LMFDB - Embedded newform 4007.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46958 q^{2} +0.828101 q^{3} +4.09882 q^{4} -3.19925 q^{5} -2.04506 q^{6} -2.79800 q^{7} -5.18321 q^{8} -2.31425 q^{9} +O(q^{10})$	\(q-2.46958 q^{2} +0.828101 q^{3} +4.09882 q^{4} -3.19925 q^{5} -2.04506 q^{6} -2.79800 q^{7} -5.18321 q^{8} -2.31425 q^{9} +7.90080 q^{10} +0.691706 q^{11} +3.39424 q^{12} -3.72300 q^{13} +6.90988 q^{14} -2.64930 q^{15} +4.60270 q^{16} -2.82586 q^{17} +5.71522 q^{18} +7.05978 q^{19} -13.1132 q^{20} -2.31703 q^{21} -1.70822 q^{22} +3.71255 q^{23} -4.29222 q^{24} +5.23520 q^{25} +9.19424 q^{26} -4.40074 q^{27} -11.4685 q^{28} +9.10469 q^{29} +6.54266 q^{30} -4.64746 q^{31} -1.00031 q^{32} +0.572803 q^{33} +6.97869 q^{34} +8.95150 q^{35} -9.48569 q^{36} +1.32468 q^{37} -17.4347 q^{38} -3.08302 q^{39} +16.5824 q^{40} +8.56235 q^{41} +5.72208 q^{42} -1.76866 q^{43} +2.83518 q^{44} +7.40386 q^{45} -9.16844 q^{46} +6.51138 q^{47} +3.81150 q^{48} +0.828806 q^{49} -12.9288 q^{50} -2.34010 q^{51} -15.2599 q^{52} +0.560577 q^{53} +10.8680 q^{54} -2.21294 q^{55} +14.5026 q^{56} +5.84622 q^{57} -22.4848 q^{58} +5.52949 q^{59} -10.8590 q^{60} +0.0266662 q^{61} +11.4773 q^{62} +6.47527 q^{63} -6.73505 q^{64} +11.9108 q^{65} -1.41458 q^{66} -3.42907 q^{67} -11.5827 q^{68} +3.07437 q^{69} -22.1064 q^{70} +11.8136 q^{71} +11.9952 q^{72} -4.57642 q^{73} -3.27139 q^{74} +4.33528 q^{75} +28.9368 q^{76} -1.93539 q^{77} +7.61376 q^{78} +6.51702 q^{79} -14.7252 q^{80} +3.29849 q^{81} -21.1454 q^{82} -3.55093 q^{83} -9.49708 q^{84} +9.04065 q^{85} +4.36784 q^{86} +7.53961 q^{87} -3.58526 q^{88} -3.67580 q^{89} -18.2844 q^{90} +10.4170 q^{91} +15.2171 q^{92} -3.84857 q^{93} -16.0804 q^{94} -22.5860 q^{95} -0.828358 q^{96} -1.78437 q^{97} -2.04680 q^{98} -1.60078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * 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 $

$2$	−2.46958	−1.74626	−0.873128	−	0.487491i	$-0.837912\pi$
$2$	−2.46958	−1.74626	−0.873128	+	0.487491i	$0.837912\pi$
$3$	0.828101	0.478104	0.239052	−	0.971007i	$-0.423163\pi$
$3$	0.828101	0.478104	0.239052	+	0.971007i	$0.423163\pi$
$4$	4.09882	2.04941
$5$	−3.19925	−1.43075	−0.715374	−	0.698742i	$-0.753744\pi$
$5$	−3.19925	−1.43075	−0.715374	+	0.698742i	$0.753744\pi$
$6$	−2.04506	−0.834893
$7$	−2.79800	−1.05754	−0.528772	−	0.848764i	$-0.677347\pi$
$7$	−2.79800	−1.05754	−0.528772	+	0.848764i	$0.677347\pi$
$8$	−5.18321	−1.83254
$9$	−2.31425	−0.771416
$10$	7.90080	2.49845
$11$	0.691706	0.208557	0.104279	−	0.994548i	$-0.466747\pi$
$11$	0.691706	0.208557	0.104279	+	0.994548i	$0.466747\pi$
$12$	3.39424	0.979833
$13$	−3.72300	−1.03257	−0.516287	−	0.856416i	$-0.672686\pi$
$13$	−3.72300	−1.03257	−0.516287	+	0.856416i	$0.672686\pi$
$14$	6.90988	1.84674
$15$	−2.64930	−0.684047
$16$	4.60270	1.15067
$17$	−2.82586	−0.685373	−0.342686	−	0.939450i	$-0.611337\pi$
$17$	−2.82586	−0.685373	−0.342686	+	0.939450i	$0.611337\pi$
$18$	5.71522	1.34709
$19$	7.05978	1.61963	0.809813	−	0.586688i	$-0.199569\pi$
$19$	7.05978	1.61963	0.809813	+	0.586688i	$0.199569\pi$
$20$	−13.1132	−2.93219
$21$	−2.31703	−0.505617
$22$	−1.70822	−0.364194
$23$	3.71255	0.774120	0.387060	−	0.922054i	$-0.373491\pi$
$23$	3.71255	0.774120	0.387060	+	0.922054i	$0.373491\pi$
$24$	−4.29222	−0.876146
$25$	5.23520	1.04704
$26$	9.19424	1.80314
$27$	−4.40074	−0.846922
$28$	−11.4685	−2.16734
$29$	9.10469	1.69070	0.845350	−	0.534213i	$-0.179392\pi$
$29$	9.10469	1.69070	0.845350	+	0.534213i	$0.179392\pi$
$30$	6.54266	1.19452
$31$	−4.64746	−0.834708	−0.417354	−	0.908744i	$-0.637042\pi$
$31$	−4.64746	−0.834708	−0.417354	+	0.908744i	$0.637042\pi$
$32$	−1.00031	−0.176831
$33$	0.572803	0.0997122
$34$	6.97869	1.19684
$35$	8.95150	1.51308
$36$	−9.48569	−1.58095
$37$	1.32468	0.217775	0.108888	−	0.994054i	$-0.465271\pi$
$37$	1.32468	0.217775	0.108888	+	0.994054i	$0.465271\pi$
$38$	−17.4347	−2.82828
$39$	−3.08302	−0.493678
$40$	16.5824	2.62190
$41$	8.56235	1.33721	0.668607	−	0.743616i	$-0.266891\pi$
$41$	8.56235	1.33721	0.668607	+	0.743616i	$0.266891\pi$
$42$	5.72208	0.882937
$43$	−1.76866	−0.269718	−0.134859	−	0.990865i	$-0.543058\pi$
$43$	−1.76866	−0.269718	−0.134859	+	0.990865i	$0.543058\pi$
$44$	2.83518	0.427419
$45$	7.40386	1.10370
$46$	−9.16844	−1.35181
$47$	6.51138	0.949782	0.474891	−	0.880045i	$-0.342487\pi$
$47$	6.51138	0.949782	0.474891	+	0.880045i	$0.342487\pi$
$48$	3.81150	0.550142
$49$	0.828806	0.118401
$50$	−12.9288	−1.82840
$51$	−2.34010	−0.327680
$52$	−15.2599	−2.11617
$53$	0.560577	0.0770011	0.0385006	−	0.999259i	$-0.487742\pi$
$53$	0.560577	0.0770011	0.0385006	+	0.999259i	$0.487742\pi$
$54$	10.8680	1.47894
$55$	−2.21294	−0.298393
$56$	14.5026	1.93799
$57$	5.84622	0.774350
$58$	−22.4848	−2.95239
$59$	5.52949	0.719878	0.359939	−	0.932976i	$-0.382798\pi$
$59$	5.52949	0.719878	0.359939	+	0.932976i	$0.382798\pi$
$60$	−10.8590	−1.40189
$61$	0.0266662	0.00341426	0.00170713	−	0.999999i	$-0.499457\pi$
$61$	0.0266662	0.00341426	0.00170713	+	0.999999i	$0.499457\pi$
$62$	11.4773	1.45761
$63$	6.47527	0.815807
$64$	−6.73505	−0.841881
$65$	11.9108	1.47735
$66$	−1.41458	−0.174123
$67$	−3.42907	−0.418927	−0.209463	−	0.977816i	$-0.567172\pi$
$67$	−3.42907	−0.418927	−0.209463	+	0.977816i	$0.567172\pi$
$68$	−11.5827	−1.40461
$69$	3.07437	0.370110
$70$	−22.1064	−2.64223
$71$	11.8136	1.40202	0.701011	−	0.713151i	$-0.252732\pi$
$71$	11.8136	1.40202	0.701011	+	0.713151i	$0.252732\pi$
$72$	11.9952	1.41365
$73$	−4.57642	−0.535630	−0.267815	−	0.963470i	$-0.586302\pi$
