LMFDB - Embedded newform 4025.2.a.bd.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.294301 q^{2} -3.07644 q^{3} -1.91339 q^{4} -0.905400 q^{6} -1.00000 q^{7} -1.15171 q^{8} +6.46449 q^{9} +O(q^{10})$	\(q+0.294301 q^{2} -3.07644 q^{3} -1.91339 q^{4} -0.905400 q^{6} -1.00000 q^{7} -1.15171 q^{8} +6.46449 q^{9} +5.13162 q^{11} +5.88642 q^{12} +3.95886 q^{13} -0.294301 q^{14} +3.48782 q^{16} +5.37860 q^{17} +1.90251 q^{18} +6.36536 q^{19} +3.07644 q^{21} +1.51024 q^{22} -1.00000 q^{23} +3.54318 q^{24} +1.16510 q^{26} -10.6583 q^{27} +1.91339 q^{28} -0.211470 q^{29} +3.95315 q^{31} +3.32990 q^{32} -15.7871 q^{33} +1.58293 q^{34} -12.3691 q^{36} -10.3059 q^{37} +1.87333 q^{38} -12.1792 q^{39} -7.39183 q^{41} +0.905400 q^{42} +6.61739 q^{43} -9.81877 q^{44} -0.294301 q^{46} -5.58540 q^{47} -10.7301 q^{48} +1.00000 q^{49} -16.5469 q^{51} -7.57484 q^{52} +9.63081 q^{53} -3.13675 q^{54} +1.15171 q^{56} -19.5826 q^{57} -0.0622359 q^{58} +5.55942 q^{59} +4.28938 q^{61} +1.16342 q^{62} -6.46449 q^{63} -5.99565 q^{64} -4.64617 q^{66} +0.973230 q^{67} -10.2913 q^{68} +3.07644 q^{69} +10.8877 q^{71} -7.44524 q^{72} -3.89355 q^{73} -3.03304 q^{74} -12.1794 q^{76} -5.13162 q^{77} -3.58436 q^{78} +14.7496 q^{79} +13.3962 q^{81} -2.17542 q^{82} +7.12278 q^{83} -5.88642 q^{84} +1.94750 q^{86} +0.650576 q^{87} -5.91015 q^{88} -3.82796 q^{89} -3.95886 q^{91} +1.91339 q^{92} -12.1616 q^{93} -1.64379 q^{94} -10.2442 q^{96} +18.7554 q^{97} +0.294301 q^{98} +33.1733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.294301	0.208102	0.104051	−	0.994572i	$-0.466819\pi$
$2$	0.294301	0.208102	0.104051	+	0.994572i	$0.466819\pi$
$3$	−3.07644	−1.77618	−0.888092	−	0.459666i	$-0.847969\pi$
$3$	−3.07644	−1.77618	−0.888092	+	0.459666i	$0.847969\pi$
$4$	−1.91339	−0.956693
$5$	0	0
$5$	0	0
$6$	−0.905400	−0.369628
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.15171	−0.407192
$9$	6.46449	2.15483
$10$	0	0
$11$	5.13162	1.54724	0.773620	−	0.633649i	$-0.218444\pi$
$11$	5.13162	1.54724	0.773620	+	0.633649i	$0.218444\pi$
$12$	5.88642	1.69926
$13$	3.95886	1.09799	0.548996	−	0.835825i	$-0.315010\pi$
$13$	3.95886	1.09799	0.548996	+	0.835825i	$0.315010\pi$
$14$	−0.294301	−0.0786553
$15$	0	0
$16$	3.48782	0.871956
$17$	5.37860	1.30450	0.652251	−	0.758003i	$-0.273825\pi$
$17$	5.37860	1.30450	0.652251	+	0.758003i	$0.273825\pi$
$18$	1.90251	0.448425
$19$	6.36536	1.46031	0.730156	−	0.683280i	$-0.239447\pi$
$19$	6.36536	1.46031	0.730156	+	0.683280i	$0.239447\pi$
$20$	0	0
$21$	3.07644	0.671335
$22$	1.51024	0.321984
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.54318	0.723249
$25$	0	0
$26$	1.16510	0.228495
$27$	−10.6583	−2.05119
$28$	1.91339	0.361596
$29$	−0.211470	−0.0392690	−0.0196345	−	0.999807i	$-0.506250\pi$
$29$	−0.211470	−0.0392690	−0.0196345	+	0.999807i	$0.506250\pi$
$30$	0	0
$31$	3.95315	0.710006	0.355003	−	0.934865i	$-0.384480\pi$
$31$	3.95315	0.710006	0.355003	+	0.934865i	$0.384480\pi$
$32$	3.32990	0.588648
$33$	−15.7871	−2.74818
$34$	1.58293	0.271470
$35$	0	0
$36$	−12.3691	−2.06151
$37$	−10.3059	−1.69428	−0.847140	−	0.531370i	$-0.821678\pi$
$37$	−10.3059	−1.69428	−0.847140	+	0.531370i	$0.821678\pi$
$38$	1.87333	0.303894
$39$	−12.1792	−1.95024
$40$	0	0
$41$	−7.39183	−1.15441	−0.577205	−	0.816600i	$-0.695856\pi$
$41$	−7.39183	−1.15441	−0.577205	+	0.816600i	$0.695856\pi$
$42$	0.905400	0.139706
$43$	6.61739	1.00914	0.504571	−	0.863370i	$-0.331651\pi$
$43$	6.61739	1.00914	0.504571	+	0.863370i	$0.331651\pi$
$44$	−9.81877	−1.48024
$45$	0	0
$46$	−0.294301	−0.0433923
$47$	−5.58540	−0.814715	−0.407357	−	0.913269i	$-0.633550\pi$
$47$	−5.58540	−0.814715	−0.407357	+	0.913269i	$0.633550\pi$
$48$	−10.7301	−1.54875
$49$	1.00000	0.142857
$50$	0	0
$51$	−16.5469	−2.31703
$52$	−7.57484	−1.05044
$53$	9.63081	1.32289	0.661447	−	0.749992i	$-0.269943\pi$
$53$	9.63081	1.32289	0.661447	+	0.749992i	$0.269943\pi$
$54$	−3.13675	−0.426858
$55$	0	0
$56$	1.15171	0.153904
$57$	−19.5826	−2.59378
$58$	−0.0622359	−0.00817197
$59$	5.55942	0.723775	0.361887	−	0.932222i	$-0.382133\pi$
$59$	5.55942	0.723775	0.361887	+	0.932222i	$0.382133\pi$
$60$	0	0
$61$	4.28938	0.549199	0.274600	−	0.961559i	$-0.411455\pi$
$61$	4.28938	0.549199	0.274600	+	0.961559i	$0.411455\pi$
$62$	1.16342	0.147754
$63$	−6.46449	−0.814449
$64$	−5.99565	−0.749457
$65$	0	0
$66$	−4.64617	−0.571903
$67$	0.973230	0.118899	0.0594495	−	0.998231i	$-0.481065\pi$
$67$	0.973230	0.118899	0.0594495	+	0.998231i	$0.481065\pi$
$68$	−10.2913	−1.24801
$69$	3.07644	0.370360
$70$	0	0
$71$	10.8877	1.29213	0.646067	−	0.763281i	$-0.276413\pi$
$71$	10.8877	1.29213	0.646067	+	0.763281i	$0.276413\pi$
$72$	−7.44524	−0.877430
$73$	−3.89355	−0.455706	−0.227853	−	0.973696i	$-0.573171\pi$
$73$	−3.89355	−0.455706	−0.227853	+	0.973696i	$0.573171\pi$
$74$	−3.03304	−0.352584
$75$	0	0
$76$	−12.1794	−1.39707
$77$	−5.13162	−0.584802
$78$	−3.58436	−0.405848
$79$	14.7496	1.65946	0.829731	−	0.558164i	$-0.188494\pi$
$79$	14.7496	1.65946	0.829731	+	0.558164i	$0.188494\pi$
$80$	0	0
$81$	13.3962	1.48846
$82$	−2.17542	−0.240235
$83$	7.12278	0.781827	0.390914	−	0.920427i	$-0.372159\pi$
