LMFDB - Embedded newform 3822.2.a.br.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$30.5188236525$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
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	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -6.41421 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +3.24264 q^{17} +1.00000 q^{18} -4.65685 q^{19} -1.00000 q^{20} -6.41421 q^{22} -2.17157 q^{23} +1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} +7.48528 q^{29} -1.00000 q^{30} +1.41421 q^{31} +1.00000 q^{32} -6.41421 q^{33} +3.24264 q^{34} +1.00000 q^{36} -8.41421 q^{37} -4.65685 q^{38} -1.00000 q^{39} -1.00000 q^{40} -5.17157 q^{41} -8.65685 q^{43} -6.41421 q^{44} -1.00000 q^{45} -2.17157 q^{46} +6.00000 q^{47} +1.00000 q^{48} -4.00000 q^{50} +3.24264 q^{51} -1.00000 q^{52} -5.65685 q^{53} +1.00000 q^{54} +6.41421 q^{55} -4.65685 q^{57} +7.48528 q^{58} -11.0711 q^{59} -1.00000 q^{60} +10.4142 q^{61} +1.41421 q^{62} +1.00000 q^{64} +1.00000 q^{65} -6.41421 q^{66} -15.5563 q^{67} +3.24264 q^{68} -2.17157 q^{69} -5.75736 q^{71} +1.00000 q^{72} +11.0000 q^{73} -8.41421 q^{74} -4.00000 q^{75} -4.65685 q^{76} -1.00000 q^{78} +2.24264 q^{79} -1.00000 q^{80} +1.00000 q^{81} -5.17157 q^{82} -3.65685 q^{83} -3.24264 q^{85} -8.65685 q^{86} +7.48528 q^{87} -6.41421 q^{88} -14.2426 q^{89} -1.00000 q^{90} -2.17157 q^{92} +1.41421 q^{93} +6.00000 q^{94} +4.65685 q^{95} +1.00000 q^{96} +7.31371 q^{97} -6.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 10 q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} - 10 q^{22} - 10 q^{23} + 2 q^{24} - 8 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{29} - 2 q^{30} + 2 q^{32} - 10 q^{33} - 2 q^{34} + 2 q^{36} - 14 q^{37} + 2 q^{38} - 2 q^{39} - 2 q^{40} - 16 q^{41} - 6 q^{43} - 10 q^{44} - 2 q^{45} - 10 q^{46} + 12 q^{47} + 2 q^{48} - 8 q^{50} - 2 q^{51} - 2 q^{52} + 2 q^{54} + 10 q^{55} + 2 q^{57} - 2 q^{58} - 8 q^{59} - 2 q^{60} + 18 q^{61} + 2 q^{64} + 2 q^{65} - 10 q^{66} - 2 q^{68} - 10 q^{69} - 20 q^{71} + 2 q^{72} + 22 q^{73} - 14 q^{74} - 8 q^{75} + 2 q^{76} - 2 q^{78} - 4 q^{79} - 2 q^{80} + 2 q^{81} - 16 q^{82} + 4 q^{83} + 2 q^{85} - 6 q^{86} - 2 q^{87} - 10 q^{88} - 20 q^{89} - 2 q^{90} - 10 q^{92} + 12 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 10 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 10 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 - 10 * q^22 - 10 * q^23 + 2 * q^24 - 8 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^29 - 2 * q^30 + 2 * q^32 - 10 * q^33 - 2 * q^34 + 2 * q^36 - 14 * q^37 + 2 * q^38 - 2 * q^39 - 2 * q^40 - 16 * q^41 - 6 * q^43 - 10 * q^44 - 2 * q^45 - 10 * q^46 + 12 * q^47 + 2 * q^48 - 8 * q^50 - 2 * q^51 - 2 * q^52 + 2 * q^54 + 10 * q^55 + 2 * q^57 - 2 * q^58 - 8 * q^59 - 2 * q^60 + 18 * q^61 + 2 * q^64 + 2 * q^65 - 10 * q^66 - 2 * q^68 - 10 * q^69 - 20 * q^71 + 2 * q^72 + 22 * q^73 - 14 * q^74 - 8 * q^75 + 2 * q^76 - 2 * q^78 - 4 * q^79 - 2 * q^80 + 2 * q^81 - 16 * q^82 + 4 * q^83 + 2 * q^85 - 6 * q^86 - 2 * q^87 - 10 * q^88 - 20 * q^89 - 2 * q^90 - 10 * q^92 + 12 * q^94 - 2 * q^95 + 2 * q^96 - 8 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−6.41421	−1.93396	−0.966979	−	0.254856i	$-0.917972\pi$
$11$	−6.41421	−1.93396	−0.966979	+	0.254856i	$0.917972\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	3.24264	0.786456	0.393228	−	0.919441i	$-0.371358\pi$
$17$	3.24264	0.786456	0.393228	+	0.919441i	$0.371358\pi$
$18$	1.00000	0.235702
$19$	−4.65685	−1.06836	−0.534178	−	0.845372i	$-0.679379\pi$
$19$	−4.65685	−1.06836	−0.534178	+	0.845372i	$0.679379\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−6.41421	−1.36751
$23$	−2.17157	−0.452804	−0.226402	−	0.974034i	$-0.572696\pi$
$23$	−2.17157	−0.452804	−0.226402	+	0.974034i	$0.572696\pi$
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	7.48528	1.38998	0.694991	−	0.719019i	$-0.255408\pi$
$29$	7.48528	1.38998	0.694991	+	0.719019i	$0.255408\pi$
$30$	−1.00000	−0.182574
$31$	1.41421	0.254000	0.127000	−	0.991903i	$-0.459465\pi$
$31$	1.41421	0.254000	0.127000	+	0.991903i	$0.459465\pi$
$32$	1.00000	0.176777
$33$	−6.41421	−1.11657
$34$	3.24264	0.556108
$35$	0	0
$36$	1.00000	0.166667
$37$	−8.41421	−1.38329	−0.691644	−	0.722238i	$-0.743113\pi$
$37$	−8.41421	−1.38329	−0.691644	+	0.722238i	$0.743113\pi$
$38$	−4.65685	−0.755442
$39$	−1.00000	−0.160128
$40$	−1.00000	−0.158114
$41$	−5.17157	−0.807664	−0.403832	−	0.914833i	$-0.632322\pi$
$41$	−5.17157	−0.807664	−0.403832	+	0.914833i	$0.632322\pi$
$42$	0	0
$43$	−8.65685	−1.32016	−0.660079	−	0.751196i	$-0.729477\pi$
$43$	−8.65685	−1.32016	−0.660079	+	0.751196i	$0.729477\pi$
$44$	−6.41421	−0.966979
$45$	−1.00000	−0.149071
$46$	−2.17157	−0.320181
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.00000	−0.565685
$51$	3.24264	0.454061
$52$	−1.00000	−0.138675
$53$	−5.65685	−0.777029	−0.388514	−	0.921443i	$-0.627012\pi$
$53$	−5.65685	−0.777029	−0.388514	+	0.921443i	$0.627012\pi$
$54$	1.00000	0.136083
$55$	6.41421	0.864892
$56$	0	0
$57$	−4.65685	−0.616815
$58$	7.48528	0.982866
$59$	−11.0711	−1.44133	−0.720665	−	0.693283i	$-0.756163\pi$
$59$	−11.0711	−1.44133	−0.720665	+	0.693283i	$0.756163\pi$
$60$	−1.00000	−0.129099
$61$	10.4142	1.33340	0.666702	−	0.745325i	$-0.267706\pi$
$61$	10.4142	1.33340	0.666702	+	0.745325i	$0.267706\pi$
$62$	1.41421	0.179605
$63$	0	0
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−6.41421	−0.789535
$67$	−15.5563	−1.90051	−0.950255	−	0.311472i	$-0.899178\pi$
