LMFDB - Embedded newform 4033.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96262 q^{2} -1.03474 q^{3} +1.85187 q^{4} +3.48986 q^{5} +2.03080 q^{6} -2.58926 q^{7} +0.290726 q^{8} -1.92931 q^{9} +O(q^{10})$	\(q-1.96262 q^{2} -1.03474 q^{3} +1.85187 q^{4} +3.48986 q^{5} +2.03080 q^{6} -2.58926 q^{7} +0.290726 q^{8} -1.92931 q^{9} -6.84926 q^{10} +5.41222 q^{11} -1.91620 q^{12} +1.24515 q^{13} +5.08173 q^{14} -3.61110 q^{15} -4.27432 q^{16} +1.57417 q^{17} +3.78650 q^{18} +5.32024 q^{19} +6.46276 q^{20} +2.67922 q^{21} -10.6221 q^{22} +0.541267 q^{23} -0.300827 q^{24} +7.17912 q^{25} -2.44376 q^{26} +5.10056 q^{27} -4.79497 q^{28} -3.46260 q^{29} +7.08721 q^{30} +4.16239 q^{31} +7.80740 q^{32} -5.60024 q^{33} -3.08949 q^{34} -9.03616 q^{35} -3.57283 q^{36} +1.00000 q^{37} -10.4416 q^{38} -1.28841 q^{39} +1.01459 q^{40} +3.40187 q^{41} -5.25828 q^{42} +0.894280 q^{43} +10.0227 q^{44} -6.73302 q^{45} -1.06230 q^{46} -5.44804 q^{47} +4.42282 q^{48} -0.295722 q^{49} -14.0899 q^{50} -1.62886 q^{51} +2.30586 q^{52} +9.67344 q^{53} -10.0104 q^{54} +18.8879 q^{55} -0.752767 q^{56} -5.50507 q^{57} +6.79575 q^{58} -4.87176 q^{59} -6.68728 q^{60} -0.171290 q^{61} -8.16918 q^{62} +4.99549 q^{63} -6.77431 q^{64} +4.34541 q^{65} +10.9911 q^{66} -2.32810 q^{67} +2.91516 q^{68} -0.560071 q^{69} +17.7345 q^{70} -12.8303 q^{71} -0.560902 q^{72} +15.9341 q^{73} -1.96262 q^{74} -7.42853 q^{75} +9.85237 q^{76} -14.0136 q^{77} +2.52866 q^{78} +10.9404 q^{79} -14.9168 q^{80} +0.510174 q^{81} -6.67657 q^{82} +12.9999 q^{83} +4.96155 q^{84} +5.49363 q^{85} -1.75513 q^{86} +3.58289 q^{87} +1.57347 q^{88} -7.68383 q^{89} +13.2144 q^{90} -3.22403 q^{91} +1.00235 q^{92} -4.30700 q^{93} +10.6924 q^{94} +18.5669 q^{95} -8.07864 q^{96} +0.658094 q^{97} +0.580389 q^{98} -10.4418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−1.96262	−1.38778	−0.693890	−	0.720081i	$-0.744105\pi$
$2$	−1.96262	−1.38778	−0.693890	+	0.720081i	$0.744105\pi$
$3$	−1.03474	−0.597408	−0.298704	−	0.954346i	$-0.596554\pi$
$3$	−1.03474	−0.597408	−0.298704	+	0.954346i	$0.596554\pi$
$4$	1.85187	0.925934
$5$	3.48986	1.56071	0.780356	−	0.625335i	$-0.215038\pi$
$5$	3.48986	1.56071	0.780356	+	0.625335i	$0.215038\pi$
$6$	2.03080	0.829071
$7$	−2.58926	−0.978649	−0.489325	−	0.872102i	$-0.662757\pi$
$7$	−2.58926	−0.978649	−0.489325	+	0.872102i	$0.662757\pi$
$8$	0.290726	0.102787
$9$	−1.92931	−0.643104
$10$	−6.84926	−2.16593
$11$	5.41222	1.63184	0.815922	−	0.578162i	$-0.196230\pi$
$11$	5.41222	1.63184	0.815922	+	0.578162i	$0.196230\pi$
$12$	−1.91620	−0.553160
$13$	1.24515	0.345344	0.172672	−	0.984979i	$-0.444760\pi$
$13$	1.24515	0.345344	0.172672	+	0.984979i	$0.444760\pi$
$14$	5.08173	1.35815
$15$	−3.61110	−0.932382
$16$	−4.27432	−1.06858
$17$	1.57417	0.381792	0.190896	−	0.981610i	$-0.438861\pi$
$17$	1.57417	0.381792	0.190896	+	0.981610i	$0.438861\pi$
$18$	3.78650	0.892487
$19$	5.32024	1.22055	0.610273	−	0.792191i	$-0.291060\pi$
$19$	5.32024	1.22055	0.610273	+	0.792191i	$0.291060\pi$
$20$	6.46276	1.44512
$21$	2.67922	0.584653
$22$	−10.6221	−2.26464
$23$	0.541267	0.112862	0.0564310	−	0.998407i	$-0.482028\pi$
$23$	0.541267	0.112862	0.0564310	+	0.998407i	$0.482028\pi$
$24$	−0.300827	−0.0614060
$25$	7.17912	1.43582
$26$	−2.44376	−0.479261
$27$	5.10056	0.981603
$28$	−4.79497	−0.906164
$29$	−3.46260	−0.642988	−0.321494	−	0.946912i	$-0.604185\pi$
$29$	−3.46260	−0.642988	−0.321494	+	0.946912i	$0.604185\pi$
$30$	7.08721	1.29394
$31$	4.16239	0.747588	0.373794	−	0.927512i	$-0.378057\pi$
$31$	4.16239	0.747588	0.373794	+	0.927512i	$0.378057\pi$
$32$	7.80740	1.38017
$33$	−5.60024	−0.974877
$34$	−3.08949	−0.529844
$35$	−9.03616	−1.52739
$36$	−3.57283	−0.595472
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−10.4416	−1.69385
$39$	−1.28841	−0.206311
$40$	1.01459	0.160421
$41$	3.40187	0.531283	0.265641	−	0.964072i	$-0.414416\pi$
$41$	3.40187	0.531283	0.265641	+	0.964072i	$0.414416\pi$
$42$	−5.25828	−0.811370
$43$	0.894280	0.136376	0.0681882	−	0.997672i	$-0.478278\pi$
$43$	0.894280	0.136376	0.0681882	+	0.997672i	$0.478278\pi$
$44$	10.0227	1.51098
$45$	−6.73302	−1.00370
$46$	−1.06230	−0.156628
$47$	−5.44804	−0.794679	−0.397339	−	0.917672i	$-0.630066\pi$
$47$	−5.44804	−0.794679	−0.397339	+	0.917672i	$0.630066\pi$
$48$	4.42282	0.638378
$49$	−0.295722	−0.0422460
$50$	−14.0899	−1.99261
$51$	−1.62886	−0.228086
$52$	2.30586	0.319765
$53$	9.67344	1.32875	0.664374	−	0.747400i	$-0.268698\pi$
$53$	9.67344	1.32875	0.664374	+	0.747400i	$0.268698\pi$
$54$	−10.0104	−1.36225
$55$	18.8879	2.54684
$56$	−0.752767	−0.100593
$57$	−5.50507	−0.729164
$58$	6.79575	0.892326
$59$	−4.87176	−0.634250	−0.317125	−	0.948384i	$-0.602717\pi$
$59$	−4.87176	−0.634250	−0.317125	+	0.948384i	$0.602717\pi$
$60$	−6.68728	−0.863324
$61$	−0.171290	−0.0219315	−0.0109657	−	0.999940i	$-0.503491\pi$
$61$	−0.171290	−0.0219315	−0.0109657	+	0.999940i	$0.503491\pi$
$62$	−8.16918	−1.03749
$63$	4.99549	0.629373
$64$	−6.77431	−0.846789
$65$	4.34541	0.538982
$66$	10.9911	1.35291
$67$	−2.32810	−0.284422	−0.142211	−	0.989836i	$-0.545421\pi$
$67$	−2.32810	−0.284422	−0.142211	+	0.989836i	$0.545421\pi$
$68$	2.91516	0.353514
$69$	−0.560071	−0.0674246
$70$	17.7345	2.11968
$71$	−12.8303	−1.52267	−0.761335	−	0.648358i	$-0.775456\pi$
$71$	−12.8303	−1.52267	−0.761335	+	0.648358i	$0.775456\pi$
$72$	−0.560902	−0.0661029
$73$	15.9341	1.86494	0.932472	−	0.361242i	$-0.117647\pi$
$73$	15.9341	1.86494	0.932472	+	0.361242i	$0.117647\pi$
$74$	−1.96262	−0.228150
$75$	−7.42853	−0.857772