$83$	7.12278	0.781827	0.390914	+	0.920427i	$0.372159\pi$
$84$	−5.88642	−0.642261
$85$	0	0
$86$	1.94750	0.210005
$87$	0.650576	0.0697490
$88$	−5.91015	−0.630025
$89$	−3.82796	−0.405763	−0.202881	−	0.979203i	$-0.565031\pi$
$89$	−3.82796	−0.405763	−0.202881	+	0.979203i	$0.565031\pi$
$90$	0	0
$91$	−3.95886	−0.415002
$92$	1.91339	0.199484
$93$	−12.1616	−1.26110
$94$	−1.64379	−0.169544
$95$	0	0
$96$	−10.2442	−1.04555
$97$	18.7554	1.90432	0.952159	−	0.305603i	$-0.0988580\pi$
$97$	18.7554	1.90432	0.952159	+	0.305603i	$0.0988580\pi$
$98$	0.294301	0.0297289
$99$	33.1733	3.33404
$100$	0	0
$101$	9.00264	0.895796	0.447898	−	0.894085i	$-0.352173\pi$
$101$	9.00264	0.895796	0.447898	+	0.894085i	$0.352173\pi$
$102$	−4.86978	−0.482180
$103$	−0.481470	−0.0474407	−0.0237203	−	0.999719i	$-0.507551\pi$
$103$	−0.481470	−0.0474407	−0.0237203	+	0.999719i	$0.507551\pi$
$104$	−4.55948	−0.447094
$105$	0	0
$106$	2.83436	0.275297
$107$	1.02213	0.0988128	0.0494064	−	0.998779i	$-0.484267\pi$
$107$	1.02213	0.0988128	0.0494064	+	0.998779i	$0.484267\pi$
$108$	20.3935	1.96236
$109$	−2.86911	−0.274811	−0.137405	−	0.990515i	$-0.543876\pi$
$109$	−2.86911	−0.274811	−0.137405	+	0.990515i	$0.543876\pi$
$110$	0	0
$111$	31.7055	3.00935
$112$	−3.48782	−0.329568
$113$	−9.35957	−0.880474	−0.440237	−	0.897882i	$-0.645106\pi$
$113$	−9.35957	−0.880474	−0.440237	+	0.897882i	$0.645106\pi$
$114$	−5.76319	−0.539772
$115$	0	0
$116$	0.404624	0.0375684
$117$	25.5920	2.36599
$118$	1.63614	0.150619
$119$	−5.37860	−0.493055
$120$	0	0
$121$	15.3335	1.39395
$122$	1.26237	0.114290
$123$	22.7405	2.05044
$124$	−7.56390	−0.679259
$125$	0	0
$126$	−1.90251	−0.169489
$127$	−5.22869	−0.463971	−0.231985	−	0.972719i	$-0.574522\pi$
$127$	−5.22869	−0.463971	−0.231985	+	0.972719i	$0.574522\pi$
$128$	−8.42432	−0.744612
$129$	−20.3580	−1.79242
$130$	0	0
$131$	−8.29697	−0.724909	−0.362455	−	0.932001i	$-0.618061\pi$
$131$	−8.29697	−0.724909	−0.362455	+	0.932001i	$0.618061\pi$
$132$	30.2069	2.62917
$133$	−6.36536	−0.551946
$134$	0.286423	0.0247431
$135$	0	0
$136$	−6.19460	−0.531183
$137$	−18.4414	−1.57555	−0.787776	−	0.615962i	$-0.788767\pi$
$137$	−18.4414	−1.57555	−0.787776	+	0.615962i	$0.788767\pi$
$138$	0.905400	0.0770728
$139$	−0.532199	−0.0451406	−0.0225703	−	0.999745i	$-0.507185\pi$
$139$	−0.532199	−0.0451406	−0.0225703	+	0.999745i	$0.507185\pi$
$140$	0	0
$141$	17.1832	1.44708
$142$	3.20427	0.268896
$143$	20.3154	1.69886
$144$	22.5470	1.87892
$145$	0	0
$146$	−1.14588	−0.0948334
$147$	−3.07644	−0.253741
$148$	19.7192	1.62091
$149$	−16.8353	−1.37920	−0.689599	−	0.724191i	$-0.742213\pi$
$149$	−16.8353	−1.37920	−0.689599	+	0.724191i	$0.742213\pi$
$150$	0	0
$151$	−13.1724	−1.07196	−0.535979	−	0.844231i	$-0.680057\pi$
$151$	−13.1724	−1.07196	−0.535979	+	0.844231i	$0.680057\pi$
$152$	−7.33107	−0.594628
$153$	34.7699	2.81098
$154$	−1.51024	−0.121699
$155$	0	0
$156$	23.3036	1.86578
$157$	−4.10230	−0.327399	−0.163700	−	0.986510i	$-0.552343\pi$
$157$	−4.10230	−0.327399	−0.163700	+	0.986510i	$0.552343\pi$
$158$	4.34083	0.345338
$159$	−29.6286	−2.34970
$160$	0	0
$161$	1.00000	0.0788110
$162$	3.94251	0.309753
$163$	−8.32406	−0.651990	−0.325995	−	0.945371i	$-0.605699\pi$
$163$	−8.32406	−0.651990	−0.325995	+	0.945371i	$0.605699\pi$
$164$	14.1434	1.10442
$165$	0	0
$166$	2.09624	0.162700
$167$	2.13317	0.165070	0.0825349	−	0.996588i	$-0.473698\pi$
$167$	2.13317	0.165070	0.0825349	+	0.996588i	$0.473698\pi$
$168$	−3.54318	−0.273362
$169$	2.67261	0.205585
$170$	0	0
$171$	41.1488	3.14673
$172$	−12.6616	−0.965440
$173$	−1.24896	−0.0949570	−0.0474785	−	0.998872i	$-0.515119\pi$
$173$	−1.24896	−0.0949570	−0.0474785	+	0.998872i	$0.515119\pi$
$174$	0.191465	0.0145149
$175$	0	0
$176$	17.8982	1.34913
$177$	−17.1032	−1.28556
$178$	−1.12657	−0.0844402
$179$	−8.80921	−0.658431	−0.329216	−	0.944255i	$-0.606784\pi$
$179$	−8.80921	−0.658431	−0.329216	+	0.944255i	$0.606784\pi$
$180$	0	0
$181$	11.6558	0.866365	0.433183	−	0.901306i	$-0.357391\pi$
$181$	11.6558	0.866365	0.433183	+	0.901306i	$0.357391\pi$
$182$	−1.16510	−0.0863628
$183$	−13.1960	−0.975479
$184$	1.15171	0.0849055
$185$	0	0
$186$	−3.57918	−0.262438
$187$	27.6009	2.01838
$188$	10.6870	0.779432
$189$	10.6583	0.775278
$190$	0	0
$191$	5.33098	0.385736	0.192868	−	0.981225i	$-0.438221\pi$
$191$	5.33098	0.385736	0.192868	+	0.981225i	$0.438221\pi$
$192$	18.4453	1.33117
$193$	−12.4322	−0.894887	−0.447444	−	0.894312i	$-0.647665\pi$
$193$	−12.4322	−0.894887	−0.447444	+	0.894312i	$0.647665\pi$
$194$	5.51972	0.396293
$195$	0	0
$196$	−1.91339	−0.136670
$197$	−6.41924	−0.457352	−0.228676	−	0.973503i	$-0.573440\pi$
$197$	−6.41924	−0.457352	−0.228676	+	0.973503i	$0.573440\pi$
$198$	9.76293	0.693821
$199$	23.4004	1.65881	0.829406	−	0.558647i	$-0.188679\pi$
$199$	23.4004	1.65881	0.829406	+	0.558647i	$0.188679\pi$
$200$	0	0
$201$	−2.99408	−0.211186
$202$	2.64949	0.186417
$203$	0.211470	0.0148423
$204$	31.6607	2.21669
$205$	0	0
$206$	−0.141697	−0.00987251
$207$	−6.46449	−0.449313
$208$	13.8078	0.957400
$209$	32.6646	2.25946
$210$	0	0
$211$	−24.0312	−1.65438	−0.827189	−	0.561924i	$-0.810061\pi$
$211$	−24.0312	−1.65438	−0.827189	+	0.561924i	$0.810061\pi$