$73$	−4.57642	−0.535630	−0.267815	+	0.963470i	$0.586302\pi$
$74$	−3.27139	−0.380292
$75$	4.33528	0.500595
$76$	28.9368	3.31928
$77$	−1.93539	−0.220559
$78$	7.61376	0.862089
$79$	6.51702	0.733222	0.366611	−	0.930374i	$-0.380518\pi$
$79$	6.51702	0.733222	0.366611	+	0.930374i	$0.380518\pi$
$80$	−14.7252	−1.64633
$81$	3.29849	0.366499
$82$	−21.1454	−2.33512
$83$	−3.55093	−0.389765	−0.194883	−	0.980827i	$-0.562433\pi$
$83$	−3.55093	−0.389765	−0.194883	+	0.980827i	$0.562433\pi$
$84$	−9.49708	−1.03622
$85$	9.04065	0.980596
$86$	4.36784	0.470997
$87$	7.53961	0.808331
$88$	−3.58526	−0.382190
$89$	−3.67580	−0.389634	−0.194817	−	0.980840i	$-0.562411\pi$
$89$	−3.67580	−0.389634	−0.194817	+	0.980840i	$0.562411\pi$
$90$	−18.2844	−1.92735
$91$	10.4170	1.09199
$92$	15.2171	1.58649
$93$	−3.84857	−0.399078
$94$	−16.0804	−1.65856
$95$	−22.5860	−2.31728
$96$	−0.828358	−0.0845439
$97$	−1.78437	−0.181176	−0.0905879	−	0.995888i	$-0.528875\pi$
$97$	−1.78437	−0.181176	−0.0905879	+	0.995888i	$0.528875\pi$
$98$	−2.04680	−0.206758
$99$	−1.60078	−0.160884
$100$	21.4582	2.14582
$101$	3.94967	0.393006	0.196503	−	0.980503i	$-0.437041\pi$
$101$	3.94967	0.393006	0.196503	+	0.980503i	$0.437041\pi$
$102$	5.77907	0.572213
$103$	2.12831	0.209709	0.104854	−	0.994488i	$-0.466562\pi$
$103$	2.12831	0.209709	0.104854	+	0.994488i	$0.466562\pi$
$104$	19.2971	1.89223
$105$	7.41275	0.723411
$106$	−1.38439	−0.134464
$107$	−7.68687	−0.743118	−0.371559	−	0.928409i	$-0.621177\pi$
$107$	−7.68687	−0.743118	−0.371559	+	0.928409i	$0.621177\pi$
$108$	−18.0378	−1.73569
$109$	−13.6680	−1.30916	−0.654580	−	0.755992i	$-0.727155\pi$
$109$	−13.6680	−1.30916	−0.654580	+	0.755992i	$0.727155\pi$
$110$	5.46503	0.521071
$111$	1.09697	0.104119
$112$	−12.8783	−1.21689
$113$	−13.3985	−1.26042	−0.630212	−	0.776423i	$-0.717032\pi$
$113$	−13.3985	−1.26042	−0.630212	+	0.776423i	$0.717032\pi$
$114$	−14.4377	−1.35221
$115$	−11.8774	−1.10757
$116$	37.3185	3.46494
$117$	8.61595	0.796544
$118$	−13.6555	−1.25709
$119$	7.90677	0.724812
$120$	13.7319	1.25354
$121$	−10.5215	−0.956504
$122$	−0.0658544	−0.00596218
$123$	7.09050	0.639328
$124$	−19.0491	−1.71066
$125$	−0.752478	−0.0673037
$126$	−15.9912	−1.42461
$127$	4.86863	0.432021	0.216011	−	0.976391i	$-0.430695\pi$
$127$	4.86863	0.432021	0.216011	+	0.976391i	$0.430695\pi$
$128$	18.6334	1.64697
$129$	−1.46463	−0.128953
$130$	−29.4147	−2.57984
$131$	7.20840	0.629800	0.314900	−	0.949125i	$-0.398029\pi$
$131$	7.20840	0.629800	0.314900	+	0.949125i	$0.398029\pi$
$132$	2.34782	0.204351
$133$	−19.7533	−1.71283
$134$	8.46835	0.731554
$135$	14.0791	1.21173
$136$	14.6470	1.25597
$137$	−4.99681	−0.426906	−0.213453	−	0.976953i	$-0.568471\pi$
$137$	−4.99681	−0.426906	−0.213453	+	0.976953i	$0.568471\pi$
$138$	−7.59239	−0.646307
$139$	−14.7244	−1.24891	−0.624454	−	0.781062i	$-0.714678\pi$
$139$	−14.7244	−1.24891	−0.624454	+	0.781062i	$0.714678\pi$
$140$	36.6906	3.10092
$141$	5.39208	0.454095
$142$	−29.1747	−2.44829
$143$	−2.57522	−0.215351
$144$	−10.6518	−0.887649
$145$	−29.1282	−2.41897
$146$	11.3018	0.935346
$147$	0.686335	0.0566080
$148$	5.42961	0.446311
$149$	−13.0311	−1.06755	−0.533775	−	0.845626i	$-0.679227\pi$
$149$	−13.0311	−1.06755	−0.533775	+	0.845626i	$0.679227\pi$
$150$	−10.7063	−0.874167
$151$	0.0843221	0.00686203	0.00343102	−	0.999994i	$-0.498908\pi$
$151$	0.0843221	0.00686203	0.00343102	+	0.999994i	$0.498908\pi$
$152$	−36.5923	−2.96803
$153$	6.53975	0.528707
$154$	4.77961	0.385152
$155$	14.8684	1.19426
$156$	−12.6368	−1.01175
$157$	17.0365	1.35966	0.679830	−	0.733370i	$-0.262053\pi$
$157$	17.0365	1.35966	0.679830	+	0.733370i	$0.262053\pi$
$158$	−16.0943	−1.28039
$159$	0.464214	0.0368146
$160$	3.20024	0.253001
$161$	−10.3877	−0.818667
$162$	−8.14588	−0.640001
$163$	−21.0704	−1.65036	−0.825181	−	0.564869i	$-0.808927\pi$
$163$	−21.0704	−1.65036	−0.825181	+	0.564869i	$0.808927\pi$
$164$	35.0956	2.74050
$165$	−1.83254	−0.142663
$166$	8.76931	0.680630
$167$	−16.5984	−1.28442	−0.642212	−	0.766527i	$-0.721983\pi$
$167$	−16.5984	−1.28442	−0.642212	+	0.766527i	$0.721983\pi$
$168$	12.0096	0.926563
$169$	0.860726	0.0662097
$170$	−22.3266	−1.71237
$171$	−16.3381	−1.24941
$172$	−7.24942	−0.552763
$173$	−9.17299	−0.697410	−0.348705	−	0.937233i	$-0.613378\pi$
$173$	−9.17299	−0.697410	−0.348705	+	0.937233i	$0.613378\pi$
$174$	−18.6197	−1.41155
$175$	−14.6481	−1.10729
$176$	3.18371	0.239981
$177$	4.57897	0.344177
$178$	9.07768	0.680401
$179$	2.94955	0.220460	0.110230	−	0.993906i	$-0.464841\pi$
$179$	2.94955	0.220460	0.110230	+	0.993906i	$0.464841\pi$
$180$	30.3471	2.26194
$181$	−4.10780	−0.305330	−0.152665	−	0.988278i	$-0.548786\pi$
$181$	−4.10780	−0.305330	−0.152665	+	0.988278i	$0.548786\pi$
$182$	−25.7255	−1.90690
$183$	0.0220824	0.00163237
$184$	−19.2429	−1.41861
$185$	−4.23797	−0.311582
$186$	9.50434	0.696892
$187$	−1.95467	−0.142939
$188$	26.6890	1.94649
$189$	12.3133	0.895658
$190$	55.7780	4.04656
$191$	−7.50188	−0.542817	−0.271408	−	0.962464i	$-0.587489\pi$
$191$	−7.50188	−0.542817	−0.271408	+	0.962464i	$0.587489\pi$
$192$	−5.57730	−0.402507
$193$	13.6966	0.985900	0.492950	−	0.870058i	$-0.335919\pi$
$193$	13.6966	0.985900	0.492950	+	0.870058i	$0.335919\pi$
$194$	4.40665	0.316379
$195$	9.86336	0.706330
$196$	3.39713	0.242652
$197$	18.7109	1.33310	0.666548	−	0.745462i	$-0.267771\pi$
$197$	18.7109	1.33310	0.666548	+	0.745462i	$0.267771\pi$
$198$	3.95325	0.280945
$199$	−9.81530	−0.695788	−0.347894	−	0.937534i	$-0.613103\pi$
$199$	−9.81530	−0.695788	−0.347894	+	0.937534i	$0.613103\pi$
$200$	−27.1351	−1.91874
