LMFDB - Embedded newform 9025.2.a.cd.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.593847$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} +1.14614 q^{6} -1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +O(q^{10})$	\(q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} +1.14614 q^{6} -1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +0.196653 q^{11} +3.17944 q^{12} -5.28245 q^{13} +0.629785 q^{14} +2.00844 q^{16} -0.704965 q^{17} -0.430558 q^{18} +2.04684 q^{21} -0.116781 q^{22} -6.62298 q^{23} -4.18038 q^{24} +3.13697 q^{26} +4.39076 q^{27} +1.74704 q^{28} +3.38126 q^{29} -7.91823 q^{31} -5.52463 q^{32} -0.379546 q^{33} +0.418641 q^{34} -1.19438 q^{36} -1.09727 q^{37} +10.1953 q^{39} +1.35463 q^{41} -1.21551 q^{42} -9.00810 q^{43} -0.323955 q^{44} +3.93303 q^{46} -4.81938 q^{47} -3.87636 q^{48} -5.87530 q^{49} +1.36061 q^{51} +8.70203 q^{52} -5.32420 q^{53} -2.60744 q^{54} -2.29704 q^{56} -2.00795 q^{58} +10.9822 q^{59} +11.7524 q^{61} +4.70221 q^{62} -0.768911 q^{63} -0.736100 q^{64} +0.225392 q^{66} -3.05599 q^{67} +1.16132 q^{68} +12.7826 q^{69} -2.50478 q^{71} +1.57040 q^{72} -6.55421 q^{73} +0.651609 q^{74} -0.208554 q^{77} -6.05445 q^{78} +12.2632 q^{79} -10.6494 q^{81} -0.804441 q^{82} +4.03175 q^{83} -3.37185 q^{84} +5.34943 q^{86} -6.52596 q^{87} +0.425943 q^{88} -17.5253 q^{89} +5.60214 q^{91} +10.9103 q^{92} +15.2825 q^{93} +2.86197 q^{94} +10.6627 q^{96} -1.33950 q^{97} +3.48903 q^{98} +0.142580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9	$ 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} + 12 q^{14} - 12 q^{16} + 9 q^{17} - 6 q^{18} + 12 q^{21} - 12 q^{22} + 15 q^{24} + 21 q^{26} - 6 q^{27} + 15 q^{28} + 15 q^{29} + 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} + 18 q^{41} - 36 q^{42} + 6 q^{43} - 24 q^{44} + 21 q^{46} - 21 q^{47} - 15 q^{48} + 3 q^{49} + 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} + 36 q^{56} - 18 q^{58} + 27 q^{59} + 12 q^{61} + 6 q^{62} + 15 q^{63} + 24 q^{64} + 3 q^{66} - 36 q^{67} - 3 q^{68} + 27 q^{69} - 6 q^{71} - 12 q^{72} + 9 q^{73} - 9 q^{74} - 12 q^{77} - 54 q^{78} + 45 q^{79} - 15 q^{81} + 48 q^{82} - 12 q^{84} - 9 q^{86} - 45 q^{87} - 39 q^{88} - 9 q^{89} + 51 q^{91} + 54 q^{92} - 9 q^{93} + 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 + 12 * q^14 - 12 * q^16 + 9 * q^17 - 6 * q^18 + 12 * q^21 - 12 * q^22 + 15 * q^24 + 21 * q^26 - 6 * q^27 + 15 * q^28 + 15 * q^29 + 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 + 18 * q^41 - 36 * q^42 + 6 * q^43 - 24 * q^44 + 21 * q^46 - 21 * q^47 - 15 * q^48 + 3 * q^49 + 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 + 36 * q^56 - 18 * q^58 + 27 * q^59 + 12 * q^61 + 6 * q^62 + 15 * q^63 + 24 * q^64 + 3 * q^66 - 36 * q^67 - 3 * q^68 + 27 * q^69 - 6 * q^71 - 12 * q^72 + 9 * q^73 - 9 * q^74 - 12 * q^77 - 54 * q^78 + 45 * q^79 - 15 * q^81 + 48 * q^82 - 12 * q^84 - 9 * q^86 - 45 * q^87 - 39 * q^88 - 9 * q^89 + 51 * q^91 + 54 * q^92 - 9 * q^93 + 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.593847	−0.419913	−0.209956	−	0.977711i	$-0.567332\pi$
$2$	−0.593847	−0.419913	−0.209956	+	0.977711i	$0.567332\pi$
$3$	−1.93003	−1.11431	−0.557153	−	0.830410i	$-0.688106\pi$
$3$	−1.93003	−1.11431	−0.557153	+	0.830410i	$0.688106\pi$
$4$	−1.64735	−0.823673
$5$	0	0
$5$	0	0
$6$	1.14614	0.467911
$7$	−1.06052	−0.400838	−0.200419	−	0.979710i	$-0.564230\pi$
$7$	−1.06052	−0.400838	−0.200419	+	0.979710i	$0.564230\pi$
$8$	2.16596	0.765784
$9$	0.725033	0.241678
$10$	0	0
$11$	0.196653	0.0592930	0.0296465	−	0.999560i	$-0.490562\pi$
$11$	0.196653	0.0592930	0.0296465	+	0.999560i	$0.490562\pi$
$12$	3.17944	0.917824
$13$	−5.28245	−1.46509	−0.732544	−	0.680719i	$-0.761667\pi$
$13$	−5.28245	−1.46509	−0.732544	+	0.680719i	$0.761667\pi$
$14$	0.629785	0.168317
$15$	0	0
$16$	2.00844	0.502111
$17$	−0.704965	−0.170979	−0.0854896	−	0.996339i	$-0.527245\pi$
$17$	−0.704965	−0.170979	−0.0854896	+	0.996339i	$0.527245\pi$
$18$	−0.430558	−0.101484
$19$	0	0
$19$	0	0
$20$	0	0
$21$	2.04684	0.446656
$22$	−0.116781	−0.0248979
$23$	−6.62298	−1.38099	−0.690493	−	0.723339i	$-0.742606\pi$
$23$	−6.62298	−1.38099	−0.690493	+	0.723339i	$0.742606\pi$
$24$	−4.18038	−0.853318
$25$	0	0
$26$	3.13697	0.615210
$27$	4.39076	0.845003
$28$	1.74704	0.330160
$29$	3.38126	0.627885	0.313942	−	0.949442i	$-0.398350\pi$
$29$	3.38126	0.627885	0.313942	+	0.949442i	$0.398350\pi$
$30$	0	0
$31$	−7.91823	−1.42216	−0.711078	−	0.703113i	$-0.751793\pi$
$31$	−7.91823	−1.42216	−0.711078	+	0.703113i	$0.751793\pi$
$32$	−5.52463	−0.976627
$33$	−0.379546	−0.0660705
$34$	0.418641	0.0717964
$35$	0	0
$36$	−1.19438	−0.199063
$37$	−1.09727	−0.180390	−0.0901949	−	0.995924i	$-0.528749\pi$
$37$	−1.09727	−0.180390	−0.0901949	+	0.995924i	$0.528749\pi$
$38$	0	0
$39$	10.1953	1.63256
$40$	0	0
$41$	1.35463	0.211557	0.105779	−	0.994390i	$-0.466267\pi$
$41$	1.35463	0.211557	0.105779	+	0.994390i	$0.466267\pi$
$42$	−1.21551	−0.187557
$43$	−9.00810	−1.37372	−0.686861	−	0.726789i	$-0.741012\pi$
$43$	−9.00810	−1.37372	−0.686861	+	0.726789i	$0.741012\pi$
$44$	−0.323955	−0.0488381
$45$	0	0
$46$	3.93303	0.579894
$47$	−4.81938	−0.702978	−0.351489	−	0.936192i	$-0.614325\pi$
$47$	−4.81938	−0.702978	−0.351489	+	0.936192i	$0.614325\pi$
$48$	−3.87636	−0.559505
$49$	−5.87530	−0.839329
$50$	0	0
$51$	1.36061	0.190523
$52$	8.70203	1.20675
$53$	−5.32420	−0.731335	−0.365668	−	0.930746i	$-0.619159\pi$
$53$	−5.32420	−0.731335	−0.365668	+	0.930746i	$0.619159\pi$
$54$	−2.60744	−0.354828
$55$	0	0
