LMFDB - Embedded newform 4034.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.19422 q^{3} +1.00000 q^{4} +1.77357 q^{5} +1.19422 q^{6} +2.63831 q^{7} -1.00000 q^{8} -1.57384 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.19422 q^{3} +1.00000 q^{4} +1.77357 q^{5} +1.19422 q^{6} +2.63831 q^{7} -1.00000 q^{8} -1.57384 q^{9} -1.77357 q^{10} -1.87386 q^{11} -1.19422 q^{12} -6.18761 q^{13} -2.63831 q^{14} -2.11803 q^{15} +1.00000 q^{16} +5.03502 q^{17} +1.57384 q^{18} +0.622057 q^{19} +1.77357 q^{20} -3.15072 q^{21} +1.87386 q^{22} -4.47785 q^{23} +1.19422 q^{24} -1.85446 q^{25} +6.18761 q^{26} +5.46217 q^{27} +2.63831 q^{28} +9.96239 q^{29} +2.11803 q^{30} +3.49715 q^{31} -1.00000 q^{32} +2.23781 q^{33} -5.03502 q^{34} +4.67922 q^{35} -1.57384 q^{36} +3.56037 q^{37} -0.622057 q^{38} +7.38938 q^{39} -1.77357 q^{40} -10.7727 q^{41} +3.15072 q^{42} +0.549121 q^{43} -1.87386 q^{44} -2.79130 q^{45} +4.47785 q^{46} -4.29974 q^{47} -1.19422 q^{48} -0.0393351 q^{49} +1.85446 q^{50} -6.01293 q^{51} -6.18761 q^{52} +1.92790 q^{53} -5.46217 q^{54} -3.32343 q^{55} -2.63831 q^{56} -0.742873 q^{57} -9.96239 q^{58} -9.34767 q^{59} -2.11803 q^{60} -4.71913 q^{61} -3.49715 q^{62} -4.15226 q^{63} +1.00000 q^{64} -10.9742 q^{65} -2.23781 q^{66} -0.131982 q^{67} +5.03502 q^{68} +5.34754 q^{69} -4.67922 q^{70} -4.03353 q^{71} +1.57384 q^{72} -7.70992 q^{73} -3.56037 q^{74} +2.21463 q^{75} +0.622057 q^{76} -4.94383 q^{77} -7.38938 q^{78} +8.76970 q^{79} +1.77357 q^{80} -1.80154 q^{81} +10.7727 q^{82} -8.41319 q^{83} -3.15072 q^{84} +8.92996 q^{85} -0.549121 q^{86} -11.8973 q^{87} +1.87386 q^{88} +1.49477 q^{89} +2.79130 q^{90} -16.3248 q^{91} -4.47785 q^{92} -4.17637 q^{93} +4.29974 q^{94} +1.10326 q^{95} +1.19422 q^{96} -2.31972 q^{97} +0.0393351 q^{98} +2.94915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	−1.19422	−0.689484	−0.344742	−	0.938697i	$-0.612034\pi$
$3$	−1.19422	−0.689484	−0.344742	+	0.938697i	$0.612034\pi$
$4$	1.00000	0.500000
$5$	1.77357	0.793164	0.396582	−	0.917999i	$-0.370196\pi$
$5$	1.77357	0.793164	0.396582	+	0.917999i	$0.370196\pi$
$6$	1.19422	0.487539
$7$	2.63831	0.997186	0.498593	−	0.866836i	$-0.333850\pi$
$7$	2.63831	0.997186	0.498593	+	0.866836i	$0.333850\pi$
$8$	−1.00000	−0.353553
$9$	−1.57384	−0.524612
$10$	−1.77357	−0.560852
$11$	−1.87386	−0.564991	−0.282496	−	0.959269i	$-0.591162\pi$
$11$	−1.87386	−0.564991	−0.282496	+	0.959269i	$0.591162\pi$
$12$	−1.19422	−0.344742
$13$	−6.18761	−1.71614	−0.858068	−	0.513537i	$-0.828335\pi$
$13$	−6.18761	−1.71614	−0.858068	+	0.513537i	$0.828335\pi$
$14$	−2.63831	−0.705117
$15$	−2.11803	−0.546874
$16$	1.00000	0.250000
$17$	5.03502	1.22117	0.610586	−	0.791950i	$-0.290934\pi$
$17$	5.03502	1.22117	0.610586	+	0.791950i	$0.290934\pi$
$18$	1.57384	0.370957
$19$	0.622057	0.142710	0.0713548	−	0.997451i	$-0.477268\pi$
$19$	0.622057	0.142710	0.0713548	+	0.997451i	$0.477268\pi$
$20$	1.77357	0.396582
$21$	−3.15072	−0.687544
$22$	1.87386	0.399509
$23$	−4.47785	−0.933696	−0.466848	−	0.884337i	$-0.654611\pi$
$23$	−4.47785	−0.933696	−0.466848	+	0.884337i	$0.654611\pi$
$24$	1.19422	0.243769
$25$	−1.85446	−0.370891
$26$	6.18761	1.21349
$27$	5.46217	1.05120
$28$	2.63831	0.498593
$29$	9.96239	1.84997	0.924985	−	0.380005i	$-0.124078\pi$
$29$	9.96239	1.84997	0.924985	+	0.380005i	$0.124078\pi$
$30$	2.11803	0.386698
$31$	3.49715	0.628107	0.314054	−	0.949405i	$-0.398313\pi$
$31$	3.49715	0.628107	0.314054	+	0.949405i	$0.398313\pi$
$32$	−1.00000	−0.176777
$33$	2.23781	0.389553
$34$	−5.03502	−0.863499
$35$	4.67922	0.790932
$36$	−1.57384	−0.262306
$37$	3.56037	0.585321	0.292661	−	0.956216i	$-0.405459\pi$
$37$	3.56037	0.585321	0.292661	+	0.956216i	$0.405459\pi$
$38$	−0.622057	−0.100911
$39$	7.38938	1.18325
$40$	−1.77357	−0.280426
$41$	−10.7727	−1.68241	−0.841207	−	0.540713i	$-0.818154\pi$
$41$	−10.7727	−1.68241	−0.841207	+	0.540713i	$0.818154\pi$
$42$	3.15072	0.486167
$43$	0.549121	0.0837402	0.0418701	−	0.999123i	$-0.486668\pi$
$43$	0.549121	0.0837402	0.0418701	+	0.999123i	$0.486668\pi$
$44$	−1.87386	−0.282496
$45$	−2.79130	−0.416103
$46$	4.47785	0.660223
$47$	−4.29974	−0.627181	−0.313590	−	0.949558i	$-0.601532\pi$
$47$	−4.29974	−0.627181	−0.313590	+	0.949558i	$0.601532\pi$
$48$	−1.19422	−0.172371
$49$	−0.0393351	−0.00561931
$50$	1.85446	0.262260
$51$	−6.01293	−0.841979
$52$	−6.18761	−0.858068
$53$	1.92790	0.264817	0.132409	−	0.991195i	$-0.457729\pi$
$53$	1.92790	0.264817	0.132409	+	0.991195i	$0.457729\pi$
$54$	−5.46217	−0.743307
$55$	−3.32343	−0.448131
$56$	−2.63831	−0.352559
$57$	−0.742873	−0.0983960
$58$	−9.96239	−1.30813
$59$	−9.34767	−1.21696	−0.608482	−	0.793568i	$-0.708221\pi$
$59$	−9.34767	−1.21696	−0.608482	+	0.793568i	$0.708221\pi$
$60$	−2.11803	−0.273437
$61$	−4.71913	−0.604223	−0.302111	−	0.953273i	$-0.597691\pi$
$61$	−4.71913	−0.604223	−0.302111	+	0.953273i	$0.597691\pi$
$62$	−3.49715	−0.444139
$63$	−4.15226	−0.523136
$64$	1.00000	0.125000
$65$	−10.9742	−1.36118
$66$	−2.23781	−0.275455
$67$	−0.131982	−0.0161242	−0.00806211	−	0.999968i	$-0.502566\pi$
$67$	−0.131982	−0.0161242	−0.00806211	+	0.999968i	$0.502566\pi$
$68$	5.03502	0.610586
$69$	5.34754	0.643769
$70$	−4.67922	−0.559274
$71$	−4.03353	−0.478692	−0.239346	−	0.970934i	$-0.576933\pi$
$71$	−4.03353	−0.478692	−0.239346	+	0.970934i	$0.576933\pi$
$72$	1.57384	0.185478
$73$	−7.70992	−0.902378	−0.451189	−	0.892428i	$-0.649000\pi$
$73$	−7.70992	−0.902378	−0.451189	+	0.892428i	$0.649000\pi$
$74$	−3.56037	−0.413885
$75$	2.21463	0.255724
$76$	0.622057	0.0713548
$77$	−4.94383	−0.563402
