LMFDB - Embedded newform 1122.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(1,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, 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("1122.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.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:	$8.95921510679$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	1122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.00000 q^{12} +5.65685 q^{13} +4.82843 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +2.82843 q^{19} +4.82843 q^{21} -1.00000 q^{22} +4.82843 q^{23} +1.00000 q^{24} -5.00000 q^{25} -5.65685 q^{26} -1.00000 q^{27} -4.82843 q^{28} -6.48528 q^{29} -6.82843 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -8.82843 q^{37} -2.82843 q^{38} -5.65685 q^{39} +11.6569 q^{41} -4.82843 q^{42} -6.82843 q^{43} +1.00000 q^{44} -4.82843 q^{46} -8.82843 q^{47} -1.00000 q^{48} +16.3137 q^{49} +5.00000 q^{50} -1.00000 q^{51} +5.65685 q^{52} -4.00000 q^{53} +1.00000 q^{54} +4.82843 q^{56} -2.82843 q^{57} +6.48528 q^{58} -1.17157 q^{59} -5.65685 q^{61} +6.82843 q^{62} -4.82843 q^{63} +1.00000 q^{64} +1.00000 q^{66} -9.65685 q^{67} +1.00000 q^{68} -4.82843 q^{69} -3.17157 q^{71} -1.00000 q^{72} +6.48528 q^{73} +8.82843 q^{74} +5.00000 q^{75} +2.82843 q^{76} -4.82843 q^{77} +5.65685 q^{78} -16.8284 q^{79} +1.00000 q^{81} -11.6569 q^{82} +9.65685 q^{83} +4.82843 q^{84} +6.82843 q^{86} +6.48528 q^{87} -1.00000 q^{88} +2.00000 q^{89} -27.3137 q^{91} +4.82843 q^{92} +6.82843 q^{93} +8.82843 q^{94} +1.00000 q^{96} -15.6569 q^{97} -16.3137 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 2 q^{24} - 10 q^{25} - 2 q^{27} - 4 q^{28} + 4 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{36} - 12 q^{37} + 12 q^{41} - 4 q^{42} - 8 q^{43} + 2 q^{44} - 4 q^{46} - 12 q^{47} - 2 q^{48} + 10 q^{49} + 10 q^{50} - 2 q^{51} - 8 q^{53} + 2 q^{54} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 8 q^{62} - 4 q^{63} + 2 q^{64} + 2 q^{66} - 8 q^{67} + 2 q^{68} - 4 q^{69} - 12 q^{71} - 2 q^{72} - 4 q^{73} + 12 q^{74} + 10 q^{75} - 4 q^{77} - 28 q^{79} + 2 q^{81} - 12 q^{82} + 8 q^{83} + 4 q^{84} + 8 q^{86} - 4 q^{87} - 2 q^{88} + 4 q^{89} - 32 q^{91} + 4 q^{92} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 20 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 2 * q^24 - 10 * q^25 - 2 * q^27 - 4 * q^28 + 4 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^36 - 12 * q^37 + 12 * q^41 - 4 * q^42 - 8 * q^43 + 2 * q^44 - 4 * q^46 - 12 * q^47 - 2 * q^48 + 10 * q^49 + 10 * q^50 - 2 * q^51 - 8 * q^53 + 2 * q^54 + 4 * q^56 - 4 * q^58 - 8 * q^59 + 8 * q^62 - 4 * q^63 + 2 * q^64 + 2 * q^66 - 8 * q^67 + 2 * q^68 - 4 * q^69 - 12 * q^71 - 2 * q^72 - 4 * q^73 + 12 * q^74 + 10 * q^75 - 4 * q^77 - 28 * q^79 + 2 * q^81 - 12 * q^82 + 8 * q^83 + 4 * q^84 + 8 * q^86 - 4 * q^87 - 2 * q^88 + 4 * q^89 - 32 * q^91 + 4 * q^92 + 8 * q^93 + 12 * q^94 + 2 * q^96 - 20 * q^97 - 10 * q^98 + 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
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	1.00000	0.408248
$7$	−4.82843	−1.82497	−0.912487	−	0.409106i	$-0.865841\pi$
$7$	−4.82843	−1.82497	−0.912487	+	0.409106i	$0.865841\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	5.65685	1.56893	0.784465	−	0.620174i	$-0.212938\pi$
$13$	5.65685	1.56893	0.784465	+	0.620174i	$0.212938\pi$
$14$	4.82843	1.29045
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	0	0
$21$	4.82843	1.05365
$22$	−1.00000	−0.213201
$23$	4.82843	1.00680	0.503398	−	0.864054i	$-0.332083\pi$
$23$	4.82843	1.00680	0.503398	+	0.864054i	$0.332083\pi$
$24$	1.00000	0.204124
$25$	−5.00000	−1.00000
$26$	−5.65685	−1.10940
$27$	−1.00000	−0.192450
$28$	−4.82843	−0.912487
$29$	−6.48528	−1.20429	−0.602143	−	0.798388i	$-0.705686\pi$
$29$	−6.48528	−1.20429	−0.602143	+	0.798388i	$0.705686\pi$
$30$	0	0
$31$	−6.82843	−1.22642	−0.613211	−	0.789919i	$-0.710122\pi$
$31$	−6.82843	−1.22642	−0.613211	+	0.789919i	$0.710122\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.82843	−1.45138	−0.725692	−	0.688019i	$-0.758480\pi$
$37$	−8.82843	−1.45138	−0.725692	+	0.688019i	$0.758480\pi$
$38$	−2.82843	−0.458831
$39$	−5.65685	−0.905822
$40$	0	0
$41$	11.6569	1.82049	0.910247	−	0.414065i	$-0.135891\pi$
$41$	11.6569	1.82049	0.910247	+	0.414065i	$0.135891\pi$
$42$	−4.82843	−0.745042
$43$	−6.82843	−1.04133	−0.520663	−	0.853762i	$-0.674315\pi$
$43$	−6.82843	−1.04133	−0.520663	+	0.853762i	$0.674315\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−4.82843	−0.711913
$47$	−8.82843	−1.28776	−0.643879	−	0.765127i	$-0.722676\pi$
$47$	−8.82843	−1.28776	−0.643879	+	0.765127i	$0.722676\pi$
$48$	−1.00000	−0.144338
$49$	16.3137	2.33053
$50$	5.00000	0.707107
$51$	−1.00000	−0.140028
$52$	5.65685	0.784465
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.82843	0.645226
$57$	−2.82843	−0.374634
$58$	6.48528	0.851559
$59$	−1.17157	−0.152526	−0.0762629	−	0.997088i	$-0.524299\pi$
$59$	−1.17157	−0.152526	−0.0762629	+	0.997088i	$0.524299\pi$
$60$	0	0
$61$	−5.65685	−0.724286	−0.362143	−	0.932123i	$-0.617955\pi$
$61$	−5.65685	−0.724286	−0.362143	+	0.932123i	$0.617955\pi$
$62$	6.82843	0.867211
$63$	−4.82843	−0.608325
$64$	1.00000	0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	−9.65685	−1.17977	−0.589886	−	0.807486i	$-0.700827\pi$
$67$	−9.65685	−1.17977	−0.589886	+	0.807486i	$0.700827\pi$
