LMFDB - Embedded newform 6018.2.a.z.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 $ x^11 - 4x^10 - 27x^9 + 117x^8 + 200x^7 - 1023x^6 - 484x^5 + 3403x^4 + 562x^3 - 4372x^2 - 692x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$3.59322$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.59322 q^{5} -1.00000 q^{6} +3.34551 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.59322 q^{5} -1.00000 q^{6} +3.34551 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.59322 q^{10} -3.90055 q^{11} -1.00000 q^{12} +4.00699 q^{13} +3.34551 q^{14} -3.59322 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.67278 q^{19} +3.59322 q^{20} -3.34551 q^{21} -3.90055 q^{22} -5.58722 q^{23} -1.00000 q^{24} +7.91124 q^{25} +4.00699 q^{26} -1.00000 q^{27} +3.34551 q^{28} +2.22628 q^{29} -3.59322 q^{30} +0.830709 q^{31} +1.00000 q^{32} +3.90055 q^{33} -1.00000 q^{34} +12.0212 q^{35} +1.00000 q^{36} +4.39474 q^{37} -3.67278 q^{38} -4.00699 q^{39} +3.59322 q^{40} -0.806935 q^{41} -3.34551 q^{42} +12.0789 q^{43} -3.90055 q^{44} +3.59322 q^{45} -5.58722 q^{46} -4.08803 q^{47} -1.00000 q^{48} +4.19247 q^{49} +7.91124 q^{50} +1.00000 q^{51} +4.00699 q^{52} +8.74497 q^{53} -1.00000 q^{54} -14.0155 q^{55} +3.34551 q^{56} +3.67278 q^{57} +2.22628 q^{58} -1.00000 q^{59} -3.59322 q^{60} +7.47207 q^{61} +0.830709 q^{62} +3.34551 q^{63} +1.00000 q^{64} +14.3980 q^{65} +3.90055 q^{66} +7.50116 q^{67} -1.00000 q^{68} +5.58722 q^{69} +12.0212 q^{70} +3.47662 q^{71} +1.00000 q^{72} -0.169296 q^{73} +4.39474 q^{74} -7.91124 q^{75} -3.67278 q^{76} -13.0493 q^{77} -4.00699 q^{78} +10.9721 q^{79} +3.59322 q^{80} +1.00000 q^{81} -0.806935 q^{82} -16.4673 q^{83} -3.34551 q^{84} -3.59322 q^{85} +12.0789 q^{86} -2.22628 q^{87} -3.90055 q^{88} +12.1589 q^{89} +3.59322 q^{90} +13.4055 q^{91} -5.58722 q^{92} -0.830709 q^{93} -4.08803 q^{94} -13.1971 q^{95} -1.00000 q^{96} +17.7603 q^{97} +4.19247 q^{98} -3.90055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * 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
$5$	3.59322	1.60694	0.803469	−	0.595347i	$-0.202985\pi$
$5$	3.59322	1.60694	0.803469	+	0.595347i	$0.202985\pi$
$6$	−1.00000	−0.408248
$7$	3.34551	1.26449	0.632243	−	0.774770i	$-0.282135\pi$
$7$	3.34551	1.26449	0.632243	+	0.774770i	$0.282135\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.59322	1.13628
$11$	−3.90055	−1.17606	−0.588029	−	0.808840i	$-0.700096\pi$
$11$	−3.90055	−1.17606	−0.588029	+	0.808840i	$0.700096\pi$
$12$	−1.00000	−0.288675
$13$	4.00699	1.11134	0.555670	−	0.831403i	$-0.312462\pi$
$13$	4.00699	1.11134	0.555670	+	0.831403i	$0.312462\pi$
$14$	3.34551	0.894126
$15$	−3.59322	−0.927766
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−3.67278	−0.842594	−0.421297	−	0.906923i	$-0.638425\pi$
$19$	−3.67278	−0.842594	−0.421297	+	0.906923i	$0.638425\pi$
$20$	3.59322	0.803469
$21$	−3.34551	−0.730051
$22$	−3.90055	−0.831599
$23$	−5.58722	−1.16501	−0.582507	−	0.812825i	$-0.697928\pi$
$23$	−5.58722	−1.16501	−0.582507	+	0.812825i	$0.697928\pi$
$24$	−1.00000	−0.204124
$25$	7.91124	1.58225
$26$	4.00699	0.785836
$27$	−1.00000	−0.192450
$28$	3.34551	0.632243
$29$	2.22628	0.413411	0.206705	−	0.978403i	$-0.433726\pi$
$29$	2.22628	0.413411	0.206705	+	0.978403i	$0.433726\pi$
$30$	−3.59322	−0.656029
$31$	0.830709	0.149200	0.0745998	−	0.997214i	$-0.476232\pi$
$31$	0.830709	0.149200	0.0745998	+	0.997214i	$0.476232\pi$
$32$	1.00000	0.176777
$33$	3.90055	0.678998
$34$	−1.00000	−0.171499
$35$	12.0212	2.03195
$36$	1.00000	0.166667
$37$	4.39474	0.722491	0.361245	−	0.932471i	$-0.382352\pi$
$37$	4.39474	0.722491	0.361245	+	0.932471i	$0.382352\pi$
$38$	−3.67278	−0.595804
$39$	−4.00699	−0.641632
$40$	3.59322	0.568138
$41$	−0.806935	−0.126022	−0.0630110	−	0.998013i	$-0.520070\pi$
$41$	−0.806935	−0.126022	−0.0630110	+	0.998013i	$0.520070\pi$
$42$	−3.34551	−0.516224
$43$	12.0789	1.84202	0.921011	−	0.389537i	$-0.127365\pi$
$43$	12.0789	1.84202	0.921011	+	0.389537i	$0.127365\pi$
$44$	−3.90055	−0.588029
$45$	3.59322	0.535646
$46$	−5.58722	−0.823790
$47$	−4.08803	−0.596301	−0.298151	−	0.954519i	$-0.596370\pi$
$47$	−4.08803	−0.596301	−0.298151	+	0.954519i	$0.596370\pi$
$48$	−1.00000	−0.144338
$49$	4.19247	0.598924
$50$	7.91124	1.11882
$51$	1.00000	0.140028
$52$	4.00699	0.555670
$53$	8.74497	1.20121	0.600607	−	0.799544i	$-0.294926\pi$
$53$	8.74497	1.20121	0.600607	+	0.799544i	$0.294926\pi$
$54$	−1.00000	−0.136083
$55$	−14.0155	−1.88985
$56$	3.34551	0.447063
$57$	3.67278	0.486472
$58$	2.22628	0.292325
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−3.59322	−0.463883
$61$	7.47207	0.956701	0.478350	−	0.878169i	$-0.341235\pi$
$61$	7.47207	0.956701	0.478350	+	0.878169i	$0.341235\pi$
$62$	0.830709	0.105500
$63$	3.34551	0.421495
$64$	1.00000	0.125000
$65$	14.3980	1.78585
$66$	3.90055	0.480124
$67$	7.50116	0.916413	0.458206	−	0.888846i	$-0.348492\pi$
$67$	7.50116	0.916413	0.458206	+	0.888846i	$0.348492\pi$
$68$	−1.00000	−0.121268
$69$	5.58722	0.672622
$70$	12.0212	1.43680
$71$	3.47662	0.412598	0.206299	−	0.978489i	$-0.433858\pi$
$71$	3.47662	0.412598	0.206299	+	0.978489i	$0.433858\pi$
$72$	1.00000	0.117851
$73$	−0.169296	−0.0198146	−0.00990732	−	0.999951i	$-0.503154\pi$
$73$	−0.169296	−0.0198146	−0.00990732	+	0.999951i	$0.503154\pi$
$74$	4.39474	0.510878
$75$	−7.91124	−0.913511
$76$	−3.67278	−0.421297
$77$	−13.0493	−1.48711
$78$	−4.00699	−0.453703
$79$	10.9721	1.23446	0.617230	−	0.786783i	$-0.288255\pi$
$79$	10.9721	1.23446	0.617230	+	0.786783i	$0.288255\pi$
