LMFDB - Embedded newform 3525.2.a.s.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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
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			$-1.41421$ 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)

$f(q)$	$=$	$q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +3.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +3.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} -2.82843 q^{11} +1.82843 q^{12} +3.58579 q^{13} -1.24264 q^{14} +3.00000 q^{16} +7.24264 q^{17} -0.414214 q^{18} +1.24264 q^{19} -3.00000 q^{21} +1.17157 q^{22} +0.171573 q^{23} -1.58579 q^{24} -1.48528 q^{26} -1.00000 q^{27} -5.48528 q^{28} -0.171573 q^{29} +2.00000 q^{31} -4.41421 q^{32} +2.82843 q^{33} -3.00000 q^{34} -1.82843 q^{36} +7.65685 q^{37} -0.514719 q^{38} -3.58579 q^{39} -4.65685 q^{41} +1.24264 q^{42} -0.828427 q^{43} +5.17157 q^{44} -0.0710678 q^{46} +1.00000 q^{47} -3.00000 q^{48} +2.00000 q^{49} -7.24264 q^{51} -6.55635 q^{52} -10.0711 q^{53} +0.414214 q^{54} +4.75736 q^{56} -1.24264 q^{57} +0.0710678 q^{58} +6.41421 q^{59} -3.00000 q^{61} -0.828427 q^{62} +3.00000 q^{63} -4.17157 q^{64} -1.17157 q^{66} +16.1421 q^{67} -13.2426 q^{68} -0.171573 q^{69} -4.75736 q^{71} +1.58579 q^{72} -8.48528 q^{73} -3.17157 q^{74} -2.27208 q^{76} -8.48528 q^{77} +1.48528 q^{78} -4.00000 q^{79} +1.00000 q^{81} +1.92893 q^{82} -1.65685 q^{83} +5.48528 q^{84} +0.343146 q^{86} +0.171573 q^{87} -4.48528 q^{88} +7.31371 q^{89} +10.7574 q^{91} -0.313708 q^{92} -2.00000 q^{93} -0.414214 q^{94} +4.41421 q^{96} -12.4853 q^{97} -0.828427 q^{98} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{12} + 10 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} - 6 q^{21} + 8 q^{22} + 6 q^{23} - 6 q^{24} + 14 q^{26} - 2 q^{27} + 6 q^{28} - 6 q^{29} + 4 q^{31} - 6 q^{32} - 6 q^{34} + 2 q^{36} + 4 q^{37} - 18 q^{38} - 10 q^{39} + 2 q^{41} - 6 q^{42} + 4 q^{43} + 16 q^{44} + 14 q^{46} + 2 q^{47} - 6 q^{48} + 4 q^{49} - 6 q^{51} + 18 q^{52} - 6 q^{53} - 2 q^{54} + 18 q^{56} + 6 q^{57} - 14 q^{58} + 10 q^{59} - 6 q^{61} + 4 q^{62} + 6 q^{63} - 14 q^{64} - 8 q^{66} + 4 q^{67} - 18 q^{68} - 6 q^{69} - 18 q^{71} + 6 q^{72} - 12 q^{74} - 30 q^{76} - 14 q^{78} - 8 q^{79} + 2 q^{81} + 18 q^{82} + 8 q^{83} - 6 q^{84} + 12 q^{86} + 6 q^{87} + 8 q^{88} - 8 q^{89} + 30 q^{91} + 22 q^{92} - 4 q^{93} + 2 q^{94} + 6 q^{96} - 8 q^{97} + 4 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^12 + 10 * q^13 + 6 * q^14 + 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 - 6 * q^21 + 8 * q^22 + 6 * q^23 - 6 * q^24 + 14 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + 4 * q^31 - 6 * q^32 - 6 * q^34 + 2 * q^36 + 4 * q^37 - 18 * q^38 - 10 * q^39 + 2 * q^41 - 6 * q^42 + 4 * q^43 + 16 * q^44 + 14 * q^46 + 2 * q^47 - 6 * q^48 + 4 * q^49 - 6 * q^51 + 18 * q^52 - 6 * q^53 - 2 * q^54 + 18 * q^56 + 6 * q^57 - 14 * q^58 + 10 * q^59 - 6 * q^61 + 4 * q^62 + 6 * q^63 - 14 * q^64 - 8 * q^66 + 4 * q^67 - 18 * q^68 - 6 * q^69 - 18 * q^71 + 6 * q^72 - 12 * q^74 - 30 * q^76 - 14 * q^78 - 8 * q^79 + 2 * q^81 + 18 * q^82 + 8 * q^83 - 6 * q^84 + 12 * q^86 + 6 * q^87 + 8 * q^88 - 8 * q^89 + 30 * q^91 + 22 * q^92 - 4 * q^93 + 2 * q^94 + 6 * q^96 - 8 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.414214	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82843	−0.914214
$5$	0	0
$5$	0	0
$6$	0.414214	0.169102
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	1.58579	0.560660
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.82843	−0.852803	−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843	−0.852803	−0.426401	+	0.904534i	$0.640219\pi$
$12$	1.82843	0.527821
$13$	3.58579	0.994518	0.497259	−	0.867602i	$-0.334340\pi$
$13$	3.58579	0.994518	0.497259	+	0.867602i	$0.334340\pi$
$14$	−1.24264	−0.332110
$15$	0	0
$16$	3.00000	0.750000
$17$	7.24264	1.75660	0.878299	−	0.478111i	$-0.158678\pi$
$17$	7.24264	1.75660	0.878299	+	0.478111i	$0.158678\pi$
$18$	−0.414214	−0.0976311
$19$	1.24264	0.285081	0.142541	−	0.989789i	$-0.454473\pi$
$19$	1.24264	0.285081	0.142541	+	0.989789i	$0.454473\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	1.17157	0.249780
$23$	0.171573	0.0357754	0.0178877	−	0.999840i	$-0.494306\pi$
$23$	0.171573	0.0357754	0.0178877	+	0.999840i	$0.494306\pi$
$24$	−1.58579	−0.323697
$25$	0	0
$26$	−1.48528	−0.291288
$27$	−1.00000	−0.192450
$28$	−5.48528	−1.03662
$29$	−0.171573	−0.0318603	−0.0159301	−	0.999873i	$-0.505071\pi$
$29$	−0.171573	−0.0318603	−0.0159301	+	0.999873i	$0.505071\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−4.41421	−0.780330
$33$	2.82843	0.492366
$34$	−3.00000	−0.514496
$35$	0	0
$36$	−1.82843	−0.304738
$37$	7.65685	1.25878	0.629390	−	0.777090i	$-0.283305\pi$
$37$	7.65685	1.25878	0.629390	+	0.777090i	$0.283305\pi$
$38$	−0.514719	−0.0834984
$39$	−3.58579	−0.574185
$40$	0	0
$41$	−4.65685	−0.727278	−0.363639	−	0.931540i	$-0.618466\pi$
$41$	−4.65685	−0.727278	−0.363639	+	0.931540i	$0.618466\pi$
$42$	1.24264	0.191744
$43$	−0.828427	−0.126334	−0.0631670	−	0.998003i	$-0.520120\pi$
$43$	−0.828427	−0.126334	−0.0631670	+	0.998003i	$0.520120\pi$
$44$	5.17157	0.779644
$45$	0	0
$46$	−0.0710678	−0.0104784
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−3.00000	−0.433013
$49$	2.00000	0.285714
$50$	0	0
$51$	−7.24264	−1.01417
$52$	−6.55635	−0.909202
$53$	−10.0711	−1.38337	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	−10.0711	−1.38337	−0.691684	+	0.722200i	$0.743131\pi$