$68$	1.00000	0.121268
$69$	−4.82843	−0.581274
$70$	0	0
$71$	−3.17157	−0.376396	−0.188198	−	0.982131i	$-0.560265\pi$
$71$	−3.17157	−0.376396	−0.188198	+	0.982131i	$0.560265\pi$
$72$	−1.00000	−0.117851
$73$	6.48528	0.759045	0.379522	−	0.925183i	$-0.376088\pi$
$73$	6.48528	0.759045	0.379522	+	0.925183i	$0.376088\pi$
$74$	8.82843	1.02628
$75$	5.00000	0.577350
$76$	2.82843	0.324443
$77$	−4.82843	−0.550250
$78$	5.65685	0.640513
$79$	−16.8284	−1.89335	−0.946673	−	0.322196i	$-0.895579\pi$
$79$	−16.8284	−1.89335	−0.946673	+	0.322196i	$0.895579\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−11.6569	−1.28728
$83$	9.65685	1.05998	0.529989	−	0.848005i	$-0.322196\pi$
$83$	9.65685	1.05998	0.529989	+	0.848005i	$0.322196\pi$
$84$	4.82843	0.526825
$85$	0	0
$86$	6.82843	0.736328
$87$	6.48528	0.695295
$88$	−1.00000	−0.106600
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	−27.3137	−2.86325
$92$	4.82843	0.503398
$93$	6.82843	0.708075
$94$	8.82843	0.910583
$95$	0	0
$96$	1.00000	0.102062
$97$	−15.6569	−1.58971	−0.794856	−	0.606798i	$-0.792454\pi$
$97$	−15.6569	−1.58971	−0.794856	+	0.606798i	$0.792454\pi$
$98$	−16.3137	−1.64793
$99$	1.00000	0.100504
$100$	−5.00000	−0.500000
$101$	17.3137	1.72278	0.861389	−	0.507946i	$-0.169595\pi$
$101$	17.3137	1.72278	0.861389	+	0.507946i	$0.169595\pi$
$102$	1.00000	0.0990148
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	−5.65685	−0.554700
$105$	0	0
$106$	4.00000	0.388514
$107$	−9.65685	−0.933563	−0.466782	−	0.884373i	$-0.654587\pi$
$107$	−9.65685	−0.933563	−0.466782	+	0.884373i	$0.654587\pi$
$108$	−1.00000	−0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	8.82843	0.837957
$112$	−4.82843	−0.456243
$113$	−1.51472	−0.142493	−0.0712464	−	0.997459i	$-0.522698\pi$
$113$	−1.51472	−0.142493	−0.0712464	+	0.997459i	$0.522698\pi$
$114$	2.82843	0.264906
$115$	0	0
$116$	−6.48528	−0.602143
$117$	5.65685	0.522976
$118$	1.17157	0.107852
$119$	−4.82843	−0.442621
$120$	0	0
$121$	1.00000	0.0909091
$122$	5.65685	0.512148
$123$	−11.6569	−1.05106
$124$	−6.82843	−0.613211
$125$	0	0
$126$	4.82843	0.430150
$127$	6.48528	0.575476	0.287738	−	0.957709i	$-0.407097\pi$
$127$	6.48528	0.575476	0.287738	+	0.957709i	$0.407097\pi$
$128$	−1.00000	−0.0883883
$129$	6.82843	0.601209
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	−1.00000	−0.0870388
$133$	−13.6569	−1.18420
$134$	9.65685	0.834225
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	−18.9706	−1.62076	−0.810382	−	0.585901i	$-0.800741\pi$
$137$	−18.9706	−1.62076	−0.810382	+	0.585901i	$0.800741\pi$
$138$	4.82843	0.411023
$139$	−17.6569	−1.49763	−0.748817	−	0.662776i	$-0.769378\pi$
$139$	−17.6569	−1.49763	−0.748817	+	0.662776i	$0.769378\pi$
$140$	0	0
$141$	8.82843	0.743488
$142$	3.17157	0.266152
$143$	5.65685	0.473050
$144$	1.00000	0.0833333
$145$	0	0
$146$	−6.48528	−0.536726
$147$	−16.3137	−1.34553
$148$	−8.82843	−0.725692
$149$	4.34315	0.355804	0.177902	−	0.984048i	$-0.443069\pi$
$149$	4.34315	0.355804	0.177902	+	0.984048i	$0.443069\pi$
$150$	−5.00000	−0.408248
$151$	0.828427	0.0674164	0.0337082	−	0.999432i	$-0.489268\pi$
$151$	0.828427	0.0674164	0.0337082	+	0.999432i	$0.489268\pi$
$152$	−2.82843	−0.229416
$153$	1.00000	0.0808452
$154$	4.82843	0.389086
$155$	0	0
$156$	−5.65685	−0.452911
$157$	−22.9706	−1.83325	−0.916625	−	0.399748i	$-0.869098\pi$
$157$	−22.9706	−1.83325	−0.916625	+	0.399748i	$0.869098\pi$
$158$	16.8284	1.33880
$159$	4.00000	0.317221
$160$	0	0
$161$	−23.3137	−1.83738
$162$	−1.00000	−0.0785674
$163$	9.65685	0.756383	0.378192	−	0.925727i	$-0.376546\pi$
$163$	9.65685	0.756383	0.378192	+	0.925727i	$0.376546\pi$
$164$	11.6569	0.910247
$165$	0	0
$166$	−9.65685	−0.749517
$167$	14.1421	1.09435	0.547176	−	0.837018i	$-0.315703\pi$
$167$	14.1421	1.09435	0.547176	+	0.837018i	$0.315703\pi$
$168$	−4.82843	−0.372521
$169$	19.0000	1.46154
$170$	0	0
$171$	2.82843	0.216295
$172$	−6.82843	−0.520663
$173$	−16.8284	−1.27944	−0.639721	−	0.768607i	$-0.720950\pi$
$173$	−16.8284	−1.27944	−0.639721	+	0.768607i	$0.720950\pi$
$174$	−6.48528	−0.491648
$175$	24.1421	1.82497
$176$	1.00000	0.0753778
$177$	1.17157	0.0880608
$178$	−2.00000	−0.149906
$179$	4.48528	0.335246	0.167623	−	0.985851i	$-0.446391\pi$
$179$	4.48528	0.335246	0.167623	+	0.985851i	$0.446391\pi$
$180$	0	0
$181$	8.82843	0.656212	0.328106	−	0.944641i	$-0.393590\pi$
$181$	8.82843	0.656212	0.328106	+	0.944641i	$0.393590\pi$
$182$	27.3137	2.02463
$183$	5.65685	0.418167
$184$	−4.82843	−0.355956
$185$	0	0
$186$	−6.82843	−0.500685
$187$	1.00000	0.0731272
$188$	−8.82843	−0.643879
$189$	4.82843	0.351216
$190$	0	0
$191$	24.1421	1.74686	0.873432	−	0.486946i	$-0.161889\pi$
$191$	24.1421	1.74686	0.873432	+	0.486946i	$0.161889\pi$
$192$	−1.00000	−0.0721688
$193$	26.4853	1.90645	0.953226	−	0.302258i	$-0.0977404\pi$
$193$	26.4853	1.90645	0.953226	+	0.302258i	$0.0977404\pi$
$194$	15.6569	1.12410
$195$	0	0
$196$	16.3137	1.16526
$197$	−20.1421	−1.43507	−0.717534	−	0.696524i	$-0.754729\pi$
$197$	−20.1421	−1.43507	−0.717534	+	0.696524i	$0.754729\pi$
$198$	−1.00000	−0.0710669
$199$	6.14214	0.435404	0.217702	−	0.976015i	$-0.430144\pi$
$199$	6.14214	0.435404	0.217702	+	0.976015i	$0.430144\pi$
$200$	5.00000	0.353553
$201$	9.65685	0.681142
$202$	−17.3137	−1.21819
$203$	31.3137	2.19779
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	12.0000	0.836080
$207$	4.82843	0.335599
