LMFDB - Embedded newform 1875.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.4
Root			$1.33826$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} -1.82709 q^{6} -1.44512 q^{7} -1.20906 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} -1.82709 q^{6} -1.44512 q^{7} -1.20906 q^{8} +1.00000 q^{9} -2.12920 q^{11} -1.33826 q^{12} +5.70353 q^{13} -2.64037 q^{14} -4.88558 q^{16} -4.15622 q^{17} +1.82709 q^{18} +1.70353 q^{19} +1.44512 q^{21} -3.89025 q^{22} +0.323478 q^{23} +1.20906 q^{24} +10.4209 q^{26} -1.00000 q^{27} -1.93395 q^{28} -8.74724 q^{29} -8.45991 q^{31} -6.50828 q^{32} +2.12920 q^{33} -7.59378 q^{34} +1.33826 q^{36} -1.75170 q^{37} +3.11251 q^{38} -5.70353 q^{39} -6.87802 q^{41} +2.64037 q^{42} +11.1411 q^{43} -2.84943 q^{44} +0.591023 q^{46} -12.5982 q^{47} +4.88558 q^{48} -4.91161 q^{49} +4.15622 q^{51} +7.63282 q^{52} -8.34451 q^{53} -1.82709 q^{54} +1.74724 q^{56} -1.70353 q^{57} -15.9820 q^{58} -2.12474 q^{59} -5.38952 q^{61} -15.4570 q^{62} -1.44512 q^{63} -2.12007 q^{64} +3.89025 q^{66} +7.13078 q^{67} -5.56210 q^{68} -0.323478 q^{69} +2.67461 q^{71} -1.20906 q^{72} -6.28253 q^{73} -3.20052 q^{74} +2.27977 q^{76} +3.07697 q^{77} -10.4209 q^{78} +8.37092 q^{79} +1.00000 q^{81} -12.5668 q^{82} +14.5872 q^{83} +1.93395 q^{84} +20.3558 q^{86} +8.74724 q^{87} +2.57433 q^{88} +2.68119 q^{89} -8.24232 q^{91} +0.432897 q^{92} +8.45991 q^{93} -23.0181 q^{94} +6.50828 q^{96} -8.55105 q^{97} -8.97397 q^{98} -2.12920 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9} - 6 q^{11} - q^{12} + 7 q^{13} - 10 q^{14} - 9 q^{16} - 7 q^{17} + q^{18} - 9 q^{19} - 5 q^{21} + 6 q^{22} + 10 q^{23} + 3 q^{24} - 2 q^{26} - 4 q^{27} + 5 q^{28} - 28 q^{29} - 10 q^{31} + 6 q^{33} + 7 q^{34} + q^{36} - 10 q^{37} - 6 q^{38} - 7 q^{39} + 10 q^{42} + q^{43} - 9 q^{44} + 5 q^{46} - 23 q^{47} + 9 q^{48} - 3 q^{49} + 7 q^{51} + 13 q^{52} - q^{54} + 9 q^{57} - 2 q^{58} + 4 q^{59} - 43 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} - 6 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 27 q^{71} - 3 q^{72} + 15 q^{73} + 5 q^{74} + 9 q^{76} - 15 q^{77} + 2 q^{78} + 10 q^{79} + 4 q^{81} - 20 q^{82} + 3 q^{83} - 5 q^{84} + 24 q^{86} + 28 q^{87} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 15 q^{92} + 10 q^{93} - 22 q^{94} + 13 q^{97} - 42 q^{98} - 6 q^{99}+O(q^{100}) $ 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9 - 6 * q^11 - q^12 + 7 * q^13 - 10 * q^14 - 9 * q^16 - 7 * q^17 + q^18 - 9 * q^19 - 5 * q^21 + 6 * q^22 + 10 * q^23 + 3 * q^24 - 2 * q^26 - 4 * q^27 + 5 * q^28 - 28 * q^29 - 10 * q^31 + 6 * q^33 + 7 * q^34 + q^36 - 10 * q^37 - 6 * q^38 - 7 * q^39 + 10 * q^42 + q^43 - 9 * q^44 + 5 * q^46 - 23 * q^47 + 9 * q^48 - 3 * q^49 + 7 * q^51 + 13 * q^52 - q^54 + 9 * q^57 - 2 * q^58 + 4 * q^59 - 43 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 - 6 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 27 * q^71 - 3 * q^72 + 15 * q^73 + 5 * q^74 + 9 * q^76 - 15 * q^77 + 2 * q^78 + 10 * q^79 + 4 * q^81 - 20 * q^82 + 3 * q^83 - 5 * q^84 + 24 * q^86 + 28 * q^87 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 15 * q^92 + 10 * q^93 - 22 * q^94 + 13 * q^97 - 42 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.82709	1.29195	0.645974	−	0.763359i	$-0.276451\pi$
$2$	1.82709	1.29195	0.645974	+	0.763359i	$0.276451\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.33826	0.669131
$5$	0	0
$5$	0	0
$6$	−1.82709	−0.745907
$7$	−1.44512	−0.546206	−0.273103	−	0.961985i	$-0.588050\pi$
$7$	−1.44512	−0.546206	−0.273103	+	0.961985i	$0.588050\pi$
$8$	−1.20906	−0.427466
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.12920	−0.641979	−0.320990	−	0.947083i	$-0.604015\pi$
$11$	−2.12920	−0.641979	−0.320990	+	0.947083i	$0.604015\pi$
$12$	−1.33826	−0.386323
$13$	5.70353	1.58188	0.790938	−	0.611897i	$-0.209593\pi$
$13$	5.70353	1.58188	0.790938	+	0.611897i	$0.209593\pi$
$14$	−2.64037	−0.705670
$15$	0	0
$16$	−4.88558	−1.22139
$17$	−4.15622	−1.00803	−0.504015	−	0.863695i	$-0.668144\pi$
$17$	−4.15622	−1.00803	−0.504015	+	0.863695i	$0.668144\pi$
$18$	1.82709	0.430649
$19$	1.70353	0.390817	0.195409	−	0.980722i	$-0.437397\pi$
$19$	1.70353	0.390817	0.195409	+	0.980722i	$0.437397\pi$
$20$	0	0
$21$	1.44512	0.315352
$22$	−3.89025	−0.829404
$23$	0.323478	0.0674497	0.0337249	−	0.999431i	$-0.489263\pi$
$23$	0.323478	0.0674497	0.0337249	+	0.999431i	$0.489263\pi$
$24$	1.20906	0.246798
$25$	0	0
$26$	10.4209	2.04370
$27$	−1.00000	−0.192450
$28$	−1.93395	−0.365483
$29$	−8.74724	−1.62432	−0.812161	−	0.583434i	$-0.801709\pi$
$29$	−8.74724	−1.62432	−0.812161	+	0.583434i	$0.801709\pi$
$30$	0	0
$31$	−8.45991	−1.51944	−0.759722	−	0.650248i	$-0.774665\pi$
$31$	−8.45991	−1.51944	−0.759722	+	0.650248i	$0.774665\pi$
$32$	−6.50828	−1.15051
$33$	2.12920	0.370647
$34$	−7.59378	−1.30232
$35$	0	0
$36$	1.33826	0.223044
$37$	−1.75170	−0.287978	−0.143989	−	0.989579i	$-0.545993\pi$
$37$	−1.75170	−0.287978	−0.143989	+	0.989579i	$0.545993\pi$
$38$	3.11251	0.504916
$39$	−5.70353	−0.913296
$40$	0	0
$41$	−6.87802	−1.07417	−0.537083	−	0.843529i	$-0.680474\pi$
$41$	−6.87802	−1.07417	−0.537083	+	0.843529i	$0.680474\pi$
$42$	2.64037	0.407419
$43$	11.1411	1.69900	0.849501	−	0.527587i	$-0.176903\pi$
$43$	11.1411	1.69900	0.849501	+	0.527587i	$0.176903\pi$
$44$	−2.84943	−0.429568
$45$	0	0
$46$	0.591023	0.0871416
$47$	−12.5982	−1.83764	−0.918822	−	0.394673i	$-0.870858\pi$
$47$	−12.5982	−1.83764	−0.918822	+	0.394673i	$0.870858\pi$
$48$	4.88558	0.705173
$49$	−4.91161	−0.701659
$50$	0	0
$51$	4.15622	0.581987
