LMFDB - Embedded newform 3822.2.a.bs.1.2

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			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.41421 q^{10} -2.41421 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.41421 q^{15} +1.00000 q^{16} -3.24264 q^{17} +1.00000 q^{18} +3.00000 q^{19} +1.41421 q^{20} -2.41421 q^{22} +5.07107 q^{23} +1.00000 q^{24} -3.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} +5.00000 q^{29} +1.41421 q^{30} +1.17157 q^{31} +1.00000 q^{32} -2.41421 q^{33} -3.24264 q^{34} +1.00000 q^{36} +9.07107 q^{37} +3.00000 q^{38} +1.00000 q^{39} +1.41421 q^{40} +7.41421 q^{41} -0.828427 q^{43} -2.41421 q^{44} +1.41421 q^{45} +5.07107 q^{46} +9.00000 q^{47} +1.00000 q^{48} -3.00000 q^{50} -3.24264 q^{51} +1.00000 q^{52} -10.3137 q^{53} +1.00000 q^{54} -3.41421 q^{55} +3.00000 q^{57} +5.00000 q^{58} +10.4142 q^{59} +1.41421 q^{60} +3.24264 q^{61} +1.17157 q^{62} +1.00000 q^{64} +1.41421 q^{65} -2.41421 q^{66} -3.34315 q^{67} -3.24264 q^{68} +5.07107 q^{69} -1.00000 q^{71} +1.00000 q^{72} +13.0711 q^{73} +9.07107 q^{74} -3.00000 q^{75} +3.00000 q^{76} +1.00000 q^{78} -9.31371 q^{79} +1.41421 q^{80} +1.00000 q^{81} +7.41421 q^{82} +3.65685 q^{83} -4.58579 q^{85} -0.828427 q^{86} +5.00000 q^{87} -2.41421 q^{88} +2.24264 q^{89} +1.41421 q^{90} +5.07107 q^{92} +1.17157 q^{93} +9.00000 q^{94} +4.24264 q^{95} +1.00000 q^{96} -11.8995 q^{97} -2.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.397584\pi$
$5$	1.41421	0.632456	0.316228	+	0.948683i	$0.397584\pi$
$6$	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
$11$	−2.41421	−0.727913	−0.363956	−	0.931416i	$-0.618574\pi$
$11$	−2.41421	−0.727913	−0.363956	+	0.931416i	$0.618574\pi$
$12$	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
$17$	−3.24264	−0.786456	−0.393228	−	0.919441i	$-0.628642\pi$
$17$	−3.24264	−0.786456	−0.393228	+	0.919441i	$0.628642\pi$
$18$	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
$22$	−2.41421	−0.514712
$23$	5.07107	1.05739	0.528695	−	0.848812i	$-0.322681\pi$
$23$	5.07107	1.05739	0.528695	+	0.848812i	$0.322681\pi$
$24$	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
$31$	1.17157	0.210421	0.105210	−	0.994450i	$-0.466448\pi$
$31$	1.17157	0.210421	0.105210	+	0.994450i	$0.466448\pi$
$32$	1.00000	0.176777
$33$	−2.41421	−0.420261
$34$	−3.24264	−0.556108
$35$	0	0
$36$	1.00000	0.166667
$37$	9.07107	1.49127	0.745637	−	0.666352i	$-0.232145\pi$
$37$	9.07107	1.49127	0.745637	+	0.666352i	$0.232145\pi$
$38$	3.00000	0.486664
$39$	1.00000	0.160128
$40$	1.41421	0.223607
$41$	7.41421	1.15791	0.578953	−	0.815361i	$-0.303462\pi$
$41$	7.41421	1.15791	0.578953	+	0.815361i	$0.303462\pi$
$42$	0	0
$43$	−0.828427	−0.126334	−0.0631670	−	0.998003i	$-0.520120\pi$
$43$	−0.828427	−0.126334	−0.0631670	+	0.998003i	$0.520120\pi$
$44$	−2.41421	−0.363956
$45$	1.41421	0.210819
$46$	5.07107	0.747688
$47$	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
$51$	−3.24264	−0.454061
$52$	1.00000	0.138675
$53$	−10.3137	−1.41670	−0.708348	−	0.705863i	$-0.750559\pi$
$53$	−10.3137	−1.41670	−0.708348	+	0.705863i	$0.750559\pi$
$54$	1.00000	0.136083
$55$	−3.41421	−0.460372
$56$	0	0
$57$	3.00000	0.397360
$58$	5.00000	0.656532
$59$	10.4142	1.35582	0.677908	−	0.735147i	$-0.262887\pi$
$59$	10.4142	1.35582	0.677908	+	0.735147i	$0.262887\pi$
$60$	1.41421	0.182574
$61$	3.24264	0.415178	0.207589	−	0.978216i	$-0.433438\pi$
$61$	3.24264	0.415178	0.207589	+	0.978216i	$0.433438\pi$
$62$	1.17157	0.148790
$63$	0	0
$64$	1.00000	0.125000
$65$	1.41421	0.175412
$66$	−2.41421	−0.297169
$67$	−3.34315	−0.408430	−0.204215	−	0.978926i	$-0.565464\pi$
$67$	−3.34315	−0.408430	−0.204215	+	0.978926i	$0.565464\pi$
$68$	−3.24264	−0.393228
$69$	5.07107	0.610485
$70$	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
$73$	13.0711	1.52985	0.764926	−	0.644118i	$-0.222775\pi$
$73$	13.0711	1.52985	0.764926	+	0.644118i	$0.222775\pi$
$74$	9.07107	1.05449
$75$	−3.00000	−0.346410
$76$	3.00000	0.344124
$77$	0	0
$78$	1.00000	0.113228
$79$	−9.31371	−1.04787	−0.523937	−	0.851757i	$-0.675537\pi$
$79$	−9.31371	−1.04787	−0.523937	+	0.851757i	$0.675537\pi$
$80$	1.41421	0.158114
$81$	1.00000	0.111111
$82$	7.41421	0.818763
$83$	3.65685	0.401392	0.200696	−	0.979654i	$-0.435680\pi$
$83$	3.65685	0.401392	0.200696	+	0.979654i	$0.435680\pi$
$84$	0	0
$85$	−4.58579	−0.497398
$86$	−0.828427	−0.0893316
$87$	5.00000	0.536056
$88$	−2.41421	−0.257356
$89$	2.24264	0.237719	0.118860	−	0.992911i	$-0.462076\pi$
$89$	2.24264	0.237719	0.118860	+	0.992911i	$0.462076\pi$
$90$	1.41421	0.149071
$91$	0	0
$92$	5.07107	0.528695
$93$	1.17157	0.121486
$94$	9.00000	0.928279
$95$	4.24264	0.435286
$96$	1.00000	0.102062
$97$	−11.8995	−1.20821	−0.604105	−	0.796904i	$-0.706469\pi$
$97$	−11.8995	−1.20821	−0.604105	+	0.796904i	$0.706469\pi$
$98$	0	0
$99$	−2.41421	−0.242638
$100$	−3.00000	−0.300000
$101$	−6.82843	−0.679454	−0.339727	−	0.940524i	$-0.610335\pi$
$101$	−6.82843	−0.679454	−0.339727	+	0.940524i	$0.610335\pi$
$102$	−3.24264	−0.321069
