LMFDB - Embedded newform 4225.2.a.bi.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4225,2,Mod(1,4225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4225, 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("4225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4225 = 5^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4225.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:	$33.7367948540$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4752.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 4x + 1 $ x^4 - 2x^3 - 3x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.21969$ of defining polynomial
Character	$\chi$	$=$	4225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21969 q^{2} -2.33225 q^{3} -0.512364 q^{4} +2.84461 q^{6} -3.60020 q^{7} +3.06430 q^{8} +2.43937 q^{9} +O(q^{10})$	\(q-1.21969 q^{2} -2.33225 q^{3} -0.512364 q^{4} +2.84461 q^{6} -3.60020 q^{7} +3.06430 q^{8} +2.43937 q^{9} +5.37182 q^{11} +1.19496 q^{12} +4.39111 q^{14} -2.71276 q^{16} +1.13186 q^{17} -2.97527 q^{18} +2.26795 q^{19} +8.39654 q^{21} -6.55193 q^{22} +3.89287 q^{23} -7.14670 q^{24} +1.30752 q^{27} +1.84461 q^{28} -0.0247279 q^{29} +5.46410 q^{31} -2.81988 q^{32} -12.5284 q^{33} -1.38051 q^{34} -1.24985 q^{36} +8.70406 q^{37} -2.76619 q^{38} +3.73205 q^{41} -10.2412 q^{42} +1.13186 q^{43} -2.75232 q^{44} -4.74809 q^{46} -2.58535 q^{47} +6.32681 q^{48} +5.96141 q^{49} -2.63977 q^{51} +4.43937 q^{53} -1.59476 q^{54} -11.0321 q^{56} -5.28942 q^{57} +0.0301603 q^{58} -0.171425 q^{59} +3.36023 q^{61} -6.66449 q^{62} -8.78222 q^{63} +8.86488 q^{64} +15.2807 q^{66} -6.39980 q^{67} -0.579922 q^{68} -9.07914 q^{69} -10.7973 q^{71} +7.47497 q^{72} +4.70308 q^{73} -10.6162 q^{74} -1.16202 q^{76} -19.3396 q^{77} -11.9826 q^{79} -10.3676 q^{81} -4.55193 q^{82} +12.1286 q^{83} -4.30209 q^{84} -1.38051 q^{86} +0.0576715 q^{87} +16.4608 q^{88} -16.1540 q^{89} -1.99457 q^{92} -12.7436 q^{93} +3.15332 q^{94} +6.57666 q^{96} -12.1682 q^{97} -7.27105 q^{98} +13.1039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9} + 10 q^{12} + 2 q^{14} + 2 q^{16} + 2 q^{17} - 20 q^{18} + 16 q^{19} + 4 q^{21} - 12 q^{22} + 10 q^{23} - 24 q^{24} + 2 q^{27} - 8 q^{28} + 8 q^{29} + 8 q^{31} - 4 q^{32} - 18 q^{33} - 4 q^{34} + 20 q^{36} + 2 q^{37} - 8 q^{38} + 8 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{44} + 16 q^{46} - 8 q^{47} + 28 q^{48} + 12 q^{49} + 4 q^{51} + 12 q^{53} - 16 q^{54} + 12 q^{56} + 14 q^{57} - 22 q^{58} + 12 q^{59} + 28 q^{61} - 4 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{66} - 30 q^{67} - 14 q^{68} - 16 q^{69} + 4 q^{71} - 12 q^{72} + 8 q^{73} - 10 q^{74} + 20 q^{76} - 18 q^{77} - 8 q^{79} - 8 q^{81} - 4 q^{82} + 12 q^{83} - 28 q^{84} - 4 q^{86} + 22 q^{87} + 18 q^{88} - 12 q^{89} - 22 q^{92} - 8 q^{93} - 32 q^{94} + 4 q^{96} - 2 q^{97} + 24 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9 + 10 * q^12 + 2 * q^14 + 2 * q^16 + 2 * q^17 - 20 * q^18 + 16 * q^19 + 4 * q^21 - 12 * q^22 + 10 * q^23 - 24 * q^24 + 2 * q^27 - 8 * q^28 + 8 * q^29 + 8 * q^31 - 4 * q^32 - 18 * q^33 - 4 * q^34 + 20 * q^36 + 2 * q^37 - 8 * q^38 + 8 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^44 + 16 * q^46 - 8 * q^47 + 28 * q^48 + 12 * q^49 + 4 * q^51 + 12 * q^53 - 16 * q^54 + 12 * q^56 + 14 * q^57 - 22 * q^58 + 12 * q^59 + 28 * q^61 - 4 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^66 - 30 * q^67 - 14 * q^68 - 16 * q^69 + 4 * q^71 - 12 * q^72 + 8 * q^73 - 10 * q^74 + 20 * q^76 - 18 * q^77 - 8 * q^79 - 8 * q^81 - 4 * q^82 + 12 * q^83 - 28 * q^84 - 4 * q^86 + 22 * q^87 + 18 * q^88 - 12 * q^89 - 22 * q^92 - 8 * q^93 - 32 * q^94 + 4 * q^96 - 2 * q^97 + 24 * q^98 + 24 * 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 $

$2$	−1.21969	−0.862449	−0.431224	−	0.902245i	$-0.641918\pi$
$2$	−1.21969	−0.862449	−0.431224	+	0.902245i	$0.641918\pi$
$3$	−2.33225	−1.34652	−0.673262	−	0.739404i	$-0.735107\pi$
$3$	−2.33225	−1.34652	−0.673262	+	0.739404i	$0.735107\pi$
$4$	−0.512364	−0.256182
$5$	0	0
$5$	0	0
$6$	2.84461	1.16131
$7$	−3.60020	−1.36075	−0.680373	−	0.732866i	$-0.738182\pi$
$7$	−3.60020	−1.36075	−0.680373	+	0.732866i	$0.738182\pi$
$8$	3.06430	1.08339
$9$	2.43937	0.813125
$10$	0	0
$11$	5.37182	1.61966	0.809832	−	0.586662i	$-0.199558\pi$
$11$	5.37182	1.61966	0.809832	+	0.586662i	$0.199558\pi$
$12$	1.19496	0.344955
$13$	0	0
$13$	0	0
$14$	4.39111	1.17357
$15$	0	0
$16$	−2.71276	−0.678189
$17$	1.13186	0.274515	0.137258	−	0.990535i	$-0.456171\pi$
$17$	1.13186	0.274515	0.137258	+	0.990535i	$0.456171\pi$
$18$	−2.97527	−0.701278
$19$	2.26795	0.520303	0.260152	−	0.965568i	$-0.416227\pi$
$19$	2.26795	0.520303	0.260152	+	0.965568i	$0.416227\pi$
$20$	0	0
$21$	8.39654	1.83228
$22$	−6.55193	−1.39688
$23$	3.89287	0.811720	0.405860	−	0.913935i	$-0.366972\pi$
$23$	3.89287	0.811720	0.405860	+	0.913935i	$0.366972\pi$
$24$	−7.14670	−1.45881
$25$	0	0
$26$	0	0
$27$	1.30752	0.251632
$28$	1.84461	0.348599
$29$	−0.0247279	−0.00459185	−0.00229593	−	0.999997i	$-0.500731\pi$
$29$	−0.0247279	−0.00459185	−0.00229593	+	0.999997i	$0.500731\pi$
$30$	0	0
$31$	5.46410	0.981382	0.490691	−	0.871334i	$-0.336744\pi$
$31$	5.46410	0.981382	0.490691	+	0.871334i	$0.336744\pi$
$32$	−2.81988	−0.498490
$33$	−12.5284	−2.18091
$34$	−1.38051	−0.236755
$35$	0	0
$36$	−1.24985	−0.208308
$37$	8.70406	1.43094	0.715470	−	0.698644i	$-0.246213\pi$
$37$	8.70406	1.43094	0.715470	+	0.698644i	$0.246213\pi$
$38$	−2.76619	−0.448735
$39$	0	0
$40$	0	0
$41$	3.73205	0.582848	0.291424	−	0.956594i	$-0.405871\pi$
$41$	3.73205	0.582848	0.291424	+	0.956594i	$0.405871\pi$
$42$	−10.2412	−1.58024
$43$	1.13186	0.172606	0.0863031	−	0.996269i	$-0.472495\pi$
