LMFDB - Embedded newform 6005.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49553 q^{2} -3.37079 q^{3} +4.22769 q^{4} -1.00000 q^{5} +8.41191 q^{6} -2.54255 q^{7} -5.55927 q^{8} +8.36220 q^{9} +O(q^{10})$	\(q-2.49553 q^{2} -3.37079 q^{3} +4.22769 q^{4} -1.00000 q^{5} +8.41191 q^{6} -2.54255 q^{7} -5.55927 q^{8} +8.36220 q^{9} +2.49553 q^{10} +2.76883 q^{11} -14.2506 q^{12} +2.63137 q^{13} +6.34503 q^{14} +3.37079 q^{15} +5.41797 q^{16} -6.32712 q^{17} -20.8682 q^{18} -2.54178 q^{19} -4.22769 q^{20} +8.57041 q^{21} -6.90970 q^{22} +2.38647 q^{23} +18.7391 q^{24} +1.00000 q^{25} -6.56666 q^{26} -18.0748 q^{27} -10.7491 q^{28} -5.08410 q^{29} -8.41191 q^{30} +6.70873 q^{31} -2.40219 q^{32} -9.33312 q^{33} +15.7895 q^{34} +2.54255 q^{35} +35.3528 q^{36} -2.20483 q^{37} +6.34309 q^{38} -8.86977 q^{39} +5.55927 q^{40} -0.311506 q^{41} -21.3877 q^{42} +1.74635 q^{43} +11.7057 q^{44} -8.36220 q^{45} -5.95551 q^{46} +6.34335 q^{47} -18.2628 q^{48} -0.535416 q^{49} -2.49553 q^{50} +21.3274 q^{51} +11.1246 q^{52} +13.7921 q^{53} +45.1064 q^{54} -2.76883 q^{55} +14.1348 q^{56} +8.56778 q^{57} +12.6875 q^{58} -8.36864 q^{59} +14.2506 q^{60} +10.9900 q^{61} -16.7419 q^{62} -21.2614 q^{63} -4.84120 q^{64} -2.63137 q^{65} +23.2911 q^{66} +15.4877 q^{67} -26.7491 q^{68} -8.04428 q^{69} -6.34503 q^{70} -1.49881 q^{71} -46.4878 q^{72} -12.6663 q^{73} +5.50224 q^{74} -3.37079 q^{75} -10.7458 q^{76} -7.03989 q^{77} +22.1348 q^{78} +12.7944 q^{79} -5.41797 q^{80} +35.8398 q^{81} +0.777375 q^{82} +11.5499 q^{83} +36.2330 q^{84} +6.32712 q^{85} -4.35809 q^{86} +17.1374 q^{87} -15.3927 q^{88} -18.3789 q^{89} +20.8682 q^{90} -6.69039 q^{91} +10.0892 q^{92} -22.6137 q^{93} -15.8300 q^{94} +2.54178 q^{95} +8.09727 q^{96} +11.9251 q^{97} +1.33615 q^{98} +23.1535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.49553	−1.76461	−0.882304	−	0.470679i	$-0.844009\pi$
$2$	−2.49553	−1.76461	−0.882304	+	0.470679i	$0.844009\pi$
$3$	−3.37079	−1.94612	−0.973062	−	0.230543i	$-0.925950\pi$
$3$	−3.37079	−1.94612	−0.973062	+	0.230543i	$0.925950\pi$
$4$	4.22769	2.11384
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	8.41191	3.43415
$7$	−2.54255	−0.960995	−0.480498	−	0.876996i	$-0.659544\pi$
$7$	−2.54255	−0.960995	−0.480498	+	0.876996i	$0.659544\pi$
$8$	−5.55927	−1.96550
$9$	8.36220	2.78740
$10$	2.49553	0.789157
$11$	2.76883	0.834833	0.417416	−	0.908715i	$-0.362936\pi$
$11$	2.76883	0.834833	0.417416	+	0.908715i	$0.362936\pi$
$12$	−14.2506	−4.11380
$13$	2.63137	0.729810	0.364905	−	0.931045i	$-0.381102\pi$
$13$	2.63137	0.729810	0.364905	+	0.931045i	$0.381102\pi$
$14$	6.34503	1.69578
$15$	3.37079	0.870333
$16$	5.41797	1.35449
$17$	−6.32712	−1.53455	−0.767276	−	0.641317i	$-0.778388\pi$
$17$	−6.32712	−1.53455	−0.767276	+	0.641317i	$0.778388\pi$
$18$	−20.8682	−4.91867
$19$	−2.54178	−0.583123	−0.291562	−	0.956552i	$-0.594175\pi$
$19$	−2.54178	−0.583123	−0.291562	+	0.956552i	$0.594175\pi$
$20$	−4.22769	−0.945340
$21$	8.57041	1.87022
$22$	−6.90970	−1.47315
$23$	2.38647	0.497613	0.248807	−	0.968553i	$-0.419962\pi$
$23$	2.38647	0.497613	0.248807	+	0.968553i	$0.419962\pi$
$24$	18.7391	3.82511
$25$	1.00000	0.200000
$26$	−6.56666	−1.28783
$27$	−18.0748	−3.47850
$28$	−10.7491	−2.03139
$29$	−5.08410	−0.944094	−0.472047	−	0.881573i	$-0.656485\pi$
$29$	−5.08410	−0.944094	−0.472047	+	0.881573i	$0.656485\pi$
$30$	−8.41191	−1.53580
$31$	6.70873	1.20492	0.602461	−	0.798148i	$-0.294187\pi$
$31$	6.70873	1.20492	0.602461	+	0.798148i	$0.294187\pi$
$32$	−2.40219	−0.424651
$33$	−9.33312	−1.62469
$34$	15.7895	2.70788
$35$	2.54255	0.429770
$36$	35.3528	5.89213
$37$	−2.20483	−0.362473	−0.181236	−	0.983440i	$-0.558010\pi$
$37$	−2.20483	−0.362473	−0.181236	+	0.983440i	$0.558010\pi$
$38$	6.34309	1.02898
$39$	−8.86977	−1.42030
$40$	5.55927	0.878998
$41$	−0.311506	−0.0486491	−0.0243246	−	0.999704i	$-0.507744\pi$
$41$	−0.311506	−0.0486491	−0.0243246	+	0.999704i	$0.507744\pi$
$42$	−21.3877	−3.30020
$43$	1.74635	0.266317	0.133158	−	0.991095i	$-0.457488\pi$
$43$	1.74635	0.266317	0.133158	+	0.991095i	$0.457488\pi$
$44$	11.7057	1.76471
$45$	−8.36220	−1.24656
$46$	−5.95551	−0.878092
$47$	6.34335	0.925273	0.462636	−	0.886548i	$-0.346904\pi$
$47$	6.34335	0.925273	0.462636	+	0.886548i	$0.346904\pi$
$48$	−18.2628	−2.63601
$49$	−0.535416	−0.0764880
$50$	−2.49553	−0.352922
$51$	21.3274	2.98643
$52$	11.1246	1.54270
$53$	13.7921	1.89449	0.947246	−	0.320508i	$-0.103854\pi$
$53$	13.7921	1.89449	0.947246	+	0.320508i	$0.103854\pi$
$54$	45.1064	6.13820
$55$	−2.76883	−0.373348
$56$	14.1348	1.88884
$57$	8.56778	1.13483
$58$	12.6875	1.66596
$59$	−8.36864	−1.08950	−0.544752	−	0.838597i	$-0.683376\pi$
$59$	−8.36864	−1.08950	−0.544752	+	0.838597i	$0.683376\pi$
$60$	14.2506	1.83975
$61$	10.9900	1.40712	0.703560	−	0.710636i	$-0.251593\pi$
$61$	10.9900	1.40712	0.703560	+	0.710636i	$0.251593\pi$
$62$	−16.7419	−2.12622
$63$	−21.2614	−2.67868
$64$	−4.84120	−0.605150
$65$	−2.63137	−0.326381
$66$	23.2911	2.86694
$67$	15.4877	1.89212	0.946061	−	0.323988i	$-0.105024\pi$
$67$	15.4877	1.89212	0.946061	+	0.323988i	$0.105024\pi$
$68$	−26.7491	−3.24380
$69$	−8.04428	−0.968417
$70$	−6.34503	−0.758376
$71$	−1.49881	−0.177876	−0.0889380	−	0.996037i	$-0.528347\pi$
$71$	−1.49881	−0.177876	−0.0889380	+	0.996037i	$0.528347\pi$
$72$	−46.4878	−5.47863
$73$	−12.6663	−1.48248	−0.741239	−	0.671242i	$-0.765761\pi$
$73$	−12.6663	−1.48248	−0.741239	+	0.671242i	$0.765761\pi$
$74$	5.50224	0.639622
$75$	−3.37079	−0.389225
