LMFDB - Embedded newform 3525.2.a.bf.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.16553$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.16553 q^{2} +1.00000 q^{3} -0.641537 q^{4} +1.16553 q^{6} +4.15990 q^{7} -3.07879 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.16553 q^{2} +1.00000 q^{3} -0.641537 q^{4} +1.16553 q^{6} +4.15990 q^{7} -3.07879 q^{8} +1.00000 q^{9} -3.81209 q^{11} -0.641537 q^{12} -4.61360 q^{13} +4.84850 q^{14} -2.30535 q^{16} -1.23057 q^{17} +1.16553 q^{18} -2.53013 q^{19} +4.15990 q^{21} -4.44310 q^{22} -2.58264 q^{23} -3.07879 q^{24} -5.37729 q^{26} +1.00000 q^{27} -2.66873 q^{28} -5.43386 q^{29} -6.09333 q^{31} +3.47062 q^{32} -3.81209 q^{33} -1.43427 q^{34} -0.641537 q^{36} -1.49075 q^{37} -2.94894 q^{38} -4.61360 q^{39} +5.04423 q^{41} +4.84850 q^{42} -12.3022 q^{43} +2.44560 q^{44} -3.01015 q^{46} -1.00000 q^{47} -2.30535 q^{48} +10.3048 q^{49} -1.23057 q^{51} +2.95979 q^{52} -6.27544 q^{53} +1.16553 q^{54} -12.8075 q^{56} -2.53013 q^{57} -6.33333 q^{58} +2.67129 q^{59} +12.7902 q^{61} -7.10197 q^{62} +4.15990 q^{63} +8.65583 q^{64} -4.44310 q^{66} -11.3306 q^{67} +0.789458 q^{68} -2.58264 q^{69} -3.49400 q^{71} -3.07879 q^{72} +14.2798 q^{73} -1.73752 q^{74} +1.62317 q^{76} -15.8579 q^{77} -5.37729 q^{78} +5.30405 q^{79} +1.00000 q^{81} +5.87921 q^{82} +5.94379 q^{83} -2.66873 q^{84} -14.3386 q^{86} -5.43386 q^{87} +11.7366 q^{88} -1.23460 q^{89} -19.1921 q^{91} +1.65686 q^{92} -6.09333 q^{93} -1.16553 q^{94} +3.47062 q^{96} +14.5416 q^{97} +12.0106 q^{98} -3.81209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * 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 $

$2$	1.16553	0.824155	0.412077	−	0.911149i	$-0.364803\pi$
$2$	1.16553	0.824155	0.412077	+	0.911149i	$0.364803\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.641537	−0.320769
$5$	0	0
$5$	0	0
$6$	1.16553	0.475826
$7$	4.15990	1.57230	0.786148	−	0.618038i	$-0.212072\pi$
$7$	4.15990	1.57230	0.786148	+	0.618038i	$0.212072\pi$
$8$	−3.07879	−1.08852
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.81209	−1.14939	−0.574694	−	0.818369i	$-0.694879\pi$
$11$	−3.81209	−1.14939	−0.574694	+	0.818369i	$0.694879\pi$
$12$	−0.641537	−0.185196
$13$	−4.61360	−1.27958	−0.639791	−	0.768549i	$-0.720979\pi$
$13$	−4.61360	−1.27958	−0.639791	+	0.768549i	$0.720979\pi$
$14$	4.84850	1.29582
$15$	0	0
$16$	−2.30535	−0.576339
$17$	−1.23057	−0.298457	−0.149229	−	0.988803i	$-0.547679\pi$
$17$	−1.23057	−0.298457	−0.149229	+	0.988803i	$0.547679\pi$
$18$	1.16553	0.274718
$19$	−2.53013	−0.580452	−0.290226	−	0.956958i	$-0.593730\pi$
$19$	−2.53013	−0.580452	−0.290226	+	0.956958i	$0.593730\pi$
$20$	0	0
$21$	4.15990	0.907766
$22$	−4.44310	−0.947273
$23$	−2.58264	−0.538517	−0.269259	−	0.963068i	$-0.586779\pi$
$23$	−2.58264	−0.538517	−0.269259	+	0.963068i	$0.586779\pi$
$24$	−3.07879	−0.628456
$25$	0	0
$26$	−5.37729	−1.05457
$27$	1.00000	0.192450
$28$	−2.66873	−0.504343
$29$	−5.43386	−1.00904	−0.504521	−	0.863399i	$-0.668331\pi$
$29$	−5.43386	−1.00904	−0.504521	+	0.863399i	$0.668331\pi$
$30$	0	0
$31$	−6.09333	−1.09439	−0.547197	−	0.837004i	$-0.684305\pi$
$31$	−6.09333	−1.09439	−0.547197	+	0.837004i	$0.684305\pi$
$32$	3.47062	0.613526
$33$	−3.81209	−0.663599
$34$	−1.43427	−0.245975
$35$	0	0
$36$	−0.641537	−0.106923
$37$	−1.49075	−0.245078	−0.122539	−	0.992464i	$-0.539104\pi$
$37$	−1.49075	−0.245078	−0.122539	+	0.992464i	$0.539104\pi$
$38$	−2.94894	−0.478382
$39$	−4.61360	−0.738767
$40$	0	0
$41$	5.04423	0.787777	0.393888	−	0.919158i	$-0.371130\pi$
$41$	5.04423	0.787777	0.393888	+	0.919158i	$0.371130\pi$
$42$	4.84850	0.748139
$43$	−12.3022	−1.87607	−0.938037	−	0.346534i	$-0.887359\pi$
$43$	−12.3022	−1.87607	−0.938037	+	0.346534i	$0.887359\pi$
$44$	2.44560	0.368687
$45$	0	0
$46$	−3.01015	−0.443822
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−2.30535	−0.332749
$49$	10.3048	1.47212
$50$	0	0
$51$	−1.23057	−0.172314
$52$	2.95979	0.410450
$53$	−6.27544	−0.861998	−0.430999	−	0.902352i	$-0.641839\pi$
$53$	−6.27544	−0.861998	−0.430999	+	0.902352i	$0.641839\pi$
$54$	1.16553	0.158609
$55$	0	0
$56$	−12.8075	−1.71147
$57$	−2.53013	−0.335124
$58$	−6.33333	−0.831607
$59$	2.67129	0.347772	0.173886	−	0.984766i	$-0.444368\pi$
$59$	2.67129	0.347772	0.173886	+	0.984766i	$0.444368\pi$
$60$	0	0
$61$	12.7902	1.63762	0.818811	−	0.574064i	$-0.194634\pi$
$61$	12.7902	1.63762	0.818811	+	0.574064i	$0.194634\pi$
$62$	−7.10197	−0.901951
$63$	4.15990	0.524099
$64$	8.65583	1.08198
$65$	0	0
$66$	−4.44310	−0.546908
$67$	−11.3306	−1.38425	−0.692127	−	0.721776i	$-0.743326\pi$
$67$	−11.3306	−1.38425	−0.692127	+	0.721776i	$0.743326\pi$
$68$	0.789458	0.0957358
$69$	−2.58264	−0.310913
$70$	0	0
$71$	−3.49400	−0.414661	−0.207331	−	0.978271i	$-0.566478\pi$
$71$	−3.49400	−0.414661	−0.207331	+	0.978271i	$0.566478\pi$
$72$	−3.07879	−0.362839
$73$	14.2798	1.67132	0.835662	−	0.549244i	$-0.185084\pi$
$73$	14.2798	1.67132	0.835662	+	0.549244i	$0.185084\pi$
$74$	−1.73752	−0.201982
$75$	0	0
$76$	1.62317	0.186191
$77$	−15.8579	−1.80718
$78$	−5.37729	−0.608858
$79$	5.30405	0.596752	0.298376	−	0.954448i	$-0.403555\pi$
