LMFDB - Embedded newform 6041.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71484 q^{2} +1.06768 q^{3} +5.37033 q^{4} +2.50113 q^{5} -2.89858 q^{6} -1.00000 q^{7} -9.14989 q^{8} -1.86006 q^{9} +O(q^{10})$	\(q-2.71484 q^{2} +1.06768 q^{3} +5.37033 q^{4} +2.50113 q^{5} -2.89858 q^{6} -1.00000 q^{7} -9.14989 q^{8} -1.86006 q^{9} -6.79016 q^{10} -2.18966 q^{11} +5.73380 q^{12} -0.421123 q^{13} +2.71484 q^{14} +2.67041 q^{15} +14.0998 q^{16} +5.68970 q^{17} +5.04975 q^{18} -2.04217 q^{19} +13.4319 q^{20} -1.06768 q^{21} +5.94457 q^{22} -1.82469 q^{23} -9.76916 q^{24} +1.25566 q^{25} +1.14328 q^{26} -5.18899 q^{27} -5.37033 q^{28} +3.44345 q^{29} -7.24972 q^{30} -1.99809 q^{31} -19.9788 q^{32} -2.33786 q^{33} -15.4466 q^{34} -2.50113 q^{35} -9.98913 q^{36} +4.47567 q^{37} +5.54417 q^{38} -0.449625 q^{39} -22.8851 q^{40} +2.06227 q^{41} +2.89858 q^{42} -1.20849 q^{43} -11.7592 q^{44} -4.65225 q^{45} +4.95374 q^{46} -6.44408 q^{47} +15.0541 q^{48} +1.00000 q^{49} -3.40890 q^{50} +6.07478 q^{51} -2.26157 q^{52} -9.57258 q^{53} +14.0873 q^{54} -5.47663 q^{55} +9.14989 q^{56} -2.18039 q^{57} -9.34840 q^{58} +3.26018 q^{59} +14.3410 q^{60} -8.20107 q^{61} +5.42448 q^{62} +1.86006 q^{63} +26.0396 q^{64} -1.05328 q^{65} +6.34690 q^{66} +7.81360 q^{67} +30.5555 q^{68} -1.94819 q^{69} +6.79016 q^{70} -3.28979 q^{71} +17.0193 q^{72} +10.0602 q^{73} -12.1507 q^{74} +1.34064 q^{75} -10.9671 q^{76} +2.18966 q^{77} +1.22066 q^{78} +0.512133 q^{79} +35.2654 q^{80} +0.0399948 q^{81} -5.59872 q^{82} -6.84734 q^{83} -5.73380 q^{84} +14.2307 q^{85} +3.28085 q^{86} +3.67650 q^{87} +20.0352 q^{88} +3.99073 q^{89} +12.6301 q^{90} +0.421123 q^{91} -9.79921 q^{92} -2.13332 q^{93} +17.4946 q^{94} -5.10774 q^{95} -21.3310 q^{96} -2.55471 q^{97} -2.71484 q^{98} +4.07290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.71484	−1.91968	−0.959839	−	0.280551i	$-0.909483\pi$
$2$	−2.71484	−1.91968	−0.959839	+	0.280551i	$0.909483\pi$
$3$	1.06768	0.616426	0.308213	−	0.951317i	$-0.400269\pi$
$3$	1.06768	0.616426	0.308213	+	0.951317i	$0.400269\pi$
$4$	5.37033	2.68517
$5$	2.50113	1.11854	0.559270	−	0.828986i	$-0.311082\pi$
$5$	2.50113	1.11854	0.559270	+	0.828986i	$0.311082\pi$
$6$	−2.89858	−1.18334
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−9.14989	−3.23498
$9$	−1.86006	−0.620020
$10$	−6.79016	−2.14724
$11$	−2.18966	−0.660208	−0.330104	−	0.943945i	$-0.607084\pi$
$11$	−2.18966	−0.660208	−0.330104	+	0.943945i	$0.607084\pi$
$12$	5.73380	1.65520
$13$	−0.421123	−0.116799	−0.0583993	−	0.998293i	$-0.518600\pi$
$13$	−0.421123	−0.116799	−0.0583993	+	0.998293i	$0.518600\pi$
$14$	2.71484	0.725570
$15$	2.67041	0.689496
$16$	14.0998	3.52495
$17$	5.68970	1.37995	0.689977	−	0.723831i	$-0.257621\pi$
$17$	5.68970	1.37995	0.689977	+	0.723831i	$0.257621\pi$
$18$	5.04975	1.19024
$19$	−2.04217	−0.468507	−0.234253	−	0.972176i	$-0.575265\pi$
$19$	−2.04217	−0.468507	−0.234253	+	0.972176i	$0.575265\pi$
$20$	13.4319	3.00346
$21$	−1.06768	−0.232987
$22$	5.94457	1.26739
$23$	−1.82469	−0.380475	−0.190238	−	0.981738i	$-0.560926\pi$
$23$	−1.82469	−0.380475	−0.190238	+	0.981738i	$0.560926\pi$
$24$	−9.76916	−1.99412
$25$	1.25566	0.251131
$26$	1.14328	0.224216
$27$	−5.18899	−0.998621
$28$	−5.37033	−1.01490
$29$	3.44345	0.639432	0.319716	−	0.947513i	$-0.396412\pi$
$29$	3.44345	0.639432	0.319716	+	0.947513i	$0.396412\pi$
$30$	−7.24972	−1.32361
$31$	−1.99809	−0.358868	−0.179434	−	0.983770i	$-0.557427\pi$
$31$	−1.99809	−0.358868	−0.179434	+	0.983770i	$0.557427\pi$
$32$	−19.9788	−3.53179
$33$	−2.33786	−0.406969
$34$	−15.4466	−2.64907
$35$	−2.50113	−0.422768
$36$	−9.98913	−1.66486
$37$	4.47567	0.735796	0.367898	−	0.929866i	$-0.380078\pi$
$37$	4.47567	0.735796	0.367898	+	0.929866i	$0.380078\pi$
$38$	5.54417	0.899382
$39$	−0.449625	−0.0719976
$40$	−22.8851	−3.61845
$41$	2.06227	0.322073	0.161036	−	0.986948i	$-0.448516\pi$
$41$	2.06227	0.322073	0.161036	+	0.986948i	$0.448516\pi$
$42$	2.89858	0.447260
$43$	−1.20849	−0.184293	−0.0921464	−	0.995745i	$-0.529373\pi$
$43$	−1.20849	−0.184293	−0.0921464	+	0.995745i	$0.529373\pi$
$44$	−11.7592	−1.77277
$45$	−4.65225	−0.693517
$46$	4.95374	0.730390
$47$	−6.44408	−0.939966	−0.469983	−	0.882675i	$-0.655740\pi$
$47$	−6.44408	−0.939966	−0.469983	+	0.882675i	$0.655740\pi$
$48$	15.0541	2.17287
$49$	1.00000	0.142857
$50$	−3.40890	−0.482091
$51$	6.07478	0.850639
$52$	−2.26157	−0.313623
$53$	−9.57258	−1.31490	−0.657448	−	0.753500i	$-0.728364\pi$
$53$	−9.57258	−1.31490	−0.657448	+	0.753500i	$0.728364\pi$
$54$	14.0873	1.91703
$55$	−5.47663	−0.738469
$56$	9.14989	1.22271
$57$	−2.18039	−0.288800
$58$	−9.34840	−1.22750
$59$	3.26018	0.424439	0.212220	−	0.977222i	$-0.431931\pi$
$59$	3.26018	0.424439	0.212220	+	0.977222i	$0.431931\pi$
$60$	14.3410	1.85141
$61$	−8.20107	−1.05004	−0.525020	−	0.851090i	$-0.675942\pi$
$61$	−8.20107	−1.05004	−0.525020	+	0.851090i	$0.675942\pi$
$62$	5.42448	0.688910
$63$	1.86006	0.234345
$64$	26.0396	3.25495
$65$	−1.05328	−0.130644
$66$	6.34690	0.781250
$67$	7.81360	0.954584	0.477292	−	0.878745i	$-0.341618\pi$
$67$	7.81360	0.954584	0.477292	+	0.878745i	$0.341618\pi$
$68$	30.5555	3.70540
$69$	−1.94819	−0.234535
$70$	6.79016	0.811579
$71$	−3.28979	−0.390426	−0.195213	−	0.980761i	$-0.562540\pi$
$71$	−3.28979	−0.390426	−0.195213	+	0.980761i	$0.562540\pi$
$72$	17.0193	2.00575
$73$	10.0602	1.17746	0.588730	−	0.808329i	$-0.299628\pi$
$73$	10.0602	1.17746	0.588730	+	0.808329i	$0.299628\pi$
$74$	−12.1507	−1.41249
$75$	1.34064	0.154804
$76$	−10.9671	−1.25802
