LMFDB - Embedded newform 9282.2.a.bm.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.45841.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 7x - 1 $ x^4 - 2x^3 - 7x^2 + 7*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.174808$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.825192 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.825192 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.825192 q^{10} -0.576323 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +0.825192 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.54576 q^{19} -0.825192 q^{20} -1.00000 q^{21} -0.576323 q^{22} -6.61595 q^{23} -1.00000 q^{24} -4.31906 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.19228 q^{29} +0.825192 q^{30} +6.69841 q^{31} +1.00000 q^{32} +0.576323 q^{33} -1.00000 q^{34} -0.825192 q^{35} +1.00000 q^{36} +5.19615 q^{37} +1.54576 q^{38} +1.00000 q^{39} -0.825192 q^{40} -6.84266 q^{41} -1.00000 q^{42} +4.37096 q^{43} -0.576323 q^{44} -0.825192 q^{45} -6.61595 q^{46} -11.6900 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.31906 q^{50} +1.00000 q^{51} -1.00000 q^{52} -4.72057 q^{53} -1.00000 q^{54} +0.475577 q^{55} +1.00000 q^{56} -1.54576 q^{57} +5.19228 q^{58} -7.77247 q^{59} +0.825192 q^{60} +0.248870 q^{61} +6.69841 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.825192 q^{65} +0.576323 q^{66} +14.9869 q^{67} -1.00000 q^{68} +6.61595 q^{69} -0.825192 q^{70} +4.34492 q^{71} +1.00000 q^{72} -2.22753 q^{73} +5.19615 q^{74} +4.31906 q^{75} +1.54576 q^{76} -0.576323 q^{77} +1.00000 q^{78} -11.6900 q^{79} -0.825192 q^{80} +1.00000 q^{81} -6.84266 q^{82} -17.3144 q^{83} -1.00000 q^{84} +0.825192 q^{85} +4.37096 q^{86} -5.19228 q^{87} -0.576323 q^{88} +2.84266 q^{89} -0.825192 q^{90} -1.00000 q^{91} -6.61595 q^{92} -6.69841 q^{93} -11.6900 q^{94} -1.27555 q^{95} -1.00000 q^{96} -6.59461 q^{97} +1.00000 q^{98} -0.576323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} - 3 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 11 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 4 q^{24} - 2 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 9 q^{29} + 2 q^{30} + 11 q^{31} + 4 q^{32} + 3 q^{33} - 4 q^{34} - 2 q^{35} + 4 q^{36} + q^{37} - 11 q^{38} + 4 q^{39} - 2 q^{40} + 5 q^{41} - 4 q^{42} - q^{43} - 3 q^{44} - 2 q^{45} + 4 q^{46} - 13 q^{47} - 4 q^{48} + 4 q^{49} - 2 q^{50} + 4 q^{51} - 4 q^{52} - 3 q^{53} - 4 q^{54} - 2 q^{55} + 4 q^{56} + 11 q^{57} - 9 q^{58} - 12 q^{59} + 2 q^{60} - q^{61} + 11 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} + 3 q^{66} + 11 q^{67} - 4 q^{68} - 4 q^{69} - 2 q^{70} - 11 q^{71} + 4 q^{72} - 28 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 3 q^{77} + 4 q^{78} - 13 q^{79} - 2 q^{80} + 4 q^{81} + 5 q^{82} - 23 q^{83} - 4 q^{84} + 2 q^{85} - q^{86} + 9 q^{87} - 3 q^{88} - 21 q^{89} - 2 q^{90} - 4 q^{91} + 4 q^{92} - 11 q^{93} - 13 q^{94} - 11 q^{95} - 4 q^{96} - 17 q^{97} + 4 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 - 3 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 11 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 4 * q^24 - 2 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 9 * q^29 + 2 * q^30 + 11 * q^31 + 4 * q^32 + 3 * q^33 - 4 * q^34 - 2 * q^35 + 4 * q^36 + q^37 - 11 * q^38 + 4 * q^39 - 2 * q^40 + 5 * q^41 - 4 * q^42 - q^43 - 3 * q^44 - 2 * q^45 + 4 * q^46 - 13 * q^47 - 4 * q^48 + 4 * q^49 - 2 * q^50 + 4 * q^51 - 4 * q^52 - 3 * q^53 - 4 * q^54 - 2 * q^55 + 4 * q^56 + 11 * q^57 - 9 * q^58 - 12 * q^59 + 2 * q^60 - q^61 + 11 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 + 3 * q^66 + 11 * q^67 - 4 * q^68 - 4 * q^69 - 2 * q^70 - 11 * q^71 + 4 * q^72 - 28 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 3 * q^77 + 4 * q^78 - 13 * q^79 - 2 * q^80 + 4 * q^81 + 5 * q^82 - 23 * q^83 - 4 * q^84 + 2 * q^85 - q^86 + 9 * q^87 - 3 * q^88 - 21 * q^89 - 2 * q^90 - 4 * q^91 + 4 * q^92 - 11 * q^93 - 13 * q^94 - 11 * q^95 - 4 * q^96 - 17 * q^97 + 4 * q^98 - 3 * 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
$5$	−0.825192	−0.369037	−0.184519	−	0.982829i	$-0.559073\pi$
$5$	−0.825192	−0.369037	−0.184519	+	0.982829i	$0.559073\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.825192	−0.260949
$11$	−0.576323	−0.173768	−0.0868839	−	0.996218i	$-0.527691\pi$
$11$	−0.576323	−0.173768	−0.0868839	+	0.996218i	$0.527691\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.00000	0.267261
$15$	0.825192	0.213064
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	1.54576	0.354623	0.177311	−	0.984155i	$-0.443260\pi$
$19$	1.54576	0.354623	0.177311	+	0.984155i	$0.443260\pi$
$20$	−0.825192	−0.184519
$21$	−1.00000	−0.218218
$22$	−0.576323	−0.122872
$23$	−6.61595	−1.37952	−0.689761	−	0.724037i	$-0.742284\pi$
$23$	−6.61595	−1.37952	−0.689761	+	0.724037i	$0.742284\pi$
$24$	−1.00000	−0.204124
$25$	−4.31906	−0.863812
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	5.19228	0.964181	0.482091	−	0.876121i	$-0.339878\pi$
$29$	5.19228	0.964181	0.482091	+	0.876121i	$0.339878\pi$
$30$	0.825192	0.150659
$31$	6.69841	1.20307	0.601535	−	0.798846i	$-0.294556\pi$
$31$	6.69841	1.20307	0.601535	+	0.798846i	$0.294556\pi$
$32$	1.00000	0.176777
$33$	0.576323	0.100325
$34$	−1.00000	−0.171499
$35$	−0.825192	−0.139483
$36$	1.00000	0.166667
$37$	5.19615	0.854242	0.427121	−	0.904195i	$-0.359528\pi$
$37$	5.19615	0.854242	0.427121	+	0.904195i	$0.359528\pi$
$38$	1.54576	0.250756
$39$	1.00000	0.160128
$40$	−0.825192	−0.130474
$41$	−6.84266	−1.06864	−0.534322	−	0.845281i	$-0.679433\pi$
$41$	−6.84266	−1.06864	−0.534322	+	0.845281i	$0.679433\pi$
$42$	−1.00000	−0.154303
$43$	4.37096	0.666565	0.333282	−	0.942827i	$-0.391844\pi$
$43$	4.37096	0.666565	0.333282	+	0.942827i	$0.391844\pi$
$44$	−0.576323	−0.0868839
$45$	−0.825192	−0.123012
$46$	−6.61595	−0.975469
$47$	−11.6900	−1.70516	−0.852582	−	0.522594i	$-0.824965\pi$
$47$	−11.6900	−1.70516	−0.852582	+	0.522594i	$0.824965\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.31906	−0.610807