$43$	1.13186	0.172606	0.0863031	+	0.996269i	$0.472495\pi$
$44$	−2.75232	−0.414929
$45$	0	0
$46$	−4.74809	−0.700067
$47$	−2.58535	−0.377113	−0.188556	−	0.982062i	$-0.560381\pi$
$47$	−2.58535	−0.377113	−0.188556	+	0.982062i	$0.560381\pi$
$48$	6.32681	0.913197
$49$	5.96141	0.851630
$50$	0	0
$51$	−2.63977	−0.369641
$52$	0	0
$53$	4.43937	0.609795	0.304897	−	0.952385i	$-0.401378\pi$
$53$	4.43937	0.609795	0.304897	+	0.952385i	$0.401378\pi$
$54$	−1.59476	−0.217020
$55$	0	0
$56$	−11.0321	−1.47422
$57$	−5.28942	−0.700600
$58$	0.0301603	0.00396024
$59$	−0.171425	−0.0223176	−0.0111588	−	0.999938i	$-0.503552\pi$
$59$	−0.171425	−0.0223176	−0.0111588	+	0.999938i	$0.503552\pi$
$60$	0	0
$61$	3.36023	0.430234	0.215117	−	0.976588i	$-0.430987\pi$
$61$	3.36023	0.430234	0.215117	+	0.976588i	$0.430987\pi$
$62$	−6.66449	−0.846391
$63$	−8.78222	−1.10646
$64$	8.86488	1.10811
$65$	0	0
$66$	15.2807	1.88093
$67$	−6.39980	−0.781861	−0.390930	−	0.920420i	$-0.627847\pi$
$67$	−6.39980	−0.781861	−0.390930	+	0.920420i	$0.627847\pi$
$68$	−0.579922	−0.0703258
$69$	−9.07914	−1.09300
$70$	0	0
$71$	−10.7973	−1.28141	−0.640703	−	0.767788i	$-0.721357\pi$
$71$	−10.7973	−1.28141	−0.640703	+	0.767788i	$0.721357\pi$
$72$	7.47497	0.880933
$73$	4.70308	0.550454	0.275227	−	0.961379i	$-0.411247\pi$
$73$	4.70308	0.550454	0.275227	+	0.961379i	$0.411247\pi$
$74$	−10.6162	−1.23411
$75$	0	0
$76$	−1.16202	−0.133292
$77$	−19.3396	−2.20395
$78$	0	0
$79$	−11.9826	−1.34815	−0.674075	−	0.738663i	$-0.735457\pi$
$79$	−11.9826	−1.34815	−0.674075	+	0.738663i	$0.735457\pi$
$80$	0	0
$81$	−10.3676	−1.15195
$82$	−4.55193	−0.502677
$83$	12.1286	1.33129	0.665643	−	0.746270i	$-0.268157\pi$
$83$	12.1286	1.33129	0.665643	+	0.746270i	$0.268157\pi$
$84$	−4.30209	−0.469396
$85$	0	0
$86$	−1.38051	−0.148864
$87$	0.0576715	0.00618303
$88$	16.4608	1.75473
$89$	−16.1540	−1.71232	−0.856162	−	0.516707i	$-0.827158\pi$
$89$	−16.1540	−1.71232	−0.856162	+	0.516707i	$0.827158\pi$
$90$	0	0
$91$	0	0
$92$	−1.99457	−0.207948
$93$	−12.7436	−1.32145
$94$	3.15332	0.325240
$95$	0	0
$96$	6.57666	0.671228
$97$	−12.1682	−1.23549	−0.617745	−	0.786379i	$-0.711954\pi$
$97$	−12.1682	−1.23549	−0.617745	+	0.786379i	$0.711954\pi$
$98$	−7.27105	−0.734487
$99$	13.1039	1.31699
$100$	0	0
$101$	−4.05441	−0.403429	−0.201714	−	0.979444i	$-0.564651\pi$
$101$	−4.05441	−0.403429	−0.201714	+	0.979444i	$0.564651\pi$
$102$	3.21969	0.318797
$103$	17.9035	1.76408	0.882041	−	0.471173i	$-0.156169\pi$
$103$	17.9035	1.76408	0.882041	+	0.471173i	$0.156169\pi$
$104$	0	0
$105$	0	0
$106$	−5.41465	−0.525917
$107$	9.13186	0.882810	0.441405	−	0.897308i	$-0.354480\pi$
$107$	9.13186	0.882810	0.441405	+	0.897308i	$0.354480\pi$
$108$	−0.669925	−0.0644636
$109$	7.37605	0.706498	0.353249	−	0.935529i	$-0.385077\pi$
$109$	7.37605	0.706498	0.353249	+	0.935529i	$0.385077\pi$
$110$	0	0
$111$	−20.3000	−1.92679
$112$	9.76645	0.922843
$113$	−7.07588	−0.665643	−0.332821	−	0.942990i	$-0.608001\pi$
$113$	−7.07588	−0.665643	−0.332821	+	0.942990i	$0.608001\pi$
$114$	6.45143	0.604232
$115$	0	0
$116$	0.0126697	0.00117635
$117$	0	0
$118$	0.209084	0.0192478
$119$	−4.07490	−0.373545
$120$	0	0
$121$	17.8564	1.62331
$122$	−4.09843	−0.371055
$123$	−8.70406	−0.784819
$124$	−2.79961	−0.251412
$125$	0	0
$126$	10.7116	0.954262
$127$	11.4361	1.01479	0.507395	−	0.861713i	$-0.330608\pi$
$127$	11.4361	1.01479	0.507395	+	0.861713i	$0.330608\pi$
$128$	−5.17262	−0.457199
$129$	−2.63977	−0.232418
$130$	0	0
$131$	−10.5680	−0.923328	−0.461664	−	0.887055i	$-0.652747\pi$
$131$	−10.5680	−0.923328	−0.461664	+	0.887055i	$0.652747\pi$
$132$	6.41910	0.558711
$133$	−8.16506	−0.708001
$134$	7.80576	0.674315
$135$	0	0
$136$	3.46834	0.297408
$137$	−3.78672	−0.323522	−0.161761	−	0.986830i	$-0.551717\pi$
$137$	−3.78672	−0.323522	−0.161761	+	0.986830i	$0.551717\pi$
$138$	11.0737	0.942656
$139$	2.01386	0.170814	0.0854068	−	0.996346i	$-0.472781\pi$
$139$	2.01386	0.170814	0.0854068	+	0.996346i	$0.472781\pi$
$140$	0	0
$141$	6.02968	0.507791
$142$	13.1694	1.10515
$143$	0	0
$144$	−6.61742	−0.551452
$145$	0	0
$146$	−5.73629	−0.474739
$147$	−13.9035	−1.14674
$148$	−4.45965	−0.366581
$149$	−5.51780	−0.452035	−0.226018	−	0.974123i	$-0.572571\pi$
$149$	−5.51780	−0.452035	−0.226018	+	0.974123i	$0.572571\pi$
$150$	0	0
$151$	−4.88961	−0.397911	−0.198956	−	0.980009i	$-0.563755\pi$
$151$	−4.88961	−0.397911	−0.198956	+	0.980009i	$0.563755\pi$
$152$	6.94967	0.563693
$153$	2.76102	0.223215
$154$	23.5882	1.90079
$155$	0	0
$156$	0	0
$157$	−10.0405	−0.801323	−0.400661	−	0.916226i	$-0.631220\pi$
$157$	−10.0405	−0.801323	−0.400661	+	0.916226i	$0.631220\pi$
$158$	14.6150	1.16271
$159$	−10.3537	−0.821103
$160$	0	0
$161$	−14.0151	−1.10454
$162$	12.6452	0.993501
$163$	−6.78124	−0.531148	−0.265574	−	0.964090i	$-0.585561\pi$
$163$	−6.78124	−0.531148	−0.265574	+	0.964090i	$0.585561\pi$
$164$	−1.91217	−0.149315
$165$	0	0
$166$	−14.7931	−1.14817
$167$	−10.4898	−0.811726	−0.405863	−	0.913934i	$-0.633029\pi$
$167$	−10.4898	−0.811726	−0.405863	+	0.913934i	$0.633029\pi$
$168$	25.7295	1.98507
$169$	0	0
$170$	0	0
$171$	5.53238	0.423071
$172$	−0.579922	−0.0442186
$173$	4.45845	0.338970	0.169485	−	0.985533i	$-0.445790\pi$
$173$	4.45845	0.338970	0.169485	+	0.985533i	$0.445790\pi$
$174$	−0.0703412	−0.00533255
$175$	0	0
$176$	−14.5724	−1.09844
$177$	0.399804	0.0300511
$178$	19.7029	1.47679
$179$	18.6313	1.39257	0.696284	−	0.717766i	$-0.254835\pi$
$179$	18.6313	1.39257	0.696284	+	0.717766i	$0.254835\pi$
$180$	0	0
$181$	18.0900	1.34462	0.672310	−	0.740270i	$-0.265302\pi$
$181$	18.0900	1.34462	0.672310	+	0.740270i	$0.265302\pi$
$182$	0	0
$183$	−7.83690	−0.579320
$184$	11.9289	0.879412
$185$	0	0
$186$	15.5432	1.13969
$187$	6.08012	0.444622
