LMFDB - Embedded newform 8009.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8009,2,Mod(1,8009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8009 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8009.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:	$63.9521869788$
Analytic rank:	$0$
Dimension:	$361$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82633 q^{2} +2.37476 q^{3} +5.98811 q^{4} +1.91635 q^{5} -6.71185 q^{6} -2.63274 q^{7} -11.2717 q^{8} +2.63950 q^{9} +O(q^{10})$	\(q-2.82633 q^{2} +2.37476 q^{3} +5.98811 q^{4} +1.91635 q^{5} -6.71185 q^{6} -2.63274 q^{7} -11.2717 q^{8} +2.63950 q^{9} -5.41622 q^{10} -3.16674 q^{11} +14.2203 q^{12} +4.93719 q^{13} +7.44098 q^{14} +4.55087 q^{15} +19.8813 q^{16} +6.05436 q^{17} -7.46007 q^{18} +5.84823 q^{19} +11.4753 q^{20} -6.25214 q^{21} +8.95023 q^{22} -4.72607 q^{23} -26.7676 q^{24} -1.32762 q^{25} -13.9541 q^{26} -0.856112 q^{27} -15.7652 q^{28} +2.96381 q^{29} -12.8622 q^{30} +7.25902 q^{31} -33.6475 q^{32} -7.52025 q^{33} -17.1116 q^{34} -5.04524 q^{35} +15.8056 q^{36} +0.951141 q^{37} -16.5290 q^{38} +11.7247 q^{39} -21.6005 q^{40} -6.37198 q^{41} +17.6706 q^{42} +12.7899 q^{43} -18.9628 q^{44} +5.05819 q^{45} +13.3574 q^{46} -7.95296 q^{47} +47.2133 q^{48} -0.0686714 q^{49} +3.75228 q^{50} +14.3777 q^{51} +29.5645 q^{52} +4.78999 q^{53} +2.41965 q^{54} -6.06856 q^{55} +29.6755 q^{56} +13.8882 q^{57} -8.37669 q^{58} +2.85411 q^{59} +27.2511 q^{60} -6.05178 q^{61} -20.5164 q^{62} -6.94911 q^{63} +55.3363 q^{64} +9.46137 q^{65} +21.2547 q^{66} -0.520352 q^{67} +36.2542 q^{68} -11.2233 q^{69} +14.2595 q^{70} +5.78349 q^{71} -29.7516 q^{72} +0.373361 q^{73} -2.68823 q^{74} -3.15278 q^{75} +35.0199 q^{76} +8.33720 q^{77} -33.1377 q^{78} +11.3847 q^{79} +38.0994 q^{80} -9.95155 q^{81} +18.0093 q^{82} -7.07335 q^{83} -37.4385 q^{84} +11.6022 q^{85} -36.1484 q^{86} +7.03834 q^{87} +35.6945 q^{88} +5.17978 q^{89} -14.2961 q^{90} -12.9984 q^{91} -28.3003 q^{92} +17.2385 q^{93} +22.4777 q^{94} +11.2072 q^{95} -79.9049 q^{96} -8.37025 q^{97} +0.194088 q^{98} -8.35859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) $ 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9} + 65 q^{10} + 33 q^{11} + 52 q^{12} + 89 q^{13} + 32 q^{14} + 55 q^{15} + 512 q^{16} + 42 q^{17} + 34 q^{18} + 191 q^{19} + 48 q^{20} + 53 q^{21} + 61 q^{22} + 52 q^{23} + 139 q^{24} + 458 q^{25} + 57 q^{26} + 80 q^{27} + 194 q^{28} + 47 q^{29} + 32 q^{30} + 254 q^{31} + 55 q^{32} + 40 q^{33} + 122 q^{34} + 93 q^{35} + 519 q^{36} + 43 q^{37} + 25 q^{38} + 210 q^{39} + 184 q^{40} + 54 q^{41} + 48 q^{42} + 151 q^{43} + 56 q^{44} + 82 q^{45} + 101 q^{46} + 117 q^{47} + 77 q^{48} + 563 q^{49} + 38 q^{50} + 143 q^{51} + 241 q^{52} + 14 q^{53} + 164 q^{54} + 452 q^{55} + 52 q^{56} + 21 q^{57} + 55 q^{58} + 125 q^{59} + 39 q^{60} + 227 q^{61} + 58 q^{62} + 292 q^{63} + 710 q^{64} + 15 q^{65} + 105 q^{66} + 120 q^{67} + 125 q^{68} + 136 q^{69} + 88 q^{70} + 105 q^{71} + 78 q^{72} + 108 q^{73} + 41 q^{74} + 128 q^{75} + 461 q^{76} + 28 q^{77} + 13 q^{78} + 400 q^{79} + 59 q^{80} + 485 q^{81} + 175 q^{82} + 97 q^{83} + 76 q^{84} + 144 q^{85} - 14 q^{86} + 327 q^{87} + 145 q^{88} + 52 q^{89} + 60 q^{90} + 192 q^{91} + 11 q^{92} + 32 q^{93} + 366 q^{94} + 182 q^{95} + 275 q^{96} + 117 q^{97} + 42 q^{98} + 111 q^{99}+O(q^{100}) \) 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9 + 65 * q^10 + 33 * q^11 + 52 * q^12 + 89 * q^13 + 32 * q^14 + 55 * q^15 + 512 * q^16 + 42 * q^17 + 34 * q^18 + 191 * q^19 + 48 * q^20 + 53 * q^21 + 61 * q^22 + 52 * q^23 + 139 * q^24 + 458 * q^25 + 57 * q^26 + 80 * q^27 + 194 * q^28 + 47 * q^29 + 32 * q^30 + 254 * q^31 + 55 * q^32 + 40 * q^33 + 122 * q^34 + 93 * q^35 + 519 * q^36 + 43 * q^37 + 25 * q^38 + 210 * q^39 + 184 * q^40 + 54 * q^41 + 48 * q^42 + 151 * q^43 + 56 * q^44 + 82 * q^45 + 101 * q^46 + 117 * q^47 + 77 * q^48 + 563 * q^49 + 38 * q^50 + 143 * q^51 + 241 * q^52 + 14 * q^53 + 164 * q^54 + 452 * q^55 + 52 * q^56 + 21 * q^57 + 55 * q^58 + 125 * q^59 + 39 * q^60 + 227 * q^61 + 58 * q^62 + 292 * q^63 + 710 * q^64 + 15 * q^65 + 105 * q^66 + 120 * q^67 + 125 * q^68 + 136 * q^69 + 88 * q^70 + 105 * q^71 + 78 * q^72 + 108 * q^73 + 41 * q^74 + 128 * q^75 + 461 * q^76 + 28 * q^77 + 13 * q^78 + 400 * q^79 + 59 * q^80 + 485 * q^81 + 175 * q^82 + 97 * q^83 + 76 * q^84 + 144 * q^85 - 14 * q^86 + 327 * q^87 + 145 * q^88 + 52 * q^89 + 60 * q^90 + 192 * q^91 + 11 * q^92 + 32 * q^93 + 366 * q^94 + 182 * q^95 + 275 * q^96 + 117 * q^97 + 42 * q^98 + 111 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.82633	−1.99851	−0.999257	−	0.0385464i	$-0.987727\pi$
$2$	−2.82633	−1.99851	−0.999257	+	0.0385464i	$0.987727\pi$
$3$	2.37476	1.37107	0.685535	−	0.728040i	$-0.259568\pi$
$3$	2.37476	1.37107	0.685535	+	0.728040i	$0.259568\pi$
$4$	5.98811	2.99406
$5$	1.91635	0.857016	0.428508	−	0.903538i	$-0.359039\pi$
$5$	1.91635	0.857016	0.428508	+	0.903538i	$0.359039\pi$
$6$	−6.71185	−2.74010
$7$	−2.63274	−0.995083	−0.497541	−	0.867440i	$-0.665764\pi$
$7$	−2.63274	−0.995083	−0.497541	+	0.867440i	$0.665764\pi$
$8$	−11.2717	−3.98515
$9$	2.63950	0.879832
$10$	−5.41622	−1.71276
$11$	−3.16674	−0.954808	−0.477404	−	0.878684i	$-0.658422\pi$
$11$	−3.16674	−0.954808	−0.477404	+	0.878684i	$0.658422\pi$
$12$	14.2203	4.10506
$13$	4.93719	1.36933	0.684666	−	0.728857i	$-0.259948\pi$
$13$	4.93719	1.36933	0.684666	+	0.728857i	$0.259948\pi$
$14$	7.44098	1.98869
$15$	4.55087	1.17503
$16$	19.8813	4.97032
$17$	6.05436	1.46840	0.734198	−	0.678935i	$-0.237558\pi$
$17$	6.05436	1.46840	0.734198	+	0.678935i	$0.237558\pi$
$18$	−7.46007	−1.75836
$19$	5.84823	1.34168	0.670838	−	0.741604i	$-0.265935\pi$
$19$	5.84823	1.34168	0.670838	+	0.741604i	$0.265935\pi$
$20$	11.4753	2.56595
$21$	−6.25214	−1.36433
$22$	8.95023	1.90820
$23$	−4.72607	−0.985455	−0.492727	−	0.870184i	$-0.664000\pi$
$23$	−4.72607	−0.985455	−0.492727	+	0.870184i	$0.664000\pi$
$24$	−26.7676	−5.46392
$25$	−1.32762	−0.265524
$26$	−13.9541	−2.73663
$27$	−0.856112	−0.164759
$28$	−15.7652	−2.97933
$29$	2.96381	0.550365	0.275183	−	0.961392i	$-0.411262\pi$
$29$	2.96381	0.550365	0.275183	+	0.961392i	$0.411262\pi$
