LMFDB - Embedded newform 2738.2.a.q.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, 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("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.37902897.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 15x^{4} - x^{3} + 60x^{2} - 64 $ x^6 - 15x^4 - x^3 + 60x^2 - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.90773$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.90773 q^{3} +1.00000 q^{4} -0.347296 q^{5} -2.90773 q^{6} +1.00984 q^{7} -1.00000 q^{8} +5.45490 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.90773 q^{3} +1.00000 q^{4} -0.347296 q^{5} -2.90773 q^{6} +1.00984 q^{7} -1.00000 q^{8} +5.45490 q^{9} +0.347296 q^{10} -5.46475 q^{11} +2.90773 q^{12} -6.36263 q^{13} -1.00984 q^{14} -1.00984 q^{15} +1.00000 q^{16} -0.522244 q^{17} -5.45490 q^{18} -5.00984 q^{19} -0.347296 q^{20} +2.93636 q^{21} +5.46475 q^{22} -1.44298 q^{23} -2.90773 q^{24} -4.87939 q^{25} +6.36263 q^{26} +7.13820 q^{27} +1.00984 q^{28} +6.33429 q^{29} +1.00984 q^{30} -3.30777 q^{31} -1.00000 q^{32} -15.8900 q^{33} +0.522244 q^{34} -0.350715 q^{35} +5.45490 q^{36} +5.00984 q^{38} -18.5008 q^{39} +0.347296 q^{40} -1.10049 q^{41} -2.93636 q^{42} +6.27037 q^{43} -5.46475 q^{44} -1.89447 q^{45} +1.44298 q^{46} -11.4382 q^{47} +2.90773 q^{48} -5.98021 q^{49} +4.87939 q^{50} -1.51855 q^{51} -6.36263 q^{52} +0.0922684 q^{53} -7.13820 q^{54} +1.89789 q^{55} -1.00984 q^{56} -14.5673 q^{57} -6.33429 q^{58} -2.99016 q^{59} -1.00984 q^{60} -3.81583 q^{61} +3.30777 q^{62} +5.50860 q^{63} +1.00000 q^{64} +2.20972 q^{65} +15.8900 q^{66} -1.16475 q^{67} -0.522244 q^{68} -4.19581 q^{69} +0.350715 q^{70} +0.312892 q^{71} -5.45490 q^{72} +13.2325 q^{73} -14.1879 q^{75} -5.00984 q^{76} -5.51855 q^{77} +18.5008 q^{78} -9.30676 q^{79} -0.347296 q^{80} +4.39126 q^{81} +1.10049 q^{82} +9.46475 q^{83} +2.93636 q^{84} +0.181374 q^{85} -6.27037 q^{86} +18.4184 q^{87} +5.46475 q^{88} +15.7678 q^{89} +1.89447 q^{90} -6.42527 q^{91} -1.44298 q^{92} -9.61810 q^{93} +11.4382 q^{94} +1.73990 q^{95} -2.90773 q^{96} +0.929128 q^{97} +5.98021 q^{98} -29.8097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 3 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^7 - 6 * q^8 + 12 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} - 3 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{11} + 3 q^{14} + 3 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 21 q^{19} + 6 q^{21} + 3 q^{22} - 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28} + 6 q^{29} - 3 q^{30} - 21 q^{31} - 6 q^{32} - 3 q^{33} + 3 q^{34} + 3 q^{35} + 12 q^{36} + 21 q^{38} - 27 q^{39} + 18 q^{41} - 6 q^{42} - 18 q^{43} - 3 q^{44} - 6 q^{45} + 21 q^{46} - 9 q^{47} + 15 q^{49} + 18 q^{50} + 18 q^{53} + 3 q^{54} + 3 q^{55} + 3 q^{56} - 6 q^{57} - 6 q^{58} - 27 q^{59} + 3 q^{60} + 24 q^{61} + 21 q^{62} - 36 q^{63} + 6 q^{64} + 3 q^{65} + 3 q^{66} + 9 q^{67} - 3 q^{68} - 27 q^{69} - 3 q^{70} - 12 q^{72} + 27 q^{73} - 3 q^{75} - 21 q^{76} - 24 q^{77} + 27 q^{78} - 21 q^{79} - 6 q^{81} - 18 q^{82} + 27 q^{83} + 6 q^{84} - 3 q^{85} + 18 q^{86} + 3 q^{88} + 21 q^{89} + 6 q^{90} + 24 q^{91} - 21 q^{92} - 54 q^{93} + 9 q^{94} - 3 q^{95} - 42 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^11 + 3 * q^14 + 3 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 21 * q^19 + 6 * q^21 + 3 * q^22 - 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 + 6 * q^29 - 3 * q^30 - 21 * q^31 - 6 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^35 + 12 * q^36 + 21 * q^38 - 27 * q^39 + 18 * q^41 - 6 * q^42 - 18 * q^43 - 3 * q^44 - 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 + 18 * q^50 + 18 * q^53 + 3 * q^54 + 3 * q^55 + 3 * q^56 - 6 * q^57 - 6 * q^58 - 27 * q^59 + 3 * q^60 + 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 + 3 * q^66 + 9 * q^67 - 3 * q^68 - 27 * q^69 - 3 * q^70 - 12 * q^72 + 27 * q^73 - 3 * q^75 - 21 * q^76 - 24 * q^77 + 27 * q^78 - 21 * q^79 - 6 * q^81 - 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 + 3 * q^88 + 21 * q^89 + 6 * q^90 + 24 * q^91 - 21 * q^92 - 54 * q^93 + 9 * q^94 - 3 * q^95 - 42 * q^97 - 15 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.90773	1.67878	0.839390	−	0.543530i	$-0.182913\pi$
$3$	2.90773	1.67878	0.839390	+	0.543530i	$0.182913\pi$
$4$	1.00000	0.500000
$5$	−0.347296	−0.155316	−0.0776578	−	0.996980i	$-0.524744\pi$
$5$	−0.347296	−0.155316	−0.0776578	+	0.996980i	$0.524744\pi$
$6$	−2.90773	−1.18708
$7$	1.00984	0.381685	0.190843	−	0.981621i	$-0.438878\pi$
$7$	1.00984	0.381685	0.190843	+	0.981621i	$0.438878\pi$
$8$	−1.00000	−0.353553
$9$	5.45490	1.81830
$10$	0.347296	0.109825
$11$	−5.46475	−1.64768	−0.823842	−	0.566820i	$-0.808174\pi$
$11$	−5.46475	−1.64768	−0.823842	+	0.566820i	$0.808174\pi$
$12$	2.90773	0.839390
$13$	−6.36263	−1.76468	−0.882339	−	0.470615i	$-0.844032\pi$
$13$	−6.36263	−1.76468	−0.882339	+	0.470615i	$0.844032\pi$
$14$	−1.00984	−0.269892
$15$	−1.00984	−0.260741
$16$	1.00000	0.250000
$17$	−0.522244	−0.126663	−0.0633314	−	0.997993i	$-0.520173\pi$
$17$	−0.522244	−0.126663	−0.0633314	+	0.997993i	$0.520173\pi$
$18$	−5.45490	−1.28573
$19$	−5.00984	−1.14934	−0.574669	−	0.818386i	$-0.694869\pi$
$19$	−5.00984	−1.14934	−0.574669	+	0.818386i	$0.694869\pi$
$20$	−0.347296	−0.0776578
$21$	2.93636	0.640766
$22$	5.46475	1.16509
$23$	−1.44298	−0.300883	−0.150441	−	0.988619i	$-0.548070\pi$
$23$	−1.44298	−0.300883	−0.150441	+	0.988619i	$0.548070\pi$
$24$	−2.90773	−0.593538
$25$	−4.87939	−0.975877
$26$	6.36263	1.24782
$27$	7.13820	1.37375
$28$	1.00984	0.190843
$29$	6.33429	1.17625	0.588124	−	0.808771i	$-0.299867\pi$
$29$	6.33429	1.17625	0.588124	+	0.808771i	$0.299867\pi$
$30$	1.00984	0.184372
$31$	−3.30777	−0.594092	−0.297046	−	0.954863i	$-0.596002\pi$
$31$	−3.30777	−0.594092	−0.297046	+	0.954863i	$0.596002\pi$
$32$	−1.00000	−0.176777
$33$	−15.8900	−2.76610
$34$	0.522244	0.0895642
$35$	−0.350715	−0.0592817
$36$	5.45490	0.909151
$37$	0	0
$37$	0	0
$38$	5.00984	0.812704
$39$	−18.5008	−2.96250
$40$	0.347296	0.0549124
$41$	−1.10049	−0.171868	−0.0859338	−	0.996301i	$-0.527387\pi$
