LMFDB - Embedded newform 4425.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4425,2,Mod(1,4425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4425, 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("4425.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4425 = 3 \cdot 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4425.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:	$35.3338028944$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.86081$ of defining polynomial
Character	$\chi$	$=$	4425.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +1.86081 q^{6} -1.13919 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +1.86081 q^{6} -1.13919 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.398207 q^{11} +1.46260 q^{12} -2.39821 q^{13} -2.11982 q^{14} -4.78600 q^{16} -7.10941 q^{17} +1.86081 q^{18} +1.53740 q^{19} -1.13919 q^{21} +0.740987 q^{22} -3.25901 q^{23} -1.00000 q^{24} -4.46260 q^{26} +1.00000 q^{27} -1.66618 q^{28} -3.93561 q^{29} +7.78600 q^{31} -6.90582 q^{32} +0.398207 q^{33} -13.2292 q^{34} +1.46260 q^{36} -1.25901 q^{37} +2.86081 q^{38} -2.39821 q^{39} -7.50761 q^{41} -2.11982 q^{42} +9.69182 q^{43} +0.582418 q^{44} -6.06439 q^{46} -8.71120 q^{47} -4.78600 q^{48} -5.70224 q^{49} -7.10941 q^{51} -3.50761 q^{52} -10.7666 q^{53} +1.86081 q^{54} +1.13919 q^{56} +1.53740 q^{57} -7.32340 q^{58} +1.00000 q^{59} +0.989588 q^{61} +14.4882 q^{62} -1.13919 q^{63} -3.27839 q^{64} +0.740987 q^{66} -5.45219 q^{67} -10.3982 q^{68} -3.25901 q^{69} +15.0450 q^{71} -1.00000 q^{72} -4.73202 q^{73} -2.34278 q^{74} +2.24860 q^{76} -0.453636 q^{77} -4.46260 q^{78} +7.04502 q^{79} +1.00000 q^{81} -13.9702 q^{82} -13.0796 q^{83} -1.66618 q^{84} +18.0346 q^{86} -3.93561 q^{87} -0.398207 q^{88} -16.4328 q^{89} +2.73202 q^{91} -4.76663 q^{92} +7.78600 q^{93} -16.2099 q^{94} -6.90582 q^{96} -14.7666 q^{97} -10.6108 q^{98} +0.398207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 2 q^{4} - 9 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 2 * q^4 - 9 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 2 q^{4} - 9 q^{7} - 3 q^{8} + 3 q^{9} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 8 q^{14} - 4 q^{16} - 3 q^{17} + 7 q^{19} - 9 q^{21} + 11 q^{22} - q^{23} - 3 q^{24} - 11 q^{26} + 3 q^{27} - 9 q^{28} - 11 q^{29} + 13 q^{31} + 4 q^{32} - 2 q^{33} - 7 q^{34} + 2 q^{36} + 5 q^{37} + 3 q^{38} - 4 q^{39} - q^{41} + 8 q^{42} - 6 q^{43} - 15 q^{44} - 19 q^{46} - 11 q^{47} - 4 q^{48} + 14 q^{49} - 3 q^{51} + 11 q^{52} - 2 q^{53} + 9 q^{56} + 7 q^{57} - 14 q^{58} + 3 q^{59} - q^{61} + 2 q^{62} - 9 q^{63} - 21 q^{64} + 11 q^{66} - 10 q^{67} - 28 q^{68} - q^{69} + 26 q^{71} - 3 q^{72} - 7 q^{73} - 19 q^{74} - 6 q^{76} + 17 q^{77} - 11 q^{78} + 2 q^{79} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 9 q^{84} + 31 q^{86} - 11 q^{87} + 2 q^{88} - 23 q^{89} + q^{91} + 16 q^{92} + 13 q^{93} + 4 q^{94} + 4 q^{96} - 14 q^{97} - 51 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 2 * q^4 - 9 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 8 * q^14 - 4 * q^16 - 3 * q^17 + 7 * q^19 - 9 * q^21 + 11 * q^22 - q^23 - 3 * q^24 - 11 * q^26 + 3 * q^27 - 9 * q^28 - 11 * q^29 + 13 * q^31 + 4 * q^32 - 2 * q^33 - 7 * q^34 + 2 * q^36 + 5 * q^37 + 3 * q^38 - 4 * q^39 - q^41 + 8 * q^42 - 6 * q^43 - 15 * q^44 - 19 * q^46 - 11 * q^47 - 4 * q^48 + 14 * q^49 - 3 * q^51 + 11 * q^52 - 2 * q^53 + 9 * q^56 + 7 * q^57 - 14 * q^58 + 3 * q^59 - q^61 + 2 * q^62 - 9 * q^63 - 21 * q^64 + 11 * q^66 - 10 * q^67 - 28 * q^68 - q^69 + 26 * q^71 - 3 * q^72 - 7 * q^73 - 19 * q^74 - 6 * q^76 + 17 * q^77 - 11 * q^78 + 2 * q^79 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 9 * q^84 + 31 * q^86 - 11 * q^87 + 2 * q^88 - 23 * q^89 + q^91 + 16 * q^92 + 13 * q^93 + 4 * q^94 + 4 * q^96 - 14 * q^97 - 51 * q^98 - 2 * 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 $

$2$	1.86081	1.31579	0.657894	−	0.753110i	$-0.271447\pi$
$2$	1.86081	1.31579	0.657894	+	0.753110i	$0.271447\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.46260	0.731299
$5$	0	0
$5$	0	0
$6$	1.86081	0.759671
$7$	−1.13919	−0.430575	−0.215287	−	0.976551i	$-0.569069\pi$
$7$	−1.13919	−0.430575	−0.215287	+	0.976551i	$0.569069\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0.398207	0.120064	0.0600320	−	0.998196i	$-0.480880\pi$
$11$	0.398207	0.120064	0.0600320	+	0.998196i	$0.480880\pi$
$12$	1.46260	0.422216
$13$	−2.39821	−0.665143	−0.332572	−	0.943078i	$-0.607916\pi$
$13$	−2.39821	−0.665143	−0.332572	+	0.943078i	$0.607916\pi$
$14$	−2.11982	−0.566545
$15$	0	0
$16$	−4.78600	−1.19650
$17$	−7.10941	−1.72428	−0.862142	−	0.506666i	$-0.830878\pi$
$17$	−7.10941	−1.72428	−0.862142	+	0.506666i	$0.830878\pi$
$18$	1.86081	0.438596
$19$	1.53740	0.352704	0.176352	−	0.984327i	$-0.443570\pi$
$19$	1.53740	0.352704	0.176352	+	0.984327i	$0.443570\pi$
$20$	0	0
$21$	−1.13919	−0.248593
$22$	0.740987	0.157979
$23$	−3.25901	−0.679551	−0.339776	−	0.940507i	$-0.610351\pi$
$23$	−3.25901	−0.679551	−0.339776	+	0.940507i	$0.610351\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−4.46260	−0.875188
$27$	1.00000	0.192450
$28$	−1.66618	−0.314879
$29$	−3.93561	−0.730824	−0.365412	−	0.930846i	$-0.619072\pi$
$29$	−3.93561	−0.730824	−0.365412	+	0.930846i	$0.619072\pi$
$30$	0	0
$31$	7.78600	1.39841	0.699204	−	0.714923i	$-0.253538\pi$
$31$	7.78600	1.39841	0.699204	+	0.714923i	$0.253538\pi$
$32$	−6.90582	−1.22079
$33$	0.398207	0.0693190
$34$	−13.2292	−2.26879
$35$	0	0
$36$	1.46260	0.243766
$37$	−1.25901	−0.206981	−0.103490	−	0.994630i	$-0.533001\pi$
$37$	−1.25901	−0.206981	−0.103490	+	0.994630i	$0.533001\pi$
$38$	2.86081	0.464084
$39$	−2.39821	−0.384021
$40$	0	0