$79$	5.30405	0.596752	0.298376	+	0.954448i	$0.403555\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.87921	0.649250
$83$	5.94379	0.652415	0.326208	−	0.945298i	$-0.394229\pi$
$83$	5.94379	0.652415	0.326208	+	0.945298i	$0.394229\pi$
$84$	−2.66873	−0.291183
$85$	0	0
$86$	−14.3386	−1.54618
$87$	−5.43386	−0.582571
$88$	11.7366	1.25113
$89$	−1.23460	−0.130868	−0.0654338	−	0.997857i	$-0.520843\pi$
$89$	−1.23460	−0.130868	−0.0654338	+	0.997857i	$0.520843\pi$
$90$	0	0
$91$	−19.1921	−2.01188
$92$	1.65686	0.172740
$93$	−6.09333	−0.631849
$94$	−1.16553	−0.120215
$95$	0	0
$96$	3.47062	0.354219
$97$	14.5416	1.47647	0.738236	−	0.674542i	$-0.235659\pi$
$97$	14.5416	1.47647	0.738236	+	0.674542i	$0.235659\pi$
$98$	12.0106	1.21325
$99$	−3.81209	−0.383129
$100$	0	0
$101$	−5.91317	−0.588382	−0.294191	−	0.955747i	$-0.595050\pi$
$101$	−5.91317	−0.588382	−0.294191	+	0.955747i	$0.595050\pi$
$102$	−1.43427	−0.142014
$103$	3.70244	0.364813	0.182406	−	0.983223i	$-0.441611\pi$
$103$	3.70244	0.364813	0.182406	+	0.983223i	$0.441611\pi$
$104$	14.2043	1.39285
$105$	0	0
$106$	−7.31422	−0.710420
$107$	−18.6364	−1.80165	−0.900826	−	0.434181i	$-0.857038\pi$
$107$	−18.6364	−1.80165	−0.900826	+	0.434181i	$0.857038\pi$
$108$	−0.641537	−0.0617320
$109$	−11.8589	−1.13588	−0.567940	−	0.823070i	$-0.692259\pi$
$109$	−11.8589	−1.13588	−0.567940	+	0.823070i	$0.692259\pi$
$110$	0	0
$111$	−1.49075	−0.141496
$112$	−9.59006	−0.906175
$113$	−12.2064	−1.14828	−0.574142	−	0.818755i	$-0.694664\pi$
$113$	−12.2064	−1.14828	−0.574142	+	0.818755i	$0.694664\pi$
$114$	−2.94894	−0.276194
$115$	0	0
$116$	3.48602	0.323669
$117$	−4.61360	−0.426527
$118$	3.11347	0.286618
$119$	−5.11906	−0.469263
$120$	0	0
$121$	3.53200	0.321091
$122$	14.9074	1.34965
$123$	5.04423	0.454823
$124$	3.90910	0.351048
$125$	0	0
$126$	4.84850	0.431939
$127$	11.6492	1.03370	0.516850	−	0.856076i	$-0.327105\pi$
$127$	11.6492	1.03370	0.516850	+	0.856076i	$0.327105\pi$
$128$	3.14739	0.278193
$129$	−12.3022	−1.08315
$130$	0	0
$131$	−2.96872	−0.259378	−0.129689	−	0.991555i	$-0.541398\pi$
$131$	−2.96872	−0.259378	−0.129689	+	0.991555i	$0.541398\pi$
$132$	2.44560	0.212862
$133$	−10.5251	−0.912642
$134$	−13.2062	−1.14084
$135$	0	0
$136$	3.78868	0.324876
$137$	−8.98119	−0.767315	−0.383658	−	0.923475i	$-0.625336\pi$
$137$	−8.98119	−0.767315	−0.383658	+	0.923475i	$0.625336\pi$
$138$	−3.01015	−0.256241
$139$	−15.3614	−1.30293	−0.651467	−	0.758677i	$-0.725846\pi$
$139$	−15.3614	−1.30293	−0.651467	+	0.758677i	$0.725846\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−4.07236	−0.341745
$143$	17.5874	1.47073
$144$	−2.30535	−0.192113
$145$	0	0
$146$	16.6435	1.37743
$147$	10.3048	0.849926
$148$	0.956372	0.0786133
$149$	10.6569	0.873046	0.436523	−	0.899693i	$-0.356210\pi$
$149$	10.6569	0.873046	0.436523	+	0.899693i	$0.356210\pi$
$150$	0	0
$151$	5.11859	0.416545	0.208272	−	0.978071i	$-0.433216\pi$
$151$	5.11859	0.416545	0.208272	+	0.978071i	$0.433216\pi$
$152$	7.78975	0.631832
$153$	−1.23057	−0.0994858
$154$	−18.4829	−1.48939
$155$	0	0
$156$	2.95979	0.236973
$157$	−11.5178	−0.919221	−0.459611	−	0.888121i	$-0.652011\pi$
$157$	−11.5178	−0.919221	−0.459611	+	0.888121i	$0.652011\pi$
$158$	6.18204	0.491816
$159$	−6.27544	−0.497675
$160$	0	0
$161$	−10.7435	−0.846709
$162$	1.16553	0.0915728
$163$	6.71301	0.525804	0.262902	−	0.964823i	$-0.415320\pi$
$163$	6.71301	0.525804	0.262902	+	0.964823i	$0.415320\pi$
$164$	−3.23606	−0.252694
$165$	0	0
$166$	6.92767	0.537691
$167$	16.8981	1.30761	0.653806	−	0.756662i	$-0.273171\pi$
$167$	16.8981	1.30761	0.653806	+	0.756662i	$0.273171\pi$
$168$	−12.8075	−0.988119
$169$	8.28526	0.637328
$170$	0	0
$171$	−2.53013	−0.193484
$172$	7.89235	0.601786
$173$	−13.5026	−1.02658	−0.513292	−	0.858214i	$-0.671574\pi$
$173$	−13.5026	−1.02658	−0.513292	+	0.858214i	$0.671574\pi$
$174$	−6.33333	−0.480129
$175$	0	0
$176$	8.78821	0.662436
$177$	2.67129	0.200787
$178$	−1.43897	−0.107855
$179$	−5.85657	−0.437741	−0.218870	−	0.975754i	$-0.570237\pi$
$179$	−5.85657	−0.437741	−0.218870	+	0.975754i	$0.570237\pi$
$180$	0	0
$181$	18.2839	1.35903	0.679515	−	0.733662i	$-0.262190\pi$
$181$	18.2839	1.35903	0.679515	+	0.733662i	$0.262190\pi$
$182$	−22.3690	−1.65810
$183$	12.7902	0.945481
$184$	7.95141	0.586186
$185$	0	0
$186$	−7.10197	−0.520741
$187$	4.69104	0.343043
$188$	0.641537	0.0467889
$189$	4.15990	0.302589
$190$	0	0
$191$	−5.42659	−0.392655	−0.196327	−	0.980538i	$-0.562902\pi$
$191$	−5.42659	−0.392655	−0.196327	+	0.980538i	$0.562902\pi$
$192$	8.65583	0.624681
$193$	17.7710	1.27918	0.639592	−	0.768715i	$-0.279104\pi$
$193$	17.7710	1.27918	0.639592	+	0.768715i	$0.279104\pi$
$194$	16.9487	1.21684
$195$	0	0
$196$	−6.61092	−0.472208
$197$	−2.41574	−0.172114	−0.0860571	−	0.996290i	$-0.527427\pi$
$197$	−2.41574	−0.172114	−0.0860571	+	0.996290i	$0.527427\pi$
$198$	−4.44310	−0.315758
$199$	−7.71405	−0.546834	−0.273417	−	0.961896i	$-0.588154\pi$
$199$	−7.71405	−0.546834	−0.273417	+	0.961896i	$0.588154\pi$
$200$	0	0
$201$	−11.3306	−0.799200
$202$	−6.89198	−0.484918
$203$	−22.6043	−1.58651
$204$	0.789458	0.0552731
$205$	0	0
$206$	4.31531	0.300662
$207$	−2.58264	−0.179506
