LMFDB - Embedded newform 3525.2.a.bc.1.7

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} - 15x^{2} + 1 $ x^7 - 3x^6 - 5x^5 + 18x^4 - 15x^2 + 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			1.7
Root			$2.49904$ 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)

$f(q)$	$=$	$q+2.49904 q^{2} +1.00000 q^{3} +4.24521 q^{4} +2.49904 q^{6} -0.534565 q^{7} +5.61086 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.49904 q^{2} +1.00000 q^{3} +4.24521 q^{4} +2.49904 q^{6} -0.534565 q^{7} +5.61086 q^{8} +1.00000 q^{9} +2.28099 q^{11} +4.24521 q^{12} +5.44670 q^{13} -1.33590 q^{14} +5.53137 q^{16} +2.12796 q^{17} +2.49904 q^{18} -1.01939 q^{19} -0.534565 q^{21} +5.70028 q^{22} -8.05859 q^{23} +5.61086 q^{24} +13.6115 q^{26} +1.00000 q^{27} -2.26934 q^{28} +4.73003 q^{29} -1.87955 q^{31} +2.60139 q^{32} +2.28099 q^{33} +5.31785 q^{34} +4.24521 q^{36} -2.45084 q^{37} -2.54750 q^{38} +5.44670 q^{39} -4.95867 q^{41} -1.33590 q^{42} +4.70001 q^{43} +9.68325 q^{44} -20.1387 q^{46} -1.00000 q^{47} +5.53137 q^{48} -6.71424 q^{49} +2.12796 q^{51} +23.1224 q^{52} +5.57514 q^{53} +2.49904 q^{54} -2.99937 q^{56} -1.01939 q^{57} +11.8205 q^{58} +3.29110 q^{59} -8.37125 q^{61} -4.69707 q^{62} -0.534565 q^{63} -4.56176 q^{64} +5.70028 q^{66} -7.39089 q^{67} +9.03361 q^{68} -8.05859 q^{69} +8.19182 q^{71} +5.61086 q^{72} +12.6180 q^{73} -6.12476 q^{74} -4.32753 q^{76} -1.21934 q^{77} +13.6115 q^{78} +10.3346 q^{79} +1.00000 q^{81} -12.3919 q^{82} -0.831352 q^{83} -2.26934 q^{84} +11.7455 q^{86} +4.73003 q^{87} +12.7983 q^{88} +7.72743 q^{89} -2.91161 q^{91} -34.2104 q^{92} -1.87955 q^{93} -2.49904 q^{94} +2.60139 q^{96} -10.8616 q^{97} -16.7792 q^{98} +2.28099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.49904	1.76709	0.883544	−	0.468347i	$-0.155150\pi$
$2$	2.49904	1.76709	0.883544	+	0.468347i	$0.155150\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.24521	2.12260
$5$	0	0
$5$	0	0
$6$	2.49904	1.02023
$7$	−0.534565	−0.202047	−0.101023	−	0.994884i	$-0.532212\pi$
$7$	−0.534565	−0.202047	−0.101023	+	0.994884i	$0.532212\pi$
$8$	5.61086	1.98374
$9$	1.00000	0.333333
$10$	0	0
$11$	2.28099	0.687743	0.343871	−	0.939017i	$-0.388262\pi$
$11$	2.28099	0.687743	0.343871	+	0.939017i	$0.388262\pi$
$12$	4.24521	1.22549
$13$	5.44670	1.51064	0.755321	−	0.655355i	$-0.227481\pi$
$13$	5.44670	1.51064	0.755321	+	0.655355i	$0.227481\pi$
$14$	−1.33590	−0.357034
$15$	0	0
$16$	5.53137	1.38284
$17$	2.12796	0.516105	0.258053	−	0.966131i	$-0.416919\pi$
$17$	2.12796	0.516105	0.258053	+	0.966131i	$0.416919\pi$
$18$	2.49904	0.589030
$19$	−1.01939	−0.233864	−0.116932	−	0.993140i	$-0.537306\pi$
$19$	−1.01939	−0.233864	−0.116932	+	0.993140i	$0.537306\pi$
$20$	0	0
$21$	−0.534565	−0.116652
$22$	5.70028	1.21530
$23$	−8.05859	−1.68033	−0.840166	−	0.542329i	$-0.817543\pi$
$23$	−8.05859	−1.68033	−0.840166	+	0.542329i	$0.817543\pi$
$24$	5.61086	1.14531
$25$	0	0
$26$	13.6115	2.66944
$27$	1.00000	0.192450
$28$	−2.26934	−0.428865
$29$	4.73003	0.878345	0.439173	−	0.898403i	$-0.355272\pi$
$29$	4.73003	0.878345	0.439173	+	0.898403i	$0.355272\pi$
$30$	0	0
$31$	−1.87955	−0.337577	−0.168788	−	0.985652i	$-0.553985\pi$
$31$	−1.87955	−0.337577	−0.168788	+	0.985652i	$0.553985\pi$
$32$	2.60139	0.459865
$33$	2.28099	0.397069
$34$	5.31785	0.912004
$35$	0	0
$36$	4.24521	0.707534
$37$	−2.45084	−0.402916	−0.201458	−	0.979497i	$-0.564568\pi$
$37$	−2.45084	−0.402916	−0.201458	+	0.979497i	$0.564568\pi$
$38$	−2.54750	−0.413259
$39$	5.44670	0.872169
$40$	0	0
$41$	−4.95867	−0.774415	−0.387207	−	0.921993i	$-0.626560\pi$
$41$	−4.95867	−0.774415	−0.387207	+	0.921993i	$0.626560\pi$
$42$	−1.33590	−0.206134
$43$	4.70001	0.716745	0.358373	−	0.933579i	$-0.383332\pi$
$43$	4.70001	0.716745	0.358373	+	0.933579i	$0.383332\pi$
$44$	9.68325	1.45981
$45$	0	0
$46$	−20.1387	−2.96930
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	5.53137	0.798384
$49$	−6.71424	−0.959177
$50$	0	0
$51$	2.12796	0.297973
$52$	23.1224	3.20649
$53$	5.57514	0.765805	0.382902	−	0.923789i	$-0.374925\pi$
$53$	5.57514	0.765805	0.382902	+	0.923789i	$0.374925\pi$
$54$	2.49904	0.340076
$55$	0	0
$56$	−2.99937	−0.400808
$57$	−1.01939	−0.135022
$58$	11.8205	1.55211
$59$	3.29110	0.428464	0.214232	−	0.976783i	$-0.431275\pi$
$59$	3.29110	0.428464	0.214232	+	0.976783i	$0.431275\pi$
$60$	0	0
$61$	−8.37125	−1.07183	−0.535914	−	0.844273i	$-0.680033\pi$
$61$	−8.37125	−1.07183	−0.535914	+	0.844273i	$0.680033\pi$
$62$	−4.69707	−0.596529
$63$	−0.534565	−0.0673489
$64$	−4.56176	−0.570220
$65$	0	0
$66$	5.70028	0.701655
$67$	−7.39089	−0.902941	−0.451471	−	0.892286i	$-0.649100\pi$
$67$	−7.39089	−0.902941	−0.451471	+	0.892286i	$0.649100\pi$
$68$	9.03361	1.09549
$69$	−8.05859	−0.970140
$70$	0	0
$71$	8.19182	0.972190	0.486095	−	0.873906i	$-0.338421\pi$
$71$	8.19182	0.972190	0.486095	+	0.873906i	$0.338421\pi$
$72$	5.61086	0.661247
$73$	12.6180	1.47682	0.738411	−	0.674351i	$-0.235576\pi$
$73$	12.6180	1.47682	0.738411	+	0.674351i	$0.235576\pi$
$74$	−6.12476	−0.711989
$75$	0	0
$76$	−4.32753	−0.496401
$77$	−1.21934	−0.138956
$78$	13.6115	1.54120
$79$	10.3346	1.16274	0.581369	−	0.813640i	$-0.302517\pi$
$79$	10.3346	1.16274	0.581369	+	0.813640i	$0.302517\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−12.3919	−1.36846
$83$	−0.831352	−0.0912527	−0.0456264	−	0.998959i	$-0.514528\pi$
