LMFDB - Embedded newform 8041.2.a.h.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21900 q^{2} -1.42344 q^{3} +2.92394 q^{4} -3.24388 q^{5} +3.15861 q^{6} +4.34231 q^{7} -2.05022 q^{8} -0.973808 q^{9} +O(q^{10})$	\(q-2.21900 q^{2} -1.42344 q^{3} +2.92394 q^{4} -3.24388 q^{5} +3.15861 q^{6} +4.34231 q^{7} -2.05022 q^{8} -0.973808 q^{9} +7.19815 q^{10} -1.00000 q^{11} -4.16207 q^{12} -2.33927 q^{13} -9.63557 q^{14} +4.61748 q^{15} -1.29845 q^{16} -1.00000 q^{17} +2.16088 q^{18} +0.168561 q^{19} -9.48490 q^{20} -6.18104 q^{21} +2.21900 q^{22} -0.985765 q^{23} +2.91837 q^{24} +5.52274 q^{25} +5.19083 q^{26} +5.65649 q^{27} +12.6967 q^{28} -0.164955 q^{29} -10.2462 q^{30} -2.02106 q^{31} +6.98170 q^{32} +1.42344 q^{33} +2.21900 q^{34} -14.0859 q^{35} -2.84736 q^{36} +9.45602 q^{37} -0.374035 q^{38} +3.32982 q^{39} +6.65066 q^{40} -5.59501 q^{41} +13.7157 q^{42} -1.00000 q^{43} -2.92394 q^{44} +3.15891 q^{45} +2.18741 q^{46} -7.32264 q^{47} +1.84827 q^{48} +11.8557 q^{49} -12.2549 q^{50} +1.42344 q^{51} -6.83989 q^{52} -2.00710 q^{53} -12.5517 q^{54} +3.24388 q^{55} -8.90270 q^{56} -0.239936 q^{57} +0.366034 q^{58} +3.01087 q^{59} +13.5012 q^{60} +6.96961 q^{61} +4.48473 q^{62} -4.22858 q^{63} -12.8955 q^{64} +7.58831 q^{65} -3.15861 q^{66} -6.46785 q^{67} -2.92394 q^{68} +1.40318 q^{69} +31.2566 q^{70} +10.3156 q^{71} +1.99652 q^{72} -3.32324 q^{73} -20.9829 q^{74} -7.86130 q^{75} +0.492861 q^{76} -4.34231 q^{77} -7.38886 q^{78} +16.8936 q^{79} +4.21201 q^{80} -5.13027 q^{81} +12.4153 q^{82} -15.1788 q^{83} -18.0730 q^{84} +3.24388 q^{85} +2.21900 q^{86} +0.234804 q^{87} +2.05022 q^{88} -13.5804 q^{89} -7.00962 q^{90} -10.1578 q^{91} -2.88232 q^{92} +2.87687 q^{93} +16.2489 q^{94} -0.546790 q^{95} -9.93805 q^{96} +9.61282 q^{97} -26.3077 q^{98} +0.973808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.21900	−1.56907	−0.784533	−	0.620087i	$-0.787097\pi$
$2$	−2.21900	−1.56907	−0.784533	+	0.620087i	$0.787097\pi$
$3$	−1.42344	−0.821826	−0.410913	−	0.911675i	$-0.634790\pi$
$3$	−1.42344	−0.821826	−0.410913	+	0.911675i	$0.634790\pi$
$4$	2.92394	1.46197
$5$	−3.24388	−1.45071	−0.725353	−	0.688377i	$-0.758323\pi$
$5$	−3.24388	−1.45071	−0.725353	+	0.688377i	$0.758323\pi$
$6$	3.15861	1.28950
$7$	4.34231	1.64124	0.820620	−	0.571475i	$-0.193628\pi$
$7$	4.34231	1.64124	0.820620	+	0.571475i	$0.193628\pi$
$8$	−2.05022	−0.724863
$9$	−0.973808	−0.324603
$10$	7.19815	2.27625
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.16207	−1.20148
$13$	−2.33927	−0.648797	−0.324399	−	0.945920i	$-0.605162\pi$
$13$	−2.33927	−0.648797	−0.324399	+	0.945920i	$0.605162\pi$
$14$	−9.63557	−2.57521
$15$	4.61748	1.19223
$16$	−1.29845	−0.324613
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.16088	0.509323
$19$	0.168561	0.0386704	0.0193352	−	0.999813i	$-0.493845\pi$
$19$	0.168561	0.0386704	0.0193352	+	0.999813i	$0.493845\pi$
$20$	−9.48490	−2.12089
$21$	−6.18104	−1.34881
$22$	2.21900	0.473091
$23$	−0.985765	−0.205546	−0.102773	−	0.994705i	$-0.532772\pi$
$23$	−0.985765	−0.205546	−0.102773	+	0.994705i	$0.532772\pi$
$24$	2.91837	0.595711
$25$	5.52274	1.10455
$26$	5.19083	1.01801
$27$	5.65649	1.08859
$28$	12.6967	2.39944
$29$	−0.164955	−0.0306314	−0.0153157	−	0.999883i	$-0.504875\pi$
$29$	−0.164955	−0.0306314	−0.0153157	+	0.999883i	$0.504875\pi$
$30$	−10.2462	−1.87068
$31$	−2.02106	−0.362993	−0.181497	−	0.983392i	$-0.558094\pi$
$31$	−2.02106	−0.362993	−0.181497	+	0.983392i	$0.558094\pi$
$32$	6.98170	1.23420
$33$	1.42344	0.247790
$34$	2.21900	0.380555
$35$	−14.0859	−2.38096
$36$	−2.84736	−0.474560
$37$	9.45602	1.55456	0.777280	−	0.629154i	$-0.216599\pi$
$37$	9.45602	1.55456	0.777280	+	0.629154i	$0.216599\pi$
$38$	−0.374035	−0.0606765
$39$	3.32982	0.533198
$40$	6.65066	1.05156
$41$	−5.59501	−0.873793	−0.436897	−	0.899512i	$-0.643922\pi$
$41$	−5.59501	−0.873793	−0.436897	+	0.899512i	$0.643922\pi$
$42$	13.7157	2.11638
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−2.92394	−0.440801
$45$	3.15891	0.470903
$46$	2.18741	0.322516
$47$	−7.32264	−1.06812	−0.534059	−	0.845447i	$-0.679334\pi$
$47$	−7.32264	−1.06812	−0.534059	+	0.845447i	$0.679334\pi$
$48$	1.84827	0.266775
$49$	11.8557	1.69367
$50$	−12.2549	−1.73311
$51$	1.42344	0.199322
$52$	−6.83989	−0.948522
$53$	−2.00710	−0.275697	−0.137848	−	0.990453i	$-0.544019\pi$
$53$	−2.00710	−0.275697	−0.137848	+	0.990453i	$0.544019\pi$
$54$	−12.5517	−1.70807
$55$	3.24388	0.437404
$56$	−8.90270	−1.18967
$57$	−0.239936	−0.0317804
$58$	0.366034	0.0480627
$59$	3.01087	0.391982	0.195991	−	0.980606i	$-0.437208\pi$
$59$	3.01087	0.391982	0.195991	+	0.980606i	$0.437208\pi$
$60$	13.5012	1.74300
$61$	6.96961	0.892367	0.446184	−	0.894941i	$-0.352783\pi$
$61$	6.96961	0.892367	0.446184	+	0.894941i	$0.352783\pi$
$62$	4.48473	0.569561
$63$	−4.22858	−0.532751
$64$	−12.8955	−1.61193
$65$	7.58831	0.941214
$66$	−3.15861	−0.388799
$67$	−6.46785	−0.790173	−0.395087	−	0.918644i	$-0.629285\pi$
$67$	−6.46785	−0.790173	−0.395087	+	0.918644i	$0.629285\pi$
$68$	−2.92394	−0.354580
$69$	1.40318	0.168923
$70$	31.2566	3.73588
$71$	10.3156	1.22424	0.612119	−	0.790766i	$-0.290317\pi$
$71$	10.3156	1.22424	0.612119	+	0.790766i	$0.290317\pi$
$72$	1.99652	0.235292
$73$	−3.32324	−0.388956	−0.194478	−	0.980907i	$-0.562301\pi$
$73$	−3.32324	−0.388956	−0.194478	+	0.980907i	$0.562301\pi$
$74$	−20.9829	−2.43921
$75$	−7.86130	−0.907745
$76$	0.492861	0.0565351
$77$	−4.34231	−0.494852
$78$	−7.38886	−0.836623
$79$	16.8936	1.90068	0.950339	−	0.311217i	$-0.100737\pi$