$56$	−2.29704	−0.306955
$57$	0	0
$58$	−2.00795	−0.263657
$59$	10.9822	1.42976	0.714878	−	0.699250i	$-0.246482\pi$
$59$	10.9822	1.42976	0.714878	+	0.699250i	$0.246482\pi$
$60$	0	0
$61$	11.7524	1.50475	0.752373	−	0.658737i	$-0.228909\pi$
$61$	11.7524	1.50475	0.752373	+	0.658737i	$0.228909\pi$
$62$	4.70221	0.597182
$63$	−0.768911	−0.0968737
$64$	−0.736100	−0.0920125
$65$	0	0
$66$	0.225392	0.0277439
$67$	−3.05599	−0.373349	−0.186674	−	0.982422i	$-0.559771\pi$
$67$	−3.05599	−0.373349	−0.186674	+	0.982422i	$0.559771\pi$
$68$	1.16132	0.140831
$69$	12.7826	1.53884
$70$	0	0
$71$	−2.50478	−0.297262	−0.148631	−	0.988893i	$-0.547487\pi$
$71$	−2.50478	−0.297262	−0.148631	+	0.988893i	$0.547487\pi$
$72$	1.57040	0.185073
$73$	−6.55421	−0.767112	−0.383556	−	0.923518i	$-0.625301\pi$
$73$	−6.55421	−0.767112	−0.383556	+	0.923518i	$0.625301\pi$
$74$	0.651609	0.0757480
$75$	0	0
$76$	0	0
$77$	−0.208554	−0.0237669
$78$	−6.05445	−0.685532
$79$	12.2632	1.37972	0.689859	−	0.723944i	$-0.257672\pi$
$79$	12.2632	1.37972	0.689859	+	0.723944i	$0.257672\pi$
$80$	0	0
$81$	−10.6494	−1.18327
$82$	−0.804441	−0.0888356
$83$	4.03175	0.442542	0.221271	−	0.975212i	$-0.428979\pi$
$83$	4.03175	0.442542	0.221271	+	0.975212i	$0.428979\pi$
$84$	−3.37185	−0.367899
$85$	0	0
$86$	5.34943	0.576844
$87$	−6.52596	−0.699656
$88$	0.425943	0.0454056
$89$	−17.5253	−1.85768	−0.928840	−	0.370482i	$-0.879193\pi$
$89$	−17.5253	−1.85768	−0.928840	+	0.370482i	$0.879193\pi$
$90$	0	0
$91$	5.60214	0.587264
$92$	10.9103	1.13748
$93$	15.2825	1.58472
$94$	2.86197	0.295190
$95$	0	0
$96$	10.6627	1.08826
$97$	−1.33950	−0.136006	−0.0680028	−	0.997685i	$-0.521663\pi$
$97$	−1.33950	−0.136006	−0.0680028	+	0.997685i	$0.521663\pi$
$98$	3.48903	0.352445
$99$	0.142580	0.0143298
$100$	0	0
$101$	−17.9348	−1.78458	−0.892288	−	0.451467i	$-0.850901\pi$
$101$	−17.9348	−1.78458	−0.892288	+	0.451467i	$0.850901\pi$
$102$	−0.807992	−0.0800031
$103$	−11.6234	−1.14528	−0.572641	−	0.819806i	$-0.694081\pi$
$103$	−11.6234	−1.14528	−0.572641	+	0.819806i	$0.694081\pi$
$104$	−11.4416	−1.12194
$105$	0	0
$106$	3.16176	0.307097
$107$	2.49645	0.241341	0.120671	−	0.992693i	$-0.461496\pi$
$107$	2.49645	0.241341	0.120671	+	0.992693i	$0.461496\pi$
$108$	−7.23311	−0.696006
$109$	2.07673	0.198915	0.0994574	−	0.995042i	$-0.468289\pi$
$109$	2.07673	0.198915	0.0994574	+	0.995042i	$0.468289\pi$
$110$	0	0
$111$	2.11776	0.201009
$112$	−2.12999	−0.201265
$113$	−15.3786	−1.44669	−0.723347	−	0.690484i	$-0.757397\pi$
$113$	−15.3786	−1.44669	−0.723347	+	0.690484i	$0.757397\pi$
$114$	0	0
$115$	0	0
$116$	−5.57011	−0.517172
$117$	−3.82995	−0.354079
$118$	−6.52172	−0.600373
$119$	0.747628	0.0685350
$120$	0	0
$121$	−10.9613	−0.996484
$122$	−6.97915	−0.631863
$123$	−2.61448	−0.235740
$124$	13.0441	1.17139
$125$	0	0
$126$	0.456615	0.0406785
$127$	−7.60725	−0.675035	−0.337517	−	0.941319i	$-0.609587\pi$
$127$	−7.60725	−0.675035	−0.337517	+	0.941319i	$0.609587\pi$
$128$	11.4864	1.01526
$129$	17.3859	1.53075
$130$	0	0
$131$	−20.8602	−1.82256	−0.911281	−	0.411784i	$-0.864906\pi$
$131$	−20.8602	−1.82256	−0.911281	+	0.411784i	$0.864906\pi$
$132$	0.625244	0.0544205
$133$	0	0
$134$	1.81479	0.156774
$135$	0	0
$136$	−1.52693	−0.130933
$137$	−19.2161	−1.64174	−0.820869	−	0.571116i	$-0.806511\pi$
$137$	−19.2161	−1.64174	−0.820869	+	0.571116i	$0.806511\pi$
$138$	−7.59089	−0.646179
$139$	−19.6484	−1.66656	−0.833279	−	0.552852i	$-0.813539\pi$
$139$	−19.6484	−1.66656	−0.833279	+	0.552852i	$0.813539\pi$
$140$	0	0
$141$	9.30156	0.783333
$142$	1.48745	0.124824
$143$	−1.03881	−0.0868695
$144$	1.45619	0.121349
$145$	0	0
$146$	3.89219	0.322120
$147$	11.3395	0.935269
$148$	1.80758	0.148582
$149$	−8.65464	−0.709016	−0.354508	−	0.935053i	$-0.615352\pi$
$149$	−8.65464	−0.709016	−0.354508	+	0.935053i	$0.615352\pi$
$150$	0	0
$151$	4.95316	0.403083	0.201541	−	0.979480i	$-0.435405\pi$
$151$	4.95316	0.403083	0.201541	+	0.979480i	$0.435405\pi$
$152$	0	0
$153$	−0.511123	−0.0413218
$154$	0.123849	0.00998003
$155$	0	0
$156$	−16.7952	−1.34469
$157$	13.8649	1.10654	0.553269	−	0.833003i	$-0.313380\pi$
$157$	13.8649	1.10654	0.553269	+	0.833003i	$0.313380\pi$
$158$	−7.28246	−0.579362
$159$	10.2759	0.814931
$160$	0	0
$161$	7.02379	0.553552
$162$	6.32412	0.496870
$163$	6.35093	0.497444	0.248722	−	0.968575i	$-0.419990\pi$
$163$	6.35093	0.497444	0.248722	+	0.968575i	$0.419990\pi$
$164$	−2.23154	−0.174254
$165$	0	0
$166$	−2.39424	−0.185829
$167$	19.7001	1.52444	0.762220	−	0.647318i	$-0.224110\pi$
$167$	19.7001	1.52444	0.762220	+	0.647318i	$0.224110\pi$
$168$	4.43337	0.342042
$169$	14.9043	1.14648
$170$	0	0
$171$	0	0
$172$	14.8395	1.13150
$173$	8.91767	0.677998	0.338999	−	0.940787i	$-0.389912\pi$
$173$	8.91767	0.677998	0.338999	+	0.940787i	$0.389912\pi$
$174$	3.87542	0.293795
$175$	0	0
$176$	0.394966	0.0297716
$177$	−21.1959	−1.59318
$178$	10.4073	0.780064
$179$	−1.77208	−0.132451	−0.0662257	−	0.997805i	$-0.521096\pi$
$179$	−1.77208	−0.132451	−0.0662257	+	0.997805i	$0.521096\pi$
$180$	0	0
$181$	−8.54886	−0.635432	−0.317716	−	0.948186i	$-0.602916\pi$
$181$	−8.54886	−0.635432	−0.317716	+	0.948186i	$0.602916\pi$
$182$	−3.32681	−0.246600
$183$	−22.6826	−1.67675
$184$	−14.3451	−1.05754
$185$	0	0
$186$	−9.07544	−0.665443
$187$	−0.138633	−0.0101379
$188$	7.93918	0.579024
$189$	−4.65649	−0.338710
$190$	0	0
$191$	−12.3918	−0.896636	−0.448318	−	0.893874i	$-0.647977\pi$
$191$	−12.3918	−0.896636	−0.448318	+	0.893874i	$0.647977\pi$
$192$	1.42070	0.102530
$193$	1.52571	0.109823	0.0549115	−	0.998491i	$-0.482512\pi$
