LMFDB - Embedded newform 8041.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20984 q^{2} +0.750857 q^{3} +2.88340 q^{4} +0.114086 q^{5} -1.65928 q^{6} +4.65666 q^{7} -1.95217 q^{8} -2.43621 q^{9} +O(q^{10})$	\(q-2.20984 q^{2} +0.750857 q^{3} +2.88340 q^{4} +0.114086 q^{5} -1.65928 q^{6} +4.65666 q^{7} -1.95217 q^{8} -2.43621 q^{9} -0.252113 q^{10} -1.00000 q^{11} +2.16502 q^{12} +2.48632 q^{13} -10.2905 q^{14} +0.0856625 q^{15} -1.45281 q^{16} +1.00000 q^{17} +5.38365 q^{18} -2.42814 q^{19} +0.328956 q^{20} +3.49649 q^{21} +2.20984 q^{22} +4.62083 q^{23} -1.46580 q^{24} -4.98698 q^{25} -5.49436 q^{26} -4.08182 q^{27} +13.4270 q^{28} -4.44553 q^{29} -0.189300 q^{30} +4.53728 q^{31} +7.11482 q^{32} -0.750857 q^{33} -2.20984 q^{34} +0.531261 q^{35} -7.02458 q^{36} -4.13773 q^{37} +5.36581 q^{38} +1.86687 q^{39} -0.222716 q^{40} -9.31993 q^{41} -7.72668 q^{42} +1.00000 q^{43} -2.88340 q^{44} -0.277938 q^{45} -10.2113 q^{46} -9.87769 q^{47} -1.09085 q^{48} +14.6845 q^{49} +11.0204 q^{50} +0.750857 q^{51} +7.16904 q^{52} -2.96581 q^{53} +9.02017 q^{54} -0.114086 q^{55} -9.09060 q^{56} -1.82319 q^{57} +9.82391 q^{58} +0.00102671 q^{59} +0.246999 q^{60} +1.83175 q^{61} -10.0267 q^{62} -11.3446 q^{63} -12.8170 q^{64} +0.283654 q^{65} +1.65928 q^{66} -10.9311 q^{67} +2.88340 q^{68} +3.46959 q^{69} -1.17400 q^{70} -8.21270 q^{71} +4.75591 q^{72} +13.0734 q^{73} +9.14373 q^{74} -3.74451 q^{75} -7.00131 q^{76} -4.65666 q^{77} -4.12548 q^{78} +5.13529 q^{79} -0.165745 q^{80} +4.24378 q^{81} +20.5956 q^{82} +7.99483 q^{83} +10.0818 q^{84} +0.114086 q^{85} -2.20984 q^{86} -3.33796 q^{87} +1.95217 q^{88} -14.1732 q^{89} +0.614200 q^{90} +11.5779 q^{91} +13.3237 q^{92} +3.40685 q^{93} +21.8281 q^{94} -0.277018 q^{95} +5.34221 q^{96} -13.1489 q^{97} -32.4503 q^{98} +2.43621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.20984	−1.56259	−0.781297	−	0.624160i	$-0.785442\pi$
$2$	−2.20984	−1.56259	−0.781297	+	0.624160i	$0.785442\pi$
$3$	0.750857	0.433508	0.216754	−	0.976226i	$-0.430453\pi$
$3$	0.750857	0.433508	0.216754	+	0.976226i	$0.430453\pi$
$4$	2.88340	1.44170
$5$	0.114086	0.0510209	0.0255105	−	0.999675i	$-0.491879\pi$
$5$	0.114086	0.0510209	0.0255105	+	0.999675i	$0.491879\pi$
$6$	−1.65928	−0.677396
$7$	4.65666	1.76005	0.880026	−	0.474926i	$-0.157525\pi$
$7$	4.65666	1.76005	0.880026	+	0.474926i	$0.157525\pi$
$8$	−1.95217	−0.690197
$9$	−2.43621	−0.812071
$10$	−0.252113	−0.0797250
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.16502	0.624988
$13$	2.48632	0.689580	0.344790	−	0.938680i	$-0.387950\pi$
$13$	2.48632	0.689580	0.344790	+	0.938680i	$0.387950\pi$
$14$	−10.2905	−2.75025
$15$	0.0856625	0.0221180
$16$	−1.45281	−0.363202
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.38365	1.26894
$19$	−2.42814	−0.557054	−0.278527	−	0.960428i	$-0.589846\pi$
$19$	−2.42814	−0.557054	−0.278527	+	0.960428i	$0.589846\pi$
$20$	0.328956	0.0735568
$21$	3.49649	0.762996
$22$	2.20984	0.471140
$23$	4.62083	0.963511	0.481755	−	0.876306i	$-0.339999\pi$
$23$	4.62083	0.963511	0.481755	+	0.876306i	$0.339999\pi$
$24$	−1.46580	−0.299206
$25$	−4.98698	−0.997397
$26$	−5.49436	−1.07753
$27$	−4.08182	−0.785547
$28$	13.4270	2.53747
$29$	−4.44553	−0.825514	−0.412757	−	0.910841i	$-0.635434\pi$
$29$	−4.44553	−0.825514	−0.412757	+	0.910841i	$0.635434\pi$
$30$	−0.189300	−0.0345614
$31$	4.53728	0.814919	0.407460	−	0.913223i	$-0.366415\pi$
$31$	4.53728	0.814919	0.407460	+	0.913223i	$0.366415\pi$
$32$	7.11482	1.25773
$33$	−0.750857	−0.130707
$34$	−2.20984	−0.378985
$35$	0.531261	0.0897994
$36$	−7.02458	−1.17076
$37$	−4.13773	−0.680239	−0.340119	−	0.940382i	$-0.610467\pi$
$37$	−4.13773	−0.680239	−0.340119	+	0.940382i	$0.610467\pi$
$38$	5.36581	0.870450
$39$	1.86687	0.298938
$40$	−0.222716	−0.0352145
$41$	−9.31993	−1.45553	−0.727764	−	0.685827i	$-0.759441\pi$
$41$	−9.31993	−1.45553	−0.727764	+	0.685827i	$0.759441\pi$
$42$	−7.72668	−1.19225
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−2.88340	−0.434689
$45$	−0.277938	−0.0414326
$46$	−10.2113	−1.50558
$47$	−9.87769	−1.44081	−0.720404	−	0.693554i	$-0.756044\pi$
$47$	−9.87769	−1.44081	−0.720404	+	0.693554i	$0.756044\pi$
$48$	−1.09085	−0.157451
$49$	14.6845	2.09778
$50$	11.0204	1.55853
$51$	0.750857	0.105141
$52$	7.16904	0.994167
$53$	−2.96581	−0.407385	−0.203692	−	0.979035i	$-0.565294\pi$
$53$	−2.96581	−0.407385	−0.203692	+	0.979035i	$0.565294\pi$
$54$	9.02017	1.22749
$55$	−0.114086	−0.0153834
$56$	−9.09060	−1.21478
$57$	−1.82319	−0.241487
$58$	9.82391	1.28994
$59$	0.00102671	0.000133666 0	6.68329e−5	−	1.00000i	$-0.499979\pi$
$59$	0.00102671	0.000133666 0	6.68329e−5		1.00000i	$0.499979\pi$
$60$	0.246999	0.0318874
$61$	1.83175	0.234531	0.117266	−	0.993101i	$-0.462587\pi$
$61$	1.83175	0.234531	0.117266	+	0.993101i	$0.462587\pi$
$62$	−10.0267	−1.27339
$63$	−11.3446	−1.42929
$64$	−12.8170	−1.60213
$65$	0.283654	0.0351830
$66$	1.65928	0.204243
$67$	−10.9311	−1.33545	−0.667725	−	0.744408i	$-0.732732\pi$
$67$	−10.9311	−1.33545	−0.667725	+	0.744408i	$0.732732\pi$
$68$	2.88340	0.349664
$69$	3.46959	0.417689
$70$	−1.17400	−0.140320
$71$	−8.21270	−0.974668	−0.487334	−	0.873216i	$-0.662031\pi$
$71$	−8.21270	−0.974668	−0.487334	+	0.873216i	$0.662031\pi$
$72$	4.75591	0.560489
$73$	13.0734	1.53012	0.765062	−	0.643957i	$-0.222708\pi$
$73$	13.0734	1.53012	0.765062	+	0.643957i	$0.222708\pi$
$74$	9.14373	1.06294
$75$	−3.74451	−0.432379
$76$	−7.00131	−0.803105
$77$	−4.65666	−0.530675
$78$	−4.12548	−0.467119
$79$	5.13529	0.577765	0.288882	−	0.957365i	$-0.406716\pi$
