LMFDB - Embedded newform 8029.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.63972 q^{2} +1.31150 q^{3} +0.688696 q^{4} +3.72445 q^{5} -2.15050 q^{6} +1.00000 q^{7} +2.15018 q^{8} -1.27996 q^{9} +O(q^{10})$	\(q-1.63972 q^{2} +1.31150 q^{3} +0.688696 q^{4} +3.72445 q^{5} -2.15050 q^{6} +1.00000 q^{7} +2.15018 q^{8} -1.27996 q^{9} -6.10708 q^{10} -0.578957 q^{11} +0.903227 q^{12} +2.70150 q^{13} -1.63972 q^{14} +4.88464 q^{15} -4.90309 q^{16} -6.64597 q^{17} +2.09878 q^{18} +1.60086 q^{19} +2.56502 q^{20} +1.31150 q^{21} +0.949330 q^{22} -4.61943 q^{23} +2.81997 q^{24} +8.87156 q^{25} -4.42972 q^{26} -5.61318 q^{27} +0.688696 q^{28} -7.29396 q^{29} -8.00946 q^{30} +1.00000 q^{31} +3.73936 q^{32} -0.759305 q^{33} +10.8976 q^{34} +3.72445 q^{35} -0.881502 q^{36} -1.00000 q^{37} -2.62496 q^{38} +3.54303 q^{39} +8.00824 q^{40} -3.11039 q^{41} -2.15050 q^{42} -2.34551 q^{43} -0.398726 q^{44} -4.76714 q^{45} +7.57460 q^{46} -7.18993 q^{47} -6.43042 q^{48} +1.00000 q^{49} -14.5469 q^{50} -8.71622 q^{51} +1.86051 q^{52} -1.53926 q^{53} +9.20407 q^{54} -2.15630 q^{55} +2.15018 q^{56} +2.09953 q^{57} +11.9601 q^{58} -5.28657 q^{59} +3.36403 q^{60} -5.49785 q^{61} -1.63972 q^{62} -1.27996 q^{63} +3.67466 q^{64} +10.0616 q^{65} +1.24505 q^{66} +12.5282 q^{67} -4.57706 q^{68} -6.05841 q^{69} -6.10708 q^{70} -9.56293 q^{71} -2.75214 q^{72} -6.72747 q^{73} +1.63972 q^{74} +11.6351 q^{75} +1.10250 q^{76} -0.578957 q^{77} -5.80960 q^{78} +13.2661 q^{79} -18.2613 q^{80} -3.52183 q^{81} +5.10019 q^{82} -9.80853 q^{83} +0.903227 q^{84} -24.7526 q^{85} +3.84599 q^{86} -9.56606 q^{87} -1.24486 q^{88} -5.79883 q^{89} +7.81680 q^{90} +2.70150 q^{91} -3.18139 q^{92} +1.31150 q^{93} +11.7895 q^{94} +5.96231 q^{95} +4.90419 q^{96} +11.6854 q^{97} -1.63972 q^{98} +0.741041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−1.63972	−1.15946	−0.579730	−	0.814809i	$-0.696842\pi$
$2$	−1.63972	−1.15946	−0.579730	+	0.814809i	$0.696842\pi$
$3$	1.31150	0.757197	0.378599	−	0.925561i	$-0.376406\pi$
$3$	1.31150	0.757197	0.378599	+	0.925561i	$0.376406\pi$
$4$	0.688696	0.344348
$5$	3.72445	1.66563	0.832813	−	0.553554i	$-0.186729\pi$
$5$	3.72445	1.66563	0.832813	+	0.553554i	$0.186729\pi$
$6$	−2.15050	−0.877940
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.15018	0.760202
$9$	−1.27996	−0.426653
$10$	−6.10708	−1.93123
$11$	−0.578957	−0.174562	−0.0872811	−	0.996184i	$-0.527818\pi$
$11$	−0.578957	−0.174562	−0.0872811	+	0.996184i	$0.527818\pi$
$12$	0.903227	0.260739
$13$	2.70150	0.749262	0.374631	−	0.927174i	$-0.377769\pi$
$13$	2.70150	0.749262	0.374631	+	0.927174i	$0.377769\pi$
$14$	−1.63972	−0.438235
$15$	4.88464	1.26121
$16$	−4.90309	−1.22577
$17$	−6.64597	−1.61189	−0.805943	−	0.591993i	$-0.798341\pi$
$17$	−6.64597	−1.61189	−0.805943	+	0.591993i	$0.798341\pi$
$18$	2.09878	0.494687
$19$	1.60086	0.367261	0.183631	−	0.982995i	$-0.441215\pi$
$19$	1.60086	0.367261	0.183631	+	0.982995i	$0.441215\pi$
$20$	2.56502	0.573555
$21$	1.31150	0.286194
$22$	0.949330	0.202398
$23$	−4.61943	−0.963219	−0.481609	−	0.876386i	$-0.659948\pi$
$23$	−4.61943	−0.963219	−0.481609	+	0.876386i	$0.659948\pi$
$24$	2.81997	0.575623
$25$	8.87156	1.77431
$26$	−4.42972	−0.868740
$27$	−5.61318	−1.08026
$28$	0.688696	0.130151
$29$	−7.29396	−1.35446	−0.677228	−	0.735774i	$-0.736819\pi$
$29$	−7.29396	−1.35446	−0.677228	+	0.735774i	$0.736819\pi$
$30$	−8.00946	−1.46232
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	3.73936	0.661032
$33$	−0.759305	−0.132178
$34$	10.8976	1.86892
$35$	3.72445	0.629548
$36$	−0.881502	−0.146917
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−2.62496	−0.425825
$39$	3.54303	0.567339
$40$	8.00824	1.26621
$41$	−3.11039	−0.485762	−0.242881	−	0.970056i	$-0.578092\pi$
$41$	−3.11039	−0.485762	−0.242881	+	0.970056i	$0.578092\pi$
$42$	−2.15050	−0.331830
$43$	−2.34551	−0.357687	−0.178843	−	0.983878i	$-0.557236\pi$
$43$	−2.34551	−0.357687	−0.178843	+	0.983878i	$0.557236\pi$
$44$	−0.398726	−0.0601101
$45$	−4.76714	−0.710644
$46$	7.57460	1.11681
$47$	−7.18993	−1.04876	−0.524379	−	0.851485i	$-0.675703\pi$
$47$	−7.18993	−1.04876	−0.524379	+	0.851485i	$0.675703\pi$
$48$	−6.43042	−0.928151
$49$	1.00000	0.142857
$50$	−14.5469	−2.05724
$51$	−8.71622	−1.22051
$52$	1.86051	0.258007
$53$	−1.53926	−0.211433	−0.105717	−	0.994396i	$-0.533714\pi$
$53$	−1.53926	−0.211433	−0.105717	+	0.994396i	$0.533714\pi$
$54$	9.20407	1.25252
$55$	−2.15630	−0.290755
$56$	2.15018	0.287330
$57$	2.09953	0.278089
$58$	11.9601	1.57044
$59$	−5.28657	−0.688253	−0.344126	−	0.938923i	$-0.611825\pi$
$59$	−5.28657	−0.688253	−0.344126	+	0.938923i	$0.611825\pi$
$60$	3.36403	0.434294
$61$	−5.49785	−0.703927	−0.351964	−	0.936014i	$-0.614486\pi$
$61$	−5.49785	−0.703927	−0.351964	+	0.936014i	$0.614486\pi$
$62$	−1.63972	−0.208245
$63$	−1.27996	−0.161260
$64$	3.67466	0.459332
$65$	10.0616	1.24799
$66$	1.24505	0.153255
$67$	12.5282	1.53057	0.765285	−	0.643692i	$-0.222598\pi$
$67$	12.5282	1.53057	0.765285	+	0.643692i	$0.222598\pi$
$68$	−4.57706	−0.555049
$69$	−6.05841	−0.729346
$70$	−6.10708	−0.729935
$71$	−9.56293	−1.13491	−0.567455	−	0.823404i	$-0.692072\pi$
$71$	−9.56293	−1.13491	−0.567455	+	0.823404i	$0.692072\pi$
$72$	−2.75214	−0.324342
$73$	−6.72747	−0.787390	−0.393695	−	0.919241i	$-0.628803\pi$
$73$	−6.72747	−0.787390	−0.393695	+	0.919241i	$0.628803\pi$
$74$	1.63972	0.190614
$75$	11.6351	1.34350
$76$	1.10250	0.126466
$77$	−0.578957	−0.0659783
$78$	−5.80960	−0.657807
$79$	13.2661	1.49255	0.746274	−	0.665639i	$-0.231841\pi$
