LMFDB - Embedded newform 9025.2.a.cd.1.3

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			1.3
Root			$-1.46231$ 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)

$f(q)$	$=$	$q-1.46231 q^{2} +1.51036 q^{3} +0.138346 q^{4} -2.20860 q^{6} -4.07172 q^{7} +2.72231 q^{8} -0.718827 q^{9} +O(q^{10})$	\(q-1.46231 q^{2} +1.51036 q^{3} +0.138346 q^{4} -2.20860 q^{6} -4.07172 q^{7} +2.72231 q^{8} -0.718827 q^{9} -0.621006 q^{11} +0.208951 q^{12} -5.09329 q^{13} +5.95412 q^{14} -4.25755 q^{16} +0.266483 q^{17} +1.05115 q^{18} -6.14975 q^{21} +0.908102 q^{22} +5.84174 q^{23} +4.11166 q^{24} +7.44796 q^{26} -5.61675 q^{27} -0.563305 q^{28} -4.07754 q^{29} +6.48991 q^{31} +0.781227 q^{32} -0.937939 q^{33} -0.389681 q^{34} -0.0994465 q^{36} -8.83927 q^{37} -7.69267 q^{39} +4.48083 q^{41} +8.99283 q^{42} +1.80073 q^{43} -0.0859133 q^{44} -8.54242 q^{46} -11.5465 q^{47} -6.43041 q^{48} +9.57894 q^{49} +0.402485 q^{51} -0.704633 q^{52} -2.52292 q^{53} +8.21342 q^{54} -11.0845 q^{56} +5.96263 q^{58} -0.890444 q^{59} +2.16991 q^{61} -9.49025 q^{62} +2.92687 q^{63} +7.37271 q^{64} +1.37156 q^{66} -14.0788 q^{67} +0.0368668 q^{68} +8.82310 q^{69} +1.64668 q^{71} -1.95687 q^{72} -1.79675 q^{73} +12.9257 q^{74} +2.52856 q^{77} +11.2491 q^{78} -5.14647 q^{79} -6.32681 q^{81} -6.55236 q^{82} -13.7833 q^{83} -0.850790 q^{84} -2.63322 q^{86} -6.15854 q^{87} -1.69057 q^{88} +0.000747238 q^{89} +20.7385 q^{91} +0.808178 q^{92} +9.80207 q^{93} +16.8845 q^{94} +1.17993 q^{96} -10.4225 q^{97} -14.0074 q^{98} +0.446396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.46231	−1.03401	−0.517004	−	0.855983i	$-0.672953\pi$
$2$	−1.46231	−1.03401	−0.517004	+	0.855983i	$0.672953\pi$
$3$	1.51036	0.872004	0.436002	−	0.899946i	$-0.356394\pi$
$3$	1.51036	0.872004	0.436002	+	0.899946i	$0.356394\pi$
$4$	0.138346	0.0691728
$5$	0	0
$5$	0	0
$6$	−2.20860	−0.901659
$7$	−4.07172	−1.53897	−0.769484	−	0.638667i	$-0.779486\pi$
$7$	−4.07172	−1.53897	−0.769484	+	0.638667i	$0.779486\pi$
$8$	2.72231	0.962483
$9$	−0.718827	−0.239609
$10$	0	0
$11$	−0.621006	−0.187240	−0.0936201	−	0.995608i	$-0.529844\pi$
$11$	−0.621006	−0.187240	−0.0936201	+	0.995608i	$0.529844\pi$
$12$	0.208951	0.0603189
$13$	−5.09329	−1.41262	−0.706312	−	0.707901i	$-0.749642\pi$
$13$	−5.09329	−1.41262	−0.706312	+	0.707901i	$0.749642\pi$
$14$	5.95412	1.59130
$15$	0	0
$16$	−4.25755	−1.06439
$17$	0.266483	0.0646317	0.0323159	−	0.999478i	$-0.489712\pi$
$17$	0.266483	0.0646317	0.0323159	+	0.999478i	$0.489712\pi$
$18$	1.05115	0.247758
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−6.14975	−1.34199
$22$	0.908102	0.193608
$23$	5.84174	1.21809	0.609043	−	0.793137i	$-0.291554\pi$
$23$	5.84174	1.21809	0.609043	+	0.793137i	$0.291554\pi$
$24$	4.11166	0.839289
$25$	0	0
$26$	7.44796	1.46066
$27$	−5.61675	−1.08094
$28$	−0.563305	−0.106455
$29$	−4.07754	−0.757181	−0.378591	−	0.925564i	$-0.623591\pi$
$29$	−4.07754	−0.757181	−0.378591	+	0.925564i	$0.623591\pi$
$30$	0	0
$31$	6.48991	1.16562	0.582811	−	0.812608i	$-0.301953\pi$
$31$	6.48991	1.16562	0.582811	+	0.812608i	$0.301953\pi$
$32$	0.781227	0.138103
$33$	−0.937939	−0.163274
$34$	−0.389681	−0.0668297
$35$	0	0
$36$	−0.0994465	−0.0165744
$37$	−8.83927	−1.45317	−0.726584	−	0.687078i	$-0.758893\pi$
$37$	−8.83927	−1.45317	−0.726584	+	0.687078i	$0.758893\pi$
$38$	0	0
$39$	−7.69267	−1.23181
$40$	0	0
$41$	4.48083	0.699788	0.349894	−	0.936789i	$-0.386218\pi$
$41$	4.48083	0.699788	0.349894	+	0.936789i	$0.386218\pi$
$42$	8.99283	1.38762
$43$	1.80073	0.274608	0.137304	−	0.990529i	$-0.456156\pi$
$43$	1.80073	0.274608	0.137304	+	0.990529i	$0.456156\pi$
$44$	−0.0859133	−0.0129519
$45$	0	0
$46$	−8.54242	−1.25951
$47$	−11.5465	−1.68423	−0.842113	−	0.539301i	$-0.818688\pi$
$47$	−11.5465	−1.68423	−0.842113	+	0.539301i	$0.818688\pi$
$48$	−6.43041	−0.928150
$49$	9.57894	1.36842
$50$	0	0
$51$	0.402485	0.0563591
$52$	−0.704633	−0.0977151
$53$	−2.52292	−0.346550	−0.173275	−	0.984873i	$-0.555435\pi$
$53$	−2.52292	−0.346550	−0.173275	+	0.984873i	$0.555435\pi$
$54$	8.21342	1.11770
$55$	0	0
$56$	−11.0845	−1.48123
$57$	0	0
$58$	5.96263	0.782931
$59$	−0.890444	−0.115926	−0.0579630	−	0.998319i	$-0.518461\pi$
$59$	−0.890444	−0.115926	−0.0579630	+	0.998319i	$0.518461\pi$
$60$	0	0
$61$	2.16991	0.277828	0.138914	−	0.990304i	$-0.455639\pi$
$61$	2.16991	0.277828	0.138914	+	0.990304i	$0.455639\pi$
$62$	−9.49025	−1.20526
$63$	2.92687	0.368751
$64$	7.37271	0.921588
$65$	0	0
$66$	1.37156	0.168827
$67$	−14.0788	−1.72000	−0.859999	−	0.510296i	$-0.829536\pi$
$67$	−14.0788	−1.72000	−0.859999	+	0.510296i	$0.829536\pi$
$68$	0.0368668	0.00447075
$69$	8.82310	1.06218
$70$	0	0
$71$	1.64668	0.195425	0.0977125	−	0.995215i	$-0.468847\pi$
$71$	1.64668	0.195425	0.0977125	+	0.995215i	$0.468847\pi$
$72$	−1.95687	−0.230620
$73$	−1.79675	−0.210294	−0.105147	−	0.994457i	$-0.533531\pi$
$73$	−1.79675	−0.210294	−0.105147	+	0.994457i	$0.533531\pi$
$74$	12.9257	1.50259
$75$	0	0
$76$	0	0
$77$	2.52856	0.288157
$78$	11.2491	1.27371
$79$	−5.14647	−0.579023	−0.289511	−	0.957175i	$-0.593493\pi$
$79$	−5.14647	−0.579023	−0.289511	+	0.957175i	$0.593493\pi$
$80$	0	0
$81$	−6.32681	−0.702978
$82$	−6.55236	−0.723587