$52$	7.63282	1.05848
$53$	−8.34451	−1.14621	−0.573103	−	0.819483i	$-0.694261\pi$
$53$	−8.34451	−1.14621	−0.573103	+	0.819483i	$0.694261\pi$
$54$	−1.82709	−0.248636
$55$	0	0
$56$	1.74724	0.233485
$57$	−1.70353	−0.225639
$58$	−15.9820	−2.09854
$59$	−2.12474	−0.276617	−0.138309	−	0.990389i	$-0.544167\pi$
$59$	−2.12474	−0.276617	−0.138309	+	0.990389i	$0.544167\pi$
$60$	0	0
$61$	−5.38952	−0.690058	−0.345029	−	0.938592i	$-0.612131\pi$
$61$	−5.38952	−0.690058	−0.345029	+	0.938592i	$0.612131\pi$
$62$	−15.4570	−1.96304
$63$	−1.44512	−0.182069
$64$	−2.12007	−0.265008
$65$	0	0
$66$	3.89025	0.478857
$67$	7.13078	0.871164	0.435582	−	0.900149i	$-0.356543\pi$
$67$	7.13078	0.871164	0.435582	+	0.900149i	$0.356543\pi$
$68$	−5.56210	−0.674504
$69$	−0.323478	−0.0389421
$70$	0	0
$71$	2.67461	0.317418	0.158709	−	0.987325i	$-0.449267\pi$
$71$	2.67461	0.317418	0.158709	+	0.987325i	$0.449267\pi$
$72$	−1.20906	−0.142489
$73$	−6.28253	−0.735315	−0.367657	−	0.929961i	$-0.619840\pi$
$73$	−6.28253	−0.735315	−0.367657	+	0.929961i	$0.619840\pi$
$74$	−3.20052	−0.372053
$75$	0	0
$76$	2.27977	0.261508
$77$	3.07697	0.350653
$78$	−10.4209	−1.17993
$79$	8.37092	0.941802	0.470901	−	0.882186i	$-0.343929\pi$
$79$	8.37092	0.941802	0.470901	+	0.882186i	$0.343929\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−12.5668	−1.38777
$83$	14.5872	1.60115	0.800577	−	0.599230i	$-0.204527\pi$
$83$	14.5872	1.60115	0.800577	+	0.599230i	$0.204527\pi$
$84$	1.93395	0.211012
$85$	0	0
$86$	20.3558	2.19502
$87$	8.74724	0.937802
$88$	2.57433	0.274424
$89$	2.68119	0.284206	0.142103	−	0.989852i	$-0.454614\pi$
$89$	2.68119	0.284206	0.142103	+	0.989852i	$0.454614\pi$
$90$	0	0
$91$	−8.24232	−0.864030
$92$	0.432897	0.0451327
$93$	8.45991	0.877252
$94$	−23.0181	−2.37414
$95$	0	0
$96$	6.50828	0.664249
$97$	−8.55105	−0.868228	−0.434114	−	0.900858i	$-0.642939\pi$
$97$	−8.55105	−0.868228	−0.434114	+	0.900858i	$0.642939\pi$
$98$	−8.97397	−0.906507
$99$	−2.12920	−0.213993
$100$	0	0
$101$	9.85377	0.980487	0.490243	−	0.871586i	$-0.336908\pi$
$101$	9.85377	0.980487	0.490243	+	0.871586i	$0.336908\pi$
$102$	7.59378	0.751897
$103$	16.1279	1.58913	0.794564	−	0.607180i	$-0.207699\pi$
$103$	16.1279	1.58913	0.794564	+	0.607180i	$0.207699\pi$
$104$	−6.89590	−0.676198
$105$	0	0
$106$	−15.2462	−1.48084
$107$	1.81198	0.175170	0.0875852	−	0.996157i	$-0.472085\pi$
$107$	1.81198	0.175170	0.0875852	+	0.996157i	$0.472085\pi$
$108$	−1.33826	−0.128774
$109$	−18.4646	−1.76859	−0.884293	−	0.466933i	$-0.845359\pi$
$109$	−18.4646	−1.76859	−0.884293	+	0.466933i	$0.845359\pi$
$110$	0	0
$111$	1.75170	0.166264
$112$	7.06027	0.667133
$113$	−13.3653	−1.25730	−0.628650	−	0.777689i	$-0.716392\pi$
$113$	−13.3653	−1.25730	−0.628650	+	0.777689i	$0.716392\pi$
$114$	−3.11251	−0.291513
$115$	0	0
$116$	−11.7061	−1.08688
$117$	5.70353	0.527292
$118$	−3.88209	−0.357375
$119$	6.00625	0.550592
$120$	0	0
$121$	−6.46649	−0.587863
$122$	−9.84715	−0.891519
$123$	6.87802	0.620170
$124$	−11.3216	−1.01671
$125$	0	0
$126$	−2.64037	−0.235223
$127$	−1.01381	−0.0899608	−0.0449804	−	0.998988i	$-0.514323\pi$
$127$	−1.01381	−0.0899608	−0.0449804	+	0.998988i	$0.514323\pi$
$128$	9.14301	0.808136
$129$	−11.1411	−0.980919
$130$	0	0
$131$	2.08550	0.182211	0.0911055	−	0.995841i	$-0.470960\pi$
$131$	2.08550	0.182211	0.0911055	+	0.995841i	$0.470960\pi$
$132$	2.84943	0.248011
$133$	−2.46182	−0.213467
$134$	13.0286	1.12550
$135$	0	0
$136$	5.02510	0.430899
$137$	16.9365	1.44698	0.723492	−	0.690333i	$-0.242536\pi$
$137$	16.9365	1.44698	0.723492	+	0.690333i	$0.242536\pi$
$138$	−0.591023	−0.0503112
$139$	14.8883	1.26281	0.631406	−	0.775452i	$-0.282478\pi$
$139$	14.8883	1.26281	0.631406	+	0.775452i	$0.282478\pi$
$140$	0	0
$141$	12.5982	1.06096
$142$	4.88676	0.410088
$143$	−12.1440	−1.01553
$144$	−4.88558	−0.407132
$145$	0	0
$146$	−11.4788	−0.949989
$147$	4.91161	0.405103
$148$	−2.34424	−0.192695
$149$	−4.70991	−0.385851	−0.192925	−	0.981213i	$-0.561798\pi$
$149$	−4.70991	−0.385851	−0.192925	+	0.981213i	$0.561798\pi$
$150$	0	0
$151$	−9.63091	−0.783752	−0.391876	−	0.920018i	$-0.628174\pi$
$151$	−9.63091	−0.783752	−0.391876	+	0.920018i	$0.628174\pi$
$152$	−2.05967	−0.167061
$153$	−4.15622	−0.336010
$154$	5.62190	0.453025
$155$	0	0
$156$	−7.63282	−0.611114
$157$	18.5557	1.48091	0.740454	−	0.672107i	$-0.234611\pi$
$157$	18.5557	1.48091	0.740454	+	0.672107i	$0.234611\pi$
$158$	15.2944	1.21676
$159$	8.34451	0.661763
$160$	0	0
$161$	−0.467465	−0.0368414
$162$	1.82709	0.143550
$163$	0.451705	0.0353803	0.0176902	−	0.999844i	$-0.494369\pi$
$163$	0.451705	0.0353803	0.0176902	+	0.999844i	$0.494369\pi$
$164$	−9.20459	−0.718758
$165$	0	0
$166$	26.6521	2.06861
$167$	4.72648	0.365746	0.182873	−	0.983137i	$-0.441460\pi$
$167$	4.72648	0.365746	0.182873	+	0.983137i	$0.441460\pi$
$168$	−1.74724	−0.134802
$169$	19.5303	1.50233
$170$	0	0
$171$	1.70353	0.130272
$172$	14.9097	1.13685
$173$	2.29489	0.174477	0.0872385	−	0.996187i	$-0.472196\pi$
$173$	2.29489	0.174477	0.0872385	+	0.996187i	$0.472196\pi$
$174$	15.9820	1.21159
$175$	0	0
$176$	10.4024	0.784110
$177$	2.12474	0.159705
$178$	4.89878	0.367179
$179$	2.68757	0.200878	0.100439	−	0.994943i	$-0.467975\pi$
$179$	2.68757	0.200878	0.100439	+	0.994943i	$0.467975\pi$
$180$	0	0
$181$	−23.9088	−1.77712	−0.888562	−	0.458756i	$-0.848295\pi$
$181$	−23.9088	−1.77712	−0.888562	+	0.458756i	$0.848295\pi$
$182$	−15.0595	−1.11628
$183$	5.38952	0.398405
$184$	−0.391103	−0.0288325
$185$	0	0
$186$	15.4570	1.13336
$187$	8.84943	0.647135
$188$	−16.8597	−1.22962
$189$	1.44512	0.105117
$190$	0	0
