LMFDB - Embedded newform 4025.2.a.x.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 $ x^12 - 2x^11 - 14x^10 + 26x^9 + 71x^8 - 120x^7 - 162x^6 + 244x^5 + 170x^4 - 210x^3 - 81x^2 + 58*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.76402$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.76402 q^{2} +1.09514 q^{3} +1.11176 q^{4} +1.93184 q^{6} +1.00000 q^{7} -1.56687 q^{8} -1.80068 q^{9} +O(q^{10})$	\(q+1.76402 q^{2} +1.09514 q^{3} +1.11176 q^{4} +1.93184 q^{6} +1.00000 q^{7} -1.56687 q^{8} -1.80068 q^{9} -0.239415 q^{11} +1.21753 q^{12} -1.56322 q^{13} +1.76402 q^{14} -4.98751 q^{16} -2.69399 q^{17} -3.17643 q^{18} -5.14265 q^{19} +1.09514 q^{21} -0.422332 q^{22} -1.00000 q^{23} -1.71593 q^{24} -2.75756 q^{26} -5.25739 q^{27} +1.11176 q^{28} -3.60222 q^{29} +6.22882 q^{31} -5.66433 q^{32} -0.262192 q^{33} -4.75225 q^{34} -2.00193 q^{36} +3.81695 q^{37} -9.07173 q^{38} -1.71194 q^{39} +0.415994 q^{41} +1.93184 q^{42} -9.10002 q^{43} -0.266173 q^{44} -1.76402 q^{46} +1.83656 q^{47} -5.46200 q^{48} +1.00000 q^{49} -2.95028 q^{51} -1.73794 q^{52} +5.48048 q^{53} -9.27414 q^{54} -1.56687 q^{56} -5.63190 q^{57} -6.35439 q^{58} -12.8080 q^{59} -6.75035 q^{61} +10.9878 q^{62} -1.80068 q^{63} -0.0169674 q^{64} -0.462511 q^{66} -12.1247 q^{67} -2.99508 q^{68} -1.09514 q^{69} -4.71473 q^{71} +2.82142 q^{72} -0.958501 q^{73} +6.73318 q^{74} -5.71741 q^{76} -0.239415 q^{77} -3.01990 q^{78} +5.66990 q^{79} -0.355531 q^{81} +0.733822 q^{82} -9.94097 q^{83} +1.21753 q^{84} -16.0526 q^{86} -3.94492 q^{87} +0.375131 q^{88} +14.2918 q^{89} -1.56322 q^{91} -1.11176 q^{92} +6.82141 q^{93} +3.23972 q^{94} -6.20321 q^{96} -3.79620 q^{97} +1.76402 q^{98} +0.431109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * 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 $

$2$	1.76402	1.24735	0.623675	−	0.781684i	$-0.285639\pi$
$2$	1.76402	1.24735	0.623675	+	0.781684i	$0.285639\pi$
$3$	1.09514	0.632277	0.316139	−	0.948713i	$-0.397614\pi$
$3$	1.09514	0.632277	0.316139	+	0.948713i	$0.397614\pi$
$4$	1.11176	0.555882
$5$	0	0
$5$	0	0
$6$	1.93184	0.788671
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.56687	−0.553971
$9$	−1.80068	−0.600226
$10$	0	0
$11$	−0.239415	−0.0721863	−0.0360931	−	0.999348i	$-0.511491\pi$
$11$	−0.239415	−0.0721863	−0.0360931	+	0.999348i	$0.511491\pi$
$12$	1.21753	0.351471
$13$	−1.56322	−0.433561	−0.216780	−	0.976220i	$-0.569556\pi$
$13$	−1.56322	−0.433561	−0.216780	+	0.976220i	$0.569556\pi$
$14$	1.76402	0.471454
$15$	0	0
$16$	−4.98751	−1.24688
$17$	−2.69399	−0.653388	−0.326694	−	0.945130i	$-0.605935\pi$
$17$	−2.69399	−0.653388	−0.326694	+	0.945130i	$0.605935\pi$
$18$	−3.17643	−0.748691
$19$	−5.14265	−1.17980	−0.589902	−	0.807475i	$-0.700834\pi$
$19$	−5.14265	−1.17980	−0.589902	+	0.807475i	$0.700834\pi$
$20$	0	0
$21$	1.09514	0.238978
$22$	−0.422332	−0.0900415
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.71593	−0.350263
$25$	0	0
$26$	−2.75756	−0.540802
$27$	−5.25739	−1.01179
$28$	1.11176	0.210104
$29$	−3.60222	−0.668916	−0.334458	−	0.942411i	$-0.608553\pi$
$29$	−3.60222	−0.668916	−0.334458	+	0.942411i	$0.608553\pi$
$30$	0	0
$31$	6.22882	1.11873	0.559365	−	0.828922i	$-0.311045\pi$
$31$	6.22882	1.11873	0.559365	+	0.828922i	$0.311045\pi$
$32$	−5.66433	−1.00132
$33$	−0.262192	−0.0456417
$34$	−4.75225	−0.815004
$35$	0	0
$36$	−2.00193	−0.333655
$37$	3.81695	0.627503	0.313752	−	0.949505i	$-0.398414\pi$
$37$	3.81695	0.627503	0.313752	+	0.949505i	$0.398414\pi$
$38$	−9.07173	−1.47163
$39$	−1.71194	−0.274130
$40$	0	0
$41$	0.415994	0.0649674	0.0324837	−	0.999472i	$-0.489658\pi$
$41$	0.415994	0.0649674	0.0324837	+	0.999472i	$0.489658\pi$
$42$	1.93184	0.298090
$43$	−9.10002	−1.38774	−0.693870	−	0.720101i	$-0.744096\pi$
$43$	−9.10002	−1.38774	−0.693870	+	0.720101i	$0.744096\pi$
$44$	−0.266173	−0.0401270
$45$	0	0
$46$	−1.76402	−0.260090
$47$	1.83656	0.267889	0.133945	−	0.990989i	$-0.457236\pi$
$47$	1.83656	0.267889	0.133945	+	0.990989i	$0.457236\pi$
$48$	−5.46200	−0.788372
$49$	1.00000	0.142857
$50$	0	0
$51$	−2.95028	−0.413122
$52$	−1.73794	−0.241008
$53$	5.48048	0.752802	0.376401	−	0.926457i	$-0.377162\pi$
$53$	5.48048	0.752802	0.376401	+	0.926457i	$0.377162\pi$
$54$	−9.27414	−1.26205
$55$	0	0
$56$	−1.56687	−0.209381
$57$	−5.63190	−0.745963
$58$	−6.35439	−0.834372
$59$	−12.8080	−1.66746	−0.833729	−	0.552175i	$-0.813798\pi$
$59$	−12.8080	−1.66746	−0.833729	+	0.552175i	$0.813798\pi$
$60$	0	0
$61$	−6.75035	−0.864293	−0.432147	−	0.901803i	$-0.642244\pi$
$61$	−6.75035	−0.864293	−0.432147	+	0.901803i	$0.642244\pi$
$62$	10.9878	1.39545
$63$	−1.80068	−0.226864
$64$	−0.0169674	−0.00212092
$65$	0	0
$66$	−0.462511	−0.0569312
$67$	−12.1247	−1.48127	−0.740635	−	0.671907i	$-0.765475\pi$
$67$	−12.1247	−1.48127	−0.740635	+	0.671907i	$0.765475\pi$
$68$	−2.99508	−0.363207
$69$	−1.09514	−0.131839
$70$	0	0
$71$	−4.71473	−0.559535	−0.279768	−	0.960068i	$-0.590257\pi$
$71$	−4.71473	−0.559535	−0.279768	+	0.960068i	$0.590257\pi$
$72$	2.82142	0.332508
$73$	−0.958501	−0.112184	−0.0560920	−	0.998426i	$-0.517864\pi$
$73$	−0.958501	−0.112184	−0.0560920	+	0.998426i	$0.517864\pi$
$74$	6.73318	0.782716
$75$	0	0
