LMFDB - Embedded newform 4011.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.254102 q^{2} -1.00000 q^{3} -1.93543 q^{4} -1.93543 q^{5} +0.254102 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.254102 q^{2} -1.00000 q^{3} -1.93543 q^{4} -1.93543 q^{5} +0.254102 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.491797 q^{10} +3.87086 q^{11} +1.93543 q^{12} +5.68133 q^{13} +0.254102 q^{14} +1.93543 q^{15} +3.61676 q^{16} -5.69774 q^{17} -0.254102 q^{18} +2.31867 q^{19} +3.74590 q^{20} +1.00000 q^{21} -0.983593 q^{22} -3.50820 q^{23} -1.00000 q^{24} -1.25410 q^{25} -1.44364 q^{26} -1.00000 q^{27} +1.93543 q^{28} +3.00000 q^{29} -0.491797 q^{30} -0.826873 q^{31} -2.91903 q^{32} -3.87086 q^{33} +1.44780 q^{34} +1.93543 q^{35} -1.93543 q^{36} -3.44364 q^{37} -0.589178 q^{38} -5.68133 q^{39} -1.93543 q^{40} +2.82687 q^{41} -0.254102 q^{42} +3.49180 q^{43} -7.49180 q^{44} -1.93543 q^{45} +0.891440 q^{46} -3.66492 q^{47} -3.61676 q^{48} +1.00000 q^{49} +0.318669 q^{50} +5.69774 q^{51} -10.9958 q^{52} -1.27051 q^{53} +0.254102 q^{54} -7.49180 q^{55} -1.00000 q^{56} -2.31867 q^{57} -0.762305 q^{58} -10.4876 q^{59} -3.74590 q^{60} +2.38324 q^{61} +0.210110 q^{62} -1.00000 q^{63} -6.49180 q^{64} -10.9958 q^{65} +0.983593 q^{66} -3.06457 q^{67} +11.0276 q^{68} +3.50820 q^{69} -0.491797 q^{70} +8.72532 q^{71} +1.00000 q^{72} +5.55636 q^{73} +0.875034 q^{74} +1.25410 q^{75} -4.48763 q^{76} -3.87086 q^{77} +1.44364 q^{78} +8.18953 q^{79} -7.00000 q^{80} +1.00000 q^{81} -0.718313 q^{82} -9.69774 q^{83} -1.93543 q^{84} +11.0276 q^{85} -0.887271 q^{86} -3.00000 q^{87} +3.87086 q^{88} +3.91903 q^{89} +0.491797 q^{90} -5.68133 q^{91} +6.78989 q^{92} +0.826873 q^{93} +0.931263 q^{94} -4.48763 q^{95} +2.91903 q^{96} -10.4548 q^{97} -0.254102 q^{98} +3.87086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 2 q^{15} - 4 q^{16} - 7 q^{17} + 14 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 5 q^{26} - 3 q^{27} - 2 q^{28} + 9 q^{29} - 3 q^{30} - 8 q^{31} - 4 q^{32} + 4 q^{33} + 27 q^{34} - 2 q^{35} + 2 q^{36} - q^{37} - 5 q^{38} - 10 q^{39} + 2 q^{40} + 14 q^{41} + 12 q^{43} - 24 q^{44} + 2 q^{45} + 16 q^{46} - 7 q^{47} + 4 q^{48} + 3 q^{49} + 8 q^{50} + 7 q^{51} - q^{52} - 24 q^{55} - 3 q^{56} - 14 q^{57} - q^{59} - 12 q^{60} + 22 q^{61} + 21 q^{62} - 3 q^{63} - 21 q^{64} - q^{65} + 6 q^{66} - 17 q^{67} + 15 q^{68} + 9 q^{69} - 3 q^{70} - 2 q^{71} + 3 q^{72} + 26 q^{73} + 19 q^{74} + 3 q^{75} + 17 q^{76} + 4 q^{77} - 5 q^{78} + 16 q^{79} - 21 q^{80} + 3 q^{81} - 21 q^{82} - 19 q^{83} + 2 q^{84} + 15 q^{85} + 16 q^{86} - 9 q^{87} - 4 q^{88} + 7 q^{89} + 3 q^{90} - 10 q^{91} + 8 q^{93} - 37 q^{94} + 17 q^{95} + 4 q^{96} - 7 q^{97} - 4 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 2 * q^15 - 4 * q^16 - 7 * q^17 + 14 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 5 * q^26 - 3 * q^27 - 2 * q^28 + 9 * q^29 - 3 * q^30 - 8 * q^31 - 4 * q^32 + 4 * q^33 + 27 * q^34 - 2 * q^35 + 2 * q^36 - q^37 - 5 * q^38 - 10 * q^39 + 2 * q^40 + 14 * q^41 + 12 * q^43 - 24 * q^44 + 2 * q^45 + 16 * q^46 - 7 * q^47 + 4 * q^48 + 3 * q^49 + 8 * q^50 + 7 * q^51 - q^52 - 24 * q^55 - 3 * q^56 - 14 * q^57 - q^59 - 12 * q^60 + 22 * q^61 + 21 * q^62 - 3 * q^63 - 21 * q^64 - q^65 + 6 * q^66 - 17 * q^67 + 15 * q^68 + 9 * q^69 - 3 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 19 * q^74 + 3 * q^75 + 17 * q^76 + 4 * q^77 - 5 * q^78 + 16 * q^79 - 21 * q^80 + 3 * q^81 - 21 * q^82 - 19 * q^83 + 2 * q^84 + 15 * q^85 + 16 * q^86 - 9 * q^87 - 4 * q^88 + 7 * q^89 + 3 * q^90 - 10 * q^91 + 8 * q^93 - 37 * q^94 + 17 * q^95 + 4 * q^96 - 7 * q^97 - 4 * 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 $

$2$	−0.254102	−0.179677	−0.0898385	−	0.995956i	$-0.528635\pi$
$2$	−0.254102	−0.179677	−0.0898385	+	0.995956i	$0.528635\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.93543	−0.967716
$5$	−1.93543	−0.865552	−0.432776	−	0.901502i	$-0.642466\pi$
$5$	−1.93543	−0.865552	−0.432776	+	0.901502i	$0.642466\pi$
$6$	0.254102	0.103737
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.491797	0.155520
$11$	3.87086	1.16711	0.583555	−	0.812074i	$-0.301661\pi$
$11$	3.87086	1.16711	0.583555	+	0.812074i	$0.301661\pi$
$12$	1.93543	0.558711
$13$	5.68133	1.57572	0.787859	−	0.615856i	$-0.211190\pi$
$13$	5.68133	1.57572	0.787859	+	0.615856i	$0.211190\pi$
$14$	0.254102	0.0679115
$15$	1.93543	0.499726
$16$	3.61676	0.904191
$17$	−5.69774	−1.38190	−0.690952	−	0.722900i	$-0.742808\pi$
$17$	−5.69774	−1.38190	−0.690952	+	0.722900i	$0.742808\pi$
$18$	−0.254102	−0.0598923
$19$	2.31867	0.531939	0.265970	−	0.963981i	$-0.414308\pi$
$19$	2.31867	0.531939	0.265970	+	0.963981i	$0.414308\pi$
$20$	3.74590	0.837608
$21$	1.00000	0.218218
$22$	−0.983593	−0.209703
$23$	−3.50820	−0.731511	−0.365755	−	0.930711i	$-0.619189\pi$
$23$	−3.50820	−0.731511	−0.365755	+	0.930711i	$0.619189\pi$
$24$	−1.00000	−0.204124
$25$	−1.25410	−0.250820
$26$	−1.44364	−0.283120
$27$	−1.00000	−0.192450
$28$	1.93543	0.365762
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	−0.491797	−0.0897894
$31$	−0.826873	−0.148511	−0.0742554	−	0.997239i	$-0.523658\pi$
$31$	−0.826873	−0.148511	−0.0742554	+	0.997239i	$0.523658\pi$
$32$	−2.91903	−0.516016
$33$	−3.87086	−0.673831
$34$	1.44780	0.248296
$35$	1.93543	0.327148
$36$	−1.93543	−0.322572
$37$	−3.44364	−0.566130	−0.283065	−	0.959101i	$-0.591351\pi$
$37$	−3.44364	−0.566130	−0.283065	+	0.959101i	$0.591351\pi$
$38$	−0.589178	−0.0955773
$39$	−5.68133	−0.909741
$40$	−1.93543	−0.306019
$41$	2.82687	0.441483	0.220742	−	0.975332i	$-0.429152\pi$
$41$	2.82687	0.441483	0.220742	+	0.975332i	$0.429152\pi$
$42$	−0.254102	−0.0392087
$43$	3.49180	0.532494	0.266247	−	0.963905i	$-0.414216\pi$
$43$	3.49180	0.532494	0.266247	+	0.963905i	$0.414216\pi$
$44$	−7.49180	−1.12943
$45$	−1.93543	−0.288517
$46$	0.891440	0.131436
$47$	−3.66492	−0.534584	−0.267292	−	0.963616i	$-0.586129\pi$
$47$	−3.66492	−0.534584	−0.267292	+	0.963616i	$0.586129\pi$