$201$	−2.83961	−0.200291
$202$	−9.75401	−0.686290
$203$	−25.4749	−1.78799
$204$	−9.59166	−0.671550
$205$	−27.3931	−1.91322
$206$	−5.25603	−0.366205
$207$	−8.59176	−0.597169
$208$	−17.1358	−1.18816
$209$	4.88330	0.337785
$210$	−18.3064	−1.26326
$211$	1.31968	0.0908507	0.0454253	−	0.998968i	$-0.485536\pi$
$211$	1.31968	0.0908507	0.0454253	+	0.998968i	$0.485536\pi$
$212$	2.29770	0.157807
$213$	9.78289	0.670313
$214$	18.9833	1.29767
$215$	5.65838	0.385899
$216$	22.8099	1.55202
$217$	13.0036	0.882741
$218$	33.7543	2.28613
$219$	−3.78974	−0.256087
$220$	−9.07045	−0.611530
$221$	10.5207	0.707698
$222$	−2.70904	−0.181819
$223$	20.1761	1.35109	0.675546	−	0.737317i	$-0.263908\pi$
$223$	20.1761	1.35109	0.675546	+	0.737317i	$0.263908\pi$
$224$	2.79887	0.187007
$225$	−12.1156	−0.807704
$226$	33.0886	2.20102
$227$	−13.0704	−0.867514	−0.433757	−	0.901030i	$-0.642812\pi$
$227$	−13.0704	−0.867514	−0.433757	+	0.901030i	$0.642812\pi$
$228$	23.9626	1.58696
$229$	27.9868	1.84942	0.924709	−	0.380675i	$-0.124308\pi$
$229$	27.9868	1.84942	0.924709	+	0.380675i	$0.124308\pi$
$230$	29.3321	1.93410
$231$	−1.60270	−0.105450
$232$	−47.1915	−3.09827
$233$	−0.916406	−0.0600358	−0.0300179	−	0.999549i	$-0.509556\pi$
$233$	−0.916406	−0.0600358	−0.0300179	+	0.999549i	$0.509556\pi$
$234$	−21.2778	−1.39097
$235$	−20.8315	−1.35890
$236$	22.6644	1.47533
$237$	5.39675	0.350557
$238$	−19.5264	−1.26571
$239$	−7.50766	−0.485630	−0.242815	−	0.970073i	$-0.578071\pi$
$239$	−7.50766	−0.485630	−0.242815	+	0.970073i	$0.578071\pi$
$240$	−12.1939	−0.787115
$241$	14.7460	0.949876	0.474938	−	0.880019i	$-0.342470\pi$
$241$	14.7460	0.949876	0.474938	+	0.880019i	$0.342470\pi$
$242$	25.9838	1.67030
$243$	15.9337	1.02215
$244$	0.109300	0.00699723
$245$	−2.65156	−0.169402
$246$	−17.5105	−1.11643
$247$	−26.2836	−1.67238
$248$	24.0887	1.52964
$249$	−2.94053	−0.186349
$250$	1.85830	0.117529
$251$	8.60851	0.543365	0.271682	−	0.962387i	$-0.412420\pi$
$251$	8.60851	0.543365	0.271682	+	0.962387i	$0.412420\pi$
$252$	26.5410	1.67192
$253$	2.56799	0.161448
$254$	−12.0235	−0.754420
$255$	7.48657	0.468827
$256$	−32.5465	−2.03415
$257$	14.5270	0.906170	0.453085	−	0.891467i	$-0.350323\pi$
$257$	14.5270	0.906170	0.453085	+	0.891467i	$0.350323\pi$
$258$	3.61702	0.225186
$259$	−3.70644	−0.230307
$260$	48.8203	3.02771
$261$	−21.0705	−1.30423
$262$	−17.8017	−1.09979
$263$	−9.75796	−0.601702	−0.300851	−	0.953671i	$-0.597271\pi$
$263$	−9.75796	−0.601702	−0.300851	+	0.953671i	$0.597271\pi$
$264$	−2.96895	−0.182727
$265$	−1.79343	−0.110169
$266$	48.7823	2.99103
$267$	−3.04393	−0.186286
$268$	−14.0551	−0.858553
$269$	−11.5274	−0.702840	−0.351420	−	0.936218i	$-0.614301\pi$
$269$	−11.5274	−0.702840	−0.351420	+	0.936218i	$0.614301\pi$
$270$	−34.7693	−2.11600
$271$	−1.99220	−0.121017	−0.0605086	−	0.998168i	$-0.519272\pi$
$271$	−1.99220	−0.121017	−0.0605086	+	0.998168i	$0.519272\pi$
$272$	−13.0066	−0.788641
$273$	8.62629	0.522087
$274$	12.3400	0.745488
$275$	3.62122	0.218368
$276$	12.6013	0.758508
$277$	8.18283	0.491658	0.245829	−	0.969313i	$-0.420940\pi$
$277$	8.18283	0.491658	0.245829	+	0.969313i	$0.420940\pi$
$278$	36.3631	2.18091
$279$	10.7554	0.643907
$280$	−46.3975	−2.77278
$281$	28.0906	1.67575	0.837874	−	0.545864i	$-0.183799\pi$
$281$	28.0906	1.67575	0.837874	+	0.545864i	$0.183799\pi$
$282$	−13.3162	−0.792966
$283$	16.9536	1.00778	0.503892	−	0.863766i	$-0.331901\pi$
$283$	16.9536	1.00778	0.503892	+	0.863766i	$0.331901\pi$
$284$	48.4220	2.87332
$285$	−18.7035	−1.10790
$286$	6.35971	0.376058
$287$	−23.9575	−1.41416
$288$	2.31497	0.136411
$289$	−9.01449	−0.530264
$290$	71.9344	4.22413
$291$	−1.47764	−0.0866210
$292$	−18.7579	−1.09772
$293$	30.7687	1.79752	0.898762	−	0.438436i	$-0.144467\pi$
$293$	30.7687	1.79752	0.898762	+	0.438436i	$0.144467\pi$
$294$	−1.69496	−0.0988520
$295$	−17.6902	−1.02996
$296$	−6.86607	−0.399082
$297$	−3.04402	−0.176632
$298$	32.1814	1.86422
$299$	−13.8218	−0.799337
$300$	17.7695	1.02592
$301$	4.94871	0.285239
$302$	−0.208240	−0.0119829
$303$	3.27072	0.187898
$304$	32.4940	1.86366
$305$	−0.0853120	−0.00488495
$306$	−16.1504	−0.923259
$307$	−31.0057	−1.76959	−0.884795	−	0.465980i	$-0.845702\pi$
$307$	−31.0057	−1.76959	−0.884795	+	0.465980i	$0.845702\pi$
$308$	−7.93283	−0.452015
$309$	1.76246	0.100263
$310$	−36.7186	−2.08548
$311$	−25.3927	−1.43989	−0.719944	−	0.694032i	$-0.755832\pi$
$311$	−25.3927	−1.43989	−0.719944	+	0.694032i	$0.755832\pi$
$312$	15.9799	0.904686
$313$	−28.7379	−1.62436	−0.812182	−	0.583404i	$-0.801720\pi$
$313$	−28.7379	−1.62436	−0.812182	+	0.583404i	$0.801720\pi$
$314$	−42.0730	−2.37432
$315$	−20.7160	−1.16721
$316$	26.7121	1.50267
$317$	0.423503	0.0237863	0.0118931	−	0.999929i	$-0.496214\pi$
$317$	0.423503	0.0237863	0.0118931	+	0.999929i	$0.496214\pi$
$318$	−1.14641	−0.0642877
$319$	6.29777	0.352608
$320$	21.5471	1.20452
$321$	−6.36551	−0.355288
$322$	25.6533	1.42960
$323$	−19.9500	−1.11005
$324$	13.5199	0.751107
$325$	−19.4907	−1.08115
$326$	52.0350	2.88195
$327$	−11.3185	−0.625916
$328$	−44.3804	−2.45050
$329$	−18.2188	−1.00444
$330$	4.52560	0.249126
$331$	22.3709	1.22962	0.614808	−	0.788677i	$-0.289233\pi$
$331$	22.3709	1.22962	0.614808	+	0.788677i	$0.289233\pi$
$332$	−14.5546	−0.798789
$333$	−3.06563	−0.167995
$334$	40.9911	2.24293
$335$	10.9704	0.599379
$336$	−10.6646	−0.581800
$337$	29.7227	1.61910	0.809548	−	0.587053i	$-0.199712\pi$
$337$	29.7227	1.61910	0.809548	+	0.587053i	$0.199712\pi$
$338$	−2.12563	−0.115619
$339$	−11.0953	−0.602614
$340$	37.0560	2.00964
$341$	−3.21467	−0.174084
