LMFDB - Embedded newform 3525.2.a.be.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 24x^{5} + 8x^{4} - 47x^{3} + 8x^{2} + 13x + 2 $ x^8 - 3x^7 - 7x^6 + 24x^5 + 8x^4 - 47x^3 + 8x^2 + 13*x + 2
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			1.3
Root			$-0.267165$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.267165 q^{2} -1.00000 q^{3} -1.92862 q^{4} +0.267165 q^{6} +0.207232 q^{7} +1.04959 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.267165 q^{2} -1.00000 q^{3} -1.92862 q^{4} +0.267165 q^{6} +0.207232 q^{7} +1.04959 q^{8} +1.00000 q^{9} -1.27329 q^{11} +1.92862 q^{12} +5.37648 q^{13} -0.0553651 q^{14} +3.57683 q^{16} -0.969832 q^{17} -0.267165 q^{18} +6.42820 q^{19} -0.207232 q^{21} +0.340179 q^{22} -5.87315 q^{23} -1.04959 q^{24} -1.43641 q^{26} -1.00000 q^{27} -0.399672 q^{28} -9.93423 q^{29} +5.97938 q^{31} -3.05479 q^{32} +1.27329 q^{33} +0.259105 q^{34} -1.92862 q^{36} +1.19082 q^{37} -1.71739 q^{38} -5.37648 q^{39} +2.24060 q^{41} +0.0553651 q^{42} +6.20192 q^{43} +2.45570 q^{44} +1.56910 q^{46} +1.00000 q^{47} -3.57683 q^{48} -6.95706 q^{49} +0.969832 q^{51} -10.3692 q^{52} +8.64084 q^{53} +0.267165 q^{54} +0.217508 q^{56} -6.42820 q^{57} +2.65408 q^{58} -9.70796 q^{59} -10.1014 q^{61} -1.59748 q^{62} +0.207232 q^{63} -6.33753 q^{64} -0.340179 q^{66} -4.36482 q^{67} +1.87044 q^{68} +5.87315 q^{69} +9.54225 q^{71} +1.04959 q^{72} +11.7305 q^{73} -0.318145 q^{74} -12.3976 q^{76} -0.263866 q^{77} +1.43641 q^{78} -15.7821 q^{79} +1.00000 q^{81} -0.598611 q^{82} -1.79347 q^{83} +0.399672 q^{84} -1.65694 q^{86} +9.93423 q^{87} -1.33644 q^{88} -7.28256 q^{89} +1.11418 q^{91} +11.3271 q^{92} -5.97938 q^{93} -0.267165 q^{94} +3.05479 q^{96} +0.290073 q^{97} +1.85868 q^{98} -1.27329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.267165	−0.188914	−0.0944571	−	0.995529i	$-0.530112\pi$
$2$	−0.267165	−0.188914	−0.0944571	+	0.995529i	$0.530112\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.92862	−0.964311
$5$	0	0
$5$	0	0
$6$	0.267165	0.109070
$7$	0.207232	0.0783262	0.0391631	−	0.999233i	$-0.487531\pi$
$7$	0.207232	0.0783262	0.0391631	+	0.999233i	$0.487531\pi$
$8$	1.04959	0.371086
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.27329	−0.383912	−0.191956	−	0.981404i	$-0.561483\pi$
$11$	−1.27329	−0.383912	−0.191956	+	0.981404i	$0.561483\pi$
$12$	1.92862	0.556745
$13$	5.37648	1.49117	0.745584	−	0.666412i	$-0.232171\pi$
$13$	5.37648	1.49117	0.745584	+	0.666412i	$0.232171\pi$
$14$	−0.0553651	−0.0147969
$15$	0	0
$16$	3.57683	0.894208
$17$	−0.969832	−0.235219	−0.117609	−	0.993060i	$-0.537523\pi$
$17$	−0.969832	−0.235219	−0.117609	+	0.993060i	$0.537523\pi$
$18$	−0.267165	−0.0629714
$19$	6.42820	1.47473	0.737365	−	0.675494i	$-0.236070\pi$
$19$	6.42820	1.47473	0.737365	+	0.675494i	$0.236070\pi$
$20$	0	0
$21$	−0.207232	−0.0452216
$22$	0.340179	0.0725265
$23$	−5.87315	−1.22464	−0.612318	−	0.790611i	$-0.709763\pi$
$23$	−5.87315	−1.22464	−0.612318	+	0.790611i	$0.709763\pi$
$24$	−1.04959	−0.214247
$25$	0	0
$26$	−1.43641	−0.281703
$27$	−1.00000	−0.192450
$28$	−0.399672	−0.0755308
$29$	−9.93423	−1.84474	−0.922370	−	0.386307i	$-0.873751\pi$
$29$	−9.93423	−1.84474	−0.922370	+	0.386307i	$0.873751\pi$
$30$	0	0
$31$	5.97938	1.07393	0.536964	−	0.843605i	$-0.319571\pi$
$31$	5.97938	1.07393	0.536964	+	0.843605i	$0.319571\pi$
$32$	−3.05479	−0.540015
$33$	1.27329	0.221652
$34$	0.259105	0.0444362
$35$	0	0
$36$	−1.92862	−0.321437
$37$	1.19082	0.195769	0.0978846	−	0.995198i	$-0.468792\pi$
$37$	1.19082	0.195769	0.0978846	+	0.995198i	$0.468792\pi$
$38$	−1.71739	−0.278598
$39$	−5.37648	−0.860926
$40$	0	0
$41$	2.24060	0.349923	0.174962	−	0.984575i	$-0.444020\pi$
$41$	2.24060	0.349923	0.174962	+	0.984575i	$0.444020\pi$
$42$	0.0553651	0.00854301
$43$	6.20192	0.945783	0.472892	−	0.881121i	$-0.343210\pi$
$43$	6.20192	0.945783	0.472892	+	0.881121i	$0.343210\pi$
$44$	2.45570	0.370211
$45$	0	0
$46$	1.56910	0.231351
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−3.57683	−0.516271
$49$	−6.95706	−0.993865
$50$	0	0
$51$	0.969832	0.135804
$52$	−10.3692	−1.43795
$53$	8.64084	1.18691	0.593455	−	0.804867i	$-0.297763\pi$
$53$	8.64084	1.18691	0.593455	+	0.804867i	$0.297763\pi$
$54$	0.267165	0.0363566
$55$	0	0
$56$	0.217508	0.0290658
$57$	−6.42820	−0.851436
$58$	2.65408	0.348498
$59$	−9.70796	−1.26387	−0.631934	−	0.775022i	$-0.717739\pi$
$59$	−9.70796	−1.26387	−0.631934	+	0.775022i	$0.717739\pi$
$60$	0	0
$61$	−10.1014	−1.29335	−0.646676	−	0.762765i	$-0.723841\pi$
$61$	−10.1014	−1.29335	−0.646676	+	0.762765i	$0.723841\pi$
$62$	−1.59748	−0.202880
$63$	0.207232	0.0261087
$64$	−6.33753	−0.792191
$65$	0	0
$66$	−0.340179	−0.0418732
$67$	−4.36482	−0.533248	−0.266624	−	0.963801i	$-0.585908\pi$
$67$	−4.36482	−0.533248	−0.266624	+	0.963801i	$0.585908\pi$
$68$	1.87044	0.226824
$69$	5.87315	0.707044
$70$	0	0
$71$	9.54225	1.13246	0.566229	−	0.824248i	$-0.308402\pi$
$71$	9.54225	1.13246	0.566229	+	0.824248i	$0.308402\pi$
$72$	1.04959	0.123695
$73$	11.7305	1.37295	0.686476	−	0.727153i	$-0.259157\pi$
$73$	11.7305	1.37295	0.686476	+	0.727153i	$0.259157\pi$
$74$	−0.318145	−0.0369836
$75$	0	0
$76$	−12.3976	−1.42210
$77$	−0.263866	−0.0300704
$78$	1.43641	0.162641
$79$	−15.7821	−1.77563	−0.887814	−	0.460202i	$-0.847777\pi$
$79$	−15.7821	−1.77563	−0.887814	+	0.460202i	$0.847777\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.598611	−0.0661055