$48$	−3.61676	−0.522035
$49$	1.00000	0.142857
$50$	0.318669	0.0450667
$51$	5.69774	0.797843
$52$	−10.9958	−1.52485
$53$	−1.27051	−0.174518	−0.0872589	−	0.996186i	$-0.527811\pi$
$53$	−1.27051	−0.174518	−0.0872589	+	0.996186i	$0.527811\pi$
$54$	0.254102	0.0345789
$55$	−7.49180	−1.01019
$56$	−1.00000	−0.133631
$57$	−2.31867	−0.307115
$58$	−0.762305	−0.100096
$59$	−10.4876	−1.36537	−0.682686	−	0.730711i	$-0.739188\pi$
$59$	−10.4876	−1.36537	−0.682686	+	0.730711i	$0.739188\pi$
$60$	−3.74590	−0.483593
$61$	2.38324	0.305142	0.152571	−	0.988292i	$-0.451245\pi$
$61$	2.38324	0.305142	0.152571	+	0.988292i	$0.451245\pi$
$62$	0.210110	0.0266840
$63$	−1.00000	−0.125988
$64$	−6.49180	−0.811475
$65$	−10.9958	−1.36386
$66$	0.983593	0.121072
$67$	−3.06457	−0.374397	−0.187198	−	0.982322i	$-0.559941\pi$
$67$	−3.06457	−0.374397	−0.187198	+	0.982322i	$0.559941\pi$
$68$	11.0276	1.33729
$69$	3.50820	0.422338
$70$	−0.491797	−0.0587809
$71$	8.72532	1.03551	0.517753	−	0.855530i	$-0.326769\pi$
$71$	8.72532	1.03551	0.517753	+	0.855530i	$0.326769\pi$
$72$	1.00000	0.117851
$73$	5.55636	0.650323	0.325162	−	0.945658i	$-0.394581\pi$
$73$	5.55636	0.650323	0.325162	+	0.945658i	$0.394581\pi$
$74$	0.875034	0.101721
$75$	1.25410	0.144811
$76$	−4.48763	−0.514766
$77$	−3.87086	−0.441126
$78$	1.44364	0.163460
$79$	8.18953	0.921395	0.460697	−	0.887557i	$-0.347599\pi$
$79$	8.18953	0.921395	0.460697	+	0.887557i	$0.347599\pi$
$80$	−7.00000	−0.782624
$81$	1.00000	0.111111
$82$	−0.718313	−0.0793244
$83$	−9.69774	−1.06446	−0.532232	−	0.846598i	$-0.678647\pi$
$83$	−9.69774	−1.06446	−0.532232	+	0.846598i	$0.678647\pi$
$84$	−1.93543	−0.211173
$85$	11.0276	1.19611
$86$	−0.887271	−0.0956769
$87$	−3.00000	−0.321634
$88$	3.87086	0.412636
$89$	3.91903	0.415416	0.207708	−	0.978191i	$-0.433400\pi$
$89$	3.91903	0.415416	0.207708	+	0.978191i	$0.433400\pi$
$90$	0.491797	0.0518399
$91$	−5.68133	−0.595565
$92$	6.78989	0.707895
$93$	0.826873	0.0857427
$94$	0.931263	0.0960525
$95$	−4.48763	−0.460421
$96$	2.91903	0.297922
$97$	−10.4548	−1.06153	−0.530763	−	0.847520i	$-0.678094\pi$
$97$	−10.4548	−1.06153	−0.530763	+	0.847520i	$0.678094\pi$
$98$	−0.254102	−0.0256681
$99$	3.87086	0.389037
$100$	2.42723	0.242723
$101$	−0.854458	−0.0850217	−0.0425109	−	0.999096i	$-0.513536\pi$
$101$	−0.854458	−0.0850217	−0.0425109	+	0.999096i	$0.513536\pi$
$102$	−1.44780	−0.143354
$103$	0.491797	0.0484582	0.0242291	−	0.999706i	$-0.492287\pi$
$103$	0.491797	0.0484582	0.0242291	+	0.999706i	$0.492287\pi$
$104$	5.68133	0.557100
$105$	−1.93543	−0.188879
$106$	0.322838	0.0313568
$107$	−15.0440	−1.45436	−0.727179	−	0.686448i	$-0.759169\pi$
$107$	−15.0440	−1.45436	−0.727179	+	0.686448i	$0.759169\pi$
$108$	1.93543	0.186237
$109$	−13.0880	−1.25360	−0.626801	−	0.779180i	$-0.715636\pi$
$109$	−13.0880	−1.25360	−0.626801	+	0.779180i	$0.715636\pi$
$110$	1.90368	0.181509
$111$	3.44364	0.326855
$112$	−3.61676	−0.341752
$113$	4.52461	0.425640	0.212820	−	0.977091i	$-0.431735\pi$
$113$	4.52461	0.425640	0.212820	+	0.977091i	$0.431735\pi$
$114$	0.589178	0.0551816
$115$	6.78989	0.633161
$116$	−5.80630	−0.539101
$117$	5.68133	0.525239
$118$	2.66492	0.245326
$119$	5.69774	0.522311
$120$	1.93543	0.176680
$121$	3.98359	0.362145
$122$	−0.605585	−0.0548270
$123$	−2.82687	−0.254891
$124$	1.60036	0.143716
$125$	12.1044	1.08265
$126$	0.254102	0.0226372
$127$	−9.29392	−0.824702	−0.412351	−	0.911025i	$-0.635292\pi$
$127$	−9.29392	−0.824702	−0.412351	+	0.911025i	$0.635292\pi$
$128$	7.48763	0.661819
$129$	−3.49180	−0.307436
$130$	2.79406	0.245055
$131$	9.67716	0.845498	0.422749	−	0.906247i	$-0.361065\pi$
$131$	9.67716	0.845498	0.422749	+	0.906247i	$0.361065\pi$
$132$	7.49180	0.652077
$133$	−2.31867	−0.201054
$134$	0.778712	0.0672705
$135$	1.93543	0.166575
$136$	−5.69774	−0.488577
$137$	17.6608	1.50886	0.754430	−	0.656380i	$-0.227913\pi$
$137$	17.6608	1.50886	0.754430	+	0.656380i	$0.227913\pi$
$138$	−0.891440	−0.0758844
$139$	12.4876	1.05919	0.529593	−	0.848252i	$-0.322345\pi$
$139$	12.4876	1.05919	0.529593	+	0.848252i	$0.322345\pi$
$140$	−3.74590	−0.316586
$141$	3.66492	0.308642
$142$	−2.21712	−0.186057
$143$	21.9917	1.83904
$144$	3.61676	0.301397
$145$	−5.80630	−0.482187
$146$	−1.41188	−0.116848
$147$	−1.00000	−0.0824786
$148$	6.66492	0.547853
$149$	9.53162	0.780861	0.390430	−	0.920632i	$-0.372326\pi$
$149$	9.53162	0.780861	0.390430	+	0.920632i	$0.372326\pi$
$150$	−0.318669	−0.0260192
$151$	18.9313	1.54060	0.770302	−	0.637679i	$-0.220105\pi$
$151$	18.9313	1.54060	0.770302	+	0.637679i	$0.220105\pi$
$152$	2.31867	0.188069
$153$	−5.69774	−0.460635
$154$	0.983593	0.0792602
$155$	1.60036	0.128544
$156$	10.9958	0.880371
$157$	1.34625	0.107443	0.0537214	−	0.998556i	$-0.482892\pi$
$157$	1.34625	0.107443	0.0537214	+	0.998556i	$0.482892\pi$
$158$	−2.08097	−0.165553
$159$	1.27051	0.100758
$160$	5.64958	0.446638
$161$	3.50820	0.276485
$162$	−0.254102	−0.0199641
$163$	15.9313	1.24783	0.623916	−	0.781491i	$-0.285541\pi$
$163$	15.9313	1.24783	0.623916	+	0.781491i	$0.285541\pi$
$164$	−5.47122	−0.427231
$165$	7.49180	0.583236
$166$	2.46421	0.191260
$167$	14.9630	1.15787	0.578937	−	0.815373i	$-0.303468\pi$
$167$	14.9630	1.15787	0.578937	+	0.815373i	$0.303468\pi$
$168$	1.00000	0.0771517
$169$	19.2775	1.48289
$170$	−2.80213	−0.214913
$171$	2.31867	0.177313
$172$	−6.75814	−0.515303
$173$	−24.5358	−1.86542	−0.932711	−	0.360625i	$-0.882563\pi$
$173$	−24.5358	−1.86542	−0.932711	+	0.360625i	$0.882563\pi$
$174$	0.762305	0.0577902
$175$	1.25410	0.0948012
$176$	14.0000	1.05529
$177$	10.4876	0.788298
$178$	−0.995831	−0.0746407
$179$	9.06457	0.677518	0.338759	−	0.940873i	$-0.389993\pi$
$179$	9.06457	0.677518	0.338759	+	0.940873i	$0.389993\pi$
$180$	3.74590	0.279203
$181$	−3.87503	−0.288029	−0.144014	−	0.989576i	$-0.546001\pi$
$181$	−3.87503	−0.288029	−0.144014	+	0.989576i	$0.546001\pi$
$182$	1.44364	0.107009
$183$	−2.38324	−0.176174
$184$	−3.50820	−0.258628
$185$	6.66492	0.490015
$186$	−0.210110	−0.0154060
$187$	−22.0552	−1.61283
$188$	7.09321	0.517326
