LMFDB - Embedded newform 2671.2.a.b.1.70

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.70
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.632093 q^{2} +1.44371 q^{3} -1.60046 q^{4} +3.81685 q^{5} +0.912557 q^{6} +5.06733 q^{7} -2.27582 q^{8} -0.915708 q^{9} +O(q^{10})$	\(q+0.632093 q^{2} +1.44371 q^{3} -1.60046 q^{4} +3.81685 q^{5} +0.912557 q^{6} +5.06733 q^{7} -2.27582 q^{8} -0.915708 q^{9} +2.41260 q^{10} +0.203431 q^{11} -2.31059 q^{12} -0.0723923 q^{13} +3.20302 q^{14} +5.51041 q^{15} +1.76239 q^{16} -2.98928 q^{17} -0.578812 q^{18} +1.18317 q^{19} -6.10871 q^{20} +7.31574 q^{21} +0.128587 q^{22} +1.99112 q^{23} -3.28562 q^{24} +9.56833 q^{25} -0.0457586 q^{26} -5.65314 q^{27} -8.11005 q^{28} +4.82007 q^{29} +3.48309 q^{30} -6.41563 q^{31} +5.66564 q^{32} +0.293694 q^{33} -1.88950 q^{34} +19.3412 q^{35} +1.46555 q^{36} +11.7708 q^{37} +0.747872 q^{38} -0.104513 q^{39} -8.68647 q^{40} +0.854404 q^{41} +4.62422 q^{42} +1.93498 q^{43} -0.325582 q^{44} -3.49512 q^{45} +1.25858 q^{46} -6.53182 q^{47} +2.54437 q^{48} +18.6778 q^{49} +6.04807 q^{50} -4.31565 q^{51} +0.115861 q^{52} -9.85586 q^{53} -3.57331 q^{54} +0.776463 q^{55} -11.5323 q^{56} +1.70815 q^{57} +3.04673 q^{58} +6.25230 q^{59} -8.81919 q^{60} -5.00283 q^{61} -4.05527 q^{62} -4.64019 q^{63} +0.0564356 q^{64} -0.276310 q^{65} +0.185642 q^{66} -3.02827 q^{67} +4.78422 q^{68} +2.87460 q^{69} +12.2254 q^{70} +2.95636 q^{71} +2.08399 q^{72} -16.4425 q^{73} +7.44021 q^{74} +13.8139 q^{75} -1.89361 q^{76} +1.03085 q^{77} -0.0660621 q^{78} -4.77625 q^{79} +6.72676 q^{80} -5.41436 q^{81} +0.540062 q^{82} +4.76453 q^{83} -11.7085 q^{84} -11.4096 q^{85} +1.22309 q^{86} +6.95877 q^{87} -0.462972 q^{88} +1.03642 q^{89} -2.20924 q^{90} -0.366835 q^{91} -3.18671 q^{92} -9.26230 q^{93} -4.12871 q^{94} +4.51597 q^{95} +8.17953 q^{96} -5.45958 q^{97} +11.8061 q^{98} -0.186283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * 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 $

$2$	0.632093	0.446957	0.223478	−	0.974709i	$-0.428259\pi$
$2$	0.632093	0.446957	0.223478	+	0.974709i	$0.428259\pi$
$3$	1.44371	0.833525	0.416763	−	0.909015i	$-0.363165\pi$
$3$	1.44371	0.833525	0.416763	+	0.909015i	$0.363165\pi$
$4$	−1.60046	−0.800229
$5$	3.81685	1.70695	0.853473	−	0.521137i	$-0.174492\pi$
$5$	3.81685	1.70695	0.853473	+	0.521137i	$0.174492\pi$
$6$	0.912557	0.372550
$7$	5.06733	1.91527	0.957634	−	0.287987i	$-0.0929859\pi$
$7$	5.06733	1.91527	0.957634	+	0.287987i	$0.0929859\pi$
$8$	−2.27582	−0.804625
$9$	−0.915708	−0.305236
$10$	2.41260	0.762932
$11$	0.203431	0.0613366	0.0306683	−	0.999530i	$-0.490236\pi$
$11$	0.203431	0.0613366	0.0306683	+	0.999530i	$0.490236\pi$
$12$	−2.31059	−0.667011
$13$	−0.0723923	−0.0200780	−0.0100390	−	0.999950i	$-0.503196\pi$
$13$	−0.0723923	−0.0200780	−0.0100390	+	0.999950i	$0.503196\pi$
$14$	3.20302	0.856043
$15$	5.51041	1.42278
$16$	1.76239	0.440597
$17$	−2.98928	−0.725007	−0.362504	−	0.931982i	$-0.618078\pi$
$17$	−2.98928	−0.725007	−0.362504	+	0.931982i	$0.618078\pi$
$18$	−0.578812	−0.136427
$19$	1.18317	0.271437	0.135719	−	0.990747i	$-0.456666\pi$
$19$	1.18317	0.271437	0.135719	+	0.990747i	$0.456666\pi$
$20$	−6.10871	−1.36595
$21$	7.31574	1.59642
$22$	0.128587	0.0274148
$23$	1.99112	0.415178	0.207589	−	0.978216i	$-0.433438\pi$
$23$	1.99112	0.415178	0.207589	+	0.978216i	$0.433438\pi$
$24$	−3.28562	−0.670675
$25$	9.56833	1.91367
$26$	−0.0457586	−0.00897401
$27$	−5.65314	−1.08795
$28$	−8.11005	−1.53265
$29$	4.82007	0.895064	0.447532	−	0.894268i	$-0.352303\pi$
$29$	4.82007	0.895064	0.447532	+	0.894268i	$0.352303\pi$
$30$	3.48309	0.635923
$31$	−6.41563	−1.15228	−0.576141	−	0.817350i	$-0.695442\pi$
$31$	−6.41563	−1.15228	−0.576141	+	0.817350i	$0.695442\pi$
$32$	5.66564	1.00155
$33$	0.293694	0.0511256
$34$	−1.88950	−0.324047
$35$	19.3412	3.26926
$36$	1.46555	0.244259
$37$	11.7708	1.93510	0.967551	−	0.252676i	$-0.0813107\pi$
$37$	11.7708	1.93510	0.967551	+	0.252676i	$0.0813107\pi$
$38$	0.747872	0.121321
$39$	−0.104513	−0.0167355
$40$	−8.68647	−1.37345
$41$	0.854404	0.133435	0.0667177	−	0.997772i	$-0.478747\pi$
$41$	0.854404	0.133435	0.0667177	+	0.997772i	$0.478747\pi$
$42$	4.62422	0.713533
$43$	1.93498	0.295082	0.147541	−	0.989056i	$-0.452864\pi$
$43$	1.93498	0.295082	0.147541	+	0.989056i	$0.452864\pi$
$44$	−0.325582	−0.0490834
$45$	−3.49512	−0.521021
$46$	1.25858	0.185567
$47$	−6.53182	−0.952764	−0.476382	−	0.879239i	$-0.658052\pi$
$47$	−6.53182	−0.952764	−0.476382	+	0.879239i	$0.658052\pi$
$48$	2.54437	0.367248
$49$	18.6778	2.66825
$50$	6.04807	0.855326
$51$	−4.31565	−0.604312
$52$	0.115861	0.0160670
$53$	−9.85586	−1.35381	−0.676903	−	0.736072i	$-0.736678\pi$
$53$	−9.85586	−1.35381	−0.676903	+	0.736072i	$0.736678\pi$
$54$	−3.57331	−0.486265
$55$	0.776463	0.104698
$56$	−11.5323	−1.54107
$57$	1.70815	0.226250
$58$	3.04673	0.400055
$59$	6.25230	0.813980	0.406990	−	0.913433i	$-0.366578\pi$
$59$	6.25230	0.813980	0.406990	+	0.913433i	$0.366578\pi$
$60$	−8.81919	−1.13855
$61$	−5.00283	−0.640547	−0.320273	−	0.947325i	$-0.603775\pi$
$61$	−5.00283	−0.640547	−0.320273	+	0.947325i	$0.603775\pi$
$62$	−4.05527	−0.515020
$63$	−4.64019	−0.584609
$64$	0.0564356	0.00705445
$65$	−0.276310	−0.0342721
$66$	0.185642	0.0228509
$67$	−3.02827	−0.369962	−0.184981	−	0.982742i	$-0.559222\pi$
$67$	−3.02827	−0.369962	−0.184981	+	0.982742i	$0.559222\pi$
$68$	4.78422	0.580172
$69$	2.87460	0.346061
$70$	12.2254	1.46122
$71$	2.95636	0.350855	0.175428	−	0.984492i	$-0.443869\pi$
$71$	2.95636	0.350855	0.175428	+	0.984492i	$0.443869\pi$
$72$	2.08399	0.245601
