LMFDB - Embedded newform 6019.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51903 q^{2} +1.84872 q^{3} +4.34553 q^{4} -3.50196 q^{5} -4.65699 q^{6} +1.30916 q^{7} -5.90847 q^{8} +0.417768 q^{9} +O(q^{10})$	\(q-2.51903 q^{2} +1.84872 q^{3} +4.34553 q^{4} -3.50196 q^{5} -4.65699 q^{6} +1.30916 q^{7} -5.90847 q^{8} +0.417768 q^{9} +8.82155 q^{10} +4.97264 q^{11} +8.03367 q^{12} +1.00000 q^{13} -3.29782 q^{14} -6.47414 q^{15} +6.19257 q^{16} +2.78816 q^{17} -1.05237 q^{18} +2.26572 q^{19} -15.2179 q^{20} +2.42027 q^{21} -12.5263 q^{22} -5.95629 q^{23} -10.9231 q^{24} +7.26370 q^{25} -2.51903 q^{26} -4.77383 q^{27} +5.68899 q^{28} -5.45742 q^{29} +16.3086 q^{30} +3.81309 q^{31} -3.78236 q^{32} +9.19303 q^{33} -7.02346 q^{34} -4.58462 q^{35} +1.81542 q^{36} -3.25330 q^{37} -5.70743 q^{38} +1.84872 q^{39} +20.6912 q^{40} +0.130374 q^{41} -6.09674 q^{42} -3.83937 q^{43} +21.6088 q^{44} -1.46301 q^{45} +15.0041 q^{46} -5.49126 q^{47} +11.4483 q^{48} -5.28610 q^{49} -18.2975 q^{50} +5.15452 q^{51} +4.34553 q^{52} -8.30820 q^{53} +12.0254 q^{54} -17.4140 q^{55} -7.73512 q^{56} +4.18868 q^{57} +13.7474 q^{58} +1.73343 q^{59} -28.1336 q^{60} -4.91024 q^{61} -9.60531 q^{62} +0.546925 q^{63} -2.85726 q^{64} -3.50196 q^{65} -23.1576 q^{66} +6.97375 q^{67} +12.1160 q^{68} -11.0115 q^{69} +11.5488 q^{70} -1.24255 q^{71} -2.46837 q^{72} +0.687614 q^{73} +8.19518 q^{74} +13.4286 q^{75} +9.84576 q^{76} +6.50998 q^{77} -4.65699 q^{78} -10.5040 q^{79} -21.6861 q^{80} -10.0788 q^{81} -0.328416 q^{82} -7.11721 q^{83} +10.5174 q^{84} -9.76401 q^{85} +9.67149 q^{86} -10.0893 q^{87} -29.3807 q^{88} -10.8687 q^{89} +3.68536 q^{90} +1.30916 q^{91} -25.8833 q^{92} +7.04934 q^{93} +13.8327 q^{94} -7.93445 q^{95} -6.99252 q^{96} +19.4993 q^{97} +13.3159 q^{98} +2.07741 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.51903	−1.78123	−0.890613	−	0.454762i	$-0.849724\pi$
$2$	−2.51903	−1.78123	−0.890613	+	0.454762i	$0.849724\pi$
$3$	1.84872	1.06736	0.533680	−	0.845687i	$-0.320809\pi$
$3$	1.84872	1.06736	0.533680	+	0.845687i	$0.320809\pi$
$4$	4.34553	2.17277
$5$	−3.50196	−1.56612	−0.783061	−	0.621945i	$-0.786343\pi$
$5$	−3.50196	−1.56612	−0.783061	+	0.621945i	$0.786343\pi$
$6$	−4.65699	−1.90121
$7$	1.30916	0.494816	0.247408	−	0.968911i	$-0.420421\pi$
$7$	1.30916	0.494816	0.247408	+	0.968911i	$0.420421\pi$
$8$	−5.90847	−2.08896
$9$	0.417768	0.139256
$10$	8.82155	2.78962
$11$	4.97264	1.49931	0.749654	−	0.661830i	$-0.230220\pi$
$11$	4.97264	1.49931	0.749654	+	0.661830i	$0.230220\pi$
$12$	8.03367	2.31912
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.29782	−0.881378
$15$	−6.47414	−1.67162
$16$	6.19257	1.54814
$17$	2.78816	0.676228	0.338114	−	0.941105i	$-0.390211\pi$
$17$	2.78816	0.676228	0.338114	+	0.941105i	$0.390211\pi$
$18$	−1.05237	−0.248046
$19$	2.26572	0.519792	0.259896	−	0.965637i	$-0.416312\pi$
$19$	2.26572	0.519792	0.259896	+	0.965637i	$0.416312\pi$
$20$	−15.2179	−3.40282
$21$	2.42027	0.528146
$22$	−12.5263	−2.67061
$23$	−5.95629	−1.24197	−0.620986	−	0.783821i	$-0.713268\pi$
$23$	−5.95629	−1.24197	−0.620986	+	0.783821i	$0.713268\pi$
$24$	−10.9231	−2.22967
$25$	7.26370	1.45274
$26$	−2.51903	−0.494023
$27$	−4.77383	−0.918723
$28$	5.68899	1.07512
$29$	−5.45742	−1.01342	−0.506709	−	0.862117i	$-0.669138\pi$
$29$	−5.45742	−1.01342	−0.506709	+	0.862117i	$0.669138\pi$
$30$	16.3086	2.97752
$31$	3.81309	0.684851	0.342426	−	0.939545i	$-0.388751\pi$
$31$	3.81309	0.684851	0.342426	+	0.939545i	$0.388751\pi$
$32$	−3.78236	−0.668633
$33$	9.19303	1.60030
$34$	−7.02346	−1.20451
$35$	−4.58462	−0.774942
$36$	1.81542	0.302571
$37$	−3.25330	−0.534840	−0.267420	−	0.963580i	$-0.586171\pi$
$37$	−3.25330	−0.534840	−0.267420	+	0.963580i	$0.586171\pi$
$38$	−5.70743	−0.925867
$39$	1.84872	0.296032
$40$	20.6912	3.27157
$41$	0.130374	0.0203610	0.0101805	−	0.999948i	$-0.496759\pi$
$41$	0.130374	0.0203610	0.0101805	+	0.999948i	$0.496759\pi$
$42$	−6.09674	−0.940747
$43$	−3.83937	−0.585498	−0.292749	−	0.956189i	$-0.594570\pi$
$43$	−3.83937	−0.585498	−0.292749	+	0.956189i	$0.594570\pi$
$44$	21.6088	3.25765
$45$	−1.46301	−0.218092
$46$	15.0041	2.21223
$47$	−5.49126	−0.800983	−0.400492	−	0.916300i	$-0.631161\pi$
$47$	−5.49126	−0.800983	−0.400492	+	0.916300i	$0.631161\pi$
$48$	11.4483	1.65242
$49$	−5.28610	−0.755158
$50$	−18.2975	−2.58766
$51$	5.15452	0.721778
$52$	4.34553	0.602617
$53$	−8.30820	−1.14122	−0.570610	−	0.821221i	$-0.693293\pi$
$53$	−8.30820	−1.14122	−0.570610	+	0.821221i	$0.693293\pi$
$54$	12.0254	1.63645
$55$	−17.4140	−2.34810
$56$	−7.73512	−1.03365
$57$	4.18868	0.554805
$58$	13.7474	1.80513
$59$	1.73343	0.225674	0.112837	−	0.993614i	$-0.464006\pi$
$59$	1.73343	0.225674	0.112837	+	0.993614i	$0.464006\pi$
$60$	−28.1336	−3.63203
$61$	−4.91024	−0.628692	−0.314346	−	0.949308i	$-0.601785\pi$
$61$	−4.91024	−0.628692	−0.314346	+	0.949308i	$0.601785\pi$
$62$	−9.60531	−1.21988
$63$	0.546925	0.0689060
$64$	−2.85726	−0.357157
$65$	−3.50196	−0.434364
$66$	−23.1576	−2.85050
$67$	6.97375	0.851979	0.425989	−	0.904728i	$-0.359926\pi$
$67$	6.97375	0.851979	0.425989	+	0.904728i	$0.359926\pi$
$68$	12.1160	1.46928
$69$	−11.0115	−1.32563
$70$	11.5488	1.38035
$71$	−1.24255	−0.147464	−0.0737318	−	0.997278i	$-0.523491\pi$
$71$	−1.24255	−0.147464	−0.0737318	+	0.997278i	$0.523491\pi$
$72$	−2.46837	−0.290900
$73$	0.687614	0.0804791	0.0402396	−	0.999190i	$-0.487188\pi$
$73$	0.687614	0.0804791	0.0402396	+	0.999190i	$0.487188\pi$
$74$	8.19518	0.952670
$75$	13.4286	1.55060
