LMFDB - Embedded newform 4730.2.a.bd.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
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} - 3 x^{10} - 25 x^{9} + 72 x^{8} + 216 x^{7} - 572 x^{6} - 767 x^{5} + 1665 x^{4} + 993 x^{3} + \cdots + 64 $ x^11 - 3x^10 - 25x^9 + 72x^8 + 216x^7 - 572x^6 - 767x^5 + 1665x^4 + 993x^3 - 1256x^2 + 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.66316$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.66316 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.66316 q^{6} -1.80847 q^{7} +1.00000 q^{8} +4.09240 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.66316 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.66316 q^{6} -1.80847 q^{7} +1.00000 q^{8} +4.09240 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.66316 q^{12} -0.569541 q^{13} -1.80847 q^{14} +2.66316 q^{15} +1.00000 q^{16} +5.29897 q^{17} +4.09240 q^{18} -0.637886 q^{19} +1.00000 q^{20} -4.81624 q^{21} +1.00000 q^{22} +8.02367 q^{23} +2.66316 q^{24} +1.00000 q^{25} -0.569541 q^{26} +2.90924 q^{27} -1.80847 q^{28} -6.56288 q^{29} +2.66316 q^{30} +2.17150 q^{31} +1.00000 q^{32} +2.66316 q^{33} +5.29897 q^{34} -1.80847 q^{35} +4.09240 q^{36} +9.60661 q^{37} -0.637886 q^{38} -1.51678 q^{39} +1.00000 q^{40} -5.21481 q^{41} -4.81624 q^{42} -1.00000 q^{43} +1.00000 q^{44} +4.09240 q^{45} +8.02367 q^{46} -4.29609 q^{47} +2.66316 q^{48} -3.72943 q^{49} +1.00000 q^{50} +14.1120 q^{51} -0.569541 q^{52} -3.99842 q^{53} +2.90924 q^{54} +1.00000 q^{55} -1.80847 q^{56} -1.69879 q^{57} -6.56288 q^{58} +15.0589 q^{59} +2.66316 q^{60} +1.81477 q^{61} +2.17150 q^{62} -7.40100 q^{63} +1.00000 q^{64} -0.569541 q^{65} +2.66316 q^{66} -7.94237 q^{67} +5.29897 q^{68} +21.3683 q^{69} -1.80847 q^{70} +5.65378 q^{71} +4.09240 q^{72} -14.4414 q^{73} +9.60661 q^{74} +2.66316 q^{75} -0.637886 q^{76} -1.80847 q^{77} -1.51678 q^{78} +8.69071 q^{79} +1.00000 q^{80} -4.52944 q^{81} -5.21481 q^{82} -14.9463 q^{83} -4.81624 q^{84} +5.29897 q^{85} -1.00000 q^{86} -17.4780 q^{87} +1.00000 q^{88} +6.18481 q^{89} +4.09240 q^{90} +1.03000 q^{91} +8.02367 q^{92} +5.78305 q^{93} -4.29609 q^{94} -0.637886 q^{95} +2.66316 q^{96} +9.24903 q^{97} -3.72943 q^{98} +4.09240 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9} + 11 q^{10} + 11 q^{11} + 3 q^{12} + q^{13} + 5 q^{14} + 3 q^{15} + 11 q^{16} + 8 q^{17} + 26 q^{18} + q^{19} + 11 q^{20} + 11 q^{22} + 20 q^{23} + 3 q^{24} + 11 q^{25} + q^{26} + 18 q^{27} + 5 q^{28} + 9 q^{29} + 3 q^{30} + 12 q^{31} + 11 q^{32} + 3 q^{33} + 8 q^{34} + 5 q^{35} + 26 q^{36} + 19 q^{37} + q^{38} - 18 q^{39} + 11 q^{40} + 9 q^{41} - 11 q^{43} + 11 q^{44} + 26 q^{45} + 20 q^{46} + 15 q^{47} + 3 q^{48} + 2 q^{49} + 11 q^{50} - 25 q^{51} + q^{52} + 35 q^{53} + 18 q^{54} + 11 q^{55} + 5 q^{56} - 25 q^{57} + 9 q^{58} + 13 q^{59} + 3 q^{60} + 9 q^{61} + 12 q^{62} + 22 q^{63} + 11 q^{64} + q^{65} + 3 q^{66} - q^{67} + 8 q^{68} + 12 q^{69} + 5 q^{70} + 14 q^{71} + 26 q^{72} - 20 q^{73} + 19 q^{74} + 3 q^{75} + q^{76} + 5 q^{77} - 18 q^{78} - 23 q^{79} + 11 q^{80} + 71 q^{81} + 9 q^{82} + 12 q^{83} + 8 q^{85} - 11 q^{86} + 6 q^{87} + 11 q^{88} - q^{89} + 26 q^{90} - 17 q^{91} + 20 q^{92} + 7 q^{93} + 15 q^{94} + q^{95} + 3 q^{96} + 17 q^{97} + 2 q^{98} + 26 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9 + 11 * q^10 + 11 * q^11 + 3 * q^12 + q^13 + 5 * q^14 + 3 * q^15 + 11 * q^16 + 8 * q^17 + 26 * q^18 + q^19 + 11 * q^20 + 11 * q^22 + 20 * q^23 + 3 * q^24 + 11 * q^25 + q^26 + 18 * q^27 + 5 * q^28 + 9 * q^29 + 3 * q^30 + 12 * q^31 + 11 * q^32 + 3 * q^33 + 8 * q^34 + 5 * q^35 + 26 * q^36 + 19 * q^37 + q^38 - 18 * q^39 + 11 * q^40 + 9 * q^41 - 11 * q^43 + 11 * q^44 + 26 * q^45 + 20 * q^46 + 15 * q^47 + 3 * q^48 + 2 * q^49 + 11 * q^50 - 25 * q^51 + q^52 + 35 * q^53 + 18 * q^54 + 11 * q^55 + 5 * q^56 - 25 * q^57 + 9 * q^58 + 13 * q^59 + 3 * q^60 + 9 * q^61 + 12 * q^62 + 22 * q^63 + 11 * q^64 + q^65 + 3 * q^66 - q^67 + 8 * q^68 + 12 * q^69 + 5 * q^70 + 14 * q^71 + 26 * q^72 - 20 * q^73 + 19 * q^74 + 3 * q^75 + q^76 + 5 * q^77 - 18 * q^78 - 23 * q^79 + 11 * q^80 + 71 * q^81 + 9 * q^82 + 12 * q^83 + 8 * q^85 - 11 * q^86 + 6 * q^87 + 11 * q^88 - q^89 + 26 * q^90 - 17 * q^91 + 20 * q^92 + 7 * q^93 + 15 * q^94 + q^95 + 3 * q^96 + 17 * q^97 + 2 * q^98 + 26 * 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
$3$	2.66316	1.53757	0.768787	−	0.639505i	$-0.220861\pi$
$3$	2.66316	1.53757	0.768787	+	0.639505i	$0.220861\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.66316	1.08723
$7$	−1.80847	−0.683538	−0.341769	−	0.939784i	$-0.611026\pi$
$7$	−1.80847	−0.683538	−0.341769	+	0.939784i	$0.611026\pi$
$8$	1.00000	0.353553
$9$	4.09240	1.36413
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.66316	0.768787
$13$	−0.569541	−0.157962	−0.0789812	−	0.996876i	$-0.525167\pi$
$13$	−0.569541	−0.157962	−0.0789812	+	0.996876i	$0.525167\pi$
$14$	−1.80847	−0.483334
$15$	2.66316	0.687624
$16$	1.00000	0.250000
$17$	5.29897	1.28519	0.642595	−	0.766206i	$-0.277858\pi$
$17$	5.29897	1.28519	0.642595	+	0.766206i	$0.277858\pi$
$18$	4.09240	0.964589
$19$	−0.637886	−0.146341	−0.0731705	−	0.997319i	$-0.523312\pi$
$19$	−0.637886	−0.146341	−0.0731705	+	0.997319i	$0.523312\pi$
$20$	1.00000	0.223607
$21$	−4.81624	−1.05099
$22$	1.00000	0.213201
$23$	8.02367	1.67305	0.836525	−	0.547928i	$-0.184583\pi$
$23$	8.02367	1.67305	0.836525	+	0.547928i	$0.184583\pi$
$24$	2.66316	0.543615
$25$	1.00000	0.200000
$26$	−0.569541	−0.111696
$27$	2.90924	0.559884
$28$	−1.80847	−0.341769
$29$	−6.56288	−1.21870	−0.609348	−	0.792903i	$-0.708569\pi$
$29$	−6.56288	−1.21870	−0.609348	+	0.792903i	$0.708569\pi$
$30$	2.66316	0.486224
$31$	2.17150	0.390013	0.195007	−	0.980802i	$-0.437527\pi$
$31$	2.17150	0.390013	0.195007	+	0.980802i	$0.437527\pi$
$32$	1.00000	0.176777
$33$	2.66316	0.463596
$34$	5.29897	0.908766
$35$	−1.80847	−0.305687
$36$	4.09240	0.682067
$37$	9.60661	1.57932	0.789658	−	0.613547i	$-0.210258\pi$
$37$	9.60661	1.57932	0.789658	+	0.613547i	$0.210258\pi$
$38$	−0.637886	−0.103479
$39$	−1.51678	−0.242879
