LMFDB - Embedded newform 8035.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51924 q^{2} -1.73731 q^{3} +4.34657 q^{4} +1.00000 q^{5} +4.37670 q^{6} -5.14815 q^{7} -5.91158 q^{8} +0.0182398 q^{9} +O(q^{10})$	\(q-2.51924 q^{2} -1.73731 q^{3} +4.34657 q^{4} +1.00000 q^{5} +4.37670 q^{6} -5.14815 q^{7} -5.91158 q^{8} +0.0182398 q^{9} -2.51924 q^{10} +1.49876 q^{11} -7.55134 q^{12} -5.55026 q^{13} +12.9694 q^{14} -1.73731 q^{15} +6.19955 q^{16} -2.59367 q^{17} -0.0459504 q^{18} +4.66946 q^{19} +4.34657 q^{20} +8.94393 q^{21} -3.77574 q^{22} +1.25547 q^{23} +10.2702 q^{24} +1.00000 q^{25} +13.9825 q^{26} +5.18024 q^{27} -22.3768 q^{28} -2.96767 q^{29} +4.37670 q^{30} -6.58366 q^{31} -3.79500 q^{32} -2.60381 q^{33} +6.53409 q^{34} -5.14815 q^{35} +0.0792806 q^{36} +11.5124 q^{37} -11.7635 q^{38} +9.64252 q^{39} -5.91158 q^{40} +1.49195 q^{41} -22.5319 q^{42} +9.01775 q^{43} +6.51448 q^{44} +0.0182398 q^{45} -3.16283 q^{46} -2.14466 q^{47} -10.7705 q^{48} +19.5035 q^{49} -2.51924 q^{50} +4.50601 q^{51} -24.1246 q^{52} -8.39169 q^{53} -13.0503 q^{54} +1.49876 q^{55} +30.4337 q^{56} -8.11228 q^{57} +7.47628 q^{58} -8.30122 q^{59} -7.55134 q^{60} +1.72561 q^{61} +16.5858 q^{62} -0.0939012 q^{63} -2.83859 q^{64} -5.55026 q^{65} +6.55962 q^{66} -14.6099 q^{67} -11.2736 q^{68} -2.18114 q^{69} +12.9694 q^{70} +2.20528 q^{71} -0.107826 q^{72} -11.1249 q^{73} -29.0024 q^{74} -1.73731 q^{75} +20.2961 q^{76} -7.71585 q^{77} -24.2918 q^{78} -0.117660 q^{79} +6.19955 q^{80} -9.05439 q^{81} -3.75858 q^{82} -9.42988 q^{83} +38.8754 q^{84} -2.59367 q^{85} -22.7179 q^{86} +5.15576 q^{87} -8.86005 q^{88} -17.9566 q^{89} -0.0459504 q^{90} +28.5736 q^{91} +5.45699 q^{92} +11.4378 q^{93} +5.40293 q^{94} +4.66946 q^{95} +6.59309 q^{96} -15.3455 q^{97} -49.1340 q^{98} +0.0273371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.51924	−1.78137	−0.890686	−	0.454619i	$-0.849775\pi$
$2$	−2.51924	−1.78137	−0.890686	+	0.454619i	$0.849775\pi$
$3$	−1.73731	−1.00304	−0.501518	−	0.865147i	$-0.667225\pi$
$3$	−1.73731	−1.00304	−0.501518	+	0.865147i	$0.667225\pi$
$4$	4.34657	2.17329
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.37670	1.78678
$7$	−5.14815	−1.94582	−0.972910	−	0.231186i	$-0.925739\pi$
$7$	−5.14815	−1.94582	−0.972910	+	0.231186i	$0.925739\pi$
$8$	−5.91158	−2.09006
$9$	0.0182398	0.00607993
$10$	−2.51924	−0.796654
$11$	1.49876	0.451893	0.225947	−	0.974140i	$-0.427452\pi$
$11$	1.49876	0.451893	0.225947	+	0.974140i	$0.427452\pi$
$12$	−7.55134	−2.17988
$13$	−5.55026	−1.53937	−0.769683	−	0.638426i	$-0.779586\pi$
$13$	−5.55026	−1.53937	−0.769683	+	0.638426i	$0.779586\pi$
$14$	12.9694	3.46623
$15$	−1.73731	−0.448571
$16$	6.19955	1.54989
$17$	−2.59367	−0.629058	−0.314529	−	0.949248i	$-0.601847\pi$
$17$	−2.59367	−0.629058	−0.314529	+	0.949248i	$0.601847\pi$
$18$	−0.0459504	−0.0108306
$19$	4.66946	1.07125	0.535623	−	0.844457i	$-0.320077\pi$
$19$	4.66946	1.07125	0.535623	+	0.844457i	$0.320077\pi$
$20$	4.34657	0.971923
$21$	8.94393	1.95173
$22$	−3.77574	−0.804990
$23$	1.25547	0.261783	0.130892	−	0.991397i	$-0.458216\pi$
$23$	1.25547	0.261783	0.130892	+	0.991397i	$0.458216\pi$
$24$	10.2702	2.09640
$25$	1.00000	0.200000
$26$	13.9825	2.74218
$27$	5.18024	0.996937
$28$	−22.3768	−4.22882
$29$	−2.96767	−0.551083	−0.275541	−	0.961289i	$-0.588857\pi$
$29$	−2.96767	−0.551083	−0.275541	+	0.961289i	$0.588857\pi$
$30$	4.37670	0.799072
$31$	−6.58366	−1.18246	−0.591230	−	0.806503i	$-0.701357\pi$
$31$	−6.58366	−1.18246	−0.591230	+	0.806503i	$0.701357\pi$