$76$	9.84576	1.12939
$77$	6.50998	0.741881
$78$	−4.65699	−0.527300
$79$	−10.5040	−1.18180	−0.590898	−	0.806746i	$-0.701227\pi$
$79$	−10.5040	−1.18180	−0.590898	+	0.806746i	$0.701227\pi$
$80$	−21.6861	−2.42458
$81$	−10.0788	−1.11986
$82$	−0.328416	−0.0362674
$83$	−7.11721	−0.781215	−0.390607	−	0.920557i	$-0.627735\pi$
$83$	−7.11721	−0.781215	−0.390607	+	0.920557i	$0.627735\pi$
$84$	10.5174	1.14754
$85$	−9.76401	−1.05906
$86$	9.67149	1.04290
$87$	−10.0893	−1.08168
$88$	−29.3807	−3.13199
$89$	−10.8687	−1.15208	−0.576041	−	0.817420i	$-0.695403\pi$
$89$	−10.8687	−1.15208	−0.576041	+	0.817420i	$0.695403\pi$
$90$	3.68536	0.388471
$91$	1.30916	0.137237
$92$	−25.8833	−2.69852
$93$	7.04934	0.730983
$94$	13.8327	1.42673
$95$	−7.93445	−0.814058
$96$	−6.99252	−0.713671
$97$	19.4993	1.97986	0.989929	−	0.141568i	$-0.0452144\pi$
$97$	19.4993	1.97986	0.989929	+	0.141568i	$0.0452144\pi$
$98$	13.3159	1.34511
$99$	2.07741	0.208788
$100$	31.5646	3.15646
$101$	−3.11740	−0.310193	−0.155096	−	0.987899i	$-0.549569\pi$
$101$	−3.11740	−0.310193	−0.155096	+	0.987899i	$0.549569\pi$
$102$	−12.9844	−1.28565
$103$	18.6957	1.84215	0.921073	−	0.389389i	$-0.127314\pi$
$103$	18.6957	1.84215	0.921073	+	0.389389i	$0.127314\pi$
$104$	−5.90847	−0.579373
$105$	−8.47568	−0.827141
$106$	20.9286	2.03277
$107$	11.6805	1.12920	0.564600	−	0.825365i	$-0.309030\pi$
$107$	11.6805	1.12920	0.564600	+	0.825365i	$0.309030\pi$
$108$	−20.7448	−1.99617
$109$	−1.05701	−0.101244	−0.0506218	−	0.998718i	$-0.516120\pi$
$109$	−1.05701	−0.101244	−0.0506218	+	0.998718i	$0.516120\pi$
$110$	43.8664	4.18250
$111$	−6.01445	−0.570866
$112$	8.10706	0.766045
$113$	5.39324	0.507353	0.253677	−	0.967289i	$-0.418360\pi$
$113$	5.39324	0.507353	0.253677	+	0.967289i	$0.418360\pi$
$114$	−10.5514	−0.988232
$115$	20.8587	1.94508
$116$	−23.7154	−2.20192
$117$	0.417768	0.0386227
$118$	−4.36658	−0.401976
$119$	3.65014	0.334608
$120$	38.2523	3.49194
$121$	13.7272	1.24793
$122$	12.3691	1.11984
$123$	0.241025	0.0217325
$124$	16.5699	1.48802
$125$	−7.92738	−0.709047
$126$	−1.37772	−0.122737
$127$	2.53314	0.224779	0.112390	−	0.993664i	$-0.464149\pi$
$127$	2.53314	0.224779	0.112390	+	0.993664i	$0.464149\pi$
$128$	14.7622	1.30481
$129$	−7.09792	−0.624937
$130$	8.82155	0.773701
$131$	7.50778	0.655957	0.327979	−	0.944685i	$-0.393633\pi$
$131$	7.50778	0.655957	0.327979	+	0.944685i	$0.393633\pi$
$132$	39.9486	3.47708
$133$	2.96619	0.257201
$134$	−17.5671	−1.51757
$135$	16.7177	1.43883
$136$	−16.4737	−1.41261
$137$	1.35961	0.116159	0.0580795	−	0.998312i	$-0.481502\pi$
$137$	1.35961	0.116159	0.0580795	+	0.998312i	$0.481502\pi$
$138$	27.7384	2.36125
$139$	−10.0386	−0.851464	−0.425732	−	0.904849i	$-0.639983\pi$
$139$	−10.0386	−0.851464	−0.425732	+	0.904849i	$0.639983\pi$
$140$	−19.9226	−1.68377
$141$	−10.1518	−0.854937
$142$	3.13003	0.262666
$143$	4.97264	0.415833
$144$	2.58706	0.215588
$145$	19.1117	1.58714
$146$	−1.73212	−0.143351
$147$	−9.77253	−0.806025
$148$	−14.1373	−1.16208
$149$	−19.6141	−1.60685	−0.803426	−	0.595404i	$-0.796992\pi$
$149$	−19.6141	−1.60685	−0.803426	+	0.595404i	$0.796992\pi$
$150$	−33.8270	−2.76196
$151$	5.91713	0.481529	0.240764	−	0.970584i	$-0.422602\pi$
$151$	5.91713	0.481529	0.240764	+	0.970584i	$0.422602\pi$
$152$	−13.3869	−1.08582
$153$	1.16480	0.0941687
$154$	−16.3989	−1.32146
$155$	−13.3533	−1.07256
$156$	8.03367	0.643208
$157$	5.80536	0.463319	0.231659	−	0.972797i	$-0.425585\pi$
$157$	5.80536	0.463319	0.231659	+	0.972797i	$0.425585\pi$
$158$	26.4600	2.10505
$159$	−15.3595	−1.21809
$160$	13.2457	1.04716
$161$	−7.79773	−0.614548
$162$	25.3888	1.99473
$163$	6.05607	0.474348	0.237174	−	0.971467i	$-0.423779\pi$
$163$	6.05607	0.474348	0.237174	+	0.971467i	$0.423779\pi$
$164$	0.566543	0.0442396
$165$	−32.1936	−2.50627
$166$	17.9285	1.39152
$167$	−11.2192	−0.868171	−0.434086	−	0.900872i	$-0.642928\pi$
$167$	−11.2192	−0.868171	−0.434086	+	0.900872i	$0.642928\pi$
$168$	−14.3001	−1.10328
$169$	1.00000	0.0769231
$170$	24.5959	1.88642
$171$	0.946545	0.0723841
$172$	−16.6841	−1.27215
$173$	−21.1351	−1.60687	−0.803436	−	0.595391i	$-0.796997\pi$
$173$	−21.1351	−1.60687	−0.803436	+	0.595391i	$0.796997\pi$
$174$	25.4152	1.92672
$175$	9.50934	0.718838
$176$	30.7935	2.32114
$177$	3.20464	0.240875
$178$	27.3787	2.05212
$179$	−5.66611	−0.423505	−0.211753	−	0.977323i	$-0.567917\pi$
$179$	−5.66611	−0.423505	−0.211753	+	0.977323i	$0.567917\pi$
$180$	−6.35753	−0.473863
$181$	−5.79084	−0.430429	−0.215215	−	0.976567i	$-0.569045\pi$
$181$	−5.79084	−0.430429	−0.215215	+	0.976567i	$0.569045\pi$
$182$	−3.29782	−0.244450
$183$	−9.07767	−0.671041
$184$	35.1926	2.59443
$185$	11.3929	0.837625
$186$	−17.7575	−1.30205
$187$	13.8645	1.01387
$188$	−23.8625	−1.74035
$189$	−6.24970	−0.454599
$190$	19.9872	1.45002
$191$	6.12169	0.442950	0.221475	−	0.975166i	$-0.428913\pi$
$191$	6.12169	0.442950	0.221475	+	0.975166i	$0.428913\pi$
$192$	−5.28227	−0.381215
$193$	0.689664	0.0496431	0.0248216	−	0.999692i	$-0.492098\pi$
$193$	0.689664	0.0496431	0.0248216	+	0.999692i	$0.492098\pi$
$194$	−49.1195	−3.52657
$195$	−6.47414	−0.463623
$196$	−22.9709	−1.64078
$197$	−8.96147	−0.638478	−0.319239	−	0.947674i	$-0.603427\pi$
$197$	−8.96147	−0.638478	−0.319239	+	0.947674i	$0.603427\pi$
$198$	−5.23307	−0.371898
$199$	12.2725	0.869975	0.434988	−	0.900436i	$-0.356753\pi$
$199$	12.2725	0.869975	0.434988	+	0.900436i	$0.356753\pi$
$200$	−42.9174	−3.03471
$201$	12.8925	0.909367
$202$	7.85283	0.552523
$203$	−7.14463	−0.501455
$204$	22.3991	1.56825