$79$	13.2661	1.49255	0.746274	+	0.665639i	$0.231841\pi$
$80$	−18.2613	−2.04168
$81$	−3.52183	−0.391315
$82$	5.10019	0.563221
$83$	−9.80853	−1.07663	−0.538313	−	0.842745i	$-0.680938\pi$
$83$	−9.80853	−1.07663	−0.538313	+	0.842745i	$0.680938\pi$
$84$	0.903227	0.0985502
$85$	−24.7526	−2.68480
$86$	3.84599	0.414724
$87$	−9.56606	−1.02559
$88$	−1.24486	−0.132703
$89$	−5.79883	−0.614675	−0.307338	−	0.951601i	$-0.599438\pi$
$89$	−5.79883	−0.614675	−0.307338	+	0.951601i	$0.599438\pi$
$90$	7.81680	0.823963
$91$	2.70150	0.283195
$92$	−3.18139	−0.331682
$93$	1.31150	0.135997
$94$	11.7895	1.21599
$95$	5.96231	0.611720
$96$	4.90419	0.500531
$97$	11.6854	1.18648	0.593238	−	0.805027i	$-0.297849\pi$
$97$	11.6854	1.18648	0.593238	+	0.805027i	$0.297849\pi$
$98$	−1.63972	−0.165637
$99$	0.741041	0.0744774
$100$	6.10981	0.610981
$101$	−8.57970	−0.853712	−0.426856	−	0.904320i	$-0.640379\pi$
$101$	−8.57970	−0.853712	−0.426856	+	0.904320i	$0.640379\pi$
$102$	14.2922	1.41514
$103$	−4.93983	−0.486735	−0.243368	−	0.969934i	$-0.578252\pi$
$103$	−4.93983	−0.486735	−0.243368	+	0.969934i	$0.578252\pi$
$104$	5.80871	0.569591
$105$	4.88464	0.476692
$106$	2.52396	0.245148
$107$	11.8705	1.14756	0.573781	−	0.819009i	$-0.305476\pi$
$107$	11.8705	1.14756	0.573781	+	0.819009i	$0.305476\pi$
$108$	−3.86577	−0.371984
$109$	−10.8217	−1.03653	−0.518266	−	0.855219i	$-0.673422\pi$
$109$	−10.8217	−1.03653	−0.518266	+	0.855219i	$0.673422\pi$
$110$	3.53574	0.337119
$111$	−1.31150	−0.124482
$112$	−4.90309	−0.463298
$113$	−18.3800	−1.72904	−0.864521	−	0.502597i	$-0.832378\pi$
$113$	−18.3800	−1.72904	−0.864521	+	0.502597i	$0.832378\pi$
$114$	−3.44265	−0.322433
$115$	−17.2049	−1.60436
$116$	−5.02332	−0.466404
$117$	−3.45781	−0.319675
$118$	8.66852	0.798001
$119$	−6.64597	−0.609235
$120$	10.5028	0.958773
$121$	−10.6648	−0.969528
$122$	9.01495	0.816176
$123$	−4.07929	−0.367817
$124$	0.688696	0.0618467
$125$	14.4194	1.28971
$126$	2.09878	0.186974
$127$	13.8299	1.22720	0.613602	−	0.789615i	$-0.289720\pi$
$127$	13.8299	1.22720	0.613602	+	0.789615i	$0.289720\pi$
$128$	−13.5041	−1.19361
$129$	−3.07614	−0.270839
$130$	−16.4983	−1.44700
$131$	−2.88303	−0.251891	−0.125946	−	0.992037i	$-0.540196\pi$
$131$	−2.88303	−0.251891	−0.125946	+	0.992037i	$0.540196\pi$
$132$	−0.522930	−0.0455152
$133$	1.60086	0.138812
$134$	−20.5429	−1.77463
$135$	−20.9060	−1.79930
$136$	−14.2900	−1.22536
$137$	−2.17123	−0.185501	−0.0927503	−	0.995689i	$-0.529566\pi$
$137$	−2.17123	−0.185501	−0.0927503	+	0.995689i	$0.529566\pi$
$138$	9.93412	0.845648
$139$	−6.58145	−0.558231	−0.279115	−	0.960258i	$-0.590041\pi$
$139$	−6.58145	−0.558231	−0.279115	+	0.960258i	$0.590041\pi$
$140$	2.56502	0.216783
$141$	−9.42962	−0.794117
$142$	15.6806	1.31588
$143$	−1.56406	−0.130793
$144$	6.27575	0.522979
$145$	−27.1660	−2.25602
$146$	11.0312	0.912948
$147$	1.31150	0.108171
$148$	−0.688696	−0.0566105
$149$	11.7372	0.961545	0.480772	−	0.876845i	$-0.340356\pi$
$149$	11.7372	0.961545	0.480772	+	0.876845i	$0.340356\pi$
$150$	−19.0783	−1.55774
$151$	3.98756	0.324503	0.162251	−	0.986749i	$-0.448124\pi$
$151$	3.98756	0.324503	0.162251	+	0.986749i	$0.448124\pi$
$152$	3.44212	0.279193
$153$	8.50657	0.687715
$154$	0.949330	0.0764992
$155$	3.72445	0.299155
$156$	2.44007	0.195362
$157$	−5.57040	−0.444566	−0.222283	−	0.974982i	$-0.571351\pi$
$157$	−5.57040	−0.444566	−0.222283	+	0.974982i	$0.571351\pi$
$158$	−21.7527	−1.73055
$159$	−2.01874	−0.160096
$160$	13.9271	1.10103
$161$	−4.61943	−0.364062
$162$	5.77484	0.453714
$163$	3.74496	0.293328	0.146664	−	0.989186i	$-0.453146\pi$
$163$	3.74496	0.293328	0.146664	+	0.989186i	$0.453146\pi$
$164$	−2.14211	−0.167271
$165$	−2.82800	−0.220159
$166$	16.0833	1.24830
$167$	−20.6060	−1.59454	−0.797268	−	0.603625i	$-0.793722\pi$
$167$	−20.6060	−1.59454	−0.797268	+	0.603625i	$0.793722\pi$
$168$	2.81997	0.217565
$169$	−5.70187	−0.438606
$170$	40.5875	3.11292
$171$	−2.04903	−0.156693
$172$	−1.61534	−0.123169
$173$	12.4182	0.944139	0.472069	−	0.881561i	$-0.343507\pi$
$173$	12.4182	0.944139	0.472069	+	0.881561i	$0.343507\pi$
$174$	15.6857	1.18913
$175$	8.87156	0.670627
$176$	2.83868	0.213974
$177$	−6.93335	−0.521143
$178$	9.50849	0.712691
$179$	−23.9071	−1.78690	−0.893452	−	0.449159i	$-0.851724\pi$
$179$	−23.9071	−1.78690	−0.893452	+	0.449159i	$0.851724\pi$
$180$	−3.28311	−0.244709
$181$	20.2575	1.50573	0.752864	−	0.658177i	$-0.228672\pi$
$181$	20.2575	1.50573	0.752864	+	0.658177i	$0.228672\pi$
$182$	−4.42972	−0.328353
$183$	−7.21045	−0.533012
$184$	−9.93260	−0.732241
$185$	−3.72445	−0.273827
$186$	−2.15050	−0.157683
$187$	3.84774	0.281374
$188$	−4.95167	−0.361138
$189$	−5.61318	−0.408299
$190$	−9.77655	−0.709265
$191$	26.1242	1.89028	0.945140	−	0.326665i	$-0.105925\pi$
$191$	26.1242	1.89028	0.945140	+	0.326665i	$0.105925\pi$
$192$	4.81933	0.347805
$193$	0.655840	0.0472084	0.0236042	−	0.999721i	$-0.492486\pi$
$193$	0.655840	0.0472084	0.0236042	+	0.999721i	$0.492486\pi$
$194$	−19.1609	−1.37567
$195$	13.1959	0.944975
$196$	0.688696	0.0491926
$197$	1.06618	0.0759619	0.0379810	−	0.999278i	$-0.487907\pi$
$197$	1.06618	0.0759619	0.0379810	+	0.999278i	$0.487907\pi$
$198$	−1.21510	−0.0863536
$199$	−21.9367	−1.55505	−0.777524	−	0.628853i	$-0.783525\pi$
$199$	−21.9367	−1.55505	−0.777524	+	0.628853i	$0.783525\pi$
$200$	19.0754	1.34884
$201$	16.4308	1.15894
$202$	14.0683	0.989845
$203$	−7.29396	−0.511936
$204$	−6.00283	−0.420282
$205$	−11.5845	−0.809098
$206$	8.09995	0.564350
$207$	5.91268	0.410960
$208$	−13.2457	−0.918425
