LMFDB - Embedded newform 6001.2.a.b.1.3

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:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.75487 q^{2} -1.38395 q^{3} +5.58934 q^{4} +1.31563 q^{5} +3.81261 q^{6} -4.81832 q^{7} -9.88817 q^{8} -1.08468 q^{9} +O(q^{10})$	\(q-2.75487 q^{2} -1.38395 q^{3} +5.58934 q^{4} +1.31563 q^{5} +3.81261 q^{6} -4.81832 q^{7} -9.88817 q^{8} -1.08468 q^{9} -3.62439 q^{10} -5.09469 q^{11} -7.73536 q^{12} +5.27345 q^{13} +13.2739 q^{14} -1.82076 q^{15} +16.0620 q^{16} +1.00000 q^{17} +2.98816 q^{18} +6.13889 q^{19} +7.35348 q^{20} +6.66832 q^{21} +14.0352 q^{22} -3.61162 q^{23} +13.6847 q^{24} -3.26912 q^{25} -14.5277 q^{26} +5.65300 q^{27} -26.9312 q^{28} -6.73759 q^{29} +5.01598 q^{30} -6.43208 q^{31} -24.4725 q^{32} +7.05080 q^{33} -2.75487 q^{34} -6.33912 q^{35} -6.06265 q^{36} +5.38614 q^{37} -16.9119 q^{38} -7.29819 q^{39} -13.0092 q^{40} -3.59917 q^{41} -18.3704 q^{42} +11.4833 q^{43} -28.4760 q^{44} -1.42704 q^{45} +9.94955 q^{46} -4.09995 q^{47} -22.2290 q^{48} +16.2162 q^{49} +9.00603 q^{50} -1.38395 q^{51} +29.4751 q^{52} +13.0616 q^{53} -15.5733 q^{54} -6.70272 q^{55} +47.6444 q^{56} -8.49592 q^{57} +18.5612 q^{58} -10.3127 q^{59} -10.1769 q^{60} +1.62534 q^{61} +17.7196 q^{62} +5.22634 q^{63} +35.2946 q^{64} +6.93789 q^{65} -19.4241 q^{66} -8.49693 q^{67} +5.58934 q^{68} +4.99830 q^{69} +17.4635 q^{70} +5.46230 q^{71} +10.7255 q^{72} -4.51414 q^{73} -14.8381 q^{74} +4.52431 q^{75} +34.3123 q^{76} +24.5479 q^{77} +20.1056 q^{78} -12.2658 q^{79} +21.1316 q^{80} -4.56942 q^{81} +9.91527 q^{82} -0.164706 q^{83} +37.2715 q^{84} +1.31563 q^{85} -31.6350 q^{86} +9.32448 q^{87} +50.3772 q^{88} +3.49655 q^{89} +3.93131 q^{90} -25.4092 q^{91} -20.1865 q^{92} +8.90167 q^{93} +11.2948 q^{94} +8.07649 q^{95} +33.8687 q^{96} +14.0705 q^{97} -44.6736 q^{98} +5.52612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.75487	−1.94799	−0.973995	−	0.226568i	$-0.927249\pi$
$2$	−2.75487	−1.94799	−0.973995	+	0.226568i	$0.927249\pi$
$3$	−1.38395	−0.799024	−0.399512	−	0.916728i	$-0.630820\pi$
$3$	−1.38395	−0.799024	−0.399512	+	0.916728i	$0.630820\pi$
$4$	5.58934	2.79467
$5$	1.31563	0.588367	0.294183	−	0.955749i	$-0.404952\pi$
$5$	1.31563	0.588367	0.294183	+	0.955749i	$0.404952\pi$
$6$	3.81261	1.55649
$7$	−4.81832	−1.82115	−0.910577	−	0.413339i	$-0.864362\pi$
$7$	−4.81832	−1.82115	−0.910577	+	0.413339i	$0.864362\pi$
$8$	−9.88817	−3.49600
$9$	−1.08468	−0.361561
$10$	−3.62439	−1.14613
$11$	−5.09469	−1.53611	−0.768054	−	0.640385i	$-0.778775\pi$
$11$	−5.09469	−1.53611	−0.768054	+	0.640385i	$0.778775\pi$
$12$	−7.73536	−2.23301
$13$	5.27345	1.46259	0.731295	−	0.682061i	$-0.238916\pi$
$13$	5.27345	1.46259	0.731295	+	0.682061i	$0.238916\pi$
$14$	13.2739	3.54759
$15$	−1.82076	−0.470119
$16$	16.0620	4.01550
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.98816	0.704317
$19$	6.13889	1.40836	0.704179	−	0.710022i	$-0.251315\pi$
$19$	6.13889	1.40836	0.704179	+	0.710022i	$0.251315\pi$
$20$	7.35348	1.64429
$21$	6.66832	1.45515
$22$	14.0352	2.99232
$23$	−3.61162	−0.753074	−0.376537	−	0.926402i	$-0.622885\pi$
$23$	−3.61162	−0.753074	−0.376537	+	0.926402i	$0.622885\pi$
$24$	13.6847	2.79339
$25$	−3.26912	−0.653825
$26$	−14.5277	−2.84911
$27$	5.65300	1.08792
$28$	−26.9312	−5.08952
$29$	−6.73759	−1.25114	−0.625569	−	0.780169i	$-0.715133\pi$
$29$	−6.73759	−1.25114	−0.625569	+	0.780169i	$0.715133\pi$
$30$	5.01598	0.915788
$31$	−6.43208	−1.15523	−0.577617	−	0.816308i	$-0.696017\pi$
$31$	−6.43208	−1.15523	−0.577617	+	0.816308i	$0.696017\pi$
$32$	−24.4725	−4.32616
$33$	7.05080	1.22739
$34$	−2.75487	−0.472457
$35$	−6.33912	−1.07151
$36$	−6.06265	−1.01044
$37$	5.38614	0.885475	0.442738	−	0.896651i	$-0.354007\pi$
$37$	5.38614	0.885475	0.442738	+	0.896651i	$0.354007\pi$
$38$	−16.9119	−2.74347
$39$	−7.29819	−1.16865
$40$	−13.0092	−2.05693
$41$	−3.59917	−0.562096	−0.281048	−	0.959694i	$-0.590682\pi$
$41$	−3.59917	−0.562096	−0.281048	+	0.959694i	$0.590682\pi$
$42$	−18.3704	−2.83461
$43$	11.4833	1.75118	0.875591	−	0.483053i	$-0.160472\pi$
$43$	11.4833	1.75118	0.875591	+	0.483053i	$0.160472\pi$
$44$	−28.4760	−4.29291
$45$	−1.42704	−0.212730
$46$	9.94955	1.46698
$47$	−4.09995	−0.598039	−0.299020	−	0.954247i	$-0.596660\pi$
$47$	−4.09995	−0.598039	−0.299020	+	0.954247i	$0.596660\pi$
$48$	−22.2290	−3.20848
$49$	16.2162	2.31660
$50$	9.00603	1.27364
$51$	−1.38395	−0.193792
$52$	29.4751	4.08746
$53$	13.0616	1.79414	0.897072	−	0.441883i	$-0.145690\pi$
$53$	13.0616	1.79414	0.897072	+	0.441883i	$0.145690\pi$
$54$	−15.5733	−2.11926
$55$	−6.70272	−0.903795
$56$	47.6444	6.36675
$57$	−8.49592	−1.12531
$58$	18.5612	2.43721
$59$	−10.3127	−1.34260	−0.671299	−	0.741186i	$-0.734263\pi$
$59$	−10.3127	−1.34260	−0.671299	+	0.741186i	$0.734263\pi$
$60$	−10.1769	−1.31383
$61$	1.62534	0.208103	0.104052	−	0.994572i	$-0.466819\pi$
$61$	1.62534	0.208103	0.104052	+	0.994572i	$0.466819\pi$
$62$	17.7196	2.25039
$63$	5.22634	0.658457
$64$	35.2946	4.41182
$65$	6.93789	0.860540
$66$	−19.4241	−2.39094
$67$	−8.49693	−1.03806	−0.519032	−	0.854755i	$-0.673708\pi$
$67$	−8.49693	−1.03806	−0.519032	+	0.854755i	$0.673708\pi$
$68$	5.58934	0.677807
$69$	4.99830	0.601724
$70$	17.4635	2.08728
$71$	5.46230	0.648256	0.324128	−	0.946013i	$-0.394929\pi$
$71$	5.46230	0.648256	0.324128	+	0.946013i	$0.394929\pi$
$72$	10.7255	1.26401
$73$	−4.51414	−0.528340	−0.264170	−	0.964476i	$-0.585098\pi$
$73$	−4.51414	−0.528340	−0.264170	+	0.964476i	$0.585098\pi$