$40$	1.00000	0.158114
$41$	−5.21481	−0.814416	−0.407208	−	0.913335i	$-0.633498\pi$
$41$	−5.21481	−0.814416	−0.407208	+	0.913335i	$0.633498\pi$
$42$	−4.81624	−0.743162
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	4.09240	0.610060
$46$	8.02367	1.18303
$47$	−4.29609	−0.626649	−0.313325	−	0.949646i	$-0.601443\pi$
$47$	−4.29609	−0.626649	−0.313325	+	0.949646i	$0.601443\pi$
$48$	2.66316	0.384394
$49$	−3.72943	−0.532776
$50$	1.00000	0.141421
$51$	14.1120	1.97607
$52$	−0.569541	−0.0789812
$53$	−3.99842	−0.549225	−0.274612	−	0.961555i	$-0.588550\pi$
$53$	−3.99842	−0.549225	−0.274612	+	0.961555i	$0.588550\pi$
$54$	2.90924	0.395898
$55$	1.00000	0.134840
$56$	−1.80847	−0.241667
$57$	−1.69879	−0.225010
$58$	−6.56288	−0.861748
$59$	15.0589	1.96050	0.980251	−	0.197757i	$-0.0633656\pi$
$59$	15.0589	1.96050	0.980251	+	0.197757i	$0.0633656\pi$
$60$	2.66316	0.343812
$61$	1.81477	0.232358	0.116179	−	0.993228i	$-0.462935\pi$
$61$	1.81477	0.232358	0.116179	+	0.993228i	$0.462935\pi$
$62$	2.17150	0.275781
$63$	−7.40100	−0.932438
$64$	1.00000	0.125000
$65$	−0.569541	−0.0706429
$66$	2.66316	0.327812
$67$	−7.94237	−0.970315	−0.485158	−	0.874427i	$-0.661238\pi$
$67$	−7.94237	−0.970315	−0.485158	+	0.874427i	$0.661238\pi$
$68$	5.29897	0.642595
$69$	21.3683	2.57244
$70$	−1.80847	−0.216154
$71$	5.65378	0.670981	0.335490	−	0.942044i	$-0.391098\pi$
$71$	5.65378	0.670981	0.335490	+	0.942044i	$0.391098\pi$
$72$	4.09240	0.482294
$73$	−14.4414	−1.69023	−0.845117	−	0.534582i	$-0.820469\pi$
$73$	−14.4414	−1.69023	−0.845117	+	0.534582i	$0.820469\pi$
$74$	9.60661	1.11675
$75$	2.66316	0.307515
$76$	−0.637886	−0.0731705
$77$	−1.80847	−0.206094
$78$	−1.51678	−0.171741
$79$	8.69071	0.977782	0.488891	−	0.872345i	$-0.337402\pi$
$79$	8.69071	0.977782	0.488891	+	0.872345i	$0.337402\pi$
$80$	1.00000	0.111803
$81$	−4.52944	−0.503271
$82$	−5.21481	−0.575879
$83$	−14.9463	−1.64057	−0.820284	−	0.571957i	$-0.806185\pi$
$83$	−14.9463	−1.64057	−0.820284	+	0.571957i	$0.806185\pi$
$84$	−4.81624	−0.525495
$85$	5.29897	0.574754
$86$	−1.00000	−0.107833
$87$	−17.4780	−1.87384
$88$	1.00000	0.106600
$89$	6.18481	0.655589	0.327794	−	0.944749i	$-0.393695\pi$
$89$	6.18481	0.655589	0.327794	+	0.944749i	$0.393695\pi$
$90$	4.09240	0.431377
$91$	1.03000	0.107973
$92$	8.02367	0.836525
$93$	5.78305	0.599674
$94$	−4.29609	−0.443108
$95$	−0.637886	−0.0654457
$96$	2.66316	0.271807
$97$	9.24903	0.939096	0.469548	−	0.882907i	$-0.344417\pi$
$97$	9.24903	0.939096	0.469548	+	0.882907i	$0.344417\pi$
$98$	−3.72943	−0.376729
$99$	4.09240	0.411302
$100$	1.00000	0.100000
$101$	−7.27588	−0.723977	−0.361988	−	0.932183i	$-0.617902\pi$
$101$	−7.27588	−0.723977	−0.361988	+	0.932183i	$0.617902\pi$
$102$	14.1120	1.39730
$103$	−12.5358	−1.23519	−0.617596	−	0.786496i	$-0.711893\pi$
$103$	−12.5358	−1.23519	−0.617596	+	0.786496i	$0.711893\pi$
$104$	−0.569541	−0.0558481
$105$	−4.81624	−0.470017
$106$	−3.99842	−0.388361
$107$	16.7546	1.61972	0.809862	−	0.586620i	$-0.199542\pi$
$107$	16.7546	1.61972	0.809862	+	0.586620i	$0.199542\pi$
$108$	2.90924	0.279942
$109$	−3.76805	−0.360913	−0.180457	−	0.983583i	$-0.557758\pi$
$109$	−3.76805	−0.360913	−0.180457	+	0.983583i	$0.557758\pi$
$110$	1.00000	0.0953463
$111$	25.5839	2.42832
$112$	−1.80847	−0.170884
$113$	14.7325	1.38592	0.692960	−	0.720976i	$-0.256306\pi$
$113$	14.7325	1.38592	0.692960	+	0.720976i	$0.256306\pi$
$114$	−1.69879	−0.159106
$115$	8.02367	0.748211
$116$	−6.56288	−0.609348
$117$	−2.33079	−0.215482
$118$	15.0589	1.38628
$119$	−9.58304	−0.878476
$120$	2.66316	0.243112
$121$	1.00000	0.0909091
$122$	1.81477	0.164302
$123$	−13.8879	−1.25223
$124$	2.17150	0.195007
$125$	1.00000	0.0894427
$126$	−7.40100	−0.659333
$127$	8.40034	0.745410	0.372705	−	0.927950i	$-0.378430\pi$
$127$	8.40034	0.745410	0.372705	+	0.927950i	$0.378430\pi$
$128$	1.00000	0.0883883
$129$	−2.66316	−0.234478
$130$	−0.569541	−0.0499521
$131$	1.12644	0.0984177	0.0492089	−	0.998789i	$-0.484330\pi$
$131$	1.12644	0.0984177	0.0492089	+	0.998789i	$0.484330\pi$
$132$	2.66316	0.231798
$133$	1.15360	0.100030
$134$	−7.94237	−0.686117
$135$	2.90924	0.250388
$136$	5.29897	0.454383
$137$	−13.9156	−1.18889	−0.594444	−	0.804137i	$-0.702628\pi$
$137$	−13.9156	−1.18889	−0.594444	+	0.804137i	$0.702628\pi$
$138$	21.3683	1.81899
$139$	1.37493	0.116620	0.0583098	−	0.998299i	$-0.481429\pi$
$139$	1.37493	0.116620	0.0583098	+	0.998299i	$0.481429\pi$
$140$	−1.80847	−0.152844
$141$	−11.4412	−0.963520
$142$	5.65378	0.474455
$143$	−0.569541	−0.0476274
$144$	4.09240	0.341034
$145$	−6.56288	−0.545017
$146$	−14.4414	−1.19518
$147$	−9.93206	−0.819183
$148$	9.60661	0.789658
$149$	19.1244	1.56673	0.783367	−	0.621560i	$-0.213501\pi$
$149$	19.1244	1.56673	0.783367	+	0.621560i	$0.213501\pi$
$150$	2.66316	0.217446
$151$	14.6959	1.19593	0.597967	−	0.801521i	$-0.295976\pi$
$151$	14.6959	1.19593	0.597967	+	0.801521i	$0.295976\pi$
$152$	−0.637886	−0.0517394
$153$	21.6855	1.75317
$154$	−1.80847	−0.145731
$155$	2.17150	0.174419
$156$	−1.51678	−0.121439
$157$	−8.79165	−0.701650	−0.350825	−	0.936441i	$-0.614099\pi$
$157$	−8.79165	−0.701650	−0.350825	+	0.936441i	$0.614099\pi$
$158$	8.69071	0.691396
$159$	−10.6484	−0.844474
$160$	1.00000	0.0790569
$161$	−14.5106	−1.14359
$162$	−4.52944	−0.355866
$163$	3.04738	0.238689	0.119344	−	0.992853i	$-0.461921\pi$
$163$	3.04738	0.238689	0.119344	+	0.992853i	$0.461921\pi$
$164$	−5.21481	−0.407208
$165$	2.66316	0.207326
$166$	−14.9463	−1.16006
$167$	−14.6308	−1.13216	−0.566081	−	0.824350i	$-0.691541\pi$
$167$	−14.6308	−1.13216	−0.566081	+	0.824350i	$0.691541\pi$
$168$	−4.81624	−0.371581
$169$	−12.6756	−0.975048
$170$	5.29897	0.406413
$171$	−2.61049	−0.199629
$172$	−1.00000	−0.0762493
$173$	7.52284	0.571951	0.285975	−	0.958237i	$-0.407682\pi$
$173$	7.52284	0.571951	0.285975	+	0.958237i	$0.407682\pi$
$174$	−17.4780	−1.32500
$175$	−1.80847	−0.136708
$176$	1.00000	0.0753778
$177$	40.1042	3.01442
$178$	6.18481	0.463571
$179$	−21.2354	−1.58721	−0.793605	−	0.608433i	$-0.791798\pi$
$179$	−21.2354	−1.58721	−0.793605	+	0.608433i	$0.791798\pi$
$180$	4.09240	0.305030