$208$	5.65685	0.392232
$209$	2.82843	0.195646
$210$	0	0
$211$	−16.9706	−1.16830	−0.584151	−	0.811645i	$-0.698572\pi$
$211$	−16.9706	−1.16830	−0.584151	+	0.811645i	$0.698572\pi$
$212$	−4.00000	−0.274721
$213$	3.17157	0.217313
$214$	9.65685	0.660129
$215$	0	0
$216$	1.00000	0.0680414
$217$	32.9706	2.23819
$218$	−4.00000	−0.270914
$219$	−6.48528	−0.438235
$220$	0	0
$221$	5.65685	0.380521
$222$	−8.82843	−0.592525
$223$	−2.34315	−0.156909	−0.0784543	−	0.996918i	$-0.524998\pi$
$223$	−2.34315	−0.156909	−0.0784543	+	0.996918i	$0.524998\pi$
$224$	4.82843	0.322613
$225$	−5.00000	−0.333333
$226$	1.51472	0.100758
$227$	−12.9706	−0.860886	−0.430443	−	0.902618i	$-0.641643\pi$
$227$	−12.9706	−0.860886	−0.430443	+	0.902618i	$0.641643\pi$
$228$	−2.82843	−0.187317
$229$	12.3431	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$229$	12.3431	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$230$	0	0
$231$	4.82843	0.317687
$232$	6.48528	0.425780
$233$	−5.31371	−0.348113	−0.174056	−	0.984736i	$-0.555687\pi$
$233$	−5.31371	−0.348113	−0.174056	+	0.984736i	$0.555687\pi$
$234$	−5.65685	−0.369800
$235$	0	0
$236$	−1.17157	−0.0762629
$237$	16.8284	1.09312
$238$	4.82843	0.312980
$239$	0.686292	0.0443925	0.0221963	−	0.999754i	$-0.492934\pi$
$239$	0.686292	0.0443925	0.0221963	+	0.999754i	$0.492934\pi$
$240$	0	0
$241$	−8.82843	−0.568689	−0.284344	−	0.958722i	$-0.591776\pi$
$241$	−8.82843	−0.568689	−0.284344	+	0.958722i	$0.591776\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−5.65685	−0.362143
$245$	0	0
$246$	11.6569	0.743214
$247$	16.0000	1.01806
$248$	6.82843	0.433606
$249$	−9.65685	−0.611978
$250$	0	0
$251$	12.4853	0.788064	0.394032	−	0.919097i	$-0.371080\pi$
$251$	12.4853	0.788064	0.394032	+	0.919097i	$0.371080\pi$
$252$	−4.82843	−0.304162
$253$	4.82843	0.303561
$254$	−6.48528	−0.406923
$255$	0	0
$256$	1.00000	0.0625000
$257$	−20.6274	−1.28670	−0.643351	−	0.765571i	$-0.722457\pi$
$257$	−20.6274	−1.28670	−0.643351	+	0.765571i	$0.722457\pi$
$258$	−6.82843	−0.425119
$259$	42.6274	2.64874
$260$	0	0
$261$	−6.48528	−0.401429
$262$	4.00000	0.247121
$263$	−24.9706	−1.53975	−0.769875	−	0.638194i	$-0.779682\pi$
$263$	−24.9706	−1.53975	−0.769875	+	0.638194i	$0.779682\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	13.6569	0.837355
$267$	−2.00000	−0.122398
$268$	−9.65685	−0.589886
$269$	−11.3137	−0.689809	−0.344904	−	0.938638i	$-0.612089\pi$
$269$	−11.3137	−0.689809	−0.344904	+	0.938638i	$0.612089\pi$
$270$	0	0
$271$	4.82843	0.293306	0.146653	−	0.989188i	$-0.453150\pi$
$271$	4.82843	0.293306	0.146653	+	0.989188i	$0.453150\pi$
$272$	1.00000	0.0606339
$273$	27.3137	1.65310
$274$	18.9706	1.14605
$275$	−5.00000	−0.301511
$276$	−4.82843	−0.290637
$277$	−2.34315	−0.140786	−0.0703930	−	0.997519i	$-0.522425\pi$
$277$	−2.34315	−0.140786	−0.0703930	+	0.997519i	$0.522425\pi$
$278$	17.6569	1.05899
$279$	−6.82843	−0.408807
$280$	0	0
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	−8.82843	−0.525725
$283$	−16.9706	−1.00880	−0.504398	−	0.863472i	$-0.668285\pi$
$283$	−16.9706	−1.00880	−0.504398	+	0.863472i	$0.668285\pi$
$284$	−3.17157	−0.188198
$285$	0	0
$286$	−5.65685	−0.334497
$287$	−56.2843	−3.32236
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	15.6569	0.917821
$292$	6.48528	0.379522
$293$	16.6274	0.971384	0.485692	−	0.874130i	$-0.338568\pi$
$293$	16.6274	0.971384	0.485692	+	0.874130i	$0.338568\pi$
$294$	16.3137	0.951435
$295$	0	0
$296$	8.82843	0.513142
$297$	−1.00000	−0.0580259
$298$	−4.34315	−0.251592
$299$	27.3137	1.57959
$300$	5.00000	0.288675
$301$	32.9706	1.90039
$302$	−0.828427	−0.0476706
$303$	−17.3137	−0.994647
$304$	2.82843	0.162221
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	−2.82843	−0.161427	−0.0807134	−	0.996737i	$-0.525720\pi$
$307$	−2.82843	−0.161427	−0.0807134	+	0.996737i	$0.525720\pi$
$308$	−4.82843	−0.275125
$309$	12.0000	0.682656
$310$	0	0
$311$	−24.8284	−1.40789	−0.703945	−	0.710254i	$-0.748580\pi$
$311$	−24.8284	−1.40789	−0.703945	+	0.710254i	$0.748580\pi$
$312$	5.65685	0.320256
$313$	−3.65685	−0.206698	−0.103349	−	0.994645i	$-0.532956\pi$
$313$	−3.65685	−0.206698	−0.103349	+	0.994645i	$0.532956\pi$
$314$	22.9706	1.29630
$315$	0	0
$316$	−16.8284	−0.946673
$317$	12.9706	0.728499	0.364250	−	0.931301i	$-0.381325\pi$
$317$	12.9706	0.728499	0.364250	+	0.931301i	$0.381325\pi$
$318$	−4.00000	−0.224309
$319$	−6.48528	−0.363106
$320$	0	0
$321$	9.65685	0.538993
$322$	23.3137	1.29922
$323$	2.82843	0.157378
$324$	1.00000	0.0555556
$325$	−28.2843	−1.56893
$326$	−9.65685	−0.534844
$327$	−4.00000	−0.221201
$328$	−11.6569	−0.643642
$329$	42.6274	2.35013
$330$	0	0
$331$	15.3137	0.841718	0.420859	−	0.907126i	$-0.361729\pi$
$331$	15.3137	0.841718	0.420859	+	0.907126i	$0.361729\pi$
$332$	9.65685	0.529989
$333$	−8.82843	−0.483795
$334$	−14.1421	−0.773823
$335$	0	0
$336$	4.82843	0.263412
$337$	12.1421	0.661424	0.330712	−	0.943732i	$-0.392711\pi$
$337$	12.1421	0.661424	0.330712	+	0.943732i	$0.392711\pi$
$338$	−19.0000	−1.03346
$339$	1.51472	0.0822682
$340$	0	0
$341$	−6.82843	−0.369780
$342$	−2.82843	−0.152944
$343$	−44.9706	−2.42818
$344$	6.82843	0.368164
$345$	0	0
$346$	16.8284	0.904702
$347$	14.3431	0.769980	0.384990	−	0.922921i	$-0.374205\pi$
$347$	14.3431	0.769980	0.384990	+	0.922921i	$0.374205\pi$
$348$	6.48528	0.347648
$349$	−28.2843	−1.51402	−0.757011	−	0.653402i	$-0.773341\pi$