$76$	−10.7458	−1.23263
$77$	−7.03989	−0.802270
$78$	22.1348	2.50627
$79$	12.7944	1.43949	0.719743	−	0.694241i	$-0.244260\pi$
$79$	12.7944	1.43949	0.719743	+	0.694241i	$0.244260\pi$
$80$	−5.41797	−0.605748
$81$	35.8398	3.98220
$82$	0.777375	0.0858467
$83$	11.5499	1.26777	0.633885	−	0.773427i	$-0.281459\pi$
$83$	11.5499	1.26777	0.633885	+	0.773427i	$0.281459\pi$
$84$	36.2330	3.95335
$85$	6.32712	0.686272
$86$	−4.35809	−0.469945
$87$	17.1374	1.83732
$88$	−15.3927	−1.64086
$89$	−18.3789	−1.94816	−0.974081	−	0.226201i	$-0.927369\pi$
$89$	−18.3789	−1.94816	−0.974081	+	0.226201i	$0.927369\pi$
$90$	20.8682	2.19970
$91$	−6.69039	−0.701344
$92$	10.0892	1.05188
$93$	−22.6137	−2.34493
$94$	−15.8300	−1.63274
$95$	2.54178	0.260781
$96$	8.09727	0.826425
$97$	11.9251	1.21081	0.605405	−	0.795917i	$-0.293011\pi$
$97$	11.9251	1.21081	0.605405	+	0.795917i	$0.293011\pi$
$98$	1.33615	0.134971
$99$	23.1535	2.32701
$100$	4.22769	0.422769
$101$	0.581619	0.0578733	0.0289366	−	0.999581i	$-0.490788\pi$
$101$	0.581619	0.0578733	0.0289366	+	0.999581i	$0.490788\pi$
$102$	−53.2232	−5.26988
$103$	−0.833506	−0.0821278	−0.0410639	−	0.999157i	$-0.513075\pi$
$103$	−0.833506	−0.0821278	−0.0410639	+	0.999157i	$0.513075\pi$
$104$	−14.6285	−1.43444
$105$	−8.57041	−0.836386
$106$	−34.4187	−3.34304
$107$	−16.9484	−1.63846	−0.819231	−	0.573464i	$-0.805599\pi$
$107$	−16.9484	−1.63846	−0.819231	+	0.573464i	$0.805599\pi$
$108$	−76.4148	−7.35302
$109$	−15.8276	−1.51601	−0.758005	−	0.652249i	$-0.773826\pi$
$109$	−15.8276	−1.51601	−0.758005	+	0.652249i	$0.773826\pi$
$110$	6.90970	0.658814
$111$	7.43203	0.705417
$112$	−13.7755	−1.30166
$113$	2.09370	0.196958	0.0984792	−	0.995139i	$-0.468602\pi$
$113$	2.09370	0.196958	0.0984792	+	0.995139i	$0.468602\pi$
$114$	−21.3812	−2.00253
$115$	−2.38647	−0.222539
$116$	−21.4940	−1.99567
$117$	22.0040	2.03427
$118$	20.8842	1.92255
$119$	16.0870	1.47470
$120$	−18.7391	−1.71064
$121$	−3.33360	−0.303055
$122$	−27.4258	−2.48302
$123$	1.05002	0.0946773
$124$	28.3624	2.54702
$125$	−1.00000	−0.0894427
$126$	53.0584	4.72682
$127$	17.1926	1.52560	0.762799	−	0.646635i	$-0.223824\pi$
$127$	17.1926	1.52560	0.762799	+	0.646635i	$0.223824\pi$
$128$	16.8858	1.49250
$129$	−5.88659	−0.518285
$130$	6.56666	0.575934
$131$	−14.8305	−1.29575	−0.647873	−	0.761748i	$-0.724341\pi$
$131$	−14.8305	−1.29575	−0.647873	+	0.761748i	$0.724341\pi$
$132$	−39.4575	−3.43434
$133$	6.46260	0.560379
$134$	−38.6501	−3.33886
$135$	18.0748	1.55563
$136$	35.1742	3.01616
$137$	11.6645	0.996566	0.498283	−	0.867015i	$-0.333964\pi$
$137$	11.6645	0.996566	0.498283	+	0.867015i	$0.333964\pi$
$138$	20.0748	1.70888
$139$	−19.7738	−1.67719	−0.838597	−	0.544753i	$-0.816623\pi$
$139$	−19.7738	−1.67719	−0.838597	+	0.544753i	$0.816623\pi$
$140$	10.7491	0.908467
$141$	−21.3821	−1.80070
$142$	3.74033	0.313882
$143$	7.28580	0.609269
$144$	45.3062	3.77552
$145$	5.08410	0.422212
$146$	31.6092	2.61599
$147$	1.80477	0.148855
$148$	−9.32135	−0.766211
$149$	23.1153	1.89368	0.946838	−	0.321711i	$-0.104258\pi$
$149$	23.1153	1.89368	0.946838	+	0.321711i	$0.104258\pi$
$150$	8.41191	0.686830
$151$	11.3492	0.923582	0.461791	−	0.886989i	$-0.347207\pi$
$151$	11.3492	0.923582	0.461791	+	0.886989i	$0.347207\pi$
$152$	14.1304	1.14613
$153$	−52.9086	−4.27741
$154$	17.5683	1.41569
$155$	−6.70873	−0.538858
$156$	−37.4986	−3.00229
$157$	4.60093	0.367194	0.183597	−	0.983002i	$-0.441226\pi$
$157$	4.60093	0.367194	0.183597	+	0.983002i	$0.441226\pi$
$158$	−31.9289	−2.54013
$159$	−46.4903	−3.68692
$160$	2.40219	0.189910
$161$	−6.06773	−0.478204
$162$	−89.4395	−7.02703
$163$	9.24056	0.723776	0.361888	−	0.932221i	$-0.382132\pi$
$163$	9.24056	0.723776	0.361888	+	0.932221i	$0.382132\pi$
$164$	−1.31695	−0.102837
$165$	9.33312	0.726583
$166$	−28.8233	−2.23712
$167$	−10.4065	−0.805279	−0.402640	−	0.915359i	$-0.631907\pi$
$167$	−10.4065	−0.805279	−0.402640	+	0.915359i	$0.631907\pi$
$168$	−47.6452	−3.67591
$169$	−6.07591	−0.467378
$170$	−15.7895	−1.21100
$171$	−21.2548	−1.62540
$172$	7.38304	0.562952
$173$	−5.50780	−0.418750	−0.209375	−	0.977835i	$-0.567143\pi$
$173$	−5.50780	−0.418750	−0.209375	+	0.977835i	$0.567143\pi$
$174$	−42.7670	−3.24216
$175$	−2.54255	−0.192199
$176$	15.0014	1.13078
$177$	28.2089	2.12031
$178$	45.8652	3.43774
$179$	7.47603	0.558785	0.279393	−	0.960177i	$-0.409867\pi$
$179$	7.47603	0.558785	0.279393	+	0.960177i	$0.409867\pi$
$180$	−35.3528	−2.63504
$181$	4.90918	0.364897	0.182448	−	0.983215i	$-0.441598\pi$
$181$	4.90918	0.364897	0.182448	+	0.983215i	$0.441598\pi$
$182$	16.6961	1.23760
$183$	−37.0448	−2.73843
$184$	−13.2670	−0.978058
$185$	2.20483	0.162103
$186$	56.4332	4.13788
$187$	−17.5187	−1.28109
$188$	26.8177	1.95588
$189$	45.9563	3.34283
$190$	−6.34309	−0.460176
$191$	5.92847	0.428969	0.214485	−	0.976727i	$-0.431193\pi$
$191$	5.92847	0.428969	0.214485	+	0.976727i	$0.431193\pi$
$192$	16.3186	1.17770
$193$	−11.2342	−0.808655	−0.404327	−	0.914614i	$-0.632494\pi$
$193$	−11.2342	−0.808655	−0.404327	+	0.914614i	$0.632494\pi$
$194$	−29.7595	−2.13661
$195$	8.86977	0.635178
$196$	−2.26357	−0.161684
$197$	−10.0793	−0.718118	−0.359059	−	0.933315i	$-0.616902\pi$
$197$	−10.0793	−0.718118	−0.359059	+	0.933315i	$0.616902\pi$
$198$	−57.7803	−4.10627
$199$	−6.18163	−0.438204	−0.219102	−	0.975702i	$-0.570313\pi$
$199$	−6.18163	−0.438204	−0.219102	+	0.975702i	$0.570313\pi$
$200$	−5.55927	−0.393100
$201$	−52.2057	−3.68231
$202$	−1.45145	−0.102124
$203$	12.9266	0.907270
$204$	90.1655	6.31285