$342$	40.3482	2.18178
$343$	17.2670	0.932331
$344$	9.16733	0.494269
$345$	−9.83567	−0.529535
$346$	22.6534	1.21786
$347$	−23.7876	−1.27699	−0.638493	−	0.769628i	$-0.720442\pi$
$347$	−23.7876	−1.27699	−0.638493	+	0.769628i	$0.720442\pi$
$348$	30.9035	1.65660
$349$	1.59600	0.0854321	0.0427160	−	0.999087i	$-0.486399\pi$
$349$	1.59600	0.0854321	0.0427160	+	0.999087i	$0.486399\pi$
$350$	36.1747	1.93362
$351$	16.3839	0.874510
$352$	−0.691921	−0.0368795
$353$	34.7688	1.85055	0.925277	−	0.379291i	$-0.123832\pi$
$353$	34.7688	1.85055	0.925277	+	0.379291i	$0.123832\pi$
$354$	−11.3081	−0.601021
$355$	−37.7948	−2.00594
$356$	−15.0664	−0.798520
$357$	6.54760	0.346536
$358$	−7.28415	−0.384979
$359$	24.9042	1.31439	0.657196	−	0.753720i	$-0.271743\pi$
$359$	24.9042	1.31439	0.657196	+	0.753720i	$0.271743\pi$
$360$	−38.3757	−2.02258
$361$	30.8406	1.62319
$362$	10.1445	0.533185
$363$	−8.71290	−0.457309
$364$	42.6972	2.23794
$365$	14.6411	0.766351
$366$	−0.0545341	−0.00285054
$367$	−13.8329	−0.722073	−0.361036	−	0.932552i	$-0.617577\pi$
$367$	−13.8329	−0.722073	−0.361036	+	0.932552i	$0.617577\pi$
$368$	17.0877	0.890760
$369$	−19.8154	−1.03155
$370$	10.4660	0.544102
$371$	−1.56849	−0.0814321
$372$	−15.7746	−0.817874
$373$	−8.81886	−0.456623	−0.228312	−	0.973588i	$-0.573320\pi$
$373$	−8.81886	−0.456623	−0.228312	+	0.973588i	$0.573320\pi$
$374$	4.82721	0.249609
$375$	−0.623128	−0.0321782
$376$	−33.7498	−1.74051
$377$	−33.8968	−1.74577
$378$	−30.4086	−1.56405
$379$	−1.75805	−0.0903052	−0.0451526	−	0.998980i	$-0.514377\pi$
$379$	−1.75805	−0.0903052	−0.0451526	+	0.998980i	$0.514377\pi$
$380$	−92.5761	−4.74905
$381$	4.03172	0.206551
$382$	18.5265	0.947897
$383$	−26.6406	−1.36127	−0.680636	−	0.732622i	$-0.738296\pi$
$383$	−26.6406	−1.36127	−0.680636	+	0.732622i	$0.738296\pi$
$384$	15.4303	0.787424
$385$	6.19181	0.315564
$386$	−33.8247	−1.72163
$387$	4.09312	0.208065
$388$	−7.31383	−0.371304
$389$	−23.2497	−1.17881	−0.589404	−	0.807839i	$-0.700637\pi$
$389$	−23.2497	−1.17881	−0.589404	+	0.807839i	$0.700637\pi$
$390$	−24.3583	−1.23343
$391$	−10.4912	−0.530561
$392$	−4.29587	−0.216974
$393$	5.96928	0.301110
$394$	−46.2080	−2.32793
$395$	−20.8496	−1.04906
$396$	−6.56131	−0.329718
$397$	0.499291	0.0250587	0.0125293	−	0.999922i	$-0.496012\pi$
$397$	0.499291	0.0250587	0.0125293	+	0.999922i	$0.496012\pi$
$398$	24.2397	1.21502
$399$	−16.3577	−0.818910
$400$	24.0961	1.20480
$401$	−34.6873	−1.73220	−0.866102	−	0.499868i	$-0.833382\pi$
$401$	−34.6873	−1.73220	−0.866102	+	0.499868i	$0.833382\pi$
$402$	7.01265	0.349759
$403$	17.3025	0.861898
$404$	16.1890	0.805432
$405$	−10.5527	−0.524368
$406$	62.9124	3.12229
$407$	0.916287	0.0454186
$408$	12.1292	0.600486
$409$	−35.2345	−1.74223	−0.871117	−	0.491075i	$-0.836604\pi$
$409$	−35.2345	−1.74223	−0.871117	+	0.491075i	$0.836604\pi$
$410$	67.6495	3.34097
$411$	−4.13787	−0.204106
$412$	8.72356	0.429779
$413$	−15.4715	−0.761303
$414$	21.2180	1.04281
$415$	11.3603	0.557656
$416$	3.72415	0.182592
$417$	−12.1933	−0.597108
$418$	−12.0597	−0.589859
$419$	14.1605	0.691784	0.345892	−	0.938274i	$-0.387576\pi$
$419$	14.1605	0.691784	0.345892	+	0.938274i	$0.387576\pi$
$420$	30.3835	1.48257
$421$	32.4683	1.58241	0.791204	−	0.611552i	$-0.209454\pi$
$421$	32.4683	1.58241	0.791204	+	0.611552i	$0.209454\pi$
$422$	−3.25906	−0.158649
$423$	−15.0689	−0.732677
$424$	−2.90559	−0.141108
$425$	−14.7940	−0.717613
$426$	−24.1596	−1.17054
$427$	−0.0746122	−0.00361074
$428$	−31.5071	−1.52295
$429$	−2.13254	−0.102960
$430$	−13.9738	−0.673878
$431$	19.4421	0.936493	0.468246	−	0.883598i	$-0.344886\pi$
$431$	19.4421	0.936493	0.468246	+	0.883598i	$0.344886\pi$
$432$	−20.2553	−0.974531
$433$	−37.6748	−1.81053	−0.905267	−	0.424842i	$-0.860330\pi$
$433$	−37.6748	−1.81053	−0.905267	+	0.424842i	$0.860330\pi$
$434$	−32.1134	−1.54149
$435$	−24.1211	−1.15652
$436$	−56.0229	−2.68301
$437$	26.2098	1.25378
$438$	9.35906	0.447193
$439$	3.69508	0.176357	0.0881783	−	0.996105i	$-0.471895\pi$
$439$	3.69508	0.176357	0.0881783	+	0.996105i	$0.471895\pi$
$440$	11.4701	0.546817
$441$	−1.91806	−0.0913363
$442$	−25.9817	−1.23582
$443$	−25.5786	−1.21528	−0.607639	−	0.794214i	$-0.707883\pi$
$443$	−25.5786	−1.21528	−0.607639	+	0.794214i	$0.707883\pi$
$444$	4.49627	0.213383
$445$	11.7598	0.557468
$446$	−49.8265	−2.35935
$447$	−10.7911	−0.510401
$448$	18.8447	0.890327
$449$	2.70956	0.127872	0.0639361	−	0.997954i	$-0.479635\pi$
$449$	2.70956	0.127872	0.0639361	+	0.997954i	$0.479635\pi$
$450$	29.9203	1.41046
$451$	5.92263	0.278886
$452$	−54.9180	−2.58313
$453$	0.0698272	0.00328077
$454$	32.2784	1.51490
$455$	−33.3264	−1.56237
$456$	−30.3021	−1.41903
$457$	1.22481	0.0572943	0.0286472	−	0.999590i	$-0.490880\pi$
$457$	1.22481	0.0572943	0.0286472	+	0.999590i	$0.490880\pi$
$458$	−69.1156	−3.22956
$459$	12.4359	0.580457
$460$	−48.6833	−2.26987
$461$	1.21702	0.0566823	0.0283411	−	0.999598i	$-0.490978\pi$
$461$	1.21702	0.0566823	0.0283411	+	0.999598i	$0.490978\pi$
$462$	3.95800	0.184143
$463$	−15.1912	−0.705996	−0.352998	−	0.935624i	$-0.614838\pi$
$463$	−15.1912	−0.705996	−0.352998	+	0.935624i	$0.614838\pi$
$464$	41.9061	1.94544
$465$	12.3125	0.570980
$466$	2.26314	0.104838
$467$	−16.5369	−0.765235	−0.382617	−	0.923907i	$-0.624977\pi$
$467$	−16.5369	−0.765235	−0.382617	+	0.923907i	$0.624977\pi$
$468$	35.3152	1.63245
$469$	9.59453	0.443034
$470$	51.4451	2.37299
$471$	14.1079	0.650060
$472$	−28.6605	−1.31921
$473$	−1.22339	−0.0562517
$474$	−13.3277	−0.612162
$475$	36.9594	1.69581
$476$	32.4084	1.48544
