LMFDB - Embedded newform 3525.2.a.bg.1.1

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			1.1
Root			$-2.04563$ 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)

$f(q)$	$=$	$q-2.04563 q^{2} -1.00000 q^{3} +2.18458 q^{4} +2.04563 q^{6} +1.36348 q^{7} -0.377587 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.04563 q^{2} -1.00000 q^{3} +2.18458 q^{4} +2.04563 q^{6} +1.36348 q^{7} -0.377587 q^{8} +1.00000 q^{9} -6.09961 q^{11} -2.18458 q^{12} -1.01507 q^{13} -2.78918 q^{14} -3.59676 q^{16} +3.16235 q^{17} -2.04563 q^{18} -2.69173 q^{19} -1.36348 q^{21} +12.4775 q^{22} +8.33386 q^{23} +0.377587 q^{24} +2.07646 q^{26} -1.00000 q^{27} +2.97864 q^{28} +8.92659 q^{29} -6.61741 q^{31} +8.11280 q^{32} +6.09961 q^{33} -6.46898 q^{34} +2.18458 q^{36} -0.367805 q^{37} +5.50627 q^{38} +1.01507 q^{39} +1.21758 q^{41} +2.78918 q^{42} -8.55376 q^{43} -13.3251 q^{44} -17.0480 q^{46} +1.00000 q^{47} +3.59676 q^{48} -5.14091 q^{49} -3.16235 q^{51} -2.21751 q^{52} +0.984720 q^{53} +2.04563 q^{54} -0.514833 q^{56} +2.69173 q^{57} -18.2605 q^{58} -1.26900 q^{59} +3.49647 q^{61} +13.5367 q^{62} +1.36348 q^{63} -9.40223 q^{64} -12.4775 q^{66} -9.10384 q^{67} +6.90841 q^{68} -8.33386 q^{69} -9.72541 q^{71} -0.377587 q^{72} +6.26521 q^{73} +0.752392 q^{74} -5.88031 q^{76} -8.31671 q^{77} -2.07646 q^{78} +8.41933 q^{79} +1.00000 q^{81} -2.49072 q^{82} -1.75703 q^{83} -2.97864 q^{84} +17.4978 q^{86} -8.92659 q^{87} +2.30313 q^{88} -5.21004 q^{89} -1.38404 q^{91} +18.2060 q^{92} +6.61741 q^{93} -2.04563 q^{94} -8.11280 q^{96} -16.2597 q^{97} +10.5164 q^{98} -6.09961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.04563	−1.44648	−0.723238	−	0.690599i	$-0.757347\pi$
$2$	−2.04563	−1.44648	−0.723238	+	0.690599i	$0.757347\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.18458	1.09229
$5$	0	0
$5$	0	0
$6$	2.04563	0.835123
$7$	1.36348	0.515348	0.257674	−	0.966232i	$-0.417044\pi$
$7$	1.36348	0.515348	0.257674	+	0.966232i	$0.417044\pi$
$8$	−0.377587	−0.133497
$9$	1.00000	0.333333
$10$	0	0
$11$	−6.09961	−1.83910	−0.919551	−	0.392971i	$-0.871447\pi$
$11$	−6.09961	−1.83910	−0.919551	+	0.392971i	$0.871447\pi$
$12$	−2.18458	−0.630635
$13$	−1.01507	−0.281531	−0.140765	−	0.990043i	$-0.544956\pi$
$13$	−1.01507	−0.281531	−0.140765	+	0.990043i	$0.544956\pi$
$14$	−2.78918	−0.745438
$15$	0	0
$16$	−3.59676	−0.899191
$17$	3.16235	0.766982	0.383491	−	0.923545i	$-0.374722\pi$
$17$	3.16235	0.766982	0.383491	+	0.923545i	$0.374722\pi$
$18$	−2.04563	−0.482158
$19$	−2.69173	−0.617525	−0.308763	−	0.951139i	$-0.599915\pi$
$19$	−2.69173	−0.617525	−0.308763	+	0.951139i	$0.599915\pi$
$20$	0	0
$21$	−1.36348	−0.297536
$22$	12.4775	2.66022
$23$	8.33386	1.73773	0.868865	−	0.495049i	$-0.164850\pi$
$23$	8.33386	1.73773	0.868865	+	0.495049i	$0.164850\pi$
$24$	0.377587	0.0770745
$25$	0	0
$26$	2.07646	0.407227
$27$	−1.00000	−0.192450
$28$	2.97864	0.562910
$29$	8.92659	1.65763	0.828813	−	0.559525i	$-0.189016\pi$
$29$	8.92659	1.65763	0.828813	+	0.559525i	$0.189016\pi$
$30$	0	0
$31$	−6.61741	−1.18852	−0.594261	−	0.804272i	$-0.702555\pi$
$31$	−6.61741	−1.18852	−0.594261	+	0.804272i	$0.702555\pi$
$32$	8.11280	1.43415
$33$	6.09961	1.06181
$34$	−6.46898	−1.10942
$35$	0	0
$36$	2.18458	0.364097
$37$	−0.367805	−0.0604668	−0.0302334	−	0.999543i	$-0.509625\pi$
$37$	−0.367805	−0.0604668	−0.0302334	+	0.999543i	$0.509625\pi$
$38$	5.50627	0.893235
$39$	1.01507	0.162542
$40$	0	0
$41$	1.21758	0.190155	0.0950774	−	0.995470i	$-0.469690\pi$
$41$	1.21758	0.190155	0.0950774	+	0.995470i	$0.469690\pi$
$42$	2.78918	0.430379
$43$	−8.55376	−1.30444	−0.652218	−	0.758031i	$-0.726162\pi$
$43$	−8.55376	−1.30444	−0.652218	+	0.758031i	$0.726162\pi$
$44$	−13.3251	−2.00883
$45$	0	0
$46$	−17.0480	−2.51358
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	3.59676	0.519148
$49$	−5.14091	−0.734416
$50$	0	0
$51$	−3.16235	−0.442817
$52$	−2.21751	−0.307514
$53$	0.984720	0.135262	0.0676309	−	0.997710i	$-0.478456\pi$
$53$	0.984720	0.135262	0.0676309	+	0.997710i	$0.478456\pi$
$54$	2.04563	0.278374
$55$	0	0
$56$	−0.514833	−0.0687974
$57$	2.69173	0.356528
$58$	−18.2605	−2.39772
$59$	−1.26900	−0.165209	−0.0826046	−	0.996582i	$-0.526324\pi$
$59$	−1.26900	−0.165209	−0.0826046	+	0.996582i	$0.526324\pi$
$60$	0	0
$61$	3.49647	0.447677	0.223839	−	0.974626i	$-0.428141\pi$
$61$	3.49647	0.447677	0.223839	+	0.974626i	$0.428141\pi$
$62$	13.5367	1.71917
$63$	1.36348	0.171783
$64$	−9.40223	−1.17528
$65$	0	0
$66$	−12.4775	−1.53588
$67$	−9.10384	−1.11221	−0.556106	−	0.831112i	$-0.687705\pi$
$67$	−9.10384	−1.11221	−0.556106	+	0.831112i	$0.687705\pi$
$68$	6.90841	0.837767
$69$	−8.33386	−1.00328
$70$	0	0
$71$	−9.72541	−1.15419	−0.577097	−	0.816676i	$-0.695815\pi$
$71$	−9.72541	−1.15419	−0.577097	+	0.816676i	$0.695815\pi$
$72$	−0.377587	−0.0444990
$73$	6.26521	0.733287	0.366644	−	0.930361i	$-0.380507\pi$
$73$	6.26521	0.733287	0.366644	+	0.930361i	$0.380507\pi$
$74$	0.752392	0.0874638
$75$	0	0
$76$	−5.88031	−0.674517
$77$	−8.31671	−0.947777
$78$	−2.07646	−0.235113
$79$	8.41933	0.947249	0.473624	−	0.880727i	$-0.342945\pi$
