LMFDB - Embedded newform 4034.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.51773 q^{3} +1.00000 q^{4} +3.18361 q^{5} -2.51773 q^{6} +3.34442 q^{7} +1.00000 q^{8} +3.33897 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.51773 q^{3} +1.00000 q^{4} +3.18361 q^{5} -2.51773 q^{6} +3.34442 q^{7} +1.00000 q^{8} +3.33897 q^{9} +3.18361 q^{10} +4.39578 q^{11} -2.51773 q^{12} -1.65607 q^{13} +3.34442 q^{14} -8.01549 q^{15} +1.00000 q^{16} +0.437905 q^{17} +3.33897 q^{18} +6.06633 q^{19} +3.18361 q^{20} -8.42036 q^{21} +4.39578 q^{22} -0.910588 q^{23} -2.51773 q^{24} +5.13540 q^{25} -1.65607 q^{26} -0.853442 q^{27} +3.34442 q^{28} +2.74018 q^{29} -8.01549 q^{30} +7.69663 q^{31} +1.00000 q^{32} -11.0674 q^{33} +0.437905 q^{34} +10.6474 q^{35} +3.33897 q^{36} -2.14712 q^{37} +6.06633 q^{38} +4.16955 q^{39} +3.18361 q^{40} -1.40688 q^{41} -8.42036 q^{42} -7.88297 q^{43} +4.39578 q^{44} +10.6300 q^{45} -0.910588 q^{46} -6.37112 q^{47} -2.51773 q^{48} +4.18517 q^{49} +5.13540 q^{50} -1.10253 q^{51} -1.65607 q^{52} +8.11955 q^{53} -0.853442 q^{54} +13.9945 q^{55} +3.34442 q^{56} -15.2734 q^{57} +2.74018 q^{58} -6.11888 q^{59} -8.01549 q^{60} -0.584661 q^{61} +7.69663 q^{62} +11.1669 q^{63} +1.00000 q^{64} -5.27230 q^{65} -11.0674 q^{66} -14.0603 q^{67} +0.437905 q^{68} +2.29262 q^{69} +10.6474 q^{70} -4.06322 q^{71} +3.33897 q^{72} +5.02776 q^{73} -2.14712 q^{74} -12.9296 q^{75} +6.06633 q^{76} +14.7013 q^{77} +4.16955 q^{78} +2.79445 q^{79} +3.18361 q^{80} -7.86818 q^{81} -1.40688 q^{82} -12.6416 q^{83} -8.42036 q^{84} +1.39412 q^{85} -7.88297 q^{86} -6.89904 q^{87} +4.39578 q^{88} +4.54074 q^{89} +10.6300 q^{90} -5.53861 q^{91} -0.910588 q^{92} -19.3780 q^{93} -6.37112 q^{94} +19.3128 q^{95} -2.51773 q^{96} -10.5365 q^{97} +4.18517 q^{98} +14.6774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−2.51773	−1.45361	−0.726807	−	0.686842i	$-0.758996\pi$
$3$	−2.51773	−1.45361	−0.726807	+	0.686842i	$0.758996\pi$
$4$	1.00000	0.500000
$5$	3.18361	1.42376	0.711878	−	0.702303i	$-0.247845\pi$
$5$	3.18361	1.42376	0.711878	+	0.702303i	$0.247845\pi$
$6$	−2.51773	−1.02786
$7$	3.34442	1.26407	0.632037	−	0.774938i	$-0.282219\pi$
$7$	3.34442	1.26407	0.632037	+	0.774938i	$0.282219\pi$
$8$	1.00000	0.353553
$9$	3.33897	1.11299
$10$	3.18361	1.00675
$11$	4.39578	1.32538	0.662689	−	0.748895i	$-0.269415\pi$
$11$	4.39578	1.32538	0.662689	+	0.748895i	$0.269415\pi$
$12$	−2.51773	−0.726807
$13$	−1.65607	−0.459312	−0.229656	−	0.973272i	$-0.573760\pi$
$13$	−1.65607	−0.459312	−0.229656	+	0.973272i	$0.573760\pi$
$14$	3.34442	0.893835
$15$	−8.01549	−2.06959
$16$	1.00000	0.250000
$17$	0.437905	0.106207	0.0531037	−	0.998589i	$-0.483089\pi$
$17$	0.437905	0.106207	0.0531037	+	0.998589i	$0.483089\pi$
$18$	3.33897	0.787003
$19$	6.06633	1.39171	0.695856	−	0.718182i	$-0.255025\pi$
$19$	6.06633	1.39171	0.695856	+	0.718182i	$0.255025\pi$
$20$	3.18361	0.711878
$21$	−8.42036	−1.83747
$22$	4.39578	0.937183
$23$	−0.910588	−0.189871	−0.0949354	−	0.995483i	$-0.530264\pi$
$23$	−0.910588	−0.189871	−0.0949354	+	0.995483i	$0.530264\pi$
$24$	−2.51773	−0.513930
$25$	5.13540	1.02708
$26$	−1.65607	−0.324783
$27$	−0.853442	−0.164245
$28$	3.34442	0.632037
$29$	2.74018	0.508839	0.254419	−	0.967094i	$-0.418116\pi$
$29$	2.74018	0.508839	0.254419	+	0.967094i	$0.418116\pi$
$30$	−8.01549	−1.46342
$31$	7.69663	1.38236	0.691178	−	0.722685i	$-0.257092\pi$
$31$	7.69663	1.38236	0.691178	+	0.722685i	$0.257092\pi$
$32$	1.00000	0.176777
$33$	−11.0674	−1.92659
$34$	0.437905	0.0751000
$35$	10.6474	1.79973
$36$	3.33897	0.556495
$37$	−2.14712	−0.352984	−0.176492	−	0.984302i	$-0.556475\pi$
$37$	−2.14712	−0.352984	−0.176492	+	0.984302i	$0.556475\pi$
$38$	6.06633	0.984088
$39$	4.16955	0.667662
$40$	3.18361	0.503374
$41$	−1.40688	−0.219718	−0.109859	−	0.993947i	$-0.535040\pi$
$41$	−1.40688	−0.219718	−0.109859	+	0.993947i	$0.535040\pi$
$42$	−8.42036	−1.29929
$43$	−7.88297	−1.20214	−0.601071	−	0.799196i	$-0.705259\pi$
$43$	−7.88297	−1.20214	−0.601071	+	0.799196i	$0.705259\pi$
$44$	4.39578	0.662689
$45$	10.6300	1.58463
$46$	−0.910588	−0.134259
$47$	−6.37112	−0.929323	−0.464662	−	0.885488i	$-0.653824\pi$
$47$	−6.37112	−0.929323	−0.464662	+	0.885488i	$0.653824\pi$
$48$	−2.51773	−0.363403
$49$	4.18517	0.597882
$50$	5.13540	0.726255
$51$	−1.10253	−0.154385
$52$	−1.65607	−0.229656
$53$	8.11955	1.11531	0.557653	−	0.830074i	$-0.311702\pi$
$53$	8.11955	1.11531	0.557653	+	0.830074i	$0.311702\pi$
$54$	−0.853442	−0.116139
$55$	13.9945	1.88701
$56$	3.34442	0.446917
$57$	−15.2734	−2.02301
$58$	2.74018	0.359803
$59$	−6.11888	−0.796611	−0.398305	−	0.917253i	$-0.630402\pi$
$59$	−6.11888	−0.796611	−0.398305	+	0.917253i	$0.630402\pi$
$60$	−8.01549	−1.03479
$61$	−0.584661	−0.0748581	−0.0374291	−	0.999299i	$-0.511917\pi$
$61$	−0.584661	−0.0748581	−0.0374291	+	0.999299i	$0.511917\pi$
$62$	7.69663	0.977473
$63$	11.1669	1.40690
$64$	1.00000	0.125000
$65$	−5.27230	−0.653948
$66$	−11.0674	−1.36230
$67$	−14.0603	−1.71774	−0.858869	−	0.512195i	$-0.828832\pi$
$67$	−14.0603	−1.71774	−0.858869	+	0.512195i	$0.828832\pi$
$68$	0.437905	0.0531037
$69$	2.29262	0.275999
$70$	10.6474	1.27260
$71$	−4.06322	−0.482216	−0.241108	−	0.970498i	$-0.577511\pi$
$71$	−4.06322	−0.482216	−0.241108	+	0.970498i	$0.577511\pi$
$72$	3.33897	0.393502
$73$	5.02776	0.588455	0.294228	−	0.955735i	$-0.404938\pi$
$73$	5.02776	0.588455	0.294228	+	0.955735i	$0.404938\pi$
$74$	−2.14712	−0.249597
$75$	−12.9296	−1.49298
$76$	6.06633	0.695856
$77$	14.7013	1.67537
$78$	4.16955	0.472108