$76$	9.85237	1.13014
$77$	−14.0136	−1.59700
$78$	2.52866	0.286314
$79$	10.9404	1.23089	0.615446	−	0.788179i	$-0.288976\pi$
$79$	10.9404	1.23089	0.615446	+	0.788179i	$0.288976\pi$
$80$	−14.9168	−1.66775
$81$	0.510174	0.0566860
$82$	−6.67657	−0.737304
$83$	12.9999	1.42692	0.713460	−	0.700695i	$-0.247127\pi$
$83$	12.9999	1.42692	0.713460	+	0.700695i	$0.247127\pi$
$84$	4.96155	0.541350
$85$	5.49363	0.595868
$86$	−1.75513	−0.189260
$87$	3.58289	0.384126
$88$	1.57347	0.167733
$89$	−7.68383	−0.814485	−0.407242	−	0.913320i	$-0.633510\pi$
$89$	−7.68383	−0.814485	−0.407242	+	0.913320i	$0.633510\pi$
$90$	13.2144	1.39291
$91$	−3.22403	−0.337970
$92$	1.00235	0.104503
$93$	−4.30700	−0.446615
$94$	10.6924	1.10284
$95$	18.5669	1.90492
$96$	−8.07864	−0.824523
$97$	0.658094	0.0668193	0.0334096	−	0.999442i	$-0.489363\pi$
$97$	0.658094	0.0668193	0.0334096	+	0.999442i	$0.489363\pi$
$98$	0.580389	0.0586281
$99$	−10.4418	−1.04945
$100$	13.2948	1.32948
$101$	−14.0427	−1.39730	−0.698648	−	0.715466i	$-0.746215\pi$
$101$	−14.0427	−1.39730	−0.698648	+	0.715466i	$0.746215\pi$
$102$	3.19683	0.316533
$103$	11.1308	1.09675	0.548374	−	0.836233i	$-0.315247\pi$
$103$	11.1308	1.09675	0.548374	+	0.836233i	$0.315247\pi$
$104$	0.361999	0.0354970
$105$	9.35009	0.912475
$106$	−18.9853	−1.84401
$107$	9.13189	0.882813	0.441407	−	0.897307i	$-0.354480\pi$
$107$	9.13189	0.882813	0.441407	+	0.897307i	$0.354480\pi$
$108$	9.44556	0.908900
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−37.0697	−3.53445
$111$	−1.03474	−0.0982133
$112$	11.0673	1.04577
$113$	3.07986	0.289729	0.144864	−	0.989452i	$-0.453725\pi$
$113$	3.07986	0.289729	0.144864	+	0.989452i	$0.453725\pi$
$114$	10.8043	1.01192
$115$	1.88895	0.176145
$116$	−6.41227	−0.595364
$117$	−2.40229	−0.222092
$118$	9.56141	0.880199
$119$	−4.07594	−0.373641
$120$	−1.04984	−0.0958371
$121$	18.2921	1.66292
$122$	0.336178	0.0304361
$123$	−3.52005	−0.317393
$124$	7.70820	0.692217
$125$	7.60481	0.680195
$126$	−9.80424	−0.873431
$127$	−9.50813	−0.843710	−0.421855	−	0.906663i	$-0.638621\pi$
$127$	−9.50813	−0.843710	−0.421855	+	0.906663i	$0.638621\pi$
$128$	−2.31943	−0.205011
$129$	−0.925348	−0.0814724
$130$	−8.52839	−0.747989
$131$	−4.89270	−0.427477	−0.213738	−	0.976891i	$-0.568564\pi$
$131$	−4.89270	−0.427477	−0.213738	+	0.976891i	$0.568564\pi$
$132$	−10.3709	−0.902672
$133$	−13.7755	−1.19449
$134$	4.56917	0.394716
$135$	17.8002	1.53200
$136$	0.457653	0.0392434
$137$	−7.08113	−0.604982	−0.302491	−	0.953152i	$-0.597818\pi$
$137$	−7.08113	−0.604982	−0.302491	+	0.953152i	$0.597818\pi$
$138$	1.09921	0.0935706
$139$	−20.1285	−1.70728	−0.853640	−	0.520864i	$-0.825610\pi$
$139$	−20.1285	−1.70728	−0.853640	+	0.520864i	$0.825610\pi$
$140$	−16.7338	−1.41426
$141$	5.63732	0.474748
$142$	25.1809	2.11313
$143$	6.73904	0.563547
$144$	8.24649	0.687208
$145$	−12.0840	−1.00352
$146$	−31.2725	−2.58813
$147$	0.305995	0.0252381
$148$	1.85187	0.152223
$149$	−6.25724	−0.512613	−0.256307	−	0.966596i	$-0.582506\pi$
$149$	−6.25724	−0.512613	−0.256307	+	0.966596i	$0.582506\pi$
$150$	14.5794	1.19040
$151$	−8.91111	−0.725176	−0.362588	−	0.931950i	$-0.618107\pi$
$151$	−8.91111	−0.725176	−0.362588	+	0.931950i	$0.618107\pi$
$152$	1.54673	0.125457
$153$	−3.03706	−0.245532
$154$	27.5034	2.21629
$155$	14.5262	1.16677
$156$	−2.38597	−0.191030
$157$	8.13236	0.649033	0.324517	−	0.945880i	$-0.394798\pi$
$157$	8.13236	0.649033	0.324517	+	0.945880i	$0.394798\pi$
$158$	−21.4718	−1.70821
$159$	−10.0095	−0.793805
$160$	27.2467	2.15404
$161$	−1.40148	−0.110452
$162$	−1.00128	−0.0786677
$163$	0.189580	0.0148491	0.00742454	−	0.999972i	$-0.497637\pi$
$163$	0.189580	0.0148491	0.00742454	+	0.999972i	$0.497637\pi$
$164$	6.29981	0.491933
$165$	−19.5441	−1.52150
$166$	−25.5138	−1.98025
$167$	2.73207	0.211414	0.105707	−	0.994397i	$-0.466289\pi$
$167$	2.73207	0.211414	0.105707	+	0.994397i	$0.466289\pi$
$168$	0.778919	0.0600949
$169$	−11.4496	−0.880738
$170$	−10.7819	−0.826934
$171$	−10.2644	−0.784937
$172$	1.65609	0.126276
$173$	5.75053	0.437205	0.218602	−	0.975814i	$-0.429850\pi$
$173$	5.75053	0.437205	0.218602	+	0.975814i	$0.429850\pi$
$174$	−7.03184	−0.533083
$175$	−18.5886	−1.40517
$176$	−23.1335	−1.74376
$177$	5.04101	0.378906
$178$	15.0804	1.13033
$179$	−1.15948	−0.0866636	−0.0433318	−	0.999061i	$-0.513797\pi$
$179$	−1.15948	−0.0866636	−0.0433318	+	0.999061i	$0.513797\pi$
$180$	−12.4687	−0.929360
$181$	−9.12591	−0.678323	−0.339162	−	0.940728i	$-0.610143\pi$
$181$	−9.12591	−0.678323	−0.339162	+	0.940728i	$0.610143\pi$
$182$	6.32754	0.469029
$183$	0.177241	0.0131020
$184$	0.157361	0.0116008
$185$	3.48986	0.256580
$186$	8.45299	0.619803
$187$	8.51975	0.623026
$188$	−10.0891	−0.735820
$189$	−13.2067	−0.960645
$190$	−36.4397	−2.64361
$191$	21.3538	1.54510	0.772552	−	0.634952i	$-0.218980\pi$
$191$	21.3538	1.54510	0.772552	+	0.634952i	$0.218980\pi$
$192$	7.00965	0.505878
$193$	−18.2224	−1.31168	−0.655838	−	0.754902i	$-0.727685\pi$
$193$	−18.2224	−1.31168	−0.655838	+	0.754902i	$0.727685\pi$
$194$	−1.29159	−0.0927305
$195$	−4.49638	−0.321992
$196$	−0.547638	−0.0391170
$197$	2.13452	0.152079	0.0760393	−	0.997105i	$-0.475773\pi$
$197$	2.13452	0.152079	0.0760393	+	0.997105i	$0.475773\pi$
$198$	20.4934	1.45640
$199$	19.4706	1.38024	0.690118	−	0.723697i	$-0.257559\pi$
$199$	19.4706	1.38024	0.690118	+	0.723697i	$0.257559\pi$
$200$	2.08716	0.147584
$201$	2.40898	0.169916
$202$	27.5604	1.93914
$203$	8.96557	0.629260
$204$	−3.01643	−0.211192
$205$	11.8720	0.829180
$206$	−21.8455	−1.52204
$207$	−1.04427	−0.0725819