$83$	−0.831352	−0.0912527	−0.0456264	+	0.998959i	$0.514528\pi$
$84$	−2.26934	−0.247605
$85$	0	0
$86$	11.7455	1.26655
$87$	4.73003	0.507113
$88$	12.7983	1.36430
$89$	7.72743	0.819106	0.409553	−	0.912286i	$-0.365685\pi$
$89$	7.72743	0.819106	0.409553	+	0.912286i	$0.365685\pi$
$90$	0	0
$91$	−2.91161	−0.305220
$92$	−34.2104	−3.56668
$93$	−1.87955	−0.194900
$94$	−2.49904	−0.257756
$95$	0	0
$96$	2.60139	0.265503
$97$	−10.8616	−1.10283	−0.551416	−	0.834230i	$-0.685912\pi$
$97$	−10.8616	−1.10283	−0.551416	+	0.834230i	$0.685912\pi$
$98$	−16.7792	−1.69495
$99$	2.28099	0.229248
$100$	0	0
$101$	−10.9521	−1.08977	−0.544887	−	0.838509i	$-0.683428\pi$
$101$	−10.9521	−1.08977	−0.544887	+	0.838509i	$0.683428\pi$
$102$	5.31785	0.526546
$103$	8.08078	0.796223	0.398112	−	0.917337i	$-0.369666\pi$
$103$	8.08078	0.796223	0.398112	+	0.917337i	$0.369666\pi$
$104$	30.5607	2.99672
$105$	0	0
$106$	13.9325	1.35325
$107$	13.0931	1.26576	0.632879	−	0.774251i	$-0.281873\pi$
$107$	13.0931	1.26576	0.632879	+	0.774251i	$0.281873\pi$
$108$	4.24521	0.408495
$109$	−4.06396	−0.389257	−0.194628	−	0.980877i	$-0.562350\pi$
$109$	−4.06396	−0.389257	−0.194628	+	0.980877i	$0.562350\pi$
$110$	0	0
$111$	−2.45084	−0.232624
$112$	−2.95688	−0.279399
$113$	4.02484	0.378625	0.189312	−	0.981917i	$-0.439374\pi$
$113$	4.02484	0.378625	0.189312	+	0.981917i	$0.439374\pi$
$114$	−2.54750	−0.238595
$115$	0	0
$116$	20.0800	1.86438
$117$	5.44670	0.503547
$118$	8.22459	0.757135
$119$	−1.13753	−0.104277
$120$	0	0
$121$	−5.79711	−0.527010
$122$	−20.9201	−1.89402
$123$	−4.95867	−0.447108
$124$	−7.97908	−0.716542
$125$	0	0
$126$	−1.33590	−0.119011
$127$	−9.92886	−0.881044	−0.440522	−	0.897742i	$-0.645207\pi$
$127$	−9.92886	−0.881044	−0.440522	+	0.897742i	$0.645207\pi$
$128$	−16.6028	−1.46749
$129$	4.70001	0.413813
$130$	0	0
$131$	−5.41092	−0.472754	−0.236377	−	0.971661i	$-0.575960\pi$
$131$	−5.41092	−0.472754	−0.236377	+	0.971661i	$0.575960\pi$
$132$	9.68325	0.842819
$133$	0.544931	0.0472515
$134$	−18.4701	−1.59558
$135$	0	0
$136$	11.9397	1.02382
$137$	−16.1227	−1.37746	−0.688728	−	0.725019i	$-0.741831\pi$
$137$	−16.1227	−1.37746	−0.688728	+	0.725019i	$0.741831\pi$
$138$	−20.1387	−1.71432
$139$	4.49918	0.381615	0.190808	−	0.981627i	$-0.438889\pi$
$139$	4.49918	0.381615	0.190808	+	0.981627i	$0.438889\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	20.4717	1.71795
$143$	12.4238	1.03893
$144$	5.53137	0.460947
$145$	0	0
$146$	31.5328	2.60968
$147$	−6.71424	−0.553781
$148$	−10.4043	−0.855231
$149$	−11.6856	−0.957319	−0.478659	−	0.878001i	$-0.658877\pi$
$149$	−11.6856	−0.957319	−0.478659	+	0.878001i	$0.658877\pi$
$150$	0	0
$151$	−5.90737	−0.480735	−0.240367	−	0.970682i	$-0.577268\pi$
$151$	−5.90737	−0.480735	−0.240367	+	0.970682i	$0.577268\pi$
$152$	−5.71967	−0.463926
$153$	2.12796	0.172035
$154$	−3.04717	−0.245548
$155$	0	0
$156$	23.1224	1.85127
$157$	−9.45273	−0.754410	−0.377205	−	0.926130i	$-0.623115\pi$
$157$	−9.45273	−0.754410	−0.377205	+	0.926130i	$0.623115\pi$
$158$	25.8267	2.05466
$159$	5.57514	0.442138
$160$	0	0
$161$	4.30784	0.339505
$162$	2.49904	0.196343
$163$	18.2578	1.43006	0.715029	−	0.699095i	$-0.246414\pi$
$163$	18.2578	1.43006	0.715029	+	0.699095i	$0.246414\pi$
$164$	−21.0506	−1.64378
$165$	0	0
$166$	−2.07758	−0.161252
$167$	2.87439	0.222427	0.111213	−	0.993797i	$-0.464526\pi$
$167$	2.87439	0.222427	0.111213	+	0.993797i	$0.464526\pi$
$168$	−2.99937	−0.231407
$169$	16.6665	1.28204
$170$	0	0
$171$	−1.01939	−0.0779548
$172$	19.9525	1.52137
$173$	−8.71147	−0.662321	−0.331161	−	0.943574i	$-0.607440\pi$
$173$	−8.71147	−0.662321	−0.331161	+	0.943574i	$0.607440\pi$
$174$	11.8205	0.896113
$175$	0	0
$176$	12.6170	0.951040
$177$	3.29110	0.247374
$178$	19.3112	1.44743
$179$	13.9957	1.04609	0.523046	−	0.852305i	$-0.324796\pi$
$179$	13.9957	1.04609	0.523046	+	0.852305i	$0.324796\pi$
$180$	0	0
$181$	4.24568	0.315579	0.157789	−	0.987473i	$-0.449563\pi$
$181$	4.24568	0.315579	0.157789	+	0.987473i	$0.449563\pi$
$182$	−7.27624	−0.539351
$183$	−8.37125	−0.618820
$184$	−45.2157	−3.33334
$185$	0	0
$186$	−4.69707	−0.344406
$187$	4.85384	0.354948
$188$	−4.24521	−0.309614
$189$	−0.534565	−0.0388839
$190$	0	0
$191$	3.81549	0.276079	0.138039	−	0.990427i	$-0.455920\pi$
$191$	3.81549	0.276079	0.138039	+	0.990427i	$0.455920\pi$
$192$	−4.56176	−0.329217
$193$	−15.4332	−1.11091	−0.555453	−	0.831548i	$-0.687455\pi$
$193$	−15.4332	−1.11091	−0.555453	+	0.831548i	$0.687455\pi$
$194$	−27.1437	−1.94880
$195$	0	0
$196$	−28.5033	−2.03595
$197$	−22.7445	−1.62048	−0.810241	−	0.586097i	$-0.800664\pi$
$197$	−22.7445	−1.62048	−0.810241	+	0.586097i	$0.800664\pi$
$198$	5.70028	0.405101
$199$	−15.8679	−1.12485	−0.562424	−	0.826849i	$-0.690131\pi$
$199$	−15.8679	−1.12485	−0.562424	+	0.826849i	$0.690131\pi$
$200$	0	0
$201$	−7.39089	−0.521313
$202$	−27.3698	−1.92573
$203$	−2.52851	−0.177467
$204$	9.03361	0.632480
$205$	0	0
$206$	20.1942	1.40700
$207$	−8.05859	−0.560111
$208$	30.1277	2.08898
$209$	−2.32522	−0.160839
$210$	0	0
$211$	3.08924	0.212672	0.106336	−	0.994330i	$-0.466088\pi$
$211$	3.08924	0.212672	0.106336	+	0.994330i	$0.466088\pi$
$212$	23.6676	1.62550
$213$	8.19182	0.561294
$214$	32.7202	2.23671
$215$	0	0
$216$	5.61086	0.381771
$217$	1.00474	0.0682063
$218$	−10.1560	−0.687851
$219$	12.6180	0.852644
$220$	0	0
$221$	11.5903	0.779650