$83$	−13.7833	−1.51292	−0.756459	−	0.654041i	$-0.773072\pi$
$83$	−13.7833	−1.51292	−0.756459	+	0.654041i	$0.773072\pi$
$84$	−0.850790	−0.0928288
$85$	0	0
$86$	−2.63322	−0.283947
$87$	−6.15854	−0.660265
$88$	−1.69057	−0.180216
$89$	0.000747238 0	7.92071e−5 0	3.96035e−5	−	1.00000i	$-0.499987\pi$
$89$	0.000747238 0	7.92071e−5 0	3.96035e−5		1.00000i	$0.499987\pi$
$90$	0	0
$91$	20.7385	2.17398
$92$	0.808178	0.0842584
$93$	9.80207	1.01643
$94$	16.8845	1.74150
$95$	0	0
$96$	1.17993	0.120426
$97$	−10.4225	−1.05825	−0.529123	−	0.848545i	$-0.677479\pi$
$97$	−10.4225	−1.05825	−0.529123	+	0.848545i	$0.677479\pi$
$98$	−14.0074	−1.41496
$99$	0.446396	0.0448645
$100$	0	0
$101$	−12.2197	−1.21591	−0.607955	−	0.793972i	$-0.708010\pi$
$101$	−12.2197	−1.21591	−0.607955	+	0.793972i	$0.708010\pi$
$102$	−0.588557	−0.0582758
$103$	−7.80372	−0.768924	−0.384462	−	0.923141i	$-0.625613\pi$
$103$	−7.80372	−0.768924	−0.384462	+	0.923141i	$0.625613\pi$
$104$	−13.8655	−1.35963
$105$	0	0
$106$	3.68929	0.358336
$107$	5.70414	0.551440	0.275720	−	0.961238i	$-0.411084\pi$
$107$	5.70414	0.551440	0.275720	+	0.961238i	$0.411084\pi$
$108$	−0.777052	−0.0747719
$109$	6.73318	0.644922	0.322461	−	0.946583i	$-0.395490\pi$
$109$	6.73318	0.644922	0.322461	+	0.946583i	$0.395490\pi$
$110$	0	0
$111$	−13.3504	−1.26717
$112$	17.3356	1.63806
$113$	−4.78878	−0.450490	−0.225245	−	0.974302i	$-0.572318\pi$
$113$	−4.78878	−0.450490	−0.225245	+	0.974302i	$0.572318\pi$
$114$	0	0
$115$	0	0
$116$	−0.564110	−0.0523763
$117$	3.66119	0.338477
$118$	1.30210	0.119868
$119$	−1.08505	−0.0994661
$120$	0	0
$121$	−10.6144	−0.964941
$122$	−3.17308	−0.287277
$123$	6.76765	0.610218
$124$	0.897850	0.0806293
$125$	0	0
$126$	−4.27998	−0.381291
$127$	18.4967	1.64131	0.820656	−	0.571422i	$-0.193608\pi$
$127$	18.4967	1.64131	0.820656	+	0.571422i	$0.193608\pi$
$128$	−12.3436	−1.09103
$129$	2.71974	0.239459
$130$	0	0
$131$	−19.5844	−1.71110	−0.855549	−	0.517721i	$-0.826780\pi$
$131$	−19.5844	−1.71110	−0.855549	+	0.517721i	$0.826780\pi$
$132$	−0.129760	−0.0112941
$133$	0	0
$134$	20.5875	1.77849
$135$	0	0
$136$	0.725451	0.0622069
$137$	2.35667	0.201343	0.100672	−	0.994920i	$-0.467901\pi$
$137$	2.35667	0.201343	0.100672	+	0.994920i	$0.467901\pi$
$138$	−12.9021	−1.09830
$139$	3.83050	0.324899	0.162449	−	0.986717i	$-0.448061\pi$
$139$	3.83050	0.324899	0.162449	+	0.986717i	$0.448061\pi$
$140$	0	0
$141$	−17.4393	−1.46865
$142$	−2.40795	−0.202071
$143$	3.16296	0.264500
$144$	3.06044	0.255037
$145$	0	0
$146$	2.62741	0.217446
$147$	14.4676	1.19327
$148$	−1.22287	−0.100520
$149$	18.1856	1.48982	0.744910	−	0.667165i	$-0.232492\pi$
$149$	18.1856	1.48982	0.744910	+	0.667165i	$0.232492\pi$
$150$	0	0
$151$	2.29340	0.186634	0.0933170	−	0.995636i	$-0.470253\pi$
$151$	2.29340	0.186634	0.0933170	+	0.995636i	$0.470253\pi$
$152$	0	0
$153$	−0.191556	−0.0154863
$154$	−3.69754	−0.297956
$155$	0	0
$156$	−1.06425	−0.0852079
$157$	20.8445	1.66357	0.831787	−	0.555095i	$-0.187318\pi$
$157$	20.8445	1.66357	0.831787	+	0.555095i	$0.187318\pi$
$158$	7.52572	0.598714
$159$	−3.81051	−0.302193
$160$	0	0
$161$	−23.7859	−1.87460
$162$	9.25174	0.726885
$163$	7.91691	0.620100	0.310050	−	0.950720i	$-0.399654\pi$
$163$	7.91691	0.620100	0.310050	+	0.950720i	$0.399654\pi$
$164$	0.619903	0.0484063
$165$	0	0
$166$	20.1555	1.56437
$167$	14.0935	1.09059	0.545293	−	0.838246i	$-0.316418\pi$
$167$	14.0935	1.09059	0.545293	+	0.838246i	$0.316418\pi$
$168$	−16.7415	−1.29164
$169$	12.9416	0.995505
$170$	0	0
$171$	0	0
$172$	0.249122	0.0189954
$173$	−10.5128	−0.799273	−0.399636	−	0.916674i	$-0.630864\pi$
$173$	−10.5128	−0.799273	−0.399636	+	0.916674i	$0.630864\pi$
$174$	9.00569	0.682719
$175$	0	0
$176$	2.64396	0.199296
$177$	−1.34489	−0.101088
$178$	−0.00109269	−8.19008e−5 0
$179$	−5.00329	−0.373963	−0.186982	−	0.982363i	$-0.559871\pi$
$179$	−5.00329	−0.373963	−0.186982	+	0.982363i	$0.559871\pi$
$180$	0	0
$181$	26.4916	1.96911	0.984553	−	0.175089i	$-0.0560214\pi$
$181$	26.4916	1.96911	0.984553	+	0.175089i	$0.0560214\pi$
$182$	−30.3260	−2.24791
$183$	3.27733	0.242267
$184$	15.9030	1.17239
$185$	0	0
$186$	−14.3337	−1.05099
$187$	−0.165488	−0.0121017
$188$	−1.59740	−0.116503
$189$	22.8699	1.66354
$190$	0	0
$191$	−0.143815	−0.0104061	−0.00520303	−	0.999986i	$-0.501656\pi$
$191$	−0.143815	−0.0104061	−0.00520303	+	0.999986i	$0.501656\pi$
$192$	11.1354	0.803629
$193$	2.06115	0.148365	0.0741823	−	0.997245i	$-0.476365\pi$
$193$	2.06115	0.148365	0.0741823	+	0.997245i	$0.476365\pi$
$194$	15.2409	1.09423
$195$	0	0
$196$	1.32520	0.0946574
$197$	−18.2483	−1.30014	−0.650068	−	0.759876i	$-0.725259\pi$
$197$	−18.2483	−1.30014	−0.650068	+	0.759876i	$0.725259\pi$
$198$	−0.652768	−0.0463902
$199$	8.00301	0.567318	0.283659	−	0.958925i	$-0.408452\pi$
$199$	8.00301	0.567318	0.283659	+	0.958925i	$0.408452\pi$
$200$	0	0
$201$	−21.2640	−1.49984
$202$	17.8690	1.25726
$203$	16.6026	1.16528
$204$	0.0556819	0.00389851
$205$	0	0
$206$	11.4115	0.795073
$207$	−4.19920	−0.291865
$208$	21.6849	1.50358
$209$	0	0
$210$	0	0
$211$	14.0828	0.969501	0.484750	−	0.874653i	$-0.338910\pi$
$211$	14.0828	0.969501	0.484750	+	0.874653i	$0.338910\pi$
$212$	−0.349035	−0.0239718