$205$	−0.456563	−0.0318877
$206$	−47.0952	−3.28128
$207$	−2.48835	−0.172952
$208$	6.19257	0.429378
$209$	11.2666	0.779328
$210$	21.3505	1.47333
$211$	−6.56722	−0.452106	−0.226053	−	0.974115i	$-0.572582\pi$
$211$	−6.56722	−0.452106	−0.226053	+	0.974115i	$0.572582\pi$
$212$	−36.1035	−2.47960
$213$	−2.29713	−0.157397
$214$	−29.4237	−2.01136
$215$	13.4453	0.916962
$216$	28.2060	1.91918
$217$	4.99194	0.338875
$218$	2.66265	0.180338
$219$	1.27121	0.0859001
$220$	−75.6730	−5.10187
$221$	2.78816	0.187552
$222$	15.1506	1.01684
$223$	5.29565	0.354623	0.177311	−	0.984155i	$-0.443260\pi$
$223$	5.29565	0.354623	0.177311	+	0.984155i	$0.443260\pi$
$224$	−4.95171	−0.330850
$225$	3.03454	0.202303
$226$	−13.5858	−0.903711
$227$	−5.06625	−0.336259	−0.168129	−	0.985765i	$-0.553773\pi$
$227$	−5.06625	−0.336259	−0.168129	+	0.985765i	$0.553773\pi$
$228$	18.2021	1.20546
$229$	−3.19428	−0.211084	−0.105542	−	0.994415i	$-0.533658\pi$
$229$	−3.19428	−0.211084	−0.105542	+	0.994415i	$0.533658\pi$
$230$	−52.5437	−3.46463
$231$	12.0351	0.791854
$232$	32.2450	2.11699
$233$	29.7735	1.95053	0.975263	−	0.221047i	$-0.0709474\pi$
$233$	29.7735	1.95053	0.975263	+	0.221047i	$0.0709474\pi$
$234$	−1.05237	−0.0687957
$235$	19.2302	1.25444
$236$	7.53269	0.490336
$237$	−19.4190	−1.26140
$238$	−9.19483	−0.596012
$239$	4.54501	0.293992	0.146996	−	0.989137i	$-0.453039\pi$
$239$	4.54501	0.293992	0.146996	+	0.989137i	$0.453039\pi$
$240$	−40.0916	−2.58790
$241$	−15.8513	−1.02107	−0.510535	−	0.859857i	$-0.670553\pi$
$241$	−15.8513	−1.02107	−0.510535	+	0.859857i	$0.670553\pi$
$242$	−34.5793	−2.22284
$243$	−4.31136	−0.276574
$244$	−21.3376	−1.36600
$245$	18.5117	1.18267
$246$	−0.607149	−0.0387104
$247$	2.26572	0.144164
$248$	−22.5295	−1.43063
$249$	−13.1577	−0.833837
$250$	19.9693	1.26297
$251$	−23.4432	−1.47972	−0.739862	−	0.672759i	$-0.765109\pi$
$251$	−23.4432	−1.47972	−0.739862	+	0.672759i	$0.765109\pi$
$252$	2.37668	0.149717
$253$	−29.6185	−1.86210
$254$	−6.38105	−0.400383
$255$	−18.0509	−1.13039
$256$	−31.4721	−1.96700
$257$	−19.2424	−1.20031	−0.600155	−	0.799884i	$-0.704894\pi$
$257$	−19.2424	−1.20031	−0.600155	+	0.799884i	$0.704894\pi$
$258$	17.8799	1.11315
$259$	−4.25909	−0.264647
$260$	−15.2179	−0.943772
$261$	−2.27994	−0.141125
$262$	−18.9123	−1.16841
$263$	−22.3546	−1.37844	−0.689221	−	0.724551i	$-0.742047\pi$
$263$	−22.3546	−1.37844	−0.689221	+	0.724551i	$0.742047\pi$
$264$	−54.3167	−3.34296
$265$	29.0950	1.78729
$266$	−7.47193	−0.458133
$267$	−20.0932	−1.22969
$268$	30.3046	1.85115
$269$	−22.4153	−1.36669	−0.683343	−	0.730098i	$-0.739475\pi$
$269$	−22.4153	−1.36669	−0.683343	+	0.730098i	$0.739475\pi$
$270$	−42.1125	−2.56289
$271$	−14.8964	−0.904891	−0.452446	−	0.891792i	$-0.649448\pi$
$271$	−14.8964	−0.904891	−0.452446	+	0.891792i	$0.649448\pi$
$272$	17.2659	1.04690
$273$	2.42027	0.146481
$274$	−3.42490	−0.206906
$275$	36.1198	2.17811
$276$	−47.8509	−2.88029
$277$	−15.7661	−0.947295	−0.473648	−	0.880714i	$-0.657063\pi$
$277$	−15.7661	−0.947295	−0.473648	+	0.880714i	$0.657063\pi$
$278$	25.2876	1.51665
$279$	1.59299	0.0953697
$280$	27.0881	1.61882
$281$	−0.347700	−0.0207420	−0.0103710	−	0.999946i	$-0.503301\pi$
$281$	−0.347700	−0.0207420	−0.0103710	+	0.999946i	$0.503301\pi$
$282$	25.5728	1.52284
$283$	−8.83836	−0.525386	−0.262693	−	0.964880i	$-0.584611\pi$
$283$	−8.83836	−0.525386	−0.262693	+	0.964880i	$0.584611\pi$
$284$	−5.39954	−0.320404
$285$	−14.6686	−0.868892
$286$	−12.5263	−0.740693
$287$	0.170680	0.0100749
$288$	−1.58015	−0.0931111
$289$	−9.22618	−0.542716
$290$	−48.1429	−2.82705
$291$	36.0488	2.11322
$292$	2.98805	0.174862
$293$	6.33766	0.370250	0.185125	−	0.982715i	$-0.440731\pi$
$293$	6.33766	0.370250	0.185125	+	0.982715i	$0.440731\pi$
$294$	24.6173	1.43571
$295$	−6.07041	−0.353433
$296$	19.2220	1.11726
$297$	−23.7385	−1.37745
$298$	49.4087	2.86217
$299$	−5.95629	−0.344461
$300$	58.3542	3.36908
$301$	−5.02634	−0.289713
$302$	−14.9054	−0.857712
$303$	−5.76320	−0.331087
$304$	14.0306	0.804712
$305$	17.1955	0.984609
$306$	−2.93418	−0.167736
$307$	−20.3084	−1.15906	−0.579530	−	0.814951i	$-0.696764\pi$
$307$	−20.3084	−1.15906	−0.579530	+	0.814951i	$0.696764\pi$
$308$	28.2893	1.61193
$309$	34.5632	1.96623
$310$	33.6374	1.91047
$311$	8.53539	0.483998	0.241999	−	0.970277i	$-0.422197\pi$
$311$	8.53539	0.483998	0.241999	+	0.970277i	$0.422197\pi$
$312$	−10.9231	−0.618399
$313$	−10.8200	−0.611582	−0.305791	−	0.952099i	$-0.598921\pi$
$313$	−10.8200	−0.611582	−0.305791	+	0.952099i	$0.598921\pi$
$314$	−14.6239	−0.825275
$315$	−1.91531	−0.107915
$316$	−45.6456	−2.56777
$317$	16.7605	0.941363	0.470681	−	0.882303i	$-0.344008\pi$
$317$	16.7605	0.941363	0.470681	+	0.882303i	$0.344008\pi$
$318$	38.6912	2.16970
$319$	−27.1378	−1.51943
$320$	10.0060	0.559352
$321$	21.5940	1.20526
$322$	19.6428	1.09465
$323$	6.31719	0.351498
$324$	−43.7976	−2.43320
$325$	7.26370	0.402918
$326$	−15.2554	−0.844921
$327$	−1.95412	−0.108063
$328$	−0.770309	−0.0425332
$329$	−7.18894	−0.396339
$330$	81.0967	4.46423
$331$	6.57897	0.361613	0.180806	−	0.983519i	$-0.442129\pi$
$331$	6.57897	0.361613	0.180806	+	0.983519i	$0.442129\pi$
$332$	−30.9280	−1.69740
$333$	−1.35913	−0.0744796
$334$	28.2616	1.54641
$335$	−24.4218	−1.33430
$336$	14.9877	0.817646
$337$	−10.8853	−0.592958	−0.296479	−	0.955039i	$-0.595812\pi$
$337$	−10.8853	−0.592958	−0.296479	+	0.955039i	$0.595812\pi$
$338$	−2.51903	−0.137017
$339$	9.97059	0.541528
$340$	−42.4298	−2.30108
$341$	18.9611	1.02680
$342$	−2.38438	−0.128932