$76$	−5.71741	−0.655832
$77$	−0.239415	−0.0272838
$78$	−3.01990	−0.341936
$79$	5.66990	0.637913	0.318957	−	0.947769i	$-0.396668\pi$
$79$	5.66990	0.637913	0.318957	+	0.947769i	$0.396668\pi$
$80$	0	0
$81$	−0.355531	−0.0395034
$82$	0.733822	0.0810370
$83$	−9.94097	−1.09116	−0.545582	−	0.838058i	$-0.683691\pi$
$83$	−9.94097	−1.09116	−0.545582	+	0.838058i	$0.683691\pi$
$84$	1.21753	0.132844
$85$	0	0
$86$	−16.0526	−1.73100
$87$	−3.94492	−0.422940
$88$	0.375131	0.0399891
$89$	14.2918	1.51493	0.757463	−	0.652878i	$-0.226439\pi$
$89$	14.2918	1.51493	0.757463	+	0.652878i	$0.226439\pi$
$90$	0	0
$91$	−1.56322	−0.163870
$92$	−1.11176	−0.115909
$93$	6.82141	0.707347
$94$	3.23972	0.334152
$95$	0	0
$96$	−6.20321	−0.633113
$97$	−3.79620	−0.385445	−0.192723	−	0.981253i	$-0.561732\pi$
$97$	−3.79620	−0.385445	−0.192723	+	0.981253i	$0.561732\pi$
$98$	1.76402	0.178193
$99$	0.431109	0.0433281
$100$	0	0
$101$	3.46673	0.344952	0.172476	−	0.985014i	$-0.444823\pi$
$101$	3.46673	0.344952	0.172476	+	0.985014i	$0.444823\pi$
$102$	−5.20436	−0.515308
$103$	−1.13062	−0.111403	−0.0557016	−	0.998447i	$-0.517740\pi$
$103$	−1.13062	−0.111403	−0.0557016	+	0.998447i	$0.517740\pi$
$104$	2.44936	0.240180
$105$	0	0
$106$	9.66767	0.939007
$107$	6.68600	0.646360	0.323180	−	0.946337i	$-0.395248\pi$
$107$	6.68600	0.646360	0.323180	+	0.946337i	$0.395248\pi$
$108$	−5.84498	−0.562433
$109$	11.1590	1.06884	0.534420	−	0.845219i	$-0.320530\pi$
$109$	11.1590	1.06884	0.534420	+	0.845219i	$0.320530\pi$
$110$	0	0
$111$	4.18008	0.396756
$112$	−4.98751	−0.471275
$113$	8.54045	0.803418	0.401709	−	0.915767i	$-0.368416\pi$
$113$	8.54045	0.803418	0.401709	+	0.915767i	$0.368416\pi$
$114$	−9.93478	−0.930477
$115$	0	0
$116$	−4.00482	−0.371838
$117$	2.81486	0.260234
$118$	−22.5935	−2.07990
$119$	−2.69399	−0.246958
$120$	0	0
$121$	−10.9427	−0.994789
$122$	−11.9077	−1.07808
$123$	0.455570	0.0410774
$124$	6.92498	0.621881
$125$	0	0
$126$	−3.17643	−0.282979
$127$	22.1551	1.96595	0.982975	−	0.183739i	$-0.0588202\pi$
$127$	22.1551	1.96595	0.982975	+	0.183739i	$0.0588202\pi$
$128$	11.2987	0.998676
$129$	−9.96575	−0.877436
$130$	0	0
$131$	7.54983	0.659631	0.329816	−	0.944045i	$-0.393013\pi$
$131$	7.54983	0.659631	0.329816	+	0.944045i	$0.393013\pi$
$132$	−0.291495	−0.0253714
$133$	−5.14265	−0.445924
$134$	−21.3882	−1.84766
$135$	0	0
$136$	4.22112	0.361958
$137$	−21.1563	−1.80750	−0.903752	−	0.428056i	$-0.859199\pi$
$137$	−21.1563	−1.80750	−0.903752	+	0.428056i	$0.859199\pi$
$138$	−1.93184	−0.164449
$139$	9.75790	0.827654	0.413827	−	0.910356i	$-0.364192\pi$
$139$	9.75790	0.827654	0.413827	+	0.910356i	$0.364192\pi$
$140$	0	0
$141$	2.01128	0.169380
$142$	−8.31687	−0.697936
$143$	0.374259	0.0312971
$144$	8.98089	0.748408
$145$	0	0
$146$	−1.69081	−0.139933
$147$	1.09514	0.0903253
$148$	4.24355	0.348818
$149$	7.80358	0.639295	0.319647	−	0.947537i	$-0.396436\pi$
$149$	7.80358	0.639295	0.319647	+	0.947537i	$0.396436\pi$
$150$	0	0
$151$	−19.5503	−1.59098	−0.795491	−	0.605966i	$-0.792787\pi$
$151$	−19.5503	−1.59098	−0.795491	+	0.605966i	$0.792787\pi$
$152$	8.05784	0.653577
$153$	4.85100	0.392180
$154$	−0.422332	−0.0340325
$155$	0	0
$156$	−1.90328	−0.152384
$157$	5.04078	0.402298	0.201149	−	0.979561i	$-0.435532\pi$
$157$	5.04078	0.402298	0.201149	+	0.979561i	$0.435532\pi$
$158$	10.0018	0.795701
$159$	6.00187	0.475979
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−0.627163	−0.0492746
$163$	8.64158	0.676860	0.338430	−	0.940991i	$-0.390104\pi$
$163$	8.64158	0.676860	0.338430	+	0.940991i	$0.390104\pi$
$164$	0.462487	0.0361142
$165$	0	0
$166$	−17.5361	−1.36106
$167$	3.10339	0.240148	0.120074	−	0.992765i	$-0.461687\pi$
$167$	3.10339	0.240148	0.120074	+	0.992765i	$0.461687\pi$
$168$	−1.71593	−0.132387
$169$	−10.5563	−0.812025
$170$	0	0
$171$	9.26025	0.708149
$172$	−10.1171	−0.771419
$173$	−3.16904	−0.240938	−0.120469	−	0.992717i	$-0.538440\pi$
$173$	−3.16904	−0.240938	−0.120469	+	0.992717i	$0.538440\pi$
$174$	−6.95892	−0.527554
$175$	0	0
$176$	1.19408	0.0900074
$177$	−14.0265	−1.05429
$178$	25.2110	1.88964
$179$	12.6355	0.944423	0.472211	−	0.881485i	$-0.343456\pi$
$179$	12.6355	0.944423	0.472211	+	0.881485i	$0.343456\pi$
$180$	0	0
$181$	−0.478228	−0.0355464	−0.0177732	−	0.999842i	$-0.505658\pi$
$181$	−0.478228	−0.0355464	−0.0177732	+	0.999842i	$0.505658\pi$
$182$	−2.75756	−0.204404
$183$	−7.39255	−0.546473
$184$	1.56687	0.115511
$185$	0	0
$186$	12.0331	0.882309
$187$	0.644981	0.0471657
$188$	2.04182	0.148915
$189$	−5.25739	−0.382419
$190$	0	0
$191$	−0.621857	−0.0449960	−0.0224980	−	0.999747i	$-0.507162\pi$
$191$	−0.621857	−0.0449960	−0.0224980	+	0.999747i	$0.507162\pi$
$192$	−0.0185816	−0.00134101
$193$	−24.9647	−1.79700	−0.898500	−	0.438974i	$-0.855342\pi$
$193$	−24.9647	−1.79700	−0.898500	+	0.438974i	$0.855342\pi$
$194$	−6.69656	−0.480785
$195$	0	0
$196$	1.11176	0.0794117
$197$	−17.6971	−1.26086	−0.630431	−	0.776245i	$-0.717122\pi$
$197$	−17.6971	−1.26086	−0.630431	+	0.776245i	$0.717122\pi$
$198$	0.760484	0.0540452
$199$	−10.9106	−0.773431	−0.386716	−	0.922199i	$-0.626390\pi$
$199$	−10.9106	−0.773431	−0.386716	+	0.922199i	$0.626390\pi$
$200$	0	0
$201$	−13.2782	−0.936574
$202$	6.11537	0.430276
