LMFDB - Embedded newform 4019.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56992 q^{2} -0.512548 q^{3} +4.60446 q^{4} -4.01178 q^{5} +1.31721 q^{6} +0.174790 q^{7} -6.69325 q^{8} -2.73729 q^{9} +O(q^{10})$	\(q-2.56992 q^{2} -0.512548 q^{3} +4.60446 q^{4} -4.01178 q^{5} +1.31721 q^{6} +0.174790 q^{7} -6.69325 q^{8} -2.73729 q^{9} +10.3099 q^{10} -2.58944 q^{11} -2.36001 q^{12} +0.398828 q^{13} -0.449196 q^{14} +2.05623 q^{15} +7.99217 q^{16} +2.25702 q^{17} +7.03461 q^{18} +4.68238 q^{19} -18.4721 q^{20} -0.0895884 q^{21} +6.65465 q^{22} -6.94815 q^{23} +3.43062 q^{24} +11.0944 q^{25} -1.02496 q^{26} +2.94064 q^{27} +0.804815 q^{28} +0.630382 q^{29} -5.28434 q^{30} -1.13200 q^{31} -7.15268 q^{32} +1.32722 q^{33} -5.80034 q^{34} -0.701220 q^{35} -12.6038 q^{36} -5.41546 q^{37} -12.0333 q^{38} -0.204419 q^{39} +26.8519 q^{40} -0.895817 q^{41} +0.230235 q^{42} -7.33763 q^{43} -11.9230 q^{44} +10.9814 q^{45} +17.8562 q^{46} -5.63962 q^{47} -4.09637 q^{48} -6.96945 q^{49} -28.5116 q^{50} -1.15683 q^{51} +1.83639 q^{52} -4.48874 q^{53} -7.55720 q^{54} +10.3883 q^{55} -1.16991 q^{56} -2.39995 q^{57} -1.62003 q^{58} -1.04664 q^{59} +9.46784 q^{60} -12.2950 q^{61} +2.90914 q^{62} -0.478452 q^{63} +2.39745 q^{64} -1.60001 q^{65} -3.41083 q^{66} -0.160326 q^{67} +10.3923 q^{68} +3.56126 q^{69} +1.80207 q^{70} -1.67171 q^{71} +18.3214 q^{72} -4.74138 q^{73} +13.9173 q^{74} -5.68640 q^{75} +21.5598 q^{76} -0.452609 q^{77} +0.525339 q^{78} -11.5976 q^{79} -32.0628 q^{80} +6.70466 q^{81} +2.30217 q^{82} -13.2985 q^{83} -0.412507 q^{84} -9.05465 q^{85} +18.8571 q^{86} -0.323101 q^{87} +17.3318 q^{88} -5.97171 q^{89} -28.2213 q^{90} +0.0697113 q^{91} -31.9925 q^{92} +0.580204 q^{93} +14.4933 q^{94} -18.7847 q^{95} +3.66610 q^{96} +19.2705 q^{97} +17.9109 q^{98} +7.08807 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.56992	−1.81720	−0.908602	−	0.417662i	$-0.862849\pi$
$2$	−2.56992	−1.81720	−0.908602	+	0.417662i	$0.862849\pi$
$3$	−0.512548	−0.295920	−0.147960	−	0.988993i	$-0.547271\pi$
$3$	−0.512548	−0.295920	−0.147960	+	0.988993i	$0.547271\pi$
$4$	4.60446	2.30223
$5$	−4.01178	−1.79412	−0.897061	−	0.441906i	$-0.854302\pi$
$5$	−4.01178	−1.79412	−0.897061	+	0.441906i	$0.854302\pi$
$6$	1.31721	0.537747
$7$	0.174790	0.0660645	0.0330322	−	0.999454i	$-0.489484\pi$
$7$	0.174790	0.0660645	0.0330322	+	0.999454i	$0.489484\pi$
$8$	−6.69325	−2.36642
$9$	−2.73729	−0.912431
$10$	10.3099	3.26029
$11$	−2.58944	−0.780747	−0.390373	−	0.920657i	$-0.627654\pi$
$11$	−2.58944	−0.780747	−0.390373	+	0.920657i	$0.627654\pi$
$12$	−2.36001	−0.681276
$13$	0.398828	0.110615	0.0553075	−	0.998469i	$-0.482386\pi$
$13$	0.398828	0.110615	0.0553075	+	0.998469i	$0.482386\pi$
$14$	−0.449196	−0.120053
$15$	2.05623	0.530917
$16$	7.99217	1.99804
$17$	2.25702	0.547407	0.273703	−	0.961814i	$-0.411751\pi$
$17$	2.25702	0.547407	0.273703	+	0.961814i	$0.411751\pi$
$18$	7.03461	1.65807
$19$	4.68238	1.07421	0.537106	−	0.843515i	$-0.319518\pi$
$19$	4.68238	1.07421	0.537106	+	0.843515i	$0.319518\pi$
$20$	−18.4721	−4.13049
$21$	−0.0895884	−0.0195498
$22$	6.65465	1.41878
$23$	−6.94815	−1.44879	−0.724395	−	0.689385i	$-0.757881\pi$
$23$	−6.94815	−1.44879	−0.724395	+	0.689385i	$0.757881\pi$
$24$	3.43062	0.700272
$25$	11.0944	2.21888
$26$	−1.02496	−0.201010
$27$	2.94064	0.565927
$28$	0.804815	0.152096
$29$	0.630382	0.117059	0.0585295	−	0.998286i	$-0.481359\pi$
$29$	0.630382	0.117059	0.0585295	+	0.998286i	$0.481359\pi$
$30$	−5.28434	−0.964784
$31$	−1.13200	−0.203313	−0.101656	−	0.994820i	$-0.532414\pi$
$31$	−1.13200	−0.203313	−0.101656	+	0.994820i	$0.532414\pi$
$32$	−7.15268	−1.26443
$33$	1.32722	0.231039
$34$	−5.80034	−0.994750
$35$	−0.701220	−0.118528
$36$	−12.6038	−2.10063
$37$	−5.41546	−0.890296	−0.445148	−	0.895457i	$-0.646849\pi$
$37$	−5.41546	−0.890296	−0.445148	+	0.895457i	$0.646849\pi$
$38$	−12.0333	−1.95206
$39$	−0.204419	−0.0327332
$40$	26.8519	4.24565
$41$	−0.895817	−0.139903	−0.0699516	−	0.997550i	$-0.522284\pi$
$41$	−0.895817	−0.139903	−0.0699516	+	0.997550i	$0.522284\pi$
$42$	0.230235	0.0355260
$43$	−7.33763	−1.11898	−0.559489	−	0.828838i	$-0.689003\pi$
$43$	−7.33763	−1.11898	−0.559489	+	0.828838i	$0.689003\pi$
$44$	−11.9230	−1.79746
$45$	10.9814	1.63701
$46$	17.8562	2.63275
$47$	−5.63962	−0.822623	−0.411311	−	0.911495i	$-0.634929\pi$
$47$	−5.63962	−0.822623	−0.411311	+	0.911495i	$0.634929\pi$
$48$	−4.09637	−0.591260
$49$	−6.96945	−0.995635
$50$	−28.5116	−4.03215
$51$	−1.15683	−0.161989
$52$	1.83639	0.254662
$53$	−4.48874	−0.616576	−0.308288	−	0.951293i	$-0.599756\pi$
$53$	−4.48874	−0.616576	−0.308288	+	0.951293i	$0.599756\pi$
$54$	−7.55720	−1.02840
$55$	10.3883	1.40076
$56$	−1.16991	−0.156336
$57$	−2.39995	−0.317881
$58$	−1.62003	−0.212720
$59$	−1.04664	−0.136260	−0.0681302	−	0.997676i	$-0.521703\pi$
$59$	−1.04664	−0.136260	−0.0681302	+	0.997676i	$0.521703\pi$
$60$	9.46784	1.22229
$61$	−12.2950	−1.57422	−0.787108	−	0.616815i	$-0.788423\pi$
$61$	−12.2950	−1.57422	−0.787108	+	0.616815i	$0.788423\pi$
$62$	2.90914	0.369461
$63$	−0.478452	−0.0602793
$64$	2.39745	0.299682
$65$	−1.60001	−0.198457
$66$	−3.41083	−0.419844
$67$	−0.160326	−0.0195869	−0.00979345	−	0.999952i	$-0.503117\pi$
$67$	−0.160326	−0.0195869	−0.00979345	+	0.999952i	$0.503117\pi$
$68$	10.3923	1.26026
$69$	3.56126	0.428726
$70$	1.80207	0.215389
$71$	−1.67171	−0.198395	−0.0991977	−	0.995068i	$-0.531628\pi$
$71$	−1.67171	−0.198395	−0.0991977	+	0.995068i	$0.531628\pi$
$72$	18.3214	2.15920
$73$	−4.74138	−0.554937	−0.277468	−	0.960735i	$-0.589495\pi$
