LMFDB - Embedded newform 8018.2.a.j.1.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.45
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.14966 q^{3} +1.00000 q^{4} +1.08282 q^{5} +3.14966 q^{6} -1.59853 q^{7} +1.00000 q^{8} +6.92039 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.14966 q^{3} +1.00000 q^{4} +1.08282 q^{5} +3.14966 q^{6} -1.59853 q^{7} +1.00000 q^{8} +6.92039 q^{9} +1.08282 q^{10} +5.80588 q^{11} +3.14966 q^{12} +2.89874 q^{13} -1.59853 q^{14} +3.41050 q^{15} +1.00000 q^{16} +3.40555 q^{17} +6.92039 q^{18} -1.00000 q^{19} +1.08282 q^{20} -5.03483 q^{21} +5.80588 q^{22} +2.00239 q^{23} +3.14966 q^{24} -3.82751 q^{25} +2.89874 q^{26} +12.3479 q^{27} -1.59853 q^{28} -3.53612 q^{29} +3.41050 q^{30} -3.83801 q^{31} +1.00000 q^{32} +18.2866 q^{33} +3.40555 q^{34} -1.73091 q^{35} +6.92039 q^{36} +3.57988 q^{37} -1.00000 q^{38} +9.13005 q^{39} +1.08282 q^{40} -4.86480 q^{41} -5.03483 q^{42} -7.60434 q^{43} +5.80588 q^{44} +7.49350 q^{45} +2.00239 q^{46} -7.58790 q^{47} +3.14966 q^{48} -4.44470 q^{49} -3.82751 q^{50} +10.7263 q^{51} +2.89874 q^{52} -11.2908 q^{53} +12.3479 q^{54} +6.28670 q^{55} -1.59853 q^{56} -3.14966 q^{57} -3.53612 q^{58} +8.16716 q^{59} +3.41050 q^{60} -4.47892 q^{61} -3.83801 q^{62} -11.0624 q^{63} +1.00000 q^{64} +3.13880 q^{65} +18.2866 q^{66} +14.6513 q^{67} +3.40555 q^{68} +6.30685 q^{69} -1.73091 q^{70} -9.60188 q^{71} +6.92039 q^{72} -8.36956 q^{73} +3.57988 q^{74} -12.0554 q^{75} -1.00000 q^{76} -9.28087 q^{77} +9.13005 q^{78} +1.39020 q^{79} +1.08282 q^{80} +18.1306 q^{81} -4.86480 q^{82} +4.62327 q^{83} -5.03483 q^{84} +3.68758 q^{85} -7.60434 q^{86} -11.1376 q^{87} +5.80588 q^{88} -1.72278 q^{89} +7.49350 q^{90} -4.63371 q^{91} +2.00239 q^{92} -12.0884 q^{93} -7.58790 q^{94} -1.08282 q^{95} +3.14966 q^{96} -18.1621 q^{97} -4.44470 q^{98} +40.1790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	3.14966	1.81846	0.909230	−	0.416294i	$-0.136671\pi$
$3$	3.14966	1.81846	0.909230	+	0.416294i	$0.136671\pi$
$4$	1.00000	0.500000
$5$	1.08282	0.484250	0.242125	−	0.970245i	$-0.422156\pi$
$5$	1.08282	0.484250	0.242125	+	0.970245i	$0.422156\pi$
$6$	3.14966	1.28585
$7$	−1.59853	−0.604187	−0.302094	−	0.953278i	$-0.597686\pi$
$7$	−1.59853	−0.604187	−0.302094	+	0.953278i	$0.597686\pi$
$8$	1.00000	0.353553
$9$	6.92039	2.30680
$10$	1.08282	0.342416
$11$	5.80588	1.75054	0.875270	−	0.483635i	$-0.160684\pi$
$11$	5.80588	1.75054	0.875270	+	0.483635i	$0.160684\pi$
$12$	3.14966	0.909230
$13$	2.89874	0.803965	0.401982	−	0.915647i	$-0.368321\pi$
$13$	2.89874	0.803965	0.401982	+	0.915647i	$0.368321\pi$
$14$	−1.59853	−0.427225
$15$	3.41050	0.880588
$16$	1.00000	0.250000
$17$	3.40555	0.825967	0.412983	−	0.910739i	$-0.364487\pi$
$17$	3.40555	0.825967	0.412983	+	0.910739i	$0.364487\pi$
$18$	6.92039	1.63115
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.08282	0.242125
$21$	−5.03483	−1.09869
$22$	5.80588	1.23782
$23$	2.00239	0.417527	0.208763	−	0.977966i	$-0.433056\pi$
$23$	2.00239	0.417527	0.208763	+	0.977966i	$0.433056\pi$
$24$	3.14966	0.642923
$25$	−3.82751	−0.765502
$26$	2.89874	0.568489
$27$	12.3479	2.37636
$28$	−1.59853	−0.302094
$29$	−3.53612	−0.656641	−0.328321	−	0.944566i	$-0.606483\pi$
$29$	−3.53612	−0.656641	−0.328321	+	0.944566i	$0.606483\pi$
$30$	3.41050	0.622670
$31$	−3.83801	−0.689326	−0.344663	−	0.938726i	$-0.612007\pi$
$31$	−3.83801	−0.689326	−0.344663	+	0.938726i	$0.612007\pi$
$32$	1.00000	0.176777
$33$	18.2866	3.18329
$34$	3.40555	0.584047
$35$	−1.73091	−0.292577
$36$	6.92039	1.15340
$37$	3.57988	0.588528	0.294264	−	0.955724i	$-0.404926\pi$
$37$	3.57988	0.588528	0.294264	+	0.955724i	$0.404926\pi$
$38$	−1.00000	−0.162221
$39$	9.13005	1.46198
$40$	1.08282	0.171208
$41$	−4.86480	−0.759754	−0.379877	−	0.925037i	$-0.624034\pi$
$41$	−4.86480	−0.759754	−0.379877	+	0.925037i	$0.624034\pi$
$42$	−5.03483	−0.776891
$43$	−7.60434	−1.15965	−0.579826	−	0.814741i	$-0.696879\pi$
$43$	−7.60434	−1.15965	−0.579826	+	0.814741i	$0.696879\pi$
$44$	5.80588	0.875270
$45$	7.49350	1.11706
$46$	2.00239	0.295236
$47$	−7.58790	−1.10681	−0.553405	−	0.832913i	$-0.686672\pi$
$47$	−7.58790	−1.10681	−0.553405	+	0.832913i	$0.686672\pi$
$48$	3.14966	0.454615
$49$	−4.44470	−0.634958
$50$	−3.82751	−0.541292
$51$	10.7263	1.50199
$52$	2.89874	0.401982
$53$	−11.2908	−1.55091	−0.775456	−	0.631402i	$-0.782480\pi$
$53$	−11.2908	−1.55091	−0.775456	+	0.631402i	$0.782480\pi$
$54$	12.3479	1.68034
$55$	6.28670	0.847698
$56$	−1.59853	−0.213612
$57$	−3.14966	−0.417183
$58$	−3.53612	−0.464316
$59$	8.16716	1.06327	0.531637	−	0.846972i	$-0.321577\pi$
$59$	8.16716	1.06327	0.531637	+	0.846972i	$0.321577\pi$
$60$	3.41050	0.440294
$61$	−4.47892	−0.573467	−0.286733	−	0.958010i	$-0.592569\pi$
$61$	−4.47892	−0.573467	−0.286733	+	0.958010i	$0.592569\pi$
$62$	−3.83801	−0.487427
$63$	−11.0624	−1.39374
$64$	1.00000	0.125000
$65$	3.13880	0.389320
$66$	18.2866	2.25092
$67$	14.6513	1.78994	0.894968	−	0.446131i	$-0.147198\pi$
$67$	14.6513	1.78994	0.894968	+	0.446131i	$0.147198\pi$
$68$	3.40555	0.412983
$69$	6.30685	0.759256
$70$	−1.73091	−0.206883
$71$	−9.60188	−1.13953	−0.569767	−	0.821806i	$-0.692967\pi$
$71$	−9.60188	−1.13953	−0.569767	+	0.821806i	$0.692967\pi$
$72$	6.92039	0.815575
$73$	−8.36956	−0.979583	−0.489791	−	0.871840i	$-0.662927\pi$
$73$	−8.36956	−0.979583	−0.489791	+	0.871840i	$0.662927\pi$
$74$	3.57988	0.416152
$75$	−12.0554	−1.39204
$76$	−1.00000	−0.114708
$77$	−9.28087	−1.05765
$78$	9.13005	1.03377