$191$	−3.91824	−0.283514	−0.141757	−	0.989902i	$-0.545275\pi$
$191$	−3.91824	−0.283514	−0.141757	+	0.989902i	$0.545275\pi$
$192$	2.12007	0.153003
$193$	−8.54752	−0.615264	−0.307632	−	0.951505i	$-0.599537\pi$
$193$	−8.54752	−0.615264	−0.307632	+	0.951505i	$0.599537\pi$
$194$	−15.6236	−1.12171
$195$	0	0
$196$	−6.57302	−0.469502
$197$	2.45235	0.174723	0.0873614	−	0.996177i	$-0.472157\pi$
$197$	2.45235	0.174723	0.0873614	+	0.996177i	$0.472157\pi$
$198$	−3.89025	−0.276468
$199$	−10.4345	−0.739680	−0.369840	−	0.929095i	$-0.620588\pi$
$199$	−10.4345	−0.739680	−0.369840	+	0.929095i	$0.620588\pi$
$200$	0	0
$201$	−7.13078	−0.502967
$202$	18.0037	1.26674
$203$	12.6409	0.887214
$204$	5.56210	0.389425
$205$	0	0
$206$	29.4671	2.05307
$207$	0.323478	0.0224832
$208$	−27.8651	−1.93209
$209$	−3.62717	−0.250897
$210$	0	0
$211$	19.2618	1.32604	0.663018	−	0.748604i	$-0.269275\pi$
$211$	19.2618	1.32604	0.663018	+	0.748604i	$0.269275\pi$
$212$	−11.1671	−0.766962
$213$	−2.67461	−0.183261
$214$	3.31065	0.226311
$215$	0	0
$216$	1.20906	0.0822659
$217$	12.2256	0.829929
$218$	−33.7365	−2.28492
$219$	6.28253	0.424534
$220$	0	0
$221$	−23.7051	−1.59458
$222$	3.20052	0.214805
$223$	7.61706	0.510076	0.255038	−	0.966931i	$-0.417912\pi$
$223$	7.61706	0.510076	0.255038	+	0.966931i	$0.417912\pi$
$224$	9.40528	0.628417
$225$	0	0
$226$	−24.4196	−1.62437
$227$	−1.31803	−0.0874810	−0.0437405	−	0.999043i	$-0.513927\pi$
$227$	−1.31803	−0.0874810	−0.0437405	+	0.999043i	$0.513927\pi$
$228$	−2.27977	−0.150982
$229$	1.12632	0.0744292	0.0372146	−	0.999307i	$-0.488151\pi$
$229$	1.12632	0.0744292	0.0372146	+	0.999307i	$0.488151\pi$
$230$	0	0
$231$	−3.07697	−0.202450
$232$	10.5759	0.694342
$233$	26.6071	1.74309	0.871543	−	0.490319i	$-0.163120\pi$
$233$	26.6071	1.74309	0.871543	+	0.490319i	$0.163120\pi$
$234$	10.4209	0.681234
$235$	0	0
$236$	−2.84345	−0.185093
$237$	−8.37092	−0.543750
$238$	10.9740	0.711337
$239$	−24.8692	−1.60865	−0.804326	−	0.594188i	$-0.797473\pi$
$239$	−24.8692	−1.60865	−0.804326	+	0.594188i	$0.797473\pi$
$240$	0	0
$241$	−12.3532	−0.795743	−0.397871	−	0.917441i	$-0.630251\pi$
$241$	−12.3532	−0.795743	−0.397871	+	0.917441i	$0.630251\pi$
$242$	−11.8149	−0.759488
$243$	−1.00000	−0.0641500
$244$	−7.21259	−0.461739
$245$	0	0
$246$	12.5668	0.801228
$247$	9.71616	0.618224
$248$	10.2285	0.649511
$249$	−14.5872	−0.924426
$250$	0	0
$251$	−29.0986	−1.83669	−0.918343	−	0.395786i	$-0.870472\pi$
$251$	−29.0986	−1.83669	−0.918343	+	0.395786i	$0.870472\pi$
$252$	−1.93395	−0.121828
$253$	−0.688750	−0.0433013
$254$	−1.85232	−0.116225
$255$	0	0
$256$	20.9452	1.30908
$257$	−12.0500	−0.751656	−0.375828	−	0.926690i	$-0.622642\pi$
$257$	−12.0500	−0.751656	−0.375828	+	0.926690i	$0.622642\pi$
$258$	−20.3558	−1.26730
$259$	2.53143	0.157296
$260$	0	0
$261$	−8.74724	−0.541440
$262$	3.81040	0.235407
$263$	−1.02892	−0.0634460	−0.0317230	−	0.999497i	$-0.510099\pi$
$263$	−1.02892	−0.0634460	−0.0317230	+	0.999497i	$0.510099\pi$
$264$	−2.57433	−0.158439
$265$	0	0
$266$	−4.49797	−0.275788
$267$	−2.68119	−0.164086
$268$	9.54285	0.582922
$269$	23.9072	1.45765	0.728824	−	0.684701i	$-0.240067\pi$
$269$	23.9072	1.45765	0.728824	+	0.684701i	$0.240067\pi$
$270$	0	0
$271$	3.72214	0.226104	0.113052	−	0.993589i	$-0.463937\pi$
$271$	3.72214	0.226104	0.113052	+	0.993589i	$0.463937\pi$
$272$	20.3055	1.23120
$273$	8.24232	0.498848
$274$	30.9445	1.86943
$275$	0	0
$276$	−0.432897	−0.0260574
$277$	−17.5802	−1.05629	−0.528147	−	0.849153i	$-0.677113\pi$
$277$	−17.5802	−1.05629	−0.528147	+	0.849153i	$0.677113\pi$
$278$	27.2024	1.63149
$279$	−8.45991	−0.506481
$280$	0	0
$281$	13.2536	0.790644	0.395322	−	0.918543i	$-0.370633\pi$
$281$	13.2536	0.790644	0.395322	+	0.918543i	$0.370633\pi$
$282$	23.0181	1.37071
$283$	12.0996	0.719249	0.359624	−	0.933097i	$-0.382905\pi$
$283$	12.0996	0.719249	0.359624	+	0.933097i	$0.382905\pi$
$284$	3.57933	0.212394
$285$	0	0
$286$	−22.1882	−1.31201
$287$	9.93960	0.586716
$288$	−6.50828	−0.383504
$289$	0.274126	0.0161251
$290$	0	0
$291$	8.55105	0.501272
$292$	−8.40767	−0.492022
$293$	3.61673	0.211291	0.105646	−	0.994404i	$-0.466309\pi$
$293$	3.61673	0.211291	0.105646	+	0.994404i	$0.466309\pi$
$294$	8.97397	0.523372
$295$	0	0
$296$	2.11791	0.123101
$297$	2.12920	0.123549
$298$	−8.60543	−0.498499
$299$	1.84497	0.106697
$300$	0	0
$301$	−16.1003	−0.928005
$302$	−17.5965	−1.01257
$303$	−9.85377	−0.566084
$304$	−8.32275	−0.477342
$305$	0	0
$306$	−7.59378	−0.434108
$307$	14.8273	0.846238	0.423119	−	0.906074i	$-0.360935\pi$
$307$	14.8273	0.846238	0.423119	+	0.906074i	$0.360935\pi$
$308$	4.11778	0.234633
$309$	−16.1279	−0.917484
$310$	0	0
$311$	−6.61579	−0.375147	−0.187574	−	0.982251i	$-0.560062\pi$
$311$	−6.61579	−0.375147	−0.187574	+	0.982251i	$0.560062\pi$
$312$	6.89590	0.390403
$313$	−7.17823	−0.405737	−0.202869	−	0.979206i	$-0.565026\pi$
$313$	−7.17823	−0.405737	−0.202869	+	0.979206i	$0.565026\pi$
$314$	33.9030	1.91326
$315$	0	0
$316$	11.2025	0.630189
$317$	−9.75255	−0.547758	−0.273879	−	0.961764i	$-0.588307\pi$
$317$	−9.75255	−0.547758	−0.273879	+	0.961764i	$0.588307\pi$
$318$	15.2462	0.854963
$319$	18.6247	1.04278
$320$	0	0
$321$	−1.81198	−0.101135
$322$	−0.854102	−0.0475972
$323$	−7.08025	−0.393956
$324$	1.33826	0.0743478
$325$	0	0
$326$	0.825307	0.0457095
$327$	18.4646	1.02109
$328$	8.31592	0.459170
$329$	18.2060	1.00373
$330$	0	0
$331$	6.68822	0.367618	0.183809	−	0.982962i	$-0.441157\pi$
$331$	6.68822	0.367618	0.183809	+	0.982962i	$0.441157\pi$
$332$	19.5215	1.07138
$333$	−1.75170	−0.0959928
$334$	8.63570	0.472525
$335$	0	0
