0.945898	−	0.324465i	$-0.894816\pi$
$157$	−23.7041	−1.89180	−0.945898	+	0.324465i	$0.894816\pi$
$158$	3.15723	0.251175
$159$	−3.70922	−0.294160
$160$	−15.5463	−1.22905
$161$	0	0
$162$	−6.07569	−0.477351
$163$	−13.8126	−1.08189	−0.540943	−	0.841059i	$-0.681933\pi$
$163$	−13.8126	−1.08189	−0.540943	+	0.841059i	$0.681933\pi$
$164$	2.17725	0.170015
$165$	0.862494	0.0671451
$166$	7.16414	0.556045
$167$	−1.71884	−0.133008	−0.0665041	−	0.997786i	$-0.521185\pi$
$167$	−1.71884	−0.133008	−0.0665041	+	0.997786i	$0.521185\pi$
$168$	0	0
$169$	−0.0498291	−0.00383300
$170$	0.707470	0.0542604
$171$	2.82740	0.216217
$172$	−8.94008	−0.681674
$173$	19.4541	1.47907	0.739533	−	0.673120i	$-0.235046\pi$
$173$	19.4541	1.47907	0.739533	+	0.673120i	$0.235046\pi$
$174$	−1.05513	−0.0799895
$175$	0	0
$176$	−0.367712	−0.0277173
$177$	3.62436	0.272423
$178$	−4.38957	−0.329012
$179$	7.90128	0.590569	0.295285	−	0.955409i	$-0.404586\pi$
$179$	7.90128	0.590569	0.295285	+	0.955409i	$0.404586\pi$
$180$	10.1298	0.755033
$181$	−13.4760	−1.00167	−0.500833	−	0.865544i	$-0.666973\pi$
$181$	−13.4760	−1.00167	−0.500833	+	0.865544i	$0.666973\pi$
$182$	0	0
$183$	−2.92881	−0.216504
$184$	20.0777	1.48015
$185$	15.7081	1.15488
$186$	−0.890787	−0.0653157
$187$	0.252670	0.0184771
$188$	−2.74489	−0.200192
$189$	0	0
$190$	2.17343	0.157677
$191$	−4.38725	−0.317450	−0.158725	−	0.987323i	$-0.550738\pi$
$191$	−4.38725	−0.317450	−0.158725	+	0.987323i	$0.550738\pi$
$192$	−1.56891	−0.113226
$193$	0.459974	0.0331096	0.0165548	−	0.999863i	$-0.494730\pi$
$193$	0.459974	0.0331096	0.0165548	+	0.999863i	$0.494730\pi$
$194$	−13.4668	−0.966859
$195$	−3.99854	−0.286342
$196$	0	0
$197$	9.13456	0.650811	0.325405	−	0.945575i	$-0.394499\pi$
$197$	9.13456	0.650811	0.325405	+	0.945575i	$0.394499\pi$
$198$	−1.78354	−0.126751
$199$	8.27347	0.586491	0.293245	−	0.956037i	$-0.405265\pi$
$199$	8.27347	0.586491	0.293245	+	0.956037i	$0.405265\pi$
$200$	5.84284	0.413151
$201$	−5.22353	−0.368440
$202$	−10.9251	−0.768688
$203$	0	0
$204$	−0.181159	−0.0126836
$205$	−4.34686	−0.303598
$206$	14.7976	1.03100
$207$	−20.9172	−1.45384
$208$	1.70472	0.118201
$209$	0.776233	0.0536932
$210$	0	0
$211$	0.184808	0.0127227	0.00636137	−	0.999980i	$-0.497975\pi$
$211$	0.184808	0.0127227	0.00636137	+	0.999980i	$0.497975\pi$
$212$	−11.9601	−0.821422
$213$	−5.95493	−0.408025
$214$	0.532219	0.0363817
$215$	17.8488	1.21728
$216$	6.57047	0.447064
$217$	0	0
$218$	−1.14019	−0.0772234
$219$	−5.77259	−0.390075
$220$	2.78104	0.187498
$221$	−1.17139	−0.0787959
$222$	1.98294	0.133086
$223$	15.0422	1.00730	0.503652	−	0.863907i	$-0.331990\pi$
$223$	15.0422	1.00730	0.503652	+	0.863907i	$0.331990\pi$
$224$	0	0
$225$	−6.08712	−0.405808
$226$	−14.2221	−0.946042
$227$	−5.10981	−0.339150	−0.169575	−	0.985517i	$-0.554240\pi$
$227$	−5.10981	−0.339150	−0.169575	+	0.985517i	$0.554240\pi$
$228$	−0.556541	−0.0368578
$229$	−17.5561	−1.16014	−0.580069	−	0.814567i	$-0.696975\pi$
$229$	−17.5561	−1.16014	−0.580069	+	0.814567i	$0.696975\pi$
$230$	−16.0791	−1.06022
$231$	0	0
$232$	−8.48162	−0.556846
$233$	6.71835	0.440134	0.220067	−	0.975485i	$-0.429372\pi$
$233$	6.71835	0.440134	0.220067	+	0.975485i	$0.429372\pi$
$234$	8.26855	0.540532
$235$	5.48015	0.357486
$236$	11.6864	0.760723
$237$	1.61408	0.104845
$238$	0	0
$239$	−22.7940	−1.47442	−0.737212	−	0.675662i	$-0.763858\pi$
$239$	−22.7940	−1.47442	−0.737212	+	0.675662i	$0.763858\pi$
$240$	−0.526356	−0.0339761
$241$	19.9138	1.28276	0.641379	−	0.767224i	$-0.278363\pi$
$241$	19.9138	1.28276	0.641379	+	0.767224i	$0.278363\pi$
$242$	8.44952	0.543156
$243$	−10.3691	−0.665180
$244$	−9.44369	−0.604571
$245$	0	0
$246$	−0.548734	−0.0349860
$247$	−3.59863	−0.228976
$248$	−7.16053	−0.454694
$249$	3.66254	0.232104
$250$	6.18796	0.391361
$251$	−10.6217	−0.670433	−0.335216	−	0.942141i	$-0.608809\pi$
$251$	−10.6217	−0.670433	−0.335216	+	0.942141i	$0.608809\pi$
$252$	0	0
$253$	−5.74259	−0.361034
$254$	8.36188	0.524671
$255$	0.361681	0.0226494
$256$	−14.5064	−0.906652
$257$	14.9646	0.933464	0.466732	−	0.884399i	$-0.345431\pi$
$257$	14.9646	0.933464	0.466732	+	0.884399i	$0.345431\pi$
$258$	2.25317	0.140276
$259$	0	0
$260$	−12.8930	−0.799588
$261$	8.83623	0.546949
$262$	16.3913	1.01266
$263$	26.0271	1.60490	0.802450	−	0.596719i	$-0.203529\pi$
$263$	26.0271	1.60490	0.802450	+	0.596719i	$0.203529\pi$
$264$	0.875213	0.0538656
$265$	23.8782	1.46682
$266$	0	0
$267$	−2.24409	−0.137336
$268$	−16.8428	−1.02884
$269$	−0.914869	−0.0557805	−0.0278903	−	0.999611i	$-0.508879\pi$