$80$	3.59322	0.401734
$81$	1.00000	0.111111
$82$	−0.806935	−0.0891110
$83$	−16.4673	−1.80752	−0.903761	−	0.428037i	$-0.859205\pi$
$83$	−16.4673	−1.80752	−0.903761	+	0.428037i	$0.859205\pi$
$84$	−3.34551	−0.365026
$85$	−3.59322	−0.389740
$86$	12.0789	1.30251
$87$	−2.22628	−0.238683
$88$	−3.90055	−0.415800
$89$	12.1589	1.28884	0.644421	−	0.764671i	$-0.277099\pi$
$89$	12.1589	1.28884	0.644421	+	0.764671i	$0.277099\pi$
$90$	3.59322	0.378759
$91$	13.4055	1.40527
$92$	−5.58722	−0.582507
$93$	−0.830709	−0.0861405
$94$	−4.08803	−0.421649
$95$	−13.1971	−1.35400
$96$	−1.00000	−0.102062
$97$	17.7603	1.80329	0.901643	−	0.432482i	$-0.142362\pi$
$97$	17.7603	1.80329	0.901643	+	0.432482i	$0.142362\pi$
$98$	4.19247	0.423503
$99$	−3.90055	−0.392020
$100$	7.91124	0.791124
$101$	−12.6201	−1.25575	−0.627876	−	0.778314i	$-0.716075\pi$
$101$	−12.6201	−1.25575	−0.627876	+	0.778314i	$0.716075\pi$
$102$	1.00000	0.0990148
$103$	−6.74912	−0.665010	−0.332505	−	0.943101i	$-0.607894\pi$
$103$	−6.74912	−0.665010	−0.332505	+	0.943101i	$0.607894\pi$
$104$	4.00699	0.392918
$105$	−12.0212	−1.17315
$106$	8.74497	0.849386
$107$	4.77758	0.461866	0.230933	−	0.972970i	$-0.425822\pi$
$107$	4.77758	0.461866	0.230933	+	0.972970i	$0.425822\pi$
$108$	−1.00000	−0.0962250
$109$	−2.76691	−0.265022	−0.132511	−	0.991182i	$-0.542304\pi$
$109$	−2.76691	−0.265022	−0.132511	+	0.991182i	$0.542304\pi$
$110$	−14.0155	−1.33633
$111$	−4.39474	−0.417130
$112$	3.34551	0.316121
$113$	12.8922	1.21280	0.606400	−	0.795160i	$-0.292613\pi$
$113$	12.8922	1.21280	0.606400	+	0.795160i	$0.292613\pi$
$114$	3.67278	0.343987
$115$	−20.0761	−1.87211
$116$	2.22628	0.206705
$117$	4.00699	0.370447
$118$	−1.00000	−0.0920575
$119$	−3.34551	−0.306683
$120$	−3.59322	−0.328015
$121$	4.21426	0.383114
$122$	7.47207	0.676489
$123$	0.806935	0.0727589
$124$	0.830709	0.0745998
$125$	10.4607	0.935635
$126$	3.34551	0.298042
$127$	9.70989	0.861614	0.430807	−	0.902444i	$-0.358229\pi$
$127$	9.70989	0.861614	0.430807	+	0.902444i	$0.358229\pi$
$128$	1.00000	0.0883883
$129$	−12.0789	−1.06349
$130$	14.3980	1.26279
$131$	13.0873	1.14344	0.571722	−	0.820447i	$-0.306276\pi$
$131$	13.0873	1.14344	0.571722	+	0.820447i	$0.306276\pi$
$132$	3.90055	0.339499
$133$	−12.2873	−1.06545
$134$	7.50116	0.648002
$135$	−3.59322	−0.309255
$136$	−1.00000	−0.0857493
$137$	−16.5772	−1.41628	−0.708142	−	0.706070i	$-0.750467\pi$
$137$	−16.5772	−1.41628	−0.708142	+	0.706070i	$0.750467\pi$
$138$	5.58722	0.475615
$139$	−2.86728	−0.243199	−0.121600	−	0.992579i	$-0.538802\pi$
$139$	−2.86728	−0.243199	−0.121600	+	0.992579i	$0.538802\pi$
$140$	12.0212	1.01597
$141$	4.08803	0.344275
$142$	3.47662	0.291751
$143$	−15.6295	−1.30700
$144$	1.00000	0.0833333
$145$	7.99953	0.664325
$146$	−0.169296	−0.0140111
$147$	−4.19247	−0.345789
$148$	4.39474	0.361245
$149$	13.5395	1.10920	0.554599	−	0.832118i	$-0.312872\pi$
$149$	13.5395	1.10920	0.554599	+	0.832118i	$0.312872\pi$
$150$	−7.91124	−0.645950
$151$	−10.1936	−0.829547	−0.414773	−	0.909925i	$-0.636139\pi$
$151$	−10.1936	−0.829547	−0.414773	+	0.909925i	$0.636139\pi$
$152$	−3.67278	−0.297902
$153$	−1.00000	−0.0808452
$154$	−13.0493	−1.05155
$155$	2.98492	0.239755
$156$	−4.00699	−0.320816
$157$	−11.4533	−0.914074	−0.457037	−	0.889448i	$-0.651089\pi$
$157$	−11.4533	−0.914074	−0.457037	+	0.889448i	$0.651089\pi$
$158$	10.9721	0.872894
$159$	−8.74497	−0.693521
$160$	3.59322	0.284069
$161$	−18.6921	−1.47314
$162$	1.00000	0.0785674
$163$	0.322411	0.0252532	0.0126266	−	0.999920i	$-0.495981\pi$
$163$	0.322411	0.0252532	0.0126266	+	0.999920i	$0.495981\pi$
$164$	−0.806935	−0.0630110
$165$	14.0155	1.09111
$166$	−16.4673	−1.27811
$167$	−8.62367	−0.667319	−0.333660	−	0.942694i	$-0.608284\pi$
$167$	−8.62367	−0.667319	−0.333660	+	0.942694i	$0.608284\pi$
$168$	−3.34551	−0.258112
$169$	3.05599	0.235076
$170$	−3.59322	−0.275587
$171$	−3.67278	−0.280865
$172$	12.0789	0.921011
$173$	−21.0431	−1.59988	−0.799940	−	0.600080i	$-0.795135\pi$
$173$	−21.0431	−1.59988	−0.799940	+	0.600080i	$0.795135\pi$
$174$	−2.22628	−0.168774
$175$	26.4672	2.00073
$176$	−3.90055	−0.294015
$177$	1.00000	0.0751646
$178$	12.1589	0.911348
$179$	−12.5182	−0.935652	−0.467826	−	0.883821i	$-0.654963\pi$
$179$	−12.5182	−0.935652	−0.467826	+	0.883821i	$0.654963\pi$
$180$	3.59322	0.267823
$181$	−1.70669	−0.126857	−0.0634287	−	0.997986i	$-0.520204\pi$
$181$	−1.70669	−0.126857	−0.0634287	+	0.997986i	$0.520204\pi$
$182$	13.4055	0.993678
$183$	−7.47207	−0.552351
$184$	−5.58722	−0.411895
$185$	15.7913	1.16100
$186$	−0.830709	−0.0609105
$187$	3.90055	0.285236
$188$	−4.08803	−0.298151
$189$	−3.34551	−0.243350
$190$	−13.1971	−0.957419
$191$	−15.1416	−1.09561	−0.547806	−	0.836606i	$-0.684537\pi$
$191$	−15.1416	−1.09561	−0.547806	+	0.836606i	$0.684537\pi$
$192$	−1.00000	−0.0721688
$193$	−1.89570	−0.136455	−0.0682277	−	0.997670i	$-0.521734\pi$
$193$	−1.89570	−0.136455	−0.0682277	+	0.997670i	$0.521734\pi$
$194$	17.7603	1.27512
$195$	−14.3980	−1.03106
$196$	4.19247	0.299462
$197$	−22.4461	−1.59922	−0.799611	−	0.600519i	$-0.794961\pi$
$197$	−22.4461	−1.59922	−0.799611	+	0.600519i	$0.794961\pi$
$198$	−3.90055	−0.277200
$199$	−9.87304	−0.699881	−0.349941	−	0.936772i	$-0.613798\pi$
$199$	−9.87304	−0.699881	−0.349941	+	0.936772i	$0.613798\pi$
$200$	7.91124	0.559409
$201$	−7.50116	−0.529091
$202$	−12.6201	−0.887950
$203$	7.44807	0.522752
$204$	1.00000	0.0700140
$205$	−2.89949	−0.202510
$206$	−6.74912	−0.470233
$207$	−5.58722	−0.388338
$208$	4.00699	0.277835
