LMFDB - Embedded newform 6014.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.26246 q^{3} +1.00000 q^{4} +2.97735 q^{5} -1.26246 q^{6} +1.38275 q^{7} +1.00000 q^{8} -1.40619 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.26246 q^{3} +1.00000 q^{4} +2.97735 q^{5} -1.26246 q^{6} +1.38275 q^{7} +1.00000 q^{8} -1.40619 q^{9} +2.97735 q^{10} -4.03185 q^{11} -1.26246 q^{12} -5.15458 q^{13} +1.38275 q^{14} -3.75878 q^{15} +1.00000 q^{16} +4.51797 q^{17} -1.40619 q^{18} -8.09538 q^{19} +2.97735 q^{20} -1.74567 q^{21} -4.03185 q^{22} +3.34096 q^{23} -1.26246 q^{24} +3.86459 q^{25} -5.15458 q^{26} +5.56265 q^{27} +1.38275 q^{28} -3.63921 q^{29} -3.75878 q^{30} +1.00000 q^{31} +1.00000 q^{32} +5.09005 q^{33} +4.51797 q^{34} +4.11692 q^{35} -1.40619 q^{36} +11.0295 q^{37} -8.09538 q^{38} +6.50746 q^{39} +2.97735 q^{40} +2.12020 q^{41} -1.74567 q^{42} -5.77876 q^{43} -4.03185 q^{44} -4.18672 q^{45} +3.34096 q^{46} -1.60653 q^{47} -1.26246 q^{48} -5.08800 q^{49} +3.86459 q^{50} -5.70376 q^{51} -5.15458 q^{52} -9.85335 q^{53} +5.56265 q^{54} -12.0042 q^{55} +1.38275 q^{56} +10.2201 q^{57} -3.63921 q^{58} -2.44665 q^{59} -3.75878 q^{60} +5.95559 q^{61} +1.00000 q^{62} -1.94441 q^{63} +1.00000 q^{64} -15.3470 q^{65} +5.09005 q^{66} -15.0141 q^{67} +4.51797 q^{68} -4.21783 q^{69} +4.11692 q^{70} -7.81799 q^{71} -1.40619 q^{72} +2.73055 q^{73} +11.0295 q^{74} -4.87890 q^{75} -8.09538 q^{76} -5.57503 q^{77} +6.50746 q^{78} -10.4772 q^{79} +2.97735 q^{80} -2.80405 q^{81} +2.12020 q^{82} -2.48316 q^{83} -1.74567 q^{84} +13.4516 q^{85} -5.77876 q^{86} +4.59436 q^{87} -4.03185 q^{88} -0.210119 q^{89} -4.18672 q^{90} -7.12749 q^{91} +3.34096 q^{92} -1.26246 q^{93} -1.60653 q^{94} -24.1027 q^{95} -1.26246 q^{96} -1.00000 q^{97} -5.08800 q^{98} +5.66955 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.26246	−0.728882	−0.364441	−	0.931226i	$-0.618740\pi$
$3$	−1.26246	−0.728882	−0.364441	+	0.931226i	$0.618740\pi$
$4$	1.00000	0.500000
$5$	2.97735	1.33151	0.665755	−	0.746171i	$-0.268110\pi$
$5$	2.97735	1.33151	0.665755	+	0.746171i	$0.268110\pi$
$6$	−1.26246	−0.515398
$7$	1.38275	0.522630	0.261315	−	0.965254i	$-0.415844\pi$
$7$	1.38275	0.522630	0.261315	+	0.965254i	$0.415844\pi$
$8$	1.00000	0.353553
$9$	−1.40619	−0.468730
$10$	2.97735	0.941520
$11$	−4.03185	−1.21565	−0.607824	−	0.794072i	$-0.707957\pi$
$11$	−4.03185	−1.21565	−0.607824	+	0.794072i	$0.707957\pi$
$12$	−1.26246	−0.364441
$13$	−5.15458	−1.42962	−0.714812	−	0.699317i	$-0.753488\pi$
$13$	−5.15458	−1.42962	−0.714812	+	0.699317i	$0.753488\pi$
$14$	1.38275	0.369555
$15$	−3.75878	−0.970514
$16$	1.00000	0.250000
$17$	4.51797	1.09577	0.547884	−	0.836554i	$-0.315434\pi$
$17$	4.51797	1.09577	0.547884	+	0.836554i	$0.315434\pi$
$18$	−1.40619	−0.331442
$19$	−8.09538	−1.85721	−0.928603	−	0.371074i	$-0.878990\pi$
$19$	−8.09538	−1.85721	−0.928603	+	0.371074i	$0.878990\pi$
$20$	2.97735	0.665755
$21$	−1.74567	−0.380936
$22$	−4.03185	−0.859593
$23$	3.34096	0.696638	0.348319	−	0.937376i	$-0.386753\pi$
$23$	3.34096	0.696638	0.348319	+	0.937376i	$0.386753\pi$
$24$	−1.26246	−0.257699
$25$	3.86459	0.772918
$26$	−5.15458	−1.01090
$27$	5.56265	1.07053
$28$	1.38275	0.261315
$29$	−3.63921	−0.675785	−0.337892	−	0.941185i	$-0.609714\pi$
$29$	−3.63921	−0.675785	−0.337892	+	0.941185i	$0.609714\pi$
$30$	−3.75878	−0.686257
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	5.09005	0.886064
$34$	4.51797	0.774825
$35$	4.11692	0.695887
$36$	−1.40619	−0.234365
$37$	11.0295	1.81323	0.906615	−	0.421958i	$-0.138657\pi$
$37$	11.0295	1.81323	0.906615	+	0.421958i	$0.138657\pi$
$38$	−8.09538	−1.31324
$39$	6.50746	1.04203
$40$	2.97735	0.470760
$41$	2.12020	0.331119	0.165559	−	0.986200i	$-0.447057\pi$
$41$	2.12020	0.331119	0.165559	+	0.986200i	$0.447057\pi$
$42$	−1.74567	−0.269362
$43$	−5.77876	−0.881253	−0.440626	−	0.897691i	$-0.645244\pi$
$43$	−5.77876	−0.881253	−0.440626	+	0.897691i	$0.645244\pi$
$44$	−4.03185	−0.607824
$45$	−4.18672	−0.624119
$46$	3.34096	0.492598
$47$	−1.60653	−0.234336	−0.117168	−	0.993112i	$-0.537382\pi$
$47$	−1.60653	−0.234336	−0.117168	+	0.993112i	$0.537382\pi$
$48$	−1.26246	−0.182221
$49$	−5.08800	−0.726858
$50$	3.86459	0.546536
$51$	−5.70376	−0.798686
$52$	−5.15458	−0.714812
$53$	−9.85335	−1.35346	−0.676731	−	0.736230i	$-0.736604\pi$
$53$	−9.85335	−1.35346	−0.676731	+	0.736230i	$0.736604\pi$
$54$	5.56265	0.756980
$55$	−12.0042	−1.61865
$56$	1.38275	0.184778
$57$	10.2201	1.35369
$58$	−3.63921	−0.477852
$59$	−2.44665	−0.318527	−0.159263	−	0.987236i	$-0.550912\pi$
$59$	−2.44665	−0.318527	−0.159263	+	0.987236i	$0.550912\pi$
$60$	−3.75878	−0.485257
$61$	5.95559	0.762535	0.381267	−	0.924465i	$-0.375488\pi$
$61$	5.95559	0.762535	0.381267	+	0.924465i	$0.375488\pi$
$62$	1.00000	0.127000
$63$	−1.94441	−0.244973
$64$	1.00000	0.125000
$65$	−15.3470	−1.90356
$66$	5.09005	0.626542
$67$	−15.0141	−1.83426	−0.917132	−	0.398585i	$-0.869501\pi$
$67$	−15.0141	−1.83426	−0.917132	+	0.398585i	$0.869501\pi$
$68$	4.51797	0.547884
$69$	−4.21783	−0.507767
$70$	4.11692	0.492067
$71$	−7.81799	−0.927825	−0.463912	−	0.885881i	$-0.653555\pi$
$71$	−7.81799	−0.927825	−0.463912	+	0.885881i	$0.653555\pi$
$72$	−1.40619	−0.165721
$73$	2.73055	0.319586	0.159793	−	0.987151i	$-0.448917\pi$
$73$	2.73055	0.319586	0.159793	+	0.987151i	$0.448917\pi$
$74$	11.0295	1.28215
$75$	−4.87890	−0.563366
$76$	−8.09538	−0.928603
$77$	−5.57503	−0.635334
$78$	6.50746	0.736824
$79$	−10.4772	−1.17878	−0.589391	−	0.807848i	$-0.700632\pi$
