LMFDB - Embedded newform 6001.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98791 q^{2} +3.32266 q^{3} +1.95179 q^{4} +2.27659 q^{5} -6.60516 q^{6} +3.45158 q^{7} +0.0958417 q^{8} +8.04010 q^{9} +O(q^{10})$	\(q-1.98791 q^{2} +3.32266 q^{3} +1.95179 q^{4} +2.27659 q^{5} -6.60516 q^{6} +3.45158 q^{7} +0.0958417 q^{8} +8.04010 q^{9} -4.52565 q^{10} +6.11215 q^{11} +6.48514 q^{12} -0.519759 q^{13} -6.86143 q^{14} +7.56433 q^{15} -4.09410 q^{16} +1.00000 q^{17} -15.9830 q^{18} -2.29689 q^{19} +4.44341 q^{20} +11.4684 q^{21} -12.1504 q^{22} -3.58377 q^{23} +0.318450 q^{24} +0.182842 q^{25} +1.03323 q^{26} +16.7466 q^{27} +6.73675 q^{28} -8.65933 q^{29} -15.0372 q^{30} +5.26218 q^{31} +7.94702 q^{32} +20.3086 q^{33} -1.98791 q^{34} +7.85781 q^{35} +15.6926 q^{36} -0.510060 q^{37} +4.56602 q^{38} -1.72698 q^{39} +0.218192 q^{40} -7.51375 q^{41} -22.7982 q^{42} -9.58623 q^{43} +11.9296 q^{44} +18.3040 q^{45} +7.12422 q^{46} -8.88367 q^{47} -13.6033 q^{48} +4.91339 q^{49} -0.363474 q^{50} +3.32266 q^{51} -1.01446 q^{52} +2.49427 q^{53} -33.2906 q^{54} +13.9148 q^{55} +0.330805 q^{56} -7.63181 q^{57} +17.2140 q^{58} -12.5070 q^{59} +14.7640 q^{60} +8.80445 q^{61} -10.4607 q^{62} +27.7510 q^{63} -7.60976 q^{64} -1.18328 q^{65} -40.3717 q^{66} +14.5651 q^{67} +1.95179 q^{68} -11.9077 q^{69} -15.6206 q^{70} +13.0879 q^{71} +0.770577 q^{72} -1.80598 q^{73} +1.01395 q^{74} +0.607523 q^{75} -4.48305 q^{76} +21.0966 q^{77} +3.43309 q^{78} -7.14739 q^{79} -9.32057 q^{80} +31.5229 q^{81} +14.9367 q^{82} +8.73442 q^{83} +22.3839 q^{84} +2.27659 q^{85} +19.0566 q^{86} -28.7720 q^{87} +0.585799 q^{88} +3.08245 q^{89} -36.3867 q^{90} -1.79399 q^{91} -6.99477 q^{92} +17.4844 q^{93} +17.6599 q^{94} -5.22908 q^{95} +26.4053 q^{96} -10.9579 q^{97} -9.76738 q^{98} +49.1423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.98791	−1.40566	−0.702832	−	0.711355i	$-0.748082\pi$
$2$	−1.98791	−1.40566	−0.702832	+	0.711355i	$0.748082\pi$
$3$	3.32266	1.91834	0.959171	−	0.282828i	$-0.0912727\pi$
$3$	3.32266	1.91834	0.959171	+	0.282828i	$0.0912727\pi$
$4$	1.95179	0.975894
$5$	2.27659	1.01812	0.509060	−	0.860731i	$-0.329993\pi$
$5$	2.27659	1.01812	0.509060	+	0.860731i	$0.329993\pi$
$6$	−6.60516	−2.69654
$7$	3.45158	1.30457	0.652287	−	0.757972i	$-0.273810\pi$
$7$	3.45158	1.30457	0.652287	+	0.757972i	$0.273810\pi$
$8$	0.0958417	0.0338852
$9$	8.04010	2.68003
$10$	−4.52565	−1.43114
$11$	6.11215	1.84288	0.921442	−	0.388517i	$-0.127012\pi$
$11$	6.11215	1.84288	0.921442	+	0.388517i	$0.127012\pi$
$12$	6.48514	1.87210
$13$	−0.519759	−0.144155	−0.0720776	−	0.997399i	$-0.522963\pi$
$13$	−0.519759	−0.144155	−0.0720776	+	0.997399i	$0.522963\pi$
$14$	−6.86143	−1.83379
$15$	7.56433	1.95310
$16$	−4.09410	−1.02353
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−15.9830	−3.76723
$19$	−2.29689	−0.526944	−0.263472	−	0.964667i	$-0.584868\pi$
$19$	−2.29689	−0.526944	−0.263472	+	0.964667i	$0.584868\pi$
$20$	4.44341	0.993577
$21$	11.4684	2.50262
$22$	−12.1504	−2.59048
$23$	−3.58377	−0.747269	−0.373634	−	0.927576i	$-0.621889\pi$
$23$	−3.58377	−0.747269	−0.373634	+	0.927576i	$0.621889\pi$
$24$	0.318450	0.0650033
$25$	0.182842	0.0365685
$26$	1.03323	0.202634
$27$	16.7466	3.22288
$28$	6.73675	1.27313
$29$	−8.65933	−1.60800	−0.803998	−	0.594632i	$-0.797298\pi$
$29$	−8.65933	−1.60800	−0.803998	+	0.594632i	$0.797298\pi$
$30$	−15.0372	−2.74541
$31$	5.26218	0.945115	0.472557	−	0.881300i	$-0.343331\pi$
$31$	5.26218	0.945115	0.472557	+	0.881300i	$0.343331\pi$
$32$	7.94702	1.40485
$33$	20.3086	3.53528
$34$	−1.98791	−0.340924
$35$	7.85781	1.32821
$36$	15.6926	2.61543
$37$	−0.510060	−0.0838534	−0.0419267	−	0.999121i	$-0.513350\pi$
$37$	−0.510060	−0.0838534	−0.0419267	+	0.999121i	$0.513350\pi$
$38$	4.56602	0.740706
$39$	−1.72698	−0.276539
$40$	0.218192	0.0344992
$41$	−7.51375	−1.17345	−0.586726	−	0.809786i	$-0.699583\pi$
$41$	−7.51375	−1.17345	−0.586726	+	0.809786i	$0.699583\pi$
$42$	−22.7982	−3.51784
$43$	−9.58623	−1.46189	−0.730943	−	0.682438i	$-0.760920\pi$
$43$	−9.58623	−1.46189	−0.730943	+	0.682438i	$0.760920\pi$
$44$	11.9296	1.79846
$45$	18.3040	2.72859
$46$	7.12422	1.05041
$47$	−8.88367	−1.29582	−0.647908	−	0.761718i	$-0.724356\pi$
$47$	−8.88367	−1.29582	−0.647908	+	0.761718i	$0.724356\pi$
$48$	−13.6033	−1.96347
$49$	4.91339	0.701913
$50$	−0.363474	−0.0514030
$51$	3.32266	0.465266
$52$	−1.01446	−0.140680
$53$	2.49427	0.342615	0.171307	−	0.985218i	$-0.445201\pi$
$53$	2.49427	0.342615	0.171307	+	0.985218i	$0.445201\pi$
$54$	−33.2906	−4.53028
$55$	13.9148	1.87628
$56$	0.330805	0.0442057
$57$	−7.63181	−1.01086
$58$	17.2140	2.26030
$59$	−12.5070	−1.62827	−0.814136	−	0.580674i	$-0.802789\pi$
$59$	−12.5070	−1.62827	−0.814136	+	0.580674i	$0.802789\pi$
$60$	14.7640	1.90602
$61$	8.80445	1.12729	0.563647	−	0.826016i	$-0.309398\pi$
$61$	8.80445	1.12729	0.563647	+	0.826016i	$0.309398\pi$
$62$	−10.4607	−1.32851
$63$	27.7510	3.49630
$64$	−7.60976	−0.951221
$65$	−1.18328	−0.146767
$66$	−40.3717	−4.96942
$67$	14.5651	1.77941	0.889704	−	0.456537i	$-0.150910\pi$
$67$	14.5651	1.77941	0.889704	+	0.456537i	$0.150910\pi$
$68$	1.95179	0.236689
$69$	−11.9077	−1.43352
$70$	−15.6206	−1.86702
$71$	13.0879	1.55325	0.776626	−	0.629962i	$-0.216930\pi$
$71$	13.0879	1.55325	0.776626	+	0.629962i	$0.216930\pi$
$72$	0.770577	0.0908134
$73$	−1.80598	−0.211374	−0.105687	−	0.994399i	$-0.533704\pi$
$73$	−1.80598	−0.211374	−0.105687	+	0.994399i	$0.533704\pi$
$74$	1.01395	0.117870
$75$	0.607523	0.0701508