$269$	−0.914869	−0.0557805	−0.0278903	+	0.999611i	$0.508879\pi$
$270$	−5.26191	−0.320230
$271$	−27.7522	−1.68582	−0.842912	−	0.538051i	$-0.819161\pi$
$271$	−27.7522	−1.68582	−0.842912	+	0.538051i	$0.819161\pi$
$272$	−0.154197	−0.00934959
$273$	0	0
$274$	1.62245	0.0980159
$275$	−1.67116	−0.100775
$276$	4.11730	0.247833
$277$	−16.2469	−0.976179	−0.488089	−	0.872794i	$-0.662306\pi$
$277$	−16.2469	−0.976179	−0.488089	+	0.872794i	$0.662306\pi$
$278$	−5.78937	−0.347223
$279$	7.45991	0.446613
$280$	0	0
$281$	0.0584578	0.00348730	0.00174365	−	0.999998i	$-0.499445\pi$
$281$	0.0584578	0.00348730	0.00174365	+	0.999998i	$0.499445\pi$
$282$	0.691797	0.0411959
$283$	−8.06662	−0.479511	−0.239755	−	0.970833i	$-0.577067\pi$
$283$	−8.06662	−0.479511	−0.239755	+	0.970833i	$0.577067\pi$
$284$	−19.2012	−1.13938
$285$	1.11113	0.0658175
$286$	2.27004	0.134231
$287$	0	0
$288$	16.4352	0.968451
$289$	−16.8940	−0.993767
$290$	6.79244	0.398866
$291$	−6.88466	−0.403586
$292$	−18.6132	−1.08926
$293$	−9.93565	−0.580447	−0.290224	−	0.956959i	$-0.593730\pi$
$293$	−9.93565	−0.580447	−0.290224	+	0.956959i	$0.593730\pi$
$294$	0	0
$295$	−23.3319	−1.35843
$296$	15.9397	0.926477
$297$	−1.87927	−0.109046
$298$	0.176202	0.0102071
$299$	26.6228	1.53964
$300$	1.19818	0.0691770
$301$	0	0
$302$	7.33580	0.422128
$303$	−5.58527	−0.320865
$304$	−0.473713	−0.0271693
$305$	18.8542	1.07959
$306$	−0.747917	−0.0427556
$307$	−9.55008	−0.545052	−0.272526	−	0.962148i	$-0.587859\pi$
$307$	−9.55008	−0.545052	−0.272526	+	0.962148i	$0.587859\pi$
$308$	0	0
$309$	7.56500	0.430358
$310$	5.73446	0.325695
$311$	−6.03378	−0.342145	−0.171072	−	0.985258i	$-0.554723\pi$
$311$	−6.03378	−0.342145	−0.171072	+	0.985258i	$0.554723\pi$
$312$	−4.05751	−0.229711
$313$	−19.1208	−1.08077	−0.540386	−	0.841417i	$-0.681722\pi$
$313$	−19.1208	−1.08077	−0.540386	+	0.841417i	$0.681722\pi$
$314$	19.2632	1.08709
$315$	0	0
$316$	5.20445	0.292773
$317$	6.68265	0.375335	0.187668	−	0.982233i	$-0.439907\pi$
$317$	6.68265	0.375335	0.187668	+	0.982233i	$0.439907\pi$
$318$	3.01431	0.169034
$319$	2.42590	0.135824
$320$	10.0999	0.564601
$321$	0.272088	0.0151864
$322$	0	0
$323$	0.325508	0.0181118
$324$	−10.0153	−0.556407
$325$	7.74752	0.429755
$326$	11.2248	0.621686
$327$	−0.582902	−0.0322345
$328$	−4.41096	−0.243555
$329$	0	0
$330$	−0.700908	−0.0385837
$331$	−3.18440	−0.175030	−0.0875152	−	0.996163i	$-0.527893\pi$
$331$	−3.18440	−0.175030	−0.0875152	+	0.996163i	$0.527893\pi$
$332$	11.8096	0.648133
$333$	−16.6061	−0.910011
$334$	1.39682	0.0764307
$335$	33.6266	1.83722
$336$	0	0
$337$	−31.9364	−1.73969	−0.869844	−	0.493326i	$-0.835781\pi$
$337$	−31.9364	−1.73969	−0.869844	+	0.493326i	$0.835781\pi$
$338$	0.0404937	0.00220257
$339$	−7.27081	−0.394896
$340$	1.16621	0.0632467
$341$	2.04804	0.110908
$342$	−2.29769	−0.124245
$343$	0	0
$344$	18.1120	0.976532
$345$	−8.22016	−0.442558
$346$	−15.8094	−0.849919
$347$	−8.71229	−0.467700	−0.233850	−	0.972273i	$-0.575133\pi$
$347$	−8.71229	−0.467700	−0.233850	+	0.972273i	$0.575133\pi$
$348$	−1.73931	−0.0932368
$349$	−7.84439	−0.419901	−0.209950	−	0.977712i	$-0.567330\pi$
$349$	−7.84439	−0.419901	−0.209950	+	0.977712i	$0.567330\pi$
$350$	0	0
$351$	8.71235	0.465031
$352$	4.51211	0.240496
$353$	−7.70723	−0.410214	−0.205107	−	0.978740i	$-0.565754\pi$
$353$	−7.70723	−0.410214	−0.205107	+	0.978740i	$0.565754\pi$
$354$	−2.94534	−0.156543
$355$	38.3350	2.03461
$356$	−7.23588	−0.383501
$357$	0	0
$358$	−6.42099	−0.339360
$359$	13.0874	0.690728	0.345364	−	0.938469i	$-0.387755\pi$
$359$	13.0874	0.690728	0.345364	+	0.938469i	$0.387755\pi$
$360$	−20.5223	−1.08162
$361$	1.00000	0.0526316
$362$	10.9513	0.575589
$363$	4.31967	0.226724
$364$	0	0
$365$	37.1611	1.94510
$366$	2.38010	0.124410
$367$	−11.0310	−0.575811	−0.287906	−	0.957659i	$-0.592959\pi$
$367$	−11.0310	−0.575811	−0.287906	+	0.957659i	$0.592959\pi$
$368$	3.50454	0.182687
$369$	4.59538	0.239226
$370$	−12.7652	−0.663631
$371$	0	0
$372$	−1.46840	−0.0761328
$373$	26.7768	1.38645	0.693226	−	0.720720i	$-0.256189\pi$
$373$	26.7768	1.38645	0.693226	+	0.720720i	$0.256189\pi$
$374$	−0.205333	−0.0106175
$375$	3.16349	0.163362
$376$	5.56096	0.286785
$377$	−11.2465	−0.579225
$378$	0	0
$379$	29.8101	1.53124	0.765622	−	0.643291i	$-0.222432\pi$
$379$	29.8101	1.53124	0.765622	+	0.643291i	$0.222432\pi$
$380$	3.58274	0.183791
$381$	4.27486	0.219008
$382$	3.56531	0.182417
$383$	−22.8918	−1.16972	−0.584858	−	0.811135i	$-0.698850\pi$
$383$	−22.8918	−1.16972	−0.584858	+	0.811135i	$0.698850\pi$