$79$	−10.4772	−1.17878	−0.589391	+	0.807848i	$0.700632\pi$
$80$	2.97735	0.332877
$81$	−2.80405	−0.311561
$82$	2.12020	0.234136
$83$	−2.48316	−0.272562	−0.136281	−	0.990670i	$-0.543515\pi$
$83$	−2.48316	−0.272562	−0.136281	+	0.990670i	$0.543515\pi$
$84$	−1.74567	−0.190468
$85$	13.4516	1.45903
$86$	−5.77876	−0.623140
$87$	4.59436	0.492568
$88$	−4.03185	−0.429796
$89$	−0.210119	−0.0222725	−0.0111363	−	0.999938i	$-0.503545\pi$
$89$	−0.210119	−0.0222725	−0.0111363	+	0.999938i	$0.503545\pi$
$90$	−4.18672	−0.441319
$91$	−7.12749	−0.747164
$92$	3.34096	0.348319
$93$	−1.26246	−0.130911
$94$	−1.60653	−0.165701
$95$	−24.1027	−2.47289
$96$	−1.26246	−0.128849
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−5.08800	−0.513966
$99$	5.66955	0.569811
$100$	3.86459	0.386459
$101$	7.47905	0.744193	0.372097	−	0.928194i	$-0.378639\pi$
$101$	7.47905	0.744193	0.372097	+	0.928194i	$0.378639\pi$
$102$	−5.70376	−0.564756
$103$	−14.0172	−1.38115	−0.690577	−	0.723259i	$-0.742643\pi$
$103$	−14.0172	−1.38115	−0.690577	+	0.723259i	$0.742643\pi$
$104$	−5.15458	−0.505448
$105$	−5.19746	−0.507220
$106$	−9.85335	−0.957042
$107$	−3.89965	−0.376993	−0.188497	−	0.982074i	$-0.560361\pi$
$107$	−3.89965	−0.376993	−0.188497	+	0.982074i	$0.560361\pi$
$108$	5.56265	0.535266
$109$	−14.2557	−1.36545	−0.682727	−	0.730674i	$-0.739206\pi$
$109$	−14.2557	−1.36545	−0.682727	+	0.730674i	$0.739206\pi$
$110$	−12.0042	−1.14456
$111$	−13.9243	−1.32163
$112$	1.38275	0.130658
$113$	−3.09144	−0.290818	−0.145409	−	0.989372i	$-0.546450\pi$
$113$	−3.09144	−0.290818	−0.145409	+	0.989372i	$0.546450\pi$
$114$	10.2201	0.957200
$115$	9.94719	0.927581
$116$	−3.63921	−0.337892
$117$	7.24833	0.670108
$118$	−2.44665	−0.225232
$119$	6.24722	0.572681
$120$	−3.75878	−0.343129
$121$	5.25579	0.477800
$122$	5.95559	0.539194
$123$	−2.67667	−0.241347
$124$	1.00000	0.0898027
$125$	−3.38051	−0.302362
$126$	−1.94441	−0.173222
$127$	13.4699	1.19526	0.597631	−	0.801771i	$-0.296109\pi$
$127$	13.4699	1.19526	0.597631	+	0.801771i	$0.296109\pi$
$128$	1.00000	0.0883883
$129$	7.29546	0.642330
$130$	−15.3470	−1.34602
$131$	−14.9048	−1.30224	−0.651120	−	0.758975i	$-0.725700\pi$
$131$	−14.9048	−1.30224	−0.651120	+	0.758975i	$0.725700\pi$
$132$	5.09005	0.443032
$133$	−11.1939	−0.970632
$134$	−15.0141	−1.29702
$135$	16.5619	1.42542
$136$	4.51797	0.387413
$137$	−22.8475	−1.95199	−0.975996	−	0.217789i	$-0.930116\pi$
$137$	−22.8475	−1.95199	−0.975996	+	0.217789i	$0.930116\pi$
$138$	−4.21783	−0.359046
$139$	17.2086	1.45962	0.729808	−	0.683652i	$-0.239609\pi$
$139$	17.2086	1.45962	0.729808	+	0.683652i	$0.239609\pi$
$140$	4.11692	0.347944
$141$	2.02818	0.170804
$142$	−7.81799	−0.656071
$143$	20.7825	1.73792
$144$	−1.40619	−0.117183
$145$	−10.8352	−0.899814
$146$	2.73055	0.225982
$147$	6.42341	0.529794
$148$	11.0295	0.906615
$149$	4.46987	0.366186	0.183093	−	0.983096i	$-0.441389\pi$
$149$	4.46987	0.366186	0.183093	+	0.983096i	$0.441389\pi$
$150$	−4.87890	−0.398360
$151$	20.8930	1.70025	0.850123	−	0.526584i	$-0.176527\pi$
$151$	20.8930	1.70025	0.850123	+	0.526584i	$0.176527\pi$
$152$	−8.09538	−0.656622
$153$	−6.35313	−0.513620
$154$	−5.57503	−0.449249
$155$	2.97735	0.239146
$156$	6.50746	0.521014
$157$	−5.06904	−0.404554	−0.202277	−	0.979328i	$-0.564834\pi$
$157$	−5.06904	−0.404554	−0.202277	+	0.979328i	$0.564834\pi$
$158$	−10.4772	−0.833524
$159$	12.4395	0.986515
$160$	2.97735	0.235380
$161$	4.61971	0.364084
$162$	−2.80405	−0.220307
$163$	0.100192	0.00784764	0.00392382	−	0.999992i	$-0.498751\pi$
$163$	0.100192	0.00784764	0.00392382	+	0.999992i	$0.498751\pi$
$164$	2.12020	0.165559
$165$	15.1548	1.17980
$166$	−2.48316	−0.192730
$167$	−9.48903	−0.734283	−0.367141	−	0.930165i	$-0.619664\pi$
$167$	−9.48903	−0.734283	−0.367141	+	0.930165i	$0.619664\pi$
$168$	−1.74567	−0.134681
$169$	13.5697	1.04382
$170$	13.4516	1.03169
$171$	11.3836	0.870529
$172$	−5.77876	−0.440626
$173$	0.417593	0.0317490	0.0158745	−	0.999874i	$-0.494947\pi$
$173$	0.417593	0.0317490	0.0158745	+	0.999874i	$0.494947\pi$
$174$	4.59436	0.348298
$175$	5.34376	0.403950
$176$	−4.03185	−0.303912
$177$	3.08880	0.232168
$178$	−0.210119	−0.0157491
$179$	6.86451	0.513078	0.256539	−	0.966534i	$-0.417418\pi$
$179$	6.86451	0.513078	0.256539	+	0.966534i	$0.417418\pi$
$180$	−4.18672	−0.312060
$181$	−3.98348	−0.296090	−0.148045	−	0.988981i	$-0.547298\pi$
$181$	−3.98348	−0.296090	−0.148045	+	0.988981i	$0.547298\pi$
$182$	−7.12749	−0.528325
$183$	−7.51870	−0.555798
$184$	3.34096	0.246299
$185$	32.8385	2.41433
$186$	−1.26246	−0.0925682
$187$	−18.2158	−1.33207
$188$	−1.60653	−0.117168
$189$	7.69175	0.559492
$190$	−24.1027	−1.74860
$191$	4.70146	0.340186	0.170093	−	0.985428i	$-0.445593\pi$
$191$	4.70146	0.340186	0.170093	+	0.985428i	$0.445593\pi$
$192$	−1.26246	−0.0911103
$193$	−3.40989	−0.245449	−0.122725	−	0.992441i	$-0.539163\pi$
$193$	−3.40989	−0.245449	−0.122725	+	0.992441i	$0.539163\pi$
$194$	−1.00000	−0.0717958
$195$	19.3750	1.38747
$196$	−5.08800	−0.363429
$197$	−13.0051	−0.926577	−0.463288	−	0.886208i	$-0.653331\pi$
$197$	−13.0051	−0.926577	−0.463288	+	0.886208i	$0.653331\pi$
$198$	5.66955	0.402917
$199$	19.0838	1.35282	0.676408	−	0.736528i	$-0.263536\pi$
$199$	19.0838	1.35282	0.676408	+	0.736528i	$0.263536\pi$
$200$	3.86459	0.273268
$201$	18.9547	1.33696
$202$	7.47905	0.526224
$203$	−5.03212	−0.353185
$204$	−5.70376	−0.399343
$205$	6.31256	0.440888
$206$	−14.0172	−0.976623
$207$	−4.69803	−0.326536
$208$	−5.15458	−0.357406
$209$	32.6393	2.25771
$210$	−5.19746	−0.358659