$349$	−28.2843	−1.51402	−0.757011	+	0.653402i	$0.773341\pi$
$350$	−24.1421	−1.29045
$351$	−5.65685	−0.301941
$352$	−1.00000	−0.0533002
$353$	−11.6569	−0.620432	−0.310216	−	0.950666i	$-0.600401\pi$
$353$	−11.6569	−0.620432	−0.310216	+	0.950666i	$0.600401\pi$
$354$	−1.17157	−0.0622684
$355$	0	0
$356$	2.00000	0.106000
$357$	4.82843	0.255547
$358$	−4.48528	−0.237054
$359$	−6.34315	−0.334778	−0.167389	−	0.985891i	$-0.553534\pi$
$359$	−6.34315	−0.334778	−0.167389	+	0.985891i	$0.553534\pi$
$360$	0	0
$361$	−11.0000	−0.578947
$362$	−8.82843	−0.464012
$363$	−1.00000	−0.0524864
$364$	−27.3137	−1.43163
$365$	0	0
$366$	−5.65685	−0.295689
$367$	27.1127	1.41527	0.707636	−	0.706577i	$-0.249762\pi$
$367$	27.1127	1.41527	0.707636	+	0.706577i	$0.249762\pi$
$368$	4.82843	0.251699
$369$	11.6569	0.606832
$370$	0	0
$371$	19.3137	1.00272
$372$	6.82843	0.354037
$373$	18.3431	0.949772	0.474886	−	0.880047i	$-0.342489\pi$
$373$	18.3431	0.949772	0.474886	+	0.880047i	$0.342489\pi$
$374$	−1.00000	−0.0517088
$375$	0	0
$376$	8.82843	0.455291
$377$	−36.6863	−1.88944
$378$	−4.82843	−0.248347
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	−6.48528	−0.332251
$382$	−24.1421	−1.23522
$383$	−16.1421	−0.824825	−0.412412	−	0.910997i	$-0.635314\pi$
$383$	−16.1421	−0.824825	−0.412412	+	0.910997i	$0.635314\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−26.4853	−1.34807
$387$	−6.82843	−0.347108
$388$	−15.6569	−0.794856
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	4.82843	0.244184
$392$	−16.3137	−0.823967
$393$	4.00000	0.201773
$394$	20.1421	1.01475
$395$	0	0
$396$	1.00000	0.0502519
$397$	25.7990	1.29481	0.647407	−	0.762144i	$-0.275853\pi$
$397$	25.7990	1.29481	0.647407	+	0.762144i	$0.275853\pi$
$398$	−6.14214	−0.307877
$399$	13.6569	0.683698
$400$	−5.00000	−0.250000
$401$	−22.4853	−1.12286	−0.561431	−	0.827524i	$-0.689749\pi$
$401$	−22.4853	−1.12286	−0.561431	+	0.827524i	$0.689749\pi$
$402$	−9.65685	−0.481640
$403$	−38.6274	−1.92417
$404$	17.3137	0.861389
$405$	0	0
$406$	−31.3137	−1.55407
$407$	−8.82843	−0.437609
$408$	1.00000	0.0495074
$409$	22.9706	1.13582	0.567911	−	0.823090i	$-0.307752\pi$
$409$	22.9706	1.13582	0.567911	+	0.823090i	$0.307752\pi$
$410$	0	0
$411$	18.9706	0.935749
$412$	−12.0000	−0.591198
$413$	5.65685	0.278356
$414$	−4.82843	−0.237304
$415$	0	0
$416$	−5.65685	−0.277350
$417$	17.6569	0.864660
$418$	−2.82843	−0.138343
$419$	−11.3137	−0.552711	−0.276355	−	0.961056i	$-0.589127\pi$
$419$	−11.3137	−0.552711	−0.276355	+	0.961056i	$0.589127\pi$
$420$	0	0
$421$	−8.62742	−0.420475	−0.210237	−	0.977650i	$-0.567424\pi$
$421$	−8.62742	−0.420475	−0.210237	+	0.977650i	$0.567424\pi$
$422$	16.9706	0.826114
$423$	−8.82843	−0.429253
$424$	4.00000	0.194257
$425$	−5.00000	−0.242536
$426$	−3.17157	−0.153663
$427$	27.3137	1.32180
$428$	−9.65685	−0.466782
$429$	−5.65685	−0.273115
$430$	0	0
$431$	−4.48528	−0.216048	−0.108024	−	0.994148i	$-0.534452\pi$
$431$	−4.48528	−0.216048	−0.108024	+	0.994148i	$0.534452\pi$
$432$	−1.00000	−0.0481125
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	−32.9706	−1.58264
$435$	0	0
$436$	4.00000	0.191565
$437$	13.6569	0.653296
$438$	6.48528	0.309879
$439$	9.51472	0.454113	0.227056	−	0.973882i	$-0.427090\pi$
$439$	9.51472	0.454113	0.227056	+	0.973882i	$0.427090\pi$
$440$	0	0
$441$	16.3137	0.776843
$442$	−5.65685	−0.269069
$443$	29.4558	1.39949	0.699745	−	0.714393i	$-0.253297\pi$
$443$	29.4558	1.39949	0.699745	+	0.714393i	$0.253297\pi$
$444$	8.82843	0.418979
$445$	0	0
$446$	2.34315	0.110951
$447$	−4.34315	−0.205424
$448$	−4.82843	−0.228122
$449$	31.1716	1.47108	0.735539	−	0.677483i	$-0.236929\pi$
$449$	31.1716	1.47108	0.735539	+	0.677483i	$0.236929\pi$
$450$	5.00000	0.235702
$451$	11.6569	0.548900
$452$	−1.51472	−0.0712464
$453$	−0.828427	−0.0389229
$454$	12.9706	0.608739
$455$	0	0
$456$	2.82843	0.132453
$457$	−18.9706	−0.887405	−0.443703	−	0.896174i	$-0.646335\pi$
$457$	−18.9706	−0.887405	−0.443703	+	0.896174i	$0.646335\pi$
$458$	−12.3431	−0.576757
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	7.65685	0.356615	0.178308	−	0.983975i	$-0.442938\pi$
$461$	7.65685	0.356615	0.178308	+	0.983975i	$0.442938\pi$
$462$	−4.82843	−0.224639
$463$	−18.6274	−0.865689	−0.432845	−	0.901468i	$-0.642490\pi$
$463$	−18.6274	−0.865689	−0.432845	+	0.901468i	$0.642490\pi$
$464$	−6.48528	−0.301072
$465$	0	0
$466$	5.31371	0.246153
$467$	3.79899	0.175796	0.0878981	−	0.996129i	$-0.471985\pi$
$467$	3.79899	0.175796	0.0878981	+	0.996129i	$0.471985\pi$
$468$	5.65685	0.261488
$469$	46.6274	2.15305
$470$	0	0
$471$	22.9706	1.05843
$472$	1.17157	0.0539260
$473$	−6.82843	−0.313971
$474$	−16.8284	−0.772955
$475$	−14.1421	−0.648886
$476$	−4.82843	−0.221311
$477$	−4.00000	−0.183147
$478$	−0.686292	−0.0313902
$479$	−26.1421	−1.19446	−0.597232	−	0.802068i	$-0.703733\pi$
$479$	−26.1421	−1.19446	−0.597232	+	0.802068i	$0.703733\pi$
$480$	0	0
$481$	−49.9411	−2.27712
$482$	8.82843	0.402124
$483$	23.3137	1.06081
$484$	1.00000	0.0454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	0.485281	0.0219902	0.0109951	−	0.999940i	$-0.496500\pi$
$487$	0.485281	0.0219902	0.0109951	+	0.999940i	$0.496500\pi$
$488$	5.65685	0.256074
$489$	−9.65685	−0.436698
$490$	0	0
$491$	40.2843	1.81800	0.909002	−	0.416792i	$-0.136846\pi$
$491$	40.2843	1.81800	0.909002	+	0.416792i	$0.136846\pi$
$492$	−11.6569	−0.525532
$493$	−6.48528	−0.292082
$494$	−16.0000	−0.719874