$67$	−15.5563	−1.90051	−0.950255	+	0.311472i	$0.899178\pi$
$68$	3.24264	0.393228
$69$	−2.17157	−0.261427
$70$	0	0
$71$	−5.75736	−0.683273	−0.341636	−	0.939832i	$-0.610981\pi$
$71$	−5.75736	−0.683273	−0.341636	+	0.939832i	$0.610981\pi$
$72$	1.00000	0.117851
$73$	11.0000	1.28745	0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000	1.28745	0.643726	+	0.765256i	$0.277388\pi$
$74$	−8.41421	−0.978132
$75$	−4.00000	−0.461880
$76$	−4.65685	−0.534178
$77$	0	0
$78$	−1.00000	−0.113228
$79$	2.24264	0.252317	0.126158	−	0.992010i	$-0.459735\pi$
$79$	2.24264	0.252317	0.126158	+	0.992010i	$0.459735\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−5.17157	−0.571105
$83$	−3.65685	−0.401392	−0.200696	−	0.979654i	$-0.564320\pi$
$83$	−3.65685	−0.401392	−0.200696	+	0.979654i	$0.564320\pi$
$84$	0	0
$85$	−3.24264	−0.351714
$86$	−8.65685	−0.933493
$87$	7.48528	0.802506
$88$	−6.41421	−0.683757
$89$	−14.2426	−1.50972	−0.754858	−	0.655888i	$-0.772294\pi$
$89$	−14.2426	−1.50972	−0.754858	+	0.655888i	$0.772294\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−2.17157	−0.226402
$93$	1.41421	0.146647
$94$	6.00000	0.618853
$95$	4.65685	0.477783
$96$	1.00000	0.102062
$97$	7.31371	0.742595	0.371297	−	0.928514i	$-0.378913\pi$
$97$	7.31371	0.742595	0.371297	+	0.928514i	$0.378913\pi$
$98$	0	0
$99$	−6.41421	−0.644653
$100$	−4.00000	−0.400000
$101$	−12.5858	−1.25233	−0.626166	−	0.779690i	$-0.715377\pi$
$101$	−12.5858	−1.25233	−0.626166	+	0.779690i	$0.715377\pi$
$102$	3.24264	0.321069
$103$	1.58579	0.156252	0.0781261	−	0.996943i	$-0.475106\pi$
$103$	1.58579	0.156252	0.0781261	+	0.996943i	$0.475106\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−5.65685	−0.549442
$107$	−17.5563	−1.69724	−0.848618	−	0.529006i	$-0.822565\pi$
$107$	−17.5563	−1.69724	−0.848618	+	0.529006i	$0.822565\pi$
$108$	1.00000	0.0962250
$109$	0.899495	0.0861560	0.0430780	−	0.999072i	$-0.486284\pi$
$109$	0.899495	0.0861560	0.0430780	+	0.999072i	$0.486284\pi$
$110$	6.41421	0.611571
$111$	−8.41421	−0.798642
$112$	0	0
$113$	4.58579	0.431394	0.215697	−	0.976460i	$-0.430798\pi$
$113$	4.58579	0.431394	0.215697	+	0.976460i	$0.430798\pi$
$114$	−4.65685	−0.436154
$115$	2.17157	0.202500
$116$	7.48528	0.694991
$117$	−1.00000	−0.0924500
$118$	−11.0711	−1.01917
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	30.1421	2.74019
$122$	10.4142	0.942859
$123$	−5.17157	−0.466305
$124$	1.41421	0.127000
$125$	9.00000	0.804984
$126$	0	0
$127$	6.72792	0.597007	0.298503	−	0.954409i	$-0.403513\pi$
$127$	6.72792	0.597007	0.298503	+	0.954409i	$0.403513\pi$
$128$	1.00000	0.0883883
$129$	−8.65685	−0.762194
$130$	1.00000	0.0877058
$131$	−5.72792	−0.500451	−0.250225	−	0.968188i	$-0.580505\pi$
$131$	−5.72792	−0.500451	−0.250225	+	0.968188i	$0.580505\pi$
$132$	−6.41421	−0.558286
$133$	0	0
$134$	−15.5563	−1.34386
$135$	−1.00000	−0.0860663
$136$	3.24264	0.278054
$137$	−6.41421	−0.548003	−0.274002	−	0.961729i	$-0.588347\pi$
$137$	−6.41421	−0.548003	−0.274002	+	0.961729i	$0.588347\pi$
$138$	−2.17157	−0.184857
$139$	19.7990	1.67933	0.839664	−	0.543106i	$-0.182752\pi$
$139$	19.7990	1.67933	0.839664	+	0.543106i	$0.182752\pi$
$140$	0	0
$141$	6.00000	0.505291
$142$	−5.75736	−0.483147
$143$	6.41421	0.536383
$144$	1.00000	0.0833333
$145$	−7.48528	−0.621619
$146$	11.0000	0.910366
$147$	0	0
$148$	−8.41421	−0.691644
$149$	8.48528	0.695141	0.347571	−	0.937654i	$-0.387007\pi$
$149$	8.48528	0.695141	0.347571	+	0.937654i	$0.387007\pi$
$150$	−4.00000	−0.326599
$151$	−6.41421	−0.521981	−0.260991	−	0.965341i	$-0.584049\pi$
$151$	−6.41421	−0.521981	−0.260991	+	0.965341i	$0.584049\pi$
$152$	−4.65685	−0.377721
$153$	3.24264	0.262152
$154$	0	0
$155$	−1.41421	−0.113592
$156$	−1.00000	−0.0800641
$157$	8.41421	0.671527	0.335764	−	0.941946i	$-0.391006\pi$
$157$	8.41421	0.671527	0.335764	+	0.941946i	$0.391006\pi$
$158$	2.24264	0.178415
$159$	−5.65685	−0.448618
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−0.343146	−0.0268772	−0.0134386	−	0.999910i	$-0.504278\pi$
$163$	−0.343146	−0.0268772	−0.0134386	+	0.999910i	$0.504278\pi$
$164$	−5.17157	−0.403832
$165$	6.41421	0.499346
$166$	−3.65685	−0.283827
$167$	23.1421	1.79079	0.895396	−	0.445270i	$-0.146892\pi$
$167$	23.1421	1.79079	0.895396	+	0.445270i	$0.146892\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−3.24264	−0.248699
$171$	−4.65685	−0.356119
$172$	−8.65685	−0.660079
$173$	−17.8995	−1.36087	−0.680437	−	0.732807i	$-0.738210\pi$
$173$	−17.8995	−1.36087	−0.680437	+	0.732807i	$0.738210\pi$
$174$	7.48528	0.567458
$175$	0	0
$176$	−6.41421	−0.483490
$177$	−11.0711	−0.832152
$178$	−14.2426	−1.06753
$179$	−6.10051	−0.455973	−0.227987	−	0.973664i	$-0.573214\pi$
$179$	−6.10051	−0.455973	−0.227987	+	0.973664i	$0.573214\pi$
$180$	−1.00000	−0.0745356
$181$	22.8284	1.69682	0.848412	−	0.529337i	$-0.177559\pi$
$181$	22.8284	1.69682	0.848412	+	0.529337i	$0.177559\pi$
$182$	0	0
$183$	10.4142	0.769841
$184$	−2.17157	−0.160090
$185$	8.41421	0.618625
$186$	1.41421	0.103695
$187$	−20.7990	−1.52097
$188$	6.00000	0.437595
$189$	0	0
$190$	4.65685	0.337844
$191$	−21.9706	−1.58973	−0.794867	−	0.606784i	$-0.792459\pi$
$191$	−21.9706	−1.58973	−0.794867	+	0.606784i	$0.792459\pi$
$192$	1.00000	0.0721688
$193$	5.75736	0.414424	0.207212	−	0.978296i	$-0.433561\pi$
$193$	5.75736	0.414424	0.207212	+	0.978296i	$0.433561\pi$
$194$	7.31371	0.525094
$195$	1.00000	0.0716115
$196$	0	0
$197$	4.58579	0.326724	0.163362	−	0.986566i	$-0.447766\pi$
$197$	4.58579	0.326724	0.163362	+	0.986566i	$0.447766\pi$