$211$	17.2879	1.19015	0.595074	−	0.803671i	$-0.297123\pi$
$211$	17.2879	1.19015	0.595074	+	0.803671i	$0.297123\pi$
$212$	−9.85335	−0.676731
$213$	9.86991	0.676275
$214$	−3.89965	−0.266574
$215$	−17.2054	−1.17340
$216$	5.56265	0.378490
$217$	1.38275	0.0938671
$218$	−14.2557	−0.965521
$219$	−3.44721	−0.232941
$220$	−12.0042	−0.809323
$221$	−23.2882	−1.56654
$222$	−13.9243	−0.934535
$223$	−15.4701	−1.03595	−0.517977	−	0.855395i	$-0.673315\pi$
$223$	−15.4701	−1.03595	−0.517977	+	0.855395i	$0.673315\pi$
$224$	1.38275	0.0923888
$225$	−5.43435	−0.362290
$226$	−3.09144	−0.205639
$227$	−25.3509	−1.68260	−0.841298	−	0.540572i	$-0.818208\pi$
$227$	−25.3509	−1.68260	−0.841298	+	0.540572i	$0.818208\pi$
$228$	10.2201	0.676843
$229$	−4.22301	−0.279064	−0.139532	−	0.990218i	$-0.544560\pi$
$229$	−4.22301	−0.279064	−0.139532	+	0.990218i	$0.544560\pi$
$230$	9.94719	0.655899
$231$	7.03827	0.463084
$232$	−3.63921	−0.238926
$233$	−6.16002	−0.403556	−0.201778	−	0.979431i	$-0.564672\pi$
$233$	−6.16002	−0.403556	−0.201778	+	0.979431i	$0.564672\pi$
$234$	7.24833	0.473838
$235$	−4.78319	−0.312021
$236$	−2.44665	−0.159263
$237$	13.2271	0.859193
$238$	6.24722	0.404947
$239$	15.9507	1.03176	0.515882	−	0.856660i	$-0.327464\pi$
$239$	15.9507	1.03176	0.515882	+	0.856660i	$0.327464\pi$
$240$	−3.75878	−0.242629
$241$	9.34596	0.602026	0.301013	−	0.953620i	$-0.402675\pi$
$241$	9.34596	0.602026	0.301013	+	0.953620i	$0.402675\pi$
$242$	5.25579	0.337855
$243$	−13.1479	−0.843440
$244$	5.95559	0.381267
$245$	−15.1488	−0.967818
$246$	−2.67667	−0.170658
$247$	41.7283	2.65511
$248$	1.00000	0.0635001
$249$	3.13489	0.198665
$250$	−3.38051	−0.213802
$251$	−21.1653	−1.33594	−0.667972	−	0.744186i	$-0.732838\pi$
$251$	−21.1653	−1.33594	−0.667972	+	0.744186i	$0.732838\pi$
$252$	−1.94441	−0.122486
$253$	−13.4702	−0.846867
$254$	13.4699	0.845179
$255$	−16.9821	−1.06346
$256$	1.00000	0.0625000
$257$	9.23156	0.575849	0.287925	−	0.957653i	$-0.407035\pi$
$257$	9.23156	0.575849	0.287925	+	0.957653i	$0.407035\pi$
$258$	7.29546	0.454196
$259$	15.2510	0.947649
$260$	−15.3470	−0.951779
$261$	5.11743	0.316761
$262$	−14.9048	−0.920822
$263$	−21.0376	−1.29724	−0.648618	−	0.761114i	$-0.724653\pi$
$263$	−21.0376	−1.29724	−0.648618	+	0.761114i	$0.724653\pi$
$264$	5.09005	0.313271
$265$	−29.3368	−1.80215
$266$	−11.1939	−0.686341
$267$	0.265267	0.0162341
$268$	−15.0141	−0.917132
$269$	30.2392	1.84371	0.921857	−	0.387529i	$-0.126671\pi$
$269$	30.2392	1.84371	0.921857	+	0.387529i	$0.126671\pi$
$270$	16.5619	1.00793
$271$	−24.6890	−1.49975	−0.749876	−	0.661578i	$-0.769887\pi$
$271$	−24.6890	−1.49975	−0.749876	+	0.661578i	$0.769887\pi$
$272$	4.51797	0.273942
$273$	8.99818	0.544595
$274$	−22.8475	−1.38027
$275$	−15.5814	−0.939596
$276$	−4.21783	−0.253884
$277$	3.07172	0.184562	0.0922808	−	0.995733i	$-0.470584\pi$
$277$	3.07172	0.184562	0.0922808	+	0.995733i	$0.470584\pi$
$278$	17.2086	1.03210
$279$	−1.40619	−0.0841865
$280$	4.11692	0.246033
$281$	−5.59659	−0.333864	−0.166932	−	0.985968i	$-0.553386\pi$
$281$	−5.59659	−0.333864	−0.166932	+	0.985968i	$0.553386\pi$
$282$	2.02818	0.120776
$283$	−13.1881	−0.783954	−0.391977	−	0.919975i	$-0.628209\pi$
$283$	−13.1881	−0.783954	−0.391977	+	0.919975i	$0.628209\pi$
$284$	−7.81799	−0.463912
$285$	30.4288	1.80245
$286$	20.7825	1.22889
$287$	2.93170	0.173053
$288$	−1.40619	−0.0828606
$289$	3.41203	0.200708
$290$	−10.8352	−0.636265
$291$	1.26246	0.0740068
$292$	2.73055	0.159793
$293$	−0.820293	−0.0479221	−0.0239610	−	0.999713i	$-0.507628\pi$
$293$	−0.820293	−0.0479221	−0.0239610	+	0.999713i	$0.507628\pi$
$294$	6.42341	0.374621
$295$	−7.28452	−0.424121
$296$	11.0295	0.641074
$297$	−22.4277	−1.30139
$298$	4.46987	0.258933
$299$	−17.2212	−0.995930
$300$	−4.87890	−0.281683
$301$	−7.99058	−0.460569
$302$	20.8930	1.20226
$303$	−9.44201	−0.542429
$304$	−8.09538	−0.464302
$305$	17.7318	1.01532
$306$	−6.35313	−0.363184
$307$	25.7336	1.46869	0.734347	−	0.678774i	$-0.237488\pi$
$307$	25.7336	1.46869	0.734347	+	0.678774i	$0.237488\pi$
$308$	−5.57503	−0.317667
$309$	17.6961	1.00670
$310$	2.97735	0.169102
$311$	6.38895	0.362284	0.181142	−	0.983457i	$-0.442021\pi$
$311$	6.38895	0.362284	0.181142	+	0.983457i	$0.442021\pi$
$312$	6.50746	0.368412
$313$	25.2330	1.42626	0.713128	−	0.701034i	$-0.247278\pi$
$313$	25.2330	1.42626	0.713128	+	0.701034i	$0.247278\pi$
$314$	−5.06904	−0.286063
$315$	−5.78918	−0.326183
$316$	−10.4772	−0.589391
$317$	13.5451	0.760768	0.380384	−	0.924829i	$-0.375792\pi$
$317$	13.5451	0.760768	0.380384	+	0.924829i	$0.375792\pi$
$318$	12.4395	0.697571
$319$	14.6727	0.821516
$320$	2.97735	0.166439
$321$	4.92315	0.274784
$322$	4.61971	0.257446
$323$	−36.5746	−2.03507
$324$	−2.80405	−0.155781
$325$	−19.9203	−1.10498
$326$	0.100192	0.00554912
$327$	17.9973	0.995255
$328$	2.12020	0.117068
$329$	−2.22143	−0.122471
$330$	15.1548	0.834247
$331$	−19.9526	−1.09670	−0.548348	−	0.836250i	$-0.684743\pi$
$331$	−19.9526	−1.09670	−0.548348	+	0.836250i	$0.684743\pi$
$332$	−2.48316	−0.136281
$333$	−15.5095	−0.849917
$334$	−9.48903	−0.519216
$335$	−44.7021	−2.44234
$336$	−1.74567	−0.0952340
$337$	27.9172	1.52075	0.760373	−	0.649487i	$-0.225016\pi$
$337$	27.9172	1.52075	0.760373	+	0.649487i	$0.225016\pi$
$338$	13.5697	0.738094
$339$	3.90282	0.211972
$340$	13.4516	0.729513
$341$	−4.03185	−0.218337
$342$	11.3836	0.615557
$343$	−16.7147	−0.902508
$344$	−5.77876	−0.311570
$345$	−12.5579	−0.676097
$346$	0.417593	0.0224499
$347$	2.66422	0.143023	0.0715114	−	0.997440i	$-0.477218\pi$
