LMFDB - Embedded newform 6013.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57881 q^{2} +1.45096 q^{3} +4.65028 q^{4} +4.21886 q^{5} -3.74175 q^{6} -1.00000 q^{7} -6.83459 q^{8} -0.894725 q^{9} +O(q^{10})$	\(q-2.57881 q^{2} +1.45096 q^{3} +4.65028 q^{4} +4.21886 q^{5} -3.74175 q^{6} -1.00000 q^{7} -6.83459 q^{8} -0.894725 q^{9} -10.8797 q^{10} -2.52769 q^{11} +6.74736 q^{12} +0.125057 q^{13} +2.57881 q^{14} +6.12138 q^{15} +8.32456 q^{16} -3.77162 q^{17} +2.30733 q^{18} +6.44998 q^{19} +19.6189 q^{20} -1.45096 q^{21} +6.51844 q^{22} -7.12018 q^{23} -9.91669 q^{24} +12.7988 q^{25} -0.322498 q^{26} -5.65108 q^{27} -4.65028 q^{28} -8.59243 q^{29} -15.7859 q^{30} -9.88638 q^{31} -7.79832 q^{32} -3.66757 q^{33} +9.72630 q^{34} -4.21886 q^{35} -4.16072 q^{36} +8.44978 q^{37} -16.6333 q^{38} +0.181452 q^{39} -28.8342 q^{40} +2.95291 q^{41} +3.74175 q^{42} +3.95820 q^{43} -11.7545 q^{44} -3.77472 q^{45} +18.3616 q^{46} -5.36484 q^{47} +12.0786 q^{48} +1.00000 q^{49} -33.0057 q^{50} -5.47245 q^{51} +0.581549 q^{52} -6.27265 q^{53} +14.5731 q^{54} -10.6640 q^{55} +6.83459 q^{56} +9.35864 q^{57} +22.1583 q^{58} +2.08576 q^{59} +28.4662 q^{60} -8.35286 q^{61} +25.4951 q^{62} +0.894725 q^{63} +3.46130 q^{64} +0.527597 q^{65} +9.45798 q^{66} -8.75828 q^{67} -17.5391 q^{68} -10.3311 q^{69} +10.8797 q^{70} +8.38423 q^{71} +6.11508 q^{72} +13.0385 q^{73} -21.7904 q^{74} +18.5705 q^{75} +29.9942 q^{76} +2.52769 q^{77} -0.467931 q^{78} -2.15745 q^{79} +35.1202 q^{80} -5.51529 q^{81} -7.61500 q^{82} +16.9078 q^{83} -6.74736 q^{84} -15.9119 q^{85} -10.2075 q^{86} -12.4672 q^{87} +17.2757 q^{88} -11.1622 q^{89} +9.73431 q^{90} -0.125057 q^{91} -33.1108 q^{92} -14.3447 q^{93} +13.8349 q^{94} +27.2116 q^{95} -11.3150 q^{96} +1.24670 q^{97} -2.57881 q^{98} +2.26159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) $ 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * 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 $

$2$	−2.57881	−1.82350	−0.911748	−	0.410749i	$-0.865267\pi$
$2$	−2.57881	−1.82350	−0.911748	+	0.410749i	$0.865267\pi$
$3$	1.45096	0.837710	0.418855	−	0.908053i	$-0.362432\pi$
$3$	1.45096	0.837710	0.418855	+	0.908053i	$0.362432\pi$
$4$	4.65028	2.32514
$5$	4.21886	1.88673	0.943366	−	0.331753i	$-0.107640\pi$
$5$	4.21886	1.88673	0.943366	+	0.331753i	$0.107640\pi$
$6$	−3.74175	−1.52756
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.83459	−2.41639
$9$	−0.894725	−0.298242
$10$	−10.8797	−3.44045
$11$	−2.52769	−0.762127	−0.381064	−	0.924549i	$-0.624442\pi$
$11$	−2.52769	−0.762127	−0.381064	+	0.924549i	$0.624442\pi$
$12$	6.74736	1.94779
$13$	0.125057	0.0346845	0.0173423	−	0.999850i	$-0.494480\pi$
$13$	0.125057	0.0346845	0.0173423	+	0.999850i	$0.494480\pi$
$14$	2.57881	0.689217
$15$	6.12138	1.58053
$16$	8.32456	2.08114
$17$	−3.77162	−0.914752	−0.457376	−	0.889273i	$-0.651211\pi$
$17$	−3.77162	−0.914752	−0.457376	+	0.889273i	$0.651211\pi$
$18$	2.30733	0.543843
$19$	6.44998	1.47973	0.739863	−	0.672757i	$-0.234890\pi$
$19$	6.44998	1.47973	0.739863	+	0.672757i	$0.234890\pi$
$20$	19.6189	4.38692
$21$	−1.45096	−0.316625
$22$	6.51844	1.38974
$23$	−7.12018	−1.48466	−0.742330	−	0.670034i	$-0.766279\pi$
$23$	−7.12018	−1.48466	−0.742330	+	0.670034i	$0.766279\pi$
$24$	−9.91669	−2.02423
$25$	12.7988	2.55976
$26$	−0.322498	−0.0632471
$27$	−5.65108	−1.08755
$28$	−4.65028	−0.878821
$29$	−8.59243	−1.59557	−0.797787	−	0.602939i	$-0.793996\pi$
$29$	−8.59243	−1.59557	−0.797787	+	0.602939i	$0.793996\pi$
$30$	−15.7859	−2.88210
$31$	−9.88638	−1.77565	−0.887823	−	0.460185i	$-0.847783\pi$
$31$	−9.88638	−1.77565	−0.887823	+	0.460185i	$0.847783\pi$
$32$	−7.79832	−1.37856
$33$	−3.66757	−0.638442
$34$	9.72630	1.66805
$35$	−4.21886	−0.713118
$36$	−4.16072	−0.693454
$37$	8.44978	1.38914	0.694568	−	0.719427i	$-0.255596\pi$
$37$	8.44978	1.38914	0.694568	+	0.719427i	$0.255596\pi$
$38$	−16.6333	−2.69828
$39$	0.181452	0.0290556
$40$	−28.8342	−4.55908
$41$	2.95291	0.461167	0.230583	−	0.973053i	$-0.425937\pi$
$41$	2.95291	0.461167	0.230583	+	0.973053i	$0.425937\pi$
$42$	3.74175	0.577364
$43$	3.95820	0.603620	0.301810	−	0.953368i	$-0.402409\pi$
$43$	3.95820	0.603620	0.301810	+	0.953368i	$0.402409\pi$
$44$	−11.7545	−1.77205
$45$	−3.77472	−0.562702
$46$	18.3616	2.70727
$47$	−5.36484	−0.782543	−0.391271	−	0.920275i	$-0.627965\pi$
$47$	−5.36484	−0.782543	−0.391271	+	0.920275i	$0.627965\pi$
$48$	12.0786	1.74339
$49$	1.00000	0.142857
$50$	−33.0057	−4.66771
$51$	−5.47245	−0.766297
$52$	0.581549	0.0806464
$53$	−6.27265	−0.861615	−0.430808	−	0.902444i	$-0.641771\pi$
$53$	−6.27265	−0.861615	−0.430808	+	0.902444i	$0.641771\pi$
$54$	14.5731	1.98314
$55$	−10.6640	−1.43793
$56$	6.83459	0.913310
$57$	9.35864	1.23958
$58$	22.1583	2.90952
$59$	2.08576	0.271543	0.135771	−	0.990740i	$-0.456649\pi$
$59$	2.08576	0.271543	0.135771	+	0.990740i	$0.456649\pi$
$60$	28.4662	3.67497
$61$	−8.35286	−1.06947	−0.534737	−	0.845019i	$-0.679589\pi$
$61$	−8.35286	−1.06947	−0.534737	+	0.845019i	$0.679589\pi$
$62$	25.4951	3.23788
$63$	0.894725	0.112725
$64$	3.46130	0.432663
$65$	0.527597	0.0654404
$66$	9.45798	1.16420
$67$	−8.75828	−1.06999	−0.534997	−	0.844854i	$-0.679687\pi$
$67$	−8.75828	−1.06999	−0.534997	+	0.844854i	$0.679687\pi$
$68$	−17.5391	−2.12693
$69$	−10.3311	−1.24371
$70$	10.8797	1.30037
$71$	8.38423	0.995025	0.497512	−	0.867457i	$-0.334247\pi$
$71$	8.38423	0.995025	0.497512	+	0.867457i	$0.334247\pi$
$72$	6.11508	0.720669
$73$	13.0385	1.52604	0.763021	−	0.646374i	$-0.223715\pi$