$203$	−3.60222	−0.252826
$204$	−3.28002	−0.229647
$205$	0	0
$206$	−1.99443	−0.138959
$207$	1.80068	0.125156
$208$	7.79660	0.540597
$209$	1.23123	0.0851657
$210$	0	0
$211$	1.87424	0.129028	0.0645142	−	0.997917i	$-0.479450\pi$
$211$	1.87424	0.129028	0.0645142	+	0.997917i	$0.479450\pi$
$212$	6.09300	0.418469
$213$	−5.16327	−0.353781
$214$	11.7942	0.806237
$215$	0	0
$216$	8.23763	0.560500
$217$	6.22882	0.422840
$218$	19.6847	1.33322
$219$	−1.04969	−0.0709314
$220$	0	0
$221$	4.21131	0.283283
$222$	7.37375	0.494894
$223$	13.6469	0.913861	0.456931	−	0.889502i	$-0.348949\pi$
$223$	13.6469	0.913861	0.456931	+	0.889502i	$0.348949\pi$
$224$	−5.66433	−0.378464
$225$	0	0
$226$	15.0655	1.00214
$227$	−8.57243	−0.568972	−0.284486	−	0.958680i	$-0.591823\pi$
$227$	−8.57243	−0.568972	−0.284486	+	0.958680i	$0.591823\pi$
$228$	−6.26134	−0.414667
$229$	8.43311	0.557276	0.278638	−	0.960396i	$-0.410117\pi$
$229$	8.43311	0.557276	0.278638	+	0.960396i	$0.410117\pi$
$230$	0	0
$231$	−0.262192	−0.0172510
$232$	5.64420	0.370560
$233$	6.14423	0.402522	0.201261	−	0.979538i	$-0.435496\pi$
$233$	6.14423	0.402522	0.201261	+	0.979538i	$0.435496\pi$
$234$	4.96547	0.324603
$235$	0	0
$236$	−14.2394	−0.926909
$237$	6.20931	0.403338
$238$	−4.75225	−0.308042
$239$	−12.1158	−0.783708	−0.391854	−	0.920027i	$-0.628166\pi$
$239$	−12.1158	−0.783708	−0.391854	+	0.920027i	$0.628166\pi$
$240$	0	0
$241$	−30.0022	−1.93261	−0.966307	−	0.257394i	$-0.917136\pi$
$241$	−30.0022	−1.93261	−0.966307	+	0.257394i	$0.917136\pi$
$242$	−19.3031	−1.24085
$243$	15.3828	0.986809
$244$	−7.50479	−0.480445
$245$	0	0
$246$	0.803634	0.0512379
$247$	8.03911	0.511516
$248$	−9.75973	−0.619743
$249$	−10.8867	−0.689918
$250$	0	0
$251$	−5.95066	−0.375603	−0.187801	−	0.982207i	$-0.560136\pi$
$251$	−5.95066	−0.375603	−0.187801	+	0.982207i	$0.560136\pi$
$252$	−2.00193	−0.126110
$253$	0.239415	0.0150519
$254$	39.0821	2.45223
$255$	0	0
$256$	19.9651	1.24782
$257$	−21.7782	−1.35849	−0.679243	−	0.733914i	$-0.737692\pi$
$257$	−21.7782	−1.35849	−0.679243	+	0.733914i	$0.737692\pi$
$258$	−17.5798	−1.09447
$259$	3.81695	0.237174
$260$	0	0
$261$	6.48644	0.401500
$262$	13.3180	0.822791
$263$	2.83030	0.174523	0.0872617	−	0.996185i	$-0.472188\pi$
$263$	2.83030	0.174523	0.0872617	+	0.996185i	$0.472188\pi$
$264$	0.410819	0.0252842
$265$	0	0
$266$	−9.07173	−0.556223
$267$	15.6514	0.957853
$268$	−13.4798	−0.823412
$269$	11.5117	0.701881	0.350941	−	0.936398i	$-0.385862\pi$
$269$	11.5117	0.701881	0.350941	+	0.936398i	$0.385862\pi$
$270$	0	0
$271$	−18.2773	−1.11027	−0.555134	−	0.831761i	$-0.687333\pi$
$271$	−18.2773	−1.11027	−0.555134	+	0.831761i	$0.687333\pi$
$272$	13.4363	0.814695
$273$	−1.71194	−0.103612
$274$	−37.3201	−2.25459
$275$	0	0
$276$	−1.21753	−0.0732868
$277$	24.3453	1.46277	0.731383	−	0.681967i	$-0.238875\pi$
$277$	24.3453	1.46277	0.731383	+	0.681967i	$0.238875\pi$
$278$	17.2131	1.03237
$279$	−11.2161	−0.671490
$280$	0	0
$281$	−5.77851	−0.344717	−0.172359	−	0.985034i	$-0.555139\pi$
$281$	−5.77851	−0.344717	−0.172359	+	0.985034i	$0.555139\pi$
$282$	3.54793	0.211276
$283$	9.79515	0.582261	0.291131	−	0.956683i	$-0.405969\pi$
$283$	9.79515	0.582261	0.291131	+	0.956683i	$0.405969\pi$
$284$	−5.24166	−0.311036
$285$	0	0
$286$	0.660200	0.0390385
$287$	0.415994	0.0245554
$288$	10.1996	0.601019
$289$	−9.74243	−0.573084
$290$	0	0
$291$	−4.15735	−0.243708
$292$	−1.06563	−0.0623611
$293$	19.4669	1.13727	0.568633	−	0.822591i	$-0.307472\pi$
$293$	19.4669	1.13727	0.568633	+	0.822591i	$0.307472\pi$
$294$	1.93184	0.112667
$295$	0	0
$296$	−5.98066	−0.347619
$297$	1.25870	0.0730371
$298$	13.7657	0.797424
$299$	1.56322	0.0904036
$300$	0	0
$301$	−9.10002	−0.524516
$302$	−34.4871	−1.98451
$303$	3.79654	0.218105
$304$	25.6490	1.47107
$305$	0	0
$306$	8.55726	0.489186
$307$	20.3450	1.16115	0.580574	−	0.814207i	$-0.302828\pi$
$307$	20.3450	1.16115	0.580574	+	0.814207i	$0.302828\pi$
$308$	−0.266173	−0.0151666
$309$	−1.23818	−0.0704377
$310$	0	0
$311$	−5.84893	−0.331662	−0.165831	−	0.986154i	$-0.553031\pi$
$311$	−5.84893	−0.331662	−0.165831	+	0.986154i	$0.553031\pi$
$312$	2.68239	0.151860
$313$	−20.4807	−1.15764	−0.578820	−	0.815455i	$-0.696487\pi$
$313$	−20.4807	−1.15764	−0.578820	+	0.815455i	$0.696487\pi$
$314$	8.89204	0.501807
$315$	0	0
$316$	6.30359	0.354604
$317$	0.656263	0.0368594	0.0184297	−	0.999830i	$-0.494133\pi$
$317$	0.656263	0.0368594	0.0184297	+	0.999830i	$0.494133\pi$
$318$	10.5874	0.593713
$319$	0.862425	0.0482865
$320$	0	0
$321$	7.32208	0.408679
$322$	−1.76402	−0.0983049
$323$	13.8542	0.770870
$324$	−0.395266	−0.0219592
$325$	0	0
$326$	15.2439	0.844282
$327$	12.2206	0.675803
$328$	−0.651807	−0.0359900
$329$	1.83656	0.101253
$330$	0	0
$331$	−26.1523	−1.43746	−0.718731	−	0.695288i	$-0.755277\pi$
$331$	−26.1523	−1.43746	−0.718731	+	0.695288i	$0.755277\pi$
$332$	−11.0520	−0.606558
$333$	−6.87310	−0.376644
$334$	5.47444	0.299548
$335$	0	0
$336$	−5.46200	−0.297977
$337$	14.4626	0.787828	0.393914	−	0.919147i	$-0.371121\pi$
$337$	14.4626	0.787828	0.393914	+	0.919147i	$0.371121\pi$
$338$	−18.6216	−1.01288
$339$	9.35295	0.507983
$340$	0	0
$341$	−1.49127	−0.0807569
$342$	16.3353	0.883309
