LMFDB - Embedded newform 4022.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.25505 q^{3} +1.00000 q^{4} -0.797463 q^{5} +3.25505 q^{6} -4.64387 q^{7} -1.00000 q^{8} +7.59538 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.25505 q^{3} +1.00000 q^{4} -0.797463 q^{5} +3.25505 q^{6} -4.64387 q^{7} -1.00000 q^{8} +7.59538 q^{9} +0.797463 q^{10} +3.29116 q^{11} -3.25505 q^{12} -5.46593 q^{13} +4.64387 q^{14} +2.59579 q^{15} +1.00000 q^{16} +0.500935 q^{17} -7.59538 q^{18} +1.04346 q^{19} -0.797463 q^{20} +15.1160 q^{21} -3.29116 q^{22} -3.58028 q^{23} +3.25505 q^{24} -4.36405 q^{25} +5.46593 q^{26} -14.9582 q^{27} -4.64387 q^{28} -7.31349 q^{29} -2.59579 q^{30} +8.16522 q^{31} -1.00000 q^{32} -10.7129 q^{33} -0.500935 q^{34} +3.70332 q^{35} +7.59538 q^{36} +0.468123 q^{37} -1.04346 q^{38} +17.7919 q^{39} +0.797463 q^{40} -0.438581 q^{41} -15.1160 q^{42} +9.00734 q^{43} +3.29116 q^{44} -6.05703 q^{45} +3.58028 q^{46} +2.38201 q^{47} -3.25505 q^{48} +14.5655 q^{49} +4.36405 q^{50} -1.63057 q^{51} -5.46593 q^{52} +1.85098 q^{53} +14.9582 q^{54} -2.62458 q^{55} +4.64387 q^{56} -3.39653 q^{57} +7.31349 q^{58} -3.16436 q^{59} +2.59579 q^{60} -9.13080 q^{61} -8.16522 q^{62} -35.2719 q^{63} +1.00000 q^{64} +4.35888 q^{65} +10.7129 q^{66} +6.82104 q^{67} +0.500935 q^{68} +11.6540 q^{69} -3.70332 q^{70} -2.40916 q^{71} -7.59538 q^{72} +5.41933 q^{73} -0.468123 q^{74} +14.2052 q^{75} +1.04346 q^{76} -15.2837 q^{77} -17.7919 q^{78} +17.6423 q^{79} -0.797463 q^{80} +25.9036 q^{81} +0.438581 q^{82} +16.9341 q^{83} +15.1160 q^{84} -0.399477 q^{85} -9.00734 q^{86} +23.8058 q^{87} -3.29116 q^{88} -5.40042 q^{89} +6.05703 q^{90} +25.3831 q^{91} -3.58028 q^{92} -26.5782 q^{93} -2.38201 q^{94} -0.832123 q^{95} +3.25505 q^{96} +8.63364 q^{97} -14.5655 q^{98} +24.9976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.25505	−1.87931	−0.939653	−	0.342129i	$-0.888852\pi$
$3$	−3.25505	−1.87931	−0.939653	+	0.342129i	$0.888852\pi$
$4$	1.00000	0.500000
$5$	−0.797463	−0.356636	−0.178318	−	0.983973i	$-0.557066\pi$
$5$	−0.797463	−0.356636	−0.178318	+	0.983973i	$0.557066\pi$
$6$	3.25505	1.32887
$7$	−4.64387	−1.75522	−0.877609	−	0.479377i	$-0.840863\pi$
$7$	−4.64387	−1.75522	−0.877609	+	0.479377i	$0.840863\pi$
$8$	−1.00000	−0.353553
$9$	7.59538	2.53179
$10$	0.797463	0.252180
$11$	3.29116	0.992322	0.496161	−	0.868230i	$-0.334742\pi$
$11$	3.29116	0.992322	0.496161	+	0.868230i	$0.334742\pi$
$12$	−3.25505	−0.939653
$13$	−5.46593	−1.51598	−0.757988	−	0.652268i	$-0.773818\pi$
$13$	−5.46593	−1.51598	−0.757988	+	0.652268i	$0.773818\pi$
$14$	4.64387	1.24113
$15$	2.59579	0.670229
$16$	1.00000	0.250000
$17$	0.500935	0.121495	0.0607473	−	0.998153i	$-0.480652\pi$
$17$	0.500935	0.121495	0.0607473	+	0.998153i	$0.480652\pi$
$18$	−7.59538	−1.79025
$19$	1.04346	0.239387	0.119693	−	0.992811i	$-0.461809\pi$
$19$	1.04346	0.239387	0.119693	+	0.992811i	$0.461809\pi$
$20$	−0.797463	−0.178318
$21$	15.1160	3.29859
$22$	−3.29116	−0.701678
$23$	−3.58028	−0.746539	−0.373270	−	0.927723i	$-0.621763\pi$
$23$	−3.58028	−0.746539	−0.373270	+	0.927723i	$0.621763\pi$
$24$	3.25505	0.664435
$25$	−4.36405	−0.872810
$26$	5.46593	1.07196
$27$	−14.9582	−2.87871
$28$	−4.64387	−0.877609
$29$	−7.31349	−1.35808	−0.679041	−	0.734101i	$-0.737604\pi$
$29$	−7.31349	−1.35808	−0.679041	+	0.734101i	$0.737604\pi$
$30$	−2.59579	−0.473924
$31$	8.16522	1.46652	0.733258	−	0.679950i	$-0.237999\pi$
$31$	8.16522	1.46652	0.733258	+	0.679950i	$0.237999\pi$
$32$	−1.00000	−0.176777
$33$	−10.7129	−1.86488
$34$	−0.500935	−0.0859096
$35$	3.70332	0.625975
$36$	7.59538	1.26590
$37$	0.468123	0.0769589	0.0384795	−	0.999259i	$-0.487749\pi$
$37$	0.468123	0.0769589	0.0384795	+	0.999259i	$0.487749\pi$
$38$	−1.04346	−0.169272
$39$	17.7919	2.84898
$40$	0.797463	0.126090
$41$	−0.438581	−0.0684948	−0.0342474	−	0.999413i	$-0.510903\pi$
$41$	−0.438581	−0.0684948	−0.0342474	+	0.999413i	$0.510903\pi$
$42$	−15.1160	−2.33246
$43$	9.00734	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$43$	9.00734	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$44$	3.29116	0.496161
$45$	−6.05703	−0.902929
$46$	3.58028	0.527883
$47$	2.38201	0.347452	0.173726	−	0.984794i	$-0.444419\pi$
$47$	2.38201	0.347452	0.173726	+	0.984794i	$0.444419\pi$
$48$	−3.25505	−0.469827
$49$	14.5655	2.08079
$50$	4.36405	0.617170
$51$	−1.63057	−0.228326
$52$	−5.46593	−0.757988
$53$	1.85098	0.254252	0.127126	−	0.991887i	$-0.459425\pi$
$53$	1.85098	0.254252	0.127126	+	0.991887i	$0.459425\pi$
$54$	14.9582	2.03555
$55$	−2.62458	−0.353898
$56$	4.64387	0.620563
$57$	−3.39653	−0.449881
$58$	7.31349	0.960309
$59$	−3.16436	−0.411964	−0.205982	−	0.978556i	$-0.566039\pi$
$59$	−3.16436	−0.411964	−0.205982	+	0.978556i	$0.566039\pi$
$60$	2.59579	0.335115
$61$	−9.13080	−1.16908	−0.584540	−	0.811365i	$-0.698725\pi$
$61$	−9.13080	−1.16908	−0.584540	+	0.811365i	$0.698725\pi$
$62$	−8.16522	−1.03698
$63$	−35.2719	−4.44385
$64$	1.00000	0.125000
$65$	4.35888	0.540652
$66$	10.7129	1.31867
$67$	6.82104	0.833323	0.416661	−	0.909062i	$-0.363200\pi$
$67$	6.82104	0.833323	0.416661	+	0.909062i	$0.363200\pi$
$68$	0.500935	0.0607473
$69$	11.6540	1.40298
$70$	−3.70332	−0.442631
$71$	−2.40916	−0.285915	−0.142957	−	0.989729i	$-0.545661\pi$
$71$	−2.40916	−0.285915	−0.142957	+	0.989729i	$0.545661\pi$
$72$	−7.59538	−0.895124
$73$	5.41933	0.634284	0.317142	−	0.948378i	$-0.397277\pi$
$73$	5.41933	0.634284	0.317142	+	0.948378i	$0.397277\pi$
$74$	−0.468123	−0.0544182
$75$	14.2052	1.64028
$76$	1.04346	0.119693
