LMFDB - Embedded newform 1875.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, 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("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.82709$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.95630 q^{2} +1.00000 q^{3} +1.82709 q^{4} +1.95630 q^{6} -4.57433 q^{7} -0.338261 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.95630 q^{2} +1.00000 q^{3} +1.82709 q^{4} +1.95630 q^{6} -4.57433 q^{7} -0.338261 q^{8} +1.00000 q^{9} -4.16535 q^{11} +1.82709 q^{12} -3.75638 q^{13} -8.94874 q^{14} -4.31592 q^{16} +3.26755 q^{17} +1.95630 q^{18} -0.243625 q^{19} -4.57433 q^{21} -8.14866 q^{22} +0.654182 q^{23} -0.338261 q^{24} -7.34858 q^{26} +1.00000 q^{27} -8.35772 q^{28} -8.54732 q^{29} -3.90694 q^{31} -7.76669 q^{32} -4.16535 q^{33} +6.39228 q^{34} +1.82709 q^{36} +10.6151 q^{37} -0.476602 q^{38} -3.75638 q^{39} +0.769579 q^{41} -8.94874 q^{42} +3.90345 q^{43} -7.61048 q^{44} +1.27977 q^{46} +7.67555 q^{47} -4.31592 q^{48} +13.9245 q^{49} +3.26755 q^{51} -6.86324 q^{52} -12.1197 q^{53} +1.95630 q^{54} +1.54732 q^{56} -0.243625 q^{57} -16.7211 q^{58} +4.90248 q^{59} -14.7035 q^{61} -7.64313 q^{62} -4.57433 q^{63} -6.56210 q^{64} -8.14866 q^{66} +0.316897 q^{67} +5.97010 q^{68} +0.654182 q^{69} +0.446705 q^{71} -0.338261 q^{72} -11.1172 q^{73} +20.7664 q^{74} -0.445125 q^{76} +19.0537 q^{77} -7.34858 q^{78} +9.80731 q^{79} +1.00000 q^{81} +1.50552 q^{82} -8.86482 q^{83} -8.35772 q^{84} +7.63631 q^{86} -8.54732 q^{87} +1.40898 q^{88} -7.81040 q^{89} +17.1829 q^{91} +1.19525 q^{92} -3.90694 q^{93} +15.0156 q^{94} -7.76669 q^{96} +8.15938 q^{97} +27.2404 q^{98} -4.16535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 4 q^{3} + q^{4} - q^{6} - 5 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 + 4 * q^3 + q^4 - q^6 - 5 * q^7 + 3 * q^8 + 4 * q^9	$ 4 q - q^{2} + 4 q^{3} + q^{4} - q^{6} - 5 q^{7} + 3 q^{8} + 4 q^{9} - 6 q^{11} + q^{12} - 7 q^{13} - 10 q^{14} - 9 q^{16} + 7 q^{17} - q^{18} - 9 q^{19} - 5 q^{21} - 6 q^{22} - 10 q^{23} + 3 q^{24} - 2 q^{26} + 4 q^{27} - 5 q^{28} - 28 q^{29} - 10 q^{31} - 6 q^{33} + 7 q^{34} + q^{36} + 10 q^{37} + 6 q^{38} - 7 q^{39} - 10 q^{42} - q^{43} - 9 q^{44} + 5 q^{46} + 23 q^{47} - 9 q^{48} - 3 q^{49} + 7 q^{51} - 13 q^{52} - q^{54} - 9 q^{57} + 2 q^{58} + 4 q^{59} - 43 q^{61} + 10 q^{62} - 5 q^{63} - 7 q^{64} - 6 q^{66} - 8 q^{67} + 3 q^{68} - 10 q^{69} - 27 q^{71} + 3 q^{72} - 15 q^{73} + 5 q^{74} + 9 q^{76} + 15 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{81} + 20 q^{82} - 3 q^{83} - 5 q^{84} + 24 q^{86} - 28 q^{87} + 3 q^{88} - 9 q^{89} + 5 q^{91} + 15 q^{92} - 10 q^{93} - 22 q^{94} - 13 q^{97} + 42 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q - q^2 + 4 * q^3 + q^4 - q^6 - 5 * q^7 + 3 * q^8 + 4 * q^9 - 6 * q^11 + q^12 - 7 * q^13 - 10 * q^14 - 9 * q^16 + 7 * q^17 - q^18 - 9 * q^19 - 5 * q^21 - 6 * q^22 - 10 * q^23 + 3 * q^24 - 2 * q^26 + 4 * q^27 - 5 * q^28 - 28 * q^29 - 10 * q^31 - 6 * q^33 + 7 * q^34 + q^36 + 10 * q^37 + 6 * q^38 - 7 * q^39 - 10 * q^42 - q^43 - 9 * q^44 + 5 * q^46 + 23 * q^47 - 9 * q^48 - 3 * q^49 + 7 * q^51 - 13 * q^52 - q^54 - 9 * q^57 + 2 * q^58 + 4 * q^59 - 43 * q^61 + 10 * q^62 - 5 * q^63 - 7 * q^64 - 6 * q^66 - 8 * q^67 + 3 * q^68 - 10 * q^69 - 27 * q^71 + 3 * q^72 - 15 * q^73 + 5 * q^74 + 9 * q^76 + 15 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^81 + 20 * q^82 - 3 * q^83 - 5 * q^84 + 24 * q^86 - 28 * q^87 + 3 * q^88 - 9 * q^89 + 5 * q^91 + 15 * q^92 - 10 * q^93 - 22 * q^94 - 13 * q^97 + 42 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.95630	1.38331	0.691655	−	0.722228i	$-0.256882\pi$
$2$	1.95630	1.38331	0.691655	+	0.722228i	$0.256882\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.82709	0.913545
$5$	0	0
$5$	0	0
$6$	1.95630	0.798654
$7$	−4.57433	−1.72893	−0.864467	−	0.502690i	$-0.832344\pi$
$7$	−4.57433	−1.72893	−0.864467	+	0.502690i	$0.832344\pi$
$8$	−0.338261	−0.119593
$9$	1.00000	0.333333
$10$	0	0
$11$	−4.16535	−1.25590	−0.627950	−	0.778253i	$-0.716106\pi$
$11$	−4.16535	−1.25590	−0.627950	+	0.778253i	$0.716106\pi$
$12$	1.82709	0.527436
$13$	−3.75638	−1.04183	−0.520915	−	0.853608i	$-0.674409\pi$
$13$	−3.75638	−1.04183	−0.520915	+	0.853608i	$0.674409\pi$
$14$	−8.94874	−2.39165
$15$	0	0
$16$	−4.31592	−1.07898
$17$	3.26755	0.792496	0.396248	−	0.918143i	$-0.370312\pi$
$17$	3.26755	0.792496	0.396248	+	0.918143i	$0.370312\pi$
$18$	1.95630	0.461103
$19$	−0.243625	−0.0558914	−0.0279457	−	0.999609i	$-0.508897\pi$
$19$	−0.243625	−0.0558914	−0.0279457	+	0.999609i	$0.508897\pi$
$20$	0	0
$21$	−4.57433	−0.998200
$22$	−8.14866	−1.73730
$23$	0.654182	0.136406	0.0682032	−	0.997671i	$-0.478273\pi$
$23$	0.654182	0.136406	0.0682032	+	0.997671i	$0.478273\pi$
$24$	−0.338261	−0.0690473
$25$	0	0
$26$	−7.34858	−1.44117
$27$	1.00000	0.192450
$28$	−8.35772	−1.57946
$29$	−8.54732	−1.58720	−0.793599	−	0.608442i	$-0.791795\pi$
$29$	−8.54732	−1.58720	−0.793599	+	0.608442i	$0.791795\pi$
$30$	0	0
$31$	−3.90694	−0.701708	−0.350854	−	0.936430i	$-0.614109\pi$
$31$	−3.90694	−0.701708	−0.350854	+	0.936430i	$0.614109\pi$
$32$	−7.76669	−1.37297
$33$	−4.16535	−0.725095
$34$	6.39228	1.09627
$35$	0	0
$36$	1.82709	0.304515
$37$	10.6151	1.74512	0.872560	−	0.488507i	$-0.162458\pi$
$37$	10.6151	1.74512	0.872560	+	0.488507i	$0.162458\pi$
$38$	−0.476602	−0.0773151
$39$	−3.75638	−0.601501
$40$	0	0
$41$	0.769579	0.120188	0.0600940	−	0.998193i	$-0.480860\pi$
$41$	0.769579	0.120188	0.0600940	+	0.998193i	$0.480860\pi$
$42$	−8.94874	−1.38082
$43$	3.90345	0.595271	0.297636	−	0.954680i	$-0.403802\pi$
$43$	3.90345	0.595271	0.297636	+	0.954680i	$0.403802\pi$
