LMFDB - Embedded newform 4022.2.a.e.1.7

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:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.56517 q^{3} +1.00000 q^{4} +1.93763 q^{5} +2.56517 q^{6} -4.25391 q^{7} -1.00000 q^{8} +3.58009 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.56517 q^{3} +1.00000 q^{4} +1.93763 q^{5} +2.56517 q^{6} -4.25391 q^{7} -1.00000 q^{8} +3.58009 q^{9} -1.93763 q^{10} -1.60787 q^{11} -2.56517 q^{12} +0.921449 q^{13} +4.25391 q^{14} -4.97035 q^{15} +1.00000 q^{16} +7.21995 q^{17} -3.58009 q^{18} -2.67019 q^{19} +1.93763 q^{20} +10.9120 q^{21} +1.60787 q^{22} +0.490534 q^{23} +2.56517 q^{24} -1.24559 q^{25} -0.921449 q^{26} -1.48803 q^{27} -4.25391 q^{28} +6.73297 q^{29} +4.97035 q^{30} -9.32348 q^{31} -1.00000 q^{32} +4.12446 q^{33} -7.21995 q^{34} -8.24250 q^{35} +3.58009 q^{36} -4.99591 q^{37} +2.67019 q^{38} -2.36367 q^{39} -1.93763 q^{40} -6.91979 q^{41} -10.9120 q^{42} -4.79643 q^{43} -1.60787 q^{44} +6.93689 q^{45} -0.490534 q^{46} +9.79727 q^{47} -2.56517 q^{48} +11.0958 q^{49} +1.24559 q^{50} -18.5204 q^{51} +0.921449 q^{52} -1.18872 q^{53} +1.48803 q^{54} -3.11546 q^{55} +4.25391 q^{56} +6.84950 q^{57} -6.73297 q^{58} +0.965789 q^{59} -4.97035 q^{60} -14.3800 q^{61} +9.32348 q^{62} -15.2294 q^{63} +1.00000 q^{64} +1.78543 q^{65} -4.12446 q^{66} +5.16658 q^{67} +7.21995 q^{68} -1.25830 q^{69} +8.24250 q^{70} +9.73690 q^{71} -3.58009 q^{72} -0.507148 q^{73} +4.99591 q^{74} +3.19515 q^{75} -2.67019 q^{76} +6.83973 q^{77} +2.36367 q^{78} -7.76563 q^{79} +1.93763 q^{80} -6.92322 q^{81} +6.91979 q^{82} +8.80351 q^{83} +10.9120 q^{84} +13.9896 q^{85} +4.79643 q^{86} -17.2712 q^{87} +1.60787 q^{88} -2.21832 q^{89} -6.93689 q^{90} -3.91976 q^{91} +0.490534 q^{92} +23.9163 q^{93} -9.79727 q^{94} -5.17385 q^{95} +2.56517 q^{96} -1.70082 q^{97} -11.0958 q^{98} -5.75632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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
$3$	−2.56517	−1.48100	−0.740500	−	0.672056i	$-0.765411\pi$
$3$	−2.56517	−1.48100	−0.740500	+	0.672056i	$0.765411\pi$
$4$	1.00000	0.500000
$5$	1.93763	0.866534	0.433267	−	0.901266i	$-0.357361\pi$
$5$	1.93763	0.866534	0.433267	+	0.901266i	$0.357361\pi$
$6$	2.56517	1.04723
$7$	−4.25391	−1.60783	−0.803913	−	0.594746i	$-0.797253\pi$
$7$	−4.25391	−1.60783	−0.803913	+	0.594746i	$0.797253\pi$
$8$	−1.00000	−0.353553
$9$	3.58009	1.19336
$10$	−1.93763	−0.612732
$11$	−1.60787	−0.484791	−0.242395	−	0.970178i	$-0.577933\pi$
$11$	−1.60787	−0.484791	−0.242395	+	0.970178i	$0.577933\pi$
$12$	−2.56517	−0.740500
$13$	0.921449	0.255564	0.127782	−	0.991802i	$-0.459214\pi$
$13$	0.921449	0.255564	0.127782	+	0.991802i	$0.459214\pi$
$14$	4.25391	1.13691
$15$	−4.97035	−1.28334
$16$	1.00000	0.250000
$17$	7.21995	1.75109	0.875547	−	0.483133i	$-0.160501\pi$
$17$	7.21995	1.75109	0.875547	+	0.483133i	$0.160501\pi$
$18$	−3.58009	−0.843836
$19$	−2.67019	−0.612585	−0.306292	−	0.951938i	$-0.599088\pi$
$19$	−2.67019	−0.612585	−0.306292	+	0.951938i	$0.599088\pi$
$20$	1.93763	0.433267
$21$	10.9120	2.38119
$22$	1.60787	0.342799
$23$	0.490534	0.102283	0.0511417	−	0.998691i	$-0.483714\pi$
$23$	0.490534	0.102283	0.0511417	+	0.998691i	$0.483714\pi$
$24$	2.56517	0.523613
$25$	−1.24559	−0.249118
$26$	−0.921449	−0.180711
$27$	−1.48803	−0.286372
$28$	−4.25391	−0.803913
$29$	6.73297	1.25028	0.625141	−	0.780512i	$-0.285042\pi$
$29$	6.73297	1.25028	0.625141	+	0.780512i	$0.285042\pi$
$30$	4.97035	0.907457
$31$	−9.32348	−1.67455	−0.837274	−	0.546784i	$-0.815852\pi$
$31$	−9.32348	−1.67455	−0.837274	+	0.546784i	$0.815852\pi$
$32$	−1.00000	−0.176777
$33$	4.12446	0.717976
$34$	−7.21995	−1.23821
$35$	−8.24250	−1.39324
$36$	3.58009	0.596682
$37$	−4.99591	−0.821322	−0.410661	−	0.911788i	$-0.634702\pi$
$37$	−4.99591	−0.821322	−0.410661	+	0.911788i	$0.634702\pi$
$38$	2.67019	0.433163
$39$	−2.36367	−0.378490
$40$	−1.93763	−0.306366
$41$	−6.91979	−1.08069	−0.540345	−	0.841444i	$-0.681706\pi$
$41$	−6.91979	−1.08069	−0.540345	+	0.841444i	$0.681706\pi$
$42$	−10.9120	−1.68376
$43$	−4.79643	−0.731449	−0.365724	−	0.930723i	$-0.619179\pi$
$43$	−4.79643	−0.731449	−0.365724	+	0.930723i	$0.619179\pi$
$44$	−1.60787	−0.242395
$45$	6.93689	1.03409
$46$	−0.490534	−0.0723253
$47$	9.79727	1.42908	0.714539	−	0.699595i	$-0.246636\pi$
$47$	9.79727	1.42908	0.714539	+	0.699595i	$0.246636\pi$
$48$	−2.56517	−0.370250
$49$	11.0958	1.58511
$50$	1.24559	0.176153
$51$	−18.5204	−2.59337
$52$	0.921449	0.127782
$53$	−1.18872	−0.163284	−0.0816419	−	0.996662i	$-0.526016\pi$
$53$	−1.18872	−0.163284	−0.0816419	+	0.996662i	$0.526016\pi$
$54$	1.48803	0.202495
$55$	−3.11546	−0.420088
$56$	4.25391	0.568453
$57$	6.84950	0.907238
$58$	−6.73297	−0.884083
$59$	0.965789	0.125735	0.0628675	−	0.998022i	$-0.479975\pi$
$59$	0.965789	0.125735	0.0628675	+	0.998022i	$0.479975\pi$
$60$	−4.97035	−0.641669
$61$	−14.3800	−1.84117	−0.920583	−	0.390548i	$-0.872286\pi$
$61$	−14.3800	−1.84117	−0.920583	+	0.390548i	$0.872286\pi$
$62$	9.32348	1.18408
$63$	−15.2294	−1.91872
$64$	1.00000	0.125000
$65$	1.78543	0.221455
$66$	−4.12446	−0.507686
$67$	5.16658	0.631199	0.315599	−	0.948893i	$-0.397794\pi$
$67$	5.16658	0.631199	0.315599	+	0.948893i	$0.397794\pi$
$68$	7.21995	0.875547
$69$	−1.25830	−0.151482
$70$	8.24250	0.985168
$71$	9.73690	1.15556	0.577779	−	0.816194i	$-0.303920\pi$
$71$	9.73690	1.15556	0.577779	+	0.816194i	$0.303920\pi$
$72$	−3.58009	−0.421918
$73$	−0.507148	−0.0593571	−0.0296786	−	0.999559i	$-0.509448\pi$
$73$	−0.507148	−0.0593571	−0.0296786	+	0.999559i	$0.509448\pi$