$77$	−15.2837	−1.74174
$78$	−17.7919	−2.01454
$79$	17.6423	1.98492	0.992459	−	0.122575i	$-0.0391152\pi$
$79$	17.6423	1.98492	0.992459	+	0.122575i	$0.0391152\pi$
$80$	−0.797463	−0.0891591
$81$	25.9036	2.87818
$82$	0.438581	0.0484331
$83$	16.9341	1.85876	0.929379	−	0.369127i	$-0.120343\pi$
$83$	16.9341	1.85876	0.929379	+	0.369127i	$0.120343\pi$
$84$	15.1160	1.64930
$85$	−0.399477	−0.0433294
$86$	−9.00734	−0.971286
$87$	23.8058	2.55225
$88$	−3.29116	−0.350839
$89$	−5.40042	−0.572443	−0.286221	−	0.958163i	$-0.592399\pi$
$89$	−5.40042	−0.572443	−0.286221	+	0.958163i	$0.592399\pi$
$90$	6.05703	0.638467
$91$	25.3831	2.66087
$92$	−3.58028	−0.373270
$93$	−26.5782	−2.75603
$94$	−2.38201	−0.245686
$95$	−0.832123	−0.0853740
$96$	3.25505	0.332218
$97$	8.63364	0.876613	0.438307	−	0.898825i	$-0.355578\pi$
$97$	8.63364	0.876613	0.438307	+	0.898825i	$0.355578\pi$
$98$	−14.5655	−1.47134
$99$	24.9976	2.51235
$100$	−4.36405	−0.436405
$101$	3.68699	0.366869	0.183435	−	0.983032i	$-0.441278\pi$
$101$	3.68699	0.366869	0.183435	+	0.983032i	$0.441278\pi$
$102$	1.63057	0.161451
$103$	−0.642945	−0.0633512	−0.0316756	−	0.999498i	$-0.510084\pi$
$103$	−0.642945	−0.0633512	−0.0316756	+	0.999498i	$0.510084\pi$
$104$	5.46593	0.535979
$105$	−12.0545	−1.17640
$106$	−1.85098	−0.179783
$107$	14.8632	1.43688	0.718440	−	0.695589i	$-0.244856\pi$
$107$	14.8632	1.43688	0.718440	+	0.695589i	$0.244856\pi$
$108$	−14.9582	−1.43935
$109$	−5.33705	−0.511197	−0.255598	−	0.966783i	$-0.582272\pi$
$109$	−5.33705	−0.511197	−0.255598	+	0.966783i	$0.582272\pi$
$110$	2.62458	0.250244
$111$	−1.52376	−0.144629
$112$	−4.64387	−0.438804
$113$	0.936689	0.0881162	0.0440581	−	0.999029i	$-0.485971\pi$
$113$	0.936689	0.0881162	0.0440581	+	0.999029i	$0.485971\pi$
$114$	3.39653	0.318114
$115$	2.85514	0.266243
$116$	−7.31349	−0.679041
$117$	−41.5158	−3.83814
$118$	3.16436	0.291303
$119$	−2.32628	−0.213249
$120$	−2.59579	−0.236962
$121$	−0.168257	−0.0152961
$122$	9.13080	0.826664
$123$	1.42760	0.128723
$124$	8.16522	0.733258
$125$	7.46749	0.667912
$126$	35.2719	3.14227
$127$	−5.76042	−0.511154	−0.255577	−	0.966789i	$-0.582266\pi$
$127$	−5.76042	−0.511154	−0.255577	+	0.966789i	$0.582266\pi$
$128$	−1.00000	−0.0883883
$129$	−29.3194	−2.58143
$130$	−4.35888	−0.382299
$131$	−11.5139	−1.00597	−0.502986	−	0.864295i	$-0.667765\pi$
$131$	−11.5139	−1.00597	−0.502986	+	0.864295i	$0.667765\pi$
$132$	−10.7129	−0.932439
$133$	−4.84570	−0.420176
$134$	−6.82104	−0.589248
$135$	11.9286	1.02665
$136$	−0.500935	−0.0429548
$137$	9.42587	0.805306	0.402653	−	0.915353i	$-0.368088\pi$
$137$	9.42587	0.805306	0.402653	+	0.915353i	$0.368088\pi$
$138$	−11.6540	−0.992054
$139$	−22.3373	−1.89463	−0.947314	−	0.320306i	$-0.896214\pi$
$139$	−22.3373	−1.89463	−0.947314	+	0.320306i	$0.896214\pi$
$140$	3.70332	0.312987
$141$	−7.75357	−0.652968
$142$	2.40916	0.202172
$143$	−17.9893	−1.50434
$144$	7.59538	0.632948
$145$	5.83224	0.484341
$146$	−5.41933	−0.448507
$147$	−47.4116	−3.91044
$148$	0.468123	0.0384795
$149$	8.40318	0.688415	0.344208	−	0.938894i	$-0.388148\pi$
$149$	8.40318	0.688415	0.344208	+	0.938894i	$0.388148\pi$
$150$	−14.2052	−1.15985
$151$	13.4752	1.09659	0.548297	−	0.836284i	$-0.315276\pi$
$151$	13.4752	1.09659	0.548297	+	0.836284i	$0.315276\pi$
$152$	−1.04346	−0.0846360
$153$	3.80479	0.307599
$154$	15.2837	1.23160
$155$	−6.51146	−0.523013
$156$	17.7919	1.42449
$157$	−10.0291	−0.800411	−0.400205	−	0.916425i	$-0.631061\pi$
$157$	−10.0291	−0.800411	−0.400205	+	0.916425i	$0.631061\pi$
$158$	−17.6423	−1.40355
$159$	−6.02504	−0.477817
$160$	0.797463	0.0630450
$161$	16.6263	1.31034
$162$	−25.9036	−2.03518
$163$	1.08496	0.0849810	0.0424905	−	0.999097i	$-0.486471\pi$
$163$	1.08496	0.0849810	0.0424905	+	0.999097i	$0.486471\pi$
$164$	−0.438581	−0.0342474
$165$	8.54315	0.665083
$166$	−16.9341	−1.31434
$167$	12.7847	0.989309	0.494654	−	0.869090i	$-0.335295\pi$
$167$	12.7847	0.989309	0.494654	+	0.869090i	$0.335295\pi$
$168$	−15.1160	−1.16623
$169$	16.8764	1.29818
$170$	0.399477	0.0306385
$171$	7.92549	0.606077
$172$	9.00734	0.686803
$173$	−20.7837	−1.58016	−0.790079	−	0.613005i	$-0.789960\pi$
$173$	−20.7837	−1.58016	−0.790079	+	0.613005i	$0.789960\pi$
$174$	−23.8058	−1.80471
$175$	20.2661	1.53197
$176$	3.29116	0.248081
$177$	10.3002	0.774207
$178$	5.40042	0.404778
$179$	9.04968	0.676404	0.338202	−	0.941073i	$-0.390181\pi$
$179$	9.04968	0.676404	0.338202	+	0.941073i	$0.390181\pi$
$180$	−6.05703	−0.451465
$181$	−11.0003	−0.817649	−0.408825	−	0.912613i	$-0.634061\pi$
$181$	−11.0003	−0.817649	−0.408825	+	0.912613i	$0.634061\pi$
$182$	−25.3831	−1.88152
$183$	29.7213	2.19706
$184$	3.58028	0.263942
$185$	−0.373311	−0.0274464
$186$	26.5782	1.94881
$187$	1.64866	0.120562
$188$	2.38201	0.173726
$189$	69.4639	5.05276
$190$	0.832123	0.0603686
$191$	−23.0080	−1.66480	−0.832399	−	0.554177i	$-0.813033\pi$
$191$	−23.0080	−1.66480	−0.832399	+	0.554177i	$0.813033\pi$
$192$	−3.25505	−0.234913
$193$	8.61447	0.620083	0.310042	−	0.950723i	$-0.399657\pi$
$193$	8.61447	0.620083	0.310042	+	0.950723i	$0.399657\pi$
$194$	−8.63364	−0.619859
$195$	−14.1884	−1.01605
$196$	14.5655	1.04039
$197$	3.13474	0.223341	0.111670	−	0.993745i	$-0.464380\pi$
$197$	3.13474	0.223341	0.111670	+	0.993745i	$0.464380\pi$
$198$	−24.9976	−1.77650
$199$	−7.42889	−0.526620	−0.263310	−	0.964711i	$-0.584814\pi$
$199$	−7.42889	−0.526620	−0.263310	+	0.964711i	$0.584814\pi$
$200$	4.36405	0.308585
$201$	−22.2029	−1.56607
$202$	−3.68699	−0.259416
$203$	33.9629	2.38373
$204$	−1.63057	−0.114163
$205$	0.349752	0.0244277
