LMFDB - Embedded newform 4017.2.a.g.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.67605 q^{2} -1.00000 q^{3} +5.16126 q^{4} -1.98695 q^{5} -2.67605 q^{6} +0.0781664 q^{7} +8.45968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.67605 q^{2} -1.00000 q^{3} +5.16126 q^{4} -1.98695 q^{5} -2.67605 q^{6} +0.0781664 q^{7} +8.45968 q^{8} +1.00000 q^{9} -5.31717 q^{10} +3.41115 q^{11} -5.16126 q^{12} -1.00000 q^{13} +0.209177 q^{14} +1.98695 q^{15} +12.3160 q^{16} +4.69600 q^{17} +2.67605 q^{18} +1.61286 q^{19} -10.2551 q^{20} -0.0781664 q^{21} +9.12843 q^{22} -1.87590 q^{23} -8.45968 q^{24} -1.05205 q^{25} -2.67605 q^{26} -1.00000 q^{27} +0.403437 q^{28} -2.33675 q^{29} +5.31717 q^{30} -2.02031 q^{31} +16.0390 q^{32} -3.41115 q^{33} +12.5667 q^{34} -0.155312 q^{35} +5.16126 q^{36} +10.2129 q^{37} +4.31610 q^{38} +1.00000 q^{39} -16.8089 q^{40} +3.38329 q^{41} -0.209177 q^{42} +5.80365 q^{43} +17.6058 q^{44} -1.98695 q^{45} -5.02000 q^{46} +1.16815 q^{47} -12.3160 q^{48} -6.99389 q^{49} -2.81533 q^{50} -4.69600 q^{51} -5.16126 q^{52} +4.15341 q^{53} -2.67605 q^{54} -6.77778 q^{55} +0.661263 q^{56} -1.61286 q^{57} -6.25327 q^{58} -1.92710 q^{59} +10.2551 q^{60} +0.0325665 q^{61} -5.40645 q^{62} +0.0781664 q^{63} +18.2891 q^{64} +1.98695 q^{65} -9.12843 q^{66} +7.23125 q^{67} +24.2373 q^{68} +1.87590 q^{69} -0.415624 q^{70} +7.99341 q^{71} +8.45968 q^{72} -2.29309 q^{73} +27.3302 q^{74} +1.05205 q^{75} +8.32439 q^{76} +0.266638 q^{77} +2.67605 q^{78} +13.6725 q^{79} -24.4713 q^{80} +1.00000 q^{81} +9.05387 q^{82} -2.42289 q^{83} -0.403437 q^{84} -9.33070 q^{85} +15.5309 q^{86} +2.33675 q^{87} +28.8573 q^{88} +4.51097 q^{89} -5.31717 q^{90} -0.0781664 q^{91} -9.68199 q^{92} +2.02031 q^{93} +3.12604 q^{94} -3.20467 q^{95} -16.0390 q^{96} +8.99421 q^{97} -18.7160 q^{98} +3.41115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	2.67605	1.89225	0.946127	−	0.323795i	$-0.104959\pi$
$2$	2.67605	1.89225	0.946127	+	0.323795i	$0.104959\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.16126	2.58063
$5$	−1.98695	−0.888589	−0.444295	−	0.895881i	$-0.646546\pi$
$5$	−1.98695	−0.888589	−0.444295	+	0.895881i	$0.646546\pi$
$6$	−2.67605	−1.09249
$7$	0.0781664	0.0295441	0.0147721	−	0.999891i	$-0.495298\pi$
$7$	0.0781664	0.0295441	0.0147721	+	0.999891i	$0.495298\pi$
$8$	8.45968	2.99095
$9$	1.00000	0.333333
$10$	−5.31717	−1.68144
$11$	3.41115	1.02850	0.514251	−	0.857640i	$-0.328070\pi$
$11$	3.41115	1.02850	0.514251	+	0.857640i	$0.328070\pi$
$12$	−5.16126	−1.48993
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.209177	0.0559050
$15$	1.98695	0.513027
$16$	12.3160	3.07901
$17$	4.69600	1.13895	0.569474	−	0.822010i	$-0.307147\pi$
$17$	4.69600	1.13895	0.569474	+	0.822010i	$0.307147\pi$
$18$	2.67605	0.630752
$19$	1.61286	0.370016	0.185008	−	0.982737i	$-0.440769\pi$
$19$	1.61286	0.370016	0.185008	+	0.982737i	$0.440769\pi$
$20$	−10.2551	−2.29312
$21$	−0.0781664	−0.0170573
$22$	9.12843	1.94619
$23$	−1.87590	−0.391152	−0.195576	−	0.980689i	$-0.562658\pi$
$23$	−1.87590	−0.391152	−0.195576	+	0.980689i	$0.562658\pi$
$24$	−8.45968	−1.72683
$25$	−1.05205	−0.210409
$26$	−2.67605	−0.524817
$27$	−1.00000	−0.192450
$28$	0.403437	0.0762424
$29$	−2.33675	−0.433924	−0.216962	−	0.976180i	$-0.569615\pi$
$29$	−2.33675	−0.433924	−0.216962	+	0.976180i	$0.569615\pi$
$30$	5.31717	0.970778
$31$	−2.02031	−0.362858	−0.181429	−	0.983404i	$-0.558072\pi$
$31$	−2.02031	−0.362858	−0.181429	+	0.983404i	$0.558072\pi$
$32$	16.0390	2.83532
$33$	−3.41115	−0.593806
$34$	12.5667	2.15518
$35$	−0.155312	−0.0262526
$36$	5.16126	0.860209
$37$	10.2129	1.67899	0.839493	−	0.543371i	$-0.182852\pi$
$37$	10.2129	1.67899	0.839493	+	0.543371i	$0.182852\pi$
$38$	4.31610	0.700164
$39$	1.00000	0.160128
$40$	−16.8089	−2.65773
$41$	3.38329	0.528382	0.264191	−	0.964470i	$-0.414895\pi$
$41$	3.38329	0.528382	0.264191	+	0.964470i	$0.414895\pi$
$42$	−0.209177	−0.0322768
$43$	5.80365	0.885048	0.442524	−	0.896757i	$-0.354083\pi$
$43$	5.80365	0.885048	0.442524	+	0.896757i	$0.354083\pi$
$44$	17.6058	2.65418
$45$	−1.98695	−0.296196
$46$	−5.02000	−0.740159
$47$	1.16815	0.170393	0.0851963	−	0.996364i	$-0.472848\pi$
$47$	1.16815	0.170393	0.0851963	+	0.996364i	$0.472848\pi$
$48$	−12.3160	−1.77767
$49$	−6.99389	−0.999127
$50$	−2.81533	−0.398148
$51$	−4.69600	−0.657572
$52$	−5.16126	−0.715737
$53$	4.15341	0.570514	0.285257	−	0.958451i	$-0.407921\pi$
$53$	4.15341	0.570514	0.285257	+	0.958451i	$0.407921\pi$
$54$	−2.67605	−0.364165
$55$	−6.77778	−0.913916
$56$	0.661263	0.0883650
$57$	−1.61286	−0.213629
$58$	−6.25327	−0.821094
$59$	−1.92710	−0.250887	−0.125444	−	0.992101i	$-0.540035\pi$
$59$	−1.92710	−0.250887	−0.125444	+	0.992101i	$0.540035\pi$
$60$	10.2551	1.32393
$61$	0.0325665	0.00416972	0.00208486	−	0.999998i	$-0.499336\pi$
$61$	0.0325665	0.00416972	0.00208486	+	0.999998i	$0.499336\pi$
$62$	−5.40645	−0.686619
$63$	0.0781664	0.00984804
$64$	18.2891	2.28614
$65$	1.98695	0.246450
$66$	−9.12843	−1.12363
$67$	7.23125	0.883438	0.441719	−	0.897153i	$-0.354369\pi$
$67$	7.23125	0.883438	0.441719	+	0.897153i	$0.354369\pi$
$68$	24.2373	2.93920
$69$	1.87590	0.225832
$70$	−0.415624	−0.0496766
$71$	7.99341	0.948643	0.474321	−	0.880352i	$-0.342693\pi$
$71$	7.99341	0.948643	0.474321	+	0.880352i	$0.342693\pi$
$72$	8.45968	0.996983
$73$	−2.29309	−0.268386	−0.134193	−	0.990955i	$-0.542844\pi$
$73$	−2.29309	−0.268386	−0.134193	+	0.990955i	$0.542844\pi$
$74$	27.3302	3.17707
$75$	1.05205	0.121480
$76$	8.32439	0.954873
$77$	0.266638	0.0303862
$78$	2.67605	0.303003