$79$	16.8936	1.90068	0.950339	+	0.311217i	$0.100737\pi$
$80$	4.21201	0.470917
$81$	−5.13027	−0.570030
$82$	12.4153	1.37104
$83$	−15.1788	−1.66609	−0.833043	−	0.553209i	$-0.813403\pi$
$83$	−15.1788	−1.66609	−0.833043	+	0.553209i	$0.813403\pi$
$84$	−18.0730	−1.97192
$85$	3.24388	0.351848
$86$	2.21900	0.239280
$87$	0.234804	0.0251736
$88$	2.05022	0.218554
$89$	−13.5804	−1.43952	−0.719759	−	0.694225i	$-0.755747\pi$
$89$	−13.5804	−1.43952	−0.719759	+	0.694225i	$0.755747\pi$
$90$	−7.00962	−0.738879
$91$	−10.1578	−1.06483
$92$	−2.88232	−0.300502
$93$	2.87687	0.298317
$94$	16.2489	1.67595
$95$	−0.546790	−0.0560994
$96$	−9.93805	−1.01430
$97$	9.61282	0.976034	0.488017	−	0.872834i	$-0.337720\pi$
$97$	9.61282	0.976034	0.488017	+	0.872834i	$0.337720\pi$
$98$	−26.3077	−2.65748
$99$	0.973808	0.0978714
$100$	16.1482	1.61482
$101$	17.8966	1.78078	0.890388	−	0.455203i	$-0.150433\pi$
$101$	17.8966	1.78078	0.890388	+	0.455203i	$0.150433\pi$
$102$	−3.15861	−0.312749
$103$	−8.07670	−0.795821	−0.397911	−	0.917424i	$-0.630265\pi$
$103$	−8.07670	−0.795821	−0.397911	+	0.917424i	$0.630265\pi$
$104$	4.79602	0.470289
$105$	20.0505	1.95673
$106$	4.45375	0.432587
$107$	−1.69407	−0.163772	−0.0818861	−	0.996642i	$-0.526094\pi$
$107$	−1.69407	−0.163772	−0.0818861	+	0.996642i	$0.526094\pi$
$108$	16.5392	1.59149
$109$	−14.5207	−1.39083	−0.695413	−	0.718610i	$-0.744779\pi$
$109$	−14.5207	−1.39083	−0.695413	+	0.718610i	$0.744779\pi$
$110$	−7.19815	−0.686316
$111$	−13.4601	−1.27758
$112$	−5.63828	−0.532767
$113$	−13.6497	−1.28406	−0.642028	−	0.766681i	$-0.721907\pi$
$113$	−13.6497	−1.28406	−0.642028	+	0.766681i	$0.721907\pi$
$114$	0.532418	0.0498655
$115$	3.19770	0.298187
$116$	−0.482319	−0.0447822
$117$	2.27800	0.210601
$118$	−6.68111	−0.615046
$119$	−4.34231	−0.398059
$120$	−9.46685	−0.864201
$121$	1.00000	0.0909091
$122$	−15.4655	−1.40018
$123$	7.96418	0.718106
$124$	−5.90946	−0.530686
$125$	−1.69569	−0.151667
$126$	9.38320	0.835922
$127$	11.1503	0.989430	0.494715	−	0.869055i	$-0.335272\pi$
$127$	11.1503	0.989430	0.494715	+	0.869055i	$0.335272\pi$
$128$	14.6516	1.29503
$129$	1.42344	0.125327
$130$	−16.8384	−1.47683
$131$	21.5713	1.88469	0.942347	−	0.334639i	$-0.108614\pi$
$131$	21.5713	1.88469	0.942347	+	0.334639i	$0.108614\pi$
$132$	4.16207	0.362261
$133$	0.731942	0.0634675
$134$	14.3521	1.23983
$135$	−18.3490	−1.57923
$136$	2.05022	0.175805
$137$	−21.9329	−1.87385	−0.936925	−	0.349531i	$-0.886341\pi$
$137$	−21.9329	−1.87385	−0.936925	+	0.349531i	$0.886341\pi$
$138$	−3.11365	−0.265052
$139$	−9.26739	−0.786050	−0.393025	−	0.919528i	$-0.628571\pi$
$139$	−9.26739	−0.786050	−0.393025	+	0.919528i	$0.628571\pi$
$140$	−41.1864	−3.48089
$141$	10.4234	0.877806
$142$	−22.8903	−1.92091
$143$	2.33927	0.195620
$144$	1.26444	0.105370
$145$	0.535094	0.0444371
$146$	7.37427	0.610299
$147$	−16.8759	−1.39190
$148$	27.6489	2.27272
$149$	6.26008	0.512846	0.256423	−	0.966565i	$-0.417456\pi$
$149$	6.26008	0.512846	0.256423	+	0.966565i	$0.417456\pi$
$150$	17.4442	1.42431
$151$	−2.44911	−0.199306	−0.0996530	−	0.995022i	$-0.531773\pi$
$151$	−2.44911	−0.199306	−0.0996530	+	0.995022i	$0.531773\pi$
$152$	−0.345586	−0.0280308
$153$	0.973808	0.0787277
$154$	9.63557	0.776456
$155$	6.55607	0.526597
$156$	9.73620	0.779520
$157$	5.17777	0.413231	0.206615	−	0.978422i	$-0.433755\pi$
$157$	5.17777	0.413231	0.206615	+	0.978422i	$0.433755\pi$
$158$	−37.4868	−2.98229
$159$	2.85700	0.226575
$160$	−22.6478	−1.79046
$161$	−4.28050	−0.337350
$162$	11.3841	0.894415
$163$	−5.60922	−0.439348	−0.219674	−	0.975573i	$-0.570499\pi$
$163$	−5.60922	−0.439348	−0.219674	+	0.975573i	$0.570499\pi$
$164$	−16.3595	−1.27746
$165$	−4.61748	−0.359470
$166$	33.6816	2.61420
$167$	0.291785	0.0225790	0.0112895	−	0.999936i	$-0.496406\pi$
$167$	0.291785	0.0225790	0.0112895	+	0.999936i	$0.496406\pi$
$168$	12.6725	0.977704
$169$	−7.52781	−0.579062
$170$	−7.19815	−0.552073
$171$	−0.164146	−0.0125525
$172$	−2.92394	−0.222948
$173$	15.5846	1.18488	0.592438	−	0.805616i	$-0.298166\pi$
$173$	15.5846	1.18488	0.592438	+	0.805616i	$0.298166\pi$
$174$	−0.521029	−0.0394991
$175$	23.9814	1.81283
$176$	1.29845	0.0978744
$177$	−4.28580	−0.322141
$178$	30.1348	2.25870
$179$	−1.74084	−0.130117	−0.0650584	−	0.997881i	$-0.520723\pi$
$179$	−1.74084	−0.130117	−0.0650584	+	0.997881i	$0.520723\pi$
$180$	9.23648	0.688447
$181$	9.83878	0.731311	0.365655	−	0.930750i	$-0.380845\pi$
$181$	9.83878	0.731311	0.365655	+	0.930750i	$0.380845\pi$
$182$	22.5402	1.67079
$183$	−9.92085	−0.733370
$184$	2.02104	0.148993
$185$	−30.6742	−2.25521
$186$	−6.38376	−0.468080
$187$	1.00000	0.0731272
$188$	−21.4110	−1.56156
$189$	24.5623	1.78664
$190$	1.21332	0.0880238
$191$	9.64636	0.697986	0.348993	−	0.937125i	$-0.386524\pi$
$191$	9.64636	0.697986	0.348993	+	0.937125i	$0.386524\pi$
$192$	18.3560	1.32473
$193$	5.68852	0.409468	0.204734	−	0.978818i	$-0.434367\pi$
$193$	5.68852	0.409468	0.204734	+	0.978818i	$0.434367\pi$
$194$	−21.3308	−1.53146
$195$	−10.8015	−0.773513
$196$	34.6653	2.47609
$197$	−10.8928	−0.776081	−0.388040	−	0.921642i	$-0.626848\pi$
$197$	−10.8928	−0.776081	−0.388040	+	0.921642i	$0.626848\pi$
$198$	−2.16088	−0.153567
$199$	−8.27232	−0.586409	−0.293205	−	0.956050i	$-0.594722\pi$
$199$	−8.27232	−0.586409	−0.293205	+	0.956050i	$0.594722\pi$
$200$	−11.3228	−0.800645
$201$	9.20661	0.649384
$202$	−39.7124	−2.79416
$203$	−0.716286	−0.0502734
$204$	4.16207	0.291403
$205$	18.1495	1.26762
$206$	17.9222	1.24870
$207$	0.959946	0.0667208
$208$	3.03743	0.210608
$209$	−0.168561	−0.0116596