$79$	1.39020	0.156409	0.0782047	−	0.996937i	$-0.475081\pi$
$79$	1.39020	0.156409	0.0782047	+	0.996937i	$0.475081\pi$
$80$	1.08282	0.121062
$81$	18.1306	2.01451
$82$	−4.86480	−0.537227
$83$	4.62327	0.507470	0.253735	−	0.967274i	$-0.418341\pi$
$83$	4.62327	0.507470	0.253735	+	0.967274i	$0.418341\pi$
$84$	−5.03483	−0.549345
$85$	3.68758	0.399974
$86$	−7.60434	−0.819997
$87$	−11.1376	−1.19408
$88$	5.80588	0.618909
$89$	−1.72278	−0.182614	−0.0913071	−	0.995823i	$-0.529104\pi$
$89$	−1.72278	−0.182614	−0.0913071	+	0.995823i	$0.529104\pi$
$90$	7.49350	0.789884
$91$	−4.63371	−0.485745
$92$	2.00239	0.208763
$93$	−12.0884	−1.25351
$94$	−7.58790	−0.782632
$95$	−1.08282	−0.111094
$96$	3.14966	0.321461
$97$	−18.1621	−1.84408	−0.922040	−	0.387094i	$-0.873479\pi$
$97$	−18.1621	−1.84408	−0.922040	+	0.387094i	$0.873479\pi$
$98$	−4.44470	−0.448983
$99$	40.1790	4.03814
$100$	−3.82751	−0.382751
$101$	0.106008	0.0105482	0.00527408	−	0.999986i	$-0.498321\pi$
$101$	0.106008	0.0105482	0.00527408	+	0.999986i	$0.498321\pi$
$102$	10.7263	1.06207
$103$	0.668408	0.0658602	0.0329301	−	0.999458i	$-0.489516\pi$
$103$	0.668408	0.0658602	0.0329301	+	0.999458i	$0.489516\pi$
$104$	2.89874	0.284245
$105$	−5.45179	−0.532040
$106$	−11.2908	−1.09666
$107$	8.95206	0.865428	0.432714	−	0.901531i	$-0.357556\pi$
$107$	8.95206	0.865428	0.432714	+	0.901531i	$0.357556\pi$
$108$	12.3479	1.18818
$109$	0.384301	0.0368094	0.0184047	−	0.999831i	$-0.494141\pi$
$109$	0.384301	0.0368094	0.0184047	+	0.999831i	$0.494141\pi$
$110$	6.28670	0.599413
$111$	11.2754	1.07021
$112$	−1.59853	−0.151047
$113$	20.6174	1.93953	0.969763	−	0.244051i	$-0.0784763\pi$
$113$	20.6174	1.93953	0.969763	+	0.244051i	$0.0784763\pi$
$114$	−3.14966	−0.294993
$115$	2.16822	0.202187
$116$	−3.53612	−0.328321
$117$	20.0604	1.85458
$118$	8.16716	0.751848
$119$	−5.44387	−0.499039
$120$	3.41050	0.311335
$121$	22.7083	2.06439
$122$	−4.47892	−0.405502
$123$	−15.3225	−1.38158
$124$	−3.83801	−0.344663
$125$	−9.55856	−0.854944
$126$	−11.0624	−0.985521
$127$	−10.7218	−0.951405	−0.475703	−	0.879606i	$-0.657806\pi$
$127$	−10.7218	−0.951405	−0.475703	+	0.879606i	$0.657806\pi$
$128$	1.00000	0.0883883
$129$	−23.9511	−2.10878
$130$	3.13880	0.275291
$131$	−10.0558	−0.878577	−0.439289	−	0.898346i	$-0.644769\pi$
$131$	−10.0558	−0.878577	−0.439289	+	0.898346i	$0.644769\pi$
$132$	18.2866	1.59164
$133$	1.59853	0.138610
$134$	14.6513	1.26568
$135$	13.3705	1.15075
$136$	3.40555	0.292023
$137$	1.42682	0.121901	0.0609505	−	0.998141i	$-0.480587\pi$
$137$	1.42682	0.121901	0.0609505	+	0.998141i	$0.480587\pi$
$138$	6.30685	0.536875
$139$	−9.82584	−0.833417	−0.416708	−	0.909040i	$-0.636816\pi$
$139$	−9.82584	−0.833417	−0.416708	+	0.909040i	$0.636816\pi$
$140$	−1.73091	−0.146289
$141$	−23.8993	−2.01269
$142$	−9.60188	−0.805772
$143$	16.8297	1.40737
$144$	6.92039	0.576699
$145$	−3.82897	−0.317978
$146$	−8.36956	−0.692670
$147$	−13.9993	−1.15465
$148$	3.57988	0.294264
$149$	14.9637	1.22587	0.612937	−	0.790132i	$-0.289988\pi$
$149$	14.9637	1.22587	0.612937	+	0.790132i	$0.289988\pi$
$150$	−12.0554	−0.984317
$151$	8.71115	0.708903	0.354451	−	0.935074i	$-0.384668\pi$
$151$	8.71115	0.708903	0.354451	+	0.935074i	$0.384668\pi$
$152$	−1.00000	−0.0811107
$153$	23.5677	1.90534
$154$	−9.28087	−0.747874
$155$	−4.15585	−0.333806
$156$	9.13005	0.730989
$157$	−16.3756	−1.30692	−0.653459	−	0.756962i	$-0.726683\pi$
$157$	−16.3756	−1.30692	−0.653459	+	0.756962i	$0.726683\pi$
$158$	1.39020	0.110598
$159$	−35.5623	−2.82027
$160$	1.08282	0.0856040
$161$	−3.20088	−0.252264
$162$	18.1306	1.42447
$163$	13.3644	1.04678	0.523390	−	0.852093i	$-0.324667\pi$
$163$	13.3644	1.04678	0.523390	+	0.852093i	$0.324667\pi$
$164$	−4.86480	−0.379877
$165$	19.8010	1.54150
$166$	4.62327	0.358836
$167$	−17.3824	−1.34509	−0.672544	−	0.740057i	$-0.734799\pi$
$167$	−17.3824	−1.34509	−0.672544	+	0.740057i	$0.734799\pi$
$168$	−5.03483	−0.388446
$169$	−4.59733	−0.353641
$170$	3.68758	0.282824
$171$	−6.92039	−0.529215
$172$	−7.60434	−0.579826
$173$	7.74831	0.589093	0.294547	−	0.955637i	$-0.404831\pi$
$173$	7.74831	0.589093	0.294547	+	0.955637i	$0.404831\pi$
$174$	−11.1376	−0.844339
$175$	6.11839	0.462507
$176$	5.80588	0.437635
$177$	25.7238	1.93352
$178$	−1.72278	−0.129128
$179$	−10.5455	−0.788205	−0.394103	−	0.919066i	$-0.628945\pi$
$179$	−10.5455	−0.788205	−0.394103	+	0.919066i	$0.628945\pi$
$180$	7.49350	0.558532
$181$	5.35671	0.398161	0.199081	−	0.979983i	$-0.436204\pi$
$181$	5.35671	0.398161	0.199081	+	0.979983i	$0.436204\pi$
$182$	−4.63371	−0.343474
$183$	−14.1071	−1.04283
$184$	2.00239	0.147618
$185$	3.87634	0.284994
$186$	−12.0884	−0.886367
$187$	19.7722	1.44589
$188$	−7.58790	−0.553405
$189$	−19.7385	−1.43576
$190$	−1.08282	−0.0785557
$191$	18.6539	1.34975	0.674873	−	0.737934i	$-0.264198\pi$
$191$	18.6539	1.34975	0.674873	+	0.737934i	$0.264198\pi$
$192$	3.14966	0.227307
$193$	10.0454	0.723081	0.361541	−	0.932356i	$-0.382251\pi$
$193$	10.0454	0.723081	0.361541	+	0.932356i	$0.382251\pi$
$194$	−18.1621	−1.30396
$195$	9.88615	0.707962
$196$	−4.44470	−0.317479
$197$	−24.3580	−1.73544	−0.867718	−	0.497056i	$-0.834414\pi$
$197$	−24.3580	−1.73544	−0.867718	+	0.497056i	$0.834414\pi$
$198$	40.1790	2.85539
$199$	−6.07220	−0.430447	−0.215224	−	0.976565i	$-0.569048\pi$
$199$	−6.07220	−0.430447	−0.215224	+	0.976565i	$0.569048\pi$
$200$	−3.82751	−0.270646
$201$	46.1465	3.25493
$202$	0.106008	0.00745868
$203$	5.65259	0.396734
$204$	10.7263	0.750994
$205$	−5.26768	−0.367911
$206$	0.668408	0.0465702