$188$	1.32464	0.0966095
$189$	−4.70732	−0.342407
$190$	0	0
$191$	27.3363	1.97799	0.988994	−	0.147958i	$-0.0472701\pi$
$191$	27.3363	1.97799	0.988994	+	0.147958i	$0.0472701\pi$
$192$	−20.6751	−1.49210
$193$	−21.7674	−1.56685	−0.783425	−	0.621486i	$-0.786529\pi$
$193$	−21.7674	−1.56685	−0.783425	+	0.621486i	$0.786529\pi$
$194$	14.8413	1.06555
$195$	0	0
$196$	−3.05441	−0.218172
$197$	1.69672	0.120886	0.0604432	−	0.998172i	$-0.480749\pi$
$197$	1.69672	0.120886	0.0604432	+	0.998172i	$0.480749\pi$
$198$	−15.9826	−1.13583
$199$	25.3255	1.79527	0.897637	−	0.440735i	$-0.145282\pi$
$199$	25.3255	1.79527	0.897637	+	0.440735i	$0.145282\pi$
$200$	0	0
$201$	14.9259	1.05279
$202$	4.94511	0.347937
$203$	0.0890252	0.00624834
$204$	1.35252	0.0946954
$205$	0	0
$206$	−21.8366	−1.52143
$207$	9.49617	0.660030
$208$	0	0
$209$	12.1830	0.842716
$210$	0	0
$211$	−0.335507	−0.0230973	−0.0115486	−	0.999933i	$-0.503676\pi$
$211$	−0.335507	−0.0230973	−0.0115486	+	0.999933i	$0.503676\pi$
$212$	−2.27458	−0.156218
$213$	25.1820	1.72544
$214$	−11.1380	−0.761378
$215$	0	0
$216$	4.00663	0.272616
$217$	−19.6718	−1.33541
$218$	−8.99648	−0.609318
$219$	−10.9688	−0.741200
$220$	0	0
$221$	0	0
$222$	24.7597	1.66176
$223$	12.2968	0.823452	0.411726	−	0.911308i	$-0.364926\pi$
$223$	12.2968	0.823452	0.411726	+	0.911308i	$0.364926\pi$
$224$	10.1521	0.678318
$225$	0	0
$226$	8.63036	0.574083
$227$	7.63227	0.506571	0.253286	−	0.967392i	$-0.418489\pi$
$227$	7.63227	0.506571	0.253286	+	0.967392i	$0.418489\pi$
$228$	2.71011	0.179481
$229$	−14.4008	−0.951631	−0.475815	−	0.879545i	$-0.657847\pi$
$229$	−14.4008	−0.951631	−0.475815	+	0.879545i	$0.657847\pi$
$230$	0	0
$231$	45.1047	2.96767
$232$	−0.0757736	−0.00497478
$233$	−9.49617	−0.622115	−0.311057	−	0.950391i	$-0.600683\pi$
$233$	−9.49617	−0.622115	−0.311057	+	0.950391i	$0.600683\pi$
$234$	0	0
$235$	0	0
$236$	0.0878318	0.00571736
$237$	27.9464	1.81531
$238$	4.97010	0.322164
$239$	−19.9143	−1.28815	−0.644076	−	0.764962i	$-0.722758\pi$
$239$	−19.9143	−1.28815	−0.644076	+	0.764962i	$0.722758\pi$
$240$	0	0
$241$	23.2664	1.49872	0.749360	−	0.662163i	$-0.230361\pi$
$241$	23.2664	1.49872	0.749360	+	0.662163i	$0.230361\pi$
$242$	−21.7792	−1.40002
$243$	20.2572	1.29950
$244$	−1.72166	−0.110218
$245$	0	0
$246$	10.6162	0.676866
$247$	0	0
$248$	16.7436	1.06322
$249$	−28.2869	−1.79261
$250$	0	0
$251$	11.8402	0.747344	0.373672	−	0.927561i	$-0.378099\pi$
$251$	11.8402	0.747344	0.373672	+	0.927561i	$0.378099\pi$
$252$	4.49969	0.283454
$253$	20.9118	1.31471
$254$	−13.9485	−0.875205
$255$	0	0
$256$	−11.4208	−0.713800
$257$	5.55002	0.346201	0.173100	−	0.984904i	$-0.444621\pi$
$257$	5.55002	0.346201	0.173100	+	0.984904i	$0.444621\pi$
$258$	3.21969	0.200449
$259$	−31.3363	−1.94714
$260$	0	0
$261$	−0.0603205	−0.00373375
$262$	12.8896	0.796323
$263$	−6.85967	−0.422985	−0.211493	−	0.977380i	$-0.567832\pi$
$263$	−6.85967	−0.422985	−0.211493	+	0.977380i	$0.567832\pi$
$264$	−38.3907	−2.36279
$265$	0	0
$266$	9.95882	0.610614
$267$	37.6752	2.30568
$268$	3.27903	0.200299
$269$	−1.42199	−0.0867001	−0.0433501	−	0.999060i	$-0.513803\pi$
$269$	−1.42199	−0.0867001	−0.0433501	+	0.999060i	$0.513803\pi$
$270$	0	0
$271$	−9.96947	−0.605602	−0.302801	−	0.953054i	$-0.597922\pi$
$271$	−9.96947	−0.605602	−0.302801	+	0.953054i	$0.597922\pi$
$272$	−3.07045	−0.186173
$273$	0	0
$274$	4.61862	0.279021
$275$	0	0
$276$	4.65182	0.280007
$277$	17.5237	1.05290	0.526449	−	0.850206i	$-0.323523\pi$
$277$	17.5237	1.05290	0.526449	+	0.850206i	$0.323523\pi$
$278$	−2.45628	−0.147318
$279$	13.3290	0.797986
$280$	0	0
$281$	10.7352	0.640406	0.320203	−	0.947349i	$-0.396249\pi$
$281$	10.7352	0.640406	0.320203	+	0.947349i	$0.396249\pi$
$282$	−7.35433	−0.437944
$283$	−1.31838	−0.0783698	−0.0391849	−	0.999232i	$-0.512476\pi$
$283$	−1.31838	−0.0783698	−0.0391849	+	0.999232i	$0.512476\pi$
$284$	5.53216	0.328273
$285$	0	0
$286$	0	0
$287$	−13.4361	−0.793109
$288$	−6.87875	−0.405334
$289$	−15.7189	−0.924641
$290$	0	0
$291$	28.3792	1.66362
$292$	−2.40969	−0.141016
$293$	−18.7427	−1.09496	−0.547479	−	0.836820i	$-0.684412\pi$
$293$	−18.7427	−1.09496	−0.547479	+	0.836820i	$0.684412\pi$
$294$	16.9579	0.989004
$295$	0	0
$296$	26.6718	1.55027
$297$	7.02375	0.407559
$298$	6.72998	0.389857
$299$	0	0
$300$	0	0
$301$	−4.07490	−0.234873
$302$	5.96380	0.343178
$303$	9.45589	0.543226
$304$	−6.15239	−0.352864
$305$	0	0
$306$	−3.36758	−0.192512
$307$	−14.3043	−0.816387	−0.408194	−	0.912895i	$-0.633841\pi$
$307$	−14.3043	−0.816387	−0.408194	+	0.912895i	$0.633841\pi$
$308$	9.90891	0.564612
$309$	−41.7553	−2.37538
$310$	0	0
$311$	2.76102	0.156563	0.0782815	−	0.996931i	$-0.475057\pi$
$311$	2.76102	0.156563	0.0782815	+	0.996931i	$0.475057\pi$
$312$	0	0
$313$	16.3858	0.926179	0.463090	−	0.886311i	$-0.346741\pi$
$313$	16.3858	0.926179	0.463090	+	0.886311i	$0.346741\pi$
$314$	12.2463	0.691100
$315$	0	0
$316$	6.13946	0.345372
$317$	−1.78575	−0.100297	−0.0501487	−	0.998742i	$-0.515970\pi$
$317$	−1.78575	−0.100297	−0.0501487	+	0.998742i	$0.515970\pi$
$318$	12.6283	0.708159
$319$	−0.132834	−0.00743725
$320$	0	0
$321$	−21.2977	−1.18872
$322$	17.0940	0.952613
$323$	2.56699	0.142831
$324$	5.31197	0.295110
$325$	0	0
$326$	8.27099	0.458088
$327$	−17.2028	−0.951316
$328$	11.4361	0.631454
$329$	9.30778	0.513155
$330$	0	0
$331$	7.22440	0.397089	0.198545	−	0.980092i	$-0.436379\pi$
$331$	7.22440	0.397089	0.198545	+	0.980092i	$0.436379\pi$
$332$	−6.21425	−0.341052
$333$	21.2325	1.16353
$334$	12.7943	0.700072
$335$	0	0
$336$	−22.7778	−1.24263
$337$	4.36219	0.237624	0.118812	−	0.992917i	$-0.462091\pi$
$337$	4.36219	0.237624	0.118812	+	0.992917i	$0.462091\pi$
$338$	0	0
$339$	16.5027	0.896303
$340$	0	0