$384$	−3.55494	−0.181412
$385$	0	0
$386$	−0.373799	−0.0190259
$387$	−18.8692	−0.959177
$388$	−22.1990	−1.12698
$389$	27.3586	1.38714	0.693568	−	0.720391i	$-0.256038\pi$
$389$	27.3586	1.38714	0.693568	+	0.720391i	$0.256038\pi$
$390$	3.24942	0.164541
$391$	−2.40812	−0.121784
$392$	0	0
$393$	8.37975	0.422703
$394$	−7.42322	−0.373976
$395$	−10.3906	−0.522810
$396$	−2.94004	−0.147743
$397$	3.57302	0.179325	0.0896624	−	0.995972i	$-0.471421\pi$
$397$	3.57302	0.179325	0.0896624	+	0.995972i	$0.471421\pi$
$398$	−6.72345	−0.337016
$399$	0	0
$400$	1.01986	0.0509930
$401$	39.4060	1.96784	0.983921	−	0.178602i	$-0.0571576\pi$
$401$	39.4060	1.96784	0.983921	+	0.178602i	$0.0571576\pi$
$402$	4.24491	0.211717
$403$	−9.49477	−0.472968
$404$	−18.0092	−0.895993
$405$	19.9955	0.993584
$406$	0	0
$407$	−4.55904	−0.225983
$408$	0.367015	0.0181699
$409$	24.5723	1.21502	0.607512	−	0.794310i	$-0.292168\pi$
$409$	24.5723	1.21502	0.607512	+	0.794310i	$0.292168\pi$
$410$	3.53249	0.174457
$411$	0.829450	0.0409137
$412$	24.3927	1.20174
$413$	0	0
$414$	16.9984	0.835425
$415$	−23.5777	−1.15738
$416$	−20.9182	−1.02560
$417$	−2.95971	−0.144938
$418$	−0.630807	−0.0308538
$419$	12.2693	0.599393	0.299696	−	0.954035i	$-0.403115\pi$
$419$	12.2693	0.599393	0.299696	+	0.954035i	$0.403115\pi$
$420$	0	0
$421$	−17.9316	−0.873930	−0.436965	−	0.899478i	$-0.643947\pi$
$421$	−17.9316	−0.873930	−0.436965	+	0.899478i	$0.643947\pi$
$422$	−0.150185	−0.00731089
$423$	−5.79346	−0.281688
$424$	24.2303	1.17673
$425$	−0.700789	−0.0339932
$426$	4.83929	0.234464
$427$	0	0
$428$	0.877324	0.0424070
$429$	1.16052	0.0560304
$430$	−14.5048	−0.699486
$431$	23.5279	1.13330	0.566651	−	0.823958i	$-0.308239\pi$
$431$	23.5279	1.13330	0.566651	+	0.823958i	$0.308239\pi$
$432$	1.14687	0.0551786
$433$	−12.8377	−0.616940	−0.308470	−	0.951234i	$-0.599817\pi$
$433$	−12.8377	−0.616940	−0.308470	+	0.951234i	$0.599817\pi$
$434$	0	0
$435$	3.47252	0.166494
$436$	−1.87952	−0.0900126
$437$	−7.39803	−0.353896
$438$	4.69110	0.224150
$439$	−28.9808	−1.38318	−0.691590	−	0.722290i	$-0.743089\pi$
$439$	−28.9808	−1.38318	−0.691590	+	0.722290i	$0.743089\pi$
$440$	−5.63420	−0.268600
$441$	0	0
$442$	0.951928	0.0452786
$443$	−4.92200	−0.233852	−0.116926	−	0.993141i	$-0.537304\pi$
$443$	−4.92200	−0.233852	−0.116926	+	0.993141i	$0.537304\pi$
$444$	3.26873	0.155127
$445$	14.4464	0.684823
$446$	−12.2241	−0.578828
$447$	0.0900803	0.00426065
$448$	0	0
$449$	34.6319	1.63438	0.817189	−	0.576370i	$-0.195531\pi$
$449$	34.6319	1.63438	0.817189	+	0.576370i	$0.195531\pi$
$450$	4.94671	0.233190
$451$	1.26161	0.0594071
$452$	−23.4441	−1.10272
$453$	3.75030	0.176204
$454$	4.15250	0.194886
$455$	0	0
$456$	1.12751	0.0528006
$457$	−1.38413	−0.0647471	−0.0323735	−	0.999476i	$-0.510307\pi$
$457$	−1.38413	−0.0647471	−0.0323735	+	0.999476i	$0.510307\pi$
$458$	14.2670	0.666652
$459$	−0.788060	−0.0367835
$460$	−26.5052	−1.23581
$461$	−41.1947	−1.91863	−0.959315	−	0.282340i	$-0.908890\pi$
$461$	−41.1947	−1.91863	−0.959315	+	0.282340i	$0.908890\pi$
$462$	0	0
$463$	18.7796	0.872762	0.436381	−	0.899762i	$-0.356260\pi$
$463$	18.7796	0.872762	0.436381	+	0.899762i	$0.356260\pi$
$464$	−1.48046	−0.0687284
$465$	2.93164	0.135952
$466$	−5.45968	−0.252915
$467$	26.4277	1.22293	0.611464	−	0.791272i	$-0.290581\pi$
$467$	26.4277	1.22293	0.611464	+	0.791272i	$0.290581\pi$
$468$	13.6301	0.630051
$469$	0	0
$470$	−4.45346	−0.205423
$471$	9.84797	0.453771
$472$	−23.6759	−1.08977
$473$	−5.18035	−0.238193
$474$	−1.31168	−0.0602475
$475$	−2.15291	−0.0987821
$476$	0	0
$477$	−25.2433	−1.15581
$478$	18.5236	0.847251
$479$	−8.41420	−0.384454	−0.192227	−	0.981350i	$-0.561571\pi$
$479$	−8.41420	−0.384454	−0.192227	+	0.981350i	$0.561571\pi$
$480$	6.45879	0.294802
$481$	21.1358	0.963711
$482$	−16.1830	−0.737113
$483$	0	0
$484$	13.9284	0.633109
$485$	44.3201	2.01247
$486$	8.42650	0.382234
$487$	−24.3482	−1.10332	−0.551661	−	0.834069i	$-0.686006\pi$
$487$	−24.3482	−1.10332	−0.551661	+	0.834069i	$0.686006\pi$
$488$	19.1323	0.866077
$489$	5.73850	0.259504
$490$	0	0
$491$	1.35722	0.0612507	0.0306253	−	0.999531i	$-0.490250\pi$
$491$	1.35722	0.0612507	0.0306253	+	0.999531i	$0.490250\pi$
$492$	−0.904548	−0.0407802
$493$	1.01728	0.0458162
$494$	2.92444	0.131577
$495$	5.86976	0.263826
$496$	−1.24986	−0.0561204
$497$	0	0
$498$	−2.97637	−0.133374
$499$	−24.9253	−1.11581	−0.557904	−	0.829905i	$-0.688394\pi$
$499$	−24.9253	−1.11581	−0.557904	+	0.829905i	$0.688394\pi$
$500$	10.2004	0.456176
$501$	0.714100	0.0319036