$103$	−10.4853	−1.03315	−0.516573	−	0.856243i	$-0.672792\pi$
$103$	−10.4853	−1.03315	−0.516573	+	0.856243i	$0.672792\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−10.3137	−1.00176
$107$	2.34315	0.226520	0.113260	−	0.993565i	$-0.463871\pi$
$107$	2.34315	0.226520	0.113260	+	0.993565i	$0.463871\pi$
$108$	1.00000	0.0962250
$109$	−9.65685	−0.924959	−0.462479	−	0.886630i	$-0.653040\pi$
$109$	−9.65685	−0.924959	−0.462479	+	0.886630i	$0.653040\pi$
$110$	−3.41421	−0.325532
$111$	9.07107	0.860988
$112$	0	0
$113$	8.07107	0.759262	0.379631	−	0.925138i	$-0.376051\pi$
$113$	8.07107	0.759262	0.379631	+	0.925138i	$0.376051\pi$
$114$	3.00000	0.280976
$115$	7.17157	0.668753
$116$	5.00000	0.464238
$117$	1.00000	0.0924500
$118$	10.4142	0.958706
$119$	0	0
$120$	1.41421	0.129099
$121$	−5.17157	−0.470143
$122$	3.24264	0.293575
$123$	7.41421	0.668517
$124$	1.17157	0.105210
$125$	−11.3137	−1.01193
$126$	0	0
$127$	−9.89949	−0.878438	−0.439219	−	0.898380i	$-0.644745\pi$
$127$	−9.89949	−0.878438	−0.439219	+	0.898380i	$0.644745\pi$
$128$	1.00000	0.0883883
$129$	−0.828427	−0.0729389
$130$	1.41421	0.124035
$131$	−9.89949	−0.864923	−0.432461	−	0.901652i	$-0.642355\pi$
$131$	−9.89949	−0.864923	−0.432461	+	0.901652i	$0.642355\pi$
$132$	−2.41421	−0.210130
$133$	0	0
$134$	−3.34315	−0.288804
$135$	1.41421	0.121716
$136$	−3.24264	−0.278054
$137$	1.07107	0.0915075	0.0457537	−	0.998953i	$-0.485431\pi$
$137$	1.07107	0.0915075	0.0457537	+	0.998953i	$0.485431\pi$
$138$	5.07107	0.431678
$139$	21.2132	1.79928	0.899640	−	0.436632i	$-0.143829\pi$
$139$	21.2132	1.79928	0.899640	+	0.436632i	$0.143829\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	−1.00000	−0.0839181
$143$	−2.41421	−0.201887
$144$	1.00000	0.0833333
$145$	7.07107	0.587220
$146$	13.0711	1.08177
$147$	0	0
$148$	9.07107	0.745637
$149$	−3.89949	−0.319459	−0.159730	−	0.987161i	$-0.551062\pi$
$149$	−3.89949	−0.319459	−0.159730	+	0.987161i	$0.551062\pi$
$150$	−3.00000	−0.244949
$151$	−10.4142	−0.847497	−0.423748	−	0.905780i	$-0.639286\pi$
$151$	−10.4142	−0.847497	−0.423748	+	0.905780i	$0.639286\pi$
$152$	3.00000	0.243332
$153$	−3.24264	−0.262152
$154$	0	0
$155$	1.65685	0.133082
$156$	1.00000	0.0800641
$157$	22.0711	1.76146	0.880731	−	0.473616i	$-0.157052\pi$
$157$	22.0711	1.76146	0.880731	+	0.473616i	$0.157052\pi$
$158$	−9.31371	−0.740959
$159$	−10.3137	−0.817930
$160$	1.41421	0.111803
$161$	0	0
$162$	1.00000	0.0785674
$163$	−11.1421	−0.872719	−0.436360	−	0.899772i	$-0.643732\pi$
$163$	−11.1421	−0.872719	−0.436360	+	0.899772i	$0.643732\pi$
$164$	7.41421	0.578953
$165$	−3.41421	−0.265796
$166$	3.65685	0.283827
$167$	−10.3137	−0.798099	−0.399049	−	0.916929i	$-0.630660\pi$
$167$	−10.3137	−0.798099	−0.399049	+	0.916929i	$0.630660\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−4.58579	−0.351714
$171$	3.00000	0.229416
$172$	−0.828427	−0.0631670
$173$	−2.31371	−0.175908	−0.0879540	−	0.996125i	$-0.528033\pi$
$173$	−2.31371	−0.175908	−0.0879540	+	0.996125i	$0.528033\pi$
$174$	5.00000	0.379049
$175$	0	0
$176$	−2.41421	−0.181978
$177$	10.4142	0.782780
$178$	2.24264	0.168093
$179$	−23.6569	−1.76820	−0.884098	−	0.467301i	$-0.845226\pi$
$179$	−23.6569	−1.76820	−0.884098	+	0.467301i	$0.845226\pi$
$180$	1.41421	0.105409
$181$	−14.4142	−1.07140	−0.535700	−	0.844408i	$-0.679952\pi$
$181$	−14.4142	−1.07140	−0.535700	+	0.844408i	$0.679952\pi$
$182$	0	0
$183$	3.24264	0.239703
$184$	5.07107	0.373844
$185$	12.8284	0.943165
$186$	1.17157	0.0859039
$187$	7.82843	0.572471
$188$	9.00000	0.656392
$189$	0	0
$190$	4.24264	0.307794
$191$	13.6569	0.988175	0.494088	−	0.869412i	$-0.335502\pi$
$191$	13.6569	0.988175	0.494088	+	0.869412i	$0.335502\pi$
$192$	1.00000	0.0721688
$193$	−24.2426	−1.74502	−0.872512	−	0.488593i	$-0.837510\pi$
$193$	−24.2426	−1.74502	−0.872512	+	0.488593i	$0.837510\pi$
$194$	−11.8995	−0.854334
$195$	1.41421	0.101274
$196$	0	0
$197$	−21.5563	−1.53583	−0.767913	−	0.640554i	$-0.778705\pi$
$197$	−21.5563	−1.53583	−0.767913	+	0.640554i	$0.778705\pi$
$198$	−2.41421	−0.171571
$199$	13.4142	0.950908	0.475454	−	0.879740i	$-0.342284\pi$
$199$	13.4142	0.950908	0.475454	+	0.879740i	$0.342284\pi$
$200$	−3.00000	−0.212132
$201$	−3.34315	−0.235807
$202$	−6.82843	−0.480446
$203$	0	0
$204$	−3.24264	−0.227030
$205$	10.4853	0.732324
$206$	−10.4853	−0.730544
$207$	5.07107	0.352464
$208$	1.00000	0.0693375
$209$	−7.24264	−0.500984
$210$	0	0
$211$	8.38478	0.577232	0.288616	−	0.957445i	$-0.406805\pi$
$211$	8.38478	0.577232	0.288616	+	0.957445i	$0.406805\pi$
$212$	−10.3137	−0.708348
$213$	−1.00000	−0.0685189
$214$	2.34315	0.160174
$215$	−1.17157	−0.0799006
$216$	1.00000	0.0680414
$217$	0	0
$218$	−9.65685	−0.654045
$219$	13.0711	0.883261
$220$	−3.41421	−0.230186
$221$	−3.24264	−0.218124
$222$	9.07107	0.608810
$223$	−15.3848	−1.03024	−0.515120	−	0.857118i	$-0.672253\pi$
$223$	−15.3848	−1.03024	−0.515120	+	0.857118i	$0.672253\pi$
$224$	0	0
$225$	−3.00000	−0.200000
$226$	8.07107	0.536879
$227$	2.14214	0.142179	0.0710893	−	0.997470i	$-0.477352\pi$
$227$	2.14214	0.142179	0.0710893	+	0.997470i	$0.477352\pi$