$78$	−7.38938	−0.836682
$79$	8.76970	0.986668	0.493334	−	0.869840i	$-0.335778\pi$
$79$	8.76970	0.986668	0.493334	+	0.869840i	$0.335778\pi$
$80$	1.77357	0.198291
$81$	−1.80154	−0.200171
$82$	10.7727	1.18965
$83$	−8.41319	−0.923468	−0.461734	−	0.887018i	$-0.652773\pi$
$83$	−8.41319	−0.923468	−0.461734	+	0.887018i	$0.652773\pi$
$84$	−3.15072	−0.343772
$85$	8.92996	0.968590
$86$	−0.549121	−0.0592133
$87$	−11.8973	−1.27552
$88$	1.87386	0.199755
$89$	1.49477	0.158445	0.0792225	−	0.996857i	$-0.474756\pi$
$89$	1.49477	0.158445	0.0792225	+	0.996857i	$0.474756\pi$
$90$	2.79130	0.294229
$91$	−16.3248	−1.71131
$92$	−4.47785	−0.466848
$93$	−4.17637	−0.433070
$94$	4.29974	0.443484
$95$	1.10326	0.113192
$96$	1.19422	0.121885
$97$	−2.31972	−0.235532	−0.117766	−	0.993041i	$-0.537573\pi$
$97$	−2.31972	−0.235532	−0.117766	+	0.993041i	$0.537573\pi$
$98$	0.0393351	0.00397345
$99$	2.94915	0.296401
$100$	−1.85446	−0.185446
$101$	13.9457	1.38765	0.693827	−	0.720142i	$-0.255923\pi$
$101$	13.9457	1.38765	0.693827	+	0.720142i	$0.255923\pi$
$102$	6.01293	0.595369
$103$	11.9285	1.17535	0.587677	−	0.809096i	$-0.300043\pi$
$103$	11.9285	1.17535	0.587677	+	0.809096i	$0.300043\pi$
$104$	6.18761	0.606745
$105$	−5.58802	−0.545335
$106$	−1.92790	−0.187254
$107$	−6.18261	−0.597695	−0.298848	−	0.954301i	$-0.596602\pi$
$107$	−6.18261	−0.597695	−0.298848	+	0.954301i	$0.596602\pi$
$108$	5.46217	0.525598
$109$	−6.13855	−0.587966	−0.293983	−	0.955811i	$-0.594981\pi$
$109$	−6.13855	−0.587966	−0.293983	+	0.955811i	$0.594981\pi$
$110$	3.32343	0.316876
$111$	−4.25187	−0.403570
$112$	2.63831	0.249297
$113$	−7.83247	−0.736817	−0.368408	−	0.929664i	$-0.620097\pi$
$113$	−7.83247	−0.736817	−0.368408	+	0.929664i	$0.620097\pi$
$114$	0.742873	0.0695765
$115$	−7.94177	−0.740574
$116$	9.96239	0.924985
$117$	9.73828	0.900305
$118$	9.34767	0.860523
$119$	13.2839	1.21774
$120$	2.11803	0.193349
$121$	−7.48863	−0.680785
$122$	4.71913	0.427250
$123$	12.8650	1.16000
$124$	3.49715	0.314054
$125$	−12.1568	−1.08734
$126$	4.15226	0.369913
$127$	13.4776	1.19595	0.597974	−	0.801516i	$-0.295973\pi$
$127$	13.4776	1.19595	0.597974	+	0.801516i	$0.295973\pi$
$128$	−1.00000	−0.0883883
$129$	−0.655772	−0.0577375
$130$	10.9742	0.962497
$131$	−1.28123	−0.111942	−0.0559710	−	0.998432i	$-0.517825\pi$
$131$	−1.28123	−0.111942	−0.0559710	+	0.998432i	$0.517825\pi$
$132$	2.23781	0.194776
$133$	1.64118	0.142308
$134$	0.131982	0.0114015
$135$	9.68753	0.833770
$136$	−5.03502	−0.431750
$137$	9.32624	0.796795	0.398397	−	0.917213i	$-0.369566\pi$
$137$	9.32624	0.796795	0.398397	+	0.917213i	$0.369566\pi$
$138$	−5.34754	−0.455213
$139$	−21.5792	−1.83032	−0.915161	−	0.403089i	$-0.867936\pi$
$139$	−21.5792	−1.83032	−0.915161	+	0.403089i	$0.867936\pi$
$140$	4.67922	0.395466
$141$	5.13484	0.432431
$142$	4.03353	0.338486
$143$	11.5947	0.969602
$144$	−1.57384	−0.131153
$145$	17.6690	1.46733
$146$	7.70992	0.638077
$147$	0.0469749	0.00387442
$148$	3.56037	0.292661
$149$	−3.50468	−0.287114	−0.143557	−	0.989642i	$-0.545854\pi$
$149$	−3.50468	−0.287114	−0.143557	+	0.989642i	$0.545854\pi$
$150$	−2.21463	−0.180824
$151$	−16.3697	−1.33215	−0.666073	−	0.745887i	$-0.732026\pi$
$151$	−16.3697	−1.33215	−0.666073	+	0.745887i	$0.732026\pi$
$152$	−0.622057	−0.0504555
$153$	−7.92430	−0.640641
$154$	4.94383	0.398385
$155$	6.20244	0.498192
$156$	7.38938	0.591624
$157$	−9.47080	−0.755852	−0.377926	−	0.925836i	$-0.623363\pi$
$157$	−9.47080	−0.755852	−0.377926	+	0.925836i	$0.623363\pi$
$158$	−8.76970	−0.697680
$159$	−2.30234	−0.182587
$160$	−1.77357	−0.140213
$161$	−11.8139	−0.931069
$162$	1.80154	0.141542
$163$	−4.02756	−0.315463	−0.157731	−	0.987482i	$-0.550418\pi$
$163$	−4.02756	−0.315463	−0.157731	+	0.987482i	$0.550418\pi$
$164$	−10.7727	−0.841207
$165$	3.96891	0.308979
$166$	8.41319	0.652990
$167$	−1.96186	−0.151814	−0.0759068	−	0.997115i	$-0.524185\pi$
$167$	−1.96186	−0.151814	−0.0759068	+	0.997115i	$0.524185\pi$
$168$	3.15072	0.243084
$169$	25.2866	1.94512
$170$	−8.92996	−0.684896
$171$	−0.979015	−0.0748671
$172$	0.549121	0.0418701
$173$	−13.7452	−1.04503	−0.522513	−	0.852631i	$-0.675005\pi$
$173$	−13.7452	−1.04503	−0.522513	+	0.852631i	$0.675005\pi$
$174$	11.8973	0.901932
$175$	−4.89262	−0.369848
$176$	−1.87386	−0.141248
$177$	11.1632	0.839077
$178$	−1.49477	−0.112038
$179$	−7.84370	−0.586266	−0.293133	−	0.956072i	$-0.594698\pi$
$179$	−7.84370	−0.586266	−0.293133	+	0.956072i	$0.594698\pi$
$180$	−2.79130	−0.208052
$181$	−4.37236	−0.324995	−0.162497	−	0.986709i	$-0.551955\pi$
$181$	−4.37236	−0.324995	−0.162497	+	0.986709i	$0.551955\pi$
$182$	16.3248	1.21008
$183$	5.63568	0.416602
$184$	4.47785	0.330111
$185$	6.31456	0.464256
$186$	4.17637	0.306227
$187$	−9.43495	−0.689952
$188$	−4.29974	−0.313590
$189$	14.4109	1.04824
$190$	−1.10326	−0.0800389
$191$	1.36718	0.0989255	0.0494628	−	0.998776i	$-0.484249\pi$
$191$	1.36718	0.0989255	0.0494628	+	0.998776i	$0.484249\pi$
$192$	−1.19422	−0.0861855
$193$	10.8364	0.780023	0.390012	−	0.920810i	$-0.372471\pi$
$193$	10.8364	0.780023	0.390012	+	0.920810i	$0.372471\pi$
$194$	2.31972	0.166546
$195$	13.1056	0.938509
$196$	−0.0393351	−0.00280965
$197$	18.2678	1.30153	0.650765	−	0.759279i	$-0.274448\pi$
$197$	18.2678	1.30153	0.650765	+	0.759279i	$0.274448\pi$
$198$	−2.94915	−0.209587
$199$	−11.5750	−0.820533	−0.410267	−	0.911966i	$-0.634564\pi$
$199$	−11.5750	−0.820533	−0.410267	+	0.911966i	$0.634564\pi$
$200$	1.85446	0.131130
$201$	0.157616	0.0111174
$202$	−13.9457	−0.981219
$203$	26.2838	1.84476
$204$	−6.01293	−0.420989
$205$	−19.1061	−1.33443