$74$	4.99591	0.580763
$75$	3.19515	0.368944
$76$	−2.67019	−0.306292
$77$	6.83973	0.779460
$78$	2.36367	0.267633
$79$	−7.76563	−0.873701	−0.436851	−	0.899534i	$-0.643906\pi$
$79$	−7.76563	−0.873701	−0.436851	+	0.899534i	$0.643906\pi$
$80$	1.93763	0.216634
$81$	−6.92322	−0.769247
$82$	6.91979	0.764163
$83$	8.80351	0.966310	0.483155	−	0.875535i	$-0.339491\pi$
$83$	8.80351	0.966310	0.483155	+	0.875535i	$0.339491\pi$
$84$	10.9120	1.19060
$85$	13.9896	1.51738
$86$	4.79643	0.517212
$87$	−17.2712	−1.85167
$88$	1.60787	0.171399
$89$	−2.21832	−0.235142	−0.117571	−	0.993065i	$-0.537511\pi$
$89$	−2.21832	−0.235142	−0.117571	+	0.993065i	$0.537511\pi$
$90$	−6.93689	−0.731213
$91$	−3.91976	−0.410903
$92$	0.490534	0.0511417
$93$	23.9163	2.48001
$94$	−9.79727	−1.01051
$95$	−5.17385	−0.530826
$96$	2.56517	0.261806
$97$	−1.70082	−0.172692	−0.0863462	−	0.996265i	$-0.527519\pi$
$97$	−1.70082	−0.172692	−0.0863462	+	0.996265i	$0.527519\pi$
$98$	−11.0958	−1.12084
$99$	−5.75632	−0.578532
$100$	−1.24559	−0.124559
$101$	−4.68052	−0.465729	−0.232865	−	0.972509i	$-0.574810\pi$
$101$	−4.68052	−0.465729	−0.232865	+	0.972509i	$0.574810\pi$
$102$	18.5204	1.83379
$103$	6.18897	0.609817	0.304909	−	0.952382i	$-0.401374\pi$
$103$	6.18897	0.609817	0.304909	+	0.952382i	$0.401374\pi$
$104$	−0.921449	−0.0903555
$105$	21.1434	2.06339
$106$	1.18872	0.115459
$107$	−13.9722	−1.35075	−0.675374	−	0.737475i	$-0.736018\pi$
$107$	−13.9722	−1.35075	−0.675374	+	0.737475i	$0.736018\pi$
$108$	−1.48803	−0.143186
$109$	19.4810	1.86595	0.932973	−	0.359946i	$-0.117205\pi$
$109$	19.4810	1.86595	0.932973	+	0.359946i	$0.117205\pi$
$110$	3.11546	0.297047
$111$	12.8153	1.21638
$112$	−4.25391	−0.401957
$113$	−2.32364	−0.218590	−0.109295	−	0.994009i	$-0.534859\pi$
$113$	−2.32364	−0.218590	−0.109295	+	0.994009i	$0.534859\pi$
$114$	−6.84950	−0.641514
$115$	0.950473	0.0886321
$116$	6.73297	0.625141
$117$	3.29887	0.304981
$118$	−0.965789	−0.0889080
$119$	−30.7130	−2.81546
$120$	4.97035	0.453729
$121$	−8.41476	−0.764978
$122$	14.3800	1.30190
$123$	17.7504	1.60050
$124$	−9.32348	−0.837274
$125$	−12.1016	−1.08240
$126$	15.2294	1.35674
$127$	−19.3081	−1.71332	−0.856660	−	0.515882i	$-0.827464\pi$
$127$	−19.3081	−1.71332	−0.856660	+	0.515882i	$0.827464\pi$
$128$	−1.00000	−0.0883883
$129$	12.3037	1.08328
$130$	−1.78543	−0.156592
$131$	−7.10981	−0.621187	−0.310593	−	0.950543i	$-0.600528\pi$
$131$	−7.10981	−0.621187	−0.310593	+	0.950543i	$0.600528\pi$
$132$	4.12446	0.358988
$133$	11.3588	0.984930
$134$	−5.16658	−0.446325
$135$	−2.88325	−0.248151
$136$	−7.21995	−0.619105
$137$	18.3315	1.56616	0.783082	−	0.621919i	$-0.213647\pi$
$137$	18.3315	1.56616	0.783082	+	0.621919i	$0.213647\pi$
$138$	1.25830	0.107114
$139$	13.5780	1.15167	0.575837	−	0.817564i	$-0.304676\pi$
$139$	13.5780	1.15167	0.575837	+	0.817564i	$0.304676\pi$
$140$	−8.24250	−0.696619
$141$	−25.1317	−2.11647
$142$	−9.73690	−0.817102
$143$	−1.48157	−0.123895
$144$	3.58009	0.298341
$145$	13.0460	1.08341
$146$	0.507148	0.0419718
$147$	−28.4625	−2.34755
$148$	−4.99591	−0.410661
$149$	13.4878	1.10496	0.552481	−	0.833525i	$-0.313681\pi$
$149$	13.4878	1.10496	0.552481	+	0.833525i	$0.313681\pi$
$150$	−3.19515	−0.260883
$151$	−6.67937	−0.543559	−0.271780	−	0.962360i	$-0.587612\pi$
$151$	−6.67937	−0.543559	−0.271780	+	0.962360i	$0.587612\pi$
$152$	2.67019	0.216581
$153$	25.8481	2.08969
$154$	−6.83973	−0.551161
$155$	−18.0655	−1.45105
$156$	−2.36367	−0.189245
$157$	5.43243	0.433555	0.216778	−	0.976221i	$-0.430445\pi$
$157$	5.43243	0.433555	0.216778	+	0.976221i	$0.430445\pi$
$158$	7.76563	0.617800
$159$	3.04928	0.241823
$160$	−1.93763	−0.153183
$161$	−2.08669	−0.164454
$162$	6.92322	0.543940
$163$	0.788543	0.0617634	0.0308817	−	0.999523i	$-0.490168\pi$
$163$	0.788543	0.0617634	0.0308817	+	0.999523i	$0.490168\pi$
$164$	−6.91979	−0.540345
$165$	7.99167	0.622151
$166$	−8.80351	−0.683285
$167$	5.55098	0.429547	0.214774	−	0.976664i	$-0.431099\pi$
$167$	5.55098	0.429547	0.214774	+	0.976664i	$0.431099\pi$
$168$	−10.9120	−0.841879
$169$	−12.1509	−0.934687
$170$	−13.9896	−1.07295
$171$	−9.55954	−0.731036
$172$	−4.79643	−0.365724
$173$	1.24445	0.0946135	0.0473068	−	0.998880i	$-0.484936\pi$
$173$	1.24445	0.0946135	0.0473068	+	0.998880i	$0.484936\pi$
$174$	17.2712	1.30933
$175$	5.29863	0.400539
$176$	−1.60787	−0.121198
$177$	−2.47741	−0.186214
$178$	2.21832	0.166270
$179$	−18.9407	−1.41569	−0.707846	−	0.706367i	$-0.750333\pi$
$179$	−18.9407	−1.41569	−0.707846	+	0.706367i	$0.750333\pi$
$180$	6.93689	0.517045
$181$	−16.3989	−1.21892	−0.609459	−	0.792818i	$-0.708613\pi$
$181$	−16.3989	−1.21892	−0.609459	+	0.792818i	$0.708613\pi$
$182$	3.91976	0.290552
$183$	36.8870	2.72677
$184$	−0.490534	−0.0361626
$185$	−9.68022	−0.711704
$186$	−23.9163	−1.75363
$187$	−11.6087	−0.848915
$188$	9.79727	0.714539
$189$	6.32995	0.460436
$190$	5.17385	0.375350
$191$	7.64872	0.553442	0.276721	−	0.960950i	$-0.410752\pi$
$191$	7.64872	0.553442	0.276721	+	0.960950i	$0.410752\pi$
$192$	−2.56517	−0.185125
$193$	3.79642	0.273272	0.136636	−	0.990621i	$-0.456371\pi$
$193$	3.79642	0.273272	0.136636	+	0.990621i	$0.456371\pi$
$194$	1.70082	0.122112
$195$	−4.57992	−0.327975
$196$	11.0958	0.792554
$197$	8.49181	0.605016	0.302508	−	0.953147i	$-0.402176\pi$
$197$	8.49181	0.605016	0.302508	+	0.953147i	$0.402176\pi$
$198$	5.75632	0.409084
$199$	2.65040	0.187882	0.0939410	−	0.995578i	$-0.470053\pi$
$199$	2.65040	0.187882	0.0939410	+	0.995578i	$0.470053\pi$
$200$	1.24559	0.0880765
$201$	−13.2532	−0.934806
$202$	4.68052	0.329320