$73$	13.0385	1.52604	0.763021	+	0.646374i	$0.223715\pi$
$74$	−21.7904	−2.53308
$75$	18.5705	2.14434
$76$	29.9942	3.44057
$77$	2.52769	0.288057
$78$	−0.467931	−0.0529827
$79$	−2.15745	−0.242732	−0.121366	−	0.992608i	$-0.538727\pi$
$79$	−2.15745	−0.242732	−0.121366	+	0.992608i	$0.538727\pi$
$80$	35.1202	3.92655
$81$	−5.51529	−0.612810
$82$	−7.61500	−0.840936
$83$	16.9078	1.85588	0.927939	−	0.372733i	$-0.121579\pi$
$83$	16.9078	1.85588	0.927939	+	0.372733i	$0.121579\pi$
$84$	−6.74736	−0.736197
$85$	−15.9119	−1.72589
$86$	−10.2075	−1.10070
$87$	−12.4672	−1.33663
$88$	17.2757	1.84160
$89$	−11.1622	−1.18319	−0.591593	−	0.806236i	$-0.701501\pi$
$89$	−11.1622	−1.18319	−0.591593	+	0.806236i	$0.701501\pi$
$90$	9.73431	1.02609
$91$	−0.125057	−0.0131095
$92$	−33.1108	−3.45204
$93$	−14.3447	−1.48748
$94$	13.8349	1.42696
$95$	27.2116	2.79185
$96$	−11.3150	−1.15484
$97$	1.24670	0.126583	0.0632915	−	0.997995i	$-0.479840\pi$
$97$	1.24670	0.126583	0.0632915	+	0.997995i	$0.479840\pi$
$98$	−2.57881	−0.260500
$99$	2.26159	0.227298
$100$	59.5180	5.95180
$101$	7.50919	0.747193	0.373596	−	0.927591i	$-0.378125\pi$
$101$	7.50919	0.747193	0.373596	+	0.927591i	$0.378125\pi$
$102$	14.1124	1.39734
$103$	−2.96305	−0.291958	−0.145979	−	0.989288i	$-0.546633\pi$
$103$	−2.96305	−0.291958	−0.145979	+	0.989288i	$0.546633\pi$
$104$	−0.854711	−0.0838113
$105$	−6.12138	−0.597386
$106$	16.1760	1.57115
$107$	−12.4867	−1.20713	−0.603567	−	0.797312i	$-0.706254\pi$
$107$	−12.4867	−1.20713	−0.603567	+	0.797312i	$0.706254\pi$
$108$	−26.2791	−2.52871
$109$	12.7949	1.22553	0.612766	−	0.790264i	$-0.290057\pi$
$109$	12.7949	1.22553	0.612766	+	0.790264i	$0.290057\pi$
$110$	27.5004	2.62206
$111$	12.2603	1.16369
$112$	−8.32456	−0.786597
$113$	−15.4233	−1.45090	−0.725452	−	0.688273i	$-0.758369\pi$
$113$	−15.4233	−1.45090	−0.725452	+	0.688273i	$0.758369\pi$
$114$	−24.1342	−2.26037
$115$	−30.0391	−2.80116
$116$	−39.9572	−3.70993
$117$	−0.111891	−0.0103444
$118$	−5.37879	−0.495157
$119$	3.77162	0.345744
$120$	−41.8371	−3.81919
$121$	−4.61078	−0.419162
$122$	21.5405	1.95018
$123$	4.28454	0.386324
$124$	−45.9744	−4.12863
$125$	32.9020	2.94285
$126$	−2.30733	−0.205553
$127$	−15.3163	−1.35910	−0.679552	−	0.733628i	$-0.737826\pi$
$127$	−15.3163	−1.35910	−0.679552	+	0.733628i	$0.737826\pi$
$128$	6.67059	0.589602
$129$	5.74317	0.505658
$130$	−1.36057	−0.119330
$131$	8.59766	0.751181	0.375591	−	0.926786i	$-0.377440\pi$
$131$	8.59766	0.751181	0.375591	+	0.926786i	$0.377440\pi$
$132$	−17.0552	−1.48447
$133$	−6.44998	−0.559284
$134$	22.5860	1.95113
$135$	−23.8411	−2.05192
$136$	25.7774	2.21040
$137$	−6.27437	−0.536056	−0.268028	−	0.963411i	$-0.586372\pi$
$137$	−6.27437	−0.536056	−0.268028	+	0.963411i	$0.586372\pi$
$138$	26.6419	2.26791
$139$	1.85317	0.157184	0.0785921	−	0.996907i	$-0.474958\pi$
$139$	1.85317	0.157184	0.0785921	+	0.996907i	$0.474958\pi$
$140$	−19.6189	−1.65810
$141$	−7.78416	−0.655544
$142$	−21.6214	−1.81442
$143$	−0.316105	−0.0264340
$144$	−7.44819	−0.620683
$145$	−36.2503	−3.01042
$146$	−33.6239	−2.78273
$147$	1.45096	0.119673
$148$	39.2939	3.22994
$149$	−2.46286	−0.201765	−0.100883	−	0.994898i	$-0.532167\pi$
$149$	−2.46286	−0.201765	−0.100883	+	0.994898i	$0.532167\pi$
$150$	−47.8898	−3.91019
$151$	−5.82225	−0.473808	−0.236904	−	0.971533i	$-0.576133\pi$
$151$	−5.82225	−0.473808	−0.236904	+	0.971533i	$0.576133\pi$
$152$	−44.0829	−3.57560
$153$	3.37456	0.272817
$154$	−6.51844	−0.525271
$155$	−41.7093	−3.35017
$156$	0.843803	0.0675583
$157$	−10.0171	−0.799455	−0.399728	−	0.916634i	$-0.630895\pi$
$157$	−10.0171	−0.799455	−0.399728	+	0.916634i	$0.630895\pi$
$158$	5.56365	0.442620
$159$	−9.10135	−0.721784
$160$	−32.9000	−2.60098
$161$	7.12018	0.561149
$162$	14.2229	1.11746
$163$	−22.9933	−1.80098	−0.900488	−	0.434882i	$-0.856790\pi$
$163$	−22.9933	−1.80098	−0.900488	+	0.434882i	$0.856790\pi$
$164$	13.7319	1.07228
$165$	−15.4730	−1.20457
$166$	−43.6022	−3.38419
$167$	−15.2053	−1.17662	−0.588311	−	0.808635i	$-0.700207\pi$
$167$	−15.2053	−1.17662	−0.588311	+	0.808635i	$0.700207\pi$
$168$	9.91669	0.765089
$169$	−12.9844	−0.998797
$170$	41.0339	3.14716
$171$	−5.77096	−0.441316
$172$	18.4067	1.40350
$173$	−3.57902	−0.272108	−0.136054	−	0.990701i	$-0.543442\pi$
$173$	−3.57902	−0.272108	−0.136054	+	0.990701i	$0.543442\pi$
$174$	32.1507	2.43734
$175$	−12.7988	−0.967498
$176$	−21.0419	−1.58609
$177$	3.02635	0.227474
$178$	28.7851	2.15754
$179$	−21.2407	−1.58760	−0.793802	−	0.608176i	$-0.791901\pi$
$179$	−21.2407	−1.58760	−0.793802	+	0.608176i	$0.791901\pi$
$180$	−17.5535	−1.30836
$181$	−14.2079	−1.05606	−0.528031	−	0.849225i	$-0.677070\pi$
$181$	−14.2079	−1.05606	−0.528031	+	0.849225i	$0.677070\pi$
$182$	0.322498	0.0239051
$183$	−12.1196	−0.895909
$184$	48.6635	3.58752
$185$	35.6485	2.62093
$186$	36.9923	2.71241
$187$	9.53348	0.697157
$188$	−24.9480	−1.81952
$189$	5.65108	0.411055
$190$	−70.1736	−5.09093
$191$	−8.13676	−0.588756	−0.294378	−	0.955689i	$-0.595112\pi$
$191$	−8.13676	−0.588756	−0.294378	+	0.955689i	$0.595112\pi$
$192$	5.02220	0.362446
$193$	−1.46405	−0.105385	−0.0526924	−	0.998611i	$-0.516780\pi$
$193$	−1.46405	−0.105385	−0.0526924	+	0.998611i	$0.516780\pi$
$194$	−3.21500	−0.230824
$195$	0.765520	0.0548201
$196$	4.65028	0.332163
$197$	3.29414	0.234698	0.117349	−	0.993091i	$-0.462560\pi$
$197$	3.29414	0.234698	0.117349	+	0.993091i	$0.462560\pi$
$198$	−5.83222	−0.414478
$199$	−17.4846	−1.23945	−0.619725	−	0.784819i	$-0.712756\pi$
$199$	−17.4846	−1.23945	−0.619725	+	0.784819i	$0.712756\pi$