$207$	13.8573	0.963149
$208$	2.89874	0.200991
$209$	−5.80588	−0.401601
$210$	−5.45179	−0.376209
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−11.2908	−0.775456
$213$	−30.2427	−2.07220
$214$	8.95206	0.611950
$215$	−8.23409	−0.561561
$216$	12.3479	0.840169
$217$	6.13516	0.416482
$218$	0.384301	0.0260282
$219$	−26.3613	−1.78133
$220$	6.28670	0.423849
$221$	9.87179	0.664048
$222$	11.2754	0.756756
$223$	−7.58504	−0.507932	−0.253966	−	0.967213i	$-0.581735\pi$
$223$	−7.58504	−0.507932	−0.253966	+	0.967213i	$0.581735\pi$
$224$	−1.59853	−0.106806
$225$	−26.4879	−1.76586
$226$	20.6174	1.37145
$227$	1.84000	0.122125	0.0610624	−	0.998134i	$-0.480551\pi$
$227$	1.84000	0.122125	0.0610624	+	0.998134i	$0.480551\pi$
$228$	−3.14966	−0.208592
$229$	−28.9472	−1.91289	−0.956444	−	0.291916i	$-0.905707\pi$
$229$	−28.9472	−1.91289	−0.956444	+	0.291916i	$0.905707\pi$
$230$	2.16822	0.142968
$231$	−29.2316	−1.92330
$232$	−3.53612	−0.232158
$233$	11.1199	0.728486	0.364243	−	0.931304i	$-0.381328\pi$
$233$	11.1199	0.728486	0.364243	+	0.931304i	$0.381328\pi$
$234$	20.0604	1.31139
$235$	−8.21629	−0.535972
$236$	8.16716	0.531637
$237$	4.37865	0.284424
$238$	−5.44387	−0.352874
$239$	23.6838	1.53198	0.765989	−	0.642854i	$-0.222250\pi$
$239$	23.6838	1.53198	0.765989	+	0.642854i	$0.222250\pi$
$240$	3.41050	0.220147
$241$	−15.8242	−1.01933	−0.509664	−	0.860373i	$-0.670230\pi$
$241$	−15.8242	−1.01933	−0.509664	+	0.860373i	$0.670230\pi$
$242$	22.7083	1.45974
$243$	20.0616	1.28695
$244$	−4.47892	−0.286733
$245$	−4.81279	−0.307478
$246$	−15.3225	−0.976926
$247$	−2.89874	−0.184442
$248$	−3.83801	−0.243714
$249$	14.5618	0.922814
$250$	−9.55856	−0.604537
$251$	22.6483	1.42955	0.714775	−	0.699355i	$-0.246529\pi$
$251$	22.6483	1.42955	0.714775	+	0.699355i	$0.246529\pi$
$252$	−11.0624	−0.696868
$253$	11.6256	0.730897
$254$	−10.7218	−0.672745
$255$	11.6146	0.727337
$256$	1.00000	0.0625000
$257$	21.3365	1.33094	0.665468	−	0.746426i	$-0.268232\pi$
$257$	21.3365	1.33094	0.665468	+	0.746426i	$0.268232\pi$
$258$	−23.9511	−1.49113
$259$	−5.72254	−0.355581
$260$	3.13880	0.194660
$261$	−24.4713	−1.51474
$262$	−10.0558	−0.621248
$263$	2.30130	0.141904	0.0709521	−	0.997480i	$-0.477396\pi$
$263$	2.30130	0.141904	0.0709521	+	0.997480i	$0.477396\pi$
$264$	18.2866	1.12546
$265$	−12.2259	−0.751028
$266$	1.59853	0.0980121
$267$	−5.42617	−0.332076
$268$	14.6513	0.894968
$269$	−4.54737	−0.277258	−0.138629	−	0.990344i	$-0.544270\pi$
$269$	−4.54737	−0.277258	−0.138629	+	0.990344i	$0.544270\pi$
$270$	13.3705	0.813703
$271$	−10.2889	−0.625004	−0.312502	−	0.949917i	$-0.601167\pi$
$271$	−10.2889	−0.625004	−0.312502	+	0.949917i	$0.601167\pi$
$272$	3.40555	0.206492
$273$	−14.5946	−0.883308
$274$	1.42682	0.0861971
$275$	−22.2221	−1.34004
$276$	6.30685	0.379628
$277$	19.8552	1.19299	0.596493	−	0.802618i	$-0.296560\pi$
$277$	19.8552	1.19299	0.596493	+	0.802618i	$0.296560\pi$
$278$	−9.82584	−0.589315
$279$	−26.5605	−1.59013
$280$	−1.73091	−0.103442
$281$	−11.4627	−0.683809	−0.341904	−	0.939735i	$-0.611072\pi$
$281$	−11.4627	−0.683809	−0.341904	+	0.939735i	$0.611072\pi$
$282$	−23.8993	−1.42319
$283$	13.5285	0.804186	0.402093	−	0.915599i	$-0.368283\pi$
$283$	13.5285	0.804186	0.402093	+	0.915599i	$0.368283\pi$
$284$	−9.60188	−0.569767
$285$	−3.41050	−0.202021
$286$	16.8297	0.995162
$287$	7.77652	0.459034
$288$	6.92039	0.407788
$289$	−5.40223	−0.317779
$290$	−3.82897	−0.224845
$291$	−57.2045	−3.35339
$292$	−8.36956	−0.489791
$293$	−1.84105	−0.107555	−0.0537776	−	0.998553i	$-0.517126\pi$
$293$	−1.84105	−0.107555	−0.0537776	+	0.998553i	$0.517126\pi$
$294$	−13.9993	−0.816457
$295$	8.84352	0.514890
$296$	3.57988	0.208076
$297$	71.6905	4.15990
$298$	14.9637	0.866823
$299$	5.80440	0.335677
$300$	−12.0554	−0.696018
$301$	12.1558	0.700646
$302$	8.71115	0.501270
$303$	0.333889	0.0191814
$304$	−1.00000	−0.0573539
$305$	−4.84984	−0.277701
$306$	23.5677	1.34728
$307$	−23.4408	−1.33783	−0.668917	−	0.743337i	$-0.733242\pi$
$307$	−23.4408	−1.33783	−0.668917	+	0.743337i	$0.733242\pi$
$308$	−9.28087	−0.528827
$309$	2.10526	0.119764
$310$	−4.15585	−0.236036
$311$	34.1635	1.93723	0.968616	−	0.248561i	$-0.0799578\pi$
$311$	34.1635	1.93723	0.968616	+	0.248561i	$0.0799578\pi$
$312$	9.13005	0.516887
$313$	−12.0149	−0.679124	−0.339562	−	0.940584i	$-0.610279\pi$
$313$	−12.0149	−0.679124	−0.339562	+	0.940584i	$0.610279\pi$
$314$	−16.3756	−0.924130
$315$	−11.9786	−0.674916
$316$	1.39020	0.0782047
$317$	30.3908	1.70691	0.853457	−	0.521163i	$-0.174502\pi$
$317$	30.3908	1.70691	0.853457	+	0.521163i	$0.174502\pi$
$318$	−35.5623	−1.99423
$319$	−20.5303	−1.14948
$320$	1.08282	0.0605312
$321$	28.1960	1.57375
$322$	−3.20088	−0.178378
$323$	−3.40555	−0.189490
$324$	18.1306	1.00726
$325$	−11.0949	−0.615437
$326$	13.3644	0.740186
$327$	1.21042	0.0669364
$328$	−4.86480	−0.268614
$329$	12.1295	0.668720
$330$	19.8010	1.09001
$331$	4.96856	0.273097	0.136548	−	0.990633i	$-0.456399\pi$
$331$	4.96856	0.273097	0.136548	+	0.990633i	$0.456399\pi$
$332$	4.62327	0.253735
$333$	24.7741	1.35761
$334$	−17.3824	−0.951121
$335$	15.8646	0.866776
$336$	−5.03483	−0.274673
$337$	−11.0861	−0.603901	−0.301950	−	0.953324i	$-0.597638\pi$
$337$	−11.0861	−0.603901	−0.301950	+	0.953324i	$0.597638\pi$
$338$	−4.59733	−0.250062
$339$	64.9380	3.52695
$340$	3.68758	0.199987
$341$	−22.2830	−1.20669
$342$	−6.92039	−0.374212
$343$	18.2947	0.987821
$344$	−7.60434	−0.409999
$345$	6.82915	0.367669
$346$	7.74831	0.416552
$347$	24.6640	1.32403	0.662017	−	0.749489i	$-0.269701\pi$