$213$	2.48707	0.170411
$214$	−8.34121	−0.570193
$215$	0	0
$216$	−15.2906	−1.04039
$217$	−26.4251	−1.79386
$218$	−9.84599	−0.666855
$219$	−2.71374	−0.183377
$220$	0	0
$221$	−1.35728	−0.0913003
$222$	19.5225	1.31026
$223$	4.90610	0.328537	0.164268	−	0.986416i	$-0.447474\pi$
$223$	4.90610	0.328537	0.164268	+	0.986416i	$0.447474\pi$
$224$	−3.18094	−0.212536
$225$	0	0
$226$	7.00267	0.465811
$227$	2.65246	0.176050	0.0880250	−	0.996118i	$-0.471944\pi$
$227$	2.65246	0.176050	0.0880250	+	0.996118i	$0.471944\pi$
$228$	0	0
$229$	−23.1372	−1.52895	−0.764473	−	0.644655i	$-0.777001\pi$
$229$	−23.1372	−1.52895	−0.764473	+	0.644655i	$0.777001\pi$
$230$	0	0
$231$	3.81903	0.251274
$232$	−11.1004	−0.728774
$233$	28.9098	1.89394	0.946971	−	0.321319i	$-0.104126\pi$
$233$	28.9098	1.89394	0.946971	+	0.321319i	$0.104126\pi$
$234$	−5.35379	−0.349988
$235$	0	0
$236$	−0.123189	−0.00801892
$237$	−7.77299	−0.504910
$238$	1.58667	0.102849
$239$	−20.7473	−1.34203	−0.671016	−	0.741443i	$-0.734142\pi$
$239$	−20.7473	−1.34203	−0.671016	+	0.741443i	$0.734142\pi$
$240$	0	0
$241$	−6.19740	−0.399209	−0.199605	−	0.979877i	$-0.563966\pi$
$241$	−6.19740	−0.399209	−0.199605	+	0.979877i	$0.563966\pi$
$242$	15.5215	0.997757
$243$	7.29453	0.467944
$244$	0.300197	0.0192182
$245$	0	0
$246$	−9.89639	−0.630971
$247$	0	0
$248$	17.6676	1.12189
$249$	−20.8177	−1.31927
$250$	0	0
$251$	7.78995	0.491697	0.245849	−	0.969308i	$-0.420933\pi$
$251$	7.78995	0.491697	0.245849	+	0.969308i	$0.420933\pi$
$252$	0.404919	0.0255075
$253$	−3.62775	−0.228075
$254$	−27.0478	−1.69713
$255$	0	0
$256$	3.30477	0.206548
$257$	20.1572	1.25737	0.628686	−	0.777659i	$-0.283593\pi$
$257$	20.1572	1.25737	0.628686	+	0.777659i	$0.283593\pi$
$258$	−3.97709	−0.247603
$259$	35.9911	2.23638
$260$	0	0
$261$	2.93105	0.181427
$262$	28.6385	1.76929
$263$	−10.6858	−0.658914	−0.329457	−	0.944171i	$-0.606866\pi$
$263$	−10.6858	−0.658914	−0.329457	+	0.944171i	$0.606866\pi$
$264$	−2.55336	−0.157149
$265$	0	0
$266$	0	0
$267$	0.00112860	6.90689e−5 0
$268$	−1.94774	−0.118977
$269$	23.9260	1.45879	0.729396	−	0.684092i	$-0.239801\pi$
$269$	23.9260	1.45879	0.729396	+	0.684092i	$0.239801\pi$
$270$	0	0
$271$	25.9701	1.57757	0.788787	−	0.614667i	$-0.210709\pi$
$271$	25.9701	1.57757	0.788787	+	0.614667i	$0.210709\pi$
$272$	−1.13457	−0.0687932
$273$	31.3224	1.89572
$274$	−3.44617	−0.208191
$275$	0	0
$276$	1.22064	0.0734737
$277$	1.83370	0.110176	0.0550882	−	0.998481i	$-0.482456\pi$
$277$	1.83370	0.110176	0.0550882	+	0.998481i	$0.482456\pi$
$278$	−5.60137	−0.335948
$279$	−4.66513	−0.279294
$280$	0	0
$281$	13.6844	0.816345	0.408173	−	0.912905i	$-0.366166\pi$
$281$	13.6844	0.816345	0.408173	+	0.912905i	$0.366166\pi$
$282$	25.5016	1.51860
$283$	−10.5363	−0.626319	−0.313159	−	0.949701i	$-0.601387\pi$
$283$	−10.5363	−0.626319	−0.313159	+	0.949701i	$0.601387\pi$
$284$	0.227811	0.0135181
$285$	0	0
$286$	−4.62522	−0.273495
$287$	−18.2447	−1.07695
$288$	−0.561567	−0.0330907
$289$	−16.9290	−0.995823
$290$	0	0
$291$	−15.7417	−0.922794
$292$	−0.248573	−0.0145466
$293$	23.9043	1.39650	0.698251	−	0.715853i	$-0.253962\pi$
$293$	23.9043	1.39650	0.698251	+	0.715853i	$0.253962\pi$
$294$	−21.1561	−1.23385
$295$	0	0
$296$	−24.0633	−1.39865
$297$	3.48803	0.202396
$298$	−26.5929	−1.54049
$299$	−29.7536	−1.72070
$300$	0	0
$301$	−7.33206	−0.422613
$302$	−3.35366	−0.192981
$303$	−18.4561	−1.06028
$304$	0	0
$305$	0	0
$306$	0.280113	0.0160130
$307$	15.6686	0.894256	0.447128	−	0.894470i	$-0.352447\pi$
$307$	15.6686	0.894256	0.447128	+	0.894470i	$0.352447\pi$
$308$	0.349815	0.0199326
$309$	−11.7864	−0.670505
$310$	0	0
$311$	−3.51210	−0.199153	−0.0995764	−	0.995030i	$-0.531749\pi$
$311$	−3.51210	−0.199153	−0.0995764	+	0.995030i	$0.531749\pi$
$312$	−20.9419	−1.18560
$313$	−1.17307	−0.0663061	−0.0331530	−	0.999450i	$-0.510555\pi$
$313$	−1.17307	−0.0663061	−0.0331530	+	0.999450i	$0.510555\pi$
$314$	−30.4811	−1.72015
$315$	0	0
$316$	−0.711991	−0.0400526
$317$	−1.31161	−0.0736673	−0.0368336	−	0.999321i	$-0.511727\pi$
$317$	−1.31161	−0.0736673	−0.0368336	+	0.999321i	$0.511727\pi$
$318$	5.57214	0.312470
$319$	2.53218	0.141775
$320$	0	0
$321$	8.61527	0.480858
$322$	34.7824	1.93835
$323$	0	0
$324$	−0.875285	−0.0486270
$325$	0	0
$326$	−11.5770	−0.641189
$327$	10.1695	0.562375
$328$	12.1982	0.673534
$329$	47.0140	2.59197
$330$	0	0
$331$	12.7249	0.699423	0.349712	−	0.936857i	$-0.386280\pi$
$331$	12.7249	0.699423	0.349712	+	0.936857i	$0.386280\pi$
$332$	−1.90686	−0.104653
$333$	6.35391	0.348192
$334$	−20.6090	−1.12767
$335$	0	0
$336$	26.1829	1.42839
$337$	15.2196	0.829064	0.414532	−	0.910035i	$-0.363945\pi$
$337$	15.2196	0.829064	0.414532	+	0.910035i	$0.363945\pi$
$338$	−18.9246	−1.02936
$339$	−7.23276	−0.392829
$340$	0	0
$341$	−4.03027	−0.218251
$342$	0	0
$343$	−10.5007	−0.566987
$344$	4.90214	0.264306
$345$	0	0
$346$	15.3729	0.826455
$347$	−20.0179	−1.07462	−0.537308	−	0.843386i	$-0.680559\pi$
$347$	−20.0179	−1.07462	−0.537308	+	0.843386i	$0.680559\pi$
$348$	−0.852006	−0.0456723
$349$	22.2816	1.19271	0.596353	−	0.802722i	$-0.296616\pi$
$349$	22.2816	1.19271	0.596353	+	0.802722i	$0.296616\pi$
$350$	0	0
$351$	28.6077	1.52697
$352$	−0.485146	−0.0258584