$203$	−28.6415	−2.01024
$204$	−18.5204	−1.29669
$205$	−13.4080	−0.936455
$206$	−6.18897	−0.431206
$207$	1.75616	0.122061
$208$	0.921449	0.0638910
$209$	4.29332	0.296975
$210$	−21.1434	−1.45903
$211$	25.2776	1.74018	0.870092	−	0.492889i	$-0.164059\pi$
$211$	25.2776	1.74018	0.870092	+	0.492889i	$0.164059\pi$
$212$	−1.18872	−0.0816419
$213$	−24.9768	−1.71138
$214$	13.9722	0.955123
$215$	−9.29370	−0.633825
$216$	1.48803	0.101248
$217$	39.6613	2.69238
$218$	−19.4810	−1.31942
$219$	1.30092	0.0879080
$220$	−3.11546	−0.210044
$221$	6.65281	0.447517
$222$	−12.8153	−0.860110
$223$	14.2056	0.951275	0.475638	−	0.879641i	$-0.342217\pi$
$223$	14.2056	0.951275	0.475638	+	0.879641i	$0.342217\pi$
$224$	4.25391	0.284226
$225$	−4.45933	−0.297288
$226$	2.32364	0.154566
$227$	18.4125	1.22208	0.611040	−	0.791599i	$-0.290751\pi$
$227$	18.4125	1.22208	0.611040	+	0.791599i	$0.290751\pi$
$228$	6.84950	0.453619
$229$	−23.7197	−1.56744	−0.783722	−	0.621112i	$-0.786681\pi$
$229$	−23.7197	−1.56744	−0.783722	+	0.621112i	$0.786681\pi$
$230$	−0.950473	−0.0626723
$231$	−17.5451	−1.15438
$232$	−6.73297	−0.442041
$233$	10.9070	0.714543	0.357271	−	0.934001i	$-0.383707\pi$
$233$	10.9070	0.714543	0.357271	+	0.934001i	$0.383707\pi$
$234$	−3.29887	−0.215654
$235$	18.9835	1.23835
$236$	0.965789	0.0628675
$237$	19.9201	1.29395
$238$	30.7130	1.99083
$239$	29.5525	1.91159	0.955796	−	0.294030i	$-0.0949967\pi$
$239$	29.5525	1.91159	0.955796	+	0.294030i	$0.0949967\pi$
$240$	−4.97035	−0.320835
$241$	16.7861	1.08129	0.540644	−	0.841252i	$-0.318181\pi$
$241$	16.7861	1.08129	0.540644	+	0.841252i	$0.318181\pi$
$242$	8.41476	0.540921
$243$	22.2233	1.42563
$244$	−14.3800	−0.920583
$245$	21.4995	1.37355
$246$	−17.7504	−1.13173
$247$	−2.46045	−0.156555
$248$	9.32348	0.592042
$249$	−22.5825	−1.43111
$250$	12.1016	0.765375
$251$	7.87366	0.496981	0.248491	−	0.968634i	$-0.420065\pi$
$251$	7.87366	0.496981	0.248491	+	0.968634i	$0.420065\pi$
$252$	−15.2294	−0.959361
$253$	−0.788714	−0.0495861
$254$	19.3081	1.21150
$255$	−35.8856	−2.24725
$256$	1.00000	0.0625000
$257$	11.8102	0.736697	0.368349	−	0.929688i	$-0.379923\pi$
$257$	11.8102	0.736697	0.368349	+	0.929688i	$0.379923\pi$
$258$	−12.3037	−0.765992
$259$	21.2521	1.32054
$260$	1.78543	0.110727
$261$	24.1047	1.49204
$262$	7.10981	0.439246
$263$	15.0981	0.930987	0.465494	−	0.885051i	$-0.345877\pi$
$263$	15.0981	0.930987	0.465494	+	0.885051i	$0.345877\pi$
$264$	−4.12446	−0.253843
$265$	−2.30331	−0.141491
$266$	−11.3588	−0.696451
$267$	5.69037	0.348245
$268$	5.16658	0.315599
$269$	14.7007	0.896316	0.448158	−	0.893954i	$-0.352080\pi$
$269$	14.7007	0.896316	0.448158	+	0.893954i	$0.352080\pi$
$270$	2.88325	0.175469
$271$	−10.6157	−0.644857	−0.322429	−	0.946594i	$-0.604499\pi$
$271$	−10.6157	−0.644857	−0.322429	+	0.946594i	$0.604499\pi$
$272$	7.21995	0.437774
$273$	10.0548	0.608547
$274$	−18.3315	−1.10745
$275$	2.00275	0.120770
$276$	−1.25830	−0.0757409
$277$	−11.0921	−0.666462	−0.333231	−	0.942845i	$-0.608139\pi$
$277$	−11.0921	−0.666462	−0.333231	+	0.942845i	$0.608139\pi$
$278$	−13.5780	−0.814357
$279$	−33.3789	−1.99834
$280$	8.24250	0.492584
$281$	−16.7397	−0.998604	−0.499302	−	0.866428i	$-0.666410\pi$
$281$	−16.7397	−0.998604	−0.499302	+	0.866428i	$0.666410\pi$
$282$	25.1317	1.49657
$283$	31.0731	1.84711	0.923553	−	0.383471i	$-0.125271\pi$
$283$	31.0731	1.84711	0.923553	+	0.383471i	$0.125271\pi$
$284$	9.73690	0.577779
$285$	13.2718	0.786153
$286$	1.48157	0.0876071
$287$	29.4362	1.73756
$288$	−3.58009	−0.210959
$289$	35.1276	2.06633
$290$	−13.0460	−0.766088
$291$	4.36290	0.255758
$292$	−0.507148	−0.0296786
$293$	−22.1638	−1.29482	−0.647411	−	0.762141i	$-0.724148\pi$
$293$	−22.1638	−1.29482	−0.647411	+	0.762141i	$0.724148\pi$
$294$	28.4625	1.65997
$295$	1.87134	0.108954
$296$	4.99591	0.290381
$297$	2.39256	0.138830
$298$	−13.4878	−0.781326
$299$	0.452002	0.0261399
$300$	3.19515	0.184472
$301$	20.4036	1.17604
$302$	6.67937	0.384354
$303$	12.0063	0.689746
$304$	−2.67019	−0.153146
$305$	−27.8630	−1.59543
$306$	−25.8481	−1.47764
$307$	0.572692	0.0326852	0.0163426	−	0.999866i	$-0.494798\pi$
$307$	0.572692	0.0326852	0.0163426	+	0.999866i	$0.494798\pi$
$308$	6.83973	0.389730
$309$	−15.8758	−0.903140
$310$	18.0655	1.02605
$311$	29.2722	1.65988	0.829938	−	0.557856i	$-0.188376\pi$
$311$	29.2722	1.65988	0.829938	+	0.557856i	$0.188376\pi$
$312$	2.36367	0.133817
$313$	19.9954	1.13021	0.565104	−	0.825020i	$-0.308836\pi$
$313$	19.9954	1.13021	0.565104	+	0.825020i	$0.308836\pi$
$314$	−5.43243	−0.306570
$315$	−29.5089	−1.66264
$316$	−7.76563	−0.436851
$317$	33.8042	1.89863	0.949317	−	0.314322i	$-0.101777\pi$
$317$	33.8042	1.89863	0.949317	+	0.314322i	$0.101777\pi$
$318$	−3.04928	−0.170995
$319$	−10.8257	−0.606125
$320$	1.93763	0.108317
$321$	35.8412	2.00046
$322$	2.08669	0.116287
$323$	−19.2787	−1.07269
$324$	−6.92322	−0.384623
$325$	−1.14775	−0.0636656
$326$	−0.788543	−0.0436733
$327$	−49.9722	−2.76347
$328$	6.91979	0.382082
$329$	−41.6767	−2.29771
$330$	−7.99167	−0.439927
$331$	−10.9843	−0.603753	−0.301877	−	0.953347i	$-0.597613\pi$
$331$	−10.9843	−0.603753	−0.301877	+	0.953347i	$0.597613\pi$
$332$	8.80351	0.483155
$333$	−17.8858	−0.980136
$334$	−5.55098	−0.303736
$335$	10.0109	0.546955
$336$	10.9120	0.595298
$337$	−26.5134	−1.44428	−0.722139	−	0.691748i	$-0.756841\pi$
$337$	−26.5134	−1.44428	−0.722139	+	0.691748i	$0.756841\pi$
$338$	12.1509	0.660924
$339$	5.96053	0.323732
$340$	13.9896	0.758692
$341$	14.9909	0.811805
$342$	9.55954	0.516921
$343$	−17.4230	−0.940751