$44$	−7.61048	−1.14732
$45$	0	0
$46$	1.27977	0.188692
$47$	7.67555	1.11959	0.559797	−	0.828630i	$-0.310879\pi$
$47$	7.67555	1.11959	0.559797	+	0.828630i	$0.310879\pi$
$48$	−4.31592	−0.622949
$49$	13.9245	1.98921
$50$	0	0
$51$	3.26755	0.457548
$52$	−6.86324	−0.951760
$53$	−12.1197	−1.66477	−0.832387	−	0.554195i	$-0.813026\pi$
$53$	−12.1197	−1.66477	−0.832387	+	0.554195i	$0.813026\pi$
$54$	1.95630	0.266218
$55$	0	0
$56$	1.54732	0.206769
$57$	−0.243625	−0.0322689
$58$	−16.7211	−2.19559
$59$	4.90248	0.638248	0.319124	−	0.947713i	$-0.396611\pi$
$59$	4.90248	0.638248	0.319124	+	0.947713i	$0.396611\pi$
$60$	0	0
$61$	−14.7035	−1.88259	−0.941297	−	0.337579i	$-0.890392\pi$
$61$	−14.7035	−1.88259	−0.941297	+	0.337579i	$0.890392\pi$
$62$	−7.64313	−0.970679
$63$	−4.57433	−0.576311
$64$	−6.56210	−0.820263
$65$	0	0
$66$	−8.14866	−1.00303
$67$	0.316897	0.0387151	0.0193576	−	0.999813i	$-0.493838\pi$
$67$	0.316897	0.0387151	0.0193576	+	0.999813i	$0.493838\pi$
$68$	5.97010	0.723981
$69$	0.654182	0.0787542
$70$	0	0
$71$	0.446705	0.0530141	0.0265070	−	0.999649i	$-0.491562\pi$
$71$	0.446705	0.0530141	0.0265070	+	0.999649i	$0.491562\pi$
$72$	−0.338261	−0.0398645
$73$	−11.1172	−1.30117	−0.650584	−	0.759434i	$-0.725476\pi$
$73$	−11.1172	−1.30117	−0.650584	+	0.759434i	$0.725476\pi$
$74$	20.7664	2.41404
$75$	0	0
$76$	−0.445125	−0.0510593
$77$	19.0537	2.17137
$78$	−7.34858	−0.832063
$79$	9.80731	1.10341	0.551704	−	0.834040i	$-0.313978\pi$
$79$	9.80731	1.10341	0.551704	+	0.834040i	$0.313978\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.50552	0.166257
$83$	−8.86482	−0.973040	−0.486520	−	0.873669i	$-0.661734\pi$
$83$	−8.86482	−0.973040	−0.486520	+	0.873669i	$0.661734\pi$
$84$	−8.35772	−0.911902
$85$	0	0
$86$	7.63631	0.823444
$87$	−8.54732	−0.916369
$88$	1.40898	0.150197
$89$	−7.81040	−0.827900	−0.413950	−	0.910300i	$-0.635851\pi$
$89$	−7.81040	−0.827900	−0.413950	+	0.910300i	$0.635851\pi$
$90$	0	0
$91$	17.1829	1.80126
$92$	1.19525	0.124613
$93$	−3.90694	−0.405131
$94$	15.0156	1.54874
$95$	0	0
$96$	−7.76669	−0.792685
$97$	8.15938	0.828459	0.414230	−	0.910172i	$-0.364051\pi$
$97$	8.15938	0.828459	0.414230	+	0.910172i	$0.364051\pi$
$98$	27.2404	2.75170
$99$	−4.16535	−0.418634
$100$	0	0
$101$	−9.54383	−0.949646	−0.474823	−	0.880081i	$-0.657488\pi$
$101$	−9.54383	−0.949646	−0.474823	+	0.880081i	$0.657488\pi$
$102$	6.39228	0.632930
$103$	9.86698	0.972222	0.486111	−	0.873897i	$-0.338415\pi$
$103$	9.86698	0.972222	0.486111	+	0.873897i	$0.338415\pi$
$104$	1.27064	0.124596
$105$	0	0
$106$	−23.7098	−2.30290
$107$	16.1273	1.55908	0.779542	−	0.626350i	$-0.215452\pi$
$107$	16.1273	1.55908	0.779542	+	0.626350i	$0.215452\pi$
$108$	1.82709	0.175812
$109$	−2.44236	−0.233936	−0.116968	−	0.993136i	$-0.537318\pi$
$109$	−2.44236	−0.233936	−0.116968	+	0.993136i	$0.537318\pi$
$110$	0	0
$111$	10.6151	1.00755
$112$	19.7424	1.86549
$113$	10.9293	1.02814	0.514070	−	0.857748i	$-0.328137\pi$
$113$	10.9293	1.02814	0.514070	+	0.857748i	$0.328137\pi$
$114$	−0.476602	−0.0446379
$115$	0	0
$116$	−15.6167	−1.44998
$117$	−3.75638	−0.347277
$118$	9.59069	0.882895
$119$	−14.9468	−1.37017
$120$	0	0
$121$	6.35016	0.577287
$122$	−28.7645	−2.60421
$123$	0.769579	0.0693906
$124$	−7.13834	−0.641042
$125$	0	0
$126$	−8.94874	−0.797217
$127$	−12.8613	−1.14126	−0.570629	−	0.821208i	$-0.693301\pi$
$127$	−12.8613	−1.14126	−0.570629	+	0.821208i	$0.693301\pi$
$128$	2.69598	0.238293
$129$	3.90345	0.343680
$130$	0	0
$131$	2.37441	0.207453	0.103727	−	0.994606i	$-0.466923\pi$
$131$	2.37441	0.207453	0.103727	+	0.994606i	$0.466923\pi$
$132$	−7.61048	−0.662407
$133$	1.11442	0.0966325
$134$	0.619944	0.0535550
$135$	0	0
$136$	−1.10528	−0.0947773
$137$	−12.5026	−1.06817	−0.534086	−	0.845430i	$-0.679344\pi$
$137$	−12.5026	−1.06817	−0.534086	+	0.845430i	$0.679344\pi$
$138$	1.27977	0.108941
$139$	−0.356135	−0.0302070	−0.0151035	−	0.999886i	$-0.504808\pi$
$139$	−0.356135	−0.0302070	−0.0151035	+	0.999886i	$0.504808\pi$
$140$	0	0
$141$	7.67555	0.646398
$142$	0.873886	0.0733349
$143$	15.6466	1.30844
$144$	−4.31592	−0.359660
$145$	0	0
$146$	−21.7485	−1.79992
$147$	13.9245	1.14847
$148$	19.3948	1.59425
$149$	−15.0317	−1.23144	−0.615722	−	0.787964i	$-0.711135\pi$
$149$	−15.0317	−1.23144	−0.615722	+	0.787964i	$0.711135\pi$
$150$	0	0
$151$	−5.65576	−0.460259	−0.230130	−	0.973160i	$-0.573915\pi$
$151$	−5.65576	−0.460259	−0.230130	+	0.973160i	$0.573915\pi$
$152$	0.0824089	0.00668424
$153$	3.26755	0.264165
$154$	37.2746	3.00368
$155$	0	0
$156$	−6.86324	−0.549499
$157$	−6.69480	−0.534303	−0.267151	−	0.963655i	$-0.586082\pi$
$157$	−6.69480	−0.534303	−0.267151	+	0.963655i	$0.586082\pi$
$158$	19.1860	1.52636
$159$	−12.1197	−0.961158
$160$	0	0
$161$	−2.99244	−0.235838
$162$	1.95630	0.153701
$163$	13.8314	1.08336	0.541681	−	0.840584i	$-0.317788\pi$
$163$	13.8314	1.08336	0.541681	+	0.840584i	$0.317788\pi$
$164$	1.40609	0.109797
$165$	0	0
$166$	−17.3422	−1.34602
$167$	13.5017	1.04479	0.522397	−	0.852703i	$-0.325038\pi$
$167$	13.5017	1.04479	0.522397	+	0.852703i	$0.325038\pi$
$168$	1.54732	0.119378
$169$	1.11035	0.0854118
$170$	0	0
$171$	−0.243625	−0.0186305
$172$	7.13196	0.543807
$173$	−13.7259	−1.04356	−0.521779	−	0.853080i	$-0.674732\pi$
$173$	−13.7259	−1.04356	−0.521779	+	0.853080i	$0.674732\pi$
$174$	−16.7211	−1.26762
$175$	0	0
$176$	17.9773	1.35509
$177$	4.90248	0.368493
$178$	−15.2794	−1.14524
$179$	4.46491	0.333723	0.166861	−	0.985980i	$-0.446637\pi$
$179$	4.46491	0.333723	0.166861	+	0.985980i	$0.446637\pi$
$180$	0	0
$181$	−14.0032	−1.04085	−0.520423	−	0.853908i	$-0.674226\pi$
$181$	−14.0032	−1.04085	−0.520423	+	0.853908i	$0.674226\pi$