$353$	26.2150	1.39528	0.697642	−	0.716447i	$-0.254233\pi$
$353$	26.2150	1.39528	0.697642	+	0.716447i	$0.254233\pi$
$354$	1.96664	0.104526
$355$	0	0
$356$	0.000103377 0	5.47897e−6 0
$357$	−1.63881	−0.0867348
$358$	7.31635	0.386681
$359$	28.2782	1.49247	0.746234	−	0.665683i	$-0.231860\pi$
$359$	28.2782	1.49247	0.746234	+	0.665683i	$0.231860\pi$
$360$	0	0
$361$	0	0
$362$	−38.7389	−2.03607
$363$	−16.0314	−0.841432
$364$	2.86907	0.150380
$365$	0	0
$366$	−4.79247	−0.250507
$367$	9.59488	0.500848	0.250424	−	0.968136i	$-0.419430\pi$
$367$	9.59488	0.500848	0.250424	+	0.968136i	$0.419430\pi$
$368$	−24.8715	−1.29652
$369$	−3.22094	−0.167676
$370$	0	0
$371$	10.2727	0.533330
$372$	1.35607	0.0703091
$373$	13.0401	0.675189	0.337595	−	0.941292i	$-0.390387\pi$
$373$	13.0401	0.675189	0.337595	+	0.941292i	$0.390387\pi$
$374$	0.241994	0.0125132
$375$	0	0
$376$	−31.4331	−1.62104
$377$	20.7681	1.06961
$378$	−33.4428	−1.72011
$379$	−9.93895	−0.510530	−0.255265	−	0.966871i	$-0.582163\pi$
$379$	−9.93895	−0.510530	−0.255265	+	0.966871i	$0.582163\pi$
$380$	0	0
$381$	27.9365	1.43123
$382$	0.210301	0.0107599
$383$	−18.0285	−0.921212	−0.460606	−	0.887605i	$-0.652368\pi$
$383$	−18.0285	−0.921212	−0.460606	+	0.887605i	$0.652368\pi$
$384$	−18.6433	−0.951385
$385$	0	0
$386$	−3.01403	−0.153410
$387$	−1.29441	−0.0657986
$388$	−1.44191	−0.0732017
$389$	24.3511	1.23465	0.617325	−	0.786708i	$-0.288216\pi$
$389$	24.3511	1.23465	0.617325	+	0.786708i	$0.288216\pi$
$390$	0	0
$391$	1.55673	0.0787270
$392$	26.0769	1.31708
$393$	−29.5794	−1.49208
$394$	26.6846	1.34435
$395$	0	0
$396$	0.0617568	0.00310340
$397$	19.9719	1.00236	0.501180	−	0.865343i	$-0.332900\pi$
$397$	19.9719	1.00236	0.501180	+	0.865343i	$0.332900\pi$
$398$	−11.7029	−0.586611
$399$	0	0
$400$	0	0
$401$	16.4037	0.819163	0.409581	−	0.912274i	$-0.365675\pi$
$401$	16.4037	0.819163	0.409581	+	0.912274i	$0.365675\pi$
$402$	31.0945	1.55085
$403$	−33.0550	−1.64659
$404$	−1.69055	−0.0841078
$405$	0	0
$406$	−24.2782	−1.20491
$407$	5.48924	0.272091
$408$	1.09569	0.0542447
$409$	−8.33303	−0.412042	−0.206021	−	0.978548i	$-0.566052\pi$
$409$	−8.33303	−0.412042	−0.206021	+	0.978548i	$0.566052\pi$
$410$	0	0
$411$	3.55940	0.175572
$412$	−1.07961	−0.0531886
$413$	3.62564	0.178406
$414$	6.14053	0.301790
$415$	0	0
$416$	−3.97901	−0.195087
$417$	5.78542	0.283313
$418$	0	0
$419$	−11.6553	−0.569397	−0.284698	−	0.958617i	$-0.591893\pi$
$419$	−11.6553	−0.569397	−0.284698	+	0.958617i	$0.591893\pi$
$420$	0	0
$421$	−21.1916	−1.03282	−0.516408	−	0.856343i	$-0.672731\pi$
$421$	−21.1916	−1.03282	−0.516408	+	0.856343i	$0.672731\pi$
$422$	−20.5934	−1.00247
$423$	8.29992	0.403556
$424$	−6.86819	−0.333549
$425$	0	0
$426$	−3.63687	−0.176207
$427$	−8.83527	−0.427569
$428$	0.789142	0.0381446
$429$	4.77719	0.230645
$430$	0	0
$431$	−0.392264	−0.0188947	−0.00944734	−	0.999955i	$-0.503007\pi$
$431$	−0.392264	−0.0188947	−0.00944734	+	0.999955i	$0.503007\pi$
$432$	23.9136	1.15054
$433$	12.9711	0.623354	0.311677	−	0.950188i	$-0.399109\pi$
$433$	12.9711	0.623354	0.311677	+	0.950188i	$0.399109\pi$
$434$	38.6417	1.85486
$435$	0	0
$436$	0.931506	0.0446110
$437$	0	0
$438$	3.96832	0.189614
$439$	5.44800	0.260019	0.130009	−	0.991513i	$-0.458499\pi$
$439$	5.44800	0.260019	0.130009	+	0.991513i	$0.458499\pi$
$440$	0	0
$441$	−6.88560	−0.327886
$442$	1.98476	0.0944052
$443$	−24.7427	−1.17556	−0.587780	−	0.809021i	$-0.699998\pi$
$443$	−24.7427	−1.17556	−0.587780	+	0.809021i	$0.699998\pi$
$444$	−1.84697	−0.0876535
$445$	0	0
$446$	−7.17423	−0.339710
$447$	27.4667	1.29913
$448$	−30.0196	−1.41829
$449$	−34.5619	−1.63108	−0.815538	−	0.578704i	$-0.803559\pi$
$449$	−34.5619	−1.63108	−0.815538	+	0.578704i	$0.803559\pi$
$450$	0	0
$451$	−2.78262	−0.131029
$452$	−0.662506	−0.0311617
$453$	3.46385	0.162746
$454$	−3.87872	−0.182037
$455$	0	0
$456$	0	0
$457$	11.6425	0.544613	0.272307	−	0.962211i	$-0.412214\pi$
$457$	11.6425	0.544613	0.272307	+	0.962211i	$0.412214\pi$
$458$	33.8337	1.58094
$459$	−1.49677	−0.0698633
$460$	0	0
$461$	2.98973	0.139246	0.0696228	−	0.997573i	$-0.477820\pi$
$461$	2.98973	0.139246	0.0696228	+	0.997573i	$0.477820\pi$
$462$	−5.58460	−0.259819
$463$	8.48715	0.394431	0.197216	−	0.980360i	$-0.436810\pi$
$463$	8.48715	0.394431	0.197216	+	0.980360i	$0.436810\pi$
$464$	17.3604	0.805934
$465$	0	0
$466$	−42.2750	−1.95835
$467$	−17.9302	−0.829712	−0.414856	−	0.909887i	$-0.636168\pi$
$467$	−17.9302	−0.829712	−0.414856	+	0.909887i	$0.636168\pi$
$468$	0.506510	0.0234134
$469$	57.3249	2.64702
$470$	0	0
$471$	31.4826	1.45064
$472$	−2.42407	−0.111577
$473$	−1.11826	−0.0514177
$474$	11.3665	0.522081
$475$	0	0
$476$	−0.150111	−0.00688034
$477$	1.81355	0.0830366
$478$	30.3389	1.38767
$479$	3.38955	0.154873	0.0774363	−	0.996997i	$-0.475327\pi$
$479$	3.38955	0.154873	0.0774363	+	0.996997i	$0.475327\pi$
$480$	0	0
$481$	45.0210	2.05278
$482$	9.06250	0.412786
$483$	−35.9252	−1.63465
$484$	−1.46845	−0.0667476
$485$	0	0
$486$	−10.6668	−0.483858
$487$	−11.1620	−0.505797	−0.252899	−	0.967493i	$-0.581384\pi$
$487$	−11.1620	−0.505797	−0.252899	+	0.967493i	$0.581384\pi$
$488$	5.90717	0.267405
$489$	11.9573	0.540730
$490$	0	0
