LMFDB - Embedded newform 4730.2.a.y.1.7

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} - 6x^{5} + 46x^{4} + 26x^{3} - 52x^{2} - 20x + 20 $ x^8 - 13x^6 - 6x^5 + 46x^4 + 26x^3 - 52x^2 - 20x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.24275$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.54582 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.54582 q^{6} +1.88573 q^{7} -1.00000 q^{8} +3.48118 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.54582 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.54582 q^{6} +1.88573 q^{7} -1.00000 q^{8} +3.48118 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.54582 q^{12} +4.02188 q^{13} -1.88573 q^{14} +2.54582 q^{15} +1.00000 q^{16} -1.30952 q^{17} -3.48118 q^{18} +3.46884 q^{19} +1.00000 q^{20} +4.80073 q^{21} +1.00000 q^{22} +9.00897 q^{23} -2.54582 q^{24} +1.00000 q^{25} -4.02188 q^{26} +1.22499 q^{27} +1.88573 q^{28} +2.56866 q^{29} -2.54582 q^{30} -0.578666 q^{31} -1.00000 q^{32} -2.54582 q^{33} +1.30952 q^{34} +1.88573 q^{35} +3.48118 q^{36} -3.03228 q^{37} -3.46884 q^{38} +10.2390 q^{39} -1.00000 q^{40} +7.32408 q^{41} -4.80073 q^{42} -1.00000 q^{43} -1.00000 q^{44} +3.48118 q^{45} -9.00897 q^{46} -5.84380 q^{47} +2.54582 q^{48} -3.44401 q^{49} -1.00000 q^{50} -3.33381 q^{51} +4.02188 q^{52} -1.34973 q^{53} -1.22499 q^{54} -1.00000 q^{55} -1.88573 q^{56} +8.83103 q^{57} -2.56866 q^{58} -7.46945 q^{59} +2.54582 q^{60} -11.1010 q^{61} +0.578666 q^{62} +6.56457 q^{63} +1.00000 q^{64} +4.02188 q^{65} +2.54582 q^{66} -3.85628 q^{67} -1.30952 q^{68} +22.9352 q^{69} -1.88573 q^{70} +3.78619 q^{71} -3.48118 q^{72} +7.39622 q^{73} +3.03228 q^{74} +2.54582 q^{75} +3.46884 q^{76} -1.88573 q^{77} -10.2390 q^{78} +9.14400 q^{79} +1.00000 q^{80} -7.32494 q^{81} -7.32408 q^{82} -10.3109 q^{83} +4.80073 q^{84} -1.30952 q^{85} +1.00000 q^{86} +6.53933 q^{87} +1.00000 q^{88} -15.2229 q^{89} -3.48118 q^{90} +7.58419 q^{91} +9.00897 q^{92} -1.47318 q^{93} +5.84380 q^{94} +3.46884 q^{95} -2.54582 q^{96} +8.82093 q^{97} +3.44401 q^{98} -3.48118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9	\( 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9} - 8 q^{10} - 8 q^{11} + 3 q^{12} + 6 q^{13} - 11 q^{14} + 3 q^{15} + 8 q^{16} + 9 q^{17} - 3 q^{18} + 9 q^{19} + 8 q^{20} + 21 q^{21} + 8 q^{22} - 2 q^{23} - 3 q^{24} + 8 q^{25} - 6 q^{26} + 24 q^{27} + 11 q^{28} - 10 q^{29} - 3 q^{30} + 6 q^{31} - 8 q^{32} - 3 q^{33} - 9 q^{34} + 11 q^{35} + 3 q^{36} + 16 q^{37} - 9 q^{38} + 6 q^{39} - 8 q^{40} - 4 q^{41} - 21 q^{42} - 8 q^{43} - 8 q^{44} + 3 q^{45} + 2 q^{46} - 11 q^{47} + 3 q^{48} + 11 q^{49} - 8 q^{50} + 38 q^{51} + 6 q^{52} - 15 q^{53} - 24 q^{54} - 8 q^{55} - 11 q^{56} - 2 q^{57} + 10 q^{58} - 7 q^{59} + 3 q^{60} + 2 q^{61} - 6 q^{62} + 33 q^{63} + 8 q^{64} + 6 q^{65} + 3 q^{66} + 4 q^{67} + 9 q^{68} - 4 q^{69} - 11 q^{70} - 3 q^{71} - 3 q^{72} + 32 q^{73} - 16 q^{74} + 3 q^{75} + 9 q^{76} - 11 q^{77} - 6 q^{78} + 45 q^{79} + 8 q^{80} + 20 q^{81} + 4 q^{82} + 39 q^{83} + 21 q^{84} + 9 q^{85} + 8 q^{86} + 2 q^{87} + 8 q^{88} - 22 q^{89} - 3 q^{90} + 18 q^{91} - 2 q^{92} + 18 q^{93} + 11 q^{94} + 9 q^{95} - 3 q^{96} + 30 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9 - 8 * q^10 - 8 * q^11 + 3 * q^12 + 6 * q^13 - 11 * q^14 + 3 * q^15 + 8 * q^16 + 9 * q^17 - 3 * q^18 + 9 * q^19 + 8 * q^20 + 21 * q^21 + 8 * q^22 - 2 * q^23 - 3 * q^24 + 8 * q^25 - 6 * q^26 + 24 * q^27 + 11 * q^28 - 10 * q^29 - 3 * q^30 + 6 * q^31 - 8 * q^32 - 3 * q^33 - 9 * q^34 + 11 * q^35 + 3 * q^36 + 16 * q^37 - 9 * q^38 + 6 * q^39 - 8 * q^40 - 4 * q^41 - 21 * q^42 - 8 * q^43 - 8 * q^44 + 3 * q^45 + 2 * q^46 - 11 * q^47 + 3 * q^48 + 11 * q^49 - 8 * q^50 + 38 * q^51 + 6 * q^52 - 15 * q^53 - 24 * q^54 - 8 * q^55 - 11 * q^56 - 2 * q^57 + 10 * q^58 - 7 * q^59 + 3 * q^60 + 2 * q^61 - 6 * q^62 + 33 * q^63 + 8 * q^64 + 6 * q^65 + 3 * q^66 + 4 * q^67 + 9 * q^68 - 4 * q^69 - 11 * q^70 - 3 * q^71 - 3 * q^72 + 32 * q^73 - 16 * q^74 + 3 * q^75 + 9 * q^76 - 11 * q^77 - 6 * q^78 + 45 * q^79 + 8 * q^80 + 20 * q^81 + 4 * q^82 + 39 * q^83 + 21 * q^84 + 9 * q^85 + 8 * q^86 + 2 * q^87 + 8 * q^88 - 22 * q^89 - 3 * q^90 + 18 * q^91 - 2 * q^92 + 18 * q^93 + 11 * q^94 + 9 * q^95 - 3 * q^96 + 30 * q^97 - 11 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.54582	1.46983	0.734914	−	0.678161i	$-0.237223\pi$
$3$	2.54582	1.46983	0.734914	+	0.678161i	$0.237223\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.54582	−1.03932
$7$	1.88573	0.712740	0.356370	−	0.934345i	$-0.384014\pi$
$7$	1.88573	0.712740	0.356370	+	0.934345i	$0.384014\pi$
$8$	−1.00000	−0.353553
$9$	3.48118	1.16039
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.54582	0.734914
$13$	4.02188	1.11547	0.557734	−	0.830020i	$-0.311671\pi$
$13$	4.02188	1.11547	0.557734	+	0.830020i	$0.311671\pi$
$14$	−1.88573	−0.503983
$15$	2.54582	0.657327
$16$	1.00000	0.250000
$17$	−1.30952	−0.317606	−0.158803	−	0.987310i	$-0.550764\pi$
$17$	−1.30952	−0.317606	−0.158803	+	0.987310i	$0.550764\pi$
$18$	−3.48118	−0.820521
$19$	3.46884	0.795807	0.397903	−	0.917427i	$-0.369738\pi$
$19$	3.46884	0.795807	0.397903	+	0.917427i	$0.369738\pi$
$20$	1.00000	0.223607
$21$	4.80073	1.04760
$22$	1.00000	0.213201
$23$	9.00897	1.87850	0.939250	−	0.343234i	$-0.111522\pi$
$23$	9.00897	1.87850	0.939250	+	0.343234i	$0.111522\pi$
$24$	−2.54582	−0.519662
$25$	1.00000	0.200000
$26$	−4.02188	−0.788755
$27$	1.22499	0.235749
$28$	1.88573	0.356370
$29$	2.56866	0.476988	0.238494	−	0.971144i	$-0.423346\pi$
$29$	2.56866	0.476988	0.238494	+	0.971144i	$0.423346\pi$
$30$	−2.54582	−0.464800
$31$	−0.578666	−0.103932	−0.0519658	−	0.998649i	$-0.516549\pi$
$31$	−0.578666	−0.103932	−0.0519658	+	0.998649i	$0.516549\pi$
$32$	−1.00000	−0.176777
$33$	−2.54582	−0.443170
$34$	1.30952	0.224582
$35$	1.88573	0.318747
$36$	3.48118	0.580196
$37$	−3.03228	−0.498504	−0.249252	−	0.968439i	$-0.580185\pi$
$37$	−3.03228	−0.498504	−0.249252	+	0.968439i	$0.580185\pi$
$38$	−3.46884	−0.562720
$39$	10.2390	1.63955
$40$	−1.00000	−0.158114
$41$	7.32408	1.14383	0.571914	−	0.820313i	$-0.306201\pi$