$30$	−12.8622	−2.34831
$31$	7.25902	1.30376	0.651879	−	0.758323i	$-0.273981\pi$
$31$	7.25902	1.30376	0.651879	+	0.758323i	$0.273981\pi$
$32$	−33.6475	−5.94810
$33$	−7.52025	−1.30911
$34$	−17.1116	−2.93461
$35$	−5.04524	−0.852802
$36$	15.8056	2.63427
$37$	0.951141	0.156367	0.0781833	−	0.996939i	$-0.475088\pi$
$37$	0.951141	0.156367	0.0781833	+	0.996939i	$0.475088\pi$
$38$	−16.5290	−2.68136
$39$	11.7247	1.87745
$40$	−21.6005	−3.41534
$41$	−6.37198	−0.995137	−0.497568	−	0.867425i	$-0.665774\pi$
$41$	−6.37198	−0.995137	−0.497568	+	0.867425i	$0.665774\pi$
$42$	17.6706	2.72663
$43$	12.7899	1.95044	0.975220	−	0.221238i	$-0.0710099\pi$
$43$	12.7899	1.95044	0.975220	+	0.221238i	$0.0710099\pi$
$44$	−18.9628	−2.85875
$45$	5.05819	0.754030
$46$	13.3574	1.96944
$47$	−7.95296	−1.16006	−0.580030	−	0.814595i	$-0.696959\pi$
$47$	−7.95296	−1.16006	−0.580030	+	0.814595i	$0.696959\pi$
$48$	47.2133	6.81465
$49$	−0.0686714	−0.00981020
$50$	3.75228	0.530653
$51$	14.3777	2.01327
$52$	29.5645	4.09986
$53$	4.78999	0.657956	0.328978	−	0.944338i	$-0.393296\pi$
$53$	4.78999	0.657956	0.328978	+	0.944338i	$0.393296\pi$
$54$	2.41965	0.329273
$55$	−6.06856	−0.818285
$56$	29.6755	3.96555
$57$	13.8882	1.83953
$58$	−8.37669	−1.09991
$59$	2.85411	0.371573	0.185787	−	0.982590i	$-0.440517\pi$
$59$	2.85411	0.371573	0.185787	+	0.982590i	$0.440517\pi$
$60$	27.2511	3.51810
$61$	−6.05178	−0.774851	−0.387425	−	0.921901i	$-0.626636\pi$
$61$	−6.05178	−0.774851	−0.387425	+	0.921901i	$0.626636\pi$
$62$	−20.5164	−2.60558
$63$	−6.94911	−0.875506
$64$	55.3363	6.91704
$65$	9.46137	1.17354
$66$	21.2547	2.61627
$67$	−0.520352	−0.0635711	−0.0317856	−	0.999495i	$-0.510119\pi$
$67$	−0.520352	−0.0635711	−0.0317856	+	0.999495i	$0.510119\pi$
$68$	36.2542	4.39646
$69$	−11.2233	−1.35113
$70$	14.2595	1.70434
$71$	5.78349	0.686374	0.343187	−	0.939267i	$-0.388493\pi$
$71$	5.78349	0.686374	0.343187	+	0.939267i	$0.388493\pi$
$72$	−29.7516	−3.50626
$73$	0.373361	0.0436986	0.0218493	−	0.999761i	$-0.493045\pi$
$73$	0.373361	0.0436986	0.0218493	+	0.999761i	$0.493045\pi$
$74$	−2.68823	−0.312501
$75$	−3.15278	−0.364052
$76$	35.0199	4.01705
$77$	8.33720	0.950113
$78$	−33.1377	−3.75211
$79$	11.3847	1.28088	0.640438	−	0.768009i	$-0.278753\pi$
$79$	11.3847	1.28088	0.640438	+	0.768009i	$0.278753\pi$
$80$	38.0994	4.25964
$81$	−9.95155	−1.10573
$82$	18.0093	1.98879
$83$	−7.07335	−0.776401	−0.388201	−	0.921575i	$-0.626903\pi$
$83$	−7.07335	−0.776401	−0.388201	+	0.921575i	$0.626903\pi$
$84$	−37.4385	−4.08487
$85$	11.6022	1.25844
$86$	−36.1484	−3.89798
$87$	7.03834	0.754589
$88$	35.6945	3.80505
$89$	5.17978	0.549055	0.274528	−	0.961579i	$-0.411479\pi$
$89$	5.17978	0.549055	0.274528	+	0.961579i	$0.411479\pi$
$90$	−14.2961	−1.50694
$91$	−12.9984	−1.36260
$92$	−28.3003	−2.95051
$93$	17.2385	1.78754
$94$	22.4777	2.31839
$95$	11.2072	1.14984
$96$	−79.9049	−8.15526
$97$	−8.37025	−0.849870	−0.424935	−	0.905224i	$-0.639703\pi$
$97$	−8.37025	−0.849870	−0.424935	+	0.905224i	$0.639703\pi$
$98$	0.194088	0.0196058
$99$	−8.35859	−0.840070
$100$	−7.94994	−0.794994
$101$	−0.513619	−0.0511070	−0.0255535	−	0.999673i	$-0.508135\pi$
$101$	−0.513619	−0.0511070	−0.0255535	+	0.999673i	$0.508135\pi$
$102$	−40.6359	−4.02356
$103$	4.19214	0.413064	0.206532	−	0.978440i	$-0.433782\pi$
$103$	4.19214	0.413064	0.206532	+	0.978440i	$0.433782\pi$
$104$	−55.6506	−5.45699
$105$	−11.9813	−1.16925
$106$	−13.5381	−1.31493
$107$	15.7412	1.52176	0.760882	−	0.648891i	$-0.224767\pi$
$107$	15.7412	1.52176	0.760882	+	0.648891i	$0.224767\pi$
$108$	−5.12650	−0.493297
$109$	−7.34839	−0.703848	−0.351924	−	0.936029i	$-0.614472\pi$
$109$	−7.34839	−0.703848	−0.351924	+	0.936029i	$0.614472\pi$
$110$	17.1517	1.63535
$111$	2.25873	0.214390
$112$	−52.3423	−4.94588
$113$	−5.31564	−0.500054	−0.250027	−	0.968239i	$-0.580439\pi$
$113$	−5.31564	−0.500054	−0.250027	+	0.968239i	$0.580439\pi$
$114$	−39.2524	−3.67633
$115$	−9.05679	−0.844550
$116$	17.7476	1.64783
$117$	13.0317	1.20478
$118$	−8.06664	−0.742595
$119$	−15.9396	−1.46118
$120$	−51.2960	−4.68266
$121$	−0.971769	−0.0883426
$122$	17.1043	1.54855
$123$	−15.1319	−1.36440
$124$	43.4679	3.90353
$125$	−12.1259	−1.08457
$126$	19.6404	1.74971
$127$	6.97792	0.619190	0.309595	−	0.950868i	$-0.399807\pi$
$127$	6.97792	0.619190	0.309595	+	0.950868i	$0.399807\pi$
$128$	−89.1034	−7.87570
$129$	30.3729	2.67419
$130$	−26.7409	−2.34533
$131$	13.9151	1.21577	0.607883	−	0.794027i	$-0.292019\pi$
$131$	13.9151	1.21577	0.607883	+	0.794027i	$0.292019\pi$
$132$	−45.0321	−3.91954
$133$	−15.3969	−1.33508
$134$	1.47068	0.127048
$135$	−1.64061	−0.141201
$136$	−68.2429	−5.85178
$137$	22.1190	1.88975	0.944877	−	0.327424i	$-0.106181\pi$
$137$	22.1190	1.88975	0.944877	+	0.327424i	$0.106181\pi$
$138$	31.7207	2.70025
$139$	−2.61186	−0.221535	−0.110768	−	0.993846i	$-0.535331\pi$
$139$	−2.61186	−0.221535	−0.110768	+	0.993846i	$0.535331\pi$
$140$	−30.2115	−2.55334
$141$	−18.8864	−1.59052
$142$	−16.3460	−1.37173
$143$	−15.6348	−1.30745
$144$	52.4765	4.37305
$145$	5.67968	0.471672
$146$	−1.05524	−0.0873323
$147$	−0.163078	−0.0134505
$148$	5.69554	0.468171
$149$	−4.99375	−0.409104	−0.204552	−	0.978856i	$-0.565574\pi$
$149$	−4.99375	−0.409104	−0.204552	+	0.978856i	$0.565574\pi$
$150$	8.91078	0.727562
$151$	−0.708547	−0.0576607	−0.0288304	−	0.999584i	$-0.509178\pi$
$151$	−0.708547	−0.0576607	−0.0288304	+	0.999584i	$0.509178\pi$
$152$	−65.9195	−5.34678
$153$	15.9804	1.29194
$154$	−23.5636	−1.89881
$155$	13.9108	1.11734
$156$	70.2086	5.62119
$157$	6.13568	0.489680	0.244840	−	0.969563i	$-0.421265\pi$
$157$	6.13568	0.489680	0.244840	+	0.969563i	$0.421265\pi$
$158$	−32.1768	−2.55985
$159$	11.3751	0.902103
$160$	−64.4803	−5.09762
$161$	12.4425	0.980609
$162$	28.1263	2.20981
$163$	−7.42879	−0.581867	−0.290934	−	0.956743i	$-0.593966\pi$
$163$	−7.42879	−0.581867	−0.290934	+	0.956743i	$0.593966\pi$
$164$	−38.1562	−2.97950
$165$	−14.4114	−1.12193
$166$	19.9916	1.55165
$167$	8.16519	0.631841	0.315921	−	0.948786i	$-0.397687\pi$
$167$	8.16519	0.631841	0.315921	+	0.948786i	$0.397687\pi$
$168$	70.4722	5.43705
$169$	11.3759	0.875069
$170$	−32.7917	−2.51501