$208$	−5.32219	−0.369027
$209$	28.7943	1.99174
$210$	−18.3506	−1.26631
$211$	5.50925	0.379272	0.189636	−	0.981854i	$-0.439269\pi$
$211$	5.50925	0.379272	0.189636	+	0.981854i	$0.439269\pi$
$212$	17.9139	1.23033
$213$	13.2760	0.909656
$214$	−17.9224	−1.22515
$215$	3.12091	0.212844
$216$	1.48287	0.100896
$217$	−10.7775	−0.731626
$218$	1.96262	0.132925
$219$	−16.4877	−1.11413
$220$	34.9778	2.35821
$221$	1.96008	0.131850
$222$	2.03080	0.136298
$223$	−23.9134	−1.60136	−0.800679	−	0.599093i	$-0.795528\pi$
$223$	−23.9134	−1.60136	−0.800679	+	0.599093i	$0.795528\pi$
$224$	−20.2154	−1.35070
$225$	−13.8508	−0.923383
$226$	−6.04458	−0.402080
$227$	16.1320	1.07072	0.535359	−	0.844625i	$-0.320177\pi$
$227$	16.1320	1.07072	0.535359	+	0.844625i	$0.320177\pi$
$228$	−10.1947	−0.675158
$229$	8.57243	0.566482	0.283241	−	0.959049i	$-0.408590\pi$
$229$	8.57243	0.566482	0.283241	+	0.959049i	$0.408590\pi$
$230$	−3.70728	−0.244451
$231$	14.5005	0.954062
$232$	−1.00667	−0.0660910
$233$	−20.6481	−1.35270	−0.676350	−	0.736580i	$-0.736439\pi$
$233$	−20.6481	−1.35270	−0.676350	+	0.736580i	$0.736439\pi$
$234$	4.71478	0.308215
$235$	−19.0129	−1.24027
$236$	−9.02186	−0.587273
$237$	−11.3205	−0.735345
$238$	7.99951	0.518531
$239$	3.53026	0.228353	0.114177	−	0.993460i	$-0.463577\pi$
$239$	3.53026	0.228353	0.114177	+	0.993460i	$0.463577\pi$
$240$	15.4350	0.996325
$241$	−2.64850	−0.170605	−0.0853025	−	0.996355i	$-0.527186\pi$
$241$	−2.64850	−0.170605	−0.0853025	+	0.996355i	$0.527186\pi$
$242$	−35.9004	−2.30776
$243$	−15.8296	−1.01547
$244$	−0.317207	−0.0203071
$245$	−1.03203	−0.0659338
$246$	6.90852	0.440471
$247$	6.62452	0.421508
$248$	1.21012	0.0768425
$249$	−13.4515	−0.852454
$250$	−14.9253	−0.943961
$251$	10.5017	0.662862	0.331431	−	0.943479i	$-0.392469\pi$
$251$	10.5017	0.662862	0.331431	+	0.943479i	$0.392469\pi$
$252$	9.25099	0.582758
$253$	2.92945	0.184173
$254$	18.6608	1.17088
$255$	−5.68449	−0.355976
$256$	18.1008	1.13130
$257$	−5.32676	−0.332274	−0.166137	−	0.986103i	$-0.553129\pi$
$257$	−5.32676	−0.332274	−0.166137	+	0.986103i	$0.553129\pi$
$258$	1.81610	0.113066
$259$	−2.58926	−0.160889
$260$	8.04713	0.499062
$261$	6.68042	0.413508
$262$	9.60249	0.593244
$263$	26.0978	1.60926	0.804631	−	0.593776i	$-0.202363\pi$
$263$	26.0978	1.60926	0.804631	+	0.593776i	$0.202363\pi$
$264$	−1.62814	−0.100205
$265$	33.7589	2.07379
$266$	27.0360	1.65768
$267$	7.95078	0.486580
$268$	−4.31133	−0.263356
$269$	−11.6170	−0.708303	−0.354151	−	0.935188i	$-0.615230\pi$
$269$	−11.6170	−0.708303	−0.354151	+	0.935188i	$0.615230\pi$
$270$	−34.9351	−2.12608
$271$	−26.0054	−1.57971	−0.789857	−	0.613291i	$-0.789845\pi$
$271$	−26.0054	−1.57971	−0.789857	+	0.613291i	$0.789845\pi$
$272$	−6.72851	−0.407976
$273$	3.33604	0.201906
$274$	13.8976	0.839582
$275$	38.8549	2.34304
$276$	−1.03718	−0.0624308
$277$	12.9258	0.776635	0.388317	−	0.921526i	$-0.373056\pi$
$277$	12.9258	0.776635	0.388317	+	0.921526i	$0.373056\pi$
$278$	39.5046	2.36933
$279$	−8.03055	−0.480776
$280$	−2.62705	−0.156996
$281$	10.9805	0.655039	0.327519	−	0.944844i	$-0.393787\pi$
$281$	10.9805	0.655039	0.327519	+	0.944844i	$0.393787\pi$
$282$	−11.0639	−0.658845
$283$	7.02860	0.417807	0.208903	−	0.977936i	$-0.433011\pi$
$283$	7.02860	0.417807	0.208903	+	0.977936i	$0.433011\pi$
$284$	−23.7599	−1.40989
$285$	−19.2119	−1.13802
$286$	−13.2262	−0.782080
$287$	−8.80833	−0.519940
$288$	−15.0629	−0.887591
$289$	−14.5220	−0.854235
$290$	23.7162	1.39266
$291$	−0.680956	−0.0399184
$292$	29.5078	1.72681
$293$	0.673916	0.0393706	0.0196853	−	0.999806i	$-0.493734\pi$
$293$	0.673916	0.0393706	0.0196853	+	0.999806i	$0.493734\pi$
$294$	−0.600552	−0.0350249
$295$	−17.0018	−0.989881
$296$	0.290726	0.0168981
$297$	27.6053	1.60182
$298$	12.2806	0.711394
$299$	0.673961	0.0389762
$300$	−13.7567	−0.794241
$301$	−2.31553	−0.133465
$302$	17.4891	1.00638
$303$	14.5305	0.834756
$304$	−22.7404	−1.30425
$305$	−0.597779	−0.0342288
$306$	5.96059	0.340745
$307$	22.3122	1.27343	0.636713	−	0.771101i	$-0.280294\pi$
$307$	22.3122	1.27343	0.636713	+	0.771101i	$0.280294\pi$
$308$	−25.9514	−1.47872
$309$	−11.5175	−0.655206
$310$	−28.5093	−1.61922
$311$	−6.67998	−0.378787	−0.189393	−	0.981901i	$-0.560652\pi$
$311$	−6.67998	−0.378787	−0.189393	+	0.981901i	$0.560652\pi$
$312$	−0.374576	−0.0212062
$313$	8.44126	0.477128	0.238564	−	0.971127i	$-0.423323\pi$
$313$	8.44126	0.477128	0.238564	+	0.971127i	$0.423323\pi$
$314$	−15.9607	−0.900715
$315$	17.4336	0.982270
$316$	20.2602	1.13972
$317$	−29.0662	−1.63252	−0.816261	−	0.577684i	$-0.803957\pi$
$317$	−29.0662	−1.63252	−0.816261	+	0.577684i	$0.803957\pi$
$318$	19.6448	1.10163
$319$	−18.7403	−1.04926
$320$	−23.6414	−1.32159
$321$	−9.44914	−0.527400
$322$	2.75057	0.153283
$323$	8.37496	0.465995
$324$	0.944774	0.0524875
$325$	8.93911	0.495853
$326$	−0.372074	−0.0206073
$327$	1.03474	0.0572213
$328$	0.989014	0.0546091
$329$	14.1064	0.777712
$330$	38.3575	2.11151
$331$	17.2168	0.946322	0.473161	−	0.880976i	$-0.343113\pi$
$331$	17.2168	0.946322	0.473161	+	0.880976i	$0.343113\pi$
$332$	24.0740	1.32123
$333$	−1.92931	−0.105726
$334$	−5.36201	−0.293396
$335$	−8.12473	−0.443902
$336$	−11.4518	−0.624748
$337$	−32.8879	−1.79152	−0.895759	−	0.444539i	$-0.853367\pi$
$337$	−32.8879	−1.79152	−0.895759	+	0.444539i	$0.853367\pi$
$338$	22.4712	1.22227
$339$	−3.18686	−0.173086
$340$	10.1735	0.551734
$341$	22.5278	1.21995
$342$	20.1451	1.08932
$343$	18.8905	1.01999
$344$	0.259991	0.0140178
$345$	−1.95457	−0.105230
$346$	−11.2861	−0.606744