$206$	0.642945	0.0447961
$207$	−27.1935	−1.89008
$208$	−5.46593	−0.378994
$209$	3.43420	0.237549
$210$	12.0545	0.831839
$211$	25.4173	1.74980	0.874899	−	0.484306i	$-0.160928\pi$
$211$	25.4173	1.74980	0.874899	+	0.484306i	$0.160928\pi$
$212$	1.85098	0.127126
$213$	7.84194	0.537321
$214$	−14.8632	−1.01603
$215$	−7.18302	−0.489878
$216$	14.9582	1.01778
$217$	−37.9182	−2.57406
$218$	5.33705	0.361471
$219$	−17.6402	−1.19201
$220$	−2.62458	−0.176949
$221$	−2.73808	−0.184183
$222$	1.52376	0.102268
$223$	−22.6398	−1.51607	−0.758035	−	0.652214i	$-0.773840\pi$
$223$	−22.6398	−1.51607	−0.758035	+	0.652214i	$0.773840\pi$
$224$	4.64387	0.310282
$225$	−33.1466	−2.20977
$226$	−0.936689	−0.0623076
$227$	3.37377	0.223925	0.111962	−	0.993712i	$-0.464286\pi$
$227$	3.37377	0.223925	0.111962	+	0.993712i	$0.464286\pi$
$228$	−3.39653	−0.224940
$229$	20.9551	1.38475	0.692375	−	0.721538i	$-0.256564\pi$
$229$	20.9551	1.38475	0.692375	+	0.721538i	$0.256564\pi$
$230$	−2.85514	−0.188262
$231$	49.7494	3.27327
$232$	7.31349	0.480154
$233$	−19.9855	−1.30929	−0.654646	−	0.755936i	$-0.727182\pi$
$233$	−19.9855	−1.30929	−0.654646	+	0.755936i	$0.727182\pi$
$234$	41.5158	2.71397
$235$	−1.89957	−0.123914
$236$	−3.16436	−0.205982
$237$	−57.4268	−3.73027
$238$	2.32628	0.150790
$239$	20.4182	1.32074	0.660372	−	0.750939i	$-0.270399\pi$
$239$	20.4182	1.32074	0.660372	+	0.750939i	$0.270399\pi$
$240$	2.59579	0.167557
$241$	−5.23353	−0.337121	−0.168561	−	0.985691i	$-0.553912\pi$
$241$	−5.23353	−0.337121	−0.168561	+	0.985691i	$0.553912\pi$
$242$	0.168257	0.0108159
$243$	−39.4431	−2.53027
$244$	−9.13080	−0.584540
$245$	−11.6155	−0.742086
$246$	−1.42760	−0.0910207
$247$	−5.70349	−0.362905
$248$	−8.16522	−0.518492
$249$	−55.1214	−3.49317
$250$	−7.46749	−0.472285
$251$	−15.1813	−0.958238	−0.479119	−	0.877750i	$-0.659044\pi$
$251$	−15.1813	−0.958238	−0.479119	+	0.877750i	$0.659044\pi$
$252$	−35.2719	−2.22192
$253$	−11.7833	−0.740808
$254$	5.76042	0.361441
$255$	1.30032	0.0814292
$256$	1.00000	0.0625000
$257$	25.0294	1.56129	0.780647	−	0.624972i	$-0.214890\pi$
$257$	25.0294	1.56129	0.780647	+	0.624972i	$0.214890\pi$
$258$	29.3194	1.82534
$259$	−2.17390	−0.135080
$260$	4.35888	0.270326
$261$	−55.5487	−3.43838
$262$	11.5139	0.711329
$263$	14.5472	0.897019	0.448510	−	0.893778i	$-0.351955\pi$
$263$	14.5472	0.897019	0.448510	+	0.893778i	$0.351955\pi$
$264$	10.7129	0.659334
$265$	−1.47609	−0.0906755
$266$	4.84570	0.297109
$267$	17.5786	1.07580
$268$	6.82104	0.416661
$269$	11.9319	0.727503	0.363752	−	0.931496i	$-0.381496\pi$
$269$	11.9319	0.727503	0.363752	+	0.931496i	$0.381496\pi$
$270$	−11.9286	−0.725952
$271$	−12.3245	−0.748663	−0.374331	−	0.927295i	$-0.622128\pi$
$271$	−12.3245	−0.748663	−0.374331	+	0.927295i	$0.622128\pi$
$272$	0.500935	0.0303736
$273$	−82.6233	−5.00059
$274$	−9.42587	−0.569437
$275$	−14.3628	−0.866109
$276$	11.6540	0.701488
$277$	25.3353	1.52225	0.761127	−	0.648603i	$-0.224647\pi$
$277$	25.3353	1.52225	0.761127	+	0.648603i	$0.224647\pi$
$278$	22.3373	1.33970
$279$	62.0179	3.71292
$280$	−3.70332	−0.221315
$281$	−14.7265	−0.878508	−0.439254	−	0.898363i	$-0.644757\pi$
$281$	−14.7265	−0.878508	−0.439254	+	0.898363i	$0.644757\pi$
$282$	7.75357	0.461718
$283$	−20.1841	−1.19982	−0.599909	−	0.800068i	$-0.704797\pi$
$283$	−20.1841	−1.19982	−0.599909	+	0.800068i	$0.704797\pi$
$284$	−2.40916	−0.142957
$285$	2.70861	0.160444
$286$	17.9893	1.06373
$287$	2.03671	0.120223
$288$	−7.59538	−0.447562
$289$	−16.7491	−0.985239
$290$	−5.83224	−0.342481
$291$	−28.1030	−1.64743
$292$	5.41933	0.317142
$293$	21.0281	1.22847	0.614237	−	0.789122i	$-0.289464\pi$
$293$	21.0281	1.22847	0.614237	+	0.789122i	$0.289464\pi$
$294$	47.4116	2.76510
$295$	2.52346	0.146921
$296$	−0.468123	−0.0272091
$297$	−49.2298	−2.85661
$298$	−8.40318	−0.486783
$299$	19.5695	1.13174
$300$	14.2052	0.820139
$301$	−41.8289	−2.41098
$302$	−13.4752	−0.775409
$303$	−12.0014	−0.689460
$304$	1.04346	0.0598467
$305$	7.28148	0.416936
$306$	−3.80479	−0.217505
$307$	−10.9129	−0.622830	−0.311415	−	0.950274i	$-0.600803\pi$
$307$	−10.9129	−0.622830	−0.311415	+	0.950274i	$0.600803\pi$
$308$	−15.2837	−0.870871
$309$	2.09282	0.119056
$310$	6.51146	0.369826
$311$	−2.54122	−0.144099	−0.0720496	−	0.997401i	$-0.522954\pi$
$311$	−2.54122	−0.144099	−0.0720496	+	0.997401i	$0.522954\pi$
$312$	−17.7919	−1.00727
$313$	−10.4232	−0.589154	−0.294577	−	0.955628i	$-0.595179\pi$
$313$	−10.4232	−0.589154	−0.294577	+	0.955628i	$0.595179\pi$
$314$	10.0291	0.565976
$315$	28.1281	1.58484
$316$	17.6423	0.992459
$317$	−27.7821	−1.56040	−0.780199	−	0.625531i	$-0.784882\pi$
$317$	−27.7821	−1.56040	−0.780199	+	0.625531i	$0.784882\pi$
$318$	6.02504	0.337868
$319$	−24.0699	−1.34765
$320$	−0.797463	−0.0445796
$321$	−48.3805	−2.70034
$322$	−16.6263	−0.926550
$323$	0.522707	0.0290842
$324$	25.9036	1.43909
$325$	23.8536	1.32316
$326$	−1.08496	−0.0600906
$327$	17.3724	0.960695
$328$	0.438581	0.0242166
$329$	−11.0617	−0.609854
$330$	−8.54315	−0.470285
$331$	−26.5369	−1.45860	−0.729301	−	0.684193i	$-0.760154\pi$
$331$	−26.5369	−1.45860	−0.729301	+	0.684193i	$0.760154\pi$
$332$	16.9341	0.929379
$333$	3.55557	0.194844
$334$	−12.7847	−0.699547
$335$	−5.43953	−0.297193
$336$	15.1160	0.824648
$337$	−10.3952	−0.566261	−0.283131	−	0.959081i	$-0.591373\pi$
$337$	−10.3952	−0.566261	−0.283131	+	0.959081i	$0.591373\pi$
$338$	−16.8764	−0.917955
$339$	−3.04897	−0.165597
$340$	−0.399477	−0.0216647
$341$	26.8731	1.45526
$342$	−7.92549	−0.428561
$343$	−35.1333	−1.89702
$344$	−9.00734	−0.485643