$41$	−1.10049	−0.171868	−0.0859338	+	0.996301i	$0.527387\pi$
$42$	−2.93636	−0.453090
$43$	6.27037	0.956222	0.478111	−	0.878299i	$-0.341322\pi$
$43$	6.27037	0.956222	0.478111	+	0.878299i	$0.341322\pi$
$44$	−5.46475	−0.823842
$45$	−1.89447	−0.282411
$46$	1.44298	0.212756
$47$	−11.4382	−1.66843	−0.834216	−	0.551437i	$-0.814080\pi$
$47$	−11.4382	−1.66843	−0.834216	+	0.551437i	$0.814080\pi$
$48$	2.90773	0.419695
$49$	−5.98021	−0.854316
$50$	4.87939	0.690049
$51$	−1.51855	−0.212639
$52$	−6.36263	−0.882339
$53$	0.0922684	0.0126740	0.00633702	−	0.999980i	$-0.497983\pi$
$53$	0.0922684	0.0126740	0.00633702	+	0.999980i	$0.497983\pi$
$54$	−7.13820	−0.971386
$55$	1.89789	0.255911
$56$	−1.00984	−0.134946
$57$	−14.5673	−1.92948
$58$	−6.33429	−0.831733
$59$	−2.99016	−0.389285	−0.194643	−	0.980874i	$-0.562355\pi$
$59$	−2.99016	−0.389285	−0.194643	+	0.980874i	$0.562355\pi$
$60$	−1.00984	−0.130370
$61$	−3.81583	−0.488567	−0.244284	−	0.969704i	$-0.578553\pi$
$61$	−3.81583	−0.488567	−0.244284	+	0.969704i	$0.578553\pi$
$62$	3.30777	0.420087
$63$	5.50860	0.694019
$64$	1.00000	0.125000
$65$	2.20972	0.274082
$66$	15.8900	1.95593
$67$	−1.16475	−0.142297	−0.0711485	−	0.997466i	$-0.522666\pi$
$67$	−1.16475	−0.142297	−0.0711485	+	0.997466i	$0.522666\pi$
$68$	−0.522244	−0.0633314
$69$	−4.19581	−0.505116
$70$	0.350715	0.0419185
$71$	0.312892	0.0371335	0.0185667	−	0.999828i	$-0.494090\pi$
$71$	0.312892	0.0371335	0.0185667	+	0.999828i	$0.494090\pi$
$72$	−5.45490	−0.642867
$73$	13.2325	1.54875	0.774376	−	0.632726i	$-0.218064\pi$
$73$	13.2325	1.54875	0.774376	+	0.632726i	$0.218064\pi$
$74$	0	0
$75$	−14.1879	−1.63828
$76$	−5.00984	−0.574669
$77$	−5.51855	−0.628897
$78$	18.5008	2.09481
$79$	−9.30676	−1.04709	−0.523546	−	0.851997i	$-0.675391\pi$
$79$	−9.30676	−1.04709	−0.523546	+	0.851997i	$0.675391\pi$
$80$	−0.347296	−0.0388289
$81$	4.39126	0.487918
$82$	1.10049	0.121529
$83$	9.46475	1.03889	0.519446	−	0.854504i	$-0.326139\pi$
$83$	9.46475	1.03889	0.519446	+	0.854504i	$0.326139\pi$
$84$	2.93636	0.320383
$85$	0.181374	0.0196727
$86$	−6.27037	−0.676151
$87$	18.4184	1.97466
$88$	5.46475	0.582544
$89$	15.7678	1.67138	0.835692	−	0.549198i	$-0.185067\pi$
$89$	15.7678	1.67138	0.835692	+	0.549198i	$0.185067\pi$
$90$	1.89447	0.199694
$91$	−6.42527	−0.673552
$92$	−1.44298	−0.150441
$93$	−9.61810	−0.997350
$94$	11.4382	1.17976
$95$	1.73990	0.178510
$96$	−2.90773	−0.296769
$97$	0.929128	0.0943387	0.0471693	−	0.998887i	$-0.484980\pi$
$97$	0.929128	0.0943387	0.0471693	+	0.998887i	$0.484980\pi$
$98$	5.98021	0.604093
$99$	−29.8097	−2.99598
$100$	−4.87939	−0.487939
$101$	8.56186	0.851937	0.425969	−	0.904738i	$-0.359933\pi$
$101$	8.56186	0.851937	0.425969	+	0.904738i	$0.359933\pi$
$102$	1.51855	0.150358
$103$	−4.95913	−0.488637	−0.244319	−	0.969695i	$-0.578564\pi$
$103$	−4.95913	−0.488637	−0.244319	+	0.969695i	$0.578564\pi$
$104$	6.36263	0.623908
$105$	−1.01979	−0.0995209
$106$	−0.0922684	−0.00896189
$107$	−3.56826	−0.344957	−0.172478	−	0.985013i	$-0.555177\pi$
$107$	−3.56826	−0.344957	−0.172478	+	0.985013i	$0.555177\pi$
$108$	7.13820	0.686874
$109$	0.978688	0.0937413	0.0468706	−	0.998901i	$-0.485075\pi$
$109$	0.978688	0.0937413	0.0468706	+	0.998901i	$0.485075\pi$
$110$	−1.89789	−0.180956
$111$	0	0
$112$	1.00984	0.0954213
$113$	−9.23702	−0.868946	−0.434473	−	0.900685i	$-0.643065\pi$
$113$	−9.23702	−0.868946	−0.434473	+	0.900685i	$0.643065\pi$
$114$	14.5673	1.36435
$115$	0.501143	0.0467318
$116$	6.33429	0.588124
$117$	−34.7076	−3.20871
$118$	2.99016	0.275266
$119$	−0.527386	−0.0483454
$120$	1.00984	0.0921858
$121$	18.8635	1.71486
$122$	3.81583	0.345469
$123$	−3.19993	−0.288528
$124$	−3.30777	−0.297046
$125$	3.43107	0.306885
$126$	−5.50860	−0.490746
$127$	6.77151	0.600874	0.300437	−	0.953802i	$-0.402867\pi$
$127$	6.77151	0.600874	0.300437	+	0.953802i	$0.402867\pi$
$128$	−1.00000	−0.0883883
$129$	18.2325	1.60529
$130$	−2.20972	−0.193805
$131$	15.1485	1.32353	0.661764	−	0.749712i	$-0.269808\pi$
$131$	15.1485	1.32353	0.661764	+	0.749712i	$0.269808\pi$
$132$	−15.8900	−1.38305
$133$	−5.05916	−0.438685
$134$	1.16475	0.100619
$135$	−2.47907	−0.213364
$136$	0.522244	0.0447821
$137$	−8.48173	−0.724643	−0.362321	−	0.932053i	$-0.618016\pi$
$137$	−8.48173	−0.724643	−0.362321	+	0.932053i	$0.618016\pi$
$138$	4.19581	0.357171
$139$	−18.3384	−1.55544	−0.777720	−	0.628611i	$-0.783624\pi$
$139$	−18.3384	−1.55544	−0.777720	+	0.628611i	$0.783624\pi$
$140$	−0.350715	−0.0296409
$141$	−33.2592	−2.80093
$142$	−0.312892	−0.0262573
$143$	34.7702	2.90763
$144$	5.45490	0.454575
$145$	−2.19988	−0.182690
$146$	−13.2325	−1.09513
$147$	−17.3889	−1.43421
$148$	0	0
$149$	5.45291	0.446720	0.223360	−	0.974736i	$-0.428297\pi$
$149$	5.45291	0.446720	0.223360	+	0.974736i	$0.428297\pi$
$150$	14.1879	1.15844
$151$	−15.5554	−1.26588	−0.632939	−	0.774202i	$-0.718152\pi$
$151$	−15.5554	−1.26588	−0.632939	+	0.774202i	$0.718152\pi$
$152$	5.00984	0.406352
$153$	−2.84879	−0.230311
$154$	5.51855	0.444697
$155$	1.14878	0.0922719
$156$	−18.5008	−1.48125
$157$	−4.00822	−0.319891	−0.159945	−	0.987126i	$-0.551132\pi$
$157$	−4.00822	−0.319891	−0.159945	+	0.987126i	$0.551132\pi$
$158$	9.30676	0.740406
$159$	0.268292	0.0212769
$160$	0.347296	0.0274562
$161$	−1.45719	−0.114843
$162$	−4.39126	−0.345010
$163$	−4.69223	−0.367524	−0.183762	−	0.982971i	$-0.558828\pi$
$163$	−4.69223	−0.367524	−0.183762	+	0.982971i	$0.558828\pi$
$164$	−1.10049	−0.0859338
$165$	5.51855	0.429618
$166$	−9.46475	−0.734607
$167$	0.776993	0.0601255	0.0300628	−	0.999548i	$-0.490429\pi$
$167$	0.776993	0.0601255	0.0300628	+	0.999548i	$0.490429\pi$
$168$	−2.93636	−0.226545
$169$	27.4831	2.11409
$170$	−0.181374	−0.0139107
$171$	−27.3282	−2.08984
$172$	6.27037	0.478111
$173$	10.7333	0.816041	0.408021	−	0.912973i	$-0.366219\pi$
$173$	10.7333	0.816041	0.408021	+	0.912973i	$0.366219\pi$
$174$	−18.4184	−1.39630
$175$	−4.92742	−0.372478
$176$	−5.46475	−0.411921
$177$	−8.69457	−0.653524
$178$	−15.7678	−1.18185
$179$	11.8976	0.889267	0.444633	−	0.895713i	$-0.353334\pi$
$179$	11.8976	0.889267	0.444633	+	0.895713i	$0.353334\pi$