$209$	14.3258	0.990940
$210$	−12.0212	−0.829540
$211$	−24.9099	−1.71487	−0.857436	−	0.514591i	$-0.827944\pi$
$211$	−24.9099	−1.71487	−0.857436	+	0.514591i	$0.827944\pi$
$212$	8.74497	0.600607
$213$	−3.47662	−0.238214
$214$	4.77758	0.326589
$215$	43.4023	2.96001
$216$	−1.00000	−0.0680414
$217$	2.77915	0.188661
$218$	−2.76691	−0.187399
$219$	0.169296	0.0114400
$220$	−14.0155	−0.944926
$221$	−4.00699	−0.269539
$222$	−4.39474	−0.294956
$223$	8.77122	0.587364	0.293682	−	0.955903i	$-0.405119\pi$
$223$	8.77122	0.587364	0.293682	+	0.955903i	$0.405119\pi$
$224$	3.34551	0.223532
$225$	7.91124	0.527416
$226$	12.8922	0.857578
$227$	−13.3195	−0.884046	−0.442023	−	0.897004i	$-0.645739\pi$
$227$	−13.3195	−0.884046	−0.442023	+	0.897004i	$0.645739\pi$
$228$	3.67278	0.243236
$229$	−7.01266	−0.463410	−0.231705	−	0.972786i	$-0.574430\pi$
$229$	−7.01266	−0.463410	−0.231705	+	0.972786i	$0.574430\pi$
$230$	−20.0761	−1.32378
$231$	13.0493	0.858583
$232$	2.22628	0.146163
$233$	20.0934	1.31637	0.658183	−	0.752858i	$-0.271325\pi$
$233$	20.0934	1.31637	0.658183	+	0.752858i	$0.271325\pi$
$234$	4.00699	0.261945
$235$	−14.6892	−0.958218
$236$	−1.00000	−0.0650945
$237$	−10.9721	−0.712715
$238$	−3.34551	−0.216858
$239$	6.63815	0.429386	0.214693	−	0.976682i	$-0.431125\pi$
$239$	6.63815	0.429386	0.214693	+	0.976682i	$0.431125\pi$
$240$	−3.59322	−0.231941
$241$	4.62233	0.297750	0.148875	−	0.988856i	$-0.452435\pi$
$241$	4.62233	0.297750	0.148875	+	0.988856i	$0.452435\pi$
$242$	4.21426	0.270903
$243$	−1.00000	−0.0641500
$244$	7.47207	0.478350
$245$	15.0645	0.962433
$246$	0.806935	0.0514483
$247$	−14.7168	−0.936408
$248$	0.830709	0.0527501
$249$	16.4673	1.04357
$250$	10.4607	0.661594
$251$	7.78823	0.491589	0.245794	−	0.969322i	$-0.420951\pi$
$251$	7.78823	0.491589	0.245794	+	0.969322i	$0.420951\pi$
$252$	3.34551	0.210748
$253$	21.7932	1.37013
$254$	9.70989	0.609253
$255$	3.59322	0.225016
$256$	1.00000	0.0625000
$257$	−9.34361	−0.582838	−0.291419	−	0.956595i	$-0.594127\pi$
$257$	−9.34361	−0.582838	−0.291419	+	0.956595i	$0.594127\pi$
$258$	−12.0789	−0.752002
$259$	14.7027	0.913579
$260$	14.3980	0.892927
$261$	2.22628	0.137804
$262$	13.0873	0.808537
$263$	14.6933	0.906029	0.453014	−	0.891503i	$-0.350349\pi$
$263$	14.6933	0.906029	0.453014	+	0.891503i	$0.350349\pi$
$264$	3.90055	0.240062
$265$	31.4226	1.93028
$266$	−12.2873	−0.753385
$267$	−12.1589	−0.744113
$268$	7.50116	0.458206
$269$	12.1534	0.741008	0.370504	−	0.928831i	$-0.379185\pi$
$269$	12.1534	0.741008	0.370504	+	0.928831i	$0.379185\pi$
$270$	−3.59322	−0.218676
$271$	−4.78563	−0.290706	−0.145353	−	0.989380i	$-0.546432\pi$
$271$	−4.78563	−0.290706	−0.145353	+	0.989380i	$0.546432\pi$
$272$	−1.00000	−0.0606339
$273$	−13.4055	−0.811335
$274$	−16.5772	−1.00146
$275$	−30.8581	−1.86082
$276$	5.58722	0.336311
$277$	−30.2425	−1.81709	−0.908547	−	0.417782i	$-0.862808\pi$
$277$	−30.2425	−1.81709	−0.908547	+	0.417782i	$0.862808\pi$
$278$	−2.86728	−0.171968
$279$	0.830709	0.0497332
$280$	12.0212	0.718402
$281$	23.1040	1.37827	0.689133	−	0.724635i	$-0.257991\pi$
$281$	23.1040	1.37827	0.689133	+	0.724635i	$0.257991\pi$
$282$	4.08803	0.243439
$283$	6.46915	0.384551	0.192275	−	0.981341i	$-0.438413\pi$
$283$	6.46915	0.384551	0.192275	+	0.981341i	$0.438413\pi$
$284$	3.47662	0.206299
$285$	13.1971	0.781729
$286$	−15.6295	−0.924189
$287$	−2.69961	−0.159353
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	7.99953	0.469749
$291$	−17.7603	−1.04113
$292$	−0.169296	−0.00990732
$293$	2.12098	0.123909	0.0619544	−	0.998079i	$-0.480267\pi$
$293$	2.12098	0.123909	0.0619544	+	0.998079i	$0.480267\pi$
$294$	−4.19247	−0.244510
$295$	−3.59322	−0.209205
$296$	4.39474	0.255439
$297$	3.90055	0.226333
$298$	13.5395	0.784321
$299$	−22.3879	−1.29473
$300$	−7.91124	−0.456755
$301$	40.4103	2.32921
$302$	−10.1936	−0.586578
$303$	12.6201	0.725008
$304$	−3.67278	−0.210648
$305$	26.8488	1.53736
$306$	−1.00000	−0.0571662
$307$	24.6580	1.40730	0.703652	−	0.710545i	$-0.251551\pi$
$307$	24.6580	1.40730	0.703652	+	0.710545i	$0.251551\pi$
$308$	−13.0493	−0.743555
$309$	6.74912	0.383944
$310$	2.98492	0.169532
$311$	6.05900	0.343574	0.171787	−	0.985134i	$-0.445046\pi$
$311$	6.05900	0.343574	0.171787	+	0.985134i	$0.445046\pi$
$312$	−4.00699	−0.226851
$313$	12.2293	0.691241	0.345621	−	0.938374i	$-0.387668\pi$
$313$	12.2293	0.691241	0.345621	+	0.938374i	$0.387668\pi$
$314$	−11.4533	−0.646348
$315$	12.0212	0.677316
$316$	10.9721	0.617230
$317$	−29.3613	−1.64910	−0.824549	−	0.565791i	$-0.808571\pi$
$317$	−29.3613	−1.64910	−0.824549	+	0.565791i	$0.808571\pi$
$318$	−8.74497	−0.490393
$319$	−8.68372	−0.486195
$320$	3.59322	0.200867
$321$	−4.77758	−0.266659
$322$	−18.6921	−1.04167
$323$	3.67278	0.204359
$324$	1.00000	0.0555556
$325$	31.7003	1.75841
$326$	0.322411	0.0178567
$327$	2.76691	0.153010
$328$	−0.806935	−0.0445555
$329$	−13.6766	−0.754014
$330$	14.0155	0.771529
$331$	24.1071	1.32505	0.662523	−	0.749042i	$-0.269486\pi$
$331$	24.1071	1.32505	0.662523	+	0.749042i	$0.269486\pi$
$332$	−16.4673	−0.903761
$333$	4.39474	0.240830
$334$	−8.62367	−0.471866
$335$	26.9533	1.47262
$336$	−3.34551	−0.182513
$337$	−5.36567	−0.292287	−0.146143	−	0.989263i	$-0.546686\pi$
$337$	−5.36567	−0.292287	−0.146143	+	0.989263i	$0.546686\pi$
$338$	3.05599	0.166224
$339$	−12.8922	−0.700210
$340$	−3.59322	−0.194870
$341$	−3.24022	−0.175468
$342$	−3.67278	−0.198601
$343$	−9.39264	−0.507155
$344$	12.0789	0.651253
$345$	20.0761	1.08086
$346$	−21.0431	−1.13129
$347$	6.89962	0.370391	0.185195	−	0.982702i	$-0.440708\pi$