$182$	33.6148	2.49170
$183$	−14.7035	−1.08692
$184$	−0.221284	−0.0163133
$185$	0	0
$186$	−7.64313	−0.560422
$187$	−13.6105	−0.995297
$188$	14.0239	1.02280
$189$	−4.57433	−0.332733
$190$	0	0
$191$	−4.29614	−0.310858	−0.155429	−	0.987847i	$-0.549676\pi$
$191$	−4.29614	−0.310858	−0.155429	+	0.987847i	$0.549676\pi$
$192$	−6.56210	−0.473579
$193$	−13.0436	−0.938897	−0.469449	−	0.882960i	$-0.655547\pi$
$193$	−13.0436	−0.938897	−0.469449	+	0.882960i	$0.655547\pi$
$194$	15.9621	1.14602
$195$	0	0
$196$	25.4413	1.81724
$197$	9.17856	0.653945	0.326973	−	0.945034i	$-0.393972\pi$
$197$	9.17856	0.653945	0.326973	+	0.945034i	$0.393972\pi$
$198$	−8.14866	−0.579100
$199$	0.677499	0.0480266	0.0240133	−	0.999712i	$-0.492356\pi$
$199$	0.677499	0.0480266	0.0240133	+	0.999712i	$0.492356\pi$
$200$	0	0
$201$	0.316897	0.0223522
$202$	−18.6705	−1.31365
$203$	39.0982	2.74416
$204$	5.97010	0.417991
$205$	0	0
$206$	19.3027	1.34488
$207$	0.654182	0.0454688
$208$	16.2122	1.12411
$209$	1.01478	0.0701941
$210$	0	0
$211$	−16.1662	−1.11293	−0.556464	−	0.830872i	$-0.687842\pi$
$211$	−16.1662	−1.11293	−0.556464	+	0.830872i	$0.687842\pi$
$212$	−22.1439	−1.52085
$213$	0.446705	0.0306077
$214$	31.5497	2.15670
$215$	0	0
$216$	−0.338261	−0.0230158
$217$	17.8716	1.21321
$218$	−4.77799	−0.323606
$219$	−11.1172	−0.751229
$220$	0	0
$221$	−12.2741	−0.825647
$222$	20.7664	1.39375
$223$	9.96064	0.667013	0.333507	−	0.942748i	$-0.391768\pi$
$223$	9.96064	0.667013	0.333507	+	0.942748i	$0.391768\pi$
$224$	35.5274	2.37377
$225$	0	0
$226$	21.3809	1.42224
$227$	−24.0646	−1.59722	−0.798612	−	0.601846i	$-0.794432\pi$
$227$	−24.0646	−1.59722	−0.798612	+	0.601846i	$0.794432\pi$
$228$	−0.445125	−0.0294791
$229$	−15.3847	−1.01665	−0.508326	−	0.861165i	$-0.669735\pi$
$229$	−15.3847	−1.01665	−0.508326	+	0.861165i	$0.669735\pi$
$230$	0	0
$231$	19.0537	1.25364
$232$	2.89123	0.189818
$233$	−6.58907	−0.431664	−0.215832	−	0.976430i	$-0.569246\pi$
$233$	−6.58907	−0.431664	−0.215832	+	0.976430i	$0.569246\pi$
$234$	−7.34858	−0.480392
$235$	0	0
$236$	8.95727	0.583069
$237$	9.80731	0.637053
$238$	−29.2404	−1.89537
$239$	17.8874	1.15704	0.578520	−	0.815668i	$-0.303630\pi$
$239$	17.8874	1.15704	0.578520	+	0.815668i	$0.303630\pi$
$240$	0	0
$241$	6.22404	0.400926	0.200463	−	0.979701i	$-0.435755\pi$
$241$	6.22404	0.400926	0.200463	+	0.979701i	$0.435755\pi$
$242$	12.4228	0.798567
$243$	1.00000	0.0641500
$244$	−26.8647	−1.71984
$245$	0	0
$246$	1.50552	0.0959887
$247$	0.915147	0.0582294
$248$	1.32157	0.0839196
$249$	−8.86482	−0.561785
$250$	0	0
$251$	−7.11580	−0.449145	−0.224573	−	0.974457i	$-0.572099\pi$
$251$	−7.11580	−0.449145	−0.224573	+	0.974457i	$0.572099\pi$
$252$	−8.35772	−0.526487
$253$	−2.72490	−0.171313
$254$	−25.1606	−1.57871
$255$	0	0
$256$	18.3983	1.14990
$257$	−7.15589	−0.446372	−0.223186	−	0.974776i	$-0.571646\pi$
$257$	−7.15589	−0.446372	−0.223186	+	0.974776i	$0.571646\pi$
$258$	7.63631	0.475416
$259$	−48.5572	−3.01720
$260$	0	0
$261$	−8.54732	−0.529066
$262$	4.64505	0.286972
$263$	1.30967	0.0807577	0.0403789	−	0.999184i	$-0.487144\pi$
$263$	1.30967	0.0807577	0.0403789	+	0.999184i	$0.487144\pi$
$264$	1.40898	0.0867165
$265$	0	0
$266$	2.18014	0.133673
$267$	−7.81040	−0.477989
$268$	0.579000	0.0353680
$269$	−20.9745	−1.27884	−0.639418	−	0.768859i	$-0.720825\pi$
$269$	−20.9745	−1.27884	−0.639418	+	0.768859i	$0.720825\pi$
$270$	0	0
$271$	9.65260	0.586354	0.293177	−	0.956058i	$-0.405288\pi$
$271$	9.65260	0.586354	0.293177	+	0.956058i	$0.405288\pi$
$272$	−14.1025	−0.855088
$273$	17.1829	1.03996
$274$	−24.4588	−1.47761
$275$	0	0
$276$	1.19525	0.0719456
$277$	−20.0455	−1.20442	−0.602210	−	0.798338i	$-0.705713\pi$
$277$	−20.0455	−1.20442	−0.602210	+	0.798338i	$0.705713\pi$
$278$	−0.696706	−0.0417857
$279$	−3.90694	−0.233903
$280$	0	0
$281$	−4.42685	−0.264084	−0.132042	−	0.991244i	$-0.542153\pi$
$281$	−4.42685	−0.264084	−0.132042	+	0.991244i	$0.542153\pi$
$282$	15.0156	0.894168
$283$	−11.2028	−0.665938	−0.332969	−	0.942938i	$-0.608050\pi$
$283$	−11.2028	−0.665938	−0.332969	+	0.942938i	$0.608050\pi$
$284$	0.816170	0.0484308
$285$	0	0
$286$	30.6094	1.80997
$287$	−3.52031	−0.207797
$288$	−7.76669	−0.457657
$289$	−6.32315	−0.371950
$290$	0	0
$291$	8.15938	0.478311
$292$	−20.3121	−1.18868
$293$	26.6504	1.55693	0.778465	−	0.627688i	$-0.215998\pi$
$293$	26.6504	1.55693	0.778465	+	0.627688i	$0.215998\pi$
$294$	27.2404	1.58869
$295$	0	0
$296$	−3.59069	−0.208705
$297$	−4.16535	−0.241698
$298$	−29.4064	−1.70347
$299$	−2.45735	−0.142112
$300$	0	0
$301$	−17.8557	−1.02918
$302$	−11.0643	−0.636681
$303$	−9.54383	−0.548279
$304$	1.05147	0.0603057
$305$	0	0
$306$	6.39228	0.365423
$307$	9.48870	0.541549	0.270774	−	0.962643i	$-0.412720\pi$
$307$	9.48870	0.541549	0.270774	+	0.962643i	$0.412720\pi$
$308$	34.8128	1.98364
$309$	9.86698	0.561313
$310$	0	0
$311$	11.5152	0.652969	0.326485	−	0.945203i	$-0.394136\pi$
$311$	11.5152	0.652969	0.326485	+	0.945203i	$0.394136\pi$
$312$	1.27064	0.0719356
$313$	2.14459	0.121219	0.0606097	−	0.998162i	$-0.480695\pi$
$313$	2.14459	0.121219	0.0606097	+	0.998162i	$0.480695\pi$
$314$	−13.0970	−0.739106
$315$	0	0
$316$	17.9188	1.00801
$317$	0.735614	0.0413162	0.0206581	−	0.999787i	$-0.493424\pi$
$317$	0.735614	0.0413162	0.0206581	+	0.999787i	$0.493424\pi$
$318$	−23.7098	−1.32958
$319$	35.6026	1.99336
$320$	0	0
$321$	16.1273	0.900138
$322$	−5.85410	−0.326236
$323$	−0.796056	−0.0442937
$324$	1.82709	0.101505
$325$	0	0
$326$	27.0584	1.49862
$327$	−2.44236	−0.135063
$328$	−0.260319	−0.0143737
$329$	−35.1105	−1.93570
$330$	0	0
$331$	11.1178	0.611089	0.305544	−	0.952178i	$-0.401162\pi$