$345$	−9.29363	−0.500352
$346$	20.7837	1.11734
$347$	−21.2535	−1.14095	−0.570474	−	0.821315i	$-0.693241\pi$
$347$	−21.2535	−1.14095	−0.570474	+	0.821315i	$0.693241\pi$
$348$	23.8058	1.27613
$349$	−5.17202	−0.276852	−0.138426	−	0.990373i	$-0.544204\pi$
$349$	−5.17202	−0.276852	−0.138426	+	0.990373i	$0.544204\pi$
$350$	−20.2661	−1.08327
$351$	81.7605	4.36405
$352$	−3.29116	−0.175419
$353$	4.72490	0.251481	0.125741	−	0.992063i	$-0.459869\pi$
$353$	4.72490	0.251481	0.125741	+	0.992063i	$0.459869\pi$
$354$	−10.3002	−0.547447
$355$	1.92122	0.101968
$356$	−5.40042	−0.286221
$357$	7.57216	0.400761
$358$	−9.04968	−0.478290
$359$	12.6683	0.668609	0.334305	−	0.942465i	$-0.391499\pi$
$359$	12.6683	0.668609	0.334305	+	0.942465i	$0.391499\pi$
$360$	6.05703	0.319234
$361$	−17.9112	−0.942694
$362$	11.0003	0.578165
$363$	0.547684	0.0287460
$364$	25.3831	1.33043
$365$	−4.32172	−0.226209
$366$	−29.7213	−1.55356
$367$	−23.2954	−1.21601	−0.608005	−	0.793933i	$-0.708030\pi$
$367$	−23.2954	−1.21601	−0.608005	+	0.793933i	$0.708030\pi$
$368$	−3.58028	−0.186635
$369$	−3.33119	−0.173415
$370$	0.373311	0.0194075
$371$	−8.59572	−0.446267
$372$	−26.5782	−1.37802
$373$	−9.95015	−0.515199	−0.257600	−	0.966252i	$-0.582932\pi$
$373$	−9.95015	−0.515199	−0.257600	+	0.966252i	$0.582932\pi$
$374$	−1.64866	−0.0852501
$375$	−24.3071	−1.25521
$376$	−2.38201	−0.122843
$377$	39.9750	2.05882
$378$	−69.4639	−3.57284
$379$	28.1826	1.44765	0.723823	−	0.689986i	$-0.242383\pi$
$379$	28.1826	1.44765	0.723823	+	0.689986i	$0.242383\pi$
$380$	−0.832123	−0.0426870
$381$	18.7505	0.960616
$382$	23.0080	1.17719
$383$	7.23818	0.369854	0.184927	−	0.982752i	$-0.440795\pi$
$383$	7.23818	0.369854	0.184927	+	0.982752i	$0.440795\pi$
$384$	3.25505	0.166109
$385$	12.1882	0.621169
$386$	−8.61447	−0.438465
$387$	68.4141	3.47768
$388$	8.63364	0.438307
$389$	−33.5857	−1.70286	−0.851432	−	0.524465i	$-0.824265\pi$
$389$	−33.5857	−1.70286	−0.851432	+	0.524465i	$0.824265\pi$
$390$	14.1884	0.718457
$391$	−1.79349	−0.0907005
$392$	−14.5655	−0.735670
$393$	37.4783	1.89053
$394$	−3.13474	−0.157926
$395$	−14.0691	−0.707894
$396$	24.9976	1.25618
$397$	−22.1451	−1.11143	−0.555715	−	0.831373i	$-0.687555\pi$
$397$	−22.1451	−1.11143	−0.555715	+	0.831373i	$0.687555\pi$
$398$	7.42889	0.372377
$399$	15.7730	0.789639
$400$	−4.36405	−0.218203
$401$	1.43080	0.0714509	0.0357254	−	0.999362i	$-0.488626\pi$
$401$	1.43080	0.0714509	0.0357254	+	0.999362i	$0.488626\pi$
$402$	22.2029	1.10738
$403$	−44.6305	−2.22320
$404$	3.68699	0.183435
$405$	−20.6572	−1.02646
$406$	−33.9629	−1.68555
$407$	1.54067	0.0763681
$408$	1.63057	0.0807253
$409$	0.226475	0.0111985	0.00559923	−	0.999984i	$-0.498218\pi$
$409$	0.226475	0.0111985	0.00559923	+	0.999984i	$0.498218\pi$
$410$	−0.349752	−0.0172730
$411$	−30.6817	−1.51342
$412$	−0.642945	−0.0316756
$413$	14.6949	0.723087
$414$	27.1935	1.33649
$415$	−13.5043	−0.662901
$416$	5.46593	0.267989
$417$	72.7092	3.56059
$418$	−3.43420	−0.167972
$419$	−33.3130	−1.62744	−0.813722	−	0.581254i	$-0.802562\pi$
$419$	−33.3130	−1.62744	−0.813722	+	0.581254i	$0.802562\pi$
$420$	−12.0545	−0.588199
$421$	−30.0446	−1.46429	−0.732143	−	0.681151i	$-0.761480\pi$
$421$	−30.0446	−1.46429	−0.732143	+	0.681151i	$0.761480\pi$
$422$	−25.4173	−1.23729
$423$	18.0923	0.879676
$424$	−1.85098	−0.0898916
$425$	−2.18611	−0.106042
$426$	−7.84194	−0.379943
$427$	42.4023	2.05199
$428$	14.8632	0.718440
$429$	58.5560	2.82711
$430$	7.18302	0.346396
$431$	39.4832	1.90184	0.950920	−	0.309437i	$-0.100140\pi$
$431$	39.4832	1.90184	0.950920	+	0.309437i	$0.100140\pi$
$432$	−14.9582	−0.719677
$433$	22.0279	1.05860	0.529298	−	0.848436i	$-0.322455\pi$
$433$	22.0279	1.05860	0.529298	+	0.848436i	$0.322455\pi$
$434$	37.9182	1.82013
$435$	−18.9843	−0.910226
$436$	−5.33705	−0.255598
$437$	−3.73588	−0.178712
$438$	17.6402	0.842882
$439$	−1.43611	−0.0685420	−0.0342710	−	0.999413i	$-0.510911\pi$
$439$	−1.43611	−0.0685420	−0.0342710	+	0.999413i	$0.510911\pi$
$440$	2.62458	0.125122
$441$	110.631	5.26813
$442$	2.73808	0.130237
$443$	−18.6973	−0.888337	−0.444169	−	0.895943i	$-0.646501\pi$
$443$	−18.6973	−0.888337	−0.444169	+	0.895943i	$0.646501\pi$
$444$	−1.52376	−0.0723147
$445$	4.30663	0.204154
$446$	22.6398	1.07202
$447$	−27.3528	−1.29374
$448$	−4.64387	−0.219402
$449$	−23.2504	−1.09725	−0.548627	−	0.836067i	$-0.684849\pi$
$449$	−23.2504	−1.09725	−0.548627	+	0.836067i	$0.684849\pi$
$450$	33.1466	1.56255
$451$	−1.44344	−0.0679689
$452$	0.936689	0.0440581
$453$	−43.8624	−2.06084
$454$	−3.37377	−0.158339
$455$	−20.2421	−0.948963
$456$	3.39653	0.159057
$457$	35.4551	1.65852	0.829261	−	0.558862i	$-0.188762\pi$
$457$	35.4551	1.65852	0.829261	+	0.558862i	$0.188762\pi$
$458$	−20.9551	−0.979166
$459$	−7.49309	−0.349747
$460$	2.85514	0.133122
$461$	−32.6482	−1.52058	−0.760290	−	0.649584i	$-0.774943\pi$
$461$	−32.6482	−1.52058	−0.760290	+	0.649584i	$0.774943\pi$
$462$	−49.7494	−2.31455
$463$	−17.2910	−0.803582	−0.401791	−	0.915731i	$-0.631612\pi$
$463$	−17.2910	−0.803582	−0.401791	+	0.915731i	$0.631612\pi$
$464$	−7.31349	−0.339520
$465$	21.1952	0.982902
$466$	19.9855	0.925809
$467$	11.5812	0.535912	0.267956	−	0.963431i	$-0.413652\pi$
$467$	11.5812	0.535912	0.267956	+	0.963431i	$0.413652\pi$
$468$	−41.5158	−1.91907
$469$	−31.6760	−1.46266
$470$	1.89957	0.0876204
$471$	32.6453	1.50422
$472$	3.16436	0.145651
$473$	29.6446	1.36306
$474$	57.4268	2.63770
$475$	−4.55372	−0.208939
$476$	−2.32628	−0.106625
$477$	14.0589	0.643713
$478$	−20.4182	−0.933907