$180$	−1.89447	−0.141205
$181$	4.38667	0.326059	0.163029	−	0.986621i	$-0.447873\pi$
$181$	4.38667	0.326059	0.163029	+	0.986621i	$0.447873\pi$
$182$	6.42527	0.476273
$183$	−11.0954	−0.820197
$184$	1.44298	0.106378
$185$	0	0
$186$	9.61810	0.705233
$187$	2.85393	0.208700
$188$	−11.4382	−0.834216
$189$	7.20847	0.524339
$190$	−1.73990	−0.126226
$191$	10.4903	0.759053	0.379527	−	0.925181i	$-0.376087\pi$
$191$	10.4903	0.759053	0.379527	+	0.925181i	$0.376087\pi$
$192$	2.90773	0.209847
$193$	−9.82949	−0.707542	−0.353771	−	0.935332i	$-0.615101\pi$
$193$	−9.82949	−0.707542	−0.353771	+	0.935332i	$0.615101\pi$
$194$	−0.929128	−0.0667075
$195$	6.42527	0.460123
$196$	−5.98021	−0.427158
$197$	−12.0631	−0.859460	−0.429730	−	0.902958i	$-0.641391\pi$
$197$	−12.0631	−0.859460	−0.429730	+	0.902958i	$0.641391\pi$
$198$	29.8097	2.11848
$199$	9.29990	0.659252	0.329626	−	0.944112i	$-0.393077\pi$
$199$	9.29990	0.659252	0.329626	+	0.944112i	$0.393077\pi$
$200$	4.87939	0.345025
$201$	−3.38678	−0.238885
$202$	−8.56186	−0.602411
$203$	6.39665	0.448957
$204$	−1.51855	−0.106320
$205$	0.382196	0.0266937
$206$	4.95913	0.345519
$207$	−7.87134	−0.547096
$208$	−6.36263	−0.441169
$209$	27.3775	1.89374
$210$	1.01979	0.0703719
$211$	−4.40004	−0.302911	−0.151455	−	0.988464i	$-0.548396\pi$
$211$	−4.40004	−0.302911	−0.151455	+	0.988464i	$0.548396\pi$
$212$	0.0922684	0.00633702
$213$	0.909807	0.0623389
$214$	3.56826	0.243921
$215$	−2.17768	−0.148516
$216$	−7.13820	−0.485693
$217$	−3.34033	−0.226756
$218$	−0.978688	−0.0662851
$219$	38.4767	2.60001
$220$	1.89789	0.127956
$221$	3.32285	0.223519
$222$	0	0
$223$	11.2311	0.752092	0.376046	−	0.926601i	$-0.377283\pi$
$223$	11.2311	0.752092	0.376046	+	0.926601i	$0.377283\pi$
$224$	−1.00984	−0.0674731
$225$	−26.6166	−1.77444
$226$	9.23702	0.614438
$227$	15.1539	1.00580	0.502901	−	0.864344i	$-0.332266\pi$
$227$	15.1539	1.00580	0.502901	+	0.864344i	$0.332266\pi$
$228$	−14.5673	−0.964742
$229$	−15.5617	−1.02835	−0.514173	−	0.857686i	$-0.671901\pi$
$229$	−15.5617	−1.02835	−0.514173	+	0.857686i	$0.671901\pi$
$230$	−0.501143	−0.0330444
$231$	−16.0465	−1.05578
$232$	−6.33429	−0.415866
$233$	13.5871	0.890122	0.445061	−	0.895500i	$-0.353182\pi$
$233$	13.5871	0.890122	0.445061	+	0.895500i	$0.353182\pi$
$234$	34.7076	2.26890
$235$	3.97244	0.259134
$236$	−2.99016	−0.194643
$237$	−27.0616	−1.75784
$238$	0.527386	0.0341853
$239$	19.4945	1.26099	0.630496	−	0.776192i	$-0.282852\pi$
$239$	19.4945	1.26099	0.630496	+	0.776192i	$0.282852\pi$
$240$	−1.00984	−0.0651852
$241$	−1.44363	−0.0929924	−0.0464962	−	0.998918i	$-0.514806\pi$
$241$	−1.44363	−0.0929924	−0.0464962	+	0.998918i	$0.514806\pi$
$242$	−18.8635	−1.21259
$243$	−8.64599	−0.554641
$244$	−3.81583	−0.244284
$245$	2.07691	0.132689
$246$	3.19993	0.204020
$247$	31.8758	2.02821
$248$	3.30777	0.210043
$249$	27.5209	1.74407
$250$	−3.43107	−0.217000
$251$	−10.0729	−0.635797	−0.317898	−	0.948125i	$-0.602977\pi$
$251$	−10.0729	−0.635797	−0.317898	+	0.948125i	$0.602977\pi$
$252$	5.50860	0.347009
$253$	7.88554	0.495760
$254$	−6.77151	−0.424882
$255$	0.527386	0.0330262
$256$	1.00000	0.0625000
$257$	6.98500	0.435712	0.217856	−	0.975981i	$-0.430094\pi$
$257$	6.98500	0.435712	0.217856	+	0.975981i	$0.430094\pi$
$258$	−18.2325	−1.13511
$259$	0	0
$260$	2.20972	0.137041
$261$	34.5529	2.13877
$262$	−15.1485	−0.935875
$263$	2.66284	0.164198	0.0820990	−	0.996624i	$-0.473838\pi$
$263$	2.66284	0.164198	0.0820990	+	0.996624i	$0.473838\pi$
$264$	15.8900	0.977963
$265$	−0.0320445	−0.00196848
$266$	5.05916	0.310197
$267$	45.8486	2.80589
$268$	−1.16475	−0.0711485
$269$	2.41504	0.147247	0.0736236	−	0.997286i	$-0.476544\pi$
$269$	2.41504	0.147247	0.0736236	+	0.997286i	$0.476544\pi$
$270$	2.47907	0.150871
$271$	−25.2506	−1.53386	−0.766932	−	0.641729i	$-0.778218\pi$
$271$	−25.2506	−1.53386	−0.766932	+	0.641729i	$0.778218\pi$
$272$	−0.522244	−0.0316657
$273$	−18.6830	−1.13074
$274$	8.48173	0.512400
$275$	26.6646	1.60794
$276$	−4.19581	−0.252558
$277$	17.7320	1.06541	0.532706	−	0.846301i	$-0.321175\pi$
$277$	17.7320	1.06541	0.532706	+	0.846301i	$0.321175\pi$
$278$	18.3384	1.09986
$279$	−18.0435	−1.08024
$280$	0.350715	0.0209593
$281$	−19.7493	−1.17815	−0.589073	−	0.808080i	$-0.700507\pi$
$281$	−19.7493	−1.17815	−0.589073	+	0.808080i	$0.700507\pi$
$282$	33.2592	1.98056
$283$	−24.3494	−1.44742	−0.723711	−	0.690103i	$-0.757565\pi$
$283$	−24.3494	−1.44742	−0.723711	+	0.690103i	$0.757565\pi$
$284$	0.312892	0.0185667
$285$	5.05916	0.299679
$286$	−34.7702	−2.05600
$287$	−1.11132	−0.0655994
$288$	−5.45490	−0.321433
$289$	−16.7273	−0.983957
$290$	2.19988	0.129181
$291$	2.70165	0.158374
$292$	13.2325	0.774376
$293$	−23.2486	−1.35820	−0.679098	−	0.734048i	$-0.737629\pi$
$293$	−23.2486	−1.35820	−0.679098	+	0.734048i	$0.737629\pi$
$294$	17.3889	1.01414
$295$	1.03847	0.0604621
$296$	0	0
$297$	−39.0085	−2.26350
$298$	−5.45291	−0.315879
$299$	9.18118	0.530961
$300$	−14.1879	−0.819141
$301$	6.33210	0.364976
$302$	15.5554	0.895111
$303$	24.8956	1.43021
$304$	−5.00984	−0.287334
$305$	1.32522	0.0758821
$306$	2.84879	0.162855
$307$	−10.6702	−0.608978	−0.304489	−	0.952516i	$-0.598486\pi$
$307$	−10.6702	−0.608978	−0.304489	+	0.952516i	$0.598486\pi$
$308$	−5.51855	−0.314448
$309$	−14.4198	−0.820314
$310$	−1.14878	−0.0652461
$311$	−17.0201	−0.965122	−0.482561	−	0.875862i	$-0.660293\pi$
$311$	−17.0201	−0.965122	−0.482561	+	0.875862i	$0.660293\pi$
$312$	18.5008	1.04740
$313$	−10.9104	−0.616694	−0.308347	−	0.951274i	$-0.599776\pi$
$313$	−10.9104	−0.616694	−0.308347	+	0.951274i	$0.599776\pi$
$314$	4.00822	0.226197
$315$	−1.91312	−0.107792
$316$	−9.30676	−0.523546
$317$	−28.8403	−1.61983	−0.809917	−	0.586545i	$-0.800488\pi$
$317$	−28.8403	−1.61983	−0.809917	+	0.586545i	$0.800488\pi$
$318$	−0.268292	−0.0150450
$319$	−34.6153	−1.93808
$320$	−0.347296	−0.0194145
$321$	−10.3755	−0.579106
$322$	1.45719	0.0812060
$323$	2.61636	0.145578
$324$	4.39126	0.243959
$325$	31.0457	1.72211
$326$	4.69223	0.259879
$327$	2.84576	0.157371
$328$	1.10049	0.0607644
$329$	−11.5508	−0.636816
$330$	−5.51855	−0.303786