$502$	8.63171	0.385252
$503$	15.9204	0.709855	0.354927	−	0.934894i	$-0.384506\pi$
$503$	15.9204	0.709855	0.354927	+	0.934894i	$0.384506\pi$
$504$	0	0
$505$	35.9553	1.59999
$506$	4.66673	0.207461
$507$	0.0207017	0.000919394 0
$508$	13.7839	0.611564
$509$	−40.2426	−1.78372	−0.891862	−	0.452309i	$-0.850601\pi$
$509$	−40.2426	−1.78372	−0.891862	+	0.452309i	$0.850601\pi$
$510$	−0.293921	−0.0130150
$511$	0	0
$512$	−5.32486	−0.235328
$513$	−2.42102	−0.106890
$514$	−12.1610	−0.536398
$515$	−48.6998	−2.14597
$516$	3.71419	0.163508
$517$	−1.59054	−0.0699517
$518$	0	0
$519$	−8.08228	−0.354773
$520$	26.1203	1.14545
$521$	16.8018	0.736099	0.368049	−	0.929806i	$-0.380026\pi$
$521$	16.8018	0.736099	0.368049	+	0.929806i	$0.380026\pi$
$522$	−7.18078	−0.314294
$523$	27.6857	1.21061	0.605305	−	0.795994i	$-0.293051\pi$
$523$	27.6857	1.21061	0.605305	+	0.795994i	$0.293051\pi$
$524$	27.0198	1.18037
$525$	0	0
$526$	−21.1510	−0.922227
$527$	0.858832	0.0374113
$528$	0.152767	0.00664834
$529$	31.7308	1.37960
$530$	−19.4047	−0.842884
$531$	24.6658	1.07040
$532$	0	0
$533$	−5.84888	−0.253343
$534$	1.82366	0.0789177
$535$	−1.75157	−0.0757269
$536$	34.1224	1.47386
$537$	−3.28262	−0.141655
$538$	0.743470	0.0320533
$539$	0	0
$540$	−8.67387	−0.373264
$541$	24.4224	1.05000	0.525000	−	0.851102i	$-0.324065\pi$
$541$	24.4224	1.05000	0.525000	+	0.851102i	$0.324065\pi$
$542$	22.5529	0.968728
$543$	5.59867	0.240262
$544$	1.89212	0.0811241
$545$	3.75244	0.160737
$546$	0	0
$547$	32.3690	1.38400	0.691999	−	0.721899i	$-0.256730\pi$
$547$	32.3690	1.38400	0.691999	+	0.721899i	$0.256730\pi$
$548$	2.67449	0.114249
$549$	−19.9322	−0.850685
$550$	1.35807	0.0579083
$551$	3.12522	0.133139
$552$	−8.34137	−0.355032
$553$	0	0
$554$	13.2030	0.560943
$555$	−6.52598	−0.277012
$556$	−9.54334	−0.404728
$557$	−12.4618	−0.528024	−0.264012	−	0.964519i	$-0.585046\pi$
$557$	−12.4618	−0.528024	−0.264012	+	0.964519i	$0.585046\pi$
$558$	−6.06231	−0.256638
$559$	24.0162	1.01578
$560$	0	0
$561$	−0.104973	−0.00443196
$562$	−0.0475058	−0.00200391
$563$	−3.19381	−0.134603	−0.0673015	−	0.997733i	$-0.521439\pi$
$563$	−3.19381	−0.134603	−0.0673015	+	0.997733i	$0.521439\pi$
$564$	1.14038	0.0480185
$565$	46.8060	1.96914
$566$	6.55536	0.275542
$567$	0	0
$568$	38.9003	1.63222
$569$	−3.89601	−0.163329	−0.0816645	−	0.996660i	$-0.526024\pi$
$569$	−3.89601	−0.163329	−0.0816645	+	0.996660i	$0.526024\pi$
$570$	−0.902960	−0.0378209
$571$	32.7650	1.37117	0.685586	−	0.727991i	$-0.259546\pi$
$571$	32.7650	1.37117	0.685586	+	0.727991i	$0.259546\pi$
$572$	3.74200	0.156461
$573$	1.82270	0.0761444
$574$	0	0
$575$	15.9273	0.664213
$576$	−10.6773	−0.444888
$577$	11.8245	0.492259	0.246130	−	0.969237i	$-0.420841\pi$
$577$	11.8245	0.492259	0.246130	+	0.969237i	$0.420841\pi$
$578$	13.7290	0.571050
$579$	−0.191098	−0.00794176
$580$	11.1968	0.464923
$581$	0	0
$582$	5.59483	0.231913
$583$	−6.93030	−0.287024
$584$	37.7091	1.56041
$585$	−27.2123	−1.12509
$586$	8.07423	0.333543
$587$	−4.35009	−0.179547	−0.0897737	−	0.995962i	$-0.528614\pi$
$587$	−4.35009	−0.179547	−0.0897737	+	0.995962i	$0.528614\pi$
$588$	0	0
$589$	2.63844	0.108715
$590$	18.9607	0.780599
$591$	−3.79499	−0.156105
$592$	2.78225	0.114350
$593$	−13.4135	−0.550827	−0.275414	−	0.961326i	$-0.588815\pi$
$593$	−13.4135	−0.550827	−0.275414	+	0.961326i	$0.588815\pi$
$594$	1.52719	0.0626615
$595$	0	0
$596$	0.290456	0.0118976
$597$	−3.43725	−0.140677
$598$	−21.6351	−0.884724
$599$	−0.499846	−0.0204232	−0.0102116	−	0.999948i	$-0.503251\pi$
$599$	−0.499846	−0.0204232	−0.0102116	+	0.999948i	$0.503251\pi$
$600$	−2.42743	−0.0990994
$601$	−29.2094	−1.19148	−0.595739	−	0.803178i	$-0.703141\pi$
$601$	−29.2094	−1.19148	−0.595739	+	0.803178i	$0.703141\pi$
$602$	0	0
$603$	−35.5491	−1.44767
$604$	12.0925	0.492038
$605$	−27.8079	−1.13055
$606$	4.53888	0.184379
$607$	−10.3886	−0.421662	−0.210831	−	0.977523i	$-0.567617\pi$
$607$	−10.3886	−0.421662	−0.210831	+	0.977523i	$0.567617\pi$
$608$	5.81282	0.235741
$609$	0	0
$610$	−15.3219	−0.620367
$611$	7.37376	0.298310
$612$	−1.23289	−0.0498365
$613$	−5.75183	−0.232314	−0.116157	−	0.993231i	$-0.537058\pi$
$613$	−5.75183	−0.232314	−0.116157	+	0.993231i	$0.537058\pi$
$614$	7.76089	0.313204
$615$	1.80592	0.0728218
$616$	0	0
$617$	8.80141	0.354331	0.177166	−	0.984181i	$-0.443307\pi$
$617$	8.80141	0.354331	0.177166	+	0.984181i	$0.443307\pi$
$618$	−6.14771	−0.247297
$619$	−10.3405	−0.415619	−0.207810	−	0.978169i	$-0.566633\pi$
$619$	−10.3405	−0.415619	−0.207810	+	0.978169i	$0.566633\pi$