$54$	0.414214	0.0563673
$55$	0	0
$56$	4.75736	0.635729
$57$	−1.24264	−0.164592
$58$	0.0710678	0.00933166
$59$	6.41421	0.835059	0.417530	−	0.908663i	$-0.362896\pi$
$59$	6.41421	0.835059	0.417530	+	0.908663i	$0.362896\pi$
$60$	0	0
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	−0.828427	−0.105210
$63$	3.00000	0.377964
$64$	−4.17157	−0.521447
$65$	0	0
$66$	−1.17157	−0.144211
$67$	16.1421	1.97208	0.986038	−	0.166521i	$-0.0532534\pi$
$67$	16.1421	1.97208	0.986038	+	0.166521i	$0.0532534\pi$
$68$	−13.2426	−1.60591
$69$	−0.171573	−0.0206549
$70$	0	0
$71$	−4.75736	−0.564595	−0.282297	−	0.959327i	$-0.591096\pi$
$71$	−4.75736	−0.564595	−0.282297	+	0.959327i	$0.591096\pi$
$72$	1.58579	0.186887
$73$	−8.48528	−0.993127	−0.496564	−	0.868000i	$-0.665405\pi$
$73$	−8.48528	−0.993127	−0.496564	+	0.868000i	$0.665405\pi$
$74$	−3.17157	−0.368688
$75$	0	0
$76$	−2.27208	−0.260625
$77$	−8.48528	−0.966988
$78$	1.48528	0.168175
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	1.92893	0.213015
$83$	−1.65685	−0.181863	−0.0909317	−	0.995857i	$-0.528984\pi$
$83$	−1.65685	−0.181863	−0.0909317	+	0.995857i	$0.528984\pi$
$84$	5.48528	0.598493
$85$	0	0
$86$	0.343146	0.0370024
$87$	0.171573	0.0183945
$88$	−4.48528	−0.478133
$89$	7.31371	0.775252	0.387626	−	0.921817i	$-0.373295\pi$
$89$	7.31371	0.775252	0.387626	+	0.921817i	$0.373295\pi$
$90$	0	0
$91$	10.7574	1.12768
$92$	−0.313708	−0.0327064
$93$	−2.00000	−0.207390
$94$	−0.414214	−0.0427229
$95$	0	0
$96$	4.41421	0.450524
$97$	−12.4853	−1.26769	−0.633844	−	0.773461i	$-0.718524\pi$
$97$	−12.4853	−1.26769	−0.633844	+	0.773461i	$0.718524\pi$
$98$	−0.828427	−0.0836838
$99$	−2.82843	−0.284268
$100$	0	0
$101$	4.34315	0.432159	0.216080	−	0.976376i	$-0.430673\pi$
$101$	4.34315	0.432159	0.216080	+	0.976376i	$0.430673\pi$
$102$	3.00000	0.297044
$103$	13.8284	1.36256	0.681278	−	0.732025i	$-0.261425\pi$
$103$	13.8284	1.36256	0.681278	+	0.732025i	$0.261425\pi$
$104$	5.68629	0.557587
$105$	0	0
$106$	4.17157	0.405179
$107$	9.65685	0.933563	0.466782	−	0.884373i	$-0.345413\pi$
$107$	9.65685	0.933563	0.466782	+	0.884373i	$0.345413\pi$
$108$	1.82843	0.175940
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	0	0
$111$	−7.65685	−0.726756
$112$	9.00000	0.850420
$113$	−14.8284	−1.39494	−0.697471	−	0.716613i	$-0.745691\pi$
$113$	−14.8284	−1.39494	−0.697471	+	0.716613i	$0.745691\pi$
$114$	0.514719	0.0482078
$115$	0	0
$116$	0.313708	0.0291271
$117$	3.58579	0.331506
$118$	−2.65685	−0.244583
$119$	21.7279	1.99180
$120$	0	0
$121$	−3.00000	−0.272727
$122$	1.24264	0.112503
$123$	4.65685	0.419894
$124$	−3.65685	−0.328395
$125$	0	0
$126$	−1.24264	−0.110703
$127$	3.51472	0.311881	0.155940	−	0.987766i	$-0.450159\pi$
$127$	3.51472	0.311881	0.155940	+	0.987766i	$0.450159\pi$
$128$	10.5563	0.933058
$129$	0.828427	0.0729389
$130$	0	0
$131$	−6.00000	−0.524222	−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000	−0.524222	−0.262111	+	0.965038i	$0.584419\pi$
$132$	−5.17157	−0.450128
$133$	3.72792	0.323252
$134$	−6.68629	−0.577608
$135$	0	0
$136$	11.4853	0.984855
$137$	−9.17157	−0.783580	−0.391790	−	0.920055i	$-0.628144\pi$
$137$	−9.17157	−0.783580	−0.391790	+	0.920055i	$0.628144\pi$
$138$	0.0710678	0.00604969
$139$	−4.89949	−0.415570	−0.207785	−	0.978175i	$-0.566625\pi$
$139$	−4.89949	−0.415570	−0.207785	+	0.978175i	$0.566625\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	1.97056	0.165366
$143$	−10.1421	−0.848128
$144$	3.00000	0.250000
$145$	0	0
$146$	3.51472	0.290880
$147$	−2.00000	−0.164957
$148$	−14.0000	−1.15079
$149$	12.8284	1.05095	0.525473	−	0.850810i	$-0.323888\pi$
$149$	12.8284	1.05095	0.525473	+	0.850810i	$0.323888\pi$
$150$	0	0
$151$	6.07107	0.494056	0.247028	−	0.969008i	$-0.420546\pi$
$151$	6.07107	0.494056	0.247028	+	0.969008i	$0.420546\pi$
$152$	1.97056	0.159834
$153$	7.24264	0.585533
$154$	3.51472	0.283224
$155$	0	0
$156$	6.55635	0.524928
$157$	2.34315	0.187003	0.0935017	−	0.995619i	$-0.470194\pi$
$157$	2.34315	0.187003	0.0935017	+	0.995619i	$0.470194\pi$
$158$	1.65685	0.131812
$159$	10.0711	0.798688
$160$	0	0
$161$	0.514719	0.0405655
$162$	−0.414214	−0.0325437
$163$	20.0000	1.56652	0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000	1.56652	0.783260	+	0.621694i	$0.213555\pi$
$164$	8.51472	0.664888
$165$	0	0
$166$	0.686292	0.0532666
$167$	23.6274	1.82834	0.914172	−	0.405326i	$-0.132842\pi$
$167$	23.6274	1.82834	0.914172	+	0.405326i	$0.132842\pi$
$168$	−4.75736	−0.367038
$169$	−0.142136	−0.0109335
$170$	0	0
$171$	1.24264	0.0950271
$172$	1.51472	0.115496
$173$	−1.58579	−0.120565	−0.0602826	−	0.998181i	$-0.519200\pi$
$173$	−1.58579	−0.120565	−0.0602826	+	0.998181i	$0.519200\pi$
$174$	−0.0710678	−0.00538764
$175$	0	0
$176$	−8.48528	−0.639602
$177$	−6.41421	−0.482122
$178$	−3.02944	−0.227066
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	2.48528	0.184730	0.0923648	−	0.995725i	$-0.470557\pi$
$181$	2.48528	0.184730	0.0923648	+	0.995725i	$0.470557\pi$
$182$	−4.45584	−0.330289
$183$	3.00000	0.221766
$184$	0.272078	0.0200579
$185$	0	0
$186$	0.828427	0.0607432
$187$	−20.4853	−1.49803
$188$	−1.82843	−0.133352
$189$	−3.00000	−0.218218
$190$	0	0
$191$	−11.6569	−0.843460	−0.421730	−	0.906721i	$-0.638577\pi$
$191$	−11.6569	−0.843460	−0.421730	+	0.906721i	$0.638577\pi$
$192$	4.17157	0.301057
$193$	0.485281	0.0349313	0.0174657	−	0.999847i	$-0.494440\pi$
$193$	0.485281	0.0349313	0.0174657	+	0.999847i	$0.494440\pi$
