LMFDB - Embedded newform 5929.2.a.bq.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, 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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
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} - 11x^{5} - x^{4} + 33x^{3} - x^{2} - 27x + 9 $ x^7 - 11x^5 - x^4 + 33x^3 - x^2 - 27*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 847)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.35905$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35905 q^{2} +2.65247 q^{3} +3.56512 q^{4} +3.32612 q^{5} -6.25730 q^{6} -3.69218 q^{8} +4.03558 q^{9} +O(q^{10})$	\(q-2.35905 q^{2} +2.65247 q^{3} +3.56512 q^{4} +3.32612 q^{5} -6.25730 q^{6} -3.69218 q^{8} +4.03558 q^{9} -7.84648 q^{10} +9.45635 q^{12} -0.793934 q^{13} +8.82241 q^{15} +1.57982 q^{16} +0.676528 q^{17} -9.52013 q^{18} +7.49630 q^{19} +11.8580 q^{20} -0.508843 q^{23} -9.79340 q^{24} +6.06306 q^{25} +1.87293 q^{26} +2.74683 q^{27} +2.93118 q^{29} -20.8125 q^{30} -1.78498 q^{31} +3.65750 q^{32} -1.59596 q^{34} +14.3873 q^{36} +9.83208 q^{37} -17.6841 q^{38} -2.10588 q^{39} -12.2806 q^{40} +3.91944 q^{41} -1.64982 q^{43} +13.4228 q^{45} +1.20039 q^{46} +11.6075 q^{47} +4.19041 q^{48} -14.3031 q^{50} +1.79447 q^{51} -2.83047 q^{52} -5.93353 q^{53} -6.47992 q^{54} +19.8837 q^{57} -6.91480 q^{58} +4.74527 q^{59} +31.4529 q^{60} -2.43036 q^{61} +4.21087 q^{62} -11.7879 q^{64} -2.64072 q^{65} -2.60692 q^{67} +2.41190 q^{68} -1.34969 q^{69} -12.5441 q^{71} -14.9001 q^{72} -0.512265 q^{73} -23.1944 q^{74} +16.0821 q^{75} +26.7252 q^{76} +4.96789 q^{78} -10.3206 q^{79} +5.25465 q^{80} -4.82085 q^{81} -9.24614 q^{82} -6.10655 q^{83} +2.25021 q^{85} +3.89201 q^{86} +7.77486 q^{87} +1.74455 q^{89} -31.6651 q^{90} -1.81408 q^{92} -4.73461 q^{93} -27.3826 q^{94} +24.9336 q^{95} +9.70141 q^{96} -3.03917 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{3} + 8 q^{4} + 4 q^{5} + 2 q^{6} + 3 q^{8} + 10 q^{9}+O(q^{10}) $ 7 * q + 3 * q^3 + 8 * q^4 + 4 * q^5 + 2 * q^6 + 3 * q^8 + 10 * q^9	$ 7 q + 3 q^{3} + 8 q^{4} + 4 q^{5} + 2 q^{6} + 3 q^{8} + 10 q^{9} - 6 q^{10} + 13 q^{12} - 6 q^{13} - q^{15} + 6 q^{16} + 3 q^{17} - 14 q^{18} + 9 q^{19} + 2 q^{20} - 6 q^{23} - 4 q^{24} + 7 q^{25} + 25 q^{26} + 12 q^{27} - 6 q^{29} - 16 q^{30} + 14 q^{31} + 36 q^{32} + 8 q^{34} - 2 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} - 18 q^{40} + 10 q^{41} - 17 q^{43} + 12 q^{45} - 16 q^{46} + 30 q^{47} + 56 q^{48} - 21 q^{50} + 20 q^{51} + 37 q^{52} - 10 q^{53} + 7 q^{54} + 31 q^{57} - 13 q^{58} + 20 q^{59} + 42 q^{60} - 7 q^{61} - 26 q^{62} + 21 q^{64} - 12 q^{65} + 7 q^{67} - 7 q^{68} + 9 q^{69} - 11 q^{71} + q^{72} + 6 q^{73} - 8 q^{74} - q^{75} + 56 q^{76} + 15 q^{78} + 14 q^{79} + 12 q^{80} + 35 q^{81} - 7 q^{82} - 17 q^{83} + 2 q^{85} + 15 q^{87} + 40 q^{89} - 68 q^{90} - 26 q^{92} - 19 q^{94} - 20 q^{95} + 63 q^{96} - 22 q^{97}+O(q^{100}) $ 7 * q + 3 * q^3 + 8 * q^4 + 4 * q^5 + 2 * q^6 + 3 * q^8 + 10 * q^9 - 6 * q^10 + 13 * q^12 - 6 * q^13 - q^15 + 6 * q^16 + 3 * q^17 - 14 * q^18 + 9 * q^19 + 2 * q^20 - 6 * q^23 - 4 * q^24 + 7 * q^25 + 25 * q^26 + 12 * q^27 - 6 * q^29 - 16 * q^30 + 14 * q^31 + 36 * q^32 + 8 * q^34 - 2 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 - 18 * q^40 + 10 * q^41 - 17 * q^43 + 12 * q^45 - 16 * q^46 + 30 * q^47 + 56 * q^48 - 21 * q^50 + 20 * q^51 + 37 * q^52 - 10 * q^53 + 7 * q^54 + 31 * q^57 - 13 * q^58 + 20 * q^59 + 42 * q^60 - 7 * q^61 - 26 * q^62 + 21 * q^64 - 12 * q^65 + 7 * q^67 - 7 * q^68 + 9 * q^69 - 11 * q^71 + q^72 + 6 * q^73 - 8 * q^74 - q^75 + 56 * q^76 + 15 * q^78 + 14 * q^79 + 12 * q^80 + 35 * q^81 - 7 * q^82 - 17 * q^83 + 2 * q^85 + 15 * q^87 + 40 * q^89 - 68 * q^90 - 26 * q^92 - 19 * q^94 - 20 * q^95 + 63 * q^96 - 22 * q^97

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 $

$2$	−2.35905	−1.66810	−0.834050	−	0.551689i	$-0.813984\pi$
$2$	−2.35905	−1.66810	−0.834050	+	0.551689i	$0.813984\pi$
$3$	2.65247	1.53140	0.765701	−	0.643197i	$-0.222392\pi$
$3$	2.65247	1.53140	0.765701	+	0.643197i	$0.222392\pi$
$4$	3.56512	1.78256
$5$	3.32612	1.48749	0.743743	−	0.668466i	$-0.233049\pi$
$5$	3.32612	1.48749	0.743743	+	0.668466i	$0.233049\pi$
$6$	−6.25730	−2.55453
$7$	0	0
$7$	0	0
$8$	−3.69218	−1.30538
$9$	4.03558	1.34519
$10$	−7.84648	−2.48127
$11$	0	0
$11$	0	0
$12$	9.45635	2.72981
$13$	−0.793934	−0.220198	−0.110099	−	0.993921i	$-0.535117\pi$
$13$	−0.793934	−0.220198	−0.110099	+	0.993921i	$0.535117\pi$
$14$	0	0
$15$	8.82241	2.27794
$16$	1.57982	0.394954
$17$	0.676528	0.164082	0.0820411	−	0.996629i	$-0.473856\pi$
$17$	0.676528	0.164082	0.0820411	+	0.996629i	$0.473856\pi$
$18$	−9.52013	−2.24392
$19$	7.49630	1.71977	0.859884	−	0.510489i	$-0.170536\pi$
$19$	7.49630	1.71977	0.859884	+	0.510489i	$0.170536\pi$
$20$	11.8580	2.65153
$21$	0	0
$22$	0	0
$23$	−0.508843	−0.106101	−0.0530505	−	0.998592i	$-0.516894\pi$
$23$	−0.508843	−0.106101	−0.0530505	+	0.998592i	$0.516894\pi$
$24$	−9.79340	−1.99907
$25$	6.06306	1.21261
$26$	1.87293	0.367312
$27$	2.74683	0.528629
$28$	0	0
$29$	2.93118	0.544307	0.272153	−	0.962254i	$-0.412264\pi$
$29$	2.93118	0.544307	0.272153	+	0.962254i	$0.412264\pi$
$30$	−20.8125	−3.79983
$31$	−1.78498	−0.320593	−0.160296	−	0.987069i	$-0.551245\pi$
$31$	−1.78498	−0.320593	−0.160296	+	0.987069i	$0.551245\pi$
$32$	3.65750	0.646562
$33$	0	0
$34$	−1.59596	−0.273705
$35$	0	0
$36$	14.3873	2.39788
$37$	9.83208	1.61638	0.808192	−	0.588919i	$-0.200446\pi$
$37$	9.83208	1.61638	0.808192	+	0.588919i	$0.200446\pi$
$38$	−17.6841	−2.86875
$39$	−2.10588	−0.337211
$40$	−12.2806	−1.94174
$41$	3.91944	0.612113	0.306056	−	0.952013i	$-0.400990\pi$
$41$	3.91944	0.612113	0.306056	+	0.952013i	$0.400990\pi$
$42$	0	0