$331$	−3.95955	−0.217637	−0.108818	−	0.994062i	$-0.534707\pi$
$331$	−3.95955	−0.217637	−0.108818	+	0.994062i	$0.534707\pi$
$332$	9.46475	0.519446
$333$	0	0
$334$	−0.776993	−0.0425152
$335$	0.404514	0.0221009
$336$	2.93636	0.160191
$337$	−4.27678	−0.232971	−0.116485	−	0.993192i	$-0.537163\pi$
$337$	−4.27678	−0.232971	−0.116485	+	0.993192i	$0.537163\pi$
$338$	−27.4831	−1.49488
$339$	−26.8588	−1.45877
$340$	0.181374	0.00983636
$341$	18.0761	0.978876
$342$	27.3282	1.47774
$343$	−13.1080	−0.707765
$344$	−6.27037	−0.338076
$345$	1.45719	0.0784524
$346$	−10.7333	−0.577028
$347$	10.1280	0.543701	0.271850	−	0.962339i	$-0.412364\pi$
$347$	10.1280	0.543701	0.271850	+	0.962339i	$0.412364\pi$
$348$	18.4184	0.987330
$349$	−7.19087	−0.384918	−0.192459	−	0.981305i	$-0.561646\pi$
$349$	−7.19087	−0.384918	−0.192459	+	0.981305i	$0.561646\pi$
$350$	4.92742	0.263382
$351$	−45.4178	−2.42422
$352$	5.46475	0.291272
$353$	34.0550	1.81256	0.906282	−	0.422674i	$-0.138908\pi$
$353$	34.0550	1.81256	0.906282	+	0.422674i	$0.138908\pi$
$354$	8.69457	0.462111
$355$	−0.108666	−0.00576741
$356$	15.7678	0.835692
$357$	−1.53350	−0.0811612
$358$	−11.8976	−0.628807
$359$	9.87953	0.521422	0.260711	−	0.965417i	$-0.416043\pi$
$359$	9.87953	0.521422	0.260711	+	0.965417i	$0.416043\pi$
$360$	1.89447	0.0998472
$361$	6.09854	0.320976
$362$	−4.38667	−0.230559
$363$	54.8499	2.87887
$364$	−6.42527	−0.336776
$365$	−4.59561	−0.240545
$366$	11.0954	0.579967
$367$	−33.9039	−1.76977	−0.884885	−	0.465809i	$-0.845763\pi$
$367$	−33.9039	−1.76977	−0.884885	+	0.465809i	$0.845763\pi$
$368$	−1.44298	−0.0752207
$369$	−6.00307	−0.312507
$370$	0	0
$371$	0.0931767	0.00483749
$372$	−9.61810	−0.498675
$373$	31.3540	1.62345	0.811725	−	0.584039i	$-0.198529\pi$
$373$	31.3540	1.62345	0.811725	+	0.584039i	$0.198529\pi$
$374$	−2.85393	−0.147573
$375$	9.97664	0.515192
$376$	11.4382	0.589880
$377$	−40.3028	−2.07570
$378$	−7.20847	−0.370764
$379$	10.6544	0.547281	0.273641	−	0.961832i	$-0.411772\pi$
$379$	10.6544	0.547281	0.273641	+	0.961832i	$0.411772\pi$
$380$	1.73990	0.0892550
$381$	19.6897	1.00874
$382$	−10.4903	−0.536732
$383$	−19.4015	−0.991372	−0.495686	−	0.868502i	$-0.665083\pi$
$383$	−19.4015	−0.991372	−0.495686	+	0.868502i	$0.665083\pi$
$384$	−2.90773	−0.148385
$385$	1.91657	0.0976775
$386$	9.82949	0.500308
$387$	34.2042	1.73870
$388$	0.929128	0.0471693
$389$	−18.6990	−0.948078	−0.474039	−	0.880504i	$-0.657204\pi$
$389$	−18.6990	−0.948078	−0.474039	+	0.880504i	$0.657204\pi$
$390$	−6.42527	−0.325356
$391$	0.753590	0.0381107
$392$	5.98021	0.302046
$393$	44.0477	2.22191
$394$	12.0631	0.607730
$395$	3.23220	0.162630
$396$	−29.8097	−1.49799
$397$	−23.8632	−1.19766	−0.598829	−	0.800877i	$-0.704367\pi$
$397$	−23.8632	−1.19766	−0.598829	+	0.800877i	$0.704367\pi$
$398$	−9.29990	−0.466162
$399$	−14.7107	−0.736456
$400$	−4.87939	−0.243969
$401$	−17.8350	−0.890638	−0.445319	−	0.895372i	$-0.646910\pi$
$401$	−17.8350	−0.890638	−0.445319	+	0.895372i	$0.646910\pi$
$402$	3.38678	0.168917
$403$	21.0461	1.04838
$404$	8.56186	0.425969
$405$	−1.52507	−0.0757813
$406$	−6.39665	−0.317460
$407$	0	0
$408$	1.51855	0.0751792
$409$	9.98668	0.493810	0.246905	−	0.969040i	$-0.420586\pi$
$409$	9.98668	0.493810	0.246905	+	0.969040i	$0.420586\pi$
$410$	−0.382196	−0.0188753
$411$	−24.6626	−1.21652
$412$	−4.95913	−0.244319
$413$	−3.01959	−0.148584
$414$	7.87134	0.386855
$415$	−3.28707	−0.161356
$416$	6.36263	0.311954
$417$	−53.3231	−2.61124
$418$	−27.3775	−1.33908
$419$	36.0291	1.76014	0.880068	−	0.474848i	$-0.157497\pi$
$419$	36.0291	1.76014	0.880068	+	0.474848i	$0.157497\pi$
$420$	−1.01979	−0.0497605
$421$	−22.3336	−1.08847	−0.544235	−	0.838933i	$-0.683180\pi$
$421$	−22.3336	−1.08847	−0.544235	+	0.838933i	$0.683180\pi$
$422$	4.40004	0.214190
$423$	−62.3943	−3.03371
$424$	−0.0922684	−0.00448095
$425$	2.54823	0.123607
$426$	−0.909807	−0.0440803
$427$	−3.85340	−0.186479
$428$	−3.56826	−0.172478
$429$	101.102	4.88127
$430$	2.17768	0.105017
$431$	−31.2560	−1.50555	−0.752774	−	0.658279i	$-0.771285\pi$
$431$	−31.2560	−1.50555	−0.752774	+	0.658279i	$0.771285\pi$
$432$	7.13820	0.343437
$433$	5.42187	0.260558	0.130279	−	0.991477i	$-0.458413\pi$
$433$	5.42187	0.260558	0.130279	+	0.991477i	$0.458413\pi$
$434$	3.34033	0.160341
$435$	−6.39665	−0.306696
$436$	0.978688	0.0468706
$437$	7.22912	0.345816
$438$	−38.4767	−1.83849
$439$	15.4292	0.736397	0.368199	−	0.929747i	$-0.379975\pi$
$439$	15.4292	0.736397	0.368199	+	0.929747i	$0.379975\pi$
$440$	−1.89789	−0.0904782
$441$	−32.6215	−1.55340
$442$	−3.32285	−0.158052
$443$	−8.45523	−0.401720	−0.200860	−	0.979620i	$-0.564374\pi$
$443$	−8.45523	−0.401720	−0.200860	+	0.979620i	$0.564374\pi$
$444$	0	0
$445$	−5.47610	−0.259592
$446$	−11.2311	−0.531810
$447$	15.8556	0.749944
$448$	1.00984	0.0477107
$449$	−36.3945	−1.71756	−0.858782	−	0.512342i	$-0.828778\pi$
$449$	−36.3945	−1.71756	−0.858782	+	0.512342i	$0.828778\pi$
$450$	26.6166	1.25472
$451$	6.01390	0.283183
$452$	−9.23702	−0.434473
$453$	−45.2308	−2.12513
$454$	−15.1539	−0.711209
$455$	2.23147	0.104613
$456$	14.5673	0.682176
$457$	−13.0415	−0.610054	−0.305027	−	0.952344i	$-0.598665\pi$
$457$	−13.0415	−0.610054	−0.305027	+	0.952344i	$0.598665\pi$
$458$	15.5617	0.727151
$459$	−3.72788	−0.174003
$460$	0.501143	0.0233659
$461$	−17.6483	−0.821964	−0.410982	−	0.911644i	$-0.634814\pi$
$461$	−17.6483	−0.821964	−0.410982	+	0.911644i	$0.634814\pi$
$462$	16.0465	0.746548
$463$	−26.4940	−1.23128	−0.615640	−	0.788028i	$-0.711102\pi$
$463$	−26.4940	−1.23128	−0.615640	+	0.788028i	$0.711102\pi$
$464$	6.33429	0.294062
$465$	3.34033	0.154904
$466$	−13.5871	−0.629411
$467$	19.0975	0.883727	0.441864	−	0.897082i	$-0.354317\pi$
$467$	19.0975	0.883727	0.441864	+	0.897082i	$0.354317\pi$
$468$	−34.7076	−1.60436
$469$	−1.17622	−0.0543127
$470$	−3.97244	−0.183235
$471$	−11.6548	−0.537026
$472$	2.99016	0.137633
$473$	−34.2660	−1.57555
$474$	27.0616	1.24298
$475$	24.4450	1.12161
$476$	−0.527386	−0.0241727
$477$	0.503315	0.0230452
$478$	−19.4945	−0.891656
$479$	−19.1825	−0.876471	−0.438236	−	0.898860i	$-0.644396\pi$