$74$	−14.8381	−1.72490
$75$	4.52431	0.522422
$76$	34.3123	3.93589
$77$	24.5479	2.79749
$78$	20.1056	2.27651
$79$	−12.2658	−1.38001	−0.690006	−	0.723804i	$-0.742392\pi$
$79$	−12.2658	−1.38001	−0.690006	+	0.723804i	$0.742392\pi$
$80$	21.1316	2.36259
$81$	−4.56942	−0.507713
$82$	9.91527	1.09496
$83$	−0.164706	−0.0180788	−0.00903939	−	0.999959i	$-0.502877\pi$
$83$	−0.164706	−0.0180788	−0.00903939	+	0.999959i	$0.502877\pi$
$84$	37.2715	4.06665
$85$	1.31563	0.142700
$86$	−31.6350	−3.41129
$87$	9.32448	0.999690
$88$	50.3772	5.37023
$89$	3.49655	0.370633	0.185317	−	0.982679i	$-0.440669\pi$
$89$	3.49655	0.370633	0.185317	+	0.982679i	$0.440669\pi$
$90$	3.93131	0.414396
$91$	−25.4092	−2.66360
$92$	−20.1865	−2.10459
$93$	8.90167	0.923061
$94$	11.2948	1.16497
$95$	8.07649	0.828631
$96$	33.8687	3.45671
$97$	14.0705	1.42864	0.714320	−	0.699819i	$-0.246736\pi$
$97$	14.0705	1.42864	0.714320	+	0.699819i	$0.246736\pi$
$98$	−44.6736	−4.51272
$99$	5.52612	0.555396
$100$	−18.2722	−1.82722
$101$	0.940015	0.0935350	0.0467675	−	0.998906i	$-0.485108\pi$
$101$	0.940015	0.0935350	0.0467675	+	0.998906i	$0.485108\pi$
$102$	3.81261	0.377505
$103$	8.90741	0.877674	0.438837	−	0.898567i	$-0.355391\pi$
$103$	8.90741	0.877674	0.438837	+	0.898567i	$0.355391\pi$
$104$	−52.1447	−5.11321
$105$	8.77302	0.856159
$106$	−35.9830	−3.49498
$107$	19.5910	1.89394	0.946968	−	0.321329i	$-0.104130\pi$
$107$	19.5910	1.89394	0.946968	+	0.321329i	$0.104130\pi$
$108$	31.5965	3.04037
$109$	0.372597	0.0356883	0.0178441	−	0.999841i	$-0.494320\pi$
$109$	0.372597	0.0356883	0.0178441	+	0.999841i	$0.494320\pi$
$110$	18.4652	1.76058
$111$	−7.45414	−0.707516
$112$	−77.3919	−7.31285
$113$	17.0229	1.60138	0.800690	−	0.599078i	$-0.204466\pi$
$113$	17.0229	1.60138	0.800690	+	0.599078i	$0.204466\pi$
$114$	23.4052	2.19210
$115$	−4.75154	−0.443084
$116$	−37.6586	−3.49652
$117$	−5.72001	−0.528815
$118$	28.4102	2.61537
$119$	−4.81832	−0.441695
$120$	18.0040	1.64353
$121$	14.9559	1.35963
$122$	−4.47761	−0.405384
$123$	4.98108	0.449128
$124$	−35.9510	−3.22850
$125$	−10.8791	−0.973055
$126$	−14.3979	−1.28267
$127$	−8.22937	−0.730239	−0.365119	−	0.930961i	$-0.618972\pi$
$127$	−8.22937	−0.730239	−0.365119	+	0.930961i	$0.618972\pi$
$128$	−48.2872	−4.26803
$129$	−15.8923	−1.39924
$130$	−19.1130	−1.67632
$131$	6.83787	0.597427	0.298714	−	0.954343i	$-0.403442\pi$
$131$	6.83787	0.597427	0.298714	+	0.954343i	$0.403442\pi$
$132$	39.4093	3.43014
$133$	−29.5791	−2.56484
$134$	23.4080	2.02214
$135$	7.43724	0.640096
$136$	−9.88817	−0.847904
$137$	0.806727	0.0689233	0.0344617	−	0.999406i	$-0.489028\pi$
$137$	0.806727	0.0689233	0.0344617	+	0.999406i	$0.489028\pi$
$138$	−13.7697	−1.17215
$139$	2.93234	0.248717	0.124359	−	0.992237i	$-0.460313\pi$
$139$	2.93234	0.248717	0.124359	+	0.992237i	$0.460313\pi$
$140$	−35.4314	−2.99450
$141$	5.67413	0.477848
$142$	−15.0480	−1.26280
$143$	−26.8666	−2.24670
$144$	−17.4222	−1.45185
$145$	−8.86415	−0.736128
$146$	12.4359	1.02920
$147$	−22.4424	−1.85102
$148$	30.1049	2.47461
$149$	10.8265	0.886942	0.443471	−	0.896289i	$-0.353747\pi$
$149$	10.8265	0.886942	0.443471	+	0.896289i	$0.353747\pi$
$150$	−12.4639	−1.01767
$151$	−0.0538371	−0.00438120	−0.00219060	−	0.999998i	$-0.500697\pi$
$151$	−0.0538371	−0.00438120	−0.00219060	+	0.999998i	$0.500697\pi$
$152$	−60.7024	−4.92362
$153$	−1.08468	−0.0876913
$154$	−67.6263	−5.44948
$155$	−8.46222	−0.679702
$156$	−40.7920	−3.26598
$157$	−7.41195	−0.591538	−0.295769	−	0.955259i	$-0.595576\pi$
$157$	−7.41195	−0.591538	−0.295769	+	0.955259i	$0.595576\pi$
$158$	33.7908	2.68825
$159$	−18.0766	−1.43357
$160$	−32.1967	−2.54537
$161$	17.4019	1.37146
$162$	12.5882	0.989021
$163$	10.5688	0.827815	0.413907	−	0.910319i	$-0.364164\pi$
$163$	10.5688	0.827815	0.413907	+	0.910319i	$0.364164\pi$
$164$	−20.1170	−1.57087
$165$	9.27623	0.722154
$166$	0.453743	0.0352173
$167$	8.09223	0.626196	0.313098	−	0.949721i	$-0.398633\pi$
$167$	8.09223	0.626196	0.313098	+	0.949721i	$0.398633\pi$
$168$	−65.9375	−5.08719
$169$	14.8092	1.13917
$170$	−3.62439	−0.277978
$171$	−6.65874	−0.509207
$172$	64.1839	4.89397
$173$	−4.69446	−0.356913	−0.178457	−	0.983948i	$-0.557110\pi$
$173$	−4.69446	−0.356913	−0.178457	+	0.983948i	$0.557110\pi$
$174$	−25.6878	−1.94739
$175$	15.7517	1.19072
$176$	−81.8310	−6.16824
$177$	14.2723	1.07277
$178$	−9.63255	−0.721990
$179$	−1.54529	−0.115500	−0.0577501	−	0.998331i	$-0.518393\pi$
$179$	−1.54529	−0.115500	−0.0577501	+	0.998331i	$0.518393\pi$
$180$	−7.97619	−0.594510
$181$	5.86638	0.436044	0.218022	−	0.975944i	$-0.430039\pi$
$181$	5.86638	0.436044	0.218022	+	0.975944i	$0.430039\pi$
$182$	69.9991	5.18867
$183$	−2.24939	−0.166280
$184$	35.7123	2.63274
$185$	7.08615	0.520984
$186$	−24.5230	−1.79811
$187$	−5.09469	−0.372561
$188$	−22.9160	−1.67132
$189$	−27.2379	−1.98127
$190$	−22.2497	−1.61417
$191$	−24.3587	−1.76253	−0.881266	−	0.472621i	$-0.843308\pi$
$191$	−24.3587	−1.76253	−0.881266	+	0.472621i	$0.843308\pi$
$192$	−48.8460	−3.52515
$193$	7.18898	0.517474	0.258737	−	0.965948i	$-0.416694\pi$
$193$	7.18898	0.517474	0.258737	+	0.965948i	$0.416694\pi$
$194$	−38.7624	−2.78298
$195$	−9.60170	−0.687592
$196$	90.6379	6.47413
$197$	−18.1768	−1.29505	−0.647523	−	0.762046i	$-0.724195\pi$
$197$	−18.1768	−1.29505	−0.647523	+	0.762046i	$0.724195\pi$
$198$	−15.2238	−1.08191
$199$	−9.60114	−0.680607	−0.340304	−	0.940316i	$-0.610530\pi$
$199$	−9.60114	−0.680607	−0.340304	+	0.940316i	$0.610530\pi$
$200$	32.3257	2.28577
$201$	11.7593	0.829439
$202$	−2.58962	−0.182205