$77$	2.18966	0.249535
$78$	1.22066	0.138212
$79$	0.512133	0.0576195	0.0288097	−	0.999585i	$-0.490828\pi$
$79$	0.512133	0.0576195	0.0288097	+	0.999585i	$0.490828\pi$
$80$	35.2654	3.94279
$81$	0.0399948	0.00444387
$82$	−5.59872	−0.618276
$83$	−6.84734	−0.751593	−0.375797	−	0.926702i	$-0.622631\pi$
$83$	−6.84734	−0.751593	−0.375797	+	0.926702i	$0.622631\pi$
$84$	−5.73380	−0.625608
$85$	14.2307	1.54353
$86$	3.28085	0.353783
$87$	3.67650	0.394162
$88$	20.0352	2.13576
$89$	3.99073	0.423017	0.211508	−	0.977376i	$-0.432162\pi$
$89$	3.99073	0.423017	0.211508	+	0.977376i	$0.432162\pi$
$90$	12.6301	1.33133
$91$	0.421123	0.0441457
$92$	−9.79921	−1.02164
$93$	−2.13332	−0.221215
$94$	17.4946	1.80443
$95$	−5.10774	−0.524044
$96$	−21.3310	−2.17709
$97$	−2.55471	−0.259392	−0.129696	−	0.991554i	$-0.541400\pi$
$97$	−2.55471	−0.259392	−0.129696	+	0.991554i	$0.541400\pi$
$98$	−2.71484	−0.274240
$99$	4.07290	0.409342
$100$	6.74329	0.674329
$101$	9.30158	0.925542	0.462771	−	0.886478i	$-0.346855\pi$
$101$	9.30158	0.925542	0.462771	+	0.886478i	$0.346855\pi$
$102$	−16.4920	−1.63295
$103$	−10.2860	−1.01351	−0.506753	−	0.862092i	$-0.669154\pi$
$103$	−10.2860	−1.01351	−0.506753	+	0.862092i	$0.669154\pi$
$104$	3.85323	0.377840
$105$	−2.67041	−0.260605
$106$	25.9880	2.52418
$107$	3.76785	0.364252	0.182126	−	0.983275i	$-0.441702\pi$
$107$	3.76785	0.364252	0.182126	+	0.983275i	$0.441702\pi$
$108$	−27.8666	−2.68146
$109$	−4.38678	−0.420178	−0.210089	−	0.977682i	$-0.567375\pi$
$109$	−4.38678	−0.420178	−0.210089	+	0.977682i	$0.567375\pi$
$110$	14.8682	1.41762
$111$	4.77858	0.453563
$112$	−14.0998	−1.33230
$113$	0.886561	0.0834006	0.0417003	−	0.999130i	$-0.486723\pi$
$113$	0.886561	0.0834006	0.0417003	+	0.999130i	$0.486723\pi$
$114$	5.91940	0.554402
$115$	−4.56380	−0.425576
$116$	18.4925	1.71698
$117$	0.783314	0.0724174
$118$	−8.85085	−0.814787
$119$	−5.68970	−0.521573
$120$	−24.4339	−2.23050
$121$	−6.20538	−0.564125
$122$	22.2646	2.01574
$123$	2.20185	0.198534
$124$	−10.7304	−0.963619
$125$	−9.36510	−0.837640
$126$	−5.04975	−0.449868
$127$	−2.48338	−0.220365	−0.110182	−	0.993911i	$-0.535143\pi$
$127$	−2.48338	−0.220365	−0.110182	+	0.993911i	$0.535143\pi$
$128$	−30.7357	−2.71667
$129$	−1.29028	−0.113603
$130$	2.85949	0.250794
$131$	−3.50809	−0.306503	−0.153252	−	0.988187i	$-0.548974\pi$
$131$	−3.50809	−0.306503	−0.153252	+	0.988187i	$0.548974\pi$
$132$	−12.5551	−1.09278
$133$	2.04217	0.177079
$134$	−21.2126	−1.83249
$135$	−12.9783	−1.11700
$136$	−52.0601	−4.46412
$137$	14.3027	1.22196	0.610981	−	0.791645i	$-0.290775\pi$
$137$	14.3027	1.22196	0.610981	+	0.791645i	$0.290775\pi$
$138$	5.28902	0.450231
$139$	−6.53650	−0.554419	−0.277209	−	0.960810i	$-0.589410\pi$
$139$	−6.53650	−0.554419	−0.277209	+	0.960810i	$0.589410\pi$
$140$	−13.4319	−1.13520
$141$	−6.88022	−0.579419
$142$	8.93123	0.749492
$143$	0.922117	0.0771113
$144$	−26.2264	−2.18554
$145$	8.61252	0.715231
$146$	−27.3119	−2.26035
$147$	1.06768	0.0880608
$148$	24.0358	1.97573
$149$	0.211359	0.0173152	0.00865762	−	0.999963i	$-0.497244\pi$
$149$	0.211359	0.0173152	0.00865762	+	0.999963i	$0.497244\pi$
$150$	−3.63961	−0.297173
$151$	−13.0408	−1.06124	−0.530621	−	0.847609i	$-0.678041\pi$
$151$	−13.0408	−1.06124	−0.530621	+	0.847609i	$0.678041\pi$
$152$	18.6857	1.51561
$153$	−10.5832	−0.855598
$154$	−5.94457	−0.479027
$155$	−4.99748	−0.401408
$156$	−2.41463	−0.193325
$157$	−20.0071	−1.59674	−0.798370	−	0.602168i	$-0.794304\pi$
$157$	−20.0071	−1.59674	−0.798370	+	0.602168i	$0.794304\pi$
$158$	−1.39036	−0.110611
$159$	−10.2205	−0.810535
$160$	−49.9696	−3.95045
$161$	1.82469	0.143806
$162$	−0.108579	−0.00853079
$163$	−6.17486	−0.483652	−0.241826	−	0.970320i	$-0.577746\pi$
$163$	−6.17486	−0.483652	−0.241826	+	0.970320i	$0.577746\pi$
$164$	11.0751	0.864818
$165$	−5.84729	−0.455211
$166$	18.5894	1.44282
$167$	−6.27989	−0.485952	−0.242976	−	0.970032i	$-0.578124\pi$
$167$	−6.27989	−0.485952	−0.242976	+	0.970032i	$0.578124\pi$
$168$	9.76916	0.753707
$169$	−12.8227	−0.986358
$170$	−38.6339	−2.96309
$171$	3.79856	0.290483
$172$	−6.48999	−0.494857
$173$	−14.8210	−1.12682	−0.563411	−	0.826177i	$-0.690511\pi$
$173$	−14.8210	−1.12682	−0.563411	+	0.826177i	$0.690511\pi$
$174$	−9.98110	−0.756665
$175$	−1.25566	−0.0949186
$176$	−30.8738	−2.32720
$177$	3.48083	0.261635
$178$	−10.8342	−0.812056
$179$	−2.69670	−0.201561	−0.100780	−	0.994909i	$-0.532134\pi$
$179$	−2.69670	−0.201561	−0.100780	+	0.994909i	$0.532134\pi$
$180$	−24.9841	−1.86221
$181$	−14.7844	−1.09892	−0.549458	−	0.835521i	$-0.685166\pi$
$181$	−14.7844	−1.09892	−0.549458	+	0.835521i	$0.685166\pi$
$182$	−1.14328	−0.0847455
$183$	−8.75612	−0.647271
$184$	16.6958	1.23083
$185$	11.1942	0.823017
$186$	5.79162	0.424662
$187$	−12.4585	−0.911056
$188$	−34.6069	−2.52396
$189$	5.18899	0.377443
$190$	13.8667	1.00600
$191$	−9.73159	−0.704153	−0.352077	−	0.935971i	$-0.614524\pi$
$191$	−9.73159	−0.704153	−0.352077	+	0.935971i	$0.614524\pi$
$192$	27.8020	2.00644
$193$	−20.0003	−1.43965	−0.719827	−	0.694153i	$-0.755779\pi$
$193$	−20.0003	−1.43965	−0.719827	+	0.694153i	$0.755779\pi$
$194$	6.93562	0.497948
$195$	−1.12457	−0.0805322
$196$	5.37033	0.383595
$197$	22.1390	1.57734	0.788669	−	0.614819i	$-0.210771\pi$
$197$	22.1390	1.57734	0.788669	+	0.614819i	$0.210771\pi$
$198$	−11.0573	−0.785805
$199$	11.7170	0.830598	0.415299	−	0.909685i	$-0.363677\pi$
$199$	11.7170	0.830598	0.415299	+	0.909685i	$0.363677\pi$
$200$	−11.4891	−0.812403
$201$	8.34243	0.588430
$202$	−25.2523	−1.77674
$203$	−3.44345	−0.241683