$76$	−4.48305	−0.514241
$77$	21.0966	2.40418
$78$	3.43309	0.388721
$79$	−7.14739	−0.804144	−0.402072	−	0.915608i	$-0.631710\pi$
$79$	−7.14739	−0.804144	−0.402072	+	0.915608i	$0.631710\pi$
$80$	−9.32057	−1.04207
$81$	31.5229	3.50254
$82$	14.9367	1.64948
$83$	8.73442	0.958727	0.479364	−	0.877616i	$-0.340867\pi$
$83$	8.73442	0.958727	0.479364	+	0.877616i	$0.340867\pi$
$84$	22.3839	2.44229
$85$	2.27659	0.246930
$86$	19.0566	2.05492
$87$	−28.7720	−3.08469
$88$	0.585799	0.0624464
$89$	3.08245	0.326740	0.163370	−	0.986565i	$-0.447764\pi$
$89$	3.08245	0.326740	0.163370	+	0.986565i	$0.447764\pi$
$90$	−36.3867	−3.83549
$91$	−1.79399	−0.188061
$92$	−6.99477	−0.729255
$93$	17.4844	1.81305
$94$	17.6599	1.82148
$95$	−5.22908	−0.536492
$96$	26.4053	2.69498
$97$	−10.9579	−1.11261	−0.556303	−	0.830979i	$-0.687781\pi$
$97$	−10.9579	−1.11261	−0.556303	+	0.830979i	$0.687781\pi$
$98$	−9.76738	−0.986654
$99$	49.1423	4.93899
$100$	0.356869	0.0356869
$101$	1.58029	0.157245	0.0786226	−	0.996904i	$-0.474948\pi$
$101$	1.58029	0.157245	0.0786226	+	0.996904i	$0.474948\pi$
$102$	−6.60516	−0.654008
$103$	−9.32901	−0.919214	−0.459607	−	0.888122i	$-0.652010\pi$
$103$	−9.32901	−0.919214	−0.459607	+	0.888122i	$0.652010\pi$
$104$	−0.0498146	−0.00488472
$105$	26.1089	2.54797
$106$	−4.95839	−0.481602
$107$	17.5778	1.69931	0.849654	−	0.527340i	$-0.176811\pi$
$107$	17.5778	1.69931	0.849654	+	0.527340i	$0.176811\pi$
$108$	32.6857	3.14518
$109$	−3.85129	−0.368886	−0.184443	−	0.982843i	$-0.559048\pi$
$109$	−3.85129	−0.368886	−0.184443	+	0.982843i	$0.559048\pi$
$110$	−27.6615	−2.63742
$111$	−1.69476	−0.160859
$112$	−14.1311	−1.33526
$113$	2.91228	0.273964	0.136982	−	0.990574i	$-0.456260\pi$
$113$	2.91228	0.273964	0.136982	+	0.990574i	$0.456260\pi$
$114$	15.1714	1.42093
$115$	−8.15877	−0.760809
$116$	−16.9012	−1.56923
$117$	−4.17891	−0.386341
$118$	24.8628	2.28881
$119$	3.45158	0.316406
$120$	0.724979	0.0661812
$121$	26.3584	2.39622
$122$	−17.5025	−1.58460
$123$	−24.9657	−2.25108
$124$	10.2707	0.922332
$125$	−10.9667	−0.980889
$126$	−55.1665	−4.91463
$127$	4.18509	0.371366	0.185683	−	0.982610i	$-0.440550\pi$
$127$	4.18509	0.371366	0.185683	+	0.982610i	$0.440550\pi$
$128$	−0.766511	−0.0677507
$129$	−31.8518	−2.80440
$130$	2.35225	0.206306
$131$	−20.6711	−1.80604	−0.903022	−	0.429594i	$-0.858657\pi$
$131$	−20.6711	−1.80604	−0.903022	+	0.429594i	$0.858657\pi$
$132$	39.6381	3.45006
$133$	−7.92791	−0.687437
$134$	−28.9541	−2.50125
$135$	38.1250	3.28127
$136$	0.0958417	0.00821836
$137$	−15.3648	−1.31270	−0.656352	−	0.754454i	$-0.727902\pi$
$137$	−15.3648	−1.31270	−0.656352	+	0.754454i	$0.727902\pi$
$138$	23.6714	2.01504
$139$	5.52109	0.468292	0.234146	−	0.972201i	$-0.424771\pi$
$139$	5.52109	0.468292	0.234146	+	0.972201i	$0.424771\pi$
$140$	15.3368	1.29619
$141$	−29.5175	−2.48582
$142$	−26.0176	−2.18335
$143$	−3.17685	−0.265661
$144$	−32.9170	−2.74308
$145$	−19.7137	−1.63713
$146$	3.59013	0.297122
$147$	16.3255	1.34651
$148$	−0.995529	−0.0818320
$149$	−12.1874	−0.998431	−0.499216	−	0.866478i	$-0.666378\pi$
$149$	−12.1874	−0.998431	−0.499216	+	0.866478i	$0.666378\pi$
$150$	−1.20770	−0.0986085
$151$	−2.77927	−0.226173	−0.113087	−	0.993585i	$-0.536074\pi$
$151$	−2.77927	−0.226173	−0.113087	+	0.993585i	$0.536074\pi$
$152$	−0.220138	−0.0178556
$153$	8.04010	0.650003
$154$	−41.9381	−3.37947
$155$	11.9798	0.962240
$156$	−3.37071	−0.269873
$157$	17.3186	1.38218	0.691089	−	0.722770i	$-0.257131\pi$
$157$	17.3186	1.38218	0.691089	+	0.722770i	$0.257131\pi$
$158$	14.2084	1.13036
$159$	8.28763	0.657252
$160$	18.0921	1.43030
$161$	−12.3697	−0.974867
$162$	−62.6647	−4.92340
$163$	−4.76349	−0.373105	−0.186553	−	0.982445i	$-0.559732\pi$
$163$	−4.76349	−0.373105	−0.186553	+	0.982445i	$0.559732\pi$
$164$	−14.6653	−1.14516
$165$	46.2343	3.59934
$166$	−17.3632	−1.34765
$167$	14.1762	1.09699	0.548495	−	0.836154i	$-0.315201\pi$
$167$	14.1762	1.09699	0.548495	+	0.836154i	$0.315201\pi$
$168$	1.09915	0.0848016
$169$	−12.7299	−0.979219
$170$	−4.52565	−0.347101
$171$	−18.4673	−1.41223
$172$	−18.7103	−1.42665
$173$	−3.29081	−0.250196	−0.125098	−	0.992144i	$-0.539924\pi$
$173$	−3.29081	−0.250196	−0.125098	+	0.992144i	$0.539924\pi$
$174$	57.1962	4.33604
$175$	0.631094	0.0477062
$176$	−25.0238	−1.88624
$177$	−41.5566	−3.12358
$178$	−6.12764	−0.459286
$179$	18.8422	1.40834	0.704168	−	0.710034i	$-0.251320\pi$
$179$	18.8422	1.40834	0.704168	+	0.710034i	$0.251320\pi$
$180$	35.7255	2.66282
$181$	23.9360	1.77915	0.889574	−	0.456791i	$-0.151001\pi$
$181$	23.9360	1.77915	0.889574	+	0.456791i	$0.151001\pi$
$182$	3.56629	0.264351
$183$	29.2542	2.16254
$184$	−0.343475	−0.0253213
$185$	−1.16120	−0.0853728
$186$	−34.7575	−2.54854
$187$	6.11215	0.446965
$188$	−17.3390	−1.26458
$189$	57.8020	4.20448
$190$	10.3949	0.754128
$191$	−5.68454	−0.411319	−0.205659	−	0.978624i	$-0.565934\pi$
$191$	−5.68454	−0.411319	−0.205659	+	0.978624i	$0.565934\pi$
$192$	−25.2847	−1.82477
$193$	−4.23541	−0.304872	−0.152436	−	0.988313i	$-0.548712\pi$
$193$	−4.23541	−0.304872	−0.152436	+	0.988313i	$0.548712\pi$
$194$	21.7833	1.56395
$195$	−3.93163	−0.281550
$196$	9.58989	0.684992
$197$	27.6564	1.97044	0.985219	−	0.171298i	$-0.0547961\pi$
$197$	27.6564	1.97044	0.985219	+	0.171298i	$0.0547961\pi$
$198$	−97.6905	−6.94256
$199$	−12.1198	−0.859152	−0.429576	−	0.903031i	$-0.641337\pi$
$199$	−12.1198	−0.859152	−0.429576	+	0.903031i	$0.641337\pi$
$200$	0.0175239	0.00123913
$201$	48.3949	3.41351
$202$	−3.14148	−0.221034
$203$	−29.8883	−2.09775