$73$	−4.74138	−0.554937	−0.277468	+	0.960735i	$0.589495\pi$
$74$	13.9173	1.61785
$75$	−5.68640	−0.656609
$76$	21.5598	2.47308
$77$	−0.452609	−0.0515796
$78$	0.525339	0.0594829
$79$	−11.5976	−1.30483	−0.652416	−	0.757861i	$-0.726245\pi$
$79$	−11.5976	−1.30483	−0.652416	+	0.757861i	$0.726245\pi$
$80$	−32.0628	−3.58473
$81$	6.70466	0.744962
$82$	2.30217	0.254233
$83$	−13.2985	−1.45970	−0.729848	−	0.683610i	$-0.760409\pi$
$83$	−13.2985	−1.45970	−0.729848	+	0.683610i	$0.760409\pi$
$84$	−0.412507	−0.0450082
$85$	−9.05465	−0.982115
$86$	18.8571	2.03341
$87$	−0.323101	−0.0346401
$88$	17.3318	1.84758
$89$	−5.97171	−0.633000	−0.316500	−	0.948592i	$-0.602508\pi$
$89$	−5.97171	−0.633000	−0.316500	+	0.948592i	$0.602508\pi$
$90$	−28.2213	−2.97479
$91$	0.0697113	0.00730773
$92$	−31.9925	−3.33545
$93$	0.580204	0.0601643
$94$	14.4933	1.49487
$95$	−18.7847	−1.92727
$96$	3.66610	0.374169
$97$	19.2705	1.95662	0.978309	−	0.207150i	$-0.0664189\pi$
$97$	19.2705	1.95662	0.978309	+	0.207150i	$0.0664189\pi$
$98$	17.9109	1.80927
$99$	7.08807	0.712378
$100$	51.0837	5.10837
$101$	11.8236	1.17649	0.588244	−	0.808683i	$-0.299819\pi$
$101$	11.8236	1.17649	0.588244	+	0.808683i	$0.299819\pi$
$102$	2.97295	0.294366
$103$	−11.3188	−1.11528	−0.557639	−	0.830084i	$-0.688293\pi$
$103$	−11.3188	−1.11528	−0.557639	+	0.830084i	$0.688293\pi$
$104$	−2.66946	−0.261762
$105$	0.359409	0.0350747
$106$	11.5357	1.12044
$107$	−8.45807	−0.817672	−0.408836	−	0.912608i	$-0.634065\pi$
$107$	−8.45807	−0.817672	−0.408836	+	0.912608i	$0.634065\pi$
$108$	13.5401	1.30289
$109$	4.42938	0.424258	0.212129	−	0.977242i	$-0.431960\pi$
$109$	4.42938	0.424258	0.212129	+	0.977242i	$0.431960\pi$
$110$	−26.6970	−2.54546
$111$	2.77569	0.263456
$112$	1.39695	0.132000
$113$	−3.80020	−0.357492	−0.178746	−	0.983895i	$-0.557204\pi$
$113$	−3.80020	−0.357492	−0.178746	+	0.983895i	$0.557204\pi$
$114$	6.16766	0.577654
$115$	27.8745	2.59931
$116$	2.90257	0.269497
$117$	−1.09171	−0.100929
$118$	2.68977	0.247613
$119$	0.394504	0.0361641
$120$	−13.7629	−1.25637
$121$	−4.29478	−0.390434
$122$	31.5972	2.86067
$123$	0.459150	0.0414001
$124$	−5.21224	−0.468073
$125$	−24.4493	−2.18681
$126$	1.22958	0.109540
$127$	19.0502	1.69043	0.845216	−	0.534425i	$-0.179472\pi$
$127$	19.0502	1.69043	0.845216	+	0.534425i	$0.179472\pi$
$128$	8.14411	0.719844
$129$	3.76089	0.331128
$130$	4.11189	0.360637
$131$	−13.8019	−1.20587	−0.602937	−	0.797789i	$-0.706003\pi$
$131$	−13.8019	−1.20587	−0.602937	+	0.797789i	$0.706003\pi$
$132$	6.11112	0.531904
$133$	0.818434	0.0709672
$134$	0.412024	0.0355934
$135$	−11.7972	−1.01534
$136$	−15.1068	−1.29540
$137$	−14.0926	−1.20401	−0.602005	−	0.798492i	$-0.705631\pi$
$137$	−14.0926	−1.20401	−0.602005	+	0.798492i	$0.705631\pi$
$138$	−9.15215	−0.779083
$139$	−10.8242	−0.918100	−0.459050	−	0.888410i	$-0.651810\pi$
$139$	−10.8242	−0.918100	−0.459050	+	0.888410i	$0.651810\pi$
$140$	−3.22874	−0.272878
$141$	2.89058	0.243431
$142$	4.29615	0.360525
$143$	−1.03274	−0.0863624
$144$	−21.8769	−1.82308
$145$	−2.52895	−0.210018
$146$	12.1849	1.00843
$147$	3.57218	0.294628
$148$	−24.9353	−2.04967
$149$	21.9810	1.80076	0.900379	−	0.435107i	$-0.143289\pi$
$149$	21.9810	1.80076	0.900379	+	0.435107i	$0.143289\pi$
$150$	14.6136	1.19319
$151$	8.92831	0.726576	0.363288	−	0.931677i	$-0.381654\pi$
$151$	8.92831	0.726576	0.363288	+	0.931677i	$0.381654\pi$
$152$	−31.3404	−2.54204
$153$	−6.17812	−0.499471
$154$	1.16317	0.0937307
$155$	4.54133	0.364768
$156$	−0.941239	−0.0753594
$157$	−18.2329	−1.45514	−0.727572	−	0.686032i	$-0.759351\pi$
$157$	−18.2329	−1.45514	−0.727572	+	0.686032i	$0.759351\pi$
$158$	29.8049	2.37115
$159$	2.30070	0.182457
$160$	28.6950	2.26854
$161$	−1.21447	−0.0957136
$162$	−17.2304	−1.35375
$163$	10.7884	0.845013	0.422507	−	0.906360i	$-0.361150\pi$
$163$	10.7884	0.845013	0.422507	+	0.906360i	$0.361150\pi$
$164$	−4.12476	−0.322090
$165$	−5.32450	−0.414512
$166$	34.1759	2.65256
$167$	−9.11401	−0.705263	−0.352632	−	0.935762i	$-0.614713\pi$
$167$	−9.11401	−0.705263	−0.352632	+	0.935762i	$0.614713\pi$
$168$	0.599638	0.0462631
$169$	−12.8409	−0.987764
$170$	23.2697	1.78470
$171$	−12.8170	−0.980144
$172$	−33.7859	−2.57615
$173$	17.8845	1.35974	0.679868	−	0.733334i	$-0.262037\pi$
$173$	17.8845	1.35974	0.679868	+	0.733334i	$0.262037\pi$
$174$	0.830343	0.0629482
$175$	1.93919	0.146589
$176$	−20.6953	−1.55996
$177$	0.536452	0.0403222
$178$	15.3468	1.15029
$179$	8.01910	0.599376	0.299688	−	0.954037i	$-0.403117\pi$
$179$	8.01910	0.599376	0.299688	+	0.954037i	$0.403117\pi$
$180$	50.5636	3.76879
$181$	13.0832	0.972465	0.486232	−	0.873830i	$-0.338371\pi$
$181$	13.0832	0.972465	0.486232	+	0.873830i	$0.338371\pi$
$182$	−0.179152	−0.0132796
$183$	6.30179	0.465842
$184$	46.5058	3.42845
$185$	21.7256	1.59730
$186$	−1.49107	−0.109331
$187$	−5.84442	−0.427386
$188$	−25.9674	−1.89387
$189$	0.513995	0.0373876
$190$	48.2750	3.50224
$191$	13.0640	0.945278	0.472639	−	0.881256i	$-0.343301\pi$
$191$	13.0640	0.945278	0.472639	+	0.881256i	$0.343301\pi$
$192$	−1.22881	−0.0886818
$193$	−24.3629	−1.75368	−0.876840	−	0.480782i	$-0.840353\pi$
$193$	−24.3629	−1.75368	−0.876840	+	0.480782i	$0.840353\pi$
$194$	−49.5234	−3.55558
$195$	0.820083	0.0587274
$196$	−32.0906	−2.29218
$197$	−4.09035	−0.291426	−0.145713	−	0.989327i	$-0.546548\pi$
$197$	−4.09035	−0.291426	−0.145713	+	0.989327i	$0.546548\pi$
$198$	−18.2157	−1.29454
$199$	−1.09274	−0.0774623	−0.0387312	−	0.999250i	$-0.512332\pi$
$199$	−1.09274	−0.0774623	−0.0387312	+	0.999250i	$0.512332\pi$
$200$	−74.2575	−5.25080
$201$	0.0821747	0.00579616