$193$	1.52571	0.109823	0.0549115	+	0.998491i	$0.482512\pi$
$194$	0.795457	0.0571105
$195$	0	0
$196$	9.67866	0.691333
$197$	−13.7625	−0.980538	−0.490269	−	0.871571i	$-0.663101\pi$
$197$	−13.7625	−0.980538	−0.490269	+	0.871571i	$0.663101\pi$
$198$	−0.0846704	−0.00601727
$199$	−14.2917	−1.01311	−0.506556	−	0.862207i	$-0.669082\pi$
$199$	−14.2917	−1.01311	−0.506556	+	0.862207i	$0.669082\pi$
$200$	0	0
$201$	5.89817	0.416025
$202$	10.6505	0.749366
$203$	−3.58589	−0.251680
$204$	−2.24139	−0.156929
$205$	0	0
$206$	6.90249	0.480919
$207$	−4.80188	−0.333754
$208$	−10.6095	−0.735637
$209$	0	0
$210$	0	0
$211$	−1.75603	−0.120890	−0.0604452	−	0.998172i	$-0.519252\pi$
$211$	−1.75603	−0.120890	−0.0604452	+	0.998172i	$0.519252\pi$
$212$	8.77080	0.602381
$213$	4.83430	0.331241
$214$	−1.48251	−0.101342
$215$	0	0
$216$	9.51024	0.647090
$217$	8.39743	0.570055
$218$	−1.23326	−0.0835269
$219$	12.6498	0.854797
$220$	0	0
$221$	3.72394	0.250500
$222$	−1.25763	−0.0844064
$223$	−16.7418	−1.12111	−0.560557	−	0.828116i	$-0.689413\pi$
$223$	−16.7418	−1.12111	−0.560557	+	0.828116i	$0.689413\pi$
$224$	5.85898	0.391469
$225$	0	0
$226$	9.13251	0.607486
$227$	16.3212	1.08328	0.541638	−	0.840612i	$-0.317804\pi$
$227$	16.3212	1.08328	0.541638	+	0.840612i	$0.317804\pi$
$228$	0	0
$229$	10.0335	0.663033	0.331517	−	0.943449i	$-0.392440\pi$
$229$	10.0335	0.663033	0.331517	+	0.943449i	$0.392440\pi$
$230$	0	0
$231$	0.402516	0.0264836
$232$	7.32370	0.480824
$233$	−10.9230	−0.715589	−0.357794	−	0.933800i	$-0.616471\pi$
$233$	−10.9230	−0.715589	−0.357794	+	0.933800i	$0.616471\pi$
$234$	2.27440	0.148682
$235$	0	0
$236$	−18.0914	−1.17765
$237$	−23.6684	−1.53743
$238$	−0.443977	−0.0287787
$239$	−11.8665	−0.767581	−0.383790	−	0.923420i	$-0.625382\pi$
$239$	−11.8665	−0.767581	−0.383790	+	0.923420i	$0.625382\pi$
$240$	0	0
$241$	−3.22626	−0.207821	−0.103911	−	0.994587i	$-0.533136\pi$
$241$	−3.22626	−0.207821	−0.103911	+	0.994587i	$0.533136\pi$
$242$	6.50935	0.418437
$243$	7.38147	0.473521
$244$	−19.3604	−1.23942
$245$	0	0
$246$	1.55260	0.0989901
$247$	0	0
$248$	−17.1506	−1.08906
$249$	−7.78142	−0.493127
$250$	0	0
$251$	−1.75483	−0.110764	−0.0553820	−	0.998465i	$-0.517638\pi$
$251$	−1.75483	−0.110764	−0.0553820	+	0.998465i	$0.517638\pi$
$252$	1.26666	0.0797922
$253$	−1.30243	−0.0818828
$254$	4.51754	0.283456
$255$	0	0
$256$	−5.34896	−0.334310
$257$	24.2332	1.51163	0.755814	−	0.654787i	$-0.227241\pi$
$257$	24.2332	1.51163	0.755814	+	0.654787i	$0.227241\pi$
$258$	−10.3246	−0.642780
$259$	1.16367	0.0723071
$260$	0	0
$261$	2.45153	0.151746
$262$	12.3877	0.765318
$263$	−12.6925	−0.782651	−0.391325	−	0.920252i	$-0.627983\pi$
$263$	−12.6925	−0.782651	−0.391325	+	0.920252i	$0.627983\pi$
$264$	−0.822084	−0.0505958
$265$	0	0
$266$	0	0
$267$	33.8245	2.07002
$268$	5.03428	0.307517
$269$	−28.2663	−1.72342	−0.861712	−	0.507398i	$-0.830608\pi$
$269$	−28.2663	−1.72342	−0.861712	+	0.507398i	$0.830608\pi$
$270$	0	0
$271$	8.18674	0.497309	0.248654	−	0.968592i	$-0.420012\pi$
$271$	8.18674	0.497309	0.248654	+	0.968592i	$0.420012\pi$
$272$	−1.41588	−0.0858505
$273$	−10.8123	−0.654391
$274$	11.4114	0.689387
$275$	0	0
$276$	−21.0573	−1.26750
$277$	25.0575	1.50556	0.752779	−	0.658273i	$-0.228713\pi$
$277$	25.0575	1.50556	0.752779	+	0.658273i	$0.228713\pi$
$278$	11.6682	0.699810
$279$	−5.74098	−0.343703
$280$	0	0
$281$	24.5418	1.46404	0.732019	−	0.681284i	$-0.238578\pi$
$281$	24.5418	1.46404	0.732019	+	0.681284i	$0.238578\pi$
$282$	−5.52370	−0.328932
$283$	−25.7298	−1.52948	−0.764739	−	0.644340i	$-0.777132\pi$
$283$	−25.7298	−1.52948	−0.764739	+	0.644340i	$0.777132\pi$
$284$	4.12623	0.244847
$285$	0	0
$286$	0.616893	0.0364776
$287$	−1.43661	−0.0848002
$288$	−4.00554	−0.236029
$289$	−16.5030	−0.970766
$290$	0	0
$291$	2.58528	0.151552
$292$	10.7970	0.631849
$293$	−5.45848	−0.318888	−0.159444	−	0.987207i	$-0.550970\pi$
$293$	−5.45848	−0.318888	−0.159444	+	0.987207i	$0.550970\pi$
$294$	−6.73394	−0.392731
$295$	0	0
$296$	−2.37664	−0.138140
$297$	0.863455	0.0501028
$298$	5.13953	0.297725
$299$	34.9856	2.02327
$300$	0	0
$301$	9.55325	0.550640
$302$	−2.94142	−0.169260
$303$	34.6147	1.98856
$304$	0	0
$305$	0	0
$306$	0.303529	0.0173516
$307$	−3.70644	−0.211538	−0.105769	−	0.994391i	$-0.533730\pi$
$307$	−3.70644	−0.211538	−0.105769	+	0.994391i	$0.533730\pi$
$308$	0.343560	0.0195762
$309$	22.4335	1.27620
$310$	0	0
$311$	−1.73452	−0.0983555	−0.0491777	−	0.998790i	$-0.515660\pi$
$311$	−1.73452	−0.0983555	−0.0491777	+	0.998790i	$0.515660\pi$
$312$	22.0827	1.25019
$313$	−3.96847	−0.224311	−0.112156	−	0.993691i	$-0.535776\pi$
$313$	−3.96847	−0.224311	−0.112156	+	0.993691i	$0.535776\pi$
$314$	−8.23361	−0.464650
$315$	0	0
$316$	−20.2017	−1.13644
$317$	−26.7159	−1.50052	−0.750258	−	0.661146i	$-0.770071\pi$
$317$	−26.7159	−1.50052	−0.750258	+	0.661146i	$0.770071\pi$
$318$	−6.10230	−0.342200
$319$	0.664935	0.0372292
$320$	0	0
$321$	−4.81824	−0.268928
$322$	−4.17105	−0.232444
$323$	0	0
$324$	17.5433	0.974627
$325$	0	0
$326$	−3.77148	−0.208883
$327$	−4.00817	−0.221652
$328$	2.93407	0.162007
$329$	5.11104	0.281781
$330$	0	0
$331$	19.1145	1.05063	0.525314	−	0.850908i	$-0.323948\pi$
$331$	19.1145	1.05063	0.525314	+	0.850908i	$0.323948\pi$
$332$	−6.64169	−0.364510
$333$	−0.795555	−0.0435962
$334$	−11.6988	−0.640132
$335$	0	0
$336$	4.11095	0.224271
$337$	−12.2171	−0.665510	−0.332755	−	0.943013i	$-0.607978\pi$
$337$	−12.2171	−0.665510	−0.332755	+	0.943013i	$0.607978\pi$
$338$	−8.85087	−0.481424
$339$	29.6812	1.61206
$340$	0	0
$341$	−1.55714	−0.0843239
$342$	0	0