$620$	9.45283	0.379635
$621$	17.9107	0.718733
$622$	4.90337	0.196607
$623$	0	0
$624$	−0.708232	−0.0283520
$625$	−31.1295	−1.24518
$626$	15.5386	0.621046
$627$	−0.322489	−0.0128790
$628$	31.7540	1.26712
$629$	−1.91181	−0.0762287
$630$	0	0
$631$	−11.7193	−0.466537	−0.233268	−	0.972412i	$-0.574942\pi$
$631$	−11.7193	−0.466537	−0.233268	+	0.972412i	$0.574942\pi$
$632$	−10.5439	−0.419412
$633$	−0.0767794	−0.00305171
$634$	−5.43067	−0.215680
$635$	−27.5195	−1.09208
$636$	4.96886	0.197028
$637$	0	0
$638$	−1.97141	−0.0780488
$639$	−40.5267	−1.60321
$640$	22.8850	0.904609
$641$	8.92703	0.352597	0.176298	−	0.984337i	$-0.443588\pi$
$641$	8.92703	0.352597	0.176298	+	0.984337i	$0.443588\pi$
$642$	−0.221112	−0.00872661
$643$	4.69125	0.185005	0.0925024	−	0.995712i	$-0.470513\pi$
$643$	4.69125	0.185005	0.0925024	+	0.995712i	$0.470513\pi$
$644$	0	0
$645$	−7.41534	−0.291979
$646$	−0.264525	−0.0104076
$647$	−22.7660	−0.895023	−0.447511	−	0.894278i	$-0.647690\pi$
$647$	−22.7660	−0.895023	−0.447511	+	0.894278i	$0.647690\pi$
$648$	20.2904	0.797080
$649$	6.77174	0.265814
$650$	−6.29604	−0.246951
$651$	0	0
$652$	18.5033	0.724646
$653$	−31.0267	−1.21417	−0.607084	−	0.794638i	$-0.707661\pi$
$653$	−31.0267	−1.21417	−0.607084	+	0.794638i	$0.707661\pi$
$654$	0.473696	0.0185230
$655$	−53.9448	−2.10780
$656$	−0.769927	−0.0300606
$657$	−39.2857	−1.53268
$658$	0	0
$659$	−41.6208	−1.62131	−0.810657	−	0.585521i	$-0.800890\pi$
$659$	−41.6208	−1.62131	−0.810657	+	0.585521i	$0.800890\pi$
$660$	−1.15539	−0.0449737
$661$	−42.1933	−1.64113	−0.820565	−	0.571554i	$-0.806341\pi$
$661$	−42.1933	−1.64113	−0.820565	+	0.571554i	$0.806341\pi$
$662$	2.58781	0.100578
$663$	0.486657	0.0189002
$664$	−23.9253	−0.928483
$665$	0	0
$666$	13.4950	0.522921
$667$	−23.1204	−0.895227
$668$	2.30256	0.0890886
$669$	−6.24936	−0.241614
$670$	−27.3267	−1.05572
$671$	−5.47217	−0.211251
$672$	0	0
$673$	−13.7641	−0.530569	−0.265284	−	0.964170i	$-0.585466\pi$
$673$	−13.7641	−0.530569	−0.265284	+	0.964170i	$0.585466\pi$
$674$	25.9532	0.999680
$675$	5.21222	0.200618
$676$	0.0667508	0.00256734
$677$	10.1128	0.388665	0.194332	−	0.980936i	$-0.437746\pi$
$677$	10.1128	0.388665	0.194332	+	0.980936i	$0.437746\pi$
$678$	5.90864	0.226920
$679$	0	0
$680$	−2.36266	−0.0906040
$681$	2.12289	0.0813494
$682$	−1.66434	−0.0637310
$683$	−40.1694	−1.53704	−0.768519	−	0.639827i	$-0.779006\pi$
$683$	−40.1694	−1.53704	−0.768519	+	0.639827i	$0.779006\pi$
$684$	−3.78757	−0.144821
$685$	−5.33960	−0.204016
$686$	0	0
$687$	7.29374	0.278274
$688$	3.16142	0.120528
$689$	32.1290	1.22402
$690$	6.68013	0.254308
$691$	−22.9646	−0.873614	−0.436807	−	0.899555i	$-0.643891\pi$
$691$	−22.9646	−0.873614	−0.436807	+	0.899555i	$0.643891\pi$
$692$	−26.0606	−0.990677
$693$	0	0
$694$	7.08006	0.268756
$695$	19.0532	0.722729
$696$	3.52372	0.133566
$697$	0.529050	0.0200392
$698$	6.37476	0.241288
$699$	−2.79117	−0.105572
$700$	0	0
$701$	21.3937	0.808028	0.404014	−	0.914753i	$-0.367615\pi$
$701$	21.3937	0.808028	0.404014	+	0.914753i	$0.367615\pi$
$702$	−7.08011	−0.267221
$703$	−5.87329	−0.221515
$704$	−2.93135	−0.110479
$705$	−2.27675	−0.0857474
$706$	6.26329	0.235722
$707$	0	0
$708$	−4.85518	−0.182469
$709$	30.0245	1.12759	0.563797	−	0.825913i	$-0.309340\pi$
$709$	30.0245	1.12759	0.563797	+	0.825913i	$0.309340\pi$
$710$	−31.1530	−1.16915
$711$	10.9847	0.411958
$712$	14.6594	0.549384
$713$	−19.5192	−0.731000
$714$	0	0
$715$	−7.47087	−0.279395
$716$	−10.5845	−0.395562
$717$	9.46987	0.353659
$718$	−10.6355	−0.396914
$719$	16.5061	0.615574	0.307787	−	0.951455i	$-0.400412\pi$
$719$	16.5061	0.615574	0.307787	+	0.951455i	$0.400412\pi$
$720$	−3.58215	−0.133499
$721$	0	0
$722$	−0.812652	−0.0302438
$723$	−8.27325	−0.307685
$724$	18.0525	0.670914
$725$	−6.72830	−0.249883
$726$	−3.51039	−0.130283
$727$	25.5691	0.948306	0.474153	−	0.880442i	$-0.342754\pi$
$727$	25.5691	0.948306	0.474153	+	0.880442i	$0.342754\pi$
$728$	0	0
$729$	−18.1212	−0.671156
$730$	−30.1991	−1.11772
$731$	−2.17235	−0.0803471
$732$	3.92342	0.145014
$733$	−8.61247	−0.318109	−0.159054	−	0.987270i	$-0.550845\pi$
$733$	−8.61247	−0.318109	−0.159054	+	0.987270i	$0.550845\pi$
$734$	8.96433	0.330880
$735$	0	0
$736$	−43.0034	−1.58513
$737$	−9.75963	−0.359501
$738$	−3.73445	−0.137467
$739$	−13.0819	−0.481226	−0.240613	−	0.970621i	$-0.577348\pi$
$739$	−13.0819	−0.481226	−0.240613	+	0.970621i	$0.577348\pi$
$740$	−21.0425	−0.773537
$741$	1.49507	0.0549227
$742$	0	0
$743$	−3.01016	−0.110432	−0.0552160	−	0.998474i	$-0.517585\pi$