$209$	−0.926827	−0.0641100
$210$	−8.00946	−0.552705
$211$	2.29048	0.157683	0.0788416	−	0.996887i	$-0.474878\pi$
$211$	2.29048	0.157683	0.0788416	+	0.996887i	$0.474878\pi$
$212$	−1.06008	−0.0728065
$213$	−12.5418	−0.859351
$214$	−19.4643	−1.33055
$215$	−8.73574	−0.595773
$216$	−12.0693	−0.821214
$217$	1.00000	0.0678844
$218$	17.7446	1.20182
$219$	−8.82310	−0.596210
$220$	−1.48503	−0.100121
$221$	−17.9541	−1.20773
$222$	2.15050	0.144332
$223$	0.455261	0.0304866	0.0152433	−	0.999884i	$-0.495148\pi$
$223$	0.455261	0.0304866	0.0152433	+	0.999884i	$0.495148\pi$
$224$	3.73936	0.249847
$225$	−11.3552	−0.757015
$226$	30.1381	2.00476
$227$	−21.4366	−1.42280	−0.711399	−	0.702788i	$-0.751938\pi$
$227$	−21.4366	−1.42280	−0.711399	+	0.702788i	$0.751938\pi$
$228$	1.44594	0.0957595
$229$	−10.3032	−0.680854	−0.340427	−	0.940271i	$-0.610572\pi$
$229$	−10.3032	−0.680854	−0.340427	+	0.940271i	$0.610572\pi$
$230$	28.2112	1.86019
$231$	−0.759305	−0.0499586
$232$	−15.6833	−1.02966
$233$	−28.6637	−1.87782	−0.938912	−	0.344158i	$-0.888164\pi$
$233$	−28.6637	−1.87782	−0.938912	+	0.344158i	$0.888164\pi$
$234$	5.66986	0.370650
$235$	−26.7786	−1.74684
$236$	−3.64084	−0.236998
$237$	17.3985	1.13015
$238$	10.8976	0.706384
$239$	25.0735	1.62187	0.810934	−	0.585137i	$-0.198959\pi$
$239$	25.0735	1.62187	0.810934	+	0.585137i	$0.198959\pi$
$240$	−23.9498	−1.54595
$241$	13.8383	0.891404	0.445702	−	0.895181i	$-0.352954\pi$
$241$	13.8383	0.891404	0.445702	+	0.895181i	$0.352954\pi$
$242$	17.4873	1.12413
$243$	12.2206	0.783955
$244$	−3.78635	−0.242396
$245$	3.72445	0.237947
$246$	6.68891	0.426470
$247$	4.32472	0.275175
$248$	2.15018	0.136536
$249$	−12.8639	−0.815218
$250$	−23.6439	−1.49537
$251$	−17.6097	−1.11152	−0.555758	−	0.831344i	$-0.687572\pi$
$251$	−17.6097	−1.11152	−0.555758	+	0.831344i	$0.687572\pi$
$252$	−0.881502	−0.0555294
$253$	2.67446	0.168142
$254$	−22.6772	−1.42289
$255$	−32.4632	−2.03292
$256$	14.7938	0.924610
$257$	23.7750	1.48304	0.741521	−	0.670930i	$-0.234105\pi$
$257$	23.7750	1.48304	0.741521	+	0.670930i	$0.234105\pi$
$258$	5.04403	0.314028
$259$	−1.00000	−0.0621370
$260$	6.92940	0.429743
$261$	9.33597	0.577882
$262$	4.72737	0.292058
$263$	14.2535	0.878910	0.439455	−	0.898265i	$-0.355172\pi$
$263$	14.2535	0.878910	0.439455	+	0.898265i	$0.355172\pi$
$264$	−1.63264	−0.100482
$265$	−5.73289	−0.352168
$266$	−2.62496	−0.160947
$267$	−7.60519	−0.465430
$268$	8.62815	0.527048
$269$	3.13088	0.190893	0.0954465	−	0.995435i	$-0.469572\pi$
$269$	3.13088	0.190893	0.0954465	+	0.995435i	$0.469572\pi$
$270$	34.2801	2.08622
$271$	−15.2421	−0.925893	−0.462947	−	0.886386i	$-0.653208\pi$
$271$	−15.2421	−0.925893	−0.462947	+	0.886386i	$0.653208\pi$
$272$	32.5858	1.97580
$273$	3.54303	0.214434
$274$	3.56022	0.215081
$275$	−5.13625	−0.309728
$276$	−4.17240	−0.251149
$277$	7.38688	0.443834	0.221917	−	0.975066i	$-0.428769\pi$
$277$	7.38688	0.443834	0.221917	+	0.975066i	$0.428769\pi$
$278$	10.7918	0.647247
$279$	−1.27996	−0.0766291
$280$	8.00824	0.478584
$281$	22.2428	1.32690	0.663448	−	0.748223i	$-0.269093\pi$
$281$	22.2428	1.32690	0.663448	+	0.748223i	$0.269093\pi$
$282$	15.4620	0.920747
$283$	−33.6283	−1.99900	−0.999498	−	0.0316840i	$-0.989913\pi$
$283$	−33.6283	−1.99900	−0.999498	+	0.0316840i	$0.989913\pi$
$284$	−6.58595	−0.390804
$285$	7.81959	0.463193
$286$	2.56462	0.151649
$287$	−3.11039	−0.183601
$288$	−4.78623	−0.282031
$289$	27.1690	1.59817
$290$	44.5448	2.61576
$291$	15.3255	0.898396
$292$	−4.63318	−0.271136
$293$	2.82404	0.164982	0.0824911	−	0.996592i	$-0.473712\pi$
$293$	2.82404	0.164982	0.0824911	+	0.996592i	$0.473712\pi$
$294$	−2.15050	−0.125420
$295$	−19.6896	−1.14637
$296$	−2.15018	−0.124977
$297$	3.24979	0.188572
$298$	−19.2457	−1.11487
$299$	−12.4794	−0.721704
$300$	8.01303	0.462633
$301$	−2.34551	−0.135193
$302$	−6.53850	−0.376248
$303$	−11.2523	−0.646428
$304$	−7.84914	−0.450179
$305$	−20.4765	−1.17248
$306$	−13.9484	−0.797378
$307$	12.2142	0.697103	0.348551	−	0.937290i	$-0.386674\pi$
$307$	12.2142	0.697103	0.348551	+	0.937290i	$0.386674\pi$
$308$	−0.398726	−0.0227195
$309$	−6.47860	−0.368555
$310$	−6.10708	−0.346859
$311$	11.2879	0.640078	0.320039	−	0.947404i	$-0.396304\pi$
$311$	11.2879	0.640078	0.320039	+	0.947404i	$0.396304\pi$
$312$	7.61815	0.431293
$313$	0.287922	0.0162743	0.00813716	−	0.999967i	$-0.497410\pi$
$313$	0.287922	0.0162743	0.00813716	+	0.999967i	$0.497410\pi$
$314$	9.13392	0.515457
$315$	−4.76714	−0.268598
$316$	9.13628	0.513956
$317$	13.4518	0.755527	0.377764	−	0.925902i	$-0.376693\pi$
$317$	13.4518	0.755527	0.377764	+	0.925902i	$0.376693\pi$
$318$	3.31018	0.185625
$319$	4.22289	0.236437
$320$	13.6861	0.765076
$321$	15.5682	0.868930
$322$	7.57460	0.422116
$323$	−10.6392	−0.591983
$324$	−2.42547	−0.134748
$325$	23.9666	1.32943
$326$	−6.14071	−0.340102
$327$	−14.1927	−0.784859
$328$	−6.68790	−0.369277
$329$	−7.18993	−0.396394
$330$	4.63713	0.255266
$331$	19.3494	1.06354	0.531770	−	0.846889i	$-0.321527\pi$
$331$	19.3494	1.06354	0.531770	+	0.846889i	$0.321527\pi$
$332$	−6.75509	−0.370734
$333$	1.27996	0.0701413
$334$	33.7881	1.84880
$335$	46.6609	2.54936
$336$	−6.43042	−0.350808
$337$	16.1394	0.879169	0.439584	−	0.898201i	$-0.355126\pi$
$337$	16.1394	0.879169	0.439584	+	0.898201i	$0.355126\pi$
$338$	9.34950	0.508546
$339$	−24.1054	−1.30923
$340$	−17.0470	−0.924505
$341$	−0.578957	−0.0313523
$342$	3.35984	0.181679
$343$	1.00000	0.0539949
$344$	−5.04326	−0.271914
$345$	−22.5643	−1.21482
$346$	−20.3624	−1.09469
$347$	27.0682	1.45310	0.726549	−	0.687115i	$-0.241123\pi$