$41$	−7.50761	−1.17249	−0.586246	−	0.810133i	$-0.699395\pi$
$41$	−7.50761	−1.17249	−0.586246	+	0.810133i	$0.699395\pi$
$42$	−2.11982	−0.327095
$43$	9.69182	1.47799	0.738995	−	0.673711i	$-0.235301\pi$
$43$	9.69182	1.47799	0.738995	+	0.673711i	$0.235301\pi$
$44$	0.582418	0.0878028
$45$	0	0
$46$	−6.06439	−0.894146
$47$	−8.71120	−1.27066	−0.635330	−	0.772241i	$-0.719136\pi$
$47$	−8.71120	−1.27066	−0.635330	+	0.772241i	$0.719136\pi$
$48$	−4.78600	−0.690800
$49$	−5.70224	−0.814605
$50$	0	0
$51$	−7.10941	−0.995516
$52$	−3.50761	−0.486419
$53$	−10.7666	−1.47891	−0.739455	−	0.673206i	$-0.764917\pi$
$53$	−10.7666	−1.47891	−0.739455	+	0.673206i	$0.764917\pi$
$54$	1.86081	0.253224
$55$	0	0
$56$	1.13919	0.152231
$57$	1.53740	0.203634
$58$	−7.32340	−0.961610
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	0.989588	0.126704	0.0633519	−	0.997991i	$-0.479821\pi$
$61$	0.989588	0.126704	0.0633519	+	0.997991i	$0.479821\pi$
$62$	14.4882	1.84001
$63$	−1.13919	−0.143525
$64$	−3.27839	−0.409799
$65$	0	0
$66$	0.740987	0.0912092
$67$	−5.45219	−0.666091	−0.333045	−	0.942911i	$-0.608076\pi$
$67$	−5.45219	−0.666091	−0.333045	+	0.942911i	$0.608076\pi$
$68$	−10.3982	−1.26097
$69$	−3.25901	−0.392339
$70$	0	0
$71$	15.0450	1.78551	0.892757	−	0.450538i	$-0.148768\pi$
$71$	15.0450	1.78551	0.892757	+	0.450538i	$0.148768\pi$
$72$	−1.00000	−0.117851
$73$	−4.73202	−0.553842	−0.276921	−	0.960893i	$-0.589314\pi$
$73$	−4.73202	−0.553842	−0.276921	+	0.960893i	$0.589314\pi$
$74$	−2.34278	−0.272343
$75$	0	0
$76$	2.24860	0.257932
$77$	−0.453636	−0.0516966
$78$	−4.46260	−0.505290
$79$	7.04502	0.792626	0.396313	−	0.918115i	$-0.370289\pi$
$79$	7.04502	0.792626	0.396313	+	0.918115i	$0.370289\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−13.9702	−1.54275
$83$	−13.0796	−1.43567	−0.717837	−	0.696211i	$-0.754868\pi$
$83$	−13.0796	−1.43567	−0.717837	+	0.696211i	$0.754868\pi$
$84$	−1.66618	−0.181796
$85$	0	0
$86$	18.0346	1.94472
$87$	−3.93561	−0.421942
$88$	−0.398207	−0.0424491
$89$	−16.4328	−1.74187	−0.870937	−	0.491394i	$-0.836487\pi$
$89$	−16.4328	−1.74187	−0.870937	+	0.491394i	$0.836487\pi$
$90$	0	0
$91$	2.73202	0.286394
$92$	−4.76663	−0.496955
$93$	7.78600	0.807371
$94$	−16.2099	−1.67192
$95$	0	0
$96$	−6.90582	−0.704822
$97$	−14.7666	−1.49932	−0.749662	−	0.661821i	$-0.769784\pi$
$97$	−14.7666	−1.49932	−0.749662	+	0.661821i	$0.769784\pi$
$98$	−10.6108	−1.07185
$99$	0.398207	0.0400214
$100$	0	0
$101$	−0.278388	−0.0277007	−0.0138503	−	0.999904i	$-0.504409\pi$
$101$	−0.278388	−0.0277007	−0.0138503	+	0.999904i	$0.504409\pi$
$102$	−13.2292	−1.30989
$103$	15.0152	1.47949	0.739747	−	0.672885i	$-0.234945\pi$
$103$	15.0152	1.47949	0.739747	+	0.672885i	$0.234945\pi$
$104$	2.39821	0.235164
$105$	0	0
$106$	−20.0346	−1.94593
$107$	−1.16898	−0.113010	−0.0565048	−	0.998402i	$-0.517996\pi$
$107$	−1.16898	−0.113010	−0.0565048	+	0.998402i	$0.517996\pi$
$108$	1.46260	0.140739
$109$	−4.89059	−0.468434	−0.234217	−	0.972184i	$-0.575253\pi$
$109$	−4.89059	−0.468434	−0.234217	+	0.972184i	$0.575253\pi$
$110$	0	0
$111$	−1.25901	−0.119500
$112$	5.45219	0.515183
$113$	15.5630	1.46405	0.732024	−	0.681279i	$-0.238576\pi$
$113$	15.5630	1.46405	0.732024	+	0.681279i	$0.238576\pi$
$114$	2.86081	0.267939
$115$	0	0
$116$	−5.75622	−0.534451
$117$	−2.39821	−0.221714
$118$	1.86081	0.171301
$119$	8.09899	0.742434
$120$	0	0
$121$	−10.8414	−0.985585
$122$	1.84143	0.166715
$123$	−7.50761	−0.676939
$124$	11.3878	1.02265
$125$	0	0
$126$	−2.11982	−0.188848
$127$	−4.39821	−0.390278	−0.195139	−	0.980776i	$-0.562516\pi$
$127$	−4.39821	−0.390278	−0.195139	+	0.980776i	$0.562516\pi$
$128$	7.71120	0.681580
$129$	9.69182	0.853318
$130$	0	0
$131$	17.6620	1.54314	0.771570	−	0.636145i	$-0.219472\pi$
$131$	17.6620	1.54314	0.771570	+	0.636145i	$0.219472\pi$
$132$	0.582418	0.0506929
$133$	−1.75140	−0.151866
$134$	−10.1455	−0.876434
$135$	0	0
$136$	7.10941	0.609627
$137$	10.7666	0.919855	0.459928	−	0.887956i	$-0.347875\pi$
$137$	10.7666	0.919855	0.459928	+	0.887956i	$0.347875\pi$
$138$	−6.06439	−0.516235
$139$	9.82061	0.832973	0.416486	−	0.909142i	$-0.363261\pi$
$139$	9.82061	0.832973	0.416486	+	0.909142i	$0.363261\pi$
$140$	0	0
$141$	−8.71120	−0.733615
$142$	27.9959	2.34936
$143$	−0.954984	−0.0798598
$144$	−4.78600	−0.398834
$145$	0	0
$146$	−8.80538	−0.728738
$147$	−5.70224	−0.470313
$148$	−1.84143	−0.151365
$149$	−5.01938	−0.411203	−0.205602	−	0.978636i	$-0.565915\pi$
$149$	−5.01938	−0.411203	−0.205602	+	0.978636i	$0.565915\pi$
$150$	0	0
$151$	7.35801	0.598786	0.299393	−	0.954130i	$-0.403216\pi$
$151$	7.35801	0.598786	0.299393	+	0.954130i	$0.403216\pi$
$152$	−1.53740	−0.124700
$153$	−7.10941	−0.574761
$154$	−0.844128	−0.0680218
$155$	0	0
$156$	−3.50761	−0.280834
$157$	1.73057	0.138115	0.0690574	−	0.997613i	$-0.478001\pi$
$157$	1.73057	0.138115	0.0690574	+	0.997613i	$0.478001\pi$
$158$	13.1094	1.04293
$159$	−10.7666	−0.853849
$160$	0	0
$161$	3.71265	0.292598
$162$	1.86081	0.146199
$163$	8.58242	0.672227	0.336113	−	0.941822i	$-0.390887\pi$
$163$	8.58242	0.672227	0.336113	+	0.941822i	$0.390887\pi$
$164$	−10.9806	−0.857443
$165$	0	0
$166$	−24.3386	−1.88904
$167$	−6.49239	−0.502396	−0.251198	−	0.967936i	$-0.580825\pi$
$167$	−6.49239	−0.502396	−0.251198	+	0.967936i	$0.580825\pi$
$168$	1.13919	0.0878907
$169$	−7.24860	−0.557585
$170$	0	0
$171$	1.53740	0.117568
$172$	14.1752	1.08085
$173$	20.5437	1.56191	0.780953	−	0.624590i	$-0.214734\pi$
$173$	20.5437	1.56191	0.780953	+	0.624590i	$0.214734\pi$
$174$	−7.32340	−0.555186
$175$	0	0
$176$	−1.90582	−0.143657
$177$	1.00000	0.0751646
$178$	−30.5783	−2.29194
$179$	−23.9702	−1.79162	−0.895809	−	0.444439i	$-0.853403\pi$
$179$	−23.9702	−1.79162	−0.895809	+	0.444439i	$0.853403\pi$