$210$	−44.4920	−3.07024
$211$	18.0157	1.24025	0.620126	−	0.784502i	$-0.287081\pi$
$211$	18.0157	1.24025	0.620126	+	0.784502i	$0.287081\pi$
$212$	−5.86865	−0.403060
$213$	−14.6837	−1.00611
$214$	3.75914	0.256970
$215$	3.24388	0.221231
$216$	−11.5971	−0.789080
$217$	−8.77608	−0.595759
$218$	32.2213	2.18230
$219$	4.73045	0.319654
$220$	9.48490	0.639472
$221$	2.33927	0.157356
$222$	29.8679	2.00460
$223$	14.8218	0.992539	0.496269	−	0.868169i	$-0.334703\pi$
$223$	14.8218	0.992539	0.496269	+	0.868169i	$0.334703\pi$
$224$	30.3167	2.02562
$225$	−5.37809	−0.358539
$226$	30.2886	2.01477
$227$	20.7575	1.37772	0.688861	−	0.724893i	$-0.258111\pi$
$227$	20.7575	1.37772	0.688861	+	0.724893i	$0.258111\pi$
$228$	−0.701560	−0.0464619
$229$	−13.6355	−0.901061	−0.450530	−	0.892761i	$-0.648765\pi$
$229$	−13.6355	−0.901061	−0.450530	+	0.892761i	$0.648765\pi$
$230$	−7.09568	−0.467875
$231$	6.18104	0.406682
$232$	0.338194	0.0222035
$233$	−4.77207	−0.312628	−0.156314	−	0.987707i	$-0.549961\pi$
$233$	−4.77207	−0.312628	−0.156314	+	0.987707i	$0.549961\pi$
$234$	−5.05488	−0.330448
$235$	23.7538	1.54952
$236$	8.80361	0.573066
$237$	−24.0471	−1.56203
$238$	9.63557	0.624581
$239$	−12.8869	−0.833585	−0.416793	−	0.909002i	$-0.636846\pi$
$239$	−12.8869	−0.833585	−0.416793	+	0.909002i	$0.636846\pi$
$240$	−5.99556	−0.387012
$241$	7.31671	0.471311	0.235656	−	0.971837i	$-0.424276\pi$
$241$	7.31671	0.471311	0.235656	+	0.971837i	$0.424276\pi$
$242$	−2.21900	−0.142642
$243$	−9.66682	−0.620127
$244$	20.3787	1.30461
$245$	−38.4583	−2.45701
$246$	−17.6725	−1.12676
$247$	−0.394309	−0.0250893
$248$	4.14362	0.263120
$249$	21.6061	1.36923
$250$	3.76273	0.237976
$251$	4.82277	0.304411	0.152205	−	0.988349i	$-0.451362\pi$
$251$	4.82277	0.304411	0.152205	+	0.988349i	$0.451362\pi$
$252$	−12.3641	−0.778866
$253$	0.985765	0.0619745
$254$	−24.7425	−1.55248
$255$	−4.61748	−0.289158
$256$	−6.72084	−0.420053
$257$	25.9570	1.61915	0.809576	−	0.587016i	$-0.199697\pi$
$257$	25.9570	1.61915	0.809576	+	0.587016i	$0.199697\pi$
$258$	−3.15861	−0.196647
$259$	41.0610	2.55141
$260$	22.1878	1.37603
$261$	0.160635	0.00994303
$262$	−47.8666	−2.95721
$263$	23.7089	1.46195	0.730977	−	0.682402i	$-0.239065\pi$
$263$	23.7089	1.46195	0.730977	+	0.682402i	$0.239065\pi$
$264$	−2.91837	−0.179614
$265$	6.51079	0.399955
$266$	−1.62418	−0.0995847
$267$	19.3309	1.18303
$268$	−18.9116	−1.15521
$269$	14.9628	0.912299	0.456149	−	0.889903i	$-0.349228\pi$
$269$	14.9628	0.912299	0.456149	+	0.889903i	$0.349228\pi$
$270$	40.7163	2.47791
$271$	24.2901	1.47552	0.737758	−	0.675065i	$-0.235885\pi$
$271$	24.2901	1.47552	0.737758	+	0.675065i	$0.235885\pi$
$272$	1.29845	0.0787301
$273$	14.4591	0.875106
$274$	48.6689	2.94020
$275$	−5.52274	−0.333034
$276$	4.10282	0.246961
$277$	9.35781	0.562256	0.281128	−	0.959670i	$-0.409291\pi$
$277$	9.35781	0.562256	0.281128	+	0.959670i	$0.409291\pi$
$278$	20.5643	1.23337
$279$	1.96813	0.117829
$280$	28.8793	1.72587
$281$	−31.2948	−1.86689	−0.933445	−	0.358721i	$-0.883213\pi$
$281$	−31.2948	−1.86689	−0.933445	+	0.358721i	$0.883213\pi$
$282$	−23.1294	−1.37734
$283$	6.46574	0.384348	0.192174	−	0.981361i	$-0.438446\pi$
$283$	6.46574	0.384348	0.192174	+	0.981361i	$0.438446\pi$
$284$	30.1622	1.78980
$285$	0.778324	0.0461039
$286$	−5.19083	−0.306940
$287$	−24.2953	−1.43410
$288$	−6.79884	−0.400625
$289$	1.00000	0.0588235
$290$	−1.18737	−0.0697248
$291$	−13.6833	−0.802129
$292$	−9.71697	−0.568643
$293$	30.3716	1.77433	0.887165	−	0.461453i	$-0.152672\pi$
$293$	30.3716	1.77433	0.887165	+	0.461453i	$0.152672\pi$
$294$	37.4475	2.18398
$295$	−9.76689	−0.568650
$296$	−19.3869	−1.12684
$297$	−5.65649	−0.328223
$298$	−13.8911	−0.804689
$299$	2.30597	0.133358
$300$	−22.9860	−1.32710
$301$	−4.34231	−0.250287
$302$	5.43457	0.312724
$303$	−25.4748	−1.46349
$304$	−0.218868	−0.0125529
$305$	−22.6086	−1.29456
$306$	−2.16088	−0.123529
$307$	24.6632	1.40761	0.703803	−	0.710396i	$-0.251484\pi$
$307$	24.6632	1.40761	0.703803	+	0.710396i	$0.251484\pi$
$308$	−12.6967	−0.723460
$309$	11.4967	0.654026
$310$	−14.5479	−0.826265
$311$	5.99308	0.339836	0.169918	−	0.985458i	$-0.445650\pi$
$311$	5.99308	0.339836	0.169918	+	0.985458i	$0.445650\pi$
$312$	−6.82687	−0.386495
$313$	−23.0932	−1.30530	−0.652652	−	0.757658i	$-0.726343\pi$
$313$	−23.0932	−1.30530	−0.652652	+	0.757658i	$0.726343\pi$
$314$	−11.4894	−0.648387
$315$	13.7170	0.772865
$316$	49.3959	2.77873
$317$	25.1608	1.41317	0.706586	−	0.707627i	$-0.250234\pi$
$317$	25.1608	1.41317	0.706586	+	0.707627i	$0.250234\pi$
$318$	−6.33966	−0.355511
$319$	0.164955	0.00923571
$320$	41.8313	2.33844
$321$	2.41142	0.134592
$322$	9.49840	0.529325
$323$	−0.168561	−0.00937896
$324$	−15.0006	−0.833367
$325$	−12.9192	−0.716627
$326$	12.4468	0.689367
$327$	20.6693	1.14302
$328$	11.4710	0.633380
$329$	−31.7972	−1.75304
$330$	10.2462	0.564032
$331$	−1.95642	−0.107535	−0.0537673	−	0.998553i	$-0.517123\pi$
$331$	−1.95642	−0.107535	−0.0537673	+	0.998553i	$0.517123\pi$
$332$	−44.3818	−2.43577
$333$	−9.20836	−0.504615
$334$	−0.647469	−0.0354279
$335$	20.9809	1.14631
$336$	8.02577	0.437842
$337$	0.349007	0.0190116	0.00950581	−	0.999955i	$-0.496974\pi$
$337$	0.349007	0.0190116	0.00950581	+	0.999955i	$0.496974\pi$
$338$	16.7042	0.908587
$339$	19.4296	1.05527
$340$	9.48490	0.514391
$341$	2.02106	0.109447
$342$	0.364239	0.0196958
$343$	21.0848	1.13847
$344$	2.05022	0.110541
$345$	−4.55174	−0.245058
$346$	−34.5822	−1.85915
$347$	−5.08045	−0.272733	−0.136366	−	0.990658i	$-0.543542\pi$