$347$	22.1417	1.18863	0.594313	−	0.804234i	$-0.297424\pi$
$347$	22.1417	1.18863	0.594313	+	0.804234i	$0.297424\pi$
$348$	6.63504	0.355675
$349$	0.414563	0.0221910	0.0110955	−	0.999938i	$-0.496468\pi$
$349$	0.414563	0.0221910	0.0110955	+	0.999938i	$0.496468\pi$
$350$	36.4823	1.95006
$351$	6.35099	0.338991
$352$	42.2554	2.25222
$353$	0.453157	0.0241191	0.0120595	−	0.999927i	$-0.496161\pi$
$353$	0.453157	0.0241191	0.0120595	+	0.999927i	$0.496161\pi$
$354$	−9.89358	−0.525838
$355$	−44.7758	−2.37645
$356$	−14.2294	−0.754159
$357$	4.21754	0.223216
$358$	2.27562	0.120270
$359$	21.1368	1.11556	0.557779	−	0.829989i	$-0.311654\pi$
$359$	21.1368	1.11556	0.557779	+	0.829989i	$0.311654\pi$
$360$	−1.95747	−0.103168
$361$	9.30491	0.489732
$362$	17.9107	0.941364
$363$	−18.9276	−0.993440
$364$	−5.97048	−0.312938
$365$	55.6077	2.91064
$366$	−0.347857	−0.0181828
$367$	21.9006	1.14320	0.571601	−	0.820532i	$-0.306323\pi$
$367$	21.9006	1.14320	0.571601	+	0.820532i	$0.306323\pi$
$368$	−2.31355	−0.120602
$369$	−6.56327	−0.341670
$370$	−6.84926	−0.356076
$371$	−25.0471	−1.30038
$372$	−7.97599	−0.413536
$373$	26.3361	1.36363	0.681815	−	0.731525i	$-0.261191\pi$
$373$	26.3361	1.36363	0.681815	+	0.731525i	$0.261191\pi$
$374$	−16.7210	−0.864623
$375$	−7.86901	−0.406354
$376$	−1.58389	−0.0816829
$377$	−4.31147	−0.222052
$378$	25.9197	1.33316
$379$	29.3425	1.50722	0.753611	−	0.657320i	$-0.228310\pi$
$379$	29.3425	1.50722	0.753611	+	0.657320i	$0.228310\pi$
$380$	34.3834	1.76383
$381$	9.83845	0.504039
$382$	−41.9092	−2.14426
$383$	30.5748	1.56230	0.781149	−	0.624344i	$-0.214634\pi$
$383$	30.5748	1.56230	0.781149	+	0.624344i	$0.214634\pi$
$384$	2.40001	0.122475
$385$	−48.9056	−2.49246
$386$	35.7636	1.82032
$387$	−1.72534	−0.0877042
$388$	1.21870	0.0618702
$389$	8.58760	0.435409	0.217704	−	0.976015i	$-0.430143\pi$
$389$	8.58760	0.435409	0.217704	+	0.976015i	$0.430143\pi$
$390$	8.82467	0.446855
$391$	0.852046	0.0430898
$392$	−0.0859741	−0.00434235
$393$	5.06267	0.255378
$394$	−4.18926	−0.211052
$395$	38.1805	1.92107
$396$	−19.3369	−0.971717
$397$	26.6916	1.33962	0.669808	−	0.742535i	$-0.266377\pi$
$397$	26.6916	1.33962	0.669808	+	0.742535i	$0.266377\pi$
$398$	−38.2134	−1.91546
$399$	14.2541	0.713596
$400$	−30.6859	−1.53429
$401$	−4.96338	−0.247859	−0.123930	−	0.992291i	$-0.539550\pi$
$401$	−4.96338	−0.247859	−0.123930	+	0.992291i	$0.539550\pi$
$402$	−4.72790	−0.235806
$403$	5.18282	0.258175
$404$	−26.0051	−1.29380
$405$	1.78043	0.0884705
$406$	−17.5960	−0.873274
$407$	5.41222	0.268274
$408$	−0.473552	−0.0234443
$409$	11.6087	0.574011	0.287006	−	0.957929i	$-0.407340\pi$
$409$	11.6087	0.574011	0.287006	+	0.957929i	$0.407340\pi$
$410$	−23.3003	−1.15072
$411$	7.32714	0.361421
$412$	20.6127	1.01552
$413$	12.6143	0.620708
$414$	2.04951	0.100728
$415$	45.3677	2.22701
$416$	9.72142	0.476632
$417$	20.8278	1.01994
$418$	−56.5121	−2.76410
$419$	27.8511	1.36062	0.680308	−	0.732926i	$-0.261846\pi$
$419$	27.8511	1.36062	0.680308	+	0.732926i	$0.261846\pi$
$420$	17.3151	0.844892
$421$	38.2834	1.86582	0.932910	−	0.360110i	$-0.117261\pi$
$421$	38.2834	1.86582	0.932910	+	0.360110i	$0.117261\pi$
$422$	−10.8125	−0.526346
$423$	10.5110	0.511061
$424$	2.81232	0.136579
$425$	11.3012	0.548186
$426$	−26.0557	−1.26240
$427$	0.443516	0.0214632
$428$	16.9111	0.817427
$429$	−6.97317	−0.336668
$430$	−6.12515	−0.295381
$431$	25.1623	1.21203	0.606014	−	0.795454i	$-0.292768\pi$
$431$	25.1623	1.21203	0.606014	+	0.795454i	$0.292768\pi$
$432$	−21.8014	−1.04892
$433$	4.87160	0.234114	0.117057	−	0.993125i	$-0.462654\pi$
$433$	4.87160	0.234114	0.117057	+	0.993125i	$0.462654\pi$
$434$	21.1522	1.01534
$435$	12.5038	0.599511
$436$	−1.85187	−0.0886884
$437$	2.87967	0.137753
$438$	32.3590	1.54617
$439$	−4.55786	−0.217535	−0.108767	−	0.994067i	$-0.534690\pi$
$439$	−4.55786	−0.217535	−0.108767	+	0.994067i	$0.534690\pi$
$440$	5.49120	0.261783
$441$	0.570539	0.0271685
$442$	−3.84690	−0.182978
$443$	−4.29707	−0.204160	−0.102080	−	0.994776i	$-0.532550\pi$
$443$	−4.29707	−0.204160	−0.102080	+	0.994776i	$0.532550\pi$
$444$	−1.91620	−0.0909390
$445$	−26.8155	−1.27118
$446$	46.9328	2.22233
$447$	6.47462	0.306239
$448$	17.5405	0.828709
$449$	19.2045	0.906318	0.453159	−	0.891430i	$-0.350297\pi$
$449$	19.2045	0.906318	0.453159	+	0.891430i	$0.350297\pi$
$450$	27.1837	1.28145
$451$	18.4117	0.866971
$452$	5.70349	0.268270
$453$	9.22069	0.433226
$454$	−31.6609	−1.48592
$455$	−11.2514	−0.527474
$456$	−1.60047	−0.0749488
$457$	−20.9272	−0.978933	−0.489467	−	0.872022i	$-0.662809\pi$
$457$	−20.9272	−0.978933	−0.489467	+	0.872022i	$0.662809\pi$
$458$	−16.8244	−0.786153
$459$	8.02915	0.374769
$460$	3.49808	0.163099
$461$	16.3236	0.760268	0.380134	−	0.924931i	$-0.375878\pi$
$461$	16.3236	0.760268	0.380134	+	0.924931i	$0.375878\pi$
$462$	−28.4589	−1.32403
$463$	26.2942	1.22200	0.610998	−	0.791632i	$-0.290768\pi$
$463$	26.2942	1.22200	0.610998	+	0.791632i	$0.290768\pi$
$464$	14.8002	0.687084
$465$	−15.0308	−0.697037
$466$	40.5243	1.87725
$467$	−29.4061	−1.36075	−0.680376	−	0.732863i	$-0.738184\pi$
$467$	−29.4061	−1.36075	−0.680376	+	0.732863i	$0.738184\pi$
$468$	−4.44872	−0.205642
$469$	6.02806	0.278350
$470$	37.3151	1.72122
$471$	−8.41489	−0.387738
$472$	−1.41635	−0.0651928
$473$	4.84004	0.222545
$474$	22.2178	1.02050
$475$	38.1946	1.75249
$476$	−7.54810	−0.345967
$477$	−18.6631	−0.854523
$478$	−6.92855	−0.316904
$479$	−29.6102	−1.35293	−0.676463	−	0.736477i	$-0.736488\pi$
$479$	−29.6102	−1.35293	−0.676463	+	0.736477i	$0.736488\pi$
$480$	−28.1933	−1.28684