$198$	−6.41421	−0.455838
$199$	−16.5563	−1.17365	−0.586824	−	0.809714i	$-0.699622\pi$
$199$	−16.5563	−1.17365	−0.586824	+	0.809714i	$0.699622\pi$
$200$	−4.00000	−0.282843
$201$	−15.5563	−1.09726
$202$	−12.5858	−0.885533
$203$	0	0
$204$	3.24264	0.227030
$205$	5.17157	0.361198
$206$	1.58579	0.110487
$207$	−2.17157	−0.150935
$208$	−1.00000	−0.0693375
$209$	29.8701	2.06616
$210$	0	0
$211$	12.6569	0.871334	0.435667	−	0.900108i	$-0.356513\pi$
$211$	12.6569	0.871334	0.435667	+	0.900108i	$0.356513\pi$
$212$	−5.65685	−0.388514
$213$	−5.75736	−0.394488
$214$	−17.5563	−1.20013
$215$	8.65685	0.590393
$216$	1.00000	0.0680414
$217$	0	0
$218$	0.899495	0.0609215
$219$	11.0000	0.743311
$220$	6.41421	0.432446
$221$	−3.24264	−0.218124
$222$	−8.41421	−0.564725
$223$	−14.0000	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$223$	−14.0000	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	4.58579	0.305042
$227$	5.07107	0.336579	0.168289	−	0.985738i	$-0.446176\pi$
$227$	5.07107	0.336579	0.168289	+	0.985738i	$0.446176\pi$
$228$	−4.65685	−0.308408
$229$	−3.89949	−0.257686	−0.128843	−	0.991665i	$-0.541126\pi$
$229$	−3.89949	−0.257686	−0.128843	+	0.991665i	$0.541126\pi$
$230$	2.17157	0.143189
$231$	0	0
$232$	7.48528	0.491433
$233$	−6.14214	−0.402385	−0.201192	−	0.979552i	$-0.564482\pi$
$233$	−6.14214	−0.402385	−0.201192	+	0.979552i	$0.564482\pi$
$234$	−1.00000	−0.0653720
$235$	−6.00000	−0.391397
$236$	−11.0711	−0.720665
$237$	2.24264	0.145675
$238$	0	0
$239$	−20.3848	−1.31858	−0.659291	−	0.751888i	$-0.729143\pi$
$239$	−20.3848	−1.31858	−0.659291	+	0.751888i	$0.729143\pi$
$240$	−1.00000	−0.0645497
$241$	14.9706	0.964339	0.482169	−	0.876078i	$-0.339849\pi$
$241$	14.9706	0.964339	0.482169	+	0.876078i	$0.339849\pi$
$242$	30.1421	1.93761
$243$	1.00000	0.0641500
$244$	10.4142	0.666702
$245$	0	0
$246$	−5.17157	−0.329727
$247$	4.65685	0.296309
$248$	1.41421	0.0898027
$249$	−3.65685	−0.231744
$250$	9.00000	0.569210
$251$	6.55635	0.413833	0.206917	−	0.978359i	$-0.433657\pi$
$251$	6.55635	0.413833	0.206917	+	0.978359i	$0.433657\pi$
$252$	0	0
$253$	13.9289	0.875704
$254$	6.72792	0.422147
$255$	−3.24264	−0.203062
$256$	1.00000	0.0625000
$257$	−2.82843	−0.176432	−0.0882162	−	0.996101i	$-0.528117\pi$
$257$	−2.82843	−0.176432	−0.0882162	+	0.996101i	$0.528117\pi$
$258$	−8.65685	−0.538952
$259$	0	0
$260$	1.00000	0.0620174
$261$	7.48528	0.463327
$262$	−5.72792	−0.353872
$263$	26.6274	1.64192	0.820958	−	0.570988i	$-0.193440\pi$
$263$	26.6274	1.64192	0.820958	+	0.570988i	$0.193440\pi$
$264$	−6.41421	−0.394768
$265$	5.65685	0.347498
$266$	0	0
$267$	−14.2426	−0.871635
$268$	−15.5563	−0.950255
$269$	−13.2132	−0.805623	−0.402812	−	0.915283i	$-0.631967\pi$
$269$	−13.2132	−0.805623	−0.402812	+	0.915283i	$0.631967\pi$
$270$	−1.00000	−0.0608581
$271$	28.3848	1.72425	0.862126	−	0.506694i	$-0.169132\pi$
$271$	28.3848	1.72425	0.862126	+	0.506694i	$0.169132\pi$
$272$	3.24264	0.196614
$273$	0	0
$274$	−6.41421	−0.387497
$275$	25.6569	1.54717
$276$	−2.17157	−0.130713
$277$	−4.58579	−0.275533	−0.137767	−	0.990465i	$-0.543992\pi$
$277$	−4.58579	−0.275533	−0.137767	+	0.990465i	$0.543992\pi$
$278$	19.7990	1.18746
$279$	1.41421	0.0846668
$280$	0	0
$281$	26.9706	1.60893	0.804464	−	0.594001i	$-0.202452\pi$
$281$	26.9706	1.60893	0.804464	+	0.594001i	$0.202452\pi$
$282$	6.00000	0.357295
$283$	−8.48528	−0.504398	−0.252199	−	0.967675i	$-0.581154\pi$
$283$	−8.48528	−0.504398	−0.252199	+	0.967675i	$0.581154\pi$
$284$	−5.75736	−0.341636
$285$	4.65685	0.275848
$286$	6.41421	0.379280
$287$	0	0
$288$	1.00000	0.0589256
$289$	−6.48528	−0.381487
$290$	−7.48528	−0.439551
$291$	7.31371	0.428737
$292$	11.0000	0.643726
$293$	−19.7990	−1.15667	−0.578335	−	0.815800i	$-0.696297\pi$
$293$	−19.7990	−1.15667	−0.578335	+	0.815800i	$0.696297\pi$
$294$	0	0
$295$	11.0711	0.644582
$296$	−8.41421	−0.489066
$297$	−6.41421	−0.372190
$298$	8.48528	0.491539
$299$	2.17157	0.125585
$300$	−4.00000	−0.230940
$301$	0	0
$302$	−6.41421	−0.369097
$303$	−12.5858	−0.723035
$304$	−4.65685	−0.267089
$305$	−10.4142	−0.596316
$306$	3.24264	0.185369
$307$	21.3137	1.21644	0.608219	−	0.793769i	$-0.291884\pi$
$307$	21.3137	1.21644	0.608219	+	0.793769i	$0.291884\pi$
$308$	0	0
$309$	1.58579	0.0902122
$310$	−1.41421	−0.0803219
$311$	12.8284	0.727433	0.363717	−	0.931510i	$-0.381508\pi$
$311$	12.8284	0.727433	0.363717	+	0.931510i	$0.381508\pi$
$312$	−1.00000	−0.0566139
$313$	15.8995	0.898693	0.449346	−	0.893358i	$-0.351657\pi$
$313$	15.8995	0.898693	0.449346	+	0.893358i	$0.351657\pi$
$314$	8.41421	0.474842
$315$	0	0
$316$	2.24264	0.126158
$317$	−15.4142	−0.865748	−0.432874	−	0.901454i	$-0.642501\pi$
$317$	−15.4142	−0.865748	−0.432874	+	0.901454i	$0.642501\pi$
$318$	−5.65685	−0.317221
$319$	−48.0122	−2.68817
$320$	−1.00000	−0.0559017
$321$	−17.5563	−0.979900
$322$	0	0
$323$	−15.1005	−0.840215
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−0.343146	−0.0190051
$327$	0.899495	0.0497422
$328$	−5.17157	−0.285552
$329$	0	0
$330$	6.41421	0.353091
$331$	3.75736	0.206523	0.103262	−	0.994654i	$-0.467072\pi$
$331$	3.75736	0.206523	0.103262	+	0.994654i	$0.467072\pi$
$332$	−3.65685	−0.200696
$333$	−8.41421	−0.461096
$334$	23.1421	1.26628
$335$	15.5563	0.849934
$336$	0	0
$337$	−27.8284	−1.51591	−0.757956	−	0.652306i	$-0.773802\pi$
$337$	−27.8284	−1.51591	−0.757956	+	0.652306i	$0.773802\pi$
$338$	1.00000	0.0543928
$339$	4.58579	0.249066
$340$	−3.24264	−0.175857
$341$	−9.07107	−0.491226
$342$	−4.65685	−0.251814
$343$	0	0