$331$	11.1178	0.611089	0.305544	+	0.952178i	$0.401162\pi$
$332$	−16.1968	−0.888917
$333$	10.6151	0.581706
$334$	26.4133	1.44527
$335$	0	0
$336$	19.7424	1.07704
$337$	14.2506	0.776282	0.388141	−	0.921600i	$-0.373117\pi$
$337$	14.2506	0.776282	0.388141	+	0.921600i	$0.373117\pi$
$338$	2.17218	0.118151
$339$	10.9293	0.593597
$340$	0	0
$341$	16.2738	0.881275
$342$	−0.476602	−0.0257717
$343$	−31.6749	−1.71028
$344$	−1.32039	−0.0711905
$345$	0	0
$346$	−26.8519	−1.44357
$347$	0.174615	0.00937383	0.00468691	−	0.999989i	$-0.498508\pi$
$347$	0.174615	0.00937383	0.00468691	+	0.999989i	$0.498508\pi$
$348$	−15.6167	−0.837144
$349$	−18.6640	−0.999059	−0.499530	−	0.866297i	$-0.666494\pi$
$349$	−18.6640	−0.999059	−0.499530	+	0.866297i	$0.666494\pi$
$350$	0	0
$351$	−3.75638	−0.200500
$352$	32.3510	1.72431
$353$	8.67239	0.461585	0.230792	−	0.973003i	$-0.425868\pi$
$353$	8.67239	0.461585	0.230792	+	0.973003i	$0.425868\pi$
$354$	9.59069	0.509740
$355$	0	0
$356$	−14.2703	−0.756325
$357$	−14.9468	−0.791070
$358$	8.73468	0.461642
$359$	13.7180	0.724008	0.362004	−	0.932177i	$-0.382093\pi$
$359$	13.7180	0.724008	0.362004	+	0.932177i	$0.382093\pi$
$360$	0	0
$361$	−18.9406	−0.996876
$362$	−27.3943	−1.43981
$363$	6.35016	0.333297
$364$	31.3947	1.64553
$365$	0	0
$366$	−28.7645	−1.50354
$367$	−0.530351	−0.0276841	−0.0138421	−	0.999904i	$-0.504406\pi$
$367$	−0.530351	−0.0276841	−0.0138421	+	0.999904i	$0.504406\pi$
$368$	−2.82340	−0.147180
$369$	0.769579	0.0400627
$370$	0	0
$371$	55.4397	2.87828
$372$	−7.13834	−0.370106
$373$	−29.3489	−1.51963	−0.759813	−	0.650142i	$-0.774710\pi$
$373$	−29.3489	−1.51963	−0.759813	+	0.650142i	$0.774710\pi$
$374$	−26.6261	−1.37680
$375$	0	0
$376$	−2.59634	−0.133896
$377$	32.1069	1.65359
$378$	−8.94874	−0.460273
$379$	4.84634	0.248940	0.124470	−	0.992223i	$-0.460277\pi$
$379$	4.84634	0.248940	0.124470	+	0.992223i	$0.460277\pi$
$380$	0	0
$381$	−12.8613	−0.658906
$382$	−8.40451	−0.430012
$383$	21.3587	1.09138	0.545689	−	0.837988i	$-0.316268\pi$
$383$	21.3587	1.09138	0.545689	+	0.837988i	$0.316268\pi$
$384$	2.69598	0.137578
$385$	0	0
$386$	−25.5171	−1.29879
$387$	3.90345	0.198424
$388$	14.9079	0.756835
$389$	10.4329	0.528971	0.264486	−	0.964390i	$-0.414798\pi$
$389$	10.4329	0.528971	0.264486	+	0.964390i	$0.414798\pi$
$390$	0	0
$391$	2.13757	0.108102
$392$	−4.71011	−0.237897
$393$	2.37441	0.119773
$394$	17.9560	0.904608
$395$	0	0
$396$	−7.61048	−0.382441
$397$	16.3146	0.818806	0.409403	−	0.912354i	$-0.365737\pi$
$397$	16.3146	0.818806	0.409403	+	0.912354i	$0.365737\pi$
$398$	1.32539	0.0664357
$399$	1.11442	0.0557908
$400$	0	0
$401$	10.3272	0.515718	0.257859	−	0.966183i	$-0.416983\pi$
$401$	10.3272	0.515718	0.257859	+	0.966183i	$0.416983\pi$
$402$	0.619944	0.0309200
$403$	14.6759	0.731061
$404$	−17.4374	−0.867545
$405$	0	0
$406$	76.4877	3.79602
$407$	−44.2158	−2.19170
$408$	−1.10528	−0.0547197
$409$	26.8421	1.32726	0.663629	−	0.748062i	$-0.269015\pi$
$409$	26.8421	1.32726	0.663629	+	0.748062i	$0.269015\pi$
$410$	0	0
$411$	−12.5026	−0.616710
$412$	18.0279	0.888169
$413$	−22.4255	−1.10349
$414$	1.27977	0.0628974
$415$	0	0
$416$	29.1746	1.43040
$417$	−0.356135	−0.0174400
$418$	1.98522	0.0971001
$419$	5.04882	0.246651	0.123325	−	0.992366i	$-0.460644\pi$
$419$	5.04882	0.246651	0.123325	+	0.992366i	$0.460644\pi$
$420$	0	0
$421$	−23.2026	−1.13082	−0.565412	−	0.824809i	$-0.691283\pi$
$421$	−23.2026	−1.13082	−0.565412	+	0.824809i	$0.691283\pi$
$422$	−31.6259	−1.53952
$423$	7.67555	0.373198
$424$	4.09964	0.199096
$425$	0	0
$426$	0.873886	0.0423399
$427$	67.2588	3.25488
$428$	29.4660	1.42429
$429$	15.6466	0.755426
$430$	0	0
$431$	−39.7692	−1.91561	−0.957807	−	0.287413i	$-0.907205\pi$
$431$	−39.7692	−1.91561	−0.957807	+	0.287413i	$0.907205\pi$
$432$	−4.31592	−0.207650
$433$	18.3272	0.880750	0.440375	−	0.897814i	$-0.354846\pi$
$433$	18.3272	0.880750	0.440375	+	0.897814i	$0.354846\pi$
$434$	34.9622	1.67824
$435$	0	0
$436$	−4.46242	−0.213711
$437$	−0.159375	−0.00762394
$438$	−21.7485	−1.03918
$439$	−37.2170	−1.77627	−0.888135	−	0.459582i	$-0.847999\pi$
$439$	−37.2170	−1.77627	−0.888135	+	0.459582i	$0.847999\pi$
$440$	0	0
$441$	13.9245	0.663071
$442$	−24.0118	−1.14213
$443$	−8.41969	−0.400032	−0.200016	−	0.979793i	$-0.564099\pi$
$443$	−8.41969	−0.400032	−0.200016	+	0.979793i	$0.564099\pi$
$444$	19.3948	0.920438
$445$	0	0
$446$	19.4859	0.922686
$447$	−15.0317	−0.710974
$448$	30.0172	1.41818
$449$	3.31527	0.156457	0.0782287	−	0.996935i	$-0.475074\pi$
$449$	3.31527	0.156457	0.0782287	+	0.996935i	$0.475074\pi$
$450$	0	0
$451$	−3.20557	−0.150944
$452$	19.9688	0.939253
$453$	−5.65576	−0.265731
$454$	−47.0775	−2.20946
$455$	0	0
$456$	0.0824089	0.00385915
$457$	2.57124	0.120277	0.0601387	−	0.998190i	$-0.480846\pi$
$457$	2.57124	0.120277	0.0601387	+	0.998190i	$0.480846\pi$
$458$	−30.0971	−1.40634
$459$	3.26755	0.152516
$460$	0	0
$461$	34.8861	1.62481	0.812404	−	0.583095i	$-0.198159\pi$
$461$	34.8861	1.62481	0.812404	+	0.583095i	$0.198159\pi$
$462$	37.2746	1.73417
$463$	−8.24992	−0.383406	−0.191703	−	0.981453i	$-0.561401\pi$
$463$	−8.24992	−0.383406	−0.191703	+	0.981453i	$0.561401\pi$
$464$	36.8895	1.71255
$465$	0	0
$466$	−12.8902	−0.597125
$467$	24.4499	1.13140	0.565702	−	0.824609i	$-0.308605\pi$
$467$	24.4499	1.13140	0.565702	+	0.824609i	$0.308605\pi$
$468$	−6.86324	−0.317253
$469$	−1.44959	−0.0669359
$470$	0	0
$471$	−6.69480	−0.308480
$472$	−1.65832	−0.0763303
$473$	−16.2593	−0.747602
$474$	19.1860	0.881242
$475$	0	0
$476$	−27.3092	−1.25172
$477$	−12.1197	−0.554925
$478$	34.9930	1.60054
$479$	4.79732	0.219195	0.109598	−	0.993976i	$-0.465044\pi$
$479$	4.79732	0.219195	0.109598	+	0.993976i	$0.465044\pi$