$200$	−87.4744	−6.18538
$201$	−12.7079	−0.896345
$202$	−19.3648	−1.36250
$203$	8.59243	0.603070
$204$	−25.4485	−1.78175
$205$	12.4579	0.870098
$206$	7.64117	0.532385
$207$	6.37060	0.442788
$208$	1.04104	0.0721833
$209$	−16.3035	−1.12774
$210$	15.7859	1.08933
$211$	21.6230	1.48859	0.744295	−	0.667851i	$-0.232786\pi$
$211$	21.6230	1.48859	0.744295	+	0.667851i	$0.232786\pi$
$212$	−29.1696	−2.00338
$213$	12.1651	0.833542
$214$	32.2009	2.20121
$215$	16.6991	1.13887
$216$	38.6228	2.62795
$217$	9.88638	0.671131
$218$	−32.9957	−2.23475
$219$	18.9183	1.27838
$220$	−49.5905	−3.34339
$221$	−0.471666	−0.0317277
$222$	−31.6169	−2.12199
$223$	11.8317	0.792311	0.396155	−	0.918183i	$-0.370344\pi$
$223$	11.8317	0.792311	0.396155	+	0.918183i	$0.370344\pi$
$224$	7.79832	0.521047
$225$	−11.4514	−0.763427
$226$	39.7739	2.64572
$227$	−25.4985	−1.69240	−0.846199	−	0.532867i	$-0.821114\pi$
$227$	−25.4985	−1.69240	−0.846199	+	0.532867i	$0.821114\pi$
$228$	43.5203	2.88220
$229$	26.7289	1.76630	0.883149	−	0.469093i	$-0.155419\pi$
$229$	26.7289	1.76630	0.883149	+	0.469093i	$0.155419\pi$
$230$	77.4651	5.10790
$231$	3.66757	0.241308
$232$	58.7257	3.85553
$233$	7.07910	0.463767	0.231884	−	0.972744i	$-0.425511\pi$
$233$	7.07910	0.463767	0.231884	+	0.972744i	$0.425511\pi$
$234$	0.288547	0.0188629
$235$	−22.6335	−1.47645
$236$	9.69937	0.631375
$237$	−3.13036	−0.203339
$238$	−9.72630	−0.630463
$239$	26.7538	1.73056	0.865279	−	0.501291i	$-0.167141\pi$
$239$	26.7538	1.73056	0.865279	+	0.501291i	$0.167141\pi$
$240$	50.9578	3.28931
$241$	18.9834	1.22283	0.611413	−	0.791312i	$-0.290602\pi$
$241$	18.9834	1.22283	0.611413	+	0.791312i	$0.290602\pi$
$242$	11.8903	0.764341
$243$	8.95078	0.574193
$244$	−38.8431	−2.48668
$245$	4.21886	0.269533
$246$	−11.0490	−0.704461
$247$	0.806613	0.0513236
$248$	67.5693	4.29065
$249$	24.5325	1.55469
$250$	−84.8482	−5.36627
$251$	−26.9571	−1.70152	−0.850760	−	0.525555i	$-0.823858\pi$
$251$	−26.9571	−1.70152	−0.850760	+	0.525555i	$0.823858\pi$
$252$	4.16072	0.262101
$253$	17.9976	1.13150
$254$	39.4979	2.47832
$255$	−23.0875	−1.44580
$256$	−24.1248	−1.50780
$257$	−8.32145	−0.519078	−0.259539	−	0.965733i	$-0.583571\pi$
$257$	−8.32145	−0.519078	−0.259539	+	0.965733i	$0.583571\pi$
$258$	−14.8106	−0.922066
$259$	−8.44978	−0.525044
$260$	2.45348	0.152158
$261$	7.68786	0.475867
$262$	−22.1718	−1.36978
$263$	21.3538	1.31673	0.658365	−	0.752699i	$-0.271248\pi$
$263$	21.3538	1.31673	0.658365	+	0.752699i	$0.271248\pi$
$264$	25.0663	1.54272
$265$	−26.4635	−1.62564
$266$	16.6333	1.01985
$267$	−16.1958	−0.991168
$268$	−40.7285	−2.48789
$269$	−0.668006	−0.0407290	−0.0203645	−	0.999793i	$-0.506483\pi$
$269$	−0.668006	−0.0407290	−0.0203645	+	0.999793i	$0.506483\pi$
$270$	61.4818	3.74166
$271$	15.6694	0.951845	0.475923	−	0.879487i	$-0.342114\pi$
$271$	15.6694	0.951845	0.475923	+	0.879487i	$0.342114\pi$
$272$	−31.3971	−1.90373
$273$	−0.181452	−0.0109820
$274$	16.1804	0.977496
$275$	−32.3514	−1.95086
$276$	−48.0424	−2.89181
$277$	−15.9313	−0.957218	−0.478609	−	0.878028i	$-0.658859\pi$
$277$	−15.9313	−0.957218	−0.478609	+	0.878028i	$0.658859\pi$
$278$	−4.77899	−0.286625
$279$	8.84559	0.529572
$280$	28.8342	1.72317
$281$	−8.14089	−0.485645	−0.242823	−	0.970071i	$-0.578073\pi$
$281$	−8.14089	−0.485645	−0.242823	+	0.970071i	$0.578073\pi$
$282$	20.0739	1.19538
$283$	−30.9103	−1.83743	−0.918713	−	0.394925i	$-0.870771\pi$
$283$	−30.9103	−1.83743	−0.918713	+	0.394925i	$0.870771\pi$
$284$	38.9890	2.31357
$285$	39.4828	2.33876
$286$	0.815175	0.0482023
$287$	−2.95291	−0.174305
$288$	6.97736	0.411145
$289$	−2.77489	−0.163229
$290$	93.4827	5.48949
$291$	1.80891	0.106040
$292$	60.6327	3.54826
$293$	−12.3185	−0.719653	−0.359826	−	0.933019i	$-0.617164\pi$
$293$	−12.3185	−0.719653	−0.359826	+	0.933019i	$0.617164\pi$
$294$	−3.74175	−0.218223
$295$	8.79953	0.512328
$296$	−57.7508	−3.35669
$297$	14.2842	0.828852
$298$	6.35125	0.367918
$299$	−0.890426	−0.0514947
$300$	86.3580	4.98588
$301$	−3.95820	−0.228147
$302$	15.0145	0.863987
$303$	10.8955	0.625931
$304$	53.6932	3.07952
$305$	−35.2395	−2.01781
$306$	−8.70237	−0.497481
$307$	−12.2800	−0.700857	−0.350429	−	0.936589i	$-0.613964\pi$
$307$	−12.2800	−0.700857	−0.350429	+	0.936589i	$0.613964\pi$
$308$	11.7545	0.669773
$309$	−4.29926	−0.244577
$310$	107.560	6.10902
$311$	−12.8499	−0.728649	−0.364325	−	0.931272i	$-0.618700\pi$
$311$	−12.8499	−0.728649	−0.364325	+	0.931272i	$0.618700\pi$
$312$	−1.24015	−0.0702096
$313$	10.9619	0.619601	0.309801	−	0.950802i	$-0.399738\pi$
$313$	10.9619	0.619601	0.309801	+	0.950802i	$0.399738\pi$
$314$	25.8324	1.45780
$315$	3.77472	0.212681
$316$	−10.0327	−0.564385
$317$	13.4731	0.756724	0.378362	−	0.925658i	$-0.376487\pi$
$317$	13.4731	0.756724	0.378362	+	0.925658i	$0.376487\pi$
$318$	23.4707	1.31617
$319$	21.7190	1.21603
$320$	14.6028	0.816319
$321$	−18.1177	−1.01123
$322$	−18.3616	−1.02325
$323$	−24.3269	−1.35358
$324$	−25.6477	−1.42487
$325$	1.60058	0.0887839
$326$	59.2955	3.28407
$327$	18.5649	1.02664
$328$	−20.1819	−1.11436
$329$	5.36484	0.295773
$330$	39.9019	2.19653
$331$	−2.29791	−0.126305	−0.0631524	−	0.998004i	$-0.520115\pi$
$331$	−2.29791	−0.126305	−0.0631524	+	0.998004i	$0.520115\pi$
$332$	78.6263	4.31518
$333$	−7.56023	−0.414298
$334$	39.2116	2.14557
$335$	−36.9500	−2.01879
$336$	−12.0786	−0.658940
$337$	−28.6927	−1.56299	−0.781496	−	0.623911i	$-0.785543\pi$
$337$	−28.6927	−1.56299	−0.781496	+	0.623911i	$0.785543\pi$
$338$	33.4843	1.82130
$339$	−22.3786	−1.21544
