LMFDB - Embedded newform 2671.2.a.b.1.46

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			1.46
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)

$f(q)$	$=$	$q-0.686018 q^{2} +2.32419 q^{3} -1.52938 q^{4} +1.52841 q^{5} -1.59443 q^{6} +3.39702 q^{7} +2.42122 q^{8} +2.40185 q^{9} +O(q^{10})$	\(q-0.686018 q^{2} +2.32419 q^{3} -1.52938 q^{4} +1.52841 q^{5} -1.59443 q^{6} +3.39702 q^{7} +2.42122 q^{8} +2.40185 q^{9} -1.04851 q^{10} +2.77898 q^{11} -3.55457 q^{12} -0.00660131 q^{13} -2.33042 q^{14} +3.55230 q^{15} +1.39776 q^{16} +3.74218 q^{17} -1.64771 q^{18} -4.86661 q^{19} -2.33751 q^{20} +7.89532 q^{21} -1.90643 q^{22} +8.82217 q^{23} +5.62736 q^{24} -2.66398 q^{25} +0.00452861 q^{26} -1.39022 q^{27} -5.19534 q^{28} -6.09468 q^{29} -2.43694 q^{30} +7.98616 q^{31} -5.80132 q^{32} +6.45888 q^{33} -2.56720 q^{34} +5.19203 q^{35} -3.67333 q^{36} +8.78969 q^{37} +3.33858 q^{38} -0.0153427 q^{39} +3.70060 q^{40} +1.02799 q^{41} -5.41633 q^{42} -2.07265 q^{43} -4.25012 q^{44} +3.67099 q^{45} -6.05217 q^{46} -11.9583 q^{47} +3.24866 q^{48} +4.53977 q^{49} +1.82753 q^{50} +8.69753 q^{51} +0.0100959 q^{52} -5.58976 q^{53} +0.953717 q^{54} +4.24741 q^{55} +8.22493 q^{56} -11.3109 q^{57} +4.18106 q^{58} -1.30986 q^{59} -5.43282 q^{60} +2.28934 q^{61} -5.47865 q^{62} +8.15913 q^{63} +1.18428 q^{64} -0.0100895 q^{65} -4.43090 q^{66} -2.93717 q^{67} -5.72322 q^{68} +20.5044 q^{69} -3.56182 q^{70} +5.01480 q^{71} +5.81539 q^{72} +15.6452 q^{73} -6.02988 q^{74} -6.19158 q^{75} +7.44289 q^{76} +9.44027 q^{77} +0.0105253 q^{78} -5.10732 q^{79} +2.13635 q^{80} -10.4367 q^{81} -0.705217 q^{82} -9.18405 q^{83} -12.0749 q^{84} +5.71957 q^{85} +1.42187 q^{86} -14.1652 q^{87} +6.72852 q^{88} -10.7101 q^{89} -2.51837 q^{90} -0.0224248 q^{91} -13.4925 q^{92} +18.5613 q^{93} +8.20363 q^{94} -7.43815 q^{95} -13.4834 q^{96} -15.3552 q^{97} -3.11436 q^{98} +6.67469 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.686018	−0.485088	−0.242544	−	0.970140i	$-0.577982\pi$
$2$	−0.686018	−0.485088	−0.242544	+	0.970140i	$0.577982\pi$
$3$	2.32419	1.34187	0.670935	−	0.741516i	$-0.265893\pi$
$3$	2.32419	1.34187	0.670935	+	0.741516i	$0.265893\pi$
$4$	−1.52938	−0.764690
$5$	1.52841	0.683524	0.341762	−	0.939787i	$-0.388976\pi$
$5$	1.52841	0.683524	0.341762	+	0.939787i	$0.388976\pi$
$6$	−1.59443	−0.650925
$7$	3.39702	1.28395	0.641977	−	0.766724i	$-0.278114\pi$
$7$	3.39702	1.28395	0.641977	+	0.766724i	$0.278114\pi$
$8$	2.42122	0.856029
$9$	2.40185	0.800615
$10$	−1.04851	−0.331569
$11$	2.77898	0.837895	0.418947	−	0.908010i	$-0.362399\pi$
$11$	2.77898	0.837895	0.418947	+	0.908010i	$0.362399\pi$
$12$	−3.55457	−1.02611
$13$	−0.00660131	−0.00183087	−0.000915437	−	1.00000i	$-0.500291\pi$
$13$	−0.00660131	−0.00183087	−0.000915437		1.00000i	$0.500291\pi$
$14$	−2.33042	−0.622830
$15$	3.55230	0.917200
$16$	1.39776	0.349441
$17$	3.74218	0.907612	0.453806	−	0.891100i	$-0.350066\pi$
$17$	3.74218	0.907612	0.453806	+	0.891100i	$0.350066\pi$
$18$	−1.64771	−0.388369
$19$	−4.86661	−1.11648	−0.558238	−	0.829681i	$-0.688523\pi$
$19$	−4.86661	−1.11648	−0.558238	+	0.829681i	$0.688523\pi$
$20$	−2.33751	−0.522684
$21$	7.89532	1.72290
$22$	−1.90643	−0.406453
$23$	8.82217	1.83955	0.919775	−	0.392446i	$-0.128371\pi$
$23$	8.82217	1.83955	0.919775	+	0.392446i	$0.128371\pi$
$24$	5.62736	1.14868
$25$	−2.66398	−0.532795
$26$	0.00452861	0.000888134 0
$27$	−1.39022	−0.267548
$28$	−5.19534	−0.981827
$29$	−6.09468	−1.13175	−0.565877	−	0.824490i	$-0.691462\pi$
$29$	−6.09468	−1.13175	−0.565877	+	0.824490i	$0.691462\pi$
$30$	−2.43694	−0.444922
$31$	7.98616	1.43436	0.717178	−	0.696890i	$-0.245433\pi$
$31$	7.98616	1.43436	0.717178	+	0.696890i	$0.245433\pi$
$32$	−5.80132	−1.02554
$33$	6.45888	1.12435
$34$	−2.56720	−0.440271
$35$	5.19203	0.877613
$36$	−3.67333	−0.612222
$37$	8.78969	1.44502	0.722508	−	0.691362i	$-0.242989\pi$
$37$	8.78969	1.44502	0.722508	+	0.691362i	$0.242989\pi$
$38$	3.33858	0.541589
$39$	−0.0153427	−0.00245679
$40$	3.70060	0.585116
$41$	1.02799	0.160544	0.0802722	−	0.996773i	$-0.474421\pi$
$41$	1.02799	0.160544	0.0802722	+	0.996773i	$0.474421\pi$
$42$	−5.41633	−0.835757
$43$	−2.07265	−0.316076	−0.158038	−	0.987433i	$-0.550517\pi$
$43$	−2.07265	−0.316076	−0.158038	+	0.987433i	$0.550517\pi$
$44$	−4.25012	−0.640730
$45$	3.67099	0.547240
$46$	−6.05217	−0.892343
$47$	−11.9583	−1.74430	−0.872152	−	0.489235i	$-0.837276\pi$
$47$	−11.9583	−1.74430	−0.872152	+	0.489235i	$0.837276\pi$
$48$	3.24866	0.468904
$49$	4.53977	0.648538
$50$	1.82753	0.258452
$51$	8.69753	1.21790
$52$	0.0100959	0.00140005
$53$	−5.58976	−0.767813	−0.383906	−	0.923372i	$-0.625421\pi$
$53$	−5.58976	−0.767813	−0.383906	+	0.923372i	$0.625421\pi$
$54$	0.953717	0.129784
$55$	4.24741	0.572721
$56$	8.22493	1.09910
$57$	−11.3109	−1.49817
$58$	4.18106	0.549000
$59$	−1.30986	−0.170529	−0.0852646	−	0.996358i	$-0.527174\pi$
$59$	−1.30986	−0.170529	−0.0852646	+	0.996358i	$0.527174\pi$
$60$	−5.43282	−0.701374
$61$	2.28934	0.293120	0.146560	−	0.989202i	$-0.453180\pi$
$61$	2.28934	0.293120	0.146560	+	0.989202i	$0.453180\pi$
$62$	−5.47865	−0.695789
$63$	8.15913	1.02795
$64$	1.18428	0.148036
$65$	−0.0100895	−0.00125145
$66$	−4.43090	−0.545407
$67$	−2.93717	−0.358832	−0.179416	−	0.983773i	$-0.557421\pi$
$67$	−2.93717	−0.358832	−0.179416	+	0.983773i	$0.557421\pi$
$68$	−5.72322	−0.694042
$69$	20.5044	2.46844
$70$	−3.56182	−0.425719
$71$	5.01480	0.595147	0.297573	−	0.954699i	$-0.403823\pi$
$71$	5.01480	0.595147	0.297573	+	0.954699i	$0.403823\pi$
$72$	5.81539	0.685350
$73$	15.6452	1.83113	0.915564	−	0.402171i	$-0.131744\pi$