$43$	−1.64982	−0.251595	−0.125798	−	0.992056i	$-0.540149\pi$
$43$	−1.64982	−0.251595	−0.125798	+	0.992056i	$0.540149\pi$
$44$	0	0
$45$	13.4228	2.00095
$46$	1.20039	0.176987
$47$	11.6075	1.69312	0.846562	−	0.532289i	$-0.178668\pi$
$47$	11.6075	1.69312	0.846562	+	0.532289i	$0.178668\pi$
$48$	4.19041	0.604833
$49$	0	0
$50$	−14.3031	−2.02276
$51$	1.79447	0.251276
$52$	−2.83047	−0.392515
$53$	−5.93353	−0.815032	−0.407516	−	0.913198i	$-0.633605\pi$
$53$	−5.93353	−0.815032	−0.407516	+	0.913198i	$0.633605\pi$
$54$	−6.47992	−0.881805
$55$	0	0
$56$	0	0
$57$	19.8837	2.63366
$58$	−6.91480	−0.907958
$59$	4.74527	0.617781	0.308891	−	0.951098i	$-0.400042\pi$
$59$	4.74527	0.617781	0.308891	+	0.951098i	$0.400042\pi$
$60$	31.4529	4.06056
$61$	−2.43036	−0.311176	−0.155588	−	0.987822i	$-0.549727\pi$
$61$	−2.43036	−0.311176	−0.155588	+	0.987822i	$0.549727\pi$
$62$	4.21087	0.534781
$63$	0	0
$64$	−11.7879	−1.47348
$65$	−2.64072	−0.327541
$66$	0	0
$67$	−2.60692	−0.318486	−0.159243	−	0.987239i	$-0.550905\pi$
$67$	−2.60692	−0.318486	−0.159243	+	0.987239i	$0.550905\pi$
$68$	2.41190	0.292486
$69$	−1.34969	−0.162483
$70$	0	0
$71$	−12.5441	−1.48871	−0.744356	−	0.667783i	$-0.767243\pi$
$71$	−12.5441	−1.48871	−0.744356	+	0.667783i	$0.767243\pi$
$72$	−14.9001	−1.75599
$73$	−0.512265	−0.0599561	−0.0299780	−	0.999551i	$-0.509544\pi$
$73$	−0.512265	−0.0599561	−0.0299780	+	0.999551i	$0.509544\pi$
$74$	−23.1944	−2.69629
$75$	16.0821	1.85700
$76$	26.7252	3.06559
$77$	0	0
$78$	4.96789	0.562502
$79$	−10.3206	−1.16116	−0.580582	−	0.814202i	$-0.697175\pi$
$79$	−10.3206	−1.16116	−0.580582	+	0.814202i	$0.697175\pi$
$80$	5.25465	0.587488
$81$	−4.82085	−0.535650
$82$	−9.24614	−1.02107
$83$	−6.10655	−0.670281	−0.335141	−	0.942168i	$-0.608784\pi$
$83$	−6.10655	−0.670281	−0.335141	+	0.942168i	$0.608784\pi$
$84$	0	0
$85$	2.25021	0.244070
$86$	3.89201	0.419686
$87$	7.77486	0.833553
$88$	0	0
$89$	1.74455	0.184922	0.0924611	−	0.995716i	$-0.470527\pi$
$89$	1.74455	0.184922	0.0924611	+	0.995716i	$0.470527\pi$
$90$	−31.6651	−3.33779
$91$	0	0
$92$	−1.81408	−0.189131
$93$	−4.73461	−0.490956
$94$	−27.3826	−2.82430
$95$	24.9336	2.55813
$96$	9.70141	0.990146
$97$	−3.03917	−0.308581	−0.154291	−	0.988026i	$-0.549309\pi$
$97$	−3.03917	−0.308581	−0.154291	+	0.988026i	$0.549309\pi$
$98$	0	0
$99$	0	0
$100$	21.6155	2.16155
$101$	−14.6675	−1.45947	−0.729733	−	0.683732i	$-0.760356\pi$
$101$	−14.6675	−1.45947	−0.729733	+	0.683732i	$0.760356\pi$
$102$	−4.23324	−0.419153
$103$	−8.54820	−0.842279	−0.421139	−	0.906996i	$-0.638370\pi$
$103$	−8.54820	−0.842279	−0.421139	+	0.906996i	$0.638370\pi$
$104$	2.93135	0.287443
$105$	0	0
$106$	13.9975	1.35956
$107$	−6.19766	−0.599151	−0.299575	−	0.954073i	$-0.596845\pi$
$107$	−6.19766	−0.599151	−0.299575	+	0.954073i	$0.596845\pi$
$108$	9.79278	0.942311
$109$	12.5527	1.20233	0.601165	−	0.799125i	$-0.294703\pi$
$109$	12.5527	1.20233	0.601165	+	0.799125i	$0.294703\pi$
$110$	0	0
$111$	26.0793	2.47533
$112$	0	0
$113$	3.12995	0.294441	0.147220	−	0.989104i	$-0.452967\pi$
$113$	3.12995	0.294441	0.147220	+	0.989104i	$0.452967\pi$
$114$	−46.9066	−4.39320
$115$	−1.69247	−0.157824
$116$	10.4500	0.970258
$117$	−3.20398	−0.296208
$118$	−11.1943	−1.03052
$119$	0	0
$120$	−32.5740	−2.97358
$121$	0	0
$122$	5.73335	0.519073
$123$	10.3962	0.937391
$124$	−6.36367	−0.571475
$125$	3.53586	0.316257
$126$	0	0
$127$	17.8817	1.58675	0.793374	−	0.608734i	$-0.208322\pi$
$127$	17.8817	1.58675	0.793374	+	0.608734i	$0.208322\pi$
$128$	20.4932	1.81136
$129$	−4.37609	−0.385294
$130$	6.22959	0.546371
$131$	9.04057	0.789878	0.394939	−	0.918707i	$-0.370766\pi$
$131$	9.04057	0.789878	0.394939	+	0.918707i	$0.370766\pi$
$132$	0	0
$133$	0	0
$134$	6.14985	0.531266
$135$	9.13630	0.786327
$136$	−2.49787	−0.214190
$137$	−17.5407	−1.49860	−0.749301	−	0.662229i	$-0.769611\pi$
$137$	−17.5407	−1.49860	−0.749301	+	0.662229i	$0.769611\pi$
$138$	3.18398	0.271039
$139$	−14.4410	−1.22487	−0.612435	−	0.790521i	$-0.709810\pi$
$139$	−14.4410	−1.22487	−0.612435	+	0.790521i	$0.709810\pi$
$140$	0	0
$141$	30.7884	2.59285
$142$	29.5922	2.48332
$143$	0	0
$144$	6.37547	0.531289
$145$	9.74946	0.809648
$146$	1.20846	0.100013
$147$	0	0
$148$	35.0525	2.88130
$149$	5.36028	0.439131	0.219566	−	0.975598i	$-0.429536\pi$
$149$	5.36028	0.439131	0.219566	+	0.975598i	$0.429536\pi$
$150$	−37.9384	−3.09766
$151$	17.4025	1.41619	0.708097	−	0.706115i	$-0.249554\pi$
$151$	17.4025	1.41619	0.708097	+	0.706115i	$0.249554\pi$
$152$	−27.6777	−2.24496
$153$	2.73018	0.220722
$154$	0	0
$155$	−5.93707	−0.476877
$156$	−7.50772	−0.601099
$157$	−20.3501	−1.62412	−0.812058	−	0.583577i	$-0.801653\pi$
$157$	−20.3501	−1.62412	−0.812058	+	0.583577i	$0.801653\pi$
$158$	24.3469	1.93694
$159$	−15.7385	−1.24814
$160$	12.1653	0.961751
$161$	0	0
$162$	11.3726	0.893517
$163$	19.1904	1.50311	0.751554	−	0.659671i	$-0.229304\pi$
$163$	19.1904	1.50311	0.751554	+	0.659671i	$0.229304\pi$
$164$	13.9732	1.09113
$165$	0	0
$166$	14.4057	1.11810
$167$	3.03331	0.234724	0.117362	−	0.993089i	$-0.462556\pi$
$167$	3.03331	0.234724	0.117362	+	0.993089i	$0.462556\pi$
$168$	0	0
$169$	−12.3697	−0.951513
$170$	−5.30836	−0.407133
$171$	30.2519	2.31342
$172$	−5.88180	−0.448483
$173$	−13.1838	−1.00235	−0.501173	−	0.865347i	$-0.667098\pi$
$173$	−13.1838	−1.00235	−0.501173	+	0.865347i	$0.667098\pi$
$174$	−18.3413	−1.39045
$175$	0	0
$176$	0	0
$177$	12.5867	0.946071
$178$	−4.11549	−0.308469
$179$	8.66931	0.647975	0.323987	−	0.946061i	$-0.394976\pi$
$179$	8.66931	0.647975	0.323987	+	0.946061i	$0.394976\pi$
$180$	47.8538	3.56682
$181$	1.85452	0.137846	0.0689228	−	0.997622i	$-0.478044\pi$
$181$	1.85452	0.137846	0.0689228	+	0.997622i	$0.478044\pi$
$182$	0	0
$183$	−6.44645	−0.476536
$184$	1.87874	0.138503
$185$	32.7026	2.40435