$180$	0	0
$181$	14.7112	1.09347	0.546737	−	0.837304i	$-0.315870\pi$
$181$	14.7112	1.09347	0.546737	+	0.837304i	$0.315870\pi$
$182$	5.08377	0.376834
$183$	0.989588	0.0731524
$184$	3.25901	0.240258
$185$	0	0
$186$	14.4882	1.06233
$187$	−2.83102	−0.207025
$188$	−12.7410	−0.929232
$189$	−1.13919	−0.0828642
$190$	0	0
$191$	2.91623	0.211011	0.105506	−	0.994419i	$-0.466354\pi$
$191$	2.91623	0.211011	0.105506	+	0.994419i	$0.466354\pi$
$192$	−3.27839	−0.236597
$193$	0.646809	0.0465583	0.0232791	−	0.999729i	$-0.492589\pi$
$193$	0.646809	0.0465583	0.0232791	+	0.999729i	$0.492589\pi$
$194$	−27.4778	−1.97279
$195$	0	0
$196$	−8.34008	−0.595720
$197$	5.87122	0.418307	0.209153	−	0.977883i	$-0.432929\pi$
$197$	5.87122	0.418307	0.209153	+	0.977883i	$0.432929\pi$
$198$	0.740987	0.0526596
$199$	11.1004	0.786890	0.393445	−	0.919348i	$-0.371283\pi$
$199$	11.1004	0.786890	0.393445	+	0.919348i	$0.371283\pi$
$200$	0	0
$201$	−5.45219	−0.384568
$202$	−0.518027	−0.0364482
$203$	4.48342	0.314675
$204$	−10.3982	−0.728020
$205$	0	0
$206$	27.9404	1.94670
$207$	−3.25901	−0.226517
$208$	11.4778	0.795844
$209$	0.612205	0.0423471
$210$	0	0
$211$	−13.4778	−0.927852	−0.463926	−	0.885874i	$-0.653560\pi$
$211$	−13.4778	−0.927852	−0.463926	+	0.885874i	$0.653560\pi$
$212$	−15.7473	−1.08153
$213$	15.0450	1.03087
$214$	−2.17525	−0.148697
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−8.86977	−0.602119
$218$	−9.10044	−0.616360
$219$	−4.73202	−0.319761
$220$	0	0
$221$	17.0498	1.14690
$222$	−2.34278	−0.157237
$223$	−16.7368	−1.12078	−0.560391	−	0.828228i	$-0.689349\pi$
$223$	−16.7368	−1.12078	−0.560391	+	0.828228i	$0.689349\pi$
$224$	7.86707	0.525641
$225$	0	0
$226$	28.9598	1.92638
$227$	14.0346	0.931509	0.465755	−	0.884914i	$-0.345783\pi$
$227$	14.0346	0.931509	0.465755	+	0.884914i	$0.345783\pi$
$228$	2.24860	0.148917
$229$	−12.2445	−0.809136	−0.404568	−	0.914508i	$-0.632578\pi$
$229$	−12.2445	−0.809136	−0.404568	+	0.914508i	$0.632578\pi$
$230$	0	0
$231$	−0.453636	−0.0298470
$232$	3.93561	0.258385
$233$	−1.87122	−0.122588	−0.0612938	−	0.998120i	$-0.519523\pi$
$233$	−1.87122	−0.122588	−0.0612938	+	0.998120i	$0.519523\pi$
$234$	−4.46260	−0.291729
$235$	0	0
$236$	1.46260	0.0952070
$237$	7.04502	0.457623
$238$	15.0707	0.976886
$239$	−13.9910	−0.905005	−0.452502	−	0.891763i	$-0.649469\pi$
$239$	−13.9910	−0.905005	−0.452502	+	0.891763i	$0.649469\pi$
$240$	0	0
$241$	27.5333	1.77357	0.886786	−	0.462179i	$-0.152932\pi$
$241$	27.5333	1.77357	0.886786	+	0.462179i	$0.152932\pi$
$242$	−20.1738	−1.29682
$243$	1.00000	0.0641500
$244$	1.44737	0.0926583
$245$	0	0
$246$	−13.9702	−0.890708
$247$	−3.68701	−0.234599
$248$	−7.78600	−0.494412
$249$	−13.0796	−0.828887
$250$	0	0
$251$	−2.61702	−0.165185	−0.0825925	−	0.996583i	$-0.526320\pi$
$251$	−2.61702	−0.165185	−0.0825925	+	0.996583i	$0.526320\pi$
$252$	−1.66618	−0.104960
$253$	−1.29776	−0.0815897
$254$	−8.18421	−0.513523
$255$	0	0
$256$	20.9058	1.30661
$257$	−20.3892	−1.27185	−0.635923	−	0.771752i	$-0.719380\pi$
$257$	−20.3892	−1.27185	−0.635923	+	0.771752i	$0.719380\pi$
$258$	18.0346	1.12279
$259$	1.43426	0.0891206
$260$	0	0
$261$	−3.93561	−0.243608
$262$	32.8656	2.03044
$263$	23.8552	1.47098	0.735488	−	0.677538i	$-0.236953\pi$
$263$	23.8552	1.47098	0.735488	+	0.677538i	$0.236953\pi$
$264$	−0.398207	−0.0245080
$265$	0	0
$266$	−3.25901	−0.199823
$267$	−16.4328	−1.00567
$268$	−7.97436	−0.487112
$269$	−28.2999	−1.72547	−0.862737	−	0.505653i	$-0.831252\pi$
$269$	−28.2999	−1.72547	−0.862737	+	0.505653i	$0.831252\pi$
$270$	0	0
$271$	−23.4134	−1.42226	−0.711132	−	0.703058i	$-0.751817\pi$
$271$	−23.4134	−1.42226	−0.711132	+	0.703058i	$0.751817\pi$
$272$	34.0256	2.06311
$273$	2.73202	0.165350
$274$	20.0346	1.21033
$275$	0	0
$276$	−4.76663	−0.286917
$277$	−15.6918	−0.942830	−0.471415	−	0.881911i	$-0.656257\pi$
$277$	−15.6918	−0.942830	−0.471415	+	0.881911i	$0.656257\pi$
$278$	18.2742	1.09602
$279$	7.78600	0.466136
$280$	0	0
$281$	−5.63158	−0.335952	−0.167976	−	0.985791i	$-0.553723\pi$
$281$	−5.63158	−0.335952	−0.167976	+	0.985791i	$0.553723\pi$
$282$	−16.2099	−0.965283
$283$	−10.8310	−0.643837	−0.321919	−	0.946767i	$-0.604328\pi$
$283$	−10.8310	−0.643837	−0.321919	+	0.946767i	$0.604328\pi$
$284$	22.0048	1.30575
$285$	0	0
$286$	−1.77704	−0.105079
$287$	8.55263	0.504846
$288$	−6.90582	−0.406929
$289$	33.5437	1.97316
$290$	0	0
$291$	−14.7666	−0.865635
$292$	−6.92105	−0.405024
$293$	−33.9959	−1.98606	−0.993029	−	0.117866i	$-0.962395\pi$
$293$	−33.9959	−1.98606	−0.993029	+	0.117866i	$0.962395\pi$
$294$	−10.6108	−0.618832
$295$	0	0
$296$	1.25901	0.0731787
$297$	0.398207	0.0231063
$298$	−9.34008	−0.541056
$299$	7.81579	0.451999
$300$	0	0
$301$	−11.0409	−0.636385
$302$	13.6918	0.787876
$303$	−0.278388	−0.0159930
$304$	−7.35801	−0.422011
$305$	0	0
$306$	−13.2292	−0.756265
$307$	4.25756	0.242992	0.121496	−	0.992592i	$-0.461231\pi$
$307$	4.25756	0.242992	0.121496	+	0.992592i	$0.461231\pi$
$308$	−0.663487	−0.0378057
$309$	15.0152	0.854187
$310$	0	0
$311$	21.5374	1.22127	0.610637	−	0.791911i	$-0.290913\pi$
$311$	21.5374	1.22127	0.610637	+	0.791911i	$0.290913\pi$
$312$	2.39821	0.135772
$313$	3.96540	0.224137	0.112069	−	0.993700i	$-0.464252\pi$
$313$	3.96540	0.224137	0.112069	+	0.993700i	$0.464252\pi$
$314$	3.22026	0.181730
$315$	0	0
$316$	10.3040	0.579647
$317$	−7.58097	−0.425790	−0.212895	−	0.977075i	$-0.568289\pi$
$317$	−7.58097	−0.425790	−0.212895	+	0.977075i	$0.568289\pi$
$318$	−20.0346	−1.12348
$319$	−1.56719	−0.0877457
$320$	0	0
$321$	−1.16898	−0.0652462
$322$	6.90852	0.384997
$323$	−10.9300	−0.608162
$324$	1.46260	0.0812555
$325$	0	0
$326$	15.9702	0.884508
$327$	−4.89059	−0.270450
$328$	7.50761	0.414539
$329$	9.92375	0.547114
