LMFDB - Embedded newform 1911.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.375116.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 7x^{2} + 2x - 2 $ x^5 - x^4 - 6x^3 + 7x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.44025$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14957 q^{2} +1.00000 q^{3} +2.62066 q^{4} +3.73093 q^{5} -2.14957 q^{6} -1.33415 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.14957 q^{2} +1.00000 q^{3} +2.62066 q^{4} +3.73093 q^{5} -2.14957 q^{6} -1.33415 q^{8} +1.00000 q^{9} -8.01989 q^{10} +0.528912 q^{11} +2.62066 q^{12} +1.00000 q^{13} +3.73093 q^{15} -2.37346 q^{16} +3.80524 q^{17} -2.14957 q^{18} -3.88050 q^{19} +9.77749 q^{20} -1.13693 q^{22} -2.43608 q^{23} -1.33415 q^{24} +8.91980 q^{25} -2.14957 q^{26} +1.00000 q^{27} -3.56822 q^{29} -8.01989 q^{30} +4.99412 q^{31} +7.77023 q^{32} +0.528912 q^{33} -8.17964 q^{34} +2.62066 q^{36} +9.45167 q^{37} +8.34141 q^{38} +1.00000 q^{39} -4.97763 q^{40} -5.21465 q^{41} +10.3457 q^{43} +1.38610 q^{44} +3.73093 q^{45} +5.23653 q^{46} -11.5477 q^{47} -2.37346 q^{48} -19.1738 q^{50} +3.80524 q^{51} +2.62066 q^{52} +7.62994 q^{53} -2.14957 q^{54} +1.97333 q^{55} -3.88050 q^{57} +7.67014 q^{58} +13.4643 q^{59} +9.77749 q^{60} +5.80524 q^{61} -10.7352 q^{62} -11.9558 q^{64} +3.73093 q^{65} -1.13693 q^{66} +6.15975 q^{67} +9.97225 q^{68} -2.43608 q^{69} -6.88638 q^{71} -1.33415 q^{72} -6.45597 q^{73} -20.3171 q^{74} +8.91980 q^{75} -10.1695 q^{76} -2.14957 q^{78} -3.70905 q^{79} -8.85520 q^{80} +1.00000 q^{81} +11.2093 q^{82} -2.16853 q^{83} +14.1971 q^{85} -22.2388 q^{86} -3.56822 q^{87} -0.705650 q^{88} +1.46383 q^{89} -8.01989 q^{90} -6.38413 q^{92} +4.99412 q^{93} +24.8227 q^{94} -14.4778 q^{95} +7.77023 q^{96} +11.6089 q^{97} +0.528912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{3} + 6 q^{4} + 3 q^{5} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^3 + 6 * q^4 + 3 * q^5 + 3 * q^8 + 5 * q^9	$ 5 q + 5 q^{3} + 6 q^{4} + 3 q^{5} + 3 q^{8} + 5 q^{9} + 2 q^{10} - q^{11} + 6 q^{12} + 5 q^{13} + 3 q^{15} + 13 q^{17} + 7 q^{19} + 13 q^{20} - 19 q^{22} - 4 q^{23} + 3 q^{24} + 16 q^{25} + 5 q^{27} - 12 q^{29} + 2 q^{30} + 6 q^{31} + 21 q^{32} - q^{33} + 7 q^{34} + 6 q^{36} + 11 q^{37} + 14 q^{38} + 5 q^{39} + 11 q^{40} + 10 q^{41} + 10 q^{43} - 29 q^{44} + 3 q^{45} + q^{46} - 4 q^{47} - 29 q^{50} + 13 q^{51} + 6 q^{52} - 9 q^{53} - 12 q^{55} + 7 q^{57} + 34 q^{58} + 7 q^{59} + 13 q^{60} + 23 q^{61} - 24 q^{62} - 13 q^{64} + 3 q^{65} - 19 q^{66} + 25 q^{67} + 20 q^{68} - 4 q^{69} - 27 q^{71} + 3 q^{72} + 18 q^{73} + 15 q^{74} + 16 q^{75} + 2 q^{76} + 8 q^{79} + 41 q^{80} + 5 q^{81} + 26 q^{82} + 12 q^{83} + 10 q^{85} - 19 q^{86} - 12 q^{87} - 36 q^{88} + 29 q^{89} + 2 q^{90} - 50 q^{92} + 6 q^{93} - 2 q^{94} - 33 q^{95} + 21 q^{96} + 13 q^{97} - q^{99}+O(q^{100}) $ 5 * q + 5 * q^3 + 6 * q^4 + 3 * q^5 + 3 * q^8 + 5 * q^9 + 2 * q^10 - q^11 + 6 * q^12 + 5 * q^13 + 3 * q^15 + 13 * q^17 + 7 * q^19 + 13 * q^20 - 19 * q^22 - 4 * q^23 + 3 * q^24 + 16 * q^25 + 5 * q^27 - 12 * q^29 + 2 * q^30 + 6 * q^31 + 21 * q^32 - q^33 + 7 * q^34 + 6 * q^36 + 11 * q^37 + 14 * q^38 + 5 * q^39 + 11 * q^40 + 10 * q^41 + 10 * q^43 - 29 * q^44 + 3 * q^45 + q^46 - 4 * q^47 - 29 * q^50 + 13 * q^51 + 6 * q^52 - 9 * q^53 - 12 * q^55 + 7 * q^57 + 34 * q^58 + 7 * q^59 + 13 * q^60 + 23 * q^61 - 24 * q^62 - 13 * q^64 + 3 * q^65 - 19 * q^66 + 25 * q^67 + 20 * q^68 - 4 * q^69 - 27 * q^71 + 3 * q^72 + 18 * q^73 + 15 * q^74 + 16 * q^75 + 2 * q^76 + 8 * q^79 + 41 * q^80 + 5 * q^81 + 26 * q^82 + 12 * q^83 + 10 * q^85 - 19 * q^86 - 12 * q^87 - 36 * q^88 + 29 * q^89 + 2 * q^90 - 50 * q^92 + 6 * q^93 - 2 * q^94 - 33 * q^95 + 21 * q^96 + 13 * q^97 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.14957	−1.51998	−0.759989	−	0.649937i	$-0.774795\pi$
$2$	−2.14957	−1.51998	−0.759989	+	0.649937i	$0.774795\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.62066	1.31033
$5$	3.73093	1.66852	0.834260	−	0.551371i	$-0.185895\pi$
$5$	3.73093	1.66852	0.834260	+	0.551371i	$0.185895\pi$
$6$	−2.14957	−0.877559
$7$	0	0
$7$	0	0
$8$	−1.33415	−0.471695
$9$	1.00000	0.333333
$10$	−8.01989	−2.53611
$11$	0.528912	0.159473	0.0797365	−	0.996816i	$-0.474592\pi$
$11$	0.528912	0.159473	0.0797365	+	0.996816i	$0.474592\pi$
$12$	2.62066	0.756519
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	3.73093	0.963321
$16$	−2.37346	−0.593365
$17$	3.80524	0.922907	0.461453	−	0.887164i	$-0.347328\pi$
$17$	3.80524	0.922907	0.461453	+	0.887164i	$0.347328\pi$
$18$	−2.14957	−0.506659
$19$	−3.88050	−0.890247	−0.445124	−	0.895469i	$-0.646840\pi$
$19$	−3.88050	−0.890247	−0.445124	+	0.895469i	$0.646840\pi$
$20$	9.77749	2.18631
$21$	0	0
$22$	−1.13693	−0.242395
$23$	−2.43608	−0.507957	−0.253979	−	0.967210i	$-0.581739\pi$
$23$	−2.43608	−0.507957	−0.253979	+	0.967210i	$0.581739\pi$
$24$	−1.33415	−0.272333
$25$	8.91980	1.78396
$26$	−2.14957	−0.421566
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.56822	−0.662602	−0.331301	−	0.943525i	$-0.607487\pi$
$29$	−3.56822	−0.662602	−0.331301	+	0.943525i	$0.607487\pi$
$30$	−8.01989	−1.46423
$31$	4.99412	0.896971	0.448485	−	0.893790i	$-0.351964\pi$
$31$	4.99412	0.896971	0.448485	+	0.893790i	$0.351964\pi$
$32$	7.77023	1.37360
$33$	0.528912	0.0920717
$34$	−8.17964	−1.40280
$35$	0	0
$36$	2.62066	0.436777
$37$	9.45167	1.55385	0.776923	−	0.629596i	$-0.216779\pi$
$37$	9.45167	1.55385	0.776923	+	0.629596i	$0.216779\pi$
$38$	8.34141	1.35316
$39$	1.00000	0.160128
$40$	−4.97763	−0.787032
$41$	−5.21465	−0.814392	−0.407196	−	0.913341i	$-0.633493\pi$
$41$	−5.21465	−0.814392	−0.407196	+	0.913341i	$0.633493\pi$
$42$	0	0
$43$	10.3457	1.57771	0.788853	−	0.614582i	$-0.210675\pi$
$43$	10.3457	1.57771	0.788853	+	0.614582i	$0.210675\pi$