$204$	6.48514	0.454050
$205$	−17.1057	−1.19471
$206$	18.5452	1.29211
$207$	−28.8139	−2.00270
$208$	2.12795	0.147546
$209$	−14.0390	−0.971096
$210$	−51.9021	−3.58159
$211$	−1.67037	−0.114993	−0.0574964	−	0.998346i	$-0.518312\pi$
$211$	−1.67037	−0.114993	−0.0574964	+	0.998346i	$0.518312\pi$
$212$	4.86829	0.334356
$213$	43.4868	2.97967
$214$	−34.9431	−2.38866
$215$	−21.8239	−1.48838
$216$	1.60502	0.109208
$217$	18.1628	1.23297
$218$	7.65602	0.518531
$219$	−6.00068	−0.405488
$220$	27.1588	1.83105
$221$	−0.519759	−0.0349628
$222$	3.36903	0.226114
$223$	−16.6458	−1.11468	−0.557342	−	0.830283i	$-0.688179\pi$
$223$	−16.6458	−1.11468	−0.557342	+	0.830283i	$0.688179\pi$
$224$	27.4298	1.83273
$225$	1.47007	0.0980047
$226$	−5.78935	−0.385102
$227$	−20.0237	−1.32902	−0.664509	−	0.747281i	$-0.731359\pi$
$227$	−20.0237	−1.32902	−0.664509	+	0.747281i	$0.731359\pi$
$228$	−14.8957	−0.986490
$229$	20.9662	1.38549	0.692743	−	0.721185i	$-0.256402\pi$
$229$	20.9662	1.38549	0.692743	+	0.721185i	$0.256402\pi$
$230$	16.2189	1.06944
$231$	70.0968	4.61203
$232$	−0.829925	−0.0544872
$233$	4.78629	0.313560	0.156780	−	0.987634i	$-0.449889\pi$
$233$	4.78629	0.313560	0.156780	+	0.987634i	$0.449889\pi$
$234$	8.30731	0.543066
$235$	−20.2244	−1.31930
$236$	−24.4110	−1.58902
$237$	−23.7484	−1.54262
$238$	−6.86143	−0.444760
$239$	10.5393	0.681733	0.340866	−	0.940112i	$-0.389280\pi$
$239$	10.5393	0.681733	0.340866	+	0.940112i	$0.389280\pi$
$240$	−30.9691	−1.99905
$241$	−21.7438	−1.40064	−0.700321	−	0.713828i	$-0.746960\pi$
$241$	−21.7438	−1.40064	−0.700321	+	0.713828i	$0.746960\pi$
$242$	−52.3981	−3.36828
$243$	54.5003	3.49619
$244$	17.1844	1.10012
$245$	11.1858	0.714631
$246$	49.6295	3.16426
$247$	1.19383	0.0759617
$248$	0.504336	0.0320254
$249$	29.0216	1.83917
$250$	21.8008	1.37880
$251$	6.16434	0.389090	0.194545	−	0.980894i	$-0.437677\pi$
$251$	6.16434	0.389090	0.194545	+	0.980894i	$0.437677\pi$
$252$	54.1641	3.41202
$253$	−21.9046	−1.37713
$254$	−8.31958	−0.522017
$255$	7.56433	0.473697
$256$	16.7433	1.04646
$257$	−11.3099	−0.705495	−0.352748	−	0.935719i	$-0.614753\pi$
$257$	−11.3099	−0.705495	−0.352748	+	0.935719i	$0.614753\pi$
$258$	63.3186	3.94204
$259$	−1.76051	−0.109393
$260$	−2.30950	−0.143229
$261$	−69.6218	−4.30948
$262$	41.0923	2.53869
$263$	−9.99459	−0.616293	−0.308146	−	0.951339i	$-0.599709\pi$
$263$	−9.99459	−0.616293	−0.308146	+	0.951339i	$0.599709\pi$
$264$	1.94641	0.119794
$265$	5.67843	0.348823
$266$	15.7600	0.966306
$267$	10.2420	0.626798
$268$	28.4280	1.73651
$269$	9.84186	0.600069	0.300034	−	0.953928i	$-0.403002\pi$
$269$	9.84186	0.600069	0.300034	+	0.953928i	$0.403002\pi$
$270$	−75.7890	−4.61237
$271$	−22.4923	−1.36631	−0.683153	−	0.730275i	$-0.739392\pi$
$271$	−22.4923	−1.36631	−0.683153	+	0.730275i	$0.739392\pi$
$272$	−4.09410	−0.248241
$273$	−5.96082	−0.360765
$274$	30.5439	1.84522
$275$	1.11756	0.0673914
$276$	−23.2413	−1.39896
$277$	−25.0668	−1.50612	−0.753058	−	0.657954i	$-0.771422\pi$
$277$	−25.0668	−1.50612	−0.753058	+	0.657954i	$0.771422\pi$
$278$	−10.9754	−0.658262
$279$	42.3084	2.53294
$280$	0.753106	0.0450067
$281$	−19.3328	−1.15330	−0.576649	−	0.816992i	$-0.695640\pi$
$281$	−19.3328	−1.15330	−0.576649	+	0.816992i	$0.695640\pi$
$282$	58.6781	3.49423
$283$	8.00938	0.476108	0.238054	−	0.971252i	$-0.423490\pi$
$283$	8.00938	0.476108	0.238054	+	0.971252i	$0.423490\pi$
$284$	25.5449	1.51581
$285$	−17.3745	−1.02917
$286$	6.31529	0.373431
$287$	−25.9343	−1.53085
$288$	63.8948	3.76504
$289$	1.00000	0.0588235
$290$	39.1891	2.30126
$291$	−36.4094	−2.13436
$292$	−3.52490	−0.206279
$293$	−8.26867	−0.483061	−0.241530	−	0.970393i	$-0.577649\pi$
$293$	−8.26867	−0.483061	−0.241530	+	0.970393i	$0.577649\pi$
$294$	−32.4537	−1.89274
$295$	−28.4732	−1.65778
$296$	−0.0488851	−0.00284139
$297$	102.357	5.93938
$298$	24.2275	1.40346
$299$	1.86270	0.107723
$300$	1.18576	0.0684597
$301$	−33.0876	−1.90714
$302$	5.52493	0.317924
$303$	5.25079	0.301650
$304$	9.40371	0.539340
$305$	20.0441	1.14772
$306$	−15.9830	−0.913687
$307$	−24.4083	−1.39306	−0.696529	−	0.717529i	$-0.745273\pi$
$307$	−24.4083	−1.39306	−0.696529	+	0.717529i	$0.745273\pi$
$308$	41.1760	2.34622
$309$	−30.9972	−1.76337
$310$	−23.8148	−1.35259
$311$	11.7842	0.668222	0.334111	−	0.942534i	$-0.391564\pi$
$311$	11.7842	0.668222	0.334111	+	0.942534i	$0.391564\pi$
$312$	−0.165517	−0.00937057
$313$	−1.55691	−0.0880020	−0.0440010	−	0.999031i	$-0.514010\pi$
$313$	−1.55691	−0.0880020	−0.0440010	+	0.999031i	$0.514010\pi$
$314$	−34.4279	−1.94288
$315$	63.1776	3.55965
$316$	−13.9502	−0.784759
$317$	20.6816	1.16159	0.580797	−	0.814048i	$-0.302741\pi$
$317$	20.6816	1.16159	0.580797	+	0.814048i	$0.302741\pi$
$318$	−16.4751	−0.923876
$319$	−52.9271	−2.96335
$320$	−17.3243	−0.968457
$321$	58.4051	3.25985
$322$	24.5898	1.37034
$323$	−2.29689	−0.127803
$324$	61.5260	3.41811
$325$	−0.0950339	−0.00527153
$326$	9.46939	0.524461
$327$	−12.7965	−0.707650
$328$	−0.720131	−0.0397626
$329$	−30.6627	−1.69049
$330$	−91.9097	−5.05946
$331$	11.4097	0.627135	0.313567	−	0.949566i	$-0.398476\pi$
$331$	11.4097	0.627135	0.313567	+	0.949566i	$0.398476\pi$
$332$	17.0477	0.935616
$333$	−4.10093	−0.224730
$334$	−28.1811	−1.54200
$335$	33.1587	1.81165
$336$	−46.9529	−2.56149
$337$	4.08606	0.222582	0.111291	−	0.993788i	$-0.464501\pi$
$337$	4.08606	0.222582	0.111291	+	0.993788i	$0.464501\pi$
$338$	25.3058	1.37645
$339$	9.67652	0.525557
$340$	4.44341	0.240978
$341$	32.1632	1.74174
$342$	36.7112	1.98512
$343$	−7.20210	−0.388877
