LMFDB - Embedded newform 3822.2.a.bs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.41421 q^{10} +0.414214 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.41421 q^{15} +1.00000 q^{16} +5.24264 q^{17} +1.00000 q^{18} +3.00000 q^{19} -1.41421 q^{20} +0.414214 q^{22} -9.07107 q^{23} +1.00000 q^{24} -3.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} +5.00000 q^{29} -1.41421 q^{30} +6.82843 q^{31} +1.00000 q^{32} +0.414214 q^{33} +5.24264 q^{34} +1.00000 q^{36} -5.07107 q^{37} +3.00000 q^{38} +1.00000 q^{39} -1.41421 q^{40} +4.58579 q^{41} +4.82843 q^{43} +0.414214 q^{44} -1.41421 q^{45} -9.07107 q^{46} +9.00000 q^{47} +1.00000 q^{48} -3.00000 q^{50} +5.24264 q^{51} +1.00000 q^{52} +12.3137 q^{53} +1.00000 q^{54} -0.585786 q^{55} +3.00000 q^{57} +5.00000 q^{58} +7.58579 q^{59} -1.41421 q^{60} -5.24264 q^{61} +6.82843 q^{62} +1.00000 q^{64} -1.41421 q^{65} +0.414214 q^{66} -14.6569 q^{67} +5.24264 q^{68} -9.07107 q^{69} -1.00000 q^{71} +1.00000 q^{72} -1.07107 q^{73} -5.07107 q^{74} -3.00000 q^{75} +3.00000 q^{76} +1.00000 q^{78} +13.3137 q^{79} -1.41421 q^{80} +1.00000 q^{81} +4.58579 q^{82} -7.65685 q^{83} -7.41421 q^{85} +4.82843 q^{86} +5.00000 q^{87} +0.414214 q^{88} -6.24264 q^{89} -1.41421 q^{90} -9.07107 q^{92} +6.82843 q^{93} +9.00000 q^{94} -4.24264 q^{95} +1.00000 q^{96} +7.89949 q^{97} +0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 6 q^{19} - 2 q^{22} - 4 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 2 q^{27} + 10 q^{29} + 8 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{34} + 2 q^{36} + 4 q^{37} + 6 q^{38} + 2 q^{39} + 12 q^{41} + 4 q^{43} - 2 q^{44} - 4 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{50} + 2 q^{51} + 2 q^{52} + 2 q^{53} + 2 q^{54} - 4 q^{55} + 6 q^{57} + 10 q^{58} + 18 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} - 2 q^{66} - 18 q^{67} + 2 q^{68} - 4 q^{69} - 2 q^{71} + 2 q^{72} + 12 q^{73} + 4 q^{74} - 6 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} + 2 q^{81} + 12 q^{82} - 4 q^{83} - 12 q^{85} + 4 q^{86} + 10 q^{87} - 2 q^{88} - 4 q^{89} - 4 q^{92} + 8 q^{93} + 18 q^{94} + 2 q^{96} - 4 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 6 * q^19 - 2 * q^22 - 4 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 2 * q^27 + 10 * q^29 + 8 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^34 + 2 * q^36 + 4 * q^37 + 6 * q^38 + 2 * q^39 + 12 * q^41 + 4 * q^43 - 2 * q^44 - 4 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^50 + 2 * q^51 + 2 * q^52 + 2 * q^53 + 2 * q^54 - 4 * q^55 + 6 * q^57 + 10 * q^58 + 18 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 2 * q^66 - 18 * q^67 + 2 * q^68 - 4 * q^69 - 2 * q^71 + 2 * q^72 + 12 * q^73 + 4 * q^74 - 6 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 + 2 * q^81 + 12 * q^82 - 4 * q^83 - 12 * q^85 + 4 * q^86 + 10 * q^87 - 2 * q^88 - 4 * q^89 - 4 * q^92 + 8 * q^93 + 18 * q^94 + 2 * q^96 - 4 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.41421	−0.632456	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	−1.41421	−0.632456	−0.316228	+	0.948683i	$0.602416\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.41421	−0.447214
$11$	0.414214	0.124890	0.0624450	−	0.998048i	$-0.480110\pi$
$11$	0.414214	0.124890	0.0624450	+	0.998048i	$0.480110\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−1.41421	−0.365148
$16$	1.00000	0.250000
$17$	5.24264	1.27153	0.635764	−	0.771884i	$-0.280685\pi$
$17$	5.24264	1.27153	0.635764	+	0.771884i	$0.280685\pi$
$18$	1.00000	0.235702
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−1.41421	−0.316228
$21$	0	0
$22$	0.414214	0.0883106
$23$	−9.07107	−1.89145	−0.945724	−	0.324970i	$-0.894646\pi$
$23$	−9.07107	−1.89145	−0.945724	+	0.324970i	$0.894646\pi$
$24$	1.00000	0.204124
$25$	−3.00000	−0.600000
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	−1.41421	−0.258199
$31$	6.82843	1.22642	0.613211	−	0.789919i	$-0.289878\pi$
$31$	6.82843	1.22642	0.613211	+	0.789919i	$0.289878\pi$
$32$	1.00000	0.176777
$33$	0.414214	0.0721053
$34$	5.24264	0.899105
$35$	0	0
$36$	1.00000	0.166667
$37$	−5.07107	−0.833678	−0.416839	−	0.908980i	$-0.636862\pi$
$37$	−5.07107	−0.833678	−0.416839	+	0.908980i	$0.636862\pi$
$38$	3.00000	0.486664
$39$	1.00000	0.160128
$40$	−1.41421	−0.223607
$41$	4.58579	0.716180	0.358090	−	0.933687i	$-0.383428\pi$
$41$	4.58579	0.716180	0.358090	+	0.933687i	$0.383428\pi$
$42$	0	0
$43$	4.82843	0.736328	0.368164	−	0.929761i	$-0.379986\pi$
$43$	4.82843	0.736328	0.368164	+	0.929761i	$0.379986\pi$
$44$	0.414214	0.0624450
$45$	−1.41421	−0.210819
$46$	−9.07107	−1.33746
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−3.00000	−0.424264
$51$	5.24264	0.734117
$52$	1.00000	0.138675
$53$	12.3137	1.69142	0.845709	−	0.533644i	$-0.179178\pi$
$53$	12.3137	1.69142	0.845709	+	0.533644i	$0.179178\pi$
$54$	1.00000	0.136083
$55$	−0.585786	−0.0789874
$56$	0	0
$57$	3.00000	0.397360
$58$	5.00000	0.656532
$59$	7.58579	0.987585	0.493793	−	0.869580i	$-0.335610\pi$
$59$	7.58579	0.987585	0.493793	+	0.869580i	$0.335610\pi$
$60$	−1.41421	−0.182574
$61$	−5.24264	−0.671251	−0.335626	−	0.941995i	$-0.608948\pi$
$61$	−5.24264	−0.671251	−0.335626	+	0.941995i	$0.608948\pi$
$62$	6.82843	0.867211
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.41421	−0.175412
$66$	0.414214	0.0509862
$67$	−14.6569	−1.79062	−0.895310	−	0.445444i	$-0.853046\pi$
$67$	−14.6569	−1.79062	−0.895310	+	0.445444i	$0.853046\pi$
$68$	5.24264	0.635764
$69$	−9.07107	−1.09203