$479$	−24.9323	−1.13918	−0.569592	−	0.821927i	$-0.692899\pi$
$479$	−24.9323	−1.13918	−0.569592	+	0.821927i	$0.692899\pi$
$480$	−2.59579	−0.118481
$481$	−2.55873	−0.116668
$482$	5.23353	0.238381
$483$	−54.1196	−2.46253
$484$	−0.168257	−0.00764803
$485$	−6.88501	−0.312632
$486$	39.4431	1.78917
$487$	−12.2668	−0.555861	−0.277930	−	0.960601i	$-0.589648\pi$
$487$	−12.2668	−0.555861	−0.277930	+	0.960601i	$0.589648\pi$
$488$	9.13080	0.413332
$489$	−3.53162	−0.159705
$490$	11.6155	0.524734
$491$	5.08039	0.229275	0.114637	−	0.993407i	$-0.463429\pi$
$491$	5.08039	0.229275	0.114637	+	0.993407i	$0.463429\pi$
$492$	1.42760	0.0643614
$493$	−3.66358	−0.165000
$494$	5.70349	0.256612
$495$	−19.9347	−0.895997
$496$	8.16522	0.366629
$497$	11.1878	0.501842
$498$	55.1214	2.47005
$499$	−5.97482	−0.267470	−0.133735	−	0.991017i	$-0.542697\pi$
$499$	−5.97482	−0.267470	−0.133735	+	0.991017i	$0.542697\pi$
$500$	7.46749	0.333956
$501$	−41.6149	−1.85921
$502$	15.1813	0.677577
$503$	−31.1379	−1.38837	−0.694185	−	0.719796i	$-0.744235\pi$
$503$	−31.1379	−1.38837	−0.694185	+	0.719796i	$0.744235\pi$
$504$	35.2719	1.57114
$505$	−2.94024	−0.130839
$506$	11.7833	0.523830
$507$	−54.9336	−2.43969
$508$	−5.76042	−0.255577
$509$	6.04026	0.267730	0.133865	−	0.991000i	$-0.457261\pi$
$509$	6.04026	0.267730	0.133865	+	0.991000i	$0.457261\pi$
$510$	−1.30032	−0.0575791
$511$	−25.1667	−1.11331
$512$	−1.00000	−0.0441942
$513$	−15.6083	−0.689124
$514$	−25.0294	−1.10400
$515$	0.512725	0.0225934
$516$	−29.3194	−1.29071
$517$	7.83958	0.344784
$518$	2.17390	0.0955157
$519$	67.6521	2.96960
$520$	−4.35888	−0.191150
$521$	40.8061	1.78775	0.893874	−	0.448318i	$-0.147977\pi$
$521$	40.8061	1.78775	0.893874	+	0.448318i	$0.147977\pi$
$522$	55.5487	2.43130
$523$	14.1782	0.619968	0.309984	−	0.950742i	$-0.399676\pi$
$523$	14.1782	0.619968	0.309984	+	0.950742i	$0.399676\pi$
$524$	−11.5139	−0.502986
$525$	−65.9672	−2.87905
$526$	−14.5472	−0.634288
$527$	4.09024	0.178174
$528$	−10.7129	−0.466219
$529$	−10.1816	−0.442679
$530$	1.47609	0.0641172
$531$	−24.0345	−1.04301
$532$	−4.84570	−0.210088
$533$	2.39725	0.103837
$534$	−17.5786	−0.760702
$535$	−11.8529	−0.512444
$536$	−6.82104	−0.294624
$537$	−29.4572	−1.27117
$538$	−11.9319	−0.514422
$539$	47.9375	2.06481
$540$	11.9286	0.513326
$541$	42.2637	1.81706	0.908529	−	0.417821i	$-0.137206\pi$
$541$	42.2637	1.81706	0.908529	+	0.417821i	$0.137206\pi$
$542$	12.3245	0.529384
$543$	35.8067	1.53661
$544$	−0.500935	−0.0214774
$545$	4.25610	0.182311
$546$	82.6233	3.53595
$547$	−0.558937	−0.0238984	−0.0119492	−	0.999929i	$-0.503804\pi$
$547$	−0.558937	−0.0238984	−0.0119492	+	0.999929i	$0.503804\pi$
$548$	9.42587	0.402653
$549$	−69.3519	−2.95987
$550$	14.3628	0.612432
$551$	−7.63136	−0.325107
$552$	−11.6540	−0.496027
$553$	−81.9287	−3.48396
$554$	−25.3353	−1.07640
$555$	1.21515	0.0515801
$556$	−22.3373	−0.947314
$557$	−6.26417	−0.265422	−0.132711	−	0.991155i	$-0.542368\pi$
$557$	−6.26417	−0.265422	−0.132711	+	0.991155i	$0.542368\pi$
$558$	−62.0179	−2.62543
$559$	−49.2335	−2.08235
$560$	3.70332	0.156494
$561$	−5.36647	−0.226573
$562$	14.7265	0.621199
$563$	39.5779	1.66801	0.834005	−	0.551757i	$-0.186042\pi$
$563$	39.5779	1.66801	0.834005	+	0.551757i	$0.186042\pi$
$564$	−7.75357	−0.326484
$565$	−0.746975	−0.0314255
$566$	20.1841	0.848400
$567$	−120.293	−5.05183
$568$	2.40916	0.101086
$569$	−26.4440	−1.10859	−0.554294	−	0.832321i	$-0.687012\pi$
$569$	−26.4440	−1.10859	−0.554294	+	0.832321i	$0.687012\pi$
$570$	−2.70861	−0.113451
$571$	−35.8862	−1.50179	−0.750895	−	0.660422i	$-0.770378\pi$
$571$	−35.8862	−1.50179	−0.750895	+	0.660422i	$0.770378\pi$
$572$	−17.9893	−0.752169
$573$	74.8921	3.12866
$574$	−2.03671	−0.0850107
$575$	15.6245	0.651587
$576$	7.59538	0.316474
$577$	−26.8905	−1.11946	−0.559732	−	0.828673i	$-0.689096\pi$
$577$	−26.8905	−1.11946	−0.559732	+	0.828673i	$0.689096\pi$
$578$	16.7491	0.696669
$579$	−28.0406	−1.16533
$580$	5.83224	0.242171
$581$	−78.6397	−3.26252
$582$	28.1030	1.16491
$583$	6.09188	0.252300
$584$	−5.41933	−0.224253
$585$	33.1073	1.36882
$586$	−21.0281	−0.868662
$587$	−6.40928	−0.264539	−0.132270	−	0.991214i	$-0.542226\pi$
$587$	−6.40928	−0.264539	−0.132270	+	0.991214i	$0.542226\pi$
$588$	−47.4116	−1.95522
$589$	8.52010	0.351065
$590$	−2.52346	−0.103889
$591$	−10.2037	−0.419726
$592$	0.468123	0.0192397
$593$	20.5906	0.845555	0.422778	−	0.906233i	$-0.361055\pi$
$593$	20.5906	0.845555	0.422778	+	0.906233i	$0.361055\pi$
$594$	49.2298	2.01992
$595$	1.85512	0.0760525
$596$	8.40318	0.344208
$597$	24.1814	0.989680
$598$	−19.5695	−0.800258
$599$	29.2853	1.19656	0.598282	−	0.801285i	$-0.295850\pi$
$599$	29.2853	1.19656	0.598282	+	0.801285i	$0.295850\pi$
$600$	−14.2052	−0.579926
$601$	29.4176	1.19997	0.599985	−	0.800011i	$-0.295173\pi$
$601$	29.4176	1.19997	0.599985	+	0.800011i	$0.295173\pi$
$602$	41.8289	1.70482
$603$	51.8084	2.10980
$604$	13.4752	0.548297
$605$	0.134178	0.00545513
$606$	12.0014	0.487522
$607$	15.4491	0.627062	0.313531	−	0.949578i	$-0.398488\pi$
$607$	15.4491	0.627062	0.313531	+	0.949578i	$0.398488\pi$
$608$	−1.04346	−0.0423180
$609$	−110.551	−4.47976
$610$	−7.28148	−0.294819
$611$	−13.0199	−0.526729
$612$	3.80479	0.153800
$613$	1.19710	0.0483504	0.0241752	−	0.999708i	$-0.492304\pi$
$613$	1.19710	0.0483504	0.0241752	+	0.999708i	$0.492304\pi$
$614$	10.9129	0.440407
$615$	−1.13846	−0.0459072
$616$	15.2837	0.615799
$617$	44.2004	1.77944	0.889720	−	0.456507i	$-0.150900\pi$
$617$	44.2004	1.77944	0.889720	+	0.456507i	$0.150900\pi$
$618$	−2.09282	−0.0841856