$73$	15.6452	1.83113	0.915564	+	0.402171i	$0.131744\pi$
$74$	−6.02988	−0.700960
$75$	−6.19158	−0.714942
$76$	7.44289	0.853758
$77$	9.44027	1.07582
$78$	0.0105253	0.00119176
$79$	−5.10732	−0.574618	−0.287309	−	0.957838i	$-0.592761\pi$
$79$	−5.10732	−0.574618	−0.287309	+	0.957838i	$0.592761\pi$
$80$	2.13635	0.238851
$81$	−10.4367	−1.15963
$82$	−0.705217	−0.0778782
$83$	−9.18405	−1.00808	−0.504040	−	0.863680i	$-0.668154\pi$
$83$	−9.18405	−1.00808	−0.504040	+	0.863680i	$0.668154\pi$
$84$	−12.0749	−1.31748
$85$	5.71957	0.620374
$86$	1.42187	0.153325
$87$	−14.1652	−1.51867
$88$	6.72852	0.717263
$89$	−10.7101	−1.13526	−0.567632	−	0.823283i	$-0.692140\pi$
$89$	−10.7101	−1.13526	−0.567632	+	0.823283i	$0.692140\pi$
$90$	−2.51837	−0.265459
$91$	−0.0224248	−0.00235076
$92$	−13.4925	−1.40669
$93$	18.5613	1.92472
$94$	8.20363	0.846140
$95$	−7.43815	−0.763138
$96$	−13.4834	−1.37614
$97$	−15.3552	−1.55909	−0.779543	−	0.626349i	$-0.784549\pi$
$97$	−15.3552	−1.55909	−0.779543	+	0.626349i	$0.784549\pi$
$98$	−3.11436	−0.314598
$99$	6.67469	0.670832
$100$	4.07423	0.407423
$101$	−13.8370	−1.37684	−0.688418	−	0.725314i	$-0.741695\pi$
$101$	−13.8370	−1.37684	−0.688418	+	0.725314i	$0.741695\pi$
$102$	−5.96666	−0.590787
$103$	12.5589	1.23747	0.618735	−	0.785600i	$-0.287646\pi$
$103$	12.5589	1.23747	0.618735	+	0.785600i	$0.287646\pi$
$104$	−0.0159832	−0.00156728
$105$	12.0672	1.17764
$106$	3.83467	0.372456
$107$	7.72899	0.747190	0.373595	−	0.927592i	$-0.378125\pi$
$107$	7.72899	0.747190	0.373595	+	0.927592i	$0.378125\pi$
$108$	2.12618	0.204592
$109$	−2.25672	−0.216155	−0.108077	−	0.994142i	$-0.534469\pi$
$109$	−2.25672	−0.216155	−0.108077	+	0.994142i	$0.534469\pi$
$110$	−2.91380	−0.277820
$111$	20.4289	1.93902
$112$	4.74823	0.448666
$113$	−2.56661	−0.241447	−0.120723	−	0.992686i	$-0.538521\pi$
$113$	−2.56661	−0.241447	−0.120723	+	0.992686i	$0.538521\pi$
$114$	7.75948	0.726742
$115$	13.4839	1.25738
$116$	9.32108	0.865441
$117$	−0.0158553	−0.00146583
$118$	0.898586	0.0827216
$119$	12.7123	1.16533
$120$	8.60089	0.785150
$121$	−3.27725	−0.297932
$122$	−1.57053	−0.142189
$123$	2.38923	0.215430
$124$	−12.2139	−1.09684
$125$	−11.7137	−1.04770
$126$	−5.59730	−0.498648
$127$	6.05389	0.537196	0.268598	−	0.963252i	$-0.413440\pi$
$127$	6.05389	0.537196	0.268598	+	0.963252i	$0.413440\pi$
$128$	10.7902	0.953728
$129$	−4.81723	−0.424133
$130$	0.00692156	0.000607061 0
$131$	10.1503	0.886836	0.443418	−	0.896315i	$-0.353766\pi$
$131$	10.1503	0.886836	0.443418	+	0.896315i	$0.353766\pi$
$132$	−9.87808	−0.859776
$133$	−16.5320	−1.43350
$134$	2.01495	0.174065
$135$	−2.12482	−0.182876
$136$	9.06063	0.776943
$137$	17.5304	1.49773	0.748863	−	0.662725i	$-0.230600\pi$
$137$	17.5304	1.49773	0.748863	+	0.662725i	$0.230600\pi$
$138$	−14.0664	−1.19741
$139$	−3.77537	−0.320222	−0.160111	−	0.987099i	$-0.551185\pi$
$139$	−3.77537	−0.320222	−0.160111	+	0.987099i	$0.551185\pi$
$140$	−7.94059	−0.671102
$141$	−27.7934	−2.34063
$142$	−3.44024	−0.288698
$143$	−0.0183449	−0.00153408
$144$	3.35721	0.279768
$145$	−9.31514	−0.773581
$146$	−10.7329	−0.888258
$147$	10.5513	0.870254
$148$	−13.4428	−1.10499
$149$	15.6799	1.28455	0.642274	−	0.766475i	$-0.277991\pi$
$149$	15.6799	1.28455	0.642274	+	0.766475i	$0.277991\pi$
$150$	4.24753	0.346810
$151$	−3.71211	−0.302087	−0.151043	−	0.988527i	$-0.548263\pi$
$151$	−3.71211	−0.302087	−0.151043	+	0.988527i	$0.548263\pi$
$152$	−11.7831	−0.955737
$153$	8.98814	0.726648
$154$	−6.47619	−0.521866
$155$	12.2061	0.980417
$156$	0.0234648	0.00187869
$157$	−0.547953	−0.0437314	−0.0218657	−	0.999761i	$-0.506961\pi$
$157$	−0.547953	−0.0437314	−0.0218657	+	0.999761i	$0.506961\pi$
$158$	3.50371	0.278740
$159$	−12.9916	−1.03030
$160$	−8.86677	−0.700980
$161$	29.9691	2.36190
$162$	7.15974	0.562522
$163$	0.152506	0.0119452	0.00597260	−	0.999982i	$-0.498099\pi$
$163$	0.152506	0.0119452	0.00597260	+	0.999982i	$0.498099\pi$
$164$	−1.57218	−0.122767
$165$	9.87178	0.768517
$166$	6.30042	0.489007
$167$	9.58630	0.741810	0.370905	−	0.928671i	$-0.379047\pi$
$167$	9.58630	0.741810	0.370905	+	0.928671i	$0.379047\pi$
$168$	19.1163	1.47485
$169$	−13.0000	−0.999997
$170$	−3.92373	−0.300936
$171$	−11.6888	−0.893868
$172$	3.16987	0.241700
$173$	19.6290	1.49236	0.746182	−	0.665742i	$-0.231885\pi$
$173$	19.6290	1.49236	0.746182	+	0.665742i	$0.231885\pi$
$174$	9.71756	0.736686
$175$	−9.04959	−0.684085
$176$	3.88436	0.292795
$177$	−3.04436	−0.228828
$178$	7.34728	0.550702
$179$	10.5252	0.786688	0.393344	−	0.919391i	$-0.371318\pi$
$179$	10.5252	0.786688	0.393344	+	0.919391i	$0.371318\pi$
$180$	−5.61435	−0.418469
$181$	5.14958	0.382765	0.191382	−	0.981516i	$-0.438703\pi$
$181$	5.14958	0.382765	0.191382	+	0.981516i	$0.438703\pi$
$182$	0.0153838	0.00114032
$183$	5.32086	0.393329
$184$	21.3604	1.57471
$185$	13.4342	0.987703
$186$	−12.7334	−0.933658
$187$	10.3995	0.760484
$188$	18.2888	1.33385
$189$	−4.72262	−0.343520
$190$	5.10270	0.370189
$191$	−4.30242	−0.311312	−0.155656	−	0.987811i	$-0.549749\pi$
$191$	−4.30242	−0.311312	−0.155656	+	0.987811i	$0.549749\pi$
$192$	2.75250	0.198645
$193$	−9.79725	−0.705221	−0.352611	−	0.935770i	$-0.614706\pi$
$193$	−9.79725	−0.705221	−0.352611	+	0.935770i	$0.614706\pi$
$194$	10.5339	0.756293
$195$	−0.0234498	−0.00167928
$196$	−6.94303	−0.495931
$197$	−9.97949	−0.711009	−0.355505	−	0.934675i	$-0.615691\pi$
$197$	−9.97949	−0.711009	−0.355505	+	0.934675i	$0.615691\pi$
$198$	−4.57895	−0.325412
$199$	11.5218	0.816761	0.408380	−	0.912812i	$-0.366094\pi$
$199$	11.5218	0.816761	0.408380	+	0.912812i	$0.366094\pi$
$200$	−6.45006	−0.456088
$201$	−6.82652	−0.481506