$73$	−16.4425	−1.92445	−0.962227	−	0.272248i	$-0.912233\pi$
$73$	−16.4425	−1.92445	−0.962227	+	0.272248i	$0.912233\pi$
$74$	7.44021	0.864907
$75$	13.8139	1.59509
$76$	−1.89361	−0.217212
$77$	1.03085	0.117476
$78$	−0.0660621	−0.00748006
$79$	−4.77625	−0.537370	−0.268685	−	0.963228i	$-0.586589\pi$
$79$	−4.77625	−0.537370	−0.268685	+	0.963228i	$0.586589\pi$
$80$	6.72676	0.752075
$81$	−5.41436	−0.601595
$82$	0.540062	0.0596399
$83$	4.76453	0.522975	0.261488	−	0.965207i	$-0.415787\pi$
$83$	4.76453	0.522975	0.261488	+	0.965207i	$0.415787\pi$
$84$	−11.7085	−1.27751
$85$	−11.4096	−1.23755
$86$	1.22309	0.131889
$87$	6.95877	0.746058
$88$	−0.462972	−0.0493530
$89$	1.03642	0.109860	0.0549302	−	0.998490i	$-0.482506\pi$
$89$	1.03642	0.109860	0.0549302	+	0.998490i	$0.482506\pi$
$90$	−2.20924	−0.232874
$91$	−0.366835	−0.0384548
$92$	−3.18671	−0.332238
$93$	−9.26230	−0.960456
$94$	−4.12871	−0.425844
$95$	4.51597	0.463329
$96$	8.17953	0.834819
$97$	−5.45958	−0.554337	−0.277168	−	0.960821i	$-0.589396\pi$
$97$	−5.45958	−0.554337	−0.277168	+	0.960821i	$0.589396\pi$
$98$	11.8061	1.19260
$99$	−0.186283	−0.0187221
$100$	−15.3137	−1.53137
$101$	9.97254	0.992305	0.496152	−	0.868235i	$-0.334746\pi$
$101$	9.97254	0.992305	0.496152	+	0.868235i	$0.334746\pi$
$102$	−2.72789	−0.270101
$103$	−12.8755	−1.26866	−0.634331	−	0.773061i	$-0.718725\pi$
$103$	−12.8755	−1.26866	−0.634331	+	0.773061i	$0.718725\pi$
$104$	0.164752	0.0161553
$105$	27.9231	2.72501
$106$	−6.22981	−0.605093
$107$	−3.54065	−0.342288	−0.171144	−	0.985246i	$-0.554746\pi$
$107$	−3.54065	−0.342288	−0.171144	+	0.985246i	$0.554746\pi$
$108$	9.04761	0.870607
$109$	17.7761	1.70264	0.851319	−	0.524648i	$-0.175803\pi$
$109$	17.7761	1.70264	0.851319	+	0.524648i	$0.175803\pi$
$110$	0.490797	0.0467956
$111$	16.9935	1.61296
$112$	8.93058	0.843861
$113$	9.96985	0.937885	0.468942	−	0.883229i	$-0.344635\pi$
$113$	9.96985	0.937885	0.468942	+	0.883229i	$0.344635\pi$
$114$	1.07971	0.101124
$115$	7.59982	0.708687
$116$	−7.71432	−0.716256
$117$	0.0662902	0.00612853
$118$	3.95203	0.363814
$119$	−15.1477	−1.38858
$120$	−12.5407	−1.14481
$121$	−10.9586	−0.996238
$122$	−3.16225	−0.286297
$123$	1.23351	0.111222
$124$	10.2680	0.922090
$125$	17.4366	1.55958
$126$	−2.93303	−0.261295
$127$	−10.7989	−0.958248	−0.479124	−	0.877747i	$-0.659046\pi$
$127$	−10.7989	−0.958248	−0.479124	+	0.877747i	$0.659046\pi$
$128$	−11.2956	−0.998400
$129$	2.79355	0.245958
$130$	−0.174654	−0.0153182
$131$	7.41163	0.647557	0.323778	−	0.946133i	$-0.395047\pi$
$131$	7.41163	0.647557	0.323778	+	0.946133i	$0.395047\pi$
$132$	−0.470046	−0.0409122
$133$	5.99550	0.519875
$134$	−1.91415	−0.165357
$135$	−21.5772	−1.85707
$136$	6.80308	0.583359
$137$	−18.8242	−1.60826	−0.804130	−	0.594453i	$-0.797369\pi$
$137$	−18.8242	−1.60826	−0.804130	+	0.594453i	$0.797369\pi$
$138$	1.81701	0.154675
$139$	11.4996	0.975379	0.487690	−	0.873017i	$-0.337840\pi$
$139$	11.4996	0.975379	0.487690	+	0.873017i	$0.337840\pi$
$140$	−30.9548	−2.61616
$141$	−9.43004	−0.794152
$142$	1.86869	0.156817
$143$	−0.0147268	−0.00123152
$144$	−1.61383	−0.134486
$145$	18.3975	1.52783
$146$	−10.3932	−0.860148
$147$	26.9653	2.22406
$148$	−18.8386	−1.54853
$149$	2.06031	0.168787	0.0843937	−	0.996432i	$-0.473105\pi$
$149$	2.06031	0.168787	0.0843937	+	0.996432i	$0.473105\pi$
$150$	8.73164	0.712936
$151$	−9.97648	−0.811874	−0.405937	−	0.913901i	$-0.633055\pi$
$151$	−9.97648	−0.811874	−0.405937	+	0.913901i	$0.633055\pi$
$152$	−2.69268	−0.218405
$153$	2.73731	0.221298
$154$	0.651592	0.0525068
$155$	−24.4875	−1.96688
$156$	0.167269	0.0133923
$157$	−11.1065	−0.886397	−0.443198	−	0.896424i	$-0.646156\pi$
$157$	−11.1065	−0.886397	−0.443198	+	0.896424i	$0.646156\pi$
$158$	−3.01903	−0.240181
$159$	−14.2290	−1.12843
$160$	21.6249	1.70960
$161$	10.0897	0.795178
$162$	−3.42237	−0.268887
$163$	2.08180	0.163059	0.0815294	−	0.996671i	$-0.474020\pi$
$163$	2.08180	0.163059	0.0815294	+	0.996671i	$0.474020\pi$
$164$	−1.36744	−0.106779
$165$	1.12099	0.0872686
$166$	3.01163	0.233747
$167$	6.68460	0.517270	0.258635	−	0.965975i	$-0.416727\pi$
$167$	6.68460	0.517270	0.258635	+	0.965975i	$0.416727\pi$
$168$	−16.6493	−1.28452
$169$	−12.9948	−0.999597
$170$	−7.21195	−0.553131
$171$	−1.08344	−0.0828524
$172$	−3.09686	−0.236133
$173$	−0.0438630	−0.00333484	−0.00166742	−	0.999999i	$-0.500531\pi$
$173$	−0.0438630	−0.00333484	−0.00166742	+	0.999999i	$0.500531\pi$
$174$	4.39858	0.333456
$175$	48.4858	3.66518
$176$	0.358523	0.0270247
$177$	9.02649	0.678472
$178$	0.655114	0.0491029
$179$	21.9841	1.64317	0.821584	−	0.570087i	$-0.193090\pi$
$179$	21.9841	1.64317	0.821584	+	0.570087i	$0.193090\pi$
$180$	5.59379	0.416937
$181$	−10.5337	−0.782962	−0.391481	−	0.920186i	$-0.628037\pi$
$181$	−10.5337	−0.782962	−0.391481	+	0.920186i	$0.628037\pi$
$182$	−0.231874	−0.0171876
$183$	−7.22262	−0.533912
$184$	−4.53145	−0.334063
$185$	44.9272	3.30311
$186$	−5.85463	−0.429282
$187$	−0.608111	−0.0444695
$188$	10.4539	0.762429
$189$	−28.6463	−2.08371
$190$	2.85451	0.207088
$191$	20.1185	1.45572	0.727862	−	0.685723i	$-0.240514\pi$
$191$	20.1185	1.45572	0.727862	+	0.685723i	$0.240514\pi$
$192$	0.0814765	0.00588006
$193$	20.6297	1.48496	0.742479	−	0.669869i	$-0.233650\pi$
$193$	20.6297	1.48496	0.742479	+	0.669869i	$0.233650\pi$
$194$	−3.45096	−0.247765
$195$	−0.398912	−0.0285666
$196$	−29.8930	−2.13522
$197$	−14.7206	−1.04880	−0.524401	−	0.851471i	$-0.675711\pi$
$197$	−14.7206	−1.04880	−0.524401	+	0.851471i	$0.675711\pi$
$198$	−0.117748	−0.00836799
$199$	7.67657	0.544178	0.272089	−	0.962272i	$-0.412286\pi$
$199$	7.67657	0.544178	0.272089	+	0.962272i	$0.412286\pi$