$208$	10.6360	0.737472
$209$	9.64507	0.667164
$210$	0	0
$211$	1.21651	0.0837481	0.0418740	−	0.999123i	$-0.486667\pi$
$211$	1.21651	0.0837481	0.0418740	+	0.999123i	$0.486667\pi$
$212$	4.02593	0.276502
$213$	−3.49400	−0.239405
$214$	−21.7213	−1.48484
$215$	0	0
$216$	−3.07879	−0.209485
$217$	−25.3477	−1.72071
$218$	−13.8220	−0.936141
$219$	14.2798	0.964939
$220$	0	0
$221$	5.67736	0.381901
$222$	−1.73752	−0.116614
$223$	28.0985	1.88161	0.940806	−	0.338945i	$-0.110070\pi$
$223$	28.0985	1.88161	0.940806	+	0.338945i	$0.110070\pi$
$224$	14.4375	0.964644
$225$	0	0
$226$	−14.2270	−0.946365
$227$	25.5840	1.69807	0.849034	−	0.528339i	$-0.177185\pi$
$227$	25.5840	1.69807	0.849034	+	0.528339i	$0.177185\pi$
$228$	1.62317	0.107497
$229$	−28.8181	−1.90435	−0.952176	−	0.305550i	$-0.901160\pi$
$229$	−28.8181	−1.90435	−0.952176	+	0.305550i	$0.901160\pi$
$230$	0	0
$231$	−15.8579	−1.04337
$232$	16.7297	1.09836
$233$	7.58573	0.496957	0.248479	−	0.968637i	$-0.420069\pi$
$233$	7.58573	0.496957	0.248479	+	0.968637i	$0.420069\pi$
$234$	−5.37729	−0.351524
$235$	0	0
$236$	−1.71373	−0.111555
$237$	5.30405	0.344535
$238$	−5.96642	−0.386746
$239$	−6.26770	−0.405424	−0.202712	−	0.979238i	$-0.564976\pi$
$239$	−6.26770	−0.405424	−0.202712	+	0.979238i	$0.564976\pi$
$240$	0	0
$241$	3.08604	0.198790	0.0993948	−	0.995048i	$-0.468309\pi$
$241$	3.08604	0.198790	0.0993948	+	0.995048i	$0.468309\pi$
$242$	4.11665	0.264628
$243$	1.00000	0.0641500
$244$	−8.20541	−0.525298
$245$	0	0
$246$	5.87921	0.374845
$247$	11.6730	0.742735
$248$	18.7601	1.19127
$249$	5.94379	0.376672
$250$	0	0
$251$	−28.3257	−1.78790	−0.893950	−	0.448166i	$-0.852077\pi$
$251$	−28.3257	−1.78790	−0.893950	+	0.448166i	$0.852077\pi$
$252$	−2.66873	−0.168114
$253$	9.84524	0.618965
$254$	13.5775	0.851928
$255$	0	0
$256$	−13.6433	−0.852705
$257$	−31.1489	−1.94301	−0.971506	−	0.237015i	$-0.923831\pi$
$257$	−31.1489	−1.94301	−0.971506	+	0.237015i	$0.923831\pi$
$258$	−14.3386	−0.892685
$259$	−6.20138	−0.385335
$260$	0	0
$261$	−5.43386	−0.336348
$262$	−3.46014	−0.213768
$263$	−20.2925	−1.25129	−0.625643	−	0.780109i	$-0.715164\pi$
$263$	−20.2925	−1.25129	−0.625643	+	0.780109i	$0.715164\pi$
$264$	11.7366	0.722339
$265$	0	0
$266$	−12.2673	−0.752158
$267$	−1.23460	−0.0755565
$268$	7.26901	0.444025
$269$	−12.3091	−0.750498	−0.375249	−	0.926924i	$-0.622443\pi$
$269$	−12.3091	−0.750498	−0.375249	+	0.926924i	$0.622443\pi$
$270$	0	0
$271$	4.15010	0.252101	0.126050	−	0.992024i	$-0.459770\pi$
$271$	4.15010	0.252101	0.126050	+	0.992024i	$0.459770\pi$
$272$	2.83690	0.172013
$273$	−19.1921	−1.16156
$274$	−10.4679	−0.632387
$275$	0	0
$276$	1.65686	0.0997312
$277$	26.8137	1.61108	0.805541	−	0.592540i	$-0.201875\pi$
$277$	26.8137	1.61108	0.805541	+	0.592540i	$0.201875\pi$
$278$	−17.9042	−1.07382
$279$	−6.09333	−0.364798
$280$	0	0
$281$	−6.98903	−0.416930	−0.208465	−	0.978030i	$-0.566847\pi$
$281$	−6.98903	−0.416930	−0.208465	+	0.978030i	$0.566847\pi$
$282$	−1.16553	−0.0694064
$283$	−20.1757	−1.19932	−0.599660	−	0.800255i	$-0.704697\pi$
$283$	−20.1757	−1.19932	−0.599660	+	0.800255i	$0.704697\pi$
$284$	2.24153	0.133010
$285$	0	0
$286$	20.4987	1.21211
$287$	20.9835	1.23862
$288$	3.47062	0.204509
$289$	−15.4857	−0.910923
$290$	0	0
$291$	14.5416	0.852442
$292$	−9.16102	−0.536108
$293$	−2.10609	−0.123039	−0.0615196	−	0.998106i	$-0.519595\pi$
$293$	−2.10609	−0.123039	−0.0615196	+	0.998106i	$0.519595\pi$
$294$	12.0106	0.700471
$295$	0	0
$296$	4.58971	0.266772
$297$	−3.81209	−0.221200
$298$	12.4209	0.719525
$299$	11.9153	0.689077
$300$	0	0
$301$	−51.1762	−2.94975
$302$	5.96587	0.343297
$303$	−5.91317	−0.339703
$304$	5.83285	0.334537
$305$	0	0
$306$	−1.43427	−0.0819917
$307$	17.1013	0.976020	0.488010	−	0.872838i	$-0.337723\pi$
$307$	17.1013	0.976020	0.488010	+	0.872838i	$0.337723\pi$
$308$	10.1734	0.579686
$309$	3.70244	0.210625
$310$	0	0
$311$	30.7032	1.74102	0.870510	−	0.492150i	$-0.163789\pi$
$311$	30.7032	1.74102	0.870510	+	0.492150i	$0.163789\pi$
$312$	14.2043	0.804161
$313$	1.89191	0.106937	0.0534686	−	0.998570i	$-0.482972\pi$
$313$	1.89191	0.106937	0.0534686	+	0.998570i	$0.482972\pi$
$314$	−13.4244	−0.757581
$315$	0	0
$316$	−3.40275	−0.191420
$317$	−18.9576	−1.06476	−0.532382	−	0.846504i	$-0.678703\pi$
$317$	−18.9576	−1.06476	−0.532382	+	0.846504i	$0.678703\pi$
$318$	−7.31422	−0.410161
$319$	20.7143	1.15978
$320$	0	0
$321$	−18.6364	−1.04018
$322$	−12.5219	−0.697819
$323$	3.11351	0.173240
$324$	−0.641537	−0.0356410
$325$	0	0
$326$	7.82422	0.433344
$327$	−11.8589	−0.655801
$328$	−15.5302	−0.857509
$329$	−4.15990	−0.229343
$330$	0	0
$331$	−34.7036	−1.90748	−0.953742	−	0.300626i	$-0.902804\pi$
$331$	−34.7036	−1.90748	−0.953742	+	0.300626i	$0.902804\pi$
$332$	−3.81316	−0.209274
$333$	−1.49075	−0.0816926
$334$	19.6952	1.07768
$335$	0	0
$336$	−9.59006	−0.523180
$337$	−0.0144912	−0.000789386 0	−0.000394693	−	1.00000i	$-0.500126\pi$
$337$	−0.0144912	−0.000789386 0	−0.000394693		1.00000i	$0.500126\pi$
$338$	9.65673	0.525257
$339$	−12.2064	−0.662963
$340$	0	0
$341$	23.2283	1.25788
$342$	−2.94894	−0.159461
$343$	13.7477	0.742305
$344$	37.8761	2.04214
$345$	0	0
$346$	−15.7377	−0.846064