$171$	15.4364	1.18045
$172$	76.5873	5.83973
$173$	3.78294	0.287612	0.143806	−	0.989606i	$-0.454066\pi$
$173$	3.78294	0.287612	0.143806	+	0.989606i	$0.454066\pi$
$174$	−19.8926	−1.50806
$175$	3.49528	0.264218
$176$	−62.9588	−4.74570
$177$	6.77783	0.509453
$178$	−14.6397	−1.09729
$179$	7.89071	0.589780	0.294890	−	0.955531i	$-0.404717\pi$
$179$	7.89071	0.589780	0.294890	+	0.955531i	$0.404717\pi$
$180$	30.2890	2.25761
$181$	21.0582	1.56524	0.782622	−	0.622497i	$-0.213882\pi$
$181$	21.0582	1.56524	0.782622	+	0.622497i	$0.213882\pi$
$182$	36.7376	2.72317
$183$	−14.3715	−1.06237
$184$	53.2709	3.92718
$185$	1.82272	0.134009
$186$	−48.7215	−3.57243
$187$	−19.1726	−1.40204
$188$	−47.6233	−3.47328
$189$	2.25392	0.163949
$190$	−31.6753	−2.29797
$191$	13.6077	0.984616	0.492308	−	0.870421i	$-0.336153\pi$
$191$	13.6077	0.984616	0.492308	+	0.870421i	$0.336153\pi$
$192$	131.411	9.48374
$193$	−14.9992	−1.07967	−0.539835	−	0.841771i	$-0.681513\pi$
$193$	−14.9992	−1.07967	−0.539835	+	0.841771i	$0.681513\pi$
$194$	23.6571	1.69848
$195$	22.4685	1.60900
$196$	−0.411212	−0.0293723
$197$	5.16028	0.367655	0.183828	−	0.982959i	$-0.441151\pi$
$197$	5.16028	0.367655	0.183828	+	0.982959i	$0.441151\pi$
$198$	23.6241	1.67889
$199$	5.51806	0.391165	0.195582	−	0.980687i	$-0.437340\pi$
$199$	5.51806	0.391165	0.195582	+	0.980687i	$0.437340\pi$
$200$	14.9645	1.05815
$201$	−1.23571	−0.0871604
$202$	1.45165	0.102138
$203$	−7.80294	−0.547659
$204$	86.0950	6.02786
$205$	−12.2109	−0.852848
$206$	−11.8483	−0.825513
$207$	−12.4745	−0.867035
$208$	98.1577	6.80601
$209$	−18.5198	−1.28104
$210$	33.8629	2.33676
$211$	−11.2530	−0.774689	−0.387344	−	0.921935i	$-0.626608\pi$
$211$	−11.2530	−0.774689	−0.387344	+	0.921935i	$0.626608\pi$
$212$	28.6830	1.96996
$213$	13.7344	0.941067
$214$	−44.4899	−3.04127
$215$	24.5098	1.67156
$216$	9.64984	0.656589
$217$	−19.1111	−1.29735
$218$	20.7689	1.40665
$219$	0.886644	0.0599138
$220$	−36.3393	−2.44999
$221$	29.8915	2.01072
$222$	−6.38392	−0.428460
$223$	−26.6493	−1.78457	−0.892283	−	0.451476i	$-0.850898\pi$
$223$	−26.6493	−1.78457	−0.892283	+	0.451476i	$0.850898\pi$
$224$	88.5853	5.91885
$225$	−3.50425	−0.233616
$226$	15.0237	0.999364
$227$	18.0166	1.19580	0.597901	−	0.801570i	$-0.296002\pi$
$227$	18.0166	1.19580	0.597901	+	0.801570i	$0.296002\pi$
$228$	83.1639	5.50766
$229$	−15.6209	−1.03226	−0.516130	−	0.856510i	$-0.672628\pi$
$229$	−15.6209	−1.03226	−0.516130	+	0.856510i	$0.672628\pi$
$230$	25.5974	1.68785
$231$	19.7989	1.30267
$232$	−33.4072	−2.19329
$233$	−18.5511	−1.21533	−0.607663	−	0.794195i	$-0.707893\pi$
$233$	−18.5511	−1.21533	−0.607663	+	0.794195i	$0.707893\pi$
$234$	−36.8318	−2.40777
$235$	−15.2406	−0.994189
$236$	17.0907	1.11251
$237$	27.0359	1.75617
$238$	45.0504	2.92018
$239$	−8.60649	−0.556707	−0.278354	−	0.960479i	$-0.589789\pi$
$239$	−8.60649	−0.556707	−0.278354	+	0.960479i	$0.589789\pi$
$240$	90.4770	5.84027
$241$	25.4917	1.64206	0.821032	−	0.570883i	$-0.193399\pi$
$241$	25.4917	1.64206	0.821032	+	0.570883i	$0.193399\pi$
$242$	2.74653	0.176554
$243$	−21.0642	−1.35127
$244$	−36.2387	−2.31995
$245$	−0.131598	−0.00840750
$246$	42.7678	2.72678
$247$	28.8739	1.83720
$248$	−81.8216	−5.19567
$249$	−16.7975	−1.06450
$250$	34.2718	2.16754
$251$	−21.6700	−1.36780	−0.683899	−	0.729577i	$-0.739717\pi$
$251$	−21.6700	−1.36780	−0.683899	+	0.729577i	$0.739717\pi$
$252$	−41.6121	−2.62131
$253$	14.9662	0.940920
$254$	−19.7219	−1.23746
$255$	27.5526	1.72541
$256$	141.162	8.82265
$257$	−22.0475	−1.37528	−0.687642	−	0.726050i	$-0.741354\pi$
$257$	−22.0475	−1.37528	−0.687642	+	0.726050i	$0.741354\pi$
$258$	−85.8438	−5.34440
$259$	−2.50411	−0.155598
$260$	56.6558	3.51364
$261$	7.82296	0.484229
$262$	−39.3285	−2.42973
$263$	−15.2119	−0.938007	−0.469003	−	0.883196i	$-0.655387\pi$
$263$	−15.2119	−0.938007	−0.469003	+	0.883196i	$0.655387\pi$
$264$	84.7660	5.21699
$265$	9.17927	0.563878
$266$	43.5166	2.66817
$267$	12.3007	0.752793
$268$	−3.11593	−0.190336
$269$	−3.19483	−0.194792	−0.0973960	−	0.995246i	$-0.531051\pi$
$269$	−3.19483	−0.194792	−0.0973960	+	0.995246i	$0.531051\pi$
$270$	4.63689	0.282192
$271$	29.7673	1.80824	0.904118	−	0.427283i	$-0.140529\pi$
$271$	29.7673	1.80824	0.904118	+	0.427283i	$0.140529\pi$
$272$	120.368	7.29840
$273$	−30.8680	−1.86822
$274$	−62.5155	−3.77670
$275$	4.20422	0.253524
$276$	−67.2064	−4.04535
$277$	−29.6080	−1.77897	−0.889487	−	0.456961i	$-0.848938\pi$
$277$	−29.6080	−1.77897	−0.889487	+	0.456961i	$0.848938\pi$
$278$	7.38198	0.442742
$279$	19.1602	1.14709
$280$	56.8685	3.39854
$281$	27.2512	1.62567	0.812834	−	0.582496i	$-0.197924\pi$
$281$	27.2512	1.62567	0.812834	+	0.582496i	$0.197924\pi$
$282$	53.3791	3.17868
$283$	13.8577	0.823757	0.411879	−	0.911239i	$-0.364873\pi$
$283$	13.8577	0.823757	0.411879	+	0.911239i	$0.364873\pi$
$284$	34.6322	2.05504
$285$	26.6145	1.57651
$286$	44.1890	2.61295
$287$	16.7758	0.990243
$288$	−88.8125	−5.23333
$289$	19.6552	1.15619
$290$	−16.0526	−0.942643
$291$	−19.8774	−1.16523
$292$	2.23573	0.130836
$293$	4.09263	0.239094	0.119547	−	0.992829i	$-0.461856\pi$
$293$	4.09263	0.239094	0.119547	+	0.992829i	$0.461856\pi$
$294$	0.460912	0.0268809
$295$	5.46946	0.318444
$296$	−10.7210	−0.623144
$297$	2.71108	0.157313
$298$	14.1140	0.817599
$299$	−23.3336	−1.34941
$300$	−18.8792	−1.08999
$301$	−33.6725	−1.94085
$302$	2.00258	0.115236
$303$	−1.21972	−0.0700713
$304$	116.270	6.66856
$305$	−11.5973	−0.664059
$306$	−45.1659	−2.58196
$307$	32.4082	1.84963	0.924816	−	0.380414i	$-0.124219\pi$
$307$	32.4082	1.84963	0.924816	+	0.380414i	$0.124219\pi$
$308$	49.9241	2.84469
$309$	9.95533	0.566339
$310$	−39.3164	−2.23302
$311$	−1.12813	−0.0639703	−0.0319852	−	0.999488i	$-0.510183\pi$
$311$	−1.12813	−0.0639703	−0.0319852	+	0.999488i	$0.510183\pi$
$312$	−132.157	−7.48191
$313$	19.6021	1.10797	0.553987	−	0.832525i	$-0.313106\pi$
$313$	19.6021	1.10797	0.553987	+	0.832525i	$0.313106\pi$
$314$	−17.3414	−0.978633
$315$	−13.3169	−0.750322
$316$	68.1728	3.83502
$317$	−1.94679	−0.109343	−0.0546714	−	0.998504i	$-0.517411\pi$
$317$	−1.94679	−0.109343	−0.0546714	+	0.998504i	$0.517411\pi$
$318$	−32.1497	−1.80287
$319$	−9.38561	−0.525493