$336$	−7.06027	−0.385169
$337$	−20.8191	−1.13409	−0.567045	−	0.823687i	$-0.691914\pi$
$337$	−20.8191	−1.13409	−0.567045	+	0.823687i	$0.691914\pi$
$338$	35.6836	1.94093
$339$	13.3653	0.725902
$340$	0	0
$341$	18.0129	0.975452
$342$	3.11251	0.168305
$343$	17.2138	0.929456
$344$	−13.4702	−0.726266
$345$	0	0
$346$	4.19297	0.225415
$347$	−30.9907	−1.66367	−0.831835	−	0.555023i	$-0.812709\pi$
$347$	−30.9907	−1.66367	−0.831835	+	0.555023i	$0.812709\pi$
$348$	11.7061	0.627512
$349$	−7.45484	−0.399048	−0.199524	−	0.979893i	$-0.563940\pi$
$349$	−7.45484	−0.399048	−0.199524	+	0.979893i	$0.563940\pi$
$350$	0	0
$351$	−5.70353	−0.304432
$352$	13.8575	0.738605
$353$	−3.68948	−0.196371	−0.0981856	−	0.995168i	$-0.531304\pi$
$353$	−3.68948	−0.196371	−0.0981856	+	0.995168i	$0.531304\pi$
$354$	3.88209	0.206331
$355$	0	0
$356$	3.58814	0.190171
$357$	−6.00625	−0.317884
$358$	4.91043	0.259524
$359$	−9.92989	−0.524079	−0.262040	−	0.965057i	$-0.584395\pi$
$359$	−9.92989	−0.524079	−0.262040	+	0.965057i	$0.584395\pi$
$360$	0	0
$361$	−16.0980	−0.847262
$362$	−43.6835	−2.29595
$363$	6.46649	0.339403
$364$	−11.0304	−0.578149
$365$	0	0
$366$	9.84715	0.514719
$367$	−12.5507	−0.655142	−0.327571	−	0.944826i	$-0.606230\pi$
$367$	−12.5507	−0.655142	−0.327571	+	0.944826i	$0.606230\pi$
$368$	−1.58038	−0.0823828
$369$	−6.87802	−0.358056
$370$	0	0
$371$	12.0589	0.626065
$372$	11.3216	0.586996
$373$	14.8576	0.769299	0.384650	−	0.923063i	$-0.374322\pi$
$373$	14.8576	0.769299	0.384650	+	0.923063i	$0.374322\pi$
$374$	16.1687	0.836064
$375$	0	0
$376$	15.2320	0.785530
$377$	−49.8902	−2.56947
$378$	2.64037	0.135806
$379$	11.2957	0.580223	0.290112	−	0.956993i	$-0.406308\pi$
$379$	11.2957	0.580223	0.290112	+	0.956993i	$0.406308\pi$
$380$	0	0
$381$	1.01381	0.0519389
$382$	−7.15898	−0.366285
$383$	−3.04968	−0.155831	−0.0779157	−	0.996960i	$-0.524827\pi$
$383$	−3.04968	−0.155831	−0.0779157	+	0.996960i	$0.524827\pi$
$384$	−9.14301	−0.466577
$385$	0	0
$386$	−15.6171	−0.794889
$387$	11.1411	0.566334
$388$	−11.4435	−0.580958
$389$	−21.3939	−1.08472	−0.542358	−	0.840148i	$-0.682468\pi$
$389$	−21.3939	−1.08472	−0.542358	+	0.840148i	$0.682468\pi$
$390$	0	0
$391$	−1.34444	−0.0679914
$392$	5.93842	0.299936
$393$	−2.08550	−0.105200
$394$	4.48067	0.225733
$395$	0	0
$396$	−2.84943	−0.143189
$397$	34.4305	1.72802	0.864009	−	0.503476i	$-0.167946\pi$
$397$	34.4305	1.72802	0.864009	+	0.503476i	$0.167946\pi$
$398$	−19.0647	−0.955629
$399$	2.46182	0.123245
$400$	0	0
$401$	36.2976	1.81262	0.906309	−	0.422616i	$-0.138888\pi$
$401$	36.2976	1.81262	0.906309	+	0.422616i	$0.138888\pi$
$402$	−13.0286	−0.649807
$403$	−48.2514	−2.40357
$404$	13.1869	0.656074
$405$	0	0
$406$	23.0960	1.14623
$407$	3.72974	0.184876
$408$	−5.02510	−0.248780
$409$	24.9896	1.23566	0.617828	−	0.786313i	$-0.288013\pi$
$409$	24.9896	1.23566	0.617828	+	0.786313i	$0.288013\pi$
$410$	0	0
$411$	−16.9365	−0.835416
$412$	21.5833	1.06333
$413$	3.07051	0.151090
$414$	0.591023	0.0290472
$415$	0	0
$416$	−37.1202	−1.81997
$417$	−14.8883	−0.729085
$418$	−6.62717	−0.324146
$419$	2.70313	0.132057	0.0660284	−	0.997818i	$-0.478967\pi$
$419$	2.70313	0.132057	0.0660284	+	0.997818i	$0.478967\pi$
$420$	0	0
$421$	26.6496	1.29882	0.649411	−	0.760438i	$-0.275016\pi$
$421$	26.6496	1.29882	0.649411	+	0.760438i	$0.275016\pi$
$422$	35.1930	1.71317
$423$	−12.5982	−0.612548
$424$	10.0890	0.489965
$425$	0	0
$426$	−4.88676	−0.236764
$427$	7.78853	0.376914
$428$	2.42490	0.117212
$429$	12.1440	0.586317
$430$	0	0
$431$	33.6242	1.61962	0.809811	−	0.586691i	$-0.199570\pi$
$431$	33.6242	1.61962	0.809811	+	0.586691i	$0.199570\pi$
$432$	4.88558	0.235058
$433$	5.34260	0.256749	0.128375	−	0.991726i	$-0.459024\pi$
$433$	5.34260	0.256749	0.128375	+	0.991726i	$0.459024\pi$
$434$	22.3373	1.07223
$435$	0	0
$436$	−24.7104	−1.18341
$437$	0.551055	0.0263605
$438$	11.4788	0.548476
$439$	26.9690	1.28716	0.643580	−	0.765379i	$-0.277448\pi$
$439$	26.9690	1.28716	0.643580	+	0.765379i	$0.277448\pi$
$440$	0	0
$441$	−4.91161	−0.233886
$442$	−43.3114	−2.06011
$443$	16.8670	0.801374	0.400687	−	0.916215i	$-0.368771\pi$
$443$	16.8670	0.801374	0.400687	+	0.916215i	$0.368771\pi$
$444$	2.34424	0.111253
$445$	0	0
$446$	13.9171	0.658992
$447$	4.70991	0.222771
$448$	3.06376	0.144749
$449$	21.5942	1.01909	0.509546	−	0.860443i	$-0.329813\pi$
$449$	21.5942	1.01909	0.509546	+	0.860443i	$0.329813\pi$
$450$	0	0
$451$	14.6447	0.689593
$452$	−17.8862	−0.841297
$453$	9.63091	0.452500
$454$	−2.40817	−0.113021
$455$	0	0
$456$	2.05967	0.0964528
$457$	−5.60699	−0.262284	−0.131142	−	0.991364i	$-0.541864\pi$
$457$	−5.60699	−0.262284	−0.131142	+	0.991364i	$0.541864\pi$
$458$	2.05788	0.0961587
$459$	4.15622	0.193996
$460$	0	0
$461$	−9.54504	−0.444557	−0.222278	−	0.974983i	$-0.571349\pi$
$461$	−9.54504	−0.444557	−0.222278	+	0.974983i	$0.571349\pi$
$462$	−5.62190	−0.261554
$463$	−23.5262	−1.09336	−0.546678	−	0.837343i	$-0.684108\pi$
$463$	−23.5262	−1.09336	−0.546678	+	0.837343i	$0.684108\pi$
$464$	42.7353	1.98394
$465$	0	0
$466$	48.6135	2.25198
$467$	−36.5834	−1.69288	−0.846439	−	0.532486i	$-0.821258\pi$
$467$	−36.5834	−1.69288	−0.846439	+	0.532486i	$0.821258\pi$
$468$	7.63282	0.352827
$469$	−10.3049	−0.475835
$470$	0	0
$471$	−18.5557	−0.855003
$472$	2.56893	0.118245
$473$	−23.7217	−1.09072
$474$	−15.2944	−0.702496
$475$	0	0
$476$	8.03793	0.368418
$477$	−8.34451	−0.382069
$478$	−45.4382	−2.07830
$479$	29.2750	1.33761	0.668804	−	0.743439i	$-0.266807\pi$
$479$	29.2750	1.33761	0.668804	+	0.743439i	$0.266807\pi$
$480$	0	0
$481$	−9.99091	−0.455546
$482$	−22.5705	−1.02806