$41$	7.32408	1.14383	0.571914	+	0.820313i	$0.306201\pi$
$42$	−4.80073	−0.740769
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	3.48118	0.518943
$46$	−9.00897	−1.32830
$47$	−5.84380	−0.852405	−0.426203	−	0.904628i	$-0.640149\pi$
$47$	−5.84380	−0.852405	−0.426203	+	0.904628i	$0.640149\pi$
$48$	2.54582	0.367457
$49$	−3.44401	−0.492002
$50$	−1.00000	−0.141421
$51$	−3.33381	−0.466826
$52$	4.02188	0.557734
$53$	−1.34973	−0.185400	−0.0927000	−	0.995694i	$-0.529550\pi$
$53$	−1.34973	−0.185400	−0.0927000	+	0.995694i	$0.529550\pi$
$54$	−1.22499	−0.166700
$55$	−1.00000	−0.134840
$56$	−1.88573	−0.251992
$57$	8.83103	1.16970
$58$	−2.56866	−0.337281
$59$	−7.46945	−0.972440	−0.486220	−	0.873836i	$-0.661625\pi$
$59$	−7.46945	−0.972440	−0.486220	+	0.873836i	$0.661625\pi$
$60$	2.54582	0.328663
$61$	−11.1010	−1.42134	−0.710669	−	0.703527i	$-0.751608\pi$
$61$	−11.1010	−1.42134	−0.710669	+	0.703527i	$0.751608\pi$
$62$	0.578666	0.0734907
$63$	6.56457	0.827058
$64$	1.00000	0.125000
$65$	4.02188	0.498852
$66$	2.54582	0.313368
$67$	−3.85628	−0.471120	−0.235560	−	0.971860i	$-0.575692\pi$
$67$	−3.85628	−0.471120	−0.235560	+	0.971860i	$0.575692\pi$
$68$	−1.30952	−0.158803
$69$	22.9352	2.76107
$70$	−1.88573	−0.225388
$71$	3.78619	0.449338	0.224669	−	0.974435i	$-0.427870\pi$
$71$	3.78619	0.449338	0.224669	+	0.974435i	$0.427870\pi$
$72$	−3.48118	−0.410261
$73$	7.39622	0.865663	0.432831	−	0.901475i	$-0.357515\pi$
$73$	7.39622	0.865663	0.432831	+	0.901475i	$0.357515\pi$
$74$	3.03228	0.352495
$75$	2.54582	0.293965
$76$	3.46884	0.397903
$77$	−1.88573	−0.214899
$78$	−10.2390	−1.15933
$79$	9.14400	1.02878	0.514390	−	0.857556i	$-0.328018\pi$
$79$	9.14400	1.02878	0.514390	+	0.857556i	$0.328018\pi$
$80$	1.00000	0.111803
$81$	−7.32494	−0.813882
$82$	−7.32408	−0.808809
$83$	−10.3109	−1.13176	−0.565882	−	0.824486i	$-0.691464\pi$
$83$	−10.3109	−1.13176	−0.565882	+	0.824486i	$0.691464\pi$
$84$	4.80073	0.523802
$85$	−1.30952	−0.142038
$86$	1.00000	0.107833
$87$	6.53933	0.701090
$88$	1.00000	0.106600
$89$	−15.2229	−1.61363	−0.806813	−	0.590807i	$-0.798809\pi$
$89$	−15.2229	−1.61363	−0.806813	+	0.590807i	$0.798809\pi$
$90$	−3.48118	−0.366948
$91$	7.58419	0.795039
$92$	9.00897	0.939250
$93$	−1.47318	−0.152761
$94$	5.84380	0.602742
$95$	3.46884	0.355896
$96$	−2.54582	−0.259831
$97$	8.82093	0.895630	0.447815	−	0.894126i	$-0.352202\pi$
$97$	8.82093	0.895630	0.447815	+	0.894126i	$0.352202\pi$
$98$	3.44401	0.347898
$99$	−3.48118	−0.349872
$100$	1.00000	0.100000
$101$	17.5879	1.75006	0.875030	−	0.484068i	$-0.160841\pi$
$101$	17.5879	1.75006	0.875030	+	0.484068i	$0.160841\pi$
$102$	3.33381	0.330096
$103$	13.8177	1.36150	0.680750	−	0.732516i	$-0.261654\pi$
$103$	13.8177	1.36150	0.680750	+	0.732516i	$0.261654\pi$
$104$	−4.02188	−0.394377
$105$	4.80073	0.468503
$106$	1.34973	0.131098
$107$	−17.9699	−1.73721	−0.868606	−	0.495504i	$-0.834983\pi$
$107$	−17.9699	−1.73721	−0.868606	+	0.495504i	$0.834983\pi$
$108$	1.22499	0.117875
$109$	2.83424	0.271471	0.135736	−	0.990745i	$-0.456660\pi$
$109$	2.83424	0.271471	0.135736	+	0.990745i	$0.456660\pi$
$110$	1.00000	0.0953463
$111$	−7.71963	−0.732715
$112$	1.88573	0.178185
$113$	−18.5804	−1.74789	−0.873946	−	0.486022i	$-0.838447\pi$
$113$	−18.5804	−1.74789	−0.873946	+	0.486022i	$0.838447\pi$
$114$	−8.83103	−0.827102
$115$	9.00897	0.840091
$116$	2.56866	0.238494
$117$	14.0009	1.29438
$118$	7.46945	0.687619
$119$	−2.46941	−0.226371
$120$	−2.54582	−0.232400
$121$	1.00000	0.0909091
$122$	11.1010	1.00504
$123$	18.6458	1.68123
$124$	−0.578666	−0.0519658
$125$	1.00000	0.0894427
$126$	−6.56457	−0.584819
$127$	−13.3389	−1.18364	−0.591818	−	0.806072i	$-0.701590\pi$
$127$	−13.3389	−1.18364	−0.591818	+	0.806072i	$0.701590\pi$
$128$	−1.00000	−0.0883883
$129$	−2.54582	−0.224147
$130$	−4.02188	−0.352742
$131$	14.4886	1.26587	0.632937	−	0.774203i	$-0.281849\pi$
$131$	14.4886	1.26587	0.632937	+	0.774203i	$0.281849\pi$
$132$	−2.54582	−0.221585
$133$	6.54131	0.567203
$134$	3.85628	0.333132
$135$	1.22499	0.105430
$136$	1.30952	0.112291
$137$	2.86988	0.245191	0.122595	−	0.992457i	$-0.460878\pi$
$137$	2.86988	0.245191	0.122595	+	0.992457i	$0.460878\pi$
$138$	−22.9352	−1.95237
$139$	11.7871	0.999768	0.499884	−	0.866092i	$-0.333376\pi$
$139$	11.7871	0.999768	0.499884	+	0.866092i	$0.333376\pi$
$140$	1.88573	0.159374
$141$	−14.8772	−1.25289
$142$	−3.78619	−0.317730
$143$	−4.02188	−0.336326
$144$	3.48118	0.290098
$145$	2.56866	0.213316
$146$	−7.39622	−0.612116
$147$	−8.76782	−0.723157
$148$	−3.03228	−0.249252
$149$	15.3007	1.25348	0.626742	−	0.779227i	$-0.284388\pi$
$149$	15.3007	1.25348	0.626742	+	0.779227i	$0.284388\pi$
$150$	−2.54582	−0.207865
$151$	−3.70288	−0.301336	−0.150668	−	0.988584i	$-0.548142\pi$
$151$	−3.70288	−0.301336	−0.150668	+	0.988584i	$0.548142\pi$
$152$	−3.46884	−0.281360
$153$	−4.55869	−0.368548
$154$	1.88573	0.151957
$155$	−0.578666	−0.0464796
$156$	10.2390	0.819773
$157$	−3.86398	−0.308379	−0.154190	−	0.988041i	$-0.549277\pi$
$157$	−3.86398	−0.308379	−0.154190	+	0.988041i	$0.549277\pi$
$158$	−9.14400	−0.727458
$159$	−3.43617	−0.272506
$160$	−1.00000	−0.0790569
$161$	16.9885	1.33888
$162$	7.32494	0.575501
$163$	20.7557	1.62571	0.812856	−	0.582464i	$-0.197911\pi$
$163$	20.7557	1.62571	0.812856	+	0.582464i	$0.197911\pi$
$164$	7.32408	0.571914
$165$	−2.54582	−0.198191
$166$	10.3109	0.800278
$167$	−18.3858	−1.42273	−0.711367	−	0.702821i	$-0.751924\pi$
$167$	−18.3858	−1.42273	−0.711367	+	0.702821i	$0.751924\pi$
$168$	−4.80073	−0.370384
$169$	3.17549	0.244269
$170$	1.30952	0.100436
$171$	12.0757	0.923448
$172$	−1.00000	−0.0762493
$173$	20.1718	1.53364	0.766818	−	0.641864i	$-0.221839\pi$
$173$	20.1718	1.53364	0.766818	+	0.641864i	$0.221839\pi$
$174$	−6.53933	−0.495746
$175$	1.88573	0.142548
$176$	−1.00000	−0.0753778
$177$	−19.0159	−1.42932
$178$	15.2229	1.14101
$179$	4.82989	0.361003	0.180502	−	0.983575i	$-0.442228\pi$
$179$	4.82989	0.361003	0.180502	+	0.983575i	$0.442228\pi$
$180$	3.48118	0.259472
$181$	−8.79785	−0.653939	−0.326969	−	0.945035i	$-0.606027\pi$
