LMFDB - Embedded newform 8029.2.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95127 q^{2} +1.43500 q^{3} +1.80747 q^{4} -4.32832 q^{5} -2.80008 q^{6} -1.00000 q^{7} +0.375685 q^{8} -0.940772 q^{9} +O(q^{10})$	\(q-1.95127 q^{2} +1.43500 q^{3} +1.80747 q^{4} -4.32832 q^{5} -2.80008 q^{6} -1.00000 q^{7} +0.375685 q^{8} -0.940772 q^{9} +8.44573 q^{10} +3.57804 q^{11} +2.59372 q^{12} +2.13860 q^{13} +1.95127 q^{14} -6.21114 q^{15} -4.34800 q^{16} -1.12670 q^{17} +1.83570 q^{18} -4.84311 q^{19} -7.82329 q^{20} -1.43500 q^{21} -6.98172 q^{22} +0.655980 q^{23} +0.539108 q^{24} +13.7343 q^{25} -4.17300 q^{26} -5.65501 q^{27} -1.80747 q^{28} +3.31506 q^{29} +12.1196 q^{30} -1.00000 q^{31} +7.73276 q^{32} +5.13449 q^{33} +2.19850 q^{34} +4.32832 q^{35} -1.70041 q^{36} +1.00000 q^{37} +9.45024 q^{38} +3.06890 q^{39} -1.62608 q^{40} -0.351635 q^{41} +2.80008 q^{42} +5.04357 q^{43} +6.46718 q^{44} +4.07196 q^{45} -1.28000 q^{46} -2.41695 q^{47} -6.23938 q^{48} +1.00000 q^{49} -26.7994 q^{50} -1.61682 q^{51} +3.86546 q^{52} -4.15290 q^{53} +11.0345 q^{54} -15.4869 q^{55} -0.375685 q^{56} -6.94987 q^{57} -6.46858 q^{58} -8.94054 q^{59} -11.2264 q^{60} -5.32850 q^{61} +1.95127 q^{62} +0.940772 q^{63} -6.39273 q^{64} -9.25655 q^{65} -10.0188 q^{66} -9.48741 q^{67} -2.03648 q^{68} +0.941332 q^{69} -8.44573 q^{70} +0.462137 q^{71} -0.353434 q^{72} +11.7862 q^{73} -1.95127 q^{74} +19.7088 q^{75} -8.75377 q^{76} -3.57804 q^{77} -5.98826 q^{78} -12.3090 q^{79} +18.8195 q^{80} -5.29263 q^{81} +0.686136 q^{82} +7.22722 q^{83} -2.59372 q^{84} +4.87672 q^{85} -9.84138 q^{86} +4.75711 q^{87} +1.34421 q^{88} +3.24926 q^{89} -7.94550 q^{90} -2.13860 q^{91} +1.18566 q^{92} -1.43500 q^{93} +4.71613 q^{94} +20.9625 q^{95} +11.0965 q^{96} -5.77276 q^{97} -1.95127 q^{98} -3.36612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−1.95127	−1.37976	−0.689879	−	0.723924i	$-0.742336\pi$
$2$	−1.95127	−1.37976	−0.689879	+	0.723924i	$0.742336\pi$
$3$	1.43500	0.828498	0.414249	−	0.910164i	$-0.364044\pi$
$3$	1.43500	0.828498	0.414249	+	0.910164i	$0.364044\pi$
$4$	1.80747	0.903733
$5$	−4.32832	−1.93568	−0.967841	−	0.251563i	$-0.919056\pi$
$5$	−4.32832	−1.93568	−0.967841	+	0.251563i	$0.919056\pi$
$6$	−2.80008	−1.14313
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.375685	0.132825
$9$	−0.940772	−0.313591
$10$	8.44573	2.67077
$11$	3.57804	1.07882	0.539409	−	0.842044i	$-0.318648\pi$
$11$	3.57804	1.07882	0.539409	+	0.842044i	$0.318648\pi$
$12$	2.59372	0.748742
$13$	2.13860	0.593142	0.296571	−	0.955011i	$-0.404157\pi$
$13$	2.13860	0.593142	0.296571	+	0.955011i	$0.404157\pi$
$14$	1.95127	0.521500
$15$	−6.21114	−1.60371
$16$	−4.34800	−1.08700
$17$	−1.12670	−0.273265	−0.136633	−	0.990622i	$-0.543628\pi$
$17$	−1.12670	−0.273265	−0.136633	+	0.990622i	$0.543628\pi$
$18$	1.83570	0.432679
$19$	−4.84311	−1.11109	−0.555543	−	0.831488i	$-0.687490\pi$
$19$	−4.84311	−1.11109	−0.555543	+	0.831488i	$0.687490\pi$
$20$	−7.82329	−1.74934
$21$	−1.43500	−0.313143
$22$	−6.98172	−1.48851
$23$	0.655980	0.136781	0.0683907	−	0.997659i	$-0.478214\pi$
$23$	0.655980	0.136781	0.0683907	+	0.997659i	$0.478214\pi$
$24$	0.539108	0.110045
$25$	13.7343	2.74687
$26$	−4.17300	−0.818393
$27$	−5.65501	−1.08831
$28$	−1.80747	−0.341579
$29$	3.31506	0.615591	0.307795	−	0.951453i	$-0.400409\pi$
$29$	3.31506	0.615591	0.307795	+	0.951453i	$0.400409\pi$
$30$	12.1196	2.21273
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.73276	1.36697
$33$	5.13449	0.893799
$34$	2.19850	0.377040
$35$	4.32832	0.731619
$36$	−1.70041	−0.283402
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	9.45024	1.53303
$39$	3.06890	0.491417
$40$	−1.62608	−0.257106
$41$	−0.351635	−0.0549162	−0.0274581	−	0.999623i	$-0.508741\pi$
$41$	−0.351635	−0.0549162	−0.0274581	+	0.999623i	$0.508741\pi$
$42$	2.80008	0.432062
$43$	5.04357	0.769137	0.384569	−	0.923096i	$-0.374350\pi$
$43$	5.04357	0.769137	0.384569	+	0.923096i	$0.374350\pi$
$44$	6.46718	0.974964
$45$	4.07196	0.607012
$46$	−1.28000	−0.188725
$47$	−2.41695	−0.352548	−0.176274	−	0.984341i	$-0.556405\pi$
$47$	−2.41695	−0.352548	−0.176274	+	0.984341i	$0.556405\pi$
$48$	−6.23938	−0.900577
$49$	1.00000	0.142857
$50$	−26.7994	−3.79001
$51$	−1.61682	−0.226400
$52$	3.86546	0.536042
$53$	−4.15290	−0.570445	−0.285222	−	0.958461i	$-0.592067\pi$
$53$	−4.15290	−0.570445	−0.285222	+	0.958461i	$0.592067\pi$
$54$	11.0345	1.50160
$55$	−15.4869	−2.08825
$56$	−0.375685	−0.0502030
$57$	−6.94987	−0.920533
$58$	−6.46858	−0.849367
$59$	−8.94054	−1.16396	−0.581979	−	0.813204i	$-0.697722\pi$
$59$	−8.94054	−1.16396	−0.581979	+	0.813204i	$0.697722\pi$
$60$	−11.2264	−1.44933
$61$	−5.32850	−0.682245	−0.341122	−	0.940019i	$-0.610807\pi$
$61$	−5.32850	−0.682245	−0.341122	+	0.940019i	$0.610807\pi$
$62$	1.95127	0.247812
$63$	0.940772	0.118526
$64$	−6.39273	−0.799092
$65$	−9.25655	−1.14813
$66$	−10.0188	−1.23323
$67$	−9.48741	−1.15907	−0.579536	−	0.814947i	$-0.696766\pi$
$67$	−9.48741	−1.15907	−0.579536	+	0.814947i	$0.696766\pi$
$68$	−2.03648	−0.246959
$69$	0.941332	0.113323
$70$	−8.44573	−1.00946
$71$	0.462137	0.0548456	0.0274228	−	0.999624i	$-0.491270\pi$
$71$	0.462137	0.0548456	0.0274228	+	0.999624i	$0.491270\pi$
$72$	−0.353434	−0.0416526
$73$	11.7862	1.37947	0.689737	−	0.724060i	$-0.257726\pi$
$73$	11.7862	1.37947	0.689737	+	0.724060i	$0.257726\pi$
$74$	−1.95127	−0.226831
$75$	19.7088	2.27577
$76$	−8.75377	−1.00413
$77$	−3.57804	−0.407755
$78$	−5.98826	−0.678037
$79$	−12.3090	−1.38487	−0.692437	−	0.721478i	$-0.743463\pi$