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	1.00000	0.117851
$73$	−1.07107	−0.125359	−0.0626795	−	0.998034i	$-0.519965\pi$
$73$	−1.07107	−0.125359	−0.0626795	+	0.998034i	$0.519965\pi$
$74$	−5.07107	−0.589500
$75$	−3.00000	−0.346410
$76$	3.00000	0.344124
$77$	0	0
$78$	1.00000	0.113228
$79$	13.3137	1.49791	0.748955	−	0.662621i	$-0.230556\pi$
$79$	13.3137	1.49791	0.748955	+	0.662621i	$0.230556\pi$
$80$	−1.41421	−0.158114
$81$	1.00000	0.111111
$82$	4.58579	0.506415
$83$	−7.65685	−0.840449	−0.420224	−	0.907420i	$-0.638049\pi$
$83$	−7.65685	−0.840449	−0.420224	+	0.907420i	$0.638049\pi$
$84$	0	0
$85$	−7.41421	−0.804184
$86$	4.82843	0.520663
$87$	5.00000	0.536056
$88$	0.414214	0.0441553
$89$	−6.24264	−0.661719	−0.330859	−	0.943680i	$-0.607339\pi$
$89$	−6.24264	−0.661719	−0.330859	+	0.943680i	$0.607339\pi$
$90$	−1.41421	−0.149071
$91$	0	0
$92$	−9.07107	−0.945724
$93$	6.82843	0.708075
$94$	9.00000	0.928279
$95$	−4.24264	−0.435286
$96$	1.00000	0.102062
$97$	7.89949	0.802072	0.401036	−	0.916062i	$-0.368650\pi$
$97$	7.89949	0.802072	0.401036	+	0.916062i	$0.368650\pi$
$98$	0	0
$99$	0.414214	0.0416300
$100$	−3.00000	−0.300000
$101$	−1.17157	−0.116576	−0.0582879	−	0.998300i	$-0.518564\pi$
$101$	−1.17157	−0.116576	−0.0582879	+	0.998300i	$0.518564\pi$
$102$	5.24264	0.519099
$103$	6.48528	0.639014	0.319507	−	0.947584i	$-0.396483\pi$
$103$	6.48528	0.639014	0.319507	+	0.947584i	$0.396483\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	12.3137	1.19601
$107$	13.6569	1.32026	0.660129	−	0.751152i	$-0.270502\pi$
$107$	13.6569	1.32026	0.660129	+	0.751152i	$0.270502\pi$
$108$	1.00000	0.0962250
$109$	1.65685	0.158698	0.0793489	−	0.996847i	$-0.474716\pi$
$109$	1.65685	0.158698	0.0793489	+	0.996847i	$0.474716\pi$
$110$	−0.585786	−0.0558525
$111$	−5.07107	−0.481324
$112$	0	0
$113$	−6.07107	−0.571118	−0.285559	−	0.958361i	$-0.592179\pi$
$113$	−6.07107	−0.571118	−0.285559	+	0.958361i	$0.592179\pi$
$114$	3.00000	0.280976
$115$	12.8284	1.19626
$116$	5.00000	0.464238
$117$	1.00000	0.0924500
$118$	7.58579	0.698328
$119$	0	0
$120$	−1.41421	−0.129099
$121$	−10.8284	−0.984402
$122$	−5.24264	−0.474646
$123$	4.58579	0.413486
$124$	6.82843	0.613211
$125$	11.3137	1.01193
$126$	0	0
$127$	9.89949	0.878438	0.439219	−	0.898380i	$-0.355255\pi$
$127$	9.89949	0.878438	0.439219	+	0.898380i	$0.355255\pi$
$128$	1.00000	0.0883883
$129$	4.82843	0.425119
$130$	−1.41421	−0.124035
$131$	9.89949	0.864923	0.432461	−	0.901652i	$-0.357645\pi$
$131$	9.89949	0.864923	0.432461	+	0.901652i	$0.357645\pi$
$132$	0.414214	0.0360527
$133$	0	0
$134$	−14.6569	−1.26616
$135$	−1.41421	−0.121716
$136$	5.24264	0.449553
$137$	−13.0711	−1.11674	−0.558368	−	0.829593i	$-0.688572\pi$
$137$	−13.0711	−1.11674	−0.558368	+	0.829593i	$0.688572\pi$
$138$	−9.07107	−0.772181
$139$	−21.2132	−1.79928	−0.899640	−	0.436632i	$-0.856171\pi$
$139$	−21.2132	−1.79928	−0.899640	+	0.436632i	$0.856171\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	−1.00000	−0.0839181
$143$	0.414214	0.0346383
$144$	1.00000	0.0833333
$145$	−7.07107	−0.587220
$146$	−1.07107	−0.0886422
$147$	0	0
$148$	−5.07107	−0.416839
$149$	15.8995	1.30254	0.651269	−	0.758847i	$-0.274237\pi$
$149$	15.8995	1.30254	0.651269	+	0.758847i	$0.274237\pi$
$150$	−3.00000	−0.244949
$151$	−7.58579	−0.617323	−0.308661	−	0.951172i	$-0.599881\pi$
$151$	−7.58579	−0.617323	−0.308661	+	0.951172i	$0.599881\pi$
$152$	3.00000	0.243332
$153$	5.24264	0.423842
$154$	0	0
$155$	−9.65685	−0.775657
$156$	1.00000	0.0800641
$157$	7.92893	0.632798	0.316399	−	0.948626i	$-0.397526\pi$
$157$	7.92893	0.632798	0.316399	+	0.948626i	$0.397526\pi$
$158$	13.3137	1.05918
$159$	12.3137	0.976541
$160$	−1.41421	−0.111803
$161$	0	0
$162$	1.00000	0.0785674
$163$	17.1421	1.34268	0.671338	−	0.741151i	$-0.265720\pi$
$163$	17.1421	1.34268	0.671338	+	0.741151i	$0.265720\pi$
$164$	4.58579	0.358090
$165$	−0.585786	−0.0456034
$166$	−7.65685	−0.594287
$167$	12.3137	0.952863	0.476432	−	0.879211i	$-0.341930\pi$
$167$	12.3137	0.952863	0.476432	+	0.879211i	$0.341930\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−7.41421	−0.568644
$171$	3.00000	0.229416
$172$	4.82843	0.368164
$173$	20.3137	1.54442	0.772211	−	0.635366i	$-0.219151\pi$
$173$	20.3137	1.54442	0.772211	+	0.635366i	$0.219151\pi$
$174$	5.00000	0.379049
$175$	0	0
$176$	0.414214	0.0312225
$177$	7.58579	0.570183
$178$	−6.24264	−0.467906
$179$	−12.3431	−0.922570	−0.461285	−	0.887252i	$-0.652611\pi$
$179$	−12.3431	−0.922570	−0.461285	+	0.887252i	$0.652611\pi$
$180$	−1.41421	−0.105409
$181$	−11.5858	−0.861165	−0.430582	−	0.902551i	$-0.641692\pi$
$181$	−11.5858	−0.861165	−0.430582	+	0.902551i	$0.641692\pi$
$182$	0	0
$183$	−5.24264	−0.387547
$184$	−9.07107	−0.668728
$185$	7.17157	0.527265
$186$	6.82843	0.500685
$187$	2.17157	0.158801
$188$	9.00000	0.656392
$189$	0	0
$190$	−4.24264	−0.307794
$191$	2.34315	0.169544	0.0847720	−	0.996400i	$-0.472984\pi$
$191$	2.34315	0.169544	0.0847720	+	0.996400i	$0.472984\pi$
$192$	1.00000	0.0721688
$193$	−15.7574	−1.13424	−0.567120	−	0.823635i	$-0.691942\pi$
$193$	−15.7574	−1.13424	−0.567120	+	0.823635i	$0.691942\pi$
$194$	7.89949	0.567151
$195$	−1.41421	−0.101274
$196$	0	0
$197$	9.55635	0.680862	0.340431	−	0.940270i	$-0.389427\pi$
$197$	9.55635	0.680862	0.340431	+	0.940270i	$0.389427\pi$
$198$	0.414214	0.0294369
$199$	10.5858	0.750407	0.375203	−	0.926943i	$-0.377573\pi$
$199$	10.5858	0.750407	0.375203	+	0.926943i	$0.377573\pi$
$200$	−3.00000	−0.212132
$201$	−14.6569	−1.03381
$202$	−1.17157	−0.0824316
$203$	0	0
$204$	5.24264	0.367058
$205$	−6.48528	−0.452952