$205$	0.311506	0.0217566
$206$	2.08004	0.144923
$207$	19.9561	1.38705
$208$	14.2567	0.988522
$209$	−7.03773	−0.486810
$210$	21.3877	1.47589
$211$	6.88824	0.474206	0.237103	−	0.971484i	$-0.423802\pi$
$211$	6.88824	0.474206	0.237103	+	0.971484i	$0.423802\pi$
$212$	58.3087	4.00466
$213$	5.05217	0.346169
$214$	42.2952	2.89124
$215$	−1.74635	−0.119100
$216$	100.483	6.83700
$217$	−17.0573	−1.15793
$218$	39.4983	2.67516
$219$	42.6954	2.88509
$220$	−11.7057	−0.789201
$221$	−16.6490	−1.11993
$222$	−18.5469	−1.24478
$223$	−5.93533	−0.397459	−0.198729	−	0.980054i	$-0.563681\pi$
$223$	−5.93533	−0.397459	−0.198729	+	0.980054i	$0.563681\pi$
$224$	6.10770	0.408088
$225$	8.36220	0.557480
$226$	−5.22489	−0.347554
$227$	−28.5026	−1.89178	−0.945892	−	0.324481i	$-0.894810\pi$
$227$	−28.5026	−1.89178	−0.945892	+	0.324481i	$0.894810\pi$
$228$	36.2219	2.39885
$229$	−1.34373	−0.0887959	−0.0443979	−	0.999014i	$-0.514137\pi$
$229$	−1.34373	−0.0887959	−0.0443979	+	0.999014i	$0.514137\pi$
$230$	5.95551	0.392695
$231$	23.7300	1.56132
$232$	28.2639	1.85562
$233$	−8.13603	−0.533009	−0.266505	−	0.963834i	$-0.585869\pi$
$233$	−8.13603	−0.533009	−0.266505	+	0.963834i	$0.585869\pi$
$234$	−54.9118	−3.58969
$235$	−6.34335	−0.413795
$236$	−35.3800	−2.30304
$237$	−43.1273	−2.80142
$238$	−40.1458	−2.60226
$239$	−1.97410	−0.127694	−0.0638470	−	0.997960i	$-0.520337\pi$
$239$	−1.97410	−0.127694	−0.0638470	+	0.997960i	$0.520337\pi$
$240$	18.2628	1.17886
$241$	12.2366	0.788231	0.394115	−	0.919061i	$-0.371051\pi$
$241$	12.2366	0.788231	0.394115	+	0.919061i	$0.371051\pi$
$242$	8.31911	0.534773
$243$	−66.5839	−4.27136
$244$	46.4621	2.97443
$245$	0.535416	0.0342065
$246$	−2.62036	−0.167068
$247$	−6.68834	−0.425569
$248$	−37.2956	−2.36827
$249$	−38.9324	−2.46724
$250$	2.49553	0.157831
$251$	−2.45844	−0.155175	−0.0775875	−	0.996986i	$-0.524722\pi$
$251$	−2.45844	−0.155175	−0.0775875	+	0.996986i	$0.524722\pi$
$252$	−89.8864	−5.66231
$253$	6.60772	0.415424
$254$	−42.9048	−2.69208
$255$	−21.3274	−1.33557
$256$	−32.4566	−2.02854
$257$	−21.2301	−1.32430	−0.662148	−	0.749373i	$-0.730355\pi$
$257$	−21.2301	−1.32430	−0.662148	+	0.749373i	$0.730355\pi$
$258$	14.6902	0.914571
$259$	5.60591	0.348334
$260$	−11.1246	−0.689918
$261$	−42.5143	−2.63157
$262$	37.0100	2.28648
$263$	−27.7514	−1.71122	−0.855611	−	0.517619i	$-0.826819\pi$
$263$	−27.7514	−1.71122	−0.855611	+	0.517619i	$0.826819\pi$
$264$	51.8854	3.19332
$265$	−13.7921	−0.847242
$266$	−16.1276	−0.988849
$267$	61.9514	3.79136
$268$	65.4771	3.99965
$269$	−21.7657	−1.32708	−0.663539	−	0.748142i	$-0.730946\pi$
$269$	−21.7657	−1.32708	−0.663539	+	0.748142i	$0.730946\pi$
$270$	−45.1064	−2.74509
$271$	8.75470	0.531810	0.265905	−	0.963999i	$-0.414329\pi$
$271$	8.75470	0.531810	0.265905	+	0.963999i	$0.414329\pi$
$272$	−34.2802	−2.07854
$273$	22.5519	1.36490
$274$	−29.1092	−1.75855
$275$	2.76883	0.166967
$276$	−34.0087	−2.04708
$277$	−17.9312	−1.07738	−0.538692	−	0.842503i	$-0.681081\pi$
$277$	−17.9312	−1.07738	−0.538692	+	0.842503i	$0.681081\pi$
$278$	49.3462	2.95959
$279$	56.0997	3.35860
$280$	−14.1348	−0.844713
$281$	−8.03689	−0.479440	−0.239720	−	0.970842i	$-0.577056\pi$
$281$	−8.03689	−0.479440	−0.239720	+	0.970842i	$0.577056\pi$
$282$	53.3597	3.17752
$283$	15.4780	0.920071	0.460036	−	0.887901i	$-0.347837\pi$
$283$	15.4780	0.920071	0.460036	+	0.887901i	$0.347837\pi$
$284$	−6.33650	−0.376002
$285$	−8.56778	−0.507512
$286$	−18.1819	−1.07512
$287$	0.792022	0.0467516
$288$	−20.0876	−1.18367
$289$	23.0324	1.35485
$290$	−12.6875	−0.745039
$291$	−40.1970	−2.35639
$292$	−53.5491	−3.13373
$293$	1.10989	0.0648402	0.0324201	−	0.999474i	$-0.489679\pi$
$293$	1.10989	0.0648402	0.0324201	+	0.999474i	$0.489679\pi$
$294$	−4.50387	−0.262671
$295$	8.36864	0.487241
$296$	12.2573	0.712440
$297$	−50.0461	−2.90397
$298$	−57.6849	−3.34160
$299$	6.27967	0.363163
$300$	−14.2506	−0.822761
$301$	−4.44020	−0.255929
$302$	−28.3222	−1.62976
$303$	−1.96051	−0.112629
$304$	−13.7713	−0.789836
$305$	−10.9900	−0.629283
$306$	132.035	7.54796
$307$	27.0880	1.54599	0.772997	−	0.634410i	$-0.218757\pi$
$307$	27.0880	1.54599	0.772997	+	0.634410i	$0.218757\pi$
$308$	−29.7625	−1.69587
$309$	2.80957	0.159831
$310$	16.7419	0.950873
$311$	7.71568	0.437516	0.218758	−	0.975779i	$-0.429799\pi$
$311$	7.71568	0.437516	0.218758	+	0.975779i	$0.429799\pi$
$312$	49.3095	2.79160
$313$	−25.0634	−1.41667	−0.708334	−	0.705877i	$-0.750553\pi$
$313$	−25.0634	−1.41667	−0.708334	+	0.705877i	$0.750553\pi$
$314$	−11.4818	−0.647954
$315$	21.2614	1.19794
$316$	54.0909	3.04285
$317$	−1.31428	−0.0738174	−0.0369087	−	0.999319i	$-0.511751\pi$
$317$	−1.31428	−0.0738174	−0.0369087	+	0.999319i	$0.511751\pi$
$318$	116.018	6.50597
$319$	−14.0770	−0.788161
$320$	4.84120	0.270631
$321$	57.1294	3.18865
$322$	15.1422	0.843843
$323$	16.0821	0.894833
$324$	151.520	8.41775
$325$	2.63137	0.145962
$326$	−23.0601	−1.27718
$327$	53.3515	2.95034
$328$	1.73175	0.0956198
$329$	−16.1283	−0.889183
$330$	−23.2911	−1.28213
$331$	9.08647	0.499438	0.249719	−	0.968318i	$-0.419662\pi$
$331$	9.08647	0.499438	0.249719	+	0.968318i	$0.419662\pi$
$332$	48.8295	2.67987
$333$	−18.4373	−1.01036
$334$	25.9698	1.42100
$335$	−15.4877	−0.846183
$336$	46.4342	2.53320
$337$	−18.9286	−1.03111	−0.515554	−	0.856857i	$-0.672414\pi$
$337$	−18.9286	−1.03111	−0.515554	+	0.856857i	$0.672414\pi$
$338$	15.1626	0.824739
$339$	−7.05740	−0.383305
$340$	26.7491	1.45067
$341$	18.5753	1.00591
$342$	53.0422	2.86819
$343$	19.1592	1.03450