$206$	−11.9285	−0.831100
$207$	7.04740	0.489828
$208$	−6.18761	−0.429034
$209$	−1.16565	−0.0806297
$210$	5.58802	0.385610
$211$	−18.5020	−1.27373	−0.636864	−	0.770976i	$-0.719769\pi$
$211$	−18.5020	−1.27373	−0.636864	+	0.770976i	$0.719769\pi$
$212$	1.92790	0.132409
$213$	4.81692	0.330050
$214$	6.18261	0.422634
$215$	0.973904	0.0664197
$216$	−5.46217	−0.371654
$217$	9.22656	0.626340
$218$	6.13855	0.415755
$219$	9.20735	0.622175
$220$	−3.32343	−0.224065
$221$	−31.1548	−2.09570
$222$	4.25187	0.285367
$223$	−24.4391	−1.63656	−0.818282	−	0.574817i	$-0.805073\pi$
$223$	−24.4391	−1.63656	−0.818282	+	0.574817i	$0.805073\pi$
$224$	−2.63831	−0.176279
$225$	2.91861	0.194574
$226$	7.83247	0.521008
$227$	−0.259743	−0.0172397	−0.00861986	−	0.999963i	$-0.502744\pi$
$227$	−0.259743	−0.0172397	−0.00861986	+	0.999963i	$0.502744\pi$
$228$	−0.742873	−0.0491980
$229$	3.88857	0.256964	0.128482	−	0.991712i	$-0.458990\pi$
$229$	3.88857	0.256964	0.128482	+	0.991712i	$0.458990\pi$
$230$	7.94177	0.523665
$231$	5.90403	0.388457
$232$	−9.96239	−0.654063
$233$	16.5787	1.08610	0.543052	−	0.839699i	$-0.317269\pi$
$233$	16.5787	1.08610	0.543052	+	0.839699i	$0.317269\pi$
$234$	−9.73828	−0.636612
$235$	−7.62588	−0.497457
$236$	−9.34767	−0.608482
$237$	−10.4730	−0.680292
$238$	−13.2839	−0.861070
$239$	6.32840	0.409350	0.204675	−	0.978830i	$-0.434386\pi$
$239$	6.32840	0.409350	0.204675	+	0.978830i	$0.434386\pi$
$240$	−2.11803	−0.136718
$241$	3.05912	0.197055	0.0985276	−	0.995134i	$-0.468587\pi$
$241$	3.05912	0.197055	0.0985276	+	0.995134i	$0.468587\pi$
$242$	7.48863	0.481387
$243$	−14.2351	−0.913181
$244$	−4.71913	−0.302111
$245$	−0.0697636	−0.00445703
$246$	−12.8650	−0.820242
$247$	−3.84905	−0.244909
$248$	−3.49715	−0.222069
$249$	10.0472	0.636716
$250$	12.1568	0.768866
$251$	16.0962	1.01598	0.507992	−	0.861362i	$-0.330388\pi$
$251$	16.0962	1.01598	0.507992	+	0.861362i	$0.330388\pi$
$252$	−4.15226	−0.261568
$253$	8.39088	0.527530
$254$	−13.4776	−0.845663
$255$	−10.6643	−0.667827
$256$	1.00000	0.0625000
$257$	0.462204	0.0288315	0.0144158	−	0.999896i	$-0.495411\pi$
$257$	0.462204	0.0288315	0.0144158	+	0.999896i	$0.495411\pi$
$258$	0.655772	0.0408266
$259$	9.39335	0.583674
$260$	−10.9742	−0.680588
$261$	−15.6792	−0.970516
$262$	1.28123	0.0791549
$263$	−28.3698	−1.74936	−0.874678	−	0.484705i	$-0.838927\pi$
$263$	−28.3698	−1.74936	−0.874678	+	0.484705i	$0.838927\pi$
$264$	−2.23781	−0.137728
$265$	3.41926	0.210044
$266$	−1.64118	−0.100627
$267$	−1.78508	−0.109245
$268$	−0.131982	−0.00806211
$269$	21.5218	1.31221	0.656103	−	0.754671i	$-0.272204\pi$
$269$	21.5218	1.31221	0.656103	+	0.754671i	$0.272204\pi$
$270$	−9.68753	−0.589565
$271$	18.7267	1.13756	0.568782	−	0.822488i	$-0.307415\pi$
$271$	18.7267	1.13756	0.568782	+	0.822488i	$0.307415\pi$
$272$	5.03502	0.305293
$273$	19.4955	1.17992
$274$	−9.32624	−0.563419
$275$	3.47500	0.209550
$276$	5.34754	0.321884
$277$	−31.1016	−1.86872	−0.934358	−	0.356335i	$-0.884026\pi$
$277$	−31.1016	−1.86872	−0.934358	+	0.356335i	$0.884026\pi$
$278$	21.5792	1.29423
$279$	−5.50394	−0.329512
$280$	−4.67922	−0.279637
$281$	−24.8077	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$281$	−24.8077	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$282$	−5.13484	−0.305775
$283$	−26.1781	−1.55613	−0.778063	−	0.628186i	$-0.783798\pi$
$283$	−26.1781	−1.55613	−0.778063	+	0.628186i	$0.783798\pi$
$284$	−4.03353	−0.239346
$285$	−1.31754	−0.0780441
$286$	−11.5947	−0.685612
$287$	−28.4217	−1.67768
$288$	1.57384	0.0927391
$289$	8.35145	0.491262
$290$	−17.6690	−1.03756
$291$	2.77026	0.162395
$292$	−7.70992	−0.451189
$293$	8.51636	0.497531	0.248765	−	0.968564i	$-0.419975\pi$
$293$	8.51636	0.497531	0.248765	+	0.968564i	$0.419975\pi$
$294$	−0.0469749	−0.00273963
$295$	−16.5787	−0.965251
$296$	−3.56037	−0.206942
$297$	−10.2354	−0.593916
$298$	3.50468	0.203021
$299$	27.7072	1.60235
$300$	2.21463	0.127862
$301$	1.44875	0.0835046
$302$	16.3697	0.941969
$303$	−16.6543	−0.956765
$304$	0.622057	0.0356774
$305$	−8.36970	−0.479247
$306$	7.92430	0.453002
$307$	−1.78407	−0.101822	−0.0509112	−	0.998703i	$-0.516213\pi$
$307$	−1.78407	−0.101822	−0.0509112	+	0.998703i	$0.516213\pi$
$308$	−4.94383	−0.281701
$309$	−14.2453	−0.810387
$310$	−6.20244	−0.352275
$311$	−3.16159	−0.179277	−0.0896387	−	0.995974i	$-0.528571\pi$
$311$	−3.16159	−0.179277	−0.0896387	+	0.995974i	$0.528571\pi$
$312$	−7.38938	−0.418341
$313$	−29.5650	−1.67111	−0.835557	−	0.549403i	$-0.814855\pi$
$313$	−29.5650	−1.67111	−0.835557	+	0.549403i	$0.814855\pi$
$314$	9.47080	0.534468
$315$	−7.36432	−0.414932
$316$	8.76970	0.493334
$317$	17.2692	0.969933	0.484967	−	0.874533i	$-0.338832\pi$
$317$	17.2692	0.969933	0.484967	+	0.874533i	$0.338832\pi$
$318$	2.30234	0.129109
$319$	−18.6682	−1.04522
$320$	1.77357	0.0991455
$321$	7.38340	0.412101
$322$	11.8139	0.658365
$323$	3.13207	0.174273
$324$	−1.80154	−0.100085
$325$	11.4747	0.636499
$326$	4.02756	0.223066
$327$	7.33079	0.405393
$328$	10.7727	0.594823
$329$	−11.3440	−0.625416
$330$	−3.96891	−0.218481
$331$	−31.6593	−1.74015	−0.870077	−	0.492916i	$-0.835931\pi$
$331$	−31.6593	−1.74015	−0.870077	+	0.492916i	$0.835931\pi$
$332$	−8.41319	−0.461734
$333$	−5.60344	−0.307066
$334$	1.96186	0.107348
$335$	−0.234080	−0.0127891
$336$	−3.15072	−0.171886
$337$	−20.7608	−1.13091	−0.565457	−	0.824778i	$-0.691300\pi$
$337$	−20.7608	−1.13091	−0.565457	+	0.824778i	$0.691300\pi$
$338$	−25.2866	−1.37541
$339$	9.35370	0.508023
$340$	8.92996	0.484295
$341$	−6.55319	−0.354875
$342$	0.979015	0.0529391
$343$	−18.5719	−1.00279