$340$	−73.9950	−4.01294
$341$	24.9897	1.35327
$342$	14.8822	0.804739
$343$	−1.00000	−0.0539949
$344$	−27.0526	−1.45858
$345$	−43.5854	−2.34656
$346$	9.22964	0.496188
$347$	−26.6413	−1.43018	−0.715090	−	0.699032i	$-0.753614\pi$
$347$	−26.6413	−1.43018	−0.715090	+	0.699032i	$0.753614\pi$
$348$	−57.9762	−3.10785
$349$	1.01497	0.0543302	0.0271651	−	0.999631i	$-0.491352\pi$
$349$	1.01497	0.0543302	0.0271651	+	0.999631i	$0.491352\pi$
$350$	33.0057	1.76423
$351$	−0.706705	−0.0377211
$352$	19.7117	1.05064
$353$	−16.3916	−0.872439	−0.436220	−	0.899840i	$-0.643683\pi$
$353$	−16.3916	−0.872439	−0.436220	+	0.899840i	$0.643683\pi$
$354$	−7.80438	−0.414798
$355$	35.3719	1.87734
$356$	−51.9072	−2.75108
$357$	5.47245	0.289633
$358$	54.7758	2.89499
$359$	−18.5786	−0.980540	−0.490270	−	0.871571i	$-0.663102\pi$
$359$	−18.5786	−0.980540	−0.490270	+	0.871571i	$0.663102\pi$
$360$	25.7987	1.35971
$361$	22.6022	1.18959
$362$	36.6394	1.92573
$363$	−6.69004	−0.351136
$364$	−0.581549	−0.0304815
$365$	55.0077	2.87923
$366$	31.2543	1.63369
$367$	23.0102	1.20112	0.600562	−	0.799578i	$-0.294944\pi$
$367$	23.0102	1.20112	0.600562	+	0.799578i	$0.294944\pi$
$368$	−59.2724	−3.08979
$369$	−2.64204	−0.137539
$370$	−91.9308	−4.77925
$371$	6.27265	0.325660
$372$	−66.7069	−3.45859
$373$	15.9299	0.824821	0.412411	−	0.910998i	$-0.364687\pi$
$373$	15.9299	0.824821	0.412411	+	0.910998i	$0.364687\pi$
$374$	−24.5851	−1.27126
$375$	47.7394	2.46525
$376$	36.6665	1.89093
$377$	−1.07454	−0.0553417
$378$	−14.5731	−0.749558
$379$	−9.94902	−0.511047	−0.255523	−	0.966803i	$-0.582248\pi$
$379$	−9.94902	−0.511047	−0.255523	+	0.966803i	$0.582248\pi$
$380$	126.541	6.49144
$381$	−22.2233	−1.13853
$382$	20.9832	1.07359
$383$	5.45135	0.278551	0.139275	−	0.990254i	$-0.455523\pi$
$383$	5.45135	0.278551	0.139275	+	0.990254i	$0.455523\pi$
$384$	9.67873	0.493916
$385$	10.6640	0.543487
$386$	3.77552	0.192169
$387$	−3.54150	−0.180025
$388$	5.79750	0.294323
$389$	28.3296	1.43637	0.718183	−	0.695854i	$-0.244974\pi$
$389$	28.3296	1.43637	0.718183	+	0.695854i	$0.244974\pi$
$390$	−1.97413	−0.0999642
$391$	26.8546	1.35810
$392$	−6.83459	−0.345199
$393$	12.4748	0.629272
$394$	−8.49498	−0.427971
$395$	−9.10196	−0.457969
$396$	10.5170	0.528500
$397$	6.42823	0.322624	0.161312	−	0.986903i	$-0.448428\pi$
$397$	6.42823	0.322624	0.161312	+	0.986903i	$0.448428\pi$
$398$	45.0895	2.26013
$399$	−9.35864	−0.468518
$400$	106.544	5.32722
$401$	20.2368	1.01058	0.505288	−	0.862951i	$-0.331386\pi$
$401$	20.2368	1.01058	0.505288	+	0.862951i	$0.331386\pi$
$402$	32.7713	1.63448
$403$	−1.23636	−0.0615874
$404$	34.9199	1.73733
$405$	−23.2683	−1.15621
$406$	−22.1583	−1.09970
$407$	−21.3584	−1.05870
$408$	37.4020	1.85167
$409$	4.54237	0.224606	0.112303	−	0.993674i	$-0.464177\pi$
$409$	4.54237	0.224606	0.112303	+	0.993674i	$0.464177\pi$
$410$	−32.1266	−1.58662
$411$	−9.10384	−0.449059
$412$	−13.7790	−0.678845
$413$	−2.08576	−0.102633
$414$	−16.4286	−0.807422
$415$	71.3319	3.50154
$416$	−0.975233	−0.0478147
$417$	2.68888	0.131675
$418$	42.0438	2.05643
$419$	11.0113	0.537938	0.268969	−	0.963149i	$-0.413317\pi$
$419$	11.0113	0.537938	0.268969	+	0.963149i	$0.413317\pi$
$420$	−28.4662	−1.38901
$421$	32.0089	1.56002	0.780010	−	0.625767i	$-0.215214\pi$
$421$	32.0089	1.56002	0.780010	+	0.625767i	$0.215214\pi$
$422$	−55.7618	−2.71444
$423$	4.80006	0.233387
$424$	42.8710	2.08200
$425$	−48.2722	−2.34154
$426$	−31.3717	−1.51996
$427$	8.35286	0.404223
$428$	−58.0667	−2.80676
$429$	−0.458654	−0.0221440
$430$	−43.0639	−2.07672
$431$	−30.0812	−1.44896	−0.724480	−	0.689296i	$-0.757920\pi$
$431$	−30.0812	−1.44896	−0.724480	+	0.689296i	$0.757920\pi$
$432$	−47.0427	−2.26334
$433$	−20.7772	−0.998490	−0.499245	−	0.866461i	$-0.666389\pi$
$433$	−20.7772	−0.998490	−0.499245	+	0.866461i	$0.666389\pi$
$434$	−25.4951	−1.22381
$435$	−52.5976	−2.52186
$436$	59.5000	2.84953
$437$	−45.9250	−2.19689
$438$	−48.7868	−2.33112
$439$	11.7213	0.559425	0.279713	−	0.960084i	$-0.409761\pi$
$439$	11.7213	0.559425	0.279713	+	0.960084i	$0.409761\pi$
$440$	72.8838	3.47460
$441$	−0.894725	−0.0426060
$442$	1.21634	0.0578554
$443$	24.2930	1.15419	0.577097	−	0.816675i	$-0.304185\pi$
$443$	24.2930	1.15419	0.577097	+	0.816675i	$0.304185\pi$
$444$	57.0137	2.70575
$445$	−47.0916	−2.23236
$446$	−30.5118	−1.44478
$447$	−3.57350	−0.169021
$448$	−3.46130	−0.163531
$449$	−20.1771	−0.952216	−0.476108	−	0.879387i	$-0.657953\pi$
$449$	−20.1771	−0.952216	−0.476108	+	0.879387i	$0.657953\pi$
$450$	29.5310	1.39211
$451$	−7.46404	−0.351468
$452$	−71.7228	−3.37356
$453$	−8.44782	−0.396913
$454$	65.7560	3.08608
$455$	−0.527597	−0.0247341
$456$	−63.9624	−2.99531
$457$	4.29216	0.200779	0.100389	−	0.994948i	$-0.467991\pi$
$457$	4.29216	0.200779	0.100389	+	0.994948i	$0.467991\pi$
$458$	−68.9290	−3.22084
$459$	21.3137	0.994839
$460$	−139.690	−6.51308
$461$	3.68236	0.171505	0.0857523	−	0.996316i	$-0.472671\pi$
$461$	3.68236	0.171505	0.0857523	+	0.996316i	$0.472671\pi$
$462$	−9.45798	−0.440025
$463$	14.5606	0.676686	0.338343	−	0.941023i	$-0.390134\pi$
$463$	14.5606	0.676686	0.338343	+	0.941023i	$0.390134\pi$
$464$	−71.5282	−3.32061
$465$	−60.5183	−2.80647
$466$	−18.2557	−0.845678
$467$	3.53799	0.163719	0.0818593	−	0.996644i	$-0.473914\pi$
$467$	3.53799	0.163719	0.0818593	+	0.996644i	$0.473914\pi$
$468$	−0.520327	−0.0240521
$469$	8.75828	0.404420
$470$	58.3677	2.69230
$471$	−14.5344	−0.669712
$472$	−14.2553	−0.656153
$473$	−10.0051	−0.460035
$474$	8.07261	0.370787
$475$	82.5519	3.78774
