LMFDB - Embedded newform 4011.2.a.k.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.640778 q^{2} +1.00000 q^{3} -1.58940 q^{4} -2.69509 q^{5} +0.640778 q^{6} +1.00000 q^{7} -2.30001 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.640778 q^{2} +1.00000 q^{3} -1.58940 q^{4} -2.69509 q^{5} +0.640778 q^{6} +1.00000 q^{7} -2.30001 q^{8} +1.00000 q^{9} -1.72696 q^{10} -4.58265 q^{11} -1.58940 q^{12} -2.02368 q^{13} +0.640778 q^{14} -2.69509 q^{15} +1.70501 q^{16} +0.863602 q^{17} +0.640778 q^{18} -5.46546 q^{19} +4.28358 q^{20} +1.00000 q^{21} -2.93646 q^{22} +0.350104 q^{23} -2.30001 q^{24} +2.26351 q^{25} -1.29673 q^{26} +1.00000 q^{27} -1.58940 q^{28} +1.76679 q^{29} -1.72696 q^{30} -0.00536166 q^{31} +5.69256 q^{32} -4.58265 q^{33} +0.553377 q^{34} -2.69509 q^{35} -1.58940 q^{36} +6.05079 q^{37} -3.50215 q^{38} -2.02368 q^{39} +6.19874 q^{40} +0.147836 q^{41} +0.640778 q^{42} -3.30155 q^{43} +7.28368 q^{44} -2.69509 q^{45} +0.224339 q^{46} +5.31875 q^{47} +1.70501 q^{48} +1.00000 q^{49} +1.45041 q^{50} +0.863602 q^{51} +3.21645 q^{52} +3.84814 q^{53} +0.640778 q^{54} +12.3507 q^{55} -2.30001 q^{56} -5.46546 q^{57} +1.13212 q^{58} +11.1101 q^{59} +4.28358 q^{60} +4.48726 q^{61} -0.00343563 q^{62} +1.00000 q^{63} +0.237651 q^{64} +5.45401 q^{65} -2.93646 q^{66} -0.615312 q^{67} -1.37261 q^{68} +0.350104 q^{69} -1.72696 q^{70} -12.4200 q^{71} -2.30001 q^{72} -4.90798 q^{73} +3.87722 q^{74} +2.26351 q^{75} +8.68681 q^{76} -4.58265 q^{77} -1.29673 q^{78} -16.1304 q^{79} -4.59515 q^{80} +1.00000 q^{81} +0.0947303 q^{82} +12.6202 q^{83} -1.58940 q^{84} -2.32748 q^{85} -2.11556 q^{86} +1.76679 q^{87} +10.5402 q^{88} +14.1782 q^{89} -1.72696 q^{90} -2.02368 q^{91} -0.556456 q^{92} -0.00536166 q^{93} +3.40814 q^{94} +14.7299 q^{95} +5.69256 q^{96} -7.12096 q^{97} +0.640778 q^{98} -4.58265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * 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 $

$2$	0.640778	0.453099	0.226549	−	0.974000i	$-0.427256\pi$
$2$	0.640778	0.453099	0.226549	+	0.974000i	$0.427256\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.58940	−0.794702
$5$	−2.69509	−1.20528	−0.602640	−	0.798013i	$-0.705885\pi$
$5$	−2.69509	−1.20528	−0.602640	+	0.798013i	$0.705885\pi$
$6$	0.640778	0.261597
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.30001	−0.813177
$9$	1.00000	0.333333
$10$	−1.72696	−0.546111
$11$	−4.58265	−1.38172	−0.690861	−	0.722988i	$-0.742768\pi$
$11$	−4.58265	−1.38172	−0.690861	+	0.722988i	$0.742768\pi$
$12$	−1.58940	−0.458821
$13$	−2.02368	−0.561269	−0.280634	−	0.959815i	$-0.590545\pi$
$13$	−2.02368	−0.561269	−0.280634	+	0.959815i	$0.590545\pi$
$14$	0.640778	0.171255
$15$	−2.69509	−0.695869
$16$	1.70501	0.426252
$17$	0.863602	0.209454	0.104727	−	0.994501i	$-0.466603\pi$
$17$	0.863602	0.209454	0.104727	+	0.994501i	$0.466603\pi$
$18$	0.640778	0.151033
$19$	−5.46546	−1.25386	−0.626931	−	0.779075i	$-0.715689\pi$
$19$	−5.46546	−1.25386	−0.626931	+	0.779075i	$0.715689\pi$
$20$	4.28358	0.957838
$21$	1.00000	0.218218
$22$	−2.93646	−0.626056
$23$	0.350104	0.0730016	0.0365008	−	0.999334i	$-0.488379\pi$
$23$	0.350104	0.0730016	0.0365008	+	0.999334i	$0.488379\pi$
$24$	−2.30001	−0.469488
$25$	2.26351	0.452702
$26$	−1.29673	−0.254310
$27$	1.00000	0.192450
$28$	−1.58940	−0.300369
$29$	1.76679	0.328084	0.164042	−	0.986453i	$-0.447547\pi$
$29$	1.76679	0.328084	0.164042	+	0.986453i	$0.447547\pi$
$30$	−1.72696	−0.315297
$31$	−0.00536166	−0.000962982 0	−0.000481491	−	1.00000i	$-0.500153\pi$
$31$	−0.00536166	−0.000962982 0	−0.000481491		1.00000i	$0.500153\pi$
$32$	5.69256	1.00631
$33$	−4.58265	−0.797737
$34$	0.553377	0.0949034
$35$	−2.69509	−0.455553
$36$	−1.58940	−0.264901
$37$	6.05079	0.994744	0.497372	−	0.867537i	$-0.334298\pi$
$37$	6.05079	0.994744	0.497372	+	0.867537i	$0.334298\pi$
$38$	−3.50215	−0.568123
$39$	−2.02368	−0.324049
$40$	6.19874	0.980107
$41$	0.147836	0.0230882	0.0115441	−	0.999933i	$-0.496325\pi$
$41$	0.147836	0.0230882	0.0115441	+	0.999933i	$0.496325\pi$
$42$	0.640778	0.0988743
$43$	−3.30155	−0.503482	−0.251741	−	0.967795i	$-0.581003\pi$
$43$	−3.30155	−0.503482	−0.251741	+	0.967795i	$0.581003\pi$
$44$	7.28368	1.09806
$45$	−2.69509	−0.401760
$46$	0.224339	0.0330769
$47$	5.31875	0.775820	0.387910	−	0.921697i	$-0.373197\pi$
$47$	5.31875	0.775820	0.387910	+	0.921697i	$0.373197\pi$
$48$	1.70501	0.246097
$49$	1.00000	0.142857
$50$	1.45041	0.205119
$51$	0.863602	0.120928
$52$	3.21645	0.446041
$53$	3.84814	0.528583	0.264292	−	0.964443i	$-0.414862\pi$
$53$	3.84814	0.528583	0.264292	+	0.964443i	$0.414862\pi$
$54$	0.640778	0.0871989
$55$	12.3507	1.66536
$56$	−2.30001	−0.307352
$57$	−5.46546	−0.723917
$58$	1.13212	0.148655
$59$	11.1101	1.44641	0.723207	−	0.690632i	$-0.242667\pi$
$59$	11.1101	1.44641	0.723207	+	0.690632i	$0.242667\pi$
$60$	4.28358	0.553008
$61$	4.48726	0.574535	0.287267	−	0.957850i	$-0.407253\pi$
$61$	4.48726	0.574535	0.287267	+	0.957850i	$0.407253\pi$
$62$	−0.00343563	−0.000436326 0
$63$	1.00000	0.125988
$64$	0.237651	0.0297063
$65$	5.45401	0.676487
$66$	−2.93646	−0.361454
$67$	−0.615312	−0.0751723	−0.0375861	−	0.999293i	$-0.511967\pi$
$67$	−0.615312	−0.0751723	−0.0375861	+	0.999293i	$0.511967\pi$
$68$	−1.37261	−0.166454
$69$	0.350104	0.0421475
$70$	−1.72696	−0.206411
$71$	−12.4200	−1.47398	−0.736990	−	0.675904i	$-0.763754\pi$
$71$	−12.4200	−1.47398	−0.736990	+	0.675904i	$0.763754\pi$
$72$	−2.30001	−0.271059
$73$	−4.90798	−0.574435	−0.287218	−	0.957865i	$-0.592730\pi$
$73$	−4.90798	−0.574435	−0.287218	+	0.957865i	$0.592730\pi$
$74$	3.87722	0.450717
$75$	2.26351	0.261368