$202$	9.49245	0.667886
$203$	−20.7038	−1.45312
$204$	−13.3018	−0.931314
$205$	1.57118	0.109736
$206$	−8.61565	−0.600281
$207$	21.1895	1.47277
$208$	−0.00922706	−0.000639782 0
$209$	−13.5242	−0.935490
$210$	−8.27834	−0.571260
$211$	3.00726	0.207029	0.103514	−	0.994628i	$-0.466991\pi$
$211$	3.00726	0.207029	0.103514	+	0.994628i	$0.466991\pi$
$212$	8.54887	0.587139
$213$	11.6553	0.798610
$214$	−5.30222	−0.362453
$215$	−3.16785	−0.216046
$216$	−3.36603	−0.229029
$217$	27.1292	1.84165
$218$	1.54815	0.104854
$219$	36.3623	2.45714
$220$	−6.49591	−0.437954
$221$	−0.0247033	−0.00166172
$222$	−14.0146	−0.940597
$223$	10.1382	0.678907	0.339454	−	0.940623i	$-0.389758\pi$
$223$	10.1382	0.678907	0.339454	+	0.940623i	$0.389758\pi$
$224$	−19.7072	−1.31674
$225$	−6.39846	−0.426564
$226$	1.76074	0.117123
$227$	−8.73108	−0.579502	−0.289751	−	0.957102i	$-0.593573\pi$
$227$	−8.73108	−0.579502	−0.289751	+	0.957102i	$0.593573\pi$
$228$	17.2987	1.14563
$229$	4.88120	0.322559	0.161279	−	0.986909i	$-0.448438\pi$
$229$	4.88120	0.322559	0.161279	+	0.986909i	$0.448438\pi$
$230$	−9.25016	−0.609938
$231$	21.9410	1.44361
$232$	−14.7565	−0.968815
$233$	−6.56725	−0.430235	−0.215118	−	0.976588i	$-0.569013\pi$
$233$	−6.56725	−0.430235	−0.215118	+	0.976588i	$0.569013\pi$
$234$	0.0108770	0.000711054 0
$235$	−18.2772	−1.19227
$236$	2.00327	0.130402
$237$	−11.8704	−0.771063
$238$	−8.72084	−0.565288
$239$	14.4179	0.932616	0.466308	−	0.884622i	$-0.345584\pi$
$239$	14.4179	0.932616	0.466308	+	0.884622i	$0.345584\pi$
$240$	4.96527	0.320507
$241$	6.54196	0.421404	0.210702	−	0.977550i	$-0.432425\pi$
$241$	6.54196	0.421404	0.210702	+	0.977550i	$0.432425\pi$
$242$	2.24825	0.144523
$243$	−20.0861	−1.28853
$244$	−3.50127	−0.224146
$245$	6.93861	0.443291
$246$	−1.63906	−0.104502
$247$	0.0321260	0.00204413
$248$	19.3362	1.22785
$249$	−21.3455	−1.35271
$250$	8.03578	0.508227
$251$	−24.4517	−1.54338	−0.771688	−	0.636001i	$-0.780587\pi$
$251$	−24.4517	−1.54338	−0.771688	+	0.636001i	$0.780587\pi$
$252$	−12.4784	−0.786066
$253$	24.5167	1.54135
$254$	−4.15308	−0.260587
$255$	13.2934	0.832462
$256$	−9.77084	−0.610678
$257$	5.14243	0.320776	0.160388	−	0.987054i	$-0.448725\pi$
$257$	5.14243	0.320776	0.160388	+	0.987054i	$0.448725\pi$
$258$	3.30470	0.205742
$259$	29.8588	1.85534
$260$	0.0154306	0.000956968 0
$261$	−14.6385	−0.906099
$262$	−6.96328	−0.430193
$263$	21.0327	1.29693	0.648466	−	0.761244i	$-0.275411\pi$
$263$	21.0327	1.29693	0.648466	+	0.761244i	$0.275411\pi$
$264$	15.6383	0.962473
$265$	−8.54342	−0.524818
$266$	11.3412	0.695376
$267$	−24.8922	−1.52338
$268$	4.49204	0.274395
$269$	−32.5840	−1.98668	−0.993340	−	0.115224i	$-0.963242\pi$
$269$	−32.5840	−1.98668	−0.993340	+	0.115224i	$0.963242\pi$
$270$	1.45767	0.0887107
$271$	−14.4067	−0.875143	−0.437572	−	0.899184i	$-0.644161\pi$
$271$	−14.4067	−0.875143	−0.437572	+	0.899184i	$0.644161\pi$
$272$	5.23068	0.317157
$273$	−0.0521194	−0.00315441
$274$	−12.0262	−0.726528
$275$	−7.40315	−0.446426
$276$	−31.3590	−1.88759
$277$	1.12890	0.0678288	0.0339144	−	0.999425i	$-0.489203\pi$
$277$	1.12890	0.0678288	0.0339144	+	0.999425i	$0.489203\pi$
$278$	2.58997	0.155336
$279$	19.1815	1.14837
$280$	12.5710	0.751263
$281$	−4.21795	−0.251622	−0.125811	−	0.992054i	$-0.540153\pi$
$281$	−4.21795	−0.251622	−0.125811	+	0.992054i	$0.540153\pi$
$282$	19.0668	1.13541
$283$	−20.4085	−1.21316	−0.606580	−	0.795023i	$-0.707459\pi$
$283$	−20.4085	−1.21316	−0.606580	+	0.795023i	$0.707459\pi$
$284$	−7.66953	−0.455103
$285$	−17.2877	−1.02403
$286$	0.0125849	0.000744163 0
$287$	3.49209	0.206132
$288$	−13.9339	−0.821062
$289$	−2.99608	−0.176240
$290$	6.39035	0.375254
$291$	−35.6884	−2.09209
$292$	−23.9274	−1.40025
$293$	32.1107	1.87593	0.937963	−	0.346736i	$-0.112710\pi$
$293$	32.1107	1.87593	0.937963	+	0.346736i	$0.112710\pi$
$294$	−7.23836	−0.422150
$295$	−2.00200	−0.116561
$296$	21.2818	1.23698
$297$	−3.86340	−0.224177
$298$	−10.7567	−0.623119
$299$	−0.0582379	−0.00336798
$300$	9.46928	0.546709
$301$	−7.04084	−0.405827
$302$	2.54657	0.146539
$303$	−32.1599	−1.84754
$304$	−6.80236	−0.390142
$305$	3.49904	0.200355
$306$	−6.16602	−0.352488
$307$	0.329040	0.0187793	0.00938964	−	0.999956i	$-0.497011\pi$
$307$	0.329040	0.0187793	0.00938964	+	0.999956i	$0.497011\pi$
$308$	−14.4378	−0.822668
$309$	29.1893	1.66052
$310$	−8.37359	−0.475588
$311$	−8.90310	−0.504849	−0.252424	−	0.967617i	$-0.581228\pi$
$311$	−8.90310	−0.504849	−0.252424	+	0.967617i	$0.581228\pi$
$312$	−0.0371479	−0.00210309
$313$	−17.1883	−0.971543	−0.485771	−	0.874086i	$-0.661461\pi$
$313$	−17.1883	−0.971543	−0.485771	+	0.874086i	$0.661461\pi$
$314$	0.375906	0.0212136
$315$	12.4705	0.702631
$316$	7.81103	0.439405
$317$	−7.84214	−0.440459	−0.220229	−	0.975448i	$-0.570681\pi$
$317$	−7.84214	−0.440459	−0.220229	+	0.975448i	$0.570681\pi$
$318$	8.91250	0.499788
$319$	−16.9370	−0.948291
$320$	1.81007	0.101186
$321$	17.9636	1.00263
$322$	−20.5593	−1.14573
$323$	−18.2117	−1.01333
$324$	15.9616	0.886758
$325$	0.0175857	0.000975481 0
$326$	−0.104622	−0.00579447
$327$	−5.24504	−0.290051
$328$	2.48898	0.137431
$329$	−40.6228	−2.23961
$330$	−6.77222	−0.372798
$331$	5.59016	0.307263	0.153632	−	0.988128i	$-0.450903\pi$
$331$	5.59016	0.307263	0.153632	+	0.988128i	$0.450903\pi$
$332$	14.0459	0.770869
$333$	21.1115	1.15690
$334$	−6.57637	−0.359843
$335$	−4.48918	−0.245270
$336$	11.0358	0.602051
$337$	10.9895	0.598634	0.299317	−	0.954154i	$-0.403241\pi$
$337$	10.9895	0.598634	0.299317	+	0.954154i	$0.403241\pi$
$338$	8.91820	0.485086
$339$	−5.96529	−0.323990
$340$	−8.74739	−0.474394
$341$	22.1934	1.20184
