LMFDB - Embedded newform 6005.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36067 q^{2} +1.42227 q^{3} +3.57275 q^{4} -1.00000 q^{5} -3.35751 q^{6} -1.80334 q^{7} -3.71273 q^{8} -0.977139 q^{9} +O(q^{10})$	\(q-2.36067 q^{2} +1.42227 q^{3} +3.57275 q^{4} -1.00000 q^{5} -3.35751 q^{6} -1.80334 q^{7} -3.71273 q^{8} -0.977139 q^{9} +2.36067 q^{10} -2.47714 q^{11} +5.08142 q^{12} -1.37437 q^{13} +4.25708 q^{14} -1.42227 q^{15} +1.61903 q^{16} +3.43636 q^{17} +2.30670 q^{18} -0.783711 q^{19} -3.57275 q^{20} -2.56484 q^{21} +5.84769 q^{22} +2.09971 q^{23} -5.28052 q^{24} +1.00000 q^{25} +3.24443 q^{26} -5.65658 q^{27} -6.44288 q^{28} +0.723089 q^{29} +3.35751 q^{30} +7.03722 q^{31} +3.60348 q^{32} -3.52316 q^{33} -8.11209 q^{34} +1.80334 q^{35} -3.49107 q^{36} +0.374005 q^{37} +1.85008 q^{38} -1.95473 q^{39} +3.71273 q^{40} +6.29483 q^{41} +6.05474 q^{42} +6.94285 q^{43} -8.85018 q^{44} +0.977139 q^{45} -4.95672 q^{46} -3.03606 q^{47} +2.30270 q^{48} -3.74797 q^{49} -2.36067 q^{50} +4.88744 q^{51} -4.91028 q^{52} -6.81469 q^{53} +13.3533 q^{54} +2.47714 q^{55} +6.69532 q^{56} -1.11465 q^{57} -1.70697 q^{58} +6.39592 q^{59} -5.08142 q^{60} +3.11201 q^{61} -16.6125 q^{62} +1.76211 q^{63} -11.7447 q^{64} +1.37437 q^{65} +8.31702 q^{66} +6.49133 q^{67} +12.2772 q^{68} +2.98637 q^{69} -4.25708 q^{70} +8.68287 q^{71} +3.62785 q^{72} -5.07379 q^{73} -0.882901 q^{74} +1.42227 q^{75} -2.80000 q^{76} +4.46712 q^{77} +4.61447 q^{78} +2.48138 q^{79} -1.61903 q^{80} -5.11378 q^{81} -14.8600 q^{82} -1.19566 q^{83} -9.16353 q^{84} -3.43636 q^{85} -16.3898 q^{86} +1.02843 q^{87} +9.19694 q^{88} +6.88880 q^{89} -2.30670 q^{90} +2.47846 q^{91} +7.50175 q^{92} +10.0088 q^{93} +7.16712 q^{94} +0.783711 q^{95} +5.12513 q^{96} -15.5180 q^{97} +8.84770 q^{98} +2.42051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−2.36067	−1.66924	−0.834622	−	0.550824i	$-0.814314\pi$
$2$	−2.36067	−1.66924	−0.834622	+	0.550824i	$0.814314\pi$
$3$	1.42227	0.821150	0.410575	−	0.911827i	$-0.365328\pi$
$3$	1.42227	0.821150	0.410575	+	0.911827i	$0.365328\pi$
$4$	3.57275	1.78637
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.35751	−1.37070
$7$	−1.80334	−0.681598	−0.340799	−	0.940136i	$-0.610698\pi$
$7$	−1.80334	−0.681598	−0.340799	+	0.940136i	$0.610698\pi$
$8$	−3.71273	−1.31265
$9$	−0.977139	−0.325713
$10$	2.36067	0.746508
$11$	−2.47714	−0.746885	−0.373442	−	0.927653i	$-0.621823\pi$
$11$	−2.47714	−0.746885	−0.373442	+	0.927653i	$0.621823\pi$
$12$	5.08142	1.46688
$13$	−1.37437	−0.381182	−0.190591	−	0.981670i	$-0.561040\pi$
$13$	−1.37437	−0.381182	−0.190591	+	0.981670i	$0.561040\pi$
$14$	4.25708	1.13775
$15$	−1.42227	−0.367229
$16$	1.61903	0.404757
$17$	3.43636	0.833439	0.416720	−	0.909035i	$-0.363180\pi$
$17$	3.43636	0.833439	0.416720	+	0.909035i	$0.363180\pi$
$18$	2.30670	0.543694
$19$	−0.783711	−0.179796	−0.0898978	−	0.995951i	$-0.528654\pi$
$19$	−0.783711	−0.179796	−0.0898978	+	0.995951i	$0.528654\pi$
$20$	−3.57275	−0.798891
$21$	−2.56484	−0.559694
$22$	5.84769	1.24673
$23$	2.09971	0.437821	0.218910	−	0.975745i	$-0.429750\pi$
$23$	2.09971	0.437821	0.218910	+	0.975745i	$0.429750\pi$
$24$	−5.28052	−1.07788
$25$	1.00000	0.200000
$26$	3.24443	0.636285
$27$	−5.65658	−1.08861
$28$	−6.44288	−1.21759
$29$	0.723089	0.134274	0.0671372	−	0.997744i	$-0.478613\pi$
$29$	0.723089	0.134274	0.0671372	+	0.997744i	$0.478613\pi$
$30$	3.35751	0.612995
$31$	7.03722	1.26392	0.631961	−	0.775000i	$-0.282250\pi$
$31$	7.03722	1.26392	0.631961	+	0.775000i	$0.282250\pi$
$32$	3.60348	0.637011
$33$	−3.52316	−0.613304
$34$	−8.11209	−1.39121
$35$	1.80334	0.304820
$36$	−3.49107	−0.581845
$37$	0.374005	0.0614860	0.0307430	−	0.999527i	$-0.490213\pi$
$37$	0.374005	0.0614860	0.0307430	+	0.999527i	$0.490213\pi$
$38$	1.85008	0.300123
$39$	−1.95473	−0.313007
$40$	3.71273	0.587034
$41$	6.29483	0.983087	0.491543	−	0.870853i	$-0.336433\pi$
$41$	6.29483	0.983087	0.491543	+	0.870853i	$0.336433\pi$
$42$	6.05474	0.934266
$43$	6.94285	1.05878	0.529388	−	0.848380i	$-0.322422\pi$
$43$	6.94285	1.05878	0.529388	+	0.848380i	$0.322422\pi$
$44$	−8.85018	−1.33422
$45$	0.977139	0.145663
$46$	−4.95672	−0.730829
$47$	−3.03606	−0.442855	−0.221427	−	0.975177i	$-0.571072\pi$
$47$	−3.03606	−0.442855	−0.221427	+	0.975177i	$0.571072\pi$
$48$	2.30270	0.332366
$49$	−3.74797	−0.535424
$50$	−2.36067	−0.333849
$51$	4.88744	0.684378
$52$	−4.91028	−0.680933
$53$	−6.81469	−0.936070	−0.468035	−	0.883710i	$-0.655038\pi$
$53$	−6.81469	−0.936070	−0.468035	+	0.883710i	$0.655038\pi$
$54$	13.3533	1.81715
$55$	2.47714	0.334017
$56$	6.69532	0.894699
$57$	−1.11465	−0.147639
$58$	−1.70697	−0.224137
$59$	6.39592	0.832677	0.416339	−	0.909210i	$-0.363313\pi$
$59$	6.39592	0.832677	0.416339	+	0.909210i	$0.363313\pi$
$60$	−5.08142	−0.656009
$61$	3.11201	0.398452	0.199226	−	0.979954i	$-0.436157\pi$
$61$	3.11201	0.398452	0.199226	+	0.979954i	$0.436157\pi$
$62$	−16.6125	−2.10979
$63$	1.76211	0.222005
$64$	−11.7447	−1.46808
$65$	1.37437	0.170470
$66$	8.31702	1.02375
$67$	6.49133	0.793043	0.396521	−	0.918026i	$-0.370217\pi$
$67$	6.49133	0.793043	0.396521	+	0.918026i	$0.370217\pi$
$68$	12.2772	1.48883
$69$	2.98637	0.359516
$70$	−4.25708	−0.508819
$71$	8.68287	1.03047	0.515234	−	0.857050i	$-0.327705\pi$
$71$	8.68287	1.03047	0.515234	+	0.857050i	$0.327705\pi$
$72$	3.62785	0.427547
$73$	−5.07379	−0.593842	−0.296921	−	0.954902i	$-0.595960\pi$
$73$	−5.07379	−0.593842	−0.296921	+	0.954902i	$0.595960\pi$
$74$	−0.882901	−0.102635
$75$	1.42227	0.164230
$76$	−2.80000	−0.321182
$77$	4.46712	0.509075