$202$	−30.3856	−2.13792
$203$	0.110185	0.00773344
$204$	−5.32658	−0.372935
$205$	3.59382	0.251003
$206$	29.0884	2.02669
$207$	19.0191	1.32192
$208$	3.18750	0.221013
$209$	−12.1248	−0.838687
$210$	−0.923651	−0.0637379
$211$	−0.793960	−0.0546585	−0.0273292	−	0.999626i	$-0.508700\pi$
$211$	−0.793960	−0.0546585	−0.0273292	+	0.999626i	$0.508700\pi$
$212$	−20.6682	−1.41950
$213$	0.856831	0.0587091
$214$	21.7365	1.48588
$215$	29.4370	2.00758
$216$	−19.6825	−1.33922
$217$	−0.197862	−0.0134318
$218$	−11.3831	−0.770963
$219$	2.43019	0.164217
$220$	47.8325	3.22486
$221$	0.900162	0.0605514
$222$	−7.13328	−0.478754
$223$	12.6126	0.844604	0.422302	−	0.906455i	$-0.361222\pi$
$223$	12.6126	0.844604	0.422302	+	0.906455i	$0.361222\pi$
$224$	−1.25022	−0.0835337
$225$	−30.3686	−2.02457
$226$	9.76618	0.649637
$227$	−0.0602946	−0.00400189	−0.00200095	−	0.999998i	$-0.500637\pi$
$227$	−0.0602946	−0.00400189	−0.00200095	+	0.999998i	$0.500637\pi$
$228$	−11.0505	−0.731835
$229$	−12.6478	−0.835790	−0.417895	−	0.908495i	$-0.637232\pi$
$229$	−12.6478	−0.835790	−0.417895	+	0.908495i	$0.637232\pi$
$230$	−71.6350	−4.72347
$231$	0.231984	0.0152634
$232$	−4.21931	−0.277011
$233$	−20.1291	−1.31870	−0.659349	−	0.751837i	$-0.729168\pi$
$233$	−20.1291	−1.31870	−0.659349	+	0.751837i	$0.729168\pi$
$234$	2.80560	0.183408
$235$	22.6249	1.47589
$236$	−4.81920	−0.313703
$237$	5.94433	0.386126
$238$	−1.01384	−0.0657176
$239$	1.78805	0.115659	0.0578296	−	0.998326i	$-0.481582\pi$
$239$	1.78805	0.115659	0.0578296	+	0.998326i	$0.481582\pi$
$240$	16.4337	1.06079
$241$	−5.20792	−0.335471	−0.167736	−	0.985832i	$-0.553646\pi$
$241$	−5.20792	−0.335471	−0.167736	+	0.985832i	$0.553646\pi$
$242$	11.0372	0.709499
$243$	−12.2584	−0.786376
$244$	−56.6120	−3.62421
$245$	27.9599	1.78629
$246$	−1.17998	−0.0752325
$247$	1.86747	0.118824
$248$	7.57675	0.481124
$249$	6.81610	0.431953
$250$	62.8326	3.97388
$251$	−2.36503	−0.149279	−0.0746397	−	0.997211i	$-0.523781\pi$
$251$	−2.36503	−0.149279	−0.0746397	+	0.997211i	$0.523781\pi$
$252$	−2.20302	−0.138777
$253$	17.9919	1.13114
$254$	−48.9574	−3.07186
$255$	4.64095	0.290627
$256$	−25.7246	−1.60779
$257$	−16.6165	−1.03651	−0.518254	−	0.855227i	$-0.673418\pi$
$257$	−16.6165	−1.03651	−0.518254	+	0.855227i	$0.673418\pi$
$258$	−9.66517	−0.601727
$259$	−0.946569	−0.0588170
$260$	−7.36720	−0.456894
$261$	−1.72554	−0.106808
$262$	35.4696	2.19132
$263$	2.31251	0.142595	0.0712976	−	0.997455i	$-0.477286\pi$
$263$	2.31251	0.142595	0.0712976	+	0.997455i	$0.477286\pi$
$264$	−8.88339	−0.546735
$265$	18.0078	1.10621
$266$	−2.10331	−0.128962
$267$	3.06079	0.187317
$268$	−0.738214	−0.0450936
$269$	21.4277	1.30647	0.653235	−	0.757155i	$-0.273411\pi$
$269$	21.4277	1.30647	0.653235	+	0.757155i	$0.273411\pi$
$270$	30.3178	1.84508
$271$	−7.55774	−0.459100	−0.229550	−	0.973297i	$-0.573725\pi$
$271$	−7.55774	−0.459100	−0.229550	+	0.973297i	$0.573725\pi$
$272$	18.0384	1.09374
$273$	−0.0357304	−0.00216250
$274$	36.2167	2.18793
$275$	−28.7283	−1.73238
$276$	16.3977	0.987027
$277$	20.5725	1.23608	0.618041	−	0.786146i	$-0.287927\pi$
$277$	20.5725	1.23608	0.618041	+	0.786146i	$0.287927\pi$
$278$	27.8174	1.66838
$279$	3.09861	0.185509
$280$	4.69344	0.280487
$281$	5.75989	0.343606	0.171803	−	0.985131i	$-0.445041\pi$
$281$	5.75989	0.343606	0.171803	+	0.985131i	$0.445041\pi$
$282$	−7.42854	−0.442363
$283$	−7.06564	−0.420009	−0.210004	−	0.977700i	$-0.567348\pi$
$283$	−7.06564	−0.420009	−0.210004	+	0.977700i	$0.567348\pi$
$284$	−7.69732	−0.456752
$285$	9.62805	0.570317
$286$	2.65406	0.156938
$287$	−0.156580	−0.00924263
$288$	19.5790	1.15370
$289$	−11.9059	−0.700346
$290$	6.49920	0.381646
$291$	−9.87704	−0.579002
$292$	−21.8315	−1.27759
$293$	−18.5086	−1.08129	−0.540643	−	0.841252i	$-0.681819\pi$
$293$	−18.5086	−1.08129	−0.540643	+	0.841252i	$0.681819\pi$
$294$	−9.18020	−0.535400
$295$	4.19887	0.244468
$296$	36.2471	2.10682
$297$	−7.61463	−0.441845
$298$	−56.4894	−3.27234
$299$	−2.77112	−0.160258
$300$	−26.1828	−1.51167
$301$	−1.28255	−0.0739247
$302$	−22.9450	−1.32034
$303$	−6.06015	−0.348146
$304$	37.4223	2.14632
$305$	49.3249	2.82434
$306$	15.8772	0.907641
$307$	−27.4308	−1.56556	−0.782779	−	0.622300i	$-0.786199\pi$
$307$	−27.4308	−1.56556	−0.782779	+	0.622300i	$0.786199\pi$
$308$	−2.08402	−0.118748
$309$	5.80145	0.330033
$310$	−11.6708	−0.662858
$311$	27.2558	1.54554	0.772768	−	0.634688i	$-0.218872\pi$
$311$	27.2558	1.54554	0.772768	+	0.634688i	$0.218872\pi$
$312$	1.36823	0.0774606
$313$	−20.6383	−1.16655	−0.583273	−	0.812276i	$-0.698228\pi$
$313$	−20.6383	−1.16655	−0.583273	+	0.812276i	$0.698228\pi$
$314$	46.8570	2.64429
$315$	1.91944	0.108148
$316$	−53.4008	−3.00403
$317$	32.0421	1.79966	0.899832	−	0.436236i	$-0.143689\pi$
$317$	32.0421	1.79966	0.899832	+	0.436236i	$0.143689\pi$
$318$	−5.91259	−0.331562
$319$	−1.63234	−0.0913935
$320$	−9.61806	−0.537666
$321$	4.33517	0.241965
$322$	3.12108	0.173931
$323$	10.5682	0.588031
$324$	30.8714	1.71508
$325$	4.42475	0.245441
$326$	−27.7253	−1.53556
$327$	−2.27027	−0.125546
$328$	5.99593	0.331070
$329$	−0.985750	−0.0543461
$330$	13.6835	0.753252
$331$	4.50548	0.247644	0.123822	−	0.992304i	$-0.460485\pi$
$331$	4.50548	0.247644	0.123822	+	0.992304i	$0.460485\pi$
$332$	−61.2323	−3.36056
$333$	14.8237	0.812334
$334$	23.4222	1.28161
$335$	0.643192	0.0351413
$336$	−0.716005	−0.0390613
$337$	19.3280	1.05286	0.526431	−	0.850218i	$-0.323530\pi$
$337$	19.3280	1.05286	0.526431	+	0.850218i	$0.323530\pi$
$338$	33.0001	1.79497
$339$	1.94778	0.105789
$340$	−41.6918	−2.26106
$341$	2.93125	0.158736