$83$	−1.79347	−0.196859	−0.0984295	−	0.995144i	$-0.531382\pi$
$83$	−1.79347	−0.196859	−0.0984295	+	0.995144i	$0.531382\pi$
$84$	0.399672	0.0436077
$85$	0	0
$86$	−1.65694	−0.178672
$87$	9.93423	1.06506
$88$	−1.33644	−0.142465
$89$	−7.28256	−0.771949	−0.385975	−	0.922509i	$-0.626135\pi$
$89$	−7.28256	−0.771949	−0.385975	+	0.922509i	$0.626135\pi$
$90$	0	0
$91$	1.11418	0.116797
$92$	11.3271	1.18093
$93$	−5.97938	−0.620033
$94$	−0.267165	−0.0275560
$95$	0	0
$96$	3.05479	0.311778
$97$	0.290073	0.0294524	0.0147262	−	0.999892i	$-0.495312\pi$
$97$	0.290073	0.0294524	0.0147262	+	0.999892i	$0.495312\pi$
$98$	1.85868	0.187755
$99$	−1.27329	−0.127971
$100$	0	0
$101$	−5.63344	−0.560548	−0.280274	−	0.959920i	$-0.590425\pi$
$101$	−5.63344	−0.560548	−0.280274	+	0.959920i	$0.590425\pi$
$102$	−0.259105	−0.0256552
$103$	11.3273	1.11612	0.558058	−	0.829802i	$-0.311547\pi$
$103$	11.3273	1.11612	0.558058	+	0.829802i	$0.311547\pi$
$104$	5.64311	0.553352
$105$	0	0
$106$	−2.30853	−0.224224
$107$	8.10431	0.783474	0.391737	−	0.920077i	$-0.371874\pi$
$107$	8.10431	0.783474	0.391737	+	0.920077i	$0.371874\pi$
$108$	1.92862	0.185582
$109$	13.2362	1.26780	0.633899	−	0.773416i	$-0.281454\pi$
$109$	13.2362	1.26780	0.633899	+	0.773416i	$0.281454\pi$
$110$	0	0
$111$	−1.19082	−0.113027
$112$	0.741232	0.0700399
$113$	16.4518	1.54766	0.773830	−	0.633394i	$-0.218339\pi$
$113$	16.4518	1.54766	0.773830	+	0.633394i	$0.218339\pi$
$114$	1.71739	0.160848
$115$	0	0
$116$	19.1594	1.77890
$117$	5.37648	0.497056
$118$	2.59363	0.238763
$119$	−0.200980	−0.0184238
$120$	0	0
$121$	−9.37873	−0.852611
$122$	2.69874	0.244333
$123$	−2.24060	−0.202028
$124$	−11.5320	−1.03560
$125$	0	0
$126$	−0.0553651	−0.00493231
$127$	−4.51985	−0.401072	−0.200536	−	0.979686i	$-0.564268\pi$
$127$	−4.51985	−0.401072	−0.200536	+	0.979686i	$0.564268\pi$
$128$	7.80274	0.689671
$129$	−6.20192	−0.546048
$130$	0	0
$131$	20.5471	1.79520	0.897602	−	0.440806i	$-0.145307\pi$
$131$	20.5471	1.79520	0.897602	+	0.440806i	$0.145307\pi$
$132$	−2.45570	−0.213741
$133$	1.33213	0.115510
$134$	1.16613	0.100738
$135$	0	0
$136$	−1.01793	−0.0872865
$137$	14.7837	1.26306	0.631528	−	0.775353i	$-0.282428\pi$
$137$	14.7837	1.26306	0.631528	+	0.775353i	$0.282428\pi$
$138$	−1.56910	−0.133571
$139$	18.5218	1.57100	0.785500	−	0.618862i	$-0.212406\pi$
$139$	18.5218	1.57100	0.785500	+	0.618862i	$0.212406\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−2.54936	−0.213937
$143$	−6.84583	−0.572477
$144$	3.57683	0.298069
$145$	0	0
$146$	−3.13398	−0.259370
$147$	6.95706	0.573808
$148$	−2.29664	−0.188783
$149$	−1.52423	−0.124870	−0.0624349	−	0.998049i	$-0.519887\pi$
$149$	−1.52423	−0.124870	−0.0624349	+	0.998049i	$0.519887\pi$
$150$	0	0
$151$	22.2961	1.81443	0.907215	−	0.420666i	$-0.138204\pi$
$151$	22.2961	1.81443	0.907215	+	0.420666i	$0.138204\pi$
$152$	6.74698	0.547252
$153$	−0.969832	−0.0784063
$154$	0.0704959	0.00568072
$155$	0	0
$156$	10.3692	0.830201
$157$	16.4590	1.31357	0.656787	−	0.754076i	$-0.271915\pi$
$157$	16.4590	1.31357	0.656787	+	0.754076i	$0.271915\pi$
$158$	4.21644	0.335442
$159$	−8.64084	−0.685263
$160$	0	0
$161$	−1.21710	−0.0959211
$162$	−0.267165	−0.0209905
$163$	7.71004	0.603897	0.301948	−	0.953324i	$-0.402363\pi$
$163$	7.71004	0.603897	0.301948	+	0.953324i	$0.402363\pi$
$164$	−4.32128	−0.337435
$165$	0	0
$166$	0.479153	0.0371895
$167$	−10.0987	−0.781458	−0.390729	−	0.920506i	$-0.627777\pi$
$167$	−10.0987	−0.781458	−0.390729	+	0.920506i	$0.627777\pi$
$168$	−0.217508	−0.0167811
$169$	15.9066	1.22358
$170$	0	0
$171$	6.42820	0.491577
$172$	−11.9612	−0.912030
$173$	−19.8597	−1.50990	−0.754952	−	0.655781i	$-0.772340\pi$
$173$	−19.8597	−1.50990	−0.754952	+	0.655781i	$0.772340\pi$
$174$	−2.65408	−0.201205
$175$	0	0
$176$	−4.55435	−0.343297
$177$	9.70796	0.729695
$178$	1.94565	0.145832
$179$	−12.2276	−0.913931	−0.456966	−	0.889484i	$-0.651064\pi$
$179$	−12.2276	−0.913931	−0.456966	+	0.889484i	$0.651064\pi$
$180$	0	0
$181$	−10.1323	−0.753126	−0.376563	−	0.926391i	$-0.622894\pi$
$181$	−10.1323	−0.753126	−0.376563	+	0.926391i	$0.622894\pi$
$182$	−0.297669	−0.0220647
$183$	10.1014	0.746717
$184$	−6.16441	−0.454446
$185$	0	0
$186$	1.59748	0.117133
$187$	1.23488	0.0903034
$188$	−1.92862	−0.140659
$189$	−0.207232	−0.0150739
$190$	0	0
$191$	−4.90791	−0.355124	−0.177562	−	0.984110i	$-0.556821\pi$
$191$	−4.90791	−0.355124	−0.177562	+	0.984110i	$0.556821\pi$
$192$	6.33753	0.457372
$193$	3.01983	0.217372	0.108686	−	0.994076i	$-0.465336\pi$
$193$	3.01983	0.217372	0.108686	+	0.994076i	$0.465336\pi$
$194$	−0.0774974	−0.00556399
$195$	0	0
$196$	13.4175	0.958395
$197$	−7.63855	−0.544224	−0.272112	−	0.962266i	$-0.587722\pi$
$197$	−7.63855	−0.544224	−0.272112	+	0.962266i	$0.587722\pi$
$198$	0.340179	0.0241755
$199$	14.8893	1.05547	0.527737	−	0.849408i	$-0.323041\pi$
$199$	14.8893	1.05547	0.527737	+	0.849408i	$0.323041\pi$
$200$	0	0
$201$	4.36482	0.307871
$202$	1.50506	0.105896
$203$	−2.05869	−0.144491
$204$	−1.87044	−0.130957
$205$	0	0
$206$	−3.02627	−0.210850
$207$	−5.87315	−0.408212
$208$	19.2308	1.33341
$209$	−8.18498	−0.566167
$210$	0	0
$211$	−4.94144	−0.340183	−0.170091	−	0.985428i	$-0.554406\pi$
$211$	−4.94144	−0.340183	−0.170091	+	0.985428i	$0.554406\pi$
$212$	−16.6649	−1.14455
$213$	−9.54225	−0.653824
$214$	−2.16519	−0.148009
$215$	0	0
$216$	−1.04959	−0.0714156
$217$	1.23912	0.0841167
$218$	−3.53625	−0.239505