$481$	1.24515	0.0567742
$482$	5.19800	0.236762
$483$	1.45017	0.0659851
$484$	33.8745	1.53975
$485$	2.29665	0.104286
$486$	31.0674	1.40925
$487$	10.3597	0.469444	0.234722	−	0.972062i	$-0.424582\pi$
$487$	10.3597	0.469444	0.234722	+	0.972062i	$0.424582\pi$
$488$	−0.0497987	−0.00225428
$489$	−0.196167	−0.00887096
$490$	2.02548	0.0915016
$491$	−27.7722	−1.25334	−0.626671	−	0.779284i	$-0.715583\pi$
$491$	−27.7722	−1.25334	−0.626671	+	0.779284i	$0.715583\pi$
$492$	−6.51868	−0.293885
$493$	−5.45072	−0.245488
$494$	−13.0014	−0.584960
$495$	−36.4406	−1.63788
$496$	−17.7914	−0.798857
$497$	33.2209	1.49016
$498$	26.4001	1.18302
$499$	33.9045	1.51777	0.758886	−	0.651223i	$-0.225744\pi$
$499$	33.9045	1.51777	0.758886	+	0.651223i	$0.225744\pi$
$500$	14.0831	0.629816
$501$	−2.82698	−0.126300
$502$	−20.6108	−0.919907
$503$	−39.0108	−1.73941	−0.869703	−	0.493575i	$-0.835690\pi$
$503$	−39.0108	−1.73941	−0.869703	+	0.493575i	$0.835690\pi$
$504$	1.45232	0.0646915
$505$	−49.0069	−2.18078
$506$	−5.74940	−0.255592
$507$	11.8474	0.526160
$508$	−17.6078	−0.781220
$509$	19.1299	0.847920	0.423960	−	0.905681i	$-0.360640\pi$
$509$	19.1299	0.847920	0.423960	+	0.905681i	$0.360640\pi$
$510$	11.1565	0.494017
$511$	−41.2575	−1.82513
$512$	−30.8860	−1.36498
$513$	27.1362	1.19809
$514$	10.4544	0.461124
$515$	38.8448	1.71171
$516$	−1.71362	−0.0754380
$517$	−29.4860	−1.29679
$518$	5.08173	0.223278
$519$	−5.95031	−0.261190
$520$	1.26333	0.0554005
$521$	−8.04701	−0.352546	−0.176273	−	0.984341i	$-0.556404\pi$
$521$	−8.04701	−0.352546	−0.176273	+	0.984341i	$0.556404\pi$
$522$	−13.1111	−0.573858
$523$	33.8634	1.48074	0.740371	−	0.672198i	$-0.234650\pi$
$523$	33.8634	1.48074	0.740371	+	0.672198i	$0.234650\pi$
$524$	−9.06063	−0.395815
$525$	19.2344	0.839458
$526$	−51.2201	−2.23330
$527$	6.55231	0.285423
$528$	23.9372	1.04173
$529$	−22.7070	−0.987262
$530$	−66.2559	−2.87797
$531$	9.39915	0.407888
$532$	−25.5104	−1.10602
$533$	4.23585	0.183475
$534$	−15.6043	−0.675266
$535$	31.8690	1.37782
$536$	−0.676840	−0.0292350
$537$	1.19976	0.0517735
$538$	22.7998	0.982968
$539$	−1.60051	−0.0689389
$540$	32.9637	1.41853
$541$	−9.47001	−0.407148	−0.203574	−	0.979060i	$-0.565256\pi$
$541$	−9.47001	−0.407148	−0.203574	+	0.979060i	$0.565256\pi$
$542$	51.0386	2.19230
$543$	9.44295	0.405236
$544$	12.2902	0.526937
$545$	−3.48986	−0.149489
$546$	−6.54737	−0.280201
$547$	−26.3719	−1.12758	−0.563791	−	0.825917i	$-0.690658\pi$
$547$	−26.3719	−1.12758	−0.563791	+	0.825917i	$0.690658\pi$
$548$	−13.1133	−0.560174
$549$	0.330472	0.0141042
$550$	−76.2574	−3.25163
$551$	−18.4218	−0.784796
$552$	−0.162827	−0.00693040
$553$	−28.3276	−1.20461
$554$	−25.3684	−1.07780
$555$	−3.61110	−0.153283
$556$	−37.2754	−1.58083
$557$	44.1072	1.86888	0.934442	−	0.356115i	$-0.115899\pi$
$557$	44.1072	1.86888	0.934442	+	0.356115i	$0.115899\pi$
$558$	15.7609	0.667212
$559$	1.11352	0.0470967
$560$	38.6234	1.63214
$561$	−8.81573	−0.372201
$562$	−21.5504	−0.909050
$563$	0.715150	0.0301400	0.0150700	−	0.999886i	$-0.495203\pi$
$563$	0.715150	0.0301400	0.0150700	+	0.999886i	$0.495203\pi$
$564$	10.4396	0.439585
$565$	10.7483	0.452183
$566$	−13.7945	−0.579824
$567$	−1.32097	−0.0554757
$568$	−3.73009	−0.156511
$569$	−11.0535	−0.463388	−0.231694	−	0.972789i	$-0.574427\pi$
$569$	−11.0535	−0.463388	−0.231694	+	0.972789i	$0.574427\pi$
$570$	37.7056	1.57931
$571$	10.1651	0.425396	0.212698	−	0.977118i	$-0.431775\pi$
$571$	10.1651	0.425396	0.212698	+	0.977118i	$0.431775\pi$
$572$	12.4798	0.521808
$573$	−22.0956	−0.923057
$574$	17.2874	0.721562
$575$	3.88582	0.162050
$576$	13.0697	0.544573
$577$	−38.0920	−1.58579	−0.792895	−	0.609358i	$-0.791427\pi$
$577$	−38.0920	−1.58579	−0.792895	+	0.609358i	$0.791427\pi$
$578$	28.5011	1.18549
$579$	18.8555	0.783606
$580$	−22.3779	−0.929193
$581$	−33.6601	−1.39645
$582$	1.33646	0.0553979
$583$	52.3547	2.16831
$584$	4.63246	0.191693
$585$	−8.38365	−0.346621
$586$	−1.32264	−0.0546377
$587$	10.2540	0.423226	0.211613	−	0.977354i	$-0.432128\pi$
$587$	10.2540	0.423226	0.211613	+	0.977354i	$0.432128\pi$
$588$	0.566663	0.0233688
$589$	22.1449	0.912465
$590$	33.3680	1.37374
$591$	−2.20868	−0.0908530
$592$	−4.27432	−0.175674
$593$	−17.3289	−0.711614	−0.355807	−	0.934559i	$-0.615794\pi$
$593$	−17.3289	−0.711614	−0.355807	+	0.934559i	$0.615794\pi$
$594$	−54.1787	−2.22298
$595$	−14.2245	−0.583146
$596$	−11.5876	−0.474646
$597$	−20.1471	−0.824564
$598$	−1.32273	−0.0540904
$599$	12.7294	0.520108	0.260054	−	0.965594i	$-0.416260\pi$
$599$	12.7294	0.520108	0.260054	+	0.965594i	$0.416260\pi$
$600$	−2.15967	−0.0881681
$601$	6.84116	0.279057	0.139528	−	0.990218i	$-0.455441\pi$
$601$	6.84116	0.279057	0.139528	+	0.990218i	$0.455441\pi$
$602$	4.54449	0.185220
$603$	4.49163	0.182913
$604$	−16.5022	−0.671465
$605$	63.8368	2.59533
$606$	−28.5178	−1.15846
$607$	21.3114	0.865004	0.432502	−	0.901633i	$-0.357631\pi$
$607$	21.3114	0.865004	0.432502	+	0.901633i	$0.357631\pi$
$608$	41.5372	1.68456
$609$	−9.27704	−0.375925
$610$	1.17321	0.0475020
$611$	−6.78366	−0.274437
$612$	−5.62424	−0.227346
$613$	−26.1915	−1.05786	−0.528932	−	0.848664i	$-0.677407\pi$
$613$	−26.1915	−1.05786	−0.528932	+	0.848664i	$0.677407\pi$
$614$	−43.7904	−1.76724
$615$	−12.2845	−0.495359
$616$	−4.07414	−0.164152
$617$	28.6698	1.15420	0.577101	−	0.816673i	$-0.304184\pi$
$617$	28.6698	1.15420	0.577101	+	0.816673i	$0.304184\pi$
$618$	22.6044	0.909282
$619$	−0.156419	−0.00628701	−0.00314350	−	0.999995i	$-0.501001\pi$
$619$	−0.156419	−0.00628701	−0.00314350	+	0.999995i	$0.501001\pi$