$79$	8.41933	0.947249	0.473624	+	0.880727i	$0.342945\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.49072	−0.275054
$83$	−1.75703	−0.192859	−0.0964294	−	0.995340i	$-0.530742\pi$
$83$	−1.75703	−0.192859	−0.0964294	+	0.995340i	$0.530742\pi$
$84$	−2.97864	−0.324996
$85$	0	0
$86$	17.4978	1.88684
$87$	−8.92659	−0.957031
$88$	2.30313	0.245515
$89$	−5.21004	−0.552263	−0.276132	−	0.961120i	$-0.589053\pi$
$89$	−5.21004	−0.552263	−0.276132	+	0.961120i	$0.589053\pi$
$90$	0	0
$91$	−1.38404	−0.145086
$92$	18.2060	1.89811
$93$	6.61741	0.686193
$94$	−2.04563	−0.210990
$95$	0	0
$96$	−8.11280	−0.828010
$97$	−16.2597	−1.65093	−0.825463	−	0.564456i	$-0.809086\pi$
$97$	−16.2597	−1.65093	−0.825463	+	0.564456i	$0.809086\pi$
$98$	10.5164	1.06232
$99$	−6.09961	−0.613034
$100$	0	0
$101$	11.1182	1.10631	0.553153	−	0.833080i	$-0.313425\pi$
$101$	11.1182	1.10631	0.553153	+	0.833080i	$0.313425\pi$
$102$	6.46898	0.640524
$103$	14.4660	1.42538	0.712690	−	0.701480i	$-0.247477\pi$
$103$	14.4660	1.42538	0.712690	+	0.701480i	$0.247477\pi$
$104$	0.383278	0.0375835
$105$	0	0
$106$	−2.01437	−0.195653
$107$	7.22963	0.698915	0.349458	−	0.936952i	$-0.386366\pi$
$107$	7.22963	0.698915	0.349458	+	0.936952i	$0.386366\pi$
$108$	−2.18458	−0.210212
$109$	14.8987	1.42704	0.713518	−	0.700637i	$-0.247101\pi$
$109$	14.8987	1.42704	0.713518	+	0.700637i	$0.247101\pi$
$110$	0	0
$111$	0.367805	0.0349105
$112$	−4.90413	−0.463396
$113$	17.1562	1.61392	0.806958	−	0.590609i	$-0.201113\pi$
$113$	17.1562	1.61392	0.806958	+	0.590609i	$0.201113\pi$
$114$	−5.50627	−0.515709
$115$	0	0
$116$	19.5009	1.81061
$117$	−1.01507	−0.0938436
$118$	2.59589	0.238971
$119$	4.31181	0.395263
$120$	0	0
$121$	26.2052	2.38229
$122$	−7.15247	−0.647554
$123$	−1.21758	−0.109786
$124$	−14.4563	−1.29821
$125$	0	0
$126$	−2.78918	−0.248479
$127$	−0.761521	−0.0675741	−0.0337870	−	0.999429i	$-0.510757\pi$
$127$	−0.761521	−0.0675741	−0.0337870	+	0.999429i	$0.510757\pi$
$128$	3.00783	0.265857
$129$	8.55376	0.753117
$130$	0	0
$131$	−4.04625	−0.353523	−0.176761	−	0.984254i	$-0.556562\pi$
$131$	−4.04625	−0.353523	−0.176761	+	0.984254i	$0.556562\pi$
$132$	13.3251	1.15980
$133$	−3.67013	−0.318240
$134$	18.6230	1.60879
$135$	0	0
$136$	−1.19406	−0.102390
$137$	−2.02543	−0.173044	−0.0865219	−	0.996250i	$-0.527575\pi$
$137$	−2.02543	−0.173044	−0.0865219	+	0.996250i	$0.527575\pi$
$138$	17.0480	1.45122
$139$	10.7449	0.911371	0.455686	−	0.890141i	$-0.349394\pi$
$139$	10.7449	0.911371	0.455686	+	0.890141i	$0.349394\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	19.8945	1.66951
$143$	6.19155	0.517764
$144$	−3.59676	−0.299730
$145$	0	0
$146$	−12.8163	−1.06068
$147$	5.14091	0.424015
$148$	−0.803501	−0.0660474
$149$	−9.95572	−0.815604	−0.407802	−	0.913070i	$-0.633705\pi$
$149$	−9.95572	−0.815604	−0.407802	+	0.913070i	$0.633705\pi$
$150$	0	0
$151$	−21.3728	−1.73929	−0.869647	−	0.493674i	$-0.835654\pi$
$151$	−21.3728	−1.73929	−0.869647	+	0.493674i	$0.835654\pi$
$152$	1.01636	0.0824377
$153$	3.16235	0.255661
$154$	17.0129	1.37094
$155$	0	0
$156$	2.21751	0.177543
$157$	3.04297	0.242855	0.121428	−	0.992600i	$-0.461253\pi$
$157$	3.04297	0.242855	0.121428	+	0.992600i	$0.461253\pi$
$158$	−17.2228	−1.37017
$159$	−0.984720	−0.0780934
$160$	0	0
$161$	11.3631	0.895536
$162$	−2.04563	−0.160719
$163$	9.45808	0.740814	0.370407	−	0.928870i	$-0.379218\pi$
$163$	9.45808	0.740814	0.370407	+	0.928870i	$0.379218\pi$
$164$	2.65991	0.207704
$165$	0	0
$166$	3.59422	0.278966
$167$	−7.24917	−0.560958	−0.280479	−	0.959860i	$-0.590493\pi$
$167$	−7.24917	−0.560958	−0.280479	+	0.959860i	$0.590493\pi$
$168$	0.514833	0.0397202
$169$	−11.9696	−0.920740
$170$	0	0
$171$	−2.69173	−0.205842
$172$	−18.6864	−1.42482
$173$	−20.0219	−1.52224	−0.761118	−	0.648613i	$-0.775349\pi$
$173$	−20.0219	−1.52224	−0.761118	+	0.648613i	$0.775349\pi$
$174$	18.2605	1.38432
$175$	0	0
$176$	21.9389	1.65370
$177$	1.26900	0.0953836
$178$	10.6578	0.798835
$179$	−10.7051	−0.800133	−0.400067	−	0.916486i	$-0.631013\pi$
$179$	−10.7051	−0.800133	−0.400067	+	0.916486i	$0.631013\pi$
$180$	0	0
$181$	−23.1690	−1.72214	−0.861069	−	0.508488i	$-0.830205\pi$
$181$	−23.1690	−1.72214	−0.861069	+	0.508488i	$0.830205\pi$
$182$	2.83122	0.209864
$183$	−3.49647	−0.258466
$184$	−3.14675	−0.231982
$185$	0	0
$186$	−13.5367	−0.992562
$187$	−19.2891	−1.41056
$188$	2.18458	0.159327
$189$	−1.36348	−0.0991788
$190$	0	0
$191$	−18.3588	−1.32839	−0.664196	−	0.747558i	$-0.731226\pi$
$191$	−18.3588	−1.32839	−0.664196	+	0.747558i	$0.731226\pi$
$192$	9.40223	0.678547
$193$	7.32709	0.527416	0.263708	−	0.964603i	$-0.415054\pi$
$193$	7.32709	0.527416	0.263708	+	0.964603i	$0.415054\pi$
$194$	33.2613	2.38802
$195$	0	0
$196$	−11.2308	−0.802197
$197$	−19.9850	−1.42387	−0.711936	−	0.702244i	$-0.752182\pi$
$197$	−19.9850	−1.42387	−0.711936	+	0.702244i	$0.752182\pi$
$198$	12.4775	0.886738
$199$	−22.9100	−1.62405	−0.812024	−	0.583624i	$-0.801634\pi$
$199$	−22.9100	−1.62405	−0.812024	+	0.583624i	$0.801634\pi$
$200$	0	0
$201$	9.10384	0.642135
$202$	−22.7437	−1.60024
$203$	12.1713	0.854255
$204$	−6.90841	−0.483685
$205$	0	0
$206$	−29.5921	−2.06178
$207$	8.33386	0.579243
$208$	3.65098	0.253150
$209$	16.4185	1.13569
$210$	0	0