$79$	13.6725	1.53827	0.769136	−	0.639085i	$-0.220687\pi$
$79$	13.6725	1.53827	0.769136	+	0.639085i	$0.220687\pi$
$80$	−24.4713	−2.73598
$81$	1.00000	0.111111
$82$	9.05387	0.999833
$83$	−2.42289	−0.265946	−0.132973	−	0.991120i	$-0.542452\pi$
$83$	−2.42289	−0.265946	−0.132973	+	0.991120i	$0.542452\pi$
$84$	−0.403437	−0.0440186
$85$	−9.33070	−1.01206
$86$	15.5309	1.67474
$87$	2.33675	0.250526
$88$	28.8573	3.07620
$89$	4.51097	0.478162	0.239081	−	0.971000i	$-0.423154\pi$
$89$	4.51097	0.478162	0.239081	+	0.971000i	$0.423154\pi$
$90$	−5.31717	−0.560479
$91$	−0.0781664	−0.00819407
$92$	−9.68199	−1.00942
$93$	2.02031	0.209496
$94$	3.12604	0.322426
$95$	−3.20467	−0.328792
$96$	−16.0390	−1.63697
$97$	8.99421	0.913223	0.456612	−	0.889666i	$-0.349063\pi$
$97$	8.99421	0.913223	0.456612	+	0.889666i	$0.349063\pi$
$98$	−18.7160	−1.89060
$99$	3.41115	0.342834
$100$	−5.42988	−0.542988
$101$	−6.74833	−0.671484	−0.335742	−	0.941954i	$-0.608987\pi$
$101$	−6.74833	−0.671484	−0.335742	+	0.941954i	$0.608987\pi$
$102$	−12.5667	−1.24429
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−8.45968	−0.829540
$105$	0.155312	0.0151569
$106$	11.1147	1.07956
$107$	1.84516	0.178378	0.0891892	−	0.996015i	$-0.471572\pi$
$107$	1.84516	0.178378	0.0891892	+	0.996015i	$0.471572\pi$
$108$	−5.16126	−0.496642
$109$	16.2941	1.56069	0.780345	−	0.625349i	$-0.215044\pi$
$109$	16.2941	1.56069	0.780345	+	0.625349i	$0.215044\pi$
$110$	−18.1377	−1.72936
$111$	−10.2129	−0.969363
$112$	0.962701	0.0909667
$113$	−0.307605	−0.0289371	−0.0144685	−	0.999895i	$-0.504606\pi$
$113$	−0.307605	−0.0289371	−0.0144685	+	0.999895i	$0.504606\pi$
$114$	−4.31610	−0.404240
$115$	3.72731	0.347573
$116$	−12.0606	−1.11980
$117$	−1.00000	−0.0924500
$118$	−5.15702	−0.474743
$119$	0.367069	0.0336492
$120$	16.8089	1.53444
$121$	0.635975	0.0578159
$122$	0.0871498	0.00789017
$123$	−3.38329	−0.305061
$124$	−10.4273	−0.936401
$125$	12.0251	1.07556
$126$	0.209177	0.0186350
$127$	−12.8059	−1.13634	−0.568170	−	0.822911i	$-0.692348\pi$
$127$	−12.8059	−1.13634	−0.568170	+	0.822911i	$0.692348\pi$
$128$	16.8647	1.49064
$129$	−5.80365	−0.510983
$130$	5.31717	0.466347
$131$	−17.8357	−1.55831	−0.779156	−	0.626830i	$-0.784352\pi$
$131$	−17.8357	−1.55831	−0.779156	+	0.626830i	$0.784352\pi$
$132$	−17.6058	−1.53239
$133$	0.126072	0.0109318
$134$	19.3512	1.67169
$135$	1.98695	0.171009
$136$	39.7267	3.40653
$137$	−6.41753	−0.548286	−0.274143	−	0.961689i	$-0.588394\pi$
$137$	−6.41753	−0.548286	−0.274143	+	0.961689i	$0.588394\pi$
$138$	5.02000	0.427331
$139$	−19.7218	−1.67278	−0.836389	−	0.548136i	$-0.815337\pi$
$139$	−19.7218	−1.67278	−0.836389	+	0.548136i	$0.815337\pi$
$140$	−0.801607	−0.0677481
$141$	−1.16815	−0.0983762
$142$	21.3908	1.79507
$143$	−3.41115	−0.285255
$144$	12.3160	1.02634
$145$	4.64300	0.385580
$146$	−6.13642	−0.507854
$147$	6.99389	0.576846
$148$	52.7112	4.33284
$149$	−2.84240	−0.232858	−0.116429	−	0.993199i	$-0.537145\pi$
$149$	−2.84240	−0.232858	−0.116429	+	0.993199i	$0.537145\pi$
$150$	2.81533	0.229871
$151$	8.48014	0.690104	0.345052	−	0.938584i	$-0.387861\pi$
$151$	8.48014	0.690104	0.345052	+	0.938584i	$0.387861\pi$
$152$	13.6443	1.10670
$153$	4.69600	0.379649
$154$	0.713536	0.0574984
$155$	4.01424	0.322431
$156$	5.16126	0.413231
$157$	−7.34154	−0.585918	−0.292959	−	0.956125i	$-0.594640\pi$
$157$	−7.34154	−0.585918	−0.292959	+	0.956125i	$0.594640\pi$
$158$	36.5882	2.91080
$159$	−4.15341	−0.329387
$160$	−31.8686	−2.51944
$161$	−0.146632	−0.0115562
$162$	2.67605	0.210251
$163$	−12.4077	−0.971849	−0.485925	−	0.874001i	$-0.661517\pi$
$163$	−12.4077	−0.971849	−0.485925	+	0.874001i	$0.661517\pi$
$164$	17.4620	1.36356
$165$	6.77778	0.527649
$166$	−6.48377	−0.503238
$167$	−0.633803	−0.0490452	−0.0245226	−	0.999699i	$-0.507807\pi$
$167$	−0.633803	−0.0490452	−0.0245226	+	0.999699i	$0.507807\pi$
$168$	−0.661263	−0.0510175
$169$	1.00000	0.0769231
$170$	−24.9694	−1.91507
$171$	1.61286	0.123339
$172$	29.9541	2.28398
$173$	2.07948	0.158100	0.0790500	−	0.996871i	$-0.474811\pi$
$173$	2.07948	0.158100	0.0790500	+	0.996871i	$0.474811\pi$
$174$	6.25327	0.474059
$175$	−0.0822347	−0.00621636
$176$	42.0119	3.16677
$177$	1.92710	0.144850
$178$	12.0716	0.904804
$179$	10.5489	0.788464	0.394232	−	0.919011i	$-0.371011\pi$
$179$	10.5489	0.788464	0.394232	+	0.919011i	$0.371011\pi$
$180$	−10.2551	−0.764373
$181$	18.3019	1.36037	0.680185	−	0.733040i	$-0.261899\pi$
$181$	18.3019	1.36037	0.680185	+	0.733040i	$0.261899\pi$
$182$	−0.209177	−0.0155053
$183$	−0.0325665	−0.00240739
$184$	−15.8695	−1.16992
$185$	−20.2924	−1.49193
$186$	5.40645	0.396420
$187$	16.0188	1.17141
$188$	6.02914	0.439720
$189$	−0.0781664	−0.00568577
$190$	−8.57586	−0.622159
$191$	13.9348	1.00829	0.504144	−	0.863619i	$-0.331808\pi$
$191$	13.9348	1.00829	0.504144	+	0.863619i	$0.331808\pi$
$192$	−18.2891	−1.31990
$193$	7.39625	0.532394	0.266197	−	0.963919i	$-0.414233\pi$
$193$	7.39625	0.532394	0.266197	+	0.963919i	$0.414233\pi$
$194$	24.0690	1.72805
$195$	−1.98695	−0.142288
$196$	−36.0973	−2.57838
$197$	−26.9283	−1.91856	−0.959281	−	0.282455i	$-0.908851\pi$
$197$	−26.9283	−1.91856	−0.959281	+	0.282455i	$0.908851\pi$
$198$	9.12843	0.648729
$199$	−4.21235	−0.298606	−0.149303	−	0.988792i	$-0.547703\pi$
$199$	−4.21235	−0.298606	−0.149303	+	0.988792i	$0.547703\pi$
$200$	−8.89998	−0.629324
$201$	−7.23125	−0.510053
$202$	−18.0589	−1.27062
$203$	−0.182655	−0.0128199
$204$	−24.2373	−1.69695
$205$	−6.72242	−0.469514
$206$	2.67605	0.186449
$207$	−1.87590	−0.130384
$208$	−12.3160	−0.853964
$209$	5.50172	0.380562
$210$	0.415624	0.0286808