$206$	6.48528	0.451851
$207$	−9.07107	−0.630483
$208$	1.00000	0.0693375
$209$	1.24264	0.0859553
$210$	0	0
$211$	−28.3848	−1.95409	−0.977044	−	0.213036i	$-0.931665\pi$
$211$	−28.3848	−1.95409	−0.977044	+	0.213036i	$0.931665\pi$
$212$	12.3137	0.845709
$213$	−1.00000	−0.0685189
$214$	13.6569	0.933563
$215$	−6.82843	−0.465695
$216$	1.00000	0.0680414
$217$	0	0
$218$	1.65685	0.112216
$219$	−1.07107	−0.0723761
$220$	−0.585786	−0.0394937
$221$	5.24264	0.352658
$222$	−5.07107	−0.340348
$223$	21.3848	1.43203	0.716015	−	0.698085i	$-0.245964\pi$
$223$	21.3848	1.43203	0.716015	+	0.698085i	$0.245964\pi$
$224$	0	0
$225$	−3.00000	−0.200000
$226$	−6.07107	−0.403841
$227$	−26.1421	−1.73511	−0.867557	−	0.497337i	$-0.834311\pi$
$227$	−26.1421	−1.73511	−0.867557	+	0.497337i	$0.834311\pi$
$228$	3.00000	0.198680
$229$	−7.17157	−0.473911	−0.236955	−	0.971521i	$-0.576150\pi$
$229$	−7.17157	−0.473911	−0.236955	+	0.971521i	$0.576150\pi$
$230$	12.8284	0.845881
$231$	0	0
$232$	5.00000	0.328266
$233$	−3.72792	−0.244224	−0.122112	−	0.992516i	$-0.538967\pi$
$233$	−3.72792	−0.244224	−0.122112	+	0.992516i	$0.538967\pi$
$234$	1.00000	0.0653720
$235$	−12.7279	−0.830278
$236$	7.58579	0.493793
$237$	13.3137	0.864818
$238$	0	0
$239$	−2.51472	−0.162664	−0.0813318	−	0.996687i	$-0.525917\pi$
$239$	−2.51472	−0.162664	−0.0813318	+	0.996687i	$0.525917\pi$
$240$	−1.41421	−0.0912871
$241$	−16.4853	−1.06191	−0.530955	−	0.847400i	$-0.678167\pi$
$241$	−16.4853	−1.06191	−0.530955	+	0.847400i	$0.678167\pi$
$242$	−10.8284	−0.696078
$243$	1.00000	0.0641500
$244$	−5.24264	−0.335626
$245$	0	0
$246$	4.58579	0.292379
$247$	3.00000	0.190885
$248$	6.82843	0.433606
$249$	−7.65685	−0.485233
$250$	11.3137	0.715542
$251$	12.8284	0.809723	0.404862	−	0.914378i	$-0.367320\pi$
$251$	12.8284	0.809723	0.404862	+	0.914378i	$0.367320\pi$
$252$	0	0
$253$	−3.75736	−0.236223
$254$	9.89949	0.621150
$255$	−7.41421	−0.464296
$256$	1.00000	0.0625000
$257$	−21.7990	−1.35978	−0.679892	−	0.733312i	$-0.737973\pi$
$257$	−21.7990	−1.35978	−0.679892	+	0.733312i	$0.737973\pi$
$258$	4.82843	0.300605
$259$	0	0
$260$	−1.41421	−0.0877058
$261$	5.00000	0.309492
$262$	9.89949	0.611593
$263$	−7.55635	−0.465944	−0.232972	−	0.972483i	$-0.574845\pi$
$263$	−7.55635	−0.465944	−0.232972	+	0.972483i	$0.574845\pi$
$264$	0.414214	0.0254931
$265$	−17.4142	−1.06975
$266$	0	0
$267$	−6.24264	−0.382043
$268$	−14.6569	−0.895310
$269$	−3.68629	−0.224757	−0.112379	−	0.993665i	$-0.535847\pi$
$269$	−3.68629	−0.224757	−0.112379	+	0.993665i	$0.535847\pi$
$270$	−1.41421	−0.0860663
$271$	−15.3848	−0.934559	−0.467279	−	0.884110i	$-0.654766\pi$
$271$	−15.3848	−0.934559	−0.467279	+	0.884110i	$0.654766\pi$
$272$	5.24264	0.317882
$273$	0	0
$274$	−13.0711	−0.789652
$275$	−1.24264	−0.0749341
$276$	−9.07107	−0.546014
$277$	−16.4142	−0.986235	−0.493117	−	0.869963i	$-0.664143\pi$
$277$	−16.4142	−0.986235	−0.493117	+	0.869963i	$0.664143\pi$
$278$	−21.2132	−1.27228
$279$	6.82843	0.408807
$280$	0	0
$281$	7.31371	0.436299	0.218150	−	0.975915i	$-0.429998\pi$
$281$	7.31371	0.436299	0.218150	+	0.975915i	$0.429998\pi$
$282$	9.00000	0.535942
$283$	17.0711	1.01477	0.507385	−	0.861720i	$-0.330612\pi$
$283$	17.0711	1.01477	0.507385	+	0.861720i	$0.330612\pi$
$284$	−1.00000	−0.0593391
$285$	−4.24264	−0.251312
$286$	0.414214	0.0244930
$287$	0	0
$288$	1.00000	0.0589256
$289$	10.4853	0.616781
$290$	−7.07107	−0.415227
$291$	7.89949	0.463077
$292$	−1.07107	−0.0626795
$293$	−18.7279	−1.09410	−0.547048	−	0.837101i	$-0.684249\pi$
$293$	−18.7279	−1.09410	−0.547048	+	0.837101i	$0.684249\pi$
$294$	0	0
$295$	−10.7279	−0.624604
$296$	−5.07107	−0.294750
$297$	0.414214	0.0240351
$298$	15.8995	0.921033
$299$	−9.07107	−0.524593
$300$	−3.00000	−0.173205
$301$	0	0
$302$	−7.58579	−0.436513
$303$	−1.17157	−0.0673051
$304$	3.00000	0.172062
$305$	7.41421	0.424537
$306$	5.24264	0.299702
$307$	−19.6274	−1.12020	−0.560098	−	0.828426i	$-0.689237\pi$
$307$	−19.6274	−1.12020	−0.560098	+	0.828426i	$0.689237\pi$
$308$	0	0
$309$	6.48528	0.368935
$310$	−9.65685	−0.548472
$311$	−6.58579	−0.373446	−0.186723	−	0.982413i	$-0.559787\pi$
$311$	−6.58579	−0.373446	−0.186723	+	0.982413i	$0.559787\pi$
$312$	1.00000	0.0566139
$313$	18.1421	1.02545	0.512727	−	0.858552i	$-0.328635\pi$
$313$	18.1421	1.02545	0.512727	+	0.858552i	$0.328635\pi$
$314$	7.92893	0.447456
$315$	0	0
$316$	13.3137	0.748955
$317$	0.828427	0.0465291	0.0232646	−	0.999729i	$-0.492594\pi$
$317$	0.828427	0.0465291	0.0232646	+	0.999729i	$0.492594\pi$
$318$	12.3137	0.690518
$319$	2.07107	0.115958
$320$	−1.41421	−0.0790569
$321$	13.6569	0.762251
$322$	0	0
$323$	15.7279	0.875125
$324$	1.00000	0.0555556
$325$	−3.00000	−0.166410
$326$	17.1421	0.949415
$327$	1.65685	0.0916242
$328$	4.58579	0.253208
$329$	0	0
$330$	−0.585786	−0.0322465
$331$	−22.4853	−1.23590	−0.617951	−	0.786216i	$-0.712037\pi$
$331$	−22.4853	−1.23590	−0.617951	+	0.786216i	$0.712037\pi$
$332$	−7.65685	−0.420224
$333$	−5.07107	−0.277893
$334$	12.3137	0.673776
$335$	20.7279	1.13249
$336$	0	0
$337$	28.6569	1.56104	0.780519	−	0.625132i	$-0.214955\pi$
$337$	28.6569	1.56104	0.780519	+	0.625132i	$0.214955\pi$
$338$	1.00000	0.0543928
$339$	−6.07107	−0.329735
$340$	−7.41421	−0.402092
$341$	2.82843	0.153168
$342$	3.00000	0.162221
$343$	0	0
$344$	4.82843	0.260331
$345$	12.8284	0.690659
$346$	20.3137	1.09207
$347$	5.75736	0.309071	0.154536	−	0.987987i	$-0.450612\pi$
$347$	5.75736	0.309071	0.154536	+	0.987987i	$0.450612\pi$
$348$	5.00000	0.268028
$349$	5.41421	0.289816	0.144908	−	0.989445i	$-0.453711\pi$