$495$	0	0
$496$	−6.82843	−0.306605
$497$	15.3137	0.686914
$498$	9.65685	0.432734
$499$	−36.0000	−1.61158	−0.805791	−	0.592200i	$-0.798259\pi$
$499$	−36.0000	−1.61158	−0.805791	+	0.592200i	$0.798259\pi$
$500$	0	0
$501$	−14.1421	−0.631824
$502$	−12.4853	−0.557245
$503$	30.1421	1.34397	0.671986	−	0.740564i	$-0.265442\pi$
$503$	30.1421	1.34397	0.671986	+	0.740564i	$0.265442\pi$
$504$	4.82843	0.215075
$505$	0	0
$506$	−4.82843	−0.214650
$507$	−19.0000	−0.843820
$508$	6.48528	0.287738
$509$	−4.00000	−0.177297	−0.0886484	−	0.996063i	$-0.528255\pi$
$509$	−4.00000	−0.177297	−0.0886484	+	0.996063i	$0.528255\pi$
$510$	0	0
$511$	−31.3137	−1.38524
$512$	−1.00000	−0.0441942
$513$	−2.82843	−0.124878
$514$	20.6274	0.909836
$515$	0	0
$516$	6.82843	0.300605
$517$	−8.82843	−0.388274
$518$	−42.6274	−1.87294
$519$	16.8284	0.738686
$520$	0	0
$521$	−22.4853	−0.985098	−0.492549	−	0.870285i	$-0.663935\pi$
$521$	−22.4853	−0.985098	−0.492549	+	0.870285i	$0.663935\pi$
$522$	6.48528	0.283853
$523$	3.51472	0.153688	0.0768440	−	0.997043i	$-0.475516\pi$
$523$	3.51472	0.153688	0.0768440	+	0.997043i	$0.475516\pi$
$524$	−4.00000	−0.174741
$525$	−24.1421	−1.05365
$526$	24.9706	1.08877
$527$	−6.82843	−0.297451
$528$	−1.00000	−0.0435194
$529$	0.313708	0.0136395
$530$	0	0
$531$	−1.17157	−0.0508419
$532$	−13.6569	−0.592100
$533$	65.9411	2.85623
$534$	2.00000	0.0865485
$535$	0	0
$536$	9.65685	0.417113
$537$	−4.48528	−0.193554
$538$	11.3137	0.487769
$539$	16.3137	0.702681
$540$	0	0
$541$	2.62742	0.112961	0.0564807	−	0.998404i	$-0.482012\pi$
$541$	2.62742	0.112961	0.0564807	+	0.998404i	$0.482012\pi$
$542$	−4.82843	−0.207399
$543$	−8.82843	−0.378864
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	−27.3137	−1.16892
$547$	37.9411	1.62225	0.811123	−	0.584876i	$-0.198857\pi$
$547$	37.9411	1.62225	0.811123	+	0.584876i	$0.198857\pi$
$548$	−18.9706	−0.810382
$549$	−5.65685	−0.241429
$550$	5.00000	0.213201
$551$	−18.3431	−0.781444
$552$	4.82843	0.205512
$553$	81.2548	3.45531
$554$	2.34315	0.0995507
$555$	0	0
$556$	−17.6569	−0.748817
$557$	27.9411	1.18390	0.591952	−	0.805973i	$-0.298358\pi$
$557$	27.9411	1.18390	0.591952	+	0.805973i	$0.298358\pi$
$558$	6.82843	0.289070
$559$	−38.6274	−1.63377
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	−26.0000	−1.09674
$563$	−36.9706	−1.55812	−0.779062	−	0.626947i	$-0.784304\pi$
$563$	−36.9706	−1.55812	−0.779062	+	0.626947i	$0.784304\pi$
$564$	8.82843	0.371744
$565$	0	0
$566$	16.9706	0.713326
$567$	−4.82843	−0.202775
$568$	3.17157	0.133076
$569$	−25.3137	−1.06121	−0.530603	−	0.847621i	$-0.678034\pi$
$569$	−25.3137	−1.06121	−0.530603	+	0.847621i	$0.678034\pi$
$570$	0	0
$571$	−16.2843	−0.681476	−0.340738	−	0.940158i	$-0.610677\pi$
$571$	−16.2843	−0.681476	−0.340738	+	0.940158i	$0.610677\pi$
$572$	5.65685	0.236525
$573$	−24.1421	−1.00855
$574$	56.2843	2.34926
$575$	−24.1421	−1.00680
$576$	1.00000	0.0416667
$577$	2.68629	0.111832	0.0559159	−	0.998435i	$-0.482192\pi$
$577$	2.68629	0.111832	0.0559159	+	0.998435i	$0.482192\pi$
$578$	−1.00000	−0.0415945
$579$	−26.4853	−1.10069
$580$	0	0
$581$	−46.6274	−1.93443
$582$	−15.6569	−0.648997
$583$	−4.00000	−0.165663
$584$	−6.48528	−0.268363
$585$	0	0
$586$	−16.6274	−0.686872
$587$	34.1421	1.40920	0.704598	−	0.709606i	$-0.251127\pi$
$587$	34.1421	1.40920	0.704598	+	0.709606i	$0.251127\pi$
$588$	−16.3137	−0.672766
$589$	−19.3137	−0.795807
$590$	0	0
$591$	20.1421	0.828537
$592$	−8.82843	−0.362846
$593$	0.627417	0.0257649	0.0128825	−	0.999917i	$-0.495899\pi$
$593$	0.627417	0.0257649	0.0128825	+	0.999917i	$0.495899\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	4.34315	0.177902
$597$	−6.14214	−0.251381
$598$	−27.3137	−1.11694
$599$	−41.1127	−1.67982	−0.839910	−	0.542726i	$-0.817392\pi$
$599$	−41.1127	−1.67982	−0.839910	+	0.542726i	$0.817392\pi$
$600$	−5.00000	−0.204124
$601$	−24.1421	−0.984778	−0.492389	−	0.870375i	$-0.663876\pi$
$601$	−24.1421	−0.984778	−0.492389	+	0.870375i	$0.663876\pi$
$602$	−32.9706	−1.34378
$603$	−9.65685	−0.393258
$604$	0.828427	0.0337082
$605$	0	0
$606$	17.3137	0.703321
$607$	−0.828427	−0.0336248	−0.0168124	−	0.999859i	$-0.505352\pi$
$607$	−0.828427	−0.0336248	−0.0168124	+	0.999859i	$0.505352\pi$
$608$	−2.82843	−0.114708
$609$	−31.3137	−1.26890
$610$	0	0
$611$	−49.9411	−2.02040
$612$	1.00000	0.0404226
$613$	−6.34315	−0.256197	−0.128099	−	0.991761i	$-0.540887\pi$
$613$	−6.34315	−0.256197	−0.128099	+	0.991761i	$0.540887\pi$
$614$	2.82843	0.114146
$615$	0	0
$616$	4.82843	0.194543
$617$	−0.142136	−0.00572216	−0.00286108	−	0.999996i	$-0.500911\pi$
$617$	−0.142136	−0.00572216	−0.00286108	+	0.999996i	$0.500911\pi$
$618$	−12.0000	−0.482711
$619$	20.9706	0.842878	0.421439	−	0.906857i	$-0.361525\pi$
$619$	20.9706	0.842878	0.421439	+	0.906857i	$0.361525\pi$
$620$	0	0
$621$	−4.82843	−0.193758
$622$	24.8284	0.995529
$623$	−9.65685	−0.386894
$624$	−5.65685	−0.226455
$625$	25.0000	1.00000
$626$	3.65685	0.146157
$627$	−2.82843	−0.112956
$628$	−22.9706	−0.916625
$629$	−8.82843	−0.352012
$630$	0	0
$631$	−24.9706	−0.994062	−0.497031	−	0.867733i	$-0.665577\pi$
$631$	−24.9706	−0.994062	−0.497031	+	0.867733i	$0.665577\pi$
$632$	16.8284	0.669399
$633$	16.9706	0.674519
$634$	−12.9706	−0.515127
$635$	0	0
$636$	4.00000	0.158610
$637$	92.2843	3.65644
$638$	6.48528	0.256755
$639$	−3.17157	−0.125465
$640$	0	0
$641$	2.48528	0.0981627	0.0490814	−	0.998795i	$-0.484371\pi$