$341$	29.3521	1.58951
$342$	−6.74777	−0.364877
$343$	3.73913	0.201894
$344$	3.46834	0.187000
$345$	0	0
$346$	−5.43792	−0.292344
$347$	26.7072	1.43372	0.716858	−	0.697219i	$-0.245580\pi$
$347$	26.7072	1.43372	0.716858	+	0.697219i	$0.245580\pi$
$348$	−0.0295488	−0.00158398
$349$	23.5711	1.26173	0.630865	−	0.775892i	$-0.282700\pi$
$349$	23.5711	1.26173	0.630865	+	0.775892i	$0.282700\pi$
$350$	0	0
$351$	0	0
$352$	−15.1479	−0.807385
$353$	−5.73727	−0.305364	−0.152682	−	0.988275i	$-0.548791\pi$
$353$	−5.73727	−0.305364	−0.152682	+	0.988275i	$0.548791\pi$
$354$	−0.487636	−0.0259176
$355$	0	0
$356$	8.27675	0.438667
$357$	9.50367	0.502988
$358$	−22.7243	−1.20102
$359$	−24.7583	−1.30669	−0.653347	−	0.757059i	$-0.726636\pi$
$359$	−24.7583	−1.30669	−0.653347	+	0.757059i	$0.726636\pi$
$360$	0	0
$361$	−13.8564	−0.729285
$362$	−22.0641	−1.15967
$363$	−41.6455	−2.18582
$364$	0	0
$365$	0	0
$366$	9.55856	0.499634
$367$	−26.0535	−1.35998	−0.679992	−	0.733220i	$-0.738017\pi$
$367$	−26.0535	−1.35998	−0.679992	+	0.733220i	$0.738017\pi$
$368$	−10.5604	−0.550499
$369$	9.10387	0.473928
$370$	0	0
$371$	−15.9826	−0.829776
$372$	6.52938	0.338532
$373$	−13.2045	−0.683702	−0.341851	−	0.939754i	$-0.611054\pi$
$373$	−13.2045	−0.683702	−0.341851	+	0.939754i	$0.611054\pi$
$374$	−7.41584	−0.383464
$375$	0	0
$376$	−7.92229	−0.408561
$377$	0	0
$378$	5.74146	0.295309
$379$	25.9977	1.33541	0.667707	−	0.744425i	$-0.267276\pi$
$379$	25.9977	1.33541	0.667707	+	0.744425i	$0.267276\pi$
$380$	0	0
$381$	−26.6718	−1.36644
$382$	−33.3418	−1.70591
$383$	9.60020	0.490547	0.245274	−	0.969454i	$-0.421122\pi$
$383$	9.60020	0.490547	0.245274	+	0.969454i	$0.421122\pi$
$384$	12.0638	0.615629
$385$	0	0
$386$	26.5494	1.35133
$387$	2.76102	0.140350
$388$	6.23453	0.316510
$389$	5.63129	0.285518	0.142759	−	0.989758i	$-0.454403\pi$
$389$	5.63129	0.285518	0.142759	+	0.989758i	$0.454403\pi$
$390$	0	0
$391$	4.40617	0.222829
$392$	18.2675	0.922650
$393$	24.6471	1.24328
$394$	−2.06947	−0.104258
$395$	0	0
$396$	−6.71395	−0.337389
$397$	16.7658	0.841452	0.420726	−	0.907188i	$-0.361775\pi$
$397$	16.7658	0.841452	0.420726	+	0.907188i	$0.361775\pi$
$398$	−30.8891	−1.54833
$399$	19.0429	0.953339
$400$	0	0
$401$	−13.8780	−0.693036	−0.346518	−	0.938043i	$-0.612636\pi$
$401$	−13.8780	−0.693036	−0.346518	+	0.938043i	$0.612636\pi$
$402$	−18.2050	−0.907980
$403$	0	0
$404$	2.07733	0.103351
$405$	0	0
$406$	−0.108583	−0.00538888
$407$	46.7566	2.31764
$408$	−8.08903	−0.400466
$409$	29.4251	1.45498	0.727489	−	0.686120i	$-0.240687\pi$
$409$	29.4251	1.45498	0.727489	+	0.686120i	$0.240687\pi$
$410$	0	0
$411$	8.83157	0.435629
$412$	−9.17310	−0.451926
$413$	0.617162	0.0303686
$414$	−11.5824	−0.569242
$415$	0	0
$416$	0	0
$417$	−4.69683	−0.230005
$418$	−14.8595	−0.726800
$419$	6.96793	0.340406	0.170203	−	0.985409i	$-0.445558\pi$
$419$	6.96793	0.340406	0.170203	+	0.985409i	$0.445558\pi$
$420$	0	0
$421$	7.12125	0.347069	0.173534	−	0.984828i	$-0.444481\pi$
$421$	7.12125	0.347069	0.173534	+	0.984828i	$0.444481\pi$
$422$	0.409213	0.0199202
$423$	−6.30664	−0.306640
$424$	13.6036	0.660647
$425$	0	0
$426$	−30.7142	−1.48811
$427$	−12.0975	−0.585439
$428$	−4.67883	−0.226160
$429$	0	0
$430$	0	0
$431$	30.2144	1.45537	0.727687	−	0.685909i	$-0.240595\pi$
$431$	30.2144	1.45537	0.727687	+	0.685909i	$0.240595\pi$
$432$	−3.54698	−0.170654
$433$	−1.20013	−0.0576745	−0.0288373	−	0.999584i	$-0.509180\pi$
$433$	−1.20013	−0.0576745	−0.0288373	+	0.999584i	$0.509180\pi$
$434$	23.9935	1.15172
$435$	0	0
$436$	−3.77922	−0.180992
$437$	8.82884	0.422341
$438$	13.3784	0.639247
$439$	−16.5541	−0.790084	−0.395042	−	0.918663i	$-0.629270\pi$
$439$	−16.5541	−0.790084	−0.395042	+	0.918663i	$0.629270\pi$
$440$	0	0
$441$	14.5421	0.692481
$442$	0	0
$443$	−4.55949	−0.216628	−0.108314	−	0.994117i	$-0.534545\pi$
$443$	−4.55949	−0.216628	−0.108314	+	0.994117i	$0.534545\pi$
$444$	10.4010	0.493610
$445$	0	0
$446$	−14.9982	−0.710185
$447$	12.8689	0.608676
$448$	−31.9153	−1.50786
$449$	13.8522	0.653724	0.326862	−	0.945072i	$-0.394009\pi$
$449$	13.8522	0.653724	0.326862	+	0.945072i	$0.394009\pi$
$450$	0	0
$451$	20.0479	0.944018
$452$	3.62542	0.170526
$453$	11.4038	0.535796
$454$	−9.30897	−0.436892
$455$	0	0
$456$	−16.2083	−0.759025
$457$	−40.1146	−1.87648	−0.938240	−	0.345984i	$-0.887545\pi$
$457$	−40.1146	−1.87648	−0.938240	+	0.345984i	$0.887545\pi$
$458$	17.5644	0.820733
$459$	1.47992	0.0690768
$460$	0	0
$461$	−7.53900	−0.351126	−0.175563	−	0.984468i	$-0.556175\pi$
$461$	−7.53900	−0.351126	−0.175563	+	0.984468i	$0.556175\pi$
$462$	−55.0136	−2.55946
$463$	−23.3031	−1.08299	−0.541494	−	0.840705i	$-0.682141\pi$
$463$	−23.3031	−1.08299	−0.541494	+	0.840705i	$0.682141\pi$
$464$	0.0670807	0.00311414
$465$	0	0
$466$	11.5824	0.536542
$467$	22.6297	1.04718	0.523589	−	0.851971i	$-0.324593\pi$
$467$	22.6297	1.04718	0.523589	+	0.851971i	$0.324593\pi$
$468$	0	0
$469$	23.0405	1.06391
$470$	0	0
$471$	23.4170	1.07900
$472$	−0.525296	−0.0241787
$473$	6.08012	0.279564
$474$	−34.0859	−1.56562
$475$	0	0
$476$	2.08783	0.0956956
$477$	10.8293	0.495839
$478$	24.2893	1.11096
$479$	20.6448	0.943286	0.471643	−	0.881790i	$-0.343661\pi$
$479$	20.6448	0.943286	0.471643	+	0.881790i	$0.343661\pi$
$480$	0	0
$481$	0	0
$482$	−28.3777	−1.29257
$483$	32.6867	1.48730
$484$	−9.14898	−0.415863
$485$	0	0
$486$	−24.7074	−1.12075
$487$	−3.03605	−0.137576	−0.0687882	−	0.997631i	$-0.521913\pi$
$487$	−3.03605	−0.137576	−0.0687882	+	0.997631i	$0.521913\pi$
$488$	10.2968	0.466112
$489$	15.8155	0.715203
$490$	0	0
$491$	10.6680	0.481441	0.240720	−	0.970595i	$-0.422616\pi$
$491$	10.6680	0.481441	0.240720	+	0.970595i	$0.422616\pi$
$492$	4.45965	0.201056
$493$	−0.0279884	−0.00126053
