LMFDB - Embedded newform 1122.2.a.p.1.2

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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.828427 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.828427 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.00000 q^{12} -5.65685 q^{13} -0.828427 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -2.82843 q^{19} -0.828427 q^{21} -1.00000 q^{22} -0.828427 q^{23} +1.00000 q^{24} -5.00000 q^{25} +5.65685 q^{26} -1.00000 q^{27} +0.828427 q^{28} +10.4853 q^{29} -1.17157 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -3.17157 q^{37} +2.82843 q^{38} +5.65685 q^{39} +0.343146 q^{41} +0.828427 q^{42} -1.17157 q^{43} +1.00000 q^{44} +0.828427 q^{46} -3.17157 q^{47} -1.00000 q^{48} -6.31371 q^{49} +5.00000 q^{50} -1.00000 q^{51} -5.65685 q^{52} -4.00000 q^{53} +1.00000 q^{54} -0.828427 q^{56} +2.82843 q^{57} -10.4853 q^{58} -6.82843 q^{59} +5.65685 q^{61} +1.17157 q^{62} +0.828427 q^{63} +1.00000 q^{64} +1.00000 q^{66} +1.65685 q^{67} +1.00000 q^{68} +0.828427 q^{69} -8.82843 q^{71} -1.00000 q^{72} -10.4853 q^{73} +3.17157 q^{74} +5.00000 q^{75} -2.82843 q^{76} +0.828427 q^{77} -5.65685 q^{78} -11.1716 q^{79} +1.00000 q^{81} -0.343146 q^{82} -1.65685 q^{83} -0.828427 q^{84} +1.17157 q^{86} -10.4853 q^{87} -1.00000 q^{88} +2.00000 q^{89} -4.68629 q^{91} -0.828427 q^{92} +1.17157 q^{93} +3.17157 q^{94} +1.00000 q^{96} -4.34315 q^{97} +6.31371 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	0.828427	0.313116	0.156558	−	0.987669i	$-0.449960\pi$
$7$	0.828427	0.313116	0.156558	+	0.987669i	$0.449960\pi$
$8$	−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	$-0.787062\pi$
$13$	−5.65685	−1.56893	−0.784465	+	0.620174i	$0.787062\pi$
$14$	−0.828427	−0.221406
$15$	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	$-0.605177\pi$
$19$	−2.82843	−0.648886	−0.324443	+	0.945905i	$0.605177\pi$
$20$	0	0
$21$	−0.828427	−0.180778
$22$	−1.00000	−0.213201
$23$	−0.828427	−0.172739	−0.0863695	−	0.996263i	$-0.527527\pi$
$23$	−0.828427	−0.172739	−0.0863695	+	0.996263i	$0.527527\pi$
$24$	1.00000	0.204124
$25$	−5.00000	−1.00000
$26$	5.65685	1.10940
$27$	−1.00000	−0.192450
$28$	0.828427	0.156558
$29$	10.4853	1.94707	0.973534	−	0.228543i	$-0.0733960\pi$
$29$	10.4853	1.94707	0.973534	+	0.228543i	$0.0733960\pi$
$30$	0	0
$31$	−1.17157	−0.210421	−0.105210	−	0.994450i	$-0.533552\pi$
$31$	−1.17157	−0.210421	−0.105210	+	0.994450i	$0.533552\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−3.17157	−0.521403	−0.260702	−	0.965419i	$-0.583954\pi$
$37$	−3.17157	−0.521403	−0.260702	+	0.965419i	$0.583954\pi$
$38$	2.82843	0.458831
$39$	5.65685	0.905822
$40$	0	0
$41$	0.343146	0.0535904	0.0267952	−	0.999641i	$-0.491470\pi$
$41$	0.343146	0.0535904	0.0267952	+	0.999641i	$0.491470\pi$
$42$	0.828427	0.127829
$43$	−1.17157	−0.178663	−0.0893316	−	0.996002i	$-0.528473\pi$
$43$	−1.17157	−0.178663	−0.0893316	+	0.996002i	$0.528473\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	0.828427	0.122145
$47$	−3.17157	−0.462621	−0.231311	−	0.972880i	$-0.574301\pi$
$47$	−3.17157	−0.462621	−0.231311	+	0.972880i	$0.574301\pi$
$48$	−1.00000	−0.144338
$49$	−6.31371	−0.901958
$50$	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
$56$	−0.828427	−0.110703
$57$	2.82843	0.374634
$58$	−10.4853	−1.37678
$59$	−6.82843	−0.888985	−0.444493	−	0.895782i	$-0.646616\pi$
$59$	−6.82843	−0.888985	−0.444493	+	0.895782i	$0.646616\pi$
$60$	0	0
$61$	5.65685	0.724286	0.362143	−	0.932123i	$-0.382045\pi$
$61$	5.65685	0.724286	0.362143	+	0.932123i	$0.382045\pi$
$62$	1.17157	0.148790
$63$	0.828427	0.104372
$64$	1.00000	0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	1.65685	0.202417	0.101208	−	0.994865i	$-0.467729\pi$
$67$	1.65685	0.202417	0.101208	+	0.994865i	$0.467729\pi$
$68$	1.00000	0.121268
$69$	0.828427	0.0997309
$70$	0	0
$71$	−8.82843	−1.04774	−0.523871	−	0.851798i	$-0.675513\pi$
$71$	−8.82843	−1.04774	−0.523871	+	0.851798i	$0.675513\pi$
$72$	−1.00000	−0.117851
$73$	−10.4853	−1.22721	−0.613605	−	0.789613i	$-0.710281\pi$
$73$	−10.4853	−1.22721	−0.613605	+	0.789613i	$0.710281\pi$
$74$	3.17157	0.368688
$75$	5.00000	0.577350
$76$	−2.82843	−0.324443
$77$	0.828427	0.0944080
$78$	−5.65685	−0.640513
$79$	−11.1716	−1.25690	−0.628450	−	0.777850i	$-0.716310\pi$
$79$	−11.1716	−1.25690	−0.628450	+	0.777850i	$0.716310\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.343146	−0.0378941
$83$	−1.65685	−0.181863	−0.0909317	−	0.995857i	$-0.528984\pi$
$83$	−1.65685	−0.181863	−0.0909317	+	0.995857i	$0.528984\pi$
$84$	−0.828427	−0.0903888
$85$	0	0
$86$	1.17157	0.126334
$87$	−10.4853	−1.12414
$88$	−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
$91$	−4.68629	−0.491257
$92$	−0.828427	−0.0863695
$93$	1.17157	0.121486
$94$	3.17157	0.327123
$95$	0	0
$96$	1.00000	0.102062
$97$	−4.34315	−0.440980	−0.220490	−	0.975389i	$-0.570766\pi$
$97$	−4.34315	−0.440980	−0.220490	+	0.975389i	$0.570766\pi$