$212$	−18.4275	−1.26560
$213$	−33.4954	−2.29507
$214$	0.300813	0.0205632
$215$	0	0
$216$	12.2753	0.835229
$217$	−3.95315	−0.268357
$218$	−0.844382	−0.0571888
$219$	11.9783	0.809417
$220$	0	0
$221$	21.2931	1.43233
$222$	9.33096	0.626253
$223$	−1.64269	−0.110002	−0.0550012	−	0.998486i	$-0.517516\pi$
$223$	−1.64269	−0.110002	−0.0550012	+	0.998486i	$0.517516\pi$
$224$	−3.32990	−0.222488
$225$	0	0
$226$	−2.75453	−0.183229
$227$	16.6973	1.10824	0.554120	−	0.832437i	$-0.313055\pi$
$227$	16.6973	1.10824	0.554120	+	0.832437i	$0.313055\pi$
$228$	37.4692	2.48146
$229$	−28.2034	−1.86374	−0.931868	−	0.362799i	$-0.881821\pi$
$229$	−28.2034	−1.86374	−0.931868	+	0.362799i	$0.881821\pi$
$230$	0	0
$231$	15.7871	1.03872
$232$	0.243553	0.0159900
$233$	−14.8131	−0.970441	−0.485221	−	0.874392i	$-0.661261\pi$
$233$	−14.8131	−0.970441	−0.485221	+	0.874392i	$0.661261\pi$
$234$	7.53177	0.492367
$235$	0	0
$236$	−10.6373	−0.692430
$237$	−45.3763	−2.94751
$238$	−1.58293	−0.102606
$239$	19.6605	1.27173	0.635867	−	0.771799i	$-0.280643\pi$
$239$	19.6605	1.27173	0.635867	+	0.771799i	$0.280643\pi$
$240$	0	0
$241$	−5.50661	−0.354712	−0.177356	−	0.984147i	$-0.556754\pi$
$241$	−5.50661	−0.354712	−0.177356	+	0.984147i	$0.556754\pi$
$242$	4.51266	0.290085
$243$	−9.23763	−0.592594
$244$	−8.20725	−0.525415
$245$	0	0
$246$	6.69256	0.426702
$247$	25.1996	1.60341
$248$	−4.55290	−0.289109
$249$	−21.9128	−1.38867
$250$	0	0
$251$	29.0814	1.83560	0.917802	−	0.397039i	$-0.129962\pi$
$251$	29.0814	1.83560	0.917802	+	0.397039i	$0.129962\pi$
$252$	12.3691	0.779178
$253$	−5.13162	−0.322622
$254$	−1.53881	−0.0965534
$255$	0	0
$256$	9.51202	0.594501
$257$	−1.12696	−0.0702977	−0.0351488	−	0.999382i	$-0.511191\pi$
$257$	−1.12696	−0.0702977	−0.0351488	+	0.999382i	$0.511191\pi$
$258$	−5.99138	−0.373007
$259$	10.3059	0.640378
$260$	0	0
$261$	−1.36705	−0.0846181
$262$	−2.44181	−0.150855
$263$	−9.73182	−0.600090	−0.300045	−	0.953925i	$-0.597002\pi$
$263$	−9.73182	−0.600090	−0.300045	+	0.953925i	$0.597002\pi$
$264$	18.1822	1.11904
$265$	0	0
$266$	−1.87333	−0.114861
$267$	11.7765	0.720710
$268$	−1.86217	−0.113750
$269$	22.3027	1.35982	0.679911	−	0.733295i	$-0.262018\pi$
$269$	22.3027	1.35982	0.679911	+	0.733295i	$0.262018\pi$
$270$	0	0
$271$	−1.57380	−0.0956016	−0.0478008	−	0.998857i	$-0.515221\pi$
$271$	−1.57380	−0.0956016	−0.0478008	+	0.998857i	$0.515221\pi$
$272$	18.7596	1.13747
$273$	12.1792	0.737120
$274$	−5.42731	−0.327876
$275$	0	0
$276$	−5.88642	−0.354321
$277$	0.352588	0.0211850	0.0105925	−	0.999944i	$-0.496628\pi$
$277$	0.352588	0.0211850	0.0105925	+	0.999944i	$0.496628\pi$
$278$	−0.156627	−0.00939385
$279$	25.5551	1.52994
$280$	0	0
$281$	10.5378	0.628635	0.314318	−	0.949318i	$-0.398224\pi$
$281$	10.5378	0.628635	0.314318	+	0.949318i	$0.398224\pi$
$282$	5.05702	0.301141
$283$	15.5619	0.925062	0.462531	−	0.886603i	$-0.346941\pi$
$283$	15.5619	0.925062	0.462531	+	0.886603i	$0.346941\pi$
$284$	−20.8324	−1.23618
$285$	0	0
$286$	5.97884	0.353536
$287$	7.39183	0.436326
$288$	21.5261	1.26844
$289$	11.9293	0.701723
$290$	0	0
$291$	−57.6998	−3.38242
$292$	7.44987	0.435971
$293$	14.7142	0.859613	0.429807	−	0.902921i	$-0.358582\pi$
$293$	14.7142	0.859613	0.429807	+	0.902921i	$0.358582\pi$
$294$	−0.905400	−0.0528040
$295$	0	0
$296$	11.8695	0.689898
$297$	−54.6943	−3.17369
$298$	−4.95463	−0.287014
$299$	−3.95886	−0.228947
$300$	0	0
$301$	−6.61739	−0.381420
$302$	−3.87666	−0.223077
$303$	−27.6961	−1.59110
$304$	22.2012	1.27333
$305$	0	0
$306$	10.2328	0.584971
$307$	−5.97288	−0.340890	−0.170445	−	0.985367i	$-0.554521\pi$
$307$	−5.97288	−0.340890	−0.170445	+	0.985367i	$0.554521\pi$
$308$	9.81877	0.559476
$309$	1.48122	0.0842634
$310$	0	0
$311$	−21.7888	−1.23553	−0.617765	−	0.786363i	$-0.711962\pi$
$311$	−21.7888	−1.23553	−0.617765	+	0.786363i	$0.711962\pi$
$312$	14.0270	0.794121
$313$	−1.79930	−0.101703	−0.0508513	−	0.998706i	$-0.516193\pi$
$313$	−1.79930	−0.101703	−0.0508513	+	0.998706i	$0.516193\pi$
$314$	−1.20731	−0.0681325
$315$	0	0
$316$	−28.2217	−1.58760
$317$	9.88480	0.555185	0.277593	−	0.960699i	$-0.410463\pi$
$317$	9.88480	0.555185	0.277593	+	0.960699i	$0.410463\pi$
$318$	−8.71973	−0.488978
$319$	−1.08518	−0.0607587
$320$	0	0
$321$	−3.14452	−0.175510
$322$	0.294301	0.0164008
$323$	34.2367	1.90498
$324$	−25.6321	−1.42400
$325$	0	0
$326$	−2.44978	−0.135681
$327$	8.82665	0.488115
$328$	8.51327	0.470067
$329$	5.58540	0.307933
$330$	0	0
$331$	−11.0244	−0.605957	−0.302979	−	0.952997i	$-0.597981\pi$
$331$	−11.0244	−0.605957	−0.302979	+	0.952997i	$0.597981\pi$
$332$	−13.6286	−0.747969
$333$	−66.6224	−3.65089
$334$	0.627795	0.0343514
$335$	0	0
$336$	10.7301	0.585374
$337$	4.37744	0.238454	0.119227	−	0.992867i	$-0.461958\pi$
$337$	4.37744	0.238454	0.119227	+	0.992867i	$0.461958\pi$
$338$	0.786552	0.0427828
$339$	28.7942	1.56388
$340$	0	0
$341$	20.2860	1.09855
$342$	12.1101	0.654841
$343$	−1.00000	−0.0539949
$344$	−7.62134	−0.410915
$345$	0	0
$346$	−0.367572	−0.0197608
$347$	24.1591	1.29693	0.648463	−	0.761246i	$-0.275412\pi$
$347$	24.1591	1.29693	0.648463	+	0.761246i	$0.275412\pi$