$79$	2.79445	0.314400	0.157200	−	0.987567i	$-0.449753\pi$
$79$	2.79445	0.314400	0.157200	+	0.987567i	$0.449753\pi$
$80$	3.18361	0.355939
$81$	−7.86818	−0.874242
$82$	−1.40688	−0.155364
$83$	−12.6416	−1.38759	−0.693796	−	0.720172i	$-0.744063\pi$
$83$	−12.6416	−1.38759	−0.693796	+	0.720172i	$0.744063\pi$
$84$	−8.42036	−0.918737
$85$	1.39412	0.151213
$86$	−7.88297	−0.850043
$87$	−6.89904	−0.739655
$88$	4.39578	0.468592
$89$	4.54074	0.481318	0.240659	−	0.970610i	$-0.422636\pi$
$89$	4.54074	0.481318	0.240659	+	0.970610i	$0.422636\pi$
$90$	10.6300	1.12050
$91$	−5.53861	−0.580604
$92$	−0.910588	−0.0949354
$93$	−19.3780	−2.00941
$94$	−6.37112	−0.657131
$95$	19.3128	1.98146
$96$	−2.51773	−0.256965
$97$	−10.5365	−1.06982	−0.534911	−	0.844908i	$-0.679655\pi$
$97$	−10.5365	−1.06982	−0.534911	+	0.844908i	$0.679655\pi$
$98$	4.18517	0.422766
$99$	14.6774	1.47513
$100$	5.13540	0.513540
$101$	5.07975	0.505454	0.252727	−	0.967538i	$-0.418672\pi$
$101$	5.07975	0.505454	0.252727	+	0.967538i	$0.418672\pi$
$102$	−1.10253	−0.109166
$103$	−2.18522	−0.215316	−0.107658	−	0.994188i	$-0.534335\pi$
$103$	−2.18522	−0.215316	−0.107658	+	0.994188i	$0.534335\pi$
$104$	−1.65607	−0.162391
$105$	−26.8072	−2.61611
$106$	8.11955	0.788640
$107$	−3.85364	−0.372545	−0.186273	−	0.982498i	$-0.559641\pi$
$107$	−3.85364	−0.372545	−0.186273	+	0.982498i	$0.559641\pi$
$108$	−0.853442	−0.0821225
$109$	18.5633	1.77804	0.889021	−	0.457866i	$-0.151386\pi$
$109$	18.5633	1.77804	0.889021	+	0.457866i	$0.151386\pi$
$110$	13.9945	1.33432
$111$	5.40587	0.513102
$112$	3.34442	0.316018
$113$	−15.9965	−1.50483	−0.752414	−	0.658691i	$-0.771110\pi$
$113$	−15.9965	−1.50483	−0.752414	+	0.658691i	$0.771110\pi$
$114$	−15.2734	−1.43048
$115$	−2.89896	−0.270330
$116$	2.74018	0.254419
$117$	−5.52958	−0.511210
$118$	−6.11888	−0.563289
$119$	1.46454	0.134254
$120$	−8.01549	−0.731710
$121$	8.32287	0.756625
$122$	−0.584661	−0.0529327
$123$	3.54215	0.319385
$124$	7.69663	0.691178
$125$	0.431051	0.0385544
$126$	11.1669	0.994830
$127$	−11.7614	−1.04366	−0.521829	−	0.853050i	$-0.674750\pi$
$127$	−11.7614	−1.04366	−0.521829	+	0.853050i	$0.674750\pi$
$128$	1.00000	0.0883883
$129$	19.8472	1.74745
$130$	−5.27230	−0.462411
$131$	−22.5045	−1.96623	−0.983113	−	0.183001i	$-0.941419\pi$
$131$	−22.5045	−1.96623	−0.983113	+	0.183001i	$0.941419\pi$
$132$	−11.0674	−0.963293
$133$	20.2884	1.75923
$134$	−14.0603	−1.21462
$135$	−2.71703	−0.233845
$136$	0.437905	0.0375500
$137$	−0.172412	−0.0147301	−0.00736506	−	0.999973i	$-0.502344\pi$
$137$	−0.172412	−0.0147301	−0.00736506	+	0.999973i	$0.502344\pi$
$138$	2.29262	0.195161
$139$	−16.8581	−1.42989	−0.714945	−	0.699181i	$-0.753548\pi$
$139$	−16.8581	−1.42989	−0.714945	+	0.699181i	$0.753548\pi$
$140$	10.6474	0.899866
$141$	16.0408	1.35088
$142$	−4.06322	−0.340978
$143$	−7.27973	−0.608762
$144$	3.33897	0.278248
$145$	8.72368	0.724462
$146$	5.02776	0.416101
$147$	−10.5371	−0.869089
$148$	−2.14712	−0.176492
$149$	14.8882	1.21969	0.609843	−	0.792522i	$-0.291232\pi$
$149$	14.8882	1.21969	0.609843	+	0.792522i	$0.291232\pi$
$150$	−12.9296	−1.05569
$151$	22.1203	1.80012	0.900061	−	0.435764i	$-0.143522\pi$
$151$	22.1203	1.80012	0.900061	+	0.435764i	$0.143522\pi$
$152$	6.06633	0.492044
$153$	1.46215	0.118208
$154$	14.7013	1.18467
$155$	24.5031	1.96814
$156$	4.16955	0.333831
$157$	−5.70304	−0.455152	−0.227576	−	0.973760i	$-0.573080\pi$
$157$	−5.70304	−0.455152	−0.227576	+	0.973760i	$0.573080\pi$
$158$	2.79445	0.222315
$159$	−20.4428	−1.62122
$160$	3.18361	0.251687
$161$	−3.04539	−0.240011
$162$	−7.86818	−0.618183
$163$	−14.6908	−1.15067	−0.575336	−	0.817917i	$-0.695129\pi$
$163$	−14.6908	−1.15067	−0.575336	+	0.817917i	$0.695129\pi$
$164$	−1.40688	−0.109859
$165$	−35.2343	−2.74299
$166$	−12.6416	−0.981175
$167$	17.6785	1.36800	0.684000	−	0.729482i	$-0.260239\pi$
$167$	17.6785	1.36800	0.684000	+	0.729482i	$0.260239\pi$
$168$	−8.42036	−0.649645
$169$	−10.2574	−0.789033
$170$	1.39412	0.106924
$171$	20.2553	1.54896
$172$	−7.88297	−0.601071
$173$	20.7270	1.57585	0.787924	−	0.615773i	$-0.211156\pi$
$173$	20.7270	1.57585	0.787924	+	0.615773i	$0.211156\pi$
$174$	−6.89904	−0.523015
$175$	17.1749	1.29830
$176$	4.39578	0.331344
$177$	15.4057	1.15796
$178$	4.54074	0.340343
$179$	13.8040	1.03176	0.515881	−	0.856661i	$-0.327465\pi$
$179$	13.8040	1.03176	0.515881	+	0.856661i	$0.327465\pi$
$180$	10.6300	0.792313
$181$	−16.0579	−1.19357	−0.596785	−	0.802401i	$-0.703556\pi$
$181$	−16.0579	−1.19357	−0.596785	+	0.802401i	$0.703556\pi$
$182$	−5.53861	−0.410549
$183$	1.47202	0.108815
$184$	−0.910588	−0.0671295
$185$	−6.83560	−0.502563
$186$	−19.3780	−1.42087
$187$	1.92493	0.140765
$188$	−6.37112	−0.464662
$189$	−2.85427	−0.207618
$190$	19.3128	1.40110
$191$	−20.7159	−1.49895	−0.749475	−	0.662032i	$-0.769694\pi$
$191$	−20.7159	−1.49895	−0.749475	+	0.662032i	$0.769694\pi$
$192$	−2.51773	−0.181702
$193$	26.8620	1.93357	0.966786	−	0.255589i	$-0.0822693\pi$
$193$	26.8620	1.93357	0.966786	+	0.255589i	$0.0822693\pi$
$194$	−10.5365	−0.756479
$195$	13.2742	0.950587
$196$	4.18517	0.298941
$197$	−15.6396	−1.11427	−0.557136	−	0.830421i	$-0.688100\pi$
$197$	−15.6396	−1.11427	−0.557136	+	0.830421i	$0.688100\pi$
$198$	14.6774	1.04308
$199$	−5.44692	−0.386122	−0.193061	−	0.981187i	$-0.561842\pi$
$199$	−5.44692	−0.386122	−0.193061	+	0.981187i	$0.561842\pi$
$200$	5.13540	0.363127
$201$	35.4000	2.49693
$202$	5.07975	0.357410
$203$	9.16433	0.643210
$204$	−1.10253	−0.0771923
$205$	−4.47896	−0.312824
$206$	−2.18522	−0.152251
$207$	−3.04043	−0.211324