$330$	0	0
$331$	−0.667633	−0.0366964	−0.0183482	−	0.999832i	$-0.505841\pi$
$331$	−0.667633	−0.0366964	−0.0183482	+	0.999832i	$0.505841\pi$
$332$	−19.1302	−1.04991
$333$	−1.25901	−0.0689935
$334$	−12.0811	−0.661047
$335$	0	0
$336$	5.45219	0.297441
$337$	−7.47783	−0.407343	−0.203672	−	0.979039i	$-0.565287\pi$
$337$	−7.47783	−0.407343	−0.203672	+	0.979039i	$0.565287\pi$
$338$	−13.4882	−0.733664
$339$	15.5630	0.845268
$340$	0	0
$341$	3.10044	0.167898
$342$	2.86081	0.154695
$343$	14.4703	0.781323
$344$	−9.69182	−0.522548
$345$	0	0
$346$	38.2278	2.05514
$347$	29.0200	1.55788	0.778939	−	0.627100i	$-0.215758\pi$
$347$	29.0200	1.55788	0.778939	+	0.627100i	$0.215758\pi$
$348$	−5.75622	−0.308566
$349$	−16.8746	−0.903276	−0.451638	−	0.892201i	$-0.649160\pi$
$349$	−16.8746	−0.903276	−0.451638	+	0.892201i	$0.649160\pi$
$350$	0	0
$351$	−2.39821	−0.128007
$352$	−2.74995	−0.146573
$353$	2.98062	0.158643	0.0793213	−	0.996849i	$-0.474725\pi$
$353$	2.98062	0.158643	0.0793213	+	0.996849i	$0.474725\pi$
$354$	1.86081	0.0989007
$355$	0	0
$356$	−24.0346	−1.27383
$357$	8.09899	0.428644
$358$	−44.6039	−2.35739
$359$	−1.85039	−0.0976600	−0.0488300	−	0.998807i	$-0.515549\pi$
$359$	−1.85039	−0.0976600	−0.0488300	+	0.998807i	$0.515549\pi$
$360$	0	0
$361$	−16.6364	−0.875600
$362$	27.3747	1.43878
$363$	−10.8414	−0.569028
$364$	3.99585	0.209440
$365$	0	0
$366$	1.84143	0.0962531
$367$	−7.97021	−0.416042	−0.208021	−	0.978124i	$-0.566702\pi$
$367$	−7.97021	−0.416042	−0.208021	+	0.978124i	$0.566702\pi$
$368$	15.5976	0.813084
$369$	−7.50761	−0.390831
$370$	0	0
$371$	12.2653	0.636782
$372$	11.3878	0.590430
$373$	−1.31859	−0.0682739	−0.0341369	−	0.999417i	$-0.510868\pi$
$373$	−1.31859	−0.0682739	−0.0341369	+	0.999417i	$0.510868\pi$
$374$	−5.26798	−0.272401
$375$	0	0
$376$	8.71120	0.449246
$377$	9.43841	0.486103
$378$	−2.11982	−0.109032
$379$	20.5783	1.05703	0.528517	−	0.848922i	$-0.322748\pi$
$379$	20.5783	1.05703	0.528517	+	0.848922i	$0.322748\pi$
$380$	0	0
$381$	−4.39821	−0.225327
$382$	5.42655	0.277646
$383$	−21.8802	−1.11803	−0.559013	−	0.829159i	$-0.688820\pi$
$383$	−21.8802	−1.11803	−0.559013	+	0.829159i	$0.688820\pi$
$384$	7.71120	0.393511
$385$	0	0
$386$	1.20359	0.0612609
$387$	9.69182	0.492663
$388$	−21.5976	−1.09645
$389$	−6.29921	−0.319383	−0.159691	−	0.987167i	$-0.551050\pi$
$389$	−6.29921	−0.319383	−0.159691	+	0.987167i	$0.551050\pi$
$390$	0	0
$391$	23.1697	1.17174
$392$	5.70224	0.288006
$393$	17.6620	0.890932
$394$	10.9252	0.550403
$395$	0	0
$396$	0.582418	0.0292676
$397$	12.1198	0.608276	0.304138	−	0.952628i	$-0.401632\pi$
$397$	12.1198	0.608276	0.304138	+	0.952628i	$0.401632\pi$
$398$	20.6558	1.03538
$399$	−1.75140	−0.0876796
$400$	0	0
$401$	−16.3338	−0.815672	−0.407836	−	0.913055i	$-0.633716\pi$
$401$	−16.3338	−0.815672	−0.407836	+	0.913055i	$0.633716\pi$
$402$	−10.1455	−0.506010
$403$	−18.6724	−0.930141
$404$	−0.407170	−0.0202575
$405$	0	0
$406$	8.34278	0.414045
$407$	−0.501348	−0.0248509
$408$	7.10941	0.351968
$409$	37.0665	1.83282	0.916410	−	0.400240i	$-0.131073\pi$
$409$	37.0665	1.83282	0.916410	+	0.400240i	$0.131073\pi$
$410$	0	0
$411$	10.7666	0.531079
$412$	21.9612	1.08195
$413$	−1.13919	−0.0560561
$414$	−6.06439	−0.298049
$415$	0	0
$416$	16.5616	0.811999
$417$	9.82061	0.480917
$418$	1.13919	0.0557198
$419$	14.6468	0.715543	0.357772	−	0.933809i	$-0.383537\pi$
$419$	14.6468	0.715543	0.357772	+	0.933809i	$0.383537\pi$
$420$	0	0
$421$	−3.32340	−0.161973	−0.0809864	−	0.996715i	$-0.525807\pi$
$421$	−3.32340	−0.161973	−0.0809864	+	0.996715i	$0.525807\pi$
$422$	−25.0796	−1.22086
$423$	−8.71120	−0.423553
$424$	10.7666	0.522874
$425$	0	0
$426$	27.9959	1.35640
$427$	−1.12733	−0.0545555
$428$	−1.70975	−0.0826439
$429$	−0.954984	−0.0461071
$430$	0	0
$431$	2.73202	0.131597	0.0657985	−	0.997833i	$-0.479041\pi$
$431$	2.73202	0.131597	0.0657985	+	0.997833i	$0.479041\pi$
$432$	−4.78600	−0.230267
$433$	36.1038	1.73504	0.867519	−	0.497404i	$-0.165713\pi$
$433$	36.1038	1.73504	0.867519	+	0.497404i	$0.165713\pi$
$434$	−16.5049	−0.792261
$435$	0	0
$436$	−7.15297	−0.342565
$437$	−5.01041	−0.239681
$438$	−8.80538	−0.420737
$439$	−37.9571	−1.81159	−0.905797	−	0.423712i	$-0.860727\pi$
$439$	−37.9571	−1.81159	−0.905797	+	0.423712i	$0.860727\pi$
$440$	0	0
$441$	−5.70224	−0.271535
$442$	31.7264	1.50907
$443$	−1.84625	−0.0877179	−0.0438589	−	0.999038i	$-0.513965\pi$
$443$	−1.84625	−0.0877179	−0.0438589	+	0.999038i	$0.513965\pi$
$444$	−1.84143	−0.0873904
$445$	0	0
$446$	−31.1440	−1.47471
$447$	−5.01938	−0.237408
$448$	3.73472	0.176449
$449$	27.9494	1.31901	0.659507	−	0.751699i	$-0.270765\pi$
$449$	27.9494	1.31901	0.659507	+	0.751699i	$0.270765\pi$
$450$	0	0
$451$	−2.98959	−0.140774
$452$	22.7625	1.07066
$453$	7.35801	0.345709
$454$	26.1157	1.22567
$455$	0	0
$456$	−1.53740	−0.0719954
$457$	23.2501	1.08759	0.543796	−	0.839218i	$-0.316987\pi$
$457$	23.2501	1.08759	0.543796	+	0.839218i	$0.316987\pi$
$458$	−22.7846	−1.06465
$459$	−7.10941	−0.331839
$460$	0	0
$461$	20.4447	0.952203	0.476102	−	0.879390i	$-0.342049\pi$
$461$	20.4447	0.952203	0.476102	+	0.879390i	$0.342049\pi$
$462$	−0.844128	−0.0392724
$463$	12.6122	0.586139	0.293069	−	0.956091i	$-0.405323\pi$
$463$	12.6122	0.586139	0.293069	+	0.956091i	$0.405323\pi$
$464$	18.8358	0.874432
$465$	0	0
$466$	−3.48197	−0.161299
$467$	1.89204	0.0875533	0.0437766	−	0.999041i	$-0.486061\pi$
$467$	1.89204	0.0875533	0.0437766	+	0.999041i	$0.486061\pi$
$468$	−3.50761	−0.162140
$469$	6.21110	0.286802
$470$	0	0
$471$	1.73057	0.0797407
$472$	−1.00000	−0.0460287
$473$	3.85936	0.177453
$474$	13.1094	0.602135
$475$	0	0
$476$	11.8456	0.542941
$477$	−10.7666	−0.492970
$478$	−26.0346	−1.19080