$344$	4.79643	0.258606
$345$	−2.43812	−0.131264
$346$	−1.24445	−0.0669019
$347$	18.7792	1.00812	0.504060	−	0.863669i	$-0.331839\pi$
$347$	18.7792	1.00812	0.504060	+	0.863669i	$0.331839\pi$
$348$	−17.2712	−0.925834
$349$	−15.8952	−0.850848	−0.425424	−	0.904994i	$-0.639875\pi$
$349$	−15.8952	−0.850848	−0.425424	+	0.904994i	$0.639875\pi$
$350$	−5.29863	−0.283224
$351$	−1.37115	−0.0731863
$352$	1.60787	0.0856997
$353$	−7.63278	−0.406252	−0.203126	−	0.979153i	$-0.565110\pi$
$353$	−7.63278	−0.406252	−0.203126	+	0.979153i	$0.565110\pi$
$354$	2.47741	0.131673
$355$	18.8665	1.00133
$356$	−2.21832	−0.117571
$357$	78.7840	4.16969
$358$	18.9407	1.00105
$359$	−18.3617	−0.969093	−0.484547	−	0.874765i	$-0.661015\pi$
$359$	−18.3617	−0.969093	−0.484547	+	0.874765i	$0.661015\pi$
$360$	−6.93689	−0.365606
$361$	−11.8701	−0.624740
$362$	16.3989	0.861905
$363$	21.5853	1.13293
$364$	−3.91976	−0.205451
$365$	−0.982664	−0.0514350
$366$	−36.8870	−1.92812
$367$	−4.18562	−0.218487	−0.109244	−	0.994015i	$-0.534843\pi$
$367$	−4.18562	−0.218487	−0.109244	+	0.994015i	$0.534843\pi$
$368$	0.490534	0.0255708
$369$	−24.7735	−1.28966
$370$	9.68022	0.503251
$371$	5.05672	0.262532
$372$	23.9163	1.24000
$373$	−0.534949	−0.0276986	−0.0138493	−	0.999904i	$-0.504409\pi$
$373$	−0.534949	−0.0276986	−0.0138493	+	0.999904i	$0.504409\pi$
$374$	11.6087	0.600273
$375$	31.0428	1.60304
$376$	−9.79727	−0.505256
$377$	6.20409	0.319527
$378$	−6.32995	−0.325578
$379$	27.9110	1.43369	0.716845	−	0.697232i	$-0.245585\pi$
$379$	27.9110	1.43369	0.716845	+	0.697232i	$0.245585\pi$
$380$	−5.17385	−0.265413
$381$	49.5286	2.53743
$382$	−7.64872	−0.391343
$383$	18.1022	0.924979	0.462490	−	0.886625i	$-0.346956\pi$
$383$	18.1022	0.924979	0.462490	+	0.886625i	$0.346956\pi$
$384$	2.56517	0.130903
$385$	13.2529	0.675429
$386$	−3.79642	−0.193233
$387$	−17.1717	−0.872884
$388$	−1.70082	−0.0863462
$389$	32.3945	1.64247	0.821233	−	0.570593i	$-0.193287\pi$
$389$	32.3945	1.64247	0.821233	+	0.570593i	$0.193287\pi$
$390$	4.57992	0.231913
$391$	3.54163	0.179108
$392$	−11.0958	−0.560420
$393$	18.2379	0.919978
$394$	−8.49181	−0.427811
$395$	−15.0469	−0.757092
$396$	−5.75632	−0.289266
$397$	32.6339	1.63785	0.818925	−	0.573901i	$-0.194570\pi$
$397$	32.6339	1.63785	0.818925	+	0.573901i	$0.194570\pi$
$398$	−2.65040	−0.132853
$399$	−29.1372	−1.45868
$400$	−1.24559	−0.0622795
$401$	27.9538	1.39595	0.697973	−	0.716124i	$-0.254085\pi$
$401$	27.9538	1.39595	0.697973	+	0.716124i	$0.254085\pi$
$402$	13.2532	0.661007
$403$	−8.59111	−0.427954
$404$	−4.68052	−0.232865
$405$	−13.4146	−0.666579
$406$	28.6415	1.42145
$407$	8.03277	0.398170
$408$	18.5204	0.916896
$409$	−17.2373	−0.852327	−0.426164	−	0.904646i	$-0.640135\pi$
$409$	−17.2373	−0.852327	−0.426164	+	0.904646i	$0.640135\pi$
$410$	13.4080	0.662174
$411$	−47.0233	−2.31949
$412$	6.18897	0.304909
$413$	−4.10838	−0.202160
$414$	−1.75616	−0.0863104
$415$	17.0579	0.837341
$416$	−0.921449	−0.0451777
$417$	−34.8300	−1.70563
$418$	−4.29332	−0.209993
$419$	−4.00613	−0.195712	−0.0978562	−	0.995201i	$-0.531199\pi$
$419$	−4.00613	−0.195712	−0.0978562	+	0.995201i	$0.531199\pi$
$420$	21.1434	1.03169
$421$	−18.5298	−0.903088	−0.451544	−	0.892249i	$-0.649127\pi$
$421$	−18.5298	−0.903088	−0.451544	+	0.892249i	$0.649127\pi$
$422$	−25.2776	−1.23050
$423$	35.0751	1.70541
$424$	1.18872	0.0577295
$425$	−8.99310	−0.436229
$426$	24.9768	1.21013
$427$	61.1711	2.96028
$428$	−13.9722	−0.675374
$429$	3.80048	0.183489
$430$	9.29370	0.448182
$431$	4.22383	0.203455	0.101727	−	0.994812i	$-0.467563\pi$
$431$	4.22383	0.203455	0.101727	+	0.994812i	$0.467563\pi$
$432$	−1.48803	−0.0715930
$433$	5.07151	0.243721	0.121861	−	0.992547i	$-0.461114\pi$
$433$	5.07151	0.243721	0.121861	+	0.992547i	$0.461114\pi$
$434$	−39.6613	−1.90380
$435$	−33.4652	−1.60453
$436$	19.4810	0.932973
$437$	−1.30982	−0.0626572
$438$	−1.30092	−0.0621603
$439$	11.6302	0.555080	0.277540	−	0.960714i	$-0.410481\pi$
$439$	11.6302	0.555080	0.277540	+	0.960714i	$0.410481\pi$
$440$	3.11546	0.148524
$441$	39.7238	1.89161
$442$	−6.65281	−0.316442
$443$	−17.9955	−0.854990	−0.427495	−	0.904018i	$-0.640604\pi$
$443$	−17.9955	−0.854990	−0.427495	+	0.904018i	$0.640604\pi$
$444$	12.8153	0.608190
$445$	−4.29829	−0.203758
$446$	−14.2056	−0.672653
$447$	−34.5984	−1.63645
$448$	−4.25391	−0.200978
$449$	−3.14783	−0.148555	−0.0742777	−	0.997238i	$-0.523665\pi$
$449$	−3.14783	−0.148555	−0.0742777	+	0.997238i	$0.523665\pi$
$450$	4.45933	0.210215
$451$	11.1261	0.523909
$452$	−2.32364	−0.109295
$453$	17.1337	0.805011
$454$	−18.4125	−0.864142
$455$	−7.59505	−0.356061
$456$	−6.84950	−0.320757
$457$	16.3646	0.765504	0.382752	−	0.923851i	$-0.374976\pi$
$457$	16.3646	0.765504	0.382752	+	0.923851i	$0.374976\pi$
$458$	23.7197	1.10835
$459$	−10.7435	−0.501464
$460$	0.950473	0.0443160
$461$	−16.4219	−0.764844	−0.382422	−	0.923988i	$-0.624910\pi$
$461$	−16.4219	−0.764844	−0.382422	+	0.923988i	$0.624910\pi$
$462$	17.5451	0.816271
$463$	23.2373	1.07993	0.539965	−	0.841688i	$-0.318438\pi$
$463$	23.2373	1.07993	0.539965	+	0.841688i	$0.318438\pi$
$464$	6.73297	0.312570
$465$	46.3410	2.14901
$466$	−10.9070	−0.505258
$467$	−6.80259	−0.314786	−0.157393	−	0.987536i	$-0.550309\pi$
$467$	−6.80259	−0.314786	−0.157393	+	0.987536i	$0.550309\pi$
$468$	3.29887	0.152490
$469$	−21.9782	−1.01486
$470$	−18.9835	−0.875643
$471$	−13.9351	−0.642096
$472$	−0.965789	−0.0444540
$473$	7.71203	0.354600
$474$	−19.9201	−0.914963
$475$	3.32597	0.152606
$476$	−30.7130	−1.40773
$477$	−4.25574	−0.194857
$478$	−29.5525	−1.35170