$619$	−37.9236	−1.52428	−0.762139	−	0.647414i	$-0.775851\pi$
$619$	−37.9236	−1.52428	−0.762139	+	0.647414i	$0.775851\pi$
$620$	−6.51146	−0.261507
$621$	53.5545	2.14907
$622$	2.54122	0.101894
$623$	25.0788	1.00476
$624$	17.7919	0.712246
$625$	15.8652	0.634608
$626$	10.4232	0.416595
$627$	−11.1785	−0.446427
$628$	−10.0291	−0.400205
$629$	0.234499	0.00935009
$630$	−28.1281	−1.12065
$631$	2.08576	0.0830329	0.0415164	−	0.999138i	$-0.486781\pi$
$631$	2.08576	0.0830329	0.0415164	+	0.999138i	$0.486781\pi$
$632$	−17.6423	−0.701775
$633$	−82.7346	−3.28841
$634$	27.7821	1.10337
$635$	4.59372	0.182296
$636$	−6.02504	−0.238909
$637$	−79.6142	−3.15443
$638$	24.0699	0.952936
$639$	−18.2985	−0.723876
$640$	0.797463	0.0315225
$641$	25.2216	0.996195	0.498098	−	0.867121i	$-0.334032\pi$
$641$	25.2216	0.996195	0.498098	+	0.867121i	$0.334032\pi$
$642$	48.3805	1.90943
$643$	2.49060	0.0982198	0.0491099	−	0.998793i	$-0.484362\pi$
$643$	2.49060	0.0982198	0.0491099	+	0.998793i	$0.484362\pi$
$644$	16.6263	0.655170
$645$	23.3811	0.920631
$646$	−0.522707	−0.0205656
$647$	38.2554	1.50398	0.751988	−	0.659176i	$-0.229095\pi$
$647$	38.2554	1.50398	0.751988	+	0.659176i	$0.229095\pi$
$648$	−25.9036	−1.01759
$649$	−10.4144	−0.408801
$650$	−23.8536	−0.935615
$651$	123.426	4.83744
$652$	1.08496	0.0424905
$653$	23.1997	0.907874	0.453937	−	0.891034i	$-0.350019\pi$
$653$	23.1997	0.907874	0.453937	+	0.891034i	$0.350019\pi$
$654$	−17.3724	−0.679314
$655$	9.18189	0.358766
$656$	−0.438581	−0.0171237
$657$	41.1618	1.60588
$658$	11.0617	0.431232
$659$	32.8123	1.27819	0.639094	−	0.769129i	$-0.279310\pi$
$659$	32.8123	1.27819	0.639094	+	0.769129i	$0.279310\pi$
$660$	8.54315	0.332542
$661$	38.6679	1.50401	0.752003	−	0.659159i	$-0.229088\pi$
$661$	38.6679	1.50401	0.752003	+	0.659159i	$0.229088\pi$
$662$	26.5369	1.03139
$663$	8.91259	0.346136
$664$	−16.9341	−0.657170
$665$	3.86427	0.149850
$666$	−3.55557	−0.137775
$667$	26.1843	1.01386
$668$	12.7847	0.494654
$669$	73.6936	2.84916
$670$	5.43953	0.210147
$671$	−30.0510	−1.16010
$672$	−15.1160	−0.583114
$673$	−36.1893	−1.39499	−0.697497	−	0.716588i	$-0.745703\pi$
$673$	−36.1893	−1.39499	−0.697497	+	0.716588i	$0.745703\pi$
$674$	10.3952	0.400407
$675$	65.2784	2.51257
$676$	16.8764	0.649092
$677$	8.48103	0.325952	0.162976	−	0.986630i	$-0.447891\pi$
$677$	8.48103	0.325952	0.162976	+	0.986630i	$0.447891\pi$
$678$	3.04897	0.117095
$679$	−40.0935	−1.53865
$680$	0.399477	0.0153193
$681$	−10.9818	−0.420823
$682$	−26.8731	−1.02902
$683$	31.9768	1.22356	0.611779	−	0.791029i	$-0.290454\pi$
$683$	31.9768	1.22356	0.611779	+	0.791029i	$0.290454\pi$
$684$	7.92549	0.303039
$685$	−7.51678	−0.287202
$686$	35.1333	1.34140
$687$	−68.2099	−2.60237
$688$	9.00734	0.343401
$689$	−10.1173	−0.385440
$690$	9.29363	0.353803
$691$	−19.7668	−0.751964	−0.375982	−	0.926627i	$-0.622694\pi$
$691$	−19.7668	−0.751964	−0.375982	+	0.926627i	$0.622694\pi$
$692$	−20.7837	−0.790079
$693$	−116.086	−4.40973
$694$	21.2535	0.806773
$695$	17.8132	0.675693
$696$	−23.8058	−0.902357
$697$	−0.219700	−0.00832175
$698$	5.17202	0.195764
$699$	65.0538	2.46056
$700$	20.2661	0.765986
$701$	2.60206	0.0982785	0.0491393	−	0.998792i	$-0.484352\pi$
$701$	2.60206	0.0982785	0.0491393	+	0.998792i	$0.484352\pi$
$702$	−81.7605	−3.08585
$703$	0.488469	0.0184229
$704$	3.29116	0.124040
$705$	6.18319	0.232872
$706$	−4.72490	−0.177824
$707$	−17.1219	−0.643936
$708$	10.3002	0.387103
$709$	−17.3221	−0.650544	−0.325272	−	0.945621i	$-0.605456\pi$
$709$	−17.3221	−0.650544	−0.325272	+	0.945621i	$0.605456\pi$
$710$	−1.92122	−0.0721020
$711$	134.000	5.02540
$712$	5.40042	0.202389
$713$	−29.2337	−1.09481
$714$	−7.57216	−0.283381
$715$	14.3458	0.536502
$716$	9.04968	0.338202
$717$	−66.4624	−2.48208
$718$	−12.6683	−0.472778
$719$	48.4121	1.80547	0.902733	−	0.430201i	$-0.141557\pi$
$719$	48.4121	1.80547	0.902733	+	0.430201i	$0.141557\pi$
$720$	−6.05703	−0.225732
$721$	2.98575	0.111195
$722$	17.9112	0.666585
$723$	17.0354	0.633554
$724$	−11.0003	−0.408825
$725$	31.9165	1.18535
$726$	−0.547684	−0.0203265
$727$	31.5434	1.16988	0.584940	−	0.811076i	$-0.301118\pi$
$727$	31.5434	1.16988	0.584940	+	0.811076i	$0.301118\pi$
$728$	−25.3831	−0.940759
$729$	50.6785	1.87698
$730$	4.32172	0.159954
$731$	4.51209	0.166886
$732$	29.7213	1.09853
$733$	−47.0479	−1.73776	−0.868878	−	0.495027i	$-0.835158\pi$
$733$	−47.0479	−1.73776	−0.868878	+	0.495027i	$0.835158\pi$
$734$	23.2954	0.859849
$735$	37.8090	1.39461
$736$	3.58028	0.131971
$737$	22.4492	0.826925
$738$	3.33119	0.122623
$739$	10.9277	0.401982	0.200991	−	0.979593i	$-0.435584\pi$
$739$	10.9277	0.401982	0.200991	+	0.979593i	$0.435584\pi$
$740$	−0.373311	−0.0137232
$741$	18.5652	0.682009
$742$	8.59572	0.315559
$743$	−17.1113	−0.627752	−0.313876	−	0.949464i	$-0.601628\pi$
$743$	−17.1113	−0.627752	−0.313876	+	0.949464i	$0.601628\pi$
$744$	26.5782	0.974405
$745$	−6.70123	−0.245514
$746$	9.95015	0.364301
$747$	128.621	4.70599
$748$	1.64866	0.0602809
$749$	−69.0228	−2.52204
$750$	24.3071	0.887569
$751$	−10.2253	−0.373127	−0.186564	−	0.982443i	$-0.559735\pi$
$751$	−10.2253	−0.373127	−0.186564	+	0.982443i	$0.559735\pi$
$752$	2.38201	0.0868630
$753$	49.4161	1.80082
$754$	−39.9750	−1.45581
$755$	−10.7460	−0.391086
$756$	69.4639	2.52638
$757$	26.1613	0.950850	0.475425	−	0.879756i	$-0.342294\pi$
$757$	26.1613	0.950850	0.475425	+	0.879756i	$0.342294\pi$
$758$	−28.1826	−1.02364
$759$	38.3552	1.39220
$760$	0.832123	0.0301843
$761$	28.0192	1.01570	0.507848	−	0.861446i	$-0.330441\pi$
$761$	28.0192	1.01570	0.507848	+	0.861446i	$0.330441\pi$