$76$	8.68681	0.996446
$77$	−4.58265	−0.522242
$78$	−1.29673	−0.146826
$79$	−16.1304	−1.81481	−0.907407	−	0.420252i	$-0.861942\pi$
$79$	−16.1304	−1.81481	−0.907407	+	0.420252i	$0.861942\pi$
$80$	−4.59515	−0.513753
$81$	1.00000	0.111111
$82$	0.0947303	0.0104612
$83$	12.6202	1.38525	0.692623	−	0.721300i	$-0.256455\pi$
$83$	12.6202	1.38525	0.692623	+	0.721300i	$0.256455\pi$
$84$	−1.58940	−0.173418
$85$	−2.32748	−0.252451
$86$	−2.11556	−0.228127
$87$	1.76679	0.189419
$88$	10.5402	1.12358
$89$	14.1782	1.50288	0.751442	−	0.659799i	$-0.229358\pi$
$89$	14.1782	1.50288	0.751442	+	0.659799i	$0.229358\pi$
$90$	−1.72696	−0.182037
$91$	−2.02368	−0.212140
$92$	−0.556456	−0.0580145
$93$	−0.00536166	−0.000555978 0
$94$	3.40814	0.351523
$95$	14.7299	1.51126
$96$	5.69256	0.580994
$97$	−7.12096	−0.723024	−0.361512	−	0.932367i	$-0.617739\pi$
$97$	−7.12096	−0.723024	−0.361512	+	0.932367i	$0.617739\pi$
$98$	0.640778	0.0647284
$99$	−4.58265	−0.460574
$100$	−3.59763	−0.359763
$101$	6.32254	0.629116	0.314558	−	0.949238i	$-0.398144\pi$
$101$	6.32254	0.629116	0.314558	+	0.949238i	$0.398144\pi$
$102$	0.553377	0.0547925
$103$	−2.01762	−0.198802	−0.0994009	−	0.995047i	$-0.531693\pi$
$103$	−2.01762	−0.198802	−0.0994009	+	0.995047i	$0.531693\pi$
$104$	4.65450	0.456411
$105$	−2.69509	−0.263014
$106$	2.46581	0.239500
$107$	15.1930	1.46876	0.734380	−	0.678739i	$-0.237473\pi$
$107$	15.1930	1.46876	0.734380	+	0.678739i	$0.237473\pi$
$108$	−1.58940	−0.152940
$109$	15.7978	1.51315	0.756577	−	0.653904i	$-0.226870\pi$
$109$	15.7978	1.51315	0.756577	+	0.653904i	$0.226870\pi$
$110$	7.91403	0.754574
$111$	6.05079	0.574316
$112$	1.70501	0.161108
$113$	17.0794	1.60669	0.803346	−	0.595512i	$-0.203051\pi$
$113$	17.0794	1.60669	0.803346	+	0.595512i	$0.203051\pi$
$114$	−3.50215	−0.328006
$115$	−0.943560	−0.0879875
$116$	−2.80814	−0.260729
$117$	−2.02368	−0.187090
$118$	7.11912	0.655368
$119$	0.863602	0.0791663
$120$	6.19874	0.565865
$121$	10.0007	0.909154
$122$	2.87534	0.260321
$123$	0.147836	0.0133300
$124$	0.00852183	0.000765283 0
$125$	7.37509	0.659648
$126$	0.640778	0.0570851
$127$	−5.50211	−0.488233	−0.244117	−	0.969746i	$-0.578498\pi$
$127$	−5.50211	−0.488233	−0.244117	+	0.969746i	$0.578498\pi$
$128$	−11.2328	−0.992851
$129$	−3.30155	−0.290685
$130$	3.49481	0.306515
$131$	−12.8660	−1.12411	−0.562056	−	0.827099i	$-0.689989\pi$
$131$	−12.8660	−1.12411	−0.562056	+	0.827099i	$0.689989\pi$
$132$	7.28368	0.633963
$133$	−5.46546	−0.473915
$134$	−0.394278	−0.0340605
$135$	−2.69509	−0.231956
$136$	−1.98629	−0.170323
$137$	7.61623	0.650699	0.325349	−	0.945594i	$-0.394518\pi$
$137$	7.61623	0.650699	0.325349	+	0.945594i	$0.394518\pi$
$138$	0.224339	0.0190970
$139$	−1.38770	−0.117703	−0.0588514	−	0.998267i	$-0.518744\pi$
$139$	−1.38770	−0.117703	−0.0588514	+	0.998267i	$0.518744\pi$
$140$	4.28358	0.362029
$141$	5.31875	0.447920
$142$	−7.95845	−0.667859
$143$	9.27384	0.775517
$144$	1.70501	0.142084
$145$	−4.76165	−0.395434
$146$	−3.14492	−0.260276
$147$	1.00000	0.0824786
$148$	−9.61715	−0.790525
$149$	−0.388309	−0.0318115	−0.0159057	−	0.999873i	$-0.505063\pi$
$149$	−0.388309	−0.0318115	−0.0159057	+	0.999873i	$0.505063\pi$
$150$	1.45041	0.118425
$151$	−11.0530	−0.899482	−0.449741	−	0.893159i	$-0.648484\pi$
$151$	−11.0530	−0.899482	−0.449741	+	0.893159i	$0.648484\pi$
$152$	12.5706	1.01961
$153$	0.863602	0.0698181
$154$	−2.93646	−0.236627
$155$	0.0144501	0.00116066
$156$	3.21645	0.257522
$157$	−2.14991	−0.171581	−0.0857907	−	0.996313i	$-0.527342\pi$
$157$	−2.14991	−0.171581	−0.0857907	+	0.996313i	$0.527342\pi$
$158$	−10.3360	−0.822290
$159$	3.84814	0.305178
$160$	−15.3420	−1.21289
$161$	0.350104	0.0275920
$162$	0.640778	0.0503443
$163$	10.1076	0.791692	0.395846	−	0.918317i	$-0.370451\pi$
$163$	10.1076	0.791692	0.395846	+	0.918317i	$0.370451\pi$
$164$	−0.234972	−0.0183482
$165$	12.3507	0.961497
$166$	8.08674	0.627653
$167$	−13.4878	−1.04372	−0.521858	−	0.853033i	$-0.674761\pi$
$167$	−13.4878	−1.04372	−0.521858	+	0.853033i	$0.674761\pi$
$168$	−2.30001	−0.177450
$169$	−8.90470	−0.684977
$170$	−1.49140	−0.114385
$171$	−5.46546	−0.417954
$172$	5.24749	0.400118
$173$	−17.9360	−1.36365	−0.681824	−	0.731516i	$-0.738813\pi$
$173$	−17.9360	−1.36365	−0.681824	+	0.731516i	$0.738813\pi$
$174$	1.13212	0.0858257
$175$	2.26351	0.171105
$176$	−7.81346	−0.588962
$177$	11.1101	0.835087
$178$	9.08508	0.680955
$179$	21.3336	1.59455	0.797274	−	0.603618i	$-0.206275\pi$
$179$	21.3336	1.59455	0.797274	+	0.603618i	$0.206275\pi$
$180$	4.28358	0.319279
$181$	−0.691691	−0.0514130	−0.0257065	−	0.999670i	$-0.508184\pi$
$181$	−0.691691	−0.0514130	−0.0257065	+	0.999670i	$0.508184\pi$
$182$	−1.29673	−0.0961202
$183$	4.48726	0.331708
$184$	−0.805242	−0.0593632
$185$	−16.3074	−1.19895
$186$	−0.00343563	−0.000251913 0
$187$	−3.95759	−0.289407
$188$	−8.45364	−0.616545
$189$	1.00000	0.0727393
$190$	9.43860	0.684748
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	0.237651	0.0171510
$193$	8.17867	0.588713	0.294357	−	0.955696i	$-0.404895\pi$
$193$	8.17867	0.588713	0.294357	+	0.955696i	$0.404895\pi$
$194$	−4.56296	−0.327601
$195$	5.45401	0.390570
$196$	−1.58940	−0.113529
$197$	24.0885	1.71623	0.858116	−	0.513456i	$-0.171635\pi$
$197$	24.0885	1.71623	0.858116	+	0.513456i	$0.171635\pi$
$198$	−2.93646	−0.208685
$199$	7.34236	0.520486	0.260243	−	0.965543i	$-0.416197\pi$
$199$	7.34236	0.520486	0.260243	+	0.965543i	$0.416197\pi$
$200$	−5.20610	−0.368127
$201$	−0.615312	−0.0434007
$202$	4.05135	0.285052
$203$	1.76679	0.124004
$204$	−1.37261	−0.0961020
$205$	−0.398432	−0.0278277
$206$	−1.29285	−0.0900768