$347$	30.3323	1.62832	0.814162	−	0.580638i	$-0.197197\pi$
$347$	30.3323	1.62832	0.814162	+	0.580638i	$0.197197\pi$
$348$	3.48602	0.186871
$349$	−4.89284	−0.261908	−0.130954	−	0.991388i	$-0.541804\pi$
$349$	−4.89284	−0.261908	−0.130954	+	0.991388i	$0.541804\pi$
$350$	0	0
$351$	−4.61360	−0.246256
$352$	−13.2303	−0.705178
$353$	24.2132	1.28874	0.644369	−	0.764715i	$-0.277120\pi$
$353$	24.2132	1.28874	0.644369	+	0.764715i	$0.277120\pi$
$354$	3.11347	0.165479
$355$	0	0
$356$	0.792044	0.0419783
$357$	−5.11906	−0.270929
$358$	−6.82602	−0.360766
$359$	−8.29577	−0.437834	−0.218917	−	0.975743i	$-0.570252\pi$
$359$	−8.29577	−0.437834	−0.218917	+	0.975743i	$0.570252\pi$
$360$	0	0
$361$	−12.5984	−0.663076
$362$	21.3104	1.12005
$363$	3.53200	0.185382
$364$	12.3125	0.645348
$365$	0	0
$366$	14.9074	0.779223
$367$	−11.0837	−0.578564	−0.289282	−	0.957244i	$-0.593417\pi$
$367$	−11.0837	−0.578564	−0.289282	+	0.957244i	$0.593417\pi$
$368$	5.95390	0.310368
$369$	5.04423	0.262592
$370$	0	0
$371$	−26.1052	−1.35532
$372$	3.90910	0.202677
$373$	1.43233	0.0741634	0.0370817	−	0.999312i	$-0.488194\pi$
$373$	1.43233	0.0741634	0.0370817	+	0.999312i	$0.488194\pi$
$374$	5.46756	0.282721
$375$	0	0
$376$	3.07879	0.158777
$377$	25.0696	1.29115
$378$	4.84850	0.249380
$379$	−12.1820	−0.625749	−0.312874	−	0.949795i	$-0.601292\pi$
$379$	−12.1820	−0.625749	−0.312874	+	0.949795i	$0.601292\pi$
$380$	0	0
$381$	11.6492	0.596807
$382$	−6.32486	−0.323608
$383$	−22.4757	−1.14846	−0.574228	−	0.818696i	$-0.694698\pi$
$383$	−22.4757	−1.14846	−0.574228	+	0.818696i	$0.694698\pi$
$384$	3.14739	0.160615
$385$	0	0
$386$	20.7126	1.05425
$387$	−12.3022	−0.625358
$388$	−9.32896	−0.473606
$389$	7.90866	0.400985	0.200492	−	0.979695i	$-0.435746\pi$
$389$	7.90866	0.400985	0.200492	+	0.979695i	$0.435746\pi$
$390$	0	0
$391$	3.17812	0.160725
$392$	−31.7264	−1.60242
$393$	−2.96872	−0.149752
$394$	−2.81562	−0.141849
$395$	0	0
$396$	2.44560	0.122896
$397$	22.6540	1.13697	0.568486	−	0.822693i	$-0.307529\pi$
$397$	22.6540	1.13697	0.568486	+	0.822693i	$0.307529\pi$
$398$	−8.99096	−0.450676
$399$	−10.5251	−0.526914
$400$	0	0
$401$	33.4361	1.66972	0.834859	−	0.550464i	$-0.185549\pi$
$401$	33.4361	1.66972	0.834859	+	0.550464i	$0.185549\pi$
$402$	−13.2062	−0.658664
$403$	28.1122	1.40037
$404$	3.79352	0.188735
$405$	0	0
$406$	−26.3461	−1.30753
$407$	5.68287	0.281689
$408$	3.78868	0.187567
$409$	14.3473	0.709430	0.354715	−	0.934974i	$-0.384578\pi$
$409$	14.3473	0.709430	0.354715	+	0.934974i	$0.384578\pi$
$410$	0	0
$411$	−8.98119	−0.443010
$412$	−2.37526	−0.117020
$413$	11.1123	0.546801
$414$	−3.01015	−0.147941
$415$	0	0
$416$	−16.0121	−0.785056
$417$	−15.3614	−0.752250
$418$	11.2416	0.549846
$419$	−8.05906	−0.393711	−0.196855	−	0.980433i	$-0.563073\pi$
$419$	−8.05906	−0.393711	−0.196855	+	0.980433i	$0.563073\pi$
$420$	0	0
$421$	0.407998	0.0198846	0.00994231	−	0.999951i	$-0.496835\pi$
$421$	0.407998	0.0198846	0.00994231	+	0.999951i	$0.496835\pi$
$422$	1.41788	0.0690214
$423$	−1.00000	−0.0486217
$424$	19.3208	0.938301
$425$	0	0
$426$	−4.07236	−0.197307
$427$	53.2061	2.57483
$428$	11.9560	0.577913
$429$	17.5874	0.849129
$430$	0	0
$431$	−11.7588	−0.566402	−0.283201	−	0.959061i	$-0.591396\pi$
$431$	−11.7588	−0.566402	−0.283201	+	0.959061i	$0.591396\pi$
$432$	−2.30535	−0.110916
$433$	4.25415	0.204442	0.102221	−	0.994762i	$-0.467405\pi$
$433$	4.25415	0.204442	0.102221	+	0.994762i	$0.467405\pi$
$434$	−29.5435	−1.41813
$435$	0	0
$436$	7.60795	0.364355
$437$	6.53441	0.312583
$438$	16.6435	0.795259
$439$	−4.77103	−0.227709	−0.113854	−	0.993497i	$-0.536320\pi$
$439$	−4.77103	−0.227709	−0.113854	+	0.993497i	$0.536320\pi$
$440$	0	0
$441$	10.3048	0.490705
$442$	6.61714	0.314745
$443$	−6.80236	−0.323190	−0.161595	−	0.986857i	$-0.551664\pi$
$443$	−6.80236	−0.323190	−0.161595	+	0.986857i	$0.551664\pi$
$444$	0.956372	0.0453874
$445$	0	0
$446$	32.7496	1.55074
$447$	10.6569	0.504053
$448$	36.0074	1.70119
$449$	−1.56203	−0.0737165	−0.0368583	−	0.999321i	$-0.511735\pi$
$449$	−1.56203	−0.0737165	−0.0368583	+	0.999321i	$0.511735\pi$
$450$	0	0
$451$	−19.2291	−0.905461
$452$	7.83088	0.368334
$453$	5.11859	0.240492
$454$	29.8189	1.39947
$455$	0	0
$456$	7.78975	0.364788
$457$	4.03564	0.188779	0.0943896	−	0.995535i	$-0.469910\pi$
$457$	4.03564	0.188779	0.0943896	+	0.995535i	$0.469910\pi$
$458$	−33.5884	−1.56948
$459$	−1.23057	−0.0574382
$460$	0	0
$461$	18.7992	0.875567	0.437784	−	0.899080i	$-0.355764\pi$
$461$	18.7992	0.875567	0.437784	+	0.899080i	$0.355764\pi$
$462$	−18.4829	−0.859902
$463$	35.4554	1.64775	0.823876	−	0.566771i	$-0.191807\pi$
$463$	35.4554	1.64775	0.823876	+	0.566771i	$0.191807\pi$
$464$	12.5270	0.581550
$465$	0	0
$466$	8.84140	0.409570
$467$	41.6376	1.92676	0.963379	−	0.268143i	$-0.0864099\pi$
$467$	41.6376	1.92676	0.963379	+	0.268143i	$0.0864099\pi$
$468$	2.95979	0.136817
$469$	−47.1343	−2.17646
$470$	0	0
$471$	−11.5178	−0.530713
$472$	−8.22435	−0.378557
$473$	46.8972	2.15634
$474$	6.18204	0.283950
$475$	0	0
$476$	3.28407	0.150525
$477$	−6.27544	−0.287333
$478$	−7.30520	−0.334132
$479$	−23.2251	−1.06118	−0.530591	−	0.847628i	$-0.678030\pi$