$79$	−12.3090	−1.38487	−0.692437	+	0.721478i	$0.743463\pi$
$80$	18.8195	2.10409
$81$	−5.29263	−0.588070
$82$	0.686136	0.0757711
$83$	7.22722	0.793291	0.396645	−	0.917972i	$-0.370174\pi$
$83$	7.22722	0.793291	0.396645	+	0.917972i	$0.370174\pi$
$84$	−2.59372	−0.282998
$85$	4.87672	0.528955
$86$	−9.84138	−1.06122
$87$	4.75711	0.510016
$88$	1.34421	0.143294
$89$	3.24926	0.344421	0.172210	−	0.985060i	$-0.444909\pi$
$89$	3.24926	0.344421	0.172210	+	0.985060i	$0.444909\pi$
$90$	−7.94550	−0.837530
$91$	−2.13860	−0.224187
$92$	1.18566	0.123614
$93$	−1.43500	−0.148803
$94$	4.71613	0.486431
$95$	20.9625	2.15071
$96$	11.0965	1.13253
$97$	−5.77276	−0.586134	−0.293067	−	0.956092i	$-0.594676\pi$
$97$	−5.77276	−0.586134	−0.293067	+	0.956092i	$0.594676\pi$
$98$	−1.95127	−0.197108
$99$	−3.36612	−0.338307
$100$	24.8243	2.48243
$101$	2.27831	0.226701	0.113350	−	0.993555i	$-0.463842\pi$
$101$	2.27831	0.226701	0.113350	+	0.993555i	$0.463842\pi$
$102$	3.15485	0.312377
$103$	−0.0202063	−0.00199099	−0.000995495	−	1.00000i	$-0.500317\pi$
$103$	−0.0202063	−0.00199099	−0.000995495		1.00000i	$0.500317\pi$
$104$	0.803441	0.0787839
$105$	6.21114	0.606145
$106$	8.10344	0.787076
$107$	18.8992	1.82706	0.913529	−	0.406773i	$-0.133346\pi$
$107$	18.8992	1.82706	0.913529	+	0.406773i	$0.133346\pi$
$108$	−10.2212	−0.983540
$109$	−10.3493	−0.991285	−0.495643	−	0.868527i	$-0.665067\pi$
$109$	−10.3493	−0.991285	−0.495643	+	0.868527i	$0.665067\pi$
$110$	30.2191	2.88128
$111$	1.43500	0.136204
$112$	4.34800	0.410847
$113$	−10.8790	−1.02341	−0.511706	−	0.859161i	$-0.670986\pi$
$113$	−10.8790	−1.02341	−0.511706	+	0.859161i	$0.670986\pi$
$114$	13.5611	1.27011
$115$	−2.83929	−0.264765
$116$	5.99186	0.556330
$117$	−2.01194	−0.186004
$118$	17.4454	1.60598
$119$	1.12670	0.103285
$120$	−2.33343	−0.213012
$121$	1.80234	0.163849
$122$	10.3974	0.941333
$123$	−0.504597	−0.0454980
$124$	−1.80747	−0.162315
$125$	−37.8049	−3.38138
$126$	−1.83570	−0.163537
$127$	−5.73269	−0.508694	−0.254347	−	0.967113i	$-0.581861\pi$
$127$	−5.73269	−0.508694	−0.254347	+	0.967113i	$0.581861\pi$
$128$	−2.99155	−0.264418
$129$	7.23753	0.637229
$130$	18.0621	1.58415
$131$	−0.784642	−0.0685545	−0.0342772	−	0.999412i	$-0.510913\pi$
$131$	−0.784642	−0.0685545	−0.0342772	+	0.999412i	$0.510913\pi$
$132$	9.28041	0.807756
$133$	4.84311	0.419951
$134$	18.5125	1.59924
$135$	24.4767	2.10662
$136$	−0.423285	−0.0362964
$137$	7.61077	0.650232	0.325116	−	0.945674i	$-0.394597\pi$
$137$	7.61077	0.650232	0.325116	+	0.945674i	$0.394597\pi$
$138$	−1.83680	−0.156358
$139$	−12.4632	−1.05712	−0.528559	−	0.848897i	$-0.677267\pi$
$139$	−12.4632	−1.05712	−0.528559	+	0.848897i	$0.677267\pi$
$140$	7.82329	0.661189
$141$	−3.46832	−0.292086
$142$	−0.901756	−0.0756737
$143$	7.65200	0.639892
$144$	4.09047	0.340873
$145$	−14.3486	−1.19159
$146$	−22.9982	−1.90334
$147$	1.43500	0.118357
$148$	1.80747	0.148573
$149$	10.8652	0.890115	0.445057	−	0.895502i	$-0.353183\pi$
$149$	10.8652	0.890115	0.445057	+	0.895502i	$0.353183\pi$
$150$	−38.4572	−3.14002
$151$	10.3696	0.843867	0.421933	−	0.906627i	$-0.361352\pi$
$151$	10.3696	0.843867	0.421933	+	0.906627i	$0.361352\pi$
$152$	−1.81949	−0.147580
$153$	1.05997	0.0856934
$154$	6.98172	0.562603
$155$	4.32832	0.347659
$156$	5.54693	0.444110
$157$	−20.9784	−1.67426	−0.837128	−	0.547007i	$-0.815767\pi$
$157$	−20.9784	−1.67426	−0.837128	+	0.547007i	$0.815767\pi$
$158$	24.0183	1.91079
$159$	−5.95941	−0.472612
$160$	−33.4698	−2.64602
$161$	−0.655980	−0.0516985
$162$	10.3274	0.811395
$163$	8.80997	0.690050	0.345025	−	0.938594i	$-0.387870\pi$
$163$	8.80997	0.690050	0.345025	+	0.938594i	$0.387870\pi$
$164$	−0.635569	−0.0496296
$165$	−22.2237	−1.73011
$166$	−14.1023	−1.09455
$167$	1.74279	0.134861	0.0674307	−	0.997724i	$-0.478520\pi$
$167$	1.74279	0.134861	0.0674307	+	0.997724i	$0.478520\pi$
$168$	−0.539108	−0.0415931
$169$	−8.42637	−0.648183
$170$	−9.51582	−0.729830
$171$	4.55627	0.348426
$172$	9.11608	0.695095
$173$	6.92553	0.526538	0.263269	−	0.964722i	$-0.415199\pi$
$173$	6.92553	0.526538	0.263269	+	0.964722i	$0.415199\pi$
$174$	−9.28242	−0.703699
$175$	−13.7343	−1.03822
$176$	−15.5573	−1.17267
$177$	−12.8297	−0.964338
$178$	−6.34019	−0.475217
$179$	4.45668	0.333108	0.166554	−	0.986032i	$-0.446736\pi$
$179$	4.45668	0.333108	0.166554	+	0.986032i	$0.446736\pi$
$180$	7.35993	0.548577
$181$	−11.4867	−0.853801	−0.426901	−	0.904299i	$-0.640395\pi$
$181$	−11.4867	−0.853801	−0.426901	+	0.904299i	$0.640395\pi$
$182$	4.17300	0.309323
$183$	−7.64640	−0.565238
$184$	0.246442	0.0181679
$185$	−4.32832	−0.318224
$186$	2.80008	0.205312
$187$	−4.03138	−0.294804
$188$	−4.36856	−0.318610
$189$	5.65501	0.411342
$190$	−40.9036	−2.96746
$191$	−6.88651	−0.498290	−0.249145	−	0.968466i	$-0.580150\pi$
$191$	−6.88651	−0.498290	−0.249145	+	0.968466i	$0.580150\pi$
$192$	−9.17358	−0.662046
$193$	6.97885	0.502348	0.251174	−	0.967942i	$-0.419183\pi$
$193$	6.97885	0.502348	0.251174	+	0.967942i	$0.419183\pi$
$194$	11.2642	0.808724
$195$	−13.2832	−0.951227
$196$	1.80747	0.129105
$197$	6.12352	0.436282	0.218141	−	0.975917i	$-0.430001\pi$
$197$	6.12352	0.436282	0.218141	+	0.975917i	$0.430001\pi$
$198$	6.56821	0.466782
$199$	10.1911	0.722424	0.361212	−	0.932484i	$-0.382363\pi$
$199$	10.1911	0.722424	0.361212	+	0.932484i	$0.382363\pi$
$200$	5.15978	0.364851
$201$	−13.6144	−0.960289
$202$	−4.44561	−0.312792
$203$	−3.31506	−0.232671
$204$	−2.92235	−0.204605
$205$	1.52199	0.106300
$206$	0.0394281	0.00274708
$207$	−0.617128	−0.0428933
$208$	−9.29864	−0.644745