$620$	26.9005	1.08035
$621$	2.76076	0.110786
$622$	13.1102	0.525673
$623$	19.8955	0.797095
$624$	5.50709	0.220460
$625$	−9.35586	−0.374234
$626$	−16.5670	−0.662149
$627$	−29.7946	−1.18988
$628$	15.0601	0.600962
$629$	1.57417	0.0627663
$630$	−34.2154	−1.36317
$631$	−11.6621	−0.464262	−0.232131	−	0.972684i	$-0.574570\pi$
$631$	−11.6621	−0.464262	−0.232131	+	0.972684i	$0.574570\pi$
$632$	3.18067	0.126520
$633$	−5.70064	−0.226580
$634$	57.0459	2.26558
$635$	−33.1820	−1.31679
$636$	−18.5363	−0.735011
$637$	−0.368219	−0.0145894
$638$	36.7801	1.45614
$639$	24.7535	0.979235
$640$	−8.09449	−0.319963
$641$	−26.3124	−1.03928	−0.519638	−	0.854386i	$-0.673933\pi$
$641$	−26.3124	−1.03928	−0.519638	+	0.854386i	$0.673933\pi$
$642$	18.5450	0.731915
$643$	−1.48585	−0.0585961	−0.0292981	−	0.999571i	$-0.509327\pi$
$643$	−1.48585	−0.0585961	−0.0292981	+	0.999571i	$0.509327\pi$
$644$	−2.59536	−0.102271
$645$	−3.22933	−0.127155
$646$	−16.4368	−0.646699
$647$	−20.2282	−0.795251	−0.397626	−	0.917548i	$-0.630166\pi$
$647$	−20.2282	−0.795251	−0.397626	+	0.917548i	$0.630166\pi$
$648$	0.148321	0.00582660
$649$	−26.3670	−1.03500
$650$	−17.5441	−0.688134
$651$	11.1519	0.437079
$652$	0.351078	0.0137493
$653$	28.5744	1.11820	0.559102	−	0.829099i	$-0.311146\pi$
$653$	28.5744	1.11820	0.559102	+	0.829099i	$0.311146\pi$
$654$	−2.03080	−0.0794106
$655$	−17.0748	−0.667168
$656$	−14.5407	−0.567718
$657$	−30.7418	−1.19935
$658$	−27.6855	−1.07929
$659$	−1.47999	−0.0576521	−0.0288260	−	0.999584i	$-0.509177\pi$
$659$	−1.47999	−0.0576521	−0.0288260	+	0.999584i	$0.509177\pi$
$660$	−36.1930	−1.40881
$661$	−23.9376	−0.931064	−0.465532	−	0.885031i	$-0.654137\pi$
$661$	−23.9376	−0.931064	−0.465532	+	0.885031i	$0.654137\pi$
$662$	−33.7900	−1.31329
$663$	−2.02818	−0.0787680
$664$	3.77941	0.146669
$665$	−48.0745	−1.86425
$666$	3.78650	0.146724
$667$	−1.87419	−0.0725689
$668$	5.05943	0.195755
$669$	24.7442	0.956665
$670$	15.9457	0.616038
$671$	−0.927061	−0.0357888
$672$	20.9177	0.806919
$673$	−32.8577	−1.26657	−0.633285	−	0.773919i	$-0.718294\pi$
$673$	−32.8577	−1.26657	−0.633285	+	0.773919i	$0.718294\pi$
$674$	64.5464	2.48623
$675$	36.6175	1.40941
$676$	−21.2031	−0.815505
$677$	4.93887	0.189816	0.0949082	−	0.995486i	$-0.469744\pi$
$677$	4.93887	0.189816	0.0949082	+	0.995486i	$0.469744\pi$
$678$	6.25458	0.240206
$679$	−1.70398	−0.0653926
$680$	1.59714	0.0612477
$681$	−16.6924	−0.639655
$682$	−44.2134	−1.69302
$683$	17.9362	0.686311	0.343156	−	0.939279i	$-0.388504\pi$
$683$	17.9362	0.686311	0.343156	+	0.939279i	$0.388504\pi$
$684$	−19.0083	−0.726800
$685$	−24.7122	−0.944203
$686$	−37.0749	−1.41553
$687$	−8.87024	−0.338421
$688$	−3.82244	−0.145729
$689$	12.0449	0.458875
$690$	3.83607	0.146037
$691$	−9.34015	−0.355316	−0.177658	−	0.984092i	$-0.556852\pi$
$691$	−9.34015	−0.355316	−0.177658	+	0.984092i	$0.556852\pi$
$692$	10.6492	0.404823
$693$	27.0367	1.02704
$694$	−43.4556	−1.64955
$695$	−70.2457	−2.66457
$696$	1.04164	0.0394833
$697$	5.35512	0.202840
$698$	−0.813628	−0.0307963
$699$	21.3654	0.808114
$700$	−34.4237	−1.30109
$701$	19.9900	0.755011	0.377505	−	0.926007i	$-0.376782\pi$
$701$	19.9900	0.755011	0.377505	+	0.926007i	$0.376782\pi$
$702$	−12.4646	−0.470444
$703$	5.32024	0.200656
$704$	−36.6640	−1.38183
$705$	19.6734	0.740944
$706$	−0.889373	−0.0334720
$707$	36.3601	1.36746
$708$	9.33529	0.350842
$709$	18.2840	0.686671	0.343336	−	0.939213i	$-0.388443\pi$
$709$	18.2840	0.686671	0.343336	+	0.939213i	$0.388443\pi$
$710$	87.8777	3.29799
$711$	−21.1074	−0.791591
$712$	−2.23389	−0.0837187
$713$	2.25296	0.0843742
$714$	−8.27742	−0.309775
$715$	23.5183	0.879535
$716$	−2.14720	−0.0802448
$717$	−3.65290	−0.136420
$718$	−41.4835	−1.54815
$719$	−4.24470	−0.158301	−0.0791503	−	0.996863i	$-0.525221\pi$
$719$	−4.24470	−0.158301	−0.0791503	+	0.996863i	$0.525221\pi$
$720$	28.7791	1.07253
$721$	−28.8205	−1.07333
$722$	−18.2620	−0.679640
$723$	2.74051	0.101921
$724$	−16.9000	−0.628083
$725$	−24.8584	−0.923217
$726$	37.1476	1.37868
$727$	1.79717	0.0666532	0.0333266	−	0.999445i	$-0.489390\pi$
$727$	1.79717	0.0666532	0.0333266	+	0.999445i	$0.489390\pi$
$728$	−0.937311	−0.0347391
$729$	14.8490	0.549963
$730$	−109.137	−4.03933
$731$	1.40775	0.0520675
$732$	0.328227	0.0121316
$733$	24.0113	0.886877	0.443439	−	0.896305i	$-0.353758\pi$
$733$	24.0113	0.886877	0.443439	+	0.896305i	$0.353758\pi$
$734$	−42.9825	−1.58651
$735$	1.06788	0.0393894
$736$	4.22589	0.155768
$737$	−12.6002	−0.464133
$738$	12.8812	0.474163
$739$	0.427427	0.0157231	0.00786157	−	0.999969i	$-0.497498\pi$
$739$	0.427427	0.0157231	0.00786157	+	0.999969i	$0.497498\pi$
$740$	6.46276	0.237576
$741$	−6.85466	−0.251812
$742$	49.1578	1.80464
$743$	47.4922	1.74232	0.871160	−	0.490999i	$-0.163368\pi$
$743$	47.4922	1.74232	0.871160	+	0.490999i	$0.163368\pi$
$744$	−1.25216	−0.0459063
$745$	−21.8369	−0.800042
$746$	−51.6876	−1.89242
$747$	−25.0808	−0.917658
$748$	15.7774	0.576881
$749$	−23.6449	−0.863964
$750$	15.4439	0.563930
$751$	25.8412	0.942958	0.471479	−	0.881877i	$-0.343720\pi$
$751$	25.8412	0.942958	0.471479	+	0.881877i	$0.343720\pi$
$752$	23.2867	0.849178
$753$	−10.8665	−0.395999
$754$	8.46176	0.308159
$755$	−31.0985	−1.13179
$756$	−24.4570	−0.889494
$757$	−49.8137	−1.81051	−0.905255	−	0.424868i	$-0.860321\pi$
$757$	−49.8137	−1.81051	−0.905255	+	0.424868i	$0.860321\pi$
$758$	−57.5881	−2.09169
$759$	−3.03123	−0.110027
$760$	5.39788	0.195802
$761$	−6.48467	−0.235069	−0.117534	−	0.993069i	$-0.537499\pi$
$761$	−6.48467	−0.235069	−0.117534	+	0.993069i	$0.537499\pi$