$348$	−1.24480	−0.0667285
$349$	−18.0096	−0.964031	−0.482015	−	0.876163i	$-0.660095\pi$
$349$	−18.0096	−0.964031	−0.482015	+	0.876163i	$0.660095\pi$
$350$	0	0
$351$	−42.1948	−2.25219
$352$	17.0878	0.910781
$353$	2.07792	0.110596	0.0552982	−	0.998470i	$-0.482389\pi$
$353$	2.07792	0.110596	0.0552982	+	0.998470i	$0.482389\pi$
$354$	−5.03350	−0.267527
$355$	0	0
$356$	7.32437	0.388191
$357$	16.5469	0.875757
$358$	−2.59256	−0.137021
$359$	−18.5094	−0.976889	−0.488445	−	0.872595i	$-0.662436\pi$
$359$	−18.5094	−0.976889	−0.488445	+	0.872595i	$0.662436\pi$
$360$	0	0
$361$	21.5177	1.13251
$362$	3.43030	0.180293
$363$	−47.1726	−2.47592
$364$	7.57484	0.397029
$365$	0	0
$366$	−3.88361	−0.202999
$367$	−3.76425	−0.196492	−0.0982462	−	0.995162i	$-0.531323\pi$
$367$	−3.76425	−0.196492	−0.0982462	+	0.995162i	$0.531323\pi$
$368$	−3.48782	−0.181815
$369$	−47.7844	−2.48756
$370$	0	0
$371$	−9.63081	−0.500007
$372$	23.2699	1.20649
$373$	−10.4068	−0.538843	−0.269421	−	0.963022i	$-0.586832\pi$
$373$	−10.4068	−0.538843	−0.269421	+	0.963022i	$0.586832\pi$
$374$	8.12297	0.420029
$375$	0	0
$376$	6.43279	0.331746
$377$	−0.837182	−0.0431171
$378$	3.13675	0.161337
$379$	1.64474	0.0844849	0.0422424	−	0.999107i	$-0.486550\pi$
$379$	1.64474	0.0844849	0.0422424	+	0.999107i	$0.486550\pi$
$380$	0	0
$381$	16.0857	0.824098
$382$	1.56891	0.0802725
$383$	24.5244	1.25314	0.626568	−	0.779367i	$-0.284459\pi$
$383$	24.5244	1.25314	0.626568	+	0.779367i	$0.284459\pi$
$384$	25.9169	1.32257
$385$	0	0
$386$	−3.65880	−0.186228
$387$	42.7780	2.17453
$388$	−35.8863	−1.82185
$389$	21.4335	1.08672	0.543362	−	0.839499i	$-0.317151\pi$
$389$	21.4335	1.08672	0.543362	+	0.839499i	$0.317151\pi$
$390$	0	0
$391$	−5.37860	−0.272007
$392$	−1.15171	−0.0581703
$393$	25.5251	1.28757
$394$	−1.88919	−0.0951760
$395$	0	0
$396$	−63.4733	−3.18966
$397$	−6.92640	−0.347626	−0.173813	−	0.984779i	$-0.555609\pi$
$397$	−6.92640	−0.347626	−0.173813	+	0.984779i	$0.555609\pi$
$398$	6.88676	0.345202
$399$	19.5826	0.980358
$400$	0	0
$401$	−10.6909	−0.533878	−0.266939	−	0.963713i	$-0.586012\pi$
$401$	−10.6909	−0.533878	−0.266939	+	0.963713i	$0.586012\pi$
$402$	−0.881162	−0.0439484
$403$	15.6500	0.779581
$404$	−17.2255	−0.857002
$405$	0	0
$406$	0.0622359	0.00308872
$407$	−52.8860	−2.62146
$408$	19.0573	0.943479
$409$	−3.92285	−0.193973	−0.0969863	−	0.995286i	$-0.530920\pi$
$409$	−3.92285	−0.193973	−0.0969863	+	0.995286i	$0.530920\pi$
$410$	0	0
$411$	56.7338	2.79847
$412$	0.921239	0.0453862
$413$	−5.55942	−0.273561
$414$	−1.90251	−0.0935031
$415$	0	0
$416$	13.1826	0.646331
$417$	1.63728	0.0801780
$418$	9.61321	0.470198
$419$	−27.2617	−1.33182	−0.665912	−	0.746031i	$-0.731957\pi$
$419$	−27.2617	−1.33182	−0.665912	+	0.746031i	$0.731957\pi$
$420$	0	0
$421$	29.9487	1.45961	0.729804	−	0.683656i	$-0.239611\pi$
$421$	29.9487	1.45961	0.729804	+	0.683656i	$0.239611\pi$
$422$	−7.07242	−0.344280
$423$	−36.1068	−1.75557
$424$	−11.0919	−0.538672
$425$	0	0
$426$	−9.85774	−0.477609
$427$	−4.28938	−0.207578
$428$	−1.95573	−0.0945336
$429$	−62.4991	−3.01748
$430$	0	0
$431$	−21.8040	−1.05026	−0.525130	−	0.851022i	$-0.675983\pi$
$431$	−21.8040	−1.05026	−0.525130	+	0.851022i	$0.675983\pi$
$432$	−37.1743	−1.78855
$433$	10.6541	0.512004	0.256002	−	0.966676i	$-0.417595\pi$
$433$	10.6541	0.512004	0.256002	+	0.966676i	$0.417595\pi$
$434$	−1.16342	−0.0558457
$435$	0	0
$436$	5.48972	0.262910
$437$	−6.36536	−0.304496
$438$	3.52522	0.168442
$439$	35.9660	1.71656	0.858281	−	0.513180i	$-0.171533\pi$
$439$	35.9660	1.71656	0.858281	+	0.513180i	$0.171533\pi$
$440$	0	0
$441$	6.46449	0.307833
$442$	6.26659	0.298071
$443$	−13.2930	−0.631571	−0.315785	−	0.948831i	$-0.602268\pi$
$443$	−13.2930	−0.631571	−0.315785	+	0.948831i	$0.602268\pi$
$444$	−60.6649	−2.87903
$445$	0	0
$446$	−0.483444	−0.0228917
$447$	51.7927	2.44971
$448$	5.99565	0.283268
$449$	−12.9466	−0.610987	−0.305494	−	0.952194i	$-0.598821\pi$
$449$	−12.9466	−0.610987	−0.305494	+	0.952194i	$0.598821\pi$
$450$	0	0
$451$	−37.9320	−1.78615
$452$	17.9085	0.842344
$453$	40.5243	1.90400
$454$	4.91404	0.230627
$455$	0	0
$456$	22.5536	1.05617
$457$	−26.4971	−1.23948	−0.619742	−	0.784805i	$-0.712763\pi$
$457$	−26.4971	−1.23948	−0.619742	+	0.784805i	$0.712763\pi$
$458$	−8.30030	−0.387847
$459$	−57.3267	−2.67578
$460$	0	0
$461$	−2.71603	−0.126498	−0.0632491	−	0.997998i	$-0.520146\pi$
$461$	−2.71603	−0.126498	−0.0632491	+	0.997998i	$0.520146\pi$
$462$	4.64617	0.216159
$463$	37.3829	1.73733	0.868665	−	0.495399i	$-0.164978\pi$
$463$	37.3829	1.73733	0.868665	+	0.495399i	$0.164978\pi$
$464$	−0.737571	−0.0342409
$465$	0	0
$466$	−4.35952	−0.201951
$467$	41.1915	1.90612	0.953058	−	0.302789i	$-0.0979177\pi$
$467$	41.1915	1.90612	0.953058	+	0.302789i	$0.0979177\pi$
$468$	−48.9675	−2.26352
$469$	−0.973230	−0.0449396
$470$	0	0
$471$	12.6205	0.581522
$472$	−6.40286	−0.294715
$473$	33.9579	1.56139
$474$	−13.3543	−0.613383
$475$	0	0
$476$	10.2913	0.471703
$477$	62.2583	2.85061
$478$	5.78611	0.264651
$479$	1.26221	0.0576716	0.0288358	−	0.999584i	$-0.490820\pi$
$479$	1.26221	0.0576716	0.0288358	+	0.999584i	$0.490820\pi$
$480$	0	0
$481$	−40.7997	−1.86031