$494$	0	0
$495$	0	0
$496$	−14.8228	−0.665562
$497$	38.8725	1.74367
$498$	34.5011	1.54603
$499$	33.9143	1.51821	0.759107	−	0.650966i	$-0.225636\pi$
$499$	33.9143	1.51821	0.759107	+	0.650966i	$0.225636\pi$
$500$	0	0
$501$	24.4648	1.09301
$502$	−14.4413	−0.644546
$503$	12.6276	0.563037	0.281518	−	0.959556i	$-0.409162\pi$
$503$	12.6276	0.563037	0.281518	+	0.959556i	$0.409162\pi$
$504$	−26.9113	−1.19873
$505$	0	0
$506$	−25.5058	−1.13387
$507$	0	0
$508$	−5.85945	−0.259971
$509$	−24.1526	−1.07055	−0.535273	−	0.844679i	$-0.679791\pi$
$509$	−24.1526	−1.07055	−0.535273	+	0.844679i	$0.679791\pi$
$510$	0	0
$511$	−16.9320	−0.749029
$512$	24.2750	1.07281
$513$	2.96539	0.130925
$514$	−6.76929	−0.298581
$515$	0	0
$516$	1.35252	0.0595414
$517$	−13.8880	−0.610796
$518$	38.2205	1.67931
$519$	−10.3982	−0.456431
$520$	0	0
$521$	−24.7521	−1.08441	−0.542205	−	0.840246i	$-0.682410\pi$
$521$	−24.7521	−1.08441	−0.542205	+	0.840246i	$0.682410\pi$
$522$	0.0735722	0.00322017
$523$	−37.0326	−1.61932	−0.809662	−	0.586897i	$-0.800350\pi$
$523$	−37.0326	−1.61932	−0.809662	+	0.586897i	$0.800350\pi$
$524$	5.41465	0.236540
$525$	0	0
$526$	8.36665	0.364803
$527$	6.18457	0.269404
$528$	33.9865	1.47907
$529$	−7.84554	−0.341111
$530$	0	0
$531$	−0.418169	−0.0181470
$532$	4.18348	0.181377
$533$	0	0
$534$	−45.9519	−1.98854
$535$	0	0
$536$	−19.6109	−0.847062
$537$	−43.4528	−1.87512
$538$	1.73438	0.0747744
$539$	32.0236	1.37935
$540$	0	0
$541$	−8.38144	−0.360346	−0.180173	−	0.983635i	$-0.557666\pi$
$541$	−8.38144	−0.360346	−0.180173	+	0.983635i	$0.557666\pi$
$542$	12.1596	0.522301
$543$	−42.1903	−1.81056
$544$	−3.19170	−0.136843
$545$	0	0
$546$	0	0
$547$	22.7842	0.974181	0.487091	−	0.873351i	$-0.338058\pi$
$547$	22.7842	0.974181	0.487091	+	0.873351i	$0.338058\pi$
$548$	1.94018	0.0828804
$549$	8.19687	0.349834
$550$	0	0
$551$	−0.0560816	−0.00238915
$552$	−27.8212	−1.18415
$553$	43.1398	1.83449
$554$	−21.3735	−0.908071
$555$	0	0
$556$	−1.03183	−0.0437594
$557$	28.1527	1.19287	0.596435	−	0.802662i	$-0.296583\pi$
$557$	28.1527	1.19287	0.596435	+	0.802662i	$0.296583\pi$
$558$	−16.2572	−0.688222
$559$	0	0
$560$	0	0
$561$	−14.1803	−0.598694
$562$	−13.0935	−0.552317
$563$	18.1303	0.764101	0.382050	−	0.924142i	$-0.375218\pi$
$563$	18.1303	0.764101	0.382050	+	0.924142i	$0.375218\pi$
$564$	−3.08939	−0.130087
$565$	0	0
$566$	1.60801	0.0675899
$567$	37.3253	1.56752
$568$	−33.0862	−1.38827
$569$	40.5985	1.70198	0.850988	−	0.525185i	$-0.176004\pi$
$569$	40.5985	1.70198	0.850988	+	0.525185i	$0.176004\pi$
$570$	0	0
$571$	24.7159	1.03433	0.517164	−	0.855886i	$-0.326988\pi$
$571$	24.7159	1.03433	0.517164	+	0.855886i	$0.326988\pi$
$572$	0	0
$573$	−63.7551	−2.66341
$574$	16.3879	0.684016
$575$	0	0
$576$	21.6248	0.901032
$577$	−23.0691	−0.960379	−0.480189	−	0.877165i	$-0.659432\pi$
$577$	−23.0691	−0.960379	−0.480189	+	0.877165i	$0.659432\pi$
$578$	19.1721	0.797456
$579$	50.7669	2.10980
$580$	0	0
$581$	−43.6653	−1.81154
$582$	−34.6137	−1.43478
$583$	23.8475	0.987662
$584$	14.4116	0.596358
$585$	0	0
$586$	22.8602	0.944345
$587$	20.3523	0.840030	0.420015	−	0.907517i	$-0.362025\pi$
$587$	20.3523	0.840030	0.420015	+	0.907517i	$0.362025\pi$
$588$	7.12364	0.293774
$589$	12.3923	0.510616
$590$	0	0
$591$	−3.95717	−0.162776
$592$	−23.6120	−0.970447
$593$	−10.3834	−0.426395	−0.213198	−	0.977009i	$-0.568388\pi$
$593$	−10.3834	−0.426395	−0.213198	+	0.977009i	$0.568388\pi$
$594$	−8.56677	−0.351499
$595$	0	0
$596$	2.82712	0.115803
$597$	−59.0652	−2.41738
$598$	0	0
$599$	−31.5965	−1.29100	−0.645499	−	0.763761i	$-0.723351\pi$
$599$	−31.5965	−1.29100	−0.645499	+	0.763761i	$0.723351\pi$
$600$	0	0
$601$	−43.8845	−1.79009	−0.895044	−	0.445979i	$-0.852856\pi$
$601$	−43.8845	−1.79009	−0.895044	+	0.445979i	$0.852856\pi$
$602$	4.97010	0.202566
$603$	−15.6115	−0.635750
$604$	2.50526	0.101938
$605$	0	0
$606$	−11.5332	−0.468505
$607$	−2.17540	−0.0882968	−0.0441484	−	0.999025i	$-0.514057\pi$
$607$	−2.17540	−0.0882968	−0.0441484	+	0.999025i	$0.514057\pi$
$608$	−6.39535	−0.259366
$609$	−0.207629	−0.00841354
$610$	0	0
$611$	0	0
$612$	−1.41465	−0.0571837
$613$	14.7620	0.596231	0.298116	−	0.954530i	$-0.403642\pi$
$613$	14.7620	0.596231	0.298116	+	0.954530i	$0.403642\pi$
$614$	17.4467	0.704092
$615$	0	0
$616$	−59.2622	−2.38774
$617$	20.2972	0.817134	0.408567	−	0.912728i	$-0.366029\pi$
$617$	20.2972	0.817134	0.408567	+	0.912728i	$0.366029\pi$
$618$	50.9284	2.04864
$619$	9.94207	0.399605	0.199803	−	0.979836i	$-0.435970\pi$
$619$	9.94207	0.399605	0.199803	+	0.979836i	$0.435970\pi$
$620$	0	0
$621$	5.09000	0.204255
$622$	−3.36758	−0.135028
$623$	58.1577	2.33004
$624$	0	0
$625$	0	0
$626$	−19.9855	−0.798782
$627$	−28.4138	−1.13474
$628$	5.14441	0.205284
$629$	9.85174	0.392815
$630$	0	0
$631$	0.973420	0.0387512	0.0193756	−	0.999812i	$-0.493832\pi$
$631$	0.973420	0.0387512	0.0193756	+	0.999812i	$0.493832\pi$
$632$	−36.7183	−1.46058
$633$	0.782485	0.0311010
$634$	2.17805	0.0865014
$635$	0	0
$636$	5.30487	0.210352
$637$	0	0
$638$	0.162015	0.00641425
$639$	−26.3387	−1.04194
$640$	0	0
$641$	−12.6209	−0.498497	−0.249249	−	0.968440i	$-0.580184\pi$
$641$	−12.6209	−0.498497	−0.249249	+	0.968440i	$0.580184\pi$
$642$	25.9766	1.02521
$643$	−9.96043	−0.392801	−0.196401	−	0.980524i	$-0.562925\pi$
$643$	−9.96043	−0.392801	−0.196401	+	0.980524i	$0.562925\pi$
$644$	7.18083	0.282964
$645$	0	0
$646$	−3.13092	−0.123185
$647$	36.2763	1.42617	0.713084	−	0.701079i	$-0.247298\pi$
$647$	36.2763	1.42617	0.713084	+	0.701079i	$0.247298\pi$
$648$	−31.7693	−1.24802
$649$	−0.920861	−0.0361470
$650$	0	0
$651$	45.8796	1.79816
$652$	3.47447	0.136071
$653$	−13.7554	−0.538289	−0.269145	−	0.963100i	$-0.586741\pi$