$347$	−5.08045	−0.272733	−0.136366	+	0.990658i	$0.543542\pi$
$348$	0.686554	0.0368031
$349$	−32.3442	−1.73135	−0.865673	−	0.500610i	$-0.833109\pi$
$349$	−32.3442	−1.73135	−0.865673	+	0.500610i	$0.833109\pi$
$350$	−53.2147	−2.84445
$351$	−13.2321	−0.706276
$352$	−6.98170	−0.372126
$353$	5.66174	0.301344	0.150672	−	0.988584i	$-0.451856\pi$
$353$	5.66174	0.301344	0.150672	+	0.988584i	$0.451856\pi$
$354$	9.51018	0.505460
$355$	−33.4626	−1.77601
$356$	−39.7082	−2.10453
$357$	6.18104	0.327135
$358$	3.86292	0.204162
$359$	6.37066	0.336231	0.168115	−	0.985767i	$-0.446232\pi$
$359$	6.37066	0.336231	0.168115	+	0.985767i	$0.446232\pi$
$360$	−6.47647	−0.341340
$361$	−18.9716	−0.998505
$362$	−21.8322	−1.14748
$363$	−1.42344	−0.0747114
$364$	−29.7009	−1.55675
$365$	10.7802	0.564261
$366$	22.0143	1.15071
$367$	−8.19238	−0.427639	−0.213819	−	0.976873i	$-0.568590\pi$
$367$	−8.19238	−0.427639	−0.213819	+	0.976873i	$0.568590\pi$
$368$	1.27997	0.0667229
$369$	5.44846	0.283636
$370$	68.0659	3.53858
$371$	−8.71546	−0.452484
$372$	8.41179	0.436131
$373$	−0.765166	−0.0396188	−0.0198094	−	0.999804i	$-0.506306\pi$
$373$	−0.765166	−0.0396188	−0.0198094	+	0.999804i	$0.506306\pi$
$374$	−2.21900	−0.114742
$375$	2.41372	0.124644
$376$	15.0130	0.774239
$377$	0.385875	0.0198735
$378$	−54.5035	−2.80336
$379$	−33.4549	−1.71846	−0.859231	−	0.511587i	$-0.829058\pi$
$379$	−33.4549	−1.71846	−0.859231	+	0.511587i	$0.829058\pi$
$380$	−1.59878	−0.0820157
$381$	−15.8718	−0.813139
$382$	−21.4052	−1.09519
$383$	19.3524	0.988864	0.494432	−	0.869216i	$-0.335376\pi$
$383$	19.3524	0.988864	0.494432	+	0.869216i	$0.335376\pi$
$384$	−20.8557	−1.06429
$385$	14.0859	0.717885
$386$	−12.6228	−0.642483
$387$	0.973808	0.0495015
$388$	28.1073	1.42693
$389$	−11.0838	−0.561972	−0.280986	−	0.959712i	$-0.590662\pi$
$389$	−11.0838	−0.561972	−0.280986	+	0.959712i	$0.590662\pi$
$390$	23.9685	1.21369
$391$	0.985765	0.0498523
$392$	−24.3067	−1.22768
$393$	−30.7055	−1.54889
$394$	24.1711	1.21772
$395$	−54.8007	−2.75732
$396$	2.84736	0.143085
$397$	21.4575	1.07692	0.538460	−	0.842651i	$-0.319006\pi$
$397$	21.4575	1.07692	0.538460	+	0.842651i	$0.319006\pi$
$398$	18.3562	0.920115
$399$	−1.04188	−0.0521592
$400$	−7.17100	−0.358550
$401$	3.91375	0.195443	0.0977216	−	0.995214i	$-0.468845\pi$
$401$	3.91375	0.195443	0.0977216	+	0.995214i	$0.468845\pi$
$402$	−20.4294	−1.01893
$403$	4.72781	0.235509
$404$	52.3285	2.60344
$405$	16.6420	0.826946
$406$	1.58944	0.0788824
$407$	−9.45602	−0.468718
$408$	−2.91837	−0.144481
$409$	−16.9893	−0.840067	−0.420033	−	0.907509i	$-0.637982\pi$
$409$	−16.9893	−0.840067	−0.420033	+	0.907509i	$0.637982\pi$
$410$	−40.2737	−1.98898
$411$	31.2202	1.53998
$412$	−23.6158	−1.16347
$413$	13.0741	0.643336
$414$	−2.13012	−0.104689
$415$	49.2380	2.41700
$416$	−16.3321	−0.800746
$417$	13.1916	0.645996
$418$	0.374035	0.0182947
$419$	−10.3589	−0.506066	−0.253033	−	0.967458i	$-0.581428\pi$
$419$	−10.3589	−0.506066	−0.253033	+	0.967458i	$0.581428\pi$
$420$	58.6265	2.86068
$421$	−33.5034	−1.63286	−0.816429	−	0.577446i	$-0.804049\pi$
$421$	−33.5034	−1.63286	−0.816429	+	0.577446i	$0.804049\pi$
$422$	−39.9768	−1.94604
$423$	7.13085	0.346714
$424$	4.11500	0.199842
$425$	−5.52274	−0.267892
$426$	32.5830	1.57865
$427$	30.2642	1.46459
$428$	−4.95337	−0.239430
$429$	−3.32982	−0.160765
$430$	−7.19815	−0.347126
$431$	−20.9487	−1.00906	−0.504532	−	0.863393i	$-0.668335\pi$
$431$	−20.9487	−1.00906	−0.504532	+	0.863393i	$0.668335\pi$
$432$	−7.34468	−0.353371
$433$	−10.7961	−0.518828	−0.259414	−	0.965766i	$-0.583529\pi$
$433$	−10.7961	−0.518828	−0.259414	+	0.965766i	$0.583529\pi$
$434$	19.4741	0.934786
$435$	−0.761676	−0.0365196
$436$	−42.4575	−2.03335
$437$	−0.166161	−0.00794856
$438$	−10.4969	−0.501559
$439$	14.5954	0.696601	0.348301	−	0.937383i	$-0.386759\pi$
$439$	14.5954	0.696601	0.348301	+	0.937383i	$0.386759\pi$
$440$	−6.65066	−0.317058
$441$	−11.5452	−0.549769
$442$	−5.19083	−0.246903
$443$	21.2294	1.00864	0.504320	−	0.863517i	$-0.331743\pi$
$443$	21.2294	1.00864	0.504320	+	0.863517i	$0.331743\pi$
$444$	−39.3566	−1.86778
$445$	44.0531	2.08832
$446$	−32.8894	−1.55736
$447$	−8.91087	−0.421470
$448$	−55.9961	−2.64557
$449$	−37.2701	−1.75888	−0.879442	−	0.476006i	$-0.842084\pi$
$449$	−37.2701	−1.75888	−0.879442	+	0.476006i	$0.842084\pi$
$450$	11.9340	0.562572
$451$	5.59501	0.263459
$452$	−39.9110	−1.87725
$453$	3.48618	0.163795
$454$	−46.0607	−2.16174
$455$	32.9508	1.54476
$456$	0.491923	0.0230364
$457$	7.90582	0.369819	0.184909	−	0.982756i	$-0.440801\pi$
$457$	7.90582	0.369819	0.184909	+	0.982756i	$0.440801\pi$
$458$	30.2572	1.41382
$459$	−5.65649	−0.264022
$460$	9.34988	0.435941
$461$	39.3929	1.83471	0.917355	−	0.398069i	$-0.130320\pi$
$461$	39.3929	1.83471	0.917355	+	0.398069i	$0.130320\pi$
$462$	−13.7157	−0.638112
$463$	−14.1083	−0.655670	−0.327835	−	0.944735i	$-0.606319\pi$
$463$	−14.1083	−0.655670	−0.327835	+	0.944735i	$0.606319\pi$
$464$	0.214186	0.00994333
$465$	−9.33220	−0.432771
$466$	10.5892	0.490535
$467$	−16.3544	−0.756792	−0.378396	−	0.925644i	$-0.623524\pi$
$467$	−16.3544	−0.756792	−0.378396	+	0.925644i	$0.623524\pi$
$468$	6.66074	0.307893
$469$	−28.0854	−1.29686
$470$	−52.7095	−2.43131
$471$	−7.37026	−0.339604
$472$	−6.17295	−0.284133
$473$	1.00000	0.0459800
$474$	53.3604	2.45092
$475$	0.930915	0.0427133
$476$	−12.6967	−0.581951
$477$	1.95453	0.0894919
$478$	28.5960	1.30795
$479$	−27.5008	−1.25654	−0.628272	−	0.777994i	$-0.716238\pi$
$479$	−27.5008	−1.25654	−0.628272	+	0.777994i	$0.716238\pi$