$211$	13.2169	0.909886	0.454943	−	0.890521i	$-0.349660\pi$
$211$	13.2169	0.909886	0.454943	+	0.890521i	$0.349660\pi$
$212$	2.15120	0.147745
$213$	9.72541	0.666374
$214$	−14.7891	−1.01096
$215$	0	0
$216$	0.377587	0.0256915
$217$	−9.02272	−0.612502
$218$	−30.4771	−2.06417
$219$	−6.26521	−0.423364
$220$	0	0
$221$	−3.21001	−0.215929
$222$	−0.752392	−0.0504972
$223$	−4.02328	−0.269419	−0.134709	−	0.990885i	$-0.543010\pi$
$223$	−4.02328	−0.269419	−0.134709	+	0.990885i	$0.543010\pi$
$224$	11.0617	0.739089
$225$	0	0
$226$	−35.0951	−2.33449
$227$	13.6120	0.903459	0.451729	−	0.892155i	$-0.350807\pi$
$227$	13.6120	0.903459	0.451729	+	0.892155i	$0.350807\pi$
$228$	5.88031	0.389433
$229$	−3.66550	−0.242223	−0.121112	−	0.992639i	$-0.538646\pi$
$229$	−3.66550	−0.242223	−0.121112	+	0.992639i	$0.538646\pi$
$230$	0	0
$231$	8.31671	0.547200
$232$	−3.37056	−0.221288
$233$	14.8068	0.970025	0.485012	−	0.874507i	$-0.338815\pi$
$233$	14.8068	0.970025	0.485012	+	0.874507i	$0.338815\pi$
$234$	2.07646	0.135742
$235$	0	0
$236$	−2.77223	−0.180457
$237$	−8.41933	−0.546894
$238$	−8.82034	−0.571738
$239$	6.56545	0.424684	0.212342	−	0.977195i	$-0.431891\pi$
$239$	6.56545	0.424684	0.212342	+	0.977195i	$0.431891\pi$
$240$	0	0
$241$	18.8548	1.21454	0.607271	−	0.794495i	$-0.292264\pi$
$241$	18.8548	1.21454	0.607271	+	0.794495i	$0.292264\pi$
$242$	−53.6061	−3.44593
$243$	−1.00000	−0.0641500
$244$	7.63833	0.488994
$245$	0	0
$246$	2.49072	0.158803
$247$	2.73230	0.173852
$248$	2.49864	0.158664
$249$	1.75703	0.111347
$250$	0	0
$251$	−10.6512	−0.672299	−0.336149	−	0.941809i	$-0.609125\pi$
$251$	−10.6512	−0.672299	−0.336149	+	0.941809i	$0.609125\pi$
$252$	2.97864	0.187637
$253$	−50.8333	−3.19586
$254$	1.55779	0.0977442
$255$	0	0
$256$	12.6516	0.790723
$257$	−2.52666	−0.157609	−0.0788045	−	0.996890i	$-0.525110\pi$
$257$	−2.52666	−0.157609	−0.0788045	+	0.996890i	$0.525110\pi$
$258$	−17.4978	−1.08937
$259$	−0.501496	−0.0311615
$260$	0	0
$261$	8.92659	0.552542
$262$	8.27711	0.511362
$263$	0.838403	0.0516981	0.0258491	−	0.999666i	$-0.491771\pi$
$263$	0.838403	0.0516981	0.0258491	+	0.999666i	$0.491771\pi$
$264$	−2.30313	−0.141748
$265$	0	0
$266$	7.50770	0.460327
$267$	5.21004	0.318849
$268$	−19.8881	−1.21486
$269$	18.5059	1.12833	0.564163	−	0.825664i	$-0.309199\pi$
$269$	18.5059	1.12833	0.564163	+	0.825664i	$0.309199\pi$
$270$	0	0
$271$	−9.34396	−0.567605	−0.283803	−	0.958883i	$-0.591596\pi$
$271$	−9.34396	−0.567605	−0.283803	+	0.958883i	$0.591596\pi$
$272$	−11.3742	−0.689663
$273$	1.38404	0.0837657
$274$	4.14326	0.250304
$275$	0	0
$276$	−18.2060	−1.09587
$277$	5.24338	0.315044	0.157522	−	0.987515i	$-0.449649\pi$
$277$	5.24338	0.315044	0.157522	+	0.987515i	$0.449649\pi$
$278$	−21.9801	−1.31828
$279$	−6.61741	−0.396174
$280$	0	0
$281$	−18.6402	−1.11198	−0.555990	−	0.831189i	$-0.687661\pi$
$281$	−18.6402	−1.11198	−0.555990	+	0.831189i	$0.687661\pi$
$282$	2.04563	0.121815
$283$	−31.9964	−1.90199	−0.950993	−	0.309213i	$-0.899934\pi$
$283$	−31.9964	−1.90199	−0.950993	+	0.309213i	$0.899934\pi$
$284$	−21.2460	−1.26072
$285$	0	0
$286$	−12.6656	−0.748933
$287$	1.66016	0.0979959
$288$	8.11280	0.478052
$289$	−6.99957	−0.411739
$290$	0	0
$291$	16.2597	0.953162
$292$	13.6869	0.800963
$293$	−11.2636	−0.658029	−0.329014	−	0.944325i	$-0.606716\pi$
$293$	−11.2636	−0.658029	−0.329014	+	0.944325i	$0.606716\pi$
$294$	−10.5164	−0.613328
$295$	0	0
$296$	0.138878	0.00807214
$297$	6.09961	0.353935
$298$	20.3657	1.17975
$299$	−8.45948	−0.489225
$300$	0	0
$301$	−11.6629	−0.672239
$302$	43.7208	2.51585
$303$	−11.1182	−0.638726
$304$	9.68152	0.555273
$305$	0	0
$306$	−6.46898	−0.369807
$307$	−21.9312	−1.25168	−0.625841	−	0.779951i	$-0.715244\pi$
$307$	−21.9312	−1.25168	−0.625841	+	0.779951i	$0.715244\pi$
$308$	−18.1685	−1.03525
$309$	−14.4660	−0.822943
$310$	0	0
$311$	−15.9766	−0.905952	−0.452976	−	0.891523i	$-0.649638\pi$
$311$	−15.9766	−0.905952	−0.452976	+	0.891523i	$0.649638\pi$
$312$	−0.383278	−0.0216989
$313$	17.0027	0.961049	0.480525	−	0.876981i	$-0.340446\pi$
$313$	17.0027	0.961049	0.480525	+	0.876981i	$0.340446\pi$
$314$	−6.22477	−0.351284
$315$	0	0
$316$	18.3927	1.03467
$317$	7.77937	0.436933	0.218466	−	0.975844i	$-0.429895\pi$
$317$	7.77937	0.436933	0.218466	+	0.975844i	$0.429895\pi$
$318$	2.01437	0.112960
$319$	−54.4487	−3.04854
$320$	0	0
$321$	−7.22963	−0.403519
$322$	−23.2446	−1.29537
$323$	−8.51218	−0.473630
$324$	2.18458	0.121366
$325$	0	0
$326$	−19.3477	−1.07157
$327$	−14.8987	−0.823899
$328$	−0.459744	−0.0253851
$329$	1.36348	0.0751712
$330$	0	0
$331$	7.22374	0.397052	0.198526	−	0.980096i	$-0.436385\pi$
$331$	7.22374	0.397052	0.198526	+	0.980096i	$0.436385\pi$
$332$	−3.83837	−0.210658
$333$	−0.367805	−0.0201556
$334$	14.8291	0.811412
$335$	0	0
$336$	4.90413	0.267542
$337$	13.5364	0.737372	0.368686	−	0.929554i	$-0.379808\pi$
$337$	13.5364	0.737372	0.368686	+	0.929554i	$0.379808\pi$
$338$	24.4854	1.33183
$339$	−17.1562	−0.931794
$340$	0	0
$341$	40.3636	2.18581
$342$	5.50627	0.297745
$343$	−16.5539	−0.893828
$344$	3.22979	0.174138
$345$	0	0
$346$	40.9573	2.20188
$347$	25.7242	1.38095	0.690473	−	0.723358i	$-0.257403\pi$