$477$	−1.29731	−0.0593999
$478$	18.5408	0.848035
$479$	7.04189	0.321752	0.160876	−	0.986975i	$-0.448568\pi$
$479$	7.04189	0.321752	0.160876	+	0.986975i	$0.448568\pi$
$480$	2.65012	0.120961
$481$	−4.93177	−0.224869
$482$	−36.4165	−1.65873
$483$	−8.60208	−0.391408
$484$	−43.1259	−1.96027
$485$	5.70866	0.259217
$486$	−39.3495	−1.78493
$487$	13.6402	0.618095	0.309047	−	0.951047i	$-0.399990\pi$
$487$	13.6402	0.618095	0.309047	+	0.951047i	$0.399990\pi$
$488$	−0.138217	−0.00625677
$489$	−17.4484	−0.789045
$490$	6.54823	0.295819
$491$	−36.1508	−1.63146	−0.815731	−	0.578432i	$-0.803665\pi$
$491$	−36.1508	−1.63146	−0.815731	+	0.578432i	$0.803665\pi$
$492$	29.0627	1.31025
$493$	−25.7286	−1.15876
$494$	64.9094	2.92041
$495$	5.12130	0.230185
$496$	−21.3908	−0.960477
$497$	−33.0546	−1.48270
$498$	7.26187	0.325412
$499$	−38.9225	−1.74241	−0.871206	−	0.490918i	$-0.836661\pi$
$499$	−38.9225	−1.74241	−0.871206	+	0.490918i	$0.836661\pi$
$500$	−3.08427	−0.137933
$501$	−13.7452	−0.614089
$502$	−21.2594	−0.948854
$503$	−4.62911	−0.206402	−0.103201	−	0.994661i	$-0.532908\pi$
$503$	−4.62911	−0.206402	−0.103201	+	0.994661i	$0.532908\pi$
$504$	−33.5626	−1.49500
$505$	−12.6360	−0.562293
$506$	−6.34186	−0.281930
$507$	0.712768	0.0316552
$508$	19.9557	0.885389
$509$	−4.55639	−0.201958	−0.100979	−	0.994889i	$-0.532198\pi$
$509$	−4.55639	−0.201958	−0.100979	+	0.994889i	$0.532198\pi$
$510$	−18.4887	−0.818692
$511$	12.8048	0.566452
$512$	43.1093	1.90518
$513$	−31.0682	−1.37170
$514$	−35.8756	−1.58241
$515$	−6.80900	−0.300040
$516$	−6.00325	−0.264279
$517$	4.50396	0.198084
$518$	9.15336	0.402175
$519$	−7.59617	−0.333435
$520$	−61.7362	−2.70731
$521$	24.5354	1.07491	0.537457	−	0.843291i	$-0.319385\pi$
$521$	24.5354	1.07491	0.537457	+	0.843291i	$0.319385\pi$
$522$	52.0353	2.27752
$523$	−23.0112	−1.00621	−0.503104	−	0.864226i	$-0.667809\pi$
$523$	−23.0112	−1.00621	−0.503104	+	0.864226i	$0.667809\pi$
$524$	29.5459	1.29072
$525$	−12.1301	−0.529402
$526$	24.0981	1.05073
$527$	13.1331	0.572086
$528$	2.63644	0.114736
$529$	−9.21697	−0.400738
$530$	4.42901	0.192384
$531$	−12.7966	−0.555325
$532$	−80.9652	−3.51029
$533$	−31.8776	−1.38077
$534$	7.51724	0.325303
$535$	24.5922	1.06321
$536$	17.7736	0.767701
$537$	2.44253	0.105403
$538$	28.4679	1.22734
$539$	0.573290	0.0246933
$540$	57.7075	2.48334
$541$	−21.8918	−0.941200	−0.470600	−	0.882347i	$-0.655962\pi$
$541$	−21.8918	−0.941200	−0.470600	+	0.882347i	$0.655962\pi$
$542$	4.91988	0.211327
$543$	−3.40167	−0.145980
$544$	2.82674	0.121195
$545$	43.7275	1.87308
$546$	−21.3033	−0.911698
$547$	−10.6486	−0.455302	−0.227651	−	0.973743i	$-0.573104\pi$
$547$	−10.6486	−0.455302	−0.227651	+	0.973743i	$0.573104\pi$
$548$	−20.4810	−0.874907
$549$	−0.0617123	−0.00263382
$550$	−8.94290	−0.381326
$551$	64.2772	2.73830
$552$	−15.9351	−0.678242
$553$	−18.2346	−0.775415
$554$	−20.2081	−0.858562
$555$	−3.50947	−0.148969
$556$	−60.3527	−2.55952
$557$	9.84193	0.417016	0.208508	−	0.978021i	$-0.433139\pi$
$557$	9.84193	0.417016	0.208508	+	0.978021i	$0.433139\pi$
$558$	−26.5612	−1.12443
$559$	6.58472	0.278504
$560$	41.2011	1.74106
$561$	−1.61866	−0.0683400
$562$	−69.3721	−2.92628
$563$	9.32940	0.393187	0.196594	−	0.980485i	$-0.437012\pi$
$563$	9.32940	0.393187	0.196594	+	0.980485i	$0.437012\pi$
$564$	22.1012	0.930628
$565$	42.8651	1.80335
$566$	−41.8682	−1.75985
$567$	−9.22918	−0.387589
$568$	−61.2326	−2.56926
$569$	−6.58971	−0.276255	−0.138128	−	0.990414i	$-0.544108\pi$
$569$	−6.58971	−0.276255	−0.138128	+	0.990414i	$0.544108\pi$
$570$	46.1898	1.93468
$571$	−22.4006	−0.937438	−0.468719	−	0.883347i	$-0.655284\pi$
$571$	−22.4006	−0.937438	−0.468719	+	0.883347i	$0.655284\pi$
$572$	−10.5554	−0.441342
$573$	−6.21231	−0.259523
$574$	59.1649	2.46949
$575$	19.4360	0.810535
$576$	15.5866	0.649441
$577$	22.3821	0.931780	0.465890	−	0.884843i	$-0.345734\pi$
$577$	22.3821	0.931780	0.465890	+	0.884843i	$0.345734\pi$
$578$	22.2620	0.925977
$579$	11.3421	0.471363
$580$	−119.391	−4.95745
$581$	9.93551	0.412194
$582$	3.64916	0.151262
$583$	0.387754	0.0160591
$584$	23.7205	0.981563
$585$	−27.5646	−1.13965
$586$	−75.9857	−3.13894
$587$	−8.76021	−0.361572	−0.180786	−	0.983522i	$-0.557864\pi$
$587$	−8.76021	−0.361572	−0.180786	+	0.983522i	$0.557864\pi$
$588$	2.81316	0.116013
$589$	−32.8100	−1.35191
$590$	43.6874	1.79858
$591$	15.4945	0.637359
$592$	6.09708	0.250589
$593$	−26.8963	−1.10450	−0.552248	−	0.833680i	$-0.686230\pi$
$593$	−26.8963	−1.10450	−0.552248	+	0.833680i	$0.686230\pi$
$594$	7.51744	0.308444
$595$	−25.2957	−1.03702
$596$	−53.4122	−2.18785
$597$	−8.12806	−0.332659
$598$	34.1341	1.39585
$599$	4.89583	0.200038	0.100019	−	0.994986i	$-0.468110\pi$
$599$	4.89583	0.200038	0.100019	+	0.994986i	$0.468110\pi$
$600$	−22.4706	−0.917360
$601$	9.59868	0.391538	0.195769	−	0.980650i	$-0.437280\pi$
$601$	9.59868	0.391538	0.195769	+	0.980650i	$0.437280\pi$
$602$	−12.2212	−0.498100
$603$	7.93571	0.323167
$604$	0.345621	0.0140631
$605$	33.6611	1.36852
$606$	−8.07731	−0.328118
$607$	−2.57042	−0.104330	−0.0521652	−	0.998638i	$-0.516612\pi$
$607$	−2.57042	−0.104330	−0.0521652	+	0.998638i	$0.516612\pi$
$608$	−7.06197	−0.286401
$609$	−21.0958	−0.854846
$610$	0.210685	0.00853038
$611$	−24.2419	−0.980721
$612$	26.8053	1.08354
$613$	11.2272	0.453461	0.226730	−	0.973958i	$-0.427196\pi$
$613$	11.2272	0.453461	0.226730	+	0.973958i	$0.427196\pi$
$614$	76.5711	3.09016
$615$	−22.6843	−0.914718
$616$	10.0315	0.404183
$617$	20.7774	0.836468	0.418234	−	0.908339i	$-0.362649\pi$
$617$	20.7774	0.836468	0.418234	+	0.908339i	$0.362649\pi$