$79$	5.13529	0.577765	0.288882	+	0.957365i	$0.406716\pi$
$80$	−0.165745	−0.0185309
$81$	4.24378	0.471531
$82$	20.5956	2.27440
$83$	7.99483	0.877547	0.438773	−	0.898598i	$-0.355413\pi$
$83$	7.99483	0.877547	0.438773	+	0.898598i	$0.355413\pi$
$84$	10.0818	1.10001
$85$	0.114086	0.0123744
$86$	−2.20984	−0.238293
$87$	−3.33796	−0.357867
$88$	1.95217	0.208102
$89$	−14.1732	−1.50235	−0.751176	−	0.660102i	$-0.770513\pi$
$89$	−14.1732	−1.50235	−0.751176	+	0.660102i	$0.770513\pi$
$90$	0.614200	0.0647424
$91$	11.5779	1.21370
$92$	13.3237	1.38909
$93$	3.40685	0.353274
$94$	21.8281	2.25140
$95$	−0.277018	−0.0284214
$96$	5.34221	0.545237
$97$	−13.1489	−1.33507	−0.667533	−	0.744580i	$-0.732650\pi$
$97$	−13.1489	−1.33507	−0.667533	+	0.744580i	$0.732650\pi$
$98$	−32.4503	−3.27798
$99$	2.43621	0.244849
$100$	−14.3795	−1.43795
$101$	−4.68091	−0.465768	−0.232884	−	0.972505i	$-0.574816\pi$
$101$	−4.68091	−0.465768	−0.232884	+	0.972505i	$0.574816\pi$
$102$	−1.65928	−0.164293
$103$	−6.23555	−0.614407	−0.307204	−	0.951644i	$-0.599393\pi$
$103$	−6.23555	−0.614407	−0.307204	+	0.951644i	$0.599393\pi$
$104$	−4.85372	−0.475946
$105$	0.398901	0.0389287
$106$	6.55396	0.636577
$107$	4.26628	0.412437	0.206219	−	0.978506i	$-0.433884\pi$
$107$	4.26628	0.412437	0.206219	+	0.978506i	$0.433884\pi$
$108$	−11.7695	−1.13252
$109$	−11.3114	−1.08344	−0.541718	−	0.840560i	$-0.682226\pi$
$109$	−11.3114	−1.08344	−0.541718	+	0.840560i	$0.682226\pi$
$110$	0.252113	0.0240380
$111$	−3.10684	−0.294889
$112$	−6.76523	−0.639254
$113$	7.64233	0.718930	0.359465	−	0.933159i	$-0.382959\pi$
$113$	7.64233	0.718930	0.359465	+	0.933159i	$0.382959\pi$
$114$	4.02896	0.377347
$115$	0.527174	0.0491592
$116$	−12.8182	−1.19014
$117$	−6.05720	−0.559988
$118$	−0.00226886	−0.000208865 0
$119$	4.65666	0.426875
$120$	−0.167228	−0.0152657
$121$	1.00000	0.0909091
$122$	−4.04787	−0.366477
$123$	−6.99794	−0.630983
$124$	13.0828	1.17487
$125$	−1.13938	−0.101909
$126$	25.0698	2.23340
$127$	0.939159	0.0833369	0.0416685	−	0.999131i	$-0.486733\pi$
$127$	0.939159	0.0833369	0.0416685	+	0.999131i	$0.486733\pi$
$128$	14.0939	1.24574
$129$	0.750857	0.0661093
$130$	−0.626831	−0.0549767
$131$	−14.3213	−1.25126	−0.625629	−	0.780121i	$-0.715158\pi$
$131$	−14.3213	−1.25126	−0.625629	+	0.780121i	$0.715158\pi$
$132$	−2.16502	−0.188441
$133$	−11.3070	−0.980444
$134$	24.1561	2.08677
$135$	−0.465680	−0.0400793
$136$	−1.95217	−0.167397
$137$	−20.7605	−1.77369	−0.886843	−	0.462072i	$-0.847106\pi$
$137$	−20.7605	−1.77369	−0.886843	+	0.462072i	$0.847106\pi$
$138$	−7.66724	−0.652678
$139$	1.08117	0.0917036	0.0458518	−	0.998948i	$-0.485400\pi$
$139$	1.08117	0.0917036	0.0458518	+	0.998948i	$0.485400\pi$
$140$	1.53184	0.129464
$141$	−7.41673	−0.624602
$142$	18.1488	1.52301
$143$	−2.48632	−0.207916
$144$	3.53935	0.294946
$145$	−0.507174	−0.0421185
$146$	−28.8901	−2.39096
$147$	11.0259	0.909404
$148$	−11.9307	−0.980700
$149$	−1.31801	−0.107976	−0.0539878	−	0.998542i	$-0.517193\pi$
$149$	−1.31801	−0.107976	−0.0539878	+	0.998542i	$0.517193\pi$
$150$	8.27478	0.675633
$151$	7.93258	0.645544	0.322772	−	0.946477i	$-0.395385\pi$
$151$	7.93258	0.645544	0.322772	+	0.946477i	$0.395385\pi$
$152$	4.74015	0.384477
$153$	−2.43621	−0.196956
$154$	10.2905	0.829230
$155$	0.517641	0.0415779
$156$	5.38293	0.430979
$157$	−14.1768	−1.13143	−0.565717	−	0.824599i	$-0.691401\pi$
$157$	−14.1768	−1.13143	−0.565717	+	0.824599i	$0.691401\pi$
$158$	−11.3482	−0.902812
$159$	−2.22690	−0.176604
$160$	0.811703	0.0641708
$161$	21.5176	1.69583
$162$	−9.37807	−0.736811
$163$	−10.3860	−0.813493	−0.406747	−	0.913541i	$-0.633337\pi$
$163$	−10.3860	−0.813493	−0.406747	+	0.913541i	$0.633337\pi$
$164$	−26.8731	−2.09844
$165$	−0.0856625	−0.00666881
$166$	−17.6673	−1.37125
$167$	−11.3738	−0.880127	−0.440064	−	0.897967i	$-0.645044\pi$
$167$	−11.3738	−0.880127	−0.440064	+	0.897967i	$0.645044\pi$
$168$	−6.82574	−0.526617
$169$	−6.81823	−0.524480
$170$	−0.252113	−0.0193361
$171$	5.91548	0.452368
$172$	2.88340	0.219857
$173$	−1.16678	−0.0887089	−0.0443544	−	0.999016i	$-0.514123\pi$
$173$	−1.16678	−0.0887089	−0.0443544	+	0.999016i	$0.514123\pi$
$174$	7.37636	0.559200
$175$	−23.2227	−1.75547
$176$	1.45281	0.109509
$177$	0.000770910 0	5.79451e−5 0
$178$	31.3204	2.34757
$179$	16.3612	1.22289	0.611446	−	0.791286i	$-0.290588\pi$
$179$	16.3612	1.22289	0.611446	+	0.791286i	$0.290588\pi$
$180$	−0.801407	−0.0597334
$181$	7.39009	0.549301	0.274651	−	0.961544i	$-0.411438\pi$
$181$	7.39009	0.549301	0.274651	+	0.961544i	$0.411438\pi$
$182$	−25.5854	−1.89651
$183$	1.37538	0.101671
$184$	−9.02066	−0.665012
$185$	−0.472058	−0.0347064
$186$	−7.52859	−0.552023
$187$	−1.00000	−0.0731272
$188$	−28.4813	−2.07721
$189$	−19.0076	−1.38260
$190$	0.612165	0.0444111
$191$	−6.93051	−0.501474	−0.250737	−	0.968055i	$-0.580673\pi$
$191$	−6.93051	−0.501474	−0.250737	+	0.968055i	$0.580673\pi$
$192$	−9.62374	−0.694534
$193$	3.01599	0.217096	0.108548	−	0.994091i	$-0.465380\pi$
$193$	3.01599	0.217096	0.108548	+	0.994091i	$0.465380\pi$
$194$	29.0569	2.08617
$195$	0.212984	0.0152521
$196$	42.3412	3.02437
$197$	−19.3333	−1.37744	−0.688719	−	0.725028i	$-0.741827\pi$
$197$	−19.3333	−1.37744	−0.688719	+	0.725028i	$0.741827\pi$
$198$	−5.38365	−0.382599
$199$	18.8796	1.33834	0.669170	−	0.743110i	$-0.266650\pi$
$199$	18.8796	1.33834	0.669170	+	0.743110i	$0.266650\pi$
$200$	9.73545	0.688400
$201$	−8.20772	−0.578928
$202$	10.3441	0.727806
$203$	−20.7013	−1.45295
$204$	2.16502	0.151582
$205$	−1.06328	−0.0742624
$206$	13.7796	0.960069
$207$	−11.2573	−0.782439
$208$	−3.61214	−0.250457