$186$	11.1692	0.818964
$187$	0	0
$188$	41.3820	3.01809
$189$	0	0
$190$	−58.8195	−4.26722
$191$	11.2843	0.816503	0.408251	−	0.912870i	$-0.366139\pi$
$191$	11.2843	0.816503	0.408251	+	0.912870i	$0.366139\pi$
$192$	−31.2669	−2.25650
$193$	6.59354	0.474614	0.237307	−	0.971435i	$-0.423735\pi$
$193$	6.59354	0.474614	0.237307	+	0.971435i	$0.423735\pi$
$194$	7.16956	0.514744
$195$	−7.00442	−0.501597
$196$	0	0
$197$	14.3199	1.02025	0.510125	−	0.860100i	$-0.329599\pi$
$197$	14.3199	1.02025	0.510125	+	0.860100i	$0.329599\pi$
$198$	0	0
$199$	12.5710	0.891131	0.445566	−	0.895249i	$-0.353003\pi$
$199$	12.5710	0.891131	0.445566	+	0.895249i	$0.353003\pi$
$200$	−22.3859	−1.58292
$201$	−6.91476	−0.487730
$202$	34.6013	2.43454
$203$	0	0
$204$	6.39748	0.447913
$205$	13.0365	0.910509
$206$	20.1656	1.40501
$207$	−2.05348	−0.142726
$208$	−1.25427	−0.0869680
$209$	0	0
$210$	0	0
$211$	−22.0451	−1.51765	−0.758824	−	0.651296i	$-0.774226\pi$
$211$	−22.0451	−1.51765	−0.758824	+	0.651296i	$0.774226\pi$
$212$	−21.1537	−1.45284
$213$	−33.2728	−2.27982
$214$	14.6206	0.999443
$215$	−5.48750	−0.374244
$216$	−10.1418	−0.690063
$217$	0	0
$218$	−29.6124	−2.00561
$219$	−1.35877	−0.0918168
$220$	0	0
$221$	−0.537119	−0.0361305
$222$	−61.5223	−4.12910
$223$	−15.0462	−1.00757	−0.503783	−	0.863830i	$-0.668059\pi$
$223$	−15.0462	−1.00757	−0.503783	+	0.863830i	$0.668059\pi$
$224$	0	0
$225$	24.4679	1.63120
$226$	−7.38370	−0.491156
$227$	2.19290	0.145548	0.0727741	−	0.997348i	$-0.476815\pi$
$227$	2.19290	0.145548	0.0727741	+	0.997348i	$0.476815\pi$
$228$	70.8876	4.69465
$229$	3.06065	0.202254	0.101127	−	0.994874i	$-0.467755\pi$
$229$	3.06065	0.202254	0.101127	+	0.994874i	$0.467755\pi$
$230$	3.99262	0.263266
$231$	0	0
$232$	−10.8225	−0.710530
$233$	9.73977	0.638073	0.319037	−	0.947742i	$-0.396641\pi$
$233$	9.73977	0.638073	0.319037	+	0.947742i	$0.396641\pi$
$234$	7.55836	0.494105
$235$	38.6078	2.51850
$236$	16.9174	1.10123
$237$	−27.3752	−1.77821
$238$	0	0
$239$	25.1364	1.62594	0.812968	−	0.582308i	$-0.197850\pi$
$239$	25.1364	1.62594	0.812968	+	0.582308i	$0.197850\pi$
$240$	13.9378	0.899681
$241$	9.01901	0.580965	0.290483	−	0.956880i	$-0.406184\pi$
$241$	9.01901	0.580965	0.290483	+	0.956880i	$0.406184\pi$
$242$	0	0
$243$	−21.0276	−1.34892
$244$	−8.66452	−0.554689
$245$	0	0
$246$	−24.5251	−1.56366
$247$	−5.95157	−0.378689
$248$	6.59049	0.418497
$249$	−16.1974	−1.02647
$250$	−8.34126	−0.527548
$251$	26.0157	1.64210	0.821048	−	0.570859i	$-0.193390\pi$
$251$	26.0157	1.64210	0.821048	+	0.570859i	$0.193390\pi$
$252$	0	0
$253$	0	0
$254$	−42.1839	−2.64685
$255$	5.96861	0.373769
$256$	−24.7686	−1.54804
$257$	1.28503	0.0801582	0.0400791	−	0.999197i	$-0.487239\pi$
$257$	1.28503	0.0801582	0.0400791	+	0.999197i	$0.487239\pi$
$258$	10.3234	0.642708
$259$	0	0
$260$	−9.41447	−0.583861
$261$	11.8290	0.732198
$262$	−21.3271	−1.31760
$263$	1.90743	0.117617	0.0588085	−	0.998269i	$-0.481270\pi$
$263$	1.90743	0.117617	0.0588085	+	0.998269i	$0.481270\pi$
$264$	0	0
$265$	−19.7356	−1.21235
$266$	0	0
$267$	4.62737	0.283190
$268$	−9.29396	−0.567719
$269$	23.8768	1.45579	0.727896	−	0.685688i	$-0.240498\pi$
$269$	23.8768	1.45579	0.727896	+	0.685688i	$0.240498\pi$
$270$	−21.5530	−1.31167
$271$	−16.5914	−1.00786	−0.503929	−	0.863745i	$-0.668113\pi$
$271$	−16.5914	−1.00786	−0.503929	+	0.863745i	$0.668113\pi$
$272$	1.06879	0.0648049
$273$	0	0
$274$	41.3794	2.49982
$275$	0	0
$276$	−4.81180	−0.289636
$277$	−8.05154	−0.483770	−0.241885	−	0.970305i	$-0.577766\pi$
$277$	−8.05154	−0.483770	−0.241885	+	0.970305i	$0.577766\pi$
$278$	34.0670	2.04321
$279$	−7.20344	−0.431259
$280$	0	0
$281$	5.15806	0.307704	0.153852	−	0.988094i	$-0.450832\pi$
$281$	5.15806	0.307704	0.153852	+	0.988094i	$0.450832\pi$
$282$	−72.6315	−4.32514
$283$	−3.53272	−0.209999	−0.104999	−	0.994472i	$-0.533484\pi$
$283$	−3.53272	−0.209999	−0.104999	+	0.994472i	$0.533484\pi$
$284$	−44.7212	−2.65371
$285$	66.1354	3.91753
$286$	0	0
$287$	0	0
$288$	14.7601	0.869750
$289$	−16.5423	−0.973077
$290$	−22.9995	−1.35057
$291$	−8.06130	−0.472562
$292$	−1.82628	−0.106875
$293$	−6.02347	−0.351895	−0.175947	−	0.984400i	$-0.556299\pi$
$293$	−6.02347	−0.351895	−0.175947	+	0.984400i	$0.556299\pi$
$294$	0	0
$295$	15.7833	0.918940
$296$	−36.3018	−2.11000
$297$	0	0
$298$	−12.6452	−0.732515
$299$	0.403988	0.0233632
$300$	57.3344	3.31020
$301$	0	0
$302$	−41.0533	−2.36235
$303$	−38.9049	−2.23503
$304$	11.8428	0.679230
$305$	−8.08367	−0.462870
$306$	−6.44063	−0.368186
$307$	−27.6588	−1.57857	−0.789287	−	0.614025i	$-0.789549\pi$
$307$	−27.6588	−1.57857	−0.789287	+	0.614025i	$0.789549\pi$
$308$	0	0
$309$	−22.6738	−1.28987
$310$	14.0058	0.795478
$311$	14.4958	0.821980	0.410990	−	0.911640i	$-0.365183\pi$
$311$	14.4958	0.821980	0.410990	+	0.911640i	$0.365183\pi$
$312$	7.77531	0.440190
$313$	23.6328	1.33580	0.667902	−	0.744249i	$-0.267193\pi$
$313$	23.6328	1.33580	0.667902	+	0.744249i	$0.267193\pi$
$314$	48.0069	2.70919
$315$	0	0
$316$	−36.7943	−2.06984
$317$	25.6388	1.44002	0.720008	−	0.693965i	$-0.244138\pi$
$317$	25.6388	1.44002	0.720008	+	0.693965i	$0.244138\pi$
$318$	37.1278	2.08203
$319$	0	0
$320$	−39.2078	−2.19178
$321$	−16.4391	−0.917541
$322$	0	0
$323$	5.07145	0.282183
$324$	−17.1869	−0.954826
$325$	−4.81367	−0.267014
$326$	−45.2711	−2.50734
$327$	33.2956	1.84125
$328$	−14.4713	−0.799043
$329$	0	0
$330$	0	0
$331$	19.4990	1.07176	0.535880	−	0.844294i	$-0.319980\pi$
$331$	19.4990	1.07176	0.535880	+	0.844294i	$0.319980\pi$
$332$	−21.7706	−1.19481
$333$	39.6781	2.17435
$334$	−7.15572	−0.391543
$335$	−8.67091	−0.473743
$336$	0	0
$337$	12.5762	0.685072	0.342536	−	0.939505i	$-0.388714\pi$
$337$	12.5762	0.685072	0.342536	+	0.939505i	$0.388714\pi$
$338$	29.1807	1.58722