$618$	−4.35252	−0.175084
$619$	12.8422	0.516173	0.258086	−	0.966122i	$-0.416908\pi$
$619$	12.8422	0.516173	0.258086	+	0.966122i	$0.416908\pi$
$620$	60.9428	2.44752
$621$	−16.3380	−0.655619
$622$	62.7093	2.51441
$623$	10.2849	0.412055
$624$	−14.1902	−0.568063
$625$	−23.7687	−0.950746
$626$	70.9706	2.83656
$627$	4.04386	0.161496
$628$	69.8296	2.78650
$629$	−3.74335	−0.149257
$630$	51.1598	2.03826
$631$	−34.3899	−1.36904	−0.684520	−	0.728994i	$-0.739988\pi$
$631$	−34.3899	−1.36904	−0.684520	+	0.728994i	$0.739988\pi$
$632$	−33.7791	−1.34366
$633$	1.09283	0.0434361
$634$	−1.04587	−0.0415370
$635$	−15.5760	−0.618114
$636$	1.90273	0.0754482
$637$	−3.08564	−0.122258
$638$	−15.5528	−0.615743
$639$	−27.3397	−1.08154
$640$	−59.6128	−2.35640
$641$	8.61805	0.340393	0.170196	−	0.985410i	$-0.445560\pi$
$641$	8.61805	0.340393	0.170196	+	0.985410i	$0.445560\pi$
$642$	15.7201	0.620424
$643$	−39.8460	−1.57137	−0.785686	−	0.618626i	$-0.787690\pi$
$643$	−39.8460	−1.57137	−0.785686	+	0.618626i	$0.787690\pi$
$644$	−42.5774	−1.67778
$645$	4.68572	0.184500
$646$	49.2681	1.93843
$647$	20.5864	0.809334	0.404667	−	0.914464i	$-0.367387\pi$
$647$	20.5864	0.809334	0.404667	+	0.914464i	$0.367387\pi$
$648$	−17.0968	−0.671624
$649$	3.82478	0.150136
$650$	48.1337	1.88796
$651$	10.7683	0.422042
$652$	−86.3638	−3.38227
$653$	14.6269	0.572396	0.286198	−	0.958170i	$-0.407608\pi$
$653$	14.6269	0.572396	0.286198	+	0.958170i	$0.407608\pi$
$654$	27.9520	1.09301
$655$	−23.0615	−0.901086
$656$	39.4099	1.53870
$657$	10.5910	0.413193
$658$	44.9929	1.75400
$659$	−14.1419	−0.550891	−0.275446	−	0.961317i	$-0.588825\pi$
$659$	−14.1419	−0.550891	−0.275446	+	0.961317i	$0.588825\pi$
$660$	−7.51125	−0.292375
$661$	11.0993	0.431711	0.215856	−	0.976425i	$-0.430746\pi$
$661$	11.0993	0.431711	0.215856	+	0.976425i	$0.430746\pi$
$662$	−55.2467	−2.14723
$663$	8.71220	0.338354
$664$	18.4052	0.714261
$665$	63.1957	2.45062
$666$	7.57081	0.293363
$667$	33.8016	1.30880
$668$	−68.0339	−2.63231
$669$	16.7079	0.645964
$670$	−27.0924	−1.04667
$671$	0.0184452	0.000712069 0
$672$	2.31775	0.0894090
$673$	−34.5710	−1.33261	−0.666306	−	0.745678i	$-0.732126\pi$
$673$	−34.5710	−1.33261	−0.666306	+	0.745678i	$0.732126\pi$
$674$	−73.4025	−2.82736
$675$	−23.0388	−0.886762
$676$	3.52796	0.135691
$677$	−9.50775	−0.365412	−0.182706	−	0.983168i	$-0.558486\pi$
$677$	−9.50775	−0.365412	−0.182706	+	0.983168i	$0.558486\pi$
$678$	27.4007	1.05232
$679$	4.99268	0.191602
$680$	−46.8595	−1.79698
$681$	−10.8236	−0.414762
$682$	7.93889	0.303996
$683$	14.9435	0.571797	0.285898	−	0.958260i	$-0.407708\pi$
$683$	14.9435	0.571797	0.285898	+	0.958260i	$0.407708\pi$
$684$	−66.9669	−2.56054
$685$	15.9861	0.610796
$686$	−42.6422	−1.62809
$687$	23.1759	0.884215
$688$	−8.14060	−0.310358
$689$	−2.08703	−0.0795094
$690$	24.2900	0.924703
$691$	21.0409	0.800432	0.400216	−	0.916421i	$-0.368935\pi$
$691$	21.0409	0.800432	0.400216	+	0.916421i	$0.368935\pi$
$692$	−37.5985	−1.42928
$693$	4.47898	0.170142
$694$	58.7454	2.22995
$695$	47.1070	1.78687
$696$	−39.0794	−1.48130
$697$	−24.1960	−0.916491
$698$	−3.94146	−0.149186
$699$	−0.758877	−0.0287034
$700$	−60.0400	−2.26930
$701$	−11.6837	−0.441287	−0.220643	−	0.975355i	$-0.570816\pi$
$701$	−11.6837	−0.441287	−0.220643	+	0.975355i	$0.570816\pi$
$702$	−40.4614	−1.52712
$703$	9.35193	0.352715
$704$	−4.65867	−0.175580
$705$	−17.2506	−0.649696
$706$	−85.8642	−3.23154
$707$	−11.0512	−0.415622
$708$	18.7684	0.705360
$709$	14.9808	0.562617	0.281308	−	0.959617i	$-0.409232\pi$
$709$	14.9808	0.562617	0.281308	+	0.959617i	$0.409232\pi$
$710$	93.3373	3.50289
$711$	−15.0820	−0.565620
$712$	19.0524	0.714020
$713$	−17.2539	−0.646164
$714$	−16.1698	−0.605141
$715$	8.23878	0.308113
$716$	12.0897	0.451813
$717$	−6.21710	−0.232182
$718$	−61.5028	−2.29526
$719$	−11.0264	−0.411215	−0.205608	−	0.978634i	$-0.565917\pi$
$719$	−11.0264	−0.411215	−0.205608	+	0.978634i	$0.565917\pi$
$720$	34.0777	1.27000
$721$	−5.95501	−0.221776
$722$	−76.1632	−2.83450
$723$	12.2112	0.454140
$724$	−16.8371	−0.625747
$725$	47.6649	1.77023
$726$	21.5172	0.798578
$727$	48.0519	1.78215	0.891073	−	0.453860i	$-0.149953\pi$
$727$	48.0519	1.78215	0.891073	+	0.453860i	$0.149953\pi$
$728$	−53.9932	−2.00112
$729$	3.29924	0.122194
$730$	−36.1574	−1.33825
$731$	4.99799	0.184857
$732$	0.0905116	0.00334541
$733$	−29.0292	−1.07222	−0.536109	−	0.844148i	$-0.680107\pi$
$733$	−29.0292	−1.07222	−0.536109	+	0.844148i	$0.680107\pi$
$734$	34.1615	1.26092
$735$	−2.19576	−0.0809917
$736$	−3.71370	−0.136889
$737$	−2.37191	−0.0873703
$738$	48.9357	1.80135
$739$	−35.1820	−1.29419	−0.647096	−	0.762409i	$-0.724017\pi$
$739$	−35.1820	−1.29419	−0.647096	+	0.762409i	$0.724017\pi$
$740$	−17.3707	−0.638559
$741$	−21.7655	−0.799574
$742$	3.87352	0.142201
$743$	−8.63616	−0.316830	−0.158415	−	0.987373i	$-0.550638\pi$
$743$	−8.63616	−0.316830	−0.158415	+	0.987373i	$0.550638\pi$
$744$	19.9479	0.731326
$745$	41.6898	1.52740
$746$	21.7789	0.797381
$747$	8.21774	0.300671
$748$	−8.01183	−0.292942
$749$	21.5079	0.785880
$750$	1.53886	0.0561913
$751$	−32.8541	−1.19886	−0.599432	−	0.800426i	$-0.704607\pi$
$751$	−32.8541	−1.19886	−0.599432	+	0.800426i	$0.704607\pi$
$752$	29.9699	1.09289
$753$	7.12872	0.259785
$754$	83.7108	3.04857
$755$	−0.269767	−0.00981784
$756$	50.4699	1.83557
$757$	−23.2337	−0.844444	−0.422222	−	0.906493i	$-0.638750\pi$
$757$	−23.2337	−0.844444	−0.422222	+	0.906493i	$0.638750\pi$
$758$	4.34166	0.157696
$759$	2.12656	0.0771892
$760$	117.068	4.24650