$204$	32.6236	2.28411
$205$	5.15801	0.360251
$206$	27.9247	1.94560
$207$	3.39404	0.235902
$208$	−5.93775	−0.411709
$209$	4.47167	0.309312
$210$	7.24972	0.500278
$211$	0.705406	0.0485622	0.0242811	−	0.999705i	$-0.492270\pi$
$211$	0.705406	0.0485622	0.0242811	+	0.999705i	$0.492270\pi$
$212$	−51.4079	−3.53071
$213$	−3.51244	−0.240668
$214$	−10.2291	−0.699246
$215$	−3.02259	−0.206139
$216$	47.4787	3.23052
$217$	1.99809	0.135639
$218$	11.9094	0.806606
$219$	10.7411	0.725817
$220$	−29.4113	−1.98291
$221$	−2.39606	−0.161177
$222$	−12.9731	−0.870695
$223$	−20.7782	−1.39141	−0.695705	−	0.718328i	$-0.744908\pi$
$223$	−20.7782	−1.39141	−0.695705	+	0.718328i	$0.744908\pi$
$224$	19.9788	1.33489
$225$	−2.33559	−0.155706
$226$	−2.40687	−0.160102
$227$	12.9427	0.859040	0.429520	−	0.903057i	$-0.358683\pi$
$227$	12.9427	0.859040	0.429520	+	0.903057i	$0.358683\pi$
$228$	−11.7094	−0.775475
$229$	−19.2138	−1.26968	−0.634842	−	0.772642i	$-0.718935\pi$
$229$	−19.2138	−1.26968	−0.634842	+	0.772642i	$0.718935\pi$
$230$	12.3900	0.816970
$231$	2.33786	0.153820
$232$	−31.5072	−2.06855
$233$	13.8390	0.906622	0.453311	−	0.891352i	$-0.350243\pi$
$233$	13.8390	0.906622	0.453311	+	0.891352i	$0.350243\pi$
$234$	−2.12657	−0.139018
$235$	−16.1175	−1.05139
$236$	17.5082	1.13969
$237$	0.546794	0.0355181
$238$	15.4466	1.00125
$239$	−21.4520	−1.38762	−0.693808	−	0.720160i	$-0.744069\pi$
$239$	−21.4520	−1.38762	−0.693808	+	0.720160i	$0.744069\pi$
$240$	37.6522	2.43044
$241$	1.71676	0.110586	0.0552932	−	0.998470i	$-0.482391\pi$
$241$	1.71676	0.110586	0.0552932	+	0.998470i	$0.482391\pi$
$242$	16.8466	1.08294
$243$	15.6097	1.00136
$244$	−44.0425	−2.81953
$245$	2.50113	0.159791
$246$	−5.97765	−0.381121
$247$	0.860007	0.0547209
$248$	18.2823	1.16093
$249$	−7.31077	−0.463301
$250$	25.4247	1.60800
$251$	−17.4367	−1.10059	−0.550296	−	0.834970i	$-0.685485\pi$
$251$	−17.4367	−1.10059	−0.550296	+	0.834970i	$0.685485\pi$
$252$	9.98913	0.629256
$253$	3.99546	0.251193
$254$	6.74197	0.423029
$255$	15.1938	0.951473
$256$	31.3630	1.96019
$257$	24.6015	1.53460	0.767300	−	0.641288i	$-0.221600\pi$
$257$	24.6015	1.53460	0.767300	+	0.641288i	$0.221600\pi$
$258$	3.50290	0.218081
$259$	−4.47567	−0.278105
$260$	−5.65648	−0.350800
$261$	−6.40502	−0.396461
$262$	9.52388	0.588387
$263$	−3.44592	−0.212485	−0.106242	−	0.994340i	$-0.533882\pi$
$263$	−3.44592	−0.212485	−0.106242	+	0.994340i	$0.533882\pi$
$264$	21.3912	1.31653
$265$	−23.9423	−1.47076
$266$	−5.54417	−0.339935
$267$	4.26082	0.260758
$268$	41.9616	2.56321
$269$	23.4845	1.43188	0.715938	−	0.698164i	$-0.245999\pi$
$269$	23.4845	1.43188	0.715938	+	0.698164i	$0.245999\pi$
$270$	35.2341	2.14428
$271$	−3.71535	−0.225691	−0.112846	−	0.993613i	$-0.535997\pi$
$271$	−3.71535	−0.225691	−0.112846	+	0.993613i	$0.535997\pi$
$272$	80.2235	4.86426
$273$	0.449625	0.0272125
$274$	−38.8295	−2.34577
$275$	−2.74946	−0.165799
$276$	−10.4624	−0.629764
$277$	2.61147	0.156908	0.0784540	−	0.996918i	$-0.475002\pi$
$277$	2.61147	0.156908	0.0784540	+	0.996918i	$0.475002\pi$
$278$	17.7455	1.06431
$279$	3.71656	0.222505
$280$	22.8851	1.36765
$281$	4.83579	0.288479	0.144239	−	0.989543i	$-0.453926\pi$
$281$	4.83579	0.288479	0.144239	+	0.989543i	$0.453926\pi$
$282$	18.6787	1.11230
$283$	−11.9352	−0.709476	−0.354738	−	0.934966i	$-0.615430\pi$
$283$	−11.9352	−0.709476	−0.354738	+	0.934966i	$0.615430\pi$
$284$	−17.6672	−1.04836
$285$	−5.45344	−0.323034
$286$	−2.50340	−0.148029
$287$	−2.06227	−0.121732
$288$	37.1618	2.18978
$289$	15.3726	0.904272
$290$	−23.3816	−1.37301
$291$	−2.72761	−0.159896
$292$	54.0268	3.16168
$293$	−1.02603	−0.0599414	−0.0299707	−	0.999551i	$-0.509541\pi$
$293$	−1.02603	−0.0599414	−0.0299707	+	0.999551i	$0.509541\pi$
$294$	−2.89858	−0.169048
$295$	8.15413	0.474752
$296$	−40.9519	−2.38028
$297$	11.3621	0.659298
$298$	−0.573806	−0.0332397
$299$	0.768421	0.0444389
$300$	7.19967	0.415673
$301$	1.20849	0.0696561
$302$	35.4035	2.03724
$303$	9.93112	0.570528
$304$	−28.7942	−1.65146
$305$	−20.5119	−1.17451
$306$	28.7316	1.64247
$307$	−24.2308	−1.38293	−0.691464	−	0.722411i	$-0.743034\pi$
$307$	−24.2308	−1.38293	−0.691464	+	0.722411i	$0.743034\pi$
$308$	11.7592	0.670043
$309$	−10.9821	−0.624750
$310$	13.5673	0.770573
$311$	−22.2646	−1.26251	−0.631255	−	0.775575i	$-0.717460\pi$
$311$	−22.2646	−1.26251	−0.631255	+	0.775575i	$0.717460\pi$
$312$	4.11402	0.232910
$313$	20.4001	1.15308	0.576541	−	0.817068i	$-0.304402\pi$
$313$	20.4001	1.15308	0.576541	+	0.817068i	$0.304402\pi$
$314$	54.3159	3.06523
$315$	4.65225	0.262125
$316$	2.75032	0.154718
$317$	0.334501	0.0187875	0.00939373	−	0.999956i	$-0.497010\pi$
$317$	0.334501	0.0187875	0.00939373	+	0.999956i	$0.497010\pi$
$318$	27.7469	1.55597
$319$	−7.53999	−0.422158
$320$	65.1285	3.64080
$321$	4.02286	0.224534
$322$	−4.95374	−0.276061
$323$	−11.6193	−0.646518
$324$	0.214785	0.0119325
$325$	−0.528785	−0.0293317
$326$	16.7637	0.928457
$327$	−4.68368	−0.259008
$328$	−18.8696	−1.04190
$329$	6.44408	0.355274
$330$	15.8744	0.873859
$331$	−1.25670	−0.0690747	−0.0345373	−	0.999403i	$-0.510996\pi$
$331$	−1.25670	−0.0690747	−0.0345373	+	0.999403i	$0.510996\pi$
$332$	−36.7725	−2.01815
$333$	−8.32501	−0.456208
$334$	17.0489	0.932872
$335$	19.5428	1.06774
$336$	−15.0541	−0.821267
$337$	−12.6064	−0.686713	−0.343356	−	0.939205i	$-0.611564\pi$
$337$	−12.6064	−0.686713	−0.343356	+	0.939205i	$0.611564\pi$
$338$	34.8114	1.89349
$339$	0.946563	0.0514103
$340$	76.4234	4.14464
$341$	4.37514	0.236927
$342$	−10.3125	−0.557635
$343$	−1.00000	−0.0539949