$181$	−8.79785	−0.653939	−0.326969	+	0.945035i	$0.606027\pi$
$182$	−7.58419	−0.562177
$183$	−28.2611	−2.08912
$184$	−9.00897	−0.664150
$185$	−3.03228	−0.222938
$186$	1.47318	0.108019
$187$	1.30952	0.0957619
$188$	−5.84380	−0.426203
$189$	2.31000	0.168028
$190$	−3.46884	−0.251656
$191$	−25.8139	−1.86783	−0.933915	−	0.357496i	$-0.883631\pi$
$191$	−25.8139	−1.86783	−0.933915	+	0.357496i	$0.883631\pi$
$192$	2.54582	0.183728
$193$	12.9052	0.928938	0.464469	−	0.885589i	$-0.346245\pi$
$193$	12.9052	0.928938	0.464469	+	0.885589i	$0.346245\pi$
$194$	−8.82093	−0.633306
$195$	10.2390	0.733227
$196$	−3.44401	−0.246001
$197$	9.37465	0.667916	0.333958	−	0.942588i	$-0.391616\pi$
$197$	9.37465	0.667916	0.333958	+	0.942588i	$0.391616\pi$
$198$	3.48118	0.247397
$199$	27.2377	1.93083	0.965415	−	0.260720i	$-0.0839598\pi$
$199$	27.2377	1.93083	0.965415	+	0.260720i	$0.0839598\pi$
$200$	−1.00000	−0.0707107
$201$	−9.81739	−0.692465
$202$	−17.5879	−1.23748
$203$	4.84381	0.339968
$204$	−3.33381	−0.233413
$205$	7.32408	0.511536
$206$	−13.8177	−0.962726
$207$	31.3618	2.17980
$208$	4.02188	0.278867
$209$	−3.46884	−0.239945
$210$	−4.80073	−0.331282
$211$	−6.15703	−0.423867	−0.211934	−	0.977284i	$-0.567976\pi$
$211$	−6.15703	−0.423867	−0.211934	+	0.977284i	$0.567976\pi$
$212$	−1.34973	−0.0927000
$213$	9.63894	0.660450
$214$	17.9699	1.22839
$215$	−1.00000	−0.0681994
$216$	−1.22499	−0.0833500
$217$	−1.09121	−0.0740762
$218$	−2.83424	−0.191959
$219$	18.8294	1.27237
$220$	−1.00000	−0.0674200
$221$	−5.26674	−0.354280
$222$	7.71963	0.518108
$223$	24.5836	1.64624	0.823120	−	0.567867i	$-0.192231\pi$
$223$	24.5836	1.64624	0.823120	+	0.567867i	$0.192231\pi$
$224$	−1.88573	−0.125996
$225$	3.48118	0.232079
$226$	18.5804	1.23595
$227$	−1.28819	−0.0854999	−0.0427500	−	0.999086i	$-0.513612\pi$
$227$	−1.28819	−0.0854999	−0.0427500	+	0.999086i	$0.513612\pi$
$228$	8.83103	0.584849
$229$	6.34291	0.419152	0.209576	−	0.977792i	$-0.432792\pi$
$229$	6.34291	0.419152	0.209576	+	0.977792i	$0.432792\pi$
$230$	−9.00897	−0.594034
$231$	−4.80073	−0.315865
$232$	−2.56866	−0.168641
$233$	10.3313	0.676824	0.338412	−	0.940998i	$-0.390110\pi$
$233$	10.3313	0.676824	0.338412	+	0.940998i	$0.390110\pi$
$234$	−14.0009	−0.915265
$235$	−5.84380	−0.381207
$236$	−7.46945	−0.486220
$237$	23.2789	1.51213
$238$	2.46941	0.160068
$239$	6.32585	0.409185	0.204593	−	0.978847i	$-0.434413\pi$
$239$	6.32585	0.409185	0.204593	+	0.978847i	$0.434413\pi$
$240$	2.54582	0.164332
$241$	−8.02708	−0.517070	−0.258535	−	0.966002i	$-0.583240\pi$
$241$	−8.02708	−0.517070	−0.258535	+	0.966002i	$0.583240\pi$
$242$	−1.00000	−0.0642824
$243$	−22.3229	−1.43201
$244$	−11.1010	−0.710669
$245$	−3.44401	−0.220030
$246$	−18.6458	−1.18881
$247$	13.9513	0.887697
$248$	0.578666	0.0367454
$249$	−26.2496	−1.66350
$250$	−1.00000	−0.0632456
$251$	−18.1796	−1.14748	−0.573742	−	0.819036i	$-0.694509\pi$
$251$	−18.1796	−1.14748	−0.573742	+	0.819036i	$0.694509\pi$
$252$	6.56457	0.413529
$253$	−9.00897	−0.566389
$254$	13.3389	0.836957
$255$	−3.33381	−0.208771
$256$	1.00000	0.0625000
$257$	−15.3465	−0.957288	−0.478644	−	0.878009i	$-0.658872\pi$
$257$	−15.3465	−0.957288	−0.478644	+	0.878009i	$0.658872\pi$
$258$	2.54582	0.158496
$259$	−5.71807	−0.355304
$260$	4.02188	0.249426
$261$	8.94196	0.553493
$262$	−14.4886	−0.895108
$263$	−24.9263	−1.53702	−0.768511	−	0.639837i	$-0.779002\pi$
$263$	−24.9263	−1.53702	−0.768511	+	0.639837i	$0.779002\pi$
$264$	2.54582	0.156684
$265$	−1.34973	−0.0829134
$266$	−6.54131	−0.401073
$267$	−38.7547	−2.37175
$268$	−3.85628	−0.235560
$269$	−25.4536	−1.55193	−0.775966	−	0.630775i	$-0.782737\pi$
$269$	−25.4536	−1.55193	−0.775966	+	0.630775i	$0.782737\pi$
$270$	−1.22499	−0.0745505
$271$	16.8479	1.02344	0.511719	−	0.859153i	$-0.329009\pi$
$271$	16.8479	1.02344	0.511719	+	0.859153i	$0.329009\pi$
$272$	−1.30952	−0.0794016
$273$	19.3079	1.16857
$274$	−2.86988	−0.173376
$275$	−1.00000	−0.0603023
$276$	22.9352	1.38054
$277$	14.6537	0.880456	0.440228	−	0.897886i	$-0.354898\pi$
$277$	14.6537	0.880456	0.440228	+	0.897886i	$0.354898\pi$
$278$	−11.7871	−0.706943
$279$	−2.01444	−0.120601
$280$	−1.88573	−0.112694
$281$	−11.1561	−0.665520	−0.332760	−	0.943012i	$-0.607980\pi$
$281$	−11.1561	−0.665520	−0.332760	+	0.943012i	$0.607980\pi$
$282$	14.8772	0.885926
$283$	−14.3015	−0.850136	−0.425068	−	0.905161i	$-0.639750\pi$
$283$	−14.3015	−0.850136	−0.425068	+	0.905161i	$0.639750\pi$
$284$	3.78619	0.224669
$285$	8.83103	0.523105
$286$	4.02188	0.237819
$287$	13.8113	0.815253
$288$	−3.48118	−0.205130
$289$	−15.2851	−0.899126
$290$	−2.56866	−0.150837
$291$	22.4565	1.31642
$292$	7.39622	0.432831
$293$	−19.8150	−1.15760	−0.578802	−	0.815468i	$-0.696480\pi$
$293$	−19.8150	−1.15760	−0.578802	+	0.815468i	$0.696480\pi$
$294$	8.76782	0.511349
$295$	−7.46945	−0.434888
$296$	3.03228	0.176248
$297$	−1.22499	−0.0710811
$298$	−15.3007	−0.886347
$299$	36.2330	2.09541
$300$	2.54582	0.146983
$301$	−1.88573	−0.108692
$302$	3.70288	0.213077
$303$	44.7755	2.57229
$304$	3.46884	0.198952
$305$	−11.1010	−0.635642
$306$	4.55869	0.260603
$307$	10.9313	0.623883	0.311941	−	0.950101i	$-0.399021\pi$
$307$	10.9313	0.623883	0.311941	+	0.950101i	$0.399021\pi$
$308$	−1.88573	−0.107450
$309$	35.1774	2.00117
$310$	0.578666	0.0328660
$311$	−3.59952	−0.204110	−0.102055	−	0.994779i	$-0.532542\pi$
$311$	−3.59952	−0.204110	−0.102055	+	0.994779i	$0.532542\pi$
$312$	−10.2390	−0.579667
$313$	−10.2185	−0.577585	−0.288792	−	0.957392i	$-0.593254\pi$
$313$	−10.2185	−0.577585	−0.288792	+	0.957392i	$0.593254\pi$
$314$	3.86398	0.218057
$315$	6.56457	0.369872
$316$	9.14400	0.514390
$317$	−19.7247	−1.10785	−0.553926	−	0.832566i	$-0.686871\pi$
$317$	−19.7247	−1.10785	−0.553926	+	0.832566i	$0.686871\pi$
$318$	3.43617	0.192691
$319$	−2.56866	−0.143817
$320$	1.00000	0.0559017
$321$	−45.7479	−2.55340
$322$	−16.9885	−0.946733
$323$	−4.54253	−0.252753
$324$	−7.32494	−0.406941
$325$	4.02188	0.223094
$326$	−20.7557	−1.14955
$327$	7.21546	0.399016
$328$	−7.32408	−0.404405
$329$	−11.0198	−0.607544
$330$	2.54582	0.140143
$331$	26.8913	1.47808	0.739040	−	0.673661i	$-0.235279\pi$