$344$	−8.65685	−0.466746
$345$	2.17157	0.116914
$346$	−17.8995	−0.962283
$347$	−13.4142	−0.720113	−0.360056	−	0.932931i	$-0.617243\pi$
$347$	−13.4142	−0.720113	−0.360056	+	0.932931i	$0.617243\pi$
$348$	7.48528	0.401253
$349$	−23.8995	−1.27931	−0.639655	−	0.768662i	$-0.720923\pi$
$349$	−23.8995	−1.27931	−0.639655	+	0.768662i	$0.720923\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−6.41421	−0.341879
$353$	−15.1716	−0.807501	−0.403751	−	0.914869i	$-0.632294\pi$
$353$	−15.1716	−0.807501	−0.403751	+	0.914869i	$0.632294\pi$
$354$	−11.0711	−0.588421
$355$	5.75736	0.305569
$356$	−14.2426	−0.754858
$357$	0	0
$358$	−6.10051	−0.322422
$359$	−6.14214	−0.324170	−0.162085	−	0.986777i	$-0.551822\pi$
$359$	−6.14214	−0.324170	−0.162085	+	0.986777i	$0.551822\pi$
$360$	−1.00000	−0.0527046
$361$	2.68629	0.141384
$362$	22.8284	1.19984
$363$	30.1421	1.58205
$364$	0	0
$365$	−11.0000	−0.575766
$366$	10.4142	0.544360
$367$	−6.34315	−0.331110	−0.165555	−	0.986201i	$-0.552941\pi$
$367$	−6.34315	−0.331110	−0.165555	+	0.986201i	$0.552941\pi$
$368$	−2.17157	−0.113201
$369$	−5.17157	−0.269221
$370$	8.41421	0.437434
$371$	0	0
$372$	1.41421	0.0733236
$373$	30.8701	1.59839	0.799195	−	0.601071i	$-0.205259\pi$
$373$	30.8701	1.59839	0.799195	+	0.601071i	$0.205259\pi$
$374$	−20.7990	−1.07549
$375$	9.00000	0.464758
$376$	6.00000	0.309426
$377$	−7.48528	−0.385512
$378$	0	0
$379$	11.8995	0.611236	0.305618	−	0.952154i	$-0.401137\pi$
$379$	11.8995	0.611236	0.305618	+	0.952154i	$0.401137\pi$
$380$	4.65685	0.238892
$381$	6.72792	0.344682
$382$	−21.9706	−1.12411
$383$	−22.3137	−1.14018	−0.570089	−	0.821583i	$-0.693091\pi$
$383$	−22.3137	−1.14018	−0.570089	+	0.821583i	$0.693091\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	5.75736	0.293042
$387$	−8.65685	−0.440053
$388$	7.31371	0.371297
$389$	29.6569	1.50366	0.751831	−	0.659356i	$-0.229171\pi$
$389$	29.6569	1.50366	0.751831	+	0.659356i	$0.229171\pi$
$390$	1.00000	0.0506370
$391$	−7.04163	−0.356111
$392$	0	0
$393$	−5.72792	−0.288935
$394$	4.58579	0.231029
$395$	−2.24264	−0.112839
$396$	−6.41421	−0.322326
$397$	−11.6569	−0.585041	−0.292520	−	0.956259i	$-0.594494\pi$
$397$	−11.6569	−0.585041	−0.292520	+	0.956259i	$0.594494\pi$
$398$	−16.5563	−0.829895
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−23.7990	−1.18846	−0.594232	−	0.804293i	$-0.702544\pi$
$401$	−23.7990	−1.18846	−0.594232	+	0.804293i	$0.702544\pi$
$402$	−15.5563	−0.775880
$403$	−1.41421	−0.0704470
$404$	−12.5858	−0.626166
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	53.9706	2.67522
$408$	3.24264	0.160535
$409$	−8.79899	−0.435082	−0.217541	−	0.976051i	$-0.569804\pi$
$409$	−8.79899	−0.435082	−0.217541	+	0.976051i	$0.569804\pi$
$410$	5.17157	0.255406
$411$	−6.41421	−0.316390
$412$	1.58579	0.0781261
$413$	0	0
$414$	−2.17157	−0.106727
$415$	3.65685	0.179508
$416$	−1.00000	−0.0490290
$417$	19.7990	0.969561
$418$	29.8701	1.46099
$419$	22.0711	1.07824	0.539121	−	0.842228i	$-0.318757\pi$
$419$	22.0711	1.07824	0.539121	+	0.842228i	$0.318757\pi$
$420$	0	0
$421$	−35.4558	−1.72801	−0.864006	−	0.503481i	$-0.832052\pi$
$421$	−35.4558	−1.72801	−0.864006	+	0.503481i	$0.832052\pi$
$422$	12.6569	0.616126
$423$	6.00000	0.291730
$424$	−5.65685	−0.274721
$425$	−12.9706	−0.629165
$426$	−5.75736	−0.278945
$427$	0	0
$428$	−17.5563	−0.848618
$429$	6.41421	0.309681
$430$	8.65685	0.417471
$431$	13.5147	0.650981	0.325491	−	0.945545i	$-0.394471\pi$
$431$	13.5147	0.650981	0.325491	+	0.945545i	$0.394471\pi$
$432$	1.00000	0.0481125
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	−7.48528	−0.358892
$436$	0.899495	0.0430780
$437$	10.1127	0.483756
$438$	11.0000	0.525600
$439$	−2.07107	−0.0988467	−0.0494233	−	0.998778i	$-0.515738\pi$
$439$	−2.07107	−0.0988467	−0.0494233	+	0.998778i	$0.515738\pi$
$440$	6.41421	0.305786
$441$	0	0
$442$	−3.24264	−0.154237
$443$	−9.79899	−0.465564	−0.232782	−	0.972529i	$-0.574783\pi$
$443$	−9.79899	−0.465564	−0.232782	+	0.972529i	$0.574783\pi$
$444$	−8.41421	−0.399321
$445$	14.2426	0.675166
$446$	−14.0000	−0.662919
$447$	8.48528	0.401340
$448$	0	0
$449$	21.0416	0.993016	0.496508	−	0.868032i	$-0.334615\pi$
$449$	21.0416	0.993016	0.496508	+	0.868032i	$0.334615\pi$
$450$	−4.00000	−0.188562
$451$	33.1716	1.56199
$452$	4.58579	0.215697
$453$	−6.41421	−0.301366
$454$	5.07107	0.237997
$455$	0	0
$456$	−4.65685	−0.218077
$457$	39.6985	1.85702	0.928508	−	0.371311i	$-0.121092\pi$
$457$	39.6985	1.85702	0.928508	+	0.371311i	$0.121092\pi$
$458$	−3.89949	−0.182211
$459$	3.24264	0.151354
$460$	2.17157	0.101250
$461$	−33.4853	−1.55957	−0.779783	−	0.626050i	$-0.784670\pi$
$461$	−33.4853	−1.55957	−0.779783	+	0.626050i	$0.784670\pi$
$462$	0	0
$463$	24.0711	1.11868	0.559339	−	0.828939i	$-0.311055\pi$
$463$	24.0711	1.11868	0.559339	+	0.828939i	$0.311055\pi$
$464$	7.48528	0.347495
$465$	−1.41421	−0.0655826
$466$	−6.14214	−0.284529
$467$	10.4142	0.481912	0.240956	−	0.970536i	$-0.422539\pi$
$467$	10.4142	0.481912	0.240956	+	0.970536i	$0.422539\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	−6.00000	−0.276759
$471$	8.41421	0.387706
$472$	−11.0711	−0.509587
$473$	55.5269	2.55313
$474$	2.24264	0.103008
$475$	18.6274	0.854685
$476$	0	0
$477$	−5.65685	−0.259010
$478$	−20.3848	−0.932378
$479$	−33.1421	−1.51430	−0.757151	−	0.653239i	$-0.773410\pi$
$479$	−33.1421	−1.51430	−0.757151	+	0.653239i	$0.773410\pi$
$480$	−1.00000	−0.0456435
$481$	8.41421	0.383655
$482$	14.9706	0.681890
$483$	0	0
$484$	30.1421	1.37010
$485$	−7.31371	−0.332098
$486$	1.00000	0.0453609