$344$	−0.549121	−0.0296066
$345$	9.48423	0.510614
$346$	13.7452	0.738945
$347$	23.4011	1.25624	0.628118	−	0.778118i	$-0.283826\pi$
$347$	23.4011	1.25624	0.628118	+	0.778118i	$0.283826\pi$
$348$	−11.8973	−0.637762
$349$	2.62440	0.140481	0.0702404	−	0.997530i	$-0.477623\pi$
$349$	2.62440	0.140481	0.0702404	+	0.997530i	$0.477623\pi$
$350$	4.89262	0.261522
$351$	−33.7978	−1.80399
$352$	1.87386	0.0998773
$353$	21.5488	1.14693	0.573463	−	0.819231i	$-0.305600\pi$
$353$	21.5488	1.14693	0.573463	+	0.819231i	$0.305600\pi$
$354$	−11.1632	−0.593317
$355$	−7.15374	−0.379681
$356$	1.49477	0.0792225
$357$	−15.8640	−0.839610
$358$	7.84370	0.414552
$359$	11.5665	0.610456	0.305228	−	0.952279i	$-0.401267\pi$
$359$	11.5665	0.610456	0.305228	+	0.952279i	$0.401267\pi$
$360$	2.79130	0.147115
$361$	−18.6130	−0.979634
$362$	4.37236	0.229806
$363$	8.94308	0.469390
$364$	−16.3248	−0.855653
$365$	−13.6741	−0.715733
$366$	−5.63568	−0.294582
$367$	−22.8497	−1.19274	−0.596371	−	0.802709i	$-0.703391\pi$
$367$	−22.8497	−1.19274	−0.596371	+	0.802709i	$0.703391\pi$
$368$	−4.47785	−0.233424
$369$	16.9545	0.882614
$370$	−6.31456	−0.328278
$371$	5.08639	0.264072
$372$	−4.17637	−0.216535
$373$	14.5260	0.752126	0.376063	−	0.926594i	$-0.377278\pi$
$373$	14.5260	0.752126	0.376063	+	0.926594i	$0.377278\pi$
$374$	9.43495	0.487870
$375$	14.5180	0.749704
$376$	4.29974	0.221742
$377$	−61.6434	−3.17480
$378$	−14.4109	−0.741216
$379$	13.1494	0.675440	0.337720	−	0.941247i	$-0.390344\pi$
$379$	13.1494	0.675440	0.337720	+	0.941247i	$0.390344\pi$
$380$	1.10326	0.0565960
$381$	−16.0953	−0.824587
$382$	−1.36718	−0.0699509
$383$	−9.88391	−0.505044	−0.252522	−	0.967591i	$-0.581260\pi$
$383$	−9.88391	−0.505044	−0.252522	+	0.967591i	$0.581260\pi$
$384$	1.19422	0.0609424
$385$	−8.76822	−0.446870
$386$	−10.8364	−0.551560
$387$	−0.864226	−0.0439311
$388$	−2.31972	−0.117766
$389$	31.5402	1.59915	0.799576	−	0.600565i	$-0.205057\pi$
$389$	31.5402	1.59915	0.799576	+	0.600565i	$0.205057\pi$
$390$	−13.1056	−0.663626
$391$	−22.5461	−1.14020
$392$	0.0393351	0.00198672
$393$	1.53008	0.0771822
$394$	−18.2678	−0.920321
$395$	15.5537	0.782590
$396$	2.94915	0.148201
$397$	−22.7053	−1.13955	−0.569774	−	0.821801i	$-0.692969\pi$
$397$	−22.7053	−1.13955	−0.569774	+	0.821801i	$0.692969\pi$
$398$	11.5750	0.580205
$399$	−1.95993	−0.0981191
$400$	−1.85446	−0.0927228
$401$	−28.3742	−1.41694	−0.708471	−	0.705740i	$-0.750615\pi$
$401$	−28.3742	−1.41694	−0.708471	+	0.705740i	$0.750615\pi$
$402$	−0.157616	−0.00786118
$403$	−21.6390	−1.07792
$404$	13.9457	0.693827
$405$	−3.19515	−0.158768
$406$	−26.2838	−1.30445
$407$	−6.67165	−0.330702
$408$	6.01293	0.297684
$409$	−8.05371	−0.398230	−0.199115	−	0.979976i	$-0.563807\pi$
$409$	−8.05371	−0.398230	−0.199115	+	0.979976i	$0.563807\pi$
$410$	19.1061	0.943584
$411$	−11.1376	−0.549377
$412$	11.9285	0.587677
$413$	−24.6620	−1.21354
$414$	−7.04740	−0.346361
$415$	−14.9214	−0.732461
$416$	6.18761	0.303373
$417$	25.7703	1.26198
$418$	1.16565	0.0570138
$419$	13.2494	0.647273	0.323637	−	0.946181i	$-0.395094\pi$
$419$	13.2494	0.647273	0.323637	+	0.946181i	$0.395094\pi$
$420$	−5.58802	−0.272668
$421$	1.39349	0.0679147	0.0339574	−	0.999423i	$-0.489189\pi$
$421$	1.39349	0.0679147	0.0339574	+	0.999423i	$0.489189\pi$
$422$	18.5020	0.900662
$423$	6.76708	0.329027
$424$	−1.92790	−0.0936271
$425$	−9.33723	−0.452922
$426$	−4.81692	−0.233381
$427$	−12.4505	−0.602522
$428$	−6.18261	−0.298848
$429$	−13.8467	−0.668525
$430$	−0.973904	−0.0469658
$431$	−1.41772	−0.0682893	−0.0341446	−	0.999417i	$-0.510871\pi$
$431$	−1.41772	−0.0682893	−0.0341446	+	0.999417i	$0.510871\pi$
$432$	5.46217	0.262799
$433$	23.7914	1.14334	0.571670	−	0.820484i	$-0.306296\pi$
$433$	23.7914	1.14334	0.571670	+	0.820484i	$0.306296\pi$
$434$	−9.22656	−0.442889
$435$	−21.1007	−1.01170
$436$	−6.13855	−0.293983
$437$	−2.78548	−0.133247
$438$	−9.20735	−0.439944
$439$	−29.8879	−1.42647	−0.713237	−	0.700923i	$-0.752772\pi$
$439$	−29.8879	−1.42647	−0.713237	+	0.700923i	$0.752772\pi$
$440$	3.32343	0.158438
$441$	0.0619070	0.00294795
$442$	31.1548	1.48188
$443$	−13.3101	−0.632384	−0.316192	−	0.948695i	$-0.602404\pi$
$443$	−13.3101	−0.632384	−0.316192	+	0.948695i	$0.602404\pi$
$444$	−4.25187	−0.201785
$445$	2.65107	0.125673
$446$	24.4391	1.15723
$447$	4.18536	0.197961
$448$	2.63831	0.124648
$449$	−15.2233	−0.718430	−0.359215	−	0.933255i	$-0.616956\pi$
$449$	−15.2233	−0.718430	−0.359215	+	0.933255i	$0.616956\pi$
$450$	−2.91861	−0.137585
$451$	20.1866	0.950549
$452$	−7.83247	−0.368408
$453$	19.5490	0.918493
$454$	0.259743	0.0121903
$455$	−28.9532	−1.35735
$456$	0.742873	0.0347882
$457$	26.0013	1.21629	0.608145	−	0.793826i	$-0.291914\pi$
$457$	26.0013	1.21629	0.608145	+	0.793826i	$0.291914\pi$
$458$	−3.88857	−0.181701
$459$	27.5022	1.28369
$460$	−7.94177	−0.370287
$461$	8.30709	0.386900	0.193450	−	0.981110i	$-0.438032\pi$
$461$	8.30709	0.386900	0.193450	+	0.981110i	$0.438032\pi$
$462$	−5.90403	−0.274680
$463$	23.3100	1.08331	0.541653	−	0.840602i	$-0.317799\pi$
$463$	23.3100	1.08331	0.541653	+	0.840602i	$0.317799\pi$
$464$	9.96239	0.462492
$465$	−7.40708	−0.343495
$466$	−16.5787	−0.767991
$467$	28.3852	1.31351	0.656754	−	0.754105i	$-0.271929\pi$
$467$	28.3852	1.31351	0.656754	+	0.754105i	$0.271929\pi$
$468$	9.73828	0.450152
$469$	−0.348210	−0.0160789
$470$	7.62588	0.351755
$471$	11.3102	0.521148
$472$	9.34767	0.430261
$473$	−1.02898	−0.0473125
$474$	10.4730	0.481039
$475$	−1.15358	−0.0529297
$476$	13.2839	0.608868
$477$	−3.03420	−0.138926
$478$	−6.32840	−0.289454