$189$	1.00000	0.0727393
$190$	1.14031	0.0827271
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	6.49180	0.468505
$193$	19.7253	1.41986	0.709930	−	0.704272i	$-0.248727\pi$
$193$	19.7253	1.41986	0.709930	+	0.704272i	$0.248727\pi$
$194$	2.65659	0.190732
$195$	10.9958	0.787428
$196$	−1.93543	−0.138245
$197$	−7.09215	−0.505295	−0.252647	−	0.967558i	$-0.581301\pi$
$197$	−7.09215	−0.505295	−0.252647	+	0.967558i	$0.581301\pi$
$198$	−0.983593	−0.0699009
$199$	8.54102	0.605457	0.302728	−	0.953077i	$-0.402103\pi$
$199$	8.54102	0.605457	0.302728	+	0.953077i	$0.402103\pi$
$200$	−1.25410	−0.0886784
$201$	3.06457	0.216158
$202$	0.217119	0.0152765
$203$	−3.00000	−0.210559
$204$	−11.0276	−0.772085
$205$	−5.47122	−0.382127
$206$	−0.124966	−0.00870682
$207$	−3.50820	−0.243837
$208$	20.5480	1.42475
$209$	8.97526	0.620831
$210$	0.491797	0.0339372
$211$	22.2775	1.53365	0.766824	−	0.641858i	$-0.221836\pi$
$211$	22.2775	1.53365	0.766824	+	0.641858i	$0.221836\pi$
$212$	2.45898	0.168884
$213$	−8.72532	−0.597849
$214$	3.82270	0.261315
$215$	−6.75814	−0.460901
$216$	−1.00000	−0.0680414
$217$	0.826873	0.0561318
$218$	3.32568	0.225243
$219$	−5.55636	−0.375464
$220$	14.4999	0.977581
$221$	−32.3707	−2.17749
$222$	−0.875034	−0.0587284
$223$	7.27051	0.486869	0.243435	−	0.969917i	$-0.421726\pi$
$223$	7.27051	0.486869	0.243435	+	0.969917i	$0.421726\pi$
$224$	2.91903	0.195036
$225$	−1.25410	−0.0836068
$226$	−1.14971	−0.0764776
$227$	−4.78572	−0.317639	−0.158820	−	0.987308i	$-0.550769\pi$
$227$	−4.78572	−0.317639	−0.158820	+	0.987308i	$0.550769\pi$
$228$	4.48763	0.297200
$229$	−5.13614	−0.339406	−0.169703	−	0.985495i	$-0.554281\pi$
$229$	−5.13614	−0.339406	−0.169703	+	0.985495i	$0.554281\pi$
$230$	−1.72532	−0.113764
$231$	3.87086	0.254684
$232$	3.00000	0.196960
$233$	24.7089	1.61873	0.809367	−	0.587303i	$-0.199810\pi$
$233$	24.7089	1.61873	0.809367	+	0.587303i	$0.199810\pi$
$234$	−1.44364	−0.0943734
$235$	7.09321	0.462710
$236$	20.2981	1.32129
$237$	−8.18953	−0.531967
$238$	−1.44780	−0.0938472
$239$	−0.399644	−0.0258508	−0.0129254	−	0.999916i	$-0.504114\pi$
$239$	−0.399644	−0.0258508	−0.0129254	+	0.999916i	$0.504114\pi$
$240$	7.00000	0.451848
$241$	−14.5962	−0.940223	−0.470112	−	0.882607i	$-0.655786\pi$
$241$	−14.5962	−0.940223	−0.470112	+	0.882607i	$0.655786\pi$
$242$	−1.01224	−0.0650691
$243$	−1.00000	−0.0641500
$244$	−4.61259	−0.295291
$245$	−1.93543	−0.123650
$246$	0.718313	0.0457980
$247$	13.1731	0.838186
$248$	−0.826873	−0.0525065
$249$	9.69774	0.614569
$250$	−3.07575	−0.194527
$251$	−8.63734	−0.545184	−0.272592	−	0.962130i	$-0.587881\pi$
$251$	−8.63734	−0.545184	−0.272592	+	0.962130i	$0.587881\pi$
$252$	1.93543	0.121921
$253$	−13.5798	−0.853753
$254$	2.36160	0.148180
$255$	−11.0276	−0.690574
$256$	11.0810	0.692561
$257$	14.5204	0.905760	0.452880	−	0.891571i	$-0.350397\pi$
$257$	14.5204	0.905760	0.452880	+	0.891571i	$0.350397\pi$
$258$	0.887271	0.0552391
$259$	3.44364	0.213977
$260$	21.2817	1.31983
$261$	3.00000	0.185695
$262$	−2.45898	−0.151916
$263$	−12.3749	−0.763069	−0.381534	−	0.924355i	$-0.624604\pi$
$263$	−12.3749	−0.763069	−0.381534	+	0.924355i	$0.624604\pi$
$264$	−3.87086	−0.238235
$265$	2.45898	0.151054
$266$	0.589178	0.0361248
$267$	−3.91903	−0.239840
$268$	5.93126	0.362310
$269$	9.26111	0.564660	0.282330	−	0.959317i	$-0.408893\pi$
$269$	9.26111	0.564660	0.282330	+	0.959317i	$0.408893\pi$
$270$	−0.491797	−0.0299298
$271$	2.12497	0.129083	0.0645413	−	0.997915i	$-0.479442\pi$
$271$	2.12497	0.129083	0.0645413	+	0.997915i	$0.479442\pi$
$272$	−20.6074	−1.24951
$273$	5.68133	0.343850
$274$	−4.48763	−0.271108
$275$	−4.85446	−0.292735
$276$	−6.78989	−0.408703
$277$	14.5522	0.874357	0.437178	−	0.899375i	$-0.355978\pi$
$277$	14.5522	0.874357	0.437178	+	0.899375i	$0.355978\pi$
$278$	−3.17313	−0.190312
$279$	−0.826873	−0.0495036
$280$	1.93543	0.115664
$281$	13.9641	0.833027	0.416513	−	0.909130i	$-0.363252\pi$
$281$	13.9641	0.833027	0.416513	+	0.909130i	$0.363252\pi$
$282$	−0.931263	−0.0554559
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	−16.8873	−1.00208
$285$	4.48763	0.265824
$286$	−5.58812	−0.330432
$287$	−2.82687	−0.166865
$288$	−2.91903	−0.172005
$289$	15.4642	0.909659
$290$	1.47539	0.0866379
$291$	10.4548	0.612872
$292$	−10.7540	−0.629328
$293$	8.46421	0.494485	0.247242	−	0.968954i	$-0.420476\pi$
$293$	8.46421	0.494485	0.247242	+	0.968954i	$0.420476\pi$
$294$	0.254102	0.0148195
$295$	20.2981	1.18180
$296$	−3.44364	−0.200157
$297$	−3.87086	−0.224610
$298$	−2.42200	−0.140303
$299$	−19.9313	−1.15265
$300$	−2.42723	−0.140136
$301$	−3.49180	−0.201264
$302$	−4.81047	−0.276811
$303$	0.854458	0.0490873
$304$	8.38608	0.480975
$305$	−4.61259	−0.264116
$306$	1.44780	0.0827655
$307$	−20.5275	−1.17156	−0.585782	−	0.810469i	$-0.699212\pi$
$307$	−20.5275	−1.17156	−0.585782	+	0.810469i	$0.699212\pi$
$308$	7.49180	0.426885
$309$	−0.491797	−0.0279773
$310$	−0.406653	−0.0230964
$311$	−12.3103	−0.698055	−0.349027	−	0.937113i	$-0.613488\pi$
$311$	−12.3103	−0.698055	−0.349027	+	0.937113i	$0.613488\pi$
$312$	−5.68133	−0.321642
$313$	−25.5686	−1.44522	−0.722611	−	0.691254i	$-0.757058\pi$
$313$	−25.5686	−1.44522	−0.722611	+	0.691254i	$0.757058\pi$
$314$	−0.342086	−0.0193050
$315$	1.93543	0.109049
$316$	−15.8503	−0.891648
$317$	−31.3861	−1.76282	−0.881409	−	0.472354i	$-0.843404\pi$
$317$	−31.3861	−1.76282	−0.881409	+	0.472354i	$0.843404\pi$
$318$	−0.322838	−0.0181039
$319$	11.6126	0.650180
$320$	12.5644	0.702373
$321$	15.0440	0.839674
$322$	−0.891440	−0.0496780
$323$	−13.2112	−0.735089
$324$	−1.93543	−0.107524
$325$	−7.12497	−0.395222
$326$	−4.04816	−0.224207
$327$	13.0880	0.723767
$328$	2.82687	0.156088
$329$	3.66492	0.202054
$330$	−1.90368	−0.104794
$331$	25.3749	1.39473	0.697365	−	0.716716i	$-0.254356\pi$
$331$	25.3749	1.39473	0.697365	+	0.716716i	$0.254356\pi$
$332$	18.7693	1.03010
$333$	−3.44364	−0.188710
$334$	−3.80213	−0.208043
$335$	5.93126	0.324060
$336$	3.61676	0.197311
$337$	28.3913	1.54657	0.773286	−	0.634057i	$-0.218611\pi$