$203$	32.4638	2.27852
$204$	−7.73536	−0.541584
$205$	−4.73517	−0.330719
$206$	−24.5388	−1.70970
$207$	3.91745	0.272282
$208$	84.7021	5.87304
$209$	−31.2758	−2.16339
$210$	−24.1686	−1.66779
$211$	16.9496	1.16686	0.583429	−	0.812164i	$-0.301711\pi$
$211$	16.9496	1.16686	0.583429	+	0.812164i	$0.301711\pi$
$212$	73.0055	5.01404
$213$	−7.55956	−0.517972
$214$	−53.9708	−3.68937
$215$	15.1077	1.03034
$216$	−55.8978	−3.80336
$217$	30.9918	2.10386
$218$	−1.02646	−0.0695205
$219$	6.24734	0.422156
$220$	−37.4638	−2.52581
$221$	5.27345	0.354730
$222$	20.5352	1.37823
$223$	10.8772	0.728391	0.364196	−	0.931322i	$-0.381344\pi$
$223$	10.8772	0.728391	0.364196	+	0.931322i	$0.381344\pi$
$224$	117.916	7.87861
$225$	3.54596	0.236397
$226$	−46.8960	−3.11947
$227$	−16.7208	−1.10980	−0.554899	−	0.831918i	$-0.687243\pi$
$227$	−16.7208	−1.10980	−0.554899	+	0.831918i	$0.687243\pi$
$228$	−47.4866	−3.14487
$229$	−5.12306	−0.338541	−0.169271	−	0.985570i	$-0.554141\pi$
$229$	−5.12306	−0.338541	−0.169271	+	0.985570i	$0.554141\pi$
$230$	13.0899	0.863123
$231$	−33.9730	−2.23526
$232$	66.6224	4.37397
$233$	17.1101	1.12092	0.560461	−	0.828181i	$-0.310624\pi$
$233$	17.1101	1.12092	0.560461	+	0.828181i	$0.310624\pi$
$234$	15.7579	1.03013
$235$	−5.39401	−0.351866
$236$	−57.6411	−3.75212
$237$	16.9753	1.10266
$238$	13.2739	0.860417
$239$	−10.8259	−0.700269	−0.350135	−	0.936699i	$-0.613864\pi$
$239$	−10.8259	−0.700269	−0.350135	+	0.936699i	$0.613864\pi$
$240$	−29.2451	−1.88776
$241$	8.02923	0.517208	0.258604	−	0.965983i	$-0.416738\pi$
$241$	8.02923	0.517208	0.258604	+	0.965983i	$0.416738\pi$
$242$	−41.2017	−2.64854
$243$	−10.6351	−0.682244
$244$	9.08457	0.581580
$245$	21.3345	1.36301
$246$	−13.7222	−0.874898
$247$	32.3731	2.05985
$248$	63.6015	4.03870
$249$	0.227944	0.0144454
$250$	29.9705	1.89550
$251$	27.3790	1.72815	0.864074	−	0.503365i	$-0.167905\pi$
$251$	27.3790	1.72815	0.864074	+	0.503365i	$0.167905\pi$
$252$	29.2118	1.84017
$253$	18.4001	1.15680
$254$	22.6709	1.42250
$255$	−1.82076	−0.114021
$256$	62.4361	3.90226
$257$	−13.4438	−0.838604	−0.419302	−	0.907847i	$-0.637725\pi$
$257$	−13.4438	−0.838604	−0.419302	+	0.907847i	$0.637725\pi$
$258$	43.7812	2.72570
$259$	−25.9521	−1.61259
$260$	38.7782	2.40492
$261$	7.30813	0.452362
$262$	−18.8375	−1.16378
$263$	17.1270	1.05610	0.528048	−	0.849214i	$-0.322924\pi$
$263$	17.1270	1.05610	0.528048	+	0.849214i	$0.322924\pi$
$264$	−69.7196	−4.29094
$265$	17.1842	1.05561
$266$	81.4868	4.99628
$267$	−4.83905	−0.296145
$268$	−47.4922	−2.90105
$269$	−2.30480	−0.140526	−0.0702630	−	0.997529i	$-0.522384\pi$
$269$	−2.30480	−0.140526	−0.0702630	+	0.997529i	$0.522384\pi$
$270$	−20.4887	−1.24690
$271$	−2.55742	−0.155352	−0.0776762	−	0.996979i	$-0.524750\pi$
$271$	−2.55742	−0.155352	−0.0776762	+	0.996979i	$0.524750\pi$
$272$	16.0620	0.973902
$273$	35.1650	2.12828
$274$	−2.22243	−0.134262
$275$	16.6552	1.00435
$276$	27.9372	1.68162
$277$	−11.1856	−0.672078	−0.336039	−	0.941848i	$-0.609087\pi$
$277$	−11.1856	−0.672078	−0.336039	+	0.941848i	$0.609087\pi$
$278$	−8.07822	−0.484499
$279$	6.97675	0.417687
$280$	62.6823	3.74598
$281$	6.12385	0.365318	0.182659	−	0.983176i	$-0.441530\pi$
$281$	6.12385	0.365318	0.182659	+	0.983176i	$0.441530\pi$
$282$	−15.6315	−0.930843
$283$	−25.8471	−1.53645	−0.768226	−	0.640178i	$-0.778860\pi$
$283$	−25.8471	−1.53645	−0.768226	+	0.640178i	$0.778860\pi$
$284$	30.5306	1.81166
$285$	−11.1775	−0.662096
$286$	74.0141	4.37655
$287$	17.3420	1.02366
$288$	26.5448	1.56417
$289$	1.00000	0.0588235
$290$	24.4196	1.43397
$291$	−19.4728	−1.14152
$292$	−25.2310	−1.47653
$293$	11.4962	0.671617	0.335808	−	0.941930i	$-0.390991\pi$
$293$	11.4962	0.671617	0.335808	+	0.941930i	$0.390991\pi$
$294$	61.8261	3.60577
$295$	−13.5677	−0.789940
$296$	−53.2590	−3.09562
$297$	−28.8003	−1.67116
$298$	−29.8257	−1.72775
$299$	−19.0457	−1.10144
$300$	25.2879	1.46000
$301$	−55.3301	−3.18917
$302$	0.148314	0.00853454
$303$	−1.30093	−0.0747367
$304$	98.6029	5.65526
$305$	2.13834	0.122441
$306$	2.98816	0.170822
$307$	6.71400	0.383188	0.191594	−	0.981474i	$-0.438634\pi$
$307$	6.71400	0.383188	0.191594	+	0.981474i	$0.438634\pi$
$308$	137.206	7.81805
$309$	−12.3274	−0.701282
$310$	23.3123	1.32405
$311$	0.693118	0.0393031	0.0196515	−	0.999807i	$-0.493744\pi$
$311$	0.693118	0.0393031	0.0196515	+	0.999807i	$0.493744\pi$
$312$	72.1657	4.08558
$313$	−0.300505	−0.0169855	−0.00849277	−	0.999964i	$-0.502703\pi$
$313$	−0.300505	−0.0169855	−0.00849277	+	0.999964i	$0.502703\pi$
$314$	20.4190	1.15231
$315$	6.87592	0.387414
$316$	−68.5577	−3.85667
$317$	−27.9780	−1.57140	−0.785701	−	0.618606i	$-0.787698\pi$
$317$	−27.9780	−1.57140	−0.785701	+	0.618606i	$0.787698\pi$
$318$	49.7987	2.79257
$319$	34.3259	1.92188
$320$	46.4345	2.59577
$321$	−27.1130	−1.51330
$322$	−47.9401	−2.67160
$323$	6.13889	0.341577
$324$	−25.5400	−1.41889
$325$	−17.2396	−0.956278
$326$	−29.1158	−1.61258
$327$	−0.515655	−0.0285158
$328$	35.5892	1.96509
$329$	19.7549	1.08912
$330$	−25.5549	−1.40675
$331$	−3.91937	−0.215428	−0.107714	−	0.994182i	$-0.534353\pi$
$331$	−3.91937	−0.215428	−0.107714	+	0.994182i	$0.534353\pi$
$332$	−0.920594	−0.0505242
$333$	−5.84224	−0.320153
$334$	−22.2931	−1.21982
$335$	−11.1788	−0.610763
$336$	107.107	5.84314
$337$	−27.8817	−1.51881	−0.759405	−	0.650618i	$-0.774510\pi$
$337$	−27.8817	−1.51881	−0.759405	+	0.650618i	$0.774510\pi$
$338$	−40.7976	−2.21910
$339$	−23.5589	−1.27954
$340$	7.35348	0.398799
$341$	32.7695	1.77457
$342$	18.3440	0.991930