$482$	−1.62060	−0.0738164
$483$	−3.07644	−0.139983
$484$	−29.3389	−1.33359
$485$	0	0
$486$	−2.71864	−0.123320
$487$	31.5628	1.43024	0.715122	−	0.698999i	$-0.246371\pi$
$487$	31.5628	1.43024	0.715122	+	0.698999i	$0.246371\pi$
$488$	−4.94014	−0.223630
$489$	25.6085	1.15806
$490$	0	0
$491$	−27.9514	−1.26143	−0.630714	−	0.776015i	$-0.717238\pi$
$491$	−27.9514	−1.26143	−0.630714	+	0.776015i	$0.717238\pi$
$492$	−43.5114	−1.96165
$493$	−1.13741	−0.0512265
$494$	7.41626	0.333673
$495$	0	0
$496$	13.7879	0.619094
$497$	−10.8877	−0.488381
$498$	−6.44897	−0.288985
$499$	23.9124	1.07046	0.535232	−	0.844705i	$-0.320224\pi$
$499$	23.9124	1.07046	0.535232	+	0.844705i	$0.320224\pi$
$500$	0	0
$501$	−6.56258	−0.293194
$502$	8.55869	0.381993
$503$	20.6663	0.921464	0.460732	−	0.887539i	$-0.347587\pi$
$503$	20.6663	0.921464	0.460732	+	0.887539i	$0.347587\pi$
$504$	7.44524	0.331637
$505$	0	0
$506$	−1.51024	−0.0671384
$507$	−8.22213	−0.365158
$508$	10.0045	0.443878
$509$	0.612536	0.0271502	0.0135751	−	0.999908i	$-0.495679\pi$
$509$	0.612536	0.0271502	0.0135751	+	0.999908i	$0.495679\pi$
$510$	0	0
$511$	3.89355	0.172241
$512$	19.6480	0.868329
$513$	−67.8439	−2.99538
$514$	−0.331665	−0.0146291
$515$	0	0
$516$	38.9527	1.71480
$517$	−28.6621	−1.26056
$518$	3.03304	0.133264
$519$	3.84237	0.168661
$520$	0	0
$521$	−35.1468	−1.53981	−0.769905	−	0.638159i	$-0.779696\pi$
$521$	−35.1468	−1.53981	−0.769905	+	0.638159i	$0.779696\pi$
$522$	−0.402323	−0.0176092
$523$	−5.43127	−0.237493	−0.118746	−	0.992925i	$-0.537888\pi$
$523$	−5.43127	−0.237493	−0.118746	+	0.992925i	$0.537888\pi$
$524$	15.8753	0.693516
$525$	0	0
$526$	−2.86408	−0.124880
$527$	21.2624	0.926204
$528$	−55.0627	−2.39630
$529$	1.00000	0.0434783
$530$	0	0
$531$	35.9388	1.55961
$532$	12.1794	0.528043
$533$	−29.2632	−1.26753
$534$	3.46583	0.149981
$535$	0	0
$536$	−1.12088	−0.0484147
$537$	27.1010	1.16949
$538$	6.56372	0.282982
$539$	5.13162	0.221034
$540$	0	0
$541$	−37.1845	−1.59868	−0.799342	−	0.600876i	$-0.794819\pi$
$541$	−37.1845	−1.59868	−0.799342	+	0.600876i	$0.794819\pi$
$542$	−0.463171	−0.0198949
$543$	−35.8582	−1.53882
$544$	17.9102	0.767892
$545$	0	0
$546$	3.58436	0.153396
$547$	−23.2330	−0.993372	−0.496686	−	0.867930i	$-0.665450\pi$
$547$	−23.2330	−0.993372	−0.496686	+	0.867930i	$0.665450\pi$
$548$	35.2855	1.50732
$549$	27.7287	1.18343
$550$	0	0
$551$	−1.34608	−0.0573451
$552$	−3.54318	−0.150808
$553$	−14.7496	−0.627217
$554$	0.103767	0.00440864
$555$	0	0
$556$	1.01830	0.0431857
$557$	−10.4323	−0.442033	−0.221016	−	0.975270i	$-0.570937\pi$
$557$	−10.4323	−0.442033	−0.221016	+	0.975270i	$0.570937\pi$
$558$	7.52089	0.318385
$559$	26.1973	1.10803
$560$	0	0
$561$	−84.9125	−3.58501
$562$	3.10130	0.130820
$563$	31.1211	1.31160	0.655799	−	0.754935i	$-0.272332\pi$
$563$	31.1211	1.31160	0.655799	+	0.754935i	$0.272332\pi$
$564$	−32.8780	−1.38442
$565$	0	0
$566$	4.57990	0.192507
$567$	−13.3962	−0.562586
$568$	−12.5395	−0.526147
$569$	−19.1533	−0.802947	−0.401474	−	0.915871i	$-0.631502\pi$
$569$	−19.1533	−0.802947	−0.401474	+	0.915871i	$0.631502\pi$
$570$	0	0
$571$	−7.47099	−0.312651	−0.156326	−	0.987706i	$-0.549965\pi$
$571$	−7.47099	−0.312651	−0.156326	+	0.987706i	$0.549965\pi$
$572$	−38.8712	−1.62529
$573$	−16.4004	−0.685138
$574$	2.17542	0.0908003
$575$	0	0
$576$	−38.7589	−1.61495
$577$	46.4776	1.93489	0.967443	−	0.253089i	$-0.0814464\pi$
$577$	46.4776	1.93489	0.967443	+	0.253089i	$0.0814464\pi$
$578$	3.51080	0.146030
$579$	38.2468	1.58948
$580$	0	0
$581$	−7.12278	−0.295503
$582$	−16.9811	−0.703889
$583$	49.4216	2.04683
$584$	4.48426	0.185560
$585$	0	0
$586$	4.33041	0.178887
$587$	16.3078	0.673095	0.336547	−	0.941667i	$-0.390741\pi$
$587$	16.3078	0.673095	0.336547	+	0.941667i	$0.390741\pi$
$588$	5.88642	0.242752
$589$	25.1632	1.03683
$590$	0	0
$591$	19.7484	0.812341
$592$	−35.9452	−1.47734
$593$	33.4569	1.37391	0.686955	−	0.726700i	$-0.258947\pi$
$593$	33.4569	1.37391	0.686955	+	0.726700i	$0.258947\pi$
$594$	−16.0966	−0.660451
$595$	0	0
$596$	32.2124	1.31947
$597$	−71.9900	−2.94635
$598$	−1.16510	−0.0476444
$599$	11.6032	0.474096	0.237048	−	0.971498i	$-0.423820\pi$
$599$	11.6032	0.474096	0.237048	+	0.971498i	$0.423820\pi$
$600$	0	0
$601$	−19.4574	−0.793682	−0.396841	−	0.917887i	$-0.629894\pi$
$601$	−19.4574	−0.793682	−0.396841	+	0.917887i	$0.629894\pi$
$602$	−1.94750	−0.0793743
$603$	6.29144	0.256207
$604$	25.2040	1.02554
$605$	0	0
$606$	−8.15099	−0.331111
$607$	−27.8988	−1.13238	−0.566189	−	0.824275i	$-0.691583\pi$
$607$	−27.8988	−1.13238	−0.566189	+	0.824275i	$0.691583\pi$
$608$	21.1960	0.859611
$609$	−0.650576	−0.0263627
$610$	0	0
$611$	−22.1119	−0.894550
$612$	−66.5282	−2.68924
$613$	32.3662	1.30726	0.653630	−	0.756814i	$-0.273245\pi$
$613$	32.3662	1.30726	0.653630	+	0.756814i	$0.273245\pi$
$614$	−1.75782	−0.0709400
$615$	0	0
$616$	5.91015	0.238127
$617$	−5.75136	−0.231541	−0.115771	−	0.993276i	$-0.536934\pi$
$617$	−5.75136	−0.231541	−0.115771	+	0.993276i	$0.536934\pi$
$618$	0.435923	0.0175354
$619$	35.0247	1.40776	0.703881	−	0.710318i	$-0.251449\pi$
$619$	35.0247	1.40776	0.703881	+	0.710318i	$0.251449\pi$
$620$	0	0