$211$	−9.89604	−0.681272	−0.340636	−	0.940195i	$-0.610642\pi$
$211$	−9.89604	−0.681272	−0.340636	+	0.940195i	$0.610642\pi$
$212$	21.4368	1.47228
$213$	−7.99341	−0.547699
$214$	4.93774	0.337537
$215$	−11.5315	−0.786444
$216$	−8.45968	−0.575609
$217$	−0.157920	−0.0107203
$218$	43.6038	2.95322
$219$	2.29309	0.154952
$220$	−34.9818	−2.35848
$221$	−4.69600	−0.315887
$222$	−27.3302	−1.83428
$223$	−18.9322	−1.26779	−0.633896	−	0.773418i	$-0.718545\pi$
$223$	−18.9322	−1.26779	−0.633896	+	0.773418i	$0.718545\pi$
$224$	1.25371	0.0837671
$225$	−1.05205	−0.0701365
$226$	−0.823168	−0.0547563
$227$	3.07891	0.204354	0.102177	−	0.994766i	$-0.467419\pi$
$227$	3.07891	0.204354	0.102177	+	0.994766i	$0.467419\pi$
$228$	−8.32439	−0.551296
$229$	−16.3773	−1.08224	−0.541120	−	0.840946i	$-0.681999\pi$
$229$	−16.3773	−1.08224	−0.541120	+	0.840946i	$0.681999\pi$
$230$	9.97447	0.657697
$231$	−0.266638	−0.0175435
$232$	−19.7682	−1.29784
$233$	−15.0068	−0.983130	−0.491565	−	0.870841i	$-0.663575\pi$
$233$	−15.0068	−0.983130	−0.491565	+	0.870841i	$0.663575\pi$
$234$	−2.67605	−0.174939
$235$	−2.32106	−0.151409
$236$	−9.94626	−0.647447
$237$	−13.6725	−0.888122
$238$	0.982297	0.0636729
$239$	−1.53264	−0.0991383	−0.0495691	−	0.998771i	$-0.515785\pi$
$239$	−1.53264	−0.0991383	−0.0495691	+	0.998771i	$0.515785\pi$
$240$	24.4713	1.57962
$241$	−22.4585	−1.44668	−0.723340	−	0.690492i	$-0.757394\pi$
$241$	−22.4585	−1.44668	−0.723340	+	0.690492i	$0.757394\pi$
$242$	1.70190	0.109402
$243$	−1.00000	−0.0641500
$244$	0.168084	0.0107605
$245$	13.8965	0.887814
$246$	−9.05387	−0.577254
$247$	−1.61286	−0.102624
$248$	−17.0912	−1.08529
$249$	2.42289	0.153544
$250$	32.1798	2.03523
$251$	15.2958	0.965462	0.482731	−	0.875769i	$-0.339645\pi$
$251$	15.2958	0.965462	0.482731	+	0.875769i	$0.339645\pi$
$252$	0.403437	0.0254141
$253$	−6.39898	−0.402300
$254$	−34.2693	−2.15024
$255$	9.33070	0.584311
$256$	8.55245	0.534528
$257$	16.5937	1.03509	0.517544	−	0.855656i	$-0.326846\pi$
$257$	16.5937	1.03509	0.517544	+	0.855656i	$0.326846\pi$
$258$	−15.5309	−0.966909
$259$	0.798303	0.0496042
$260$	10.2551	0.635996
$261$	−2.33675	−0.144641
$262$	−47.7292	−2.94872
$263$	−21.2489	−1.31026	−0.655132	−	0.755515i	$-0.727387\pi$
$263$	−21.2489	−1.31026	−0.655132	+	0.755515i	$0.727387\pi$
$264$	−28.8573	−1.77604
$265$	−8.25259	−0.506953
$266$	0.337374	0.0206857
$267$	−4.51097	−0.276067
$268$	37.3223	2.27982
$269$	−3.82408	−0.233158	−0.116579	−	0.993181i	$-0.537193\pi$
$269$	−3.82408	−0.233158	−0.116579	+	0.993181i	$0.537193\pi$
$270$	5.31717	0.323593
$271$	3.72119	0.226046	0.113023	−	0.993592i	$-0.463947\pi$
$271$	3.72119	0.226046	0.113023	+	0.993592i	$0.463947\pi$
$272$	57.8362	3.50683
$273$	0.0781664	0.00473085
$274$	−17.1736	−1.03750
$275$	−3.58869	−0.216406
$276$	9.68199	0.582787
$277$	−17.8720	−1.07383	−0.536914	−	0.843637i	$-0.680410\pi$
$277$	−17.8720	−1.07383	−0.536914	+	0.843637i	$0.680410\pi$
$278$	−52.7765	−3.16532
$279$	−2.02031	−0.120953
$280$	−1.31389	−0.0785202
$281$	−9.40496	−0.561053	−0.280526	−	0.959846i	$-0.590509\pi$
$281$	−9.40496	−0.561053	−0.280526	+	0.959846i	$0.590509\pi$
$282$	−3.12604	−0.186153
$283$	−15.2249	−0.905027	−0.452513	−	0.891758i	$-0.649473\pi$
$283$	−15.2249	−0.905027	−0.452513	+	0.891758i	$0.649473\pi$
$284$	41.2560	2.44809
$285$	3.20467	0.189828
$286$	−9.12843	−0.539775
$287$	0.264460	0.0156106
$288$	16.0390	0.945108
$289$	5.05243	0.297202
$290$	12.4249	0.729616
$291$	−8.99421	−0.527250
$292$	−11.8352	−0.692603
$293$	−1.07212	−0.0626342	−0.0313171	−	0.999509i	$-0.509970\pi$
$293$	−1.07212	−0.0626342	−0.0313171	+	0.999509i	$0.509970\pi$
$294$	18.7160	1.09154
$295$	3.82905	0.222936
$296$	86.3977	5.02176
$297$	−3.41115	−0.197935
$298$	−7.60641	−0.440628
$299$	1.87590	0.108486
$300$	5.42988	0.313494
$301$	0.453650	0.0261480
$302$	22.6933	1.30585
$303$	6.74833	0.387681
$304$	19.8641	1.13928
$305$	−0.0647080	−0.00370517
$306$	12.5667	0.718393
$307$	−15.3099	−0.873782	−0.436891	−	0.899515i	$-0.643920\pi$
$307$	−15.3099	−0.873782	−0.436891	+	0.899515i	$0.643920\pi$
$308$	1.37619	0.0784154
$309$	−1.00000	−0.0568880
$310$	10.7423	0.610122
$311$	30.4553	1.72696	0.863480	−	0.504383i	$-0.168280\pi$
$311$	30.4553	1.72696	0.863480	+	0.504383i	$0.168280\pi$
$312$	8.45968	0.478935
$313$	−30.0770	−1.70005	−0.850027	−	0.526740i	$-0.823414\pi$
$313$	−30.0770	−1.70005	−0.850027	+	0.526740i	$0.823414\pi$
$314$	−19.6463	−1.10871
$315$	−0.155312	−0.00875086
$316$	70.5671	3.96971
$317$	0.259083	0.0145515	0.00727577	−	0.999974i	$-0.497684\pi$
$317$	0.259083	0.0145515	0.00727577	+	0.999974i	$0.497684\pi$
$318$	−11.1147	−0.623283
$319$	−7.97102	−0.446291
$320$	−36.3395	−2.03144
$321$	−1.84516	−0.102987
$322$	−0.392395	−0.0218673
$323$	7.57400	0.421429
$324$	5.16126	0.286736
$325$	1.05205	0.0583571
$326$	−33.2038	−1.83899
$327$	−16.2941	−0.901065
$328$	28.6216	1.58036
$329$	0.0913103	0.00503410
$330$	18.1377	0.998447
$331$	−21.6707	−1.19113	−0.595564	−	0.803308i	$-0.703071\pi$
$331$	−21.6707	−1.19113	−0.595564	+	0.803308i	$0.703071\pi$
$332$	−12.5051	−0.686309
$333$	10.2129	0.559662
$334$	−1.69609	−0.0928059
$335$	−14.3681	−0.785014
$336$	−0.962701	−0.0525196
$337$	−3.38225	−0.184243	−0.0921216	−	0.995748i	$-0.529365\pi$
$337$	−3.38225	−0.184243	−0.0921216	+	0.995748i	$0.529365\pi$
$338$	2.67605	0.145558
$339$	0.307605	0.0167068
$340$	−48.1581	−2.61174
$341$	−6.89158	−0.373200
$342$	4.31610	0.233388
$343$	−1.09385	−0.0590625
$344$	49.0970	2.64713
$345$	−3.72731	−0.200671
$346$	5.56480	0.299166
$347$	1.00469	0.0539344	0.0269672	−	0.999636i	$-0.491415\pi$