$347$	25.7242	1.38095	0.690473	+	0.723358i	$0.257403\pi$
$348$	−19.5009	−1.04536
$349$	−30.6245	−1.63929	−0.819646	−	0.572870i	$-0.805830\pi$
$349$	−30.6245	−1.63929	−0.819646	+	0.572870i	$0.805830\pi$
$350$	0	0
$351$	1.01507	0.0541806
$352$	−49.4849	−2.63756
$353$	−23.9161	−1.27292	−0.636462	−	0.771308i	$-0.719603\pi$
$353$	−23.9161	−1.27292	−0.636462	+	0.771308i	$0.719603\pi$
$354$	−2.59589	−0.137970
$355$	0	0
$356$	−11.3818	−0.603232
$357$	−4.31181	−0.228205
$358$	21.8985	1.15737
$359$	28.4996	1.50415	0.752077	−	0.659076i	$-0.229052\pi$
$359$	28.4996	1.50415	0.752077	+	0.659076i	$0.229052\pi$
$360$	0	0
$361$	−11.7546	−0.618663
$362$	47.3951	2.49103
$363$	−26.2052	−1.37542
$364$	−3.02354	−0.158477
$365$	0	0
$366$	7.15247	0.373865
$367$	35.1577	1.83522	0.917609	−	0.397485i	$-0.130117\pi$
$367$	35.1577	1.83522	0.917609	+	0.397485i	$0.130117\pi$
$368$	−29.9749	−1.56255
$369$	1.21758	0.0633849
$370$	0	0
$371$	1.34265	0.0697069
$372$	14.4563	0.749523
$373$	−30.9187	−1.60091	−0.800456	−	0.599392i	$-0.795409\pi$
$373$	−30.9187	−1.60091	−0.800456	+	0.599392i	$0.795409\pi$
$374$	39.4582	2.04034
$375$	0	0
$376$	−0.377587	−0.0194725
$377$	−9.06115	−0.466673
$378$	2.78918	0.143460
$379$	−10.6258	−0.545813	−0.272906	−	0.962041i	$-0.587985\pi$
$379$	−10.6258	−0.545813	−0.272906	+	0.962041i	$0.587985\pi$
$380$	0	0
$381$	0.761521	0.0390139
$382$	37.5551	1.92149
$383$	13.5818	0.693999	0.347000	−	0.937865i	$-0.387200\pi$
$383$	13.5818	0.693999	0.347000	+	0.937865i	$0.387200\pi$
$384$	−3.00783	−0.153493
$385$	0	0
$386$	−14.9885	−0.762894
$387$	−8.55376	−0.434812
$388$	−35.5207	−1.80329
$389$	−35.6919	−1.80965	−0.904826	−	0.425781i	$-0.859999\pi$
$389$	−35.6919	−1.80965	−0.904826	+	0.425781i	$0.859999\pi$
$390$	0	0
$391$	26.3546	1.33281
$392$	1.94114	0.0980424
$393$	4.04625	0.204106
$394$	40.8818	2.05960
$395$	0	0
$396$	−13.3251	−0.669611
$397$	−18.5860	−0.932804	−0.466402	−	0.884573i	$-0.654450\pi$
$397$	−18.5860	−0.932804	−0.466402	+	0.884573i	$0.654450\pi$
$398$	46.8653	2.34915
$399$	3.67013	0.183736
$400$	0	0
$401$	23.9733	1.19717	0.598584	−	0.801060i	$-0.295730\pi$
$401$	23.9733	1.19717	0.598584	+	0.801060i	$0.295730\pi$
$402$	−18.6230	−0.928833
$403$	6.71716	0.334605
$404$	24.2887	1.20841
$405$	0	0
$406$	−24.8978	−1.23566
$407$	2.24347	0.111205
$408$	1.19406	0.0591147
$409$	4.48372	0.221706	0.110853	−	0.993837i	$-0.464642\pi$
$409$	4.48372	0.221706	0.110853	+	0.993837i	$0.464642\pi$
$410$	0	0
$411$	2.02543	0.0999069
$412$	31.6022	1.55693
$413$	−1.73025	−0.0851402
$414$	−17.0480	−0.837861
$415$	0	0
$416$	−8.23510	−0.403759
$417$	−10.7449	−0.526180
$418$	−33.5861	−1.64275
$419$	13.0168	0.635913	0.317956	−	0.948105i	$-0.397003\pi$
$419$	13.0168	0.635913	0.317956	+	0.948105i	$0.397003\pi$
$420$	0	0
$421$	−12.9993	−0.633549	−0.316774	−	0.948501i	$-0.602600\pi$
$421$	−12.9993	−0.633549	−0.316774	+	0.948501i	$0.602600\pi$
$422$	−27.0367	−1.31613
$423$	1.00000	0.0486217
$424$	−0.371817	−0.0180570
$425$	0	0
$426$	−19.8945	−0.963894
$427$	4.76738	0.230710
$428$	15.7937	0.763419
$429$	−6.19155	−0.298931
$430$	0	0
$431$	−26.9050	−1.29597	−0.647984	−	0.761654i	$-0.724388\pi$
$431$	−26.9050	−1.29597	−0.647984	+	0.761654i	$0.724388\pi$
$432$	3.59676	0.173049
$433$	−1.31361	−0.0631282	−0.0315641	−	0.999502i	$-0.510049\pi$
$433$	−1.31361	−0.0631282	−0.0315641	+	0.999502i	$0.510049\pi$
$434$	18.4571	0.885970
$435$	0	0
$436$	32.5474	1.55874
$437$	−22.4325	−1.07309
$438$	12.8163	0.612385
$439$	4.37790	0.208946	0.104473	−	0.994528i	$-0.466684\pi$
$439$	4.37790	0.208946	0.104473	+	0.994528i	$0.466684\pi$
$440$	0	0
$441$	−5.14091	−0.244805
$442$	6.56649	0.312336
$443$	−24.5311	−1.16551	−0.582754	−	0.812649i	$-0.698025\pi$
$443$	−24.5311	−1.16551	−0.582754	+	0.812649i	$0.698025\pi$
$444$	0.803501	0.0381325
$445$	0	0
$446$	8.23012	0.389708
$447$	9.95572	0.470889
$448$	−12.8198	−0.605678
$449$	−22.7169	−1.07207	−0.536037	−	0.844194i	$-0.680079\pi$
$449$	−22.7169	−1.07207	−0.536037	+	0.844194i	$0.680079\pi$
$450$	0	0
$451$	−7.42679	−0.349714
$452$	37.4790	1.76287
$453$	21.3728	1.00418
$454$	−27.8450	−1.30683
$455$	0	0
$456$	−1.01636	−0.0475955
$457$	−10.7824	−0.504380	−0.252190	−	0.967678i	$-0.581151\pi$
$457$	−10.7824	−0.504380	−0.252190	+	0.967678i	$0.581151\pi$
$458$	7.49825	0.350370
$459$	−3.16235	−0.147606
$460$	0	0
$461$	−18.0877	−0.842427	−0.421214	−	0.906962i	$-0.638396\pi$
$461$	−18.0877	−0.842427	−0.421214	+	0.906962i	$0.638396\pi$
$462$	−17.0129	−0.791511
$463$	−37.7010	−1.75211	−0.876057	−	0.482208i	$-0.839835\pi$
$463$	−37.7010	−1.75211	−0.876057	+	0.482208i	$0.839835\pi$
$464$	−32.1069	−1.49052
$465$	0	0
$466$	−30.2891	−1.40312
$467$	−19.4983	−0.902275	−0.451138	−	0.892454i	$-0.648982\pi$
$467$	−19.4983	−0.902275	−0.451138	+	0.892454i	$0.648982\pi$
$468$	−2.21751	−0.102505
$469$	−12.4129	−0.573176
$470$	0	0
$471$	−3.04297	−0.140213
$472$	0.479156	0.0220549
$473$	52.1746	2.39899
$474$	17.2228	0.791069
$475$	0	0
$476$	9.41949	0.431742
$477$	0.984720	0.0450872
$478$	−13.4304	−0.614294
$479$	−14.2927	−0.653049	−0.326524	−	0.945189i	$-0.605878\pi$
$479$	−14.2927	−0.653049	−0.326524	+	0.945189i	$0.605878\pi$
$480$	0	0