$347$	24.6640	1.32403	0.662017	+	0.749489i	$0.269701\pi$
$348$	−11.1376	−0.597038
$349$	25.0300	1.33982	0.669911	−	0.742441i	$-0.266332\pi$
$349$	25.0300	1.33982	0.669911	+	0.742441i	$0.266332\pi$
$350$	6.11839	0.327042
$351$	35.7933	1.91051
$352$	5.80588	0.309455
$353$	33.1854	1.76628	0.883140	−	0.469109i	$-0.155425\pi$
$353$	33.1854	1.76628	0.883140	+	0.469109i	$0.155425\pi$
$354$	25.7238	1.36721
$355$	−10.3971	−0.551819
$356$	−1.72278	−0.0913071
$357$	−17.1464	−0.907482
$358$	−10.5455	−0.557345
$359$	2.26997	0.119804	0.0599022	−	0.998204i	$-0.480921\pi$
$359$	2.26997	0.119804	0.0599022	+	0.998204i	$0.480921\pi$
$360$	7.49350	0.394942
$361$	1.00000	0.0526316
$362$	5.35671	0.281542
$363$	71.5234	3.75401
$364$	−4.63371	−0.242873
$365$	−9.06269	−0.474363
$366$	−14.1071	−0.737389
$367$	−11.1384	−0.581419	−0.290709	−	0.956811i	$-0.593891\pi$
$367$	−11.1384	−0.581419	−0.290709	+	0.956811i	$0.593891\pi$
$368$	2.00239	0.104382
$369$	−33.6663	−1.75260
$370$	3.87634	0.201521
$371$	18.0487	0.937041
$372$	−12.0884	−0.626756
$373$	−35.8338	−1.85540	−0.927702	−	0.373321i	$-0.878219\pi$
$373$	−35.8338	−1.85540	−0.927702	+	0.373321i	$0.878219\pi$
$374$	19.7722	1.02240
$375$	−30.1063	−1.55468
$376$	−7.58790	−0.391316
$377$	−10.2503	−0.527917
$378$	−19.7385	−1.01524
$379$	6.08629	0.312631	0.156316	−	0.987707i	$-0.450038\pi$
$379$	6.08629	0.312631	0.156316	+	0.987707i	$0.450038\pi$
$380$	−1.08282	−0.0555472
$381$	−33.7701	−1.73009
$382$	18.6539	0.954414
$383$	13.7620	0.703205	0.351602	−	0.936149i	$-0.385637\pi$
$383$	13.7620	0.703205	0.351602	+	0.936149i	$0.385637\pi$
$384$	3.14966	0.160731
$385$	−10.0495	−0.512168
$386$	10.0454	0.511296
$387$	−52.6250	−2.67508
$388$	−18.1621	−0.922040
$389$	36.9641	1.87415	0.937077	−	0.349124i	$-0.113521\pi$
$389$	36.9641	1.87415	0.937077	+	0.349124i	$0.113521\pi$
$390$	9.88615	0.500605
$391$	6.81923	0.344863
$392$	−4.44470	−0.224491
$393$	−31.6723	−1.59766
$394$	−24.3580	−1.22714
$395$	1.50533	0.0757412
$396$	40.1790	2.01907
$397$	15.2165	0.763694	0.381847	−	0.924226i	$-0.375288\pi$
$397$	15.2165	0.763694	0.381847	+	0.924226i	$0.375288\pi$
$398$	−6.07220	−0.304372
$399$	5.03483	0.252057
$400$	−3.82751	−0.191376
$401$	34.3279	1.71425	0.857127	−	0.515106i	$-0.172247\pi$
$401$	34.3279	1.71425	0.857127	+	0.515106i	$0.172247\pi$
$402$	46.1465	2.30158
$403$	−11.1254	−0.554194
$404$	0.106008	0.00527408
$405$	19.6321	0.975526
$406$	5.65259	0.280534
$407$	20.7843	1.03024
$408$	10.7263	0.531033
$409$	6.99065	0.345665	0.172833	−	0.984951i	$-0.444708\pi$
$409$	6.99065	0.345665	0.172833	+	0.984951i	$0.444708\pi$
$410$	−5.26768	−0.260152
$411$	4.49399	0.221672
$412$	0.668408	0.0329301
$413$	−13.0554	−0.642416
$414$	13.8573	0.681049
$415$	5.00615	0.245742
$416$	2.89874	0.142122
$417$	−30.9481	−1.51553
$418$	−5.80588	−0.283975
$419$	12.3753	0.604572	0.302286	−	0.953217i	$-0.402250\pi$
$419$	12.3753	0.604572	0.302286	+	0.953217i	$0.402250\pi$
$420$	−5.45179	−0.266020
$421$	40.1368	1.95615	0.978074	−	0.208259i	$-0.0667796\pi$
$421$	40.1368	1.95615	0.978074	+	0.208259i	$0.0667796\pi$
$422$	−1.00000	−0.0486792
$423$	−52.5112	−2.55318
$424$	−11.2908	−0.548330
$425$	−13.0348	−0.632280
$426$	−30.2427	−1.46526
$427$	7.15968	0.346481
$428$	8.95206	0.432714
$429$	53.0080	2.55925
$430$	−8.23409	−0.397083
$431$	−34.6133	−1.66727	−0.833633	−	0.552319i	$-0.813743\pi$
$431$	−34.6133	−1.66727	−0.833633	+	0.552319i	$0.813743\pi$
$432$	12.3479	0.594089
$433$	26.9920	1.29715	0.648577	−	0.761149i	$-0.275365\pi$
$433$	26.9920	1.29715	0.648577	+	0.761149i	$0.275365\pi$
$434$	6.13516	0.294497
$435$	−12.0600	−0.578231
$436$	0.384301	0.0184047
$437$	−2.00239	−0.0957872
$438$	−26.3613	−1.25959
$439$	−2.99789	−0.143081	−0.0715406	−	0.997438i	$-0.522792\pi$
$439$	−2.99789	−0.143081	−0.0715406	+	0.997438i	$0.522792\pi$
$440$	6.28670	0.299706
$441$	−30.7591	−1.46472
$442$	9.87179	0.469553
$443$	−3.46699	−0.164722	−0.0823608	−	0.996603i	$-0.526246\pi$
$443$	−3.46699	−0.164722	−0.0823608	+	0.996603i	$0.526246\pi$
$444$	11.2754	0.535107
$445$	−1.86545	−0.0884308
$446$	−7.58504	−0.359162
$447$	47.1306	2.22920
$448$	−1.59853	−0.0755234
$449$	−28.9706	−1.36721	−0.683603	−	0.729854i	$-0.739588\pi$
$449$	−28.9706	−1.36721	−0.683603	+	0.729854i	$0.739588\pi$
$450$	−26.4879	−1.24865
$451$	−28.2444	−1.32998
$452$	20.6174	0.969763
$453$	27.4372	1.28911
$454$	1.84000	0.0863553
$455$	−5.01746	−0.235222
$456$	−3.14966	−0.147497
$457$	36.9879	1.73022	0.865111	−	0.501581i	$-0.167248\pi$
$457$	36.9879	1.73022	0.865111	+	0.501581i	$0.167248\pi$
$458$	−28.9472	−1.35262
$459$	42.0514	1.96279
$460$	2.16822	0.101094
$461$	6.84579	0.318840	0.159420	−	0.987211i	$-0.449038\pi$
$461$	6.84579	0.318840	0.159420	+	0.987211i	$0.449038\pi$
$462$	−29.2316	−1.35998
$463$	−27.0341	−1.25638	−0.628191	−	0.778059i	$-0.716205\pi$
$463$	−27.0341	−1.25638	−0.628191	+	0.778059i	$0.716205\pi$
$464$	−3.53612	−0.164160
$465$	−13.0895	−0.607013
$466$	11.1199	0.515117
$467$	−31.5885	−1.46174	−0.730871	−	0.682516i	$-0.760886\pi$
$467$	−31.5885	−1.46174	−0.730871	+	0.682516i	$0.760886\pi$
$468$	20.0604	0.927291
$469$	−23.4205	−1.08146
$470$	−8.21629	−0.378989
$471$	−51.5777	−2.37658
$472$	8.16716	0.375924
$473$	−44.1499	−2.03001
$474$	4.37865	0.201118
$475$	3.82751	0.175618
$476$	−5.44387	−0.249519
$477$	−78.1368	−3.57764
$478$	23.6838	1.08327
$479$	14.6566	0.669678	0.334839	−	0.942275i	$-0.391318\pi$
$479$	14.6566	0.669678	0.334839	+	0.942275i	$0.391318\pi$
$480$	3.41050	0.155668