$347$	27.0682	1.45310	0.726549	+	0.687115i	$0.241123\pi$
$348$	−6.58811	−0.353160
$349$	−36.2681	−1.94138	−0.970692	−	0.240326i	$-0.922746\pi$
$349$	−36.2681	−1.94138	−0.970692	+	0.240326i	$0.922746\pi$
$350$	−14.5469	−0.777565
$351$	−15.1640	−0.809396
$352$	−2.16493	−0.115391
$353$	−5.85926	−0.311857	−0.155928	−	0.987768i	$-0.549837\pi$
$353$	−5.85926	−0.311857	−0.155928	+	0.987768i	$0.549837\pi$
$354$	11.3688	0.604244
$355$	−35.6167	−1.89034
$356$	−3.99363	−0.211662
$357$	−8.71622	−0.461311
$358$	39.2011	2.07184
$359$	−4.56090	−0.240715	−0.120358	−	0.992731i	$-0.538404\pi$
$359$	−4.56090	−0.240715	−0.120358	+	0.992731i	$0.538404\pi$
$360$	−10.2502	−0.540233
$361$	−16.4373	−0.865119
$362$	−33.2167	−1.74583
$363$	−13.9869	−0.734124
$364$	1.86051	0.0975175
$365$	−25.0561	−1.31150
$366$	11.8231	0.618006
$367$	−21.8907	−1.14269	−0.571343	−	0.820711i	$-0.693577\pi$
$367$	−21.8907	−1.14269	−0.571343	+	0.820711i	$0.693577\pi$
$368$	22.6495	1.18069
$369$	3.98117	0.207252
$370$	6.10708	0.317492
$371$	−1.53926	−0.0799142
$372$	0.903227	0.0468302
$373$	16.1431	0.835856	0.417928	−	0.908480i	$-0.362756\pi$
$373$	16.1431	0.835856	0.417928	+	0.908480i	$0.362756\pi$
$374$	−6.30923	−0.326242
$375$	18.9111	0.976567
$376$	−15.4596	−0.797269
$377$	−19.7047	−1.01484
$378$	9.20407	0.473406
$379$	10.3284	0.530532	0.265266	−	0.964175i	$-0.414540\pi$
$379$	10.3284	0.530532	0.265266	+	0.964175i	$0.414540\pi$
$380$	4.10622	0.210645
$381$	18.1380	0.929235
$382$	−42.8365	−2.19170
$383$	16.6952	0.853083	0.426542	−	0.904468i	$-0.359732\pi$
$383$	16.6952	0.853083	0.426542	+	0.904468i	$0.359732\pi$
$384$	−17.7107	−0.903797
$385$	−2.15630	−0.109895
$386$	−1.07540	−0.0547363
$387$	3.00215	0.152608
$388$	8.04771	0.408561
$389$	24.4276	1.23853	0.619264	−	0.785183i	$-0.287431\pi$
$389$	24.4276	1.23853	0.619264	+	0.785183i	$0.287431\pi$
$390$	−21.6376	−1.09566
$391$	30.7006	1.55260
$392$	2.15018	0.108600
$393$	−3.78110	−0.190731
$394$	−1.74824	−0.0880749
$395$	49.4088	2.48603
$396$	0.510352	0.0256461
$397$	7.54132	0.378488	0.189244	−	0.981930i	$-0.439396\pi$
$397$	7.54132	0.378488	0.189244	+	0.981930i	$0.439396\pi$
$398$	35.9701	1.80302
$399$	2.09953	0.105108
$400$	−43.4980	−2.17490
$401$	23.4179	1.16944	0.584718	−	0.811237i	$-0.301205\pi$
$401$	23.4179	1.16944	0.584718	+	0.811237i	$0.301205\pi$
$402$	−26.9421	−1.34375
$403$	2.70150	0.134572
$404$	−5.90880	−0.293974
$405$	−13.1169	−0.651784
$406$	11.9601	0.593569
$407$	0.578957	0.0286978
$408$	−18.7414	−0.927838
$409$	21.5417	1.06517	0.532585	−	0.846377i	$-0.321221\pi$
$409$	21.5417	1.06517	0.532585	+	0.846377i	$0.321221\pi$
$410$	18.9954	0.938117
$411$	−2.84758	−0.140461
$412$	−3.40204	−0.167606
$413$	−5.28657	−0.260135
$414$	−9.69517	−0.476492
$415$	−36.5314	−1.79326
$416$	10.1019	0.495286
$417$	−8.63159	−0.422691
$418$	1.51974	0.0743329
$419$	−15.8409	−0.773877	−0.386939	−	0.922105i	$-0.626467\pi$
$419$	−15.8409	−0.773877	−0.386939	+	0.922105i	$0.626467\pi$
$420$	3.36403	0.164148
$421$	16.9385	0.825533	0.412767	−	0.910837i	$-0.364562\pi$
$421$	16.9385	0.825533	0.412767	+	0.910837i	$0.364562\pi$
$422$	−3.75576	−0.182827
$423$	9.20280	0.447456
$424$	−3.30967	−0.160732
$425$	−58.9601	−2.85999
$426$	20.5651	0.996383
$427$	−5.49785	−0.266059
$428$	8.17515	0.395161
$429$	−2.05126	−0.0990360
$430$	14.3242	0.690775
$431$	24.0402	1.15797	0.578987	−	0.815337i	$-0.303448\pi$
$431$	24.0402	1.15797	0.578987	+	0.815337i	$0.303448\pi$
$432$	27.5219	1.32415
$433$	−5.43628	−0.261251	−0.130625	−	0.991432i	$-0.541699\pi$
$433$	−5.43628	−0.261251	−0.130625	+	0.991432i	$0.541699\pi$
$434$	−1.63972	−0.0787093
$435$	−35.6284	−1.70825
$436$	−7.45287	−0.356928
$437$	−7.39505	−0.353753
$438$	14.4674	0.691281
$439$	−17.8945	−0.854058	−0.427029	−	0.904238i	$-0.640440\pi$
$439$	−17.8945	−0.854058	−0.427029	+	0.904238i	$0.640440\pi$
$440$	−4.63643	−0.221033
$441$	−1.27996	−0.0609504
$442$	29.4398	1.40031
$443$	−20.3245	−0.965645	−0.482823	−	0.875718i	$-0.660388\pi$
$443$	−20.3245	−0.965645	−0.482823	+	0.875718i	$0.660388\pi$
$444$	−0.903227	−0.0428653
$445$	−21.5975	−1.02382
$446$	−0.746503	−0.0353480
$447$	15.3933	0.728079
$448$	3.67466	0.173611
$449$	39.1273	1.84653	0.923266	−	0.384161i	$-0.125509\pi$
$449$	39.1273	1.84653	0.923266	+	0.384161i	$0.125509\pi$
$450$	18.6194	0.877728
$451$	1.80078	0.0847956
$452$	−12.6582	−0.595392
$453$	5.22970	0.245713
$454$	35.1501	1.64968
$455$	10.0616	0.471696
$456$	4.51436	0.211404
$457$	−1.78591	−0.0835413	−0.0417707	−	0.999127i	$-0.513300\pi$
$457$	−1.78591	−0.0835413	−0.0417707	+	0.999127i	$0.513300\pi$
$458$	16.8944	0.789423
$459$	37.3051	1.74125
$460$	−11.8489	−0.552459
$461$	−31.9248	−1.48689	−0.743443	−	0.668799i	$-0.766809\pi$
$461$	−31.9248	−1.48689	−0.743443	+	0.668799i	$0.766809\pi$
$462$	1.24505	0.0579250
$463$	−11.1489	−0.518133	−0.259066	−	0.965860i	$-0.583415\pi$
$463$	−11.1489	−0.518133	−0.259066	+	0.965860i	$0.583415\pi$
$464$	35.7630	1.66025
$465$	4.88464	0.226520
$466$	47.0006	2.17726
$467$	7.93368	0.367127	0.183563	−	0.983008i	$-0.441237\pi$
$467$	7.93368	0.367127	0.183563	+	0.983008i	$0.441237\pi$
$468$	−2.38138	−0.110079
$469$	12.5282	0.578501
$470$	43.9094	2.02539
$471$	−7.30560	−0.336624
$472$	−11.3671	−0.523211
$473$	1.35795	0.0624386
$474$	−28.5287	−1.31037
$475$	14.2021	0.651636
$476$	−4.57706	−0.209789
$477$	1.97018	0.0902085
$478$	−41.1136	−1.88049
$479$	28.5082	1.30257	0.651287	−	0.758832i	$-0.274230\pi$
$479$	28.5082	1.30257	0.651287	+	0.758832i	$0.274230\pi$