$347$	2.66422	0.143023	0.0715114	+	0.997440i	$0.477218\pi$
$348$	4.59436	0.246284
$349$	−14.8379	−0.794254	−0.397127	−	0.917764i	$-0.629993\pi$
$349$	−14.8379	−0.794254	−0.397127	+	0.917764i	$0.629993\pi$
$350$	5.34376	0.285636
$351$	−28.6731	−1.53046
$352$	−4.03185	−0.214898
$353$	−7.67611	−0.408558	−0.204279	−	0.978913i	$-0.565485\pi$
$353$	−7.67611	−0.408558	−0.204279	+	0.978913i	$0.565485\pi$
$354$	3.08880	0.164168
$355$	−23.2769	−1.23541
$356$	−0.210119	−0.0111363
$357$	−7.88687	−0.417417
$358$	6.86451	0.362801
$359$	−9.18418	−0.484722	−0.242361	−	0.970186i	$-0.577922\pi$
$359$	−9.18418	−0.484722	−0.242361	+	0.970186i	$0.577922\pi$
$360$	−4.18672	−0.220659
$361$	46.5351	2.44922
$362$	−3.98348	−0.209367
$363$	−6.63524	−0.348260
$364$	−7.12749	−0.373582
$365$	8.12978	0.425532
$366$	−7.51870	−0.393009
$367$	4.30473	0.224705	0.112353	−	0.993668i	$-0.464161\pi$
$367$	4.30473	0.224705	0.112353	+	0.993668i	$0.464161\pi$
$368$	3.34096	0.174160
$369$	−2.98140	−0.155206
$370$	32.8385	1.70719
$371$	−13.6247	−0.707360
$372$	−1.26246	−0.0654556
$373$	6.60585	0.342038	0.171019	−	0.985268i	$-0.445294\pi$
$373$	6.60585	0.342038	0.171019	+	0.985268i	$0.445294\pi$
$374$	−18.2158	−0.941914
$375$	4.26776	0.220386
$376$	−1.60653	−0.0828504
$377$	18.7586	0.966118
$378$	7.69175	0.395621
$379$	3.53482	0.181571	0.0907857	−	0.995870i	$-0.471062\pi$
$379$	3.53482	0.181571	0.0907857	+	0.995870i	$0.471062\pi$
$380$	−24.1027	−1.23644
$381$	−17.0053	−0.871206
$382$	4.70146	0.240548
$383$	37.5393	1.91817	0.959085	−	0.283118i	$-0.0913688\pi$
$383$	37.5393	1.91817	0.959085	+	0.283118i	$0.0913688\pi$
$384$	−1.26246	−0.0644247
$385$	−16.5988	−0.845954
$386$	−3.40989	−0.173559
$387$	8.12604	0.413070
$388$	−1.00000	−0.0507673
$389$	26.7240	1.35496	0.677480	−	0.735541i	$-0.263072\pi$
$389$	26.7240	1.35496	0.677480	+	0.735541i	$0.263072\pi$
$390$	19.3750	0.981089
$391$	15.0943	0.763354
$392$	−5.08800	−0.256983
$393$	18.8167	0.949179
$394$	−13.0051	−0.655189
$395$	−31.1944	−1.56956
$396$	5.66955	0.284906
$397$	−23.6971	−1.18932	−0.594662	−	0.803976i	$-0.702714\pi$
$397$	−23.6971	−1.18932	−0.594662	+	0.803976i	$0.702714\pi$
$398$	19.0838	0.956585
$399$	14.1318	0.707477
$400$	3.86459	0.193230
$401$	−8.68735	−0.433825	−0.216913	−	0.976191i	$-0.569599\pi$
$401$	−8.68735	−0.433825	−0.216913	+	0.976191i	$0.569599\pi$
$402$	18.9547	0.945375
$403$	−5.15458	−0.256768
$404$	7.47905	0.372097
$405$	−8.34863	−0.414847
$406$	−5.03212	−0.249740
$407$	−44.4691	−2.20425
$408$	−5.70376	−0.282378
$409$	−38.1044	−1.88414	−0.942070	−	0.335416i	$-0.891123\pi$
$409$	−38.1044	−1.88414	−0.942070	+	0.335416i	$0.891123\pi$
$410$	6.31256	0.311755
$411$	28.8441	1.42277
$412$	−14.0172	−0.690577
$413$	−3.38310	−0.166472
$414$	−4.69803	−0.230896
$415$	−7.39322	−0.362919
$416$	−5.15458	−0.252724
$417$	−21.7252	−1.06389
$418$	32.6393	1.59644
$419$	−26.0169	−1.27101	−0.635503	−	0.772098i	$-0.719207\pi$
$419$	−26.0169	−1.27101	−0.635503	+	0.772098i	$0.719207\pi$
$420$	−5.19746	−0.253610
$421$	13.7768	0.671442	0.335721	−	0.941961i	$-0.391020\pi$
$421$	13.7768	0.671442	0.335721	+	0.941961i	$0.391020\pi$
$422$	17.2879	0.841562
$423$	2.25909	0.109841
$424$	−9.85335	−0.478521
$425$	17.4601	0.846939
$426$	9.86991	0.478199
$427$	8.23508	0.398524
$428$	−3.89965	−0.188497
$429$	−26.2371	−1.26674
$430$	−17.2054	−0.829717
$431$	27.8018	1.33917	0.669583	−	0.742737i	$-0.266473\pi$
$431$	27.8018	1.33917	0.669583	+	0.742737i	$0.266473\pi$
$432$	5.56265	0.267633
$433$	11.3585	0.545853	0.272927	−	0.962035i	$-0.412008\pi$
$433$	11.3585	0.545853	0.272927	+	0.962035i	$0.412008\pi$
$434$	1.38275	0.0663741
$435$	13.6790	0.655859
$436$	−14.2557	−0.682727
$437$	−27.0463	−1.29380
$438$	−3.44721	−0.164714
$439$	33.8184	1.61406	0.807031	−	0.590509i	$-0.201073\pi$
$439$	33.8184	1.61406	0.807031	+	0.590509i	$0.201073\pi$
$440$	−12.0042	−0.572278
$441$	7.15471	0.340700
$442$	−23.2882	−1.10771
$443$	−28.9255	−1.37429	−0.687146	−	0.726520i	$-0.741137\pi$
$443$	−28.9255	−1.37429	−0.687146	+	0.726520i	$0.741137\pi$
$444$	−13.9243	−0.660816
$445$	−0.625596	−0.0296561
$446$	−15.4701	−0.732530
$447$	−5.64304	−0.266907
$448$	1.38275	0.0653288
$449$	20.4904	0.967003	0.483501	−	0.875344i	$-0.339365\pi$
$449$	20.4904	0.967003	0.483501	+	0.875344i	$0.339365\pi$
$450$	−5.43435	−0.256178
$451$	−8.54831	−0.402524
$452$	−3.09144	−0.145409
$453$	−26.3766	−1.23928
$454$	−25.3509	−1.18977
$455$	−21.2210	−0.994856
$456$	10.2201	0.478600
$457$	39.1892	1.83320	0.916598	−	0.399811i	$-0.130924\pi$
$457$	39.1892	1.83320	0.916598	+	0.399811i	$0.130924\pi$
$458$	−4.22301	−0.197328
$459$	25.1319	1.17305
$460$	9.94719	0.463790
$461$	36.8717	1.71729	0.858643	−	0.512574i	$-0.171308\pi$
$461$	36.8717	1.71729	0.858643	+	0.512574i	$0.171308\pi$
$462$	7.03827	0.327450
$463$	−26.9203	−1.25109	−0.625547	−	0.780187i	$-0.715124\pi$
$463$	−26.9203	−1.25109	−0.625547	+	0.780187i	$0.715124\pi$
$464$	−3.63921	−0.168946
$465$	−3.75878	−0.174309
$466$	−6.16002	−0.285358
$467$	26.7081	1.23590	0.617952	−	0.786216i	$-0.287963\pi$
$467$	26.7081	1.23590	0.617952	+	0.786216i	$0.287963\pi$
$468$	7.24833	0.335054
$469$	−20.7607	−0.958641
$470$	−4.78319	−0.220632
$471$	6.39947	0.294872
$472$	−2.44665	−0.112616
$473$	23.2991	1.07129
$474$	13.2271	0.607541
$475$	−31.2853	−1.43547
$476$	6.24722	0.286341
$477$	13.8557	0.634409
$478$	15.9507	0.729567
$479$	−36.1782	−1.65303	−0.826513	−	0.562917i	$-0.809679\pi$
$479$	−36.1782	−1.65303	−0.826513	+	0.562917i	$0.809679\pi$