$480$	32.2378	1.47145
$481$	−22.1202	−1.00859
$482$	−16.2358	−0.739518
$483$	6.09305	0.277243
$484$	2.92394	0.132906
$485$	−31.1828	−1.41594
$486$	21.4506	0.973021
$487$	35.0151	1.58668	0.793342	−	0.608776i	$-0.208339\pi$
$487$	35.0151	1.58668	0.793342	+	0.608776i	$0.208339\pi$
$488$	−14.2892	−0.646844
$489$	7.98441	0.361067
$490$	85.3389	3.85522
$491$	5.81085	0.262240	0.131120	−	0.991367i	$-0.458143\pi$
$491$	5.81085	0.262240	0.131120	+	0.991367i	$0.458143\pi$
$492$	23.2868	1.04985
$493$	0.164955	0.00742920
$494$	0.874970	0.0393667
$495$	−3.15891	−0.141983
$496$	2.62425	0.117832
$497$	44.7936	2.00927
$498$	−47.9438	−2.14842
$499$	35.4872	1.58862	0.794312	−	0.607510i	$-0.207831\pi$
$499$	35.4872	1.58862	0.794312	+	0.607510i	$0.207831\pi$
$500$	−4.95810	−0.221733
$501$	−0.415339	−0.0185560
$502$	−10.7017	−0.477641
$503$	−38.0822	−1.69800	−0.849001	−	0.528392i	$-0.822795\pi$
$503$	−38.0822	−1.69800	−0.849001	+	0.528392i	$0.822795\pi$
$504$	8.66952	0.386171
$505$	−58.0543	−2.58338
$506$	−2.18741	−0.0972421
$507$	10.7154	0.475888
$508$	32.6029	1.44652
$509$	−20.6921	−0.917163	−0.458582	−	0.888652i	$-0.651642\pi$
$509$	−20.6921	−0.917163	−0.458582	+	0.888652i	$0.651642\pi$
$510$	10.2462	0.453707
$511$	−14.4306	−0.638371
$512$	−14.3896	−0.635937
$513$	0.953461	0.0420964
$514$	−57.5984	−2.54056
$515$	26.1998	1.15450
$516$	4.16207	0.183225
$517$	7.32264	0.322050
$518$	−91.1142	−4.00333
$519$	−22.1838	−0.973761
$520$	−15.5577	−0.682251
$521$	−22.0626	−0.966578	−0.483289	−	0.875461i	$-0.660558\pi$
$521$	−22.0626	−0.966578	−0.483289	+	0.875461i	$0.660558\pi$
$522$	−0.356447	−0.0156013
$523$	−4.39028	−0.191974	−0.0959868	−	0.995383i	$-0.530601\pi$
$523$	−4.39028	−0.191974	−0.0959868	+	0.995383i	$0.530601\pi$
$524$	63.0732	2.75537
$525$	−34.1362	−1.48983
$526$	−52.6099	−2.29390
$527$	2.02106	0.0880388
$528$	−1.84827	−0.0804357
$529$	−22.0283	−0.957751
$530$	−14.4474	−0.627556
$531$	−2.93201	−0.127238
$532$	2.14016	0.0927876
$533$	13.0882	0.566915
$534$	−42.8952	−1.85626
$535$	5.49537	0.237585
$536$	13.2605	0.572767
$537$	2.47799	0.106933
$538$	−33.2024	−1.43146
$539$	−11.8557	−0.510660
$540$	−53.6513	−2.30878
$541$	−4.27903	−0.183970	−0.0919850	−	0.995760i	$-0.529321\pi$
$541$	−4.27903	−0.183970	−0.0919850	+	0.995760i	$0.529321\pi$
$542$	−53.8995	−2.31518
$543$	−14.0049	−0.601010
$544$	−6.98170	−0.299338
$545$	47.1032	2.01768
$546$	−32.0847	−1.37310
$547$	21.4055	0.915235	0.457617	−	0.889149i	$-0.348703\pi$
$547$	21.4055	0.915235	0.457617	+	0.889149i	$0.348703\pi$
$548$	−64.1304	−2.73951
$549$	−6.78707	−0.289665
$550$	12.2549	0.522552
$551$	−0.0278049	−0.00118453
$552$	−2.87683	−0.122446
$553$	73.3572	3.11947
$554$	−20.7649	−0.882218
$555$	43.6630	1.85339
$556$	−27.0973	−1.14918
$557$	10.6371	0.450708	0.225354	−	0.974277i	$-0.427646\pi$
$557$	10.6371	0.450708	0.225354	+	0.974277i	$0.427646\pi$
$558$	−4.36726	−0.184881
$559$	2.33927	0.0989406
$560$	18.2899	0.772888
$561$	−1.42344	−0.0600978
$562$	69.4430	2.92928
$563$	8.95936	0.377592	0.188796	−	0.982016i	$-0.439541\pi$
$563$	8.95936	0.377592	0.188796	+	0.982016i	$0.439541\pi$
$564$	30.4773	1.28333
$565$	44.2780	1.86279
$566$	−14.3474	−0.603068
$567$	−22.2772	−0.935556
$568$	−21.1493	−0.887404
$569$	−40.1706	−1.68404	−0.842019	−	0.539448i	$-0.818633\pi$
$569$	−40.1706	−1.68404	−0.842019	+	0.539448i	$0.818633\pi$
$570$	−1.72710	−0.0723402
$571$	−17.0870	−0.715069	−0.357534	−	0.933900i	$-0.616382\pi$
$571$	−17.0870	−0.715069	−0.357534	+	0.933900i	$0.616382\pi$
$572$	6.83989	0.285990
$573$	−13.7311	−0.573623
$574$	53.9111	2.25021
$575$	−5.44412	−0.227035
$576$	12.5577	0.523238
$577$	−13.8811	−0.577880	−0.288940	−	0.957347i	$-0.593303\pi$
$577$	−13.8811	−0.577880	−0.288940	+	0.957347i	$0.593303\pi$
$578$	−2.21900	−0.0922980
$579$	−8.09728	−0.336511
$580$	1.56458	0.0649658
$581$	−65.9109	−2.73444
$582$	30.3632	1.25859
$583$	2.00710	0.0831257
$584$	6.81339	0.281940
$585$	−7.38956	−0.305521
$586$	−67.3945	−2.78404
$587$	−27.8595	−1.14988	−0.574942	−	0.818194i	$-0.694975\pi$
$587$	−27.8595	−1.14988	−0.574942	+	0.818194i	$0.694975\pi$
$588$	−49.3441	−2.03492
$589$	−0.340671	−0.0140371
$590$	21.6727	0.892251
$591$	15.5053	0.637803
$592$	−12.2782	−0.504630
$593$	0.353922	0.0145338	0.00726692	−	0.999974i	$-0.497687\pi$
$593$	0.353922	0.0145338	0.00726692	+	0.999974i	$0.497687\pi$
$594$	12.5517	0.515004
$595$	14.0859	0.577467
$596$	18.3041	0.749765
$597$	11.7752	0.481926
$598$	−5.11694	−0.209247
$599$	−40.0065	−1.63462	−0.817311	−	0.576196i	$-0.804536\pi$
$599$	−40.0065	−1.63462	−0.817311	+	0.576196i	$0.804536\pi$
$600$	16.1174	0.657991
$601$	9.80601	0.399995	0.199998	−	0.979796i	$-0.435907\pi$
$601$	9.80601	0.399995	0.199998	+	0.979796i	$0.435907\pi$
$602$	9.63557	0.392717
$603$	6.29844	0.256492
$604$	−7.16106	−0.291380
$605$	−3.24388	−0.131882
$606$	56.5284	2.29631
$607$	43.3038	1.75765	0.878824	−	0.477147i	$-0.158329\pi$
$607$	43.3038	1.75765	0.878824	+	0.477147i	$0.158329\pi$
$608$	1.17684	0.0477271
$609$	1.01959	0.0413160
$610$	50.1683	2.03126
$611$	17.1297	0.692992
$612$	2.84736	0.115098
$613$	3.97962	0.160735	0.0803677	−	0.996765i	$-0.474391\pi$
$613$	3.97962	0.160735	0.0803677	+	0.996765i	$0.474391\pi$
$614$	−54.7276	−2.20863
$615$	−25.8348	−1.04176
$616$	8.90270	0.358700
$617$	−24.9581	−1.00478	−0.502388	−	0.864642i	$-0.667545\pi$
$617$	−24.9581	−1.00478	−0.502388	+	0.864642i	$0.667545\pi$
$618$	−25.5112	−1.02621
$619$	9.98236	0.401225	0.200612	−	0.979671i	$-0.435707\pi$