$342$	32.9387	1.78112
$343$	−2.44172	−0.131841
$344$	49.1126	2.64798
$345$	−14.2870	−0.769187
$346$	−45.9617	−2.47092
$347$	−1.13051	−0.0606888	−0.0303444	−	0.999540i	$-0.509660\pi$
$347$	−1.13051	−0.0606888	−0.0303444	+	0.999540i	$0.509660\pi$
$348$	−1.48771	−0.0797496
$349$	4.63733	0.248230	0.124115	−	0.992268i	$-0.460391\pi$
$349$	4.63733	0.248230	0.124115	+	0.992268i	$0.460391\pi$
$350$	−4.98355	−0.266382
$351$	1.17281	0.0626000
$352$	18.5215	0.987198
$353$	−31.6375	−1.68390	−0.841948	−	0.539559i	$-0.818591\pi$
$353$	−31.6375	−1.68390	−0.841948	+	0.539559i	$0.818591\pi$
$354$	−1.37864	−0.0732736
$355$	6.70653	0.355945
$356$	−27.4965	−1.45731
$357$	−0.202202	−0.0107017
$358$	−20.6084	−1.08919
$359$	−31.5339	−1.66429	−0.832147	−	0.554555i	$-0.812888\pi$
$359$	−31.5339	−1.66429	−0.832147	+	0.554555i	$0.812888\pi$
$360$	−73.5014	−3.87387
$361$	2.92467	0.153930
$362$	−33.6227	−1.76717
$363$	2.20128	0.115537
$364$	0.320983	0.0168241
$365$	19.0214	0.995624
$366$	−16.1951	−0.846530
$367$	3.92030	0.204638	0.102319	−	0.994752i	$-0.467374\pi$
$367$	3.92030	0.204638	0.102319	+	0.994752i	$0.467374\pi$
$368$	−55.5308	−2.89474
$369$	2.45212	0.127652
$370$	−55.8331	−2.90262
$371$	−0.784587	−0.0407337
$372$	2.67153	0.138512
$373$	0.304601	0.0157717	0.00788583	−	0.999969i	$-0.497490\pi$
$373$	0.304601	0.0157717	0.00788583	+	0.999969i	$0.497490\pi$
$374$	15.0197	0.776648
$375$	12.5314	0.647121
$376$	37.7474	1.94667
$377$	0.251414	0.0129485
$378$	−1.32092	−0.0679410
$379$	11.4602	0.588673	0.294336	−	0.955702i	$-0.404901\pi$
$379$	11.4602	0.588673	0.294336	+	0.955702i	$0.404901\pi$
$380$	−86.4934	−4.43702
$381$	−9.76415	−0.500232
$382$	−33.5734	−1.71776
$383$	−4.60659	−0.235386	−0.117693	−	0.993050i	$-0.537550\pi$
$383$	−4.60659	−0.235386	−0.117693	+	0.993050i	$0.537550\pi$
$384$	−4.17425	−0.213016
$385$	1.81577	0.0925402
$386$	62.6106	3.18680
$387$	20.0853	1.02099
$388$	88.7301	4.50459
$389$	25.8731	1.31182	0.655909	−	0.754840i	$-0.272285\pi$
$389$	25.8731	1.31182	0.655909	+	0.754840i	$0.272285\pi$
$390$	−2.10754	−0.106720
$391$	−15.6821	−0.793078
$392$	46.6483	2.35609
$393$	7.07412	0.356842
$394$	10.5119	0.529580
$395$	46.5270	2.34103
$396$	32.6368	1.64006
$397$	−14.3705	−0.721234	−0.360617	−	0.932714i	$-0.617434\pi$
$397$	−14.3705	−0.721234	−0.360617	+	0.932714i	$0.617434\pi$
$398$	2.80825	0.140765
$399$	−0.419487	−0.0210006
$400$	88.6681	4.43340
$401$	31.0413	1.55013	0.775065	−	0.631882i	$-0.217717\pi$
$401$	31.0413	1.55013	0.775065	+	0.631882i	$0.217717\pi$
$402$	−0.211182	−0.0105328
$403$	−0.451473	−0.0224895
$404$	54.4412	2.70855
$405$	−26.8976	−1.33655
$406$	−0.283165	−0.0140532
$407$	14.0230	0.695096
$408$	7.74295	0.383333
$409$	−0.951862	−0.0470666	−0.0235333	−	0.999723i	$-0.507492\pi$
$409$	−0.951862	−0.0470666	−0.0235333	+	0.999723i	$0.507492\pi$
$410$	−9.23582	−0.456125
$411$	7.22313	0.356291
$412$	−52.1172	−2.56763
$413$	−0.182942	−0.00900197
$414$	−48.8776	−2.40220
$415$	53.3505	2.61887
$416$	−2.85269	−0.139865
$417$	5.54794	0.271684
$418$	31.1596	1.52407
$419$	22.8013	1.11391	0.556957	−	0.830541i	$-0.311969\pi$
$419$	22.8013	1.11391	0.556957	+	0.830541i	$0.311969\pi$
$420$	1.65489	0.0807502
$421$	20.6793	1.00785	0.503924	−	0.863748i	$-0.331889\pi$
$421$	20.6793	1.00785	0.503924	+	0.863748i	$0.331889\pi$
$422$	2.04041	0.0993256
$423$	15.4373	0.750587
$424$	30.0443	1.45908
$425$	25.0402	1.21463
$426$	−2.20198	−0.106686
$427$	−2.14905	−0.104000
$428$	−38.9449	−1.88247
$429$	0.529331	0.0255563
$430$	−75.6505	−3.64819
$431$	30.6022	1.47405	0.737027	−	0.675863i	$-0.236229\pi$
$431$	30.6022	1.47405	0.737027	+	0.675863i	$0.236229\pi$
$432$	23.5021	1.13074
$433$	−10.9444	−0.525953	−0.262976	−	0.964802i	$-0.584704\pi$
$433$	−10.9444	−0.525953	−0.262976	+	0.964802i	$0.584704\pi$
$434$	0.508489	0.0244082
$435$	1.29621	0.0621486
$436$	20.3949	0.976739
$437$	−32.5339	−1.55631
$438$	−6.24538	−0.298416
$439$	17.6597	0.842852	0.421426	−	0.906863i	$-0.361530\pi$
$439$	17.6597	0.842852	0.421426	+	0.906863i	$0.361530\pi$
$440$	−69.5314	−3.31478
$441$	19.0774	0.908449
$442$	−2.31334	−0.110034
$443$	18.6611	0.886615	0.443307	−	0.896370i	$-0.353805\pi$
$443$	18.6611	0.886615	0.443307	+	0.896370i	$0.353805\pi$
$444$	12.7805	0.606538
$445$	23.9572	1.13568
$446$	−32.4134	−1.53482
$447$	−11.2663	−0.532880
$448$	0.419051	0.0197983
$449$	24.8067	1.17070	0.585351	−	0.810780i	$-0.300957\pi$
$449$	24.8067	1.17070	0.585351	+	0.810780i	$0.300957\pi$
$450$	78.0447	3.67906
$451$	2.31967	0.109229
$452$	−17.4979	−0.823030
$453$	−4.57619	−0.215008
$454$	0.154952	0.00727226
$455$	−0.279666	−0.0131110
$456$	16.0634	0.752240
$457$	−15.3687	−0.718915	−0.359458	−	0.933161i	$-0.617038\pi$
$457$	−15.3687	−0.718915	−0.359458	+	0.933161i	$0.617038\pi$
$458$	32.5038	1.51880
$459$	6.63707	0.309792
$460$	128.347	5.98421
$461$	4.68495	0.218200	0.109100	−	0.994031i	$-0.465203\pi$
$461$	4.68495	0.218200	0.109100	+	0.994031i	$0.465203\pi$
$462$	−0.596180	−0.0277368
$463$	−1.49220	−0.0693483	−0.0346741	−	0.999399i	$-0.511039\pi$
$463$	−1.49220	−0.0693483	−0.0346741	+	0.999399i	$0.511039\pi$
$464$	5.03812	0.233889
$465$	−2.32765	−0.107942
$466$	51.7300	2.39634
$467$	−19.2068	−0.888785	−0.444393	−	0.895832i	$-0.646580\pi$
$467$	−19.2068	−0.888785	−0.444393	+	0.895832i	$0.646580\pi$
$468$	−5.02674	−0.232361
$469$	−0.0280234	−0.00129400
$470$	−58.1441	−2.68199
$471$	9.34524	0.430606
$472$	7.00540	0.322450
$473$	19.0004	0.873639
$474$	−15.2764	−0.701670
$475$	51.9481	2.38354
$476$	1.81648	0.0832582
$477$	12.2870	0.562583
$478$	−4.59513	−0.210176