$219$	−11.7305	−0.792674
$220$	0	0
$221$	−5.21428	−0.350751
$222$	0.318145	0.0213525
$223$	−18.3690	−1.23008	−0.615041	−	0.788495i	$-0.710860\pi$
$223$	−18.3690	−1.23008	−0.615041	+	0.788495i	$0.710860\pi$
$224$	−0.633048	−0.0422973
$225$	0	0
$226$	−4.39536	−0.292375
$227$	29.0700	1.92944	0.964721	−	0.263274i	$-0.0848024\pi$
$227$	29.0700	1.92944	0.964721	+	0.263274i	$0.0848024\pi$
$228$	12.3976	0.821049
$229$	−0.499997	−0.0330407	−0.0165204	−	0.999864i	$-0.505259\pi$
$229$	−0.499997	−0.0330407	−0.0165204	+	0.999864i	$0.505259\pi$
$230$	0	0
$231$	0.263866	0.0173611
$232$	−10.4269	−0.684558
$233$	27.0992	1.77533	0.887663	−	0.460494i	$-0.152328\pi$
$233$	27.0992	1.77533	0.887663	+	0.460494i	$0.152328\pi$
$234$	−1.43641	−0.0939010
$235$	0	0
$236$	18.7230	1.21876
$237$	15.7821	1.02516
$238$	0.0536948	0.00348052
$239$	25.1215	1.62497	0.812487	−	0.582979i	$-0.198113\pi$
$239$	25.1215	1.62497	0.812487	+	0.582979i	$0.198113\pi$
$240$	0	0
$241$	−7.98036	−0.514060	−0.257030	−	0.966403i	$-0.582744\pi$
$241$	−7.98036	−0.514060	−0.257030	+	0.966403i	$0.582744\pi$
$242$	2.50567	0.161070
$243$	−1.00000	−0.0641500
$244$	19.4818	1.24719
$245$	0	0
$246$	0.598611	0.0381660
$247$	34.5611	2.19907
$248$	6.27590	0.398520
$249$	1.79347	0.113657
$250$	0	0
$251$	−29.7735	−1.87929	−0.939645	−	0.342151i	$-0.888844\pi$
$251$	−29.7735	−1.87929	−0.939645	+	0.342151i	$0.888844\pi$
$252$	−0.399672	−0.0251769
$253$	7.47824	0.470153
$254$	1.20755	0.0757682
$255$	0	0
$256$	10.5904	0.661902
$257$	−3.24067	−0.202148	−0.101074	−	0.994879i	$-0.532228\pi$
$257$	−3.24067	−0.202148	−0.101074	+	0.994879i	$0.532228\pi$
$258$	1.65694	0.103156
$259$	0.246775	0.0153339
$260$	0	0
$261$	−9.93423	−0.614914
$262$	−5.48946	−0.339140
$263$	14.9421	0.921367	0.460684	−	0.887564i	$-0.347604\pi$
$263$	14.9421	0.921367	0.460684	+	0.887564i	$0.347604\pi$
$264$	1.33644	0.0822520
$265$	0	0
$266$	−0.355898	−0.0218215
$267$	7.28256	0.445685
$268$	8.41809	0.514217
$269$	12.7592	0.777941	0.388970	−	0.921250i	$-0.372831\pi$
$269$	12.7592	0.777941	0.388970	+	0.921250i	$0.372831\pi$
$270$	0	0
$271$	9.13747	0.555062	0.277531	−	0.960717i	$-0.410484\pi$
$271$	9.13747	0.555062	0.277531	+	0.960717i	$0.410484\pi$
$272$	−3.46893	−0.210334
$273$	−1.11418	−0.0674331
$274$	−3.94968	−0.238609
$275$	0	0
$276$	−11.3271	−0.681811
$277$	3.04812	0.183144	0.0915720	−	0.995798i	$-0.470811\pi$
$277$	3.04812	0.183144	0.0915720	+	0.995798i	$0.470811\pi$
$278$	−4.94838	−0.296784
$279$	5.97938	0.357976
$280$	0	0
$281$	−8.19048	−0.488603	−0.244302	−	0.969699i	$-0.578559\pi$
$281$	−8.19048	−0.488603	−0.244302	+	0.969699i	$0.578559\pi$
$282$	0.267165	0.0159095
$283$	6.63076	0.394158	0.197079	−	0.980388i	$-0.436854\pi$
$283$	6.63076	0.394158	0.197079	+	0.980388i	$0.436854\pi$
$284$	−18.4034	−1.09204
$285$	0	0
$286$	1.82897	0.108149
$287$	0.464324	0.0274082
$288$	−3.05479	−0.180005
$289$	−16.0594	−0.944672
$290$	0	0
$291$	−0.290073	−0.0170044
$292$	−22.6237	−1.32395
$293$	−18.2716	−1.06744	−0.533719	−	0.845662i	$-0.679206\pi$
$293$	−18.2716	−1.06744	−0.533719	+	0.845662i	$0.679206\pi$
$294$	−1.85868	−0.108401
$295$	0	0
$296$	1.24987	0.0726473
$297$	1.27329	0.0738839
$298$	0.407221	0.0235897
$299$	−31.5769	−1.82614
$300$	0	0
$301$	1.28523	0.0740796
$302$	−5.95674	−0.342772
$303$	5.63344	0.323633
$304$	22.9926	1.31872
$305$	0	0
$306$	0.259105	0.0148121
$307$	18.1634	1.03664	0.518319	−	0.855187i	$-0.326558\pi$
$307$	18.1634	1.03664	0.518319	+	0.855187i	$0.326558\pi$
$308$	0.508899	0.0289972
$309$	−11.3273	−0.644389
$310$	0	0
$311$	28.0180	1.58876	0.794379	−	0.607423i	$-0.207797\pi$
$311$	28.0180	1.58876	0.794379	+	0.607423i	$0.207797\pi$
$312$	−5.64311	−0.319478
$313$	12.6852	0.717009	0.358504	−	0.933528i	$-0.383287\pi$
$313$	12.6852	0.717009	0.358504	+	0.933528i	$0.383287\pi$
$314$	−4.39728	−0.248153
$315$	0	0
$316$	30.4378	1.71226
$317$	34.8739	1.95871	0.979355	−	0.202146i	$-0.0647915\pi$
$317$	34.8739	1.95871	0.979355	+	0.202146i	$0.0647915\pi$
$318$	2.30853	0.129456
$319$	12.6492	0.708218
$320$	0	0
$321$	−8.10431	−0.452339
$322$	0.325167	0.0181209
$323$	−6.23427	−0.346884
$324$	−1.92862	−0.107146
$325$	0	0
$326$	−2.05985	−0.114085
$327$	−13.2362	−0.731963
$328$	2.35172	0.129852
$329$	0.207232	0.0114250
$330$	0	0
$331$	20.3577	1.11896	0.559480	−	0.828844i	$-0.311001\pi$
$331$	20.3577	1.11896	0.559480	+	0.828844i	$0.311001\pi$
$332$	3.45893	0.189833
$333$	1.19082	0.0652564
$334$	2.69801	0.147629
$335$	0	0
$336$	−0.741232	−0.0404375
$337$	−29.3333	−1.59789	−0.798943	−	0.601407i	$-0.794607\pi$
$337$	−29.3333	−1.59789	−0.798943	+	0.601407i	$0.794607\pi$
$338$	−4.24968	−0.231152
$339$	−16.4518	−0.893542
$340$	0	0
$341$	−7.61350	−0.412294
$342$	−1.71739	−0.0928659
$343$	−2.89234	−0.156172
$344$	6.50948	0.350967
$345$	0	0
$346$	5.30581	0.285242
$347$	29.5486	1.58625	0.793127	−	0.609057i	$-0.208452\pi$
$347$	29.5486	1.58625	0.793127	+	0.609057i	$0.208452\pi$
$348$	−19.1594	−1.02705
$349$	0.661771	0.0354238	0.0177119	−	0.999843i	$-0.494362\pi$
$349$	0.661771	0.0354238	0.0177119	+	0.999843i	$0.494362\pi$
$350$	0	0
$351$	−5.37648	−0.286975
$352$	3.88964	0.207318
$353$	−4.99309	−0.265756	−0.132878	−	0.991132i	$-0.542422\pi$
$353$	−4.99309	−0.265756	−0.132878	+	0.991132i	$0.542422\pi$
$354$	−2.59363	−0.137850
$355$	0	0
$356$	14.0453	0.744400
$357$	0.200980	0.0106370
$358$	3.26678	0.172655
$359$	−17.0698	−0.900910	−0.450455	−	0.892799i	$-0.648738\pi$