$349$	5.41421	0.289816	0.144908	+	0.989445i	$0.453711\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	0.414214	0.0220777
$353$	12.6274	0.672090	0.336045	−	0.941846i	$-0.390911\pi$
$353$	12.6274	0.672090	0.336045	+	0.941846i	$0.390911\pi$
$354$	7.58579	0.403180
$355$	1.41421	0.0750587
$356$	−6.24264	−0.330859
$357$	0	0
$358$	−12.3431	−0.652356
$359$	−15.4558	−0.815728	−0.407864	−	0.913043i	$-0.633726\pi$
$359$	−15.4558	−0.815728	−0.407864	+	0.913043i	$0.633726\pi$
$360$	−1.41421	−0.0745356
$361$	−10.0000	−0.526316
$362$	−11.5858	−0.608935
$363$	−10.8284	−0.568345
$364$	0	0
$365$	1.51472	0.0792840
$366$	−5.24264	−0.274037
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	−9.07107	−0.472862
$369$	4.58579	0.238727
$370$	7.17157	0.372832
$371$	0	0
$372$	6.82843	0.354037
$373$	−11.1005	−0.574762	−0.287381	−	0.957816i	$-0.592785\pi$
$373$	−11.1005	−0.574762	−0.287381	+	0.957816i	$0.592785\pi$
$374$	2.17157	0.112289
$375$	11.3137	0.584237
$376$	9.00000	0.464140
$377$	5.00000	0.257513
$378$	0	0
$379$	−33.6569	−1.72884	−0.864418	−	0.502773i	$-0.832313\pi$
$379$	−33.6569	−1.72884	−0.864418	+	0.502773i	$0.832313\pi$
$380$	−4.24264	−0.217643
$381$	9.89949	0.507166
$382$	2.34315	0.119886
$383$	6.48528	0.331382	0.165691	−	0.986178i	$-0.447015\pi$
$383$	6.48528	0.331382	0.165691	+	0.986178i	$0.447015\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−15.7574	−0.802028
$387$	4.82843	0.245443
$388$	7.89949	0.401036
$389$	23.0000	1.16615	0.583073	−	0.812420i	$-0.301850\pi$
$389$	23.0000	1.16615	0.583073	+	0.812420i	$0.301850\pi$
$390$	−1.41421	−0.0716115
$391$	−47.5563	−2.40503
$392$	0	0
$393$	9.89949	0.499363
$394$	9.55635	0.481442
$395$	−18.8284	−0.947361
$396$	0.414214	0.0208150
$397$	−19.7574	−0.991593	−0.495797	−	0.868439i	$-0.665124\pi$
$397$	−19.7574	−0.991593	−0.495797	+	0.868439i	$0.665124\pi$
$398$	10.5858	0.530618
$399$	0	0
$400$	−3.00000	−0.150000
$401$	19.0711	0.952364	0.476182	−	0.879347i	$-0.342020\pi$
$401$	19.0711	0.952364	0.476182	+	0.879347i	$0.342020\pi$
$402$	−14.6569	−0.731017
$403$	6.82843	0.340148
$404$	−1.17157	−0.0582879
$405$	−1.41421	−0.0702728
$406$	0	0
$407$	−2.10051	−0.104118
$408$	5.24264	0.259549
$409$	−2.58579	−0.127859	−0.0639295	−	0.997954i	$-0.520363\pi$
$409$	−2.58579	−0.127859	−0.0639295	+	0.997954i	$0.520363\pi$
$410$	−6.48528	−0.320285
$411$	−13.0711	−0.644748
$412$	6.48528	0.319507
$413$	0	0
$414$	−9.07107	−0.445819
$415$	10.8284	0.531547
$416$	1.00000	0.0490290
$417$	−21.2132	−1.03882
$418$	1.24264	0.0607795
$419$	−27.4558	−1.34131	−0.670653	−	0.741771i	$-0.733986\pi$
$419$	−27.4558	−1.34131	−0.670653	+	0.741771i	$0.733986\pi$
$420$	0	0
$421$	10.5858	0.515920	0.257960	−	0.966156i	$-0.416950\pi$
$421$	10.5858	0.515920	0.257960	+	0.966156i	$0.416950\pi$
$422$	−28.3848	−1.38175
$423$	9.00000	0.437595
$424$	12.3137	0.598007
$425$	−15.7279	−0.762916
$426$	−1.00000	−0.0484502
$427$	0	0
$428$	13.6569	0.660129
$429$	0.414214	0.0199984
$430$	−6.82843	−0.329296
$431$	14.4853	0.697731	0.348866	−	0.937173i	$-0.386567\pi$
$431$	14.4853	0.697731	0.348866	+	0.937173i	$0.386567\pi$
$432$	1.00000	0.0481125
$433$	−19.0000	−0.913082	−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000	−0.913082	−0.456541	+	0.889702i	$0.650912\pi$
$434$	0	0
$435$	−7.07107	−0.339032
$436$	1.65685	0.0793489
$437$	−27.2132	−1.30178
$438$	−1.07107	−0.0511776
$439$	−10.5858	−0.505232	−0.252616	−	0.967567i	$-0.581291\pi$
$439$	−10.5858	−0.505232	−0.252616	+	0.967567i	$0.581291\pi$
$440$	−0.585786	−0.0279263
$441$	0	0
$442$	5.24264	0.249367
$443$	22.7279	1.07984	0.539918	−	0.841718i	$-0.318455\pi$
$443$	22.7279	1.07984	0.539918	+	0.841718i	$0.318455\pi$
$444$	−5.07107	−0.240662
$445$	8.82843	0.418508
$446$	21.3848	1.01260
$447$	15.8995	0.752020
$448$	0	0
$449$	−33.9411	−1.60178	−0.800890	−	0.598811i	$-0.795640\pi$
$449$	−33.9411	−1.60178	−0.800890	+	0.598811i	$0.795640\pi$
$450$	−3.00000	−0.141421
$451$	1.89949	0.0894437
$452$	−6.07107	−0.285559
$453$	−7.58579	−0.356411
$454$	−26.1421	−1.22691
$455$	0	0
$456$	3.00000	0.140488
$457$	−15.2132	−0.711644	−0.355822	−	0.934554i	$-0.615799\pi$
$457$	−15.2132	−0.711644	−0.355822	+	0.934554i	$0.615799\pi$
$458$	−7.17157	−0.335106
$459$	5.24264	0.244706
$460$	12.8284	0.598128
$461$	−33.4558	−1.55819	−0.779097	−	0.626903i	$-0.784322\pi$
$461$	−33.4558	−1.55819	−0.779097	+	0.626903i	$0.784322\pi$
$462$	0	0
$463$	−37.9411	−1.76327	−0.881637	−	0.471929i	$-0.843558\pi$
$463$	−37.9411	−1.76327	−0.881637	+	0.471929i	$0.843558\pi$
$464$	5.00000	0.232119
$465$	−9.65685	−0.447826
$466$	−3.72792	−0.172693
$467$	−0.242641	−0.0112281	−0.00561404	−	0.999984i	$-0.501787\pi$
$467$	−0.242641	−0.0112281	−0.00561404	+	0.999984i	$0.501787\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	−12.7279	−0.587095
$471$	7.92893	0.365346
$472$	7.58579	0.349164
$473$	2.00000	0.0919601
$474$	13.3137	0.611519
$475$	−9.00000	−0.412948
$476$	0	0
$477$	12.3137	0.563806
$478$	−2.51472	−0.115021
$479$	−31.1421	−1.42292	−0.711460	−	0.702726i	$-0.751966\pi$
$479$	−31.1421	−1.42292	−0.711460	+	0.702726i	$0.751966\pi$
$480$	−1.41421	−0.0645497
$481$	−5.07107	−0.231221
$482$	−16.4853	−0.750884
$483$	0	0
$484$	−10.8284	−0.492201
$485$	−11.1716	−0.507275
$486$	1.00000	0.0453609
$487$	−23.7279	−1.07521	−0.537607	−	0.843195i	$-0.680672\pi$
$487$	−23.7279	−1.07521	−0.537607	+	0.843195i	$0.680672\pi$
$488$	−5.24264	−0.237323
$489$	17.1421	0.775194
$490$	0	0
$491$	−26.2843	−1.18619	−0.593096	−	0.805132i	$-0.702095\pi$