$483$	0.467465	0.0212704
$484$	−8.65385	−0.393357
$485$	0	0
$486$	−1.82709	−0.0828785
$487$	−21.2869	−0.964600	−0.482300	−	0.876006i	$-0.660199\pi$
$487$	−21.2869	−0.964600	−0.482300	+	0.876006i	$0.660199\pi$
$488$	6.51624	0.294976
$489$	−0.451705	−0.0204268
$490$	0	0
$491$	−33.1940	−1.49803	−0.749013	−	0.662556i	$-0.769472\pi$
$491$	−33.1940	−1.49803	−0.749013	+	0.662556i	$0.769472\pi$
$492$	9.20459	0.414975
$493$	36.3554	1.63737
$494$	17.7523	0.798714
$495$	0	0
$496$	41.3316	1.85584
$497$	−3.86515	−0.173376
$498$	−26.6521	−1.19431
$499$	4.72872	0.211686	0.105843	−	0.994383i	$-0.466246\pi$
$499$	4.72872	0.211686	0.105843	+	0.994383i	$0.466246\pi$
$500$	0	0
$501$	−4.72648	−0.211163
$502$	−53.1657	−2.37290
$503$	−0.400444	−0.0178549	−0.00892745	−	0.999960i	$-0.502842\pi$
$503$	−0.400444	−0.0178549	−0.00892745	+	0.999960i	$0.502842\pi$
$504$	1.74724	0.0778282
$505$	0	0
$506$	−1.25841	−0.0559431
$507$	−19.5303	−0.867371
$508$	−1.35674	−0.0601956
$509$	−27.6104	−1.22381	−0.611904	−	0.790932i	$-0.709596\pi$
$509$	−27.6104	−1.22381	−0.611904	+	0.790932i	$0.709596\pi$
$510$	0	0
$511$	9.07905	0.401633
$512$	19.9828	0.883126
$513$	−1.70353	−0.0752128
$514$	−22.0164	−0.971100
$515$	0	0
$516$	−14.9097	−0.656363
$517$	26.8242	1.17973
$518$	4.62516	0.203218
$519$	−2.29489	−0.100734
$520$	0	0
$521$	−28.7374	−1.25901	−0.629505	−	0.776996i	$-0.716742\pi$
$521$	−28.7374	−1.25901	−0.629505	+	0.776996i	$0.716742\pi$
$522$	−15.9820	−0.699513
$523$	18.0660	0.789969	0.394985	−	0.918688i	$-0.370750\pi$
$523$	18.0660	0.789969	0.394985	+	0.918688i	$0.370750\pi$
$524$	2.79094	0.121923
$525$	0	0
$526$	−1.87993	−0.0819690
$527$	35.1612	1.53165
$528$	−10.4024	−0.452706
$529$	−22.8954	−0.995451
$530$	0	0
$531$	−2.12474	−0.0922058
$532$	−3.29456	−0.142837
$533$	−39.2290	−1.69920
$534$	−4.89878	−0.211991
$535$	0	0
$536$	−8.62152	−0.372393
$537$	−2.68757	−0.115977
$538$	43.6807	1.88321
$539$	10.4578	0.450451
$540$	0	0
$541$	−5.26032	−0.226159	−0.113079	−	0.993586i	$-0.536071\pi$
$541$	−5.26032	−0.226159	−0.113079	+	0.993586i	$0.536071\pi$
$542$	6.80068	0.292114
$543$	23.9088	1.02602
$544$	27.0498	1.15975
$545$	0	0
$546$	15.0595	0.644486
$547$	−36.7888	−1.57297	−0.786487	−	0.617607i	$-0.788102\pi$
$547$	−36.7888	−1.57297	−0.786487	+	0.617607i	$0.788102\pi$
$548$	22.6655	0.968221
$549$	−5.38952	−0.230019
$550$	0	0
$551$	−14.9012	−0.634813
$552$	0.391103	0.0166464
$553$	−12.0970	−0.514418
$554$	−32.1207	−1.36468
$555$	0	0
$556$	19.9245	0.844986
$557$	23.3475	0.989266	0.494633	−	0.869102i	$-0.335302\pi$
$557$	23.3475	0.989266	0.494633	+	0.869102i	$0.335302\pi$
$558$	−15.4570	−0.654348
$559$	63.5436	2.68761
$560$	0	0
$561$	−8.84943	−0.373623
$562$	24.2156	1.02147
$563$	−29.2369	−1.23219	−0.616095	−	0.787672i	$-0.711286\pi$
$563$	−29.2369	−1.23219	−0.616095	+	0.787672i	$0.711286\pi$
$564$	16.8597	0.709923
$565$	0	0
$566$	22.1071	0.929232
$567$	−1.44512	−0.0606895
$568$	−3.23376	−0.135685
$569$	−20.2530	−0.849051	−0.424526	−	0.905416i	$-0.639559\pi$
$569$	−20.2530	−0.849051	−0.424526	+	0.905416i	$0.639559\pi$
$570$	0	0
$571$	−4.57564	−0.191484	−0.0957422	−	0.995406i	$-0.530522\pi$
$571$	−4.57564	−0.191484	−0.0957422	+	0.995406i	$0.530522\pi$
$572$	−16.2518	−0.679523
$573$	3.91824	0.163687
$574$	18.1606	0.758007
$575$	0	0
$576$	−2.12007	−0.0883361
$577$	−31.3502	−1.30513	−0.652564	−	0.757734i	$-0.726306\pi$
$577$	−31.3502	−1.30513	−0.652564	+	0.757734i	$0.726306\pi$
$578$	0.500853	0.0208327
$579$	8.54752	0.355223
$580$	0	0
$581$	−21.0803	−0.874559
$582$	15.6236	0.647617
$583$	17.7672	0.735841
$584$	7.59594	0.314322
$585$	0	0
$586$	6.60809	0.272978
$587$	−4.67218	−0.192842	−0.0964208	−	0.995341i	$-0.530739\pi$
$587$	−4.67218	−0.192842	−0.0964208	+	0.995341i	$0.530739\pi$
$588$	6.57302	0.271067
$589$	−14.4117	−0.593825
$590$	0	0
$591$	−2.45235	−0.100876
$592$	8.55809	0.351735
$593$	−7.37978	−0.303051	−0.151526	−	0.988453i	$-0.548419\pi$
$593$	−7.37978	−0.303051	−0.151526	+	0.988453i	$0.548419\pi$
$594$	3.89025	0.159619
$595$	0	0
$596$	−6.30309	−0.258185
$597$	10.4345	0.427055
$598$	3.37092	0.137847
$599$	−46.7505	−1.91018	−0.955088	−	0.296323i	$-0.904239\pi$
$599$	−46.7505	−1.91018	−0.955088	+	0.296323i	$0.904239\pi$
$600$	0	0
$601$	32.3225	1.31846	0.659230	−	0.751941i	$-0.270882\pi$
$601$	32.3225	1.31846	0.659230	+	0.751941i	$0.270882\pi$
$602$	−29.4167	−1.19893
$603$	7.13078	0.290388
$604$	−12.8887	−0.524433
$605$	0	0
$606$	−18.0037	−0.731352
$607$	−14.0891	−0.571858	−0.285929	−	0.958251i	$-0.592302\pi$
$607$	−14.0891	−0.571858	−0.285929	+	0.958251i	$0.592302\pi$
$608$	−11.0871	−0.449640
$609$	−12.6409	−0.512233
$610$	0	0
$611$	−71.8545	−2.90692
$612$	−5.56210	−0.224835
$613$	−12.2959	−0.496625	−0.248313	−	0.968680i	$-0.579876\pi$
$613$	−12.2959	−0.496625	−0.248313	+	0.968680i	$0.579876\pi$
$614$	27.0908	1.09330
$615$	0	0
$616$	−3.72023	−0.149892
$617$	−1.96969	−0.0792969	−0.0396485	−	0.999214i	$-0.512624\pi$
$617$	−1.96969	−0.0792969	−0.0396485	+	0.999214i	$0.512624\pi$
$618$	−29.4671	−1.18534
$619$	14.9714	0.601749	0.300875	−	0.953664i	$-0.402721\pi$
$619$	14.9714	0.601749	0.300875	+	0.953664i	$0.402721\pi$
$620$	0	0
$621$	−0.323478	−0.0129807
$622$	−12.0877	−0.484671
$623$	−3.87466	−0.155235
$624$	27.8651	1.11550
$625$	0	0
$626$	−13.1153	−0.524192
$627$	3.62717	0.144855
$628$	24.8324	0.990921
$629$	7.28046	0.290291
$630$	0	0
$631$	18.0729	0.719472	0.359736	−	0.933054i	$-0.382867\pi$
$631$	18.0729	0.719472	0.359736	+	0.933054i	$0.382867\pi$
$632$	−10.1209	−0.402588
$633$	−19.2618	−0.765587