$344$	−0.918761	−0.0495363
$345$	−27.1089	−1.45949
$346$	6.54183	0.351691
$347$	10.3687	0.556622	0.278311	−	0.960491i	$-0.410225\pi$
$347$	10.3687	0.556622	0.278311	+	0.960491i	$0.410225\pi$
$348$	−56.1569	−3.01033
$349$	24.9847	1.33740	0.668700	−	0.743532i	$-0.266851\pi$
$349$	24.9847	1.33740	0.668700	+	0.743532i	$0.266851\pi$
$350$	−1.25456	−0.0670590
$351$	−8.70417	−0.464594
$352$	48.5734	2.58897
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	82.6107	4.39071
$355$	29.7958	1.58140
$356$	6.01630	0.318863
$357$	11.4684	0.606974
$358$	−37.4567	−1.97965
$359$	−4.28903	−0.226366	−0.113183	−	0.993574i	$-0.536105\pi$
$359$	−4.28903	−0.226366	−0.113183	+	0.993574i	$0.536105\pi$
$360$	1.75428	0.0924589
$361$	−13.7243	−0.722330
$362$	−47.5826	−2.50089
$363$	87.5801	4.59676
$364$	−3.50149	−0.183528
$365$	−4.11148	−0.215205
$366$	−58.1548	−3.03980
$367$	1.52370	0.0795362	0.0397681	−	0.999209i	$-0.487338\pi$
$367$	1.52370	0.0795362	0.0397681	+	0.999209i	$0.487338\pi$
$368$	14.6723	0.764848
$369$	−60.4113	−3.14489
$370$	2.30835	0.120006
$371$	8.60918	0.446966
$372$	34.1259	1.76935
$373$	−9.41826	−0.487659	−0.243830	−	0.969818i	$-0.578404\pi$
$373$	−9.41826	−0.487659	−0.243830	+	0.969818i	$0.578404\pi$
$374$	−12.1504	−0.628283
$375$	−36.4386	−1.88168
$376$	−0.851427	−0.0439090
$377$	4.50076	0.231801
$378$	−114.905	−5.91009
$379$	8.75710	0.449822	0.224911	−	0.974379i	$-0.427791\pi$
$379$	8.75710	0.449822	0.224911	+	0.974379i	$0.427791\pi$
$380$	−10.2060	−0.523559
$381$	13.9056	0.712407
$382$	11.3004	0.578176
$383$	9.52987	0.486953	0.243477	−	0.969907i	$-0.421712\pi$
$383$	9.52987	0.486953	0.243477	+	0.969907i	$0.421712\pi$
$384$	−2.54686	−0.129969
$385$	48.0281	2.44774
$386$	8.41962	0.428547
$387$	−77.0742	−3.91790
$388$	−21.3875	−1.08579
$389$	−11.8121	−0.598900	−0.299450	−	0.954112i	$-0.596803\pi$
$389$	−11.8121	−0.598900	−0.299450	+	0.954112i	$0.596803\pi$
$390$	7.81573	0.395765
$391$	−3.58377	−0.181239
$392$	0.470908	0.0237844
$393$	−68.6832	−3.46461
$394$	−54.9785	−2.76978
$395$	−16.2716	−0.818715
$396$	95.9153	4.81993
$397$	−0.0218522	−0.00109673	−0.000548366	−	1.00000i	$-0.500175\pi$
$397$	−0.0218522	−0.00109673	−0.000548366		1.00000i	$0.500175\pi$
$398$	24.0931	1.20768
$399$	−26.3418	−1.31874
$400$	−0.748575	−0.0374287
$401$	17.7171	0.884752	0.442376	−	0.896830i	$-0.354136\pi$
$401$	17.7171	0.884752	0.442376	+	0.896830i	$0.354136\pi$
$402$	−96.2047	−4.79826
$403$	−2.73506	−0.136243
$404$	3.08440	0.153455
$405$	71.7645	3.56601
$406$	59.4153	2.94873
$407$	−3.11757	−0.154532
$408$	0.318450	0.0157656
$409$	6.36231	0.314596	0.157298	−	0.987551i	$-0.449722\pi$
$409$	6.36231	0.314596	0.157298	+	0.987551i	$0.449722\pi$
$410$	34.0046	1.67937
$411$	−51.0521	−2.51822
$412$	−18.2082	−0.897055
$413$	−43.1689	−2.12420
$414$	57.2794	2.81513
$415$	19.8847	0.976100
$416$	−4.13054	−0.202516
$417$	18.3447	0.898345
$418$	27.9082	1.36504
$419$	−16.0527	−0.784225	−0.392113	−	0.919917i	$-0.628256\pi$
$419$	−16.0527	−0.784225	−0.392113	+	0.919917i	$0.628256\pi$
$420$	50.9590	2.48654
$421$	−26.1103	−1.27254	−0.636269	−	0.771468i	$-0.719523\pi$
$421$	−26.1103	−1.27254	−0.636269	+	0.771468i	$0.719523\pi$
$422$	3.32054	0.161641
$423$	−71.4256	−3.47283
$424$	0.239056	0.0116096
$425$	0.182842	0.00886915
$426$	−86.4479	−4.18841
$427$	30.3893	1.47064
$428$	34.3081	1.65834
$429$	−10.5556	−0.509629
$430$	43.3839	2.09216
$431$	−8.92201	−0.429758	−0.214879	−	0.976641i	$-0.568936\pi$
$431$	−8.92201	−0.429758	−0.214879	+	0.976641i	$0.568936\pi$
$432$	−68.5621	−3.29869
$433$	−9.96225	−0.478755	−0.239378	−	0.970927i	$-0.576943\pi$
$433$	−9.96225	−0.478755	−0.239378	+	0.970927i	$0.576943\pi$
$434$	−36.1060	−1.73315
$435$	−65.5020	−3.14058
$436$	−7.51690	−0.359994
$437$	8.23155	0.393768
$438$	11.9288	0.569981
$439$	−4.17571	−0.199296	−0.0996478	−	0.995023i	$-0.531772\pi$
$439$	−4.17571	−0.199296	−0.0996478	+	0.995023i	$0.531772\pi$
$440$	1.33362	0.0635779
$441$	39.5041	1.88115
$442$	1.03323	0.0491460
$443$	33.5286	1.59299	0.796496	−	0.604644i	$-0.206685\pi$
$443$	33.5286	1.59299	0.796496	+	0.604644i	$0.206685\pi$
$444$	−3.30781	−0.156982
$445$	7.01747	0.332660
$446$	33.0903	1.56687
$447$	−40.4947	−1.91533
$448$	−26.2657	−1.24094
$449$	13.8952	0.655755	0.327878	−	0.944720i	$-0.393667\pi$
$449$	13.8952	0.655755	0.327878	+	0.944720i	$0.393667\pi$
$450$	−2.92237	−0.137762
$451$	−45.9252	−2.16253
$452$	5.68415	0.267360
$453$	−9.23457	−0.433878
$454$	39.8052	1.86815
$455$	−4.08417	−0.191469
$456$	−0.731446	−0.0342531
$457$	−30.2156	−1.41343	−0.706713	−	0.707500i	$-0.749823\pi$
$457$	−30.2156	−1.41343	−0.706713	+	0.707500i	$0.749823\pi$
$458$	−41.6789	−1.94753
$459$	16.7466	0.781662
$460$	−15.9242	−0.742469
$461$	23.3696	1.08843	0.544216	−	0.838945i	$-0.316827\pi$
$461$	23.3696	1.08843	0.544216	+	0.838945i	$0.316827\pi$
$462$	−139.346	−6.48297
$463$	−0.162094	−0.00753316	−0.00376658	−	0.999993i	$-0.501199\pi$
$463$	−0.162094	−0.00753316	−0.00376658	+	0.999993i	$0.501199\pi$
$464$	35.4522	1.64582
$465$	39.8048	1.84591
$466$	−9.51472	−0.440761
$467$	32.7777	1.51677	0.758386	−	0.651806i	$-0.225988\pi$
$467$	32.7777	1.51677	0.758386	+	0.651806i	$0.225988\pi$
$468$	−8.15635	−0.377028
$469$	50.2725	2.32137
$470$	40.2044	1.85449
$471$	57.5440	2.65149
$472$	−1.19869	−0.0551743
$473$	−58.5925	−2.69409
$474$	47.2096	2.16841
$475$	−0.419969	−0.0192695
$476$	6.73675	0.308778
$477$	20.0542	0.918219
$478$	−20.9512	−0.958288
$479$	23.8671	1.09052	0.545258	−	0.838269i	$-0.316432\pi$