$481$	10.3771	0.473156
$482$	−15.8242	−0.720774
$483$	−10.0817	−0.458733
$484$	22.7083	1.03219
$485$	−19.6662	−0.892995
$486$	20.0616	0.910012
$487$	−26.0487	−1.18038	−0.590189	−	0.807265i	$-0.700947\pi$
$487$	−26.0487	−1.18038	−0.590189	+	0.807265i	$0.700947\pi$
$488$	−4.47892	−0.202751
$489$	42.0934	1.90353
$490$	−4.81279	−0.217420
$491$	−40.4320	−1.82467	−0.912334	−	0.409446i	$-0.865722\pi$
$491$	−40.4320	−1.82467	−0.912334	+	0.409446i	$0.865722\pi$
$492$	−15.3225	−0.690791
$493$	−12.0424	−0.542364
$494$	−2.89874	−0.130420
$495$	43.5064	1.95547
$496$	−3.83801	−0.172332
$497$	15.3489	0.688492
$498$	14.5618	0.652528
$499$	12.5359	0.561186	0.280593	−	0.959827i	$-0.409469\pi$
$499$	12.5359	0.561186	0.280593	+	0.959827i	$0.409469\pi$
$500$	−9.55856	−0.427472
$501$	−54.7486	−2.44599
$502$	22.6483	1.01084
$503$	−11.1251	−0.496045	−0.248022	−	0.968754i	$-0.579781\pi$
$503$	−11.1251	−0.496045	−0.248022	+	0.968754i	$0.579781\pi$
$504$	−11.0624	−0.492760
$505$	0.114787	0.00510795
$506$	11.6256	0.516822
$507$	−14.4800	−0.643081
$508$	−10.7218	−0.475703
$509$	30.8656	1.36809	0.684047	−	0.729438i	$-0.260218\pi$
$509$	30.8656	1.36809	0.684047	+	0.729438i	$0.260218\pi$
$510$	11.6146	0.514305
$511$	13.3790	0.591851
$512$	1.00000	0.0441942
$513$	−12.3479	−0.545173
$514$	21.3365	0.941114
$515$	0.723762	0.0318928
$516$	−23.9511	−1.05439
$517$	−44.0545	−1.93751
$518$	−5.72254	−0.251434
$519$	24.4046	1.07124
$520$	3.13880	0.137645
$521$	27.8090	1.21834	0.609168	−	0.793041i	$-0.291504\pi$
$521$	27.8090	1.21834	0.609168	+	0.793041i	$0.291504\pi$
$522$	−24.4713	−1.07108
$523$	33.1472	1.44942	0.724712	−	0.689051i	$-0.241973\pi$
$523$	33.1472	1.44942	0.724712	+	0.689051i	$0.241973\pi$
$524$	−10.0558	−0.439289
$525$	19.2709	0.841050
$526$	2.30130	0.100341
$527$	−13.0705	−0.569361
$528$	18.2866	0.795821
$529$	−18.9904	−0.825671
$530$	−12.2259	−0.531057
$531$	56.5199	2.45275
$532$	1.59853	0.0693050
$533$	−14.1018	−0.610815
$534$	−5.42617	−0.234813
$535$	9.69342	0.419083
$536$	14.6513	0.632838
$537$	−33.2147	−1.43332
$538$	−4.54737	−0.196051
$539$	−25.8054	−1.11152
$540$	13.3705	0.575375
$541$	1.21683	0.0523156	0.0261578	−	0.999658i	$-0.491673\pi$
$541$	1.21683	0.0523156	0.0261578	+	0.999658i	$0.491673\pi$
$542$	−10.2889	−0.441945
$543$	16.8718	0.724040
$544$	3.40555	0.146012
$545$	0.416127	0.0178249
$546$	−14.5946	−0.624593
$547$	1.16033	0.0496120	0.0248060	−	0.999692i	$-0.492103\pi$
$547$	1.16033	0.0496120	0.0248060	+	0.999692i	$0.492103\pi$
$548$	1.42682	0.0609505
$549$	−30.9958	−1.32287
$550$	−22.2221	−0.947553
$551$	3.53612	0.150644
$552$	6.30685	0.268437
$553$	−2.22227	−0.0945005
$554$	19.8552	0.843569
$555$	12.2092	0.518251
$556$	−9.82584	−0.416708
$557$	32.5171	1.37780	0.688898	−	0.724859i	$-0.258095\pi$
$557$	32.5171	1.37780	0.688898	+	0.724859i	$0.258095\pi$
$558$	−26.5605	−1.12439
$559$	−22.0430	−0.932319
$560$	−1.73091	−0.0731444
$561$	62.2759	2.62929
$562$	−11.4627	−0.483526
$563$	−4.29658	−0.181079	−0.0905396	−	0.995893i	$-0.528859\pi$
$563$	−4.29658	−0.181079	−0.0905396	+	0.995893i	$0.528859\pi$
$564$	−23.8993	−1.00634
$565$	22.3249	0.939214
$566$	13.5285	0.568645
$567$	−28.9823	−1.21714
$568$	−9.60188	−0.402886
$569$	17.5661	0.736407	0.368204	−	0.929745i	$-0.379973\pi$
$569$	17.5661	0.736407	0.368204	+	0.929745i	$0.379973\pi$
$570$	−3.41050	−0.142850
$571$	10.7350	0.449246	0.224623	−	0.974446i	$-0.427885\pi$
$571$	10.7350	0.449246	0.224623	+	0.974446i	$0.427885\pi$
$572$	16.8297	0.703686
$573$	58.7534	2.45446
$574$	7.77652	0.324586
$575$	−7.66416	−0.319618
$576$	6.92039	0.288349
$577$	−18.3486	−0.763861	−0.381930	−	0.924191i	$-0.624741\pi$
$577$	−18.3486	−0.763861	−0.381930	+	0.924191i	$0.624741\pi$
$578$	−5.40223	−0.224703
$579$	31.6395	1.31489
$580$	−3.82897	−0.158989
$581$	−7.39044	−0.306607
$582$	−57.2045	−2.37120
$583$	−65.5531	−2.71493
$584$	−8.36956	−0.346335
$585$	21.7217	0.898081
$586$	−1.84105	−0.0760530
$587$	−35.3702	−1.45988	−0.729942	−	0.683509i	$-0.760453\pi$
$587$	−35.3702	−1.45988	−0.729942	+	0.683509i	$0.760453\pi$
$588$	−13.9993	−0.577323
$589$	3.83801	0.158142
$590$	8.84352	0.364082
$591$	−76.7196	−3.15582
$592$	3.57988	0.147132
$593$	−1.85973	−0.0763699	−0.0381850	−	0.999271i	$-0.512158\pi$
$593$	−1.85973	−0.0763699	−0.0381850	+	0.999271i	$0.512158\pi$
$594$	71.6905	2.94150
$595$	−5.89470	−0.241659
$596$	14.9637	0.612937
$597$	−19.1254	−0.782751
$598$	5.80440	0.237359
$599$	−12.9633	−0.529665	−0.264833	−	0.964294i	$-0.585317\pi$
$599$	−12.9633	−0.529665	−0.264833	+	0.964294i	$0.585317\pi$
$600$	−12.0554	−0.492159
$601$	−28.6224	−1.16753	−0.583766	−	0.811922i	$-0.698422\pi$
$601$	−28.6224	−1.16753	−0.583766	+	0.811922i	$0.698422\pi$
$602$	12.1558	0.495432
$603$	101.392	4.12902
$604$	8.71115	0.354451
$605$	24.5889	0.999679
$606$	0.333889	0.0135633
$607$	−27.4096	−1.11252	−0.556261	−	0.831007i	$-0.687765\pi$
$607$	−27.4096	−1.11252	−0.556261	+	0.831007i	$0.687765\pi$
$608$	−1.00000	−0.0405554
$609$	17.8038	0.721445
$610$	−4.84984	−0.196364
$611$	−21.9953	−0.889836
$612$	23.5677	0.952669
$613$	−30.6254	−1.23695	−0.618475	−	0.785805i	$-0.712249\pi$
$613$	−30.6254	−1.23695	−0.618475	+	0.785805i	$0.712249\pi$
$614$	−23.4408	−0.945992
$615$	−16.5914	−0.669030
$616$	−9.28087	−0.373937
$617$	−15.6437	−0.629791	−0.314895	−	0.949126i	$-0.601969\pi$
$617$	−15.6437	−0.629791	−0.314895	+	0.949126i	$0.601969\pi$
$618$	2.10526	0.0846860
$619$	8.86214	0.356199	0.178100	−	0.984012i	$-0.443005\pi$
$619$	8.86214	0.356199	0.178100	+	0.984012i	$0.443005\pi$