$44$	1.38610	0.208962
$45$	3.73093	0.556174
$46$	5.23653	0.772084
$47$	−11.5477	−1.68441	−0.842204	−	0.539159i	$-0.818742\pi$
$47$	−11.5477	−1.68441	−0.842204	+	0.539159i	$0.818742\pi$
$48$	−2.37346	−0.342580
$49$	0	0
$50$	−19.1738	−2.71158
$51$	3.80524	0.532840
$52$	2.62066	0.363420
$53$	7.62994	1.04805	0.524026	−	0.851702i	$-0.324429\pi$
$53$	7.62994	1.04805	0.524026	+	0.851702i	$0.324429\pi$
$54$	−2.14957	−0.292520
$55$	1.97333	0.266084
$56$	0	0
$57$	−3.88050	−0.513984
$58$	7.67014	1.00714
$59$	13.4643	1.75290	0.876452	−	0.481489i	$-0.159904\pi$
$59$	13.4643	1.75290	0.876452	+	0.481489i	$0.159904\pi$
$60$	9.77749	1.26227
$61$	5.80524	0.743285	0.371643	−	0.928376i	$-0.378795\pi$
$61$	5.80524	0.743285	0.371643	+	0.928376i	$0.378795\pi$
$62$	−10.7352	−1.36337
$63$	0	0
$64$	−11.9558	−1.49447
$65$	3.73093	0.462764
$66$	−1.13693	−0.139947
$67$	6.15975	0.752533	0.376267	−	0.926511i	$-0.377208\pi$
$67$	6.15975	0.752533	0.376267	+	0.926511i	$0.377208\pi$
$68$	9.97225	1.20931
$69$	−2.43608	−0.293269
$70$	0	0
$71$	−6.88638	−0.817263	−0.408631	−	0.912700i	$-0.633994\pi$
$71$	−6.88638	−0.817263	−0.408631	+	0.912700i	$0.633994\pi$
$72$	−1.33415	−0.157232
$73$	−6.45597	−0.755614	−0.377807	−	0.925884i	$-0.623322\pi$
$73$	−6.45597	−0.755614	−0.377807	+	0.925884i	$0.623322\pi$
$74$	−20.3171	−2.36181
$75$	8.91980	1.02997
$76$	−10.1695	−1.16652
$77$	0	0
$78$	−2.14957	−0.243391
$79$	−3.70905	−0.417301	−0.208650	−	0.977990i	$-0.566907\pi$
$79$	−3.70905	−0.417301	−0.208650	+	0.977990i	$0.566907\pi$
$80$	−8.85520	−0.990042
$81$	1.00000	0.111111
$82$	11.2093	1.23786
$83$	−2.16853	−0.238027	−0.119013	−	0.992893i	$-0.537973\pi$
$83$	−2.16853	−0.238027	−0.119013	+	0.992893i	$0.537973\pi$
$84$	0	0
$85$	14.1971	1.53989
$86$	−22.2388	−2.39808
$87$	−3.56822	−0.382553
$88$	−0.705650	−0.0752225
$89$	1.46383	0.155166	0.0775830	−	0.996986i	$-0.475280\pi$
$89$	1.46383	0.155166	0.0775830	+	0.996986i	$0.475280\pi$
$90$	−8.01989	−0.845371
$91$	0	0
$92$	−6.38413	−0.665592
$93$	4.99412	0.517866
$94$	24.8227	2.56026
$95$	−14.4778	−1.48540
$96$	7.77023	0.793046
$97$	11.6089	1.17871	0.589353	−	0.807876i	$-0.299383\pi$
$97$	11.6089	1.17871	0.589353	+	0.807876i	$0.299383\pi$
$98$	0	0
$99$	0.528912	0.0531576
$100$	23.3758	2.33758
$101$	−12.6410	−1.25783	−0.628913	−	0.777476i	$-0.716500\pi$
$101$	−12.6410	−1.25783	−0.628913	+	0.777476i	$0.716500\pi$
$102$	−8.17964	−0.809905
$103$	−13.8963	−1.36925	−0.684624	−	0.728897i	$-0.740034\pi$
$103$	−13.8963	−1.36925	−0.684624	+	0.728897i	$0.740034\pi$
$104$	−1.33415	−0.130825
$105$	0	0
$106$	−16.4011	−1.59302
$107$	−15.6037	−1.50847	−0.754234	−	0.656606i	$-0.771991\pi$
$107$	−15.6037	−1.50847	−0.754234	+	0.656606i	$0.771991\pi$
$108$	2.62066	0.252173
$109$	4.85566	0.465088	0.232544	−	0.972586i	$-0.425295\pi$
$109$	4.85566	0.465088	0.232544	+	0.972586i	$0.425295\pi$
$110$	−4.24182	−0.404441
$111$	9.45167	0.897113
$112$	0	0
$113$	−4.32152	−0.406534	−0.203267	−	0.979123i	$-0.565156\pi$
$113$	−4.32152	−0.406534	−0.203267	+	0.979123i	$0.565156\pi$
$114$	8.34141	0.781245
$115$	−9.08883	−0.847537
$116$	−9.35109	−0.868227
$117$	1.00000	0.0924500
$118$	−28.9425	−2.66437
$119$	0	0
$120$	−4.97763	−0.454393
$121$	−10.7203	−0.974568
$122$	−12.4788	−1.12978
$123$	−5.21465	−0.470189
$124$	13.0879	1.17533
$125$	14.6245	1.30805
$126$	0	0
$127$	−17.2976	−1.53491	−0.767457	−	0.641101i	$-0.778478\pi$
$127$	−17.2976	−1.53491	−0.767457	+	0.641101i	$0.778478\pi$
$128$	10.1593	0.897963
$129$	10.3457	0.910889
$130$	−8.01989	−0.703391
$131$	12.5511	1.09659	0.548296	−	0.836284i	$-0.315277\pi$
$131$	12.5511	1.09659	0.548296	+	0.836284i	$0.315277\pi$
$132$	1.38610	0.120644
$133$	0	0
$134$	−13.2408	−1.14383
$135$	3.73093	0.321107
$136$	−5.07678	−0.435330
$137$	4.86350	0.415517	0.207759	−	0.978180i	$-0.433383\pi$
$137$	4.86350	0.415517	0.207759	+	0.978180i	$0.433383\pi$
$138$	5.23653	0.445763
$139$	16.4230	1.39298	0.696490	−	0.717567i	$-0.254744\pi$
$139$	16.4230	1.39298	0.696490	+	0.717567i	$0.254744\pi$
$140$	0	0
$141$	−11.5477	−0.972493
$142$	14.8028	1.24222
$143$	0.528912	0.0442298
$144$	−2.37346	−0.197788
$145$	−13.3128	−1.10556
$146$	13.8776	1.14852
$147$	0	0
$148$	24.7696	2.03605
$149$	8.77319	0.718728	0.359364	−	0.933198i	$-0.382994\pi$
$149$	8.77319	0.718728	0.359364	+	0.933198i	$0.382994\pi$
$150$	−19.1738	−1.56553
$151$	15.6060	1.27000	0.634998	−	0.772513i	$-0.281001\pi$
$151$	15.6060	1.27000	0.634998	+	0.772513i	$0.281001\pi$
$152$	5.17718	0.419925
$153$	3.80524	0.307636
$154$	0	0
$155$	18.6327	1.49661
$156$	2.62066	0.209821
$157$	15.0461	1.20081	0.600405	−	0.799696i	$-0.295006\pi$
$157$	15.0461	1.20081	0.600405	+	0.799696i	$0.295006\pi$
$158$	7.97287	0.634288
$159$	7.62994	0.605094
$160$	28.9902	2.29187
$161$	0	0
$162$	−2.14957	−0.168886
$163$	−6.63561	−0.519741	−0.259871	−	0.965643i	$-0.583680\pi$
$163$	−6.63561	−0.519741	−0.259871	+	0.965643i	$0.583680\pi$
$164$	−13.6658	−1.06712
$165$	1.97333	0.153624
$166$	4.66140	0.361795
$167$	−14.1593	−1.09568	−0.547839	−	0.836584i	$-0.684549\pi$
$167$	−14.1593	−1.09568	−0.547839	+	0.836584i	$0.684549\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−30.5176	−2.34060
$171$	−3.88050	−0.296749
$172$	27.1126	2.06731
$173$	−1.05826	−0.0804581	−0.0402290	−	0.999190i	$-0.512809\pi$
$173$	−1.05826	−0.0804581	−0.0402290	+	0.999190i	$0.512809\pi$
$174$	7.67014	0.581472
$175$	0	0
$176$	−1.25535	−0.0946257
$177$	13.4643	1.01204
$178$	−3.14661	−0.235849
$179$	−16.1559	−1.20755	−0.603774	−	0.797155i	$-0.706337\pi$
$179$	−16.1559	−1.20755	−0.603774	+	0.797155i	$0.706337\pi$
$180$	9.77749	0.728771
$181$	8.79784	0.653938	0.326969	−	0.945035i	$-0.393973\pi$
$181$	8.79784	0.653938	0.326969	+	0.945035i	$0.393973\pi$
$182$	0	0
$183$	5.80524	0.429136
$184$	3.25010	0.239601