$491$	22.9830	1.03721	0.518604	−	0.855015i	$-0.326452\pi$
$491$	22.9830	1.03721	0.518604	+	0.855015i	$0.326452\pi$
$492$	0.936274	0.0422105
$493$	−1.08660	−0.0489379
$494$	0	0
$495$	0	0
$496$	−27.6311	−1.24067
$497$	−6.70483	−0.300753
$498$	30.4419	1.36414
$499$	0.980732	0.0439036	0.0219518	−	0.999759i	$-0.493012\pi$
$499$	0.980732	0.0439036	0.0219518	+	0.999759i	$0.493012\pi$
$500$	0	0
$501$	21.2862	0.950995
$502$	−11.3913	−0.508419
$503$	−3.57195	−0.159265	−0.0796326	−	0.996824i	$-0.525375\pi$
$503$	−3.57195	−0.159265	−0.0796326	+	0.996824i	$0.525375\pi$
$504$	7.96785	0.354916
$505$	0	0
$506$	5.30489	0.235831
$507$	19.5464	0.868085
$508$	2.55893	0.113534
$509$	12.9903	0.575783	0.287892	−	0.957663i	$-0.407046\pi$
$509$	12.9903	0.575783	0.287892	+	0.957663i	$0.407046\pi$
$510$	0	0
$511$	7.31589	0.323636
$512$	19.8547	0.877460
$513$	0	0
$514$	−29.4761	−1.30013
$515$	0	0
$516$	0.376263	0.0165641
$517$	7.17042	0.315355
$518$	−52.6301	−2.31243
$519$	−15.8781	−0.696969
$520$	0	0
$521$	−22.9197	−1.00413	−0.502064	−	0.864830i	$-0.667426\pi$
$521$	−22.9197	−1.00413	−0.502064	+	0.864830i	$0.667426\pi$
$522$	−4.28610	−0.187597
$523$	1.97236	0.0862455	0.0431227	−	0.999070i	$-0.486269\pi$
$523$	1.97236	0.0862455	0.0431227	+	0.999070i	$0.486269\pi$
$524$	−2.70942	−0.118361
$525$	0	0
$526$	15.6259	0.681323
$527$	1.72945	0.0753362
$528$	3.99332	0.173787
$529$	11.1259	0.483735
$530$	0	0
$531$	0.640075	0.0277769
$532$	0	0
$533$	−22.8222	−0.988538
$534$	−0.00165035	−7.14178e−5 0
$535$	0	0
$536$	−38.3269	−1.65547
$537$	−7.55674	−0.326098
$538$	−34.9871	−1.50840
$539$	−5.94858	−0.256223
$540$	0	0
$541$	−27.5270	−1.18348	−0.591739	−	0.806129i	$-0.701559\pi$
$541$	−27.5270	−1.18348	−0.591739	+	0.806129i	$0.701559\pi$
$542$	−37.9764	−1.63122
$543$	40.0117	1.71707
$544$	0.208184	0.00892582
$545$	0	0
$546$	−45.8031	−1.96019
$547$	8.34646	0.356869	0.178434	−	0.983952i	$-0.442897\pi$
$547$	8.34646	0.356869	0.178434	+	0.983952i	$0.442897\pi$
$548$	0.326034	0.0139275
$549$	−1.55979	−0.0665702
$550$	0	0
$551$	0	0
$552$	24.0192	1.02233
$553$	20.9550	0.891097
$554$	−2.68144	−0.113923
$555$	0	0
$556$	0.529933	0.0224742
$557$	−23.8334	−1.00985	−0.504926	−	0.863163i	$-0.668480\pi$
$557$	−23.8334	−1.00985	−0.504926	+	0.863163i	$0.668480\pi$
$558$	6.82185	0.288792
$559$	−9.17161	−0.387918
$560$	0	0
$561$	−0.249945	−0.0105527
$562$	−20.0109	−0.844108
$563$	−19.6274	−0.827198	−0.413599	−	0.910459i	$-0.635728\pi$
$563$	−19.6274	−0.827198	−0.413599	+	0.910459i	$0.635728\pi$
$564$	−2.41264	−0.101591
$565$	0	0
$566$	15.4073	0.647618
$567$	25.7610	1.08186
$568$	4.48278	0.188093
$569$	−23.7705	−0.996510	−0.498255	−	0.867030i	$-0.666026\pi$
$569$	−23.7705	−0.996510	−0.498255	+	0.867030i	$0.666026\pi$
$570$	0	0
$571$	−17.5361	−0.733865	−0.366933	−	0.930248i	$-0.619592\pi$
$571$	−17.5361	−0.733865	−0.366933	+	0.930248i	$0.619592\pi$
$572$	0.437581	0.0182962
$573$	−0.217211	−0.00907412
$574$	26.6794	1.11358
$575$	0	0
$576$	−5.29970	−0.220821
$577$	25.9280	1.07940	0.539699	−	0.841858i	$-0.318538\pi$
$577$	25.9280	1.07940	0.539699	+	0.841858i	$0.318538\pi$
$578$	24.7554	1.02969
$579$	3.11306	0.129375
$580$	0	0
$581$	56.1220	2.32833
$582$	23.0192	0.954177
$583$	1.56675	0.0648882
$584$	−4.89133	−0.202405
$585$	0	0
$586$	−34.9554	−1.44399
$587$	4.04205	0.166833	0.0834166	−	0.996515i	$-0.473417\pi$
$587$	4.04205	0.166833	0.0834166	+	0.996515i	$0.473417\pi$
$588$	2.00153	0.0825416
$589$	0	0
$590$	0	0
$591$	−27.5614	−1.13372
$592$	37.6337	1.54673
$593$	−18.8561	−0.774329	−0.387165	−	0.922011i	$-0.626545\pi$
$593$	−18.8561	−0.774329	−0.387165	+	0.922011i	$0.626545\pi$
$594$	−5.10058	−0.209279
$595$	0	0
$596$	2.51589	0.103055
$597$	12.0874	0.494704
$598$	43.5090	1.77922
$599$	38.8211	1.58619	0.793094	−	0.609099i	$-0.208469\pi$
$599$	38.8211	1.58619	0.793094	+	0.609099i	$0.208469\pi$
$600$	0	0
$601$	−0.358419	−0.0146202	−0.00731011	−	0.999973i	$-0.502327\pi$
$601$	−0.358419	−0.0146202	−0.00731011	+	0.999973i	$0.502327\pi$
$602$	10.7217	0.436985
$603$	10.1202	0.412127
$604$	0.317281	0.0129100
$605$	0	0
$606$	26.9886	1.09634
$607$	4.56885	0.185444	0.0927219	−	0.995692i	$-0.470443\pi$
$607$	4.56885	0.185444	0.0927219	+	0.995692i	$0.470443\pi$
$608$	0	0
$609$	25.0759	1.01613
$610$	0	0
$611$	58.8095	2.37918
$612$	−0.0265008	−0.00107123
$613$	−16.8926	−0.682287	−0.341143	−	0.940011i	$-0.610814\pi$
$613$	−16.8926	−0.682287	−0.341143	+	0.940011i	$0.610814\pi$
$614$	−22.9124	−0.924668
$615$	0	0
$616$	6.88354	0.277346
$617$	−24.3654	−0.980914	−0.490457	−	0.871465i	$-0.663170\pi$
$617$	−24.3654	−0.980914	−0.490457	+	0.871465i	$0.663170\pi$
$618$	17.2353	0.693307
$619$	−33.3232	−1.33937	−0.669687	−	0.742644i	$-0.733572\pi$
$619$	−33.3232	−1.33937	−0.669687	+	0.742644i	$0.733572\pi$
$620$	0	0
$621$	−32.8116	−1.31668
$622$	5.13577	0.205926
$623$	−0.00304255	−0.000121897 0
$624$	32.7519	1.31113
$625$	0	0
$626$	1.71540	0.0685610
$627$	0	0
$628$	2.88375	0.115074
$629$	−2.35552	−0.0939207
$630$	0	0
$631$	37.5315	1.49411	0.747053	−	0.664765i	$-0.231468\pi$
$631$	37.5315	1.49411	0.747053	+	0.664765i	$0.231468\pi$
$632$	−14.0103	−0.557300
$633$	21.2701	0.845409
$634$	1.91798	0.0761725