$479$	−24.3774	−1.11383	−0.556917	−	0.830568i	$-0.688016\pi$
$479$	−24.3774	−1.11383	−0.556917	+	0.830568i	$0.688016\pi$
$480$	2.11803	0.0966745
$481$	−22.0302	−1.00449
$482$	−3.05912	−0.139339
$483$	14.1085	0.641957
$484$	−7.48863	−0.340392
$485$	−4.11418	−0.186815
$486$	14.2351	0.645716
$487$	28.7707	1.30372	0.651862	−	0.758338i	$-0.273988\pi$
$487$	28.7707	1.30372	0.651862	+	0.758338i	$0.273988\pi$
$488$	4.71913	0.213625
$489$	4.80980	0.217507
$490$	0.0697636	0.00315160
$491$	−11.4581	−0.517099	−0.258549	−	0.965998i	$-0.583244\pi$
$491$	−11.4581	−0.517099	−0.258549	+	0.965998i	$0.583244\pi$
$492$	12.8650	0.579999
$493$	50.1609	2.25913
$494$	3.84905	0.173177
$495$	5.23053	0.235095
$496$	3.49715	0.157027
$497$	−10.6417	−0.477345
$498$	−10.0472	−0.450226
$499$	−3.43695	−0.153859	−0.0769295	−	0.997037i	$-0.524512\pi$
$499$	−3.43695	−0.153859	−0.0769295	+	0.997037i	$0.524512\pi$
$500$	−12.1568	−0.543671
$501$	2.34290	0.104673
$502$	−16.0962	−0.718409
$503$	17.9063	0.798402	0.399201	−	0.916863i	$-0.369287\pi$
$503$	17.9063	0.798402	0.399201	+	0.916863i	$0.369287\pi$
$504$	4.15226	0.184956
$505$	24.7337	1.10064
$506$	−8.39088	−0.373020
$507$	−30.1977	−1.34113
$508$	13.4776	0.597974
$509$	4.08079	0.180878	0.0904390	−	0.995902i	$-0.471173\pi$
$509$	4.08079	0.180878	0.0904390	+	0.995902i	$0.471173\pi$
$510$	10.6643	0.472225
$511$	−20.3411	−0.899839
$512$	−1.00000	−0.0441942
$513$	3.39778	0.150016
$514$	−0.462204	−0.0203870
$515$	21.1561	0.932248
$516$	−0.655772	−0.0288688
$517$	8.05712	0.354352
$518$	−9.39335	−0.412720
$519$	16.4148	0.720528
$520$	10.9742	0.481248
$521$	7.13648	0.312655	0.156327	−	0.987705i	$-0.450034\pi$
$521$	7.13648	0.312655	0.156327	+	0.987705i	$0.450034\pi$
$522$	15.6792	0.686258
$523$	−15.4767	−0.676749	−0.338375	−	0.941012i	$-0.609877\pi$
$523$	−15.4767	−0.676749	−0.338375	+	0.941012i	$0.609877\pi$
$524$	−1.28123	−0.0559710
$525$	5.84288	0.255004
$526$	28.3698	1.23698
$527$	17.6082	0.767027
$528$	2.23781	0.0973881
$529$	−2.94886	−0.128211
$530$	−3.41926	−0.148523
$531$	14.7117	0.638433
$532$	1.64118	0.0711540
$533$	66.6573	2.88725
$534$	1.78508	0.0772481
$535$	−10.9653	−0.474070
$536$	0.131982	0.00570077
$537$	9.36711	0.404221
$538$	−21.5218	−0.927870
$539$	0.0737087	0.00317486
$540$	9.68753	0.416885
$541$	17.5669	0.755259	0.377629	−	0.925957i	$-0.376739\pi$
$541$	17.5669	0.755259	0.377629	+	0.925957i	$0.376739\pi$
$542$	−18.7267	−0.804379
$543$	5.22156	0.224079
$544$	−5.03502	−0.215875
$545$	−10.8871	−0.466354
$546$	−19.4955	−0.834328
$547$	−2.17095	−0.0928232	−0.0464116	−	0.998922i	$-0.514779\pi$
$547$	−2.17095	−0.0928232	−0.0464116	+	0.998922i	$0.514779\pi$
$548$	9.32624	0.398397
$549$	7.42713	0.316982
$550$	−3.47500	−0.148174
$551$	6.19717	0.264008
$552$	−5.34754	−0.227607
$553$	23.1372	0.983892
$554$	31.1016	1.32138
$555$	−7.54098	−0.320097
$556$	−21.5792	−0.915161
$557$	35.1809	1.49066	0.745331	−	0.666695i	$-0.232292\pi$
$557$	35.1809	1.49066	0.745331	+	0.666695i	$0.232292\pi$
$558$	5.50394	0.233000
$559$	−3.39775	−0.143709
$560$	4.67922	0.197733
$561$	11.2674	0.475711
$562$	24.8077	1.04645
$563$	−23.1749	−0.976705	−0.488352	−	0.872646i	$-0.662402\pi$
$563$	−23.1749	−0.976705	−0.488352	+	0.872646i	$0.662402\pi$
$564$	5.13484	0.216216
$565$	−13.8914	−0.584416
$566$	26.1781	1.10035
$567$	−4.75300	−0.199607
$568$	4.03353	0.169243
$569$	−2.94176	−0.123325	−0.0616624	−	0.998097i	$-0.519640\pi$
$569$	−2.94176	−0.123325	−0.0616624	+	0.998097i	$0.519640\pi$
$570$	1.31754	0.0551855
$571$	−25.7228	−1.07647	−0.538233	−	0.842796i	$-0.680908\pi$
$571$	−25.7228	−1.07647	−0.538233	+	0.842796i	$0.680908\pi$
$572$	11.5947	0.484801
$573$	−1.63271	−0.0682076
$574$	28.4217	1.18630
$575$	8.30397	0.346300
$576$	−1.57384	−0.0655765
$577$	−28.8296	−1.20019	−0.600097	−	0.799927i	$-0.704871\pi$
$577$	−28.8296	−1.20019	−0.600097	+	0.799927i	$0.704871\pi$
$578$	−8.35145	−0.347375
$579$	−12.9411	−0.537814
$580$	17.6690	0.733664
$581$	−22.1966	−0.920870
$582$	−2.77026	−0.114831
$583$	−3.61262	−0.149620
$584$	7.70992	0.319039
$585$	17.2715	0.714089
$586$	−8.51636	−0.351807
$587$	−24.2063	−0.999101	−0.499551	−	0.866285i	$-0.666502\pi$
$587$	−24.2063	−0.999101	−0.499551	+	0.866285i	$0.666502\pi$
$588$	0.0469749	0.00193721
$589$	2.17543	0.0896369
$590$	16.5787	0.682536
$591$	−21.8159	−0.897384
$592$	3.56037	0.146330
$593$	7.00440	0.287636	0.143818	−	0.989604i	$-0.454062\pi$
$593$	7.00440	0.287636	0.143818	+	0.989604i	$0.454062\pi$
$594$	10.2354	0.419962
$595$	23.5600	0.965864
$596$	−3.50468	−0.143557
$597$	13.8232	0.565745
$598$	−27.7072	−1.13303
$599$	−33.2646	−1.35915	−0.679577	−	0.733605i	$-0.737836\pi$
$599$	−33.2646	−1.35915	−0.679577	+	0.733605i	$0.737836\pi$
$600$	−2.21463	−0.0904119
$601$	14.5923	0.595234	0.297617	−	0.954685i	$-0.403808\pi$
$601$	14.5923	0.595234	0.297617	+	0.954685i	$0.403808\pi$
$602$	−1.44875	−0.0590466
$603$	0.207719	0.00845896
$604$	−16.3697	−0.666073
$605$	−13.2816	−0.539974
$606$	16.6543	0.676535
$607$	−29.8150	−1.21015	−0.605077	−	0.796167i	$-0.706858\pi$
$607$	−29.8150	−1.21015	−0.605077	+	0.796167i	$0.706858\pi$
$608$	−0.622057	−0.0252277
$609$	−31.3887	−1.27194
$610$	8.36970	0.338879
$611$	26.6051	1.07633
$612$	−7.92430	−0.320321
$613$	36.6620	1.48076	0.740381	−	0.672187i	$-0.234645\pi$
$613$	36.6620	1.48076	0.740381	+	0.672187i	$0.234645\pi$
$614$	1.78407	0.0719993
$615$	22.8169	0.920068
$616$	4.94383	0.199193
$617$	24.4886	0.985875	0.492937	−	0.870065i	$-0.335923\pi$
$617$	24.4886	0.985875	0.492937	+	0.870065i	$0.335923\pi$
$618$	14.2453	0.573030