$347$	6.89962	0.370391	0.185195	+	0.982702i	$0.440708\pi$
$348$	−2.22628	−0.119341
$349$	1.99380	0.106726	0.0533628	−	0.998575i	$-0.483006\pi$
$349$	1.99380	0.106726	0.0533628	+	0.998575i	$0.483006\pi$
$350$	26.4672	1.41473
$351$	−4.00699	−0.213877
$352$	−3.90055	−0.207900
$353$	12.3308	0.656300	0.328150	−	0.944626i	$-0.393575\pi$
$353$	12.3308	0.656300	0.328150	+	0.944626i	$0.393575\pi$
$354$	1.00000	0.0531494
$355$	12.4922	0.663020
$356$	12.1589	0.644421
$357$	3.34551	0.177063
$358$	−12.5182	−0.661606
$359$	−27.2027	−1.43570	−0.717852	−	0.696196i	$-0.754874\pi$
$359$	−27.2027	−1.43570	−0.717852	+	0.696196i	$0.754874\pi$
$360$	3.59322	0.189379
$361$	−5.51068	−0.290036
$362$	−1.70669	−0.0897017
$363$	−4.21426	−0.221191
$364$	13.4055	0.702637
$365$	−0.608319	−0.0318409
$366$	−7.47207	−0.390571
$367$	−20.4147	−1.06564	−0.532818	−	0.846230i	$-0.678867\pi$
$367$	−20.4147	−1.06564	−0.532818	+	0.846230i	$0.678867\pi$
$368$	−5.58722	−0.291254
$369$	−0.806935	−0.0420073
$370$	15.7913	0.820949
$371$	29.2564	1.51892
$372$	−0.830709	−0.0430702
$373$	−9.95331	−0.515363	−0.257682	−	0.966230i	$-0.582959\pi$
$373$	−9.95331	−0.515363	−0.257682	+	0.966230i	$0.582959\pi$
$374$	3.90055	0.201692
$375$	−10.4607	−0.540189
$376$	−4.08803	−0.210824
$377$	8.92070	0.459440
$378$	−3.34551	−0.172075
$379$	−12.5156	−0.642884	−0.321442	−	0.946929i	$-0.604167\pi$
$379$	−12.5156	−0.642884	−0.321442	+	0.946929i	$0.604167\pi$
$380$	−13.1971	−0.676998
$381$	−9.70989	−0.497453
$382$	−15.1416	−0.774714
$383$	16.1436	0.824899	0.412449	−	0.910981i	$-0.364673\pi$
$383$	16.1436	0.824899	0.412449	+	0.910981i	$0.364673\pi$
$384$	−1.00000	−0.0510310
$385$	−46.8891	−2.38969
$386$	−1.89570	−0.0964885
$387$	12.0789	0.614007
$388$	17.7603	0.901643
$389$	13.8274	0.701075	0.350537	−	0.936549i	$-0.385999\pi$
$389$	13.8274	0.701075	0.350537	+	0.936549i	$0.385999\pi$
$390$	−14.3980	−0.729071
$391$	5.58722	0.282558
$392$	4.19247	0.211752
$393$	−13.0873	−0.660168
$394$	−22.4461	−1.13082
$395$	39.4252	1.98370
$396$	−3.90055	−0.196010
$397$	−22.7156	−1.14006	−0.570032	−	0.821622i	$-0.693069\pi$
$397$	−22.7156	−1.14006	−0.570032	+	0.821622i	$0.693069\pi$
$398$	−9.87304	−0.494891
$399$	12.2873	0.615136
$400$	7.91124	0.395562
$401$	−2.48748	−0.124219	−0.0621094	−	0.998069i	$-0.519783\pi$
$401$	−2.48748	−0.124219	−0.0621094	+	0.998069i	$0.519783\pi$
$402$	−7.50116	−0.374124
$403$	3.32864	0.165812
$404$	−12.6201	−0.627876
$405$	3.59322	0.178549
$406$	7.44807	0.369641
$407$	−17.1419	−0.849691
$408$	1.00000	0.0495074
$409$	−7.76514	−0.383961	−0.191981	−	0.981399i	$-0.561491\pi$
$409$	−7.76514	−0.383961	−0.191981	+	0.981399i	$0.561491\pi$
$410$	−2.89949	−0.143196
$411$	16.5772	0.817693
$412$	−6.74912	−0.332505
$413$	−3.34551	−0.164622
$414$	−5.58722	−0.274597
$415$	−59.1707	−2.90458
$416$	4.00699	0.196459
$417$	2.86728	0.140411
$418$	14.3258	0.700700
$419$	4.81906	0.235427	0.117713	−	0.993048i	$-0.462444\pi$
$419$	4.81906	0.235427	0.117713	+	0.993048i	$0.462444\pi$
$420$	−12.0212	−0.586573
$421$	−9.81170	−0.478193	−0.239096	−	0.970996i	$-0.576851\pi$
$421$	−9.81170	−0.478193	−0.239096	+	0.970996i	$0.576851\pi$
$422$	−24.9099	−1.21260
$423$	−4.08803	−0.198767
$424$	8.74497	0.424693
$425$	−7.91124	−0.383751
$426$	−3.47662	−0.168443
$427$	24.9979	1.20973
$428$	4.77758	0.230933
$429$	15.6295	0.754597
$430$	43.4023	2.09305
$431$	40.3904	1.94554	0.972770	−	0.231774i	$-0.0744530\pi$
$431$	40.3904	1.94554	0.972770	+	0.231774i	$0.0744530\pi$
$432$	−1.00000	−0.0481125
$433$	−33.3421	−1.60232	−0.801160	−	0.598450i	$-0.795783\pi$
$433$	−33.3421	−1.60232	−0.801160	+	0.598450i	$0.795783\pi$
$434$	2.77915	0.133403
$435$	−7.99953	−0.383548
$436$	−2.76691	−0.132511
$437$	20.5206	0.981634
$438$	0.169296	0.00808929
$439$	13.4335	0.641144	0.320572	−	0.947224i	$-0.396125\pi$
$439$	13.4335	0.641144	0.320572	+	0.947224i	$0.396125\pi$
$440$	−14.0155	−0.668164
$441$	4.19247	0.199641
$442$	−4.00699	−0.190593
$443$	−33.6679	−1.59961	−0.799804	−	0.600261i	$-0.795063\pi$
$443$	−33.6679	−1.59961	−0.799804	+	0.600261i	$0.795063\pi$
$444$	−4.39474	−0.208565
$445$	43.6896	2.07109
$446$	8.77122	0.415329
$447$	−13.5395	−0.640396
$448$	3.34551	0.158061
$449$	36.2186	1.70926	0.854631	−	0.519236i	$-0.173783\pi$
$449$	36.2186	1.70926	0.854631	+	0.519236i	$0.173783\pi$
$450$	7.91124	0.372939
$451$	3.14749	0.148209
$452$	12.8922	0.606400
$453$	10.1936	0.478939
$454$	−13.3195	−0.625115
$455$	48.1687	2.25819
$456$	3.67278	0.171994
$457$	−3.55382	−0.166241	−0.0831203	−	0.996540i	$-0.526489\pi$
$457$	−3.55382	−0.166241	−0.0831203	+	0.996540i	$0.526489\pi$
$458$	−7.01266	−0.327680
$459$	1.00000	0.0466760
$460$	−20.0761	−0.936053
$461$	34.9053	1.62570	0.812851	−	0.582471i	$-0.197914\pi$
$461$	34.9053	1.62570	0.812851	+	0.582471i	$0.197914\pi$
$462$	13.0493	0.607110
$463$	−24.2262	−1.12589	−0.562943	−	0.826496i	$-0.690331\pi$
$463$	−24.2262	−1.12589	−0.562943	+	0.826496i	$0.690331\pi$
$464$	2.22628	0.103353
$465$	−2.98492	−0.138422
$466$	20.0934	0.930811
$467$	−27.7161	−1.28255	−0.641275	−	0.767311i	$-0.721594\pi$
$467$	−27.7161	−1.28255	−0.641275	+	0.767311i	$0.721594\pi$
$468$	4.00699	0.185223
$469$	25.0952	1.15879
$470$	−14.6892	−0.677563
$471$	11.4533	0.527741
$472$	−1.00000	−0.0460287
$473$	−47.1145	−2.16633
$474$	−10.9721	−0.503966
$475$	−29.0562	−1.33319
$476$	−3.34551	−0.153341
$477$	8.74497	0.400405
$478$	6.63815	0.303622
$479$	−38.4860	−1.75847	−0.879234	−	0.476390i	$-0.841945\pi$