$491$	−26.2843	−1.18619	−0.593096	+	0.805132i	$0.702095\pi$
$492$	4.58579	0.206743
$493$	26.2132	1.18058
$494$	3.00000	0.134976
$495$	−0.585786	−0.0263291
$496$	6.82843	0.306605
$497$	0	0
$498$	−7.65685	−0.343112
$499$	−30.0000	−1.34298	−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000	−1.34298	−0.671492	+	0.741012i	$0.734346\pi$
$500$	11.3137	0.505964
$501$	12.3137	0.550136
$502$	12.8284	0.572561
$503$	35.7990	1.59620	0.798099	−	0.602526i	$-0.205839\pi$
$503$	35.7990	1.59620	0.798099	+	0.602526i	$0.205839\pi$
$504$	0	0
$505$	1.65685	0.0737290
$506$	−3.75736	−0.167035
$507$	1.00000	0.0444116
$508$	9.89949	0.439219
$509$	12.9706	0.574910	0.287455	−	0.957794i	$-0.407191\pi$
$509$	12.9706	0.574910	0.287455	+	0.957794i	$0.407191\pi$
$510$	−7.41421	−0.328307
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.00000	0.132453
$514$	−21.7990	−0.961512
$515$	−9.17157	−0.404148
$516$	4.82843	0.212560
$517$	3.72792	0.163954
$518$	0	0
$519$	20.3137	0.891673
$520$	−1.41421	−0.0620174
$521$	−14.0000	−0.613351	−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000	−0.613351	−0.306676	+	0.951814i	$0.599217\pi$
$522$	5.00000	0.218844
$523$	−3.85786	−0.168693	−0.0843463	−	0.996437i	$-0.526880\pi$
$523$	−3.85786	−0.168693	−0.0843463	+	0.996437i	$0.526880\pi$
$524$	9.89949	0.432461
$525$	0	0
$526$	−7.55635	−0.329472
$527$	35.7990	1.55943
$528$	0.414214	0.0180263
$529$	59.2843	2.57758
$530$	−17.4142	−0.756425
$531$	7.58579	0.329195
$532$	0	0
$533$	4.58579	0.198632
$534$	−6.24264	−0.270145
$535$	−19.3137	−0.835004
$536$	−14.6569	−0.633080
$537$	−12.3431	−0.532646
$538$	−3.68629	−0.158927
$539$	0	0
$540$	−1.41421	−0.0608581
$541$	12.8701	0.553327	0.276663	−	0.960967i	$-0.410771\pi$
$541$	12.8701	0.553327	0.276663	+	0.960967i	$0.410771\pi$
$542$	−15.3848	−0.660833
$543$	−11.5858	−0.497194
$544$	5.24264	0.224776
$545$	−2.34315	−0.100369
$546$	0	0
$547$	−5.75736	−0.246167	−0.123083	−	0.992396i	$-0.539278\pi$
$547$	−5.75736	−0.246167	−0.123083	+	0.992396i	$0.539278\pi$
$548$	−13.0711	−0.558368
$549$	−5.24264	−0.223750
$550$	−1.24264	−0.0529864
$551$	15.0000	0.639021
$552$	−9.07107	−0.386090
$553$	0	0
$554$	−16.4142	−0.697373
$555$	7.17157	0.304416
$556$	−21.2132	−0.899640
$557$	−10.9706	−0.464838	−0.232419	−	0.972616i	$-0.574664\pi$
$557$	−10.9706	−0.464838	−0.232419	+	0.972616i	$0.574664\pi$
$558$	6.82843	0.289070
$559$	4.82843	0.204221
$560$	0	0
$561$	2.17157	0.0916839
$562$	7.31371	0.308510
$563$	−0.485281	−0.0204522	−0.0102261	−	0.999948i	$-0.503255\pi$
$563$	−0.485281	−0.0204522	−0.0102261	+	0.999948i	$0.503255\pi$
$564$	9.00000	0.378968
$565$	8.58579	0.361207
$566$	17.0711	0.717551
$567$	0	0
$568$	−1.00000	−0.0419591
$569$	−25.5858	−1.07261	−0.536306	−	0.844024i	$-0.680181\pi$
$569$	−25.5858	−1.07261	−0.536306	+	0.844024i	$0.680181\pi$
$570$	−4.24264	−0.177705
$571$	−1.65685	−0.0693372	−0.0346686	−	0.999399i	$-0.511038\pi$
$571$	−1.65685	−0.0693372	−0.0346686	+	0.999399i	$0.511038\pi$
$572$	0.414214	0.0173191
$573$	2.34315	0.0978863
$574$	0	0
$575$	27.2132	1.13487
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	10.4853	0.436130
$579$	−15.7574	−0.654854
$580$	−7.07107	−0.293610
$581$	0	0
$582$	7.89949	0.327445
$583$	5.10051	0.211241
$584$	−1.07107	−0.0443211
$585$	−1.41421	−0.0584705
$586$	−18.7279	−0.773643
$587$	11.2426	0.464033	0.232017	−	0.972712i	$-0.425468\pi$
$587$	11.2426	0.464033	0.232017	+	0.972712i	$0.425468\pi$
$588$	0	0
$589$	20.4853	0.844081
$590$	−10.7279	−0.441662
$591$	9.55635	0.393096
$592$	−5.07107	−0.208420
$593$	−28.5858	−1.17388	−0.586939	−	0.809631i	$-0.699667\pi$
$593$	−28.5858	−1.17388	−0.586939	+	0.809631i	$0.699667\pi$
$594$	0.414214	0.0169954
$595$	0	0
$596$	15.8995	0.651269
$597$	10.5858	0.433247
$598$	−9.07107	−0.370944
$599$	−14.8701	−0.607574	−0.303787	−	0.952740i	$-0.598251\pi$
$599$	−14.8701	−0.607574	−0.303787	+	0.952740i	$0.598251\pi$
$600$	−3.00000	−0.122474
$601$	−17.8284	−0.727237	−0.363618	−	0.931548i	$-0.618459\pi$
$601$	−17.8284	−0.727237	−0.363618	+	0.931548i	$0.618459\pi$
$602$	0	0
$603$	−14.6569	−0.596873
$604$	−7.58579	−0.308661
$605$	15.3137	0.622591
$606$	−1.17157	−0.0475919
$607$	27.0711	1.09878	0.549390	−	0.835566i	$-0.314860\pi$
$607$	27.0711	1.09878	0.549390	+	0.835566i	$0.314860\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	7.41421	0.300193
$611$	9.00000	0.364101
$612$	5.24264	0.211921
$613$	−35.7990	−1.44591	−0.722954	−	0.690896i	$-0.757216\pi$
$613$	−35.7990	−1.44591	−0.722954	+	0.690896i	$0.757216\pi$
$614$	−19.6274	−0.792098
$615$	−6.48528	−0.261512
$616$	0	0
$617$	−6.48528	−0.261088	−0.130544	−	0.991443i	$-0.541672\pi$
$617$	−6.48528	−0.261088	−0.130544	+	0.991443i	$0.541672\pi$
$618$	6.48528	0.260876
$619$	43.4558	1.74664	0.873319	−	0.487149i	$-0.161963\pi$
$619$	43.4558	1.74664	0.873319	+	0.487149i	$0.161963\pi$
$620$	−9.65685	−0.387829
$621$	−9.07107	−0.364009
$622$	−6.58579	−0.264066
$623$	0	0
$624$	1.00000	0.0400320
$625$	−1.00000	−0.0400000
$626$	18.1421	0.725106
$627$	1.24264	0.0496263
$628$	7.92893	0.316399
$629$	−26.5858	−1.06004
$630$	0	0
$631$	36.6274	1.45811	0.729057	−	0.684453i	$-0.239959\pi$
$631$	36.6274	1.45811	0.729057	+	0.684453i	$0.239959\pi$
$632$	13.3137	0.529591
$633$	−28.3848	−1.12819
$634$	0.828427	0.0329010
$635$	−14.0000	−0.555573
$636$	12.3137	0.488270
$637$	0	0
$638$	2.07107	0.0819944
$639$	−1.00000	−0.0395594
$640$	−1.41421	−0.0559017
$641$	33.1716	1.31020	0.655099	−	0.755543i	$-0.272627\pi$
$641$	33.1716	1.31020	0.655099	+	0.755543i	$0.272627\pi$
$642$	13.6569	0.538993