$343$	1.00000	0.0539949
$344$	14.2585	0.768767
$345$	0	0
$346$	−5.59025	−0.300534
$347$	2.11370	0.113470	0.0567348	−	0.998389i	$-0.481931\pi$
$347$	2.11370	0.113470	0.0567348	+	0.998389i	$0.481931\pi$
$348$	−4.38582	−0.235105
$349$	25.2203	1.35001	0.675006	−	0.737812i	$-0.264141\pi$
$349$	25.2203	1.35001	0.675006	+	0.737812i	$0.264141\pi$
$350$	0	0
$351$	8.21849	0.438670
$352$	1.35612	0.0722817
$353$	7.24294	0.385503	0.192751	−	0.981248i	$-0.438259\pi$
$353$	7.24294	0.385503	0.192751	+	0.981248i	$0.438259\pi$
$354$	−24.7430	−1.31507
$355$	0	0
$356$	15.8891	0.842120
$357$	−2.95028	−0.156146
$358$	22.2893	1.17803
$359$	−18.4361	−0.973021	−0.486510	−	0.873675i	$-0.661730\pi$
$359$	−18.4361	−0.973021	−0.486510	+	0.873675i	$0.661730\pi$
$360$	0	0
$361$	7.44681	0.391938
$362$	−0.843604	−0.0443388
$363$	−11.9837	−0.628982
$364$	−1.73794	−0.0910926
$365$	0	0
$366$	−13.0406	−0.681643
$367$	22.0938	1.15329	0.576644	−	0.816996i	$-0.304362\pi$
$367$	22.0938	1.15329	0.576644	+	0.816996i	$0.304362\pi$
$368$	4.98751	0.259992
$369$	−0.749071	−0.0389951
$370$	0	0
$371$	5.48048	0.284532
$372$	7.58379	0.393201
$373$	12.5896	0.651867	0.325933	−	0.945393i	$-0.394321\pi$
$373$	12.5896	0.651867	0.325933	+	0.945393i	$0.394321\pi$
$374$	1.13776	0.0588321
$375$	0	0
$376$	−2.87764	−0.148403
$377$	5.63108	0.290015
$378$	−9.27414	−0.477011
$379$	−3.95376	−0.203091	−0.101546	−	0.994831i	$-0.532379\pi$
$379$	−3.95376	−0.203091	−0.101546	+	0.994831i	$0.532379\pi$
$380$	0	0
$381$	24.2629	1.24303
$382$	−1.09697	−0.0561258
$383$	17.9072	0.915013	0.457507	−	0.889206i	$-0.348743\pi$
$383$	17.9072	0.915013	0.457507	+	0.889206i	$0.348743\pi$
$384$	12.3736	0.631440
$385$	0	0
$386$	−44.0382	−2.24149
$387$	16.3862	0.832957
$388$	−4.22047	−0.214262
$389$	9.57056	0.485247	0.242623	−	0.970121i	$-0.421992\pi$
$389$	9.57056	0.485247	0.242623	+	0.970121i	$0.421992\pi$
$390$	0	0
$391$	2.69399	0.136241
$392$	−1.56687	−0.0791387
$393$	8.26809	0.417070
$394$	−31.2179	−1.57274
$395$	0	0
$396$	0.479291	0.0240853
$397$	29.4768	1.47940	0.739700	−	0.672937i	$-0.234967\pi$
$397$	29.4768	1.47940	0.739700	+	0.672937i	$0.234967\pi$
$398$	−19.2465	−0.964739
$399$	−5.63190	−0.281948
$400$	0	0
$401$	−17.4842	−0.873121	−0.436560	−	0.899675i	$-0.643803\pi$
$401$	−17.4842	−0.873121	−0.436560	+	0.899675i	$0.643803\pi$
$402$	−23.4230	−1.16824
$403$	−9.73705	−0.485037
$404$	3.85418	0.191753
$405$	0	0
$406$	−6.35439	−0.315363
$407$	−0.913835	−0.0452971
$408$	4.62270	0.228858
$409$	−30.2892	−1.49770	−0.748852	−	0.662737i	$-0.769395\pi$
$409$	−30.2892	−1.49770	−0.748852	+	0.662737i	$0.769395\pi$
$410$	0	0
$411$	−23.1690	−1.14284
$412$	−1.25698	−0.0619270
$413$	−12.8080	−0.630240
$414$	3.17643	0.156113
$415$	0	0
$416$	8.85462	0.434133
$417$	10.6862	0.523307
$418$	2.17191	0.106231
$419$	−6.62316	−0.323562	−0.161781	−	0.986827i	$-0.551724\pi$
$419$	−6.62316	−0.323562	−0.161781	+	0.986827i	$0.551724\pi$
$420$	0	0
$421$	−27.6057	−1.34542	−0.672709	−	0.739907i	$-0.734869\pi$
$421$	−27.6057	−1.34542	−0.672709	+	0.739907i	$0.734869\pi$
$422$	3.30620	0.160943
$423$	−3.30704	−0.160794
$424$	−8.58718	−0.417030
$425$	0	0
$426$	−9.10811	−0.441289
$427$	−6.75035	−0.326672
$428$	7.43325	0.359300
$429$	0.409865	0.0197884
$430$	0	0
$431$	26.7573	1.28885	0.644427	−	0.764666i	$-0.277096\pi$
$431$	26.7573	1.28885	0.644427	+	0.764666i	$0.277096\pi$
$432$	26.2213	1.26157
$433$	8.23574	0.395784	0.197892	−	0.980224i	$-0.436590\pi$
$433$	8.23574	0.395784	0.197892	+	0.980224i	$0.436590\pi$
$434$	10.9878	0.527429
$435$	0	0
$436$	12.4062	0.594149
$437$	5.14265	0.246006
$438$	−1.85167	−0.0884763
$439$	−32.1946	−1.53656	−0.768281	−	0.640112i	$-0.778888\pi$
$439$	−32.1946	−1.53656	−0.768281	+	0.640112i	$0.778888\pi$
$440$	0	0
$441$	−1.80068	−0.0857465
$442$	7.42883	0.353353
$443$	−20.8271	−0.989525	−0.494763	−	0.869028i	$-0.664745\pi$
$443$	−20.8271	−0.989525	−0.494763	+	0.869028i	$0.664745\pi$
$444$	4.64727	0.220549
$445$	0	0
$446$	24.0733	1.13990
$447$	8.54599	0.404211
$448$	−0.0169674	−0.000801633 0
$449$	−11.7635	−0.555152	−0.277576	−	0.960704i	$-0.589531\pi$
$449$	−11.7635	−0.555152	−0.277576	+	0.960704i	$0.589531\pi$
$450$	0	0
$451$	−0.0995951	−0.00468975
$452$	9.49496	0.446605
$453$	−21.4102	−1.00594
$454$	−15.1219	−0.709707
$455$	0	0
$456$	8.82443	0.413242
$457$	−14.7843	−0.691581	−0.345790	−	0.938312i	$-0.612389\pi$
$457$	−14.7843	−0.691581	−0.345790	+	0.938312i	$0.612389\pi$
$458$	14.8762	0.695118
$459$	14.1634	0.661089
$460$	0	0
$461$	34.9035	1.62562	0.812808	−	0.582531i	$-0.197938\pi$
$461$	34.9035	1.62562	0.812808	+	0.582531i	$0.197938\pi$
$462$	−0.462511	−0.0215180
$463$	−19.5820	−0.910052	−0.455026	−	0.890478i	$-0.650370\pi$
$463$	−19.5820	−0.910052	−0.455026	+	0.890478i	$0.650370\pi$
$464$	17.9661	0.834056
$465$	0	0
$466$	10.8385	0.502086
$467$	37.8670	1.75227	0.876137	−	0.482062i	$-0.160112\pi$
$467$	37.8670	1.75227	0.876137	+	0.482062i	$0.160112\pi$
$468$	3.12946	0.144659
$469$	−12.1247	−0.559868
$470$	0	0
$471$	5.52034	0.254364
$472$	20.0684	0.923723
$473$	2.17868	0.100176
$474$	10.9533	0.503104
$475$	0	0
$476$	−2.99508	−0.137279
$477$	−9.86857	−0.451851
$478$	−21.3726	−0.977558