$200$	−21.7758	−1.53978
$201$	−4.37193	−0.308372
$202$	6.30357	0.443518
$203$	24.4248	1.71429
$204$	6.90702	0.483588
$205$	3.26113	0.227767
$206$	−8.13852	−0.567038
$207$	−1.82329	−0.126727
$208$	−0.127583	−0.00884631
$209$	0.240692	0.0166490
$210$	17.6500	1.21796
$211$	−12.0026	−0.826294	−0.413147	−	0.910664i	$-0.635570\pi$
$211$	−12.0026	−0.826294	−0.413147	+	0.910664i	$0.635570\pi$
$212$	15.7739	1.08336
$213$	4.26812	0.292447
$214$	−2.23802	−0.152988
$215$	7.38553	0.503689
$216$	12.8655	0.875389
$217$	−32.5101	−2.20693
$218$	11.2361	0.761006
$219$	−23.7382	−1.60408
$220$	−1.24270	−0.0837827
$221$	0.216401	0.0145567
$222$	10.7415	0.720922
$223$	16.8582	1.12891	0.564454	−	0.825465i	$-0.309087\pi$
$223$	16.8582	1.12891	0.564454	+	0.825465i	$0.309087\pi$
$224$	28.7096	1.91824
$225$	−8.76179	−0.584119
$226$	6.30187	0.419194
$227$	−22.3887	−1.48599	−0.742995	−	0.669297i	$-0.766595\pi$
$227$	−22.3887	−1.48599	−0.742995	+	0.669297i	$0.766595\pi$
$228$	−2.73382	−0.181052
$229$	4.77292	0.315403	0.157702	−	0.987487i	$-0.449592\pi$
$229$	4.77292	0.315403	0.157702	+	0.987487i	$0.449592\pi$
$230$	4.80379	0.316753
$231$	1.48824	0.0979193
$232$	−10.9696	−0.720191
$233$	−16.3112	−1.06858	−0.534291	−	0.845300i	$-0.679421\pi$
$233$	−16.3112	−1.06858	−0.534291	+	0.845300i	$0.679421\pi$
$234$	0.0419016	0.00273919
$235$	−24.9310	−1.62632
$236$	−10.0065	−0.651370
$237$	−6.89551	−0.447911
$238$	−9.57473	−0.620637
$239$	−17.4615	−1.12949	−0.564746	−	0.825265i	$-0.691026\pi$
$239$	−17.4615	−1.12949	−0.564746	+	0.825265i	$0.691026\pi$
$240$	9.71148	0.626873
$241$	−3.20860	−0.206684	−0.103342	−	0.994646i	$-0.532954\pi$
$241$	−3.20860	−0.206684	−0.103342	+	0.994646i	$0.532954\pi$
$242$	−6.92686	−0.445275
$243$	9.14267	0.586502
$244$	8.00682	0.512584
$245$	71.2903	4.55457
$246$	0.779692	0.0497114
$247$	−0.0856522	−0.00544992
$248$	14.6009	0.927155
$249$	6.87859	0.435913
$250$	11.0215	0.697064
$251$	14.2130	0.897116	0.448558	−	0.893754i	$-0.351938\pi$
$251$	14.2130	0.897116	0.448558	+	0.893754i	$0.351938\pi$
$252$	7.42643	0.467821
$253$	0.405055	0.0254656
$254$	−6.82591	−0.428295
$255$	−16.4722	−1.03153
$256$	−7.25274	−0.453296
$257$	−20.4189	−1.27369	−0.636847	−	0.770990i	$-0.719762\pi$
$257$	−20.4189	−1.27369	−0.636847	+	0.770990i	$0.719762\pi$
$258$	1.76578	0.109933
$259$	59.6463	3.70624
$260$	0.442223	0.0274255
$261$	−4.41377	−0.273206
$262$	4.68483	0.289430
$263$	11.7573	0.724987	0.362493	−	0.931986i	$-0.381926\pi$
$263$	11.7573	0.724987	0.362493	+	0.931986i	$0.381926\pi$
$264$	−0.668396	−0.0411369
$265$	−37.6183	−2.31087
$266$	3.78971	0.232362
$267$	1.49629	0.0915714
$268$	4.84662	0.296054
$269$	24.4948	1.49347	0.746736	−	0.665121i	$-0.231620\pi$
$269$	24.4948	1.49347	0.746736	+	0.665121i	$0.231620\pi$
$270$	−13.6388	−0.830029
$271$	13.1035	0.795981	0.397991	−	0.917389i	$-0.369708\pi$
$271$	13.1035	0.795981	0.397991	+	0.917389i	$0.369708\pi$
$272$	−5.26827	−0.319436
$273$	−0.529603	−0.0320530
$274$	−11.8986	−0.718823
$275$	1.94649	0.117378
$276$	−4.60068	−0.276929
$277$	14.1022	0.847317	0.423659	−	0.905822i	$-0.360746\pi$
$277$	14.1022	0.847317	0.423659	+	0.905822i	$0.360746\pi$
$278$	7.26878	0.435953
$279$	5.87485	0.351718
$280$	−44.0172	−2.63053
$281$	−14.2572	−0.850512	−0.425256	−	0.905073i	$-0.639816\pi$
$281$	−14.2572	−0.850512	−0.425256	+	0.905073i	$0.639816\pi$
$282$	−5.96066	−0.354952
$283$	−4.42746	−0.263185	−0.131592	−	0.991304i	$-0.542009\pi$
$283$	−4.42746	−0.263185	−0.131592	+	0.991304i	$0.542009\pi$
$284$	−4.73153	−0.280765
$285$	6.51974	0.386196
$286$	−0.00930871	−0.000550435 0
$287$	4.32954	0.255565
$288$	−5.18807	−0.305710
$289$	−8.06419	−0.474364
$290$	11.6289	0.682872
$291$	−7.88204	−0.462054
$292$	26.3156	1.54000
$293$	9.98201	0.583155	0.291578	−	0.956547i	$-0.405820\pi$
$293$	9.98201	0.583155	0.291578	+	0.956547i	$0.405820\pi$
$294$	17.0445	0.994058
$295$	23.8641	1.38942
$296$	−26.7882	−1.55703
$297$	−1.15002	−0.0667310
$298$	1.30231	0.0754407
$299$	−0.144142	−0.00833595
$300$	−22.1085	−1.27644
$301$	9.80519	0.565162
$302$	−6.30606	−0.362873
$303$	14.3974	0.827111
$304$	2.08520	0.119594
$305$	−19.0950	−1.09338
$306$	1.73023	0.0989108
$307$	−32.1151	−1.83291	−0.916453	−	0.400142i	$-0.868961\pi$
$307$	−32.1151	−1.83291	−0.916453	+	0.400142i	$0.868961\pi$
$308$	−1.64983	−0.0940078
$309$	−18.5885	−1.05746
$310$	−15.4784	−0.879112
$311$	−5.07779	−0.287935	−0.143968	−	0.989582i	$-0.545986\pi$
$311$	−5.07779	−0.287935	−0.143968	+	0.989582i	$0.545986\pi$
$312$	0.237854	0.0134658
$313$	−28.1423	−1.59070	−0.795350	−	0.606151i	$-0.792713\pi$
$313$	−28.1423	−1.59070	−0.795350	+	0.606151i	$0.792713\pi$
$314$	−7.02035	−0.396181
$315$	−17.7109	−0.997896
$316$	7.64419	0.430019
$317$	4.57557	0.256990	0.128495	−	0.991710i	$-0.458985\pi$
$317$	4.57557	0.256990	0.128495	+	0.991710i	$0.458985\pi$
$318$	−8.99403	−0.504360
$319$	0.980548	0.0549002
$320$	0.215406	0.0120416
$321$	−5.11167	−0.285305
$322$	6.37761	0.355410
$323$	−3.53682	−0.196794
$324$	8.66545	0.481414
$325$	−0.692673	−0.0384226
$326$	1.31589	0.0728803
$327$	25.6634	1.41919
$328$	−1.94447	−0.107366
$329$	−33.0988	−1.82480
$330$	0.708567	0.0390053
$331$	29.4846	1.62062	0.810310	−	0.586001i	$-0.199299\pi$
$331$	29.4846	1.62062	0.810310	+	0.586001i	$0.199299\pi$
$332$	−7.62544	−0.418500
$333$	−10.7786	−0.590663
$334$	4.22529	0.231197
$335$	−11.5584	−0.631505
$336$	12.8932	0.703379
$337$	−33.3444	−1.81639	−0.908193	−	0.418552i	$-0.862538\pi$
$337$	−33.3444	−1.81639	−0.908193	+	0.418552i	$0.862538\pi$
$338$	−8.21389	−0.446777
$339$	14.3936	0.781750