$208$	−1.65607	−0.114828
$209$	26.6662	1.84454
$210$	−26.8072	−1.84987
$211$	12.1769	0.838289	0.419145	−	0.907919i	$-0.362330\pi$
$211$	12.1769	0.838289	0.419145	+	0.907919i	$0.362330\pi$
$212$	8.11955	0.557653
$213$	10.2301	0.700955
$214$	−3.85364	−0.263429
$215$	−25.0963	−1.71156
$216$	−0.853442	−0.0580694
$217$	25.7408	1.74740
$218$	18.5633	1.25727
$219$	−12.6586	−0.855386
$220$	13.9945	0.943506
$221$	−0.725202	−0.0487823
$222$	5.40587	0.362818
$223$	4.34013	0.290637	0.145318	−	0.989385i	$-0.453579\pi$
$223$	4.34013	0.290637	0.145318	+	0.989385i	$0.453579\pi$
$224$	3.34442	0.223459
$225$	17.1469	1.14313
$226$	−15.9965	−1.06407
$227$	−0.764918	−0.0507694	−0.0253847	−	0.999678i	$-0.508081\pi$
$227$	−0.764918	−0.0507694	−0.0253847	+	0.999678i	$0.508081\pi$
$228$	−15.2734	−1.01150
$229$	25.2083	1.66581	0.832904	−	0.553417i	$-0.186676\pi$
$229$	25.2083	1.66581	0.832904	+	0.553417i	$0.186676\pi$
$230$	−2.89896	−0.191152
$231$	−37.0141	−2.43535
$232$	2.74018	0.179902
$233$	7.59456	0.497536	0.248768	−	0.968563i	$-0.419974\pi$
$233$	7.59456	0.497536	0.248768	+	0.968563i	$0.419974\pi$
$234$	−5.52958	−0.361480
$235$	−20.2832	−1.32313
$236$	−6.11888	−0.398305
$237$	−7.03568	−0.457017
$238$	1.46454	0.0949319
$239$	−1.10323	−0.0713622	−0.0356811	−	0.999363i	$-0.511360\pi$
$239$	−1.10323	−0.0713622	−0.0356811	+	0.999363i	$0.511360\pi$
$240$	−8.01549	−0.517397
$241$	10.8256	0.697341	0.348671	−	0.937245i	$-0.386633\pi$
$241$	10.8256	0.697341	0.348671	+	0.937245i	$0.386633\pi$
$242$	8.32287	0.535015
$243$	22.3703	1.43505
$244$	−0.584661	−0.0374291
$245$	13.3240	0.851238
$246$	3.54215	0.225839
$247$	−10.0463	−0.639230
$248$	7.69663	0.488736
$249$	31.8281	2.01702
$250$	0.431051	0.0272621
$251$	−3.32831	−0.210081	−0.105041	−	0.994468i	$-0.533497\pi$
$251$	−3.32831	−0.210081	−0.105041	+	0.994468i	$0.533497\pi$
$252$	11.1669	0.703451
$253$	−4.00275	−0.251650
$254$	−11.7614	−0.737977
$255$	−3.51002	−0.219806
$256$	1.00000	0.0625000
$257$	−4.53769	−0.283053	−0.141527	−	0.989934i	$-0.545201\pi$
$257$	−4.53769	−0.283053	−0.141527	+	0.989934i	$0.545201\pi$
$258$	19.8472	1.23563
$259$	−7.18088	−0.446198
$260$	−5.27230	−0.326974
$261$	9.14939	0.566333
$262$	−22.5045	−1.39033
$263$	12.6658	0.781009	0.390505	−	0.920601i	$-0.372301\pi$
$263$	12.6658	0.781009	0.390505	+	0.920601i	$0.372301\pi$
$264$	−11.0674	−0.681151
$265$	25.8495	1.58792
$266$	20.2884	1.24396
$267$	−11.4324	−0.699650
$268$	−14.0603	−0.858869
$269$	9.39941	0.573092	0.286546	−	0.958066i	$-0.407493\pi$
$269$	9.39941	0.573092	0.286546	+	0.958066i	$0.407493\pi$
$270$	−2.71703	−0.165353
$271$	20.7315	1.25935	0.629674	−	0.776860i	$-0.283188\pi$
$271$	20.7315	1.25935	0.629674	+	0.776860i	$0.283188\pi$
$272$	0.437905	0.0265519
$273$	13.9447	0.843974
$274$	−0.172412	−0.0104158
$275$	22.5741	1.36127
$276$	2.29262	0.137999
$277$	18.1194	1.08869	0.544344	−	0.838862i	$-0.316779\pi$
$277$	18.1194	1.08869	0.544344	+	0.838862i	$0.316779\pi$
$278$	−16.8581	−1.01108
$279$	25.6988	1.53855
$280$	10.6474	0.636301
$281$	6.87701	0.410248	0.205124	−	0.978736i	$-0.434240\pi$
$281$	6.87701	0.410248	0.205124	+	0.978736i	$0.434240\pi$
$282$	16.0408	0.955214
$283$	0.126831	0.00753930	0.00376965	−	0.999993i	$-0.498800\pi$
$283$	0.126831	0.00753930	0.00376965	+	0.999993i	$0.498800\pi$
$284$	−4.06322	−0.241108
$285$	−48.6246	−2.88027
$286$	−7.27973	−0.430459
$287$	−4.70520	−0.277739
$288$	3.33897	0.196751
$289$	−16.8082	−0.988720
$290$	8.72368	0.512272
$291$	26.5282	1.55511
$292$	5.02776	0.294228
$293$	24.1920	1.41331	0.706656	−	0.707557i	$-0.250203\pi$
$293$	24.1920	1.41331	0.706656	+	0.707557i	$0.250203\pi$
$294$	−10.5371	−0.614539
$295$	−19.4802	−1.13418
$296$	−2.14712	−0.124799
$297$	−3.75154	−0.217687
$298$	14.8882	0.862449
$299$	1.50800	0.0872099
$300$	−12.9296	−0.746488
$301$	−26.3640	−1.51960
$302$	22.1203	1.27288
$303$	−12.7895	−0.734735
$304$	6.06633	0.347928
$305$	−1.86133	−0.106580
$306$	1.46215	0.0835856
$307$	3.47382	0.198261	0.0991307	−	0.995074i	$-0.468394\pi$
$307$	3.47382	0.198261	0.0991307	+	0.995074i	$0.468394\pi$
$308$	14.7013	0.837687
$309$	5.50179	0.312986
$310$	24.5031	1.39168
$311$	10.1173	0.573699	0.286850	−	0.957976i	$-0.407392\pi$
$311$	10.1173	0.573699	0.286850	+	0.957976i	$0.407392\pi$
$312$	4.16955	0.236054
$313$	−3.16036	−0.178634	−0.0893170	−	0.996003i	$-0.528468\pi$
$313$	−3.16036	−0.178634	−0.0893170	+	0.996003i	$0.528468\pi$
$314$	−5.70304	−0.321841
$315$	35.5512	2.00308
$316$	2.79445	0.157200
$317$	16.6310	0.934091	0.467045	−	0.884233i	$-0.345318\pi$
$317$	16.6310	0.934091	0.467045	+	0.884233i	$0.345318\pi$
$318$	−20.4428	−1.14638
$319$	12.0452	0.674404
$320$	3.18361	0.177969
$321$	9.70243	0.541537
$322$	−3.04539	−0.169713
$323$	2.65647	0.147810
$324$	−7.86818	−0.437121
$325$	−8.50459	−0.471750
$326$	−14.6908	−0.813648
$327$	−46.7374	−2.58459
$328$	−1.40688	−0.0776819
$329$	−21.3077	−1.17473
$330$	−35.2343	−1.93958
$331$	−12.5326	−0.688855	−0.344427	−	0.938813i	$-0.611927\pi$
$331$	−12.5326	−0.688855	−0.344427	+	0.938813i	$0.611927\pi$
$332$	−12.6416	−0.693796
$333$	−7.16917	−0.392868
$334$	17.6785	0.967323
$335$	−44.7625	−2.44564
$336$	−8.42036	−0.459368
$337$	−2.50968	−0.136711	−0.0683556	−	0.997661i	$-0.521775\pi$
$337$	−2.50968	−0.136711	−0.0683556	+	0.997661i	$0.521775\pi$
$338$	−10.2574	−0.557930
$339$	40.2750	2.18744
$340$	1.39412	0.0756067
$341$	33.8327	1.83214
$342$	20.2553	1.09528
$343$	−9.41397	−0.508307
$344$	−7.88297	−0.425021
$345$	7.29881	0.392955
$346$	20.7270	1.11429