$339$	8.30208	0.450907
$340$	8.02226	0.435068
$341$	0	0
$342$	−71.3657	−3.85902
$343$	0	0
$344$	6.09144	0.328429
$345$	−4.48922	−0.241692
$346$	31.1012	1.67201
$347$	−26.6951	−1.43307	−0.716533	−	0.697553i	$-0.754272\pi$
$347$	−26.6951	−1.43307	−0.716533	+	0.697553i	$0.754272\pi$
$348$	27.7183	1.48586
$349$	−12.1521	−0.650488	−0.325244	−	0.945630i	$-0.605446\pi$
$349$	−12.1521	−0.650488	−0.325244	+	0.945630i	$0.605446\pi$
$350$	0	0
$351$	−2.18081	−0.116403
$352$	0	0
$353$	−31.0014	−1.65004	−0.825018	−	0.565106i	$-0.808835\pi$
$353$	−31.0014	−1.65004	−0.825018	+	0.565106i	$0.808835\pi$
$354$	−29.6926	−1.57814
$355$	−41.7232	−2.21444
$356$	6.21953	0.329635
$357$	0	0
$358$	−20.4513	−1.08089
$359$	5.89396	0.311072	0.155536	−	0.987830i	$-0.450290\pi$
$359$	5.89396	0.311072	0.155536	+	0.987830i	$0.450290\pi$
$360$	−49.5595	−2.61201
$361$	37.1945	1.95760
$362$	−4.37491	−0.229940
$363$	0	0
$364$	0	0
$365$	−1.70385	−0.0891837
$366$	15.2075	0.794909
$367$	21.7508	1.13538	0.567690	−	0.823242i	$-0.307837\pi$
$367$	21.7508	1.13538	0.567690	+	0.823242i	$0.307837\pi$
$368$	−0.803878	−0.0419051
$369$	15.8172	0.823410
$370$	−77.1472	−4.01069
$371$	0	0
$372$	−16.8794	−0.875158
$373$	−25.2083	−1.30524	−0.652619	−	0.757686i	$-0.726330\pi$
$373$	−25.2083	−1.30524	−0.652619	+	0.757686i	$0.726330\pi$
$374$	0	0
$375$	9.37874	0.484316
$376$	−42.8570	−2.21018
$377$	−2.32717	−0.119855
$378$	0	0
$379$	1.79889	0.0924029	0.0462014	−	0.998932i	$-0.485288\pi$
$379$	1.79889	0.0924029	0.0462014	+	0.998932i	$0.485288\pi$
$380$	88.8910	4.56001
$381$	47.4307	2.42995
$382$	−26.6202	−1.36201
$383$	−21.0066	−1.07339	−0.536693	−	0.843778i	$-0.680327\pi$
$383$	−21.0066	−1.07339	−0.536693	+	0.843778i	$0.680327\pi$
$384$	54.3574	2.77391
$385$	0	0
$386$	−15.5545	−0.791703
$387$	−6.65798	−0.338444
$388$	−10.8350	−0.550064
$389$	−21.0133	−1.06542	−0.532709	−	0.846299i	$-0.678826\pi$
$389$	−21.0133	−1.06542	−0.532709	+	0.846299i	$0.678826\pi$
$390$	16.5238	0.836714
$391$	−0.344247	−0.0174093
$392$	0	0
$393$	23.9798	1.20962
$394$	−33.7814	−1.70188
$395$	−34.3277	−1.72721
$396$	0	0
$397$	−16.7210	−0.839205	−0.419602	−	0.907708i	$-0.637830\pi$
$397$	−16.7210	−0.839205	−0.419602	+	0.907708i	$0.637830\pi$
$398$	−29.6555	−1.48650
$399$	0	0
$400$	9.57852	0.478926
$401$	−22.5761	−1.12740	−0.563698	−	0.825981i	$-0.690622\pi$
$401$	−22.5761	−1.12740	−0.563698	+	0.825981i	$0.690622\pi$
$402$	16.3123	0.813582
$403$	1.41716	0.0705938
$404$	−52.2912	−2.60158
$405$	−16.0347	−0.796771
$406$	0	0
$407$	0	0
$408$	−6.62551	−0.328011
$409$	−8.44206	−0.417433	−0.208717	−	0.977976i	$-0.566929\pi$
$409$	−8.44206	−0.417433	−0.208717	+	0.977976i	$0.566929\pi$
$410$	−30.7538	−1.51882
$411$	−46.5261	−2.29496
$412$	−30.4753	−1.50141
$413$	0	0
$414$	4.84425	0.238082
$415$	−20.3111	−0.997033
$416$	−2.90382	−0.142371
$417$	−38.3043	−1.87577
$418$	0	0
$419$	1.89905	0.0927747	0.0463874	−	0.998924i	$-0.485229\pi$
$419$	1.89905	0.0927747	0.0463874	+	0.998924i	$0.485229\pi$
$420$	0	0
$421$	10.7348	0.523182	0.261591	−	0.965179i	$-0.415753\pi$
$421$	10.7348	0.523182	0.261591	+	0.965179i	$0.415753\pi$
$422$	52.0055	2.53159
$423$	46.8429	2.27758
$424$	21.9077	1.06393
$425$	4.10183	0.198968
$426$	78.4923	3.80296
$427$	0	0
$428$	−22.0954	−1.06802
$429$	0	0
$430$	12.9453	0.624277
$431$	−11.2719	−0.542947	−0.271474	−	0.962446i	$-0.587511\pi$
$431$	−11.2719	−0.542947	−0.271474	+	0.962446i	$0.587511\pi$
$432$	4.33949	0.208784
$433$	3.68638	0.177156	0.0885782	−	0.996069i	$-0.471768\pi$
$433$	3.68638	0.177156	0.0885782	+	0.996069i	$0.471768\pi$
$434$	0	0
$435$	25.8601	1.23990
$436$	44.7518	2.14322
$437$	−3.81444	−0.182469
$438$	3.20539	0.153160
$439$	−25.3116	−1.20806	−0.604029	−	0.796963i	$-0.706439\pi$
$439$	−25.3116	−1.20806	−0.604029	+	0.796963i	$0.706439\pi$
$440$	0	0
$441$	0	0
$442$	1.26709	0.0602693
$443$	27.7722	1.31950	0.659748	−	0.751487i	$-0.270663\pi$
$443$	27.7722	1.31950	0.659748	+	0.751487i	$0.270663\pi$
$444$	92.9755	4.41242
$445$	5.80259	0.275069
$446$	35.4947	1.68072
$447$	14.2180	0.672486
$448$	0	0
$449$	7.12882	0.336430	0.168215	−	0.985750i	$-0.446200\pi$
$449$	7.12882	0.336430	0.168215	+	0.985750i	$0.446200\pi$
$450$	−57.7211	−2.72100
$451$	0	0
$452$	11.1586	0.524857
$453$	46.1595	2.16876
$454$	−5.17317	−0.242789
$455$	0	0
$456$	−73.4142	−3.43793
$457$	9.43858	0.441518	0.220759	−	0.975328i	$-0.429147\pi$
$457$	9.43858	0.441518	0.220759	+	0.975328i	$0.429147\pi$
$458$	−7.22023	−0.337379
$459$	1.85831	0.0867385
$460$	−6.03386	−0.281330
$461$	26.4814	1.23336	0.616681	−	0.787213i	$-0.288477\pi$
$461$	26.4814	1.23336	0.616681	+	0.787213i	$0.288477\pi$
$462$	0	0
$463$	−16.8153	−0.781474	−0.390737	−	0.920502i	$-0.627780\pi$
$463$	−16.8153	−0.781474	−0.390737	+	0.920502i	$0.627780\pi$
$464$	4.63073	0.214976
$465$	−15.7479	−0.730290
$466$	−22.9766	−1.06437
$467$	16.6996	0.772764	0.386382	−	0.922339i	$-0.373725\pi$
$467$	16.6996	0.772764	0.386382	+	0.922339i	$0.373725\pi$
$468$	−11.4226	−0.528009
$469$	0	0
$470$	−91.0778	−4.20111
$471$	−53.9780	−2.48717
$472$	−17.5204	−0.806442
$473$	0	0
$474$	64.5794	2.96623
$475$	45.4505	2.08541
$476$	0	0
$477$	−23.9452	−1.09638
$478$	−59.2979	−2.71223
$479$	5.23785	0.239323	0.119662	−	0.992815i	$-0.461819\pi$
$479$	5.23785	0.239323	0.119662	+	0.992815i	$0.461819\pi$
$480$	32.2680	1.47283
$481$	−7.80602	−0.355924
$482$	−21.2763	−0.969108
$483$	0	0
$484$	0	0
$485$	−10.1086	−0.459010
$486$	49.6052	2.25014
$487$	−21.2181	−0.961482	−0.480741	−	0.876863i	$-0.659632\pi$
$487$	−21.2181	−0.961482	−0.480741	+	0.876863i	$0.659632\pi$
$488$	8.97335	0.406204
$489$	50.9019	2.30186
$490$	0	0
$491$	−9.43930	−0.425989	−0.212995	−	0.977053i	$-0.568322\pi$
$491$	−9.43930	−0.425989	−0.212995	+	0.977053i	$0.568322\pi$