$479$	11.8330	0.540661	0.270331	−	0.962768i	$-0.412867\pi$
$479$	11.8330	0.540661	0.270331	+	0.962768i	$0.412867\pi$
$480$	4.97035	0.226864
$481$	−4.60347	−0.209900
$482$	−16.7861	−0.764586
$483$	5.35270	0.243556
$484$	−8.41476	−0.382489
$485$	−3.29556	−0.149644
$486$	−22.2233	−1.00807
$487$	29.5293	1.33810	0.669050	−	0.743217i	$-0.266701\pi$
$487$	29.5293	1.33810	0.669050	+	0.743217i	$0.266701\pi$
$488$	14.3800	0.650950
$489$	−2.02275	−0.0914717
$490$	−21.4995	−0.971247
$491$	19.5477	0.882177	0.441089	−	0.897464i	$-0.354592\pi$
$491$	19.5477	0.882177	0.441089	+	0.897464i	$0.354592\pi$
$492$	17.7504	0.800251
$493$	48.6117	2.18936
$494$	2.46045	0.110701
$495$	−11.1536	−0.501318
$496$	−9.32348	−0.418637
$497$	−41.4199	−1.85794
$498$	22.5825	1.01195
$499$	18.2240	0.815820	0.407910	−	0.913022i	$-0.366258\pi$
$499$	18.2240	0.815820	0.407910	+	0.913022i	$0.366258\pi$
$500$	−12.1016	−0.541202
$501$	−14.2392	−0.636160
$502$	−7.87366	−0.351419
$503$	−22.3377	−0.995988	−0.497994	−	0.867180i	$-0.665930\pi$
$503$	−22.3377	−0.995988	−0.497994	+	0.867180i	$0.665930\pi$
$504$	15.2294	0.678371
$505$	−9.06912	−0.403571
$506$	0.788714	0.0350626
$507$	31.1692	1.38427
$508$	−19.3081	−0.856660
$509$	−15.9706	−0.707885	−0.353943	−	0.935267i	$-0.615159\pi$
$509$	−15.9706	−0.707885	−0.353943	+	0.935267i	$0.615159\pi$
$510$	35.8856	1.58904
$511$	2.15736	0.0954360
$512$	−1.00000	−0.0441942
$513$	3.97333	0.175427
$514$	−11.8102	−0.520924
$515$	11.9919	0.528428
$516$	12.3037	0.541638
$517$	−15.7527	−0.692804
$518$	−21.2521	−0.933766
$519$	−3.19222	−0.140123
$520$	−1.78543	−0.0782961
$521$	32.5780	1.42727	0.713634	−	0.700519i	$-0.247048\pi$
$521$	32.5780	1.42727	0.713634	+	0.700519i	$0.247048\pi$
$522$	−24.1047	−1.05503
$523$	23.9741	1.04831	0.524157	−	0.851622i	$-0.324380\pi$
$523$	23.9741	1.04831	0.524157	+	0.851622i	$0.324380\pi$
$524$	−7.10981	−0.310593
$525$	−13.5919	−0.593198
$526$	−15.0981	−0.658308
$527$	−67.3151	−2.93229
$528$	4.12446	0.179494
$529$	−22.7594	−0.989538
$530$	2.30331	0.100049
$531$	3.45761	0.150048
$532$	11.3588	0.492465
$533$	−6.37624	−0.276185
$534$	−5.69037	−0.246246
$535$	−27.0730	−1.17047
$536$	−5.16658	−0.223162
$537$	48.5860	2.09664
$538$	−14.7007	−0.633791
$539$	−17.8405	−0.768446
$540$	−2.88325	−0.124076
$541$	20.8007	0.894291	0.447145	−	0.894461i	$-0.352441\pi$
$541$	20.8007	0.894291	0.447145	+	0.894461i	$0.352441\pi$
$542$	10.6157	0.455983
$543$	42.0658	1.80522
$544$	−7.21995	−0.309553
$545$	37.7471	1.61691
$546$	−10.0548	−0.430308
$547$	−15.4228	−0.659433	−0.329716	−	0.944080i	$-0.606953\pi$
$547$	−15.4228	−0.659433	−0.329716	+	0.944080i	$0.606953\pi$
$548$	18.3315	0.783082
$549$	−51.4816	−2.19718
$550$	−2.00275	−0.0853974
$551$	−17.9783	−0.765903
$552$	1.25830	0.0535569
$553$	33.0343	1.40476
$554$	11.0921	0.471260
$555$	24.8314	1.05403
$556$	13.5780	0.575837
$557$	38.9720	1.65130	0.825648	−	0.564186i	$-0.190810\pi$
$557$	38.9720	1.65130	0.825648	+	0.564186i	$0.190810\pi$
$558$	33.3789	1.41304
$559$	−4.41966	−0.186932
$560$	−8.24250	−0.348309
$561$	29.7784	1.25724
$562$	16.7397	0.706120
$563$	4.11999	0.173637	0.0868184	−	0.996224i	$-0.472330\pi$
$563$	4.11999	0.173637	0.0868184	+	0.996224i	$0.472330\pi$
$564$	−25.1317	−1.05823
$565$	−4.50236	−0.189415
$566$	−31.0731	−1.30610
$567$	29.4508	1.23682
$568$	−9.73690	−0.408551
$569$	−13.5710	−0.568926	−0.284463	−	0.958687i	$-0.591815\pi$
$569$	−13.5710	−0.568926	−0.284463	+	0.958687i	$0.591815\pi$
$570$	−13.2718	−0.555894
$571$	32.2701	1.35046	0.675231	−	0.737606i	$-0.264044\pi$
$571$	32.2701	1.35046	0.675231	+	0.737606i	$0.264044\pi$
$572$	−1.48157	−0.0619475
$573$	−19.6203	−0.819648
$574$	−29.4362	−1.22864
$575$	−0.611004	−0.0254806
$576$	3.58009	0.149170
$577$	42.4253	1.76619	0.883094	−	0.469196i	$-0.155456\pi$
$577$	42.4253	1.76619	0.883094	+	0.469196i	$0.155456\pi$
$578$	−35.1276	−1.46112
$579$	−9.73846	−0.404717
$580$	13.0460	0.541706
$581$	−37.4493	−1.55366
$582$	−4.36290	−0.180848
$583$	1.91131	0.0791585
$584$	0.507148	0.0209859
$585$	6.39199	0.264276
$586$	22.1638	0.915578
$587$	−45.8918	−1.89416	−0.947078	−	0.321004i	$-0.895980\pi$
$587$	−45.8918	−1.89416	−0.947078	+	0.321004i	$0.895980\pi$
$588$	−28.4625	−1.17377
$589$	24.8955	1.02580
$590$	−1.87134	−0.0770419
$591$	−21.7829	−0.896029
$592$	−4.99591	−0.205331
$593$	−40.9534	−1.68176	−0.840878	−	0.541225i	$-0.817961\pi$
$593$	−40.9534	−1.68176	−0.840878	+	0.541225i	$0.817961\pi$
$594$	−2.39256	−0.0981680
$595$	−59.5104	−2.43969
$596$	13.4878	0.552481
$597$	−6.79873	−0.278254
$598$	−0.452002	−0.0184837
$599$	28.4167	1.16108	0.580538	−	0.814233i	$-0.302842\pi$
$599$	28.4167	1.16108	0.580538	+	0.814233i	$0.302842\pi$
$600$	−3.19515	−0.130441
$601$	−2.59379	−0.105803	−0.0529014	−	0.998600i	$-0.516847\pi$
$601$	−2.59379	−0.105803	−0.0529014	+	0.998600i	$0.516847\pi$
$602$	−20.4036	−0.831588
$603$	18.4968	0.753249
$604$	−6.67937	−0.271780
$605$	−16.3047	−0.662880
$606$	−12.0063	−0.487724
$607$	42.6617	1.73159	0.865793	−	0.500402i	$-0.166814\pi$
$607$	42.6617	1.73159	0.865793	+	0.500402i	$0.166814\pi$
$608$	2.67019	0.108291
$609$	73.4702	2.97716
$610$	27.8630	1.12814
$611$	9.02768	0.365221
$612$	25.8481	1.04485
$613$	13.5825	0.548590	0.274295	−	0.961646i	$-0.411556\pi$
$613$	13.5825	0.548590	0.274295	+	0.961646i	$0.411556\pi$
$614$	−0.572692	−0.0231120
$615$	34.3938	1.38689
$616$	−6.83973	−0.275581
$617$	17.4021	0.700584	0.350292	−	0.936641i	$-0.386082\pi$
$617$	17.4021	0.700584	0.350292	+	0.936641i	$0.386082\pi$
$618$	15.8758	0.638616