$343$	−16.0845	−0.868479
$344$	22.6848	1.22308
$345$	38.5619	2.07610
$346$	53.2401	2.86220
$347$	28.2712	1.51768	0.758840	−	0.651278i	$-0.225767\pi$
$347$	28.2712	1.51768	0.758840	+	0.651278i	$0.225767\pi$
$348$	−43.8431	−2.35024
$349$	23.0389	1.23325	0.616623	−	0.787259i	$-0.288500\pi$
$349$	23.0389	1.23325	0.616623	+	0.787259i	$0.288500\pi$
$350$	−23.9543	−1.28041
$351$	−4.77383	−0.254808
$352$	−18.8083	−1.00249
$353$	−31.0898	−1.65474	−0.827371	−	0.561656i	$-0.810165\pi$
$353$	−31.0898	−1.65474	−0.827371	+	0.561656i	$0.810165\pi$
$354$	−8.07258	−0.429053
$355$	4.35136	0.230946
$356$	−47.2304	−2.50321
$357$	6.74809	0.357147
$358$	14.2731	0.754358
$359$	−19.3505	−1.02128	−0.510640	−	0.859795i	$-0.670591\pi$
$359$	−19.3505	−1.02128	−0.510640	+	0.859795i	$0.670591\pi$
$360$	8.64412	0.455585
$361$	−13.8665	−0.729816
$362$	14.5873	0.766692
$363$	25.3777	1.33199
$364$	5.68899	0.298184
$365$	−2.40799	−0.126040
$366$	22.8670	1.19527
$367$	3.89260	0.203192	0.101596	−	0.994826i	$-0.467605\pi$
$367$	3.89260	0.203192	0.101596	+	0.994826i	$0.467605\pi$
$368$	−36.8848	−1.92275
$369$	0.0544660	0.00283538
$370$	−28.6992	−1.49200
$371$	−10.8768	−0.564693
$372$	30.6331	1.58825
$373$	−28.3393	−1.46735	−0.733676	−	0.679499i	$-0.762197\pi$
$373$	−28.3393	−1.46735	−0.733676	+	0.679499i	$0.762197\pi$
$374$	−34.9252	−1.80594
$375$	−14.6555	−0.756807
$376$	32.4450	1.67322
$377$	−5.45742	−0.281072
$378$	15.7432	0.809743
$379$	−18.2907	−0.939532	−0.469766	−	0.882791i	$-0.655662\pi$
$379$	−18.2907	−0.939532	−0.469766	+	0.882791i	$0.655662\pi$
$380$	−34.4794	−1.76876
$381$	4.68306	0.239920
$382$	−15.4207	−0.788994
$383$	−28.1862	−1.44025	−0.720124	−	0.693846i	$-0.755915\pi$
$383$	−28.1862	−1.44025	−0.720124	+	0.693846i	$0.755915\pi$
$384$	27.2913	1.39270
$385$	−22.7977	−1.16188
$386$	−1.73729	−0.0884256
$387$	−1.60396	−0.0815341
$388$	84.7349	4.30176
$389$	21.4390	1.08700	0.543499	−	0.839410i	$-0.317099\pi$
$389$	21.4390	1.08700	0.543499	+	0.839410i	$0.317099\pi$
$390$	16.3086	0.825817
$391$	−16.6071	−0.839856
$392$	31.2328	1.57749
$393$	13.8798	0.700142
$394$	22.5742	1.13727
$395$	36.7847	1.85084
$396$	9.02745	0.453647
$397$	−11.9659	−0.600551	−0.300275	−	0.953853i	$-0.597079\pi$
$397$	−11.9659	−0.600551	−0.300275	+	0.953853i	$0.597079\pi$
$398$	−30.9149	−1.54962
$399$	5.48365	0.274526
$400$	44.9810	2.24905
$401$	−5.29679	−0.264509	−0.132254	−	0.991216i	$-0.542222\pi$
$401$	−5.29679	−0.264509	−0.132254	+	0.991216i	$0.542222\pi$
$402$	−32.4767	−1.61979
$403$	3.81309	0.189944
$404$	−13.5467	−0.673976
$405$	35.2954	1.75384
$406$	17.9976	0.893205
$407$	−16.1775	−0.801890
$408$	−30.4554	−1.50776
$409$	7.49494	0.370601	0.185300	−	0.982682i	$-0.440674\pi$
$409$	7.49494	0.370601	0.185300	+	0.982682i	$0.440674\pi$
$410$	1.15010	0.0567993
$411$	2.51353	0.123983
$412$	81.2429	4.00255
$413$	2.26934	0.111667
$414$	6.26823	0.308067
$415$	24.9241	1.22348
$416$	−3.78236	−0.185445
$417$	−18.5586	−0.908819
$418$	−28.3810	−1.38816
$419$	4.03536	0.197140	0.0985701	−	0.995130i	$-0.468573\pi$
$419$	4.03536	0.197140	0.0985701	+	0.995130i	$0.468573\pi$
$420$	−36.8313	−1.79718
$421$	23.5786	1.14915	0.574575	−	0.818452i	$-0.305168\pi$
$421$	23.5786	1.14915	0.574575	+	0.818452i	$0.305168\pi$
$422$	16.5431	0.805303
$423$	−2.29407	−0.111542
$424$	49.0888	2.38396
$425$	20.2523	0.982383
$426$	5.78654	0.280359
$427$	−6.42829	−0.311087
$428$	50.7581	2.45349
$429$	9.19303	0.443844
$430$	−33.8692	−1.63332
$431$	−5.25825	−0.253281	−0.126640	−	0.991949i	$-0.540419\pi$
$431$	−5.25825	−0.253281	−0.126640	+	0.991949i	$0.540419\pi$
$432$	−29.5623	−1.42231
$433$	−24.0887	−1.15763	−0.578815	−	0.815459i	$-0.696485\pi$
$433$	−24.0887	−1.15763	−0.578815	+	0.815459i	$0.696485\pi$
$434$	−12.5749	−0.603613
$435$	35.3321	1.69405
$436$	−4.59328	−0.219978
$437$	−13.4953	−0.645567
$438$	−3.20221	−0.153008
$439$	−3.29273	−0.157153	−0.0785767	−	0.996908i	$-0.525038\pi$
$439$	−3.29273	−0.157153	−0.0785767	+	0.996908i	$0.525038\pi$
$440$	102.890	4.90509
$441$	−2.20836	−0.105160
$442$	−7.02346	−0.334072
$443$	24.4736	1.16278	0.581388	−	0.813626i	$-0.302510\pi$
$443$	24.4736	1.16278	0.581388	+	0.813626i	$0.302510\pi$
$444$	−26.1360	−1.24036
$445$	38.0618	1.80430
$446$	−13.3399	−0.631663
$447$	−36.2610	−1.71509
$448$	−3.74060	−0.176727
$449$	22.1516	1.04540	0.522700	−	0.852517i	$-0.324925\pi$
$449$	22.1516	1.04540	0.522700	+	0.852517i	$0.324925\pi$
$450$	−7.64411	−0.360347
$451$	0.648302	0.0305273
$452$	23.4365	1.10236
$453$	10.9391	0.513964
$454$	12.7620	0.598953
$455$	−4.58462	−0.214930
$456$	−24.7487	−1.15896
$457$	26.7263	1.25020	0.625101	−	0.780544i	$-0.285058\pi$
$457$	26.7263	1.25020	0.625101	+	0.780544i	$0.285058\pi$
$458$	8.04649	0.375988
$459$	−13.3102	−0.621266
$460$	90.6420	4.22621
$461$	5.81161	0.270674	0.135337	−	0.990800i	$-0.456788\pi$
$461$	5.81161	0.270674	0.135337	+	0.990800i	$0.456788\pi$
$462$	−30.3169	−1.41047
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−33.7955	−1.56892
$465$	−24.6865	−1.14481
$466$	−75.0004	−3.47433
$467$	17.1595	0.794049	0.397024	−	0.917808i	$-0.370043\pi$
$467$	17.1595	0.794049	0.397024	+	0.917808i	$0.370043\pi$
$468$	1.81542	0.0839180
$469$	9.12974	0.421572
$470$	−48.4414	−2.23444
$471$	10.7325	0.494527
$472$	−10.2419	−0.471424
$473$	−19.0918	−0.877842
$474$	48.9172	2.24684
$475$	16.4575	0.755122
$476$	15.8618	0.727024
$477$	−3.47090	−0.158922
$478$	−11.4490	−0.523667
$479$	34.5249	1.57748	0.788742	−	0.614724i	$-0.210733\pi$
$479$	34.5249	1.57748	0.788742	+	0.614724i	$0.210733\pi$