$207$	0.350104	0.0243339
$208$	−3.45040	−0.239242
$209$	25.0463	1.73249
$210$	−1.72696	−0.119171
$211$	−16.2622	−1.11953	−0.559767	−	0.828650i	$-0.689109\pi$
$211$	−16.2622	−1.11953	−0.559767	+	0.828650i	$0.689109\pi$
$212$	−6.11625	−0.420066
$213$	−12.4200	−0.851003
$214$	9.73532	0.665493
$215$	8.89797	0.606837
$216$	−2.30001	−0.156496
$217$	−0.00536166	−0.000363973 0
$218$	10.1229	0.685609
$219$	−4.90798	−0.331650
$220$	−19.6302	−1.32347
$221$	−1.74766	−0.117560
$222$	3.87722	0.260222
$223$	20.2732	1.35760	0.678798	−	0.734325i	$-0.262501\pi$
$223$	20.2732	1.35760	0.678798	+	0.734325i	$0.262501\pi$
$224$	5.69256	0.380350
$225$	2.26351	0.150901
$226$	10.9441	0.727991
$227$	3.16890	0.210327	0.105164	−	0.994455i	$-0.466463\pi$
$227$	3.16890	0.210327	0.105164	+	0.994455i	$0.466463\pi$
$228$	8.68681	0.575298
$229$	20.7242	1.36949	0.684747	−	0.728781i	$-0.259913\pi$
$229$	20.7242	1.36949	0.684747	+	0.728781i	$0.259913\pi$
$230$	−0.604613	−0.0398670
$231$	−4.58265	−0.301516
$232$	−4.06363	−0.266791
$233$	9.92388	0.650135	0.325068	−	0.945691i	$-0.394613\pi$
$233$	9.92388	0.650135	0.325068	+	0.945691i	$0.394613\pi$
$234$	−1.29673	−0.0847701
$235$	−14.3345	−0.935081
$236$	−17.6584	−1.14947
$237$	−16.1304	−1.04778
$238$	0.553377	0.0358701
$239$	−15.3964	−0.995912	−0.497956	−	0.867202i	$-0.665916\pi$
$239$	−15.3964	−0.995912	−0.497956	+	0.867202i	$0.665916\pi$
$240$	−4.59515	−0.296616
$241$	19.9170	1.28297	0.641484	−	0.767136i	$-0.278319\pi$
$241$	19.9170	1.28297	0.641484	+	0.767136i	$0.278319\pi$
$242$	6.40823	0.411937
$243$	1.00000	0.0641500
$244$	−7.13207	−0.456584
$245$	−2.69509	−0.172183
$246$	0.0947303	0.00603979
$247$	11.0604	0.703754
$248$	0.0123319	0.000783075 0
$249$	12.6202	0.799772
$250$	4.72580	0.298886
$251$	−3.59699	−0.227040	−0.113520	−	0.993536i	$-0.536213\pi$
$251$	−3.59699	−0.227040	−0.113520	+	0.993536i	$0.536213\pi$
$252$	−1.58940	−0.100123
$253$	−1.60440	−0.100868
$254$	−3.52563	−0.221218
$255$	−2.32748	−0.145753
$256$	−7.67306	−0.479566
$257$	0.614071	0.0383047	0.0191523	−	0.999817i	$-0.493903\pi$
$257$	0.614071	0.0383047	0.0191523	+	0.999817i	$0.493903\pi$
$258$	−2.11556	−0.131709
$259$	6.05079	0.375978
$260$	−8.66862	−0.537605
$261$	1.76679	0.109361
$262$	−8.24429	−0.509334
$263$	1.77648	0.109543	0.0547713	−	0.998499i	$-0.482557\pi$
$263$	1.77648	0.109543	0.0547713	+	0.998499i	$0.482557\pi$
$264$	10.5402	0.648702
$265$	−10.3711	−0.637091
$266$	−3.50215	−0.214730
$267$	14.1782	0.867691
$268$	0.977978	0.0597395
$269$	−2.42432	−0.147814	−0.0739068	−	0.997265i	$-0.523547\pi$
$269$	−2.42432	−0.147814	−0.0739068	+	0.997265i	$0.523547\pi$
$270$	−1.72696	−0.105099
$271$	8.68589	0.527630	0.263815	−	0.964573i	$-0.415019\pi$
$271$	8.68589	0.527630	0.263815	+	0.964573i	$0.415019\pi$
$272$	1.47245	0.0892803
$273$	−2.02368	−0.122479
$274$	4.88032	0.294831
$275$	−10.3729	−0.625508
$276$	−0.556456	−0.0334947
$277$	24.5578	1.47553	0.737767	−	0.675056i	$-0.235880\pi$
$277$	24.5578	1.47553	0.737767	+	0.675056i	$0.235880\pi$
$278$	−0.889205	−0.0533310
$279$	−0.00536166	−0.000320994 0
$280$	6.19874	0.370445
$281$	−11.0053	−0.656523	−0.328262	−	0.944587i	$-0.606463\pi$
$281$	−11.0053	−0.656523	−0.328262	+	0.944587i	$0.606463\pi$
$282$	3.40814	0.202952
$283$	−8.46339	−0.503097	−0.251548	−	0.967845i	$-0.580940\pi$
$283$	−8.46339	−0.503097	−0.251548	+	0.967845i	$0.580940\pi$
$284$	19.7404	1.17137
$285$	14.7299	0.872524
$286$	5.94248	0.351386
$287$	0.147836	0.00872650
$288$	5.69256	0.335437
$289$	−16.2542	−0.956129
$290$	−3.05116	−0.179170
$291$	−7.12096	−0.417438
$292$	7.80075	0.456504
$293$	−8.35510	−0.488110	−0.244055	−	0.969761i	$-0.578478\pi$
$293$	−8.35510	−0.488110	−0.244055	+	0.969761i	$0.578478\pi$
$294$	0.640778	0.0373710
$295$	−29.9428	−1.74333
$296$	−13.9169	−0.808903
$297$	−4.58265	−0.265912
$298$	−0.248820	−0.0144137
$299$	−0.708499	−0.0409735
$300$	−3.59763	−0.207709
$301$	−3.30155	−0.190298
$302$	−7.08254	−0.407554
$303$	6.32254	0.363220
$304$	−9.31865	−0.534461
$305$	−12.0936	−0.692476
$306$	0.553377	0.0316345
$307$	4.99550	0.285108	0.142554	−	0.989787i	$-0.454469\pi$
$307$	4.99550	0.285108	0.142554	+	0.989787i	$0.454469\pi$
$308$	7.28368	0.415026
$309$	−2.01762	−0.114778
$310$	0.00925934	0.000525895 0
$311$	4.36761	0.247665	0.123832	−	0.992303i	$-0.460482\pi$
$311$	4.36761	0.247665	0.123832	+	0.992303i	$0.460482\pi$
$312$	4.65450	0.263509
$313$	9.33715	0.527767	0.263883	−	0.964555i	$-0.414997\pi$
$313$	9.33715	0.527767	0.263883	+	0.964555i	$0.414997\pi$
$314$	−1.37761	−0.0777433
$315$	−2.69509	−0.151851
$316$	25.6378	1.44224
$317$	22.0436	1.23809	0.619046	−	0.785355i	$-0.287519\pi$
$317$	22.0436	1.23809	0.619046	+	0.785355i	$0.287519\pi$
$318$	2.46581	0.138276
$319$	−8.09657	−0.453321
$320$	−0.640490	−0.0358045
$321$	15.1930	0.847989
$322$	0.224339	0.0125019
$323$	−4.71998	−0.262627
$324$	−1.58940	−0.0883002
$325$	−4.58063	−0.254087
$326$	6.47676	0.358715
$327$	15.7978	0.873620
$328$	−0.340025	−0.0187748
$329$	5.31875	0.293232
$330$	7.91403	0.435653
$331$	6.75119	0.371079	0.185539	−	0.982637i	$-0.440597\pi$
$331$	6.75119	0.371079	0.185539	+	0.982637i	$0.440597\pi$
$332$	−20.0586	−1.10086
$333$	6.05079	0.331581
$334$	−8.64268	−0.472906
$335$	1.65832	0.0906037
$336$	1.70501	0.0930158
$337$	−25.2359	−1.37469	−0.687343	−	0.726333i	$-0.741223\pi$
$337$	−25.2359	−1.37469	−0.687343	+	0.726333i	$0.741223\pi$
$338$	−5.70594	−0.310362
$339$	17.0794	0.927625
$340$	3.69931	0.200623
$341$	0.0245706	0.00133057
$342$	−3.50215	−0.189374
$343$	1.00000	0.0539949
$344$	7.59360	0.409420
$345$	−0.943560	−0.0507996