$78$	4.61447	0.522486
$79$	2.48138	0.279177	0.139588	−	0.990210i	$-0.455422\pi$
$79$	2.48138	0.279177	0.139588	+	0.990210i	$0.455422\pi$
$80$	−1.61903	−0.181013
$81$	−5.11378	−0.568198
$82$	−14.8600	−1.64101
$83$	−1.19566	−0.131240	−0.0656202	−	0.997845i	$-0.520903\pi$
$83$	−1.19566	−0.131240	−0.0656202	+	0.997845i	$0.520903\pi$
$84$	−9.16353	−0.999823
$85$	−3.43636	−0.372725
$86$	−16.3898	−1.76735
$87$	1.02843	0.110259
$88$	9.19694	0.980397
$89$	6.88880	0.730211	0.365105	−	0.930966i	$-0.381033\pi$
$89$	6.88880	0.730211	0.365105	+	0.930966i	$0.381033\pi$
$90$	−2.30670	−0.243147
$91$	2.47846	0.259813
$92$	7.50175	0.782111
$93$	10.0088	1.03787
$94$	7.16712	0.739232
$95$	0.783711	0.0804071
$96$	5.12513	0.523081
$97$	−15.5180	−1.57561	−0.787807	−	0.615922i	$-0.788784\pi$
$97$	−15.5180	−1.57561	−0.787807	+	0.615922i	$0.788784\pi$
$98$	8.84770	0.893753
$99$	2.42051	0.243270
$100$	3.57275	0.357275
$101$	−9.54086	−0.949351	−0.474676	−	0.880161i	$-0.657435\pi$
$101$	−9.54086	−0.949351	−0.474676	+	0.880161i	$0.657435\pi$
$102$	−11.5376	−1.14239
$103$	14.8738	1.46556	0.732782	−	0.680464i	$-0.238222\pi$
$103$	14.8738	1.46556	0.732782	+	0.680464i	$0.238222\pi$
$104$	5.10267	0.500358
$105$	2.56484	0.250303
$106$	16.0872	1.56253
$107$	0.0352599	0.00340870	0.00170435	−	0.999999i	$-0.499457\pi$
$107$	0.0352599	0.00340870	0.00170435	+	0.999999i	$0.499457\pi$
$108$	−20.2095	−1.94466
$109$	−16.8764	−1.61646	−0.808232	−	0.588864i	$-0.799575\pi$
$109$	−16.8764	−1.61646	−0.808232	+	0.588864i	$0.799575\pi$
$110$	−5.84769	−0.557556
$111$	0.531937	0.0504892
$112$	−2.91966	−0.275882
$113$	7.99228	0.751851	0.375925	−	0.926650i	$-0.377325\pi$
$113$	7.99228	0.751851	0.375925	+	0.926650i	$0.377325\pi$
$114$	2.63132	0.246446
$115$	−2.09971	−0.195799
$116$	2.58342	0.239864
$117$	1.34295	0.124156
$118$	−15.0986	−1.38994
$119$	−6.19692	−0.568071
$120$	5.28052	0.482043
$121$	−4.86380	−0.442163
$122$	−7.34642	−0.665113
$123$	8.95296	0.807261
$124$	25.1422	2.25784
$125$	−1.00000	−0.0894427
$126$	−4.15976	−0.370581
$127$	6.32252	0.561033	0.280516	−	0.959849i	$-0.409494\pi$
$127$	6.32252	0.561033	0.280516	+	0.959849i	$0.409494\pi$
$128$	20.5183	1.81358
$129$	9.87463	0.869413
$130$	−3.24443	−0.284555
$131$	−15.1999	−1.32802	−0.664009	−	0.747725i	$-0.731146\pi$
$131$	−15.1999	−1.32802	−0.664009	+	0.747725i	$0.731146\pi$
$132$	−12.5874	−1.09559
$133$	1.41330	0.122548
$134$	−15.3239	−1.32378
$135$	5.65658	0.486841
$136$	−12.7583	−1.09401
$137$	9.99845	0.854225	0.427112	−	0.904199i	$-0.359531\pi$
$137$	9.99845	0.854225	0.427112	+	0.904199i	$0.359531\pi$
$138$	−7.04982	−0.600120
$139$	1.84482	0.156475	0.0782377	−	0.996935i	$-0.475071\pi$
$139$	1.84482	0.156475	0.0782377	+	0.996935i	$0.475071\pi$
$140$	6.44288	0.544522
$141$	−4.31810	−0.363650
$142$	−20.4974	−1.72010
$143$	3.40450	0.284699
$144$	−1.58202	−0.131835
$145$	−0.723089	−0.0600493
$146$	11.9775	0.991267
$147$	−5.33063	−0.439663
$148$	1.33622	0.109837
$149$	3.46024	0.283474	0.141737	−	0.989904i	$-0.454731\pi$
$149$	3.46024	0.283474	0.141737	+	0.989904i	$0.454731\pi$
$150$	−3.35751	−0.274140
$151$	−19.0218	−1.54797	−0.773986	−	0.633202i	$-0.781740\pi$
$151$	−19.0218	−1.54797	−0.773986	+	0.633202i	$0.781740\pi$
$152$	2.90971	0.236009
$153$	−3.35780	−0.271462
$154$	−10.5454	−0.849771
$155$	−7.03722	−0.565243
$156$	−6.98376	−0.559148
$157$	−19.6740	−1.57016	−0.785078	−	0.619397i	$-0.787377\pi$
$157$	−19.6740	−1.57016	−0.785078	+	0.619397i	$0.787377\pi$
$158$	−5.85770	−0.466014
$159$	−9.69236	−0.768654
$160$	−3.60348	−0.284880
$161$	−3.78650	−0.298418
$162$	12.0719	0.948461
$163$	−2.36594	−0.185315	−0.0926574	−	0.995698i	$-0.529536\pi$
$163$	−2.36594	−0.185315	−0.0926574	+	0.995698i	$0.529536\pi$
$164$	22.4898	1.75616
$165$	3.52316	0.274278
$166$	2.82255	0.219072
$167$	−5.65903	−0.437909	−0.218954	−	0.975735i	$-0.570265\pi$
$167$	−5.65903	−0.437909	−0.218954	+	0.975735i	$0.570265\pi$
$168$	9.52257	0.734682
$169$	−11.1111	−0.854700
$170$	8.11209	0.622169
$171$	0.765795	0.0585618
$172$	24.8051	1.89137
$173$	20.1494	1.53193	0.765966	−	0.642881i	$-0.222261\pi$
$173$	20.1494	1.53193	0.765966	+	0.642881i	$0.222261\pi$
$174$	−2.42778	−0.184050
$175$	−1.80334	−0.136320
$176$	−4.01055	−0.302307
$177$	9.09674	0.683753
$178$	−16.2621	−1.21890
$179$	−17.9245	−1.33974	−0.669869	−	0.742479i	$-0.733650\pi$
$179$	−17.9245	−1.33974	−0.669869	+	0.742479i	$0.733650\pi$
$180$	3.49107	0.260209
$181$	−25.1269	−1.86767	−0.933836	−	0.357702i	$-0.883560\pi$
$181$	−25.1269	−1.86767	−0.933836	+	0.357702i	$0.883560\pi$
$182$	−5.85081	−0.433691
$183$	4.42613	0.327189
$184$	−7.79568	−0.574705
$185$	−0.374005	−0.0274974
$186$	−23.6275	−1.73246
$187$	−8.51233	−0.622483
$188$	−10.8471	−0.791104
$189$	10.2007	0.741994
$190$	−1.85008	−0.134219
$191$	−14.4853	−1.04812	−0.524058	−	0.851682i	$-0.675583\pi$
$191$	−14.4853	−1.04812	−0.524058	+	0.851682i	$0.675583\pi$
$192$	−16.7041	−1.20552
$193$	−0.591360	−0.0425670	−0.0212835	−	0.999773i	$-0.506775\pi$
$193$	−0.591360	−0.0425670	−0.0212835	+	0.999773i	$0.506775\pi$
$194$	36.6328	2.63008
$195$	1.95473	0.139981
$196$	−13.3905	−0.956467
$197$	8.32864	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$197$	8.32864	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$198$	−5.71401	−0.406077
$199$	−4.77772	−0.338684	−0.169342	−	0.985557i	$-0.554164\pi$
$199$	−4.77772	−0.338684	−0.169342	+	0.985557i	$0.554164\pi$
$200$	−3.71273	−0.262530
$201$	9.23245	0.651207
$202$	22.5228	1.58470
$203$	−1.30398	−0.0915211
$204$	17.4616	1.22256
$205$	−6.29483	−0.439650