$479$	−38.4860	−1.75847	−0.879234	+	0.476390i	$0.841945\pi$
$480$	−3.59322	−0.164007
$481$	17.6097	0.802933
$482$	4.62233	0.210541
$483$	18.6921	0.850520
$484$	4.21426	0.191557
$485$	63.8167	2.89777
$486$	−1.00000	−0.0453609
$487$	8.78340	0.398014	0.199007	−	0.979998i	$-0.436228\pi$
$487$	8.78340	0.398014	0.199007	+	0.979998i	$0.436228\pi$
$488$	7.47207	0.338245
$489$	−0.322411	−0.0145799
$490$	15.0645	0.680543
$491$	7.15524	0.322912	0.161456	−	0.986880i	$-0.448381\pi$
$491$	7.15524	0.322912	0.161456	+	0.986880i	$0.448381\pi$
$492$	0.806935	0.0363794
$493$	−2.22628	−0.100267
$494$	−14.7168	−0.662140
$495$	−14.0155	−0.629951
$496$	0.830709	0.0372999
$497$	11.6311	0.521725
$498$	16.4673	0.737918
$499$	−19.6359	−0.879026	−0.439513	−	0.898236i	$-0.644849\pi$
$499$	−19.6359	−0.879026	−0.439513	+	0.898236i	$0.644849\pi$
$500$	10.4607	0.467817
$501$	8.62367	0.385277
$502$	7.78823	0.347606
$503$	11.4982	0.512681	0.256340	−	0.966587i	$-0.417483\pi$
$503$	11.4982	0.512681	0.256340	+	0.966587i	$0.417483\pi$
$504$	3.34551	0.149021
$505$	−45.3470	−2.01791
$506$	21.7932	0.968825
$507$	−3.05599	−0.135721
$508$	9.70989	0.430807
$509$	−5.71551	−0.253335	−0.126668	−	0.991945i	$-0.540428\pi$
$509$	−5.71551	−0.253335	−0.126668	+	0.991945i	$0.540428\pi$
$510$	3.59322	0.159110
$511$	−0.566384	−0.0250553
$512$	1.00000	0.0441942
$513$	3.67278	0.162157
$514$	−9.34361	−0.412129
$515$	−24.2511	−1.06863
$516$	−12.0789	−0.531746
$517$	15.9456	0.701285
$518$	14.7027	0.645998
$519$	21.0431	0.923691
$520$	14.3980	0.631394
$521$	−18.9096	−0.828443	−0.414221	−	0.910176i	$-0.635946\pi$
$521$	−18.9096	−0.828443	−0.414221	+	0.910176i	$0.635946\pi$
$522$	2.22628	0.0974418
$523$	−32.4221	−1.41772	−0.708860	−	0.705349i	$-0.750790\pi$
$523$	−32.4221	−1.41772	−0.708860	+	0.705349i	$0.750790\pi$
$524$	13.0873	0.571722
$525$	−26.4672	−1.15512
$526$	14.6933	0.640659
$527$	−0.830709	−0.0361862
$528$	3.90055	0.169749
$529$	8.21698	0.357260
$530$	31.4226	1.36491
$531$	−1.00000	−0.0433963
$532$	−12.2873	−0.532724
$533$	−3.23338	−0.140053
$534$	−12.1589	−0.526167
$535$	17.1669	0.742190
$536$	7.50116	0.324001
$537$	12.5182	0.540199
$538$	12.1534	0.523972
$539$	−16.3529	−0.704370
$540$	−3.59322	−0.154628
$541$	−40.5496	−1.74336	−0.871682	−	0.490072i	$-0.836970\pi$
$541$	−40.5496	−1.74336	−0.871682	+	0.490072i	$0.836970\pi$
$542$	−4.78563	−0.205560
$543$	1.70669	0.0732412
$544$	−1.00000	−0.0428746
$545$	−9.94211	−0.425873
$546$	−13.4055	−0.573700
$547$	4.45896	0.190651	0.0953257	−	0.995446i	$-0.469611\pi$
$547$	4.45896	0.190651	0.0953257	+	0.995446i	$0.469611\pi$
$548$	−16.5772	−0.708142
$549$	7.47207	0.318900
$550$	−30.8581	−1.31580
$551$	−8.17665	−0.348337
$552$	5.58722	0.237808
$553$	36.7074	1.56096
$554$	−30.2425	−1.28488
$555$	−15.7913	−0.670302
$556$	−2.86728	−0.121600
$557$	−16.0301	−0.679216	−0.339608	−	0.940567i	$-0.610294\pi$
$557$	−16.0301	−0.679216	−0.339608	+	0.940567i	$0.610294\pi$
$558$	0.830709	0.0351667
$559$	48.4002	2.04711
$560$	12.0212	0.507987
$561$	−3.90055	−0.164681
$562$	23.1040	0.974582
$563$	−20.1064	−0.847384	−0.423692	−	0.905806i	$-0.639266\pi$
$563$	−20.1064	−0.847384	−0.423692	+	0.905806i	$0.639266\pi$
$564$	4.08803	0.172137
$565$	46.3246	1.94889
$566$	6.46915	0.271918
$567$	3.34551	0.140498
$568$	3.47662	0.145876
$569$	−32.2801	−1.35325	−0.676627	−	0.736326i	$-0.736559\pi$
$569$	−32.2801	−1.35325	−0.676627	+	0.736326i	$0.736559\pi$
$570$	13.1971	0.552766
$571$	16.1257	0.674840	0.337420	−	0.941354i	$-0.390446\pi$
$571$	16.1257	0.674840	0.337420	+	0.941354i	$0.390446\pi$
$572$	−15.6295	−0.653500
$573$	15.1416	0.632551
$574$	−2.69961	−0.112680
$575$	−44.2018	−1.84334
$576$	1.00000	0.0416667
$577$	−23.4609	−0.976688	−0.488344	−	0.872651i	$-0.662399\pi$
$577$	−23.4609	−0.976688	−0.488344	+	0.872651i	$0.662399\pi$
$578$	1.00000	0.0415945
$579$	1.89570	0.0787825
$580$	7.99953	0.332162
$581$	−55.0916	−2.28559
$582$	−17.7603	−0.736188
$583$	−34.1101	−1.41270
$584$	−0.169296	−0.00700553
$585$	14.3980	0.595284
$586$	2.12098	0.0876168
$587$	17.1609	0.708307	0.354154	−	0.935187i	$-0.384769\pi$
$587$	17.1609	0.708307	0.354154	+	0.935187i	$0.384769\pi$
$588$	−4.19247	−0.172894
$589$	−3.05101	−0.125715
$590$	−3.59322	−0.147931
$591$	22.4461	0.923311
$592$	4.39474	0.180623
$593$	−15.1402	−0.621731	−0.310866	−	0.950454i	$-0.600619\pi$
$593$	−15.1402	−0.621731	−0.310866	+	0.950454i	$0.600619\pi$
$594$	3.90055	0.160041
$595$	−12.0212	−0.492820
$596$	13.5395	0.554599
$597$	9.87304	0.404077
$598$	−22.3879	−0.915511
$599$	−20.9400	−0.855585	−0.427793	−	0.903877i	$-0.640709\pi$
$599$	−20.9400	−0.855585	−0.427793	+	0.903877i	$0.640709\pi$
$600$	−7.91124	−0.322975
$601$	−8.00463	−0.326516	−0.163258	−	0.986583i	$-0.552200\pi$
$601$	−8.00463	−0.326516	−0.163258	+	0.986583i	$0.552200\pi$
$602$	40.4103	1.64700
$603$	7.50116	0.305471
$604$	−10.1936	−0.414773
$605$	15.1427	0.615640
$606$	12.6201	0.512658
$607$	44.7868	1.81784	0.908919	−	0.416972i	$-0.136909\pi$
$607$	44.7868	1.81784	0.908919	+	0.416972i	$0.136909\pi$
$608$	−3.67278	−0.148951
$609$	−7.44807	−0.301811
$610$	26.8488	1.08708
$611$	−16.3807	−0.662693
$612$	−1.00000	−0.0404226
$613$	−27.8309	−1.12408	−0.562040	−	0.827110i	$-0.689983\pi$
$613$	−27.8309	−1.12408	−0.562040	+	0.827110i	$0.689983\pi$
$614$	24.6580	0.995115
$615$	2.89949	0.116919
$616$	−13.0493	−0.525773
$617$	27.6682	1.11388	0.556940	−	0.830552i	$-0.311975\pi$
$617$	27.6682	1.11388	0.556940	+	0.830552i	$0.311975\pi$
$618$	6.74912	0.271489