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	−4.72057	−0.648421	−0.324210	−	0.945985i	$-0.605099\pi$
$53$	−4.72057	−0.648421	−0.324210	+	0.945985i	$0.605099\pi$
$54$	−1.00000	−0.136083
$55$	0.475577	0.0641268
$56$	1.00000	0.133631
$57$	−1.54576	−0.204742
$58$	5.19228	0.681779
$59$	−7.77247	−1.01189	−0.505945	−	0.862566i	$-0.668856\pi$
$59$	−7.77247	−1.01189	−0.505945	+	0.862566i	$0.668856\pi$
$60$	0.825192	0.106532
$61$	0.248870	0.0318645	0.0159323	−	0.999873i	$-0.494928\pi$
$61$	0.248870	0.0318645	0.0159323	+	0.999873i	$0.494928\pi$
$62$	6.69841	0.850699
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0.825192	0.102353
$66$	0.576323	0.0709404
$67$	14.9869	1.83094	0.915471	−	0.402383i	$-0.131818\pi$
$67$	14.9869	1.83094	0.915471	+	0.402383i	$0.131818\pi$
$68$	−1.00000	−0.121268
$69$	6.61595	0.796467
$70$	−0.825192	−0.0986293
$71$	4.34492	0.515647	0.257824	−	0.966192i	$-0.416995\pi$
$71$	4.34492	0.515647	0.257824	+	0.966192i	$0.416995\pi$
$72$	1.00000	0.117851
$73$	−2.22753	−0.260712	−0.130356	−	0.991467i	$-0.541612\pi$
$73$	−2.22753	−0.260712	−0.130356	+	0.991467i	$0.541612\pi$
$74$	5.19615	0.604040
$75$	4.31906	0.498722
$76$	1.54576	0.177311
$77$	−0.576323	−0.0656781
$78$	1.00000	0.113228
$79$	−11.6900	−1.31523	−0.657615	−	0.753354i	$-0.728434\pi$
$79$	−11.6900	−1.31523	−0.657615	+	0.753354i	$0.728434\pi$
$80$	−0.825192	−0.0922593
$81$	1.00000	0.111111
$82$	−6.84266	−0.755645
$83$	−17.3144	−1.90050	−0.950249	−	0.311491i	$-0.899172\pi$
$83$	−17.3144	−1.90050	−0.950249	+	0.311491i	$0.899172\pi$
$84$	−1.00000	−0.109109
$85$	0.825192	0.0895047
$86$	4.37096	0.471332
$87$	−5.19228	−0.556670
$88$	−0.576323	−0.0614362
$89$	2.84266	0.301321	0.150661	−	0.988586i	$-0.451860\pi$
$89$	2.84266	0.301321	0.150661	+	0.988586i	$0.451860\pi$
$90$	−0.825192	−0.0869829
$91$	−1.00000	−0.104828
$92$	−6.61595	−0.689761
$93$	−6.69841	−0.694593
$94$	−11.6900	−1.20573
$95$	−1.27555	−0.130869
$96$	−1.00000	−0.102062
$97$	−6.59461	−0.669581	−0.334791	−	0.942293i	$-0.608666\pi$
$97$	−6.59461	−0.669581	−0.334791	+	0.942293i	$0.608666\pi$
$98$	1.00000	0.101015
$99$	−0.576323	−0.0579226
$100$	−4.31906	−0.431906
$101$	9.58540	0.953782	0.476891	−	0.878962i	$-0.341764\pi$
$101$	9.58540	0.953782	0.476891	+	0.878962i	$0.341764\pi$
$102$	1.00000	0.0990148
$103$	−1.69471	−0.166985	−0.0834924	−	0.996508i	$-0.526607\pi$
$103$	−1.69471	−0.166985	−0.0834924	+	0.996508i	$0.526607\pi$
$104$	−1.00000	−0.0980581
$105$	0.825192	0.0805305
$106$	−4.72057	−0.458503
$107$	−5.04803	−0.488011	−0.244006	−	0.969774i	$-0.578462\pi$
$107$	−5.04803	−0.488011	−0.244006	+	0.969774i	$0.578462\pi$
$108$	−1.00000	−0.0962250
$109$	−10.3671	−0.992986	−0.496493	−	0.868041i	$-0.665379\pi$
$109$	−10.3671	−0.992986	−0.496493	+	0.868041i	$0.665379\pi$
$110$	0.475577	0.0453445
$111$	−5.19615	−0.493197
$112$	1.00000	0.0944911
$113$	−4.84348	−0.455636	−0.227818	−	0.973704i	$-0.573159\pi$
$113$	−4.84348	−0.455636	−0.227818	+	0.973704i	$0.573159\pi$
$114$	−1.54576	−0.144774
$115$	5.45943	0.509095
$116$	5.19228	0.482091
$117$	−1.00000	−0.0924500
$118$	−7.77247	−0.715514
$119$	−1.00000	−0.0916698
$120$	0.825192	0.0753294
$121$	−10.6679	−0.969805
$122$	0.248870	0.0225316
$123$	6.84266	0.616982
$124$	6.69841	0.601535
$125$	7.69001	0.687816
$126$	1.00000	0.0890871
$127$	3.91754	0.347626	0.173813	−	0.984779i	$-0.444391\pi$
$127$	3.91754	0.347626	0.173813	+	0.984779i	$0.444391\pi$
$128$	1.00000	0.0883883
$129$	−4.37096	−0.384841
$130$	0.825192	0.0723742
$131$	15.3762	1.34342	0.671710	−	0.740814i	$-0.265560\pi$
$131$	15.3762	1.34342	0.671710	+	0.740814i	$0.265560\pi$
$132$	0.576323	0.0501624
$133$	1.54576	0.134035
$134$	14.9869	1.29467
$135$	0.825192	0.0710212
$136$	−1.00000	−0.0857493
$137$	−2.73804	−0.233927	−0.116963	−	0.993136i	$-0.537316\pi$
$137$	−2.73804	−0.233927	−0.116963	+	0.993136i	$0.537316\pi$
$138$	6.61595	0.563187
$139$	−0.374831	−0.0317928	−0.0158964	−	0.999874i	$-0.505060\pi$
$139$	−0.374831	−0.0317928	−0.0158964	+	0.999874i	$0.505060\pi$
$140$	−0.825192	−0.0697415
$141$	11.6900	0.984477
$142$	4.34492	0.364618
$143$	0.576323	0.0481945
$144$	1.00000	0.0833333
$145$	−4.28463	−0.355819
$146$	−2.22753	−0.184352
$147$	−1.00000	−0.0824786
$148$	5.19615	0.427121
$149$	−7.02586	−0.575581	−0.287791	−	0.957693i	$-0.592921\pi$
$149$	−7.02586	−0.575581	−0.287791	+	0.957693i	$0.592921\pi$
$150$	4.31906	0.352650
$151$	16.5122	1.34374	0.671870	−	0.740669i	$-0.265491\pi$
$151$	16.5122	1.34374	0.671870	+	0.740669i	$0.265491\pi$
$152$	1.54576	0.125378
$153$	−1.00000	−0.0808452
$154$	−0.576323	−0.0464414
$155$	−5.52748	−0.443978
$156$	1.00000	0.0800641
$157$	−13.4015	−1.06956	−0.534779	−	0.844992i	$-0.679605\pi$
$157$	−13.4015	−1.06956	−0.534779	+	0.844992i	$0.679605\pi$
$158$	−11.6900	−0.930008
$159$	4.72057	0.374366
$160$	−0.825192	−0.0652372
$161$	−6.61595	−0.521410
$162$	1.00000	0.0785674
$163$	−9.23578	−0.723402	−0.361701	−	0.932294i	$-0.617804\pi$
$163$	−9.23578	−0.723402	−0.361701	+	0.932294i	$0.617804\pi$
$164$	−6.84266	−0.534322
$165$	−0.475577	−0.0370236
$166$	−17.3144	−1.34386
$167$	−1.07406	−0.0831134	−0.0415567	−	0.999136i	$-0.513232\pi$
$167$	−1.07406	−0.0831134	−0.0415567	+	0.999136i	$0.513232\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	0.825192	0.0632894
$171$	1.54576	0.118208
$172$	4.37096	0.333282
$173$	−0.720573	−0.0547841	−0.0273921	−	0.999625i	$-0.508720\pi$
$173$	−0.720573	−0.0547841	−0.0273921	+	0.999625i	$0.508720\pi$
$174$	−5.19228	−0.393625
$175$	−4.31906	−0.326490
$176$	−0.576323	−0.0434419
$177$	7.77247	0.584215
$178$	2.84266	0.213066
$179$	8.90295	0.665438	0.332719	−	0.943026i	$-0.392034\pi$
$179$	8.90295	0.665438	0.332719	+	0.943026i	$0.392034\pi$
$180$	−0.825192	−0.0615062
$181$	−18.1396	−1.34830	−0.674151	−	0.738593i	$-0.735490\pi$
$181$	−18.1396	−1.34830	−0.674151	+	0.738593i	$0.735490\pi$
$182$	−1.00000	−0.0741249
$183$	−0.248870	−0.0183970
$184$	−6.61595	−0.487735
$185$	−4.28782	−0.315247
$186$	−6.69841	−0.491151
$187$	0.576323	0.0421449
$188$	−11.6900	−0.852582
$189$	−1.00000	−0.0727393