$479$	−29.0215	−1.32603	−0.663014	−	0.748607i	$-0.730723\pi$
$479$	−29.0215	−1.32603	−0.663014	+	0.748607i	$0.730723\pi$
$480$	0	0
$481$	−5.96676	−0.272061
$482$	−52.9245	−2.41064
$483$	−1.09514	−0.0498304
$484$	−12.1657	−0.552985
$485$	0	0
$486$	27.1356	1.23090
$487$	29.3348	1.32929	0.664643	−	0.747161i	$-0.268583\pi$
$487$	29.3348	1.32929	0.664643	+	0.747161i	$0.268583\pi$
$488$	10.5769	0.478793
$489$	9.46370	0.427963
$490$	0	0
$491$	−28.5788	−1.28974	−0.644871	−	0.764291i	$-0.723089\pi$
$491$	−28.5788	−1.28974	−0.644871	+	0.764291i	$0.723089\pi$
$492$	0.506486	0.0228342
$493$	9.70434	0.437062
$494$	14.1811	0.638040
$495$	0	0
$496$	−31.0663	−1.39492
$497$	−4.71473	−0.211485
$498$	−19.2044	−0.860569
$499$	−23.4533	−1.04992	−0.524958	−	0.851128i	$-0.675919\pi$
$499$	−23.4533	−1.04992	−0.524958	+	0.851128i	$0.675919\pi$
$500$	0	0
$501$	3.39864	0.151840
$502$	−10.4971	−0.468508
$503$	26.9666	1.20238	0.601191	−	0.799106i	$-0.294693\pi$
$503$	26.9666	1.20238	0.601191	+	0.799106i	$0.294693\pi$
$504$	2.82142	0.125676
$505$	0	0
$506$	0.422332	0.0187750
$507$	−11.5606	−0.513425
$508$	24.6313	1.09284
$509$	9.80906	0.434779	0.217389	−	0.976085i	$-0.430246\pi$
$509$	9.80906	0.434779	0.217389	+	0.976085i	$0.430246\pi$
$510$	0	0
$511$	−0.958501	−0.0424016
$512$	12.6214	0.557791
$513$	27.0369	1.19371
$514$	−38.4171	−1.69451
$515$	0	0
$516$	−11.0796	−0.487751
$517$	−0.439699	−0.0193379
$518$	6.73318	0.295839
$519$	−3.47053	−0.152339
$520$	0	0
$521$	0.445651	0.0195243	0.00976217	−	0.999952i	$-0.496893\pi$
$521$	0.445651	0.0195243	0.00976217	+	0.999952i	$0.496893\pi$
$522$	11.4422	0.500812
$523$	−13.1584	−0.575376	−0.287688	−	0.957724i	$-0.592887\pi$
$523$	−13.1584	−0.575376	−0.287688	+	0.957724i	$0.592887\pi$
$524$	8.39362	0.366677
$525$	0	0
$526$	4.99269	0.217692
$527$	−16.7804	−0.730964
$528$	1.30768	0.0569096
$529$	1.00000	0.0434783
$530$	0	0
$531$	23.0630	1.00085
$532$	−5.71741	−0.247881
$533$	−0.650292	−0.0281673
$534$	27.6094	1.19478
$535$	0	0
$536$	18.9978	0.820581
$537$	13.8376	0.597137
$538$	20.3069	0.875492
$539$	−0.239415	−0.0103123
$540$	0	0
$541$	−35.1191	−1.50989	−0.754943	−	0.655790i	$-0.772336\pi$
$541$	−35.1191	−1.50989	−0.754943	+	0.655790i	$0.772336\pi$
$542$	−32.2416	−1.38489
$543$	−0.523725	−0.0224752
$544$	15.2596	0.654252
$545$	0	0
$546$	−3.01990	−0.129240
$547$	−41.3726	−1.76897	−0.884483	−	0.466572i	$-0.845489\pi$
$547$	−41.3726	−1.76897	−0.884483	+	0.466572i	$0.845489\pi$
$548$	−23.5208	−1.00476
$549$	12.1552	0.518771
$550$	0	0
$551$	18.5250	0.789190
$552$	1.71593	0.0730349
$553$	5.66990	0.241109
$554$	42.9456	1.82458
$555$	0	0
$556$	10.8485	0.460078
$557$	−10.0357	−0.425227	−0.212614	−	0.977136i	$-0.568198\pi$
$557$	−10.0357	−0.425227	−0.212614	+	0.977136i	$0.568198\pi$
$558$	−19.7854	−0.837583
$559$	14.2254	0.601669
$560$	0	0
$561$	0.706342	0.0298218
$562$	−10.1934	−0.429983
$563$	46.9517	1.97878	0.989389	−	0.145290i	$-0.0464115\pi$
$563$	46.9517	1.97878	0.989389	+	0.145290i	$0.0464115\pi$
$564$	2.23607	0.0941554
$565$	0	0
$566$	17.2788	0.726283
$567$	−0.355531	−0.0149309
$568$	7.38735	0.309966
$569$	−11.9187	−0.499659	−0.249829	−	0.968290i	$-0.580375\pi$
$569$	−11.9187	−0.499659	−0.249829	+	0.968290i	$0.580375\pi$
$570$	0	0
$571$	17.4004	0.728185	0.364093	−	0.931363i	$-0.381379\pi$
$571$	17.4004	0.728185	0.364093	+	0.931363i	$0.381379\pi$
$572$	0.416088	0.0173975
$573$	−0.681018	−0.0284499
$574$	0.733822	0.0306291
$575$	0	0
$576$	0.0305527	0.00127303
$577$	−18.9569	−0.789184	−0.394592	−	0.918856i	$-0.629114\pi$
$577$	−18.9569	−0.789184	−0.394592	+	0.918856i	$0.629114\pi$
$578$	−17.1858	−0.714836
$579$	−27.3398	−1.13620
$580$	0	0
$581$	−9.94097	−0.412421
$582$	−7.33365	−0.303990
$583$	−1.31211	−0.0543420
$584$	1.50184	0.0621467
$585$	0	0
$586$	34.3399	1.41857
$587$	13.8885	0.573242	0.286621	−	0.958044i	$-0.407468\pi$
$587$	13.8885	0.573242	0.286621	+	0.958044i	$0.407468\pi$
$588$	1.21753	0.0502102
$589$	−32.0326	−1.31988
$590$	0	0
$591$	−19.3807	−0.797215
$592$	−19.0371	−0.782420
$593$	1.96736	0.0807899	0.0403950	−	0.999184i	$-0.487138\pi$
$593$	1.96736	0.0807899	0.0403950	+	0.999184i	$0.487138\pi$
$594$	2.22037	0.0911028
$595$	0	0
$596$	8.67574	0.355372
$597$	−11.9486	−0.489023
$598$	2.75756	0.112765
$599$	−36.6332	−1.49679	−0.748395	−	0.663253i	$-0.769175\pi$
$599$	−36.6332	−1.49679	−0.748395	+	0.663253i	$0.769175\pi$
$600$	0	0
$601$	40.3821	1.64722	0.823611	−	0.567156i	$-0.191956\pi$
$601$	40.3821	1.64722	0.823611	+	0.567156i	$0.191956\pi$
$602$	−16.0526	−0.654255
$603$	21.8327	0.889097
$604$	−21.7353	−0.884398
$605$	0	0
$606$	6.69717	0.272054
$607$	1.68034	0.0682028	0.0341014	−	0.999418i	$-0.489143\pi$
$607$	1.68034	0.0682028	0.0341014	+	0.999418i	$0.489143\pi$
$608$	29.1296	1.18136
$609$	−3.94492	−0.159856
$610$	0	0
$611$	−2.87095	−0.116146
$612$	5.39317	0.218006
$613$	−4.47924	−0.180915	−0.0904575	−	0.995900i	$-0.528833\pi$
$613$	−4.47924	−0.180915	−0.0904575	+	0.995900i	$0.528833\pi$
$614$	35.8889	1.44836
$615$	0	0
$616$	0.375131	0.0151145
$617$	5.58000	0.224642	0.112321	−	0.993672i	$-0.464171\pi$
$617$	5.58000	0.224642	0.112321	+	0.993672i	$0.464171\pi$
$618$	−2.18418	−0.0878604
