LMFDB - Embedded newform 8013.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24374 q^{2} -1.00000 q^{3} +3.03438 q^{4} +2.67702 q^{5} +2.24374 q^{6} -0.787815 q^{7} -2.32089 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.24374 q^{2} -1.00000 q^{3} +3.03438 q^{4} +2.67702 q^{5} +2.24374 q^{6} -0.787815 q^{7} -2.32089 q^{8} +1.00000 q^{9} -6.00654 q^{10} -5.88697 q^{11} -3.03438 q^{12} -2.84511 q^{13} +1.76766 q^{14} -2.67702 q^{15} -0.861281 q^{16} -5.55030 q^{17} -2.24374 q^{18} -1.86863 q^{19} +8.12310 q^{20} +0.787815 q^{21} +13.2089 q^{22} -0.552759 q^{23} +2.32089 q^{24} +2.16643 q^{25} +6.38370 q^{26} -1.00000 q^{27} -2.39053 q^{28} -0.159227 q^{29} +6.00654 q^{30} -5.77990 q^{31} +6.57428 q^{32} +5.88697 q^{33} +12.4534 q^{34} -2.10900 q^{35} +3.03438 q^{36} -0.113823 q^{37} +4.19274 q^{38} +2.84511 q^{39} -6.21307 q^{40} -6.88130 q^{41} -1.76766 q^{42} -4.07920 q^{43} -17.8633 q^{44} +2.67702 q^{45} +1.24025 q^{46} +5.69248 q^{47} +0.861281 q^{48} -6.37935 q^{49} -4.86091 q^{50} +5.55030 q^{51} -8.63317 q^{52} -12.0811 q^{53} +2.24374 q^{54} -15.7595 q^{55} +1.82843 q^{56} +1.86863 q^{57} +0.357264 q^{58} -1.39489 q^{59} -8.12310 q^{60} -11.1198 q^{61} +12.9686 q^{62} -0.787815 q^{63} -13.0284 q^{64} -7.61642 q^{65} -13.2089 q^{66} -8.57370 q^{67} -16.8417 q^{68} +0.552759 q^{69} +4.73205 q^{70} +3.34231 q^{71} -2.32089 q^{72} -3.77345 q^{73} +0.255389 q^{74} -2.16643 q^{75} -5.67015 q^{76} +4.63785 q^{77} -6.38370 q^{78} +15.2345 q^{79} -2.30567 q^{80} +1.00000 q^{81} +15.4399 q^{82} +5.73088 q^{83} +2.39053 q^{84} -14.8582 q^{85} +9.15269 q^{86} +0.159227 q^{87} +13.6630 q^{88} +0.944385 q^{89} -6.00654 q^{90} +2.24142 q^{91} -1.67728 q^{92} +5.77990 q^{93} -12.7725 q^{94} -5.00237 q^{95} -6.57428 q^{96} -0.199388 q^{97} +14.3136 q^{98} -5.88697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) $ 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * 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 $

$2$	−2.24374	−1.58657	−0.793283	−	0.608853i	$-0.791630\pi$
$2$	−2.24374	−1.58657	−0.793283	+	0.608853i	$0.791630\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.03438	1.51719
$5$	2.67702	1.19720	0.598600	−	0.801048i	$-0.295724\pi$
$5$	2.67702	1.19720	0.598600	+	0.801048i	$0.295724\pi$
$6$	2.24374	0.916004
$7$	−0.787815	−0.297766	−0.148883	−	0.988855i	$-0.547568\pi$
$7$	−0.787815	−0.297766	−0.148883	+	0.988855i	$0.547568\pi$
$8$	−2.32089	−0.820559
$9$	1.00000	0.333333
$10$	−6.00654	−1.89944
$11$	−5.88697	−1.77499	−0.887495	−	0.460818i	$-0.847556\pi$
$11$	−5.88697	−1.77499	−0.887495	+	0.460818i	$0.847556\pi$
$12$	−3.03438	−0.875951
$13$	−2.84511	−0.789092	−0.394546	−	0.918876i	$-0.629098\pi$
$13$	−2.84511	−0.789092	−0.394546	+	0.918876i	$0.629098\pi$
$14$	1.76766	0.472426
$15$	−2.67702	−0.691203
$16$	−0.861281	−0.215320
$17$	−5.55030	−1.34614	−0.673072	−	0.739577i	$-0.735026\pi$
$17$	−5.55030	−1.34614	−0.673072	+	0.739577i	$0.735026\pi$
$18$	−2.24374	−0.528855
$19$	−1.86863	−0.428694	−0.214347	−	0.976758i	$-0.568762\pi$
$19$	−1.86863	−0.428694	−0.214347	+	0.976758i	$0.568762\pi$
$20$	8.12310	1.81638
$21$	0.787815	0.171915
$22$	13.2089	2.81614
$23$	−0.552759	−0.115258	−0.0576291	−	0.998338i	$-0.518354\pi$
$23$	−0.552759	−0.115258	−0.0576291	+	0.998338i	$0.518354\pi$
$24$	2.32089	0.473750
$25$	2.16643	0.433286
$26$	6.38370	1.25195
$27$	−1.00000	−0.192450
$28$	−2.39053	−0.451769
$29$	−0.159227	−0.0295677	−0.0147838	−	0.999891i	$-0.504706\pi$
$29$	−0.159227	−0.0295677	−0.0147838	+	0.999891i	$0.504706\pi$
$30$	6.00654	1.09664
$31$	−5.77990	−1.03810	−0.519050	−	0.854744i	$-0.673714\pi$
$31$	−5.77990	−1.03810	−0.519050	+	0.854744i	$0.673714\pi$
$32$	6.57428	1.16218
$33$	5.88697	1.02479
$34$	12.4534	2.13575
$35$	−2.10900	−0.356485
$36$	3.03438	0.505731
$37$	−0.113823	−0.0187124	−0.00935619	−	0.999956i	$-0.502978\pi$
$37$	−0.113823	−0.0187124	−0.00935619	+	0.999956i	$0.502978\pi$
$38$	4.19274	0.680152
$39$	2.84511	0.455583
$40$	−6.21307	−0.982373
$41$	−6.88130	−1.07468	−0.537339	−	0.843366i	$-0.680570\pi$
$41$	−6.88130	−1.07468	−0.537339	+	0.843366i	$0.680570\pi$
$42$	−1.76766	−0.272755
$43$	−4.07920	−0.622073	−0.311036	−	0.950398i	$-0.600676\pi$
$43$	−4.07920	−0.622073	−0.311036	+	0.950398i	$0.600676\pi$
$44$	−17.8633	−2.69300
$45$	2.67702	0.399066
$46$	1.24025	0.182865
$47$	5.69248	0.830334	0.415167	−	0.909745i	$-0.363723\pi$
$47$	5.69248	0.830334	0.415167	+	0.909745i	$0.363723\pi$
$48$	0.861281	0.124315
$49$	−6.37935	−0.911335
$50$	−4.86091	−0.687437
$51$	5.55030	0.777197
$52$	−8.63317	−1.19720
$53$	−12.0811	−1.65946	−0.829731	−	0.558164i	$-0.811506\pi$
$53$	−12.0811	−1.65946	−0.829731	+	0.558164i	$0.811506\pi$
$54$	2.24374	0.305335
$55$	−15.7595	−2.12502
$56$	1.82843	0.244335
$57$	1.86863	0.247507
$58$	0.357264	0.0469110
$59$	−1.39489	−0.181600	−0.0907999	−	0.995869i	$-0.528942\pi$
$59$	−1.39489	−0.181600	−0.0907999	+	0.995869i	$0.528942\pi$
$60$	−8.12310	−1.04869
$61$	−11.1198	−1.42375	−0.711873	−	0.702308i	$-0.752153\pi$
$61$	−11.1198	−1.42375	−0.711873	+	0.702308i	$0.752153\pi$
$62$	12.9686	1.64702
$63$	−0.787815	−0.0992554
$64$	−13.0284	−1.62855
$65$	−7.61642	−0.944701
$66$	−13.2089	−1.62590
$67$	−8.57370	−1.04744	−0.523722	−	0.851889i	$-0.675457\pi$
$67$	−8.57370	−1.04744	−0.523722	+	0.851889i	$0.675457\pi$
$68$	−16.8417	−2.04236
$69$	0.552759	0.0665443
$70$	4.73205	0.565588
$71$	3.34231	0.396659	0.198329	−	0.980135i	$-0.436448\pi$
$71$	3.34231	0.396659	0.198329	+	0.980135i	$0.436448\pi$
$72$	−2.32089	−0.273520
$73$	−3.77345	−0.441649	−0.220824	−	0.975314i	$-0.570875\pi$
$73$	−3.77345	−0.441649	−0.220824	+	0.975314i	$0.570875\pi$
$74$	0.255389	0.0296884
$75$	−2.16643	−0.250158
$76$	−5.67015	−0.650411