$222$	−6.12476	−0.411067
$223$	−5.16188	−0.345665	−0.172832	−	0.984951i	$-0.555292\pi$
$223$	−5.16188	−0.345665	−0.172832	+	0.984951i	$0.555292\pi$
$224$	−1.39061	−0.0929141
$225$	0	0
$226$	10.0582	0.669063
$227$	14.5232	0.963937	0.481969	−	0.876189i	$-0.339922\pi$
$227$	14.5232	0.963937	0.481969	+	0.876189i	$0.339922\pi$
$228$	−4.32753	−0.286598
$229$	−12.1255	−0.801275	−0.400637	−	0.916237i	$-0.631211\pi$
$229$	−12.1255	−0.801275	−0.400637	+	0.916237i	$0.631211\pi$
$230$	0	0
$231$	−1.21934	−0.0802264
$232$	26.5396	1.74241
$233$	−2.73012	−0.178856	−0.0894279	−	0.995993i	$-0.528504\pi$
$233$	−2.73012	−0.178856	−0.0894279	+	0.995993i	$0.528504\pi$
$234$	13.6115	0.889813
$235$	0	0
$236$	13.9714	0.909460
$237$	10.3346	0.671307
$238$	−2.84274	−0.184267
$239$	−23.9431	−1.54875	−0.774376	−	0.632726i	$-0.781936\pi$
$239$	−23.9431	−1.54875	−0.774376	+	0.632726i	$0.781936\pi$
$240$	0	0
$241$	−12.7368	−0.820452	−0.410226	−	0.911984i	$-0.634550\pi$
$241$	−12.7368	−0.820452	−0.410226	+	0.911984i	$0.634550\pi$
$242$	−14.4872	−0.931273
$243$	1.00000	0.0641500
$244$	−35.5377	−2.27507
$245$	0	0
$246$	−12.3919	−0.790080
$247$	−5.55231	−0.353285
$248$	−10.5459	−0.669665
$249$	−0.831352	−0.0526848
$250$	0	0
$251$	4.59985	0.290340	0.145170	−	0.989407i	$-0.453627\pi$
$251$	4.59985	0.290340	0.145170	+	0.989407i	$0.453627\pi$
$252$	−2.26934	−0.142955
$253$	−18.3815	−1.15564
$254$	−24.8126	−1.55688
$255$	0	0
$256$	−32.3676	−2.02297
$257$	−21.4598	−1.33862	−0.669312	−	0.742981i	$-0.733411\pi$
$257$	−21.4598	−1.33862	−0.669312	+	0.742981i	$0.733411\pi$
$258$	11.7455	0.731245
$259$	1.31014	0.0814079
$260$	0	0
$261$	4.73003	0.292782
$262$	−13.5221	−0.835399
$263$	26.4842	1.63308	0.816542	−	0.577286i	$-0.195888\pi$
$263$	26.4842	1.63308	0.816542	+	0.577286i	$0.195888\pi$
$264$	12.7983	0.787681
$265$	0	0
$266$	1.36181	0.0834976
$267$	7.72743	0.472911
$268$	−31.3759	−1.91659
$269$	−18.9269	−1.15399	−0.576997	−	0.816747i	$-0.695775\pi$
$269$	−18.9269	−1.15399	−0.576997	+	0.816747i	$0.695775\pi$
$270$	0	0
$271$	3.58283	0.217642	0.108821	−	0.994061i	$-0.465293\pi$
$271$	3.58283	0.217642	0.108821	+	0.994061i	$0.465293\pi$
$272$	11.7705	0.713692
$273$	−2.91161	−0.176219
$274$	−40.2913	−2.43409
$275$	0	0
$276$	−34.2104	−2.05922
$277$	13.8090	0.829700	0.414850	−	0.909890i	$-0.363834\pi$
$277$	13.8090	0.829700	0.414850	+	0.909890i	$0.363834\pi$
$278$	11.2436	0.674348
$279$	−1.87955	−0.112526
$280$	0	0
$281$	−18.1689	−1.08387	−0.541934	−	0.840421i	$-0.682308\pi$
$281$	−18.1689	−1.08387	−0.541934	+	0.840421i	$0.682308\pi$
$282$	−2.49904	−0.148816
$283$	−16.6494	−0.989705	−0.494852	−	0.868977i	$-0.664778\pi$
$283$	−16.6494	−0.989705	−0.494852	+	0.868977i	$0.664778\pi$
$284$	34.7760	2.06357
$285$	0	0
$286$	31.0477	1.83589
$287$	2.65073	0.156468
$288$	2.60139	0.153288
$289$	−12.4718	−0.733635
$290$	0	0
$291$	−10.8616	−0.636721
$292$	53.5659	3.13471
$293$	28.4051	1.65944	0.829722	−	0.558177i	$-0.188499\pi$
$293$	28.4051	1.65944	0.829722	+	0.558177i	$0.188499\pi$
$294$	−16.7792	−0.978581
$295$	0	0
$296$	−13.7514	−0.799281
$297$	2.28099	0.132356
$298$	−29.2027	−1.69167
$299$	−43.8927	−2.53838
$300$	0	0
$301$	−2.51246	−0.144816
$302$	−14.7628	−0.849501
$303$	−10.9521	−0.629182
$304$	−5.63863	−0.323398
$305$	0	0
$306$	5.31785	0.304001
$307$	−10.1616	−0.579951	−0.289976	−	0.957034i	$-0.593647\pi$
$307$	−10.1616	−0.579951	−0.289976	+	0.957034i	$0.593647\pi$
$308$	−5.17633	−0.294949
$309$	8.08078	0.459700
$310$	0	0
$311$	−4.38105	−0.248427	−0.124213	−	0.992256i	$-0.539641\pi$
$311$	−4.38105	−0.248427	−0.124213	+	0.992256i	$0.539641\pi$
$312$	30.5607	1.73016
$313$	−9.20443	−0.520265	−0.260132	−	0.965573i	$-0.583766\pi$
$313$	−9.20443	−0.520265	−0.260132	+	0.965573i	$0.583766\pi$
$314$	−23.6228	−1.33311
$315$	0	0
$316$	43.8727	2.46803
$317$	1.10272	0.0619352	0.0309676	−	0.999520i	$-0.490141\pi$
$317$	1.10272	0.0619352	0.0309676	+	0.999520i	$0.490141\pi$
$318$	13.9325	0.781297
$319$	10.7891	0.604076
$320$	0	0
$321$	13.0931	0.730785
$322$	10.7655	0.599936
$323$	−2.16922	−0.120699
$324$	4.24521	0.235845
$325$	0	0
$326$	45.6269	2.52704
$327$	−4.06396	−0.224737
$328$	−27.8224	−1.53624
$329$	0.534565	0.0294715
$330$	0	0
$331$	−27.9050	−1.53380	−0.766900	−	0.641767i	$-0.778202\pi$
$331$	−27.9050	−1.53380	−0.766900	+	0.641767i	$0.778202\pi$
$332$	−3.52926	−0.193693
$333$	−2.45084	−0.134305
$334$	7.18321	0.393048
$335$	0	0
$336$	−2.95688	−0.161311
$337$	−19.5221	−1.06343	−0.531717	−	0.846922i	$-0.678453\pi$
$337$	−19.5221	−1.06343	−0.531717	+	0.846922i	$0.678453\pi$
$338$	41.6503	2.26548
$339$	4.02484	0.218599
$340$	0	0
$341$	−4.28722	−0.232166
$342$	−2.54750	−0.137753
$343$	7.33116	0.395845
$344$	26.3711	1.42184
$345$	0	0
$346$	−21.7703	−1.17038
$347$	0.589517	0.0316469	0.0158235	−	0.999875i	$-0.494963\pi$
$347$	0.589517	0.0316469	0.0158235	+	0.999875i	$0.494963\pi$
$348$	20.0800	1.07640
$349$	−19.4759	−1.04252	−0.521260	−	0.853398i	$-0.674538\pi$
$349$	−19.4759	−1.04252	−0.521260	+	0.853398i	$0.674538\pi$
$350$	0	0
$351$	5.44670	0.290723
$352$	5.93373	0.316269
$353$	15.7738	0.839555	0.419778	−	0.907627i	$-0.362108\pi$
$353$	15.7738	0.839555	0.419778	+	0.907627i	$0.362108\pi$
$354$	8.22459	0.437132
$355$	0	0
$356$	32.8045	1.73864
$357$	−1.13753	−0.0602045
$358$	34.9759	1.84854
$359$	21.8041	1.15078	0.575389	−	0.817880i	$-0.304851\pi$