$619$	9.98236	0.401225	0.200612	+	0.979671i	$0.435707\pi$
$620$	19.1696	0.769869
$621$	−5.57597	−0.223756
$622$	−13.2986	−0.533226
$623$	−58.9702	−2.36259
$624$	−4.32361	−0.173083
$625$	−22.1131	−0.884523
$626$	51.2436	2.04811
$627$	0.239936	0.00958214
$628$	15.1395	0.604131
$629$	−9.45602	−0.377036
$630$	−30.4379	−1.21268
$631$	31.2136	1.24259	0.621296	−	0.783576i	$-0.286606\pi$
$631$	31.2136	1.24259	0.621296	+	0.783576i	$0.286606\pi$
$632$	−34.6356	−1.37773
$633$	−25.6443	−1.01927
$634$	−55.8317	−2.21736
$635$	−36.1702	−1.43537
$636$	8.35369	0.331245
$637$	−27.7336	−1.09885
$638$	−0.366034	−0.0144914
$639$	−10.0454	−0.397391
$640$	−47.5279	−1.87870
$641$	12.4159	0.490397	0.245198	−	0.969473i	$-0.421147\pi$
$641$	12.4159	0.490397	0.245198	+	0.969473i	$0.421147\pi$
$642$	−5.35093	−0.211184
$643$	26.7222	1.05382	0.526910	−	0.849921i	$-0.323351\pi$
$643$	26.7222	1.05382	0.526910	+	0.849921i	$0.323351\pi$
$644$	−12.5159	−0.493196
$645$	−4.61748	−0.181813
$646$	0.374035	0.0147162
$647$	−30.5218	−1.19993	−0.599967	−	0.800025i	$-0.704820\pi$
$647$	−30.5218	−1.19993	−0.599967	+	0.800025i	$0.704820\pi$
$648$	10.5182	0.413194
$649$	−3.01087	−0.118187
$650$	28.6676	1.12444
$651$	12.4923	0.489610
$652$	−16.4010	−0.642314
$653$	1.07982	0.0422566	0.0211283	−	0.999777i	$-0.493274\pi$
$653$	1.07982	0.0422566	0.0211283	+	0.999777i	$0.493274\pi$
$654$	−45.8652	−1.79347
$655$	−69.9746	−2.73414
$656$	7.26484	0.283644
$657$	3.23620	0.126256
$658$	70.5579	2.75063
$659$	8.32386	0.324252	0.162126	−	0.986770i	$-0.448165\pi$
$659$	8.32386	0.324252	0.162126	+	0.986770i	$0.448165\pi$
$660$	−13.5012	−0.525535
$661$	31.1013	1.20970	0.604850	−	0.796340i	$-0.293233\pi$
$661$	31.1013	1.20970	0.604850	+	0.796340i	$0.293233\pi$
$662$	4.34129	0.168729
$663$	−3.32982	−0.129320
$664$	31.1198	1.20768
$665$	−2.37433	−0.0920726
$666$	20.4333	0.791774
$667$	0.162607	0.00629616
$668$	0.853162	0.0330098
$669$	−21.0979	−0.815694
$670$	−46.5565	−1.79863
$671$	−6.96961	−0.269059
$672$	−43.1541	−1.66471
$673$	−35.9020	−1.38392	−0.691961	−	0.721935i	$-0.743253\pi$
$673$	−35.9020	−1.38392	−0.691961	+	0.721935i	$0.743253\pi$
$674$	−0.774445	−0.0298305
$675$	31.2393	1.20240
$676$	−22.0109	−0.846572
$677$	9.10901	0.350088	0.175044	−	0.984561i	$-0.443993\pi$
$677$	9.10901	0.350088	0.175044	+	0.984561i	$0.443993\pi$
$678$	−43.1142	−1.65579
$679$	41.7418	1.60191
$680$	−6.65066	−0.255041
$681$	−29.5471	−1.13225
$682$	−4.48473	−0.171729
$683$	−25.4418	−0.973503	−0.486751	−	0.873541i	$-0.661818\pi$
$683$	−25.4418	−0.973503	−0.486751	+	0.873541i	$0.661818\pi$
$684$	−0.479952	−0.0183514
$685$	71.1475	2.71840
$686$	−46.7871	−1.78634
$687$	19.4094	0.740515
$688$	1.29845	0.0495030
$689$	4.69516	0.178871
$690$	10.1003	0.384512
$691$	38.0233	1.44648	0.723238	−	0.690599i	$-0.242653\pi$
$691$	38.0233	1.44648	0.723238	+	0.690599i	$0.242653\pi$
$692$	45.5684	1.73225
$693$	4.22858	0.160630
$694$	11.2735	0.427936
$695$	30.0623	1.14033
$696$	−0.481400	−0.0182474
$697$	5.59501	0.211926
$698$	71.7717	2.71660
$699$	6.79277	0.256926
$700$	70.1203	2.65030
$701$	−38.7308	−1.46284	−0.731422	−	0.681925i	$-0.761143\pi$
$701$	−38.7308	−1.46284	−0.731422	+	0.681925i	$0.761143\pi$
$702$	29.3619	1.10819
$703$	1.59391	0.0601156
$704$	12.8955	0.486016
$705$	−33.8121	−1.27344
$706$	−12.5634	−0.472829
$707$	77.7125	2.92268
$708$	−12.5314	−0.470960
$709$	20.8392	0.782632	0.391316	−	0.920256i	$-0.372020\pi$
$709$	20.8392	0.782632	0.391316	+	0.920256i	$0.372020\pi$
$710$	74.2533	2.78668
$711$	−16.4511	−0.616965
$712$	27.8428	1.04345
$713$	1.99229	0.0746119
$714$	−13.7157	−0.513297
$715$	−7.58831	−0.283787
$716$	−5.09012	−0.190227
$717$	18.3438	0.685062
$718$	−14.1365	−0.527568
$719$	−7.75544	−0.289229	−0.144615	−	0.989488i	$-0.546194\pi$
$719$	−7.75544	−0.289229	−0.144615	+	0.989488i	$0.546194\pi$
$720$	−4.10169	−0.152861
$721$	−35.0716	−1.30613
$722$	42.0979	1.56672
$723$	−10.4149	−0.387335
$724$	28.7680	1.06915
$725$	−0.911003	−0.0338338
$726$	3.15861	0.117227
$727$	50.5169	1.87357	0.936783	−	0.349910i	$-0.113788\pi$
$727$	50.5169	1.87357	0.936783	+	0.349910i	$0.113788\pi$
$728$	20.8258	0.771857
$729$	29.1510	1.07967
$730$	−23.9212	−0.885364
$731$	1.00000	0.0369863
$732$	−29.0080	−1.07217
$733$	−0.907654	−0.0335250	−0.0167625	−	0.999859i	$-0.505336\pi$
$733$	−0.907654	−0.0335250	−0.0167625	+	0.999859i	$0.505336\pi$
$734$	18.1789	0.670994
$735$	54.7433	2.01924
$736$	−6.88231	−0.253685
$737$	6.46785	0.238246
$738$	−12.0901	−0.445043
$739$	34.5219	1.26991	0.634954	−	0.772550i	$-0.281019\pi$
$739$	34.5219	1.26991	0.634954	+	0.772550i	$0.281019\pi$
$740$	−89.6895	−3.29705
$741$	0.561276	0.0206190
$742$	19.3396	0.709978
$743$	4.82868	0.177147	0.0885736	−	0.996070i	$-0.471769\pi$
$743$	4.82868	0.177147	0.0885736	+	0.996070i	$0.471769\pi$
$744$	−5.89821	−0.216239
$745$	−20.3069	−0.743988
$746$	1.69790	0.0621645
$747$	14.7812	0.540816
$748$	2.92394	0.106910
$749$	−7.35620	−0.268790
$750$	−5.35604	−0.195575
$751$	−15.1984	−0.554598	−0.277299	−	0.960784i	$-0.589439\pi$
$751$	−15.1984	−0.554598	−0.277299	+	0.960784i	$0.589439\pi$
$752$	9.50809	0.346724
$753$	−6.86494	−0.250172
$754$	−0.856254	−0.0311829
$755$	7.94462	0.289134
$756$	71.8186	2.61202
$757$	5.94453	0.216057	0.108029	−	0.994148i	$-0.465546\pi$
$757$	5.94453	0.216057	0.108029	+	0.994148i	$0.465546\pi$
$758$	74.2363	2.69638
$759$	−1.40318	−0.0509322
$760$	1.12104	0.0406644
$761$	−1.82834	−0.0662772	−0.0331386	−	0.999451i	$-0.510550\pi$
$761$	−1.82834	−0.0662772	−0.0331386	+	0.999451i	$0.510550\pi$