$206$	−35.1122	−2.44638
$207$	−2.05171	−0.142604
$208$	−2.22515	−0.154286
$209$	1.94136	0.134287
$210$	−6.05474	−0.417816
$211$	−8.00888	−0.551354	−0.275677	−	0.961250i	$-0.588902\pi$
$211$	−8.00888	−0.551354	−0.275677	+	0.961250i	$0.588902\pi$
$212$	−24.3472	−1.67217
$213$	12.3494	0.846168
$214$	−0.0832368	−0.00568995
$215$	−6.94285	−0.473499
$216$	21.0014	1.42896
$217$	−12.6905	−0.861486
$218$	39.8395	2.69827
$219$	−7.21632	−0.487633
$220$	8.85018	0.596679
$221$	−4.72283	−0.317692
$222$	−1.25573	−0.0842788
$223$	12.5455	0.840111	0.420055	−	0.907498i	$-0.362011\pi$
$223$	12.5455	0.840111	0.420055	+	0.907498i	$0.362011\pi$
$224$	−6.49829	−0.434186
$225$	−0.977139	−0.0651426
$226$	−18.8671	−1.25502
$227$	−25.3113	−1.67997	−0.839986	−	0.542608i	$-0.817437\pi$
$227$	−25.3113	−1.67997	−0.839986	+	0.542608i	$0.817437\pi$
$228$	−3.98237	−0.263739
$229$	−1.29433	−0.0855318	−0.0427659	−	0.999085i	$-0.513617\pi$
$229$	−1.29433	−0.0855318	−0.0427659	+	0.999085i	$0.513617\pi$
$230$	4.95672	0.326837
$231$	6.35346	0.418027
$232$	−2.68464	−0.176255
$233$	−20.5824	−1.34840	−0.674199	−	0.738549i	$-0.735511\pi$
$233$	−20.5824	−1.34840	−0.674199	+	0.738549i	$0.735511\pi$
$234$	−3.17026	−0.207246
$235$	3.03606	0.198051
$236$	22.8510	1.48747
$237$	3.52919	0.229246
$238$	14.6289	0.948248
$239$	−23.9994	−1.55239	−0.776197	−	0.630490i	$-0.782854\pi$
$239$	−23.9994	−1.55239	−0.776197	+	0.630490i	$0.782854\pi$
$240$	−2.30270	−0.148639
$241$	4.58276	0.295202	0.147601	−	0.989047i	$-0.452845\pi$
$241$	4.58276	0.295202	0.147601	+	0.989047i	$0.452845\pi$
$242$	11.4818	0.738078
$243$	9.69654	0.622033
$244$	11.1184	0.711784
$245$	3.74797	0.239449
$246$	−21.1350	−1.34752
$247$	1.07711	0.0685349
$248$	−26.1273	−1.65908
$249$	−1.70055	−0.107768
$250$	2.36067	0.149302
$251$	−4.06436	−0.256540	−0.128270	−	0.991739i	$-0.540942\pi$
$251$	−4.06436	−0.256540	−0.128270	+	0.991739i	$0.540942\pi$
$252$	6.29558	0.396585
$253$	−5.20128	−0.327002
$254$	−14.9254	−0.936500
$255$	−4.88744	−0.306063
$256$	−24.9475	−1.55922
$257$	−7.15683	−0.446431	−0.223215	−	0.974769i	$-0.571655\pi$
$257$	−7.15683	−0.446431	−0.223215	+	0.974769i	$0.571655\pi$
$258$	−23.3107	−1.45126
$259$	−0.674458	−0.0419088
$260$	4.91028	0.304523
$261$	−0.706559	−0.0437349
$262$	35.8818	2.21678
$263$	23.7097	1.46200	0.731000	−	0.682377i	$-0.239054\pi$
$263$	23.7097	1.46200	0.731000	+	0.682377i	$0.239054\pi$
$264$	13.0806	0.805053
$265$	6.81469	0.418623
$266$	−3.33632	−0.204563
$267$	9.79775	0.599612
$268$	23.1919	1.41667
$269$	7.06181	0.430566	0.215283	−	0.976552i	$-0.430933\pi$
$269$	7.06181	0.430566	0.215283	+	0.976552i	$0.430933\pi$
$270$	−13.3533	−0.812656
$271$	−10.8636	−0.659917	−0.329959	−	0.943995i	$-0.607035\pi$
$271$	−10.8636	−0.659917	−0.329959	+	0.943995i	$0.607035\pi$
$272$	5.56356	0.337340
$273$	3.52504	0.213345
$274$	−23.6030	−1.42591
$275$	−2.47714	−0.149377
$276$	10.6695	0.642230
$277$	−21.4894	−1.29117	−0.645586	−	0.763687i	$-0.723387\pi$
$277$	−21.4894	−1.29117	−0.645586	+	0.763687i	$0.723387\pi$
$278$	−4.35500	−0.261196
$279$	−6.87634	−0.411676
$280$	−6.69532	−0.400122
$281$	−6.22409	−0.371298	−0.185649	−	0.982616i	$-0.559439\pi$
$281$	−6.22409	−0.371298	−0.185649	+	0.982616i	$0.559439\pi$
$282$	10.1936	0.607020
$283$	−27.3859	−1.62792	−0.813960	−	0.580921i	$-0.802693\pi$
$283$	−27.3859	−1.62792	−0.813960	+	0.580921i	$0.802693\pi$
$284$	31.0217	1.84080
$285$	1.11465	0.0660263
$286$	−8.03690	−0.475232
$287$	−11.3517	−0.670070
$288$	−3.52110	−0.207483
$289$	−5.19145	−0.305379
$290$	1.70697	0.100237
$291$	−22.0708	−1.29382
$292$	−18.1274	−1.06082
$293$	27.4550	1.60394	0.801969	−	0.597365i	$-0.203786\pi$
$293$	27.4550	1.60394	0.801969	+	0.597365i	$0.203786\pi$
$294$	12.5838	0.733905
$295$	−6.39592	−0.372385
$296$	−1.38858	−0.0807096
$297$	14.0121	0.813065
$298$	−8.16848	−0.473188
$299$	−2.88579	−0.166889
$300$	5.08142	0.293376
$301$	−12.5203	−0.721659
$302$	44.9041	2.58394
$303$	−13.5697	−0.779560
$304$	−1.26885	−0.0727736
$305$	−3.11201	−0.178193
$306$	7.92664	0.453136
$307$	−7.68744	−0.438745	−0.219373	−	0.975641i	$-0.570401\pi$
$307$	−7.68744	−0.438745	−0.219373	+	0.975641i	$0.570401\pi$
$308$	15.9599	0.909399
$309$	21.1547	1.20345
$310$	16.6125	0.943528
$311$	−12.1767	−0.690476	−0.345238	−	0.938515i	$-0.612202\pi$
$311$	−12.1767	−0.690476	−0.345238	+	0.938515i	$0.612202\pi$
$312$	7.25739	0.410869
$313$	11.6831	0.660370	0.330185	−	0.943916i	$-0.392889\pi$
$313$	11.6831	0.660370	0.330185	+	0.943916i	$0.392889\pi$
$314$	46.4438	2.62097
$315$	−1.76211	−0.0992838
$316$	8.86533	0.498714
$317$	24.4973	1.37590	0.687952	−	0.725756i	$-0.258510\pi$
$317$	24.4973	1.37590	0.687952	+	0.725756i	$0.258510\pi$
$318$	22.8804	1.28307
$319$	−1.79119	−0.100287
$320$	11.7447	0.656547
$321$	0.0501492	0.00279906
$322$	8.93866	0.498132
$323$	−2.69311	−0.149849
$324$	−18.2703	−1.01501
$325$	−1.37437	−0.0762364
$326$	5.58520	0.309336
$327$	−24.0028	−1.32736
$328$	−23.3710	−1.29045
$329$	5.47504	0.301849
$330$	−8.31702	−0.457837
$331$	21.1583	1.16297	0.581483	−	0.813559i	$-0.302473\pi$
$331$	21.1583	1.16297	0.581483	+	0.813559i	$0.302473\pi$
$332$	−4.27178	−0.234444
$333$	−0.365455	−0.0200268
$334$	13.3591	0.730976
$335$	−6.49133	−0.354659
$336$	−4.15255	−0.226540
$337$	−0.177253	−0.00965561	−0.00482780	−	0.999988i	$-0.501537\pi$
$337$	−0.177253	−0.00965561	−0.00482780	+	0.999988i	$0.501537\pi$
$338$	26.2296	1.42670
$339$	11.3672	0.617382
$340$	−12.2772	−0.665827
$341$	−17.4321	−0.944003
$342$	−1.80779	−0.0977539
$343$	19.3822	1.04654