$181$	7.45611	0.554208	0.277104	−	0.960840i	$-0.410625\pi$
$181$	7.45611	0.554208	0.277104	+	0.960840i	$0.410625\pi$
$182$	1.03000	0.0763486
$183$	4.83302	0.357267
$184$	8.02367	0.591513
$185$	9.60661	0.706292
$186$	5.78305	0.424034
$187$	5.29897	0.387499
$188$	−4.29609	−0.313325
$189$	−5.26128	−0.382702
$190$	−0.637886	−0.0462771
$191$	3.97014	0.287269	0.143634	−	0.989631i	$-0.454121\pi$
$191$	3.97014	0.287269	0.143634	+	0.989631i	$0.454121\pi$
$192$	2.66316	0.192197
$193$	−27.1516	−1.95441	−0.977207	−	0.212290i	$-0.931908\pi$
$193$	−27.1516	−1.95441	−0.977207	+	0.212290i	$0.931908\pi$
$194$	9.24903	0.664041
$195$	−1.51678	−0.108619
$196$	−3.72943	−0.266388
$197$	5.62459	0.400736	0.200368	−	0.979721i	$-0.435786\pi$
$197$	5.62459	0.400736	0.200368	+	0.979721i	$0.435786\pi$
$198$	4.09240	0.290835
$199$	1.33397	0.0945628	0.0472814	−	0.998882i	$-0.484944\pi$
$199$	1.33397	0.0945628	0.0472814	+	0.998882i	$0.484944\pi$
$200$	1.00000	0.0707107
$201$	−21.1518	−1.49193
$202$	−7.27588	−0.511929
$203$	11.8688	0.833025
$204$	14.1120	0.988037
$205$	−5.21481	−0.364218
$206$	−12.5358	−0.873412
$207$	32.8361	2.28227
$208$	−0.569541	−0.0394906
$209$	−0.637886	−0.0441235
$210$	−4.81624	−0.332352
$211$	−27.9750	−1.92588	−0.962938	−	0.269723i	$-0.913068\pi$
$211$	−27.9750	−1.92588	−0.962938	+	0.269723i	$0.913068\pi$
$212$	−3.99842	−0.274612
$213$	15.0569	1.03168
$214$	16.7546	1.14532
$215$	−1.00000	−0.0681994
$216$	2.90924	0.197949
$217$	−3.92710	−0.266589
$218$	−3.76805	−0.255204
$219$	−38.4596	−2.59886
$220$	1.00000	0.0674200
$221$	−3.01798	−0.203012
$222$	25.5839	1.71708
$223$	−9.28952	−0.622073	−0.311036	−	0.950398i	$-0.600676\pi$
$223$	−9.28952	−0.622073	−0.311036	+	0.950398i	$0.600676\pi$
$224$	−1.80847	−0.120834
$225$	4.09240	0.272827
$226$	14.7325	0.979993
$227$	22.1290	1.46875	0.734377	−	0.678742i	$-0.237475\pi$
$227$	22.1290	1.46875	0.734377	+	0.678742i	$0.237475\pi$
$228$	−1.69879	−0.112505
$229$	21.5005	1.42080	0.710398	−	0.703800i	$-0.248515\pi$
$229$	21.5005	1.42080	0.710398	+	0.703800i	$0.248515\pi$
$230$	8.02367	0.529065
$231$	−4.81624	−0.316886
$232$	−6.56288	−0.430874
$233$	24.6743	1.61647	0.808233	−	0.588862i	$-0.200424\pi$
$233$	24.6743	1.61647	0.808233	+	0.588862i	$0.200424\pi$
$234$	−2.33079	−0.152369
$235$	−4.29609	−0.280246
$236$	15.0589	0.980251
$237$	23.1447	1.50341
$238$	−9.58304	−0.621176
$239$	18.8221	1.21750	0.608750	−	0.793362i	$-0.291671\pi$
$239$	18.8221	1.21750	0.608750	+	0.793362i	$0.291671\pi$
$240$	2.66316	0.171906
$241$	−15.4771	−0.996969	−0.498484	−	0.866899i	$-0.666110\pi$
$241$	−15.4771	−0.996969	−0.498484	+	0.866899i	$0.666110\pi$
$242$	1.00000	0.0642824
$243$	−20.7903	−1.33370
$244$	1.81477	0.116179
$245$	−3.72943	−0.238265
$246$	−13.8879	−0.885457
$247$	0.363302	0.0231164
$248$	2.17150	0.137890
$249$	−39.8043	−2.52249
$250$	1.00000	0.0632456
$251$	−31.2651	−1.97344	−0.986719	−	0.162436i	$-0.948065\pi$
$251$	−31.2651	−1.97344	−0.986719	+	0.162436i	$0.948065\pi$
$252$	−7.40100	−0.466219
$253$	8.02367	0.504444
$254$	8.40034	0.527084
$255$	14.1120	0.883727
$256$	1.00000	0.0625000
$257$	−4.60816	−0.287449	−0.143725	−	0.989618i	$-0.545908\pi$
$257$	−4.60816	−0.287449	−0.143725	+	0.989618i	$0.545908\pi$
$258$	−2.66316	−0.165801
$259$	−17.3733	−1.07952
$260$	−0.569541	−0.0353214
$261$	−26.8580	−1.66247
$262$	1.12644	0.0695918
$263$	−21.6381	−1.33426	−0.667130	−	0.744942i	$-0.732477\pi$
$263$	−21.6381	−1.33426	−0.667130	+	0.744942i	$0.732477\pi$
$264$	2.66316	0.163906
$265$	−3.99842	−0.245621
$266$	1.15360	0.0707316
$267$	16.4711	1.00802
$268$	−7.94237	−0.485158
$269$	30.3578	1.85095	0.925475	−	0.378810i	$-0.123667\pi$
$269$	30.3578	1.85095	0.925475	+	0.378810i	$0.123667\pi$
$270$	2.90924	0.177051
$271$	−21.6234	−1.31353	−0.656763	−	0.754097i	$-0.728075\pi$
$271$	−21.6234	−1.31353	−0.656763	+	0.754097i	$0.728075\pi$
$272$	5.29897	0.321297
$273$	2.74305	0.166017
$274$	−13.9156	−0.840670
$275$	1.00000	0.0603023
$276$	21.3683	1.28622
$277$	−26.7074	−1.60469	−0.802346	−	0.596859i	$-0.796415\pi$
$277$	−26.7074	−1.60469	−0.802346	+	0.596859i	$0.796415\pi$
$278$	1.37493	0.0824625
$279$	8.88666	0.532030
$280$	−1.80847	−0.108077
$281$	20.2064	1.20541	0.602707	−	0.797963i	$-0.294089\pi$
$281$	20.2064	1.20541	0.602707	+	0.797963i	$0.294089\pi$
$282$	−11.4412	−0.681311
$283$	−31.5317	−1.87436	−0.937182	−	0.348841i	$-0.886575\pi$
$283$	−31.5317	−1.87436	−0.937182	+	0.348841i	$0.886575\pi$
$284$	5.65378	0.335490
$285$	−1.69879	−0.100628
$286$	−0.569541	−0.0336777
$287$	9.43083	0.556684
$288$	4.09240	0.241147
$289$	11.0791	0.651713
$290$	−6.56288	−0.385385
$291$	24.6316	1.44393
$292$	−14.4414	−0.845117
$293$	−21.1852	−1.23765	−0.618826	−	0.785528i	$-0.712391\pi$
$293$	−21.1852	−1.23765	−0.618826	+	0.785528i	$0.712391\pi$
$294$	−9.93206	−0.579250
$295$	15.0589	0.876763
$296$	9.60661	0.558373
$297$	2.90924	0.168811
$298$	19.1244	1.10785
$299$	−4.56981	−0.264279
$300$	2.66316	0.153757
$301$	1.80847	0.104239
$302$	14.6959	0.845653
$303$	−19.3768	−1.11317
$304$	−0.637886	−0.0365853
$305$	1.81477	0.103913
$306$	21.6855	1.23968
$307$	4.68211	0.267222	0.133611	−	0.991034i	$-0.457343\pi$
$307$	4.68211	0.267222	0.133611	+	0.991034i	$0.457343\pi$
$308$	−1.80847	−0.103047
$309$	−33.3849	−1.89920
$310$	2.17150	0.123333
$311$	−23.0414	−1.30656	−0.653278	−	0.757118i	$-0.726607\pi$
$311$	−23.0414	−1.30656	−0.653278	+	0.757118i	$0.726607\pi$
$312$	−1.51678	−0.0858706
$313$	−30.9092	−1.74709	−0.873546	−	0.486741i	$-0.838186\pi$
$313$	−30.9092	−1.74709	−0.873546	+	0.486741i	$0.838186\pi$
$314$	−8.79165	−0.496141
$315$	−7.40100	−0.416999
$316$	8.69071	0.488891
$317$	11.1978	0.628929	0.314465	−	0.949269i	$-0.398175\pi$
$317$	11.1978	0.628929	0.314465	+	0.949269i	$0.398175\pi$
$318$	−10.6484	−0.597133
$319$	−6.56288	−0.367451
$320$	1.00000	0.0559017
$321$	44.6200	2.49045
$322$	−14.5106	−0.808643
$323$	−3.38014	−0.188076
$324$	−4.52944	−0.251636
$325$	−0.569541	−0.0315925
$326$	3.04738	0.168779
$327$	−10.0349	−0.554931
$328$	−5.21481	−0.287940
$329$	7.76935	0.428338
$330$	2.66316	0.146602