$480$	18.2654	0.833698
$481$	−2.70150	−0.123178
$482$	−22.6910	−1.03355
$483$	−6.05841	−0.275667
$484$	−7.34481	−0.333855
$485$	43.5219	1.97623
$486$	−20.0385	−0.908964
$487$	−11.8338	−0.536240	−0.268120	−	0.963386i	$-0.586402\pi$
$487$	−11.8338	−0.536240	−0.268120	+	0.963386i	$0.586402\pi$
$488$	−11.8213	−0.535127
$489$	4.91153	0.222107
$490$	−6.10708	−0.275890
$491$	26.9887	1.21798	0.608992	−	0.793176i	$-0.291574\pi$
$491$	26.9887	1.21798	0.608992	+	0.793176i	$0.291574\pi$
$492$	−2.80939	−0.126657
$493$	48.4755	2.18323
$494$	−7.09135	−0.319055
$495$	2.75997	0.124052
$496$	−4.90309	−0.220155
$497$	−9.56293	−0.428956
$498$	21.0933	0.945213
$499$	12.1632	0.544501	0.272251	−	0.962226i	$-0.412232\pi$
$499$	12.1632	0.544501	0.272251	+	0.962226i	$0.412232\pi$
$500$	9.93061	0.444110
$501$	−27.0248	−1.20738
$502$	28.8751	1.28876
$503$	8.31360	0.370685	0.185343	−	0.982674i	$-0.440661\pi$
$503$	8.31360	0.370685	0.185343	+	0.982674i	$0.440661\pi$
$504$	−2.75214	−0.122590
$505$	−31.9547	−1.42197
$506$	−4.38537	−0.194953
$507$	−7.47803	−0.332111
$508$	9.52459	0.422585
$509$	−20.8149	−0.922605	−0.461302	−	0.887243i	$-0.652618\pi$
$509$	−20.8149	−0.922605	−0.461302	+	0.887243i	$0.652618\pi$
$510$	53.2306	2.35709
$511$	−6.72747	−0.297606
$512$	2.75060	0.121560
$513$	−8.98589	−0.396737
$514$	−38.9844	−1.71953
$515$	−18.3982	−0.810719
$516$	−2.11853	−0.0932630
$517$	4.16266	0.183074
$518$	1.63972	0.0720454
$519$	16.2865	0.714899
$520$	21.6343	0.948726
$521$	22.0490	0.965985	0.482993	−	0.875624i	$-0.339550\pi$
$521$	22.0490	0.965985	0.482993	+	0.875624i	$0.339550\pi$
$522$	−15.3084	−0.670031
$523$	27.8154	1.21628	0.608142	−	0.793828i	$-0.291915\pi$
$523$	27.8154	1.21628	0.608142	+	0.793828i	$0.291915\pi$
$524$	−1.98553	−0.0867383
$525$	11.6351	0.507797
$526$	−23.3718	−1.01906
$527$	−6.64597	−0.289503
$528$	3.72294	0.162020
$529$	−1.66082	−0.0722097
$530$	9.40036	0.408325
$531$	6.76659	0.293645
$532$	1.10250	0.0477996
$533$	−8.40274	−0.363963
$534$	12.4704	0.539648
$535$	44.2110	1.91141
$536$	26.9380	1.16354
$537$	−31.3543	−1.35304
$538$	−5.13377	−0.221333
$539$	−0.578957	−0.0249375
$540$	−14.3979	−0.619587
$541$	27.1447	1.16704	0.583521	−	0.812098i	$-0.301675\pi$
$541$	27.1447	1.16704	0.583521	+	0.812098i	$0.301675\pi$
$542$	24.9929	1.07354
$543$	26.5678	1.14013
$544$	−24.8517	−1.06551
$545$	−40.3050	−1.72648
$546$	−5.80960	−0.248628
$547$	−4.18129	−0.178779	−0.0893895	−	0.995997i	$-0.528492\pi$
$547$	−4.18129	−0.178779	−0.0893895	+	0.995997i	$0.528492\pi$
$548$	−1.49532	−0.0638768
$549$	7.03701	0.300332
$550$	8.42204	0.359117
$551$	−11.6766	−0.497439
$552$	−13.0266	−0.554451
$553$	13.2661	0.564130
$554$	−12.1124	−0.514608
$555$	−4.88464	−0.207341
$556$	−4.53262	−0.192226
$557$	−25.2626	−1.07041	−0.535206	−	0.844722i	$-0.679766\pi$
$557$	−25.2626	−1.07041	−0.535206	+	0.844722i	$0.679766\pi$
$558$	2.09878	0.0888484
$559$	−6.33640	−0.268001
$560$	−18.2613	−0.771682
$561$	5.04632	0.213056
$562$	−36.4721	−1.53848
$563$	−16.0142	−0.674917	−0.337458	−	0.941340i	$-0.609567\pi$
$563$	−16.0142	−0.674917	−0.337458	+	0.941340i	$0.609567\pi$
$564$	−6.49414	−0.273453
$565$	−68.4553	−2.87994
$566$	55.1412	2.31776
$567$	−3.52183	−0.147903
$568$	−20.5620	−0.862762
$569$	−22.2794	−0.934001	−0.467001	−	0.884257i	$-0.654665\pi$
$569$	−22.2794	−0.934001	−0.467001	+	0.884257i	$0.654665\pi$
$570$	−12.8220	−0.537054
$571$	−9.19190	−0.384669	−0.192335	−	0.981329i	$-0.561606\pi$
$571$	−9.19190	−0.384669	−0.192335	+	0.981329i	$0.561606\pi$
$572$	−1.07716	−0.0450383
$573$	34.2620	1.43131
$574$	5.10019	0.212878
$575$	−40.9816	−1.70905
$576$	−4.70341	−0.195975
$577$	41.1948	1.71496	0.857482	−	0.514514i	$-0.172028\pi$
$577$	41.1948	1.71496	0.857482	+	0.514514i	$0.172028\pi$
$578$	−44.5496	−1.85302
$579$	0.860137	0.0357461
$580$	−18.7091	−0.776855
$581$	−9.80853	−0.406926
$582$	−25.1296	−1.04165
$583$	0.891163	0.0369082
$584$	−14.4652	−0.598576
$585$	−12.8785	−0.532459
$586$	−4.63065	−0.191290
$587$	−31.2445	−1.28960	−0.644799	−	0.764352i	$-0.723059\pi$
$587$	−31.2445	−1.28960	−0.644799	+	0.764352i	$0.723059\pi$
$588$	0.903227	0.0372485
$589$	1.60086	0.0659621
$590$	32.2855	1.32917
$591$	1.39829	0.0575182
$592$	4.90309	0.201516
$593$	38.3221	1.57370	0.786849	−	0.617145i	$-0.211711\pi$
$593$	38.3221	1.57370	0.786849	+	0.617145i	$0.211711\pi$
$594$	−5.32876	−0.218642
$595$	−24.7526	−1.01476
$596$	8.08333	0.331106
$597$	−28.7700	−1.17748
$598$	20.4628	0.836787
$599$	−6.83489	−0.279266	−0.139633	−	0.990203i	$-0.544592\pi$
$599$	−6.83489	−0.279266	−0.139633	+	0.990203i	$0.544592\pi$
$600$	25.0175	1.02133
$601$	33.6816	1.37390	0.686950	−	0.726705i	$-0.258949\pi$
$601$	33.6816	1.37390	0.686950	+	0.726705i	$0.258949\pi$
$602$	3.84599	0.156751
$603$	−16.0356	−0.653021
$604$	2.74622	0.111742
$605$	−39.7206	−1.61487
$606$	18.4507	0.749508
$607$	−16.7511	−0.679908	−0.339954	−	0.940442i	$-0.610412\pi$
$607$	−16.7511	−0.679908	−0.339954	+	0.940442i	$0.610412\pi$
$608$	5.98618	0.242772
$609$	−9.56606	−0.387636
$610$	33.5758	1.35944
$611$	−19.4236	−0.785796
$612$	5.85844	0.236813
$613$	−7.58646	−0.306414	−0.153207	−	0.988194i	$-0.548960\pi$
$613$	−7.58646	−0.306414	−0.153207	+	0.988194i	$0.548960\pi$
$614$	−20.0280	−0.808263
$615$	−15.1931	−0.612646
$616$	−1.24486	−0.0501569
$617$	−23.3584	−0.940374	−0.470187	−	0.882567i	$-0.655813\pi$
$617$	−23.3584	−0.940374	−0.470187	+	0.882567i	$0.655813\pi$
$618$	10.6231	0.427324
$619$	−34.2218	−1.37549	−0.687745	−	0.725952i	$-0.741399\pi$