$320$	106.044	5.92801
$321$	37.3817	2.08644
$322$	−35.1666	−1.95976
$323$	35.4073	1.97011
$324$	−59.5910	−3.31061
$325$	−6.55472	−0.363590
$326$	20.9962	1.16287
$327$	−17.4507	−0.965025
$328$	71.8231	3.96577
$329$	20.9381	1.15435
$330$	40.7313	2.24218
$331$	−0.453291	−0.0249151	−0.0124576	−	0.999922i	$-0.503965\pi$
$331$	−0.453291	−0.0249151	−0.0124576	+	0.999922i	$0.503965\pi$
$332$	−42.3560	−2.32459
$333$	2.51053	0.137576
$334$	−23.0775	−1.26274
$335$	−0.997174	−0.0544814
$336$	−124.300	−6.78114
$337$	22.7201	1.23765	0.618823	−	0.785531i	$-0.287610\pi$
$337$	22.7201	1.23765	0.618823	+	0.785531i	$0.287610\pi$
$338$	−32.1520	−1.74884
$339$	−12.6234	−0.685608
$340$	69.4755	3.76784
$341$	−22.9874	−1.24484
$342$	−43.6282	−2.35914
$343$	18.6100	1.00484
$344$	−144.164	−7.77279
$345$	−21.5077	−1.15794
$346$	−10.6918	−0.574796
$347$	−24.2474	−1.30167	−0.650833	−	0.759221i	$-0.725580\pi$
$347$	−24.2474	−1.30167	−0.650833	+	0.759221i	$0.725580\pi$
$348$	42.1464	2.25928
$349$	22.7072	1.21549	0.607743	−	0.794134i	$-0.292075\pi$
$349$	22.7072	1.21549	0.607743	+	0.794134i	$0.292075\pi$
$350$	−9.87880	−0.528044
$351$	−4.22679	−0.225609
$352$	106.553	5.67929
$353$	−31.4178	−1.67220	−0.836101	−	0.548575i	$-0.815170\pi$
$353$	−31.4178	−1.67220	−0.836101	+	0.548575i	$0.815170\pi$
$354$	−19.1564	−1.01815
$355$	11.0832	0.588234
$356$	31.0171	1.64390
$357$	−37.8527	−2.00337
$358$	−22.3017	−1.17868
$359$	22.9848	1.21309	0.606546	−	0.795049i	$-0.292555\pi$
$359$	22.9848	1.21309	0.606546	+	0.795049i	$0.292555\pi$
$360$	−57.0144	−3.00492
$361$	15.2018	0.800095
$362$	−59.5174	−3.12816
$363$	−2.30772	−0.121124
$364$	−77.8356	−4.07970
$365$	0.715489	0.0374504
$366$	40.6186	2.12317
$367$	−31.3391	−1.63589	−0.817945	−	0.575297i	$-0.804886\pi$
$367$	−31.3391	−1.63589	−0.817945	+	0.575297i	$0.804886\pi$
$368$	−93.9604	−4.89802
$369$	−16.8188	−0.875553
$370$	−5.15159	−0.267818
$371$	−12.6108	−0.654720
$372$	103.226	5.35201
$373$	26.9767	1.39680	0.698400	−	0.715708i	$-0.253896\pi$
$373$	26.9767	1.39680	0.698400	+	0.715708i	$0.253896\pi$
$374$	54.1879	2.80199
$375$	−28.7961	−1.48703
$376$	89.6435	4.62301
$377$	14.6329	0.753633
$378$	−6.37032	−0.327654
$379$	−2.11396	−0.108587	−0.0542935	−	0.998525i	$-0.517291\pi$
$379$	−2.11396	−0.108587	−0.0542935	+	0.998525i	$0.517291\pi$
$380$	67.1102	3.44268
$381$	16.5709	0.848953
$382$	−38.4597	−1.96777
$383$	−33.2625	−1.69964	−0.849818	−	0.527076i	$-0.823288\pi$
$383$	−33.2625	−1.69964	−0.849818	+	0.527076i	$0.823288\pi$
$384$	−211.599	−10.7981
$385$	15.9770	0.814261
$386$	42.3927	2.15773
$387$	33.7589	1.71606
$388$	−50.1220	−2.54456
$389$	4.42545	0.224379	0.112190	−	0.993687i	$-0.464214\pi$
$389$	4.42545	0.224379	0.112190	+	0.993687i	$0.464214\pi$
$390$	−63.5033	−3.21561
$391$	−28.6133	−1.44704
$392$	0.774044	0.0390951
$393$	33.0450	1.66690
$394$	−14.5846	−0.734764
$395$	21.8170	1.09773
$396$	−50.0522	−2.51522
$397$	−35.4328	−1.77832	−0.889160	−	0.457597i	$-0.848710\pi$
$397$	−35.4328	−1.77832	−0.889160	+	0.457597i	$0.848710\pi$
$398$	−15.5958	−0.781748
$399$	−36.5639	−1.83049
$400$	−26.3948	−1.31974
$401$	−18.4074	−0.919219	−0.459610	−	0.888121i	$-0.652011\pi$
$401$	−18.4074	−0.919219	−0.459610	+	0.888121i	$0.652011\pi$
$402$	3.49252	0.174191
$403$	35.8392	1.78528
$404$	−3.07561	−0.153017
$405$	−19.0706	−0.947626
$406$	22.0536	1.09450
$407$	−3.01202	−0.149300
$408$	−162.061	−8.02320
$409$	17.4839	0.864521	0.432261	−	0.901749i	$-0.357716\pi$
$409$	17.4839	0.864521	0.432261	+	0.901749i	$0.357716\pi$
$410$	34.5120	1.70443
$411$	52.5274	2.59099
$412$	25.1030	1.23674
$413$	−7.51413	−0.369746
$414$	35.2569	1.73278
$415$	−13.5550	−0.665388
$416$	−166.124	−8.14492
$417$	−6.20256	−0.303741
$418$	52.3430	2.56018
$419$	38.0965	1.86113	0.930567	−	0.366121i	$-0.119314\pi$
$419$	38.0965	1.86113	0.930567	+	0.366121i	$0.119314\pi$
$420$	−71.7451	−3.50080
$421$	−6.14306	−0.299394	−0.149697	−	0.988732i	$-0.547830\pi$
$421$	−6.14306	−0.299394	−0.149697	+	0.988732i	$0.547830\pi$
$422$	31.8047	1.54823
$423$	−20.9918	−1.02066
$424$	−53.9913	−2.62205
$425$	−8.03788	−0.389895
$426$	−38.8179	−1.88074
$427$	15.9328	0.771041
$428$	94.2604	4.55625
$429$	−37.1289	−1.79260
$430$	−69.2728	−3.34063
$431$	30.1693	1.45320	0.726601	−	0.687060i	$-0.241099\pi$
$431$	30.1693	1.45320	0.726601	+	0.687060i	$0.241099\pi$
$432$	−17.0206	−0.818904
$433$	31.9704	1.53640	0.768200	−	0.640210i	$-0.221153\pi$
$433$	31.9704	1.53640	0.768200	+	0.640210i	$0.221153\pi$
$434$	54.0143	2.59277
$435$	13.4879	0.646695
$436$	−44.0030	−2.10736
$437$	−27.6392	−1.32216
$438$	−2.50594	−0.119739
$439$	−14.3747	−0.686067	−0.343034	−	0.939323i	$-0.611454\pi$
$439$	−14.3747	−0.686067	−0.343034	+	0.939323i	$0.611454\pi$
$440$	68.4031	3.26099
$441$	−0.181258	−0.00863133
$442$	−84.4832	−4.01846
$443$	36.7247	1.74484	0.872421	−	0.488755i	$-0.162549\pi$
$443$	36.7247	1.74484	0.872421	+	0.488755i	$0.162549\pi$
$444$	13.5256	0.641894
$445$	9.92624	0.470549
$446$	75.3195	3.56648
$447$	−11.8590	−0.560910
$448$	−145.686	−6.88303
$449$	2.83954	0.134006	0.0670031	−	0.997753i	$-0.478656\pi$
$449$	2.83954	0.134006	0.0670031	+	0.997753i	$0.478656\pi$
$450$	9.90414	0.466886
$451$	20.1784	0.950164
$452$	−31.8307	−1.49719
$453$	−1.68263	−0.0790569
$454$	−50.9207	−2.38983
$455$	−24.9093	−1.16777
$456$	−156.543	−7.33081
$457$	−15.2665	−0.714136	−0.357068	−	0.934078i	$-0.616224\pi$
$457$	−15.2665	−0.714136	−0.357068	+	0.934078i	$0.616224\pi$
$458$	44.1498	2.06298
$459$	−5.18321	−0.241931
$460$	−54.2331	−2.52863
$461$	21.6555	1.00860	0.504298	−	0.863530i	$-0.331751\pi$
$461$	21.6555	1.00860	0.504298	+	0.863530i	$0.331751\pi$
$462$	−55.9581	−2.60340
$463$	−20.9807	−0.975055	−0.487528	−	0.873108i	$-0.662101\pi$
$463$	−20.9807	−0.975055	−0.487528	+	0.873108i	$0.662101\pi$
$464$	58.9243	2.73549
$465$	33.0348	1.53195
$466$	52.4316	2.42885
$467$	13.5250	0.625862	0.312931	−	0.949776i	$-0.398689\pi$
$467$	13.5250	0.625862	0.312931	+	0.949776i	$0.398689\pi$
$468$	78.0353	3.60718
$469$	1.36995	0.0632585
$470$	43.0750	1.98690
$471$	14.5708	0.671386
$472$	−32.1707	−1.48078
$473$	−40.5022	−1.86229
$474$	−76.4123	−3.50973
$475$	−7.76423	−0.356247