$479$	−19.1825	−0.876471	−0.438236	+	0.898860i	$0.644396\pi$
$480$	1.00984	0.0460929
$481$	0	0
$482$	1.44363	0.0657556
$483$	−4.23712	−0.192795
$484$	18.8635	0.857430
$485$	−0.322683	−0.0146523
$486$	8.64599	0.392190
$487$	35.7577	1.62034	0.810168	−	0.586197i	$-0.199376\pi$
$487$	35.7577	1.62034	0.810168	+	0.586197i	$0.199376\pi$
$488$	3.81583	0.172735
$489$	−13.6438	−0.616992
$490$	−2.07691	−0.0938251
$491$	29.7732	1.34364	0.671822	−	0.740713i	$-0.265512\pi$
$491$	29.7732	1.34364	0.671822	+	0.740713i	$0.265512\pi$
$492$	−3.19993	−0.144264
$493$	−3.30805	−0.148987
$494$	−31.8758	−1.43416
$495$	10.3528	0.465323
$496$	−3.30777	−0.148523
$497$	0.315973	0.0141733
$498$	−27.5209	−1.23324
$499$	−24.8179	−1.11100	−0.555501	−	0.831516i	$-0.687473\pi$
$499$	−24.8179	−1.11100	−0.555501	+	0.831516i	$0.687473\pi$
$500$	3.43107	0.153442
$501$	2.25929	0.100938
$502$	10.0729	0.449576
$503$	−13.6252	−0.607518	−0.303759	−	0.952749i	$-0.598242\pi$
$503$	−13.6252	−0.607518	−0.303759	+	0.952749i	$0.598242\pi$
$504$	−5.50860	−0.245373
$505$	−2.97350	−0.132319
$506$	−7.88554	−0.350555
$507$	79.9135	3.54909
$508$	6.77151	0.300437
$509$	21.1010	0.935285	0.467643	−	0.883918i	$-0.345103\pi$
$509$	21.1010	0.935285	0.467643	+	0.883918i	$0.345103\pi$
$510$	−0.527386	−0.0233530
$511$	13.3628	0.591136
$512$	−1.00000	−0.0441942
$513$	−35.7613	−1.57890
$514$	−6.98500	−0.308095
$515$	1.72229	0.0758930
$516$	18.2325	0.802643
$517$	62.5069	2.74905
$518$	0	0
$519$	31.2097	1.36995
$520$	−2.20972	−0.0969026
$521$	2.94157	0.128872	0.0644362	−	0.997922i	$-0.479475\pi$
$521$	2.94157	0.128872	0.0644362	+	0.997922i	$0.479475\pi$
$522$	−34.5529	−1.51234
$523$	−10.8441	−0.474180	−0.237090	−	0.971488i	$-0.576194\pi$
$523$	−10.8441	−0.474180	−0.237090	+	0.971488i	$0.576194\pi$
$524$	15.1485	0.661764
$525$	−14.3276	−0.625308
$526$	−2.66284	−0.116105
$527$	1.72746	0.0752494
$528$	−15.8900	−0.691524
$529$	−20.9178	−0.909469
$530$	0.0320445	0.00139192
$531$	−16.3110	−0.707837
$532$	−5.05916	−0.219343
$533$	7.00202	0.303291
$534$	−45.8486	−1.98406
$535$	1.23924	0.0535772
$536$	1.16475	0.0503096
$537$	34.5950	1.49288
$538$	−2.41504	−0.104120
$539$	32.6804	1.40764
$540$	−2.47907	−0.106682
$541$	−8.87735	−0.381667	−0.190834	−	0.981622i	$-0.561119\pi$
$541$	−8.87735	−0.381667	−0.190834	+	0.981622i	$0.561119\pi$
$542$	25.2506	1.08461
$543$	12.7553	0.547381
$544$	0.522244	0.0223910
$545$	−0.339895	−0.0145595
$546$	18.6830	0.799557
$547$	36.5299	1.56190	0.780952	−	0.624591i	$-0.214734\pi$
$547$	36.5299	1.56190	0.780952	+	0.624591i	$0.214734\pi$
$548$	−8.48173	−0.362321
$549$	−20.8150	−0.888362
$550$	−26.6646	−1.13698
$551$	−31.7338	−1.35191
$552$	4.19581	0.178586
$553$	−9.39838	−0.399660
$554$	−17.7320	−0.753360
$555$	0	0
$556$	−18.3384	−0.777720
$557$	−36.7236	−1.55603	−0.778014	−	0.628246i	$-0.783773\pi$
$557$	−36.7236	−1.55603	−0.778014	+	0.628246i	$0.783773\pi$
$558$	18.0435	0.763844
$559$	−39.8961	−1.68742
$560$	−0.350715	−0.0148204
$561$	8.29847	0.350362
$562$	19.7493	0.833074
$563$	−0.476912	−0.0200995	−0.0100497	−	0.999950i	$-0.503199\pi$
$563$	−0.476912	−0.0200995	−0.0100497	+	0.999950i	$0.503199\pi$
$564$	−33.2592	−1.40047
$565$	3.20798	0.134961
$566$	24.3494	1.02348
$567$	4.43449	0.186231
$568$	−0.312892	−0.0131287
$569$	−9.09812	−0.381413	−0.190706	−	0.981647i	$-0.561078\pi$
$569$	−9.09812	−0.381413	−0.190706	+	0.981647i	$0.561078\pi$
$570$	−5.05916	−0.211905
$571$	25.5966	1.07118	0.535592	−	0.844477i	$-0.320089\pi$
$571$	25.5966	1.07118	0.535592	+	0.844477i	$0.320089\pi$
$572$	34.7702	1.45381
$573$	30.5030	1.27428
$574$	1.11132	0.0463858
$575$	7.04087	0.293625
$576$	5.45490	0.227288
$577$	−15.4291	−0.642322	−0.321161	−	0.947025i	$-0.604073\pi$
$577$	−15.4291	−0.642322	−0.321161	+	0.947025i	$0.604073\pi$
$578$	16.7273	0.695762
$579$	−28.5815	−1.18781
$580$	−2.19988	−0.0913449
$581$	9.55792	0.396530
$582$	−2.70165	−0.111987
$583$	−0.504223	−0.0208828
$584$	−13.2325	−0.547567
$585$	12.0538	0.498364
$586$	23.2486	0.960390
$587$	−16.2385	−0.670235	−0.335118	−	0.942176i	$-0.608776\pi$
$587$	−16.2385	−0.670235	−0.335118	+	0.942176i	$0.608776\pi$
$588$	−17.3889	−0.717104
$589$	16.5714	0.682813
$590$	−1.03847	−0.0427531
$591$	−35.0762	−1.44284
$592$	0	0
$593$	−27.0626	−1.11133	−0.555663	−	0.831407i	$-0.687536\pi$
$593$	−27.0626	−1.11133	−0.555663	+	0.831407i	$0.687536\pi$
$594$	39.0085	1.60054
$595$	0.183159	0.00750879
$596$	5.45291	0.223360
$597$	27.0416	1.10674
$598$	−9.18118	−0.375446
$599$	−39.8486	−1.62817	−0.814085	−	0.580746i	$-0.802761\pi$
$599$	−39.8486	−1.62817	−0.814085	+	0.580746i	$0.802761\pi$
$600$	14.1879	0.579220
$601$	35.6736	1.45516	0.727578	−	0.686025i	$-0.240646\pi$
$601$	35.6736	1.45516	0.727578	+	0.686025i	$0.240646\pi$
$602$	−6.33210	−0.258077
$603$	−6.35360	−0.258739
$604$	−15.5554	−0.632939
$605$	−6.55121	−0.266345
$606$	−24.8956	−1.01131
$607$	12.7478	0.517417	0.258709	−	0.965955i	$-0.416703\pi$
$607$	12.7478	0.517417	0.258709	+	0.965955i	$0.416703\pi$
$608$	5.00984	0.203176
$609$	18.5997	0.753699
$610$	−1.32522	−0.0536568
$611$	72.7771	2.94425
$612$	−2.84879	−0.115156
$613$	−4.09270	−0.165303	−0.0826513	−	0.996579i	$-0.526339\pi$
$613$	−4.09270	−0.165303	−0.0826513	+	0.996579i	$0.526339\pi$
$614$	10.6702	0.430613
$615$	1.11132	0.0448129
$616$	5.51855	0.222349
$617$	47.2712	1.90307	0.951534	−	0.307545i	$-0.0995073\pi$
$617$	47.2712	1.90307	0.951534	+	0.307545i	$0.0995073\pi$
$618$	14.4198	0.580050
$619$	−21.0337	−0.845416	−0.422708	−	0.906266i	$-0.638920\pi$
$619$	−21.0337	−0.845416	−0.422708	+	0.906266i	$0.638920\pi$
$620$	1.14878	0.0461359
$621$	−10.3003	−0.413337
$622$	17.0201	0.682444
$623$	15.9230	0.637943
$624$	−18.5008	−0.740626
$625$	23.2053	0.928213
$626$	10.9104	0.436068
$627$	79.6065	3.17918
$628$	−4.00822	−0.159945
$629$	0	0
$630$	1.91312	0.0762205
$631$	32.7576	1.30406	0.652030	−	0.758193i	$-0.273918\pi$
$631$	32.7576	1.30406	0.652030	+	0.758193i	$0.273918\pi$
$632$	9.30676	0.370203
$633$	−12.7941	−0.508521
$634$	28.8403	1.14540
$635$	−2.35172	−0.0933252
$636$	0.268292	0.0106385
$637$	38.0499	1.50759
$638$	34.6153	1.37043