$98$	6.31371	0.637781
$99$	1.00000	0.100504
$100$	−5.00000	−0.500000
$101$	−5.31371	−0.528734	−0.264367	−	0.964422i	$-0.585163\pi$
$101$	−5.31371	−0.528734	−0.264367	+	0.964422i	$0.585163\pi$
$102$	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
$107$	1.65685	0.160174	0.0800871	−	0.996788i	$-0.474480\pi$
$107$	1.65685	0.160174	0.0800871	+	0.996788i	$0.474480\pi$
$108$	−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
$111$	3.17157	0.301032
$112$	0.828427	0.0782790
$113$	−18.4853	−1.73895	−0.869474	−	0.493978i	$-0.835542\pi$
$113$	−18.4853	−1.73895	−0.869474	+	0.493978i	$0.835542\pi$
$114$	−2.82843	−0.264906
$115$	0	0
$116$	10.4853	0.973534
$117$	−5.65685	−0.522976
$118$	6.82843	0.628608
$119$	0.828427	0.0759418
$120$	0	0
$121$	1.00000	0.0909091
$122$	−5.65685	−0.512148
$123$	−0.343146	−0.0309404
$124$	−1.17157	−0.105210
$125$	0	0
$126$	−0.828427	−0.0738022
$127$	−10.4853	−0.930418	−0.465209	−	0.885201i	$-0.654021\pi$
$127$	−10.4853	−0.930418	−0.465209	+	0.885201i	$0.654021\pi$
$128$	−1.00000	−0.0883883
$129$	1.17157	0.103151
$130$	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
$133$	−2.34315	−0.203177
$134$	−1.65685	−0.143130
$135$	0	0
$136$	−1.00000	−0.0857493
$137$	14.9706	1.27902	0.639511	−	0.768782i	$-0.279137\pi$
$137$	14.9706	1.27902	0.639511	+	0.768782i	$0.279137\pi$
$138$	−0.828427	−0.0705204
$139$	−6.34315	−0.538019	−0.269009	−	0.963138i	$-0.586696\pi$
$139$	−6.34315	−0.538019	−0.269009	+	0.963138i	$0.586696\pi$
$140$	0	0
$141$	3.17157	0.267095
$142$	8.82843	0.740865
$143$	−5.65685	−0.473050
$144$	1.00000	0.0833333
$145$	0	0
$146$	10.4853	0.867768
$147$	6.31371	0.520746
$148$	−3.17157	−0.260702
$149$	15.6569	1.28266	0.641330	−	0.767265i	$-0.278383\pi$
$149$	15.6569	1.28266	0.641330	+	0.767265i	$0.278383\pi$
$150$	−5.00000	−0.408248
$151$	−4.82843	−0.392932	−0.196466	−	0.980511i	$-0.562947\pi$
$151$	−4.82843	−0.392932	−0.196466	+	0.980511i	$0.562947\pi$
$152$	2.82843	0.229416
$153$	1.00000	0.0808452
$154$	−0.828427	−0.0667566
$155$	0	0
$156$	5.65685	0.452911
$157$	10.9706	0.875546	0.437773	−	0.899085i	$-0.355767\pi$
$157$	10.9706	0.875546	0.437773	+	0.899085i	$0.355767\pi$
$158$	11.1716	0.888763
$159$	4.00000	0.317221
$160$	0	0
$161$	−0.686292	−0.0540873
$162$	−1.00000	−0.0785674
$163$	−1.65685	−0.129775	−0.0648874	−	0.997893i	$-0.520669\pi$
$163$	−1.65685	−0.129775	−0.0648874	+	0.997893i	$0.520669\pi$
$164$	0.343146	0.0267952
$165$	0	0
$166$	1.65685	0.128597
$167$	−14.1421	−1.09435	−0.547176	−	0.837018i	$-0.684297\pi$
$167$	−14.1421	−1.09435	−0.547176	+	0.837018i	$0.684297\pi$
$168$	0.828427	0.0639145
$169$	19.0000	1.46154
$170$	0	0
$171$	−2.82843	−0.216295
$172$	−1.17157	−0.0893316
$173$	−11.1716	−0.849359	−0.424679	−	0.905344i	$-0.639613\pi$
$173$	−11.1716	−0.849359	−0.424679	+	0.905344i	$0.639613\pi$
$174$	10.4853	0.794887
$175$	−4.14214	−0.313116
$176$	1.00000	0.0753778
$177$	6.82843	0.513256
$178$	−2.00000	−0.149906
$179$	−12.4853	−0.933194	−0.466597	−	0.884470i	$-0.654520\pi$
$179$	−12.4853	−0.933194	−0.466597	+	0.884470i	$0.654520\pi$
$180$	0	0
$181$	3.17157	0.235741	0.117871	−	0.993029i	$-0.462393\pi$
$181$	3.17157	0.235741	0.117871	+	0.993029i	$0.462393\pi$
$182$	4.68629	0.347371
$183$	−5.65685	−0.418167
$184$	0.828427	0.0610725
$185$	0	0
$186$	−1.17157	−0.0859039
$187$	1.00000	0.0731272
$188$	−3.17157	−0.231311
$189$	−0.828427	−0.0602592
$190$	0	0
$191$	−4.14214	−0.299714	−0.149857	−	0.988708i	$-0.547881\pi$
$191$	−4.14214	−0.299714	−0.149857	+	0.988708i	$0.547881\pi$
$192$	−1.00000	−0.0721688
$193$	9.51472	0.684884	0.342442	−	0.939539i	$-0.388746\pi$
$193$	9.51472	0.684884	0.342442	+	0.939539i	$0.388746\pi$
$194$	4.34315	0.311820
$195$	0	0
$196$	−6.31371	−0.450979
$197$	8.14214	0.580103	0.290052	−	0.957011i	$-0.406328\pi$
$197$	8.14214	0.580103	0.290052	+	0.957011i	$0.406328\pi$
$198$	−1.00000	−0.0710669
$199$	−22.1421	−1.56961	−0.784807	−	0.619740i	$-0.787238\pi$
$199$	−22.1421	−1.56961	−0.784807	+	0.619740i	$0.787238\pi$
$200$	5.00000	0.353553
$201$	−1.65685	−0.116865
$202$	5.31371	0.373871
$203$	8.68629	0.609658
$204$	−1.00000	−0.0700140
$205$	0	0
$206$	12.0000	0.836080
$207$	−0.828427	−0.0575797
$208$	−5.65685	−0.392232
$209$	−2.82843	−0.195646
$210$	0	0
$211$	16.9706	1.16830	0.584151	−	0.811645i	$-0.301428\pi$
$211$	16.9706	1.16830	0.584151	+	0.811645i	$0.301428\pi$
$212$	−4.00000	−0.274721
$213$	8.82843	0.604914
$214$	−1.65685	−0.113260
$215$	0	0
$216$	1.00000	0.0680414
$217$	−0.970563	−0.0658861
$218$	−4.00000	−0.270914
$219$	10.4853	0.708530
$220$	0	0
$221$	−5.65685	−0.380521
$222$	−3.17157	−0.212862
$223$	−13.6569	−0.914531	−0.457265	−	0.889330i	$-0.651171\pi$
$223$	−13.6569	−0.914531	−0.457265	+	0.889330i	$0.651171\pi$
$224$	−0.828427	−0.0553516
$225$	−5.00000	−0.333333
$226$	18.4853	1.22962
$227$	20.9706	1.39187	0.695933	−	0.718107i	$-0.254991\pi$
$227$	20.9706	1.39187	0.695933	+	0.718107i	$0.254991\pi$
$228$	2.82843	0.187317