$77$	4.63785	0.528532
$78$	−6.38370	−0.722812
$79$	15.2345	1.71402	0.857010	−	0.515301i	$-0.172320\pi$
$79$	15.2345	1.71402	0.857010	+	0.515301i	$0.172320\pi$
$80$	−2.30567	−0.257781
$81$	1.00000	0.111111
$82$	15.4399	1.70505
$83$	5.73088	0.629046	0.314523	−	0.949250i	$-0.398155\pi$
$83$	5.73088	0.629046	0.314523	+	0.949250i	$0.398155\pi$
$84$	2.39053	0.260829
$85$	−14.8582	−1.61160
$86$	9.15269	0.986960
$87$	0.159227	0.0170709
$88$	13.6630	1.45648
$89$	0.944385	0.100105	0.0500523	−	0.998747i	$-0.484061\pi$
$89$	0.944385	0.100105	0.0500523	+	0.998747i	$0.484061\pi$
$90$	−6.00654	−0.633145
$91$	2.24142	0.234965
$92$	−1.67728	−0.174869
$93$	5.77990	0.599348
$94$	−12.7725	−1.31738
$95$	−5.00237	−0.513232
$96$	−6.57428	−0.670985
$97$	−0.199388	−0.0202448	−0.0101224	−	0.999949i	$-0.503222\pi$
$97$	−0.199388	−0.0202448	−0.0101224	+	0.999949i	$0.503222\pi$
$98$	14.3136	1.44589
$99$	−5.88697	−0.591663
$100$	6.57378	0.657378
$101$	1.83391	0.182481	0.0912404	−	0.995829i	$-0.470917\pi$
$101$	1.83391	0.182481	0.0912404	+	0.995829i	$0.470917\pi$
$102$	−12.4534	−1.23307
$103$	−4.45758	−0.439218	−0.219609	−	0.975588i	$-0.570478\pi$
$103$	−4.45758	−0.439218	−0.219609	+	0.975588i	$0.570478\pi$
$104$	6.60320	0.647497
$105$	2.10900	0.205817
$106$	27.1068	2.63285
$107$	6.82555	0.659851	0.329925	−	0.944007i	$-0.392976\pi$
$107$	6.82555	0.659851	0.329925	+	0.944007i	$0.392976\pi$
$108$	−3.03438	−0.291984
$109$	16.5895	1.58898	0.794492	−	0.607275i	$-0.207737\pi$
$109$	16.5895	1.58898	0.794492	+	0.607275i	$0.207737\pi$
$110$	35.3604	3.37148
$111$	0.113823	0.0108036
$112$	0.678531	0.0641151
$113$	−0.828624	−0.0779504	−0.0389752	−	0.999240i	$-0.512409\pi$
$113$	−0.828624	−0.0779504	−0.0389752	+	0.999240i	$0.512409\pi$
$114$	−4.19274	−0.392686
$115$	−1.47975	−0.137987
$116$	−0.483155	−0.0448598
$117$	−2.84511	−0.263031
$118$	3.12979	0.288120
$119$	4.37261	0.400836
$120$	6.21307	0.567173
$121$	23.6565	2.15059
$122$	24.9500	2.25887
$123$	6.88130	0.620466
$124$	−17.5384	−1.57500
$125$	−7.58552	−0.678470
$126$	1.76766	0.157475
$127$	4.40176	0.390593	0.195296	−	0.980744i	$-0.437433\pi$
$127$	4.40176	0.390593	0.195296	+	0.980744i	$0.437433\pi$
$128$	16.0839	1.42163
$129$	4.07920	0.359154
$130$	17.0893	1.49883
$131$	7.66473	0.669671	0.334835	−	0.942277i	$-0.391319\pi$
$131$	7.66473	0.669671	0.334835	+	0.942277i	$0.391319\pi$
$132$	17.8633	1.55480
$133$	1.47214	0.127651
$134$	19.2372	1.66184
$135$	−2.67702	−0.230401
$136$	12.8816	1.10459
$137$	−0.926703	−0.0791736	−0.0395868	−	0.999216i	$-0.512604\pi$
$137$	−0.926703	−0.0791736	−0.0395868	+	0.999216i	$0.512604\pi$
$138$	−1.24025	−0.105577
$139$	−5.73977	−0.486841	−0.243420	−	0.969921i	$-0.578269\pi$
$139$	−5.73977	−0.486841	−0.243420	+	0.969921i	$0.578269\pi$
$140$	−6.39951	−0.540857
$141$	−5.69248	−0.479393
$142$	−7.49928	−0.629325
$143$	16.7491	1.40063
$144$	−0.861281	−0.0717735
$145$	−0.426253	−0.0353984
$146$	8.46665	0.700705
$147$	6.37935	0.526160
$148$	−0.345382	−0.0283903
$149$	6.44621	0.528094	0.264047	−	0.964510i	$-0.414943\pi$
$149$	6.44621	0.528094	0.264047	+	0.964510i	$0.414943\pi$
$150$	4.86091	0.396892
$151$	12.4736	1.01509	0.507545	−	0.861625i	$-0.330553\pi$
$151$	12.4736	1.01509	0.507545	+	0.861625i	$0.330553\pi$
$152$	4.33690	0.351769
$153$	−5.55030	−0.448715
$154$	−10.4061	−0.838551
$155$	−15.4729	−1.24281
$156$	8.63317	0.691206
$157$	6.08453	0.485598	0.242799	−	0.970077i	$-0.421934\pi$
$157$	6.08453	0.485598	0.242799	+	0.970077i	$0.421934\pi$
$158$	−34.1824	−2.71940
$159$	12.0811	0.958091
$160$	17.5995	1.39136
$161$	0.435472	0.0343200
$162$	−2.24374	−0.176285
$163$	10.9798	0.860003	0.430001	−	0.902828i	$-0.358513\pi$
$163$	10.9798	0.860003	0.430001	+	0.902828i	$0.358513\pi$
$164$	−20.8805	−1.63049
$165$	15.7595	1.22688
$166$	−12.8586	−0.998023
$167$	−13.4742	−1.04267	−0.521334	−	0.853353i	$-0.674566\pi$
$167$	−13.4742	−1.04267	−0.521334	+	0.853353i	$0.674566\pi$
$168$	−1.82843	−0.141067
$169$	−4.90533	−0.377333
$170$	33.3381	2.55691
$171$	−1.86863	−0.142898
$172$	−12.3779	−0.943804
$173$	−8.60358	−0.654118	−0.327059	−	0.945004i	$-0.606058\pi$
$173$	−8.60358	−0.654118	−0.327059	+	0.945004i	$0.606058\pi$
$174$	−0.357264	−0.0270841
$175$	−1.70675	−0.129018
$176$	5.07034	0.382191
$177$	1.39489	0.104847
$178$	−2.11896	−0.158823
$179$	7.32437	0.547449	0.273724	−	0.961808i	$-0.411744\pi$
$179$	7.32437	0.547449	0.273724	+	0.961808i	$0.411744\pi$
$180$	8.12310	0.605460
$181$	−5.08863	−0.378235	−0.189117	−	0.981955i	$-0.560563\pi$
$181$	−5.08863	−0.378235	−0.189117	+	0.981955i	$0.560563\pi$
$182$	−5.02918	−0.372788
$183$	11.1198	0.822001
$184$	1.28289	0.0945761
$185$	−0.304706	−0.0224024
$186$	−12.9686	−0.950905
$187$	32.6744	2.38939
$188$	17.2732	1.25978
$189$	0.787815	0.0573051
$190$	11.2240	0.814277
$191$	3.99488	0.289059	0.144530	−	0.989500i	$-0.453833\pi$
$191$	3.99488	0.289059	0.144530	+	0.989500i	$0.453833\pi$
$192$	13.0284	0.940246
$193$	−23.2009	−1.67004	−0.835020	−	0.550219i	$-0.814544\pi$
$193$	−23.2009	−1.67004	−0.835020	+	0.550219i	$0.814544\pi$
$194$	0.447376	0.0321197
$195$	7.61642	0.545423
$196$	−19.3574	−1.38267
$197$	20.2683	1.44405	0.722027	−	0.691865i	$-0.243211\pi$
$197$	20.2683	1.44405	0.722027	+	0.691865i	$0.243211\pi$
$198$	13.2089	0.938713
$199$	6.44545	0.456906	0.228453	−	0.973555i	$-0.426633\pi$
$199$	6.44545	0.456906	0.228453	+	0.973555i	$0.426633\pi$
$200$	−5.02805	−0.355537
$201$	8.57370	0.604742
$202$	−4.11482	−0.289518
$203$	0.125441	0.00880425
$204$	16.8417	1.17916
$205$	−18.4214	−1.28660
$206$	10.0017	0.696848
$207$	−0.552759	−0.0384194
$208$	2.45044	0.169908
$209$	11.0006	0.760927
$210$	−4.73205	−0.326542
$211$	3.13315	0.215695	0.107847	−	0.994167i	$-0.465604\pi$