$343$	13.6545	0.737273
$344$	−19.5112	−1.05197
$345$	0	0
$346$	−5.29573	−0.284700
$347$	3.96425	0.212812	0.106406	−	0.994323i	$-0.466066\pi$
$347$	3.96425	0.212812	0.106406	+	0.994323i	$0.466066\pi$
$348$	10.7505	0.576288
$349$	−24.8326	−1.32926	−0.664628	−	0.747174i	$-0.731410\pi$
$349$	−24.8326	−1.32926	−0.664628	+	0.747174i	$0.731410\pi$
$350$	0	0
$351$	−23.1940	−1.23800
$352$	−1.08643	−0.0579071
$353$	−14.0216	−0.746297	−0.373148	−	0.927772i	$-0.621722\pi$
$353$	−14.0216	−0.746297	−0.373148	+	0.927772i	$0.621722\pi$
$354$	12.5871	0.668999
$355$	0	0
$356$	28.8703	1.53012
$357$	−1.44295	−0.0763689
$358$	1.05234	0.0556180
$359$	−17.5130	−0.924301	−0.462151	−	0.886801i	$-0.652922\pi$
$359$	−17.5130	−0.924301	−0.462151	+	0.886801i	$0.652922\pi$
$360$	0	0
$361$	0	0
$362$	5.07671	0.266826
$363$	21.1557	1.11039
$364$	−9.22866	−0.483713
$365$	0	0
$366$	13.4700	0.704088
$367$	−18.2965	−0.955068	−0.477534	−	0.878613i	$-0.658469\pi$
$367$	−18.2965	−0.955068	−0.477534	+	0.878613i	$0.658469\pi$
$368$	−13.3019	−0.693408
$369$	0.982150	0.0511287
$370$	0	0
$371$	5.64641	0.293147
$372$	−25.1755	−1.30529
$373$	7.71339	0.399384	0.199692	−	0.979859i	$-0.436006\pi$
$373$	7.71339	0.399384	0.199692	+	0.979859i	$0.436006\pi$
$374$	0.0823269	0.00425702
$375$	0	0
$376$	−10.4386	−0.538329
$377$	−17.8614	−0.919907
$378$	2.76524	0.142228
$379$	12.7900	0.656977	0.328488	−	0.944508i	$-0.393461\pi$
$379$	12.7900	0.656977	0.328488	+	0.944508i	$0.393461\pi$
$380$	0	0
$381$	14.6823	0.752195
$382$	7.35880	0.376509
$383$	16.1868	0.827106	0.413553	−	0.910480i	$-0.364288\pi$
$383$	16.1868	0.827106	0.413553	+	0.910480i	$0.364288\pi$
$384$	−22.1691	−1.13131
$385$	0	0
$386$	−0.906038	−0.0461161
$387$	−6.53117	−0.331998
$388$	2.20662	0.112024
$389$	−2.77039	−0.140465	−0.0702323	−	0.997531i	$-0.522374\pi$
$389$	−2.77039	−0.140465	−0.0702323	+	0.997531i	$0.522374\pi$
$390$	0	0
$391$	4.66897	0.236120
$392$	−12.7257	−0.642744
$393$	40.2609	2.03089
$394$	8.17282	0.411741
$395$	0	0
$396$	−0.234878	−0.0118031
$397$	−27.1420	−1.36222	−0.681109	−	0.732182i	$-0.738502\pi$
$397$	−27.1420	−1.36222	−0.681109	+	0.732182i	$0.738502\pi$
$398$	8.48707	0.425418
$399$	0	0
$400$	0	0
$401$	11.9676	0.597632	0.298816	−	0.954311i	$-0.403408\pi$
$401$	11.9676	0.597632	0.298816	+	0.954311i	$0.403408\pi$
$402$	−3.50261	−0.174694
$403$	41.8277	2.08359
$404$	29.5448	1.46991
$405$	0	0
$406$	2.12947	0.105684
$407$	−0.215781	−0.0106958
$408$	2.94703	0.145900
$409$	29.4536	1.45639	0.728193	−	0.685372i	$-0.240360\pi$
$409$	29.4536	1.45639	0.728193	+	0.685372i	$0.240360\pi$
$410$	0	0
$411$	37.0877	1.82940
$412$	19.1477	0.943339
$413$	−11.6468	−0.573101
$414$	2.85158	0.140147
$415$	0	0
$416$	29.1836	1.43084
$417$	37.9222	1.85706
$418$	0	0
$419$	19.9013	0.972243	0.486121	−	0.873891i	$-0.338411\pi$
$419$	19.9013	0.972243	0.486121	+	0.873891i	$0.338411\pi$
$420$	0	0
$421$	16.1432	0.786773	0.393386	−	0.919373i	$-0.371303\pi$
$421$	16.1432	0.786773	0.393386	+	0.919373i	$0.371303\pi$
$422$	1.04281	0.0507634
$423$	−3.49421	−0.169894
$424$	−11.5320	−0.560045
$425$	0	0
$426$	−2.87084	−0.139092
$427$	−12.4637	−0.603160
$428$	−4.11252	−0.198786
$429$	2.00494	0.0967992
$430$	0	0
$431$	−14.3829	−0.692801	−0.346401	−	0.938087i	$-0.612596\pi$
$431$	−14.3829	−0.692801	−0.346401	+	0.938087i	$0.612596\pi$
$432$	8.81860	0.424285
$433$	−31.2784	−1.50315	−0.751573	−	0.659650i	$-0.770705\pi$
$433$	−31.2784	−1.50315	−0.751573	+	0.659650i	$0.770705\pi$
$434$	−4.98678	−0.239373
$435$	0	0
$436$	−3.42110	−0.163841
$437$	0	0
$438$	−7.51207	−0.358940
$439$	3.11511	0.148676	0.0743382	−	0.997233i	$-0.476316\pi$
$439$	3.11511	0.148676	0.0743382	+	0.997233i	$0.476316\pi$
$440$	0	0
$441$	−4.25979	−0.202847
$442$	−2.21145	−0.105188
$443$	20.7826	0.987411	0.493706	−	0.869629i	$-0.335642\pi$
$443$	20.7826	0.987411	0.493706	+	0.869629i	$0.335642\pi$
$444$	−3.48869	−0.165566
$445$	0	0
$446$	9.94205	0.470770
$447$	16.7038	0.790061
$448$	0.780648	0.0368821
$449$	15.7733	0.744388	0.372194	−	0.928155i	$-0.378606\pi$
$449$	15.7733	0.744388	0.372194	+	0.928155i	$0.378606\pi$
$450$	0	0
$451$	0.266391	0.0125439
$452$	25.3338	1.19160
$453$	−9.55977	−0.449157
$454$	−9.69228	−0.454881
$455$	0	0
$456$	0	0
$457$	26.9899	1.26254	0.631268	−	0.775565i	$-0.282535\pi$
$457$	26.9899	1.26254	0.631268	+	0.775565i	$0.282535\pi$
$458$	−5.95837	−0.278416
$459$	−3.09534	−0.144478
$460$	0	0
$461$	−7.28234	−0.339172	−0.169586	−	0.985515i	$-0.554243\pi$
$461$	−7.28234	−0.339172	−0.169586	+	0.985515i	$0.554243\pi$
$462$	−0.239033	−0.0111208
$463$	−12.2146	−0.567660	−0.283830	−	0.958875i	$-0.591605\pi$
$463$	−12.2146	−0.567660	−0.283830	+	0.958875i	$0.591605\pi$
$464$	6.79107	0.315268
$465$	0	0
$466$	6.48658	0.300485
$467$	10.5737	0.489293	0.244646	−	0.969612i	$-0.421328\pi$
$467$	10.5737	0.489293	0.244646	+	0.969612i	$0.421328\pi$
$468$	6.30926	0.291646
$469$	3.24094	0.149652
$470$	0	0
$471$	−26.7597	−1.23302
$472$	23.7870	1.09488
$473$	−1.77147	−0.0814521
$474$	14.0554	0.645586
$475$	0	0
$476$	−1.23160	−0.0564504
$477$	−3.86022	−0.176747
$478$	7.04689	0.322317
$479$	1.52234	0.0695576	0.0347788	−	0.999395i	$-0.488927\pi$
$479$	1.52234	0.0695576	0.0347788	+	0.999395i	$0.488927\pi$
$480$	0	0
$481$	5.79626	0.264287
$482$	1.91590	0.0872669
$483$	−13.5562	−0.616826
$484$	18.0571	0.820777
$485$	0	0
$486$	−4.38346	−0.198838
$487$	28.9305	1.31096	0.655482	−	0.755211i	$-0.272465\pi$
$487$	28.9305	1.31096	0.655482	+	0.755211i	$0.272465\pi$
$488$	25.4554	1.15231
$489$	−12.2575	−0.554304
$490$	0	0