$762$	−19.3091	−0.699496
$763$	2.58926	0.0937376
$764$	39.5443	1.43066
$765$	−10.5989	−0.383205
$766$	−60.0066	−2.16813
$767$	−6.06610	−0.219034
$768$	−18.7296	−0.675847
$769$	−37.4272	−1.34966	−0.674829	−	0.737974i	$-0.735783\pi$
$769$	−37.4272	−1.34966	−0.674829	+	0.737974i	$0.735783\pi$
$770$	95.9831	3.45899
$771$	5.51182	0.198503
$772$	−33.7455	−1.21453
$773$	−18.9037	−0.679918	−0.339959	−	0.940440i	$-0.610413\pi$
$773$	−18.9037	−0.679918	−0.339959	+	0.940440i	$0.610413\pi$
$774$	3.38619	0.121714
$775$	29.8823	1.07340
$776$	0.191325	0.00686817
$777$	2.67922	0.0961163
$778$	−16.8542	−0.604252
$779$	18.0988	0.648455
$780$	−8.32670	−0.298144
$781$	−69.4401	−2.48476
$782$	−1.67224	−0.0597992
$783$	−17.6612	−0.631159
$784$	1.26401	0.0451432
$785$	28.3808	1.01295
$786$	−9.93609	−0.354409
$787$	−9.43418	−0.336292	−0.168146	−	0.985762i	$-0.553778\pi$
$787$	−9.43418	−0.336292	−0.168146	+	0.985762i	$0.553778\pi$
$788$	3.95286	0.140815
$789$	−27.0045	−0.961386
$790$	−74.9337	−2.66602
$791$	−7.97456	−0.283543
$792$	−3.03572	−0.107870
$793$	−0.213283	−0.00757390
$794$	−52.3855	−1.85909
$795$	−34.9318	−1.23890
$796$	36.0570	1.27801
$797$	32.2257	1.14149	0.570747	−	0.821126i	$-0.306654\pi$
$797$	32.2257	1.14149	0.570747	+	0.821126i	$0.306654\pi$
$798$	−27.9753	−0.990314
$799$	−8.57615	−0.303402
$800$	56.0503	1.98168
$801$	14.8245	0.523798
$802$	9.74121	0.343974
$803$	86.2387	3.04330
$804$	4.46111	0.157331
$805$	−4.89097	−0.172384
$806$	−10.1719	−0.358290
$807$	12.0206	0.423146
$808$	−4.08257	−0.143624
$809$	−37.1430	−1.30588	−0.652939	−	0.757410i	$-0.726464\pi$
$809$	−37.1430	−1.30588	−0.652939	+	0.757410i	$0.726464\pi$
$810$	−3.49431	−0.122778
$811$	−22.8875	−0.803687	−0.401844	−	0.915708i	$-0.631630\pi$
$811$	−22.8875	−0.803687	−0.401844	+	0.915708i	$0.631630\pi$
$812$	16.6031	0.582653
$813$	26.9088	0.943734
$814$	−10.6221	−0.372305
$815$	0.661609	0.0231751
$816$	6.96226	0.243728
$817$	4.75778	0.166454
$818$	−22.7834	−0.796602
$819$	6.22016	0.217350
$820$	21.9855	0.767766
$821$	7.61464	0.265753	0.132876	−	0.991133i	$-0.457579\pi$
$821$	7.61464	0.265753	0.132876	+	0.991133i	$0.457579\pi$
$822$	−14.3804	−0.501573
$823$	−19.0229	−0.663096	−0.331548	−	0.943438i	$-0.607571\pi$
$823$	−19.0229	−0.663096	−0.331548	+	0.943438i	$0.607571\pi$
$824$	3.23601	0.112732
$825$	−40.2048	−1.39975
$826$	−24.7570	−0.861406
$827$	19.0078	0.660968	0.330484	−	0.943812i	$-0.392788\pi$
$827$	19.0078	0.660968	0.330484	+	0.943812i	$0.392788\pi$
$828$	−1.93385	−0.0672061
$829$	−12.3846	−0.430134	−0.215067	−	0.976599i	$-0.568997\pi$
$829$	−12.3846	−0.430134	−0.215067	+	0.976599i	$0.568997\pi$
$830$	−89.0395	−3.09061
$831$	−13.3748	−0.463968
$832$	−8.43506	−0.292433
$833$	−0.465516	−0.0161292
$834$	−40.8770	−1.41546
$835$	9.53453	0.329956
$836$	53.3232	1.84422
$837$	21.2305	0.733834
$838$	−54.6611	−1.88824
$839$	−4.02796	−0.139061	−0.0695303	−	0.997580i	$-0.522150\pi$
$839$	−4.02796	−0.139061	−0.0695303	+	0.997580i	$0.522150\pi$
$840$	2.71832	0.0937909
$841$	−17.0104	−0.586566
$842$	−75.1357	−2.58935
$843$	−11.3619	−0.391326
$844$	10.2024	0.351181
$845$	−39.9575	−1.37458
$846$	−20.6290	−0.709240
$847$	−47.3630	−1.62741
$848$	−41.3474	−1.41987
$849$	−7.27278	−0.249601
$850$	−22.1798	−0.760762
$851$	0.541267	0.0185544
$852$	24.5854	0.842281
$853$	40.9910	1.40350	0.701752	−	0.712421i	$-0.252401\pi$
$853$	40.9910	1.40350	0.701752	+	0.712421i	$0.252401\pi$
$854$	−0.870452	−0.0297863
$855$	−35.8213	−1.22506
$856$	2.65488	0.0907420
$857$	4.45633	0.152225	0.0761126	−	0.997099i	$-0.475749\pi$
$857$	4.45633	0.152225	0.0761126	+	0.997099i	$0.475749\pi$
$858$	13.6857	0.467221
$859$	15.7128	0.536114	0.268057	−	0.963403i	$-0.413618\pi$
$859$	15.7128	0.536114	0.268057	+	0.963403i	$0.413618\pi$
$860$	5.77952	0.197080
$861$	9.11434	0.310616
$862$	−49.3841	−1.68203
$863$	−27.2952	−0.929140	−0.464570	−	0.885536i	$-0.653791\pi$
$863$	−27.2952	−0.929140	−0.464570	+	0.885536i	$0.653791\pi$
$864$	39.8221	1.35478
$865$	20.0685	0.682351
$866$	−9.56109	−0.324899
$867$	15.0265	0.510327
$868$	−19.9585	−0.677437
$869$	59.2118	2.00862
$870$	−24.5401	−0.831989
$871$	−2.89884	−0.0982235
$872$	−0.290726	−0.00984524
$873$	−1.26967	−0.0429717
$874$	−5.65169	−0.191171
$875$	−19.6909	−0.665672
$876$	−30.5330	−1.03161
$877$	−41.6623	−1.40684	−0.703418	−	0.710777i	$-0.748344\pi$
$877$	−41.6623	−1.40684	−0.703418	+	0.710777i	$0.748344\pi$
$878$	8.94534	0.301891
$879$	−0.697329	−0.0235203
$880$	−80.7328	−2.72150
$881$	7.59924	0.256025	0.128012	−	0.991773i	$-0.459140\pi$
$881$	7.59924	0.256025	0.128012	+	0.991773i	$0.459140\pi$
$882$	−1.11975	−0.0377040
$883$	51.3036	1.72650	0.863252	−	0.504772i	$-0.168424\pi$
$883$	51.3036	1.72650	0.863252	+	0.504772i	$0.168424\pi$
$884$	3.62982	0.122084
$885$	17.5924	0.591363
$886$	8.43350	0.283329
$887$	30.8945	1.03733	0.518667	−	0.854976i	$-0.326428\pi$
$887$	30.8945	1.03733	0.518667	+	0.854976i	$0.326428\pi$
$888$	−0.300827	−0.0100951
$889$	24.6190	0.825696
$890$	52.6286	1.76411
$891$	2.76117	0.0925027
$892$	−44.2844	−1.48275
$893$	−28.9849	−0.969942
$894$	−12.7072	−0.424993
$895$	−4.04642	−0.135257
$896$	6.00562	0.200634
$897$	−0.697375	−0.0232847
$898$	−37.6912	−1.25777
$899$	−14.4127	−0.480690
$900$	−25.6498	−0.854992
$901$	15.2276	0.507306
$902$	−36.1350	−1.20317
$903$	2.39597	0.0797328
$904$	0.895396	0.0297804
$905$	−31.8481	−1.05867
$906$	−18.0967	−0.601222
$907$	−45.0721	−1.49660	−0.748298	−	0.663363i	$-0.769129\pi$
$907$	−45.0721	−1.49660	−0.748298	+	0.663363i	$0.769129\pi$