$211$	3.13315	0.215695	0.107847	+	0.994167i	$0.465604\pi$
$212$	−36.6586	−2.51772
$213$	−3.34231	−0.229011
$214$	−15.3148	−1.04690
$215$	−10.9201	−0.744745
$216$	2.32089	0.157917
$217$	4.55350	0.309111
$218$	−37.2225	−2.52103
$219$	3.77345	0.254986
$220$	−47.8205	−3.22406
$221$	15.7912	1.06223
$222$	−0.255389	−0.0171406
$223$	9.36240	0.626952	0.313476	−	0.949596i	$-0.398506\pi$
$223$	9.36240	0.626952	0.313476	+	0.949596i	$0.398506\pi$
$224$	−5.17932	−0.346058
$225$	2.16643	0.144429
$226$	1.85922	0.123674
$227$	28.0526	1.86192	0.930960	−	0.365121i	$-0.118973\pi$
$227$	28.0526	1.86192	0.930960	+	0.365121i	$0.118973\pi$
$228$	5.67015	0.375515
$229$	−24.6788	−1.63082	−0.815410	−	0.578885i	$-0.803488\pi$
$229$	−24.6788	−1.63082	−0.815410	+	0.578885i	$0.803488\pi$
$230$	3.32017	0.218925
$231$	−4.63785	−0.305148
$232$	0.369548	0.0242620
$233$	17.3301	1.13533	0.567665	−	0.823260i	$-0.307847\pi$
$233$	17.3301	1.13533	0.567665	+	0.823260i	$0.307847\pi$
$234$	6.38370	0.417316
$235$	15.2389	0.994075
$236$	−4.23265	−0.275522
$237$	−15.2345	−0.989589
$238$	−9.81101	−0.635953
$239$	−1.48135	−0.0958206	−0.0479103	−	0.998852i	$-0.515256\pi$
$239$	−1.48135	−0.0958206	−0.0479103	+	0.998852i	$0.515256\pi$
$240$	2.30567	0.148830
$241$	−15.7651	−1.01552	−0.507761	−	0.861498i	$-0.669527\pi$
$241$	−15.7651	−1.01552	−0.507761	+	0.861498i	$0.669527\pi$
$242$	−53.0790	−3.41205
$243$	−1.00000	−0.0641500
$244$	−33.7418	−2.16010
$245$	−17.0776	−1.09105
$246$	−15.4399	−0.984410
$247$	5.31648	0.338279
$248$	13.4145	0.851823
$249$	−5.73088	−0.363180
$250$	17.0200	1.07644
$251$	−18.1216	−1.14382	−0.571912	−	0.820315i	$-0.693798\pi$
$251$	−18.1216	−1.14382	−0.571912	+	0.820315i	$0.693798\pi$
$252$	−2.39053	−0.150590
$253$	3.25408	0.204582
$254$	−9.87641	−0.619701
$255$	14.8582	0.930459
$256$	−10.0313	−0.626955
$257$	18.5978	1.16010	0.580051	−	0.814580i	$-0.303033\pi$
$257$	18.5978	1.16010	0.580051	+	0.814580i	$0.303033\pi$
$258$	−9.15269	−0.569821
$259$	0.0896714	0.00557191
$260$	−23.1111	−1.43329
$261$	−0.159227	−0.00985588
$262$	−17.1977	−1.06248
$263$	3.62110	0.223287	0.111643	−	0.993748i	$-0.464389\pi$
$263$	3.62110	0.223287	0.111643	+	0.993748i	$0.464389\pi$
$264$	−13.6630	−0.840901
$265$	−32.3412	−1.98671
$266$	−3.30310	−0.202526
$267$	−0.944385	−0.0577954
$268$	−26.0159	−1.58917
$269$	9.73419	0.593504	0.296752	−	0.954955i	$-0.404097\pi$
$269$	9.73419	0.593504	0.296752	+	0.954955i	$0.404097\pi$
$270$	6.00654	0.365547
$271$	−4.56549	−0.277334	−0.138667	−	0.990339i	$-0.544282\pi$
$271$	−4.56549	−0.277334	−0.138667	+	0.990339i	$0.544282\pi$
$272$	4.78037	0.289852
$273$	−2.24142	−0.135657
$274$	2.07928	0.125614
$275$	−12.7537	−0.769078
$276$	1.67728	0.100961
$277$	15.9385	0.957651	0.478826	−	0.877910i	$-0.341063\pi$
$277$	15.9385	0.957651	0.478826	+	0.877910i	$0.341063\pi$
$278$	12.8786	0.772405
$279$	−5.77990	−0.346034
$280$	4.89475	0.292517
$281$	7.39706	0.441272	0.220636	−	0.975356i	$-0.429187\pi$
$281$	7.39706	0.441272	0.220636	+	0.975356i	$0.429187\pi$
$282$	12.7725	0.760589
$283$	−2.96331	−0.176151	−0.0880753	−	0.996114i	$-0.528072\pi$
$283$	−2.96331	−0.176151	−0.0880753	+	0.996114i	$0.528072\pi$
$284$	10.1418	0.601807
$285$	5.00237	0.296315
$286$	−37.5807	−2.22219
$287$	5.42119	0.320003
$288$	6.57428	0.387393
$289$	13.8058	0.812105
$290$	0.956402	0.0561619
$291$	0.199388	0.0116884
$292$	−11.4501	−0.670066
$293$	−5.45110	−0.318457	−0.159228	−	0.987242i	$-0.550901\pi$
$293$	−5.45110	−0.318457	−0.159228	+	0.987242i	$0.550901\pi$
$294$	−14.3136	−0.834787
$295$	−3.73416	−0.217411
$296$	0.264171	0.0153546
$297$	5.88697	0.341597
$298$	−14.4636	−0.837856
$299$	1.57266	0.0909493
$300$	−6.57378	−0.379537
$301$	3.21366	0.185232
$302$	−27.9876	−1.61051
$303$	−1.83391	−0.105355
$304$	1.60942	0.0923066
$305$	−29.7680	−1.70451
$306$	12.4534	0.711916
$307$	8.93530	0.509965	0.254982	−	0.966946i	$-0.417930\pi$
$307$	8.93530	0.509965	0.254982	+	0.966946i	$0.417930\pi$
$308$	14.0730	0.801884
$309$	4.45758	0.253583
$310$	34.7172	1.97181
$311$	22.6745	1.28575	0.642876	−	0.765970i	$-0.277741\pi$
$311$	22.6745	1.28575	0.642876	+	0.765970i	$0.277741\pi$
$312$	−6.60320	−0.373833
$313$	−33.0360	−1.86730	−0.933652	−	0.358181i	$-0.883397\pi$
$313$	−33.0360	−1.86730	−0.933652	+	0.358181i	$0.883397\pi$
$314$	−13.6521	−0.770433
$315$	−2.10900	−0.118828
$316$	46.2274	2.60050
$317$	30.9785	1.73993	0.869964	−	0.493116i	$-0.164142\pi$
$317$	30.9785	1.73993	0.869964	+	0.493116i	$0.164142\pi$
$318$	−27.1068	−1.52007
$319$	0.937363	0.0524823
$320$	−34.8774	−1.94970
$321$	−6.82555	−0.380965
$322$	−0.977087	−0.0544509
$323$	10.3715	0.577084
$324$	3.03438	0.168577
$325$	−6.16374	−0.341903
$326$	−24.6358	−1.36445
$327$	−16.5895	−0.917400
$328$	15.9708	0.881837
$329$	−4.48462	−0.247245
$330$	−35.3604	−1.94652
$331$	−22.3184	−1.22673	−0.613364	−	0.789800i	$-0.710184\pi$
$331$	−22.3184	−1.22673	−0.613364	+	0.789800i	$0.710184\pi$
$332$	17.3897	0.954383
$333$	−0.113823	−0.00623746
$334$	30.2328	1.65426
$335$	−22.9520	−1.25400
$336$	−0.678531	−0.0370169
$337$	−22.9280	−1.24897	−0.624484	−	0.781037i	$-0.714691\pi$
$337$	−22.9280	−1.24897	−0.624484	+	0.781037i	$0.714691\pi$
$338$	11.0063	0.598664
$339$	0.828624	0.0450047
$340$	−45.0856	−2.44511
$341$	34.0261	1.84262
$342$	4.19274	0.226717
$343$	10.5405	0.569131
$344$	9.46739	0.510448
$345$	1.47975	0.0796668
$346$	19.3042	1.03780
$347$	7.85869	0.421877	0.210938	−	0.977499i	$-0.432348\pi$
$347$	7.85869	0.421877	0.210938	+	0.977499i	$0.432348\pi$
$348$	0.483155	0.0258998
$349$	−20.6002	−1.10270	−0.551352	−	0.834273i	$-0.685888\pi$
$349$	−20.6002	−1.10270	−0.551352	+	0.834273i	$0.685888\pi$
$350$	3.82950	0.204695
$351$	2.84511	0.151861
$352$	−38.7026	−2.06286