$342$	8.01875	0.433605
$343$	−8.35746	−0.451261
$344$	−5.01834	−0.270571
$345$	31.3390	1.68724
$346$	−13.4658	−0.723927
$347$	24.3054	1.30478	0.652391	−	0.757883i	$-0.273766\pi$
$347$	24.3054	1.30478	0.652391	+	0.757883i	$0.273766\pi$
$348$	21.6639	1.16131
$349$	−20.0716	−1.07441	−0.537204	−	0.843452i	$-0.680520\pi$
$349$	−20.0716	−1.07441	−0.537204	+	0.843452i	$0.680520\pi$
$350$	6.20818	0.331841
$351$	0.00917728	0.000489847 0
$352$	−16.1218	−0.859294
$353$	−12.6415	−0.672837	−0.336418	−	0.941713i	$-0.609216\pi$
$353$	−12.6415	−0.672837	−0.336418	+	0.941713i	$0.609216\pi$
$354$	2.08848	0.111002
$355$	7.66464	0.406797
$356$	16.3797	0.868124
$357$	29.5457	1.56372
$358$	−7.22045	−0.381613
$359$	7.67191	0.404908	0.202454	−	0.979292i	$-0.435108\pi$
$359$	7.67191	0.404908	0.202454	+	0.979292i	$0.435108\pi$
$360$	8.88827	0.468453
$361$	4.68388	0.246520
$362$	−3.53270	−0.185675
$363$	−7.61695	−0.399786
$364$	0.0342960	0.00179760
$365$	23.9122	1.25162
$366$	−3.65020	−0.190799
$367$	19.2020	1.00234	0.501169	−	0.865350i	$-0.332904\pi$
$367$	19.2020	1.00234	0.501169	+	0.865350i	$0.332904\pi$
$368$	12.3313	0.642813
$369$	2.46906	0.128534
$370$	−9.21611	−0.479123
$371$	−18.9885	−0.985836
$372$	−28.3873	−1.47181
$373$	−27.1736	−1.40700	−0.703498	−	0.710698i	$-0.748379\pi$
$373$	−27.1736	−1.40700	−0.703498	+	0.710698i	$0.748379\pi$
$374$	−7.13421	−0.368901
$375$	−27.2247	−1.40588
$376$	−28.9537	−1.49318
$377$	0.0402329	0.00207210
$378$	3.23980	0.166637
$379$	−21.3697	−1.09769	−0.548845	−	0.835924i	$-0.684932\pi$
$379$	−21.3697	−1.09769	−0.548845	+	0.835924i	$0.684932\pi$
$380$	11.3758	0.583564
$381$	14.0704	0.720847
$382$	2.95153	0.151014
$383$	17.6157	0.900121	0.450061	−	0.892998i	$-0.351402\pi$
$383$	17.6157	0.900121	0.450061	+	0.892998i	$0.351402\pi$
$384$	25.0785	1.27978
$385$	14.4286	0.735348
$386$	6.72108	0.342094
$387$	−4.97819	−0.253055
$388$	23.4840	1.19222
$389$	10.1238	0.513298	0.256649	−	0.966505i	$-0.417382\pi$
$389$	10.1238	0.513298	0.256649	+	0.966505i	$0.417382\pi$
$390$	0.0160870	0.000814597 0
$391$	33.0142	1.66960
$392$	10.9918	0.555168
$393$	23.5912	1.19002
$394$	6.84610	0.344902
$395$	−7.80605	−0.392765
$396$	−10.2081	−0.512978
$397$	9.51604	0.477596	0.238798	−	0.971069i	$-0.423247\pi$
$397$	9.51604	0.477596	0.238798	+	0.971069i	$0.423247\pi$
$398$	−7.90418	−0.396201
$399$	−38.4234	−1.92358
$400$	−3.72361	−0.186180
$401$	19.6704	0.982293	0.491147	−	0.871077i	$-0.336578\pi$
$401$	19.6704	0.982293	0.491147	+	0.871077i	$0.336578\pi$
$402$	4.68311	0.233573
$403$	−0.0527191	−0.00262613
$404$	21.1621	1.05285
$405$	−15.9515	−0.792635
$406$	14.2032	0.704891
$407$	24.4264	1.21077
$408$	21.0586	1.04256
$409$	−18.1606	−0.897982	−0.448991	−	0.893536i	$-0.648217\pi$
$409$	−18.1606	−0.897982	−0.448991	+	0.893536i	$0.648217\pi$
$410$	−1.07786	−0.0532316
$411$	40.7440	2.00975
$412$	−19.2074	−0.946280
$413$	−4.44962	−0.218952
$414$	−14.5364	−0.714424
$415$	−14.0370	−0.689047
$416$	0.0382963	0.00187763
$417$	−8.77466	−0.429697
$418$	9.27786	0.453795
$419$	−18.7200	−0.914530	−0.457265	−	0.889330i	$-0.651171\pi$
$419$	−18.7200	−0.914530	−0.457265	+	0.889330i	$0.651171\pi$
$420$	−18.4554	−0.900532
$421$	−17.1828	−0.837437	−0.418718	−	0.908116i	$-0.637521\pi$
$421$	−17.1828	−0.837437	−0.418718	+	0.908116i	$0.637521\pi$
$422$	−2.06304	−0.100427
$423$	−28.7221	−1.39652
$424$	−13.5340	−0.657270
$425$	−9.96908	−0.483571
$426$	−7.99576	−0.387396
$427$	7.77695	0.376353
$428$	−11.8206	−0.571369
$429$	−0.0426370	−0.00205854
$430$	2.17320	0.104801
$431$	−8.79330	−0.423558	−0.211779	−	0.977318i	$-0.567926\pi$
$431$	−8.79330	−0.423558	−0.211779	+	0.977318i	$0.567926\pi$
$432$	−1.94320	−0.0934923
$433$	9.32345	0.448056	0.224028	−	0.974583i	$-0.428079\pi$
$433$	9.32345	0.448056	0.224028	+	0.974583i	$0.428079\pi$
$434$	−18.6111	−0.893361
$435$	−21.6501	−1.03804
$436$	3.45138	0.165291
$437$	−42.9341	−2.05381
$438$	−24.9452	−1.19193
$439$	35.6357	1.70080	0.850400	−	0.526137i	$-0.176360\pi$
$439$	35.6357	1.70080	0.850400	+	0.526137i	$0.176360\pi$
$440$	10.2839	0.490266
$441$	10.9038	0.519230
$442$	0.0169469	0.000806081 0
$443$	−8.36847	−0.397598	−0.198799	−	0.980040i	$-0.563704\pi$
$443$	−8.36847	−0.397598	−0.198799	+	0.980040i	$0.563704\pi$
$444$	−31.2435	−1.48275
$445$	−16.3693	−0.775979
$446$	−6.95501	−0.329329
$447$	36.4430	1.72370
$448$	4.02304	0.190071
$449$	−6.30164	−0.297393	−0.148696	−	0.988883i	$-0.547508\pi$
$449$	−6.30164	−0.297393	−0.148696	+	0.988883i	$0.547508\pi$
$450$	4.38946	0.206921
$451$	2.85676	0.134519
$452$	3.92533	0.184632
$453$	−8.62763	−0.405361
$454$	5.98968	0.281109
$455$	−0.0342742	−0.00160680
$456$	−27.3862	−1.28247
$457$	17.0324	0.796742	0.398371	−	0.917224i	$-0.369576\pi$
$457$	17.0324	0.796742	0.398371	+	0.917224i	$0.369576\pi$
$458$	−3.34859	−0.156469
$459$	−5.20246	−0.242830
$460$	−20.6219	−0.961503
$461$	24.5887	1.14521	0.572604	−	0.819832i	$-0.305933\pi$
$461$	24.5887	1.14521	0.572604	+	0.819832i	$0.305933\pi$
$462$	−15.0519	−0.700277
$463$	19.4652	0.904623	0.452311	−	0.891860i	$-0.350600\pi$
$463$	19.4652	0.904623	0.452311	+	0.891860i	$0.350600\pi$
$464$	−8.51892	−0.395481
$465$	28.3692	1.31559
$466$	4.50525	0.208702
$467$	2.64248	0.122279	0.0611397	−	0.998129i	$-0.480526\pi$
$467$	2.64248	0.122279	0.0611397	+	0.998129i	$0.480526\pi$
$468$	0.0242488	0.00112090
$469$	−9.97762	−0.460724
$470$	12.5385	0.578357
$471$	−1.27355	−0.0586819
$472$	−3.17145	−0.145978
$473$	−5.75986	−0.264839
$474$	8.14328	0.374033
$475$	12.9645	0.594853
$476$	−19.4419	−0.891118
$477$	−13.4257	−0.614723
$478$	−9.89093	−0.452401