$344$	−9.70846	−0.523445
$345$	8.04428	0.433089
$346$	13.7449	0.738931
$347$	−24.9348	−1.33857	−0.669285	−	0.743005i	$-0.733400\pi$
$347$	−24.9348	−1.33857	−0.669285	+	0.743005i	$0.733400\pi$
$348$	72.4517	3.88382
$349$	19.8166	1.06076	0.530380	−	0.847760i	$-0.322049\pi$
$349$	19.8166	1.06076	0.530380	+	0.847760i	$0.322049\pi$
$350$	6.34503	0.339156
$351$	−47.5615	−2.53865
$352$	−6.65125	−0.354513
$353$	−21.7666	−1.15852	−0.579260	−	0.815143i	$-0.696658\pi$
$353$	−21.7666	−1.15852	−0.579260	+	0.815143i	$0.696658\pi$
$354$	−70.3962	−3.74152
$355$	1.49881	0.0795486
$356$	−77.7003	−4.11811
$357$	−54.2260	−2.86994
$358$	−18.6567	−0.986037
$359$	6.82387	0.360150	0.180075	−	0.983653i	$-0.442366\pi$
$359$	6.82387	0.360150	0.180075	+	0.983653i	$0.442366\pi$
$360$	46.4878	2.45012
$361$	−12.5394	−0.659967
$362$	−12.2510	−0.643900
$363$	11.2369	0.589782
$364$	−28.2849	−1.48253
$365$	12.6663	0.662984
$366$	92.4466	4.83226
$367$	21.7157	1.13355	0.566775	−	0.823873i	$-0.308191\pi$
$367$	21.7157	1.13355	0.566775	+	0.823873i	$0.308191\pi$
$368$	12.9298	0.674014
$369$	−2.60488	−0.135605
$370$	−5.50224	−0.286048
$371$	−35.0672	−1.82060
$372$	−95.6036	−4.95682
$373$	16.0828	0.832737	0.416368	−	0.909196i	$-0.363303\pi$
$373$	16.0828	0.832737	0.416368	+	0.909196i	$0.363303\pi$
$374$	43.7185	2.26063
$375$	3.37079	0.174067
$376$	−35.2644	−1.81862
$377$	−13.3781	−0.689009
$378$	−114.685	−5.89878
$379$	−2.89842	−0.148882	−0.0744410	−	0.997225i	$-0.523717\pi$
$379$	−2.89842	−0.148882	−0.0744410	+	0.997225i	$0.523717\pi$
$380$	10.7458	0.551250
$381$	−57.9527	−2.96901
$382$	−14.7947	−0.756963
$383$	0.341120	0.0174304	0.00871521	−	0.999962i	$-0.497226\pi$
$383$	0.341120	0.0174304	0.00871521	+	0.999962i	$0.497226\pi$
$384$	−56.9183	−2.90460
$385$	7.03989	0.358786
$386$	28.0353	1.42696
$387$	14.6034	0.742331
$388$	50.4156	2.55947
$389$	4.57545	0.231984	0.115992	−	0.993250i	$-0.462995\pi$
$389$	4.57545	0.231984	0.115992	+	0.993250i	$0.462995\pi$
$390$	−22.1348	−1.12084
$391$	−15.0995	−0.763613
$392$	2.97652	0.150337
$393$	49.9904	2.52168
$394$	25.1532	1.26720
$395$	−12.7944	−0.643758
$396$	97.8857	4.91894
$397$	−7.32990	−0.367877	−0.183939	−	0.982938i	$-0.558885\pi$
$397$	−7.32990	−0.367877	−0.183939	+	0.982938i	$0.558885\pi$
$398$	15.4265	0.773259
$399$	−21.7841	−1.09057
$400$	5.41797	0.270899
$401$	8.62869	0.430896	0.215448	−	0.976515i	$-0.430879\pi$
$401$	8.62869	0.430896	0.215448	+	0.976515i	$0.430879\pi$
$402$	130.281	6.49783
$403$	17.6531	0.879364
$404$	2.45891	0.122335
$405$	−35.8398	−1.78089
$406$	−32.2588	−1.60098
$407$	−6.10480	−0.302604
$408$	−118.565	−5.86982
$409$	0.391232	0.0193452	0.00967259	−	0.999953i	$-0.496921\pi$
$409$	0.391232	0.0193452	0.00967259	+	0.999953i	$0.496921\pi$
$410$	−0.777375	−0.0383918
$411$	−39.3185	−1.93944
$412$	−3.52381	−0.173605
$413$	21.2777	1.04701
$414$	−49.8012	−2.44760
$415$	−11.5499	−0.566964
$416$	−6.32104	−0.309915
$417$	66.6533	3.26403
$418$	17.5629	0.859030
$419$	22.8426	1.11593	0.557966	−	0.829864i	$-0.311582\pi$
$419$	22.8426	1.11593	0.557966	+	0.829864i	$0.311582\pi$
$420$	−36.2330	−1.76799
$421$	−12.6491	−0.616478	−0.308239	−	0.951309i	$-0.599740\pi$
$421$	−12.6491	−0.616478	−0.308239	+	0.951309i	$0.599740\pi$
$422$	−17.1898	−0.836789
$423$	53.0444	2.57911
$424$	−76.6741	−3.72362
$425$	−6.32712	−0.306910
$426$	−12.6079	−0.610853
$427$	−27.9426	−1.35224
$428$	−71.6524	−3.46345
$429$	−24.5589	−1.18571
$430$	4.35809	0.210166
$431$	23.2719	1.12097	0.560485	−	0.828165i	$-0.310615\pi$
$431$	23.2719	1.12097	0.560485	+	0.828165i	$0.310615\pi$
$432$	−97.9290	−4.71161
$433$	1.58919	0.0763714	0.0381857	−	0.999271i	$-0.487842\pi$
$433$	1.58919	0.0763714	0.0381857	+	0.999271i	$0.487842\pi$
$434$	42.5671	2.04328
$435$	−17.1374	−0.821677
$436$	−66.9142	−3.20461
$437$	−6.06587	−0.290170
$438$	−106.548	−5.09105
$439$	37.6098	1.79502	0.897509	−	0.440997i	$-0.145375\pi$
$439$	37.6098	1.79502	0.897509	+	0.440997i	$0.145375\pi$
$440$	15.3927	0.733816
$441$	−4.47725	−0.213203
$442$	41.5481	1.97624
$443$	24.4820	1.16318	0.581588	−	0.813484i	$-0.302432\pi$
$443$	24.4820	1.16318	0.581588	+	0.813484i	$0.302432\pi$
$444$	31.4203	1.49114
$445$	18.3789	0.871244
$446$	14.8118	0.701359
$447$	−77.9166	−3.68533
$448$	12.3090	0.581546
$449$	−3.86557	−0.182427	−0.0912137	−	0.995831i	$-0.529075\pi$
$449$	−3.86557	−0.182427	−0.0912137	+	0.995831i	$0.529075\pi$
$450$	−20.8682	−0.983734
$451$	−0.862507	−0.0406139
$452$	8.85149	0.416339
$453$	−38.2556	−1.79741
$454$	71.1292	3.33826
$455$	6.69039	0.313650
$456$	−47.6306	−2.23051
$457$	−27.8214	−1.30143	−0.650716	−	0.759321i	$-0.725531\pi$
$457$	−27.8214	−1.30143	−0.650716	+	0.759321i	$0.725531\pi$
$458$	3.35331	0.156690
$459$	114.362	5.33794
$460$	−10.0892	−0.470414
$461$	−26.9092	−1.25328	−0.626642	−	0.779307i	$-0.715571\pi$
$461$	−26.9092	−1.25328	−0.626642	+	0.779307i	$0.715571\pi$
$462$	−59.2190	−2.75511
$463$	1.87846	0.0872993	0.0436497	−	0.999047i	$-0.486101\pi$
$463$	1.87846	0.0872993	0.0436497	+	0.999047i	$0.486101\pi$
$464$	−27.5455	−1.27877
$465$	22.6137	1.04868
$466$	20.3037	0.940552
$467$	19.7920	0.915865	0.457933	−	0.888987i	$-0.348590\pi$
$467$	19.7920	0.915865	0.457933	+	0.888987i	$0.348590\pi$
$468$	93.0261	4.30013
$469$	−39.3783	−1.81832
$470$	15.8300	0.730185
$471$	−15.5087	−0.714605
$472$	46.5235	2.14142
$473$	4.83535	0.222330
$474$	107.626	4.94341
$475$	−2.54178	−0.116625
$476$	68.0110	3.11728
$477$	115.332	5.28071
$478$	4.92644	0.225330