$346$	−11.4930	−0.617867
$347$	1.64132	0.0881109	0.0440554	−	0.999029i	$-0.485972\pi$
$347$	1.64132	0.0881109	0.0440554	+	0.999029i	$0.485972\pi$
$348$	−2.80814	−0.150532
$349$	19.9027	1.06537	0.532684	−	0.846314i	$-0.321184\pi$
$349$	19.9027	1.06537	0.532684	+	0.846314i	$0.321184\pi$
$350$	1.45041	0.0775276
$351$	−2.02368	−0.108016
$352$	−26.0870	−1.39044
$353$	−14.3900	−0.765900	−0.382950	−	0.923769i	$-0.625092\pi$
$353$	−14.3900	−0.765900	−0.382950	+	0.923769i	$0.625092\pi$
$354$	7.11912	0.378377
$355$	33.4730	1.77656
$356$	−22.5349	−1.19434
$357$	0.863602	0.0457067
$358$	13.6701	0.722487
$359$	−4.17720	−0.220464	−0.110232	−	0.993906i	$-0.535159\pi$
$359$	−4.17720	−0.220464	−0.110232	+	0.993906i	$0.535159\pi$
$360$	6.19874	0.326702
$361$	10.8712	0.572170
$362$	−0.443220	−0.0232952
$363$	10.0007	0.524900
$364$	3.21645	0.168588
$365$	13.2274	0.692356
$366$	2.87534	0.150296
$367$	17.7694	0.927554	0.463777	−	0.885952i	$-0.346494\pi$
$367$	17.7694	0.927554	0.463777	+	0.885952i	$0.346494\pi$
$368$	0.596929	0.0311171
$369$	0.147836	0.00769605
$370$	−10.4495	−0.543241
$371$	3.84814	0.199786
$372$	0.00852183	0.000441836 0
$373$	−6.31115	−0.326779	−0.163389	−	0.986562i	$-0.552243\pi$
$373$	−6.31115	−0.326779	−0.163389	+	0.986562i	$0.552243\pi$
$374$	−2.53594	−0.131130
$375$	7.37509	0.380848
$376$	−12.2332	−0.630879
$377$	−3.57542	−0.184143
$378$	0.640778	0.0329581
$379$	−31.8501	−1.63603	−0.818016	−	0.575196i	$-0.804926\pi$
$379$	−31.8501	−1.63603	−0.818016	+	0.575196i	$0.804926\pi$
$380$	−23.4117	−1.20100
$381$	−5.50211	−0.281882
$382$	0.640778	0.0327851
$383$	−21.7452	−1.11113	−0.555565	−	0.831473i	$-0.687498\pi$
$383$	−21.7452	−1.11113	−0.555565	+	0.831473i	$0.687498\pi$
$384$	−11.2328	−0.573223
$385$	12.3507	0.629448
$386$	5.24071	0.266745
$387$	−3.30155	−0.167827
$388$	11.3181	0.574588
$389$	−8.18237	−0.414863	−0.207431	−	0.978250i	$-0.566510\pi$
$389$	−8.18237	−0.414863	−0.207431	+	0.978250i	$0.566510\pi$
$390$	3.49481	0.176967
$391$	0.302350	0.0152905
$392$	−2.30001	−0.116168
$393$	−12.8660	−0.649006
$394$	15.4354	0.777623
$395$	43.4729	2.18736
$396$	7.28368	0.366019
$397$	−8.68375	−0.435825	−0.217912	−	0.975968i	$-0.569925\pi$
$397$	−8.68375	−0.435825	−0.217912	+	0.975968i	$0.569925\pi$
$398$	4.70482	0.235832
$399$	−5.46546	−0.273615
$400$	3.85930	0.192965
$401$	−14.7832	−0.738237	−0.369119	−	0.929382i	$-0.620340\pi$
$401$	−14.7832	−0.738237	−0.369119	+	0.929382i	$0.620340\pi$
$402$	−0.394278	−0.0196648
$403$	0.0108503	0.000540492 0
$404$	−10.0491	−0.499960
$405$	−2.69509	−0.133920
$406$	1.13212	0.0561861
$407$	−27.7287	−1.37446
$408$	−1.98629	−0.0983362
$409$	14.8588	0.734723	0.367361	−	0.930078i	$-0.380261\pi$
$409$	14.8588	0.734723	0.367361	+	0.930078i	$0.380261\pi$
$410$	−0.255307	−0.0126087
$411$	7.61623	0.375681
$412$	3.20681	0.157988
$413$	11.1101	0.546693
$414$	0.224339	0.0110256
$415$	−34.0125	−1.66961
$416$	−11.5199	−0.564811
$417$	−1.38770	−0.0679557
$418$	16.0491	0.784988
$419$	−25.1575	−1.22903	−0.614513	−	0.788907i	$-0.710647\pi$
$419$	−25.1575	−1.22903	−0.614513	+	0.788907i	$0.710647\pi$
$420$	4.28358	0.209017
$421$	−27.5798	−1.34416	−0.672079	−	0.740479i	$-0.734599\pi$
$421$	−27.5798	−1.34416	−0.672079	+	0.740479i	$0.734599\pi$
$422$	−10.4204	−0.507259
$423$	5.31875	0.258607
$424$	−8.85078	−0.429832
$425$	1.95477	0.0948203
$426$	−7.95845	−0.385588
$427$	4.48726	0.217154
$428$	−24.1477	−1.16723
$429$	9.27384	0.447745
$430$	5.70163	0.274957
$431$	−28.5787	−1.37659	−0.688293	−	0.725433i	$-0.741640\pi$
$431$	−28.5787	−1.37659	−0.688293	+	0.725433i	$0.741640\pi$
$432$	1.70501	0.0820322
$433$	25.8786	1.24365	0.621823	−	0.783158i	$-0.286392\pi$
$433$	25.8786	1.24365	0.621823	+	0.783158i	$0.286392\pi$
$434$	−0.00343563	−0.000164916 0
$435$	−4.76165	−0.228304
$436$	−25.1091	−1.20251
$437$	−1.91348	−0.0915340
$438$	−3.14492	−0.150270
$439$	−4.52055	−0.215754	−0.107877	−	0.994164i	$-0.534405\pi$
$439$	−4.52055	−0.215754	−0.107877	+	0.994164i	$0.534405\pi$
$440$	−28.4067	−1.35423
$441$	1.00000	0.0476190
$442$	−1.11986	−0.0532664
$443$	24.0832	1.14423	0.572115	−	0.820174i	$-0.306123\pi$
$443$	24.0832	1.14423	0.572115	+	0.820174i	$0.306123\pi$
$444$	−9.61715	−0.456410
$445$	−38.2115	−1.81140
$446$	12.9907	0.615125
$447$	−0.388309	−0.0183664
$448$	0.237651	0.0112279
$449$	27.2408	1.28557	0.642787	−	0.766045i	$-0.277778\pi$
$449$	27.2408	1.28557	0.642787	+	0.766045i	$0.277778\pi$
$450$	1.45041	0.0683729
$451$	−0.677482	−0.0319014
$452$	−27.1460	−1.27684
$453$	−11.0530	−0.519316
$454$	2.03056	0.0952991
$455$	5.45401	0.255688
$456$	12.5706	0.588673
$457$	−39.6192	−1.85331	−0.926653	−	0.375917i	$-0.877328\pi$
$457$	−39.6192	−1.85331	−0.926653	+	0.375917i	$0.877328\pi$
$458$	13.2796	0.620516
$459$	0.863602	0.0403095
$460$	1.49970	0.0699238
$461$	−4.06988	−0.189553	−0.0947766	−	0.995499i	$-0.530214\pi$
$461$	−4.06988	−0.189553	−0.0947766	+	0.995499i	$0.530214\pi$
$462$	−2.93646	−0.136617
$463$	23.6906	1.10100	0.550498	−	0.834836i	$-0.314438\pi$
$463$	23.6906	1.10100	0.550498	+	0.834836i	$0.314438\pi$
$464$	3.01239	0.139847
$465$	0.0144501	0.000670109 0
$466$	6.35901	0.294575
$467$	16.6631	0.771076	0.385538	−	0.922692i	$-0.374016\pi$
$467$	16.6631	0.771076	0.385538	+	0.922692i	$0.374016\pi$
$468$	3.21645	0.148680
$469$	−0.615312	−0.0284125
$470$	−9.18525	−0.423684
$471$	−2.14991	−0.0990625
$472$	−25.5534	−1.17619
$473$	15.1299	0.695671
$474$	−10.3360	−0.474750
$475$	−12.3711	−0.567626
$476$	−1.37261	−0.0629135
$477$	3.84814	0.176194
$478$	−9.86570	−0.451247
$479$	32.9391	1.50503	0.752513	−	0.658577i	$-0.228841\pi$