$479$	−33.9558	−1.55148	−0.775740	−	0.631052i	$-0.782623\pi$
$479$	−33.9558	−1.55148	−0.775740	+	0.631052i	$0.782623\pi$
$480$	−20.6080	−0.940624
$481$	−0.0580235	−0.00264564
$482$	−4.48790	−0.204418
$483$	69.6539	3.16936
$484$	5.01216	0.227826
$485$	−23.4690	−1.06567
$486$	13.7794	0.625048
$487$	−1.99883	−0.0905756	−0.0452878	−	0.998974i	$-0.514420\pi$
$487$	−1.99883	−0.0905756	−0.0452878	+	0.998974i	$0.514420\pi$
$488$	5.54299	0.250919
$489$	0.354453	0.0160289
$490$	−4.76001	−0.215035
$491$	−15.4149	−0.695664	−0.347832	−	0.937557i	$-0.613082\pi$
$491$	−15.4149	−0.695664	−0.347832	+	0.937557i	$0.613082\pi$
$492$	−3.65404	−0.164737
$493$	−22.8074	−1.02719
$494$	−0.0220390	−0.000991581 0
$495$	10.2016	0.458529
$496$	11.1628	0.501223
$497$	17.0354	0.764141
$498$	14.6434	0.656185
$499$	−15.8623	−0.710093	−0.355047	−	0.934849i	$-0.615535\pi$
$499$	−15.8623	−0.710093	−0.355047	+	0.934849i	$0.615535\pi$
$500$	17.9146	0.801167
$501$	22.2804	0.995413
$502$	16.7743	0.748673
$503$	33.0753	1.47475	0.737377	−	0.675481i	$-0.236064\pi$
$503$	33.0753	1.47475	0.737377	+	0.675481i	$0.236064\pi$
$504$	19.7550	0.879958
$505$	−21.1486	−0.941100
$506$	−16.8189	−0.747690
$507$	−30.2143	−1.34187
$508$	−9.25870	−0.410788
$509$	−8.14637	−0.361081	−0.180541	−	0.983568i	$-0.557785\pi$
$509$	−8.14637	−0.361081	−0.180541	+	0.983568i	$0.557785\pi$
$510$	−9.11947	−0.403817
$511$	53.1470	2.35109
$512$	−14.8774	−0.657496
$513$	6.76567	0.298711
$514$	−3.52780	−0.155605
$515$	19.1952	0.845840
$516$	7.36737	0.324330
$517$	−33.2320	−1.46154
$518$	−20.4837	−0.900000
$519$	45.6214	2.00256
$520$	−0.0244288	−0.00107127
$521$	11.3410	0.496860	0.248430	−	0.968650i	$-0.420085\pi$
$521$	11.3410	0.496860	0.248430	+	0.968650i	$0.420085\pi$
$522$	10.0423	0.439538
$523$	32.8256	1.43536	0.717682	−	0.696371i	$-0.245203\pi$
$523$	32.8256	1.43536	0.717682	+	0.696371i	$0.245203\pi$
$524$	−15.5237	−0.678154
$525$	−21.0329	−0.917953
$526$	−14.4288	−0.629126
$527$	29.8857	1.30184
$528$	9.02798	0.392892
$529$	54.8307	2.38394
$530$	5.86094	0.254583
$531$	−3.14608	−0.136528
$532$	25.2837	1.09619
$533$	−0.00678606	−0.000293937 0
$534$	17.0765	0.738971
$535$	11.8130	0.510722
$536$	−7.11151	−0.307171
$537$	24.4625	1.05563
$538$	22.3532	0.963714
$539$	12.6159	0.543407
$540$	3.24966	0.139843
$541$	−45.1470	−1.94102	−0.970511	−	0.241058i	$-0.922506\pi$
$541$	−45.1470	−1.94102	−0.970511	+	0.241058i	$0.922506\pi$
$542$	9.88323	0.424521
$543$	11.9686	0.513621
$544$	−21.7096	−0.930791
$545$	−3.44918	−0.147747
$546$	0.0357549	0.00153017
$547$	−34.0956	−1.45782	−0.728911	−	0.684609i	$-0.759973\pi$
$547$	−34.0956	−1.45782	−0.728911	+	0.684609i	$0.759973\pi$
$548$	−26.8107	−1.14530
$549$	5.49864	0.234676
$550$	5.07869	0.216556
$551$	29.6604	1.26358
$552$	49.6455	2.11305
$553$	−17.3497	−0.737784
$554$	−0.774443	−0.0329029
$555$	31.2236	1.32537
$556$	5.77397	0.244871
$557$	−8.92351	−0.378101	−0.189051	−	0.981967i	$-0.560541\pi$
$557$	−8.92351	−0.378101	−0.189051	+	0.981967i	$0.560541\pi$
$558$	−13.1589	−0.557059
$559$	0.0136822	0.000578696 0
$560$	7.25722	0.306674
$561$	24.1703	1.02047
$562$	2.89359	0.122059
$563$	42.1344	1.77575	0.887877	−	0.460082i	$-0.152180\pi$
$563$	42.1344	1.77575	0.887877	+	0.460082i	$0.152180\pi$
$564$	42.5067	1.78986
$565$	−3.92283	−0.165035
$566$	14.0006	0.588489
$567$	−35.4536	−1.48891
$568$	12.1419	0.509463
$569$	−19.8395	−0.831714	−0.415857	−	0.909430i	$-0.636518\pi$
$569$	−19.8395	−0.831714	−0.415857	+	0.909430i	$0.636518\pi$
$570$	11.8596	0.496746
$571$	−42.0739	−1.76074	−0.880369	−	0.474289i	$-0.842705\pi$
$571$	−42.0739	−1.76074	−0.880369	+	0.474289i	$0.842705\pi$
$572$	0.0280564	0.00117310
$573$	−9.99962	−0.417740
$574$	−2.39564	−0.0999920
$575$	−23.5021	−0.980104
$576$	2.84447	0.118520
$577$	23.8665	0.993575	0.496787	−	0.867872i	$-0.334513\pi$
$577$	23.8665	0.993575	0.496787	+	0.867872i	$0.334513\pi$
$578$	2.05537	0.0854920
$579$	−22.7706	−0.946315
$580$	14.2464	0.591549
$581$	−31.1984	−1.29433
$582$	24.4829	1.01485
$583$	−15.5338	−0.643346
$584$	37.8803	1.56750
$585$	−0.0242334	−0.00100193
$586$	−22.0285	−0.909988
$587$	−17.0597	−0.704131	−0.352065	−	0.935975i	$-0.614521\pi$
$587$	−17.0597	−0.704131	−0.352065	+	0.935975i	$0.614521\pi$
$588$	−16.1369	−0.665475
$589$	−38.8655	−1.60143
$590$	1.37340	0.0565422
$591$	−23.1942	−0.954082
$592$	12.2859	0.504948
$593$	−46.5637	−1.91214	−0.956072	−	0.293133i	$-0.905302\pi$
$593$	−46.5637	−1.91214	−0.956072	+	0.293133i	$0.905302\pi$
$594$	2.65036	0.108746
$595$	19.4295	0.796532
$596$	−23.9805	−0.982281
$597$	26.7789	1.09599
$598$	0.0399522	0.00163377
$599$	−37.7419	−1.54209	−0.771046	−	0.636779i	$-0.780266\pi$
$599$	−37.7419	−1.54209	−0.771046	+	0.636779i	$0.780266\pi$
$600$	−14.9912	−0.612011
$601$	−28.2023	−1.15039	−0.575197	−	0.818015i	$-0.695075\pi$
$601$	−28.2023	−1.15039	−0.575197	+	0.818015i	$0.695075\pi$
$602$	4.83014	0.196862
$603$	−7.05462	−0.287286
$604$	5.67722	0.231003
$605$	−5.00897	−0.203644
$606$	22.0622	0.896217
$607$	−19.9210	−0.808568	−0.404284	−	0.914634i	$-0.632479\pi$
$607$	−19.9210	−0.808568	−0.404284	+	0.914634i	$0.632479\pi$
$608$	28.2328	1.14499
$609$	−48.1194	−1.94990
$610$	−2.40040	−0.0971895
$611$	0.0789407	0.00319360
$612$	−13.7463	−0.555661
$613$	−46.0604	−1.86036	−0.930181	−	0.367101i	$-0.880350\pi$
$613$	−46.0604	−1.86036	−0.930181	+	0.367101i	$0.880350\pi$
$614$	−0.225727	−0.00910960
$615$	3.65172	0.147251
$616$	22.8569	0.920932
$617$	42.5271	1.71208	0.856039	−	0.516912i	$-0.172918\pi$
$617$	42.5271	1.71208	0.856039	+	0.516912i	$0.172918\pi$
$618$	−20.0244	−0.805499