$228$	3.00000	0.198680
$229$	−12.8284	−0.847726	−0.423863	−	0.905726i	$-0.639326\pi$
$229$	−12.8284	−0.847726	−0.423863	+	0.905726i	$0.639326\pi$
$230$	7.17157	0.472880
$231$	0	0
$232$	5.00000	0.328266
$233$	21.7279	1.42344	0.711722	−	0.702461i	$-0.247916\pi$
$233$	21.7279	1.42344	0.711722	+	0.702461i	$0.247916\pi$
$234$	1.00000	0.0653720
$235$	12.7279	0.830278
$236$	10.4142	0.677908
$237$	−9.31371	−0.604990
$238$	0	0
$239$	−19.4853	−1.26040	−0.630199	−	0.776434i	$-0.717027\pi$
$239$	−19.4853	−1.26040	−0.630199	+	0.776434i	$0.717027\pi$
$240$	1.41421	0.0912871
$241$	0.485281	0.0312597	0.0156299	−	0.999878i	$-0.495025\pi$
$241$	0.485281	0.0312597	0.0156299	+	0.999878i	$0.495025\pi$
$242$	−5.17157	−0.332441
$243$	1.00000	0.0641500
$244$	3.24264	0.207589
$245$	0	0
$246$	7.41421	0.472713
$247$	3.00000	0.190885
$248$	1.17157	0.0743950
$249$	3.65685	0.231744
$250$	−11.3137	−0.715542
$251$	7.17157	0.452666	0.226333	−	0.974050i	$-0.427326\pi$
$251$	7.17157	0.452666	0.226333	+	0.974050i	$0.427326\pi$
$252$	0	0
$253$	−12.2426	−0.769688
$254$	−9.89949	−0.621150
$255$	−4.58579	−0.287173
$256$	1.00000	0.0625000
$257$	17.7990	1.11027	0.555135	−	0.831760i	$-0.312666\pi$
$257$	17.7990	1.11027	0.555135	+	0.831760i	$0.312666\pi$
$258$	−0.828427	−0.0515756
$259$	0	0
$260$	1.41421	0.0877058
$261$	5.00000	0.309492
$262$	−9.89949	−0.611593
$263$	23.5563	1.45255	0.726273	−	0.687406i	$-0.241251\pi$
$263$	23.5563	1.45255	0.726273	+	0.687406i	$0.241251\pi$
$264$	−2.41421	−0.148585
$265$	−14.5858	−0.895998
$266$	0	0
$267$	2.24264	0.137247
$268$	−3.34315	−0.204215
$269$	−26.3137	−1.60438	−0.802188	−	0.597072i	$-0.796331\pi$
$269$	−26.3137	−1.60438	−0.802188	+	0.597072i	$0.796331\pi$
$270$	1.41421	0.0860663
$271$	21.3848	1.29903	0.649516	−	0.760348i	$-0.274971\pi$
$271$	21.3848	1.29903	0.649516	+	0.760348i	$0.274971\pi$
$272$	−3.24264	−0.196614
$273$	0	0
$274$	1.07107	0.0647056
$275$	7.24264	0.436748
$276$	5.07107	0.305242
$277$	−13.5858	−0.816291	−0.408145	−	0.912917i	$-0.633824\pi$
$277$	−13.5858	−0.816291	−0.408145	+	0.912917i	$0.633824\pi$
$278$	21.2132	1.27228
$279$	1.17157	0.0701402
$280$	0	0
$281$	−15.3137	−0.913539	−0.456770	−	0.889585i	$-0.650994\pi$
$281$	−15.3137	−0.913539	−0.456770	+	0.889585i	$0.650994\pi$
$282$	9.00000	0.535942
$283$	2.92893	0.174107	0.0870535	−	0.996204i	$-0.472255\pi$
$283$	2.92893	0.174107	0.0870535	+	0.996204i	$0.472255\pi$
$284$	−1.00000	−0.0593391
$285$	4.24264	0.251312
$286$	−2.41421	−0.142755
$287$	0	0
$288$	1.00000	0.0589256
$289$	−6.48528	−0.381487
$290$	7.07107	0.415227
$291$	−11.8995	−0.697561
$292$	13.0711	0.764926
$293$	6.72792	0.393049	0.196525	−	0.980499i	$-0.437034\pi$
$293$	6.72792	0.393049	0.196525	+	0.980499i	$0.437034\pi$
$294$	0	0
$295$	14.7279	0.857493
$296$	9.07107	0.527245
$297$	−2.41421	−0.140087
$298$	−3.89949	−0.225892
$299$	5.07107	0.293267
$300$	−3.00000	−0.173205
$301$	0	0
$302$	−10.4142	−0.599271
$303$	−6.82843	−0.392283
$304$	3.00000	0.172062
$305$	4.58579	0.262581
$306$	−3.24264	−0.185369
$307$	25.6274	1.46263	0.731317	−	0.682038i	$-0.238906\pi$
$307$	25.6274	1.46263	0.731317	+	0.682038i	$0.238906\pi$
$308$	0	0
$309$	−10.4853	−0.596487
$310$	1.65685	0.0941030
$311$	−9.41421	−0.533831	−0.266916	−	0.963720i	$-0.586004\pi$
$311$	−9.41421	−0.533831	−0.266916	+	0.963720i	$0.586004\pi$
$312$	1.00000	0.0566139
$313$	−10.1421	−0.573267	−0.286634	−	0.958040i	$-0.592536\pi$
$313$	−10.1421	−0.573267	−0.286634	+	0.958040i	$0.592536\pi$
$314$	22.0711	1.24554
$315$	0	0
$316$	−9.31371	−0.523937
$317$	−4.82843	−0.271191	−0.135596	−	0.990764i	$-0.543295\pi$
$317$	−4.82843	−0.271191	−0.135596	+	0.990764i	$0.543295\pi$
$318$	−10.3137	−0.578364
$319$	−12.0711	−0.675850
$320$	1.41421	0.0790569
$321$	2.34315	0.130782
$322$	0	0
$323$	−9.72792	−0.541276
$324$	1.00000	0.0555556
$325$	−3.00000	−0.166410
$326$	−11.1421	−0.617106
$327$	−9.65685	−0.534025
$328$	7.41421	0.409381
$329$	0	0
$330$	−3.41421	−0.187946
$331$	−5.51472	−0.303116	−0.151558	−	0.988448i	$-0.548429\pi$
$331$	−5.51472	−0.303116	−0.151558	+	0.988448i	$0.548429\pi$
$332$	3.65685	0.200696
$333$	9.07107	0.497091
$334$	−10.3137	−0.564341
$335$	−4.72792	−0.258314
$336$	0	0
$337$	17.3431	0.944741	0.472371	−	0.881400i	$-0.343398\pi$
$337$	17.3431	0.944741	0.472371	+	0.881400i	$0.343398\pi$
$338$	1.00000	0.0543928
$339$	8.07107	0.438360
$340$	−4.58579	−0.248699
$341$	−2.82843	−0.153168
$342$	3.00000	0.162221
$343$	0	0
$344$	−0.828427	−0.0446658
$345$	7.17157	0.386105
$346$	−2.31371	−0.124386
$347$	14.2426	0.764585	0.382293	−	0.924041i	$-0.375135\pi$
$347$	14.2426	0.764585	0.382293	+	0.924041i	$0.375135\pi$
$348$	5.00000	0.268028
$349$	2.58579	0.138414	0.0692070	−	0.997602i	$-0.477953\pi$
$349$	2.58579	0.138414	0.0692070	+	0.997602i	$0.477953\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−2.41421	−0.128678
$353$	−32.6274	−1.73658	−0.868291	−	0.496055i	$-0.834781\pi$
$353$	−32.6274	−1.73658	−0.868291	+	0.496055i	$0.834781\pi$
$354$	10.4142	0.553509
$355$	−1.41421	−0.0750587