$337$	28.3913	1.54657	0.773286	+	0.634057i	$0.218611\pi$
$338$	−4.89845	−0.266441
$339$	−4.52461	−0.245743
$340$	−21.3431	−1.15749
$341$	−3.20071	−0.173328
$342$	−0.589178	−0.0318591
$343$	−1.00000	−0.0539949
$344$	3.49180	0.188265
$345$	−6.78989	−0.365555
$346$	6.23459	0.335173
$347$	−21.9149	−1.17645	−0.588226	−	0.808697i	$-0.700173\pi$
$347$	−21.9149	−1.17645	−0.588226	+	0.808697i	$0.700173\pi$
$348$	5.80630	0.311250
$349$	16.6014	0.888653	0.444327	−	0.895865i	$-0.353443\pi$
$349$	16.6014	0.888653	0.444327	+	0.895865i	$0.353443\pi$
$350$	−0.318669	−0.0170336
$351$	−5.68133	−0.303247
$352$	−11.2992	−0.602247
$353$	−34.7745	−1.85086	−0.925431	−	0.378916i	$-0.876297\pi$
$353$	−34.7745	−1.85086	−0.925431	+	0.378916i	$0.876297\pi$
$354$	−2.66492	−0.141639
$355$	−16.8873	−0.896283
$356$	−7.58501	−0.402005
$357$	−5.69774	−0.301556
$358$	−2.30332	−0.121734
$359$	−2.22936	−0.117661	−0.0588305	−	0.998268i	$-0.518737\pi$
$359$	−2.22936	−0.117661	−0.0588305	+	0.998268i	$0.518737\pi$
$360$	−1.93543	−0.102006
$361$	−13.6238	−0.717041
$362$	0.984653	0.0517522
$363$	−3.98359	−0.209084
$364$	10.9958	0.576338
$365$	−10.7540	−0.562888
$366$	0.605585	0.0316544
$367$	20.7100	1.08105	0.540526	−	0.841327i	$-0.318225\pi$
$367$	20.7100	1.08105	0.540526	+	0.841327i	$0.318225\pi$
$368$	−12.6883	−0.661425
$369$	2.82687	0.147161
$370$	−1.69357	−0.0880444
$371$	1.27051	0.0659615
$372$	−1.60036	−0.0829746
$373$	25.0768	1.29843	0.649214	−	0.760606i	$-0.275098\pi$
$373$	25.0768	1.29843	0.649214	+	0.760606i	$0.275098\pi$
$374$	5.60426	0.289789
$375$	−12.1044	−0.625068
$376$	−3.66492	−0.189004
$377$	17.0440	0.877810
$378$	−0.254102	−0.0130696
$379$	−19.2377	−0.988174	−0.494087	−	0.869412i	$-0.664498\pi$
$379$	−19.2377	−0.988174	−0.494087	+	0.869412i	$0.664498\pi$
$380$	8.68550	0.445557
$381$	9.29392	0.476142
$382$	−0.254102	−0.0130010
$383$	−1.08514	−0.0554482	−0.0277241	−	0.999616i	$-0.508826\pi$
$383$	−1.08514	−0.0554482	−0.0277241	+	0.999616i	$0.508826\pi$
$384$	−7.48763	−0.382101
$385$	7.49180	0.381817
$386$	−5.01224	−0.255116
$387$	3.49180	0.177498
$388$	20.2346	1.02726
$389$	−5.94767	−0.301559	−0.150779	−	0.988567i	$-0.548178\pi$
$389$	−5.94767	−0.301559	−0.150779	+	0.988567i	$0.548178\pi$
$390$	−2.79406	−0.141483
$391$	19.9888	1.01088
$392$	1.00000	0.0505076
$393$	−9.67716	−0.488148
$394$	1.80213	0.0907899
$395$	−15.8503	−0.797515
$396$	−7.49180	−0.376477
$397$	16.2018	0.813144	0.406572	−	0.913619i	$-0.366724\pi$
$397$	16.2018	0.813144	0.406572	+	0.913619i	$0.366724\pi$
$398$	−2.17029	−0.108787
$399$	2.31867	0.116079
$400$	−4.53579	−0.226789
$401$	−0.891440	−0.0445164	−0.0222582	−	0.999752i	$-0.507086\pi$
$401$	−0.891440	−0.0445164	−0.0222582	+	0.999752i	$0.507086\pi$
$402$	−0.778712	−0.0388386
$403$	−4.69774	−0.234011
$404$	1.65375	0.0822769
$405$	−1.93543	−0.0961724
$406$	0.762305	0.0378326
$407$	−13.3298	−0.660736
$408$	5.69774	0.282080
$409$	12.9078	0.638252	0.319126	−	0.947712i	$-0.396611\pi$
$409$	12.9078	0.638252	0.319126	+	0.947712i	$0.396611\pi$
$410$	1.39025	0.0686594
$411$	−17.6608	−0.871141
$412$	−0.951839	−0.0468937
$413$	10.4876	0.516062
$414$	0.891440	0.0438119
$415$	18.7693	0.921349
$416$	−16.5839	−0.813095
$417$	−12.4876	−0.611522
$418$	−2.28063	−0.111549
$419$	1.55220	0.0758297	0.0379149	−	0.999281i	$-0.487928\pi$
$419$	1.55220	0.0758297	0.0379149	+	0.999281i	$0.487928\pi$
$420$	3.74590	0.182781
$421$	33.1414	1.61521	0.807606	−	0.589723i	$-0.200763\pi$
$421$	33.1414	1.61521	0.807606	+	0.589723i	$0.200763\pi$
$422$	−5.66075	−0.275561
$423$	−3.66492	−0.178195
$424$	−1.27051	−0.0617013
$425$	7.14554	0.346610
$426$	2.21712	0.107420
$427$	−2.38324	−0.115333
$428$	29.1166	1.40741
$429$	−21.9917	−1.06177
$430$	1.71725	0.0828133
$431$	−41.3449	−1.99152	−0.995758	−	0.0920163i	$-0.970669\pi$
$431$	−41.3449	−1.99152	−0.995758	+	0.0920163i	$0.970669\pi$
$432$	−3.61676	−0.174012
$433$	3.78288	0.181794	0.0908968	−	0.995860i	$-0.471027\pi$
$433$	3.78288	0.181794	0.0908968	+	0.995860i	$0.471027\pi$
$434$	−0.210110	−0.0100856
$435$	5.80630	0.278391
$436$	25.3309	1.21313
$437$	−8.13436	−0.389119
$438$	1.41188	0.0674623
$439$	9.77454	0.466513	0.233257	−	0.972415i	$-0.425062\pi$
$439$	9.77454	0.466513	0.233257	+	0.972415i	$0.425062\pi$
$440$	−7.49180	−0.357157
$441$	1.00000	0.0476190
$442$	8.22546	0.391245
$443$	23.7058	1.12630	0.563148	−	0.826356i	$-0.309590\pi$
$443$	23.7058	1.12630	0.563148	+	0.826356i	$0.309590\pi$
$444$	−6.66492	−0.316303
$445$	−7.58501	−0.359564
$446$	−1.84745	−0.0874792
$447$	−9.53162	−0.450830
$448$	6.49180	0.306709
$449$	−11.1044	−0.524049	−0.262024	−	0.965061i	$-0.584390\pi$
$449$	−11.1044	−0.524049	−0.262024	+	0.965061i	$0.584390\pi$
$450$	0.318669	0.0150222
$451$	10.9424	0.515259
$452$	−8.75708	−0.411898
$453$	−18.9313	−0.889468
$454$	1.21606	0.0570725
$455$	10.9958	0.515493
$456$	−2.31867	−0.108582
$457$	35.8737	1.67810	0.839051	−	0.544053i	$-0.183111\pi$
$457$	35.8737	1.67810	0.839051	+	0.544053i	$0.183111\pi$
$458$	1.30510	0.0609835
$459$	5.69774	0.265948
$460$	−13.1414	−0.612720
$461$	22.5603	1.05074	0.525368	−	0.850875i	$-0.323928\pi$
$461$	22.5603	1.05074	0.525368	+	0.850875i	$0.323928\pi$
$462$	−0.983593	−0.0457609
$463$	−18.5892	−0.863912	−0.431956	−	0.901895i	$-0.642176\pi$
$463$	−18.5892	−0.863912	−0.431956	+	0.901895i	$0.642176\pi$
$464$	10.8503	0.503712
$465$	−1.60036	−0.0742147
$466$	−6.27858	−0.290849
$467$	9.03565	0.418120	0.209060	−	0.977903i	$-0.432960\pi$
$467$	9.03565	0.418120	0.209060	+	0.977903i	$0.432960\pi$
$468$	−10.9958	−0.508282
$469$	3.06457	0.141509
$470$	−1.80240	−0.0831384
$471$	−1.34625	−0.0620321
$472$	−10.4876	−0.482732
$473$	13.5163	0.621479
$474$	2.08097	0.0955823
$475$	−2.90785	−0.133421
$476$	−11.0276	−0.505449
$477$	−1.27051	−0.0581726
$478$	0.101550	0.00464480
$479$	20.8873	0.954364	0.477182	−	0.878805i	$-0.341658\pi$
$479$	20.8873	0.954364	0.477182	+	0.878805i	$0.341658\pi$
$480$	−5.64958	−0.257867
$481$	−19.5644	−0.892061