$209$	2.42814	0.167958
$210$	−0.881508	−0.0608298
$211$	−0.343098	−0.0236199	−0.0118099	−	0.999930i	$-0.503759\pi$
$211$	−0.343098	−0.0236199	−0.0118099	+	0.999930i	$0.503759\pi$
$212$	−8.55161	−0.587327
$213$	−6.16656	−0.422526
$214$	−9.42781	−0.644472
$215$	0.114086	0.00778062
$216$	7.96841	0.542182
$217$	21.1286	1.43430
$218$	24.9964	1.69297
$219$	9.81625	0.663320
$220$	−0.328956	−0.0221782
$221$	2.48632	0.167248
$222$	6.86563	0.460791
$223$	−1.80310	−0.120744	−0.0603721	−	0.998176i	$-0.519229\pi$
$223$	−1.80310	−0.120744	−0.0603721	+	0.998176i	$0.519229\pi$
$224$	33.1313	2.21368
$225$	12.1494	0.809957
$226$	−16.8883	−1.12340
$227$	−3.64167	−0.241706	−0.120853	−	0.992670i	$-0.538563\pi$
$227$	−3.64167	−0.241706	−0.120853	+	0.992670i	$0.538563\pi$
$228$	−5.25698	−0.348152
$229$	24.0210	1.58735	0.793676	−	0.608340i	$-0.208164\pi$
$229$	24.0210	1.58735	0.793676	+	0.608340i	$0.208164\pi$
$230$	−1.16497	−0.0768159
$231$	−3.49649	−0.230052
$232$	8.67844	0.569767
$233$	−5.24993	−0.343934	−0.171967	−	0.985103i	$-0.555012\pi$
$233$	−5.24993	−0.343934	−0.171967	+	0.985103i	$0.555012\pi$
$234$	13.3854	0.875034
$235$	−1.12691	−0.0735114
$236$	0.00296041	0.000192706 0
$237$	3.85587	0.250466
$238$	−10.2905	−0.667033
$239$	6.73217	0.435468	0.217734	−	0.976008i	$-0.430134\pi$
$239$	6.73217	0.435468	0.217734	+	0.976008i	$0.430134\pi$
$240$	−0.124451	−0.00803328
$241$	−27.5795	−1.77655	−0.888277	−	0.459308i	$-0.848098\pi$
$241$	−27.5795	−1.77655	−0.888277	+	0.459308i	$0.848098\pi$
$242$	−2.20984	−0.142054
$243$	15.4319	0.989959
$244$	5.28166	0.338123
$245$	1.67530	0.107031
$246$	15.4643	0.985970
$247$	−6.03713	−0.384133
$248$	−8.85755	−0.562455
$249$	6.00298	0.380423
$250$	2.51784	0.159242
$251$	2.95090	0.186259	0.0931297	−	0.995654i	$-0.470313\pi$
$251$	2.95090	0.186259	0.0931297	+	0.995654i	$0.470313\pi$
$252$	−32.7111	−2.06060
$253$	−4.62083	−0.290509
$254$	−2.07539	−0.130222
$255$	0.0856625	0.00536439
$256$	−5.51130	−0.344456
$257$	−6.51885	−0.406635	−0.203317	−	0.979113i	$-0.565172\pi$
$257$	−6.51885	−0.406635	−0.203317	+	0.979113i	$0.565172\pi$
$258$	−1.65928	−0.103302
$259$	−19.2680	−1.19725
$260$	0.817889	0.0507233
$261$	10.8303	0.670376
$262$	31.6478	1.95521
$263$	−21.6219	−1.33326	−0.666631	−	0.745388i	$-0.732264\pi$
$263$	−21.6219	−1.33326	−0.666631	+	0.745388i	$0.732264\pi$
$264$	1.46580	0.0902139
$265$	−0.338358	−0.0207852
$266$	24.9868	1.53204
$267$	−10.6420	−0.651281
$268$	−31.5188	−1.92532
$269$	8.20177	0.500071	0.250035	−	0.968237i	$-0.419558\pi$
$269$	8.20177	0.500071	0.250035	+	0.968237i	$0.419558\pi$
$270$	1.02908	0.0626277
$271$	10.2794	0.624427	0.312213	−	0.950012i	$-0.398930\pi$
$271$	10.2794	0.624427	0.312213	+	0.950012i	$0.398930\pi$
$272$	−1.45281	−0.0880894
$273$	8.69337	0.526146
$274$	45.8773	2.77155
$275$	4.98698	0.300726
$276$	10.0042	0.602182
$277$	4.08105	0.245206	0.122603	−	0.992456i	$-0.460876\pi$
$277$	4.08105	0.245206	0.122603	+	0.992456i	$0.460876\pi$
$278$	−2.38921	−0.143295
$279$	−11.0538	−0.661772
$280$	−1.03711	−0.0619793
$281$	−17.5969	−1.04974	−0.524871	−	0.851182i	$-0.675886\pi$
$281$	−17.5969	−1.04974	−0.524871	+	0.851182i	$0.675886\pi$
$282$	16.3898	0.975999
$283$	−18.5864	−1.10484	−0.552422	−	0.833564i	$-0.686296\pi$
$283$	−18.5864	−1.10484	−0.552422	+	0.833564i	$0.686296\pi$
$284$	−23.6805	−1.40518
$285$	−0.208001	−0.0123209
$286$	5.49436	0.324889
$287$	−43.3997	−2.56181
$288$	−17.3332	−1.02137
$289$	1.00000	0.0588235
$290$	1.12077	0.0658141
$291$	−9.87293	−0.578762
$292$	37.6958	2.20598
$293$	−12.0587	−0.704478	−0.352239	−	0.935910i	$-0.614580\pi$
$293$	−12.0587	−0.704478	−0.352239	+	0.935910i	$0.614580\pi$
$294$	−24.3656	−1.42103
$295$	0.000117133 0	6.81975e−6 0
$296$	8.07756	0.469499
$297$	4.08182	0.236851
$298$	2.91259	0.168722
$299$	11.4889	0.664418
$300$	−10.7969	−0.623361
$301$	4.65666	0.268405
$302$	−17.5297	−1.00872
$303$	−3.51470	−0.201914
$304$	3.52763	0.202323
$305$	0.208977	0.0119660
$306$	5.38365	0.307763
$307$	16.0132	0.913923	0.456962	−	0.889486i	$-0.348938\pi$
$307$	16.0132	0.913923	0.456962	+	0.889486i	$0.348938\pi$
$308$	−13.4270	−0.765075
$309$	−4.68201	−0.266350
$310$	−1.14390	−0.0649694
$311$	5.70637	0.323579	0.161789	−	0.986825i	$-0.448274\pi$
$311$	5.70637	0.323579	0.161789	+	0.986825i	$0.448274\pi$
$312$	−3.64445	−0.206326
$313$	33.2537	1.87961	0.939806	−	0.341707i	$-0.111005\pi$
$313$	33.2537	1.87961	0.939806	+	0.341707i	$0.111005\pi$
$314$	31.3286	1.76797
$315$	−1.29426	−0.0729235
$316$	14.8071	0.832964
$317$	25.1113	1.41039	0.705197	−	0.709012i	$-0.250859\pi$
$317$	25.1113	1.41039	0.705197	+	0.709012i	$0.250859\pi$
$318$	4.92109	0.275961
$319$	4.44553	0.248902
$320$	−1.46224	−0.0817419
$321$	3.20337	0.178795
$322$	−47.5506	−2.64989
$323$	−2.42814	−0.135106
$324$	12.2365	0.679806
$325$	−12.3992	−0.687785
$326$	22.9514	1.27116
$327$	−8.49325	−0.469678
$328$	18.1941	1.00460
$329$	−45.9970	−2.53590
$330$	0.189300	0.0104206
$331$	28.9347	1.59039	0.795196	−	0.606352i	$-0.207368\pi$
$331$	28.9347	1.59039	0.795196	+	0.606352i	$0.207368\pi$
$332$	23.0523	1.26516
$333$	10.0804	0.552402
$334$	25.1342	1.37528
$335$	−1.24709	−0.0681359
$336$	−5.07972	−0.277121
$337$	−13.1526	−0.716470	−0.358235	−	0.933631i	$-0.616621\pi$
$337$	−13.1526	−0.716470	−0.358235	+	0.933631i	$0.616621\pi$
$338$	15.0672	0.819549
$339$	5.73830	0.311661
$340$	0.328956	0.0178402
$341$	−4.53728	−0.245707
$342$	−13.0723	−0.706867
$343$	35.7839	1.93215
$344$	−1.95217	−0.105254
$345$	0.395832	0.0213109
$346$	2.57841	0.138616
$347$	22.7644	1.22206	0.611029	−	0.791609i	$-0.290756\pi$