$356$	2.24264	0.118860
$357$	0	0
$358$	−23.6569	−1.25030
$359$	35.4558	1.87129	0.935644	−	0.352945i	$-0.114820\pi$
$359$	35.4558	1.87129	0.935644	+	0.352945i	$0.114820\pi$
$360$	1.41421	0.0745356
$361$	−10.0000	−0.526316
$362$	−14.4142	−0.757594
$363$	−5.17157	−0.271437
$364$	0	0
$365$	18.4853	0.967564
$366$	3.24264	0.169496
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	5.07107	0.264348
$369$	7.41421	0.385969
$370$	12.8284	0.666918
$371$	0	0
$372$	1.17157	0.0607432
$373$	−30.8995	−1.59992	−0.799958	−	0.600057i	$-0.795145\pi$
$373$	−30.8995	−1.59992	−0.799958	+	0.600057i	$0.795145\pi$
$374$	7.82843	0.404798
$375$	−11.3137	−0.584237
$376$	9.00000	0.464140
$377$	5.00000	0.257513
$378$	0	0
$379$	−22.3431	−1.14769	−0.573845	−	0.818964i	$-0.694549\pi$
$379$	−22.3431	−1.14769	−0.573845	+	0.818964i	$0.694549\pi$
$380$	4.24264	0.217643
$381$	−9.89949	−0.507166
$382$	13.6569	0.698745
$383$	−10.4853	−0.535773	−0.267886	−	0.963450i	$-0.586325\pi$
$383$	−10.4853	−0.535773	−0.267886	+	0.963450i	$0.586325\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−24.2426	−1.23392
$387$	−0.828427	−0.0421113
$388$	−11.8995	−0.604105
$389$	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
$391$	−16.4437	−0.831591
$392$	0	0
$393$	−9.89949	−0.499363
$394$	−21.5563	−1.08599
$395$	−13.1716	−0.662734
$396$	−2.41421	−0.121319
$397$	−28.2426	−1.41746	−0.708729	−	0.705481i	$-0.750731\pi$
$397$	−28.2426	−1.41746	−0.708729	+	0.705481i	$0.750731\pi$
$398$	13.4142	0.672394
$399$	0	0
$400$	−3.00000	−0.150000
$401$	4.92893	0.246139	0.123070	−	0.992398i	$-0.460726\pi$
$401$	4.92893	0.246139	0.123070	+	0.992398i	$0.460726\pi$
$402$	−3.34315	−0.166741
$403$	1.17157	0.0583602
$404$	−6.82843	−0.339727
$405$	1.41421	0.0702728
$406$	0	0
$407$	−21.8995	−1.08552
$408$	−3.24264	−0.160535
$409$	−5.41421	−0.267716	−0.133858	−	0.991001i	$-0.542737\pi$
$409$	−5.41421	−0.267716	−0.133858	+	0.991001i	$0.542737\pi$
$410$	10.4853	0.517831
$411$	1.07107	0.0528319
$412$	−10.4853	−0.516573
$413$	0	0
$414$	5.07107	0.249229
$415$	5.17157	0.253863
$416$	1.00000	0.0490290
$417$	21.2132	1.03882
$418$	−7.24264	−0.354249
$419$	23.4558	1.14589	0.572946	−	0.819593i	$-0.305800\pi$
$419$	23.4558	1.14589	0.572946	+	0.819593i	$0.305800\pi$
$420$	0	0
$421$	13.4142	0.653769	0.326884	−	0.945064i	$-0.394001\pi$
$421$	13.4142	0.653769	0.326884	+	0.945064i	$0.394001\pi$
$422$	8.38478	0.408165
$423$	9.00000	0.437595
$424$	−10.3137	−0.500878
$425$	9.72792	0.471874
$426$	−1.00000	−0.0484502
$427$	0	0
$428$	2.34315	0.113260
$429$	−2.41421	−0.116559
$430$	−1.17157	−0.0564983
$431$	−2.48528	−0.119712	−0.0598559	−	0.998207i	$-0.519064\pi$
$431$	−2.48528	−0.119712	−0.0598559	+	0.998207i	$0.519064\pi$
$432$	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
$436$	−9.65685	−0.462479
$437$	15.2132	0.727746
$438$	13.0711	0.624560
$439$	−13.4142	−0.640225	−0.320113	−	0.947379i	$-0.603721\pi$
$439$	−13.4142	−0.640225	−0.320113	+	0.947379i	$0.603721\pi$
$440$	−3.41421	−0.162766
$441$	0	0
$442$	−3.24264	−0.154237
$443$	−2.72792	−0.129607	−0.0648037	−	0.997898i	$-0.520642\pi$
$443$	−2.72792	−0.129607	−0.0648037	+	0.997898i	$0.520642\pi$
$444$	9.07107	0.430494
$445$	3.17157	0.150347
$446$	−15.3848	−0.728490
$447$	−3.89949	−0.184440
$448$	0	0
$449$	33.9411	1.60178	0.800890	−	0.598811i	$-0.204360\pi$
$449$	33.9411	1.60178	0.800890	+	0.598811i	$0.204360\pi$
$450$	−3.00000	−0.141421
$451$	−17.8995	−0.842854
$452$	8.07107	0.379631
$453$	−10.4142	−0.489302
$454$	2.14214	0.100535
$455$	0	0
$456$	3.00000	0.140488
$457$	27.2132	1.27298	0.636490	−	0.771285i	$-0.280386\pi$
$457$	27.2132	1.27298	0.636490	+	0.771285i	$0.280386\pi$
$458$	−12.8284	−0.599433
$459$	−3.24264	−0.151354
$460$	7.17157	0.334376
$461$	17.4558	0.813000	0.406500	−	0.913651i	$-0.366749\pi$
$461$	17.4558	0.813000	0.406500	+	0.913651i	$0.366749\pi$
$462$	0	0
$463$	29.9411	1.39148	0.695741	−	0.718293i	$-0.255076\pi$
$463$	29.9411	1.39148	0.695741	+	0.718293i	$0.255076\pi$
$464$	5.00000	0.232119
$465$	1.65685	0.0768348
$466$	21.7279	1.00653
$467$	8.24264	0.381424	0.190712	−	0.981646i	$-0.438920\pi$
$467$	8.24264	0.381424	0.190712	+	0.981646i	$0.438920\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	12.7279	0.587095
$471$	22.0711	1.01698
$472$	10.4142	0.479353
$473$	2.00000	0.0919601
$474$	−9.31371	−0.427793
$475$	−9.00000	−0.412948
$476$	0	0
$477$	−10.3137	−0.472232
$478$	−19.4853	−0.891236
$479$	−2.85786	−0.130579	−0.0652896	−	0.997866i	$-0.520797\pi$
$479$	−2.85786	−0.130579	−0.0652896	+	0.997866i	$0.520797\pi$
$480$	1.41421	0.0645497
$481$	9.07107	0.413605
$482$	0.485281	0.0221040
$483$	0	0
$484$	−5.17157	−0.235071
$485$	−16.8284	−0.764140
$486$	1.00000	0.0453609
$487$	1.72792	0.0782996	0.0391498	−	0.999233i	$-0.487535\pi$
$487$	1.72792	0.0782996	0.0391498	+	0.999233i	$0.487535\pi$
$488$	3.24264	0.146787
$489$	−11.1421	−0.503865
$490$	0	0
$491$	30.2843	1.36671	0.683355	−	0.730086i	$-0.260520\pi$
$491$	30.2843	1.36671	0.683355	+	0.730086i	$0.260520\pi$
$492$	7.41421	0.334259