$185$	35.2635	2.59262
$186$	−10.7352	−0.787145
$187$	2.01264	0.147179
$188$	−30.2626	−2.20713
$189$	0	0
$190$	31.1212	2.25777
$191$	5.19862	0.376159	0.188079	−	0.982154i	$-0.439774\pi$
$191$	5.19862	0.376159	0.188079	+	0.982154i	$0.439774\pi$
$192$	−11.9558	−0.862832
$193$	−14.1552	−1.01892	−0.509458	−	0.860495i	$-0.670154\pi$
$193$	−14.1552	−1.01892	−0.509458	+	0.860495i	$0.670154\pi$
$194$	−24.9542	−1.79161
$195$	3.73093	0.267177
$196$	0	0
$197$	20.4646	1.45804	0.729020	−	0.684492i	$-0.239976\pi$
$197$	20.4646	1.45804	0.729020	+	0.684492i	$0.239976\pi$
$198$	−1.13693	−0.0807984
$199$	−20.7931	−1.47398	−0.736991	−	0.675902i	$-0.763754\pi$
$199$	−20.7931	−1.47398	−0.736991	+	0.675902i	$0.763754\pi$
$200$	−11.9004	−0.841485
$201$	6.15975	0.434475
$202$	27.1727	1.91187
$203$	0	0
$204$	9.97225	0.698197
$205$	−19.4555	−1.35883
$206$	29.8712	2.08123
$207$	−2.43608	−0.169319
$208$	−2.37346	−0.164570
$209$	−2.05244	−0.141970
$210$	0	0
$211$	1.47513	0.101552	0.0507761	−	0.998710i	$-0.483831\pi$
$211$	1.47513	0.101552	0.0507761	+	0.998710i	$0.483831\pi$
$212$	19.9955	1.37330
$213$	−6.88638	−0.471847
$214$	33.5413	2.29284
$215$	38.5991	2.63243
$216$	−1.33415	−0.0907777
$217$	0	0
$218$	−10.4376	−0.706924
$219$	−6.45597	−0.436254
$220$	5.17143	0.348658
$221$	3.80524	0.255968
$222$	−20.3171	−1.36359
$223$	18.9314	1.26774	0.633869	−	0.773441i	$-0.281466\pi$
$223$	18.9314	1.26774	0.633869	+	0.773441i	$0.281466\pi$
$224$	0	0
$225$	8.91980	0.594654
$226$	9.28941	0.617922
$227$	6.43602	0.427174	0.213587	−	0.976924i	$-0.431485\pi$
$227$	6.43602	0.427174	0.213587	+	0.976924i	$0.431485\pi$
$228$	−10.1695	−0.673489
$229$	18.4074	1.21640	0.608199	−	0.793785i	$-0.291892\pi$
$229$	18.4074	1.21640	0.608199	+	0.793785i	$0.291892\pi$
$230$	19.5371	1.28824
$231$	0	0
$232$	4.76055	0.312546
$233$	−14.8076	−0.970075	−0.485038	−	0.874493i	$-0.661194\pi$
$233$	−14.8076	−0.970075	−0.485038	+	0.874493i	$0.661194\pi$
$234$	−2.14957	−0.140522
$235$	−43.0837	−2.81047
$236$	35.2854	2.29688
$237$	−3.70905	−0.240929
$238$	0	0
$239$	1.48600	0.0961213	0.0480606	−	0.998844i	$-0.484696\pi$
$239$	1.48600	0.0961213	0.0480606	+	0.998844i	$0.484696\pi$
$240$	−8.85520	−0.571601
$241$	27.1228	1.74713	0.873565	−	0.486707i	$-0.161802\pi$
$241$	27.1228	1.74713	0.873565	+	0.486707i	$0.161802\pi$
$242$	23.0440	1.48132
$243$	1.00000	0.0641500
$244$	15.2136	0.973949
$245$	0	0
$246$	11.2093	0.714677
$247$	−3.88050	−0.246910
$248$	−6.66293	−0.423096
$249$	−2.16853	−0.137425
$250$	−31.4364	−1.98821
$251$	3.04811	0.192395	0.0961974	−	0.995362i	$-0.469332\pi$
$251$	3.04811	0.192395	0.0961974	+	0.995362i	$0.469332\pi$
$252$	0	0
$253$	−1.28847	−0.0810055
$254$	37.1824	2.33303
$255$	14.1971	0.889055
$256$	2.07338	0.129586
$257$	20.1383	1.25619	0.628096	−	0.778136i	$-0.283834\pi$
$257$	20.1383	1.25619	0.628096	+	0.778136i	$0.283834\pi$
$258$	−22.2388	−1.38453
$259$	0	0
$260$	9.77749	0.606374
$261$	−3.56822	−0.220867
$262$	−26.9794	−1.66680
$263$	−20.0617	−1.23706	−0.618529	−	0.785762i	$-0.712271\pi$
$263$	−20.0617	−1.23706	−0.618529	+	0.785762i	$0.712271\pi$
$264$	−0.705650	−0.0434297
$265$	28.4667	1.74870
$266$	0	0
$267$	1.46383	0.0895851
$268$	16.1426	0.986067
$269$	−19.0100	−1.15906	−0.579530	−	0.814951i	$-0.696764\pi$
$269$	−19.0100	−1.15906	−0.579530	+	0.814951i	$0.696764\pi$
$270$	−8.01989	−0.488075
$271$	16.8274	1.02219	0.511096	−	0.859524i	$-0.329240\pi$
$271$	16.8274	1.02219	0.511096	+	0.859524i	$0.329240\pi$
$272$	−9.03159	−0.547621
$273$	0	0
$274$	−10.4544	−0.631576
$275$	4.71779	0.284493
$276$	−6.38413	−0.384280
$277$	−23.0432	−1.38453	−0.692267	−	0.721641i	$-0.743388\pi$
$277$	−23.0432	−1.38453	−0.692267	+	0.721641i	$0.743388\pi$
$278$	−35.3024	−2.11730
$279$	4.99412	0.298990
$280$	0	0
$281$	−17.7086	−1.05641	−0.528203	−	0.849118i	$-0.677134\pi$
$281$	−17.7086	−1.05641	−0.528203	+	0.849118i	$0.677134\pi$
$282$	24.8227	1.47817
$283$	17.3781	1.03302	0.516510	−	0.856281i	$-0.327231\pi$
$283$	17.3781	1.03302	0.516510	+	0.856281i	$0.327231\pi$
$284$	−18.0469	−1.07088
$285$	−14.4778	−0.857594
$286$	−1.13693	−0.0672283
$287$	0	0
$288$	7.77023	0.457865
$289$	−2.52013	−0.148243
$290$	28.6167	1.68043
$291$	11.6089	0.680526
$292$	−16.9189	−0.990104
$293$	−31.0543	−1.81421	−0.907105	−	0.420905i	$-0.861712\pi$
$293$	−31.0543	−1.81421	−0.907105	+	0.420905i	$0.861712\pi$
$294$	0	0
$295$	50.2343	2.92476
$296$	−12.6100	−0.732941
$297$	0.528912	0.0306906
$298$	−18.8586	−1.09245
$299$	−2.43608	−0.140882
$300$	23.3758	1.34960
$301$	0	0
$302$	−33.5462	−1.93037
$303$	−12.6410	−0.726206
$304$	9.21021	0.528242
$305$	21.6589	1.24019
$306$	−8.17964	−0.467599
$307$	−15.7951	−0.901474	−0.450737	−	0.892657i	$-0.648839\pi$
$307$	−15.7951	−0.901474	−0.450737	+	0.892657i	$0.648839\pi$
$308$	0	0
$309$	−13.8963	−0.790536
$310$	−40.0523	−2.27482
$311$	6.58699	0.373514	0.186757	−	0.982406i	$-0.440202\pi$
$311$	6.58699	0.373514	0.186757	+	0.982406i	$0.440202\pi$
$312$	−1.33415	−0.0755316
$313$	−12.9625	−0.732682	−0.366341	−	0.930481i	$-0.619390\pi$
$313$	−12.9625	−0.732682	−0.366341	+	0.930481i	$0.619390\pi$
$314$	−32.3427	−1.82520
$315$	0	0
$316$	−9.72016	−0.546802
$317$	24.9452	1.40106	0.700532	−	0.713621i	$-0.252946\pi$
$317$	24.9452	1.40106	0.700532	+	0.713621i	$0.252946\pi$
$318$	−16.4011	−0.919728
$319$	−1.88727	−0.105667
$320$	−44.6060	−2.49355
$321$	−15.6037	−0.870914
$322$	0	0
$323$	−14.7662	−0.821615
$324$	2.62066	0.145592
$325$	8.91980	0.494782
$326$	14.2637	0.789995
$327$	4.85566	0.268519
$328$	6.95715	0.384144
$329$	0	0
$330$	−4.24182	−0.233504
$331$	4.37115	0.240260	0.120130	−	0.992758i	$-0.461669\pi$
$331$	4.37115	0.240260	0.120130	+	0.992758i	$0.461669\pi$
$332$	−5.68297	−0.311893
$333$	9.45167	0.517949
$334$	30.4364	1.66541
$335$	22.9816	1.25562