$620$	−4.15585	−0.166903
$621$	24.7253	0.992192
$622$	34.1635	1.36983
$623$	2.75391	0.110333
$624$	9.13005	0.365494
$625$	8.78740	0.351496
$626$	−12.0149	−0.480213
$627$	−18.2866	−0.730296
$628$	−16.3756	−0.653459
$629$	12.1914	0.486105
$630$	−11.9786	−0.477238
$631$	−3.44021	−0.136953	−0.0684763	−	0.997653i	$-0.521814\pi$
$631$	−3.44021	−0.136953	−0.0684763	+	0.997653i	$0.521814\pi$
$632$	1.39020	0.0552991
$633$	−3.14966	−0.125188
$634$	30.3908	1.20697
$635$	−11.6097	−0.460718
$636$	−35.5623	−1.41014
$637$	−12.8840	−0.510484
$638$	−20.5303	−0.812803
$639$	−66.4487	−2.62867
$640$	1.08282	0.0428020
$641$	−37.9018	−1.49703	−0.748515	−	0.663118i	$-0.769233\pi$
$641$	−37.9018	−1.49703	−0.748515	+	0.663118i	$0.769233\pi$
$642$	28.1960	1.11281
$643$	−36.0191	−1.42045	−0.710227	−	0.703973i	$-0.751408\pi$
$643$	−36.0191	−1.42045	−0.710227	+	0.703973i	$0.751408\pi$
$644$	−3.20088	−0.126132
$645$	−25.9346	−1.02118
$646$	−3.40555	−0.133990
$647$	3.85348	0.151496	0.0757480	−	0.997127i	$-0.475866\pi$
$647$	3.85348	0.151496	0.0757480	+	0.997127i	$0.475866\pi$
$648$	18.1306	0.712237
$649$	47.4176	1.86130
$650$	−11.0949	−0.435180
$651$	19.3237	0.757356
$652$	13.3644	0.523390
$653$	33.9404	1.32819	0.664096	−	0.747648i	$-0.268817\pi$
$653$	33.9404	1.32819	0.664096	+	0.747648i	$0.268817\pi$
$654$	1.21042	0.0473312
$655$	−10.8885	−0.425451
$656$	−4.86480	−0.189938
$657$	−57.9206	−2.25970
$658$	12.1295	0.472856
$659$	−24.3748	−0.949507	−0.474753	−	0.880119i	$-0.657463\pi$
$659$	−24.3748	−0.949507	−0.474753	+	0.880119i	$0.657463\pi$
$660$	19.8010	0.770752
$661$	−21.2741	−0.827467	−0.413734	−	0.910398i	$-0.635776\pi$
$661$	−21.2741	−0.827467	−0.413734	+	0.910398i	$0.635776\pi$
$662$	4.96856	0.193109
$663$	31.0928	1.20755
$664$	4.62327	0.179418
$665$	1.73091	0.0671219
$666$	24.7741	0.959978
$667$	−7.08069	−0.274165
$668$	−17.3824	−0.672544
$669$	−23.8903	−0.923653
$670$	15.8646	0.612903
$671$	−26.0041	−1.00388
$672$	−5.03483	−0.194223
$673$	−7.41903	−0.285982	−0.142991	−	0.989724i	$-0.545672\pi$
$673$	−7.41903	−0.285982	−0.142991	+	0.989724i	$0.545672\pi$
$674$	−11.0861	−0.427022
$675$	−47.2617	−1.81911
$676$	−4.59733	−0.176820
$677$	2.07054	0.0795772	0.0397886	−	0.999208i	$-0.487332\pi$
$677$	2.07054	0.0795772	0.0397886	+	0.999208i	$0.487332\pi$
$678$	64.9380	2.49393
$679$	29.0326	1.11417
$680$	3.68758	0.141412
$681$	5.79537	0.222079
$682$	−22.2830	−0.853260
$683$	4.73814	0.181300	0.0906499	−	0.995883i	$-0.471106\pi$
$683$	4.73814	0.181300	0.0906499	+	0.995883i	$0.471106\pi$
$684$	−6.92039	−0.264608
$685$	1.54498	0.0590305
$686$	18.2947	0.698495
$687$	−91.1741	−3.47851
$688$	−7.60434	−0.289913
$689$	−32.7291	−1.24688
$690$	6.82915	0.259981
$691$	10.7447	0.408748	0.204374	−	0.978893i	$-0.434484\pi$
$691$	10.7447	0.408748	0.204374	+	0.978893i	$0.434484\pi$
$692$	7.74831	0.294547
$693$	−64.2272	−2.43979
$694$	24.6640	0.936233
$695$	−10.6396	−0.403582
$696$	−11.1376	−0.422170
$697$	−16.5673	−0.627532
$698$	25.0300	0.947398
$699$	35.0238	1.32472
$700$	6.11839	0.231253
$701$	−19.7540	−0.746097	−0.373049	−	0.927812i	$-0.621688\pi$
$701$	−19.7540	−0.746097	−0.373049	+	0.927812i	$0.621688\pi$
$702$	35.7933	1.35093
$703$	−3.57988	−0.135018
$704$	5.80588	0.218817
$705$	−25.8786	−0.974643
$706$	33.1854	1.24895
$707$	−0.169457	−0.00637307
$708$	25.7238	0.966760
$709$	3.33196	0.125134	0.0625672	−	0.998041i	$-0.480071\pi$
$709$	3.33196	0.125134	0.0625672	+	0.998041i	$0.480071\pi$
$710$	−10.3971	−0.390195
$711$	9.62070	0.360804
$712$	−1.72278	−0.0645638
$713$	−7.68518	−0.287812
$714$	−17.1464	−0.641687
$715$	18.2235	0.681519
$716$	−10.5455	−0.394103
$717$	74.5960	2.78584
$718$	2.26997	0.0847145
$719$	−7.09847	−0.264728	−0.132364	−	0.991201i	$-0.542257\pi$
$719$	−7.09847	−0.264728	−0.132364	+	0.991201i	$0.542257\pi$
$720$	7.49350	0.279266
$721$	−1.06847	−0.0397919
$722$	1.00000	0.0372161
$723$	−49.8410	−1.85361
$724$	5.35671	0.199081
$725$	13.5345	0.502660
$726$	71.5234	2.65448
$727$	−28.0388	−1.03990	−0.519950	−	0.854197i	$-0.674049\pi$
$727$	−28.0388	−1.03990	−0.519950	+	0.854197i	$0.674049\pi$
$728$	−4.63371	−0.171737
$729$	8.79548	0.325759
$730$	−9.06269	−0.335425
$731$	−25.8970	−0.957834
$732$	−14.1071	−0.521413
$733$	5.03396	0.185933	0.0929667	−	0.995669i	$-0.470365\pi$
$733$	5.03396	0.185933	0.0929667	+	0.995669i	$0.470365\pi$
$734$	−11.1384	−0.411125
$735$	−15.1587	−0.559136
$736$	2.00239	0.0738090
$737$	85.0635	3.13335
$738$	−33.6663	−1.23927
$739$	30.3065	1.11484	0.557421	−	0.830230i	$-0.311791\pi$
$739$	30.3065	1.11484	0.557421	+	0.830230i	$0.311791\pi$
$740$	3.87634	0.142497
$741$	−9.13005	−0.335401
$742$	18.0487	0.662588
$743$	−21.6437	−0.794030	−0.397015	−	0.917812i	$-0.629954\pi$
$743$	−21.6437	−0.794030	−0.397015	+	0.917812i	$0.629954\pi$
$744$	−12.0884	−0.443183
$745$	16.2029	0.593629
$746$	−35.8338	−1.31197
$747$	31.9948	1.17063
$748$	19.7722	0.722944
$749$	−14.3101	−0.522881
$750$	−30.1063	−1.09933
$751$	35.2880	1.28768	0.643839	−	0.765161i	$-0.277341\pi$
$751$	35.2880	1.28768	0.643839	+	0.765161i	$0.277341\pi$
$752$	−7.58790	−0.276702
$753$	71.3346	2.59958
$754$	−10.2503	−0.373293
$755$	9.43256	0.343286
$756$	−19.7385	−0.717882
$757$	−3.11569	−0.113242	−0.0566208	−	0.998396i	$-0.518033\pi$
$757$	−3.11569	−0.113242	−0.0566208	+	0.998396i	$0.518033\pi$
$758$	6.08629	0.221064
$759$	36.6168	1.32911
$760$	−1.08282	−0.0392778
$761$	1.71532	0.0621804	0.0310902	−	0.999517i	$-0.490102\pi$
$761$	1.71532	0.0621804	0.0310902	+	0.999517i	$0.490102\pi$