$331$	−24.5819	−1.35115	−0.675573	−	0.737293i	$-0.736104\pi$
$331$	−24.5819	−1.35115	−0.675573	+	0.737293i	$0.736104\pi$
$332$	−14.9463	−0.820284
$333$	39.3141	2.15440
$334$	−14.6308	−0.800559
$335$	−7.94237	−0.433938
$336$	−4.81624	−0.262748
$337$	6.18969	0.337174	0.168587	−	0.985687i	$-0.446080\pi$
$337$	6.18969	0.337174	0.168587	+	0.985687i	$0.446080\pi$
$338$	−12.6756	−0.689463
$339$	39.2350	2.13095
$340$	5.29897	0.287377
$341$	2.17150	0.117593
$342$	−2.61049	−0.141159
$343$	19.4039	1.04771
$344$	−1.00000	−0.0539164
$345$	21.3683	1.15043
$346$	7.52284	0.404430
$347$	19.5559	1.04982	0.524909	−	0.851159i	$-0.324099\pi$
$347$	19.5559	1.04982	0.524909	+	0.851159i	$0.324099\pi$
$348$	−17.4780	−0.936918
$349$	20.1322	1.07765	0.538825	−	0.842418i	$-0.318868\pi$
$349$	20.1322	1.07765	0.538825	+	0.842418i	$0.318868\pi$
$350$	−1.80847	−0.0966669
$351$	−1.65693	−0.0884406
$352$	1.00000	0.0533002
$353$	7.59001	0.403976	0.201988	−	0.979388i	$-0.435260\pi$
$353$	7.59001	0.403976	0.201988	+	0.979388i	$0.435260\pi$
$354$	40.1042	2.13152
$355$	5.65378	0.300072
$356$	6.18481	0.327794
$357$	−25.5211	−1.35072
$358$	−21.2354	−1.12233
$359$	−28.2907	−1.49312	−0.746562	−	0.665316i	$-0.768297\pi$
$359$	−28.2907	−1.49312	−0.746562	+	0.665316i	$0.768297\pi$
$360$	4.09240	0.215689
$361$	−18.5931	−0.978584
$362$	7.45611	0.391884
$363$	2.66316	0.139779
$364$	1.03000	0.0539866
$365$	−14.4414	−0.755895
$366$	4.83302	0.252626
$367$	13.6974	0.714999	0.357499	−	0.933913i	$-0.383629\pi$
$367$	13.6974	0.714999	0.357499	+	0.933913i	$0.383629\pi$
$368$	8.02367	0.418263
$369$	−21.3411	−1.11097
$370$	9.60661	0.499424
$371$	7.23102	0.375416
$372$	5.78305	0.299837
$373$	−34.8868	−1.80637	−0.903185	−	0.429252i	$-0.858777\pi$
$373$	−34.8868	−1.80637	−0.903185	+	0.429252i	$0.858777\pi$
$374$	5.29897	0.274003
$375$	2.66316	0.137525
$376$	−4.29609	−0.221554
$377$	3.73783	0.192508
$378$	−5.26128	−0.270611
$379$	−9.61413	−0.493845	−0.246922	−	0.969035i	$-0.579419\pi$
$379$	−9.61413	−0.493845	−0.246922	+	0.969035i	$0.579419\pi$
$380$	−0.637886	−0.0327228
$381$	22.3714	1.14612
$382$	3.97014	0.203130
$383$	−21.4023	−1.09361	−0.546803	−	0.837262i	$-0.684155\pi$
$383$	−21.4023	−1.09361	−0.546803	+	0.837262i	$0.684155\pi$
$384$	2.66316	0.135904
$385$	−1.80847	−0.0921682
$386$	−27.1516	−1.38198
$387$	−4.09240	−0.208029
$388$	9.24903	0.469548
$389$	−27.8898	−1.41407	−0.707035	−	0.707178i	$-0.749968\pi$
$389$	−27.8898	−1.41407	−0.707035	+	0.707178i	$0.749968\pi$
$390$	−1.51678	−0.0768050
$391$	42.5172	2.15019
$392$	−3.72943	−0.188365
$393$	2.99989	0.151325
$394$	5.62459	0.283363
$395$	8.69071	0.437277
$396$	4.09240	0.205651
$397$	−14.7227	−0.738912	−0.369456	−	0.929248i	$-0.620456\pi$
$397$	−14.7227	−0.738912	−0.369456	+	0.929248i	$0.620456\pi$
$398$	1.33397	0.0668660
$399$	3.07221	0.153803
$400$	1.00000	0.0500000
$401$	15.0702	0.752571	0.376286	−	0.926504i	$-0.377201\pi$
$401$	15.0702	0.752571	0.376286	+	0.926504i	$0.377201\pi$
$402$	−21.1518	−1.05496
$403$	−1.23676	−0.0616074
$404$	−7.27588	−0.361988
$405$	−4.52944	−0.225070
$406$	11.8688	0.589037
$407$	9.60661	0.476182
$408$	14.1120	0.698648
$409$	−8.36968	−0.413854	−0.206927	−	0.978356i	$-0.566346\pi$
$409$	−8.36968	−0.413854	−0.206927	+	0.978356i	$0.566346\pi$
$410$	−5.21481	−0.257541
$411$	−37.0593	−1.82800
$412$	−12.5358	−0.617596
$413$	−27.2336	−1.34008
$414$	32.8361	1.61381
$415$	−14.9463	−0.733684
$416$	−0.569541	−0.0279241
$417$	3.66164	0.179311
$418$	−0.637886	−0.0312000
$419$	−32.5091	−1.58817	−0.794086	−	0.607805i	$-0.792050\pi$
$419$	−32.5091	−1.58817	−0.794086	+	0.607805i	$0.792050\pi$
$420$	−4.81624	−0.235009
$421$	−7.14116	−0.348039	−0.174019	−	0.984742i	$-0.555676\pi$
$421$	−7.14116	−0.348039	−0.174019	+	0.984742i	$0.555676\pi$
$422$	−27.9750	−1.36180
$423$	−17.5813	−0.854834
$424$	−3.99842	−0.194180
$425$	5.29897	0.257038
$426$	15.0569	0.729510
$427$	−3.28196	−0.158825
$428$	16.7546	0.809862
$429$	−1.51678	−0.0732307
$430$	−1.00000	−0.0482243
$431$	4.77895	0.230194	0.115097	−	0.993354i	$-0.463282\pi$
$431$	4.77895	0.230194	0.115097	+	0.993354i	$0.463282\pi$
$432$	2.90924	0.139971
$433$	6.47208	0.311028	0.155514	−	0.987834i	$-0.450297\pi$
$433$	6.47208	0.311028	0.155514	+	0.987834i	$0.450297\pi$
$434$	−3.92710	−0.188507
$435$	−17.4780	−0.838005
$436$	−3.76805	−0.180457
$437$	−5.11818	−0.244836
$438$	−38.4596	−1.83767
$439$	1.54006	0.0735029	0.0367515	−	0.999324i	$-0.488299\pi$
$439$	1.54006	0.0735029	0.0367515	+	0.999324i	$0.488299\pi$
$440$	1.00000	0.0476731
$441$	−15.2623	−0.726778
$442$	−3.01798	−0.143551
$443$	−4.76324	−0.226308	−0.113154	−	0.993577i	$-0.536095\pi$
$443$	−4.76324	−0.226308	−0.113154	+	0.993577i	$0.536095\pi$
$444$	25.5839	1.21416
$445$	6.18481	0.293188
$446$	−9.28952	−0.439872
$447$	50.9313	2.40897
$448$	−1.80847	−0.0854422
$449$	31.1087	1.46811	0.734055	−	0.679090i	$-0.237626\pi$
$449$	31.1087	1.46811	0.734055	+	0.679090i	$0.237626\pi$
$450$	4.09240	0.192918
$451$	−5.21481	−0.245556
$452$	14.7325	0.692960
$453$	39.1374	1.83884
$454$	22.1290	1.03857
$455$	1.03000	0.0482871
$456$	−1.69879	−0.0795531
$457$	12.7017	0.594161	0.297080	−	0.954852i	$-0.403987\pi$
$457$	12.7017	0.594161	0.297080	+	0.954852i	$0.403987\pi$
$458$	21.5005	1.00465
$459$	15.4160	0.719558
$460$	8.02367	0.374106
$461$	−29.9663	−1.39567	−0.697835	−	0.716259i	$-0.745853\pi$
$461$	−29.9663	−1.39567	−0.697835	+	0.716259i	$0.745853\pi$
$462$	−4.81624	−0.224072
$463$	28.5419	1.32646	0.663228	−	0.748418i	$-0.269186\pi$
$463$	28.5419	1.32646	0.663228	+	0.748418i	$0.269186\pi$
$464$	−6.56288	−0.304674
$465$	5.78305	0.268182
$466$	24.6743	1.14301
$467$	21.0670	0.974865	0.487432	−	0.873161i	$-0.337934\pi$
$467$	21.0670	0.974865	0.487432	+	0.873161i	$0.337934\pi$
$468$	−2.33079	−0.107741
$469$	14.3636	0.663247
$470$	−4.29609	−0.198164
$471$	−23.4135	−1.07884
$472$	15.0589	0.693142
$473$	−1.00000	−0.0459800
$474$	23.1447	1.06307
$475$	−0.637886	−0.0292682
$476$	−9.58304	−0.439238
$477$	−16.3631	−0.749217
$478$	18.8221	0.860902
$479$	−15.6180	−0.713607	−0.356803	−	0.934180i	$-0.616133\pi$