$476$	17.5391	0.803903
$477$	5.61230	0.256970
$478$	−68.9930	−3.15567
$479$	−21.1512	−0.966425	−0.483213	−	0.875503i	$-0.660530\pi$
$479$	−21.1512	−0.966425	−0.483213	+	0.875503i	$0.660530\pi$
$480$	−47.7365	−2.17886
$481$	1.05670	0.0481815
$482$	−48.9545	−2.22982
$483$	10.3311	0.470080
$484$	−21.4414	−0.974611
$485$	5.25965	0.238828
$486$	−23.0824	−1.04704
$487$	−14.2430	−0.645411	−0.322706	−	0.946499i	$-0.604592\pi$
$487$	−14.2430	−0.645411	−0.322706	+	0.946499i	$0.604592\pi$
$488$	57.0883	2.58427
$489$	−33.3623	−1.50870
$490$	−10.8797	−0.491493
$491$	−43.2166	−1.95034	−0.975169	−	0.221461i	$-0.928917\pi$
$491$	−43.2166	−1.95034	−0.975169	+	0.221461i	$0.928917\pi$
$492$	19.9243	0.898258
$493$	32.4074	1.45955
$494$	−2.08011	−0.0935884
$495$	9.54133	0.428851
$496$	−82.2997	−3.69537
$497$	−8.38423	−0.376084
$498$	−63.2649	−2.83497
$499$	−16.9785	−0.760064	−0.380032	−	0.924973i	$-0.624087\pi$
$499$	−16.9785	−0.760064	−0.380032	+	0.924973i	$0.624087\pi$
$500$	153.004	6.84253
$501$	−22.0622	−0.985668
$502$	69.5174	3.10271
$503$	−10.4158	−0.464416	−0.232208	−	0.972666i	$-0.574595\pi$
$503$	−10.4158	−0.464416	−0.232208	+	0.972666i	$0.574595\pi$
$504$	−6.11508	−0.272387
$505$	31.6802	1.40975
$506$	−46.4125	−2.06329
$507$	−18.8397	−0.836702
$508$	−71.2252	−3.16011
$509$	27.2777	1.20906	0.604530	−	0.796582i	$-0.293361\pi$
$509$	27.2777	1.20906	0.604530	+	0.796582i	$0.293361\pi$
$510$	59.5384	2.63641
$511$	−13.0385	−0.576790
$512$	48.8722	2.15987
$513$	−36.4493	−1.60928
$514$	21.4595	0.946537
$515$	−12.5007	−0.550847
$516$	26.7074	1.17573
$517$	13.5607	0.596397
$518$	21.7904	0.957416
$519$	−5.19301	−0.227948
$520$	−3.60591	−0.158129
$521$	28.5955	1.25279	0.626396	−	0.779505i	$-0.284529\pi$
$521$	28.5955	1.25279	0.626396	+	0.779505i	$0.284529\pi$
$522$	−19.8256	−0.867741
$523$	30.0642	1.31462	0.657309	−	0.753622i	$-0.271695\pi$
$523$	30.0642	1.31462	0.657309	+	0.753622i	$0.271695\pi$
$524$	39.9816	1.74660
$525$	−18.5705	−0.810483
$526$	−55.0674	−2.40105
$527$	37.2876	1.62428
$528$	−30.5309	−1.32869
$529$	27.6970	1.20422
$530$	68.2443	2.96434
$531$	−1.86618	−0.0809854
$532$	−29.9942	−1.30041
$533$	0.369281	0.0159953
$534$	41.7660	1.80739
$535$	−52.6796	−2.27754
$536$	59.8592	2.58552
$537$	−30.8193	−1.32995
$538$	1.72266	0.0742692
$539$	−2.52769	−0.108875
$540$	−110.868	−4.77099
$541$	−2.04113	−0.0877549	−0.0438774	−	0.999037i	$-0.513971\pi$
$541$	−2.04113	−0.0877549	−0.0438774	+	0.999037i	$0.513971\pi$
$542$	−40.4083	−1.73569
$543$	−20.6150	−0.884674
$544$	29.4123	1.26104
$545$	53.9800	2.31225
$546$	0.467931	0.0200256
$547$	38.7673	1.65757	0.828786	−	0.559566i	$-0.189032\pi$
$547$	38.7673	1.65757	0.828786	+	0.559566i	$0.189032\pi$
$548$	−29.1776	−1.24641
$549$	7.47351	0.318962
$550$	83.4282	3.55739
$551$	−55.4210	−2.36101
$552$	70.6086	3.00530
$553$	2.15745	0.0917439
$554$	41.0838	1.74548
$555$	51.7244	2.19558
$556$	8.61778	0.365475
$557$	18.6044	0.788293	0.394147	−	0.919048i	$-0.371040\pi$
$557$	18.6044	0.788293	0.394147	+	0.919048i	$0.371040\pi$
$558$	−22.8111	−0.965672
$559$	0.494999	0.0209362
$560$	−35.1202	−1.48410
$561$	13.8327	0.584016
$562$	20.9939	0.885572
$563$	15.7396	0.663346	0.331673	−	0.943394i	$-0.392387\pi$
$563$	15.7396	0.663346	0.331673	+	0.943394i	$0.392387\pi$
$564$	−36.1985	−1.52423
$565$	−65.0689	−2.73747
$566$	79.7119	3.35054
$567$	5.51529	0.231620
$568$	−57.3027	−2.40437
$569$	20.1025	0.842741	0.421371	−	0.906889i	$-0.361549\pi$
$569$	20.1025	0.842741	0.421371	+	0.906889i	$0.361549\pi$
$570$	−101.819	−4.26472
$571$	28.3667	1.18711	0.593555	−	0.804793i	$-0.297724\pi$
$571$	28.3667	1.18711	0.593555	+	0.804793i	$0.297724\pi$
$572$	−1.46998	−0.0614628
$573$	−11.8061	−0.493207
$574$	7.61500	0.317844
$575$	−91.1297	−3.80037
$576$	−3.09692	−0.129038
$577$	−27.4917	−1.14449	−0.572247	−	0.820081i	$-0.693928\pi$
$577$	−27.4917	−1.14449	−0.572247	+	0.820081i	$0.693928\pi$
$578$	7.15594	0.297648
$579$	−2.12428	−0.0882820
$580$	−168.574	−6.99965
$581$	−16.9078	−0.701456
$582$	−4.66483	−0.193363
$583$	15.8553	0.656660
$584$	−89.1128	−3.68751
$585$	−0.472054	−0.0195170
$586$	31.7671	1.31228
$587$	7.18698	0.296639	0.148319	−	0.988940i	$-0.452614\pi$
$587$	7.18698	0.296639	0.148319	+	0.988940i	$0.452614\pi$
$588$	6.74736	0.278256
$589$	−63.7669	−2.62747
$590$	−22.6924	−0.934229
$591$	4.77966	0.196609
$592$	70.3407	2.89099
$593$	−26.2882	−1.07953	−0.539764	−	0.841817i	$-0.681486\pi$
$593$	−26.2882	−1.07953	−0.539764	+	0.841817i	$0.681486\pi$
$594$	−36.8362	−1.51141
$595$	15.9119	0.652326
$596$	−11.4530	−0.469132
$597$	−25.3694	−1.03830
$598$	2.29624	0.0939004
$599$	27.4542	1.12175	0.560873	−	0.827902i	$-0.310465\pi$
$599$	27.4542	1.12175	0.560873	+	0.827902i	$0.310465\pi$
$600$	−126.922	−5.18155
$601$	8.39212	0.342322	0.171161	−	0.985243i	$-0.445248\pi$
$601$	8.39212	0.342322	0.171161	+	0.985243i	$0.445248\pi$
$602$	10.2075	0.416025
$603$	7.83625	0.319117
$604$	−27.0751	−1.10167
$605$	−19.4523	−0.790846
$606$	−28.0975	−1.14138
$607$	−6.00797	−0.243856	−0.121928	−	0.992539i	$-0.538908\pi$
$607$	−6.00797	−0.243856	−0.121928	+	0.992539i	$0.538908\pi$
$608$	−50.2990	−2.03989
$609$	12.4672	0.505198
$610$	90.8762	3.67947
$611$	−0.670910	−0.0271421
$612$	15.6927	0.634338
$613$	−16.5327	−0.667749	−0.333875	−	0.942617i	$-0.608356\pi$
$613$	−16.5327	−0.667749	−0.333875	+	0.942617i	$0.608356\pi$
$614$	31.6679	1.27801
$615$	18.0759	0.728890
$616$	−17.2757	−0.696058
$617$	−5.13713	−0.206813	−0.103406	−	0.994639i	$-0.532974\pi$