$491$	−14.7582	−0.666027	−0.333013	−	0.942922i	$-0.608065\pi$
$491$	−14.7582	−0.666027	−0.333013	+	0.942922i	$0.608065\pi$
$492$	4.30695	0.194172
$493$	−2.38367	−0.107355
$494$	0	0
$495$	0	0
$496$	−15.9033	−0.714080
$497$	2.65636	0.119154
$498$	4.62097	0.207071
$499$	22.4539	1.00518	0.502588	−	0.864526i	$-0.332381\pi$
$499$	22.4539	1.00518	0.502588	+	0.864526i	$0.332381\pi$
$500$	0	0
$501$	−38.0219	−1.69869
$502$	1.04210	0.0465112
$503$	43.9991	1.96182	0.980912	−	0.194455i	$-0.0622937\pi$
$503$	43.9991	1.96182	0.980912	+	0.194455i	$0.0622937\pi$
$504$	−1.66543	−0.0741843
$505$	0	0
$506$	0.773441	0.0343837
$507$	−28.7658	−1.27753
$508$	12.5318	0.556008
$509$	13.9423	0.617981	0.308990	−	0.951065i	$-0.400009\pi$
$509$	13.9423	0.617981	0.308990	+	0.951065i	$0.400009\pi$
$510$	0	0
$511$	6.95086	0.307488
$512$	−19.7963	−0.874883
$513$	0	0
$514$	−14.3908	−0.634752
$515$	0	0
$516$	−28.6407	−1.26084
$517$	−0.947743	−0.0416817
$518$	−0.691043	−0.0303627
$519$	−17.2114	−0.755497
$520$	0	0
$521$	−25.7694	−1.12898	−0.564489	−	0.825440i	$-0.690927\pi$
$521$	−25.7694	−1.12898	−0.564489	+	0.825440i	$0.690927\pi$
$522$	−1.45583	−0.0637200
$523$	−20.9485	−0.916015	−0.458008	−	0.888948i	$-0.651437\pi$
$523$	−20.9485	−0.916015	−0.458008	+	0.888948i	$0.651437\pi$
$524$	34.3639	1.50120
$525$	0	0
$526$	7.53737	0.328645
$527$	5.58208	0.243159
$528$	−0.762297	−0.0331747
$529$	20.8638	0.907124
$530$	0	0
$531$	7.96243	0.345540
$532$	0	0
$533$	−7.15575	−0.309950
$534$	−20.0865	−0.869230
$535$	0	0
$536$	−6.61917	−0.285905
$537$	3.42017	0.147591
$538$	16.7858	0.723688
$539$	−1.15539	−0.0497663
$540$	0	0
$541$	9.53234	0.409827	0.204914	−	0.978780i	$-0.434309\pi$
$541$	9.53234	0.409827	0.204914	+	0.978780i	$0.434309\pi$
$542$	−4.86167	−0.208826
$543$	16.4996	0.708065
$544$	3.89467	0.166983
$545$	0	0
$546$	6.42086	0.274787
$547$	13.6538	0.583793	0.291896	−	0.956450i	$-0.405714\pi$
$547$	13.6538	0.583793	0.291896	+	0.956450i	$0.405714\pi$
$548$	31.6555	1.35226
$549$	8.52091	0.363664
$550$	0	0
$551$	0	0
$552$	27.6866	1.17842
$553$	−13.0054	−0.553044
$554$	−14.8803	−0.632203
$555$	0	0
$556$	32.3678	1.37270
$557$	−8.56312	−0.362831	−0.181416	−	0.983407i	$-0.558068\pi$
$557$	−8.56312	−0.362831	−0.181416	+	0.983407i	$0.558068\pi$
$558$	3.40926	0.144326
$559$	47.5849	2.01263
$560$	0	0
$561$	0.267567	0.0112967
$562$	−14.5740	−0.614769
$563$	−14.2191	−0.599263	−0.299631	−	0.954055i	$-0.596864\pi$
$563$	−14.2191	−0.599263	−0.299631	+	0.954055i	$0.596864\pi$
$564$	−15.3229	−0.645210
$565$	0	0
$566$	15.2795	0.642247
$567$	11.2939	0.474300
$568$	−5.42526	−0.227639
$569$	−30.2404	−1.26774	−0.633872	−	0.773438i	$-0.718535\pi$
$569$	−30.2404	−1.26774	−0.633872	+	0.773438i	$0.718535\pi$
$570$	0	0
$571$	−32.2109	−1.34798	−0.673992	−	0.738739i	$-0.735422\pi$
$571$	−32.2109	−1.34798	−0.673992	+	0.738739i	$0.735422\pi$
$572$	1.71128	0.0715521
$573$	23.9165	0.999127
$574$	0.853124	0.0356087
$575$	0	0
$576$	−0.533697	−0.0222374
$577$	44.7931	1.86476	0.932381	−	0.361478i	$-0.117728\pi$
$577$	44.7931	1.86476	0.932381	+	0.361478i	$0.117728\pi$
$578$	9.80026	0.407637
$579$	−2.94467	−0.122377
$580$	0	0
$581$	−4.27575	−0.177388
$582$	−1.53526	−0.0636386
$583$	−1.04702	−0.0433630
$584$	−14.1962	−0.587442
$585$	0	0
$586$	3.24150	0.133905
$587$	8.76880	0.361927	0.180964	−	0.983490i	$-0.442078\pi$
$587$	8.76880	0.361927	0.180964	+	0.983490i	$0.442078\pi$
$588$	−18.6801	−0.770356
$589$	0	0
$590$	0	0
$591$	26.5621	1.09262
$592$	−2.20380	−0.0905756
$593$	−10.4206	−0.427924	−0.213962	−	0.976842i	$-0.568637\pi$
$593$	−10.4206	−0.427924	−0.213962	+	0.976842i	$0.568637\pi$
$594$	−0.512760	−0.0210388
$595$	0	0
$596$	14.2572	0.583997
$597$	27.5835	1.12892
$598$	−20.7761	−0.849596
$599$	−18.9458	−0.774104	−0.387052	−	0.922058i	$-0.626507\pi$
$599$	−18.9458	−0.774104	−0.387052	+	0.922058i	$0.626507\pi$
$600$	0	0
$601$	4.83652	0.197286	0.0986429	−	0.995123i	$-0.468550\pi$
$601$	4.83652	0.197286	0.0986429	+	0.995123i	$0.468550\pi$
$602$	−5.67317	−0.231221
$603$	−2.21570	−0.0902301
$604$	−8.15957	−0.332008
$605$	0	0
$606$	−20.5558	−0.835023
$607$	−19.4767	−0.790537	−0.395268	−	0.918566i	$-0.629348\pi$
$607$	−19.4767	−0.790537	−0.395268	+	0.918566i	$0.629348\pi$
$608$	0	0
$609$	6.92090	0.280449
$610$	0	0
$611$	25.4581	1.02993
$612$	0.841997	0.0340357
$613$	37.1623	1.50097	0.750485	−	0.660887i	$-0.229820\pi$
$613$	37.1623	1.50097	0.750485	+	0.660887i	$0.229820\pi$
$614$	2.20106	0.0888274
$615$	0	0
$616$	−0.451720	−0.0182003
$617$	14.1365	0.569116	0.284558	−	0.958659i	$-0.408153\pi$
$617$	14.1365	0.569116	0.284558	+	0.958659i	$0.408153\pi$
$618$	−13.3220	−0.535891
$619$	31.9110	1.28261	0.641306	−	0.767286i	$-0.278393\pi$
$619$	31.9110	1.28261	0.641306	+	0.767286i	$0.278393\pi$
$620$	0	0
$621$	−29.0799	−1.16694
$622$	1.03004	0.0413007
$623$	18.5859	0.744629
$624$	20.4767	0.819724
$625$	0	0
$626$	2.35666	0.0941912
$627$	0	0
$628$	−22.8403	−0.911426
$629$	0.773535	0.0308429
$630$	0	0
$631$	4.30611	0.171424	0.0857118	−	0.996320i	$-0.472684\pi$
$631$	4.30611	0.171424	0.0857118	+	0.996320i	$0.472684\pi$
$632$	26.5617	1.05657
$633$	3.38921	0.134709
$634$	15.8652	0.630086
$635$	0	0
$636$	−16.9279	−0.671237
$637$	31.0360	1.22969
$638$	−0.394869	−0.0156330
$639$	−1.81605	−0.0718417
$640$	0	0
$641$	−32.0886	−1.26742	−0.633711	−	0.773570i	$-0.718469\pi$
$641$	−32.0886	−1.26742	−0.633711	+	0.773570i	$0.718469\pi$
$642$	2.86129	0.112926
$643$	19.2873	0.760618	0.380309	−	0.924859i	$-0.375818\pi$
$643$	19.2873	0.760618	0.380309	+	0.924859i	$0.375818\pi$