$190$	−1.27555	−0.0925384
$191$	−5.39682	−0.390500	−0.195250	−	0.980753i	$-0.562552\pi$
$191$	−5.39682	−0.390500	−0.195250	+	0.980753i	$0.562552\pi$
$192$	−1.00000	−0.0721688
$193$	−5.27086	−0.379405	−0.189702	−	0.981842i	$-0.560752\pi$
$193$	−5.27086	−0.379405	−0.189702	+	0.981842i	$0.560752\pi$
$194$	−6.59461	−0.473465
$195$	−0.825192	−0.0590932
$196$	1.00000	0.0714286
$197$	2.51603	0.179260	0.0896298	−	0.995975i	$-0.471432\pi$
$197$	2.51603	0.179260	0.0896298	+	0.995975i	$0.471432\pi$
$198$	−0.576323	−0.0409575
$199$	3.79463	0.268995	0.134497	−	0.990914i	$-0.457058\pi$
$199$	3.79463	0.268995	0.134497	+	0.990914i	$0.457058\pi$
$200$	−4.31906	−0.305403
$201$	−14.9869	−1.05710
$202$	9.58540	0.674426
$203$	5.19228	0.364426
$204$	1.00000	0.0700140
$205$	5.64651	0.394369
$206$	−1.69471	−0.118076
$207$	−6.61595	−0.459841
$208$	−1.00000	−0.0693375
$209$	−0.890859	−0.0616220
$210$	0.825192	0.0569437
$211$	−19.0472	−1.31126	−0.655632	−	0.755081i	$-0.727598\pi$
$211$	−19.0472	−1.31126	−0.655632	+	0.755081i	$0.727598\pi$
$212$	−4.72057	−0.324210
$213$	−4.34492	−0.297709
$214$	−5.04803	−0.345076
$215$	−3.60688	−0.245987
$216$	−1.00000	−0.0680414
$217$	6.69841	0.454718
$218$	−10.3671	−0.702147
$219$	2.22753	0.150522
$220$	0.475577	0.0320634
$221$	1.00000	0.0672673
$222$	−5.19615	−0.348743
$223$	−16.8427	−1.12787	−0.563934	−	0.825820i	$-0.690713\pi$
$223$	−16.8427	−1.12787	−0.563934	+	0.825820i	$0.690713\pi$
$224$	1.00000	0.0668153
$225$	−4.31906	−0.287937
$226$	−4.84348	−0.322184
$227$	−20.9219	−1.38864	−0.694318	−	0.719668i	$-0.744294\pi$
$227$	−20.9219	−1.38864	−0.694318	+	0.719668i	$0.744294\pi$
$228$	−1.54576	−0.102371
$229$	−8.49304	−0.561236	−0.280618	−	0.959820i	$-0.590539\pi$
$229$	−8.49304	−0.561236	−0.280618	+	0.959820i	$0.590539\pi$
$230$	5.45943	0.359984
$231$	0.576323	0.0379192
$232$	5.19228	0.340890
$233$	25.4935	1.67014	0.835069	−	0.550145i	$-0.185428\pi$
$233$	25.4935	1.67014	0.835069	+	0.550145i	$0.185428\pi$
$234$	−1.00000	−0.0653720
$235$	9.64651	0.629269
$236$	−7.77247	−0.505945
$237$	11.6900	0.759348
$238$	−1.00000	−0.0648204
$239$	−1.09235	−0.0706583	−0.0353291	−	0.999376i	$-0.511248\pi$
$239$	−1.09235	−0.0706583	−0.0353291	+	0.999376i	$0.511248\pi$
$240$	0.825192	0.0532659
$241$	24.2578	1.56258	0.781290	−	0.624168i	$-0.214562\pi$
$241$	24.2578	1.56258	0.781290	+	0.624168i	$0.214562\pi$
$242$	−10.6679	−0.685756
$243$	−1.00000	−0.0641500
$244$	0.248870	0.0159323
$245$	−0.825192	−0.0527196
$246$	6.84266	0.436272
$247$	−1.54576	−0.0983547
$248$	6.69841	0.425349
$249$	17.3144	1.09725
$250$	7.69001	0.486359
$251$	−14.6984	−0.927755	−0.463878	−	0.885899i	$-0.653542\pi$
$251$	−14.6984	−0.927755	−0.463878	+	0.885899i	$0.653542\pi$
$252$	1.00000	0.0629941
$253$	3.81292	0.239716
$254$	3.91754	0.245808
$255$	−0.825192	−0.0516755
$256$	1.00000	0.0625000
$257$	−6.39312	−0.398792	−0.199396	−	0.979919i	$-0.563898\pi$
$257$	−6.39312	−0.398792	−0.199396	+	0.979919i	$0.563898\pi$
$258$	−4.37096	−0.272124
$259$	5.19615	0.322873
$260$	0.825192	0.0511763
$261$	5.19228	0.321394
$262$	15.3762	0.949942
$263$	−30.4234	−1.87598	−0.937992	−	0.346656i	$-0.887317\pi$
$263$	−30.4234	−1.87598	−0.937992	+	0.346656i	$0.887317\pi$
$264$	0.576323	0.0354702
$265$	3.89538	0.239291
$266$	1.54576	0.0947769
$267$	−2.84266	−0.173968
$268$	14.9869	0.915471
$269$	3.46331	0.211162	0.105581	−	0.994411i	$-0.466330\pi$
$269$	3.46331	0.211162	0.105581	+	0.994411i	$0.466330\pi$
$270$	0.825192	0.0502196
$271$	−4.70310	−0.285693	−0.142847	−	0.989745i	$-0.545626\pi$
$271$	−4.70310	−0.285693	−0.142847	+	0.989745i	$0.545626\pi$
$272$	−1.00000	−0.0606339
$273$	1.00000	0.0605228
$274$	−2.73804	−0.165411
$275$	2.48917	0.150103
$276$	6.61595	0.398234
$277$	−6.86482	−0.412467	−0.206234	−	0.978503i	$-0.566121\pi$
$277$	−6.86482	−0.412467	−0.206234	+	0.978503i	$0.566121\pi$
$278$	−0.374831	−0.0224809
$279$	6.69841	0.401023
$280$	−0.825192	−0.0493147
$281$	27.8470	1.66121	0.830607	−	0.556858i	$-0.187993\pi$
$281$	27.8470	1.66121	0.830607	+	0.556858i	$0.187993\pi$
$282$	11.6900	0.696130
$283$	29.7241	1.76692	0.883458	−	0.468510i	$-0.155209\pi$
$283$	29.7241	1.76692	0.883458	+	0.468510i	$0.155209\pi$
$284$	4.34492	0.257824
$285$	1.27555	0.0755573
$286$	0.576323	0.0340787
$287$	−6.84266	−0.403909
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−4.28463	−0.251602
$291$	6.59461	0.386583
$292$	−2.22753	−0.130356
$293$	−8.68564	−0.507420	−0.253710	−	0.967280i	$-0.581651\pi$
$293$	−8.68564	−0.507420	−0.253710	+	0.967280i	$0.581651\pi$
$294$	−1.00000	−0.0583212
$295$	6.41378	0.373425
$296$	5.19615	0.302020
$297$	0.576323	0.0334416
$298$	−7.02586	−0.406997
$299$	6.61595	0.382610
$300$	4.31906	0.249361
$301$	4.37096	0.251938
$302$	16.5122	0.950168
$303$	−9.58540	−0.550667
$304$	1.54576	0.0886557
$305$	−0.205365	−0.0117592
$306$	−1.00000	−0.0571662
$307$	7.31354	0.417406	0.208703	−	0.977979i	$-0.433076\pi$
$307$	7.31354	0.417406	0.208703	+	0.977979i	$0.433076\pi$
$308$	−0.576323	−0.0328390
$309$	1.69471	0.0964087
$310$	−5.52748	−0.313940
$311$	10.5899	0.600499	0.300250	−	0.953861i	$-0.402930\pi$
$311$	10.5899	0.600499	0.300250	+	0.953861i	$0.402930\pi$
$312$	1.00000	0.0566139
$313$	11.5380	0.652167	0.326084	−	0.945341i	$-0.394271\pi$
$313$	11.5380	0.652167	0.326084	+	0.945341i	$0.394271\pi$
$314$	−13.4015	−0.756291
$315$	−0.825192	−0.0464943
$316$	−11.6900	−0.657615
$317$	−14.8609	−0.834674	−0.417337	−	0.908752i	$-0.637037\pi$
$317$	−14.8609	−0.834674	−0.417337	+	0.908752i	$0.637037\pi$
$318$	4.72057	0.264717
$319$	−2.99243	−0.167544
$320$	−0.825192	−0.0461297
$321$	5.04803	0.281753
$322$	−6.61595	−0.368693
$323$	−1.54576	−0.0860087
$324$	1.00000	0.0555556
$325$	4.31906	0.239578
$326$	−9.23578	−0.511523
$327$	10.3671	0.573301
$328$	−6.84266	−0.377823
$329$	−11.6900	−0.644491
$330$	−0.475577	−0.0261797
$331$	−4.62452	−0.254187	−0.127093	−	0.991891i	$-0.540565\pi$
$331$	−4.62452	−0.254187	−0.127093	+	0.991891i	$0.540565\pi$
$332$	−17.3144	−0.950249
$333$	5.19615	0.284747
$334$	−1.07406	−0.0587701
$335$	−12.3671	−0.675686