$653$	−13.7554	−0.538289	−0.269145	+	0.963100i	$0.586741\pi$
$654$	20.9820	0.820461
$655$	0	0
$656$	−10.1241	−0.395281
$657$	11.4726	0.447588
$658$	−11.3526	−0.442570
$659$	−2.58183	−0.100574	−0.0502869	−	0.998735i	$-0.516014\pi$
$659$	−2.58183	−0.100574	−0.0502869	+	0.998735i	$0.516014\pi$
$660$	0	0
$661$	24.8765	0.967582	0.483791	−	0.875183i	$-0.339259\pi$
$661$	24.8765	0.967582	0.483791	+	0.875183i	$0.339259\pi$
$662$	−8.81151	−0.342469
$663$	0	0
$664$	37.1656	1.44231
$665$	0	0
$666$	−25.8970	−1.00349
$667$	−0.0962625	−0.00372730
$668$	5.37460	0.207949
$669$	−28.6791	−1.10880
$670$	0	0
$671$	18.0506	0.696834
$672$	−23.6773	−0.913370
$673$	−43.3222	−1.66995	−0.834974	−	0.550289i	$-0.814517\pi$
$673$	−43.3222	−1.66995	−0.834974	+	0.550289i	$0.814517\pi$
$674$	−5.32051	−0.204938
$675$	0	0
$676$	0	0
$677$	41.3625	1.58969	0.794845	−	0.606813i	$-0.207552\pi$
$677$	41.3625	1.58969	0.794845	+	0.606813i	$0.207552\pi$
$678$	−20.1281	−0.773016
$679$	43.8078	1.68119
$680$	0	0
$681$	−17.8003	−0.682110
$682$	−35.8004	−1.37087
$683$	−2.62688	−0.100515	−0.0502574	−	0.998736i	$-0.516004\pi$
$683$	−2.62688	−0.100515	−0.0502574	+	0.998736i	$0.516004\pi$
$684$	−2.83459	−0.108383
$685$	0	0
$686$	−4.56057	−0.174123
$687$	33.5862	1.28139
$688$	−3.07045	−0.117060
$689$	0	0
$690$	0	0
$691$	−15.2753	−0.581099	−0.290550	−	0.956860i	$-0.593838\pi$
$691$	−15.2753	−0.581099	−0.290550	+	0.956860i	$0.593838\pi$
$692$	−2.28435	−0.0868380
$693$	−47.1765	−1.79209
$694$	−32.5744	−1.23651
$695$	0	0
$696$	0.176723	0.00669865
$697$	4.22414	0.160001
$698$	−28.7493	−1.08818
$699$	22.1474	0.837692
$700$	0	0
$701$	−48.1947	−1.82029	−0.910144	−	0.414292i	$-0.864029\pi$
$701$	−48.1947	−1.82029	−0.910144	+	0.414292i	$0.864029\pi$
$702$	0	0
$703$	19.7404	0.744522
$704$	47.6205	1.79477
$705$	0	0
$706$	6.99767	0.263361
$707$	14.5967	0.548964
$708$	−0.204845	−0.00769856
$709$	−38.8699	−1.45979	−0.729896	−	0.683559i	$-0.760431\pi$
$709$	−38.8699	−1.45979	−0.729896	+	0.683559i	$0.760431\pi$
$710$	0	0
$711$	−29.2301	−1.09621
$712$	−49.5008	−1.85512
$713$	21.2711	0.796607
$714$	−11.5915	−0.433801
$715$	0	0
$716$	−9.54600	−0.356751
$717$	46.4452	1.73453
$718$	30.1974	1.12696
$719$	6.61660	0.246758	0.123379	−	0.992360i	$-0.460627\pi$
$719$	6.61660	0.246758	0.123379	+	0.992360i	$0.460627\pi$
$720$	0	0
$721$	−64.4560	−2.40047
$722$	16.9005	0.628971
$723$	−54.2629	−2.01806
$724$	−9.26867	−0.344467
$725$	0	0
$726$	50.7945	1.88516
$727$	18.3735	0.681435	0.340717	−	0.940166i	$-0.389330\pi$
$727$	18.3735	0.681435	0.340717	+	0.940166i	$0.389330\pi$
$728$	0	0
$729$	−16.1420	−0.597853
$730$	0	0
$731$	1.28110	0.0473830
$732$	4.01534	0.148411
$733$	−0.791131	−0.0292211	−0.0146105	−	0.999893i	$-0.504651\pi$
$733$	−0.791131	−0.0292211	−0.0146105	+	0.999893i	$0.504651\pi$
$734$	31.7772	1.17292
$735$	0	0
$736$	−10.9774	−0.404634
$737$	−34.3786	−1.26635
$738$	−11.1039	−0.408739
$739$	31.1853	1.14717	0.573585	−	0.819146i	$-0.305552\pi$
$739$	31.1853	1.14717	0.573585	+	0.819146i	$0.305552\pi$
$740$	0	0
$741$	0	0
$742$	19.4938	0.715639
$743$	−5.56304	−0.204088	−0.102044	−	0.994780i	$-0.532538\pi$
$743$	−5.56304	−0.204088	−0.102044	+	0.994780i	$0.532538\pi$
$744$	−39.0503	−1.43165
$745$	0	0
$746$	16.1053	0.589658
$747$	29.5862	1.08250
$748$	−3.11523	−0.113904
$749$	−32.8765	−1.20128
$750$	0	0
$751$	−35.2097	−1.28482	−0.642410	−	0.766361i	$-0.722065\pi$
$751$	−35.2097	−1.28482	−0.642410	+	0.766361i	$0.722065\pi$
$752$	7.01343	0.255754
$753$	−27.6142	−1.00632
$754$	0	0
$755$	0	0
$756$	2.41186	0.0877186
$757$	−50.0446	−1.81890	−0.909451	−	0.415810i	$-0.863498\pi$
$757$	−50.0446	−1.81890	−0.909451	+	0.415810i	$0.863498\pi$
$758$	−31.7091	−1.15173
$759$	−48.7715	−1.77029
$760$	0	0
$761$	44.8209	1.62476	0.812379	−	0.583130i	$-0.198172\pi$
$761$	44.8209	1.62476	0.812379	+	0.583130i	$0.198172\pi$
$762$	32.5313	1.17848
$763$	−26.5552	−0.961364
$764$	−14.0061	−0.506725
$765$	0	0
$766$	−11.7092	−0.423072
$767$	0	0
$768$	26.6361	0.961148
$769$	−39.3633	−1.41948	−0.709739	−	0.704465i	$-0.751187\pi$
$769$	−39.3633	−1.41948	−0.709739	+	0.704465i	$0.751187\pi$
$770$	0	0
$771$	−12.9440	−0.466168
$772$	11.1528	0.401399
$773$	−48.7805	−1.75451	−0.877256	−	0.480022i	$-0.840629\pi$
$773$	−48.7805	−1.75451	−0.877256	+	0.480022i	$0.840629\pi$
$774$	−3.36758	−0.121045
$775$	0	0
$776$	−37.2869	−1.33852
$777$	73.0840	2.62188
$778$	−6.86841	−0.246244
$779$	8.46410	0.303258
$780$	0	0
$781$	−58.0013	−2.07545
$782$	−5.37415	−0.192179
$783$	−0.0323322	−0.00115546
$784$	−16.1718	−0.577566
$785$	0	0
$786$	−30.0618	−1.07227
$787$	−39.8608	−1.42088	−0.710442	−	0.703756i	$-0.751505\pi$
$787$	−39.8608	−1.42088	−0.710442	+	0.703756i	$0.751505\pi$
$788$	−0.869338	−0.0309689
$789$	15.9984	0.569559
$790$	0	0
$791$	25.4745	0.905771
$792$	40.1541	1.42682
$793$	0	0
$794$	−20.4490	−0.725709
$795$	0	0
$796$	−12.9759	−0.459917
$797$	−26.2118	−0.928470	−0.464235	−	0.885712i	$-0.653671\pi$
$797$	−26.2118	−0.928470	−0.464235	+	0.885712i	$0.653671\pi$
$798$	−23.2264	−0.822206
$799$	−2.92625	−0.103523
$800$	0	0
$801$	−39.4057	−1.39233
$802$	16.9269	0.597708
$803$	25.2641	0.891551
$804$	−7.64750	−0.269707
$805$	0	0
$806$	0	0
$807$	3.31643	0.116744
$808$	−12.4239	−0.437072
$809$	22.2136	0.780990	0.390495	−	0.920605i	$-0.372304\pi$
$809$	22.2136	0.780990	0.390495	+	0.920605i	$0.372304\pi$
$810$	0	0
$811$	19.0950	0.670515	0.335257	−	0.942127i	$-0.391177\pi$
$811$	19.0950	0.670515	0.335257	+	0.942127i	$0.391177\pi$
$812$	−0.0456133	−0.00160071
$813$	23.2513	0.815457
$814$	−57.0284	−1.99885
$815$	0	0
$816$	7.16104	0.250686
$817$	2.56699	0.0898076
$818$	−35.8894	−1.25484
$819$	0	0
$820$	0	0
$821$	−34.1584	−1.19214	−0.596068	−	0.802934i	$-0.703271\pi$