$479$	−15.6180	−0.713607	−0.356803	+	0.934180i	$0.616133\pi$
$480$	2.66316	0.121556
$481$	−5.47136	−0.249472
$482$	−15.4771	−0.704963
$483$	−38.6439	−1.75836
$484$	1.00000	0.0454545
$485$	9.24903	0.419977
$486$	−20.7903	−0.943069
$487$	−10.7687	−0.487976	−0.243988	−	0.969778i	$-0.578456\pi$
$487$	−10.7687	−0.487976	−0.243988	+	0.969778i	$0.578456\pi$
$488$	1.81477	0.0821508
$489$	8.11564	0.367002
$490$	−3.72943	−0.168479
$491$	−18.4328	−0.831858	−0.415929	−	0.909397i	$-0.636544\pi$
$491$	−18.4328	−0.831858	−0.415929	+	0.909397i	$0.636544\pi$
$492$	−13.8879	−0.626113
$493$	−34.7765	−1.56626
$494$	0.363302	0.0163457
$495$	4.09240	0.183940
$496$	2.17150	0.0975033
$497$	−10.2247	−0.458641
$498$	−39.8043	−1.78367
$499$	−29.7862	−1.33341	−0.666706	−	0.745321i	$-0.732296\pi$
$499$	−29.7862	−1.33341	−0.666706	+	0.745321i	$0.732296\pi$
$500$	1.00000	0.0447214
$501$	−38.9640	−1.74078
$502$	−31.2651	−1.39543
$503$	28.0764	1.25186	0.625932	−	0.779878i	$-0.284719\pi$
$503$	28.0764	1.25186	0.625932	+	0.779878i	$0.284719\pi$
$504$	−7.40100	−0.329667
$505$	−7.27588	−0.323772
$506$	8.02367	0.356696
$507$	−33.7572	−1.49921
$508$	8.40034	0.372705
$509$	5.65824	0.250797	0.125399	−	0.992106i	$-0.459979\pi$
$509$	5.65824	0.250797	0.125399	+	0.992106i	$0.459979\pi$
$510$	14.1120	0.624890
$511$	26.1168	1.15534
$512$	1.00000	0.0441942
$513$	−1.85577	−0.0819340
$514$	−4.60816	−0.203257
$515$	−12.5358	−0.552394
$516$	−2.66316	−0.117239
$517$	−4.29609	−0.188942
$518$	−17.3733	−0.763338
$519$	20.0345	0.879417
$520$	−0.569541	−0.0249760
$521$	−14.7463	−0.646046	−0.323023	−	0.946391i	$-0.604699\pi$
$521$	−14.7463	−0.646046	−0.323023	+	0.946391i	$0.604699\pi$
$522$	−26.8580	−1.17554
$523$	17.3368	0.758084	0.379042	−	0.925380i	$-0.376254\pi$
$523$	17.3368	0.758084	0.379042	+	0.925380i	$0.376254\pi$
$524$	1.12644	0.0492089
$525$	−4.81624	−0.210198
$526$	−21.6381	−0.943464
$527$	11.5067	0.501241
$528$	2.66316	0.115899
$529$	41.3793	1.79910
$530$	−3.99842	−0.173680
$531$	61.6271	2.67439
$532$	1.15360	0.0500148
$533$	2.97005	0.128647
$534$	16.4711	0.712775
$535$	16.7546	0.724363
$536$	−7.94237	−0.343058
$537$	−56.5533	−2.44045
$538$	30.3578	1.30882
$539$	−3.72943	−0.160638
$540$	2.90924	0.125194
$541$	−0.283377	−0.0121833	−0.00609167	−	0.999981i	$-0.501939\pi$
$541$	−0.283377	−0.0121833	−0.00609167	+	0.999981i	$0.501939\pi$
$542$	−21.6234	−0.928803
$543$	19.8568	0.852136
$544$	5.29897	0.227192
$545$	−3.76805	−0.161405
$546$	2.74305	0.117392
$547$	−13.7243	−0.586810	−0.293405	−	0.955988i	$-0.594788\pi$
$547$	−13.7243	−0.586810	−0.293405	+	0.955988i	$0.594788\pi$
$548$	−13.9156	−0.594444
$549$	7.42677	0.316967
$550$	1.00000	0.0426401
$551$	4.18637	0.178345
$552$	21.3683	0.909495
$553$	−15.7169	−0.668351
$554$	−26.7074	−1.13469
$555$	25.5839	1.08598
$556$	1.37493	0.0583098
$557$	12.4083	0.525755	0.262877	−	0.964829i	$-0.415329\pi$
$557$	12.4083	0.525755	0.262877	+	0.964829i	$0.415329\pi$
$558$	8.88666	0.376202
$559$	0.569541	0.0240890
$560$	−1.80847	−0.0764219
$561$	14.1120	0.595809
$562$	20.2064	0.852356
$563$	−44.3876	−1.87071	−0.935357	−	0.353706i	$-0.884921\pi$
$563$	−44.3876	−1.87071	−0.935357	+	0.353706i	$0.884921\pi$
$564$	−11.4412	−0.481760
$565$	14.7325	0.619802
$566$	−31.5317	−1.32538
$567$	8.19136	0.344005
$568$	5.65378	0.237228
$569$	−33.2177	−1.39256	−0.696279	−	0.717771i	$-0.745162\pi$
$569$	−33.2177	−1.39256	−0.696279	+	0.717771i	$0.745162\pi$
$570$	−1.69879	−0.0711545
$571$	33.2458	1.39129	0.695647	−	0.718384i	$-0.255118\pi$
$571$	33.2458	1.39129	0.695647	+	0.718384i	$0.255118\pi$
$572$	−0.569541	−0.0238137
$573$	10.5731	0.441697
$574$	9.43083	0.393635
$575$	8.02367	0.334610
$576$	4.09240	0.170517
$577$	16.4993	0.686876	0.343438	−	0.939175i	$-0.388409\pi$
$577$	16.4993	0.686876	0.343438	+	0.939175i	$0.388409\pi$
$578$	11.0791	0.460830
$579$	−72.3089	−3.00506
$580$	−6.56288	−0.272509
$581$	27.0299	1.12139
$582$	24.6316	1.02101
$583$	−3.99842	−0.165598
$584$	−14.4414	−0.597588
$585$	−2.33079	−0.0963664
$586$	−21.1852	−0.875152
$587$	−39.8025	−1.64283	−0.821413	−	0.570334i	$-0.806814\pi$
$587$	−39.8025	−1.64283	−0.821413	+	0.570334i	$0.806814\pi$
$588$	−9.93206	−0.409591
$589$	−1.38517	−0.0570749
$590$	15.0589	0.619965
$591$	14.9792	0.616161
$592$	9.60661	0.394829
$593$	−19.4059	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$593$	−19.4059	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$594$	2.90924	0.119368
$595$	−9.58304	−0.392866
$596$	19.1244	0.783367
$597$	3.55258	0.145397
$598$	−4.56981	−0.186873
$599$	−39.5997	−1.61800	−0.809001	−	0.587808i	$-0.799991\pi$
$599$	−39.5997	−1.61800	−0.809001	+	0.587808i	$0.799991\pi$
$600$	2.66316	0.108723
$601$	−6.59940	−0.269195	−0.134598	−	0.990900i	$-0.542974\pi$
$601$	−6.59940	−0.269195	−0.134598	+	0.990900i	$0.542974\pi$
$602$	1.80847	0.0737078
$603$	−32.5034	−1.32364
$604$	14.6959	0.597967
$605$	1.00000	0.0406558
$606$	−19.3768	−0.787129
$607$	20.5859	0.835556	0.417778	−	0.908549i	$-0.362809\pi$
$607$	20.5859	0.835556	0.417778	+	0.908549i	$0.362809\pi$
$608$	−0.637886	−0.0258697
$609$	31.6084	1.28084
$610$	1.81477	0.0734779
$611$	2.44680	0.0989869
$612$	21.6855	0.876586
$613$	7.23459	0.292202	0.146101	−	0.989270i	$-0.453328\pi$
$613$	7.23459	0.292202	0.146101	+	0.989270i	$0.453328\pi$
$614$	4.68211	0.188954
$615$	−13.8879	−0.560012
$616$	−1.80847	−0.0728654
$617$	26.1951	1.05458	0.527288	−	0.849687i	$-0.323209\pi$
$617$	26.1951	1.05458	0.527288	+	0.849687i	$0.323209\pi$
$618$	−33.3849	−1.34294
$619$	−31.3424	−1.25976	−0.629879	−	0.776694i	$-0.716895\pi$
$619$	−31.3424	−1.25976	−0.629879	+	0.776694i	$0.716895\pi$
$620$	2.17150	0.0872096
$621$	23.3428	0.936715
$622$	−23.0414	−0.923874
$623$	−11.1851	−0.448120
$624$	−1.51678	−0.0607197
$625$	1.00000	0.0400000
$626$	−30.9092	−1.23538
$627$	−1.69879	−0.0678431
$628$	−8.79165	−0.350825
$629$	50.9051	2.02972
$630$	−7.40100	−0.294863
$631$	33.9685	1.35226	0.676132	−	0.736780i	$-0.263655\pi$
$631$	33.9685	1.35226	0.676132	+	0.736780i	$0.263655\pi$
$632$	8.69071	0.345698
$633$	−74.5017	−2.96118
$634$	11.1978	0.444720