$619$	−30.6959	−1.23377	−0.616885	−	0.787053i	$-0.711606\pi$
$619$	−30.6959	−1.23377	−0.616885	+	0.787053i	$0.711606\pi$
$620$	−18.0655	−0.725526
$621$	−0.729930	−0.0292911
$622$	−29.2722	−1.17371
$623$	9.43654	0.378067
$624$	−2.36367	−0.0946226
$625$	−17.2206	−0.688822
$626$	−19.9954	−0.799177
$627$	−11.0131	−0.439821
$628$	5.43243	0.216778
$629$	−36.0702	−1.43821
$630$	29.5089	1.17566
$631$	8.86194	0.352788	0.176394	−	0.984320i	$-0.443557\pi$
$631$	8.86194	0.352788	0.176394	+	0.984320i	$0.443557\pi$
$632$	7.76563	0.308900
$633$	−64.8414	−2.57721
$634$	−33.8042	−1.34254
$635$	−37.4120	−1.48465
$636$	3.04928	0.120912
$637$	10.2242	0.405096
$638$	10.8257	0.428595
$639$	34.8590	1.37900
$640$	−1.93763	−0.0765915
$641$	10.3517	0.408867	0.204434	−	0.978880i	$-0.434465\pi$
$641$	10.3517	0.408867	0.204434	+	0.978880i	$0.434465\pi$
$642$	−35.8412	−1.41454
$643$	−35.6986	−1.40781	−0.703907	−	0.710292i	$-0.748563\pi$
$643$	−35.6986	−1.40781	−0.703907	+	0.710292i	$0.748563\pi$
$644$	−2.08669	−0.0822270
$645$	23.8399	0.938696
$646$	19.2787	0.758509
$647$	−38.4611	−1.51206	−0.756031	−	0.654536i	$-0.772864\pi$
$647$	−38.4611	−1.51206	−0.756031	+	0.654536i	$0.772864\pi$
$648$	6.92322	0.271970
$649$	−1.55286	−0.0609552
$650$	1.14775	0.0450184
$651$	−101.738	−3.98742
$652$	0.788543	0.0308817
$653$	−6.10098	−0.238750	−0.119375	−	0.992849i	$-0.538089\pi$
$653$	−6.10098	−0.238750	−0.119375	+	0.992849i	$0.538089\pi$
$654$	49.9722	1.95407
$655$	−13.7762	−0.538280
$656$	−6.91979	−0.270173
$657$	−1.81563	−0.0708347
$658$	41.6767	1.62473
$659$	−2.42799	−0.0945810	−0.0472905	−	0.998881i	$-0.515059\pi$
$659$	−2.42799	−0.0945810	−0.0472905	+	0.998881i	$0.515059\pi$
$660$	7.99167	0.311075
$661$	−8.04605	−0.312955	−0.156478	−	0.987682i	$-0.550014\pi$
$661$	−8.04605	−0.312955	−0.156478	+	0.987682i	$0.550014\pi$
$662$	10.9843	0.426918
$663$	−17.0656	−0.662772
$664$	−8.80351	−0.341642
$665$	22.0091	0.853476
$666$	17.8858	0.693061
$667$	3.30275	0.127883
$668$	5.55098	0.214774
$669$	−36.4397	−1.40884
$670$	−10.0109	−0.386756
$671$	23.1211	0.892580
$672$	−10.9120	−0.420939
$673$	−28.2443	−1.08874	−0.544369	−	0.838846i	$-0.683231\pi$
$673$	−28.2443	−1.08874	−0.544369	+	0.838846i	$0.683231\pi$
$674$	26.5134	1.02126
$675$	1.85348	0.0713404
$676$	−12.1509	−0.467344
$677$	12.1752	0.467932	0.233966	−	0.972245i	$-0.424830\pi$
$677$	12.1752	0.467932	0.233966	+	0.972245i	$0.424830\pi$
$678$	−5.96053	−0.228913
$679$	7.23515	0.277659
$680$	−13.9896	−0.536476
$681$	−47.2312	−1.80990
$682$	−14.9909	−0.574033
$683$	8.07324	0.308914	0.154457	−	0.988000i	$-0.450637\pi$
$683$	8.07324	0.308914	0.154457	+	0.988000i	$0.450637\pi$
$684$	−9.55954	−0.365518
$685$	35.5196	1.35713
$686$	17.4230	0.665212
$687$	60.8451	2.32138
$688$	−4.79643	−0.182862
$689$	−1.09535	−0.0417294
$690$	2.43812	0.0928178
$691$	−3.27745	−0.124680	−0.0623400	−	0.998055i	$-0.519856\pi$
$691$	−3.27745	−0.124680	−0.0623400	+	0.998055i	$0.519856\pi$
$692$	1.24445	0.0473068
$693$	24.4869	0.930179
$694$	−18.7792	−0.712848
$695$	26.3092	0.997965
$696$	17.2712	0.654664
$697$	−49.9605	−1.89239
$698$	15.8952	0.601640
$699$	−27.9784	−1.05824
$700$	5.29863	0.200269
$701$	14.3865	0.543369	0.271685	−	0.962386i	$-0.412419\pi$
$701$	14.3865	0.543369	0.271685	+	0.962386i	$0.412419\pi$
$702$	1.37115	0.0517505
$703$	13.3400	0.503129
$704$	−1.60787	−0.0605989
$705$	−48.6958	−1.83399
$706$	7.63278	0.287263
$707$	19.9105	0.748812
$708$	−2.47741	−0.0931068
$709$	−2.62265	−0.0984958	−0.0492479	−	0.998787i	$-0.515682\pi$
$709$	−2.62265	−0.0984958	−0.0492479	+	0.998787i	$0.515682\pi$
$710$	−18.8665	−0.708047
$711$	−27.8017	−1.04264
$712$	2.21832	0.0831351
$713$	−4.57348	−0.171278
$714$	−78.7840	−2.94842
$715$	−2.87073	−0.107359
$716$	−18.9407	−0.707846
$717$	−75.8071	−2.83107
$718$	18.3617	0.685252
$719$	17.9898	0.670908	0.335454	−	0.942057i	$-0.391110\pi$
$719$	17.9898	0.670908	0.335454	+	0.942057i	$0.391110\pi$
$720$	6.93689	0.258523
$721$	−26.3273	−0.980481
$722$	11.8701	0.441758
$723$	−43.0592	−1.60139
$724$	−16.3989	−0.609459
$725$	−8.38653	−0.311468
$726$	−21.5853	−0.801104
$727$	−30.6672	−1.13738	−0.568692	−	0.822550i	$-0.692551\pi$
$727$	−30.6672	−1.13738	−0.568692	+	0.822550i	$0.692551\pi$
$728$	3.91976	0.145276
$729$	−36.2369	−1.34211
$730$	0.982664	0.0363700
$731$	−34.6300	−1.28084
$732$	36.8870	1.36338
$733$	35.4464	1.30924	0.654621	−	0.755958i	$-0.272828\pi$
$733$	35.4464	1.30924	0.654621	+	0.755958i	$0.272828\pi$
$734$	4.18562	0.154494
$735$	−55.1497	−2.03423
$736$	−0.490534	−0.0180813
$737$	−8.30719	−0.305999
$738$	24.7735	0.911925
$739$	−47.1703	−1.73519	−0.867594	−	0.497273i	$-0.834335\pi$
$739$	−47.1703	−1.73519	−0.867594	+	0.497273i	$0.834335\pi$
$740$	−9.68022	−0.355852
$741$	6.31146	0.231857
$742$	−5.05672	−0.185638
$743$	42.1826	1.54753	0.773764	−	0.633474i	$-0.218372\pi$
$743$	42.1826	1.54753	0.773764	+	0.633474i	$0.218372\pi$
$744$	−23.9163	−0.876815
$745$	26.1343	0.957488
$746$	0.534949	0.0195859
$747$	31.5174	1.15316
$748$	−11.6087	−0.424457
$749$	59.4367	2.17177
$750$	−31.0428	−1.13352
$751$	−37.2317	−1.35860	−0.679302	−	0.733859i	$-0.737717\pi$
$751$	−37.2317	−1.35860	−0.679302	+	0.733859i	$0.737717\pi$
$752$	9.79727	0.357270
$753$	−20.1973	−0.736030
$754$	−6.20409	−0.225940
$755$	−12.9421	−0.471013
$756$	6.32995	0.230218
$757$	−4.69849	−0.170769	−0.0853847	−	0.996348i	$-0.527212\pi$
$757$	−4.69849	−0.170769	−0.0853847	+	0.996348i	$0.527212\pi$
$758$	−27.9110	−1.01377
$759$	2.02319	0.0734370
$760$	5.17385	0.187675
$761$	−17.4396	−0.632186	−0.316093	−	0.948728i	$-0.602371\pi$