$344$	11.0575	0.596183
$345$	−4.87268	−0.262336
$346$	40.2366	2.16314
$347$	17.5597	0.942656	0.471328	−	0.881958i	$-0.343775\pi$
$347$	17.5597	0.942656	0.471328	+	0.881958i	$0.343775\pi$
$348$	19.7440	1.05839
$349$	20.1615	1.07922	0.539611	−	0.841915i	$-0.318571\pi$
$349$	20.1615	1.07922	0.539611	+	0.841915i	$0.318571\pi$
$350$	3.40890	0.182213
$351$	2.18520	0.116637
$352$	43.7469	2.33172
$353$	−8.70701	−0.463427	−0.231714	−	0.972784i	$-0.574433\pi$
$353$	−8.70701	−0.463427	−0.231714	+	0.972784i	$0.574433\pi$
$354$	−9.44988	−0.502255
$355$	−8.22819	−0.436707
$356$	21.4315	1.13587
$357$	−6.07478	−0.321511
$358$	7.32108	0.386931
$359$	13.0003	0.686131	0.343066	−	0.939311i	$-0.388535\pi$
$359$	13.0003	0.686131	0.343066	+	0.939311i	$0.388535\pi$
$360$	42.5676	2.24351
$361$	−14.8295	−0.780501
$362$	40.1372	2.10957
$363$	−6.62536	−0.347741
$364$	2.26157	0.118538
$365$	25.1620	1.31704
$366$	23.7714	1.24255
$367$	−17.3935	−0.907935	−0.453968	−	0.891018i	$-0.649992\pi$
$367$	−17.3935	−0.907935	−0.453968	+	0.891018i	$0.649992\pi$
$368$	−25.7278	−1.34115
$369$	−3.83594	−0.199691
$370$	−30.3905	−1.57993
$371$	9.57258	0.496984
$372$	−11.4566	−0.593999
$373$	6.76726	0.350395	0.175198	−	0.984533i	$-0.443944\pi$
$373$	6.76726	0.350395	0.175198	+	0.984533i	$0.443944\pi$
$374$	33.8228	1.74894
$375$	−9.99893	−0.516342
$376$	58.9627	3.04077
$377$	−1.45012	−0.0746848
$378$	−14.0873	−0.724570
$379$	−17.8261	−0.915666	−0.457833	−	0.889038i	$-0.651374\pi$
$379$	−17.8261	−0.915666	−0.457833	+	0.889038i	$0.651374\pi$
$380$	−27.4303	−1.40714
$381$	−2.65146	−0.135838
$382$	26.4197	1.35175
$383$	19.8866	1.01616	0.508079	−	0.861310i	$-0.330356\pi$
$383$	19.8866	1.01616	0.508079	+	0.861310i	$0.330356\pi$
$384$	−32.8159	−1.67463
$385$	5.47663	0.279115
$386$	54.2976	2.76367
$387$	2.24786	0.114265
$388$	−13.7196	−0.696509
$389$	−34.4075	−1.74453	−0.872266	−	0.489033i	$-0.837350\pi$
$389$	−34.4075	−1.74453	−0.872266	+	0.489033i	$0.837350\pi$
$390$	3.05302	0.154596
$391$	−10.3820	−0.525038
$392$	−9.14989	−0.462139
$393$	−3.74552	−0.188936
$394$	−60.1037	−3.02798
$395$	1.28091	0.0644497
$396$	21.8728	1.09915
$397$	−7.54185	−0.378515	−0.189257	−	0.981928i	$-0.560608\pi$
$397$	−7.54185	−0.378515	−0.189257	+	0.981928i	$0.560608\pi$
$398$	−31.8098	−1.59448
$399$	2.18039	0.109156
$400$	17.7045	0.885224
$401$	13.5431	0.676309	0.338155	−	0.941091i	$-0.390197\pi$
$401$	13.5431	0.676309	0.338155	+	0.941091i	$0.390197\pi$
$402$	−22.6483	−1.12960
$403$	0.841442	0.0419152
$404$	49.9526	2.48523
$405$	0.100032	0.00497064
$406$	9.34840	0.463953
$407$	−9.80020	−0.485778
$408$	−55.5835	−2.75180
$409$	21.4115	1.05873	0.529366	−	0.848393i	$-0.322430\pi$
$409$	21.4115	1.05873	0.529366	+	0.848393i	$0.322430\pi$
$410$	−14.0031	−0.691566
$411$	15.2707	0.753249
$412$	−55.2390	−2.72143
$413$	−3.26018	−0.160423
$414$	−9.21426	−0.452856
$415$	−17.1261	−0.840687
$416$	8.41354	0.412508
$417$	−6.97889	−0.341758
$418$	−12.1398	−0.593779
$419$	−27.4314	−1.34011	−0.670056	−	0.742311i	$-0.733730\pi$
$419$	−27.4314	−1.34011	−0.670056	+	0.742311i	$0.733730\pi$
$420$	−14.3410	−0.699768
$421$	−17.4048	−0.848256	−0.424128	−	0.905602i	$-0.639419\pi$
$421$	−17.4048	−0.848256	−0.424128	+	0.905602i	$0.639419\pi$
$422$	−1.91506	−0.0932238
$423$	11.9864	0.582797
$424$	87.5881	4.25365
$425$	7.14430	0.346549
$426$	9.53570	0.462006
$427$	8.20107	0.396878
$428$	20.2346	0.978076
$429$	0.984526	0.0475334
$430$	8.20583	0.395720
$431$	0.824195	0.0397001	0.0198500	−	0.999803i	$-0.493681\pi$
$431$	0.824195	0.0397001	0.0198500	+	0.999803i	$0.493681\pi$
$432$	−73.1637	−3.52009
$433$	−17.2281	−0.827928	−0.413964	−	0.910293i	$-0.635856\pi$
$433$	−17.2281	−0.827928	−0.413964	+	0.910293i	$0.635856\pi$
$434$	−5.42448	−0.260384
$435$	9.19541	0.440886
$436$	−23.5585	−1.12825
$437$	3.72634	0.178255
$438$	−29.1603	−1.39334
$439$	−16.6734	−0.795776	−0.397888	−	0.917434i	$-0.630257\pi$
$439$	−16.6734	−0.795776	−0.397888	+	0.917434i	$0.630257\pi$
$440$	50.1106	2.38893
$441$	−1.86006	−0.0885742
$442$	6.50491	0.309407
$443$	−34.5926	−1.64354	−0.821772	−	0.569817i	$-0.807014\pi$
$443$	−34.5926	−1.64354	−0.821772	+	0.569817i	$0.807014\pi$
$444$	25.6626	1.21789
$445$	9.98134	0.473161
$446$	56.4093	2.67106
$447$	0.225664	0.0106736
$448$	−26.0396	−1.23026
$449$	−35.1613	−1.65937	−0.829683	−	0.558234i	$-0.811479\pi$
$449$	−35.1613	−1.65937	−0.829683	+	0.558234i	$0.811479\pi$
$450$	6.34075	0.298906
$451$	−4.51568	−0.212635
$452$	4.76112	0.223944
$453$	−13.9234	−0.654176
$454$	−35.1374	−1.64908
$455$	1.05328	0.0493787
$456$	19.9503	0.934260
$457$	−7.02526	−0.328628	−0.164314	−	0.986408i	$-0.552541\pi$
$457$	−7.02526	−0.328628	−0.164314	+	0.986408i	$0.552541\pi$
$458$	52.1623	2.43739
$459$	−29.5238	−1.37805
$460$	−24.5091	−1.14274
$461$	3.89217	0.181276	0.0906382	−	0.995884i	$-0.471109\pi$
$461$	3.89217	0.181276	0.0906382	+	0.995884i	$0.471109\pi$
$462$	−6.34690	−0.295285
$463$	34.2311	1.59085	0.795427	−	0.606050i	$-0.207247\pi$
$463$	34.2311	1.59085	0.795427	+	0.606050i	$0.207247\pi$
$464$	48.5519	2.25397
$465$	−5.33572	−0.247438
$466$	−37.5706	−1.74042
$467$	1.19189	0.0551542	0.0275771	−	0.999620i	$-0.491221\pi$
$467$	1.19189	0.0551542	0.0275771	+	0.999620i	$0.491221\pi$
$468$	4.20665	0.194453
$469$	−7.81360	−0.360799
$470$	43.7563	2.01833
$471$	−21.3612	−0.984271
$472$	−29.8303	−1.37305
$473$	2.64618	0.121672
$474$	−1.48446	−0.0681834
$475$	−2.56427	−0.117657
$476$	−30.5555	−1.40051
$477$	17.8056	0.815261
$478$	58.2387	2.66378