$194$	5.17157	0.371297
$195$	0	0
$196$	−3.65685	−0.261204
$197$	−21.7279	−1.54805	−0.774025	−	0.633155i	$-0.781760\pi$
$197$	−21.7279	−1.54805	−0.774025	+	0.633155i	$0.781760\pi$
$198$	1.17157	0.0832601
$199$	2.75736	0.195464	0.0977320	−	0.995213i	$-0.468841\pi$
$199$	2.75736	0.195464	0.0977320	+	0.995213i	$0.468841\pi$
$200$	0	0
$201$	−16.1421	−1.13858
$202$	−1.79899	−0.126576
$203$	−0.514719	−0.0361262
$204$	13.2426	0.927170
$205$	0	0
$206$	−5.72792	−0.399083
$207$	0.171573	0.0119251
$208$	10.7574	0.745889
$209$	−3.51472	−0.243118
$210$	0	0
$211$	10.9706	0.755245	0.377622	−	0.925960i	$-0.376742\pi$
$211$	10.9706	0.755245	0.377622	+	0.925960i	$0.376742\pi$
$212$	18.4142	1.26469
$213$	4.75736	0.325969
$214$	−4.00000	−0.273434
$215$	0	0
$216$	−1.58579	−0.107899
$217$	6.00000	0.407307
$218$	−2.48528	−0.168324
$219$	8.48528	0.573382
$220$	0	0
$221$	25.9706	1.74697
$222$	3.17157	0.212862
$223$	17.7990	1.19191	0.595954	−	0.803018i	$-0.296774\pi$
$223$	17.7990	1.19191	0.595954	+	0.803018i	$0.296774\pi$
$224$	−13.2426	−0.884811
$225$	0	0
$226$	6.14214	0.408569
$227$	−3.82843	−0.254102	−0.127051	−	0.991896i	$-0.540551\pi$
$227$	−3.82843	−0.254102	−0.127051	+	0.991896i	$0.540551\pi$
$228$	2.27208	0.150472
$229$	−26.6274	−1.75959	−0.879795	−	0.475354i	$-0.842320\pi$
$229$	−26.6274	−1.75959	−0.879795	+	0.475354i	$0.842320\pi$
$230$	0	0
$231$	8.48528	0.558291
$232$	−0.272078	−0.0178628
$233$	13.3137	0.872210	0.436105	−	0.899896i	$-0.356358\pi$
$233$	13.3137	0.872210	0.436105	+	0.899896i	$0.356358\pi$
$234$	−1.48528	−0.0970959
$235$	0	0
$236$	−11.7279	−0.763423
$237$	4.00000	0.259828
$238$	−9.00000	−0.583383
$239$	−2.68629	−0.173762	−0.0868809	−	0.996219i	$-0.527690\pi$
$239$	−2.68629	−0.173762	−0.0868809	+	0.996219i	$0.527690\pi$
$240$	0	0
$241$	25.0000	1.61039	0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000	1.61039	0.805196	+	0.593009i	$0.202060\pi$
$242$	1.24264	0.0798800
$243$	−1.00000	−0.0641500
$244$	5.48528	0.351159
$245$	0	0
$246$	−1.92893	−0.122984
$247$	4.45584	0.283519
$248$	3.17157	0.201395
$249$	1.65685	0.104999
$250$	0	0
$251$	10.0711	0.635680	0.317840	−	0.948144i	$-0.397042\pi$
$251$	10.0711	0.635680	0.317840	+	0.948144i	$0.397042\pi$
$252$	−5.48528	−0.345540
$253$	−0.485281	−0.0305094
$254$	−1.45584	−0.0913478
$255$	0	0
$256$	3.97056	0.248160
$257$	8.14214	0.507892	0.253946	−	0.967218i	$-0.418271\pi$
$257$	8.14214	0.507892	0.253946	+	0.967218i	$0.418271\pi$
$258$	−0.343146	−0.0213633
$259$	22.9706	1.42732
$260$	0	0
$261$	−0.171573	−0.0106201
$262$	2.48528	0.153541
$263$	8.82843	0.544384	0.272192	−	0.962243i	$-0.412251\pi$
$263$	8.82843	0.544384	0.272192	+	0.962243i	$0.412251\pi$
$264$	4.48528	0.276050
$265$	0	0
$266$	−1.54416	−0.0946783
$267$	−7.31371	−0.447592
$268$	−29.5147	−1.80290
$269$	−4.34315	−0.264806	−0.132403	−	0.991196i	$-0.542269\pi$
$269$	−4.34315	−0.264806	−0.132403	+	0.991196i	$0.542269\pi$
$270$	0	0
$271$	−6.14214	−0.373108	−0.186554	−	0.982445i	$-0.559732\pi$
$271$	−6.14214	−0.373108	−0.186554	+	0.982445i	$0.559732\pi$
$272$	21.7279	1.31745
$273$	−10.7574	−0.651065
$274$	3.79899	0.229505
$275$	0	0
$276$	0.313708	0.0188830
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	2.02944	0.121718
$279$	2.00000	0.119737
$280$	0	0
$281$	18.7990	1.12145	0.560727	−	0.828001i	$-0.310522\pi$
$281$	18.7990	1.12145	0.560727	+	0.828001i	$0.310522\pi$
$282$	0.414214	0.0246661
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	8.69848	0.516160
$285$	0	0
$286$	4.20101	0.248411
$287$	−13.9706	−0.824656
$288$	−4.41421	−0.260110
$289$	35.4558	2.08564
$290$	0	0
$291$	12.4853	0.731900
$292$	15.5147	0.907930
$293$	29.1127	1.70078	0.850391	−	0.526151i	$-0.176365\pi$
$293$	29.1127	1.70078	0.850391	+	0.526151i	$0.176365\pi$
$294$	0.828427	0.0483149
$295$	0	0
$296$	12.1421	0.705747
$297$	2.82843	0.164122
$298$	−5.31371	−0.307815
$299$	0.615224	0.0355793
$300$	0	0
$301$	−2.48528	−0.143249
$302$	−2.51472	−0.144706
$303$	−4.34315	−0.249507
$304$	3.72792	0.213811
$305$	0	0
$306$	−3.00000	−0.171499
$307$	32.4558	1.85235	0.926176	−	0.377090i	$-0.123075\pi$
$307$	32.4558	1.85235	0.926176	+	0.377090i	$0.123075\pi$
$308$	15.5147	0.884033
$309$	−13.8284	−0.786672
$310$	0	0
$311$	13.3137	0.754951	0.377476	−	0.926020i	$-0.376792\pi$
$311$	13.3137	0.754951	0.377476	+	0.926020i	$0.376792\pi$
$312$	−5.68629	−0.321923
$313$	−15.2426	−0.861565	−0.430782	−	0.902456i	$-0.641762\pi$
$313$	−15.2426	−0.861565	−0.430782	+	0.902456i	$0.641762\pi$
$314$	−0.970563	−0.0547720
$315$	0	0
$316$	7.31371	0.411428
$317$	−21.1716	−1.18911	−0.594557	−	0.804053i	$-0.702673\pi$
$317$	−21.1716	−1.18911	−0.594557	+	0.804053i	$0.702673\pi$
$318$	−4.17157	−0.233930
$319$	0.485281	0.0271705
$320$	0	0
$321$	−9.65685	−0.538993
$322$	−0.213203	−0.0118814
$323$	9.00000	0.500773
$324$	−1.82843	−0.101579
$325$	0	0
$326$	−8.28427	−0.458823
$327$	−6.00000	−0.331801
$328$	−7.38478	−0.407756
$329$	3.00000	0.165395
$330$	0	0
$331$	−24.0000	−1.31916	−0.659580	−	0.751635i	$-0.729266\pi$
$331$	−24.0000	−1.31916	−0.659580	+	0.751635i	$0.729266\pi$
$332$	3.02944	0.166262
$333$	7.65685	0.419593
$334$	−9.78680	−0.535510
$335$	0	0
$336$	−9.00000	−0.490990
$337$	36.6274	1.99522	0.997611	−	0.0690779i	$-0.0220057\pi$
$337$	36.6274	1.99522	0.997611	+	0.0690779i	$0.0220057\pi$
$338$	0.0588745	0.00320235
$339$	14.8284	0.805370
$340$	0	0
$341$	−5.65685	−0.306336
$342$	−0.514719	−0.0278328
$343$	−15.0000	−0.809924