$821$	−34.1584	−1.19214	−0.596068	+	0.802934i	$0.703271\pi$
$822$	−10.7718	−0.375708
$823$	−4.07940	−0.142199	−0.0710995	−	0.997469i	$-0.522651\pi$
$823$	−4.07940	−0.142199	−0.0710995	+	0.997469i	$0.522651\pi$
$824$	54.8616	1.91119
$825$	0	0
$826$	−0.752744	−0.0261913
$827$	54.8780	1.90830	0.954148	−	0.299337i	$-0.0967654\pi$
$827$	54.8780	1.90830	0.954148	+	0.299337i	$0.0967654\pi$
$828$	−4.86550	−0.169088
$829$	8.14950	0.283044	0.141522	−	0.989935i	$-0.454800\pi$
$829$	8.14950	0.283044	0.141522	+	0.989935i	$0.454800\pi$
$830$	0	0
$831$	−40.8697	−1.41775
$832$	0	0
$833$	6.74745	0.233785
$834$	5.72866	0.198367
$835$	0	0
$836$	−6.24213	−0.215889
$837$	7.14441	0.246947
$838$	−8.49869	−0.293582
$839$	−21.8865	−0.755606	−0.377803	−	0.925886i	$-0.623320\pi$
$839$	−21.8865	−0.755606	−0.377803	+	0.925886i	$0.623320\pi$
$840$	0	0
$841$	−28.9994	−0.999979
$842$	−8.68570	−0.299329
$843$	−25.0370	−0.862321
$844$	0.171902	0.00591710
$845$	0	0
$846$	7.69213	0.264461
$847$	−64.2866	−2.20891
$848$	−12.0429	−0.413556
$849$	3.07480	0.105527
$850$	0	0
$851$	33.8838	1.16152
$852$	−12.9024	−0.442028
$853$	19.2240	0.658217	0.329108	−	0.944292i	$-0.393252\pi$
$853$	19.2240	0.658217	0.329108	+	0.944292i	$0.393252\pi$
$854$	14.7552	0.504911
$855$	0	0
$856$	27.9827	0.956430
$857$	27.8197	0.950302	0.475151	−	0.879904i	$-0.342393\pi$
$857$	27.8197	0.950302	0.475151	+	0.879904i	$0.342393\pi$
$858$	0	0
$859$	45.7355	1.56048	0.780238	−	0.625482i	$-0.215098\pi$
$859$	45.7355	1.56048	0.780238	+	0.625482i	$0.215098\pi$
$860$	0	0
$861$	31.3363	1.06794
$862$	−36.8521	−1.25519
$863$	−54.8186	−1.86605	−0.933024	−	0.359814i	$-0.882840\pi$
$863$	−54.8186	−1.86605	−0.933024	+	0.359814i	$0.882840\pi$
$864$	−3.68705	−0.125436
$865$	0	0
$866$	1.46378	0.0497413
$867$	36.6604	1.24505
$868$	10.0791	0.342108
$869$	−64.3684	−2.18355
$870$	0	0
$871$	0	0
$872$	22.6024	0.765415
$873$	−29.6827	−1.00461
$874$	−10.7684	−0.364247
$875$	0	0
$876$	5.61999	0.189882
$877$	27.3794	0.924537	0.462269	−	0.886740i	$-0.347036\pi$
$877$	27.3794	0.924537	0.462269	+	0.886740i	$0.347036\pi$
$878$	20.1908	0.681407
$879$	43.7125	1.47439
$880$	0	0
$881$	−34.4426	−1.16040	−0.580200	−	0.814474i	$-0.697026\pi$
$881$	−34.4426	−1.16040	−0.580200	+	0.814474i	$0.697026\pi$
$882$	−17.7368	−0.597230
$883$	17.3592	0.584183	0.292092	−	0.956390i	$-0.405649\pi$
$883$	17.3592	0.584183	0.292092	+	0.956390i	$0.405649\pi$
$884$	0	0
$885$	0	0
$886$	5.56115	0.186831
$887$	31.1427	1.04567	0.522835	−	0.852434i	$-0.324874\pi$
$887$	31.1427	1.04567	0.522835	+	0.852434i	$0.324874\pi$
$888$	−62.2053	−2.08747
$889$	−41.1722	−1.38087
$890$	0	0
$891$	−55.6927	−1.86578
$892$	−6.30042	−0.210954
$893$	−5.86345	−0.196213
$894$	−15.6960	−0.524952
$895$	0	0
$896$	18.6224	0.622132
$897$	0	0
$898$	−16.8953	−0.563804
$899$	−0.135116	−0.00450636
$900$	0	0
$901$	5.02473	0.167398
$902$	−24.4521	−0.814167
$903$	9.50367	0.316262
$904$	−21.6826	−0.721152
$905$	0	0
$906$	−13.9090	−0.462097
$907$	−17.6057	−0.584587	−0.292294	−	0.956329i	$-0.594418\pi$
$907$	−17.6057	−0.584587	−0.292294	+	0.956329i	$0.594418\pi$
$908$	−3.91050	−0.129774
$909$	−9.89022	−0.328038
$910$	0	0
$911$	50.0232	1.65734	0.828671	−	0.559737i	$-0.189098\pi$
$911$	50.0232	1.65734	0.828671	+	0.559737i	$0.189098\pi$
$912$	14.3489	0.475139
$913$	65.1526	2.15624
$914$	48.9272	1.61837
$915$	0	0
$916$	7.37844	0.243791
$917$	38.0468	1.25641
$918$	−1.80504	−0.0595752
$919$	−7.61556	−0.251214	−0.125607	−	0.992080i	$-0.540088\pi$
$919$	−7.61556	−0.251214	−0.125607	+	0.992080i	$0.540088\pi$
$920$	0	0
$921$	33.3611	1.09928
$922$	9.19522	0.302828
$923$	0	0
$924$	−23.1100	−0.760264
$925$	0	0
$926$	28.4225	0.934022
$927$	43.6733	1.43442
$928$	0.0697297	0.00228899
$929$	−14.1239	−0.463391	−0.231695	−	0.972788i	$-0.574427\pi$
$929$	−14.1239	−0.463391	−0.231695	+	0.972788i	$0.574427\pi$
$930$	0	0
$931$	13.5202	0.443106
$932$	4.86550	0.159375
$933$	−6.43937	−0.210816
$934$	−27.6012	−0.903138
$935$	0	0
$936$	0	0
$937$	23.9317	0.781815	0.390908	−	0.920430i	$-0.372161\pi$
$937$	23.9317	0.781815	0.390908	+	0.920430i	$0.372161\pi$
$938$	−28.1023	−0.917571
$939$	−38.2157	−1.24712
$940$	0	0
$941$	−25.3591	−0.826683	−0.413342	−	0.910576i	$-0.635638\pi$
$941$	−25.3591	−0.826683	−0.413342	+	0.910576i	$0.635638\pi$
$942$	−28.5614	−0.930582
$943$	14.5284	0.473110
$944$	0.465033	0.0151355
$945$	0	0
$946$	−7.41584	−0.241110
$947$	−41.4223	−1.34604	−0.673021	−	0.739623i	$-0.735004\pi$
$947$	−41.4223	−1.34604	−0.673021	+	0.739623i	$0.735004\pi$
$948$	−14.3187	−0.465051
$949$	0	0
$950$	0	0
$951$	4.16480	0.135053
$952$	−12.4867	−0.404696
$953$	−24.3026	−0.787237	−0.393619	−	0.919274i	$-0.628777\pi$
$953$	−24.3026	−0.787237	−0.393619	+	0.919274i	$0.628777\pi$
$954$	−13.2083	−0.427636
$955$	0	0
$956$	10.2034	0.330001
$957$	0.309801	0.0100144
$958$	−25.1802	−0.813536
$959$	13.6329	0.440231
$960$	0	0
$961$	−1.14359	−0.0368901
$962$	0	0
$963$	22.2760	0.717834
$964$	−11.9209	−0.383945
$965$	0	0
$966$	−39.8675	−1.28272
$967$	−23.6784	−0.761445	−0.380722	−	0.924689i	$-0.624325\pi$
$967$	−23.6784	−0.761445	−0.380722	+	0.924689i	$0.624325\pi$
$968$	54.7173	1.75868
$969$	−5.98685	−0.192325
$970$	0	0
$971$	−16.9722	−0.544663	−0.272332	−	0.962203i	$-0.587795\pi$
$971$	−16.9722	−0.544663	−0.272332	+	0.962203i	$0.587795\pi$
$972$	−10.3791	−0.332908
$973$	−7.25030	−0.232434
$974$	3.70303	0.118653
$975$	0	0
$976$	−9.11550	−0.291780
$977$	−24.9994	−0.799802	−0.399901	−	0.916558i	$-0.630956\pi$
$977$	−24.9994	−0.799802	−0.399901	+	0.916558i	$0.630956\pi$
$978$	−19.2900	−0.616826
$979$	−86.7765	−2.77339
$980$	0	0
$981$	17.9930	0.574471
$982$	−13.0116	−0.415218
$983$	27.3418	0.872068	0.436034	−	0.899930i	$-0.356383\pi$