$619$	25.5661	1.02759	0.513794	−	0.857914i	$-0.328240\pi$
$619$	25.5661	1.02759	0.513794	+	0.857914i	$0.328240\pi$
$620$	6.20244	0.249096
$621$	−24.4588	−0.981497
$622$	3.16159	0.126768
$623$	3.94365	0.157999
$624$	7.38938	0.295812
$625$	−12.2887	−0.491549
$626$	29.5650	1.18166
$627$	1.39204	0.0555929
$628$	−9.47080	−0.377926
$629$	17.9265	0.714778
$630$	7.36432	0.293401
$631$	−35.5516	−1.41529	−0.707644	−	0.706569i	$-0.750242\pi$
$631$	−35.5516	−1.41529	−0.707644	+	0.706569i	$0.750242\pi$
$632$	−8.76970	−0.348840
$633$	22.0954	0.878215
$634$	−17.2692	−0.685846
$635$	23.9035	0.948582
$636$	−2.30234	−0.0912937
$637$	0.243391	0.00964349
$638$	18.6682	0.739080
$639$	6.34811	0.251127
$640$	−1.77357	−0.0701064
$641$	−13.2899	−0.524918	−0.262459	−	0.964943i	$-0.584533\pi$
$641$	−13.2899	−0.524918	−0.262459	+	0.964943i	$0.584533\pi$
$642$	−7.38340	−0.291400
$643$	−21.0667	−0.830788	−0.415394	−	0.909642i	$-0.636356\pi$
$643$	−21.0667	−0.830788	−0.415394	+	0.909642i	$0.636356\pi$
$644$	−11.8139	−0.465535
$645$	−1.16306	−0.0457953
$646$	−3.13207	−0.123230
$647$	−0.270667	−0.0106410	−0.00532051	−	0.999986i	$-0.501694\pi$
$647$	−0.270667	−0.0106410	−0.00532051	+	0.999986i	$0.501694\pi$
$648$	1.80154	0.0707710
$649$	17.5163	0.687574
$650$	−11.4747	−0.450073
$651$	−11.0186	−0.431851
$652$	−4.02756	−0.157731
$653$	−1.90523	−0.0745575	−0.0372787	−	0.999305i	$-0.511869\pi$
$653$	−1.90523	−0.0745575	−0.0372787	+	0.999305i	$0.511869\pi$
$654$	−7.33079	−0.286656
$655$	−2.27236	−0.0887883
$656$	−10.7727	−0.420603
$657$	12.1341	0.473398
$658$	11.3440	0.442236
$659$	−44.6719	−1.74017	−0.870085	−	0.492902i	$-0.835936\pi$
$659$	−44.6719	−1.74017	−0.870085	+	0.492902i	$0.835936\pi$
$660$	3.96891	0.154489
$661$	−15.7093	−0.611020	−0.305510	−	0.952189i	$-0.598827\pi$
$661$	−15.7093	−0.611020	−0.305510	+	0.952189i	$0.598827\pi$
$662$	31.6593	1.23047
$663$	37.2057	1.44495
$664$	8.41319	0.326495
$665$	2.91074	0.112874
$666$	5.60344	0.217129
$667$	−44.6101	−1.72731
$668$	−1.96186	−0.0759068
$669$	29.1857	1.12838
$670$	0.234080	0.00904329
$671$	8.84301	0.341381
$672$	3.15072	0.121542
$673$	−47.2620	−1.82182	−0.910909	−	0.412608i	$-0.864618\pi$
$673$	−47.2620	−1.82182	−0.910909	+	0.412608i	$0.864618\pi$
$674$	20.7608	0.799676
$675$	−10.1294	−0.389879
$676$	25.2866	0.972560
$677$	12.2389	0.470379	0.235190	−	0.971950i	$-0.424429\pi$
$677$	12.2389	0.470379	0.235190	+	0.971950i	$0.424429\pi$
$678$	−9.35370	−0.359227
$679$	−6.12013	−0.234869
$680$	−8.92996	−0.342448
$681$	0.310190	0.0118865
$682$	6.55319	0.250935
$683$	1.83806	0.0703313	0.0351656	−	0.999381i	$-0.488804\pi$
$683$	1.83806	0.0703313	0.0351656	+	0.999381i	$0.488804\pi$
$684$	−0.979015	−0.0374336
$685$	16.5407	0.631989
$686$	18.5719	0.709080
$687$	−4.64381	−0.177172
$688$	0.549121	0.0209350
$689$	−11.9291	−0.454462
$690$	−9.48423	−0.361059
$691$	−2.95049	−0.112242	−0.0561209	−	0.998424i	$-0.517873\pi$
$691$	−2.95049	−0.112242	−0.0561209	+	0.998424i	$0.517873\pi$
$692$	−13.7452	−0.522513
$693$	7.78078	0.295567
$694$	−23.4011	−0.888293
$695$	−38.2721	−1.45174
$696$	11.8973	0.450966
$697$	−54.2408	−2.05452
$698$	−2.62440	−0.0993350
$699$	−19.7986	−0.748851
$700$	−4.89262	−0.184924
$701$	−30.2617	−1.14297	−0.571485	−	0.820612i	$-0.693633\pi$
$701$	−30.2617	−1.14297	−0.571485	+	0.820612i	$0.693633\pi$
$702$	33.7978	1.27562
$703$	2.21475	0.0835310
$704$	−1.87386	−0.0706239
$705$	9.10698	0.342989
$706$	−21.5488	−0.810999
$707$	36.7932	1.38375
$708$	11.1632	0.419538
$709$	6.34042	0.238119	0.119060	−	0.992887i	$-0.462012\pi$
$709$	6.34042	0.238119	0.119060	+	0.992887i	$0.462012\pi$
$710$	7.15374	0.268475
$711$	−13.8021	−0.517618
$712$	−1.49477	−0.0560188
$713$	−15.6597	−0.586461
$714$	15.8640	0.593694
$715$	20.5641	0.769053
$716$	−7.84370	−0.293133
$717$	−7.55750	−0.282240
$718$	−11.5665	−0.431658
$719$	35.2670	1.31524	0.657619	−	0.753351i	$-0.271564\pi$
$719$	35.2670	1.31524	0.657619	+	0.753351i	$0.271564\pi$
$720$	−2.79130	−0.104026
$721$	31.4711	1.17205
$722$	18.6130	0.692706
$723$	−3.65326	−0.135866
$724$	−4.37236	−0.162497
$725$	−18.4748	−0.686137
$726$	−8.94308	−0.331909
$727$	−8.58089	−0.318247	−0.159124	−	0.987259i	$-0.550867\pi$
$727$	−8.58089	−0.318247	−0.159124	+	0.987259i	$0.550867\pi$
$728$	16.3248	0.605038
$729$	22.4044	0.829794
$730$	13.6741	0.506100
$731$	2.76484	0.102261
$732$	5.63568	0.208301
$733$	13.7145	0.506557	0.253278	−	0.967393i	$-0.418491\pi$
$733$	13.7145	0.506557	0.253278	+	0.967393i	$0.418491\pi$
$734$	22.8497	0.843396
$735$	0.0833131	0.00307305
$736$	4.47785	0.165056
$737$	0.247317	0.00911005
$738$	−16.9545	−0.624102
$739$	−39.2282	−1.44303	−0.721516	−	0.692397i	$-0.756555\pi$
$739$	−39.2282	−1.44303	−0.721516	+	0.692397i	$0.756555\pi$
$740$	6.31456	0.232128
$741$	4.59661	0.168861
$742$	−5.08639	−0.186727
$743$	−42.5549	−1.56119	−0.780595	−	0.625037i	$-0.785084\pi$
$743$	−42.5549	−1.56119	−0.780595	+	0.625037i	$0.785084\pi$
$744$	4.17637	0.153113
$745$	−6.21578	−0.227729
$746$	−14.5260	−0.531833
$747$	13.2410	0.484462
$748$	−9.43495	−0.344976
$749$	−16.3116	−0.596014
$750$	−14.5180	−0.530121
$751$	−29.2031	−1.06564	−0.532819	−	0.846229i	$-0.678867\pi$
$751$	−29.2031	−1.06564	−0.532819	+	0.846229i	$0.678867\pi$
$752$	−4.29974	−0.156795
$753$	−19.2224	−0.700504
$754$	61.6434	2.24492
$755$	−29.0327	−1.05661
$756$	14.4109	0.524119
$757$	54.1411	1.96779	0.983895	−	0.178747i	$-0.0572044\pi$
$757$	54.1411	1.96779	0.983895	+	0.178747i	$0.0572044\pi$
$758$	−13.1494	−0.477608
$759$	−10.0206	−0.363724
$760$	−1.10326	−0.0400194