$639$	1.70680	0.0675198
$640$	0.347296	0.0137281
$641$	20.0323	0.791229	0.395614	−	0.918417i	$-0.370532\pi$
$641$	20.0323	0.791229	0.395614	+	0.918417i	$0.370532\pi$
$642$	10.3755	0.409490
$643$	13.3924	0.528143	0.264071	−	0.964503i	$-0.414935\pi$
$643$	13.3924	0.528143	0.264071	+	0.964503i	$0.414935\pi$
$644$	−1.45719	−0.0574213
$645$	−6.33210	−0.249326
$646$	−2.61636	−0.102939
$647$	−14.7797	−0.581049	−0.290525	−	0.956867i	$-0.593830\pi$
$647$	−14.7797	−0.581049	−0.290525	+	0.956867i	$0.593830\pi$
$648$	−4.39126	−0.172505
$649$	16.3404	0.641419
$650$	−31.0457	−1.21771
$651$	−9.71278	−0.380674
$652$	−4.69223	−0.183762
$653$	27.1356	1.06190	0.530949	−	0.847404i	$-0.321836\pi$
$653$	27.1356	1.06190	0.530949	+	0.847404i	$0.321836\pi$
$654$	−2.84576	−0.111278
$655$	−5.26101	−0.205565
$656$	−1.10049	−0.0429669
$657$	72.1822	2.81610
$658$	11.5508	0.450297
$659$	31.6449	1.23271	0.616355	−	0.787468i	$-0.288609\pi$
$659$	31.6449	1.23271	0.616355	+	0.787468i	$0.288609\pi$
$660$	5.51855	0.214809
$661$	−33.9896	−1.32204	−0.661022	−	0.750367i	$-0.729877\pi$
$661$	−33.9896	−1.32204	−0.661022	+	0.750367i	$0.729877\pi$
$662$	3.95955	0.153892
$663$	9.66196	0.375239
$664$	−9.46475	−0.367303
$665$	1.75703	0.0681347
$666$	0	0
$667$	−9.14028	−0.353913
$668$	0.776993	0.0300628
$669$	32.6571	1.26260
$670$	−0.404514	−0.0156277
$671$	20.8526	0.805004
$672$	−2.93636	−0.113272
$673$	39.6475	1.52830	0.764149	−	0.645039i	$-0.223159\pi$
$673$	39.6475	1.52830	0.764149	+	0.645039i	$0.223159\pi$
$674$	4.27678	0.164735
$675$	−34.8300	−1.34061
$676$	27.4831	1.05704
$677$	19.3061	0.741992	0.370996	−	0.928634i	$-0.379016\pi$
$677$	19.3061	0.741992	0.370996	+	0.928634i	$0.379016\pi$
$678$	26.8588	1.03151
$679$	0.938275	0.0360077
$680$	−0.181374	−0.00695536
$681$	44.0636	1.68852
$682$	−18.0761	−0.692170
$683$	−2.02310	−0.0774117	−0.0387058	−	0.999251i	$-0.512324\pi$
$683$	−2.02310	−0.0774117	−0.0387058	+	0.999251i	$0.512324\pi$
$684$	−27.3282	−1.04492
$685$	2.94567	0.112548
$686$	13.1080	0.500466
$687$	−45.2493	−1.72637
$688$	6.27037	0.239055
$689$	−0.587070	−0.0223656
$690$	−1.45719	−0.0554742
$691$	−1.39530	−0.0530798	−0.0265399	−	0.999648i	$-0.508449\pi$
$691$	−1.39530	−0.0530798	−0.0265399	+	0.999648i	$0.508449\pi$
$692$	10.7333	0.408021
$693$	−30.1031	−1.14352
$694$	−10.1280	−0.384455
$695$	6.36885	0.241584
$696$	−18.4184	−0.698148
$697$	0.574725	0.0217692
$698$	7.19087	0.272178
$699$	39.5077	1.49432
$700$	−4.92742	−0.186239
$701$	45.2003	1.70719	0.853596	−	0.520936i	$-0.174417\pi$
$701$	45.2003	1.70719	0.853596	+	0.520936i	$0.174417\pi$
$702$	45.4178	1.71418
$703$	0	0
$704$	−5.46475	−0.205960
$705$	11.5508	0.435028
$706$	−34.0550	−1.28168
$707$	8.64615	0.325172
$708$	−8.69457	−0.326762
$709$	28.5445	1.07201	0.536005	−	0.844215i	$-0.319933\pi$
$709$	28.5445	1.07201	0.536005	+	0.844215i	$0.319933\pi$
$710$	0.108666	0.00407817
$711$	−50.7675	−1.90393
$712$	−15.7678	−0.590924
$713$	4.77305	0.178752
$714$	1.53350	0.0573896
$715$	−12.0756	−0.451600
$716$	11.8976	0.444633
$717$	56.6847	2.11693
$718$	−9.87953	−0.368701
$719$	−17.8740	−0.666589	−0.333294	−	0.942823i	$-0.608160\pi$
$719$	−17.8740	−0.666589	−0.333294	+	0.942823i	$0.608160\pi$
$720$	−1.89447	−0.0706027
$721$	−5.00795	−0.186506
$722$	−6.09854	−0.226964
$723$	−4.19769	−0.156114
$724$	4.38667	0.163029
$725$	−30.9074	−1.14787
$726$	−54.8499	−2.03567
$727$	17.4477	0.647099	0.323550	−	0.946211i	$-0.395124\pi$
$727$	17.4477	0.647099	0.323550	+	0.946211i	$0.395124\pi$
$728$	6.42527	0.238136
$729$	−38.3140	−1.41904
$730$	4.59561	0.170091
$731$	−3.27466	−0.121118
$732$	−11.0954	−0.410098
$733$	−43.8731	−1.62049	−0.810244	−	0.586092i	$-0.800666\pi$
$733$	−43.8731	−1.62049	−0.810244	+	0.586092i	$0.800666\pi$
$734$	33.9039	1.25142
$735$	6.03909	0.222755
$736$	1.44298	0.0531891
$737$	6.36507	0.234460
$738$	6.00307	0.220976
$739$	39.5017	1.45309	0.726546	−	0.687118i	$-0.241124\pi$
$739$	39.5017	1.45309	0.726546	+	0.687118i	$0.241124\pi$
$740$	0	0
$741$	92.6863	3.40492
$742$	−0.0931767	−0.00342062
$743$	19.8910	0.729730	0.364865	−	0.931060i	$-0.381115\pi$
$743$	19.8910	0.729730	0.364865	+	0.931060i	$0.381115\pi$
$744$	9.61810	0.352617
$745$	−1.89378	−0.0693826
$746$	−31.3540	−1.14795
$747$	51.6293	1.88902
$748$	2.85393	0.104350
$749$	−3.60339	−0.131665
$750$	−9.97664	−0.364296
$751$	−33.2367	−1.21283	−0.606413	−	0.795150i	$-0.707392\pi$
$751$	−33.2367	−1.21283	−0.606413	+	0.795150i	$0.707392\pi$
$752$	−11.4382	−0.417108
$753$	−29.2893	−1.06736
$754$	40.3028	1.46774
$755$	5.40232	0.196611
$756$	7.20847	0.262170
$757$	−43.4094	−1.57774	−0.788871	−	0.614558i	$-0.789334\pi$
$757$	−43.4094	−1.57774	−0.788871	+	0.614558i	$0.789334\pi$
$758$	−10.6544	−0.386986
$759$	22.9290	0.832271
$760$	−1.73990	−0.0631128
$761$	25.2861	0.916619	0.458309	−	0.888793i	$-0.348455\pi$
$761$	25.2861	0.916619	0.458309	+	0.888793i	$0.348455\pi$
$762$	−19.6897	−0.713284
$763$	0.988323	0.0357797
$764$	10.4903	0.379527
$765$	0.989375	0.0357709
$766$	19.4015	0.701006
$767$	19.0253	0.686963
$768$	2.90773	0.104924
$769$	−27.7983	−1.00243	−0.501216	−	0.865322i	$-0.667114\pi$
$769$	−27.7983	−1.00243	−0.501216	+	0.865322i	$0.667114\pi$
$770$	−1.91657	−0.0690684
$771$	20.3105	0.731465
$772$	−9.82949	−0.353771
$773$	−0.986707	−0.0354894	−0.0177447	−	0.999843i	$-0.505649\pi$
$773$	−0.986707	−0.0354894	−0.0177447	+	0.999843i	$0.505649\pi$
$774$	−34.2042	−1.22945
$775$	16.1399	0.579761
$776$	−0.929128	−0.0333538
$777$	0	0
$778$	18.6990	0.670392
$779$	5.51328	0.197534
$780$	6.42527	0.230062
$781$	−1.70988	−0.0611842
$782$	−0.753590	−0.0269483
$783$	45.2154	1.61587
$784$	−5.98021	−0.213579
$785$	1.39204	0.0496841
$786$	−44.0477	−1.57113
$787$	25.7979	0.919597	0.459799	−	0.888023i	$-0.347922\pi$
$787$	25.7979	0.919597	0.459799	+	0.888023i	$0.347922\pi$
$788$	−12.0631	−0.429730
$789$	7.74283	0.275652
$790$	−3.23220	−0.114997
$791$	−9.32796	−0.331664
$792$	29.8097	1.05924
$793$	24.2787	0.862163
$794$	23.8632	0.846872
$795$	−0.0931767	−0.00330464
$796$	9.29990	0.329626
$797$	−15.1068	−0.535112	−0.267556	−	0.963542i	$-0.586216\pi$