$479$	3.24121	0.148095	0.0740474	−	0.997255i	$-0.476408\pi$
$479$	3.24121	0.148095	0.0740474	+	0.997255i	$0.476408\pi$
$480$	−14.7076	−0.671305
$481$	−2.15984	−0.0984802
$482$	13.3839	0.609620
$483$	0.622474	0.0283235
$484$	−19.7751	−0.898870
$485$	−77.3088	−3.51041
$486$	31.5030	1.42901
$487$	27.7722	1.25848	0.629240	−	0.777211i	$-0.283366\pi$
$487$	27.7722	1.25848	0.629240	+	0.777211i	$0.283366\pi$
$488$	82.2937	3.72526
$489$	−5.52958	−0.250056
$490$	−71.8546	−3.24606
$491$	6.44648	0.290925	0.145463	−	0.989364i	$-0.453533\pi$
$491$	6.44648	0.290925	0.145463	+	0.989364i	$0.453533\pi$
$492$	2.11414	0.0953127
$493$	1.42278	0.0640789
$494$	−4.79923	−0.215927
$495$	−28.4358	−1.27809
$496$	−9.04711	−0.406227
$497$	−0.292198	−0.0131069
$498$	−17.5168	−0.784947
$499$	27.7902	1.24406	0.622031	−	0.782993i	$-0.286308\pi$
$499$	27.7902	1.24406	0.622031	+	0.782993i	$0.286308\pi$
$500$	−112.576	−5.03455
$501$	4.67137	0.208701
$502$	6.07793	0.271271
$503$	−10.2084	−0.455171	−0.227586	−	0.973758i	$-0.573083\pi$
$503$	−10.2084	−0.455171	−0.227586	+	0.973758i	$0.573083\pi$
$504$	3.20240	0.142646
$505$	−47.4335	−2.11076
$506$	−46.2376	−2.05551
$507$	6.58160	0.292299
$508$	87.7160	3.89177
$509$	12.3770	0.548603	0.274301	−	0.961644i	$-0.411553\pi$
$509$	12.3770	0.548603	0.274301	+	0.961644i	$0.411553\pi$
$510$	−11.9268	−0.528129
$511$	−0.828747	−0.0366616
$512$	49.8218	2.20183
$513$	13.7692	0.607925
$514$	42.7030	1.88355
$515$	45.4087	2.00094
$516$	17.3169	0.762334
$517$	14.6035	0.642260
$518$	2.43260	0.106882
$519$	−9.16669	−0.402373
$520$	10.7093	0.469633
$521$	7.79555	0.341529	0.170765	−	0.985312i	$-0.445376\pi$
$521$	7.79555	0.341529	0.170765	+	0.985312i	$0.445376\pi$
$522$	4.43450	0.194093
$523$	24.1473	1.05589	0.527944	−	0.849279i	$-0.322963\pi$
$523$	24.1473	1.05589	0.527944	+	0.849279i	$0.322963\pi$
$524$	−63.5502	−2.77620
$525$	−0.993928	−0.0433786
$526$	−5.94295	−0.259125
$527$	−2.55494	−0.111295
$528$	10.6073	0.461625
$529$	25.2768	1.09899
$530$	−46.2786	−2.01021
$531$	2.86495	0.124328
$532$	3.76845	0.163383
$533$	−0.357277	−0.0154754
$534$	−7.86598	−0.340394
$535$	33.9319	1.46700
$536$	1.07310	0.0463509
$537$	−4.11018	−0.177367
$538$	−55.0674	−2.37412
$539$	18.0470	0.777339
$540$	−54.3198	−2.33755
$541$	15.3824	0.661341	0.330670	−	0.943746i	$-0.392725\pi$
$541$	15.3824	0.661341	0.330670	+	0.943746i	$0.392725\pi$
$542$	19.4227	0.834278
$543$	−6.70576	−0.287772
$544$	−16.1437	−0.692156
$545$	−17.7697	−0.761170
$546$	0.0918241	0.00392971
$547$	−19.1251	−0.817732	−0.408866	−	0.912594i	$-0.634076\pi$
$547$	−19.1251	−0.817732	−0.408866	+	0.912594i	$0.634076\pi$
$548$	−64.8888	−2.77191
$549$	33.6551	1.43636
$550$	73.8292	3.14809
$551$	2.95169	0.125746
$552$	−23.8364	−1.01455
$553$	−2.02715	−0.0862031
$554$	−52.8696	−2.24621
$555$	−11.1354	−0.472673
$556$	−49.8398	−2.11368
$557$	−12.1660	−0.515491	−0.257745	−	0.966213i	$-0.582980\pi$
$557$	−12.1660	−0.515491	−0.257745	+	0.966213i	$0.582980\pi$
$558$	−7.96317	−0.337108
$559$	−2.92646	−0.123776
$560$	−5.60426	−0.236823
$561$	2.99555	0.126472
$562$	−14.8024	−0.624403
$563$	25.6074	1.07922	0.539611	−	0.841915i	$-0.318571\pi$
$563$	25.6074	1.07922	0.539611	+	0.841915i	$0.318571\pi$
$564$	13.3096	0.560434
$565$	15.2455	0.641385
$566$	18.1581	0.763242
$567$	1.17191	0.0492155
$568$	11.1892	0.469487
$569$	−25.5284	−1.07021	−0.535103	−	0.844787i	$-0.679727\pi$
$569$	−25.5284	−1.07021	−0.535103	+	0.844787i	$0.679727\pi$
$570$	−24.7433	−1.03638
$571$	−14.7060	−0.615428	−0.307714	−	0.951479i	$-0.599564\pi$
$571$	−14.7060	−0.615428	−0.307714	+	0.951479i	$0.599564\pi$
$572$	−4.75523	−0.198826
$573$	−6.69593	−0.279727
$574$	0.402397	0.0167957
$575$	−77.0854	−3.21469
$576$	−6.56254	−0.273439
$577$	47.4299	1.97453	0.987266	−	0.159076i	$-0.0508514\pi$
$577$	47.4299	1.97453	0.987266	+	0.159076i	$0.0508514\pi$
$578$	30.5971	1.27267
$579$	12.4872	0.518949
$580$	−11.6445	−0.483511
$581$	−2.32444	−0.0964340
$582$	25.3832	1.05217
$583$	11.6233	0.481389
$584$	31.7353	1.31321
$585$	4.37970	0.181078
$586$	47.5656	1.96492
$587$	−7.17019	−0.295945	−0.147973	−	0.988991i	$-0.547275\pi$
$587$	−7.17019	−0.295945	−0.147973	+	0.988991i	$0.547275\pi$
$588$	16.4480	0.678303
$589$	−5.30044	−0.218401
$590$	−10.7907	−0.444248
$591$	2.09650	0.0862386
$592$	−43.2813	−1.77885
$593$	−23.6639	−0.971761	−0.485881	−	0.874025i	$-0.661501\pi$
$593$	−23.6639	−0.971761	−0.485881	+	0.874025i	$0.661501\pi$
$594$	19.5689	0.802924
$595$	−1.58266	−0.0648829
$596$	101.211	4.14576
$597$	0.560083	0.0229227
$598$	7.12155	0.291222
$599$	−23.6792	−0.967508	−0.483754	−	0.875204i	$-0.660727\pi$
$599$	−23.6792	−0.967508	−0.483754	+	0.875204i	$0.660727\pi$
$600$	38.0605	1.55382
$601$	−22.2412	−0.907236	−0.453618	−	0.891196i	$-0.649867\pi$
$601$	−22.2412	−0.907236	−0.453618	+	0.891196i	$0.649867\pi$
$602$	3.29603	0.134336
$603$	0.438859	0.0178717
$604$	41.1101	1.67275
$605$	17.2297	0.700487
$606$	15.5741	0.632653
$607$	−18.0900	−0.734251	−0.367126	−	0.930171i	$-0.619658\pi$
$607$	−18.0900	−0.734251	−0.367126	+	0.930171i	$0.619658\pi$
$608$	−33.4916	−1.35826
$609$	−0.0564749	−0.00228848
$610$	−126.761	−5.13240
$611$	−2.24924	−0.0909945
$612$	−28.4469	−1.14990
$613$	−2.00063	−0.0808047	−0.0404024	−	0.999183i	$-0.512864\pi$
$613$	−2.00063	−0.0808047	−0.0404024	+	0.999183i	$0.512864\pi$
$614$	70.4948	2.84494
$615$	−1.84201	−0.0742769
$616$	3.02943	0.122059
$617$	8.84164	0.355951	0.177975	−	0.984035i	$-0.443045\pi$
$617$	8.84164	0.355951	0.177975	+	0.984035i	$0.443045\pi$
$618$	−14.9092	−0.599737