$619$	15.7193	0.631813	0.315907	−	0.948790i	$-0.397691\pi$
$619$	15.7193	0.631813	0.315907	+	0.948790i	$0.397691\pi$
$620$	−18.6678	−0.749715
$621$	−12.2648	−0.492168
$622$	6.10769	0.244896
$623$	−36.3823	−1.45763
$624$	−0.0214454	−0.000858504 0
$625$	−4.58335	−0.183334
$626$	11.7915	0.471283
$627$	−31.4328	−1.25531
$628$	0.838029	0.0334410
$629$	32.8926	1.31151
$630$	−8.55495	−0.340837
$631$	−26.0352	−1.03645	−0.518223	−	0.855245i	$-0.673406\pi$
$631$	−26.0352	−1.03645	−0.518223	+	0.855245i	$0.673406\pi$
$632$	−12.3659	−0.491890
$633$	6.98944	0.277805
$634$	5.37985	0.213661
$635$	9.25280	0.367186
$636$	19.8692	0.787864
$637$	−0.0299684	−0.00118739
$638$	11.6191	0.460004
$639$	12.0448	0.476484
$640$	16.4918	0.651896
$641$	−0.696080	−0.0274935	−0.0137468	−	0.999906i	$-0.504376\pi$
$641$	−0.696080	−0.0274935	−0.0137468	+	0.999906i	$0.504376\pi$
$642$	−12.3234	−0.486364
$643$	18.5052	0.729776	0.364888	−	0.931051i	$-0.381107\pi$
$643$	18.5052	0.729776	0.364888	+	0.931051i	$0.381107\pi$
$644$	−45.8342	−1.80612
$645$	−7.36268	−0.289905
$646$	12.4936	0.491553
$647$	−9.29926	−0.365592	−0.182796	−	0.983151i	$-0.558515\pi$
$647$	−9.29926	−0.365592	−0.182796	+	0.983151i	$0.558515\pi$
$648$	−25.2694	−0.992678
$649$	−3.64008	−0.142885
$650$	−0.0120641	−0.000473194 0
$651$	63.0533	2.47125
$652$	−0.233240	−0.00913438
$653$	−21.2245	−0.830579	−0.415289	−	0.909689i	$-0.636320\pi$
$653$	−21.2245	−0.830579	−0.415289	+	0.909689i	$0.636320\pi$
$654$	3.59819	0.140700
$655$	15.5138	0.606173
$656$	1.43688	0.0561008
$657$	37.5773	1.46603
$658$	27.8679	1.08641
$659$	6.62803	0.258191	0.129096	−	0.991632i	$-0.458793\pi$
$659$	6.62803	0.258191	0.129096	+	0.991632i	$0.458793\pi$
$660$	−15.0977	−0.587677
$661$	−45.5010	−1.76978	−0.884892	−	0.465796i	$-0.845768\pi$
$661$	−45.5010	−1.76978	−0.884892	+	0.465796i	$0.845768\pi$
$662$	−3.83495	−0.149050
$663$	−0.0574151	−0.00222982
$664$	−22.2366	−0.862947
$665$	−25.2676	−0.979835
$666$	−14.4829	−0.561199
$667$	−53.7683	−2.08192
$668$	−14.6611	−0.567255
$669$	23.5632	0.911005
$670$	3.07966	0.118978
$671$	6.36204	0.245604
$672$	−45.8033	−1.76690
$673$	−38.0047	−1.46497	−0.732487	−	0.680781i	$-0.761641\pi$
$673$	−38.0047	−1.46497	−0.732487	+	0.680781i	$0.761641\pi$
$674$	−7.53897	−0.290390
$675$	3.70352	0.142548
$676$	19.8819	0.764687
$677$	1.58248	0.0608196	0.0304098	−	0.999538i	$-0.490319\pi$
$677$	1.58248	0.0608196	0.0304098	+	0.999538i	$0.490319\pi$
$678$	4.09229	0.157164
$679$	−52.1620	−2.00180
$680$	13.8483	0.531059
$681$	−20.2927	−0.777617
$682$	−15.2251	−0.582998
$683$	−28.8817	−1.10513	−0.552564	−	0.833471i	$-0.686350\pi$
$683$	−28.8817	−1.10513	−0.552564	+	0.833471i	$0.686350\pi$
$684$	17.8767	0.683532
$685$	26.7936	1.02373
$686$	5.73337	0.218901
$687$	11.3448	0.432832
$688$	−2.89707	−0.110450
$689$	0.0368997	0.00140577
$690$	−21.4991	−0.818457
$691$	39.3469	1.49683	0.748413	−	0.663233i	$-0.230816\pi$
$691$	39.3469	1.49683	0.748413	+	0.663233i	$0.230816\pi$
$692$	−30.0202	−1.14120
$693$	22.6741	0.861317
$694$	−16.6739	−0.632933
$695$	−5.77029	−0.218880
$696$	−34.2970	−1.30002
$697$	3.84691	0.145712
$698$	13.7695	0.521182
$699$	−15.2635	−0.577320
$700$	13.8403	0.523113
$701$	−10.5179	−0.397257	−0.198629	−	0.980075i	$-0.563649\pi$
$701$	−10.5179	−0.397257	−0.198629	+	0.980075i	$0.563649\pi$
$702$	−0.00629578	−0.000237619 0
$703$	−42.7760	−1.61333
$704$	3.29111	0.124038
$705$	−42.4796	−1.59988
$706$	8.67226	0.326385
$707$	−47.0047	−1.76779
$708$	4.65598	0.174982
$709$	−50.5544	−1.89861	−0.949306	−	0.314353i	$-0.898212\pi$
$709$	−50.5544	−1.89861	−0.949306	+	0.314353i	$0.898212\pi$
$710$	−5.25808	−0.197332
$711$	−12.2670	−0.460048
$712$	−25.9314	−0.971819
$713$	70.4553	2.63857
$714$	−20.2689	−0.758544
$715$	−0.0280385	−0.00104858
$716$	−16.0970	−0.601572
$717$	33.5099	1.25145
$718$	−5.26307	−0.196416
$719$	−32.3377	−1.20599	−0.602996	−	0.797744i	$-0.706027\pi$
$719$	−32.3377	−1.20599	−0.602996	+	0.797744i	$0.706027\pi$
$720$	5.13118	0.191228
$721$	42.6630	1.58885
$722$	−3.21322	−0.119584
$723$	15.2047	0.565470
$724$	−7.87566	−0.292696
$725$	16.2361	0.602993
$726$	5.22536	0.193931
$727$	4.15520	0.154108	0.0770539	−	0.997027i	$-0.475449\pi$
$727$	4.15520	0.154108	0.0770539	+	0.997027i	$0.475449\pi$
$728$	−0.0542953	−0.00201232
$729$	−15.3739	−0.569403
$730$	−16.4042	−0.607145
$731$	−7.75623	−0.286875
$732$	−8.13761	−0.300775
$733$	0.694632	0.0256568	0.0128284	−	0.999918i	$-0.495916\pi$
$733$	0.694632	0.0256568	0.0128284	+	0.999918i	$0.495916\pi$
$734$	−13.1729	−0.486222
$735$	16.1266	0.594839
$736$	−51.1803	−1.88653
$737$	−8.16233	−0.300663
$738$	−1.69382	−0.0623504
$739$	−44.2854	−1.62906	−0.814532	−	0.580119i	$-0.803006\pi$
$739$	−44.2854	−1.62906	−0.814532	+	0.580119i	$0.803006\pi$
$740$	−20.5460	−0.755287
$741$	0.0746668	0.00274295
$742$	13.0265	0.478217
$743$	−9.92011	−0.363934	−0.181967	−	0.983305i	$-0.558246\pi$
$743$	−9.92011	−0.363934	−0.181967	+	0.983305i	$0.558246\pi$
$744$	44.9410	1.64762
$745$	23.9653	0.878019
$746$	18.6416	0.682516
$747$	−22.0587	−0.807085
$748$	−15.9047	−0.581534
$749$	26.2556	0.959357
$750$	18.6767	0.681975
$751$	−25.8179	−0.942109	−0.471055	−	0.882104i	$-0.656127\pi$
$751$	−25.8179	−0.942109	−0.471055	+	0.882104i	$0.656127\pi$
$752$	−16.7149	−0.609531
$753$	−56.8303	−2.07101
$754$	−0.0276005	−0.00100515
$755$	−5.67360	−0.206484
$756$	7.22267	0.262686
$757$	21.1952	0.770352	0.385176	−	0.922843i	$-0.374141\pi$
$757$	21.1952	0.770352	0.385176	+	0.922843i	$0.374141\pi$
$758$	14.6600	0.532476
$759$	56.9813	2.06829
$760$	−18.0094	−0.653269
$761$	−13.5930	−0.492745	−0.246372	−	0.969175i	$-0.579239\pi$