$479$	−3.51658	−0.160677	−0.0803383	−	0.996768i	$-0.525600\pi$
$479$	−3.51658	−0.160677	−0.0803383	+	0.996768i	$0.525600\pi$
$480$	0	0
$481$	3.01938	0.137672
$482$	51.2340	2.33365
$483$	3.71265	0.168931
$484$	−15.8567	−0.720757
$485$	0	0
$486$	1.86081	0.0844079
$487$	−21.2203	−0.961582	−0.480791	−	0.876835i	$-0.659650\pi$
$487$	−21.2203	−0.961582	−0.480791	+	0.876835i	$0.659650\pi$
$488$	−0.989588	−0.0447965
$489$	8.58242	0.388110
$490$	0	0
$491$	12.4536	0.562025	0.281012	−	0.959704i	$-0.409330\pi$
$491$	12.4536	0.562025	0.281012	+	0.959704i	$0.409330\pi$
$492$	−10.9806	−0.495045
$493$	27.9798	1.26015
$494$	−6.86081	−0.308682
$495$	0	0
$496$	−37.2638	−1.67320
$497$	−17.1392	−0.768798
$498$	−24.3386	−1.09064
$499$	33.0755	1.48066	0.740331	−	0.672243i	$-0.234669\pi$
$499$	33.0755	1.48066	0.740331	+	0.672243i	$0.234669\pi$
$500$	0	0
$501$	−6.49239	−0.290058
$502$	−4.86977	−0.217348
$503$	−12.5824	−0.561022	−0.280511	−	0.959851i	$-0.590504\pi$
$503$	−12.5824	−0.561022	−0.280511	+	0.959851i	$0.590504\pi$
$504$	1.13919	0.0507437
$505$	0	0
$506$	−2.41489	−0.107355
$507$	−7.24860	−0.321922
$508$	−6.43281	−0.285410
$509$	28.0465	1.24314	0.621569	−	0.783360i	$-0.286496\pi$
$509$	28.0465	1.24314	0.621569	+	0.783360i	$0.286496\pi$
$510$	0	0
$511$	5.39069	0.238470
$512$	23.4793	1.03765
$513$	1.53740	0.0678779
$514$	−37.9404	−1.67348
$515$	0	0
$516$	14.1752	0.624030
$517$	−3.46886	−0.152560
$518$	2.66888	0.117264
$519$	20.5437	0.901767
$520$	0	0
$521$	−37.7956	−1.65586	−0.827928	−	0.560834i	$-0.810481\pi$
$521$	−37.7956	−1.65586	−0.827928	+	0.560834i	$0.810481\pi$
$522$	−7.32340	−0.320537
$523$	17.1946	0.751868	0.375934	−	0.926646i	$-0.377322\pi$
$523$	17.1946	0.751868	0.375934	+	0.926646i	$0.377322\pi$
$524$	25.8325	1.12850
$525$	0	0
$526$	44.3899	1.93549
$527$	−55.3539	−2.41125
$528$	−1.90582	−0.0829402
$529$	−12.3788	−0.538210
$530$	0	0
$531$	1.00000	0.0433963
$532$	−2.56159	−0.111059
$533$	18.0048	0.779875
$534$	−30.5783	−1.32325
$535$	0	0
$536$	5.45219	0.235499
$537$	−23.9702	−1.03439
$538$	−52.6606	−2.27036
$539$	−2.27067	−0.0978048
$540$	0	0
$541$	−3.94939	−0.169797	−0.0848987	−	0.996390i	$-0.527057\pi$
$541$	−3.94939	−0.169797	−0.0848987	+	0.996390i	$0.527057\pi$
$542$	−43.5679	−1.87140
$543$	14.7112	0.631318
$544$	49.0963	2.10499
$545$	0	0
$546$	5.08377	0.217565
$547$	−17.1094	−0.731545	−0.365773	−	0.930704i	$-0.619195\pi$
$547$	−17.1094	−0.731545	−0.365773	+	0.930704i	$0.619195\pi$
$548$	15.7473	0.672689
$549$	0.989588	0.0422346
$550$	0	0
$551$	−6.05061	−0.257765
$552$	3.25901	0.138713
$553$	−8.02564	−0.341285
$554$	−29.1994	−1.24057
$555$	0	0
$556$	14.3636	0.609152
$557$	−3.29362	−0.139555	−0.0697775	−	0.997563i	$-0.522229\pi$
$557$	−3.29362	−0.139555	−0.0697775	+	0.997563i	$0.522229\pi$
$558$	14.4882	0.613336
$559$	−23.2430	−0.983074
$560$	0	0
$561$	−2.83102	−0.119526
$562$	−10.4793	−0.442042
$563$	−3.10459	−0.130843	−0.0654214	−	0.997858i	$-0.520839\pi$
$563$	−3.10459	−0.130843	−0.0654214	+	0.997858i	$0.520839\pi$
$564$	−12.7410	−0.536492
$565$	0	0
$566$	−20.1544	−0.847154
$567$	−1.13919	−0.0478417
$568$	−15.0450	−0.631275
$569$	14.4024	0.603778	0.301889	−	0.953343i	$-0.402383\pi$
$569$	14.4024	0.603778	0.301889	+	0.953343i	$0.402383\pi$
$570$	0	0
$571$	−34.1198	−1.42787	−0.713935	−	0.700212i	$-0.753089\pi$
$571$	−34.1198	−1.42787	−0.713935	+	0.700212i	$0.753089\pi$
$572$	−1.39676	−0.0584014
$573$	2.91623	0.121827
$574$	15.9148	0.664270
$575$	0	0
$576$	−3.27839	−0.136600
$577$	43.6143	1.81569	0.907844	−	0.419308i	$-0.137727\pi$
$577$	43.6143	1.81569	0.907844	+	0.419308i	$0.137727\pi$
$578$	62.4183	2.59626
$579$	0.646809	0.0268804
$580$	0	0
$581$	14.9002	0.618166
$582$	−27.4778	−1.13899
$583$	−4.28735	−0.177564
$584$	4.73202	0.195813
$585$	0	0
$586$	−63.2597	−2.61323
$587$	−10.6170	−0.438211	−0.219106	−	0.975701i	$-0.570314\pi$
$587$	−10.6170	−0.438211	−0.219106	+	0.975701i	$0.570314\pi$
$588$	−8.34008	−0.343939
$589$	11.9702	0.493224
$590$	0	0
$591$	5.87122	0.241510
$592$	6.02564	0.247652
$593$	0.621168	0.0255083	0.0127541	−	0.999919i	$-0.495940\pi$
$593$	0.621168	0.0255083	0.0127541	+	0.999919i	$0.495940\pi$
$594$	0.740987	0.0304031
$595$	0	0
$596$	−7.34133	−0.300713
$597$	11.1004	0.454311
$598$	14.5437	0.594735
$599$	3.01523	0.123199	0.0615995	−	0.998101i	$-0.480380\pi$
$599$	3.01523	0.123199	0.0615995	+	0.998101i	$0.480380\pi$
$600$	0	0
$601$	−6.24378	−0.254689	−0.127345	−	0.991859i	$-0.540645\pi$
$601$	−6.24378	−0.254689	−0.127345	+	0.991859i	$0.540645\pi$
$602$	−20.5449	−0.837348
$603$	−5.45219	−0.222030
$604$	10.7618	0.437892
$605$	0	0
$606$	−0.518027	−0.0210434
$607$	0.526989	0.0213898	0.0106949	−	0.999943i	$-0.496596\pi$
$607$	0.526989	0.0213898	0.0106949	+	0.999943i	$0.496596\pi$
$608$	−10.6170	−0.430577
$609$	4.48342	0.181677
$610$	0	0
$611$	20.8913	0.845170
$612$	−10.3982	−0.420323
$613$	−44.6564	−1.80366	−0.901828	−	0.432094i	$-0.857775\pi$
$613$	−44.6564	−1.80366	−0.901828	+	0.432094i	$0.857775\pi$
$614$	7.92250	0.319726
$615$	0	0
$616$	0.453636	0.0182775
$617$	44.5831	1.79485	0.897424	−	0.441170i	$-0.145436\pi$
$617$	44.5831	1.79485	0.897424	+	0.441170i	$0.145436\pi$
$618$	27.9404	1.12393
$619$	−39.6531	−1.59379	−0.796896	−	0.604117i	$-0.793526\pi$
$619$	−39.6531	−1.59379	−0.796896	+	0.604117i	$0.793526\pi$
$620$	0	0
$621$	−3.25901	−0.130780
$622$	40.0769	1.60694
$623$	18.7202	0.750007
$624$	11.4778	0.459481
$625$	0	0
$626$	7.37883	0.294917
$627$	0.612205	0.0244491
$628$	2.53114	0.101003
$629$	8.95084	0.356893
$630$	0	0
$631$	−6.30818	−0.251125	−0.125562	−	0.992086i	$-0.540073\pi$
$631$	−6.30818	−0.251125	−0.125562	+	0.992086i	$0.540073\pi$
$632$	−7.04502	−0.280236
$633$	−13.4778	−0.535696
$634$	−14.1067	−0.560249
$635$	0	0