$479$	−28.3027	−1.29319	−0.646593	−	0.762836i	$-0.723807\pi$
$479$	−28.3027	−1.29319	−0.646593	+	0.762836i	$0.723807\pi$
$480$	−8.09727	−0.369588
$481$	−5.80173	−0.264536
$482$	−30.5369	−1.39092
$483$	20.4530	0.930644
$484$	−14.0934	−0.640610
$485$	−11.9251	−0.541491
$486$	166.162	7.53727
$487$	−23.2358	−1.05292	−0.526458	−	0.850201i	$-0.676480\pi$
$487$	−23.2358	−1.05292	−0.526458	+	0.850201i	$0.676480\pi$
$488$	−61.0962	−2.76569
$489$	−31.1480	−1.40856
$490$	−1.33615	−0.0603610
$491$	28.0774	1.26712	0.633559	−	0.773695i	$-0.281594\pi$
$491$	28.0774	1.26712	0.633559	+	0.773695i	$0.281594\pi$
$492$	4.43916	0.200133
$493$	32.1677	1.44876
$494$	16.6910	0.750963
$495$	−23.1535	−1.04067
$496$	36.3477	1.63206
$497$	3.81081	0.170938
$498$	97.1571	4.35371
$499$	−8.99837	−0.402822	−0.201411	−	0.979507i	$-0.564553\pi$
$499$	−8.99837	−0.402822	−0.201411	+	0.979507i	$0.564553\pi$
$500$	−4.22769	−0.189068
$501$	35.0781	1.56717
$502$	6.13511	0.273823
$503$	−29.5397	−1.31711	−0.658556	−	0.752532i	$-0.728832\pi$
$503$	−29.5397	−1.31711	−0.658556	+	0.752532i	$0.728832\pi$
$504$	118.198	5.26494
$505$	−0.581619	−0.0258817
$506$	−16.4898	−0.733060
$507$	20.4806	0.909576
$508$	72.6851	3.22488
$509$	9.25090	0.410039	0.205019	−	0.978758i	$-0.434274\pi$
$509$	9.25090	0.410039	0.205019	+	0.978758i	$0.434274\pi$
$510$	53.2232	2.35676
$511$	32.2047	1.42465
$512$	47.2250	2.08707
$513$	45.9422	2.02840
$514$	52.9804	2.33687
$515$	0.833506	0.0367287
$516$	−24.8867	−1.09557
$517$	17.5636	0.772448
$518$	−13.9897	−0.614674
$519$	18.5656	0.814940
$520$	14.6285	0.641501
$521$	8.15514	0.357283	0.178642	−	0.983914i	$-0.442830\pi$
$521$	8.15514	0.357283	0.178642	+	0.983914i	$0.442830\pi$
$522$	106.096	4.64369
$523$	1.94196	0.0849158	0.0424579	−	0.999098i	$-0.486481\pi$
$523$	1.94196	0.0849158	0.0424579	+	0.999098i	$0.486481\pi$
$524$	−62.6987	−2.73901
$525$	8.57041	0.374043
$526$	69.2545	3.01964
$527$	−42.4469	−1.84902
$528$	−50.5666	−2.20063
$529$	−17.3048	−0.752381
$530$	34.4187	1.49505
$531$	−69.9802	−3.03688
$532$	27.3219	1.18455
$533$	−0.819687	−0.0355046
$534$	−154.602	−6.69028
$535$	16.9484	0.732742
$536$	−86.1003	−3.71897
$537$	−25.2001	−1.08747
$538$	54.3170	2.34177
$539$	−1.48247	−0.0638546
$540$	76.4148	3.28837
$541$	35.5115	1.52676	0.763380	−	0.645950i	$-0.223538\pi$
$541$	35.5115	1.52676	0.763380	+	0.645950i	$0.223538\pi$
$542$	−21.8476	−0.938437
$543$	−16.5478	−0.710134
$544$	15.1989	0.651650
$545$	15.8276	0.677980
$546$	−56.2790	−2.40852
$547$	9.59771	0.410368	0.205184	−	0.978723i	$-0.434221\pi$
$547$	9.59771	0.410368	0.205184	+	0.978723i	$0.434221\pi$
$548$	49.3139	2.10658
$549$	91.9003	3.92221
$550$	−6.90970	−0.294631
$551$	12.9226	0.550523
$552$	44.7203	1.90342
$553$	−32.5305	−1.38334
$554$	44.7480	1.90116
$555$	−7.43203	−0.315472
$556$	−83.5975	−3.54533
$557$	−23.3329	−0.988647	−0.494324	−	0.869278i	$-0.664584\pi$
$557$	−23.3329	−0.988647	−0.494324	+	0.869278i	$0.664584\pi$
$558$	−139.999	−5.92662
$559$	4.59530	0.194360
$560$	13.7755	0.582121
$561$	59.0518	2.49317
$562$	20.0563	0.846025
$563$	−29.5266	−1.24440	−0.622199	−	0.782859i	$-0.713761\pi$
$563$	−29.5266	−1.24440	−0.622199	+	0.782859i	$0.713761\pi$
$564$	−90.3968	−3.80639
$565$	−2.09370	−0.0880824
$566$	−38.6258	−1.62357
$567$	−91.1247	−3.82688
$568$	8.33229	0.349615
$569$	−26.9378	−1.12929	−0.564645	−	0.825334i	$-0.690987\pi$
$569$	−26.9378	−1.12929	−0.564645	+	0.825334i	$0.690987\pi$
$570$	21.3812	0.895559
$571$	17.0420	0.713187	0.356593	−	0.934260i	$-0.383938\pi$
$571$	17.0420	0.713187	0.356593	+	0.934260i	$0.383938\pi$
$572$	30.8021	1.28790
$573$	−19.9836	−0.834828
$574$	−1.97652	−0.0824983
$575$	2.38647	0.0995226
$576$	−40.4831	−1.68679
$577$	19.6145	0.816562	0.408281	−	0.912856i	$-0.366128\pi$
$577$	19.6145	0.816562	0.408281	+	0.912856i	$0.366128\pi$
$578$	−57.4782	−2.39078
$579$	37.8681	1.57374
$580$	21.4940	0.892490
$581$	−29.3664	−1.21832
$582$	100.313	4.15810
$583$	38.1880	1.58158
$584$	70.4154	2.91381
$585$	−22.0040	−0.909754
$586$	−2.76976	−0.114418
$587$	16.5147	0.681635	0.340818	−	0.940129i	$-0.389296\pi$
$587$	16.5147	0.681635	0.340818	+	0.940129i	$0.389296\pi$
$588$	7.63001	0.314656
$589$	−17.0521	−0.702618
$590$	−20.8842	−0.859790
$591$	33.9751	1.39755
$592$	−11.9457	−0.490967
$593$	18.5396	0.761329	0.380665	−	0.924713i	$-0.375695\pi$
$593$	18.5396	0.761329	0.380665	+	0.924713i	$0.375695\pi$
$594$	124.892	5.12437
$595$	−16.0870	−0.659505
$596$	97.7241	4.00294
$597$	20.8370	0.852800
$598$	−15.6711	−0.640840
$599$	16.8408	0.688098	0.344049	−	0.938952i	$-0.388201\pi$
$599$	16.8408	0.688098	0.344049	+	0.938952i	$0.388201\pi$
$600$	18.7391	0.765021
$601$	21.5829	0.880385	0.440192	−	0.897904i	$-0.354910\pi$
$601$	21.5829	0.880385	0.440192	+	0.897904i	$0.354910\pi$
$602$	11.0807	0.451615
$603$	129.511	5.27410
$604$	47.9807	1.95231
$605$	3.33360	0.135530
$606$	4.89253	0.198745
$607$	43.9671	1.78457	0.892285	−	0.451473i	$-0.149101\pi$
$607$	43.9671	1.78457	0.892285	+	0.451473i	$0.149101\pi$
$608$	6.10583	0.247624
$609$	−43.5728	−1.76566
$610$	27.4258	1.11044
$611$	16.6917	0.675273
$612$	−223.681	−9.04178
$613$	−0.763895	−0.0308534	−0.0154267	−	0.999881i	$-0.504911\pi$
$613$	−0.763895	−0.0308534	−0.0154267	+	0.999881i	$0.504911\pi$
$614$	−67.5990	−2.72807
$615$	−1.05002	−0.0423410
$616$	39.1367	1.57686
$617$	8.64472	0.348023	0.174012	−	0.984744i	$-0.444327\pi$
$617$	8.64472	0.348023	0.174012	+	0.984744i	$0.444327\pi$
$618$	−7.01138	−0.282039