$479$	32.9391	1.50503	0.752513	+	0.658577i	$0.228841\pi$
$480$	−15.3420	−0.700261
$481$	−12.2449	−0.558319
$482$	12.7624	0.581311
$483$	0.350104	0.0159303
$484$	−15.8951	−0.722506
$485$	19.1916	0.871447
$486$	0.640778	0.0290663
$487$	21.8369	0.989527	0.494763	−	0.869028i	$-0.335255\pi$
$487$	21.8369	0.989527	0.494763	+	0.869028i	$0.335255\pi$
$488$	−10.3208	−0.467199
$489$	10.1076	0.457084
$490$	−1.72696	−0.0780159
$491$	38.4075	1.73331	0.866654	−	0.498910i	$-0.166266\pi$
$491$	38.4075	1.73331	0.866654	+	0.498910i	$0.166266\pi$
$492$	−0.234972	−0.0105933
$493$	1.52580	0.0687186
$494$	7.08724	0.318870
$495$	12.3507	0.555121
$496$	−0.00914167	−0.000410473 0
$497$	−12.4200	−0.557112
$498$	8.08674	0.362376
$499$	−22.8928	−1.02482	−0.512412	−	0.858740i	$-0.671248\pi$
$499$	−22.8928	−1.02482	−0.512412	+	0.858740i	$0.671248\pi$
$500$	−11.7220	−0.524223
$501$	−13.4878	−0.602589
$502$	−2.30488	−0.102872
$503$	0.775087	0.0345594	0.0172797	−	0.999851i	$-0.494499\pi$
$503$	0.775087	0.0345594	0.0172797	+	0.999851i	$0.494499\pi$
$504$	−2.30001	−0.102451
$505$	−17.0398	−0.758262
$506$	−1.02807	−0.0457031
$507$	−8.90470	−0.395472
$508$	8.74507	0.388000
$509$	−18.3928	−0.815246	−0.407623	−	0.913150i	$-0.633642\pi$
$509$	−18.3928	−0.815246	−0.407623	+	0.913150i	$0.633642\pi$
$510$	−1.49140	−0.0660404
$511$	−4.90798	−0.217116
$512$	17.5489	0.775561
$513$	−5.46546	−0.241306
$514$	0.393483	0.0173558
$515$	5.43766	0.239612
$516$	5.24749	0.231008
$517$	−24.3740	−1.07197
$518$	3.87722	0.170355
$519$	−17.9360	−0.787302
$520$	−12.5443	−0.550103
$521$	−8.47303	−0.371210	−0.185605	−	0.982624i	$-0.559425\pi$
$521$	−8.47303	−0.371210	−0.185605	+	0.982624i	$0.559425\pi$
$522$	1.13212	0.0495515
$523$	−19.0573	−0.833320	−0.416660	−	0.909062i	$-0.636799\pi$
$523$	−19.0573	−0.833320	−0.416660	+	0.909062i	$0.636799\pi$
$524$	20.4493	0.893333
$525$	2.26351	0.0987876
$526$	1.13833	0.0496336
$527$	−0.00463034	−0.000201701 0
$528$	−7.81346	−0.340037
$529$	−22.8774	−0.994671
$530$	−6.64557	−0.288665
$531$	11.1101	0.482138
$532$	8.68681	0.376621
$533$	−0.299174	−0.0129587
$534$	9.08508	0.393150
$535$	−40.9464	−1.77027
$536$	1.41522	0.0611284
$537$	21.3336	0.920612
$538$	−1.55345	−0.0669742
$539$	−4.58265	−0.197389
$540$	4.28358	0.184336
$541$	−14.7317	−0.633367	−0.316683	−	0.948531i	$-0.602569\pi$
$541$	−14.7317	−0.633367	−0.316683	+	0.948531i	$0.602569\pi$
$542$	5.56573	0.239069
$543$	−0.691691	−0.0296833
$544$	4.91610	0.210776
$545$	−42.5765	−1.82378
$546$	−1.29673	−0.0554950
$547$	−22.9327	−0.980531	−0.490266	−	0.871573i	$-0.663100\pi$
$547$	−22.9327	−0.980531	−0.490266	+	0.871573i	$0.663100\pi$
$548$	−12.1053	−0.517111
$549$	4.48726	0.191512
$550$	−6.64671	−0.283417
$551$	−9.65630	−0.411372
$552$	−0.805242	−0.0342734
$553$	−16.1304	−0.685936
$554$	15.7361	0.668562
$555$	−16.3074	−0.692212
$556$	2.20561	0.0935386
$557$	−36.5399	−1.54824	−0.774122	−	0.633036i	$-0.781809\pi$
$557$	−36.5399	−1.54824	−0.774122	+	0.633036i	$0.781809\pi$
$558$	−0.00343563	−0.000145442 0
$559$	6.68129	0.282589
$560$	−4.59515	−0.194181
$561$	−3.95759	−0.167089
$562$	−7.05198	−0.297470
$563$	19.1556	0.807313	0.403657	−	0.914911i	$-0.367739\pi$
$563$	19.1556	0.807313	0.403657	+	0.914911i	$0.367739\pi$
$564$	−8.45364	−0.355963
$565$	−46.0305	−1.93652
$566$	−5.42316	−0.227952
$567$	1.00000	0.0419961
$568$	28.5661	1.19861
$569$	−12.6082	−0.528565	−0.264283	−	0.964445i	$-0.585135\pi$
$569$	−12.6082	−0.528565	−0.264283	+	0.964445i	$0.585135\pi$
$570$	9.43860	0.395339
$571$	33.0533	1.38324	0.691620	−	0.722262i	$-0.256898\pi$
$571$	33.0533	1.38324	0.691620	+	0.722262i	$0.256898\pi$
$572$	−14.7399	−0.616305
$573$	1.00000	0.0417756
$574$	0.0947303	0.00395397
$575$	0.792463	0.0330480
$576$	0.237651	0.00990211
$577$	−1.72375	−0.0717605	−0.0358803	−	0.999356i	$-0.511423\pi$
$577$	−1.72375	−0.0717605	−0.0358803	+	0.999356i	$0.511423\pi$
$578$	−10.4153	−0.433221
$579$	8.17867	0.339894
$580$	7.56818	0.314252
$581$	12.6202	0.523573
$582$	−4.56296	−0.189141
$583$	−17.6347	−0.730355
$584$	11.2884	0.467117
$585$	5.45401	0.225496
$586$	−5.35377	−0.221162
$587$	33.4458	1.38045	0.690227	−	0.723593i	$-0.257511\pi$
$587$	33.4458	1.38045	0.690227	+	0.723593i	$0.257511\pi$
$588$	−1.58940	−0.0655459
$589$	0.0293039	0.00120745
$590$	−19.1867	−0.789903
$591$	24.0885	0.990867
$592$	10.3167	0.424012
$593$	18.1088	0.743640	0.371820	−	0.928305i	$-0.378734\pi$
$593$	18.1088	0.743640	0.371820	+	0.928305i	$0.378734\pi$
$594$	−2.93646	−0.120485
$595$	−2.32748	−0.0954176
$596$	0.617179	0.0252806
$597$	7.34236	0.300503
$598$	−0.453991	−0.0185651
$599$	−28.3111	−1.15676	−0.578379	−	0.815768i	$-0.696315\pi$
$599$	−28.3111	−1.15676	−0.578379	+	0.815768i	$0.696315\pi$
$600$	−5.20610	−0.212538
$601$	4.59316	0.187359	0.0936795	−	0.995602i	$-0.470137\pi$
$601$	4.59316	0.187359	0.0936795	+	0.995602i	$0.470137\pi$
$602$	−2.11556	−0.0862239
$603$	−0.615312	−0.0250574
$604$	17.5677	0.714820
$605$	−26.9528	−1.09579
$606$	4.05135	0.164575
$607$	−36.5406	−1.48314	−0.741568	−	0.670878i	$-0.765917\pi$
$607$	−36.5406	−1.48314	−0.741568	+	0.670878i	$0.765917\pi$
$608$	−31.1124	−1.26178
$609$	1.76679	0.0715938
$610$	−7.74930	−0.313760
$611$	−10.7635	−0.435444
$612$	−1.37261	−0.0554845
$613$	23.1359	0.934448	0.467224	−	0.884139i	$-0.345254\pi$
$613$	23.1359	0.934448	0.467224	+	0.884139i	$0.345254\pi$
$614$	3.20101	0.129182
$615$	−0.398432	−0.0160663
$616$	10.5402	0.424675
$617$	−39.4707	−1.58903	−0.794515	−	0.607245i	$-0.792275\pi$
$617$	−39.4707	−1.58903	−0.794515	+	0.607245i	$0.792275\pi$
$618$	−1.29285	−0.0520059