$641$	2.48528	0.0981627	0.0490814	+	0.998795i	$0.484371\pi$
$642$	−9.65685	−0.381126
$643$	31.3137	1.23489	0.617446	−	0.786613i	$-0.288167\pi$
$643$	31.3137	1.23489	0.617446	+	0.786613i	$0.288167\pi$
$644$	−23.3137	−0.918689
$645$	0	0
$646$	−2.82843	−0.111283
$647$	−7.17157	−0.281944	−0.140972	−	0.990014i	$-0.545023\pi$
$647$	−7.17157	−0.281944	−0.140972	+	0.990014i	$0.545023\pi$
$648$	−1.00000	−0.0392837
$649$	−1.17157	−0.0459883
$650$	28.2843	1.10940
$651$	−32.9706	−1.29222
$652$	9.65685	0.378192
$653$	−20.9706	−0.820642	−0.410321	−	0.911941i	$-0.634583\pi$
$653$	−20.9706	−0.820642	−0.410321	+	0.911941i	$0.634583\pi$
$654$	4.00000	0.156412
$655$	0	0
$656$	11.6569	0.455124
$657$	6.48528	0.253015
$658$	−42.6274	−1.66179
$659$	24.6863	0.961641	0.480821	−	0.876819i	$-0.340339\pi$
$659$	24.6863	0.961641	0.480821	+	0.876819i	$0.340339\pi$
$660$	0	0
$661$	−16.3431	−0.635675	−0.317837	−	0.948145i	$-0.602957\pi$
$661$	−16.3431	−0.635675	−0.317837	+	0.948145i	$0.602957\pi$
$662$	−15.3137	−0.595184
$663$	−5.65685	−0.219694
$664$	−9.65685	−0.374759
$665$	0	0
$666$	8.82843	0.342095
$667$	−31.3137	−1.21247
$668$	14.1421	0.547176
$669$	2.34315	0.0905912
$670$	0	0
$671$	−5.65685	−0.218380
$672$	−4.82843	−0.186261
$673$	−39.4558	−1.52091	−0.760456	−	0.649390i	$-0.775024\pi$
$673$	−39.4558	−1.52091	−0.760456	+	0.649390i	$0.775024\pi$
$674$	−12.1421	−0.467698
$675$	5.00000	0.192450
$676$	19.0000	0.730769
$677$	26.4853	1.01791	0.508956	−	0.860793i	$-0.330032\pi$
$677$	26.4853	1.01791	0.508956	+	0.860793i	$0.330032\pi$
$678$	−1.51472	−0.0581724
$679$	75.5980	2.90118
$680$	0	0
$681$	12.9706	0.497033
$682$	6.82843	0.261474
$683$	6.62742	0.253591	0.126796	−	0.991929i	$-0.459531\pi$
$683$	6.62742	0.253591	0.126796	+	0.991929i	$0.459531\pi$
$684$	2.82843	0.108148
$685$	0	0
$686$	44.9706	1.71698
$687$	−12.3431	−0.470920
$688$	−6.82843	−0.260331
$689$	−22.6274	−0.862036
$690$	0	0
$691$	16.2843	0.619483	0.309741	−	0.950821i	$-0.399758\pi$
$691$	16.2843	0.619483	0.309741	+	0.950821i	$0.399758\pi$
$692$	−16.8284	−0.639721
$693$	−4.82843	−0.183417
$694$	−14.3431	−0.544458
$695$	0	0
$696$	−6.48528	−0.245824
$697$	11.6569	0.441535
$698$	28.2843	1.07058
$699$	5.31371	0.200983
$700$	24.1421	0.912487
$701$	−14.9706	−0.565430	−0.282715	−	0.959204i	$-0.591235\pi$
$701$	−14.9706	−0.565430	−0.282715	+	0.959204i	$0.591235\pi$
$702$	5.65685	0.213504
$703$	−24.9706	−0.941783
$704$	1.00000	0.0376889
$705$	0	0
$706$	11.6569	0.438711
$707$	−83.5980	−3.14403
$708$	1.17157	0.0440304
$709$	21.5147	0.808002	0.404001	−	0.914758i	$-0.367619\pi$
$709$	21.5147	0.808002	0.404001	+	0.914758i	$0.367619\pi$
$710$	0	0
$711$	−16.8284	−0.631115
$712$	−2.00000	−0.0749532
$713$	−32.9706	−1.23476
$714$	−4.82843	−0.180699
$715$	0	0
$716$	4.48528	0.167623
$717$	−0.686292	−0.0256300
$718$	6.34315	0.236724
$719$	−23.4558	−0.874755	−0.437378	−	0.899278i	$-0.644093\pi$
$719$	−23.4558	−0.874755	−0.437378	+	0.899278i	$0.644093\pi$
$720$	0	0
$721$	57.9411	2.15784
$722$	11.0000	0.409378
$723$	8.82843	0.328333
$724$	8.82843	0.328106
$725$	32.4264	1.20429
$726$	1.00000	0.0371135
$727$	41.6569	1.54497	0.772484	−	0.635035i	$-0.219014\pi$
$727$	41.6569	1.54497	0.772484	+	0.635035i	$0.219014\pi$
$728$	27.3137	1.01231
$729$	1.00000	0.0370370
$730$	0	0
$731$	−6.82843	−0.252559
$732$	5.65685	0.209083
$733$	5.65685	0.208941	0.104470	−	0.994528i	$-0.466685\pi$
$733$	5.65685	0.208941	0.104470	+	0.994528i	$0.466685\pi$
$734$	−27.1127	−1.00075
$735$	0	0
$736$	−4.82843	−0.177978
$737$	−9.65685	−0.355715
$738$	−11.6569	−0.429095
$739$	−0.201010	−0.00739428	−0.00369714	−	0.999993i	$-0.501177\pi$
$739$	−0.201010	−0.00739428	−0.00369714	+	0.999993i	$0.501177\pi$
$740$	0	0
$741$	−16.0000	−0.587775
$742$	−19.3137	−0.709029
$743$	49.4558	1.81436	0.907179	−	0.420744i	$-0.138231\pi$
$743$	49.4558	1.81436	0.907179	+	0.420744i	$0.138231\pi$
$744$	−6.82843	−0.250342
$745$	0	0
$746$	−18.3431	−0.671590
$747$	9.65685	0.353326
$748$	1.00000	0.0365636
$749$	46.6274	1.70373
$750$	0	0
$751$	−25.1716	−0.918524	−0.459262	−	0.888301i	$-0.651886\pi$
$751$	−25.1716	−0.918524	−0.459262	+	0.888301i	$0.651886\pi$
$752$	−8.82843	−0.321940
$753$	−12.4853	−0.454989
$754$	36.6863	1.33604
$755$	0	0
$756$	4.82843	0.175608
$757$	2.68629	0.0976349	0.0488175	−	0.998808i	$-0.484455\pi$
$757$	2.68629	0.0976349	0.0488175	+	0.998808i	$0.484455\pi$
$758$	−12.0000	−0.435860
$759$	−4.82843	−0.175261
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	6.48528	0.234937
$763$	−19.3137	−0.699203
$764$	24.1421	0.873432
$765$	0	0
$766$	16.1421	0.583239
$767$	−6.62742	−0.239302
$768$	−1.00000	−0.0360844
$769$	−52.9117	−1.90804	−0.954022	−	0.299736i	$-0.903101\pi$
$769$	−52.9117	−1.90804	−0.954022	+	0.299736i	$0.903101\pi$
$770$	0	0
$771$	20.6274	0.742878
$772$	26.4853	0.953226
$773$	−34.6274	−1.24546	−0.622731	−	0.782436i	$-0.713977\pi$
$773$	−34.6274	−1.24546	−0.622731	+	0.782436i	$0.713977\pi$
$774$	6.82843	0.245443
$775$	34.1421	1.22642
$776$	15.6569	0.562048
$777$	−42.6274	−1.52925
$778$	12.0000	0.430221
$779$	32.9706	1.18129
$780$	0	0
$781$	−3.17157	−0.113488
$782$	−4.82843	−0.172664
$783$	6.48528	0.231765
$784$	16.3137	0.582632
$785$	0	0
$786$	−4.00000	−0.142675
$787$	45.2548	1.61316	0.806580	−	0.591125i	$-0.201316\pi$
$787$	45.2548	1.61316	0.806580	+	0.591125i	$0.201316\pi$
$788$	−20.1421	−0.717534