$344$	−1.31371	−0.0708304
$345$	0	0
$346$	0.656854	0.0353127
$347$	25.4558	1.36654	0.683271	−	0.730165i	$-0.260557\pi$
$347$	25.4558	1.36654	0.683271	+	0.730165i	$0.260557\pi$
$348$	−0.313708	−0.0168165
$349$	−30.4853	−1.63184	−0.815920	−	0.578165i	$-0.803769\pi$
$349$	−30.4853	−1.63184	−0.815920	+	0.578165i	$0.803769\pi$
$350$	0	0
$351$	−3.58579	−0.191395
$352$	12.4853	0.665468
$353$	−10.8284	−0.576339	−0.288170	−	0.957579i	$-0.593047\pi$
$353$	−10.8284	−0.576339	−0.288170	+	0.957579i	$0.593047\pi$
$354$	2.65685	0.141210
$355$	0	0
$356$	−13.3726	−0.708745
$357$	−21.7279	−1.14996
$358$	−4.97056	−0.262702
$359$	−18.8284	−0.993726	−0.496863	−	0.867829i	$-0.665515\pi$
$359$	−18.8284	−0.993726	−0.496863	+	0.867829i	$0.665515\pi$
$360$	0	0
$361$	−17.4558	−0.918729
$362$	−1.02944	−0.0541060
$363$	3.00000	0.157459
$364$	−19.6690	−1.03094
$365$	0	0
$366$	−1.24264	−0.0649539
$367$	22.0000	1.14839	0.574195	−	0.818718i	$-0.305315\pi$
$367$	22.0000	1.14839	0.574195	+	0.818718i	$0.305315\pi$
$368$	0.514719	0.0268316
$369$	−4.65685	−0.242426
$370$	0	0
$371$	−30.2132	−1.56859
$372$	3.65685	0.189599
$373$	29.4558	1.52517	0.762583	−	0.646891i	$-0.223931\pi$
$373$	29.4558	1.52517	0.762583	+	0.646891i	$0.223931\pi$
$374$	8.48528	0.438763
$375$	0	0
$376$	1.58579	0.0817807
$377$	−0.615224	−0.0316856
$378$	1.24264	0.0639145
$379$	32.4853	1.66866	0.834328	−	0.551268i	$-0.185856\pi$
$379$	32.4853	1.66866	0.834328	+	0.551268i	$0.185856\pi$
$380$	0	0
$381$	−3.51472	−0.180064
$382$	4.82843	0.247044
$383$	−25.4558	−1.30073	−0.650366	−	0.759621i	$-0.725385\pi$
$383$	−25.4558	−1.30073	−0.650366	+	0.759621i	$0.725385\pi$
$384$	−10.5563	−0.538701
$385$	0	0
$386$	−0.201010	−0.0102311
$387$	−0.828427	−0.0421113
$388$	22.8284	1.15894
$389$	−25.8284	−1.30955	−0.654777	−	0.755822i	$-0.727237\pi$
$389$	−25.8284	−1.30955	−0.654777	+	0.755822i	$0.727237\pi$
$390$	0	0
$391$	1.24264	0.0628430
$392$	3.17157	0.160189
$393$	6.00000	0.302660
$394$	9.00000	0.453413
$395$	0	0
$396$	5.17157	0.259881
$397$	20.4853	1.02813	0.514063	−	0.857752i	$-0.328140\pi$
$397$	20.4853	1.02813	0.514063	+	0.857752i	$0.328140\pi$
$398$	−1.14214	−0.0572501
$399$	−3.72792	−0.186630
$400$	0	0
$401$	−14.4853	−0.723360	−0.361680	−	0.932302i	$-0.617797\pi$
$401$	−14.4853	−0.723360	−0.361680	+	0.932302i	$0.617797\pi$
$402$	6.68629	0.333482
$403$	7.17157	0.357241
$404$	−7.94113	−0.395086
$405$	0	0
$406$	0.213203	0.0105811
$407$	−21.6569	−1.07349
$408$	−11.4853	−0.568606
$409$	−25.6569	−1.26865	−0.634325	−	0.773067i	$-0.718722\pi$
$409$	−25.6569	−1.26865	−0.634325	+	0.773067i	$0.718722\pi$
$410$	0	0
$411$	9.17157	0.452400
$412$	−25.2843	−1.24567
$413$	19.2426	0.946868
$414$	−0.0710678	−0.00349279
$415$	0	0
$416$	−15.8284	−0.776052
$417$	4.89949	0.239929
$418$	1.45584	0.0712077
$419$	8.48528	0.414533	0.207267	−	0.978285i	$-0.433543\pi$
$419$	8.48528	0.414533	0.207267	+	0.978285i	$0.433543\pi$
$420$	0	0
$421$	38.6274	1.88259	0.941293	−	0.337592i	$-0.109612\pi$
$421$	38.6274	1.88259	0.941293	+	0.337592i	$0.109612\pi$
$422$	−4.54416	−0.221206
$423$	1.00000	0.0486217
$424$	−15.9706	−0.775599
$425$	0	0
$426$	−1.97056	−0.0954741
$427$	−9.00000	−0.435541
$428$	−17.6569	−0.853476
$429$	10.1421	0.489667
$430$	0	0
$431$	−33.0416	−1.59156	−0.795780	−	0.605586i	$-0.792939\pi$
$431$	−33.0416	−1.59156	−0.795780	+	0.605586i	$0.792939\pi$
$432$	−3.00000	−0.144338
$433$	−15.5858	−0.749005	−0.374503	−	0.927226i	$-0.622187\pi$
$433$	−15.5858	−0.749005	−0.374503	+	0.927226i	$0.622187\pi$
$434$	−2.48528	−0.119297
$435$	0	0
$436$	−10.9706	−0.525395
$437$	0.213203	0.0101989
$438$	−3.51472	−0.167940
$439$	−14.3431	−0.684561	−0.342280	−	0.939598i	$-0.611199\pi$
$439$	−14.3431	−0.684561	−0.342280	+	0.939598i	$0.611199\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	−10.7574	−0.511675
$443$	3.68629	0.175141	0.0875705	−	0.996158i	$-0.472090\pi$
$443$	3.68629	0.175141	0.0875705	+	0.996158i	$0.472090\pi$
$444$	14.0000	0.664411
$445$	0	0
$446$	−7.37258	−0.349102
$447$	−12.8284	−0.606764
$448$	−12.5147	−0.591265
$449$	−17.8284	−0.841375	−0.420688	−	0.907205i	$-0.638211\pi$
$449$	−17.8284	−0.841375	−0.420688	+	0.907205i	$0.638211\pi$
$450$	0	0
$451$	13.1716	0.620225
$452$	27.1127	1.27527
$453$	−6.07107	−0.285244
$454$	1.58579	0.0744246
$455$	0	0
$456$	−1.97056	−0.0922801
$457$	−16.9706	−0.793849	−0.396925	−	0.917851i	$-0.629923\pi$
$457$	−16.9706	−0.793849	−0.396925	+	0.917851i	$0.629923\pi$
$458$	11.0294	0.515372
$459$	−7.24264	−0.338058
$460$	0	0
$461$	1.02944	0.0479457	0.0239728	−	0.999713i	$-0.492368\pi$
$461$	1.02944	0.0479457	0.0239728	+	0.999713i	$0.492368\pi$
$462$	−3.51472	−0.163520
$463$	12.1421	0.564293	0.282146	−	0.959371i	$-0.408954\pi$
$463$	12.1421	0.564293	0.282146	+	0.959371i	$0.408954\pi$
$464$	−0.514719	−0.0238952
$465$	0	0
$466$	−5.51472	−0.255464
$467$	−35.7696	−1.65522	−0.827609	−	0.561305i	$-0.810299\pi$
$467$	−35.7696	−1.65522	−0.827609	+	0.561305i	$0.810299\pi$
$468$	−6.55635	−0.303067
$469$	48.4264	2.23612
$470$	0	0
$471$	−2.34315	−0.107966
$472$	10.1716	0.468185
$473$	2.34315	0.107738
$474$	−1.65685	−0.0761018
$475$	0	0
$476$	−39.7279	−1.82093
$477$	−10.0711	−0.461123
$478$	1.11270	0.0508936
$479$	−18.8995	−0.863540	−0.431770	−	0.901984i	$-0.642111\pi$
$479$	−18.8995	−0.863540	−0.431770	+	0.901984i	$0.642111\pi$
$480$	0	0
$481$	27.4558	1.25188
$482$	−10.3553	−0.471673
$483$	−0.514719	−0.0234205
$484$	5.48528	0.249331
$485$	0	0
$486$	0.414214	0.0187891