$343$	−44.4067	−2.39774
$344$	−113.549	−6.12213
$345$	6.57590	0.354034
$346$	12.9326	0.695264
$347$	−5.18556	−0.278376	−0.139188	−	0.990266i	$-0.544449\pi$
$347$	−5.18556	−0.278376	−0.139188	+	0.990266i	$0.544449\pi$
$348$	52.1177	2.79380
$349$	−12.9154	−0.691346	−0.345673	−	0.938355i	$-0.612349\pi$
$349$	−12.9154	−0.691346	−0.345673	+	0.938355i	$0.612349\pi$
$350$	−43.3939	−2.31950
$351$	29.8108	1.59118
$352$	124.680	6.64545
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−39.3183	−2.08974
$355$	7.18636	0.381412
$356$	19.5434	1.03580
$357$	6.66832	0.352925
$358$	4.25707	0.224993
$359$	−27.8674	−1.47079	−0.735393	−	0.677641i	$-0.763002\pi$
$359$	−27.8674	−1.47079	−0.735393	+	0.677641i	$0.763002\pi$
$360$	14.1108	0.743704
$361$	18.6860	0.983473
$362$	−16.1611	−0.849410
$363$	−20.6982	−1.08638
$364$	−142.020	−7.44389
$365$	−5.93892	−0.310857
$366$	6.19679	0.323911
$367$	6.50514	0.339565	0.169783	−	0.985482i	$-0.445693\pi$
$367$	6.50514	0.339565	0.169783	+	0.985482i	$0.445693\pi$
$368$	−58.0098	−3.02397
$369$	3.90396	0.203232
$370$	−19.5215	−1.01487
$371$	−62.9348	−3.26741
$372$	49.7544	2.57965
$373$	27.7373	1.43618	0.718092	−	0.695948i	$-0.245016\pi$
$373$	27.7373	1.43618	0.718092	+	0.695948i	$0.245016\pi$
$374$	14.0352	0.725745
$375$	15.0561	0.777495
$376$	40.5410	2.09074
$377$	−35.5303	−1.82990
$378$	75.0371	3.85949
$379$	−15.4252	−0.792341	−0.396171	−	0.918177i	$-0.629661\pi$
$379$	−15.4252	−0.792341	−0.396171	+	0.918177i	$0.629661\pi$
$380$	45.1422	2.31575
$381$	11.3890	0.583479
$382$	67.1051	3.43339
$383$	8.25417	0.421768	0.210884	−	0.977511i	$-0.432366\pi$
$383$	8.25417	0.421768	0.210884	+	0.977511i	$0.432366\pi$
$384$	66.8271	3.41026
$385$	32.2959	1.64595
$386$	−19.8047	−1.00803
$387$	−12.4557	−0.633158
$388$	78.6446	3.99257
$389$	−22.3600	−1.13370	−0.566848	−	0.823823i	$-0.691837\pi$
$389$	−22.3600	−1.13370	−0.566848	+	0.823823i	$0.691837\pi$
$390$	26.4515	1.33942
$391$	−3.61162	−0.182647
$392$	−160.349	−8.09883
$393$	−9.46327	−0.477359
$394$	50.0749	2.52274
$395$	−16.1372	−0.811953
$396$	30.8873	1.55215
$397$	−24.5964	−1.23446	−0.617228	−	0.786784i	$-0.711745\pi$
$397$	−24.5964	−1.23446	−0.617228	+	0.786784i	$0.711745\pi$
$398$	26.4500	1.32582
$399$	40.9361	2.04937
$400$	−52.5087	−2.62543
$401$	17.0749	0.852681	0.426341	−	0.904563i	$-0.359802\pi$
$401$	17.0749	0.852681	0.426341	+	0.904563i	$0.359802\pi$
$402$	−32.3955	−1.61574
$403$	−33.9192	−1.68964
$404$	5.25406	0.261399
$405$	−6.01166	−0.298722
$406$	−89.4338	−4.43853
$407$	−27.4407	−1.36019
$408$	13.6847	0.677496
$409$	32.9225	1.62791	0.813956	−	0.580927i	$-0.197310\pi$
$409$	32.9225	1.62791	0.813956	+	0.580927i	$0.197310\pi$
$410$	13.0448	0.644237
$411$	−1.11647	−0.0550714
$412$	49.7865	2.45281
$413$	49.6899	2.44508
$414$	−10.7921	−0.530402
$415$	−0.216691	−0.0106369
$416$	−129.054	−6.32741
$417$	−4.05821	−0.198731
$418$	86.1608	4.21426
$419$	26.0108	1.27071	0.635355	−	0.772220i	$-0.280854\pi$
$419$	26.0108	1.27071	0.635355	+	0.772220i	$0.280854\pi$
$420$	49.0354	2.39268
$421$	−6.62047	−0.322662	−0.161331	−	0.986900i	$-0.551579\pi$
$421$	−6.62047	−0.322662	−0.161331	+	0.986900i	$0.551579\pi$
$422$	−46.6940	−2.27303
$423$	4.44714	0.216227
$424$	−129.155	−6.27232
$425$	−3.26912	−0.158576
$426$	20.8256	1.00901
$427$	−7.83141	−0.378988
$428$	109.501	5.29292
$429$	37.1820	1.79517
$430$	−41.6199	−2.00709
$431$	28.2510	1.36080	0.680401	−	0.732840i	$-0.261806\pi$
$431$	28.2510	1.36080	0.680401	+	0.732840i	$0.261806\pi$
$432$	90.7985	4.36854
$433$	−12.4363	−0.597651	−0.298825	−	0.954308i	$-0.596595\pi$
$433$	−12.4363	−0.597651	−0.298825	+	0.954308i	$0.596595\pi$
$434$	−85.3785	−4.09830
$435$	12.2675	0.588184
$436$	2.08257	0.0997369
$437$	−22.1713	−1.06060
$438$	−17.2106	−0.822356
$439$	32.0340	1.52890	0.764450	−	0.644683i	$-0.223011\pi$
$439$	32.0340	1.52890	0.764450	+	0.644683i	$0.223011\pi$
$440$	66.2777	3.15966
$441$	−17.5894	−0.837592
$442$	−14.5277	−0.691012
$443$	−33.6093	−1.59683	−0.798414	−	0.602109i	$-0.794327\pi$
$443$	−33.6093	−1.59683	−0.798414	+	0.602109i	$0.794327\pi$
$444$	−41.6637	−1.97727
$445$	4.60015	0.218068
$446$	−29.9653	−1.41890
$447$	−14.9833	−0.708688
$448$	−170.061	−8.03461
$449$	−13.2498	−0.625295	−0.312648	−	0.949869i	$-0.601216\pi$
$449$	−13.2498	−0.625295	−0.312648	+	0.949869i	$0.601216\pi$
$450$	−9.76867	−0.460500
$451$	18.3367	0.863441
$452$	95.1468	4.47533
$453$	0.0745079	0.00350068
$454$	46.0637	2.16188
$455$	−33.4290	−1.56718
$456$	84.0091	3.93409
$457$	−25.2382	−1.18059	−0.590297	−	0.807186i	$-0.700989\pi$
$457$	−25.2382	−1.18059	−0.590297	+	0.807186i	$0.700989\pi$
$458$	14.1134	0.659475
$459$	5.65300	0.263859
$460$	−26.5580	−1.23827
$461$	−0.317499	−0.0147874	−0.00739369	−	0.999973i	$-0.502354\pi$
$461$	−0.317499	−0.0147874	−0.00739369	+	0.999973i	$0.502354\pi$
$462$	93.5915	4.35427
$463$	32.0904	1.49137	0.745684	−	0.666300i	$-0.232123\pi$
$463$	32.0904	1.49137	0.745684	+	0.666300i	$0.232123\pi$
$464$	−108.219	−5.02395
$465$	11.7113	0.543098
$466$	−47.1362	−2.18354
$467$	3.11978	0.144366	0.0721832	−	0.997391i	$-0.477003\pi$
$467$	3.11978	0.144366	0.0721832	+	0.997391i	$0.477003\pi$
$468$	−31.9711	−1.47786
$469$	40.9409	1.89048
$470$	14.8598	0.685432
$471$	10.2578	0.472653
$472$	101.974	4.69372
$473$	−58.5038	−2.69001
$474$	−46.7647	−2.14798
$475$	−20.0688	−0.920819
$476$	−26.9312	−1.23439
$477$	−14.1676	−0.648692
$478$	29.8240	1.36412
$479$	−1.51347	−0.0691524	−0.0345762	−	0.999402i	$-0.511008\pi$