$229$	23.6569	1.56329	0.781644	−	0.623724i	$-0.214381\pi$
$229$	23.6569	1.56329	0.781644	+	0.623724i	$0.214381\pi$
$230$	0	0
$231$	−0.828427	−0.0545065
$232$	−10.4853	−0.688392
$233$	17.3137	1.13426	0.567129	−	0.823629i	$-0.308054\pi$
$233$	17.3137	1.13426	0.567129	+	0.823629i	$0.308054\pi$
$234$	5.65685	0.369800
$235$	0	0
$236$	−6.82843	−0.444493
$237$	11.1716	0.725672
$238$	−0.828427	−0.0536990
$239$	23.3137	1.50804	0.754019	−	0.656852i	$-0.228113\pi$
$239$	23.3137	1.50804	0.754019	+	0.656852i	$0.228113\pi$
$240$	0	0
$241$	−3.17157	−0.204299	−0.102149	−	0.994769i	$-0.532572\pi$
$241$	−3.17157	−0.204299	−0.102149	+	0.994769i	$0.532572\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	5.65685	0.362143
$245$	0	0
$246$	0.343146	0.0218782
$247$	16.0000	1.01806
$248$	1.17157	0.0743950
$249$	1.65685	0.104999
$250$	0	0
$251$	−4.48528	−0.283108	−0.141554	−	0.989931i	$-0.545210\pi$
$251$	−4.48528	−0.283108	−0.141554	+	0.989931i	$0.545210\pi$
$252$	0.828427	0.0521860
$253$	−0.828427	−0.0520828
$254$	10.4853	0.657905
$255$	0	0
$256$	1.00000	0.0625000
$257$	24.6274	1.53622	0.768108	−	0.640320i	$-0.221198\pi$
$257$	24.6274	1.53622	0.768108	+	0.640320i	$0.221198\pi$
$258$	−1.17157	−0.0729389
$259$	−2.62742	−0.163260
$260$	0	0
$261$	10.4853	0.649023
$262$	4.00000	0.247121
$263$	8.97056	0.553149	0.276574	−	0.960993i	$-0.410801\pi$
$263$	8.97056	0.553149	0.276574	+	0.960993i	$0.410801\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	2.34315	0.143667
$267$	−2.00000	−0.122398
$268$	1.65685	0.101208
$269$	11.3137	0.689809	0.344904	−	0.938638i	$-0.387911\pi$
$269$	11.3137	0.689809	0.344904	+	0.938638i	$0.387911\pi$
$270$	0	0
$271$	−0.828427	−0.0503234	−0.0251617	−	0.999683i	$-0.508010\pi$
$271$	−0.828427	−0.0503234	−0.0251617	+	0.999683i	$0.508010\pi$
$272$	1.00000	0.0606339
$273$	4.68629	0.283627
$274$	−14.9706	−0.904405
$275$	−5.00000	−0.301511
$276$	0.828427	0.0498655
$277$	−13.6569	−0.820561	−0.410280	−	0.911959i	$-0.634569\pi$
$277$	−13.6569	−0.820561	−0.410280	+	0.911959i	$0.634569\pi$
$278$	6.34315	0.380437
$279$	−1.17157	−0.0701402
$280$	0	0
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	−3.17157	−0.188864
$283$	16.9706	1.00880	0.504398	−	0.863472i	$-0.331715\pi$
$283$	16.9706	1.00880	0.504398	+	0.863472i	$0.331715\pi$
$284$	−8.82843	−0.523871
$285$	0	0
$286$	5.65685	0.334497
$287$	0.284271	0.0167800
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0	0
$291$	4.34315	0.254600
$292$	−10.4853	−0.613605
$293$	−28.6274	−1.67243	−0.836216	−	0.548401i	$-0.815237\pi$
$293$	−28.6274	−1.67243	−0.836216	+	0.548401i	$0.815237\pi$
$294$	−6.31371	−0.368223
$295$	0	0
$296$	3.17157	0.184344
$297$	−1.00000	−0.0580259
$298$	−15.6569	−0.906977
$299$	4.68629	0.271015
$300$	5.00000	0.288675
$301$	−0.970563	−0.0559423
$302$	4.82843	0.277845
$303$	5.31371	0.305265
$304$	−2.82843	−0.162221
$305$	0	0
$306$	−1.00000	−0.0571662
$307$	2.82843	0.161427	0.0807134	−	0.996737i	$-0.474280\pi$
$307$	2.82843	0.161427	0.0807134	+	0.996737i	$0.474280\pi$
$308$	0.828427	0.0472040
$309$	12.0000	0.682656
$310$	0	0
$311$	−19.1716	−1.08712	−0.543560	−	0.839370i	$-0.682924\pi$
$311$	−19.1716	−1.08712	−0.543560	+	0.839370i	$0.682924\pi$
$312$	−5.65685	−0.320256
$313$	7.65685	0.432791	0.216395	−	0.976306i	$-0.430570\pi$
$313$	7.65685	0.432791	0.216395	+	0.976306i	$0.430570\pi$
$314$	−10.9706	−0.619105
$315$	0	0
$316$	−11.1716	−0.628450
$317$	−20.9706	−1.17782	−0.588912	−	0.808197i	$-0.700444\pi$
$317$	−20.9706	−1.17782	−0.588912	+	0.808197i	$0.700444\pi$
$318$	−4.00000	−0.224309
$319$	10.4853	0.587063
$320$	0	0
$321$	−1.65685	−0.0924766
$322$	0.686292	0.0382455
$323$	−2.82843	−0.157378
$324$	1.00000	0.0555556
$325$	28.2843	1.56893
$326$	1.65685	0.0917647
$327$	−4.00000	−0.221201
$328$	−0.343146	−0.0189471
$329$	−2.62742	−0.144854
$330$	0	0
$331$	−7.31371	−0.401998	−0.200999	−	0.979591i	$-0.564419\pi$
$331$	−7.31371	−0.401998	−0.200999	+	0.979591i	$0.564419\pi$
$332$	−1.65685	−0.0909317
$333$	−3.17157	−0.173801
$334$	14.1421	0.773823
$335$	0	0
$336$	−0.828427	−0.0451944
$337$	−16.1421	−0.879318	−0.439659	−	0.898165i	$-0.644901\pi$
$337$	−16.1421	−0.879318	−0.439659	+	0.898165i	$0.644901\pi$
$338$	−19.0000	−1.03346
$339$	18.4853	1.00398
$340$	0	0
$341$	−1.17157	−0.0634442
$342$	2.82843	0.152944
$343$	−11.0294	−0.595534
$344$	1.17157	0.0631670
$345$	0	0
$346$	11.1716	0.600587
$347$	25.6569	1.37733	0.688666	−	0.725079i	$-0.258197\pi$
$347$	25.6569	1.37733	0.688666	+	0.725079i	$0.258197\pi$
$348$	−10.4853	−0.562070
$349$	28.2843	1.51402	0.757011	−	0.653402i	$-0.226659\pi$
$349$	28.2843	1.51402	0.757011	+	0.653402i	$0.226659\pi$
$350$	4.14214	0.221406
$351$	5.65685	0.301941
$352$	−1.00000	−0.0533002
$353$	−0.343146	−0.0182638	−0.00913190	−	0.999958i	$-0.502907\pi$
$353$	−0.343146	−0.0182638	−0.00913190	+	0.999958i	$0.502907\pi$
$354$	−6.82843	−0.362927
$355$	0	0
$356$	2.00000	0.106000
$357$	−0.828427	−0.0438450
$358$	12.4853	0.659868