$336$	−1.00000	−0.0545545
$337$	−33.9874	−1.85141	−0.925706	−	0.378243i	$-0.876528\pi$
$337$	−33.9874	−1.85141	−0.925706	+	0.378243i	$0.876528\pi$
$338$	1.00000	0.0543928
$339$	4.84348	0.263062
$340$	0.825192	0.0447523
$341$	−3.86044	−0.209055
$342$	1.54576	0.0835854
$343$	1.00000	0.0539949
$344$	4.37096	0.235666
$345$	−5.45943	−0.293926
$346$	−0.720573	−0.0387382
$347$	11.9945	0.643898	0.321949	−	0.946757i	$-0.395662\pi$
$347$	11.9945	0.643898	0.321949	+	0.946757i	$0.395662\pi$
$348$	−5.19228	−0.278335
$349$	2.41528	0.129287	0.0646435	−	0.997908i	$-0.479409\pi$
$349$	2.41528	0.129287	0.0646435	+	0.997908i	$0.479409\pi$
$350$	−4.31906	−0.230863
$351$	1.00000	0.0533761
$352$	−0.576323	−0.0307181
$353$	−30.2487	−1.60998	−0.804989	−	0.593290i	$-0.797829\pi$
$353$	−30.2487	−1.60998	−0.804989	+	0.593290i	$0.797829\pi$
$354$	7.77247	0.413102
$355$	−3.58540	−0.190293
$356$	2.84266	0.150661
$357$	1.00000	0.0529256
$358$	8.90295	0.470536
$359$	−25.5884	−1.35051	−0.675253	−	0.737586i	$-0.735966\pi$
$359$	−25.5884	−1.35051	−0.675253	+	0.737586i	$0.735966\pi$
$360$	−0.825192	−0.0434915
$361$	−16.6106	−0.874243
$362$	−18.1396	−0.953394
$363$	10.6679	0.559917
$364$	−1.00000	−0.0524142
$365$	1.83814	0.0962126
$366$	−0.248870	−0.0130086
$367$	−16.5930	−0.866146	−0.433073	−	0.901359i	$-0.642571\pi$
$367$	−16.5930	−0.866146	−0.433073	+	0.901359i	$0.642571\pi$
$368$	−6.61595	−0.344880
$369$	−6.84266	−0.356215
$370$	−4.28782	−0.222913
$371$	−4.72057	−0.245080
$372$	−6.69841	−0.347296
$373$	31.6433	1.63843	0.819214	−	0.573487i	$-0.194410\pi$
$373$	31.6433	1.63843	0.819214	+	0.573487i	$0.194410\pi$
$374$	0.576323	0.0298009
$375$	−7.69001	−0.397111
$376$	−11.6900	−0.602866
$377$	−5.19228	−0.267416
$378$	−1.00000	−0.0514344
$379$	−29.5426	−1.51750	−0.758750	−	0.651382i	$-0.774190\pi$
$379$	−29.5426	−1.51750	−0.758750	+	0.651382i	$0.774190\pi$
$380$	−1.27555	−0.0654345
$381$	−3.91754	−0.200702
$382$	−5.39682	−0.276125
$383$	−18.8983	−0.965656	−0.482828	−	0.875715i	$-0.660390\pi$
$383$	−18.8983	−0.965656	−0.482828	+	0.875715i	$0.660390\pi$
$384$	−1.00000	−0.0510310
$385$	0.475577	0.0242376
$386$	−5.27086	−0.268280
$387$	4.37096	0.222188
$388$	−6.59461	−0.334791
$389$	−5.26651	−0.267023	−0.133511	−	0.991047i	$-0.542625\pi$
$389$	−5.26651	−0.267023	−0.133511	+	0.991047i	$0.542625\pi$
$390$	−0.825192	−0.0417852
$391$	6.61595	0.334583
$392$	1.00000	0.0505076
$393$	−15.3762	−0.775624
$394$	2.51603	0.126756
$395$	9.64651	0.485369
$396$	−0.576323	−0.0289613
$397$	−25.1930	−1.26440	−0.632199	−	0.774806i	$-0.717847\pi$
$397$	−25.1930	−1.26440	−0.632199	+	0.774806i	$0.717847\pi$
$398$	3.79463	0.190208
$399$	−1.54576	−0.0773850
$400$	−4.31906	−0.215953
$401$	12.9305	0.645718	0.322859	−	0.946447i	$-0.395356\pi$
$401$	12.9305	0.645718	0.322859	+	0.946447i	$0.395356\pi$
$402$	−14.9869	−0.747479
$403$	−6.69841	−0.333672
$404$	9.58540	0.476891
$405$	−0.825192	−0.0410041
$406$	5.19228	0.257688
$407$	−2.99466	−0.148440
$408$	1.00000	0.0495074
$409$	−38.8616	−1.92158	−0.960792	−	0.277271i	$-0.910570\pi$
$409$	−38.8616	−1.92158	−0.960792	+	0.277271i	$0.910570\pi$
$410$	5.64651	0.278861
$411$	2.73804	0.135058
$412$	−1.69471	−0.0834924
$413$	−7.77247	−0.382458
$414$	−6.61595	−0.325156
$415$	14.2877	0.701355
$416$	−1.00000	−0.0490290
$417$	0.374831	0.0183556
$418$	−0.890859	−0.0435733
$419$	−15.4159	−0.753117	−0.376559	−	0.926393i	$-0.622893\pi$
$419$	−15.4159	−0.753117	−0.376559	+	0.926393i	$0.622893\pi$
$420$	0.825192	0.0402653
$421$	18.6595	0.909406	0.454703	−	0.890643i	$-0.349745\pi$
$421$	18.6595	0.909406	0.454703	+	0.890643i	$0.349745\pi$
$422$	−19.0472	−0.927203
$423$	−11.6900	−0.568388
$424$	−4.72057	−0.229251
$425$	4.31906	0.209505
$426$	−4.34492	−0.210512
$427$	0.248870	0.0120437
$428$	−5.04803	−0.244006
$429$	−0.576323	−0.0278251
$430$	−3.60688	−0.173939
$431$	19.5029	0.939423	0.469712	−	0.882820i	$-0.344358\pi$
$431$	19.5029	0.939423	0.469712	+	0.882820i	$0.344358\pi$
$432$	−1.00000	−0.0481125
$433$	−28.1913	−1.35479	−0.677393	−	0.735621i	$-0.736890\pi$
$433$	−28.1913	−1.35479	−0.677393	+	0.735621i	$0.736890\pi$
$434$	6.69841	0.321534
$435$	4.28463	0.205432
$436$	−10.3671	−0.496493
$437$	−10.2267	−0.489210
$438$	2.22753	0.106435
$439$	−3.24870	−0.155052	−0.0775259	−	0.996990i	$-0.524702\pi$
$439$	−3.24870	−0.155052	−0.0775259	+	0.996990i	$0.524702\pi$
$440$	0.475577	0.0226722
$441$	1.00000	0.0476190
$442$	1.00000	0.0475651
$443$	32.5073	1.54447	0.772235	−	0.635338i	$-0.219139\pi$
$443$	32.5073	1.54447	0.772235	+	0.635338i	$0.219139\pi$
$444$	−5.19615	−0.246598
$445$	−2.34574	−0.111199
$446$	−16.8427	−0.797523
$447$	7.02586	0.332312
$448$	1.00000	0.0472456
$449$	−2.23528	−0.105489	−0.0527446	−	0.998608i	$-0.516797\pi$
$449$	−2.23528	−0.105489	−0.0527446	+	0.998608i	$0.516797\pi$
$450$	−4.31906	−0.203602
$451$	3.94358	0.185696
$452$	−4.84348	−0.227818
$453$	−16.5122	−0.775809
$454$	−20.9219	−0.981914
$455$	0.825192	0.0386856
$456$	−1.54576	−0.0723871
$457$	−27.0249	−1.26417	−0.632086	−	0.774898i	$-0.717801\pi$
$457$	−27.0249	−1.26417	−0.632086	+	0.774898i	$0.717801\pi$
$458$	−8.49304	−0.396854
$459$	1.00000	0.0466760
$460$	5.45943	0.254547
$461$	−29.4547	−1.37184	−0.685922	−	0.727675i	$-0.740601\pi$
$461$	−29.4547	−1.37184	−0.685922	+	0.727675i	$0.740601\pi$
$462$	0.576323	0.0268130
$463$	−1.94440	−0.0903639	−0.0451820	−	0.998979i	$-0.514387\pi$
$463$	−1.94440	−0.0903639	−0.0451820	+	0.998979i	$0.514387\pi$
$464$	5.19228	0.241045
$465$	5.52748	0.256331
$466$	25.4935	1.18097
$467$	−14.3978	−0.666251	−0.333126	−	0.942882i	$-0.608103\pi$
$467$	−14.3978	−0.666251	−0.333126	+	0.942882i	$0.608103\pi$
$468$	−1.00000	−0.0462250
$469$	14.9869	0.692031
$470$	9.64651	0.444960
$471$	13.4015	0.617509
$472$	−7.77247	−0.357757
$473$	−2.51908	−0.115827
$474$	11.6900	0.536940
$475$	−6.67625	−0.306327
$476$	−1.00000	−0.0458349
$477$	−4.72057	−0.216140
$478$	−1.09235	−0.0499629
$479$	−12.3090	−0.562414	−0.281207	−	0.959647i	$-0.590735\pi$
$479$	−12.3090	−0.562414	−0.281207	+	0.959647i	$0.590735\pi$