$761$	34.6083	1.25455	0.627276	−	0.778797i	$-0.284170\pi$
$761$	34.6083	1.25455	0.627276	+	0.778797i	$0.284170\pi$
$762$	−9.95666	−0.360692
$763$	38.2432	1.38450
$764$	−30.7489	−1.11245
$765$	−20.9223	−0.756447
$766$	65.7911	2.37713
$767$	−20.5863	−0.743327
$768$	−26.9518	−0.972538
$769$	21.2802	0.767383	0.383692	−	0.923461i	$-0.374653\pi$
$769$	21.2802	0.767383	0.383692	+	0.923461i	$0.374653\pi$
$770$	−15.2912	−0.551055
$771$	12.0298	0.433244
$772$	56.1397	2.02051
$773$	−16.0759	−0.578212	−0.289106	−	0.957297i	$-0.593358\pi$
$773$	−16.0759	−0.578212	−0.289106	+	0.957297i	$0.593358\pi$
$774$	−10.1083	−0.363335
$775$	−24.3304	−0.873973
$776$	9.24878	0.332012
$777$	−3.06931	−0.110111
$778$	57.4170	2.05850
$779$	60.4484	2.16579
$780$	40.4281	1.44756
$781$	8.17157	0.292402
$782$	25.9088	0.926495
$783$	−40.0674	−1.43189
$784$	3.81474	0.136241
$785$	−54.5040	−1.94533
$786$	−14.7416	−0.525816
$787$	28.2571	1.00726	0.503629	−	0.863920i	$-0.331998\pi$
$787$	28.2571	1.00726	0.503629	+	0.863920i	$0.331998\pi$
$788$	76.6926	2.73206
$789$	−8.08058	−0.287676
$790$	51.4897	1.83192
$791$	37.4890	1.33295
$792$	8.29717	0.294827
$793$	−0.0992784	−0.00352548
$794$	−1.23304	−0.0437589
$795$	−1.48514	−0.0526724
$796$	−40.2312	−1.42596
$797$	18.7268	0.663337	0.331669	−	0.943396i	$-0.392388\pi$
$797$	18.7268	0.663337	0.331669	+	0.943396i	$0.392388\pi$
$798$	40.3967	1.43003
$799$	−18.4003	−0.650955
$800$	−5.23683	−0.185150
$801$	8.50671	0.300570
$802$	85.6632	3.02487
$803$	−3.16554	−0.111709
$804$	−11.6391	−0.410478
$805$	33.2329	1.17131
$806$	−42.7299	−1.50509
$807$	−9.54588	−0.336031
$808$	−20.4719	−0.720200
$809$	23.1653	0.814450	0.407225	−	0.913328i	$-0.366497\pi$
$809$	23.1653	0.814450	0.407225	+	0.913328i	$0.366497\pi$
$810$	26.0607	0.915680
$811$	−28.6937	−1.00757	−0.503785	−	0.863829i	$-0.668060\pi$
$811$	−28.6937	−1.00757	−0.503785	+	0.863829i	$0.668060\pi$
$812$	−104.417	−3.66433
$813$	−1.64974	−0.0578589
$814$	−2.26284	−0.0793126
$815$	67.4095	2.36125
$816$	−10.7708	−0.377053
$817$	−12.4864	−0.436842
$818$	87.0144	3.04239
$819$	−24.1074	−0.842381
$820$	−112.279	−3.92097
$821$	−48.3536	−1.68755	−0.843775	−	0.536696i	$-0.819672\pi$
$821$	−48.3536	−1.68755	−0.843775	+	0.536696i	$0.819672\pi$
$822$	10.2188	0.356421
$823$	−16.5704	−0.577609	−0.288805	−	0.957388i	$-0.593258\pi$
$823$	−16.5704	−0.577609	−0.288805	+	0.957388i	$0.593258\pi$
$824$	−11.0315	−0.384299
$825$	2.99874	0.104403
$826$	38.2081	1.32943
$827$	−0.254194	−0.00883919	−0.00441960	−	0.999990i	$-0.501407\pi$
$827$	−0.254194	−0.00883919	−0.00441960	+	0.999990i	$0.501407\pi$
$828$	−35.2161	−1.22384
$829$	−10.0788	−0.350050	−0.175025	−	0.984564i	$-0.556001\pi$
$829$	−10.0788	−0.350050	−0.175025	+	0.984564i	$0.556001\pi$
$830$	−28.0552	−0.973811
$831$	6.77621	0.235064
$832$	25.0746	0.869305
$833$	−2.34209	−0.0811487
$834$	30.1123	1.04270
$835$	53.1025	1.83769
$836$	20.0158	0.692260
$837$	20.4522	0.706933
$838$	−34.9704	−1.20803
$839$	8.31888	0.287200	0.143600	−	0.989636i	$-0.454132\pi$
$839$	8.31888	0.287200	0.143600	+	0.989636i	$0.454132\pi$
$840$	−38.4218	−1.32568
$841$	53.8955	1.85846
$842$	−80.1831	−2.76329
$843$	23.2619	0.801182
$844$	5.40914	0.186190
$845$	−2.75368	−0.0947294
$846$	37.2140	1.27944
$847$	29.4393	1.01155
$848$	2.58016	0.0886032
$849$	14.0393	0.481826
$850$	36.5349	1.25314
$851$	4.91793	0.168584
$852$	40.0983	1.37375
$853$	13.2939	0.455174	0.227587	−	0.973758i	$-0.426916\pi$
$853$	13.2939	0.455174	0.227587	+	0.973758i	$0.426916\pi$
$854$	0.184261	0.00630527
$855$	52.2697	1.78758
$856$	39.8426	1.36179
$857$	24.5943	0.840125	0.420063	−	0.907495i	$-0.362008\pi$
$857$	24.5943	0.840125	0.420063	+	0.907495i	$0.362008\pi$
$858$	5.26649	0.179795
$859$	5.51762	0.188259	0.0941294	−	0.995560i	$-0.469993\pi$
$859$	5.51762	0.188259	0.0941294	+	0.995560i	$0.469993\pi$
$860$	23.1927	0.790865
$861$	−19.8392	−0.676118
$862$	−48.0138	−1.63536
$863$	54.1575	1.84354	0.921771	−	0.387734i	$-0.126742\pi$
$863$	54.1575	1.84354	0.921771	+	0.387734i	$0.126742\pi$
$864$	4.40210	0.149762
$865$	29.3467	0.997818
$866$	93.0409	3.16166
$867$	−7.46491	−0.253522
$868$	53.2994	1.80910
$869$	4.50786	0.152919
$870$	59.5690	2.01958
$871$	12.7664	0.432573
$872$	70.8443	2.39909
$873$	4.12949	0.139762
$874$	−64.7272	−2.18943
$875$	2.10543	0.0711766
$876$	−15.5335	−0.524827
$877$	−43.3424	−1.46357	−0.731784	−	0.681536i	$-0.761312\pi$
$877$	−43.3424	−1.46357	−0.731784	+	0.681536i	$0.761312\pi$
$878$	−9.12529	−0.307964
$879$	25.4796	0.859405
$880$	−10.1855	−0.343353
$881$	54.3858	1.83230	0.916152	−	0.400832i	$-0.131279\pi$
$881$	54.3858	1.83230	0.916152	+	0.400832i	$0.131279\pi$
$882$	4.73681	0.159497
$883$	0.0287618	0.000967911 0	0.000483955	−	1.00000i	$-0.499846\pi$
$883$	0.0287618	0.000967911 0	0.000483955		1.00000i	$0.499846\pi$
$884$	43.1224	1.45036
$885$	−14.6493	−0.492430
$886$	63.1684	2.12219
$887$	−16.6600	−0.559386	−0.279693	−	0.960089i	$-0.590233\pi$
$887$	−16.6600	−0.559386	−0.279693	+	0.960089i	$0.590233\pi$
$888$	−5.68580	−0.190803
$889$	−13.6224	−0.456882
$890$	−29.0418	−0.973482
$891$	2.28159	0.0764360
$892$	82.6983	2.76894
$893$	45.9689	1.53829
$894$	26.6494	0.891290
$895$	−9.43636	−0.315423
$896$	−52.1361	−1.74175
$897$	−11.4459	−0.382166
$898$	−6.69148	−0.223298
$899$	−42.3137	−1.41124
$900$	−49.6595	−1.65532
$901$	−1.58411	−0.0527745
$902$	−14.6264	−0.487006
$903$	4.09803	0.136374
$904$	69.4472	2.30978
$905$	13.1419	0.436851
$906$	−0.172444	−0.00572906
$907$	40.8779	1.35733	0.678664	−	0.734449i	$-0.262559\pi$