$347$	6.29608	0.337991	0.168996	−	0.985617i	$-0.445948\pi$
$347$	6.29608	0.337991	0.168996	+	0.985617i	$0.445948\pi$
$348$	−6.89904	−0.369827
$349$	25.6196	1.37138	0.685692	−	0.727891i	$-0.259500\pi$
$349$	25.6196	1.37138	0.685692	+	0.727891i	$0.259500\pi$
$350$	17.1749	0.918039
$351$	1.41336	0.0754397
$352$	4.39578	0.234296
$353$	−2.73598	−0.145621	−0.0728107	−	0.997346i	$-0.523197\pi$
$353$	−2.73598	−0.145621	−0.0728107	+	0.997346i	$0.523197\pi$
$354$	15.4057	0.818804
$355$	−12.9357	−0.686557
$356$	4.54074	0.240659
$357$	−3.68732	−0.195153
$358$	13.8040	0.729565
$359$	−27.0672	−1.42855	−0.714277	−	0.699863i	$-0.753244\pi$
$359$	−27.0672	−1.42855	−0.714277	+	0.699863i	$0.753244\pi$
$360$	10.6300	0.560250
$361$	17.8003	0.936860
$362$	−16.0579	−0.843982
$363$	−20.9548	−1.09984
$364$	−5.53861	−0.290302
$365$	16.0065	0.837816
$366$	1.47202	0.0769437
$367$	−18.0955	−0.944579	−0.472289	−	0.881443i	$-0.656572\pi$
$367$	−18.0955	−0.944579	−0.472289	+	0.881443i	$0.656572\pi$
$368$	−0.910588	−0.0474677
$369$	−4.69753	−0.244544
$370$	−6.83560	−0.355366
$371$	27.1552	1.40983
$372$	−19.3780	−1.00470
$373$	−21.7061	−1.12390	−0.561949	−	0.827172i	$-0.689948\pi$
$373$	−21.7061	−1.12390	−0.561949	+	0.827172i	$0.689948\pi$
$374$	1.92493	0.0995358
$375$	−1.08527	−0.0560432
$376$	−6.37112	−0.328565
$377$	−4.53794	−0.233716
$378$	−2.85427	−0.146808
$379$	−30.4578	−1.56451	−0.782256	−	0.622957i	$-0.785931\pi$
$379$	−30.4578	−1.56451	−0.782256	+	0.622957i	$0.785931\pi$
$380$	19.3128	0.990728
$381$	29.6121	1.51707
$382$	−20.7159	−1.05992
$383$	20.8528	1.06553	0.532765	−	0.846263i	$-0.321153\pi$
$383$	20.8528	1.06553	0.532765	+	0.846263i	$0.321153\pi$
$384$	−2.51773	−0.128482
$385$	46.8034	2.38532
$386$	26.8620	1.36724
$387$	−26.3210	−1.33797
$388$	−10.5365	−0.534911
$389$	−27.8182	−1.41044	−0.705219	−	0.708989i	$-0.749152\pi$
$389$	−27.8182	−1.41044	−0.705219	+	0.708989i	$0.749152\pi$
$390$	13.2742	0.672167
$391$	−0.398751	−0.0201657
$392$	4.18517	0.211383
$393$	56.6602	2.85813
$394$	−15.6396	−0.787910
$395$	8.89646	0.447629
$396$	14.6774	0.737566
$397$	−33.5752	−1.68509	−0.842546	−	0.538624i	$-0.818944\pi$
$397$	−33.5752	−1.68509	−0.842546	+	0.538624i	$0.818944\pi$
$398$	−5.44692	−0.273029
$399$	−51.0807	−2.55723
$400$	5.13540	0.256770
$401$	−19.4435	−0.970962	−0.485481	−	0.874247i	$-0.661355\pi$
$401$	−19.4435	−0.970962	−0.485481	+	0.874247i	$0.661355\pi$
$402$	35.4000	1.76559
$403$	−12.7462	−0.634932
$404$	5.07975	0.252727
$405$	−25.0492	−1.24471
$406$	9.16433	0.454818
$407$	−9.43826	−0.467837
$408$	−1.10253	−0.0545832
$409$	−17.6302	−0.871758	−0.435879	−	0.900005i	$-0.643562\pi$
$409$	−17.6302	−0.871758	−0.435879	+	0.900005i	$0.643562\pi$
$410$	−4.47896	−0.221200
$411$	0.434086	0.0214119
$412$	−2.18522	−0.107658
$413$	−20.4641	−1.00697
$414$	−3.04043	−0.149429
$415$	−40.2458	−1.97559
$416$	−1.65607	−0.0811956
$417$	42.4443	2.07851
$418$	26.6662	1.30429
$419$	11.1342	0.543941	0.271971	−	0.962306i	$-0.412325\pi$
$419$	11.1342	0.543941	0.271971	+	0.962306i	$0.412325\pi$
$420$	−26.8072	−1.30806
$421$	−7.21336	−0.351558	−0.175779	−	0.984430i	$-0.556244\pi$
$421$	−7.21336	−0.351558	−0.175779	+	0.984430i	$0.556244\pi$
$422$	12.1769	0.592760
$423$	−21.2730	−1.03433
$424$	8.11955	0.394320
$425$	2.24881	0.109083
$426$	10.2301	0.495650
$427$	−1.95535	−0.0946262
$428$	−3.85364	−0.186273
$429$	18.3284	0.884904
$430$	−25.0963	−1.21025
$431$	−3.95857	−0.190678	−0.0953389	−	0.995445i	$-0.530393\pi$
$431$	−3.95857	−0.190678	−0.0953389	+	0.995445i	$0.530393\pi$
$432$	−0.853442	−0.0410613
$433$	−4.67256	−0.224549	−0.112274	−	0.993677i	$-0.535814\pi$
$433$	−4.67256	−0.224549	−0.112274	+	0.993677i	$0.535814\pi$
$434$	25.7408	1.23560
$435$	−21.9639	−1.05309
$436$	18.5633	0.889021
$437$	−5.52393	−0.264245
$438$	−12.6586	−0.604849
$439$	2.05782	0.0982145	0.0491072	−	0.998794i	$-0.484362\pi$
$439$	2.05782	0.0982145	0.0491072	+	0.998794i	$0.484362\pi$
$440$	13.9945	0.667160
$441$	13.9742	0.665437
$442$	−0.725202	−0.0344943
$443$	−6.66947	−0.316876	−0.158438	−	0.987369i	$-0.550646\pi$
$443$	−6.66947	−0.316876	−0.158438	+	0.987369i	$0.550646\pi$
$444$	5.40587	0.256551
$445$	14.4560	0.685279
$446$	4.34013	0.205511
$447$	−37.4844	−1.77295
$448$	3.34442	0.158009
$449$	−5.68669	−0.268371	−0.134186	−	0.990956i	$-0.542842\pi$
$449$	−5.68669	−0.268371	−0.134186	+	0.990956i	$0.542842\pi$
$450$	17.1469	0.808315
$451$	−6.18433	−0.291209
$452$	−15.9965	−0.752414
$453$	−55.6929	−2.61668
$454$	−0.764918	−0.0358994
$455$	−17.6328	−0.826638
$456$	−15.2734	−0.715242
$457$	1.91582	0.0896185	0.0448092	−	0.998996i	$-0.485732\pi$
$457$	1.91582	0.0896185	0.0448092	+	0.998996i	$0.485732\pi$
$458$	25.2083	1.17790
$459$	−0.373726	−0.0174440
$460$	−2.89896	−0.135165
$461$	−5.00120	−0.232929	−0.116465	−	0.993195i	$-0.537156\pi$
$461$	−5.00120	−0.232929	−0.116465	+	0.993195i	$0.537156\pi$
$462$	−37.0141	−1.72205
$463$	−7.48957	−0.348070	−0.174035	−	0.984739i	$-0.555681\pi$
$463$	−7.48957	−0.348070	−0.174035	+	0.984739i	$0.555681\pi$
$464$	2.74018	0.127210
$465$	−61.6922	−2.86091
$466$	7.59456	0.351811
$467$	−6.23078	−0.288326	−0.144163	−	0.989554i	$-0.546049\pi$
$467$	−6.23078	−0.288326	−0.144163	+	0.989554i	$0.546049\pi$
$468$	−5.52958	−0.255605
$469$	−47.0236	−2.17135
$470$	−20.2832	−0.935593
$471$	14.3587	0.661615
$472$	−6.11888	−0.281644
$473$	−34.6518	−1.59329
$474$	−7.03568	−0.323160
$475$	31.1530	1.42940
$476$	1.46454	0.0671270
$477$	27.1109	1.24132
$478$	−1.10323	−0.0504607
$479$	−5.99882	−0.274093	−0.137046	−	0.990565i	$-0.543761\pi$