$761$	−13.5930	−0.492745	−0.246372	+	0.969175i	$0.579239\pi$
$762$	−9.65253	−0.349674
$763$	−7.66613	−0.277533
$764$	6.58003	0.238057
$765$	13.7375	0.496681
$766$	−12.0847	−0.436638
$767$	0.00864678	0.000312217 0
$768$	−22.7093	−0.819450
$769$	−23.2843	−0.839652	−0.419826	−	0.907605i	$-0.637909\pi$
$769$	−23.2843	−0.839652	−0.419826	+	0.907605i	$0.637909\pi$
$770$	−9.89825	−0.356708
$771$	11.9520	0.430440
$772$	14.9837	0.539276
$773$	37.4363	1.34649	0.673245	−	0.739420i	$-0.264900\pi$
$773$	37.4363	1.34649	0.673245	+	0.739420i	$0.264900\pi$
$774$	3.41512	0.122754
$775$	−21.2749	−0.764219
$776$	−37.1783	−1.33462
$777$	69.3974	2.48962
$778$	−6.94512	−0.248995
$779$	−5.00281	−0.179244
$780$	0.0358637	0.00128413
$781$	13.9360	0.498670
$782$	−22.6483	−0.809901
$783$	8.47296	0.302799
$784$	6.34552	0.226626
$785$	−0.837495	−0.0298915
$786$	−16.1840	−0.577263
$787$	10.1629	0.362267	0.181134	−	0.983459i	$-0.442023\pi$
$787$	10.1629	0.362267	0.181134	+	0.983459i	$0.442023\pi$
$788$	15.2624	0.543701
$789$	48.8839	1.74031
$790$	5.35509	0.190526
$791$	−8.71885	−0.310007
$792$	16.1609	0.574252
$793$	−0.0151126	−0.000536666 0
$794$	−6.52817	−0.231676
$795$	−19.8565	−0.704238
$796$	−17.6213	−0.624569
$797$	2.70469	0.0958050	0.0479025	−	0.998852i	$-0.484746\pi$
$797$	2.70469	0.0958050	0.0479025	+	0.998852i	$0.484746\pi$
$798$	26.3591	0.933104
$799$	−44.7503	−1.58315
$800$	15.4546	0.546402
$801$	−25.7239	−0.908909
$802$	−13.4942	−0.476498
$803$	43.4777	1.53429
$804$	10.4403	0.368203
$805$	45.8050	1.61441
$806$	0.0361662	0.00127390
$807$	−75.7312	−2.66587
$808$	−33.5025	−1.17861
$809$	31.2004	1.09695	0.548473	−	0.836168i	$-0.315209\pi$
$809$	31.2004	1.09695	0.548473	+	0.836168i	$0.315209\pi$
$810$	10.9430	0.384497
$811$	14.8703	0.522168	0.261084	−	0.965316i	$-0.415920\pi$
$811$	14.8703	0.522168	0.261084	+	0.965316i	$0.415920\pi$
$812$	31.6639	1.11119
$813$	−33.4838	−1.17433
$814$	−16.7569	−0.587331
$815$	0.233091	0.00816483
$816$	12.1571	0.425583
$817$	10.0868	0.352892
$818$	12.4585	0.435600
$819$	−0.0538609	−0.00188205
$820$	−2.40293	−0.0839140
$821$	18.3961	0.642028	0.321014	−	0.947074i	$-0.395976\pi$
$821$	18.3961	0.642028	0.321014	+	0.947074i	$0.395976\pi$
$822$	−27.9511	−0.974906
$823$	28.6587	0.998978	0.499489	−	0.866320i	$-0.333521\pi$
$823$	28.6587	0.998978	0.499489	+	0.866320i	$0.333521\pi$
$824$	30.4079	1.05931
$825$	−17.2063	−0.599046
$826$	3.05252	0.106211
$827$	−33.5589	−1.16696	−0.583479	−	0.812128i	$-0.698309\pi$
$827$	−33.5589	−1.16696	−0.583479	+	0.812128i	$0.698309\pi$
$828$	−32.4068	−1.12621
$829$	3.27463	0.113733	0.0568664	−	0.998382i	$-0.481889\pi$
$829$	3.27463	0.113733	0.0568664	+	0.998382i	$0.481889\pi$
$830$	9.62960	0.334248
$831$	2.62377	0.0910174
$832$	−0.00781783	−0.000271034 0
$833$	16.9886	0.588621
$834$	6.01957	0.208441
$835$	14.6518	0.507045
$836$	20.6837	0.715360
$837$	−11.1025	−0.383760
$838$	12.8422	0.443627
$839$	−45.1159	−1.55757	−0.778786	−	0.627289i	$-0.784164\pi$
$839$	−45.1159	−1.55757	−0.778786	+	0.627289i	$0.784164\pi$
$840$	29.2174	1.00810
$841$	8.14513	0.280867
$842$	11.7877	0.406230
$843$	−9.80331	−0.337644
$844$	−4.59925	−0.158313
$845$	−19.8692	−0.683521
$846$	19.7039	0.677433
$847$	−11.1329	−0.382531
$848$	−7.81316	−0.268305
$849$	−47.4332	−1.62790
$850$	6.83896	0.234575
$851$	77.5442	2.65818
$852$	−17.8254	−0.610689
$853$	−37.1146	−1.27078	−0.635390	−	0.772192i	$-0.719161\pi$
$853$	−37.1146	−1.27078	−0.635390	+	0.772192i	$0.719161\pi$
$854$	−5.33512	−0.182564
$855$	−17.8653	−0.610980
$856$	18.7136	0.639616
$857$	58.1666	1.98693	0.993467	−	0.114118i	$-0.0364041\pi$
$857$	58.1666	1.98693	0.993467	+	0.114118i	$0.0364041\pi$
$858$	0.0292498	0.000998570 0
$859$	32.2598	1.10069	0.550345	−	0.834938i	$-0.314496\pi$
$859$	32.2598	1.10069	0.550345	+	0.834938i	$0.314496\pi$
$860$	4.84485	0.165208
$861$	8.11628	0.276602
$862$	6.03236	0.205463
$863$	1.00307	0.0341448	0.0170724	−	0.999854i	$-0.494565\pi$
$863$	1.00307	0.0341448	0.0170724	+	0.999854i	$0.494565\pi$
$864$	8.06513	0.274381
$865$	30.0010	1.02007
$866$	−6.39605	−0.217347
$867$	−6.96346	−0.236492
$868$	−41.4908	−1.40829
$869$	−14.1932	−0.481470
$870$	14.8524	0.503543
$871$	0.0193891	0.000656976 0
$872$	−5.46401	−0.185035
$873$	−36.8809	−1.24823
$874$	29.4535	0.996280
$875$	−39.7916	−1.34520
$876$	−55.6118	−1.87895
$877$	−1.24540	−0.0420542	−0.0210271	−	0.999779i	$-0.506694\pi$
$877$	−1.24540	−0.0420542	−0.0210271	+	0.999779i	$0.506694\pi$
$878$	−24.4467	−0.825037
$879$	74.6312	2.51725
$880$	5.93688	0.200132
$881$	−17.1772	−0.578716	−0.289358	−	0.957221i	$-0.593442\pi$
$881$	−17.1772	−0.578716	−0.289358	+	0.957221i	$0.593442\pi$
$882$	−7.48022	−0.251872
$883$	24.9222	0.838700	0.419350	−	0.907825i	$-0.362258\pi$
$883$	24.9222	0.838700	0.419350	+	0.907825i	$0.362258\pi$
$884$	0.0377807	0.00127070
$885$	−4.65301	−0.156409
$886$	5.74092	0.192870
$887$	20.6512	0.693399	0.346699	−	0.937976i	$-0.387302\pi$
$887$	20.6512	0.693399	0.346699	+	0.937976i	$0.387302\pi$
$888$	49.4628	1.65986
$889$	20.5652	0.689735
$890$	11.2296	0.376418
$891$	−29.0033	−0.971648
$892$	−15.5052	−0.519153
$893$	58.1966	1.94747
$894$	−25.0006	−0.836144
$895$	16.0867	0.537720
$896$	36.6546	1.22454
$897$	−0.135356	−0.00451940
$898$	4.32304	0.144262
$899$	−48.6731	−1.62334
$900$	9.78568	0.326189
$901$	−20.9179	−0.696876
$902$	−1.95979	−0.0652537
$903$	−16.3642	−0.544568
$904$	−6.21433	−0.206685
$905$	7.87064	0.261629
$906$	5.91871	0.196636
$907$	−27.6506	−0.918122	−0.459061	−	0.888405i	$-0.651814\pi$
$907$	−27.6506	−0.918122	−0.459061	+	0.888405i	$0.651814\pi$
$908$	13.3531	0.443140