$347$	1.00469	0.0539344	0.0269672	+	0.999636i	$0.491415\pi$
$348$	12.0606	0.646514
$349$	−27.2904	−1.46082	−0.730410	−	0.683009i	$-0.760671\pi$
$349$	−27.2904	−1.46082	−0.730410	+	0.683009i	$0.760671\pi$
$350$	−0.220064	−0.0117629
$351$	1.00000	0.0533761
$352$	54.7115	2.91613
$353$	11.1521	0.593568	0.296784	−	0.954945i	$-0.404086\pi$
$353$	11.1521	0.593568	0.296784	+	0.954945i	$0.404086\pi$
$354$	5.15702	0.274093
$355$	−15.8825	−0.842954
$356$	23.2823	1.23396
$357$	−0.367069	−0.0194274
$358$	28.2295	1.49198
$359$	−2.59534	−0.136977	−0.0684884	−	0.997652i	$-0.521818\pi$
$359$	−2.59534	−0.136977	−0.0684884	+	0.997652i	$0.521818\pi$
$360$	−16.8089	−0.885908
$361$	−16.3987	−0.863088
$362$	48.9769	2.57417
$363$	−0.635975	−0.0333800
$364$	−0.403437	−0.0211458
$365$	4.55624	0.238484
$366$	−0.0871498	−0.00455539
$367$	−19.5143	−1.01864	−0.509318	−	0.860578i	$-0.670102\pi$
$367$	−19.5143	−1.01864	−0.509318	+	0.860578i	$0.670102\pi$
$368$	−23.1036	−1.20436
$369$	3.38329	0.176127
$370$	−54.3036	−2.82311
$371$	0.324657	0.0168553
$372$	10.4273	0.540631
$373$	−6.49554	−0.336326	−0.168163	−	0.985759i	$-0.553784\pi$
$373$	−6.49554	−0.336326	−0.168163	+	0.985759i	$0.553784\pi$
$374$	42.8671	2.21661
$375$	−12.0251	−0.620973
$376$	9.88220	0.509636
$377$	2.33675	0.120349
$378$	−0.209177	−0.0107589
$379$	−6.88815	−0.353820	−0.176910	−	0.984227i	$-0.556610\pi$
$379$	−6.88815	−0.353820	−0.176910	+	0.984227i	$0.556610\pi$
$380$	−16.5401	−0.848490
$381$	12.8059	0.656066
$382$	37.2903	1.90794
$383$	8.08893	0.413325	0.206662	−	0.978412i	$-0.433740\pi$
$383$	8.08893	0.413325	0.206662	+	0.978412i	$0.433740\pi$
$384$	−16.8647	−0.860621
$385$	−0.529795	−0.0270008
$386$	19.7928	1.00742
$387$	5.80365	0.295016
$388$	46.4214	2.35669
$389$	31.6115	1.60277	0.801383	−	0.598152i	$-0.204098\pi$
$389$	31.6115	1.60277	0.801383	+	0.598152i	$0.204098\pi$
$390$	−5.31717	−0.269245
$391$	−8.80922	−0.445501
$392$	−59.1661	−2.98834
$393$	17.8357	0.899692
$394$	−72.0615	−3.63041
$395$	−27.1665	−1.36689
$396$	17.6058	0.884727
$397$	37.0283	1.85840	0.929198	−	0.369581i	$-0.120499\pi$
$397$	37.0283	1.85840	0.929198	+	0.369581i	$0.120499\pi$
$398$	−11.2725	−0.565038
$399$	−0.126072	−0.00631148
$400$	−12.9571	−0.647853
$401$	−1.07202	−0.0535342	−0.0267671	−	0.999642i	$-0.508521\pi$
$401$	−1.07202	−0.0535342	−0.0267671	+	0.999642i	$0.508521\pi$
$402$	−19.3512	−0.965151
$403$	2.02031	0.100639
$404$	−34.8298	−1.73285
$405$	−1.98695	−0.0987321
$406$	−0.488796	−0.0242585
$407$	34.8377	1.72684
$408$	−39.7267	−1.96676
$409$	−27.4749	−1.35855	−0.679273	−	0.733886i	$-0.737705\pi$
$409$	−27.4749	−1.35855	−0.679273	+	0.733886i	$0.737705\pi$
$410$	−17.9895	−0.888440
$411$	6.41753	0.316553
$412$	5.16126	0.254277
$413$	−0.150635	−0.00741224
$414$	−5.02000	−0.246720
$415$	4.81414	0.236317
$416$	−16.0390	−0.786377
$417$	19.7218	0.965779
$418$	14.7229	0.720120
$419$	13.0418	0.637135	0.318567	−	0.947900i	$-0.396798\pi$
$419$	13.0418	0.637135	0.318567	+	0.947900i	$0.396798\pi$
$420$	0.801607	0.0391144
$421$	8.81593	0.429662	0.214831	−	0.976651i	$-0.431080\pi$
$421$	8.81593	0.429662	0.214831	+	0.976651i	$0.431080\pi$
$422$	−26.4823	−1.28914
$423$	1.16815	0.0567975
$424$	35.1365	1.70638
$425$	−4.94041	−0.239645
$426$	−21.3908	−1.03639
$427$	0.00254561	0.000123191 0
$428$	9.52334	0.460328
$429$	3.41115	0.164692
$430$	−30.8590	−1.48815
$431$	−0.407034	−0.0196061	−0.00980306	−	0.999952i	$-0.503120\pi$
$431$	−0.407034	−0.0196061	−0.00980306	+	0.999952i	$0.503120\pi$
$432$	−12.3160	−0.592556
$433$	−3.78436	−0.181865	−0.0909324	−	0.995857i	$-0.528985\pi$
$433$	−3.78436	−0.181865	−0.0909324	+	0.995857i	$0.528985\pi$
$434$	−0.422602	−0.0202856
$435$	−4.64300	−0.222615
$436$	84.0979	4.02756
$437$	−3.02557	−0.144732
$438$	6.13642	0.293209
$439$	8.42124	0.401924	0.200962	−	0.979599i	$-0.435593\pi$
$439$	8.42124	0.401924	0.200962	+	0.979599i	$0.435593\pi$
$440$	−57.3379	−2.73348
$441$	−6.99389	−0.333042
$442$	−12.5667	−0.597739
$443$	−13.2073	−0.627497	−0.313749	−	0.949506i	$-0.601585\pi$
$443$	−13.2073	−0.627497	−0.313749	+	0.949506i	$0.601585\pi$
$444$	−52.7112	−2.50156
$445$	−8.96305	−0.424889
$446$	−50.6635	−2.39898
$447$	2.84240	0.134441
$448$	1.42960	0.0675421
$449$	27.7854	1.31128	0.655638	−	0.755075i	$-0.272400\pi$
$449$	27.7854	1.31128	0.655638	+	0.755075i	$0.272400\pi$
$450$	−2.81533	−0.132716
$451$	11.5409	0.543442
$452$	−1.58763	−0.0746758
$453$	−8.48014	−0.398432
$454$	8.23931	0.386690
$455$	0.155312	0.00728116
$456$	−13.6443	−0.638953
$457$	11.3542	0.531126	0.265563	−	0.964094i	$-0.414442\pi$
$457$	11.3542	0.531126	0.265563	+	0.964094i	$0.414442\pi$
$458$	−43.8264	−2.04787
$459$	−4.69600	−0.219191
$460$	19.2376	0.896957
$461$	33.8865	1.57825	0.789125	−	0.614233i	$-0.210534\pi$
$461$	33.8865	1.57825	0.789125	+	0.614233i	$0.210534\pi$
$462$	−0.713536	−0.0331967
$463$	−14.4858	−0.673213	−0.336607	−	0.941645i	$-0.609279\pi$
$463$	−14.4858	−0.673213	−0.336607	+	0.941645i	$0.609279\pi$
$464$	−28.7795	−1.33606
$465$	−4.01424	−0.186156
$466$	−40.1591	−1.86033
$467$	−13.1878	−0.610261	−0.305130	−	0.952311i	$-0.598700\pi$
$467$	−13.1878	−0.610261	−0.305130	+	0.952311i	$0.598700\pi$
$468$	−5.16126	−0.238579
$469$	0.565241	0.0261004
$470$	−6.21127	−0.286504
$471$	7.34154	0.338280
$472$	−16.3027	−0.750391
$473$	19.7971	0.910274
$474$	−36.5882	−1.68055
$475$	−1.69681	−0.0778548
$476$	1.89454	0.0868361
$477$	4.15341	0.190171
$478$	−4.10143	−0.187595
$479$	8.77939	0.401141	0.200570	−	0.979679i	$-0.435721\pi$