$353$	19.9224	1.06036	0.530180	−	0.847885i	$-0.322124\pi$
$353$	19.9224	1.06036	0.530180	+	0.847885i	$0.322124\pi$
$354$	−3.12979	−0.166346
$355$	8.94742	0.474879
$356$	2.86563	0.151878
$357$	−4.37261	−0.231423
$358$	−16.4340	−0.868564
$359$	−14.3721	−0.758531	−0.379266	−	0.925288i	$-0.623823\pi$
$359$	−14.3721	−0.758531	−0.379266	+	0.925288i	$0.623823\pi$
$360$	−6.21307	−0.327458
$361$	−15.5082	−0.816221
$362$	11.4176	0.600094
$363$	−23.6565	−1.24164
$364$	6.80134	0.356487
$365$	−10.1016	−0.528741
$366$	−24.9500	−1.30416
$367$	−28.8646	−1.50672	−0.753361	−	0.657607i	$-0.771569\pi$
$367$	−28.8646	−1.50672	−0.753361	+	0.657607i	$0.771569\pi$
$368$	0.476081	0.0248174
$369$	−6.88130	−0.358226
$370$	0.683682	0.0355429
$371$	9.51765	0.494132
$372$	17.5384	0.909326
$373$	25.1563	1.30254	0.651272	−	0.758844i	$-0.274236\pi$
$373$	25.1563	1.30254	0.651272	+	0.758844i	$0.274236\pi$
$374$	−73.3131	−3.79093
$375$	7.58552	0.391715
$376$	−13.2116	−0.681338
$377$	0.453018	0.0233316
$378$	−1.76766	−0.0909184
$379$	−26.1924	−1.34541	−0.672706	−	0.739910i	$-0.734868\pi$
$379$	−26.1924	−1.34541	−0.672706	+	0.739910i	$0.734868\pi$
$380$	−15.1791	−0.778672
$381$	−4.40176	−0.225509
$382$	−8.96348	−0.458611
$383$	11.2339	0.574023	0.287012	−	0.957927i	$-0.407338\pi$
$383$	11.2339	0.574023	0.287012	+	0.957927i	$0.407338\pi$
$384$	−16.0839	−0.820778
$385$	12.4156	0.632758
$386$	52.0570	2.64963
$387$	−4.07920	−0.207358
$388$	−0.605021	−0.0307153
$389$	4.86638	0.246736	0.123368	−	0.992361i	$-0.460631\pi$
$389$	4.86638	0.246736	0.123368	+	0.992361i	$0.460631\pi$
$390$	−17.0893	−0.865350
$391$	3.06797	0.155154
$392$	14.8058	0.747805
$393$	−7.66473	−0.386635
$394$	−45.4768	−2.29109
$395$	40.7831	2.05202
$396$	−17.8633	−0.897667
$397$	−3.93228	−0.197356	−0.0986778	−	0.995119i	$-0.531461\pi$
$397$	−3.93228	−0.197356	−0.0986778	+	0.995119i	$0.531461\pi$
$398$	−14.4619	−0.724911
$399$	−1.47214	−0.0736991
$400$	−1.86591	−0.0932953
$401$	−21.8801	−1.09264	−0.546320	−	0.837576i	$-0.683972\pi$
$401$	−21.8801	−1.09264	−0.546320	+	0.837576i	$0.683972\pi$
$402$	−19.2372	−0.959463
$403$	16.4445	0.819158
$404$	5.56479	0.276859
$405$	2.67702	0.133022
$406$	−0.281458	−0.0139685
$407$	0.670072	0.0332143
$408$	−12.8816	−0.637736
$409$	−23.0317	−1.13884	−0.569422	−	0.822045i	$-0.692833\pi$
$409$	−23.0317	−1.13884	−0.569422	+	0.822045i	$0.692833\pi$
$410$	41.3328	2.04128
$411$	0.926703	0.0457109
$412$	−13.5260	−0.666378
$413$	1.09892	0.0540743
$414$	1.24025	0.0609549
$415$	15.3417	0.753093
$416$	−18.7046	−0.917067
$417$	5.73977	0.281078
$418$	−24.6825	−1.20726
$419$	13.3367	0.651541	0.325770	−	0.945449i	$-0.394376\pi$
$419$	13.3367	0.651541	0.325770	+	0.945449i	$0.394376\pi$
$420$	6.39951	0.312264
$421$	1.35227	0.0659055	0.0329528	−	0.999457i	$-0.489509\pi$
$421$	1.35227	0.0659055	0.0329528	+	0.999457i	$0.489509\pi$
$422$	−7.02999	−0.342214
$423$	5.69248	0.276778
$424$	28.0388	1.36169
$425$	−12.0243	−0.583265
$426$	7.49928	0.363341
$427$	8.76036	0.423944
$428$	20.7113	1.00112
$429$	−16.7491	−0.808654
$430$	24.5019	1.18159
$431$	11.7447	0.565723	0.282862	−	0.959161i	$-0.408716\pi$
$431$	11.7447	0.565723	0.282862	+	0.959161i	$0.408716\pi$
$432$	0.861281	0.0414384
$433$	−9.42123	−0.452755	−0.226378	−	0.974040i	$-0.572688\pi$
$433$	−9.42123	−0.452755	−0.226378	+	0.974040i	$0.572688\pi$
$434$	−10.2169	−0.490426
$435$	0.426253	0.0204373
$436$	50.3388	2.41079
$437$	1.03290	0.0494105
$438$	−8.46665	−0.404552
$439$	−30.5243	−1.45685	−0.728423	−	0.685128i	$-0.759746\pi$
$439$	−30.5243	−1.45685	−0.728423	+	0.685128i	$0.759746\pi$
$440$	36.5762	1.74370
$441$	−6.37935	−0.303778
$442$	−35.4314	−1.68530
$443$	33.0230	1.56897	0.784486	−	0.620146i	$-0.212927\pi$
$443$	33.0230	1.56897	0.784486	+	0.620146i	$0.212927\pi$
$444$	0.345382	0.0163911
$445$	2.52814	0.119845
$446$	−21.0068	−0.994701
$447$	−6.44621	−0.304895
$448$	10.2640	0.484928
$449$	27.0309	1.27567	0.637833	−	0.770175i	$-0.279831\pi$
$449$	27.0309	1.27567	0.637833	+	0.770175i	$0.279831\pi$
$450$	−4.86091	−0.229146
$451$	40.5100	1.90754
$452$	−2.51436	−0.118266
$453$	−12.4736	−0.586062
$454$	−62.9429	−2.95406
$455$	6.00033	0.281300
$456$	−4.33690	−0.203094
$457$	−6.94949	−0.325083	−0.162542	−	0.986702i	$-0.551969\pi$
$457$	−6.94949	−0.325083	−0.162542	+	0.986702i	$0.551969\pi$
$458$	55.3728	2.58740
$459$	5.55030	0.259066
$460$	−4.49011	−0.209353
$461$	−25.5062	−1.18794	−0.593972	−	0.804486i	$-0.702441\pi$
$461$	−25.5062	−1.18794	−0.593972	+	0.804486i	$0.702441\pi$
$462$	10.4061	0.484137
$463$	−16.5146	−0.767497	−0.383748	−	0.923438i	$-0.625367\pi$
$463$	−16.5146	−0.767497	−0.383748	+	0.923438i	$0.625367\pi$
$464$	0.137139	0.00636652
$465$	15.4729	0.717539
$466$	−38.8842	−1.80128
$467$	30.7774	1.42421	0.712104	−	0.702074i	$-0.247742\pi$
$467$	30.7774	1.42421	0.712104	+	0.702074i	$0.247742\pi$
$468$	−8.63317	−0.399068
$469$	6.75449	0.311893
$470$	−34.1921	−1.57717
$471$	−6.08453	−0.280360
$472$	3.23740	0.149013
$473$	24.0142	1.10417
$474$	34.1824	1.57005
$475$	−4.04826	−0.185747
$476$	13.2682	0.608146
$477$	−12.0811	−0.553154
$478$	3.32377	0.152026
$479$	−14.9934	−0.685068	−0.342534	−	0.939505i	$-0.611285\pi$
$479$	−14.9934	−0.685068	−0.342534	+	0.939505i	$0.611285\pi$
$480$	−17.5995	−0.803302
$481$	0.323839	0.0147658
$482$	35.3729	1.61119
$483$	−0.435472	−0.0198146
$484$	71.7828	3.26285
$485$	−0.533766	−0.0242371
$486$	2.24374	0.101778
$487$	30.9928	1.40442	0.702208	−	0.711971i	$-0.252197\pi$
$487$	30.9928	1.40442	0.702208	+	0.711971i	$0.252197\pi$
$488$	25.8079	1.16827
$489$	−10.9798	−0.496523
$490$	38.3178	1.73102
$491$	−30.3711	−1.37063	−0.685315	−	0.728247i	$-0.740335\pi$
$491$	−30.3711	−1.37063	−0.685315	+	0.728247i	$0.740335\pi$