$359$	−17.6569	−0.931893	−0.465947	−	0.884813i	$-0.654286\pi$
$359$	−17.6569	−0.931893	−0.465947	+	0.884813i	$0.654286\pi$
$360$	0	0
$361$	−11.0000	−0.578947
$362$	−3.17157	−0.166694
$363$	−1.00000	−0.0524864
$364$	−4.68629	−0.245628
$365$	0	0
$366$	5.65685	0.295689
$367$	−35.1127	−1.83287	−0.916434	−	0.400186i	$-0.868946\pi$
$367$	−35.1127	−1.83287	−0.916434	+	0.400186i	$0.868946\pi$
$368$	−0.828427	−0.0431847
$369$	0.343146	0.0178635
$370$	0	0
$371$	−3.31371	−0.172039
$372$	1.17157	0.0607432
$373$	29.6569	1.53557	0.767787	−	0.640705i	$-0.221358\pi$
$373$	29.6569	1.53557	0.767787	+	0.640705i	$0.221358\pi$
$374$	−1.00000	−0.0517088
$375$	0	0
$376$	3.17157	0.163561
$377$	−59.3137	−3.05481
$378$	0.828427	0.0426097
$379$	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
$381$	10.4853	0.537177
$382$	4.14214	0.211930
$383$	12.1421	0.620434	0.310217	−	0.950666i	$-0.399598\pi$
$383$	12.1421	0.620434	0.310217	+	0.950666i	$0.399598\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−9.51472	−0.484286
$387$	−1.17157	−0.0595544
$388$	−4.34315	−0.220490
$389$	−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
$391$	−0.828427	−0.0418954
$392$	6.31371	0.318890
$393$	4.00000	0.201773
$394$	−8.14214	−0.410195
$395$	0	0
$396$	1.00000	0.0502519
$397$	−13.7990	−0.692551	−0.346276	−	0.938133i	$-0.612554\pi$
$397$	−13.7990	−0.692551	−0.346276	+	0.938133i	$0.612554\pi$
$398$	22.1421	1.10988
$399$	2.34315	0.117304
$400$	−5.00000	−0.250000
$401$	−5.51472	−0.275392	−0.137696	−	0.990475i	$-0.543970\pi$
$401$	−5.51472	−0.275392	−0.137696	+	0.990475i	$0.543970\pi$
$402$	1.65685	0.0826364
$403$	6.62742	0.330135
$404$	−5.31371	−0.264367
$405$	0	0
$406$	−8.68629	−0.431093
$407$	−3.17157	−0.157209
$408$	1.00000	0.0495074
$409$	−10.9706	−0.542459	−0.271230	−	0.962515i	$-0.587430\pi$
$409$	−10.9706	−0.542459	−0.271230	+	0.962515i	$0.587430\pi$
$410$	0	0
$411$	−14.9706	−0.738443
$412$	−12.0000	−0.591198
$413$	−5.65685	−0.278356
$414$	0.828427	0.0407150
$415$	0	0
$416$	5.65685	0.277350
$417$	6.34315	0.310625
$418$	2.82843	0.138343
$419$	11.3137	0.552711	0.276355	−	0.961056i	$-0.410873\pi$
$419$	11.3137	0.552711	0.276355	+	0.961056i	$0.410873\pi$
$420$	0	0
$421$	36.6274	1.78511	0.892556	−	0.450937i	$-0.148910\pi$
$421$	36.6274	1.78511	0.892556	+	0.450937i	$0.148910\pi$
$422$	−16.9706	−0.826114
$423$	−3.17157	−0.154207
$424$	4.00000	0.194257
$425$	−5.00000	−0.242536
$426$	−8.82843	−0.427739
$427$	4.68629	0.226786
$428$	1.65685	0.0800871
$429$	5.65685	0.273115
$430$	0	0
$431$	12.4853	0.601395	0.300697	−	0.953720i	$-0.402781\pi$
$431$	12.4853	0.601395	0.300697	+	0.953720i	$0.402781\pi$
$432$	−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	$0.546051\pi$
$434$	0.970563	0.0465885
$435$	0	0
$436$	4.00000	0.191565
$437$	2.34315	0.112088
$438$	−10.4853	−0.501006
$439$	26.4853	1.26407	0.632037	−	0.774938i	$-0.282219\pi$
$439$	26.4853	1.26407	0.632037	+	0.774938i	$0.282219\pi$
$440$	0	0
$441$	−6.31371	−0.300653
$442$	5.65685	0.269069
$443$	−21.4558	−1.01940	−0.509699	−	0.860353i	$-0.670243\pi$
$443$	−21.4558	−1.01940	−0.509699	+	0.860353i	$0.670243\pi$
$444$	3.17157	0.150516
$445$	0	0
$446$	13.6569	0.646671
$447$	−15.6569	−0.740544
$448$	0.828427	0.0391395
$449$	36.8284	1.73804	0.869020	−	0.494776i	$-0.164750\pi$
$449$	36.8284	1.73804	0.869020	+	0.494776i	$0.164750\pi$
$450$	5.00000	0.235702
$451$	0.343146	0.0161581
$452$	−18.4853	−0.869474
$453$	4.82843	0.226859
$454$	−20.9706	−0.984197
$455$	0	0
$456$	−2.82843	−0.132453
$457$	14.9706	0.700293	0.350147	−	0.936695i	$-0.386132\pi$
$457$	14.9706	0.700293	0.350147	+	0.936695i	$0.386132\pi$
$458$	−23.6569	−1.10541
$459$	−1.00000	−0.0466760
$460$	0	0
$461$	−3.65685	−0.170317	−0.0851583	−	0.996367i	$-0.527140\pi$
$461$	−3.65685	−0.170317	−0.0851583	+	0.996367i	$0.527140\pi$
$462$	0.828427	0.0385419
$463$	26.6274	1.23748	0.618741	−	0.785595i	$-0.287643\pi$
$463$	26.6274	1.23748	0.618741	+	0.785595i	$0.287643\pi$
$464$	10.4853	0.486767
$465$	0	0
$466$	−17.3137	−0.802042
$467$	−35.7990	−1.65658	−0.828290	−	0.560300i	$-0.810686\pi$
$467$	−35.7990	−1.65658	−0.828290	+	0.560300i	$0.810686\pi$
$468$	−5.65685	−0.261488
$469$	1.37258	0.0633800
$470$	0	0
$471$	−10.9706	−0.505497
$472$	6.82843	0.314304
$473$	−1.17157	−0.0538690
$474$	−11.1716	−0.513127
$475$	14.1421	0.648886
$476$	0.828427	0.0379709
$477$	−4.00000	−0.183147
$478$	−23.3137	−1.06634
$479$	2.14214	0.0978767	0.0489383	−	0.998802i	$-0.484416\pi$
$479$	2.14214	0.0978767	0.0489383	+	0.998802i	$0.484416\pi$
$480$	0	0
$481$	17.9411	0.818045
$482$	3.17157	0.144461
$483$	0.686292	0.0312273
$484$	1.00000	0.0454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	−16.4853	−0.747019	−0.373510	−	0.927626i	$-0.621846\pi$
$487$	−16.4853	−0.747019	−0.373510	+	0.927626i	$0.621846\pi$
$488$	−5.65685	−0.256074
$489$	1.65685	0.0749255
$490$	0	0
$491$	−16.2843	−0.734899	−0.367449	−	0.930043i	$-0.619769\pi$
$491$	−16.2843	−0.734899	−0.367449	+	0.930043i	$0.619769\pi$