$762$	35.2195	1.27587
$763$	−63.0532	−2.28268
$764$	28.2054	1.02044
$765$	−3.15891	−0.114211
$766$	−42.9430	−1.55159
$767$	−7.04324	−0.254317
$768$	9.56674	0.345210
$769$	−5.30186	−0.191190	−0.0955950	−	0.995420i	$-0.530475\pi$
$769$	−5.30186	−0.191190	−0.0955950	+	0.995420i	$0.530475\pi$
$770$	−31.2566	−1.12641
$771$	−36.9483	−1.33066
$772$	16.6329	0.598631
$773$	−0.739334	−0.0265920	−0.0132960	−	0.999912i	$-0.504232\pi$
$773$	−0.739334	−0.0265920	−0.0132960	+	0.999912i	$0.504232\pi$
$774$	−2.16088	−0.0776711
$775$	−11.1618	−0.400943
$776$	−19.7084	−0.707490
$777$	−58.4480	−2.09681
$778$	24.5950	0.881772
$779$	−0.943098	−0.0337900
$780$	−31.5830	−1.13085
$781$	−10.3156	−0.369121
$782$	−2.18741	−0.0782215
$783$	−0.933067	−0.0333451
$784$	−15.3940	−0.549786
$785$	−16.7960	−0.599476
$786$	68.1354	2.43031
$787$	−40.0836	−1.42883	−0.714413	−	0.699724i	$-0.753306\pi$
$787$	−40.0836	−1.42883	−0.714413	+	0.699724i	$0.753306\pi$
$788$	−31.8499	−1.13461
$789$	−33.7483	−1.20147
$790$	121.603	4.32643
$791$	−59.2713	−2.10744
$792$	−1.99652	−0.0709433
$793$	−16.3038	−0.578965
$794$	−47.6140	−1.68976
$795$	−9.26775	−0.328693
$796$	−24.1878	−0.857313
$797$	11.3744	0.402903	0.201452	−	0.979498i	$-0.435434\pi$
$797$	11.3744	0.402903	0.201452	+	0.979498i	$0.435434\pi$
$798$	2.31192	0.0818412
$799$	7.32264	0.259057
$800$	38.5581	1.36323
$801$	13.2247	0.467271
$802$	−8.68459	−0.306663
$803$	3.32324	0.117275
$804$	26.9196	0.949381
$805$	13.8854	0.489396
$806$	−10.4910	−0.369529
$807$	−21.2987	−0.749750
$808$	−36.6919	−1.29082
$809$	−8.25575	−0.290257	−0.145128	−	0.989413i	$-0.546360\pi$
$809$	−8.25575	−0.290257	−0.145128	+	0.989413i	$0.546360\pi$
$810$	−36.9285	−1.29753
$811$	−30.8723	−1.08407	−0.542036	−	0.840355i	$-0.682346\pi$
$811$	−30.8723	−1.08407	−0.542036	+	0.840355i	$0.682346\pi$
$812$	−2.09438	−0.0734983
$813$	−34.5755	−1.21262
$814$	20.9829	0.735449
$815$	18.1956	0.637365
$816$	−1.84827	−0.0647024
$817$	−0.168561	−0.00589719
$818$	37.6992	1.31812
$819$	9.89179	0.345647
$820$	53.0681	1.85322
$821$	6.02126	0.210143	0.105072	−	0.994465i	$-0.466493\pi$
$821$	6.02126	0.210143	0.105072	+	0.994465i	$0.466493\pi$
$822$	−69.2774	−2.41633
$823$	−30.1880	−1.05229	−0.526144	−	0.850395i	$-0.676363\pi$
$823$	−30.1880	−1.05229	−0.526144	+	0.850395i	$0.676363\pi$
$824$	16.5590	0.576861
$825$	7.86130	0.273695
$826$	−29.0115	−1.00944
$827$	−15.1863	−0.528078	−0.264039	−	0.964512i	$-0.585055\pi$
$827$	−15.1863	−0.528078	−0.264039	+	0.964512i	$0.585055\pi$
$828$	2.80683	0.0975439
$829$	−34.7492	−1.20689	−0.603445	−	0.797404i	$-0.706206\pi$
$829$	−34.7492	−1.20689	−0.603445	+	0.797404i	$0.706206\pi$
$830$	−109.259	−3.79243
$831$	−13.3203	−0.462077
$832$	30.1660	1.04582
$833$	−11.8557	−0.410775
$834$	−29.2721	−1.01361
$835$	−0.946514	−0.0327555
$836$	−0.492861	−0.0170460
$837$	−11.4321	−0.395152
$838$	22.9864	0.794051
$839$	−31.6224	−1.09173	−0.545863	−	0.837875i	$-0.683798\pi$
$839$	−31.6224	−1.09173	−0.545863	+	0.837875i	$0.683798\pi$
$840$	−41.1080	−1.41836
$841$	−28.9728	−0.999062
$842$	74.3440	2.56206
$843$	44.5464	1.53426
$844$	52.6769	1.81321
$845$	24.4193	0.840049
$846$	−15.8233	−0.544017
$847$	4.34231	0.149204
$848$	2.60612	0.0894946
$849$	−9.20362	−0.315867
$850$	12.2549	0.420341
$851$	−9.32141	−0.319534
$852$	−42.9342	−1.47090
$853$	−50.8142	−1.73985	−0.869923	−	0.493187i	$-0.835832\pi$
$853$	−50.8142	−1.73985	−0.869923	+	0.493187i	$0.835832\pi$
$854$	−67.1562	−2.29804
$855$	0.532468	0.0182100
$856$	3.47323	0.118712
$857$	−52.4053	−1.79013	−0.895066	−	0.445933i	$-0.852872\pi$
$857$	−52.4053	−1.79013	−0.895066	+	0.445933i	$0.852872\pi$
$858$	7.38886	0.252251
$859$	−18.1811	−0.620331	−0.310165	−	0.950683i	$-0.600384\pi$
$859$	−18.1811	−0.620331	−0.310165	+	0.950683i	$0.600384\pi$
$860$	9.48490	0.323433
$861$	34.5829	1.17858
$862$	46.4851	1.58329
$863$	−23.2488	−0.791399	−0.395699	−	0.918380i	$-0.629498\pi$
$863$	−23.2488	−0.791399	−0.395699	+	0.918380i	$0.629498\pi$
$864$	39.4919	1.34354
$865$	−50.5545	−1.71891
$866$	23.9565	0.814076
$867$	−1.42344	−0.0483427
$868$	−25.6607	−0.870982
$869$	−16.8936	−0.573076
$870$	1.69016	0.0573016
$871$	15.1300	0.512662
$872$	29.7706	1.00816
$873$	−9.36104	−0.316823
$874$	0.368711	0.0124718
$875$	−7.36322	−0.248922
$876$	13.8316	0.467325
$877$	−49.2444	−1.66286	−0.831432	−	0.555626i	$-0.812478\pi$
$877$	−49.2444	−1.66286	−0.831432	+	0.555626i	$0.812478\pi$
$878$	−32.3872	−1.09301
$879$	−43.2323	−1.45819
$880$	−4.21201	−0.141987
$881$	17.8498	0.601375	0.300687	−	0.953723i	$-0.402784\pi$
$881$	17.8498	0.601375	0.300687	+	0.953723i	$0.402784\pi$
$882$	25.6186	0.862624
$883$	11.7793	0.396404	0.198202	−	0.980161i	$-0.436490\pi$
$883$	11.7793	0.396404	0.198202	+	0.980161i	$0.436490\pi$
$884$	6.83989	0.230050
$885$	13.9026	0.467331
$886$	−47.1080	−1.58262
$887$	44.1033	1.48084	0.740422	−	0.672142i	$-0.234626\pi$
$887$	44.1033	1.48084	0.740422	+	0.672142i	$0.234626\pi$
$888$	27.5962	0.926068
$889$	48.4181	1.62389
$890$	−97.7536	−3.27671
$891$	5.13027	0.171871
$892$	43.3380	1.45106
$893$	−1.23431	−0.0413046
$894$	19.7732	0.661314
$895$	5.64708	0.188761
$896$	63.6217	2.12545
$897$	−3.28242	−0.109597
$898$	82.7021	2.75981
$899$	0.333384	0.0111190
$900$	−15.7252	−0.524174
$901$	2.00710	0.0668663
$902$	−12.4153	−0.413384
$903$	6.18104	0.205692
$904$	27.9849	0.930765
$905$	−31.9158	−1.06092
$906$	−7.73581	−0.257005
$907$	−55.7734	−1.85193	−0.925963	−	0.377615i	$-0.876744\pi$
$907$	−55.7734	−1.85193	−0.925963	+	0.377615i	$0.876744\pi$