$492$	20.8805	0.941366
$493$	0.883755	0.0398023
$494$	−11.9288	−0.536702
$495$	−15.7595	−0.708339
$496$	4.97812	0.223524
$497$	−2.63312	−0.118112
$498$	12.8586	0.576209
$499$	−16.0816	−0.719911	−0.359956	−	0.932969i	$-0.617208\pi$
$499$	−16.0816	−0.719911	−0.359956	+	0.932969i	$0.617208\pi$
$500$	−23.0174	−1.02937
$501$	13.4742	0.601985
$502$	40.6602	1.81475
$503$	−16.9566	−0.756058	−0.378029	−	0.925794i	$-0.623398\pi$
$503$	−16.9566	−0.756058	−0.378029	+	0.925794i	$0.623398\pi$
$504$	1.82843	0.0814450
$505$	4.90941	0.218466
$506$	−7.30131	−0.324583
$507$	4.90533	0.217853
$508$	13.3566	0.592604
$509$	−11.1019	−0.492083	−0.246041	−	0.969259i	$-0.579130\pi$
$509$	−11.1019	−0.492083	−0.246041	+	0.969259i	$0.579130\pi$
$510$	−33.3381	−1.47624
$511$	2.97278	0.131508
$512$	−9.66019	−0.426924
$513$	1.86863	0.0825022
$514$	−41.7288	−1.84058
$515$	−11.9330	−0.525831
$516$	12.3779	0.544905
$517$	−33.5115	−1.47383
$518$	−0.201200	−0.00884021
$519$	8.60358	0.377655
$520$	17.6769	0.775183
$521$	−2.28457	−0.100089	−0.0500444	−	0.998747i	$-0.515936\pi$
$521$	−2.28457	−0.100089	−0.0500444	+	0.998747i	$0.515936\pi$
$522$	0.357264	0.0156370
$523$	−0.426777	−0.0186616	−0.00933082	−	0.999956i	$-0.502970\pi$
$523$	−0.426777	−0.0186616	−0.00933082	+	0.999956i	$0.502970\pi$
$524$	23.2577	1.01602
$525$	1.70675	0.0744885
$526$	−8.12482	−0.354259
$527$	32.0802	1.39743
$528$	−5.07034	−0.220658
$529$	−22.6945	−0.986716
$530$	72.5654	3.15204
$531$	−1.39489	−0.0605333
$532$	4.46703	0.193671
$533$	19.5781	0.848020
$534$	2.11896	0.0916963
$535$	18.2721	0.789973
$536$	19.8986	0.859490
$537$	−7.32437	−0.316070
$538$	−21.8410	−0.941633
$539$	37.5550	1.61761
$540$	−8.12310	−0.349563
$541$	−20.6871	−0.889406	−0.444703	−	0.895678i	$-0.646691\pi$
$541$	−20.6871	−0.889406	−0.444703	+	0.895678i	$0.646691\pi$
$542$	10.2438	0.440008
$543$	5.08863	0.218374
$544$	−36.4892	−1.56446
$545$	44.4103	1.90233
$546$	5.02918	0.215229
$547$	44.7099	1.91166	0.955828	−	0.293927i	$-0.0949623\pi$
$547$	44.7099	1.91166	0.955828	+	0.293927i	$0.0949623\pi$
$548$	−2.81197	−0.120122
$549$	−11.1198	−0.474582
$550$	28.6161	1.22019
$551$	0.297536	0.0126755
$552$	−1.28289	−0.0546036
$553$	−12.0020	−0.510377
$554$	−35.7619	−1.51938
$555$	0.304706	0.0129341
$556$	−17.4167	−0.738631
$557$	−21.4994	−0.910960	−0.455480	−	0.890246i	$-0.650532\pi$
$557$	−21.4994	−0.910960	−0.455480	+	0.890246i	$0.650532\pi$
$558$	12.9686	0.549005
$559$	11.6058	0.490873
$560$	1.81644	0.0767586
$561$	−32.6744	−1.37952
$562$	−16.5971	−0.700107
$563$	−1.75414	−0.0739283	−0.0369641	−	0.999317i	$-0.511769\pi$
$563$	−1.75414	−0.0739283	−0.0369641	+	0.999317i	$0.511769\pi$
$564$	−17.2732	−0.727332
$565$	−2.21824	−0.0933222
$566$	6.64891	0.279474
$567$	−0.787815	−0.0330851
$568$	−7.75713	−0.325482
$569$	−6.15896	−0.258197	−0.129098	−	0.991632i	$-0.541208\pi$
$569$	−6.15896	−0.258197	−0.129098	+	0.991632i	$0.541208\pi$
$570$	−11.2240	−0.470123
$571$	24.3238	1.01792	0.508960	−	0.860790i	$-0.330030\pi$
$571$	24.3238	1.01792	0.508960	+	0.860790i	$0.330030\pi$
$572$	50.8232	2.12503
$573$	−3.99488	−0.166888
$574$	−12.1638	−0.507706
$575$	−1.19751	−0.0499397
$576$	−13.0284	−0.542851
$577$	0.997231	0.0415153	0.0207576	−	0.999785i	$-0.493392\pi$
$577$	0.997231	0.0415153	0.0207576	+	0.999785i	$0.493392\pi$
$578$	−30.9766	−1.28846
$579$	23.2009	0.964198
$580$	−1.29341	−0.0537061
$581$	−4.51488	−0.187309
$582$	−0.447376	−0.0185443
$583$	71.1209	2.94553
$584$	8.75777	0.362399
$585$	−7.61642	−0.314900
$586$	12.2309	0.505253
$587$	−26.7142	−1.10261	−0.551306	−	0.834303i	$-0.685870\pi$
$587$	−26.7142	−1.10261	−0.551306	+	0.834303i	$0.685870\pi$
$588$	19.3574	0.798285
$589$	10.8005	0.445028
$590$	8.37849	0.344937
$591$	−20.2683	−0.833725
$592$	0.0980336	0.00402915
$593$	−8.38782	−0.344446	−0.172223	−	0.985058i	$-0.555095\pi$
$593$	−8.38782	−0.344446	−0.172223	+	0.985058i	$0.555095\pi$
$594$	−13.2089	−0.541966
$595$	11.7056	0.479881
$596$	19.5603	0.801220
$597$	−6.44545	−0.263795
$598$	−3.52865	−0.144297
$599$	23.5435	0.961963	0.480981	−	0.876731i	$-0.340280\pi$
$599$	23.5435	0.961963	0.480981	+	0.876731i	$0.340280\pi$
$600$	5.02805	0.205269
$601$	20.3652	0.830713	0.415356	−	0.909659i	$-0.363657\pi$
$601$	20.3652	0.830713	0.415356	+	0.909659i	$0.363657\pi$
$602$	−7.21063	−0.293883
$603$	−8.57370	−0.349148
$604$	37.8498	1.54009
$605$	63.3288	2.57468
$606$	4.11482	0.167153
$607$	31.4860	1.27798	0.638989	−	0.769216i	$-0.279353\pi$
$607$	31.4860	1.27798	0.638989	+	0.769216i	$0.279353\pi$
$608$	−12.2849	−0.498219
$609$	−0.125441	−0.00508314
$610$	66.7917	2.70432
$611$	−16.1957	−0.655210
$612$	−16.8417	−0.680787
$613$	33.5258	1.35409	0.677046	−	0.735940i	$-0.263260\pi$
$613$	33.5258	1.35409	0.677046	+	0.735940i	$0.263260\pi$
$614$	−20.0485	−0.809093
$615$	18.4214	0.742821
$616$	−10.7639	−0.433692
$617$	−29.6323	−1.19295	−0.596477	−	0.802630i	$-0.703433\pi$
$617$	−29.6323	−1.19295	−0.596477	+	0.802630i	$0.703433\pi$
$618$	−10.0017	−0.402326
$619$	−37.5640	−1.50982	−0.754911	−	0.655827i	$-0.772320\pi$
$619$	−37.5640	−1.50982	−0.754911	+	0.655827i	$0.772320\pi$
$620$	−46.9507	−1.88559
$621$	0.552759	0.0221814
$622$	−50.8758	−2.03993
$623$	−0.744001	−0.0298078
$624$	−2.45044	−0.0980962
$625$	−31.1387	−1.24555
$626$	74.1243	2.96260
$627$	−11.0006	−0.439322
$628$	18.4628	0.736745
$629$	0.631751	0.0251896
$630$	4.73205	0.188529
$631$	18.9935	0.756119	0.378060	−	0.925781i	$-0.376591\pi$
$631$	18.9935	0.756119	0.378060	+	0.925781i	$0.376591\pi$
$632$	−35.3577	−1.40645
$633$	−3.13315	−0.124532
$634$	−69.5079	−2.76051
$635$	11.7836	0.467617
$636$	36.6586	1.45361
$637$	18.1500	0.719128
$638$	−2.10320	−0.0832666
$639$	3.34231	0.132220
$640$	43.0569	1.70197