$619$	−34.5286	−1.38782	−0.693912	−	0.720060i	$-0.744114\pi$
$619$	−34.5286	−1.38782	−0.693912	+	0.720060i	$0.744114\pi$
$620$	0	0
$621$	5.25739	0.210972
$622$	−10.3176	−0.413699
$623$	14.2918	0.572588
$624$	8.53833	0.341807
$625$	0	0
$626$	−36.1284	−1.44398
$627$	1.34836	0.0538483
$628$	5.60416	0.223630
$629$	−10.2828	−0.410003
$630$	0	0
$631$	34.8386	1.38690	0.693451	−	0.720504i	$-0.256089\pi$
$631$	34.8386	1.38690	0.693451	+	0.720504i	$0.256089\pi$
$632$	−8.88397	−0.353385
$633$	2.05255	0.0815817
$634$	1.15766	0.0459766
$635$	0	0
$636$	6.67266	0.264588
$637$	−1.56322	−0.0619372
$638$	1.52133	0.0602302
$639$	8.48971	0.335848
$640$	0	0
$641$	27.4139	1.08278	0.541391	−	0.840771i	$-0.317898\pi$
$641$	27.4139	1.08278	0.541391	+	0.840771i	$0.317898\pi$
$642$	12.9163	0.509765
$643$	33.6303	1.32625	0.663126	−	0.748508i	$-0.269229\pi$
$643$	33.6303	1.32625	0.663126	+	0.748508i	$0.269229\pi$
$644$	−1.11176	−0.0438096
$645$	0	0
$646$	24.4391	0.961545
$647$	12.6817	0.498568	0.249284	−	0.968430i	$-0.419805\pi$
$647$	12.6817	0.498568	0.249284	+	0.968430i	$0.419805\pi$
$648$	0.557069	0.0218837
$649$	3.06642	0.120368
$650$	0	0
$651$	6.82141	0.267352
$652$	9.60739	0.376254
$653$	−1.13312	−0.0443423	−0.0221711	−	0.999754i	$-0.507058\pi$
$653$	−1.13312	−0.0443423	−0.0221711	+	0.999754i	$0.507058\pi$
$654$	21.5575	0.842963
$655$	0	0
$656$	−2.07477	−0.0810063
$657$	1.72595	0.0673357
$658$	3.23972	0.126297
$659$	38.8660	1.51401	0.757003	−	0.653412i	$-0.226663\pi$
$659$	38.8660	1.51401	0.757003	+	0.653412i	$0.226663\pi$
$660$	0	0
$661$	19.7711	0.769008	0.384504	−	0.923123i	$-0.374372\pi$
$661$	19.7711	0.769008	0.384504	+	0.923123i	$0.374372\pi$
$662$	−46.1332	−1.79302
$663$	4.61196	0.179114
$664$	15.5762	0.604473
$665$	0	0
$666$	−12.1243	−0.469806
$667$	3.60222	0.139479
$668$	3.45024	0.133494
$669$	14.9452	0.577813
$670$	0	0
$671$	1.61613	0.0623901
$672$	−6.20321	−0.239294
$673$	−21.4304	−0.826080	−0.413040	−	0.910713i	$-0.635533\pi$
$673$	−21.4304	−0.826080	−0.413040	+	0.910713i	$0.635533\pi$
$674$	25.5123	0.982698
$675$	0	0
$676$	−11.7361	−0.451390
$677$	19.2421	0.739533	0.369766	−	0.929125i	$-0.379438\pi$
$677$	19.2421	0.739533	0.369766	+	0.929125i	$0.379438\pi$
$678$	16.4988	0.633632
$679$	−3.79620	−0.145685
$680$	0	0
$681$	−9.38798	−0.359748
$682$	−2.63063	−0.100732
$683$	−41.1126	−1.57313	−0.786564	−	0.617508i	$-0.788142\pi$
$683$	−41.1126	−1.57313	−0.786564	+	0.617508i	$0.788142\pi$
$684$	10.2952	0.393647
$685$	0	0
$686$	1.76402	0.0673506
$687$	9.23541	0.352353
$688$	45.3864	1.73034
$689$	−8.56722	−0.326385
$690$	0	0
$691$	−10.2082	−0.388340	−0.194170	−	0.980968i	$-0.562201\pi$
$691$	−10.2082	−0.388340	−0.194170	+	0.980968i	$0.562201\pi$
$692$	−3.52322	−0.133933
$693$	0.431109	0.0163765
$694$	3.72862	0.141536
$695$	0	0
$696$	6.18117	0.234296
$697$	−1.12068	−0.0424489
$698$	44.4891	1.68394
$699$	6.72877	0.254506
$700$	0	0
$701$	−19.5382	−0.737949	−0.368975	−	0.929439i	$-0.620291\pi$
$701$	−19.5382	−0.737949	−0.368975	+	0.929439i	$0.620291\pi$
$702$	14.4976	0.547176
$703$	−19.6292	−0.740331
$704$	0.00406224	0.000153101 0
$705$	0	0
$706$	12.7767	0.480857
$707$	3.46673	0.130380
$708$	−15.5941	−0.586063
$709$	−4.59444	−0.172548	−0.0862740	−	0.996271i	$-0.527496\pi$
$709$	−4.59444	−0.172548	−0.0862740	+	0.996271i	$0.527496\pi$
$710$	0	0
$711$	−10.2097	−0.382892
$712$	−22.3933	−0.839225
$713$	−6.22882	−0.233271
$714$	−5.20436	−0.194768
$715$	0	0
$716$	14.0477	0.524987
$717$	−13.2685	−0.495520
$718$	−32.5216	−1.21370
$719$	6.62616	0.247114	0.123557	−	0.992337i	$-0.460570\pi$
$719$	6.62616	0.247114	0.123557	+	0.992337i	$0.460570\pi$
$720$	0	0
$721$	−1.13062	−0.0421064
$722$	13.1363	0.488883
$723$	−32.8565	−1.22195
$724$	−0.531677	−0.0197596
$725$	0	0
$726$	−21.1395	−0.784561
$727$	−38.1675	−1.41555	−0.707777	−	0.706436i	$-0.750302\pi$
$727$	−38.1675	−1.41555	−0.707777	+	0.706436i	$0.750302\pi$
$728$	2.44936	0.0907795
$729$	17.9129	0.663440
$730$	0	0
$731$	24.5153	0.906732
$732$	−8.21877	−0.303774
$733$	34.4849	1.27373	0.636864	−	0.770977i	$-0.280231\pi$
$733$	34.4849	1.27373	0.636864	+	0.770977i	$0.280231\pi$
$734$	38.9739	1.43855
$735$	0	0
$736$	5.66433	0.208790
$737$	2.90284	0.106927
$738$	−1.32138	−0.0486405
$739$	28.0779	1.03286	0.516430	−	0.856329i	$-0.327260\pi$
$739$	28.0779	1.03286	0.516430	+	0.856329i	$0.327260\pi$
$740$	0	0
$741$	8.80392	0.323420
$742$	9.66767	0.354911
$743$	−19.6190	−0.719750	−0.359875	−	0.933001i	$-0.617181\pi$
$743$	−19.6190	−0.719750	−0.359875	+	0.933001i	$0.617181\pi$
$744$	−10.6882	−0.391849
$745$	0	0
$746$	22.2084	0.813106
$747$	17.9005	0.654944
$748$	0.717066	0.0262185
$749$	6.68600	0.244301
$750$	0	0
$751$	15.0536	0.549313	0.274657	−	0.961542i	$-0.411436\pi$
$751$	15.0536	0.549313	0.274657	+	0.961542i	$0.411436\pi$
$752$	−9.15984	−0.334025
$753$	−6.51679	−0.237485
$754$	9.93334	0.361751
$755$	0	0
$756$	−5.84498	−0.212580
$757$	−38.1645	−1.38711	−0.693555	−	0.720403i	$-0.743957\pi$
$757$	−38.1645	−1.38711	−0.693555	+	0.720403i	$0.743957\pi$
$758$	−6.97451	−0.253326
$759$	0.262192	0.00951696
$760$	0	0
$761$	53.5124	1.93982	0.969911	−	0.243461i	$-0.0782826\pi$