$476$	−95.4479	−4.37485
$477$	12.6432	0.578890
$478$	24.3247	1.11259
$479$	−0.416803	−0.0190442	−0.00952210	−	0.999955i	$-0.503031\pi$
$479$	−0.416803	−0.0190442	−0.00952210	+	0.999955i	$0.503031\pi$
$480$	−153.125	−6.98919
$481$	4.69597	0.214118
$482$	−72.0478	−3.28169
$483$	29.5481	1.34448
$484$	−5.81906	−0.264503
$485$	−16.0403	−0.728352
$486$	59.5344	2.70053
$487$	30.1701	1.36714	0.683568	−	0.729887i	$-0.260427\pi$
$487$	30.1701	1.36714	0.683568	+	0.729887i	$0.260427\pi$
$488$	68.2139	3.08790
$489$	−17.6416	−0.797781
$490$	0.371939	0.0168025
$491$	−14.7224	−0.664411	−0.332205	−	0.943207i	$-0.607793\pi$
$491$	−14.7224	−0.664411	−0.332205	+	0.943207i	$0.607793\pi$
$492$	−90.6118	−4.08510
$493$	17.9439	0.808155
$494$	−81.6069	−3.67167
$495$	−16.0180	−0.719953
$496$	144.319	6.48010
$497$	−15.2264	−0.682999
$498$	47.4753	2.12742
$499$	14.4588	0.647267	0.323633	−	0.946183i	$-0.395096\pi$
$499$	14.4588	0.647267	0.323633	+	0.946183i	$0.395096\pi$
$500$	−72.6113	−3.24728
$501$	19.3904	0.866298
$502$	61.2464	2.73356
$503$	8.78342	0.391633	0.195817	−	0.980641i	$-0.437264\pi$
$503$	8.78342	0.391633	0.195817	+	0.980641i	$0.437264\pi$
$504$	78.3283	3.48902
$505$	−0.984272	−0.0437995
$506$	−42.2995	−1.88044
$507$	27.0150	1.19978
$508$	41.7846	1.85389
$509$	−10.5816	−0.469023	−0.234511	−	0.972113i	$-0.575349\pi$
$509$	−10.5816	−0.469023	−0.234511	+	0.972113i	$0.575349\pi$
$510$	−77.8725	−3.44825
$511$	−0.982963	−0.0434837
$512$	−220.764	−9.75649
$513$	−5.00674	−0.221053
$514$	62.3133	2.74852
$515$	8.03358	0.354002
$516$	181.877	8.00667
$517$	25.1850	1.10763
$518$	7.07743	0.310964
$519$	8.98359	0.394336
$520$	−106.646	−4.67673
$521$	22.0704	0.966921	0.483461	−	0.875366i	$-0.339380\pi$
$521$	22.0704	0.966921	0.483461	+	0.875366i	$0.339380\pi$
$522$	−22.1102	−0.967738
$523$	11.2453	0.491724	0.245862	−	0.969305i	$-0.420929\pi$
$523$	11.2453	0.491724	0.245862	+	0.969305i	$0.420929\pi$
$524$	83.3251	3.64007
$525$	8.30046	0.362262
$526$	42.9938	1.87462
$527$	43.9487	1.91444
$528$	−149.512	−6.50668
$529$	−0.664216	−0.0288789
$530$	−25.9436	−1.12692
$531$	7.53341	0.326922
$532$	−92.1983	−3.99730
$533$	−31.4597	−1.36267
$534$	−34.7659	−1.50447
$535$	30.1657	1.30418
$536$	5.86525	0.253340
$537$	18.7386	0.808629
$538$	9.02962	0.389294
$539$	0.217464	0.00936685
$540$	−9.82414	−0.422764
$541$	19.8407	0.853018	0.426509	−	0.904483i	$-0.359743\pi$
$541$	19.8407	0.853018	0.426509	+	0.904483i	$0.359743\pi$
$542$	−84.1321	−3.61378
$543$	50.0083	2.14606
$544$	−203.714	−8.73417
$545$	−14.0821	−0.603209
$546$	87.2430	3.73366
$547$	21.1685	0.905099	0.452549	−	0.891739i	$-0.350515\pi$
$547$	21.1685	0.905099	0.452549	+	0.891739i	$0.350515\pi$
$548$	132.451	5.65803
$549$	−15.9736	−0.681739
$550$	−11.8825	−0.506672
$551$	17.3330	0.738412
$552$	126.506	5.38444
$553$	−29.9729	−1.27458
$554$	83.6819	3.55530
$555$	4.32852	0.183735
$556$	−15.6401	−0.663290
$557$	−8.25165	−0.349634	−0.174817	−	0.984601i	$-0.555933\pi$
$557$	−8.25165	−0.349634	−0.174817	+	0.984601i	$0.555933\pi$
$558$	−54.1528	−2.29247
$559$	63.1462	2.67080
$560$	−100.306	−4.23870
$561$	−45.5303	−1.92229
$562$	−77.0206	−3.24892
$563$	−2.20462	−0.0929135	−0.0464568	−	0.998920i	$-0.514793\pi$
$563$	−2.20462	−0.0929135	−0.0464568	+	0.998920i	$0.514793\pi$
$564$	−113.094	−4.76211
$565$	−10.1866	−0.428554
$566$	−39.1665	−1.64629
$567$	26.1999	1.10029
$568$	−65.1898	−2.73530
$569$	−28.1507	−1.18014	−0.590070	−	0.807352i	$-0.700900\pi$
$569$	−28.1507	−1.18014	−0.590070	+	0.807352i	$0.700900\pi$
$570$	−75.2212	−3.15067
$571$	−1.14825	−0.0480527	−0.0240263	−	0.999711i	$-0.507649\pi$
$571$	−1.14825	−0.0480527	−0.0240263	+	0.999711i	$0.507649\pi$
$572$	−93.6230	−3.91457
$573$	32.3150	1.34998
$574$	−47.4138	−1.97901
$575$	6.27443	0.261662
$576$	146.060	6.08583
$577$	3.10757	0.129370	0.0646850	−	0.997906i	$-0.479396\pi$
$577$	3.10757	0.129370	0.0646850	+	0.997906i	$0.479396\pi$
$578$	−55.5520	−2.31066
$579$	−35.6196	−1.48030
$580$	34.0106	1.41221
$581$	18.6223	0.772584
$582$	56.1799	2.32873
$583$	−15.1686	−0.628221
$584$	−4.20842	−0.174145
$585$	24.9732	1.03252
$586$	−11.5671	−0.477833
$587$	−28.3036	−1.16821	−0.584107	−	0.811677i	$-0.698555\pi$
$587$	−28.3036	−1.16821	−0.584107	+	0.811677i	$0.698555\pi$
$588$	−0.976531	−0.0402715
$589$	42.4524	1.74922
$590$	−15.4585	−0.636415
$591$	12.2544	0.504081
$592$	18.9099	0.777192
$593$	9.58285	0.393520	0.196760	−	0.980452i	$-0.436958\pi$
$593$	9.58285	0.393520	0.196760	+	0.980452i	$0.436958\pi$
$594$	−7.66240	−0.314392
$595$	−30.5457	−1.25225
$596$	−29.9031	−1.22488
$597$	13.1041	0.536314
$598$	65.9482	2.69682
$599$	20.9405	0.855606	0.427803	−	0.903872i	$-0.359288\pi$
$599$	20.9405	0.855606	0.427803	+	0.903872i	$0.359288\pi$
$600$	35.5372	1.45080
$601$	34.6326	1.41269	0.706346	−	0.707867i	$-0.250342\pi$
$601$	34.6326	1.41269	0.706346	+	0.707867i	$0.250342\pi$
$602$	95.1693	3.87881
$603$	−1.37347	−0.0559319
$604$	−4.24286	−0.172640
$605$	−1.86224	−0.0757110
$606$	3.44733	0.140038
$607$	0.824640	0.0334711	0.0167356	−	0.999860i	$-0.494673\pi$
$607$	0.824640	0.0334711	0.0167356	+	0.999860i	$0.494673\pi$
$608$	−196.779	−7.98042
$609$	−18.5301	−0.750879
$610$	32.7777	1.32713
$611$	−39.2653	−1.58851
$612$	95.6927	3.86815
$613$	10.4010	0.420091	0.210045	−	0.977692i	$-0.432639\pi$
$613$	10.4010	0.420091	0.210045	+	0.977692i	$0.432639\pi$
$614$	−91.5960	−3.69652
$615$	−28.9980	−1.16931
$616$	−93.9745	−3.78634
$617$	−36.4909	−1.46907	−0.734533	−	0.678572i	$-0.762599\pi$
$617$	−36.4909	−1.46907	−0.734533	+	0.678572i	$0.762599\pi$
$618$	−28.1370	−1.13184
$619$	−4.01223	−0.161265	−0.0806326	−	0.996744i	$-0.525694\pi$
$619$	−4.01223	−0.161265	−0.0806326	+	0.996744i	$0.525694\pi$
$620$	83.2994	3.34539
$621$	4.04605	0.162362
$622$	3.18846	0.127846
$623$	−13.6370	−0.546355
$624$	233.101	9.33152
$625$	−16.5993	−0.663973
$626$	−55.4018	−2.21430
$627$	−43.9802	−1.75640
$628$	36.7411	1.46613
$629$	5.75855	0.229608
$630$	37.6379	1.49953
$631$	25.5068	1.01541	0.507704	−	0.861532i	$-0.330494\pi$
$631$	25.5068	1.01541	0.507704	+	0.861532i	$0.330494\pi$
$632$	−128.325	−5.10449
$633$	−26.7232	−1.06215
$634$	5.50227	0.218523