$641$	−8.08703	−0.319418	−0.159709	−	0.987164i	$-0.551056\pi$
$641$	−8.08703	−0.319418	−0.159709	+	0.987164i	$0.551056\pi$
$642$	15.3148	0.604426
$643$	−10.3790	−0.409307	−0.204654	−	0.978834i	$-0.565607\pi$
$643$	−10.3790	−0.409307	−0.204654	+	0.978834i	$0.565607\pi$
$644$	1.32139	0.0520700
$645$	10.9201	0.429979
$646$	−23.2709	−0.915582
$647$	31.7171	1.24693	0.623464	−	0.781852i	$-0.285725\pi$
$647$	31.7171	1.24693	0.623464	+	0.781852i	$0.285725\pi$
$648$	−2.32089	−0.0911733
$649$	8.21171	0.322338
$650$	13.8298	0.542451
$651$	−4.55350	−0.178466
$652$	33.3169	1.30479
$653$	−10.1008	−0.395274	−0.197637	−	0.980275i	$-0.563327\pi$
$653$	−10.1008	−0.395274	−0.197637	+	0.980275i	$0.563327\pi$
$654$	37.2225	1.45552
$655$	20.5186	0.801729
$656$	5.92673	0.231400
$657$	−3.77345	−0.147216
$658$	10.0623	0.392271
$659$	14.2913	0.556708	0.278354	−	0.960479i	$-0.410211\pi$
$659$	14.2913	0.556708	0.278354	+	0.960479i	$0.410211\pi$
$660$	47.8205	1.86141
$661$	19.4462	0.756371	0.378186	−	0.925730i	$-0.376548\pi$
$661$	19.4462	0.756371	0.378186	+	0.925730i	$0.376548\pi$
$662$	50.0767	1.94629
$663$	−15.7912	−0.613280
$664$	−13.3008	−0.516169
$665$	3.94094	0.152823
$666$	0.255389	0.00989614
$667$	0.0880139	0.00340791
$668$	−40.8860	−1.58193
$669$	−9.36240	−0.361971
$670$	51.4983	1.98955
$671$	65.4621	2.52714
$672$	5.17932	0.199797
$673$	−14.2119	−0.547827	−0.273914	−	0.961754i	$-0.588318\pi$
$673$	−14.2119	−0.547827	−0.273914	+	0.961754i	$0.588318\pi$
$674$	51.4446	1.98157
$675$	−2.16643	−0.0833859
$676$	−14.8847	−0.572487
$677$	−34.3220	−1.31910	−0.659552	−	0.751659i	$-0.729254\pi$
$677$	−34.3220	−1.31910	−0.659552	+	0.751659i	$0.729254\pi$
$678$	−1.85922	−0.0714029
$679$	0.157081	0.00602822
$680$	34.4844	1.32242
$681$	−28.0526	−1.07498
$682$	−76.3459	−2.92344
$683$	−48.3879	−1.85151	−0.925756	−	0.378122i	$-0.876570\pi$
$683$	−48.3879	−1.85151	−0.925756	+	0.378122i	$0.876570\pi$
$684$	−5.67015	−0.216804
$685$	−2.48080	−0.0947866
$686$	−23.6501	−0.902964
$687$	24.6788	0.941554
$688$	3.51334	0.133945
$689$	34.3720	1.30947
$690$	−3.32017	−0.126397
$691$	−37.6891	−1.43376	−0.716880	−	0.697196i	$-0.754431\pi$
$691$	−37.6891	−1.43376	−0.716880	+	0.697196i	$0.754431\pi$
$692$	−26.1066	−0.992423
$693$	4.63785	0.176177
$694$	−17.6329	−0.669335
$695$	−15.3655	−0.582845
$696$	−0.369548	−0.0140077
$697$	38.1932	1.44667
$698$	46.2216	1.74951
$699$	−17.3301	−0.655483
$700$	−5.17892	−0.195745
$701$	−5.57190	−0.210448	−0.105224	−	0.994449i	$-0.533556\pi$
$701$	−5.57190	−0.210448	−0.105224	+	0.994449i	$0.533556\pi$
$702$	−6.38370	−0.240937
$703$	0.212693	0.00802188
$704$	76.6980	2.89067
$705$	−15.2389	−0.573929
$706$	−44.7007	−1.68233
$707$	−1.44478	−0.0543366
$708$	4.23265	0.159073
$709$	−27.9186	−1.04851	−0.524253	−	0.851562i	$-0.675656\pi$
$709$	−27.9186	−1.04851	−0.524253	+	0.851562i	$0.675656\pi$
$710$	−20.0757	−0.753428
$711$	15.2345	0.571340
$712$	−2.19182	−0.0821418
$713$	3.19489	0.119650
$714$	9.81101	0.367168
$715$	44.8377	1.67683
$716$	22.2249	0.830585
$717$	1.48135	0.0553220
$718$	32.2473	1.20346
$719$	−16.3289	−0.608965	−0.304483	−	0.952518i	$-0.598484\pi$
$719$	−16.3289	−0.608965	−0.304483	+	0.952518i	$0.598484\pi$
$720$	−2.30567	−0.0859271
$721$	3.51175	0.130784
$722$	34.7964	1.29499
$723$	15.7651	0.586312
$724$	−15.4408	−0.573855
$725$	−0.344953	−0.0128112
$726$	53.0790	1.96995
$727$	41.2386	1.52946	0.764728	−	0.644353i	$-0.222873\pi$
$727$	41.2386	1.52946	0.764728	+	0.644353i	$0.222873\pi$
$728$	−5.20210	−0.192803
$729$	1.00000	0.0370370
$730$	22.6654	0.838883
$731$	22.6408	0.837400
$732$	33.7418	1.24713
$733$	5.66380	0.209197	0.104599	−	0.994515i	$-0.466644\pi$
$733$	5.66380	0.209197	0.104599	+	0.994515i	$0.466644\pi$
$734$	64.7648	2.39051
$735$	17.0776	0.629918
$736$	−3.63399	−0.133951
$737$	50.4731	1.85920
$738$	15.4399	0.568349
$739$	22.7170	0.835657	0.417829	−	0.908526i	$-0.362791\pi$
$739$	22.7170	0.835657	0.417829	+	0.908526i	$0.362791\pi$
$740$	−0.924595	−0.0339888
$741$	−5.31648	−0.195306
$742$	−21.3552	−0.783972
$743$	26.0510	0.955717	0.477858	−	0.878437i	$-0.341413\pi$
$743$	26.0510	0.955717	0.477858	+	0.878437i	$0.341413\pi$
$744$	−13.4145	−0.491800
$745$	17.2566	0.632234
$746$	−56.4443	−2.06657
$747$	5.73088	0.209682
$748$	99.1468	3.62517
$749$	−5.37727	−0.196481
$750$	−17.0200	−0.621481
$751$	−36.8696	−1.34539	−0.672695	−	0.739920i	$-0.734864\pi$
$751$	−36.8696	−1.34539	−0.672695	+	0.739920i	$0.734864\pi$
$752$	−4.90283	−0.178788
$753$	18.1216	0.660387
$754$	−1.01646	−0.0370171
$755$	33.3922	1.21526
$756$	2.39053	0.0869429
$757$	30.1985	1.09758	0.548791	−	0.835960i	$-0.315088\pi$
$757$	30.1985	1.09758	0.548791	+	0.835960i	$0.315088\pi$
$758$	58.7690	2.13459
$759$	−3.25408	−0.118115
$760$	11.6100	0.421137
$761$	2.81258	0.101956	0.0509780	−	0.998700i	$-0.483766\pi$
$761$	2.81258	0.101956	0.0509780	+	0.998700i	$0.483766\pi$
$762$	9.87641	0.357785
$763$	−13.0694	−0.473146
$764$	12.1220	0.438558
$765$	−14.8582	−0.537201
$766$	−25.2059	−0.910726
$767$	3.96863	0.143299
$768$	10.0313	0.361973
$769$	7.80393	0.281417	0.140708	−	0.990051i	$-0.455062\pi$
$769$	7.80393	0.281417	0.140708	+	0.990051i	$0.455062\pi$
$770$	−27.8574	−1.00391
$771$	−18.5978	−0.669785
$772$	−70.4006	−2.53377
$773$	−18.6020	−0.669066	−0.334533	−	0.942384i	$-0.608579\pi$
$773$	−18.6020	−0.669066	−0.334533	+	0.942384i	$0.608579\pi$
$774$	9.15269	0.328987
$775$	−12.5217	−0.449794
$776$	0.462759	0.0166121
$777$	−0.0896714	−0.00321695
$778$	−10.9189	−0.391462
$779$	12.8586	0.460708
$780$	23.1111	0.827512
$781$	−19.6761	−0.704065
$782$	−6.88374	−0.246162
$783$	0.159227	0.00569030
$784$	5.49441	0.196229
$785$	16.2884	0.581357
$786$	17.1977	0.613421
$787$	38.3219	1.36603	0.683015	−	0.730404i	$-0.260668\pi$