$761$	53.5124	1.93982	0.969911	+	0.243461i	$0.0782826\pi$
$762$	42.8002	1.55049
$763$	11.1590	0.403984
$764$	−0.691358	−0.0250125
$765$	0	0
$766$	31.5886	1.14134
$767$	20.0218	0.722944
$768$	21.8645	0.788967
$769$	−11.0805	−0.399574	−0.199787	−	0.979839i	$-0.564025\pi$
$769$	−11.0805	−0.399574	−0.199787	+	0.979839i	$0.564025\pi$
$770$	0	0
$771$	−23.8501	−0.858939
$772$	−27.7549	−0.998919
$773$	−18.3391	−0.659611	−0.329805	−	0.944049i	$-0.606983\pi$
$773$	−18.3391	−0.659611	−0.329805	+	0.944049i	$0.606983\pi$
$774$	28.9056	1.03899
$775$	0	0
$776$	5.94813	0.213525
$777$	4.18008	0.149960
$778$	16.8826	0.605272
$779$	−2.13931	−0.0766488
$780$	0	0
$781$	1.12878	0.0403908
$782$	4.75225	0.169940
$783$	18.9383	0.676800
$784$	−4.98751	−0.178125
$785$	0	0
$786$	14.5851	0.520232
$787$	31.0160	1.10560	0.552801	−	0.833314i	$-0.313559\pi$
$787$	31.0160	1.10560	0.552801	+	0.833314i	$0.313559\pi$
$788$	−19.6749	−0.700891
$789$	3.09956	0.110347
$790$	0	0
$791$	8.54045	0.303663
$792$	−0.675490	−0.0240025
$793$	10.5523	0.374723
$794$	51.9977	1.84533
$795$	0	0
$796$	−12.1300	−0.429936
$797$	7.94631	0.281473	0.140736	−	0.990047i	$-0.455053\pi$
$797$	7.94631	0.281473	0.140736	+	0.990047i	$0.455053\pi$
$798$	−9.93478	−0.351687
$799$	−4.94766	−0.175036
$800$	0	0
$801$	−25.7349	−0.909297
$802$	−30.8425	−1.08909
$803$	0.229479	0.00809815
$804$	−14.7622	−0.520624
$805$	0	0
$806$	−17.1763	−0.605011
$807$	12.6069	0.443784
$808$	−5.43190	−0.191093
$809$	−19.1548	−0.673446	−0.336723	−	0.941604i	$-0.609319\pi$
$809$	−19.1548	−0.673446	−0.336723	+	0.941604i	$0.609319\pi$
$810$	0	0
$811$	−38.9385	−1.36732	−0.683658	−	0.729802i	$-0.739612\pi$
$811$	−38.9385	−1.36732	−0.683658	+	0.729802i	$0.739612\pi$
$812$	−4.00482	−0.140542
$813$	−20.0162	−0.701997
$814$	−1.61202	−0.0565014
$815$	0	0
$816$	14.7146	0.515113
$817$	46.7982	1.63726
$818$	−53.4307	−1.86816
$819$	2.81486	0.0983593
$820$	0	0
$821$	−8.65182	−0.301951	−0.150975	−	0.988538i	$-0.548241\pi$
$821$	−8.65182	−0.301951	−0.150975	+	0.988538i	$0.548241\pi$
$822$	−40.8706	−1.42553
$823$	−11.1297	−0.387957	−0.193979	−	0.981006i	$-0.562139\pi$
$823$	−11.1297	−0.387957	−0.193979	+	0.981006i	$0.562139\pi$
$824$	1.77153	0.0617141
$825$	0	0
$826$	−22.5935	−0.786129
$827$	37.1410	1.29152	0.645759	−	0.763541i	$-0.276541\pi$
$827$	37.1410	1.29152	0.645759	+	0.763541i	$0.276541\pi$
$828$	2.00193	0.0695718
$829$	−13.1062	−0.455198	−0.227599	−	0.973755i	$-0.573087\pi$
$829$	−13.1062	−0.455198	−0.227599	+	0.973755i	$0.573087\pi$
$830$	0	0
$831$	26.6614	0.924874
$832$	0.0265238	0.000919548 0
$833$	−2.69399	−0.0933412
$834$	18.8507	0.652747
$835$	0	0
$836$	1.36883	0.0473420
$837$	−32.7474	−1.13191
$838$	−11.6834	−0.403596
$839$	10.9543	0.378184	0.189092	−	0.981959i	$-0.439446\pi$
$839$	10.9543	0.378184	0.189092	+	0.981959i	$0.439446\pi$
$840$	0	0
$841$	−16.0240	−0.552552
$842$	−48.6969	−1.67821
$843$	−6.32826	−0.217957
$844$	2.08372	0.0717245
$845$	0	0
$846$	−5.83369	−0.200566
$847$	−10.9427	−0.375995
$848$	−27.3339	−0.938651
$849$	10.7270	0.368150
$850$	0	0
$851$	−3.81695	−0.130844
$852$	−5.74034	−0.196661
$853$	51.9504	1.77875	0.889375	−	0.457179i	$-0.151140\pi$
$853$	51.9504	1.77875	0.889375	+	0.457179i	$0.151140\pi$
$854$	−11.9077	−0.407475
$855$	0	0
$856$	−10.4761	−0.358065
$857$	−43.9344	−1.50077	−0.750385	−	0.661001i	$-0.770132\pi$
$857$	−43.9344	−1.50077	−0.750385	+	0.661001i	$0.770132\pi$
$858$	0.723009	0.0246831
$859$	−45.3622	−1.54774	−0.773869	−	0.633346i	$-0.781681\pi$
$859$	−45.3622	−1.54774	−0.773869	+	0.633346i	$0.781681\pi$
$860$	0	0
$861$	0.455570	0.0155258
$862$	47.2004	1.60765
$863$	−46.3089	−1.57637	−0.788186	−	0.615437i	$-0.788980\pi$
$863$	−46.3089	−1.57637	−0.788186	+	0.615437i	$0.788980\pi$
$864$	29.7796	1.01312
$865$	0	0
$866$	14.5280	0.493682
$867$	−10.6693	−0.362348
$868$	6.92498	0.235049
$869$	−1.35746	−0.0460486
$870$	0	0
$871$	18.9537	0.642221
$872$	−17.4847	−0.592106
$873$	6.83572	0.231354
$874$	9.07173	0.306856
$875$	0	0
$876$	−1.16701	−0.0394295
$877$	−7.61440	−0.257120	−0.128560	−	0.991702i	$-0.541036\pi$
$877$	−7.61440	−0.257120	−0.128560	+	0.991702i	$0.541036\pi$
$878$	−56.7918	−1.91663
$879$	21.3189	0.719068
$880$	0	0
$881$	18.3719	0.618964	0.309482	−	0.950905i	$-0.399844\pi$
$881$	18.3719	0.618964	0.309482	+	0.950905i	$0.399844\pi$
$882$	−3.17643	−0.106956
$883$	−23.6116	−0.794595	−0.397298	−	0.917690i	$-0.630052\pi$
$883$	−23.6116	−0.794595	−0.397298	+	0.917690i	$0.630052\pi$
$884$	4.68198	0.157472
$885$	0	0
$886$	−36.7394	−1.23428
$887$	1.90523	0.0639714	0.0319857	−	0.999488i	$-0.489817\pi$
$887$	1.90523	0.0639714	0.0319857	+	0.999488i	$0.489817\pi$
$888$	−6.54963	−0.219791
$889$	22.1551	0.743059
$890$	0	0
$891$	0.0851193	0.00285160
$892$	15.1721	0.507999
$893$	−9.44476	−0.316057
$894$	15.0753	0.504193
$895$	0	0
$896$	11.2987	0.377464
$897$	1.71194	0.0571601
$898$	−20.7510	−0.692469
$899$	−22.4376	−0.748336
$900$	0	0
$901$	−14.7644	−0.491872
$902$	−0.175688	−0.00584976
$903$	−9.96575	−0.331640
$904$	−13.3817	−0.445070
$905$	0	0
$906$	−37.7681	−1.25476
$907$	0.0436569	0.00144960	0.000724802	−	1.00000i	$-0.499769\pi$
$907$	0.0436569	0.00144960	0.000724802		1.00000i	$0.499769\pi$