$761$	9.28220	0.336479	0.168240	−	0.985746i	$-0.446192\pi$
$761$	9.28220	0.336479	0.168240	+	0.985746i	$0.446192\pi$
$762$	16.0953	0.583071
$763$	−16.1954	−0.586312
$764$	1.36718	0.0494628
$765$	−14.0543	−0.508134
$766$	9.88391	0.357120
$767$	57.8398	2.08847
$768$	−1.19422	−0.0430927
$769$	−40.2774	−1.45244	−0.726219	−	0.687463i	$-0.758724\pi$
$769$	−40.2774	−1.45244	−0.726219	+	0.687463i	$0.758724\pi$
$770$	8.76822	0.315985
$771$	−0.551974	−0.0198789
$772$	10.8364	0.390012
$773$	30.3962	1.09328	0.546638	−	0.837369i	$-0.315907\pi$
$773$	30.3962	1.09328	0.546638	+	0.837369i	$0.315907\pi$
$774$	0.864226	0.0310640
$775$	−6.48531	−0.232959
$776$	2.31972	0.0832731
$777$	−11.2177	−0.402434
$778$	−31.5402	−1.13077
$779$	−6.70123	−0.240097
$780$	13.1056	0.469255
$781$	7.55828	0.270457
$782$	22.5461	0.806246
$783$	54.4163	1.94468
$784$	−0.0393351	−0.00140483
$785$	−16.7971	−0.599515
$786$	−1.53008	−0.0545760
$787$	22.0039	0.784353	0.392177	−	0.919890i	$-0.371722\pi$
$787$	22.0039	0.784353	0.392177	+	0.919890i	$0.371722\pi$
$788$	18.2678	0.650765
$789$	33.8798	1.20615
$790$	−15.5537	−0.553374
$791$	−20.6645	−0.734744
$792$	−2.94915	−0.104794
$793$	29.2001	1.03693
$794$	22.7053	0.805782
$795$	−4.08336	−0.144822
$796$	−11.5750	−0.410267
$797$	10.7006	0.379034	0.189517	−	0.981877i	$-0.439308\pi$
$797$	10.7006	0.379034	0.189517	+	0.981877i	$0.439308\pi$
$798$	1.95993	0.0693807
$799$	−21.6493	−0.765896
$800$	1.85446	0.0655649
$801$	−2.35252	−0.0831221
$802$	28.3742	1.00193
$803$	14.4473	0.509836
$804$	0.157616	0.00555870
$805$	−20.9528	−0.738490
$806$	21.6390	0.762202
$807$	−25.7018	−0.904746
$808$	−13.9457	−0.490610
$809$	0.880381	0.0309525	0.0154763	−	0.999880i	$-0.495074\pi$
$809$	0.880381	0.0309525	0.0154763	+	0.999880i	$0.495074\pi$
$810$	3.19515	0.112266
$811$	42.1152	1.47887	0.739433	−	0.673231i	$-0.235094\pi$
$811$	42.1152	1.47887	0.739433	+	0.673231i	$0.235094\pi$
$812$	26.2838	0.922382
$813$	−22.3638	−0.784332
$814$	6.67165	0.233841
$815$	−7.14316	−0.250214
$816$	−6.01293	−0.210495
$817$	0.341584	0.0119505
$818$	8.05371	0.281591
$819$	25.6926	0.897772
$820$	−19.1061	−0.667215
$821$	−17.2652	−0.602559	−0.301280	−	0.953536i	$-0.597414\pi$
$821$	−17.2652	−0.602559	−0.301280	+	0.953536i	$0.597414\pi$
$822$	11.1376	0.388468
$823$	33.9987	1.18512	0.592559	−	0.805527i	$-0.298118\pi$
$823$	33.9987	1.18512	0.592559	+	0.805527i	$0.298118\pi$
$824$	−11.9285	−0.415550
$825$	−4.14992	−0.144482
$826$	24.6620	0.858102
$827$	−30.2703	−1.05260	−0.526300	−	0.850299i	$-0.676421\pi$
$827$	−30.2703	−1.05260	−0.526300	+	0.850299i	$0.676421\pi$
$828$	7.04740	0.244914
$829$	17.5186	0.608446	0.304223	−	0.952601i	$-0.401603\pi$
$829$	17.5186	0.608446	0.304223	+	0.952601i	$0.401603\pi$
$830$	14.9214	0.517928
$831$	37.1423	1.28845
$832$	−6.18761	−0.214517
$833$	−0.198053	−0.00686214
$834$	−25.7703	−0.892353
$835$	−3.47950	−0.120413
$836$	−1.16565	−0.0403148
$837$	19.1020	0.660263
$838$	−13.2494	−0.457691
$839$	−34.3836	−1.18705	−0.593526	−	0.804815i	$-0.702265\pi$
$839$	−34.3836	−1.18705	−0.593526	+	0.804815i	$0.702265\pi$
$840$	5.58802	0.192805
$841$	70.2492	2.42239
$842$	−1.39349	−0.0480230
$843$	29.6259	1.02037
$844$	−18.5020	−0.636864
$845$	44.8474	1.54280
$846$	−6.76708	−0.232657
$847$	−19.7573	−0.678869
$848$	1.92790	0.0662043
$849$	31.2624	1.07292
$850$	9.33723	0.320264
$851$	−15.9428	−0.546512
$852$	4.81692	0.165025
$853$	43.3944	1.48580	0.742899	−	0.669404i	$-0.233450\pi$
$853$	43.3944	1.48580	0.742899	+	0.669404i	$0.233450\pi$
$854$	12.4505	0.426048
$855$	−1.73635	−0.0593819
$856$	6.18261	0.211317
$857$	24.4238	0.834301	0.417151	−	0.908837i	$-0.363029\pi$
$857$	24.4238	0.834301	0.417151	+	0.908837i	$0.363029\pi$
$858$	13.8467	0.472718
$859$	−9.99289	−0.340953	−0.170476	−	0.985362i	$-0.554531\pi$
$859$	−9.99289	−0.340953	−0.170476	+	0.985362i	$0.554531\pi$
$860$	0.973904	0.0332098
$861$	33.9418	1.15673
$862$	1.41772	0.0482878
$863$	−14.3077	−0.487041	−0.243521	−	0.969896i	$-0.578302\pi$
$863$	−14.3077	−0.487041	−0.243521	+	0.969896i	$0.578302\pi$
$864$	−5.46217	−0.185827
$865$	−24.3780	−0.828876
$866$	−23.7914	−0.808463
$867$	−9.97348	−0.338717
$868$	9.22656	0.313170
$869$	−16.4332	−0.557459
$870$	21.1007	0.715380
$871$	0.816656	0.0276713
$872$	6.13855	0.207877
$873$	3.65086	0.123563
$874$	2.78548	0.0942201
$875$	−32.0735	−1.08428
$876$	9.20735	0.311088
$877$	3.73475	0.126114	0.0630569	−	0.998010i	$-0.479915\pi$
$877$	3.73475	0.126114	0.0630569	+	0.998010i	$0.479915\pi$
$878$	29.8879	1.00867
$879$	−10.1704	−0.343040
$880$	−3.32343	−0.112033
$881$	−3.16166	−0.106519	−0.0532595	−	0.998581i	$-0.516961\pi$
$881$	−3.16166	−0.106519	−0.0532595	+	0.998581i	$0.516961\pi$
$882$	−0.0619070	−0.00208452
$883$	50.1141	1.68647	0.843236	−	0.537543i	$-0.180648\pi$
$883$	50.1141	1.68647	0.843236	+	0.537543i	$0.180648\pi$
$884$	−31.1548	−1.04785
$885$	19.7987	0.665525
$886$	13.3101	0.447163
$887$	8.03219	0.269694	0.134847	−	0.990866i	$-0.456946\pi$
$887$	8.03219	0.269694	0.134847	+	0.990866i	$0.456946\pi$
$888$	4.25187	0.142683
$889$	35.5582	1.19258
$890$	−2.65107	−0.0888641
$891$	3.37583	0.113095
$892$	−24.4391	−0.818282
$893$	−2.67468	−0.0895047
$894$	−4.18536	−0.139979
$895$	−13.9113	−0.465005
$896$	−2.63831	−0.0881397
$897$	−33.0885	−1.10479
$898$	15.2233	0.508007
$899$	34.8400	1.16198
$900$	2.91861	0.0972869
$901$	9.70702	0.323388
$902$	−20.1866	−0.672140
$903$	−1.73013	−0.0575751
$904$	7.83247	0.260504
$905$	−7.75468	−0.257774
$906$	−19.5490	−0.649473
$907$	−26.0749	−0.865801	−0.432901	−	0.901442i	$-0.642510\pi$