$743$	−3.01016	−0.110432	−0.0552160	+	0.998474i	$0.517585\pi$
$744$	2.97487	0.109064
$745$	−0.579894	−0.0212457
$746$	−21.7603	−0.796699
$747$	24.9256	0.911982
$748$	−0.338476	−0.0123759
$749$	0	0
$750$	−2.57081	−0.0938728
$751$	39.6223	1.44584	0.722919	−	0.690933i	$-0.242800\pi$
$751$	39.6223	1.44584	0.722919	+	0.690933i	$0.242800\pi$
$752$	0.970658	0.0353963
$753$	4.41281	0.160812
$754$	9.13950	0.332841
$755$	−24.1426	−0.878640
$756$	0	0
$757$	−27.3743	−0.994935	−0.497467	−	0.867483i	$-0.665737\pi$
$757$	−27.3743	−0.994935	−0.497467	+	0.867483i	$0.665737\pi$
$758$	−24.2253	−0.879901
$759$	2.38578	0.0865984
$760$	−7.25838	−0.263289
$761$	23.5356	0.853165	0.426582	−	0.904449i	$-0.359717\pi$
$761$	23.5356	0.853165	0.426582	+	0.904449i	$0.359717\pi$
$762$	−3.47398	−0.125849
$763$	0	0
$764$	5.87715	0.212628
$765$	2.46145	0.0889937
$766$	18.6031	0.672156
$767$	−31.3940	−1.13357
$768$	6.02675	0.217472
$769$	12.9066	0.465424	0.232712	−	0.972546i	$-0.425240\pi$
$769$	12.9066	0.465424	0.232712	+	0.972546i	$0.425240\pi$
$770$	0	0
$771$	−6.21709	−0.223903
$772$	−0.616179	−0.0221768
$773$	25.1232	0.903619	0.451810	−	0.892114i	$-0.350779\pi$
$773$	25.1232	0.903619	0.451810	+	0.892114i	$0.350779\pi$
$774$	15.3341	0.551173
$775$	−5.68030	−0.204043
$776$	44.9736	1.61446
$777$	0	0
$778$	−22.2330	−0.797092
$779$	1.62530	0.0582326
$780$	5.35644	0.191791
$781$	−11.1262	−0.398126
$782$	1.95696	0.0699808
$783$	−7.56620	−0.270394
$784$	0	0
$785$	−63.3965	−2.26272
$786$	−6.80982	−0.242898
$787$	−29.1922	−1.04059	−0.520296	−	0.853986i	$-0.674178\pi$
$787$	−29.1922	−1.04059	−0.520296	+	0.853986i	$0.674178\pi$
$788$	−12.2366	−0.435912
$789$	−10.8131	−0.384955
$790$	8.44397	0.300423
$791$	0	0
$792$	5.95632	0.211648
$793$	25.3691	0.900884
$794$	−2.90362	−0.103046
$795$	−9.92028	−0.351836
$796$	−11.0831	−0.392831
$797$	−16.6956	−0.591388	−0.295694	−	0.955283i	$-0.595551\pi$
$797$	−16.6956	−0.591388	−0.295694	+	0.955283i	$0.595551\pi$
$798$	0	0
$799$	−0.666981	−0.0235961
$800$	−12.5145	−0.442453
$801$	−15.2723	−0.539620
$802$	−32.0234	−1.13078
$803$	−10.7855	−0.380612
$804$	6.99743	0.246780
$805$	0	0
$806$	7.71594	0.271782
$807$	0.380086	0.0133797
$808$	36.4855	1.28355
$809$	31.8024	1.11811	0.559057	−	0.829129i	$-0.311163\pi$
$809$	31.8024	1.11811	0.559057	+	0.829129i	$0.311163\pi$
$810$	−16.2494	−0.570945
$811$	13.2927	0.466771	0.233385	−	0.972384i	$-0.425020\pi$
$811$	13.2927	0.466771	0.233385	+	0.972384i	$0.425020\pi$
$812$	0	0
$813$	11.5298	0.404366
$814$	3.70492	0.129857
$815$	−36.9417	−1.29401
$816$	0.0640619	0.00224262
$817$	−6.67371	−0.233483
$818$	−19.9688	−0.698192
$819$	0	0
$820$	5.82304	0.203349
$821$	−10.7591	−0.375495	−0.187748	−	0.982217i	$-0.560119\pi$
$821$	−10.7591	−0.375495	−0.187748	+	0.982217i	$0.560119\pi$
$822$	−0.674054	−0.0235103
$823$	−4.65306	−0.162195	−0.0810977	−	0.996706i	$-0.525843\pi$
$823$	−4.65306	−0.162195	−0.0810977	+	0.996706i	$0.525843\pi$
$824$	−49.4180	−1.72156
$825$	0.694289	0.0241720
$826$	0	0
$827$	−40.8916	−1.42194	−0.710970	−	0.703222i	$-0.751744\pi$
$827$	−40.8916	−1.42194	−0.710970	+	0.703222i	$0.751744\pi$
$828$	28.0206	0.973782
$829$	17.0449	0.591993	0.295997	−	0.955189i	$-0.404348\pi$
$829$	17.0449	0.591993	0.295997	+	0.955189i	$0.404348\pi$
$830$	19.1604	0.665068
$831$	6.74982	0.234149
$832$	13.5898	0.471142
$833$	0	0
$834$	2.40521	0.0832858
$835$	−4.59703	−0.159087
$836$	−1.03984	−0.0359636
$837$	−6.38769	−0.220791
$838$	−9.97064	−0.344430
$839$	−30.4387	−1.05086	−0.525431	−	0.850836i	$-0.676096\pi$
$839$	−30.4387	−1.05086	−0.525431	+	0.850836i	$0.676096\pi$
$840$	0	0
$841$	−19.2330	−0.663208
$842$	14.5721	0.502188
$843$	−0.0242865	−0.000836472 0
$844$	−0.247569	−0.00852167
$845$	−0.133267	−0.00458454
$846$	4.70807	0.161867
$847$	0	0
$848$	4.22936	0.145237
$849$	3.35131	0.115017
$850$	0.569497	0.0195336
$851$	43.4508	1.48947
$852$	7.97721	0.273295
$853$	2.87727	0.0985157	0.0492579	−	0.998786i	$-0.484314\pi$
$853$	2.87727	0.0985157	0.0492579	+	0.998786i	$0.484314\pi$
$854$	0	0
$855$	7.56185	0.258610
$856$	−1.77740	−0.0607502
$857$	52.3613	1.78863	0.894315	−	0.447439i	$-0.147664\pi$
$857$	52.3613	1.78863	0.894315	+	0.447439i	$0.147664\pi$
$858$	−0.943099	−0.0321969
$859$	8.20928	0.280097	0.140049	−	0.990145i	$-0.455274\pi$
$859$	8.20928	0.280097	0.140049	+	0.990145i	$0.455274\pi$
$860$	−23.9102	−0.815330
$861$	0	0
$862$	−19.1200	−0.651231
$863$	−18.0505	−0.614448	−0.307224	−	0.951637i	$-0.599400\pi$