$331$	26.8913	1.47808	0.739040	+	0.673661i	$0.235279\pi$
$332$	−10.3109	−0.565882
$333$	−10.5559	−0.578460
$334$	18.3858	1.00603
$335$	−3.85628	−0.210691
$336$	4.80073	0.261901
$337$	18.4909	1.00726	0.503632	−	0.863919i	$-0.331997\pi$
$337$	18.4909	1.00726	0.503632	+	0.863919i	$0.331997\pi$
$338$	−3.17549	−0.172724
$339$	−47.3022	−2.56910
$340$	−1.30952	−0.0710189
$341$	0.578666	0.0313365
$342$	−12.0757	−0.652976
$343$	−19.6946	−1.06341
$344$	1.00000	0.0539164
$345$	22.9352	1.23479
$346$	−20.1718	−1.08444
$347$	35.7798	1.92076	0.960380	−	0.278694i	$-0.0899015\pi$
$347$	35.7798	1.92076	0.960380	+	0.278694i	$0.0899015\pi$
$348$	6.53933	0.350545
$349$	31.2632	1.67348	0.836740	−	0.547600i	$-0.184459\pi$
$349$	31.2632	1.67348	0.836740	+	0.547600i	$0.184459\pi$
$350$	−1.88573	−0.100797
$351$	4.92676	0.262971
$352$	1.00000	0.0533002
$353$	23.4108	1.24603	0.623016	−	0.782209i	$-0.285907\pi$
$353$	23.4108	1.24603	0.623016	+	0.782209i	$0.285907\pi$
$354$	19.0159	1.01068
$355$	3.78619	0.200950
$356$	−15.2229	−0.806813
$357$	−6.28667	−0.332726
$358$	−4.82989	−0.255268
$359$	4.81585	0.254171	0.127085	−	0.991892i	$-0.459438\pi$
$359$	4.81585	0.254171	0.127085	+	0.991892i	$0.459438\pi$
$360$	−3.48118	−0.183474
$361$	−6.96714	−0.366692
$362$	8.79785	0.462405
$363$	2.54582	0.133621
$364$	7.58419	0.397519
$365$	7.39622	0.387136
$366$	28.2611	1.47723
$367$	13.3164	0.695110	0.347555	−	0.937660i	$-0.387012\pi$
$367$	13.3164	0.695110	0.347555	+	0.937660i	$0.387012\pi$
$368$	9.00897	0.469625
$369$	25.4964	1.32729
$370$	3.03228	0.157641
$371$	−2.54523	−0.132142
$372$	−1.47318	−0.0763807
$373$	−4.76510	−0.246728	−0.123364	−	0.992362i	$-0.539368\pi$
$373$	−4.76510	−0.246728	−0.123364	+	0.992362i	$0.539368\pi$
$374$	−1.30952	−0.0677139
$375$	2.54582	0.131465
$376$	5.84380	0.301371
$377$	10.3308	0.532065
$378$	−2.31000	−0.118814
$379$	−35.9696	−1.84764	−0.923818	−	0.382833i	$-0.874949\pi$
$379$	−35.9696	−1.84764	−0.923818	+	0.382833i	$0.874949\pi$
$380$	3.46884	0.177948
$381$	−33.9584	−1.73974
$382$	25.8139	1.32075
$383$	−8.54489	−0.436623	−0.218312	−	0.975879i	$-0.570055\pi$
$383$	−8.54489	−0.436623	−0.218312	+	0.975879i	$0.570055\pi$
$384$	−2.54582	−0.129916
$385$	−1.88573	−0.0961059
$386$	−12.9052	−0.656858
$387$	−3.48118	−0.176958
$388$	8.82093	0.447815
$389$	−20.0156	−1.01483	−0.507416	−	0.861701i	$-0.669399\pi$
$389$	−20.0156	−1.01483	−0.507416	+	0.861701i	$0.669399\pi$
$390$	−10.2390	−0.518470
$391$	−11.7975	−0.596623
$392$	3.44401	0.173949
$393$	36.8853	1.86062
$394$	−9.37465	−0.472288
$395$	9.14400	0.460085
$396$	−3.48118	−0.174936
$397$	−5.66695	−0.284416	−0.142208	−	0.989837i	$-0.545420\pi$
$397$	−5.66695	−0.284416	−0.142208	+	0.989837i	$0.545420\pi$
$398$	−27.2377	−1.36530
$399$	16.6530	0.833691
$400$	1.00000	0.0500000
$401$	−5.73776	−0.286530	−0.143265	−	0.989684i	$-0.545760\pi$
$401$	−5.73776	−0.286530	−0.143265	+	0.989684i	$0.545760\pi$
$402$	9.81739	0.489647
$403$	−2.32732	−0.115932
$404$	17.5879	0.875030
$405$	−7.32494	−0.363979
$406$	−4.84381	−0.240394
$407$	3.03228	0.150305
$408$	3.33381	0.165048
$409$	−21.2782	−1.05214	−0.526069	−	0.850442i	$-0.676335\pi$
$409$	−21.2782	−1.05214	−0.526069	+	0.850442i	$0.676335\pi$
$410$	−7.32408	−0.361710
$411$	7.30620	0.360388
$412$	13.8177	0.680750
$413$	−14.0854	−0.693097
$414$	−31.3618	−1.54135
$415$	−10.3109	−0.506140
$416$	−4.02188	−0.197189
$417$	30.0078	1.46949
$418$	3.46884	0.169667
$419$	−6.69994	−0.327313	−0.163657	−	0.986517i	$-0.552329\pi$
$419$	−6.69994	−0.327313	−0.163657	+	0.986517i	$0.552329\pi$
$420$	4.80073	0.234252
$421$	6.15631	0.300040	0.150020	−	0.988683i	$-0.452066\pi$
$421$	6.15631	0.300040	0.150020	+	0.988683i	$0.452066\pi$
$422$	6.15703	0.299720
$423$	−20.3433	−0.989125
$424$	1.34973	0.0655488
$425$	−1.30952	−0.0635212
$426$	−9.63894	−0.467008
$427$	−20.9335	−1.01304
$428$	−17.9699	−0.868606
$429$	−10.2390	−0.494341
$430$	1.00000	0.0482243
$431$	1.05991	0.0510539	0.0255269	−	0.999674i	$-0.491874\pi$
$431$	1.05991	0.0510539	0.0255269	+	0.999674i	$0.491874\pi$
$432$	1.22499	0.0589373
$433$	−25.4349	−1.22232	−0.611161	−	0.791506i	$-0.709297\pi$
$433$	−25.4349	−1.22232	−0.611161	+	0.791506i	$0.709297\pi$
$434$	1.09121	0.0523798
$435$	6.53933	0.313537
$436$	2.83424	0.135736
$437$	31.2507	1.49492
$438$	−18.8294	−0.899705
$439$	−38.9399	−1.85850	−0.929250	−	0.369451i	$-0.879546\pi$
$439$	−38.9399	−1.85850	−0.929250	+	0.369451i	$0.879546\pi$
$440$	1.00000	0.0476731
$441$	−11.9892	−0.570915
$442$	5.26674	0.250513
$443$	35.1847	1.67168	0.835838	−	0.548976i	$-0.184982\pi$
$443$	35.1847	1.67168	0.835838	+	0.548976i	$0.184982\pi$
$444$	−7.71963	−0.366357
$445$	−15.2229	−0.721635
$446$	−24.5836	−1.16407
$447$	38.9528	1.84240
$448$	1.88573	0.0890925
$449$	14.8270	0.699729	0.349865	−	0.936800i	$-0.386228\pi$
$449$	14.8270	0.699729	0.349865	+	0.936800i	$0.386228\pi$
$450$	−3.48118	−0.164104
$451$	−7.32408	−0.344877
$452$	−18.5804	−0.873946
$453$	−9.42686	−0.442912
$454$	1.28819	0.0604576
$455$	7.58419	0.355552
$456$	−8.83103	−0.413551
$457$	−25.8340	−1.20846	−0.604231	−	0.796809i	$-0.706520\pi$
$457$	−25.8340	−1.20846	−0.604231	+	0.796809i	$0.706520\pi$
$458$	−6.34291	−0.296385
$459$	−1.60415	−0.0748754
$460$	9.00897	0.420045
$461$	−35.2941	−1.64381	−0.821904	−	0.569626i	$-0.807088\pi$
$461$	−35.2941	−1.64381	−0.821904	+	0.569626i	$0.807088\pi$
$462$	4.80073	0.223350
$463$	−24.0128	−1.11597	−0.557985	−	0.829851i	$-0.688425\pi$
$463$	−24.0128	−1.11597	−0.557985	+	0.829851i	$0.688425\pi$
$464$	2.56866	0.119247
$465$	−1.47318	−0.0683170
$466$	−10.3313	−0.478587
$467$	−14.9797	−0.693177	−0.346589	−	0.938017i	$-0.612660\pi$
$467$	−14.9797	−0.693177	−0.346589	+	0.938017i	$0.612660\pi$
$468$	14.0009	0.647190
$469$	−7.27192	−0.335786
$470$	5.84380	0.269554
$471$	−9.83698	−0.453264
$472$	7.46945	0.343810
$473$	1.00000	0.0459800
$474$	−23.2789	−1.06924
$475$	3.46884	0.159161
$476$	−2.46941	−0.113185
$477$	−4.69866	−0.215137
$478$	−6.32585	−0.289338
$479$	11.7264	0.535795	0.267897	−	0.963447i	$-0.413671\pi$