$635$	0	0
$636$	−0.527167	−0.0209035
$637$	−48.7883	−1.93306
$638$	−3.70282	−0.146596
$639$	−1.18368	−0.0468256
$640$	0	0
$641$	7.04598	0.278300	0.139150	−	0.990271i	$-0.455563\pi$
$641$	7.04598	0.278300	0.139150	+	0.990271i	$0.455563\pi$
$642$	−12.5982	−0.497211
$643$	−15.2815	−0.602645	−0.301323	−	0.953522i	$-0.597428\pi$
$643$	−15.2815	−0.602645	−0.301323	+	0.953522i	$0.597428\pi$
$644$	−3.29068	−0.129671
$645$	0	0
$646$	0	0
$647$	−23.8972	−0.939495	−0.469748	−	0.882801i	$-0.655655\pi$
$647$	−23.8972	−0.939495	−0.469748	+	0.882801i	$0.655655\pi$
$648$	−17.2235	−0.676605
$649$	0.552971	0.0217060
$650$	0	0
$651$	−39.9113	−1.56425
$652$	1.09527	0.0428940
$653$	27.1407	1.06210	0.531050	−	0.847341i	$-0.321798\pi$
$653$	27.1407	1.06210	0.531050	+	0.847341i	$0.321798\pi$
$654$	−14.8709	−0.581500
$655$	0	0
$656$	−19.0774	−0.744846
$657$	1.29156	0.0503884
$658$	−68.7490	−2.68012
$659$	45.8304	1.78530	0.892650	−	0.450750i	$-0.148844\pi$
$659$	45.8304	1.78530	0.892650	+	0.450750i	$0.148844\pi$
$660$	0	0
$661$	−18.3884	−0.715226	−0.357613	−	0.933870i	$-0.616409\pi$
$661$	−18.3884	−0.715226	−0.357613	+	0.933870i	$0.616409\pi$
$662$	−18.6077	−0.723209
$663$	−2.04997	−0.0796142
$664$	−37.5226	−1.45616
$665$	0	0
$666$	−9.29138	−0.360034
$667$	−23.8199	−0.922312
$668$	1.94977	0.0754388
$669$	7.40995	0.286485
$670$	0	0
$671$	−1.34753	−0.0520207
$672$	−4.80435	−0.185332
$673$	−5.81977	−0.224336	−0.112168	−	0.993689i	$-0.535779\pi$
$673$	−5.81977	−0.224336	−0.112168	+	0.993689i	$0.535779\pi$
$674$	−22.2557	−0.857259
$675$	0	0
$676$	1.79041	0.0688619
$677$	17.8836	0.687324	0.343662	−	0.939093i	$-0.388332\pi$
$677$	17.8836	0.687324	0.343662	+	0.939093i	$0.388332\pi$
$678$	10.5765	0.406189
$679$	42.4376	1.62861
$680$	0	0
$681$	4.00616	0.153516
$682$	5.89350	0.225674
$683$	−13.4534	−0.514779	−0.257390	−	0.966308i	$-0.582862\pi$
$683$	−13.4534	−0.514779	−0.257390	+	0.966308i	$0.582862\pi$
$684$	0	0
$685$	0	0
$686$	15.3553	0.586269
$687$	−34.9453	−1.33325
$688$	−7.66668	−0.292290
$689$	12.8500	0.489545
$690$	0	0
$691$	2.31515	0.0880724	0.0440362	−	0.999030i	$-0.485978\pi$
$691$	2.31515	0.0880724	0.0440362	+	0.999030i	$0.485978\pi$
$692$	−1.45440	−0.0552879
$693$	−1.81760	−0.0690449
$694$	29.2723	1.11116
$695$	0	0
$696$	−16.7655	−0.635494
$697$	1.19407	0.0452285
$698$	−32.5825	−1.23327
$699$	43.6640	1.65152
$700$	0	0
$701$	3.12614	0.118073	0.0590364	−	0.998256i	$-0.481197\pi$
$701$	3.12614	0.118073	0.0590364	+	0.998256i	$0.481197\pi$
$702$	−41.8333	−1.57890
$703$	0	0
$704$	−4.57849	−0.172558
$705$	0	0
$706$	−38.3344	−1.44273
$707$	49.7554	1.87124
$708$	−0.186059	−0.00699253
$709$	−28.1738	−1.05809	−0.529045	−	0.848594i	$-0.677450\pi$
$709$	−28.1738	−1.05809	−0.529045	+	0.848594i	$0.677450\pi$
$710$	0	0
$711$	3.69942	0.138739
$712$	0.00203422	7.62355e−5 0
$713$	37.9124	1.41983
$714$	2.39644	0.0896845
$715$	0	0
$716$	−0.692183	−0.0258681
$717$	−31.3358	−1.17026
$718$	−41.3515	−1.54322
$719$	−1.21291	−0.0452338	−0.0226169	−	0.999744i	$-0.507200\pi$
$719$	−1.21291	−0.0452338	−0.0226169	+	0.999744i	$0.507200\pi$
$720$	0	0
$721$	31.7746	1.18335
$722$	0	0
$723$	−9.36027	−0.348112
$724$	3.66499	0.136208
$725$	0	0
$726$	23.4429	0.870048
$727$	−35.7719	−1.32671	−0.663354	−	0.748306i	$-0.730868\pi$
$727$	−35.7719	−1.32671	−0.663354	+	0.748306i	$0.730868\pi$
$728$	56.4566	2.09242
$729$	29.9977	1.11103
$730$	0	0
$731$	0.479864	0.0177484
$732$	0.453404	0.0167583
$733$	−37.8471	−1.39791	−0.698957	−	0.715164i	$-0.746352\pi$
$733$	−37.8471	−1.39791	−0.698957	+	0.715164i	$0.746352\pi$
$734$	−14.0307	−0.517881
$735$	0	0
$736$	4.56373	0.168221
$737$	8.74301	0.322053
$738$	4.71001	0.173378
$739$	7.54675	0.277612	0.138806	−	0.990320i	$-0.455674\pi$
$739$	7.54675	0.277612	0.138806	+	0.990320i	$0.455674\pi$
$740$	0	0
$741$	0	0
$742$	−15.0218	−0.551467
$743$	−9.17584	−0.336629	−0.168314	−	0.985733i	$-0.553832\pi$
$743$	−9.17584	−0.336629	−0.168314	+	0.985733i	$0.553832\pi$
$744$	26.6843	0.978294
$745$	0	0
$746$	−19.0686	−0.698151
$747$	9.90784	0.362509
$748$	−0.0228945	−0.000837105 0
$749$	−23.2257	−0.848648
$750$	0	0
$751$	−10.4714	−0.382105	−0.191053	−	0.981580i	$-0.561190\pi$
$751$	−10.4714	−0.382105	−0.191053	+	0.981580i	$0.561190\pi$
$752$	49.1597	1.79267
$753$	11.7656	0.428762
$754$	−30.3694	−1.10599
$755$	0	0
$756$	3.16394	0.115071
$757$	53.0755	1.92906	0.964532	−	0.263967i	$-0.0850310\pi$
$757$	53.0755	1.92906	0.964532	+	0.263967i	$0.0850310\pi$
$758$	14.5338	0.527892
$759$	−5.47919	−0.198882
$760$	0	0
$761$	−16.6886	−0.604960	−0.302480	−	0.953156i	$-0.597815\pi$
$761$	−16.6886	−0.604960	−0.302480	+	0.953156i	$0.597815\pi$
$762$	−40.8518	−1.47990
$763$	−27.4157	−0.992514
$764$	−0.0198961	−0.000719816 0
$765$	0	0
$766$	26.3632	0.952541
$767$	4.53529	0.163760
$768$	4.99138	0.180111
$769$	−6.17780	−0.222777	−0.111389	−	0.993777i	$-0.535530\pi$
$769$	−6.17780	−0.222777	−0.111389	+	0.993777i	$0.535530\pi$
$770$	0	0
$771$	30.4445	1.09643
$772$	0.285150	0.0102628
$773$	28.1558	1.01270	0.506348	−	0.862330i	$-0.330995\pi$
$773$	28.1558	1.01270	0.506348	+	0.862330i	$0.330995\pi$
$774$	1.89283	0.0680363
$775$	0	0
$776$	−28.3733	−1.01854
$777$	54.3593	1.95013