$619$	−34.2218	−1.37549	−0.687745	+	0.725952i	$0.741399\pi$
$620$	2.56502	0.103014
$621$	25.9297	1.04052
$622$	−18.5090	−0.742144
$623$	−5.79883	−0.232325
$624$	−17.3718	−0.695429
$625$	9.34674	0.373870
$626$	−0.472113	−0.0188694
$627$	−1.21554	−0.0485439
$628$	−3.83631	−0.153085
$629$	6.64597	0.264992
$630$	7.81680	0.311429
$631$	−10.6298	−0.423165	−0.211582	−	0.977360i	$-0.567862\pi$
$631$	−10.6298	−0.423165	−0.211582	+	0.977360i	$0.567862\pi$
$632$	28.5244	1.13464
$633$	3.00397	0.119397
$634$	−22.0572	−0.876004
$635$	51.5088	2.04406
$636$	−1.39030	−0.0551289
$637$	2.70150	0.107037
$638$	−6.92438	−0.274139
$639$	12.2401	0.484213
$640$	−50.2956	−1.98811
$641$	−10.7906	−0.426204	−0.213102	−	0.977030i	$-0.568357\pi$
$641$	−10.7906	−0.426204	−0.213102	+	0.977030i	$0.568357\pi$
$642$	−25.5275	−1.00749
$643$	−33.5373	−1.32258	−0.661291	−	0.750129i	$-0.729991\pi$
$643$	−33.5373	−1.32258	−0.661291	+	0.750129i	$0.729991\pi$
$644$	−3.18139	−0.125364
$645$	−11.4570	−0.451117
$646$	17.4454	0.686381
$647$	−37.1379	−1.46004	−0.730021	−	0.683425i	$-0.760490\pi$
$647$	−37.1379	−1.46004	−0.730021	+	0.683425i	$0.760490\pi$
$648$	−7.57257	−0.297479
$649$	3.06070	0.120143
$650$	−39.2985	−1.54142
$651$	1.31150	0.0514019
$652$	2.57914	0.101007
$653$	−5.27027	−0.206242	−0.103121	−	0.994669i	$-0.532883\pi$
$653$	−5.27027	−0.206242	−0.103121	+	0.994669i	$0.532883\pi$
$654$	23.2721	0.910013
$655$	−10.7377	−0.419557
$656$	15.2505	0.595433
$657$	8.61087	0.335942
$658$	11.7895	0.459603
$659$	−34.0946	−1.32814	−0.664068	−	0.747672i	$-0.731172\pi$
$659$	−34.0946	−1.32814	−0.664068	+	0.747672i	$0.731172\pi$
$660$	−1.94763	−0.0758113
$661$	−0.767012	−0.0298333	−0.0149167	−	0.999889i	$-0.504748\pi$
$661$	−0.767012	−0.0298333	−0.0149167	+	0.999889i	$0.504748\pi$
$662$	−31.7277	−1.23313
$663$	−23.5469	−0.914486
$664$	−21.0901	−0.818453
$665$	5.96231	0.231209
$666$	−2.09878	−0.0813260
$667$	33.6940	1.30464
$668$	−14.1912	−0.549075
$669$	0.597077	0.0230843
$670$	−76.5110	−2.95588
$671$	3.18302	0.122879
$672$	4.90419	0.189183
$673$	−22.2499	−0.857670	−0.428835	−	0.903383i	$-0.641076\pi$
$673$	−22.2499	−0.857670	−0.428835	+	0.903383i	$0.641076\pi$
$674$	−26.4642	−1.01936
$675$	−49.7977	−1.91671
$676$	−3.92686	−0.151033
$677$	−20.6341	−0.793034	−0.396517	−	0.918027i	$-0.629781\pi$
$677$	−20.6341	−0.793034	−0.396517	+	0.918027i	$0.629781\pi$
$678$	39.5262	1.51799
$679$	11.6854	0.448446
$680$	−53.2225	−2.04099
$681$	−28.1142	−1.07734
$682$	0.949330	0.0363517
$683$	33.0073	1.26299	0.631494	−	0.775381i	$-0.282442\pi$
$683$	33.0073	1.26299	0.631494	+	0.775381i	$0.282442\pi$
$684$	−1.41116	−0.0539569
$685$	−8.08664	−0.308975
$686$	−1.63972	−0.0626050
$687$	−13.5127	−0.515540
$688$	11.5002	0.438443
$689$	−4.15831	−0.158419
$690$	36.9992	1.40853
$691$	19.6939	0.749190	0.374595	−	0.927189i	$-0.377782\pi$
$691$	19.6939	0.749190	0.374595	+	0.927189i	$0.377782\pi$
$692$	8.55237	0.325112
$693$	0.741041	0.0281498
$694$	−44.3844	−1.68481
$695$	−24.5123	−0.929804
$696$	−20.5687	−0.779656
$697$	20.6716	0.782992
$698$	59.4696	2.25096
$699$	−37.5926	−1.42188
$700$	6.10981	0.230929
$701$	−30.8734	−1.16607	−0.583036	−	0.812446i	$-0.698135\pi$
$701$	−30.8734	−1.16607	−0.583036	+	0.812446i	$0.698135\pi$
$702$	24.8648	0.938463
$703$	−1.60086	−0.0603774
$704$	−2.12747	−0.0801820
$705$	−35.1202	−1.32270
$706$	9.60756	0.361585
$707$	−8.57970	−0.322673
$708$	−4.77497	−0.179454
$709$	36.2906	1.36292	0.681462	−	0.731854i	$-0.261344\pi$
$709$	36.2906	1.36292	0.681462	+	0.731854i	$0.261344\pi$
$710$	58.4015	2.19177
$711$	−16.9800	−0.636800
$712$	−12.4685	−0.467278
$713$	−4.61943	−0.172999
$714$	14.2922	0.534872
$715$	−5.82525	−0.217852
$716$	−16.4648	−0.615317
$717$	32.8840	1.22807
$718$	7.47862	0.279100
$719$	25.3424	0.945110	0.472555	−	0.881301i	$-0.343332\pi$
$719$	25.3424	0.945110	0.472555	+	0.881301i	$0.343332\pi$
$720$	23.3737	0.871088
$721$	−4.93983	−0.183969
$722$	26.9526	1.00307
$723$	18.1490	0.674968
$724$	13.9512	0.518494
$725$	−64.7088	−2.40323
$726$	22.9347	0.851187
$727$	40.4114	1.49878	0.749388	−	0.662131i	$-0.230348\pi$
$727$	40.4114	1.49878	0.749388	+	0.662131i	$0.230348\pi$
$728$	5.80871	0.215285
$729$	26.5929	0.984923
$730$	41.0852	1.52063
$731$	15.5882	0.576550
$732$	−4.96581	−0.183541
$733$	19.1287	0.706534	0.353267	−	0.935522i	$-0.385071\pi$
$733$	19.1287	0.706534	0.353267	+	0.935522i	$0.385071\pi$
$734$	35.8947	1.32490
$735$	4.88464	0.180172
$736$	−17.2737	−0.636718
$737$	−7.25332	−0.267180
$738$	−6.52802	−0.240300
$739$	−4.98062	−0.183215	−0.0916076	−	0.995795i	$-0.529201\pi$
$739$	−4.98062	−0.183215	−0.0916076	+	0.995795i	$0.529201\pi$
$740$	−2.56502	−0.0942919
$741$	5.67188	0.208362
$742$	2.52396	0.0926573
$743$	−37.9440	−1.39203	−0.696016	−	0.718026i	$-0.745046\pi$
$743$	−37.9440	−1.39203	−0.696016	+	0.718026i	$0.745046\pi$
$744$	2.81997	0.103385
$745$	43.7145	1.60157
$746$	−26.4702	−0.969142
$747$	12.5545	0.459345
$748$	2.64992	0.0968907
$749$	11.8705	0.433738
$750$	−31.0091	−1.13229
$751$	−13.3454	−0.486981	−0.243490	−	0.969903i	$-0.578292\pi$
$751$	−13.3454	−0.486981	−0.243490	+	0.969903i	$0.578292\pi$
$752$	35.2529	1.28554
$753$	−23.0952	−0.841637
$754$	32.3102	1.17667
$755$	14.8515	0.540501
$756$	−3.86577	−0.140597
$757$	−14.6247	−0.531543	−0.265772	−	0.964036i	$-0.585627\pi$
$757$	−14.6247	−0.531543	−0.265772	+	0.964036i	$0.585627\pi$
$758$	−16.9357	−0.615131
$759$	3.50756	0.127316
$760$	12.8200	0.465031
$761$	51.9916	1.88469	0.942347	−	0.334638i	$-0.108614\pi$
$761$	51.9916	1.88469	0.942347	+	0.334638i	$0.108614\pi$