$908$	60.6936	2.01419
$909$	−17.4278	−0.578045
$910$	−73.1177	−2.42383
$911$	49.7052	1.64681	0.823403	−	0.567457i	$-0.192073\pi$
$911$	49.7052	1.64681	0.823403	+	0.567457i	$0.192073\pi$
$912$	0.311546	0.0103163
$913$	15.1788	0.502344
$914$	−17.5430	−0.580270
$915$	32.1820	1.06390
$916$	−39.8695	−1.31732
$917$	93.6693	3.09323
$918$	12.5517	0.414269
$919$	−12.9447	−0.427006	−0.213503	−	0.976942i	$-0.568487\pi$
$919$	−12.9447	−0.427006	−0.213503	+	0.976942i	$0.568487\pi$
$920$	−6.55599	−0.216145
$921$	−35.1067	−1.15681
$922$	−87.4127	−2.87878
$923$	−24.1310	−0.794282
$924$	18.0730	0.594558
$925$	52.2231	1.71709
$926$	31.3063	1.02879
$927$	7.86516	0.258326
$928$	−1.15167	−0.0378053
$929$	−31.3268	−1.02780	−0.513899	−	0.857851i	$-0.671799\pi$
$929$	−31.3268	−1.02780	−0.513899	+	0.857851i	$0.671799\pi$
$930$	20.7081	0.679046
$931$	1.99840	0.0654949
$932$	−13.9532	−0.457054
$933$	−8.53081	−0.279286
$934$	36.2904	1.18746
$935$	−3.24388	−0.106086
$936$	−4.67041	−0.152657
$937$	−33.6348	−1.09880	−0.549401	−	0.835559i	$-0.685144\pi$
$937$	−33.6348	−1.09880	−0.549401	+	0.835559i	$0.685144\pi$
$938$	62.3214	2.03486
$939$	32.8718	1.07273
$940$	69.4546	2.26536
$941$	10.7913	0.351787	0.175894	−	0.984409i	$-0.443719\pi$
$941$	10.7913	0.351787	0.175894	+	0.984409i	$0.443719\pi$
$942$	16.3546	0.532861
$943$	5.51536	0.179605
$944$	−3.90947	−0.127242
$945$	−79.6769	−2.59189
$946$	−2.21900	−0.0721458
$947$	−36.8685	−1.19807	−0.599033	−	0.800724i	$-0.704448\pi$
$947$	−36.8685	−1.19807	−0.599033	+	0.800724i	$0.704448\pi$
$948$	−70.3122	−2.28364
$949$	7.77397	0.252354
$950$	−2.06570	−0.0670201
$951$	−35.8150	−1.16138
$952$	8.90270	0.288538
$953$	−24.7583	−0.802000	−0.401000	−	0.916078i	$-0.631337\pi$
$953$	−24.7583	−0.802000	−0.401000	+	0.916078i	$0.631337\pi$
$954$	−4.33710	−0.140419
$955$	−31.2916	−1.01257
$956$	−37.6806	−1.21868
$957$	−0.234804	−0.00759014
$958$	61.0242	1.97160
$959$	−95.2393	−3.07544
$960$	−59.5445	−1.92179
$961$	−26.9153	−0.868236
$962$	49.0846	1.58255
$963$	1.64970	0.0531609
$964$	21.3936	0.689043
$965$	−18.4528	−0.594018
$966$	−13.5204	−0.435013
$967$	−26.4393	−0.850232	−0.425116	−	0.905139i	$-0.639767\pi$
$967$	−26.4393	−0.850232	−0.425116	+	0.905139i	$0.639767\pi$
$968$	−2.05022	−0.0658966
$969$	0.239936	0.00770787
$970$	69.1945	2.22170
$971$	12.3613	0.396692	0.198346	−	0.980132i	$-0.436443\pi$
$971$	12.3613	0.396692	0.198346	+	0.980132i	$0.436443\pi$
$972$	−28.2652	−0.906607
$973$	−40.2419	−1.29010
$974$	−77.6983	−2.48961
$975$	18.3897	0.588942
$976$	−9.04970	−0.289674
$977$	−8.22409	−0.263112	−0.131556	−	0.991309i	$-0.541997\pi$
$977$	−8.22409	−0.263112	−0.131556	+	0.991309i	$0.541997\pi$
$978$	−17.7174	−0.566539
$979$	13.5804	0.434031
$980$	−112.450	−3.59208
$981$	14.1403	0.451466
$982$	−12.8942	−0.411472
$983$	−36.9045	−1.17707	−0.588535	−	0.808471i	$-0.700295\pi$
$983$	−36.9045	−1.17707	−0.588535	+	0.808471i	$0.700295\pi$
$984$	−16.3283	−0.520528
$985$	35.3349	1.12586
$986$	−0.366034	−0.0116569
$987$	45.2615	1.44069
$988$	−1.15294	−0.0366798
$989$	0.985765	0.0313455
$990$	7.00962	0.222780
$991$	−31.6841	−1.00648	−0.503239	−	0.864147i	$-0.667858\pi$
$991$	−31.6841	−1.00648	−0.503239	+	0.864147i	$0.667858\pi$
$992$	−14.1104	−0.448007
$993$	2.78486	0.0883747
$994$	−99.3968	−3.15267
$995$	26.8344	0.850707
$996$	63.1750	2.00178
$997$	21.2341	0.672489	0.336245	−	0.941775i	$-0.390843\pi$
$997$	21.2341	0.672489	0.336245	+	0.941775i	$0.390843\pi$
$998$	−78.7459	−2.49266
$999$	53.4879	1.69228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.11	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.11	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21900 q^{2} -1.42344 q^{3} +2.92394 q^{4} -3.24388 q^{5} +3.15861 q^{6} +4.34231 q^{7} -2.05022 q^{8} -0.973808 q^{9} +O(q^{10})\)	\(q-2.21900 q^{2} -1.42344 q^{3} +2.92394 q^{4} -3.24388 q^{5} +3.15861 q^{6} +4.34231 q^{7} -2.05022 q^{8} -0.973808 q^{9} +7.19815 q^{10} -1.00000 q^{11} -4.16207 q^{12} -2.33927 q^{13} -9.63557 q^{14} +4.61748 q^{15} -1.29845 q^{16} -1.00000 q^{17} +2.16088 q^{18} +0.168561 q^{19} -9.48490 q^{20} -6.18104 q^{21} +2.21900 q^{22} -0.985765 q^{23} +2.91837 q^{24} +5.52274 q^{25} +5.19083 q^{26} +5.65649 q^{27} +12.6967 q^{28} -0.164955 q^{29} -10.2462 q^{30} -2.02106 q^{31} +6.98170 q^{32} +1.42344 q^{33} +2.21900 q^{34} -14.0859 q^{35} -2.84736 q^{36} +9.45602 q^{37} -0.374035 q^{38} +3.32982 q^{39} +6.65066 q^{40} -5.59501 q^{41} +13.7157 q^{42} -1.00000 q^{43} -2.92394 q^{44} +3.15891 q^{45} +2.18741 q^{46} -7.32264 q^{47} +1.84827 q^{48} +11.8557 q^{49} -12.2549 q^{50} +1.42344 q^{51} -6.83989 q^{52} -2.00710 q^{53} -12.5517 q^{54} +3.24388 q^{55} -8.90270 q^{56} -0.239936 q^{57} +0.366034 q^{58} +3.01087 q^{59} +13.5012 q^{60} +6.96961 q^{61} +4.48473 q^{62} -4.22858 q^{63} -12.8955 q^{64} +7.58831 q^{65} -3.15861 q^{66} -6.46785 q^{67} -2.92394 q^{68} +1.40318 q^{69} +31.2566 q^{70} +10.3156 q^{71} +1.99652 q^{72} -3.32324 q^{73} -20.9829 q^{74} -7.86130 q^{75} +0.492861 q^{76} -4.34231 q^{77} -7.38886 q^{78} +16.8936 q^{79} +4.21201 q^{80} -5.13027 q^{81} +12.4153 q^{82} -15.1788 q^{83} -18.0730 q^{84} +3.24388 q^{85} +2.21900 q^{86} +0.234804 q^{87} +2.05022 q^{88} -13.5804 q^{89} -7.00962 q^{90} -10.1578 q^{91} -2.88232 q^{92} +2.87687 q^{93} +16.2489 q^{94} -0.546790 q^{95} -9.93805 q^{96} +9.61282 q^{97} -26.3077 q^{98} +0.973808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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