$619$	25.4737	1.02387	0.511937	−	0.859023i	$-0.328928\pi$
$619$	25.4737	1.02387	0.511937	+	0.859023i	$0.328928\pi$
$620$	2.98492	0.119877
$621$	5.58722	0.224207
$622$	6.05900	0.242944
$623$	40.6778	1.62972
$624$	−4.00699	−0.160408
$625$	−1.96852	−0.0787410
$626$	12.2293	0.488781
$627$	−14.3258	−0.572119
$628$	−11.4533	−0.457037
$629$	−4.39474	−0.175230
$630$	12.0212	0.478935
$631$	1.75059	0.0696899	0.0348450	−	0.999393i	$-0.488906\pi$
$631$	1.75059	0.0696899	0.0348450	+	0.999393i	$0.488906\pi$
$632$	10.9721	0.436447
$633$	24.9099	0.990081
$634$	−29.3613	−1.16609
$635$	34.8898	1.38456
$636$	−8.74497	−0.346761
$637$	16.7992	0.665608
$638$	−8.68372	−0.343792
$639$	3.47662	0.137533
$640$	3.59322	0.142035
$641$	21.0640	0.831977	0.415989	−	0.909370i	$-0.363436\pi$
$641$	21.0640	0.831977	0.415989	+	0.909370i	$0.363436\pi$
$642$	−4.77758	−0.188556
$643$	41.2314	1.62601	0.813004	−	0.582258i	$-0.197831\pi$
$643$	41.2314	1.62601	0.813004	+	0.582258i	$0.197831\pi$
$644$	−18.6921	−0.736572
$645$	−43.4023	−1.70896
$646$	3.67278	0.144504
$647$	−17.0401	−0.669914	−0.334957	−	0.942233i	$-0.608722\pi$
$647$	−17.0401	−0.669914	−0.334957	+	0.942233i	$0.608722\pi$
$648$	1.00000	0.0392837
$649$	3.90055	0.153110
$650$	31.7003	1.24339
$651$	−2.77915	−0.108923
$652$	0.322411	0.0126266
$653$	−41.1955	−1.61211	−0.806053	−	0.591844i	$-0.798400\pi$
$653$	−41.1955	−1.61211	−0.806053	+	0.591844i	$0.798400\pi$
$654$	2.76691	0.108195
$655$	47.0256	1.83744
$656$	−0.806935	−0.0315055
$657$	−0.169296	−0.00660488
$658$	−13.6766	−0.533169
$659$	34.2014	1.33230	0.666149	−	0.745819i	$-0.267942\pi$
$659$	34.2014	1.33230	0.666149	+	0.745819i	$0.267942\pi$
$660$	14.0155	0.545553
$661$	27.2794	1.06104	0.530522	−	0.847671i	$-0.321996\pi$
$661$	27.2794	1.06104	0.530522	+	0.847671i	$0.321996\pi$
$662$	24.1071	0.936949
$663$	4.00699	0.155619
$664$	−16.4673	−0.639056
$665$	−44.1511	−1.71211
$666$	4.39474	0.170293
$667$	−12.4387	−0.481630
$668$	−8.62367	−0.333660
$669$	−8.77122	−0.339115
$670$	26.9533	1.04130
$671$	−29.1451	−1.12514
$672$	−3.34551	−0.129056
$673$	−10.7968	−0.416185	−0.208092	−	0.978109i	$-0.566725\pi$
$673$	−10.7968	−0.416185	−0.208092	+	0.978109i	$0.566725\pi$
$674$	−5.36567	−0.206678
$675$	−7.91124	−0.304504
$676$	3.05599	0.117538
$677$	26.5989	1.02228	0.511140	−	0.859498i	$-0.329224\pi$
$677$	26.5989	1.02228	0.511140	+	0.859498i	$0.329224\pi$
$678$	−12.8922	−0.495123
$679$	59.4173	2.28023
$680$	−3.59322	−0.137794
$681$	13.3195	0.510404
$682$	−3.24022	−0.124074
$683$	−24.2951	−0.929627	−0.464813	−	0.885409i	$-0.653879\pi$
$683$	−24.2951	−0.929627	−0.464813	+	0.885409i	$0.653879\pi$
$684$	−3.67278	−0.140432
$685$	−59.5655	−2.27588
$686$	−9.39264	−0.358613
$687$	7.01266	0.267550
$688$	12.0789	0.460505
$689$	35.0410	1.33496
$690$	20.0761	0.764284
$691$	−23.1125	−0.879241	−0.439620	−	0.898184i	$-0.644887\pi$
$691$	−23.1125	−0.879241	−0.439620	+	0.898184i	$0.644887\pi$
$692$	−21.0431	−0.799940
$693$	−13.0493	−0.495703
$694$	6.89962	0.261906
$695$	−10.3028	−0.390806
$696$	−2.22628	−0.0843871
$697$	0.806935	0.0305648
$698$	1.99380	0.0754664
$699$	−20.0934	−0.760004
$700$	26.4672	1.00036
$701$	31.5612	1.19205	0.596024	−	0.802966i	$-0.296746\pi$
$701$	31.5612	1.19205	0.596024	+	0.802966i	$0.296746\pi$
$702$	−4.00699	−0.151234
$703$	−16.1409	−0.608766
$704$	−3.90055	−0.147007
$705$	14.6892	0.553228
$706$	12.3308	0.464074
$707$	−42.2209	−1.58788
$708$	1.00000	0.0375823
$709$	−3.32313	−0.124803	−0.0624013	−	0.998051i	$-0.519876\pi$
$709$	−3.32313	−0.124803	−0.0624013	+	0.998051i	$0.519876\pi$
$710$	12.4922	0.468826
$711$	10.9721	0.411486
$712$	12.1589	0.455674
$713$	−4.64135	−0.173820
$714$	3.34551	0.125203
$715$	−56.1601	−2.10027
$716$	−12.5182	−0.467826
$717$	−6.63815	−0.247906
$718$	−27.2027	−1.01520
$719$	−37.3760	−1.39389	−0.696945	−	0.717124i	$-0.745458\pi$
$719$	−37.3760	−1.39389	−0.696945	+	0.717124i	$0.745458\pi$
$720$	3.59322	0.133911
$721$	−22.5793	−0.840896
$722$	−5.51068	−0.205086
$723$	−4.62233	−0.171906
$724$	−1.70669	−0.0634287
$725$	17.6127	0.654118
$726$	−4.21426	−0.156406
$727$	16.6385	0.617086	0.308543	−	0.951210i	$-0.400159\pi$
$727$	16.6385	0.617086	0.308543	+	0.951210i	$0.400159\pi$
$728$	13.4055	0.496839
$729$	1.00000	0.0370370
$730$	−0.608319	−0.0225149
$731$	−12.0789	−0.446756
$732$	−7.47207	−0.276176
$733$	42.5985	1.57341	0.786706	−	0.617328i	$-0.211785\pi$
$733$	42.5985	1.57341	0.786706	+	0.617328i	$0.211785\pi$
$734$	−20.4147	−0.753519
$735$	−15.0645	−0.555661
$736$	−5.58722	−0.205947
$737$	−29.2586	−1.07776
$738$	−0.806935	−0.0297037
$739$	4.42398	0.162739	0.0813694	−	0.996684i	$-0.474071\pi$
$739$	4.42398	0.162739	0.0813694	+	0.996684i	$0.474071\pi$
$740$	15.7913	0.580499
$741$	14.7168	0.540635
$742$	29.2564	1.07404
$743$	27.7275	1.01722	0.508612	−	0.860996i	$-0.330159\pi$
$743$	27.7275	1.01722	0.508612	+	0.860996i	$0.330159\pi$
$744$	−0.830709	−0.0304553
$745$	48.6504	1.78241
$746$	−9.95331	−0.364417
$747$	−16.4673	−0.602508
$748$	3.90055	0.142618
$749$	15.9835	0.584023
$750$	−10.4607	−0.381971
$751$	0.00849090	0.000309837 0	0.000154919	−	1.00000i	$-0.499951\pi$
$751$	0.00849090	0.000309837 0	0.000154919		1.00000i	$0.499951\pi$
$752$	−4.08803	−0.149075
$753$	−7.78823	−0.283819
$754$	8.92070	0.324873
$755$	−36.6280	−1.33303
$756$	−3.34551	−0.121675
$757$	52.6491	1.91356	0.956782	−	0.290805i	$-0.0939230\pi$
$757$	52.6491	1.91356	0.956782	+	0.290805i	$0.0939230\pi$
$758$	−12.5156	−0.454587
$759$	−21.7932	−0.791043
$760$	−13.1971	−0.478710