$479$	3.14503	0.143700	0.0718500	−	0.997415i	$-0.477110\pi$
$479$	3.14503	0.143700	0.0718500	+	0.997415i	$0.477110\pi$
$480$	−53.3516	−2.43516
$481$	−1.88481	−0.0859398
$482$	−4.66072	−0.212290
$483$	1.94819	0.0886457
$484$	−33.3249	−1.51477
$485$	−6.38967	−0.290140
$486$	−42.3777	−1.92229
$487$	−35.5382	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$487$	−35.5382	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$488$	75.0389	3.39685
$489$	−6.59277	−0.298136
$490$	−6.79016	−0.306748
$491$	9.10277	0.410802	0.205401	−	0.978678i	$-0.434150\pi$
$491$	9.10277	0.410802	0.205401	+	0.978678i	$0.434150\pi$
$492$	11.8246	0.533096
$493$	19.5922	0.882387
$494$	−2.33478	−0.105047
$495$	10.1869	0.457865
$496$	−28.1726	−1.26499
$497$	3.28979	0.147567
$498$	19.8475	0.889389
$499$	4.49685	0.201307	0.100653	−	0.994922i	$-0.467907\pi$
$499$	4.49685	0.201307	0.100653	+	0.994922i	$0.467907\pi$
$500$	−50.2937	−2.24920
$501$	−6.70491	−0.299553
$502$	47.3376	2.11278
$503$	21.0503	0.938588	0.469294	−	0.883042i	$-0.344508\pi$
$503$	21.0503	0.938588	0.469294	+	0.883042i	$0.344508\pi$
$504$	−17.0193	−0.758102
$505$	23.2645	1.03526
$506$	−10.8470	−0.482209
$507$	−13.6905	−0.608016
$508$	−13.3366	−0.591715
$509$	31.8349	1.41106	0.705528	−	0.708682i	$-0.250710\pi$
$509$	31.8349	1.41106	0.705528	+	0.708682i	$0.250710\pi$
$510$	−41.2487	−1.82652
$511$	−10.0602	−0.445038
$512$	−23.6741	−1.04626
$513$	10.5968	0.467861
$514$	−66.7890	−2.94594
$515$	−25.7265	−1.13365
$516$	−6.92923	−0.305042
$517$	14.1104	0.620573
$518$	12.1507	0.533871
$519$	−15.8241	−0.694602
$520$	9.63743	0.422629
$521$	10.0972	0.442367	0.221184	−	0.975232i	$-0.429008\pi$
$521$	10.0972	0.442367	0.221184	+	0.975232i	$0.429008\pi$
$522$	17.3886	0.761077
$523$	−2.75679	−0.120546	−0.0602729	−	0.998182i	$-0.519197\pi$
$523$	−2.75679	−0.120546	−0.0602729	+	0.998182i	$0.519197\pi$
$524$	−18.8396	−0.823011
$525$	−1.34064	−0.0585103
$526$	9.35510	0.407902
$527$	−11.3685	−0.495221
$528$	−32.9633	−1.43454
$529$	−19.6705	−0.855239
$530$	64.9993	2.82339
$531$	−6.06412	−0.263161
$532$	10.9671	0.475486
$533$	−0.868470	−0.0376176
$534$	−11.5674	−0.500572
$535$	9.42388	0.407430
$536$	−71.4936	−3.08805
$537$	−2.87921	−0.124247
$538$	−63.7566	−2.74874
$539$	−2.18966	−0.0943154
$540$	−69.6980	−2.99932
$541$	−17.1695	−0.738174	−0.369087	−	0.929395i	$-0.620330\pi$
$541$	−17.1695	−0.738174	−0.369087	+	0.929395i	$0.620330\pi$
$542$	10.0866	0.433255
$543$	−15.7850	−0.677400
$544$	−113.673	−4.87371
$545$	−10.9719	−0.469986
$546$	−1.22066	−0.0522393
$547$	4.02120	0.171934	0.0859670	−	0.996298i	$-0.472602\pi$
$547$	4.02120	0.171934	0.0859670	+	0.996298i	$0.472602\pi$
$548$	76.8102	3.28117
$549$	15.2545	0.651045
$550$	7.46433	0.318280
$551$	−7.03212	−0.299578
$552$	17.8257	0.758714
$553$	−0.512133	−0.0217781
$554$	−7.08971	−0.301213
$555$	11.9519	0.507328
$556$	−35.1032	−1.48871
$557$	−5.78165	−0.244977	−0.122488	−	0.992470i	$-0.539087\pi$
$557$	−5.78165	−0.244977	−0.122488	+	0.992470i	$0.539087\pi$
$558$	−10.0899	−0.427138
$559$	0.508923	0.0215251
$560$	−35.2654	−1.49024
$561$	−13.3017	−0.561598
$562$	−13.1284	−0.553787
$563$	−2.11014	−0.0889316	−0.0444658	−	0.999011i	$-0.514159\pi$
$563$	−2.11014	−0.0889316	−0.0444658	+	0.999011i	$0.514159\pi$
$564$	−36.9491	−1.55584
$565$	2.21740	0.0932869
$566$	32.4022	1.36197
$567$	−0.0399948	−0.00167962
$568$	30.1012	1.26302
$569$	−33.9773	−1.42440	−0.712201	−	0.701975i	$-0.752302\pi$
$569$	−33.9773	−1.42440	−0.712201	+	0.701975i	$0.752302\pi$
$570$	14.8052	0.620121
$571$	32.5248	1.36112	0.680560	−	0.732692i	$-0.261736\pi$
$571$	32.5248	1.36112	0.680560	+	0.732692i	$0.261736\pi$
$572$	4.95207	0.207057
$573$	−10.3902	−0.434058
$574$	5.59872	0.233686
$575$	−2.29119	−0.0955491
$576$	−48.4352	−2.01814
$577$	28.3630	1.18077	0.590384	−	0.807122i	$-0.298976\pi$
$577$	28.3630	1.18077	0.590384	+	0.807122i	$0.298976\pi$
$578$	−41.7342	−1.73591
$579$	−21.3539	−0.887440
$580$	46.2521	1.92051
$581$	6.84734	0.284076
$582$	7.40502	0.306948
$583$	20.9607	0.868104
$584$	−92.0500	−3.80906
$585$	1.95917	0.0810017
$586$	2.78551	0.115068
$587$	24.8518	1.02574	0.512872	−	0.858465i	$-0.328582\pi$
$587$	24.8518	1.02574	0.512872	+	0.858465i	$0.328582\pi$
$588$	5.73380	0.236458
$589$	4.08045	0.168132
$590$	−22.1371	−0.911371
$591$	23.6374	0.972311
$592$	63.1060	2.59364
$593$	15.9476	0.654888	0.327444	−	0.944871i	$-0.393813\pi$
$593$	15.9476	0.654888	0.327444	+	0.944871i	$0.393813\pi$
$594$	−30.8463	−1.26564
$595$	−14.2307	−0.583401
$596$	1.13507	0.0464943
$597$	12.5100	0.512002
$598$	−2.08614	−0.0853084
$599$	−21.1764	−0.865243	−0.432622	−	0.901576i	$-0.642411\pi$
$599$	−21.1764	−0.865243	−0.432622	+	0.901576i	$0.642411\pi$
$600$	−12.2667	−0.500786
$601$	−15.5255	−0.633300	−0.316650	−	0.948542i	$-0.602558\pi$
$601$	−15.5255	−0.633300	−0.316650	+	0.948542i	$0.602558\pi$
$602$	−3.28085	−0.133717
$603$	−14.5338	−0.591861
$604$	−70.0331	−2.84961
$605$	−15.5205	−0.630997
$606$	−26.9613	−1.09523
$607$	15.2789	0.620153	0.310076	−	0.950712i	$-0.399645\pi$
$607$	15.2789	0.620153	0.310076	+	0.950712i	$0.399645\pi$
$608$	40.8002	1.65467
$609$	−3.67650	−0.148979
$610$	55.6866	2.25468
$611$	2.71375	0.109787
$612$	−56.8351	−2.29742
$613$	6.19858	0.250358	0.125179	−	0.992134i	$-0.460049\pi$
$613$	6.19858	0.250358	0.125179	+	0.992134i	$0.460049\pi$
$614$	65.7828	2.65478
$615$	5.50710	0.222068
$616$	−20.0352	−0.807240
$617$	−16.3900	−0.659838	−0.329919	−	0.944009i	$-0.607021\pi$
$617$	−16.3900	−0.659838	−0.329919	+	0.944009i	$0.607021\pi$