$344$	−25.7769	−1.38980
$345$	−2.98637	−0.160781
$346$	−47.5660	−2.55717
$347$	14.0806	0.755886	0.377943	−	0.925829i	$-0.376631\pi$
$347$	14.0806	0.755886	0.377943	+	0.925829i	$0.376631\pi$
$348$	3.67432	0.196964
$349$	−25.7630	−1.37906	−0.689532	−	0.724255i	$-0.742184\pi$
$349$	−25.7630	−1.37906	−0.689532	+	0.724255i	$0.742184\pi$
$350$	4.25708	0.227551
$351$	7.77424	0.414958
$352$	−8.92631	−0.475774
$353$	23.3583	1.24324	0.621618	−	0.783321i	$-0.286476\pi$
$353$	23.3583	1.24324	0.621618	+	0.783321i	$0.286476\pi$
$354$	−21.4744	−1.14135
$355$	−8.68287	−0.460839
$356$	24.6119	1.30443
$357$	−8.81371	−0.466471
$358$	42.3137	2.23635
$359$	9.64115	0.508840	0.254420	−	0.967094i	$-0.418115\pi$
$359$	9.64115	0.508840	0.254420	+	0.967094i	$0.418115\pi$
$360$	−3.62785	−0.191205
$361$	−18.3858	−0.967674
$362$	59.3164	3.11760
$363$	−6.91765	−0.363082
$364$	8.85490	0.464123
$365$	5.07379	0.265574
$366$	−10.4486	−0.546158
$367$	0.371417	0.0193878	0.00969391	−	0.999953i	$-0.496914\pi$
$367$	0.371417	0.0193878	0.00969391	+	0.999953i	$0.496914\pi$
$368$	3.39950	0.177211
$369$	−6.15092	−0.320204
$370$	0.882901	0.0458998
$371$	12.2892	0.638024
$372$	35.7591	1.85402
$373$	−9.26159	−0.479547	−0.239774	−	0.970829i	$-0.577073\pi$
$373$	−9.26159	−0.479547	−0.239774	+	0.970829i	$0.577073\pi$
$374$	20.0948	1.03908
$375$	−1.42227	−0.0734459
$376$	11.2721	0.581313
$377$	−0.993793	−0.0511829
$378$	−24.0805	−1.23857
$379$	−8.66332	−0.445005	−0.222502	−	0.974932i	$-0.571423\pi$
$379$	−8.66332	−0.445005	−0.222502	+	0.974932i	$0.571423\pi$
$380$	2.80000	0.143637
$381$	8.99235	0.460692
$382$	34.1949	1.74956
$383$	29.1957	1.49183	0.745915	−	0.666041i	$-0.232012\pi$
$383$	29.1957	1.49183	0.745915	+	0.666041i	$0.232012\pi$
$384$	29.1826	1.48922
$385$	−4.46712	−0.227665
$386$	1.39600	0.0710547
$387$	−6.78413	−0.344857
$388$	−55.4419	−2.81464
$389$	7.79021	0.394979	0.197490	−	0.980305i	$-0.436721\pi$
$389$	7.79021	0.394979	0.197490	+	0.980305i	$0.436721\pi$
$390$	−4.61447	−0.233663
$391$	7.21537	0.364897
$392$	13.9152	0.702824
$393$	−21.6184	−1.09050
$394$	−19.6611	−0.990514
$395$	−2.48138	−0.124852
$396$	8.64786	0.434571
$397$	23.8454	1.19677	0.598383	−	0.801210i	$-0.295810\pi$
$397$	23.8454	1.19677	0.598383	+	0.801210i	$0.295810\pi$
$398$	11.2786	0.565346
$399$	2.01009	0.100631
$400$	1.61903	0.0809514
$401$	6.99963	0.349545	0.174772	−	0.984609i	$-0.444081\pi$
$401$	6.99963	0.349545	0.174772	+	0.984609i	$0.444081\pi$
$402$	−21.7947	−1.08702
$403$	−9.67174	−0.481784
$404$	−34.0871	−1.69590
$405$	5.11378	0.254106
$406$	3.07825	0.152771
$407$	−0.926461	−0.0459230
$408$	−18.1457	−0.898348
$409$	13.5011	0.667585	0.333793	−	0.942647i	$-0.391671\pi$
$409$	13.5011	0.667585	0.333793	+	0.942647i	$0.391671\pi$
$410$	14.8600	0.733882
$411$	14.2205	0.701447
$412$	53.1405	2.61804
$413$	−11.5340	−0.567551
$414$	4.84341	0.238041
$415$	1.19566	0.0586925
$416$	−4.95252	−0.242817
$417$	2.62384	0.128490
$418$	−4.58290	−0.224157
$419$	7.59190	0.370888	0.185444	−	0.982655i	$-0.440628\pi$
$419$	7.59190	0.370888	0.185444	+	0.982655i	$0.440628\pi$
$420$	9.16353	0.447134
$421$	−9.47314	−0.461693	−0.230846	−	0.972990i	$-0.574149\pi$
$421$	−9.47314	−0.461693	−0.230846	+	0.972990i	$0.574149\pi$
$422$	18.9063	0.920344
$423$	2.96665	0.144244
$424$	25.3011	1.22873
$425$	3.43636	0.166688
$426$	−29.1528	−1.41246
$427$	−5.61201	−0.271584
$428$	0.125975	0.00608922
$429$	4.84214	0.233780
$430$	16.3898	0.790384
$431$	−17.3454	−0.835501	−0.417750	−	0.908562i	$-0.637181\pi$
$431$	−17.3454	−0.835501	−0.417750	+	0.908562i	$0.637181\pi$
$432$	−9.15816	−0.440622
$433$	2.43383	0.116963	0.0584813	−	0.998289i	$-0.481374\pi$
$433$	2.43383	0.116963	0.0584813	+	0.998289i	$0.481374\pi$
$434$	29.9580	1.43803
$435$	−1.02843	−0.0493095
$436$	−60.2950	−2.88761
$437$	−1.64557	−0.0787183
$438$	17.0353	0.813979
$439$	−1.32277	−0.0631322	−0.0315661	−	0.999502i	$-0.510049\pi$
$439$	−1.32277	−0.0631322	−0.0315661	+	0.999502i	$0.510049\pi$
$440$	−9.19694	−0.438447
$441$	3.66228	0.174395
$442$	11.1490	0.530305
$443$	−3.78018	−0.179602	−0.0898010	−	0.995960i	$-0.528623\pi$
$443$	−3.78018	−0.179602	−0.0898010	+	0.995960i	$0.528623\pi$
$444$	1.90048	0.0901926
$445$	−6.88880	−0.326560
$446$	−29.6158	−1.40235
$447$	4.92141	0.232775
$448$	21.1796	1.00064
$449$	27.5616	1.30071	0.650357	−	0.759629i	$-0.274619\pi$
$449$	27.5616	1.30071	0.650357	+	0.759629i	$0.274619\pi$
$450$	2.30670	0.108739
$451$	−15.5931	−0.734252
$452$	28.5544	1.34309
$453$	−27.0542	−1.27112
$454$	59.7516	2.80428
$455$	−2.47846	−0.116192
$456$	4.13840	0.193798
$457$	−19.2807	−0.901912	−0.450956	−	0.892546i	$-0.648917\pi$
$457$	−19.2807	−0.901912	−0.450956	+	0.892546i	$0.648917\pi$
$458$	3.05548	0.142773
$459$	−19.4380	−0.907289
$460$	−7.50175	−0.349771
$461$	2.54208	0.118396	0.0591982	−	0.998246i	$-0.481146\pi$
$461$	2.54208	0.118396	0.0591982	+	0.998246i	$0.481146\pi$
$462$	−14.9984	−0.697789
$463$	−6.86436	−0.319014	−0.159507	−	0.987197i	$-0.550990\pi$
$463$	−6.86436	−0.319014	−0.159507	+	0.987197i	$0.550990\pi$
$464$	1.17070	0.0543485
$465$	−10.0088	−0.464149
$466$	48.5882	2.25081
$467$	−34.6820	−1.60489	−0.802447	−	0.596724i	$-0.796469\pi$
$467$	−34.6820	−1.60489	−0.802447	+	0.596724i	$0.796469\pi$
$468$	4.79803	0.221789
$469$	−11.7061	−0.540536
$470$	−7.16712	−0.330595
$471$	−27.9818	−1.28933
$472$	−23.7463	−1.09301
$473$	−17.1984	−0.790783
$474$	−8.33125	−0.382667
$475$	−0.783711	−0.0359591
$476$	−22.1400	−1.01479
$477$	6.65890	0.304890
$478$	56.6547	2.59132
$479$	26.3090	1.20209	0.601045	−	0.799216i	$-0.294751\pi$