$479$	−5.99882	−0.274093	−0.137046	+	0.990565i	$0.543761\pi$
$480$	−8.01549	−0.365855
$481$	3.55578	0.162130
$482$	10.8256	0.493095
$483$	7.66749	0.348883
$484$	8.32287	0.378312
$485$	−33.5442	−1.52317
$486$	22.3703	1.01474
$487$	−27.6837	−1.25447	−0.627233	−	0.778831i	$-0.715813\pi$
$487$	−27.6837	−1.25447	−0.627233	+	0.778831i	$0.715813\pi$
$488$	−0.584661	−0.0264663
$489$	36.9875	1.67263
$490$	13.3240	0.601916
$491$	−31.2593	−1.41071	−0.705355	−	0.708854i	$-0.749213\pi$
$491$	−31.2593	−1.41071	−0.705355	+	0.708854i	$0.749213\pi$
$492$	3.54215	0.159692
$493$	1.19994	0.0540425
$494$	−10.0463	−0.452004
$495$	46.7271	2.10023
$496$	7.69663	0.345589
$497$	−13.5891	−0.609556
$498$	31.8281	1.42625
$499$	17.8189	0.797683	0.398842	−	0.917020i	$-0.369412\pi$
$499$	17.8189	0.797683	0.398842	+	0.917020i	$0.369412\pi$
$500$	0.431051	0.0192772
$501$	−44.5096	−1.98854
$502$	−3.32831	−0.148550
$503$	6.96487	0.310548	0.155274	−	0.987871i	$-0.450374\pi$
$503$	6.96487	0.310548	0.155274	+	0.987871i	$0.450374\pi$
$504$	11.1669	0.497415
$505$	16.1720	0.719643
$506$	−4.00275	−0.177944
$507$	25.8254	1.14695
$508$	−11.7614	−0.521829
$509$	28.1001	1.24551	0.622757	−	0.782415i	$-0.286012\pi$
$509$	28.1001	1.24551	0.622757	+	0.782415i	$0.286012\pi$
$510$	−3.51002	−0.155426
$511$	16.8150	0.743851
$512$	1.00000	0.0441942
$513$	−5.17726	−0.228582
$514$	−4.53769	−0.200149
$515$	−6.95688	−0.306557
$516$	19.8472	0.873725
$517$	−28.0060	−1.23170
$518$	−7.18088	−0.315510
$519$	−52.1851	−2.29067
$520$	−5.27230	−0.231205
$521$	−27.1116	−1.18778	−0.593890	−	0.804546i	$-0.702409\pi$
$521$	−27.1116	−1.18778	−0.593890	+	0.804546i	$0.702409\pi$
$522$	9.14939	0.400458
$523$	33.7768	1.47695	0.738477	−	0.674278i	$-0.235545\pi$
$523$	33.7768	1.47695	0.738477	+	0.674278i	$0.235545\pi$
$524$	−22.5045	−0.983113
$525$	−43.2419	−1.88723
$526$	12.6658	0.552257
$527$	3.37039	0.146816
$528$	−11.0674	−0.481646
$529$	−22.1708	−0.963949
$530$	25.8495	1.12283
$531$	−20.4308	−0.886621
$532$	20.2884	0.879613
$533$	2.32990	0.100919
$534$	−11.4324	−0.494727
$535$	−12.2685	−0.530413
$536$	−14.0603	−0.607312
$537$	−34.7548	−1.49978
$538$	9.39941	0.405238
$539$	18.3971	0.792419
$540$	−2.71703	−0.116922
$541$	28.9579	1.24500	0.622498	−	0.782621i	$-0.286118\pi$
$541$	28.9579	1.24500	0.622498	+	0.782621i	$0.286118\pi$
$542$	20.7315	0.890493
$543$	40.4294	1.73499
$544$	0.437905	0.0187750
$545$	59.0984	2.53150
$546$	13.9447	0.596779
$547$	−31.1440	−1.33162	−0.665810	−	0.746121i	$-0.731914\pi$
$547$	−31.1440	−1.33162	−0.665810	+	0.746121i	$0.731914\pi$
$548$	−0.172412	−0.00736506
$549$	−1.95217	−0.0833164
$550$	22.5741	0.962562
$551$	16.6228	0.708157
$552$	2.29262	0.0975803
$553$	9.34583	0.397425
$554$	18.1194	0.769818
$555$	17.2102	0.730532
$556$	−16.8581	−0.714945
$557$	−28.6070	−1.21212	−0.606060	−	0.795419i	$-0.707251\pi$
$557$	−28.6070	−1.21212	−0.606060	+	0.795419i	$0.707251\pi$
$558$	25.6988	1.08792
$559$	13.0548	0.552158
$560$	10.6474	0.449933
$561$	−4.84646	−0.204618
$562$	6.87701	0.290089
$563$	35.0156	1.47573	0.737866	−	0.674947i	$-0.235833\pi$
$563$	35.0156	1.47573	0.737866	+	0.674947i	$0.235833\pi$
$564$	16.0408	0.675438
$565$	−50.9268	−2.14251
$566$	0.126831	0.00533109
$567$	−26.3145	−1.10511
$568$	−4.06322	−0.170489
$569$	−6.23052	−0.261197	−0.130599	−	0.991435i	$-0.541690\pi$
$569$	−6.23052	−0.261197	−0.130599	+	0.991435i	$0.541690\pi$
$570$	−48.6246	−2.03666
$571$	2.58529	0.108191	0.0540955	−	0.998536i	$-0.482772\pi$
$571$	2.58529	0.108191	0.0540955	+	0.998536i	$0.482772\pi$
$572$	−7.27973	−0.304381
$573$	52.1571	2.17889
$574$	−4.70520	−0.196391
$575$	−4.67623	−0.195012
$576$	3.33897	0.139124
$577$	−6.50698	−0.270889	−0.135445	−	0.990785i	$-0.543246\pi$
$577$	−6.50698	−0.270889	−0.135445	+	0.990785i	$0.543246\pi$
$578$	−16.8082	−0.699131
$579$	−67.6314	−2.81066
$580$	8.72368	0.362231
$581$	−42.2787	−1.75402
$582$	26.5282	1.09963
$583$	35.6917	1.47820
$584$	5.02776	0.208050
$585$	−17.6041	−0.727838
$586$	24.1920	0.999363
$587$	27.7013	1.14336	0.571678	−	0.820478i	$-0.306293\pi$
$587$	27.7013	1.14336	0.571678	+	0.820478i	$0.306293\pi$
$588$	−10.5371	−0.434544
$589$	46.6903	1.92384
$590$	−19.4802	−0.801986
$591$	39.3762	1.61972
$592$	−2.14712	−0.0882460
$593$	−15.5154	−0.637141	−0.318571	−	0.947899i	$-0.603203\pi$
$593$	−15.5154	−0.637141	−0.318571	+	0.947899i	$0.603203\pi$
$594$	−3.75154	−0.153928
$595$	4.66253	0.191145
$596$	14.8882	0.609843
$597$	13.7139	0.561272
$598$	1.50800	0.0616667
$599$	29.8959	1.22151	0.610756	−	0.791819i	$-0.290866\pi$
$599$	29.8959	1.22151	0.610756	+	0.791819i	$0.290866\pi$
$600$	−12.9296	−0.527847
$601$	2.95486	0.120531	0.0602657	−	0.998182i	$-0.480805\pi$
$601$	2.95486	0.120531	0.0602657	+	0.998182i	$0.480805\pi$
$602$	−26.3640	−1.07452
$603$	−46.9469	−1.91183
$604$	22.1203	0.900061
$605$	26.4968	1.07725
$606$	−12.7895	−0.519536
$607$	22.9224	0.930391	0.465195	−	0.885208i	$-0.345984\pi$
$607$	22.9224	0.930391	0.465195	+	0.885208i	$0.345984\pi$
$608$	6.06633	0.246022
$609$	−23.0733	−0.934978
$610$	−1.86133	−0.0753632
$611$	10.5510	0.426849
$612$	1.46215	0.0591040
$613$	43.4209	1.75376	0.876878	−	0.480714i	$-0.159622\pi$
$613$	43.4209	1.75376	0.876878	+	0.480714i	$0.159622\pi$
$614$	3.47382	0.140192
$615$	11.2768	0.454725
$616$	14.7013	0.592334
$617$	13.8734	0.558523	0.279262	−	0.960215i	$-0.409910\pi$
$617$	13.8734	0.558523	0.279262	+	0.960215i	$0.409910\pi$
$618$	5.50179	0.221314
$619$	−12.9730	−0.521431	−0.260715	−	0.965416i	$-0.583958\pi$