$619$	0.000980310 0	3.94020e−5 0	1.97010e−5	−	1.00000i	$-0.499994\pi$
$619$	0.000980310 0	3.94020e−5 0	1.97010e−5		1.00000i	$0.499994\pi$
$620$	20.9104	0.839781
$621$	−20.4320	−0.819909
$622$	−70.0452	−2.80856
$623$	−1.04380	−0.0418188
$624$	−1.63375	−0.0654023
$625$	42.6133	1.70453
$626$	53.0387	2.11985
$627$	6.21453	0.248184
$628$	−83.9527	−3.35008
$629$	−12.2228	−0.487354
$630$	−4.93281	−0.196528
$631$	9.38662	0.373676	0.186838	−	0.982391i	$-0.440176\pi$
$631$	9.38662	0.373676	0.186838	+	0.982391i	$0.440176\pi$
$632$	77.6257	3.08778
$633$	0.406943	0.0161745
$634$	−82.3455	−3.27036
$635$	−76.4252	−3.03284
$636$	10.5935	0.420058
$637$	−2.77961	−0.110132
$638$	4.19498	0.166081
$639$	4.57596	0.181022
$640$	−32.6724	−1.29149
$641$	−37.6904	−1.48868	−0.744341	−	0.667800i	$-0.767236\pi$
$641$	−37.6904	−1.48868	−0.744341	+	0.667800i	$0.767236\pi$
$642$	−11.1410	−0.439701
$643$	6.82903	0.269311	0.134655	−	0.990892i	$-0.457007\pi$
$643$	6.82903	0.269311	0.134655	+	0.990892i	$0.457007\pi$
$644$	−5.59198	−0.220355
$645$	−15.0879	−0.594084
$646$	−27.1594	−1.06857
$647$	−6.28402	−0.247050	−0.123525	−	0.992341i	$-0.539420\pi$
$647$	−6.28402	−0.247050	−0.123525	+	0.992341i	$0.539420\pi$
$648$	−44.8760	−1.76290
$649$	2.71021	0.106385
$650$	−11.3712	−0.446017
$651$	0.101414	0.00397472
$652$	49.6748	1.94542
$653$	−17.1976	−0.672995	−0.336497	−	0.941684i	$-0.609242\pi$
$653$	−17.1976	−0.672995	−0.336497	+	0.941684i	$0.609242\pi$
$654$	5.83440	0.228143
$655$	55.3700	2.16349
$656$	−7.15952	−0.279532
$657$	12.9786	0.506342
$658$	2.53329	0.0987581
$659$	−4.88317	−0.190221	−0.0951106	−	0.995467i	$-0.530320\pi$
$659$	−4.88317	−0.190221	−0.0951106	+	0.995467i	$0.530320\pi$
$660$	−24.5165	−0.954302
$661$	−34.3667	−1.33671	−0.668355	−	0.743843i	$-0.733001\pi$
$661$	−34.3667	−1.33671	−0.668355	+	0.743843i	$0.733001\pi$
$662$	−11.5787	−0.450019
$663$	−0.461376	−0.0179184
$664$	89.0099	3.45426
$665$	−3.28338	−0.127324
$666$	−38.0957	−1.47618
$667$	−4.37999	−0.169594
$668$	−41.9651	−1.62368
$669$	−6.46458	−0.249935
$670$	−1.65295	−0.0638589
$671$	31.8373	1.22906
$672$	0.640797	0.0247193
$673$	15.1142	0.582611	0.291305	−	0.956630i	$-0.405910\pi$
$673$	15.1142	0.582611	0.291305	+	0.956630i	$0.405910\pi$
$674$	−49.6713	−1.91327
$675$	32.6246	1.25572
$676$	−59.1256	−2.27406
$677$	−7.83617	−0.301169	−0.150584	−	0.988597i	$-0.548115\pi$
$677$	−7.83617	−0.301169	−0.150584	+	0.988597i	$0.548115\pi$
$678$	−5.00564	−0.192240
$679$	3.36829	0.129263
$680$	60.6051	2.32410
$681$	0.0309039	0.00118424
$682$	−7.53305	−0.288456
$683$	29.5937	1.13237	0.566186	−	0.824278i	$-0.308419\pi$
$683$	29.5937	1.13237	0.566186	+	0.824278i	$0.308419\pi$
$684$	−59.0156	−2.25652
$685$	56.5363	2.16014
$686$	6.27502	0.239581
$687$	6.48261	0.247327
$688$	−58.6436	−2.23577
$689$	−1.79024	−0.0682026
$690$	36.7164	1.39777
$691$	9.26567	0.352483	0.176241	−	0.984347i	$-0.443606\pi$
$691$	9.26567	0.352483	0.176241	+	0.984347i	$0.443606\pi$
$692$	82.3487	3.13043
$693$	1.23893	0.0470629
$694$	2.90531	0.110284
$695$	43.4245	1.64718
$696$	2.16260	0.0819731
$697$	−2.02187	−0.0765839
$698$	−11.9175	−0.451085
$699$	10.3171	0.390229
$700$	8.92892	0.337482
$701$	−38.6769	−1.46081	−0.730403	−	0.683016i	$-0.760668\pi$
$701$	−38.6769	−1.46081	−0.730403	+	0.683016i	$0.760668\pi$
$702$	−3.01402	−0.113757
$703$	−25.3572	−0.956367
$704$	−6.20807	−0.233976
$705$	−11.5964	−0.436744
$706$	81.3058	3.05998
$707$	2.06664	0.0777241
$708$	2.47007	0.0928310
$709$	31.4982	1.18294	0.591470	−	0.806327i	$-0.298548\pi$
$709$	31.4982	1.18294	0.591470	+	0.806327i	$0.298548\pi$
$710$	−17.2352	−0.646826
$711$	31.7461	1.19057
$712$	39.9702	1.49795
$713$	7.86530	0.294558
$714$	0.519643	0.0194472
$715$	4.14314	0.154945
$716$	36.9237	1.37990
$717$	−0.916461	−0.0342259
$718$	81.0394	3.02436
$719$	40.6575	1.51627	0.758134	−	0.652099i	$-0.226111\pi$
$719$	40.6575	1.51627	0.758134	+	0.652099i	$0.226111\pi$
$720$	87.7653	3.27082
$721$	−1.97842	−0.0736802
$722$	−7.51616	−0.279723
$723$	2.66931	0.0992727
$724$	60.2410	2.23884
$725$	6.99370	0.259739
$726$	−5.65710	−0.209955
$727$	−22.3344	−0.828336	−0.414168	−	0.910200i	$-0.635927\pi$
$727$	−22.3344	−0.828336	−0.414168	+	0.910200i	$0.635927\pi$
$728$	−0.466595	−0.0172932
$729$	−13.8310	−0.512258
$730$	−48.8833	−1.80925
$731$	−16.5612	−0.612536
$732$	29.0164	1.07248
$733$	35.8980	1.32592	0.662962	−	0.748653i	$-0.269299\pi$
$733$	35.8980	1.32592	0.662962	+	0.748653i	$0.269299\pi$
$734$	−10.0748	−0.371869
$735$	−14.3308	−0.528599
$736$	49.6979	1.83189
$737$	0.415155	0.0152924
$738$	−6.30173	−0.231970
$739$	5.85171	0.215259	0.107629	−	0.994191i	$-0.465674\pi$
$739$	5.85171	0.215259	0.107629	+	0.994191i	$0.465674\pi$
$740$	100.035	3.67736
$741$	−0.957166	−0.0351624
$742$	2.01632	0.0740215
$743$	11.2665	0.413327	0.206664	−	0.978412i	$-0.433739\pi$
$743$	11.2665	0.413327	0.206664	+	0.978412i	$0.433739\pi$
$744$	−3.88345	−0.142374
$745$	−88.1831	−3.23078
$746$	−0.782800	−0.0286603
$747$	36.4018	1.33187
$748$	−26.9104	−0.983942
$749$	−1.47839	−0.0540191
$750$	−32.2048	−1.17595
$751$	31.2868	1.14167	0.570835	−	0.821065i	$-0.306619\pi$
$751$	31.2868	1.14167	0.570835	+	0.821065i	$0.306619\pi$
$752$	−45.0728	−1.64363
$753$	1.21219	0.0441747
$754$	−0.646113	−0.0235301
$755$	−35.8184	−1.30357
$756$	2.36667	0.0860750
$757$	−23.4806	−0.853416	−0.426708	−	0.904390i	$-0.640327\pi$
$757$	−23.4806	−0.853416	−0.426708	+	0.904390i	$0.640327\pi$
$758$	−29.4518	−1.06974
$759$	−9.22170	−0.334726
$760$	125.731	4.56073
$761$	35.2910	1.27930	0.639648	−	0.768668i	$-0.279080\pi$