$617$	−5.13713	−0.206813	−0.103406	+	0.994639i	$0.532974\pi$
$618$	11.0870	0.445985
$619$	10.7117	0.430542	0.215271	−	0.976554i	$-0.430937\pi$
$619$	10.7117	0.430542	0.215271	+	0.976554i	$0.430937\pi$
$620$	−193.960	−7.78961
$621$	40.2367	1.61464
$622$	33.1374	1.32869
$623$	11.1622	0.447203
$624$	1.51051	0.0604687
$625$	74.8151	2.99261
$626$	−28.2686	−1.12984
$627$	−23.6557	−0.944719
$628$	−46.5826	−1.85885
$629$	−31.8694	−1.27071
$630$	−9.73431	−0.387824
$631$	38.2070	1.52100	0.760498	−	0.649341i	$-0.224955\pi$
$631$	38.2070	1.52100	0.760498	+	0.649341i	$0.224955\pi$
$632$	14.7452	0.586534
$633$	31.3741	1.24701
$634$	−34.7446	−1.37988
$635$	−64.6174	−2.56426
$636$	−42.3238	−1.67825
$637$	0.125057	0.00495493
$638$	−56.0093	−2.21743
$639$	−7.50158	−0.296758
$640$	28.1423	1.11242
$641$	22.2813	0.880059	0.440030	−	0.897983i	$-0.354968\pi$
$641$	22.2813	0.880059	0.440030	+	0.897983i	$0.354968\pi$
$642$	46.7221	1.84397
$643$	13.5921	0.536020	0.268010	−	0.963416i	$-0.413634\pi$
$643$	13.5921	0.536020	0.268010	+	0.963416i	$0.413634\pi$
$644$	33.1108	1.30475
$645$	24.2297	0.954042
$646$	62.7344	2.46825
$647$	−0.779039	−0.0306272	−0.0153136	−	0.999883i	$-0.504875\pi$
$647$	−0.779039	−0.0306272	−0.0153136	+	0.999883i	$0.504875\pi$
$648$	37.6947	1.48079
$649$	−5.27215	−0.206950
$650$	−4.12759	−0.161897
$651$	14.3447	0.562213
$652$	−106.925	−4.18752
$653$	6.50410	0.254525	0.127263	−	0.991869i	$-0.459381\pi$
$653$	6.50410	0.254525	0.127263	+	0.991869i	$0.459381\pi$
$654$	−47.8754	−1.87208
$655$	36.2723	1.41728
$656$	24.5817	0.959752
$657$	−11.6659	−0.455129
$658$	−13.8349	−0.539342
$659$	40.5681	1.58031	0.790154	−	0.612909i	$-0.210001\pi$
$659$	40.5681	1.58031	0.790154	+	0.612909i	$0.210001\pi$
$660$	−71.9537	−2.80079
$661$	−32.5834	−1.26735	−0.633673	−	0.773601i	$-0.718454\pi$
$661$	−32.5834	−1.26735	−0.633673	+	0.773601i	$0.718454\pi$
$662$	5.92589	0.230316
$663$	−0.684367	−0.0265786
$664$	−115.558	−4.48452
$665$	−27.2116	−1.05522
$666$	19.4964	0.755472
$667$	61.1796	2.36888
$668$	−70.7089	−2.73581
$669$	17.1673	0.663727
$670$	95.2871	3.68126
$671$	21.1134	0.815075
$672$	11.3150	0.436487
$673$	−7.96819	−0.307151	−0.153576	−	0.988137i	$-0.549079\pi$
$673$	−7.96819	−0.307151	−0.153576	+	0.988137i	$0.549079\pi$
$674$	73.9932	2.85011
$675$	−72.3270	−2.78387
$676$	−60.3809	−2.32234
$677$	−16.5914	−0.637660	−0.318830	−	0.947812i	$-0.603290\pi$
$677$	−16.5914	−0.637660	−0.318830	+	0.947812i	$0.603290\pi$
$678$	57.7102	2.21635
$679$	−1.24670	−0.0478439
$680$	108.751	4.17043
$681$	−36.9973	−1.41774
$682$	−64.4438	−2.46768
$683$	1.77881	0.0680643	0.0340322	−	0.999421i	$-0.489165\pi$
$683$	1.77881	0.0680643	0.0340322	+	0.999421i	$0.489165\pi$
$684$	−26.8366	−1.02612
$685$	−26.4707	−1.01139
$686$	2.57881	0.0984596
$687$	38.7825	1.47965
$688$	32.9503	1.25622
$689$	−0.784437	−0.0298847
$690$	112.399	4.27894
$691$	11.9474	0.454499	0.227250	−	0.973837i	$-0.427027\pi$
$691$	11.9474	0.454499	0.227250	+	0.973837i	$0.427027\pi$
$692$	−16.6435	−0.632690
$693$	−2.26159	−0.0859106
$694$	68.7030	2.60793
$695$	7.81829	0.296564
$696$	85.2084	3.22982
$697$	−11.1372	−0.421853
$698$	−2.61742	−0.0990709
$699$	10.2715	0.388503
$700$	−59.5180	−2.24957
$701$	−50.9366	−1.92385	−0.961925	−	0.273313i	$-0.911881\pi$
$701$	−50.9366	−1.92385	−0.961925	+	0.273313i	$0.911881\pi$
$702$	1.82246	0.0687844
$703$	54.5009	2.05554
$704$	−8.74910	−0.329744
$705$	−32.8403	−1.23684
$706$	42.2710	1.59089
$707$	−7.50919	−0.282412
$708$	14.0734	0.528909
$709$	17.9563	0.674363	0.337182	−	0.941440i	$-0.390526\pi$
$709$	17.9563	0.674363	0.337182	+	0.941440i	$0.390526\pi$
$710$	−91.2175	−3.42333
$711$	1.93032	0.0723927
$712$	76.2887	2.85904
$713$	70.3928	2.63623
$714$	−14.1124	−0.528145
$715$	−1.33360	−0.0498739
$716$	−98.7752	−3.69140
$717$	38.8186	1.44971
$718$	47.9107	1.78801
$719$	−13.2429	−0.493876	−0.246938	−	0.969031i	$-0.579424\pi$
$719$	−13.2429	−0.493876	−0.246938	+	0.969031i	$0.579424\pi$
$720$	−31.4229	−1.17106
$721$	2.96305	0.110350
$722$	−58.2869	−2.16922
$723$	27.5440	1.02437
$724$	−66.0706	−2.45549
$725$	−109.973	−4.08428
$726$	17.2524	0.640296
$727$	−23.9179	−0.887066	−0.443533	−	0.896258i	$-0.646275\pi$
$727$	−23.9179	−0.887066	−0.443533	+	0.896258i	$0.646275\pi$
$728$	0.854711	0.0316777
$729$	29.5331	1.09382
$730$	−141.855	−5.25027
$731$	−14.9288	−0.552162
$732$	−56.3597	−2.08311
$733$	−10.2871	−0.379962	−0.189981	−	0.981788i	$-0.560843\pi$
$733$	−10.2871	−0.379962	−0.189981	+	0.981788i	$0.560843\pi$
$734$	−59.3391	−2.19024
$735$	6.12138	0.225791
$736$	55.5255	2.04670
$737$	22.1382	0.815472
$738$	6.81333	0.250802
$739$	3.36594	0.123818	0.0619091	−	0.998082i	$-0.480281\pi$
$739$	3.36594	0.123818	0.0619091	+	0.998082i	$0.480281\pi$
$740$	165.775	6.09403
$741$	1.17036	0.0429943
$742$	−16.1760	−0.593840
$743$	49.1083	1.80161	0.900804	−	0.434226i	$-0.142978\pi$
$743$	49.1083	1.80161	0.900804	+	0.434226i	$0.142978\pi$
$744$	98.0401	3.59432
$745$	−10.3905	−0.380677
$746$	−41.0804	−1.50406
$747$	−15.1279	−0.553500
$748$	44.3334	1.62099
$749$	12.4867	0.456254
$750$	−123.111	−4.49538
$751$	10.1045	0.368719	0.184359	−	0.982859i	$-0.440979\pi$
$751$	10.1045	0.368719	0.184359	+	0.982859i	$0.440979\pi$
$752$	−44.6600	−1.62858
$753$	−39.1136	−1.42538
$754$	2.77104	0.100915
$755$	−24.5632	−0.893948
$756$	26.2791	0.955762
$757$	−16.4441	−0.597670	−0.298835	−	0.954305i	$-0.596598\pi$
$757$	−16.4441	−0.597670	−0.298835	+	0.954305i	$0.596598\pi$
$758$	25.6567	0.931892
$759$	26.1137	0.947869