$787$	38.3219	1.36603	0.683015	+	0.730404i	$0.260668\pi$
$788$	61.5017	2.19091
$789$	−3.62110	−0.128915
$790$	−91.5069	−3.25567
$791$	0.652803	0.0232110
$792$	13.6630	0.485495
$793$	31.6371	1.12347
$794$	8.82303	0.313118
$795$	32.3412	1.14703
$796$	19.5580	0.693214
$797$	−22.5236	−0.797827	−0.398914	−	0.916989i	$-0.630613\pi$
$797$	−22.5236	−0.797827	−0.398914	+	0.916989i	$0.630613\pi$
$798$	3.30310	0.116929
$799$	−31.5949	−1.11775
$800$	14.2427	0.503556
$801$	0.944385	0.0333682
$802$	49.0933	1.73355
$803$	22.2142	0.783922
$804$	26.0159	0.917510
$805$	1.16577	0.0410879
$806$	−36.8972	−1.29965
$807$	−9.73419	−0.342660
$808$	−4.25631	−0.149736
$809$	−7.61854	−0.267854	−0.133927	−	0.990991i	$-0.542759\pi$
$809$	−7.61854	−0.267854	−0.133927	+	0.990991i	$0.542759\pi$
$810$	−6.00654	−0.211048
$811$	−24.9822	−0.877244	−0.438622	−	0.898672i	$-0.644533\pi$
$811$	−24.9822	−0.877244	−0.438622	+	0.898672i	$0.644533\pi$
$812$	0.380637	0.0133577
$813$	4.56549	0.160119
$814$	−1.50347	−0.0526966
$815$	29.3931	1.02959
$816$	−4.78037	−0.167346
$817$	7.62254	0.266679
$818$	51.6772	1.80685
$819$	2.24142	0.0783217
$820$	−55.8975	−1.95203
$821$	−2.31326	−0.0807334	−0.0403667	−	0.999185i	$-0.512853\pi$
$821$	−2.31326	−0.0807334	−0.0403667	+	0.999185i	$0.512853\pi$
$822$	−2.07928	−0.0725234
$823$	−27.9691	−0.974942	−0.487471	−	0.873139i	$-0.662081\pi$
$823$	−27.9691	−0.974942	−0.487471	+	0.873139i	$0.662081\pi$
$824$	10.3456	0.360404
$825$	12.7537	0.444027
$826$	−2.46569	−0.0857924
$827$	13.3404	0.463892	0.231946	−	0.972729i	$-0.425491\pi$
$827$	13.3404	0.463892	0.231946	+	0.972729i	$0.425491\pi$
$828$	−1.67728	−0.0582896
$829$	16.9448	0.588517	0.294258	−	0.955726i	$-0.404927\pi$
$829$	16.9448	0.588517	0.294258	+	0.955726i	$0.404927\pi$
$830$	−34.4228	−1.19483
$831$	−15.9385	−0.552900
$832$	37.0674	1.28508
$833$	35.4073	1.22679
$834$	−12.8786	−0.445948
$835$	−36.0708	−1.24828
$836$	33.3800	1.15447
$837$	5.77990	0.199783
$838$	−29.9241	−1.03371
$839$	−49.8424	−1.72075	−0.860375	−	0.509662i	$-0.829771\pi$
$839$	−49.8424	−1.72075	−0.860375	+	0.509662i	$0.829771\pi$
$840$	−4.89475	−0.168885
$841$	−28.9746	−0.999126
$842$	−3.03414	−0.104563
$843$	−7.39706	−0.254768
$844$	9.50718	0.327251
$845$	−13.1317	−0.451743
$846$	−12.7725	−0.439126
$847$	−18.6369	−0.640372
$848$	10.4052	0.357316
$849$	2.96331	0.101701
$850$	26.9795	0.925389
$851$	0.0629166	0.00215675
$852$	−10.1418	−0.347454
$853$	24.7961	0.849003	0.424501	−	0.905427i	$-0.360449\pi$
$853$	24.7961	0.849003	0.424501	+	0.905427i	$0.360449\pi$
$854$	−19.6560	−0.672615
$855$	−5.00237	−0.171077
$856$	−15.8414	−0.541447
$857$	−30.3603	−1.03709	−0.518544	−	0.855051i	$-0.673526\pi$
$857$	−30.3603	−1.03709	−0.518544	+	0.855051i	$0.673526\pi$
$858$	37.5807	1.28298
$859$	−21.2962	−0.726617	−0.363309	−	0.931669i	$-0.618353\pi$
$859$	−21.2962	−0.726617	−0.363309	+	0.931669i	$0.618353\pi$
$860$	−33.1358	−1.12992
$861$	−5.42119	−0.184754
$862$	−26.3521	−0.897557
$863$	−21.3866	−0.728009	−0.364004	−	0.931397i	$-0.618591\pi$
$863$	−21.3866	−0.728009	−0.364004	+	0.931397i	$0.618591\pi$
$864$	−6.57428	−0.223662
$865$	−23.0319	−0.783109
$866$	21.1388	0.718326
$867$	−13.8058	−0.468869
$868$	13.8171	0.468981
$869$	−89.6853	−3.04237
$870$	−0.956402	−0.0324251
$871$	24.3931	0.826530
$872$	−38.5024	−1.30386
$873$	−0.199388	−0.00674827
$874$	−2.31757	−0.0783930
$875$	5.97599	0.202025
$876$	11.4501	0.386863
$877$	49.8992	1.68498	0.842488	−	0.538715i	$-0.181090\pi$
$877$	49.8992	1.68498	0.842488	+	0.538715i	$0.181090\pi$
$878$	68.4887	2.31138
$879$	5.45110	0.183861
$880$	13.5734	0.457559
$881$	−20.2087	−0.680850	−0.340425	−	0.940272i	$-0.610571\pi$
$881$	−20.2087	−0.680850	−0.340425	+	0.940272i	$0.610571\pi$
$882$	14.3136	0.481965
$883$	−47.0127	−1.58210	−0.791052	−	0.611749i	$-0.790466\pi$
$883$	−47.0127	−1.58210	−0.791052	+	0.611749i	$0.790466\pi$
$884$	47.9166	1.61161
$885$	3.73416	0.125522
$886$	−74.0952	−2.48928
$887$	−10.6841	−0.358738	−0.179369	−	0.983782i	$-0.557406\pi$
$887$	−10.6841	−0.358738	−0.179369	+	0.983782i	$0.557406\pi$
$888$	−0.264171	−0.00886499
$889$	−3.46777	−0.116305
$890$	−5.67249	−0.190142
$891$	−5.88697	−0.197221
$892$	28.4091	0.951207
$893$	−10.6372	−0.355959
$894$	14.4636	0.483736
$895$	19.6075	0.655405
$896$	−12.6711	−0.423313
$897$	−1.57266	−0.0525096
$898$	−60.6503	−2.02393
$899$	0.920315	0.0306942
$900$	6.57378	0.219126
$901$	67.0535	2.23387
$902$	−90.8941	−3.02644
$903$	−3.21366	−0.106944
$904$	1.92315	0.0639630
$905$	−13.6223	−0.452822
$906$	27.9876	0.929827
$907$	−3.01392	−0.100075	−0.0500377	−	0.998747i	$-0.515934\pi$
$907$	−3.01392	−0.100075	−0.0500377	+	0.998747i	$0.515934\pi$
$908$	85.1225	2.82489
$909$	1.83391	0.0608270
$910$	−13.4632	−0.446301
$911$	−18.8927	−0.625943	−0.312972	−	0.949762i	$-0.601325\pi$
$911$	−18.8927	−0.625943	−0.312972	+	0.949762i	$0.601325\pi$
$912$	−1.60942	−0.0532932
$913$	−33.7375	−1.11655
$914$	15.5929	0.515766
$915$	29.7680	0.984098
$916$	−74.8849	−2.47427
$917$	−6.03839	−0.199405
$918$	−12.4534	−0.411025
$919$	−6.23328	−0.205617	−0.102809	−	0.994701i	$-0.532783\pi$
$919$	−6.23328	−0.205617	−0.102809	+	0.994701i	$0.532783\pi$
$920$	3.43433	0.113226
$921$	−8.93530	−0.294428
$922$	57.2295	1.88475
$923$	−9.50924	−0.313000
$924$	−14.0730	−0.462968
$925$	−0.246589	−0.00810781
$926$	37.0544	1.21768
$927$	−4.45758	−0.146406
$928$	−1.04680	−0.0343629
$929$	47.5621	1.56046	0.780231	−	0.625491i	$-0.215101\pi$
$929$	47.5621	1.56046	0.780231	+	0.625491i	$0.215101\pi$
$930$	−34.7172	−1.13842
$931$	11.9207	0.390684
$932$	52.5861	1.72251
$933$	−22.6745	−0.742330
$934$	−69.0566	−2.25960
$935$	87.4701	2.86058
$936$	6.60320	0.215832
$937$	34.9081	1.14040	0.570199	−	0.821507i	$-0.306866\pi$