$480$	0.825192	0.0376647
$481$	−5.19615	−0.236924
$482$	24.2578	1.10491
$483$	6.61595	0.301036
$484$	−10.6679	−0.484902
$485$	5.44182	0.247100
$486$	−1.00000	−0.0453609
$487$	41.1805	1.86607	0.933034	−	0.359790i	$-0.117151\pi$
$487$	41.1805	1.86607	0.933034	+	0.359790i	$0.117151\pi$
$488$	0.248870	0.0112658
$489$	9.23578	0.417656
$490$	−0.825192	−0.0372784
$491$	−16.8870	−0.762099	−0.381049	−	0.924555i	$-0.624437\pi$
$491$	−16.8870	−0.762099	−0.381049	+	0.924555i	$0.624437\pi$
$492$	6.84266	0.308491
$493$	−5.19228	−0.233848
$494$	−1.54576	−0.0695472
$495$	0.475577	0.0213756
$496$	6.69841	0.300767
$497$	4.34492	0.194896
$498$	17.3144	0.775875
$499$	6.04283	0.270514	0.135257	−	0.990811i	$-0.456814\pi$
$499$	6.04283	0.270514	0.135257	+	0.990811i	$0.456814\pi$
$500$	7.69001	0.343908
$501$	1.07406	0.0479856
$502$	−14.6984	−0.656022
$503$	−11.3373	−0.505507	−0.252754	−	0.967531i	$-0.581336\pi$
$503$	−11.3373	−0.505507	−0.252754	+	0.967531i	$0.581336\pi$
$504$	1.00000	0.0445435
$505$	−7.90979	−0.351981
$506$	3.81292	0.169505
$507$	−1.00000	−0.0444116
$508$	3.91754	0.173813
$509$	−34.6761	−1.53699	−0.768496	−	0.639855i	$-0.778994\pi$
$509$	−34.6761	−1.53699	−0.768496	+	0.639855i	$0.778994\pi$
$510$	−0.825192	−0.0365401
$511$	−2.22753	−0.0985400
$512$	1.00000	0.0441942
$513$	−1.54576	−0.0682472
$514$	−6.39312	−0.281988
$515$	1.39846	0.0616236
$516$	−4.37096	−0.192421
$517$	6.73722	0.296303
$518$	5.19615	0.228306
$519$	0.720573	0.0316296
$520$	0.825192	0.0361871
$521$	−14.5631	−0.638019	−0.319010	−	0.947751i	$-0.603350\pi$
$521$	−14.5631	−0.638019	−0.319010	+	0.947751i	$0.603350\pi$
$522$	5.19228	0.227260
$523$	3.66785	0.160384	0.0801920	−	0.996779i	$-0.474447\pi$
$523$	3.66785	0.160384	0.0801920	+	0.996779i	$0.474447\pi$
$524$	15.3762	0.671710
$525$	4.31906	0.188499
$526$	−30.4234	−1.32652
$527$	−6.69841	−0.291787
$528$	0.576323	0.0250812
$529$	20.7708	0.903080
$530$	3.89538	0.169205
$531$	−7.77247	−0.337297
$532$	1.54576	0.0670174
$533$	6.84266	0.296389
$534$	−2.84266	−0.123014
$535$	4.16559	0.180094
$536$	14.9869	0.647336
$537$	−8.90295	−0.384191
$538$	3.46331	0.149314
$539$	−0.576323	−0.0248240
$540$	0.825192	0.0355106
$541$	7.62435	0.327796	0.163898	−	0.986477i	$-0.447593\pi$
$541$	7.62435	0.327796	0.163898	+	0.986477i	$0.447593\pi$
$542$	−4.70310	−0.202016
$543$	18.1396	0.778443
$544$	−1.00000	−0.0428746
$545$	8.55484	0.366449
$546$	1.00000	0.0427960
$547$	−11.6014	−0.496039	−0.248019	−	0.968755i	$-0.579780\pi$
$547$	−11.6014	−0.496039	−0.248019	+	0.968755i	$0.579780\pi$
$548$	−2.73804	−0.116963
$549$	0.248870	0.0106215
$550$	2.48917	0.106139
$551$	8.02604	0.341921
$552$	6.61595	0.281594
$553$	−11.6900	−0.497110
$554$	−6.86482	−0.291658
$555$	4.28782	0.182008
$556$	−0.374831	−0.0158964
$557$	14.4961	0.614219	0.307110	−	0.951674i	$-0.400638\pi$
$557$	14.4961	0.614219	0.307110	+	0.951674i	$0.400638\pi$
$558$	6.69841	0.283566
$559$	−4.37096	−0.184872
$560$	−0.825192	−0.0348707
$561$	−0.576323	−0.0243324
$562$	27.8470	1.17466
$563$	4.59461	0.193640	0.0968199	−	0.995302i	$-0.469133\pi$
$563$	4.59461	0.193640	0.0968199	+	0.995302i	$0.469133\pi$
$564$	11.6900	0.492238
$565$	3.99680	0.168147
$566$	29.7241	1.24940
$567$	1.00000	0.0419961
$568$	4.34492	0.182309
$569$	−13.6108	−0.570593	−0.285296	−	0.958439i	$-0.592092\pi$
$569$	−13.6108	−0.570593	−0.285296	+	0.958439i	$0.592092\pi$
$570$	1.27555	0.0534270
$571$	41.0608	1.71834	0.859170	−	0.511689i	$-0.170980\pi$
$571$	41.0608	1.71834	0.859170	+	0.511689i	$0.170980\pi$
$572$	0.576323	0.0240973
$573$	5.39682	0.225455
$574$	−6.84266	−0.285607
$575$	28.5747	1.19165
$576$	1.00000	0.0416667
$577$	20.1221	0.837693	0.418847	−	0.908057i	$-0.362434\pi$
$577$	20.1221	0.837693	0.418847	+	0.908057i	$0.362434\pi$
$578$	1.00000	0.0415945
$579$	5.27086	0.219049
$580$	−4.28463	−0.177909
$581$	−17.3144	−0.718321
$582$	6.59461	0.273355
$583$	2.72057	0.112675
$584$	−2.22753	−0.0921758
$585$	0.825192	0.0341175
$586$	−8.68564	−0.358800
$587$	−2.74438	−0.113273	−0.0566363	−	0.998395i	$-0.518038\pi$
$587$	−2.74438	−0.113273	−0.0566363	+	0.998395i	$0.518038\pi$
$588$	−1.00000	−0.0412393
$589$	10.3542	0.426636
$590$	6.41378	0.264051
$591$	−2.51603	−0.103496
$592$	5.19615	0.213560
$593$	−38.6983	−1.58915	−0.794574	−	0.607168i	$-0.792306\pi$
$593$	−38.6983	−1.58915	−0.794574	+	0.607168i	$0.792306\pi$
$594$	0.576323	0.0236468
$595$	0.825192	0.0338296
$596$	−7.02586	−0.287791
$597$	−3.79463	−0.155304
$598$	6.61595	0.270546
$599$	−24.4883	−1.00057	−0.500283	−	0.865862i	$-0.666771\pi$
$599$	−24.4883	−1.00057	−0.500283	+	0.865862i	$0.666771\pi$
$600$	4.31906	0.176325
$601$	24.5396	1.00099	0.500496	−	0.865739i	$-0.333151\pi$
$601$	24.5396	1.00099	0.500496	+	0.865739i	$0.333151\pi$
$602$	4.37096	0.178147
$603$	14.9869	0.610314
$604$	16.5122	0.671870
$605$	8.80303	0.357894
$606$	−9.58540	−0.389380
$607$	20.9496	0.850318	0.425159	−	0.905119i	$-0.360218\pi$
$607$	20.9496	0.850318	0.425159	+	0.905119i	$0.360218\pi$
$608$	1.54576	0.0626890
$609$	−5.19228	−0.210402
$610$	−0.205365	−0.00831500
$611$	11.6900	0.472927
$612$	−1.00000	−0.0404226
$613$	−4.14038	−0.167228	−0.0836141	−	0.996498i	$-0.526646\pi$
$613$	−4.14038	−0.167228	−0.0836141	+	0.996498i	$0.526646\pi$
$614$	7.31354	0.295151
$615$	−5.64651	−0.227689
$616$	−0.576323	−0.0232207
$617$	10.3593	0.417051	0.208526	−	0.978017i	$-0.433134\pi$
$617$	10.3593	0.417051	0.208526	+	0.978017i	$0.433134\pi$
$618$	1.69471	0.0681712
$619$	−20.7287	−0.833155	−0.416577	−	0.909100i	$-0.636771\pi$
$619$	−20.7287	−0.833155	−0.416577	+	0.909100i	$0.636771\pi$
$620$	−5.52748	−0.221989
$621$	6.61595	0.265489
$622$	10.5899	0.424617
$623$	2.84266	0.113889
$624$	1.00000	0.0400320
$625$	15.2495	0.609982
$626$	11.5380	0.461152
$627$	0.890859	0.0355775
$628$	−13.4015	−0.534779
$629$	−5.19615	−0.207184
$630$	−0.825192	−0.0328764
$631$	43.9564	1.74987	0.874937	−	0.484236i	$-0.160902\pi$
$631$	43.9564	1.74987	0.874937	+	0.484236i	$0.160902\pi$
$632$	−11.6900	−0.465004
$633$	19.0472	0.757058
$634$	−14.8609	−0.590204