$644$	−11.5706	−0.455946
$645$	0	0
$646$	0	0
$647$	−7.19470	−0.282853	−0.141426	−	0.989949i	$-0.545169\pi$
$647$	−7.19470	−0.282853	−0.141426	+	0.989949i	$0.545169\pi$
$648$	−23.0663	−0.906129
$649$	2.15967	0.0847745
$650$	0	0
$651$	−16.2073	−0.635215
$652$	−10.4622	−0.409731
$653$	44.8697	1.75589	0.877944	−	0.478763i	$-0.158915\pi$
$653$	44.8697	1.75589	0.877944	+	0.478763i	$0.158915\pi$
$654$	2.38023	0.0930746
$655$	0	0
$656$	2.72069	0.106225
$657$	−4.75202	−0.185394
$658$	−3.03517	−0.118323
$659$	4.96593	0.193445	0.0967226	−	0.995311i	$-0.469164\pi$
$659$	4.96593	0.193445	0.0967226	+	0.995311i	$0.469164\pi$
$660$	0	0
$661$	1.68450	0.0655195	0.0327598	−	0.999463i	$-0.489570\pi$
$661$	1.68450	0.0655195	0.0327598	+	0.999463i	$0.489570\pi$
$662$	−11.3511	−0.441172
$663$	−7.18734	−0.279133
$664$	8.73263	0.338892
$665$	0	0
$666$	0.472438	0.0183066
$667$	−22.3940	−0.867101
$668$	−32.4529	−1.25564
$669$	32.3122	1.24926
$670$	0	0
$671$	2.31115	0.0892209
$672$	−11.3080	−0.436217
$673$	−0.429596	−0.0165597	−0.00827986	−	0.999966i	$-0.502636\pi$
$673$	−0.429596	−0.0165597	−0.00827986	+	0.999966i	$0.502636\pi$
$674$	7.25511	0.279456
$675$	0	0
$676$	−24.5525	−0.944329
$677$	13.9059	0.534447	0.267223	−	0.963635i	$-0.413894\pi$
$677$	13.9059	0.534447	0.267223	+	0.963635i	$0.413894\pi$
$678$	−17.6261	−0.676925
$679$	1.42056	0.0545163
$680$	0	0
$681$	−31.5005	−1.20710
$682$	0.924703	0.0354087
$683$	19.7531	0.755831	0.377916	−	0.925840i	$-0.376641\pi$
$683$	19.7531	0.755831	0.377916	+	0.925840i	$0.376641\pi$
$684$	0	0
$685$	0	0
$686$	−8.10867	−0.309591
$687$	−19.3650	−0.738822
$688$	−18.0923	−0.689761
$689$	28.1248	1.07147
$690$	0	0
$691$	12.1130	0.460800	0.230400	−	0.973096i	$-0.425997\pi$
$691$	12.1130	0.460800	0.230400	+	0.973096i	$0.425997\pi$
$692$	−14.6905	−0.558449
$693$	−0.151208	−0.00574393
$694$	−2.35415	−0.0893625
$695$	0	0
$696$	−14.1350	−0.535785
$697$	−0.954965	−0.0361719
$698$	14.7467	0.558172
$699$	21.0817	0.797385
$700$	0	0
$701$	−20.3516	−0.768670	−0.384335	−	0.923194i	$-0.625569\pi$
$701$	−20.3516	−0.768670	−0.384335	+	0.923194i	$0.625569\pi$
$702$	13.7737	0.519854
$703$	0	0
$704$	−0.144756	−0.00545570
$705$	0	0
$706$	8.32670	0.313380
$707$	19.0201	0.715326
$708$	34.9171	1.31226
$709$	39.8887	1.49805	0.749027	−	0.662540i	$-0.230522\pi$
$709$	39.8887	1.49805	0.749027	+	0.662540i	$0.230522\pi$
$710$	0	0
$711$	8.89123	0.333447
$712$	−37.9592	−1.42258
$713$	52.4423	1.96398
$714$	0.856890	0.0320683
$715$	0	0
$716$	2.91923	0.109097
$717$	22.9028	0.855320
$718$	10.4000	0.388126
$719$	24.1535	0.900772	0.450386	−	0.892834i	$-0.351286\pi$
$719$	24.1535	0.900772	0.450386	+	0.892834i	$0.351286\pi$
$720$	0	0
$721$	12.3268	0.459073
$722$	0	0
$723$	6.22679	0.231577
$724$	14.0829	0.523388
$725$	0	0
$726$	−12.5633	−0.466266
$727$	33.1287	1.22868	0.614338	−	0.789043i	$-0.289423\pi$
$727$	33.1287	1.22868	0.614338	+	0.789043i	$0.289423\pi$
$728$	12.1340	0.449717
$729$	17.7018	0.655622
$730$	0	0
$731$	6.35040	0.234878
$732$	37.3661	1.38109
$733$	20.2774	0.748962	0.374481	−	0.927235i	$-0.377821\pi$
$733$	20.2774	0.748962	0.374481	+	0.927235i	$0.377821\pi$
$734$	10.8653	0.401045
$735$	0	0
$736$	36.5895	1.34871
$737$	−0.600969	−0.0221370
$738$	−0.583246	−0.0214696
$739$	−25.6142	−0.942232	−0.471116	−	0.882071i	$-0.656149\pi$
$739$	−25.6142	−0.942232	−0.471116	+	0.882071i	$0.656149\pi$
$740$	0	0
$741$	0	0
$742$	−3.35310	−0.123096
$743$	23.8850	0.876255	0.438127	−	0.898913i	$-0.355642\pi$
$743$	23.8850	0.876255	0.438127	+	0.898913i	$0.355642\pi$
$744$	33.1013	1.21355
$745$	0	0
$746$	−4.58057	−0.167707
$747$	2.92315	0.106953
$748$	0.228377	0.00835029
$749$	−2.64753	−0.0967387
$750$	0	0
$751$	49.1093	1.79203	0.896013	−	0.444029i	$-0.146451\pi$
$751$	49.1093	1.79203	0.896013	+	0.444029i	$0.146451\pi$
$752$	−9.67944	−0.352973
$753$	3.38688	0.123425
$754$	10.6069	0.386281
$755$	0	0
$756$	7.67085	0.278986
$757$	21.3259	0.775104	0.387552	−	0.921848i	$-0.373321\pi$
$757$	21.3259	0.775104	0.387552	+	0.921848i	$0.373321\pi$
$758$	−7.59528	−0.275873
$759$	2.51373	0.0912425
$760$	0	0
$761$	11.4807	0.416176	0.208088	−	0.978110i	$-0.433276\pi$
$761$	11.4807	0.416176	0.208088	+	0.978110i	$0.433276\pi$
$762$	−8.71901	−0.315856
$763$	−2.20241	−0.0797327
$764$	20.4135	0.738535
$765$	0	0
$766$	−9.61247	−0.347313
$767$	−58.0127	−2.09472
$768$	10.3237	0.372523
$769$	0.115723	0.00417309	0.00208655	−	0.999998i	$-0.499336\pi$
$769$	0.115723	0.00417309	0.00208655	+	0.999998i	$0.499336\pi$
$770$	0	0
$771$	−46.7710	−1.68442
$772$	−2.51337	−0.0904583
$773$	34.3645	1.23600	0.618002	−	0.786177i	$-0.287942\pi$
$773$	34.3645	1.23600	0.618002	+	0.786177i	$0.287942\pi$
$774$	3.87851	0.139410
$775$	0	0
$776$	−2.90131	−0.104151
$777$	−2.24593	−0.0805722
$778$	1.64519	0.0589829
$779$	0	0
$780$	0	0
$781$	−0.492571	−0.0176256
$782$	−2.77265	−0.0991498
$783$	14.8463	0.530565
$784$	−11.8002	−0.421436
$785$	0	0
$786$	−23.9088	−0.852798
$787$	5.70731	0.203444	0.101722	−	0.994813i	$-0.467565\pi$
$787$	5.70731	0.203444	0.101722	+	0.994813i	$0.467565\pi$
$788$	22.6716	0.807643
$789$	24.4969	0.872112
$790$	0	0
$791$	16.3093	0.579890
$792$	0.308822	0.0109735
$793$	−62.0817	−2.20459
$794$	16.1182	0.572013
$795$	0	0
$796$	23.5434	0.834473
$797$	−39.6776	−1.40545	−0.702726	−	0.711461i	$-0.748034\pi$
$797$	−39.6776	−1.40545	−0.702726	+	0.711461i	$0.748034\pi$
$798$	0	0
$799$	3.39749	0.120195
$800$	0	0
$801$	−12.7064	−0.448960
$802$	−7.10690	−0.250953
$803$	−1.28890	−0.0454844
$804$	−9.71633	−0.342669