$635$	8.40034	0.333357
$636$	−10.6484	−0.422237
$637$	2.12406	0.0841585
$638$	−6.56288	−0.259827
$639$	23.1376	0.915308
$640$	1.00000	0.0395285
$641$	28.5282	1.12680	0.563398	−	0.826186i	$-0.309494\pi$
$641$	28.5282	1.12680	0.563398	+	0.826186i	$0.309494\pi$
$642$	44.6200	1.76101
$643$	33.2471	1.31114	0.655568	−	0.755136i	$-0.272429\pi$
$643$	33.2471	1.31114	0.655568	+	0.755136i	$0.272429\pi$
$644$	−14.5106	−0.571797
$645$	−2.66316	−0.104862
$646$	−3.38014	−0.132990
$647$	15.1049	0.593833	0.296917	−	0.954903i	$-0.404042\pi$
$647$	15.1049	0.593833	0.296917	+	0.954903i	$0.404042\pi$
$648$	−4.52944	−0.177933
$649$	15.0589	0.591114
$650$	−0.569541	−0.0223392
$651$	−10.4585	−0.409900
$652$	3.04738	0.119344
$653$	12.1339	0.474834	0.237417	−	0.971408i	$-0.423699\pi$
$653$	12.1339	0.474834	0.237417	+	0.971408i	$0.423699\pi$
$654$	−10.0349	−0.392396
$655$	1.12644	0.0440137
$656$	−5.21481	−0.203604
$657$	−59.0999	−2.30571
$658$	7.76935	0.302881
$659$	−20.1778	−0.786017	−0.393009	−	0.919535i	$-0.628566\pi$
$659$	−20.1778	−0.786017	−0.393009	+	0.919535i	$0.628566\pi$
$660$	2.66316	0.103663
$661$	14.0186	0.545262	0.272631	−	0.962119i	$-0.412106\pi$
$661$	14.0186	0.545262	0.272631	+	0.962119i	$0.412106\pi$
$662$	−24.5819	−0.955404
$663$	−8.03736	−0.312145
$664$	−14.9463	−0.580028
$665$	1.15360	0.0447346
$666$	39.3141	1.52339
$667$	−52.6584	−2.03894
$668$	−14.6308	−0.566081
$669$	−24.7395	−0.956483
$670$	−7.94237	−0.306841
$671$	1.81477	0.0700584
$672$	−4.81624	−0.185791
$673$	29.1587	1.12399	0.561993	−	0.827142i	$-0.310035\pi$
$673$	29.1587	1.12399	0.561993	+	0.827142i	$0.310035\pi$
$674$	6.18969	0.238418
$675$	2.90924	0.111977
$676$	−12.6756	−0.487524
$677$	8.93287	0.343318	0.171659	−	0.985156i	$-0.445087\pi$
$677$	8.93287	0.343318	0.171659	+	0.985156i	$0.445087\pi$
$678$	39.2350	1.50681
$679$	−16.7266	−0.641908
$680$	5.29897	0.203206
$681$	58.9330	2.25832
$682$	2.17150	0.0831511
$683$	4.51535	0.172775	0.0863876	−	0.996262i	$-0.472468\pi$
$683$	4.51535	0.172775	0.0863876	+	0.996262i	$0.472468\pi$
$684$	−2.61049	−0.0998144
$685$	−13.9156	−0.531687
$686$	19.4039	0.740843
$687$	57.2593	2.18458
$688$	−1.00000	−0.0381246
$689$	2.27726	0.0867568
$690$	21.3683	0.813477
$691$	36.7315	1.39733	0.698666	−	0.715448i	$-0.253777\pi$
$691$	36.7315	1.39733	0.698666	+	0.715448i	$0.253777\pi$
$692$	7.52284	0.285975
$693$	−7.40100	−0.281141
$694$	19.5559	0.742333
$695$	1.37493	0.0521539
$696$	−17.4780	−0.662501
$697$	−27.6331	−1.04668
$698$	20.1322	0.762014
$699$	65.7115	2.48544
$700$	−1.80847	−0.0683538
$701$	21.1662	0.799438	0.399719	−	0.916638i	$-0.369108\pi$
$701$	21.1662	0.799438	0.399719	+	0.916638i	$0.369108\pi$
$702$	−1.65693	−0.0625370
$703$	−6.12792	−0.231119
$704$	1.00000	0.0376889
$705$	−11.4412	−0.430899
$706$	7.59001	0.285654
$707$	13.1582	0.494866
$708$	40.1042	1.50721
$709$	21.9879	0.825775	0.412887	−	0.910782i	$-0.364520\pi$
$709$	21.9879	0.825775	0.412887	+	0.910782i	$0.364520\pi$
$710$	5.65378	0.212183
$711$	35.5659	1.33383
$712$	6.18481	0.231786
$713$	17.4234	0.652512
$714$	−25.5211	−0.955105
$715$	−0.569541	−0.0212996
$716$	−21.2354	−0.793605
$717$	50.1262	1.87200
$718$	−28.2907	−1.05580
$719$	16.7349	0.624107	0.312054	−	0.950065i	$-0.398983\pi$
$719$	16.7349	0.624107	0.312054	+	0.950065i	$0.398983\pi$
$720$	4.09240	0.152515
$721$	22.6707	0.844300
$722$	−18.5931	−0.691964
$723$	−41.2180	−1.53291
$724$	7.45611	0.277104
$725$	−6.56288	−0.243739
$726$	2.66316	0.0988390
$727$	4.13462	0.153344	0.0766722	−	0.997056i	$-0.475570\pi$
$727$	4.13462	0.153344	0.0766722	+	0.997056i	$0.475570\pi$
$728$	1.03000	0.0381743
$729$	−41.7796	−1.54739
$730$	−14.4414	−0.534499
$731$	−5.29897	−0.195990
$732$	4.83302	0.178633
$733$	−20.2142	−0.746628	−0.373314	−	0.927705i	$-0.621779\pi$
$733$	−20.2142	−0.746628	−0.373314	+	0.927705i	$0.621779\pi$
$734$	13.6974	0.505580
$735$	−9.93206	−0.366350
$736$	8.02367	0.295756
$737$	−7.94237	−0.292561
$738$	−21.3411	−0.785577
$739$	46.0976	1.69573	0.847864	−	0.530214i	$-0.177888\pi$
$739$	46.0976	1.69573	0.847864	+	0.530214i	$0.177888\pi$
$740$	9.60661	0.353146
$741$	0.967531	0.0355431
$742$	7.23102	0.265459
$743$	−25.1031	−0.920943	−0.460472	−	0.887674i	$-0.652320\pi$
$743$	−25.1031	−0.920943	−0.460472	+	0.887674i	$0.652320\pi$
$744$	5.78305	0.212017
$745$	19.1244	0.700664
$746$	−34.8868	−1.27730
$747$	−61.1662	−2.23796
$748$	5.29897	0.193750
$749$	−30.3001	−1.10714
$750$	2.66316	0.0972447
$751$	42.8552	1.56381	0.781904	−	0.623398i	$-0.214249\pi$
$751$	42.8552	1.56381	0.781904	+	0.623398i	$0.214249\pi$
$752$	−4.29609	−0.156662
$753$	−83.2640	−3.03431
$754$	3.73783	0.136124
$755$	14.6959	0.534838
$756$	−5.26128	−0.191351
$757$	−0.389159	−0.0141442	−0.00707211	−	0.999975i	$-0.502251\pi$
$757$	−0.389159	−0.0141442	−0.00707211	+	0.999975i	$0.502251\pi$
$758$	−9.61413	−0.349201
$759$	21.3683	0.775620
$760$	−0.637886	−0.0231385
$761$	−9.82012	−0.355979	−0.177990	−	0.984032i	$-0.556959\pi$
$761$	−9.82012	−0.355979	−0.177990	+	0.984032i	$0.556959\pi$
$762$	22.3714	0.810431
$763$	6.81440	0.246698
$764$	3.97014	0.143634
$765$	21.6855	0.784042
$766$	−21.4023	−0.773296
$767$	−8.57667	−0.309685
$768$	2.66316	0.0960984
$769$	38.2141	1.37803	0.689017	−	0.724745i	$-0.258042\pi$
$769$	38.2141	1.37803	0.689017	+	0.724745i	$0.258042\pi$
$770$	−1.80847	−0.0651728
$771$	−12.2723	−0.441975
$772$	−27.1516	−0.977207
$773$	50.6950	1.82337	0.911686	−	0.410888i	$-0.134781\pi$
$773$	50.6950	1.82337	0.911686	+	0.410888i	$0.134781\pi$
$774$	−4.09240	−0.147098
$775$	2.17150	0.0780026
$776$	9.24903	0.332021
$777$	−46.2677	−1.65985
$778$	−27.8898	−0.999899
$779$	3.32645	0.119182
$780$	−1.51678	−0.0543093
$781$	5.65378	0.202308
$782$	42.5172	1.52041
$783$	−19.0930	−0.682329
$784$	−3.72943	−0.133194
$785$	−8.79165	−0.313787
$786$	2.99989	0.107003
$787$	8.59258	0.306293	0.153146	−	0.988204i	$-0.451059\pi$
$787$	8.59258	0.306293	0.153146	+	0.988204i	$0.451059\pi$
$788$	5.62459	0.200368
$789$	−57.6255	−2.05152
$790$	8.69071	0.309202
$791$	−26.6434	−0.947329
$792$	4.09240	0.145417
$793$	−1.03359	−0.0367037