$479$	11.7264	0.535795	0.267897	+	0.963447i	$0.413671\pi$
$480$	−2.54582	−0.116200
$481$	−12.1955	−0.556065
$482$	8.02708	0.365624
$483$	43.2496	1.96793
$484$	1.00000	0.0454545
$485$	8.82093	0.400538
$486$	22.3229	1.01259
$487$	−18.7699	−0.850547	−0.425273	−	0.905065i	$-0.639822\pi$
$487$	−18.7699	−0.850547	−0.425273	+	0.905065i	$0.639822\pi$
$488$	11.1010	0.502519
$489$	52.8402	2.38952
$490$	3.44401	0.155585
$491$	29.3472	1.32442	0.662211	−	0.749317i	$-0.269618\pi$
$491$	29.3472	1.32442	0.662211	+	0.749317i	$0.269618\pi$
$492$	18.6458	0.840615
$493$	−3.36372	−0.151494
$494$	−13.9513	−0.627696
$495$	−3.48118	−0.156467
$496$	−0.578666	−0.0259829
$497$	7.13975	0.320261
$498$	26.2496	1.17627
$499$	−24.3687	−1.09089	−0.545447	−	0.838145i	$-0.683640\pi$
$499$	−24.3687	−1.09089	−0.545447	+	0.838145i	$0.683640\pi$
$500$	1.00000	0.0447214
$501$	−46.8068	−2.09117
$502$	18.1796	0.811393
$503$	−36.3028	−1.61866	−0.809331	−	0.587353i	$-0.800170\pi$
$503$	−36.3028	−1.61866	−0.809331	+	0.587353i	$0.800170\pi$
$504$	−6.56457	−0.292409
$505$	17.5879	0.782651
$506$	9.00897	0.400497
$507$	8.08422	0.359033
$508$	−13.3389	−0.591818
$509$	−2.83695	−0.125745	−0.0628727	−	0.998022i	$-0.520026\pi$
$509$	−2.83695	−0.125745	−0.0628727	+	0.998022i	$0.520026\pi$
$510$	3.33381	0.147623
$511$	13.9473	0.616992
$512$	−1.00000	−0.0441942
$513$	4.24929	0.187611
$514$	15.3465	0.676905
$515$	13.8177	0.608881
$516$	−2.54582	−0.112073
$517$	5.84380	0.257010
$518$	5.71807	0.251238
$519$	51.3538	2.25418
$520$	−4.02188	−0.176371
$521$	−22.0171	−0.964587	−0.482293	−	0.876010i	$-0.660196\pi$
$521$	−22.0171	−0.964587	−0.482293	+	0.876010i	$0.660196\pi$
$522$	−8.94196	−0.391379
$523$	−4.79328	−0.209595	−0.104798	−	0.994494i	$-0.533419\pi$
$523$	−4.79328	−0.209595	−0.104798	+	0.994494i	$0.533419\pi$
$524$	14.4886	0.632937
$525$	4.80073	0.209521
$526$	24.9263	1.08684
$527$	0.757777	0.0330093
$528$	−2.54582	−0.110792
$529$	58.1615	2.52876
$530$	1.34973	0.0586286
$531$	−26.0025	−1.12841
$532$	6.54131	0.283602
$533$	29.4565	1.27590
$534$	38.7547	1.67708
$535$	−17.9699	−0.776905
$536$	3.85628	0.166566
$537$	12.2960	0.530612
$538$	25.4536	1.09738
$539$	3.44401	0.148344
$540$	1.22499	0.0527151
$541$	36.4649	1.56775	0.783875	−	0.620919i	$-0.213240\pi$
$541$	36.4649	1.56775	0.783875	+	0.620919i	$0.213240\pi$
$542$	−16.8479	−0.723681
$543$	−22.3977	−0.961177
$544$	1.30952	0.0561454
$545$	2.83424	0.121406
$546$	−19.3079	−0.826304
$547$	−25.0250	−1.06999	−0.534996	−	0.844855i	$-0.679687\pi$
$547$	−25.0250	−1.06999	−0.534996	+	0.844855i	$0.679687\pi$
$548$	2.86988	0.122595
$549$	−38.6446	−1.64931
$550$	1.00000	0.0426401
$551$	8.91027	0.379590
$552$	−22.9352	−0.976186
$553$	17.2431	0.733253
$554$	−14.6537	−0.622576
$555$	−7.71963	−0.327680
$556$	11.7871	0.499884
$557$	−18.1591	−0.769426	−0.384713	−	0.923036i	$-0.625700\pi$
$557$	−18.1591	−0.769426	−0.384713	+	0.923036i	$0.625700\pi$
$558$	2.01444	0.0852781
$559$	−4.02188	−0.170107
$560$	1.88573	0.0796868
$561$	3.33381	0.140753
$562$	11.1561	0.470594
$563$	−33.5177	−1.41260	−0.706300	−	0.707912i	$-0.749637\pi$
$563$	−33.5177	−1.41260	−0.706300	+	0.707912i	$0.749637\pi$
$564$	−14.8772	−0.626444
$565$	−18.5804	−0.781681
$566$	14.3015	0.601137
$567$	−13.8129	−0.580086
$568$	−3.78619	−0.158865
$569$	5.30005	0.222190	0.111095	−	0.993810i	$-0.464564\pi$
$569$	5.30005	0.222190	0.111095	+	0.993810i	$0.464564\pi$
$570$	−8.83103	−0.369891
$571$	−18.9909	−0.794746	−0.397373	−	0.917657i	$-0.630078\pi$
$571$	−18.9909	−0.794746	−0.397373	+	0.917657i	$0.630078\pi$
$572$	−4.02188	−0.168163
$573$	−65.7175	−2.74539
$574$	−13.8113	−0.576471
$575$	9.00897	0.375700
$576$	3.48118	0.145049
$577$	38.5557	1.60510	0.802548	−	0.596588i	$-0.203477\pi$
$577$	38.5557	1.60510	0.802548	+	0.596588i	$0.203477\pi$
$578$	15.2851	0.635778
$579$	32.8543	1.36538
$580$	2.56866	0.106658
$581$	−19.4435	−0.806654
$582$	−22.4565	−0.930850
$583$	1.34973	0.0559002
$584$	−7.39622	−0.306058
$585$	14.0009	0.578865
$586$	19.8150	0.818550
$587$	5.37415	0.221815	0.110908	−	0.993831i	$-0.464624\pi$
$587$	5.37415	0.221815	0.110908	+	0.993831i	$0.464624\pi$
$588$	−8.76782	−0.361579
$589$	−2.00730	−0.0827094
$590$	7.46945	0.307513
$591$	23.8661	0.981722
$592$	−3.03228	−0.124626
$593$	14.3477	0.589190	0.294595	−	0.955622i	$-0.404815\pi$
$593$	14.3477	0.589190	0.294595	+	0.955622i	$0.404815\pi$
$594$	1.22499	0.0502619
$595$	−2.46941	−0.101236
$596$	15.3007	0.626742
$597$	69.3422	2.83799
$598$	−36.2330	−1.48168
$599$	−4.68203	−0.191303	−0.0956514	−	0.995415i	$-0.530493\pi$
$599$	−4.68203	−0.191303	−0.0956514	+	0.995415i	$0.530493\pi$
$600$	−2.54582	−0.103932
$601$	30.9657	1.26312	0.631559	−	0.775328i	$-0.282415\pi$
$601$	30.9657	1.26312	0.631559	+	0.775328i	$0.282415\pi$
$602$	1.88573	0.0768567
$603$	−13.4244	−0.546684
$604$	−3.70288	−0.150668
$605$	1.00000	0.0406558
$606$	−44.7755	−1.81888
$607$	42.8732	1.74017	0.870086	−	0.492901i	$-0.164063\pi$
$607$	42.8732	1.74017	0.870086	+	0.492901i	$0.164063\pi$
$608$	−3.46884	−0.140680
$609$	12.3314	0.499695
$610$	11.1010	0.449466
$611$	−23.5030	−0.950831
$612$	−4.55869	−0.184274
$613$	35.7002	1.44192	0.720959	−	0.692977i	$-0.243701\pi$
$613$	35.7002	1.44192	0.720959	+	0.692977i	$0.243701\pi$
$614$	−10.9313	−0.441152
$615$	18.6458	0.751869
$616$	1.88573	0.0759784
$617$	23.9066	0.962443	0.481222	−	0.876599i	$-0.340193\pi$
$617$	23.9066	0.962443	0.481222	+	0.876599i	$0.340193\pi$
$618$	−35.1774	−1.41504
$619$	5.94717	0.239037	0.119519	−	0.992832i	$-0.461865\pi$
$619$	5.94717	0.239037	0.119519	+	0.992832i	$0.461865\pi$
$620$	−0.578666	−0.0232398
$621$	11.0359	0.442855
$622$	3.59952	0.144328
$623$	−28.7063	−1.15010
$624$	10.2390	0.409886
$625$	1.00000	0.0400000
$626$	10.2185	0.408414
$627$	−8.83103	−0.352677
$628$	−3.86398	−0.154190
$629$	3.97084	0.158328
$630$	−6.56457	−0.261539
$631$	2.88435	0.114824	0.0574121	−	0.998351i	$-0.481715\pi$
$631$	2.88435	0.114824	0.0574121	+	0.998351i	$0.481715\pi$
$632$	−9.14400	−0.363729
$633$	−15.6747	−0.623012
$634$	19.7247	0.783369
$635$	−13.3389	−0.529338
$636$	−3.43617	−0.136253