$482$	3.70892	0.168936
$483$	−3.50820	−0.159629
$484$	−7.70998	−0.350453
$485$	20.2346	0.918805
$486$	0.254102	0.0115263
$487$	−8.16195	−0.369853	−0.184927	−	0.982752i	$-0.559205\pi$
$487$	−8.16195	−0.369853	−0.184927	+	0.982752i	$0.559205\pi$
$488$	2.38324	0.107884
$489$	−15.9313	−0.720437
$490$	0.491797	0.0222171
$491$	−18.8175	−0.849221	−0.424610	−	0.905376i	$-0.639589\pi$
$491$	−18.8175	−0.849221	−0.424610	+	0.905376i	$0.639589\pi$
$492$	5.47122	0.246662
$493$	−17.0932	−0.769840
$494$	−3.34731	−0.150603
$495$	−7.49180	−0.336731
$496$	−2.99060	−0.134282
$497$	−8.72532	−0.391384
$498$	−2.46421	−0.110424
$499$	23.2252	1.03970	0.519851	−	0.854257i	$-0.325987\pi$
$499$	23.2252	1.03970	0.519851	+	0.854257i	$0.325987\pi$
$500$	−23.4272	−1.04770
$501$	−14.9630	−0.668498
$502$	2.19476	0.0979570
$503$	−4.32568	−0.192872	−0.0964362	−	0.995339i	$-0.530744\pi$
$503$	−4.32568	−0.192872	−0.0964362	+	0.995339i	$0.530744\pi$
$504$	−1.00000	−0.0445435
$505$	1.65375	0.0735907
$506$	3.45065	0.153400
$507$	−19.2775	−0.856145
$508$	17.9878	0.798078
$509$	−31.7540	−1.40747	−0.703735	−	0.710463i	$-0.748486\pi$
$509$	−31.7540	−1.40747	−0.703735	+	0.710463i	$0.748486\pi$
$510$	2.80213	0.124080
$511$	−5.55636	−0.245799
$512$	−17.7909	−0.786256
$513$	−2.31867	−0.102372
$514$	−3.68967	−0.162744
$515$	−0.951839	−0.0419430
$516$	6.75814	0.297510
$517$	−14.1864	−0.623918
$518$	−0.875034	−0.0384468
$519$	24.5358	1.07700
$520$	−10.9958	−0.482199
$521$	9.08514	0.398027	0.199014	−	0.979997i	$-0.436226\pi$
$521$	9.08514	0.398027	0.199014	+	0.979997i	$0.436226\pi$
$522$	−0.762305	−0.0333652
$523$	−30.3983	−1.32923	−0.664613	−	0.747188i	$-0.731403\pi$
$523$	−30.3983	−1.32923	−0.664613	+	0.747188i	$0.731403\pi$
$524$	−18.7295	−0.818202
$525$	−1.25410	−0.0547335
$526$	3.14448	0.137106
$527$	4.71130	0.205228
$528$	−14.0000	−0.609272
$529$	−10.6925	−0.464892
$530$	−0.624832	−0.0271410
$531$	−10.4876	−0.455124
$532$	4.48763	0.194563
$533$	16.0604	0.695653
$534$	0.995831	0.0430938
$535$	29.1166	1.25882
$536$	−3.06457	−0.132369
$537$	−9.06457	−0.391165
$538$	−2.35326	−0.101456
$539$	3.87086	0.166730
$540$	−3.74590	−0.161198
$541$	33.8984	1.45741	0.728704	−	0.684829i	$-0.240123\pi$
$541$	33.8984	1.45741	0.728704	+	0.684829i	$0.240123\pi$
$542$	−0.539958	−0.0231932
$543$	3.87503	0.166294
$544$	16.6318	0.713084
$545$	25.3309	1.08506
$546$	−1.44364	−0.0617819
$547$	−11.6454	−0.497922	−0.248961	−	0.968514i	$-0.580089\pi$
$547$	−11.6454	−0.497922	−0.248961	+	0.968514i	$0.580089\pi$
$548$	−34.1812	−1.46015
$549$	2.38324	0.101714
$550$	1.23353	0.0525977
$551$	6.95601	0.296336
$552$	3.50820	0.149319
$553$	−8.18953	−0.348254
$554$	−3.69774	−0.157102
$555$	−6.66492	−0.282910
$556$	−24.1690	−1.02499
$557$	27.8545	1.18023	0.590116	−	0.807319i	$-0.299082\pi$
$557$	27.8545	1.18023	0.590116	+	0.807319i	$0.299082\pi$
$558$	0.210110	0.00889466
$559$	19.8381	0.839060
$560$	7.00000	0.295804
$561$	22.0552	0.931170
$562$	−3.54830	−0.149676
$563$	16.0151	0.674955	0.337478	−	0.941334i	$-0.390426\pi$
$563$	16.0151	0.674955	0.337478	+	0.941334i	$0.390426\pi$
$564$	−7.09321	−0.298678
$565$	−8.75708	−0.368413
$566$	−2.03281	−0.0854455
$567$	−1.00000	−0.0419961
$568$	8.72532	0.366106
$569$	5.21117	0.218464	0.109232	−	0.994016i	$-0.465161\pi$
$569$	5.21117	0.218464	0.109232	+	0.994016i	$0.465161\pi$
$570$	−1.14031	−0.0477625
$571$	26.3902	1.10440	0.552199	−	0.833713i	$-0.313789\pi$
$571$	26.3902	1.10440	0.552199	+	0.833713i	$0.313789\pi$
$572$	−42.5634	−1.77966
$573$	−1.00000	−0.0417756
$574$	0.718313	0.0299818
$575$	4.39964	0.183478
$576$	−6.49180	−0.270492
$577$	−18.0122	−0.749859	−0.374930	−	0.927053i	$-0.622333\pi$
$577$	−18.0122	−0.749859	−0.374930	+	0.927053i	$0.622333\pi$
$578$	−3.92948	−0.163445
$579$	−19.7253	−0.819756
$580$	11.2377	0.466620
$581$	9.69774	0.402330
$582$	−2.65659	−0.110119
$583$	−4.91797	−0.203681
$584$	5.55636	0.229924
$585$	−10.9958	−0.454622
$586$	−2.15077	−0.0888475
$587$	−10.1854	−0.420395	−0.210198	−	0.977659i	$-0.567411\pi$
$587$	−10.1854	−0.420395	−0.210198	+	0.977659i	$0.567411\pi$
$588$	1.93543	0.0798159
$589$	−1.91724	−0.0789987
$590$	−5.15778	−0.212342
$591$	7.09215	0.291732
$592$	−12.4548	−0.511890
$593$	33.3627	1.37004	0.685020	−	0.728524i	$-0.259793\pi$
$593$	33.3627	1.37004	0.685020	+	0.728524i	$0.259793\pi$
$594$	0.983593	0.0403573
$595$	−11.0276	−0.452087
$596$	−18.4478	−0.755652
$597$	−8.54102	−0.349561
$598$	5.06457	0.207106
$599$	−7.12391	−0.291075	−0.145537	−	0.989353i	$-0.546491\pi$
$599$	−7.12391	−0.291075	−0.145537	+	0.989353i	$0.546491\pi$
$600$	1.25410	0.0511985
$601$	21.4835	0.876329	0.438164	−	0.898895i	$-0.355629\pi$
$601$	21.4835	0.876329	0.438164	+	0.898895i	$0.355629\pi$
$602$	0.887271	0.0361625
$603$	−3.06457	−0.124799
$604$	−36.6402	−1.49087
$605$	−7.70998	−0.313455
$606$	−0.217119	−0.00881986
$607$	−0.450645	−0.0182911	−0.00914556	−	0.999958i	$-0.502911\pi$
$607$	−0.450645	−0.0182911	−0.00914556	+	0.999958i	$0.502911\pi$
$608$	−6.76826	−0.274489
$609$	3.00000	0.121566
$610$	1.17207	0.0474556
$611$	−20.8216	−0.842354
$612$	11.0276	0.445764
$613$	43.2130	1.74535	0.872677	−	0.488297i	$-0.162382\pi$
$613$	43.2130	1.74535	0.872677	+	0.488297i	$0.162382\pi$
$614$	5.21606	0.210503
$615$	5.47122	0.220621
$616$	−3.87086	−0.155962
$617$	29.4587	1.18596	0.592982	−	0.805216i	$-0.297951\pi$
$617$	29.4587	1.18596	0.592982	+	0.805216i	$0.297951\pi$
$618$	0.124966	0.00502688
$619$	30.8451	1.23977	0.619884	−	0.784694i	$-0.287180\pi$
$619$	30.8451	1.23977	0.619884	+	0.784694i	$0.287180\pi$
$620$	−3.09738	−0.124394
$621$	3.50820	0.140779
$622$	3.12808	0.125424
$623$	−3.91903	−0.157012
$624$	−20.5480	−0.822579
$625$	−17.1567	−0.686269
$626$	6.49702	0.259673
$627$	−8.97526	−0.358437
$628$	−2.60558	−0.103974
$629$	19.6209	0.782338
$630$	−0.491797	−0.0195936
$631$	12.6014	0.501654	0.250827	−	0.968032i	$-0.419297\pi$
$631$	12.6014	0.501654	0.250827	+	0.968032i	$0.419297\pi$
$632$	8.18953	0.325762
$633$	−22.2775	−0.885452