$359$	−17.0698	−0.900910	−0.450455	+	0.892799i	$0.648738\pi$
$360$	0	0
$361$	22.3218	1.17483
$362$	2.70699	0.142276
$363$	9.37873	0.492255
$364$	−2.14883	−0.112629
$365$	0	0
$366$	−2.69874	−0.141065
$367$	6.07188	0.316949	0.158475	−	0.987363i	$-0.449342\pi$
$367$	6.07188	0.316949	0.158475	+	0.987363i	$0.449342\pi$
$368$	−21.0073	−1.09508
$369$	2.24060	0.116641
$370$	0	0
$371$	1.79065	0.0929661
$372$	11.5320	0.597905
$373$	19.3121	0.999944	0.499972	−	0.866042i	$-0.333344\pi$
$373$	19.3121	0.999944	0.499972	+	0.866042i	$0.333344\pi$
$374$	−0.329917	−0.0170596
$375$	0	0
$376$	1.04959	0.0541285
$377$	−53.4112	−2.75082
$378$	0.0553651	0.00284767
$379$	−4.68181	−0.240488	−0.120244	−	0.992744i	$-0.538368\pi$
$379$	−4.68181	−0.240488	−0.120244	+	0.992744i	$0.538368\pi$
$380$	0	0
$381$	4.51985	0.231559
$382$	1.31122	0.0670880
$383$	−5.78171	−0.295432	−0.147716	−	0.989030i	$-0.547192\pi$
$383$	−5.78171	−0.295432	−0.147716	+	0.989030i	$0.547192\pi$
$384$	−7.80274	−0.398182
$385$	0	0
$386$	−0.806794	−0.0410647
$387$	6.20192	0.315261
$388$	−0.559441	−0.0284013
$389$	1.93198	0.0979553	0.0489777	−	0.998800i	$-0.484404\pi$
$389$	1.93198	0.0979553	0.0489777	+	0.998800i	$0.484404\pi$
$390$	0	0
$391$	5.69597	0.288058
$392$	−7.30206	−0.368810
$393$	−20.5471	−1.03646
$394$	2.04076	0.102812
$395$	0	0
$396$	2.45570	0.123404
$397$	−30.9953	−1.55561	−0.777805	−	0.628506i	$-0.783667\pi$
$397$	−30.9953	−1.55561	−0.777805	+	0.628506i	$0.783667\pi$
$398$	−3.97790	−0.199394
$399$	−1.33213	−0.0666897
$400$	0	0
$401$	36.2628	1.81088	0.905438	−	0.424478i	$-0.139542\pi$
$401$	36.2628	1.81088	0.905438	+	0.424478i	$0.139542\pi$
$402$	−1.16613	−0.0581612
$403$	32.1480	1.60141
$404$	10.8648	0.540543
$405$	0	0
$406$	0.550009	0.0272965
$407$	−1.51626	−0.0751582
$408$	1.01793	0.0503949
$409$	−0.0369376	−0.00182645	−0.000913223	−	1.00000i	$-0.500291\pi$
$409$	−0.0369376	−0.00182645	−0.000913223		1.00000i	$0.500291\pi$
$410$	0	0
$411$	−14.7837	−0.729225
$412$	−21.8462	−1.07628
$413$	−2.01180	−0.0989940
$414$	1.56910	0.0771171
$415$	0	0
$416$	−16.4240	−0.805253
$417$	−18.5218	−0.907017
$418$	2.18674	0.106957
$419$	0.362309	0.0176999	0.00884997	−	0.999961i	$-0.497183\pi$
$419$	0.362309	0.0176999	0.00884997	+	0.999961i	$0.497183\pi$
$420$	0	0
$421$	12.6406	0.616063	0.308032	−	0.951376i	$-0.400330\pi$
$421$	12.6406	0.616063	0.308032	+	0.951376i	$0.400330\pi$
$422$	1.32018	0.0642654
$423$	1.00000	0.0486217
$424$	9.06934	0.440446
$425$	0	0
$426$	2.54936	0.123517
$427$	−2.09333	−0.101303
$428$	−15.6302	−0.755513
$429$	6.84583	0.330520
$430$	0	0
$431$	6.98498	0.336455	0.168227	−	0.985748i	$-0.446196\pi$
$431$	6.98498	0.336455	0.168227	+	0.985748i	$0.446196\pi$
$432$	−3.57683	−0.172090
$433$	−22.4312	−1.07797	−0.538987	−	0.842314i	$-0.681193\pi$
$433$	−22.4312	−1.07797	−0.538987	+	0.842314i	$0.681193\pi$
$434$	−0.331049	−0.0158908
$435$	0	0
$436$	−25.5276	−1.22255
$437$	−37.7538	−1.80601
$438$	3.13398	0.149747
$439$	19.9828	0.953726	0.476863	−	0.878978i	$-0.341774\pi$
$439$	19.9828	0.953726	0.476863	+	0.878978i	$0.341774\pi$
$440$	0	0
$441$	−6.95706	−0.331288
$442$	1.39307	0.0662618
$443$	0.382306	0.0181639	0.00908196	−	0.999959i	$-0.497109\pi$
$443$	0.382306	0.0181639	0.00908196	+	0.999959i	$0.497109\pi$
$444$	2.29664	0.108994
$445$	0	0
$446$	4.90756	0.232380
$447$	1.52423	0.0720936
$448$	−1.31334	−0.0620493
$449$	33.6928	1.59006	0.795030	−	0.606570i	$-0.207455\pi$
$449$	33.6928	1.59006	0.795030	+	0.606570i	$0.207455\pi$
$450$	0	0
$451$	−2.85294	−0.134340
$452$	−31.7294	−1.49243
$453$	−22.2961	−1.04756
$454$	−7.76648	−0.364499
$455$	0	0
$456$	−6.74698	−0.315956
$457$	10.9263	0.511110	0.255555	−	0.966795i	$-0.417742\pi$
$457$	10.9263	0.511110	0.255555	+	0.966795i	$0.417742\pi$
$458$	0.133582	0.00624186
$459$	0.969832	0.0452679
$460$	0	0
$461$	−35.9233	−1.67311	−0.836557	−	0.547880i	$-0.815435\pi$
$461$	−35.9233	−1.67311	−0.836557	+	0.547880i	$0.815435\pi$
$462$	−0.0704959	−0.00327977
$463$	−25.5389	−1.18690	−0.593448	−	0.804873i	$-0.702234\pi$
$463$	−25.5389	−1.18690	−0.593448	+	0.804873i	$0.702234\pi$
$464$	−35.5331	−1.64958
$465$	0	0
$466$	−7.23996	−0.335384
$467$	27.9327	1.29257	0.646285	−	0.763096i	$-0.276322\pi$
$467$	27.9327	1.29257	0.646285	+	0.763096i	$0.276322\pi$
$468$	−10.3692	−0.479317
$469$	−0.904529	−0.0417673
$470$	0	0
$471$	−16.4590	−0.758393
$472$	−10.1894	−0.469005
$473$	−7.89685	−0.363098
$474$	−4.21644	−0.193667
$475$	0	0
$476$	0.387614	0.0177663
$477$	8.64084	0.395637
$478$	−6.71159	−0.306981
$479$	17.2921	0.790096	0.395048	−	0.918660i	$-0.370728\pi$
$479$	17.2921	0.790096	0.395048	+	0.918660i	$0.370728\pi$
$480$	0	0
$481$	6.40241	0.291925
$482$	2.13207	0.0971133
$483$	1.21710	0.0553801
$484$	18.0880	0.822183
$485$	0	0
$486$	0.267165	0.0121189
$487$	5.99955	0.271866	0.135933	−	0.990718i	$-0.456597\pi$
$487$	5.99955	0.271866	0.135933	+	0.990718i	$0.456597\pi$
$488$	−10.6023	−0.479945
$489$	−7.71004	−0.348660
$490$	0	0
$491$	−21.8555	−0.986323	−0.493161	−	0.869938i	$-0.664159\pi$
$491$	−21.8555	−0.986323	−0.493161	+	0.869938i	$0.664159\pi$
$492$	4.32128	0.194818
$493$	9.63454	0.433918
$494$	−9.23352	−0.415436
$495$	0	0
$496$	21.3872	0.960315
$497$	1.97746	0.0887010
$498$	−0.479153	−0.0214713
$499$	34.1218	1.52750	0.763752	−	0.645510i	$-0.223355\pi$
$499$	34.1218	1.52750	0.763752	+	0.645510i	$0.223355\pi$
$500$	0	0
$501$	10.0987	0.451175