$487$	8.34315	0.378064	0.189032	−	0.981971i	$-0.439465\pi$
$487$	8.34315	0.378064	0.189032	+	0.981971i	$0.439465\pi$
$488$	10.4142	0.471429
$489$	−0.343146	−0.0155176
$490$	0	0
$491$	24.8284	1.12049	0.560246	−	0.828327i	$-0.310707\pi$
$491$	24.8284	1.12049	0.560246	+	0.828327i	$0.310707\pi$
$492$	−5.17157	−0.233153
$493$	24.2721	1.09316
$494$	4.65685	0.209522
$495$	6.41421	0.288297
$496$	1.41421	0.0635001
$497$	0	0
$498$	−3.65685	−0.163868
$499$	22.0416	0.986719	0.493359	−	0.869826i	$-0.335769\pi$
$499$	22.0416	0.986719	0.493359	+	0.869826i	$0.335769\pi$
$500$	9.00000	0.402492
$501$	23.1421	1.03391
$502$	6.55635	0.292624
$503$	22.3848	0.998088	0.499044	−	0.866577i	$-0.333685\pi$
$503$	22.3848	0.998088	0.499044	+	0.866577i	$0.333685\pi$
$504$	0	0
$505$	12.5858	0.560060
$506$	13.9289	0.619217
$507$	1.00000	0.0444116
$508$	6.72792	0.298503
$509$	18.7990	0.833251	0.416625	−	0.909078i	$-0.363213\pi$
$509$	18.7990	0.833251	0.416625	+	0.909078i	$0.363213\pi$
$510$	−3.24264	−0.143587
$511$	0	0
$512$	1.00000	0.0441942
$513$	−4.65685	−0.205605
$514$	−2.82843	−0.124757
$515$	−1.58579	−0.0698781
$516$	−8.65685	−0.381097
$517$	−38.4853	−1.69258
$518$	0	0
$519$	−17.8995	−0.785701
$520$	1.00000	0.0438529
$521$	−9.24264	−0.404927	−0.202464	−	0.979290i	$-0.564895\pi$
$521$	−9.24264	−0.404927	−0.202464	+	0.979290i	$0.564895\pi$
$522$	7.48528	0.327622
$523$	13.7574	0.601567	0.300784	−	0.953692i	$-0.402752\pi$
$523$	13.7574	0.601567	0.300784	+	0.953692i	$0.402752\pi$
$524$	−5.72792	−0.250225
$525$	0	0
$526$	26.6274	1.16101
$527$	4.58579	0.199760
$528$	−6.41421	−0.279143
$529$	−18.2843	−0.794968
$530$	5.65685	0.245718
$531$	−11.0711	−0.480443
$532$	0	0
$533$	5.17157	0.224006
$534$	−14.2426	−0.616339
$535$	17.5563	0.759027
$536$	−15.5563	−0.671932
$537$	−6.10051	−0.263256
$538$	−13.2132	−0.569662
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	11.3848	0.489470	0.244735	−	0.969590i	$-0.421299\pi$
$541$	11.3848	0.489470	0.244735	+	0.969590i	$0.421299\pi$
$542$	28.3848	1.21923
$543$	22.8284	0.979662
$544$	3.24264	0.139027
$545$	−0.899495	−0.0385301
$546$	0	0
$547$	17.5147	0.748875	0.374438	−	0.927252i	$-0.377836\pi$
$547$	17.5147	0.748875	0.374438	+	0.927252i	$0.377836\pi$
$548$	−6.41421	−0.274002
$549$	10.4142	0.444468
$550$	25.6569	1.09401
$551$	−34.8579	−1.48499
$552$	−2.17157	−0.0924283
$553$	0	0
$554$	−4.58579	−0.194831
$555$	8.41421	0.357163
$556$	19.7990	0.839664
$557$	−28.4853	−1.20696	−0.603480	−	0.797378i	$-0.706220\pi$
$557$	−28.4853	−1.20696	−0.603480	+	0.797378i	$0.706220\pi$
$558$	1.41421	0.0598684
$559$	8.65685	0.366146
$560$	0	0
$561$	−20.7990	−0.878134
$562$	26.9706	1.13768
$563$	−23.2426	−0.979561	−0.489780	−	0.871846i	$-0.662923\pi$
$563$	−23.2426	−0.979561	−0.489780	+	0.871846i	$0.662923\pi$
$564$	6.00000	0.252646
$565$	−4.58579	−0.192925
$566$	−8.48528	−0.356663
$567$	0	0
$568$	−5.75736	−0.241573
$569$	−9.79899	−0.410795	−0.205398	−	0.978679i	$-0.565849\pi$
$569$	−9.79899	−0.410795	−0.205398	+	0.978679i	$0.565849\pi$
$570$	4.65685	0.195054
$571$	−44.6274	−1.86760	−0.933800	−	0.357796i	$-0.883528\pi$
$571$	−44.6274	−1.86760	−0.933800	+	0.357796i	$0.883528\pi$
$572$	6.41421	0.268192
$573$	−21.9706	−0.917833
$574$	0	0
$575$	8.68629	0.362243
$576$	1.00000	0.0416667
$577$	6.14214	0.255700	0.127850	−	0.991793i	$-0.459192\pi$
$577$	6.14214	0.255700	0.127850	+	0.991793i	$0.459192\pi$
$578$	−6.48528	−0.269752
$579$	5.75736	0.239268
$580$	−7.48528	−0.310809
$581$	0	0
$582$	7.31371	0.303163
$583$	36.2843	1.50274
$584$	11.0000	0.455183
$585$	1.00000	0.0413449
$586$	−19.7990	−0.817889
$587$	8.82843	0.364388	0.182194	−	0.983263i	$-0.441680\pi$
$587$	8.82843	0.364388	0.182194	+	0.983263i	$0.441680\pi$
$588$	0	0
$589$	−6.58579	−0.271363
$590$	11.0711	0.455789
$591$	4.58579	0.188634
$592$	−8.41421	−0.345822
$593$	15.8995	0.652914	0.326457	−	0.945212i	$-0.394145\pi$
$593$	15.8995	0.652914	0.326457	+	0.945212i	$0.394145\pi$
$594$	−6.41421	−0.263178
$595$	0	0
$596$	8.48528	0.347571
$597$	−16.5563	−0.677606
$598$	2.17157	0.0888022
$599$	−1.68629	−0.0689000	−0.0344500	−	0.999406i	$-0.510968\pi$
$599$	−1.68629	−0.0689000	−0.0344500	+	0.999406i	$0.510968\pi$
$600$	−4.00000	−0.163299
$601$	−9.45584	−0.385712	−0.192856	−	0.981227i	$-0.561775\pi$
$601$	−9.45584	−0.385712	−0.192856	+	0.981227i	$0.561775\pi$
$602$	0	0
$603$	−15.5563	−0.633504
$604$	−6.41421	−0.260991
$605$	−30.1421	−1.22545
$606$	−12.5858	−0.511263
$607$	−19.7279	−0.800732	−0.400366	−	0.916355i	$-0.631117\pi$
$607$	−19.7279	−0.800732	−0.400366	+	0.916355i	$0.631117\pi$
$608$	−4.65685	−0.188860
$609$	0	0
$610$	−10.4142	−0.421659
$611$	−6.00000	−0.242734
$612$	3.24264	0.131076
$613$	25.8701	1.04488	0.522441	−	0.852676i	$-0.325022\pi$
$613$	25.8701	1.04488	0.522441	+	0.852676i	$0.325022\pi$
$614$	21.3137	0.860151
$615$	5.17157	0.208538
$616$	0	0
$617$	15.2426	0.613646	0.306823	−	0.951767i	$-0.400734\pi$
$617$	15.2426	0.613646	0.306823	+	0.951767i	$0.400734\pi$
$618$	1.58579	0.0637897
$619$	−25.8284	−1.03813	−0.519066	−	0.854734i	$-0.673720\pi$
$619$	−25.8284	−1.03813	−0.519066	+	0.854734i	$0.673720\pi$
$620$	−1.41421	−0.0567962
$621$	−2.17157	−0.0871422
$622$	12.8284	0.514373
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	11.0000	0.440000
$626$	15.8995	0.635472
$627$	29.8701	1.19290
$628$	8.41421	0.335764
$629$	−27.2843	−1.08790
$630$	0	0
$631$	7.04163	0.280323	0.140161	−	0.990129i	$-0.455238\pi$
$631$	7.04163	0.280323	0.140161	+	0.990129i	$0.455238\pi$