$480$	0	0
$481$	−39.8745	−1.81812
$482$	12.1761	0.554605
$483$	−2.99244	−0.136161
$484$	11.6023	0.527378
$485$	0	0
$486$	1.95630	0.0887394
$487$	−20.2715	−0.918589	−0.459294	−	0.888284i	$-0.651898\pi$
$487$	−20.2715	−0.918589	−0.459294	+	0.888284i	$0.651898\pi$
$488$	4.97364	0.225146
$489$	13.8314	0.625479
$490$	0	0
$491$	36.2638	1.63656	0.818281	−	0.574818i	$-0.194927\pi$
$491$	36.2638	1.63656	0.818281	+	0.574818i	$0.194927\pi$
$492$	1.40609	0.0633915
$493$	−27.9287	−1.25785
$494$	1.79030	0.0805493
$495$	0	0
$496$	16.8621	0.757129
$497$	−2.04337	−0.0916579
$498$	−17.3422	−0.777123
$499$	2.39550	0.107237	0.0536187	−	0.998561i	$-0.482924\pi$
$499$	2.39550	0.107237	0.0536187	+	0.998561i	$0.482924\pi$
$500$	0	0
$501$	13.5017	0.603212
$502$	−13.9206	−0.621307
$503$	−22.7079	−1.01249	−0.506247	−	0.862389i	$-0.668968\pi$
$503$	−22.7079	−1.01249	−0.506247	+	0.862389i	$0.668968\pi$
$504$	1.54732	0.0689230
$505$	0	0
$506$	−5.33070	−0.236979
$507$	1.11035	0.0493125
$508$	−23.4988	−1.04259
$509$	14.9257	0.661569	0.330784	−	0.943706i	$-0.392687\pi$
$509$	14.9257	0.661569	0.330784	+	0.943706i	$0.392687\pi$
$510$	0	0
$511$	50.8536	2.24963
$512$	30.6006	1.35237
$513$	−0.243625	−0.0107563
$514$	−13.9990	−0.617470
$515$	0	0
$516$	7.13196	0.313967
$517$	−31.9714	−1.40610
$518$	−94.9922	−4.17372
$519$	−13.7259	−0.602499
$520$	0	0
$521$	−5.56462	−0.243790	−0.121895	−	0.992543i	$-0.538897\pi$
$521$	−5.56462	−0.243790	−0.121895	+	0.992543i	$0.538897\pi$
$522$	−16.7211	−0.731862
$523$	−22.6133	−0.988811	−0.494405	−	0.869231i	$-0.664614\pi$
$523$	−22.6133	−0.988811	−0.494405	+	0.869231i	$0.664614\pi$
$524$	4.33826	0.189518
$525$	0	0
$526$	2.56210	0.111713
$527$	−12.7661	−0.556101
$528$	17.9773	0.782363
$529$	−22.5720	−0.981393
$530$	0	0
$531$	4.90248	0.212749
$532$	2.03615	0.0882782
$533$	−2.89083	−0.125216
$534$	−15.2794	−0.661206
$535$	0	0
$536$	−0.107194	−0.00463007
$537$	4.46491	0.192675
$538$	−41.0323	−1.76903
$539$	−58.0004	−2.49825
$540$	0	0
$541$	−12.5382	−0.539059	−0.269529	−	0.962992i	$-0.586868\pi$
$541$	−12.5382	−0.539059	−0.269529	+	0.962992i	$0.586868\pi$
$542$	18.8833	0.811109
$543$	−14.0032	−0.600933
$544$	−25.3780	−1.08807
$545$	0	0
$546$	33.6148	1.43858
$547$	5.45889	0.233405	0.116703	−	0.993167i	$-0.462768\pi$
$547$	5.45889	0.233405	0.116703	+	0.993167i	$0.462768\pi$
$548$	−22.8435	−0.975824
$549$	−14.7035	−0.627532
$550$	0	0
$551$	2.08234	0.0887107
$552$	−0.221284	−0.00941849
$553$	−44.8618	−1.90772
$554$	−39.2150	−1.66608
$555$	0	0
$556$	−0.650692	−0.0275955
$557$	4.84648	0.205352	0.102676	−	0.994715i	$-0.467260\pi$
$557$	4.84648	0.205352	0.102676	+	0.994715i	$0.467260\pi$
$558$	−7.64313	−0.323560
$559$	−14.6628	−0.620172
$560$	0	0
$561$	−13.6105	−0.574635
$562$	−8.66023	−0.365310
$563$	−37.5755	−1.58362	−0.791809	−	0.610769i	$-0.790861\pi$
$563$	−37.5755	−1.58362	−0.791809	+	0.610769i	$0.790861\pi$
$564$	14.0239	0.590514
$565$	0	0
$566$	−21.9160	−0.921198
$567$	−4.57433	−0.192104
$568$	−0.151103	−0.00634014
$569$	17.0619	0.715272	0.357636	−	0.933861i	$-0.383583\pi$
$569$	17.0619	0.715272	0.357636	+	0.933861i	$0.383583\pi$
$570$	0	0
$571$	−28.6234	−1.19785	−0.598925	−	0.800805i	$-0.704405\pi$
$571$	−28.6234	−1.19785	−0.598925	+	0.800805i	$0.704405\pi$
$572$	28.5878	1.19532
$573$	−4.29614	−0.179474
$574$	−6.88676	−0.287448
$575$	0	0
$576$	−6.56210	−0.273421
$577$	−2.22388	−0.0925815	−0.0462907	−	0.998928i	$-0.514740\pi$
$577$	−2.22388	−0.0925815	−0.0462907	+	0.998928i	$0.514740\pi$
$578$	−12.3699	−0.514522
$579$	−13.0436	−0.542073
$580$	0	0
$581$	40.5506	1.68232
$582$	15.9621	0.661652
$583$	50.4830	2.09079
$584$	3.76051	0.155611
$585$	0	0
$586$	52.1360	2.15372
$587$	29.8085	1.23033	0.615164	−	0.788399i	$-0.289090\pi$
$587$	29.8085	1.23033	0.615164	+	0.788399i	$0.289090\pi$
$588$	25.4413	1.04918
$589$	0.951829	0.0392194
$590$	0	0
$591$	9.17856	0.377555
$592$	−45.8141	−1.88295
$593$	43.9251	1.80379	0.901895	−	0.431956i	$-0.142177\pi$
$593$	43.9251	1.80379	0.901895	+	0.431956i	$0.142177\pi$
$594$	−8.14866	−0.334344
$595$	0	0
$596$	−27.4642	−1.12498
$597$	0.677499	0.0277282
$598$	−4.80731	−0.196585
$599$	43.1539	1.76322	0.881610	−	0.471978i	$-0.156460\pi$
$599$	43.1539	1.76322	0.881610	+	0.471978i	$0.156460\pi$
$600$	0	0
$601$	37.7365	1.53931	0.769653	−	0.638463i	$-0.220429\pi$
$601$	37.7365	1.53931	0.769653	+	0.638463i	$0.220429\pi$
$602$	−34.9310	−1.42368
$603$	0.316897	0.0129050
$604$	−10.3336	−0.420468
$605$	0	0
$606$	−18.6705	−0.758439
$607$	−45.6549	−1.85308	−0.926538	−	0.376202i	$-0.877230\pi$
$607$	−45.6549	−1.85308	−0.926538	+	0.376202i	$0.877230\pi$
$608$	1.89216	0.0767372
$609$	39.0982	1.58434
$610$	0	0
$611$	−28.8322	−1.16643
$612$	5.97010	0.241327
$613$	39.0685	1.57796	0.788980	−	0.614418i	$-0.210609\pi$
$613$	39.0685	1.57796	0.788980	+	0.614418i	$0.210609\pi$
$614$	18.5627	0.749130
$615$	0	0
$616$	−6.44512	−0.259681
$617$	27.4125	1.10359	0.551794	−	0.833981i	$-0.313944\pi$
$617$	27.4125	1.10359	0.551794	+	0.833981i	$0.313944\pi$
$618$	19.3027	0.776469
$619$	−22.8242	−0.917384	−0.458692	−	0.888595i	$-0.651682\pi$
$619$	−22.8242	−0.917384	−0.458692	+	0.888595i	$0.651682\pi$
$620$	0	0
$621$	0.654182	0.0262514
$622$	22.5272	0.903259
$623$	35.7273	1.43139
$624$	16.2122	0.649008
$625$	0	0
$626$	4.19545	0.167684
$627$	1.01478	0.0405266
$628$	−12.2320	−0.488110
$629$	34.6855	1.38300
$630$	0	0
$631$	10.0638	0.400632	0.200316	−	0.979731i	$-0.435803\pi$
$631$	10.0638	0.400632	0.200316	+	0.979731i	$0.435803\pi$
$632$	−3.31743	−0.131960
$633$	−16.1662	−0.642549
$634$	1.43908	0.0571531
$635$	0	0
$636$	−22.1439	−0.878061