$762$	−29.7412	−1.07741
$763$	−10.8217	−0.391772
$764$	17.9916	0.650914
$765$	31.6823	1.14548
$766$	−27.3755	−0.989116
$767$	−14.2817	−0.515682
$768$	19.4021	0.700112
$769$	−49.4381	−1.78278	−0.891391	−	0.453235i	$-0.850270\pi$
$769$	−49.4381	−1.78278	−0.891391	+	0.453235i	$0.850270\pi$
$770$	3.53574	0.127419
$771$	31.1810	1.12295
$772$	0.451674	0.0162561
$773$	−25.0187	−0.899861	−0.449931	−	0.893063i	$-0.648551\pi$
$773$	−25.0187	−0.899861	−0.449931	+	0.893063i	$0.648551\pi$
$774$	−4.92270	−0.176943
$775$	8.87156	0.318676
$776$	25.1258	0.901962
$777$	−1.31150	−0.0470499
$778$	−40.0545	−1.43602
$779$	−4.97929	−0.178402
$780$	9.08794	0.325400
$781$	5.53653	0.198113
$782$	−50.3406	−1.80018
$783$	40.9423	1.46316
$784$	−4.90309	−0.175110
$785$	−20.7467	−0.740481
$786$	6.19996	0.221145
$787$	−28.4775	−1.01511	−0.507556	−	0.861619i	$-0.669451\pi$
$787$	−28.4775	−1.01511	−0.507556	+	0.861619i	$0.669451\pi$
$788$	0.734272	0.0261573
$789$	18.6935	0.665508
$790$	−81.0169	−2.88245
$791$	−18.3800	−0.653516
$792$	1.59337	0.0566179
$793$	−14.8525	−0.527426
$794$	−12.3657	−0.438842
$795$	−7.51870	−0.266661
$796$	−15.1077	−0.535478
$797$	10.3889	0.367995	0.183997	−	0.982927i	$-0.441096\pi$
$797$	10.3889	0.367995	0.183997	+	0.982927i	$0.441096\pi$
$798$	−3.44265	−0.121868
$799$	47.7841	1.69048
$800$	33.1740	1.17288
$801$	7.42226	0.262253
$802$	−38.3990	−1.35591
$803$	3.89492	0.137449
$804$	11.3159	0.399079
$805$	−17.2049	−0.606392
$806$	−4.42972	−0.156030
$807$	4.10616	0.144544
$808$	−18.4479	−0.648994
$809$	−36.5471	−1.28493	−0.642463	−	0.766316i	$-0.722088\pi$
$809$	−36.5471	−1.28493	−0.642463	+	0.766316i	$0.722088\pi$
$810$	21.5081	0.755718
$811$	49.2372	1.72895	0.864476	−	0.502674i	$-0.167650\pi$
$811$	49.2372	1.72895	0.864476	+	0.502674i	$0.167650\pi$
$812$	−5.02332	−0.176284
$813$	−19.9901	−0.701084
$814$	−0.949330	−0.0332740
$815$	13.9479	0.488575
$816$	42.7364	1.49607
$817$	−3.75482	−0.131365
$818$	−35.3225	−1.23502
$819$	−3.45781	−0.120826
$820$	−7.97821	−0.278611
$821$	−12.5383	−0.437590	−0.218795	−	0.975771i	$-0.570213\pi$
$821$	−12.5383	−0.437590	−0.218795	+	0.975771i	$0.570213\pi$
$822$	4.66924	0.162858
$823$	−28.4126	−0.990400	−0.495200	−	0.868779i	$-0.664905\pi$
$823$	−28.4126	−0.990400	−0.495200	+	0.868779i	$0.664905\pi$
$824$	−10.6215	−0.370017
$825$	−6.73621	−0.234525
$826$	8.66852	0.301616
$827$	21.0520	0.732050	0.366025	−	0.930605i	$-0.380718\pi$
$827$	21.0520	0.732050	0.366025	+	0.930605i	$0.380718\pi$
$828$	4.07204	0.141513
$829$	−29.4997	−1.02457	−0.512284	−	0.858816i	$-0.671201\pi$
$829$	−29.4997	−1.02457	−0.512284	+	0.858816i	$0.671201\pi$
$830$	59.9014	2.07921
$831$	9.68792	0.336070
$832$	9.92710	0.344160
$833$	−6.64597	−0.230269
$834$	14.1534	0.490093
$835$	−76.7459	−2.65590
$836$	−0.638302	−0.0220761
$837$	−5.61318	−0.194020
$838$	25.9747	0.897280
$839$	7.22193	0.249329	0.124664	−	0.992199i	$-0.460215\pi$
$839$	7.22193	0.249329	0.124664	+	0.992199i	$0.460215\pi$
$840$	10.5028	0.362382
$841$	24.2019	0.834549
$842$	−27.7745	−0.957173
$843$	29.1715	1.00472
$844$	1.57744	0.0542979
$845$	−21.2364	−0.730553
$846$	−15.0901	−0.518807
$847$	−10.6648	−0.366447
$848$	7.54711	0.259169
$849$	−44.1037	−1.51363
$850$	96.6784	3.31604
$851$	4.61943	0.158352
$852$	−8.63750	−0.295916
$853$	−6.51967	−0.223229	−0.111615	−	0.993752i	$-0.535602\pi$
$853$	−6.51967	−0.223229	−0.111615	+	0.993752i	$0.535602\pi$
$854$	9.01495	0.308485
$855$	−7.63151	−0.260992
$856$	25.5236	0.872379
$857$	4.50385	0.153849	0.0769243	−	0.997037i	$-0.475490\pi$
$857$	4.50385	0.153849	0.0769243	+	0.997037i	$0.475490\pi$
$858$	3.36351	0.114828
$859$	11.3825	0.388365	0.194183	−	0.980965i	$-0.437795\pi$
$859$	11.3825	0.388365	0.194183	+	0.980965i	$0.437795\pi$
$860$	−6.01627	−0.205153
$861$	−4.07929	−0.139022
$862$	−39.4192	−1.34262
$863$	12.5481	0.427143	0.213571	−	0.976927i	$-0.431490\pi$
$863$	12.5481	0.427143	0.213571	+	0.976927i	$0.431490\pi$
$864$	−20.9897	−0.714084
$865$	46.2510	1.57258
$866$	8.91399	0.302910
$867$	35.6322	1.21013
$868$	0.688696	0.0233759
$869$	−7.68048	−0.260543
$870$	58.4207	1.98065
$871$	33.8451	1.14680
$872$	−23.2686	−0.787974
$873$	−14.9569	−0.506213
$874$	12.1258	0.410163
$875$	14.4194	0.487466
$876$	−6.07643	−0.205304
$877$	17.3901	0.587224	0.293612	−	0.955925i	$-0.405143\pi$
$877$	17.3901	0.587224	0.293612	+	0.955925i	$0.405143\pi$
$878$	29.3421	0.990247
$879$	3.70374	0.124924
$880$	10.5725	0.356400
$881$	−46.3239	−1.56069	−0.780346	−	0.625348i	$-0.784957\pi$
$881$	−46.3239	−1.56069	−0.780346	+	0.625348i	$0.784957\pi$
$882$	2.09878	0.0706695
$883$	5.12198	0.172368	0.0861842	−	0.996279i	$-0.472533\pi$
$883$	5.12198	0.172368	0.0861842	+	0.996279i	$0.472533\pi$
$884$	−12.3649	−0.415878
$885$	−25.8230	−0.868029
$886$	33.3265	1.11963
$887$	−5.84064	−0.196110	−0.0980548	−	0.995181i	$-0.531262\pi$
$887$	−5.84064	−0.196110	−0.0980548	+	0.995181i	$0.531262\pi$
$888$	−2.81997	−0.0946318
$889$	13.8299	0.463840
$890$	35.4139	1.18708
$891$	2.03899	0.0683088
$892$	0.313537	0.0104980
$893$	−11.5100	−0.385169
$894$	−25.2408	−0.844178
$895$	−89.0410	−2.97631
$896$	−13.5041	−0.451142
$897$	−16.3668	−0.546472
$898$	−64.1580	−2.14098
$899$	−7.29396	−0.243267
$900$	−7.82029	−0.260676
$901$	10.2299	0.340806
$902$	−2.95279	−0.0983172
$903$	−3.07614	−0.102368
$904$	−39.5202	−1.31442
$905$	75.4481	2.50798
$906$	−8.57527	−0.284894
$907$	−46.0574	−1.52931	−0.764655	−	0.644440i	$-0.777091\pi$
$907$	−46.0574	−1.52931	−0.764655	+	0.644440i	$0.777091\pi$