$209$	−17.3288	−1.19866
$210$	−12.1196	−0.836334
$211$	−8.22093	−0.565952	−0.282976	−	0.959127i	$-0.591322\pi$
$211$	−8.22093	−0.565952	−0.282976	+	0.959127i	$0.591322\pi$
$212$	−7.50623	−0.515530
$213$	0.663168	0.0454395
$214$	−36.8776	−2.52090
$215$	−21.8302	−1.48880
$216$	−2.12450	−0.144554
$217$	1.00000	0.0678844
$218$	20.1944	1.36773
$219$	16.9133	1.14289
$220$	−27.9920	−1.88722
$221$	−2.40957	−0.162085
$222$	−2.80008	−0.187929
$223$	−17.4364	−1.16763	−0.583815	−	0.811887i	$-0.698441\pi$
$223$	−17.4364	−1.16763	−0.583815	+	0.811887i	$0.698441\pi$
$224$	−7.73276	−0.516667
$225$	−12.9209	−0.861391
$226$	21.2279	1.41206
$227$	−23.0238	−1.52815	−0.764073	−	0.645130i	$-0.776803\pi$
$227$	−23.0238	−1.52815	−0.764073	+	0.645130i	$0.776803\pi$
$228$	−12.5617	−0.831917
$229$	14.3024	0.945129	0.472564	−	0.881296i	$-0.343328\pi$
$229$	14.3024	0.945129	0.472564	+	0.881296i	$0.343328\pi$
$230$	5.54023	0.365312
$231$	−5.13449	−0.337824
$232$	1.24542	0.0817657
$233$	13.7521	0.900930	0.450465	−	0.892794i	$-0.351258\pi$
$233$	13.7521	0.900930	0.450465	+	0.892794i	$0.351258\pi$
$234$	3.92584	0.256640
$235$	10.4613	0.682421
$236$	−16.1597	−1.05191
$237$	−17.6635	−1.14737
$238$	−2.19850	−0.142508
$239$	3.57010	0.230930	0.115465	−	0.993312i	$-0.463164\pi$
$239$	3.57010	0.230930	0.115465	+	0.993312i	$0.463164\pi$
$240$	27.0060	1.74323
$241$	10.8587	0.699473	0.349736	−	0.936848i	$-0.386271\pi$
$241$	10.8587	0.699473	0.349736	+	0.936848i	$0.386271\pi$
$242$	−3.51686	−0.226072
$243$	9.37010	0.601092
$244$	−9.63109	−0.616567
$245$	−4.32832	−0.276526
$246$	0.984607	0.0627762
$247$	−10.3575	−0.659032
$248$	−0.375685	−0.0238560
$249$	10.3711	0.657240
$250$	73.7677	4.66548
$251$	16.5362	1.04375	0.521877	−	0.853021i	$-0.325232\pi$
$251$	16.5362	1.04375	0.521877	+	0.853021i	$0.325232\pi$
$252$	1.70041	0.107116
$253$	2.34712	0.147562
$254$	11.1860	0.701875
$255$	6.99810	0.438238
$256$	18.6228	1.16393
$257$	−19.5663	−1.22051	−0.610257	−	0.792203i	$-0.708934\pi$
$257$	−19.5663	−1.22051	−0.610257	+	0.792203i	$0.708934\pi$
$258$	−14.1224	−0.879222
$259$	−1.00000	−0.0621370
$260$	−16.7309	−1.03761
$261$	−3.11871	−0.193044
$262$	1.53105	0.0945886
$263$	6.42585	0.396235	0.198117	−	0.980178i	$-0.436517\pi$
$263$	6.42585	0.396235	0.198117	+	0.980178i	$0.436517\pi$
$264$	1.92895	0.118719
$265$	17.9751	1.10420
$266$	−9.45024	−0.579431
$267$	4.66269	0.285352
$268$	−17.1482	−1.04749
$269$	−11.5027	−0.701330	−0.350665	−	0.936501i	$-0.614044\pi$
$269$	−11.5027	−0.701330	−0.350665	+	0.936501i	$0.614044\pi$
$270$	−47.7607	−2.90662
$271$	−2.65935	−0.161544	−0.0807720	−	0.996733i	$-0.525739\pi$
$271$	−2.65935	−0.161544	−0.0807720	+	0.996733i	$0.525739\pi$
$272$	4.89890	0.297039
$273$	−3.06890	−0.185738
$274$	−14.8507	−0.897163
$275$	49.1419	2.96337
$276$	1.70143	0.102414
$277$	−4.06139	−0.244025	−0.122013	−	0.992529i	$-0.538935\pi$
$277$	−4.06139	−0.244025	−0.122013	+	0.992529i	$0.538935\pi$
$278$	24.3192	1.45857
$279$	0.940772	0.0563225
$280$	1.62608	0.0971771
$281$	−7.38869	−0.440772	−0.220386	−	0.975413i	$-0.570732\pi$
$281$	−7.38869	−0.440772	−0.220386	+	0.975413i	$0.570732\pi$
$282$	6.76765	0.403008
$283$	18.6953	1.11132	0.555660	−	0.831410i	$-0.312466\pi$
$283$	18.6953	1.11132	0.555660	+	0.831410i	$0.312466\pi$
$284$	0.835298	0.0495658
$285$	30.0813	1.78186
$286$	−14.9311	−0.882897
$287$	0.351635	0.0207564
$288$	−7.27476	−0.428670
$289$	−15.7305	−0.925326
$290$	27.9981	1.64410
$291$	−8.28391	−0.485611
$292$	21.3032	1.24668
$293$	8.54570	0.499245	0.249623	−	0.968343i	$-0.419693\pi$
$293$	8.54570	0.499245	0.249623	+	0.968343i	$0.419693\pi$
$294$	−2.80008	−0.163304
$295$	38.6975	2.25305
$296$	0.375685	0.0218362
$297$	−20.2338	−1.17409
$298$	−21.2010	−1.22814
$299$	1.40288	0.0811307
$300$	35.6229	2.05669
$301$	−5.04357	−0.290706
$302$	−20.2339	−1.16433
$303$	3.26938	0.187821
$304$	21.0578	1.20775
$305$	23.0634	1.32061
$306$	−2.06829	−0.118236
$307$	25.6610	1.46455	0.732274	−	0.681010i	$-0.238459\pi$
$307$	25.6610	1.46455	0.732274	+	0.681010i	$0.238459\pi$
$308$	−6.46718	−0.368502
$309$	−0.0289961	−0.00164953
$310$	−8.44573	−0.479685
$311$	16.4617	0.933456	0.466728	−	0.884401i	$-0.345433\pi$
$311$	16.4617	0.933456	0.466728	+	0.884401i	$0.345433\pi$
$312$	1.15294	0.0652723
$313$	−15.1014	−0.853582	−0.426791	−	0.904350i	$-0.640356\pi$
$313$	−15.1014	−0.853582	−0.426791	+	0.904350i	$0.640356\pi$
$314$	40.9345	2.31007
$315$	−4.07196	−0.229429
$316$	−22.2482	−1.25156
$317$	7.99488	0.449037	0.224519	−	0.974470i	$-0.427919\pi$
$317$	7.99488	0.449037	0.224519	+	0.974470i	$0.427919\pi$
$318$	11.6284	0.652091
$319$	11.8614	0.664111
$320$	27.6698	1.54679
$321$	27.1204	1.51371
$322$	1.28000	0.0713314
$323$	5.45675	0.303621
$324$	−9.56626	−0.531459
$325$	29.3723	1.62928
$326$	−17.1907	−0.952102
$327$	−14.8513	−0.821278
$328$	−0.132104	−0.00729423
$329$	2.41695	0.133251
$330$	43.3645	2.38714
$331$	8.33579	0.458176	0.229088	−	0.973406i	$-0.426426\pi$
$331$	8.33579	0.458176	0.229088	+	0.973406i	$0.426426\pi$
$332$	13.0630	0.716923
$333$	−0.940772	−0.0515540
$334$	−3.40066	−0.186076
$335$	41.0645	2.24359
$336$	6.23938	0.340386
$337$	13.7611	0.749615	0.374807	−	0.927103i	$-0.377709\pi$
$337$	13.7611	0.749615	0.374807	+	0.927103i	$0.377709\pi$
$338$	16.4422	0.894335
$339$	−15.6114	−0.847895
$340$	8.81451	0.478034
$341$	−3.57804	−0.193761
$342$	−8.89052	−0.480744
$343$	−1.00000	−0.0539949
$344$	1.89479	0.102160
$345$	−4.07438	−0.219357
$346$	−13.5136	−0.726496
$347$	−12.3359	−0.662226	−0.331113	−	0.943591i	$-0.607424\pi$