$805$	0	0
$806$	−24.8392	−0.874924
$807$	54.5549	1.92042
$808$	−38.8460	−1.36660
$809$	−23.7933	−0.836528	−0.418264	−	0.908325i	$-0.637361\pi$
$809$	−23.7933	−0.836528	−0.418264	+	0.908325i	$0.637361\pi$
$810$	0	0
$811$	15.5784	0.547032	0.273516	−	0.961868i	$-0.411813\pi$
$811$	15.5784	0.547032	0.273516	+	0.961868i	$0.411813\pi$
$812$	5.90721	0.207302
$813$	−15.8007	−0.554154
$814$	0.128141	0.00449132
$815$	0	0
$816$	2.73270	0.0956637
$817$	0	0
$818$	−17.4909	−0.611555
$819$	4.06173	0.141928
$820$	0	0
$821$	49.3819	1.72344	0.861720	−	0.507385i	$-0.169388\pi$
$821$	49.3819	1.72344	0.861720	+	0.507385i	$0.169388\pi$
$822$	−22.0244	−0.768188
$823$	−7.56905	−0.263840	−0.131920	−	0.991260i	$-0.542114\pi$
$823$	−7.56905	−0.263840	−0.131920	+	0.991260i	$0.542114\pi$
$824$	−25.1758	−0.877039
$825$	0	0
$826$	6.91640	0.240652
$827$	−32.0613	−1.11488	−0.557440	−	0.830217i	$-0.688216\pi$
$827$	−32.0613	−1.11488	−0.557440	+	0.830217i	$0.688216\pi$
$828$	7.91036	0.274904
$829$	−13.0362	−0.452766	−0.226383	−	0.974038i	$-0.572690\pi$
$829$	−13.0362	−0.452766	−0.226383	+	0.974038i	$0.572690\pi$
$830$	0	0
$831$	−48.3618	−1.67765
$832$	3.88841	0.134807
$833$	4.14188	0.143508
$834$	−22.5199	−0.779802
$835$	0	0
$836$	0	0
$837$	−34.7671	−1.20173
$838$	−11.8183	−0.408257
$839$	9.00794	0.310989	0.155494	−	0.987837i	$-0.450303\pi$
$839$	9.00794	0.310989	0.155494	+	0.987837i	$0.450303\pi$
$840$	0	0
$841$	−17.5671	−0.605760
$842$	−9.58660	−0.330376
$843$	−47.3664	−1.63139
$844$	2.89280	0.0995742
$845$	0	0
$846$	2.07502	0.0713408
$847$	11.6247	0.399429
$848$	−10.6933	−0.367211
$849$	49.6594	1.70431
$850$	0	0
$851$	7.26718	0.249116
$852$	−7.96377	−0.272834
$853$	−19.5224	−0.668434	−0.334217	−	0.942496i	$-0.608472\pi$
$853$	−19.5224	−0.668434	−0.334217	+	0.942496i	$0.608472\pi$
$854$	7.40152	0.253275
$855$	0	0
$856$	5.40722	0.184815
$857$	−20.6184	−0.704311	−0.352155	−	0.935942i	$-0.614551\pi$
$857$	−20.6184	−0.704311	−0.352155	+	0.935942i	$0.614551\pi$
$858$	−1.19062	−0.0406472
$859$	16.9711	0.579046	0.289523	−	0.957171i	$-0.406503\pi$
$859$	16.9711	0.579046	0.289523	+	0.957171i	$0.406503\pi$
$860$	0	0
$861$	2.77270	0.0944934
$862$	8.54125	0.290916
$863$	−7.17739	−0.244321	−0.122161	−	0.992510i	$-0.538982\pi$
$863$	−7.17739	−0.244321	−0.122161	+	0.992510i	$0.538982\pi$
$864$	−24.2574	−0.825252
$865$	0	0
$866$	18.5746	0.631191
$867$	31.8514	1.08173
$868$	−13.8335	−0.469539
$869$	2.41159	0.0818077
$870$	0	0
$871$	16.1431	0.546989
$872$	4.49813	0.152326
$873$	−0.971182	−0.0328695
$874$	0	0
$875$	0	0
$876$	−20.8387	−0.704074
$877$	−1.52300	−0.0514280	−0.0257140	−	0.999669i	$-0.508186\pi$
$877$	−1.52300	−0.0514280	−0.0257140	+	0.999669i	$0.508186\pi$
$878$	−1.84990	−0.0624311
$879$	10.5350	0.355338
$880$	0	0
$881$	51.5139	1.73555	0.867774	−	0.496960i	$-0.165550\pi$
$881$	51.5139	1.73555	0.867774	+	0.496960i	$0.165550\pi$
$882$	2.52966	0.0851781
$883$	−3.44935	−0.116080	−0.0580400	−	0.998314i	$-0.518485\pi$
$883$	−3.44935	−0.116080	−0.0580400	+	0.998314i	$0.518485\pi$
$884$	−6.13463	−0.206330
$885$	0	0
$886$	−12.3417	−0.414627
$887$	−36.9520	−1.24073	−0.620364	−	0.784314i	$-0.713015\pi$
$887$	−36.9520	−1.24073	−0.620364	+	0.784314i	$0.713015\pi$
$888$	4.58700	0.153930
$889$	8.06763	0.270580
$890$	0	0
$891$	−2.09424	−0.0701596
$892$	27.5795	0.923431
$893$	0	0
$894$	−9.91947	−0.331757
$895$	0	0
$896$	−12.1815	−0.406957
$897$	−67.5233	−2.25454
$898$	−9.36692	−0.312578
$899$	−26.7736	−0.892951
$900$	0	0
$901$	3.75337	0.125043
$902$	−0.158195	−0.00526733
$903$	−18.4381	−0.613582
$904$	−33.3094	−1.10786
$905$	0	0
$906$	5.67704	0.188607
$907$	−23.0663	−0.765905	−0.382952	−	0.923768i	$-0.625093\pi$
$907$	−23.0663	−0.765905	−0.382952	+	0.923768i	$0.625093\pi$
$908$	−26.8867	−0.892265
$909$	−13.0033	−0.431292
$910$	0	0
$911$	−22.8760	−0.757915	−0.378957	−	0.925414i	$-0.623717\pi$
$911$	−22.8760	−0.757915	−0.378957	+	0.925414i	$0.623717\pi$
$912$	0	0
$913$	0.792855	0.0262397
$914$	−16.0279	−0.530155
$915$	0	0
$916$	−16.5287	−0.546123
$917$	22.1226	0.730553
$918$	1.83815	0.0606681
$919$	−12.9324	−0.426601	−0.213301	−	0.976987i	$-0.568421\pi$
$919$	−12.9324	−0.426601	−0.213301	+	0.976987i	$0.568421\pi$
$920$	0	0
$921$	7.15355	0.235718
$922$	4.32459	0.142423
$923$	13.2314	0.435516
$924$	−0.663083	−0.0218138
$925$	0	0
$926$	7.25359	0.238368
$927$	−8.42731	−0.276789
$928$	−18.6802	−0.613209
$929$	−12.3880	−0.406437	−0.203219	−	0.979133i	$-0.565140\pi$
$929$	−12.3880	−0.406437	−0.203219	+	0.979133i	$0.565140\pi$
$930$	0	0
$931$	0	0
$932$	17.9939	0.589411
$933$	3.34768	0.109598
$934$	−6.27916	−0.205460
$935$	0	0
$936$	−8.29554	−0.271148
$937$	10.6696	0.348561	0.174280	−	0.984696i	$-0.444240\pi$
$937$	10.6696	0.348561	0.174280	+	0.984696i	$0.444240\pi$
$938$	−1.92462	−0.0628410
$939$	7.65929	0.249951
$940$	0	0
$941$	−12.7892	−0.416917	−0.208459	−	0.978031i	$-0.566845\pi$
$941$	−12.7892	−0.416917	−0.208459	+	0.978031i	$0.566845\pi$
$942$	15.8912	0.517762
$943$	−8.97167	−0.292158
$944$	22.0570	0.717895
$945$	0	0
$946$	1.05198	0.0342028
$947$	−14.1158	−0.458703	−0.229351	−	0.973344i	$-0.573661\pi$
$947$	−14.1158	−0.458703	−0.229351	+	0.973344i	$0.573661\pi$
$948$	38.9901	1.26634
$949$	34.6223	1.12389
$950$	0	0
$951$	51.5626	1.67203
$952$	1.61934	0.0524830
$953$	−43.7008	−1.41561	−0.707803	−	0.706410i	$-0.750314\pi$
$953$	−43.7008	−1.41561	−0.707803	+	0.706410i	$0.750314\pi$
$954$	2.29238	0.0742185
$955$	0	0
$956$	19.5483	0.632236
$957$	−1.28335	−0.0414847
$958$	−0.904038	−0.0292081
$959$	20.3790	0.658072