$643$	36.3137	1.43207	0.716036	−	0.698063i	$-0.245954\pi$
$643$	36.3137	1.43207	0.716036	+	0.698063i	$0.245954\pi$
$644$	0	0
$645$	−6.82843	−0.268869
$646$	15.7279	0.618807
$647$	28.6274	1.12546	0.562730	−	0.826641i	$-0.309751\pi$
$647$	28.6274	1.12546	0.562730	+	0.826641i	$0.309751\pi$
$648$	1.00000	0.0392837
$649$	3.14214	0.123340
$650$	−3.00000	−0.117670
$651$	0	0
$652$	17.1421	0.671338
$653$	15.1127	0.591406	0.295703	−	0.955280i	$-0.404446\pi$
$653$	15.1127	0.591406	0.295703	+	0.955280i	$0.404446\pi$
$654$	1.65685	0.0647881
$655$	−14.0000	−0.547025
$656$	4.58579	0.179045
$657$	−1.07107	−0.0417863
$658$	0	0
$659$	30.7279	1.19699	0.598495	−	0.801127i	$-0.295766\pi$
$659$	30.7279	1.19699	0.598495	+	0.801127i	$0.295766\pi$
$660$	−0.585786	−0.0228017
$661$	−13.5563	−0.527281	−0.263640	−	0.964621i	$-0.584923\pi$
$661$	−13.5563	−0.527281	−0.263640	+	0.964621i	$0.584923\pi$
$662$	−22.4853	−0.873915
$663$	5.24264	0.203607
$664$	−7.65685	−0.297144
$665$	0	0
$666$	−5.07107	−0.196500
$667$	−45.3553	−1.75617
$668$	12.3137	0.476432
$669$	21.3848	0.826783
$670$	20.7279	0.800789
$671$	−2.17157	−0.0838326
$672$	0	0
$673$	−1.17157	−0.0451608	−0.0225804	−	0.999745i	$-0.507188\pi$
$673$	−1.17157	−0.0451608	−0.0225804	+	0.999745i	$0.507188\pi$
$674$	28.6569	1.10382
$675$	−3.00000	−0.115470
$676$	1.00000	0.0384615
$677$	28.1716	1.08272	0.541361	−	0.840790i	$-0.317909\pi$
$677$	28.1716	1.08272	0.541361	+	0.840790i	$0.317909\pi$
$678$	−6.07107	−0.233158
$679$	0	0
$680$	−7.41421	−0.284322
$681$	−26.1421	−1.00177
$682$	2.82843	0.108306
$683$	5.45584	0.208762	0.104381	−	0.994537i	$-0.466714\pi$
$683$	5.45584	0.208762	0.104381	+	0.994537i	$0.466714\pi$
$684$	3.00000	0.114708
$685$	18.4853	0.706286
$686$	0	0
$687$	−7.17157	−0.273613
$688$	4.82843	0.184082
$689$	12.3137	0.469115
$690$	12.8284	0.488370
$691$	11.1421	0.423867	0.211933	−	0.977284i	$-0.432024\pi$
$691$	11.1421	0.423867	0.211933	+	0.977284i	$0.432024\pi$
$692$	20.3137	0.772211
$693$	0	0
$694$	5.75736	0.218546
$695$	30.0000	1.13796
$696$	5.00000	0.189525
$697$	24.0416	0.910642
$698$	5.41421	0.204931
$699$	−3.72792	−0.141003
$700$	0	0
$701$	48.4853	1.83126	0.915632	−	0.402018i	$-0.131691\pi$
$701$	48.4853	1.83126	0.915632	+	0.402018i	$0.131691\pi$
$702$	1.00000	0.0377426
$703$	−15.2132	−0.573777
$704$	0.414214	0.0156113
$705$	−12.7279	−0.479361
$706$	12.6274	0.475239
$707$	0	0
$708$	7.58579	0.285091
$709$	−32.0416	−1.20335	−0.601674	−	0.798741i	$-0.705499\pi$
$709$	−32.0416	−1.20335	−0.601674	+	0.798741i	$0.705499\pi$
$710$	1.41421	0.0530745
$711$	13.3137	0.499303
$712$	−6.24264	−0.233953
$713$	−61.9411	−2.31971
$714$	0	0
$715$	−0.585786	−0.0219072
$716$	−12.3431	−0.461285
$717$	−2.51472	−0.0939139
$718$	−15.4558	−0.576807
$719$	−22.2843	−0.831063	−0.415532	−	0.909579i	$-0.636404\pi$
$719$	−22.2843	−0.831063	−0.415532	+	0.909579i	$0.636404\pi$
$720$	−1.41421	−0.0527046
$721$	0	0
$722$	−10.0000	−0.372161
$723$	−16.4853	−0.613094
$724$	−11.5858	−0.430582
$725$	−15.0000	−0.557086
$726$	−10.8284	−0.401881
$727$	−38.8284	−1.44007	−0.720033	−	0.693939i	$-0.755874\pi$
$727$	−38.8284	−1.44007	−0.720033	+	0.693939i	$0.755874\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.51472	0.0560623
$731$	25.3137	0.936261
$732$	−5.24264	−0.193774
$733$	−29.0122	−1.07159	−0.535795	−	0.844348i	$-0.679988\pi$
$733$	−29.0122	−1.07159	−0.535795	+	0.844348i	$0.679988\pi$
$734$	14.0000	0.516749
$735$	0	0
$736$	−9.07107	−0.334364
$737$	−6.07107	−0.223631
$738$	4.58579	0.168805
$739$	6.97056	0.256416	0.128208	−	0.991747i	$-0.459077\pi$
$739$	6.97056	0.256416	0.128208	+	0.991747i	$0.459077\pi$
$740$	7.17157	0.263632
$741$	3.00000	0.110208
$742$	0	0
$743$	11.4853	0.421354	0.210677	−	0.977556i	$-0.432433\pi$
$743$	11.4853	0.421354	0.210677	+	0.977556i	$0.432433\pi$
$744$	6.82843	0.250342
$745$	−22.4853	−0.823797
$746$	−11.1005	−0.406418
$747$	−7.65685	−0.280150
$748$	2.17157	0.0794006
$749$	0	0
$750$	11.3137	0.413118
$751$	−34.3431	−1.25320	−0.626600	−	0.779341i	$-0.715554\pi$
$751$	−34.3431	−1.25320	−0.626600	+	0.779341i	$0.715554\pi$
$752$	9.00000	0.328196
$753$	12.8284	0.467494
$754$	5.00000	0.182089
$755$	10.7279	0.390429
$756$	0	0
$757$	23.4437	0.852074	0.426037	−	0.904706i	$-0.359909\pi$
$757$	23.4437	0.852074	0.426037	+	0.904706i	$0.359909\pi$
$758$	−33.6569	−1.22247
$759$	−3.75736	−0.136384
$760$	−4.24264	−0.153897
$761$	−17.8579	−0.647347	−0.323674	−	0.946169i	$-0.604918\pi$
$761$	−17.8579	−0.647347	−0.323674	+	0.946169i	$0.604918\pi$
$762$	9.89949	0.358621
$763$	0	0
$764$	2.34315	0.0847720
$765$	−7.41421	−0.268061
$766$	6.48528	0.234323
$767$	7.58579	0.273907
$768$	1.00000	0.0360844
$769$	−6.92893	−0.249864	−0.124932	−	0.992165i	$-0.539871\pi$
$769$	−6.92893	−0.249864	−0.124932	+	0.992165i	$0.539871\pi$
$770$	0	0
$771$	−21.7990	−0.785071
$772$	−15.7574	−0.567120
$773$	−29.5980	−1.06457	−0.532283	−	0.846567i	$-0.678666\pi$
$773$	−29.5980	−1.06457	−0.532283	+	0.846567i	$0.678666\pi$
$774$	4.82843	0.173554
$775$	−20.4853	−0.735853
$776$	7.89949	0.283575
$777$	0	0
$778$	23.0000	0.824590
$779$	13.7574	0.492909
$780$	−1.41421	−0.0506370
$781$	−0.414214	−0.0148217
$782$	−47.5563	−1.70061
$783$	5.00000	0.178685
$784$	0	0
$785$	−11.2132	−0.400216
$786$	9.89949	0.353103
$787$	−8.17157	−0.291285	−0.145643	−	0.989337i	$-0.546525\pi$
$787$	−8.17157	−0.291285	−0.145643	+	0.989337i	$0.546525\pi$
$788$	9.55635	0.340431
$789$	−7.55635	−0.269013
$790$	−18.8284	−0.669885
$791$	0	0
$792$	0.414214	0.0147184
$793$	−5.24264	−0.186172