$340$	18.2606	0.990323
$341$	−1.30514	−0.0706771
$342$	−0.684832	−0.0370315
$343$	59.1751	3.19516
$344$	−4.40368	−0.237430
$345$	10.9719	0.590708
$346$	−0.0277255	−0.00149053
$347$	−31.4707	−1.68943	−0.844717	−	0.535213i	$-0.820231\pi$
$347$	−31.4707	−1.68943	−0.844717	+	0.535213i	$0.820231\pi$
$348$	−11.1372	−0.597018
$349$	15.3928	0.823956	0.411978	−	0.911194i	$-0.364838\pi$
$349$	15.3928	0.823956	0.411978	+	0.911194i	$0.364838\pi$
$350$	30.6475	1.63818
$351$	0.409244	0.0218438
$352$	1.15256	0.0614319
$353$	12.0436	0.641016	0.320508	−	0.947246i	$-0.396146\pi$
$353$	12.0436	0.641016	0.320508	+	0.947246i	$0.396146\pi$
$354$	5.70558	0.303248
$355$	11.2840	0.598891
$356$	−1.65875	−0.0879135
$357$	−21.8688	−1.15742
$358$	13.8960	0.734426
$359$	−2.90286	−0.153207	−0.0766036	−	0.997062i	$-0.524408\pi$
$359$	−2.90286	−0.153207	−0.0766036	+	0.997062i	$0.524408\pi$
$360$	7.95427	0.419227
$361$	−17.6001	−0.926322
$362$	−6.65826	−0.349950
$363$	−15.8210	−0.830389
$364$	0.587105	0.0307727
$365$	−62.7587	−3.28494
$366$	−4.56537	−0.238636
$367$	−7.81803	−0.408098	−0.204049	−	0.978961i	$-0.565410\pi$
$367$	−7.81803	−0.408098	−0.204049	+	0.978961i	$0.565410\pi$
$368$	3.50913	0.182926
$369$	−0.782384	−0.0407293
$370$	28.3982	1.47635
$371$	−49.9428	−2.59290
$372$	14.8239	0.768585
$373$	−13.1119	−0.678907	−0.339454	−	0.940623i	$-0.610242\pi$
$373$	−13.1119	−0.678907	−0.339454	+	0.940623i	$0.610242\pi$
$374$	−0.384383	−0.0198760
$375$	25.1734	1.29995
$376$	14.8653	0.766617
$377$	−0.348936	−0.0179711
$378$	−18.1071	−0.931329
$379$	13.0237	0.668982	0.334491	−	0.942399i	$-0.391436\pi$
$379$	13.0237	0.668982	0.334491	+	0.942399i	$0.391436\pi$
$380$	−7.22763	−0.370769
$381$	−15.5905	−0.798723
$382$	12.7168	0.650646
$383$	−19.4276	−0.992705	−0.496353	−	0.868121i	$-0.665328\pi$
$383$	−19.4276	−0.992705	−0.496353	+	0.868121i	$0.665328\pi$
$384$	−16.3076	−0.832191
$385$	3.93459	0.200525
$386$	13.0399	0.663713
$387$	−1.77188	−0.0900697
$388$	8.73784	0.443597
$389$	9.99007	0.506517	0.253258	−	0.967399i	$-0.418498\pi$
$389$	9.99007	0.506517	0.253258	+	0.967399i	$0.418498\pi$
$390$	−0.252149	−0.0127681
$391$	−5.95203	−0.301007
$392$	−42.5073	−2.14694
$393$	10.7002	0.539755
$394$	−9.30481	−0.468770
$395$	−18.2302	−0.917261
$396$	0.298138	0.0149820
$397$	0.0605059	0.00303670	0.00151835	−	0.999999i	$-0.499517\pi$
$397$	0.0605059	0.00303670	0.00151835	+	0.999999i	$0.499517\pi$
$398$	4.85230	0.243224
$399$	8.65574	0.433329
$400$	16.8631	0.843154
$401$	34.5944	1.72756	0.863781	−	0.503867i	$-0.168090\pi$
$401$	34.5944	1.72756	0.863781	+	0.503867i	$0.168090\pi$
$402$	−2.76347	−0.137829
$403$	0.464443	0.0231355
$404$	−15.9606	−0.794071
$405$	−20.6658	−1.02689
$406$	15.4388	0.766213
$407$	2.39453	0.118693
$408$	9.82166	0.486244
$409$	14.2637	0.705294	0.352647	−	0.935756i	$-0.385282\pi$
$409$	14.2637	0.705294	0.352647	+	0.935756i	$0.385282\pi$
$410$	2.06134	0.101802
$411$	−27.1767	−1.34053
$412$	20.6067	1.01522
$413$	31.6824	1.55899
$414$	−1.15249	−0.0566417
$415$	18.1855	0.892691
$416$	−0.410149	−0.0201092
$417$	16.6020	0.813003
$418$	0.152140	0.00744141
$419$	−17.3874	−0.849431	−0.424716	−	0.905327i	$-0.639626\pi$
$419$	−17.3874	−0.849431	−0.424716	+	0.905327i	$0.639626\pi$
$420$	−44.6897	−2.18063
$421$	19.9533	0.972465	0.486232	−	0.873829i	$-0.338371\pi$
$421$	19.9533	0.972465	0.486232	+	0.873829i	$0.338371\pi$
$422$	−7.58676	−0.369318
$423$	5.98124	0.290818
$424$	22.4302	1.08931
$425$	−28.6024	−1.38742
$426$	2.69785	0.130711
$427$	−25.3510	−1.22682
$428$	5.66667	0.273909
$429$	−0.0212612	−0.00102650
$430$	4.66834	0.225127
$431$	−35.1591	−1.69355	−0.846777	−	0.531948i	$-0.821460\pi$
$431$	−35.1591	−1.69355	−0.846777	+	0.531948i	$0.821460\pi$
$432$	−9.96301	−0.479346
$433$	−16.4558	−0.790813	−0.395407	−	0.918506i	$-0.629396\pi$
$433$	−16.4558	−0.790813	−0.395407	+	0.918506i	$0.629396\pi$
$434$	−20.5494	−0.986403
$435$	26.5605	1.27348
$436$	−28.4499	−1.36250
$437$	2.35583	0.112695
$438$	−15.0048	−0.716955
$439$	−28.3933	−1.35514	−0.677568	−	0.735460i	$-0.736966\pi$
$439$	−28.3933	−1.35514	−0.677568	+	0.735460i	$0.736966\pi$
$440$	−1.76709	−0.0842429
$441$	−17.1034	−0.814447
$442$	0.136786	0.00650622
$443$	−24.2174	−1.15060	−0.575301	−	0.817942i	$-0.695115\pi$
$443$	−24.2174	−1.15060	−0.575301	+	0.817942i	$0.695115\pi$
$444$	−27.1975	−1.29073
$445$	3.95586	0.187526
$446$	10.6559	0.504573
$447$	2.97449	0.140688
$448$	0.285978	0.0135112
$449$	−38.0728	−1.79677	−0.898383	−	0.439213i	$-0.855257\pi$
$449$	−38.0728	−1.79677	−0.898383	+	0.439213i	$0.855257\pi$
$450$	−5.53826	−0.261076
$451$	0.173812	0.00818448
$452$	−15.9563	−0.750523
$453$	−14.4031	−0.676718
$454$	−14.1517	−0.664173
$455$	−1.40015	−0.0656403
$456$	−3.88744	−0.182046
$457$	25.1866	1.17818	0.589091	−	0.808067i	$-0.299486\pi$
$457$	25.1866	1.17818	0.589091	+	0.808067i	$0.299486\pi$
$458$	3.01693	0.140972
$459$	16.8988	0.788769
$460$	−12.1632	−0.567112
$461$	−11.4031	−0.531097	−0.265548	−	0.964098i	$-0.585553\pi$
$461$	−11.4031	−0.531097	−0.265548	+	0.964098i	$0.585553\pi$
$462$	0.940708	0.0437657
$463$	−5.79535	−0.269333	−0.134666	−	0.990891i	$-0.542996\pi$
$463$	−5.79535	−0.269333	−0.134666	+	0.990891i	$0.542996\pi$
$464$	8.49482	0.394362
$465$	−35.3528	−1.63945
$466$	−10.3102	−0.477610
$467$	16.6862	0.772145	0.386073	−	0.922468i	$-0.373831\pi$
$467$	16.6862	0.772145	0.386073	+	0.922468i	$0.373831\pi$
$468$	−0.106095	−0.00490423
$469$	−15.3452	−0.708576
$470$	−15.7587	−0.726893
$471$	−16.0346	−0.738834
$472$	−14.2291	−0.654948
$473$	0.393635	0.0180993
$474$	−4.35860	−0.200197
$475$	11.3209	0.519440