$480$	24.4875	1.11770
$481$	−3.25330	−0.148338
$482$	39.9299	1.81876
$483$	−14.4158	−0.655943
$484$	59.6519	2.71145
$485$	−68.2858	−3.10070
$486$	10.8605	0.492641
$487$	0.612246	0.0277435	0.0138717	−	0.999904i	$-0.495584\pi$
$487$	0.612246	0.0277435	0.0138717	+	0.999904i	$0.495584\pi$
$488$	29.0120	1.31331
$489$	11.1960	0.506300
$490$	−46.6316	−2.10660
$491$	−21.3389	−0.963011	−0.481506	−	0.876443i	$-0.659910\pi$
$491$	−21.3389	−0.963011	−0.481506	+	0.876443i	$0.659910\pi$
$492$	1.04738	0.0472195
$493$	−15.2162	−0.685301
$494$	−5.70743	−0.256789
$495$	−7.27500	−0.326987
$496$	23.6128	1.06025
$497$	−1.62670	−0.0729673
$498$	33.1448	1.48525
$499$	0.252920	0.0113223	0.00566113	−	0.999984i	$-0.498198\pi$
$499$	0.252920	0.0113223	0.00566113	+	0.999984i	$0.498198\pi$
$500$	−34.4487	−1.54059
$501$	−20.7412	−0.926651
$502$	59.0543	2.63572
$503$	31.7882	1.41737	0.708684	−	0.705526i	$-0.249289\pi$
$503$	31.7882	1.41737	0.708684	+	0.705526i	$0.249289\pi$
$504$	−3.23149	−0.143942
$505$	10.9170	0.485800
$506$	74.6101	3.31682
$507$	1.84872	0.0821046
$508$	11.0078	0.488393
$509$	−3.03975	−0.134735	−0.0673673	−	0.997728i	$-0.521460\pi$
$509$	−3.03975	−0.134735	−0.0673673	+	0.997728i	$0.521460\pi$
$510$	45.4709	2.01348
$511$	0.900196	0.0398223
$512$	49.7547	2.19887
$513$	−10.8162	−0.477545
$514$	48.4723	2.13802
$515$	−65.4717	−2.88503
$516$	−30.8442	−1.35784
$517$	−27.3061	−1.20092
$518$	10.7288	0.471396
$519$	−39.0729	−1.71511
$520$	20.6912	0.907369
$521$	31.1366	1.36412	0.682059	−	0.731297i	$-0.261085\pi$
$521$	31.1366	1.36412	0.682059	+	0.731297i	$0.261085\pi$
$522$	5.74324	0.251375
$523$	26.5566	1.16124	0.580619	−	0.814175i	$-0.302811\pi$
$523$	26.5566	1.16124	0.580619	+	0.814175i	$0.302811\pi$
$524$	32.6253	1.42524
$525$	17.5801	0.767259
$526$	56.3119	2.45532
$527$	10.6315	0.463115
$528$	56.9285	2.47749
$529$	12.4774	0.542497
$530$	−73.2912	−3.18357
$531$	0.724173	0.0314264
$532$	12.8897	0.558838
$533$	0.130374	0.00564711
$534$	50.6156	2.19035
$535$	−40.9047	−1.76847
$536$	−41.2042	−1.77975
$537$	−10.4751	−0.452032
$538$	56.4649	2.43438
$539$	−26.2859	−1.13221
$540$	72.6474	3.12625
$541$	7.80752	0.335672	0.167836	−	0.985815i	$-0.446322\pi$
$541$	7.80752	0.335672	0.167836	+	0.985815i	$0.446322\pi$
$542$	37.5245	1.61182
$543$	−10.7056	−0.459423
$544$	−10.5458	−0.452148
$545$	3.70162	0.158560
$546$	−6.09674	−0.260916
$547$	12.3082	0.526261	0.263130	−	0.964760i	$-0.415245\pi$
$547$	12.3082	0.526261	0.263130	+	0.964760i	$0.415245\pi$
$548$	5.90821	0.252386
$549$	−2.05134	−0.0875492
$550$	−90.9870	−3.87970
$551$	−12.3650	−0.526766
$552$	65.0612	2.76919
$553$	−13.7515	−0.584771
$554$	39.7154	1.68735
$555$	21.0623	0.894046
$556$	−43.6231	−1.85003
$557$	−0.113552	−0.00481134	−0.00240567	−	0.999997i	$-0.500766\pi$
$557$	−0.113552	−0.00481134	−0.00240567	+	0.999997i	$0.500766\pi$
$558$	−4.01279	−0.169875
$559$	−3.83937	−0.162388
$560$	−28.3906	−1.19972
$561$	25.6316	1.08217
$562$	0.875867	0.0369462
$563$	−35.5044	−1.49633	−0.748166	−	0.663511i	$-0.769066\pi$
$563$	−35.5044	−1.49633	−0.748166	+	0.663511i	$0.769066\pi$
$564$	−44.1150	−1.85758
$565$	−18.8869	−0.794577
$566$	22.2641	0.935830
$567$	−13.1947	−0.554126
$568$	7.34157	0.308045
$569$	−15.0461	−0.630765	−0.315383	−	0.948965i	$-0.602133\pi$
$569$	−15.0461	−0.630765	−0.315383	+	0.948965i	$0.602133\pi$
$570$	36.9507	1.54769
$571$	−43.9468	−1.83912	−0.919558	−	0.392954i	$-0.871453\pi$
$571$	−43.9468	−1.83912	−0.919558	+	0.392954i	$0.871453\pi$
$572$	21.6088	0.903508
$573$	11.3173	0.472787
$574$	−0.429948	−0.0179457
$575$	−43.2647	−1.80426
$576$	−1.19367	−0.0497363
$577$	37.4673	1.55978	0.779891	−	0.625915i	$-0.215274\pi$
$577$	37.4673	1.55978	0.779891	+	0.625915i	$0.215274\pi$
$578$	23.2410	0.966700
$579$	1.27500	0.0529870
$580$	83.0503	3.44848
$581$	−9.31755	−0.386557
$582$	−90.8082	−3.76412
$583$	−41.3137	−1.71104
$584$	−4.06275	−0.168118
$585$	−1.46301	−0.0604878
$586$	−15.9648	−0.659499
$587$	−35.2447	−1.45470	−0.727352	−	0.686264i	$-0.759249\pi$
$587$	−35.2447	−1.45470	−0.727352	+	0.686264i	$0.759249\pi$
$588$	−42.4668	−1.75130
$589$	8.63940	0.355980
$590$	15.2916	0.629544
$591$	−16.5673	−0.681486
$592$	−20.1463	−0.828008
$593$	9.25113	0.379898	0.189949	−	0.981794i	$-0.439168\pi$
$593$	9.25113	0.379898	0.189949	+	0.981794i	$0.439168\pi$
$594$	59.7982	2.45355
$595$	−12.7826	−0.524037
$596$	−85.2338	−3.49131
$597$	22.6884	0.928576
$598$	15.0041	0.613563
$599$	−26.9490	−1.10111	−0.550553	−	0.834800i	$-0.685583\pi$
$599$	−26.9490	−1.10111	−0.550553	+	0.834800i	$0.685583\pi$
$600$	−79.3422	−3.23913
$601$	−46.6809	−1.90415	−0.952076	−	0.305861i	$-0.901056\pi$
$601$	−46.6809	−1.90415	−0.952076	+	0.305861i	$0.901056\pi$
$602$	12.6615	0.516045
$603$	2.91341	0.118643
$604$	25.7131	1.04625
$605$	−48.0720	−1.95441
$606$	14.5177	0.589741
$607$	−42.5461	−1.72689	−0.863446	−	0.504441i	$-0.831699\pi$
$607$	−42.5461	−1.72689	−0.863446	+	0.504441i	$0.831699\pi$
$608$	−8.56977	−0.347550
$609$	−13.2084	−0.535233
$610$	−43.3159	−1.75381
$611$	−5.49126	−0.222153
$612$	5.06169	0.204607
$613$	29.8494	1.20561	0.602803	−	0.797890i	$-0.294050\pi$
$613$	29.8494	1.20561	0.602803	+	0.797890i	$0.294050\pi$
$614$	51.1575	2.06455
$615$	−0.844057	−0.0340357
$616$	−38.4640	−1.54976
$617$	−29.9741	−1.20671	−0.603357	−	0.797471i	$-0.706170\pi$
$617$	−29.9741	−1.20671	−0.603357	+	0.797471i	$0.706170\pi$
$618$	−87.0659	−3.50230
$619$	−31.6689	−1.27288	−0.636440	−	0.771326i	$-0.719594\pi$