$637$	−52.3056	−2.07242
$638$	69.6492	2.75744
$639$	0.446705	0.0176714
$640$	0	0
$641$	−42.7831	−1.68983	−0.844916	−	0.534899i	$-0.820350\pi$
$641$	−42.7831	−1.68983	−0.844916	+	0.534899i	$0.820350\pi$
$642$	31.5497	1.24517
$643$	−10.1067	−0.398571	−0.199285	−	0.979941i	$-0.563862\pi$
$643$	−10.1067	−0.398571	−0.199285	+	0.979941i	$0.563862\pi$
$644$	−5.46747	−0.215448
$645$	0	0
$646$	−1.55732	−0.0612719
$647$	16.7580	0.658826	0.329413	−	0.944186i	$-0.393149\pi$
$647$	16.7580	0.658826	0.329413	+	0.944186i	$0.393149\pi$
$648$	−0.338261	−0.0132882
$649$	−20.4205	−0.801576
$650$	0	0
$651$	17.8716	0.700445
$652$	25.2713	0.989700
$653$	−20.7798	−0.813175	−0.406588	−	0.913612i	$-0.633281\pi$
$653$	−20.7798	−0.813175	−0.406588	+	0.913612i	$0.633281\pi$
$654$	−4.77799	−0.186834
$655$	0	0
$656$	−3.32144	−0.129680
$657$	−11.1172	−0.433723
$658$	−68.6865	−2.67768
$659$	−15.9362	−0.620785	−0.310393	−	0.950608i	$-0.600461\pi$
$659$	−15.9362	−0.620785	−0.310393	+	0.950608i	$0.600461\pi$
$660$	0	0
$661$	3.37323	0.131203	0.0656017	−	0.997846i	$-0.479103\pi$
$661$	3.37323	0.131203	0.0656017	+	0.997846i	$0.479103\pi$
$662$	21.7497	0.845325
$663$	−12.2741	−0.476688
$664$	2.99862	0.116369
$665$	0	0
$666$	20.7664	0.804680
$667$	−5.59150	−0.216504
$668$	24.6688	0.954466
$669$	9.96064	0.385100
$670$	0	0
$671$	61.2454	2.36435
$672$	35.5274	1.37050
$673$	35.2852	1.36015	0.680073	−	0.733144i	$-0.261948\pi$
$673$	35.2852	1.36015	0.680073	+	0.733144i	$0.261948\pi$
$674$	27.8785	1.07384
$675$	0	0
$676$	2.02872	0.0780276
$677$	31.2943	1.20274	0.601369	−	0.798971i	$-0.294622\pi$
$677$	31.2943	1.20274	0.601369	+	0.798971i	$0.294622\pi$
$678$	21.3809	0.821129
$679$	−37.3237	−1.43235
$680$	0	0
$681$	−24.0646	−0.922158
$682$	31.8363	1.21908
$683$	−10.8131	−0.413751	−0.206876	−	0.978367i	$-0.566330\pi$
$683$	−10.8131	−0.413751	−0.206876	+	0.978367i	$0.566330\pi$
$684$	−0.445125	−0.0170198
$685$	0	0
$686$	−61.9654	−2.36585
$687$	−15.3847	−0.586964
$688$	−16.8470	−0.642286
$689$	45.5263	1.73441
$690$	0	0
$691$	−50.9819	−1.93944	−0.969722	−	0.244210i	$-0.921471\pi$
$691$	−50.9819	−1.93944	−0.969722	+	0.244210i	$0.921471\pi$
$692$	−25.0784	−0.953338
$693$	19.0537	0.723790
$694$	0.341599	0.0129669
$695$	0	0
$696$	2.89123	0.109592
$697$	2.51463	0.0952485
$698$	−36.5122	−1.38201
$699$	−6.58907	−0.249222
$700$	0	0
$701$	5.20728	0.196676	0.0983382	−	0.995153i	$-0.468647\pi$
$701$	5.20728	0.196676	0.0983382	+	0.995153i	$0.468647\pi$
$702$	−7.34858	−0.277354
$703$	−2.58611	−0.0975372
$704$	27.3335	1.03017
$705$	0	0
$706$	16.9657	0.638514
$707$	43.6566	1.64188
$708$	8.95727	0.336635
$709$	−37.4108	−1.40499	−0.702497	−	0.711687i	$-0.747931\pi$
$709$	−37.4108	−1.40499	−0.702497	+	0.711687i	$0.747931\pi$
$710$	0	0
$711$	9.80731	0.367803
$712$	2.64195	0.0990114
$713$	−2.55585	−0.0957174
$714$	−29.2404	−1.09429
$715$	0	0
$716$	8.15780	0.304871
$717$	17.8874	0.668017
$718$	26.8364	1.00153
$719$	31.2527	1.16553	0.582764	−	0.812641i	$-0.301971\pi$
$719$	31.2527	1.16553	0.582764	+	0.812641i	$0.301971\pi$
$720$	0	0
$721$	−45.1348	−1.68091
$722$	−37.0535	−1.37899
$723$	6.22404	0.231475
$724$	−25.5850	−0.950861
$725$	0	0
$726$	12.4228	0.461053
$727$	−1.21933	−0.0452225	−0.0226113	−	0.999744i	$-0.507198\pi$
$727$	−1.21933	−0.0452225	−0.0226113	+	0.999744i	$0.507198\pi$
$728$	−5.81231	−0.215418
$729$	1.00000	0.0370370
$730$	0	0
$731$	12.7547	0.471750
$732$	−26.8647	−0.992948
$733$	13.3535	0.493221	0.246611	−	0.969115i	$-0.420683\pi$
$733$	13.3535	0.493221	0.246611	+	0.969115i	$0.420683\pi$
$734$	−1.03752	−0.0382957
$735$	0	0
$736$	−5.08083	−0.187282
$737$	−1.31999	−0.0486224
$738$	1.50552	0.0554191
$739$	−5.24691	−0.193011	−0.0965054	−	0.995332i	$-0.530766\pi$
$739$	−5.24691	−0.193011	−0.0965054	+	0.995332i	$0.530766\pi$
$740$	0	0
$741$	0.915147	0.0336188
$742$	108.456	3.98156
$743$	−42.9203	−1.57459	−0.787296	−	0.616575i	$-0.788520\pi$
$743$	−42.9203	−1.57459	−0.787296	+	0.616575i	$0.788520\pi$
$744$	1.32157	0.0484510
$745$	0	0
$746$	−57.4150	−2.10211
$747$	−8.86482	−0.324347
$748$	−24.8676	−0.909249
$749$	−73.7716	−2.69555
$750$	0	0
$751$	−20.2461	−0.738792	−0.369396	−	0.929272i	$-0.620435\pi$
$751$	−20.2461	−0.738792	−0.369396	+	0.929272i	$0.620435\pi$
$752$	−33.1270	−1.20802
$753$	−7.11580	−0.259314
$754$	62.8106	2.28743
$755$	0	0
$756$	−8.35772	−0.303967
$757$	−10.3260	−0.375306	−0.187653	−	0.982235i	$-0.560088\pi$
$757$	−10.3260	−0.375306	−0.187653	+	0.982235i	$0.560088\pi$
$758$	9.48087	0.344361
$759$	−2.72490	−0.0989075
$760$	0	0
$761$	29.2923	1.06185	0.530923	−	0.847420i	$-0.321845\pi$
$761$	29.2923	1.06185	0.530923	+	0.847420i	$0.321845\pi$
$762$	−25.1606	−0.911471
$763$	11.1722	0.404460
$764$	−7.84943	−0.283982
$765$	0	0
$766$	41.7839	1.50971
$767$	−18.4155	−0.664947
$768$	18.3983	0.663893
$769$	−22.9834	−0.828803	−0.414402	−	0.910094i	$-0.636009\pi$
$769$	−22.9834	−0.828803	−0.414402	+	0.910094i	$0.636009\pi$
$770$	0	0
$771$	−7.15589	−0.257713
$772$	−23.8318	−0.857725
$773$	54.2216	1.95022	0.975108	−	0.221732i	$-0.0711709\pi$
$773$	54.2216	1.95022	0.975108	+	0.221732i	$0.0711709\pi$
$774$	7.63631	0.274481
$775$	0	0
$776$	−2.76000	−0.0990782
$777$	−48.5572	−1.74198
$778$	20.4099	0.731731
$779$	−0.187489	−0.00671748
$780$	0	0
$781$	−1.86068	−0.0665805
$782$	4.18172	0.149538
$783$	−8.54732	−0.305456
$784$	−60.0970	−2.14632
$785$	0	0
$786$	4.64505	0.165683
$787$	−6.60711	−0.235518	−0.117759	−	0.993042i	$-0.537571\pi$
$787$	−6.60711	−0.235518	−0.117759	+	0.993042i	$0.537571\pi$
$788$	16.7701	0.597409
$789$	1.30967	0.0466255
$790$	0	0
$791$	−49.9941	−1.77759
$792$	1.40898	0.0500658
$793$	55.2320	1.96135