$493$	−16.2132	−0.730206
$494$	3.00000	0.134976
$495$	−3.41421	−0.153457
$496$	1.17157	0.0526052
$497$	0	0
$498$	3.65685	0.163868
$499$	−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
$501$	−10.3137	−0.460783
$502$	7.17157	0.320083
$503$	−3.79899	−0.169389	−0.0846943	−	0.996407i	$-0.526991\pi$
$503$	−3.79899	−0.169389	−0.0846943	+	0.996407i	$0.526991\pi$
$504$	0	0
$505$	−9.65685	−0.429724
$506$	−12.2426	−0.544252
$507$	1.00000	0.0444116
$508$	−9.89949	−0.439219
$509$	−20.9706	−0.929504	−0.464752	−	0.885441i	$-0.653856\pi$
$509$	−20.9706	−0.929504	−0.464752	+	0.885441i	$0.653856\pi$
$510$	−4.58579	−0.203062
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.00000	0.132453
$514$	17.7990	0.785080
$515$	−14.8284	−0.653419
$516$	−0.828427	−0.0364695
$517$	−21.7279	−0.955593
$518$	0	0
$519$	−2.31371	−0.101561
$520$	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
$523$	−32.1421	−1.40548	−0.702739	−	0.711448i	$-0.748040\pi$
$523$	−32.1421	−1.40548	−0.702739	+	0.711448i	$0.748040\pi$
$524$	−9.89949	−0.432461
$525$	0	0
$526$	23.5563	1.02711
$527$	−3.79899	−0.165487
$528$	−2.41421	−0.105065
$529$	2.71573	0.118075
$530$	−14.5858	−0.633566
$531$	10.4142	0.451938
$532$	0	0
$533$	7.41421	0.321145
$534$	2.24264	0.0970486
$535$	3.31371	0.143264
$536$	−3.34315	−0.144402
$537$	−23.6569	−1.02087
$538$	−26.3137	−1.13446
$539$	0	0
$540$	1.41421	0.0608581
$541$	−40.8701	−1.75714	−0.878571	−	0.477613i	$-0.841502\pi$
$541$	−40.8701	−1.75714	−0.878571	+	0.477613i	$0.841502\pi$
$542$	21.3848	0.918555
$543$	−14.4142	−0.618573
$544$	−3.24264	−0.139027
$545$	−13.6569	−0.584995
$546$	0	0
$547$	−14.2426	−0.608971	−0.304486	−	0.952517i	$-0.598485\pi$
$547$	−14.2426	−0.608971	−0.304486	+	0.952517i	$0.598485\pi$
$548$	1.07107	0.0457537
$549$	3.24264	0.138393
$550$	7.24264	0.308827
$551$	15.0000	0.639021
$552$	5.07107	0.215839
$553$	0	0
$554$	−13.5858	−0.577205
$555$	12.8284	0.544536
$556$	21.2132	0.899640
$557$	22.9706	0.973294	0.486647	−	0.873599i	$-0.338220\pi$
$557$	22.9706	0.973294	0.486647	+	0.873599i	$0.338220\pi$
$558$	1.17157	0.0495966
$559$	−0.828427	−0.0350387
$560$	0	0
$561$	7.82843	0.330516
$562$	−15.3137	−0.645970
$563$	16.4853	0.694772	0.347386	−	0.937722i	$-0.387069\pi$
$563$	16.4853	0.694772	0.347386	+	0.937722i	$0.387069\pi$
$564$	9.00000	0.378968
$565$	11.4142	0.480200
$566$	2.92893	0.123112
$567$	0	0
$568$	−1.00000	−0.0419591
$569$	−28.4142	−1.19119	−0.595593	−	0.803286i	$-0.703083\pi$
$569$	−28.4142	−1.19119	−0.595593	+	0.803286i	$0.703083\pi$
$570$	4.24264	0.177705
$571$	9.65685	0.404127	0.202063	−	0.979372i	$-0.435235\pi$
$571$	9.65685	0.404127	0.202063	+	0.979372i	$0.435235\pi$
$572$	−2.41421	−0.100943
$573$	13.6569	0.570523
$574$	0	0
$575$	−15.2132	−0.634434
$576$	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	$0.622246\pi$
$578$	−6.48528	−0.269752
$579$	−24.2426	−1.00749
$580$	7.07107	0.293610
$581$	0	0
$582$	−11.8995	−0.493250
$583$	24.8995	1.03123
$584$	13.0711	0.540885
$585$	1.41421	0.0584705
$586$	6.72792	0.277928
$587$	2.75736	0.113808	0.0569042	−	0.998380i	$-0.481877\pi$
$587$	2.75736	0.113808	0.0569042	+	0.998380i	$0.481877\pi$
$588$	0	0
$589$	3.51472	0.144821
$590$	14.7279	0.606339
$591$	−21.5563	−0.886710
$592$	9.07107	0.372819
$593$	−31.4142	−1.29003	−0.645014	−	0.764171i	$-0.723148\pi$
$593$	−31.4142	−1.29003	−0.645014	+	0.764171i	$0.723148\pi$
$594$	−2.41421	−0.0990564
$595$	0	0
$596$	−3.89949	−0.159730
$597$	13.4142	0.549007
$598$	5.07107	0.207371
$599$	38.8701	1.58819	0.794094	−	0.607795i	$-0.207946\pi$
$599$	38.8701	1.58819	0.794094	+	0.607795i	$0.207946\pi$
$600$	−3.00000	−0.122474
$601$	−12.1716	−0.496489	−0.248244	−	0.968697i	$-0.579854\pi$
$601$	−12.1716	−0.496489	−0.248244	+	0.968697i	$0.579854\pi$
$602$	0	0
$603$	−3.34315	−0.136143
$604$	−10.4142	−0.423748
$605$	−7.31371	−0.297345
$606$	−6.82843	−0.277386
$607$	12.9289	0.524769	0.262385	−	0.964963i	$-0.415491\pi$
$607$	12.9289	0.524769	0.262385	+	0.964963i	$0.415491\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	4.58579	0.185673
$611$	9.00000	0.364101
$612$	−3.24264	−0.131076
$613$	3.79899	0.153440	0.0767199	−	0.997053i	$-0.475555\pi$
$613$	3.79899	0.153440	0.0767199	+	0.997053i	$0.475555\pi$
$614$	25.6274	1.03424
$615$	10.4853	0.422807
$616$	0	0
$617$	10.4853	0.422122	0.211061	−	0.977473i	$-0.432308\pi$
$617$	10.4853	0.422122	0.211061	+	0.977473i	$0.432308\pi$
$618$	−10.4853	−0.421780
$619$	−7.45584	−0.299676	−0.149838	−	0.988711i	$-0.547875\pi$
$619$	−7.45584	−0.299676	−0.149838	+	0.988711i	$0.547875\pi$
$620$	1.65685	0.0665409
$621$	5.07107	0.203495
$622$	−9.41421	−0.377476
$623$	0	0
$624$	1.00000	0.0400320
$625$	−1.00000	−0.0400000
$626$	−10.1421	−0.405361
$627$	−7.24264	−0.289243
$628$	22.0711	0.880731
$629$	−29.4142	−1.17282
$630$	0	0
$631$	−8.62742	−0.343452	−0.171726	−	0.985145i	$-0.554934\pi$
$631$	−8.62742	−0.343452	−0.171726	+	0.985145i	$0.554934\pi$
$632$	−9.31371	−0.370479
$633$	8.38478	0.333265
$634$	−4.82843	−0.191761
$635$	−14.0000	−0.555573