$619$	−31.6689	−1.27288	−0.636440	+	0.771326i	$0.719594\pi$
$620$	−58.0271	−2.33042
$621$	28.4343	1.14103
$622$	−21.5009	−0.862109
$623$	−14.2289	−0.570069
$624$	11.4483	0.458300
$625$	−8.55716	−0.342286
$626$	27.2559	1.08937
$627$	20.8288	0.831823
$628$	25.2274	1.00668
$629$	−9.07072	−0.361673
$630$	4.82472	0.192221
$631$	−33.6881	−1.34110	−0.670550	−	0.741864i	$-0.733942\pi$
$631$	−33.6881	−1.34110	−0.670550	+	0.741864i	$0.733942\pi$
$632$	62.0628	2.46873
$633$	−12.1410	−0.482560
$634$	−42.2202	−1.67678
$635$	−8.87093	−0.352032
$636$	−66.7454	−2.64663
$637$	−5.28610	−0.209443
$638$	68.3611	2.70644
$639$	−0.519098	−0.0205352
$640$	−51.6967	−2.04349
$641$	0.988835	0.0390566	0.0195283	−	0.999809i	$-0.493784\pi$
$641$	0.988835	0.0390566	0.0195283	+	0.999809i	$0.493784\pi$
$642$	−54.3961	−2.14684
$643$	−17.0494	−0.672361	−0.336180	−	0.941798i	$-0.609135\pi$
$643$	−17.0494	−0.672361	−0.336180	+	0.941798i	$0.609135\pi$
$644$	−33.8853	−1.33527
$645$	24.8566	0.978728
$646$	−15.9132	−0.626097
$647$	27.9743	1.09978	0.549891	−	0.835237i	$-0.314669\pi$
$647$	27.9743	1.09978	0.549891	+	0.835237i	$0.314669\pi$
$648$	59.5501	2.33935
$649$	8.61975	0.338355
$650$	−18.2975	−0.717687
$651$	9.22871	0.361702
$652$	26.3168	1.03065
$653$	−41.3589	−1.61850	−0.809249	−	0.587466i	$-0.800126\pi$
$653$	−41.3589	−1.61850	−0.809249	+	0.587466i	$0.800126\pi$
$654$	4.92250	0.192485
$655$	−26.2919	−1.02731
$656$	0.807348	0.0315217
$657$	0.287263	0.0112072
$658$	18.1092	0.705969
$659$	31.8941	1.24242	0.621209	−	0.783645i	$-0.286642\pi$
$659$	31.8941	1.24242	0.621209	+	0.783645i	$0.286642\pi$
$660$	−139.898	−5.44553
$661$	−14.6452	−0.569634	−0.284817	−	0.958582i	$-0.591933\pi$
$661$	−14.6452	−0.569634	−0.284817	+	0.958582i	$0.591933\pi$
$662$	−16.5726	−0.644114
$663$	5.15452	0.200185
$664$	42.0518	1.63193
$665$	−10.3875	−0.402808
$666$	3.42368	0.132665
$667$	32.5060	1.25864
$668$	−48.7536	−1.88633
$669$	9.79017	0.378510
$670$	61.5192	2.37669
$671$	−24.4169	−0.942604
$672$	−9.15432	−0.353136
$673$	11.7736	0.453839	0.226920	−	0.973914i	$-0.427135\pi$
$673$	11.7736	0.453839	0.226920	+	0.973914i	$0.427135\pi$
$674$	27.4203	1.05619
$675$	−34.6756	−1.33467
$676$	4.34553	0.167136
$677$	−43.7521	−1.68153	−0.840764	−	0.541402i	$-0.817894\pi$
$677$	−43.7521	−1.68153	−0.840764	+	0.541402i	$0.817894\pi$
$678$	−25.1163	−0.964584
$679$	25.5277	0.979664
$680$	57.6903	2.21232
$681$	−9.36608	−0.358909
$682$	−47.7638	−1.82897
$683$	0.225168	0.00861582	0.00430791	−	0.999991i	$-0.498629\pi$
$683$	0.225168	0.00861582	0.00430791	+	0.999991i	$0.498629\pi$
$684$	4.11324	0.157274
$685$	−4.76129	−0.181919
$686$	40.5173	1.54696
$687$	−5.90532	−0.225302
$688$	−23.7756	−0.906435
$689$	−8.30820	−0.316517
$690$	−97.1386	−3.69801
$691$	22.6687	0.862356	0.431178	−	0.902267i	$-0.358098\pi$
$691$	22.6687	0.862356	0.431178	+	0.902267i	$0.358098\pi$
$692$	−91.8433	−3.49136
$693$	2.71966	0.103311
$694$	−71.2162	−2.70333
$695$	35.1548	1.33350
$696$	59.6120	2.25959
$697$	0.363502	0.0137686
$698$	−58.0359	−2.19669
$699$	55.0429	2.08191
$700$	41.3231	1.56187
$701$	44.4207	1.67775	0.838873	−	0.544328i	$-0.183215\pi$
$701$	44.4207	1.67775	0.838873	+	0.544328i	$0.183215\pi$
$702$	12.0254	0.453870
$703$	−7.37107	−0.278005
$704$	−14.2081	−0.535489
$705$	35.5512	1.33894
$706$	78.3162	2.94747
$707$	−4.08117	−0.153488
$708$	13.9258	0.523365
$709$	22.5968	0.848641	0.424321	−	0.905512i	$-0.360513\pi$
$709$	22.5968	0.848641	0.424321	+	0.905512i	$0.360513\pi$
$710$	−10.9612	−0.411367
$711$	−4.38825	−0.164572
$712$	64.2175	2.40665
$713$	−22.7119	−0.850567
$714$	−16.9987	−0.636159
$715$	−17.4140	−0.651246
$716$	−24.6223	−0.920177
$717$	8.40246	0.313796
$718$	48.7445	1.81913
$719$	−33.9658	−1.26671	−0.633355	−	0.773861i	$-0.718323\pi$
$719$	−33.9658	−1.26671	−0.633355	+	0.773861i	$0.718323\pi$
$720$	−9.05977	−0.337638
$721$	24.4757	0.911523
$722$	34.9302	1.29997
$723$	−29.3046	−1.08985
$724$	−25.1643	−0.935222
$725$	−39.6411	−1.47223
$726$	−63.9274	−2.37257
$727$	−4.49289	−0.166632	−0.0833161	−	0.996523i	$-0.526551\pi$
$727$	−4.49289	−0.166632	−0.0833161	+	0.996523i	$0.526551\pi$
$728$	−7.73512	−0.286683
$729$	22.2658	0.824660
$730$	6.06582	0.224506
$731$	−10.7048	−0.395930
$732$	−39.4473	−1.45801
$733$	17.2725	0.637973	0.318987	−	0.947759i	$-0.396657\pi$
$733$	17.2725	0.637973	0.318987	+	0.947759i	$0.396657\pi$
$734$	−9.80558	−0.361931
$735$	34.2230	1.26233
$736$	22.5288	0.830424
$737$	34.6780	1.27738
$738$	−0.137202	−0.00505046
$739$	−31.0733	−1.14305	−0.571525	−	0.820585i	$-0.693648\pi$
$739$	−31.0733	−1.14305	−0.571525	+	0.820585i	$0.693648\pi$
$740$	49.5083	1.81996
$741$	4.18868	0.153875
$742$	27.3989	1.00585
$743$	−27.4261	−1.00617	−0.503083	−	0.864238i	$-0.667801\pi$
$743$	−27.4261	−1.00617	−0.503083	+	0.864238i	$0.667801\pi$
$744$	−41.6508	−1.52699
$745$	68.6878	2.51653
$746$	71.3876	2.61369
$747$	−2.97334	−0.108789
$748$	60.2487	2.20291
$749$	15.2917	0.558746
$750$	36.9177	1.34804
$751$	−8.31839	−0.303542	−0.151771	−	0.988416i	$-0.548498\pi$
$751$	−8.31839	−0.303542	−0.151771	+	0.988416i	$0.548498\pi$
$752$	−34.0050	−1.24004
$753$	−43.3400	−1.57940
$754$	13.7474	0.500652
$755$	−20.7215	−0.754133
$756$	−27.1582	−0.987736
$757$	27.1267	0.985938	0.492969	−	0.870047i	$-0.335912\pi$
$757$	27.1267	0.985938	0.492969	+	0.870047i	$0.335912\pi$
$758$	46.0750	1.67352
$759$	−54.7564	−1.98753
$760$	46.8805	1.70053
$761$	−28.4703	−1.03205	−0.516023	−	0.856575i	$-0.672588\pi$
$761$	−28.4703	−1.03205	−0.516023	+	0.856575i	$0.672588\pi$