$479$	8.77939	0.401141	0.200570	+	0.979679i	$0.435721\pi$
$480$	31.8686	1.45460
$481$	−10.2129	−0.465667
$482$	−60.1002	−2.73749
$483$	0.146632	0.00667200
$484$	3.28243	0.149201
$485$	−17.8710	−0.811480
$486$	−2.67605	−0.121388
$487$	1.43077	0.0648342	0.0324171	−	0.999474i	$-0.489680\pi$
$487$	1.43077	0.0648342	0.0324171	+	0.999474i	$0.489680\pi$
$488$	0.275503	0.0124714
$489$	12.4077	0.561098
$490$	37.1877	1.67997
$491$	−24.4644	−1.10406	−0.552032	−	0.833823i	$-0.686148\pi$
$491$	−24.4644	−1.10406	−0.552032	+	0.833823i	$0.686148\pi$
$492$	−17.4620	−0.787250
$493$	−10.9734	−0.494217
$494$	−4.31610	−0.194191
$495$	−6.77778	−0.304639
$496$	−24.8822	−1.11724
$497$	0.624816	0.0280268
$498$	6.48377	0.290545
$499$	17.8097	0.797271	0.398635	−	0.917110i	$-0.369484\pi$
$499$	17.8097	0.797271	0.398635	+	0.917110i	$0.369484\pi$
$500$	62.0645	2.77561
$501$	0.633803	0.0283162
$502$	40.9324	1.82690
$503$	−23.0826	−1.02920	−0.514601	−	0.857430i	$-0.672060\pi$
$503$	−23.0826	−1.02920	−0.514601	+	0.857430i	$0.672060\pi$
$504$	0.661263	0.0294550
$505$	13.4086	0.596673
$506$	−17.1240	−0.761255
$507$	−1.00000	−0.0444116
$508$	−66.0945	−2.93247
$509$	−12.9086	−0.572162	−0.286081	−	0.958205i	$-0.592353\pi$
$509$	−12.9086	−0.572162	−0.286081	+	0.958205i	$0.592353\pi$
$510$	24.9694	1.10567
$511$	−0.179242	−0.00792921
$512$	−10.8425	−0.479176
$513$	−1.61286	−0.0712096
$514$	44.4057	1.95865
$515$	−1.98695	−0.0875553
$516$	−29.9541	−1.31866
$517$	3.98475	0.175249
$518$	2.13630	0.0938637
$519$	−2.07948	−0.0912791
$520$	16.8089	0.737120
$521$	25.9738	1.13793	0.568966	−	0.822361i	$-0.307343\pi$
$521$	25.9738	1.13793	0.568966	+	0.822361i	$0.307343\pi$
$522$	−6.25327	−0.273698
$523$	12.7146	0.555972	0.277986	−	0.960585i	$-0.410333\pi$
$523$	12.7146	0.555972	0.277986	+	0.960585i	$0.410333\pi$
$524$	−92.0546	−4.02142
$525$	0.0822347	0.00358902
$526$	−56.8632	−2.47935
$527$	−9.48736	−0.413276
$528$	−42.0119	−1.82833
$529$	−19.4810	−0.847000
$530$	−22.0844	−0.959284
$531$	−1.92710	−0.0836291
$532$	0.650688	0.0282109
$533$	−3.38329	−0.146547
$534$	−12.0716	−0.522389
$535$	−3.66623	−0.158505
$536$	61.1741	2.64232
$537$	−10.5489	−0.455220
$538$	−10.2334	−0.441195
$539$	−23.8572	−1.02760
$540$	10.2551	0.441311
$541$	20.6920	0.889617	0.444808	−	0.895626i	$-0.353272\pi$
$541$	20.6920	0.889617	0.444808	+	0.895626i	$0.353272\pi$
$542$	9.95809	0.427737
$543$	−18.3019	−0.785410
$544$	75.3192	3.22928
$545$	−32.3755	−1.38681
$546$	0.209177	0.00895196
$547$	30.9466	1.32318	0.661591	−	0.749865i	$-0.269881\pi$
$547$	30.9466	1.32318	0.661591	+	0.749865i	$0.269881\pi$
$548$	−33.1225	−1.41492
$549$	0.0325665	0.00138991
$550$	−9.60353	−0.409496
$551$	−3.76886	−0.160559
$552$	15.8695	0.675451
$553$	1.06873	0.0454469
$554$	−47.8265	−2.03195
$555$	20.2924	0.861365
$556$	−101.789	−4.31682
$557$	−31.9361	−1.35317	−0.676587	−	0.736363i	$-0.736542\pi$
$557$	−31.9361	−1.35317	−0.676587	+	0.736363i	$0.736542\pi$
$558$	−5.40645	−0.228873
$559$	−5.80365	−0.245468
$560$	−1.91283	−0.0808320
$561$	−16.0188	−0.676314
$562$	−25.1682	−1.06165
$563$	−3.72433	−0.156962	−0.0784810	−	0.996916i	$-0.525007\pi$
$563$	−3.72433	−0.156962	−0.0784810	+	0.996916i	$0.525007\pi$
$564$	−6.02914	−0.253872
$565$	0.611195	0.0257132
$566$	−40.7426	−1.71254
$567$	0.0781664	0.00328268
$568$	67.6217	2.83734
$569$	13.3705	0.560522	0.280261	−	0.959924i	$-0.409579\pi$
$569$	13.3705	0.560522	0.280261	+	0.959924i	$0.409579\pi$
$570$	8.57586	0.359203
$571$	−44.2752	−1.85286	−0.926429	−	0.376470i	$-0.877138\pi$
$571$	−44.2752	−1.85286	−0.926429	+	0.376470i	$0.877138\pi$
$572$	−17.6058	−0.736137
$573$	−13.9348	−0.582136
$574$	0.707708	0.0295392
$575$	1.97353	0.0823020
$576$	18.2891	0.762047
$577$	−2.70648	−0.112672	−0.0563360	−	0.998412i	$-0.517942\pi$
$577$	−2.70648	−0.112672	−0.0563360	+	0.998412i	$0.517942\pi$
$578$	13.5206	0.562381
$579$	−7.39625	−0.307378
$580$	23.9637	0.995038
$581$	−0.189388	−0.00785715
$582$	−24.0690	−0.997691
$583$	14.1679	0.586775
$584$	−19.3988	−0.802728
$585$	1.98695	0.0821501
$586$	−2.86906	−0.118520
$587$	−15.0720	−0.622089	−0.311044	−	0.950395i	$-0.600679\pi$
$587$	−15.0720	−0.622089	−0.311044	+	0.950395i	$0.600679\pi$
$588$	36.0973	1.48863
$589$	−3.25848	−0.134263
$590$	10.2467	0.421851
$591$	26.9283	1.10768
$592$	125.782	5.16962
$593$	−12.4532	−0.511391	−0.255695	−	0.966757i	$-0.582304\pi$
$593$	−12.4532	−0.511391	−0.255695	+	0.966757i	$0.582304\pi$
$594$	−9.12843	−0.374544
$595$	−0.729347	−0.0299003
$596$	−14.6704	−0.600921
$597$	4.21235	0.172400
$598$	5.02000	0.205283
$599$	16.7531	0.684512	0.342256	−	0.939607i	$-0.388809\pi$
$599$	16.7531	0.684512	0.342256	+	0.939607i	$0.388809\pi$
$600$	8.89998	0.363340
$601$	−6.98328	−0.284854	−0.142427	−	0.989805i	$-0.545491\pi$
$601$	−6.98328	−0.284854	−0.142427	+	0.989805i	$0.545491\pi$
$602$	1.21399	0.0494786
$603$	7.23125	0.294479
$604$	43.7682	1.78090
$605$	−1.26365	−0.0513746
$606$	18.0589	0.733592
$607$	4.16357	0.168994	0.0844970	−	0.996424i	$-0.473072\pi$
$607$	4.16357	0.168994	0.0844970	+	0.996424i	$0.473072\pi$
$608$	25.8687	1.04911
$609$	0.182655	0.00740157
$610$	−0.173162	−0.00701112
$611$	−1.16815	−0.0472584
$612$	24.2373	0.979733
$613$	25.8080	1.04237	0.521187	−	0.853443i	$-0.325490\pi$
$613$	25.8080	1.04237	0.521187	+	0.853443i	$0.325490\pi$
$614$	−40.9701	−1.65342
$615$	6.72242	0.271074
$616$	2.25567	0.0908835
$617$	27.4369	1.10457	0.552284	−	0.833656i	$-0.313757\pi$
$617$	27.4369	1.10457	0.552284	+	0.833656i	$0.313757\pi$
$618$	−2.67605	−0.107647
$619$	11.9361	0.479753	0.239876	−	0.970803i	$-0.422893\pi$