$760$	−185.980	−6.74620
$761$	15.1615	0.549604	0.274802	−	0.961501i	$-0.411388\pi$
$761$	15.1615	0.549604	0.274802	+	0.961501i	$0.411388\pi$
$762$	57.3098	2.07611
$763$	−12.7949	−0.463208
$764$	−37.8383	−1.36894
$765$	14.2368	0.514733
$766$	−14.0580	−0.507936
$767$	0.260838	0.00941832
$768$	−35.0040	−1.26310
$769$	48.8209	1.76053	0.880264	−	0.474484i	$-0.157365\pi$
$769$	48.8209	1.76053	0.880264	+	0.474484i	$0.157365\pi$
$770$	−27.5004	−0.991046
$771$	−12.0741	−0.434837
$772$	−6.80826	−0.245035
$773$	20.9729	0.754341	0.377171	−	0.926144i	$-0.376897\pi$
$773$	20.9729	0.754341	0.377171	+	0.926144i	$0.376897\pi$
$774$	9.13287	0.328274
$775$	−126.534	−4.54522
$776$	−8.52067	−0.305874
$777$	−12.2603	−0.439835
$778$	−73.0567	−2.61921
$779$	19.0462	0.682401
$780$	3.55989	0.127464
$781$	−21.1927	−0.758335
$782$	−69.2530	−2.47648
$783$	48.5565	1.73527
$784$	8.32456	0.297306
$785$	−42.2610	−1.50836
$786$	−32.1703	−1.14748
$787$	7.76216	0.276691	0.138345	−	0.990384i	$-0.455822\pi$
$787$	7.76216	0.276691	0.138345	+	0.990384i	$0.455822\pi$
$788$	15.3187	0.545706
$789$	30.9834	1.10304
$790$	23.4723	0.835106
$791$	15.4233	0.548390
$792$	−15.4570	−0.549241
$793$	−1.04458	−0.0370942
$794$	−16.5772	−0.588303
$795$	−38.3973	−1.36181
$796$	−81.3083	−2.88190
$797$	−12.0070	−0.425311	−0.212655	−	0.977127i	$-0.568211\pi$
$797$	−12.0070	−0.425311	−0.212655	+	0.977127i	$0.568211\pi$
$798$	24.1342	0.854341
$799$	20.2341	0.715833
$800$	−99.8091	−3.52879
$801$	9.98707	0.352876
$802$	−52.1868	−1.84278
$803$	−32.9573	−1.16304
$804$	−59.0953	−2.08413
$805$	30.0391	1.05874
$806$	3.18834	0.112304
$807$	−0.969247	−0.0341191
$808$	−51.3222	−1.80551
$809$	27.5076	0.967117	0.483558	−	0.875312i	$-0.339344\pi$
$809$	27.5076	0.967117	0.483558	+	0.875312i	$0.339344\pi$
$810$	60.0045	2.10834
$811$	1.62498	0.0570607	0.0285303	−	0.999593i	$-0.490917\pi$
$811$	1.62498	0.0570607	0.0285303	+	0.999593i	$0.490917\pi$
$812$	39.9572	1.40222
$813$	22.7355	0.797371
$814$	55.0794	1.93053
$815$	−97.0056	−3.39796
$816$	−45.5558	−1.59477
$817$	25.5303	0.893192
$818$	−11.7139	−0.409568
$819$	0.111891	0.00390980
$820$	57.9328	2.02310
$821$	10.5670	0.368790	0.184395	−	0.982852i	$-0.440967\pi$
$821$	10.5670	0.368790	0.184395	+	0.982852i	$0.440967\pi$
$822$	23.4771	0.818858
$823$	−18.9921	−0.662021	−0.331011	−	0.943627i	$-0.607390\pi$
$823$	−18.9921	−0.662021	−0.331011	+	0.943627i	$0.607390\pi$
$824$	20.2513	0.705486
$825$	−46.9405	−1.63426
$826$	5.37879	0.187152
$827$	−3.67570	−0.127816	−0.0639082	−	0.997956i	$-0.520356\pi$
$827$	−3.67570	−0.127816	−0.0639082	+	0.997956i	$0.520356\pi$
$828$	29.6251	1.02954
$829$	−43.0126	−1.49389	−0.746944	−	0.664887i	$-0.768480\pi$
$829$	−43.0126	−1.49389	−0.746944	+	0.664887i	$0.768480\pi$
$830$	−183.952	−6.38505
$831$	−23.1156	−0.801871
$832$	0.432859	0.0150067
$833$	−3.77162	−0.130679
$834$	−6.93411	−0.240109
$835$	−64.1491	−2.21997
$836$	−75.8161	−2.62215
$837$	55.8687	1.93110
$838$	−28.3961	−0.980928
$839$	−42.6327	−1.47184	−0.735922	−	0.677067i	$-0.763251\pi$
$839$	−42.6327	−1.47184	−0.735922	+	0.677067i	$0.763251\pi$
$840$	41.8371	1.44352
$841$	44.8298	1.54586
$842$	−82.5451	−2.84469
$843$	−11.8121	−0.406830
$844$	100.553	3.46118
$845$	−54.7792	−1.88446
$846$	−12.3785	−0.425580
$847$	4.61078	0.158428
$848$	−52.2171	−1.79314
$849$	−44.8495	−1.53923
$850$	124.485	4.26980
$851$	−60.1640	−2.06239
$852$	56.5714	1.93810
$853$	−14.4077	−0.493312	−0.246656	−	0.969103i	$-0.579332\pi$
$853$	−14.4077	−0.493312	−0.246656	+	0.969103i	$0.579332\pi$
$854$	−21.5405	−0.737099
$855$	−24.3469	−0.832646
$856$	85.3414	2.91691
$857$	−19.8645	−0.678558	−0.339279	−	0.940686i	$-0.610183\pi$
$857$	−19.8645	−0.678558	−0.339279	+	0.940686i	$0.610183\pi$
$858$	1.18278	0.0403796
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	77.6555	2.64803
$861$	−4.28454	−0.146017
$862$	77.5738	2.64217
$863$	51.8852	1.76619	0.883096	−	0.469192i	$-0.155455\pi$
$863$	51.8852	1.76619	0.883096	+	0.469192i	$0.155455\pi$
$864$	44.0689	1.49926
$865$	−15.0994	−0.513395
$866$	53.5806	1.82074
$867$	−4.02625	−0.136739
$868$	45.9744	1.56047
$869$	5.45335	0.184992
$870$	135.639	4.59860
$871$	−1.09528	−0.0371122
$872$	−87.4480	−2.96136
$873$	−1.11545	−0.0377523
$874$	118.432	4.00602
$875$	−32.9020	−1.11229
$876$	87.9755	2.97242
$877$	59.2246	1.99987	0.999936	−	0.0112743i	$-0.00358881\pi$
$877$	59.2246	1.99987	0.999936	+	0.0112743i	$0.00358881\pi$
$878$	−30.2270	−1.02011
$879$	−17.8736	−0.602861
$880$	−88.7729	−2.99253
$881$	6.52818	0.219940	0.109970	−	0.993935i	$-0.464925\pi$
$881$	6.52818	0.219940	0.109970	+	0.993935i	$0.464925\pi$
$882$	2.30733	0.0776918
$883$	−8.08800	−0.272183	−0.136091	−	0.990696i	$-0.543454\pi$
$883$	−8.08800	−0.272183	−0.136091	+	0.990696i	$0.543454\pi$
$884$	−2.19338	−0.0737714
$885$	12.7677	0.429183
$886$	−62.6471	−2.10467
$887$	−47.1668	−1.58370	−0.791852	−	0.610712i	$-0.790883\pi$
$887$	−47.1668	−1.58370	−0.791852	+	0.610712i	$0.790883\pi$
$888$	−83.7938	−2.81194
$889$	15.3163	0.513693
$890$	121.441	4.07070
$891$	13.9409	0.467039
$892$	55.0209	1.84223
$893$	−34.6031	−1.15795
$894$	9.21539	0.308209
$895$	−89.6115	−2.99538
$896$	−6.67059	−0.222849
$897$	−1.29197	−0.0431376
$898$	52.0330	1.73636
$899$	84.9480	2.83317
$900$	−53.2523	−1.77508
$901$	23.6581	0.788164
$902$	19.2484	0.640900
$903$	−5.74317	−0.191121
$904$	105.412	3.50595
$905$	−59.9410	−1.99251
$906$	21.7854	0.723770
$907$	−40.4429	−1.34289	−0.671443	−	0.741056i	$-0.734325\pi$
$907$	−40.4429	−1.34289	−0.671443	+	0.741056i	$0.734325\pi$