$492$	−0.343146	−0.0154702
$493$	10.4853	0.472233
$494$	−16.0000	−0.719874
$495$	0	0
$496$	−1.17157	−0.0526052
$497$	−7.31371	−0.328065
$498$	−1.65685	−0.0742454
$499$	−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
$502$	4.48528	0.200188
$503$	1.85786	0.0828381	0.0414190	−	0.999142i	$-0.486812\pi$
$503$	1.85786	0.0828381	0.0414190	+	0.999142i	$0.486812\pi$
$504$	−0.828427	−0.0369011
$505$	0	0
$506$	0.828427	0.0368281
$507$	−19.0000	−0.843820
$508$	−10.4853	−0.465209
$509$	−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
$511$	−8.68629	−0.384259
$512$	−1.00000	−0.0441942
$513$	2.82843	0.124878
$514$	−24.6274	−1.08627
$515$	0	0
$516$	1.17157	0.0515756
$517$	−3.17157	−0.139486
$518$	2.62742	0.115442
$519$	11.1716	0.490378
$520$	0	0
$521$	−5.51472	−0.241604	−0.120802	−	0.992677i	$-0.538547\pi$
$521$	−5.51472	−0.241604	−0.120802	+	0.992677i	$0.538547\pi$
$522$	−10.4853	−0.458928
$523$	20.4853	0.895759	0.447879	−	0.894094i	$-0.352179\pi$
$523$	20.4853	0.895759	0.447879	+	0.894094i	$0.352179\pi$
$524$	−4.00000	−0.174741
$525$	4.14214	0.180778
$526$	−8.97056	−0.391135
$527$	−1.17157	−0.0510345
$528$	−1.00000	−0.0435194
$529$	−22.3137	−0.970161
$530$	0	0
$531$	−6.82843	−0.296328
$532$	−2.34315	−0.101588
$533$	−1.94113	−0.0840795
$534$	2.00000	0.0865485
$535$	0	0
$536$	−1.65685	−0.0715652
$537$	12.4853	0.538780
$538$	−11.3137	−0.487769
$539$	−6.31371	−0.271951
$540$	0	0
$541$	−42.6274	−1.83270	−0.916348	−	0.400383i	$-0.868877\pi$
$541$	−42.6274	−1.83270	−0.916348	+	0.400383i	$0.868877\pi$
$542$	0.828427	0.0355840
$543$	−3.17157	−0.136105
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	−4.68629	−0.200555
$547$	−29.9411	−1.28019	−0.640095	−	0.768296i	$-0.721105\pi$
$547$	−29.9411	−1.28019	−0.640095	+	0.768296i	$0.721105\pi$
$548$	14.9706	0.639511
$549$	5.65685	0.241429
$550$	5.00000	0.213201
$551$	−29.6569	−1.26342
$552$	−0.828427	−0.0352602
$553$	−9.25483	−0.393556
$554$	13.6569	0.580224
$555$	0	0
$556$	−6.34315	−0.269009
$557$	−39.9411	−1.69236	−0.846180	−	0.532897i	$-0.821103\pi$
$557$	−39.9411	−1.69236	−0.846180	+	0.532897i	$0.821103\pi$
$558$	1.17157	0.0495966
$559$	6.62742	0.280310
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	−26.0000	−1.09674
$563$	−3.02944	−0.127676	−0.0638378	−	0.997960i	$-0.520334\pi$
$563$	−3.02944	−0.127676	−0.0638378	+	0.997960i	$0.520334\pi$
$564$	3.17157	0.133547
$565$	0	0
$566$	−16.9706	−0.713326
$567$	0.828427	0.0347907
$568$	8.82843	0.370433
$569$	−2.68629	−0.112615	−0.0563076	−	0.998413i	$-0.517933\pi$
$569$	−2.68629	−0.112615	−0.0563076	+	0.998413i	$0.517933\pi$
$570$	0	0
$571$	40.2843	1.68584	0.842922	−	0.538036i	$-0.180833\pi$
$571$	40.2843	1.68584	0.842922	+	0.538036i	$0.180833\pi$
$572$	−5.65685	−0.236525
$573$	4.14214	0.173040
$574$	−0.284271	−0.0118653
$575$	4.14214	0.172739
$576$	1.00000	0.0416667
$577$	25.3137	1.05382	0.526912	−	0.849920i	$-0.323350\pi$
$577$	25.3137	1.05382	0.526912	+	0.849920i	$0.323350\pi$
$578$	−1.00000	−0.0415945
$579$	−9.51472	−0.395418
$580$	0	0
$581$	−1.37258	−0.0569443
$582$	−4.34315	−0.180029
$583$	−4.00000	−0.165663
$584$	10.4853	0.433884
$585$	0	0
$586$	28.6274	1.18259
$587$	5.85786	0.241780	0.120890	−	0.992666i	$-0.461425\pi$
$587$	5.85786	0.241780	0.120890	+	0.992666i	$0.461425\pi$
$588$	6.31371	0.260373
$589$	3.31371	0.136539
$590$	0	0
$591$	−8.14214	−0.334923
$592$	−3.17157	−0.130351
$593$	−44.6274	−1.83263	−0.916314	−	0.400460i	$-0.868850\pi$
$593$	−44.6274	−1.83263	−0.916314	+	0.400460i	$0.868850\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	15.6569	0.641330
$597$	22.1421	0.906217
$598$	−4.68629	−0.191637
$599$	21.1127	0.862641	0.431321	−	0.902199i	$-0.358048\pi$
$599$	21.1127	0.862641	0.431321	+	0.902199i	$0.358048\pi$
$600$	−5.00000	−0.204124
$601$	4.14214	0.168961	0.0844806	−	0.996425i	$-0.473077\pi$
$601$	4.14214	0.168961	0.0844806	+	0.996425i	$0.473077\pi$
$602$	0.970563	0.0395572
$603$	1.65685	0.0674723
$604$	−4.82843	−0.196466
$605$	0	0
$606$	−5.31371	−0.215855
$607$	4.82843	0.195980	0.0979899	−	0.995187i	$-0.468759\pi$
$607$	4.82843	0.195980	0.0979899	+	0.995187i	$0.468759\pi$
$608$	2.82843	0.114708
$609$	−8.68629	−0.351986
$610$	0	0
$611$	17.9411	0.725820
$612$	1.00000	0.0404226
$613$	−17.6569	−0.713154	−0.356577	−	0.934266i	$-0.616056\pi$
$613$	−17.6569	−0.713154	−0.356577	+	0.934266i	$0.616056\pi$
$614$	−2.82843	−0.114146
$615$	0	0
$616$	−0.828427	−0.0333783
$617$	28.1421	1.13296	0.566480	−	0.824076i	$-0.308305\pi$
$617$	28.1421	1.13296	0.566480	+	0.824076i	$0.308305\pi$
$618$	−12.0000	−0.482711
$619$	−12.9706	−0.521331	−0.260665	−	0.965429i	$-0.583942\pi$
$619$	−12.9706	−0.521331	−0.260665	+	0.965429i	$0.583942\pi$
$620$	0	0
$621$	0.828427	0.0332436
$622$	19.1716	0.768710
$623$	1.65685	0.0663805
$624$	5.65685	0.226455
$625$	25.0000	1.00000
$626$	−7.65685	−0.306029
$627$	2.82843	0.112956
$628$	10.9706	0.437773
$629$	−3.17157	−0.126459
$630$	0	0