$476$	24.2432	1.11119
$477$	9.02508	0.413230
$478$	−11.0373	−0.504834
$479$	−0.873513	−0.0399118	−0.0199559	−	0.999801i	$-0.506353\pi$
$479$	−0.873513	−0.0399118	−0.0199559	+	0.999801i	$0.506353\pi$
$480$	31.2200	1.42499
$481$	−0.852113	−0.0388530
$482$	−2.02813	−0.0923789
$483$	14.5665	0.662801
$484$	17.5388	0.797219
$485$	−20.8384	−0.946223
$486$	5.77901	0.262141
$487$	−35.2690	−1.59819	−0.799096	−	0.601204i	$-0.794688\pi$
$487$	−35.2690	−1.59819	−0.799096	+	0.601204i	$0.794688\pi$
$488$	11.3856	0.515400
$489$	3.00551	0.135914
$490$	45.0620	2.03570
$491$	−20.7400	−0.935981	−0.467991	−	0.883733i	$-0.655022\pi$
$491$	−20.7400	−0.935981	−0.467991	+	0.883733i	$0.655022\pi$
$492$	−1.97418	−0.0890030
$493$	−14.4085	−0.648928
$494$	−0.0541402	−0.00243588
$495$	−0.711014	−0.0319577
$496$	−11.3068	−0.507691
$497$	14.9808	0.671982
$498$	4.34791	0.194834
$499$	−19.3501	−0.866231	−0.433115	−	0.901338i	$-0.642586\pi$
$499$	−19.3501	−0.866231	−0.433115	+	0.901338i	$0.642586\pi$
$500$	−27.9066	−1.24802
$501$	9.65061	0.431158
$502$	8.98392	0.400972
$503$	0.0252726	0.00112685	0.000563424	−	1.00000i	$-0.499821\pi$
$503$	0.0252726	0.00112685	0.000563424		1.00000i	$0.499821\pi$
$504$	10.5603	0.470391
$505$	38.0637	1.69381
$506$	0.256033	0.0113820
$507$	−18.7606	−0.833189
$508$	17.2832	0.766818
$509$	9.29179	0.411851	0.205926	−	0.978568i	$-0.433979\pi$
$509$	9.29179	0.411851	0.205926	+	0.978568i	$0.433979\pi$
$510$	−10.4119	−0.461049
$511$	−83.3197	−3.68585
$512$	18.0068	0.795796
$513$	−6.68861	−0.295309
$514$	−12.9066	−0.569286
$515$	−49.1439	−2.16554
$516$	−4.47096	−0.196823
$517$	−1.32877	−0.0584393
$518$	37.7020	1.65653
$519$	−0.0633254	−0.00277968
$520$	0.628834	0.0275762
$521$	8.62989	0.378082	0.189041	−	0.981969i	$-0.439462\pi$
$521$	8.62989	0.378082	0.189041	+	0.981969i	$0.439462\pi$
$522$	−2.78991	−0.122111
$523$	31.2882	1.36814	0.684069	−	0.729417i	$-0.260209\pi$
$523$	31.2882	1.36814	0.684069	+	0.729417i	$0.260209\pi$
$524$	−11.8620	−0.518194
$525$	69.9993	3.05502
$526$	7.43171	0.324038
$527$	19.1781	0.835413
$528$	0.517603	0.0225258
$529$	−19.0354	−0.827627
$530$	−23.7782	−1.03286
$531$	−5.72528	−0.248456
$532$	−9.59554	−0.416020
$533$	−0.0618523	−0.00267912
$534$	0.945793	0.0409285
$535$	−13.5141	−0.584267
$536$	6.89180	0.297681
$537$	31.7386	1.36962
$538$	15.4830	0.667517
$539$	3.79963	0.163662
$540$	34.5334	1.48608
$541$	25.6088	1.10101	0.550504	−	0.834832i	$-0.314436\pi$
$541$	25.6088	1.10101	0.550504	+	0.834832i	$0.314436\pi$
$542$	8.28263	0.355769
$543$	−15.2075	−0.652618
$544$	−16.9362	−0.726133
$545$	67.8485	2.90631
$546$	−0.334758	−0.0143263
$547$	3.58812	0.153417	0.0767086	−	0.997054i	$-0.475559\pi$
$547$	3.58812	0.153417	0.0767086	+	0.997054i	$0.475559\pi$
$548$	30.1274	1.28698
$549$	4.58113	0.195518
$550$	1.23036	0.0524628
$551$	5.70295	0.242954
$552$	−6.54209	−0.278450
$553$	−24.2028	−1.02921
$554$	8.91388	0.378714
$555$	64.8618	2.75323
$556$	−18.4046	−0.780527
$557$	14.3683	0.608803	0.304401	−	0.952544i	$-0.401544\pi$
$557$	14.3683	0.608803	0.304401	+	0.952544i	$0.401544\pi$
$558$	3.71345	0.157203
$559$	−0.140078	−0.00592466
$560$	34.0867	1.44043
$561$	−0.877935	−0.0370664
$562$	−9.01186	−0.380142
$563$	−41.7127	−1.75798	−0.878991	−	0.476839i	$-0.841783\pi$
$563$	−41.7127	−1.75798	−0.878991	+	0.476839i	$0.841783\pi$
$564$	15.0924	0.635504
$565$	38.0534	1.60092
$566$	−2.79856	−0.117632
$567$	−27.4363	−1.15222
$568$	−6.72815	−0.282307
$569$	34.4035	1.44227	0.721136	−	0.692794i	$-0.243620\pi$
$569$	34.4035	1.44227	0.721136	+	0.692794i	$0.243620\pi$
$570$	4.12108	0.172613
$571$	8.97006	0.375385	0.187693	−	0.982228i	$-0.439899\pi$
$571$	8.97006	0.375385	0.187693	+	0.982228i	$0.439899\pi$
$572$	0.0235696	0.000985496 0
$573$	29.0453	1.21338
$574$	2.73667	0.114226
$575$	19.0517	0.794512
$576$	−0.0516785	−0.00215327
$577$	15.9143	0.662519	0.331260	−	0.943540i	$-0.392526\pi$
$577$	15.9143	0.662519	0.331260	+	0.943540i	$0.392526\pi$
$578$	−5.09732	−0.212020
$579$	29.7833	1.23775
$580$	−29.4444	−1.22261
$581$	24.1434	1.00164
$582$	−4.98218	−0.206518
$583$	−2.00498	−0.0830379
$584$	37.4203	1.54846
$585$	0.253020	0.0104611
$586$	6.30956	0.260645
$587$	−34.0585	−1.40574	−0.702872	−	0.711316i	$-0.748099\pi$
$587$	−34.0585	−1.40574	−0.702872	+	0.711316i	$0.748099\pi$
$588$	−43.1568	−1.77976
$589$	−7.59077	−0.312772
$590$	15.0843	0.621011
$591$	−21.2523	−0.874203
$592$	20.7446	0.852599
$593$	11.8921	0.488351	0.244175	−	0.969731i	$-0.421483\pi$
$593$	11.8921	0.488351	0.244175	+	0.969731i	$0.421483\pi$
$594$	−0.726920	−0.0298259
$595$	−57.8163	−2.37024
$596$	−3.29744	−0.135069
$597$	11.0827	0.453586
$598$	−0.0911112	−0.00372581
$599$	13.3470	0.545343	0.272672	−	0.962107i	$-0.412093\pi$
$599$	13.3470	0.545343	0.272672	+	0.962107i	$0.412093\pi$
$600$	−31.4379	−1.28345
$601$	−1.42488	−0.0581219	−0.0290610	−	0.999578i	$-0.509252\pi$
$601$	−1.42488	−0.0581219	−0.0290610	+	0.999578i	$0.509252\pi$
$602$	6.19779	0.252603
$603$	2.77301	0.112926
$604$	15.9669	0.649686
$605$	−41.8274	−1.70052
$606$	9.10051	0.369683
$607$	26.0094	1.05569	0.527844	−	0.849341i	$-0.323000\pi$
$607$	26.0094	1.05569	0.527844	+	0.849341i	$0.323000\pi$
$608$	6.70340	0.271859
$609$	35.2623	1.42890
$610$	−12.0698	−0.488693
$611$	0.472853	0.0191296
$612$	−4.38095	−0.177089
$613$	−16.1065	−0.650536	−0.325268	−	0.945622i	$-0.605455\pi$
$613$	−16.1065	−0.650536	−0.325268	+	0.945622i	$0.605455\pi$
$614$	−20.2997	−0.819230
$615$	4.70812	0.189850
$616$	−2.34603	−0.0945242
$617$	−9.91620	−0.399211	−0.199606	−	0.979876i	$-0.563966\pi$