$635$	13.3721	0.530656
$636$	68.1153	2.70095
$637$	−0.339044	−0.0134334
$638$	26.5268	1.05020
$639$	15.2655	0.603894
$640$	−170.753	−6.74960
$641$	−38.8079	−1.53282	−0.766410	−	0.642351i	$-0.777959\pi$
$641$	−38.8079	−1.53282	−0.766410	+	0.642351i	$0.777959\pi$
$642$	−105.653	−4.16979
$643$	45.4964	1.79420	0.897101	−	0.441825i	$-0.145669\pi$
$643$	45.4964	1.79420	0.897101	+	0.441825i	$0.145669\pi$
$644$	74.5073	2.93600
$645$	58.2051	2.29182
$646$	−100.072	−3.93730
$647$	20.6770	0.812899	0.406449	−	0.913673i	$-0.366767\pi$
$647$	20.6770	0.812899	0.406449	+	0.913673i	$0.366767\pi$
$648$	112.171	4.40649
$649$	−9.03822	−0.354781
$650$	18.5258	0.726640
$651$	−45.3844	−1.77875
$652$	−44.4844	−1.74214
$653$	31.6499	1.23856	0.619278	−	0.785172i	$-0.287426\pi$
$653$	31.6499	1.23856	0.619278	+	0.785172i	$0.287426\pi$
$654$	49.3213	1.92861
$655$	26.6661	1.04193
$656$	−126.683	−4.94615
$657$	0.985485	0.0384474
$658$	−59.1779	−2.30699
$659$	15.1613	0.590602	0.295301	−	0.955404i	$-0.404580\pi$
$659$	15.1613	0.590602	0.295301	+	0.955404i	$0.404580\pi$
$660$	−86.2971	−3.35911
$661$	−31.9400	−1.24232	−0.621161	−	0.783683i	$-0.713339\pi$
$661$	−31.9400	−1.24232	−0.621161	+	0.783683i	$0.713339\pi$
$662$	1.28115	0.0497932
$663$	70.9853	2.75684
$664$	79.7287	3.09408
$665$	−29.5057	−1.14418
$666$	−7.09558	−0.274948
$667$	−14.0072	−0.542360
$668$	48.8941	1.89177
$669$	−63.2857	−2.44677
$670$	2.81834	0.108882
$671$	19.1644	0.739833
$672$	210.369	8.11516
$673$	−40.3862	−1.55677	−0.778387	−	0.627785i	$-0.783962\pi$
$673$	−40.3862	−1.55677	−0.778387	+	0.627785i	$0.783962\pi$
$674$	−64.2145	−2.47345
$675$	1.13659	0.0437474
$676$	68.1201	2.62000
$677$	36.9954	1.42185	0.710925	−	0.703268i	$-0.248277\pi$
$677$	36.9954	1.42185	0.710925	+	0.703268i	$0.248277\pi$
$678$	35.6778	1.37020
$679$	22.0367	0.845691
$680$	−130.777	−5.01507
$681$	42.7851	1.63953
$682$	64.9699	2.48783
$683$	14.7944	0.566092	0.283046	−	0.959106i	$-0.408655\pi$
$683$	14.7944	0.566092	0.283046	+	0.959106i	$0.408655\pi$
$684$	92.4348	3.53433
$685$	42.3877	1.61955
$686$	−52.5979	−2.00820
$687$	−37.0960	−1.41530
$688$	254.279	9.69431
$689$	23.6491	0.900959
$690$	60.7878	2.31415
$691$	−41.5526	−1.58074	−0.790368	−	0.612632i	$-0.790111\pi$
$691$	−41.5526	−1.58074	−0.790368	+	0.612632i	$0.790111\pi$
$692$	22.6527	0.861126
$693$	22.0060	0.835939
$694$	68.5309	2.60140
$695$	−5.00523	−0.189859
$696$	−79.3341	−3.00715
$697$	−38.5783	−1.46126
$698$	−64.1778	−2.42917
$699$	−44.0546	−1.66630
$700$	20.9301	0.791085
$701$	22.3931	0.845775	0.422887	−	0.906182i	$-0.361017\pi$
$701$	22.3931	0.845775	0.422887	+	0.906182i	$0.361017\pi$
$702$	11.9463	0.450884
$703$	5.56249	0.209793
$704$	−175.236	−6.60444
$705$	−36.1929	−1.36310
$706$	88.7970	3.34192
$707$	1.35223	0.0508557
$708$	40.5864	1.52533
$709$	−35.1798	−1.32121	−0.660603	−	0.750735i	$-0.729699\pi$
$709$	−35.1798	−1.32121	−0.660603	+	0.750735i	$0.729699\pi$
$710$	−31.3246	−1.17559
$711$	30.0498	1.12696
$712$	−58.3849	−2.18807
$713$	−34.3067	−1.28480
$714$	106.984	4.00377
$715$	−29.9617	−1.12050
$716$	47.2505	1.76583
$717$	−20.4384	−0.763284
$718$	−64.9625	−2.42438
$719$	13.9533	0.520369	0.260185	−	0.965559i	$-0.416217\pi$
$719$	13.9533	0.520369	0.260185	+	0.965559i	$0.416217\pi$
$720$	100.563	3.74777
$721$	−11.0368	−0.411032
$722$	−42.9652	−1.59900
$723$	60.5367	2.25138
$724$	126.099	4.68643
$725$	−3.93481	−0.146135
$726$	6.52236	0.242068
$727$	14.2239	0.527534	0.263767	−	0.964586i	$-0.415035\pi$
$727$	14.2239	0.527534	0.263767	+	0.964586i	$0.415035\pi$
$728$	146.514	5.43016
$729$	−20.1679	−0.746959
$730$	−2.02220	−0.0748451
$731$	77.4345	2.86402
$732$	−86.0584	−3.18081
$733$	16.4577	0.607880	0.303940	−	0.952691i	$-0.401698\pi$
$733$	16.4577	0.607880	0.303940	+	0.952691i	$0.401698\pi$
$734$	88.5746	3.26935
$735$	−0.312514	−0.0115273
$736$	159.021	5.86158
$737$	1.64782	0.0606982
$738$	47.5355	1.74980
$739$	−45.2534	−1.66467	−0.832337	−	0.554270i	$-0.812997\pi$
$739$	−45.2534	−1.66467	−0.832337	+	0.554270i	$0.812997\pi$
$740$	10.9146	0.401230
$741$	68.5685	2.51893
$742$	35.6422	1.30847
$743$	−11.7540	−0.431213	−0.215607	−	0.976480i	$-0.569173\pi$
$743$	−11.7540	−0.431213	−0.215607	+	0.976480i	$0.569173\pi$
$744$	−194.307	−7.12363
$745$	−9.56975	−0.350608
$746$	−76.2449	−2.79152
$747$	−18.6701	−0.683103
$748$	−114.807	−4.19778
$749$	−41.4426	−1.51428
$750$	81.3873	2.97184
$751$	−26.4661	−0.965760	−0.482880	−	0.875686i	$-0.660409\pi$
$751$	−26.4661	−0.965760	−0.482880	+	0.875686i	$0.660409\pi$
$752$	−158.115	−5.76586
$753$	−51.4611	−1.87535
$754$	−41.3573	−1.50615
$755$	−1.35782	−0.0494162
$756$	13.4967	0.490872
$757$	34.5109	1.25432	0.627159	−	0.778891i	$-0.284218\pi$
$757$	34.5109	1.25432	0.627159	+	0.778891i	$0.284218\pi$
$758$	5.97474	0.217012
$759$	35.5413	1.29007
$760$	−126.325	−4.58227
$761$	−24.4564	−0.886544	−0.443272	−	0.896387i	$-0.646182\pi$
$761$	−24.4564	−0.886544	−0.443272	+	0.896387i	$0.646182\pi$
$762$	−46.8347	−1.69664
$763$	19.3464	0.700387
$764$	81.4842	2.94799
$765$	30.6241	1.10722
$766$	94.0108	3.39675
$767$	14.0913	0.508807
$768$	335.227	12.0965
$769$	19.5683	0.705652	0.352826	−	0.935689i	$-0.385221\pi$
$769$	19.5683	0.705652	0.352826	+	0.935689i	$0.385221\pi$
$770$	−45.1561	−1.62731
$771$	−52.3575	−1.88561
$772$	−89.8172	−3.23259
$773$	−2.65425	−0.0954667	−0.0477333	−	0.998860i	$-0.515200\pi$
$773$	−2.65425	−0.0954667	−0.0477333	+	0.998860i	$0.515200\pi$
$774$	−95.4135	−3.42957
$775$	−9.63722	−0.346179
$776$	94.3470	3.38686
$777$	−5.94666	−0.213335
$778$	−12.5078	−0.448425
$779$	−37.2648	−1.33515
$780$	134.544	4.81745
$781$	−18.3148	−0.655355
$782$	80.8706	2.89193
$783$	−2.53735	−0.0906776
$784$	−1.36528	−0.0487598
$785$	11.7581	0.419664
$786$	−93.3959	−3.33132
$787$	−32.1747	−1.14690	−0.573451	−	0.819240i	$-0.694396\pi$
$787$	−32.1747	−1.14690	−0.573451	+	0.819240i	$0.694396\pi$
$788$	30.9004	1.10078
$789$	−36.1247	−1.28607
$790$	−61.6619	−2.19383
$791$	13.9947	0.497595
$792$	94.2156	3.34781
$793$	−29.8788	−1.06103
$794$	100.145	3.55400
$795$	21.7986	0.773117
$796$	33.0428	1.17117
$797$	−15.5925	−0.552316	−0.276158	−	0.961112i	$-0.589061\pi$