$908$	−118.575	−3.93506
$909$	−6.71866	−0.222844
$910$	1.36057	0.0451026
$911$	−13.7678	−0.456146	−0.228073	−	0.973644i	$-0.573243\pi$
$911$	−13.7678	−0.456146	−0.228073	+	0.973644i	$0.573243\pi$
$912$	77.9065	2.57974
$913$	−42.7378	−1.41441
$914$	−11.0687	−0.366120
$915$	−51.1310	−1.69034
$916$	124.297	4.10689
$917$	−8.59766	−0.283920
$918$	−54.9641	−1.81409
$919$	33.4025	1.10185	0.550923	−	0.834556i	$-0.314276\pi$
$919$	33.4025	1.10185	0.550923	+	0.834556i	$0.314276\pi$
$920$	205.304	6.76869
$921$	−17.8178	−0.587115
$922$	−9.49612	−0.312738
$923$	1.04850	0.0345119
$924$	17.0552	0.561076
$925$	108.147	3.55585
$926$	−37.5490	−1.23394
$927$	2.65112	0.0870742
$928$	67.0065	2.19960
$929$	26.7661	0.878168	0.439084	−	0.898446i	$-0.355303\pi$
$929$	26.7661	0.878168	0.439084	+	0.898446i	$0.355303\pi$
$930$	156.065	5.11759
$931$	6.44998	0.211390
$932$	32.9198	1.07832
$933$	−18.6446	−0.610397
$934$	−9.12382	−0.298541
$935$	40.2204	1.31535
$936$	0.764731	0.0249960
$937$	−20.0846	−0.656135	−0.328068	−	0.944654i	$-0.606397\pi$
$937$	−20.0846	−0.656135	−0.328068	+	0.944654i	$0.606397\pi$
$938$	−22.5860	−0.737458
$939$	15.9052	0.519046
$940$	−105.252	−3.43295
$941$	37.1302	1.21041	0.605205	−	0.796070i	$-0.293091\pi$
$941$	37.1302	1.21041	0.605205	+	0.796070i	$0.293091\pi$
$942$	37.4816	1.22122
$943$	−21.0252	−0.684676
$944$	17.3630	0.565118
$945$	23.8411	0.775551
$946$	25.8013	0.838872
$947$	−43.6702	−1.41909	−0.709545	−	0.704660i	$-0.751099\pi$
$947$	−43.6702	−1.41909	−0.709545	+	0.704660i	$0.751099\pi$
$948$	−14.5571	−0.472791
$949$	1.63055	0.0529300
$950$	−212.886	−6.90694
$951$	19.5489	0.633916
$952$	−25.7774	−0.835452
$953$	6.83194	0.221308	0.110654	−	0.993859i	$-0.464705\pi$
$953$	6.83194	0.221308	0.110654	+	0.993859i	$0.464705\pi$
$954$	−14.4731	−0.468583
$955$	−34.3279	−1.11082
$956$	124.413	4.02379
$957$	31.5133	1.01868
$958$	54.5451	1.76227
$959$	6.27437	0.202610
$960$	21.1880	0.683839
$961$	66.7405	2.15292
$962$	−2.72504	−0.0878588
$963$	11.1722	0.360018
$964$	88.2779	2.84324
$965$	−6.17664	−0.198833
$966$	−26.6419	−0.857189
$967$	19.5520	0.628749	0.314375	−	0.949299i	$-0.398205\pi$
$967$	19.5520	0.628749	0.314375	+	0.949299i	$0.398205\pi$
$968$	31.5128	1.01286
$969$	−35.2972	−1.13391
$970$	−13.5637	−0.435503
$971$	5.43343	0.174367	0.0871835	−	0.996192i	$-0.472213\pi$
$971$	5.43343	0.174367	0.0871835	+	0.996192i	$0.472213\pi$
$972$	41.6237	1.33508
$973$	−1.85317	−0.0594100
$974$	36.7300	1.17691
$975$	2.32237	0.0743752
$976$	−69.5339	−2.22572
$977$	−16.8531	−0.539179	−0.269590	−	0.962975i	$-0.586888\pi$
$977$	−16.8531	−0.539179	−0.269590	+	0.962975i	$0.586888\pi$
$978$	86.0352	2.75110
$979$	28.2145	0.901739
$980$	19.6189	0.626703
$981$	−11.4479	−0.365505
$982$	111.448	3.55644
$983$	6.41416	0.204580	0.102290	−	0.994755i	$-0.467383\pi$
$983$	6.41416	0.204580	0.102290	+	0.994755i	$0.467383\pi$
$984$	−29.2831	−0.933510
$985$	13.8975	0.442812
$986$	−83.5726	−2.66149
$987$	7.78416	0.247772
$988$	3.75098	0.119335
$989$	−28.1831	−0.896170
$990$	−24.6053	−0.782008
$991$	−23.1619	−0.735762	−0.367881	−	0.929873i	$-0.619917\pi$
$991$	−23.1619	−0.735762	−0.367881	+	0.929873i	$0.619917\pi$
$992$	77.0972	2.44784
$993$	−3.33417	−0.105807
$994$	21.6214	0.685788
$995$	−73.7651	−2.33851
$996$	114.083	3.61487
$997$	−16.9366	−0.536387	−0.268194	−	0.963365i	$-0.586427\pi$
$997$	−16.9366	−0.536387	−0.268194	+	0.963365i	$0.586427\pi$
$998$	43.7845	1.38597
$999$	−47.7504	−1.51075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.c.1.7	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.c.1.7	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57881 q^{2} +1.45096 q^{3} +4.65028 q^{4} +4.21886 q^{5} -3.74175 q^{6} -1.00000 q^{7} -6.83459 q^{8} -0.894725 q^{9} +O(q^{10})\)	\(q-2.57881 q^{2} +1.45096 q^{3} +4.65028 q^{4} +4.21886 q^{5} -3.74175 q^{6} -1.00000 q^{7} -6.83459 q^{8} -0.894725 q^{9} -10.8797 q^{10} -2.52769 q^{11} +6.74736 q^{12} +0.125057 q^{13} +2.57881 q^{14} +6.12138 q^{15} +8.32456 q^{16} -3.77162 q^{17} +2.30733 q^{18} +6.44998 q^{19} +19.6189 q^{20} -1.45096 q^{21} +6.51844 q^{22} -7.12018 q^{23} -9.91669 q^{24} +12.7988 q^{25} -0.322498 q^{26} -5.65108 q^{27} -4.65028 q^{28} -8.59243 q^{29} -15.7859 q^{30} -9.88638 q^{31} -7.79832 q^{32} -3.66757 q^{33} +9.72630 q^{34} -4.21886 q^{35} -4.16072 q^{36} +8.44978 q^{37} -16.6333 q^{38} +0.181452 q^{39} -28.8342 q^{40} +2.95291 q^{41} +3.74175 q^{42} +3.95820 q^{43} -11.7545 q^{44} -3.77472 q^{45} +18.3616 q^{46} -5.36484 q^{47} +12.0786 q^{48} +1.00000 q^{49} -33.0057 q^{50} -5.47245 q^{51} +0.581549 q^{52} -6.27265 q^{53} +14.5731 q^{54} -10.6640 q^{55} +6.83459 q^{56} +9.35864 q^{57} +22.1583 q^{58} +2.08576 q^{59} +28.4662 q^{60} -8.35286 q^{61} +25.4951 q^{62} +0.894725 q^{63} +3.46130 q^{64} +0.527597 q^{65} +9.45798 q^{66} -8.75828 q^{67} -17.5391 q^{68} -10.3311 q^{69} +10.8797 q^{70} +8.38423 q^{71} +6.11508 q^{72} +13.0385 q^{73} -21.7904 q^{74} +18.5705 q^{75} +29.9942 q^{76} +2.52769 q^{77} -0.467931 q^{78} -2.15745 q^{79} +35.1202 q^{80} -5.51529 q^{81} -7.61500 q^{82} +16.9078 q^{83} -6.74736 q^{84} -15.9119 q^{85} -10.2075 q^{86} -12.4672 q^{87} +17.2757 q^{88} -11.1622 q^{89} +9.73431 q^{90} -0.125057 q^{91} -33.1108 q^{92} -14.3447 q^{93} +13.8349 q^{94} +27.2116 q^{95} -11.3150 q^{96} +1.24670 q^{97} -2.57881 q^{98} +2.26159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * q^99

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