$617$	−9.91620	−0.399211	−0.199606	+	0.979876i	$0.563966\pi$
$618$	−11.7496	−0.472640
$619$	−10.2963	−0.413843	−0.206921	−	0.978358i	$-0.566344\pi$
$619$	−10.2963	−0.413843	−0.206921	+	0.978358i	$0.566344\pi$
$620$	39.1912	1.57396
$621$	−11.2561	−0.451692
$622$	−3.20964	−0.128695
$623$	5.25188	0.210412
$624$	−0.184193	−0.00737362
$625$	18.7112	0.748449
$626$	−17.7886	−0.710974
$627$	0.347490	0.0138774
$628$	17.7755	0.709321
$629$	−35.1861	−1.40296
$630$	−11.1949	−0.446017
$631$	20.9781	0.835125	0.417563	−	0.908648i	$-0.362884\pi$
$631$	20.9781	0.835125	0.417563	+	0.908648i	$0.362884\pi$
$632$	10.8699	0.432381
$633$	−17.3283	−0.688737
$634$	2.89218	0.114863
$635$	−41.2178	−1.63568
$636$	22.7729	0.903004
$637$	−1.35213	−0.0535733
$638$	0.619797	0.0245380
$639$	−2.70716	−0.107094
$640$	−43.1136	−1.70421
$641$	−13.8159	−0.545696	−0.272848	−	0.962057i	$-0.587966\pi$
$641$	−13.8159	−0.545696	−0.272848	+	0.962057i	$0.587966\pi$
$642$	−3.23105	−0.127519
$643$	19.3040	0.761277	0.380638	−	0.924724i	$-0.375704\pi$
$643$	19.3040	0.761277	0.380638	+	0.924724i	$0.375704\pi$
$644$	−16.1481	−0.636325
$645$	10.6626	0.419838
$646$	−2.23560	−0.0879585
$647$	42.9340	1.68791	0.843955	−	0.536414i	$-0.180221\pi$
$647$	42.9340	1.68791	0.843955	+	0.536414i	$0.180221\pi$
$648$	12.3221	0.484059
$649$	1.27191	0.0499267
$650$	−0.437834	−0.0171732
$651$	−46.9351	−1.83953
$652$	−3.33183	−0.130485
$653$	−19.2598	−0.753696	−0.376848	−	0.926275i	$-0.622992\pi$
$653$	−19.2598	−0.753696	−0.376848	+	0.926275i	$0.622992\pi$
$654$	16.2217	0.634318
$655$	28.2890	1.10534
$656$	1.50579	0.0587912
$657$	15.0566	0.587413
$658$	−20.9215	−0.815606
$659$	−12.2221	−0.476106	−0.238053	−	0.971252i	$-0.576509\pi$
$659$	−12.2221	−0.476106	−0.238053	+	0.971252i	$0.576509\pi$
$660$	−1.79409	−0.0698349
$661$	−28.4481	−1.10650	−0.553251	−	0.833015i	$-0.686613\pi$
$661$	−28.4481	−1.10650	−0.553251	+	0.833015i	$0.686613\pi$
$662$	18.6370	0.724348
$663$	0.312420	0.0121334
$664$	−10.8432	−0.420799
$665$	22.8839	0.887399
$666$	−6.81306	−0.264001
$667$	9.59735	0.371611
$668$	−10.6984	−0.413935
$669$	24.3383	0.940973
$670$	−7.30600	−0.282256
$671$	−1.01773	−0.0392890
$672$	41.4483	1.59890
$673$	−49.9381	−1.92497	−0.962486	−	0.271333i	$-0.912536\pi$
$673$	−49.9381	−1.92497	−0.962486	+	0.271333i	$0.912536\pi$
$674$	−21.0768	−0.811846
$675$	−54.0911	−2.08197
$676$	20.7976	0.799907
$677$	28.4876	1.09487	0.547434	−	0.836849i	$-0.315605\pi$
$677$	28.4876	1.09487	0.547434	+	0.836849i	$0.315605\pi$
$678$	9.09806	0.349409
$679$	−27.6655	−1.06170
$680$	25.9663	0.995763
$681$	−32.3227	−1.23861
$682$	−0.824967	−0.0315896
$683$	45.3525	1.73537	0.867683	−	0.497119i	$-0.165609\pi$
$683$	45.3525	1.73537	0.867683	+	0.497119i	$0.165609\pi$
$684$	1.73399	0.0663009
$685$	−71.8491	−2.74521
$686$	37.4042	1.42810
$687$	6.89070	0.262897
$688$	3.41019	0.130012
$689$	0.713488	0.0271817
$690$	6.93527	0.264021
$691$	−14.0514	−0.534542	−0.267271	−	0.963621i	$-0.586122\pi$
$691$	−14.0514	−0.534542	−0.267271	+	0.963621i	$0.586122\pi$
$692$	0.0702010	0.00266864
$693$	−0.943956	−0.0358579
$694$	−19.8924	−0.755104
$695$	43.8920	1.66492
$696$	−15.8369	−0.600297
$697$	−2.55405	−0.0967417
$698$	9.72966	0.368273
$699$	−23.5486	−0.890690
$700$	−77.5996	−2.93299
$701$	14.4410	0.545431	0.272715	−	0.962095i	$-0.412078\pi$
$701$	14.4410	0.545431	0.272715	+	0.962095i	$0.412078\pi$
$702$	0.258680	0.00976325
$703$	13.9268	0.525259
$704$	0.0114807	0.000432696 0
$705$	−35.9930	−1.35558
$706$	7.61267	0.286507
$707$	50.5341	1.90053
$708$	−14.4465	−0.542934
$709$	33.8783	1.27233	0.636163	−	0.771554i	$-0.280520\pi$
$709$	33.8783	1.27233	0.636163	+	0.771554i	$0.280520\pi$
$710$	7.13252	0.267679
$711$	4.37365	0.164025
$712$	−2.35871	−0.0883965
$713$	−12.7743	−0.478402
$714$	−13.8231	−0.517317
$715$	−0.0562100	−0.00210213
$716$	−35.1846	−1.31491
$717$	−25.2093	−0.941460
$718$	−1.83488	−0.0684770
$719$	−45.7982	−1.70798	−0.853992	−	0.520285i	$-0.825826\pi$
$719$	−45.7982	−1.70798	−0.853992	+	0.520285i	$0.825826\pi$
$720$	−6.15975	−0.229560
$721$	−65.2445	−2.42983
$722$	−11.1249	−0.414026
$723$	−4.63228	−0.172276
$724$	16.8587	0.626549
$725$	46.1200	1.71285
$726$	−10.0004	−0.371148
$727$	−11.1539	−0.413674	−0.206837	−	0.978375i	$-0.566317\pi$
$727$	−11.1539	−0.413674	−0.206837	+	0.978375i	$0.566317\pi$
$728$	0.834853	0.0309417
$729$	29.4424	1.09046
$730$	−39.6693	−1.46823
$731$	−5.78421	−0.213937
$732$	11.5595	0.427252
$733$	23.8272	0.880078	0.440039	−	0.897979i	$-0.354965\pi$
$733$	23.8272	0.880078	0.440039	+	0.897979i	$0.354965\pi$
$734$	−4.94172	−0.182402
$735$	102.922	3.79635
$736$	11.2810	0.415823
$737$	−0.616042	−0.0226922
$738$	−0.494539	−0.0182042
$739$	13.7518	0.505869	0.252934	−	0.967483i	$-0.418604\pi$
$739$	13.7518	0.505869	0.252934	+	0.967483i	$0.418604\pi$
$740$	−71.9042	−2.64325
$741$	−0.123657	−0.00454265
$742$	−31.5685	−1.15892
$743$	−15.8762	−0.582443	−0.291222	−	0.956656i	$-0.594062\pi$
$743$	−15.8762	−0.582443	−0.291222	+	0.956656i	$0.594062\pi$
$744$	21.0794	0.772807
$745$	7.86390	0.288111
$746$	−8.28792	−0.303442
$747$	−4.36292	−0.159631
$748$	0.973257	0.0355858
$749$	−17.9416	−0.655573
$750$	15.9119	0.581020
$751$	−36.1277	−1.31832	−0.659159	−	0.752003i	$-0.729088\pi$
$751$	−36.1277	−1.31832	−0.659159	+	0.752003i	$0.729088\pi$
$752$	−11.5116	−0.419784
$753$	20.5194	0.747769
$754$	−0.220560	−0.00803231
$755$	−38.0787	−1.38583
$756$	45.8472	1.66745
$757$	14.6896	0.533902	0.266951	−	0.963710i	$-0.413984\pi$
$757$	14.6896	0.533902	0.266951	+	0.963710i	$0.413984\pi$
$758$	8.23218	0.299006
$759$	0.584782	0.0212262
$760$	−10.2776	−0.372806