$632$	2.24264	0.0892075
$633$	12.6569	0.503065
$634$	−15.4142	−0.612177
$635$	−6.72792	−0.266989
$636$	−5.65685	−0.224309
$637$	0	0
$638$	−48.0122	−1.90082
$639$	−5.75736	−0.227758
$640$	−1.00000	−0.0395285
$641$	18.2426	0.720541	0.360270	−	0.932848i	$-0.382684\pi$
$641$	18.2426	0.720541	0.360270	+	0.932848i	$0.382684\pi$
$642$	−17.5563	−0.692894
$643$	34.1127	1.34527	0.672637	−	0.739973i	$-0.265162\pi$
$643$	34.1127	1.34527	0.672637	+	0.739973i	$0.265162\pi$
$644$	0	0
$645$	8.65685	0.340863
$646$	−15.1005	−0.594121
$647$	−16.6863	−0.656006	−0.328003	−	0.944677i	$-0.606376\pi$
$647$	−16.6863	−0.656006	−0.328003	+	0.944677i	$0.606376\pi$
$648$	1.00000	0.0392837
$649$	71.0122	2.78747
$650$	4.00000	0.156893
$651$	0	0
$652$	−0.343146	−0.0134386
$653$	17.0000	0.665261	0.332631	−	0.943057i	$-0.392064\pi$
$653$	17.0000	0.665261	0.332631	+	0.943057i	$0.392064\pi$
$654$	0.899495	0.0351730
$655$	5.72792	0.223808
$656$	−5.17157	−0.201916
$657$	11.0000	0.429151
$658$	0	0
$659$	−45.7990	−1.78408	−0.892038	−	0.451961i	$-0.850725\pi$
$659$	−45.7990	−1.78408	−0.892038	+	0.451961i	$0.850725\pi$
$660$	6.41421	0.249673
$661$	0.343146	0.0133468	0.00667341	−	0.999978i	$-0.497876\pi$
$661$	0.343146	0.0133468	0.00667341	+	0.999978i	$0.497876\pi$
$662$	3.75736	0.146034
$663$	−3.24264	−0.125934
$664$	−3.65685	−0.141913
$665$	0	0
$666$	−8.41421	−0.326044
$667$	−16.2548	−0.629390
$668$	23.1421	0.895396
$669$	−14.0000	−0.541271
$670$	15.5563	0.600994
$671$	−66.7990	−2.57875
$672$	0	0
$673$	7.48528	0.288536	0.144268	−	0.989539i	$-0.453917\pi$
$673$	7.48528	0.288536	0.144268	+	0.989539i	$0.453917\pi$
$674$	−27.8284	−1.07191
$675$	−4.00000	−0.153960
$676$	1.00000	0.0384615
$677$	−9.51472	−0.365680	−0.182840	−	0.983143i	$-0.558529\pi$
$677$	−9.51472	−0.365680	−0.182840	+	0.983143i	$0.558529\pi$
$678$	4.58579	0.176116
$679$	0	0
$680$	−3.24264	−0.124350
$681$	5.07107	0.194324
$682$	−9.07107	−0.347349
$683$	−1.24264	−0.0475483	−0.0237742	−	0.999717i	$-0.507568\pi$
$683$	−1.24264	−0.0475483	−0.0237742	+	0.999717i	$0.507568\pi$
$684$	−4.65685	−0.178059
$685$	6.41421	0.245075
$686$	0	0
$687$	−3.89949	−0.148775
$688$	−8.65685	−0.330039
$689$	5.65685	0.215509
$690$	2.17157	0.0826704
$691$	−24.1421	−0.918410	−0.459205	−	0.888330i	$-0.651866\pi$
$691$	−24.1421	−0.918410	−0.459205	+	0.888330i	$0.651866\pi$
$692$	−17.8995	−0.680437
$693$	0	0
$694$	−13.4142	−0.509197
$695$	−19.7990	−0.751018
$696$	7.48528	0.283729
$697$	−16.7696	−0.635192
$698$	−23.8995	−0.904609
$699$	−6.14214	−0.232317
$700$	0	0
$701$	31.5147	1.19029	0.595147	−	0.803617i	$-0.297094\pi$
$701$	31.5147	1.19029	0.595147	+	0.803617i	$0.297094\pi$
$702$	−1.00000	−0.0377426
$703$	39.1838	1.47784
$704$	−6.41421	−0.241745
$705$	−6.00000	−0.225973
$706$	−15.1716	−0.570990
$707$	0	0
$708$	−11.0711	−0.416076
$709$	−48.1421	−1.80802	−0.904008	−	0.427516i	$-0.859389\pi$
$709$	−48.1421	−1.80802	−0.904008	+	0.427516i	$0.859389\pi$
$710$	5.75736	0.216070
$711$	2.24264	0.0841056
$712$	−14.2426	−0.533766
$713$	−3.07107	−0.115012
$714$	0	0
$715$	−6.41421	−0.239878
$716$	−6.10051	−0.227987
$717$	−20.3848	−0.761283
$718$	−6.14214	−0.229222
$719$	−14.8701	−0.554560	−0.277280	−	0.960789i	$-0.589433\pi$
$719$	−14.8701	−0.554560	−0.277280	+	0.960789i	$0.589433\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	2.68629	0.0999734
$723$	14.9706	0.556761
$724$	22.8284	0.848412
$725$	−29.9411	−1.11199
$726$	30.1421	1.11868
$727$	−41.8701	−1.55287	−0.776437	−	0.630195i	$-0.782975\pi$
$727$	−41.8701	−1.55287	−0.776437	+	0.630195i	$0.782975\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−11.0000	−0.407128
$731$	−28.0711	−1.03825
$732$	10.4142	0.384920
$733$	−8.44365	−0.311873	−0.155937	−	0.987767i	$-0.549840\pi$
$733$	−8.44365	−0.311873	−0.155937	+	0.987767i	$0.549840\pi$
$734$	−6.34315	−0.234130
$735$	0	0
$736$	−2.17157	−0.0800452
$737$	99.7817	3.67551
$738$	−5.17157	−0.190368
$739$	8.34315	0.306908	0.153454	−	0.988156i	$-0.450960\pi$
$739$	8.34315	0.306908	0.153454	+	0.988156i	$0.450960\pi$
$740$	8.41421	0.309313
$741$	4.65685	0.171074
$742$	0	0
$743$	34.2843	1.25777	0.628884	−	0.777499i	$-0.283512\pi$
$743$	34.2843	1.25777	0.628884	+	0.777499i	$0.283512\pi$
$744$	1.41421	0.0518476
$745$	−8.48528	−0.310877
$746$	30.8701	1.13023
$747$	−3.65685	−0.133797
$748$	−20.7990	−0.760486
$749$	0	0
$750$	9.00000	0.328634
$751$	−21.2132	−0.774081	−0.387040	−	0.922063i	$-0.626503\pi$
$751$	−21.2132	−0.774081	−0.387040	+	0.922063i	$0.626503\pi$
$752$	6.00000	0.218797
$753$	6.55635	0.238927
$754$	−7.48528	−0.272598
$755$	6.41421	0.233437
$756$	0	0
$757$	−30.7279	−1.11683	−0.558413	−	0.829563i	$-0.688589\pi$
$757$	−30.7279	−1.11683	−0.558413	+	0.829563i	$0.688589\pi$
$758$	11.8995	0.432209
$759$	13.9289	0.505588
$760$	4.65685	0.168922
$761$	44.0833	1.59802	0.799008	−	0.601320i	$-0.205358\pi$
$761$	44.0833	1.59802	0.799008	+	0.601320i	$0.205358\pi$
$762$	6.72792	0.243727
$763$	0	0
$764$	−21.9706	−0.794867
$765$	−3.24264	−0.117238
$766$	−22.3137	−0.806227
$767$	11.0711	0.399753
$768$	1.00000	0.0360844
$769$	−28.9411	−1.04364	−0.521822	−	0.853054i	$-0.674747\pi$
$769$	−28.9411	−1.04364	−0.521822	+	0.853054i	$0.674747\pi$
$770$	0	0
$771$	−2.82843	−0.101863
$772$	5.75736	0.207212
$773$	54.2548	1.95141	0.975705	−	0.219087i	$-0.0703078\pi$
$773$	54.2548	1.95141	0.975705	+	0.219087i	$0.0703078\pi$
$774$	−8.65685	−0.311164
$775$	−5.65685	−0.203200
$776$	7.31371	0.262547
$777$	0	0
$778$	29.6569	1.06325
$779$	24.0833	0.862872
$780$	1.00000	0.0358057