$487$	−26.4558	−1.19883	−0.599414	−	0.800439i	$-0.704600\pi$
$487$	−26.4558	−1.19883	−0.599414	+	0.800439i	$0.704600\pi$
$488$	−4.75736	−0.215356
$489$	−20.0000	−0.904431
$490$	0	0
$491$	−33.7279	−1.52212	−0.761060	−	0.648682i	$-0.775321\pi$
$491$	−33.7279	−1.52212	−0.761060	+	0.648682i	$0.775321\pi$
$492$	−8.51472	−0.383873
$493$	−1.24264	−0.0559657
$494$	−1.84567	−0.0830407
$495$	0	0
$496$	6.00000	0.269408
$497$	−14.2721	−0.640190
$498$	−0.686292	−0.0307535
$499$	15.2426	0.682354	0.341177	−	0.939999i	$-0.389174\pi$
$499$	15.2426	0.682354	0.341177	+	0.939999i	$0.389174\pi$
$500$	0	0
$501$	−23.6274	−1.05560
$502$	−4.17157	−0.186186
$503$	−17.8284	−0.794930	−0.397465	−	0.917617i	$-0.630110\pi$
$503$	−17.8284	−0.794930	−0.397465	+	0.917617i	$0.630110\pi$
$504$	4.75736	0.211910
$505$	0	0
$506$	0.201010	0.00893599
$507$	0.142136	0.00631246
$508$	−6.42641	−0.285126
$509$	−33.7696	−1.49681	−0.748405	−	0.663243i	$-0.769180\pi$
$509$	−33.7696	−1.49681	−0.748405	+	0.663243i	$0.769180\pi$
$510$	0	0
$511$	−25.4558	−1.12610
$512$	−22.7574	−1.00574
$513$	−1.24264	−0.0548639
$514$	−3.37258	−0.148758
$515$	0	0
$516$	−1.51472	−0.0666818
$517$	−2.82843	−0.124394
$518$	−9.51472	−0.418053
$519$	1.58579	0.0696083
$520$	0	0
$521$	34.6274	1.51705	0.758527	−	0.651641i	$-0.225919\pi$
$521$	34.6274	1.51705	0.758527	+	0.651641i	$0.225919\pi$
$522$	0.0710678	0.00311055
$523$	−7.34315	−0.321093	−0.160547	−	0.987028i	$-0.551326\pi$
$523$	−7.34315	−0.321093	−0.160547	+	0.987028i	$0.551326\pi$
$524$	10.9706	0.479251
$525$	0	0
$526$	−3.65685	−0.159446
$527$	14.4853	0.630989
$528$	8.48528	0.369274
$529$	−22.9706	−0.998720
$530$	0	0
$531$	6.41421	0.278353
$532$	−6.81623	−0.295521
$533$	−16.6985	−0.723292
$534$	3.02944	0.131097
$535$	0	0
$536$	25.5980	1.10566
$537$	−12.0000	−0.517838
$538$	1.79899	0.0775600
$539$	−5.65685	−0.243658
$540$	0	0
$541$	39.1421	1.68285	0.841426	−	0.540372i	$-0.181717\pi$
$541$	39.1421	1.68285	0.841426	+	0.540372i	$0.181717\pi$
$542$	2.54416	0.109281
$543$	−2.48528	−0.106654
$544$	−31.9706	−1.37073
$545$	0	0
$546$	4.45584	0.190693
$547$	−1.51472	−0.0647647	−0.0323823	−	0.999476i	$-0.510309\pi$
$547$	−1.51472	−0.0647647	−0.0323823	+	0.999476i	$0.510309\pi$
$548$	16.7696	0.716360
$549$	−3.00000	−0.128037
$550$	0	0
$551$	−0.213203	−0.00908277
$552$	−0.272078	−0.0115804
$553$	−12.0000	−0.510292
$554$	−12.4264	−0.527947
$555$	0	0
$556$	8.95837	0.379919
$557$	−31.1127	−1.31829	−0.659144	−	0.752017i	$-0.729081\pi$
$557$	−31.1127	−1.31829	−0.659144	+	0.752017i	$0.729081\pi$
$558$	−0.828427	−0.0350701
$559$	−2.97056	−0.125641
$560$	0	0
$561$	20.4853	0.864889
$562$	−7.78680	−0.328466
$563$	6.34315	0.267332	0.133666	−	0.991026i	$-0.457325\pi$
$563$	6.34315	0.267332	0.133666	+	0.991026i	$0.457325\pi$
$564$	1.82843	0.0769907
$565$	0	0
$566$	0	0
$567$	3.00000	0.125988
$568$	−7.54416	−0.316546
$569$	18.2843	0.766517	0.383258	−	0.923641i	$-0.374802\pi$
$569$	18.2843	0.766517	0.383258	+	0.923641i	$0.374802\pi$
$570$	0	0
$571$	30.9706	1.29608	0.648039	−	0.761607i	$-0.275589\pi$
$571$	30.9706	1.29608	0.648039	+	0.761607i	$0.275589\pi$
$572$	18.5442	0.775370
$573$	11.6569	0.486972
$574$	5.78680	0.241536
$575$	0	0
$576$	−4.17157	−0.173816
$577$	−34.5563	−1.43860	−0.719300	−	0.694700i	$-0.755537\pi$
$577$	−34.5563	−1.43860	−0.719300	+	0.694700i	$0.755537\pi$
$578$	−14.6863	−0.610869
$579$	−0.485281	−0.0201676
$580$	0	0
$581$	−4.97056	−0.206214
$582$	−5.17157	−0.214369
$583$	28.4853	1.17974
$584$	−13.4558	−0.556807
$585$	0	0
$586$	−12.0589	−0.498148
$587$	−0.686292	−0.0283263	−0.0141631	−	0.999900i	$-0.504508\pi$
$587$	−0.686292	−0.0283263	−0.0141631	+	0.999900i	$0.504508\pi$
$588$	3.65685	0.150806
$589$	2.48528	0.102404
$590$	0	0
$591$	21.7279	0.893767
$592$	22.9706	0.944084
$593$	−43.4558	−1.78452	−0.892259	−	0.451524i	$-0.850880\pi$
$593$	−43.4558	−1.78452	−0.892259	+	0.451524i	$0.850880\pi$
$594$	−1.17157	−0.0480702
$595$	0	0
$596$	−23.4558	−0.960789
$597$	−2.75736	−0.112851
$598$	−0.254834	−0.0104209
$599$	29.7990	1.21755	0.608777	−	0.793341i	$-0.291660\pi$
$599$	29.7990	1.21755	0.608777	+	0.793341i	$0.291660\pi$
$600$	0	0
$601$	−25.4853	−1.03957	−0.519783	−	0.854298i	$-0.673987\pi$
$601$	−25.4853	−1.03957	−0.519783	+	0.854298i	$0.673987\pi$
$602$	1.02944	0.0419567
$603$	16.1421	0.657359
$604$	−11.1005	−0.451673
$605$	0	0
$606$	1.79899	0.0730790
$607$	26.4853	1.07500	0.537502	−	0.843262i	$-0.319368\pi$
$607$	26.4853	1.07500	0.537502	+	0.843262i	$0.319368\pi$
$608$	−5.48528	−0.222458
$609$	0.514719	0.0208575
$610$	0	0
$611$	3.58579	0.145065
$612$	−13.2426	−0.535302
$613$	37.3137	1.50709	0.753543	−	0.657398i	$-0.228343\pi$
$613$	37.3137	1.50709	0.753543	+	0.657398i	$0.228343\pi$
$614$	−13.4437	−0.542542
$615$	0	0
$616$	−13.4558	−0.542151
$617$	2.82843	0.113868	0.0569341	−	0.998378i	$-0.481868\pi$
$617$	2.82843	0.113868	0.0569341	+	0.998378i	$0.481868\pi$
$618$	5.72792	0.230411
$619$	2.00000	0.0803868	0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000	0.0803868	0.0401934	+	0.999192i	$0.487203\pi$
$620$	0	0
$621$	−0.171573	−0.00688498
$622$	−5.51472	−0.221120
$623$	21.9411	0.879053
$624$	−10.7574	−0.430639
$625$	0	0
$626$	6.31371	0.252347
$627$	3.51472	0.140364
$628$	−4.28427	−0.170961
$629$	55.4558	2.21117
$630$	0	0
$631$	26.0000	1.03504	0.517522	−	0.855670i	$-0.326855\pi$
$631$	26.0000	1.03504	0.517522	+	0.855670i	$0.326855\pi$
$632$	−6.34315	−0.252317
$633$	−10.9706	−0.436041