$347$	−12.3359	−0.662226	−0.331113	+	0.943591i	$0.607424\pi$
$348$	8.59832	0.460918
$349$	23.3279	1.24872	0.624358	−	0.781138i	$-0.285361\pi$
$349$	23.3279	1.24872	0.624358	+	0.781138i	$0.285361\pi$
$350$	26.7994	1.43249
$351$	−12.0938	−0.645521
$352$	27.6681	1.47471
$353$	14.3768	0.765198	0.382599	−	0.923915i	$-0.375029\pi$
$353$	14.3768	0.765198	0.382599	+	0.923915i	$0.375029\pi$
$354$	25.0342	1.33055
$355$	−2.00028	−0.106164
$356$	5.87292	0.311264
$357$	1.61682	0.0855711
$358$	−8.69619	−0.459608
$359$	35.7527	1.88695	0.943477	−	0.331437i	$-0.107533\pi$
$359$	35.7527	1.88695	0.943477	+	0.331437i	$0.107533\pi$
$360$	1.52977	0.0806261
$361$	4.45576	0.234513
$362$	22.4137	1.17804
$363$	2.58636	0.135749
$364$	−3.86546	−0.202605
$365$	−51.0145	−2.67022
$366$	14.9202	0.779893
$367$	−1.05033	−0.0548269	−0.0274134	−	0.999624i	$-0.508727\pi$
$367$	−1.05033	−0.0548269	−0.0274134	+	0.999624i	$0.508727\pi$
$368$	−2.85220	−0.148681
$369$	0.330809	0.0172212
$370$	8.44573	0.439072
$371$	4.15290	0.215608
$372$	−2.59372	−0.134478
$373$	−8.46777	−0.438445	−0.219222	−	0.975675i	$-0.570352\pi$
$373$	−8.46777	−0.438445	−0.219222	+	0.975675i	$0.570352\pi$
$374$	7.86632	0.406758
$375$	−54.2501	−2.80146
$376$	−0.908011	−0.0468271
$377$	7.08960	0.365133
$378$	−11.0345	−0.567552
$379$	30.3003	1.55642	0.778212	−	0.628002i	$-0.216127\pi$
$379$	30.3003	1.55642	0.778212	+	0.628002i	$0.216127\pi$
$380$	37.8891	1.94367
$381$	−8.22642	−0.421452
$382$	13.4375	0.687520
$383$	−8.91410	−0.455489	−0.227745	−	0.973721i	$-0.573135\pi$
$383$	−8.91410	−0.455489	−0.227745	+	0.973721i	$0.573135\pi$
$384$	−4.29288	−0.219070
$385$	15.4869	0.789284
$386$	−13.6176	−0.693119
$387$	−4.74485	−0.241194
$388$	−10.4341	−0.529709
$389$	35.1133	1.78031	0.890156	−	0.455655i	$-0.150595\pi$
$389$	35.1133	1.78031	0.890156	+	0.455655i	$0.150595\pi$
$390$	25.9191	1.31246
$391$	−0.739094	−0.0373776
$392$	0.375685	0.0189750
$393$	−1.12596	−0.0567973
$394$	−11.9487	−0.601964
$395$	53.2774	2.68068
$396$	−6.08414	−0.305740
$397$	−27.5785	−1.38412	−0.692062	−	0.721838i	$-0.743298\pi$
$397$	−27.5785	−1.38412	−0.692062	+	0.721838i	$0.743298\pi$
$398$	−19.8855	−0.996771
$399$	6.94987	0.347929
$400$	−59.7168	−2.98584
$401$	10.5189	0.525289	0.262645	−	0.964893i	$-0.415405\pi$
$401$	10.5189	0.525289	0.262645	+	0.964893i	$0.415405\pi$
$402$	26.5655	1.32497
$403$	−2.13860	−0.106531
$404$	4.11798	0.204877
$405$	22.9082	1.13832
$406$	6.46858	0.321030
$407$	3.57804	0.177357
$408$	−0.607414	−0.0300715
$409$	−19.5260	−0.965501	−0.482750	−	0.875758i	$-0.660362\pi$
$409$	−19.5260	−0.965501	−0.482750	+	0.875758i	$0.660362\pi$
$410$	−2.96982	−0.146669
$411$	10.9215	0.538716
$412$	−0.0365223	−0.00179932
$413$	8.94054	0.439935
$414$	1.20418	0.0591825
$415$	−31.2817	−1.53556
$416$	16.5373	0.810808
$417$	−17.8847	−0.875820
$418$	33.8133	1.65386
$419$	16.1564	0.789290	0.394645	−	0.918834i	$-0.370868\pi$
$419$	16.1564	0.789290	0.394645	+	0.918834i	$0.370868\pi$
$420$	11.2264	0.547794
$421$	1.16678	0.0568656	0.0284328	−	0.999596i	$-0.490948\pi$
$421$	1.16678	0.0568656	0.0284328	+	0.999596i	$0.490948\pi$
$422$	16.0413	0.780877
$423$	2.27380	0.110556
$424$	−1.56018	−0.0757691
$425$	−15.4745	−0.750623
$426$	−1.29402	−0.0626955
$427$	5.32850	0.257864
$428$	34.1597	1.65117
$429$	10.9806	0.530150
$430$	42.5966	2.05419
$431$	−15.9828	−0.769863	−0.384932	−	0.922945i	$-0.625775\pi$
$431$	−15.9828	−0.769863	−0.384932	+	0.922945i	$0.625775\pi$
$432$	24.5880	1.18299
$433$	−21.8937	−1.05214	−0.526072	−	0.850440i	$-0.676336\pi$
$433$	−21.8937	−1.05214	−0.526072	+	0.850440i	$0.676336\pi$
$434$	−1.95127	−0.0936641
$435$	−20.5903	−0.987229
$436$	−18.7061	−0.895858
$437$	−3.17699	−0.151976
$438$	−33.0024	−1.57691
$439$	−27.7220	−1.32310	−0.661549	−	0.749902i	$-0.730101\pi$
$439$	−27.7220	−1.32310	−0.661549	+	0.749902i	$0.730101\pi$
$440$	−5.81818	−0.277371
$441$	−0.940772	−0.0447987
$442$	4.70173	0.223638
$443$	32.0365	1.52210	0.761051	−	0.648692i	$-0.224684\pi$
$443$	32.0365	1.52210	0.761051	+	0.648692i	$0.224684\pi$
$444$	2.59372	0.123092
$445$	−14.0638	−0.666689
$446$	34.0232	1.61105
$447$	15.5916	0.737458
$448$	6.39273	0.302028
$449$	−13.4542	−0.634941	−0.317470	−	0.948268i	$-0.602833\pi$
$449$	−13.4542	−0.634941	−0.317470	+	0.948268i	$0.602833\pi$
$450$	25.2121	1.18851
$451$	−1.25816	−0.0592446
$452$	−19.6635	−0.924891
$453$	14.8804	0.699142
$454$	44.9258	2.10847
$455$	9.25655	0.433954
$456$	−2.61096	−0.122270
$457$	38.5991	1.80559	0.902795	−	0.430072i	$-0.141512\pi$
$457$	38.5991	1.80559	0.902795	+	0.430072i	$0.141512\pi$
$458$	−27.9079	−1.30405
$459$	6.37151	0.297397
$460$	−5.13192	−0.239277
$461$	3.86519	0.180020	0.0900100	−	0.995941i	$-0.471310\pi$
$461$	3.86519	0.180020	0.0900100	+	0.995941i	$0.471310\pi$
$462$	10.0188	0.466116
$463$	4.44575	0.206611	0.103306	−	0.994650i	$-0.467058\pi$
$463$	4.44575	0.206611	0.103306	+	0.994650i	$0.467058\pi$
$464$	−14.4139	−0.669147
$465$	6.21114	0.288035
$466$	−26.8341	−1.24307
$467$	16.9703	0.785290	0.392645	−	0.919690i	$-0.371560\pi$
$467$	16.9703	0.785290	0.392645	+	0.919690i	$0.371560\pi$
$468$	−3.63651	−0.168098
$469$	9.48741	0.438088
$470$	−20.4129	−0.941577
$471$	−30.1040	−1.38712
$472$	−3.35882	−0.154602
$473$	18.0461	0.829759
$474$	34.4663	1.58309
$475$	−66.5169	−3.05201
$476$	2.03648	0.0933417
$477$	3.90693	0.178886
$478$	−6.96623	−0.318628
$479$	3.47072	0.158581	0.0792906	−	0.996852i	$-0.474735\pi$
$479$	3.47072	0.158581	0.0792906	+	0.996852i	$0.474735\pi$
$480$	−48.0293	−2.19223