$359$	21.8041	1.15078	0.575389	+	0.817880i	$0.304851\pi$
$360$	0	0
$361$	−17.9608	−0.945307
$362$	10.6101	0.557656
$363$	−5.79711	−0.304269
$364$	−12.3604	−0.647861
$365$	0	0
$366$	−20.9201	−1.09351
$367$	30.4844	1.59127	0.795636	−	0.605775i	$-0.207137\pi$
$367$	30.4844	1.59127	0.795636	+	0.605775i	$0.207137\pi$
$368$	−44.5750	−2.32363
$369$	−4.95867	−0.258138
$370$	0	0
$371$	−2.98028	−0.154728
$372$	−7.97908	−0.413696
$373$	−10.0316	−0.519419	−0.259709	−	0.965687i	$-0.583627\pi$
$373$	−10.0316	−0.519419	−0.259709	+	0.965687i	$0.583627\pi$
$374$	12.1299	0.627224
$375$	0	0
$376$	−5.61086	−0.289358
$377$	25.7631	1.32686
$378$	−1.33590	−0.0687113
$379$	0.646905	0.0332293	0.0166146	−	0.999862i	$-0.494711\pi$
$379$	0.646905	0.0332293	0.0166146	+	0.999862i	$0.494711\pi$
$380$	0	0
$381$	−9.92886	−0.508671
$382$	9.53505	0.487856
$383$	37.5422	1.91831	0.959157	−	0.282873i	$-0.0912874\pi$
$383$	37.5422	1.91831	0.959157	+	0.282873i	$0.0912874\pi$
$384$	−16.6028	−0.847258
$385$	0	0
$386$	−38.5682	−1.96307
$387$	4.70001	0.238915
$388$	−46.1099	−2.34088
$389$	−24.6638	−1.25050	−0.625251	−	0.780424i	$-0.715003\pi$
$389$	−24.6638	−1.25050	−0.625251	+	0.780424i	$0.715003\pi$
$390$	0	0
$391$	−17.1483	−0.867228
$392$	−37.6727	−1.90276
$393$	−5.41092	−0.272945
$394$	−56.8396	−2.86354
$395$	0	0
$396$	9.68325	0.486602
$397$	33.3744	1.67501	0.837507	−	0.546427i	$-0.184012\pi$
$397$	33.3744	1.67501	0.837507	+	0.546427i	$0.184012\pi$
$398$	−39.6546	−1.98770
$399$	0.544931	0.0272807
$400$	0	0
$401$	−7.63874	−0.381460	−0.190730	−	0.981643i	$-0.561086\pi$
$401$	−7.63874	−0.381460	−0.190730	+	0.981643i	$0.561086\pi$
$402$	−18.4701	−0.921207
$403$	−10.2373	−0.509958
$404$	−46.4939	−2.31316
$405$	0	0
$406$	−6.31885	−0.313599
$407$	−5.59034	−0.277103
$408$	11.9397	0.591102
$409$	32.0984	1.58716	0.793582	−	0.608463i	$-0.208214\pi$
$409$	32.0984	1.58716	0.793582	+	0.608463i	$0.208214\pi$
$410$	0	0
$411$	−16.1227	−0.795275
$412$	34.3046	1.69007
$413$	−1.75931	−0.0865698
$414$	−20.1387	−0.989765
$415$	0	0
$416$	14.1690	0.694691
$417$	4.49918	0.220326
$418$	−5.81081	−0.284216
$419$	−10.2321	−0.499871	−0.249936	−	0.968262i	$-0.580409\pi$
$419$	−10.2321	−0.499871	−0.249936	+	0.968262i	$0.580409\pi$
$420$	0	0
$421$	−38.5005	−1.87640	−0.938199	−	0.346097i	$-0.887507\pi$
$421$	−38.5005	−1.87640	−0.938199	+	0.346097i	$0.887507\pi$
$422$	7.72015	0.375811
$423$	−1.00000	−0.0486217
$424$	31.2814	1.51916
$425$	0	0
$426$	20.4717	0.991857
$427$	4.47498	0.216559
$428$	55.5829	2.68670
$429$	12.4238	0.599828
$430$	0	0
$431$	−15.7052	−0.756494	−0.378247	−	0.925705i	$-0.623473\pi$
$431$	−15.7052	−0.756494	−0.378247	+	0.925705i	$0.623473\pi$
$432$	5.53137	0.266128
$433$	34.0232	1.63505	0.817526	−	0.575892i	$-0.195345\pi$
$433$	34.0232	1.63505	0.817526	+	0.575892i	$0.195345\pi$
$434$	2.51089	0.120527
$435$	0	0
$436$	−17.2523	−0.826237
$437$	8.21486	0.392970
$438$	31.5328	1.50670
$439$	−4.31306	−0.205851	−0.102926	−	0.994689i	$-0.532820\pi$
$439$	−4.31306	−0.205851	−0.102926	+	0.994689i	$0.532820\pi$
$440$	0	0
$441$	−6.71424	−0.319726
$442$	28.9647	1.37771
$443$	−15.4209	−0.732671	−0.366336	−	0.930483i	$-0.619388\pi$
$443$	−15.4209	−0.732671	−0.366336	+	0.930483i	$0.619388\pi$
$444$	−10.4043	−0.493768
$445$	0	0
$446$	−12.8997	−0.610820
$447$	−11.6856	−0.552708
$448$	2.43856	0.115211
$449$	32.2639	1.52263	0.761314	−	0.648383i	$-0.224555\pi$
$449$	32.2639	1.52263	0.761314	+	0.648383i	$0.224555\pi$
$450$	0	0
$451$	−11.3107	−0.532598
$452$	17.0863	0.803670
$453$	−5.90737	−0.277552
$454$	36.2940	1.70336
$455$	0	0
$456$	−5.71967	−0.267848
$457$	29.1815	1.36505	0.682527	−	0.730860i	$-0.260881\pi$
$457$	29.1815	1.36505	0.682527	+	0.730860i	$0.260881\pi$
$458$	−30.3021	−1.41592
$459$	2.12796	0.0993245
$460$	0	0
$461$	3.08132	0.143511	0.0717557	−	0.997422i	$-0.477140\pi$
$461$	3.08132	0.143511	0.0717557	+	0.997422i	$0.477140\pi$
$462$	−3.04717	−0.141767
$463$	30.2571	1.40617	0.703083	−	0.711108i	$-0.251806\pi$
$463$	30.2571	1.40617	0.703083	+	0.711108i	$0.251806\pi$
$464$	26.1636	1.21461
$465$	0	0
$466$	−6.82267	−0.316054
$467$	−23.3898	−1.08235	−0.541176	−	0.840910i	$-0.682021\pi$
$467$	−23.3898	−1.08235	−0.541176	+	0.840910i	$0.682021\pi$
$468$	23.1224	1.06883
$469$	3.95091	0.182436
$470$	0	0
$471$	−9.45273	−0.435559
$472$	18.4659	0.849962
$473$	10.7207	0.492937
$474$	25.8267	1.18626
$475$	0	0
$476$	−4.82906	−0.221339
$477$	5.57514	0.255268
$478$	−59.8349	−2.73678
$479$	22.5588	1.03074	0.515368	−	0.856969i	$-0.327655\pi$
$479$	22.5588	1.03074	0.515368	+	0.856969i	$0.327655\pi$
$480$	0	0
$481$	−13.3490	−0.608662
$482$	−31.8299	−1.44981
$483$	4.30784	0.196014
$484$	−24.6099	−1.11863
$485$	0	0
$486$	2.49904	0.113359
$487$	−11.0625	−0.501289	−0.250644	−	0.968079i	$-0.580642\pi$
$487$	−11.0625	−0.501289	−0.250644	+	0.968079i	$0.580642\pi$
$488$	−46.9699	−2.12623
$489$	18.2578	0.825644
$490$	0	0
$491$	−8.21352	−0.370671	−0.185335	−	0.982675i	$-0.559337\pi$
$491$	−8.21352	−0.370671	−0.185335	+	0.982675i	$0.559337\pi$
$492$	−21.0506	−0.949034
$493$	10.0653	0.453318
$494$	−13.8755	−0.624287
$495$	0	0
$496$	−10.3965	−0.466816
$497$	−4.37906	−0.196428
$498$	−2.07758	−0.0930987
$499$	29.6470	1.32718	0.663591	−	0.748096i	$-0.269032\pi$
$499$	29.6470	1.32718	0.663591	+	0.748096i	$0.269032\pi$
$500$	0	0
$501$	2.87439	0.128418