$634$	8.76955	0.348283
$635$	0	0
$636$	−18.4142	−0.730171
$637$	7.17157	0.284148
$638$	−0.201010	−0.00795807
$639$	−4.75736	−0.188198
$640$	0	0
$641$	31.6569	1.25037	0.625185	−	0.780476i	$-0.285023\pi$
$641$	31.6569	1.25037	0.625185	+	0.780476i	$0.285023\pi$
$642$	4.00000	0.157867
$643$	19.6863	0.776352	0.388176	−	0.921585i	$-0.373105\pi$
$643$	19.6863	0.776352	0.388176	+	0.921585i	$0.373105\pi$
$644$	−0.941125	−0.0370855
$645$	0	0
$646$	−3.72792	−0.146673
$647$	5.85786	0.230296	0.115148	−	0.993348i	$-0.463266\pi$
$647$	5.85786	0.230296	0.115148	+	0.993348i	$0.463266\pi$
$648$	1.58579	0.0622956
$649$	−18.1421	−0.712141
$650$	0	0
$651$	−6.00000	−0.235159
$652$	−36.5685	−1.43213
$653$	12.2132	0.477940	0.238970	−	0.971027i	$-0.423190\pi$
$653$	12.2132	0.477940	0.238970	+	0.971027i	$0.423190\pi$
$654$	2.48528	0.0971822
$655$	0	0
$656$	−13.9706	−0.545459
$657$	−8.48528	−0.331042
$658$	−1.24264	−0.0484432
$659$	−34.2843	−1.33553	−0.667763	−	0.744374i	$-0.732748\pi$
$659$	−34.2843	−1.33553	−0.667763	+	0.744374i	$0.732748\pi$
$660$	0	0
$661$	8.51472	0.331184	0.165592	−	0.986194i	$-0.447046\pi$
$661$	8.51472	0.331184	0.165592	+	0.986194i	$0.447046\pi$
$662$	9.94113	0.386373
$663$	−25.9706	−1.00861
$664$	−2.62742	−0.101964
$665$	0	0
$666$	−3.17157	−0.122896
$667$	−0.0294373	−0.00113981
$668$	−43.2010	−1.67150
$669$	−17.7990	−0.688149
$670$	0	0
$671$	8.48528	0.327571
$672$	13.2426	0.510846
$673$	−39.7279	−1.53140	−0.765699	−	0.643199i	$-0.777607\pi$
$673$	−39.7279	−1.53140	−0.765699	+	0.643199i	$0.777607\pi$
$674$	−15.1716	−0.584387
$675$	0	0
$676$	0.259885	0.00999556
$677$	−8.82843	−0.339304	−0.169652	−	0.985504i	$-0.554264\pi$
$677$	−8.82843	−0.339304	−0.169652	+	0.985504i	$0.554264\pi$
$678$	−6.14214	−0.235887
$679$	−37.4558	−1.43742
$680$	0	0
$681$	3.82843	0.146706
$682$	2.34315	0.0897237
$683$	14.4853	0.554264	0.277132	−	0.960832i	$-0.410616\pi$
$683$	14.4853	0.554264	0.277132	+	0.960832i	$0.410616\pi$
$684$	−2.27208	−0.0868751
$685$	0	0
$686$	6.21320	0.237221
$687$	26.6274	1.01590
$688$	−2.48528	−0.0947505
$689$	−36.1127	−1.37578
$690$	0	0
$691$	22.3553	0.850437	0.425219	−	0.905091i	$-0.360197\pi$
$691$	22.3553	0.850437	0.425219	+	0.905091i	$0.360197\pi$
$692$	2.89949	0.110222
$693$	−8.48528	−0.322329
$694$	−10.5442	−0.400251
$695$	0	0
$696$	0.272078	0.0103131
$697$	−33.7279	−1.27754
$698$	12.6274	0.477955
$699$	−13.3137	−0.503571
$700$	0	0
$701$	20.6569	0.780199	0.390099	−	0.920773i	$-0.372441\pi$
$701$	20.6569	0.780199	0.390099	+	0.920773i	$0.372441\pi$
$702$	1.48528	0.0560583
$703$	9.51472	0.358854
$704$	11.7990	0.444691
$705$	0	0
$706$	4.48528	0.168806
$707$	13.0294	0.490022
$708$	11.7279	0.440762
$709$	50.9706	1.91424	0.957120	−	0.289692i	$-0.0935530\pi$
$709$	50.9706	1.91424	0.957120	+	0.289692i	$0.0935530\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	11.5980	0.434653
$713$	0.343146	0.0128509
$714$	9.00000	0.336817
$715$	0	0
$716$	−21.9411	−0.819978
$717$	2.68629	0.100321
$718$	7.79899	0.291056
$719$	−4.07107	−0.151825	−0.0759126	−	0.997114i	$-0.524187\pi$
$719$	−4.07107	−0.151825	−0.0759126	+	0.997114i	$0.524187\pi$
$720$	0	0
$721$	41.4853	1.54499
$722$	7.23045	0.269089
$723$	−25.0000	−0.929760
$724$	−4.54416	−0.168882
$725$	0	0
$726$	−1.24264	−0.0461187
$727$	−17.1127	−0.634675	−0.317337	−	0.948313i	$-0.602789\pi$
$727$	−17.1127	−0.634675	−0.317337	+	0.948313i	$0.602789\pi$
$728$	17.0589	0.632244
$729$	1.00000	0.0370370
$730$	0	0
$731$	−6.00000	−0.221918
$732$	−5.48528	−0.202742
$733$	26.4853	0.978256	0.489128	−	0.872212i	$-0.337315\pi$
$733$	26.4853	0.978256	0.489128	+	0.872212i	$0.337315\pi$
$734$	−9.11270	−0.336356
$735$	0	0
$736$	−0.757359	−0.0279166
$737$	−45.6569	−1.68179
$738$	1.92893	0.0710050
$739$	38.7696	1.42616	0.713081	−	0.701082i	$-0.247299\pi$
$739$	38.7696	1.42616	0.713081	+	0.701082i	$0.247299\pi$
$740$	0	0
$741$	−4.45584	−0.163690
$742$	12.5147	0.459430
$743$	−37.9706	−1.39300	−0.696502	−	0.717554i	$-0.745261\pi$
$743$	−37.9706	−1.39300	−0.696502	+	0.717554i	$0.745261\pi$
$744$	−3.17157	−0.116276
$745$	0	0
$746$	−12.2010	−0.446711
$747$	−1.65685	−0.0606211
$748$	37.4558	1.36952
$749$	28.9706	1.05856
$750$	0	0
$751$	−12.2721	−0.447814	−0.223907	−	0.974610i	$-0.571881\pi$
$751$	−12.2721	−0.447814	−0.223907	+	0.974610i	$0.571881\pi$
$752$	3.00000	0.109399
$753$	−10.0711	−0.367010
$754$	0.254834	0.00928051
$755$	0	0
$756$	5.48528	0.199498
$757$	5.85786	0.212908	0.106454	−	0.994318i	$-0.466050\pi$
$757$	5.85786	0.212908	0.106454	+	0.994318i	$0.466050\pi$
$758$	−13.4558	−0.488738
$759$	0.485281	0.0176146
$760$	0	0
$761$	49.1127	1.78033	0.890167	−	0.455634i	$-0.150588\pi$
$761$	49.1127	1.78033	0.890167	+	0.455634i	$0.150588\pi$
$762$	1.45584	0.0527397
$763$	18.0000	0.651644
$764$	21.3137	0.771103
$765$	0	0
$766$	10.5442	0.380976
$767$	23.0000	0.830482
$768$	−3.97056	−0.143275
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	−8.14214	−0.293232
$772$	−0.887302	−0.0319347
$773$	6.14214	0.220917	0.110459	−	0.993881i	$-0.464768\pi$
$773$	6.14214	0.220917	0.110459	+	0.993881i	$0.464768\pi$
$774$	0.343146	0.0123341
$775$	0	0
$776$	−19.7990	−0.710742
$777$	−22.9706	−0.824064
$778$	10.6985	0.383559
$779$	−5.78680	−0.207334
$780$	0	0
$781$	13.4558	0.481488
$782$	−0.514719	−0.0184063
$783$	0.171573	0.00613151
$784$	6.00000	0.214286
$785$	0	0
$786$	−2.48528	−0.0886471
$787$	−54.4264	−1.94009	−0.970046	−	0.242922i	$-0.921894\pi$