$797$	−15.5925	−0.552316	−0.276158	+	0.961112i	$0.589061\pi$
$798$	103.342	3.65825
$799$	−48.1501	−1.70343
$800$	44.6711	1.57936
$801$	13.6720	0.483076
$802$	52.0252	1.83707
$803$	−1.18234	−0.0417238
$804$	−7.39958	−0.260963
$805$	23.8442	0.840397
$806$	−101.293	−3.56790
$807$	−7.58695	−0.267073
$808$	5.78936	0.203669
$809$	−47.0938	−1.65573	−0.827865	−	0.560927i	$-0.810445\pi$
$809$	−47.0938	−1.65573	−0.827865	+	0.560927i	$0.810445\pi$
$810$	53.8997	1.89384
$811$	12.5284	0.439933	0.219966	−	0.975507i	$-0.429405\pi$
$811$	12.5284	0.439933	0.219966	+	0.975507i	$0.429405\pi$
$812$	−46.7249	−1.63972
$813$	70.6903	2.47922
$814$	8.51293	0.298378
$815$	−14.2361	−0.498670
$816$	285.846	10.0066
$817$	74.7982	2.61686
$818$	−49.4151	−1.72776
$819$	−34.3091	−1.19886
$820$	−73.1204	−2.55347
$821$	−15.5484	−0.542643	−0.271322	−	0.962489i	$-0.587461\pi$
$821$	−15.5484	−0.542643	−0.271322	+	0.962489i	$0.587461\pi$
$822$	−148.459	−5.17812
$823$	24.7672	0.863329	0.431664	−	0.902034i	$-0.357927\pi$
$823$	24.7672	0.863329	0.431664	+	0.902034i	$0.357927\pi$
$824$	−47.2525	−1.64612
$825$	9.98403	0.347599
$826$	21.2374	0.738943
$827$	31.6401	1.10023	0.550117	−	0.835088i	$-0.314583\pi$
$827$	31.6401	1.10023	0.550117	+	0.835088i	$0.314583\pi$
$828$	−74.6984	−2.59595
$829$	−23.1216	−0.803046	−0.401523	−	0.915849i	$-0.631519\pi$
$829$	−23.1216	−0.803046	−0.401523	+	0.915849i	$0.631519\pi$
$830$	38.3108	1.32979
$831$	−70.3120	−2.43910
$832$	273.206	9.47172
$833$	−0.415761	−0.0144053
$834$	17.5304	0.607030
$835$	15.6473	0.541498
$836$	−110.899	−3.83551
$837$	−6.21454	−0.214806
$838$	−107.673	−3.71950
$839$	17.7618	0.613207	0.306603	−	0.951837i	$-0.400807\pi$
$839$	17.7618	0.613207	0.306603	+	0.951837i	$0.400807\pi$
$840$	135.049	4.65964
$841$	−20.2158	−0.697098
$842$	17.3623	0.598344
$843$	64.7150	2.22890
$844$	−67.3843	−2.31946
$845$	21.8001	0.749948
$846$	59.3297	2.03980
$847$	2.55842	0.0879082
$848$	95.2311	3.27025
$849$	32.9088	1.12943
$850$	22.7177	0.779210
$851$	−4.49516	−0.154092
$852$	82.2433	2.81761
$853$	−34.7374	−1.18939	−0.594693	−	0.803953i	$-0.702726\pi$
$853$	−34.7374	−1.18939	−0.594693	+	0.803953i	$0.702726\pi$
$854$	−45.0312	−1.54094
$855$	29.5814	1.01166
$856$	−177.431	−6.06446
$857$	−40.3474	−1.37824	−0.689120	−	0.724647i	$-0.742003\pi$
$857$	−40.3474	−1.37824	−0.689120	+	0.724647i	$0.742003\pi$
$858$	104.938	3.58254
$859$	−0.904569	−0.0308635	−0.0154317	−	0.999881i	$-0.504912\pi$
$859$	−0.904569	−0.0308635	−0.0154317	+	0.999881i	$0.504912\pi$
$860$	146.768	5.00474
$861$	39.8385	1.35769
$862$	−85.2681	−2.90424
$863$	9.34658	0.318161	0.159081	−	0.987266i	$-0.449147\pi$
$863$	9.34658	0.318161	0.159081	+	0.987266i	$0.449147\pi$
$864$	28.8061	0.980002
$865$	7.24942	0.246488
$866$	−90.3587	−3.07051
$867$	46.6765	1.58522
$868$	−114.440	−3.88433
$869$	−36.0523	−1.22299
$870$	−38.1212	−1.29243
$871$	−2.56908	−0.0870499
$872$	82.8289	2.80494
$873$	−22.0932	−0.747743
$874$	78.1173	2.64236
$875$	31.9244	1.07924
$876$	5.30932	0.179385
$877$	29.1715	0.985053	0.492527	−	0.870297i	$-0.336073\pi$
$877$	29.1715	0.985053	0.492527	+	0.870297i	$0.336073\pi$
$878$	40.6276	1.37111
$879$	9.71903	0.327815
$880$	−120.651	−4.06714
$881$	−16.1080	−0.542692	−0.271346	−	0.962482i	$-0.587469\pi$
$881$	−16.1080	−0.542692	−0.271346	+	0.962482i	$0.587469\pi$
$882$	0.512294	0.0172498
$883$	−10.0855	−0.339403	−0.169701	−	0.985496i	$-0.554280\pi$
$883$	−10.0855	−0.339403	−0.169701	+	0.985496i	$0.554280\pi$
$884$	178.994	6.02022
$885$	12.9887	0.436609
$886$	−103.796	−3.48709
$887$	−25.4937	−0.855994	−0.427997	−	0.903780i	$-0.640781\pi$
$887$	−25.4937	−0.855994	−0.427997	+	0.903780i	$0.640781\pi$
$888$	−25.4598	−0.854374
$889$	−18.3711	−0.616145
$890$	−28.0548	−0.940398
$891$	31.5140	1.05576
$892$	−159.579	−5.34309
$893$	−46.5108	−1.55642
$894$	33.5173	1.12099
$895$	15.1213	0.505450
$896$	234.586	7.83697
$897$	−55.4116	−1.85014
$898$	−8.02547	−0.267813
$899$	21.5144	0.717544
$900$	−20.9838	−0.699461
$901$	29.0003	0.966140
$902$	−57.0307	−1.89892
$903$	−79.9641	−2.66104
$904$	59.9164	1.99279
$905$	40.3548	1.34144
$906$	4.75566	0.157996
$907$	−42.3735	−1.40699	−0.703495	−	0.710700i	$-0.748378\pi$
$907$	−42.3735	−1.40699	−0.703495	+	0.710700i	$0.748378\pi$
$908$	107.885	3.58030
$909$	−1.35570	−0.0449656
$910$	70.4019	2.33380
$911$	−20.3877	−0.675474	−0.337737	−	0.941241i	$-0.609661\pi$
$911$	−20.3877	−0.675474	−0.337737	+	0.941241i	$0.609661\pi$
$912$	276.114	9.14306
$913$	22.3995	0.741314
$914$	43.1481	1.42721
$915$	−27.5408	−0.910472
$916$	−93.5398	−3.09064
$917$	−36.6348	−1.20979
$918$	14.6494	0.483503
$919$	4.15517	0.137067	0.0685333	−	0.997649i	$-0.478168\pi$
$919$	4.15517	0.137067	0.0685333	+	0.997649i	$0.478168\pi$
$920$	102.085	3.36566
$921$	76.9617	2.53597
$922$	−61.2054	−2.01569
$923$	28.5542	0.939874
$924$	118.558	3.90027
$925$	−1.26275	−0.0415191
$926$	59.2982	1.94866
$927$	11.0651	0.363426
$928$	−99.7249	−3.27363
$929$	−25.9929	−0.852800	−0.426400	−	0.904535i	$-0.640218\pi$
$929$	−25.9929	−0.852800	−0.426400	+	0.904535i	$0.640218\pi$
$930$	−93.3672	−3.06163
$931$	−0.401606	−0.0131621
$932$	−111.086	−3.63876
$933$	−2.67904	−0.0877077
$934$	−38.2260	−1.25079
$935$	−36.7413	−1.20157
$936$	−146.890	−4.80123
$937$	−26.8717	−0.877861	−0.438931	−	0.898521i	$-0.644643\pi$
$937$	−26.8717	−0.877861	−0.438931	+	0.898521i	$0.644643\pi$
$938$	−3.87193	−0.126423
$939$	46.5503	1.51911
$940$	−91.2626	−2.97666
$941$	50.1414	1.63456	0.817281	−	0.576239i	$-0.195480\pi$
$941$	50.1414	1.63456	0.817281	+	0.576239i	$0.195480\pi$
$942$	−41.1817	−1.34177
$943$	30.1145	0.980662
$944$	56.7433	1.84684
$945$	4.31929	0.140507
$946$	114.472	3.72182
$947$	−27.5469	−0.895155	−0.447578	−	0.894245i	$-0.647713\pi$
$947$	−27.5469	−0.895155	−0.447578	+	0.894245i	$0.647713\pi$
$948$	161.894	5.25808
$949$	1.84336	0.0598379
$950$	21.9442	0.711965
$951$	−4.62317	−0.149917
$952$	179.666	5.82301
$953$	−31.3292	−1.01485	−0.507427	−	0.861695i	$-0.669403\pi$
$953$	−31.3292	−1.01485	−0.507427	+	0.861695i	$0.669403\pi$
$954$	−35.7337	−1.15692
$955$	26.0770	0.843831
$956$	−51.5366	−1.66681
$957$	−22.2886	−0.720488
$958$	1.17802	0.0380601
$959$	−58.2336	−1.88046