$778$	−35.6088	−1.27664
$779$	0	0
$780$	0	0
$781$	−1.02260	−0.0365914
$782$	−2.27641	−0.0814044
$783$	22.9025	0.818470
$784$	−40.7828	−1.45653
$785$	0	0
$786$	43.2542	1.54283
$787$	5.46867	0.194937	0.0974685	−	0.995239i	$-0.468925\pi$
$787$	5.46867	0.194937	0.0974685	+	0.995239i	$0.468925\pi$
$788$	−2.52457	−0.0899339
$789$	−16.1393	−0.574576
$790$	0	0
$791$	19.4986	0.693290
$792$	1.21523	0.0431813
$793$	−11.0520	−0.392467
$794$	−29.2050	−1.03645
$795$	0	0
$796$	1.10718	0.0392429
$797$	−47.2273	−1.67288	−0.836439	−	0.548061i	$-0.815366\pi$
$797$	−47.2273	−1.67288	−0.836439	+	0.548061i	$0.815366\pi$
$798$	0	0
$799$	−3.07694	−0.108854
$800$	0	0
$801$	−0.000537135 0	−1.89787e−5 0
$802$	−23.9873	−0.847021
$803$	1.11579	0.0393755
$804$	−2.94177	−0.103748
$805$	0	0
$806$	48.3366	1.70258
$807$	36.1367	1.27207
$808$	−33.2659	−1.17029
$809$	−6.13382	−0.215654	−0.107827	−	0.994170i	$-0.534389\pi$
$809$	−6.13382	−0.215654	−0.107827	+	0.994170i	$0.534389\pi$
$810$	0	0
$811$	−26.9998	−0.948093	−0.474046	−	0.880500i	$-0.657207\pi$
$811$	−26.9998	−0.948093	−0.474046	+	0.880500i	$0.657207\pi$
$812$	2.29690	0.0806054
$813$	39.2241	1.37565
$814$	−8.02696	−0.281345
$815$	0	0
$816$	−1.71360	−0.0599880
$817$	0	0
$818$	12.1855	0.426055
$819$	−14.9074	−0.520906
$820$	0	0
$821$	−45.2474	−1.57914	−0.789572	−	0.613658i	$-0.789697\pi$
$821$	−45.2474	−1.57914	−0.789572	+	0.613658i	$0.789697\pi$
$822$	−5.20494	−0.181543
$823$	−30.1438	−1.05075	−0.525373	−	0.850872i	$-0.676074\pi$
$823$	−30.1438	−1.05075	−0.525373	+	0.850872i	$0.676074\pi$
$824$	−21.2442	−0.740076
$825$	0	0
$826$	−5.30181	−0.184473
$827$	−20.4710	−0.711846	−0.355923	−	0.934515i	$-0.615833\pi$
$827$	−20.4710	−0.711846	−0.355923	+	0.934515i	$0.615833\pi$
$828$	−0.580941	−0.0201891
$829$	20.9207	0.726606	0.363303	−	0.931671i	$-0.381649\pi$
$829$	20.9207	0.726606	0.363303	+	0.931671i	$0.381649\pi$
$830$	0	0
$831$	2.76954	0.0960743
$832$	−37.5513	−1.30186
$833$	2.55263	0.0884433
$834$	−8.46006	−0.292948
$835$	0	0
$836$	0	0
$837$	−36.4522	−1.25997
$838$	17.0436	0.588761
$839$	−4.24739	−0.146636	−0.0733180	−	0.997309i	$-0.523359\pi$
$839$	−4.24739	−0.146636	−0.0733180	+	0.997309i	$0.523359\pi$
$840$	0	0
$841$	−12.3736	−0.426677
$842$	30.9887	1.06794
$843$	20.6684	0.711856
$844$	1.94829	0.0670630
$845$	0	0
$846$	−12.1370	−0.417280
$847$	43.2187	1.48501
$848$	10.7415	0.368864
$849$	−15.9136	−0.546152
$850$	0	0
$851$	−51.6367	−1.77008
$852$	0.344075	0.0117878
$853$	1.66945	0.0571610	0.0285805	−	0.999591i	$-0.490901\pi$
$853$	1.66945	0.0571610	0.0285805	+	0.999591i	$0.490901\pi$
$854$	12.9199	0.442110
$855$	0	0
$856$	15.5284	0.530751
$857$	0.856668	0.0292632	0.0146316	−	0.999893i	$-0.495342\pi$
$857$	0.856668	0.0292632	0.0146316	+	0.999893i	$0.495342\pi$
$858$	−6.98573	−0.238489
$859$	−53.1009	−1.81178	−0.905889	−	0.423515i	$-0.860796\pi$
$859$	−53.1009	−1.81178	−0.905889	+	0.423515i	$0.860796\pi$
$860$	0	0
$861$	−27.5560	−0.939106
$862$	0.573611	0.0195373
$863$	29.5608	1.00626	0.503130	−	0.864211i	$-0.332182\pi$
$863$	29.5608	1.00626	0.503130	+	0.864211i	$0.332182\pi$
$864$	−4.38796	−0.149281
$865$	0	0
$866$	−18.9678	−0.644553
$867$	−25.5688	−0.868361
$868$	−3.65580	−0.124086
$869$	3.19598	0.108416
$870$	0	0
$871$	71.7073	2.42971
$872$	18.3298	0.620727
$873$	7.49198	0.253565
$874$	0	0
$875$	0	0
$876$	−0.375433	−0.0126847
$877$	8.79077	0.296843	0.148422	−	0.988924i	$-0.452581\pi$
$877$	8.79077	0.296843	0.148422	+	0.988924i	$0.452581\pi$
$878$	−7.96665	−0.268861
$879$	36.1039	1.21776
$880$	0	0
$881$	27.2670	0.918647	0.459324	−	0.888269i	$-0.348092\pi$
$881$	27.2670	0.918647	0.459324	+	0.888269i	$0.348092\pi$
$882$	10.0689	0.339037
$883$	8.65079	0.291122	0.145561	−	0.989349i	$-0.453501\pi$
$883$	8.65079	0.291122	0.145561	+	0.989349i	$0.453501\pi$
$884$	−0.187773	−0.00631549
$885$	0	0
$886$	36.1814	1.21554
$887$	39.6495	1.33130	0.665651	−	0.746263i	$-0.268154\pi$
$887$	39.6495	1.33130	0.665651	+	0.746263i	$0.268154\pi$
$888$	−36.3441	−1.21963
$889$	−75.3133	−2.52593
$890$	0	0
$891$	3.92898	0.131626
$892$	0.678737	0.0227258
$893$	0	0
$894$	−40.1648	−1.34331
$895$	0	0
$896$	50.2598	1.67906
$897$	−44.9386	−1.50046
$898$	50.5401	1.68655
$899$	−26.4629	−0.882587
$900$	0	0
$901$	−0.672317	−0.0223981
$902$	4.06905	0.135485
$903$	−11.0740	−0.368520
$904$	−13.0366	−0.433589
$905$	0	0
$906$	−5.06521	−0.168280
$907$	−33.3774	−1.10828	−0.554139	−	0.832424i	$-0.686952\pi$
$907$	−33.3774	−1.10828	−0.554139	+	0.832424i	$0.686952\pi$
$908$	0.366956	0.0121779
$909$	8.78388	0.291343
$910$	0	0
$911$	46.3977	1.53722	0.768611	−	0.639716i	$-0.220948\pi$
$911$	46.3977	1.53722	0.768611	+	0.639716i	$0.220948\pi$
$912$	0	0
$913$	8.55953	0.283279
$914$	−17.0249	−0.563134
$915$	0	0
$916$	−3.20092	−0.105761
$917$	79.7424	2.63333
$918$	2.18874	0.0722392
$919$	8.51995	0.281047	0.140524	−	0.990077i	$-0.455121\pi$
$919$	8.51995	0.281047	0.140524	+	0.990077i	$0.455121\pi$
$920$	0	0
$921$	23.6652	0.779795
$922$	−4.37191	−0.143981
$923$	−8.38701	−0.276062
$924$	0.528345	0.0173813
$925$	0	0
$926$	−12.4108	−0.407845
$927$	5.60953	0.184241
$928$	−3.18549	−0.104569
$929$	−47.1584	−1.54722	−0.773608	−	0.633665i	$-0.781550\pi$