$336$	0	0
$337$	2.61680	0.142546	0.0712731	−	0.997457i	$-0.477294\pi$
$337$	2.61680	0.142546	0.0712731	+	0.997457i	$0.477294\pi$
$338$	−2.14957	−0.116921
$339$	−4.32152	−0.234713
$340$	37.2057	2.01776
$341$	2.64145	0.143043
$342$	8.34141	0.451052
$343$	0	0
$344$	−13.8028	−0.744195
$345$	−9.08883	−0.489326
$346$	2.27481	0.122294
$347$	−17.0188	−0.913617	−0.456809	−	0.889565i	$-0.651008\pi$
$347$	−17.0188	−0.913617	−0.456809	+	0.889565i	$0.651008\pi$
$348$	−9.35109	−0.501271
$349$	11.1055	0.594464	0.297232	−	0.954805i	$-0.403936\pi$
$349$	11.1055	0.594464	0.297232	+	0.954805i	$0.403936\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	4.10977	0.219051
$353$	15.7257	0.836996	0.418498	−	0.908218i	$-0.362557\pi$
$353$	15.7257	0.836996	0.418498	+	0.908218i	$0.362557\pi$
$354$	−28.9425	−1.53828
$355$	−25.6926	−1.36362
$356$	3.83621	0.203319
$357$	0	0
$358$	34.7283	1.83545
$359$	−2.66357	−0.140578	−0.0702890	−	0.997527i	$-0.522392\pi$
$359$	−2.66357	−0.140578	−0.0702890	+	0.997527i	$0.522392\pi$
$360$	−4.97763	−0.262344
$361$	−3.94174	−0.207460
$362$	−18.9116	−0.993971
$363$	−10.7203	−0.562667
$364$	0	0
$365$	−24.0867	−1.26076
$366$	−12.4788	−0.652277
$367$	−13.8145	−0.721109	−0.360555	−	0.932738i	$-0.617413\pi$
$367$	−13.8145	−0.721109	−0.360555	+	0.932738i	$0.617413\pi$
$368$	5.78194	0.301404
$369$	−5.21465	−0.271464
$370$	−75.8014	−3.94073
$371$	0	0
$372$	13.0879	0.678576
$373$	1.40620	0.0728101	0.0364051	−	0.999337i	$-0.488409\pi$
$373$	1.40620	0.0728101	0.0364051	+	0.999337i	$0.488409\pi$
$374$	−4.32631	−0.223708
$375$	14.6245	0.755206
$376$	15.4064	0.794526
$377$	−3.56822	−0.183773
$378$	0	0
$379$	10.4746	0.538046	0.269023	−	0.963134i	$-0.413299\pi$
$379$	10.4746	0.538046	0.269023	+	0.963134i	$0.413299\pi$
$380$	−37.9415	−1.94636
$381$	−17.2976	−0.886183
$382$	−11.1748	−0.571753
$383$	−3.63078	−0.185524	−0.0927620	−	0.995688i	$-0.529570\pi$
$383$	−3.63078	−0.185524	−0.0927620	+	0.995688i	$0.529570\pi$
$384$	10.1593	0.518439
$385$	0	0
$386$	30.4277	1.54873
$387$	10.3457	0.525902
$388$	30.4230	1.54449
$389$	11.6835	0.592378	0.296189	−	0.955129i	$-0.404284\pi$
$389$	11.6835	0.592378	0.296189	+	0.955129i	$0.404284\pi$
$390$	−8.01989	−0.406103
$391$	−9.26987	−0.468797
$392$	0	0
$393$	12.5511	0.633118
$394$	−43.9901	−2.21619
$395$	−13.8382	−0.696275
$396$	1.38610	0.0696541
$397$	−6.67982	−0.335250	−0.167625	−	0.985851i	$-0.553610\pi$
$397$	−6.67982	−0.335250	−0.167625	+	0.985851i	$0.553610\pi$
$398$	44.6962	2.24042
$399$	0	0
$400$	−21.1708	−1.05854
$401$	−25.6428	−1.28054	−0.640271	−	0.768149i	$-0.721178\pi$
$401$	−25.6428	−1.28054	−0.640271	+	0.768149i	$0.721178\pi$
$402$	−13.2408	−0.660392
$403$	4.99412	0.248775
$404$	−33.1277	−1.64817
$405$	3.73093	0.185391
$406$	0	0
$407$	4.99910	0.247796
$408$	−5.07678	−0.251338
$409$	−22.5418	−1.11462	−0.557311	−	0.830304i	$-0.688167\pi$
$409$	−22.5418	−1.11462	−0.557311	+	0.830304i	$0.688167\pi$
$410$	41.8209	2.06539
$411$	4.86350	0.239899
$412$	−36.4176	−1.79417
$413$	0	0
$414$	5.23653	0.257361
$415$	−8.09061	−0.397152
$416$	7.77023	0.380967
$417$	16.4230	0.804237
$418$	4.41187	0.215792
$419$	−10.1169	−0.494242	−0.247121	−	0.968985i	$-0.579484\pi$
$419$	−10.1169	−0.494242	−0.247121	+	0.968985i	$0.579484\pi$
$420$	0	0
$421$	26.8426	1.30823	0.654113	−	0.756396i	$-0.273042\pi$
$421$	26.8426	1.30823	0.654113	+	0.756396i	$0.273042\pi$
$422$	−3.17090	−0.154357
$423$	−11.5477	−0.561469
$424$	−10.1795	−0.494361
$425$	33.9420	1.64643
$426$	14.8028	0.717196
$427$	0	0
$428$	−40.8920	−1.97659
$429$	0.528912	0.0255361
$430$	−82.9715	−4.00124
$431$	5.32813	0.256647	0.128323	−	0.991732i	$-0.459040\pi$
$431$	5.32813	0.256647	0.128323	+	0.991732i	$0.459040\pi$
$432$	−2.37346	−0.114193
$433$	2.75478	0.132386	0.0661932	−	0.997807i	$-0.478915\pi$
$433$	2.75478	0.132386	0.0661932	+	0.997807i	$0.478915\pi$
$434$	0	0
$435$	−13.3128	−0.638298
$436$	12.7250	0.609419
$437$	9.45320	0.452208
$438$	13.8776	0.663096
$439$	−23.9811	−1.14455	−0.572277	−	0.820060i	$-0.693940\pi$
$439$	−23.9811	−1.14455	−0.572277	+	0.820060i	$0.693940\pi$
$440$	−2.63273	−0.125510
$441$	0	0
$442$	−8.17964	−0.389066
$443$	19.6584	0.933999	0.466999	−	0.884258i	$-0.345335\pi$
$443$	19.6584	0.933999	0.466999	+	0.884258i	$0.345335\pi$
$444$	24.7696	1.17551
$445$	5.46145	0.258898
$446$	−40.6943	−1.92693
$447$	8.77319	0.414958
$448$	0	0
$449$	−18.5726	−0.876493	−0.438246	−	0.898855i	$-0.644400\pi$
$449$	−18.5726	−0.876493	−0.438246	+	0.898855i	$0.644400\pi$
$450$	−19.1738	−0.903860
$451$	−2.75809	−0.129873
$452$	−11.3252	−0.532694
$453$	15.6060	0.733233
$454$	−13.8347	−0.649294
$455$	0	0
$456$	5.17718	0.242444
$457$	8.39115	0.392521	0.196261	−	0.980552i	$-0.437120\pi$
$457$	8.39115	0.392521	0.196261	+	0.980552i	$0.437120\pi$
$458$	−39.5681	−1.84890
$459$	3.80524	0.177613
$460$	−23.8187	−1.11055
$461$	−1.50338	−0.0700195	−0.0350097	−	0.999387i	$-0.511146\pi$
$461$	−1.50338	−0.0700195	−0.0350097	+	0.999387i	$0.511146\pi$
$462$	0	0
$463$	−30.3510	−1.41053	−0.705265	−	0.708944i	$-0.749172\pi$
$463$	−30.3510	−1.41053	−0.705265	+	0.708944i	$0.749172\pi$
$464$	8.46903	0.393165
$465$	18.6327	0.864070
$466$	31.8299	1.47449
$467$	−27.0373	−1.25114	−0.625569	−	0.780169i	$-0.715133\pi$
$467$	−27.0373	−1.25114	−0.625569	+	0.780169i	$0.715133\pi$
$468$	2.62066	0.121140
$469$	0	0
$470$	92.6115	4.27185
$471$	15.0461	0.693288
$472$	−17.9635	−0.826835
$473$	5.47197	0.251601
$474$	7.97287	0.366206
$475$	−34.6133	−1.58817
$476$	0	0
$477$	7.62994	0.349351
$478$	−3.19426	−0.146102
$479$	−19.2791	−0.880885	−0.440442	−	0.897781i	$-0.645178\pi$
$479$	−19.2791	−0.880885	−0.440442	+	0.897781i	$0.645178\pi$
$480$	28.9902	1.32321
$481$	9.45167	0.430959
$482$	−58.3023	−2.65560
$483$	0	0
$484$	−28.0941	−1.27701
$485$	43.3119	1.96669