$761$	−17.4396	−0.632186	−0.316093	+	0.948728i	$0.602371\pi$
$762$	−49.5286	−1.79423
$763$	−82.8706	−3.00012
$764$	7.64872	0.276721
$765$	50.0840	1.81079
$766$	−18.1022	−0.654059
$767$	0.889925	0.0321333
$768$	−2.56517	−0.0925626
$769$	23.7892	0.857861	0.428931	−	0.903337i	$-0.358890\pi$
$769$	23.7892	0.857861	0.428931	+	0.903337i	$0.358890\pi$
$770$	−13.2529	−0.477600
$771$	−30.2951	−1.09105
$772$	3.79642	0.136636
$773$	−23.7963	−0.855893	−0.427947	−	0.903804i	$-0.640763\pi$
$773$	−23.7963	−0.855893	−0.427947	+	0.903804i	$0.640763\pi$
$774$	17.1717	0.617222
$775$	11.6132	0.417160
$776$	1.70082	0.0610560
$777$	−54.5153	−1.95573
$778$	−32.3945	−1.16140
$779$	18.4772	0.662014
$780$	−4.57992	−0.163987
$781$	−15.6557	−0.560204
$782$	−3.54163	−0.126648
$783$	−10.0189	−0.358045
$784$	11.0958	0.396277
$785$	10.5260	0.375690
$786$	−18.2379	−0.650523
$787$	50.3266	1.79395	0.896975	−	0.442081i	$-0.145760\pi$
$787$	50.3266	1.79395	0.896975	+	0.442081i	$0.145760\pi$
$788$	8.49181	0.302508
$789$	−38.7291	−1.37879
$790$	15.0469	0.535345
$791$	9.88456	0.351454
$792$	5.75632	0.204542
$793$	−13.2504	−0.470535
$794$	−32.6339	−1.15813
$795$	5.90837	0.209548
$796$	2.65040	0.0939410
$797$	−32.1205	−1.13777	−0.568883	−	0.822419i	$-0.692624\pi$
$797$	−32.1205	−1.13777	−0.568883	+	0.822419i	$0.692624\pi$
$798$	29.1372	1.03144
$799$	70.7358	2.50245
$800$	1.24559	0.0440383
$801$	−7.94179	−0.280609
$802$	−27.9538	−0.987083
$803$	0.815427	0.0287758
$804$	−13.2532	−0.467403
$805$	−4.04323	−0.142505
$806$	8.59111	0.302609
$807$	−37.7097	−1.32744
$808$	4.68052	0.164660
$809$	3.40432	0.119690	0.0598448	−	0.998208i	$-0.480939\pi$
$809$	3.40432	0.119690	0.0598448	+	0.998208i	$0.480939\pi$
$810$	13.4146	0.471342
$811$	−21.1630	−0.743133	−0.371567	−	0.928406i	$-0.621179\pi$
$811$	−21.1630	−0.743133	−0.371567	+	0.928406i	$0.621179\pi$
$812$	−28.6415	−1.00512
$813$	27.2310	0.955034
$814$	−8.03277	−0.281548
$815$	1.52790	0.0535201
$816$	−18.5204	−0.648343
$817$	12.8074	0.448074
$818$	17.2373	0.602686
$819$	−14.0331	−0.490356
$820$	−13.4080	−0.468228
$821$	−48.8874	−1.70618	−0.853090	−	0.521763i	$-0.825275\pi$
$821$	−48.8874	−1.70618	−0.853090	+	0.521763i	$0.825275\pi$
$822$	47.0233	1.64013
$823$	−27.1691	−0.947054	−0.473527	−	0.880779i	$-0.657019\pi$
$823$	−27.1691	−0.947054	−0.473527	+	0.880779i	$0.657019\pi$
$824$	−6.18897	−0.215603
$825$	−5.13738	−0.178861
$826$	4.10838	0.142949
$827$	19.7918	0.688230	0.344115	−	0.938928i	$-0.388179\pi$
$827$	19.7918	0.688230	0.344115	+	0.938928i	$0.388179\pi$
$828$	1.75616	0.0610306
$829$	50.6578	1.75942	0.879709	−	0.475513i	$-0.157738\pi$
$829$	50.6578	1.75942	0.879709	+	0.475513i	$0.157738\pi$
$830$	−17.0579	−0.592090
$831$	28.4532	0.987031
$832$	0.921449	0.0319455
$833$	80.1107	2.77567
$834$	34.8300	1.20606
$835$	10.7557	0.372218
$836$	4.29332	0.148488
$837$	13.8736	0.479543
$838$	4.00613	0.138390
$839$	2.97094	0.102568	0.0512842	−	0.998684i	$-0.483669\pi$
$839$	2.97094	0.102568	0.0512842	+	0.998684i	$0.483669\pi$
$840$	−21.1434	−0.729517
$841$	16.3329	0.563205
$842$	18.5298	0.638579
$843$	42.9400	1.47893
$844$	25.2776	0.870092
$845$	−23.5440	−0.809939
$846$	−35.0751	−1.20591
$847$	35.7956	1.22995
$848$	−1.18872	−0.0408209
$849$	−79.7078	−2.73557
$850$	8.99310	0.308461
$851$	−2.45066	−0.0840076
$852$	−24.9768	−0.855691
$853$	44.3379	1.51810	0.759051	−	0.651031i	$-0.225663\pi$
$853$	44.3379	1.51810	0.759051	+	0.651031i	$0.225663\pi$
$854$	−61.1711	−2.09323
$855$	−18.5228	−0.633468
$856$	13.9722	0.477562
$857$	35.8756	1.22549	0.612743	−	0.790282i	$-0.290066\pi$
$857$	35.8756	1.22549	0.612743	+	0.790282i	$0.290066\pi$
$858$	−3.80048	−0.129746
$859$	−20.1168	−0.686375	−0.343188	−	0.939267i	$-0.611507\pi$
$859$	−20.1168	−0.686375	−0.343188	+	0.939267i	$0.611507\pi$
$860$	−9.29370	−0.316913
$861$	−75.5088	−2.57333
$862$	−4.22383	−0.143864
$863$	−21.2816	−0.724433	−0.362216	−	0.932094i	$-0.617980\pi$
$863$	−21.2816	−0.724433	−0.362216	+	0.932094i	$0.617980\pi$
$864$	1.48803	0.0506239
$865$	2.41128	0.0819859
$866$	−5.07151	−0.172337
$867$	−90.1083	−3.06024
$868$	39.6613	1.34619
$869$	12.4861	0.423563
$870$	33.4652	1.13458
$871$	4.76074	0.161312
$872$	−19.4810	−0.659712
$873$	−6.08910	−0.206085
$874$	1.30982	0.0443053
$875$	51.4793	1.74032
$876$	1.30092	0.0439540
$877$	−11.5675	−0.390605	−0.195303	−	0.980743i	$-0.562569\pi$
$877$	−11.5675	−0.390605	−0.195303	+	0.980743i	$0.562569\pi$
$878$	−11.6302	−0.392501
$879$	56.8539	1.91763
$880$	−3.11546	−0.105022
$881$	−1.24245	−0.0418593	−0.0209297	−	0.999781i	$-0.506663\pi$
$881$	−1.24245	−0.0418593	−0.0209297	+	0.999781i	$0.506663\pi$
$882$	−39.7238	−1.33757
$883$	−3.45308	−0.116205	−0.0581027	−	0.998311i	$-0.518505\pi$
$883$	−3.45308	−0.116205	−0.0581027	+	0.998311i	$0.518505\pi$
$884$	6.65281	0.223758
$885$	−4.80030	−0.161360
$886$	17.9955	0.604569
$887$	−41.5190	−1.39407	−0.697035	−	0.717037i	$-0.745498\pi$
$887$	−41.5190	−1.39407	−0.697035	+	0.717037i	$0.745498\pi$
$888$	−12.8153	−0.430055
$889$	82.1351	2.75472
$890$	4.29829	0.144079
$891$	11.1316	0.372924
$892$	14.2056	0.475638
$893$	−26.1606	−0.875432
$894$	34.5984	1.15714
$895$	−36.7000	−1.22675
$896$	4.25391	0.142113
$897$	−1.15946	−0.0387133
$898$	3.14783	0.105044
$899$	−62.7748	−2.09366
$900$	−4.45933	−0.148644
$901$	−8.58252	−0.285925
$902$	−11.1261	−0.370459
$903$	−52.3386	−1.74172
$904$	2.32364	0.0772831
$905$	−31.7749	−1.05623
$906$	−17.1337	−0.569229
$907$	−10.2073	−0.338926	−0.169463	−	0.985537i	$-0.554203\pi$