$502$	7.95445	0.355025
$503$	17.7971	0.793533	0.396767	−	0.917919i	$-0.370132\pi$
$503$	17.7971	0.793533	0.396767	+	0.917919i	$0.370132\pi$
$504$	0.217508	0.00968860
$505$	0	0
$506$	−1.99793	−0.0888186
$507$	−15.9066	−0.706435
$508$	8.71709	0.386758
$509$	−21.7120	−0.962369	−0.481184	−	0.876619i	$-0.659793\pi$
$509$	−21.7120	−0.962369	−0.481184	+	0.876619i	$0.659793\pi$
$510$	0	0
$511$	2.43093	0.107538
$512$	−18.4349	−0.814714
$513$	−6.42820	−0.283812
$514$	0.865795	0.0381886
$515$	0	0
$516$	11.9612	0.526561
$517$	−1.27329	−0.0559993
$518$	−0.0659297	−0.00289678
$519$	19.8597	0.871743
$520$	0	0
$521$	−22.2821	−0.976197	−0.488099	−	0.872788i	$-0.662309\pi$
$521$	−22.2821	−0.976197	−0.488099	+	0.872788i	$0.662309\pi$
$522$	2.65408	0.116166
$523$	9.96039	0.435538	0.217769	−	0.976000i	$-0.430122\pi$
$523$	9.96039	0.435538	0.217769	+	0.976000i	$0.430122\pi$
$524$	−39.6275	−1.73114
$525$	0	0
$526$	−3.99200	−0.174059
$527$	−5.79899	−0.252608
$528$	4.55435	0.198203
$529$	11.4939	0.499736
$530$	0	0
$531$	−9.70796	−0.421290
$532$	−2.56917	−0.111388
$533$	12.0466	0.521794
$534$	−1.94565	−0.0841963
$535$	0	0
$536$	−4.58128	−0.197881
$537$	12.2276	0.527658
$538$	−3.40881	−0.146964
$539$	8.85837	0.381557
$540$	0	0
$541$	−4.70353	−0.202221	−0.101110	−	0.994875i	$-0.532240\pi$
$541$	−4.70353	−0.202221	−0.101110	+	0.994875i	$0.532240\pi$
$542$	−2.44121	−0.104859
$543$	10.1323	0.434818
$544$	2.96263	0.127022
$545$	0	0
$546$	0.297669	0.0127391
$547$	−41.3316	−1.76721	−0.883605	−	0.468233i	$-0.844891\pi$
$547$	−41.3316	−1.76721	−0.883605	+	0.468233i	$0.844891\pi$
$548$	−28.5121	−1.21798
$549$	−10.1014	−0.431117
$550$	0	0
$551$	−63.8592	−2.72049
$552$	6.16441	0.262375
$553$	−3.27056	−0.139078
$554$	−0.814352	−0.0345985
$555$	0	0
$556$	−35.7216	−1.51493
$557$	43.0480	1.82400	0.912001	−	0.410188i	$-0.134537\pi$
$557$	43.0480	1.82400	0.912001	+	0.410188i	$0.134537\pi$
$558$	−1.59748	−0.0676268
$559$	33.3445	1.41032
$560$	0	0
$561$	−1.23488	−0.0521367
$562$	2.18821	0.0923041
$563$	32.3647	1.36401	0.682006	−	0.731347i	$-0.261108\pi$
$563$	32.3647	1.36401	0.682006	+	0.731347i	$0.261108\pi$
$564$	1.92862	0.0812097
$565$	0	0
$566$	−1.77151	−0.0744620
$567$	0.207232	0.00870291
$568$	10.0155	0.420240
$569$	−34.4813	−1.44553	−0.722766	−	0.691093i	$-0.757129\pi$
$569$	−34.4813	−1.44553	−0.722766	+	0.691093i	$0.757129\pi$
$570$	0	0
$571$	36.6501	1.53376	0.766879	−	0.641792i	$-0.221809\pi$
$571$	36.6501	1.53376	0.766879	+	0.641792i	$0.221809\pi$
$572$	13.2030	0.552047
$573$	4.90791	0.205031
$574$	−0.124051	−0.00517779
$575$	0	0
$576$	−6.33753	−0.264064
$577$	2.62010	0.109076	0.0545381	−	0.998512i	$-0.482631\pi$
$577$	2.62010	0.109076	0.0545381	+	0.998512i	$0.482631\pi$
$578$	4.29052	0.178462
$579$	−3.01983	−0.125500
$580$	0	0
$581$	−0.371664	−0.0154192
$582$	0.0774974	0.00321237
$583$	−11.0023	−0.455669
$584$	12.3122	0.509484
$585$	0	0
$586$	4.88154	0.201654
$587$	2.63615	0.108806	0.0544028	−	0.998519i	$-0.482674\pi$
$587$	2.63615	0.108806	0.0544028	+	0.998519i	$0.482674\pi$
$588$	−13.4175	−0.553330
$589$	38.4366	1.58375
$590$	0	0
$591$	7.63855	0.314208
$592$	4.25935	0.175058
$593$	7.63049	0.313347	0.156673	−	0.987650i	$-0.449923\pi$
$593$	7.63049	0.313347	0.156673	+	0.987650i	$0.449923\pi$
$594$	−0.340179	−0.0139577
$595$	0	0
$596$	2.93967	0.120413
$597$	−14.8893	−0.609378
$598$	8.43625	0.344984
$599$	20.3053	0.829650	0.414825	−	0.909901i	$-0.363843\pi$
$599$	20.3053	0.829650	0.414825	+	0.909901i	$0.363843\pi$
$600$	0	0
$601$	−1.07475	−0.0438398	−0.0219199	−	0.999760i	$-0.506978\pi$
$601$	−1.07475	−0.0438398	−0.0219199	+	0.999760i	$0.506978\pi$
$602$	−0.343369	−0.0139947
$603$	−4.36482	−0.177749
$604$	−43.0008	−1.74968
$605$	0	0
$606$	−1.50506	−0.0611389
$607$	−17.0385	−0.691573	−0.345786	−	0.938313i	$-0.612388\pi$
$607$	−17.0385	−0.691573	−0.345786	+	0.938313i	$0.612388\pi$
$608$	−19.6368	−0.796377
$609$	2.05869	0.0834222
$610$	0	0
$611$	5.37648	0.217509
$612$	1.87044	0.0756081
$613$	−36.6117	−1.47873	−0.739366	−	0.673304i	$-0.764874\pi$
$613$	−36.6117	−1.47873	−0.739366	+	0.673304i	$0.764874\pi$
$614$	−4.85262	−0.195836
$615$	0	0
$616$	−0.276952	−0.0111587
$617$	−23.1682	−0.932716	−0.466358	−	0.884596i	$-0.654434\pi$
$617$	−23.1682	−0.932716	−0.466358	+	0.884596i	$0.654434\pi$
$618$	3.02627	0.121734
$619$	−26.4232	−1.06204	−0.531018	−	0.847360i	$-0.678190\pi$
$619$	−26.4232	−1.06204	−0.531018	+	0.847360i	$0.678190\pi$
$620$	0	0
$621$	5.87315	0.235681
$622$	−7.48545	−0.300139
$623$	−1.50918	−0.0604639
$624$	−19.2308	−0.769847
$625$	0	0
$626$	−3.38904	−0.135453
$627$	8.18498	0.326877
$628$	−31.7433	−1.26669
$629$	−1.15489	−0.0460486
$630$	0	0
$631$	−42.2696	−1.68273	−0.841363	−	0.540471i	$-0.818246\pi$
$631$	−42.2696	−1.68273	−0.841363	+	0.540471i	$0.818246\pi$
$632$	−16.5648	−0.658912
$633$	4.94144	0.196405
$634$	−9.31708	−0.370028
$635$	0	0
$636$	16.6649	0.660807
$637$	−37.4045	−1.48202
$638$	−3.37942	−0.133793
$639$	9.54225	0.377486
$640$	0	0
$641$	−2.47629	−0.0978077	−0.0489039	−	0.998803i	$-0.515573\pi$
$641$	−2.47629	−0.0978077	−0.0489039	+	0.998803i	$0.515573\pi$
$642$	2.16519	0.0854532
$643$	−38.6391	−1.52378	−0.761890	−	0.647707i	$-0.775728\pi$
$643$	−38.6391	−1.52378	−0.761890	+	0.647707i	$0.775728\pi$
$644$	2.34733	0.0924978
$645$	0	0
$646$	1.66558	0.0655314
$647$	−8.32898	−0.327446	−0.163723	−	0.986506i	$-0.552350\pi$