$479$	−1.51347	−0.0691524	−0.0345762	+	0.999402i	$0.511008\pi$
$480$	44.5586	2.03381
$481$	28.4035	1.29509
$482$	−22.1195	−1.00752
$483$	−24.0834	−1.09583
$484$	83.5936	3.79971
$485$	18.5115	0.840564
$486$	29.2985	1.32901
$487$	−9.89872	−0.448554	−0.224277	−	0.974525i	$-0.572002\pi$
$487$	−9.89872	−0.448554	−0.224277	+	0.974525i	$0.572002\pi$
$488$	−16.0716	−0.727529
$489$	−14.6267	−0.661444
$490$	−58.7739	−2.65513
$491$	−13.7986	−0.622721	−0.311360	−	0.950292i	$-0.600785\pi$
$491$	−13.7986	−0.622721	−0.311360	+	0.950292i	$0.600785\pi$
$492$	27.8409	1.25516
$493$	−6.73759	−0.303446
$494$	−89.1839	−4.01257
$495$	7.27032	0.326776
$496$	−103.312	−4.63885
$497$	−26.3191	−1.18057
$498$	−0.627958	−0.0281395
$499$	−37.5978	−1.68311	−0.841555	−	0.540172i	$-0.818359\pi$
$499$	−37.5978	−1.68311	−0.841555	+	0.540172i	$0.818359\pi$
$500$	−60.8069	−2.71937
$501$	−11.1992	−0.500345
$502$	−75.4258	−3.36642
$503$	−13.3935	−0.597187	−0.298593	−	0.954380i	$-0.596517\pi$
$503$	−13.3935	−0.597187	−0.298593	+	0.954380i	$0.596517\pi$
$504$	−51.6790	−2.30196
$505$	1.23671	0.0550329
$506$	−50.6899	−2.25344
$507$	−20.4953	−0.910226
$508$	−45.9967	−2.04078
$509$	−28.7976	−1.27643	−0.638216	−	0.769858i	$-0.720327\pi$
$509$	−28.7976	−1.27643	−0.638216	+	0.769858i	$0.720327\pi$
$510$	5.01598	0.222111
$511$	21.7506	0.962188
$512$	−75.4292	−3.33353
$513$	34.7031	1.53218
$514$	37.0361	1.63359
$515$	11.7188	0.516394
$516$	−88.8273	−3.91040
$517$	20.8880	0.918653
$518$	71.4949	3.14130
$519$	6.49690	0.285182
$520$	−68.6031	−3.00844
$521$	−2.06407	−0.0904285	−0.0452143	−	0.998977i	$-0.514397\pi$
$521$	−2.06407	−0.0904285	−0.0452143	+	0.998977i	$0.514397\pi$
$522$	−20.1330	−0.881197
$523$	20.3347	0.889175	0.444587	−	0.895736i	$-0.353350\pi$
$523$	20.3347	0.889175	0.444587	+	0.895736i	$0.353350\pi$
$524$	38.2191	1.66961
$525$	−21.7996	−0.951411
$526$	−47.1827	−2.05727
$527$	−6.43208	−0.280186
$528$	113.250	4.92858
$529$	−9.95623	−0.432880
$530$	−47.3402	−2.05633
$531$	11.1860	0.485431
$532$	−165.328	−7.16787
$533$	−18.9800	−0.822117
$534$	13.3310	0.576887
$535$	25.7745	1.11433
$536$	84.0191	3.62907
$537$	2.13860	0.0922874
$538$	6.34943	0.273743
$539$	−82.6167	−3.55855
$540$	41.5692	1.78885
$541$	31.0928	1.33679	0.668393	−	0.743809i	$-0.266983\pi$
$541$	31.0928	1.33679	0.668393	+	0.743809i	$0.266983\pi$
$542$	7.04539	0.302625
$543$	−8.11877	−0.348410
$544$	−24.4725	−1.04925
$545$	0.490199	0.0209978
$546$	−96.8752	−4.14588
$547$	16.3923	0.700884	0.350442	−	0.936584i	$-0.386031\pi$
$547$	16.3923	0.700884	0.350442	+	0.936584i	$0.386031\pi$
$548$	4.50907	0.192618
$549$	−1.76298	−0.0752420
$550$	−45.8830	−1.95646
$551$	−41.3613	−1.76205
$552$	−49.4240	−2.10363
$553$	59.1006	2.51321
$554$	30.8149	1.30920
$555$	−9.80688	−0.416279
$556$	16.3898	0.695083
$557$	−31.0733	−1.31662	−0.658310	−	0.752747i	$-0.728728\pi$
$557$	−31.0733	−1.31662	−0.658310	+	0.752747i	$0.728728\pi$
$558$	−19.2201	−0.813651
$559$	60.5564	2.56126
$560$	−101.819	−4.30263
$561$	7.05080	0.297685
$562$	−16.8704	−0.711637
$563$	7.46822	0.314748	0.157374	−	0.987539i	$-0.449697\pi$
$563$	7.46822	0.314748	0.157374	+	0.987539i	$0.449697\pi$
$564$	31.7146	1.33543
$565$	22.3958	0.942199
$566$	71.2056	2.99300
$567$	22.0169	0.924624
$568$	−54.0122	−2.26630
$569$	−4.01374	−0.168265	−0.0841324	−	0.996455i	$-0.526812\pi$
$569$	−4.01374	−0.168265	−0.0841324	+	0.996455i	$0.526812\pi$
$570$	30.7925	1.28976
$571$	−12.6101	−0.527718	−0.263859	−	0.964561i	$-0.584995\pi$
$571$	−12.6101	−0.527718	−0.263859	+	0.964561i	$0.584995\pi$
$572$	−150.166	−6.27877
$573$	33.7112	1.40831
$574$	−47.7749	−1.99409
$575$	11.8068	0.492378
$576$	−38.2834	−1.59514
$577$	−8.66150	−0.360583	−0.180291	−	0.983613i	$-0.557704\pi$
$577$	−8.66150	−0.360583	−0.180291	+	0.983613i	$0.557704\pi$
$578$	−2.75487	−0.114588
$579$	−9.94919	−0.413474
$580$	−49.5447	−2.05723
$581$	0.793604	0.0329242
$582$	53.6452	2.22367
$583$	−66.5447	−2.75600
$584$	44.6365	1.84707
$585$	−7.52540	−0.311137
$586$	−31.6707	−1.30830
$587$	21.6722	0.894508	0.447254	−	0.894407i	$-0.352402\pi$
$587$	21.6722	0.894508	0.447254	+	0.894407i	$0.352402\pi$
$588$	−125.438	−5.17299
$589$	−39.4858	−1.62698
$590$	37.3772	1.53880
$591$	25.1558	1.03477
$592$	86.5121	3.55563
$593$	41.3352	1.69743	0.848716	−	0.528849i	$-0.177376\pi$
$593$	41.3352	1.69743	0.848716	+	0.528849i	$0.177376\pi$
$594$	79.3412	3.25541
$595$	−6.33912	−0.259878
$596$	60.5130	2.47871
$597$	13.2875	0.543821
$598$	52.4684	2.14559
$599$	−32.4854	−1.32732	−0.663659	−	0.748035i	$-0.730998\pi$
$599$	−32.4854	−1.32732	−0.663659	+	0.748035i	$0.730998\pi$
$600$	−44.7371	−1.82638
$601$	−4.99245	−0.203646	−0.101823	−	0.994803i	$-0.532468\pi$
$601$	−4.99245	−0.203646	−0.101823	+	0.994803i	$0.532468\pi$
$602$	152.427	6.21248
$603$	9.21646	0.375323
$604$	−0.300914	−0.0122440
$605$	19.6764	0.799960
$606$	3.58391	0.145586
$607$	11.7942	0.478711	0.239355	−	0.970932i	$-0.423064\pi$
$607$	11.7942	0.478711	0.239355	+	0.970932i	$0.423064\pi$
$608$	−150.234	−6.09279
$609$	−44.9284	−1.82059
$610$	−5.89087	−0.238514
$611$	−21.6209	−0.874687
$612$	−6.06265	−0.245068
$613$	27.9795	1.13008	0.565042	−	0.825062i	$-0.308860\pi$
$613$	27.9795	1.13008	0.565042	+	0.825062i	$0.308860\pi$
$614$	−18.4962	−0.746447
$615$	6.55324	0.264252
$616$	−242.734	−9.78001
$617$	−7.29682	−0.293759	−0.146879	−	0.989154i	$-0.546923\pi$
$617$	−7.29682	−0.293759	−0.146879	+	0.989154i	$0.546923\pi$
$618$	33.9605	1.36609
$619$	25.9805	1.04425	0.522123	−	0.852870i	$-0.325140\pi$