$502$	11.4952	0.513057
$503$	38.3749	1.71105	0.855527	−	0.517759i	$-0.173234\pi$
$503$	38.3749	1.71105	0.855527	+	0.517759i	$0.173234\pi$
$504$	−2.99937	−0.133603
$505$	0	0
$506$	−45.9362	−2.04211
$507$	16.6665	0.740185
$508$	−42.1501	−1.87011
$509$	20.8713	0.925102	0.462551	−	0.886593i	$-0.346934\pi$
$509$	20.8713	0.925102	0.462551	+	0.886593i	$0.346934\pi$
$510$	0	0
$511$	−6.74513	−0.298387
$512$	−47.6823	−2.10728
$513$	−1.01939	−0.0450072
$514$	−53.6289	−2.36547
$515$	0	0
$516$	19.9525	0.878361
$517$	−2.28099	−0.100318
$518$	3.27408	0.143855
$519$	−8.71147	−0.382391
$520$	0	0
$521$	22.1924	0.972266	0.486133	−	0.873885i	$-0.338407\pi$
$521$	22.1924	0.972266	0.486133	+	0.873885i	$0.338407\pi$
$522$	11.8205	0.517371
$523$	0.662574	0.0289723	0.0144862	−	0.999895i	$-0.495389\pi$
$523$	0.662574	0.0289723	0.0144862	+	0.999895i	$0.495389\pi$
$524$	−22.9705	−1.00347
$525$	0	0
$526$	66.1850	2.88580
$527$	−3.99960	−0.174225
$528$	12.6170	0.549083
$529$	41.9409	1.82352
$530$	0	0
$531$	3.29110	0.142821
$532$	2.31335	0.100296
$533$	−27.0084	−1.16986
$534$	19.3112	0.835676
$535$	0	0
$536$	−41.4693	−1.79120
$537$	13.9957	0.603961
$538$	−47.2991	−2.03921
$539$	−15.3151	−0.659667
$540$	0	0
$541$	−23.4940	−1.01009	−0.505043	−	0.863094i	$-0.668523\pi$
$541$	−23.4940	−1.01009	−0.505043	+	0.863094i	$0.668523\pi$
$542$	8.95365	0.384592
$543$	4.24568	0.182200
$544$	5.53564	0.237339
$545$	0	0
$546$	−7.27624	−0.311394
$547$	29.8539	1.27646	0.638231	−	0.769845i	$-0.279667\pi$
$547$	29.8539	1.27646	0.638231	+	0.769845i	$0.279667\pi$
$548$	−68.4443	−2.92379
$549$	−8.37125	−0.357276
$550$	0	0
$551$	−4.82176	−0.205414
$552$	−45.2157	−1.92451
$553$	−5.52454	−0.234927
$554$	34.5092	1.46615
$555$	0	0
$556$	19.0999	0.810018
$557$	40.5581	1.71850	0.859250	−	0.511556i	$-0.170931\pi$
$557$	40.5581	1.71850	0.859250	+	0.511556i	$0.170931\pi$
$558$	−4.69707	−0.198843
$559$	25.5995	1.08275
$560$	0	0
$561$	4.85384	0.204929
$562$	−45.4049	−1.91529
$563$	2.98878	0.125962	0.0629811	−	0.998015i	$-0.479939\pi$
$563$	2.98878	0.125962	0.0629811	+	0.998015i	$0.479939\pi$
$564$	−4.24521	−0.178755
$565$	0	0
$566$	−41.6076	−1.74890
$567$	−0.534565	−0.0224496
$568$	45.9632	1.92857
$569$	−7.61447	−0.319215	−0.159608	−	0.987181i	$-0.551023\pi$
$569$	−7.61447	−0.319215	−0.159608	+	0.987181i	$0.551023\pi$
$570$	0	0
$571$	30.1648	1.26236	0.631180	−	0.775637i	$-0.282571\pi$
$571$	30.1648	1.26236	0.631180	+	0.775637i	$0.282571\pi$
$572$	52.7417	2.20524
$573$	3.81549	0.159394
$574$	6.62429	0.276493
$575$	0	0
$576$	−4.56176	−0.190073
$577$	26.8905	1.11947	0.559733	−	0.828673i	$-0.310904\pi$
$577$	26.8905	1.11947	0.559733	+	0.828673i	$0.310904\pi$
$578$	−31.1675	−1.29640
$579$	−15.4332	−0.641382
$580$	0	0
$581$	0.444412	0.0184373
$582$	−27.1437	−1.12514
$583$	12.7168	0.526677
$584$	70.7977	2.92963
$585$	0	0
$586$	70.9855	2.93238
$587$	16.4626	0.679483	0.339741	−	0.940519i	$-0.389660\pi$
$587$	16.4626	0.679483	0.339741	+	0.940519i	$0.389660\pi$
$588$	−28.5033	−1.17546
$589$	1.91600	0.0789472
$590$	0	0
$591$	−22.7445	−0.935586
$592$	−13.5565	−0.557170
$593$	6.36681	0.261453	0.130727	−	0.991418i	$-0.458269\pi$
$593$	6.36681	0.261453	0.130727	+	0.991418i	$0.458269\pi$
$594$	5.70028	0.233885
$595$	0	0
$596$	−49.6076	−2.03201
$597$	−15.8679	−0.649431
$598$	−109.690	−4.48554
$599$	−7.18507	−0.293574	−0.146787	−	0.989168i	$-0.546893\pi$
$599$	−7.18507	−0.293574	−0.146787	+	0.989168i	$0.546893\pi$
$600$	0	0
$601$	−2.00970	−0.0819774	−0.0409887	−	0.999160i	$-0.513051\pi$
$601$	−2.00970	−0.0819774	−0.0409887	+	0.999160i	$0.513051\pi$
$602$	−6.27875	−0.255903
$603$	−7.39089	−0.300980
$604$	−25.0780	−1.02041
$605$	0	0
$606$	−27.3698	−1.11182
$607$	−5.58993	−0.226888	−0.113444	−	0.993544i	$-0.536188\pi$
$607$	−5.58993	−0.226888	−0.113444	+	0.993544i	$0.536188\pi$
$608$	−2.65183	−0.107546
$609$	−2.52851	−0.102460
$610$	0	0
$611$	−5.44670	−0.220350
$612$	9.03361	0.365162
$613$	−30.4403	−1.22947	−0.614737	−	0.788732i	$-0.710738\pi$
$613$	−30.4403	−1.22947	−0.614737	+	0.788732i	$0.710738\pi$
$614$	−25.3942	−1.02483
$615$	0	0
$616$	−6.84153	−0.275653
$617$	38.2716	1.54076	0.770379	−	0.637587i	$-0.220067\pi$
$617$	38.2716	1.54076	0.770379	+	0.637587i	$0.220067\pi$
$618$	20.1942	0.812330
$619$	9.72912	0.391046	0.195523	−	0.980699i	$-0.437360\pi$
$619$	9.72912	0.391046	0.195523	+	0.980699i	$0.437360\pi$
$620$	0	0
$621$	−8.05859	−0.323380
$622$	−10.9484	−0.438992
$623$	−4.13081	−0.165498
$624$	30.1277	1.20607
$625$	0	0
$626$	−23.0022	−0.919354
$627$	−2.32522	−0.0928602
$628$	−40.1288	−1.60131
$629$	−5.21529	−0.207947
$630$	0	0
$631$	13.2554	0.527690	0.263845	−	0.964565i	$-0.415009\pi$
$631$	13.2554	0.527690	0.263845	+	0.964565i	$0.415009\pi$
$632$	57.9862	2.30657
$633$	3.08924	0.122786
$634$	2.75575	0.109445
$635$	0	0
$636$	23.6676	0.938483
$637$	−36.5704	−1.44897
$638$	26.9625	1.06746
$639$	8.19182	0.324063
$640$	0	0
$641$	50.2447	1.98455	0.992273	−	0.124073i	$-0.0395958\pi$
$641$	50.2447	1.98455	0.992273	+	0.124073i	$0.0395958\pi$
$642$	32.7202	1.29136
$643$	46.1775	1.82106	0.910531	−	0.413440i	$-0.135673\pi$
$643$	46.1775	1.82106	0.910531	+	0.413440i	$0.135673\pi$
$644$	18.2877	0.720635
$645$	0	0
$646$	−5.42097	−0.213285
$647$	−1.21338	−0.0477029	−0.0238514	−	0.999716i	$-0.507593\pi$
$647$	−1.21338	−0.0477029	−0.0238514	+	0.999716i	$0.507593\pi$