$619$	−12.9730	−0.521431	−0.260715	+	0.965416i	$0.583958\pi$
$620$	24.5031	0.984068
$621$	0.777135	0.0311853
$622$	10.1173	0.405667
$623$	15.1862	0.608421
$624$	4.16955	0.166915
$625$	−24.3047	−0.972187
$626$	−3.16036	−0.126313
$627$	−67.1384	−2.68125
$628$	−5.70304	−0.227576
$629$	−0.940233	−0.0374895
$630$	35.5512	1.41639
$631$	16.1694	0.643693	0.321847	−	0.946792i	$-0.395696\pi$
$631$	16.1694	0.643693	0.321847	+	0.946792i	$0.395696\pi$
$632$	2.79445	0.111157
$633$	−30.6581	−1.21855
$634$	16.6310	0.660502
$635$	−37.4438	−1.48591
$636$	−20.4428	−0.810611
$637$	−6.93095	−0.274614
$638$	12.0452	0.476875
$639$	−13.5670	−0.536702
$640$	3.18361	0.125843
$641$	−25.8442	−1.02078	−0.510392	−	0.859942i	$-0.670500\pi$
$641$	−25.8442	−1.02078	−0.510392	+	0.859942i	$0.670500\pi$
$642$	9.70243	0.382924
$643$	−27.2371	−1.07413	−0.537063	−	0.843542i	$-0.680466\pi$
$643$	−27.2371	−1.07413	−0.537063	+	0.843542i	$0.680466\pi$
$644$	−3.04539	−0.120005
$645$	63.1858	2.48794
$646$	2.65647	0.104518
$647$	13.9982	0.550326	0.275163	−	0.961398i	$-0.411268\pi$
$647$	13.9982	0.550326	0.275163	+	0.961398i	$0.411268\pi$
$648$	−7.86818	−0.309091
$649$	−26.8973	−1.05581
$650$	−8.50459	−0.333577
$651$	−64.8084	−2.54004
$652$	−14.6908	−0.575336
$653$	30.3854	1.18907	0.594536	−	0.804069i	$-0.297336\pi$
$653$	30.3854	1.18907	0.594536	+	0.804069i	$0.297336\pi$
$654$	−46.7374	−1.82758
$655$	−71.6456	−2.79942
$656$	−1.40688	−0.0549294
$657$	16.7876	0.654945
$658$	−21.3077	−0.830661
$659$	−11.4773	−0.447091	−0.223545	−	0.974694i	$-0.571763\pi$
$659$	−11.4773	−0.447091	−0.223545	+	0.974694i	$0.571763\pi$
$660$	−35.2343	−1.37149
$661$	−4.80840	−0.187025	−0.0935125	−	0.995618i	$-0.529810\pi$
$661$	−4.80840	−0.187025	−0.0935125	+	0.995618i	$0.529810\pi$
$662$	−12.5326	−0.487094
$663$	1.82586	0.0709107
$664$	−12.6416	−0.490588
$665$	64.5904	2.50471
$666$	−7.16917	−0.277800
$667$	−2.49518	−0.0966137
$668$	17.6785	0.684000
$669$	−10.9273	−0.422473
$670$	−44.7625	−1.72933
$671$	−2.57004	−0.0992153
$672$	−8.42036	−0.324823
$673$	39.2551	1.51317	0.756586	−	0.653894i	$-0.226866\pi$
$673$	39.2551	1.51317	0.756586	+	0.653894i	$0.226866\pi$
$674$	−2.50968	−0.0966694
$675$	−4.38276	−0.168693
$676$	−10.2574	−0.394516
$677$	−15.4538	−0.593937	−0.296969	−	0.954887i	$-0.595976\pi$
$677$	−15.4538	−0.593937	−0.296969	+	0.954887i	$0.595976\pi$
$678$	40.2750	1.54675
$679$	−35.2386	−1.35233
$680$	1.39412	0.0534620
$681$	1.92586	0.0737990
$682$	33.8327	1.29552
$683$	−24.9334	−0.954049	−0.477025	−	0.878890i	$-0.658285\pi$
$683$	−24.9334	−0.954049	−0.477025	+	0.878890i	$0.658285\pi$
$684$	20.2553	0.774481
$685$	−0.548892	−0.0209721
$686$	−9.41397	−0.359427
$687$	−63.4676	−2.42144
$688$	−7.88297	−0.300535
$689$	−13.4466	−0.512273
$690$	7.29881	0.277861
$691$	−16.0017	−0.608734	−0.304367	−	0.952555i	$-0.598445\pi$
$691$	−16.0017	−0.608734	−0.304367	+	0.952555i	$0.598445\pi$
$692$	20.7270	0.787924
$693$	49.0874	1.86468
$694$	6.29608	0.238996
$695$	−53.6698	−2.03581
$696$	−6.89904	−0.261508
$697$	−0.616079	−0.0233357
$698$	25.6196	0.969715
$699$	−19.1211	−0.723225
$700$	17.1749	0.649152
$701$	22.4155	0.846620	0.423310	−	0.905985i	$-0.360868\pi$
$701$	22.4155	0.846620	0.423310	+	0.905985i	$0.360868\pi$
$702$	1.41336	0.0533439
$703$	−13.0251	−0.491252
$704$	4.39578	0.165672
$705$	51.0676	1.92332
$706$	−2.73598	−0.102970
$707$	16.9888	0.638931
$708$	15.4057	0.578982
$709$	41.3395	1.55254	0.776268	−	0.630403i	$-0.217110\pi$
$709$	41.3395	1.55254	0.776268	+	0.630403i	$0.217110\pi$
$710$	−12.9357	−0.485469
$711$	9.33060	0.349925
$712$	4.54074	0.170172
$713$	−7.00846	−0.262469
$714$	−3.68732	−0.137994
$715$	−23.1758	−0.866728
$716$	13.8040	0.515881
$717$	2.77765	0.103733
$718$	−27.0672	−1.01014
$719$	9.75775	0.363903	0.181951	−	0.983308i	$-0.441759\pi$
$719$	9.75775	0.363903	0.181951	+	0.983308i	$0.441759\pi$
$720$	10.6300	0.396157
$721$	−7.30829	−0.272175
$722$	17.8003	0.662460
$723$	−27.2561	−1.01366
$724$	−16.0579	−0.596785
$725$	14.0719	0.522618
$726$	−20.9548	−0.777704
$727$	17.3195	0.642345	0.321173	−	0.947021i	$-0.395923\pi$
$727$	17.3195	0.642345	0.321173	+	0.947021i	$0.395923\pi$
$728$	−5.53861	−0.205275
$729$	−32.7179	−1.21177
$730$	16.0065	0.592425
$731$	−3.45199	−0.127676
$732$	1.47202	0.0544074
$733$	−6.81193	−0.251604	−0.125802	−	0.992055i	$-0.540150\pi$
$733$	−6.81193	−0.251604	−0.125802	+	0.992055i	$0.540150\pi$
$734$	−18.0955	−0.667918
$735$	−33.5462	−1.23737
$736$	−0.910588	−0.0335647
$737$	−61.8059	−2.27665
$738$	−4.69753	−0.172919
$739$	31.1679	1.14653	0.573266	−	0.819370i	$-0.305676\pi$
$739$	31.1679	1.14653	0.573266	+	0.819370i	$0.305676\pi$
$740$	−6.83560	−0.251282
$741$	25.2938	0.929192
$742$	27.1552	0.996899
$743$	−18.6503	−0.684212	−0.342106	−	0.939661i	$-0.611140\pi$
$743$	−18.6503	−0.684212	−0.342106	+	0.939661i	$0.611140\pi$
$744$	−19.3780	−0.710434
$745$	47.3982	1.73654
$746$	−21.7061	−0.794715
$747$	−42.2098	−1.54438
$748$	1.92493	0.0703825
$749$	−12.8882	−0.470925
$750$	−1.08527	−0.0396285
$751$	−29.1265	−1.06284	−0.531420	−	0.847108i	$-0.678341\pi$
$751$	−29.1265	−1.06284	−0.531420	+	0.847108i	$0.678341\pi$
$752$	−6.37112	−0.232331
$753$	8.37979	0.305377
$754$	−4.53794	−0.165262
$755$	70.4224	2.56293
$756$	−2.85427	−0.103809
$757$	−18.4932	−0.672146	−0.336073	−	0.941836i	$-0.609099\pi$
$757$	−18.4932	−0.672146	−0.336073	+	0.941836i	$0.609099\pi$
$758$	−30.4578	−1.10628
$759$	10.0778	0.365802
$760$	19.3128	0.700551
$761$	−6.20305	−0.224861	−0.112430	−	0.993660i	$-0.535863\pi$