$492$	37.0635	1.67095
$493$	1.98303	0.0893110
$494$	14.0400	0.631692
$495$	0	0
$496$	−2.81995	−0.126619
$497$	0	0
$498$	38.2105	1.71225
$499$	−20.4341	−0.914755	−0.457378	−	0.889273i	$-0.651211\pi$
$499$	−20.4341	−0.914755	−0.457378	+	0.889273i	$0.651211\pi$
$500$	12.6057	0.563746
$501$	8.04574	0.359457
$502$	−61.3723	−2.73918
$503$	35.2228	1.57051	0.785255	−	0.619173i	$-0.212532\pi$
$503$	35.2228	1.57051	0.785255	+	0.619173i	$0.212532\pi$
$504$	0	0
$505$	−48.7857	−2.17093
$506$	0	0
$507$	−32.8101	−1.45715
$508$	63.7505	2.82847
$509$	−25.6132	−1.13528	−0.567642	−	0.823276i	$-0.692144\pi$
$509$	−25.6132	−1.13528	−0.567642	+	0.823276i	$0.692144\pi$
$510$	−14.0802	−0.623484
$511$	0	0
$512$	17.4441	0.770929
$513$	20.5911	0.909119
$514$	−3.03146	−0.133712
$515$	−28.4323	−1.25288
$516$	−15.6013	−0.686808
$517$	0	0
$518$	0	0
$519$	−34.9696	−1.53499
$520$	9.75002	0.427567
$521$	−14.4165	−0.631598	−0.315799	−	0.948826i	$-0.602273\pi$
$521$	−14.4165	−0.631598	−0.315799	+	0.948826i	$0.602273\pi$
$522$	−27.9052	−1.22138
$523$	−13.1716	−0.575955	−0.287977	−	0.957637i	$-0.592983\pi$
$523$	−13.1716	−0.575955	−0.287977	+	0.957637i	$0.592983\pi$
$524$	32.2307	1.40800
$525$	0	0
$526$	−4.49972	−0.196197
$527$	−1.20759	−0.0526035
$528$	0	0
$529$	−22.7411	−0.988743
$530$	46.5573	2.02232
$531$	19.1499	0.831034
$532$	0	0
$533$	−3.11177	−0.134786
$534$	−10.9162	−0.472390
$535$	−20.6142	−0.891228
$536$	9.62522	0.415746
$537$	22.9951	0.992310
$538$	−56.3265	−2.42841
$539$	0	0
$540$	32.5719	1.40167
$541$	35.6561	1.53298	0.766489	−	0.642258i	$-0.222002\pi$
$541$	35.6561	1.53298	0.766489	+	0.642258i	$0.222002\pi$
$542$	39.1400	1.68121
$543$	4.91906	0.211097
$544$	2.47440	0.106089
$545$	41.7517	1.78845
$546$	0	0
$547$	0.398641	0.0170447	0.00852234	−	0.999964i	$-0.497287\pi$
$547$	0.398641	0.0170447	0.00852234	+	0.999964i	$0.497287\pi$
$548$	−62.5346	−2.67135
$549$	−9.80792	−0.418592
$550$	0	0
$551$	21.9730	0.936082
$552$	4.98330	0.212103
$553$	0	0
$554$	18.9940	0.806977
$555$	86.7427	3.68202
$556$	−51.4838	−2.18340
$557$	0.919475	0.0389594	0.0194797	−	0.999810i	$-0.493799\pi$
$557$	0.919475	0.0389594	0.0194797	+	0.999810i	$0.493799\pi$
$558$	16.9933	0.719383
$559$	1.30985	0.0554007
$560$	0	0
$561$	0	0
$562$	−12.1681	−0.513282
$563$	−26.0775	−1.09904	−0.549519	−	0.835481i	$-0.685189\pi$
$563$	−26.0775	−1.09904	−0.549519	+	0.835481i	$0.685189\pi$
$564$	109.764	4.62191
$565$	10.4106	0.437976
$566$	8.33387	0.350299
$567$	0	0
$568$	46.3152	1.94334
$569$	−28.6888	−1.20270	−0.601348	−	0.798988i	$-0.705369\pi$
$569$	−28.6888	−1.20270	−0.601348	+	0.798988i	$0.705369\pi$
$570$	−156.017	−6.53482
$571$	−17.7105	−0.741160	−0.370580	−	0.928801i	$-0.620841\pi$
$571$	−17.7105	−0.741160	−0.370580	+	0.928801i	$0.620841\pi$
$572$	0	0
$573$	29.9312	1.25039
$574$	0	0
$575$	−3.08514	−0.128659
$576$	−47.5709	−1.98212
$577$	8.31430	0.346129	0.173064	−	0.984911i	$-0.444633\pi$
$577$	8.31430	0.346129	0.173064	+	0.984911i	$0.444633\pi$
$578$	39.0241	1.62319
$579$	17.4891	0.726824
$580$	34.7579	1.44324
$581$	0	0
$582$	19.0170	0.788281
$583$	0	0
$584$	1.89138	0.0782657
$585$	−10.6568	−0.440606
$586$	14.2097	0.586995
$587$	18.4688	0.762289	0.381144	−	0.924516i	$-0.375530\pi$
$587$	18.4688	0.762289	0.381144	+	0.924516i	$0.375530\pi$
$588$	0	0
$589$	−13.3808	−0.551345
$590$	−37.2336	−1.53288
$591$	37.9831	1.56241
$592$	15.5329	0.638397
$593$	3.85511	0.158310	0.0791552	−	0.996862i	$-0.474778\pi$
$593$	3.85511	0.158310	0.0791552	+	0.996862i	$0.474778\pi$
$594$	0	0
$595$	0	0
$596$	19.1100	0.782776
$597$	33.3440	1.36468
$598$	−0.953028	−0.0389722
$599$	−29.2060	−1.19332	−0.596661	−	0.802493i	$-0.703506\pi$
$599$	−29.2060	−1.19332	−0.596661	+	0.802493i	$0.703506\pi$
$600$	−59.3779	−2.42409
$601$	44.0990	1.79883	0.899417	−	0.437092i	$-0.143992\pi$
$601$	44.0990	1.79883	0.899417	+	0.437092i	$0.143992\pi$
$602$	0	0
$603$	−10.5204	−0.428425
$604$	62.0419	2.52445
$605$	0	0
$606$	91.7787	3.72825
$607$	−30.4865	−1.23741	−0.618704	−	0.785624i	$-0.712342\pi$
$607$	−30.4865	−1.23741	−0.618704	+	0.785624i	$0.712342\pi$
$608$	27.4177	1.11194
$609$	0	0
$610$	19.0698	0.772113
$611$	−9.21558	−0.372822
$612$	9.73341	0.393450
$613$	−25.5581	−1.03228	−0.516140	−	0.856504i	$-0.672632\pi$
$613$	−25.5581	−1.03228	−0.516140	+	0.856504i	$0.672632\pi$
$614$	65.2486	2.63322
$615$	34.5789	1.39436
$616$	0	0
$617$	36.8776	1.48463	0.742317	−	0.670048i	$-0.233727\pi$
$617$	36.8776	1.48463	0.742317	+	0.670048i	$0.233727\pi$
$618$	53.4886	2.15163
$619$	0.208237	0.00836977	0.00418489	−	0.999991i	$-0.498668\pi$
$619$	0.208237	0.00836977	0.00418489	+	0.999991i	$0.498668\pi$
$620$	−21.1663	−0.850060
$621$	−1.39771	−0.0560881
$622$	−34.1963	−1.37115
$623$	0	0
$624$	−3.32691	−0.133183
$625$	−18.5546	−0.742185
$626$	−55.7509	−2.22825
$627$	0	0
$628$	−72.5505	−2.89508
$629$	6.65168	0.265220
$630$	0	0
$631$	−2.77879	−0.110622	−0.0553110	−	0.998469i	$-0.517615\pi$
$631$	−2.77879	−0.110622	−0.0553110	+	0.998469i	$0.517615\pi$
$632$	38.1057	1.51576
$633$	−58.4739	−2.32413
$634$	−60.4831	−2.40209
$635$	59.4768	2.36026
$636$	−56.1095	−2.22489
$637$	0	0
$638$	0	0
$639$	−50.6227	−2.00260
$640$	68.1626	2.69436
$641$	13.1553	0.519604	0.259802	−	0.965662i	$-0.416343\pi$
$641$	13.1553	0.519604	0.259802	+	0.965662i	$0.416343\pi$
$642$	38.7806	1.53055
$643$	−32.0151	−1.26255	−0.631277	−	0.775558i	$-0.717469\pi$
$643$	−32.0151	−1.26255	−0.631277	+	0.775558i	$0.717469\pi$
$644$	0	0
$645$	−14.5554	−0.573118
$646$	−11.9638	−0.470710
$647$	45.5265	1.78983	0.894917	−	0.446233i	$-0.147235\pi$
$647$	45.5265	1.78983	0.894917	+	0.446233i	$0.147235\pi$
$648$	17.7995	0.699229
$649$	0	0
$650$	11.3557	0.445407
$651$	0	0
$652$	68.4160	2.67938