$347$	22.7644	1.22206	0.611029	+	0.791609i	$0.290756\pi$
$348$	−9.62466	−0.515936
$349$	11.6423	0.623200	0.311600	−	0.950213i	$-0.399135\pi$
$349$	11.6423	0.623200	0.311600	+	0.950213i	$0.399135\pi$
$350$	51.3184	2.74309
$351$	−10.1487	−0.541697
$352$	−7.11482	−0.379221
$353$	−11.5931	−0.617039	−0.308519	−	0.951218i	$-0.599833\pi$
$353$	−11.5931	−0.617039	−0.308519	+	0.951218i	$0.599833\pi$
$354$	−0.00170359	−9.05447e−5 0
$355$	−0.936956	−0.0497285
$356$	−40.8669	−2.16594
$357$	3.49649	0.185054
$358$	−36.1556	−1.91088
$359$	36.7102	1.93749	0.968746	−	0.248053i	$-0.0797908\pi$
$359$	36.7102	1.93749	0.968746	+	0.248053i	$0.0797908\pi$
$360$	0.542584	0.0285967
$361$	−13.1041	−0.689690
$362$	−16.3309	−0.858335
$363$	0.750857	0.0394098
$364$	33.3838	1.74979
$365$	1.49149	0.0780683
$366$	−3.03937	−0.158870
$367$	30.9856	1.61744	0.808718	−	0.588197i	$-0.200162\pi$
$367$	30.9856	1.61744	0.808718	+	0.588197i	$0.200162\pi$
$368$	−6.71318	−0.349949
$369$	22.7053	1.18199
$370$	1.04317	0.0542320
$371$	−13.8108	−0.717019
$372$	9.82330	0.509314
$373$	15.7210	0.814003	0.407001	−	0.913427i	$-0.366574\pi$
$373$	15.7210	0.814003	0.407001	+	0.913427i	$0.366574\pi$
$374$	2.20984	0.114268
$375$	−0.855510	−0.0441783
$376$	19.2829	0.994442
$377$	−11.0530	−0.569258
$378$	42.0039	2.16045
$379$	12.0706	0.620024	0.310012	−	0.950733i	$-0.399667\pi$
$379$	12.0706	0.620024	0.310012	+	0.950733i	$0.399667\pi$
$380$	−0.798753	−0.0409752
$381$	0.705175	0.0361272
$382$	15.3153	0.783600
$383$	−25.2323	−1.28931	−0.644656	−	0.764473i	$-0.722999\pi$
$383$	−25.2323	−1.28931	−0.644656	+	0.764473i	$0.722999\pi$
$384$	10.5825	0.540037
$385$	−0.531261	−0.0270756
$386$	−6.66486	−0.339233
$387$	−2.43621	−0.123840
$388$	−37.9135	−1.92477
$389$	−14.6318	−0.741863	−0.370932	−	0.928660i	$-0.620962\pi$
$389$	−14.6318	−0.741863	−0.370932	+	0.928660i	$0.620962\pi$
$390$	−0.470661	−0.0238328
$391$	4.62083	0.233686
$392$	−28.6666	−1.44788
$393$	−10.7533	−0.542430
$394$	42.7235	2.15238
$395$	0.585866	0.0294781
$396$	7.02458	0.352998
$397$	−2.12611	−0.106707	−0.0533533	−	0.998576i	$-0.516991\pi$
$397$	−2.12611	−0.106707	−0.0533533	+	0.998576i	$0.516991\pi$
$398$	−41.7209	−2.09128
$399$	−8.48997	−0.425030
$400$	7.24513	0.362256
$401$	26.1334	1.30504	0.652519	−	0.757772i	$-0.273712\pi$
$401$	26.1334	1.30504	0.652519	+	0.757772i	$0.273712\pi$
$402$	18.1378	0.904629
$403$	11.2811	0.561952
$404$	−13.4969	−0.671498
$405$	0.484157	0.0240579
$406$	45.7466	2.27037
$407$	4.13773	0.205100
$408$	−1.46580	−0.0725680
$409$	−3.86768	−0.191244	−0.0956222	−	0.995418i	$-0.530484\pi$
$409$	−3.86768	−0.191244	−0.0956222	+	0.995418i	$0.530484\pi$
$410$	2.34967	0.116042
$411$	−15.5881	−0.768906
$412$	−17.9796	−0.885791
$413$	0.00478102	0.000235259 0
$414$	24.8769	1.22263
$415$	0.912100	0.0447732
$416$	17.6897	0.867308
$417$	0.811804	0.0397542
$418$	−5.36581	−0.262450
$419$	5.44966	0.266233	0.133117	−	0.991100i	$-0.457501\pi$
$419$	5.44966	0.266233	0.133117	+	0.991100i	$0.457501\pi$
$420$	1.15019	0.0561235
$421$	−29.5126	−1.43835	−0.719177	−	0.694827i	$-0.755481\pi$
$421$	−29.5126	−1.43835	−0.719177	+	0.694827i	$0.755481\pi$
$422$	0.758193	0.0369082
$423$	24.0642	1.17004
$424$	5.78977	0.281176
$425$	−4.98698	−0.241904
$426$	13.6271	0.660237
$427$	8.52982	0.412787
$428$	12.3014	0.594611
$429$	−1.86687	−0.0901332
$430$	−0.252113	−0.0121579
$431$	−9.21918	−0.444072	−0.222036	−	0.975038i	$-0.571270\pi$
$431$	−9.21918	−0.444072	−0.222036	+	0.975038i	$0.571270\pi$
$432$	5.93010	0.285312
$433$	−12.2353	−0.587992	−0.293996	−	0.955807i	$-0.594985\pi$
$433$	−12.2353	−0.587992	−0.293996	+	0.955807i	$0.594985\pi$
$434$	−46.6907	−2.24123
$435$	−0.380815	−0.0182587
$436$	−32.6153	−1.56199
$437$	−11.2200	−0.536728
$438$	−21.6923	−1.03650
$439$	4.24483	0.202595	0.101297	−	0.994856i	$-0.467701\pi$
$439$	4.24483	0.202595	0.101297	+	0.994856i	$0.467701\pi$
$440$	0.222716	0.0106176
$441$	−35.7745	−1.70355
$442$	−5.49436	−0.261340
$443$	−19.6944	−0.935711	−0.467855	−	0.883805i	$-0.654973\pi$
$443$	−19.6944	−0.935711	−0.467855	+	0.883805i	$0.654973\pi$
$444$	−8.95827	−0.425141
$445$	−1.61696	−0.0766514
$446$	3.98456	0.188674
$447$	−0.989637	−0.0468082
$448$	−59.6844	−2.81982
$449$	−21.8415	−1.03076	−0.515382	−	0.856961i	$-0.672350\pi$
$449$	−21.8415	−1.03076	−0.515382	+	0.856961i	$0.672350\pi$
$450$	−26.8482	−1.26563
$451$	9.31993	0.438858
$452$	22.0359	1.03648
$453$	5.95624	0.279848
$454$	8.04752	0.377689
$455$	1.32088	0.0619239
$456$	3.55918	0.166674
$457$	−4.81329	−0.225156	−0.112578	−	0.993643i	$-0.535911\pi$
$457$	−4.81329	−0.225156	−0.112578	+	0.993643i	$0.535911\pi$
$458$	−53.0826	−2.48039
$459$	−4.08182	−0.190523
$460$	1.52005	0.0708728
$461$	−5.33600	−0.248522	−0.124261	−	0.992250i	$-0.539656\pi$
$461$	−5.33600	−0.248522	−0.124261	+	0.992250i	$0.539656\pi$
$462$	7.72668	0.359478
$463$	19.4484	0.903842	0.451921	−	0.892058i	$-0.350739\pi$
$463$	19.4484	0.903842	0.451921	+	0.892058i	$0.350739\pi$
$464$	6.45850	0.299828
$465$	0.388674	0.0180243
$466$	11.6015	0.537430
$467$	30.1271	1.39411	0.697057	−	0.717015i	$-0.254492\pi$
$467$	30.1271	1.39411	0.697057	+	0.717015i	$0.254492\pi$
$468$	−17.4653	−0.807334
$469$	−50.9025	−2.35046
$470$	2.49029	0.114868
$471$	−10.6448	−0.490486
$472$	−0.00200431	−9.22558e−5 0
$473$	−1.00000	−0.0459800
$474$	−8.52086	−0.391376
$475$	12.1091	0.555604
$476$	13.4270	0.615426
$477$	7.22534	0.330826
$478$	−14.8770	−0.680459
$479$	6.47622	0.295906	0.147953	−	0.988994i	$-0.452732\pi$
$479$	6.47622	0.295906	0.147953	+	0.988994i	$0.452732\pi$