$794$	−14.7227	−0.522490
$795$	−10.6484	−0.377660
$796$	1.33397	0.0472814
$797$	1.77231	0.0627783	0.0313891	−	0.999507i	$-0.490007\pi$
$797$	1.77231	0.0627783	0.0313891	+	0.999507i	$0.490007\pi$
$798$	3.07221	0.108755
$799$	−22.7649	−0.805363
$800$	1.00000	0.0353553
$801$	25.3108	0.894311
$802$	15.0702	0.532148
$803$	−14.4414	−0.509624
$804$	−21.1518	−0.745966
$805$	−14.5106	−0.511431
$806$	−1.23676	−0.0435630
$807$	80.8476	2.84597
$808$	−7.27588	−0.255964
$809$	23.3259	0.820096	0.410048	−	0.912064i	$-0.365512\pi$
$809$	23.3259	0.820096	0.410048	+	0.912064i	$0.365512\pi$
$810$	−4.52944	−0.159148
$811$	−17.2923	−0.607215	−0.303607	−	0.952797i	$-0.598191\pi$
$811$	−17.2923	−0.607215	−0.303607	+	0.952797i	$0.598191\pi$
$812$	11.8688	0.416512
$813$	−57.5864	−2.01964
$814$	9.60661	0.336711
$815$	3.04738	0.106745
$816$	14.1120	0.494019
$817$	0.637886	0.0223168
$818$	−8.36968	−0.292639
$819$	4.21517	0.147290
$820$	−5.21481	−0.182109
$821$	−31.9634	−1.11553	−0.557765	−	0.829999i	$-0.688341\pi$
$821$	−31.9634	−1.11553	−0.557765	+	0.829999i	$0.688341\pi$
$822$	−37.0593	−1.29259
$823$	37.2846	1.29966	0.649829	−	0.760080i	$-0.274840\pi$
$823$	37.2846	1.29966	0.649829	+	0.760080i	$0.274840\pi$
$824$	−12.5358	−0.436706
$825$	2.66316	0.0927192
$826$	−27.2336	−0.947578
$827$	4.21071	0.146421	0.0732104	−	0.997317i	$-0.476676\pi$
$827$	4.21071	0.146421	0.0732104	+	0.997317i	$0.476676\pi$
$828$	32.8361	1.14113
$829$	25.2308	0.876301	0.438151	−	0.898902i	$-0.355634\pi$
$829$	25.2308	0.876301	0.438151	+	0.898902i	$0.355634\pi$
$830$	−14.9463	−0.518793
$831$	−71.1260	−2.46733
$832$	−0.569541	−0.0197453
$833$	−19.7622	−0.684718
$834$	3.66164	0.126792
$835$	−14.6308	−0.506318
$836$	−0.637886	−0.0220617
$837$	6.31743	0.218362
$838$	−32.5091	−1.12301
$839$	−4.53471	−0.156555	−0.0782777	−	0.996932i	$-0.524942\pi$
$839$	−4.53471	−0.156555	−0.0782777	+	0.996932i	$0.524942\pi$
$840$	−4.81624	−0.166176
$841$	14.0714	0.485220
$842$	−7.14116	−0.246101
$843$	53.8128	1.85341
$844$	−27.9750	−0.962938
$845$	−12.6756	−0.436055
$846$	−17.5813	−0.604459
$847$	−1.80847	−0.0621398
$848$	−3.99842	−0.137306
$849$	−83.9738	−2.88197
$850$	5.29897	0.181753
$851$	77.0802	2.64228
$852$	15.0569	0.515841
$853$	47.0150	1.60976	0.804881	−	0.593436i	$-0.202229\pi$
$853$	47.0150	1.60976	0.804881	+	0.593436i	$0.202229\pi$
$854$	−3.28196	−0.112306
$855$	−2.61049	−0.0892767
$856$	16.7546	0.572659
$857$	4.58623	0.156663	0.0783313	−	0.996927i	$-0.475041\pi$
$857$	4.58623	0.156663	0.0783313	+	0.996927i	$0.475041\pi$
$858$	−1.51678	−0.0517819
$859$	−5.78150	−0.197262	−0.0986312	−	0.995124i	$-0.531446\pi$
$859$	−5.78150	−0.197262	−0.0986312	+	0.995124i	$0.531446\pi$
$860$	−1.00000	−0.0340997
$861$	25.1158	0.855943
$862$	4.77895	0.162772
$863$	42.4588	1.44532	0.722658	−	0.691206i	$-0.242920\pi$
$863$	42.4588	1.44532	0.722658	+	0.691206i	$0.242920\pi$
$864$	2.90924	0.0989745
$865$	7.52284	0.255784
$866$	6.47208	0.219930
$867$	29.5054	1.00206
$868$	−3.92710	−0.133294
$869$	8.69071	0.294812
$870$	−17.4780	−0.592559
$871$	4.52351	0.153273
$872$	−3.76805	−0.127602
$873$	37.8508	1.28105
$874$	−5.11818	−0.173125
$875$	−1.80847	−0.0611375
$876$	−38.4596	−1.29943
$877$	−35.9656	−1.21447	−0.607236	−	0.794522i	$-0.707722\pi$
$877$	−35.9656	−1.21447	−0.607236	+	0.794522i	$0.707722\pi$
$878$	1.54006	0.0519744
$879$	−56.4195	−1.90298
$880$	1.00000	0.0337100
$881$	−16.7304	−0.563660	−0.281830	−	0.959464i	$-0.590941\pi$
$881$	−16.7304	−0.563660	−0.281830	+	0.959464i	$0.590941\pi$
$882$	−15.2623	−0.513910
$883$	−54.1583	−1.82257	−0.911286	−	0.411773i	$-0.864910\pi$
$883$	−54.1583	−1.82257	−0.911286	+	0.411773i	$0.864910\pi$
$884$	−3.01798	−0.101506
$885$	40.1042	1.34809
$886$	−4.76324	−0.160024
$887$	−27.3664	−0.918875	−0.459437	−	0.888210i	$-0.651949\pi$
$887$	−27.3664	−0.918875	−0.459437	+	0.888210i	$0.651949\pi$
$888$	25.5839	0.858539
$889$	−15.1918	−0.509516
$890$	6.18481	0.207315
$891$	−4.52944	−0.151742
$892$	−9.28952	−0.311036
$893$	2.74041	0.0917045
$894$	50.9313	1.70340
$895$	−21.2354	−0.709822
$896$	−1.80847	−0.0604168
$897$	−12.1701	−0.406349
$898$	31.1087	1.03811
$899$	−14.2513	−0.475307
$900$	4.09240	0.136413
$901$	−21.1875	−0.705858
$902$	−5.21481	−0.173634
$903$	4.81624	0.160275
$904$	14.7325	0.489997
$905$	7.45611	0.247849
$906$	39.1374	1.30025
$907$	27.9794	0.929042	0.464521	−	0.885562i	$-0.346226\pi$
$907$	27.9794	0.929042	0.464521	+	0.885562i	$0.346226\pi$
$908$	22.1290	0.734377
$909$	−29.7758	−0.987602
$910$	1.03000	0.0341441
$911$	45.5460	1.50901	0.754504	−	0.656296i	$-0.227878\pi$
$911$	45.5460	1.50901	0.754504	+	0.656296i	$0.227878\pi$
$912$	−1.69879	−0.0562525
$913$	−14.9463	−0.494650
$914$	12.7017	0.420135
$915$	4.83302	0.159775
$916$	21.5005	0.710398
$917$	−2.03714	−0.0672722
$918$	15.4160	0.508804
$919$	58.6492	1.93466	0.967329	−	0.253525i	$-0.0815899\pi$
$919$	58.6492	1.93466	0.967329	+	0.253525i	$0.0815899\pi$
$920$	8.02367	0.264533
$921$	12.4692	0.410873
$922$	−29.9663	−0.986887
$923$	−3.22006	−0.105990
$924$	−4.81624	−0.158443
$925$	9.60661	0.315863
$926$	28.5419	0.937946
$927$	−51.3016	−1.68497
$928$	−6.56288	−0.215437
$929$	3.87909	0.127269	0.0636344	−	0.997973i	$-0.479731\pi$
$929$	3.87909	0.127269	0.0636344	+	0.997973i	$0.479731\pi$
$930$	5.78305	0.189634
$931$	2.37895	0.0779670
$932$	24.6743	0.808233
$933$	−61.3628	−2.00893
$934$	21.0670	0.689333
$935$	5.29897	0.173295
$936$	−2.33079	−0.0761844
$937$	52.3484	1.71015	0.855073	−	0.518507i	$-0.173512\pi$
$937$	52.3484	1.71015	0.855073	+	0.518507i	$0.173512\pi$
$938$	14.3636	0.468987
$939$	−82.3161	−2.68629
$940$	−4.29609	−0.140123
$941$	16.1874	0.527695	0.263848	−	0.964564i	$-0.415008\pi$
$941$	16.1874	0.527695	0.263848	+	0.964564i	$0.415008\pi$
$942$	−23.4135	−0.762854
$943$	−41.8419	−1.36256
$944$	15.0589	0.490126
$945$	−5.26128	−0.171150
$946$	−1.00000	−0.0325128
$947$	48.8825	1.58847	0.794234	−	0.607612i	$-0.207873\pi$
$947$	48.8825	1.58847	0.794234	+	0.607612i	$0.207873\pi$
$948$	23.1447	0.751706
$949$	8.22495	0.266993
$950$	−0.637886	−0.0206957
$951$	29.8214	0.967025