$863$	−18.0505	−0.614448	−0.307224	+	0.951637i	$0.599400\pi$
$864$	−14.0729	−0.478771
$865$	52.0298	1.76907
$866$	10.4326	0.354513
$867$	7.01870	0.238367
$868$	0	0
$869$	3.01573	0.102302
$870$	−2.82195	−0.0956730
$871$	45.2459	1.53310
$872$	3.80777	0.128947
$873$	−46.8540	−1.58577
$874$	6.01202	0.203360
$875$	0	0
$876$	7.73294	0.261272
$877$	3.24810	0.109681	0.0548403	−	0.998495i	$-0.482535\pi$
$877$	3.24810	0.109681	0.0548403	+	0.998495i	$0.482535\pi$
$878$	23.5513	0.794819
$879$	4.12781	0.139227
$880$	−0.983441	−0.0331518
$881$	−22.5210	−0.758751	−0.379375	−	0.925243i	$-0.623861\pi$
$881$	−22.5210	−0.758751	−0.379375	+	0.925243i	$0.623861\pi$
$882$	0	0
$883$	29.6749	0.998638	0.499319	−	0.866418i	$-0.333584\pi$
$883$	29.6749	0.998638	0.499319	+	0.866418i	$0.333584\pi$
$884$	1.56918	0.0527774
$885$	9.69332	0.325837
$886$	3.99988	0.134378
$887$	34.4511	1.15675	0.578377	−	0.815769i	$-0.303686\pi$
$887$	34.4511	1.15675	0.578377	+	0.815769i	$0.303686\pi$
$888$	−6.62221	−0.222227
$889$	0	0
$890$	−11.7399	−0.393521
$891$	−5.80341	−0.194421
$892$	−20.1505	−0.674690
$893$	−2.04904	−0.0685686
$894$	−0.0732039	−0.00244831
$895$	21.1319	0.706362
$896$	0	0
$897$	−11.0605	−0.369301
$898$	−28.1436	−0.939166
$899$	8.24568	0.275009
$900$	8.15429	0.271810
$901$	−2.90618	−0.0968188
$902$	−1.02525	−0.0341372
$903$	0	0
$904$	47.4962	1.57970
$905$	−36.0415	−1.19806
$906$	−3.04769	−0.101253
$907$	−33.8042	−1.12245	−0.561225	−	0.827664i	$-0.689670\pi$
$907$	−33.8042	−1.12245	−0.561225	+	0.827664i	$0.689670\pi$
$908$	6.84509	0.227162
$909$	−38.0109	−1.26074
$910$	0	0
$911$	22.5998	0.748764	0.374382	−	0.927274i	$-0.377855\pi$
$911$	22.5998	0.748764	0.374382	+	0.927274i	$0.377855\pi$
$912$	0.196806	0.00651689
$913$	6.84308	0.226473
$914$	1.12482	0.0372057
$915$	−7.83307	−0.258953
$916$	23.5181	0.777059
$917$	0	0
$918$	0.640419	0.0211370
$919$	−12.0533	−0.397600	−0.198800	−	0.980040i	$-0.563704\pi$
$919$	−12.0533	−0.397600	−0.198800	+	0.980040i	$0.563704\pi$
$920$	53.6977	1.77036
$921$	3.96762	0.130737
$922$	33.4770	1.10251
$923$	51.5812	1.69782
$924$	0	0
$925$	12.6447	0.415754
$926$	−15.2613	−0.501517
$927$	51.4841	1.69096
$928$	18.1663	0.596339
$929$	−53.3504	−1.75037	−0.875184	−	0.483790i	$-0.839260\pi$
$929$	−53.3504	−1.75037	−0.875184	+	0.483790i	$0.839260\pi$
$930$	−2.38240	−0.0781221
$931$	0	0
$932$	−8.99988	−0.294801
$933$	2.50676	0.0820676
$934$	−21.4765	−0.702733
$935$	0.675764	0.0220999
$936$	−27.6136	−0.902579
$937$	−33.0678	−1.08028	−0.540138	−	0.841576i	$-0.681628\pi$
$937$	−33.0678	−1.08028	−0.540138	+	0.841576i	$0.681628\pi$
$938$	0	0
$939$	7.94382	0.259237
$940$	−7.34119	−0.239443
$941$	−32.0887	−1.04606	−0.523030	−	0.852314i	$-0.675199\pi$
$941$	−32.0887	−1.04606	−0.523030	+	0.852314i	$0.675199\pi$
$942$	−8.00297	−0.260751
$943$	−12.0240	−0.391557
$944$	−4.13260	−0.134505
$945$	0	0
$946$	4.20982	0.136873
$947$	23.4621	0.762414	0.381207	−	0.924490i	$-0.375508\pi$
$947$	23.4621	0.762414	0.381207	+	0.924490i	$0.375508\pi$
$948$	−2.16221	−0.0702253
$949$	50.0018	1.62313
$950$	1.74956	0.0567633
$951$	−2.77633	−0.0900288
$952$	0	0
$953$	−20.5889	−0.666940	−0.333470	−	0.942761i	$-0.608220\pi$
$953$	−20.5889	−0.666940	−0.333470	+	0.942761i	$0.608220\pi$
$954$	20.5141	0.664167
$955$	−11.7337	−0.379693
$956$	30.5348	0.987567
$957$	−1.00785	−0.0325791
$958$	6.83781	0.220920
$959$	0	0
$960$	−4.19604	−0.135427
$961$	−24.0387	−0.775441
$962$	−17.1761	−0.553779
$963$	1.85171	0.0596705
$964$	−26.6764	−0.859189
$965$	1.23020	0.0396014
$966$	0	0
$967$	25.1770	0.809639	0.404819	−	0.914397i	$-0.367334\pi$
$967$	25.1770	0.809639	0.404819	+	0.914397i	$0.367334\pi$
$968$	−28.2180	−0.906960
$969$	−0.135234	−0.00434433
$970$	−36.0168	−1.15643
$971$	32.5727	1.04531	0.522654	−	0.852545i	$-0.324942\pi$
$971$	32.5727	1.04531	0.522654	+	0.852545i	$0.324942\pi$
$972$	13.8905	0.445537
$973$	0	0
$974$	19.7866	0.634003
$975$	−3.21874	−0.103082
$976$	3.33951	0.106895
$977$	−37.7675	−1.20829	−0.604145	−	0.796874i	$-0.706485\pi$
$977$	−37.7675	−1.20829	−0.604145	+	0.796874i	$0.706485\pi$
$978$	−4.66340	−0.149119
$979$	−4.19285	−0.134004
$980$	0	0
$981$	−3.96697	−0.126656
$982$	−1.10295	−0.0351966
$983$	45.7880	1.46041	0.730205	−	0.683228i	$-0.239424\pi$
$983$	45.7880	1.46041	0.730205	+	0.683228i	$0.239424\pi$
$984$	1.83255	0.0584196
$985$	24.4303	0.778414
$986$	−0.826698	−0.0263274
$987$	0	0
$988$	4.82072	0.153368
$989$	49.3723	1.56995
$990$	−4.77007	−0.151603
$991$	−16.3860	−0.520518	−0.260259	−	0.965539i	$-0.583808\pi$