$479$	23.8671	1.09052	0.545258	+	0.838269i	$0.316432\pi$
$480$	60.1139	2.74381
$481$	0.265108	0.0120879
$482$	43.2248	1.96883
$483$	−41.1003	−1.87013
$484$	51.4460	2.33845
$485$	−24.9466	−1.13277
$486$	−108.342	−4.91448
$487$	−17.9179	−0.811939	−0.405969	−	0.913887i	$-0.633066\pi$
$487$	−17.9179	−0.811939	−0.405969	+	0.913887i	$0.633066\pi$
$488$	0.843834	0.0381986
$489$	−15.8275	−0.715743
$490$	−22.2363	−1.00453
$491$	−30.9228	−1.39553	−0.697764	−	0.716327i	$-0.745822\pi$
$491$	−30.9228	−1.39553	−0.697764	+	0.716327i	$0.745822\pi$
$492$	−48.7277	−2.19681
$493$	−8.65933	−0.389996
$494$	−2.37323	−0.106777
$495$	111.877	5.02848
$496$	−21.5439	−0.967349
$497$	45.1740	2.02633
$498$	−57.6922	−2.58525
$499$	−25.2630	−1.13093	−0.565464	−	0.824773i	$-0.691303\pi$
$499$	−25.2630	−1.13093	−0.565464	+	0.824773i	$0.691303\pi$
$500$	−21.4046	−0.957244
$501$	47.1028	2.10440
$502$	−12.2542	−0.546930
$503$	−15.6168	−0.696318	−0.348159	−	0.937436i	$-0.613193\pi$
$503$	−15.6168	−0.696318	−0.348159	+	0.937436i	$0.613193\pi$
$504$	2.65971	0.118473
$505$	3.59768	0.160094
$506$	43.5443	1.93578
$507$	−42.2970	−1.87848
$508$	8.16840	0.362414
$509$	−23.9056	−1.05960	−0.529799	−	0.848123i	$-0.677733\pi$
$509$	−23.9056	−1.05960	−0.529799	+	0.848123i	$0.677733\pi$
$510$	−15.0372	−0.665859
$511$	−6.23349	−0.275754
$512$	−31.7511	−1.40321
$513$	−38.4651	−1.69827
$514$	22.4832	0.991690
$515$	−21.2383	−0.935870
$516$	−62.1680	−2.73679
$517$	−54.2984	−2.38804
$518$	3.49974	0.153770
$519$	−10.9343	−0.479960
$520$	−0.113407	−0.00497324
$521$	25.4275	1.11400	0.556999	−	0.830513i	$-0.311953\pi$
$521$	25.4275	1.11400	0.556999	+	0.830513i	$0.311953\pi$
$522$	138.402	6.05769
$523$	−40.2729	−1.76101	−0.880506	−	0.474036i	$-0.842797\pi$
$523$	−40.2729	−1.76101	−0.880506	+	0.474036i	$0.842797\pi$
$524$	−40.3456	−1.76251
$525$	2.09691	0.0915169
$526$	19.8684	0.866301
$527$	5.26218	0.229224
$528$	−83.1456	−3.61845
$529$	−10.1566	−0.441590
$530$	−11.2882	−0.490328
$531$	−100.557	−4.36382
$532$	−15.4736	−0.670865
$533$	3.90534	0.169159
$534$	−20.3601	−0.881068
$535$	40.0173	1.73010
$536$	1.39594	0.0602956
$537$	62.6065	2.70167
$538$	−19.5647	−0.843495
$539$	30.0314	1.29354
$540$	74.4118	3.20218
$541$	0.601634	0.0258663	0.0129331	−	0.999916i	$-0.495883\pi$
$541$	0.601634	0.0258663	0.0129331	+	0.999916i	$0.495883\pi$
$542$	44.7126	1.92057
$543$	79.5313	3.41301
$544$	7.94702	0.340726
$545$	−8.76779	−0.375571
$546$	11.8496	0.507115
$547$	22.3693	0.956443	0.478221	−	0.878239i	$-0.341282\pi$
$547$	22.3693	0.956443	0.478221	+	0.878239i	$0.341282\pi$
$548$	−29.9889	−1.28106
$549$	70.7887	3.02119
$550$	−2.22161	−0.0947297
$551$	19.8896	0.847324
$552$	−1.14125	−0.0485749
$553$	−24.6698	−1.04906
$554$	49.8305	2.11709
$555$	−3.85826	−0.163774
$556$	10.7760	0.457004
$557$	40.6274	1.72144	0.860720	−	0.509079i	$-0.170014\pi$
$557$	40.6274	1.72144	0.860720	+	0.509079i	$0.170014\pi$
$558$	−84.1053	−3.56046
$559$	4.98253	0.210739
$560$	−32.1707	−1.35946
$561$	20.3086	0.857431
$562$	38.4319	1.62115
$563$	−45.0959	−1.90056	−0.950282	−	0.311389i	$-0.899206\pi$
$563$	−45.0959	−1.90056	−0.950282	+	0.311389i	$0.899206\pi$
$564$	−57.6118	−2.42589
$565$	6.63005	0.278928
$566$	−15.9219	−0.669249
$567$	108.804	4.56932
$568$	1.25437	0.0526322
$569$	35.5041	1.48841	0.744204	−	0.667952i	$-0.232829\pi$
$569$	35.5041	1.48841	0.744204	+	0.667952i	$0.232829\pi$
$570$	34.5389	1.44667
$571$	−32.2936	−1.35145	−0.675723	−	0.737156i	$-0.736168\pi$
$571$	−32.2936	−1.35145	−0.675723	+	0.737156i	$0.736168\pi$
$572$	−6.20053	−0.259257
$573$	−18.8878	−0.789050
$574$	51.5551	2.15187
$575$	−0.655266	−0.0273265
$576$	−61.1833	−2.54930
$577$	−11.0196	−0.458752	−0.229376	−	0.973338i	$-0.573668\pi$
$577$	−11.0196	−0.458752	−0.229376	+	0.973338i	$0.573668\pi$
$578$	−1.98791	−0.0826862
$579$	−14.0728	−0.584848
$580$	−38.4770	−1.59767
$581$	30.1475	1.25073
$582$	72.3787	3.00019
$583$	15.2454	0.631399
$584$	−0.173089	−0.00716246
$585$	−9.51366	−0.393341
$586$	16.4374	0.679021
$587$	6.94379	0.286601	0.143301	−	0.989679i	$-0.454228\pi$
$587$	6.94379	0.286601	0.143301	+	0.989679i	$0.454228\pi$
$588$	31.8640	1.31405
$589$	−12.0867	−0.498022
$590$	56.6023	2.33028
$591$	91.8930	3.77997
$592$	2.08824	0.0858260
$593$	−16.3044	−0.669540	−0.334770	−	0.942300i	$-0.608659\pi$
$593$	−16.3044	−0.669540	−0.334770	+	0.942300i	$0.608659\pi$
$594$	−203.477	−8.34878
$595$	7.85781	0.322139
$596$	−23.7872	−0.974363
$597$	−40.2701	−1.64815
$598$	−3.70288	−0.151422
$599$	−26.5861	−1.08628	−0.543140	−	0.839642i	$-0.682765\pi$
$599$	−26.5861	−1.08628	−0.543140	+	0.839642i	$0.682765\pi$
$600$	0.0582261	0.00237707
$601$	42.0482	1.71518	0.857591	−	0.514332i	$-0.171960\pi$
$601$	42.0482	1.71518	0.857591	+	0.514332i	$0.171960\pi$
$602$	65.7752	2.68080
$603$	117.105	4.76887
$604$	−5.42454	−0.220721
$605$	60.0072	2.43964
$606$	−10.4381	−0.424019
$607$	−16.7122	−0.678327	−0.339163	−	0.940727i	$-0.610144\pi$
$607$	−16.7122	−0.678327	−0.339163	+	0.940727i	$0.610144\pi$
$608$	−18.2535	−0.740276
$609$	−99.3089	−4.02420
$610$	−39.8459	−1.61331
$611$	4.61737	0.186799
$612$	15.6926	0.634334
$613$	−28.5506	−1.15315	−0.576574	−	0.817045i	$-0.695611\pi$
$613$	−28.5506	−1.15315	−0.576574	+	0.817045i	$0.695611\pi$
$614$	48.5216	1.95817
$615$	−56.8365	−2.29187
$616$	2.02193	0.0814660
$617$	−8.76493	−0.352863	−0.176431	−	0.984313i	$-0.556455\pi$
$617$	−8.76493	−0.352863	−0.176431	+	0.984313i	$0.556455\pi$
$618$	61.6196	2.47870