$762$	−11.7968	−0.427353
$763$	−1.38380	−0.0500969
$764$	26.6020	0.962426
$765$	−4.07909	−0.147480
$766$	71.0020	2.56541
$767$	1.73343	0.0625907
$768$	−58.1831	−2.09950
$769$	31.4072	1.13257	0.566287	−	0.824208i	$-0.308379\pi$
$769$	31.4072	1.13257	0.566287	+	0.824208i	$0.308379\pi$
$770$	57.4281	2.06957
$771$	−35.5739	−1.28116
$772$	2.99696	0.107863
$773$	−32.1786	−1.15738	−0.578692	−	0.815546i	$-0.696437\pi$
$773$	−32.1786	−1.15738	−0.578692	+	0.815546i	$0.696437\pi$
$774$	4.04044	0.145231
$775$	27.6972	0.994911
$776$	−115.211	−4.13584
$777$	−7.87387	−0.282473
$778$	−54.0055	−1.93619
$779$	0.295390	0.0105835
$780$	−28.1336	−1.00734
$781$	−6.17876	−0.221093
$782$	41.8338	1.49597
$783$	26.0528	0.931051
$784$	−32.7346	−1.16909
$785$	−20.3301	−0.725614
$786$	−34.9636	−1.24711
$787$	−36.4216	−1.29829	−0.649145	−	0.760665i	$-0.724873\pi$
$787$	−36.4216	−1.29829	−0.649145	+	0.760665i	$0.724873\pi$
$788$	−38.9423	−1.38726
$789$	−41.3274	−1.47129
$790$	−92.6619	−3.29676
$791$	7.06061	0.251046
$792$	−12.2743	−0.436149
$793$	−4.91024	−0.174368
$794$	30.1425	1.06972
$795$	53.7885	1.90768
$796$	53.3306	1.89025
$797$	27.8711	0.987246	0.493623	−	0.869676i	$-0.335672\pi$
$797$	27.8711	0.987246	0.493623	+	0.869676i	$0.335672\pi$
$798$	−13.8135	−0.488993
$799$	−15.3105	−0.541647
$800$	−27.4739	−0.971350
$801$	−4.54061	−0.160434
$802$	13.3428	0.471150
$803$	3.41926	0.120663
$804$	56.0248	1.97584
$805$	27.3073	0.962457
$806$	−9.60531	−0.338332
$807$	−41.4396	−1.45874
$808$	18.4190	0.647980
$809$	20.2381	0.711533	0.355767	−	0.934575i	$-0.384220\pi$
$809$	20.2381	0.711533	0.355767	+	0.934575i	$0.384220\pi$
$810$	−88.9104	−3.12399
$811$	−11.3243	−0.397649	−0.198825	−	0.980035i	$-0.563712\pi$
$811$	−11.3243	−0.397649	−0.198825	+	0.980035i	$0.563712\pi$
$812$	−31.0472	−1.08954
$813$	−27.5393	−0.965844
$814$	40.7517	1.42835
$815$	−21.2081	−0.742887
$816$	31.9198	1.11742
$817$	−8.69893	−0.304337
$818$	−18.8800	−0.660124
$819$	0.546925	0.0191111
$820$	−1.98401	−0.0692846
$821$	10.8870	0.379961	0.189980	−	0.981788i	$-0.439158\pi$
$821$	10.8870	0.379961	0.189980	+	0.981788i	$0.439158\pi$
$822$	−6.33168	−0.220843
$823$	−0.571448	−0.0199194	−0.00995972	−	0.999950i	$-0.503170\pi$
$823$	−0.571448	−0.0199194	−0.00995972	+	0.999950i	$0.503170\pi$
$824$	−110.463	−3.84817
$825$	66.7754	2.32482
$826$	−5.71655	−0.198904
$827$	−7.77401	−0.270329	−0.135164	−	0.990823i	$-0.543156\pi$
$827$	−7.77401	−0.270329	−0.135164	+	0.990823i	$0.543156\pi$
$828$	−10.8132	−0.375784
$829$	−28.6568	−0.995291	−0.497646	−	0.867380i	$-0.665802\pi$
$829$	−28.6568	−0.995291	−0.497646	+	0.867380i	$0.665802\pi$
$830$	−62.7848	−2.17929
$831$	−29.1472	−1.01110
$832$	−2.85726	−0.0990575
$833$	−14.7385	−0.510658
$834$	46.7497	1.61881
$835$	39.2893	1.35966
$836$	48.9594	1.69330
$837$	−18.2030	−0.629189
$838$	−10.1652	−0.351151
$839$	8.72380	0.301179	0.150589	−	0.988596i	$-0.451883\pi$
$839$	8.72380	0.301179	0.150589	+	0.988596i	$0.451883\pi$
$840$	50.0783	1.72786
$841$	0.783471	0.0270163
$842$	−59.3952	−2.04689
$843$	−0.642799	−0.0221392
$844$	−28.5381	−0.982320
$845$	−3.50196	−0.120471
$846$	5.77885	0.198681
$847$	17.9711	0.617493
$848$	−51.4491	−1.76677
$849$	−16.3396	−0.560775
$850$	−51.0163	−1.74985
$851$	19.3776	0.664256
$852$	−9.98224	−0.341986
$853$	−14.5092	−0.496787	−0.248393	−	0.968659i	$-0.579903\pi$
$853$	−14.5092	−0.496787	−0.248393	+	0.968659i	$0.579903\pi$
$854$	16.1931	0.554116
$855$	−3.31476	−0.113362
$856$	−69.0141	−2.35885
$857$	39.8950	1.36279	0.681394	−	0.731917i	$-0.261374\pi$
$857$	39.8950	1.36279	0.681394	+	0.731917i	$0.261374\pi$
$858$	−23.1576	−0.790586
$859$	−30.7628	−1.04961	−0.524807	−	0.851221i	$-0.675863\pi$
$859$	−30.7628	−1.04961	−0.524807	+	0.851221i	$0.675863\pi$
$860$	58.4269	1.99234
$861$	0.315539	0.0107536
$862$	13.2457	0.451150
$863$	−21.2810	−0.724415	−0.362208	−	0.932097i	$-0.617977\pi$
$863$	−21.2810	−0.724415	−0.362208	+	0.932097i	$0.617977\pi$
$864$	18.0563	0.614288
$865$	74.0142	2.51656
$866$	60.6803	2.06200
$867$	−17.0566	−0.579273
$868$	21.6926	0.736296
$869$	−52.2328	−1.77188
$870$	−89.0028	−3.01748
$871$	6.97375	0.236296
$872$	6.24533	0.211494
$873$	8.14620	0.275707
$874$	33.9951	1.14990
$875$	−10.3782	−0.350847
$876$	5.52406	0.186641
$877$	−6.02948	−0.203601	−0.101801	−	0.994805i	$-0.532460\pi$
$877$	−6.02948	−0.203601	−0.101801	+	0.994805i	$0.532460\pi$
$878$	8.29450	0.279926
$879$	11.7166	0.395190
$880$	−107.837	−3.63520
$881$	−15.0799	−0.508056	−0.254028	−	0.967197i	$-0.581756\pi$
$881$	−15.0799	−0.508056	−0.254028	+	0.967197i	$0.581756\pi$
$882$	5.56294	0.187314
$883$	−19.0514	−0.641129	−0.320565	−	0.947227i	$-0.603873\pi$
$883$	−19.0514	−0.641129	−0.320565	+	0.947227i	$0.603873\pi$
$884$	12.1160	0.407506
$885$	−11.2225	−0.377240
$886$	−61.6499	−2.07117
$887$	33.0441	1.10951	0.554756	−	0.832013i	$-0.312812\pi$
$887$	33.0441	1.10951	0.554756	+	0.832013i	$0.312812\pi$
$888$	35.5362	1.19252
$889$	3.31628	0.111224
$890$	−95.8790	−3.21387
$891$	−50.1182	−1.67902
$892$	23.0124	0.770512
$893$	−12.4417	−0.416345
$894$	91.3428	3.05496
$895$	19.8425	0.663261
$896$	19.3261	0.645640
$897$	−11.0115	−0.367664
$898$	−55.8007	−1.86209
$899$	−20.8097	−0.694041
$900$	13.1867	0.439556
$901$	−23.1646	−0.771724
$902$	−1.63309	−0.0543761
$903$	−9.29230	−0.309228
$904$	−31.8658	−1.05984
$905$	20.2793	0.674105
$906$	−27.5560	−0.915487
$907$	39.4279	1.30918	0.654590	−	0.755984i	$-0.272841\pi$
$907$	39.4279	1.30918	0.654590	+	0.755984i	$0.272841\pi$