$636$	−10.3137	−0.408965
$637$	0	0
$638$	−12.0711	−0.477898
$639$	−1.00000	−0.0395594
$640$	1.41421	0.0559017
$641$	38.8284	1.53363	0.766815	−	0.641868i	$-0.221840\pi$
$641$	38.8284	1.53363	0.766815	+	0.641868i	$0.221840\pi$
$642$	2.34315	0.0924766
$643$	13.6863	0.539735	0.269867	−	0.962898i	$-0.413020\pi$
$643$	13.6863	0.539735	0.269867	+	0.962898i	$0.413020\pi$
$644$	0	0
$645$	−1.17157	−0.0461306
$646$	−9.72792	−0.382740
$647$	−16.6274	−0.653691	−0.326846	−	0.945078i	$-0.605986\pi$
$647$	−16.6274	−0.653691	−0.326846	+	0.945078i	$0.605986\pi$
$648$	1.00000	0.0392837
$649$	−25.1421	−0.986915
$650$	−3.00000	−0.117670
$651$	0	0
$652$	−11.1421	−0.436360
$653$	−47.1127	−1.84366	−0.921831	−	0.387592i	$-0.873307\pi$
$653$	−47.1127	−1.84366	−0.921831	+	0.387592i	$0.873307\pi$
$654$	−9.65685	−0.377613
$655$	−14.0000	−0.547025
$656$	7.41421	0.289476
$657$	13.0711	0.509951
$658$	0	0
$659$	5.27208	0.205371	0.102685	−	0.994714i	$-0.467256\pi$
$659$	5.27208	0.205371	0.102685	+	0.994714i	$0.467256\pi$
$660$	−3.41421	−0.132898
$661$	17.5563	0.682863	0.341431	−	0.939907i	$-0.389088\pi$
$661$	17.5563	0.682863	0.341431	+	0.939907i	$0.389088\pi$
$662$	−5.51472	−0.214336
$663$	−3.24264	−0.125934
$664$	3.65685	0.141913
$665$	0	0
$666$	9.07107	0.351497
$667$	25.3553	0.981763
$668$	−10.3137	−0.399049
$669$	−15.3848	−0.594810
$670$	−4.72792	−0.182656
$671$	−7.82843	−0.302213
$672$	0	0
$673$	−6.82843	−0.263217	−0.131608	−	0.991302i	$-0.542014\pi$
$673$	−6.82843	−0.263217	−0.131608	+	0.991302i	$0.542014\pi$
$674$	17.3431	0.668033
$675$	−3.00000	−0.115470
$676$	1.00000	0.0384615
$677$	33.8284	1.30013	0.650066	−	0.759878i	$-0.274741\pi$
$677$	33.8284	1.30013	0.650066	+	0.759878i	$0.274741\pi$
$678$	8.07107	0.309967
$679$	0	0
$680$	−4.58579	−0.175857
$681$	2.14214	0.0820868
$682$	−2.82843	−0.108306
$683$	−45.4558	−1.73932	−0.869660	−	0.493652i	$-0.835662\pi$
$683$	−45.4558	−1.73932	−0.869660	+	0.493652i	$0.835662\pi$
$684$	3.00000	0.114708
$685$	1.51472	0.0578744
$686$	0	0
$687$	−12.8284	−0.489435
$688$	−0.828427	−0.0315835
$689$	−10.3137	−0.392921
$690$	7.17157	0.273017
$691$	−17.1421	−0.652118	−0.326059	−	0.945349i	$-0.605721\pi$
$691$	−17.1421	−0.652118	−0.326059	+	0.945349i	$0.605721\pi$
$692$	−2.31371	−0.0879540
$693$	0	0
$694$	14.2426	0.540643
$695$	30.0000	1.13796
$696$	5.00000	0.189525
$697$	−24.0416	−0.910642
$698$	2.58579	0.0978735
$699$	21.7279	0.821825
$700$	0	0
$701$	31.5147	1.19029	0.595147	−	0.803617i	$-0.297094\pi$
$701$	31.5147	1.19029	0.595147	+	0.803617i	$0.297094\pi$
$702$	1.00000	0.0377426
$703$	27.2132	1.02637
$704$	−2.41421	−0.0909891
$705$	12.7279	0.479361
$706$	−32.6274	−1.22795
$707$	0	0
$708$	10.4142	0.391390
$709$	16.0416	0.602456	0.301228	−	0.953552i	$-0.402603\pi$
$709$	16.0416	0.602456	0.301228	+	0.953552i	$0.402603\pi$
$710$	−1.41421	−0.0530745
$711$	−9.31371	−0.349291
$712$	2.24264	0.0840465
$713$	5.94113	0.222497
$714$	0	0
$715$	−3.41421	−0.127684
$716$	−23.6569	−0.884098
$717$	−19.4853	−0.727691
$718$	35.4558	1.32320
$719$	34.2843	1.27859	0.639294	−	0.768963i	$-0.279227\pi$
$719$	34.2843	1.27859	0.639294	+	0.768963i	$0.279227\pi$
$720$	1.41421	0.0527046
$721$	0	0
$722$	−10.0000	−0.372161
$723$	0.485281	0.0180478
$724$	−14.4142	−0.535700
$725$	−15.0000	−0.557086
$726$	−5.17157	−0.191935
$727$	−33.1716	−1.23027	−0.615133	−	0.788424i	$-0.710898\pi$
$727$	−33.1716	−1.23027	−0.615133	+	0.788424i	$0.710898\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	18.4853	0.684171
$731$	2.68629	0.0993561
$732$	3.24264	0.119851
$733$	53.0122	1.95805	0.979025	−	0.203740i	$-0.0653097\pi$
$733$	53.0122	1.95805	0.979025	+	0.203740i	$0.0653097\pi$
$734$	14.0000	0.516749
$735$	0	0
$736$	5.07107	0.186922
$737$	8.07107	0.297302
$738$	7.41421	0.272921
$739$	−26.9706	−0.992128	−0.496064	−	0.868286i	$-0.665222\pi$
$739$	−26.9706	−0.992128	−0.496064	+	0.868286i	$0.665222\pi$
$740$	12.8284	0.471582
$741$	3.00000	0.110208
$742$	0	0
$743$	−5.48528	−0.201235	−0.100618	−	0.994925i	$-0.532082\pi$
$743$	−5.48528	−0.201235	−0.100618	+	0.994925i	$0.532082\pi$
$744$	1.17157	0.0429519
$745$	−5.51472	−0.202044
$746$	−30.8995	−1.13131
$747$	3.65685	0.133797
$748$	7.82843	0.286236
$749$	0	0
$750$	−11.3137	−0.413118
$751$	−45.6569	−1.66604	−0.833021	−	0.553241i	$-0.813391\pi$
$751$	−45.6569	−1.66604	−0.833021	+	0.553241i	$0.813391\pi$
$752$	9.00000	0.328196
$753$	7.17157	0.261347
$754$	5.00000	0.182089
$755$	−14.7279	−0.536004
$756$	0	0
$757$	54.5563	1.98288	0.991442	−	0.130547i	$-0.0416734\pi$
$757$	54.5563	1.98288	0.991442	+	0.130547i	$0.0416734\pi$
$758$	−22.3431	−0.811540
$759$	−12.2426	−0.444380
$760$	4.24264	0.153897
$761$	−46.1421	−1.67265	−0.836326	−	0.548233i	$-0.815301\pi$
$761$	−46.1421	−1.67265	−0.836326	+	0.548233i	$0.815301\pi$
$762$	−9.89949	−0.358621
$763$	0	0
$764$	13.6569	0.494088
$765$	−4.58579	−0.165799
$766$	−10.4853	−0.378849
$767$	10.4142	0.376035
$768$	1.00000	0.0360844
$769$	−21.0711	−0.759842	−0.379921	−	0.925019i	$-0.624049\pi$
$769$	−21.0711	−0.759842	−0.379921	+	0.925019i	$0.624049\pi$