$634$	−17.8188	−0.707675
$635$	0	0
$636$	11.1671	0.442806
$637$	−28.0136	−1.10994
$638$	34.0289	1.34722
$639$	2.67461	0.105806
$640$	0	0
$641$	12.2381	0.483374	0.241687	−	0.970354i	$-0.422299\pi$
$641$	12.2381	0.483374	0.241687	+	0.970354i	$0.422299\pi$
$642$	−3.31065	−0.130661
$643$	−16.4453	−0.648540	−0.324270	−	0.945964i	$-0.605119\pi$
$643$	−16.4453	−0.648540	−0.324270	+	0.945964i	$0.605119\pi$
$644$	−0.625591	−0.0246517
$645$	0	0
$646$	−12.9363	−0.508971
$647$	17.3991	0.684028	0.342014	−	0.939695i	$-0.388891\pi$
$647$	17.3991	0.684028	0.342014	+	0.939695i	$0.388891\pi$
$648$	−1.20906	−0.0474962
$649$	4.52400	0.177583
$650$	0	0
$651$	−12.2256	−0.479160
$652$	0.604500	0.0236740
$653$	−28.4645	−1.11390	−0.556950	−	0.830546i	$-0.688029\pi$
$653$	−28.4645	−1.11390	−0.556950	+	0.830546i	$0.688029\pi$
$654$	33.7365	1.31920
$655$	0	0
$656$	33.6031	1.31198
$657$	−6.28253	−0.245105
$658$	33.2641	1.29677
$659$	−1.51333	−0.0589509	−0.0294754	−	0.999566i	$-0.509384\pi$
$659$	−1.51333	−0.0589509	−0.0294754	+	0.999566i	$0.509384\pi$
$660$	0	0
$661$	26.7842	1.04179	0.520893	−	0.853622i	$-0.325599\pi$
$661$	26.7842	1.04179	0.520893	+	0.853622i	$0.325599\pi$
$662$	12.2200	0.474943
$663$	23.7051	0.920630
$664$	−17.6368	−0.684439
$665$	0	0
$666$	−3.20052	−0.124018
$667$	−2.82954	−0.109560
$668$	6.32526	0.244732
$669$	−7.61706	−0.294492
$670$	0	0
$671$	11.4754	0.443003
$672$	−9.40528	−0.362817
$673$	9.31141	0.358929	0.179464	−	0.983764i	$-0.442564\pi$
$673$	9.31141	0.358929	0.179464	+	0.983764i	$0.442564\pi$
$674$	−38.0385	−1.46519
$675$	0	0
$676$	26.1366	1.00526
$677$	24.7854	0.952579	0.476290	−	0.879288i	$-0.341981\pi$
$677$	24.7854	0.952579	0.476290	+	0.879288i	$0.341981\pi$
$678$	24.4196	0.937828
$679$	12.3573	0.474231
$680$	0	0
$681$	1.31803	0.0505072
$682$	32.9112	1.26023
$683$	−37.3864	−1.43055	−0.715276	−	0.698842i	$-0.753699\pi$
$683$	−37.3864	−1.43055	−0.715276	+	0.698842i	$0.753699\pi$
$684$	2.27977	0.0871693
$685$	0	0
$686$	31.4511	1.20081
$687$	−1.12632	−0.0429717
$688$	−54.4307	−2.07515
$689$	−47.5932	−1.81316
$690$	0	0
$691$	−32.8909	−1.25123	−0.625615	−	0.780132i	$-0.715152\pi$
$691$	−32.8909	−1.25123	−0.625615	+	0.780132i	$0.715152\pi$
$692$	3.07116	0.116748
$693$	3.07697	0.116884
$694$	−56.6229	−2.14938
$695$	0	0
$696$	−10.5759	−0.400879
$697$	28.5865	1.08279
$698$	−13.6207	−0.515550
$699$	−26.6071	−1.00637
$700$	0	0
$701$	−42.3336	−1.59892	−0.799459	−	0.600721i	$-0.794880\pi$
$701$	−42.3336	−1.59892	−0.799459	+	0.600721i	$0.794880\pi$
$702$	−10.4209	−0.393311
$703$	−2.98409	−0.112547
$704$	4.51406	0.170130
$705$	0	0
$706$	−6.74101	−0.253701
$707$	−14.2399	−0.535548
$708$	2.84345	0.106864
$709$	18.3593	0.689498	0.344749	−	0.938695i	$-0.387964\pi$
$709$	18.3593	0.689498	0.344749	+	0.938695i	$0.387964\pi$
$710$	0	0
$711$	8.37092	0.313934
$712$	−3.24171	−0.121488
$713$	−2.73659	−0.102486
$714$	−10.9740	−0.410690
$715$	0	0
$716$	3.59667	0.134414
$717$	24.8692	0.928756
$718$	−18.1428	−0.677084
$719$	−19.2706	−0.718671	−0.359336	−	0.933208i	$-0.616997\pi$
$719$	−19.2706	−0.718671	−0.359336	+	0.933208i	$0.616997\pi$
$720$	0	0
$721$	−23.3068	−0.867992
$722$	−29.4125	−1.09462
$723$	12.3532	0.459422
$724$	−31.9962	−1.18913
$725$	0	0
$726$	11.8149	0.438491
$727$	17.4238	0.646214	0.323107	−	0.946362i	$-0.395273\pi$
$727$	17.4238	0.646214	0.323107	+	0.946362i	$0.395273\pi$
$728$	9.96543	0.369343
$729$	1.00000	0.0370370
$730$	0	0
$731$	−46.3048	−1.71265
$732$	7.21259	0.266585
$733$	24.2010	0.893883	0.446942	−	0.894563i	$-0.352513\pi$
$733$	24.2010	0.893883	0.446942	+	0.894563i	$0.352513\pi$
$734$	−22.9313	−0.846410
$735$	0	0
$736$	−2.10528	−0.0776018
$737$	−15.1829	−0.559269
$738$	−12.5668	−0.462589
$739$	−38.5798	−1.41918	−0.709591	−	0.704613i	$-0.751120\pi$
$739$	−38.5798	−1.41918	−0.709591	+	0.704613i	$0.751120\pi$
$740$	0	0
$741$	−9.71616	−0.356932
$742$	22.0326	0.808844
$743$	−33.8580	−1.24213	−0.621065	−	0.783759i	$-0.713300\pi$
$743$	−33.8580	−1.24213	−0.621065	+	0.783759i	$0.713300\pi$
$744$	−10.2285	−0.374995
$745$	0	0
$746$	27.1462	0.993895
$747$	14.5872	0.533718
$748$	11.8429	0.433018
$749$	−2.61853	−0.0956791
$750$	0	0
$751$	−45.9138	−1.67542	−0.837710	−	0.546115i	$-0.816106\pi$
$751$	−45.9138	−1.67542	−0.837710	+	0.546115i	$0.816106\pi$
$752$	61.5497	2.24449
$753$	29.0986	1.06041
$754$	−91.1539	−3.31963
$755$	0	0
$756$	1.93395	0.0703372
$757$	10.3561	0.376400	0.188200	−	0.982131i	$-0.439735\pi$
$757$	10.3561	0.376400	0.188200	+	0.982131i	$0.439735\pi$
$758$	20.6383	0.749618
$759$	0.688750	0.0250000
$760$	0	0
$761$	49.2652	1.78586	0.892931	−	0.450193i	$-0.148645\pi$
$761$	49.2652	1.78586	0.892931	+	0.450193i	$0.148645\pi$
$762$	1.85232	0.0671024
$763$	26.6836	0.966012
$764$	−5.24362	−0.189708
$765$	0	0
$766$	−5.57205	−0.201326
$767$	−12.1185	−0.437574
$768$	−20.9452	−0.755797
$769$	−1.26208	−0.0455116	−0.0227558	−	0.999741i	$-0.507244\pi$
$769$	−1.26208	−0.0455116	−0.0227558	+	0.999741i	$0.507244\pi$
$770$	0	0
$771$	12.0500	0.433969
$772$	−11.4388	−0.411692
$773$	−26.9903	−0.970772	−0.485386	−	0.874300i	$-0.661321\pi$
$773$	−26.9903	−0.970772	−0.485386	+	0.874300i	$0.661321\pi$
$774$	20.3558	0.731674
$775$	0	0
$776$	10.3387	0.371138
$777$	−2.53143	−0.0908146
$778$	−39.0887	−1.40140
$779$	−11.7169	−0.419803
$780$	0	0
$781$	−5.69480	−0.203776
$782$	−2.45642	−0.0878413
$783$	8.74724	0.312601
$784$	23.9961	0.857003
$785$	0	0
$786$	−3.81040	−0.135912
$787$	7.62303	0.271732	0.135866	−	0.990727i	$-0.456618\pi$
$787$	7.62303	0.271732	0.135866	+	0.990727i	$0.456618\pi$