$635$	−3.23273	−0.128287
$636$	4.72057	0.187183
$637$	−1.00000	−0.0396214
$638$	−2.99243	−0.118471
$639$	4.34492	0.171882
$640$	−0.825192	−0.0326186
$641$	25.9385	1.02451	0.512255	−	0.858833i	$-0.328810\pi$
$641$	25.9385	1.02451	0.512255	+	0.858833i	$0.328810\pi$
$642$	5.04803	0.199230
$643$	−33.5402	−1.32270	−0.661349	−	0.750078i	$-0.730016\pi$
$643$	−33.5402	−1.32270	−0.661349	+	0.750078i	$0.730016\pi$
$644$	−6.61595	−0.260705
$645$	3.60688	0.142021
$646$	−1.54576	−0.0608173
$647$	−10.4282	−0.409975	−0.204987	−	0.978765i	$-0.565715\pi$
$647$	−10.4282	−0.409975	−0.204987	+	0.978765i	$0.565715\pi$
$648$	1.00000	0.0392837
$649$	4.47945	0.175834
$650$	4.31906	0.169407
$651$	−6.69841	−0.262531
$652$	−9.23578	−0.361701
$653$	19.9249	0.779723	0.389862	−	0.920873i	$-0.372523\pi$
$653$	19.9249	0.779723	0.389862	+	0.920873i	$0.372523\pi$
$654$	10.3671	0.405385
$655$	−12.6883	−0.495772
$656$	−6.84266	−0.267161
$657$	−2.22753	−0.0869041
$658$	−11.6900	−0.455724
$659$	−48.6590	−1.89548	−0.947742	−	0.319037i	$-0.896640\pi$
$659$	−48.6590	−1.89548	−0.947742	+	0.319037i	$0.896640\pi$
$660$	−0.475577	−0.0185118
$661$	−33.1066	−1.28770	−0.643849	−	0.765152i	$-0.722664\pi$
$661$	−33.1066	−1.28770	−0.643849	+	0.765152i	$0.722664\pi$
$662$	−4.62452	−0.179737
$663$	−1.00000	−0.0388368
$664$	−17.3144	−0.671928
$665$	−1.27555	−0.0494638
$666$	5.19615	0.201347
$667$	−34.3518	−1.33011
$668$	−1.07406	−0.0415567
$669$	16.8427	0.651175
$670$	−12.3671	−0.477782
$671$	−0.143429	−0.00553702
$672$	−1.00000	−0.0385758
$673$	40.5646	1.56365	0.781824	−	0.623499i	$-0.214289\pi$
$673$	40.5646	1.56365	0.781824	+	0.623499i	$0.214289\pi$
$674$	−33.9874	−1.30915
$675$	4.31906	0.166241
$676$	1.00000	0.0384615
$677$	−21.3357	−0.819998	−0.409999	−	0.912086i	$-0.634471\pi$
$677$	−21.3357	−0.819998	−0.409999	+	0.912086i	$0.634471\pi$
$678$	4.84348	0.186013
$679$	−6.59461	−0.253078
$680$	0.825192	0.0316447
$681$	20.9219	0.801730
$682$	−3.86044	−0.147824
$683$	19.4061	0.742552	0.371276	−	0.928522i	$-0.378920\pi$
$683$	19.4061	0.742552	0.371276	+	0.928522i	$0.378920\pi$
$684$	1.54576	0.0591038
$685$	2.25941	0.0863276
$686$	1.00000	0.0381802
$687$	8.49304	0.324030
$688$	4.37096	0.166641
$689$	4.72057	0.179839
$690$	−5.45943	−0.207837
$691$	−24.1839	−0.919998	−0.459999	−	0.887919i	$-0.652150\pi$
$691$	−24.1839	−0.919998	−0.459999	+	0.887919i	$0.652150\pi$
$692$	−0.720573	−0.0273921
$693$	−0.576323	−0.0218927
$694$	11.9945	0.455304
$695$	0.309308	0.0117327
$696$	−5.19228	−0.196813
$697$	6.84266	0.259184
$698$	2.41528	0.0914198
$699$	−25.4935	−0.964255
$700$	−4.31906	−0.163245
$701$	0.218959	0.00826996	0.00413498	−	0.999991i	$-0.498684\pi$
$701$	0.218959	0.00826996	0.00413498	+	0.999991i	$0.498684\pi$
$702$	1.00000	0.0377426
$703$	8.03203	0.302934
$704$	−0.576323	−0.0217210
$705$	−9.64651	−0.363309
$706$	−30.2487	−1.13843
$707$	9.58540	0.360496
$708$	7.77247	0.292107
$709$	−37.0241	−1.39047	−0.695234	−	0.718783i	$-0.744699\pi$
$709$	−37.0241	−1.39047	−0.695234	+	0.718783i	$0.744699\pi$
$710$	−3.58540	−0.134557
$711$	−11.6900	−0.438410
$712$	2.84266	0.106533
$713$	−44.3164	−1.65966
$714$	1.00000	0.0374241
$715$	−0.475577	−0.0177856
$716$	8.90295	0.332719
$717$	1.09235	0.0407946
$718$	−25.5884	−0.954952
$719$	28.7737	1.07308	0.536538	−	0.843876i	$-0.319732\pi$
$719$	28.7737	1.07308	0.536538	+	0.843876i	$0.319732\pi$
$720$	−0.825192	−0.0307531
$721$	−1.69471	−0.0631143
$722$	−16.6106	−0.618183
$723$	−24.2578	−0.902156
$724$	−18.1396	−0.674151
$725$	−22.4257	−0.832871
$726$	10.6679	0.395921
$727$	−44.2087	−1.63961	−0.819806	−	0.572642i	$-0.805919\pi$
$727$	−44.2087	−1.63961	−0.819806	+	0.572642i	$0.805919\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	1.83814	0.0680326
$731$	−4.37096	−0.161666
$732$	−0.248870	−0.00919849
$733$	18.4883	0.682883	0.341441	−	0.939903i	$-0.389085\pi$
$733$	18.4883	0.682883	0.341441	+	0.939903i	$0.389085\pi$
$734$	−16.5930	−0.612458
$735$	0.825192	0.0304377
$736$	−6.61595	−0.243867
$737$	−8.63729	−0.318159
$738$	−6.84266	−0.251882
$739$	46.0188	1.69283	0.846415	−	0.532524i	$-0.178756\pi$
$739$	46.0188	1.69283	0.846415	+	0.532524i	$0.178756\pi$
$740$	−4.28782	−0.157623
$741$	1.54576	0.0567851
$742$	−4.72057	−0.173298
$743$	−2.83729	−0.104090	−0.0520450	−	0.998645i	$-0.516574\pi$
$743$	−2.83729	−0.104090	−0.0520450	+	0.998645i	$0.516574\pi$
$744$	−6.69841	−0.245576
$745$	5.79769	0.212411
$746$	31.6433	1.15854
$747$	−17.3144	−0.633499
$748$	0.576323	0.0210724
$749$	−5.04803	−0.184451
$750$	−7.69001	−0.280800
$751$	50.2673	1.83428	0.917141	−	0.398564i	$-0.130491\pi$
$751$	50.2673	1.83428	0.917141	+	0.398564i	$0.130491\pi$
$752$	−11.6900	−0.426291
$753$	14.6984	0.535640
$754$	−5.19228	−0.189092
$755$	−13.6257	−0.495890
$756$	−1.00000	−0.0363696
$757$	−2.36872	−0.0860928	−0.0430464	−	0.999073i	$-0.513706\pi$
$757$	−2.36872	−0.0860928	−0.0430464	+	0.999073i	$0.513706\pi$
$758$	−29.5426	−1.07303
$759$	−3.81292	−0.138400
$760$	−1.27555	−0.0462692
$761$	45.6697	1.65552	0.827762	−	0.561079i	$-0.189614\pi$
$761$	45.6697	1.65552	0.827762	+	0.561079i	$0.189614\pi$
$762$	−3.91754	−0.141918
$763$	−10.3671	−0.375314
$764$	−5.39682	−0.195250
$765$	0.825192	0.0298349
$766$	−18.8983	−0.682822
$767$	7.77247	0.280648
$768$	−1.00000	−0.0360844
$769$	9.91822	0.357660	0.178830	−	0.983880i	$-0.442769\pi$
$769$	9.91822	0.357660	0.178830	+	0.983880i	$0.442769\pi$
$770$	0.475577	0.0171386
$771$	6.39312	0.230243
$772$	−5.27086	−0.189702
$773$	−3.09787	−0.111422	−0.0557112	−	0.998447i	$-0.517743\pi$
$773$	−3.09787	−0.111422	−0.0557112	+	0.998447i	$0.517743\pi$
$774$	4.37096	0.157111
$775$	−28.9308	−1.03923
$776$	−6.59461	−0.236733
$777$	−5.19615	−0.186411
$778$	−5.26651	−0.188814
$779$	−10.5771	−0.378965
$780$	−0.825192	−0.0295466
$781$	−2.50408	−0.0896029
$782$	6.61595	0.236586
$783$	−5.19228	−0.185557
$784$	1.00000	0.0357143
$785$	11.0588	0.394706
$786$	−15.3762	−0.548449
$787$	37.2700	1.32853	0.664267	−	0.747496i	$-0.268744\pi$
$787$	37.2700	1.32853	0.664267	+	0.747496i	$0.268744\pi$
$788$	2.51603	0.0896298