$618$	29.8146	1.19932
$619$	2.77605	0.111579	0.0557895	−	0.998443i	$-0.482232\pi$
$619$	2.77605	0.111579	0.0557895	+	0.998443i	$0.482232\pi$
$620$	−26.8381	−1.07785
$621$	9.46832	0.379951
$622$	60.4448	2.42361
$623$	−3.99073	−0.159885
$624$	−6.33962	−0.253788
$625$	−29.7016	−1.18806
$626$	−55.3829	−2.21355
$627$	4.77431	0.190668
$628$	−107.445	−4.28751
$629$	25.4652	1.01536
$630$	−12.6301	−0.503195
$631$	0.0954145	0.00379839	0.00189920	−	0.999998i	$-0.499395\pi$
$631$	0.0954145	0.00379839	0.00189920	+	0.999998i	$0.499395\pi$
$632$	−4.68596	−0.186398
$633$	0.753148	0.0299350
$634$	−0.908116	−0.0360659
$635$	−6.21126	−0.246487
$636$	−54.8872	−2.17642
$637$	−0.421123	−0.0166855
$638$	20.4698	0.810408
$639$	6.11920	0.242072
$640$	−76.8739	−3.03871
$641$	−0.835404	−0.0329965	−0.0164982	−	0.999864i	$-0.505252\pi$
$641$	−0.835404	−0.0329965	−0.0164982	+	0.999864i	$0.505252\pi$
$642$	−10.9214	−0.431033
$643$	17.6821	0.697314	0.348657	−	0.937250i	$-0.386638\pi$
$643$	17.6821	0.697314	0.348657	+	0.937250i	$0.386638\pi$
$644$	9.79921	0.386143
$645$	−3.22716	−0.127069
$646$	31.5446	1.24111
$647$	−45.0790	−1.77224	−0.886119	−	0.463458i	$-0.846608\pi$
$647$	−45.0790	−1.77224	−0.886119	+	0.463458i	$0.846608\pi$
$648$	−0.365948	−0.0143758
$649$	−7.13869	−0.280218
$650$	1.43557	0.0563075
$651$	2.13332	0.0836114
$652$	−33.1610	−1.29869
$653$	40.9486	1.60244	0.801222	−	0.598367i	$-0.204184\pi$
$653$	40.9486	1.60244	0.801222	+	0.598367i	$0.204184\pi$
$654$	12.7154	0.497213
$655$	−8.77419	−0.342836
$656$	29.0776	1.13529
$657$	−18.7126	−0.730049
$658$	−17.4946	−0.682011
$659$	−16.3416	−0.636577	−0.318289	−	0.947994i	$-0.603108\pi$
$659$	−16.3416	−0.636577	−0.318289	+	0.947994i	$0.603108\pi$
$660$	−31.4019	−1.22232
$661$	−36.8304	−1.43253	−0.716267	−	0.697826i	$-0.754151\pi$
$661$	−36.8304	−1.43253	−0.716267	+	0.697826i	$0.754151\pi$
$662$	3.41174	0.132601
$663$	−2.55823	−0.0993533
$664$	62.6524	2.43139
$665$	5.10774	0.198070
$666$	22.6010	0.875772
$667$	−6.28324	−0.243288
$668$	−33.7251	−1.30486
$669$	−22.1844	−0.857700
$670$	−53.0556	−2.04972
$671$	17.9576	0.693244
$672$	21.3310	0.822861
$673$	−6.79155	−0.261795	−0.130898	−	0.991396i	$-0.541786\pi$
$673$	−6.79155	−0.261795	−0.130898	+	0.991396i	$0.541786\pi$
$674$	34.2242	1.31827
$675$	−6.51558	−0.250785
$676$	−68.8619	−2.64853
$677$	1.10357	0.0424136	0.0212068	−	0.999775i	$-0.493249\pi$
$677$	1.10357	0.0424136	0.0212068	+	0.999775i	$0.493249\pi$
$678$	−2.56976	−0.0986912
$679$	2.55471	0.0980408
$680$	−130.209	−4.99329
$681$	13.8187	0.529534
$682$	−11.8778	−0.454824
$683$	38.4616	1.47169	0.735845	−	0.677150i	$-0.236785\pi$
$683$	38.4616	1.47169	0.735845	+	0.677150i	$0.236785\pi$
$684$	20.3995	0.779996
$685$	35.7729	1.36681
$686$	2.71484	0.103653
$687$	−20.5142	−0.782666
$688$	−17.0394	−0.649623
$689$	4.03123	0.153578
$690$	13.2285	0.503601
$691$	35.9947	1.36930	0.684651	−	0.728871i	$-0.259955\pi$
$691$	35.9947	1.36930	0.684651	+	0.728871i	$0.259955\pi$
$692$	−79.5938	−3.02570
$693$	−4.07290	−0.154717
$694$	−47.6718	−1.80960
$695$	−16.3486	−0.620139
$696$	−33.6396	−1.27511
$697$	11.7337	0.444445
$698$	−54.7352	−2.07176
$699$	14.7756	0.558865
$700$	−6.74329	−0.254872
$701$	7.60107	0.287089	0.143544	−	0.989644i	$-0.454150\pi$
$701$	7.60107	0.287089	0.143544	+	0.989644i	$0.454150\pi$
$702$	−5.93247	−0.223906
$703$	−9.14010	−0.344725
$704$	−57.0180	−2.14895
$705$	−17.2083	−0.648103
$706$	23.6381	0.889632
$707$	−9.30158	−0.349822
$708$	18.6932	0.702534
$709$	−16.6448	−0.625108	−0.312554	−	0.949900i	$-0.601185\pi$
$709$	−16.6448	−0.625108	−0.312554	+	0.949900i	$0.601185\pi$
$710$	22.3382	0.838337
$711$	−0.952598	−0.0357252
$712$	−36.5148	−1.36845
$713$	3.64590	0.136540
$714$	16.4920	0.617198
$715$	2.30634	0.0862521
$716$	−14.4821	−0.541223
$717$	−22.9039	−0.855362
$718$	−35.2938	−1.31715
$719$	4.15562	0.154979	0.0774893	−	0.996993i	$-0.475310\pi$
$719$	4.15562	0.154979	0.0774893	+	0.996993i	$0.475310\pi$
$720$	−65.5958	−2.44461
$721$	10.2860	0.383069
$722$	40.2597	1.49831
$723$	1.83295	0.0681682
$724$	−79.3972	−2.95077
$725$	4.32379	0.160581
$726$	17.9868	0.667552
$727$	8.37563	0.310635	0.155317	−	0.987865i	$-0.450360\pi$
$727$	8.37563	0.310635	0.155317	+	0.987865i	$0.450360\pi$
$728$	−3.85323	−0.142810
$729$	16.5462	0.612820
$730$	−68.3106	−2.52829
$731$	−6.87593	−0.254316
$732$	−47.0233	−1.73803
$733$	37.5012	1.38514	0.692570	−	0.721351i	$-0.256479\pi$
$733$	37.5012	1.38514	0.692570	+	0.721351i	$0.256479\pi$
$734$	47.2206	1.74294
$735$	2.67041	0.0984995
$736$	36.4552	1.34376
$737$	−17.1092	−0.630224
$738$	10.4140	0.383343
$739$	22.1569	0.815056	0.407528	−	0.913193i	$-0.366391\pi$
$739$	22.1569	0.815056	0.407528	+	0.913193i	$0.366391\pi$
$740$	60.1167	2.20994
$741$	0.918212	0.0337314
$742$	−25.9880	−0.954049
$743$	34.0635	1.24967	0.624835	−	0.780757i	$-0.285166\pi$
$743$	34.0635	1.24967	0.624835	+	0.780757i	$0.285166\pi$
$744$	19.5197	0.715625
$745$	0.528638	0.0193678
$746$	−18.3720	−0.672646
$747$	12.7365	0.466003
$748$	−66.9063	−2.44634
$749$	−3.76785	−0.137674
$750$	27.1454	0.991211
$751$	34.9556	1.27555	0.637774	−	0.770224i	$-0.279855\pi$
$751$	34.9556	1.27555	0.637774	+	0.770224i	$0.279855\pi$
$752$	−90.8602	−3.31333
$753$	−18.6168	−0.678433
$754$	3.93683	0.143371
$755$	−32.6166	−1.18704
$756$	27.8666	1.01350
$757$	−45.5812	−1.65668	−0.828339	−	0.560228i	$-0.810714\pi$
$757$	−45.5812	−1.65668	−0.828339	+	0.560228i	$0.810714\pi$
$758$	48.3950	1.75779
$759$	4.26588	0.154842
$760$	46.7353	1.69527