$486$	−2.14957	−0.0975066
$487$	−14.5719	−0.660316	−0.330158	−	0.943926i	$-0.607102\pi$
$487$	−14.5719	−0.660316	−0.330158	+	0.943926i	$0.607102\pi$
$488$	−7.74509	−0.350604
$489$	−6.63561	−0.300073
$490$	0	0
$491$	16.7357	0.755271	0.377636	−	0.925954i	$-0.376737\pi$
$491$	16.7357	0.755271	0.377636	+	0.925954i	$0.376737\pi$
$492$	−13.6658	−0.616103
$493$	−13.5779	−0.611519
$494$	8.34141	0.375298
$495$	1.97333	0.0886946
$496$	−11.8533	−0.532231
$497$	0	0
$498$	4.66140	0.208882
$499$	−2.72382	−0.121935	−0.0609674	−	0.998140i	$-0.519419\pi$
$499$	−2.72382	−0.121935	−0.0609674	+	0.998140i	$0.519419\pi$
$500$	38.3258	1.71398
$501$	−14.1593	−0.632590
$502$	−6.55213	−0.292436
$503$	−6.96312	−0.310470	−0.155235	−	0.987878i	$-0.549613\pi$
$503$	−6.96312	−0.310470	−0.155235	+	0.987878i	$0.549613\pi$
$504$	0	0
$505$	−47.1626	−2.09871
$506$	2.76966	0.123126
$507$	1.00000	0.0444116
$508$	−45.3311	−2.01124
$509$	−13.6370	−0.604449	−0.302224	−	0.953237i	$-0.597729\pi$
$509$	−13.6370	−0.604449	−0.302224	+	0.953237i	$0.597729\pi$
$510$	−30.5176	−1.35134
$511$	0	0
$512$	−24.7755	−1.09493
$513$	−3.88050	−0.171328
$514$	−43.2887	−1.90938
$515$	−51.8462	−2.28462
$516$	27.1126	1.19356
$517$	−6.10773	−0.268618
$518$	0	0
$519$	−1.05826	−0.0464525
$520$	−4.97763	−0.218283
$521$	42.1653	1.84730	0.923648	−	0.383242i	$-0.125192\pi$
$521$	42.1653	1.84730	0.923648	+	0.383242i	$0.125192\pi$
$522$	7.67014	0.335713
$523$	−9.87664	−0.431875	−0.215938	−	0.976407i	$-0.569281\pi$
$523$	−9.87664	−0.431875	−0.215938	+	0.976407i	$0.569281\pi$
$524$	32.8921	1.43690
$525$	0	0
$526$	43.1241	1.88030
$527$	19.0038	0.827820
$528$	−1.25535	−0.0546322
$529$	−17.0655	−0.741979
$530$	−61.1913	−2.65798
$531$	13.4643	0.584301
$532$	0	0
$533$	−5.21465	−0.225872
$534$	−3.14661	−0.136167
$535$	−58.2163	−2.51691
$536$	−8.21805	−0.354966
$537$	−16.1559	−0.697178
$538$	40.8634	1.76175
$539$	0	0
$540$	9.77749	0.420756
$541$	−12.6880	−0.545500	−0.272750	−	0.962085i	$-0.587933\pi$
$541$	−12.6880	−0.545500	−0.272750	+	0.962085i	$0.587933\pi$
$542$	−36.1717	−1.55371
$543$	8.79784	0.377551
$544$	29.5676	1.26770
$545$	18.1161	0.776009
$546$	0	0
$547$	−32.9907	−1.41058	−0.705291	−	0.708918i	$-0.749184\pi$
$547$	−32.9907	−1.41058	−0.705291	+	0.708918i	$0.749184\pi$
$548$	12.7456	0.544465
$549$	5.80524	0.247762
$550$	−10.1412	−0.432424
$551$	13.8465	0.589879
$552$	3.25010	0.138334
$553$	0	0
$554$	49.5331	2.10446
$555$	35.2635	1.49685
$556$	43.0391	1.82526
$557$	−18.7978	−0.796489	−0.398245	−	0.917279i	$-0.630380\pi$
$557$	−18.7978	−0.796489	−0.398245	+	0.917279i	$0.630380\pi$
$558$	−10.7352	−0.454458
$559$	10.3457	0.437577
$560$	0	0
$561$	2.01264	0.0849736
$562$	38.0659	1.60571
$563$	−25.8645	−1.09006	−0.545030	−	0.838416i	$-0.683482\pi$
$563$	−25.8645	−1.09006	−0.545030	+	0.838416i	$0.683482\pi$
$564$	−30.2626	−1.27429
$565$	−16.1233	−0.678310
$566$	−37.3555	−1.57017
$567$	0	0
$568$	9.18749	0.385498
$569$	−44.0629	−1.84721	−0.923607	−	0.383341i	$-0.874774\pi$
$569$	−44.0629	−1.84721	−0.923607	+	0.383341i	$0.874774\pi$
$570$	31.1212	1.30352
$571$	6.08341	0.254583	0.127291	−	0.991865i	$-0.459372\pi$
$571$	6.08341	0.254583	0.127291	+	0.991865i	$0.459372\pi$
$572$	1.38610	0.0579557
$573$	5.19862	0.217175
$574$	0	0
$575$	−21.7293	−0.906176
$576$	−11.9558	−0.498156
$577$	1.20699	0.0502477	0.0251238	−	0.999684i	$-0.492002\pi$
$577$	1.20699	0.0502477	0.0251238	+	0.999684i	$0.492002\pi$
$578$	5.41721	0.225326
$579$	−14.1552	−0.588272
$580$	−34.8882	−1.44865
$581$	0	0
$582$	−24.9542	−1.03438
$583$	4.03557	0.167136
$584$	8.61326	0.356419
$585$	3.73093	0.154255
$586$	66.7534	2.75756
$587$	29.7974	1.22987	0.614935	−	0.788578i	$-0.289182\pi$
$587$	29.7974	1.22987	0.614935	+	0.788578i	$0.289182\pi$
$588$	0	0
$589$	−19.3797	−0.798526
$590$	−107.982	−4.44556
$591$	20.4646	0.841800
$592$	−22.4332	−0.921998
$593$	1.33274	0.0547291	0.0273646	−	0.999626i	$-0.491289\pi$
$593$	1.33274	0.0547291	0.0273646	+	0.999626i	$0.491289\pi$
$594$	−1.13693	−0.0466490
$595$	0	0
$596$	22.9916	0.941771
$597$	−20.7931	−0.851004
$598$	5.23653	0.214137
$599$	15.6611	0.639897	0.319948	−	0.947435i	$-0.396334\pi$
$599$	15.6611	0.639897	0.319948	+	0.947435i	$0.396334\pi$
$600$	−11.9004	−0.485831
$601$	9.62304	0.392532	0.196266	−	0.980551i	$-0.437118\pi$
$601$	9.62304	0.392532	0.196266	+	0.980551i	$0.437118\pi$
$602$	0	0
$603$	6.15975	0.250844
$604$	40.8980	1.66411
$605$	−39.9965	−1.62609
$606$	27.1727	1.10382
$607$	39.8297	1.61664	0.808318	−	0.588746i	$-0.200378\pi$
$607$	39.8297	1.61664	0.808318	+	0.588746i	$0.200378\pi$
$608$	−30.1524	−1.22284
$609$	0	0
$610$	−46.5574	−1.88505
$611$	−11.5477	−0.467171
$612$	9.97225	0.403104
$613$	−24.6932	−0.997350	−0.498675	−	0.866789i	$-0.666180\pi$
$613$	−24.6932	−0.997350	−0.498675	+	0.866789i	$0.666180\pi$
$614$	33.9527	1.37022
$615$	−19.4555	−0.784520
$616$	0	0
$617$	24.3968	0.982178	0.491089	−	0.871109i	$-0.336599\pi$
$617$	24.3968	0.982178	0.491089	+	0.871109i	$0.336599\pi$
$618$	29.8712	1.20160
$619$	−17.1583	−0.689649	−0.344825	−	0.938667i	$-0.612062\pi$
$619$	−17.1583	−0.689649	−0.344825	+	0.938667i	$0.612062\pi$
$620$	48.8300	1.96106
$621$	−2.43608	−0.0977565
$622$	−14.1592	−0.567733
$623$	0	0
$624$	−2.37346	−0.0950145
$625$	9.96389	0.398556
$626$	27.8638	1.11366
$627$	−2.05244	−0.0819666
$628$	39.4307	1.57346
$629$	35.9659	1.43405
$630$	0	0
$631$	−4.49651	−0.179003	−0.0895016	−	0.995987i	$-0.528527\pi$
$631$	−4.49651	−0.179003	−0.0895016	+	0.995987i	$0.528527\pi$
$632$	4.94844	0.196839
$633$	1.47513	0.0586312
$634$	−53.6216	−2.12958
$635$	−64.5361	−2.56104
$636$	19.9955	0.792872
$637$	0	0
$638$	4.05683	0.160611
$639$	−6.88638	−0.272421
$640$	37.9035	1.49827
$641$	21.6506	0.855146	0.427573	−	0.903981i	$-0.359369\pi$