$647$	−8.32898	−0.327446	−0.163723	+	0.986506i	$0.552350\pi$
$648$	1.04959	0.0412318
$649$	12.3611	0.485215
$650$	0	0
$651$	−1.23912	−0.0485648
$652$	−14.8698	−0.582345
$653$	−18.8800	−0.738832	−0.369416	−	0.929264i	$-0.620442\pi$
$653$	−18.8800	−0.738832	−0.369416	+	0.929264i	$0.620442\pi$
$654$	3.53625	0.138278
$655$	0	0
$656$	8.01426	0.312904
$657$	11.7305	0.457651
$658$	−0.0553651	−0.00215835
$659$	−13.9987	−0.545311	−0.272656	−	0.962112i	$-0.587902\pi$
$659$	−13.9987	−0.545311	−0.272656	+	0.962112i	$0.587902\pi$
$660$	0	0
$661$	5.55730	0.216154	0.108077	−	0.994143i	$-0.465531\pi$
$661$	5.55730	0.216154	0.108077	+	0.994143i	$0.465531\pi$
$662$	−5.43887	−0.211388
$663$	5.21428	0.202506
$664$	−1.88241	−0.0730517
$665$	0	0
$666$	−0.318145	−0.0123279
$667$	58.3453	2.25914
$668$	19.4765	0.753569
$669$	18.3690	0.710188
$670$	0	0
$671$	12.8620	0.496533
$672$	0.633048	0.0244204
$673$	31.0565	1.19714	0.598569	−	0.801071i	$-0.295736\pi$
$673$	31.0565	1.19714	0.598569	+	0.801071i	$0.295736\pi$
$674$	7.83683	0.301863
$675$	0	0
$676$	−30.6777	−1.17991
$677$	21.7287	0.835101	0.417550	−	0.908654i	$-0.362889\pi$
$677$	21.7287	0.835101	0.417550	+	0.908654i	$0.362889\pi$
$678$	4.39536	0.168803
$679$	0.0601123	0.00230690
$680$	0	0
$681$	−29.0700	−1.11396
$682$	2.03406	0.0778882
$683$	−1.85083	−0.0708202	−0.0354101	−	0.999373i	$-0.511274\pi$
$683$	−1.85083	−0.0708202	−0.0354101	+	0.999373i	$0.511274\pi$
$684$	−12.3976	−0.474033
$685$	0	0
$686$	0.772733	0.0295031
$687$	0.499997	0.0190761
$688$	22.1832	0.845727
$689$	46.4573	1.76988
$690$	0	0
$691$	6.56714	0.249826	0.124913	−	0.992168i	$-0.460135\pi$
$691$	6.56714	0.249826	0.124913	+	0.992168i	$0.460135\pi$
$692$	38.3018	1.45602
$693$	−0.263866	−0.0100235
$694$	−7.89436	−0.299666
$695$	0	0
$696$	10.4269	0.395230
$697$	−2.17301	−0.0823085
$698$	−0.176802	−0.00669206
$699$	−27.0992	−1.02498
$700$	0	0
$701$	−28.3117	−1.06932	−0.534659	−	0.845068i	$-0.679560\pi$
$701$	−28.3117	−1.06932	−0.534659	+	0.845068i	$0.679560\pi$
$702$	1.43641	0.0542137
$703$	7.65482	0.288707
$704$	8.06953	0.304132
$705$	0	0
$706$	1.33398	0.0502050
$707$	−1.16743	−0.0439056
$708$	−18.7230	−0.703653
$709$	18.8498	0.707920	0.353960	−	0.935260i	$-0.384835\pi$
$709$	18.8498	0.707920	0.353960	+	0.935260i	$0.384835\pi$
$710$	0	0
$711$	−15.7821	−0.591876
$712$	−7.64371	−0.286460
$713$	−35.1178	−1.31517
$714$	−0.0536948	−0.00200948
$715$	0	0
$716$	23.5824	0.881314
$717$	−25.1215	−0.938179
$718$	4.56046	0.170195
$719$	−21.6400	−0.807036	−0.403518	−	0.914972i	$-0.632213\pi$
$719$	−21.6400	−0.807036	−0.403518	+	0.914972i	$0.632213\pi$
$720$	0	0
$721$	2.34738	0.0874210
$722$	−5.96360	−0.221942
$723$	7.98036	0.296793
$724$	19.5413	0.726248
$725$	0	0
$726$	−2.50567	−0.0929941
$727$	2.30732	0.0855737	0.0427869	−	0.999084i	$-0.486376\pi$
$727$	2.30732	0.0855737	0.0427869	+	0.999084i	$0.486376\pi$
$728$	1.16943	0.0433420
$729$	1.00000	0.0370370
$730$	0	0
$731$	−6.01482	−0.222466
$732$	−19.4818	−0.720068
$733$	−18.9481	−0.699863	−0.349932	−	0.936775i	$-0.613795\pi$
$733$	−18.9481	−0.699863	−0.349932	+	0.936775i	$0.613795\pi$
$734$	−1.62219	−0.0598763
$735$	0	0
$736$	17.9412	0.661322
$737$	5.55769	0.204720
$738$	−0.598611	−0.0220352
$739$	18.6083	0.684519	0.342259	−	0.939605i	$-0.388808\pi$
$739$	18.6083	0.684519	0.342259	+	0.939605i	$0.388808\pi$
$740$	0	0
$741$	−34.5611	−1.26963
$742$	−0.478400	−0.0175626
$743$	−4.08148	−0.149735	−0.0748676	−	0.997193i	$-0.523853\pi$
$743$	−4.08148	−0.149735	−0.0748676	+	0.997193i	$0.523853\pi$
$744$	−6.27590	−0.230086
$745$	0	0
$746$	−5.15953	−0.188904
$747$	−1.79347	−0.0656196
$748$	−2.38162	−0.0870806
$749$	1.67947	0.0613665
$750$	0	0
$751$	−0.378534	−0.0138129	−0.00690645	−	0.999976i	$-0.502198\pi$
$751$	−0.378534	−0.0138129	−0.00690645	+	0.999976i	$0.502198\pi$
$752$	3.57683	0.130434
$753$	29.7735	1.08501
$754$	14.2696	0.519669
$755$	0	0
$756$	0.399672	0.0145359
$757$	24.9727	0.907649	0.453825	−	0.891091i	$-0.350059\pi$
$757$	24.9727	0.907649	0.453825	+	0.891091i	$0.350059\pi$
$758$	1.25082	0.0454317
$759$	−7.47824	−0.271443
$760$	0	0
$761$	−13.0020	−0.471322	−0.235661	−	0.971835i	$-0.575725\pi$
$761$	−13.0020	−0.471322	−0.235661	+	0.971835i	$0.575725\pi$
$762$	−1.20755	−0.0437448
$763$	2.74296	0.0993018
$764$	9.46551	0.342450
$765$	0	0
$766$	1.54467	0.0558113
$767$	−52.1947	−1.88464
$768$	−10.5904	−0.382150
$769$	30.0353	1.08310	0.541550	−	0.840669i	$-0.317838\pi$
$769$	30.0353	1.08310	0.541550	+	0.840669i	$0.317838\pi$
$770$	0	0
$771$	3.24067	0.116710
$772$	−5.82412	−0.209615
$773$	−40.8899	−1.47071	−0.735354	−	0.677683i	$-0.762984\pi$
$773$	−40.8899	−1.47071	−0.735354	+	0.677683i	$0.762984\pi$
$774$	−1.65694	−0.0595573
$775$	0	0
$776$	0.304458	0.0109294
$777$	−0.246775	−0.00885301
$778$	−0.516158	−0.0185052
$779$	14.4030	0.516042
$780$	0	0
$781$	−12.1501	−0.434764
$782$	−1.52176	−0.0544182
$783$	9.93423	0.355021
$784$	−24.8842	−0.888722
$785$	0	0
$786$	5.48946	0.195802
$787$	11.3769	0.405543	0.202772	−	0.979226i	$-0.435005\pi$
$787$	11.3769	0.405543	0.202772	+	0.979226i	$0.435005\pi$
$788$	14.7319	0.524802
$789$	−14.9421	−0.531952
$790$	0	0
$791$	3.40934	0.121222
$792$	−1.33644	−0.0474882
$793$	−54.3100	−1.92860
$794$	8.28086	0.293877
$795$	0	0
$796$	−28.7158	−1.01780
$797$	7.09623	0.251361	0.125681	−	0.992071i	$-0.459889\pi$
$797$	7.09623	0.251361	0.125681	+	0.992071i	$0.459889\pi$
$798$	0.355898	0.0125986