$909$	−33.2344	−1.10232
$910$	0.0235127	0.000779438 0
$911$	36.8550	1.22106	0.610530	−	0.791993i	$-0.290956\pi$
$911$	36.8550	1.22106	0.610530	+	0.791993i	$0.290956\pi$
$912$	−15.8100	−0.523520
$913$	−25.5223	−0.844666
$914$	−11.6845	−0.386490
$915$	8.13243	0.268850
$916$	−7.46521	−0.246657
$917$	34.4808	1.13866
$918$	3.56898	0.117794
$919$	−14.0143	−0.462289	−0.231144	−	0.972919i	$-0.574247\pi$
$919$	−14.0143	−0.462289	−0.231144	+	0.972919i	$0.574247\pi$
$920$	32.6473	1.07635
$921$	0.764749	0.0251994
$922$	−16.8683	−0.555526
$923$	−0.0331042	−0.00108964
$924$	−33.5561	−1.10391
$925$	−23.4155	−0.769898
$926$	−13.3534	−0.438821
$927$	30.1646	0.990737
$928$	35.3572	1.16066
$929$	−23.5623	−0.773054	−0.386527	−	0.922278i	$-0.626325\pi$
$929$	−23.5623	−0.773054	−0.386527	+	0.922278i	$0.626325\pi$
$930$	−19.4618	−0.638178
$931$	−22.0933	−0.724078
$932$	10.0438	0.328996
$933$	−20.6925	−0.677441
$934$	−1.81279	−0.0593162
$935$	15.8946	0.519809
$936$	−0.0383892	−0.00125479
$937$	42.3693	1.38415	0.692073	−	0.721828i	$-0.256698\pi$
$937$	42.3693	1.38415	0.692073	+	0.721828i	$0.256698\pi$
$938$	6.84482	0.223491
$939$	−39.9489	−1.30368
$940$	27.9528	0.911719
$941$	44.4840	1.45014	0.725068	−	0.688677i	$-0.241808\pi$
$941$	44.4840	1.45014	0.725068	+	0.688677i	$0.241808\pi$
$942$	0.873675	0.0284659
$943$	9.06907	0.295330
$944$	−1.83087	−0.0595898
$945$	−7.21807	−0.234804
$946$	3.95137	0.128470
$947$	43.8449	1.42477	0.712383	−	0.701791i	$-0.247616\pi$
$947$	43.8449	1.42477	0.712383	+	0.701791i	$0.247616\pi$
$948$	18.1543	0.589624
$949$	−0.103279	−0.00335257
$950$	−8.89390	−0.288556
$951$	−18.2266	−0.591038
$952$	30.7792	0.997559
$953$	0.394860	0.0127908	0.00639539	−	0.999980i	$-0.497964\pi$
$953$	0.394860	0.0127908	0.00639539	+	0.999980i	$0.497964\pi$
$954$	9.21030	0.298194
$955$	−6.57584	−0.212789
$956$	−22.0504	−0.713162
$957$	−39.3648	−1.27248
$958$	23.2943	0.752604
$959$	59.5513	1.92301
$960$	4.20694	0.135778
$961$	32.7788	1.05738
$962$	0.0398051	0.00128337
$963$	18.5638	0.598212
$964$	−10.0051	−0.322244
$965$	−14.9742	−0.482035
$966$	−47.7838	−1.53742
$967$	8.94165	0.287544	0.143772	−	0.989611i	$-0.454077\pi$
$967$	8.94165	0.287544	0.143772	+	0.989611i	$0.454077\pi$
$968$	−7.93494	−0.255039
$969$	−42.3275	−1.35975
$970$	16.1001	0.516945
$971$	−25.5519	−0.820001	−0.410000	−	0.912085i	$-0.634471\pi$
$971$	−25.5519	−0.820001	−0.410000	+	0.912085i	$0.634471\pi$
$972$	30.7193	0.985322
$973$	−12.8250	−0.411151
$974$	1.37123	0.0439371
$975$	0.0408725	0.00130897
$976$	3.19995	0.102428
$977$	2.65021	0.0847877	0.0423938	−	0.999101i	$-0.486502\pi$
$977$	2.65021	0.0847877	0.0423938	+	0.999101i	$0.486502\pi$
$978$	−0.243161	−0.00777543
$979$	−29.7631	−0.951231
$980$	−10.6118	−0.338980
$981$	−5.42030	−0.173057
$982$	10.5749	0.337458
$983$	35.8439	1.14324	0.571621	−	0.820518i	$-0.306315\pi$
$983$	35.8439	1.14324	0.571621	+	0.820518i	$0.306315\pi$
$984$	5.78485	0.184414
$985$	−15.2527	−0.485992
$986$	15.6463	0.498279
$987$	−94.4149	−3.00526
$988$	−0.0491328	−0.00156312
$989$	−18.2853	−0.581438
$990$	−6.99850	−0.222427
$991$	−30.0132	−0.953402	−0.476701	−	0.879065i	$-0.658168\pi$
$991$	−30.0132	−0.953402	−0.476701	+	0.879065i	$0.658168\pi$
$992$	−46.3303	−1.47099
$993$	12.9926	0.412307
$994$	−11.6866	−0.370675
$995$	17.6100	0.558275
$996$	32.6453	1.03441
$997$	37.7431	1.19534	0.597668	−	0.801744i	$-0.296094\pi$
$997$	37.7431	1.19534	0.597668	+	0.801744i	$0.296094\pi$
$998$	10.8818	0.344457
$999$	−12.2196	−0.386612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.46	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.46	✓	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)

\(f(q)\)	\(=\)	\(q-0.686018 q^{2} +2.32419 q^{3} -1.52938 q^{4} +1.52841 q^{5} -1.59443 q^{6} +3.39702 q^{7} +2.42122 q^{8} +2.40185 q^{9} +O(q^{10})\)	\(q-0.686018 q^{2} +2.32419 q^{3} -1.52938 q^{4} +1.52841 q^{5} -1.59443 q^{6} +3.39702 q^{7} +2.42122 q^{8} +2.40185 q^{9} -1.04851 q^{10} +2.77898 q^{11} -3.55457 q^{12} -0.00660131 q^{13} -2.33042 q^{14} +3.55230 q^{15} +1.39776 q^{16} +3.74218 q^{17} -1.64771 q^{18} -4.86661 q^{19} -2.33751 q^{20} +7.89532 q^{21} -1.90643 q^{22} +8.82217 q^{23} +5.62736 q^{24} -2.66398 q^{25} +0.00452861 q^{26} -1.39022 q^{27} -5.19534 q^{28} -6.09468 q^{29} -2.43694 q^{30} +7.98616 q^{31} -5.80132 q^{32} +6.45888 q^{33} -2.56720 q^{34} +5.19203 q^{35} -3.67333 q^{36} +8.78969 q^{37} +3.33858 q^{38} -0.0153427 q^{39} +3.70060 q^{40} +1.02799 q^{41} -5.41633 q^{42} -2.07265 q^{43} -4.25012 q^{44} +3.67099 q^{45} -6.05217 q^{46} -11.9583 q^{47} +3.24866 q^{48} +4.53977 q^{49} +1.82753 q^{50} +8.69753 q^{51} +0.0100959 q^{52} -5.58976 q^{53} +0.953717 q^{54} +4.24741 q^{55} +8.22493 q^{56} -11.3109 q^{57} +4.18106 q^{58} -1.30986 q^{59} -5.43282 q^{60} +2.28934 q^{61} -5.47865 q^{62} +8.15913 q^{63} +1.18428 q^{64} -0.0100895 q^{65} -4.43090 q^{66} -2.93717 q^{67} -5.72322 q^{68} +20.5044 q^{69} -3.56182 q^{70} +5.01480 q^{71} +5.81539 q^{72} +15.6452 q^{73} -6.02988 q^{74} -6.19158 q^{75} +7.44289 q^{76} +9.44027 q^{77} +0.0105253 q^{78} -5.10732 q^{79} +2.13635 q^{80} -10.4367 q^{81} -0.705217 q^{82} -9.18405 q^{83} -12.0749 q^{84} +5.71957 q^{85} +1.42187 q^{86} -14.1652 q^{87} +6.72852 q^{88} -10.7101 q^{89} -2.51837 q^{90} -0.0224248 q^{91} -13.4925 q^{92} +18.5613 q^{93} +8.20363 q^{94} -7.43815 q^{95} -13.4834 q^{96} -15.3552 q^{97} -3.11436 q^{98} +6.67469 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 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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