$641$	21.6506	0.855146	0.427573	+	0.903981i	$0.359369\pi$
$642$	33.5413	1.32377
$643$	−3.00336	−0.118441	−0.0592204	−	0.998245i	$-0.518861\pi$
$643$	−3.00336	−0.118441	−0.0592204	+	0.998245i	$0.518861\pi$
$644$	0	0
$645$	38.5991	1.51984
$646$	31.7411	1.24884
$647$	−31.8567	−1.25242	−0.626208	−	0.779656i	$-0.715394\pi$
$647$	−31.8567	−1.25242	−0.626208	+	0.779656i	$0.715394\pi$
$648$	−1.33415	−0.0524105
$649$	7.12144	0.279541
$650$	−19.1738	−0.752057
$651$	0	0
$652$	−17.3897	−0.681033
$653$	−23.9761	−0.938257	−0.469128	−	0.883130i	$-0.655432\pi$
$653$	−23.9761	−0.938257	−0.469128	+	0.883130i	$0.655432\pi$
$654$	−10.4376	−0.408142
$655$	46.8271	1.82969
$656$	12.3768	0.483232
$657$	−6.45597	−0.251871
$658$	0	0
$659$	23.5364	0.916849	0.458425	−	0.888733i	$-0.348414\pi$
$659$	23.5364	0.916849	0.458425	+	0.888733i	$0.348414\pi$
$660$	5.17143	0.201298
$661$	38.6096	1.50174	0.750870	−	0.660450i	$-0.229634\pi$
$661$	38.6096	1.50174	0.750870	+	0.660450i	$0.229634\pi$
$662$	−9.39609	−0.365189
$663$	3.80524	0.147783
$664$	2.89315	0.112276
$665$	0	0
$666$	−20.3171	−0.787270
$667$	8.69246	0.336573
$668$	−37.1067	−1.43570
$669$	18.9314	0.731929
$670$	−49.4005	−1.90851
$671$	3.07046	0.118534
$672$	0	0
$673$	16.6618	0.642266	0.321133	−	0.947034i	$-0.395936\pi$
$673$	16.6618	0.642266	0.321133	+	0.947034i	$0.395936\pi$
$674$	−5.62500	−0.216667
$675$	8.91980	0.343323
$676$	2.62066	0.100795
$677$	7.62777	0.293159	0.146579	−	0.989199i	$-0.453174\pi$
$677$	7.62777	0.293159	0.146579	+	0.989199i	$0.453174\pi$
$678$	9.28941	0.356758
$679$	0	0
$680$	−18.9411	−0.726357
$681$	6.43602	0.246629
$682$	−5.67799	−0.217421
$683$	1.09427	0.0418711	0.0209355	−	0.999781i	$-0.493336\pi$
$683$	1.09427	0.0418711	0.0209355	+	0.999781i	$0.493336\pi$
$684$	−10.1695	−0.388839
$685$	18.1454	0.693299
$686$	0	0
$687$	18.4074	0.702287
$688$	−24.5551	−0.936155
$689$	7.62994	0.290678
$690$	19.5371	0.743764
$691$	−5.87856	−0.223631	−0.111815	−	0.993729i	$-0.535667\pi$
$691$	−5.87856	−0.223631	−0.111815	+	0.993729i	$0.535667\pi$
$692$	−2.77334	−0.105427
$693$	0	0
$694$	36.5832	1.38868
$695$	61.2729	2.32421
$696$	4.76055	0.180448
$697$	−19.8430	−0.751608
$698$	−23.8721	−0.903572
$699$	−14.8076	−0.560073
$700$	0	0
$701$	−8.84963	−0.334246	−0.167123	−	0.985936i	$-0.553448\pi$
$701$	−8.84963	−0.334246	−0.167123	+	0.985936i	$0.553448\pi$
$702$	−2.14957	−0.0811304
$703$	−36.6772	−1.38331
$704$	−6.32354	−0.238327
$705$	−43.0837	−1.62263
$706$	−33.8036	−1.27222
$707$	0	0
$708$	35.2854	1.32611
$709$	−14.2588	−0.535502	−0.267751	−	0.963488i	$-0.586280\pi$
$709$	−14.2588	−0.535502	−0.267751	+	0.963488i	$0.586280\pi$
$710$	55.2280	2.07267
$711$	−3.70905	−0.139100
$712$	−1.95298	−0.0731909
$713$	−12.1661	−0.455623
$714$	0	0
$715$	1.97333	0.0737984
$716$	−42.3391	−1.58229
$717$	1.48600	0.0554956
$718$	5.72554	0.213675
$719$	25.8818	0.965227	0.482614	−	0.875833i	$-0.339688\pi$
$719$	25.8818	0.965227	0.482614	+	0.875833i	$0.339688\pi$
$720$	−8.85520	−0.330014
$721$	0	0
$722$	8.47305	0.315334
$723$	27.1228	1.00871
$724$	23.0562	0.856875
$725$	−31.8278	−1.18206
$726$	23.0440	0.855241
$727$	−29.9940	−1.11242	−0.556209	−	0.831043i	$-0.687744\pi$
$727$	−29.9940	−1.11242	−0.556209	+	0.831043i	$0.687744\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	51.7762	1.91632
$731$	39.3679	1.45607
$732$	15.2136	0.562310
$733$	16.6763	0.615951	0.307976	−	0.951394i	$-0.400348\pi$
$733$	16.6763	0.615951	0.307976	+	0.951394i	$0.400348\pi$
$734$	29.6952	1.09607
$735$	0	0
$736$	−18.9289	−0.697728
$737$	3.25796	0.120009
$738$	11.2093	0.412619
$739$	18.1001	0.665823	0.332911	−	0.942958i	$-0.391969\pi$
$739$	18.1001	0.665823	0.332911	+	0.942958i	$0.391969\pi$
$740$	92.4136	3.39719
$741$	−3.88050	−0.142554
$742$	0	0
$743$	−15.3219	−0.562107	−0.281054	−	0.959692i	$-0.590684\pi$
$743$	−15.3219	−0.562107	−0.281054	+	0.959692i	$0.590684\pi$
$744$	−6.66293	−0.244275
$745$	32.7321	1.19921
$746$	−3.02272	−0.110670
$747$	−2.16853	−0.0793422
$748$	5.27444	0.192853
$749$	0	0
$750$	−31.4364	−1.14790
$751$	−32.6153	−1.19015	−0.595075	−	0.803670i	$-0.702878\pi$
$751$	−32.6153	−1.19015	−0.595075	+	0.803670i	$0.702878\pi$
$752$	27.4081	0.999469
$753$	3.04811	0.111079
$754$	7.67014	0.279330
$755$	58.2247	2.11902
$756$	0	0
$757$	32.2037	1.17046	0.585232	−	0.810866i	$-0.301003\pi$
$757$	32.2037	1.17046	0.585232	+	0.810866i	$0.301003\pi$
$758$	−22.5160	−0.817817
$759$	−1.28847	−0.0467685
$760$	19.3157	0.700653
$761$	25.1610	0.912086	0.456043	−	0.889958i	$-0.349266\pi$
$761$	25.1610	0.912086	0.456043	+	0.889958i	$0.349266\pi$
$762$	37.1824	1.34698
$763$	0	0
$764$	13.6238	0.492892
$765$	14.1971	0.513296
$766$	7.80462	0.281992
$767$	13.4643	0.486168
$768$	2.07338	0.0748168
$769$	20.3041	0.732186	0.366093	−	0.930578i	$-0.380695\pi$
$769$	20.3041	0.732186	0.366093	+	0.930578i	$0.380695\pi$
$770$	0	0
$771$	20.1383	0.725263
$772$	−37.0961	−1.33512
$773$	−5.54678	−0.199504	−0.0997519	−	0.995012i	$-0.531805\pi$
$773$	−5.54678	−0.199504	−0.0997519	+	0.995012i	$0.531805\pi$
$774$	−22.2388	−0.799359
$775$	44.5466	1.60016
$776$	−15.4881	−0.555989
$777$	0	0
$778$	−25.1146	−0.900400
$779$	20.2354	0.725010
$780$	9.77749	0.350090
$781$	−3.64229	−0.130331
$782$	19.9262	0.712561
$783$	−3.56822	−0.127518
$784$	0	0
$785$	56.1359	2.00358
$786$	−26.9794	−0.962325
$787$	0.466851	0.0166414	0.00832071	−	0.999965i	$-0.497351\pi$
$787$	0.466851	0.0166414	0.00832071	+	0.999965i	$0.497351\pi$
$788$	53.6307	1.91051
$789$	−20.0617	−0.714216
$790$	29.7462	1.05832
$791$	0	0
$792$	−0.705650	−0.0250742
$793$	5.80524	0.206150
$794$	14.3587	0.509573
$795$	28.4667	1.00961
$796$	−54.4916	−1.93140
$797$	−12.2437	−0.433694	−0.216847	−	0.976206i	$-0.569577\pi$
$797$	−12.2437	−0.433694	−0.216847	+	0.976206i	$0.569577\pi$
$798$	0	0