$621$	10.6583	0.427703
$622$	−6.41247	−0.257117
$623$	3.82796	0.153364
$624$	−42.4790	−1.70052
$625$	0	0
$626$	−0.529537	−0.0211645
$627$	−100.491	−4.01321
$628$	7.84929	0.313221
$629$	−55.4313	−2.21019
$630$	0	0
$631$	30.6491	1.22012	0.610061	−	0.792355i	$-0.291145\pi$
$631$	30.6491	1.22012	0.610061	+	0.792355i	$0.291145\pi$
$632$	−16.9873	−0.675720
$633$	73.9307	2.93848
$634$	2.90911	0.115535
$635$	0	0
$636$	56.6910	2.24795
$637$	3.95886	0.156856
$638$	−0.319371	−0.0126440
$639$	70.3835	2.78433
$640$	0	0
$641$	17.2394	0.680916	0.340458	−	0.940260i	$-0.389418\pi$
$641$	17.2394	0.680916	0.340458	+	0.940260i	$0.389418\pi$
$642$	−0.925434	−0.0365240
$643$	−45.8636	−1.80868	−0.904342	−	0.426808i	$-0.859638\pi$
$643$	−45.8636	−1.80868	−0.904342	+	0.426808i	$0.859638\pi$
$644$	−1.91339	−0.0753980
$645$	0	0
$646$	10.0759	0.396431
$647$	−2.68743	−0.105654	−0.0528270	−	0.998604i	$-0.516823\pi$
$647$	−2.68743	−0.105654	−0.0528270	+	0.998604i	$0.516823\pi$
$648$	−15.4286	−0.606091
$649$	28.5288	1.11985
$650$	0	0
$651$	12.1616	0.476652
$652$	15.9271	0.623755
$653$	−19.9602	−0.781102	−0.390551	−	0.920581i	$-0.627715\pi$
$653$	−19.9602	−0.781102	−0.390551	+	0.920581i	$0.627715\pi$
$654$	2.59769	0.101578
$655$	0	0
$656$	−25.7814	−1.00659
$657$	−25.1698	−0.981969
$658$	1.64379	0.0640816
$659$	16.7049	0.650729	0.325364	−	0.945589i	$-0.394513\pi$
$659$	16.7049	0.650729	0.325364	+	0.945589i	$0.394513\pi$
$660$	0	0
$661$	39.9384	1.55342	0.776711	−	0.629857i	$-0.216886\pi$
$661$	39.9384	1.55342	0.776711	+	0.629857i	$0.216886\pi$
$662$	−3.24450	−0.126101
$663$	−65.5071	−2.54408
$664$	−8.20341	−0.318354
$665$	0	0
$666$	−19.6070	−0.759758
$667$	0.211470	0.00818816
$668$	−4.08158	−0.157921
$669$	5.05363	0.195385
$670$	0	0
$671$	22.0115	0.849743
$672$	10.2442	0.395180
$673$	32.5765	1.25573	0.627866	−	0.778321i	$-0.283928\pi$
$673$	32.5765	1.25573	0.627866	+	0.778321i	$0.283928\pi$
$674$	1.28829	0.0496229
$675$	0	0
$676$	−5.11374	−0.196682
$677$	11.1191	0.427340	0.213670	−	0.976906i	$-0.431458\pi$
$677$	11.1191	0.427340	0.213670	+	0.976906i	$0.431458\pi$
$678$	8.47415	0.325448
$679$	−18.7554	−0.719765
$680$	0	0
$681$	−51.3683	−1.96844
$682$	5.97020	0.228611
$683$	25.8940	0.990807	0.495404	−	0.868663i	$-0.335020\pi$
$683$	25.8940	0.990807	0.495404	+	0.868663i	$0.335020\pi$
$684$	−78.7335	−3.01045
$685$	0	0
$686$	−0.294301	−0.0112365
$687$	86.7662	3.31034
$688$	23.0803	0.879927
$689$	38.1271	1.45253
$690$	0	0
$691$	−27.0771	−1.03006	−0.515031	−	0.857172i	$-0.672220\pi$
$691$	−27.0771	−1.03006	−0.515031	+	0.857172i	$0.672220\pi$
$692$	2.38975	0.0908447
$693$	−33.1733	−1.26015
$694$	7.11003	0.269893
$695$	0	0
$696$	−0.749277	−0.0284013
$697$	−39.7576	−1.50593
$698$	−5.30024	−0.200617
$699$	45.5718	1.72368
$700$	0	0
$701$	28.1572	1.06348	0.531741	−	0.846907i	$-0.321538\pi$
$701$	28.1572	1.06348	0.531741	+	0.846907i	$0.321538\pi$
$702$	−12.4180	−0.468686
$703$	−65.6007	−2.47418
$704$	−30.7674	−1.15959
$705$	0	0
$706$	0.611534	0.0230154
$707$	−9.00264	−0.338579
$708$	32.7251	1.22988
$709$	−12.1541	−0.456458	−0.228229	−	0.973607i	$-0.573294\pi$
$709$	−12.1541	−0.456458	−0.228229	+	0.973607i	$0.573294\pi$
$710$	0	0
$711$	95.3488	3.57586
$712$	4.40871	0.165224
$713$	−3.95315	−0.148047
$714$	4.86978	0.182247
$715$	0	0
$716$	16.8554	0.629917
$717$	−60.4845	−2.25883
$718$	−5.44734	−0.203293
$719$	−49.0151	−1.82795	−0.913977	−	0.405765i	$-0.867005\pi$
$719$	−49.0151	−1.82795	−0.913977	+	0.405765i	$0.867005\pi$
$720$	0	0
$721$	0.481470	0.0179309
$722$	6.33270	0.235679
$723$	16.9408	0.630034
$724$	−22.3020	−0.828846
$725$	0	0
$726$	−13.8829	−0.515244
$727$	−9.01931	−0.334508	−0.167254	−	0.985914i	$-0.553490\pi$
$727$	−9.01931	−0.334508	−0.167254	+	0.985914i	$0.553490\pi$
$728$	4.55948	0.168986
$729$	−11.7695	−0.435907
$730$	0	0
$731$	35.5923	1.31643
$732$	25.2491	0.933234
$733$	27.5416	1.01727	0.508637	−	0.860981i	$-0.330150\pi$
$733$	27.5416	1.01727	0.508637	+	0.860981i	$0.330150\pi$
$734$	−1.10782	−0.0408905
$735$	0	0
$736$	−3.32990	−0.122742
$737$	4.99424	0.183965
$738$	−14.0630	−0.517666
$739$	−43.9338	−1.61613	−0.808066	−	0.589092i	$-0.799486\pi$
$739$	−43.9338	−1.61613	−0.808066	+	0.589092i	$0.799486\pi$
$740$	0	0
$741$	−77.5250	−2.84795
$742$	−2.83436	−0.104053
$743$	5.63645	0.206781	0.103391	−	0.994641i	$-0.467031\pi$
$743$	5.63645	0.206781	0.103391	+	0.994641i	$0.467031\pi$
$744$	14.0067	0.513511
$745$	0	0
$746$	−3.06273	−0.112134
$747$	46.0452	1.68470
$748$	−52.8112	−1.93097
$749$	−1.02213	−0.0373477
$750$	0	0
$751$	−22.2984	−0.813680	−0.406840	−	0.913499i	$-0.633369\pi$
$751$	−22.2984	−0.813680	−0.406840	+	0.913499i	$0.633369\pi$
$752$	−19.4809	−0.710395
$753$	−89.4673	−3.26037
$754$	−0.246384	−0.00897276
$755$	0	0
$756$	−20.3935	−0.741703
$757$	20.4751	0.744179	0.372089	−	0.928197i	$-0.378641\pi$
$757$	20.4751	0.744179	0.372089	+	0.928197i	$0.378641\pi$
$758$	0.484050	0.0175815
$759$	15.7871	0.573036
$760$	0	0
$761$	0.909333	0.0329633	0.0164816	−	0.999864i	$-0.494753\pi$
$761$	0.909333	0.0329633	0.0164816	+	0.999864i	$0.494753\pi$
$762$	4.73405	0.171497
$763$	2.86911	0.103869