$781$	36.9289	1.32142
$782$	−7.04163	−0.251808
$783$	7.48528	0.267502
$784$	0	0
$785$	−8.41421	−0.300316
$786$	−5.72792	−0.204308
$787$	−13.9706	−0.497997	−0.248998	−	0.968504i	$-0.580101\pi$
$787$	−13.9706	−0.497997	−0.248998	+	0.968504i	$0.580101\pi$
$788$	4.58579	0.163362
$789$	26.6274	0.947961
$790$	−2.24264	−0.0797896
$791$	0	0
$792$	−6.41421	−0.227919
$793$	−10.4142	−0.369820
$794$	−11.6569	−0.413686
$795$	5.65685	0.200628
$796$	−16.5563	−0.586824
$797$	6.24264	0.221126	0.110563	−	0.993869i	$-0.464735\pi$
$797$	6.24264	0.221126	0.110563	+	0.993869i	$0.464735\pi$
$798$	0	0
$799$	19.4558	0.688298
$800$	−4.00000	−0.141421
$801$	−14.2426	−0.503239
$802$	−23.7990	−0.840372
$803$	−70.5563	−2.48988
$804$	−15.5563	−0.548630
$805$	0	0
$806$	−1.41421	−0.0498135
$807$	−13.2132	−0.465127
$808$	−12.5858	−0.442766
$809$	35.8995	1.26216	0.631080	−	0.775718i	$-0.282612\pi$
$809$	35.8995	1.26216	0.631080	+	0.775718i	$0.282612\pi$
$810$	−1.00000	−0.0351364
$811$	−15.8284	−0.555811	−0.277906	−	0.960608i	$-0.589640\pi$
$811$	−15.8284	−0.555811	−0.277906	+	0.960608i	$0.589640\pi$
$812$	0	0
$813$	28.3848	0.995498
$814$	53.9706	1.89167
$815$	0.343146	0.0120199
$816$	3.24264	0.113515
$817$	40.3137	1.41040
$818$	−8.79899	−0.307649
$819$	0	0
$820$	5.17157	0.180599
$821$	−23.7990	−0.830590	−0.415295	−	0.909687i	$-0.636322\pi$
$821$	−23.7990	−0.830590	−0.415295	+	0.909687i	$0.636322\pi$
$822$	−6.41421	−0.223721
$823$	24.0416	0.838039	0.419019	−	0.907977i	$-0.362374\pi$
$823$	24.0416	0.838039	0.419019	+	0.907977i	$0.362374\pi$
$824$	1.58579	0.0552435
$825$	25.6569	0.893257
$826$	0	0
$827$	3.38478	0.117700	0.0588501	−	0.998267i	$-0.481257\pi$
$827$	3.38478	0.117700	0.0588501	+	0.998267i	$0.481257\pi$
$828$	−2.17157	−0.0754674
$829$	−8.61522	−0.299219	−0.149610	−	0.988745i	$-0.547802\pi$
$829$	−8.61522	−0.299219	−0.149610	+	0.988745i	$0.547802\pi$
$830$	3.65685	0.126931
$831$	−4.58579	−0.159079
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	19.7990	0.685583
$835$	−23.1421	−0.800867
$836$	29.8701	1.03308
$837$	1.41421	0.0488824
$838$	22.0711	0.762432
$839$	−38.9706	−1.34541	−0.672707	−	0.739909i	$-0.734868\pi$
$839$	−38.9706	−1.34541	−0.672707	+	0.739909i	$0.734868\pi$
$840$	0	0
$841$	27.0294	0.932050
$842$	−35.4558	−1.22189
$843$	26.9706	0.928916
$844$	12.6569	0.435667
$845$	−1.00000	−0.0344010
$846$	6.00000	0.206284
$847$	0	0
$848$	−5.65685	−0.194257
$849$	−8.48528	−0.291214
$850$	−12.9706	−0.444887
$851$	18.2721	0.626359
$852$	−5.75736	−0.197244
$853$	−52.9706	−1.81368	−0.906839	−	0.421478i	$-0.861512\pi$
$853$	−52.9706	−1.81368	−0.906839	+	0.421478i	$0.861512\pi$
$854$	0	0
$855$	4.65685	0.159261
$856$	−17.5563	−0.600064
$857$	30.4853	1.04136	0.520679	−	0.853753i	$-0.325679\pi$
$857$	30.4853	1.04136	0.520679	+	0.853753i	$0.325679\pi$
$858$	6.41421	0.218978
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	8.65685	0.295196
$861$	0	0
$862$	13.5147	0.460313
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	1.00000	0.0340207
$865$	17.8995	0.608601
$866$	0	0
$867$	−6.48528	−0.220252
$868$	0	0
$869$	−14.3848	−0.487970
$870$	−7.48528	−0.253775
$871$	15.5563	0.527107
$872$	0.899495	0.0304607
$873$	7.31371	0.247532
$874$	10.1127	0.342067
$875$	0	0
$876$	11.0000	0.371656
$877$	8.48528	0.286528	0.143264	−	0.989685i	$-0.454240\pi$
$877$	8.48528	0.286528	0.143264	+	0.989685i	$0.454240\pi$
$878$	−2.07107	−0.0698952
$879$	−19.7990	−0.667803
$880$	6.41421	0.216223
$881$	−53.7279	−1.81014	−0.905070	−	0.425263i	$-0.860182\pi$
$881$	−53.7279	−1.81014	−0.905070	+	0.425263i	$0.860182\pi$
$882$	0	0
$883$	−44.5980	−1.50084	−0.750421	−	0.660960i	$-0.770149\pi$
$883$	−44.5980	−1.50084	−0.750421	+	0.660960i	$0.770149\pi$
$884$	−3.24264	−0.109062
$885$	11.0711	0.372150
$886$	−9.79899	−0.329204
$887$	−2.82843	−0.0949693	−0.0474846	−	0.998872i	$-0.515121\pi$
$887$	−2.82843	−0.0949693	−0.0474846	+	0.998872i	$0.515121\pi$
$888$	−8.41421	−0.282363
$889$	0	0
$890$	14.2426	0.477414
$891$	−6.41421	−0.214884
$892$	−14.0000	−0.468755
$893$	−27.9411	−0.935014
$894$	8.48528	0.283790
$895$	6.10051	0.203917
$896$	0	0
$897$	2.17157	0.0725067
$898$	21.0416	0.702168
$899$	10.5858	0.353056
$900$	−4.00000	−0.133333
$901$	−18.3431	−0.611099
$902$	33.1716	1.10449
$903$	0	0
$904$	4.58579	0.152521
$905$	−22.8284	−0.758843
$906$	−6.41421	−0.213098
$907$	−17.5147	−0.581567	−0.290783	−	0.956789i	$-0.593916\pi$
$907$	−17.5147	−0.581567	−0.290783	+	0.956789i	$0.593916\pi$
$908$	5.07107	0.168289
$909$	−12.5858	−0.417444
$910$	0	0
$911$	−41.8284	−1.38584	−0.692919	−	0.721016i	$-0.743676\pi$
$911$	−41.8284	−1.38584	−0.692919	+	0.721016i	$0.743676\pi$
$912$	−4.65685	−0.154204
$913$	23.4558	0.776275
$914$	39.6985	1.31311
$915$	−10.4142	−0.344283
$916$	−3.89949	−0.128843
$917$	0	0
$918$	3.24264	0.107023
$919$	50.4853	1.66536	0.832678	−	0.553758i	$-0.186807\pi$
$919$	50.4853	1.66536	0.832678	+	0.553758i	$0.186807\pi$
$920$	2.17157	0.0715946
$921$	21.3137	0.702311
$922$	−33.4853	−1.10278
$923$	5.75736	0.189506
$924$	0	0
$925$	33.6569	1.10663
$926$	24.0711	0.791024
$927$	1.58579	0.0520841
$928$	7.48528	0.245716
$929$	25.1716	0.825853	0.412926	−	0.910764i	$-0.364507\pi$
$929$	25.1716	0.825853	0.412926	+	0.910764i	$0.364507\pi$
$930$	−1.41421	−0.0463739
$931$	0	0
$932$	−6.14214	−0.201192
$933$	12.8284	0.419984
$934$	10.4142	0.340763
$935$	20.7990	0.680200
$936$	−1.00000	−0.0326860
$937$	−17.2132	−0.562331	−0.281165	−	0.959659i	$-0.590721\pi$