$619$	−26.8395	−1.07877	−0.539385	−	0.842059i	$-0.681343\pi$
$619$	−26.8395	−1.07877	−0.539385	+	0.842059i	$0.681343\pi$
$620$	−28.3624	−1.13906
$621$	−43.1350	−1.73095
$622$	−19.2547	−0.772044
$623$	46.7294	1.87217
$624$	−48.0562	−1.92379
$625$	1.00000	0.0400000
$626$	62.5466	2.49987
$627$	23.7227	0.947393
$628$	19.4513	0.776191
$629$	13.9503	0.556233
$630$	−53.0584	−2.11390
$631$	−32.3421	−1.28752	−0.643760	−	0.765227i	$-0.722627\pi$
$631$	−32.3421	−1.28752	−0.643760	+	0.765227i	$0.722627\pi$
$632$	−71.1277	−2.82931
$633$	−23.2188	−0.922864
$634$	3.27983	0.130259
$635$	−17.1926	−0.682268
$636$	−196.546	−7.79357
$637$	−1.40887	−0.0558216
$638$	35.1296	1.39079
$639$	−12.5334	−0.495812
$640$	−16.8858	−0.667468
$641$	10.5032	0.414853	0.207426	−	0.978251i	$-0.433491\pi$
$641$	10.5032	0.414853	0.207426	+	0.978251i	$0.433491\pi$
$642$	−142.568	−5.62672
$643$	−28.7110	−1.13225	−0.566125	−	0.824319i	$-0.691558\pi$
$643$	−28.7110	−1.13225	−0.566125	+	0.824319i	$0.691558\pi$
$644$	−25.6525	−1.01085
$645$	5.88659	0.231784
$646$	−40.1335	−1.57903
$647$	−3.55020	−0.139573	−0.0697864	−	0.997562i	$-0.522232\pi$
$647$	−3.55020	−0.139573	−0.0697864	+	0.997562i	$0.522232\pi$
$648$	−199.243	−7.82701
$649$	−23.1713	−0.909553
$650$	−6.56666	−0.257566
$651$	57.4965	2.25347
$652$	39.0662	1.52995
$653$	28.9825	1.13417	0.567086	−	0.823658i	$-0.308071\pi$
$653$	28.9825	1.13417	0.567086	+	0.823658i	$0.308071\pi$
$654$	−133.140	−5.20620
$655$	14.8305	0.579475
$656$	−1.68773	−0.0658949
$657$	−105.918	−4.13226
$658$	40.2488	1.56906
$659$	29.6720	1.15586	0.577929	−	0.816087i	$-0.303861\pi$
$659$	29.6720	1.15586	0.577929	+	0.816087i	$0.303861\pi$
$660$	39.4575	1.53588
$661$	22.5242	0.876089	0.438045	−	0.898953i	$-0.355671\pi$
$661$	22.5242	0.876089	0.438045	+	0.898953i	$0.355671\pi$
$662$	−22.6756	−0.881312
$663$	56.1201	2.17952
$664$	−64.2093	−2.49180
$665$	−6.46260	−0.250609
$666$	46.0108	1.78288
$667$	−12.1331	−0.469794
$668$	−43.9954	−1.70223
$669$	20.0067	0.773504
$670$	38.6501	1.49318
$671$	30.4293	1.17471
$672$	−20.5878	−0.794190
$673$	2.40254	0.0926112	0.0463056	−	0.998927i	$-0.485255\pi$
$673$	2.40254	0.0926112	0.0463056	+	0.998927i	$0.485255\pi$
$674$	47.2370	1.81950
$675$	−18.0748	−0.695701
$676$	−25.6871	−0.987964
$677$	21.3213	0.819443	0.409721	−	0.912211i	$-0.365626\pi$
$677$	21.3213	0.819443	0.409721	+	0.912211i	$0.365626\pi$
$678$	17.6120	0.676384
$679$	−30.3202	−1.16358
$680$	−35.1742	−1.34887
$681$	96.0762	3.68165
$682$	−46.3553	−1.77504
$683$	−15.0172	−0.574617	−0.287309	−	0.957838i	$-0.592760\pi$
$683$	−15.0172	−0.574617	−0.287309	+	0.957838i	$0.592760\pi$
$684$	−89.8588	−3.43584
$685$	−11.6645	−0.445678
$686$	−47.8124	−1.82549
$687$	4.52941	0.172808
$688$	9.46170	0.360724
$689$	36.2921	1.38262
$690$	−20.0748	−0.764233
$691$	34.4881	1.31199	0.655995	−	0.754765i	$-0.272249\pi$
$691$	34.4881	1.31199	0.655995	+	0.754765i	$0.272249\pi$
$692$	−23.2853	−0.885173
$693$	−58.8690	−2.23625
$694$	62.2257	2.36205
$695$	19.7738	0.750064
$696$	−95.2716	−3.61126
$697$	1.97094	0.0746546
$698$	−49.4531	−1.87183
$699$	27.4248	1.03730
$700$	−10.7491	−0.406279
$701$	−32.0822	−1.21173	−0.605864	−	0.795568i	$-0.707173\pi$
$701$	−32.0822	−1.21173	−0.605864	+	0.795568i	$0.707173\pi$
$702$	118.691	4.47972
$703$	5.60419	0.211366
$704$	−13.4044	−0.505199
$705$	21.3821	0.805296
$706$	54.3193	2.04433
$707$	−1.47880	−0.0556160
$708$	119.258	4.48201
$709$	9.57955	0.359767	0.179884	−	0.983688i	$-0.442428\pi$
$709$	9.57955	0.359767	0.179884	+	0.983688i	$0.442428\pi$
$710$	−3.74033	−0.140372
$711$	106.990	4.01242
$712$	102.173	3.82911
$713$	16.0102	0.599585
$714$	135.323	5.06433
$715$	−7.28580	−0.272473
$716$	31.6063	1.18118
$717$	6.65428	0.248509
$718$	−17.0292	−0.635524
$719$	32.7704	1.22213	0.611065	−	0.791580i	$-0.290741\pi$
$719$	32.7704	1.22213	0.611065	+	0.791580i	$0.290741\pi$
$720$	−45.3062	−1.68846
$721$	2.11924	0.0789245
$722$	31.2924	1.16458
$723$	−41.2471	−1.53400
$724$	20.7545	0.771335
$725$	−5.08410	−0.188819
$726$	−28.0420	−1.04073
$727$	17.8237	0.661045	0.330523	−	0.943798i	$-0.392775\pi$
$727$	17.8237	0.661045	0.330523	+	0.943798i	$0.392775\pi$
$728$	37.1937	1.37849
$729$	116.921	4.33039
$730$	−31.6092	−1.16991
$731$	−11.0494	−0.408677
$732$	−156.614	−5.78862
$733$	−16.8833	−0.623600	−0.311800	−	0.950148i	$-0.600932\pi$
$733$	−16.8833	−0.623600	−0.311800	+	0.950148i	$0.600932\pi$
$734$	−54.1923	−2.00027
$735$	−1.80477	−0.0665700
$736$	−5.73275	−0.211312
$737$	42.8827	1.57961
$738$	6.50056	0.239289
$739$	21.1144	0.776707	0.388353	−	0.921510i	$-0.373044\pi$
$739$	21.1144	0.776707	0.388353	+	0.921510i	$0.373044\pi$
$740$	9.32135	0.342660
$741$	22.5450	0.828210
$742$	87.5114	3.21264
$743$	−45.6793	−1.67581	−0.837906	−	0.545814i	$-0.816220\pi$
$743$	−45.6793	−1.67581	−0.837906	+	0.545814i	$0.816220\pi$
$744$	125.716	4.60896
$745$	−23.1153	−0.846878
$746$	−40.1352	−1.46945
$747$	96.5829	3.53378
$748$	−74.0636	−2.70803
$749$	43.0922	1.57455
$750$	−8.41191	−0.307160
$751$	15.4329	0.563156	0.281578	−	0.959538i	$-0.409142\pi$
$751$	15.4329	0.563156	0.281578	+	0.959538i	$0.409142\pi$
$752$	34.3681	1.25328
$753$	8.28686	0.301990
$754$	33.3856	1.21583
$755$	−11.3492	−0.413038
$756$	194.289	7.06621
$757$	6.09327	0.221464	0.110732	−	0.993850i	$-0.464681\pi$
$757$	6.09327	0.221464	0.110732	+	0.993850i	$0.464681\pi$
$758$	7.23311	0.262719
$759$	−22.2732	−0.808466
$760$	−14.1304	−0.512564
$761$	−12.8746	−0.466704	−0.233352	−	0.972392i	$-0.574969\pi$