$762$	−33.7701	−1.22336
$763$	−0.614317	−0.0222398
$764$	18.6539	0.674873
$765$	25.5195	0.922659
$766$	13.7620	0.497241
$767$	23.6744	0.854835
$768$	3.14966	0.113654
$769$	28.2825	1.01989	0.509946	−	0.860206i	$-0.329665\pi$
$769$	28.2825	1.01989	0.509946	+	0.860206i	$0.329665\pi$
$770$	−10.0495	−0.362158
$771$	67.2029	2.42025
$772$	10.0454	0.361541
$773$	−20.3658	−0.732506	−0.366253	−	0.930515i	$-0.619360\pi$
$773$	−20.3658	−0.732506	−0.366253	+	0.930515i	$0.619360\pi$
$774$	−52.6250	−1.89157
$775$	14.6900	0.527681
$776$	−18.1621	−0.651981
$777$	−18.0241	−0.646610
$778$	36.9641	1.32523
$779$	4.86480	0.174299
$780$	9.88615	0.353981
$781$	−55.7474	−1.99480
$782$	6.81923	0.243855
$783$	−43.6637	−1.56041
$784$	−4.44470	−0.158739
$785$	−17.7318	−0.632874
$786$	−31.6723	−1.12971
$787$	−42.3173	−1.50845	−0.754224	−	0.656617i	$-0.771987\pi$
$787$	−42.3173	−1.50845	−0.754224	+	0.656617i	$0.771987\pi$
$788$	−24.3580	−0.867718
$789$	7.24832	0.258047
$790$	1.50533	0.0535571
$791$	−32.9576	−1.17184
$792$	40.1790	1.42770
$793$	−12.9832	−0.461047
$794$	15.2165	0.540013
$795$	−38.5073	−1.36571
$796$	−6.07220	−0.215224
$797$	−29.5477	−1.04663	−0.523317	−	0.852138i	$-0.675306\pi$
$797$	−29.5477	−1.04663	−0.523317	+	0.852138i	$0.675306\pi$
$798$	5.03483	0.178231
$799$	−25.8410	−0.914188
$800$	−3.82751	−0.135323
$801$	−11.9223	−0.421253
$802$	34.3279	1.21216
$803$	−48.5927	−1.71480
$804$	46.1465	1.62746
$805$	−3.46596	−0.122159
$806$	−11.1254	−0.391874
$807$	−14.3227	−0.504183
$808$	0.106008	0.00372934
$809$	11.9637	0.420620	0.210310	−	0.977635i	$-0.432553\pi$
$809$	11.9637	0.420620	0.210310	+	0.977635i	$0.432553\pi$
$810$	19.6321	0.689801
$811$	21.9746	0.771631	0.385816	−	0.922576i	$-0.373920\pi$
$811$	21.9746	0.771631	0.385816	+	0.922576i	$0.373920\pi$
$812$	5.65259	0.198367
$813$	−32.4065	−1.13655
$814$	20.7843	0.728491
$815$	14.4712	0.506903
$816$	10.7263	0.375497
$817$	7.60434	0.266042
$818$	6.99065	0.244422
$819$	−32.0671	−1.12052
$820$	−5.26768	−0.183955
$821$	−15.6097	−0.544783	−0.272392	−	0.962186i	$-0.587815\pi$
$821$	−15.6097	−0.544783	−0.272392	+	0.962186i	$0.587815\pi$
$822$	4.49399	0.156746
$823$	2.36151	0.0823170	0.0411585	−	0.999153i	$-0.486895\pi$
$823$	2.36151	0.0823170	0.0411585	+	0.999153i	$0.486895\pi$
$824$	0.668408	0.0232851
$825$	−69.9921	−2.43681
$826$	−13.0554	−0.454257
$827$	25.4087	0.883546	0.441773	−	0.897127i	$-0.354350\pi$
$827$	25.4087	0.883546	0.441773	+	0.897127i	$0.354350\pi$
$828$	13.8573	0.481574
$829$	−10.5911	−0.367845	−0.183923	−	0.982941i	$-0.558880\pi$
$829$	−10.5911	−0.367845	−0.183923	+	0.982941i	$0.558880\pi$
$830$	5.00615	0.173766
$831$	62.5374	2.16940
$832$	2.89874	0.100496
$833$	−15.1367	−0.524454
$834$	−30.9481	−1.07164
$835$	−18.8219	−0.651359
$836$	−5.80588	−0.200801
$837$	−47.3913	−1.63808
$838$	12.3753	0.427497
$839$	33.9187	1.17100	0.585502	−	0.810671i	$-0.300897\pi$
$839$	33.9187	1.17100	0.585502	+	0.810671i	$0.300897\pi$
$840$	−5.45179	−0.188105
$841$	−16.4958	−0.568822
$842$	40.1368	1.38321
$843$	−36.1037	−1.24348
$844$	−1.00000	−0.0344214
$845$	−4.97805	−0.171250
$846$	−52.5112	−1.80537
$847$	−36.2998	−1.24728
$848$	−11.2908	−0.387728
$849$	42.6102	1.46238
$850$	−13.0348	−0.447089
$851$	7.16830	0.245726
$852$	−30.2427	−1.03610
$853$	−8.33875	−0.285514	−0.142757	−	0.989758i	$-0.545597\pi$
$853$	−8.33875	−0.285514	−0.142757	+	0.989758i	$0.545597\pi$
$854$	7.15968	0.244999
$855$	−7.49350	−0.256272
$856$	8.95206	0.305975
$857$	29.8769	1.02057	0.510287	−	0.860004i	$-0.329539\pi$
$857$	29.8769	1.02057	0.510287	+	0.860004i	$0.329539\pi$
$858$	53.0080	1.80966
$859$	−33.0694	−1.12832	−0.564158	−	0.825667i	$-0.690799\pi$
$859$	−33.0694	−1.12832	−0.564158	+	0.825667i	$0.690799\pi$
$860$	−8.23409	−0.280780
$861$	24.4934	0.834734
$862$	−34.6133	−1.17893
$863$	2.13527	0.0726855	0.0363428	−	0.999339i	$-0.488429\pi$
$863$	2.13527	0.0726855	0.0363428	+	0.999339i	$0.488429\pi$
$864$	12.3479	0.420084
$865$	8.38999	0.285268
$866$	26.9920	0.917226
$867$	−17.0152	−0.577867
$868$	6.13516	0.208241
$869$	8.07132	0.273801
$870$	−12.0600	−0.408871
$871$	42.4701	1.43905
$872$	0.384301	0.0130141
$873$	−125.689	−4.25392
$874$	−2.00239	−0.0677318
$875$	15.2796	0.516546
$876$	−26.3613	−0.890666
$877$	−32.0771	−1.08317	−0.541584	−	0.840647i	$-0.682175\pi$
$877$	−32.0771	−1.08317	−0.541584	+	0.840647i	$0.682175\pi$
$878$	−2.99789	−0.101174
$879$	−5.79868	−0.195585
$880$	6.28670	0.211924
$881$	3.45811	0.116507	0.0582534	−	0.998302i	$-0.481447\pi$
$881$	3.45811	0.116507	0.0582534	+	0.998302i	$0.481447\pi$
$882$	−30.7591	−1.03571
$883$	25.2488	0.849688	0.424844	−	0.905267i	$-0.360329\pi$
$883$	25.2488	0.849688	0.424844	+	0.905267i	$0.360329\pi$
$884$	9.87179	0.332024
$885$	27.8541	0.936306
$886$	−3.46699	−0.116476
$887$	−51.9195	−1.74329	−0.871644	−	0.490140i	$-0.836946\pi$
$887$	−51.9195	−1.74329	−0.871644	+	0.490140i	$0.836946\pi$
$888$	11.2754	0.378378
$889$	17.1391	0.574827
$890$	−1.86545	−0.0625300
$891$	105.264	3.52648
$892$	−7.58504	−0.253966
$893$	7.58790	0.253919
$894$	47.1306	1.57628
$895$	−11.4188	−0.381688
$896$	−1.59853	−0.0534031
$897$	18.2819	0.610415
$898$	−28.9706	−0.966761
$899$	13.5717	0.452640
$900$	−26.4879	−0.882929
$901$	−38.4514	−1.28100
$902$	−28.2444	−0.940437
$903$	38.2866	1.27410
$904$	20.6174	0.685726
$905$	5.80033	0.192809
$906$	27.4372	0.911540
$907$	33.6600	1.11766	0.558830	−	0.829282i	$-0.311250\pi$
$907$	33.6600	1.11766	0.558830	+	0.829282i	$0.311250\pi$