$960$	251.828	8.12772
$961$	21.6934	0.699787
$962$	−13.2723	−0.427917
$963$	41.5489	1.33890
$964$	152.647	4.91643
$965$	−28.7437	−0.925294
$966$	−83.5124	−2.68697
$967$	33.3549	1.07262	0.536311	−	0.844021i	$-0.319818\pi$
$967$	33.3549	1.07262	0.536311	+	0.844021i	$0.319818\pi$
$968$	10.9535	0.352058
$969$	84.0838	2.70116
$970$	45.3351	1.45562
$971$	33.6207	1.07894	0.539470	−	0.842005i	$-0.318625\pi$
$971$	33.6207	1.07894	0.539470	+	0.842005i	$0.318625\pi$
$972$	−126.135	−4.04578
$973$	6.87636	0.220446
$974$	−85.2704	−2.73224
$975$	−15.5659	−0.498508
$976$	−120.317	−3.85126
$977$	40.1652	1.28500	0.642499	−	0.766286i	$-0.277898\pi$
$977$	40.1652	1.28500	0.642499	+	0.766286i	$0.277898\pi$
$978$	49.8609	1.59438
$979$	−16.4030	−0.524242
$980$	−0.788025	−0.0251725
$981$	−19.3960	−0.619268
$982$	41.6102	1.32783
$983$	22.8733	0.729545	0.364772	−	0.931097i	$-0.381147\pi$
$983$	22.8733	0.729545	0.364772	+	0.931097i	$0.381147\pi$
$984$	170.563	5.43734
$985$	9.88889	0.315086
$986$	−50.7154	−1.61511
$987$	49.7230	1.58270
$988$	172.900	5.50068
$989$	−60.4460	−1.92207
$990$	45.2719	1.43884
$991$	38.9538	1.23741	0.618703	−	0.785625i	$-0.287658\pi$
$991$	38.9538	1.23741	0.618703	+	0.785625i	$0.287658\pi$
$992$	−244.248	−7.75489
$993$	−1.07646	−0.0341604
$994$	43.0349	1.36498
$995$	10.5745	0.335234
$996$	−100.586	−3.18717
$997$	−31.1603	−0.986856	−0.493428	−	0.869787i	$-0.664256\pi$
$997$	−31.1603	−0.986856	−0.493428	+	0.869787i	$0.664256\pi$
$998$	−40.8654	−1.29357
$999$	−0.814283	−0.0257628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8009.2.a.b.1.1	✓	361

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8009.2.a.b.1.1	✓	361	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:	\( N \)	\(=\)	\( 8009 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82633 q^{2} +2.37476 q^{3} +5.98811 q^{4} +1.91635 q^{5} -6.71185 q^{6} -2.63274 q^{7} -11.2717 q^{8} +2.63950 q^{9} +O(q^{10})\)	\(q-2.82633 q^{2} +2.37476 q^{3} +5.98811 q^{4} +1.91635 q^{5} -6.71185 q^{6} -2.63274 q^{7} -11.2717 q^{8} +2.63950 q^{9} -5.41622 q^{10} -3.16674 q^{11} +14.2203 q^{12} +4.93719 q^{13} +7.44098 q^{14} +4.55087 q^{15} +19.8813 q^{16} +6.05436 q^{17} -7.46007 q^{18} +5.84823 q^{19} +11.4753 q^{20} -6.25214 q^{21} +8.95023 q^{22} -4.72607 q^{23} -26.7676 q^{24} -1.32762 q^{25} -13.9541 q^{26} -0.856112 q^{27} -15.7652 q^{28} +2.96381 q^{29} -12.8622 q^{30} +7.25902 q^{31} -33.6475 q^{32} -7.52025 q^{33} -17.1116 q^{34} -5.04524 q^{35} +15.8056 q^{36} +0.951141 q^{37} -16.5290 q^{38} +11.7247 q^{39} -21.6005 q^{40} -6.37198 q^{41} +17.6706 q^{42} +12.7899 q^{43} -18.9628 q^{44} +5.05819 q^{45} +13.3574 q^{46} -7.95296 q^{47} +47.2133 q^{48} -0.0686714 q^{49} +3.75228 q^{50} +14.3777 q^{51} +29.5645 q^{52} +4.78999 q^{53} +2.41965 q^{54} -6.06856 q^{55} +29.6755 q^{56} +13.8882 q^{57} -8.37669 q^{58} +2.85411 q^{59} +27.2511 q^{60} -6.05178 q^{61} -20.5164 q^{62} -6.94911 q^{63} +55.3363 q^{64} +9.46137 q^{65} +21.2547 q^{66} -0.520352 q^{67} +36.2542 q^{68} -11.2233 q^{69} +14.2595 q^{70} +5.78349 q^{71} -29.7516 q^{72} +0.373361 q^{73} -2.68823 q^{74} -3.15278 q^{75} +35.0199 q^{76} +8.33720 q^{77} -33.1377 q^{78} +11.3847 q^{79} +38.0994 q^{80} -9.95155 q^{81} +18.0093 q^{82} -7.07335 q^{83} -37.4385 q^{84} +11.6022 q^{85} -36.1484 q^{86} +7.03834 q^{87} +35.6945 q^{88} +5.17978 q^{89} -14.2961 q^{90} -12.9984 q^{91} -28.3003 q^{92} +17.2385 q^{93} +22.4777 q^{94} +11.2072 q^{95} -79.9049 q^{96} -8.37025 q^{97} +0.194088 q^{98} -8.35859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) \) 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9	\( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9} + 65 q^{10} + 33 q^{11} + 52 q^{12} + 89 q^{13} + 32 q^{14} + 55 q^{15} + 512 q^{16} + 42 q^{17} + 34 q^{18} + 191 q^{19} + 48 q^{20} + 53 q^{21} + 61 q^{22} + 52 q^{23} + 139 q^{24} + 458 q^{25} + 57 q^{26} + 80 q^{27} + 194 q^{28} + 47 q^{29} + 32 q^{30} + 254 q^{31} + 55 q^{32} + 40 q^{33} + 122 q^{34} + 93 q^{35} + 519 q^{36} + 43 q^{37} + 25 q^{38} + 210 q^{39} + 184 q^{40} + 54 q^{41} + 48 q^{42} + 151 q^{43} + 56 q^{44} + 82 q^{45} + 101 q^{46} + 117 q^{47} + 77 q^{48} + 563 q^{49} + 38 q^{50} + 143 q^{51} + 241 q^{52} + 14 q^{53} + 164 q^{54} + 452 q^{55} + 52 q^{56} + 21 q^{57} + 55 q^{58} + 125 q^{59} + 39 q^{60} + 227 q^{61} + 58 q^{62} + 292 q^{63} + 710 q^{64} + 15 q^{65} + 105 q^{66} + 120 q^{67} + 125 q^{68} + 136 q^{69} + 88 q^{70} + 105 q^{71} + 78 q^{72} + 108 q^{73} + 41 q^{74} + 128 q^{75} + 461 q^{76} + 28 q^{77} + 13 q^{78} + 400 q^{79} + 59 q^{80} + 485 q^{81} + 175 q^{82} + 97 q^{83} + 76 q^{84} + 144 q^{85} - 14 q^{86} + 327 q^{87} + 145 q^{88} + 52 q^{89} + 60 q^{90} + 192 q^{91} + 11 q^{92} + 32 q^{93} + 366 q^{94} + 182 q^{95} + 275 q^{96} + 117 q^{97} + 42 q^{98} + 111 q^{99}+O(q^{100}) \) 361 * q + 10 * q^2 + 23 * q^3 + 414 * q^4 + 21 * q^5 + 49 * q^6 + 106 * q^7 + 30 * q^8 + 406 * q^9 + 65 * q^10 + 33 * q^11 + 52 * q^12 + 89 * q^13 + 32 * q^14 + 55 * q^15 + 512 * q^16 + 42 * q^17 + 34 * q^18 + 191 * q^19 + 48 * q^20 + 53 * q^21 + 61 * q^22 + 52 * q^23 + 139 * q^24 + 458 * q^25 + 57 * q^26 + 80 * q^27 + 194 * q^28 + 47 * q^29 + 32 * q^30 + 254 * q^31 + 55 * q^32 + 40 * q^33 + 122 * q^34 + 93 * q^35 + 519 * q^36 + 43 * q^37 + 25 * q^38 + 210 * q^39 + 184 * q^40 + 54 * q^41 + 48 * q^42 + 151 * q^43 + 56 * q^44 + 82 * q^45 + 101 * q^46 + 117 * q^47 + 77 * q^48 + 563 * q^49 + 38 * q^50 + 143 * q^51 + 241 * q^52 + 14 * q^53 + 164 * q^54 + 452 * q^55 + 52 * q^56 + 21 * q^57 + 55 * q^58 + 125 * q^59 + 39 * q^60 + 227 * q^61 + 58 * q^62 + 292 * q^63 + 710 * q^64 + 15 * q^65 + 105 * q^66 + 120 * q^67 + 125 * q^68 + 136 * q^69 + 88 * q^70 + 105 * q^71 + 78 * q^72 + 108 * q^73 + 41 * q^74 + 128 * q^75 + 461 * q^76 + 28 * q^77 + 13 * q^78 + 400 * q^79 + 59 * q^80 + 485 * q^81 + 175 * q^82 + 97 * q^83 + 76 * q^84 + 144 * q^85 - 14 * q^86 + 327 * q^87 + 145 * q^88 + 52 * q^89 + 60 * q^90 + 192 * q^91 + 11 * q^92 + 32 * q^93 + 366 * q^94 + 182 * q^95 + 275 * q^96 + 117 * q^97 + 42 * q^98 + 111 * q^99

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