$480$	−3.75878	−0.171564
$481$	−56.8522	−2.59224
$482$	9.34596	0.425697
$483$	−5.83221	−0.265375
$484$	5.25579	0.238900
$485$	−2.97735	−0.135194
$486$	−13.1479	−0.596402
$487$	16.5383	0.749423	0.374712	−	0.927141i	$-0.377742\pi$
$487$	16.5383	0.749423	0.374712	+	0.927141i	$0.377742\pi$
$488$	5.95559	0.269597
$489$	−0.126488	−0.00572001
$490$	−15.1488	−0.684351
$491$	−23.6759	−1.06848	−0.534238	−	0.845334i	$-0.679401\pi$
$491$	−23.6759	−1.06848	−0.534238	+	0.845334i	$0.679401\pi$
$492$	−2.67667	−0.120673
$493$	−16.4418	−0.740503
$494$	41.7283	1.87744
$495$	16.8802	0.758709
$496$	1.00000	0.0449013
$497$	−10.8103	−0.484909
$498$	3.13489	0.140478
$499$	23.3612	1.04579	0.522895	−	0.852397i	$-0.324852\pi$
$499$	23.3612	1.04579	0.522895	+	0.852397i	$0.324852\pi$
$500$	−3.38051	−0.151181
$501$	11.9795	0.535206
$502$	−21.1653	−0.944655
$503$	16.1826	0.721545	0.360772	−	0.932654i	$-0.382513\pi$
$503$	16.1826	0.721545	0.360772	+	0.932654i	$0.382513\pi$
$504$	−1.94441	−0.0866109
$505$	22.2677	0.990900
$506$	−13.4702	−0.598825
$507$	−17.1312	−0.760824
$508$	13.4699	0.597631
$509$	−35.8209	−1.58773	−0.793867	−	0.608092i	$-0.791935\pi$
$509$	−35.8209	−1.58773	−0.793867	+	0.608092i	$0.791935\pi$
$510$	−16.9821	−0.751979
$511$	3.77566	0.167025
$512$	1.00000	0.0441942
$513$	−45.0317	−1.98820
$514$	9.23156	0.407187
$515$	−41.7340	−1.83902
$516$	7.29546	0.321165
$517$	6.47728	0.284870
$518$	15.2510	0.670089
$519$	−0.527195	−0.0231413
$520$	−15.3470	−0.673009
$521$	7.37675	0.323181	0.161591	−	0.986858i	$-0.448338\pi$
$521$	7.37675	0.323181	0.161591	+	0.986858i	$0.448338\pi$
$522$	5.11743	0.223984
$523$	−23.0524	−1.00801	−0.504006	−	0.863700i	$-0.668141\pi$
$523$	−23.0524	−1.00801	−0.504006	+	0.863700i	$0.668141\pi$
$524$	−14.9048	−0.651120
$525$	−6.74629	−0.294432
$526$	−21.0376	−0.917285
$527$	4.51797	0.196806
$528$	5.09005	0.221516
$529$	−11.8380	−0.514695
$530$	−29.3368	−1.27431
$531$	3.44046	0.149303
$532$	−11.1939	−0.485316
$533$	−10.9287	−0.473375
$534$	0.265267	0.0114792
$535$	−11.6106	−0.501970
$536$	−15.0141	−0.648510
$537$	−8.66618	−0.373973
$538$	30.2392	1.30370
$539$	20.5141	0.883603
$540$	16.5619	0.712712
$541$	−3.76878	−0.162033	−0.0810163	−	0.996713i	$-0.525817\pi$
$541$	−3.76878	−0.162033	−0.0810163	+	0.996713i	$0.525817\pi$
$542$	−24.6890	−1.06048
$543$	5.02899	0.215814
$544$	4.51797	0.193706
$545$	−42.4443	−1.81811
$546$	8.99818	0.385087
$547$	−17.7488	−0.758882	−0.379441	−	0.925216i	$-0.623884\pi$
$547$	−17.7488	−0.758882	−0.379441	+	0.925216i	$0.623884\pi$
$548$	−22.8475	−0.975996
$549$	−8.37470	−0.357423
$550$	−15.5814	−0.664395
$551$	29.4608	1.25507
$552$	−4.21783	−0.179523
$553$	−14.4874	−0.616067
$554$	3.07172	0.130505
$555$	−41.4573	−1.75977
$556$	17.2086	0.729808
$557$	−15.7499	−0.667345	−0.333672	−	0.942689i	$-0.608288\pi$
$557$	−15.7499	−0.667345	−0.333672	+	0.942689i	$0.608288\pi$
$558$	−1.40619	−0.0595288
$559$	29.7871	1.25986
$560$	4.11692	0.173972
$561$	22.9967	0.970921
$562$	−5.59659	−0.236078
$563$	37.1593	1.56608	0.783040	−	0.621971i	$-0.213668\pi$
$563$	37.1593	1.56608	0.783040	+	0.621971i	$0.213668\pi$
$564$	2.02818	0.0854018
$565$	−9.20427	−0.387227
$566$	−13.1881	−0.554339
$567$	−3.87730	−0.162831
$568$	−7.81799	−0.328036
$569$	25.8177	1.08233	0.541167	−	0.840915i	$-0.317983\pi$
$569$	25.8177	1.08233	0.541167	+	0.840915i	$0.317983\pi$
$570$	30.4288	1.27452
$571$	−29.3095	−1.22656	−0.613282	−	0.789864i	$-0.710151\pi$
$571$	−29.3095	−1.22656	−0.613282	+	0.789864i	$0.710151\pi$
$572$	20.7825	0.868959
$573$	−5.93541	−0.247955
$574$	2.93170	0.122367
$575$	12.9114	0.538444
$576$	−1.40619	−0.0585913
$577$	−3.59894	−0.149826	−0.0749130	−	0.997190i	$-0.523868\pi$
$577$	−3.59894	−0.149826	−0.0749130	+	0.997190i	$0.523868\pi$
$578$	3.41203	0.141922
$579$	4.30486	0.178904
$580$	−10.8352	−0.449907
$581$	−3.43358	−0.142449
$582$	1.26246	0.0523307
$583$	39.7272	1.64533
$584$	2.73055	0.112991
$585$	21.5808	0.892255
$586$	−0.820293	−0.0338860
$587$	20.1372	0.831153	0.415576	−	0.909558i	$-0.363580\pi$
$587$	20.1372	0.831153	0.415576	+	0.909558i	$0.363580\pi$
$588$	6.42341	0.264897
$589$	−8.09538	−0.333564
$590$	−7.28452	−0.299899
$591$	16.4185	0.675366
$592$	11.0295	0.453308
$593$	21.0451	0.864220	0.432110	−	0.901821i	$-0.357769\pi$
$593$	21.0451	0.864220	0.432110	+	0.901821i	$0.357769\pi$
$594$	−22.4277	−0.920221
$595$	18.6001	0.762531
$596$	4.46987	0.183093
$597$	−24.0926	−0.986043
$598$	−17.2212	−0.704229
$599$	6.75847	0.276144	0.138072	−	0.990422i	$-0.455910\pi$
$599$	6.75847	0.276144	0.138072	+	0.990422i	$0.455910\pi$
$600$	−4.87890	−0.199180
$601$	29.2687	1.19389	0.596947	−	0.802280i	$-0.296380\pi$
$601$	29.2687	1.19389	0.596947	+	0.802280i	$0.296380\pi$
$602$	−7.99058	−0.325672
$603$	21.1127	0.859775
$604$	20.8930	0.850123
$605$	15.6483	0.636195
$606$	−9.44201	−0.383555
$607$	27.8971	1.13231	0.566154	−	0.824299i	$-0.308431\pi$
$607$	27.8971	1.13231	0.566154	+	0.824299i	$0.308431\pi$
$608$	−8.09538	−0.328311
$609$	6.35286	0.257431
$610$	17.7318	0.717941
$611$	8.28098	0.335012
$612$	−6.35313	−0.256810
$613$	−31.3604	−1.26663	−0.633317	−	0.773893i	$-0.718307\pi$
$613$	−31.3604	−1.26663	−0.633317	+	0.773893i	$0.718307\pi$
$614$	25.7336	1.03852
$615$	−7.96936	−0.321356
$616$	−5.57503	−0.224625
$617$	−0.385691	−0.0155273	−0.00776367	−	0.999970i	$-0.502471\pi$
$617$	−0.385691	−0.0155273	−0.00776367	+	0.999970i	$0.502471\pi$
$618$	17.6961	0.711843
$619$	−28.3262	−1.13853	−0.569264	−	0.822155i	$-0.692772\pi$