$797$	−15.1068	−0.535112	−0.267556	+	0.963542i	$0.586216\pi$
$798$	14.7107	0.520753
$799$	5.97353	0.211328
$800$	4.87939	0.172512
$801$	86.0119	3.03908
$802$	17.8350	0.629776
$803$	−72.3125	−2.55185
$804$	−3.38678	−0.119443
$805$	0.506077	0.0178369
$806$	−21.0461	−0.741318
$807$	7.02227	0.247196
$808$	−8.56186	−0.301205
$809$	42.6899	1.50090	0.750448	−	0.660929i	$-0.229838\pi$
$809$	42.6899	1.50090	0.750448	+	0.660929i	$0.229838\pi$
$810$	1.52507	0.0535855
$811$	20.4180	0.716974	0.358487	−	0.933535i	$-0.383293\pi$
$811$	20.4180	0.716974	0.358487	+	0.933535i	$0.383293\pi$
$812$	6.39665	0.224478
$813$	−73.4219	−2.57502
$814$	0	0
$815$	1.62960	0.0570822
$816$	−1.51855	−0.0531598
$817$	−31.4136	−1.09902
$818$	−9.98668	−0.349176
$819$	−35.0492	−1.22472
$820$	0.382196	0.0133469
$821$	13.4462	0.469275	0.234637	−	0.972083i	$-0.424610\pi$
$821$	13.4462	0.469275	0.234637	+	0.972083i	$0.424610\pi$
$822$	24.6626	0.860206
$823$	−40.7832	−1.42161	−0.710807	−	0.703387i	$-0.751670\pi$
$823$	−40.7832	−1.42161	−0.710807	+	0.703387i	$0.751670\pi$
$824$	4.95913	0.172759
$825$	77.5335	2.69937
$826$	3.01959	0.105065
$827$	40.4427	1.40633	0.703165	−	0.711026i	$-0.251769\pi$
$827$	40.4427	1.40633	0.703165	+	0.711026i	$0.251769\pi$
$828$	−7.87134	−0.273548
$829$	−2.65519	−0.0922186	−0.0461093	−	0.998936i	$-0.514682\pi$
$829$	−2.65519	−0.0922186	−0.0461093	+	0.998936i	$0.514682\pi$
$830$	3.28707	0.114096
$831$	51.5598	1.78859
$832$	−6.36263	−0.220585
$833$	3.12313	0.108210
$834$	53.3231	1.84643
$835$	−0.269847	−0.00933844
$836$	27.3775	0.946872
$837$	−23.6115	−0.816133
$838$	−36.0291	−1.24460
$839$	−43.1281	−1.48895	−0.744474	−	0.667651i	$-0.767300\pi$
$839$	−43.1281	−1.48895	−0.744474	+	0.667651i	$0.767300\pi$
$840$	1.01979	0.0351860
$841$	11.1232	0.383559
$842$	22.3336	0.769665
$843$	−57.4257	−1.97785
$844$	−4.40004	−0.151455
$845$	−9.54479	−0.328351
$846$	62.3943	2.14516
$847$	19.0492	0.654537
$848$	0.0922684	0.00316851
$849$	−70.8015	−2.42990
$850$	−2.54823	−0.0874036
$851$	0	0
$852$	0.909807	0.0311695
$853$	44.9180	1.53796	0.768981	−	0.639271i	$-0.220764\pi$
$853$	44.9180	1.53796	0.768981	+	0.639271i	$0.220764\pi$
$854$	3.85340	0.131861
$855$	9.49099	0.324585
$856$	3.56826	0.121961
$857$	1.14287	0.0390395	0.0195198	−	0.999809i	$-0.493786\pi$
$857$	1.14287	0.0390395	0.0195198	+	0.999809i	$0.493786\pi$
$858$	−101.102	−3.45158
$859$	−20.6966	−0.706160	−0.353080	−	0.935593i	$-0.614866\pi$
$859$	−20.6966	−0.706160	−0.353080	+	0.935593i	$0.614866\pi$
$860$	−2.17768	−0.0742581
$861$	−3.23143	−0.110127
$862$	31.2560	1.06458
$863$	−11.0475	−0.376061	−0.188030	−	0.982163i	$-0.560210\pi$
$863$	−11.0475	−0.376061	−0.188030	+	0.982163i	$0.560210\pi$
$864$	−7.13820	−0.242847
$865$	−3.72765	−0.126744
$866$	−5.42187	−0.184243
$867$	−48.6384	−1.65185
$868$	−3.34033	−0.113378
$869$	50.8591	1.72528
$870$	6.39665	0.216867
$871$	7.41088	0.251108
$872$	−0.978688	−0.0331426
$873$	5.06830	0.171536
$874$	−7.22912	−0.244529
$875$	3.46485	0.117133
$876$	38.4767	1.30001
$877$	−12.3680	−0.417638	−0.208819	−	0.977954i	$-0.566962\pi$
$877$	−12.3680	−0.417638	−0.208819	+	0.977954i	$0.566962\pi$
$878$	−15.4292	−0.520712
$879$	−67.6006	−2.28011
$880$	1.89789	0.0639778
$881$	17.9831	0.605865	0.302933	−	0.953012i	$-0.402034\pi$
$881$	17.9831	0.605865	0.302933	+	0.953012i	$0.402034\pi$
$882$	32.6215	1.09842
$883$	10.7268	0.360986	0.180493	−	0.983576i	$-0.442231\pi$
$883$	10.7268	0.360986	0.180493	+	0.983576i	$0.442231\pi$
$884$	3.32285	0.111760
$885$	3.01959	0.101502
$886$	8.45523	0.284059
$887$	−16.7444	−0.562222	−0.281111	−	0.959675i	$-0.590703\pi$
$887$	−16.7444	−0.562222	−0.281111	+	0.959675i	$0.590703\pi$
$888$	0	0
$889$	6.83817	0.229345
$890$	5.47610	0.183559
$891$	−23.9971	−0.803934
$892$	11.2311	0.376046
$893$	57.3036	1.91759
$894$	−15.8556	−0.530291
$895$	−4.13199	−0.138117
$896$	−1.00984	−0.0337365
$897$	26.6964	0.891367
$898$	36.3945	1.21450
$899$	−20.9524	−0.698800
$900$	−26.6166	−0.887219
$901$	−0.0481866	−0.00160533
$902$	−6.01390	−0.200241
$903$	18.4120	0.612714
$904$	9.23702	0.307219
$905$	−1.52348	−0.0506421
$906$	45.2308	1.50269
$907$	−43.3824	−1.44049	−0.720244	−	0.693721i	$-0.755970\pi$
$907$	−43.3824	−1.44049	−0.720244	+	0.693721i	$0.755970\pi$
$908$	15.1539	0.502901
$909$	46.7041	1.54908
$910$	−2.23147	−0.0739726
$911$	−10.1061	−0.334831	−0.167416	−	0.985886i	$-0.553542\pi$
$911$	−10.1061	−0.334831	−0.167416	+	0.985886i	$0.553542\pi$
$912$	−14.5673	−0.482371
$913$	−51.7225	−1.71176
$914$	13.0415	0.431373
$915$	3.85340	0.127389
$916$	−15.5617	−0.514173
$917$	15.2976	0.505171
$918$	3.72788	0.123039
$919$	−2.82736	−0.0932661	−0.0466330	−	0.998912i	$-0.514849\pi$
$919$	−2.82736	−0.0932661	−0.0466330	+	0.998912i	$0.514849\pi$
$920$	−0.501143	−0.0165222
$921$	−31.0260	−1.02234
$922$	17.6483	0.581216
$923$	−1.99082	−0.0655286
$924$	−16.0465	−0.527889
$925$	0	0
$926$	26.4940	0.870646
$927$	−27.0516	−0.888490
$928$	−6.33429	−0.207933
$929$	33.4655	1.09797	0.548985	−	0.835833i	$-0.315015\pi$
$929$	33.4655	1.09797	0.548985	+	0.835833i	$0.315015\pi$
$930$	−3.34033	−0.109534
$931$	29.9599	0.981897
$932$	13.5871	0.445061
$933$	−49.4899	−1.62023
$934$	−19.0975	−0.624890
$935$	−0.991161	−0.0324144
$936$	34.7076	1.13445
$937$	46.0579	1.50465	0.752323	−	0.658794i	$-0.228933\pi$
$937$	46.0579	1.50465	0.752323	+	0.658794i	$0.228933\pi$
$938$	1.17622	0.0384048
$939$	−31.7246	−1.03529
$940$	3.97244	0.129567
$941$	−17.5337	−0.571583	−0.285791	−	0.958292i	$-0.592256\pi$
$941$	−17.5337	−0.571583	−0.285791	+	0.958292i	$0.592256\pi$
$942$	11.6548	0.379735
$943$	1.58799	0.0517120
$944$	−2.99016	−0.0973213
$945$	−2.50348	−0.0814381
$946$	34.2660	1.11408
$947$	−26.1918	−0.851118	−0.425559	−	0.904931i	$-0.639923\pi$
$947$	−26.1918	−0.851118	−0.425559	+	0.904931i	$0.639923\pi$
$948$	−27.0616	−0.878919
$949$	−84.1938	−2.73305
$950$	−24.4450	−0.793099
$951$	−83.8599	−2.71934
$952$	0.527386	0.0170927
$953$	−25.9695	−0.841235	−0.420617	−	0.907238i	$-0.638187\pi$
$953$	−25.9695	−0.841235	−0.420617	+	0.907238i	$0.638187\pi$
$954$	−0.503315	−0.0162954