$648$	5.61086	0.220416
$649$	7.50694	0.294673
$650$	0	0
$651$	1.00474	0.0393789
$652$	77.5079	3.03545
$653$	−36.4118	−1.42490	−0.712451	−	0.701722i	$-0.752415\pi$
$653$	−36.4118	−1.42490	−0.712451	+	0.701722i	$0.752415\pi$
$654$	−10.1560	−0.397131
$655$	0	0
$656$	−27.4282	−1.07089
$657$	12.6180	0.492274
$658$	1.33590	0.0520788
$659$	−14.4444	−0.562675	−0.281337	−	0.959609i	$-0.590778\pi$
$659$	−14.4444	−0.562675	−0.281337	+	0.959609i	$0.590778\pi$
$660$	0	0
$661$	30.1849	1.17406	0.587028	−	0.809567i	$-0.300298\pi$
$661$	30.1849	1.17406	0.587028	+	0.809567i	$0.300298\pi$
$662$	−69.7358	−2.71036
$663$	11.5903	0.450131
$664$	−4.66460	−0.181022
$665$	0	0
$666$	−6.12476	−0.237330
$667$	−38.1174	−1.47591
$668$	12.2024	0.472124
$669$	−5.16188	−0.199570
$670$	0	0
$671$	−19.0947	−0.737142
$672$	−1.39061	−0.0536440
$673$	15.7377	0.606643	0.303322	−	0.952888i	$-0.401904\pi$
$673$	15.7377	0.606643	0.303322	+	0.952888i	$0.401904\pi$
$674$	−48.7864	−1.87918
$675$	0	0
$676$	70.7527	2.72126
$677$	10.1309	0.389361	0.194680	−	0.980867i	$-0.437633\pi$
$677$	10.1309	0.389361	0.194680	+	0.980867i	$0.437633\pi$
$678$	10.0582	0.386284
$679$	5.80625	0.222824
$680$	0	0
$681$	14.5232	0.556529
$682$	−10.7139	−0.410258
$683$	−12.3973	−0.474369	−0.237185	−	0.971465i	$-0.576225\pi$
$683$	−12.3973	−0.474369	−0.237185	+	0.971465i	$0.576225\pi$
$684$	−4.32753	−0.165467
$685$	0	0
$686$	18.3209	0.699494
$687$	−12.1255	−0.462616
$688$	25.9975	0.991146
$689$	30.3661	1.15686
$690$	0	0
$691$	4.27653	0.162687	0.0813434	−	0.996686i	$-0.474079\pi$
$691$	4.27653	0.162687	0.0813434	+	0.996686i	$0.474079\pi$
$692$	−36.9820	−1.40585
$693$	−1.21934	−0.0463187
$694$	1.47323	0.0559229
$695$	0	0
$696$	26.5396	1.00598
$697$	−10.5518	−0.399679
$698$	−48.6711	−1.84223
$699$	−2.73012	−0.103262
$700$	0	0
$701$	−5.73609	−0.216649	−0.108325	−	0.994116i	$-0.534549\pi$
$701$	−5.73609	−0.216649	−0.108325	+	0.994116i	$0.534549\pi$
$702$	13.6115	0.513734
$703$	2.49837	0.0942278
$704$	−10.4053	−0.392165
$705$	0	0
$706$	39.4194	1.48357
$707$	5.85461	0.220185
$708$	13.9714	0.525077
$709$	2.93799	0.110338	0.0551692	−	0.998477i	$-0.482430\pi$
$709$	2.93799	0.110338	0.0551692	+	0.998477i	$0.482430\pi$
$710$	0	0
$711$	10.3346	0.387579
$712$	43.3575	1.62489
$713$	15.1465	0.567241
$714$	−2.84274	−0.106387
$715$	0	0
$716$	59.4148	2.22044
$717$	−23.9431	−0.894173
$718$	54.4894	2.03353
$719$	−22.5548	−0.841153	−0.420576	−	0.907257i	$-0.638172\pi$
$719$	−22.5548	−0.841153	−0.420576	+	0.907257i	$0.638172\pi$
$720$	0	0
$721$	−4.31971	−0.160874
$722$	−44.8849	−1.67044
$723$	−12.7368	−0.473688
$724$	18.0238	0.669849
$725$	0	0
$726$	−14.4872	−0.537671
$727$	−38.9515	−1.44463	−0.722315	−	0.691564i	$-0.756922\pi$
$727$	−38.9515	−1.44463	−0.722315	+	0.691564i	$0.756922\pi$
$728$	−16.3367	−0.605477
$729$	1.00000	0.0370370
$730$	0	0
$731$	10.0014	0.369916
$732$	−35.5377	−1.31351
$733$	−14.7475	−0.544712	−0.272356	−	0.962197i	$-0.587803\pi$
$733$	−14.7475	−0.544712	−0.272356	+	0.962197i	$0.587803\pi$
$734$	76.1817	2.81192
$735$	0	0
$736$	−20.9635	−0.772725
$737$	−16.8585	−0.620991
$738$	−12.3919	−0.456153
$739$	−53.0480	−1.95140	−0.975701	−	0.219106i	$-0.929686\pi$
$739$	−53.0480	−1.95140	−0.975701	+	0.219106i	$0.929686\pi$
$740$	0	0
$741$	−5.55231	−0.203969
$742$	−7.44784	−0.273419
$743$	33.5240	1.22988	0.614938	−	0.788575i	$-0.289181\pi$
$743$	33.5240	1.22988	0.614938	+	0.788575i	$0.289181\pi$
$744$	−10.5459	−0.386631
$745$	0	0
$746$	−25.0695	−0.917859
$747$	−0.831352	−0.0304176
$748$	20.6055	0.753413
$749$	−6.99911	−0.255742
$750$	0	0
$751$	−0.260686	−0.00951257	−0.00475628	−	0.999989i	$-0.501514\pi$
$751$	−0.260686	−0.00951257	−0.00475628	+	0.999989i	$0.501514\pi$
$752$	−5.53137	−0.201708
$753$	4.59985	0.167628
$754$	64.3829	2.34469
$755$	0	0
$756$	−2.26934	−0.0825351
$757$	43.1169	1.56711	0.783556	−	0.621321i	$-0.213404\pi$
$757$	43.1169	1.56711	0.783556	+	0.621321i	$0.213404\pi$
$758$	1.61664	0.0587191
$759$	−18.3815	−0.667207
$760$	0	0
$761$	20.5755	0.745861	0.372930	−	0.927859i	$-0.378353\pi$
$761$	20.5755	0.745861	0.372930	+	0.927859i	$0.378353\pi$
$762$	−24.8126	−0.898867
$763$	2.17245	0.0786480
$764$	16.1975	0.586006
$765$	0	0
$766$	93.8194	3.38983
$767$	17.9256	0.647256
$768$	−32.3676	−1.16796
$769$	2.30150	0.0829943	0.0414971	−	0.999139i	$-0.486787\pi$
$769$	2.30150	0.0829943	0.0414971	+	0.999139i	$0.486787\pi$
$770$	0	0
$771$	−21.4598	−0.772855
$772$	−65.5171	−2.35801
$773$	38.5028	1.38485	0.692424	−	0.721490i	$-0.256543\pi$
$773$	38.5028	1.38485	0.692424	+	0.721490i	$0.256543\pi$
$774$	11.7455	0.422184
$775$	0	0
$776$	−60.9432	−2.18773
$777$	1.31014	0.0470009
$778$	−61.6358	−2.20975
$779$	5.05483	0.181108
$780$	0	0
$781$	18.6854	0.668617
$782$	−42.8544	−1.53247
$783$	4.73003	0.169038
$784$	−37.1389	−1.32639
$785$	0	0
$786$	−13.5221	−0.482318
$787$	38.4647	1.37112	0.685559	−	0.728017i	$-0.259558\pi$
$787$	38.4647	1.37112	0.685559	+	0.728017i	$0.259558\pi$
$788$	−96.5553	−3.43964
$789$	26.4842	0.942861
$790$	0	0
$791$	−2.15154	−0.0764998
$792$	12.7983	0.454768
$793$	−45.5956	−1.61915
$794$	83.4040	2.95990
$795$	0	0
$796$	−67.3626	−2.38760
$797$	−42.3166	−1.49893	−0.749466	−	0.662043i	$-0.769690\pi$
$797$	−42.3166	−1.49893	−0.749466	+	0.662043i	$0.769690\pi$
$798$	1.36181	0.0482074
$799$	−2.12796	−0.0752817
$800$	0	0