$761$	5.33551	0.193412	0.0967060	−	0.995313i	$-0.469169\pi$
$761$	5.33551	0.193412	0.0967060	+	0.995313i	$0.469169\pi$
$762$	7.19827	0.260766
$763$	4.38678	0.158812
$764$	−52.2619	−1.89077
$765$	−26.4699	−0.957021
$766$	−53.9889	−1.95070
$767$	−1.37294	−0.0495739
$768$	33.4857	1.20831
$769$	5.69800	0.205475	0.102738	−	0.994708i	$-0.467240\pi$
$769$	5.69800	0.205475	0.102738	+	0.994708i	$0.467240\pi$
$770$	−14.8682	−0.535811
$771$	26.2665	0.945967
$772$	−107.408	−3.86571
$773$	−18.8305	−0.677287	−0.338643	−	0.940915i	$-0.609968\pi$
$773$	−18.8305	−0.677287	−0.338643	+	0.940915i	$0.609968\pi$
$774$	−6.10257	−0.219352
$775$	−2.50891	−0.0901228
$776$	23.3753	0.839125
$777$	−4.77858	−0.171431
$778$	93.4108	3.34894
$779$	−4.21151	−0.150893
$780$	−6.03931	−0.216242
$781$	7.20352	0.257762
$782$	28.1853	1.00790
$783$	−17.8680	−0.638551
$784$	14.0998	0.503564
$785$	−50.0403	−1.78602
$786$	10.1685	0.362697
$787$	36.2952	1.29379	0.646893	−	0.762581i	$-0.276068\pi$
$787$	36.2952	1.29379	0.646893	+	0.762581i	$0.276068\pi$
$788$	118.894	4.23541
$789$	−3.67914	−0.130981
$790$	−3.47746	−0.123723
$791$	−0.886561	−0.0315225
$792$	−37.2666	−1.32421
$793$	3.45366	0.122643
$794$	20.4749	0.726626
$795$	−25.5627	−0.906616
$796$	62.9243	2.23029
$797$	41.9606	1.48632	0.743160	−	0.669114i	$-0.233326\pi$
$797$	41.9606	1.48632	0.743160	+	0.669114i	$0.233326\pi$
$798$	−5.91940	−0.209544
$799$	−36.6649	−1.29711
$800$	−25.0865	−0.886942
$801$	−7.42299	−0.262279
$802$	−36.7672	−1.29830
$803$	−22.0285	−0.777369
$804$	44.8016	1.58003
$805$	4.56380	0.160853
$806$	−2.28438	−0.0804637
$807$	25.0740	0.882645
$808$	−85.1085	−2.99411
$809$	6.68720	0.235109	0.117555	−	0.993066i	$-0.462494\pi$
$809$	6.68720	0.235109	0.117555	+	0.993066i	$0.462494\pi$
$810$	−0.271571	−0.00954203
$811$	26.9492	0.946315	0.473157	−	0.880978i	$-0.343114\pi$
$811$	26.9492	0.946315	0.473157	+	0.880978i	$0.343114\pi$
$812$	−18.4925	−0.648958
$813$	−3.96680	−0.139122
$814$	26.6059	0.932538
$815$	−15.4441	−0.540984
$816$	85.6531	2.99846
$817$	2.46794	0.0863425
$818$	−58.1288	−2.03243
$819$	−0.783314	−0.0273712
$820$	27.7002	0.967333
$821$	1.13873	0.0397420	0.0198710	−	0.999803i	$-0.493674\pi$
$821$	1.13873	0.0397420	0.0198710	+	0.999803i	$0.493674\pi$
$822$	−41.4575	−1.44600
$823$	14.5543	0.507332	0.253666	−	0.967292i	$-0.418364\pi$
$823$	14.5543	0.507332	0.253666	+	0.967292i	$0.418364\pi$
$824$	94.1154	3.27866
$825$	−2.93555	−0.102203
$826$	8.85085	0.307960
$827$	−2.29308	−0.0797381	−0.0398691	−	0.999205i	$-0.512694\pi$
$827$	−2.29308	−0.0797381	−0.0398691	+	0.999205i	$0.512694\pi$
$828$	18.2271	0.633436
$829$	−1.52438	−0.0529438	−0.0264719	−	0.999650i	$-0.508427\pi$
$829$	−1.52438	−0.0529438	−0.0264719	+	0.999650i	$0.508427\pi$
$830$	46.4945	1.61385
$831$	2.78821	0.0967221
$832$	−10.9659	−0.380174
$833$	5.68970	0.197136
$834$	18.9465	0.656065
$835$	−15.7068	−0.543557
$836$	24.0144	0.830554
$837$	10.3681	0.358373
$838$	74.4718	2.57258
$839$	12.6462	0.436596	0.218298	−	0.975882i	$-0.429949\pi$
$839$	12.6462	0.436596	0.218298	+	0.975882i	$0.429949\pi$
$840$	24.4339	0.843051
$841$	−17.1427	−0.591126
$842$	47.2510	1.62838
$843$	5.16307	0.177826
$844$	3.78827	0.130397
$845$	−32.0711	−1.10328
$846$	−32.5410	−1.11878
$847$	6.20538	0.213219
$848$	−134.971	−4.63494
$849$	−12.7430	−0.437339
$850$	−19.3956	−0.665263
$851$	−8.16673	−0.279952
$852$	−18.8630	−0.646234
$853$	1.92758	0.0659991	0.0329995	−	0.999455i	$-0.489494\pi$
$853$	1.92758	0.0659991	0.0329995	+	0.999455i	$0.489494\pi$
$854$	−22.2646	−0.761877
$855$	9.50070	0.324917
$856$	−34.4754	−1.17834
$857$	−7.13238	−0.243638	−0.121819	−	0.992552i	$-0.538873\pi$
$857$	−7.13238	−0.243638	−0.121819	+	0.992552i	$0.538873\pi$
$858$	−2.67283	−0.0912488
$859$	−47.1576	−1.60900	−0.804499	−	0.593954i	$-0.797566\pi$
$859$	−47.1576	−1.60900	−0.804499	+	0.593954i	$0.797566\pi$
$860$	−16.2323	−0.553517
$861$	−2.20185	−0.0750387
$862$	−2.23755	−0.0762114
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	103.670	3.52692
$865$	−37.0693	−1.26039
$866$	46.7713	1.58936
$867$	16.4131	0.557417
$868$	10.7304	0.364214
$869$	−1.12140	−0.0380408
$870$	−24.9640	−0.846360
$871$	−3.29049	−0.111494
$872$	40.1386	1.35926
$873$	4.75191	0.160828
$874$	−10.1164	−0.342193
$875$	9.36510	0.316598
$876$	57.6833	1.94894
$877$	1.95895	0.0661490	0.0330745	−	0.999453i	$-0.489470\pi$
$877$	1.95895	0.0661490	0.0330745	+	0.999453i	$0.489470\pi$
$878$	45.2654	1.52763
$879$	−1.09547	−0.0369494
$880$	−77.2194	−2.60306
$881$	7.37470	0.248460	0.124230	−	0.992253i	$-0.460354\pi$
$881$	7.37470	0.248460	0.124230	+	0.992253i	$0.460354\pi$
$882$	5.04975	0.170034
$883$	−47.4012	−1.59518	−0.797589	−	0.603201i	$-0.793892\pi$
$883$	−47.4012	−1.59518	−0.797589	+	0.603201i	$0.793892\pi$
$884$	−12.8676	−0.432786
$885$	8.70601	0.292649
$886$	93.9132	3.15507
$887$	−16.2053	−0.544122	−0.272061	−	0.962280i	$-0.587705\pi$
$887$	−16.2053	−0.544122	−0.272061	+	0.962280i	$0.587705\pi$
$888$	−43.7235	−1.46727
$889$	2.48338	0.0832900
$890$	−27.0977	−0.908317
$891$	−0.0875751	−0.00293387
$892$	−111.586	−3.73616
$893$	13.1599	0.440381
$894$	−0.612641	−0.0204898
$895$	−6.74479	−0.225453
$896$	30.7357	1.02681
$897$	0.820428	0.0273933
$898$	95.4573	3.18545
$899$	−6.88032	−0.229472
$900$	−12.5429	−0.418097
$901$	−54.4651	−1.81449
$902$	12.2593	0.408191
$903$	1.29028	0.0429378
$904$	−8.11194	−0.269799
$905$	−36.9777	−1.22918
$906$	37.7996	1.25581
$907$	−12.6253	−0.419216	−0.209608	−	0.977785i	$-0.567219\pi$
$907$	−12.6253	−0.419216	−0.209608	+	0.977785i	$0.567219\pi$