$653$	24.9407	0.976004	0.488002	−	0.872843i	$-0.337726\pi$
$653$	24.9407	0.976004	0.488002	+	0.872843i	$0.337726\pi$
$654$	−78.5460	−3.07139
$655$	30.0700	1.17493
$656$	6.19199	0.241756
$657$	−2.06728	−0.0806524
$658$	0	0
$659$	38.4929	1.49947	0.749736	−	0.661737i	$-0.230181\pi$
$659$	38.4929	1.49947	0.749736	+	0.661737i	$0.230181\pi$
$660$	0	0
$661$	−10.9680	−0.426607	−0.213303	−	0.976986i	$-0.568422\pi$
$661$	−10.9680	−0.426607	−0.213303	+	0.976986i	$0.568422\pi$
$662$	−45.9990	−1.78780
$663$	−1.42469	−0.0553304
$664$	22.5465	0.874974
$665$	0	0
$666$	−93.6026	−3.62703
$667$	−1.49151	−0.0577516
$668$	10.8141	0.418409
$669$	−39.9095	−1.54299
$670$	20.4551	0.790250
$671$	0	0
$672$	0	0
$673$	2.41058	0.0929209	0.0464605	−	0.998920i	$-0.485206\pi$
$673$	2.41058	0.0929209	0.0464605	+	0.998920i	$0.485206\pi$
$674$	−29.6680	−1.14277
$675$	16.6542	0.641021
$676$	−44.0993	−1.69613
$677$	20.9166	0.803889	0.401945	−	0.915664i	$-0.368334\pi$
$677$	20.9166	0.803889	0.401945	+	0.915664i	$0.368334\pi$
$678$	−19.5850	−0.752158
$679$	0	0
$680$	−8.30820	−0.318605
$681$	5.81660	0.222893
$682$	0	0
$683$	20.2306	0.774102	0.387051	−	0.922058i	$-0.373494\pi$
$683$	20.2306	0.774102	0.387051	+	0.922058i	$0.373494\pi$
$684$	107.851	4.12380
$685$	−58.3424	−2.22915
$686$	0	0
$687$	8.11827	0.309731
$688$	−2.60641	−0.0993686
$689$	4.71083	0.179468
$690$	10.5903	0.403166
$691$	34.4849	1.31187	0.655933	−	0.754819i	$-0.272275\pi$
$691$	34.4849	1.31187	0.655933	+	0.754819i	$0.272275\pi$
$692$	−47.0018	−1.78674
$693$	0	0
$694$	62.9750	2.39050
$695$	−48.0325	−1.82198
$696$	−28.7062	−1.08811
$697$	2.65161	0.100437
$698$	28.6674	1.08508
$699$	25.8344	0.977147
$700$	0	0
$701$	−13.9755	−0.527849	−0.263924	−	0.964543i	$-0.585017\pi$
$701$	−13.9755	−0.527849	−0.263924	+	0.964543i	$0.585017\pi$
$702$	5.14463	0.194172
$703$	73.7042	2.77981
$704$	0	0
$705$	102.406	3.85683
$706$	73.1337	2.75242
$707$	0	0
$708$	44.8729	1.68643
$709$	25.1391	0.944119	0.472059	−	0.881567i	$-0.343511\pi$
$709$	25.1391	0.944119	0.472059	+	0.881567i	$0.343511\pi$
$710$	98.4271	3.69390
$711$	−41.6498	−1.56199
$712$	−6.44121	−0.241395
$713$	0.908277	0.0340152
$714$	0	0
$715$	0	0
$716$	30.9071	1.15505
$717$	66.6734	2.48996
$718$	−13.9042	−0.518898
$719$	18.3226	0.683318	0.341659	−	0.939824i	$-0.389011\pi$
$719$	18.3226	0.683318	0.341659	+	0.939824i	$0.389011\pi$
$720$	21.2056	0.790285
$721$	0	0
$722$	−87.7436	−3.26548
$723$	23.9226	0.889691
$724$	6.61159	0.245718
$725$	17.7719	0.660033
$726$	0	0
$727$	3.75571	0.139292	0.0696458	−	0.997572i	$-0.477813\pi$
$727$	3.75571	0.139292	0.0696458	+	0.997572i	$0.477813\pi$
$728$	0	0
$729$	−41.3126	−1.53009
$730$	4.01947	0.148767
$731$	−1.11615	−0.0412823
$732$	−22.9824	−0.849452
$733$	−17.4667	−0.645148	−0.322574	−	0.946544i	$-0.604548\pi$
$733$	−17.4667	−0.645148	−0.322574	+	0.946544i	$0.604548\pi$
$734$	−51.3111	−1.89393
$735$	0	0
$736$	−1.86110	−0.0686009
$737$	0	0
$738$	−37.3135	−1.37353
$739$	−35.8505	−1.31878	−0.659391	−	0.751800i	$-0.729186\pi$
$739$	−35.8505	−1.31878	−0.659391	+	0.751800i	$0.729186\pi$
$740$	116.589	4.28589
$741$	−15.7863	−0.579926
$742$	0	0
$743$	2.13272	0.0782419	0.0391210	−	0.999234i	$-0.487544\pi$
$743$	2.13272	0.0782419	0.0391210	+	0.999234i	$0.487544\pi$
$744$	17.4811	0.640887
$745$	17.8289	0.653201
$746$	59.4677	2.17727
$747$	−24.6435	−0.901657
$748$	0	0
$749$	0	0
$750$	−22.1249	−0.807888
$751$	−13.2246	−0.482574	−0.241287	−	0.970454i	$-0.577570\pi$
$751$	−13.2246	−0.482574	−0.241287	+	0.970454i	$0.577570\pi$
$752$	18.3377	0.668706
$753$	69.0058	2.51471
$754$	5.48990	0.199930
$755$	57.8827	2.10657
$756$	0	0
$757$	33.0990	1.20300	0.601502	−	0.798871i	$-0.294569\pi$
$757$	33.0990	1.20300	0.601502	+	0.798871i	$0.294569\pi$
$758$	−4.24368	−0.154137
$759$	0	0
$760$	−92.0593	−3.33934
$761$	−33.9029	−1.22898	−0.614490	−	0.788924i	$-0.710638\pi$
$761$	−33.9029	−1.22898	−0.614490	+	0.788924i	$0.710638\pi$
$762$	−111.891	−4.05340
$763$	0	0
$764$	40.2298	1.45546
$765$	9.08090	0.328321
$766$	49.5555	1.79051
$767$	−3.76743	−0.136034
$768$	−65.6980	−2.37067
$769$	25.4101	0.916312	0.458156	−	0.888872i	$-0.348510\pi$
$769$	25.4101	0.916312	0.458156	+	0.888872i	$0.348510\pi$
$770$	0	0
$771$	3.40851	0.122754
$772$	23.5067	0.846026
$773$	13.2786	0.477600	0.238800	−	0.971069i	$-0.423246\pi$
$773$	13.2786	0.477600	0.238800	+	0.971069i	$0.423246\pi$
$774$	15.7065	0.564559
$775$	−10.8225	−0.388754
$776$	11.2212	0.402817
$777$	0	0
$778$	49.5714	1.77722
$779$	29.3813	1.05269
$780$	−24.9716	−0.894125
$781$	0	0
$782$	0.812095	0.0290404
$783$	8.05147	0.287736
$784$	0	0
$785$	−67.6868	−2.41585
$786$	−56.5695	−2.01777
$787$	−20.1893	−0.719671	−0.359836	−	0.933016i	$-0.617167\pi$
$787$	−20.1893	−0.719671	−0.359836	+	0.933016i	$0.617167\pi$
$788$	51.0521	1.81866
$789$	5.05939	0.180119
$790$	80.9807	2.88116
$791$	0	0
$792$	0	0
$793$	1.92955	0.0685203
$794$	39.4457	1.39988
$795$	−52.3480	−1.85659
$796$	44.8169	1.58849
$797$	−3.88469	−0.137603	−0.0688014	−	0.997630i	$-0.521917\pi$
$797$	−3.88469	−0.137603	−0.0688014	+	0.997630i	$0.521917\pi$
$798$	0	0
$799$	7.85278	0.277812
$800$	22.1757	0.784028
$801$	7.04028	0.248756
$802$	53.2581	1.88061
$803$	0	0
$804$	−24.6519	−0.869406
$805$	0	0
$806$	−3.34315	−0.117757
$807$	63.3323	2.22940
$808$	54.1550	1.90516
$809$	30.6836	1.07878	0.539388	−	0.842057i	$-0.318656\pi$
$809$	30.6836	1.07878	0.539388	+	0.842057i	$0.318656\pi$
$810$	37.8267	1.32909
$811$	−21.4621	−0.753636	−0.376818	−	0.926287i	$-0.622982\pi$
$811$	−21.4621	−0.753636	−0.376818	+	0.926287i	$0.622982\pi$
$812$	0	0
$813$	−44.0083	−1.54344
$814$	0	0
$815$	63.8295	2.23585
$816$	2.83493	0.0992424
$817$	−12.3675	−0.432686
$818$	19.9152	0.696320
$819$	0	0
$820$	46.4766	1.62303