$794$	−19.7574	−0.701162
$795$	−17.4142	−0.617619
$796$	10.5858	0.375203
$797$	−36.9706	−1.30956	−0.654782	−	0.755818i	$-0.727240\pi$
$797$	−36.9706	−1.30956	−0.654782	+	0.755818i	$0.727240\pi$
$798$	0	0
$799$	47.1838	1.66924
$800$	−3.00000	−0.106066
$801$	−6.24264	−0.220573
$802$	19.0711	0.673423
$803$	−0.443651	−0.0156561
$804$	−14.6569	−0.516907
$805$	0	0
$806$	6.82843	0.240521
$807$	−3.68629	−0.129764
$808$	−1.17157	−0.0412158
$809$	35.0416	1.23200	0.615999	−	0.787747i	$-0.288753\pi$
$809$	35.0416	1.23200	0.615999	+	0.787747i	$0.288753\pi$
$810$	−1.41421	−0.0496904
$811$	26.7696	0.940006	0.470003	−	0.882665i	$-0.344253\pi$
$811$	26.7696	0.940006	0.470003	+	0.882665i	$0.344253\pi$
$812$	0	0
$813$	−15.3848	−0.539568
$814$	−2.10051	−0.0736227
$815$	−24.2426	−0.849183
$816$	5.24264	0.183529
$817$	14.4853	0.506776
$818$	−2.58579	−0.0904099
$819$	0	0
$820$	−6.48528	−0.226476
$821$	−9.61522	−0.335574	−0.167787	−	0.985823i	$-0.553662\pi$
$821$	−9.61522	−0.335574	−0.167787	+	0.985823i	$0.553662\pi$
$822$	−13.0711	−0.455906
$823$	−8.10051	−0.282366	−0.141183	−	0.989984i	$-0.545091\pi$
$823$	−8.10051	−0.282366	−0.141183	+	0.989984i	$0.545091\pi$
$824$	6.48528	0.225925
$825$	−1.24264	−0.0432632
$826$	0	0
$827$	13.5269	0.470377	0.235188	−	0.971950i	$-0.424429\pi$
$827$	13.5269	0.470377	0.235188	+	0.971950i	$0.424429\pi$
$828$	−9.07107	−0.315241
$829$	18.6985	0.649425	0.324713	−	0.945813i	$-0.394732\pi$
$829$	18.6985	0.649425	0.324713	+	0.945813i	$0.394732\pi$
$830$	10.8284	0.375860
$831$	−16.4142	−0.569403
$832$	1.00000	0.0346688
$833$	0	0
$834$	−21.2132	−0.734553
$835$	−17.4142	−0.602644
$836$	1.24264	0.0429776
$837$	6.82843	0.236025
$838$	−27.4558	−0.948446
$839$	2.51472	0.0868177	0.0434089	−	0.999057i	$-0.486178\pi$
$839$	2.51472	0.0868177	0.0434089	+	0.999057i	$0.486178\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	10.5858	0.364810
$843$	7.31371	0.251898
$844$	−28.3848	−0.977044
$845$	−1.41421	−0.0486504
$846$	9.00000	0.309426
$847$	0	0
$848$	12.3137	0.422854
$849$	17.0711	0.585878
$850$	−15.7279	−0.539463
$851$	46.0000	1.57686
$852$	−1.00000	−0.0342594
$853$	−17.6985	−0.605985	−0.302992	−	0.952993i	$-0.597986\pi$
$853$	−17.6985	−0.605985	−0.302992	+	0.952993i	$0.597986\pi$
$854$	0	0
$855$	−4.24264	−0.145095
$856$	13.6569	0.466782
$857$	−51.3848	−1.75527	−0.877635	−	0.479329i	$-0.840880\pi$
$857$	−51.3848	−1.75527	−0.877635	+	0.479329i	$0.840880\pi$
$858$	0.414214	0.0141410
$859$	0.201010	0.00685838	0.00342919	−	0.999994i	$-0.498908\pi$
$859$	0.201010	0.00685838	0.00342919	+	0.999994i	$0.498908\pi$
$860$	−6.82843	−0.232847
$861$	0	0
$862$	14.4853	0.493371
$863$	4.00000	0.136162	0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000	0.136162	0.0680808	+	0.997680i	$0.478312\pi$
$864$	1.00000	0.0340207
$865$	−28.7279	−0.976779
$866$	−19.0000	−0.645646
$867$	10.4853	0.356099
$868$	0	0
$869$	5.51472	0.187074
$870$	−7.07107	−0.239732
$871$	−14.6569	−0.496629
$872$	1.65685	0.0561082
$873$	7.89949	0.267357
$874$	−27.2132	−0.920500
$875$	0	0
$876$	−1.07107	−0.0361880
$877$	23.4142	0.790642	0.395321	−	0.918543i	$-0.370633\pi$
$877$	23.4142	0.790642	0.395321	+	0.918543i	$0.370633\pi$
$878$	−10.5858	−0.357253
$879$	−18.7279	−0.631677
$880$	−0.585786	−0.0197469
$881$	−41.1127	−1.38512	−0.692561	−	0.721359i	$-0.743518\pi$
$881$	−41.1127	−1.38512	−0.692561	+	0.721359i	$0.743518\pi$
$882$	0	0
$883$	−0.928932	−0.0312611	−0.0156305	−	0.999878i	$-0.504976\pi$
$883$	−0.928932	−0.0312611	−0.0156305	+	0.999878i	$0.504976\pi$
$884$	5.24264	0.176329
$885$	−10.7279	−0.360615
$886$	22.7279	0.763559
$887$	41.3137	1.38718	0.693589	−	0.720371i	$-0.256028\pi$
$887$	41.3137	1.38718	0.693589	+	0.720371i	$0.256028\pi$
$888$	−5.07107	−0.170174
$889$	0	0
$890$	8.82843	0.295930
$891$	0.414214	0.0138767
$892$	21.3848	0.716015
$893$	27.0000	0.903521
$894$	15.8995	0.531759
$895$	17.4558	0.583485
$896$	0	0
$897$	−9.07107	−0.302874
$898$	−33.9411	−1.13263
$899$	34.1421	1.13870
$900$	−3.00000	−0.100000
$901$	64.5563	2.15068
$902$	1.89949	0.0632463
$903$	0	0
$904$	−6.07107	−0.201921
$905$	16.3848	0.544648
$906$	−7.58579	−0.252021
$907$	−32.1005	−1.06588	−0.532940	−	0.846153i	$-0.678913\pi$
$907$	−32.1005	−1.06588	−0.532940	+	0.846153i	$0.678913\pi$
$908$	−26.1421	−0.867557
$909$	−1.17157	−0.0388586
$910$	0	0
$911$	54.0000	1.78910	0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000	1.78910	0.894550	+	0.446968i	$0.147496\pi$
$912$	3.00000	0.0993399
$913$	−3.17157	−0.104964
$914$	−15.2132	−0.503208
$915$	7.41421	0.245106
$916$	−7.17157	−0.236955
$917$	0	0
$918$	5.24264	0.173033
$919$	−25.7990	−0.851030	−0.425515	−	0.904951i	$-0.639907\pi$
$919$	−25.7990	−0.851030	−0.425515	+	0.904951i	$0.639907\pi$
$920$	12.8284	0.422941
$921$	−19.6274	−0.646745
$922$	−33.4558	−1.10181
$923$	−1.00000	−0.0329154
$924$	0	0
$925$	15.2132	0.500207
$926$	−37.9411	−1.24682
$927$	6.48528	0.213005
$928$	5.00000	0.164133
$929$	18.2843	0.599887	0.299944	−	0.953957i	$-0.403032\pi$
$929$	18.2843	0.599887	0.299944	+	0.953957i	$0.403032\pi$
$930$	−9.65685	−0.316661
$931$	0	0
$932$	−3.72792	−0.122112
$933$	−6.58579	−0.215609
$934$	−0.242641	−0.00793945
$935$	−3.07107	−0.100435
$936$	1.00000	0.0326860
$937$	40.5980	1.32628	0.663139	−	0.748496i	$-0.269224\pi$
$937$	40.5980	1.32628	0.663139	+	0.748496i	$0.269224\pi$
$938$	0	0
$939$	18.1421	0.592046
$940$	−12.7279	−0.415139
$941$	−20.9706	−0.683621	−0.341810	−	0.939769i	$-0.611040\pi$
$941$	−20.9706	−0.683621	−0.341810	+	0.939769i	$0.611040\pi$