$799$	−43.9419	−1.55455
$800$	69.3090	2.45044
$801$	1.46383	0.0517220
$802$	55.1211	1.94639
$803$	−3.41464	−0.120500
$804$	16.1426	0.569306
$805$	0	0
$806$	−10.7352	−0.378132
$807$	−19.0100	−0.669184
$808$	16.8650	0.593309
$809$	−43.8846	−1.54290	−0.771451	−	0.636289i	$-0.780469\pi$
$809$	−43.8846	−1.54290	−0.771451	+	0.636289i	$0.780469\pi$
$810$	−8.01989	−0.281790
$811$	30.2691	1.06289	0.531446	−	0.847092i	$-0.321649\pi$
$811$	30.2691	1.06289	0.531446	+	0.847092i	$0.321649\pi$
$812$	0	0
$813$	16.8274	0.590163
$814$	−10.7459	−0.376645
$815$	−24.7570	−0.867199
$816$	−9.03159	−0.316169
$817$	−40.1465	−1.40455
$818$	48.4553	1.69420
$819$	0	0
$820$	−50.9862	−1.78051
$821$	−35.0880	−1.22458	−0.612290	−	0.790633i	$-0.709752\pi$
$821$	−35.0880	−1.22458	−0.612290	+	0.790633i	$0.709752\pi$
$822$	−10.4544	−0.364641
$823$	−40.3528	−1.40661	−0.703305	−	0.710889i	$-0.748293\pi$
$823$	−40.3528	−1.40661	−0.703305	+	0.710889i	$0.748293\pi$
$824$	18.5399	0.645867
$825$	4.71779	0.164252
$826$	0	0
$827$	−26.5847	−0.924439	−0.462220	−	0.886766i	$-0.652947\pi$
$827$	−26.5847	−0.924439	−0.462220	+	0.886766i	$0.652947\pi$
$828$	−6.38413	−0.221864
$829$	14.4672	0.502468	0.251234	−	0.967926i	$-0.419164\pi$
$829$	14.4672	0.502468	0.251234	+	0.967926i	$0.419164\pi$
$830$	17.3913	0.603662
$831$	−23.0432	−0.799361
$832$	−11.9558	−0.414491
$833$	0	0
$834$	−35.3024	−1.22242
$835$	−52.8272	−1.82816
$836$	−5.37875	−0.186028
$837$	4.99412	0.172622
$838$	21.7470	0.751236
$839$	32.7480	1.13059	0.565294	−	0.824890i	$-0.308763\pi$
$839$	32.7480	1.13059	0.565294	+	0.824890i	$0.308763\pi$
$840$	0	0
$841$	−16.2678	−0.560959
$842$	−57.7000	−1.98847
$843$	−17.7086	−0.609916
$844$	3.86582	0.133067
$845$	3.73093	0.128348
$846$	24.8227	0.853421
$847$	0	0
$848$	−18.1094	−0.621878
$849$	17.3781	0.596415
$850$	−72.9608	−2.50253
$851$	−23.0250	−0.789288
$852$	−18.0469	−0.618275
$853$	4.69850	0.160873	0.0804367	−	0.996760i	$-0.474369\pi$
$853$	4.69850	0.160873	0.0804367	+	0.996760i	$0.474369\pi$
$854$	0	0
$855$	−14.4778	−0.495132
$856$	20.8177	0.711536
$857$	−17.1751	−0.586690	−0.293345	−	0.956007i	$-0.594768\pi$
$857$	−17.1751	−0.586690	−0.293345	+	0.956007i	$0.594768\pi$
$858$	−1.13693	−0.0388143
$859$	−38.2619	−1.30548	−0.652739	−	0.757583i	$-0.726380\pi$
$859$	−38.2619	−1.30548	−0.652739	+	0.757583i	$0.726380\pi$
$860$	101.155	3.44936
$861$	0	0
$862$	−11.4532	−0.390097
$863$	−7.68202	−0.261499	−0.130750	−	0.991415i	$-0.541738\pi$
$863$	−7.68202	−0.261499	−0.130750	+	0.991415i	$0.541738\pi$
$864$	7.77023	0.264349
$865$	−3.94829	−0.134246
$866$	−5.92160	−0.201224
$867$	−2.52013	−0.0855883
$868$	0	0
$869$	−1.96176	−0.0665482
$870$	28.6167	0.970198
$871$	6.15975	0.208715
$872$	−6.47820	−0.219380
$873$	11.6089	0.392902
$874$	−20.3203	−0.687345
$875$	0	0
$876$	−16.9189	−0.571637
$877$	44.3178	1.49650	0.748252	−	0.663415i	$-0.230893\pi$
$877$	44.3178	1.49650	0.748252	+	0.663415i	$0.230893\pi$
$878$	51.5490	1.73970
$879$	−31.0543	−1.04743
$880$	−4.68362	−0.157885
$881$	−25.8704	−0.871598	−0.435799	−	0.900044i	$-0.643534\pi$
$881$	−25.8704	−0.871598	−0.435799	+	0.900044i	$0.643534\pi$
$882$	0	0
$883$	11.3880	0.383236	0.191618	−	0.981470i	$-0.438627\pi$
$883$	11.3880	0.383236	0.191618	+	0.981470i	$0.438627\pi$
$884$	9.97225	0.335403
$885$	50.2343	1.68861
$886$	−42.2572	−1.41966
$887$	19.8155	0.665338	0.332669	−	0.943044i	$-0.392051\pi$
$887$	19.8155	0.665338	0.332669	+	0.943044i	$0.392051\pi$
$888$	−12.6100	−0.423163
$889$	0	0
$890$	−11.7398	−0.393518
$891$	0.528912	0.0177192
$892$	49.6127	1.66115
$893$	44.8109	1.49954
$894$	−18.8586	−0.630726
$895$	−60.2764	−2.01482
$896$	0	0
$897$	−2.43608	−0.0813383
$898$	39.9230	1.33225
$899$	−17.8201	−0.594334
$900$	23.3758	0.779193
$901$	29.0338	0.967255
$902$	5.92872	0.197405
$903$	0	0
$904$	5.76557	0.191760
$905$	32.8241	1.09111
$906$	−33.5462	−1.11450
$907$	27.1502	0.901508	0.450754	−	0.892648i	$-0.351155\pi$
$907$	27.1502	0.901508	0.450754	+	0.892648i	$0.351155\pi$
$908$	16.8666	0.559738
$909$	−12.6410	−0.419275
$910$	0	0
$911$	22.2728	0.737932	0.368966	−	0.929443i	$-0.379712\pi$
$911$	22.2728	0.737932	0.368966	+	0.929443i	$0.379712\pi$
$912$	9.21021	0.304980
$913$	−1.14696	−0.0379588
$914$	−18.0374	−0.596623
$915$	21.6589	0.716022
$916$	48.2396	1.59388
$917$	0	0
$918$	−8.17964	−0.269968
$919$	−10.7030	−0.353060	−0.176530	−	0.984295i	$-0.556487\pi$
$919$	−10.7030	−0.353060	−0.176530	+	0.984295i	$0.556487\pi$
$920$	12.1259	0.399779
$921$	−15.7951	−0.520466
$922$	3.23163	0.106428
$923$	−6.88638	−0.226668
$924$	0	0
$925$	84.3071	2.77200
$926$	65.2416	2.14397
$927$	−13.8963	−0.456416
$928$	−27.7259	−0.910147
$929$	23.5275	0.771911	0.385956	−	0.922517i	$-0.373872\pi$
$929$	23.5275	0.771911	0.385956	+	0.922517i	$0.373872\pi$
$930$	−40.0523	−1.31337
$931$	0	0
$932$	−38.8056	−1.27112
$933$	6.58699	0.215648
$934$	58.1186	1.90170
$935$	7.50900	0.245571
$936$	−1.33415	−0.0436082
$937$	7.08326	0.231400	0.115700	−	0.993284i	$-0.463089\pi$
$937$	7.08326	0.231400	0.115700	+	0.993284i	$0.463089\pi$
$938$	0	0
$939$	−12.9625	−0.423014
$940$	−112.908	−3.68264
$941$	−10.9218	−0.356040	−0.178020	−	0.984027i	$-0.556969\pi$
$941$	−10.9218	−0.356040	−0.178020	+	0.984027i	$0.556969\pi$
$942$	−32.3427	−1.05378
$943$	12.7033	0.413676
$944$	−31.9570	−1.04011
$945$	0	0
$946$	−11.7624	−0.382428
$947$	32.4458	1.05435	0.527173	−	0.849758i	$-0.323252\pi$
$947$	32.4458	1.05435	0.527173	+	0.849758i	$0.323252\pi$
$948$	−9.72016	−0.315696
$949$	−6.45597	−0.209570
$950$	74.4037	2.41398
$951$	24.9452	0.808904
$952$	0	0
$953$	−36.7070	−1.18906	−0.594528	−	0.804075i	$-0.702661\pi$
$953$	−36.7070	−1.18906	−0.594528	+	0.804075i	$0.702661\pi$
$954$	−16.4011	−0.531005
$955$	19.3957	0.627629
$956$	3.89430	0.125951
$957$	−1.88727	−0.0610069