$481$	0.373349	0.0170233
$482$	−38.5698	−1.75681
$483$	−11.3631	−0.517038
$484$	57.2475	2.60216
$485$	0	0
$486$	2.04563	0.0927914
$487$	−19.2934	−0.874267	−0.437133	−	0.899397i	$-0.644006\pi$
$487$	−19.2934	−0.874267	−0.437133	+	0.899397i	$0.644006\pi$
$488$	−1.32022	−0.0597635
$489$	−9.45808	−0.427709
$490$	0	0
$491$	−13.9091	−0.627708	−0.313854	−	0.949471i	$-0.601620\pi$
$491$	−13.9091	−0.627708	−0.313854	+	0.949471i	$0.601620\pi$
$492$	−2.65991	−0.119918
$493$	28.2290	1.27137
$494$	−5.58927	−0.251473
$495$	0	0
$496$	23.8013	1.06871
$497$	−13.2604	−0.594812
$498$	−3.59422	−0.161061
$499$	3.15305	0.141150	0.0705750	−	0.997506i	$-0.477517\pi$
$499$	3.15305	0.141150	0.0705750	+	0.997506i	$0.477517\pi$
$500$	0	0
$501$	7.24917	0.323869
$502$	21.7884	0.972464
$503$	34.8503	1.55390	0.776950	−	0.629563i	$-0.216766\pi$
$503$	34.8503	1.55390	0.776950	+	0.629563i	$0.216766\pi$
$504$	−0.514833	−0.0229325
$505$	0	0
$506$	103.986	4.62274
$507$	11.9696	0.531590
$508$	−1.66361	−0.0738106
$509$	1.89412	0.0839553	0.0419776	−	0.999119i	$-0.486634\pi$
$509$	1.89412	0.0839553	0.0419776	+	0.999119i	$0.486634\pi$
$510$	0	0
$511$	8.54251	0.377898
$512$	−31.8960	−1.40962
$513$	2.69173	0.118843
$514$	5.16861	0.227977
$515$	0	0
$516$	18.6864	0.822623
$517$	−6.09961	−0.268261
$518$	1.02587	0.0450743
$519$	20.0219	0.878864
$520$	0	0
$521$	−27.2380	−1.19332	−0.596659	−	0.802495i	$-0.703506\pi$
$521$	−27.2380	−1.19332	−0.596659	+	0.802495i	$0.703506\pi$
$522$	−18.2605	−0.799239
$523$	−19.5385	−0.854360	−0.427180	−	0.904167i	$-0.640493\pi$
$523$	−19.5385	−0.854360	−0.427180	+	0.904167i	$0.640493\pi$
$524$	−8.83937	−0.386150
$525$	0	0
$526$	−1.71506	−0.0747801
$527$	−20.9265	−0.911574
$528$	−21.9389	−0.954766
$529$	46.4532	2.01971
$530$	0	0
$531$	−1.26900	−0.0550697
$532$	−8.01770	−0.347611
$533$	−1.23594	−0.0535344
$534$	−10.6578	−0.461208
$535$	0	0
$536$	3.43749	0.148477
$537$	10.7051	0.461957
$538$	−37.8562	−1.63210
$539$	31.3576	1.35067
$540$	0	0
$541$	8.14791	0.350306	0.175153	−	0.984541i	$-0.443958\pi$
$541$	8.14791	0.350306	0.175153	+	0.984541i	$0.443958\pi$
$542$	19.1142	0.821027
$543$	23.1690	0.994277
$544$	25.6555	1.09997
$545$	0	0
$546$	−2.83122	−0.121165
$547$	−8.14002	−0.348042	−0.174021	−	0.984742i	$-0.555676\pi$
$547$	−8.14002	−0.348042	−0.174021	+	0.984742i	$0.555676\pi$
$548$	−4.42471	−0.189014
$549$	3.49647	0.149226
$550$	0	0
$551$	−24.0280	−1.02363
$552$	3.14675	0.133935
$553$	11.4796	0.488163
$554$	−10.7260	−0.455704
$555$	0	0
$556$	23.4731	0.995483
$557$	4.05381	0.171766	0.0858828	−	0.996305i	$-0.472629\pi$
$557$	4.05381	0.171766	0.0858828	+	0.996305i	$0.472629\pi$
$558$	13.5367	0.573056
$559$	8.68270	0.367239
$560$	0	0
$561$	19.2891	0.814385
$562$	38.1308	1.60845
$563$	−27.6714	−1.16621	−0.583105	−	0.812397i	$-0.698162\pi$
$563$	−27.6714	−1.16621	−0.583105	+	0.812397i	$0.698162\pi$
$564$	−2.18458	−0.0919875
$565$	0	0
$566$	65.4525	2.75118
$567$	1.36348	0.0572609
$568$	3.67218	0.154081
$569$	−26.9067	−1.12799	−0.563994	−	0.825779i	$-0.690736\pi$
$569$	−26.9067	−1.12799	−0.563994	+	0.825779i	$0.690736\pi$
$570$	0	0
$571$	−24.5857	−1.02888	−0.514440	−	0.857527i	$-0.672000\pi$
$571$	−24.5857	−1.02888	−0.514440	+	0.857527i	$0.672000\pi$
$572$	13.5260	0.565549
$573$	18.3588	0.766948
$574$	−3.39606	−0.141749
$575$	0	0
$576$	−9.40223	−0.391760
$577$	5.81843	0.242225	0.121112	−	0.992639i	$-0.461354\pi$
$577$	5.81843	0.242225	0.121112	+	0.992639i	$0.461354\pi$
$578$	14.3185	0.595571
$579$	−7.32709	−0.304504
$580$	0	0
$581$	−2.39568	−0.0993895
$582$	−33.2613	−1.37873
$583$	−6.00641	−0.248760
$584$	−2.36566	−0.0978917
$585$	0	0
$586$	23.0412	0.951822
$587$	−14.5567	−0.600818	−0.300409	−	0.953810i	$-0.597123\pi$
$587$	−14.5567	−0.600818	−0.300409	+	0.953810i	$0.597123\pi$
$588$	11.2308	0.463148
$589$	17.8123	0.733942
$590$	0	0
$591$	19.9850	0.822073
$592$	1.32291	0.0543712
$593$	8.99369	0.369327	0.184663	−	0.982802i	$-0.440881\pi$
$593$	8.99369	0.369327	0.184663	+	0.982802i	$0.440881\pi$
$594$	−12.4775	−0.511959
$595$	0	0
$596$	−21.7491	−0.890877
$597$	22.9100	0.937645
$598$	17.3049	0.707651
$599$	17.8362	0.728767	0.364383	−	0.931249i	$-0.381280\pi$
$599$	17.8362	0.728767	0.364383	+	0.931249i	$0.381280\pi$
$600$	0	0
$601$	−25.5820	−1.04351	−0.521757	−	0.853094i	$-0.674723\pi$
$601$	−25.5820	−1.04351	−0.521757	+	0.853094i	$0.674723\pi$
$602$	23.8579	0.972377
$603$	−9.10384	−0.370737
$604$	−46.6907	−1.89982
$605$	0	0
$606$	22.7437	0.923901
$607$	11.0205	0.447307	0.223653	−	0.974669i	$-0.428202\pi$
$607$	11.0205	0.447307	0.223653	+	0.974669i	$0.428202\pi$
$608$	−21.8375	−0.885627
$609$	−12.1713	−0.493204
$610$	0	0
$611$	−1.01507	−0.0410655
$612$	6.90841	0.279256
$613$	−0.429277	−0.0173383	−0.00866917	−	0.999962i	$-0.502760\pi$
$613$	−0.429277	−0.0173383	−0.00866917	+	0.999962i	$0.502760\pi$
$614$	44.8631	1.81053
$615$	0	0
$616$	3.14028	0.126525
$617$	21.1936	0.853221	0.426611	−	0.904435i	$-0.359707\pi$
$617$	21.1936	0.853221	0.426611	+	0.904435i	$0.359707\pi$
$618$	29.5921	1.19037
$619$	−39.0805	−1.57078	−0.785388	−	0.619004i	$-0.787537\pi$
$619$	−39.0805	−1.57078	−0.785388	+	0.619004i	$0.787537\pi$