$631$	8.97056	0.357112	0.178556	−	0.983930i	$-0.442857\pi$
$631$	8.97056	0.357112	0.178556	+	0.983930i	$0.442857\pi$
$632$	11.1716	0.444381
$633$	−16.9706	−0.674519
$634$	20.9706	0.832847
$635$	0	0
$636$	4.00000	0.158610
$637$	35.7157	1.41511
$638$	−10.4853	−0.415116
$639$	−8.82843	−0.349247
$640$	0	0
$641$	−14.4853	−0.572134	−0.286067	−	0.958210i	$-0.592348\pi$
$641$	−14.4853	−0.572134	−0.286067	+	0.958210i	$0.592348\pi$
$642$	1.65685	0.0653908
$643$	8.68629	0.342554	0.171277	−	0.985223i	$-0.445211\pi$
$643$	8.68629	0.342554	0.171277	+	0.985223i	$0.445211\pi$
$644$	−0.686292	−0.0270437
$645$	0	0
$646$	2.82843	0.111283
$647$	−12.8284	−0.504338	−0.252169	−	0.967683i	$-0.581144\pi$
$647$	−12.8284	−0.504338	−0.252169	+	0.967683i	$0.581144\pi$
$648$	−1.00000	−0.0392837
$649$	−6.82843	−0.268039
$650$	−28.2843	−1.10940
$651$	0.970563	0.0380394
$652$	−1.65685	−0.0648874
$653$	12.9706	0.507577	0.253789	−	0.967260i	$-0.418323\pi$
$653$	12.9706	0.507577	0.253789	+	0.967260i	$0.418323\pi$
$654$	4.00000	0.156412
$655$	0	0
$656$	0.343146	0.0133976
$657$	−10.4853	−0.409070
$658$	2.62742	0.102427
$659$	47.3137	1.84308	0.921540	−	0.388283i	$-0.126932\pi$
$659$	47.3137	1.84308	0.921540	+	0.388283i	$0.126932\pi$
$660$	0	0
$661$	−27.6569	−1.07573	−0.537863	−	0.843032i	$-0.680768\pi$
$661$	−27.6569	−1.07573	−0.537863	+	0.843032i	$0.680768\pi$
$662$	7.31371	0.284255
$663$	5.65685	0.219694
$664$	1.65685	0.0642984
$665$	0	0
$666$	3.17157	0.122896
$667$	−8.68629	−0.336335
$668$	−14.1421	−0.547176
$669$	13.6569	0.528004
$670$	0	0
$671$	5.65685	0.218380
$672$	0.828427	0.0319573
$673$	11.4558	0.441590	0.220795	−	0.975320i	$-0.429135\pi$
$673$	11.4558	0.441590	0.220795	+	0.975320i	$0.429135\pi$
$674$	16.1421	0.621772
$675$	5.00000	0.192450
$676$	19.0000	0.730769
$677$	9.51472	0.365680	0.182840	−	0.983143i	$-0.441471\pi$
$677$	9.51472	0.365680	0.182840	+	0.983143i	$0.441471\pi$
$678$	−18.4853	−0.709923
$679$	−3.59798	−0.138078
$680$	0	0
$681$	−20.9706	−0.803594
$682$	1.17157	0.0448618
$683$	−38.6274	−1.47804	−0.739019	−	0.673685i	$-0.764710\pi$
$683$	−38.6274	−1.47804	−0.739019	+	0.673685i	$0.764710\pi$
$684$	−2.82843	−0.108148
$685$	0	0
$686$	11.0294	0.421106
$687$	−23.6569	−0.902565
$688$	−1.17157	−0.0446658
$689$	22.6274	0.862036
$690$	0	0
$691$	−40.2843	−1.53249	−0.766243	−	0.642551i	$-0.777876\pi$
$691$	−40.2843	−1.53249	−0.766243	+	0.642551i	$0.777876\pi$
$692$	−11.1716	−0.424679
$693$	0.828427	0.0314693
$694$	−25.6569	−0.973921
$695$	0	0
$696$	10.4853	0.397444
$697$	0.343146	0.0129976
$698$	−28.2843	−1.07058
$699$	−17.3137	−0.654865
$700$	−4.14214	−0.156558
$701$	18.9706	0.716508	0.358254	−	0.933624i	$-0.383372\pi$
$701$	18.9706	0.716508	0.358254	+	0.933624i	$0.383372\pi$
$702$	−5.65685	−0.213504
$703$	8.97056	0.338331
$704$	1.00000	0.0376889
$705$	0	0
$706$	0.343146	0.0129145
$707$	−4.40202	−0.165555
$708$	6.82843	0.256628
$709$	38.4853	1.44535	0.722673	−	0.691191i	$-0.242913\pi$
$709$	38.4853	1.44535	0.722673	+	0.691191i	$0.242913\pi$
$710$	0	0
$711$	−11.1716	−0.418967
$712$	−2.00000	−0.0749532
$713$	0.970563	0.0363479
$714$	0.828427	0.0310031
$715$	0	0
$716$	−12.4853	−0.466597
$717$	−23.3137	−0.870666
$718$	17.6569	0.658948
$719$	27.4558	1.02393	0.511965	−	0.859006i	$-0.328918\pi$
$719$	27.4558	1.02393	0.511965	+	0.859006i	$0.328918\pi$
$720$	0	0
$721$	−9.94113	−0.370227
$722$	11.0000	0.409378
$723$	3.17157	0.117952
$724$	3.17157	0.117871
$725$	−52.4264	−1.94707
$726$	1.00000	0.0371135
$727$	30.3431	1.12536	0.562682	−	0.826673i	$-0.309769\pi$
$727$	30.3431	1.12536	0.562682	+	0.826673i	$0.309769\pi$
$728$	4.68629	0.173686
$729$	1.00000	0.0370370
$730$	0	0
$731$	−1.17157	−0.0433322
$732$	−5.65685	−0.209083
$733$	−5.65685	−0.208941	−0.104470	−	0.994528i	$-0.533315\pi$
$733$	−5.65685	−0.208941	−0.104470	+	0.994528i	$0.533315\pi$
$734$	35.1127	1.29603
$735$	0	0
$736$	0.828427	0.0305362
$737$	1.65685	0.0610310
$738$	−0.343146	−0.0126314
$739$	−39.7990	−1.46403	−0.732015	−	0.681289i	$-0.761420\pi$
$739$	−39.7990	−1.46403	−0.732015	+	0.681289i	$0.761420\pi$
$740$	0	0
$741$	−16.0000	−0.587775
$742$	3.31371	0.121650
$743$	−1.45584	−0.0534097	−0.0267049	−	0.999643i	$-0.508501\pi$
$743$	−1.45584	−0.0534097	−0.0267049	+	0.999643i	$0.508501\pi$
$744$	−1.17157	−0.0429519
$745$	0	0
$746$	−29.6569	−1.08581
$747$	−1.65685	−0.0606211
$748$	1.00000	0.0365636
$749$	1.37258	0.0501531
$750$	0	0
$751$	−30.8284	−1.12495	−0.562473	−	0.826816i	$-0.690150\pi$
$751$	−30.8284	−1.12495	−0.562473	+	0.826816i	$0.690150\pi$
$752$	−3.17157	−0.115655
$753$	4.48528	0.163453
$754$	59.3137	2.16008
$755$	0	0
$756$	−0.828427	−0.0301296
$757$	25.3137	0.920042	0.460021	−	0.887908i	$-0.347842\pi$
$757$	25.3137	0.920042	0.460021	+	0.887908i	$0.347842\pi$
$758$	−12.0000	−0.435860
$759$	0.828427	0.0300700
$760$	0	0
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	−10.4853	−0.379842
$763$	3.31371	0.119964
$764$	−4.14214	−0.149857
$765$	0	0