$761$	−12.8746	−0.466704	−0.233352	+	0.972392i	$0.574969\pi$
$762$	144.623	5.23913
$763$	40.2425	1.45688
$764$	25.0637	0.906774
$765$	52.9086	1.91292
$766$	−0.851277	−0.0307579
$767$	−22.0209	−0.795130
$768$	109.404	3.94778
$769$	11.9995	0.432711	0.216356	−	0.976315i	$-0.430583\pi$
$769$	11.9995	0.432711	0.216356	+	0.976315i	$0.430583\pi$
$770$	−17.5683	−0.633117
$771$	71.5621	2.57725
$772$	−47.4947	−1.70937
$773$	6.15449	0.221362	0.110681	−	0.993856i	$-0.464697\pi$
$773$	6.15449	0.221362	0.110681	+	0.993856i	$0.464697\pi$
$774$	−36.4432	−1.30992
$775$	6.70873	0.240985
$776$	−66.2949	−2.37985
$777$	−18.8963	−0.677902
$778$	−11.4182	−0.409362
$779$	0.791779	0.0283684
$780$	37.4986	1.34267
$781$	−4.14994	−0.148497
$782$	37.6812	1.34748
$783$	91.8943	3.28404
$784$	−2.90087	−0.103602
$785$	−4.60093	−0.164214
$786$	−124.753	−4.44978
$787$	−12.7929	−0.456018	−0.228009	−	0.973659i	$-0.573222\pi$
$787$	−12.7929	−0.456018	−0.228009	+	0.973659i	$0.573222\pi$
$788$	−42.6120	−1.51799
$789$	93.5439	3.33025
$790$	31.9289	1.13598
$791$	−5.32334	−0.189276
$792$	−128.717	−4.57374
$793$	28.9186	1.02693
$794$	18.2920	0.649159
$795$	46.4903	1.64884
$796$	−26.1340	−0.926295
$797$	8.94441	0.316827	0.158414	−	0.987373i	$-0.449362\pi$
$797$	8.94441	0.316827	0.158414	+	0.987373i	$0.449362\pi$
$798$	54.3628	1.92442
$799$	−40.1351	−1.41988
$800$	−2.40219	−0.0849303
$801$	−153.688	−5.43031
$802$	−21.5332	−0.760363
$803$	−35.0708	−1.23762
$804$	−220.709	−7.78382
$805$	6.06773	0.213859
$806$	−44.0539	−1.55173
$807$	73.3675	2.58266
$808$	−3.23338	−0.113750
$809$	−51.1059	−1.79679	−0.898394	−	0.439190i	$-0.855266\pi$
$809$	−51.1059	−1.79679	−0.898394	+	0.439190i	$0.855266\pi$
$810$	89.4395	3.14258
$811$	−5.99908	−0.210656	−0.105328	−	0.994438i	$-0.533589\pi$
$811$	−5.99908	−0.210656	−0.105328	+	0.994438i	$0.533589\pi$
$812$	54.6497	1.91783
$813$	−29.5102	−1.03497
$814$	15.2347	0.533978
$815$	−9.24056	−0.323683
$816$	115.551	4.04510
$817$	−4.43884	−0.155295
$818$	−0.976333	−0.0341367
$819$	−55.9464	−1.95493
$820$	1.31695	0.0459900
$821$	18.0838	0.631129	0.315564	−	0.948904i	$-0.397806\pi$
$821$	18.0838	0.631129	0.315564	+	0.948904i	$0.397806\pi$
$822$	98.1207	3.42235
$823$	51.0919	1.78095	0.890476	−	0.455030i	$-0.150371\pi$
$823$	51.0919	1.78095	0.890476	+	0.455030i	$0.150371\pi$
$824$	4.63369	0.161422
$825$	−9.33312	−0.324938
$826$	−53.0993	−1.84756
$827$	11.2348	0.390671	0.195336	−	0.980736i	$-0.437420\pi$
$827$	11.2348	0.390671	0.195336	+	0.980736i	$0.437420\pi$
$828$	84.3683	2.93200
$829$	20.1203	0.698808	0.349404	−	0.936972i	$-0.386384\pi$
$829$	20.1203	0.698808	0.349404	+	0.936972i	$0.386384\pi$
$830$	28.8233	1.00047
$831$	60.4424	2.09672
$832$	−12.7390	−0.441644
$833$	3.38764	0.117375
$834$	−166.336	−5.75973
$835$	10.4065	0.360132
$836$	−29.7533	−1.02904
$837$	−121.259	−4.19133
$838$	−57.0044	−1.96918
$839$	16.6247	0.573949	0.286975	−	0.957938i	$-0.407350\pi$
$839$	16.6247	0.573949	0.286975	+	0.957938i	$0.407350\pi$
$840$	47.6452	1.64392
$841$	−3.15190	−0.108686
$842$	31.5662	1.08784
$843$	27.0906	0.933051
$844$	29.1213	1.00240
$845$	6.07591	0.209018
$846$	−132.374	−4.55111
$847$	8.47586	0.291234
$848$	74.7253	2.56608
$849$	−52.1730	−1.79057
$850$	15.7895	0.541577
$851$	−5.26177	−0.180371
$852$	21.3590	0.731747
$853$	3.58561	0.122769	0.0613845	−	0.998114i	$-0.480448\pi$
$853$	3.58561	0.122769	0.0613845	+	0.998114i	$0.480448\pi$
$854$	69.7316	2.38617
$855$	21.2548	0.726900
$856$	94.2206	3.22039
$857$	24.8266	0.848061	0.424030	−	0.905648i	$-0.360615\pi$
$857$	24.8266	0.848061	0.424030	+	0.905648i	$0.360615\pi$
$858$	61.2875	2.09232
$859$	−52.6585	−1.79669	−0.898343	−	0.439295i	$-0.855228\pi$
$859$	−52.6585	−1.79669	−0.898343	+	0.439295i	$0.855228\pi$
$860$	−7.38304	−0.251760
$861$	−2.66974	−0.0909844
$862$	−58.0759	−1.97807
$863$	8.45858	0.287933	0.143967	−	0.989583i	$-0.454014\pi$
$863$	8.45858	0.287933	0.143967	+	0.989583i	$0.454014\pi$
$864$	43.4192	1.47715
$865$	5.50780	0.187271
$866$	−3.96587	−0.134766
$867$	−77.6374	−2.63670
$868$	−72.1130	−2.44767
$869$	35.4256	1.20173
$870$	42.7670	1.44994
$871$	40.7538	1.38089
$872$	87.9899	2.97972
$873$	99.7201	3.37501
$874$	15.1376	0.512036
$875$	2.54255	0.0859540
$876$	180.503	6.09862
$877$	5.25018	0.177286	0.0886430	−	0.996063i	$-0.471747\pi$
$877$	5.25018	0.177286	0.0886430	+	0.996063i	$0.471747\pi$
$878$	−93.8565	−3.16750
$879$	−3.74119	−0.126187
$880$	−15.0014	−0.505698
$881$	−39.9154	−1.34479	−0.672393	−	0.740195i	$-0.734733\pi$
$881$	−39.9154	−1.34479	−0.672393	+	0.740195i	$0.734733\pi$
$882$	11.1731	0.376219
$883$	−7.57872	−0.255044	−0.127522	−	0.991836i	$-0.540702\pi$
$883$	−7.57872	−0.255044	−0.127522	+	0.991836i	$0.540702\pi$
$884$	−70.3866	−2.36736
$885$	−28.2089	−0.948231
$886$	−61.0957	−2.05255
$887$	36.6396	1.23024	0.615119	−	0.788434i	$-0.289108\pi$
$887$	36.6396	1.23024	0.615119	+	0.788434i	$0.289108\pi$
$888$	−41.3167	−1.38650
$889$	−43.7132	−1.46609
$890$	−45.8652	−1.53741
$891$	99.2342	3.32447
$892$	−25.0927	−0.840166
$893$	−16.1234	−0.539548
$894$	194.444	6.50316
$895$	−7.47603	−0.249896
$896$	−42.9330	−1.43429
$897$	−21.1674	−0.706760
$898$	9.64665	0.321913
$899$	−34.1078	−1.13756
$900$	35.3528	1.17843
$901$	−87.2643	−2.90720
$902$	2.15242	0.0716676
$903$	14.9670	0.498070
$904$	−11.6394	−0.387121
$905$	−4.90918	−0.163187
$906$	95.4682	3.17172
$907$	−2.29603	−0.0762385	−0.0381192	−	0.999273i	$-0.512137\pi$
$907$	−2.29603	−0.0762385	−0.0381192	+	0.999273i	$0.512137\pi$