$619$	−26.3129	−1.05760	−0.528802	−	0.848745i	$-0.677358\pi$
$619$	−26.3129	−1.05760	−0.528802	+	0.848745i	$0.677358\pi$
$620$	23.3820	0.939044
$621$	−60.0159	−2.40835
$622$	−23.4260	−0.939297
$623$	10.6393	0.426256
$624$	7.07045	0.283045
$625$	−25.8808	−1.03523
$626$	3.09501	0.123701
$627$	−46.6468	−1.86289
$628$	33.8023	1.34886
$629$	−0.510060	−0.0203374
$630$	−125.591	−5.00368
$631$	−32.6007	−1.29781	−0.648906	−	0.760869i	$-0.724773\pi$
$631$	−32.6007	−1.29781	−0.648906	+	0.760869i	$0.724773\pi$
$632$	−0.685018	−0.0272486
$633$	−5.55007	−0.220595
$634$	−41.1132	−1.63281
$635$	9.52771	0.378096
$636$	16.1757	0.641408
$637$	−2.55378	−0.101184
$638$	105.214	4.16548
$639$	105.228	4.16277
$640$	−1.74503	−0.0689783
$641$	−28.2601	−1.11621	−0.558104	−	0.829771i	$-0.688471\pi$
$641$	−28.2601	−1.11621	−0.558104	+	0.829771i	$0.688471\pi$
$642$	−116.104	−4.58226
$643$	18.6631	0.736002	0.368001	−	0.929825i	$-0.380042\pi$
$643$	18.6631	0.736002	0.368001	+	0.929825i	$0.380042\pi$
$644$	−24.1430	−0.951367
$645$	−72.5134	−2.85521
$646$	4.56602	0.179648
$647$	−11.0239	−0.433395	−0.216697	−	0.976239i	$-0.569528\pi$
$647$	−11.0239	−0.433395	−0.216697	+	0.976239i	$0.569528\pi$
$648$	3.02121	0.118684
$649$	−76.4447	−3.00072
$650$	0.188919	0.00741001
$651$	60.3489	2.36526
$652$	−9.29732	−0.364111
$653$	32.4444	1.26965	0.634823	−	0.772658i	$-0.281073\pi$
$653$	32.4444	1.26965	0.634823	+	0.772658i	$0.281073\pi$
$654$	25.4384	0.994719
$655$	−47.0596	−1.83877
$656$	30.7621	1.20106
$657$	−14.5203	−0.566490
$658$	60.9547	2.37626
$659$	41.5400	1.61817	0.809085	−	0.587692i	$-0.199963\pi$
$659$	41.5400	1.61817	0.809085	+	0.587692i	$0.199963\pi$
$660$	90.2396	3.51257
$661$	38.8679	1.51178	0.755892	−	0.654696i	$-0.227203\pi$
$661$	38.8679	1.51178	0.755892	+	0.654696i	$0.227203\pi$
$662$	−22.6815	−0.881541
$663$	−1.72698	−0.0670705
$664$	0.837122	0.0324866
$665$	−18.0486	−0.699893
$666$	8.15229	0.315895
$667$	31.0331	1.20161
$668$	27.6690	1.07055
$669$	−55.3084	−2.13835
$670$	−65.9165	−2.54658
$671$	53.8142	2.07747
$672$	91.1399	3.51580
$673$	−37.7162	−1.45385	−0.726926	−	0.686715i	$-0.759052\pi$
$673$	−37.7162	−1.45385	−0.726926	+	0.686715i	$0.759052\pi$
$674$	−8.12272	−0.312876
$675$	3.06198	0.117856
$676$	−24.8460	−0.955614
$677$	6.62891	0.254770	0.127385	−	0.991853i	$-0.459342\pi$
$677$	6.62891	0.254770	0.127385	+	0.991853i	$0.459342\pi$
$678$	−19.2361	−0.738757
$679$	−37.8220	−1.45148
$680$	0.218192	0.00836728
$681$	−66.5319	−2.54951
$682$	−63.9376	−2.44830
$683$	−0.826382	−0.0316206	−0.0158103	−	0.999875i	$-0.505033\pi$
$683$	−0.826382	−0.0316206	−0.0158103	+	0.999875i	$0.505033\pi$
$684$	−36.0442	−1.37818
$685$	−34.9793	−1.33649
$686$	14.3171	0.546630
$687$	69.6637	2.65783
$688$	39.2470	1.49628
$689$	−1.29642	−0.0493897
$690$	53.8900	2.05156
$691$	−15.2014	−0.578290	−0.289145	−	0.957285i	$-0.593371\pi$
$691$	−15.2014	−0.578290	−0.289145	+	0.957285i	$0.593371\pi$
$692$	−6.42296	−0.244164
$693$	169.618	6.44327
$694$	−20.6121	−0.782424
$695$	12.5692	0.476778
$696$	−2.75756	−0.104525
$697$	−7.51375	−0.284604
$698$	−49.6673	−1.87994
$699$	15.9032	0.601516
$700$	1.23176	0.0465562
$701$	−7.96957	−0.301006	−0.150503	−	0.988610i	$-0.548089\pi$
$701$	−7.96957	−0.301006	−0.150503	+	0.988610i	$0.548089\pi$
$702$	17.3031	0.653064
$703$	1.17155	0.0441860
$704$	−46.5120	−1.75299
$705$	−67.1990	−2.53086
$706$	1.98791	0.0748160
$707$	5.45451	0.205138
$708$	−81.1096	−3.04828
$709$	27.8570	1.04619	0.523095	−	0.852274i	$-0.324777\pi$
$709$	27.8570	1.04619	0.523095	+	0.852274i	$0.324777\pi$
$710$	−59.2314	−2.22291
$711$	−57.4657	−2.15513
$712$	0.295428	0.0110716
$713$	−18.8585	−0.706255
$714$	−22.7982	−0.853202
$715$	−7.23236	−0.270475
$716$	36.7761	1.37439
$717$	35.0187	1.30780
$718$	8.52621	0.318195
$719$	35.2649	1.31516	0.657579	−	0.753385i	$-0.271581\pi$
$719$	35.2649	1.31516	0.657579	+	0.753385i	$0.271581\pi$
$720$	−74.9383	−2.79279
$721$	−32.1998	−1.19918
$722$	27.2826	1.01535
$723$	−72.2474	−2.68691
$724$	46.7180	1.73626
$725$	−1.58329	−0.0588020
$726$	−174.101	−6.46151
$727$	21.6712	0.803739	0.401870	−	0.915697i	$-0.368360\pi$
$727$	21.6712	0.803739	0.401870	+	0.915697i	$0.368360\pi$
$728$	−0.171939	−0.00637248
$729$	86.5175	3.20435
$730$	8.17325	0.302505
$731$	−9.58623	−0.354560
$732$	57.0981	2.11041
$733$	39.4947	1.45877	0.729386	−	0.684103i	$-0.239806\pi$
$733$	39.4947	1.45877	0.729386	+	0.684103i	$0.239806\pi$
$734$	−3.02897	−0.111801
$735$	37.1665	1.37091
$736$	−28.4803	−1.04980
$737$	89.0240	3.27924
$738$	120.092	4.42066
$739$	−20.2010	−0.743107	−0.371553	−	0.928412i	$-0.621175\pi$
$739$	−20.2010	−0.743107	−0.371553	+	0.928412i	$0.621175\pi$
$740$	−2.26641	−0.0833148
$741$	3.96670	0.145720
$742$	−17.1143	−0.628285
$743$	48.1858	1.76776	0.883882	−	0.467709i	$-0.154921\pi$
$743$	48.1858	1.76776	0.883882	+	0.467709i	$0.154921\pi$
$744$	1.67574	0.0614356
$745$	−27.7457	−1.01652
$746$	18.7227	0.685485
$747$	70.2256	2.56942
$748$	11.9296	0.436190
$749$	60.6711	2.21687
$750$	72.4366	2.64501
$751$	41.5491	1.51615	0.758073	−	0.652169i	$-0.226141\pi$
$751$	41.5491	1.51615	0.758073	+	0.652169i	$0.226141\pi$
$752$	36.3706	1.32630
$753$	20.4820	0.746406
$754$	−8.94712	−0.325835
$755$	−6.32724	−0.230272
$756$	112.817	4.10313
$757$	52.2517	1.89912	0.949560	−	0.313586i	$-0.101530\pi$
$757$	52.2517	1.89912	0.949560	+	0.313586i	$0.101530\pi$
$758$	−17.4083	−0.632299
$759$	−72.7815	−2.64180
$760$	−0.501164	−0.0181791
$761$	24.4842	0.887550	0.443775	−	0.896138i	$-0.353639\pi$