$761$	−43.5091	−1.57720	−0.788602	−	0.614903i	$-0.789195\pi$
$761$	−43.5091	−1.57720	−0.788602	+	0.614903i	$0.789195\pi$
$762$	−9.70989	−0.351752
$763$	−9.25673	−0.335116
$764$	−15.1416	−0.547806
$765$	−3.59322	−0.129913
$766$	16.1436	0.583291
$767$	−4.00699	−0.144684
$768$	−1.00000	−0.0360844
$769$	−31.2077	−1.12538	−0.562689	−	0.826669i	$-0.690233\pi$
$769$	−31.2077	−1.12538	−0.562689	+	0.826669i	$0.690233\pi$
$770$	−46.8891	−1.68977
$771$	9.34361	0.336502
$772$	−1.89570	−0.0682277
$773$	−19.7723	−0.711160	−0.355580	−	0.934646i	$-0.615717\pi$
$773$	−19.7723	−0.711160	−0.355580	+	0.934646i	$0.615717\pi$
$774$	12.0789	0.434169
$775$	6.57193	0.236071
$776$	17.7603	0.637558
$777$	−14.7027	−0.527455
$778$	13.8274	0.495735
$779$	2.96369	0.106185
$780$	−14.3980	−0.515531
$781$	−13.5607	−0.485240
$782$	5.58722	0.199798
$783$	−2.22628	−0.0795609
$784$	4.19247	0.149731
$785$	−41.1543	−1.46886
$786$	−13.0873	−0.466809
$787$	37.0131	1.31938	0.659688	−	0.751540i	$-0.270688\pi$
$787$	37.0131	1.31938	0.659688	+	0.751540i	$0.270688\pi$
$788$	−22.4461	−0.799611
$789$	−14.6933	−0.523096
$790$	39.4252	1.40269
$791$	43.1311	1.53357
$792$	−3.90055	−0.138600
$793$	29.9405	1.06322
$794$	−22.7156	−0.806147
$795$	−31.4226	−1.11444
$796$	−9.87304	−0.349941
$797$	−9.98915	−0.353834	−0.176917	−	0.984226i	$-0.556612\pi$
$797$	−9.98915	−0.353834	−0.176917	+	0.984226i	$0.556612\pi$
$798$	12.2873	0.434967
$799$	4.08803	0.144624
$800$	7.91124	0.279704
$801$	12.1589	0.429614
$802$	−2.48748	−0.0878360
$803$	0.660348	0.0233032
$804$	−7.50116	−0.264546
$805$	−67.1649	−2.36725
$806$	3.32864	0.117246
$807$	−12.1534	−0.427821
$808$	−12.6201	−0.443975
$809$	−24.1625	−0.849507	−0.424753	−	0.905309i	$-0.639639\pi$
$809$	−24.1625	−0.849507	−0.424753	+	0.905309i	$0.639639\pi$
$810$	3.59322	0.126253
$811$	24.4047	0.856963	0.428482	−	0.903550i	$-0.359049\pi$
$811$	24.4047	0.856963	0.428482	+	0.903550i	$0.359049\pi$
$812$	7.44807	0.261376
$813$	4.78563	0.167839
$814$	−17.1419	−0.600823
$815$	1.15849	0.0405803
$816$	1.00000	0.0350070
$817$	−44.3633	−1.55208
$818$	−7.76514	−0.271502
$819$	13.4055	0.468424
$820$	−2.89949	−0.101255
$821$	27.0811	0.945138	0.472569	−	0.881294i	$-0.343327\pi$
$821$	27.0811	0.945138	0.472569	+	0.881294i	$0.343327\pi$
$822$	16.5772	0.578196
$823$	−37.1458	−1.29482	−0.647411	−	0.762141i	$-0.724148\pi$
$823$	−37.1458	−1.29482	−0.647411	+	0.762141i	$0.724148\pi$
$824$	−6.74912	−0.235117
$825$	30.8581	1.07434
$826$	−3.34551	−0.116405
$827$	−16.0294	−0.557395	−0.278698	−	0.960379i	$-0.589903\pi$
$827$	−16.0294	−0.557395	−0.278698	+	0.960379i	$0.589903\pi$
$828$	−5.58722	−0.194169
$829$	−24.2359	−0.841748	−0.420874	−	0.907119i	$-0.638277\pi$
$829$	−24.2359	−0.841748	−0.420874	+	0.907119i	$0.638277\pi$
$830$	−59.1707	−2.05385
$831$	30.2425	1.04910
$832$	4.00699	0.138917
$833$	−4.19247	−0.145260
$834$	2.86728	0.0992857
$835$	−30.9867	−1.07234
$836$	14.3258	0.495470
$837$	−0.830709	−0.0287135
$838$	4.81906	0.166472
$839$	−28.5690	−0.986312	−0.493156	−	0.869941i	$-0.664157\pi$
$839$	−28.5690	−0.986312	−0.493156	+	0.869941i	$0.664157\pi$
$840$	−12.0212	−0.414770
$841$	−24.0437	−0.829092
$842$	−9.81170	−0.338133
$843$	−23.1040	−0.795742
$844$	−24.9099	−0.857436
$845$	10.9808	0.377752
$846$	−4.08803	−0.140550
$847$	14.0989	0.484442
$848$	8.74497	0.300303
$849$	−6.46915	−0.222020
$850$	−7.91124	−0.271353
$851$	−24.5544	−0.841712
$852$	−3.47662	−0.119107
$853$	−18.3990	−0.629970	−0.314985	−	0.949097i	$-0.601999\pi$
$853$	−18.3990	−0.629970	−0.314985	+	0.949097i	$0.601999\pi$
$854$	24.9979	0.855411
$855$	−13.1971	−0.451332
$856$	4.77758	0.163294
$857$	4.25048	0.145194	0.0725969	−	0.997361i	$-0.476871\pi$
$857$	4.25048	0.145194	0.0725969	+	0.997361i	$0.476871\pi$
$858$	15.6295	0.533581
$859$	16.0374	0.547188	0.273594	−	0.961845i	$-0.411788\pi$
$859$	16.0374	0.547188	0.273594	+	0.961845i	$0.411788\pi$
$860$	43.4023	1.48001
$861$	2.69961	0.0920025
$862$	40.3904	1.37570
$863$	−50.8731	−1.73174	−0.865870	−	0.500269i	$-0.833235\pi$
$863$	−50.8731	−1.73174	−0.865870	+	0.500269i	$0.833235\pi$
$864$	−1.00000	−0.0340207
$865$	−75.6126	−2.57091
$866$	−33.3421	−1.13301
$867$	−1.00000	−0.0339618
$868$	2.77915	0.0943304
$869$	−42.7972	−1.45180
$870$	−7.99953	−0.271210
$871$	30.0571	1.01845
$872$	−2.76691	−0.0936993
$873$	17.7603	0.601095
$874$	20.5206	0.694120
$875$	34.9965	1.18310
$876$	0.169296	0.00571999
$877$	2.01922	0.0681843	0.0340921	−	0.999419i	$-0.489146\pi$
$877$	2.01922	0.0681843	0.0340921	+	0.999419i	$0.489146\pi$
$878$	13.4335	0.453357
$879$	−2.12098	−0.0715388
$880$	−14.0155	−0.472463
$881$	6.09656	0.205398	0.102699	−	0.994712i	$-0.467252\pi$
$881$	6.09656	0.205398	0.102699	+	0.994712i	$0.467252\pi$
$882$	4.19247	0.141168
$883$	38.5474	1.29722	0.648612	−	0.761119i	$-0.275350\pi$
$883$	38.5474	1.29722	0.648612	+	0.761119i	$0.275350\pi$
$884$	−4.00699	−0.134770
$885$	3.59322	0.120785
$886$	−33.6679	−1.13109
$887$	−55.9857	−1.87982	−0.939908	−	0.341427i	$-0.889090\pi$
$887$	−55.9857	−1.87982	−0.939908	+	0.341427i	$0.889090\pi$
$888$	−4.39474	−0.147478
$889$	32.4846	1.08950
$890$	43.6896	1.46448
$891$	−3.90055	−0.130673
$892$	8.77122	0.293682
$893$	15.0145	0.502440
$894$	−13.5395	−0.452828
$895$	−44.9805	−1.50353
$896$	3.34551	0.111766
$897$	22.3879	0.747511
$898$	36.2186	1.20863
$899$	1.84939	0.0616807
$900$	7.91124	0.263708
$901$	−8.74497	−0.291337
$902$	3.14749	0.104800
$903$	−40.4103	−1.34477
$904$	12.8922	0.428789
$905$	−6.13252	−0.203852