$908$	69.5068	2.30666
$909$	−17.3015	−0.573854
$910$	−2.85949	−0.0947912
$911$	20.7035	0.685939	0.342970	−	0.939347i	$-0.388567\pi$
$911$	20.7035	0.685939	0.342970	+	0.939347i	$0.388567\pi$
$912$	−30.7430	−1.01800
$913$	14.9934	0.496208
$914$	19.0724	0.630860
$915$	−21.9002	−0.723998
$916$	−103.185	−3.40931
$917$	3.50809	0.115847
$918$	80.1522	2.64542
$919$	−9.47363	−0.312506	−0.156253	−	0.987717i	$-0.549942\pi$
$919$	−9.47363	−0.312506	−0.156253	+	0.987717i	$0.549942\pi$
$920$	41.7583	1.37673
$921$	−25.8708	−0.852472
$922$	−10.5666	−0.347993
$923$	1.38540	0.0456012
$924$	12.5551	0.413032
$925$	5.61990	0.184781
$926$	−92.9318	−3.05393
$927$	19.1325	0.628393
$928$	−68.7961	−2.25834
$929$	−23.7536	−0.779331	−0.389666	−	0.920956i	$-0.627409\pi$
$929$	−23.7536	−0.779331	−0.389666	+	0.920956i	$0.627409\pi$
$930$	14.4856	0.475001
$931$	−2.04217	−0.0669295
$932$	74.3200	2.43443
$933$	−23.7715	−0.778244
$934$	−3.23579	−0.105878
$935$	−31.1604	−1.01905
$936$	−7.16724	−0.234268
$937$	36.0280	1.17698	0.588492	−	0.808503i	$-0.299722\pi$
$937$	36.0280	1.17698	0.588492	+	0.808503i	$0.299722\pi$
$938$	21.2126	0.692617
$939$	21.7808	0.710789
$940$	−86.5563	−2.82315
$941$	−2.50605	−0.0816949	−0.0408475	−	0.999165i	$-0.513006\pi$
$941$	−2.50605	−0.0816949	−0.0408475	+	0.999165i	$0.513006\pi$
$942$	57.9921	1.88948
$943$	−3.76301	−0.122541
$944$	45.9678	1.49613
$945$	12.9783	0.422185
$946$	−7.18395	−0.233570
$947$	18.3538	0.596419	0.298209	−	0.954501i	$-0.403611\pi$
$947$	18.3538	0.596419	0.298209	+	0.954501i	$0.403611\pi$
$948$	2.93647	0.0953720
$949$	−4.23659	−0.137526
$950$	6.96156	0.225863
$951$	0.357140	0.0115811
$952$	52.0601	1.68728
$953$	−4.04237	−0.130945	−0.0654727	−	0.997854i	$-0.520856\pi$
$953$	−4.04237	−0.130945	−0.0654727	+	0.997854i	$0.520856\pi$
$954$	−48.3392	−1.56504
$955$	−24.3400	−0.787623
$956$	−115.205	−3.72598
$957$	−8.05030	−0.260229
$958$	−8.53823	−0.275858
$959$	−14.3027	−0.461858
$960$	69.5364	2.24428
$961$	−27.0076	−0.871214
$962$	5.11694	0.164977
$963$	−7.00842	−0.225843
$964$	9.21958	0.296943
$965$	−50.0234	−1.61031
$966$	−5.28902	−0.170171
$967$	52.1528	1.67712	0.838561	−	0.544808i	$-0.183398\pi$
$967$	52.1528	1.67712	0.838561	+	0.544808i	$0.183398\pi$
$968$	56.7786	1.82493
$969$	−12.4057	−0.398530
$970$	17.3469	0.556975
$971$	−38.2169	−1.22644	−0.613219	−	0.789913i	$-0.710126\pi$
$971$	−38.2169	−1.22644	−0.613219	+	0.789913i	$0.710126\pi$
$972$	83.8291	2.68882
$973$	6.53650	0.209551
$974$	96.4805	3.09143
$975$	−0.564574	−0.0180808
$976$	−115.633	−3.70133
$977$	4.15113	0.132806	0.0664032	−	0.997793i	$-0.478848\pi$
$977$	4.15113	0.132806	0.0664032	+	0.997793i	$0.478848\pi$
$978$	17.8983	0.572324
$979$	−8.73835	−0.279279
$980$	13.4319	0.429066
$981$	8.15968	0.260518
$982$	−24.7125	−0.788609
$983$	−11.0696	−0.353066	−0.176533	−	0.984295i	$-0.556488\pi$
$983$	−11.0696	−0.353066	−0.176533	+	0.984295i	$0.556488\pi$
$984$	−20.1466	−0.642252
$985$	55.3725	1.76431
$986$	−53.1895	−1.69390
$987$	6.88022	0.219000
$988$	4.61852	0.146935
$989$	2.20512	0.0701188
$990$	−27.6556	−0.878954
$991$	−52.0361	−1.65298	−0.826490	−	0.562952i	$-0.809666\pi$
$991$	−52.0361	−1.65298	−0.826490	+	0.562952i	$0.809666\pi$
$992$	39.9195	1.26744
$993$	−1.34176	−0.0425794
$994$	−8.93123	−0.283281
$995$	29.3058	0.929057
$996$	−39.2613	−1.24404
$997$	10.9217	0.345893	0.172947	−	0.984931i	$-0.444671\pi$
$997$	10.9217	0.345893	0.172947	+	0.984931i	$0.444671\pi$
$998$	−12.2082	−0.386444
$999$	−23.2242	−0.734781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.1	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.1	✓	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71484 q^{2} +1.06768 q^{3} +5.37033 q^{4} +2.50113 q^{5} -2.89858 q^{6} -1.00000 q^{7} -9.14989 q^{8} -1.86006 q^{9} +O(q^{10})\)	\(q-2.71484 q^{2} +1.06768 q^{3} +5.37033 q^{4} +2.50113 q^{5} -2.89858 q^{6} -1.00000 q^{7} -9.14989 q^{8} -1.86006 q^{9} -6.79016 q^{10} -2.18966 q^{11} +5.73380 q^{12} -0.421123 q^{13} +2.71484 q^{14} +2.67041 q^{15} +14.0998 q^{16} +5.68970 q^{17} +5.04975 q^{18} -2.04217 q^{19} +13.4319 q^{20} -1.06768 q^{21} +5.94457 q^{22} -1.82469 q^{23} -9.76916 q^{24} +1.25566 q^{25} +1.14328 q^{26} -5.18899 q^{27} -5.37033 q^{28} +3.44345 q^{29} -7.24972 q^{30} -1.99809 q^{31} -19.9788 q^{32} -2.33786 q^{33} -15.4466 q^{34} -2.50113 q^{35} -9.98913 q^{36} +4.47567 q^{37} +5.54417 q^{38} -0.449625 q^{39} -22.8851 q^{40} +2.06227 q^{41} +2.89858 q^{42} -1.20849 q^{43} -11.7592 q^{44} -4.65225 q^{45} +4.95374 q^{46} -6.44408 q^{47} +15.0541 q^{48} +1.00000 q^{49} -3.40890 q^{50} +6.07478 q^{51} -2.26157 q^{52} -9.57258 q^{53} +14.0873 q^{54} -5.47663 q^{55} +9.14989 q^{56} -2.18039 q^{57} -9.34840 q^{58} +3.26018 q^{59} +14.3410 q^{60} -8.20107 q^{61} +5.42448 q^{62} +1.86006 q^{63} +26.0396 q^{64} -1.05328 q^{65} +6.34690 q^{66} +7.81360 q^{67} +30.5555 q^{68} -1.94819 q^{69} +6.79016 q^{70} -3.28979 q^{71} +17.0193 q^{72} +10.0602 q^{73} -12.1507 q^{74} +1.34064 q^{75} -10.9671 q^{76} +2.18966 q^{77} +1.22066 q^{78} +0.512133 q^{79} +35.2654 q^{80} +0.0399948 q^{81} -5.59872 q^{82} -6.84734 q^{83} -5.73380 q^{84} +14.2307 q^{85} +3.28085 q^{86} +3.67650 q^{87} +20.0352 q^{88} +3.99073 q^{89} +12.6301 q^{90} +0.421123 q^{91} -9.79921 q^{92} -2.13332 q^{93} +17.4946 q^{94} -5.10774 q^{95} -21.3310 q^{96} -2.55471 q^{97} -2.71484 q^{98} +4.07290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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