$620$	0	0
$621$	−8.33386	−0.334426
$622$	32.6822	1.31044
$623$	−7.10380	−0.284608
$624$	−3.65098	−0.146156
$625$	0	0
$626$	−34.7811	−1.39013
$627$	−16.4185	−0.655692
$628$	6.64762	0.265269
$629$	−1.16313	−0.0463769
$630$	0	0
$631$	−1.63195	−0.0649669	−0.0324834	−	0.999472i	$-0.510342\pi$
$631$	−1.63195	−0.0649669	−0.0324834	+	0.999472i	$0.510342\pi$
$632$	−3.17903	−0.126455
$633$	−13.2169	−0.525323
$634$	−15.9137	−0.632013
$635$	0	0
$636$	−2.15120	−0.0853007
$637$	5.21841	0.206761
$638$	111.382	4.40964
$639$	−9.72541	−0.384731
$640$	0	0
$641$	33.5845	1.32651	0.663254	−	0.748395i	$-0.269175\pi$
$641$	33.5845	1.32651	0.663254	+	0.748395i	$0.269175\pi$
$642$	14.7891	0.583680
$643$	−6.01140	−0.237067	−0.118533	−	0.992950i	$-0.537819\pi$
$643$	−6.01140	−0.237067	−0.118533	+	0.992950i	$0.537819\pi$
$644$	24.8236	0.978186
$645$	0	0
$646$	17.4127	0.685095
$647$	−0.387585	−0.0152375	−0.00761877	−	0.999971i	$-0.502425\pi$
$647$	−0.387585	−0.0152375	−0.00761877	+	0.999971i	$0.502425\pi$
$648$	−0.377587	−0.0148330
$649$	7.74038	0.303836
$650$	0	0
$651$	9.02272	0.353628
$652$	20.6619	0.809184
$653$	−1.93021	−0.0755349	−0.0377674	−	0.999287i	$-0.512025\pi$
$653$	−1.93021	−0.0755349	−0.0377674	+	0.999287i	$0.512025\pi$
$654$	30.4771	1.19175
$655$	0	0
$656$	−4.37937	−0.170985
$657$	6.26521	0.244429
$658$	−2.78918	−0.108733
$659$	17.1375	0.667582	0.333791	−	0.942647i	$-0.391672\pi$
$659$	17.1375	0.667582	0.333791	+	0.942647i	$0.391672\pi$
$660$	0	0
$661$	−30.1486	−1.17264	−0.586322	−	0.810078i	$-0.699425\pi$
$661$	−30.1486	−1.17264	−0.586322	+	0.810078i	$0.699425\pi$
$662$	−14.7771	−0.574327
$663$	3.21001	0.124667
$664$	0.663430	0.0257461
$665$	0	0
$666$	0.752392	0.0291546
$667$	74.3930	2.88051
$668$	−15.8364	−0.612729
$669$	4.02328	0.155549
$670$	0	0
$671$	−21.3271	−0.823323
$672$	−11.0617	−0.426713
$673$	−20.1355	−0.776166	−0.388083	−	0.921624i	$-0.626863\pi$
$673$	−20.1355	−0.776166	−0.388083	+	0.921624i	$0.626863\pi$
$674$	−27.6903	−1.06659
$675$	0	0
$676$	−26.1486	−1.00572
$677$	−47.7942	−1.83688	−0.918441	−	0.395559i	$-0.870551\pi$
$677$	−47.7942	−1.83688	−0.918441	+	0.395559i	$0.870551\pi$
$678$	35.0951	1.34782
$679$	−22.1699	−0.850802
$680$	0	0
$681$	−13.6120	−0.521612
$682$	−82.5688	−3.16172
$683$	8.05534	0.308229	0.154115	−	0.988053i	$-0.450748\pi$
$683$	8.05534	0.308229	0.154115	+	0.988053i	$0.450748\pi$
$684$	−5.88031	−0.224839
$685$	0	0
$686$	33.8631	1.29290
$687$	3.66550	0.139848
$688$	30.7659	1.17294
$689$	−0.999564	−0.0380803
$690$	0	0
$691$	−43.4917	−1.65450	−0.827252	−	0.561831i	$-0.810097\pi$
$691$	−43.4917	−1.65450	−0.827252	+	0.561831i	$0.810097\pi$
$692$	−43.7395	−1.66273
$693$	−8.31671	−0.315926
$694$	−52.6220	−1.99750
$695$	0	0
$696$	3.37056	0.127761
$697$	3.85042	0.145845
$698$	62.6463	2.37120
$699$	−14.8068	−0.560044
$700$	0	0
$701$	3.68237	0.139081	0.0695405	−	0.997579i	$-0.477847\pi$
$701$	3.68237	0.139081	0.0695405	+	0.997579i	$0.477847\pi$
$702$	−2.07646	−0.0783710
$703$	0.990032	0.0373398
$704$	57.3499	2.16146
$705$	0	0
$706$	48.9233	1.84125
$707$	15.1595	0.570133
$708$	2.77223	0.104187
$709$	12.1787	0.457381	0.228691	−	0.973499i	$-0.426556\pi$
$709$	12.1787	0.457381	0.228691	+	0.973499i	$0.426556\pi$
$710$	0	0
$711$	8.41933	0.315750
$712$	1.96724	0.0737255
$713$	−55.1486	−2.06533
$714$	8.82034	0.330093
$715$	0	0
$716$	−23.3861	−0.873979
$717$	−6.56545	−0.245191
$718$	−58.2996	−2.17572
$719$	27.6967	1.03291	0.516455	−	0.856314i	$-0.327251\pi$
$719$	27.6967	1.03291	0.516455	+	0.856314i	$0.327251\pi$
$720$	0	0
$721$	19.7242	0.734566
$722$	24.0455	0.894880
$723$	−18.8548	−0.701217
$724$	−50.6146	−1.88108
$725$	0	0
$726$	53.6061	1.98951
$727$	−38.8927	−1.44245	−0.721225	−	0.692701i	$-0.756421\pi$
$727$	−38.8927	−1.44245	−0.721225	+	0.692701i	$0.756421\pi$
$728$	0.522593	0.0193686
$729$	1.00000	0.0370370
$730$	0	0
$731$	−27.0500	−1.00048
$732$	−7.63833	−0.282321
$733$	15.5684	0.575032	0.287516	−	0.957776i	$-0.407171\pi$
$733$	15.5684	0.575032	0.287516	+	0.957776i	$0.407171\pi$
$734$	−71.9195	−2.65460
$735$	0	0
$736$	67.6110	2.49217
$737$	55.5299	2.04547
$738$	−2.49072	−0.0916847
$739$	−11.0652	−0.407039	−0.203520	−	0.979071i	$-0.565238\pi$
$739$	−11.0652	−0.407039	−0.203520	+	0.979071i	$0.565238\pi$
$740$	0	0
$741$	−2.73230	−0.100374
$742$	−2.74656	−0.100829
$743$	24.2939	0.891258	0.445629	−	0.895218i	$-0.352980\pi$
$743$	24.2939	0.891258	0.445629	+	0.895218i	$0.352980\pi$
$744$	−2.49864	−0.0916047
$745$	0	0
$746$	63.2482	2.31568
$747$	−1.75703	−0.0642863
$748$	−42.1386	−1.54074
$749$	9.85748	0.360185
$750$	0	0
$751$	39.1625	1.42906	0.714529	−	0.699605i	$-0.246641\pi$
$751$	39.1625	1.42906	0.714529	+	0.699605i	$0.246641\pi$
$752$	−3.59676	−0.131161
$753$	10.6512	0.388152
$754$	18.5357	0.675031
$755$	0	0
$756$	−2.97864	−0.108332
$757$	−34.1665	−1.24180	−0.620900	−	0.783889i	$-0.713233\pi$
$757$	−34.1665	−1.24180	−0.620900	+	0.783889i	$0.713233\pi$
$758$	21.7365	0.789504
$759$	50.8333	1.84513
$760$	0	0
$761$	−1.47941	−0.0536284	−0.0268142	−	0.999640i	$-0.508536\pi$
$761$	−1.47941	−0.0536284	−0.0268142	+	0.999640i	$0.508536\pi$
$762$	−1.55779	−0.0564327