$908$	−22.0155	−0.730611
$909$	−1.30235	−0.0431962
$910$	11.5488	0.382839
$911$	9.42386	0.312226	0.156113	−	0.987739i	$-0.450104\pi$
$911$	9.42386	0.312226	0.156113	+	0.987739i	$0.450104\pi$
$912$	25.9387	0.858917
$913$	−35.3913	−1.17128
$914$	−67.3243	−2.22689
$915$	31.7896	1.05093
$916$	−13.8808	−0.458635
$917$	9.82887	0.324578
$918$	33.5288	1.10661
$919$	3.09820	0.102200	0.0511002	−	0.998694i	$-0.483727\pi$
$919$	3.09820	0.102200	0.0511002	+	0.998694i	$0.483727\pi$
$920$	−123.243	−4.06320
$921$	−37.5445	−1.23713
$922$	−14.6396	−0.482131
$923$	−1.24255	−0.0408990
$924$	52.2990	1.72051
$925$	−23.6310	−0.776983
$926$	−2.51903	−0.0827806
$927$	7.81048	0.256530
$928$	20.6419	0.677605
$929$	−15.3089	−0.502269	−0.251134	−	0.967952i	$-0.580804\pi$
$929$	−15.3089	−0.502269	−0.251134	+	0.967952i	$0.580804\pi$
$930$	62.1861	2.03916
$931$	−11.9768	−0.392525
$932$	129.382	4.23804
$933$	15.7796	0.516599
$934$	−43.2255	−1.41438
$935$	−48.5529	−1.58785
$936$	−2.46837	−0.0806812
$937$	−6.70570	−0.219066	−0.109533	−	0.993983i	$-0.534935\pi$
$937$	−6.70570	−0.219066	−0.109533	+	0.993983i	$0.534935\pi$
$938$	−22.9981	−0.750915
$939$	−20.0032	−0.652778
$940$	83.5653	2.72560
$941$	14.1651	0.461768	0.230884	−	0.972981i	$-0.425838\pi$
$941$	14.1651	0.461768	0.230884	+	0.972981i	$0.425838\pi$
$942$	−27.0355	−0.880865
$943$	−0.776544	−0.0252877
$944$	10.7344	0.349375
$945$	21.8862	0.711957
$946$	48.0929	1.56363
$947$	14.3954	0.467787	0.233893	−	0.972262i	$-0.424853\pi$
$947$	14.3954	0.467787	0.233893	+	0.972262i	$0.424853\pi$
$948$	−84.3860	−2.74073
$949$	0.687614	0.0223209
$950$	−41.4570	−1.34504
$951$	30.9855	1.00477
$952$	−21.5667	−0.698982
$953$	24.6164	0.797405	0.398702	−	0.917080i	$-0.369461\pi$
$953$	24.6164	0.797405	0.398702	+	0.917080i	$0.369461\pi$
$954$	8.74332	0.283075
$955$	−21.4379	−0.693714
$956$	19.7505	0.638776
$957$	−50.1703	−1.62177
$958$	−86.9694	−2.80985
$959$	1.77994	0.0574773
$960$	18.4983	0.597029
$961$	−16.4603	−0.530978
$962$	8.19518	0.264223
$963$	4.87975	0.157248
$964$	−68.8822	−2.21855
$965$	−2.41517	−0.0777472
$966$	36.3140	1.16838
$967$	8.08831	0.260102	0.130051	−	0.991507i	$-0.458486\pi$
$967$	8.08831	0.260102	0.130051	+	0.991507i	$0.458486\pi$
$968$	−81.1067	−2.60687
$969$	11.6787	0.375174
$970$	172.014	5.52304
$971$	24.2267	0.777472	0.388736	−	0.921349i	$-0.372912\pi$
$971$	24.2267	0.777472	0.388736	+	0.921349i	$0.372912\pi$
$972$	−18.7351	−0.600930
$973$	−13.1421	−0.421318
$974$	−1.54227	−0.0494174
$975$	13.4286	0.430058
$976$	−30.4070	−0.973306
$977$	42.0206	1.34436	0.672179	−	0.740388i	$-0.265358\pi$
$977$	42.0206	1.34436	0.672179	+	0.740388i	$0.265358\pi$
$978$	−28.2031	−0.901834
$979$	−54.0463	−1.72733
$980$	80.4432	2.56966
$981$	−0.441586	−0.0140988
$982$	53.7534	1.71534
$983$	−56.9646	−1.81689	−0.908445	−	0.418005i	$-0.862729\pi$
$983$	−56.9646	−1.81689	−0.908445	+	0.418005i	$0.862729\pi$
$984$	−1.42409	−0.0453982
$985$	31.3827	0.999935
$986$	38.3300	1.22068
$987$	−13.2903	−0.423036
$988$	9.84576	0.313235
$989$	22.8684	0.727173
$990$	18.3260	0.582438
$991$	−43.9237	−1.39528	−0.697641	−	0.716448i	$-0.745767\pi$
$991$	−43.9237	−1.39528	−0.697641	+	0.716448i	$0.745767\pi$
$992$	−14.4225	−0.457914
$993$	12.1627	0.385971
$994$	4.09770	0.129971
$995$	−42.9778	−1.36249
$996$	−57.1773	−1.81173
$997$	31.9166	1.01081	0.505404	−	0.862883i	$-0.331343\pi$
$997$	31.9166	1.01081	0.505404	+	0.862883i	$0.331343\pi$
$998$	−0.637115	−0.0201675
$999$	15.5307	0.491370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.7	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.7	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51903 q^{2} +1.84872 q^{3} +4.34553 q^{4} -3.50196 q^{5} -4.65699 q^{6} +1.30916 q^{7} -5.90847 q^{8} +0.417768 q^{9} +O(q^{10})\)	\(q-2.51903 q^{2} +1.84872 q^{3} +4.34553 q^{4} -3.50196 q^{5} -4.65699 q^{6} +1.30916 q^{7} -5.90847 q^{8} +0.417768 q^{9} +8.82155 q^{10} +4.97264 q^{11} +8.03367 q^{12} +1.00000 q^{13} -3.29782 q^{14} -6.47414 q^{15} +6.19257 q^{16} +2.78816 q^{17} -1.05237 q^{18} +2.26572 q^{19} -15.2179 q^{20} +2.42027 q^{21} -12.5263 q^{22} -5.95629 q^{23} -10.9231 q^{24} +7.26370 q^{25} -2.51903 q^{26} -4.77383 q^{27} +5.68899 q^{28} -5.45742 q^{29} +16.3086 q^{30} +3.81309 q^{31} -3.78236 q^{32} +9.19303 q^{33} -7.02346 q^{34} -4.58462 q^{35} +1.81542 q^{36} -3.25330 q^{37} -5.70743 q^{38} +1.84872 q^{39} +20.6912 q^{40} +0.130374 q^{41} -6.09674 q^{42} -3.83937 q^{43} +21.6088 q^{44} -1.46301 q^{45} +15.0041 q^{46} -5.49126 q^{47} +11.4483 q^{48} -5.28610 q^{49} -18.2975 q^{50} +5.15452 q^{51} +4.34553 q^{52} -8.30820 q^{53} +12.0254 q^{54} -17.4140 q^{55} -7.73512 q^{56} +4.18868 q^{57} +13.7474 q^{58} +1.73343 q^{59} -28.1336 q^{60} -4.91024 q^{61} -9.60531 q^{62} +0.546925 q^{63} -2.85726 q^{64} -3.50196 q^{65} -23.1576 q^{66} +6.97375 q^{67} +12.1160 q^{68} -11.0115 q^{69} +11.5488 q^{70} -1.24255 q^{71} -2.46837 q^{72} +0.687614 q^{73} +8.19518 q^{74} +13.4286 q^{75} +9.84576 q^{76} +6.50998 q^{77} -4.65699 q^{78} -10.5040 q^{79} -21.6861 q^{80} -10.0788 q^{81} -0.328416 q^{82} -7.11721 q^{83} +10.5174 q^{84} -9.76401 q^{85} +9.67149 q^{86} -10.0893 q^{87} -29.3807 q^{88} -10.8687 q^{89} +3.68536 q^{90} +1.30916 q^{91} -25.8833 q^{92} +7.04934 q^{93} +13.8327 q^{94} -7.93445 q^{95} -6.99252 q^{96} +19.4993 q^{97} +13.3159 q^{98} +2.07741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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