$821$	29.5100	1.02991	0.514953	−	0.857219i	$-0.327809\pi$
$821$	29.5100	1.02991	0.514953	+	0.857219i	$0.327809\pi$
$822$	109.757	3.82823
$823$	−4.73575	−0.165078	−0.0825389	−	0.996588i	$-0.526303\pi$
$823$	−4.73575	−0.165078	−0.0825389	+	0.996588i	$0.526303\pi$
$824$	31.5615	1.09950
$825$	0	0
$826$	0	0
$827$	−23.9967	−0.834448	−0.417224	−	0.908804i	$-0.636997\pi$
$827$	−23.9967	−0.834448	−0.417224	+	0.908804i	$0.636997\pi$
$828$	−7.32088	−0.254418
$829$	29.2088	1.01446	0.507232	−	0.861810i	$-0.330669\pi$
$829$	29.2088	1.01446	0.507232	+	0.861810i	$0.330669\pi$
$830$	47.9149	1.66315
$831$	−21.3564	−0.740847
$832$	9.35879	0.324458
$833$	0	0
$834$	90.3617	3.12897
$835$	10.0891	0.349149
$836$	0	0
$837$	−4.90306	−0.169474
$838$	−4.47996	−0.154758
$839$	29.0588	1.00322	0.501610	−	0.865094i	$-0.332741\pi$
$839$	29.0588	1.00322	0.501610	+	0.865094i	$0.332741\pi$
$840$	0	0
$841$	−20.4082	−0.703730
$842$	−25.3239	−0.872720
$843$	13.6816	0.471219
$844$	−78.5933	−2.70529
$845$	−41.1430	−1.41536
$846$	−110.505	−3.79923
$847$	0	0
$848$	−9.37388	−0.321900
$849$	−9.37043	−0.321592
$850$	−9.67642	−0.331898
$851$	−5.00298	−0.171500
$852$	−118.621	−4.06390
$853$	−52.3889	−1.79376	−0.896881	−	0.442273i	$-0.854172\pi$
$853$	−52.3889	−1.79376	−0.896881	+	0.442273i	$0.854172\pi$
$854$	0	0
$855$	100.621	3.44118
$856$	22.8829	0.782122
$857$	−20.7519	−0.708871	−0.354436	−	0.935080i	$-0.615327\pi$
$857$	−20.7519	−0.708871	−0.354436	+	0.935080i	$0.615327\pi$
$858$	0	0
$859$	−20.4393	−0.697381	−0.348691	−	0.937238i	$-0.613374\pi$
$859$	−20.4393	−0.697381	−0.348691	+	0.937238i	$0.613374\pi$
$860$	−19.5636	−0.667112
$861$	0	0
$862$	26.5909	0.905690
$863$	28.8935	0.983546	0.491773	−	0.870723i	$-0.336349\pi$
$863$	28.8935	0.983546	0.491773	+	0.870723i	$0.336349\pi$
$864$	10.0466	0.341791
$865$	−43.8509	−1.49097
$866$	−8.69637	−0.295515
$867$	−43.8779	−1.49017
$868$	0	0
$869$	0	0
$870$	−61.0053	−2.06827
$871$	2.06972	0.0701298
$872$	−46.3469	−1.56950
$873$	−12.2648	−0.415101
$874$	8.99845	0.304377
$875$	0	0
$876$	−4.84415	−0.163669
$877$	−38.9269	−1.31447	−0.657235	−	0.753686i	$-0.728274\pi$
$877$	−38.9269	−1.31447	−0.657235	+	0.753686i	$0.728274\pi$
$878$	59.7113	2.01516
$879$	−15.9770	−0.538892
$880$	0	0
$881$	−54.1951	−1.82588	−0.912940	−	0.408095i	$-0.866193\pi$
$881$	−54.1951	−1.82588	−0.912940	+	0.408095i	$0.866193\pi$
$882$	0	0
$883$	−21.4360	−0.721379	−0.360689	−	0.932686i	$-0.617459\pi$
$883$	−21.4360	−0.721379	−0.360689	+	0.932686i	$0.617459\pi$
$884$	−1.91489	−0.0644047
$885$	41.8647	1.40727
$886$	−65.5159	−2.20105
$887$	37.4837	1.25858	0.629290	−	0.777171i	$-0.283346\pi$
$887$	37.4837	1.25858	0.629290	+	0.777171i	$0.283346\pi$
$888$	−96.2894	−3.23126
$889$	0	0
$890$	−13.6886	−0.458843
$891$	0	0
$892$	−53.6413	−1.79604
$893$	87.0131	2.91178
$894$	−33.5409	−1.12177
$895$	28.8351	0.963853
$896$	0	0
$897$	1.07156	0.0357785
$898$	−16.8172	−0.561199
$899$	−5.23211	−0.174501
$900$	87.2310	2.90770
$901$	−4.01420	−0.133732
$902$	0	0
$903$	0	0
$904$	−11.5563	−0.384358
$905$	6.16836	0.205043
$906$	−108.893	−3.61771
$907$	−2.88194	−0.0956933	−0.0478466	−	0.998855i	$-0.515236\pi$
$907$	−2.88194	−0.0956933	−0.0478466	+	0.998855i	$0.515236\pi$
$908$	7.81795	0.259448
$909$	−59.1917	−1.96326
$910$	0	0
$911$	29.4530	0.975822	0.487911	−	0.872893i	$-0.337759\pi$
$911$	29.4530	0.975822	0.487911	+	0.872893i	$0.337759\pi$
$912$	31.4126	1.04017
$913$	0	0
$914$	−22.2661	−0.736496
$915$	−21.4417	−0.708840
$916$	10.9116	0.360529
$917$	0	0
$918$	−4.38385	−0.144688
$919$	41.7416	1.37693	0.688464	−	0.725271i	$-0.258285\pi$
$919$	41.7416	1.37693	0.688464	+	0.725271i	$0.258285\pi$
$920$	6.24892	0.206021
$921$	−73.3641	−2.41743
$922$	−62.4709	−2.05737
$923$	9.95920	0.327811
$924$	0	0
$925$	59.6125	1.96005
$926$	39.6681	1.30358
$927$	−34.4969	−1.13303
$928$	10.7208	0.351928
$929$	16.5200	0.542005	0.271003	−	0.962579i	$-0.412645\pi$
$929$	16.5200	0.542005	0.271003	+	0.962579i	$0.412645\pi$
$930$	37.1500	1.21820
$931$	0	0
$932$	34.7234	1.13740
$933$	38.4496	1.25878
$934$	−39.3951	−1.28905
$935$	0	0
$936$	11.8297	0.386666
$937$	−25.2516	−0.824935	−0.412468	−	0.910972i	$-0.635333\pi$
$937$	−25.2516	−0.824935	−0.412468	+	0.910972i	$0.635333\pi$
$938$	0	0
$939$	62.6851	2.04565
$940$	137.641	4.48937
$941$	−1.81386	−0.0591302	−0.0295651	−	0.999563i	$-0.509412\pi$
$941$	−1.81386	−0.0591302	−0.0295651	+	0.999563i	$0.509412\pi$
$942$	127.337	4.14885
$943$	−1.99438	−0.0649459
$944$	7.49665	0.243995
$945$	0	0
$946$	0	0
$947$	−29.9280	−0.972529	−0.486265	−	0.873812i	$-0.661641\pi$
$947$	−29.9280	−0.972529	−0.486265	+	0.873812i	$0.661641\pi$
$948$	−97.5956	−3.16976
$949$	0.406705	0.0132022
$950$	−107.220	−3.47867
$951$	68.0060	2.20524
$952$	0	0
$953$	−52.3251	−1.69498	−0.847488	−	0.530814i	$-0.821886\pi$
$953$	−52.3251	−1.69498	−0.847488	+	0.530814i	$0.821886\pi$
$954$	56.4879	1.82886
$955$	37.5329	1.21454
$956$	89.6141	2.89833
$957$	0	0
$958$	−12.3563	−0.399215
$959$	0	0
$960$	−103.997	−3.35650
$961$	−27.8138	−0.897220
$962$	18.4148	0.593717
$963$	−25.0112	−0.805973
$964$	32.1538	1.03560
$965$	21.9309	0.705981
$966$	0	0
$967$	−5.53907	−0.178124	−0.0890622	−	0.996026i	$-0.528387\pi$
$967$	−5.53907	−0.178124	−0.0890622	+	0.996026i	$0.528387\pi$
$968$	0	0
$969$	13.4519	0.432136
$970$	23.8468	0.765675
$971$	−12.5770	−0.403614	−0.201807	−	0.979425i	$-0.564681\pi$
$971$	−12.5770	−0.403614	−0.201807	+	0.979425i	$0.564681\pi$
$972$	−74.9659	−2.40453
$973$	0	0
$974$	50.0545	1.60385
$975$	−12.7681	−0.408906
$976$	−3.83953	−0.122900
$977$	−13.6144	−0.435564	−0.217782	−	0.975997i	$-0.569882\pi$
$977$	−13.6144	−0.435564	−0.217782	+	0.975997i	$0.569882\pi$
$978$	−120.080	−3.83974
$979$	0	0
$980$	0	0
$981$	50.6574	1.61737
$982$	22.2678	0.710593