$789$	30.4234	1.08310
$790$	9.64651	0.343207
$791$	−4.84348	−0.172214
$792$	−0.576323	−0.0204787
$793$	−0.248870	−0.00883762
$794$	−25.1930	−0.894064
$795$	−3.89538	−0.138155
$796$	3.79463	0.134497
$797$	30.9790	1.09733	0.548667	−	0.836041i	$-0.315136\pi$
$797$	30.9790	1.09733	0.548667	+	0.836041i	$0.315136\pi$
$798$	−1.54576	−0.0547195
$799$	11.6900	0.413563
$800$	−4.31906	−0.152702
$801$	2.84266	0.100440
$802$	12.9305	0.456591
$803$	1.28377	0.0453034
$804$	−14.9869	−0.528548
$805$	5.45943	0.192420
$806$	−6.69841	−0.235941
$807$	−3.46331	−0.121914
$808$	9.58540	0.337213
$809$	16.8297	0.591702	0.295851	−	0.955234i	$-0.404397\pi$
$809$	16.8297	0.591702	0.295851	+	0.955234i	$0.404397\pi$
$810$	−0.825192	−0.0289943
$811$	50.4051	1.76996	0.884981	−	0.465628i	$-0.154171\pi$
$811$	50.4051	1.76996	0.884981	+	0.465628i	$0.154171\pi$
$812$	5.19228	0.182213
$813$	4.70310	0.164945
$814$	−2.99466	−0.104963
$815$	7.62129	0.266962
$816$	1.00000	0.0350070
$817$	6.75647	0.236379
$818$	−38.8616	−1.35876
$819$	−1.00000	−0.0349428
$820$	5.64651	0.197185
$821$	−37.9508	−1.32449	−0.662247	−	0.749286i	$-0.730397\pi$
$821$	−37.9508	−1.32449	−0.662247	+	0.749286i	$0.730397\pi$
$822$	2.73804	0.0955001
$823$	47.5052	1.65593	0.827963	−	0.560783i	$-0.189500\pi$
$823$	47.5052	1.65593	0.827963	+	0.560783i	$0.189500\pi$
$824$	−1.69471	−0.0590380
$825$	−2.48917	−0.0866618
$826$	−7.77247	−0.270439
$827$	−3.57650	−0.124367	−0.0621835	−	0.998065i	$-0.519806\pi$
$827$	−3.57650	−0.124367	−0.0621835	+	0.998065i	$0.519806\pi$
$828$	−6.61595	−0.229920
$829$	15.7258	0.546179	0.273089	−	0.961989i	$-0.411955\pi$
$829$	15.7258	0.546179	0.273089	+	0.961989i	$0.411955\pi$
$830$	14.2877	0.495933
$831$	6.86482	0.238138
$832$	−1.00000	−0.0346688
$833$	−1.00000	−0.0346479
$834$	0.374831	0.0129793
$835$	0.886308	0.0306719
$836$	−0.890859	−0.0308110
$837$	−6.69841	−0.231531
$838$	−15.4159	−0.532534
$839$	4.04268	0.139569	0.0697845	−	0.997562i	$-0.477769\pi$
$839$	4.04268	0.139569	0.0697845	+	0.997562i	$0.477769\pi$
$840$	0.825192	0.0284718
$841$	−2.04028	−0.0703544
$842$	18.6595	0.643047
$843$	−27.8470	−0.959103
$844$	−19.0472	−0.655632
$845$	−0.825192	−0.0283875
$846$	−11.6900	−0.401911
$847$	−10.6679	−0.366552
$848$	−4.72057	−0.162105
$849$	−29.7241	−1.02013
$850$	4.31906	0.148142
$851$	−34.3775	−1.17844
$852$	−4.34492	−0.148855
$853$	17.5006	0.599210	0.299605	−	0.954063i	$-0.403145\pi$
$853$	17.5006	0.599210	0.299605	+	0.954063i	$0.403145\pi$
$854$	0.248870	0.00851615
$855$	−1.27555	−0.0436230
$856$	−5.04803	−0.172538
$857$	−27.2225	−0.929903	−0.464952	−	0.885336i	$-0.653928\pi$
$857$	−27.2225	−0.929903	−0.464952	+	0.885336i	$0.653928\pi$
$858$	−0.576323	−0.0196753
$859$	8.56857	0.292356	0.146178	−	0.989258i	$-0.453303\pi$
$859$	8.56857	0.292356	0.146178	+	0.989258i	$0.453303\pi$
$860$	−3.60688	−0.122994
$861$	6.84266	0.233197
$862$	19.5029	0.664273
$863$	45.3127	1.54246	0.771231	−	0.636555i	$-0.219641\pi$
$863$	45.3127	1.54246	0.771231	+	0.636555i	$0.219641\pi$
$864$	−1.00000	−0.0340207
$865$	0.594611	0.0202174
$866$	−28.1913	−0.957979
$867$	−1.00000	−0.0339618
$868$	6.69841	0.227359
$869$	6.73722	0.228545
$870$	4.28463	0.145262
$871$	−14.9869	−0.507812
$872$	−10.3671	−0.351074
$873$	−6.59461	−0.223194
$874$	−10.2267	−0.345924
$875$	7.69001	0.259970
$876$	2.22753	0.0752612
$877$	−30.0128	−1.01346	−0.506730	−	0.862105i	$-0.669146\pi$
$877$	−30.0128	−1.01346	−0.506730	+	0.862105i	$0.669146\pi$
$878$	−3.24870	−0.109638
$879$	8.68564	0.292959
$880$	0.475577	0.0160317
$881$	4.57327	0.154077	0.0770387	−	0.997028i	$-0.475454\pi$
$881$	4.57327	0.154077	0.0770387	+	0.997028i	$0.475454\pi$
$882$	1.00000	0.0336718
$883$	−3.06115	−0.103016	−0.0515079	−	0.998673i	$-0.516403\pi$
$883$	−3.06115	−0.103016	−0.0515079	+	0.998673i	$0.516403\pi$
$884$	1.00000	0.0336336
$885$	−6.41378	−0.215597
$886$	32.5073	1.09210
$887$	20.8559	0.700273	0.350137	−	0.936699i	$-0.386135\pi$
$887$	20.8559	0.700273	0.350137	+	0.936699i	$0.386135\pi$
$888$	−5.19615	−0.174371
$889$	3.91754	0.131390
$890$	−2.34574	−0.0786294
$891$	−0.576323	−0.0193075
$892$	−16.8427	−0.563934
$893$	−18.0700	−0.604690
$894$	7.02586	0.234980
$895$	−7.34665	−0.245571
$896$	1.00000	0.0334077
$897$	−6.61595	−0.220900
$898$	−2.23528	−0.0745921
$899$	34.7800	1.15998
$900$	−4.31906	−0.143969
$901$	4.72057	0.157265
$902$	3.94358	0.131307
$903$	−4.37096	−0.145456
$904$	−4.84348	−0.161092
$905$	14.9686	0.497574
$906$	−16.5122	−0.548580
$907$	−17.8027	−0.591129	−0.295565	−	0.955323i	$-0.595508\pi$
$907$	−17.8027	−0.591129	−0.295565	+	0.955323i	$0.595508\pi$
$908$	−20.9219	−0.694318
$909$	9.58540	0.317927
$910$	0.825192	0.0273549
$911$	−14.2349	−0.471624	−0.235812	−	0.971799i	$-0.575775\pi$
$911$	−14.2349	−0.471624	−0.235812	+	0.971799i	$0.575775\pi$
$912$	−1.54576	−0.0511854
$913$	9.97866	0.330245
$914$	−27.0249	−0.893904
$915$	0.205365	0.00678917
$916$	−8.49304	−0.280618
$917$	15.3762	0.507765
$918$	1.00000	0.0330049
$919$	21.3182	0.703224	0.351612	−	0.936146i	$-0.385634\pi$
$919$	21.3182	0.703224	0.351612	+	0.936146i	$0.385634\pi$
$920$	5.45943	0.179992
$921$	−7.31354	−0.240989
$922$	−29.4547	−0.970040
$923$	−4.34492	−0.143015
$924$	0.576323	0.0189596
$925$	−22.4425	−0.737904
$926$	−1.94440	−0.0638970
$927$	−1.69471	−0.0556616
$928$	5.19228	0.170445
$929$	46.7826	1.53489	0.767443	−	0.641117i	$-0.221529\pi$
$929$	46.7826	1.53489	0.767443	+	0.641117i	$0.221529\pi$
$930$	5.52748	0.181253
$931$	1.54576	0.0506604
$932$	25.4935	0.835069
$933$	−10.5899	−0.346698
$934$	−14.3978	−0.471111
$935$	−0.475577	−0.0155530
$936$	−1.00000	−0.0326860
$937$	0.794808	0.0259653	0.0129826	−	0.999916i	$-0.495867\pi$
$937$	0.794808	0.0259653	0.0129826	+	0.999916i	$0.495867\pi$
$938$	14.9869	0.489340
$939$	−11.5380	−0.376529
$940$	9.64651	0.314634
$941$	−2.09978	−0.0684509	−0.0342255	−	0.999414i	$-0.510896\pi$
$941$	−2.09978	−0.0684509	−0.0342255	+	0.999414i	$0.510896\pi$
$942$	13.4015	0.436645
$943$	45.2707	1.47422
$944$	−7.77247	−0.252972
$945$	0.825192	0.0268435
$946$	−2.51908	−0.0819024