$788$	3.28189	0.116912
$789$	1.02892	0.0366306
$790$	0	0
$791$	19.3145	0.686744
$792$	2.57433	0.0914748
$793$	−30.7393	−1.09159
$794$	62.9077	2.23251
$795$	0	0
$796$	−13.9641	−0.494943
$797$	4.98266	0.176495	0.0882474	−	0.996099i	$-0.471873\pi$
$797$	4.98266	0.176495	0.0882474	+	0.996099i	$0.471873\pi$
$798$	4.49797	0.159226
$799$	52.3610	1.85240
$800$	0	0
$801$	2.68119	0.0947353
$802$	66.3191	2.34181
$803$	13.3768	0.472057
$804$	−9.54285	−0.336550
$805$	0	0
$806$	−88.1596	−3.10529
$807$	−23.9072	−0.841574
$808$	−11.9138	−0.419125
$809$	5.74271	0.201903	0.100952	−	0.994891i	$-0.467811\pi$
$809$	5.74271	0.201903	0.100952	+	0.994891i	$0.467811\pi$
$810$	0	0
$811$	38.8021	1.36253	0.681264	−	0.732038i	$-0.261431\pi$
$811$	38.8021	1.36253	0.681264	+	0.732038i	$0.261431\pi$
$812$	16.9168	0.593662
$813$	−3.72214	−0.130541
$814$	6.81457	0.238851
$815$	0	0
$816$	−20.3055	−0.710835
$817$	18.9792	0.664000
$818$	45.6583	1.59640
$819$	−8.24232	−0.288010
$820$	0	0
$821$	−41.8919	−1.46204	−0.731019	−	0.682357i	$-0.760955\pi$
$821$	−41.8919	−1.46204	−0.731019	+	0.682357i	$0.760955\pi$
$822$	−30.9445	−1.07931
$823$	−29.2212	−1.01859	−0.509294	−	0.860593i	$-0.670093\pi$
$823$	−29.2212	−1.01859	−0.509294	+	0.860593i	$0.670093\pi$
$824$	−19.4995	−0.679299
$825$	0	0
$826$	5.61010	0.195200
$827$	7.41934	0.257996	0.128998	−	0.991645i	$-0.458824\pi$
$827$	7.41934	0.257996	0.128998	+	0.991645i	$0.458824\pi$
$828$	0.432897	0.0150442
$829$	29.7586	1.03356	0.516779	−	0.856119i	$-0.327131\pi$
$829$	29.7586	1.03356	0.516779	+	0.856119i	$0.327131\pi$
$830$	0	0
$831$	17.5802	0.609852
$832$	−12.0919	−0.419210
$833$	20.4137	0.707294
$834$	−27.2024	−0.941940
$835$	0	0
$836$	−4.85410	−0.167883
$837$	8.45991	0.292417
$838$	4.93887	0.170610
$839$	29.5793	1.02119	0.510595	−	0.859821i	$-0.329425\pi$
$839$	29.5793	1.02119	0.510595	+	0.859821i	$0.329425\pi$
$840$	0	0
$841$	47.5142	1.63842
$842$	48.6912	1.67801
$843$	−13.2536	−0.456479
$844$	25.7773	0.887291
$845$	0	0
$846$	−23.0181	−0.791380
$847$	9.34488	0.321094
$848$	40.7678	1.39997
$849$	−12.0996	−0.415258
$850$	0	0
$851$	−0.566637	−0.0194241
$852$	−3.57933	−0.122626
$853$	37.5298	1.28499	0.642497	−	0.766288i	$-0.277898\pi$
$853$	37.5298	1.28499	0.642497	+	0.766288i	$0.277898\pi$
$854$	14.2304	0.486953
$855$	0	0
$856$	−2.19078	−0.0748794
$857$	49.4333	1.68861	0.844305	−	0.535864i	$-0.180014\pi$
$857$	49.4333	1.68861	0.844305	+	0.535864i	$0.180014\pi$
$858$	22.1882	0.757492
$859$	2.82651	0.0964394	0.0482197	−	0.998837i	$-0.484645\pi$
$859$	2.82651	0.0964394	0.0482197	+	0.998837i	$0.484645\pi$
$860$	0	0
$861$	−9.93960	−0.338741
$862$	61.4345	2.09247
$863$	−33.3977	−1.13687	−0.568436	−	0.822727i	$-0.692451\pi$
$863$	−33.3977	−1.13687	−0.568436	+	0.822727i	$0.692451\pi$
$864$	6.50828	0.221416
$865$	0	0
$866$	9.76142	0.331707
$867$	−0.274126	−0.00930980
$868$	16.3611	0.555331
$869$	−17.8234	−0.604617
$870$	0	0
$871$	40.6707	1.37807
$872$	22.3247	0.756011
$873$	−8.55105	−0.289409
$874$	1.00683	0.0340564
$875$	0	0
$876$	8.40767	0.284069
$877$	9.28115	0.313402	0.156701	−	0.987646i	$-0.449914\pi$
$877$	9.28115	0.313402	0.156701	+	0.987646i	$0.449914\pi$
$878$	49.2748	1.66294
$879$	−3.61673	−0.121989
$880$	0	0
$881$	6.58736	0.221934	0.110967	−	0.993824i	$-0.464605\pi$
$881$	6.58736	0.221934	0.110967	+	0.993824i	$0.464605\pi$
$882$	−8.97397	−0.302169
$883$	−4.18883	−0.140965	−0.0704827	−	0.997513i	$-0.522454\pi$
$883$	−4.18883	−0.140965	−0.0704827	+	0.997513i	$0.522454\pi$
$884$	−31.7236	−1.06698
$885$	0	0
$886$	30.8175	1.03533
$887$	26.8716	0.902260	0.451130	−	0.892458i	$-0.351021\pi$
$887$	26.8716	0.902260	0.451130	+	0.892458i	$0.351021\pi$
$888$	−2.11791	−0.0710724
$889$	1.46508	0.0491371
$890$	0	0
$891$	−2.12920	−0.0713310
$892$	10.1936	0.341307
$893$	−21.4615	−0.718183
$894$	8.60543	0.287809
$895$	0	0
$896$	−13.2128	−0.441408
$897$	−1.84497	−0.0616016
$898$	39.4545	1.31661
$899$	74.0008	2.46807
$900$	0	0
$901$	34.6816	1.15541
$902$	26.7572	0.890918
$903$	16.1003	0.535784
$904$	16.1594	0.537453
$905$	0	0
$906$	17.5965	0.584606
$907$	−39.1821	−1.30102	−0.650511	−	0.759497i	$-0.725445\pi$
$907$	−39.1821	−1.30102	−0.650511	+	0.759497i	$0.725445\pi$
$908$	−1.76387	−0.0585362
$909$	9.85377	0.326829
$910$	0	0
$911$	54.2926	1.79880	0.899398	−	0.437132i	$-0.144006\pi$
$911$	54.2926	1.79880	0.899398	+	0.437132i	$0.144006\pi$
$912$	8.32275	0.275594
$913$	−31.0591	−1.02791
$914$	−10.2445	−0.338857
$915$	0	0
$916$	1.50731	0.0498028
$917$	−3.01381	−0.0995247
$918$	7.59378	0.250632
$919$	−28.0959	−0.926798	−0.463399	−	0.886150i	$-0.653370\pi$
$919$	−28.0959	−0.926798	−0.463399	+	0.886150i	$0.653370\pi$
$920$	0	0
$921$	−14.8273	−0.488576
$922$	−17.4396	−0.574344
$923$	15.2547	0.502116
$924$	−4.11778	−0.135465
$925$	0	0
$926$	−42.9846	−1.41256
$927$	16.1279	0.529710
$928$	56.9295	1.86880
$929$	−31.3772	−1.02945	−0.514727	−	0.857354i	$-0.672107\pi$
$929$	−31.3772	−1.02945	−0.514727	+	0.857354i	$0.672107\pi$
$930$	0	0
$931$	−8.36710	−0.274221
$932$	35.6072	1.16635
$933$	6.61579	0.216591
$934$	−66.8412	−2.18711
$935$	0	0
$936$	−6.89590	−0.225399
$937$	−49.7286	−1.62456	−0.812281	−	0.583266i	$-0.801774\pi$
$937$	−49.7286	−1.62456	−0.812281	+	0.583266i	$0.801774\pi$
$938$	−18.8279	−0.614754
$939$	7.17823	0.234253
$940$	0	0
$941$	−4.49598	−0.146565	−0.0732824	−	0.997311i	$-0.523347\pi$
$941$	−4.49598	−0.146565	−0.0732824	+	0.997311i	$0.523347\pi$
$942$	−33.9030	−1.10462
$943$	−2.22489	−0.0724523
$944$	10.3806	0.337859
$945$	0	0
$946$	−43.3417	−1.40916
$947$	−28.8993	−0.939101	−0.469551	−	0.882906i	$-0.655584\pi$