$787$	−54.4264	−1.94009	−0.970046	+	0.242922i	$0.921894\pi$
$788$	39.7279	1.41525
$789$	−8.82843	−0.314300
$790$	0	0
$791$	−44.4853	−1.58171
$792$	−4.48528	−0.159378
$793$	−10.7574	−0.382005
$794$	−8.48528	−0.301131
$795$	0	0
$796$	−5.04163	−0.178696
$797$	−39.1716	−1.38753	−0.693764	−	0.720202i	$-0.744049\pi$
$797$	−39.1716	−1.38753	−0.693764	+	0.720202i	$0.744049\pi$
$798$	1.54416	0.0546625
$799$	7.24264	0.256226
$800$	0	0
$801$	7.31371	0.258417
$802$	6.00000	0.211867
$803$	24.0000	0.846942
$804$	29.5147	1.04090
$805$	0	0
$806$	−2.97056	−0.104634
$807$	4.34315	0.152886
$808$	6.88730	0.242294
$809$	−1.02944	−0.0361931	−0.0180965	−	0.999836i	$-0.505761\pi$
$809$	−1.02944	−0.0361931	−0.0180965	+	0.999836i	$0.505761\pi$
$810$	0	0
$811$	6.00000	0.210688	0.105344	−	0.994436i	$-0.466406\pi$
$811$	6.00000	0.210688	0.105344	+	0.994436i	$0.466406\pi$
$812$	0.941125	0.0330270
$813$	6.14214	0.215414
$814$	8.97056	0.314418
$815$	0	0
$816$	−21.7279	−0.760629
$817$	−1.02944	−0.0360155
$818$	10.6274	0.371579
$819$	10.7574	0.375893
$820$	0	0
$821$	−26.5980	−0.928276	−0.464138	−	0.885763i	$-0.653636\pi$
$821$	−26.5980	−0.928276	−0.464138	+	0.885763i	$0.653636\pi$
$822$	−3.79899	−0.132505
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	21.9289	0.763931
$825$	0	0
$826$	−7.97056	−0.277331
$827$	8.68629	0.302052	0.151026	−	0.988530i	$-0.451742\pi$
$827$	8.68629	0.302052	0.151026	+	0.988530i	$0.451742\pi$
$828$	−0.313708	−0.0109021
$829$	−26.4853	−0.919872	−0.459936	−	0.887952i	$-0.652128\pi$
$829$	−26.4853	−0.919872	−0.459936	+	0.887952i	$0.652128\pi$
$830$	0	0
$831$	−30.0000	−1.04069
$832$	−14.9584	−0.518588
$833$	14.4853	0.501885
$834$	−2.02944	−0.0702737
$835$	0	0
$836$	6.42641	0.222262
$837$	−2.00000	−0.0691301
$838$	−3.51472	−0.121414
$839$	−1.02944	−0.0355401	−0.0177701	−	0.999842i	$-0.505657\pi$
$839$	−1.02944	−0.0355401	−0.0177701	+	0.999842i	$0.505657\pi$
$840$	0	0
$841$	−28.9706	−0.998985
$842$	−16.0000	−0.551396
$843$	−18.7990	−0.647472
$844$	−20.0589	−0.690455
$845$	0	0
$846$	−0.414214	−0.0142410
$847$	−9.00000	−0.309244
$848$	−30.2132	−1.03753
$849$	0	0
$850$	0	0
$851$	1.31371	0.0450333
$852$	−8.69848	−0.298005
$853$	−6.14214	−0.210303	−0.105151	−	0.994456i	$-0.533533\pi$
$853$	−6.14214	−0.210303	−0.105151	+	0.994456i	$0.533533\pi$
$854$	3.72792	0.127567
$855$	0	0
$856$	15.3137	0.523412
$857$	5.31371	0.181513	0.0907564	−	0.995873i	$-0.471072\pi$
$857$	5.31371	0.181513	0.0907564	+	0.995873i	$0.471072\pi$
$858$	−4.20101	−0.143420
$859$	−3.72792	−0.127195	−0.0635975	−	0.997976i	$-0.520257\pi$
$859$	−3.72792	−0.127195	−0.0635975	+	0.997976i	$0.520257\pi$
$860$	0	0
$861$	13.9706	0.476116
$862$	13.6863	0.466157
$863$	52.1421	1.77494	0.887469	−	0.460867i	$-0.152461\pi$
$863$	52.1421	1.77494	0.887469	+	0.460867i	$0.152461\pi$
$864$	4.41421	0.150175
$865$	0	0
$866$	6.45584	0.219379
$867$	−35.4558	−1.20414
$868$	−10.9706	−0.372365
$869$	11.3137	0.383791
$870$	0	0
$871$	57.8823	1.96127
$872$	9.51472	0.322209
$873$	−12.4853	−0.422563
$874$	−0.0883118	−0.00298719
$875$	0	0
$876$	−15.5147	−0.524194
$877$	20.2721	0.684539	0.342270	−	0.939602i	$-0.388804\pi$
$877$	20.2721	0.684539	0.342270	+	0.939602i	$0.388804\pi$
$878$	5.94113	0.200503
$879$	−29.1127	−0.981947
$880$	0	0
$881$	35.4853	1.19553	0.597765	−	0.801672i	$-0.296056\pi$
$881$	35.4853	1.19553	0.597765	+	0.801672i	$0.296056\pi$
$882$	−0.828427	−0.0278946
$883$	8.45584	0.284562	0.142281	−	0.989826i	$-0.454556\pi$
$883$	8.45584	0.284562	0.142281	+	0.989826i	$0.454556\pi$
$884$	−47.4853	−1.59710
$885$	0	0
$886$	−1.52691	−0.0512976
$887$	−20.2843	−0.681079	−0.340540	−	0.940230i	$-0.610610\pi$
$887$	−20.2843	−0.681079	−0.340540	+	0.940230i	$0.610610\pi$
$888$	−12.1421	−0.407463
$889$	10.5442	0.353640
$890$	0	0
$891$	−2.82843	−0.0947559
$892$	−32.5442	−1.08966
$893$	1.24264	0.0415834
$894$	5.31371	0.177717
$895$	0	0
$896$	31.6690	1.05799
$897$	−0.615224	−0.0205417
$898$	7.38478	0.246433
$899$	−0.343146	−0.0114446
$900$	0	0
$901$	−72.9411	−2.43002
$902$	−5.45584	−0.181660
$903$	2.48528	0.0827050
$904$	−23.5147	−0.782088
$905$	0	0
$906$	2.51472	0.0835459
$907$	−36.4558	−1.21050	−0.605248	−	0.796037i	$-0.706926\pi$
$907$	−36.4558	−1.21050	−0.605248	+	0.796037i	$0.706926\pi$
$908$	7.00000	0.232303
$909$	4.34315	0.144053
$910$	0	0
$911$	52.6274	1.74362	0.871812	−	0.489841i	$-0.162945\pi$
$911$	52.6274	1.74362	0.871812	+	0.489841i	$0.162945\pi$
$912$	−3.72792	−0.123444
$913$	4.68629	0.155094
$914$	7.02944	0.232513
$915$	0	0
$916$	48.6863	1.60864
$917$	−18.0000	−0.594412
$918$	3.00000	0.0990148
$919$	−26.7574	−0.882644	−0.441322	−	0.897349i	$-0.645490\pi$
$919$	−26.7574	−0.882644	−0.441322	+	0.897349i	$0.645490\pi$
$920$	0	0
$921$	−32.4558	−1.06946
$922$	−0.426407	−0.0140430
$923$	−17.0589	−0.561500
$924$	−15.5147	−0.510397
$925$	0	0
$926$	−5.02944	−0.165278
$927$	13.8284	0.454185
$928$	0.757359	0.0248615
$929$	−11.1716	−0.366527	−0.183264	−	0.983064i	$-0.558666\pi$
$929$	−11.1716	−0.366527	−0.183264	+	0.983064i	$0.558666\pi$
$930$	0	0
$931$	2.48528	0.0814518
$932$	−24.3431	−0.797386
$933$	−13.3137	−0.435871
$934$	14.8162	0.484802
$935$	0	0
$936$	5.68629	0.185862
$937$	−4.48528	−0.146528	−0.0732639	−	0.997313i	$-0.523342\pi$
$937$	−4.48528	−0.146528	−0.0732639	+	0.997313i	$0.523342\pi$
$938$	−20.0589	−0.654945
$939$	15.2426	0.497425
$940$	0	0
$941$	39.5980	1.29086	0.645429	−	0.763821i	$-0.276679\pi$
$941$	39.5980	1.29086	0.645429	+	0.763821i	$0.276679\pi$