$481$	2.13860	0.0975119
$482$	−21.1884	−0.965103
$483$	−0.941332	−0.0428321
$484$	3.25767	0.148076
$485$	24.9863	1.13457
$486$	−18.2836	−0.829362
$487$	39.0922	1.77144	0.885718	−	0.464224i	$-0.153667\pi$
$487$	39.0922	1.77144	0.885718	+	0.464224i	$0.153667\pi$
$488$	−2.00184	−0.0906189
$489$	12.6423	0.571705
$490$	8.44573	0.381539
$491$	−8.26877	−0.373164	−0.186582	−	0.982439i	$-0.559741\pi$
$491$	−8.26877	−0.373164	−0.186582	+	0.982439i	$0.559741\pi$
$492$	−0.912042	−0.0411180
$493$	−3.73508	−0.168220
$494$	20.2103	0.909305
$495$	14.5696	0.654855
$496$	4.34800	0.195231
$497$	−0.462137	−0.0207297
$498$	−20.2368	−0.906833
$499$	6.27155	0.280753	0.140377	−	0.990098i	$-0.455169\pi$
$499$	6.27155	0.280753	0.140377	+	0.990098i	$0.455169\pi$
$500$	−68.3311	−3.05586
$501$	2.50091	0.111732
$502$	−32.2666	−1.44013
$503$	19.8637	0.885680	0.442840	−	0.896601i	$-0.353971\pi$
$503$	19.8637	0.885680	0.442840	+	0.896601i	$0.353971\pi$
$504$	0.353434	0.0157432
$505$	−9.86126	−0.438820
$506$	−4.57987	−0.203600
$507$	−12.0919	−0.537018
$508$	−10.3616	−0.459724
$509$	2.22204	0.0984902	0.0492451	−	0.998787i	$-0.484318\pi$
$509$	2.22204	0.0984902	0.0492451	+	0.998787i	$0.484318\pi$
$510$	−13.6552	−0.604663
$511$	−11.7862	−0.521392
$512$	−30.3551	−1.34152
$513$	27.3879	1.20920
$514$	38.1793	1.68401
$515$	0.0874594	0.00385392
$516$	13.0816	0.575885
$517$	−8.64793	−0.380336
$518$	1.95127	0.0857340
$519$	9.93815	0.436236
$520$	−3.47755	−0.152501
$521$	39.5013	1.73058	0.865292	−	0.501268i	$-0.167133\pi$
$521$	39.5013	1.73058	0.865292	+	0.501268i	$0.167133\pi$
$522$	6.08546	0.266353
$523$	−20.0158	−0.875229	−0.437615	−	0.899163i	$-0.644177\pi$
$523$	−20.0158	−0.875229	−0.437615	+	0.899163i	$0.644177\pi$
$524$	−1.41821	−0.0619550
$525$	−19.7088	−0.860161
$526$	−12.5386	−0.546708
$527$	1.12670	0.0490799
$528$	−22.3247	−0.971559
$529$	−22.5697	−0.981291
$530$	−35.0743	−1.52353
$531$	8.41101	0.365007
$532$	8.75377	0.379524
$533$	−0.752008	−0.0325731
$534$	−9.09818	−0.393717
$535$	−81.8019	−3.53660
$536$	−3.56428	−0.153953
$537$	6.39533	0.275979
$538$	22.4449	0.967667
$539$	3.57804	0.154117
$540$	44.2408	1.90382
$541$	25.1801	1.08258	0.541288	−	0.840837i	$-0.317937\pi$
$541$	25.1801	1.08258	0.541288	+	0.840837i	$0.317937\pi$
$542$	5.18912	0.222892
$543$	−16.4835	−0.707373
$544$	−8.71251	−0.373546
$545$	44.7951	1.91881
$546$	5.98826	0.256274
$547$	1.18522	0.0506763	0.0253381	−	0.999679i	$-0.491934\pi$
$547$	1.18522	0.0506763	0.0253381	+	0.999679i	$0.491934\pi$
$548$	13.7562	0.587636
$549$	5.01290	0.213946
$550$	−95.8893	−4.08873
$551$	−16.0552	−0.683975
$552$	0.353644	0.0150521
$553$	12.3090	0.523433
$554$	7.92488	0.336696
$555$	−6.21114	−0.263648
$556$	−22.5269	−0.955352
$557$	45.0949	1.91073	0.955367	−	0.295423i	$-0.0954606\pi$
$557$	45.0949	1.91073	0.955367	+	0.295423i	$0.0954606\pi$
$558$	−1.83570	−0.0777115
$559$	10.7862	0.456207
$560$	−18.8195	−0.795269
$561$	−5.78503	−0.244244
$562$	14.4173	0.608159
$563$	30.1715	1.27158	0.635789	−	0.771863i	$-0.280675\pi$
$563$	30.1715	1.27158	0.635789	+	0.771863i	$0.280675\pi$
$564$	−6.26888	−0.263968
$565$	47.0878	1.98100
$566$	−36.4796	−1.53335
$567$	5.29263	0.222270
$568$	0.173618	0.00728485
$569$	−1.81371	−0.0760347	−0.0380174	−	0.999277i	$-0.512104\pi$
$569$	−1.81371	−0.0760347	−0.0380174	+	0.999277i	$0.512104\pi$
$570$	−58.6967	−2.45854
$571$	−8.28936	−0.346899	−0.173449	−	0.984843i	$-0.555491\pi$
$571$	−8.28936	−0.346899	−0.173449	+	0.984843i	$0.555491\pi$
$572$	13.8307	0.578292
$573$	−9.88215	−0.412833
$574$	−0.686136	−0.0286388
$575$	9.00944	0.375720
$576$	6.01410	0.250588
$577$	43.8111	1.82388	0.911940	−	0.410324i	$-0.134584\pi$
$577$	43.8111	1.82388	0.911940	+	0.410324i	$0.134584\pi$
$578$	30.6946	1.27673
$579$	10.0147	0.416195
$580$	−25.9347	−1.07688
$581$	−7.22722	−0.299836
$582$	16.1642	0.670026
$583$	−14.8592	−0.615406
$584$	4.42791	0.183228
$585$	8.70831	0.360044
$586$	−16.6750	−0.688838
$587$	−22.0309	−0.909311	−0.454656	−	0.890667i	$-0.650238\pi$
$587$	−22.0309	−0.909311	−0.454656	+	0.890667i	$0.650238\pi$
$588$	2.59372	0.106963
$589$	4.84311	0.199557
$590$	−75.5093	−3.10867
$591$	8.78725	0.361459
$592$	−4.34800	−0.178702
$593$	25.6705	1.05416	0.527080	−	0.849816i	$-0.323287\pi$
$593$	25.6705	1.05416	0.527080	+	0.849816i	$0.323287\pi$
$594$	39.4817	1.61996
$595$	−4.87672	−0.199926
$596$	19.6385	0.804426
$597$	14.6242	0.598527
$598$	−2.73741	−0.111941
$599$	−24.6773	−1.00829	−0.504144	−	0.863620i	$-0.668192\pi$
$599$	−24.6773	−1.00829	−0.504144	+	0.863620i	$0.668192\pi$
$600$	7.40429	0.302279
$601$	36.7856	1.50051	0.750257	−	0.661146i	$-0.229930\pi$
$601$	36.7856	1.50051	0.750257	+	0.661146i	$0.229930\pi$
$602$	9.84138	0.401105
$603$	8.92549	0.363474
$604$	18.7427	0.762630
$605$	−7.80110	−0.317160
$606$	−6.37946	−0.259148
$607$	−27.3254	−1.10910	−0.554551	−	0.832150i	$-0.687110\pi$
$607$	−27.3254	−1.10910	−0.554551	+	0.832150i	$0.687110\pi$
$608$	−37.4506	−1.51882
$609$	−4.75711	−0.192768
$610$	−45.0031	−1.82212
$611$	−5.16890	−0.209111
$612$	1.91586	0.0774440
$613$	22.0918	0.892279	0.446140	−	0.894963i	$-0.352798\pi$
$613$	22.0918	0.892279	0.446140	+	0.894963i	$0.352798\pi$
$614$	−50.0715	−2.02072
$615$	2.18406	0.0880696
$616$	−1.34421	−0.0541599
$617$	−24.0832	−0.969553	−0.484777	−	0.874638i	$-0.661099\pi$
$617$	−24.0832	−0.969553	−0.484777	+	0.874638i	$0.661099\pi$
$618$	0.0565793	0.00227595
$619$	−13.5517	−0.544690	−0.272345	−	0.962200i	$-0.587799\pi$
$619$	−13.5517	−0.544690	−0.272345	+	0.962200i	$0.587799\pi$