$761$	40.4896	1.46775	0.733873	−	0.679286i	$-0.237711\pi$
$761$	40.4896	1.46775	0.733873	+	0.679286i	$0.237711\pi$
$762$	−9.85461	−0.356995
$763$	90.0771	3.26101
$764$	−32.1988	−1.16491
$765$	10.4479	0.377744
$766$	−12.2801	−0.443697
$767$	−0.452618	−0.0163431
$768$	−10.4708	−0.377834
$769$	31.6708	1.14208	0.571040	−	0.820922i	$-0.306540\pi$
$769$	31.6708	1.14208	0.571040	+	0.820922i	$0.306540\pi$
$770$	2.48703	0.0896262
$771$	−29.4789	−1.06166
$772$	−33.0170	−1.18831
$773$	6.72418	0.241852	0.120926	−	0.992662i	$-0.461414\pi$
$773$	6.72418	0.241852	0.120926	+	0.992662i	$0.461414\pi$
$774$	−1.11999	−0.0402573
$775$	−61.3869	−2.20508
$776$	12.4251	0.446033
$777$	86.1118	3.08924
$778$	6.31465	0.226391
$779$	1.01090	0.0362194
$780$	0.638441	0.0228599
$781$	0.601414	0.0215203
$782$	−3.76224	−0.134537
$783$	−27.2485	−0.973782
$784$	32.9175	1.17562
$785$	−42.3919	−1.51303
$786$	6.76353	0.241247
$787$	13.0637	0.465671	0.232835	−	0.972516i	$-0.425200\pi$
$787$	13.0637	0.465671	0.232835	+	0.972516i	$0.425200\pi$
$788$	23.5598	0.839282
$789$	16.9741	0.604295
$790$	−11.5232	−0.409976
$791$	50.5205	1.79630
$792$	0.423947	0.0150643
$793$	0.362166	0.0128609
$794$	0.0382453	0.00135728
$795$	−54.3098	−1.92617
$796$	−12.2860	−0.435467
$797$	49.3845	1.74929	0.874644	−	0.484766i	$-0.161095\pi$
$797$	49.3845	1.74929	0.874644	+	0.484766i	$0.161095\pi$
$798$	5.47123	0.193679
$799$	19.5254	0.690761
$800$	54.2107	1.91664
$801$	−0.949059	−0.0335334
$802$	21.8669	0.772146
$803$	−3.34492	−0.118039
$804$	6.99710	0.246769
$805$	38.5108	1.35733
$806$	0.293571	0.0103406
$807$	35.3633	1.24485
$808$	−22.6957	−0.798433
$809$	16.1212	0.566790	0.283395	−	0.959003i	$-0.408539\pi$
$809$	16.1212	0.566790	0.283395	+	0.959003i	$0.408539\pi$
$810$	−13.0627	−0.458976
$811$	−14.1635	−0.497349	−0.248675	−	0.968587i	$-0.579995\pi$
$811$	−14.1635	−0.497349	−0.248675	+	0.968587i	$0.579995\pi$
$812$	−39.0909	−1.37182
$813$	18.9176	0.663470
$814$	1.51357	0.0530505
$815$	7.94590	0.278333
$816$	−7.60584	−0.266258
$817$	2.28941	0.0800963
$818$	9.01598	0.315236
$819$	0.335914	0.0117378
$820$	−5.21930	−0.182266
$821$	25.7942	0.900224	0.450112	−	0.892972i	$-0.351384\pi$
$821$	25.7942	0.900224	0.450112	+	0.892972i	$0.351384\pi$
$822$	−17.1782	−0.599157
$823$	−21.9469	−0.765023	−0.382511	−	0.923951i	$-0.624941\pi$
$823$	−21.9469	−0.765023	−0.382511	+	0.923951i	$0.624941\pi$
$824$	29.3024	1.02080
$825$	2.81016	0.0978373
$826$	20.0262	0.696801
$827$	8.50057	0.295594	0.147797	−	0.989018i	$-0.452782\pi$
$827$	8.50057	0.295594	0.147797	+	0.989018i	$0.452782\pi$
$828$	2.91810	0.101411
$829$	21.4616	0.745391	0.372695	−	0.927954i	$-0.378434\pi$
$829$	21.4616	0.745391	0.372695	+	0.927954i	$0.378434\pi$
$830$	11.4949	0.398994
$831$	20.3594	0.706260
$832$	−0.00408550	−0.000141639 0
$833$	−55.8332	−1.93450
$834$	10.4940	0.363377
$835$	25.5141	0.882952
$836$	−0.385218	−0.0133231
$837$	36.2685	1.25362
$838$	−10.9905	−0.379659
$839$	5.50510	0.190057	0.0950287	−	0.995475i	$-0.469706\pi$
$839$	5.50510	0.190057	0.0950287	+	0.995475i	$0.469706\pi$
$840$	−63.5479	−2.19261
$841$	−5.76697	−0.198861
$842$	12.6123	0.434650
$843$	−20.5832	−0.708923
$844$	19.2097	0.661225
$845$	−49.5990	−1.70626
$846$	3.78070	0.129983
$847$	−55.5309	−1.90806
$848$	−17.3698	−0.596482
$849$	−6.39195	−0.219371
$850$	−18.0794	−0.620118
$851$	23.4371	0.803412
$852$	−6.83095	−0.234025
$853$	8.29175	0.283904	0.141952	−	0.989874i	$-0.454662\pi$
$853$	8.29175	0.283904	0.141952	+	0.989874i	$0.454662\pi$
$854$	−16.0242	−0.548335
$855$	−4.13531	−0.141425
$856$	8.05790	0.275413
$857$	3.42875	0.117124	0.0585620	−	0.998284i	$-0.481348\pi$
$857$	3.42875	0.117124	0.0585620	+	0.998284i	$0.481348\pi$
$858$	−0.0134391	−0.000458802 0
$859$	−56.1340	−1.91527	−0.957633	−	0.287990i	$-0.907013\pi$
$859$	−56.1340	−1.91527	−0.957633	+	0.287990i	$0.907013\pi$
$860$	−11.8202	−0.403067
$861$	6.25059	0.213020
$862$	−22.2238	−0.756946
$863$	28.9835	0.986610	0.493305	−	0.869856i	$-0.335789\pi$
$863$	28.9835	0.986610	0.493305	+	0.869856i	$0.335789\pi$
$864$	−32.0286	−1.08964
$865$	−0.167418	−0.00569240
$866$	−10.4016	−0.353459
$867$	−11.6423	−0.395395
$868$	52.0311	1.76605
$869$	−0.971635	−0.0329604
$870$	16.7887	0.569191
$871$	0.219223	0.00742810
$872$	−40.4552	−1.36999
$873$	4.99938	0.169204
$874$	1.48911	0.0503697
$875$	88.3569	2.98701
$876$	37.9921	1.28363
$877$	−49.9132	−1.68545	−0.842724	−	0.538346i	$-0.819049\pi$
$877$	−49.9132	−1.68545	−0.842724	+	0.538346i	$0.819049\pi$
$878$	−17.9472	−0.605687
$879$	14.4111	0.486075
$880$	1.36843	0.0461297
$881$	−3.53098	−0.118962	−0.0594808	−	0.998229i	$-0.518945\pi$
$881$	−3.53098	−0.118962	−0.0594808	+	0.998229i	$0.518945\pi$
$882$	−10.8109	−0.364023
$883$	−44.2457	−1.48899	−0.744494	−	0.667629i	$-0.767309\pi$
$883$	−44.2457	−1.48899	−0.744494	+	0.667629i	$0.767309\pi$
$884$	−0.346341	−0.0116487
$885$	34.4527	1.15812
$886$	−15.3076	−0.514270
$887$	31.3892	1.05395	0.526973	−	0.849882i	$-0.323327\pi$
$887$	31.3892	1.05395	0.526973	+	0.849882i	$0.323327\pi$
$888$	−38.6743	−1.29782
$889$	−54.7215	−1.83530
$890$	2.50047	0.0838160
$891$	−1.10145	−0.0368998
$892$	−26.9808	−0.903385
$893$	−7.72824	−0.258616
$894$	1.88015	0.0628817
$895$	83.9100	2.80480
$896$	−57.2385	−1.91220
$897$	−0.208099	−0.00694823
$898$	−24.0655	−0.803077
$899$	−30.9238	−1.03137
$900$	14.0229	0.467430
$901$	29.4619	0.981519
$902$	0.109865	0.00365811
$903$	14.1558	0.471076
$904$	−22.6896	−0.754646
$905$	−40.2054	−1.33647
$906$	−9.10411	−0.302464
$907$	−10.2158	−0.339210	−0.169605	−	0.985512i	$-0.554249\pi$