$794$	31.9161	1.13266
$795$	0	0
$796$	1.23785	0.0438745
$797$	2.34163	0.0829446	0.0414723	−	0.999140i	$-0.486795\pi$
$797$	2.34163	0.0829446	0.0414723	+	0.999140i	$0.486795\pi$
$798$	2.18014	0.0771760
$799$	25.0802	0.887274
$800$	0	0
$801$	−7.81040	−0.275967
$802$	20.2031	0.713397
$803$	46.3070	1.63414
$804$	0.579000	0.0204197
$805$	0	0
$806$	28.7105	1.01128
$807$	−20.9745	−0.738337
$808$	3.22831	0.113571
$809$	−53.7248	−1.88886	−0.944432	−	0.328707i	$-0.893387\pi$
$809$	−53.7248	−1.88886	−0.944432	+	0.328707i	$0.893387\pi$
$810$	0	0
$811$	−29.5877	−1.03897	−0.519483	−	0.854481i	$-0.673875\pi$
$811$	−29.5877	−1.03897	−0.519483	+	0.854481i	$0.673875\pi$
$812$	71.4361	2.50691
$813$	9.65260	0.338532
$814$	−86.4992	−3.03180
$815$	0	0
$816$	−14.1025	−0.493685
$817$	−0.950979	−0.0332705
$818$	52.5112	1.83601
$819$	17.1829	0.600419
$820$	0	0
$821$	33.3855	1.16516	0.582580	−	0.812773i	$-0.302043\pi$
$821$	33.3855	1.16516	0.582580	+	0.812773i	$0.302043\pi$
$822$	−24.4588	−0.853100
$823$	17.5383	0.611345	0.305672	−	0.952137i	$-0.401119\pi$
$823$	17.5383	0.611345	0.305672	+	0.952137i	$0.401119\pi$
$824$	−3.33762	−0.116271
$825$	0	0
$826$	−43.8710	−1.52647
$827$	−26.6114	−0.925369	−0.462684	−	0.886523i	$-0.653114\pi$
$827$	−26.6114	−0.925369	−0.462684	+	0.886523i	$0.653114\pi$
$828$	1.19525	0.0415378
$829$	20.3212	0.705784	0.352892	−	0.935664i	$-0.385198\pi$
$829$	20.3212	0.705784	0.352892	+	0.935664i	$0.385198\pi$
$830$	0	0
$831$	−20.0455	−0.695372
$832$	24.6497	0.854575
$833$	45.4989	1.57644
$834$	−0.696706	−0.0241250
$835$	0	0
$836$	1.85410	0.0641255
$837$	−3.90694	−0.135044
$838$	9.87698	0.341195
$839$	−23.3881	−0.807448	−0.403724	−	0.914881i	$-0.632284\pi$
$839$	−23.3881	−0.807448	−0.403724	+	0.914881i	$0.632284\pi$
$840$	0	0
$841$	44.0566	1.51919
$842$	−45.3910	−1.56428
$843$	−4.42685	−0.152469
$844$	−29.5371	−1.01671
$845$	0	0
$846$	15.0156	0.516248
$847$	−29.0477	−0.998091
$848$	52.3078	1.79626
$849$	−11.2028	−0.384479
$850$	0	0
$851$	6.94424	0.238045
$852$	0.816170	0.0279615
$853$	9.81934	0.336208	0.168104	−	0.985769i	$-0.446236\pi$
$853$	9.81934	0.336208	0.168104	+	0.985769i	$0.446236\pi$
$854$	131.578	4.50251
$855$	0	0
$856$	−5.45524	−0.186456
$857$	15.9866	0.546093	0.273047	−	0.962001i	$-0.411969\pi$
$857$	15.9866	0.546093	0.273047	+	0.962001i	$0.411969\pi$
$858$	30.6094	1.04499
$859$	−20.5913	−0.702567	−0.351284	−	0.936269i	$-0.614255\pi$
$859$	−20.5913	−0.702567	−0.351284	+	0.936269i	$0.614255\pi$
$860$	0	0
$861$	−3.52031	−0.119972
$862$	−77.8002	−2.64989
$863$	−51.5169	−1.75366	−0.876828	−	0.480803i	$-0.840345\pi$
$863$	−51.5169	−1.75366	−0.876828	+	0.480803i	$0.840345\pi$
$864$	−7.76669	−0.264228
$865$	0	0
$866$	35.8534	1.21835
$867$	−6.32315	−0.214745
$868$	32.6531	1.10832
$869$	−40.8509	−1.38577
$870$	0	0
$871$	−1.19038	−0.0403346
$872$	0.826157	0.0279772
$873$	8.15938	0.276153
$874$	−0.311785	−0.0105463
$875$	0	0
$876$	−20.3121	−0.686282
$877$	−17.6050	−0.594480	−0.297240	−	0.954803i	$-0.596066\pi$
$877$	−17.6050	−0.594480	−0.297240	+	0.954803i	$0.596066\pi$
$878$	−72.8075	−2.45713
$879$	26.6504	0.898894
$880$	0	0
$881$	−47.1453	−1.58837	−0.794183	−	0.607679i	$-0.792101\pi$
$881$	−47.1453	−1.58837	−0.794183	+	0.607679i	$0.792101\pi$
$882$	27.2404	0.917232
$883$	−23.2300	−0.781751	−0.390875	−	0.920444i	$-0.627828\pi$
$883$	−23.2300	−0.781751	−0.390875	+	0.920444i	$0.627828\pi$
$884$	−22.4259	−0.754266
$885$	0	0
$886$	−16.4714	−0.553368
$887$	20.5226	0.689082	0.344541	−	0.938771i	$-0.388035\pi$
$887$	20.5226	0.689082	0.344541	+	0.938771i	$0.388035\pi$
$888$	−3.59069	−0.120496
$889$	58.8320	1.97316
$890$	0	0
$891$	−4.16535	−0.139545
$892$	18.1990	0.609347
$893$	−1.86995	−0.0625756
$894$	−29.4064	−0.983497
$895$	0	0
$896$	−12.3323	−0.411993
$897$	−2.45735	−0.0820486
$898$	6.48566	0.216429
$899$	33.3939	1.11375
$900$	0	0
$901$	−39.6018	−1.31933
$902$	−6.27104	−0.208803
$903$	−17.8557	−0.594200
$904$	−3.69695	−0.122959
$905$	0	0
$906$	−11.0643	−0.367588
$907$	−13.1950	−0.438133	−0.219066	−	0.975710i	$-0.570301\pi$
$907$	−13.1950	−0.438133	−0.219066	+	0.975710i	$0.570301\pi$
$908$	−43.9682	−1.45914
$909$	−9.54383	−0.316549
$910$	0	0
$911$	27.1021	0.897932	0.448966	−	0.893549i	$-0.351792\pi$
$911$	27.1021	0.897932	0.448966	+	0.893549i	$0.351792\pi$
$912$	1.05147	0.0348175
$913$	36.9251	1.22204
$914$	5.03010	0.166381
$915$	0	0
$916$	−28.1093	−0.928757
$917$	−10.8613	−0.358673
$918$	6.39228	0.210977
$919$	−3.80568	−0.125538	−0.0627690	−	0.998028i	$-0.519993\pi$
$919$	−3.80568	−0.125538	−0.0627690	+	0.998028i	$0.519993\pi$
$920$	0	0
$921$	9.48870	0.312663
$922$	68.2475	2.24761
$923$	−1.67799	−0.0552317
$924$	34.8128	1.14526
$925$	0	0
$926$	−16.1393	−0.530369
$927$	9.86698	0.324074
$928$	66.3844	2.17917
$929$	41.8941	1.37450	0.687250	−	0.726421i	$-0.258818\pi$
$929$	41.8941	1.37450	0.687250	+	0.726421i	$0.258818\pi$
$930$	0	0
$931$	−3.39235	−0.111180
$932$	−12.0388	−0.394345
$933$	11.5152	0.376992
$934$	47.8312	1.56508
$935$	0	0
$936$	1.27064	0.0415320
$937$	−8.55321	−0.279421	−0.139711	−	0.990192i	$-0.544617\pi$
$937$	−8.55321	−0.279421	−0.139711	+	0.990192i	$0.544617\pi$
$938$	−2.83583	−0.0925931
$939$	2.14459	0.0699861
$940$	0	0
$941$	−48.3669	−1.57672	−0.788358	−	0.615216i	$-0.789069\pi$
$941$	−48.3669	−1.57672	−0.788358	+	0.615216i	$0.789069\pi$
$942$	−13.0970	−0.426723
$943$	0.503445	0.0163944
$944$	−21.1587	−0.688657
$945$	0	0
$946$	−31.8079	−1.03416
$947$	8.71018	0.283043	0.141521	−	0.989935i	$-0.454801\pi$
$947$	8.71018	0.283043	0.141521	+	0.989935i	$0.454801\pi$
$948$	17.9188	0.581977
$949$	41.7603	1.35560
$950$	0	0
$951$	0.735614	0.0238539