$619$	−28.3262	−1.13853	−0.569264	+	0.822155i	$0.692772\pi$
$620$	2.97735	0.119573
$621$	18.5846	0.745773
$622$	6.38895	0.256174
$623$	−0.290541	−0.0116403
$624$	6.50746	0.260507
$625$	−29.3879	−1.17552
$626$	25.2330	1.00852
$627$	−41.2059	−1.64560
$628$	−5.06904	−0.202277
$629$	49.8307	1.98688
$630$	−5.78918	−0.230647
$631$	7.47065	0.297402	0.148701	−	0.988882i	$-0.452491\pi$
$631$	7.47065	0.297402	0.148701	+	0.988882i	$0.452491\pi$
$632$	−10.4772	−0.416762
$633$	−21.8253	−0.867478
$634$	13.5451	0.537944
$635$	40.1046	1.59150
$636$	12.4395	0.493257
$637$	26.2265	1.03913
$638$	14.6727	0.580900
$639$	10.9936	0.434900
$640$	2.97735	0.117690
$641$	4.24386	0.167623	0.0838113	−	0.996482i	$-0.473291\pi$
$641$	4.24386	0.167623	0.0838113	+	0.996482i	$0.473291\pi$
$642$	4.92315	0.194301
$643$	−25.3308	−0.998947	−0.499474	−	0.866329i	$-0.666473\pi$
$643$	−25.3308	−0.998947	−0.499474	+	0.866329i	$0.666473\pi$
$644$	4.61971	0.182042
$645$	21.7211	0.855268
$646$	−36.5746	−1.43901
$647$	19.2196	0.755600	0.377800	−	0.925887i	$-0.376681\pi$
$647$	19.2196	0.755600	0.377800	+	0.925887i	$0.376681\pi$
$648$	−2.80405	−0.110154
$649$	9.86452	0.387216
$650$	−19.9203	−0.781340
$651$	−1.74567	−0.0684181
$652$	0.100192	0.00392382
$653$	−1.55799	−0.0609687	−0.0304843	−	0.999535i	$-0.509705\pi$
$653$	−1.55799	−0.0609687	−0.0304843	+	0.999535i	$0.509705\pi$
$654$	17.9973	0.703751
$655$	−44.3768	−1.73394
$656$	2.12020	0.0827797
$657$	−3.83967	−0.149800
$658$	−2.22143	−0.0866002
$659$	−31.4773	−1.22618	−0.613090	−	0.790013i	$-0.710074\pi$
$659$	−31.4773	−1.22618	−0.613090	+	0.790013i	$0.710074\pi$
$660$	15.1548	0.589902
$661$	42.0160	1.63423	0.817117	−	0.576471i	$-0.195571\pi$
$661$	42.0160	1.63423	0.817117	+	0.576471i	$0.195571\pi$
$662$	−19.9526	−0.775481
$663$	29.4005	1.14182
$664$	−2.48316	−0.0963652
$665$	−33.3281	−1.29241
$666$	−15.5095	−0.600982
$667$	−12.1585	−0.470778
$668$	−9.48903	−0.367141
$669$	19.5304	0.755088
$670$	−44.7021	−1.72699
$671$	−24.0120	−0.926974
$672$	−1.74567	−0.0673406
$673$	27.0647	1.04327	0.521634	−	0.853169i	$-0.325323\pi$
$673$	27.0647	1.04327	0.521634	+	0.853169i	$0.325323\pi$
$674$	27.9172	1.07533
$675$	21.4974	0.827434
$676$	13.5697	0.521911
$677$	−15.0622	−0.578889	−0.289445	−	0.957195i	$-0.593471\pi$
$677$	−15.0622	−0.578889	−0.289445	+	0.957195i	$0.593471\pi$
$678$	3.90282	0.149887
$679$	−1.38275	−0.0530650
$680$	13.4516	0.515844
$681$	32.0045	1.22641
$682$	−4.03185	−0.154387
$683$	−23.9547	−0.916600	−0.458300	−	0.888798i	$-0.651541\pi$
$683$	−23.9547	−0.916600	−0.458300	+	0.888798i	$0.651541\pi$
$684$	11.3836	0.435265
$685$	−68.0249	−2.59910
$686$	−16.7147	−0.638169
$687$	5.33138	0.203405
$688$	−5.77876	−0.220313
$689$	50.7899	1.93494
$690$	−12.5579	−0.478073
$691$	10.3353	0.393175	0.196587	−	0.980486i	$-0.437014\pi$
$691$	10.3353	0.393175	0.196587	+	0.980486i	$0.437014\pi$
$692$	0.417593	0.0158745
$693$	7.83957	0.297800
$694$	2.66422	0.101132
$695$	51.2360	1.94349
$696$	4.59436	0.174149
$697$	9.57898	0.362830
$698$	−14.8379	−0.561622
$699$	7.77679	0.294145
$700$	5.34376	0.201975
$701$	21.8102	0.823760	0.411880	−	0.911238i	$-0.364872\pi$
$701$	21.8102	0.823760	0.411880	+	0.911238i	$0.364872\pi$
$702$	−28.6731	−1.08220
$703$	−89.2876	−3.36754
$704$	−4.03185	−0.151956
$705$	6.03859	0.227427
$706$	−7.67611	−0.288894
$707$	10.3416	0.388938
$708$	3.08880	0.116084
$709$	25.8141	0.969470	0.484735	−	0.874661i	$-0.338916\pi$
$709$	25.8141	0.969470	0.484735	+	0.874661i	$0.338916\pi$
$710$	−23.2769	−0.873565
$711$	14.7330	0.552531
$712$	−0.210119	−0.00787453
$713$	3.34096	0.125120
$714$	−7.88687	−0.295159
$715$	61.8766	2.31405
$716$	6.86451	0.256539
$717$	−20.1371	−0.752035
$718$	−9.18418	−0.342751
$719$	−41.1314	−1.53394	−0.766971	−	0.641681i	$-0.778237\pi$
$719$	−41.1314	−1.53394	−0.766971	+	0.641681i	$0.778237\pi$
$720$	−4.18672	−0.156030
$721$	−19.3822	−0.721832
$722$	46.5351	1.73186
$723$	−11.7989	−0.438806
$724$	−3.98348	−0.148045
$725$	−14.0641	−0.522326
$726$	−6.63524	−0.246257
$727$	2.70224	0.100221	0.0501103	−	0.998744i	$-0.484043\pi$
$727$	2.70224	0.100221	0.0501103	+	0.998744i	$0.484043\pi$
$728$	−7.12749	−0.264162
$729$	25.0109	0.926330
$730$	8.12978	0.300897
$731$	−26.1083	−0.965649
$732$	−7.51870	−0.277899
$733$	23.3734	0.863317	0.431658	−	0.902037i	$-0.357929\pi$
$733$	23.3734	0.863317	0.431658	+	0.902037i	$0.357929\pi$
$734$	4.30473	0.158890
$735$	19.1247	0.705426
$736$	3.34096	0.123149
$737$	60.5345	2.22982
$738$	−2.98140	−0.109747
$739$	−27.9675	−1.02880	−0.514400	−	0.857550i	$-0.671985\pi$
$739$	−27.9675	−1.02880	−0.514400	+	0.857550i	$0.671985\pi$
$740$	32.8385	1.20717
$741$	−52.6803	−1.93526
$742$	−13.6247	−0.500179
$743$	−28.8448	−1.05821	−0.529107	−	0.848555i	$-0.677473\pi$
$743$	−28.8448	−1.05821	−0.529107	+	0.848555i	$0.677473\pi$
$744$	−1.26246	−0.0462841
$745$	13.3084	0.487580
$746$	6.60585	0.241857
$747$	3.49179	0.127758
$748$	−18.2158	−0.666034
$749$	−5.39223	−0.197028
$750$	4.26776	0.155836
$751$	−44.3528	−1.61846	−0.809228	−	0.587495i	$-0.800114\pi$
$751$	−44.3528	−1.61846	−0.809228	+	0.587495i	$0.800114\pi$
$752$	−1.60653	−0.0585841
$753$	26.7204	0.973746
$754$	18.7586	0.683148
$755$	62.2056	2.26389
$756$	7.69175	0.279746
$757$	26.8216	0.974848	0.487424	−	0.873166i	$-0.337937\pi$
$757$	26.8216	0.974848	0.487424	+	0.873166i	$0.337937\pi$
$758$	3.53482	0.128390
$759$	17.0057	0.617266
$760$	−24.1027	−0.874298
$761$	29.3114	1.06254	0.531268	−	0.847204i	$-0.321716\pi$
$761$	29.3114	1.06254	0.531268	+	0.847204i	$0.321716\pi$