$908$	−9.53052	−0.316281
$909$	−6.24246	−0.207049
$910$	0	0
$911$	20.0484	0.664234	0.332117	−	0.943238i	$-0.392237\pi$
$911$	20.0484	0.664234	0.332117	+	0.943238i	$0.392237\pi$
$912$	28.0891	0.930124
$913$	2.38002	0.0787670
$914$	−26.0798	−0.862643
$915$	0	0
$916$	9.37563	0.309779
$917$	7.54983	0.249317
$918$	24.9844	0.824609
$919$	5.54638	0.182958	0.0914791	−	0.995807i	$-0.470841\pi$
$919$	5.54638	0.182958	0.0914791	+	0.995807i	$0.470841\pi$
$920$	0	0
$921$	22.2805	0.734167
$922$	61.5704	2.02771
$923$	7.37018	0.242592
$924$	−0.291495	−0.00958949
$925$	0	0
$926$	−34.5430	−1.13515
$927$	2.03588	0.0668670
$928$	20.4042	0.669800
$929$	−52.0245	−1.70687	−0.853434	−	0.521202i	$-0.825484\pi$
$929$	−52.0245	−1.70687	−0.853434	+	0.521202i	$0.825484\pi$
$930$	0	0
$931$	−5.14265	−0.168543
$932$	6.83094	0.223755
$933$	−6.40538	−0.209703
$934$	66.7981	2.18570
$935$	0	0
$936$	−4.41051	−0.144162
$937$	−31.6834	−1.03505	−0.517526	−	0.855668i	$-0.673147\pi$
$937$	−31.6834	−1.03505	−0.517526	+	0.855668i	$0.673147\pi$
$938$	−21.3882	−0.698351
$939$	−22.4292	−0.731949
$940$	0	0
$941$	−2.87642	−0.0937687	−0.0468843	−	0.998900i	$-0.514929\pi$
$941$	−2.87642	−0.0937687	−0.0468843	+	0.998900i	$0.514929\pi$
$942$	9.73799	0.317281
$943$	−0.415994	−0.0135466
$944$	63.8799	2.07911
$945$	0	0
$946$	3.84323	0.124954
$947$	−54.3056	−1.76470	−0.882348	−	0.470598i	$-0.844038\pi$
$947$	−54.3056	−1.76470	−0.882348	+	0.470598i	$0.844038\pi$
$948$	6.90329	0.224208
$949$	1.49835	0.0486386
$950$	0	0
$951$	0.718697	0.0233054
$952$	4.22112	0.136807
$953$	40.3678	1.30764	0.653820	−	0.756650i	$-0.273165\pi$
$953$	40.3678	1.30764	0.653820	+	0.756650i	$0.273165\pi$
$954$	−17.4084	−0.563616
$955$	0	0
$956$	−13.4699	−0.435649
$957$	0.944473	0.0305305
$958$	−51.1945	−1.65402
$959$	−21.1563	−0.683173
$960$	0	0
$961$	7.79820	0.251555
$962$	−10.5255	−0.339355
$963$	−12.0393	−0.387962
$964$	−33.3554	−1.07430
$965$	0	0
$966$	−1.93184	−0.0621560
$967$	−2.42820	−0.0780857	−0.0390428	−	0.999238i	$-0.512431\pi$
$967$	−2.42820	−0.0780857	−0.0390428	+	0.999238i	$0.512431\pi$
$968$	17.1457	0.551084
$969$	15.1723	0.487403
$970$	0	0
$971$	−40.3190	−1.29390	−0.646950	−	0.762533i	$-0.723956\pi$
$971$	−40.3190	−1.29390	−0.646950	+	0.762533i	$0.723956\pi$
$972$	17.1021	0.548549
$973$	9.75790	0.312824
$974$	51.7472	1.65809
$975$	0	0
$976$	33.6674	1.07767
$977$	5.41096	0.173112	0.0865560	−	0.996247i	$-0.472414\pi$
$977$	5.41096	0.173112	0.0865560	+	0.996247i	$0.472414\pi$
$978$	16.6942	0.533820
$979$	−3.42166	−0.109357
$980$	0	0
$981$	−20.0938	−0.641546
$982$	−50.4135	−1.60876
$983$	−49.3945	−1.57544	−0.787720	−	0.616034i	$-0.788739\pi$
$983$	−49.3945	−1.57544	−0.787720	+	0.616034i	$0.788739\pi$
$984$	−0.713817	−0.0227557
$985$	0	0
$986$	17.1186	0.545169
$987$	2.01128	0.0640197
$988$	8.93759	0.284343
$989$	9.10002	0.289364
$990$	0	0
$991$	−52.4435	−1.66592	−0.832961	−	0.553331i	$-0.813356\pi$
$991$	−52.4435	−1.66592	−0.832961	+	0.553331i	$0.813356\pi$
$992$	−35.2821	−1.12021
$993$	−28.6404	−0.908874
$994$	−8.31687	−0.263795
$995$	0	0
$996$	−12.1035	−0.383513
$997$	0.668249	0.0211636	0.0105818	−	0.999944i	$-0.496632\pi$
$997$	0.668249	0.0211636	0.0105818	+	0.999944i	$0.496632\pi$
$998$	−41.3721	−1.30961
$999$	−20.0672	−0.634899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.x.1.11		12
5.2	odd	4		805.2.c.b.484.21	yes	24
5.3	odd	4		805.2.c.b.484.4	✓	24
5.4	even	2		4025.2.a.y.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.4	✓	24	5.3	odd	4
805.2.c.b.484.21	yes	24	5.2	odd	4
4025.2.a.x.1.11		12	1.1	even	1	trivial
4025.2.a.y.1.2		12	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.76402 q^{2} +1.09514 q^{3} +1.11176 q^{4} +1.93184 q^{6} +1.00000 q^{7} -1.56687 q^{8} -1.80068 q^{9} +O(q^{10})\)	\(q+1.76402 q^{2} +1.09514 q^{3} +1.11176 q^{4} +1.93184 q^{6} +1.00000 q^{7} -1.56687 q^{8} -1.80068 q^{9} -0.239415 q^{11} +1.21753 q^{12} -1.56322 q^{13} +1.76402 q^{14} -4.98751 q^{16} -2.69399 q^{17} -3.17643 q^{18} -5.14265 q^{19} +1.09514 q^{21} -0.422332 q^{22} -1.00000 q^{23} -1.71593 q^{24} -2.75756 q^{26} -5.25739 q^{27} +1.11176 q^{28} -3.60222 q^{29} +6.22882 q^{31} -5.66433 q^{32} -0.262192 q^{33} -4.75225 q^{34} -2.00193 q^{36} +3.81695 q^{37} -9.07173 q^{38} -1.71194 q^{39} +0.415994 q^{41} +1.93184 q^{42} -9.10002 q^{43} -0.266173 q^{44} -1.76402 q^{46} +1.83656 q^{47} -5.46200 q^{48} +1.00000 q^{49} -2.95028 q^{51} -1.73794 q^{52} +5.48048 q^{53} -9.27414 q^{54} -1.56687 q^{56} -5.63190 q^{57} -6.35439 q^{58} -12.8080 q^{59} -6.75035 q^{61} +10.9878 q^{62} -1.80068 q^{63} -0.0169674 q^{64} -0.462511 q^{66} -12.1247 q^{67} -2.99508 q^{68} -1.09514 q^{69} -4.71473 q^{71} +2.82142 q^{72} -0.958501 q^{73} +6.73318 q^{74} -5.71741 q^{76} -0.239415 q^{77} -3.01990 q^{78} +5.66990 q^{79} -0.355531 q^{81} +0.733822 q^{82} -9.94097 q^{83} +1.21753 q^{84} -16.0526 q^{86} -3.94492 q^{87} +0.375131 q^{88} +14.2918 q^{89} -1.56322 q^{91} -1.11176 q^{92} +6.82141 q^{93} +3.23972 q^{94} -6.20321 q^{96} -3.79620 q^{97} +1.76402 q^{98} +0.431109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * q^99

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