$637$	−13.8514	−0.548812
$638$	2.56866	0.101694
$639$	13.1804	0.521409
$640$	−1.00000	−0.0395285
$641$	42.4483	1.67661	0.838303	−	0.545205i	$-0.183548\pi$
$641$	42.4483	1.67661	0.838303	+	0.545205i	$0.183548\pi$
$642$	45.7479	1.80553
$643$	−22.5246	−0.888283	−0.444142	−	0.895957i	$-0.646491\pi$
$643$	−22.5246	−0.888283	−0.444142	+	0.895957i	$0.646491\pi$
$644$	16.9885	0.669441
$645$	−2.54582	−0.100241
$646$	4.54253	0.178723
$647$	9.50984	0.373870	0.186935	−	0.982372i	$-0.440145\pi$
$647$	9.50984	0.373870	0.186935	+	0.982372i	$0.440145\pi$
$648$	7.32494	0.287751
$649$	7.46945	0.293202
$650$	−4.02188	−0.157751
$651$	−2.77802	−0.108879
$652$	20.7557	0.812856
$653$	−13.4258	−0.525394	−0.262697	−	0.964878i	$-0.584612\pi$
$653$	−13.4258	−0.525394	−0.262697	+	0.964878i	$0.584612\pi$
$654$	−7.21546	−0.282147
$655$	14.4886	0.566116
$656$	7.32408	0.285957
$657$	25.7476	1.00451
$658$	11.0198	0.429598
$659$	−12.2236	−0.476166	−0.238083	−	0.971245i	$-0.576519\pi$
$659$	−12.2236	−0.476166	−0.238083	+	0.971245i	$0.576519\pi$
$660$	−2.54582	−0.0990957
$661$	−14.8531	−0.577720	−0.288860	−	0.957371i	$-0.593276\pi$
$661$	−14.8531	−0.577720	−0.288860	+	0.957371i	$0.593276\pi$
$662$	−26.8913	−1.04516
$663$	−13.4082	−0.520730
$664$	10.3109	0.400139
$665$	6.54131	0.253661
$666$	10.5559	0.409033
$667$	23.1410	0.896022
$668$	−18.3858	−0.711367
$669$	62.5854	2.41969
$670$	3.85628	0.148981
$671$	11.1010	0.428549
$672$	−4.80073	−0.185192
$673$	0.717133	0.0276435	0.0138217	−	0.999904i	$-0.495600\pi$
$673$	0.717133	0.0276435	0.0138217	+	0.999904i	$0.495600\pi$
$674$	−18.4909	−0.712243
$675$	1.22499	0.0471499
$676$	3.17549	0.122134
$677$	42.1816	1.62117	0.810585	−	0.585620i	$-0.199149\pi$
$677$	42.1816	1.62117	0.810585	+	0.585620i	$0.199149\pi$
$678$	47.3022	1.81663
$679$	16.6339	0.638351
$680$	1.30952	0.0502180
$681$	−3.27948	−0.125670
$682$	−0.578666	−0.0221583
$683$	5.17382	0.197971	0.0989853	−	0.995089i	$-0.468440\pi$
$683$	5.17382	0.197971	0.0989853	+	0.995089i	$0.468440\pi$
$684$	12.0757	0.461724
$685$	2.86988	0.109653
$686$	19.6946	0.751944
$687$	16.1479	0.616080
$688$	−1.00000	−0.0381246
$689$	−5.42845	−0.206808
$690$	−22.9352	−0.873127
$691$	20.5255	0.780827	0.390414	−	0.920640i	$-0.372332\pi$
$691$	20.5255	0.780827	0.390414	+	0.920640i	$0.372332\pi$
$692$	20.1718	0.766818
$693$	−6.56457	−0.249367
$694$	−35.7798	−1.35818
$695$	11.7871	0.447110
$696$	−6.53933	−0.247873
$697$	−9.59106	−0.363287
$698$	−31.2632	−1.18333
$699$	26.3015	0.994815
$700$	1.88573	0.0712740
$701$	1.02844	0.0388437	0.0194218	−	0.999811i	$-0.493817\pi$
$701$	1.02844	0.0388437	0.0194218	+	0.999811i	$0.493817\pi$
$702$	−4.92676	−0.185948
$703$	−10.5185	−0.396713
$704$	−1.00000	−0.0376889
$705$	−14.8772	−0.560309
$706$	−23.4108	−0.881078
$707$	33.1661	1.24734
$708$	−19.0159	−0.714660
$709$	−26.3350	−0.989033	−0.494517	−	0.869168i	$-0.664655\pi$
$709$	−26.3350	−0.989033	−0.494517	+	0.869168i	$0.664655\pi$
$710$	−3.78619	−0.142093
$711$	31.8319	1.19379
$712$	15.2229	0.570503
$713$	−5.21319	−0.195235
$714$	6.28667	0.235273
$715$	−4.02188	−0.150410
$716$	4.82989	0.180502
$717$	16.1044	0.601432
$718$	−4.81585	−0.179726
$719$	−28.3675	−1.05793	−0.528965	−	0.848644i	$-0.677420\pi$
$719$	−28.3675	−1.05793	−0.528965	+	0.848644i	$0.677420\pi$
$720$	3.48118	0.129736
$721$	26.0565	0.970396
$722$	6.96714	0.259290
$723$	−20.4355	−0.760004
$724$	−8.79785	−0.326969
$725$	2.56866	0.0953976
$726$	−2.54582	−0.0944841
$727$	34.1926	1.26813	0.634066	−	0.773279i	$-0.281385\pi$
$727$	34.1926	1.26813	0.634066	+	0.773279i	$0.281385\pi$
$728$	−7.58419	−0.281089
$729$	−34.8552	−1.29093
$730$	−7.39622	−0.273747
$731$	1.30952	0.0484345
$732$	−28.2611	−1.04456
$733$	−34.3906	−1.27024	−0.635122	−	0.772411i	$-0.719050\pi$
$733$	−34.3906	−1.27024	−0.635122	+	0.772411i	$0.719050\pi$
$734$	−13.3164	−0.491517
$735$	−8.76782	−0.323406
$736$	−9.00897	−0.332075
$737$	3.85628	0.142048
$738$	−25.4964	−0.938536
$739$	37.0322	1.36225	0.681126	−	0.732166i	$-0.261490\pi$
$739$	37.0322	1.36225	0.681126	+	0.732166i	$0.261490\pi$
$740$	−3.03228	−0.111469
$741$	35.5173	1.30476
$742$	2.54523	0.0934385
$743$	−3.58638	−0.131572	−0.0657858	−	0.997834i	$-0.520955\pi$
$743$	−3.58638	−0.131572	−0.0657858	+	0.997834i	$0.520955\pi$
$744$	1.47318	0.0540093
$745$	15.3007	0.560575
$746$	4.76510	0.174463
$747$	−35.8940	−1.31329
$748$	1.30952	0.0478809
$749$	−33.8864	−1.23818
$750$	−2.54582	−0.0929600
$751$	−33.9263	−1.23799	−0.618994	−	0.785396i	$-0.712459\pi$
$751$	−33.9263	−1.23799	−0.618994	+	0.785396i	$0.712459\pi$
$752$	−5.84380	−0.213101
$753$	−46.2818	−1.68660
$754$	−10.3308	−0.376227
$755$	−3.70288	−0.134762
$756$	2.31000	0.0840140
$757$	51.3668	1.86696	0.933480	−	0.358630i	$-0.116756\pi$
$757$	51.3668	1.86696	0.933480	+	0.358630i	$0.116756\pi$
$758$	35.9696	1.30648
$759$	−22.9352	−0.832494
$760$	−3.46884	−0.125828
$761$	−14.3406	−0.519845	−0.259922	−	0.965630i	$-0.583697\pi$
$761$	−14.3406	−0.519845	−0.259922	+	0.965630i	$0.583697\pi$
$762$	33.9584	1.23018
$763$	5.34462	0.193488
$764$	−25.8139	−0.933915
$765$	−4.55869	−0.164820
$766$	8.54489	0.308739
$767$	−30.0412	−1.08473
$768$	2.54582	0.0918642
$769$	−31.0766	−1.12065	−0.560326	−	0.828272i	$-0.689324\pi$
$769$	−31.0766	−1.12065	−0.560326	+	0.828272i	$0.689324\pi$
$770$	1.88573	0.0679571
$771$	−39.0693	−1.40705
$772$	12.9052	0.464469
$773$	51.8926	1.86645	0.933224	−	0.359294i	$-0.116983\pi$
$773$	51.8926	1.86645	0.933224	+	0.359294i	$0.116983\pi$
$774$	3.48118	0.125128
$775$	−0.578666	−0.0207863
$776$	−8.82093	−0.316653
$777$	−14.5572	−0.522235
$778$	20.0156	0.717594
$779$	25.4061	0.910267
$780$	10.2390	0.366613
$781$	−3.78619	−0.135481
$782$	11.7975	0.421876
$783$	3.14658	0.112450
$784$	−3.44401	−0.123000
$785$	−3.86398	−0.137911
$786$	−36.8853	−1.31565
$787$	17.9831	0.641030	0.320515	−	0.947243i	$-0.396144\pi$
$787$	17.9831	0.641030	0.320515	+	0.947243i	$0.396144\pi$
$788$	9.37465	0.333958
$789$	−63.4577	−2.25916
$790$	−9.14400	−0.325329
$791$	−35.0376	−1.24579
$792$	3.48118	0.123698
$793$	−44.6469	−1.58546
$794$	5.66695	0.201112