$907$	−10.2073	−0.338926	−0.169463	+	0.985537i	$0.554203\pi$
$908$	18.4125	0.611040
$909$	−16.7567	−0.555785
$910$	7.59505	0.251773
$911$	−6.49126	−0.215065	−0.107532	−	0.994202i	$-0.534295\pi$
$911$	−6.49126	−0.215065	−0.107532	+	0.994202i	$0.534295\pi$
$912$	6.84950	0.226810
$913$	−14.1549	−0.468458
$914$	−16.3646	−0.541293
$915$	71.4734	2.36284
$916$	−23.7197	−0.783722
$917$	30.2445	0.998761
$918$	10.7435	0.354589
$919$	9.98549	0.329391	0.164695	−	0.986344i	$-0.447336\pi$
$919$	9.98549	0.329391	0.164695	+	0.986344i	$0.447336\pi$
$920$	−0.950473	−0.0313362
$921$	−1.46905	−0.0484069
$922$	16.4219	0.540826
$923$	8.97205	0.295319
$924$	−17.5451	−0.577190
$925$	6.22286	0.204606
$926$	−23.2373	−0.763625
$927$	22.1571	0.727734
$928$	−6.73297	−0.221021
$929$	3.48313	0.114278	0.0571388	−	0.998366i	$-0.481802\pi$
$929$	3.48313	0.114278	0.0571388	+	0.998366i	$0.481802\pi$
$930$	−46.3410	−1.51958
$931$	−29.6278	−0.971012
$932$	10.9070	0.357271
$933$	−75.0882	−2.45828
$934$	6.80259	0.222587
$935$	−22.4934	−0.735614
$936$	−3.29887	−0.107827
$937$	−42.4035	−1.38526	−0.692632	−	0.721291i	$-0.743549\pi$
$937$	−42.4035	−1.38526	−0.692632	+	0.721291i	$0.743549\pi$
$938$	21.9782	0.717613
$939$	−51.2916	−1.67384
$940$	18.9835	0.619173
$941$	−19.4692	−0.634679	−0.317340	−	0.948312i	$-0.602790\pi$
$941$	−19.4692	−0.634679	−0.317340	+	0.948312i	$0.602790\pi$
$942$	13.9351	0.454030
$943$	−3.39439	−0.110537
$944$	0.965789	0.0314337
$945$	12.2651	0.398984
$946$	−7.71203	−0.250740
$947$	44.4965	1.44594	0.722971	−	0.690878i	$-0.242776\pi$
$947$	44.4965	1.44594	0.722971	+	0.690878i	$0.242776\pi$
$948$	19.9201	0.646976
$949$	−0.467311	−0.0151695
$950$	−3.32597	−0.107909
$951$	−86.7135	−2.81188
$952$	30.7130	0.995414
$953$	−27.8582	−0.902415	−0.451208	−	0.892419i	$-0.649007\pi$
$953$	−27.8582	−0.902415	−0.451208	+	0.892419i	$0.649007\pi$
$954$	4.25574	0.137785
$955$	14.8204	0.479577
$956$	29.5525	0.955796
$957$	27.7699	0.897672
$958$	−11.8330	−0.382305
$959$	−77.9805	−2.51812
$960$	−4.97035	−0.160417
$961$	55.9274	1.80411
$962$	4.60347	0.148422
$963$	−50.0219	−1.61193
$964$	16.7861	0.540644
$965$	7.35606	0.236800
$966$	−5.35270	−0.172220
$967$	−30.0128	−0.965148	−0.482574	−	0.875855i	$-0.660298\pi$
$967$	−30.0128	−0.965148	−0.482574	+	0.875855i	$0.660298\pi$
$968$	8.41476	0.270460
$969$	49.4530	1.58866
$970$	3.29556	0.105814
$971$	21.5886	0.692811	0.346405	−	0.938085i	$-0.387402\pi$
$971$	21.5886	0.692811	0.346405	+	0.938085i	$0.387402\pi$
$972$	22.2233	0.712813
$973$	−57.7598	−1.85169
$974$	−29.5293	−0.946180
$975$	2.94417	0.0942888
$976$	−14.3800	−0.460291
$977$	−24.9306	−0.797600	−0.398800	−	0.917038i	$-0.630573\pi$
$977$	−24.9306	−0.797600	−0.398800	+	0.917038i	$0.630573\pi$
$978$	2.02275	0.0646803
$979$	3.56677	0.113995
$980$	21.4995	0.686775
$981$	69.7439	2.22675
$982$	−19.5477	−0.623794
$983$	26.9669	0.860111	0.430055	−	0.902802i	$-0.358494\pi$
$983$	26.9669	0.860111	0.430055	+	0.902802i	$0.358494\pi$
$984$	−17.7504	−0.565863
$985$	16.4540	0.524267
$986$	−48.6117	−1.54811
$987$	106.908	3.40291
$988$	−2.46045	−0.0782773
$989$	−2.35281	−0.0748150
$990$	11.1536	0.354485
$991$	−42.8747	−1.36196	−0.680979	−	0.732303i	$-0.738446\pi$
$991$	−42.8747	−1.36196	−0.680979	+	0.732303i	$0.738446\pi$
$992$	9.32348	0.296021
$993$	28.1767	0.894159
$994$	41.4199	1.31376
$995$	5.13550	0.162806
$996$	−22.5825	−0.715553
$997$	43.3573	1.37314	0.686569	−	0.727065i	$-0.259116\pi$
$997$	43.3573	1.37314	0.686569	+	0.727065i	$0.259116\pi$
$998$	−18.2240	−0.576872
$999$	7.43407	0.235204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.7	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.7	✓	46	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.56517 q^{3} +1.00000 q^{4} +1.93763 q^{5} +2.56517 q^{6} -4.25391 q^{7} -1.00000 q^{8} +3.58009 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.56517 q^{3} +1.00000 q^{4} +1.93763 q^{5} +2.56517 q^{6} -4.25391 q^{7} -1.00000 q^{8} +3.58009 q^{9} -1.93763 q^{10} -1.60787 q^{11} -2.56517 q^{12} +0.921449 q^{13} +4.25391 q^{14} -4.97035 q^{15} +1.00000 q^{16} +7.21995 q^{17} -3.58009 q^{18} -2.67019 q^{19} +1.93763 q^{20} +10.9120 q^{21} +1.60787 q^{22} +0.490534 q^{23} +2.56517 q^{24} -1.24559 q^{25} -0.921449 q^{26} -1.48803 q^{27} -4.25391 q^{28} +6.73297 q^{29} +4.97035 q^{30} -9.32348 q^{31} -1.00000 q^{32} +4.12446 q^{33} -7.21995 q^{34} -8.24250 q^{35} +3.58009 q^{36} -4.99591 q^{37} +2.67019 q^{38} -2.36367 q^{39} -1.93763 q^{40} -6.91979 q^{41} -10.9120 q^{42} -4.79643 q^{43} -1.60787 q^{44} +6.93689 q^{45} -0.490534 q^{46} +9.79727 q^{47} -2.56517 q^{48} +11.0958 q^{49} +1.24559 q^{50} -18.5204 q^{51} +0.921449 q^{52} -1.18872 q^{53} +1.48803 q^{54} -3.11546 q^{55} +4.25391 q^{56} +6.84950 q^{57} -6.73297 q^{58} +0.965789 q^{59} -4.97035 q^{60} -14.3800 q^{61} +9.32348 q^{62} -15.2294 q^{63} +1.00000 q^{64} +1.78543 q^{65} -4.12446 q^{66} +5.16658 q^{67} +7.21995 q^{68} -1.25830 q^{69} +8.24250 q^{70} +9.73690 q^{71} -3.58009 q^{72} -0.507148 q^{73} +4.99591 q^{74} +3.19515 q^{75} -2.67019 q^{76} +6.83973 q^{77} +2.36367 q^{78} -7.76563 q^{79} +1.93763 q^{80} -6.92322 q^{81} +6.91979 q^{82} +8.80351 q^{83} +10.9120 q^{84} +13.9896 q^{85} +4.79643 q^{86} -17.2712 q^{87} +1.60787 q^{88} -2.21832 q^{89} -6.93689 q^{90} -3.91976 q^{91} +0.490534 q^{92} +23.9163 q^{93} -9.79727 q^{94} -5.17385 q^{95} +2.56517 q^{96} -1.70082 q^{97} -11.0958 q^{98} -5.75632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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