$634$	7.97526	0.316738
$635$	17.9878	0.713823
$636$	−2.45898	−0.0975050
$637$	5.68133	0.225103
$638$	−2.95078	−0.116822
$639$	8.72532	0.345168
$640$	−14.4918	−0.572839
$641$	−1.76931	−0.0698837	−0.0349419	−	0.999389i	$-0.511125\pi$
$641$	−1.76931	−0.0698837	−0.0349419	+	0.999389i	$0.511125\pi$
$642$	−3.82270	−0.150870
$643$	46.2004	1.82197	0.910984	−	0.412442i	$-0.135324\pi$
$643$	46.2004	1.82197	0.910984	+	0.412442i	$0.135324\pi$
$644$	−6.78989	−0.267559
$645$	6.75814	0.266101
$646$	3.35698	0.132079
$647$	1.90679	0.0749636	0.0374818	−	0.999297i	$-0.488066\pi$
$647$	1.90679	0.0749636	0.0374818	+	0.999297i	$0.488066\pi$
$648$	1.00000	0.0392837
$649$	−40.5962	−1.59354
$650$	1.81047	0.0710123
$651$	−0.826873	−0.0324077
$652$	−30.8339	−1.20755
$653$	3.00106	0.117441	0.0587203	−	0.998274i	$-0.481298\pi$
$653$	3.00106	0.117441	0.0587203	+	0.998274i	$0.481298\pi$
$654$	−3.32568	−0.130044
$655$	−18.7295	−0.731822
$656$	10.2241	0.399185
$657$	5.55636	0.216774
$658$	−0.931263	−0.0363044
$659$	−39.3009	−1.53095	−0.765474	−	0.643467i	$-0.777495\pi$
$659$	−39.3009	−1.53095	−0.765474	+	0.643467i	$0.777495\pi$
$660$	−14.4999	−0.564406
$661$	−34.9864	−1.36081	−0.680407	−	0.732834i	$-0.738197\pi$
$661$	−34.9864	−1.36081	−0.680407	+	0.732834i	$0.738197\pi$
$662$	−6.44780	−0.250601
$663$	32.3707	1.25717
$664$	−9.69774	−0.376345
$665$	4.48763	0.174023
$666$	0.875034	0.0339069
$667$	−10.5246	−0.407515
$668$	−28.9599	−1.12049
$669$	−7.27051	−0.281094
$670$	−1.50714	−0.0582261
$671$	9.22519	0.356134
$672$	−2.91903	−0.112604
$673$	−22.8297	−0.880021	−0.440010	−	0.897993i	$-0.645025\pi$
$673$	−22.8297	−0.880021	−0.440010	+	0.897993i	$0.645025\pi$
$674$	−7.21428	−0.277884
$675$	1.25410	0.0482704
$676$	−37.3103	−1.43501
$677$	29.7498	1.14338	0.571689	−	0.820471i	$-0.306288\pi$
$677$	29.7498	1.14338	0.571689	+	0.820471i	$0.306288\pi$
$678$	1.14971	0.0441544
$679$	10.4548	0.401219
$680$	11.0276	0.422889
$681$	4.78572	0.183389
$682$	0.813306	0.0311431
$683$	−5.36266	−0.205197	−0.102598	−	0.994723i	$-0.532716\pi$
$683$	−5.36266	−0.205197	−0.102598	+	0.994723i	$0.532716\pi$
$684$	−4.48763	−0.171589
$685$	−34.1812	−1.30600
$686$	0.254102	0.00970165
$687$	5.13614	0.195956
$688$	12.6290	0.481476
$689$	−7.21818	−0.274991
$690$	1.72532	0.0656819
$691$	−28.1812	−1.07206	−0.536032	−	0.844198i	$-0.680077\pi$
$691$	−28.1812	−1.07206	−0.536032	+	0.844198i	$0.680077\pi$
$692$	47.4874	1.80520
$693$	−3.87086	−0.147042
$694$	5.56860	0.211381
$695$	−24.1690	−0.916781
$696$	−3.00000	−0.113715
$697$	−16.1068	−0.610088
$698$	−4.21845	−0.159671
$699$	−24.7089	−0.934577
$700$	−2.42723	−0.0917406
$701$	36.4793	1.37780	0.688902	−	0.724855i	$-0.258093\pi$
$701$	36.4793	1.37780	0.688902	+	0.724855i	$0.258093\pi$
$702$	1.44364	0.0544865
$703$	−7.98465	−0.301147
$704$	−25.1289	−0.947080
$705$	−7.09321	−0.267146
$706$	8.83627	0.332557
$707$	0.854458	0.0321352
$708$	−20.2981	−0.762849
$709$	−9.08798	−0.341306	−0.170653	−	0.985331i	$-0.554588\pi$
$709$	−9.08798	−0.341306	−0.170653	+	0.985331i	$0.554588\pi$
$710$	4.29108	0.161042
$711$	8.18953	0.307132
$712$	3.91903	0.146872
$713$	2.90084	0.108637
$714$	1.44780	0.0541827
$715$	−42.5634	−1.59178
$716$	−17.5439	−0.655645
$717$	0.399644	0.0149250
$718$	0.566483	0.0211410
$719$	−7.61676	−0.284057	−0.142029	−	0.989863i	$-0.545363\pi$
$719$	−7.61676	−0.284057	−0.142029	+	0.989863i	$0.545363\pi$
$720$	−7.00000	−0.260875
$721$	−0.491797	−0.0183155
$722$	3.46182	0.128836
$723$	14.5962	0.542838
$724$	7.49987	0.278730
$725$	−3.76231	−0.139729
$726$	1.01224	0.0375677
$727$	19.7006	0.730654	0.365327	−	0.930879i	$-0.380957\pi$
$727$	19.7006	0.730654	0.365327	+	0.930879i	$0.380957\pi$
$728$	−5.68133	−0.210564
$729$	1.00000	0.0370370
$730$	2.73260	0.101138
$731$	−19.8953	−0.735856
$732$	4.61259	0.170486
$733$	29.8726	1.10337	0.551686	−	0.834052i	$-0.313985\pi$
$733$	29.8726	1.10337	0.551686	+	0.834052i	$0.313985\pi$
$734$	−5.26244	−0.194240
$735$	1.93543	0.0713895
$736$	10.2405	0.377471
$737$	−11.8625	−0.436962
$738$	−0.718313	−0.0264415
$739$	50.0221	1.84009	0.920046	−	0.391810i	$-0.128151\pi$
$739$	50.0221	1.84009	0.920046	+	0.391810i	$0.128151\pi$
$740$	−12.8995	−0.474195
$741$	−13.1731	−0.483927
$742$	−0.322838	−0.0118518
$743$	17.2077	0.631290	0.315645	−	0.948877i	$-0.397779\pi$
$743$	17.2077	0.631290	0.315645	+	0.948877i	$0.397779\pi$
$744$	0.826873	0.0303146
$745$	−18.4478	−0.675875
$746$	−6.37206	−0.233298
$747$	−9.69774	−0.354822
$748$	42.6863	1.56077
$749$	15.0440	0.549696
$750$	3.07575	0.112310
$751$	−13.7735	−0.502602	−0.251301	−	0.967909i	$-0.580858\pi$
$751$	−13.7735	−0.502602	−0.251301	+	0.967909i	$0.580858\pi$
$752$	−13.2552	−0.483366
$753$	8.63734	0.314762
$754$	−4.33091	−0.157722
$755$	−36.6402	−1.33347
$756$	−1.93543	−0.0703910
$757$	5.99583	0.217922	0.108961	−	0.994046i	$-0.465248\pi$
$757$	5.99583	0.217922	0.108961	+	0.994046i	$0.465248\pi$
$758$	4.88833	0.177552
$759$	13.5798	0.492915
$760$	−4.48763	−0.162783
$761$	−45.0838	−1.63429	−0.817144	−	0.576434i	$-0.804444\pi$
$761$	−45.0838	−1.63429	−0.817144	+	0.576434i	$0.804444\pi$
$762$	−2.36160	−0.0855518
$763$	13.0880	0.473817
$764$	−1.93543	−0.0700215
$765$	11.0276	0.398703
$766$	0.275737	0.00996277
$767$	−59.5837	−2.15144
$768$	−11.0810	−0.399850
$769$	31.2489	1.12686	0.563432	−	0.826163i	$-0.309481\pi$
$769$	31.2489	1.12686	0.563432	+	0.826163i	$0.309481\pi$
$770$	−1.90368	−0.0686038
$771$	−14.5204	−0.522941
$772$	−38.1770	−1.37402
$773$	3.37490	0.121387	0.0606933	−	0.998156i	$-0.480669\pi$
$773$	3.37490	0.121387	0.0606933	+	0.998156i	$0.480669\pi$
$774$	−0.887271	−0.0318923
$775$	1.03698	0.0372495
$776$	−10.4548	−0.375306
$777$	−3.44364	−0.123540
$778$	1.51131	0.0541832
$779$	6.55458	0.234842
$780$	−21.2817	−0.762007
$781$	33.7745	1.20855
$782$	−5.07919	−0.181632
$783$	−3.00000	−0.107211
$784$	3.61676	0.129170
$785$	−2.60558	−0.0929973
$786$	2.45898	0.0877090
$787$	−1.01224	−0.0360824	−0.0180412	−	0.999837i	$-0.505743\pi$