$762$	−17.0053	−0.616036
$763$	−19.7121	−0.713627
$764$	4.70146	0.170093
$765$	−18.9155	−0.683890
$766$	37.5393	1.35635
$767$	12.6114	0.455373
$768$	−1.26246	−0.0455551
$769$	−21.7097	−0.782872	−0.391436	−	0.920205i	$-0.628022\pi$
$769$	−21.7097	−0.782872	−0.391436	+	0.920205i	$0.628022\pi$
$770$	−16.5988	−0.598180
$771$	−11.6545	−0.419726
$772$	−3.40989	−0.122725
$773$	45.1973	1.62564	0.812818	−	0.582518i	$-0.197932\pi$
$773$	45.1973	1.62564	0.812818	+	0.582518i	$0.197932\pi$
$774$	8.12604	0.292085
$775$	3.86459	0.138820
$776$	−1.00000	−0.0358979
$777$	−19.2538	−0.690725
$778$	26.7240	0.958102
$779$	−17.1638	−0.614956
$780$	19.3750	0.693735
$781$	31.5209	1.12791
$782$	15.0943	0.539773
$783$	−20.2437	−0.723449
$784$	−5.08800	−0.181714
$785$	−15.0923	−0.538667
$786$	18.8167	0.671171
$787$	−40.1143	−1.42992	−0.714959	−	0.699166i	$-0.753555\pi$
$787$	−40.1143	−1.42992	−0.714959	+	0.699166i	$0.753555\pi$
$788$	−13.0051	−0.463288
$789$	26.5592	0.945533
$790$	−31.1944	−1.10985
$791$	−4.27468	−0.151990
$792$	5.66955	0.201459
$793$	−30.6985	−1.09014
$794$	−23.6971	−0.840978
$795$	37.0366	1.31355
$796$	19.0838	0.676408
$797$	36.4191	1.29003	0.645016	−	0.764169i	$-0.276851\pi$
$797$	36.4191	1.29003	0.645016	+	0.764169i	$0.276851\pi$
$798$	14.1318	0.500262
$799$	−7.25824	−0.256778
$800$	3.86459	0.136634
$801$	0.295467	0.0104398
$802$	−8.68735	−0.306761
$803$	−11.0091	−0.388504
$804$	18.9547	0.668481
$805$	13.7545	0.484782
$806$	−5.15458	−0.181562
$807$	−38.1758	−1.34385
$808$	7.47905	0.263112
$809$	−15.6135	−0.548941	−0.274471	−	0.961596i	$-0.588503\pi$
$809$	−15.6135	−0.548941	−0.274471	+	0.961596i	$0.588503\pi$
$810$	−8.34863	−0.293341
$811$	−10.4358	−0.366450	−0.183225	−	0.983071i	$-0.558654\pi$
$811$	−10.4358	−0.366450	−0.183225	+	0.983071i	$0.558654\pi$
$812$	−5.03212	−0.176593
$813$	31.1689	1.09314
$814$	−44.4691	−1.55864
$815$	0.298306	0.0104492
$816$	−5.70376	−0.199672
$817$	46.7813	1.63667
$818$	−38.1044	−1.33229
$819$	10.0226	0.350219
$820$	6.31256	0.220444
$821$	−45.1929	−1.57724	−0.788621	−	0.614880i	$-0.789204\pi$
$821$	−45.1929	−1.57724	−0.788621	+	0.614880i	$0.789204\pi$
$822$	28.8441	1.00605
$823$	−48.1038	−1.67679	−0.838396	−	0.545061i	$-0.816506\pi$
$823$	−48.1038	−1.67679	−0.838396	+	0.545061i	$0.816506\pi$
$824$	−14.0172	−0.488311
$825$	19.6710	0.684855
$826$	−3.38310	−0.117713
$827$	25.6495	0.891919	0.445960	−	0.895053i	$-0.352863\pi$
$827$	25.6495	0.891919	0.445960	+	0.895053i	$0.352863\pi$
$828$	−4.69803	−0.163268
$829$	−9.83103	−0.341446	−0.170723	−	0.985319i	$-0.554610\pi$
$829$	−9.83103	−0.341446	−0.170723	+	0.985319i	$0.554610\pi$
$830$	−7.39322	−0.256622
$831$	−3.87792	−0.134524
$832$	−5.15458	−0.178703
$833$	−22.9874	−0.796467
$834$	−21.7252	−0.752283
$835$	−28.2521	−0.977705
$836$	32.6393	1.12885
$837$	5.56265	0.192273
$838$	−26.0169	−0.898738
$839$	50.1934	1.73287	0.866434	−	0.499292i	$-0.166407\pi$
$839$	50.1934	1.73287	0.866434	+	0.499292i	$0.166407\pi$
$840$	−5.19746	−0.179329
$841$	−15.7561	−0.543315
$842$	13.7768	0.474781
$843$	7.06547	0.243348
$844$	17.2879	0.595074
$845$	40.4017	1.38986
$846$	2.25909	0.0776690
$847$	7.26745	0.249712
$848$	−9.85335	−0.338366
$849$	16.6495	0.571410
$850$	17.4601	0.598876
$851$	36.8490	1.26317
$852$	9.86991	0.338137
$853$	0.875887	0.0299898	0.0149949	−	0.999888i	$-0.495227\pi$
$853$	0.875887	0.0299898	0.0149949	+	0.999888i	$0.495227\pi$
$854$	8.23508	0.281799
$855$	33.8931	1.15912
$856$	−3.89965	−0.133287
$857$	−33.5272	−1.14527	−0.572634	−	0.819811i	$-0.694078\pi$
$857$	−33.5272	−1.14527	−0.572634	+	0.819811i	$0.694078\pi$
$858$	−26.2371	−0.895719
$859$	10.9268	0.372819	0.186410	−	0.982472i	$-0.440315\pi$
$859$	10.9268	0.372819	0.186410	+	0.982472i	$0.440315\pi$
$860$	−17.2054	−0.586698
$861$	−3.70116	−0.126135
$862$	27.8018	0.946934
$863$	−15.5743	−0.530156	−0.265078	−	0.964227i	$-0.585398\pi$
$863$	−15.5743	−0.530156	−0.265078	+	0.964227i	$0.585398\pi$
$864$	5.56265	0.189245
$865$	1.24332	0.0422741
$866$	11.3585	0.385976
$867$	−4.30755	−0.146292
$868$	1.38275	0.0469336
$869$	42.2426	1.43298
$870$	13.6790	0.463762
$871$	77.3913	2.62230
$872$	−14.2557	−0.482761
$873$	1.40619	0.0475924
$874$	−27.0463	−0.914856
$875$	−4.67439	−0.158023
$876$	−3.44721	−0.116470
$877$	19.5412	0.659858	0.329929	−	0.944006i	$-0.392975\pi$
$877$	19.5412	0.659858	0.329929	+	0.944006i	$0.392975\pi$
$878$	33.8184	1.14131
$879$	1.03559	0.0349295
$880$	−12.0042	−0.404662
$881$	−8.64126	−0.291132	−0.145566	−	0.989349i	$-0.546500\pi$
$881$	−8.64126	−0.291132	−0.145566	+	0.989349i	$0.546500\pi$
$882$	7.15471	0.240912
$883$	−23.7687	−0.799879	−0.399940	−	0.916541i	$-0.630969\pi$
$883$	−23.7687	−0.799879	−0.399940	+	0.916541i	$0.630969\pi$
$884$	−23.2882	−0.783268
$885$	9.19643	0.309135
$886$	−28.9255	−0.971771
$887$	30.0960	1.01053	0.505263	−	0.862966i	$-0.331396\pi$
$887$	30.0960	1.01053	0.505263	+	0.862966i	$0.331396\pi$
$888$	−13.9243	−0.467267
$889$	18.6255	0.624680
$890$	−0.625596	−0.0209700
$891$	11.3055	0.378749
$892$	−15.4701	−0.517977
$893$	13.0055	0.435211
$894$	−5.64304	−0.188731
$895$	20.4380	0.683168
$896$	1.38275	0.0461944
$897$	21.7412	0.725916
$898$	20.4904	0.683774
$899$	−3.63921	−0.121375
$900$	−5.43435	−0.181145
$901$	−44.5171	−1.48308
$902$	−8.54831	−0.284627
$903$	10.0878	0.335701
$904$	−3.09144	−0.102820
$905$	−11.8602	−0.394246
$906$	−26.3766	−0.876303
$907$	54.0015	1.79309	0.896546	−	0.442951i	$-0.146068\pi$
$907$	54.0015	1.79309	0.896546	+	0.442951i	$0.146068\pi$