$762$	−18.7505	−0.679258
$763$	24.7846	0.897262
$764$	−23.0080	−0.832399
$765$	−3.03418	−0.109701
$766$	−7.23818	−0.261526
$767$	17.2962	0.624528
$768$	−3.25505	−0.117457
$769$	−8.52834	−0.307540	−0.153770	−	0.988107i	$-0.549141\pi$
$769$	−8.52834	−0.307540	−0.153770	+	0.988107i	$0.549141\pi$
$770$	−12.1882	−0.439233
$771$	−81.4722	−2.93415
$772$	8.61447	0.310042
$773$	−21.2153	−0.763061	−0.381531	−	0.924356i	$-0.624603\pi$
$773$	−21.2153	−0.763061	−0.381531	+	0.924356i	$0.624603\pi$
$774$	−68.4141	−2.45909
$775$	−35.6334	−1.27999
$776$	−8.63364	−0.309930
$777$	7.07617	0.253856
$778$	33.5857	1.20411
$779$	−0.457643	−0.0163967
$780$	−14.1884	−0.508026
$781$	−7.92893	−0.283720
$782$	1.79349	0.0641349
$783$	109.397	3.90952
$784$	14.5655	0.520197
$785$	7.99785	0.285456
$786$	−37.4783	−1.33681
$787$	−31.2784	−1.11495	−0.557477	−	0.830193i	$-0.688230\pi$
$787$	−31.2784	−1.11495	−0.557477	+	0.830193i	$0.688230\pi$
$788$	3.13474	0.111670
$789$	−47.3519	−1.68577
$790$	14.0691	0.500557
$791$	−4.34986	−0.154663
$792$	−24.9976	−0.888251
$793$	49.9083	1.77230
$794$	22.1451	0.785899
$795$	4.80475	0.170407
$796$	−7.42889	−0.263310
$797$	−33.5844	−1.18962	−0.594811	−	0.803866i	$-0.702773\pi$
$797$	−33.5844	−1.18962	−0.594811	+	0.803866i	$0.702773\pi$
$798$	−15.7730	−0.558359
$799$	1.19323	0.0422135
$800$	4.36405	0.154293
$801$	−41.0182	−1.44931
$802$	−1.43080	−0.0505234
$803$	17.8359	0.629415
$804$	−22.2029	−0.783035
$805$	−13.2589	−0.467315
$806$	44.6305	1.57204
$807$	−38.8391	−1.36720
$808$	−3.68699	−0.129708
$809$	−48.9858	−1.72225	−0.861125	−	0.508393i	$-0.830240\pi$
$809$	−48.9858	−1.72225	−0.861125	+	0.508393i	$0.830240\pi$
$810$	20.6572	0.725819
$811$	52.6685	1.84944	0.924720	−	0.380648i	$-0.124299\pi$
$811$	52.6685	1.84944	0.924720	+	0.380648i	$0.124299\pi$
$812$	33.9629	1.19186
$813$	40.1171	1.40697
$814$	−1.54067	−0.0540004
$815$	−0.865220	−0.0303073
$816$	−1.63057	−0.0570814
$817$	9.39882	0.328823
$818$	−0.226475	−0.00791850
$819$	192.794	6.73677
$820$	0.349752	0.0122139
$821$	3.64832	0.127327	0.0636636	−	0.997971i	$-0.479722\pi$
$821$	3.64832	0.127327	0.0636636	+	0.997971i	$0.479722\pi$
$822$	30.6817	1.07015
$823$	−36.0022	−1.25496	−0.627480	−	0.778633i	$-0.715913\pi$
$823$	−36.0022	−1.25496	−0.627480	+	0.778633i	$0.715913\pi$
$824$	0.642945	0.0223980
$825$	46.7517	1.62768
$826$	−14.6949	−0.511300
$827$	−7.17494	−0.249497	−0.124749	−	0.992188i	$-0.539812\pi$
$827$	−7.17494	−0.249497	−0.124749	+	0.992188i	$0.539812\pi$
$828$	−27.1935	−0.945041
$829$	−15.7348	−0.546493	−0.273246	−	0.961944i	$-0.588097\pi$
$829$	−15.7348	−0.546493	−0.273246	+	0.961944i	$0.588097\pi$
$830$	13.5043	0.468742
$831$	−82.4679	−2.86078
$832$	−5.46593	−0.189497
$833$	7.29638	0.252805
$834$	−72.7092	−2.51771
$835$	−10.1953	−0.352824
$836$	3.43420	0.118774
$837$	−122.137	−4.22167
$838$	33.3130	1.15078
$839$	−17.5145	−0.604668	−0.302334	−	0.953202i	$-0.597766\pi$
$839$	−17.5145	−0.604668	−0.302334	+	0.953202i	$0.597766\pi$
$840$	12.0545	0.415920
$841$	24.4872	0.844386
$842$	30.0446	1.03541
$843$	47.9355	1.65099
$844$	25.4173	0.874899
$845$	−13.4583	−0.462980
$846$	−18.0923	−0.622025
$847$	0.781362	0.0268479
$848$	1.85098	0.0635630
$849$	65.7003	2.25483
$850$	2.18611	0.0749828
$851$	−1.67601	−0.0574529
$852$	7.84194	0.268661
$853$	−37.0460	−1.26843	−0.634216	−	0.773156i	$-0.718677\pi$
$853$	−37.0460	−1.26843	−0.634216	+	0.773156i	$0.718677\pi$
$854$	−42.4023	−1.45098
$855$	−6.32029	−0.216149
$856$	−14.8632	−0.508014
$857$	9.78913	0.334390	0.167195	−	0.985924i	$-0.446529\pi$
$857$	9.78913	0.334390	0.167195	+	0.985924i	$0.446529\pi$
$858$	−58.5560	−1.99907
$859$	−1.79271	−0.0611663	−0.0305832	−	0.999532i	$-0.509736\pi$
$859$	−1.79271	−0.0611663	−0.0305832	+	0.999532i	$0.509736\pi$
$860$	−7.18302	−0.244939
$861$	−6.62961	−0.225936
$862$	−39.4832	−1.34480
$863$	49.1927	1.67454	0.837269	−	0.546791i	$-0.184151\pi$
$863$	49.1927	1.67454	0.837269	+	0.546791i	$0.184151\pi$
$864$	14.9582	0.508888
$865$	16.5743	0.563542
$866$	−22.0279	−0.748540
$867$	54.5191	1.85157
$868$	−37.9182	−1.28703
$869$	58.0638	1.96968
$870$	18.9843	0.643627
$871$	−37.2833	−1.26330
$872$	5.33705	0.180735
$873$	65.5758	2.21940
$874$	3.73588	0.126368
$875$	−34.6780	−1.17233
$876$	−17.6402	−0.596007
$877$	−2.84241	−0.0959812	−0.0479906	−	0.998848i	$-0.515282\pi$
$877$	−2.84241	−0.0959812	−0.0479906	+	0.998848i	$0.515282\pi$
$878$	1.43611	0.0484665
$879$	−68.4476	−2.30868
$880$	−2.62458	−0.0884746
$881$	49.8286	1.67877	0.839385	−	0.543538i	$-0.182915\pi$
$881$	49.8286	1.67877	0.839385	+	0.543538i	$0.182915\pi$
$882$	−110.631	−3.72513
$883$	−11.2532	−0.378702	−0.189351	−	0.981909i	$-0.560638\pi$
$883$	−11.2532	−0.378702	−0.189351	+	0.981909i	$0.560638\pi$
$884$	−2.73808	−0.0920915
$885$	−8.21399	−0.276110
$886$	18.6973	0.628149
$887$	−22.0121	−0.739094	−0.369547	−	0.929212i	$-0.620487\pi$
$887$	−22.0121	−0.739094	−0.369547	+	0.929212i	$0.620487\pi$
$888$	1.52376	0.0511342
$889$	26.7506	0.897187
$890$	−4.30663	−0.144359
$891$	85.2530	2.85608
$892$	−22.6398	−0.758035
$893$	2.48554	0.0831754
$894$	27.3528	0.914814
$895$	−7.21678	−0.241230
$896$	4.64387	0.155141
$897$	−63.6999	−2.12688
$898$	23.2504	0.775876
$899$	−59.7163	−1.99165
$900$	−33.1466	−1.10489
$901$	0.927221	0.0308902
$902$	1.44344	0.0480613
$903$	136.155	4.53096
$904$	−0.936689	−0.0311538
$905$	8.77237	0.291604
$906$	43.8624	1.45723
$907$	−0.897874	−0.0298134	−0.0149067	−	0.999889i	$-0.504745\pi$
$907$	−0.897874	−0.0298134	−0.0149067	+	0.999889i	$0.504745\pi$