$764$	−10.2002	−0.369031
$765$	0	0
$766$	7.21755	0.260781
$767$	22.0090	0.794698
$768$	−29.2632	−1.05594
$769$	3.50793	0.126499	0.0632496	−	0.997998i	$-0.479854\pi$
$769$	3.50793	0.126499	0.0632496	+	0.997998i	$0.479854\pi$
$770$	0	0
$771$	3.46702	0.124862
$772$	23.7876	0.856133
$773$	−40.9075	−1.47134	−0.735670	−	0.677340i	$-0.763132\pi$
$773$	−40.9075	−1.47134	−0.735670	+	0.677340i	$0.763132\pi$
$774$	12.5896	0.452525
$775$	0	0
$776$	−21.6008	−0.775424
$777$	−31.7055	−1.13743
$778$	6.30791	0.226150
$779$	−47.0516	−1.68580
$780$	0	0
$781$	55.8716	1.99924
$782$	−1.58293	−0.0566053
$783$	2.25391	0.0805483
$784$	3.48782	0.124565
$785$	0	0
$786$	7.51207	0.267947
$787$	−15.9735	−0.569396	−0.284698	−	0.958617i	$-0.591893\pi$
$787$	−15.9735	−0.569396	−0.284698	+	0.958617i	$0.591893\pi$
$788$	12.2825	0.437546
$789$	29.9394	1.06587
$790$	0	0
$791$	9.35957	0.332788
$792$	−38.2061	−1.35760
$793$	16.9811	0.603016
$794$	−2.03845	−0.0723418
$795$	0	0
$796$	−44.7740	−1.58697
$797$	−12.5234	−0.443601	−0.221801	−	0.975092i	$-0.571193\pi$
$797$	−12.5234	−0.443601	−0.221801	+	0.975092i	$0.571193\pi$
$798$	5.76319	0.204015
$799$	−30.0416	−1.06280
$800$	0	0
$801$	−24.7458	−0.874350
$802$	−3.14634	−0.111101
$803$	−19.9802	−0.705087
$804$	5.72884	0.202041
$805$	0	0
$806$	4.60581	0.162233
$807$	−68.6130	−2.41529
$808$	−10.3685	−0.364761
$809$	−31.8809	−1.12087	−0.560437	−	0.828197i	$-0.689367\pi$
$809$	−31.8809	−1.12087	−0.560437	+	0.828197i	$0.689367\pi$
$810$	0	0
$811$	−31.5796	−1.10891	−0.554455	−	0.832214i	$-0.687073\pi$
$811$	−31.5796	−1.10891	−0.554455	+	0.832214i	$0.687073\pi$
$812$	−0.404624	−0.0141995
$813$	4.84171	0.169806
$814$	−15.5644	−0.545532
$815$	0	0
$816$	−57.7128	−2.02035
$817$	42.1220	1.47366
$818$	−1.15450	−0.0403662
$819$	−25.5920	−0.894258
$820$	0	0
$821$	−5.97979	−0.208696	−0.104348	−	0.994541i	$-0.533276\pi$
$821$	−5.97979	−0.208696	−0.104348	+	0.994541i	$0.533276\pi$
$822$	16.6968	0.582368
$823$	10.2825	0.358425	0.179213	−	0.983810i	$-0.442645\pi$
$823$	10.2825	0.358425	0.179213	+	0.983810i	$0.442645\pi$
$824$	0.554516	0.0193175
$825$	0	0
$826$	−1.63614	−0.0569287
$827$	−22.5563	−0.784361	−0.392181	−	0.919888i	$-0.628279\pi$
$827$	−22.5563	−0.784361	−0.392181	+	0.919888i	$0.628279\pi$
$828$	12.3691	0.429855
$829$	6.99835	0.243063	0.121531	−	0.992588i	$-0.461220\pi$
$829$	6.99835	0.243063	0.121531	+	0.992588i	$0.461220\pi$
$830$	0	0
$831$	−1.08472	−0.0376284
$832$	−23.7360	−0.822897
$833$	5.37860	0.186357
$834$	0.481853	0.0166852
$835$	0	0
$836$	−62.5000	−2.16161
$837$	−42.1339	−1.45636
$838$	−8.02316	−0.277155
$839$	−10.7152	−0.369930	−0.184965	−	0.982745i	$-0.559217\pi$
$839$	−10.7152	−0.369930	−0.184965	+	0.982745i	$0.559217\pi$
$840$	0	0
$841$	−28.9553	−0.998458
$842$	8.81392	0.303748
$843$	−32.4191	−1.11657
$844$	45.9810	1.58273
$845$	0	0
$846$	−10.6263	−0.365339
$847$	−15.3335	−0.526865
$848$	33.5906	1.15350
$849$	−47.8754	−1.64308
$850$	0	0
$851$	10.3059	0.353282
$852$	64.0897	2.19568
$853$	−35.0450	−1.19992	−0.599958	−	0.800031i	$-0.704816\pi$
$853$	−35.0450	−1.19992	−0.599958	+	0.800031i	$0.704816\pi$
$854$	−1.26237	−0.0431974
$855$	0	0
$856$	−1.17720	−0.0402358
$857$	−10.2807	−0.351182	−0.175591	−	0.984463i	$-0.556184\pi$
$857$	−10.2807	−0.351182	−0.175591	+	0.984463i	$0.556184\pi$
$858$	−18.3935	−0.627945
$859$	−11.2019	−0.382205	−0.191102	−	0.981570i	$-0.561206\pi$
$859$	−11.2019	−0.382205	−0.191102	+	0.981570i	$0.561206\pi$
$860$	0	0
$861$	−22.7405	−0.774995
$862$	−6.41693	−0.218561
$863$	−26.3781	−0.897922	−0.448961	−	0.893551i	$-0.648206\pi$
$863$	−26.3781	−0.897922	−0.448961	+	0.893551i	$0.648206\pi$
$864$	−35.4911	−1.20743
$865$	0	0
$866$	3.13551	0.106549
$867$	−36.6998	−1.24639
$868$	7.56390	0.256736
$869$	75.6894	2.56759
$870$	0	0
$871$	3.85289	0.130550
$872$	3.30439	0.111901
$873$	121.244	4.10348
$874$	−1.87333	−0.0633664
$875$	0	0
$876$	−22.9191	−0.774364
$877$	49.9079	1.68527	0.842635	−	0.538485i	$-0.181003\pi$
$877$	49.9079	1.68527	0.842635	+	0.538485i	$0.181003\pi$
$878$	10.5848	0.357220
$879$	−45.2674	−1.52683
$880$	0	0
$881$	−20.7890	−0.700398	−0.350199	−	0.936675i	$-0.613886\pi$
$881$	−20.7890	−0.700398	−0.350199	+	0.936675i	$0.613886\pi$
$882$	1.90251	0.0640607
$883$	4.42580	0.148940	0.0744699	−	0.997223i	$-0.476274\pi$
$883$	4.42580	0.148940	0.0744699	+	0.997223i	$0.476274\pi$
$884$	−40.7420	−1.37030
$885$	0	0
$886$	−3.91215	−0.131431
$887$	7.03226	0.236120	0.118060	−	0.993006i	$-0.462332\pi$
$887$	7.03226	0.236120	0.118060	+	0.993006i	$0.462332\pi$
$888$	−36.5157	−1.22539
$889$	5.22869	0.175365
$890$	0	0
$891$	68.7440	2.30301
$892$	3.14309	0.105239
$893$	−35.5531	−1.18974
$894$	15.2426	0.509790
$895$	0	0
$896$	8.42432	0.281437
$897$	12.1792	0.406652
$898$	−3.81019	−0.127148
$899$	−0.835973	−0.0278813
$900$	0	0
$901$	51.8002	1.72572
$902$	−11.1634	−0.371702
$903$	20.3580	0.677472
$904$	10.7795	0.358522
$905$	0	0
$906$	11.9263	0.396226
$907$	−54.4920	−1.80938	−0.904688	−	0.426074i	$-0.859896\pi$
$907$	−54.4920	−1.80938	−0.904688	+	0.426074i	$0.859896\pi$
$908$	−31.9484	−1.06025
$909$	58.1975	1.93029
$910$	0	0