$960$	0	0
$961$	31.6984	1.02253
$962$	−3.44209	−0.110977
$963$	1.81001	0.0583268
$964$	5.31476	0.171177
$965$	0	0
$966$	8.05028	0.259013
$967$	−2.29371	−0.0737606	−0.0368803	−	0.999320i	$-0.511742\pi$
$967$	−2.29371	−0.0737606	−0.0368803	+	0.999320i	$0.511742\pi$
$968$	−23.7418	−0.763092
$969$	0	0
$970$	0	0
$971$	29.5744	0.949086	0.474543	−	0.880232i	$-0.342613\pi$
$971$	29.5744	0.949086	0.474543	+	0.880232i	$0.342613\pi$
$972$	−12.1598	−0.390027
$973$	20.8375	0.668020
$974$	−17.1803	−0.550491
$975$	0	0
$976$	23.6041	0.755549
$977$	16.3897	0.524354	0.262177	−	0.965020i	$-0.415560\pi$
$977$	16.3897	0.524354	0.262177	+	0.965020i	$0.415560\pi$
$978$	7.27909	0.232760
$979$	−3.44640	−0.110147
$980$	0	0
$981$	1.50570	0.0480733
$982$	8.76409	0.279673
$983$	51.3730	1.63854	0.819272	−	0.573404i	$-0.194378\pi$
$983$	51.3730	1.63854	0.819272	+	0.573404i	$0.194378\pi$
$984$	−5.66286	−0.180526
$985$	0	0
$986$	1.41554	0.0450799
$987$	−9.86448	−0.313990
$988$	0	0
$989$	59.6605	1.89709
$990$	0	0
$991$	48.8793	1.55270	0.776351	−	0.630301i	$-0.217068\pi$
$991$	48.8793	1.55270	0.776351	+	0.630301i	$0.217068\pi$
$992$	43.7453	1.38892
$993$	−36.8916	−1.17072
$994$	−1.57747	−0.0500343
$995$	0	0
$996$	12.8187	0.406176
$997$	−19.2225	−0.608783	−0.304392	−	0.952547i	$-0.598453\pi$
$997$	−19.2225	−0.608783	−0.304392	+	0.952547i	$0.598453\pi$
$998$	−13.3342	−0.422086
$999$	−4.81784	−0.152430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cd.1.5		9
5.4	even	2		1805.2.a.u.1.5		9
19.14	odd	18		475.2.l.b.101.2		18
19.15	odd	18		475.2.l.b.301.2		18
19.18	odd	2		9025.2.a.ce.1.5		9
95.14	odd	18		95.2.k.b.6.2	✓	18
95.33	even	36		475.2.u.c.424.3		36
95.34	odd	18		95.2.k.b.16.2	yes	18
95.52	even	36		475.2.u.c.424.4		36
95.53	even	36		475.2.u.c.149.4		36
95.72	even	36		475.2.u.c.149.3		36
95.94	odd	2		1805.2.a.t.1.5		9
285.14	even	18		855.2.bs.b.766.2		18
285.224	even	18		855.2.bs.b.586.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.2	✓	18	95.14	odd	18
95.2.k.b.16.2	yes	18	95.34	odd	18
475.2.l.b.101.2		18	19.14	odd	18
475.2.l.b.301.2		18	19.15	odd	18
475.2.u.c.149.3		36	95.72	even	36
475.2.u.c.149.4		36	95.53	even	36
475.2.u.c.424.3		36	95.33	even	36
475.2.u.c.424.4		36	95.52	even	36
855.2.bs.b.586.2		18	285.224	even	18
855.2.bs.b.766.2		18	285.14	even	18
1805.2.a.t.1.5		9	95.94	odd	2
1805.2.a.u.1.5		9	5.4	even	2
9025.2.a.cd.1.5		9	1.1	even	1	trivial
9025.2.a.ce.1.5		9	19.18	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} +1.14614 q^{6} -1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +O(q^{10})\)	\(q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} +1.14614 q^{6} -1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +0.196653 q^{11} +3.17944 q^{12} -5.28245 q^{13} +0.629785 q^{14} +2.00844 q^{16} -0.704965 q^{17} -0.430558 q^{18} +2.04684 q^{21} -0.116781 q^{22} -6.62298 q^{23} -4.18038 q^{24} +3.13697 q^{26} +4.39076 q^{27} +1.74704 q^{28} +3.38126 q^{29} -7.91823 q^{31} -5.52463 q^{32} -0.379546 q^{33} +0.418641 q^{34} -1.19438 q^{36} -1.09727 q^{37} +10.1953 q^{39} +1.35463 q^{41} -1.21551 q^{42} -9.00810 q^{43} -0.323955 q^{44} +3.93303 q^{46} -4.81938 q^{47} -3.87636 q^{48} -5.87530 q^{49} +1.36061 q^{51} +8.70203 q^{52} -5.32420 q^{53} -2.60744 q^{54} -2.29704 q^{56} -2.00795 q^{58} +10.9822 q^{59} +11.7524 q^{61} +4.70221 q^{62} -0.768911 q^{63} -0.736100 q^{64} +0.225392 q^{66} -3.05599 q^{67} +1.16132 q^{68} +12.7826 q^{69} -2.50478 q^{71} +1.57040 q^{72} -6.55421 q^{73} +0.651609 q^{74} -0.208554 q^{77} -6.05445 q^{78} +12.2632 q^{79} -10.6494 q^{81} -0.804441 q^{82} +4.03175 q^{83} -3.37185 q^{84} +5.34943 q^{86} -6.52596 q^{87} +0.425943 q^{88} -17.5253 q^{89} +5.60214 q^{91} +10.9103 q^{92} +15.2825 q^{93} +2.86197 q^{94} +10.6627 q^{96} -1.33950 q^{97} +3.48903 q^{98} +0.142580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9	\( 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} + 12 q^{14} - 12 q^{16} + 9 q^{17} - 6 q^{18} + 12 q^{21} - 12 q^{22} + 15 q^{24} + 21 q^{26} - 6 q^{27} + 15 q^{28} + 15 q^{29} + 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} + 18 q^{41} - 36 q^{42} + 6 q^{43} - 24 q^{44} + 21 q^{46} - 21 q^{47} - 15 q^{48} + 3 q^{49} + 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} + 36 q^{56} - 18 q^{58} + 27 q^{59} + 12 q^{61} + 6 q^{62} + 15 q^{63} + 24 q^{64} + 3 q^{66} - 36 q^{67} - 3 q^{68} + 27 q^{69} - 6 q^{71} - 12 q^{72} + 9 q^{73} - 9 q^{74} - 12 q^{77} - 54 q^{78} + 45 q^{79} - 15 q^{81} + 48 q^{82} - 12 q^{84} - 9 q^{86} - 45 q^{87} - 39 q^{88} - 9 q^{89} + 51 q^{91} + 54 q^{92} - 9 q^{93} + 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 3 * q^3 + 6 * q^4 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 + 12 * q^14 - 12 * q^16 + 9 * q^17 - 6 * q^18 + 12 * q^21 - 12 * q^22 + 15 * q^24 + 21 * q^26 - 6 * q^27 + 15 * q^28 + 15 * q^29 + 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 + 18 * q^41 - 36 * q^42 + 6 * q^43 - 24 * q^44 + 21 * q^46 - 21 * q^47 - 15 * q^48 + 3 * q^49 + 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 + 36 * q^56 - 18 * q^58 + 27 * q^59 + 12 * q^61 + 6 * q^62 + 15 * q^63 + 24 * q^64 + 3 * q^66 - 36 * q^67 - 3 * q^68 + 27 * q^69 - 6 * q^71 - 12 * q^72 + 9 * q^73 - 9 * q^74 - 12 * q^77 - 54 * q^78 + 45 * q^79 - 15 * q^81 + 48 * q^82 - 12 * q^84 - 9 * q^86 - 45 * q^87 - 39 * q^88 - 9 * q^89 + 51 * q^91 + 54 * q^92 - 9 * q^93 + 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * q^99

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