$789$	24.9706	0.888976
$790$	0	0
$791$	7.31371	0.260046
$792$	−1.00000	−0.0355335
$793$	−32.0000	−1.13635
$794$	−25.7990	−0.915572
$795$	0	0
$796$	6.14214	0.217702
$797$	−20.0000	−0.708436	−0.354218	−	0.935163i	$-0.615253\pi$
$797$	−20.0000	−0.708436	−0.354218	+	0.935163i	$0.615253\pi$
$798$	−13.6569	−0.483447
$799$	−8.82843	−0.312327
$800$	5.00000	0.176777
$801$	2.00000	0.0706665
$802$	22.4853	0.793983
$803$	6.48528	0.228861
$804$	9.65685	0.340571
$805$	0	0
$806$	38.6274	1.36059
$807$	11.3137	0.398261
$808$	−17.3137	−0.609094
$809$	43.2548	1.52076	0.760379	−	0.649479i	$-0.225013\pi$
$809$	43.2548	1.52076	0.760379	+	0.649479i	$0.225013\pi$
$810$	0	0
$811$	51.3137	1.80187	0.900934	−	0.433956i	$-0.142883\pi$
$811$	51.3137	1.80187	0.900934	+	0.433956i	$0.142883\pi$
$812$	31.3137	1.09890
$813$	−4.82843	−0.169340
$814$	8.82843	0.309436
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	−19.3137	−0.675701
$818$	−22.9706	−0.803147
$819$	−27.3137	−0.954418
$820$	0	0
$821$	−1.79899	−0.0627852	−0.0313926	−	0.999507i	$-0.509994\pi$
$821$	−1.79899	−0.0627852	−0.0313926	+	0.999507i	$0.509994\pi$
$822$	−18.9706	−0.661674
$823$	20.4853	0.714072	0.357036	−	0.934091i	$-0.383787\pi$
$823$	20.4853	0.714072	0.357036	+	0.934091i	$0.383787\pi$
$824$	12.0000	0.418040
$825$	5.00000	0.174078
$826$	−5.65685	−0.196827
$827$	11.0294	0.383531	0.191766	−	0.981441i	$-0.438579\pi$
$827$	11.0294	0.383531	0.191766	+	0.981441i	$0.438579\pi$
$828$	4.82843	0.167799
$829$	14.9706	0.519949	0.259975	−	0.965615i	$-0.416286\pi$
$829$	14.9706	0.519949	0.259975	+	0.965615i	$0.416286\pi$
$830$	0	0
$831$	2.34315	0.0812828
$832$	5.65685	0.196116
$833$	16.3137	0.565236
$834$	−17.6569	−0.611407
$835$	0	0
$836$	2.82843	0.0978232
$837$	6.82843	0.236025
$838$	11.3137	0.390826
$839$	−35.4558	−1.22407	−0.612036	−	0.790830i	$-0.709649\pi$
$839$	−35.4558	−1.22407	−0.612036	+	0.790830i	$0.709649\pi$
$840$	0	0
$841$	13.0589	0.450306
$842$	8.62742	0.297320
$843$	−26.0000	−0.895488
$844$	−16.9706	−0.584151
$845$	0	0
$846$	8.82843	0.303528
$847$	−4.82843	−0.165907
$848$	−4.00000	−0.137361
$849$	16.9706	0.582428
$850$	5.00000	0.171499
$851$	−42.6274	−1.46125
$852$	3.17157	0.108656
$853$	2.34315	0.0802278	0.0401139	−	0.999195i	$-0.487228\pi$
$853$	2.34315	0.0802278	0.0401139	+	0.999195i	$0.487228\pi$
$854$	−27.3137	−0.934656
$855$	0	0
$856$	9.65685	0.330064
$857$	25.3137	0.864700	0.432350	−	0.901706i	$-0.357685\pi$
$857$	25.3137	0.864700	0.432350	+	0.901706i	$0.357685\pi$
$858$	5.65685	0.193122
$859$	−21.9411	−0.748622	−0.374311	−	0.927303i	$-0.622121\pi$
$859$	−21.9411	−0.748622	−0.374311	+	0.927303i	$0.622121\pi$
$860$	0	0
$861$	56.2843	1.91816
$862$	4.48528	0.152769
$863$	10.4853	0.356923	0.178462	−	0.983947i	$-0.442888\pi$
$863$	10.4853	0.356923	0.178462	+	0.983947i	$0.442888\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	6.00000	0.203888
$867$	−1.00000	−0.0339618
$868$	32.9706	1.11909
$869$	−16.8284	−0.570865
$870$	0	0
$871$	−54.6274	−1.85098
$872$	−4.00000	−0.135457
$873$	−15.6569	−0.529904
$874$	−13.6569	−0.461950
$875$	0	0
$876$	−6.48528	−0.219117
$877$	−15.3137	−0.517107	−0.258554	−	0.965997i	$-0.583246\pi$
$877$	−15.3137	−0.517107	−0.258554	+	0.965997i	$0.583246\pi$
$878$	−9.51472	−0.321106
$879$	−16.6274	−0.560829
$880$	0	0
$881$	−4.82843	−0.162674	−0.0813369	−	0.996687i	$-0.525919\pi$
$881$	−4.82843	−0.162674	−0.0813369	+	0.996687i	$0.525919\pi$
$882$	−16.3137	−0.549311
$883$	−10.6274	−0.357641	−0.178821	−	0.983882i	$-0.557228\pi$
$883$	−10.6274	−0.357641	−0.178821	+	0.983882i	$0.557228\pi$
$884$	5.65685	0.190261
$885$	0	0
$886$	−29.4558	−0.989588
$887$	−15.5147	−0.520933	−0.260467	−	0.965483i	$-0.583876\pi$
$887$	−15.5147	−0.520933	−0.260467	+	0.965483i	$0.583876\pi$
$888$	−8.82843	−0.296263
$889$	−31.3137	−1.05023
$890$	0	0
$891$	1.00000	0.0335013
$892$	−2.34315	−0.0784543
$893$	−24.9706	−0.835608
$894$	4.34315	0.145257
$895$	0	0
$896$	4.82843	0.161306
$897$	−27.3137	−0.911978
$898$	−31.1716	−1.04021
$899$	44.2843	1.47696
$900$	−5.00000	−0.166667
$901$	−4.00000	−0.133259
$902$	−11.6569	−0.388131
$903$	−32.9706	−1.09719
$904$	1.51472	0.0503788
$905$	0	0
$906$	0.828427	0.0275226
$907$	−28.9706	−0.961952	−0.480976	−	0.876734i	$-0.659718\pi$
$907$	−28.9706	−0.961952	−0.480976	+	0.876734i	$0.659718\pi$
$908$	−12.9706	−0.430443
$909$	17.3137	0.574259
$910$	0	0
$911$	24.1421	0.799865	0.399932	−	0.916545i	$-0.369034\pi$
$911$	24.1421	0.799865	0.399932	+	0.916545i	$0.369034\pi$
$912$	−2.82843	−0.0936586
$913$	9.65685	0.319595
$914$	18.9706	0.627490
$915$	0	0
$916$	12.3431	0.407829
$917$	19.3137	0.637795
$918$	1.00000	0.0330049
$919$	−56.8284	−1.87460	−0.937298	−	0.348528i	$-0.886682\pi$
$919$	−56.8284	−1.87460	−0.937298	+	0.348528i	$0.886682\pi$
$920$	0	0
$921$	2.82843	0.0931998
$922$	−7.65685	−0.252165
$923$	−17.9411	−0.590539
$924$	4.82843	0.158844
$925$	44.1421	1.45138
$926$	18.6274	0.612135
$927$	−12.0000	−0.394132
$928$	6.48528	0.212890
$929$	−9.79899	−0.321494	−0.160747	−	0.986996i	$-0.551390\pi$
$929$	−9.79899	−0.321494	−0.160747	+	0.986996i	$0.551390\pi$
$930$	0	0
$931$	46.1421	1.51225
$932$	−5.31371	−0.174056
$933$	24.8284	0.812846
$934$	−3.79899	−0.124307
$935$	0	0
$936$	−5.65685	−0.184900
$937$	−52.6274	−1.71926	−0.859631	−	0.510915i	$-0.829307\pi$
$937$	−52.6274	−1.71926	−0.859631	+	0.510915i	$0.829307\pi$
$938$	−46.6274	−1.52244