$787$	−1.01224	−0.0360824	−0.0180412	+	0.999837i	$0.505743\pi$
$788$	13.7264	0.488982
$789$	12.3749	0.440558
$790$	4.02759	0.143295
$791$	−4.52461	−0.160877
$792$	3.87086	0.137545
$793$	13.5400	0.480818
$794$	−4.11690	−0.146103
$795$	−2.45898	−0.0872111
$796$	−16.5306	−0.585910
$797$	32.0039	1.13364	0.566818	−	0.823843i	$-0.308174\pi$
$797$	32.0039	1.13364	0.566818	+	0.823843i	$0.308174\pi$
$798$	−0.589178	−0.0208567
$799$	20.8818	0.738744
$800$	3.66075	0.129427
$801$	3.91903	0.138472
$802$	0.226517	0.00799858
$803$	21.5079	0.758999
$804$	−5.93126	−0.209180
$805$	−6.78989	−0.239312
$806$	1.19370	0.0420464
$807$	−9.26111	−0.326007
$808$	−0.854458	−0.0300597
$809$	6.40665	0.225246	0.112623	−	0.993638i	$-0.464075\pi$
$809$	6.40665	0.225246	0.112623	+	0.993638i	$0.464075\pi$
$810$	0.491797	0.0172800
$811$	3.55220	0.124734	0.0623672	−	0.998053i	$-0.480135\pi$
$811$	3.55220	0.124734	0.0623672	+	0.998053i	$0.480135\pi$
$812$	5.80630	0.203761
$813$	−2.12497	−0.0745258
$814$	3.38714	0.118719
$815$	−30.8339	−1.08006
$816$	20.6074	0.721402
$817$	8.09632	0.283254
$818$	−3.27991	−0.114679
$819$	−5.68133	−0.198522
$820$	10.5892	0.369790
$821$	13.8737	0.484196	0.242098	−	0.970252i	$-0.422165\pi$
$821$	13.8737	0.484196	0.242098	+	0.970252i	$0.422165\pi$
$822$	4.48763	0.156524
$823$	15.6126	0.544221	0.272110	−	0.962266i	$-0.412278\pi$
$823$	15.6126	0.544221	0.272110	+	0.962266i	$0.412278\pi$
$824$	0.491797	0.0171325
$825$	4.85446	0.169011
$826$	−2.66492	−0.0927246
$827$	31.0992	1.08142	0.540712	−	0.841208i	$-0.318155\pi$
$827$	31.0992	1.08142	0.540712	+	0.841208i	$0.318155\pi$
$828$	6.78989	0.235965
$829$	28.6137	0.993793	0.496897	−	0.867810i	$-0.334473\pi$
$829$	28.6137	0.993793	0.496897	+	0.867810i	$0.334473\pi$
$830$	−4.76931	−0.165545
$831$	−14.5522	−0.504810
$832$	−36.8820	−1.27865
$833$	−5.69774	−0.197415
$834$	3.17313	0.109876
$835$	−28.9599	−1.00220
$836$	−17.3710	−0.600789
$837$	0.826873	0.0285809
$838$	−0.394415	−0.0136249
$839$	4.67716	0.161474	0.0807368	−	0.996735i	$-0.474273\pi$
$839$	4.67716	0.161474	0.0807368	+	0.996735i	$0.474273\pi$
$840$	−1.93543	−0.0667788
$841$	−20.0000	−0.689655
$842$	−8.42128	−0.290216
$843$	−13.9641	−0.480948
$844$	−43.1166	−1.48414
$845$	−37.3103	−1.28351
$846$	0.931263	0.0320175
$847$	−3.98359	−0.136878
$848$	−4.59513	−0.157797
$849$	−8.00000	−0.274559
$850$	−1.81569	−0.0622778
$851$	12.0810	0.414130
$852$	16.8873	0.578548
$853$	−21.9341	−0.751009	−0.375505	−	0.926820i	$-0.622531\pi$
$853$	−21.9341	−0.751009	−0.375505	+	0.926820i	$0.622531\pi$
$854$	0.605585	0.0207227
$855$	−4.48763	−0.153474
$856$	−15.0440	−0.514193
$857$	−42.8807	−1.46478	−0.732389	−	0.680887i	$-0.761595\pi$
$857$	−42.8807	−1.46478	−0.732389	+	0.680887i	$0.761595\pi$
$858$	5.58812	0.190775
$859$	−29.7159	−1.01389	−0.506947	−	0.861977i	$-0.669226\pi$
$859$	−29.7159	−1.01389	−0.506947	+	0.861977i	$0.669226\pi$
$860$	13.0799	0.446021
$861$	2.82687	0.0963396
$862$	10.5058	0.357829
$863$	24.4548	0.832452	0.416226	−	0.909261i	$-0.363353\pi$
$863$	24.4548	0.832452	0.416226	+	0.909261i	$0.363353\pi$
$864$	2.91903	0.0993073
$865$	47.4874	1.61462
$866$	−0.961236	−0.0326641
$867$	−15.4642	−0.525192
$868$	−1.60036	−0.0543196
$869$	31.7006	1.07537
$870$	−1.47539	−0.0500204
$871$	−17.4108	−0.589943
$872$	−13.0880	−0.443215
$873$	−10.4548	−0.353842
$874$	2.06696	0.0699158
$875$	−12.1044	−0.409203
$876$	10.7540	0.363343
$877$	−17.4559	−0.589443	−0.294721	−	0.955583i	$-0.595227\pi$
$877$	−17.4559	−0.589443	−0.294721	+	0.955583i	$0.595227\pi$
$878$	−2.48373	−0.0838218
$879$	−8.46421	−0.285491
$880$	−27.0961	−0.913408
$881$	49.4915	1.66741	0.833706	−	0.552209i	$-0.186215\pi$
$881$	49.4915	1.66741	0.833706	+	0.552209i	$0.186215\pi$
$882$	−0.254102	−0.00855605
$883$	−21.5327	−0.724632	−0.362316	−	0.932055i	$-0.618014\pi$
$883$	−21.5327	−0.724632	−0.362316	+	0.932055i	$0.618014\pi$
$884$	62.6514	2.10719
$885$	−20.2981	−0.682313
$886$	−6.02369	−0.202370
$887$	−39.2775	−1.31881	−0.659405	−	0.751788i	$-0.729192\pi$
$887$	−39.2775	−1.31881	−0.659405	+	0.751788i	$0.729192\pi$
$888$	3.44364	0.115561
$889$	9.29392	0.311708
$890$	1.92736	0.0646054
$891$	3.87086	0.129679
$892$	−14.0716	−0.471151
$893$	−8.49775	−0.284366
$894$	2.42200	0.0810038
$895$	−17.5439	−0.586426
$896$	−7.48763	−0.250144
$897$	19.9313	0.665486
$898$	2.82164	0.0941595
$899$	−2.48062	−0.0827332
$900$	2.42723	0.0809076
$901$	7.23902	0.241167
$902$	−2.78049	−0.0925803
$903$	3.49180	0.116200
$904$	4.52461	0.150486
$905$	7.49987	0.249304
$906$	4.81047	0.159817
$907$	4.21295	0.139889	0.0699444	−	0.997551i	$-0.477718\pi$
$907$	4.21295	0.139889	0.0699444	+	0.997551i	$0.477718\pi$
$908$	9.26244	0.307385
$909$	−0.854458	−0.0283406
$910$	−2.79406	−0.0926222
$911$	27.5428	0.912534	0.456267	−	0.889843i	$-0.349186\pi$
$911$	27.5428	0.912534	0.456267	+	0.889843i	$0.349186\pi$
$912$	−8.38608	−0.277691
$913$	−37.5386	−1.24235
$914$	−9.11557	−0.301516
$915$	4.61259	0.152488
$916$	9.94066	0.328449
$917$	−9.67716	−0.319568
$918$	−1.44780	−0.0477847
$919$	55.8584	1.84260	0.921299	−	0.388856i	$-0.127130\pi$
$919$	55.8584	1.84260	0.921299	+	0.388856i	$0.127130\pi$
$920$	6.78989	0.223856
$921$	20.5275	0.676402
$922$	−5.73260	−0.188793
$923$	49.5714	1.63166
$924$	−7.49180	−0.246462
$925$	4.31867	0.141997
$926$	4.72354	0.155225
$927$	0.491797	0.0161527
$928$	−8.75708	−0.287465
$929$	−0.409763	−0.0134439	−0.00672194	−	0.999977i	$-0.502140\pi$
$929$	−0.409763	−0.0134439	−0.00672194	+	0.999977i	$0.502140\pi$
$930$	0.406653	0.0133347
$931$	2.31867	0.0759913
$932$	−47.8224	−1.56648
$933$	12.3103	0.403022
$934$	−2.29597	−0.0751266
$935$	42.6863	1.39599
$936$	5.68133	0.185700
$937$	26.9149	0.879270	0.439635	−	0.898177i	$-0.355108\pi$
$937$	26.9149	0.879270	0.439635	+	0.898177i	$0.355108\pi$
$938$	−0.778712	−0.0254258
$939$	25.5686	0.834400
$940$	−13.7284	−0.447772
$941$	−23.1979	−0.756229	−0.378115	−	0.925759i	$-0.623427\pi$
$941$	−23.1979	−0.756229	−0.378115	+	0.925759i	$0.623427\pi$
$942$	0.342086	0.0111457