$947$	54.4505	1.76941	0.884703	−	0.466156i	$-0.154361\pi$
$947$	54.4505	1.76941	0.884703	+	0.466156i	$0.154361\pi$
$948$	11.6900	0.379674
$949$	2.22753	0.0723086
$950$	−6.67625	−0.216606
$951$	14.8609	0.481899
$952$	−1.00000	−0.0324102
$953$	−44.4256	−1.43909	−0.719543	−	0.694448i	$-0.755649\pi$
$953$	−44.4256	−1.43909	−0.719543	+	0.694448i	$0.755649\pi$
$954$	−4.72057	−0.152834
$955$	4.45341	0.144109
$956$	−1.09235	−0.0353291
$957$	2.99243	0.0967314
$958$	−12.3090	−0.397686
$959$	−2.73804	−0.0884159
$960$	0.825192	0.0266330
$961$	13.8687	0.447377
$962$	−5.19615	−0.167531
$963$	−5.04803	−0.162670
$964$	24.2578	0.781290
$965$	4.34947	0.140014
$966$	6.61595	0.212865
$967$	24.3129	0.781850	0.390925	−	0.920423i	$-0.372155\pi$
$967$	24.3129	0.781850	0.390925	+	0.920423i	$0.372155\pi$
$968$	−10.6679	−0.342878
$969$	1.54576	0.0496571
$970$	5.44182	0.174726
$971$	−3.79511	−0.121791	−0.0608954	−	0.998144i	$-0.519396\pi$
$971$	−3.79511	−0.121791	−0.0608954	+	0.998144i	$0.519396\pi$
$972$	−1.00000	−0.0320750
$973$	−0.374831	−0.0120165
$974$	41.1805	1.31951
$975$	−4.31906	−0.138321
$976$	0.248870	0.00796613
$977$	−24.6571	−0.788850	−0.394425	−	0.918928i	$-0.629056\pi$
$977$	−24.6571	−0.788850	−0.394425	+	0.918928i	$0.629056\pi$
$978$	9.23578	0.295328
$979$	−1.63829	−0.0523599
$980$	−0.825192	−0.0263598
$981$	−10.3671	−0.330995
$982$	−16.8870	−0.538885
$983$	−16.2165	−0.517226	−0.258613	−	0.965981i	$-0.583265\pi$
$983$	−16.2165	−0.517226	−0.258613	+	0.965981i	$0.583265\pi$
$984$	6.84266	0.218136
$985$	−2.07621	−0.0661535
$986$	−5.19228	−0.165356
$987$	11.6900	0.372097
$988$	−1.54576	−0.0491773
$989$	−28.9180	−0.919540
$990$	0.475577	0.0151148
$991$	−44.5201	−1.41423	−0.707114	−	0.707100i	$-0.750003\pi$
$991$	−44.5201	−1.41423	−0.707114	+	0.707100i	$0.750003\pi$
$992$	6.69841	0.212675
$993$	4.62452	0.146755
$994$	4.34492	0.137813
$995$	−3.13130	−0.0992690
$996$	17.3144	0.548627
$997$	−35.7568	−1.13243	−0.566215	−	0.824258i	$-0.691593\pi$
$997$	−35.7568	−1.13243	−0.566215	+	0.824258i	$0.691593\pi$
$998$	6.04283	0.191282
$999$	−5.19615	−0.164399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bm.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bm.1.2	✓	4	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.825192 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.825192 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.825192 q^{10} -0.576323 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +0.825192 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.54576 q^{19} -0.825192 q^{20} -1.00000 q^{21} -0.576323 q^{22} -6.61595 q^{23} -1.00000 q^{24} -4.31906 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.19228 q^{29} +0.825192 q^{30} +6.69841 q^{31} +1.00000 q^{32} +0.576323 q^{33} -1.00000 q^{34} -0.825192 q^{35} +1.00000 q^{36} +5.19615 q^{37} +1.54576 q^{38} +1.00000 q^{39} -0.825192 q^{40} -6.84266 q^{41} -1.00000 q^{42} +4.37096 q^{43} -0.576323 q^{44} -0.825192 q^{45} -6.61595 q^{46} -11.6900 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.31906 q^{50} +1.00000 q^{51} -1.00000 q^{52} -4.72057 q^{53} -1.00000 q^{54} +0.475577 q^{55} +1.00000 q^{56} -1.54576 q^{57} +5.19228 q^{58} -7.77247 q^{59} +0.825192 q^{60} +0.248870 q^{61} +6.69841 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.825192 q^{65} +0.576323 q^{66} +14.9869 q^{67} -1.00000 q^{68} +6.61595 q^{69} -0.825192 q^{70} +4.34492 q^{71} +1.00000 q^{72} -2.22753 q^{73} +5.19615 q^{74} +4.31906 q^{75} +1.54576 q^{76} -0.576323 q^{77} +1.00000 q^{78} -11.6900 q^{79} -0.825192 q^{80} +1.00000 q^{81} -6.84266 q^{82} -17.3144 q^{83} -1.00000 q^{84} +0.825192 q^{85} +4.37096 q^{86} -5.19228 q^{87} -0.576323 q^{88} +2.84266 q^{89} -0.825192 q^{90} -1.00000 q^{91} -6.61595 q^{92} -6.69841 q^{93} -11.6900 q^{94} -1.27555 q^{95} -1.00000 q^{96} -6.59461 q^{97} +1.00000 q^{98} -0.576323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} - 3 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 11 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 4 q^{24} - 2 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 9 q^{29} + 2 q^{30} + 11 q^{31} + 4 q^{32} + 3 q^{33} - 4 q^{34} - 2 q^{35} + 4 q^{36} + q^{37} - 11 q^{38} + 4 q^{39} - 2 q^{40} + 5 q^{41} - 4 q^{42} - q^{43} - 3 q^{44} - 2 q^{45} + 4 q^{46} - 13 q^{47} - 4 q^{48} + 4 q^{49} - 2 q^{50} + 4 q^{51} - 4 q^{52} - 3 q^{53} - 4 q^{54} - 2 q^{55} + 4 q^{56} + 11 q^{57} - 9 q^{58} - 12 q^{59} + 2 q^{60} - q^{61} + 11 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} + 3 q^{66} + 11 q^{67} - 4 q^{68} - 4 q^{69} - 2 q^{70} - 11 q^{71} + 4 q^{72} - 28 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 3 q^{77} + 4 q^{78} - 13 q^{79} - 2 q^{80} + 4 q^{81} + 5 q^{82} - 23 q^{83} - 4 q^{84} + 2 q^{85} - q^{86} + 9 q^{87} - 3 q^{88} - 21 q^{89} - 2 q^{90} - 4 q^{91} + 4 q^{92} - 11 q^{93} - 13 q^{94} - 11 q^{95} - 4 q^{96} - 17 q^{97} + 4 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 - 3 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 11 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 4 * q^24 - 2 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 9 * q^29 + 2 * q^30 + 11 * q^31 + 4 * q^32 + 3 * q^33 - 4 * q^34 - 2 * q^35 + 4 * q^36 + q^37 - 11 * q^38 + 4 * q^39 - 2 * q^40 + 5 * q^41 - 4 * q^42 - q^43 - 3 * q^44 - 2 * q^45 + 4 * q^46 - 13 * q^47 - 4 * q^48 + 4 * q^49 - 2 * q^50 + 4 * q^51 - 4 * q^52 - 3 * q^53 - 4 * q^54 - 2 * q^55 + 4 * q^56 + 11 * q^57 - 9 * q^58 - 12 * q^59 + 2 * q^60 - q^61 + 11 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 + 3 * q^66 + 11 * q^67 - 4 * q^68 - 4 * q^69 - 2 * q^70 - 11 * q^71 + 4 * q^72 - 28 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 3 * q^77 + 4 * q^78 - 13 * q^79 - 2 * q^80 + 4 * q^81 + 5 * q^82 - 23 * q^83 - 4 * q^84 + 2 * q^85 - q^86 + 9 * q^87 - 3 * q^88 - 21 * q^89 - 2 * q^90 - 4 * q^91 + 4 * q^92 - 11 * q^93 - 13 * q^94 - 11 * q^95 - 4 * q^96 - 17 * q^97 + 4 * q^98 - 3 * q^99

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