$763$	20.3141	0.735420
$764$	−40.1062	−1.45099
$765$	0	0
$766$	−27.7833	−1.00385
$767$	1.28812	0.0465115
$768$	−12.6516	−0.456524
$769$	44.4471	1.60280	0.801402	−	0.598127i	$-0.204088\pi$
$769$	44.4471	1.60280	0.801402	+	0.598127i	$0.204088\pi$
$770$	0	0
$771$	2.52666	0.0909956
$772$	16.0066	0.576092
$773$	13.9509	0.501779	0.250889	−	0.968016i	$-0.419277\pi$
$773$	13.9509	0.501779	0.250889	+	0.968016i	$0.419277\pi$
$774$	17.4978	0.628945
$775$	0	0
$776$	6.13946	0.220394
$777$	0.501496	0.0179911
$778$	73.0123	2.61762
$779$	−3.27741	−0.117425
$780$	0	0
$781$	59.3212	2.12268
$782$	−53.9115	−1.92787
$783$	−8.92659	−0.319010
$784$	18.4907	0.660381
$785$	0	0
$786$	−8.27711	−0.295235
$787$	5.24787	0.187066	0.0935331	−	0.995616i	$-0.470184\pi$
$787$	5.24787	0.187066	0.0935331	+	0.995616i	$0.470184\pi$
$788$	−43.6589	−1.55528
$789$	−0.838403	−0.0298479
$790$	0	0
$791$	23.3921	0.831728
$792$	2.30313	0.0818382
$793$	−3.54917	−0.126035
$794$	38.0200	1.34928
$795$	0	0
$796$	−50.0488	−1.77393
$797$	15.1502	0.536649	0.268324	−	0.963329i	$-0.413530\pi$
$797$	15.1502	0.536649	0.268324	+	0.963329i	$0.413530\pi$
$798$	−7.50770	−0.265770
$799$	3.16235	0.111876
$800$	0	0
$801$	−5.21004	−0.184088
$802$	−49.0403	−1.73167
$803$	−38.2153	−1.34859
$804$	19.8881	0.701399
$805$	0	0
$806$	−13.7408	−0.483999
$807$	−18.5059	−0.651439
$808$	−4.19810	−0.147689
$809$	23.8183	0.837408	0.418704	−	0.908123i	$-0.362484\pi$
$809$	23.8183	0.837408	0.418704	+	0.908123i	$0.362484\pi$
$810$	0	0
$811$	16.9388	0.594803	0.297401	−	0.954753i	$-0.403880\pi$
$811$	16.9388	0.594803	0.297401	+	0.954753i	$0.403880\pi$
$812$	26.5891	0.933095
$813$	9.34396	0.327707
$814$	−4.58930	−0.160855
$815$	0	0
$816$	11.3742	0.398177
$817$	23.0244	0.805523
$818$	−9.17201	−0.320692
$819$	−1.38404	−0.0483621
$820$	0	0
$821$	−35.0142	−1.22200	−0.611002	−	0.791629i	$-0.709233\pi$
$821$	−35.0142	−1.22200	−0.611002	+	0.791629i	$0.709233\pi$
$822$	−4.14326	−0.144513
$823$	20.3228	0.708409	0.354205	−	0.935168i	$-0.384752\pi$
$823$	20.3228	0.708409	0.354205	+	0.935168i	$0.384752\pi$
$824$	−5.46217	−0.190284
$825$	0	0
$826$	3.53945	0.123153
$827$	−3.77900	−0.131409	−0.0657043	−	0.997839i	$-0.520929\pi$
$827$	−3.77900	−0.131409	−0.0657043	+	0.997839i	$0.520929\pi$
$828$	18.2060	0.632702
$829$	26.7502	0.929072	0.464536	−	0.885554i	$-0.346221\pi$
$829$	26.7502	0.929072	0.464536	+	0.885554i	$0.346221\pi$
$830$	0	0
$831$	−5.24338	−0.181891
$832$	9.54396	0.330877
$833$	−16.2574	−0.563284
$834$	21.9801	0.761107
$835$	0	0
$836$	35.8676	1.24051
$837$	6.61741	0.228731
$838$	−26.6275	−0.919832
$839$	−40.9971	−1.41538	−0.707689	−	0.706524i	$-0.750262\pi$
$839$	−40.9971	−1.41538	−0.707689	+	0.706524i	$0.750262\pi$
$840$	0	0
$841$	50.6841	1.74773
$842$	26.5918	0.916413
$843$	18.6402	0.642002
$844$	28.8733	0.993860
$845$	0	0
$846$	−2.04563	−0.0703300
$847$	35.7304	1.22771
$848$	−3.54181	−0.121626
$849$	31.9964	1.09811
$850$	0	0
$851$	−3.06524	−0.105075
$852$	21.2460	0.727875
$853$	29.0372	0.994214	0.497107	−	0.867689i	$-0.334396\pi$
$853$	29.0372	0.994214	0.497107	+	0.867689i	$0.334396\pi$
$854$	−9.75227	−0.333716
$855$	0	0
$856$	−2.72981	−0.0933031
$857$	47.5833	1.62542	0.812708	−	0.582672i	$-0.197993\pi$
$857$	47.5833	1.62542	0.812708	+	0.582672i	$0.197993\pi$
$858$	12.6656	0.432396
$859$	−18.8804	−0.644191	−0.322095	−	0.946707i	$-0.604387\pi$
$859$	−18.8804	−0.644191	−0.322095	+	0.946707i	$0.604387\pi$
$860$	0	0
$861$	−1.66016	−0.0565780
$862$	55.0376	1.87459
$863$	−12.0159	−0.409026	−0.204513	−	0.978864i	$-0.565561\pi$
$863$	−12.0159	−0.409026	−0.204513	+	0.978864i	$0.565561\pi$
$864$	−8.11280	−0.276003
$865$	0	0
$866$	2.68716	0.0913133
$867$	6.99957	0.237718
$868$	−19.7109	−0.669031
$869$	−51.3546	−1.74209
$870$	0	0
$871$	9.24107	0.313122
$872$	−5.62554	−0.190505
$873$	−16.2597	−0.550309
$874$	45.8885	1.55220
$875$	0	0
$876$	−13.6869	−0.462436
$877$	−20.2581	−0.684066	−0.342033	−	0.939688i	$-0.611115\pi$
$877$	−20.2581	−0.684066	−0.342033	+	0.939688i	$0.611115\pi$
$878$	−8.95554	−0.302235
$879$	11.2636	0.379913
$880$	0	0
$881$	−21.8467	−0.736034	−0.368017	−	0.929819i	$-0.619963\pi$
$881$	−21.8467	−0.736034	−0.368017	+	0.929819i	$0.619963\pi$
$882$	10.5164	0.354105
$883$	21.6700	0.729255	0.364627	−	0.931154i	$-0.381196\pi$
$883$	21.6700	0.729255	0.364627	+	0.931154i	$0.381196\pi$
$884$	−7.01254	−0.235857
$885$	0	0
$886$	50.1814	1.68588
$887$	−45.7596	−1.53646	−0.768228	−	0.640177i	$-0.778861\pi$
$887$	−45.7596	−1.53646	−0.768228	+	0.640177i	$0.778861\pi$
$888$	−0.138878	−0.00466045
$889$	−1.03832	−0.0348242
$890$	0	0
$891$	−6.09961	−0.204345
$892$	−8.78919	−0.294284
$893$	−2.69173	−0.0900753
$894$	−20.3657	−0.681130
$895$	0	0
$896$	4.10112	0.137009
$897$	8.45948	0.282454
$898$	46.4702	1.55073
$899$	−59.0709	−1.97013
$900$	0	0
$901$	3.11403	0.103743
$902$	15.1924	0.505853
$903$	11.6629	0.388117
$904$	−6.47793	−0.215453
$905$	0	0
$906$	−43.7208	−1.45252
$907$	−42.6881	−1.41744	−0.708718	−	0.705492i	$-0.750726\pi$
$907$	−42.6881	−1.41744	−0.708718	+	0.705492i	$0.750726\pi$
$908$	29.7365	0.986840
$909$	11.1182	0.368769
$910$	0	0
$911$	14.2697	0.472776	0.236388	−	0.971659i	$-0.424036\pi$