$801$	7.72743	0.273035
$802$	−19.0895	−0.674074
$803$	28.7814	1.01567
$804$	−31.3759	−1.10654
$805$	0	0
$806$	−25.5835	−0.901141
$807$	−18.9269	−0.666258
$808$	−61.4508	−2.16183
$809$	49.4881	1.73991	0.869954	−	0.493133i	$-0.164148\pi$
$809$	49.4881	1.73991	0.869954	+	0.493133i	$0.164148\pi$
$810$	0	0
$811$	−30.7904	−1.08120	−0.540599	−	0.841280i	$-0.681802\pi$
$811$	−30.7904	−1.08120	−0.540599	+	0.841280i	$0.681802\pi$
$812$	−10.7341	−0.376691
$813$	3.58283	0.125655
$814$	−13.9705	−0.489665
$815$	0	0
$816$	11.7705	0.412050
$817$	−4.79115	−0.167621
$818$	80.2153	2.80466
$819$	−2.91161	−0.101740
$820$	0	0
$821$	−0.559250	−0.0195180	−0.00975898	−	0.999952i	$-0.503106\pi$
$821$	−0.559250	−0.0195180	−0.00975898	+	0.999952i	$0.503106\pi$
$822$	−40.2913	−1.40532
$823$	−15.8192	−0.551422	−0.275711	−	0.961241i	$-0.588913\pi$
$823$	−15.8192	−0.551422	−0.275711	+	0.961241i	$0.588913\pi$
$824$	45.3402	1.57950
$825$	0	0
$826$	−4.39658	−0.152977
$827$	20.0715	0.697955	0.348978	−	0.937131i	$-0.386529\pi$
$827$	20.0715	0.697955	0.348978	+	0.937131i	$0.386529\pi$
$828$	−34.2104	−1.18889
$829$	−15.2956	−0.531238	−0.265619	−	0.964078i	$-0.585576\pi$
$829$	−15.2956	−0.531238	−0.265619	+	0.964078i	$0.585576\pi$
$830$	0	0
$831$	13.8090	0.479027
$832$	−24.8465	−0.861398
$833$	−14.2876	−0.495036
$834$	11.2436	0.389335
$835$	0	0
$836$	−9.87103	−0.341397
$837$	−1.87955	−0.0649667
$838$	−25.5705	−0.883317
$839$	−0.0490414	−0.00169310	−0.000846549	−	1.00000i	$-0.500269\pi$
$839$	−0.0490414	−0.00169310	−0.000846549		1.00000i	$0.500269\pi$
$840$	0	0
$841$	−6.62679	−0.228510
$842$	−96.2142	−3.31576
$843$	−18.1689	−0.625771
$844$	13.1145	0.451419
$845$	0	0
$846$	−2.49904	−0.0859188
$847$	3.09893	0.106481
$848$	30.8382	1.05899
$849$	−16.6494	−0.571406
$850$	0	0
$851$	19.7503	0.677033
$852$	34.7760	1.19141
$853$	−54.4712	−1.86506	−0.932529	−	0.361095i	$-0.882403\pi$
$853$	−54.4712	−1.86506	−0.932529	+	0.361095i	$0.882403\pi$
$854$	11.1832	0.382680
$855$	0	0
$856$	73.4636	2.51093
$857$	40.2657	1.37545	0.687725	−	0.725971i	$-0.258609\pi$
$857$	40.2657	1.37545	0.687725	+	0.725971i	$0.258609\pi$
$858$	31.0477	1.05995
$859$	−27.0404	−0.922608	−0.461304	−	0.887242i	$-0.652618\pi$
$859$	−27.0404	−0.922608	−0.461304	+	0.887242i	$0.652618\pi$
$860$	0	0
$861$	2.65073	0.0903368
$862$	−39.2480	−1.33679
$863$	−53.4320	−1.81885	−0.909424	−	0.415871i	$-0.863477\pi$
$863$	−53.4320	−1.81885	−0.909424	+	0.415871i	$0.863477\pi$
$864$	2.60139	0.0885010
$865$	0	0
$866$	85.0254	2.88928
$867$	−12.4718	−0.423565
$868$	4.26534	0.144775
$869$	23.5731	0.799664
$870$	0	0
$871$	−40.2559	−1.36402
$872$	−22.8023	−0.772184
$873$	−10.8616	−0.367611
$874$	20.5293	0.694413
$875$	0	0
$876$	53.5659	1.80982
$877$	−17.1595	−0.579434	−0.289717	−	0.957112i	$-0.593561\pi$
$877$	−17.1595	−0.579434	−0.289717	+	0.957112i	$0.593561\pi$
$878$	−10.7785	−0.363757
$879$	28.4051	0.958080
$880$	0	0
$881$	−12.9987	−0.437938	−0.218969	−	0.975732i	$-0.570269\pi$
$881$	−12.9987	−0.437938	−0.218969	+	0.975732i	$0.570269\pi$
$882$	−16.7792	−0.564984
$883$	53.7882	1.81012	0.905059	−	0.425286i	$-0.139827\pi$
$883$	53.7882	1.81012	0.905059	+	0.425286i	$0.139827\pi$
$884$	49.2034	1.65489
$885$	0	0
$886$	−38.5376	−1.29470
$887$	32.3554	1.08639	0.543194	−	0.839607i	$-0.317215\pi$
$887$	32.3554	1.08639	0.543194	+	0.839607i	$0.317215\pi$
$888$	−13.7514	−0.461465
$889$	5.30762	0.178012
$890$	0	0
$891$	2.28099	0.0764159
$892$	−21.9132	−0.733709
$893$	1.01939	0.0341126
$894$	−29.2027	−0.976684
$895$	0	0
$896$	8.87528	0.296502
$897$	−43.8927	−1.46553
$898$	80.6288	2.69062
$899$	−8.89033	−0.296509
$900$	0	0
$901$	11.8637	0.395236
$902$	−28.2658	−0.941148
$903$	−2.51246	−0.0836096
$904$	22.5828	0.751093
$905$	0	0
$906$	−14.7628	−0.490460
$907$	19.3851	0.643672	0.321836	−	0.946795i	$-0.395700\pi$
$907$	19.3851	0.643672	0.321836	+	0.946795i	$0.395700\pi$
$908$	61.6539	2.04606
$909$	−10.9521	−0.363258
$910$	0	0
$911$	11.3571	0.376278	0.188139	−	0.982142i	$-0.439754\pi$
$911$	11.3571	0.376278	0.188139	+	0.982142i	$0.439754\pi$
$912$	−5.63863	−0.186714
$913$	−1.89630	−0.0627584
$914$	72.9258	2.41217
$915$	0	0
$916$	−51.4752	−1.70079
$917$	2.89249	0.0955184
$918$	5.31785	0.175515
$919$	−55.9635	−1.84607	−0.923033	−	0.384721i	$-0.874298\pi$
$919$	−55.9635	−1.84607	−0.923033	+	0.384721i	$0.874298\pi$
$920$	0	0
$921$	−10.1616	−0.334835
$922$	7.70034	0.253597
$923$	44.6184	1.46863
$924$	−5.17633	−0.170289
$925$	0	0
$926$	75.6137	2.48482
$927$	8.08078	0.265408
$928$	12.3047	0.403920
$929$	−17.0374	−0.558977	−0.279489	−	0.960149i	$-0.590165\pi$
$929$	−17.0374	−0.558977	−0.279489	+	0.960149i	$0.590165\pi$
$930$	0	0
$931$	6.84444	0.224317
$932$	−11.5899	−0.379640
$933$	−4.38105	−0.143429
$934$	−58.4521	−1.91261
$935$	0	0
$936$	30.5607	0.998907
$937$	−49.0016	−1.60081	−0.800406	−	0.599458i	$-0.795383\pi$
$937$	−49.0016	−1.60081	−0.800406	+	0.599458i	$0.795383\pi$
$938$	9.87350	0.322381
$939$	−9.20443	−0.300375
$940$	0	0
$941$	10.6230	0.346300	0.173150	−	0.984895i	$-0.444605\pi$
$941$	10.6230	0.346300	0.173150	+	0.984895i	$0.444605\pi$
$942$	−23.6228	−0.769672
$943$	39.9599	1.30127
$944$	18.2043	0.592499
$945$	0	0
$946$	26.7914	0.871063
$947$	18.3187	0.595276	0.297638	−	0.954679i	$-0.403801\pi$
$947$	18.3187	0.595276	0.297638	+	0.954679i	$0.403801\pi$
$948$	43.8727	1.42492