$795$	−3.43617	−0.121868
$796$	27.2377	0.965415
$797$	38.5190	1.36441	0.682206	−	0.731160i	$-0.261021\pi$
$797$	38.5190	1.36441	0.682206	+	0.731160i	$0.261021\pi$
$798$	−16.6530	−0.589509
$799$	7.65259	0.270729
$800$	−1.00000	−0.0353553
$801$	−52.9937	−1.87244
$802$	5.73776	0.202607
$803$	−7.39622	−0.261007
$804$	−9.81739	−0.346233
$805$	16.9885	0.598766
$806$	2.32732	0.0819765
$807$	−64.8001	−2.28107
$808$	−17.5879	−0.618740
$809$	44.4985	1.56448	0.782242	−	0.622974i	$-0.214076\pi$
$809$	44.4985	1.56448	0.782242	+	0.622974i	$0.214076\pi$
$810$	7.32494	0.257372
$811$	−30.4919	−1.07071	−0.535357	−	0.844626i	$-0.679823\pi$
$811$	−30.4919	−1.07071	−0.535357	+	0.844626i	$0.679823\pi$
$812$	4.84381	0.169984
$813$	42.8917	1.50428
$814$	−3.03228	−0.106281
$815$	20.7557	0.727041
$816$	−3.33381	−0.116707
$817$	−3.46884	−0.121359
$818$	21.2782	0.743974
$819$	26.4019	0.922557
$820$	7.32408	0.255768
$821$	−49.8114	−1.73843	−0.869216	−	0.494433i	$-0.835376\pi$
$821$	−49.8114	−1.73843	−0.869216	+	0.494433i	$0.835376\pi$
$822$	−7.30620	−0.254833
$823$	31.6337	1.10268	0.551341	−	0.834280i	$-0.314116\pi$
$823$	31.6337	1.10268	0.551341	+	0.834280i	$0.314116\pi$
$824$	−13.8177	−0.481363
$825$	−2.54582	−0.0886339
$826$	14.0854	0.490094
$827$	−2.94683	−0.102471	−0.0512357	−	0.998687i	$-0.516316\pi$
$827$	−2.94683	−0.102471	−0.0512357	+	0.998687i	$0.516316\pi$
$828$	31.3618	1.08990
$829$	−12.6614	−0.439750	−0.219875	−	0.975528i	$-0.570565\pi$
$829$	−12.6614	−0.439750	−0.219875	+	0.975528i	$0.570565\pi$
$830$	10.3109	0.357895
$831$	37.3056	1.29412
$832$	4.02188	0.139433
$833$	4.51001	0.156263
$834$	−30.0078	−1.03908
$835$	−18.3858	−0.636266
$836$	−3.46884	−0.119972
$837$	−0.708860	−0.0245018
$838$	6.69994	0.231445
$839$	7.36525	0.254277	0.127138	−	0.991885i	$-0.459421\pi$
$839$	7.36525	0.254277	0.127138	+	0.991885i	$0.459421\pi$
$840$	−4.80073	−0.165641
$841$	−22.4020	−0.772482
$842$	−6.15631	−0.212160
$843$	−28.4015	−0.978199
$844$	−6.15703	−0.211934
$845$	3.17549	0.109240
$846$	20.3433	0.699417
$847$	1.88573	0.0647946
$848$	−1.34973	−0.0463500
$849$	−36.4090	−1.24955
$850$	1.30952	0.0449163
$851$	−27.3177	−0.936439
$852$	9.63894	0.330225
$853$	22.6021	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$853$	22.6021	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$854$	20.9335	0.716331
$855$	12.0757	0.412979
$856$	17.9699	0.614197
$857$	−40.6528	−1.38867	−0.694336	−	0.719651i	$-0.744302\pi$
$857$	−40.6528	−1.38867	−0.694336	+	0.719651i	$0.744302\pi$
$858$	10.2390	0.349552
$859$	−21.7265	−0.741298	−0.370649	−	0.928773i	$-0.620865\pi$
$859$	−21.7265	−0.741298	−0.370649	+	0.928773i	$0.620865\pi$
$860$	−1.00000	−0.0340997
$861$	35.1609	1.19828
$862$	−1.05991	−0.0361005
$863$	−43.8970	−1.49427	−0.747135	−	0.664672i	$-0.768571\pi$
$863$	−43.8970	−1.49427	−0.747135	+	0.664672i	$0.768571\pi$
$864$	−1.22499	−0.0416750
$865$	20.1718	0.685863
$866$	25.4349	0.864313
$867$	−38.9132	−1.32156
$868$	−1.09121	−0.0370381
$869$	−9.14400	−0.310189
$870$	−6.53933	−0.221704
$871$	−15.5095	−0.525519
$872$	−2.83424	−0.0959796
$873$	30.7072	1.03928
$874$	−31.2507	−1.05707
$875$	1.88573	0.0637494
$876$	18.8294	0.636187
$877$	16.4036	0.553909	0.276954	−	0.960883i	$-0.410675\pi$
$877$	16.4036	0.553909	0.276954	+	0.960883i	$0.410675\pi$
$878$	38.9399	1.31416
$879$	−50.4453	−1.70148
$880$	−1.00000	−0.0337100
$881$	−25.3259	−0.853252	−0.426626	−	0.904428i	$-0.640298\pi$
$881$	−25.3259	−0.853252	−0.426626	+	0.904428i	$0.640298\pi$
$882$	11.9892	0.403698
$883$	15.6134	0.525434	0.262717	−	0.964873i	$-0.415381\pi$
$883$	15.6134	0.525434	0.262717	+	0.964873i	$0.415381\pi$
$884$	−5.26674	−0.177140
$885$	−19.0159	−0.639211
$886$	−35.1847	−1.18205
$887$	17.4960	0.587457	0.293728	−	0.955889i	$-0.405104\pi$
$887$	17.4960	0.587457	0.293728	+	0.955889i	$0.405104\pi$
$888$	7.71963	0.259054
$889$	−25.1536	−0.843625
$890$	15.2229	0.510273
$891$	7.32494	0.245395
$892$	24.5836	0.823120
$893$	−20.2712	−0.678350
$894$	−38.9528	−1.30278
$895$	4.82989	0.161445
$896$	−1.88573	−0.0629979
$897$	92.2424	3.07989
$898$	−14.8270	−0.494783
$899$	−1.48640	−0.0495741
$900$	3.48118	0.116039
$901$	1.76751	0.0588842
$902$	7.32408	0.243865
$903$	−4.80073	−0.159758
$904$	18.5804	0.617973
$905$	−8.79785	−0.292450
$906$	9.42686	0.313186
$907$	−13.7817	−0.457615	−0.228807	−	0.973472i	$-0.573483\pi$
$907$	−13.7817	−0.457615	−0.228807	+	0.973472i	$0.573483\pi$
$908$	−1.28819	−0.0427500
$909$	61.2266	2.03076
$910$	−7.58419	−0.251413
$911$	0.620122	0.0205456	0.0102728	−	0.999947i	$-0.496730\pi$
$911$	0.620122	0.0205456	0.0102728	+	0.999947i	$0.496730\pi$
$912$	8.83103	0.292425
$913$	10.3109	0.341240
$914$	25.8340	0.854512
$915$	−28.2611	−0.934283
$916$	6.34291	0.209576
$917$	27.3216	0.902239
$918$	1.60415	0.0529449
$919$	12.9009	0.425560	0.212780	−	0.977100i	$-0.431748\pi$
$919$	12.9009	0.425560	0.212780	+	0.977100i	$0.431748\pi$
$920$	−9.00897	−0.297017
$921$	27.8291	0.917000
$922$	35.2941	1.16235
$923$	15.2276	0.501222
$924$	−4.80073	−0.157932
$925$	−3.03228	−0.0997008
$926$	24.0128	0.789110
$927$	48.1019	1.57987
$928$	−2.56866	−0.0843204
$929$	−37.9038	−1.24358	−0.621791	−	0.783183i	$-0.713595\pi$
$929$	−37.9038	−1.24358	−0.621791	+	0.783183i	$0.713595\pi$
$930$	1.47318	0.0483074
$931$	−11.9467	−0.391538
$932$	10.3313	0.338412
$933$	−9.16371	−0.300007
$934$	14.9797	0.490150
$935$	1.30952	0.0428260
$936$	−14.0009	−0.457633
$937$	−45.0425	−1.47147	−0.735737	−	0.677268i	$-0.763164\pi$
$937$	−45.0425	−1.47147	−0.735737	+	0.677268i	$0.763164\pi$
$938$	7.27192	0.237437
$939$	−26.0145	−0.848950
$940$	−5.84380	−0.190604
$941$	−58.1703	−1.89630	−0.948149	−	0.317827i	$-0.897047\pi$
$941$	−58.1703	−1.89630	−0.948149	+	0.317827i	$0.897047\pi$
$942$	9.83698	0.320506
$943$	65.9824	2.14868
$944$	−7.46945	−0.243110
$945$	2.31000	0.0751444
$946$	−1.00000	−0.0325128
$947$	44.3803	1.44216	0.721082	−	0.692849i	$-0.243645\pi$
$947$	44.3803	1.44216	0.721082	+	0.692849i	$0.243645\pi$
$948$	23.2789	0.756065
$949$	29.7467	0.965619
$950$	−3.46884	−0.112544
$951$	−50.2155	−1.62835