$479$	26.3090	1.20209	0.601045	+	0.799216i	$0.294751\pi$
$480$	−5.12513	−0.233929
$481$	−0.514021	−0.0234374
$482$	−10.8184	−0.492764
$483$	−5.38543	−0.245046
$484$	−17.3771	−0.789869
$485$	15.5180	0.704636
$486$	−22.8903	−1.03832
$487$	3.08202	0.139660	0.0698298	−	0.997559i	$-0.477754\pi$
$487$	3.08202	0.139660	0.0698298	+	0.997559i	$0.477754\pi$
$488$	−11.5541	−0.523028
$489$	−3.36502	−0.152171
$490$	−8.84770	−0.399698
$491$	32.2719	1.45641	0.728205	−	0.685359i	$-0.240355\pi$
$491$	32.2719	1.45641	0.728205	+	0.685359i	$0.240355\pi$
$492$	31.9867	1.44207
$493$	2.48479	0.111909
$494$	−2.54270	−0.114401
$495$	−2.42051	−0.108794
$496$	11.3934	0.511581
$497$	−15.6582	−0.702365
$498$	4.01443	0.179891
$499$	−22.6831	−1.01543	−0.507717	−	0.861524i	$-0.669511\pi$
$499$	−22.6831	−1.01543	−0.507717	+	0.861524i	$0.669511\pi$
$500$	−3.57275	−0.159778
$501$	−8.04869	−0.359589
$502$	9.59459	0.428228
$503$	−32.6784	−1.45706	−0.728529	−	0.685015i	$-0.759796\pi$
$503$	−32.6784	−1.45706	−0.728529	+	0.685015i	$0.759796\pi$
$504$	−6.54225	−0.291415
$505$	9.54086	0.424563
$506$	12.2785	0.545845
$507$	−15.8030	−0.701837
$508$	22.5888	1.00221
$509$	−13.3913	−0.593557	−0.296779	−	0.954946i	$-0.595912\pi$
$509$	−13.3913	−0.593557	−0.296779	+	0.954946i	$0.595912\pi$
$510$	11.5376	0.510894
$511$	9.14977	0.404762
$512$	17.8562	0.789139
$513$	4.43312	0.195727
$514$	16.8949	0.745201
$515$	−14.8738	−0.655420
$516$	35.2796	1.55310
$517$	7.52073	0.330761
$518$	1.59217	0.0699559
$519$	28.6580	1.25795
$520$	−5.10267	−0.223767
$521$	−14.5525	−0.637558	−0.318779	−	0.947829i	$-0.603273\pi$
$521$	−14.5525	−0.637558	−0.318779	+	0.947829i	$0.603273\pi$
$522$	1.66795	0.0730042
$523$	−0.103380	−0.00452048	−0.00226024	−	0.999997i	$-0.500719\pi$
$523$	−0.103380	−0.00452048	−0.00226024	+	0.999997i	$0.500719\pi$
$524$	−54.3052	−2.37234
$525$	−2.56484	−0.111939
$526$	−55.9706	−2.44043
$527$	24.1824	1.05340
$528$	−5.70410	−0.248239
$529$	−18.5912	−0.808313
$530$	−16.0872	−0.698784
$531$	−6.24970	−0.271214
$532$	5.04935	0.218917
$533$	−8.65143	−0.374735
$534$	−23.1292	−1.00090
$535$	−0.0352599	−0.00152442
$536$	−24.1006	−1.04099
$537$	−25.4935	−1.10013
$538$	−16.6706	−0.718720
$539$	9.28423	0.399900
$540$	20.2095	0.869679
$541$	7.50891	0.322833	0.161417	−	0.986886i	$-0.448394\pi$
$541$	7.50891	0.322833	0.161417	+	0.986886i	$0.448394\pi$
$542$	25.6454	1.10156
$543$	−35.7374	−1.53364
$544$	12.3828	0.530910
$545$	16.8764	0.722905
$546$	−8.32145	−0.356125
$547$	15.8978	0.679740	0.339870	−	0.940472i	$-0.389617\pi$
$547$	15.8978	0.679740	0.339870	+	0.940472i	$0.389617\pi$
$548$	35.7219	1.52596
$549$	−3.04087	−0.129781
$550$	5.84769	0.249346
$551$	−0.566693	−0.0241419
$552$	−11.0876	−0.471919
$553$	−4.47476	−0.190286
$554$	50.7293	2.15528
$555$	−0.531937	−0.0225795
$556$	6.59107	0.279524
$557$	10.9464	0.463814	0.231907	−	0.972738i	$-0.425503\pi$
$557$	10.9464	0.463814	0.231907	+	0.972738i	$0.425503\pi$
$558$	16.2327	0.687187
$559$	−9.54205	−0.403586
$560$	2.91966	0.123378
$561$	−12.1069	−0.511152
$562$	14.6930	0.619787
$563$	6.37850	0.268822	0.134411	−	0.990926i	$-0.457086\pi$
$563$	6.37850	0.268822	0.134411	+	0.990926i	$0.457086\pi$
$564$	−15.4275	−0.649615
$565$	−7.99228	−0.336238
$566$	64.6489	2.71740
$567$	9.22189	0.387283
$568$	−32.2372	−1.35264
$569$	43.3728	1.81828	0.909141	−	0.416489i	$-0.136740\pi$
$569$	43.3728	1.81828	0.909141	+	0.416489i	$0.136740\pi$
$570$	−2.63132	−0.110214
$571$	34.9213	1.46141	0.730705	−	0.682694i	$-0.239192\pi$
$571$	34.9213	1.46141	0.730705	+	0.682694i	$0.239192\pi$
$572$	12.1634	0.508579
$573$	−20.6020	−0.860661
$574$	26.7976	1.11851
$575$	2.09971	0.0875641
$576$	11.4762	0.478174
$577$	−32.3024	−1.34477	−0.672384	−	0.740202i	$-0.734730\pi$
$577$	−32.3024	−1.34477	−0.672384	+	0.740202i	$0.734730\pi$
$578$	12.2553	0.509753
$579$	−0.841075	−0.0349539
$580$	−2.58342	−0.107270
$581$	2.15617	0.0894532
$582$	52.1019	2.15969
$583$	16.8809	0.699136
$584$	18.8376	0.779506
$585$	−1.34295	−0.0555242
$586$	−64.8121	−2.67736
$587$	−27.8123	−1.14794	−0.573968	−	0.818878i	$-0.694597\pi$
$587$	−27.8123	−1.14794	−0.573968	+	0.818878i	$0.694597\pi$
$588$	−19.0450	−0.785403
$589$	−5.51515	−0.227248
$590$	15.0986	0.621601
$591$	11.8456	0.487263
$592$	0.605524	0.0248869
$593$	15.2722	0.627152	0.313576	−	0.949563i	$-0.398473\pi$
$593$	15.2722	0.627152	0.313576	+	0.949563i	$0.398473\pi$
$594$	−33.0779	−1.35720
$595$	6.19692	0.254049
$596$	12.3626	0.506391
$597$	−6.79523	−0.278110
$598$	6.81238	0.278579
$599$	−24.9412	−1.01907	−0.509535	−	0.860450i	$-0.670183\pi$
$599$	−24.9412	−1.01907	−0.509535	+	0.860450i	$0.670183\pi$
$600$	−5.28052	−0.215576
$601$	−3.82988	−0.156224	−0.0781121	−	0.996945i	$-0.524889\pi$
$601$	−3.82988	−0.156224	−0.0781121	+	0.996945i	$0.524889\pi$
$602$	29.5563	1.20462
$603$	−6.34293	−0.258304
$604$	−67.9601	−2.76526
$605$	4.86380	0.197741
$606$	32.0336	1.30127
$607$	−6.78587	−0.275430	−0.137715	−	0.990472i	$-0.543976\pi$
$607$	−6.78587	−0.275430	−0.137715	+	0.990472i	$0.543976\pi$
$608$	−2.82409	−0.114532
$609$	−1.85461	−0.0751526
$610$	7.34642	0.297448
$611$	4.17267	0.168808
$612$	−11.9966	−0.484932
$613$	−29.4869	−1.19097	−0.595483	−	0.803368i	$-0.703039\pi$
$613$	−29.4869	−1.19097	−0.595483	+	0.803368i	$0.703039\pi$
$614$	18.1475	0.732373
$615$	−8.95296	−0.361018
$616$	−16.5852	−0.668237
$617$	−7.68349	−0.309326	−0.154663	−	0.987967i	$-0.549429\pi$
$617$	−7.68349	−0.309326	−0.154663	+	0.987967i	$0.549429\pi$
$618$	−49.9391	−2.00885