$479$	−23.2251	−1.06118	−0.530591	+	0.847628i	$0.678030\pi$
$480$	0	0
$481$	6.87772	0.313597
$482$	3.59688	0.163833
$483$	−10.7435	−0.488848
$484$	−2.26591	−0.102996
$485$	0	0
$486$	1.16553	0.0528696
$487$	−4.25601	−0.192858	−0.0964291	−	0.995340i	$-0.530742\pi$
$487$	−4.25601	−0.192858	−0.0964291	+	0.995340i	$0.530742\pi$
$488$	−39.3785	−1.78258
$489$	6.71301	0.303573
$490$	0	0
$491$	29.2980	1.32220	0.661101	−	0.750297i	$-0.270089\pi$
$491$	29.2980	1.32220	0.661101	+	0.750297i	$0.270089\pi$
$492$	−3.23606	−0.145893
$493$	6.68675	0.301156
$494$	13.6052	0.612129
$495$	0	0
$496$	14.0473	0.630742
$497$	−14.5347	−0.651971
$498$	6.92767	0.310436
$499$	28.3988	1.27130	0.635651	−	0.771976i	$-0.280732\pi$
$499$	28.3988	1.27130	0.635651	+	0.771976i	$0.280732\pi$
$500$	0	0
$501$	16.8981	0.754950
$502$	−33.0145	−1.47351
$503$	−23.0789	−1.02904	−0.514518	−	0.857480i	$-0.672029\pi$
$503$	−23.0789	−1.02904	−0.514518	+	0.857480i	$0.672029\pi$
$504$	−12.8075	−0.570491
$505$	0	0
$506$	11.4749	0.510123
$507$	8.28526	0.367961
$508$	−7.47340	−0.331578
$509$	34.4963	1.52902	0.764510	−	0.644612i	$-0.222981\pi$
$509$	34.4963	1.52902	0.764510	+	0.644612i	$0.222981\pi$
$510$	0	0
$511$	59.4026	2.62782
$512$	−22.1964	−0.980954
$513$	−2.53013	−0.111708
$514$	−36.3050	−1.60134
$515$	0	0
$516$	7.89235	0.347441
$517$	3.81209	0.167655
$518$	−7.22790	−0.317576
$519$	−13.5026	−0.592698
$520$	0	0
$521$	−28.8601	−1.26438	−0.632191	−	0.774813i	$-0.717844\pi$
$521$	−28.8601	−1.26438	−0.632191	+	0.774813i	$0.717844\pi$
$522$	−6.33333	−0.277202
$523$	−2.81087	−0.122911	−0.0614553	−	0.998110i	$-0.519574\pi$
$523$	−2.81087	−0.122911	−0.0614553	+	0.998110i	$0.519574\pi$
$524$	1.90455	0.0832005
$525$	0	0
$526$	−23.6515	−1.03125
$527$	7.49828	0.326630
$528$	8.78821	0.382458
$529$	−16.3300	−0.709999
$530$	0	0
$531$	2.67129	0.115924
$532$	6.75224	0.292747
$533$	−23.2721	−1.00802
$534$	−1.43897	−0.0622702
$535$	0	0
$536$	34.8846	1.50679
$537$	−5.85657	−0.252730
$538$	−14.3466	−0.618526
$539$	−39.2828	−1.69203
$540$	0	0
$541$	−9.59709	−0.412611	−0.206305	−	0.978488i	$-0.566144\pi$
$541$	−9.59709	−0.412611	−0.206305	+	0.978488i	$0.566144\pi$
$542$	4.83707	0.207770
$543$	18.2839	0.784636
$544$	−4.27085	−0.183111
$545$	0	0
$546$	−22.3690	−0.957305
$547$	36.0808	1.54270	0.771352	−	0.636409i	$-0.219581\pi$
$547$	36.0808	1.54270	0.771352	+	0.636409i	$0.219581\pi$
$548$	5.76177	0.246131
$549$	12.7902	0.545874
$550$	0	0
$551$	13.7484	0.585700
$552$	7.95141	0.338435
$553$	22.0644	0.938272
$554$	31.2523	1.32778
$555$	0	0
$556$	9.85489	0.417941
$557$	−21.1230	−0.895008	−0.447504	−	0.894282i	$-0.647687\pi$
$557$	−21.1230	−0.895008	−0.447504	+	0.894282i	$0.647687\pi$
$558$	−7.10197	−0.300650
$559$	56.7576	2.40059
$560$	0	0
$561$	4.69104	0.198056
$562$	−8.14593	−0.343615
$563$	−11.8546	−0.499612	−0.249806	−	0.968296i	$-0.580367\pi$
$563$	−11.8546	−0.499612	−0.249806	+	0.968296i	$0.580367\pi$
$564$	0.641537	0.0270136
$565$	0	0
$566$	−23.5154	−0.988425
$567$	4.15990	0.174700
$568$	10.7573	0.451366
$569$	6.36909	0.267006	0.133503	−	0.991048i	$-0.457377\pi$
$569$	6.36909	0.267006	0.133503	+	0.991048i	$0.457377\pi$
$570$	0	0
$571$	40.2702	1.68526	0.842628	−	0.538496i	$-0.181007\pi$
$571$	40.2702	1.68526	0.842628	+	0.538496i	$0.181007\pi$
$572$	−11.2830	−0.471765
$573$	−5.42659	−0.226699
$574$	24.4570	1.02081
$575$	0	0
$576$	8.65583	0.360660
$577$	26.1825	1.08999	0.544996	−	0.838438i	$-0.316531\pi$
$577$	26.1825	1.08999	0.544996	+	0.838438i	$0.316531\pi$
$578$	−18.0491	−0.750742
$579$	17.7710	0.738537
$580$	0	0
$581$	24.7256	1.02579
$582$	16.9487	0.702544
$583$	23.9225	0.990770
$584$	−43.9646	−1.81927
$585$	0	0
$586$	−2.45472	−0.101403
$587$	4.54659	0.187658	0.0938289	−	0.995588i	$-0.470089\pi$
$587$	4.54659	0.187658	0.0938289	+	0.995588i	$0.470089\pi$
$588$	−6.61092	−0.272630
$589$	15.4169	0.635243
$590$	0	0
$591$	−2.41574	−0.0993702
$592$	3.43671	0.141248
$593$	−23.1314	−0.949891	−0.474946	−	0.880015i	$-0.657532\pi$
$593$	−23.1314	−0.949891	−0.474946	+	0.880015i	$0.657532\pi$
$594$	−4.44310	−0.182303
$595$	0	0
$596$	−6.83679	−0.280046
$597$	−7.71405	−0.315715
$598$	13.8876	0.567906
$599$	−41.6490	−1.70173	−0.850866	−	0.525383i	$-0.823922\pi$
$599$	−41.6490	−1.70173	−0.850866	+	0.525383i	$0.823922\pi$
$600$	0	0
$601$	8.66645	0.353512	0.176756	−	0.984255i	$-0.443440\pi$
$601$	8.66645	0.353512	0.176756	+	0.984255i	$0.443440\pi$
$602$	−59.6474	−2.43105
$603$	−11.3306	−0.461418
$604$	−3.28376	−0.133614
$605$	0	0
$606$	−6.89198	−0.279968
$607$	−11.3275	−0.459771	−0.229885	−	0.973218i	$-0.573835\pi$
$607$	−11.3275	−0.459771	−0.229885	+	0.973218i	$0.573835\pi$
$608$	−8.78113	−0.356122
$609$	−22.6043	−0.915974
$610$	0	0
$611$	4.61360	0.186646
$612$	0.789458	0.0319119
$613$	22.4281	0.905863	0.452931	−	0.891545i	$-0.350378\pi$
$613$	22.4281	0.905863	0.452931	+	0.891545i	$0.350378\pi$
$614$	19.9320	0.804392
$615$	0	0
$616$	48.8232	1.96714
$617$	−42.5696	−1.71379	−0.856893	−	0.515494i	$-0.827608\pi$
$617$	−42.5696	−1.71379	−0.856893	+	0.515494i	$0.827608\pi$
$618$	4.31531	0.173587
$619$	19.1959	0.771549	0.385774	−	0.922593i	$-0.373934\pi$