$480$	0.609473	0.0278185
$481$	−10.2877	−0.469079
$482$	60.9464	2.77603
$483$	16.1567	0.735154
$484$	2.88340	0.131064
$485$	−1.50011	−0.0681163
$486$	−34.1021	−1.54690
$487$	−11.3463	−0.514152	−0.257076	−	0.966391i	$-0.582759\pi$
$487$	−11.3463	−0.514152	−0.257076	+	0.966391i	$0.582759\pi$
$488$	−3.57588	−0.161873
$489$	−7.79839	−0.352656
$490$	−3.70214	−0.167246
$491$	−24.9536	−1.12614	−0.563069	−	0.826410i	$-0.690380\pi$
$491$	−24.9536	−1.12614	−0.563069	+	0.826410i	$0.690380\pi$
$492$	−20.1778	−0.909688
$493$	−4.44553	−0.200217
$494$	13.3411	0.600245
$495$	0.277938	0.0124924
$496$	−6.59179	−0.295980
$497$	−38.2437	−1.71547
$498$	−13.2656	−0.594447
$499$	−29.8327	−1.33549	−0.667747	−	0.744388i	$-0.732741\pi$
$499$	−29.8327	−1.33549	−0.667747	+	0.744388i	$0.732741\pi$
$500$	−3.28528	−0.146922
$501$	−8.54006	−0.381542
$502$	−6.52103	−0.291048
$503$	−0.682030	−0.0304102	−0.0152051	−	0.999884i	$-0.504840\pi$
$503$	−0.682030	−0.0304102	−0.0152051	+	0.999884i	$0.504840\pi$
$504$	22.1466	0.986490
$505$	−0.534027	−0.0237639
$506$	10.2113	0.453948
$507$	−5.11952	−0.227366
$508$	2.70797	0.120147
$509$	19.8110	0.878105	0.439053	−	0.898461i	$-0.355314\pi$
$509$	19.8110	0.878105	0.439053	+	0.898461i	$0.355314\pi$
$510$	−0.189300	−0.00838237
$511$	60.8783	2.69310
$512$	−16.0087	−0.707492
$513$	9.91124	0.437592
$514$	14.4056	0.635405
$515$	−0.711391	−0.0313476
$516$	2.16502	0.0953097
$517$	9.87769	0.434420
$518$	42.5792	1.87082
$519$	−0.876087	−0.0384560
$520$	−0.553742	−0.0242832
$521$	−29.4872	−1.29186	−0.645928	−	0.763398i	$-0.723530\pi$
$521$	−29.4872	−1.29186	−0.645928	+	0.763398i	$0.723530\pi$
$522$	−23.9331	−1.04753
$523$	13.7465	0.601094	0.300547	−	0.953767i	$-0.402831\pi$
$523$	13.7465	0.601094	0.300547	+	0.953767i	$0.402831\pi$
$524$	−41.2940	−1.80394
$525$	−17.4369	−0.761009
$526$	47.7809	2.08335
$527$	4.53728	0.197647
$528$	1.09085	0.0474732
$529$	−1.64789	−0.0716474
$530$	0.747717	0.0324788
$531$	−0.00250128	−0.000108546 0
$532$	−32.6027	−1.41351
$533$	−23.1723	−1.00370
$534$	23.5172	1.01769
$535$	0.486724	0.0210429
$536$	21.3395	0.921724
$537$	12.2849	0.530133
$538$	−18.1246	−0.781407
$539$	−14.6845	−0.632505
$540$	−1.34274	−0.0577823
$541$	5.59366	0.240490	0.120245	−	0.992744i	$-0.461632\pi$
$541$	5.59366	0.240490	0.120245	+	0.992744i	$0.461632\pi$
$542$	−22.7158	−0.975725
$543$	5.54890	0.238126
$544$	7.11482	0.305045
$545$	−1.29048	−0.0552779
$546$	−19.2110	−0.822153
$547$	−38.5557	−1.64852	−0.824262	−	0.566208i	$-0.808410\pi$
$547$	−38.5557	−1.64852	−0.824262	+	0.566208i	$0.808410\pi$
$548$	−59.8607	−2.55712
$549$	−4.46252	−0.190456
$550$	−11.0204	−0.469913
$551$	10.7944	0.459856
$552$	−6.77323	−0.288288
$553$	23.9133	1.01690
$554$	−9.01847	−0.383158
$555$	−0.354448	−0.0150455
$556$	3.11744	0.132209
$557$	42.3986	1.79649	0.898244	−	0.439497i	$-0.144843\pi$
$557$	42.3986	1.79649	0.898244	+	0.439497i	$0.144843\pi$
$558$	24.4271	1.03408
$559$	2.48632	0.105160
$560$	−0.771819	−0.0326153
$561$	−0.750857	−0.0317012
$562$	38.8863	1.64032
$563$	−38.2526	−1.61215	−0.806077	−	0.591811i	$-0.798413\pi$
$563$	−38.2526	−1.61215	−0.806077	+	0.591811i	$0.798413\pi$
$564$	−21.3854	−0.900488
$565$	0.871884	0.0366805
$566$	41.0729	1.72642
$567$	19.7618	0.829918
$568$	16.0326	0.672713
$569$	−27.0419	−1.13365	−0.566827	−	0.823837i	$-0.691829\pi$
$569$	−27.0419	−1.13365	−0.566827	+	0.823837i	$0.691829\pi$
$570$	0.459649	0.0192526
$571$	34.7063	1.45241	0.726206	−	0.687477i	$-0.241282\pi$
$571$	34.7063	1.45241	0.726206	+	0.687477i	$0.241282\pi$
$572$	−7.16904	−0.299753
$573$	−5.20382	−0.217393
$574$	95.9065	4.00306
$575$	−23.0440	−0.961002
$576$	31.2250	1.30104
$577$	20.8059	0.866160	0.433080	−	0.901356i	$-0.357427\pi$
$577$	20.8059	0.866160	0.433080	+	0.901356i	$0.357427\pi$
$578$	−2.20984	−0.0919173
$579$	2.26458	0.0941127
$580$	−1.46238	−0.0607222
$581$	37.2292	1.54453
$582$	21.8176	0.904369
$583$	2.96581	0.122831
$584$	−25.5215	−1.05609
$585$	−0.691043	−0.0285711
$586$	26.6478	1.10081
$587$	29.0898	1.20066	0.600332	−	0.799751i	$-0.295035\pi$
$587$	29.0898	1.20066	0.600332	+	0.799751i	$0.295035\pi$
$588$	31.7922	1.31109
$589$	−11.0172	−0.453954
$590$	−0.000258846 0	−1.06565e−5 0
$591$	−14.5165	−0.597130
$592$	6.01133	0.247064
$593$	−10.7188	−0.440168	−0.220084	−	0.975481i	$-0.570633\pi$
$593$	−10.7188	−0.440168	−0.220084	+	0.975481i	$0.570633\pi$
$594$	−9.02017	−0.370102
$595$	0.531261	0.0217796
$596$	−3.80035	−0.155668
$597$	14.1759	0.580180
$598$	−25.3885	−1.03821
$599$	45.2831	1.85022	0.925108	−	0.379704i	$-0.123974\pi$
$599$	45.2831	1.85022	0.925108	+	0.379704i	$0.123974\pi$
$600$	7.30993	0.298427
$601$	9.15360	0.373383	0.186692	−	0.982419i	$-0.440223\pi$
$601$	9.15360	0.373383	0.186692	+	0.982419i	$0.440223\pi$
$602$	−10.2905	−0.419409
$603$	26.6306	1.08448
$604$	22.8728	0.930681
$605$	0.114086	0.00463827
$606$	7.76692	0.315510
$607$	36.3496	1.47538	0.737692	−	0.675138i	$-0.235916\pi$
$607$	36.3496	1.47538	0.737692	+	0.675138i	$0.235916\pi$
$608$	−17.2758	−0.700626
$609$	−15.5437	−0.629863
$610$	−0.461806	−0.0186980
$611$	−24.5590	−0.993553
$612$	−7.02458	−0.283952
$613$	−0.803782	−0.0324645	−0.0162322	−	0.999868i	$-0.505167\pi$
$613$	−0.803782	−0.0324645	−0.0162322	+	0.999868i	$0.505167\pi$
$614$	−35.3867	−1.42809
$615$	−0.798369	−0.0321933
$616$	9.09060	0.366271
$617$	−6.69185	−0.269404	−0.134702	−	0.990886i	$-0.543008\pi$
$617$	−6.69185	−0.269404	−0.134702	+	0.990886i	$0.543008\pi$
$618$	10.3465	0.416197
$619$	16.1139	0.647674	0.323837	−	0.946113i	$-0.395027\pi$