$620$	7.82329	0.314191
$621$	−3.70958	−0.148860
$622$	−32.1212	−1.28794
$623$	−3.24926	−0.130179
$624$	−13.3436	−0.534170
$625$	94.9601	3.79840
$626$	29.4670	1.17774
$627$	−24.8669	−0.993088
$628$	−37.9177	−1.51308
$629$	−1.12670	−0.0449245
$630$	7.94550	0.316556
$631$	−32.1072	−1.27817	−0.639084	−	0.769137i	$-0.720686\pi$
$631$	−32.1072	−1.27817	−0.639084	+	0.769137i	$0.720686\pi$
$632$	−4.62432	−0.183945
$633$	−11.7970	−0.468890
$634$	−15.6002	−0.619563
$635$	24.8129	0.984670
$636$	−10.7714	−0.427116
$637$	2.13860	0.0847346
$638$	−23.1448	−0.916312
$639$	−0.434766	−0.0171991
$640$	12.9484	0.511830
$641$	19.8798	0.785207	0.392603	−	0.919708i	$-0.371575\pi$
$641$	19.8798	0.785207	0.392603	+	0.919708i	$0.371575\pi$
$642$	−52.9194	−2.08856
$643$	1.51227	0.0596382	0.0298191	−	0.999555i	$-0.490507\pi$
$643$	1.51227	0.0596382	0.0298191	+	0.999555i	$0.490507\pi$
$644$	−1.18566	−0.0467216
$645$	−31.3263	−1.23347
$646$	−10.6476	−0.418924
$647$	19.7077	0.774791	0.387395	−	0.921914i	$-0.373375\pi$
$647$	19.7077	0.774791	0.387395	+	0.921914i	$0.373375\pi$
$648$	−1.98836	−0.0781102
$649$	−31.9896	−1.25570
$650$	−57.3133	−2.24801
$651$	1.43500	0.0562421
$652$	15.9237	0.623621
$653$	−19.2508	−0.753340	−0.376670	−	0.926347i	$-0.622931\pi$
$653$	−19.2508	−0.753340	−0.376670	+	0.926347i	$0.622931\pi$
$654$	28.9789	1.13317
$655$	3.39618	0.132700
$656$	1.52891	0.0596939
$657$	−11.0882	−0.432590
$658$	−4.71613	−0.183854
$659$	40.2412	1.56758	0.783788	−	0.621029i	$-0.213285\pi$
$659$	40.2412	1.56758	0.783788	+	0.621029i	$0.213285\pi$
$660$	−40.1686	−1.56356
$661$	−14.9653	−0.582081	−0.291041	−	0.956711i	$-0.594001\pi$
$661$	−14.9653	−0.582081	−0.291041	+	0.956711i	$0.594001\pi$
$662$	−16.2654	−0.632173
$663$	−3.45773	−0.134287
$664$	2.71516	0.105369
$665$	−20.9625	−0.812892
$666$	1.83570	0.0711320
$667$	2.17461	0.0842013
$668$	3.15004	0.121879
$669$	−25.0213	−0.967379
$670$	−80.1281	−3.09562
$671$	−19.0656	−0.736018
$672$	−11.0965	−0.428058
$673$	36.3197	1.40002	0.700011	−	0.714132i	$-0.253178\pi$
$673$	36.3197	1.40002	0.700011	+	0.714132i	$0.253178\pi$
$674$	−26.8517	−1.03429
$675$	−77.6678	−2.98943
$676$	−15.2304	−0.585784
$677$	−5.38019	−0.206778	−0.103389	−	0.994641i	$-0.532969\pi$
$677$	−5.38019	−0.206778	−0.103389	+	0.994641i	$0.532969\pi$
$678$	30.4621	1.16989
$679$	5.77276	0.221538
$680$	1.83211	0.0702582
$681$	−33.0392	−1.26607
$682$	6.98172	0.267344
$683$	19.2352	0.736016	0.368008	−	0.929823i	$-0.380040\pi$
$683$	19.2352	0.736016	0.368008	+	0.929823i	$0.380040\pi$
$684$	8.23530	0.314885
$685$	−32.9418	−1.25864
$686$	1.95127	0.0745000
$687$	20.5239	0.783037
$688$	−21.9294	−0.836052
$689$	−8.88141	−0.338355
$690$	7.95024	0.302660
$691$	7.93225	0.301757	0.150879	−	0.988552i	$-0.451790\pi$
$691$	7.93225	0.301757	0.150879	+	0.988552i	$0.451790\pi$
$692$	12.5177	0.475850
$693$	3.36612	0.127868
$694$	24.0707	0.913712
$695$	53.9448	2.04624
$696$	1.78718	0.0677427
$697$	0.396188	0.0150067
$698$	−45.5192	−1.72293
$699$	19.7343	0.746419
$700$	−24.8243	−0.938272
$701$	−39.6031	−1.49579	−0.747894	−	0.663819i	$-0.768935\pi$
$701$	−39.6031	−1.49579	−0.747894	+	0.663819i	$0.768935\pi$
$702$	23.5984	0.890663
$703$	−4.84311	−0.182662
$704$	−22.8734	−0.862075
$705$	15.0120	0.565385
$706$	−28.0530	−1.05579
$707$	−2.27831	−0.0856848
$708$	−23.1892	−0.871504
$709$	−21.3949	−0.803503	−0.401752	−	0.915749i	$-0.631598\pi$
$709$	−21.3949	−0.803503	−0.401752	+	0.915749i	$0.631598\pi$
$710$	3.90309	0.146480
$711$	11.5800	0.434284
$712$	1.22070	0.0457475
$713$	−0.655980	−0.0245667
$714$	−3.15485	−0.118067
$715$	−33.1203	−1.23863
$716$	8.05529	0.301040
$717$	5.12309	0.191325
$718$	−69.7633	−2.60354
$719$	−2.24022	−0.0835461	−0.0417731	−	0.999127i	$-0.513301\pi$
$719$	−2.24022	−0.0835461	−0.0417731	+	0.999127i	$0.513301\pi$
$720$	−17.7049	−0.659821
$721$	0.0202063	0.000752523 0
$722$	−8.69440	−0.323572
$723$	15.5823	0.579512
$724$	−20.7619	−0.771609
$725$	45.5301	1.69094
$726$	−5.04669	−0.187300
$727$	2.87543	0.106644	0.0533219	−	0.998577i	$-0.483019\pi$
$727$	2.87543	0.106644	0.0533219	+	0.998577i	$0.483019\pi$
$728$	−0.803441	−0.0297775
$729$	29.3240	1.08607
$730$	99.5433	3.68426
$731$	−5.68260	−0.210178
$732$	−13.8206	−0.510825
$733$	16.8153	0.621086	0.310543	−	0.950559i	$-0.399489\pi$
$733$	16.8153	0.621086	0.310543	+	0.950559i	$0.399489\pi$
$734$	2.04949	0.0756479
$735$	−6.21114	−0.229101
$736$	5.07254	0.186976
$737$	−33.9463	−1.25043
$738$	−0.645498	−0.0237611
$739$	−0.0732843	−0.00269581	−0.00134790	−	0.999999i	$-0.500429\pi$
$739$	−0.0732843	−0.00269581	−0.00134790	+	0.999999i	$0.500429\pi$
$740$	−7.82329	−0.287590
$741$	−14.8630	−0.546007
$742$	−8.10344	−0.297487
$743$	48.6517	1.78486	0.892429	−	0.451187i	$-0.148999\pi$
$743$	48.6517	1.78486	0.892429	+	0.451187i	$0.148999\pi$
$744$	−0.539108	−0.0197647
$745$	−47.0282	−1.72298
$746$	16.5229	0.604948
$747$	−6.79917	−0.248769
$748$	−7.28658	−0.266424
$749$	−18.8992	−0.690563
$750$	105.857	3.86534
$751$	18.3218	0.668573	0.334286	−	0.942472i	$-0.391505\pi$
$751$	18.3218	0.668573	0.334286	+	0.942472i	$0.391505\pi$
$752$	10.5089	0.383220
$753$	23.7294	0.864748
$754$	−13.8337	−0.503795
$755$	−44.8829	−1.63346
$756$	10.2212	0.371743
$757$	−5.57612	−0.202668	−0.101334	−	0.994852i	$-0.532311\pi$
$757$	−5.57612	−0.202668	−0.101334	+	0.994852i	$0.532311\pi$
$758$	−59.1242	−2.14749
$759$	3.36812	0.122255
$760$	7.87531	0.285667
$761$	−4.00966	−0.145350	−0.0726750	−	0.997356i	$-0.523154\pi$