$949$	68.7263	2.23095
$950$	0	0
$951$	1.10272	0.0357583
$952$	−6.38253	−0.206859
$953$	−17.9940	−0.582884	−0.291442	−	0.956589i	$-0.594135\pi$
$953$	−17.9940	−0.582884	−0.291442	+	0.956589i	$0.594135\pi$
$954$	13.9325	0.451082
$955$	0	0
$956$	−101.644	−3.28739
$957$	10.7891	0.348763
$958$	56.3753	1.82140
$959$	8.61865	0.278311
$960$	0	0
$961$	−27.4673	−0.886042
$962$	−33.3597	−1.07556
$963$	13.0931	0.421919
$964$	−54.0705	−1.74149
$965$	0	0
$966$	10.7655	0.346373
$967$	−46.1004	−1.48249	−0.741245	−	0.671234i	$-0.765764\pi$
$967$	−46.1004	−1.48249	−0.741245	+	0.671234i	$0.765764\pi$
$968$	−32.5268	−1.04545
$969$	−2.16922	−0.0696854
$970$	0	0
$971$	−13.7544	−0.441400	−0.220700	−	0.975342i	$-0.570834\pi$
$971$	−13.7544	−0.441400	−0.220700	+	0.975342i	$0.570834\pi$
$972$	4.24521	0.136165
$973$	−2.40510	−0.0771041
$974$	−27.6456	−0.885822
$975$	0	0
$976$	−46.3044	−1.48217
$977$	3.00336	0.0960861	0.0480431	−	0.998845i	$-0.484702\pi$
$977$	3.00336	0.0960861	0.0480431	+	0.998845i	$0.484702\pi$
$978$	45.6269	1.45899
$979$	17.6261	0.563334
$980$	0	0
$981$	−4.06396	−0.129752
$982$	−20.5259	−0.655008
$983$	−15.1968	−0.484702	−0.242351	−	0.970189i	$-0.577919\pi$
$983$	−15.1968	−0.484702	−0.242351	+	0.970189i	$0.577919\pi$
$984$	−27.8224	−0.886947
$985$	0	0
$986$	25.1536	0.801054
$987$	0.534565	0.0170154
$988$	−23.5707	−0.749885
$989$	−37.8755	−1.20437
$990$	0	0
$991$	37.3755	1.18727	0.593636	−	0.804734i	$-0.297692\pi$
$991$	37.3755	1.18727	0.593636	+	0.804734i	$0.297692\pi$
$992$	−4.88944	−0.155240
$993$	−27.9050	−0.885540
$994$	−10.9435	−0.347105
$995$	0	0
$996$	−3.52926	−0.111829
$997$	2.60342	0.0824511	0.0412256	−	0.999150i	$-0.486874\pi$
$997$	2.60342	0.0824511	0.0412256	+	0.999150i	$0.486874\pi$
$998$	74.0891	2.34525
$999$	−2.45084	−0.0775413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bc.1.7	yes	7
5.4	even	2		3525.2.a.x.1.1	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.x.1.1	✓	7	5.4	even	2
3525.2.a.bc.1.7	yes	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49904 q^{2} +1.00000 q^{3} +4.24521 q^{4} +2.49904 q^{6} -0.534565 q^{7} +5.61086 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.49904 q^{2} +1.00000 q^{3} +4.24521 q^{4} +2.49904 q^{6} -0.534565 q^{7} +5.61086 q^{8} +1.00000 q^{9} +2.28099 q^{11} +4.24521 q^{12} +5.44670 q^{13} -1.33590 q^{14} +5.53137 q^{16} +2.12796 q^{17} +2.49904 q^{18} -1.01939 q^{19} -0.534565 q^{21} +5.70028 q^{22} -8.05859 q^{23} +5.61086 q^{24} +13.6115 q^{26} +1.00000 q^{27} -2.26934 q^{28} +4.73003 q^{29} -1.87955 q^{31} +2.60139 q^{32} +2.28099 q^{33} +5.31785 q^{34} +4.24521 q^{36} -2.45084 q^{37} -2.54750 q^{38} +5.44670 q^{39} -4.95867 q^{41} -1.33590 q^{42} +4.70001 q^{43} +9.68325 q^{44} -20.1387 q^{46} -1.00000 q^{47} +5.53137 q^{48} -6.71424 q^{49} +2.12796 q^{51} +23.1224 q^{52} +5.57514 q^{53} +2.49904 q^{54} -2.99937 q^{56} -1.01939 q^{57} +11.8205 q^{58} +3.29110 q^{59} -8.37125 q^{61} -4.69707 q^{62} -0.534565 q^{63} -4.56176 q^{64} +5.70028 q^{66} -7.39089 q^{67} +9.03361 q^{68} -8.05859 q^{69} +8.19182 q^{71} +5.61086 q^{72} +12.6180 q^{73} -6.12476 q^{74} -4.32753 q^{76} -1.21934 q^{77} +13.6115 q^{78} +10.3346 q^{79} +1.00000 q^{81} -12.3919 q^{82} -0.831352 q^{83} -2.26934 q^{84} +11.7455 q^{86} +4.73003 q^{87} +12.7983 q^{88} +7.72743 q^{89} -2.91161 q^{91} -34.2104 q^{92} -1.87955 q^{93} -2.49904 q^{94} +2.60139 q^{96} -10.8616 q^{97} -16.7792 q^{98} +2.28099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 5 q^{4} + 3 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 4 q^{11} + 5 q^{12} + 5 q^{13} + 5 q^{14} + 9 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} + 10 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{26} + 7 q^{27} + 2 q^{28} + 9 q^{29} + 3 q^{31} + 4 q^{33} - 20 q^{34} + 5 q^{36} + 9 q^{37} - 2 q^{38} + 5 q^{39} + 20 q^{41} + 5 q^{42} + 16 q^{43} - 5 q^{44} - q^{46} - 7 q^{47} + 9 q^{48} - 10 q^{49} + 10 q^{51} + 21 q^{52} + 3 q^{54} + 21 q^{56} + q^{57} + 19 q^{58} + 18 q^{59} - 2 q^{62} + 5 q^{63} - 30 q^{64} + 10 q^{66} + 8 q^{67} + 20 q^{68} + 10 q^{69} + 14 q^{71} + 6 q^{72} + 4 q^{73} - 17 q^{74} + 12 q^{76} + 2 q^{77} + 12 q^{78} - 21 q^{79} + 7 q^{81} - 7 q^{82} + 22 q^{83} + 2 q^{84} + 35 q^{86} + 9 q^{87} + 14 q^{88} + 2 q^{89} - 2 q^{91} + 5 q^{92} + 3 q^{93} - 3 q^{94} + 12 q^{97} + 30 q^{98} + 4 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 + 3 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 4 * q^11 + 5 * q^12 + 5 * q^13 + 5 * q^14 + 9 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + 5 * q^21 + 10 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^26 + 7 * q^27 + 2 * q^28 + 9 * q^29 + 3 * q^31 + 4 * q^33 - 20 * q^34 + 5 * q^36 + 9 * q^37 - 2 * q^38 + 5 * q^39 + 20 * q^41 + 5 * q^42 + 16 * q^43 - 5 * q^44 - q^46 - 7 * q^47 + 9 * q^48 - 10 * q^49 + 10 * q^51 + 21 * q^52 + 3 * q^54 + 21 * q^56 + q^57 + 19 * q^58 + 18 * q^59 - 2 * q^62 + 5 * q^63 - 30 * q^64 + 10 * q^66 + 8 * q^67 + 20 * q^68 + 10 * q^69 + 14 * q^71 + 6 * q^72 + 4 * q^73 - 17 * q^74 + 12 * q^76 + 2 * q^77 + 12 * q^78 - 21 * q^79 + 7 * q^81 - 7 * q^82 + 22 * q^83 + 2 * q^84 + 35 * q^86 + 9 * q^87 + 14 * q^88 + 2 * q^89 - 2 * q^91 + 5 * q^92 + 3 * q^93 - 3 * q^94 + 12 * q^97 + 30 * q^98 + 4 * q^99

Introduction

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