$907$	−10.2158	−0.339210	−0.169605	+	0.985512i	$0.554249\pi$
$908$	35.8322	1.18913
$909$	−9.13193	−0.302887
$910$	−0.885028	−0.0293384
$911$	−32.7996	−1.08670	−0.543350	−	0.839506i	$-0.682844\pi$
$911$	−32.7996	−1.08670	−0.543350	+	0.839506i	$0.682844\pi$
$912$	3.01042	0.0996849
$913$	0.969251	0.0320775
$914$	15.9203	0.526596
$915$	−27.5676	−0.911358
$916$	−7.63886	−0.252395
$917$	37.5571	1.24025
$918$	10.6816	0.352546
$919$	−25.9356	−0.855537	−0.427768	−	0.903888i	$-0.640700\pi$
$919$	−25.9356	−0.855537	−0.427768	+	0.903888i	$0.640700\pi$
$920$	−17.2958	−0.570227
$921$	−46.3648	−1.52777
$922$	−7.20784	−0.237377
$923$	−0.214018	−0.00704448
$924$	−2.38187	−0.0783579
$925$	112.627	3.70314
$926$	−3.66320	−0.120380
$927$	11.7902	0.387242
$928$	27.3087	0.896454
$929$	−15.6834	−0.514556	−0.257278	−	0.966337i	$-0.582826\pi$
$929$	−15.6834	−0.514556	−0.257278	+	0.966337i	$0.582826\pi$
$930$	−22.3462	−0.732762
$931$	22.0989	0.724264
$932$	26.1054	0.855111
$933$	−7.33085	−0.240001
$934$	10.5472	0.345116
$935$	−2.32107	−0.0759070
$936$	−0.150865	−0.00493117
$937$	−9.46697	−0.309272	−0.154636	−	0.987971i	$-0.549421\pi$
$937$	−9.46697	−0.309272	−0.154636	+	0.987971i	$0.549421\pi$
$938$	−9.69960	−0.316703
$939$	−40.6293	−1.32589
$940$	39.9010	1.30143
$941$	10.0077	0.326243	0.163121	−	0.986606i	$-0.447844\pi$
$941$	10.0077	0.326243	0.163121	+	0.986606i	$0.447844\pi$
$942$	−10.1353	−0.330227
$943$	1.70122	0.0553995
$944$	11.0190	0.358637
$945$	−109.339	−3.55678
$946$	0.248814	0.00808963
$947$	−24.4039	−0.793021	−0.396510	−	0.918030i	$-0.629779\pi$
$947$	−24.4039	−0.793021	−0.396510	+	0.918030i	$0.629779\pi$
$948$	11.0360	0.358432
$949$	1.19031	0.0386392
$950$	7.15588	0.232167
$951$	6.60579	0.214207
$952$	34.4734	1.11729
$953$	32.5746	1.05519	0.527597	−	0.849495i	$-0.323093\pi$
$953$	32.5746	1.05519	0.527597	+	0.849495i	$0.323093\pi$
$954$	5.70469	0.184696
$955$	76.7893	2.48484
$956$	27.9465	0.903853
$957$	1.41563	0.0457607
$958$	−0.552141	−0.0178389
$959$	−95.3884	−3.08025
$960$	0.310984	0.0100370
$961$	10.1604	0.327753
$962$	−0.538614	−0.0173656
$963$	3.24220	0.104479
$964$	5.13523	0.165395
$965$	78.7404	2.53474
$966$	9.20740	0.296243
$967$	20.2790	0.652128	0.326064	−	0.945348i	$-0.394277\pi$
$967$	20.2790	0.652128	0.326064	+	0.945348i	$0.394277\pi$
$968$	24.9399	0.801598
$969$	−5.10614	−0.164033
$970$	−13.1718	−0.422921
$971$	−8.05880	−0.258619	−0.129310	−	0.991604i	$-0.541276\pi$
$971$	−8.05880	−0.258619	−0.129310	+	0.991604i	$0.541276\pi$
$972$	−14.6325	−0.469336
$973$	58.2720	1.86811
$974$	−22.2933	−0.714323
$975$	−1.00002	−0.0320262
$976$	−8.81692	−0.282223
$977$	−29.2232	−0.934933	−0.467466	−	0.884011i	$-0.654833\pi$
$977$	−29.2232	−0.934933	−0.467466	+	0.884011i	$0.654833\pi$
$978$	1.89976	0.0607476
$979$	0.210840	0.00673847
$980$	−114.097	−3.64470
$981$	−16.2777	−0.519706
$982$	−13.1096	−0.418343
$983$	57.8384	1.84476	0.922379	−	0.386287i	$-0.126242\pi$
$983$	57.8384	1.84476	0.922379	+	0.386287i	$0.126242\pi$
$984$	−2.80725	−0.0894919
$985$	−56.1864	−1.79025
$986$	−9.10753	−0.290043
$987$	−47.7851	−1.52102
$988$	0.137083	0.00436119
$989$	3.85279	0.122512
$990$	−0.449426	−0.0142837
$991$	−31.0879	−0.987539	−0.493770	−	0.869593i	$-0.664381\pi$
$991$	−31.0879	−0.987539	−0.493770	+	0.869593i	$0.664381\pi$
$992$	−36.3487	−1.15407
$993$	42.5672	1.35083
$994$	9.46928	0.300347
$995$	29.3003	0.928882
$996$	−11.0089	−0.348830
$997$	37.3232	1.18204	0.591018	−	0.806658i	$-0.298726\pi$
$997$	37.3232	1.18204	0.591018	+	0.806658i	$0.298726\pi$
$998$	−12.2311	−0.387168
$999$	−66.5418	−2.10529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.70	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.70	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.632093 q^{2} +1.44371 q^{3} -1.60046 q^{4} +3.81685 q^{5} +0.912557 q^{6} +5.06733 q^{7} -2.27582 q^{8} -0.915708 q^{9} +O(q^{10})\)	\(q+0.632093 q^{2} +1.44371 q^{3} -1.60046 q^{4} +3.81685 q^{5} +0.912557 q^{6} +5.06733 q^{7} -2.27582 q^{8} -0.915708 q^{9} +2.41260 q^{10} +0.203431 q^{11} -2.31059 q^{12} -0.0723923 q^{13} +3.20302 q^{14} +5.51041 q^{15} +1.76239 q^{16} -2.98928 q^{17} -0.578812 q^{18} +1.18317 q^{19} -6.10871 q^{20} +7.31574 q^{21} +0.128587 q^{22} +1.99112 q^{23} -3.28562 q^{24} +9.56833 q^{25} -0.0457586 q^{26} -5.65314 q^{27} -8.11005 q^{28} +4.82007 q^{29} +3.48309 q^{30} -6.41563 q^{31} +5.66564 q^{32} +0.293694 q^{33} -1.88950 q^{34} +19.3412 q^{35} +1.46555 q^{36} +11.7708 q^{37} +0.747872 q^{38} -0.104513 q^{39} -8.68647 q^{40} +0.854404 q^{41} +4.62422 q^{42} +1.93498 q^{43} -0.325582 q^{44} -3.49512 q^{45} +1.25858 q^{46} -6.53182 q^{47} +2.54437 q^{48} +18.6778 q^{49} +6.04807 q^{50} -4.31565 q^{51} +0.115861 q^{52} -9.85586 q^{53} -3.57331 q^{54} +0.776463 q^{55} -11.5323 q^{56} +1.70815 q^{57} +3.04673 q^{58} +6.25230 q^{59} -8.81919 q^{60} -5.00283 q^{61} -4.05527 q^{62} -4.64019 q^{63} +0.0564356 q^{64} -0.276310 q^{65} +0.185642 q^{66} -3.02827 q^{67} +4.78422 q^{68} +2.87460 q^{69} +12.2254 q^{70} +2.95636 q^{71} +2.08399 q^{72} -16.4425 q^{73} +7.44021 q^{74} +13.8139 q^{75} -1.89361 q^{76} +1.03085 q^{77} -0.0660621 q^{78} -4.77625 q^{79} +6.72676 q^{80} -5.41436 q^{81} +0.540062 q^{82} +4.76453 q^{83} -11.7085 q^{84} -11.4096 q^{85} +1.22309 q^{86} +6.95877 q^{87} -0.462972 q^{88} +1.03642 q^{89} -2.20924 q^{90} -0.366835 q^{91} -3.18671 q^{92} -9.26230 q^{93} -4.12871 q^{94} +4.51597 q^{95} +8.17953 q^{96} -5.45958 q^{97} +11.8061 q^{98} -0.186283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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