$937$	−17.2132	−0.562331	−0.281165	+	0.959659i	$0.590721\pi$
$938$	0	0
$939$	15.8995	0.518860
$940$	−6.00000	−0.195698
$941$	11.9411	0.389270	0.194635	−	0.980876i	$-0.437648\pi$
$941$	11.9411	0.389270	0.194635	+	0.980876i	$0.437648\pi$
$942$	8.41421	0.274150
$943$	11.2304	0.365714
$944$	−11.0711	−0.360333
$945$	0	0
$946$	55.5269	1.80534
$947$	7.72792	0.251124	0.125562	−	0.992086i	$-0.459927\pi$
$947$	7.72792	0.251124	0.125562	+	0.992086i	$0.459927\pi$
$948$	2.24264	0.0728376
$949$	−11.0000	−0.357075
$950$	18.6274	0.604353
$951$	−15.4142	−0.499840
$952$	0	0
$953$	−33.9411	−1.09946	−0.549730	−	0.835342i	$-0.685270\pi$
$953$	−33.9411	−1.09946	−0.549730	+	0.835342i	$0.685270\pi$
$954$	−5.65685	−0.183147
$955$	21.9706	0.710951
$956$	−20.3848	−0.659291
$957$	−48.0122	−1.55201
$958$	−33.1421	−1.07077
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−29.0000	−0.935484
$962$	8.41421	0.271285
$963$	−17.5563	−0.565745
$964$	14.9706	0.482169
$965$	−5.75736	−0.185336
$966$	0	0
$967$	39.5858	1.27299	0.636497	−	0.771280i	$-0.280383\pi$
$967$	39.5858	1.27299	0.636497	+	0.771280i	$0.280383\pi$
$968$	30.1421	0.968805
$969$	−15.1005	−0.485098
$970$	−7.31371	−0.234829
$971$	11.7990	0.378648	0.189324	−	0.981915i	$-0.439370\pi$
$971$	11.7990	0.378648	0.189324	+	0.981915i	$0.439370\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	8.34315	0.267332
$975$	4.00000	0.128103
$976$	10.4142	0.333351
$977$	0.272078	0.00870454	0.00435227	−	0.999991i	$-0.498615\pi$
$977$	0.272078	0.00870454	0.00435227	+	0.999991i	$0.498615\pi$
$978$	−0.343146	−0.0109726
$979$	91.3553	2.91973
$980$	0	0
$981$	0.899495	0.0287187
$982$	24.8284	0.792307
$983$	11.6274	0.370857	0.185429	−	0.982658i	$-0.440633\pi$
$983$	11.6274	0.370857	0.185429	+	0.982658i	$0.440633\pi$
$984$	−5.17157	−0.164864
$985$	−4.58579	−0.146115
$986$	24.2721	0.772980
$987$	0	0
$988$	4.65685	0.148154
$989$	18.7990	0.597773
$990$	6.41421	0.203857
$991$	−19.6569	−0.624421	−0.312210	−	0.950013i	$-0.601069\pi$
$991$	−19.6569	−0.624421	−0.312210	+	0.950013i	$0.601069\pi$
$992$	1.41421	0.0449013
$993$	3.75736	0.119236
$994$	0	0
$995$	16.5563	0.524872
$996$	−3.65685	−0.115872
$997$	47.2548	1.49658	0.748288	−	0.663374i	$-0.230876\pi$
$997$	47.2548	1.49658	0.748288	+	0.663374i	$0.230876\pi$
$998$	22.0416	0.697716
$999$	−8.41421	−0.266214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.br.1.1	yes	2
7.6	odd	2		3822.2.a.bq.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bq.1.1	✓	2	7.6	odd	2
3822.2.a.br.1.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -6.41421 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +3.24264 q^{17} +1.00000 q^{18} -4.65685 q^{19} -1.00000 q^{20} -6.41421 q^{22} -2.17157 q^{23} +1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} +7.48528 q^{29} -1.00000 q^{30} +1.41421 q^{31} +1.00000 q^{32} -6.41421 q^{33} +3.24264 q^{34} +1.00000 q^{36} -8.41421 q^{37} -4.65685 q^{38} -1.00000 q^{39} -1.00000 q^{40} -5.17157 q^{41} -8.65685 q^{43} -6.41421 q^{44} -1.00000 q^{45} -2.17157 q^{46} +6.00000 q^{47} +1.00000 q^{48} -4.00000 q^{50} +3.24264 q^{51} -1.00000 q^{52} -5.65685 q^{53} +1.00000 q^{54} +6.41421 q^{55} -4.65685 q^{57} +7.48528 q^{58} -11.0711 q^{59} -1.00000 q^{60} +10.4142 q^{61} +1.41421 q^{62} +1.00000 q^{64} +1.00000 q^{65} -6.41421 q^{66} -15.5563 q^{67} +3.24264 q^{68} -2.17157 q^{69} -5.75736 q^{71} +1.00000 q^{72} +11.0000 q^{73} -8.41421 q^{74} -4.00000 q^{75} -4.65685 q^{76} -1.00000 q^{78} +2.24264 q^{79} -1.00000 q^{80} +1.00000 q^{81} -5.17157 q^{82} -3.65685 q^{83} -3.24264 q^{85} -8.65685 q^{86} +7.48528 q^{87} -6.41421 q^{88} -14.2426 q^{89} -1.00000 q^{90} -2.17157 q^{92} +1.41421 q^{93} +6.00000 q^{94} +4.65685 q^{95} +1.00000 q^{96} +7.31371 q^{97} -6.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 10 q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} - 10 q^{22} - 10 q^{23} + 2 q^{24} - 8 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{29} - 2 q^{30} + 2 q^{32} - 10 q^{33} - 2 q^{34} + 2 q^{36} - 14 q^{37} + 2 q^{38} - 2 q^{39} - 2 q^{40} - 16 q^{41} - 6 q^{43} - 10 q^{44} - 2 q^{45} - 10 q^{46} + 12 q^{47} + 2 q^{48} - 8 q^{50} - 2 q^{51} - 2 q^{52} + 2 q^{54} + 10 q^{55} + 2 q^{57} - 2 q^{58} - 8 q^{59} - 2 q^{60} + 18 q^{61} + 2 q^{64} + 2 q^{65} - 10 q^{66} - 2 q^{68} - 10 q^{69} - 20 q^{71} + 2 q^{72} + 22 q^{73} - 14 q^{74} - 8 q^{75} + 2 q^{76} - 2 q^{78} - 4 q^{79} - 2 q^{80} + 2 q^{81} - 16 q^{82} + 4 q^{83} + 2 q^{85} - 6 q^{86} - 2 q^{87} - 10 q^{88} - 20 q^{89} - 2 q^{90} - 10 q^{92} + 12 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 10 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 10 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 - 10 * q^22 - 10 * q^23 + 2 * q^24 - 8 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^29 - 2 * q^30 + 2 * q^32 - 10 * q^33 - 2 * q^34 + 2 * q^36 - 14 * q^37 + 2 * q^38 - 2 * q^39 - 2 * q^40 - 16 * q^41 - 6 * q^43 - 10 * q^44 - 2 * q^45 - 10 * q^46 + 12 * q^47 + 2 * q^48 - 8 * q^50 - 2 * q^51 - 2 * q^52 + 2 * q^54 + 10 * q^55 + 2 * q^57 - 2 * q^58 - 8 * q^59 - 2 * q^60 + 18 * q^61 + 2 * q^64 + 2 * q^65 - 10 * q^66 - 2 * q^68 - 10 * q^69 - 20 * q^71 + 2 * q^72 + 22 * q^73 - 14 * q^74 - 8 * q^75 + 2 * q^76 - 2 * q^78 - 4 * q^79 - 2 * q^80 + 2 * q^81 - 16 * q^82 + 4 * q^83 + 2 * q^85 - 6 * q^86 - 2 * q^87 - 10 * q^88 - 20 * q^89 - 2 * q^90 - 10 * q^92 + 12 * q^94 - 2 * q^95 + 2 * q^96 - 8 * q^97 - 10 * q^99

Introduction

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