$952$	2.46941	0.0800341
$953$	−26.3823	−0.854607	−0.427303	−	0.904108i	$-0.640536\pi$
$953$	−26.3823	−0.854607	−0.427303	+	0.904108i	$0.640536\pi$
$954$	4.69866	0.152125
$955$	−25.8139	−0.835319
$956$	6.32585	0.204593
$957$	−6.53933	−0.211387
$958$	−11.7264	−0.378864
$959$	5.41184	0.174757
$960$	2.54582	0.0821658
$961$	−30.6651	−0.989198
$962$	12.1955	0.393197
$963$	−62.5563	−2.01585
$964$	−8.02708	−0.258535
$965$	12.9052	0.415434
$966$	−43.2496	−1.39153
$967$	−23.6524	−0.760611	−0.380305	−	0.924861i	$-0.624181\pi$
$967$	−23.6524	−0.760611	−0.380305	+	0.924861i	$0.624181\pi$
$968$	−1.00000	−0.0321412
$969$	−11.5644	−0.371503
$970$	−8.82093	−0.283223
$971$	1.24858	0.0400688	0.0200344	−	0.999799i	$-0.493622\pi$
$971$	1.24858	0.0400688	0.0200344	+	0.999799i	$0.493622\pi$
$972$	−22.3229	−0.716007
$973$	22.2273	0.712575
$974$	18.7699	0.601427
$975$	10.2390	0.327909
$976$	−11.1010	−0.355334
$977$	5.17999	0.165723	0.0828613	−	0.996561i	$-0.473594\pi$
$977$	5.17999	0.165723	0.0828613	+	0.996561i	$0.473594\pi$
$978$	−52.8402	−1.68964
$979$	15.2229	0.486526
$980$	−3.44401	−0.110015
$981$	9.86650	0.315013
$982$	−29.3472	−0.936508
$983$	−9.03545	−0.288186	−0.144093	−	0.989564i	$-0.546026\pi$
$983$	−9.03545	−0.288186	−0.144093	+	0.989564i	$0.546026\pi$
$984$	−18.6458	−0.594405
$985$	9.37465	0.298701
$986$	3.36372	0.107123
$987$	−28.0545	−0.892984
$988$	13.9513	0.443848
$989$	−9.00897	−0.286469
$990$	3.48118	0.110639
$991$	−27.8946	−0.886103	−0.443051	−	0.896496i	$-0.646104\pi$
$991$	−27.8946	−0.886103	−0.443051	+	0.896496i	$0.646104\pi$
$992$	0.578666	0.0183727
$993$	68.4603	2.17252
$994$	−7.13975	−0.226459
$995$	27.2377	0.863493
$996$	−26.2496	−0.831749
$997$	−8.64858	−0.273903	−0.136952	−	0.990578i	$-0.543730\pi$
$997$	−8.64858	−0.273903	−0.136952	+	0.990578i	$0.543730\pi$
$998$	24.3687	0.771378
$999$	−3.71451	−0.117522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.y.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.y.1.7	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.54582 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.54582 q^{6} +1.88573 q^{7} -1.00000 q^{8} +3.48118 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.54582 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.54582 q^{6} +1.88573 q^{7} -1.00000 q^{8} +3.48118 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.54582 q^{12} +4.02188 q^{13} -1.88573 q^{14} +2.54582 q^{15} +1.00000 q^{16} -1.30952 q^{17} -3.48118 q^{18} +3.46884 q^{19} +1.00000 q^{20} +4.80073 q^{21} +1.00000 q^{22} +9.00897 q^{23} -2.54582 q^{24} +1.00000 q^{25} -4.02188 q^{26} +1.22499 q^{27} +1.88573 q^{28} +2.56866 q^{29} -2.54582 q^{30} -0.578666 q^{31} -1.00000 q^{32} -2.54582 q^{33} +1.30952 q^{34} +1.88573 q^{35} +3.48118 q^{36} -3.03228 q^{37} -3.46884 q^{38} +10.2390 q^{39} -1.00000 q^{40} +7.32408 q^{41} -4.80073 q^{42} -1.00000 q^{43} -1.00000 q^{44} +3.48118 q^{45} -9.00897 q^{46} -5.84380 q^{47} +2.54582 q^{48} -3.44401 q^{49} -1.00000 q^{50} -3.33381 q^{51} +4.02188 q^{52} -1.34973 q^{53} -1.22499 q^{54} -1.00000 q^{55} -1.88573 q^{56} +8.83103 q^{57} -2.56866 q^{58} -7.46945 q^{59} +2.54582 q^{60} -11.1010 q^{61} +0.578666 q^{62} +6.56457 q^{63} +1.00000 q^{64} +4.02188 q^{65} +2.54582 q^{66} -3.85628 q^{67} -1.30952 q^{68} +22.9352 q^{69} -1.88573 q^{70} +3.78619 q^{71} -3.48118 q^{72} +7.39622 q^{73} +3.03228 q^{74} +2.54582 q^{75} +3.46884 q^{76} -1.88573 q^{77} -10.2390 q^{78} +9.14400 q^{79} +1.00000 q^{80} -7.32494 q^{81} -7.32408 q^{82} -10.3109 q^{83} +4.80073 q^{84} -1.30952 q^{85} +1.00000 q^{86} +6.53933 q^{87} +1.00000 q^{88} -15.2229 q^{89} -3.48118 q^{90} +7.58419 q^{91} +9.00897 q^{92} -1.47318 q^{93} +5.84380 q^{94} +3.46884 q^{95} -2.54582 q^{96} +8.82093 q^{97} +3.44401 q^{98} -3.48118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9	\( 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9} - 8 q^{10} - 8 q^{11} + 3 q^{12} + 6 q^{13} - 11 q^{14} + 3 q^{15} + 8 q^{16} + 9 q^{17} - 3 q^{18} + 9 q^{19} + 8 q^{20} + 21 q^{21} + 8 q^{22} - 2 q^{23} - 3 q^{24} + 8 q^{25} - 6 q^{26} + 24 q^{27} + 11 q^{28} - 10 q^{29} - 3 q^{30} + 6 q^{31} - 8 q^{32} - 3 q^{33} - 9 q^{34} + 11 q^{35} + 3 q^{36} + 16 q^{37} - 9 q^{38} + 6 q^{39} - 8 q^{40} - 4 q^{41} - 21 q^{42} - 8 q^{43} - 8 q^{44} + 3 q^{45} + 2 q^{46} - 11 q^{47} + 3 q^{48} + 11 q^{49} - 8 q^{50} + 38 q^{51} + 6 q^{52} - 15 q^{53} - 24 q^{54} - 8 q^{55} - 11 q^{56} - 2 q^{57} + 10 q^{58} - 7 q^{59} + 3 q^{60} + 2 q^{61} - 6 q^{62} + 33 q^{63} + 8 q^{64} + 6 q^{65} + 3 q^{66} + 4 q^{67} + 9 q^{68} - 4 q^{69} - 11 q^{70} - 3 q^{71} - 3 q^{72} + 32 q^{73} - 16 q^{74} + 3 q^{75} + 9 q^{76} - 11 q^{77} - 6 q^{78} + 45 q^{79} + 8 q^{80} + 20 q^{81} + 4 q^{82} + 39 q^{83} + 21 q^{84} + 9 q^{85} + 8 q^{86} + 2 q^{87} + 8 q^{88} - 22 q^{89} - 3 q^{90} + 18 q^{91} - 2 q^{92} + 18 q^{93} + 11 q^{94} + 9 q^{95} - 3 q^{96} + 30 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9 - 8 * q^10 - 8 * q^11 + 3 * q^12 + 6 * q^13 - 11 * q^14 + 3 * q^15 + 8 * q^16 + 9 * q^17 - 3 * q^18 + 9 * q^19 + 8 * q^20 + 21 * q^21 + 8 * q^22 - 2 * q^23 - 3 * q^24 + 8 * q^25 - 6 * q^26 + 24 * q^27 + 11 * q^28 - 10 * q^29 - 3 * q^30 + 6 * q^31 - 8 * q^32 - 3 * q^33 - 9 * q^34 + 11 * q^35 + 3 * q^36 + 16 * q^37 - 9 * q^38 + 6 * q^39 - 8 * q^40 - 4 * q^41 - 21 * q^42 - 8 * q^43 - 8 * q^44 + 3 * q^45 + 2 * q^46 - 11 * q^47 + 3 * q^48 + 11 * q^49 - 8 * q^50 + 38 * q^51 + 6 * q^52 - 15 * q^53 - 24 * q^54 - 8 * q^55 - 11 * q^56 - 2 * q^57 + 10 * q^58 - 7 * q^59 + 3 * q^60 + 2 * q^61 - 6 * q^62 + 33 * q^63 + 8 * q^64 + 6 * q^65 + 3 * q^66 + 4 * q^67 + 9 * q^68 - 4 * q^69 - 11 * q^70 - 3 * q^71 - 3 * q^72 + 32 * q^73 - 16 * q^74 + 3 * q^75 + 9 * q^76 - 11 * q^77 - 6 * q^78 + 45 * q^79 + 8 * q^80 + 20 * q^81 + 4 * q^82 + 39 * q^83 + 21 * q^84 + 9 * q^85 + 8 * q^86 + 2 * q^87 + 8 * q^88 - 22 * q^89 - 3 * q^90 + 18 * q^91 - 2 * q^92 + 18 * q^93 + 11 * q^94 + 9 * q^95 - 3 * q^96 + 30 * q^97 - 11 * q^98 - 3 * q^99

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