$619$	−19.0655	−0.766306	−0.383153	−	0.923685i	$-0.625162\pi$
$619$	−19.0655	−0.766306	−0.383153	+	0.923685i	$0.625162\pi$
$620$	−0.0229671	−0.000922381 0
$621$	0.350104	0.0140492
$622$	2.79867	0.112217
$623$	14.1782	0.568037
$624$	−3.45040	−0.138126
$625$	−31.1941	−1.24776
$626$	5.98304	0.239130
$627$	25.0463	1.00025
$628$	3.41707	0.136356
$629$	5.22548	0.208353
$630$	−1.72696	−0.0688035
$631$	4.84671	0.192945	0.0964723	−	0.995336i	$-0.469244\pi$
$631$	4.84671	0.192945	0.0964723	+	0.995336i	$0.469244\pi$
$632$	37.1002	1.47577
$633$	−16.2622	−0.646363
$634$	14.1251	0.560978
$635$	14.8287	0.588458
$636$	−6.11625	−0.242525
$637$	−2.02368	−0.0801813
$638$	−5.18811	−0.205399
$639$	−12.4200	−0.491327
$640$	30.2735	1.19666
$641$	37.6293	1.48627	0.743134	−	0.669143i	$-0.233339\pi$
$641$	37.6293	1.48627	0.743134	+	0.669143i	$0.233339\pi$
$642$	9.73532	0.384223
$643$	21.1137	0.832644	0.416322	−	0.909217i	$-0.363319\pi$
$643$	21.1137	0.832644	0.416322	+	0.909217i	$0.363319\pi$
$644$	−0.556456	−0.0219274
$645$	8.89797	0.350357
$646$	−3.02446	−0.118996
$647$	21.1412	0.831146	0.415573	−	0.909560i	$-0.363581\pi$
$647$	21.1412	0.831146	0.415573	+	0.909560i	$0.363581\pi$
$648$	−2.30001	−0.0903530
$649$	−50.9138	−1.99854
$650$	−2.93517	−0.115127
$651$	−0.00536166	−0.000210140 0
$652$	−16.0651	−0.629159
$653$	36.5039	1.42851	0.714254	−	0.699887i	$-0.246766\pi$
$653$	36.5039	1.42851	0.714254	+	0.699887i	$0.246766\pi$
$654$	10.1229	0.395836
$655$	34.6752	1.35487
$656$	0.252062	0.00984137
$657$	−4.90798	−0.191478
$658$	3.40814	0.132863
$659$	−17.3314	−0.675137	−0.337569	−	0.941301i	$-0.609604\pi$
$659$	−17.3314	−0.675137	−0.337569	+	0.941301i	$0.609604\pi$
$660$	−19.6302	−0.764103
$661$	38.0507	1.48000	0.740001	−	0.672606i	$-0.234825\pi$
$661$	38.0507	1.48000	0.740001	+	0.672606i	$0.234825\pi$
$662$	4.32602	0.168135
$663$	−1.74766	−0.0678734
$664$	−29.0266	−1.12645
$665$	14.7299	0.571201
$666$	3.87722	0.150239
$667$	0.618558	0.0239507
$668$	21.4375	0.829442
$669$	20.2732	0.783809
$670$	1.06262	0.0410524
$671$	−20.5636	−0.793847
$672$	5.69256	0.219595
$673$	−20.0734	−0.773772	−0.386886	−	0.922128i	$-0.626449\pi$
$673$	−20.0734	−0.773772	−0.386886	+	0.922128i	$0.626449\pi$
$674$	−16.1706	−0.622869
$675$	2.26351	0.0871225
$676$	14.1532	0.544352
$677$	−19.7190	−0.757863	−0.378932	−	0.925425i	$-0.623708\pi$
$677$	−19.7190	−0.757863	−0.378932	+	0.925425i	$0.623708\pi$
$678$	10.9441	0.420306
$679$	−7.12096	−0.273277
$680$	5.35324	0.205287
$681$	3.16890	0.121433
$682$	0.0157443	0.000602881 0
$683$	13.7641	0.526670	0.263335	−	0.964704i	$-0.415177\pi$
$683$	13.7641	0.526670	0.263335	+	0.964704i	$0.415177\pi$
$684$	8.68681	0.332149
$685$	−20.5264	−0.784275
$686$	0.640778	0.0244650
$687$	20.7242	0.790677
$688$	−5.62917	−0.214610
$689$	−7.78743	−0.296677
$690$	−0.604613	−0.0230172
$691$	25.9909	0.988739	0.494370	−	0.869252i	$-0.335399\pi$
$691$	25.9909	0.988739	0.494370	+	0.869252i	$0.335399\pi$
$692$	28.5075	1.08369
$693$	−4.58265	−0.174081
$694$	1.05173	0.0399229
$695$	3.73996	0.141865
$696$	−4.06363	−0.154032
$697$	0.127672	0.00483591
$698$	12.7532	0.482717
$699$	9.92388	0.375356
$700$	−3.59763	−0.135978
$701$	4.33438	0.163707	0.0818537	−	0.996644i	$-0.473916\pi$
$701$	4.33438	0.163707	0.0818537	+	0.996644i	$0.473916\pi$
$702$	−1.29673	−0.0489420
$703$	−33.0704	−1.24727
$704$	−1.08907	−0.0410459
$705$	−14.3345	−0.539869
$706$	−9.22078	−0.347029
$707$	6.32254	0.237784
$708$	−17.6584	−0.663645
$709$	−18.6500	−0.700416	−0.350208	−	0.936672i	$-0.613889\pi$
$709$	−18.6500	−0.700416	−0.350208	+	0.936672i	$0.613889\pi$
$710$	21.4487	0.804957
$711$	−16.1304	−0.604938
$712$	−32.6100	−1.22211
$713$	−0.00187713	−7.02992e−5 0
$714$	0.553377	0.0207096
$715$	−24.9938	−0.934716
$716$	−33.9077	−1.26719
$717$	−15.3964	−0.574990
$718$	−2.67666	−0.0998921
$719$	−13.5058	−0.503681	−0.251841	−	0.967769i	$-0.581036\pi$
$719$	−13.5058	−0.503681	−0.251841	+	0.967769i	$0.581036\pi$
$720$	−4.59515	−0.171251
$721$	−2.01762	−0.0751400
$722$	6.96604	0.259249
$723$	19.9170	0.740722
$724$	1.09938	0.0408580
$725$	3.99914	0.148524
$726$	6.40823	0.237832
$727$	24.4324	0.906147	0.453073	−	0.891473i	$-0.350328\pi$
$727$	24.4324	0.906147	0.453073	+	0.891473i	$0.350328\pi$
$728$	4.65450	0.172507
$729$	1.00000	0.0370370
$730$	8.47585	0.313705
$731$	−2.85122	−0.105456
$732$	−7.13207	−0.263609
$733$	22.6420	0.836302	0.418151	−	0.908378i	$-0.362678\pi$
$733$	22.6420	0.836302	0.418151	+	0.908378i	$0.362678\pi$
$734$	11.3862	0.420274
$735$	−2.69509	−0.0994099
$736$	1.99298	0.0734624
$737$	2.81976	0.103867
$738$	0.0947303	0.00348707
$739$	16.2319	0.597100	0.298550	−	0.954394i	$-0.403497\pi$
$739$	16.2319	0.597100	0.298550	+	0.954394i	$0.403497\pi$
$740$	25.9191	0.952805
$741$	11.0604	0.406312
$742$	2.46581	0.0905226
$743$	13.7079	0.502896	0.251448	−	0.967871i	$-0.419093\pi$
$743$	13.7079	0.502896	0.251448	+	0.967871i	$0.419093\pi$
$744$	0.0123319	0.000452108 0
$745$	1.04653	0.0383418
$746$	−4.04405	−0.148063
$747$	12.6202	0.461748
$748$	6.29020	0.229992
$749$	15.1930	0.555139
$750$	4.72580	0.172562
$751$	−22.1375	−0.807808	−0.403904	−	0.914801i	$-0.632347\pi$
$751$	−22.1375	−0.807808	−0.403904	+	0.914801i	$0.632347\pi$
$752$	9.06852	0.330695
$753$	−3.59699	−0.131082
$754$	−2.29105	−0.0834352
$755$	29.7889	1.08413
$756$	−1.58940	−0.0578060
$757$	34.3402	1.24812	0.624058	−	0.781378i	$-0.285483\pi$
$757$	34.3402	1.24812	0.624058	+	0.781378i	$0.285483\pi$
$758$	−20.4089	−0.741284
$759$	−1.60440	−0.0582361
$760$	−33.8789	−1.22892
$761$	30.0941	1.09091	0.545454	−	0.838140i	$-0.316357\pi$