$636$	−15.7473	−0.624419
$637$	13.6751	0.541829
$638$	−2.91623	−0.115455
$639$	15.0450	0.595172
$640$	0	0
$641$	16.5062	0.651954	0.325977	−	0.945378i	$-0.394307\pi$
$641$	16.5062	0.651954	0.325977	+	0.945378i	$0.394307\pi$
$642$	−2.17525	−0.0858502
$643$	22.1455	0.873332	0.436666	−	0.899624i	$-0.356159\pi$
$643$	22.1455	0.873332	0.436666	+	0.899624i	$0.356159\pi$
$644$	5.43011	0.213976
$645$	0	0
$646$	−20.3386	−0.800213
$647$	12.4376	0.488974	0.244487	−	0.969653i	$-0.421381\pi$
$647$	12.4376	0.488974	0.244487	+	0.969653i	$0.421381\pi$
$648$	−1.00000	−0.0392837
$649$	0.398207	0.0156310
$650$	0	0
$651$	−8.86977	−0.347634
$652$	12.5526	0.491599
$653$	10.3941	0.406751	0.203376	−	0.979101i	$-0.434809\pi$
$653$	10.3941	0.406751	0.203376	+	0.979101i	$0.434809\pi$
$654$	−9.10044	−0.355856
$655$	0	0
$656$	35.9315	1.40289
$657$	−4.73202	−0.184614
$658$	18.4662	0.719886
$659$	−46.5139	−1.81192	−0.905962	−	0.423360i	$-0.860851\pi$
$659$	−46.5139	−1.81192	−0.905962	+	0.423360i	$0.860851\pi$
$660$	0	0
$661$	−31.3788	−1.22050	−0.610248	−	0.792211i	$-0.708930\pi$
$661$	−31.3788	−1.22050	−0.610248	+	0.792211i	$0.708930\pi$
$662$	−1.24234	−0.0482847
$663$	17.0498	0.662161
$664$	13.0796	0.507588
$665$	0	0
$666$	−2.34278	−0.0907809
$667$	12.8262	0.496633
$668$	−9.49575	−0.367402
$669$	−16.7368	−0.647084
$670$	0	0
$671$	0.394061	0.0152126
$672$	7.86707	0.303479
$673$	−23.2936	−0.897903	−0.448951	−	0.893556i	$-0.648202\pi$
$673$	−23.2936	−0.897903	−0.448951	+	0.893556i	$0.648202\pi$
$674$	−13.9148	−0.535977
$675$	0	0
$676$	−10.6018	−0.407761
$677$	0.775591	0.0298084	0.0149042	−	0.999889i	$-0.495256\pi$
$677$	0.775591	0.0298084	0.0149042	+	0.999889i	$0.495256\pi$
$678$	28.9598	1.11219
$679$	16.8221	0.645571
$680$	0	0
$681$	14.0346	0.537807
$682$	5.76932	0.220919
$683$	13.5810	0.519661	0.259831	−	0.965654i	$-0.416333\pi$
$683$	13.5810	0.519661	0.259831	+	0.965654i	$0.416333\pi$
$684$	2.24860	0.0859774
$685$	0	0
$686$	26.9264	1.02806
$687$	−12.2445	−0.467155
$688$	−46.3851	−1.76842
$689$	25.8206	0.983687
$690$	0	0
$691$	18.6981	0.711309	0.355654	−	0.934618i	$-0.384258\pi$
$691$	18.6981	0.711309	0.355654	+	0.934618i	$0.384258\pi$
$692$	30.0471	1.14222
$693$	−0.453636	−0.0172322
$694$	54.0007	2.04984
$695$	0	0
$696$	3.93561	0.149179
$697$	53.3747	2.02171
$698$	−31.4003	−1.18852
$699$	−1.87122	−0.0707760
$700$	0	0
$701$	−46.7625	−1.76619	−0.883097	−	0.469190i	$-0.844546\pi$
$701$	−46.7625	−1.76619	−0.883097	+	0.469190i	$0.844546\pi$
$702$	−4.46260	−0.168430
$703$	−1.93561	−0.0730029
$704$	−1.30548	−0.0492021
$705$	0	0
$706$	5.54636	0.208740
$707$	0.317138	0.0119272
$708$	1.46260	0.0549678
$709$	2.98477	0.112095	0.0560477	−	0.998428i	$-0.482150\pi$
$709$	2.98477	0.112095	0.0560477	+	0.998428i	$0.482150\pi$
$710$	0	0
$711$	7.04502	0.264209
$712$	16.4328	0.615846
$713$	−25.3747	−0.950289
$714$	15.0707	0.564005
$715$	0	0
$716$	−35.0588	−1.31021
$717$	−13.9910	−0.522505
$718$	−3.44322	−0.128500
$719$	−33.0915	−1.23410	−0.617052	−	0.786922i	$-0.711673\pi$
$719$	−33.0915	−1.23410	−0.617052	+	0.786922i	$0.711673\pi$
$720$	0	0
$721$	−17.1053	−0.637033
$722$	−30.9571	−1.15210
$723$	27.5333	1.02397
$724$	21.5166	0.799657
$725$	0	0
$726$	−20.1738	−0.748720
$727$	−25.9100	−0.960948	−0.480474	−	0.877009i	$-0.659535\pi$
$727$	−25.9100	−0.960948	−0.480474	+	0.877009i	$0.659535\pi$
$728$	−2.73202	−0.101256
$729$	1.00000	0.0370370
$730$	0	0
$731$	−68.9031	−2.54847
$732$	1.44737	0.0534963
$733$	3.43426	0.126847	0.0634237	−	0.997987i	$-0.479798\pi$
$733$	3.43426	0.126847	0.0634237	+	0.997987i	$0.479798\pi$
$734$	−14.8310	−0.547423
$735$	0	0
$736$	22.5062	0.829588
$737$	−2.17110	−0.0799735
$738$	−13.9702	−0.514251
$739$	19.0014	0.698980	0.349490	−	0.936940i	$-0.386355\pi$
$739$	19.0014	0.698980	0.349490	+	0.936940i	$0.386355\pi$
$740$	0	0
$741$	−3.68701	−0.135446
$742$	22.8233	0.837870
$743$	13.1607	0.482819	0.241409	−	0.970423i	$-0.422390\pi$
$743$	13.1607	0.482819	0.241409	+	0.970423i	$0.422390\pi$
$744$	−7.78600	−0.285449
$745$	0	0
$746$	−2.45364	−0.0898340
$747$	−13.0796	−0.478558
$748$	−4.14064	−0.151397
$749$	1.33170	0.0486591
$750$	0	0
$751$	−14.6981	−0.536341	−0.268170	−	0.963371i	$-0.586419\pi$
$751$	−14.6981	−0.536341	−0.268170	+	0.963371i	$0.586419\pi$
$752$	41.6918	1.52034
$753$	−2.61702	−0.0953696
$754$	17.5630	0.639608
$755$	0	0
$756$	−1.66618	−0.0605985
$757$	−3.27984	−0.119208	−0.0596039	−	0.998222i	$-0.518984\pi$
$757$	−3.27984	−0.119208	−0.0596039	+	0.998222i	$0.518984\pi$
$758$	38.2922	1.39083
$759$	−1.29776	−0.0471058
$760$	0	0
$761$	−15.5810	−0.564810	−0.282405	−	0.959295i	$-0.591132\pi$
$761$	−15.5810	−0.564810	−0.282405	+	0.959295i	$0.591132\pi$
$762$	−8.18421	−0.296483
$763$	5.57133	0.201696
$764$	4.26528	0.154312
$765$	0	0
$766$	−40.7148	−1.47108
$767$	−2.39821	−0.0865943
$768$	20.9058	0.754374
$769$	11.0402	0.398120	0.199060	−	0.979987i	$-0.436211\pi$
$769$	11.0402	0.398120	0.199060	+	0.979987i	$0.436211\pi$
$770$	0	0
$771$	−20.3892	−0.734301
$772$	0.946021	0.0340480
$773$	−39.8600	−1.43367	−0.716833	−	0.697245i	$-0.754409\pi$
$773$	−39.8600	−1.43367	−0.716833	+	0.697245i	$0.754409\pi$
$774$	18.0346	0.648240
$775$	0	0
$776$	14.7666	0.530091
$777$	1.43426	0.0514538
$778$	−11.7216	−0.420240
$779$	−11.5422	−0.413543
$780$	0	0
$781$	5.99104	0.214376
$782$	43.1142	1.54176
$783$	−3.93561	−0.140647
$784$	27.2909	0.974676
$785$	0	0
$786$	32.8656	1.17228
$787$	−24.0692	−0.857975	−0.428987	−	0.903311i	$-0.641129\pi$
$787$	−24.0692	−0.857975	−0.428987	+	0.903311i	$0.641129\pi$
$788$	8.58723	0.305908
$789$	23.8552	0.849268
$790$	0	0
$791$	−17.7293	−0.630382
$792$	−0.398207	−0.0141497
$793$	−2.37324	−0.0842761
$794$	22.5526	0.800363