$619$	−27.7136	−1.11390	−0.556952	−	0.830545i	$-0.688029\pi$
$619$	−27.7136	−1.11390	−0.556952	+	0.830545i	$0.688029\pi$
$620$	−25.1422	−1.00973
$621$	−11.8772	−0.476615
$622$	28.7451	1.15257
$623$	−12.4228	−0.497710
$624$	−3.16476	−0.126692
$625$	1.00000	0.0400000
$626$	−27.5800	−1.10232
$627$	2.76114	0.110269
$628$	−70.2902	−2.80489
$629$	1.28521	0.0512449
$630$	4.15976	0.165729
$631$	−31.1413	−1.23972	−0.619858	−	0.784714i	$-0.712810\pi$
$631$	−31.1413	−1.23972	−0.619858	+	0.784714i	$0.712810\pi$
$632$	−9.21268	−0.366461
$633$	−11.3908	−0.452744
$634$	−57.8299	−2.29672
$635$	−6.32252	−0.250901
$636$	−34.6283	−1.37310
$637$	5.15110	0.204094
$638$	4.22840	0.167404
$639$	−8.48437	−0.335637
$640$	−20.5183	−0.811057
$641$	−38.8251	−1.53350	−0.766750	−	0.641946i	$-0.778127\pi$
$641$	−38.8251	−1.53350	−0.766750	+	0.641946i	$0.778127\pi$
$642$	−0.118386	−0.00467230
$643$	−14.3439	−0.565667	−0.282833	−	0.959169i	$-0.591274\pi$
$643$	−14.3439	−0.565667	−0.282833	+	0.959169i	$0.591274\pi$
$644$	−13.5282	−0.533086
$645$	−9.87463	−0.388813
$646$	6.35754	0.250134
$647$	13.0601	0.513445	0.256723	−	0.966485i	$-0.417357\pi$
$647$	13.0601	0.513445	0.256723	+	0.966485i	$0.417357\pi$
$648$	18.9861	0.745845
$649$	−15.8436	−0.621914
$650$	3.24443	0.127257
$651$	−18.0493	−0.707409
$652$	−8.45291	−0.331042
$653$	−47.3252	−1.85198	−0.925990	−	0.377548i	$-0.876767\pi$
$653$	−47.3252	−1.85198	−0.925990	+	0.377548i	$0.876767\pi$
$654$	56.6626	2.21568
$655$	15.1999	0.593908
$656$	10.1915	0.397911
$657$	4.95780	0.193422
$658$	−12.9248	−0.503859
$659$	17.3767	0.676898	0.338449	−	0.940985i	$-0.390098\pi$
$659$	17.3767	0.676898	0.338449	+	0.940985i	$0.390098\pi$
$660$	12.5874	0.489963
$661$	−6.08866	−0.236821	−0.118411	−	0.992965i	$-0.537780\pi$
$661$	−6.08866	−0.236821	−0.118411	+	0.992965i	$0.537780\pi$
$662$	−49.9477	−1.94127
$663$	−6.71715	−0.260873
$664$	4.43915	0.172272
$665$	−1.41330	−0.0548053
$666$	0.862717	0.0334296
$667$	1.51828	0.0587881
$668$	−20.2183	−0.782269
$669$	17.8432	0.689857
$670$	15.3239	0.592013
$671$	−7.70887	−0.297598
$672$	−9.24235	−0.356531
$673$	25.2347	0.972725	0.486363	−	0.873757i	$-0.338323\pi$
$673$	25.2347	0.972725	0.486363	+	0.873757i	$0.338323\pi$
$674$	0.418436	0.0161176
$675$	−5.65658	−0.217722
$676$	−39.6972	−1.52681
$677$	40.8793	1.57112	0.785560	−	0.618786i	$-0.212375\pi$
$677$	40.8793	1.57112	0.785560	+	0.618786i	$0.212375\pi$
$678$	−26.8342	−1.03056
$679$	27.9842	1.07394
$680$	12.7583	0.489257
$681$	−35.9996	−1.37951
$682$	41.1515	1.57577
$683$	−24.6062	−0.941531	−0.470765	−	0.882258i	$-0.656022\pi$
$683$	−24.6062	−0.941531	−0.470765	+	0.882258i	$0.656022\pi$
$684$	2.73599	0.104613
$685$	−9.99845	−0.382021
$686$	−45.7550	−1.74693
$687$	−1.84089	−0.0702344
$688$	11.2407	0.428547
$689$	9.36592	0.356813
$690$	7.04982	0.268382
$691$	16.2062	0.616513	0.308257	−	0.951303i	$-0.400254\pi$
$691$	16.2062	0.616513	0.308257	+	0.951303i	$0.400254\pi$
$692$	71.9888	2.73660
$693$	−4.36499	−0.165812
$694$	−33.2396	−1.26176
$695$	−1.84482	−0.0699779
$696$	−3.81829	−0.144732
$697$	21.6313	0.819343
$698$	60.8179	2.30199
$699$	−29.2738	−1.10724
$700$	−6.44288	−0.243518
$701$	−37.9826	−1.43458	−0.717292	−	0.696773i	$-0.754619\pi$
$701$	−37.9826	−1.43458	−0.717292	+	0.696773i	$0.754619\pi$
$702$	−18.3524	−0.692666
$703$	−0.293112	−0.0110549
$704$	29.0931	1.09649
$705$	4.31810	0.162629
$706$	−55.1411	−2.07526
$707$	17.2054	0.647076
$708$	32.5004	1.22144
$709$	9.43859	0.354474	0.177237	−	0.984168i	$-0.443284\pi$
$709$	9.43859	0.354474	0.177237	+	0.984168i	$0.443284\pi$
$710$	20.4974	0.769252
$711$	−2.42465	−0.0909315
$712$	−25.5762	−0.958510
$713$	14.7761	0.553371
$714$	20.8062	0.778654
$715$	−3.40450	−0.127321
$716$	−64.0397	−2.39327
$717$	−34.1338	−1.27475
$718$	−22.7595	−0.849378
$719$	2.58967	0.0965783	0.0482892	−	0.998833i	$-0.484623\pi$
$719$	2.58967	0.0965783	0.0482892	+	0.998833i	$0.484623\pi$
$720$	1.58202	0.0589582
$721$	−26.8226	−0.998926
$722$	43.4027	1.61528
$723$	6.51794	0.242405
$724$	−89.7722	−3.33636
$725$	0.723089	0.0268549
$726$	16.3303	0.606073
$727$	−34.1955	−1.26824	−0.634120	−	0.773235i	$-0.718637\pi$
$727$	−34.1955	−1.26824	−0.634120	+	0.773235i	$0.718637\pi$
$728$	−9.20185	−0.341043
$729$	29.1325	1.07898
$730$	−11.9775	−0.443308
$731$	23.8581	0.882424
$732$	15.8134	0.584481
$733$	42.1512	1.55689	0.778445	−	0.627713i	$-0.216009\pi$
$733$	42.1512	1.55689	0.778445	+	0.627713i	$0.216009\pi$
$734$	−0.876792	−0.0323630
$735$	5.33063	0.196623
$736$	7.56627	0.278897
$737$	−16.0799	−0.592311
$738$	14.5203	0.534499
$739$	−0.570440	−0.0209840	−0.0104920	−	0.999945i	$-0.503340\pi$
$739$	−0.570440	−0.0209840	−0.0104920	+	0.999945i	$0.503340\pi$
$740$	−1.33622	−0.0491206
$741$	1.53194	0.0562774
$742$	−29.0107	−1.06502
$743$	27.9698	1.02611	0.513056	−	0.858355i	$-0.328513\pi$
$743$	27.9698	1.02611	0.513056	+	0.858355i	$0.328513\pi$
$744$	−37.1602	−1.36236
$745$	−3.46024	−0.126774
$746$	21.8635	0.800481
$747$	1.16832	0.0427467
$748$	−30.4124	−1.11199
$749$	−0.0635855	−0.00232337
$750$	3.35751	0.122599
$751$	−19.1040	−0.697115	−0.348558	−	0.937287i	$-0.613328\pi$
$751$	−19.1040	−0.697115	−0.348558	+	0.937287i	$0.613328\pi$
$752$	−4.91546	−0.179249
$753$	−5.78063	−0.210658
$754$	2.34601	0.0854368
$755$	19.0218	0.692274
$756$	36.4446	1.32548
$757$	49.1372	1.78592	0.892960	−	0.450136i	$-0.148624\pi$
$757$	49.1372	1.78592	0.892960	+	0.450136i	$0.148624\pi$
$758$	20.4512	0.742822
$759$	−7.39764	−0.268517
$760$	−2.90971	−0.105546
$761$	−17.9283	−0.649899	−0.324949	−	0.945731i	$-0.605347\pi$