$799$	−0.969832	−0.0343102
$800$	0	0
$801$	−7.28256	−0.257316
$802$	−9.68815	−0.342100
$803$	−14.9364	−0.527093
$804$	−8.41809	−0.296883
$805$	0	0
$806$	−8.58883	−0.302529
$807$	−12.7592	−0.449144
$808$	−5.91281	−0.208012
$809$	11.6552	0.409776	0.204888	−	0.978785i	$-0.434317\pi$
$809$	11.6552	0.409776	0.204888	+	0.978785i	$0.434317\pi$
$810$	0	0
$811$	0.0224294	0.000787602 0	0.000393801	−	1.00000i	$-0.499875\pi$
$811$	0.0224294	0.000787602 0	0.000393801		1.00000i	$0.499875\pi$
$812$	3.97043	0.139335
$813$	−9.13747	−0.320465
$814$	0.405092	0.0141985
$815$	0	0
$816$	3.46893	0.121437
$817$	39.8672	1.39478
$818$	0.00986844	0.000345042 0
$819$	1.11418	0.0389325
$820$	0	0
$821$	−41.9487	−1.46402	−0.732009	−	0.681294i	$-0.761417\pi$
$821$	−41.9487	−1.46402	−0.732009	+	0.681294i	$0.761417\pi$
$822$	3.94968	0.137761
$823$	−30.5936	−1.06643	−0.533213	−	0.845981i	$-0.679015\pi$
$823$	−30.5936	−1.06643	−0.533213	+	0.845981i	$0.679015\pi$
$824$	11.8891	0.414175
$825$	0	0
$826$	0.537482	0.0187014
$827$	33.5561	1.16686	0.583430	−	0.812163i	$-0.301710\pi$
$827$	33.5561	1.16686	0.583430	+	0.812163i	$0.301710\pi$
$828$	11.3271	0.393644
$829$	33.2808	1.15589	0.577945	−	0.816076i	$-0.303855\pi$
$829$	33.2808	1.15589	0.577945	+	0.816076i	$0.303855\pi$
$830$	0	0
$831$	−3.04812	−0.105738
$832$	−34.0736	−1.18129
$833$	6.74717	0.233776
$834$	4.94838	0.171348
$835$	0	0
$836$	15.7857	0.545961
$837$	−5.97938	−0.206678
$838$	−0.0967963	−0.00334377
$839$	30.8908	1.06647	0.533235	−	0.845967i	$-0.320976\pi$
$839$	30.8908	1.06647	0.533235	+	0.845967i	$0.320976\pi$
$840$	0	0
$841$	69.6890	2.40307
$842$	−3.37712	−0.116383
$843$	8.19048	0.282095
$844$	9.53018	0.328042
$845$	0	0
$846$	−0.267165	−0.00918533
$847$	−1.94357	−0.0667818
$848$	30.9068	1.06134
$849$	−6.63076	−0.227567
$850$	0	0
$851$	−6.99385	−0.239746
$852$	18.4034	0.630490
$853$	−11.9094	−0.407772	−0.203886	−	0.978995i	$-0.565357\pi$
$853$	−11.9094	−0.407772	−0.203886	+	0.978995i	$0.565357\pi$
$854$	0.559264	0.0191376
$855$	0	0
$856$	8.50622	0.290736
$857$	1.29588	0.0442665	0.0221332	−	0.999755i	$-0.492954\pi$
$857$	1.29588	0.0442665	0.0221332	+	0.999755i	$0.492954\pi$
$858$	−1.82897	−0.0624400
$859$	15.9383	0.543808	0.271904	−	0.962324i	$-0.412347\pi$
$859$	15.9383	0.543808	0.271904	+	0.962324i	$0.412347\pi$
$860$	0	0
$861$	−0.464324	−0.0158241
$862$	−1.86614	−0.0635611
$863$	4.41860	0.150411	0.0752054	−	0.997168i	$-0.476039\pi$
$863$	4.41860	0.150411	0.0752054	+	0.997168i	$0.476039\pi$
$864$	3.05479	0.103926
$865$	0	0
$866$	5.99283	0.203645
$867$	16.0594	0.545407
$868$	−2.38979	−0.0811147
$869$	20.0953	0.681685
$870$	0	0
$871$	−23.4674	−0.795162
$872$	13.8926	0.470463
$873$	0.290073	0.00981748
$874$	10.0865	0.341181
$875$	0	0
$876$	22.6237	0.764385
$877$	−24.5208	−0.828007	−0.414004	−	0.910275i	$-0.635870\pi$
$877$	−24.5208	−0.828007	−0.414004	+	0.910275i	$0.635870\pi$
$878$	−5.33870	−0.180172
$879$	18.2716	0.616286
$880$	0	0
$881$	28.7702	0.969293	0.484646	−	0.874710i	$-0.338948\pi$
$881$	28.7702	0.969293	0.484646	+	0.874710i	$0.338948\pi$
$882$	1.85868	0.0625851
$883$	−10.7916	−0.363167	−0.181584	−	0.983375i	$-0.558122\pi$
$883$	−10.7916	−0.363167	−0.181584	+	0.983375i	$0.558122\pi$
$884$	10.0564	0.338233
$885$	0	0
$886$	−0.102139	−0.00343142
$887$	30.3740	1.01986	0.509930	−	0.860216i	$-0.329671\pi$
$887$	30.3740	1.01986	0.509930	+	0.860216i	$0.329671\pi$
$888$	−1.24987	−0.0419430
$889$	−0.936656	−0.0314144
$890$	0	0
$891$	−1.27329	−0.0426569
$892$	35.4269	1.18618
$893$	6.42820	0.215112
$894$	−0.407221	−0.0136195
$895$	0	0
$896$	1.61697	0.0540193
$897$	31.5769	1.05432
$898$	−9.00153	−0.300385
$899$	−59.4005	−1.98112
$900$	0	0
$901$	−8.38016	−0.279184
$902$	0.762207	0.0253787
$903$	−1.28523	−0.0427699
$904$	17.2677	0.574316
$905$	0	0
$906$	5.95674	0.197899
$907$	34.6143	1.14935	0.574674	−	0.818382i	$-0.305129\pi$
$907$	34.6143	1.14935	0.574674	+	0.818382i	$0.305129\pi$
$908$	−56.0650	−1.86058
$909$	−5.63344	−0.186849
$910$	0	0
$911$	27.9342	0.925502	0.462751	−	0.886488i	$-0.346862\pi$
$911$	27.9342	0.925502	0.462751	+	0.886488i	$0.346862\pi$
$912$	−22.9926	−0.761361
$913$	2.28361	0.0755765
$914$	−2.91912	−0.0965560
$915$	0	0
$916$	0.964305	0.0318615
$917$	4.25800	0.140612
$918$	−0.259105	−0.00855175
$919$	22.8657	0.754269	0.377135	−	0.926158i	$-0.376909\pi$
$919$	22.8657	0.754269	0.377135	+	0.926158i	$0.376909\pi$
$920$	0	0
$921$	−18.1634	−0.598504
$922$	9.59745	0.316075
$923$	51.3038	1.68868
$924$	−0.508899	−0.0167415
$925$	0	0
$926$	6.82311	0.224221
$927$	11.3273	0.372038
$928$	30.3470	0.996188
$929$	−19.6394	−0.644348	−0.322174	−	0.946680i	$-0.604414\pi$
$929$	−19.6394	−0.644348	−0.322174	+	0.946680i	$0.604414\pi$
$930$	0	0
$931$	−44.7213	−1.46568
$932$	−52.2641	−1.71197
$933$	−28.0180	−0.917270
$934$	−7.46263	−0.244185
$935$	0	0
$936$	5.64311	0.184451
$937$	19.3312	0.631521	0.315761	−	0.948839i	$-0.397740\pi$
$937$	19.3312	0.631521	0.315761	+	0.948839i	$0.397740\pi$
$938$	0.241659	0.00789043
$939$	−12.6852	−0.413965
$940$	0	0
$941$	−16.7500	−0.546034	−0.273017	−	0.962009i	$-0.588021\pi$
$941$	−16.7500	−0.546034	−0.273017	+	0.962009i	$0.588021\pi$
$942$	4.39728	0.143271
$943$	−13.1594	−0.428529
$944$	−34.7237	−1.13016
$945$	0	0
$946$	2.10976	0.0685943
$947$	−51.3618	−1.66903	−0.834517	−	0.550982i	$-0.814253\pi$
$947$	−51.3618	−1.66903	−0.834517	+	0.550982i	$0.814253\pi$