$908$	−14.7633	−0.489938
$909$	10.9817	0.364239
$910$	−16.4983	−0.546913
$911$	−15.7571	−0.522055	−0.261028	−	0.965331i	$-0.584061\pi$
$911$	−15.7571	−0.522055	−0.261028	+	0.965331i	$0.584061\pi$
$912$	−10.2942	−0.340874
$913$	5.67872	0.187938
$914$	2.92840	0.0968629
$915$	−26.8550	−0.887798
$916$	−7.09576	−0.234451
$917$	−2.88303	−0.0952060
$918$	−61.1700	−2.01891
$919$	−26.8744	−0.886503	−0.443252	−	0.896397i	$-0.646175\pi$
$919$	−26.8744	−0.886503	−0.443252	+	0.896397i	$0.646175\pi$
$920$	−36.9935	−1.21964
$921$	16.0190	0.527844
$922$	52.3479	1.72399
$923$	−25.8343	−0.850346
$924$	−0.522930	−0.0172031
$925$	−8.87156	−0.291695
$926$	18.2811	0.600754
$927$	6.32277	0.207667
$928$	−27.2748	−0.895338
$929$	51.8859	1.70232	0.851161	−	0.524905i	$-0.175899\pi$
$929$	51.8859	1.70232	0.851161	+	0.524905i	$0.175899\pi$
$930$	−8.00946	−0.262640
$931$	1.60086	0.0524659
$932$	−19.7406	−0.646625
$933$	14.8041	0.484665
$934$	−13.0090	−0.425669
$935$	14.3307	0.468664
$936$	−7.43491	−0.243018
$937$	45.3708	1.48220	0.741099	−	0.671396i	$-0.234305\pi$
$937$	45.3708	1.48220	0.741099	+	0.671396i	$0.234305\pi$
$938$	−20.5429	−0.670749
$939$	0.377611	0.0123229
$940$	−18.4423	−0.601521
$941$	−38.4539	−1.25356	−0.626781	−	0.779196i	$-0.715628\pi$
$941$	−38.4539	−1.25356	−0.626781	+	0.779196i	$0.715628\pi$
$942$	11.9792	0.390302
$943$	14.3683	0.467895
$944$	25.9205	0.843641
$945$	−20.9060	−0.680073
$946$	−2.22666	−0.0723951
$947$	−46.1416	−1.49940	−0.749701	−	0.661777i	$-0.769802\pi$
$947$	−46.1416	−1.49940	−0.749701	+	0.661777i	$0.769802\pi$
$948$	11.9823	0.389166
$949$	−18.1743	−0.589962
$950$	−23.2875	−0.755546
$951$	17.6421	0.572083
$952$	−14.2900	−0.463142
$953$	−27.3629	−0.886371	−0.443185	−	0.896430i	$-0.646152\pi$
$953$	−27.3629	−0.886371	−0.443185	+	0.896430i	$0.646152\pi$
$954$	−3.23056	−0.104593
$955$	97.2984	3.14850
$956$	17.2680	0.558487
$957$	5.53834	0.179029
$958$	−46.7456	−1.51028
$959$	−2.17123	−0.0701126
$960$	17.9494	0.579313
$961$	1.00000	0.0322581
$962$	4.42972	0.142820
$963$	−15.1937	−0.489610
$964$	9.53038	0.306953
$965$	2.44265	0.0786315
$966$	9.93412	0.319625
$967$	8.11338	0.260909	0.130454	−	0.991454i	$-0.458356\pi$
$967$	8.11338	0.260909	0.130454	+	0.991454i	$0.458356\pi$
$968$	−22.9312	−0.737038
$969$	−13.9534	−0.448248
$970$	−71.3639	−2.29136
$971$	−12.5374	−0.402345	−0.201172	−	0.979556i	$-0.564475\pi$
$971$	−12.5374	−0.402345	−0.201172	+	0.979556i	$0.564475\pi$
$972$	8.41631	0.269953
$973$	−6.58145	−0.210991
$974$	19.4041	0.621749
$975$	31.4322	1.00664
$976$	26.9564	0.862855
$977$	19.7202	0.630905	0.315452	−	0.948941i	$-0.397844\pi$
$977$	19.7202	0.630905	0.315452	+	0.948941i	$0.397844\pi$
$978$	−8.05356	−0.257524
$979$	3.35728	0.107299
$980$	2.56502	0.0819364
$981$	13.8513	0.442239
$982$	−44.2541	−1.41220
$983$	−1.78068	−0.0567950	−0.0283975	−	0.999597i	$-0.509040\pi$
$983$	−1.78068	−0.0567950	−0.0283975	+	0.999597i	$0.509040\pi$
$984$	−8.77120	−0.279616
$985$	3.97093	0.126524
$986$	−79.4865	−2.53136
$987$	−9.42962	−0.300148
$988$	2.97842	0.0947560
$989$	10.8349	0.344531
$990$	−4.52559	−0.143833
$991$	33.3326	1.05885	0.529423	−	0.848358i	$-0.322408\pi$
$991$	33.3326	1.05885	0.529423	+	0.848358i	$0.322408\pi$
$992$	3.73936	0.118725
$993$	25.3768	0.805309
$994$	15.6806	0.497357
$995$	−81.7021	−2.59013
$996$	−8.85933	−0.280719
$997$	−6.71322	−0.212610	−0.106305	−	0.994334i	$-0.533902\pi$
$997$	−6.71322	−0.212610	−0.106305	+	0.994334i	$0.533902\pi$
$998$	−19.9444	−0.631328
$999$	5.61318	0.177593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.18	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.18	✓	66	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.63972 q^{2} +1.31150 q^{3} +0.688696 q^{4} +3.72445 q^{5} -2.15050 q^{6} +1.00000 q^{7} +2.15018 q^{8} -1.27996 q^{9} +O(q^{10})\)	\(q-1.63972 q^{2} +1.31150 q^{3} +0.688696 q^{4} +3.72445 q^{5} -2.15050 q^{6} +1.00000 q^{7} +2.15018 q^{8} -1.27996 q^{9} -6.10708 q^{10} -0.578957 q^{11} +0.903227 q^{12} +2.70150 q^{13} -1.63972 q^{14} +4.88464 q^{15} -4.90309 q^{16} -6.64597 q^{17} +2.09878 q^{18} +1.60086 q^{19} +2.56502 q^{20} +1.31150 q^{21} +0.949330 q^{22} -4.61943 q^{23} +2.81997 q^{24} +8.87156 q^{25} -4.42972 q^{26} -5.61318 q^{27} +0.688696 q^{28} -7.29396 q^{29} -8.00946 q^{30} +1.00000 q^{31} +3.73936 q^{32} -0.759305 q^{33} +10.8976 q^{34} +3.72445 q^{35} -0.881502 q^{36} -1.00000 q^{37} -2.62496 q^{38} +3.54303 q^{39} +8.00824 q^{40} -3.11039 q^{41} -2.15050 q^{42} -2.34551 q^{43} -0.398726 q^{44} -4.76714 q^{45} +7.57460 q^{46} -7.18993 q^{47} -6.43042 q^{48} +1.00000 q^{49} -14.5469 q^{50} -8.71622 q^{51} +1.86051 q^{52} -1.53926 q^{53} +9.20407 q^{54} -2.15630 q^{55} +2.15018 q^{56} +2.09953 q^{57} +11.9601 q^{58} -5.28657 q^{59} +3.36403 q^{60} -5.49785 q^{61} -1.63972 q^{62} -1.27996 q^{63} +3.67466 q^{64} +10.0616 q^{65} +1.24505 q^{66} +12.5282 q^{67} -4.57706 q^{68} -6.05841 q^{69} -6.10708 q^{70} -9.56293 q^{71} -2.75214 q^{72} -6.72747 q^{73} +1.63972 q^{74} +11.6351 q^{75} +1.10250 q^{76} -0.578957 q^{77} -5.80960 q^{78} +13.2661 q^{79} -18.2613 q^{80} -3.52183 q^{81} +5.10019 q^{82} -9.80853 q^{83} +0.903227 q^{84} -24.7526 q^{85} +3.84599 q^{86} -9.56606 q^{87} -1.24486 q^{88} -5.79883 q^{89} +7.81680 q^{90} +2.70150 q^{91} -3.18139 q^{92} +1.31150 q^{93} +11.7895 q^{94} +5.96231 q^{95} +4.90419 q^{96} +11.6854 q^{97} -1.63972 q^{98} +0.741041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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