$761$	24.4842	0.887550	0.443775	+	0.896138i	$0.353639\pi$
$762$	−27.6432	−1.00141
$763$	−13.2930	−0.481240
$764$	−11.0950	−0.401403
$765$	18.3040	0.661781
$766$	−18.9445	−0.684493
$767$	6.50063	0.234724
$768$	55.6323	2.00746
$769$	−13.5479	−0.488549	−0.244275	−	0.969706i	$-0.578550\pi$
$769$	−13.5479	−0.488549	−0.244275	+	0.969706i	$0.578550\pi$
$770$	−95.4756	−3.44070
$771$	−37.5792	−1.35338
$772$	−8.26662	−0.297522
$773$	5.47779	0.197022	0.0985111	−	0.995136i	$-0.468592\pi$
$773$	5.47779	0.197022	0.0985111	+	0.995136i	$0.468592\pi$
$774$	153.217	5.50726
$775$	0.962148	0.0345614
$776$	−1.05022	−0.0377009
$777$	−5.84959	−0.209853
$778$	23.4815	0.841852
$779$	17.2583	0.618343
$780$	−7.67371	−0.274763
$781$	79.9954	2.86246
$782$	7.12422	0.254762
$783$	−145.014	−5.18237
$784$	−20.1159	−0.718425
$785$	39.4273	1.40722
$786$	136.536	4.87008
$787$	15.5334	0.553707	0.276853	−	0.960912i	$-0.410708\pi$
$787$	15.5334	0.553707	0.276853	+	0.960912i	$0.410708\pi$
$788$	53.9795	1.92294
$789$	−33.2087	−1.18226
$790$	32.3466	1.15084
$791$	10.0520	0.357406
$792$	4.70988	0.167358
$793$	−4.57619	−0.162505
$794$	0.0434403	0.00154164
$795$	18.8675	0.669162
$796$	−23.6553	−0.838441
$797$	26.1497	0.926271	0.463136	−	0.886287i	$-0.346724\pi$
$797$	26.1497	0.926271	0.463136	+	0.886287i	$0.346724\pi$
$798$	52.3651	1.85370
$799$	−8.88367	−0.314282
$800$	1.45305	0.0513731
$801$	24.7832	0.875673
$802$	−35.2201	−1.24367
$803$	−11.0384	−0.389538
$804$	94.4566	3.33123
$805$	−28.1606	−0.992532
$806$	5.43706	0.191512
$807$	32.7012	1.15114
$808$	0.151458	0.00532828
$809$	−14.0108	−0.492593	−0.246297	−	0.969194i	$-0.579214\pi$
$809$	−14.0108	−0.492593	−0.246297	+	0.969194i	$0.579214\pi$
$810$	−142.661	−5.01261
$811$	12.7423	0.447443	0.223722	−	0.974653i	$-0.428179\pi$
$811$	12.7423	0.447443	0.223722	+	0.974653i	$0.428179\pi$
$812$	−58.3357	−2.04718
$813$	−74.7342	−2.62104
$814$	6.19744	0.217220
$815$	−10.8445	−0.379866
$816$	−13.6033	−0.476211
$817$	22.0186	0.770332
$818$	−12.6477	−0.442217
$819$	−14.4238	−0.504010
$820$	−33.3867	−1.16591
$821$	−44.9893	−1.57014	−0.785070	−	0.619408i	$-0.787373\pi$
$821$	−44.9893	−1.57014	−0.785070	+	0.619408i	$0.787373\pi$
$822$	101.487	3.53977
$823$	−35.8527	−1.24975	−0.624873	−	0.780726i	$-0.714849\pi$
$823$	−35.8527	−1.24975	−0.624873	+	0.780726i	$0.714849\pi$
$824$	−0.894108	−0.0311477
$825$	3.71328	0.129280
$826$	85.8159	2.98592
$827$	47.6717	1.65771	0.828853	−	0.559466i	$-0.188994\pi$
$827$	47.6717	1.65771	0.828853	+	0.559466i	$0.188994\pi$
$828$	−56.2386	−1.95443
$829$	−14.4870	−0.503155	−0.251578	−	0.967837i	$-0.580949\pi$
$829$	−14.4870	−0.503155	−0.251578	+	0.967837i	$0.580949\pi$
$830$	−39.5289	−1.37207
$831$	−83.2884	−2.88924
$832$	3.95524	0.137123
$833$	4.91339	0.170239
$834$	−36.4677	−1.26277
$835$	32.2734	1.11687
$836$	−27.4011	−0.947686
$837$	88.1233	3.04599
$838$	31.9113	1.10236
$839$	24.6718	0.851764	0.425882	−	0.904779i	$-0.359964\pi$
$839$	24.6718	0.851764	0.425882	+	0.904779i	$0.359964\pi$
$840$	2.50232	0.0863382
$841$	45.9839	1.58565
$842$	51.9049	1.78876
$843$	−64.2364	−2.21242
$844$	−3.26020	−0.112221
$845$	−28.9806	−0.996963
$846$	141.988	4.88164
$847$	90.9781	3.12604
$848$	−10.2118	−0.350675
$849$	26.6125	0.913338
$850$	−0.363474	−0.0124671
$851$	1.82794	0.0626610
$852$	84.8770	2.90784
$853$	20.1456	0.689773	0.344887	−	0.938644i	$-0.387917\pi$
$853$	20.1456	0.689773	0.344887	+	0.938644i	$0.387917\pi$
$854$	−60.4111	−2.06723
$855$	−42.0423	−1.43782
$856$	1.68469	0.0575814
$857$	21.2213	0.724907	0.362454	−	0.932002i	$-0.381939\pi$
$857$	21.2213	0.724907	0.362454	+	0.932002i	$0.381939\pi$
$858$	20.9836	0.716367
$859$	27.0128	0.921666	0.460833	−	0.887487i	$-0.347551\pi$
$859$	27.0128	0.921666	0.460833	+	0.887487i	$0.347551\pi$
$860$	−42.5956	−1.45250
$861$	−86.1710	−2.93670
$862$	17.7362	0.604096
$863$	−32.6389	−1.11104	−0.555521	−	0.831502i	$-0.687481\pi$
$863$	−32.6389	−1.11104	−0.555521	+	0.831502i	$0.687481\pi$
$864$	133.085	4.52765
$865$	−7.49181	−0.254729
$866$	19.8041	0.672969
$867$	3.32266	0.112844
$868$	35.4500	1.20325
$869$	−43.6859	−1.48194
$870$	130.212	4.41460
$871$	−7.57034	−0.256511
$872$	−0.369114	−0.0124998
$873$	−88.1026	−2.98182
$874$	−16.3636	−0.553507
$875$	−37.8523	−1.27964
$876$	−11.7120	−0.395713
$877$	52.2136	1.76313	0.881564	−	0.472065i	$-0.156491\pi$
$877$	52.2136	1.76313	0.881564	+	0.472065i	$0.156491\pi$
$878$	8.30093	0.280143
$879$	−27.4740	−0.926675
$880$	−56.9687	−1.92042
$881$	−44.6500	−1.50430	−0.752149	−	0.658993i	$-0.770983\pi$
$881$	−44.6500	−1.50430	−0.752149	+	0.658993i	$0.770983\pi$
$882$	−78.5307	−2.64427
$883$	−24.6501	−0.829543	−0.414771	−	0.909926i	$-0.636138\pi$
$883$	−24.6501	−0.829543	−0.414771	+	0.909926i	$0.636138\pi$
$884$	−1.01446	−0.0341200
$885$	−94.6070	−3.18018
$886$	−66.6518	−2.23921
$887$	5.04716	0.169467	0.0847335	−	0.996404i	$-0.472996\pi$
$887$	5.04716	0.169467	0.0847335	+	0.996404i	$0.472996\pi$
$888$	−0.162429	−0.00545075
$889$	14.4452	0.484475
$890$	−13.9501	−0.467609
$891$	192.673	6.45478
$892$	−32.4891	−1.08781
$893$	20.4049	0.682822
$894$	80.4998	2.69231
$895$	42.8960	1.43385
$896$	−2.64567	−0.0883857
$897$	6.18912	0.206649
$898$	−27.6224	−0.921772
$899$	−45.5669	−1.51974
$900$	2.86926	0.0956421
$901$	2.49427	0.0830963
$902$	91.2952	3.03980
$903$	−109.939	−3.65854
$904$	0.279118	0.00928332
$905$	54.4923	1.81139
$906$	18.3575	0.609887
$907$	22.5584	0.749039	0.374519	−	0.927219i	$-0.377808\pi$
$907$	22.5584	0.749039	0.374519	+	0.927219i	$0.377808\pi$