$908$	−25.3509	−0.841298
$909$	−10.5170	−0.348826
$910$	−21.2210	−0.703470
$911$	−2.84554	−0.0942771	−0.0471385	−	0.998888i	$-0.515010\pi$
$911$	−2.84554	−0.0942771	−0.0471385	+	0.998888i	$0.515010\pi$
$912$	10.2201	0.338421
$913$	10.0117	0.331339
$914$	39.1892	1.29627
$915$	−22.3858	−0.740051
$916$	−4.22301	−0.139532
$917$	−20.6096	−0.680589
$918$	25.1319	0.829475
$919$	45.4077	1.49786	0.748931	−	0.662648i	$-0.230567\pi$
$919$	45.4077	1.49786	0.748931	+	0.662648i	$0.230567\pi$
$920$	9.94719	0.327949
$921$	−32.4877	−1.07051
$922$	36.8717	1.21430
$923$	40.2984	1.32644
$924$	7.03827	0.231542
$925$	42.6243	1.40148
$926$	−26.9203	−0.884656
$927$	19.7108	0.647389
$928$	−3.63921	−0.119463
$929$	−25.1228	−0.824251	−0.412126	−	0.911127i	$-0.635214\pi$
$929$	−25.1228	−0.824251	−0.412126	+	0.911127i	$0.635214\pi$
$930$	−3.75878	−0.123255
$931$	41.1893	1.34993
$932$	−6.16002	−0.201778
$933$	−8.06580	−0.264063
$934$	26.7081	0.873916
$935$	−54.2346	−1.77366
$936$	7.24833	0.236919
$937$	−18.5894	−0.607289	−0.303644	−	0.952785i	$-0.598203\pi$
$937$	−18.5894	−0.607289	−0.303644	+	0.952785i	$0.598203\pi$
$938$	−20.7607	−0.677862
$939$	−31.8557	−1.03957
$940$	−4.78319	−0.156010
$941$	54.5932	1.77969	0.889844	−	0.456264i	$-0.150813\pi$
$941$	54.5932	1.77969	0.889844	+	0.456264i	$0.150813\pi$
$942$	6.39947	0.208506
$943$	7.08349	0.230670
$944$	−2.44665	−0.0796316
$945$	22.9010	0.744969
$946$	23.2991	0.757519
$947$	−33.9235	−1.10237	−0.551183	−	0.834384i	$-0.685823\pi$
$947$	−33.9235	−1.10237	−0.551183	+	0.834384i	$0.685823\pi$
$948$	13.2271	0.429596
$949$	−14.0748	−0.456888
$950$	−31.2853	−1.01503
$951$	−17.1001	−0.554510
$952$	6.24722	0.202473
$953$	11.3910	0.368991	0.184496	−	0.982833i	$-0.440935\pi$
$953$	11.3910	0.368991	0.184496	+	0.982833i	$0.440935\pi$
$954$	13.8557	0.448595
$955$	13.9979	0.452961
$956$	15.9507	0.515882
$957$	−18.5238	−0.598789
$958$	−36.1782	−1.16887
$959$	−31.5923	−1.02017
$960$	−3.75878	−0.121314
$961$	1.00000	0.0322581
$962$	−56.8522	−1.83299
$963$	5.48365	0.176708
$964$	9.34596	0.301013
$965$	−10.1524	−0.326818
$966$	−5.83221	−0.187648
$967$	7.56632	0.243317	0.121658	−	0.992572i	$-0.461179\pi$
$967$	7.56632	0.243317	0.121658	+	0.992572i	$0.461179\pi$
$968$	5.25579	0.168928
$969$	46.1741	1.48333
$970$	−2.97735	−0.0955968
$971$	−52.4423	−1.68295	−0.841477	−	0.540292i	$-0.818314\pi$
$971$	−52.4423	−1.68295	−0.841477	+	0.540292i	$0.818314\pi$
$972$	−13.1479	−0.421720
$973$	23.7952	0.762839
$974$	16.5383	0.529922
$975$	25.1487	0.805402
$976$	5.95559	0.190634
$977$	−41.0103	−1.31203	−0.656017	−	0.754746i	$-0.727760\pi$
$977$	−41.0103	−1.31203	−0.656017	+	0.754746i	$0.727760\pi$
$978$	−0.126488	−0.00404466
$979$	0.847166	0.0270755
$980$	−15.1488	−0.483909
$981$	20.0463	0.640029
$982$	−23.6759	−0.755527
$983$	−13.1871	−0.420604	−0.210302	−	0.977636i	$-0.567445\pi$
$983$	−13.1871	−0.420604	−0.210302	+	0.977636i	$0.567445\pi$
$984$	−2.67667	−0.0853290
$985$	−38.7208	−1.23375
$986$	−16.4418	−0.523615
$987$	2.80446	0.0892671
$988$	41.7283	1.32755
$989$	−19.3066	−0.613914
$990$	16.8802	0.536488
$991$	−14.5388	−0.461841	−0.230920	−	0.972973i	$-0.574174\pi$
$991$	−14.5388	−0.461841	−0.230920	+	0.972973i	$0.574174\pi$
$992$	1.00000	0.0317500
$993$	25.1894	0.799362
$994$	−10.8103	−0.342882
$995$	56.8191	1.80129
$996$	3.13489	0.0993327
$997$	−22.1152	−0.700394	−0.350197	−	0.936676i	$-0.613885\pi$
$997$	−22.1152	−0.700394	−0.350197	+	0.936676i	$0.613885\pi$
$998$	23.3612	0.739485
$999$	61.3529	1.94112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.9	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.9	✓	21	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.26246 q^{3} +1.00000 q^{4} +2.97735 q^{5} -1.26246 q^{6} +1.38275 q^{7} +1.00000 q^{8} -1.40619 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.26246 q^{3} +1.00000 q^{4} +2.97735 q^{5} -1.26246 q^{6} +1.38275 q^{7} +1.00000 q^{8} -1.40619 q^{9} +2.97735 q^{10} -4.03185 q^{11} -1.26246 q^{12} -5.15458 q^{13} +1.38275 q^{14} -3.75878 q^{15} +1.00000 q^{16} +4.51797 q^{17} -1.40619 q^{18} -8.09538 q^{19} +2.97735 q^{20} -1.74567 q^{21} -4.03185 q^{22} +3.34096 q^{23} -1.26246 q^{24} +3.86459 q^{25} -5.15458 q^{26} +5.56265 q^{27} +1.38275 q^{28} -3.63921 q^{29} -3.75878 q^{30} +1.00000 q^{31} +1.00000 q^{32} +5.09005 q^{33} +4.51797 q^{34} +4.11692 q^{35} -1.40619 q^{36} +11.0295 q^{37} -8.09538 q^{38} +6.50746 q^{39} +2.97735 q^{40} +2.12020 q^{41} -1.74567 q^{42} -5.77876 q^{43} -4.03185 q^{44} -4.18672 q^{45} +3.34096 q^{46} -1.60653 q^{47} -1.26246 q^{48} -5.08800 q^{49} +3.86459 q^{50} -5.70376 q^{51} -5.15458 q^{52} -9.85335 q^{53} +5.56265 q^{54} -12.0042 q^{55} +1.38275 q^{56} +10.2201 q^{57} -3.63921 q^{58} -2.44665 q^{59} -3.75878 q^{60} +5.95559 q^{61} +1.00000 q^{62} -1.94441 q^{63} +1.00000 q^{64} -15.3470 q^{65} +5.09005 q^{66} -15.0141 q^{67} +4.51797 q^{68} -4.21783 q^{69} +4.11692 q^{70} -7.81799 q^{71} -1.40619 q^{72} +2.73055 q^{73} +11.0295 q^{74} -4.87890 q^{75} -8.09538 q^{76} -5.57503 q^{77} +6.50746 q^{78} -10.4772 q^{79} +2.97735 q^{80} -2.80405 q^{81} +2.12020 q^{82} -2.48316 q^{83} -1.74567 q^{84} +13.4516 q^{85} -5.77876 q^{86} +4.59436 q^{87} -4.03185 q^{88} -0.210119 q^{89} -4.18672 q^{90} -7.12749 q^{91} +3.34096 q^{92} -1.26246 q^{93} -1.60653 q^{94} -24.1027 q^{95} -1.26246 q^{96} -1.00000 q^{97} -5.08800 q^{98} +5.66955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

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