$958$	41.4418	1.33892
$959$	0	0
$960$	−44.6060	−1.43965
$961$	−6.05876	−0.195444
$962$	−20.3171	−0.655048
$963$	−15.6037	−0.502822
$964$	71.0795	2.28932
$965$	−52.8122	−1.70008
$966$	0	0
$967$	−56.6977	−1.82328	−0.911638	−	0.410993i	$-0.865182\pi$
$967$	−56.6977	−1.82328	−0.911638	+	0.410993i	$0.865182\pi$
$968$	14.3025	0.459699
$969$	−14.7662	−0.474360
$970$	−93.1022	−2.98933
$971$	−28.2100	−0.905302	−0.452651	−	0.891688i	$-0.649522\pi$
$971$	−28.2100	−0.905302	−0.452651	+	0.891688i	$0.649522\pi$
$972$	2.62066	0.0840577
$973$	0	0
$974$	31.3234	1.00367
$975$	8.91980	0.285662
$976$	−13.7785	−0.441039
$977$	−26.0183	−0.832400	−0.416200	−	0.909273i	$-0.636638\pi$
$977$	−26.0183	−0.832400	−0.416200	+	0.909273i	$0.636638\pi$
$978$	14.2637	0.456104
$979$	0.774239	0.0247448
$980$	0	0
$981$	4.85566	0.155029
$982$	−35.9746	−1.14800
$983$	−17.4230	−0.555708	−0.277854	−	0.960623i	$-0.589623\pi$
$983$	−17.4230	−0.555708	−0.277854	+	0.960623i	$0.589623\pi$
$984$	6.95715	0.221786
$985$	76.3518	2.43277
$986$	29.1868	0.929496
$987$	0	0
$988$	−10.1695	−0.323534
$989$	−25.2030	−0.801407
$990$	−4.24182	−0.134814
$991$	17.1434	0.544577	0.272288	−	0.962216i	$-0.412220\pi$
$991$	17.1434	0.544577	0.272288	+	0.962216i	$0.412220\pi$
$992$	38.8055	1.23208
$993$	4.37115	0.138714
$994$	0	0
$995$	−77.5774	−2.45937
$996$	−5.68297	−0.180072
$997$	−19.1655	−0.606977	−0.303489	−	0.952835i	$-0.598151\pi$
$997$	−19.1655	−0.606977	−0.303489	+	0.952835i	$0.598151\pi$
$998$	5.85504	0.185338
$999$	9.45167	0.299038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.u.1.1		5
3.2	odd	2		5733.2.a.bp.1.5		5
7.3	odd	6		273.2.i.e.79.5	✓	10
7.5	odd	6		273.2.i.e.235.5	yes	10
7.6	odd	2		1911.2.a.t.1.1		5
21.5	even	6		819.2.j.g.235.1		10
21.17	even	6		819.2.j.g.352.1		10
21.20	even	2		5733.2.a.bq.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.5	✓	10	7.3	odd	6
273.2.i.e.235.5	yes	10	7.5	odd	6
819.2.j.g.235.1		10	21.5	even	6
819.2.j.g.352.1		10	21.17	even	6
1911.2.a.t.1.1		5	7.6	odd	2
1911.2.a.u.1.1		5	1.1	even	1	trivial
5733.2.a.bp.1.5		5	3.2	odd	2
5733.2.a.bq.1.5		5	21.20	even	2

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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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14957 q^{2} +1.00000 q^{3} +2.62066 q^{4} +3.73093 q^{5} -2.14957 q^{6} -1.33415 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.14957 q^{2} +1.00000 q^{3} +2.62066 q^{4} +3.73093 q^{5} -2.14957 q^{6} -1.33415 q^{8} +1.00000 q^{9} -8.01989 q^{10} +0.528912 q^{11} +2.62066 q^{12} +1.00000 q^{13} +3.73093 q^{15} -2.37346 q^{16} +3.80524 q^{17} -2.14957 q^{18} -3.88050 q^{19} +9.77749 q^{20} -1.13693 q^{22} -2.43608 q^{23} -1.33415 q^{24} +8.91980 q^{25} -2.14957 q^{26} +1.00000 q^{27} -3.56822 q^{29} -8.01989 q^{30} +4.99412 q^{31} +7.77023 q^{32} +0.528912 q^{33} -8.17964 q^{34} +2.62066 q^{36} +9.45167 q^{37} +8.34141 q^{38} +1.00000 q^{39} -4.97763 q^{40} -5.21465 q^{41} +10.3457 q^{43} +1.38610 q^{44} +3.73093 q^{45} +5.23653 q^{46} -11.5477 q^{47} -2.37346 q^{48} -19.1738 q^{50} +3.80524 q^{51} +2.62066 q^{52} +7.62994 q^{53} -2.14957 q^{54} +1.97333 q^{55} -3.88050 q^{57} +7.67014 q^{58} +13.4643 q^{59} +9.77749 q^{60} +5.80524 q^{61} -10.7352 q^{62} -11.9558 q^{64} +3.73093 q^{65} -1.13693 q^{66} +6.15975 q^{67} +9.97225 q^{68} -2.43608 q^{69} -6.88638 q^{71} -1.33415 q^{72} -6.45597 q^{73} -20.3171 q^{74} +8.91980 q^{75} -10.1695 q^{76} -2.14957 q^{78} -3.70905 q^{79} -8.85520 q^{80} +1.00000 q^{81} +11.2093 q^{82} -2.16853 q^{83} +14.1971 q^{85} -22.2388 q^{86} -3.56822 q^{87} -0.705650 q^{88} +1.46383 q^{89} -8.01989 q^{90} -6.38413 q^{92} +4.99412 q^{93} +24.8227 q^{94} -14.4778 q^{95} +7.77023 q^{96} +11.6089 q^{97} +0.528912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{3} + 6 q^{4} + 3 q^{5} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^3 + 6 * q^4 + 3 * q^5 + 3 * q^8 + 5 * q^9	\( 5 q + 5 q^{3} + 6 q^{4} + 3 q^{5} + 3 q^{8} + 5 q^{9} + 2 q^{10} - q^{11} + 6 q^{12} + 5 q^{13} + 3 q^{15} + 13 q^{17} + 7 q^{19} + 13 q^{20} - 19 q^{22} - 4 q^{23} + 3 q^{24} + 16 q^{25} + 5 q^{27} - 12 q^{29} + 2 q^{30} + 6 q^{31} + 21 q^{32} - q^{33} + 7 q^{34} + 6 q^{36} + 11 q^{37} + 14 q^{38} + 5 q^{39} + 11 q^{40} + 10 q^{41} + 10 q^{43} - 29 q^{44} + 3 q^{45} + q^{46} - 4 q^{47} - 29 q^{50} + 13 q^{51} + 6 q^{52} - 9 q^{53} - 12 q^{55} + 7 q^{57} + 34 q^{58} + 7 q^{59} + 13 q^{60} + 23 q^{61} - 24 q^{62} - 13 q^{64} + 3 q^{65} - 19 q^{66} + 25 q^{67} + 20 q^{68} - 4 q^{69} - 27 q^{71} + 3 q^{72} + 18 q^{73} + 15 q^{74} + 16 q^{75} + 2 q^{76} + 8 q^{79} + 41 q^{80} + 5 q^{81} + 26 q^{82} + 12 q^{83} + 10 q^{85} - 19 q^{86} - 12 q^{87} - 36 q^{88} + 29 q^{89} + 2 q^{90} - 50 q^{92} + 6 q^{93} - 2 q^{94} - 33 q^{95} + 21 q^{96} + 13 q^{97} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^3 + 6 * q^4 + 3 * q^5 + 3 * q^8 + 5 * q^9 + 2 * q^10 - q^11 + 6 * q^12 + 5 * q^13 + 3 * q^15 + 13 * q^17 + 7 * q^19 + 13 * q^20 - 19 * q^22 - 4 * q^23 + 3 * q^24 + 16 * q^25 + 5 * q^27 - 12 * q^29 + 2 * q^30 + 6 * q^31 + 21 * q^32 - q^33 + 7 * q^34 + 6 * q^36 + 11 * q^37 + 14 * q^38 + 5 * q^39 + 11 * q^40 + 10 * q^41 + 10 * q^43 - 29 * q^44 + 3 * q^45 + q^46 - 4 * q^47 - 29 * q^50 + 13 * q^51 + 6 * q^52 - 9 * q^53 - 12 * q^55 + 7 * q^57 + 34 * q^58 + 7 * q^59 + 13 * q^60 + 23 * q^61 - 24 * q^62 - 13 * q^64 + 3 * q^65 - 19 * q^66 + 25 * q^67 + 20 * q^68 - 4 * q^69 - 27 * q^71 + 3 * q^72 + 18 * q^73 + 15 * q^74 + 16 * q^75 + 2 * q^76 + 8 * q^79 + 41 * q^80 + 5 * q^81 + 26 * q^82 + 12 * q^83 + 10 * q^85 - 19 * q^86 - 12 * q^87 - 36 * q^88 + 29 * q^89 + 2 * q^90 - 50 * q^92 + 6 * q^93 - 2 * q^94 - 33 * q^95 + 21 * q^96 + 13 * q^97 - q^99

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