$939$	3.65685	0.119337
$940$	0	0
$941$	−27.1716	−0.885768	−0.442884	−	0.896579i	$-0.646045\pi$
$941$	−27.1716	−0.885768	−0.442884	+	0.896579i	$0.646045\pi$
$942$	−22.9706	−0.748421
$943$	56.2843	1.83287
$944$	−1.17157	−0.0381314
$945$	0	0
$946$	6.82843	0.222011
$947$	11.0294	0.358409	0.179204	−	0.983812i	$-0.442648\pi$
$947$	11.0294	0.358409	0.179204	+	0.983812i	$0.442648\pi$
$948$	16.8284	0.546562
$949$	36.6863	1.19089
$950$	14.1421	0.458831
$951$	−12.9706	−0.420599
$952$	4.82843	0.156490
$953$	36.6274	1.18648	0.593239	−	0.805026i	$-0.297849\pi$
$953$	36.6274	1.18648	0.593239	+	0.805026i	$0.297849\pi$
$954$	4.00000	0.129505
$955$	0	0
$956$	0.686292	0.0221963
$957$	6.48528	0.209639
$958$	26.1421	0.844614
$959$	91.5980	2.95785
$960$	0	0
$961$	15.6274	0.504110
$962$	49.9411	1.61017
$963$	−9.65685	−0.311188
$964$	−8.82843	−0.284344
$965$	0	0
$966$	−23.3137	−0.750106
$967$	21.5147	0.691867	0.345933	−	0.938259i	$-0.387562\pi$
$967$	21.5147	0.691867	0.345933	+	0.938259i	$0.387562\pi$
$968$	−1.00000	−0.0321412
$969$	−2.82843	−0.0908622
$970$	0	0
$971$	60.0833	1.92816	0.964082	−	0.265605i	$-0.0855719\pi$
$971$	60.0833	1.92816	0.964082	+	0.265605i	$0.0855719\pi$
$972$	−1.00000	−0.0320750
$973$	85.2548	2.73314
$974$	−0.485281	−0.0155494
$975$	28.2843	0.905822
$976$	−5.65685	−0.181071
$977$	38.9706	1.24678	0.623389	−	0.781912i	$-0.285755\pi$
$977$	38.9706	1.24678	0.623389	+	0.781912i	$0.285755\pi$
$978$	9.65685	0.308792
$979$	2.00000	0.0639203
$980$	0	0
$981$	4.00000	0.127710
$982$	−40.2843	−1.28552
$983$	−28.1421	−0.897595	−0.448797	−	0.893634i	$-0.648148\pi$
$983$	−28.1421	−0.897595	−0.448797	+	0.893634i	$0.648148\pi$
$984$	11.6569	0.371607
$985$	0	0
$986$	6.48528	0.206533
$987$	−42.6274	−1.35685
$988$	16.0000	0.509028
$989$	−32.9706	−1.04840
$990$	0	0
$991$	−13.8579	−0.440210	−0.220105	−	0.975476i	$-0.570640\pi$
$991$	−13.8579	−0.440210	−0.220105	+	0.975476i	$0.570640\pi$
$992$	6.82843	0.216803
$993$	−15.3137	−0.485966
$994$	−15.3137	−0.485721
$995$	0	0
$996$	−9.65685	−0.305989
$997$	−45.9411	−1.45497	−0.727485	−	0.686124i	$-0.759311\pi$
$997$	−45.9411	−1.45497	−0.727485	+	0.686124i	$0.759311\pi$
$998$	36.0000	1.13956
$999$	8.82843	0.279319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.a.p.1.1	✓	2
3.2	odd	2		3366.2.a.v.1.1		2
4.3	odd	2		8976.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.a.p.1.1	✓	2	1.1	even	1	trivial
3366.2.a.v.1.1		2	3.2	odd	2
8976.2.a.bp.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.82843 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.00000 q^{12} +5.65685 q^{13} +4.82843 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +2.82843 q^{19} +4.82843 q^{21} -1.00000 q^{22} +4.82843 q^{23} +1.00000 q^{24} -5.00000 q^{25} -5.65685 q^{26} -1.00000 q^{27} -4.82843 q^{28} -6.48528 q^{29} -6.82843 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -8.82843 q^{37} -2.82843 q^{38} -5.65685 q^{39} +11.6569 q^{41} -4.82843 q^{42} -6.82843 q^{43} +1.00000 q^{44} -4.82843 q^{46} -8.82843 q^{47} -1.00000 q^{48} +16.3137 q^{49} +5.00000 q^{50} -1.00000 q^{51} +5.65685 q^{52} -4.00000 q^{53} +1.00000 q^{54} +4.82843 q^{56} -2.82843 q^{57} +6.48528 q^{58} -1.17157 q^{59} -5.65685 q^{61} +6.82843 q^{62} -4.82843 q^{63} +1.00000 q^{64} +1.00000 q^{66} -9.65685 q^{67} +1.00000 q^{68} -4.82843 q^{69} -3.17157 q^{71} -1.00000 q^{72} +6.48528 q^{73} +8.82843 q^{74} +5.00000 q^{75} +2.82843 q^{76} -4.82843 q^{77} +5.65685 q^{78} -16.8284 q^{79} +1.00000 q^{81} -11.6569 q^{82} +9.65685 q^{83} +4.82843 q^{84} +6.82843 q^{86} +6.48528 q^{87} -1.00000 q^{88} +2.00000 q^{89} -27.3137 q^{91} +4.82843 q^{92} +6.82843 q^{93} +8.82843 q^{94} +1.00000 q^{96} -15.6569 q^{97} -16.3137 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} - 2 q^{12} + 4 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 4 q^{21} - 2 q^{22} + 4 q^{23} + 2 q^{24} - 10 q^{25} - 2 q^{27} - 4 q^{28} + 4 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 2 q^{34} + 2 q^{36} - 12 q^{37} + 12 q^{41} - 4 q^{42} - 8 q^{43} + 2 q^{44} - 4 q^{46} - 12 q^{47} - 2 q^{48} + 10 q^{49} + 10 q^{50} - 2 q^{51} - 8 q^{53} + 2 q^{54} + 4 q^{56} - 4 q^{58} - 8 q^{59} + 8 q^{62} - 4 q^{63} + 2 q^{64} + 2 q^{66} - 8 q^{67} + 2 q^{68} - 4 q^{69} - 12 q^{71} - 2 q^{72} - 4 q^{73} + 12 q^{74} + 10 q^{75} - 4 q^{77} - 28 q^{79} + 2 q^{81} - 12 q^{82} + 8 q^{83} + 4 q^{84} + 8 q^{86} - 4 q^{87} - 2 q^{88} + 4 q^{89} - 32 q^{91} + 4 q^{92} + 8 q^{93} + 12 q^{94} + 2 q^{96} - 20 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 - 2 * q^12 + 4 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 4 * q^21 - 2 * q^22 + 4 * q^23 + 2 * q^24 - 10 * q^25 - 2 * q^27 - 4 * q^28 + 4 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^36 - 12 * q^37 + 12 * q^41 - 4 * q^42 - 8 * q^43 + 2 * q^44 - 4 * q^46 - 12 * q^47 - 2 * q^48 + 10 * q^49 + 10 * q^50 - 2 * q^51 - 8 * q^53 + 2 * q^54 + 4 * q^56 - 4 * q^58 - 8 * q^59 + 8 * q^62 - 4 * q^63 + 2 * q^64 + 2 * q^66 - 8 * q^67 + 2 * q^68 - 4 * q^69 - 12 * q^71 - 2 * q^72 - 4 * q^73 + 12 * q^74 + 10 * q^75 - 4 * q^77 - 28 * q^79 + 2 * q^81 - 12 * q^82 + 8 * q^83 + 4 * q^84 + 8 * q^86 - 4 * q^87 - 2 * q^88 + 4 * q^89 - 32 * q^91 + 4 * q^92 + 8 * q^93 + 12 * q^94 + 2 * q^96 - 20 * q^97 - 10 * q^98 + 2 * q^99

Introduction

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