$770$	0	0
$771$	17.7990	0.641015
$772$	−24.2426	−0.872512
$773$	49.5980	1.78392	0.891958	−	0.452119i	$-0.149332\pi$
$773$	49.5980	1.78392	0.891958	+	0.452119i	$0.149332\pi$
$774$	−0.828427	−0.0297772
$775$	−3.51472	−0.126252
$776$	−11.8995	−0.427167
$777$	0	0
$778$	23.0000	0.824590
$779$	22.2426	0.796925
$780$	1.41421	0.0506370
$781$	2.41421	0.0863874
$782$	−16.4437	−0.588024
$783$	5.00000	0.178685
$784$	0	0
$785$	31.2132	1.11405
$786$	−9.89949	−0.353103
$787$	−13.8284	−0.492930	−0.246465	−	0.969152i	$-0.579269\pi$
$787$	−13.8284	−0.492930	−0.246465	+	0.969152i	$0.579269\pi$
$788$	−21.5563	−0.767913
$789$	23.5563	0.838628
$790$	−13.1716	−0.468624
$791$	0	0
$792$	−2.41421	−0.0857853
$793$	3.24264	0.115150
$794$	−28.2426	−1.00229
$795$	−14.5858	−0.517305
$796$	13.4142	0.475454
$797$	−3.02944	−0.107308	−0.0536541	−	0.998560i	$-0.517087\pi$
$797$	−3.02944	−0.107308	−0.0536541	+	0.998560i	$0.517087\pi$
$798$	0	0
$799$	−29.1838	−1.03245
$800$	−3.00000	−0.106066
$801$	2.24264	0.0792398
$802$	4.92893	0.174047
$803$	−31.5563	−1.11360
$804$	−3.34315	−0.117904
$805$	0	0
$806$	1.17157	0.0412669
$807$	−26.3137	−0.926286
$808$	−6.82843	−0.240223
$809$	−13.0416	−0.458519	−0.229260	−	0.973365i	$-0.573630\pi$
$809$	−13.0416	−0.458519	−0.229260	+	0.973365i	$0.573630\pi$
$810$	1.41421	0.0496904
$811$	−46.7696	−1.64230	−0.821151	−	0.570712i	$-0.806667\pi$
$811$	−46.7696	−1.64230	−0.821151	+	0.570712i	$0.806667\pi$
$812$	0	0
$813$	21.3848	0.749997
$814$	−21.8995	−0.767577
$815$	−15.7574	−0.551956
$816$	−3.24264	−0.113515
$817$	−2.48528	−0.0869490
$818$	−5.41421	−0.189304
$819$	0	0
$820$	10.4853	0.366162
$821$	−46.3848	−1.61884	−0.809420	−	0.587230i	$-0.800218\pi$
$821$	−46.3848	−1.61884	−0.809420	+	0.587230i	$0.800218\pi$
$822$	1.07107	0.0373578
$823$	−27.8995	−0.972515	−0.486258	−	0.873815i	$-0.661638\pi$
$823$	−27.8995	−0.972515	−0.486258	+	0.873815i	$0.661638\pi$
$824$	−10.4853	−0.365272
$825$	7.24264	0.252156
$826$	0	0
$827$	−51.5269	−1.79177	−0.895883	−	0.444290i	$-0.853456\pi$
$827$	−51.5269	−1.79177	−0.895883	+	0.444290i	$0.853456\pi$
$828$	5.07107	0.176232
$829$	−40.6985	−1.41352	−0.706758	−	0.707455i	$-0.749843\pi$
$829$	−40.6985	−1.41352	−0.706758	+	0.707455i	$0.749843\pi$
$830$	5.17157	0.179508
$831$	−13.5858	−0.471286
$832$	1.00000	0.0346688
$833$	0	0
$834$	21.2132	0.734553
$835$	−14.5858	−0.504762
$836$	−7.24264	−0.250492
$837$	1.17157	0.0404955
$838$	23.4558	0.810269
$839$	19.4853	0.672707	0.336353	−	0.941736i	$-0.390806\pi$
$839$	19.4853	0.672707	0.336353	+	0.941736i	$0.390806\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	13.4142	0.462284
$843$	−15.3137	−0.527432
$844$	8.38478	0.288616
$845$	1.41421	0.0486504
$846$	9.00000	0.309426
$847$	0	0
$848$	−10.3137	−0.354174
$849$	2.92893	0.100521
$850$	9.72792	0.333665
$851$	46.0000	1.57686
$852$	−1.00000	−0.0342594
$853$	41.6985	1.42773	0.713864	−	0.700284i	$-0.246943\pi$
$853$	41.6985	1.42773	0.713864	+	0.700284i	$0.246943\pi$
$854$	0	0
$855$	4.24264	0.145095
$856$	2.34315	0.0800871
$857$	−14.6152	−0.499247	−0.249623	−	0.968343i	$-0.580307\pi$
$857$	−14.6152	−0.499247	−0.249623	+	0.968343i	$0.580307\pi$
$858$	−2.41421	−0.0824199
$859$	39.7990	1.35792	0.678962	−	0.734173i	$-0.262430\pi$
$859$	39.7990	1.35792	0.678962	+	0.734173i	$0.262430\pi$
$860$	−1.17157	−0.0399503
$861$	0	0
$862$	−2.48528	−0.0846490
$863$	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
$865$	−3.27208	−0.111254
$866$	−19.0000	−0.645646
$867$	−6.48528	−0.220252
$868$	0	0
$869$	22.4853	0.762761
$870$	7.07107	0.239732
$871$	−3.34315	−0.113278
$872$	−9.65685	−0.327022
$873$	−11.8995	−0.402737
$874$	15.2132	0.514594
$875$	0	0
$876$	13.0711	0.441630
$877$	20.5858	0.695133	0.347566	−	0.937655i	$-0.387008\pi$
$877$	20.5858	0.695133	0.347566	+	0.937655i	$0.387008\pi$
$878$	−13.4142	−0.452708
$879$	6.72792	0.226927
$880$	−3.41421	−0.115093
$881$	21.1127	0.711305	0.355652	−	0.934618i	$-0.384259\pi$
$881$	21.1127	0.711305	0.355652	+	0.934618i	$0.384259\pi$
$882$	0	0
$883$	−15.0711	−0.507182	−0.253591	−	0.967312i	$-0.581612\pi$
$883$	−15.0711	−0.507182	−0.253591	+	0.967312i	$0.581612\pi$
$884$	−3.24264	−0.109062
$885$	14.7279	0.495074
$886$	−2.72792	−0.0916463
$887$	18.6863	0.627424	0.313712	−	0.949518i	$-0.398427\pi$
$887$	18.6863	0.627424	0.313712	+	0.949518i	$0.398427\pi$
$888$	9.07107	0.304405
$889$	0	0
$890$	3.17157	0.106311
$891$	−2.41421	−0.0808792
$892$	−15.3848	−0.515120
$893$	27.0000	0.903521
$894$	−3.89949	−0.130419
$895$	−33.4558	−1.11831
$896$	0	0
$897$	5.07107	0.169318
$898$	33.9411	1.13263
$899$	5.85786	0.195371
$900$	−3.00000	−0.100000
$901$	33.4437	1.11417
$902$	−17.8995	−0.595988
$903$	0	0
$904$	8.07107	0.268440
$905$	−20.3848	−0.677613
$906$	−10.4142	−0.345989
$907$	−51.8995	−1.72329	−0.861647	−	0.507508i	$-0.830567\pi$
$907$	−51.8995	−1.72329	−0.861647	+	0.507508i	$0.830567\pi$
$908$	2.14214	0.0710893
$909$	−6.82843	−0.226485
$910$	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
$913$	−8.82843	−0.292178