$619$	16.1139	0.647674	0.323837	+	0.946113i	$0.395027\pi$
$620$	1.49257	0.0599429
$621$	−18.8614	−0.756882
$622$	−12.6102	−0.505622
$623$	−65.9995	−2.64422
$624$	−2.71220	−0.108575
$625$	24.8049	0.992197
$626$	−73.4855	−2.93707
$627$	1.82319	0.0728112
$628$	−40.8775	−1.63119
$629$	−4.13773	−0.164982
$630$	2.86012	0.113950
$631$	20.8082	0.828361	0.414180	−	0.910195i	$-0.364068\pi$
$631$	20.8082	0.828361	0.414180	+	0.910195i	$0.364068\pi$
$632$	−10.0250	−0.398772
$633$	−0.257618	−0.0102394
$634$	−55.4921	−2.20387
$635$	0.107145	0.00425193
$636$	−6.42104	−0.254611
$637$	36.5102	1.44659
$638$	−9.82391	−0.388932
$639$	20.0079	0.791500
$640$	1.60792	0.0635587
$641$	−12.9771	−0.512566	−0.256283	−	0.966602i	$-0.582498\pi$
$641$	−12.9771	−0.512566	−0.256283	+	0.966602i	$0.582498\pi$
$642$	−7.07894	−0.279383
$643$	−7.75787	−0.305941	−0.152970	−	0.988231i	$-0.548884\pi$
$643$	−7.75787	−0.305941	−0.152970	+	0.988231i	$0.548884\pi$
$644$	62.0440	2.44487
$645$	0.0856625	0.00337296
$646$	5.36581	0.211115
$647$	−40.8309	−1.60523	−0.802615	−	0.596497i	$-0.796559\pi$
$647$	−40.8309	−1.60523	−0.802615	+	0.596497i	$0.796559\pi$
$648$	−8.28458	−0.325449
$649$	−0.00102671	−4.03018e−5 0
$650$	27.4003	1.07473
$651$	15.8645	0.621780
$652$	−29.9469	−1.17281
$653$	24.3575	0.953183	0.476591	−	0.879125i	$-0.341872\pi$
$653$	24.3575	0.953183	0.476591	+	0.879125i	$0.341872\pi$
$654$	18.7687	0.733916
$655$	−1.63386	−0.0638403
$656$	13.5401	0.528651
$657$	−31.8496	−1.24257
$658$	101.646	3.96258
$659$	−40.2598	−1.56830	−0.784150	−	0.620572i	$-0.786901\pi$
$659$	−40.2598	−1.56830	−0.784150	+	0.620572i	$0.786901\pi$
$660$	−0.246999	−0.00961443
$661$	16.7483	0.651434	0.325717	−	0.945467i	$-0.394394\pi$
$661$	16.7483	0.651434	0.325717	+	0.945467i	$0.394394\pi$
$662$	−63.9410	−2.48514
$663$	1.86687	0.0725031
$664$	−15.6073	−0.605680
$665$	−1.28998	−0.0500232
$666$	−22.2761	−0.863180
$667$	−20.5420	−0.795391
$668$	−32.7951	−1.26888
$669$	−1.35387	−0.0523435
$670$	2.75588	0.106469
$671$	−1.83175	−0.0707138
$672$	24.8769	0.959646
$673$	−32.6157	−1.25724	−0.628621	−	0.777712i	$-0.716380\pi$
$673$	−32.6157	−1.25724	−0.628621	+	0.777712i	$0.716380\pi$
$674$	29.0652	1.11955
$675$	20.3560	0.783502
$676$	−19.6597	−0.756142
$677$	−42.8384	−1.64641	−0.823207	−	0.567742i	$-0.807817\pi$
$677$	−42.8384	−1.64641	−0.823207	+	0.567742i	$0.807817\pi$
$678$	−12.6807	−0.487000
$679$	−61.2299	−2.34979
$680$	−0.222716	−0.00854077
$681$	−2.73438	−0.104782
$682$	10.0267	0.383941
$683$	22.4783	0.860110	0.430055	−	0.902803i	$-0.358494\pi$
$683$	22.4783	0.860110	0.430055	+	0.902803i	$0.358494\pi$
$684$	17.0567	0.652178
$685$	−2.36848	−0.0904951
$686$	−79.0768	−3.01917
$687$	18.0363	0.688129
$688$	−1.45281	−0.0553878
$689$	−7.37393	−0.280924
$690$	−0.874726	−0.0333003
$691$	−39.5969	−1.50634	−0.753168	−	0.657828i	$-0.771475\pi$
$691$	−39.5969	−1.50634	−0.753168	+	0.657828i	$0.771475\pi$
$692$	−3.36430	−0.127892
$693$	11.3446	0.430946
$694$	−50.3057	−1.90958
$695$	0.123347	0.00467880
$696$	6.51627	0.246998
$697$	−9.31993	−0.353018
$698$	−25.7277	−0.973808
$699$	−3.94195	−0.149098
$700$	−66.9603	−2.53086
$701$	43.3540	1.63746	0.818730	−	0.574179i	$-0.194679\pi$
$701$	43.3540	1.63746	0.818730	+	0.574179i	$0.194679\pi$
$702$	22.4270	0.846453
$703$	10.0470	0.378930
$704$	12.8170	0.483059
$705$	−0.846147	−0.0318677
$706$	25.6189	0.964181
$707$	−21.7974	−0.819776
$708$	0.00222284	8.35395e−5 0
$709$	−34.7125	−1.30366	−0.651828	−	0.758367i	$-0.725998\pi$
$709$	−34.7125	−1.30366	−0.651828	+	0.758367i	$0.725998\pi$
$710$	2.07052	0.0777054
$711$	−12.5107	−0.469186
$712$	27.6684	1.03692
$713$	20.9660	0.785183
$714$	−7.72668	−0.289164
$715$	−0.283654	−0.0106081
$716$	47.1758	1.76304
$717$	5.05490	0.188779
$718$	−81.1238	−3.02751
$719$	6.05332	0.225751	0.112875	−	0.993609i	$-0.463994\pi$
$719$	6.05332	0.225751	0.112875	+	0.993609i	$0.463994\pi$
$720$	0.403791	0.0150484
$721$	−29.0368	−1.08139
$722$	28.9580	1.07771
$723$	−20.7083	−0.770150
$724$	21.3086	0.791927
$725$	22.1698	0.823365
$726$	−1.65928	−0.0615815
$727$	−35.5345	−1.31790	−0.658951	−	0.752186i	$-0.729000\pi$
$727$	−35.5345	−1.31790	−0.658951	+	0.752186i	$0.729000\pi$
$728$	−22.6021	−0.837689
$729$	−1.14415	−0.0423761
$730$	−3.29596	−0.121989
$731$	1.00000	0.0369863
$732$	3.96577	0.146579
$733$	14.2633	0.526826	0.263413	−	0.964683i	$-0.415152\pi$
$733$	14.2633	0.526826	0.263413	+	0.964683i	$0.415152\pi$
$734$	−68.4733	−2.52740
$735$	1.25791	0.0463986
$736$	32.8764	1.21184
$737$	10.9311	0.402653
$738$	−50.1752	−1.84698
$739$	−4.96592	−0.182674	−0.0913371	−	0.995820i	$-0.529114\pi$
$739$	−4.96592	−0.182674	−0.0913371	+	0.995820i	$0.529114\pi$
$740$	−1.36113	−0.0500362
$741$	−4.53302	−0.166525
$742$	30.5196	1.12041
$743$	−3.69649	−0.135611	−0.0678055	−	0.997699i	$-0.521600\pi$
$743$	−3.69649	−0.135611	−0.0678055	+	0.997699i	$0.521600\pi$
$744$	−6.65075	−0.243828
$745$	−0.150367	−0.00550901
$746$	−34.7409	−1.27196
$747$	−19.4771	−0.712630
$748$	−2.88340	−0.105428
$749$	19.8666	0.725911
$750$	1.89054	0.0690328
$751$	28.0119	1.02217	0.511084	−	0.859531i	$-0.329244\pi$
$751$	28.0119	1.02217	0.511084	+	0.859531i	$0.329244\pi$
$752$	14.3504	0.523304
$753$	2.21571	0.0807448
$754$	24.4253	0.889519
$755$	0.904998	0.0329363
$756$	−54.8066	−1.99330
$757$	−42.8281	−1.55661	−0.778307	−	0.627883i	$-0.783921\pi$
$757$	−42.8281	−1.55661	−0.778307	+	0.627883i	$0.783921\pi$
$758$	−26.6740	−0.968845
$759$	−3.46959	−0.125938
$760$	0.540786	0.0196164
$761$	−38.7262	−1.40382	−0.701912	−	0.712264i	$-0.747670\pi$