$906$	10.1936	0.338661
$907$	38.2958	1.27159	0.635796	−	0.771857i	$-0.280672\pi$
$907$	38.2958	1.27159	0.635796	+	0.771857i	$0.280672\pi$
$908$	−13.3195	−0.442023
$909$	−12.6201	−0.418584
$910$	48.1687	1.59678
$911$	20.6398	0.683826	0.341913	−	0.939732i	$-0.388925\pi$
$911$	20.6398	0.683826	0.341913	+	0.939732i	$0.388925\pi$
$912$	3.67278	0.121618
$913$	64.2315	2.12575
$914$	−3.55382	−0.117550
$915$	−26.8488	−0.887594
$916$	−7.01266	−0.231705
$917$	43.7838	1.44587
$918$	1.00000	0.0330049
$919$	39.0190	1.28712	0.643558	−	0.765397i	$-0.277457\pi$
$919$	39.0190	1.28712	0.643558	+	0.765397i	$0.277457\pi$
$920$	−20.0761	−0.661889
$921$	−24.6580	−0.812508
$922$	34.9053	1.14955
$923$	13.9308	0.458537
$924$	13.0493	0.429292
$925$	34.7678	1.14316
$926$	−24.2262	−0.796122
$927$	−6.74912	−0.221670
$928$	2.22628	0.0730814
$929$	38.3425	1.25798	0.628988	−	0.777415i	$-0.283469\pi$
$929$	38.3425	1.25798	0.628988	+	0.777415i	$0.283469\pi$
$930$	−2.98492	−0.0978794
$931$	−15.3980	−0.504650
$932$	20.0934	0.658183
$933$	−6.05900	−0.198363
$934$	−27.7161	−0.906900
$935$	14.0155	0.458357
$936$	4.00699	0.130973
$937$	−26.2749	−0.858365	−0.429182	−	0.903218i	$-0.641198\pi$
$937$	−26.2749	−0.858365	−0.429182	+	0.903218i	$0.641198\pi$
$938$	25.0952	0.819389
$939$	−12.2293	−0.399088
$940$	−14.6892	−0.479109
$941$	3.13445	0.102180	0.0510900	−	0.998694i	$-0.483730\pi$
$941$	3.13445	0.102180	0.0510900	+	0.998694i	$0.483730\pi$
$942$	11.4533	0.373169
$943$	4.50852	0.146818
$944$	−1.00000	−0.0325472
$945$	−12.0212	−0.391049
$946$	−47.1145	−1.53182
$947$	39.0363	1.26851	0.634254	−	0.773125i	$-0.281307\pi$
$947$	39.0363	1.26851	0.634254	+	0.773125i	$0.281307\pi$
$948$	−10.9721	−0.356358
$949$	−0.678369	−0.0220208
$950$	−29.0562	−0.942709
$951$	29.3613	0.952107
$952$	−3.34551	−0.108429
$953$	20.0317	0.648890	0.324445	−	0.945905i	$-0.394823\pi$
$953$	20.0317	0.648890	0.324445	+	0.945905i	$0.394823\pi$
$954$	8.74497	0.283129
$955$	−54.4073	−1.76058
$956$	6.63815	0.214693
$957$	8.68372	0.280705
$958$	−38.4860	−1.24342
$959$	−55.4592	−1.79087
$960$	−3.59322	−0.115971
$961$	−30.3099	−0.977739
$962$	17.6097	0.567759
$963$	4.77758	0.153955
$964$	4.62233	0.148875
$965$	−6.81166	−0.219275
$966$	18.6921	0.601409
$967$	−32.9032	−1.05809	−0.529047	−	0.848592i	$-0.677451\pi$
$967$	−32.9032	−1.05809	−0.529047	+	0.848592i	$0.677451\pi$
$968$	4.21426	0.135451
$969$	−3.67278	−0.117987
$970$	63.8167	2.04903
$971$	−19.9725	−0.640949	−0.320475	−	0.947257i	$-0.603842\pi$
$971$	−19.9725	−0.640949	−0.320475	+	0.947257i	$0.603842\pi$
$972$	−1.00000	−0.0320750
$973$	−9.59252	−0.307522
$974$	8.78340	0.281438
$975$	−31.7003	−1.01522
$976$	7.47207	0.239175
$977$	−52.6206	−1.68348	−0.841740	−	0.539883i	$-0.818469\pi$
$977$	−52.6206	−1.68348	−0.841740	+	0.539883i	$0.818469\pi$
$978$	−0.322411	−0.0103096
$979$	−47.4264	−1.51575
$980$	15.0645	0.481217
$981$	−2.76691	−0.0883405
$982$	7.15524	0.228333
$983$	−23.9023	−0.762365	−0.381182	−	0.924500i	$-0.624483\pi$
$983$	−23.9023	−0.762365	−0.381182	+	0.924500i	$0.624483\pi$
$984$	0.806935	0.0257241
$985$	−80.6539	−2.56985
$986$	−2.22628	−0.0708993
$987$	13.6766	0.435330
$988$	−14.7168	−0.468204
$989$	−67.4877	−2.14598
$990$	−14.0155	−0.445443
$991$	15.5139	0.492816	0.246408	−	0.969166i	$-0.420750\pi$
$991$	15.5139	0.492816	0.246408	+	0.969166i	$0.420750\pi$
$992$	0.830709	0.0263750
$993$	−24.1071	−0.765016
$994$	11.6311	0.368915
$995$	−35.4760	−1.12467
$996$	16.4673	0.521787
$997$	53.3410	1.68933	0.844663	−	0.535299i	$-0.179801\pi$
$997$	53.3410	1.68933	0.844663	+	0.535299i	$0.179801\pi$
$998$	−19.6359	−0.621565
$999$	−4.39474	−0.139043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.10	✓	11	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.59322 q^{5} -1.00000 q^{6} +3.34551 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.59322 q^{5} -1.00000 q^{6} +3.34551 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.59322 q^{10} -3.90055 q^{11} -1.00000 q^{12} +4.00699 q^{13} +3.34551 q^{14} -3.59322 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.67278 q^{19} +3.59322 q^{20} -3.34551 q^{21} -3.90055 q^{22} -5.58722 q^{23} -1.00000 q^{24} +7.91124 q^{25} +4.00699 q^{26} -1.00000 q^{27} +3.34551 q^{28} +2.22628 q^{29} -3.59322 q^{30} +0.830709 q^{31} +1.00000 q^{32} +3.90055 q^{33} -1.00000 q^{34} +12.0212 q^{35} +1.00000 q^{36} +4.39474 q^{37} -3.67278 q^{38} -4.00699 q^{39} +3.59322 q^{40} -0.806935 q^{41} -3.34551 q^{42} +12.0789 q^{43} -3.90055 q^{44} +3.59322 q^{45} -5.58722 q^{46} -4.08803 q^{47} -1.00000 q^{48} +4.19247 q^{49} +7.91124 q^{50} +1.00000 q^{51} +4.00699 q^{52} +8.74497 q^{53} -1.00000 q^{54} -14.0155 q^{55} +3.34551 q^{56} +3.67278 q^{57} +2.22628 q^{58} -1.00000 q^{59} -3.59322 q^{60} +7.47207 q^{61} +0.830709 q^{62} +3.34551 q^{63} +1.00000 q^{64} +14.3980 q^{65} +3.90055 q^{66} +7.50116 q^{67} -1.00000 q^{68} +5.58722 q^{69} +12.0212 q^{70} +3.47662 q^{71} +1.00000 q^{72} -0.169296 q^{73} +4.39474 q^{74} -7.91124 q^{75} -3.67278 q^{76} -13.0493 q^{77} -4.00699 q^{78} +10.9721 q^{79} +3.59322 q^{80} +1.00000 q^{81} -0.806935 q^{82} -16.4673 q^{83} -3.34551 q^{84} -3.59322 q^{85} +12.0789 q^{86} -2.22628 q^{87} -3.90055 q^{88} +12.1589 q^{89} +3.59322 q^{90} +13.4055 q^{91} -5.58722 q^{92} -0.830709 q^{93} -4.08803 q^{94} -13.1971 q^{95} -1.00000 q^{96} +17.7603 q^{97} +4.19247 q^{98} -3.90055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

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