$761$	−6.20305	−0.224861	−0.112430	+	0.993660i	$0.535863\pi$
$762$	29.6121	1.07273
$763$	62.0836	2.24758
$764$	−20.7159	−0.749475
$765$	4.65493	0.168299
$766$	20.8528	0.753444
$767$	10.1333	0.365893
$768$	−2.51773	−0.0908508
$769$	44.5042	1.60486	0.802431	−	0.596745i	$-0.203540\pi$
$769$	44.5042	1.60486	0.802431	+	0.596745i	$0.203540\pi$
$770$	46.8034	1.68668
$771$	11.4247	0.411450
$772$	26.8620	0.966786
$773$	−9.63658	−0.346604	−0.173302	−	0.984869i	$-0.555444\pi$
$773$	−9.63658	−0.346604	−0.173302	+	0.984869i	$0.555444\pi$
$774$	−26.3210	−0.946090
$775$	39.5252	1.41979
$776$	−10.5365	−0.378239
$777$	18.0795	0.648599
$778$	−27.8182	−0.997331
$779$	−8.53460	−0.305784
$780$	13.2742	0.475294
$781$	−17.8610	−0.639118
$782$	−0.398751	−0.0142593
$783$	−2.33859	−0.0835743
$784$	4.18517	0.149470
$785$	−18.1563	−0.648026
$786$	56.6602	2.02100
$787$	6.40595	0.228347	0.114174	−	0.993461i	$-0.463578\pi$
$787$	6.40595	0.228347	0.114174	+	0.993461i	$0.463578\pi$
$788$	−15.6396	−0.557136
$789$	−31.8892	−1.13529
$790$	8.89646	0.316522
$791$	−53.4992	−1.90221
$792$	14.6774	0.521538
$793$	0.968241	0.0343832
$794$	−33.5752	−1.19154
$795$	−65.0821	−2.30822
$796$	−5.44692	−0.193061
$797$	16.3754	0.580048	0.290024	−	0.957019i	$-0.406337\pi$
$797$	16.3754	0.580048	0.290024	+	0.957019i	$0.406337\pi$
$798$	−51.0807	−1.80824
$799$	−2.78994	−0.0987010
$800$	5.13540	0.181564
$801$	15.1614	0.535702
$802$	−19.4435	−0.686574
$803$	22.1009	0.779925
$804$	35.4000	1.24846
$805$	−9.69536	−0.341717
$806$	−12.7462	−0.448965
$807$	−23.6652	−0.833055
$808$	5.07975	0.178705
$809$	−43.0960	−1.51517	−0.757587	−	0.652735i	$-0.773622\pi$
$809$	−43.0960	−1.51517	−0.757587	+	0.652735i	$0.773622\pi$
$810$	−25.0492	−0.880141
$811$	−6.88519	−0.241772	−0.120886	−	0.992666i	$-0.538573\pi$
$811$	−6.88519	−0.241772	−0.120886	+	0.992666i	$0.538573\pi$
$812$	9.16433	0.321605
$813$	−52.1963	−1.83060
$814$	−9.43826	−0.330811
$815$	−46.7698	−1.63827
$816$	−1.10253	−0.0385961
$817$	−47.8207	−1.67303
$818$	−17.6302	−0.616426
$819$	−18.4933	−0.646207
$820$	−4.47896	−0.156412
$821$	−14.5351	−0.507279	−0.253639	−	0.967299i	$-0.581628\pi$
$821$	−14.5351	−0.507279	−0.253639	+	0.967299i	$0.581628\pi$
$822$	0.434086	0.0151405
$823$	−33.3012	−1.16081	−0.580404	−	0.814329i	$-0.697105\pi$
$823$	−33.3012	−1.16081	−0.580404	+	0.814329i	$0.697105\pi$
$824$	−2.18522	−0.0761256
$825$	−56.8354	−1.97876
$826$	−20.4641	−0.712039
$827$	−39.3524	−1.36842	−0.684209	−	0.729286i	$-0.739852\pi$
$827$	−39.3524	−1.36842	−0.684209	+	0.729286i	$0.739852\pi$
$828$	−3.04043	−0.105662
$829$	51.4599	1.78728	0.893638	−	0.448788i	$-0.148144\pi$
$829$	51.4599	1.78728	0.893638	+	0.448788i	$0.148144\pi$
$830$	−40.2458	−1.39695
$831$	−45.6197	−1.58253
$832$	−1.65607	−0.0574140
$833$	1.83271	0.0634995
$834$	42.4443	1.46973
$835$	56.2814	1.94770
$836$	26.6662	0.922271
$837$	−6.56863	−0.227045
$838$	11.1342	0.384624
$839$	−39.7819	−1.37343	−0.686713	−	0.726929i	$-0.740947\pi$
$839$	−39.7819	−1.37343	−0.686713	+	0.726929i	$0.740947\pi$
$840$	−26.8072	−0.924936
$841$	−21.4914	−0.741083
$842$	−7.21336	−0.248589
$843$	−17.3145	−0.596342
$844$	12.1769	0.419145
$845$	−32.6557	−1.12339
$846$	−21.2730	−0.731380
$847$	27.8352	0.956429
$848$	8.11955	0.278826
$849$	−0.319325	−0.0109592
$850$	2.24881	0.0771337
$851$	1.95514	0.0670214
$852$	10.2301	0.350478
$853$	31.4934	1.07831	0.539157	−	0.842205i	$-0.318743\pi$
$853$	31.4934	1.07831	0.539157	+	0.842205i	$0.318743\pi$
$854$	−1.95535	−0.0669108
$855$	64.4851	2.20534
$856$	−3.85364	−0.131715
$857$	−10.0814	−0.344373	−0.172187	−	0.985064i	$-0.555083\pi$
$857$	−10.0814	−0.344373	−0.172187	+	0.985064i	$0.555083\pi$
$858$	18.3284	0.625721
$859$	−14.2783	−0.487171	−0.243585	−	0.969879i	$-0.578324\pi$
$859$	−14.2783	−0.487171	−0.243585	+	0.969879i	$0.578324\pi$
$860$	−25.0963	−0.855778
$861$	11.8464	0.403726
$862$	−3.95857	−0.134830
$863$	−36.5707	−1.24488	−0.622441	−	0.782667i	$-0.713859\pi$
$863$	−36.5707	−1.24488	−0.622441	+	0.782667i	$0.713859\pi$
$864$	−0.853442	−0.0290347
$865$	65.9869	2.24362
$866$	−4.67256	−0.158780
$867$	42.3186	1.43722
$868$	25.7408	0.873699
$869$	12.2838	0.416699
$870$	−21.9639	−0.744645
$871$	23.2849	0.788978
$872$	18.5633	0.628633
$873$	−35.1812	−1.19070
$874$	−5.52393	−0.186850
$875$	1.44162	0.0487356
$876$	−12.6586	−0.427693
$877$	−27.5853	−0.931489	−0.465745	−	0.884919i	$-0.654213\pi$
$877$	−27.5853	−0.931489	−0.465745	+	0.884919i	$0.654213\pi$
$878$	2.05782	0.0694481
$879$	−60.9090	−2.05441
$880$	13.9945	0.471753
$881$	20.8586	0.702744	0.351372	−	0.936236i	$-0.385715\pi$
$881$	20.8586	0.702744	0.351372	+	0.936236i	$0.385715\pi$
$882$	13.9742	0.470535
$883$	26.4272	0.889346	0.444673	−	0.895693i	$-0.353320\pi$
$883$	26.4272	0.889346	0.444673	+	0.895693i	$0.353320\pi$
$884$	−0.725202	−0.0243912
$885$	49.0458	1.64866
$886$	−6.66947	−0.224065
$887$	23.1562	0.777509	0.388755	−	0.921341i	$-0.372905\pi$
$887$	23.1562	0.777509	0.388755	+	0.921341i	$0.372905\pi$
$888$	5.40587	0.181409
$889$	−39.3352	−1.31926
$890$	14.4560	0.484565
$891$	−34.5868	−1.15870
$892$	4.34013	0.145318
$893$	−38.6493	−1.29335
$894$	−37.4844	−1.25367
$895$	43.9467	1.46898
$896$	3.34442	0.111729
$897$	−3.79674	−0.126769
$898$	−5.68669	−0.189767
$899$	21.0902	0.703396
$900$	17.1469	0.571565
$901$	3.55559	0.118454
$902$	−6.18433	−0.205916
$903$	66.3775	2.20890
$904$	−15.9965	−0.532037
$905$	−51.1220	−1.69935
$906$	−55.6929	−1.85027
$907$	46.3026	1.53745	0.768726	−	0.639578i	$-0.220891\pi$
$907$	46.3026	1.53745	0.768726	+	0.639578i	$0.220891\pi$