$761$	−38.7262	−1.40382	−0.701912	+	0.712264i	$0.747670\pi$
$762$	−1.55832	−0.0564521
$763$	−52.6734	−1.90690
$764$	−19.9834	−0.722975
$765$	−0.277938	−0.0100489
$766$	55.7594	2.01467
$767$	0.00255272	9.21733e−5 0
$768$	−4.13820	−0.149324
$769$	−20.7572	−0.748525	−0.374263	−	0.927323i	$-0.622104\pi$
$769$	−20.7572	−0.748525	−0.374263	+	0.927323i	$0.622104\pi$
$770$	1.17400	0.0423081
$771$	−4.89472	−0.176279
$772$	8.69631	0.312987
$773$	6.74658	0.242658	0.121329	−	0.992612i	$-0.461284\pi$
$773$	6.74658	0.242658	0.121329	+	0.992612i	$0.461284\pi$
$774$	5.38365	0.193511
$775$	−22.6273	−0.812798
$776$	25.6689	0.921459
$777$	−14.4675	−0.519019
$778$	32.3340	1.15923
$779$	22.6301	0.810809
$780$	0.614118	0.0219889
$781$	8.21270	0.293873
$782$	−10.2113	−0.365156
$783$	18.1458	0.648480
$784$	−21.3337	−0.761918
$785$	−1.61738	−0.0577268
$786$	23.7630	0.847598
$787$	11.2267	0.400188	0.200094	−	0.979777i	$-0.435875\pi$
$787$	11.2267	0.400188	0.200094	+	0.979777i	$0.435875\pi$
$788$	−55.7455	−1.98585
$789$	−16.2349	−0.577979
$790$	−1.29467	−0.0460623
$791$	35.5877	1.26535
$792$	−4.75591	−0.168994
$793$	4.55430	0.161728
$794$	4.69837	0.166739
$795$	−0.254058	−0.00901052
$796$	54.4374	1.92948
$797$	−0.768608	−0.0272255	−0.0136127	−	0.999907i	$-0.504333\pi$
$797$	−0.768608	−0.0272255	−0.0136127	+	0.999907i	$0.504333\pi$
$798$	18.7615	0.664149
$799$	−9.87769	−0.349447
$800$	−35.4815	−1.25446
$801$	34.5288	1.22002
$802$	−57.7506	−2.03925
$803$	−13.0734	−0.461350
$804$	−23.6661	−0.834640
$805$	2.45487	0.0865227
$806$	−24.9295	−0.878102
$807$	6.15836	0.216784
$808$	9.13794	0.321472
$809$	49.8688	1.75329	0.876646	−	0.481136i	$-0.159776\pi$
$809$	49.8688	1.75329	0.876646	+	0.481136i	$0.159776\pi$
$810$	−1.06991	−0.0375928
$811$	5.26885	0.185014	0.0925071	−	0.995712i	$-0.470512\pi$
$811$	5.26885	0.185014	0.0925071	+	0.995712i	$0.470512\pi$
$812$	−59.6901	−2.09471
$813$	7.71833	0.270694
$814$	−9.14373	−0.320487
$815$	−1.18490	−0.0415052
$816$	−1.09085	−0.0381874
$817$	−2.42814	−0.0849500
$818$	8.54695	0.298837
$819$	−28.2063	−0.985608
$820$	−3.06585	−0.107064
$821$	13.6830	0.477539	0.238770	−	0.971076i	$-0.423256\pi$
$821$	13.6830	0.477539	0.238770	+	0.971076i	$0.423256\pi$
$822$	34.4473	1.20149
$823$	7.56635	0.263747	0.131873	−	0.991267i	$-0.457901\pi$
$823$	7.56635	0.263747	0.131873	+	0.991267i	$0.457901\pi$
$824$	12.1729	0.424062
$825$	3.74451	0.130367
$826$	−0.0105653	−0.000367614 0
$827$	33.8998	1.17881	0.589406	−	0.807837i	$-0.299362\pi$
$827$	33.8998	1.17881	0.589406	+	0.807837i	$0.299362\pi$
$828$	−32.4594	−1.12804
$829$	24.3305	0.845032	0.422516	−	0.906355i	$-0.361147\pi$
$829$	24.3305	0.845032	0.422516	+	0.906355i	$0.361147\pi$
$830$	−2.01560	−0.0699624
$831$	3.06428	0.106299
$832$	−31.8671	−1.10479
$833$	14.6845	0.508787
$834$	−1.79396	−0.0621197
$835$	−1.29759	−0.0449049
$836$	7.00131	0.242145
$837$	−18.5203	−0.640157
$838$	−12.0429	−0.416015
$839$	3.38834	0.116979	0.0584893	−	0.998288i	$-0.481372\pi$
$839$	3.38834	0.116979	0.0584893	+	0.998288i	$0.481372\pi$
$840$	−0.778723	−0.0268685
$841$	−9.23728	−0.318527
$842$	65.2181	2.24756
$843$	−13.2127	−0.455071
$844$	−0.989289	−0.0340527
$845$	−0.777867	−0.0267594
$846$	−53.1780	−1.82830
$847$	4.65666	0.160005
$848$	4.30875	0.147963
$849$	−13.9557	−0.478959
$850$	11.0204	0.377998
$851$	−19.1198	−0.655417
$852$	−17.7807	−0.609156
$853$	−22.2634	−0.762286	−0.381143	−	0.924516i	$-0.624469\pi$
$853$	−22.2634	−0.762286	−0.381143	+	0.924516i	$0.624469\pi$
$854$	−18.8495	−0.645018
$855$	0.674874	0.0230802
$856$	−8.32852	−0.284663
$857$	−43.1652	−1.47449	−0.737247	−	0.675623i	$-0.763875\pi$
$857$	−43.1652	−1.47449	−0.737247	+	0.675623i	$0.763875\pi$
$858$	4.12548	0.140842
$859$	23.2875	0.794558	0.397279	−	0.917698i	$-0.369954\pi$
$859$	23.2875	0.794558	0.397279	+	0.917698i	$0.369954\pi$
$860$	0.328956	0.0112173
$861$	−32.5870	−1.11056
$862$	20.3729	0.693905
$863$	20.5477	0.699453	0.349726	−	0.936852i	$-0.386275\pi$
$863$	20.5477	0.699453	0.349726	+	0.936852i	$0.386275\pi$
$864$	−29.0414	−0.988009
$865$	−0.133114	−0.00452601
$866$	27.0381	0.918793
$867$	0.750857	0.0255004
$868$	60.9220	2.06783
$869$	−5.13529	−0.174203
$870$	0.841541	0.0285309
$871$	−27.1782	−0.920900
$872$	22.0818	0.747785
$873$	32.0335	1.08417
$874$	24.7945	0.838687
$875$	−5.30569	−0.179365
$876$	28.3042	0.956309
$877$	18.8632	0.636966	0.318483	−	0.947928i	$-0.396827\pi$
$877$	18.8632	0.636966	0.318483	+	0.947928i	$0.396827\pi$
$878$	−9.38041	−0.316573
$879$	−9.05437	−0.305396
$880$	0.165745	0.00558727
$881$	−40.9825	−1.38074	−0.690368	−	0.723459i	$-0.742551\pi$
$881$	−40.9825	−1.38074	−0.690368	+	0.723459i	$0.742551\pi$
$882$	79.0560	2.66195
$883$	21.8613	0.735691	0.367846	−	0.929887i	$-0.380096\pi$
$883$	21.8613	0.735691	0.367846	+	0.929887i	$0.380096\pi$
$884$	7.16904	0.241121
$885$	8.79502e−5 0	2.95641e−6 0
$886$	43.5216	1.46214
$887$	2.76245	0.0927540	0.0463770	−	0.998924i	$-0.485232\pi$
$887$	2.76245	0.0927540	0.0463770	+	0.998924i	$0.485232\pi$
$888$	6.06509	0.203531
$889$	4.37334	0.146677
$890$	3.57323	0.119775
$891$	−4.24378	−0.142172
$892$	−5.19905	−0.174077
$893$	23.9844	0.802609
$894$	2.18694	0.0731423
$895$	1.86659	0.0623931
$896$	65.6305	2.19256
$897$	8.62649	0.288030
$898$	48.2662	1.61066
$899$	−20.1706	−0.672727
$900$	35.0315	1.16772
$901$	−2.96581	−0.0988054
$902$	−20.5956	−0.685758
$903$	3.49649	0.116356
$904$	−14.9191	−0.496203
$905$	0.843108	0.0280258
$906$	−13.1623	−0.437289
$907$	−27.2878	−0.906076	−0.453038	−	0.891491i	$-0.649660\pi$