$619$	25.9805	1.04425	0.522123	+	0.852870i	$0.325140\pi$
$620$	−47.2982	−1.89954
$621$	−20.4164	−0.819284
$622$	−1.90945	−0.0765621
$623$	−16.8475	−0.674980
$624$	−117.224	−4.69270
$625$	2.03279	0.0813117
$626$	0.827853	0.0330877
$627$	43.2841	1.72860
$628$	−41.4279	−1.65315
$629$	5.38614	0.214759
$630$	−18.9423	−0.754679
$631$	−28.4391	−1.13214	−0.566071	−	0.824357i	$-0.691537\pi$
$631$	−28.4391	−1.13214	−0.566071	+	0.824357i	$0.691537\pi$
$632$	121.286	4.82452
$633$	−23.4574	−0.932348
$634$	77.0760	3.06108
$635$	−10.8268	−0.429648
$636$	−101.036	−4.00634
$637$	85.5153	3.38824
$638$	−94.5637	−3.74381
$639$	−5.92486	−0.234384
$640$	−63.5280	−2.51117
$641$	−16.9746	−0.670458	−0.335229	−	0.942137i	$-0.608814\pi$
$641$	−16.9746	−0.670458	−0.335229	+	0.942137i	$0.608814\pi$
$642$	74.6929	2.94789
$643$	−25.3326	−0.999019	−0.499509	−	0.866308i	$-0.666486\pi$
$643$	−25.3326	−0.999019	−0.499509	+	0.866308i	$0.666486\pi$
$644$	97.2652	3.83279
$645$	−20.9083	−0.823264
$646$	−16.9119	−0.665389
$647$	−36.8206	−1.44757	−0.723784	−	0.690026i	$-0.757599\pi$
$647$	−36.8206	−1.44757	−0.723784	+	0.690026i	$0.757599\pi$
$648$	45.1832	1.77496
$649$	52.5400	2.06238
$650$	47.4928	1.86282
$651$	−42.8911	−1.68104
$652$	59.0728	2.31347
$653$	38.8027	1.51847	0.759234	−	0.650818i	$-0.225574\pi$
$653$	38.8027	1.51847	0.759234	+	0.650818i	$0.225574\pi$
$654$	1.42057	0.0555485
$655$	8.99608	0.351506
$656$	−57.8099	−2.25710
$657$	4.89640	0.191027
$658$	−54.4222	−2.12160
$659$	24.4183	0.951201	0.475601	−	0.879661i	$-0.342231\pi$
$659$	24.4183	0.951201	0.475601	+	0.879661i	$0.342231\pi$
$660$	51.8480	2.01818
$661$	41.5089	1.61451	0.807254	−	0.590204i	$-0.200953\pi$
$661$	41.5089	1.61451	0.807254	+	0.590204i	$0.200953\pi$
$662$	10.7974	0.419652
$663$	−7.29819	−0.283438
$664$	1.62864	0.0632033
$665$	−38.9151	−1.50906
$666$	16.0946	0.623655
$667$	24.3336	0.942200
$668$	45.2302	1.75001
$669$	−15.0535	−0.582002
$670$	30.7962	1.18976
$671$	−8.28061	−0.319669
$672$	−163.190	−6.29520
$673$	−25.8865	−0.997850	−0.498925	−	0.866645i	$-0.666272\pi$
$673$	−25.8865	−0.997850	−0.498925	+	0.866645i	$0.666272\pi$
$674$	76.8105	2.95863
$675$	−18.4803	−0.711309
$676$	82.7738	3.18361
$677$	−23.7726	−0.913657	−0.456828	−	0.889555i	$-0.651015\pi$
$677$	−23.7726	−0.913657	−0.456828	+	0.889555i	$0.651015\pi$
$678$	64.9017	2.49254
$679$	−67.7960	−2.60177
$680$	−13.0092	−0.498878
$681$	23.1407	0.886755
$682$	−90.2758	−3.45684
$683$	−9.56096	−0.365840	−0.182920	−	0.983128i	$-0.558555\pi$
$683$	−9.56096	−0.365840	−0.182920	+	0.983128i	$0.558555\pi$
$684$	−37.2179	−1.42306
$685$	1.06135	0.0405522
$686$	122.335	4.67077
$687$	7.09006	0.270503
$688$	184.444	7.03188
$689$	68.8795	2.62410
$690$	−18.1158	−0.689656
$691$	−48.4330	−1.84248	−0.921239	−	0.388997i	$-0.872822\pi$
$691$	−48.4330	−1.84248	−0.921239	+	0.388997i	$0.872822\pi$
$692$	−26.2389	−0.997454
$693$	−26.6266	−1.01146
$694$	14.2856	0.542273
$695$	3.85786	0.146337
$696$	−92.2021	−3.49491
$697$	−3.59917	−0.136328
$698$	35.5803	1.34674
$699$	−23.6796	−0.895643
$700$	88.0415	3.32766
$701$	−11.6295	−0.439239	−0.219620	−	0.975586i	$-0.570482\pi$
$701$	−11.6295	−0.439239	−0.219620	+	0.975586i	$0.570482\pi$
$702$	−82.1250	−3.09961
$703$	33.0649	1.24707
$704$	−179.815	−6.77704
$705$	7.46504	0.281150
$706$	−2.75487	−0.103681
$707$	−4.52929	−0.170342
$708$	79.7724	2.99803
$709$	−24.1336	−0.906356	−0.453178	−	0.891420i	$-0.649710\pi$
$709$	−24.1336	−0.906356	−0.453178	+	0.891420i	$0.649710\pi$
$710$	−19.7975	−0.742987
$711$	13.3045	0.498958
$712$	−34.5745	−1.29573
$713$	23.2302	0.869977
$714$	−18.3704	−0.687494
$715$	−35.3464	−1.32188
$716$	−8.63713	−0.322785
$717$	14.9825	0.559532
$718$	76.7712	2.86508
$719$	−48.0895	−1.79344	−0.896718	−	0.442603i	$-0.854055\pi$
$719$	−48.0895	−1.79344	−0.896718	+	0.442603i	$0.854055\pi$
$720$	−22.9211	−0.854218
$721$	−42.9188	−1.59838
$722$	−51.4775	−1.91580
$723$	−11.1121	−0.413262
$724$	32.7891	1.21860
$725$	22.0260	0.818025
$726$	57.0211	2.11625
$727$	34.4811	1.27883	0.639417	−	0.768861i	$-0.279176\pi$
$727$	34.4811	1.27883	0.639417	+	0.768861i	$0.279176\pi$
$728$	251.250	9.31195
$729$	28.4268	1.05284
$730$	16.3610	0.605547
$731$	11.4833	0.424724
$732$	−12.5726	−0.464697
$733$	−35.4817	−1.31055	−0.655273	−	0.755392i	$-0.727446\pi$
$733$	−35.4817	−1.31055	−0.655273	+	0.755392i	$0.727446\pi$
$734$	−17.9208	−0.661470
$735$	−29.5259	−1.08908
$736$	88.3852	3.25792
$737$	43.2892	1.59458
$738$	−10.7549	−0.395894
$739$	8.06191	0.296562	0.148281	−	0.988945i	$-0.452626\pi$
$739$	8.06191	0.296562	0.148281	+	0.988945i	$0.452626\pi$
$740$	39.6069	1.45598
$741$	−44.8028	−1.64587
$742$	173.378	6.36489
$743$	−19.3678	−0.710536	−0.355268	−	0.934765i	$-0.615610\pi$
$743$	−19.3678	−0.710536	−0.355268	+	0.934765i	$0.615610\pi$
$744$	−88.0213	−3.22702
$745$	14.2437	0.521847
$746$	−76.4129	−2.79767
$747$	0.178653	0.00653657
$748$	−28.4760	−1.04118
$749$	−94.3958	−3.44915
$750$	−41.4777	−1.51455
$751$	−7.95756	−0.290375	−0.145188	−	0.989404i	$-0.546379\pi$
$751$	−7.95756	−0.290375	−0.145188	+	0.989404i	$0.546379\pi$
$752$	−65.8534	−2.40143
$753$	−37.8912	−1.38083
$754$	97.8815	3.56463
$755$	−0.0708296	−0.00257775
$756$	−152.242	−5.53699
$757$	−47.5578	−1.72852	−0.864260	−	0.503046i	$-0.832213\pi$
$757$	−47.5578	−1.72852	−0.864260	+	0.503046i	$0.832213\pi$
$758$	42.4946	1.54347
$759$	−25.4648	−0.924313
$760$	−79.8618	−2.89689
$761$	3.39134	0.122936	0.0614680	−	0.998109i	$-0.480422\pi$
$761$	3.39134	0.122936	0.0614680	+	0.998109i	$0.480422\pi$