$619$	11.9361	0.479753	0.239876	+	0.970803i	$0.422893\pi$
$620$	20.7185	0.832075
$621$	1.87590	0.0752772
$622$	81.4999	3.26785
$623$	0.352606	0.0141269
$624$	12.3160	0.493036
$625$	−18.6330	−0.745319
$626$	−80.4877	−3.21693
$627$	−5.50172	−0.219718
$628$	−37.8915	−1.51204
$629$	47.9597	1.91228
$630$	−0.415624	−0.0165589
$631$	−15.7171	−0.625687	−0.312844	−	0.949805i	$-0.601282\pi$
$631$	−15.7171	−0.625687	−0.312844	+	0.949805i	$0.601282\pi$
$632$	115.665	4.60090
$633$	9.89604	0.393332
$634$	0.693319	0.0275352
$635$	25.4446	1.00974
$636$	−21.4368	−0.850024
$637$	6.99389	0.277108
$638$	−21.3309	−0.844497
$639$	7.99341	0.316214
$640$	−33.5092	−1.32457
$641$	2.84004	0.112175	0.0560875	−	0.998426i	$-0.482137\pi$
$641$	2.84004	0.112175	0.0560875	+	0.998426i	$0.482137\pi$
$642$	−4.93774	−0.194877
$643$	21.7991	0.859672	0.429836	−	0.902907i	$-0.358571\pi$
$643$	21.7991	0.859672	0.429836	+	0.902907i	$0.358571\pi$
$644$	−0.756806	−0.0298223
$645$	11.5315	0.454054
$646$	20.2684	0.797451
$647$	39.0395	1.53480	0.767400	−	0.641169i	$-0.221550\pi$
$647$	39.0395	1.53480	0.767400	+	0.641169i	$0.221550\pi$
$648$	8.45968	0.332328
$649$	−6.57364	−0.258038
$650$	2.81533	0.110426
$651$	0.157920	0.00618938
$652$	−64.0395	−2.50798
$653$	31.9913	1.25192	0.625958	−	0.779857i	$-0.284708\pi$
$653$	31.9913	1.25192	0.625958	+	0.779857i	$0.284708\pi$
$654$	−43.6038	−1.70504
$655$	35.4386	1.38470
$656$	41.6688	1.62689
$657$	−2.29309	−0.0894618
$658$	0.244351	0.00952580
$659$	−4.33592	−0.168904	−0.0844518	−	0.996428i	$-0.526914\pi$
$659$	−4.33592	−0.168904	−0.0844518	+	0.996428i	$0.526914\pi$
$660$	34.9818	1.36167
$661$	−42.6439	−1.65865	−0.829327	−	0.558763i	$-0.811276\pi$
$661$	−42.6439	−1.65865	−0.829327	+	0.558763i	$0.811276\pi$
$662$	−57.9918	−2.25392
$663$	4.69600	0.182378
$664$	−20.4969	−0.795432
$665$	−0.250497	−0.00971388
$666$	27.3302	1.05902
$667$	4.38351	0.169730
$668$	−3.27122	−0.126567
$669$	18.9322	0.731960
$670$	−38.4498	−1.48545
$671$	0.111090	0.00428856
$672$	−1.25371	−0.0483630
$673$	−30.6850	−1.18282	−0.591410	−	0.806371i	$-0.701429\pi$
$673$	−30.6850	−1.18282	−0.591410	+	0.806371i	$0.701429\pi$
$674$	−9.05109	−0.348635
$675$	1.05205	0.0404933
$676$	5.16126	0.198510
$677$	19.0683	0.732856	0.366428	−	0.930446i	$-0.380581\pi$
$677$	19.0683	0.732856	0.366428	+	0.930446i	$0.380581\pi$
$678$	0.823168	0.0316136
$679$	0.703045	0.0269804
$680$	−78.9348	−3.02701
$681$	−3.07891	−0.117984
$682$	−18.4422	−0.706189
$683$	−27.7627	−1.06231	−0.531156	−	0.847274i	$-0.678242\pi$
$683$	−27.7627	−1.06231	−0.531156	+	0.847274i	$0.678242\pi$
$684$	8.32439	0.318291
$685$	12.7513	0.487201
$686$	−2.92720	−0.111761
$687$	16.3773	0.624831
$688$	71.4780	2.72507
$689$	−4.15341	−0.158232
$690$	−9.97447	−0.379722
$691$	3.75477	0.142838	0.0714191	−	0.997446i	$-0.477247\pi$
$691$	3.75477	0.142838	0.0714191	+	0.997446i	$0.477247\pi$
$692$	10.7327	0.407997
$693$	0.266638	0.0101287
$694$	2.68859	0.102058
$695$	39.1861	1.48641
$696$	19.7682	0.749311
$697$	15.8880	0.601799
$698$	−73.0304	−2.76424
$699$	15.0068	0.567611
$700$	−0.424434	−0.0160421
$701$	−24.6555	−0.931226	−0.465613	−	0.884989i	$-0.654166\pi$
$701$	−24.6555	−0.931226	−0.465613	+	0.884989i	$0.654166\pi$
$702$	2.67605	0.101001
$703$	16.4720	0.621252
$704$	62.3871	2.35130
$705$	2.32106	0.0874160
$706$	29.8437	1.12318
$707$	−0.527493	−0.0198384
$708$	9.94626	0.373803
$709$	1.52489	0.0572686	0.0286343	−	0.999590i	$-0.490884\pi$
$709$	1.52489	0.0572686	0.0286343	+	0.999590i	$0.490884\pi$
$710$	−42.5023	−1.59508
$711$	13.6725	0.512758
$712$	38.1614	1.43016
$713$	3.78989	0.141932
$714$	−0.982297	−0.0367615
$715$	6.77778	0.253475
$716$	54.4457	2.03473
$717$	1.53264	0.0572375
$718$	−6.94527	−0.259195
$719$	−3.92739	−0.146467	−0.0732334	−	0.997315i	$-0.523332\pi$
$719$	−3.92739	−0.146467	−0.0732334	+	0.997315i	$0.523332\pi$
$720$	−24.4713	−0.911992
$721$	0.0781664	0.00291107
$722$	−43.8837	−1.63318
$723$	22.4585	0.835242
$724$	94.4608	3.51061
$725$	2.45837	0.0913017
$726$	−1.70190	−0.0631635
$727$	40.8329	1.51441	0.757204	−	0.653179i	$-0.226565\pi$
$727$	40.8329	1.51441	0.757204	+	0.653179i	$0.226565\pi$
$728$	−0.661263	−0.0245080
$729$	1.00000	0.0370370
$730$	12.1927	0.451273
$731$	27.2539	1.00802
$732$	−0.168084	−0.00621257
$733$	−14.7840	−0.546058	−0.273029	−	0.962006i	$-0.588026\pi$
$733$	−14.7840	−0.546058	−0.273029	+	0.962006i	$0.588026\pi$
$734$	−52.2212	−1.92752
$735$	−13.8965	−0.512579
$736$	−30.0875	−1.10904
$737$	24.6669	0.908618
$738$	9.05387	0.333278
$739$	−5.19135	−0.190967	−0.0954835	−	0.995431i	$-0.530440\pi$
$739$	−5.19135	−0.190967	−0.0954835	+	0.995431i	$0.530440\pi$
$740$	−104.734	−3.85011
$741$	1.61286	0.0592500
$742$	0.868798	0.0318946
$743$	−0.265922	−0.00975575	−0.00487787	−	0.999988i	$-0.501553\pi$
$743$	−0.265922	−0.00975575	−0.00487787	+	0.999988i	$0.501553\pi$
$744$	17.0912	0.626592
$745$	5.64769	0.206916
$746$	−17.3824	−0.636415
$747$	−2.42289	−0.0886488
$748$	82.6770	3.02297
$749$	0.144230	0.00527003
$750$	−32.1798	−1.17504
$751$	27.4497	1.00165	0.500826	−	0.865548i	$-0.333030\pi$
$751$	27.4497	1.00165	0.500826	+	0.865548i	$0.333030\pi$
$752$	14.3870	0.524641
$753$	−15.2958	−0.557410
$754$	6.25327	0.227731
$755$	−16.8496	−0.613219
$756$	−0.403437	−0.0146729
$757$	36.0816	1.31141	0.655704	−	0.755018i	$-0.272372\pi$
$757$	36.0816	1.31141	0.655704	+	0.755018i	$0.272372\pi$
$758$	−18.4330	−0.669518
$759$	6.39898	0.232268
$760$	−27.1105	−0.983401
$761$	−46.3677	−1.68083	−0.840413	−	0.541946i	$-0.817688\pi$