$911$	6.10327	0.202210	0.101105	−	0.994876i	$-0.467762\pi$
$911$	6.10327	0.202210	0.101105	+	0.994876i	$0.467762\pi$
$912$	−68.3008	−2.26167
$913$	36.5514	1.20967
$914$	−7.79814	−0.257939
$915$	0	0
$916$	53.9641	1.78302
$917$	8.29697	0.273990
$918$	−16.8713	−0.556836
$919$	39.5800	1.30562	0.652812	−	0.757520i	$-0.273589\pi$
$919$	39.5800	1.30562	0.652812	+	0.757520i	$0.273589\pi$
$920$	0	0
$921$	18.3752	0.605484
$922$	−0.799331	−0.0263246
$923$	43.1030	1.41875
$924$	−30.2069	−0.993733
$925$	0	0
$926$	11.0018	0.361542
$927$	−3.11246	−0.102227
$928$	−0.704174	−0.0231157
$929$	−26.4534	−0.867907	−0.433954	−	0.900935i	$-0.642882\pi$
$929$	−26.4534	−0.867907	−0.433954	+	0.900935i	$0.642882\pi$
$930$	0	0
$931$	6.36536	0.208616
$932$	28.3433	0.928415
$933$	67.0320	2.19453
$934$	12.1227	0.396667
$935$	0	0
$936$	−29.4747	−0.963411
$937$	19.0681	0.622929	0.311464	−	0.950258i	$-0.399181\pi$
$937$	19.0681	0.622929	0.311464	+	0.950258i	$0.399181\pi$
$938$	−0.286423	−0.00935203
$939$	5.53545	0.180643
$940$	0	0
$941$	5.19794	0.169448	0.0847239	−	0.996404i	$-0.472999\pi$
$941$	5.19794	0.169448	0.0847239	+	0.996404i	$0.472999\pi$
$942$	3.71422	0.121016
$943$	7.39183	0.240711
$944$	19.3903	0.631099
$945$	0	0
$946$	9.99384	0.324928
$947$	−6.67752	−0.216990	−0.108495	−	0.994097i	$-0.534603\pi$
$947$	−6.67752	−0.216990	−0.108495	+	0.994097i	$0.534603\pi$
$948$	86.8225	2.81986
$949$	−15.4140	−0.500361
$950$	0	0
$951$	−30.4100	−0.986112
$952$	6.19460	0.200768
$953$	34.8232	1.12804	0.564018	−	0.825763i	$-0.309255\pi$
$953$	34.8232	1.12804	0.564018	+	0.825763i	$0.309255\pi$
$954$	18.3227	0.593219
$955$	0	0
$956$	−37.6182	−1.21666
$957$	3.33851	0.107919
$958$	0.371468	0.0120016
$959$	18.4414	0.595503
$960$	0	0
$961$	−15.3726	−0.495891
$962$	−12.0074	−0.387134
$963$	6.60754	0.212925
$964$	10.5363	0.339351
$965$	0	0
$966$	−0.905400	−0.0291308
$967$	23.9481	0.770118	0.385059	−	0.922892i	$-0.374181\pi$
$967$	23.9481	0.770118	0.385059	+	0.922892i	$0.374181\pi$
$968$	−17.6598	−0.567607
$969$	−105.327	−3.38359
$970$	0	0
$971$	−51.0744	−1.63906	−0.819528	−	0.573039i	$-0.805764\pi$
$971$	−51.0744	−1.63906	−0.819528	+	0.573039i	$0.805764\pi$
$972$	17.6752	0.566931
$973$	0.532199	0.0170615
$974$	9.28895	0.297637
$975$	0	0
$976$	14.9606	0.478877
$977$	−4.73986	−0.151642	−0.0758208	−	0.997121i	$-0.524158\pi$
$977$	−4.73986	−0.151642	−0.0758208	+	0.997121i	$0.524158\pi$
$978$	7.53660	0.240994
$979$	−19.6436	−0.627813
$980$	0	0
$981$	−18.5473	−0.592171
$982$	−8.22612	−0.262506
$983$	23.0332	0.734645	0.367323	−	0.930094i	$-0.380275\pi$
$983$	23.0332	0.734645	0.367323	+	0.930094i	$0.380275\pi$
$984$	−26.1906	−0.834925
$985$	0	0
$986$	−0.334742	−0.0106604
$987$	−17.1832	−0.546946
$988$	−48.2165	−1.53397
$989$	−6.61739	−0.210421
$990$	0	0
$991$	−8.38374	−0.266318	−0.133159	−	0.991095i	$-0.542512\pi$
$991$	−8.38374	−0.266318	−0.133159	+	0.991095i	$0.542512\pi$
$992$	13.1636	0.417944
$993$	33.9160	1.07629
$994$	−3.20427	−0.101633
$995$	0	0
$996$	41.9277	1.32853
$997$	1.50199	0.0475684	0.0237842	−	0.999717i	$-0.492429\pi$
$997$	1.50199	0.0475684	0.0237842	+	0.999717i	$0.492429\pi$
$998$	7.03743	0.222766
$999$	109.843	3.47529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.12		21
5.2	odd	4		805.2.c.c.484.23	yes	42
5.3	odd	4		805.2.c.c.484.20	✓	42
5.4	even	2		4025.2.a.be.1.10		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.20	✓	42	5.3	odd	4
805.2.c.c.484.23	yes	42	5.2	odd	4
4025.2.a.bd.1.12		21	1.1	even	1	trivial
4025.2.a.be.1.10		21	5.4	even	2

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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.294301 q^{2} -3.07644 q^{3} -1.91339 q^{4} -0.905400 q^{6} -1.00000 q^{7} -1.15171 q^{8} +6.46449 q^{9} +O(q^{10})\)	\(q+0.294301 q^{2} -3.07644 q^{3} -1.91339 q^{4} -0.905400 q^{6} -1.00000 q^{7} -1.15171 q^{8} +6.46449 q^{9} +5.13162 q^{11} +5.88642 q^{12} +3.95886 q^{13} -0.294301 q^{14} +3.48782 q^{16} +5.37860 q^{17} +1.90251 q^{18} +6.36536 q^{19} +3.07644 q^{21} +1.51024 q^{22} -1.00000 q^{23} +3.54318 q^{24} +1.16510 q^{26} -10.6583 q^{27} +1.91339 q^{28} -0.211470 q^{29} +3.95315 q^{31} +3.32990 q^{32} -15.7871 q^{33} +1.58293 q^{34} -12.3691 q^{36} -10.3059 q^{37} +1.87333 q^{38} -12.1792 q^{39} -7.39183 q^{41} +0.905400 q^{42} +6.61739 q^{43} -9.81877 q^{44} -0.294301 q^{46} -5.58540 q^{47} -10.7301 q^{48} +1.00000 q^{49} -16.5469 q^{51} -7.57484 q^{52} +9.63081 q^{53} -3.13675 q^{54} +1.15171 q^{56} -19.5826 q^{57} -0.0622359 q^{58} +5.55942 q^{59} +4.28938 q^{61} +1.16342 q^{62} -6.46449 q^{63} -5.99565 q^{64} -4.64617 q^{66} +0.973230 q^{67} -10.2913 q^{68} +3.07644 q^{69} +10.8877 q^{71} -7.44524 q^{72} -3.89355 q^{73} -3.03304 q^{74} -12.1794 q^{76} -5.13162 q^{77} -3.58436 q^{78} +14.7496 q^{79} +13.3962 q^{81} -2.17542 q^{82} +7.12278 q^{83} -5.88642 q^{84} +1.94750 q^{86} +0.650576 q^{87} -5.91015 q^{88} -3.82796 q^{89} -3.95886 q^{91} +1.91339 q^{92} -12.1616 q^{93} -1.64379 q^{94} -10.2442 q^{96} +18.7554 q^{97} +0.294301 q^{98} +33.1733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

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