$983$	30.8987	0.985517	0.492759	−	0.870166i	$-0.335989\pi$
$983$	30.8987	0.985517	0.492759	+	0.870166i	$0.335989\pi$
$984$	−38.3846	−1.22366
$985$	47.6297	1.51761
$986$	−4.67806	−0.148980
$987$	0	0
$988$	−21.2180	−0.675035
$989$	0.839500	0.0266945
$990$	0	0
$991$	−27.1884	−0.863669	−0.431834	−	0.901953i	$-0.642134\pi$
$991$	−27.1884	−0.863669	−0.431834	+	0.901953i	$0.642134\pi$
$992$	−6.52859	−0.207283
$993$	51.7203	1.64129
$994$	0	0
$995$	41.8125	1.32554
$996$	−57.7457	−1.82974
$997$	−30.0461	−0.951570	−0.475785	−	0.879562i	$-0.657836\pi$
$997$	−30.0461	−0.951570	−0.475785	+	0.879562i	$0.657836\pi$
$998$	48.2050	1.52590
$999$	27.0071	0.854467

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bq.1.1		7
7.2	even	3		847.2.e.g.606.7	yes	14
7.4	even	3		847.2.e.g.485.7	yes	14
7.6	odd	2		5929.2.a.bn.1.1		7
11.10	odd	2		5929.2.a.bp.1.7		7
77.2	odd	30		847.2.n.m.81.1		56
77.4	even	15		847.2.n.l.632.7		56
77.9	even	15		847.2.n.l.81.7		56
77.16	even	15		847.2.n.l.487.1		56
77.18	odd	30		847.2.n.m.632.1		56
77.25	even	15		847.2.n.l.9.1		56
77.30	odd	30		847.2.n.m.130.1		56
77.32	odd	6		847.2.e.f.485.1	✓	14
77.37	even	15		847.2.n.l.753.1		56
77.39	odd	30		847.2.n.m.366.1		56
77.46	odd	30		847.2.n.m.807.7		56
77.51	odd	30		847.2.n.m.753.7		56
77.53	even	15		847.2.n.l.807.1		56
77.58	even	15		847.2.n.l.130.7		56
77.60	even	15		847.2.n.l.366.7		56
77.65	odd	6		847.2.e.f.606.1	yes	14
77.72	odd	30		847.2.n.m.487.7		56
77.74	odd	30		847.2.n.m.9.7		56
77.76	even	2		5929.2.a.bo.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.e.f.485.1	✓	14	77.32	odd	6
847.2.e.f.606.1	yes	14	77.65	odd	6
847.2.e.g.485.7	yes	14	7.4	even	3
847.2.e.g.606.7	yes	14	7.2	even	3
847.2.n.l.9.1		56	77.25	even	15
847.2.n.l.81.7		56	77.9	even	15
847.2.n.l.130.7		56	77.58	even	15
847.2.n.l.366.7		56	77.60	even	15
847.2.n.l.487.1		56	77.16	even	15
847.2.n.l.632.7		56	77.4	even	15
847.2.n.l.753.1		56	77.37	even	15
847.2.n.l.807.1		56	77.53	even	15
847.2.n.m.9.7		56	77.74	odd	30
847.2.n.m.81.1		56	77.2	odd	30
847.2.n.m.130.1		56	77.30	odd	30
847.2.n.m.366.1		56	77.39	odd	30
847.2.n.m.487.7		56	77.72	odd	30
847.2.n.m.632.1		56	77.18	odd	30
847.2.n.m.753.7		56	77.51	odd	30
847.2.n.m.807.7		56	77.46	odd	30
5929.2.a.bn.1.1		7	7.6	odd	2
5929.2.a.bo.1.7		7	77.76	even	2
5929.2.a.bp.1.7		7	11.10	odd	2
5929.2.a.bq.1.1		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35905 q^{2} +2.65247 q^{3} +3.56512 q^{4} +3.32612 q^{5} -6.25730 q^{6} -3.69218 q^{8} +4.03558 q^{9} +O(q^{10})\)	\(q-2.35905 q^{2} +2.65247 q^{3} +3.56512 q^{4} +3.32612 q^{5} -6.25730 q^{6} -3.69218 q^{8} +4.03558 q^{9} -7.84648 q^{10} +9.45635 q^{12} -0.793934 q^{13} +8.82241 q^{15} +1.57982 q^{16} +0.676528 q^{17} -9.52013 q^{18} +7.49630 q^{19} +11.8580 q^{20} -0.508843 q^{23} -9.79340 q^{24} +6.06306 q^{25} +1.87293 q^{26} +2.74683 q^{27} +2.93118 q^{29} -20.8125 q^{30} -1.78498 q^{31} +3.65750 q^{32} -1.59596 q^{34} +14.3873 q^{36} +9.83208 q^{37} -17.6841 q^{38} -2.10588 q^{39} -12.2806 q^{40} +3.91944 q^{41} -1.64982 q^{43} +13.4228 q^{45} +1.20039 q^{46} +11.6075 q^{47} +4.19041 q^{48} -14.3031 q^{50} +1.79447 q^{51} -2.83047 q^{52} -5.93353 q^{53} -6.47992 q^{54} +19.8837 q^{57} -6.91480 q^{58} +4.74527 q^{59} +31.4529 q^{60} -2.43036 q^{61} +4.21087 q^{62} -11.7879 q^{64} -2.64072 q^{65} -2.60692 q^{67} +2.41190 q^{68} -1.34969 q^{69} -12.5441 q^{71} -14.9001 q^{72} -0.512265 q^{73} -23.1944 q^{74} +16.0821 q^{75} +26.7252 q^{76} +4.96789 q^{78} -10.3206 q^{79} +5.25465 q^{80} -4.82085 q^{81} -9.24614 q^{82} -6.10655 q^{83} +2.25021 q^{85} +3.89201 q^{86} +7.77486 q^{87} +1.74455 q^{89} -31.6651 q^{90} -1.81408 q^{92} -4.73461 q^{93} -27.3826 q^{94} +24.9336 q^{95} +9.70141 q^{96} -3.03917 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{3} + 8 q^{4} + 4 q^{5} + 2 q^{6} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 7 * q + 3 * q^3 + 8 * q^4 + 4 * q^5 + 2 * q^6 + 3 * q^8 + 10 * q^9	\( 7 q + 3 q^{3} + 8 q^{4} + 4 q^{5} + 2 q^{6} + 3 q^{8} + 10 q^{9} - 6 q^{10} + 13 q^{12} - 6 q^{13} - q^{15} + 6 q^{16} + 3 q^{17} - 14 q^{18} + 9 q^{19} + 2 q^{20} - 6 q^{23} - 4 q^{24} + 7 q^{25} + 25 q^{26} + 12 q^{27} - 6 q^{29} - 16 q^{30} + 14 q^{31} + 36 q^{32} + 8 q^{34} - 2 q^{36} - 8 q^{37} - 10 q^{38} + 9 q^{39} - 18 q^{40} + 10 q^{41} - 17 q^{43} + 12 q^{45} - 16 q^{46} + 30 q^{47} + 56 q^{48} - 21 q^{50} + 20 q^{51} + 37 q^{52} - 10 q^{53} + 7 q^{54} + 31 q^{57} - 13 q^{58} + 20 q^{59} + 42 q^{60} - 7 q^{61} - 26 q^{62} + 21 q^{64} - 12 q^{65} + 7 q^{67} - 7 q^{68} + 9 q^{69} - 11 q^{71} + q^{72} + 6 q^{73} - 8 q^{74} - q^{75} + 56 q^{76} + 15 q^{78} + 14 q^{79} + 12 q^{80} + 35 q^{81} - 7 q^{82} - 17 q^{83} + 2 q^{85} + 15 q^{87} + 40 q^{89} - 68 q^{90} - 26 q^{92} - 19 q^{94} - 20 q^{95} + 63 q^{96} - 22 q^{97}+O(q^{100}) \) 7 * q + 3 * q^3 + 8 * q^4 + 4 * q^5 + 2 * q^6 + 3 * q^8 + 10 * q^9 - 6 * q^10 + 13 * q^12 - 6 * q^13 - q^15 + 6 * q^16 + 3 * q^17 - 14 * q^18 + 9 * q^19 + 2 * q^20 - 6 * q^23 - 4 * q^24 + 7 * q^25 + 25 * q^26 + 12 * q^27 - 6 * q^29 - 16 * q^30 + 14 * q^31 + 36 * q^32 + 8 * q^34 - 2 * q^36 - 8 * q^37 - 10 * q^38 + 9 * q^39 - 18 * q^40 + 10 * q^41 - 17 * q^43 + 12 * q^45 - 16 * q^46 + 30 * q^47 + 56 * q^48 - 21 * q^50 + 20 * q^51 + 37 * q^52 - 10 * q^53 + 7 * q^54 + 31 * q^57 - 13 * q^58 + 20 * q^59 + 42 * q^60 - 7 * q^61 - 26 * q^62 + 21 * q^64 - 12 * q^65 + 7 * q^67 - 7 * q^68 + 9 * q^69 - 11 * q^71 + q^72 + 6 * q^73 - 8 * q^74 - q^75 + 56 * q^76 + 15 * q^78 + 14 * q^79 + 12 * q^80 + 35 * q^81 - 7 * q^82 - 17 * q^83 + 2 * q^85 + 15 * q^87 + 40 * q^89 - 68 * q^90 - 26 * q^92 - 19 * q^94 - 20 * q^95 + 63 * q^96 - 22 * q^97

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