$761$	−4.00966	−0.145350	−0.0726750	+	0.997356i	$0.523154\pi$
$762$	16.0520	0.581502
$763$	10.3493	0.374671
$764$	−12.4471	−0.450322
$765$	−4.58788	−0.165875
$766$	17.3938	0.628465
$767$	−19.1203	−0.690393
$768$	26.7237	0.964310
$769$	19.5726	0.705808	0.352904	−	0.935660i	$-0.385194\pi$
$769$	19.5726	0.705808	0.352904	+	0.935660i	$0.385194\pi$
$770$	−30.2191	−1.08902
$771$	−28.0777	−1.01119
$772$	12.6140	0.453989
$773$	46.5777	1.67528	0.837641	−	0.546221i	$-0.183934\pi$
$773$	46.5777	1.67528	0.837641	+	0.546221i	$0.183934\pi$
$774$	9.25849	0.332790
$775$	−13.7343	−0.493352
$776$	−2.16874	−0.0778531
$777$	−1.43500	−0.0514804
$778$	−68.5156	−2.45640
$779$	1.70301	0.0610167
$780$	−24.0089	−0.859656
$781$	1.65354	0.0591684
$782$	1.44217	0.0515720
$783$	−18.7467	−0.669952
$784$	−4.34800	−0.155286
$785$	90.8010	3.24083
$786$	2.19706	0.0783665
$787$	−26.9794	−0.961713	−0.480856	−	0.876799i	$-0.659674\pi$
$787$	−26.9794	−0.961713	−0.480856	+	0.876799i	$0.659674\pi$
$788$	11.0681	0.394283
$789$	9.22110	0.328280
$790$	−103.959	−3.69869
$791$	10.8790	0.386813
$792$	−1.26460	−0.0449356
$793$	−11.3956	−0.404668
$794$	53.8132	1.90976
$795$	25.7942	0.914827
$796$	18.4200	0.652879
$797$	7.14534	0.253101	0.126550	−	0.991960i	$-0.459609\pi$
$797$	7.14534	0.253101	0.126550	+	0.991960i	$0.459609\pi$
$798$	−13.5611	−0.480058
$799$	2.72318	0.0963392
$800$	106.204	3.75489
$801$	−3.05681	−0.108007
$802$	−20.5253	−0.724772
$803$	42.1715	1.48820
$804$	−24.6077	−0.867845
$805$	2.83929	0.100072
$806$	4.17300	0.146988
$807$	−16.5064	−0.581051
$808$	0.855928	0.0301114
$809$	−7.25250	−0.254984	−0.127492	−	0.991840i	$-0.540693\pi$
$809$	−7.25250	−0.254984	−0.127492	+	0.991840i	$0.540693\pi$
$810$	−44.7001	−1.57060
$811$	1.31617	0.0462169	0.0231085	−	0.999733i	$-0.492644\pi$
$811$	1.31617	0.0462169	0.0231085	+	0.999733i	$0.492644\pi$
$812$	−5.99186	−0.210273
$813$	−3.81617	−0.133839
$814$	−6.98172	−0.244709
$815$	−38.1323	−1.33572
$816$	7.02992	0.246096
$817$	−24.4266	−0.854578
$818$	38.1007	1.33216
$819$	2.01194	0.0703028
$820$	2.75094	0.0960671
$821$	−35.5102	−1.23932	−0.619658	−	0.784872i	$-0.712729\pi$
$821$	−35.5102	−1.23932	−0.619658	+	0.784872i	$0.712729\pi$
$822$	−21.3107	−0.743298
$823$	15.6991	0.547236	0.273618	−	0.961838i	$-0.411780\pi$
$823$	15.6991	0.547236	0.273618	+	0.961838i	$0.411780\pi$
$824$	−0.00759122	−0.000264453 0
$825$	70.5187	2.45515
$826$	−17.4454	−0.607004
$827$	7.19951	0.250351	0.125176	−	0.992135i	$-0.460051\pi$
$827$	7.19951	0.250351	0.125176	+	0.992135i	$0.460051\pi$
$828$	−1.11544	−0.0387641
$829$	−46.5888	−1.61809	−0.809047	−	0.587744i	$-0.800016\pi$
$829$	−46.5888	−1.61809	−0.809047	+	0.587744i	$0.800016\pi$
$830$	61.0392	2.11870
$831$	−5.82810	−0.202175
$832$	−13.6715	−0.473975
$833$	−1.12670	−0.0390379
$834$	34.8980	1.20842
$835$	−7.54336	−0.261049
$836$	−31.3213	−1.08327
$837$	5.65501	0.195466
$838$	−31.5255	−1.08903
$839$	43.0429	1.48600	0.743002	−	0.669289i	$-0.233401\pi$
$839$	43.0429	1.48600	0.743002	+	0.669289i	$0.233401\pi$
$840$	2.33343	0.0805110
$841$	−18.0104	−0.621048
$842$	−2.27671	−0.0784608
$843$	−10.6028	−0.365179
$844$	−14.8591	−0.511470
$845$	36.4720	1.25468
$846$	−4.43680	−0.152540
$847$	−1.80234	−0.0619291
$848$	18.0568	0.620073
$849$	26.8278	0.920726
$850$	30.1950	1.03568
$851$	0.655980	0.0224867
$852$	1.19865	0.0410652
$853$	5.92124	0.202739	0.101370	−	0.994849i	$-0.467677\pi$
$853$	5.92124	0.202739	0.101370	+	0.994849i	$0.467677\pi$
$854$	−10.3974	−0.355790
$855$	−19.7210	−0.674443
$856$	7.10016	0.242678
$857$	22.2837	0.761196	0.380598	−	0.924741i	$-0.375718\pi$
$857$	22.2837	0.761196	0.380598	+	0.924741i	$0.375718\pi$
$858$	−21.4262	−0.731479
$859$	1.70670	0.0582318	0.0291159	−	0.999576i	$-0.490731\pi$
$859$	1.70670	0.0582318	0.0291159	+	0.999576i	$0.490731\pi$
$860$	−39.4573	−1.34548
$861$	0.504597	0.0171966
$862$	31.1868	1.06223
$863$	−25.5790	−0.870719	−0.435359	−	0.900257i	$-0.643379\pi$
$863$	−25.5790	−0.870719	−0.435359	+	0.900257i	$0.643379\pi$
$864$	−43.7289	−1.48769
$865$	−29.9759	−1.01921
$866$	42.7206	1.45170
$867$	−22.5733	−0.766631
$868$	1.80747	0.0613494
$869$	−44.0421	−1.49403
$870$	40.1773	1.36214
$871$	−20.2898	−0.687494
$872$	−3.88808	−0.131667
$873$	5.43085	0.183806
$874$	6.19917	0.209690
$875$	37.8049	1.27804
$876$	30.5701	1.03287
$877$	50.5927	1.70840	0.854198	−	0.519948i	$-0.174049\pi$
$877$	50.5927	1.70840	0.854198	+	0.519948i	$0.174049\pi$
$878$	54.0932	1.82556
$879$	12.2631	0.413624
$880$	67.3369	2.26993
$881$	54.0592	1.82130	0.910650	−	0.413178i	$-0.135581\pi$
$881$	54.0592	1.82130	0.910650	+	0.413178i	$0.135581\pi$
$882$	1.83570	0.0618113
$883$	−39.9035	−1.34286	−0.671431	−	0.741067i	$-0.734320\pi$
$883$	−39.9035	−1.34286	−0.671431	+	0.741067i	$0.734320\pi$
$884$	−4.35521	−0.146482
$885$	55.5309	1.86665
$886$	−62.5120	−2.10013
$887$	−19.0903	−0.640990	−0.320495	−	0.947250i	$-0.603849\pi$
$887$	−19.0903	−0.640990	−0.320495	+	0.947250i	$0.603849\pi$
$888$	0.539108	0.0180913
$889$	5.73269	0.192268
$890$	27.4423	0.919869
$891$	−18.9372	−0.634421
$892$	−31.5158	−1.05523
$893$	11.7056	0.391712
$894$	−30.4235	−1.01751
$895$	−19.2899	−0.644790
$896$	2.99155	0.0999408
$897$	2.01314	0.0672167
$898$	26.2527	0.876065
$899$	−3.31506	−0.110563
$900$	−23.3540	−0.778468
$901$	4.67908	0.155883
$902$	2.45502	0.0817432
$903$	−7.23753	−0.240850
$904$	−4.08708	−0.135934
$905$	49.7182	1.65269
$906$	−29.0357	−0.964647
$907$	29.6727	0.985267	0.492634	−	0.870237i	$-0.336034\pi$
$907$	29.6727	0.985267	0.492634	+	0.870237i	$0.336034\pi$