$761$	30.0941	1.09091	0.545454	+	0.838140i	$0.316357\pi$
$762$	−3.52563	−0.127720
$763$	15.7978	0.571919
$764$	−1.58940	−0.0575026
$765$	−2.32748	−0.0841504
$766$	−13.9339	−0.503451
$767$	−22.4834	−0.811827
$768$	−7.67306	−0.276878
$769$	−22.6224	−0.815785	−0.407892	−	0.913030i	$-0.633736\pi$
$769$	−22.6224	−0.815785	−0.407892	+	0.913030i	$0.633736\pi$
$770$	7.91403	0.285202
$771$	0.614071	0.0221152
$772$	−12.9992	−0.467851
$773$	21.6047	0.777067	0.388534	−	0.921435i	$-0.372982\pi$
$773$	21.6047	0.777067	0.388534	+	0.921435i	$0.372982\pi$
$774$	−2.11556	−0.0760423
$775$	−0.0121362	−0.000435944 0
$776$	16.3783	0.587946
$777$	6.05079	0.217071
$778$	−5.24309	−0.187974
$779$	−0.807993	−0.0289494
$780$	−8.66862	−0.310386
$781$	56.9164	2.03663
$782$	0.193739	0.00692811
$783$	1.76679	0.0631398
$784$	1.70501	0.0608931
$785$	5.79419	0.206804
$786$	−8.24429	−0.294064
$787$	18.4454	0.657509	0.328755	−	0.944415i	$-0.393371\pi$
$787$	18.4454	0.657509	0.328755	+	0.944415i	$0.393371\pi$
$788$	−38.2863	−1.36389
$789$	1.77648	0.0632444
$790$	27.8565	0.991091
$791$	17.0794	0.607273
$792$	10.5402	0.374528
$793$	−9.08080	−0.322469
$794$	−5.56436	−0.197472
$795$	−10.3711	−0.367825
$796$	−11.6700	−0.413631
$797$	14.6629	0.519386	0.259693	−	0.965691i	$-0.416379\pi$
$797$	14.6629	0.519386	0.259693	+	0.965691i	$0.416379\pi$
$798$	−3.50215	−0.123975
$799$	4.59329	0.162499
$800$	12.8852	0.455559
$801$	14.1782	0.500962
$802$	−9.47275	−0.334494
$803$	22.4915	0.793709
$804$	0.977978	0.0344906
$805$	−0.943560	−0.0332561
$806$	0.00695264	0.000244896 0
$807$	−2.42432	−0.0853402
$808$	−14.5419	−0.511583
$809$	−2.32671	−0.0818029	−0.0409014	−	0.999163i	$-0.513023\pi$
$809$	−2.32671	−0.0818029	−0.0409014	+	0.999163i	$0.513023\pi$
$810$	−1.72696	−0.0606790
$811$	11.9683	0.420262	0.210131	−	0.977673i	$-0.432611\pi$
$811$	11.9683	0.420262	0.210131	+	0.977673i	$0.432611\pi$
$812$	−2.80814	−0.0985463
$813$	8.68589	0.304628
$814$	−17.7679	−0.622766
$815$	−27.2410	−0.954211
$816$	1.47245	0.0515460
$817$	18.0445	0.631296
$818$	9.52123	0.332902
$819$	−2.02368	−0.0707132
$820$	0.633269	0.0221147
$821$	0.349961	0.0122137	0.00610687	−	0.999981i	$-0.498056\pi$
$821$	0.349961	0.0122137	0.00610687	+	0.999981i	$0.498056\pi$
$822$	4.88032	0.170221
$823$	−6.39270	−0.222836	−0.111418	−	0.993774i	$-0.535539\pi$
$823$	−6.39270	−0.222836	−0.111418	+	0.993774i	$0.535539\pi$
$824$	4.64054	0.161661
$825$	−10.3729	−0.361137
$826$	7.11912	0.247706
$827$	−54.5806	−1.89795	−0.948977	−	0.315346i	$-0.897880\pi$
$827$	−54.5806	−1.89795	−0.948977	+	0.315346i	$0.897880\pi$
$828$	−0.556456	−0.0193382
$829$	29.8976	1.03839	0.519194	−	0.854656i	$-0.326232\pi$
$829$	29.8976	1.03839	0.519194	+	0.854656i	$0.326232\pi$
$830$	−21.7945	−0.756498
$831$	24.5578	0.851900
$832$	−0.480930	−0.0166732
$833$	0.863602	0.0299220
$834$	−0.889205	−0.0307907
$835$	36.3508	1.25797
$836$	−39.8086	−1.37681
$837$	−0.00536166	−0.000185326 0
$838$	−16.1204	−0.556870
$839$	3.30005	0.113930	0.0569651	−	0.998376i	$-0.481858\pi$
$839$	3.30005	0.113930	0.0569651	+	0.998376i	$0.481858\pi$
$840$	6.19874	0.213877
$841$	−25.8785	−0.892361
$842$	−17.6726	−0.609037
$843$	−11.0053	−0.379044
$844$	25.8471	0.889695
$845$	23.9990	0.825590
$846$	3.40814	0.117174
$847$	10.0007	0.343628
$848$	6.56112	0.225310
$849$	−8.46339	−0.290463
$850$	1.25257	0.0429630
$851$	2.11840	0.0726180
$852$	19.7404	0.676293
$853$	−23.4318	−0.802289	−0.401144	−	0.916015i	$-0.631387\pi$
$853$	−23.4318	−0.802289	−0.401144	+	0.916015i	$0.631387\pi$
$854$	2.87534	0.0983921
$855$	14.7299	0.503752
$856$	−34.9440	−1.19436
$857$	0.517765	0.0176865	0.00884325	−	0.999961i	$-0.497185\pi$
$857$	0.517765	0.0176865	0.00884325	+	0.999961i	$0.497185\pi$
$858$	5.94248	0.202873
$859$	35.1851	1.20050	0.600251	−	0.799812i	$-0.295068\pi$
$859$	35.1851	1.20050	0.600251	+	0.799812i	$0.295068\pi$
$860$	−14.1425	−0.482254
$861$	0.147836	0.00503825
$862$	−18.3126	−0.623730
$863$	38.9968	1.32747	0.663733	−	0.747969i	$-0.268971\pi$
$863$	38.9968	1.32747	0.663733	+	0.747969i	$0.268971\pi$
$864$	5.69256	0.193665
$865$	48.3391	1.64358
$866$	16.5824	0.563494
$867$	−16.2542	−0.552021
$868$	0.00852183	0.000289250 0
$869$	73.9201	2.50757
$870$	−3.05116	−0.103444
$871$	1.24520	0.0421919
$872$	−36.3351	−1.23046
$873$	−7.12096	−0.241008
$874$	−1.22611	−0.0414739
$875$	7.37509	0.249324
$876$	7.80075	0.263563
$877$	6.35971	0.214752	0.107376	−	0.994218i	$-0.465755\pi$
$877$	6.35971	0.214752	0.107376	+	0.994218i	$0.465755\pi$
$878$	−2.89667	−0.0977578
$879$	−8.35510	−0.281810
$880$	21.0580	0.709864
$881$	−46.9553	−1.58196	−0.790982	−	0.611839i	$-0.790430\pi$
$881$	−46.9553	−1.58196	−0.790982	+	0.611839i	$0.790430\pi$
$882$	0.640778	0.0215761
$883$	4.38218	0.147472	0.0737360	−	0.997278i	$-0.476508\pi$
$883$	4.38218	0.147472	0.0737360	+	0.997278i	$0.476508\pi$
$884$	2.77773	0.0934252
$885$	−29.9428	−1.00651
$886$	15.4320	0.518449
$887$	41.5373	1.39469	0.697344	−	0.716737i	$-0.254365\pi$
$887$	41.5373	1.39469	0.697344	+	0.716737i	$0.254365\pi$
$888$	−13.9169	−0.467021
$889$	−5.50211	−0.184535
$890$	−24.4851	−0.820742
$891$	−4.58265	−0.153525
$892$	−32.2223	−1.07888
$893$	−29.0694	−0.972771
$894$	−0.248820	−0.00832178
$895$	−57.4959	−1.92188
$896$	−11.2328	−0.375263
$897$	−0.708499	−0.0236561
$898$	17.4553	0.582492
$899$	−0.00947291	−0.000315939 0
$900$	−3.59763	−0.119921
$901$	3.32326	0.110714
$902$	−0.434116	−0.0144545
$903$	−3.30155	−0.109869
$904$	−39.2828	−1.30653
$905$	1.86417	0.0619671
$906$	−7.08254	−0.235302
$907$	−23.9385	−0.794865	−0.397432	−	0.917631i	$-0.630099\pi$
$907$	−23.9385	−0.794865	−0.397432	+	0.917631i	$0.630099\pi$