$766$	−12.1421	−0.438713
$767$	38.6274	1.39476
$768$	−1.00000	−0.0360844
$769$	48.9117	1.76380	0.881900	−	0.471436i	$-0.156264\pi$
$769$	48.9117	1.76380	0.881900	+	0.471436i	$0.156264\pi$
$770$	0	0
$771$	−24.6274	−0.886935
$772$	9.51472	0.342442
$773$	10.6274	0.382242	0.191121	−	0.981567i	$-0.438788\pi$
$773$	10.6274	0.382242	0.191121	+	0.981567i	$0.438788\pi$
$774$	1.17157	0.0421113
$775$	5.85786	0.210421
$776$	4.34315	0.155910
$777$	2.62742	0.0942581
$778$	12.0000	0.430221
$779$	−0.970563	−0.0347740
$780$	0	0
$781$	−8.82843	−0.315906
$782$	0.828427	0.0296245
$783$	−10.4853	−0.374713
$784$	−6.31371	−0.225490
$785$	0	0
$786$	−4.00000	−0.142675
$787$	−45.2548	−1.61316	−0.806580	−	0.591125i	$-0.798684\pi$
$787$	−45.2548	−1.61316	−0.806580	+	0.591125i	$0.798684\pi$
$788$	8.14214	0.290052
$789$	−8.97056	−0.319360
$790$	0	0
$791$	−15.3137	−0.544493
$792$	−1.00000	−0.0355335
$793$	−32.0000	−1.13635
$794$	13.7990	0.489708
$795$	0	0
$796$	−22.1421	−0.784807
$797$	−20.0000	−0.708436	−0.354218	−	0.935163i	$-0.615253\pi$
$797$	−20.0000	−0.708436	−0.354218	+	0.935163i	$0.615253\pi$
$798$	−2.34315	−0.0829465
$799$	−3.17157	−0.112202
$800$	5.00000	0.176777
$801$	2.00000	0.0706665
$802$	5.51472	0.194731
$803$	−10.4853	−0.370018
$804$	−1.65685	−0.0584327
$805$	0	0
$806$	−6.62742	−0.233441
$807$	−11.3137	−0.398261
$808$	5.31371	0.186936
$809$	−47.2548	−1.66139	−0.830696	−	0.556727i	$-0.812057\pi$
$809$	−47.2548	−1.66139	−0.830696	+	0.556727i	$0.812057\pi$
$810$	0	0
$811$	28.6863	1.00731	0.503656	−	0.863904i	$-0.331988\pi$
$811$	28.6863	1.00731	0.503656	+	0.863904i	$0.331988\pi$
$812$	8.68629	0.304829
$813$	0.828427	0.0290542
$814$	3.17157	0.111164
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	3.31371	0.115932
$818$	10.9706	0.383577
$819$	−4.68629	−0.163752
$820$	0	0
$821$	37.7990	1.31919	0.659597	−	0.751620i	$-0.270727\pi$
$821$	37.7990	1.31919	0.659597	+	0.751620i	$0.270727\pi$
$822$	14.9706	0.522158
$823$	3.51472	0.122515	0.0612577	−	0.998122i	$-0.480489\pi$
$823$	3.51472	0.122515	0.0612577	+	0.998122i	$0.480489\pi$
$824$	12.0000	0.418040
$825$	5.00000	0.174078
$826$	5.65685	0.196827
$827$	44.9706	1.56378	0.781890	−	0.623417i	$-0.214256\pi$
$827$	44.9706	1.56378	0.781890	+	0.623417i	$0.214256\pi$
$828$	−0.828427	−0.0287898
$829$	−18.9706	−0.658875	−0.329437	−	0.944177i	$-0.606859\pi$
$829$	−18.9706	−0.658875	−0.329437	+	0.944177i	$0.606859\pi$
$830$	0	0
$831$	13.6569	0.473751
$832$	−5.65685	−0.196116
$833$	−6.31371	−0.218757
$834$	−6.34315	−0.219645
$835$	0	0
$836$	−2.82843	−0.0978232
$837$	1.17157	0.0404955
$838$	−11.3137	−0.390826
$839$	15.4558	0.533595	0.266797	−	0.963753i	$-0.414035\pi$
$839$	15.4558	0.533595	0.266797	+	0.963753i	$0.414035\pi$
$840$	0	0
$841$	80.9411	2.79107
$842$	−36.6274	−1.26226
$843$	−26.0000	−0.895488
$844$	16.9706	0.584151
$845$	0	0
$846$	3.17157	0.109041
$847$	0.828427	0.0284651
$848$	−4.00000	−0.137361
$849$	−16.9706	−0.582428
$850$	5.00000	0.171499
$851$	2.62742	0.0900667
$852$	8.82843	0.302457
$853$	13.6569	0.467602	0.233801	−	0.972284i	$-0.424884\pi$
$853$	13.6569	0.467602	0.233801	+	0.972284i	$0.424884\pi$
$854$	−4.68629	−0.160362
$855$	0	0
$856$	−1.65685	−0.0566301
$857$	2.68629	0.0917620	0.0458810	−	0.998947i	$-0.485391\pi$
$857$	2.68629	0.0917620	0.0458810	+	0.998947i	$0.485391\pi$
$858$	−5.65685	−0.193122
$859$	45.9411	1.56749	0.783745	−	0.621082i	$-0.213307\pi$
$859$	45.9411	1.56749	0.783745	+	0.621082i	$0.213307\pi$
$860$	0	0
$861$	−0.284271	−0.00968794
$862$	−12.4853	−0.425250
$863$	−6.48528	−0.220762	−0.110381	−	0.993889i	$-0.535207\pi$
$863$	−6.48528	−0.220762	−0.110381	+	0.993889i	$0.535207\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	6.00000	0.203888
$867$	−1.00000	−0.0339618
$868$	−0.970563	−0.0329430
$869$	−11.1716	−0.378970
$870$	0	0
$871$	−9.37258	−0.317578
$872$	−4.00000	−0.135457
$873$	−4.34315	−0.146993
$874$	−2.34315	−0.0792581
$875$	0	0
$876$	10.4853	0.354265
$877$	7.31371	0.246966	0.123483	−	0.992347i	$-0.460593\pi$
$877$	7.31371	0.246966	0.123483	+	0.992347i	$0.460593\pi$
$878$	−26.4853	−0.893835
$879$	28.6274	0.965579
$880$	0	0
$881$	0.828427	0.0279104	0.0139552	−	0.999903i	$-0.495558\pi$
$881$	0.828427	0.0279104	0.0139552	+	0.999903i	$0.495558\pi$
$882$	6.31371	0.212594
$883$	34.6274	1.16531	0.582653	−	0.812721i	$-0.302015\pi$
$883$	34.6274	1.16531	0.582653	+	0.812721i	$0.302015\pi$
$884$	−5.65685	−0.190261
$885$	0	0
$886$	21.4558	0.720823
$887$	−32.4853	−1.09075	−0.545374	−	0.838192i	$-0.683613\pi$
$887$	−32.4853	−1.09075	−0.545374	+	0.838192i	$0.683613\pi$
$888$	−3.17157	−0.106431
$889$	−8.68629	−0.291329
$890$	0	0
$891$	1.00000	0.0335013
$892$	−13.6569	−0.457265
$893$	8.97056	0.300188
$894$	15.6569	0.523644
$895$	0	0
$896$	−0.828427	−0.0276758
$897$	−4.68629	−0.156471
$898$	−36.8284	−1.22898
$899$	−12.2843	−0.409703
$900$	−5.00000	−0.166667
$901$	−4.00000	−0.133259
$902$	−0.343146	−0.0114255
$903$	0.970563	0.0322983
$904$	18.4853	0.614811