$761$	35.2910	1.27930	0.639648	+	0.768668i	$0.279080\pi$
$762$	25.0930	0.909025
$763$	0.774212	0.0280283
$764$	60.1527	2.17625
$765$	24.7852	0.896112
$766$	11.8386	0.427744
$767$	−0.417428	−0.0150725
$768$	13.1851	0.475776
$769$	0.278809	0.0100541	0.00502706	−	0.999987i	$-0.498400\pi$
$769$	0.278809	0.0100541	0.00502706	+	0.999987i	$0.498400\pi$
$770$	−4.66637	−0.168164
$771$	8.51676	0.306724
$772$	−112.178	−4.03738
$773$	−19.5739	−0.704024	−0.352012	−	0.935995i	$-0.614502\pi$
$773$	−19.5739	−0.704024	−0.352012	+	0.935995i	$0.614502\pi$
$774$	−51.6174	−1.85535
$775$	−12.5588	−0.451126
$776$	−128.982	−4.63019
$777$	0.485163	0.0174051
$778$	−66.4917	−2.38384
$779$	−4.19456	−0.150286
$780$	3.77604	0.135204
$781$	4.32880	0.154897
$782$	40.3017	1.44118
$783$	1.85373	0.0662468
$784$	−55.7010	−1.98932
$785$	73.1464	2.61071
$786$	−18.1799	−0.648455
$787$	5.09792	0.181721	0.0908606	−	0.995864i	$-0.471038\pi$
$787$	5.09792	0.181721	0.0908606	+	0.995864i	$0.471038\pi$
$788$	−18.8339	−0.670929
$789$	−1.18527	−0.0421968
$790$	−119.571	−4.25413
$791$	−0.664237	−0.0236175
$792$	−47.4423	−1.68579
$793$	−4.90360	−0.174132
$794$	36.9309	1.31063
$795$	−9.22988	−0.327350
$796$	−5.03149	−0.178336
$797$	−5.29812	−0.187669	−0.0938346	−	0.995588i	$-0.529912\pi$
$797$	−5.29812	−0.187669	−0.0938346	+	0.995588i	$0.529912\pi$
$798$	1.07805	0.0381624
$799$	−12.7287	−0.450309
$800$	−79.3545	−2.80561
$801$	16.3463	0.577569
$802$	−79.7735	−2.81690
$803$	12.2775	0.433265
$804$	0.378370	0.0133441
$805$	4.87218	0.171722
$806$	1.16025	0.0408680
$807$	−10.9827	−0.386610
$808$	−79.1381	−2.78407
$809$	4.13007	0.145206	0.0726028	−	0.997361i	$-0.476869\pi$
$809$	4.13007	0.145206	0.0726028	+	0.997361i	$0.476869\pi$
$810$	69.1246	2.42879
$811$	32.2044	1.13085	0.565424	−	0.824800i	$-0.308713\pi$
$811$	32.2044	1.13085	0.565424	+	0.824800i	$0.308713\pi$
$812$	0.507341	0.0178042
$813$	3.87370	0.135857
$814$	−36.0380	−1.26313
$815$	−43.2807	−1.51606
$816$	−9.24557	−0.323660
$817$	−34.3576	−1.20202
$818$	2.44621	0.0855296
$819$	−0.190820	−0.00666780
$820$	16.5476	0.577868
$821$	−19.2471	−0.671729	−0.335865	−	0.941910i	$-0.609028\pi$
$821$	−19.2471	−0.671729	−0.335865	+	0.941910i	$0.609028\pi$
$822$	−18.5628	−0.647453
$823$	−36.9838	−1.28917	−0.644587	−	0.764531i	$-0.722971\pi$
$823$	−36.9838	−1.28917	−0.644587	+	0.764531i	$0.722971\pi$
$824$	75.7598	2.63922
$825$	14.7246	0.512646
$826$	0.470145	0.0163584
$827$	−39.0561	−1.35811	−0.679057	−	0.734086i	$-0.737611\pi$
$827$	−39.0561	−1.35811	−0.679057	+	0.734086i	$0.737611\pi$
$828$	87.5730	3.04337
$829$	9.43066	0.327540	0.163770	−	0.986499i	$-0.447634\pi$
$829$	9.43066	0.327540	0.163770	+	0.986499i	$0.447634\pi$
$830$	−137.106	−4.75903
$831$	−10.5444	−0.365781
$832$	0.956173	0.0331493
$833$	−15.7302	−0.545018
$834$	−14.2577	−0.493705
$835$	36.5634	1.26533
$836$	−55.8280	−1.93085
$837$	−3.32880	−0.115060
$838$	−58.5973	−2.02421
$839$	19.8435	0.685074	0.342537	−	0.939504i	$-0.388714\pi$
$839$	19.8435	0.685074	0.342537	+	0.939504i	$0.388714\pi$
$840$	−2.40562	−0.0830016
$841$	−28.6026	−0.986297
$842$	−53.1441	−1.83147
$843$	−2.95222	−0.101680
$844$	−3.65576	−0.125837
$845$	51.5150	1.77217
$846$	−39.6725	−1.36397
$847$	−0.750685	−0.0257938
$848$	−35.8747	−1.23194
$849$	3.62148	0.124289
$850$	−64.3512	−2.20723
$851$	37.6275	1.28985
$852$	3.94525	0.135162
$853$	25.1405	0.860795	0.430397	−	0.902640i	$-0.358373\pi$
$853$	25.1405	0.860795	0.430397	+	0.902640i	$0.358373\pi$
$854$	5.52287	0.188989
$855$	51.4192	1.75850
$856$	56.6120	1.93496
$857$	−37.9056	−1.29483	−0.647416	−	0.762137i	$-0.724150\pi$
$857$	−37.9056	−1.29483	−0.647416	+	0.762137i	$0.724150\pi$
$858$	−1.36034	−0.0464411
$859$	−35.5986	−1.21461	−0.607304	−	0.794469i	$-0.707749\pi$
$859$	−35.5986	−1.21461	−0.607304	+	0.794469i	$0.707749\pi$
$860$	135.541	4.62193
$861$	0.0802548	0.00273508
$862$	−78.6449	−2.67866
$863$	19.1710	0.652589	0.326295	−	0.945268i	$-0.394200\pi$
$863$	19.1710	0.652589	0.326295	+	0.945268i	$0.394200\pi$
$864$	−21.0335	−0.715573
$865$	−71.7488	−2.43953
$866$	28.1261	0.955764
$867$	6.10234	0.207246
$868$	−0.911049	−0.0309230
$869$	30.0314	1.01874
$870$	−3.33115	−0.112937
$871$	−0.0639424	−0.00216661
$872$	−29.6470	−1.00397
$873$	−52.7489	−1.78528
$874$	83.6093	2.82813
$875$	−4.27350	−0.144471
$876$	11.1897	0.378065
$877$	55.1035	1.86071	0.930357	−	0.366655i	$-0.119497\pi$
$877$	55.1035	1.86071	0.930357	+	0.366655i	$0.119497\pi$
$878$	−45.3840	−1.53163
$879$	9.48657	0.319974
$880$	83.0249	2.79877
$881$	51.0073	1.71848	0.859240	−	0.511573i	$-0.170937\pi$
$881$	51.0073	1.71848	0.859240	+	0.511573i	$0.170937\pi$
$882$	−49.0274	−1.65084
$883$	−56.1603	−1.88995	−0.944973	−	0.327148i	$-0.893912\pi$
$883$	−56.1603	−1.88995	−0.944973	+	0.327148i	$0.893912\pi$
$884$	4.14476	0.139403
$885$	−2.15213	−0.0723429
$886$	−47.9574	−1.61116
$887$	−15.4881	−0.520041	−0.260020	−	0.965603i	$-0.583729\pi$
$887$	−15.4881	−0.520041	−0.260020	+	0.965603i	$0.583729\pi$
$888$	−18.5784	−0.623449
$889$	3.32979	0.111677
$890$	−61.5680	−2.06376
$891$	−17.3614	−0.581627
$892$	58.0744	1.94448
$893$	−26.4068	−0.883671
$894$	28.9536	0.968352
$895$	−32.1709	−1.07535
$896$	1.42351	0.0475561
$897$	1.42033	0.0474235
$898$	−63.7512	−2.12741
$899$	−0.713591	−0.0237996
$900$	−139.831	−4.66103
$901$	−10.1312	−0.337518
$902$	−5.96135	−0.198491
$903$	0.657367	0.0218758
$904$	25.4357	0.845978
$905$	−52.4868	−1.74472
$906$	11.7604	0.390714
$907$	−39.2318	−1.30267	−0.651335	−	0.758790i	$-0.725791\pi$
$907$	−39.2318	−1.30267	−0.651335	+	0.758790i	$0.725791\pi$