$619$	19.1959	0.771549	0.385774	+	0.922593i	$0.373934\pi$
$620$	0	0
$621$	−2.58264	−0.103638
$622$	35.7856	1.43487
$623$	−5.13583	−0.205763
$624$	10.6360	0.425780
$625$	0	0
$626$	2.20508	0.0881328
$627$	9.64507	0.385187
$628$	7.38910	0.294857
$629$	1.83448	0.0731453
$630$	0	0
$631$	−30.0498	−1.19627	−0.598133	−	0.801397i	$-0.704090\pi$
$631$	−30.0498	−1.19627	−0.598133	+	0.801397i	$0.704090\pi$
$632$	−16.3301	−0.649576
$633$	1.21651	0.0483520
$634$	−22.0957	−0.877531
$635$	0	0
$636$	4.02593	0.159639
$637$	−47.5422	−1.88369
$638$	24.1432	0.955839
$639$	−3.49400	−0.138220
$640$	0	0
$641$	21.0046	0.829631	0.414815	−	0.909906i	$-0.363846\pi$
$641$	21.0046	0.829631	0.414815	+	0.909906i	$0.363846\pi$
$642$	−21.7213	−0.857273
$643$	−12.2565	−0.483351	−0.241675	−	0.970357i	$-0.577697\pi$
$643$	−12.2565	−0.483351	−0.241675	+	0.970357i	$0.577697\pi$
$644$	6.89238	0.271598
$645$	0	0
$646$	3.62889	0.142777
$647$	−12.9252	−0.508143	−0.254072	−	0.967185i	$-0.581770\pi$
$647$	−12.9252	−0.508143	−0.254072	+	0.967185i	$0.581770\pi$
$648$	−3.07879	−0.120946
$649$	−10.1832	−0.399725
$650$	0	0
$651$	−25.3477	−0.993454
$652$	−4.30665	−0.168661
$653$	−2.34399	−0.0917276	−0.0458638	−	0.998948i	$-0.514604\pi$
$653$	−2.34399	−0.0917276	−0.0458638	+	0.998948i	$0.514604\pi$
$654$	−13.8220	−0.540481
$655$	0	0
$656$	−11.6287	−0.454026
$657$	14.2798	0.557108
$658$	−4.84850	−0.189014
$659$	−12.3566	−0.481345	−0.240672	−	0.970606i	$-0.577368\pi$
$659$	−12.3566	−0.481345	−0.240672	+	0.970606i	$0.577368\pi$
$660$	0	0
$661$	34.5750	1.34481	0.672405	−	0.740184i	$-0.265261\pi$
$661$	34.5750	1.34481	0.672405	+	0.740184i	$0.265261\pi$
$662$	−40.4482	−1.57206
$663$	5.67736	0.220490
$664$	−18.2997	−0.710166
$665$	0	0
$666$	−1.73752	−0.0673274
$667$	14.0337	0.543387
$668$	−10.8407	−0.419441
$669$	28.0985	1.08635
$670$	0	0
$671$	−48.7574	−1.88226
$672$	14.4375	0.556937
$673$	−21.9687	−0.846831	−0.423416	−	0.905936i	$-0.639169\pi$
$673$	−21.9687	−0.846831	−0.423416	+	0.905936i	$0.639169\pi$
$674$	−0.0168899	−0.000650576 0
$675$	0	0
$676$	−5.31531	−0.204435
$677$	12.3690	0.475379	0.237689	−	0.971341i	$-0.423610\pi$
$677$	12.3690	0.475379	0.237689	+	0.971341i	$0.423610\pi$
$678$	−14.2270	−0.546384
$679$	60.4915	2.32145
$680$	0	0
$681$	25.5840	0.980380
$682$	27.0733	1.03669
$683$	7.40119	0.283198	0.141599	−	0.989924i	$-0.454776\pi$
$683$	7.40119	0.283198	0.141599	+	0.989924i	$0.454776\pi$
$684$	1.62317	0.0620636
$685$	0	0
$686$	16.0233	0.611774
$687$	−28.8181	−1.09948
$688$	28.3610	1.08125
$689$	28.9523	1.10300
$690$	0	0
$691$	30.0653	1.14374	0.571869	−	0.820345i	$-0.306219\pi$
$691$	30.0653	1.14374	0.571869	+	0.820345i	$0.306219\pi$
$692$	8.66242	0.329296
$693$	−15.8579	−0.602392
$694$	35.3533	1.34199
$695$	0	0
$696$	16.7297	0.634139
$697$	−6.20729	−0.235118
$698$	−5.70276	−0.215853
$699$	7.58573	0.286918
$700$	0	0
$701$	−3.69687	−0.139629	−0.0698144	−	0.997560i	$-0.522241\pi$
$701$	−3.69687	−0.139629	−0.0698144	+	0.997560i	$0.522241\pi$
$702$	−5.37729	−0.202953
$703$	3.77179	0.142256
$704$	−32.9968	−1.24361
$705$	0	0
$706$	28.2212	1.06212
$707$	−24.5982	−0.925111
$708$	−1.71373	−0.0644060
$709$	−27.5176	−1.03345	−0.516723	−	0.856153i	$-0.672848\pi$
$709$	−27.5176	−1.03345	−0.516723	+	0.856153i	$0.672848\pi$
$710$	0	0
$711$	5.30405	0.198917
$712$	3.80109	0.142452
$713$	15.7369	0.589351
$714$	−5.96642	−0.223288
$715$	0	0
$716$	3.75721	0.140414
$717$	−6.26770	−0.234072
$718$	−9.66898	−0.360843
$719$	−25.3414	−0.945074	−0.472537	−	0.881311i	$-0.656662\pi$
$719$	−25.3414	−0.945074	−0.472537	+	0.881311i	$0.656662\pi$
$720$	0	0
$721$	15.4018	0.573593
$722$	−14.6839	−0.546477
$723$	3.08604	0.114771
$724$	−11.7298	−0.435934
$725$	0	0
$726$	4.11665	0.152783
$727$	−35.6248	−1.32125	−0.660625	−	0.750716i	$-0.729709\pi$
$727$	−35.6248	−1.32125	−0.660625	+	0.750716i	$0.729709\pi$
$728$	59.0886	2.18997
$729$	1.00000	0.0370370
$730$	0	0
$731$	15.1388	0.559928
$732$	−8.20541	−0.303281
$733$	26.4007	0.975131	0.487565	−	0.873086i	$-0.337885\pi$
$733$	26.4007	0.975131	0.487565	+	0.873086i	$0.337885\pi$
$734$	−12.9184	−0.476827
$735$	0	0
$736$	−8.96337	−0.330394
$737$	43.1933	1.59104
$738$	5.87921	0.216417
$739$	−2.48916	−0.0915652	−0.0457826	−	0.998951i	$-0.514578\pi$
$739$	−2.48916	−0.0915652	−0.0457826	+	0.998951i	$0.514578\pi$
$740$	0	0
$741$	11.6730	0.428818
$742$	−30.4265	−1.11699
$743$	44.8468	1.64527	0.822634	−	0.568571i	$-0.192504\pi$
$743$	44.8468	1.64527	0.822634	+	0.568571i	$0.192504\pi$
$744$	18.7601	0.687779
$745$	0	0
$746$	1.66943	0.0611221
$747$	5.94379	0.217472
$748$	−3.00948	−0.110037
$749$	−77.5258	−2.83273
$750$	0	0
$751$	−38.4960	−1.40474	−0.702370	−	0.711812i	$-0.747875\pi$
$751$	−38.4960	−1.40474	−0.702370	+	0.711812i	$0.747875\pi$
$752$	2.30535	0.0840676
$753$	−28.3257	−1.03224
$754$	29.2194	1.06411
$755$	0	0
$756$	−2.66873	−0.0970609
$757$	1.70387	0.0619284	0.0309642	−	0.999520i	$-0.490142\pi$
$757$	1.70387	0.0619284	0.0309642	+	0.999520i	$0.490142\pi$
$758$	−14.1985	−0.515714
$759$	9.84524	0.357360
$760$	0	0
$761$	−17.2211	−0.624263	−0.312132	−	0.950039i	$-0.601043\pi$
$761$	−17.2211	−0.624263	−0.312132	+	0.950039i	$0.601043\pi$