$908$	−5.03666	−0.167147
$909$	6.32254	0.209705
$910$	3.49481	0.115852
$911$	33.9165	1.12370	0.561852	−	0.827238i	$-0.310089\pi$
$911$	33.9165	1.12370	0.561852	+	0.827238i	$0.310089\pi$
$912$	−9.31865	−0.308571
$913$	−57.8339	−1.91402
$914$	−25.3871	−0.839731
$915$	−12.0936	−0.399801
$916$	−32.9391	−1.08834
$917$	−12.8660	−0.424874
$918$	0.553377	0.0182642
$919$	10.6638	0.351767	0.175884	−	0.984411i	$-0.443722\pi$
$919$	10.6638	0.351767	0.175884	+	0.984411i	$0.443722\pi$
$920$	2.17020	0.0715494
$921$	4.99550	0.164607
$922$	−2.60789	−0.0858863
$923$	25.1341	0.827299
$924$	7.28368	0.239615
$925$	13.6960	0.450323
$926$	15.1804	0.498860
$927$	−2.01762	−0.0662672
$928$	10.0575	0.330155
$929$	43.3654	1.42277	0.711386	−	0.702802i	$-0.248068\pi$
$929$	43.3654	1.42277	0.711386	+	0.702802i	$0.248068\pi$
$930$	0.00925934	0.000303626 0
$931$	−5.46546	−0.179123
$932$	−15.7730	−0.516663
$933$	4.36761	0.142989
$934$	10.6774	0.349374
$935$	10.6661	0.348817
$936$	4.65450	0.152137
$937$	36.7898	1.20187	0.600935	−	0.799298i	$-0.294795\pi$
$937$	36.7898	1.20187	0.600935	+	0.799298i	$0.294795\pi$
$938$	−0.394278	−0.0128736
$939$	9.33715	0.304706
$940$	22.7833	0.743110
$941$	16.2968	0.531259	0.265630	−	0.964075i	$-0.414420\pi$
$941$	16.2968	0.531259	0.265630	+	0.964075i	$0.414420\pi$
$942$	−1.37761	−0.0448851
$943$	0.0517580	0.00168547
$944$	18.9428	0.616537
$945$	−2.69509	−0.0876713
$946$	9.69488	0.315208
$947$	56.3329	1.83057	0.915287	−	0.402802i	$-0.131964\pi$
$947$	56.3329	1.83057	0.915287	+	0.402802i	$0.131964\pi$
$948$	25.6378	0.832675
$949$	9.93219	0.322413
$950$	−7.92714	−0.257190
$951$	22.0436	0.714813
$952$	−1.98629	−0.0643762
$953$	−13.1640	−0.426423	−0.213212	−	0.977006i	$-0.568392\pi$
$953$	−13.1640	−0.426423	−0.213212	+	0.977006i	$0.568392\pi$
$954$	2.46581	0.0798335
$955$	−2.69509	−0.0872111
$956$	24.4711	0.791453
$957$	−8.09657	−0.261725
$958$	21.1067	0.681926
$959$	7.61623	0.245941
$960$	−0.640490	−0.0206717
$961$	−31.0000	−0.999999
$962$	−7.84626	−0.252974
$963$	15.1930	0.489586
$964$	−31.6562	−1.01958
$965$	−22.0422	−0.709565
$966$	0.224339	0.00721798
$967$	0.503327	0.0161859	0.00809296	−	0.999967i	$-0.497424\pi$
$967$	0.503327	0.0161859	0.00809296	+	0.999967i	$0.497424\pi$
$968$	−23.0017	−0.739303
$969$	−4.71998	−0.151628
$970$	12.2976	0.394851
$971$	−7.36981	−0.236508	−0.118254	−	0.992983i	$-0.537730\pi$
$971$	−7.36981	−0.236508	−0.118254	+	0.992983i	$0.537730\pi$
$972$	−1.58940	−0.0509801
$973$	−1.38770	−0.0444875
$974$	13.9926	0.448353
$975$	−4.58063	−0.146697
$976$	7.65082	0.244897
$977$	−2.63534	−0.0843120	−0.0421560	−	0.999111i	$-0.513423\pi$
$977$	−2.63534	−0.0843120	−0.0421560	+	0.999111i	$0.513423\pi$
$978$	6.47676	0.207104
$979$	−64.9737	−2.07657
$980$	4.28358	0.136834
$981$	15.7978	0.504385
$982$	24.6107	0.785359
$983$	11.2399	0.358497	0.179249	−	0.983804i	$-0.442633\pi$
$983$	11.2399	0.358497	0.179249	+	0.983804i	$0.442633\pi$
$984$	−0.340025	−0.0108396
$985$	−64.9206	−2.06854
$986$	0.977700	0.0311363
$987$	5.31875	0.169298
$988$	−17.5794	−0.559274
$989$	−1.15588	−0.0367550
$990$	7.91403	0.251525
$991$	−31.6993	−1.00696	−0.503481	−	0.864006i	$-0.667948\pi$
$991$	−31.6993	−1.00696	−0.503481	+	0.864006i	$0.667948\pi$
$992$	−0.0305215	−0.000969060 0
$993$	6.75119	0.214242
$994$	−7.95845	−0.252427
$995$	−19.7883	−0.627332
$996$	−20.0586	−0.635580
$997$	33.9517	1.07526	0.537631	−	0.843180i	$-0.319320\pi$
$997$	33.9517	1.07526	0.537631	+	0.843180i	$0.319320\pi$
$998$	−14.6692	−0.464347
$999$	6.05079	0.191439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.15	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.15	✓	27	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.640778 q^{2} +1.00000 q^{3} -1.58940 q^{4} -2.69509 q^{5} +0.640778 q^{6} +1.00000 q^{7} -2.30001 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.640778 q^{2} +1.00000 q^{3} -1.58940 q^{4} -2.69509 q^{5} +0.640778 q^{6} +1.00000 q^{7} -2.30001 q^{8} +1.00000 q^{9} -1.72696 q^{10} -4.58265 q^{11} -1.58940 q^{12} -2.02368 q^{13} +0.640778 q^{14} -2.69509 q^{15} +1.70501 q^{16} +0.863602 q^{17} +0.640778 q^{18} -5.46546 q^{19} +4.28358 q^{20} +1.00000 q^{21} -2.93646 q^{22} +0.350104 q^{23} -2.30001 q^{24} +2.26351 q^{25} -1.29673 q^{26} +1.00000 q^{27} -1.58940 q^{28} +1.76679 q^{29} -1.72696 q^{30} -0.00536166 q^{31} +5.69256 q^{32} -4.58265 q^{33} +0.553377 q^{34} -2.69509 q^{35} -1.58940 q^{36} +6.05079 q^{37} -3.50215 q^{38} -2.02368 q^{39} +6.19874 q^{40} +0.147836 q^{41} +0.640778 q^{42} -3.30155 q^{43} +7.28368 q^{44} -2.69509 q^{45} +0.224339 q^{46} +5.31875 q^{47} +1.70501 q^{48} +1.00000 q^{49} +1.45041 q^{50} +0.863602 q^{51} +3.21645 q^{52} +3.84814 q^{53} +0.640778 q^{54} +12.3507 q^{55} -2.30001 q^{56} -5.46546 q^{57} +1.13212 q^{58} +11.1101 q^{59} +4.28358 q^{60} +4.48726 q^{61} -0.00343563 q^{62} +1.00000 q^{63} +0.237651 q^{64} +5.45401 q^{65} -2.93646 q^{66} -0.615312 q^{67} -1.37261 q^{68} +0.350104 q^{69} -1.72696 q^{70} -12.4200 q^{71} -2.30001 q^{72} -4.90798 q^{73} +3.87722 q^{74} +2.26351 q^{75} +8.68681 q^{76} -4.58265 q^{77} -1.29673 q^{78} -16.1304 q^{79} -4.59515 q^{80} +1.00000 q^{81} +0.0947303 q^{82} +12.6202 q^{83} -1.58940 q^{84} -2.32748 q^{85} -2.11556 q^{86} +1.76679 q^{87} +10.5402 q^{88} +14.1782 q^{89} -1.72696 q^{90} -2.02368 q^{91} -0.556456 q^{92} -0.00536166 q^{93} +3.40814 q^{94} +14.7299 q^{95} +5.69256 q^{96} -7.12096 q^{97} +0.640778 q^{98} -4.58265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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