$914$	27.2132	0.900133
$915$	4.58579	0.151601
$916$	−12.8284	−0.423863
$917$	0	0
$918$	−3.24264	−0.107023
$919$	13.7990	0.455187	0.227593	−	0.973756i	$-0.426914\pi$
$919$	13.7990	0.455187	0.227593	+	0.973756i	$0.426914\pi$
$920$	7.17157	0.236440
$921$	25.6274	0.844452
$922$	17.4558	0.574878
$923$	−1.00000	−0.0329154
$924$	0	0
$925$	−27.2132	−0.894765
$926$	29.9411	0.983926
$927$	−10.4853	−0.344382
$928$	5.00000	0.164133
$929$	−38.2843	−1.25607	−0.628033	−	0.778187i	$-0.716140\pi$
$929$	−38.2843	−1.25607	−0.628033	+	0.778187i	$0.716140\pi$
$930$	1.65685	0.0543304
$931$	0	0
$932$	21.7279	0.711722
$933$	−9.41421	−0.308208
$934$	8.24264	0.269707
$935$	11.0711	0.362063
$936$	1.00000	0.0326860
$937$	−38.5980	−1.26094	−0.630471	−	0.776213i	$-0.717138\pi$
$937$	−38.5980	−1.26094	−0.630471	+	0.776213i	$0.717138\pi$
$938$	0	0
$939$	−10.1421	−0.330976
$940$	12.7279	0.415139
$941$	12.9706	0.422828	0.211414	−	0.977397i	$-0.432193\pi$
$941$	12.9706	0.422828	0.211414	+	0.977397i	$0.432193\pi$
$942$	22.0711	0.719114
$943$	37.5980	1.22436
$944$	10.4142	0.338954
$945$	0	0
$946$	2.00000	0.0650256
$947$	8.75736	0.284576	0.142288	−	0.989825i	$-0.454554\pi$
$947$	8.75736	0.284576	0.142288	+	0.989825i	$0.454554\pi$
$948$	−9.31371	−0.302495
$949$	13.0711	0.424305
$950$	−9.00000	−0.291999
$951$	−4.82843	−0.156572
$952$	0	0
$953$	32.2132	1.04349	0.521744	−	0.853102i	$-0.325282\pi$
$953$	32.2132	1.04349	0.521744	+	0.853102i	$0.325282\pi$
$954$	−10.3137	−0.333919
$955$	19.3137	0.624977
$956$	−19.4853	−0.630199
$957$	−12.0711	−0.390202
$958$	−2.85786	−0.0923334
$959$	0	0
$960$	1.41421	0.0456435
$961$	−29.6274	−0.955723
$962$	9.07107	0.292463
$963$	2.34315	0.0755068
$964$	0.485281	0.0156299
$965$	−34.2843	−1.10365
$966$	0	0
$967$	−27.3848	−0.880635	−0.440318	−	0.897842i	$-0.645134\pi$
$967$	−27.3848	−0.880635	−0.440318	+	0.897842i	$0.645134\pi$
$968$	−5.17157	−0.166221
$969$	−9.72792	−0.312506
$970$	−16.8284	−0.540328
$971$	26.4437	0.848617	0.424309	−	0.905518i	$-0.360517\pi$
$971$	26.4437	0.848617	0.424309	+	0.905518i	$0.360517\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	1.72792	0.0553662
$975$	−3.00000	−0.0960769
$976$	3.24264	0.103794
$977$	−14.4853	−0.463425	−0.231713	−	0.972784i	$-0.574433\pi$
$977$	−14.4853	−0.463425	−0.231713	+	0.972784i	$0.574433\pi$
$978$	−11.1421	−0.356286
$979$	−5.41421	−0.173039
$980$	0	0
$981$	−9.65685	−0.308320
$982$	30.2843	0.966410
$983$	−27.8284	−0.887589	−0.443794	−	0.896129i	$-0.646368\pi$
$983$	−27.8284	−0.887589	−0.443794	+	0.896129i	$0.646368\pi$
$984$	7.41421	0.236356
$985$	−30.4853	−0.971342
$986$	−16.2132	−0.516334
$987$	0	0
$988$	3.00000	0.0954427
$989$	−4.20101	−0.133584
$990$	−3.41421	−0.108511
$991$	15.3137	0.486456	0.243228	−	0.969969i	$-0.421794\pi$
$991$	15.3137	0.486456	0.243228	+	0.969969i	$0.421794\pi$
$992$	1.17157	0.0371975
$993$	−5.51472	−0.175004
$994$	0	0
$995$	18.9706	0.601407
$996$	3.65685	0.115872
$997$	−52.6985	−1.66898	−0.834489	−	0.551025i	$-0.814237\pi$
$997$	−52.6985	−1.66898	−0.834489	+	0.551025i	$0.814237\pi$
$998$	−30.0000	−0.949633
$999$	9.07107	0.286996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bs.1.2		2
7.2	even	3		546.2.i.h.235.1	yes	4
7.4	even	3		546.2.i.h.79.1	✓	4
7.6	odd	2		3822.2.a.bp.1.1		2
21.2	odd	6		1638.2.j.n.235.2		4
21.11	odd	6		1638.2.j.n.1171.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.h.79.1	✓	4	7.4	even	3
546.2.i.h.235.1	yes	4	7.2	even	3
1638.2.j.n.235.2		4	21.2	odd	6
1638.2.j.n.1171.2		4	21.11	odd	6
3822.2.a.bp.1.1		2	7.6	odd	2
3822.2.a.bs.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.41421 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.41421 q^{10} -2.41421 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.41421 q^{15} +1.00000 q^{16} -3.24264 q^{17} +1.00000 q^{18} +3.00000 q^{19} +1.41421 q^{20} -2.41421 q^{22} +5.07107 q^{23} +1.00000 q^{24} -3.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} +5.00000 q^{29} +1.41421 q^{30} +1.17157 q^{31} +1.00000 q^{32} -2.41421 q^{33} -3.24264 q^{34} +1.00000 q^{36} +9.07107 q^{37} +3.00000 q^{38} +1.00000 q^{39} +1.41421 q^{40} +7.41421 q^{41} -0.828427 q^{43} -2.41421 q^{44} +1.41421 q^{45} +5.07107 q^{46} +9.00000 q^{47} +1.00000 q^{48} -3.00000 q^{50} -3.24264 q^{51} +1.00000 q^{52} -10.3137 q^{53} +1.00000 q^{54} -3.41421 q^{55} +3.00000 q^{57} +5.00000 q^{58} +10.4142 q^{59} +1.41421 q^{60} +3.24264 q^{61} +1.17157 q^{62} +1.00000 q^{64} +1.41421 q^{65} -2.41421 q^{66} -3.34315 q^{67} -3.24264 q^{68} +5.07107 q^{69} -1.00000 q^{71} +1.00000 q^{72} +13.0711 q^{73} +9.07107 q^{74} -3.00000 q^{75} +3.00000 q^{76} +1.00000 q^{78} -9.31371 q^{79} +1.41421 q^{80} +1.00000 q^{81} +7.41421 q^{82} +3.65685 q^{83} -4.58579 q^{85} -0.828427 q^{86} +5.00000 q^{87} -2.41421 q^{88} +2.24264 q^{89} +1.41421 q^{90} +5.07107 q^{92} +1.17157 q^{93} +9.00000 q^{94} +4.24264 q^{95} +1.00000 q^{96} -11.8995 q^{97} -2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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