$908$	3.37377	0.111962
$909$	28.0041	0.928837
$910$	20.2421	0.671018
$911$	−24.3651	−0.807251	−0.403626	−	0.914924i	$-0.632250\pi$
$911$	−24.3651	−0.807251	−0.403626	+	0.914924i	$0.632250\pi$
$912$	−3.39653	−0.112470
$913$	55.7328	1.84449
$914$	−35.4551	−1.17275
$915$	−23.7016	−0.783551
$916$	20.9551	0.692375
$917$	53.4689	1.76570
$918$	7.49309	0.247309
$919$	53.7002	1.77140	0.885702	−	0.464253i	$-0.153677\pi$
$919$	53.7002	1.77140	0.885702	+	0.464253i	$0.153677\pi$
$920$	−2.85514	−0.0941312
$921$	35.5219	1.17049
$922$	32.6482	1.07521
$923$	13.1683	0.433440
$924$	49.7494	1.63663
$925$	−2.04291	−0.0671705
$926$	17.2910	0.568218
$927$	−4.88341	−0.160392
$928$	7.31349	0.240077
$929$	38.9927	1.27931	0.639655	−	0.768662i	$-0.279077\pi$
$929$	38.9927	1.27931	0.639655	+	0.768662i	$0.279077\pi$
$930$	−21.1952	−0.695017
$931$	15.1986	0.498113
$932$	−19.9855	−0.654646
$933$	8.27180	0.270807
$934$	−11.5812	−0.378947
$935$	−1.31474	−0.0429967
$936$	41.5158	1.35699
$937$	26.8800	0.878130	0.439065	−	0.898455i	$-0.355310\pi$
$937$	26.8800	0.878130	0.439065	+	0.898455i	$0.355310\pi$
$938$	31.6760	1.03426
$939$	33.9281	1.10720
$940$	−1.89957	−0.0619570
$941$	−31.1249	−1.01464	−0.507322	−	0.861757i	$-0.669365\pi$
$941$	−31.1249	−1.01464	−0.507322	+	0.861757i	$0.669365\pi$
$942$	−32.6453	−1.06364
$943$	1.57024	0.0511341
$944$	−3.16436	−0.102991
$945$	−55.3949	−1.80200
$946$	−29.6446	−0.963829
$947$	23.7607	0.772120	0.386060	−	0.922474i	$-0.373836\pi$
$947$	23.7607	0.772120	0.386060	+	0.922474i	$0.373836\pi$
$948$	−57.4268	−1.86513
$949$	−29.6217	−0.961560
$950$	4.55372	0.147742
$951$	90.4322	2.93247
$952$	2.32628	0.0753951
$953$	−8.63103	−0.279586	−0.139793	−	0.990181i	$-0.544644\pi$
$953$	−8.63103	−0.279586	−0.139793	+	0.990181i	$0.544644\pi$
$954$	−14.0589	−0.455174
$955$	18.3480	0.593727
$956$	20.4182	0.660372
$957$	78.3488	2.53266
$958$	24.9323	0.805525
$959$	−43.7725	−1.41349
$960$	2.59579	0.0837786
$961$	35.6708	1.15067
$962$	2.55873	0.0824967
$963$	112.892	3.63788
$964$	−5.23353	−0.168561
$965$	−6.86973	−0.221144
$966$	54.1196	1.74127
$967$	44.4514	1.42946	0.714731	−	0.699400i	$-0.246549\pi$
$967$	44.4514	1.42946	0.714731	+	0.699400i	$0.246549\pi$
$968$	0.168257	0.00540797
$969$	−1.70144	−0.0546581
$970$	6.88501	0.221064
$971$	−25.0891	−0.805146	−0.402573	−	0.915388i	$-0.631884\pi$
$971$	−25.0891	−0.805146	−0.402573	+	0.915388i	$0.631884\pi$
$972$	−39.4431	−1.26514
$973$	103.732	3.32549
$974$	12.2668	0.393053
$975$	−77.6448	−2.48662
$976$	−9.13080	−0.292270
$977$	−0.541258	−0.0173164	−0.00865819	−	0.999963i	$-0.502756\pi$
$977$	−0.541258	−0.0173164	−0.00865819	+	0.999963i	$0.502756\pi$
$978$	3.53162	0.112929
$979$	−17.7736	−0.568048
$980$	−11.6155	−0.371043
$981$	−40.5369	−1.29424
$982$	−5.08039	−0.162122
$983$	−28.5162	−0.909526	−0.454763	−	0.890613i	$-0.650276\pi$
$983$	−28.5162	−0.909526	−0.454763	+	0.890613i	$0.650276\pi$
$984$	−1.42760	−0.0455104
$985$	−2.49984	−0.0796515
$986$	3.66358	0.116672
$987$	36.0066	1.14610
$988$	−5.70349	−0.181452
$989$	−32.2488	−1.02545
$990$	19.9347	0.633566
$991$	−45.2310	−1.43681	−0.718405	−	0.695626i	$-0.755127\pi$
$991$	−45.2310	−1.43681	−0.718405	+	0.695626i	$0.755127\pi$
$992$	−8.16522	−0.259246
$993$	86.3791	2.74116
$994$	−11.1878	−0.354856
$995$	5.92427	0.187812
$996$	−55.1214	−1.74659
$997$	−1.46977	−0.0465481	−0.0232740	−	0.999729i	$-0.507409\pi$
$997$	−1.46977	−0.0465481	−0.0232740	+	0.999729i	$0.507409\pi$
$998$	5.97482	0.189130
$999$	−7.00227	−0.221542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.1	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.1	✓	37	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.25505 q^{3} +1.00000 q^{4} -0.797463 q^{5} +3.25505 q^{6} -4.64387 q^{7} -1.00000 q^{8} +7.59538 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.25505 q^{3} +1.00000 q^{4} -0.797463 q^{5} +3.25505 q^{6} -4.64387 q^{7} -1.00000 q^{8} +7.59538 q^{9} +0.797463 q^{10} +3.29116 q^{11} -3.25505 q^{12} -5.46593 q^{13} +4.64387 q^{14} +2.59579 q^{15} +1.00000 q^{16} +0.500935 q^{17} -7.59538 q^{18} +1.04346 q^{19} -0.797463 q^{20} +15.1160 q^{21} -3.29116 q^{22} -3.58028 q^{23} +3.25505 q^{24} -4.36405 q^{25} +5.46593 q^{26} -14.9582 q^{27} -4.64387 q^{28} -7.31349 q^{29} -2.59579 q^{30} +8.16522 q^{31} -1.00000 q^{32} -10.7129 q^{33} -0.500935 q^{34} +3.70332 q^{35} +7.59538 q^{36} +0.468123 q^{37} -1.04346 q^{38} +17.7919 q^{39} +0.797463 q^{40} -0.438581 q^{41} -15.1160 q^{42} +9.00734 q^{43} +3.29116 q^{44} -6.05703 q^{45} +3.58028 q^{46} +2.38201 q^{47} -3.25505 q^{48} +14.5655 q^{49} +4.36405 q^{50} -1.63057 q^{51} -5.46593 q^{52} +1.85098 q^{53} +14.9582 q^{54} -2.62458 q^{55} +4.64387 q^{56} -3.39653 q^{57} +7.31349 q^{58} -3.16436 q^{59} +2.59579 q^{60} -9.13080 q^{61} -8.16522 q^{62} -35.2719 q^{63} +1.00000 q^{64} +4.35888 q^{65} +10.7129 q^{66} +6.82104 q^{67} +0.500935 q^{68} +11.6540 q^{69} -3.70332 q^{70} -2.40916 q^{71} -7.59538 q^{72} +5.41933 q^{73} -0.468123 q^{74} +14.2052 q^{75} +1.04346 q^{76} -15.2837 q^{77} -17.7919 q^{78} +17.6423 q^{79} -0.797463 q^{80} +25.9036 q^{81} +0.438581 q^{82} +16.9341 q^{83} +15.1160 q^{84} -0.399477 q^{85} -9.00734 q^{86} +23.8058 q^{87} -3.29116 q^{88} -5.40042 q^{89} +6.05703 q^{90} +25.3831 q^{91} -3.58028 q^{92} -26.5782 q^{93} -2.38201 q^{94} -0.832123 q^{95} +3.25505 q^{96} +8.63364 q^{97} -14.5655 q^{98} +24.9976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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