$905$	0	0
$906$	−4.82843	−0.160414
$907$	4.97056	0.165045	0.0825224	−	0.996589i	$-0.473702\pi$
$907$	4.97056	0.165045	0.0825224	+	0.996589i	$0.473702\pi$
$908$	20.9706	0.695933
$909$	−5.31371	−0.176245
$910$	0	0
$911$	−4.14214	−0.137235	−0.0686175	−	0.997643i	$-0.521859\pi$
$911$	−4.14214	−0.137235	−0.0686175	+	0.997643i	$0.521859\pi$
$912$	2.82843	0.0936586
$913$	−1.65685	−0.0548339
$914$	−14.9706	−0.495182
$915$	0	0
$916$	23.6569	0.781644
$917$	−3.31371	−0.109428
$918$	1.00000	0.0330049
$919$	−51.1716	−1.68799	−0.843997	−	0.536348i	$-0.819804\pi$
$919$	−51.1716	−1.68799	−0.843997	+	0.536348i	$0.819804\pi$
$920$	0	0
$921$	−2.82843	−0.0931998
$922$	3.65685	0.120432
$923$	49.9411	1.64383
$924$	−0.828427	−0.0272533
$925$	15.8579	0.521403
$926$	−26.6274	−0.875031
$927$	−12.0000	−0.394132
$928$	−10.4853	−0.344196
$929$	29.7990	0.977673	0.488837	−	0.872375i	$-0.337421\pi$
$929$	29.7990	0.977673	0.488837	+	0.872375i	$0.337421\pi$
$930$	0	0
$931$	17.8579	0.585268
$932$	17.3137	0.567129
$933$	19.1716	0.627649
$934$	35.7990	1.17138
$935$	0	0
$936$	5.65685	0.184900
$937$	−7.37258	−0.240852	−0.120426	−	0.992722i	$-0.538426\pi$
$937$	−7.37258	−0.240852	−0.120426	+	0.992722i	$0.538426\pi$
$938$	−1.37258	−0.0448164
$939$	−7.65685	−0.249872
$940$	0	0
$941$	−32.8284	−1.07018	−0.535088	−	0.844796i	$-0.679722\pi$
$941$	−32.8284	−1.07018	−0.535088	+	0.844796i	$0.679722\pi$
$942$	10.9706	0.357440
$943$	−0.284271	−0.00925715
$944$	−6.82843	−0.222246
$945$	0	0
$946$	1.17157	0.0380911
$947$	44.9706	1.46135	0.730673	−	0.682727i	$-0.239206\pi$
$947$	44.9706	1.46135	0.730673	+	0.682727i	$0.239206\pi$
$948$	11.1716	0.362836
$949$	59.3137	1.92540
$950$	−14.1421	−0.458831
$951$	20.9706	0.680017
$952$	−0.828427	−0.0268495
$953$	−8.62742	−0.279469	−0.139735	−	0.990189i	$-0.544625\pi$
$953$	−8.62742	−0.279469	−0.139735	+	0.990189i	$0.544625\pi$
$954$	4.00000	0.129505
$955$	0	0
$956$	23.3137	0.754019
$957$	−10.4853	−0.338941
$958$	−2.14214	−0.0692093
$959$	12.4020	0.400482
$960$	0	0
$961$	−29.6274	−0.955723
$962$	−17.9411	−0.578445
$963$	1.65685	0.0533914
$964$	−3.17157	−0.102149
$965$	0	0
$966$	−0.686292	−0.0220811
$967$	38.4853	1.23760	0.618802	−	0.785547i	$-0.287618\pi$
$967$	38.4853	1.23760	0.618802	+	0.785547i	$0.287618\pi$
$968$	−1.00000	−0.0321412
$969$	2.82843	0.0908622
$970$	0	0
$971$	−36.0833	−1.15797	−0.578983	−	0.815339i	$-0.696550\pi$
$971$	−36.0833	−1.15797	−0.578983	+	0.815339i	$0.696550\pi$
$972$	−1.00000	−0.0320750
$973$	−5.25483	−0.168462
$974$	16.4853	0.528222
$975$	−28.2843	−0.905822
$976$	5.65685	0.181071
$977$	5.02944	0.160906	0.0804530	−	0.996758i	$-0.474363\pi$
$977$	5.02944	0.160906	0.0804530	+	0.996758i	$0.474363\pi$
$978$	−1.65685	−0.0529804
$979$	2.00000	0.0639203
$980$	0	0
$981$	4.00000	0.127710
$982$	16.2843	0.519652
$983$	0.142136	0.00453342	0.00226671	−	0.999997i	$-0.499278\pi$
$983$	0.142136	0.00453342	0.00226671	+	0.999997i	$0.499278\pi$
$984$	0.343146	0.0109391
$985$	0	0
$986$	−10.4853	−0.333919
$987$	2.62742	0.0836316
$988$	16.0000	0.509028
$989$	0.970563	0.0308621
$990$	0	0
$991$	−42.1421	−1.33869	−0.669345	−	0.742952i	$-0.733425\pi$
$991$	−42.1421	−1.33869	−0.669345	+	0.742952i	$0.733425\pi$
$992$	1.17157	0.0371975
$993$	7.31371	0.232094
$994$	7.31371	0.231977
$995$	0	0
$996$	1.65685	0.0524994
$997$	21.9411	0.694882	0.347441	−	0.937702i	$-0.387051\pi$
$997$	21.9411	0.694882	0.347441	+	0.937702i	$0.387051\pi$
$998$	36.0000	1.13956
$999$	3.17157	0.100344

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.828427 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +0.828427 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} -1.00000 q^{12} -5.65685 q^{13} -0.828427 q^{14} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -2.82843 q^{19} -0.828427 q^{21} -1.00000 q^{22} -0.828427 q^{23} +1.00000 q^{24} -5.00000 q^{25} +5.65685 q^{26} -1.00000 q^{27} +0.828427 q^{28} +10.4853 q^{29} -1.17157 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} -3.17157 q^{37} +2.82843 q^{38} +5.65685 q^{39} +0.343146 q^{41} +0.828427 q^{42} -1.17157 q^{43} +1.00000 q^{44} +0.828427 q^{46} -3.17157 q^{47} -1.00000 q^{48} -6.31371 q^{49} +5.00000 q^{50} -1.00000 q^{51} -5.65685 q^{52} -4.00000 q^{53} +1.00000 q^{54} -0.828427 q^{56} +2.82843 q^{57} -10.4853 q^{58} -6.82843 q^{59} +5.65685 q^{61} +1.17157 q^{62} +0.828427 q^{63} +1.00000 q^{64} +1.00000 q^{66} +1.65685 q^{67} +1.00000 q^{68} +0.828427 q^{69} -8.82843 q^{71} -1.00000 q^{72} -10.4853 q^{73} +3.17157 q^{74} +5.00000 q^{75} -2.82843 q^{76} +0.828427 q^{77} -5.65685 q^{78} -11.1716 q^{79} +1.00000 q^{81} -0.343146 q^{82} -1.65685 q^{83} -0.828427 q^{84} +1.17157 q^{86} -10.4853 q^{87} -1.00000 q^{88} +2.00000 q^{89} -4.68629 q^{91} -0.828427 q^{92} +1.17157 q^{93} +3.17157 q^{94} +1.00000 q^{96} -4.34315 q^{97} +6.31371 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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