$907$	40.8779	1.35733	0.678664	+	0.734449i	$0.262559\pi$
$908$	−53.5733	−1.77789
$909$	−9.14051	−0.303172
$910$	82.3023	2.72829
$911$	13.3539	0.442434	0.221217	−	0.975225i	$-0.428997\pi$
$911$	13.3539	0.442434	0.221217	+	0.975225i	$0.428997\pi$
$912$	26.9084	0.891025
$913$	−2.45620	−0.0812884
$914$	−3.02477	−0.100051
$915$	−0.0706470	−0.00233552
$916$	114.713	3.79022
$917$	−20.1691	−0.666042
$918$	−30.7114	−1.01363
$919$	−23.3104	−0.768939	−0.384469	−	0.923138i	$-0.625616\pi$
$919$	−23.3104	−0.768939	−0.384469	+	0.923138i	$0.625616\pi$
$920$	61.5629	2.02967
$921$	−25.6759	−0.846049
$922$	−3.00553	−0.0989818
$923$	−43.9822	−1.44769
$924$	−6.56919	−0.216111
$925$	6.93495	0.228020
$926$	37.5159	1.23285
$927$	−4.92544	−0.161773
$928$	−9.10752	−0.298969
$929$	−6.90064	−0.226403	−0.113201	−	0.993572i	$-0.536110\pi$
$929$	−6.90064	−0.226403	−0.113201	+	0.993572i	$0.536110\pi$
$930$	−30.4068	−0.997077
$931$	5.85119	0.191765
$932$	−3.75619	−0.123038
$933$	−21.0277	−0.688417
$934$	40.8391	1.33630
$935$	6.25347	0.204510
$936$	−44.6582	−1.45970
$937$	−20.4366	−0.667636	−0.333818	−	0.942638i	$-0.608337\pi$
$937$	−20.4366	−0.667636	−0.333818	+	0.942638i	$0.608337\pi$
$938$	−23.6944	−0.773651
$939$	−23.7979	−0.776616
$940$	−85.3847	−2.78494
$941$	11.2863	0.367923	0.183961	−	0.982933i	$-0.441108\pi$
$941$	11.2863	0.367923	0.183961	+	0.982933i	$0.441108\pi$
$942$	−34.8407	−1.13517
$943$	31.7882	1.03517
$944$	25.4505	0.828345
$945$	−39.3932	−1.28146
$946$	3.02126	0.0982298
$947$	−51.9121	−1.68692	−0.843459	−	0.537194i	$-0.819484\pi$
$947$	−51.9121	−1.68692	−0.843459	+	0.537194i	$0.819484\pi$
$948$	22.1203	0.718435
$949$	17.0380	0.553077
$950$	−91.2742	−2.96133
$951$	0.350703	0.0113723
$952$	−40.9824	−1.32825
$953$	−44.8806	−1.45383	−0.726913	−	0.686730i	$-0.759046\pi$
$953$	−44.8806	−1.45383	−0.726913	+	0.686730i	$0.759046\pi$
$954$	3.20382	0.103727
$955$	24.0004	0.776634
$956$	−30.7726	−0.995256
$957$	5.21519	0.168583
$958$	−17.3905	−0.561862
$959$	13.9811	0.451473
$960$	17.8432	0.575886
$961$	−9.40114	−0.303262
$962$	12.1794	0.392679
$963$	17.7893	0.573253
$964$	60.4414	1.94669
$965$	−43.8187	−1.41057
$966$	21.2435	0.683499
$967$	19.7941	0.636534	0.318267	−	0.948001i	$-0.396899\pi$
$967$	19.7941	0.636534	0.318267	+	0.948001i	$0.396899\pi$
$968$	54.5353	1.75283
$969$	−16.5206	−0.530718
$970$	−14.0980	−0.452659
$971$	10.4742	0.336132	0.168066	−	0.985776i	$-0.446248\pi$
$971$	10.4742	0.336132	0.168066	+	0.985776i	$0.446248\pi$
$972$	65.3094	2.09480
$973$	41.1989	1.32078
$974$	−33.6855	−1.07935
$975$	−16.1402	−0.516901
$976$	0.122737	0.00392870
$977$	−50.2806	−1.60862	−0.804310	−	0.594210i	$-0.797465\pi$
$977$	−50.2806	−1.60862	−0.804310	+	0.594210i	$0.797465\pi$
$978$	43.0903	1.37788
$979$	−2.54257	−0.0812610
$980$	−10.8683	−0.347174
$981$	31.6312	1.00991
$982$	89.2772	2.84895
$983$	50.3729	1.60665	0.803324	−	0.595543i	$-0.203063\pi$
$983$	50.3729	1.60665	0.803324	+	0.595543i	$0.203063\pi$
$984$	−36.7515	−1.17160
$985$	−59.8608	−1.90732
$986$	63.5389	2.02349
$987$	−15.0870	−0.480226
$988$	−107.732	−3.42740
$989$	−6.56624	−0.208794
$990$	−12.6474	−0.401962
$991$	20.0430	0.636686	0.318343	−	0.947976i	$-0.396874\pi$
$991$	20.0430	0.636686	0.318343	+	0.947976i	$0.396874\pi$
$992$	4.64890	0.147603
$993$	18.5254	0.587885
$994$	81.6309	2.58917
$995$	31.4016	0.995498
$996$	−12.0527	−0.381905
$997$	−57.6033	−1.82432	−0.912158	−	0.409839i	$-0.865585\pi$
$997$	−57.6033	−1.82432	−0.912158	+	0.409839i	$0.865585\pi$
$998$	96.1223	3.04270
$999$	−5.82955	−0.184439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.11	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.11	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46958 q^{2} +0.828101 q^{3} +4.09882 q^{4} -3.19925 q^{5} -2.04506 q^{6} -2.79800 q^{7} -5.18321 q^{8} -2.31425 q^{9} +O(q^{10})\)	\(q-2.46958 q^{2} +0.828101 q^{3} +4.09882 q^{4} -3.19925 q^{5} -2.04506 q^{6} -2.79800 q^{7} -5.18321 q^{8} -2.31425 q^{9} +7.90080 q^{10} +0.691706 q^{11} +3.39424 q^{12} -3.72300 q^{13} +6.90988 q^{14} -2.64930 q^{15} +4.60270 q^{16} -2.82586 q^{17} +5.71522 q^{18} +7.05978 q^{19} -13.1132 q^{20} -2.31703 q^{21} -1.70822 q^{22} +3.71255 q^{23} -4.29222 q^{24} +5.23520 q^{25} +9.19424 q^{26} -4.40074 q^{27} -11.4685 q^{28} +9.10469 q^{29} +6.54266 q^{30} -4.64746 q^{31} -1.00031 q^{32} +0.572803 q^{33} +6.97869 q^{34} +8.95150 q^{35} -9.48569 q^{36} +1.32468 q^{37} -17.4347 q^{38} -3.08302 q^{39} +16.5824 q^{40} +8.56235 q^{41} +5.72208 q^{42} -1.76866 q^{43} +2.83518 q^{44} +7.40386 q^{45} -9.16844 q^{46} +6.51138 q^{47} +3.81150 q^{48} +0.828806 q^{49} -12.9288 q^{50} -2.34010 q^{51} -15.2599 q^{52} +0.560577 q^{53} +10.8680 q^{54} -2.21294 q^{55} +14.5026 q^{56} +5.84622 q^{57} -22.4848 q^{58} +5.52949 q^{59} -10.8590 q^{60} +0.0266662 q^{61} +11.4773 q^{62} +6.47527 q^{63} -6.73505 q^{64} +11.9108 q^{65} -1.41458 q^{66} -3.42907 q^{67} -11.5827 q^{68} +3.07437 q^{69} -22.1064 q^{70} +11.8136 q^{71} +11.9952 q^{72} -4.57642 q^{73} -3.27139 q^{74} +4.33528 q^{75} +28.9368 q^{76} -1.93539 q^{77} +7.61376 q^{78} +6.51702 q^{79} -14.7252 q^{80} +3.29849 q^{81} -21.1454 q^{82} -3.55093 q^{83} -9.49708 q^{84} +9.04065 q^{85} +4.36784 q^{86} +7.53961 q^{87} -3.58526 q^{88} -3.67580 q^{89} -18.2844 q^{90} +10.4170 q^{91} +15.2171 q^{92} -3.84857 q^{93} -16.0804 q^{94} -22.5860 q^{95} -0.828358 q^{96} -1.78437 q^{97} -2.04680 q^{98} -1.60078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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