$908$	−0.277624	−0.00921329
$909$	−32.3646	−1.07347
$910$	0.718719	0.0238253
$911$	−5.76089	−0.190867	−0.0954335	−	0.995436i	$-0.530424\pi$
$911$	−5.76089	−0.190867	−0.0954335	+	0.995436i	$0.530424\pi$
$912$	−19.1808	−0.635139
$913$	34.4356	1.13965
$914$	39.4961	1.30642
$915$	−25.2814	−0.835778
$916$	−58.2364	−1.92418
$917$	−2.41243	−0.0796654
$918$	−17.0567	−0.562955
$919$	0.140223	0.00462552	0.00231276	−	0.999997i	$-0.499264\pi$
$919$	0.140223	0.00462552	0.00231276	+	0.999997i	$0.499264\pi$
$920$	−186.571	−6.15106
$921$	14.0596	0.463280
$922$	−12.0399	−0.396514
$923$	−0.666725	−0.0219455
$924$	1.06816	0.0351400
$925$	−60.0812	−1.97546
$926$	3.83482	0.126020
$927$	30.9830	1.01761
$928$	−4.50892	−0.148013
$929$	−47.0006	−1.54204	−0.771020	−	0.636811i	$-0.780253\pi$
$929$	−47.0006	−1.54204	−0.771020	+	0.636811i	$0.780253\pi$
$930$	5.98186	0.196153
$931$	−32.6336	−1.06952
$932$	−92.6835	−3.03595
$933$	−13.9699	−0.457355
$934$	49.3599	1.61510
$935$	23.4465	0.766783
$936$	7.30710	0.238840
$937$	5.30514	0.173311	0.0866557	−	0.996238i	$-0.472382\pi$
$937$	5.30514	0.173311	0.0866557	+	0.996238i	$0.472382\pi$
$938$	0.0720177	0.00235146
$939$	10.5781	0.345204
$940$	104.176	3.39783
$941$	−28.6096	−0.932645	−0.466322	−	0.884615i	$-0.654421\pi$
$941$	−28.6096	−0.932645	−0.466322	+	0.884615i	$0.654421\pi$
$942$	−24.0165	−0.782499
$943$	6.22428	0.202690
$944$	−8.36489	−0.272254
$945$	−2.06203	−0.0670780
$946$	−48.8294	−1.58758
$947$	−4.16170	−0.135237	−0.0676186	−	0.997711i	$-0.521540\pi$
$947$	−4.16170	−0.135237	−0.0676186	+	0.997711i	$0.521540\pi$
$948$	27.3705	0.888952
$949$	−1.89100	−0.0613844
$950$	−133.502	−4.33138
$951$	−16.4231	−0.532557
$952$	−2.64052	−0.0855796
$953$	−12.1201	−0.392607	−0.196304	−	0.980543i	$-0.562894\pi$
$953$	−12.1201	−0.392607	−0.196304	+	0.980543i	$0.562894\pi$
$954$	−31.5765	−1.02233
$955$	−52.4099	−1.69594
$956$	8.23300	0.266274
$957$	0.836653	0.0270452
$958$	−8.32964	−0.269118
$959$	−2.46324	−0.0795423
$960$	4.92972	0.159106
$961$	−29.7186	−0.958664
$962$	5.55060	0.178959
$963$	23.1522	0.746070
$964$	−23.9797	−0.772333
$965$	97.7386	3.14632
$966$	−1.59971	−0.0514697
$967$	−25.0274	−0.804828	−0.402414	−	0.915458i	$-0.631829\pi$
$967$	−25.0274	−0.804828	−0.402414	+	0.915458i	$0.631829\pi$
$968$	28.7460	0.923932
$969$	−5.41672	−0.174010
$970$	198.677	6.37914
$971$	8.47180	0.271873	0.135937	−	0.990718i	$-0.456596\pi$
$971$	8.47180	0.271873	0.135937	+	0.990718i	$0.456596\pi$
$972$	−56.4433	−1.81042
$973$	−1.89197	−0.0606538
$974$	−71.3723	−2.28692
$975$	−2.26790	−0.0726309
$976$	−98.2639	−3.14535
$977$	41.4737	1.32686	0.663431	−	0.748237i	$-0.269099\pi$
$977$	41.4737	1.32686	0.663431	+	0.748237i	$0.269099\pi$
$978$	14.2106	0.454403
$979$	15.4634	0.494213
$980$	128.740	4.11246
$981$	−12.1245	−0.387106
$982$	−16.5669	−0.528671
$983$	12.2387	0.390354	0.195177	−	0.980768i	$-0.437472\pi$
$983$	12.2387	0.390354	0.195177	+	0.980768i	$0.437472\pi$
$984$	−3.07321	−0.0979702
$985$	16.4096	0.522853
$986$	−3.65643	−0.116444
$987$	0.505244	0.0160821
$988$	8.59868	0.273560
$989$	50.9830	1.62116
$990$	73.0776	2.32256
$991$	19.8732	0.631294	0.315647	−	0.948877i	$-0.397778\pi$
$991$	19.8732	0.631294	0.315647	+	0.948877i	$0.397778\pi$
$992$	8.09682	0.257074
$993$	−2.30928	−0.0732827
$994$	0.750925	0.0238179
$995$	4.38384	0.138977
$996$	31.3845	0.994456
$997$	18.4035	0.582844	0.291422	−	0.956595i	$-0.405872\pi$
$997$	18.4035	0.582844	0.291422	+	0.956595i	$0.405872\pi$
$998$	−71.4185	−2.26071
$999$	−15.9249	−0.503842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.12	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.12	✓	186	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56992 q^{2} -0.512548 q^{3} +4.60446 q^{4} -4.01178 q^{5} +1.31721 q^{6} +0.174790 q^{7} -6.69325 q^{8} -2.73729 q^{9} +O(q^{10})\)	\(q-2.56992 q^{2} -0.512548 q^{3} +4.60446 q^{4} -4.01178 q^{5} +1.31721 q^{6} +0.174790 q^{7} -6.69325 q^{8} -2.73729 q^{9} +10.3099 q^{10} -2.58944 q^{11} -2.36001 q^{12} +0.398828 q^{13} -0.449196 q^{14} +2.05623 q^{15} +7.99217 q^{16} +2.25702 q^{17} +7.03461 q^{18} +4.68238 q^{19} -18.4721 q^{20} -0.0895884 q^{21} +6.65465 q^{22} -6.94815 q^{23} +3.43062 q^{24} +11.0944 q^{25} -1.02496 q^{26} +2.94064 q^{27} +0.804815 q^{28} +0.630382 q^{29} -5.28434 q^{30} -1.13200 q^{31} -7.15268 q^{32} +1.32722 q^{33} -5.80034 q^{34} -0.701220 q^{35} -12.6038 q^{36} -5.41546 q^{37} -12.0333 q^{38} -0.204419 q^{39} +26.8519 q^{40} -0.895817 q^{41} +0.230235 q^{42} -7.33763 q^{43} -11.9230 q^{44} +10.9814 q^{45} +17.8562 q^{46} -5.63962 q^{47} -4.09637 q^{48} -6.96945 q^{49} -28.5116 q^{50} -1.15683 q^{51} +1.83639 q^{52} -4.48874 q^{53} -7.55720 q^{54} +10.3883 q^{55} -1.16991 q^{56} -2.39995 q^{57} -1.62003 q^{58} -1.04664 q^{59} +9.46784 q^{60} -12.2950 q^{61} +2.90914 q^{62} -0.478452 q^{63} +2.39745 q^{64} -1.60001 q^{65} -3.41083 q^{66} -0.160326 q^{67} +10.3923 q^{68} +3.56126 q^{69} +1.80207 q^{70} -1.67171 q^{71} +18.3214 q^{72} -4.74138 q^{73} +13.9173 q^{74} -5.68640 q^{75} +21.5598 q^{76} -0.452609 q^{77} +0.525339 q^{78} -11.5976 q^{79} -32.0628 q^{80} +6.70466 q^{81} +2.30217 q^{82} -13.2985 q^{83} -0.412507 q^{84} -9.05465 q^{85} +18.8571 q^{86} -0.323101 q^{87} +17.3318 q^{88} -5.97171 q^{89} -28.2213 q^{90} +0.0697113 q^{91} -31.9925 q^{92} +0.580204 q^{93} +14.4933 q^{94} -18.7847 q^{95} +3.66610 q^{96} +19.2705 q^{97} +17.9109 q^{98} +7.08807 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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