$907$	−27.2878	−0.906076	−0.453038	+	0.891491i	$0.649660\pi$
$908$	−10.5004	−0.348468
$909$	11.4037	0.378237
$910$	−2.91894	−0.0967619
$911$	20.5703	0.681525	0.340762	−	0.940149i	$-0.389315\pi$
$911$	20.5703	0.681525	0.340762	+	0.940149i	$0.389315\pi$
$912$	2.64874	0.0877086
$913$	−7.99483	−0.264590
$914$	10.6366	0.351828
$915$	0.156912	0.00518735
$916$	69.2621	2.28849
$917$	−66.6894	−2.20228
$918$	9.02017	0.297710
$919$	−4.95557	−0.163469	−0.0817346	−	0.996654i	$-0.526046\pi$
$919$	−4.95557	−0.163469	−0.0817346	+	0.996654i	$0.526046\pi$
$920$	−1.02913	−0.0339295
$921$	12.0236	0.396193
$922$	11.7917	0.388340
$923$	−20.4194	−0.672112
$924$	−10.0818	−0.331666
$925$	20.6348	0.678468
$926$	−42.9778	−1.41234
$927$	15.1911	0.498943
$928$	−31.6291	−1.03828
$929$	−26.1290	−0.857264	−0.428632	−	0.903479i	$-0.641004\pi$
$929$	−26.1290	−0.857264	−0.428632	+	0.903479i	$0.641004\pi$
$930$	−0.858909	−0.0281647
$931$	−35.6560	−1.16858
$932$	−15.1376	−0.495850
$933$	4.28467	0.140274
$934$	−66.5761	−2.17844
$935$	−0.114086	−0.00373102
$936$	11.8247	0.386502
$937$	54.6458	1.78520	0.892600	−	0.450849i	$-0.148879\pi$
$937$	54.6458	1.78520	0.892600	+	0.450849i	$0.148879\pi$
$938$	112.487	3.67282
$939$	24.9688	0.814826
$940$	−3.24933	−0.105981
$941$	3.92662	0.128004	0.0640021	−	0.997950i	$-0.479614\pi$
$941$	3.92662	0.128004	0.0640021	+	0.997950i	$0.479614\pi$
$942$	23.5233	0.766430
$943$	−43.0659	−1.40242
$944$	−0.00149161	−4.85477e−5 0
$945$	−2.16851	−0.0705416
$946$	2.20984	0.0718481
$947$	−58.0611	−1.88673	−0.943366	−	0.331753i	$-0.892360\pi$
$947$	−58.0611	−1.88673	−0.943366	+	0.331753i	$0.892360\pi$
$948$	11.1180	0.361096
$949$	32.5046	1.05514
$950$	−26.7592	−0.868184
$951$	18.8550	0.611416
$952$	−9.09060	−0.294628
$953$	−59.4184	−1.92475	−0.962375	−	0.271726i	$-0.912406\pi$
$953$	−59.4184	−1.92475	−0.962375	+	0.271726i	$0.912406\pi$
$954$	−15.9669	−0.516946
$955$	−0.790675	−0.0255857
$956$	19.4115	0.627813
$957$	3.33796	0.107901
$958$	−14.3114	−0.462381
$959$	−96.6743	−3.12178
$960$	−1.09794	−0.0354357
$961$	−10.4131	−0.335907
$962$	22.7342	0.732980
$963$	−10.3936	−0.334928
$964$	−79.5228	−2.56126
$965$	0.344083	0.0110764
$966$	−35.7037	−1.14875
$967$	1.25222	0.0402685	0.0201343	−	0.999797i	$-0.493591\pi$
$967$	1.25222	0.0402685	0.0201343	+	0.999797i	$0.493591\pi$
$968$	−1.95217	−0.0627452
$969$	−1.82319	−0.0585693
$970$	3.31500	0.106438
$971$	32.0937	1.02994	0.514968	−	0.857210i	$-0.327804\pi$
$971$	32.0937	1.02994	0.514968	+	0.857210i	$0.327804\pi$
$972$	44.4964	1.42722
$973$	5.03464	0.161403
$974$	25.0736	0.803411
$975$	−9.31004	−0.298160
$976$	−2.66117	−0.0851821
$977$	29.4772	0.943060	0.471530	−	0.881850i	$-0.343702\pi$
$977$	29.4772	0.943060	0.471530	+	0.881850i	$0.343702\pi$
$978$	17.2332	0.551057
$979$	14.1732	0.452976
$980$	4.83055	0.154306
$981$	27.5570	0.879828
$982$	55.1434	1.75970
$983$	−39.7189	−1.26684	−0.633419	−	0.773809i	$-0.718349\pi$
$983$	−39.7189	−1.26684	−0.633419	+	0.773809i	$0.718349\pi$
$984$	13.6612	0.435503
$985$	−2.20566	−0.0702782
$986$	9.82391	0.312857
$987$	−34.5372	−1.09933
$988$	−17.4075	−0.553805
$989$	4.62083	0.146934
$990$	−0.614200	−0.0195206
$991$	25.1836	0.799984	0.399992	−	0.916519i	$-0.369013\pi$
$991$	25.1836	0.799984	0.399992	+	0.916519i	$0.369013\pi$
$992$	32.2819	1.02495
$993$	21.7258	0.689447
$994$	84.5126	2.68058
$995$	2.15390	0.0682833
$996$	17.3090	0.548456
$997$	−59.0134	−1.86897	−0.934486	−	0.355999i	$-0.884141\pi$
$997$	−59.0134	−1.86897	−0.934486	+	0.355999i	$0.884141\pi$
$998$	65.9255	2.08683
$999$	16.8895	0.534359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.10	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.10	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20984 q^{2} +0.750857 q^{3} +2.88340 q^{4} +0.114086 q^{5} -1.65928 q^{6} +4.65666 q^{7} -1.95217 q^{8} -2.43621 q^{9} +O(q^{10})\)	\(q-2.20984 q^{2} +0.750857 q^{3} +2.88340 q^{4} +0.114086 q^{5} -1.65928 q^{6} +4.65666 q^{7} -1.95217 q^{8} -2.43621 q^{9} -0.252113 q^{10} -1.00000 q^{11} +2.16502 q^{12} +2.48632 q^{13} -10.2905 q^{14} +0.0856625 q^{15} -1.45281 q^{16} +1.00000 q^{17} +5.38365 q^{18} -2.42814 q^{19} +0.328956 q^{20} +3.49649 q^{21} +2.20984 q^{22} +4.62083 q^{23} -1.46580 q^{24} -4.98698 q^{25} -5.49436 q^{26} -4.08182 q^{27} +13.4270 q^{28} -4.44553 q^{29} -0.189300 q^{30} +4.53728 q^{31} +7.11482 q^{32} -0.750857 q^{33} -2.20984 q^{34} +0.531261 q^{35} -7.02458 q^{36} -4.13773 q^{37} +5.36581 q^{38} +1.86687 q^{39} -0.222716 q^{40} -9.31993 q^{41} -7.72668 q^{42} +1.00000 q^{43} -2.88340 q^{44} -0.277938 q^{45} -10.2113 q^{46} -9.87769 q^{47} -1.09085 q^{48} +14.6845 q^{49} +11.0204 q^{50} +0.750857 q^{51} +7.16904 q^{52} -2.96581 q^{53} +9.02017 q^{54} -0.114086 q^{55} -9.09060 q^{56} -1.82319 q^{57} +9.82391 q^{58} +0.00102671 q^{59} +0.246999 q^{60} +1.83175 q^{61} -10.0267 q^{62} -11.3446 q^{63} -12.8170 q^{64} +0.283654 q^{65} +1.65928 q^{66} -10.9311 q^{67} +2.88340 q^{68} +3.46959 q^{69} -1.17400 q^{70} -8.21270 q^{71} +4.75591 q^{72} +13.0734 q^{73} +9.14373 q^{74} -3.74451 q^{75} -7.00131 q^{76} -4.65666 q^{77} -4.12548 q^{78} +5.13529 q^{79} -0.165745 q^{80} +4.24378 q^{81} +20.5956 q^{82} +7.99483 q^{83} +10.0818 q^{84} +0.114086 q^{85} -2.20984 q^{86} -3.33796 q^{87} +1.95217 q^{88} -14.1732 q^{89} +0.614200 q^{90} +11.5779 q^{91} +13.3237 q^{92} +3.40685 q^{93} +21.8281 q^{94} -0.277018 q^{95} +5.34221 q^{96} -13.1489 q^{97} -32.4503 q^{98} +2.43621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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