$991$	−16.3860	−0.520518	−0.260259	+	0.965539i	$0.583808\pi$
$992$	15.3368	0.486943
$993$	1.32297	0.0419832
$994$	0	0
$995$	22.1273	0.701484
$996$	−4.90633	−0.155463
$997$	−38.6659	−1.22456	−0.612281	−	0.790640i	$-0.709748\pi$
$997$	−38.6659	−1.22456	−0.612281	+	0.790640i	$0.709748\pi$
$998$	20.2556	0.641179
$999$	14.2193	0.449880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.o.1.3		7
3.2	odd	2		8379.2.a.ck.1.5		7
7.2	even	3		931.2.f.p.704.5		14
7.3	odd	6		133.2.f.d.58.5	yes	14
7.4	even	3		931.2.f.p.324.5		14
7.5	odd	6		133.2.f.d.39.5	✓	14
7.6	odd	2		931.2.a.n.1.3		7
21.5	even	6		1197.2.j.l.172.3		14
21.17	even	6		1197.2.j.l.856.3		14
21.20	even	2		8379.2.a.cl.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.5	✓	14	7.5	odd	6
133.2.f.d.58.5	yes	14	7.3	odd	6
931.2.a.n.1.3		7	7.6	odd	2
931.2.a.o.1.3		7	1.1	even	1	trivial
931.2.f.p.324.5		14	7.4	even	3
931.2.f.p.704.5		14	7.2	even	3
1197.2.j.l.172.3		14	21.5	even	6
1197.2.j.l.856.3		14	21.17	even	6
8379.2.a.ck.1.5		7	3.2	odd	2
8379.2.a.cl.1.5		7	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)

\(f(q)\)	\(=\)	\(q-0.812652 q^{2} -0.415454 q^{3} -1.33960 q^{4} +2.67449 q^{5} +0.337619 q^{6} +2.71393 q^{8} -2.82740 q^{9} +O(q^{10})\)	\(q-0.812652 q^{2} -0.415454 q^{3} -1.33960 q^{4} +2.67449 q^{5} +0.337619 q^{6} +2.71393 q^{8} -2.82740 q^{9} -2.17343 q^{10} -0.776233 q^{11} +0.556541 q^{12} +3.59863 q^{13} -1.11113 q^{15} +0.473713 q^{16} -0.325508 q^{17} +2.29769 q^{18} -1.00000 q^{19} -3.58274 q^{20} +0.630807 q^{22} +7.39803 q^{23} -1.12751 q^{24} +2.15291 q^{25} -2.92444 q^{26} +2.42102 q^{27} -3.12522 q^{29} +0.902960 q^{30} -2.63844 q^{31} -5.81282 q^{32} +0.322489 q^{33} +0.264525 q^{34} +3.78757 q^{36} +5.87329 q^{37} +0.812652 q^{38} -1.49507 q^{39} +7.25838 q^{40} -1.62530 q^{41} +6.67371 q^{43} +1.03984 q^{44} -7.56185 q^{45} -6.01202 q^{46} +2.04904 q^{47} -0.196806 q^{48} -1.74956 q^{50} +0.135234 q^{51} -4.82072 q^{52} +8.92812 q^{53} -1.96744 q^{54} -2.07603 q^{55} +0.415454 q^{57} +2.53971 q^{58} -8.72385 q^{59} +1.48846 q^{60} +7.04965 q^{61} +2.14413 q^{62} +3.77638 q^{64} +9.62452 q^{65} -0.262071 q^{66} +12.5731 q^{67} +0.436050 q^{68} -3.07354 q^{69} +14.3336 q^{71} -7.67336 q^{72} +13.8947 q^{73} -4.77294 q^{74} -0.894433 q^{75} +1.33960 q^{76} +1.21497 q^{78} -3.88509 q^{79} +1.26694 q^{80} +7.47637 q^{81} +1.32081 q^{82} -8.81575 q^{83} -0.870569 q^{85} -5.42340 q^{86} +1.29838 q^{87} -2.10664 q^{88} +5.40154 q^{89} +6.14515 q^{90} -9.91037 q^{92} +1.09615 q^{93} -1.66516 q^{94} -2.67449 q^{95} +2.41496 q^{96} +16.5714 q^{97} +2.19472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} + 22 q^{12} - 6 q^{13} + 2 q^{15} + 24 q^{16} - 19 q^{17} - 12 q^{18} - 7 q^{19} + 8 q^{20} - 6 q^{22} - q^{23} - 20 q^{24} - 3 q^{25} - 12 q^{26} + 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} + 14 q^{33} - 6 q^{34} + 46 q^{36} + 8 q^{37} - 2 q^{38} + 16 q^{39} + 10 q^{40} + 4 q^{41} + 4 q^{43} + 26 q^{44} - 14 q^{45} - 16 q^{46} - 5 q^{47} + 28 q^{48} + 16 q^{50} - 4 q^{51} - 42 q^{52} + 20 q^{53} + 24 q^{54} + 30 q^{55} - 2 q^{57} + 16 q^{59} - 44 q^{60} - 5 q^{61} - 24 q^{62} + 32 q^{64} + 26 q^{65} - 68 q^{66} - 4 q^{67} - 22 q^{68} + 36 q^{69} + 12 q^{71} - 3 q^{73} - 4 q^{74} - 18 q^{75} - 10 q^{76} - 14 q^{78} - 20 q^{79} + 4 q^{80} + 27 q^{81} + 48 q^{82} + 11 q^{83} + 26 q^{85} + 36 q^{86} + 16 q^{87} - 32 q^{88} + 10 q^{89} - 32 q^{90} - 30 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{95} + 12 q^{96} + 4 q^{97} + 15 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 + 22 * q^12 - 6 * q^13 + 2 * q^15 + 24 * q^16 - 19 * q^17 - 12 * q^18 - 7 * q^19 + 8 * q^20 - 6 * q^22 - q^23 - 20 * q^24 - 3 * q^25 - 12 * q^26 + 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 + 14 * q^33 - 6 * q^34 + 46 * q^36 + 8 * q^37 - 2 * q^38 + 16 * q^39 + 10 * q^40 + 4 * q^41 + 4 * q^43 + 26 * q^44 - 14 * q^45 - 16 * q^46 - 5 * q^47 + 28 * q^48 + 16 * q^50 - 4 * q^51 - 42 * q^52 + 20 * q^53 + 24 * q^54 + 30 * q^55 - 2 * q^57 + 16 * q^59 - 44 * q^60 - 5 * q^61 - 24 * q^62 + 32 * q^64 + 26 * q^65 - 68 * q^66 - 4 * q^67 - 22 * q^68 + 36 * q^69 + 12 * q^71 - 3 * q^73 - 4 * q^74 - 18 * q^75 - 10 * q^76 - 14 * q^78 - 20 * q^79 + 4 * q^80 + 27 * q^81 + 48 * q^82 + 11 * q^83 + 26 * q^85 + 36 * q^86 + 16 * q^87 - 32 * q^88 + 10 * q^89 - 32 * q^90 - 30 * q^92 - 4 * q^93 - 16 * q^94 - 2 * q^95 + 12 * q^96 + 4 * q^97 + 15 * q^99

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