$937$	34.9081	1.14040	0.570199	+	0.821507i	$0.306866\pi$
$938$	−15.1553	−0.494840
$939$	33.0360	1.07809
$940$	46.2406	1.50820
$941$	24.8618	0.810472	0.405236	−	0.914212i	$-0.367189\pi$
$941$	24.8618	0.810472	0.405236	+	0.914212i	$0.367189\pi$
$942$	13.6521	0.444810
$943$	3.80370	0.123865
$944$	1.20140	0.0391021
$945$	2.10900	0.0686057
$946$	−53.8816	−1.75184
$947$	58.4613	1.89974	0.949868	−	0.312652i	$-0.101217\pi$
$947$	58.4613	1.89974	0.949868	+	0.312652i	$0.101217\pi$
$948$	−46.2274	−1.50140
$949$	10.7359	0.348502
$950$	9.08326	0.294700
$951$	−30.9785	−1.00455
$952$	−10.1484	−0.328910
$953$	11.7025	0.379081	0.189540	−	0.981873i	$-0.439300\pi$
$953$	11.7025	0.379081	0.189540	+	0.981873i	$0.439300\pi$
$954$	27.1068	0.877615
$955$	10.6944	0.346061
$956$	−4.49499	−0.145378
$957$	−0.937363	−0.0303007
$958$	33.6415	1.08691
$959$	0.730071	0.0235752
$960$	34.8774	1.12566
$961$	2.40726	0.0776536
$962$	−0.726612	−0.0234269
$963$	6.82555	0.219950
$964$	−47.8375	−1.54074
$965$	−62.1094	−1.99937
$966$	0.977087	0.0314373
$967$	36.3767	1.16980	0.584898	−	0.811107i	$-0.301134\pi$
$967$	36.3767	1.16980	0.584898	+	0.811107i	$0.301134\pi$
$968$	−54.9041	−1.76468
$969$	−10.3715	−0.333180
$970$	1.19763	0.0384537
$971$	−34.2636	−1.09957	−0.549786	−	0.835306i	$-0.685291\pi$
$971$	−34.2636	−1.09957	−0.549786	+	0.835306i	$0.685291\pi$
$972$	−3.03438	−0.0973279
$973$	4.52188	0.144965
$974$	−69.5398	−2.22820
$975$	6.16374	0.197398
$976$	9.57729	0.306562
$977$	−48.1564	−1.54066	−0.770330	−	0.637645i	$-0.779909\pi$
$977$	−48.1564	−1.54066	−0.770330	+	0.637645i	$0.779909\pi$
$978$	24.6358	0.787766
$979$	−5.55957	−0.177685
$980$	−51.8201	−1.65533
$981$	16.5895	0.529661
$982$	68.1450	2.17459
$983$	6.21222	0.198139	0.0990695	−	0.995081i	$-0.468413\pi$
$983$	6.21222	0.198139	0.0990695	+	0.995081i	$0.468413\pi$
$984$	−15.9708	−0.509129
$985$	54.2585	1.72882
$986$	−1.98292	−0.0631490
$987$	4.48462	0.142747
$988$	16.1322	0.513235
$989$	2.25481	0.0716989
$990$	35.3604	1.12383
$991$	−7.66539	−0.243499	−0.121750	−	0.992561i	$-0.538850\pi$
$991$	−7.66539	−0.243499	−0.121750	+	0.992561i	$0.538850\pi$
$992$	−37.9987	−1.20646
$993$	22.3184	0.708252
$994$	5.90805	0.187392
$995$	17.2546	0.547007
$996$	−17.3897	−0.551014
$997$	−4.81440	−0.152474	−0.0762369	−	0.997090i	$-0.524291\pi$
$997$	−4.81440	−0.152474	−0.0762369	+	0.997090i	$0.524291\pi$
$998$	36.0830	1.14219
$999$	0.113823	0.00360120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.b.1.13	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.b.1.13	✓	106	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24374 q^{2} -1.00000 q^{3} +3.03438 q^{4} +2.67702 q^{5} +2.24374 q^{6} -0.787815 q^{7} -2.32089 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.24374 q^{2} -1.00000 q^{3} +3.03438 q^{4} +2.67702 q^{5} +2.24374 q^{6} -0.787815 q^{7} -2.32089 q^{8} +1.00000 q^{9} -6.00654 q^{10} -5.88697 q^{11} -3.03438 q^{12} -2.84511 q^{13} +1.76766 q^{14} -2.67702 q^{15} -0.861281 q^{16} -5.55030 q^{17} -2.24374 q^{18} -1.86863 q^{19} +8.12310 q^{20} +0.787815 q^{21} +13.2089 q^{22} -0.552759 q^{23} +2.32089 q^{24} +2.16643 q^{25} +6.38370 q^{26} -1.00000 q^{27} -2.39053 q^{28} -0.159227 q^{29} +6.00654 q^{30} -5.77990 q^{31} +6.57428 q^{32} +5.88697 q^{33} +12.4534 q^{34} -2.10900 q^{35} +3.03438 q^{36} -0.113823 q^{37} +4.19274 q^{38} +2.84511 q^{39} -6.21307 q^{40} -6.88130 q^{41} -1.76766 q^{42} -4.07920 q^{43} -17.8633 q^{44} +2.67702 q^{45} +1.24025 q^{46} +5.69248 q^{47} +0.861281 q^{48} -6.37935 q^{49} -4.86091 q^{50} +5.55030 q^{51} -8.63317 q^{52} -12.0811 q^{53} +2.24374 q^{54} -15.7595 q^{55} +1.82843 q^{56} +1.86863 q^{57} +0.357264 q^{58} -1.39489 q^{59} -8.12310 q^{60} -11.1198 q^{61} +12.9686 q^{62} -0.787815 q^{63} -13.0284 q^{64} -7.61642 q^{65} -13.2089 q^{66} -8.57370 q^{67} -16.8417 q^{68} +0.552759 q^{69} +4.73205 q^{70} +3.34231 q^{71} -2.32089 q^{72} -3.77345 q^{73} +0.255389 q^{74} -2.16643 q^{75} -5.67015 q^{76} +4.63785 q^{77} -6.38370 q^{78} +15.2345 q^{79} -2.30567 q^{80} +1.00000 q^{81} +15.4399 q^{82} +5.73088 q^{83} +2.39053 q^{84} -14.8582 q^{85} +9.15269 q^{86} +0.159227 q^{87} +13.6630 q^{88} +0.944385 q^{89} -6.00654 q^{90} +2.24142 q^{91} -1.67728 q^{92} +5.77990 q^{93} -12.7725 q^{94} -5.00237 q^{95} -6.57428 q^{96} -0.199388 q^{97} +14.3136 q^{98} -5.88697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9	\( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 106 * q + 15 * q^2 - 106 * q^3 + 109 * q^4 + 16 * q^5 - 15 * q^6 + 35 * q^7 + 48 * q^8 + 106 * q^9 - 3 * q^10 + 55 * q^11 - 109 * q^12 - 8 * q^13 + 27 * q^14 - 16 * q^15 + 111 * q^16 + 28 * q^17 + 15 * q^18 + q^19 + 54 * q^20 - 35 * q^21 + 20 * q^22 + 62 * q^23 - 48 * q^24 + 102 * q^25 + 21 * q^26 - 106 * q^27 + 79 * q^28 + 36 * q^29 + 3 * q^30 + q^31 + 111 * q^32 - 55 * q^33 - 27 * q^34 + 72 * q^35 + 109 * q^36 + 31 * q^37 + 43 * q^38 + 8 * q^39 - 13 * q^40 + 35 * q^41 - 27 * q^42 + 98 * q^43 + 121 * q^44 + 16 * q^45 + 8 * q^46 + 75 * q^47 - 111 * q^48 + 49 * q^49 + 83 * q^50 - 28 * q^51 - 18 * q^52 + 60 * q^53 - 15 * q^54 + 14 * q^55 + 85 * q^56 - q^57 + 65 * q^58 + 77 * q^59 - 54 * q^60 - 55 * q^61 + 83 * q^62 + 35 * q^63 + 122 * q^64 + 86 * q^65 - 20 * q^66 + 121 * q^67 + 80 * q^68 - 62 * q^69 - 11 * q^70 + 79 * q^71 + 48 * q^72 - 29 * q^73 + 91 * q^74 - 102 * q^75 - 10 * q^76 + 87 * q^77 - 21 * q^78 + 15 * q^79 + 108 * q^80 + 106 * q^81 + 21 * q^82 + 196 * q^83 - 79 * q^84 - 5 * q^85 + 65 * q^86 - 36 * q^87 + 84 * q^88 + 34 * q^89 - 3 * q^90 + 17 * q^91 + 162 * q^92 - q^93 - 35 * q^94 + 113 * q^95 - 111 * q^96 - 63 * q^97 + 112 * q^98 + 55 * q^99

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