$762$	13.5775	0.491861
$763$	−49.3320	−1.78594
$764$	3.48136	0.125951
$765$	0	0
$766$	−26.1961	−0.946505
$767$	−12.3243	−0.445003
$768$	−13.6433	−0.492310
$769$	1.47987	0.0533656	0.0266828	−	0.999644i	$-0.491506\pi$
$769$	1.47987	0.0533656	0.0266828	+	0.999644i	$0.491506\pi$
$770$	0	0
$771$	−31.1489	−1.12180
$772$	−11.4007	−0.410322
$773$	−33.0531	−1.18884	−0.594418	−	0.804156i	$-0.702617\pi$
$773$	−33.0531	−1.18884	−0.594418	+	0.804156i	$0.702617\pi$
$774$	−14.3386	−0.515392
$775$	0	0
$776$	−44.7705	−1.60717
$777$	−6.20138	−0.222473
$778$	9.21779	0.330474
$779$	−12.7626	−0.457266
$780$	0	0
$781$	13.3194	0.476606
$782$	3.70420	0.132462
$783$	−5.43386	−0.194190
$784$	−23.7562	−0.848437
$785$	0	0
$786$	−3.46014	−0.123419
$787$	2.79404	0.0995968	0.0497984	−	0.998759i	$-0.484142\pi$
$787$	2.79404	0.0995968	0.0497984	+	0.998759i	$0.484142\pi$
$788$	1.54979	0.0552089
$789$	−20.2925	−0.722431
$790$	0	0
$791$	−50.7776	−1.80544
$792$	11.7366	0.417043
$793$	−59.0089	−2.09547
$794$	26.4039	0.937041
$795$	0	0
$796$	4.94885	0.175407
$797$	31.7140	1.12337	0.561684	−	0.827352i	$-0.310154\pi$
$797$	31.7140	1.12337	0.561684	+	0.827352i	$0.310154\pi$
$798$	−12.2673	−0.434259
$799$	1.23057	0.0435345
$800$	0	0
$801$	−1.23460	−0.0436226
$802$	38.9708	1.37611
$803$	−54.4358	−1.92100
$804$	7.26901	0.256358
$805$	0	0
$806$	32.7656	1.15412
$807$	−12.3091	−0.433300
$808$	18.2054	0.640465
$809$	12.9229	0.454344	0.227172	−	0.973855i	$-0.427052\pi$
$809$	12.9229	0.454344	0.227172	+	0.973855i	$0.427052\pi$
$810$	0	0
$811$	−20.0140	−0.702786	−0.351393	−	0.936228i	$-0.614292\pi$
$811$	−20.0140	−0.702786	−0.351393	+	0.936228i	$0.614292\pi$
$812$	14.5015	0.508904
$813$	4.15010	0.145550
$814$	6.62356	0.232156
$815$	0	0
$816$	2.83690	0.0993115
$817$	31.1263	1.08897
$818$	16.7223	0.584680
$819$	−19.1921	−0.670627
$820$	0	0
$821$	−35.9297	−1.25396	−0.626978	−	0.779037i	$-0.715708\pi$
$821$	−35.9297	−1.25396	−0.626978	+	0.779037i	$0.715708\pi$
$822$	−10.4679	−0.365109
$823$	19.8583	0.692217	0.346108	−	0.938195i	$-0.387503\pi$
$823$	19.8583	0.692217	0.346108	+	0.938195i	$0.387503\pi$
$824$	−11.3991	−0.397105
$825$	0	0
$826$	12.9517	0.450649
$827$	−15.4529	−0.537350	−0.268675	−	0.963231i	$-0.586586\pi$
$827$	−15.4529	−0.537350	−0.268675	+	0.963231i	$0.586586\pi$
$828$	1.65686	0.0575799
$829$	−18.2545	−0.634004	−0.317002	−	0.948425i	$-0.602676\pi$
$829$	−18.2545	−0.634004	−0.317002	+	0.948425i	$0.602676\pi$
$830$	0	0
$831$	26.8137	0.930159
$832$	−39.9345	−1.38448
$833$	−12.6808	−0.439364
$834$	−17.9042	−0.619970
$835$	0	0
$836$	−6.18767	−0.214005
$837$	−6.09333	−0.210616
$838$	−9.39308	−0.324479
$839$	42.3886	1.46342	0.731709	−	0.681617i	$-0.238723\pi$
$839$	42.3886	1.46342	0.731709	+	0.681617i	$0.238723\pi$
$840$	0	0
$841$	0.526840	0.0181669
$842$	0.475535	0.0163880
$843$	−6.98903	−0.240715
$844$	−0.780437	−0.0268638
$845$	0	0
$846$	−1.16553	−0.0400718
$847$	14.6928	0.504850
$848$	14.4671	0.496803
$849$	−20.1757	−0.692427
$850$	0	0
$851$	3.85007	0.131979
$852$	2.24153	0.0767936
$853$	24.4161	0.835993	0.417997	−	0.908449i	$-0.362732\pi$
$853$	24.4161	0.835993	0.417997	+	0.908449i	$0.362732\pi$
$854$	62.0134	2.12205
$855$	0	0
$856$	57.3777	1.96113
$857$	29.3860	1.00381	0.501904	−	0.864923i	$-0.332633\pi$
$857$	29.3860	1.00381	0.501904	+	0.864923i	$0.332633\pi$
$858$	20.4987	0.699814
$859$	15.1898	0.518268	0.259134	−	0.965841i	$-0.416563\pi$
$859$	15.1898	0.518268	0.259134	+	0.965841i	$0.416563\pi$
$860$	0	0
$861$	20.9835	0.715117
$862$	−13.7053	−0.466803
$863$	−23.3323	−0.794240	−0.397120	−	0.917767i	$-0.629990\pi$
$863$	−23.3323	−0.794240	−0.397120	+	0.917767i	$0.629990\pi$
$864$	3.47062	0.118073
$865$	0	0
$866$	4.95835	0.168492
$867$	−15.4857	−0.525922
$868$	16.2615	0.551951
$869$	−20.2195	−0.685900
$870$	0	0
$871$	52.2749	1.77127
$872$	36.5112	1.23643
$873$	14.5416	0.492158
$874$	7.61606	0.257617
$875$	0	0
$876$	−9.16102	−0.309522
$877$	−29.0676	−0.981543	−0.490771	−	0.871288i	$-0.663285\pi$
$877$	−29.0676	−0.981543	−0.490771	+	0.871288i	$0.663285\pi$
$878$	−5.56078	−0.187667
$879$	−2.10609	−0.0710367
$880$	0	0
$881$	−1.61823	−0.0545196	−0.0272598	−	0.999628i	$-0.508678\pi$
$881$	−1.61823	−0.0545196	−0.0272598	+	0.999628i	$0.508678\pi$
$882$	12.0106	0.404417
$883$	−13.6728	−0.460125	−0.230063	−	0.973176i	$-0.573893\pi$
$883$	−13.6728	−0.460125	−0.230063	+	0.973176i	$0.573893\pi$
$884$	−3.64224	−0.122502
$885$	0	0
$886$	−7.92837	−0.266359
$887$	5.09087	0.170935	0.0854673	−	0.996341i	$-0.472762\pi$
$887$	5.09087	0.170935	0.0854673	+	0.996341i	$0.472762\pi$
$888$	4.58971	0.154021
$889$	48.4596	1.62528
$890$	0	0
$891$	−3.81209	−0.127710
$892$	−18.0262	−0.603562
$893$	2.53013	0.0846676
$894$	12.4209	0.415418
$895$	0	0
$896$	13.0928	0.437401
$897$	11.9153	0.397839
$898$	−1.82059	−0.0607538
$899$	33.1103	1.10429
$900$	0	0
$901$	7.72238	0.257270
$902$	−22.4121	−0.746240
$903$	−51.1762	−1.70304
$904$	37.5811	1.24993
$905$	0	0
$906$	5.96587	0.198203
$907$	18.3464	0.609181	0.304591	−	0.952483i	$-0.401480\pi$
$907$	18.3464	0.609181	0.304591	+	0.952483i	$0.401480\pi$
$908$	−16.4131	−0.544687