$955$	−3.64325	−0.117893
$956$	19.4945	0.630496
$957$	−100.652	−3.25362
$958$	19.1825	0.619759
$959$	−8.56522	−0.276586
$960$	−1.00984	−0.0325926
$961$	−20.0587	−0.647054
$962$	0	0
$963$	−19.4645	−0.627235
$964$	−1.44363	−0.0464962
$965$	3.41374	0.109892
$966$	4.23712	0.136327
$967$	−33.7691	−1.08594	−0.542970	−	0.839752i	$-0.682700\pi$
$967$	−33.7691	−1.08594	−0.542970	+	0.839752i	$0.682700\pi$
$968$	−18.8635	−0.606295
$969$	7.60768	0.244394
$970$	0.322683	0.0103607
$971$	−13.7944	−0.442683	−0.221342	−	0.975196i	$-0.571044\pi$
$971$	−13.7944	−0.442683	−0.221342	+	0.975196i	$0.571044\pi$
$972$	−8.64599	−0.277320
$973$	−18.5189	−0.593689
$974$	−35.7577	−1.14575
$975$	90.2727	2.89104
$976$	−3.81583	−0.122142
$977$	38.9852	1.24725	0.623624	−	0.781724i	$-0.285660\pi$
$977$	38.9852	1.24725	0.623624	+	0.781724i	$0.285660\pi$
$978$	13.6438	0.436279
$979$	−86.1671	−2.75391
$980$	2.07691	0.0663443
$981$	5.33865	0.170450
$982$	−29.7732	−0.950100
$983$	12.1963	0.389001	0.194501	−	0.980902i	$-0.437691\pi$
$983$	12.1963	0.389001	0.194501	+	0.980902i	$0.437691\pi$
$984$	3.19993	0.102010
$985$	4.18947	0.133488
$986$	3.30805	0.105350
$987$	−33.5866	−1.06907
$988$	31.8758	1.01410
$989$	−9.04804	−0.287711
$990$	−10.3528	−0.329033
$991$	−26.4606	−0.840549	−0.420275	−	0.907397i	$-0.638066\pi$
$991$	−26.4606	−0.840549	−0.420275	+	0.907397i	$0.638066\pi$
$992$	3.30777	0.105022
$993$	−11.5133	−0.365364
$994$	−0.315973	−0.0100220
$995$	−3.22982	−0.102392
$996$	27.5209	0.872035
$997$	13.3432	0.422584	0.211292	−	0.977423i	$-0.432233\pi$
$997$	13.3432	0.422584	0.211292	+	0.977423i	$0.432233\pi$
$998$	24.8179	0.785597
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.q.1.6		6
37.3	even	18		74.2.f.b.9.2	✓	12
37.25	even	18		74.2.f.b.33.2	yes	12
37.36	even	2		2738.2.a.t.1.6		6
111.62	odd	18		666.2.x.g.181.2		12
111.77	odd	18		666.2.x.g.379.2		12
148.3	odd	18		592.2.bc.d.305.1		12
148.99	odd	18		592.2.bc.d.33.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.9.2	✓	12	37.3	even	18
74.2.f.b.33.2	yes	12	37.25	even	18
592.2.bc.d.33.1		12	148.99	odd	18
592.2.bc.d.305.1		12	148.3	odd	18
666.2.x.g.181.2		12	111.62	odd	18
666.2.x.g.379.2		12	111.77	odd	18
2738.2.a.q.1.6		6	1.1	even	1	trivial
2738.2.a.t.1.6		6	37.36	even	2

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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.90773 q^{3} +1.00000 q^{4} -0.347296 q^{5} -2.90773 q^{6} +1.00984 q^{7} -1.00000 q^{8} +5.45490 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.90773 q^{3} +1.00000 q^{4} -0.347296 q^{5} -2.90773 q^{6} +1.00984 q^{7} -1.00000 q^{8} +5.45490 q^{9} +0.347296 q^{10} -5.46475 q^{11} +2.90773 q^{12} -6.36263 q^{13} -1.00984 q^{14} -1.00984 q^{15} +1.00000 q^{16} -0.522244 q^{17} -5.45490 q^{18} -5.00984 q^{19} -0.347296 q^{20} +2.93636 q^{21} +5.46475 q^{22} -1.44298 q^{23} -2.90773 q^{24} -4.87939 q^{25} +6.36263 q^{26} +7.13820 q^{27} +1.00984 q^{28} +6.33429 q^{29} +1.00984 q^{30} -3.30777 q^{31} -1.00000 q^{32} -15.8900 q^{33} +0.522244 q^{34} -0.350715 q^{35} +5.45490 q^{36} +5.00984 q^{38} -18.5008 q^{39} +0.347296 q^{40} -1.10049 q^{41} -2.93636 q^{42} +6.27037 q^{43} -5.46475 q^{44} -1.89447 q^{45} +1.44298 q^{46} -11.4382 q^{47} +2.90773 q^{48} -5.98021 q^{49} +4.87939 q^{50} -1.51855 q^{51} -6.36263 q^{52} +0.0922684 q^{53} -7.13820 q^{54} +1.89789 q^{55} -1.00984 q^{56} -14.5673 q^{57} -6.33429 q^{58} -2.99016 q^{59} -1.00984 q^{60} -3.81583 q^{61} +3.30777 q^{62} +5.50860 q^{63} +1.00000 q^{64} +2.20972 q^{65} +15.8900 q^{66} -1.16475 q^{67} -0.522244 q^{68} -4.19581 q^{69} +0.350715 q^{70} +0.312892 q^{71} -5.45490 q^{72} +13.2325 q^{73} -14.1879 q^{75} -5.00984 q^{76} -5.51855 q^{77} +18.5008 q^{78} -9.30676 q^{79} -0.347296 q^{80} +4.39126 q^{81} +1.10049 q^{82} +9.46475 q^{83} +2.93636 q^{84} +0.181374 q^{85} -6.27037 q^{86} +18.4184 q^{87} +5.46475 q^{88} +15.7678 q^{89} +1.89447 q^{90} -6.42527 q^{91} -1.44298 q^{92} -9.61810 q^{93} +11.4382 q^{94} +1.73990 q^{95} -2.90773 q^{96} +0.929128 q^{97} +5.98021 q^{98} -29.8097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 3 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} - 3 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{11} + 3 q^{14} + 3 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 21 q^{19} + 6 q^{21} + 3 q^{22} - 21 q^{23} - 18 q^{25} - 3 q^{27} - 3 q^{28} + 6 q^{29} - 3 q^{30} - 21 q^{31} - 6 q^{32} - 3 q^{33} + 3 q^{34} + 3 q^{35} + 12 q^{36} + 21 q^{38} - 27 q^{39} + 18 q^{41} - 6 q^{42} - 18 q^{43} - 3 q^{44} - 6 q^{45} + 21 q^{46} - 9 q^{47} + 15 q^{49} + 18 q^{50} + 18 q^{53} + 3 q^{54} + 3 q^{55} + 3 q^{56} - 6 q^{57} - 6 q^{58} - 27 q^{59} + 3 q^{60} + 24 q^{61} + 21 q^{62} - 36 q^{63} + 6 q^{64} + 3 q^{65} + 3 q^{66} + 9 q^{67} - 3 q^{68} - 27 q^{69} - 3 q^{70} - 12 q^{72} + 27 q^{73} - 3 q^{75} - 21 q^{76} - 24 q^{77} + 27 q^{78} - 21 q^{79} - 6 q^{81} - 18 q^{82} + 27 q^{83} + 6 q^{84} - 3 q^{85} + 18 q^{86} + 3 q^{88} + 21 q^{89} + 6 q^{90} + 24 q^{91} - 21 q^{92} - 54 q^{93} + 9 q^{94} - 3 q^{95} - 42 q^{97} - 15 q^{98} - 36 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^11 + 3 * q^14 + 3 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 21 * q^19 + 6 * q^21 + 3 * q^22 - 21 * q^23 - 18 * q^25 - 3 * q^27 - 3 * q^28 + 6 * q^29 - 3 * q^30 - 21 * q^31 - 6 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^35 + 12 * q^36 + 21 * q^38 - 27 * q^39 + 18 * q^41 - 6 * q^42 - 18 * q^43 - 3 * q^44 - 6 * q^45 + 21 * q^46 - 9 * q^47 + 15 * q^49 + 18 * q^50 + 18 * q^53 + 3 * q^54 + 3 * q^55 + 3 * q^56 - 6 * q^57 - 6 * q^58 - 27 * q^59 + 3 * q^60 + 24 * q^61 + 21 * q^62 - 36 * q^63 + 6 * q^64 + 3 * q^65 + 3 * q^66 + 9 * q^67 - 3 * q^68 - 27 * q^69 - 3 * q^70 - 12 * q^72 + 27 * q^73 - 3 * q^75 - 21 * q^76 - 24 * q^77 + 27 * q^78 - 21 * q^79 - 6 * q^81 - 18 * q^82 + 27 * q^83 + 6 * q^84 - 3 * q^85 + 18 * q^86 + 3 * q^88 + 21 * q^89 + 6 * q^90 + 24 * q^91 - 21 * q^92 - 54 * q^93 + 9 * q^94 - 3 * q^95 - 42 * q^97 - 15 * q^98 - 36 * q^99

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