$762$	−31.3754	−1.13661
$763$	−1.79529	−0.0649939
$764$	−136.149	−4.92569
$765$	−1.42704	−0.0515946
$766$	−22.7392	−0.821601
$767$	−54.3834	−1.96367
$768$	−86.4085	−3.11800
$769$	16.0805	0.579877	0.289939	−	0.957045i	$-0.406365\pi$
$769$	16.0805	0.579877	0.289939	+	0.957045i	$0.406365\pi$
$770$	−88.9711	−3.20629
$771$	18.6056	0.670065
$772$	40.1816	1.44617
$773$	−48.9441	−1.76040	−0.880198	−	0.474607i	$-0.842590\pi$
$773$	−48.9441	−1.76040	−0.880198	+	0.474607i	$0.842590\pi$
$774$	34.3139	1.23339
$775$	21.0273	0.755321
$776$	−139.131	−4.99452
$777$	35.9165	1.28850
$778$	61.5989	2.20843
$779$	−22.0949	−0.791633
$780$	−53.6671	−1.92159
$781$	−27.8288	−0.995792
$782$	9.94955	0.355795
$783$	−38.0875	−1.36114
$784$	260.465	9.30232
$785$	−9.75137	−0.348041
$786$	26.0701	0.929890
$787$	−32.7361	−1.16692	−0.583459	−	0.812143i	$-0.698301\pi$
$787$	−32.7361	−1.16692	−0.583459	+	0.812143i	$0.698301\pi$
$788$	−101.596	−3.61922
$789$	−23.7029	−0.843846
$790$	44.4561	1.58168
$791$	−82.0218	−2.91636
$792$	−54.6432	−1.94166
$793$	8.57114	0.304370
$794$	67.7599	2.40471
$795$	−23.7820	−0.843462
$796$	−53.6640	−1.90207
$797$	−6.87112	−0.243387	−0.121694	−	0.992568i	$-0.538833\pi$
$797$	−6.87112	−0.243387	−0.121694	+	0.992568i	$0.538833\pi$
$798$	−112.774	−3.99215
$799$	−4.09995	−0.145046
$800$	80.0035	2.82855
$801$	−3.79264	−0.134006
$802$	−47.0393	−1.66102
$803$	22.9981	0.811587
$804$	65.7268	2.31801
$805$	22.8944	0.806923
$806$	93.4432	3.29140
$807$	3.18972	0.112284
$808$	−9.29503	−0.326998
$809$	16.0637	0.564770	0.282385	−	0.959301i	$-0.408874\pi$
$809$	16.0637	0.564770	0.282385	+	0.959301i	$0.408874\pi$
$810$	16.5614	0.581907
$811$	−43.7462	−1.53614	−0.768068	−	0.640369i	$-0.778782\pi$
$811$	−43.7462	−1.53614	−0.768068	+	0.640369i	$0.778782\pi$
$812$	181.451	6.36769
$813$	3.53935	0.124130
$814$	75.5957	2.64963
$815$	13.9046	0.487059
$816$	−22.2290	−0.778171
$817$	70.4946	2.46629
$818$	−90.6973	−3.17116
$819$	27.5608	0.963054
$820$	−26.4665	−0.924249
$821$	32.7099	1.14158	0.570791	−	0.821095i	$-0.306637\pi$
$821$	32.7099	1.14158	0.570791	+	0.821095i	$0.306637\pi$
$822$	3.07574	0.107279
$823$	51.9900	1.81226	0.906129	−	0.423000i	$-0.139023\pi$
$823$	51.9900	1.81226	0.906129	+	0.423000i	$0.139023\pi$
$824$	−88.0780	−3.06834
$825$	−23.0500	−0.802496
$826$	−136.889	−4.76299
$827$	−3.56395	−0.123931	−0.0619654	−	0.998078i	$-0.519737\pi$
$827$	−3.56395	−0.123931	−0.0619654	+	0.998078i	$0.519737\pi$
$828$	21.8960	0.760937
$829$	43.5030	1.51092	0.755460	−	0.655194i	$-0.227413\pi$
$829$	43.5030	1.51092	0.755460	+	0.655194i	$0.227413\pi$
$830$	0.596957	0.0207207
$831$	15.4803	0.537006
$832$	186.124	6.45269
$833$	16.2162	0.561859
$834$	11.1799	0.387127
$835$	10.6464	0.368433
$836$	−174.811	−6.04596
$837$	−36.3605	−1.25680
$838$	−71.6565	−2.47533
$839$	−47.9142	−1.65418	−0.827091	−	0.562068i	$-0.810006\pi$
$839$	−47.9142	−1.65418	−0.827091	+	0.562068i	$0.810006\pi$
$840$	−86.7491	−2.99313
$841$	16.3951	0.565347
$842$	18.2386	0.628543
$843$	−8.47511	−0.291898
$844$	94.7370	3.26098
$845$	19.4834	0.670251
$846$	−12.2513	−0.421209
$847$	−72.0624	−2.47609
$848$	209.795	7.20439
$849$	35.7712	1.22766
$850$	9.00603	0.308904
$851$	−19.4527	−0.666828
$852$	−42.2529	−1.44756
$853$	−11.7507	−0.402337	−0.201168	−	0.979557i	$-0.564474\pi$
$853$	−11.7507	−0.402337	−0.201168	+	0.979557i	$0.564474\pi$
$854$	21.5746	0.738266
$855$	−8.76042	−0.299600
$856$	−193.719	−6.62119
$857$	39.3138	1.34293	0.671467	−	0.741035i	$-0.265665\pi$
$857$	39.3138	1.34293	0.671467	+	0.741035i	$0.265665\pi$
$858$	−102.432	−3.49697
$859$	−50.7875	−1.73285	−0.866424	−	0.499309i	$-0.833587\pi$
$859$	−50.7875	−1.73285	−0.866424	+	0.499309i	$0.833587\pi$
$860$	84.4421	2.87945
$861$	−24.0004	−0.817932
$862$	−77.8280	−2.65083
$863$	33.5353	1.14155	0.570777	−	0.821105i	$-0.306642\pi$
$863$	33.5353	1.14155	0.570777	+	0.821105i	$0.306642\pi$
$864$	−138.343	−4.70652
$865$	−6.17616	−0.209996
$866$	34.2605	1.16422
$867$	−1.38395	−0.0470014
$868$	173.224	5.87959
$869$	62.4906	2.11985
$870$	−33.7956	−1.14578
$871$	−44.8081	−1.51826
$872$	−3.68430	−0.124766
$873$	−15.2620	−0.516540
$874$	61.0792	2.06603
$875$	52.4189	1.77208
$876$	34.9185	1.17979
$877$	−3.59414	−0.121366	−0.0606828	−	0.998157i	$-0.519328\pi$
$877$	−3.59414	−0.121366	−0.0606828	+	0.998157i	$0.519328\pi$
$878$	−88.2497	−2.97828
$879$	−15.9102	−0.536638
$880$	−107.659	−3.62919
$881$	−41.9150	−1.41215	−0.706076	−	0.708136i	$-0.749536\pi$
$881$	−41.9150	−1.41215	−0.706076	+	0.708136i	$0.749536\pi$
$882$	48.4567	1.63162
$883$	−6.93214	−0.233285	−0.116643	−	0.993174i	$-0.537213\pi$
$883$	−6.93214	−0.233285	−0.116643	+	0.993174i	$0.537213\pi$
$884$	29.4751	0.991354
$885$	18.7770	0.631181
$886$	92.5896	3.11061
$887$	−10.9871	−0.368911	−0.184455	−	0.982841i	$-0.559052\pi$
$887$	−10.9871	−0.368911	−0.184455	+	0.982841i	$0.559052\pi$
$888$	73.7079	2.47347
$889$	39.6518	1.32988
$890$	−12.6728	−0.424795
$891$	23.2798	0.779903
$892$	60.7963	2.03561
$893$	−25.1691	−0.842253
$894$	41.2773	1.38052
$895$	−2.03302	−0.0679564
$896$	232.663	7.77274
$897$	26.3582	0.880076
$898$	36.5015	1.21807
$899$	43.3367	1.44536
$900$	19.8196	0.660652
$901$	13.0616	0.435144
$902$	−50.5153	−1.68197
$903$	76.5741	2.54823
$904$	−168.325	−5.59842
$905$	7.71797	0.256554
$906$	−0.205260	−0.00681930
$907$	2.94876	0.0979119	0.0489560	−	0.998801i	$-0.484411\pi$
$907$	2.94876	0.0979119	0.0489560	+	0.998801i	$0.484411\pi$
$908$	−93.4581	−3.10152