$908$	29.8743	0.991413
$909$	27.0926	0.898606
$910$	22.0822	0.732019
$911$	37.0746	1.22834	0.614169	−	0.789175i	$-0.289491\pi$
$911$	37.0746	1.22834	0.614169	+	0.789175i	$0.289491\pi$
$912$	23.5304	0.779170
$913$	70.3581	2.32851
$914$	41.0721	1.35854
$915$	0.618547	0.0204485
$916$	15.8750	0.524525
$917$	12.6685	0.418350
$918$	−15.7582	−0.520096
$919$	−6.55588	−0.216258	−0.108129	−	0.994137i	$-0.534486\pi$
$919$	−6.55588	−0.216258	−0.108129	+	0.994137i	$0.534486\pi$
$920$	0.549166	0.0181055
$921$	−23.0874	−0.760755
$922$	−32.0371	−1.05508
$923$	−15.9756	−0.525845
$924$	26.8530	0.883399
$925$	7.17912	0.236048
$926$	−51.6055	−1.69586
$927$	−21.4747	−0.705323
$928$	−27.0339	−0.887431
$929$	−26.4512	−0.867837	−0.433919	−	0.900952i	$-0.642869\pi$
$929$	−26.4512	−0.867837	−0.433919	+	0.900952i	$0.642869\pi$
$930$	29.4997	0.967335
$931$	−1.57331	−0.0515631
$932$	−38.2375	−1.25251
$933$	6.91205	0.226290
$934$	57.7129	1.88843
$935$	29.7327	0.972364
$936$	−0.698409	−0.0228282
$937$	−2.82295	−0.0922219	−0.0461109	−	0.998936i	$-0.514683\pi$
$937$	−2.82295	−0.0922219	−0.0461109	+	0.998936i	$0.514683\pi$
$938$	−11.8308	−0.386288
$939$	−8.73452	−0.285040
$940$	−35.2094	−1.14840
$941$	−23.3693	−0.761817	−0.380908	−	0.924613i	$-0.624389\pi$
$941$	−23.3693	−0.761817	−0.380908	+	0.924613i	$0.624389\pi$
$942$	16.5152	0.538095
$943$	1.84132	0.0599616
$944$	20.8235	0.677746
$945$	−46.0895	−1.49929
$946$	−9.49914	−0.308844
$947$	55.2154	1.79426	0.897129	−	0.441768i	$-0.145649\pi$
$947$	55.2154	1.79426	0.897129	+	0.441768i	$0.145649\pi$
$948$	−20.9641	−0.680881
$949$	19.8404	0.644047
$950$	−74.9614	−2.43207
$951$	30.0760	0.975281
$952$	−1.18498	−0.0384055
$953$	−18.7885	−0.608619	−0.304309	−	0.952573i	$-0.598426\pi$
$953$	−18.7885	−0.608619	−0.304309	+	0.952573i	$0.598426\pi$
$954$	36.6285	1.18589
$955$	74.5216	2.41146
$956$	6.53757	0.211440
$957$	19.3914	0.626834
$958$	58.1135	1.87756
$959$	18.3349	0.592065
$960$	24.4627	0.789531
$961$	−13.6745	−0.441113
$962$	−2.44376	−0.0787901
$963$	−17.6183	−0.567740
$964$	−4.90468	−0.157969
$965$	−63.5936	−2.04715
$966$	−2.84613	−0.0915728
$967$	−17.0809	−0.549286	−0.274643	−	0.961546i	$-0.588560\pi$
$967$	−17.0809	−0.549286	−0.274643	+	0.961546i	$0.588560\pi$
$968$	5.31799	0.170927
$969$	−8.66591	−0.278389
$970$	−4.50745	−0.144726
$971$	17.9005	0.574454	0.287227	−	0.957863i	$-0.407267\pi$
$971$	17.9005	0.574454	0.287227	+	0.957863i	$0.407267\pi$
$972$	−29.3143	−0.940256
$973$	52.1180	1.67083
$974$	−20.3322	−0.651486
$975$	−9.24966	−0.296226
$976$	0.732150	0.0234356
$977$	30.5331	0.976841	0.488420	−	0.872608i	$-0.337573\pi$
$977$	30.5331	0.976841	0.488420	+	0.872608i	$0.337573\pi$
$978$	0.385000	0.0123109
$979$	−41.5866	−1.32911
$980$	−1.91118	−0.0610504
$981$	1.92931	0.0615982
$982$	54.5063	1.73936
$983$	1.79471	0.0572423	0.0286211	−	0.999590i	$-0.490888\pi$
$983$	1.79471	0.0572423	0.0286211	+	0.999590i	$0.490888\pi$
$984$	−1.02337	−0.0326239
$985$	7.44919	0.237351
$986$	10.6977	0.340683
$987$	−14.5965	−0.464611
$988$	12.2677	0.390288
$989$	0.484044	0.0153917
$990$	71.5189	2.27302
$991$	−13.4650	−0.427731	−0.213865	−	0.976863i	$-0.568605\pi$
$991$	−13.4650	−0.427731	−0.213865	+	0.976863i	$0.568605\pi$
$992$	32.4975	1.03180
$993$	−17.8149	−0.565340
$994$	−65.1999	−2.06802
$995$	67.9498	2.15415
$996$	−24.9104	−0.789316
$997$	−30.6437	−0.970497	−0.485249	−	0.874376i	$-0.661271\pi$
$997$	−30.6437	−0.970497	−0.485249	+	0.874376i	$0.661271\pi$
$998$	−66.5415	−2.10633
$999$	5.10056	0.161375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.15	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.15	✓	85	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96262 q^{2} -1.03474 q^{3} +1.85187 q^{4} +3.48986 q^{5} +2.03080 q^{6} -2.58926 q^{7} +0.290726 q^{8} -1.92931 q^{9} +O(q^{10})\)	\(q-1.96262 q^{2} -1.03474 q^{3} +1.85187 q^{4} +3.48986 q^{5} +2.03080 q^{6} -2.58926 q^{7} +0.290726 q^{8} -1.92931 q^{9} -6.84926 q^{10} +5.41222 q^{11} -1.91620 q^{12} +1.24515 q^{13} +5.08173 q^{14} -3.61110 q^{15} -4.27432 q^{16} +1.57417 q^{17} +3.78650 q^{18} +5.32024 q^{19} +6.46276 q^{20} +2.67922 q^{21} -10.6221 q^{22} +0.541267 q^{23} -0.300827 q^{24} +7.17912 q^{25} -2.44376 q^{26} +5.10056 q^{27} -4.79497 q^{28} -3.46260 q^{29} +7.08721 q^{30} +4.16239 q^{31} +7.80740 q^{32} -5.60024 q^{33} -3.08949 q^{34} -9.03616 q^{35} -3.57283 q^{36} +1.00000 q^{37} -10.4416 q^{38} -1.28841 q^{39} +1.01459 q^{40} +3.40187 q^{41} -5.25828 q^{42} +0.894280 q^{43} +10.0227 q^{44} -6.73302 q^{45} -1.06230 q^{46} -5.44804 q^{47} +4.42282 q^{48} -0.295722 q^{49} -14.0899 q^{50} -1.62886 q^{51} +2.30586 q^{52} +9.67344 q^{53} -10.0104 q^{54} +18.8879 q^{55} -0.752767 q^{56} -5.50507 q^{57} +6.79575 q^{58} -4.87176 q^{59} -6.68728 q^{60} -0.171290 q^{61} -8.16918 q^{62} +4.99549 q^{63} -6.77431 q^{64} +4.34541 q^{65} +10.9911 q^{66} -2.32810 q^{67} +2.91516 q^{68} -0.560071 q^{69} +17.7345 q^{70} -12.8303 q^{71} -0.560902 q^{72} +15.9341 q^{73} -1.96262 q^{74} -7.42853 q^{75} +9.85237 q^{76} -14.0136 q^{77} +2.52866 q^{78} +10.9404 q^{79} -14.9168 q^{80} +0.510174 q^{81} -6.67657 q^{82} +12.9999 q^{83} +4.96155 q^{84} +5.49363 q^{85} -1.75513 q^{86} +3.58289 q^{87} +1.57347 q^{88} -7.68383 q^{89} +13.2144 q^{90} -3.22403 q^{91} +1.00235 q^{92} -4.30700 q^{93} +10.6924 q^{94} +18.5669 q^{95} -8.07864 q^{96} +0.658094 q^{97} +0.580389 q^{98} -10.4418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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