$907$	−26.0749	−0.865801	−0.432901	+	0.901442i	$0.642510\pi$
$908$	−0.259743	−0.00861986
$909$	−21.9483	−0.727979
$910$	28.9532	0.959789
$911$	9.16809	0.303752	0.151876	−	0.988400i	$-0.451468\pi$
$911$	9.16809	0.303752	0.151876	+	0.988400i	$0.451468\pi$
$912$	−0.742873	−0.0245990
$913$	15.7652	0.521751
$914$	−26.0013	−0.860048
$915$	9.99527	0.330433
$916$	3.88857	0.128482
$917$	−3.38029	−0.111627
$918$	−27.5022	−0.907706
$919$	36.2498	1.19577	0.597885	−	0.801582i	$-0.296008\pi$
$919$	36.2498	1.19577	0.597885	+	0.801582i	$0.296008\pi$
$920$	7.94177	0.261832
$921$	2.13058	0.0702049
$922$	−8.30709	−0.273579
$923$	24.9579	0.821499
$924$	5.90403	0.194228
$925$	−6.60255	−0.217090
$926$	−23.3100	−0.766013
$927$	−18.7735	−0.616604
$928$	−9.96239	−0.327031
$929$	4.63219	0.151977	0.0759886	−	0.997109i	$-0.475789\pi$
$929$	4.63219	0.151977	0.0759886	+	0.997109i	$0.475789\pi$
$930$	7.40708	0.242888
$931$	−0.0244687	−0.000801929 0
$932$	16.5787	0.543052
$933$	3.77564	0.123609
$934$	−28.3852	−0.928791
$935$	−16.7335	−0.547245
$936$	−9.73828	−0.318306
$937$	30.7156	1.00343	0.501717	−	0.865032i	$-0.332702\pi$
$937$	30.7156	1.00343	0.501717	+	0.865032i	$0.332702\pi$
$938$	0.348210	0.0113695
$939$	35.3072	1.15221
$940$	−7.62588	−0.248729
$941$	46.8420	1.52701	0.763503	−	0.645805i	$-0.223478\pi$
$941$	46.8420	1.52701	0.763503	+	0.645805i	$0.223478\pi$
$942$	−11.3102	−0.368507
$943$	48.2386	1.57086
$944$	−9.34767	−0.304241
$945$	25.5587	0.831424
$946$	1.02898	0.0334550
$947$	45.4643	1.47739	0.738696	−	0.674039i	$-0.235442\pi$
$947$	45.4643	1.47739	0.738696	+	0.674039i	$0.235442\pi$
$948$	−10.4730	−0.340146
$949$	47.7060	1.54860
$950$	1.15358	0.0374270
$951$	−20.6232	−0.668753
$952$	−13.2839	−0.430535
$953$	41.9541	1.35903	0.679514	−	0.733663i	$-0.262191\pi$
$953$	41.9541	1.35903	0.679514	+	0.733663i	$0.262191\pi$
$954$	3.03420	0.0982357
$955$	2.42478	0.0784642
$956$	6.32840	0.204675
$957$	22.2939	0.720660
$958$	24.3774	0.787599
$959$	24.6055	0.794553
$960$	−2.11803	−0.0683592
$961$	−18.7699	−0.605481
$962$	22.0302	0.710282
$963$	9.73041	0.313558
$964$	3.05912	0.0985276
$965$	19.2192	0.618686
$966$	−14.1085	−0.453932
$967$	27.1554	0.873258	0.436629	−	0.899642i	$-0.356172\pi$
$967$	27.1554	0.873258	0.436629	+	0.899642i	$0.356172\pi$
$968$	7.48863	0.240694
$969$	−3.74038	−0.120158
$970$	4.11418	0.132098
$971$	−7.14234	−0.229209	−0.114604	−	0.993411i	$-0.536560\pi$
$971$	−7.14234	−0.229209	−0.114604	+	0.993411i	$0.536560\pi$
$972$	−14.2351	−0.456591
$973$	−56.9325	−1.82517
$974$	−28.7707	−0.921872
$975$	−13.7033	−0.438856
$976$	−4.71913	−0.151056
$977$	−7.88164	−0.252156	−0.126078	−	0.992020i	$-0.540239\pi$
$977$	−7.88164	−0.252156	−0.126078	+	0.992020i	$0.540239\pi$
$978$	−4.80980	−0.153800
$979$	−2.80099	−0.0895201
$980$	−0.0697636	−0.00222852
$981$	9.66107	0.308454
$982$	11.4581	0.365644
$983$	4.98431	0.158975	0.0794874	−	0.996836i	$-0.474672\pi$
$983$	4.98431	0.158975	0.0794874	+	0.996836i	$0.474672\pi$
$984$	−12.8650	−0.410121
$985$	32.3993	1.03233
$986$	−50.1609	−1.59745
$987$	13.5473	0.431215
$988$	−3.84905	−0.122454
$989$	−2.45888	−0.0781879
$990$	−5.23053	−0.166237
$991$	−46.1083	−1.46468	−0.732340	−	0.680939i	$-0.761572\pi$
$991$	−46.1083	−1.46468	−0.732340	+	0.680939i	$0.761572\pi$
$992$	−3.49715	−0.111035
$993$	37.8083	1.19981
$994$	10.6417	0.337534
$995$	−20.5291	−0.650817
$996$	10.0472	0.318358
$997$	58.0707	1.83912	0.919558	−	0.392954i	$-0.128547\pi$
$997$	58.0707	1.83912	0.919558	+	0.392954i	$0.128547\pi$
$998$	3.43695	0.108795
$999$	19.4474	0.615287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.14	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.14	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.19422 q^{3} +1.00000 q^{4} +1.77357 q^{5} +1.19422 q^{6} +2.63831 q^{7} -1.00000 q^{8} -1.57384 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.19422 q^{3} +1.00000 q^{4} +1.77357 q^{5} +1.19422 q^{6} +2.63831 q^{7} -1.00000 q^{8} -1.57384 q^{9} -1.77357 q^{10} -1.87386 q^{11} -1.19422 q^{12} -6.18761 q^{13} -2.63831 q^{14} -2.11803 q^{15} +1.00000 q^{16} +5.03502 q^{17} +1.57384 q^{18} +0.622057 q^{19} +1.77357 q^{20} -3.15072 q^{21} +1.87386 q^{22} -4.47785 q^{23} +1.19422 q^{24} -1.85446 q^{25} +6.18761 q^{26} +5.46217 q^{27} +2.63831 q^{28} +9.96239 q^{29} +2.11803 q^{30} +3.49715 q^{31} -1.00000 q^{32} +2.23781 q^{33} -5.03502 q^{34} +4.67922 q^{35} -1.57384 q^{36} +3.56037 q^{37} -0.622057 q^{38} +7.38938 q^{39} -1.77357 q^{40} -10.7727 q^{41} +3.15072 q^{42} +0.549121 q^{43} -1.87386 q^{44} -2.79130 q^{45} +4.47785 q^{46} -4.29974 q^{47} -1.19422 q^{48} -0.0393351 q^{49} +1.85446 q^{50} -6.01293 q^{51} -6.18761 q^{52} +1.92790 q^{53} -5.46217 q^{54} -3.32343 q^{55} -2.63831 q^{56} -0.742873 q^{57} -9.96239 q^{58} -9.34767 q^{59} -2.11803 q^{60} -4.71913 q^{61} -3.49715 q^{62} -4.15226 q^{63} +1.00000 q^{64} -10.9742 q^{65} -2.23781 q^{66} -0.131982 q^{67} +5.03502 q^{68} +5.34754 q^{69} -4.67922 q^{70} -4.03353 q^{71} +1.57384 q^{72} -7.70992 q^{73} -3.56037 q^{74} +2.21463 q^{75} +0.622057 q^{76} -4.94383 q^{77} -7.38938 q^{78} +8.76970 q^{79} +1.77357 q^{80} -1.80154 q^{81} +10.7727 q^{82} -8.41319 q^{83} -3.15072 q^{84} +8.92996 q^{85} -0.549121 q^{86} -11.8973 q^{87} +1.87386 q^{88} +1.49477 q^{89} +2.79130 q^{90} -16.3248 q^{91} -4.47785 q^{92} -4.17637 q^{93} +4.29974 q^{94} +1.10326 q^{95} +1.19422 q^{96} -2.31972 q^{97} +0.0393351 q^{98} +2.94915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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