$761$	−46.3677	−1.68083	−0.840413	+	0.541946i	$0.817688\pi$
$762$	34.2693	1.24144
$763$	1.27365	0.0461092
$764$	71.9212	2.60202
$765$	−9.33070	−0.337352
$766$	21.6464	0.782116
$767$	1.92710	0.0695836
$768$	−8.55245	−0.308610
$769$	−43.7642	−1.57818	−0.789089	−	0.614279i	$-0.789447\pi$
$769$	−43.7642	−1.57818	−0.789089	+	0.614279i	$0.789447\pi$
$770$	−1.41776	−0.0510924
$771$	−16.5937	−0.597609
$772$	38.1739	1.37391
$773$	−28.7440	−1.03385	−0.516926	−	0.856030i	$-0.672924\pi$
$773$	−28.7440	−1.03385	−0.516926	+	0.856030i	$0.672924\pi$
$774$	15.5309	0.558245
$775$	2.12546	0.0763487
$776$	76.0881	2.73141
$777$	−0.798303	−0.0286390
$778$	84.5940	3.03284
$779$	5.45679	0.195510
$780$	−10.2551	−0.367193
$781$	27.2667	0.975681
$782$	−23.5739	−0.843002
$783$	2.33675	0.0835087
$784$	−86.1371	−3.07632
$785$	14.5872	0.520641
$786$	47.7292	1.70245
$787$	7.62457	0.271786	0.135893	−	0.990723i	$-0.456610\pi$
$787$	7.62457	0.271786	0.135893	+	0.990723i	$0.456610\pi$
$788$	−138.984	−4.95109
$789$	21.2489	0.756481
$790$	−72.6988	−2.58651
$791$	−0.0240444	−0.000854920 0
$792$	28.8573	1.02540
$793$	−0.0325665	−0.00115647
$794$	99.0896	3.51656
$795$	8.25259	0.292689
$796$	−21.7410	−0.770590
$797$	3.07198	0.108815	0.0544075	−	0.998519i	$-0.482673\pi$
$797$	3.07198	0.108815	0.0544075	+	0.998519i	$0.482673\pi$
$798$	−0.337374	−0.0119429
$799$	5.48565	0.194068
$800$	−16.8738	−0.596579
$801$	4.51097	0.159387
$802$	−2.86879	−0.101300
$803$	−7.82207	−0.276035
$804$	−37.3223	−1.31626
$805$	0.291350	0.0102687
$806$	5.40645	0.190434
$807$	3.82408	0.134614
$808$	−57.0887	−2.00837
$809$	42.7746	1.50388	0.751938	−	0.659234i	$-0.229119\pi$
$809$	42.7746	1.50388	0.751938	+	0.659234i	$0.229119\pi$
$810$	−5.31717	−0.186826
$811$	7.17466	0.251936	0.125968	−	0.992034i	$-0.459796\pi$
$811$	7.17466	0.251936	0.125968	+	0.992034i	$0.459796\pi$
$812$	−0.942731	−0.0330834
$813$	−3.72119	−0.130508
$814$	93.2274	3.26762
$815$	24.6535	0.863575
$816$	−57.8362	−2.02467
$817$	9.36049	0.327482
$818$	−73.5242	−2.57071
$819$	−0.0781664	−0.00273136
$820$	−34.6961	−1.21164
$821$	−42.1115	−1.46970	−0.734850	−	0.678230i	$-0.762747\pi$
$821$	−42.1115	−1.46970	−0.734850	+	0.678230i	$0.762747\pi$
$822$	17.1736	0.598999
$823$	−8.88884	−0.309845	−0.154923	−	0.987927i	$-0.549513\pi$
$823$	−8.88884	−0.309845	−0.154923	+	0.987927i	$0.549513\pi$
$824$	8.45968	0.294707
$825$	3.58869	0.124942
$826$	−0.403106	−0.0140259
$827$	19.0869	0.663715	0.331857	−	0.943330i	$-0.392325\pi$
$827$	19.0869	0.663715	0.331857	+	0.943330i	$0.392325\pi$
$828$	−9.68199	−0.336472
$829$	−41.3723	−1.43692	−0.718460	−	0.695568i	$-0.755153\pi$
$829$	−41.3723	−1.43692	−0.718460	+	0.695568i	$0.755153\pi$
$830$	12.8829	0.447172
$831$	17.8720	0.619974
$832$	−18.2891	−0.634062
$833$	−32.8433	−1.13795
$834$	52.7765	1.82750
$835$	1.25933	0.0435810
$836$	28.3958	0.982089
$837$	2.02031	0.0698320
$838$	34.9006	1.20562
$839$	13.8763	0.479063	0.239531	−	0.970889i	$-0.423006\pi$
$839$	13.8763	0.479063	0.239531	+	0.970889i	$0.423006\pi$
$840$	1.31389	0.0453336
$841$	−23.5396	−0.811710
$842$	23.5919	0.813030
$843$	9.40496	0.323924
$844$	−51.0760	−1.75811
$845$	−1.98695	−0.0683530
$846$	3.12604	0.107475
$847$	0.0497119	0.00170812
$848$	51.1535	1.75662
$849$	15.2249	0.522517
$850$	−13.2208	−0.453470
$851$	−19.1583	−0.656738
$852$	−41.2560	−1.41341
$853$	5.20393	0.178179	0.0890897	−	0.996024i	$-0.471604\pi$
$853$	5.20393	0.178179	0.0890897	+	0.996024i	$0.471604\pi$
$854$	0.00681218	0.000233108 0
$855$	−3.20467	−0.109597
$856$	15.6095	0.533521
$857$	31.3296	1.07020	0.535099	−	0.844789i	$-0.320274\pi$
$857$	31.3296	1.07020	0.535099	+	0.844789i	$0.320274\pi$
$858$	9.12843	0.311639
$859$	15.4525	0.527231	0.263616	−	0.964628i	$-0.415085\pi$
$859$	15.4525	0.527231	0.263616	+	0.964628i	$0.415085\pi$
$860$	−59.5172	−2.02952
$861$	−0.264460	−0.00901277
$862$	−1.08924	−0.0370998
$863$	21.7909	0.741771	0.370885	−	0.928679i	$-0.379054\pi$
$863$	21.7909	0.741771	0.370885	+	0.928679i	$0.379054\pi$
$864$	−16.0390	−0.545658
$865$	−4.13182	−0.140486
$866$	−10.1271	−0.344134
$867$	−5.05243	−0.171589
$868$	−0.815066	−0.0276651
$869$	46.6389	1.58212
$870$	−12.4249	−0.421244
$871$	−7.23125	−0.245022
$872$	137.843	4.66795
$873$	8.99421	0.304408
$874$	−8.09657	−0.273871
$875$	0.939958	0.0317764
$876$	11.8352	0.399875
$877$	−17.2407	−0.582178	−0.291089	−	0.956696i	$-0.594018\pi$
$877$	−17.2407	−0.582178	−0.291089	+	0.956696i	$0.594018\pi$
$878$	22.5357	0.760542
$879$	1.07212	0.0361618
$880$	−83.4754	−2.81396
$881$	−5.69584	−0.191898	−0.0959489	−	0.995386i	$-0.530589\pi$
$881$	−5.69584	−0.191898	−0.0959489	+	0.995386i	$0.530589\pi$
$882$	−18.7160	−0.630201
$883$	20.6253	0.694096	0.347048	−	0.937847i	$-0.387184\pi$
$883$	20.6253	0.694096	0.347048	+	0.937847i	$0.387184\pi$
$884$	−24.2373	−0.815187
$885$	−3.82905	−0.128712
$886$	−35.3434	−1.18738
$887$	23.3933	0.785472	0.392736	−	0.919651i	$-0.371529\pi$
$887$	23.3933	0.785472	0.392736	+	0.919651i	$0.371529\pi$
$888$	−86.3977	−2.89932
$889$	−1.00099	−0.0335722
$890$	−23.9856	−0.803999
$891$	3.41115	0.114278
$892$	−97.7137	−3.27170
$893$	1.88407	0.0630480
$894$	7.60641	0.254396
$895$	−20.9602	−0.700621
$896$	1.31825	0.0440397
$897$	−1.87590	−0.0626344
$898$	74.3553	2.48127
$899$	4.72095	0.157453
$900$	−5.42988	−0.180996
$901$	19.5044	0.649786
$902$	30.8841	1.02833
$903$	−0.453650	−0.0150965
$904$	−2.60224	−0.0865493
$905$	−36.3649	−1.20881
$906$	−22.6933	−0.753934
$907$	4.00600	0.133017	0.0665086	−	0.997786i	$-0.478814\pi$
$907$	4.00600	0.133017	0.0665086	+	0.997786i	$0.478814\pi$