$947$	−28.8993	−0.939101	−0.469551	+	0.882906i	$0.655584\pi$
$948$	−11.2025	−0.363840
$949$	−35.8326	−1.16318
$950$	0	0
$951$	9.75255	0.316248
$952$	−7.26190	−0.235359
$953$	−46.1922	−1.49631	−0.748156	−	0.663523i	$-0.769060\pi$
$953$	−46.1922	−1.49631	−0.748156	+	0.663523i	$0.769060\pi$
$954$	−15.2462	−0.493613
$955$	0	0
$956$	−33.2814	−1.07640
$957$	−18.6247	−0.602050
$958$	53.4880	1.72812
$959$	−24.4754	−0.790351
$960$	0	0
$961$	40.5701	1.30871
$962$	−18.2543	−0.588542
$963$	1.81198	0.0583901
$964$	−16.5319	−0.532456
$965$	0	0
$966$	0.854102	0.0274803
$967$	8.41820	0.270711	0.135356	−	0.990797i	$-0.456782\pi$
$967$	8.41820	0.270711	0.135356	+	0.990797i	$0.456782\pi$
$968$	7.81835	0.251291
$969$	7.08025	0.227450
$970$	0	0
$971$	26.4421	0.848567	0.424284	−	0.905529i	$-0.360526\pi$
$971$	26.4421	0.848567	0.424284	+	0.905529i	$0.360526\pi$
$972$	−1.33826	−0.0429247
$973$	−21.5155	−0.689756
$974$	−38.8931	−1.24621
$975$	0	0
$976$	26.3309	0.842833
$977$	39.8235	1.27407	0.637034	−	0.770836i	$-0.280161\pi$
$977$	39.8235	1.27407	0.637034	+	0.770836i	$0.280161\pi$
$978$	−0.825307	−0.0263904
$979$	−5.70881	−0.182454
$980$	0	0
$981$	−18.4646	−0.589529
$982$	−60.6485	−1.93537
$983$	−24.1179	−0.769242	−0.384621	−	0.923075i	$-0.625668\pi$
$983$	−24.1179	−0.769242	−0.384621	+	0.923075i	$0.625668\pi$
$984$	−8.31592	−0.265102
$985$	0	0
$986$	66.4246	2.11539
$987$	−18.2060	−0.579505
$988$	13.0028	0.413673
$989$	3.60390	0.114597
$990$	0	0
$991$	−10.4044	−0.330506	−0.165253	−	0.986251i	$-0.552844\pi$
$991$	−10.4044	−0.330506	−0.165253	+	0.986251i	$0.552844\pi$
$992$	55.0595	1.74814
$993$	−6.68822	−0.212244
$994$	−7.06198	−0.223992
$995$	0	0
$996$	−19.5215	−0.618562
$997$	−13.3642	−0.423249	−0.211624	−	0.977351i	$-0.567875\pi$
$997$	−13.3642	−0.423249	−0.211624	+	0.977351i	$0.567875\pi$
$998$	8.63980	0.273488
$999$	1.75170	0.0554215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.g.1.4	yes	4
3.2	odd	2		5625.2.a.j.1.1		4
5.2	odd	4		1875.2.b.d.1249.7		8
5.3	odd	4		1875.2.b.d.1249.2		8
5.4	even	2		1875.2.a.f.1.1	✓	4
15.14	odd	2		5625.2.a.m.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.f.1.1	✓	4	5.4	even	2
1875.2.a.g.1.4	yes	4	1.1	even	1	trivial
1875.2.b.d.1249.2		8	5.3	odd	4
1875.2.b.d.1249.7		8	5.2	odd	4
5625.2.a.j.1.1		4	3.2	odd	2
5625.2.a.m.1.4		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} -1.82709 q^{6} -1.44512 q^{7} -1.20906 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} -1.82709 q^{6} -1.44512 q^{7} -1.20906 q^{8} +1.00000 q^{9} -2.12920 q^{11} -1.33826 q^{12} +5.70353 q^{13} -2.64037 q^{14} -4.88558 q^{16} -4.15622 q^{17} +1.82709 q^{18} +1.70353 q^{19} +1.44512 q^{21} -3.89025 q^{22} +0.323478 q^{23} +1.20906 q^{24} +10.4209 q^{26} -1.00000 q^{27} -1.93395 q^{28} -8.74724 q^{29} -8.45991 q^{31} -6.50828 q^{32} +2.12920 q^{33} -7.59378 q^{34} +1.33826 q^{36} -1.75170 q^{37} +3.11251 q^{38} -5.70353 q^{39} -6.87802 q^{41} +2.64037 q^{42} +11.1411 q^{43} -2.84943 q^{44} +0.591023 q^{46} -12.5982 q^{47} +4.88558 q^{48} -4.91161 q^{49} +4.15622 q^{51} +7.63282 q^{52} -8.34451 q^{53} -1.82709 q^{54} +1.74724 q^{56} -1.70353 q^{57} -15.9820 q^{58} -2.12474 q^{59} -5.38952 q^{61} -15.4570 q^{62} -1.44512 q^{63} -2.12007 q^{64} +3.89025 q^{66} +7.13078 q^{67} -5.56210 q^{68} -0.323478 q^{69} +2.67461 q^{71} -1.20906 q^{72} -6.28253 q^{73} -3.20052 q^{74} +2.27977 q^{76} +3.07697 q^{77} -10.4209 q^{78} +8.37092 q^{79} +1.00000 q^{81} -12.5668 q^{82} +14.5872 q^{83} +1.93395 q^{84} +20.3558 q^{86} +8.74724 q^{87} +2.57433 q^{88} +2.68119 q^{89} -8.24232 q^{91} +0.432897 q^{92} +8.45991 q^{93} -23.0181 q^{94} +6.50828 q^{96} -8.55105 q^{97} -8.97397 q^{98} -2.12920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q + q^{2} - 4 q^{3} + q^{4} - q^{6} + 5 q^{7} - 3 q^{8} + 4 q^{9} - 6 q^{11} - q^{12} + 7 q^{13} - 10 q^{14} - 9 q^{16} - 7 q^{17} + q^{18} - 9 q^{19} - 5 q^{21} + 6 q^{22} + 10 q^{23} + 3 q^{24} - 2 q^{26} - 4 q^{27} + 5 q^{28} - 28 q^{29} - 10 q^{31} + 6 q^{33} + 7 q^{34} + q^{36} - 10 q^{37} - 6 q^{38} - 7 q^{39} + 10 q^{42} + q^{43} - 9 q^{44} + 5 q^{46} - 23 q^{47} + 9 q^{48} - 3 q^{49} + 7 q^{51} + 13 q^{52} - q^{54} + 9 q^{57} - 2 q^{58} + 4 q^{59} - 43 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} - 6 q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 27 q^{71} - 3 q^{72} + 15 q^{73} + 5 q^{74} + 9 q^{76} - 15 q^{77} + 2 q^{78} + 10 q^{79} + 4 q^{81} - 20 q^{82} + 3 q^{83} - 5 q^{84} + 24 q^{86} + 28 q^{87} - 3 q^{88} - 9 q^{89} + 5 q^{91} - 15 q^{92} + 10 q^{93} - 22 q^{94} + 13 q^{97} - 42 q^{98} - 6 q^{99}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 + q^4 - q^6 + 5 * q^7 - 3 * q^8 + 4 * q^9 - 6 * q^11 - q^12 + 7 * q^13 - 10 * q^14 - 9 * q^16 - 7 * q^17 + q^18 - 9 * q^19 - 5 * q^21 + 6 * q^22 + 10 * q^23 + 3 * q^24 - 2 * q^26 - 4 * q^27 + 5 * q^28 - 28 * q^29 - 10 * q^31 + 6 * q^33 + 7 * q^34 + q^36 - 10 * q^37 - 6 * q^38 - 7 * q^39 + 10 * q^42 + q^43 - 9 * q^44 + 5 * q^46 - 23 * q^47 + 9 * q^48 - 3 * q^49 + 7 * q^51 + 13 * q^52 - q^54 + 9 * q^57 - 2 * q^58 + 4 * q^59 - 43 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 - 6 * q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 27 * q^71 - 3 * q^72 + 15 * q^73 + 5 * q^74 + 9 * q^76 - 15 * q^77 + 2 * q^78 + 10 * q^79 + 4 * q^81 - 20 * q^82 + 3 * q^83 - 5 * q^84 + 24 * q^86 + 28 * q^87 - 3 * q^88 - 9 * q^89 + 5 * q^91 - 15 * q^92 + 10 * q^93 - 22 * q^94 + 13 * q^97 - 42 * q^98 - 6 * q^99

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