$948$	−30.4378	−0.988573
$949$	63.0688	2.04730
$950$	0	0
$951$	−34.8739	−1.13086
$952$	−0.210947	−0.00683682
$953$	−18.3541	−0.594548	−0.297274	−	0.954792i	$-0.596078\pi$
$953$	−18.3541	−0.594548	−0.297274	+	0.954792i	$0.596078\pi$
$954$	−2.30853	−0.0747414
$955$	0	0
$956$	−48.4499	−1.56698
$957$	−12.6492	−0.408890
$958$	−4.61985	−0.149260
$959$	3.06365	0.0989303
$960$	0	0
$961$	4.75296	0.153321
$962$	−1.71050	−0.0551488
$963$	8.10431	0.261158
$964$	15.3911	0.495714
$965$	0	0
$966$	−0.325167	−0.0104621
$967$	−47.6325	−1.53176	−0.765879	−	0.642985i	$-0.777696\pi$
$967$	−47.6325	−1.53176	−0.765879	+	0.642985i	$0.777696\pi$
$968$	−9.84383	−0.316393
$969$	6.23427	0.200274
$970$	0	0
$971$	−15.0570	−0.483203	−0.241601	−	0.970376i	$-0.577673\pi$
$971$	−15.0570	−0.483203	−0.241601	+	0.970376i	$0.577673\pi$
$972$	1.92862	0.0618606
$973$	3.83830	0.123050
$974$	−1.60287	−0.0513593
$975$	0	0
$976$	−36.1310	−1.15653
$977$	57.6863	1.84555	0.922774	−	0.385342i	$-0.125917\pi$
$977$	57.6863	1.84555	0.922774	+	0.385342i	$0.125917\pi$
$978$	2.05985	0.0658669
$979$	9.27283	0.296361
$980$	0	0
$981$	13.2362	0.422599
$982$	5.83902	0.186330
$983$	27.1491	0.865920	0.432960	−	0.901413i	$-0.357469\pi$
$983$	27.1491	0.865920	0.432960	+	0.901413i	$0.357469\pi$
$984$	−2.35172	−0.0749700
$985$	0	0
$986$	−2.57401	−0.0819732
$987$	−0.207232	−0.00659625
$988$	−66.6553	−2.12059
$989$	−36.4248	−1.15824
$990$	0	0
$991$	15.3572	0.487837	0.243918	−	0.969796i	$-0.421567\pi$
$991$	15.3572	0.487837	0.243918	+	0.969796i	$0.421567\pi$
$992$	−18.2657	−0.579937
$993$	−20.3577	−0.646032
$994$	−0.528307	−0.0167569
$995$	0	0
$996$	−3.45893	−0.109600
$997$	−50.5126	−1.59975	−0.799876	−	0.600166i	$-0.795101\pi$
$997$	−50.5126	−1.59975	−0.799876	+	0.600166i	$0.795101\pi$
$998$	−9.11617	−0.288567
$999$	−1.19082	−0.0376758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.be.1.3	yes	8
5.4	even	2		3525.2.a.bd.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.bd.1.6	✓	8	5.4	even	2
3525.2.a.be.1.3	yes	8	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-0.267165 q^{2} -1.00000 q^{3} -1.92862 q^{4} +0.267165 q^{6} +0.207232 q^{7} +1.04959 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.267165 q^{2} -1.00000 q^{3} -1.92862 q^{4} +0.267165 q^{6} +0.207232 q^{7} +1.04959 q^{8} +1.00000 q^{9} -1.27329 q^{11} +1.92862 q^{12} +5.37648 q^{13} -0.0553651 q^{14} +3.57683 q^{16} -0.969832 q^{17} -0.267165 q^{18} +6.42820 q^{19} -0.207232 q^{21} +0.340179 q^{22} -5.87315 q^{23} -1.04959 q^{24} -1.43641 q^{26} -1.00000 q^{27} -0.399672 q^{28} -9.93423 q^{29} +5.97938 q^{31} -3.05479 q^{32} +1.27329 q^{33} +0.259105 q^{34} -1.92862 q^{36} +1.19082 q^{37} -1.71739 q^{38} -5.37648 q^{39} +2.24060 q^{41} +0.0553651 q^{42} +6.20192 q^{43} +2.45570 q^{44} +1.56910 q^{46} +1.00000 q^{47} -3.57683 q^{48} -6.95706 q^{49} +0.969832 q^{51} -10.3692 q^{52} +8.64084 q^{53} +0.267165 q^{54} +0.217508 q^{56} -6.42820 q^{57} +2.65408 q^{58} -9.70796 q^{59} -10.1014 q^{61} -1.59748 q^{62} +0.207232 q^{63} -6.33753 q^{64} -0.340179 q^{66} -4.36482 q^{67} +1.87044 q^{68} +5.87315 q^{69} +9.54225 q^{71} +1.04959 q^{72} +11.7305 q^{73} -0.318145 q^{74} -12.3976 q^{76} -0.263866 q^{77} +1.43641 q^{78} -15.7821 q^{79} +1.00000 q^{81} -0.598611 q^{82} -1.79347 q^{83} +0.399672 q^{84} -1.65694 q^{86} +9.93423 q^{87} -1.33644 q^{88} -7.28256 q^{89} +1.11418 q^{91} +11.3271 q^{92} -5.97938 q^{93} -0.267165 q^{94} +3.05479 q^{96} +0.290073 q^{97} +1.85868 q^{98} -1.27329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} - 8 q^{3} + 7 q^{4} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 7 q^{12} + 10 q^{13} + q^{14} + 5 q^{16} + 6 q^{17} + 3 q^{18} - 2 q^{19} - 8 q^{21} + 10 q^{23} - 6 q^{24} - 14 q^{26} - 8 q^{27} + 44 q^{28} - 13 q^{29} + 10 q^{32} + 8 q^{33} + 28 q^{34} + 7 q^{36} + 3 q^{37} + 36 q^{38} - 10 q^{39} - 16 q^{41} - q^{42} + 25 q^{43} - 17 q^{44} - 5 q^{46} + 8 q^{47} - 5 q^{48} + 16 q^{49} - 6 q^{51} - 17 q^{52} + 4 q^{53} - 3 q^{54} + 37 q^{56} + 2 q^{57} + 15 q^{58} - 8 q^{59} + 15 q^{61} + 6 q^{62} + 8 q^{63} - 14 q^{64} + 27 q^{67} + 14 q^{68} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 28 q^{73} - 21 q^{74} + 6 q^{76} + 4 q^{77} + 14 q^{78} + 7 q^{79} + 8 q^{81} - 53 q^{82} + 60 q^{83} - 44 q^{84} - 3 q^{86} + 13 q^{87} + 54 q^{88} - 34 q^{89} + 23 q^{91} - 43 q^{92} + 3 q^{94} - 10 q^{96} + 7 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 8 * q^3 + 7 * q^4 - 3 * q^6 + 8 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 7 * q^12 + 10 * q^13 + q^14 + 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 - 8 * q^21 + 10 * q^23 - 6 * q^24 - 14 * q^26 - 8 * q^27 + 44 * q^28 - 13 * q^29 + 10 * q^32 + 8 * q^33 + 28 * q^34 + 7 * q^36 + 3 * q^37 + 36 * q^38 - 10 * q^39 - 16 * q^41 - q^42 + 25 * q^43 - 17 * q^44 - 5 * q^46 + 8 * q^47 - 5 * q^48 + 16 * q^49 - 6 * q^51 - 17 * q^52 + 4 * q^53 - 3 * q^54 + 37 * q^56 + 2 * q^57 + 15 * q^58 - 8 * q^59 + 15 * q^61 + 6 * q^62 + 8 * q^63 - 14 * q^64 + 27 * q^67 + 14 * q^68 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 28 * q^73 - 21 * q^74 + 6 * q^76 + 4 * q^77 + 14 * q^78 + 7 * q^79 + 8 * q^81 - 53 * q^82 + 60 * q^83 - 44 * q^84 - 3 * q^86 + 13 * q^87 + 54 * q^88 - 34 * q^89 + 23 * q^91 - 43 * q^92 + 3 * q^94 - 10 * q^96 + 7 * q^97 + 40 * q^98 - 8 * q^99

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