$908$	1.84000	0.0610624
$909$	0.733615	0.0243325
$910$	−5.01746	−0.166327
$911$	35.2214	1.16694	0.583469	−	0.812136i	$-0.301695\pi$
$911$	35.2214	1.16694	0.583469	+	0.812136i	$0.301695\pi$
$912$	−3.14966	−0.104296
$913$	26.8422	0.888346
$914$	36.9879	1.22345
$915$	−15.2754	−0.504988
$916$	−28.9472	−0.956444
$917$	16.0745	0.530825
$918$	42.0514	1.38790
$919$	0.694528	0.0229104	0.0114552	−	0.999934i	$-0.496354\pi$
$919$	0.694528	0.0229104	0.0114552	+	0.999934i	$0.496354\pi$
$920$	2.16822	0.0714840
$921$	−73.8305	−2.43280
$922$	6.84579	0.225454
$923$	−27.8333	−0.916145
$924$	−29.2316	−0.961650
$925$	−13.7020	−0.450519
$926$	−27.0341	−0.888397
$927$	4.62564	0.151926
$928$	−3.53612	−0.116079
$929$	−9.50311	−0.311787	−0.155894	−	0.987774i	$-0.549826\pi$
$929$	−9.50311	−0.311787	−0.155894	+	0.987774i	$0.549826\pi$
$930$	−13.0895	−0.429223
$931$	4.44470	0.145669
$932$	11.1199	0.364243
$933$	107.603	3.52278
$934$	−31.5885	−1.03361
$935$	21.4097	0.700171
$936$	20.0604	0.655694
$937$	−58.2346	−1.90244	−0.951221	−	0.308510i	$-0.900170\pi$
$937$	−58.2346	−1.90244	−0.951221	+	0.308510i	$0.900170\pi$
$938$	−23.4205	−0.764705
$939$	−37.8430	−1.23496
$940$	−8.21629	−0.267986
$941$	60.4313	1.97000	0.985002	−	0.172544i	$-0.0551988\pi$
$941$	60.4313	1.97000	0.985002	+	0.172544i	$0.0551988\pi$
$942$	−51.5777	−1.68049
$943$	−9.74121	−0.317218
$944$	8.16716	0.265818
$945$	−21.3731	−0.695268
$946$	−44.1499	−1.43544
$947$	−25.7529	−0.836857	−0.418429	−	0.908250i	$-0.637419\pi$
$947$	−25.7529	−0.836857	−0.418429	+	0.908250i	$0.637419\pi$
$948$	4.37865	0.142212
$949$	−24.2611	−0.787550
$950$	3.82751	0.124181
$951$	95.7207	3.10396
$952$	−5.44387	−0.176437
$953$	−33.3684	−1.08091	−0.540454	−	0.841373i	$-0.681748\pi$
$953$	−33.3684	−1.08091	−0.540454	+	0.841373i	$0.681748\pi$
$954$	−78.1368	−2.52977
$955$	20.1987	0.653614
$956$	23.6838	0.765989
$957$	−64.6636	−2.09028
$958$	14.6566	0.473534
$959$	−2.28081	−0.0736511
$960$	3.41050	0.110074
$961$	−16.2697	−0.524830
$962$	10.3771	0.334572
$963$	61.9517	1.99637
$964$	−15.8242	−0.509664
$965$	10.8773	0.350152
$966$	−10.0817	−0.324373
$967$	−9.65223	−0.310395	−0.155197	−	0.987883i	$-0.549601\pi$
$967$	−9.65223	−0.310395	−0.155197	+	0.987883i	$0.549601\pi$
$968$	22.7083	0.729871
$969$	−10.7263	−0.344580
$970$	−19.6662	−0.631443
$971$	−10.0878	−0.323734	−0.161867	−	0.986813i	$-0.551752\pi$
$971$	−10.0878	−0.323734	−0.161867	+	0.986813i	$0.551752\pi$
$972$	20.0616	0.643476
$973$	15.7069	0.503540
$974$	−26.0487	−0.834653
$975$	−34.9454	−1.11915
$976$	−4.47892	−0.143367
$977$	−51.1804	−1.63741	−0.818704	−	0.574216i	$-0.805307\pi$
$977$	−51.1804	−1.63741	−0.818704	+	0.574216i	$0.805307\pi$
$978$	42.0934	1.34600
$979$	−10.0022	−0.319673
$980$	−4.81279	−0.153739
$981$	2.65951	0.0849117
$982$	−40.4320	−1.29024
$983$	−11.6396	−0.371245	−0.185623	−	0.982621i	$-0.559430\pi$
$983$	−11.6396	−0.371245	−0.185623	+	0.982621i	$0.559430\pi$
$984$	−15.3225	−0.488463
$985$	−26.3752	−0.840385
$986$	−12.0424	−0.383509
$987$	38.2038	1.21604
$988$	−2.89874	−0.0922211
$989$	−15.2268	−0.484185
$990$	43.5064	1.38272
$991$	−7.43885	−0.236303	−0.118151	−	0.992996i	$-0.537697\pi$
$991$	−7.43885	−0.236303	−0.118151	+	0.992996i	$0.537697\pi$
$992$	−3.83801	−0.121857
$993$	15.6493	0.496616
$994$	15.3489	0.486837
$995$	−6.57507	−0.208444
$996$	14.5618	0.461407
$997$	18.4452	0.584164	0.292082	−	0.956393i	$-0.405652\pi$
$997$	18.4452	0.584164	0.292082	+	0.956393i	$0.405652\pi$
$998$	12.5359	0.396818
$999$	44.2040	1.39855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.45	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.45	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.14966 q^{3} +1.00000 q^{4} +1.08282 q^{5} +3.14966 q^{6} -1.59853 q^{7} +1.00000 q^{8} +6.92039 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.14966 q^{3} +1.00000 q^{4} +1.08282 q^{5} +3.14966 q^{6} -1.59853 q^{7} +1.00000 q^{8} +6.92039 q^{9} +1.08282 q^{10} +5.80588 q^{11} +3.14966 q^{12} +2.89874 q^{13} -1.59853 q^{14} +3.41050 q^{15} +1.00000 q^{16} +3.40555 q^{17} +6.92039 q^{18} -1.00000 q^{19} +1.08282 q^{20} -5.03483 q^{21} +5.80588 q^{22} +2.00239 q^{23} +3.14966 q^{24} -3.82751 q^{25} +2.89874 q^{26} +12.3479 q^{27} -1.59853 q^{28} -3.53612 q^{29} +3.41050 q^{30} -3.83801 q^{31} +1.00000 q^{32} +18.2866 q^{33} +3.40555 q^{34} -1.73091 q^{35} +6.92039 q^{36} +3.57988 q^{37} -1.00000 q^{38} +9.13005 q^{39} +1.08282 q^{40} -4.86480 q^{41} -5.03483 q^{42} -7.60434 q^{43} +5.80588 q^{44} +7.49350 q^{45} +2.00239 q^{46} -7.58790 q^{47} +3.14966 q^{48} -4.44470 q^{49} -3.82751 q^{50} +10.7263 q^{51} +2.89874 q^{52} -11.2908 q^{53} +12.3479 q^{54} +6.28670 q^{55} -1.59853 q^{56} -3.14966 q^{57} -3.53612 q^{58} +8.16716 q^{59} +3.41050 q^{60} -4.47892 q^{61} -3.83801 q^{62} -11.0624 q^{63} +1.00000 q^{64} +3.13880 q^{65} +18.2866 q^{66} +14.6513 q^{67} +3.40555 q^{68} +6.30685 q^{69} -1.73091 q^{70} -9.60188 q^{71} +6.92039 q^{72} -8.36956 q^{73} +3.57988 q^{74} -12.0554 q^{75} -1.00000 q^{76} -9.28087 q^{77} +9.13005 q^{78} +1.39020 q^{79} +1.08282 q^{80} +18.1306 q^{81} -4.86480 q^{82} +4.62327 q^{83} -5.03483 q^{84} +3.68758 q^{85} -7.60434 q^{86} -11.1376 q^{87} +5.80588 q^{88} -1.72278 q^{89} +7.49350 q^{90} -4.63371 q^{91} +2.00239 q^{92} -12.0884 q^{93} -7.58790 q^{94} -1.08282 q^{95} +3.14966 q^{96} -18.1621 q^{97} -4.44470 q^{98} +40.1790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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