$929$	−47.1584	−1.54722	−0.773608	+	0.633665i	$0.781550\pi$
$930$	0	0
$931$	0	0
$932$	3.99954	0.131009
$933$	−5.30452	−0.173662
$934$	26.2195	0.857929
$935$	0	0
$936$	9.96691	0.325779
$937$	29.5004	0.963735	0.481867	−	0.876244i	$-0.339959\pi$
$937$	29.5004	0.963735	0.481867	+	0.876244i	$0.339959\pi$
$938$	−83.8267	−2.73704
$939$	−1.77176	−0.0578192
$940$	0	0
$941$	9.49895	0.309657	0.154829	−	0.987941i	$-0.450517\pi$
$941$	9.49895	0.309657	0.154829	+	0.987941i	$0.450517\pi$
$942$	−46.0373	−1.49998
$943$	26.1759	0.852403
$944$	3.79111	0.123390
$945$	0	0
$946$	1.63524	0.0531663
$947$	9.85963	0.320395	0.160198	−	0.987085i	$-0.448787\pi$
$947$	9.85963	0.320395	0.160198	+	0.987085i	$0.448787\pi$
$948$	−1.07536	−0.0349260
$949$	9.15138	0.297066
$950$	0	0
$951$	−1.98099	−0.0642381
$952$	−2.95384	−0.0957344
$953$	53.6746	1.73869	0.869346	−	0.494204i	$-0.164540\pi$
$953$	53.6746	1.73869	0.869346	+	0.494204i	$0.164540\pi$
$954$	−2.65196	−0.0858605
$955$	0	0
$956$	−2.87030	−0.0928320
$957$	3.82449	0.123628
$958$	−4.95657	−0.160139
$959$	−9.59569	−0.309861
$960$	0	0
$961$	11.1190	0.358676
$962$	−65.8345	−2.12259
$963$	−4.10029	−0.132130
$964$	−0.857382	−0.0276144
$965$	0	0
$966$	52.5338	1.69025
$967$	−34.2375	−1.10100	−0.550502	−	0.834834i	$-0.685564\pi$
$967$	−34.2375	−1.10100	−0.550502	+	0.834834i	$0.685564\pi$
$968$	−28.8956	−0.928739
$969$	0	0
$970$	0	0
$971$	−14.1698	−0.454730	−0.227365	−	0.973810i	$-0.573011\pi$
$971$	−14.1698	−0.454730	−0.227365	+	0.973810i	$0.573011\pi$
$972$	1.00916	0.0323690
$973$	−15.5967	−0.500009
$974$	16.3222	0.522998
$975$	0	0
$976$	−9.23850	−0.295717
$977$	45.6175	1.45943	0.729717	−	0.683749i	$-0.239652\pi$
$977$	45.6175	1.45943	0.729717	+	0.683749i	$0.239652\pi$
$978$	−17.4853	−0.559119
$979$	−0.000464039 0	−1.48308e−5 0
$980$	0	0
$981$	−4.84000	−0.154529
$982$	−33.6082	−1.07248
$983$	20.1860	0.643832	0.321916	−	0.946768i	$-0.395673\pi$
$983$	20.1860	0.643832	0.321916	+	0.946768i	$0.395673\pi$
$984$	18.4237	0.587325
$985$	0	0
$986$	1.58894	0.0506022
$987$	71.0079	2.26021
$988$	0	0
$989$	10.5194	0.334496
$990$	0	0
$991$	11.0566	0.351226	0.175613	−	0.984459i	$-0.443809\pi$
$991$	11.0566	0.351226	0.175613	+	0.984459i	$0.443809\pi$
$992$	5.07010	0.160976
$993$	19.2191	0.609900
$994$	9.80452	0.310981
$995$	0	0
$996$	−2.88004	−0.0912576
$997$	−31.2270	−0.988969	−0.494485	−	0.869186i	$-0.664643\pi$
$997$	−31.2270	−0.988969	−0.494485	+	0.869186i	$0.664643\pi$
$998$	−1.43413	−0.0453967
$999$	49.6480	1.57079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cd.1.3		9
5.4	even	2		1805.2.a.u.1.7		9
19.3	odd	18		475.2.l.b.351.3		18
19.13	odd	18		475.2.l.b.226.3		18
19.18	odd	2		9025.2.a.ce.1.7		9
95.3	even	36		475.2.u.c.199.5		36
95.13	even	36		475.2.u.c.74.2		36
95.22	even	36		475.2.u.c.199.2		36
95.32	even	36		475.2.u.c.74.5		36
95.79	odd	18		95.2.k.b.66.1	yes	18
95.89	odd	18		95.2.k.b.36.1	✓	18
95.94	odd	2		1805.2.a.t.1.3		9
285.89	even	18		855.2.bs.b.226.3		18
285.269	even	18		855.2.bs.b.541.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.1	✓	18	95.89	odd	18
95.2.k.b.66.1	yes	18	95.79	odd	18
475.2.l.b.226.3		18	19.13	odd	18
475.2.l.b.351.3		18	19.3	odd	18
475.2.u.c.74.2		36	95.13	even	36
475.2.u.c.74.5		36	95.32	even	36
475.2.u.c.199.2		36	95.22	even	36
475.2.u.c.199.5		36	95.3	even	36
855.2.bs.b.226.3		18	285.89	even	18
855.2.bs.b.541.3		18	285.269	even	18
1805.2.a.t.1.3		9	95.94	odd	2
1805.2.a.u.1.7		9	5.4	even	2
9025.2.a.cd.1.3		9	1.1	even	1	trivial
9025.2.a.ce.1.7		9	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.46231 q^{2} +1.51036 q^{3} +0.138346 q^{4} -2.20860 q^{6} -4.07172 q^{7} +2.72231 q^{8} -0.718827 q^{9} +O(q^{10})\)	\(q-1.46231 q^{2} +1.51036 q^{3} +0.138346 q^{4} -2.20860 q^{6} -4.07172 q^{7} +2.72231 q^{8} -0.718827 q^{9} -0.621006 q^{11} +0.208951 q^{12} -5.09329 q^{13} +5.95412 q^{14} -4.25755 q^{16} +0.266483 q^{17} +1.05115 q^{18} -6.14975 q^{21} +0.908102 q^{22} +5.84174 q^{23} +4.11166 q^{24} +7.44796 q^{26} -5.61675 q^{27} -0.563305 q^{28} -4.07754 q^{29} +6.48991 q^{31} +0.781227 q^{32} -0.937939 q^{33} -0.389681 q^{34} -0.0994465 q^{36} -8.83927 q^{37} -7.69267 q^{39} +4.48083 q^{41} +8.99283 q^{42} +1.80073 q^{43} -0.0859133 q^{44} -8.54242 q^{46} -11.5465 q^{47} -6.43041 q^{48} +9.57894 q^{49} +0.402485 q^{51} -0.704633 q^{52} -2.52292 q^{53} +8.21342 q^{54} -11.0845 q^{56} +5.96263 q^{58} -0.890444 q^{59} +2.16991 q^{61} -9.49025 q^{62} +2.92687 q^{63} +7.37271 q^{64} +1.37156 q^{66} -14.0788 q^{67} +0.0368668 q^{68} +8.82310 q^{69} +1.64668 q^{71} -1.95687 q^{72} -1.79675 q^{73} +12.9257 q^{74} +2.52856 q^{77} +11.2491 q^{78} -5.14647 q^{79} -6.32681 q^{81} -6.55236 q^{82} -13.7833 q^{83} -0.850790 q^{84} -2.63322 q^{86} -6.15854 q^{87} -1.69057 q^{88} +0.000747238 q^{89} +20.7385 q^{91} +0.808178 q^{92} +9.80207 q^{93} +16.8845 q^{94} +1.17993 q^{96} -10.4225 q^{97} -14.0074 q^{98} +0.446396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{3} + 6 q^{4} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 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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