$908$	15.8910	0.527362
$909$	−6.74833	−0.223828
$910$	0.415624	0.0137778
$911$	27.4729	0.910216	0.455108	−	0.890436i	$-0.349601\pi$
$911$	27.4729	0.910216	0.455108	+	0.890436i	$0.349601\pi$
$912$	−19.8641	−0.657766
$913$	−8.26484	−0.273526
$914$	30.3843	1.00502
$915$	0.0647080	0.00213918
$916$	−84.5272	−2.79286
$917$	−1.39415	−0.0460390
$918$	−12.5667	−0.414764
$919$	−8.50093	−0.280420	−0.140210	−	0.990122i	$-0.544778\pi$
$919$	−8.50093	−0.280420	−0.140210	+	0.990122i	$0.544778\pi$
$920$	31.5318	1.03957
$921$	15.3099	0.504478
$922$	90.6820	2.98645
$923$	−7.99341	−0.263106
$924$	−1.37619	−0.0452732
$925$	−10.7444	−0.353274
$926$	−38.7648	−1.27389
$927$	1.00000	0.0328443
$928$	−37.4792	−1.23031
$929$	7.57882	0.248653	0.124326	−	0.992241i	$-0.460323\pi$
$929$	7.57882	0.248653	0.124326	+	0.992241i	$0.460323\pi$
$930$	−10.7423	−0.352254
$931$	−11.2802	−0.369693
$932$	−77.4541	−2.53709
$933$	−30.4553	−0.997061
$934$	−35.2914	−1.15477
$935$	−31.8285	−1.04090
$936$	−8.45968	−0.276513
$937$	−60.5706	−1.97876	−0.989378	−	0.145366i	$-0.953564\pi$
$937$	−60.5706	−1.97876	−0.989378	+	0.145366i	$0.953564\pi$
$938$	1.51261	0.0493886
$939$	30.0770	0.981526
$940$	−11.9796	−0.390730
$941$	−18.7743	−0.612024	−0.306012	−	0.952028i	$-0.598995\pi$
$941$	−18.7743	−0.612024	−0.306012	+	0.952028i	$0.598995\pi$
$942$	19.6463	0.640112
$943$	−6.34671	−0.206677
$944$	−23.7343	−0.772485
$945$	0.155312	0.00505231
$946$	52.9782	1.72247
$947$	−23.4867	−0.763214	−0.381607	−	0.924325i	$-0.624629\pi$
$947$	−23.4867	−0.763214	−0.381607	+	0.924325i	$0.624629\pi$
$948$	−70.5671	−2.29191
$949$	2.29309	0.0744367
$950$	−4.54074	−0.147321
$951$	−0.259083	−0.00840133
$952$	3.10529	0.100643
$953$	42.6285	1.38087	0.690436	−	0.723393i	$-0.257419\pi$
$953$	42.6285	1.38087	0.690436	+	0.723393i	$0.257419\pi$
$954$	11.1147	0.359853
$955$	−27.6877	−0.895954
$956$	−7.91035	−0.255839
$957$	7.97102	0.257667
$958$	23.4941	0.759060
$959$	−0.501635	−0.0161986
$960$	36.3395	1.17285
$961$	−26.9184	−0.868334
$962$	−27.3302	−0.881160
$963$	1.84516	0.0594594
$964$	−115.914	−3.73334
$965$	−14.6960	−0.473079
$966$	0.392395	0.0126251
$967$	57.8119	1.85910	0.929552	−	0.368690i	$-0.120194\pi$
$967$	57.8119	1.85910	0.929552	+	0.368690i	$0.120194\pi$
$968$	5.38015	0.172925
$969$	−7.57400	−0.243312
$970$	−47.8237	−1.53553
$971$	−33.6047	−1.07843	−0.539213	−	0.842169i	$-0.681278\pi$
$971$	−33.6047	−1.07843	−0.539213	+	0.842169i	$0.681278\pi$
$972$	−5.16126	−0.165547
$973$	−1.54158	−0.0494208
$974$	3.82881	0.122683
$975$	−1.05205	−0.0336925
$976$	0.401091	0.0128386
$977$	38.9322	1.24555	0.622776	−	0.782401i	$-0.286005\pi$
$977$	38.9322	1.24555	0.622776	+	0.782401i	$0.286005\pi$
$978$	33.2038	1.06174
$979$	15.3876	0.491790
$980$	71.7233	2.29112
$981$	16.2941	0.520230
$982$	−65.4681	−2.08917
$983$	−6.41611	−0.204642	−0.102321	−	0.994751i	$-0.532627\pi$
$983$	−6.41611	−0.204642	−0.102321	+	0.994751i	$0.532627\pi$
$984$	−28.6216	−0.912423
$985$	53.5051	1.70481
$986$	−29.3654	−0.935184
$987$	−0.0913103	−0.00290644
$988$	−8.32439	−0.264834
$989$	−10.8871	−0.346188
$990$	−18.1377	−0.576454
$991$	−11.9825	−0.380638	−0.190319	−	0.981722i	$-0.560952\pi$
$991$	−11.9825	−0.380638	−0.190319	+	0.981722i	$0.560952\pi$
$992$	−32.4037	−1.02882
$993$	21.6707	0.687698
$994$	1.67204	0.0530339
$995$	8.36971	0.265338
$996$	12.5051	0.396240
$997$	−21.6855	−0.686788	−0.343394	−	0.939191i	$-0.611577\pi$
$997$	−21.6855	−0.686788	−0.343394	+	0.939191i	$0.611577\pi$
$998$	47.6596	1.50864
$999$	−10.2129	−0.323121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.23	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.23	✓	24	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+2.67605 q^{2} -1.00000 q^{3} +5.16126 q^{4} -1.98695 q^{5} -2.67605 q^{6} +0.0781664 q^{7} +8.45968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.67605 q^{2} -1.00000 q^{3} +5.16126 q^{4} -1.98695 q^{5} -2.67605 q^{6} +0.0781664 q^{7} +8.45968 q^{8} +1.00000 q^{9} -5.31717 q^{10} +3.41115 q^{11} -5.16126 q^{12} -1.00000 q^{13} +0.209177 q^{14} +1.98695 q^{15} +12.3160 q^{16} +4.69600 q^{17} +2.67605 q^{18} +1.61286 q^{19} -10.2551 q^{20} -0.0781664 q^{21} +9.12843 q^{22} -1.87590 q^{23} -8.45968 q^{24} -1.05205 q^{25} -2.67605 q^{26} -1.00000 q^{27} +0.403437 q^{28} -2.33675 q^{29} +5.31717 q^{30} -2.02031 q^{31} +16.0390 q^{32} -3.41115 q^{33} +12.5667 q^{34} -0.155312 q^{35} +5.16126 q^{36} +10.2129 q^{37} +4.31610 q^{38} +1.00000 q^{39} -16.8089 q^{40} +3.38329 q^{41} -0.209177 q^{42} +5.80365 q^{43} +17.6058 q^{44} -1.98695 q^{45} -5.02000 q^{46} +1.16815 q^{47} -12.3160 q^{48} -6.99389 q^{49} -2.81533 q^{50} -4.69600 q^{51} -5.16126 q^{52} +4.15341 q^{53} -2.67605 q^{54} -6.77778 q^{55} +0.661263 q^{56} -1.61286 q^{57} -6.25327 q^{58} -1.92710 q^{59} +10.2551 q^{60} +0.0325665 q^{61} -5.40645 q^{62} +0.0781664 q^{63} +18.2891 q^{64} +1.98695 q^{65} -9.12843 q^{66} +7.23125 q^{67} +24.2373 q^{68} +1.87590 q^{69} -0.415624 q^{70} +7.99341 q^{71} +8.45968 q^{72} -2.29309 q^{73} +27.3302 q^{74} +1.05205 q^{75} +8.32439 q^{76} +0.266638 q^{77} +2.67605 q^{78} +13.6725 q^{79} -24.4713 q^{80} +1.00000 q^{81} +9.05387 q^{82} -2.42289 q^{83} -0.403437 q^{84} -9.33070 q^{85} +15.5309 q^{86} +2.33675 q^{87} +28.8573 q^{88} +4.51097 q^{89} -5.31717 q^{90} -0.0781664 q^{91} -9.68199 q^{92} +2.02031 q^{93} +3.12604 q^{94} -3.20467 q^{95} -16.0390 q^{96} +8.99421 q^{97} -18.7160 q^{98} +3.41115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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