$761$	−17.9283	−0.649899	−0.324949	+	0.945731i	$0.605347\pi$
$762$	−21.2279	−0.769007
$763$	30.4338	1.10178
$764$	−51.7522	−1.87233
$765$	3.35780	0.121401
$766$	−68.9213	−2.49023
$767$	−8.79036	−0.317402
$768$	−35.4822	−1.28035
$769$	−10.0519	−0.362482	−0.181241	−	0.983439i	$-0.558011\pi$
$769$	−10.0519	−0.362482	−0.181241	+	0.983439i	$0.558011\pi$
$770$	10.5454	0.380029
$771$	−10.1790	−0.366586
$772$	−2.11278	−0.0760406
$773$	−40.7599	−1.46603	−0.733016	−	0.680212i	$-0.761888\pi$
$773$	−40.7599	−1.46603	−0.733016	+	0.680212i	$0.761888\pi$
$774$	16.0151	0.575650
$775$	7.03722	0.252784
$776$	57.6142	2.06823
$777$	−0.959263	−0.0344134
$778$	−18.3901	−0.659317
$779$	−4.93333	−0.176755
$780$	6.98376	0.250059
$781$	−21.5087	−0.769640
$782$	−17.0331	−0.609102
$783$	−4.09021	−0.146172
$784$	−6.06806	−0.216717
$785$	19.6740	0.702195
$786$	51.0337	1.82031
$787$	−22.5331	−0.803219	−0.401610	−	0.915811i	$-0.631549\pi$
$787$	−22.5331	−0.803219	−0.401610	+	0.915811i	$0.631549\pi$
$788$	29.7561	1.06002
$789$	33.7216	1.20052
$790$	5.85770	0.208408
$791$	−14.4128	−0.512460
$792$	−8.98669	−0.319328
$793$	−4.27706	−0.151883
$794$	−56.2910	−1.99769
$795$	9.69236	0.343752
$796$	−17.0696	−0.605016
$797$	9.14955	0.324094	0.162047	−	0.986783i	$-0.448190\pi$
$797$	9.14955	0.324094	0.162047	+	0.986783i	$0.448190\pi$
$798$	−4.74516	−0.167977
$799$	−10.4330	−0.369092
$800$	3.60348	0.127402
$801$	−6.73131	−0.237839
$802$	−16.5238	−0.583476
$803$	12.5685	0.443532
$804$	32.9852	1.16330
$805$	3.78650	0.133456
$806$	22.8318	0.804215
$807$	10.0438	0.353559
$808$	35.4227	1.24616
$809$	−10.5686	−0.371572	−0.185786	−	0.982590i	$-0.559483\pi$
$809$	−10.5686	−0.371572	−0.185786	+	0.982590i	$0.559483\pi$
$810$	−12.0719	−0.424165
$811$	4.58555	0.161020	0.0805102	−	0.996754i	$-0.474345\pi$
$811$	4.58555	0.161020	0.0805102	+	0.996754i	$0.474345\pi$
$812$	−4.65877	−0.163491
$813$	−15.4510	−0.541891
$814$	2.18707	0.0766566
$815$	2.36594	0.0828753
$816$	7.91290	0.277007
$817$	−5.44119	−0.190363
$818$	−31.8715	−1.11436
$819$	−2.42180	−0.0846244
$820$	−22.4898	−0.785379
$821$	−28.2116	−0.984592	−0.492296	−	0.870428i	$-0.663842\pi$
$821$	−28.2116	−0.984592	−0.492296	+	0.870428i	$0.663842\pi$
$822$	−33.5699	−1.17089
$823$	−31.6513	−1.10330	−0.551648	−	0.834077i	$-0.686001\pi$
$823$	−31.6513	−1.10330	−0.551648	+	0.834077i	$0.686001\pi$
$824$	−55.2226	−1.92377
$825$	−3.52316	−0.122661
$826$	27.2279	0.947381
$827$	5.28254	0.183692	0.0918459	−	0.995773i	$-0.470723\pi$
$827$	5.28254	0.183692	0.0918459	+	0.995773i	$0.470723\pi$
$828$	−7.33025	−0.254744
$829$	37.1309	1.28961	0.644804	−	0.764348i	$-0.276939\pi$
$829$	37.1309	1.28961	0.644804	+	0.764348i	$0.276939\pi$
$830$	−2.82255	−0.0979720
$831$	−30.5638	−1.06025
$832$	16.1415	0.559607
$833$	−12.8794	−0.446243
$834$	−6.19400	−0.214481
$835$	5.65903	0.195839
$836$	6.93599	0.239886
$837$	−39.8066	−1.37592
$838$	−17.9219	−0.619103
$839$	−12.6015	−0.435053	−0.217526	−	0.976054i	$-0.569799\pi$
$839$	−12.6015	−0.435053	−0.217526	+	0.976054i	$0.569799\pi$
$840$	−9.52257	−0.328560
$841$	−28.4771	−0.981970
$842$	22.3629	0.770678
$843$	−8.85236	−0.304891
$844$	−28.6137	−0.984925
$845$	11.1111	0.382234
$846$	−7.00327	−0.240778
$847$	8.77107	0.301378
$848$	−11.0332	−0.378881
$849$	−38.9502	−1.33677
$850$	−8.11209	−0.278243
$851$	0.785303	0.0269199
$852$	44.1213	1.51157
$853$	9.78833	0.335146	0.167573	−	0.985860i	$-0.446407\pi$
$853$	9.78833	0.335146	0.167573	+	0.985860i	$0.446407\pi$
$854$	13.2481	0.453340
$855$	−0.765795	−0.0261896
$856$	−0.130911	−0.00447443
$857$	−27.1083	−0.926001	−0.463000	−	0.886358i	$-0.653227\pi$
$857$	−27.1083	−0.926001	−0.463000	+	0.886358i	$0.653227\pi$
$858$	−11.4307	−0.390237
$859$	−43.0887	−1.47017	−0.735083	−	0.677977i	$-0.762857\pi$
$859$	−43.0887	−1.47017	−0.735083	+	0.677977i	$0.762857\pi$
$860$	−24.8051	−0.845845
$861$	−16.1452	−0.550228
$862$	40.9468	1.39465
$863$	14.7007	0.500416	0.250208	−	0.968192i	$-0.419501\pi$
$863$	14.7007	0.500416	0.250208	+	0.968192i	$0.419501\pi$
$864$	−20.3834	−0.693456
$865$	−20.1494	−0.685101
$866$	−5.74547	−0.195239
$867$	−7.38366	−0.250762
$868$	−45.3399	−1.53894
$869$	−6.14671	−0.208513
$870$	2.42778	0.0823095
$871$	−8.92150	−0.302294
$872$	62.6575	2.12185
$873$	15.1632	0.513198
$874$	3.88464	0.131400
$875$	1.80334	0.0609640
$876$	−25.7821	−0.871095
$877$	12.8263	0.433114	0.216557	−	0.976270i	$-0.430517\pi$
$877$	12.8263	0.433114	0.216557	+	0.976270i	$0.430517\pi$
$878$	3.12261	0.105383
$879$	39.0485	1.31707
$880$	4.01055	0.135196
$881$	−5.22134	−0.175912	−0.0879558	−	0.996124i	$-0.528033\pi$
$881$	−5.22134	−0.175912	−0.0879558	+	0.996124i	$0.528033\pi$
$882$	−8.64543	−0.291107
$883$	−35.8681	−1.20706	−0.603529	−	0.797341i	$-0.706239\pi$
$883$	−35.8681	−1.20706	−0.603529	+	0.797341i	$0.706239\pi$
$884$	−16.8735	−0.567516
$885$	−9.09674	−0.305784
$886$	8.92375	0.299799
$887$	4.59854	0.154404	0.0772019	−	0.997015i	$-0.475401\pi$
$887$	4.59854	0.154404	0.0772019	+	0.997015i	$0.475401\pi$
$888$	−1.97494	−0.0662746
$889$	−11.4016	−0.382399
$890$	16.2621	0.545108
$891$	12.6675	0.424378
$892$	44.8220	1.50075
$893$	2.37939	0.0796234
$894$	−11.6178	−0.388558
$895$	17.9245	0.599149
$896$	−37.0014	−1.23613
$897$	−4.10438	−0.137041
$898$	−65.0638	−2.17121
$899$	5.08854	0.169712
$900$	−3.49107	−0.116369
$901$	−23.4177	−0.780157
$902$	36.8102	1.22565
$903$	−17.8073	−0.592590
$904$	−29.6732	−0.986916
$905$	25.1269	0.835248
$906$	63.8660	2.12180
$907$	−52.5466	−1.74478	−0.872391	−	0.488808i	$-0.837432\pi$