$795$	0	0
$796$	16.2355	0.575452
$797$	−10.3088	−0.365158	−0.182579	−	0.983191i	$-0.558445\pi$
$797$	−10.3088	−0.365158	−0.182579	+	0.983191i	$0.558445\pi$
$798$	−3.25901	−0.115368
$799$	61.9315	2.19098
$800$	0	0
$801$	−16.4328	−0.580625
$802$	−30.3941	−1.07325
$803$	−1.88433	−0.0664965
$804$	−7.97436	−0.281234
$805$	0	0
$806$	−34.7458	−1.22387
$807$	−28.2999	−0.996203
$808$	0.278388	0.00979367
$809$	24.7119	0.868823	0.434412	−	0.900715i	$-0.356956\pi$
$809$	24.7119	0.868823	0.434412	+	0.900715i	$0.356956\pi$
$810$	0	0
$811$	−16.3088	−0.572681	−0.286341	−	0.958128i	$-0.592439\pi$
$811$	−16.3088	−0.572681	−0.286341	+	0.958128i	$0.592439\pi$
$812$	6.55745	0.230121
$813$	−23.4134	−0.821145
$814$	−0.932912	−0.0326986
$815$	0	0
$816$	34.0256	1.19114
$817$	14.9002	0.521293
$818$	68.9736	2.41160
$819$	2.73202	0.0954646
$820$	0	0
$821$	−39.5076	−1.37883	−0.689413	−	0.724369i	$-0.742131\pi$
$821$	−39.5076	−1.37883	−0.689413	+	0.724369i	$0.742131\pi$
$822$	20.0346	0.698787
$823$	0.655771	0.0228588	0.0114294	−	0.999935i	$-0.496362\pi$
$823$	0.655771	0.0228588	0.0114294	+	0.999935i	$0.496362\pi$
$824$	−15.0152	−0.523080
$825$	0	0
$826$	−2.11982	−0.0737579
$827$	−33.5035	−1.16503	−0.582515	−	0.812820i	$-0.697931\pi$
$827$	−33.5035	−1.16503	−0.582515	+	0.812820i	$0.697931\pi$
$828$	−4.76663	−0.165652
$829$	28.1752	0.978567	0.489283	−	0.872125i	$-0.337258\pi$
$829$	28.1752	0.978567	0.489283	+	0.872125i	$0.337258\pi$
$830$	0	0
$831$	−15.6918	−0.544343
$832$	7.86226	0.272575
$833$	40.5395	1.40461
$834$	18.2742	0.632785
$835$	0	0
$836$	0.895410	0.0309684
$837$	7.78600	0.269124
$838$	27.2549	0.941504
$839$	−21.9315	−0.757158	−0.378579	−	0.925569i	$-0.623587\pi$
$839$	−21.9315	−0.757158	−0.378579	+	0.925569i	$0.623587\pi$
$840$	0	0
$841$	−13.5110	−0.465896
$842$	−6.18421	−0.213122
$843$	−5.63158	−0.193962
$844$	−19.7126	−0.678537
$845$	0	0
$846$	−16.2099	−0.557306
$847$	12.3505	0.424368
$848$	51.5291	1.76952
$849$	−10.8310	−0.371720
$850$	0	0
$851$	4.10314	0.140654
$852$	22.0048	0.753873
$853$	22.9903	0.787171	0.393586	−	0.919288i	$-0.371234\pi$
$853$	22.9903	0.787171	0.393586	+	0.919288i	$0.371234\pi$
$854$	−2.09775	−0.0717834
$855$	0	0
$856$	1.16898	0.0399550
$857$	16.5574	0.565592	0.282796	−	0.959180i	$-0.408738\pi$
$857$	16.5574	0.565592	0.282796	+	0.959180i	$0.408738\pi$
$858$	−1.77704	−0.0606671
$859$	−3.50280	−0.119514	−0.0597570	−	0.998213i	$-0.519033\pi$
$859$	−3.50280	−0.119514	−0.0597570	+	0.998213i	$0.519033\pi$
$860$	0	0
$861$	8.55263	0.291473
$862$	5.08377	0.173154
$863$	19.1994	0.653557	0.326778	−	0.945101i	$-0.394037\pi$
$863$	19.1994	0.653557	0.326778	+	0.945101i	$0.394037\pi$
$864$	−6.90582	−0.234941
$865$	0	0
$866$	67.1822	2.28294
$867$	33.5437	1.13920
$868$	−12.9729	−0.440329
$869$	2.80538	0.0951659
$870$	0	0
$871$	13.0755	0.443046
$872$	4.89059	0.165616
$873$	−14.7666	−0.499775
$874$	−9.32340	−0.315369
$875$	0	0
$876$	−6.92105	−0.233841
$877$	−52.8864	−1.78585	−0.892924	−	0.450207i	$-0.851350\pi$
$877$	−52.8864	−1.78585	−0.892924	+	0.450207i	$0.851350\pi$
$878$	−70.6308	−2.38367
$879$	−33.9959	−1.14665
$880$	0	0
$881$	−6.86562	−0.231309	−0.115654	−	0.993290i	$-0.536896\pi$
$881$	−6.86562	−0.231309	−0.115654	+	0.993290i	$0.536896\pi$
$882$	−10.6108	−0.357283
$883$	51.6233	1.73726	0.868631	−	0.495460i	$-0.165000\pi$
$883$	51.6233	1.73726	0.868631	+	0.495460i	$0.165000\pi$
$884$	24.9371	0.838724
$885$	0	0
$886$	−3.43551	−0.115418
$887$	−19.7126	−0.661886	−0.330943	−	0.943651i	$-0.607367\pi$
$887$	−19.7126	−0.661886	−0.330943	+	0.943651i	$0.607367\pi$
$888$	1.25901	0.0422497
$889$	5.01041	0.168044
$890$	0	0
$891$	0.398207	0.0133405
$892$	−24.4793	−0.819627
$893$	−13.3926	−0.448167
$894$	−9.34008	−0.312379
$895$	0	0
$896$	−8.78455	−0.293471
$897$	7.81579	0.260962
$898$	52.0084	1.73554
$899$	−30.6427	−1.02199
$900$	0	0
$901$	76.5443	2.55006
$902$	−5.56304	−0.185229
$903$	−11.0409	−0.367417
$904$	−15.5630	−0.517619
$905$	0	0
$906$	13.6918	0.454880
$907$	40.5366	1.34600	0.672998	−	0.739644i	$-0.265006\pi$
$907$	40.5366	1.34600	0.672998	+	0.739644i	$0.265006\pi$
$908$	20.5270	0.681212
$909$	−0.278388	−0.00923356
$910$	0	0
$911$	54.5949	1.80881	0.904406	−	0.426674i	$-0.140315\pi$
$911$	54.5949	1.80881	0.904406	+	0.426674i	$0.140315\pi$
$912$	−7.35801	−0.243648
$913$	−5.20840	−0.172373
$914$	43.2638	1.43104
$915$	0	0
$916$	−17.9087	−0.591721
$917$	−20.1205	−0.664437
$918$	−13.2292	−0.436630
$919$	−6.95565	−0.229446	−0.114723	−	0.993398i	$-0.536598\pi$
$919$	−6.95565	−0.229446	−0.114723	+	0.993398i	$0.536598\pi$
$920$	0	0
$921$	4.25756	0.140292
$922$	38.0436	1.25290
$923$	−36.0811	−1.18762
$924$	−0.663487	−0.0218271
$925$	0	0
$926$	23.4689	0.771235
$927$	15.0152	0.493165
$928$	27.1786	0.892182
$929$	16.5478	0.542916	0.271458	−	0.962450i	$-0.412494\pi$
$929$	16.5478	0.542916	0.271458	+	0.962450i	$0.412494\pi$
$930$	0	0
$931$	−8.76663	−0.287315
$932$	−2.73684	−0.0896482
$933$	21.5374	0.705103
$934$	3.52072	0.115202
$935$	0	0
$936$	2.39821	0.0783879
$937$	28.6766	0.936824	0.468412	−	0.883510i	$-0.344826\pi$
$937$	28.6766	0.936824	0.468412	+	0.883510i	$0.344826\pi$
$938$	11.5576	0.377371
$939$	3.96540	0.129406
$940$	0	0
$941$	−24.1198	−0.786284	−0.393142	−	0.919478i	$-0.628612\pi$
$941$	−24.1198	−0.786284	−0.393142	+	0.919478i	$0.628612\pi$
$942$	3.22026	0.104922
$943$	24.4674	0.796769
$944$	−4.78600	−0.155771
$945$	0	0
$946$	7.18151	0.233491
$947$	−33.0617	−1.07436	−0.537180	−	0.843467i	$-0.680511\pi$
$947$	−33.0617	−1.07436	−0.537180	+	0.843467i	$0.680511\pi$
$948$	10.3040	0.334659
$949$	11.3484	0.368384
$950$	0	0
$951$	−7.58097	−0.245830
$952$	−8.09899	−0.262490
$953$	6.79641	0.220157	0.110079	−	0.993923i	$-0.464890\pi$