$952$	5.05593	0.163864
$953$	−43.4534	−1.40760	−0.703798	−	0.710401i	$-0.748514\pi$
$953$	−43.4534	−1.40760	−0.703798	+	0.710401i	$0.748514\pi$
$954$	−23.7098	−0.767633
$955$	0	0
$956$	32.6819	1.05701
$957$	35.6026	1.15087
$958$	9.38497	0.303215
$959$	57.1912	1.84680
$960$	0	0
$961$	−15.7358	−0.507606
$962$	−78.0062	−2.51502
$963$	16.1273	0.519695
$964$	11.3719	0.366264
$965$	0	0
$966$	−5.85410	−0.188353
$967$	−60.2789	−1.93844	−0.969220	−	0.246197i	$-0.920819\pi$
$967$	−60.2789	−1.93844	−0.969220	+	0.246197i	$0.920819\pi$
$968$	−2.14801	−0.0690397
$969$	−0.796056	−0.0255730
$970$	0	0
$971$	5.42583	0.174123	0.0870616	−	0.996203i	$-0.472252\pi$
$971$	5.42583	0.174123	0.0870616	+	0.996203i	$0.472252\pi$
$972$	1.82709	0.0586040
$973$	1.62908	0.0522259
$974$	−39.6570	−1.27069
$975$	0	0
$976$	63.4593	2.03128
$977$	−36.5741	−1.17011	−0.585054	−	0.810994i	$-0.698927\pi$
$977$	−36.5741	−1.17011	−0.585054	+	0.810994i	$0.698927\pi$
$978$	27.0584	0.865231
$979$	32.5331	1.03976
$980$	0	0
$981$	−2.44236	−0.0779787
$982$	70.9427	2.26387
$983$	−41.0896	−1.31056	−0.655278	−	0.755388i	$-0.727449\pi$
$983$	−41.0896	−1.31056	−0.655278	+	0.755388i	$0.727449\pi$
$984$	−0.260319	−0.00829866
$985$	0	0
$986$	−54.6369	−1.73999
$987$	−35.1105	−1.11758
$988$	1.67206	0.0531952
$989$	2.55357	0.0811988
$990$	0	0
$991$	−4.20264	−0.133501	−0.0667506	−	0.997770i	$-0.521263\pi$
$991$	−4.20264	−0.133501	−0.0667506	+	0.997770i	$0.521263\pi$
$992$	30.3440	0.963424
$993$	11.1178	0.352812
$994$	−3.99744	−0.126791
$995$	0	0
$996$	−16.1968	−0.513216
$997$	−10.1577	−0.321698	−0.160849	−	0.986979i	$-0.551423\pi$
$997$	−10.1577	−0.321698	−0.160849	+	0.986979i	$0.551423\pi$
$998$	4.68631	0.148342
$999$	10.6151	0.335848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.f.1.4	✓	4
3.2	odd	2		5625.2.a.m.1.1		4
5.2	odd	4		1875.2.b.d.1249.8		8
5.3	odd	4		1875.2.b.d.1249.1		8
5.4	even	2		1875.2.a.g.1.1	yes	4
15.14	odd	2		5625.2.a.j.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.f.1.4	✓	4	1.1	even	1	trivial
1875.2.a.g.1.1	yes	4	5.4	even	2
1875.2.b.d.1249.1		8	5.3	odd	4
1875.2.b.d.1249.8		8	5.2	odd	4
5625.2.a.j.1.4		4	15.14	odd	2
5625.2.a.m.1.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+1.95630 q^{2} +1.00000 q^{3} +1.82709 q^{4} +1.95630 q^{6} -4.57433 q^{7} -0.338261 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.95630 q^{2} +1.00000 q^{3} +1.82709 q^{4} +1.95630 q^{6} -4.57433 q^{7} -0.338261 q^{8} +1.00000 q^{9} -4.16535 q^{11} +1.82709 q^{12} -3.75638 q^{13} -8.94874 q^{14} -4.31592 q^{16} +3.26755 q^{17} +1.95630 q^{18} -0.243625 q^{19} -4.57433 q^{21} -8.14866 q^{22} +0.654182 q^{23} -0.338261 q^{24} -7.34858 q^{26} +1.00000 q^{27} -8.35772 q^{28} -8.54732 q^{29} -3.90694 q^{31} -7.76669 q^{32} -4.16535 q^{33} +6.39228 q^{34} +1.82709 q^{36} +10.6151 q^{37} -0.476602 q^{38} -3.75638 q^{39} +0.769579 q^{41} -8.94874 q^{42} +3.90345 q^{43} -7.61048 q^{44} +1.27977 q^{46} +7.67555 q^{47} -4.31592 q^{48} +13.9245 q^{49} +3.26755 q^{51} -6.86324 q^{52} -12.1197 q^{53} +1.95630 q^{54} +1.54732 q^{56} -0.243625 q^{57} -16.7211 q^{58} +4.90248 q^{59} -14.7035 q^{61} -7.64313 q^{62} -4.57433 q^{63} -6.56210 q^{64} -8.14866 q^{66} +0.316897 q^{67} +5.97010 q^{68} +0.654182 q^{69} +0.446705 q^{71} -0.338261 q^{72} -11.1172 q^{73} +20.7664 q^{74} -0.445125 q^{76} +19.0537 q^{77} -7.34858 q^{78} +9.80731 q^{79} +1.00000 q^{81} +1.50552 q^{82} -8.86482 q^{83} -8.35772 q^{84} +7.63631 q^{86} -8.54732 q^{87} +1.40898 q^{88} -7.81040 q^{89} +17.1829 q^{91} +1.19525 q^{92} -3.90694 q^{93} +15.0156 q^{94} -7.76669 q^{96} +8.15938 q^{97} +27.2404 q^{98} -4.16535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 4 q^{3} + q^{4} - q^{6} - 5 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 + 4 * q^3 + q^4 - q^6 - 5 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q - q^{2} + 4 q^{3} + q^{4} - q^{6} - 5 q^{7} + 3 q^{8} + 4 q^{9} - 6 q^{11} + q^{12} - 7 q^{13} - 10 q^{14} - 9 q^{16} + 7 q^{17} - q^{18} - 9 q^{19} - 5 q^{21} - 6 q^{22} - 10 q^{23} + 3 q^{24} - 2 q^{26} + 4 q^{27} - 5 q^{28} - 28 q^{29} - 10 q^{31} - 6 q^{33} + 7 q^{34} + q^{36} + 10 q^{37} + 6 q^{38} - 7 q^{39} - 10 q^{42} - q^{43} - 9 q^{44} + 5 q^{46} + 23 q^{47} - 9 q^{48} - 3 q^{49} + 7 q^{51} - 13 q^{52} - q^{54} - 9 q^{57} + 2 q^{58} + 4 q^{59} - 43 q^{61} + 10 q^{62} - 5 q^{63} - 7 q^{64} - 6 q^{66} - 8 q^{67} + 3 q^{68} - 10 q^{69} - 27 q^{71} + 3 q^{72} - 15 q^{73} + 5 q^{74} + 9 q^{76} + 15 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{81} + 20 q^{82} - 3 q^{83} - 5 q^{84} + 24 q^{86} - 28 q^{87} + 3 q^{88} - 9 q^{89} + 5 q^{91} + 15 q^{92} - 10 q^{93} - 22 q^{94} - 13 q^{97} + 42 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q - q^2 + 4 * q^3 + q^4 - q^6 - 5 * q^7 + 3 * q^8 + 4 * q^9 - 6 * q^11 + q^12 - 7 * q^13 - 10 * q^14 - 9 * q^16 + 7 * q^17 - q^18 - 9 * q^19 - 5 * q^21 - 6 * q^22 - 10 * q^23 + 3 * q^24 - 2 * q^26 + 4 * q^27 - 5 * q^28 - 28 * q^29 - 10 * q^31 - 6 * q^33 + 7 * q^34 + q^36 + 10 * q^37 + 6 * q^38 - 7 * q^39 - 10 * q^42 - q^43 - 9 * q^44 + 5 * q^46 + 23 * q^47 - 9 * q^48 - 3 * q^49 + 7 * q^51 - 13 * q^52 - q^54 - 9 * q^57 + 2 * q^58 + 4 * q^59 - 43 * q^61 + 10 * q^62 - 5 * q^63 - 7 * q^64 - 6 * q^66 - 8 * q^67 + 3 * q^68 - 10 * q^69 - 27 * q^71 + 3 * q^72 - 15 * q^73 + 5 * q^74 + 9 * q^76 + 15 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^81 + 20 * q^82 - 3 * q^83 - 5 * q^84 + 24 * q^86 - 28 * q^87 + 3 * q^88 - 9 * q^89 + 5 * q^91 + 15 * q^92 - 10 * q^93 - 22 * q^94 - 13 * q^97 + 42 * q^98 - 6 * q^99

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