$911$	14.2697	0.472776	0.236388	+	0.971659i	$0.424036\pi$
$912$	−9.68152	−0.320587
$913$	10.7172	0.354687
$914$	22.0568	0.729573
$915$	0	0
$916$	−8.00760	−0.264578
$917$	−5.51700	−0.182187
$918$	6.46898	0.213508
$919$	−16.4907	−0.543978	−0.271989	−	0.962300i	$-0.587681\pi$
$919$	−16.4907	−0.543978	−0.271989	+	0.962300i	$0.587681\pi$
$920$	0	0
$921$	21.9312	0.722659
$922$	37.0006	1.21855
$923$	9.87201	0.324941
$924$	18.1685	0.597701
$925$	0	0
$926$	77.1221	2.53439
$927$	14.4660	0.475126
$928$	72.4197	2.37729
$929$	3.18581	0.104523	0.0522615	−	0.998633i	$-0.483357\pi$
$929$	3.18581	0.104523	0.0522615	+	0.998633i	$0.483357\pi$
$930$	0	0
$931$	13.8380	0.453521
$932$	32.3466	1.05955
$933$	15.9766	0.523051
$934$	39.8863	1.30512
$935$	0	0
$936$	0.383278	0.0125278
$937$	−32.9395	−1.07609	−0.538044	−	0.842917i	$-0.680836\pi$
$937$	−32.9395	−1.07609	−0.538044	+	0.842917i	$0.680836\pi$
$938$	25.3922	0.829085
$939$	−17.0027	−0.554862
$940$	0	0
$941$	−46.5726	−1.51822	−0.759111	−	0.650961i	$-0.774366\pi$
$941$	−46.5726	−1.51822	−0.759111	+	0.650961i	$0.774366\pi$
$942$	6.22477	0.202814
$943$	10.1472	0.330438
$944$	4.56428	0.148555
$945$	0	0
$946$	−106.730	−3.47008
$947$	4.83401	0.157084	0.0785421	−	0.996911i	$-0.474974\pi$
$947$	4.83401	0.157084	0.0785421	+	0.996911i	$0.474974\pi$
$948$	−18.3927	−0.597368
$949$	−6.35965	−0.206443
$950$	0	0
$951$	−7.77937	−0.252263
$952$	−1.62808	−0.0527664
$953$	−12.0174	−0.389280	−0.194640	−	0.980875i	$-0.562354\pi$
$953$	−12.0174	−0.389280	−0.194640	+	0.980875i	$0.562354\pi$
$954$	−2.01437	−0.0652176
$955$	0	0
$956$	14.3428	0.463878
$957$	54.4487	1.76008
$958$	29.2374	0.944619
$959$	−2.76163	−0.0891778
$960$	0	0
$961$	12.7901	0.412583
$962$	−0.763733	−0.0246237
$963$	7.22963	0.232972
$964$	41.1898	1.32663
$965$	0	0
$966$	23.2446	0.747883
$967$	−20.4699	−0.658266	−0.329133	−	0.944284i	$-0.606756\pi$
$967$	−20.4699	−0.658266	−0.329133	+	0.944284i	$0.606756\pi$
$968$	−9.89474	−0.318029
$969$	8.51218	0.273451
$970$	0	0
$971$	−4.43200	−0.142230	−0.0711148	−	0.997468i	$-0.522656\pi$
$971$	−4.43200	−0.142230	−0.0711148	+	0.997468i	$0.522656\pi$
$972$	−2.18458	−0.0700705
$973$	14.6505	0.469673
$974$	39.4670	1.26461
$975$	0	0
$976$	−12.5760	−0.402547
$977$	17.6508	0.564698	0.282349	−	0.959312i	$-0.408886\pi$
$977$	17.6508	0.564698	0.282349	+	0.959312i	$0.408886\pi$
$978$	19.3477	0.618670
$979$	31.7792	1.01567
$980$	0	0
$981$	14.8987	0.475678
$982$	28.4528	0.907965
$983$	13.0397	0.415903	0.207952	−	0.978139i	$-0.433320\pi$
$983$	13.0397	0.415903	0.207952	+	0.978139i	$0.433320\pi$
$984$	0.459744	0.0146561
$985$	0	0
$986$	−57.7459	−1.83900
$987$	−1.36348	−0.0434001
$988$	5.96894	0.189897
$989$	−71.2859	−2.26676
$990$	0	0
$991$	−11.4046	−0.362278	−0.181139	−	0.983458i	$-0.557978\pi$
$991$	−11.4046	−0.362278	−0.181139	+	0.983458i	$0.557978\pi$
$992$	−53.6857	−1.70452
$993$	−7.22374	−0.229238
$994$	27.1259	0.860380
$995$	0	0
$996$	3.83837	0.121623
$997$	39.9295	1.26458	0.632289	−	0.774732i	$-0.282115\pi$
$997$	39.9295	1.26458	0.632289	+	0.774732i	$0.282115\pi$
$998$	−6.44996	−0.204170
$999$	0.367805	0.0116368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bg.1.1		10
5.2	odd	4		705.2.c.b.424.3	✓	20
5.3	odd	4		705.2.c.b.424.18	yes	20
5.4	even	2		3525.2.a.bf.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.3	✓	20	5.2	odd	4
705.2.c.b.424.18	yes	20	5.3	odd	4
3525.2.a.bf.1.10		10	5.4	even	2
3525.2.a.bg.1.1		10	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-2.04563 q^{2} -1.00000 q^{3} +2.18458 q^{4} +2.04563 q^{6} +1.36348 q^{7} -0.377587 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.04563 q^{2} -1.00000 q^{3} +2.18458 q^{4} +2.04563 q^{6} +1.36348 q^{7} -0.377587 q^{8} +1.00000 q^{9} -6.09961 q^{11} -2.18458 q^{12} -1.01507 q^{13} -2.78918 q^{14} -3.59676 q^{16} +3.16235 q^{17} -2.04563 q^{18} -2.69173 q^{19} -1.36348 q^{21} +12.4775 q^{22} +8.33386 q^{23} +0.377587 q^{24} +2.07646 q^{26} -1.00000 q^{27} +2.97864 q^{28} +8.92659 q^{29} -6.61741 q^{31} +8.11280 q^{32} +6.09961 q^{33} -6.46898 q^{34} +2.18458 q^{36} -0.367805 q^{37} +5.50627 q^{38} +1.01507 q^{39} +1.21758 q^{41} +2.78918 q^{42} -8.55376 q^{43} -13.3251 q^{44} -17.0480 q^{46} +1.00000 q^{47} +3.59676 q^{48} -5.14091 q^{49} -3.16235 q^{51} -2.21751 q^{52} +0.984720 q^{53} +2.04563 q^{54} -0.514833 q^{56} +2.69173 q^{57} -18.2605 q^{58} -1.26900 q^{59} +3.49647 q^{61} +13.5367 q^{62} +1.36348 q^{63} -9.40223 q^{64} -12.4775 q^{66} -9.10384 q^{67} +6.90841 q^{68} -8.33386 q^{69} -9.72541 q^{71} -0.377587 q^{72} +6.26521 q^{73} +0.752392 q^{74} -5.88031 q^{76} -8.31671 q^{77} -2.07646 q^{78} +8.41933 q^{79} +1.00000 q^{81} -2.49072 q^{82} -1.75703 q^{83} -2.97864 q^{84} +17.4978 q^{86} -8.92659 q^{87} +2.30313 q^{88} -5.21004 q^{89} -1.38404 q^{91} +18.2060 q^{92} +6.61741 q^{93} -2.04563 q^{94} -8.11280 q^{96} -16.2597 q^{97} +10.5164 q^{98} -6.09961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 7 q^{4} - 3 q^{6} + 9 q^{8} + 10 q^{9}+O(q^{10}) \) 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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