$953$	6.79641	0.220157	0.110079	+	0.993923i	$0.464890\pi$
$954$	−20.0346	−0.648644
$955$	0	0
$956$	−20.4633	−0.661829
$957$	−1.56719	−0.0506600
$958$	−6.54367	−0.211416
$959$	−12.2653	−0.396067
$960$	0	0
$961$	29.6218	0.955543
$962$	5.61847	0.181147
$963$	−1.16898	−0.0376699
$964$	40.2701	1.29701
$965$	0	0
$966$	6.90852	0.222278
$967$	43.7479	1.40684	0.703419	−	0.710775i	$-0.251656\pi$
$967$	43.7479	1.40684	0.703419	+	0.710775i	$0.251656\pi$
$968$	10.8414	0.348457
$969$	−10.9300	−0.351123
$970$	0	0
$971$	30.3434	0.973768	0.486884	−	0.873467i	$-0.338134\pi$
$971$	30.3434	0.973768	0.486884	+	0.873467i	$0.338134\pi$
$972$	1.46260	0.0469129
$973$	−11.1876	−0.358657
$974$	−39.4868	−1.26524
$975$	0	0
$976$	−4.73617	−0.151601
$977$	−47.2638	−1.51210	−0.756052	−	0.654512i	$-0.772874\pi$
$977$	−47.2638	−1.51210	−0.756052	+	0.654512i	$0.772874\pi$
$978$	15.9702	0.510671
$979$	−6.54367	−0.209137
$980$	0	0
$981$	−4.89059	−0.156145
$982$	23.1738	0.739506
$983$	−30.9854	−0.988282	−0.494141	−	0.869382i	$-0.664517\pi$
$983$	−30.9854	−0.988282	−0.494141	+	0.869382i	$0.664517\pi$
$984$	7.50761	0.239334
$985$	0	0
$986$	52.0651	1.65809
$987$	9.92375	0.315876
$988$	−5.39261	−0.171562
$989$	−31.5858	−1.00437
$990$	0	0
$991$	−18.8131	−0.597618	−0.298809	−	0.954313i	$-0.596589\pi$
$991$	−18.8131	−0.597618	−0.298809	+	0.954313i	$0.596589\pi$
$992$	−53.7687	−1.70716
$993$	−0.667633	−0.0211867
$994$	−31.8927	−1.01158
$995$	0	0
$996$	−19.1302	−0.606165
$997$	−16.5020	−0.522624	−0.261312	−	0.965254i	$-0.584155\pi$
$997$	−16.5020	−0.522624	−0.261312	+	0.965254i	$0.584155\pi$
$998$	61.5470	1.94824
$999$	−1.25901	−0.0398334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4425.2.a.w.1.3		3
5.4	even	2		177.2.a.d.1.1	✓	3
15.14	odd	2		531.2.a.d.1.3		3
20.19	odd	2		2832.2.a.t.1.1		3
35.34	odd	2		8673.2.a.s.1.1		3
60.59	even	2		8496.2.a.bl.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.d.1.1	✓	3	5.4	even	2
531.2.a.d.1.3		3	15.14	odd	2
2832.2.a.t.1.1		3	20.19	odd	2
4425.2.a.w.1.3		3	1.1	even	1	trivial
8496.2.a.bl.1.3		3	60.59	even	2
8673.2.a.s.1.1		3	35.34	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:	\( N \)	\(=\)	\( 4425 = 3 \cdot 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4425.a (trivial)

\(f(q)\)	\(=\)	\(q+1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +1.86081 q^{6} -1.13919 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.86081 q^{2} +1.00000 q^{3} +1.46260 q^{4} +1.86081 q^{6} -1.13919 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.398207 q^{11} +1.46260 q^{12} -2.39821 q^{13} -2.11982 q^{14} -4.78600 q^{16} -7.10941 q^{17} +1.86081 q^{18} +1.53740 q^{19} -1.13919 q^{21} +0.740987 q^{22} -3.25901 q^{23} -1.00000 q^{24} -4.46260 q^{26} +1.00000 q^{27} -1.66618 q^{28} -3.93561 q^{29} +7.78600 q^{31} -6.90582 q^{32} +0.398207 q^{33} -13.2292 q^{34} +1.46260 q^{36} -1.25901 q^{37} +2.86081 q^{38} -2.39821 q^{39} -7.50761 q^{41} -2.11982 q^{42} +9.69182 q^{43} +0.582418 q^{44} -6.06439 q^{46} -8.71120 q^{47} -4.78600 q^{48} -5.70224 q^{49} -7.10941 q^{51} -3.50761 q^{52} -10.7666 q^{53} +1.86081 q^{54} +1.13919 q^{56} +1.53740 q^{57} -7.32340 q^{58} +1.00000 q^{59} +0.989588 q^{61} +14.4882 q^{62} -1.13919 q^{63} -3.27839 q^{64} +0.740987 q^{66} -5.45219 q^{67} -10.3982 q^{68} -3.25901 q^{69} +15.0450 q^{71} -1.00000 q^{72} -4.73202 q^{73} -2.34278 q^{74} +2.24860 q^{76} -0.453636 q^{77} -4.46260 q^{78} +7.04502 q^{79} +1.00000 q^{81} -13.9702 q^{82} -13.0796 q^{83} -1.66618 q^{84} +18.0346 q^{86} -3.93561 q^{87} -0.398207 q^{88} -16.4328 q^{89} +2.73202 q^{91} -4.76663 q^{92} +7.78600 q^{93} -16.2099 q^{94} -6.90582 q^{96} -14.7666 q^{97} -10.6108 q^{98} +0.398207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 2 q^{4} - 9 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 2 * q^4 - 9 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 2 q^{4} - 9 q^{7} - 3 q^{8} + 3 q^{9} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 8 q^{14} - 4 q^{16} - 3 q^{17} + 7 q^{19} - 9 q^{21} + 11 q^{22} - q^{23} - 3 q^{24} - 11 q^{26} + 3 q^{27} - 9 q^{28} - 11 q^{29} + 13 q^{31} + 4 q^{32} - 2 q^{33} - 7 q^{34} + 2 q^{36} + 5 q^{37} + 3 q^{38} - 4 q^{39} - q^{41} + 8 q^{42} - 6 q^{43} - 15 q^{44} - 19 q^{46} - 11 q^{47} - 4 q^{48} + 14 q^{49} - 3 q^{51} + 11 q^{52} - 2 q^{53} + 9 q^{56} + 7 q^{57} - 14 q^{58} + 3 q^{59} - q^{61} + 2 q^{62} - 9 q^{63} - 21 q^{64} + 11 q^{66} - 10 q^{67} - 28 q^{68} - q^{69} + 26 q^{71} - 3 q^{72} - 7 q^{73} - 19 q^{74} - 6 q^{76} + 17 q^{77} - 11 q^{78} + 2 q^{79} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 9 q^{84} + 31 q^{86} - 11 q^{87} + 2 q^{88} - 23 q^{89} + q^{91} + 16 q^{92} + 13 q^{93} + 4 q^{94} + 4 q^{96} - 14 q^{97} - 51 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 2 * q^4 - 9 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 8 * q^14 - 4 * q^16 - 3 * q^17 + 7 * q^19 - 9 * q^21 + 11 * q^22 - q^23 - 3 * q^24 - 11 * q^26 + 3 * q^27 - 9 * q^28 - 11 * q^29 + 13 * q^31 + 4 * q^32 - 2 * q^33 - 7 * q^34 + 2 * q^36 + 5 * q^37 + 3 * q^38 - 4 * q^39 - q^41 + 8 * q^42 - 6 * q^43 - 15 * q^44 - 19 * q^46 - 11 * q^47 - 4 * q^48 + 14 * q^49 - 3 * q^51 + 11 * q^52 - 2 * q^53 + 9 * q^56 + 7 * q^57 - 14 * q^58 + 3 * q^59 - q^61 + 2 * q^62 - 9 * q^63 - 21 * q^64 + 11 * q^66 - 10 * q^67 - 28 * q^68 - q^69 + 26 * q^71 - 3 * q^72 - 7 * q^73 - 19 * q^74 - 6 * q^76 + 17 * q^77 - 11 * q^78 + 2 * q^79 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 9 * q^84 + 31 * q^86 - 11 * q^87 + 2 * q^88 - 23 * q^89 + q^91 + 16 * q^92 + 13 * q^93 + 4 * q^94 + 4 * q^96 - 14 * q^97 - 51 * q^98 - 2 * q^99

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