$952$	−9.58304	−0.310588
$953$	−7.85715	−0.254518	−0.127259	−	0.991870i	$-0.540618\pi$
$953$	−7.85715	−0.254518	−0.127259	+	0.991870i	$0.540618\pi$
$954$	−16.3631	−0.529776
$955$	3.97014	0.128471
$956$	18.8221	0.608750
$957$	−17.4780	−0.564983
$958$	−15.6180	−0.504596
$959$	25.1659	0.812650
$960$	2.66316	0.0859530
$961$	−26.2846	−0.847890
$962$	−5.47136	−0.176404
$963$	68.5665	2.20952
$964$	−15.4771	−0.498484
$965$	−27.1516	−0.874040
$966$	−38.6439	−1.24335
$967$	34.8826	1.12175	0.560874	−	0.827901i	$-0.310465\pi$
$967$	34.8826	1.12175	0.560874	+	0.827901i	$0.310465\pi$
$968$	1.00000	0.0321412
$969$	−9.00184	−0.289181
$970$	9.24903	0.296968
$971$	31.4565	1.00949	0.504743	−	0.863270i	$-0.331587\pi$
$971$	31.4565	1.00949	0.504743	+	0.863270i	$0.331587\pi$
$972$	−20.7903	−0.666850
$973$	−2.48651	−0.0797139
$974$	−10.7687	−0.345051
$975$	−1.51678	−0.0485758
$976$	1.81477	0.0580894
$977$	−45.9562	−1.47027	−0.735135	−	0.677921i	$-0.762881\pi$
$977$	−45.9562	−1.47027	−0.735135	+	0.677921i	$0.762881\pi$
$978$	8.11564	0.259510
$979$	6.18481	0.197667
$980$	−3.72943	−0.119132
$981$	−15.4204	−0.492335
$982$	−18.4328	−0.588213
$983$	50.8860	1.62301	0.811506	−	0.584344i	$-0.198648\pi$
$983$	50.8860	1.62301	0.811506	+	0.584344i	$0.198648\pi$
$984$	−13.8879	−0.442729
$985$	5.62459	0.179214
$986$	−34.7765	−1.10751
$987$	20.6910	0.658602
$988$	0.363302	0.0115582
$989$	−8.02367	−0.255138
$990$	4.09240	0.130065
$991$	3.24437	0.103061	0.0515304	−	0.998671i	$-0.483590\pi$
$991$	3.24437	0.103061	0.0515304	+	0.998671i	$0.483590\pi$
$992$	2.17150	0.0689452
$993$	−65.4656	−2.07749
$994$	−10.2247	−0.324308
$995$	1.33397	0.0422898
$996$	−39.8043	−1.26125
$997$	19.1054	0.605075	0.302537	−	0.953138i	$-0.402166\pi$
$997$	19.1054	0.605075	0.302537	+	0.953138i	$0.402166\pi$
$998$	−29.7862	−0.942865
$999$	27.9480	0.884234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bd.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bd.1.9	✓	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.66316 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.66316 q^{6} -1.80847 q^{7} +1.00000 q^{8} +4.09240 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.66316 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.66316 q^{6} -1.80847 q^{7} +1.00000 q^{8} +4.09240 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.66316 q^{12} -0.569541 q^{13} -1.80847 q^{14} +2.66316 q^{15} +1.00000 q^{16} +5.29897 q^{17} +4.09240 q^{18} -0.637886 q^{19} +1.00000 q^{20} -4.81624 q^{21} +1.00000 q^{22} +8.02367 q^{23} +2.66316 q^{24} +1.00000 q^{25} -0.569541 q^{26} +2.90924 q^{27} -1.80847 q^{28} -6.56288 q^{29} +2.66316 q^{30} +2.17150 q^{31} +1.00000 q^{32} +2.66316 q^{33} +5.29897 q^{34} -1.80847 q^{35} +4.09240 q^{36} +9.60661 q^{37} -0.637886 q^{38} -1.51678 q^{39} +1.00000 q^{40} -5.21481 q^{41} -4.81624 q^{42} -1.00000 q^{43} +1.00000 q^{44} +4.09240 q^{45} +8.02367 q^{46} -4.29609 q^{47} +2.66316 q^{48} -3.72943 q^{49} +1.00000 q^{50} +14.1120 q^{51} -0.569541 q^{52} -3.99842 q^{53} +2.90924 q^{54} +1.00000 q^{55} -1.80847 q^{56} -1.69879 q^{57} -6.56288 q^{58} +15.0589 q^{59} +2.66316 q^{60} +1.81477 q^{61} +2.17150 q^{62} -7.40100 q^{63} +1.00000 q^{64} -0.569541 q^{65} +2.66316 q^{66} -7.94237 q^{67} +5.29897 q^{68} +21.3683 q^{69} -1.80847 q^{70} +5.65378 q^{71} +4.09240 q^{72} -14.4414 q^{73} +9.60661 q^{74} +2.66316 q^{75} -0.637886 q^{76} -1.80847 q^{77} -1.51678 q^{78} +8.69071 q^{79} +1.00000 q^{80} -4.52944 q^{81} -5.21481 q^{82} -14.9463 q^{83} -4.81624 q^{84} +5.29897 q^{85} -1.00000 q^{86} -17.4780 q^{87} +1.00000 q^{88} +6.18481 q^{89} +4.09240 q^{90} +1.03000 q^{91} +8.02367 q^{92} +5.78305 q^{93} -4.29609 q^{94} -0.637886 q^{95} +2.66316 q^{96} +9.24903 q^{97} -3.72943 q^{98} +4.09240 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9	\( 11 q + 11 q^{2} + 3 q^{3} + 11 q^{4} + 11 q^{5} + 3 q^{6} + 5 q^{7} + 11 q^{8} + 26 q^{9} + 11 q^{10} + 11 q^{11} + 3 q^{12} + q^{13} + 5 q^{14} + 3 q^{15} + 11 q^{16} + 8 q^{17} + 26 q^{18} + q^{19} + 11 q^{20} + 11 q^{22} + 20 q^{23} + 3 q^{24} + 11 q^{25} + q^{26} + 18 q^{27} + 5 q^{28} + 9 q^{29} + 3 q^{30} + 12 q^{31} + 11 q^{32} + 3 q^{33} + 8 q^{34} + 5 q^{35} + 26 q^{36} + 19 q^{37} + q^{38} - 18 q^{39} + 11 q^{40} + 9 q^{41} - 11 q^{43} + 11 q^{44} + 26 q^{45} + 20 q^{46} + 15 q^{47} + 3 q^{48} + 2 q^{49} + 11 q^{50} - 25 q^{51} + q^{52} + 35 q^{53} + 18 q^{54} + 11 q^{55} + 5 q^{56} - 25 q^{57} + 9 q^{58} + 13 q^{59} + 3 q^{60} + 9 q^{61} + 12 q^{62} + 22 q^{63} + 11 q^{64} + q^{65} + 3 q^{66} - q^{67} + 8 q^{68} + 12 q^{69} + 5 q^{70} + 14 q^{71} + 26 q^{72} - 20 q^{73} + 19 q^{74} + 3 q^{75} + q^{76} + 5 q^{77} - 18 q^{78} - 23 q^{79} + 11 q^{80} + 71 q^{81} + 9 q^{82} + 12 q^{83} + 8 q^{85} - 11 q^{86} + 6 q^{87} + 11 q^{88} - q^{89} + 26 q^{90} - 17 q^{91} + 20 q^{92} + 7 q^{93} + 15 q^{94} + q^{95} + 3 q^{96} + 17 q^{97} + 2 q^{98} + 26 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 + 3 * q^3 + 11 * q^4 + 11 * q^5 + 3 * q^6 + 5 * q^7 + 11 * q^8 + 26 * q^9 + 11 * q^10 + 11 * q^11 + 3 * q^12 + q^13 + 5 * q^14 + 3 * q^15 + 11 * q^16 + 8 * q^17 + 26 * q^18 + q^19 + 11 * q^20 + 11 * q^22 + 20 * q^23 + 3 * q^24 + 11 * q^25 + q^26 + 18 * q^27 + 5 * q^28 + 9 * q^29 + 3 * q^30 + 12 * q^31 + 11 * q^32 + 3 * q^33 + 8 * q^34 + 5 * q^35 + 26 * q^36 + 19 * q^37 + q^38 - 18 * q^39 + 11 * q^40 + 9 * q^41 - 11 * q^43 + 11 * q^44 + 26 * q^45 + 20 * q^46 + 15 * q^47 + 3 * q^48 + 2 * q^49 + 11 * q^50 - 25 * q^51 + q^52 + 35 * q^53 + 18 * q^54 + 11 * q^55 + 5 * q^56 - 25 * q^57 + 9 * q^58 + 13 * q^59 + 3 * q^60 + 9 * q^61 + 12 * q^62 + 22 * q^63 + 11 * q^64 + q^65 + 3 * q^66 - q^67 + 8 * q^68 + 12 * q^69 + 5 * q^70 + 14 * q^71 + 26 * q^72 - 20 * q^73 + 19 * q^74 + 3 * q^75 + q^76 + 5 * q^77 - 18 * q^78 - 23 * q^79 + 11 * q^80 + 71 * q^81 + 9 * q^82 + 12 * q^83 + 8 * q^85 - 11 * q^86 + 6 * q^87 + 11 * q^88 - q^89 + 26 * q^90 - 17 * q^91 + 20 * q^92 + 7 * q^93 + 15 * q^94 + q^95 + 3 * q^96 + 17 * q^97 + 2 * q^98 + 26 * q^99

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