$908$	−41.6148	−1.38104
$909$	−2.14337	−0.0710912
$910$	−18.0621	−0.598752
$911$	29.8661	0.989507	0.494754	−	0.869033i	$-0.335258\pi$
$911$	29.8661	0.989507	0.494754	+	0.869033i	$0.335258\pi$
$912$	30.2180	1.00062
$913$	25.8593	0.855817
$914$	−75.3174	−2.49128
$915$	33.0961	1.09412
$916$	25.8511	0.854144
$917$	0.784642	0.0259112
$918$	−12.4326	−0.410336
$919$	14.4183	0.475617	0.237809	−	0.971312i	$-0.423571\pi$
$919$	14.4183	0.475617	0.237809	+	0.971312i	$0.423571\pi$
$920$	−1.06668	−0.0351673
$921$	36.8235	1.21338
$922$	−7.54204	−0.248384
$923$	0.988329	0.0325312
$924$	−9.28041	−0.305303
$925$	13.7343	0.451582
$926$	−8.67487	−0.285074
$927$	0.0190096	0.000624356 0
$928$	25.6346	0.841495
$929$	−3.84196	−0.126051	−0.0630253	−	0.998012i	$-0.520075\pi$
$929$	−3.84196	−0.126051	−0.0630253	+	0.998012i	$0.520075\pi$
$930$	−12.1196	−0.397418
$931$	−4.84311	−0.158727
$932$	24.8565	0.814200
$933$	23.6225	0.773366
$934$	−33.1136	−1.08351
$935$	17.4491	0.570646
$936$	−0.755855	−0.0247059
$937$	−12.0671	−0.394215	−0.197108	−	0.980382i	$-0.563155\pi$
$937$	−12.0671	−0.394215	−0.197108	+	0.980382i	$0.563155\pi$
$938$	−18.5125	−0.604456
$939$	−21.6705	−0.707191
$940$	18.9085	0.616727
$941$	−46.5205	−1.51652	−0.758262	−	0.651950i	$-0.773951\pi$
$941$	−46.5205	−1.51652	−0.758262	+	0.651950i	$0.773951\pi$
$942$	58.7411	1.91389
$943$	−0.230666	−0.00751151
$944$	38.8734	1.26522
$945$	−24.4767	−0.796227
$946$	−35.2128	−1.14487
$947$	−56.8961	−1.84888	−0.924438	−	0.381332i	$-0.875465\pi$
$947$	−56.8961	−1.84888	−0.924438	+	0.381332i	$0.875465\pi$
$948$	−31.9261	−1.03691
$949$	25.2061	0.818224
$950$	129.793	4.21103
$951$	11.4727	0.372027
$952$	0.423285	0.0137187
$953$	−36.0312	−1.16716	−0.583582	−	0.812054i	$-0.698349\pi$
$953$	−36.0312	−1.16716	−0.583582	+	0.812054i	$0.698349\pi$
$954$	−7.62349	−0.246820
$955$	29.8070	0.964532
$956$	6.45283	0.208699
$957$	17.0211	0.550215
$958$	−6.77232	−0.218804
$959$	−7.61077	−0.245764
$960$	39.7062	1.28151
$961$	1.00000	0.0322581
$962$	−4.17300	−0.134543
$963$	−17.7799	−0.572948
$964$	19.6268	0.632137
$965$	−30.2067	−0.972387
$966$	1.83680	0.0590980
$967$	−49.6872	−1.59783	−0.798916	−	0.601442i	$-0.794593\pi$
$967$	−49.6872	−1.59783	−0.798916	+	0.601442i	$0.794593\pi$
$968$	0.677112	0.0217632
$969$	7.83044	0.251550
$970$	−48.7551	−1.56543
$971$	59.2589	1.90171	0.950855	−	0.309637i	$-0.100208\pi$
$971$	59.2589	1.90171	0.950855	+	0.309637i	$0.100208\pi$
$972$	16.9361	0.543227
$973$	12.4632	0.399553
$974$	−76.2795	−2.44415
$975$	42.1493	1.34986
$976$	23.1683	0.741599
$977$	−29.4735	−0.942940	−0.471470	−	0.881882i	$-0.656277\pi$
$977$	−29.4735	−0.942940	−0.471470	+	0.881882i	$0.656277\pi$
$978$	−24.6686	−0.788815
$979$	11.6260	0.371567
$980$	−7.82329	−0.249906
$981$	9.73635	0.310858
$982$	16.1346	0.514877
$983$	−11.0159	−0.351354	−0.175677	−	0.984448i	$-0.556211\pi$
$983$	−11.0159	−0.351354	−0.175677	+	0.984448i	$0.556211\pi$
$984$	−0.189569	−0.00604325
$985$	−26.5045	−0.844504
$986$	7.28816	0.232102
$987$	3.46832	0.110398
$988$	−18.7208	−0.595589
$989$	3.30848	0.105204
$990$	−28.4293	−0.903542
$991$	3.26630	0.103757	0.0518787	−	0.998653i	$-0.483479\pi$
$991$	3.26630	0.103757	0.0518787	+	0.998653i	$0.483479\pi$
$992$	−7.73276	−0.245515
$993$	11.9619	0.379598
$994$	0.901756	0.0286020
$995$	−44.1101	−1.39838
$996$	18.7454	0.593970
$997$	−7.29147	−0.230923	−0.115462	−	0.993312i	$-0.536835\pi$
$997$	−7.29147	−0.230923	−0.115462	+	0.993312i	$0.536835\pi$
$998$	−12.2375	−0.387372
$999$	−5.65501	−0.178917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.15	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.15	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.95127 q^{2} +1.43500 q^{3} +1.80747 q^{4} -4.32832 q^{5} -2.80008 q^{6} -1.00000 q^{7} +0.375685 q^{8} -0.940772 q^{9} +O(q^{10})\)	\(q-1.95127 q^{2} +1.43500 q^{3} +1.80747 q^{4} -4.32832 q^{5} -2.80008 q^{6} -1.00000 q^{7} +0.375685 q^{8} -0.940772 q^{9} +8.44573 q^{10} +3.57804 q^{11} +2.59372 q^{12} +2.13860 q^{13} +1.95127 q^{14} -6.21114 q^{15} -4.34800 q^{16} -1.12670 q^{17} +1.83570 q^{18} -4.84311 q^{19} -7.82329 q^{20} -1.43500 q^{21} -6.98172 q^{22} +0.655980 q^{23} +0.539108 q^{24} +13.7343 q^{25} -4.17300 q^{26} -5.65501 q^{27} -1.80747 q^{28} +3.31506 q^{29} +12.1196 q^{30} -1.00000 q^{31} +7.73276 q^{32} +5.13449 q^{33} +2.19850 q^{34} +4.32832 q^{35} -1.70041 q^{36} +1.00000 q^{37} +9.45024 q^{38} +3.06890 q^{39} -1.62608 q^{40} -0.351635 q^{41} +2.80008 q^{42} +5.04357 q^{43} +6.46718 q^{44} +4.07196 q^{45} -1.28000 q^{46} -2.41695 q^{47} -6.23938 q^{48} +1.00000 q^{49} -26.7994 q^{50} -1.61682 q^{51} +3.86546 q^{52} -4.15290 q^{53} +11.0345 q^{54} -15.4869 q^{55} -0.375685 q^{56} -6.94987 q^{57} -6.46858 q^{58} -8.94054 q^{59} -11.2264 q^{60} -5.32850 q^{61} +1.95127 q^{62} +0.940772 q^{63} -6.39273 q^{64} -9.25655 q^{65} -10.0188 q^{66} -9.48741 q^{67} -2.03648 q^{68} +0.941332 q^{69} -8.44573 q^{70} +0.462137 q^{71} -0.353434 q^{72} +11.7862 q^{73} -1.95127 q^{74} +19.7088 q^{75} -8.75377 q^{76} -3.57804 q^{77} -5.98826 q^{78} -12.3090 q^{79} +18.8195 q^{80} -5.29263 q^{81} +0.686136 q^{82} +7.22722 q^{83} -2.59372 q^{84} +4.87672 q^{85} -9.84138 q^{86} +4.75711 q^{87} +1.34421 q^{88} +3.24926 q^{89} -7.94550 q^{90} -2.13860 q^{91} +1.18566 q^{92} -1.43500 q^{93} +4.71613 q^{94} +20.9625 q^{95} +11.0965 q^{96} -5.77276 q^{97} -1.95127 q^{98} -3.36612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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