$909$	−5.91317	−0.196127
$910$	0	0
$911$	−27.6570	−0.916316	−0.458158	−	0.888871i	$-0.651491\pi$
$911$	−27.6570	−0.916316	−0.458158	+	0.888871i	$0.651491\pi$
$912$	5.83285	0.193145
$913$	−22.6582	−0.749878
$914$	4.70366	0.155583
$915$	0	0
$916$	18.4879	0.610857
$917$	−12.3496	−0.407820
$918$	−1.43427	−0.0473379
$919$	7.19193	0.237240	0.118620	−	0.992940i	$-0.462153\pi$
$919$	7.19193	0.237240	0.118620	+	0.992940i	$0.462153\pi$
$920$	0	0
$921$	17.1013	0.563505
$922$	21.9111	0.721603
$923$	16.1199	0.530593
$924$	10.1734	0.334682
$925$	0	0
$926$	41.3243	1.35800
$927$	3.70244	0.121604
$928$	−18.8589	−0.619073
$929$	−26.7260	−0.876852	−0.438426	−	0.898767i	$-0.644464\pi$
$929$	−26.7260	−0.876852	−0.438426	+	0.898767i	$0.644464\pi$
$930$	0	0
$931$	−26.0725	−0.854492
$932$	−4.86653	−0.159408
$933$	30.7032	1.00518
$934$	48.5299	1.58795
$935$	0	0
$936$	14.2043	0.464282
$937$	−27.4610	−0.897112	−0.448556	−	0.893755i	$-0.648061\pi$
$937$	−27.4610	−0.897112	−0.448556	+	0.893755i	$0.648061\pi$
$938$	−54.9364	−1.79374
$939$	1.89191	0.0617402
$940$	0	0
$941$	−44.1964	−1.44076	−0.720381	−	0.693579i	$-0.756033\pi$
$941$	−44.1964	−1.44076	−0.720381	+	0.693579i	$0.756033\pi$
$942$	−13.4244	−0.437389
$943$	−13.0274	−0.424232
$944$	−6.15827	−0.200435
$945$	0	0
$946$	54.6602	1.77715
$947$	−42.5524	−1.38277	−0.691384	−	0.722487i	$-0.742999\pi$
$947$	−42.5524	−1.38277	−0.691384	+	0.722487i	$0.742999\pi$
$948$	−3.40275	−0.110516
$949$	−65.8812	−2.13859
$950$	0	0
$951$	−18.9576	−0.614742
$952$	15.7605	0.510802
$953$	−35.9045	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$953$	−35.9045	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$954$	−7.31422	−0.236807
$955$	0	0
$956$	4.02097	0.130047
$957$	20.7143	0.669600
$958$	−27.0696	−0.874578
$959$	−37.3609	−1.20645
$960$	0	0
$961$	6.12868	0.197699
$962$	8.01620	0.258453
$963$	−18.6364	−0.600550
$964$	−1.97981	−0.0637655
$965$	0	0
$966$	−12.5219	−0.402886
$967$	−38.1824	−1.22786	−0.613932	−	0.789359i	$-0.710413\pi$
$967$	−38.1824	−1.22786	−0.613932	+	0.789359i	$0.710413\pi$
$968$	−10.8743	−0.349513
$969$	3.11351	0.100020
$970$	0	0
$971$	26.5718	0.852731	0.426365	−	0.904551i	$-0.359794\pi$
$971$	26.5718	0.852731	0.426365	+	0.904551i	$0.359794\pi$
$972$	−0.641537	−0.0205773
$973$	−63.9018	−2.04860
$974$	−4.96051	−0.158945
$975$	0	0
$976$	−29.4860	−0.943824
$977$	41.8510	1.33893	0.669466	−	0.742843i	$-0.266523\pi$
$977$	41.8510	1.33893	0.669466	+	0.742843i	$0.266523\pi$
$978$	7.82422	0.250191
$979$	4.70641	0.150418
$980$	0	0
$981$	−11.8589	−0.378627
$982$	34.1478	1.08970
$983$	23.7688	0.758108	0.379054	−	0.925375i	$-0.376249\pi$
$983$	23.7688	0.758108	0.379054	+	0.925375i	$0.376249\pi$
$984$	−15.5302	−0.495083
$985$	0	0
$986$	7.79362	0.248199
$987$	−4.15990	−0.132411
$988$	−7.48866	−0.238246
$989$	31.7723	1.01030
$990$	0	0
$991$	29.2351	0.928685	0.464342	−	0.885656i	$-0.346291\pi$
$991$	29.2351	0.928685	0.464342	+	0.885656i	$0.346291\pi$
$992$	−21.1477	−0.671439
$993$	−34.7036	−1.10129
$994$	−16.9406	−0.537325
$995$	0	0
$996$	−3.81316	−0.120825
$997$	−6.57182	−0.208132	−0.104066	−	0.994570i	$-0.533185\pi$
$997$	−6.57182	−0.208132	−0.104066	+	0.994570i	$0.533185\pi$
$998$	33.0996	1.04775
$999$	−1.49075	−0.0471653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.8		10
5.2	odd	4		705.2.c.b.424.14	yes	20
5.3	odd	4		705.2.c.b.424.7	✓	20
5.4	even	2		3525.2.a.bg.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.7	✓	20	5.3	odd	4
705.2.c.b.424.14	yes	20	5.2	odd	4
3525.2.a.bf.1.8		10	1.1	even	1	trivial
3525.2.a.bg.1.3		10	5.4	even	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+1.16553 q^{2} +1.00000 q^{3} -0.641537 q^{4} +1.16553 q^{6} +4.15990 q^{7} -3.07879 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.16553 q^{2} +1.00000 q^{3} -0.641537 q^{4} +1.16553 q^{6} +4.15990 q^{7} -3.07879 q^{8} +1.00000 q^{9} -3.81209 q^{11} -0.641537 q^{12} -4.61360 q^{13} +4.84850 q^{14} -2.30535 q^{16} -1.23057 q^{17} +1.16553 q^{18} -2.53013 q^{19} +4.15990 q^{21} -4.44310 q^{22} -2.58264 q^{23} -3.07879 q^{24} -5.37729 q^{26} +1.00000 q^{27} -2.66873 q^{28} -5.43386 q^{29} -6.09333 q^{31} +3.47062 q^{32} -3.81209 q^{33} -1.43427 q^{34} -0.641537 q^{36} -1.49075 q^{37} -2.94894 q^{38} -4.61360 q^{39} +5.04423 q^{41} +4.84850 q^{42} -12.3022 q^{43} +2.44560 q^{44} -3.01015 q^{46} -1.00000 q^{47} -2.30535 q^{48} +10.3048 q^{49} -1.23057 q^{51} +2.95979 q^{52} -6.27544 q^{53} +1.16553 q^{54} -12.8075 q^{56} -2.53013 q^{57} -6.33333 q^{58} +2.67129 q^{59} +12.7902 q^{61} -7.10197 q^{62} +4.15990 q^{63} +8.65583 q^{64} -4.44310 q^{66} -11.3306 q^{67} +0.789458 q^{68} -2.58264 q^{69} -3.49400 q^{71} -3.07879 q^{72} +14.2798 q^{73} -1.73752 q^{74} +1.62317 q^{76} -15.8579 q^{77} -5.37729 q^{78} +5.30405 q^{79} +1.00000 q^{81} +5.87921 q^{82} +5.94379 q^{83} -2.66873 q^{84} -14.3386 q^{86} -5.43386 q^{87} +11.7366 q^{88} -1.23460 q^{89} -19.1921 q^{91} +1.65686 q^{92} -6.09333 q^{93} -1.16553 q^{94} +3.47062 q^{96} +14.5416 q^{97} +12.0106 q^{98} -3.81209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

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