$942$	0.970563	0.0316226
$943$	−0.798990	−0.0260187
$944$	19.2426	0.626295
$945$	0	0
$946$	−0.970563	−0.0315557
$947$	−39.1127	−1.27099	−0.635496	−	0.772104i	$-0.719204\pi$
$947$	−39.1127	−1.27099	−0.635496	+	0.772104i	$0.719204\pi$
$948$	−7.31371	−0.237538
$949$	−30.4264	−0.987683
$950$	0	0
$951$	21.1716	0.686535
$952$	34.4558	1.11672
$953$	31.4558	1.01895	0.509477	−	0.860484i	$-0.329839\pi$
$953$	31.4558	1.01895	0.509477	+	0.860484i	$0.329839\pi$
$954$	4.17157	0.135060
$955$	0	0
$956$	4.91169	0.158855
$957$	−0.485281	−0.0156869
$958$	7.82843	0.252925
$959$	−27.5147	−0.888497
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−11.3726	−0.366667
$963$	9.65685	0.311188
$964$	−45.7107	−1.47224
$965$	0	0
$966$	0.213203	0.00685971
$967$	28.9706	0.931630	0.465815	−	0.884882i	$-0.345761\pi$
$967$	28.9706	0.931630	0.465815	+	0.884882i	$0.345761\pi$
$968$	−4.75736	−0.152907
$969$	−9.00000	−0.289122
$970$	0	0
$971$	−26.1421	−0.838941	−0.419471	−	0.907769i	$-0.637784\pi$
$971$	−26.1421	−0.838941	−0.419471	+	0.907769i	$0.637784\pi$
$972$	1.82843	0.0586468
$973$	−14.6985	−0.471212
$974$	10.9584	0.351129
$975$	0	0
$976$	−9.00000	−0.288083
$977$	53.8701	1.72346	0.861728	−	0.507371i	$-0.169382\pi$
$977$	53.8701	1.72346	0.861728	+	0.507371i	$0.169382\pi$
$978$	8.28427	0.264902
$979$	−20.6863	−0.661137
$980$	0	0
$981$	6.00000	0.191565
$982$	13.9706	0.445819
$983$	−23.6863	−0.755475	−0.377738	−	0.925913i	$-0.623298\pi$
$983$	−23.6863	−0.755475	−0.377738	+	0.925913i	$0.623298\pi$
$984$	7.38478	0.235418
$985$	0	0
$986$	0.514719	0.0163920
$987$	−3.00000	−0.0954911
$988$	−8.14719	−0.259197
$989$	−0.142136	−0.00451965
$990$	0	0
$991$	−2.97056	−0.0943630	−0.0471815	−	0.998886i	$-0.515024\pi$
$991$	−2.97056	−0.0943630	−0.0471815	+	0.998886i	$0.515024\pi$
$992$	−8.82843	−0.280303
$993$	24.0000	0.761617
$994$	5.91169	0.187507
$995$	0	0
$996$	−3.02944	−0.0959914
$997$	6.21320	0.196774	0.0983871	−	0.995148i	$-0.468632\pi$
$997$	6.21320	0.196774	0.0983871	+	0.995148i	$0.468632\pi$
$998$	−6.31371	−0.199857
$999$	−7.65685	−0.242252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.s.1.1		2
5.4	even	2		705.2.a.g.1.2	✓	2
15.14	odd	2		2115.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.a.g.1.2	✓	2	5.4	even	2
2115.2.a.n.1.1		2	15.14	odd	2
3525.2.a.s.1.1		2	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)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +3.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} -1.00000 q^{3} -1.82843 q^{4} +0.414214 q^{6} +3.00000 q^{7} +1.58579 q^{8} +1.00000 q^{9} -2.82843 q^{11} +1.82843 q^{12} +3.58579 q^{13} -1.24264 q^{14} +3.00000 q^{16} +7.24264 q^{17} -0.414214 q^{18} +1.24264 q^{19} -3.00000 q^{21} +1.17157 q^{22} +0.171573 q^{23} -1.58579 q^{24} -1.48528 q^{26} -1.00000 q^{27} -5.48528 q^{28} -0.171573 q^{29} +2.00000 q^{31} -4.41421 q^{32} +2.82843 q^{33} -3.00000 q^{34} -1.82843 q^{36} +7.65685 q^{37} -0.514719 q^{38} -3.58579 q^{39} -4.65685 q^{41} +1.24264 q^{42} -0.828427 q^{43} +5.17157 q^{44} -0.0710678 q^{46} +1.00000 q^{47} -3.00000 q^{48} +2.00000 q^{49} -7.24264 q^{51} -6.55635 q^{52} -10.0711 q^{53} +0.414214 q^{54} +4.75736 q^{56} -1.24264 q^{57} +0.0710678 q^{58} +6.41421 q^{59} -3.00000 q^{61} -0.828427 q^{62} +3.00000 q^{63} -4.17157 q^{64} -1.17157 q^{66} +16.1421 q^{67} -13.2426 q^{68} -0.171573 q^{69} -4.75736 q^{71} +1.58579 q^{72} -8.48528 q^{73} -3.17157 q^{74} -2.27208 q^{76} -8.48528 q^{77} +1.48528 q^{78} -4.00000 q^{79} +1.00000 q^{81} +1.92893 q^{82} -1.65685 q^{83} +5.48528 q^{84} +0.343146 q^{86} +0.171573 q^{87} -4.48528 q^{88} +7.31371 q^{89} +10.7574 q^{91} -0.313708 q^{92} -2.00000 q^{93} -0.414214 q^{94} +4.41421 q^{96} -12.4853 q^{97} -0.828427 q^{98} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{12} + 10 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} - 6 q^{21} + 8 q^{22} + 6 q^{23} - 6 q^{24} + 14 q^{26} - 2 q^{27} + 6 q^{28} - 6 q^{29} + 4 q^{31} - 6 q^{32} - 6 q^{34} + 2 q^{36} + 4 q^{37} - 18 q^{38} - 10 q^{39} + 2 q^{41} - 6 q^{42} + 4 q^{43} + 16 q^{44} + 14 q^{46} + 2 q^{47} - 6 q^{48} + 4 q^{49} - 6 q^{51} + 18 q^{52} - 6 q^{53} - 2 q^{54} + 18 q^{56} + 6 q^{57} - 14 q^{58} + 10 q^{59} - 6 q^{61} + 4 q^{62} + 6 q^{63} - 14 q^{64} - 8 q^{66} + 4 q^{67} - 18 q^{68} - 6 q^{69} - 18 q^{71} + 6 q^{72} - 12 q^{74} - 30 q^{76} - 14 q^{78} - 8 q^{79} + 2 q^{81} + 18 q^{82} + 8 q^{83} - 6 q^{84} + 12 q^{86} + 6 q^{87} + 8 q^{88} - 8 q^{89} + 30 q^{91} + 22 q^{92} - 4 q^{93} + 2 q^{94} + 6 q^{96} - 8 q^{97} + 4 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^12 + 10 * q^13 + 6 * q^14 + 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 - 6 * q^21 + 8 * q^22 + 6 * q^23 - 6 * q^24 + 14 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + 4 * q^31 - 6 * q^32 - 6 * q^34 + 2 * q^36 + 4 * q^37 - 18 * q^38 - 10 * q^39 + 2 * q^41 - 6 * q^42 + 4 * q^43 + 16 * q^44 + 14 * q^46 + 2 * q^47 - 6 * q^48 + 4 * q^49 - 6 * q^51 + 18 * q^52 - 6 * q^53 - 2 * q^54 + 18 * q^56 + 6 * q^57 - 14 * q^58 + 10 * q^59 - 6 * q^61 + 4 * q^62 + 6 * q^63 - 14 * q^64 - 8 * q^66 + 4 * q^67 - 18 * q^68 - 6 * q^69 - 18 * q^71 + 6 * q^72 - 12 * q^74 - 30 * q^76 - 14 * q^78 - 8 * q^79 + 2 * q^81 + 18 * q^82 + 8 * q^83 - 6 * q^84 + 12 * q^86 + 6 * q^87 + 8 * q^88 - 8 * q^89 + 30 * q^91 + 22 * q^92 - 4 * q^93 + 2 * q^94 + 6 * q^96 - 8 * q^97 + 4 * q^98

Introduction

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