$909$	−1.01962	−0.0338186
$910$	92.0927	3.05284
$911$	−9.70709	−0.321610	−0.160805	−	0.986986i	$-0.551409\pi$
$911$	−9.70709	−0.321610	−0.160805	+	0.986986i	$0.551409\pi$
$912$	−136.462	−4.51869
$913$	0.839124	0.0277710
$914$	69.5282	2.29979
$915$	−2.95936	−0.0978334
$916$	−28.6345	−0.946110
$917$	−32.9470	−1.08801
$918$	−15.5733	−0.513995
$919$	−34.8141	−1.14841	−0.574206	−	0.818711i	$-0.694689\pi$
$919$	−34.8141	−1.14841	−0.574206	+	0.818711i	$0.694689\pi$
$920$	46.9841	1.54902
$921$	−9.29184	−0.306176
$922$	0.874669	0.0288057
$923$	28.8052	0.948133
$924$	−189.887	−6.24681
$925$	−17.6079	−0.578946
$926$	−88.4050	−2.90517
$927$	−9.66171	−0.317332
$928$	164.885	5.41263
$929$	11.6150	0.381074	0.190537	−	0.981680i	$-0.438977\pi$
$929$	11.6150	0.381074	0.190537	+	0.981680i	$0.438977\pi$
$930$	−32.2631	−1.05795
$931$	99.5496	3.26261
$932$	95.6342	3.13260
$933$	−0.959240	−0.0314041
$934$	−8.59461	−0.281224
$935$	−6.70272	−0.219202
$936$	56.5604	1.84874
$937$	18.2768	0.597078	0.298539	−	0.954397i	$-0.403501\pi$
$937$	18.2768	0.597078	0.298539	+	0.954397i	$0.403501\pi$
$938$	−112.787	−3.68263
$939$	0.415884	0.0135719
$940$	−30.1489	−0.983349
$941$	−7.46183	−0.243249	−0.121624	−	0.992576i	$-0.538810\pi$
$941$	−7.46183	−0.243249	−0.121624	+	0.992576i	$0.538810\pi$
$942$	−28.2589	−0.920724
$943$	12.9988	0.423300
$944$	−165.643	−5.39121
$945$	−35.8350	−1.16571
$946$	161.171	5.24011
$947$	−10.5432	−0.342607	−0.171303	−	0.985218i	$-0.554798\pi$
$947$	−10.5432	−0.342607	−0.171303	+	0.985218i	$0.554798\pi$
$948$	94.8805	3.08158
$949$	−23.8051	−0.772745
$950$	55.2870	1.79375
$951$	38.7202	1.25559
$952$	47.6444	1.54416
$953$	25.0948	0.812900	0.406450	−	0.913673i	$-0.366767\pi$
$953$	25.0948	0.812900	0.406450	+	0.913673i	$0.366767\pi$
$954$	39.0301	1.26365
$955$	−32.0469	−1.03701
$956$	−60.5096	−1.95702
$957$	−47.5054	−1.53563
$958$	4.16943	0.134708
$959$	−3.88707	−0.125520
$960$	−64.2631	−2.07408
$961$	10.3716	0.334568
$962$	−78.2481	−2.52282
$963$	−21.2500	−0.684772
$964$	44.8781	1.44542
$965$	9.45802	0.304464
$966$	66.3467	2.13467
$967$	−23.1106	−0.743187	−0.371594	−	0.928395i	$-0.621189\pi$
$967$	−23.1106	−0.743187	−0.371594	+	0.928395i	$0.621189\pi$
$968$	−147.887	−4.75326
$969$	−8.49592	−0.272928
$970$	−50.9969	−1.63741
$971$	−13.6255	−0.437264	−0.218632	−	0.975807i	$-0.570159\pi$
$971$	−13.6255	−0.437264	−0.218632	+	0.975807i	$0.570159\pi$
$972$	−59.4434	−1.90665
$973$	−14.1289	−0.452953
$974$	27.2697	0.873778
$975$	23.8587	0.764089
$976$	26.1062	0.835640
$977$	−55.4372	−1.77359	−0.886797	−	0.462159i	$-0.847075\pi$
$977$	−55.4372	−1.77359	−0.886797	+	0.462159i	$0.847075\pi$
$978$	40.2948	1.28849
$979$	−17.8138	−0.569333
$980$	119.246	3.80916
$981$	−0.404149	−0.0129035
$982$	38.0133	1.21305
$983$	−28.6291	−0.913128	−0.456564	−	0.889691i	$-0.650920\pi$
$983$	−28.6291	−0.913128	−0.456564	+	0.889691i	$0.650920\pi$
$984$	−49.2537	−1.57015
$985$	−23.9139	−0.761961
$986$	18.5612	0.591109
$987$	−27.3398	−0.870234
$988$	180.944	5.75660
$989$	−41.4732	−1.31877
$990$	−20.0288	−0.636558
$991$	−15.6685	−0.497726	−0.248863	−	0.968539i	$-0.580057\pi$
$991$	−15.6685	−0.497726	−0.248863	+	0.968539i	$0.580057\pi$
$992$	157.409	4.99773
$993$	5.42422	0.172132
$994$	72.5059	2.29975
$995$	−12.6315	−0.400446
$996$	1.27406	0.0403700
$997$	1.25717	0.0398150	0.0199075	−	0.999802i	$-0.493663\pi$
$997$	1.25717	0.0398150	0.0199075	+	0.999802i	$0.493663\pi$
$998$	103.577	3.27868
$999$	30.4478	0.963326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.3	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.3	✓	114	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)

\(f(q)\)	\(=\)	\(q-2.75487 q^{2} -1.38395 q^{3} +5.58934 q^{4} +1.31563 q^{5} +3.81261 q^{6} -4.81832 q^{7} -9.88817 q^{8} -1.08468 q^{9} +O(q^{10})\)	\(q-2.75487 q^{2} -1.38395 q^{3} +5.58934 q^{4} +1.31563 q^{5} +3.81261 q^{6} -4.81832 q^{7} -9.88817 q^{8} -1.08468 q^{9} -3.62439 q^{10} -5.09469 q^{11} -7.73536 q^{12} +5.27345 q^{13} +13.2739 q^{14} -1.82076 q^{15} +16.0620 q^{16} +1.00000 q^{17} +2.98816 q^{18} +6.13889 q^{19} +7.35348 q^{20} +6.66832 q^{21} +14.0352 q^{22} -3.61162 q^{23} +13.6847 q^{24} -3.26912 q^{25} -14.5277 q^{26} +5.65300 q^{27} -26.9312 q^{28} -6.73759 q^{29} +5.01598 q^{30} -6.43208 q^{31} -24.4725 q^{32} +7.05080 q^{33} -2.75487 q^{34} -6.33912 q^{35} -6.06265 q^{36} +5.38614 q^{37} -16.9119 q^{38} -7.29819 q^{39} -13.0092 q^{40} -3.59917 q^{41} -18.3704 q^{42} +11.4833 q^{43} -28.4760 q^{44} -1.42704 q^{45} +9.94955 q^{46} -4.09995 q^{47} -22.2290 q^{48} +16.2162 q^{49} +9.00603 q^{50} -1.38395 q^{51} +29.4751 q^{52} +13.0616 q^{53} -15.5733 q^{54} -6.70272 q^{55} +47.6444 q^{56} -8.49592 q^{57} +18.5612 q^{58} -10.3127 q^{59} -10.1769 q^{60} +1.62534 q^{61} +17.7196 q^{62} +5.22634 q^{63} +35.2946 q^{64} +6.93789 q^{65} -19.4241 q^{66} -8.49693 q^{67} +5.58934 q^{68} +4.99830 q^{69} +17.4635 q^{70} +5.46230 q^{71} +10.7255 q^{72} -4.51414 q^{73} -14.8381 q^{74} +4.52431 q^{75} +34.3123 q^{76} +24.5479 q^{77} +20.1056 q^{78} -12.2658 q^{79} +21.1316 q^{80} -4.56942 q^{81} +9.91527 q^{82} -0.164706 q^{83} +37.2715 q^{84} +1.31563 q^{85} -31.6350 q^{86} +9.32448 q^{87} +50.3772 q^{88} +3.49655 q^{89} +3.93131 q^{90} -25.4092 q^{91} -20.1865 q^{92} +8.90167 q^{93} +11.2948 q^{94} +8.07649 q^{95} +33.8687 q^{96} +14.0705 q^{97} -44.6736 q^{98} +5.52612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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