$908$	−39.0819	−1.29698
$909$	12.7057	0.421422
$910$	8.11896	0.269141
$911$	32.6449	1.08157	0.540786	−	0.841160i	$-0.318127\pi$
$911$	32.6449	1.08157	0.540786	+	0.841160i	$0.318127\pi$
$912$	31.2454	1.03464
$913$	53.3861	1.76682
$914$	60.0659	1.98680
$915$	66.5998	2.20172
$916$	40.9216	1.35209
$917$	−71.3480	−2.35612
$918$	−33.2906	−1.09876
$919$	6.72893	0.221967	0.110984	−	0.993822i	$-0.464600\pi$
$919$	6.72893	0.221967	0.110984	+	0.993822i	$0.464600\pi$
$920$	−0.781951	−0.0257802
$921$	−81.1007	−2.67236
$922$	−46.4567	−1.52997
$923$	−6.80257	−0.223909
$924$	136.814	4.50085
$925$	−0.0932606	−0.00306639
$926$	0.322229	0.0105891
$927$	−75.0061	−2.46352
$928$	−68.8159	−2.25899
$929$	26.9571	0.884434	0.442217	−	0.896908i	$-0.354192\pi$
$929$	26.9571	0.884434	0.442217	+	0.896908i	$0.354192\pi$
$930$	−79.1284	−2.59472
$931$	−11.2855	−0.369868
$932$	9.34183	0.306002
$933$	39.1550	1.28188
$934$	−65.1592	−2.13207
$935$	13.9148	0.455064
$936$	−0.400514	−0.0130912
$937$	40.5490	1.32468	0.662339	−	0.749204i	$-0.269564\pi$
$937$	40.5490	1.32468	0.662339	+	0.749204i	$0.269564\pi$
$938$	−99.9373	−3.26307
$939$	−5.17310	−0.168818
$940$	−39.4738	−1.28749
$941$	−14.7308	−0.480209	−0.240104	−	0.970747i	$-0.577182\pi$
$941$	−14.7308	−0.480209	−0.240104	+	0.970747i	$0.577182\pi$
$942$	−114.392	−3.72710
$943$	26.9276	0.876883
$944$	51.2049	1.66658
$945$	131.591	4.28066
$946$	116.477	3.78698
$947$	−25.2505	−0.820530	−0.410265	−	0.911966i	$-0.634564\pi$
$947$	−25.2505	−0.820530	−0.410265	+	0.911966i	$0.634564\pi$
$948$	−46.3518	−1.50544
$949$	0.938677	0.0304707
$950$	0.834861	0.0270865
$951$	68.7180	2.22833
$952$	0.330805	0.0107215
$953$	−6.92681	−0.224381	−0.112191	−	0.993687i	$-0.535787\pi$
$953$	−6.92681	−0.224381	−0.112191	+	0.993687i	$0.535787\pi$
$954$	−39.8660	−1.29071
$955$	−12.9413	−0.418772
$956$	20.5705	0.665299
$957$	−175.859	−5.68472
$958$	−47.4456	−1.53290
$959$	−53.0329	−1.71252
$960$	−57.5628	−1.85783
$961$	−3.30950	−0.106758
$962$	−0.527012	−0.0169915
$963$	141.327	4.55420
$964$	−42.4393	−1.36688
$965$	−9.64228	−0.310396
$966$	81.7037	2.62877
$967$	−7.51653	−0.241715	−0.120858	−	0.992670i	$-0.538564\pi$
$967$	−7.51653	−0.241715	−0.120858	+	0.992670i	$0.538564\pi$
$968$	2.52624	0.0811963
$969$	−7.63181	−0.245169
$970$	49.5916	1.59229
$971$	−36.5222	−1.17205	−0.586027	−	0.810291i	$-0.699309\pi$
$971$	−36.5222	−1.17205	−0.586027	+	0.810291i	$0.699309\pi$
$972$	106.373	3.41191
$973$	19.0565	0.610922
$974$	35.6192	1.14131
$975$	−0.315766	−0.0101126
$976$	−36.0463	−1.15381
$977$	−29.2277	−0.935077	−0.467539	−	0.883973i	$-0.654859\pi$
$977$	−29.2277	−0.935077	−0.467539	+	0.883973i	$0.654859\pi$
$978$	31.4636	1.00610
$979$	18.8404	0.602143
$980$	21.8322	0.697404
$981$	−30.9647	−0.988628
$982$	61.4719	1.96165
$983$	−36.7686	−1.17274	−0.586369	−	0.810044i	$-0.699443\pi$
$983$	−36.7686	−1.17274	−0.586369	+	0.810044i	$0.699443\pi$
$984$	−2.39275	−0.0762782
$985$	62.9622	2.00614
$986$	17.2140	0.548204
$987$	−101.882	−3.24293
$988$	2.33011	0.0741305
$989$	34.3549	1.09242
$990$	−222.401	−7.06836
$991$	−8.57427	−0.272371	−0.136185	−	0.990683i	$-0.543484\pi$
$991$	−8.57427	−0.272371	−0.136185	+	0.990683i	$0.543484\pi$
$992$	41.8186	1.32774
$993$	37.9107	1.20306
$994$	−89.8019	−2.84834
$995$	−27.5918	−0.874720
$996$	56.6439	1.79483
$997$	47.3205	1.49866	0.749328	−	0.662199i	$-0.230377\pi$
$997$	47.3205	1.49866	0.749328	+	0.662199i	$0.230377\pi$
$998$	50.2206	1.58971
$999$	−8.54175	−0.270249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.20	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.20	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98791 q^{2} +3.32266 q^{3} +1.95179 q^{4} +2.27659 q^{5} -6.60516 q^{6} +3.45158 q^{7} +0.0958417 q^{8} +8.04010 q^{9} +O(q^{10})\)	\(q-1.98791 q^{2} +3.32266 q^{3} +1.95179 q^{4} +2.27659 q^{5} -6.60516 q^{6} +3.45158 q^{7} +0.0958417 q^{8} +8.04010 q^{9} -4.52565 q^{10} +6.11215 q^{11} +6.48514 q^{12} -0.519759 q^{13} -6.86143 q^{14} +7.56433 q^{15} -4.09410 q^{16} +1.00000 q^{17} -15.9830 q^{18} -2.29689 q^{19} +4.44341 q^{20} +11.4684 q^{21} -12.1504 q^{22} -3.58377 q^{23} +0.318450 q^{24} +0.182842 q^{25} +1.03323 q^{26} +16.7466 q^{27} +6.73675 q^{28} -8.65933 q^{29} -15.0372 q^{30} +5.26218 q^{31} +7.94702 q^{32} +20.3086 q^{33} -1.98791 q^{34} +7.85781 q^{35} +15.6926 q^{36} -0.510060 q^{37} +4.56602 q^{38} -1.72698 q^{39} +0.218192 q^{40} -7.51375 q^{41} -22.7982 q^{42} -9.58623 q^{43} +11.9296 q^{44} +18.3040 q^{45} +7.12422 q^{46} -8.88367 q^{47} -13.6033 q^{48} +4.91339 q^{49} -0.363474 q^{50} +3.32266 q^{51} -1.01446 q^{52} +2.49427 q^{53} -33.2906 q^{54} +13.9148 q^{55} +0.330805 q^{56} -7.63181 q^{57} +17.2140 q^{58} -12.5070 q^{59} +14.7640 q^{60} +8.80445 q^{61} -10.4607 q^{62} +27.7510 q^{63} -7.60976 q^{64} -1.18328 q^{65} -40.3717 q^{66} +14.5651 q^{67} +1.95179 q^{68} -11.9077 q^{69} -15.6206 q^{70} +13.0879 q^{71} +0.770577 q^{72} -1.80598 q^{73} +1.01395 q^{74} +0.607523 q^{75} -4.48305 q^{76} +21.0966 q^{77} +3.43309 q^{78} -7.14739 q^{79} -9.32057 q^{80} +31.5229 q^{81} +14.9367 q^{82} +8.73442 q^{83} +22.3839 q^{84} +2.27659 q^{85} +19.0566 q^{86} -28.7720 q^{87} +0.585799 q^{88} +3.08245 q^{89} -36.3867 q^{90} -1.79399 q^{91} -6.99477 q^{92} +17.4844 q^{93} +17.6599 q^{94} -5.22908 q^{95} +26.4053 q^{96} -10.9579 q^{97} -9.76738 q^{98} +49.1423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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