$943$	−9.91724	−0.322950
$944$	−37.9313	−1.23456
$945$	−1.93543	−0.0629596
$946$	−3.43451	−0.111665
$947$	−6.05206	−0.196666	−0.0983328	−	0.995154i	$-0.531351\pi$
$947$	−6.05206	−0.196666	−0.0983328	+	0.995154i	$0.531351\pi$
$948$	15.8503	0.514793
$949$	31.5675	1.02473
$950$	0.738889	0.0239727
$951$	31.3861	1.01776
$952$	5.69774	0.184665
$953$	29.4600	0.954304	0.477152	−	0.878821i	$-0.341669\pi$
$953$	29.4600	0.954304	0.477152	+	0.878821i	$0.341669\pi$
$954$	0.322838	0.0104523
$955$	−1.93543	−0.0626291
$956$	0.773483	0.0250162
$957$	−11.6126	−0.375382
$958$	−5.30749	−0.171477
$959$	−17.6608	−0.570296
$960$	−12.5644	−0.405515
$961$	−30.3163	−0.977945
$962$	4.97136	0.160283
$963$	−15.0440	−0.484786
$964$	28.2499	0.909869
$965$	−38.1770	−1.22896
$966$	0.891440	0.0286816
$967$	−3.75530	−0.120762	−0.0603811	−	0.998175i	$-0.519232\pi$
$967$	−3.75530	−0.120762	−0.0603811	+	0.998175i	$0.519232\pi$
$968$	3.98359	0.128038
$969$	13.2112	0.424404
$970$	−5.14164	−0.165088
$971$	−16.4600	−0.528228	−0.264114	−	0.964491i	$-0.585080\pi$
$971$	−16.4600	−0.528228	−0.264114	+	0.964491i	$0.585080\pi$
$972$	1.93543	0.0620790
$973$	−12.4876	−0.400335
$974$	2.07396	0.0664541
$975$	7.12497	0.228182
$976$	8.61960	0.275907
$977$	40.5878	1.29852	0.649260	−	0.760566i	$-0.275079\pi$
$977$	40.5878	1.29852	0.649260	+	0.760566i	$0.275079\pi$
$978$	4.04816	0.129446
$979$	15.1700	0.484836
$980$	3.74590	0.119658
$981$	−13.0880	−0.417867
$982$	4.78155	0.152585
$983$	−0.858627	−0.0273859	−0.0136930	−	0.999906i	$-0.504359\pi$
$983$	−0.858627	−0.0273859	−0.0136930	+	0.999906i	$0.504359\pi$
$984$	−2.82687	−0.0901174
$985$	13.7264	0.437359
$986$	4.34341	0.138322
$987$	−3.66492	−0.116656
$988$	−25.4957	−0.811126
$989$	−12.2499	−0.389525
$990$	1.90368	0.0605029
$991$	−12.8185	−0.407194	−0.203597	−	0.979055i	$-0.565263\pi$
$991$	−12.8185	−0.407194	−0.203597	+	0.979055i	$0.565263\pi$
$992$	2.41366	0.0766339
$993$	−25.3749	−0.805248
$994$	2.21712	0.0703228
$995$	−16.5306	−0.524054
$996$	−18.7693	−0.594728
$997$	6.49180	0.205597	0.102799	−	0.994702i	$-0.467220\pi$
$997$	6.49180	0.205597	0.102799	+	0.994702i	$0.467220\pi$
$998$	−5.90156	−0.186811
$999$	3.44364	0.108952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.e.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.e.1.2	✓	3	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.254102 q^{2} -1.00000 q^{3} -1.93543 q^{4} -1.93543 q^{5} +0.254102 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.254102 q^{2} -1.00000 q^{3} -1.93543 q^{4} -1.93543 q^{5} +0.254102 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.491797 q^{10} +3.87086 q^{11} +1.93543 q^{12} +5.68133 q^{13} +0.254102 q^{14} +1.93543 q^{15} +3.61676 q^{16} -5.69774 q^{17} -0.254102 q^{18} +2.31867 q^{19} +3.74590 q^{20} +1.00000 q^{21} -0.983593 q^{22} -3.50820 q^{23} -1.00000 q^{24} -1.25410 q^{25} -1.44364 q^{26} -1.00000 q^{27} +1.93543 q^{28} +3.00000 q^{29} -0.491797 q^{30} -0.826873 q^{31} -2.91903 q^{32} -3.87086 q^{33} +1.44780 q^{34} +1.93543 q^{35} -1.93543 q^{36} -3.44364 q^{37} -0.589178 q^{38} -5.68133 q^{39} -1.93543 q^{40} +2.82687 q^{41} -0.254102 q^{42} +3.49180 q^{43} -7.49180 q^{44} -1.93543 q^{45} +0.891440 q^{46} -3.66492 q^{47} -3.61676 q^{48} +1.00000 q^{49} +0.318669 q^{50} +5.69774 q^{51} -10.9958 q^{52} -1.27051 q^{53} +0.254102 q^{54} -7.49180 q^{55} -1.00000 q^{56} -2.31867 q^{57} -0.762305 q^{58} -10.4876 q^{59} -3.74590 q^{60} +2.38324 q^{61} +0.210110 q^{62} -1.00000 q^{63} -6.49180 q^{64} -10.9958 q^{65} +0.983593 q^{66} -3.06457 q^{67} +11.0276 q^{68} +3.50820 q^{69} -0.491797 q^{70} +8.72532 q^{71} +1.00000 q^{72} +5.55636 q^{73} +0.875034 q^{74} +1.25410 q^{75} -4.48763 q^{76} -3.87086 q^{77} +1.44364 q^{78} +8.18953 q^{79} -7.00000 q^{80} +1.00000 q^{81} -0.718313 q^{82} -9.69774 q^{83} -1.93543 q^{84} +11.0276 q^{85} -0.887271 q^{86} -3.00000 q^{87} +3.87086 q^{88} +3.91903 q^{89} +0.491797 q^{90} -5.68133 q^{91} +6.78989 q^{92} +0.826873 q^{93} +0.931263 q^{94} -4.48763 q^{95} +2.91903 q^{96} -10.4548 q^{97} -0.254102 q^{98} +3.87086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 2 q^{15} - 4 q^{16} - 7 q^{17} + 14 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 5 q^{26} - 3 q^{27} - 2 q^{28} + 9 q^{29} - 3 q^{30} - 8 q^{31} - 4 q^{32} + 4 q^{33} + 27 q^{34} - 2 q^{35} + 2 q^{36} - q^{37} - 5 q^{38} - 10 q^{39} + 2 q^{40} + 14 q^{41} + 12 q^{43} - 24 q^{44} + 2 q^{45} + 16 q^{46} - 7 q^{47} + 4 q^{48} + 3 q^{49} + 8 q^{50} + 7 q^{51} - q^{52} - 24 q^{55} - 3 q^{56} - 14 q^{57} - q^{59} - 12 q^{60} + 22 q^{61} + 21 q^{62} - 3 q^{63} - 21 q^{64} - q^{65} + 6 q^{66} - 17 q^{67} + 15 q^{68} + 9 q^{69} - 3 q^{70} - 2 q^{71} + 3 q^{72} + 26 q^{73} + 19 q^{74} + 3 q^{75} + 17 q^{76} + 4 q^{77} - 5 q^{78} + 16 q^{79} - 21 q^{80} + 3 q^{81} - 21 q^{82} - 19 q^{83} + 2 q^{84} + 15 q^{85} + 16 q^{86} - 9 q^{87} - 4 q^{88} + 7 q^{89} + 3 q^{90} - 10 q^{91} + 8 q^{93} - 37 q^{94} + 17 q^{95} + 4 q^{96} - 7 q^{97} - 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 2 * q^15 - 4 * q^16 - 7 * q^17 + 14 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 5 * q^26 - 3 * q^27 - 2 * q^28 + 9 * q^29 - 3 * q^30 - 8 * q^31 - 4 * q^32 + 4 * q^33 + 27 * q^34 - 2 * q^35 + 2 * q^36 - q^37 - 5 * q^38 - 10 * q^39 + 2 * q^40 + 14 * q^41 + 12 * q^43 - 24 * q^44 + 2 * q^45 + 16 * q^46 - 7 * q^47 + 4 * q^48 + 3 * q^49 + 8 * q^50 + 7 * q^51 - q^52 - 24 * q^55 - 3 * q^56 - 14 * q^57 - q^59 - 12 * q^60 + 22 * q^61 + 21 * q^62 - 3 * q^63 - 21 * q^64 - q^65 + 6 * q^66 - 17 * q^67 + 15 * q^68 + 9 * q^69 - 3 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 19 * q^74 + 3 * q^75 + 17 * q^76 + 4 * q^77 - 5 * q^78 + 16 * q^79 - 21 * q^80 + 3 * q^81 - 21 * q^82 - 19 * q^83 + 2 * q^84 + 15 * q^85 + 16 * q^86 - 9 * q^87 - 4 * q^88 + 7 * q^89 + 3 * q^90 - 10 * q^91 + 8 * q^93 - 37 * q^94 + 17 * q^95 + 4 * q^96 - 7 * q^97 - 4 * q^99

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