$908$	−0.764918	−0.0253847
$909$	16.9612	0.562566
$910$	−17.6328	−0.584521
$911$	−0.461564	−0.0152923	−0.00764615	−	0.999971i	$-0.502434\pi$
$911$	−0.461564	−0.0152923	−0.00764615	+	0.999971i	$0.502434\pi$
$912$	−15.2734	−0.505752
$913$	−55.5695	−1.83908
$914$	1.91582	0.0633698
$915$	4.68634	0.154926
$916$	25.2083	0.832904
$917$	−75.2645	−2.48545
$918$	−0.373726	−0.0123348
$919$	−8.18435	−0.269977	−0.134988	−	0.990847i	$-0.543100\pi$
$919$	−8.18435	−0.269977	−0.134988	+	0.990847i	$0.543100\pi$
$920$	−2.89896	−0.0955760
$921$	−8.74615	−0.288195
$922$	−5.00120	−0.164706
$923$	6.72899	0.221487
$924$	−37.0141	−1.21767
$925$	−11.0263	−0.362543
$926$	−7.48957	−0.246123
$927$	−7.29637	−0.239644
$928$	2.74018	0.0899509
$929$	25.7043	0.843331	0.421665	−	0.906751i	$-0.361446\pi$
$929$	25.7043	0.843331	0.421665	+	0.906751i	$0.361446\pi$
$930$	−61.6922	−2.02297
$931$	25.3886	0.832079
$932$	7.59456	0.248768
$933$	−25.4726	−0.833937
$934$	−6.23078	−0.203877
$935$	6.12824	0.200415
$936$	−5.52958	−0.180740
$937$	4.17527	0.136400	0.0682000	−	0.997672i	$-0.478274\pi$
$937$	4.17527	0.136400	0.0682000	+	0.997672i	$0.478274\pi$
$938$	−47.0236	−1.53537
$939$	7.95694	0.259665
$940$	−20.2832	−0.661564
$941$	−37.3633	−1.21801	−0.609004	−	0.793167i	$-0.708431\pi$
$941$	−37.3633	−1.21801	−0.609004	+	0.793167i	$0.708431\pi$
$942$	14.3587	0.467833
$943$	1.28109	0.0417180
$944$	−6.11888	−0.199153
$945$	−9.08690	−0.295597
$946$	−34.6518	−1.12663
$947$	−11.6440	−0.378380	−0.189190	−	0.981941i	$-0.560586\pi$
$947$	−11.6440	−0.378380	−0.189190	+	0.981941i	$0.560586\pi$
$948$	−7.03568	−0.228508
$949$	−8.32634	−0.270284
$950$	31.1530	1.01074
$951$	−41.8724	−1.35781
$952$	1.46454	0.0474660
$953$	−2.35260	−0.0762083	−0.0381042	−	0.999274i	$-0.512132\pi$
$953$	−2.35260	−0.0762083	−0.0381042	+	0.999274i	$0.512132\pi$
$954$	27.1109	0.877749
$955$	−65.9515	−2.13414
$956$	−1.10323	−0.0356811
$957$	−30.3267	−0.980322
$958$	−5.99882	−0.193813
$959$	−0.576618	−0.0186200
$960$	−8.01549	−0.258699
$961$	28.2381	0.910906
$962$	3.55578	0.114643
$963$	−12.8672	−0.414640
$964$	10.8256	0.348671
$965$	85.5183	2.75293
$966$	7.66749	0.246697
$967$	−40.8516	−1.31370	−0.656849	−	0.754022i	$-0.728111\pi$
$967$	−40.8516	−1.31370	−0.656849	+	0.754022i	$0.728111\pi$
$968$	8.32287	0.267507
$969$	−6.68829	−0.214859
$970$	−33.5442	−1.07704
$971$	32.9014	1.05586	0.527928	−	0.849289i	$-0.322969\pi$
$971$	32.9014	1.05586	0.527928	+	0.849289i	$0.322969\pi$
$972$	22.3703	0.717527
$973$	−56.3808	−1.80749
$974$	−27.6837	−0.887042
$975$	21.4123	0.685742
$976$	−0.584661	−0.0187145
$977$	−46.5290	−1.48859	−0.744297	−	0.667848i	$-0.767215\pi$
$977$	−46.5290	−1.48859	−0.744297	+	0.667848i	$0.767215\pi$
$978$	36.9875	1.18273
$979$	19.9601	0.637928
$980$	13.3240	0.425619
$981$	61.9824	1.97895
$982$	−31.2593	−0.997523
$983$	−29.7410	−0.948592	−0.474296	−	0.880365i	$-0.657297\pi$
$983$	−29.7410	−0.948592	−0.474296	+	0.880365i	$0.657297\pi$
$984$	3.54215	0.112919
$985$	−49.7903	−1.58645
$986$	1.19994	0.0382138
$987$	53.6471	1.70761
$988$	−10.0463	−0.319615
$989$	7.17814	0.228252
$990$	46.7271	1.48509
$991$	35.3249	1.12213	0.561066	−	0.827771i	$-0.310391\pi$
$991$	35.3249	1.12213	0.561066	+	0.827771i	$0.310391\pi$
$992$	7.69663	0.244368
$993$	31.5538	1.00133
$994$	−13.5891	−0.431021
$995$	−17.3409	−0.549743
$996$	31.8281	1.00851
$997$	−14.2769	−0.452153	−0.226077	−	0.974110i	$-0.572590\pi$
$997$	−14.2769	−0.452153	−0.226077	+	0.974110i	$0.572590\pi$
$998$	17.8189	0.564047
$999$	1.83244	0.0579759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.7	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.7	✓	52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.51773 q^{3} +1.00000 q^{4} +3.18361 q^{5} -2.51773 q^{6} +3.34442 q^{7} +1.00000 q^{8} +3.33897 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.51773 q^{3} +1.00000 q^{4} +3.18361 q^{5} -2.51773 q^{6} +3.34442 q^{7} +1.00000 q^{8} +3.33897 q^{9} +3.18361 q^{10} +4.39578 q^{11} -2.51773 q^{12} -1.65607 q^{13} +3.34442 q^{14} -8.01549 q^{15} +1.00000 q^{16} +0.437905 q^{17} +3.33897 q^{18} +6.06633 q^{19} +3.18361 q^{20} -8.42036 q^{21} +4.39578 q^{22} -0.910588 q^{23} -2.51773 q^{24} +5.13540 q^{25} -1.65607 q^{26} -0.853442 q^{27} +3.34442 q^{28} +2.74018 q^{29} -8.01549 q^{30} +7.69663 q^{31} +1.00000 q^{32} -11.0674 q^{33} +0.437905 q^{34} +10.6474 q^{35} +3.33897 q^{36} -2.14712 q^{37} +6.06633 q^{38} +4.16955 q^{39} +3.18361 q^{40} -1.40688 q^{41} -8.42036 q^{42} -7.88297 q^{43} +4.39578 q^{44} +10.6300 q^{45} -0.910588 q^{46} -6.37112 q^{47} -2.51773 q^{48} +4.18517 q^{49} +5.13540 q^{50} -1.10253 q^{51} -1.65607 q^{52} +8.11955 q^{53} -0.853442 q^{54} +13.9945 q^{55} +3.34442 q^{56} -15.2734 q^{57} +2.74018 q^{58} -6.11888 q^{59} -8.01549 q^{60} -0.584661 q^{61} +7.69663 q^{62} +11.1669 q^{63} +1.00000 q^{64} -5.27230 q^{65} -11.0674 q^{66} -14.0603 q^{67} +0.437905 q^{68} +2.29262 q^{69} +10.6474 q^{70} -4.06322 q^{71} +3.33897 q^{72} +5.02776 q^{73} -2.14712 q^{74} -12.9296 q^{75} +6.06633 q^{76} +14.7013 q^{77} +4.16955 q^{78} +2.79445 q^{79} +3.18361 q^{80} -7.86818 q^{81} -1.40688 q^{82} -12.6416 q^{83} -8.42036 q^{84} +1.39412 q^{85} -7.88297 q^{86} -6.89904 q^{87} +4.39578 q^{88} +4.54074 q^{89} +10.6300 q^{90} -5.53861 q^{91} -0.910588 q^{92} -19.3780 q^{93} -6.37112 q^{94} +19.3128 q^{95} -2.51773 q^{96} -10.5365 q^{97} +4.18517 q^{98} +14.6774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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