$983$	27.3418	0.872068	0.436034	+	0.899930i	$0.356383\pi$
$984$	−26.6718	−0.850267
$985$	0	0
$986$	0.0341370	0.00108715
$987$	−21.7080	−0.690975
$988$	0	0
$989$	4.40617	0.140108
$990$	0	0
$991$	16.0760	0.510672	0.255336	−	0.966852i	$-0.417814\pi$
$991$	16.0760	0.510672	0.255336	+	0.966852i	$0.417814\pi$
$992$	−15.4081	−0.489208
$993$	−16.8491	−0.534690
$994$	−47.4123	−1.50383
$995$	0	0
$996$	14.4932	0.459234
$997$	34.5612	1.09456	0.547282	−	0.836948i	$-0.315663\pi$
$997$	34.5612	1.09456	0.547282	+	0.836948i	$0.315663\pi$
$998$	−41.3649	−1.30938
$999$	11.3807	0.360070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4225.2.a.bi.1.2		4
5.4	even	2		845.2.a.m.1.3		4
13.2	odd	12		325.2.n.d.251.2		8
13.7	odd	12		325.2.n.d.101.2		8
13.12	even	2		4225.2.a.bl.1.3		4
15.14	odd	2		7605.2.a.cf.1.2		4
65.2	even	12		325.2.m.c.199.3		8
65.4	even	6		845.2.e.n.146.3		8
65.7	even	12		325.2.m.b.49.2		8
65.9	even	6		845.2.e.m.146.2		8
65.19	odd	12		845.2.m.g.361.2		8
65.24	odd	12		845.2.m.g.316.2		8
65.28	even	12		325.2.m.b.199.2		8
65.29	even	6		845.2.e.m.191.2		8
65.33	even	12		325.2.m.c.49.3		8
65.34	odd	4		845.2.c.g.506.6		8
65.44	odd	4		845.2.c.g.506.3		8
65.49	even	6		845.2.e.n.191.3		8
65.54	odd	12		65.2.m.a.56.3	yes	8
65.59	odd	12		65.2.m.a.36.3	✓	8
65.64	even	2		845.2.a.l.1.2		4
195.59	even	12		585.2.bu.c.361.2		8
195.119	even	12		585.2.bu.c.316.2		8
195.194	odd	2		7605.2.a.cj.1.3		4
260.59	even	12		1040.2.da.b.881.4		8
260.119	even	12		1040.2.da.b.641.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.3	✓	8	65.59	odd	12
65.2.m.a.56.3	yes	8	65.54	odd	12
325.2.m.b.49.2		8	65.7	even	12
325.2.m.b.199.2		8	65.28	even	12
325.2.m.c.49.3		8	65.33	even	12
325.2.m.c.199.3		8	65.2	even	12
325.2.n.d.101.2		8	13.7	odd	12
325.2.n.d.251.2		8	13.2	odd	12
585.2.bu.c.316.2		8	195.119	even	12
585.2.bu.c.361.2		8	195.59	even	12
845.2.a.l.1.2		4	65.64	even	2
845.2.a.m.1.3		4	5.4	even	2
845.2.c.g.506.3		8	65.44	odd	4
845.2.c.g.506.6		8	65.34	odd	4
845.2.e.m.146.2		8	65.9	even	6
845.2.e.m.191.2		8	65.29	even	6
845.2.e.n.146.3		8	65.4	even	6
845.2.e.n.191.3		8	65.49	even	6
845.2.m.g.316.2		8	65.24	odd	12
845.2.m.g.361.2		8	65.19	odd	12
1040.2.da.b.641.4		8	260.119	even	12
1040.2.da.b.881.4		8	260.59	even	12
4225.2.a.bi.1.2		4	1.1	even	1	trivial
4225.2.a.bl.1.3		4	13.12	even	2
7605.2.a.cf.1.2		4	15.14	odd	2
7605.2.a.cj.1.3		4	195.194	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:	\( N \)	\(=\)	\( 4225 = 5^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4225.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21969 q^{2} -2.33225 q^{3} -0.512364 q^{4} +2.84461 q^{6} -3.60020 q^{7} +3.06430 q^{8} +2.43937 q^{9} +O(q^{10})\)	\(q-1.21969 q^{2} -2.33225 q^{3} -0.512364 q^{4} +2.84461 q^{6} -3.60020 q^{7} +3.06430 q^{8} +2.43937 q^{9} +5.37182 q^{11} +1.19496 q^{12} +4.39111 q^{14} -2.71276 q^{16} +1.13186 q^{17} -2.97527 q^{18} +2.26795 q^{19} +8.39654 q^{21} -6.55193 q^{22} +3.89287 q^{23} -7.14670 q^{24} +1.30752 q^{27} +1.84461 q^{28} -0.0247279 q^{29} +5.46410 q^{31} -2.81988 q^{32} -12.5284 q^{33} -1.38051 q^{34} -1.24985 q^{36} +8.70406 q^{37} -2.76619 q^{38} +3.73205 q^{41} -10.2412 q^{42} +1.13186 q^{43} -2.75232 q^{44} -4.74809 q^{46} -2.58535 q^{47} +6.32681 q^{48} +5.96141 q^{49} -2.63977 q^{51} +4.43937 q^{53} -1.59476 q^{54} -11.0321 q^{56} -5.28942 q^{57} +0.0301603 q^{58} -0.171425 q^{59} +3.36023 q^{61} -6.66449 q^{62} -8.78222 q^{63} +8.86488 q^{64} +15.2807 q^{66} -6.39980 q^{67} -0.579922 q^{68} -9.07914 q^{69} -10.7973 q^{71} +7.47497 q^{72} +4.70308 q^{73} -10.6162 q^{74} -1.16202 q^{76} -19.3396 q^{77} -11.9826 q^{79} -10.3676 q^{81} -4.55193 q^{82} +12.1286 q^{83} -4.30209 q^{84} -1.38051 q^{86} +0.0576715 q^{87} +16.4608 q^{88} -16.1540 q^{89} -1.99457 q^{92} -12.7436 q^{93} +3.15332 q^{94} +6.57666 q^{96} -12.1682 q^{97} -7.27105 q^{98} +13.1039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 4 q^{6} - 10 q^{7} - 6 q^{8} + 4 q^{9} + 10 q^{12} + 2 q^{14} + 2 q^{16} + 2 q^{17} - 20 q^{18} + 16 q^{19} + 4 q^{21} - 12 q^{22} + 10 q^{23} - 24 q^{24} + 2 q^{27} - 8 q^{28} + 8 q^{29} + 8 q^{31} - 4 q^{32} - 18 q^{33} - 4 q^{34} + 20 q^{36} + 2 q^{37} - 8 q^{38} + 8 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{44} + 16 q^{46} - 8 q^{47} + 28 q^{48} + 12 q^{49} + 4 q^{51} + 12 q^{53} - 16 q^{54} + 12 q^{56} + 14 q^{57} - 22 q^{58} + 12 q^{59} + 28 q^{61} - 4 q^{62} - 4 q^{63} + 4 q^{64} + 6 q^{66} - 30 q^{67} - 14 q^{68} - 16 q^{69} + 4 q^{71} - 12 q^{72} + 8 q^{73} - 10 q^{74} + 20 q^{76} - 18 q^{77} - 8 q^{79} - 8 q^{81} - 4 q^{82} + 12 q^{83} - 28 q^{84} - 4 q^{86} + 22 q^{87} + 18 q^{88} - 12 q^{89} - 22 q^{92} - 8 q^{93} - 32 q^{94} + 4 q^{96} - 2 q^{97} + 24 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 4 * q^6 - 10 * q^7 - 6 * q^8 + 4 * q^9 + 10 * q^12 + 2 * q^14 + 2 * q^16 + 2 * q^17 - 20 * q^18 + 16 * q^19 + 4 * q^21 - 12 * q^22 + 10 * q^23 - 24 * q^24 + 2 * q^27 - 8 * q^28 + 8 * q^29 + 8 * q^31 - 4 * q^32 - 18 * q^33 - 4 * q^34 + 20 * q^36 + 2 * q^37 - 8 * q^38 + 8 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^44 + 16 * q^46 - 8 * q^47 + 28 * q^48 + 12 * q^49 + 4 * q^51 + 12 * q^53 - 16 * q^54 + 12 * q^56 + 14 * q^57 - 22 * q^58 + 12 * q^59 + 28 * q^61 - 4 * q^62 - 4 * q^63 + 4 * q^64 + 6 * q^66 - 30 * q^67 - 14 * q^68 - 16 * q^69 + 4 * q^71 - 12 * q^72 + 8 * q^73 - 10 * q^74 + 20 * q^76 - 18 * q^77 - 8 * q^79 - 8 * q^81 - 4 * q^82 + 12 * q^83 - 28 * q^84 - 4 * q^86 + 22 * q^87 + 18 * q^88 - 12 * q^89 - 22 * q^92 - 8 * q^93 - 32 * q^94 + 4 * q^96 - 2 * q^97 + 24 * q^98 + 24 * q^99

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