$907$	−52.5466	−1.74478	−0.872391	+	0.488808i	$0.837432\pi$
$908$	−90.4310	−3.00106
$909$	9.32275	0.309216
$910$	5.85081	0.193953
$911$	−9.22793	−0.305735	−0.152867	−	0.988247i	$-0.548851\pi$
$911$	−9.22793	−0.305735	−0.152867	+	0.988247i	$0.548851\pi$
$912$	−1.80465	−0.0597580
$913$	2.96180	0.0980214
$914$	45.5152	1.50551
$915$	−4.42613	−0.146323
$916$	−4.62432	−0.152792
$917$	27.4105	0.905175
$918$	45.8867	1.51449
$919$	27.8033	0.917146	0.458573	−	0.888657i	$-0.348361\pi$
$919$	27.8033	0.917146	0.458573	+	0.888657i	$0.348361\pi$
$920$	7.79568	0.257016
$921$	−10.9336	−0.360276
$922$	−6.00100	−0.197632
$923$	−11.9335	−0.392795
$924$	22.6993	0.746753
$925$	0.374005	0.0122972
$926$	16.2045	0.532512
$927$	−14.5338	−0.477353
$928$	2.60564	0.0855342
$929$	16.6944	0.547726	0.273863	−	0.961769i	$-0.411699\pi$
$929$	16.6944	0.547726	0.273863	+	0.961769i	$0.411699\pi$
$930$	23.6275	0.774778
$931$	2.93732	0.0962669
$932$	−73.5358	−2.40874
$933$	−17.3186	−0.566984
$934$	81.8727	2.67896
$935$	8.51233	0.278383
$936$	−4.98602	−0.162973
$937$	−4.52032	−0.147673	−0.0738363	−	0.997270i	$-0.523524\pi$
$937$	−4.52032	−0.147673	−0.0738363	+	0.997270i	$0.523524\pi$
$938$	27.6341	0.902287
$939$	16.6166	0.542263
$940$	10.8471	0.353792
$941$	−9.77391	−0.318620	−0.159310	−	0.987229i	$-0.550927\pi$
$941$	−9.77391	−0.318620	−0.159310	+	0.987229i	$0.550927\pi$
$942$	66.0557	2.15221
$943$	13.2173	0.430416
$944$	10.3552	0.337032
$945$	−10.2007	−0.331830
$946$	40.5997	1.32001
$947$	−41.7888	−1.35795	−0.678977	−	0.734160i	$-0.737576\pi$
$947$	−41.7888	−1.35795	−0.678977	+	0.734160i	$0.737576\pi$
$948$	12.6089	0.409519
$949$	6.97327	0.226362
$950$	1.85008	0.0600246
$951$	34.8418	1.12982
$952$	23.0075	0.745677
$953$	−3.65516	−0.118402	−0.0592012	−	0.998246i	$-0.518855\pi$
$953$	−3.65516	−0.118402	−0.0592012	+	0.998246i	$0.518855\pi$
$954$	−15.7194	−0.508936
$955$	14.4853	0.468732
$956$	−85.7439	−2.77316
$957$	−2.54756	−0.0823510
$958$	−62.1068	−2.00658
$959$	−18.0306	−0.582238
$960$	16.7041	0.539123
$961$	18.5224	0.597497
$962$	1.21343	0.0391227
$963$	−0.0344538	−0.00111026
$964$	16.3731	0.527341
$965$	0.591360	0.0190365
$966$	12.7132	0.409041
$967$	−12.2502	−0.393938	−0.196969	−	0.980410i	$-0.563110\pi$
$967$	−12.2502	−0.393938	−0.196969	+	0.980410i	$0.563110\pi$
$968$	18.0580	0.580405
$969$	−3.83034	−0.123048
$970$	−36.6328	−1.17621
$971$	−59.3467	−1.90453	−0.952263	−	0.305279i	$-0.901250\pi$
$971$	−59.3467	−1.90453	−0.952263	+	0.305279i	$0.901250\pi$
$972$	34.6433	1.11118
$973$	−3.32683	−0.106653
$974$	−7.27562	−0.233126
$975$	−1.95473	−0.0626015
$976$	5.03843	0.161276
$977$	18.0938	0.578873	0.289437	−	0.957197i	$-0.406532\pi$
$977$	18.0938	0.578873	0.289437	+	0.957197i	$0.406532\pi$
$978$	7.94368	0.254011
$979$	−17.0645	−0.545383
$980$	13.3905	0.427745
$981$	16.4906	0.526503
$982$	−76.1832	−2.43110
$983$	−3.88640	−0.123957	−0.0619785	−	0.998077i	$-0.519741\pi$
$983$	−3.88640	−0.123957	−0.0619785	+	0.998077i	$0.519741\pi$
$984$	−33.2399	−1.05965
$985$	−8.32864	−0.265372
$986$	−5.86577	−0.186804
$987$	7.78701	0.247863
$988$	3.84824	0.122429
$989$	14.5780	0.463554
$990$	5.71401	0.181603
$991$	−23.0013	−0.730660	−0.365330	−	0.930878i	$-0.619044\pi$
$991$	−23.0013	−0.730660	−0.365330	+	0.930878i	$0.619044\pi$
$992$	25.3585	0.805132
$993$	30.0929	0.954969
$994$	36.9637	1.17242
$995$	4.77772	0.151464
$996$	−6.07563	−0.192514
$997$	4.84305	0.153381	0.0766905	−	0.997055i	$-0.475565\pi$
$997$	4.84305	0.153381	0.0766905	+	0.997055i	$0.475565\pi$
$998$	53.5472	1.69501
$999$	−2.11559	−0.0669342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.7	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.7	✓	83	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36067 q^{2} +1.42227 q^{3} +3.57275 q^{4} -1.00000 q^{5} -3.35751 q^{6} -1.80334 q^{7} -3.71273 q^{8} -0.977139 q^{9} +O(q^{10})\)	\(q-2.36067 q^{2} +1.42227 q^{3} +3.57275 q^{4} -1.00000 q^{5} -3.35751 q^{6} -1.80334 q^{7} -3.71273 q^{8} -0.977139 q^{9} +2.36067 q^{10} -2.47714 q^{11} +5.08142 q^{12} -1.37437 q^{13} +4.25708 q^{14} -1.42227 q^{15} +1.61903 q^{16} +3.43636 q^{17} +2.30670 q^{18} -0.783711 q^{19} -3.57275 q^{20} -2.56484 q^{21} +5.84769 q^{22} +2.09971 q^{23} -5.28052 q^{24} +1.00000 q^{25} +3.24443 q^{26} -5.65658 q^{27} -6.44288 q^{28} +0.723089 q^{29} +3.35751 q^{30} +7.03722 q^{31} +3.60348 q^{32} -3.52316 q^{33} -8.11209 q^{34} +1.80334 q^{35} -3.49107 q^{36} +0.374005 q^{37} +1.85008 q^{38} -1.95473 q^{39} +3.71273 q^{40} +6.29483 q^{41} +6.05474 q^{42} +6.94285 q^{43} -8.85018 q^{44} +0.977139 q^{45} -4.95672 q^{46} -3.03606 q^{47} +2.30270 q^{48} -3.74797 q^{49} -2.36067 q^{50} +4.88744 q^{51} -4.91028 q^{52} -6.81469 q^{53} +13.3533 q^{54} +2.47714 q^{55} +6.69532 q^{56} -1.11465 q^{57} -1.70697 q^{58} +6.39592 q^{59} -5.08142 q^{60} +3.11201 q^{61} -16.6125 q^{62} +1.76211 q^{63} -11.7447 q^{64} +1.37437 q^{65} +8.31702 q^{66} +6.49133 q^{67} +12.2772 q^{68} +2.98637 q^{69} -4.25708 q^{70} +8.68287 q^{71} +3.62785 q^{72} -5.07379 q^{73} -0.882901 q^{74} +1.42227 q^{75} -2.80000 q^{76} +4.46712 q^{77} +4.61447 q^{78} +2.48138 q^{79} -1.61903 q^{80} -5.11378 q^{81} -14.8600 q^{82} -1.19566 q^{83} -9.16353 q^{84} -3.43636 q^{85} -16.3898 q^{86} +1.02843 q^{87} +9.19694 q^{88} +6.88880 q^{89} -2.30670 q^{90} +2.47846 q^{91} +7.50175 q^{92} +10.0088 q^{93} +7.16712 q^{94} +0.783711 q^{95} +5.12513 q^{96} -15.5180 q^{97} +8.84770 q^{98} +2.42051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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