$942$	7.92893	0.258339
$943$	−41.5980	−1.35462
$944$	7.58579	0.246896
$945$	0	0
$946$	2.00000	0.0650256
$947$	17.2426	0.560311	0.280155	−	0.959955i	$-0.409614\pi$
$947$	17.2426	0.560311	0.280155	+	0.959955i	$0.409614\pi$
$948$	13.3137	0.432409
$949$	−1.07107	−0.0347683
$950$	−9.00000	−0.291999
$951$	0.828427	0.0268636
$952$	0	0
$953$	−10.2132	−0.330838	−0.165419	−	0.986223i	$-0.552898\pi$
$953$	−10.2132	−0.330838	−0.165419	+	0.986223i	$0.552898\pi$
$954$	12.3137	0.398671
$955$	−3.31371	−0.107229
$956$	−2.51472	−0.0813318
$957$	2.07107	0.0669481
$958$	−31.1421	−1.00616
$959$	0	0
$960$	−1.41421	−0.0456435
$961$	15.6274	0.504110
$962$	−5.07107	−0.163498
$963$	13.6569	0.440086
$964$	−16.4853	−0.530955
$965$	22.2843	0.717356
$966$	0	0
$967$	9.38478	0.301794	0.150897	−	0.988549i	$-0.451784\pi$
$967$	9.38478	0.301794	0.150897	+	0.988549i	$0.451784\pi$
$968$	−10.8284	−0.348039
$969$	15.7279	0.505254
$970$	−11.1716	−0.358698
$971$	57.5563	1.84707	0.923536	−	0.383513i	$-0.125286\pi$
$971$	57.5563	1.84707	0.923536	+	0.383513i	$0.125286\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−23.7279	−0.760292
$975$	−3.00000	−0.0960769
$976$	−5.24264	−0.167813
$977$	2.48528	0.0795112	0.0397556	−	0.999209i	$-0.487342\pi$
$977$	2.48528	0.0795112	0.0397556	+	0.999209i	$0.487342\pi$
$978$	17.1421	0.548145
$979$	−2.58579	−0.0826421
$980$	0	0
$981$	1.65685	0.0528993
$982$	−26.2843	−0.838765
$983$	−22.1716	−0.707163	−0.353582	−	0.935404i	$-0.615036\pi$
$983$	−22.1716	−0.707163	−0.353582	+	0.935404i	$0.615036\pi$
$984$	4.58579	0.146190
$985$	−13.5147	−0.430615
$986$	26.2132	0.834798
$987$	0	0
$988$	3.00000	0.0954427
$989$	−43.7990	−1.39273
$990$	−0.585786	−0.0186175
$991$	−7.31371	−0.232328	−0.116164	−	0.993230i	$-0.537060\pi$
$991$	−7.31371	−0.232328	−0.116164	+	0.993230i	$0.537060\pi$
$992$	6.82843	0.216803
$993$	−22.4853	−0.713549
$994$	0	0
$995$	−14.9706	−0.474599
$996$	−7.65685	−0.242617
$997$	6.69848	0.212143	0.106072	−	0.994358i	$-0.466173\pi$
$997$	6.69848	0.212143	0.106072	+	0.994358i	$0.466173\pi$
$998$	−30.0000	−0.949633
$999$	−5.07107	−0.160441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bs.1.1		2
7.2	even	3		546.2.i.h.235.2	yes	4
7.4	even	3		546.2.i.h.79.2	✓	4
7.6	odd	2		3822.2.a.bp.1.2		2
21.2	odd	6		1638.2.j.n.235.1		4
21.11	odd	6		1638.2.j.n.1171.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.h.79.2	✓	4	7.4	even	3
546.2.i.h.235.2	yes	4	7.2	even	3
1638.2.j.n.235.1		4	21.2	odd	6
1638.2.j.n.1171.1		4	21.11	odd	6
3822.2.a.bp.1.2		2	7.6	odd	2
3822.2.a.bs.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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.41421 q^{10} +0.414214 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.41421 q^{15} +1.00000 q^{16} +5.24264 q^{17} +1.00000 q^{18} +3.00000 q^{19} -1.41421 q^{20} +0.414214 q^{22} -9.07107 q^{23} +1.00000 q^{24} -3.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} +5.00000 q^{29} -1.41421 q^{30} +6.82843 q^{31} +1.00000 q^{32} +0.414214 q^{33} +5.24264 q^{34} +1.00000 q^{36} -5.07107 q^{37} +3.00000 q^{38} +1.00000 q^{39} -1.41421 q^{40} +4.58579 q^{41} +4.82843 q^{43} +0.414214 q^{44} -1.41421 q^{45} -9.07107 q^{46} +9.00000 q^{47} +1.00000 q^{48} -3.00000 q^{50} +5.24264 q^{51} +1.00000 q^{52} +12.3137 q^{53} +1.00000 q^{54} -0.585786 q^{55} +3.00000 q^{57} +5.00000 q^{58} +7.58579 q^{59} -1.41421 q^{60} -5.24264 q^{61} +6.82843 q^{62} +1.00000 q^{64} -1.41421 q^{65} +0.414214 q^{66} -14.6569 q^{67} +5.24264 q^{68} -9.07107 q^{69} -1.00000 q^{71} +1.00000 q^{72} -1.07107 q^{73} -5.07107 q^{74} -3.00000 q^{75} +3.00000 q^{76} +1.00000 q^{78} +13.3137 q^{79} -1.41421 q^{80} +1.00000 q^{81} +4.58579 q^{82} -7.65685 q^{83} -7.41421 q^{85} +4.82843 q^{86} +5.00000 q^{87} +0.414214 q^{88} -6.24264 q^{89} -1.41421 q^{90} -9.07107 q^{92} +6.82843 q^{93} +9.00000 q^{94} -4.24264 q^{95} +1.00000 q^{96} +7.89949 q^{97} +0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 6 q^{19} - 2 q^{22} - 4 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 2 q^{27} + 10 q^{29} + 8 q^{31} + 2 q^{32} - 2 q^{33} + 2 q^{34} + 2 q^{36} + 4 q^{37} + 6 q^{38} + 2 q^{39} + 12 q^{41} + 4 q^{43} - 2 q^{44} - 4 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{50} + 2 q^{51} + 2 q^{52} + 2 q^{53} + 2 q^{54} - 4 q^{55} + 6 q^{57} + 10 q^{58} + 18 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} - 2 q^{66} - 18 q^{67} + 2 q^{68} - 4 q^{69} - 2 q^{71} + 2 q^{72} + 12 q^{73} + 4 q^{74} - 6 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} + 2 q^{81} + 12 q^{82} - 4 q^{83} - 12 q^{85} + 4 q^{86} + 10 q^{87} - 2 q^{88} - 4 q^{89} - 4 q^{92} + 8 q^{93} + 18 q^{94} + 2 q^{96} - 4 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 6 * q^19 - 2 * q^22 - 4 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 2 * q^27 + 10 * q^29 + 8 * q^31 + 2 * q^32 - 2 * q^33 + 2 * q^34 + 2 * q^36 + 4 * q^37 + 6 * q^38 + 2 * q^39 + 12 * q^41 + 4 * q^43 - 2 * q^44 - 4 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^50 + 2 * q^51 + 2 * q^52 + 2 * q^53 + 2 * q^54 - 4 * q^55 + 6 * q^57 + 10 * q^58 + 18 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 2 * q^66 - 18 * q^67 + 2 * q^68 - 4 * q^69 - 2 * q^71 + 2 * q^72 + 12 * q^73 + 4 * q^74 - 6 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 + 2 * q^81 + 12 * q^82 - 4 * q^83 - 12 * q^85 + 4 * q^86 + 10 * q^87 - 2 * q^88 - 4 * q^89 - 4 * q^92 + 8 * q^93 + 18 * q^94 + 2 * q^96 - 4 * q^97 - 2 * q^99

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