$908$	−120.500	−3.99894
$909$	4.86362	0.161316
$910$	−16.6961	−0.553470
$911$	29.5839	0.980158	0.490079	−	0.871678i	$-0.336968\pi$
$911$	29.5839	0.980158	0.490079	+	0.871678i	$0.336968\pi$
$912$	46.4200	1.53712
$913$	31.9798	1.05838
$914$	69.4294	2.29652
$915$	37.0448	1.22466
$916$	−5.68085	−0.187701
$917$	37.7073	1.24521
$918$	−285.393	−9.41938
$919$	−17.5474	−0.578836	−0.289418	−	0.957203i	$-0.593462\pi$
$919$	−17.5474	−0.578836	−0.289418	+	0.957203i	$0.593462\pi$
$920$	13.2670	0.437401
$921$	−91.3078	−3.00870
$922$	67.1527	2.21156
$923$	−3.94392	−0.129816
$924$	100.323	3.30038
$925$	−2.20483	−0.0724945
$926$	−4.68775	−0.154049
$927$	−6.96995	−0.228923
$928$	12.2130	0.400911
$929$	18.2625	0.599172	0.299586	−	0.954069i	$-0.403152\pi$
$929$	18.2625	0.599172	0.299586	+	0.954069i	$0.403152\pi$
$930$	−56.4332	−1.85052
$931$	1.36091	0.0446019
$932$	−34.3966	−1.12670
$933$	−26.0079	−0.851460
$934$	−49.3916	−1.61614
$935$	17.5187	0.572923
$936$	−122.326	−3.99836
$937$	−11.2235	−0.366656	−0.183328	−	0.983052i	$-0.558687\pi$
$937$	−11.2235	−0.366656	−0.183328	+	0.983052i	$0.558687\pi$
$938$	98.2699	3.20863
$939$	84.4835	2.75701
$940$	−26.8177	−0.874697
$941$	14.9764	0.488218	0.244109	−	0.969748i	$-0.421505\pi$
$941$	14.9764	0.488218	0.244109	+	0.969748i	$0.421505\pi$
$942$	38.7026	1.26100
$943$	−0.743400	−0.0242084
$944$	−45.3411	−1.47573
$945$	−45.9563	−1.49496
$946$	−12.0668	−0.392325
$947$	−7.65859	−0.248871	−0.124435	−	0.992228i	$-0.539712\pi$
$947$	−7.65859	−0.248871	−0.124435	+	0.992228i	$0.539712\pi$
$948$	−182.329	−5.92176
$949$	−33.3297	−1.08193
$950$	6.34309	0.205797
$951$	4.43016	0.143658
$952$	−89.4323	−2.89852
$953$	−29.9609	−0.970527	−0.485264	−	0.874368i	$-0.661276\pi$
$953$	−29.9609	−0.970527	−0.485264	+	0.874368i	$0.661276\pi$
$954$	−287.816	−9.31838
$955$	−5.92847	−0.191841
$956$	−8.34589	−0.269925
$957$	47.4506	1.53386
$958$	70.6304	2.28197
$959$	−29.6576	−0.957695
$960$	−16.3186	−0.526682
$961$	14.0070	0.451839
$962$	14.4784	0.466803
$963$	−141.726	−4.56705
$964$	51.7327	1.66620
$965$	11.2342	0.361641
$966$	−51.0412	−1.64222
$967$	25.2569	0.812208	0.406104	−	0.913827i	$-0.366887\pi$
$967$	25.2569	0.812208	0.406104	+	0.913827i	$0.366887\pi$
$968$	18.5324	0.595654
$969$	−54.2094	−1.74146
$970$	29.7595	0.955520
$971$	−32.9201	−1.05646	−0.528228	−	0.849103i	$-0.677143\pi$
$971$	−32.9201	−1.05646	−0.528228	+	0.849103i	$0.677143\pi$
$972$	−281.496	−9.02898
$973$	50.2760	1.61178
$974$	57.9858	1.85798
$975$	−8.86977	−0.284060
$976$	59.5433	1.90593
$977$	−25.1267	−0.803874	−0.401937	−	0.915667i	$-0.631663\pi$
$977$	−25.1267	−0.803874	−0.401937	+	0.915667i	$0.631663\pi$
$978$	77.7308	2.48556
$979$	−50.8880	−1.62639
$980$	2.26357	0.0723071
$981$	−132.354	−4.22573
$982$	−70.0682	−2.23597
$983$	32.6072	1.04001	0.520004	−	0.854164i	$-0.325931\pi$
$983$	32.6072	1.04001	0.520004	+	0.854164i	$0.325931\pi$
$984$	−5.83736	−0.186088
$985$	10.0793	0.321152
$986$	−80.2756	−2.55650
$987$	54.3651	1.73046
$988$	−28.2762	−0.899586
$989$	4.16762	0.132523
$990$	57.7803	1.83638
$991$	−47.4543	−1.50744	−0.753718	−	0.657198i	$-0.771741\pi$
$991$	−47.4543	−1.50744	−0.753718	+	0.657198i	$0.771741\pi$
$992$	−16.1156	−0.511672
$993$	−30.6286	−0.971968
$994$	−9.51000	−0.301639
$995$	6.18163	0.195971
$996$	−164.594	−5.21536
$997$	−43.5182	−1.37824	−0.689118	−	0.724649i	$-0.742002\pi$
$997$	−43.5182	−1.37824	−0.689118	+	0.724649i	$0.742002\pi$
$998$	22.4557	0.710824
$999$	39.8520	1.26086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.12	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.12	✓	113	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49553 q^{2} -3.37079 q^{3} +4.22769 q^{4} -1.00000 q^{5} +8.41191 q^{6} -2.54255 q^{7} -5.55927 q^{8} +8.36220 q^{9} +O(q^{10})\)	\(q-2.49553 q^{2} -3.37079 q^{3} +4.22769 q^{4} -1.00000 q^{5} +8.41191 q^{6} -2.54255 q^{7} -5.55927 q^{8} +8.36220 q^{9} +2.49553 q^{10} +2.76883 q^{11} -14.2506 q^{12} +2.63137 q^{13} +6.34503 q^{14} +3.37079 q^{15} +5.41797 q^{16} -6.32712 q^{17} -20.8682 q^{18} -2.54178 q^{19} -4.22769 q^{20} +8.57041 q^{21} -6.90970 q^{22} +2.38647 q^{23} +18.7391 q^{24} +1.00000 q^{25} -6.56666 q^{26} -18.0748 q^{27} -10.7491 q^{28} -5.08410 q^{29} -8.41191 q^{30} +6.70873 q^{31} -2.40219 q^{32} -9.33312 q^{33} +15.7895 q^{34} +2.54255 q^{35} +35.3528 q^{36} -2.20483 q^{37} +6.34309 q^{38} -8.86977 q^{39} +5.55927 q^{40} -0.311506 q^{41} -21.3877 q^{42} +1.74635 q^{43} +11.7057 q^{44} -8.36220 q^{45} -5.95551 q^{46} +6.34335 q^{47} -18.2628 q^{48} -0.535416 q^{49} -2.49553 q^{50} +21.3274 q^{51} +11.1246 q^{52} +13.7921 q^{53} +45.1064 q^{54} -2.76883 q^{55} +14.1348 q^{56} +8.56778 q^{57} +12.6875 q^{58} -8.36864 q^{59} +14.2506 q^{60} +10.9900 q^{61} -16.7419 q^{62} -21.2614 q^{63} -4.84120 q^{64} -2.63137 q^{65} +23.2911 q^{66} +15.4877 q^{67} -26.7491 q^{68} -8.04428 q^{69} -6.34503 q^{70} -1.49881 q^{71} -46.4878 q^{72} -12.6663 q^{73} +5.50224 q^{74} -3.37079 q^{75} -10.7458 q^{76} -7.03989 q^{77} +22.1348 q^{78} +12.7944 q^{79} -5.41797 q^{80} +35.8398 q^{81} +0.777375 q^{82} +11.5499 q^{83} +36.2330 q^{84} +6.32712 q^{85} -4.35809 q^{86} +17.1374 q^{87} -15.3927 q^{88} -18.3789 q^{89} +20.8682 q^{90} -6.69039 q^{91} +10.0892 q^{92} -22.6137 q^{93} -15.8300 q^{94} +2.54178 q^{95} +8.09727 q^{96} +11.9251 q^{97} +1.33615 q^{98} +23.1535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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