$32$	−3.79500	−0.670868
$33$	−2.60381	−0.453265
$34$	6.53409	1.12059
$35$	−5.14815	−0.870197
$36$	0.0792806	0.0132134
$37$	11.5124	1.89262	0.946311	−	0.323258i	$-0.104778\pi$
$37$	11.5124	1.89262	0.946311	+	0.323258i	$0.104778\pi$
$38$	−11.7635	−1.90829
$39$	9.64252	1.54404
$40$	−5.91158	−0.934703
$41$	1.49195	0.233004	0.116502	−	0.993190i	$-0.462832\pi$
$41$	1.49195	0.233004	0.116502	+	0.993190i	$0.462832\pi$
$42$	−22.5319	−3.47675
$43$	9.01775	1.37519	0.687597	−	0.726092i	$-0.258665\pi$
$43$	9.01775	1.37519	0.687597	+	0.726092i	$0.258665\pi$
$44$	6.51448	0.982094
$45$	0.0182398	0.00271903
$46$	−3.16283	−0.466334
$47$	−2.14466	−0.312831	−0.156416	−	0.987691i	$-0.549994\pi$
$47$	−2.14466	−0.312831	−0.156416	+	0.987691i	$0.549994\pi$
$48$	−10.7705	−1.55459
$49$	19.5035	2.78621
$50$	−2.51924	−0.356274
$51$	4.50601	0.630968
$52$	−24.1246	−3.34548
$53$	−8.39169	−1.15269	−0.576343	−	0.817208i	$-0.695521\pi$
$53$	−8.39169	−1.15269	−0.576343	+	0.817208i	$0.695521\pi$
$54$	−13.0503	−1.77592
$55$	1.49876	0.202093
$56$	30.4337	4.06688
$57$	−8.11228	−1.07450
$58$	7.47628	0.981683
$59$	−8.30122	−1.08073	−0.540364	−	0.841432i	$-0.681713\pi$
$59$	−8.30122	−1.08073	−0.540364	+	0.841432i	$0.681713\pi$
$60$	−7.55134	−0.974873
$61$	1.72561	0.220941	0.110471	−	0.993879i	$-0.464764\pi$
$61$	1.72561	0.220941	0.110471	+	0.993879i	$0.464764\pi$
$62$	16.5858	2.10640
$63$	−0.0939012	−0.0118304
$64$	−2.83859	−0.354823
$65$	−5.55026	−0.688426
$66$	6.55962	0.807434
$67$	−14.6099	−1.78488	−0.892441	−	0.451165i	$-0.851009\pi$
$67$	−14.6099	−1.78488	−0.892441	+	0.451165i	$0.851009\pi$
$68$	−11.2736	−1.36712
$69$	−2.18114	−0.262578
$70$	12.9694	1.55014
$71$	2.20528	0.261719	0.130859	−	0.991401i	$-0.458226\pi$
$71$	2.20528	0.261719	0.130859	+	0.991401i	$0.458226\pi$
$72$	−0.107826	−0.0127074
$73$	−11.1249	−1.30207	−0.651037	−	0.759046i	$-0.725666\pi$
$73$	−11.1249	−1.30207	−0.651037	+	0.759046i	$0.725666\pi$
$74$	−29.0024	−3.37146
$75$	−1.73731	−0.200607
$76$	20.2961	2.32813
$77$	−7.71585	−0.879303
$78$	−24.2918	−2.75051
$79$	−0.117660	−0.0132378	−0.00661891	−	0.999978i	$-0.502107\pi$
$79$	−0.117660	−0.0132378	−0.00661891	+	0.999978i	$0.502107\pi$
$80$	6.19955	0.693131
$81$	−9.05439	−1.00604
$82$	−3.75858	−0.415066
$83$	−9.42988	−1.03506	−0.517532	−	0.855664i	$-0.673149\pi$
$83$	−9.42988	−1.03506	−0.517532	+	0.855664i	$0.673149\pi$
$84$	38.8754	4.24166
$85$	−2.59367	−0.281323
$86$	−22.7179	−2.44973
$87$	5.15576	0.552755
$88$	−8.86005	−0.944485
$89$	−17.9566	−1.90339	−0.951696	−	0.307043i	$-0.900660\pi$
$89$	−17.9566	−1.90339	−0.951696	+	0.307043i	$0.900660\pi$
$90$	−0.0459504	−0.00484360
$91$	28.5736	2.99533
$92$	5.45699	0.568931
$93$	11.4378	1.18605
$94$	5.40293	0.557269
$95$	4.66946	0.479076
$96$	6.59309	0.672904
$97$	−15.3455	−1.55809	−0.779047	−	0.626965i	$-0.784297\pi$
$97$	−15.3455	−1.55809	−0.779047	+	0.626965i	$0.784297\pi$
$98$	−49.1340	−4.96328
$99$	0.0273371	0.00274748
$100$	4.34657	0.434657
$101$	−3.08894	−0.307361	−0.153681	−	0.988121i	$-0.549113\pi$
$101$	−3.08894	−0.307361	−0.153681	+	0.988121i	$0.549113\pi$
$102$	−11.3517	−1.12399
$103$	−10.0468	−0.989939	−0.494970	−	0.868910i	$-0.664821\pi$
$103$	−10.0468	−0.989939	−0.494970	+	0.868910i	$0.664821\pi$
$104$	32.8108	3.21737
$105$	8.94393	0.872838
$106$	21.1407	2.05336
$107$	6.65751	0.643606	0.321803	−	0.946807i	$-0.395711\pi$
$107$	6.65751	0.643606	0.321803	+	0.946807i	$0.395711\pi$
$108$	22.5163	2.16663
$109$	−7.58670	−0.726674	−0.363337	−	0.931658i	$-0.618363\pi$
$109$	−7.58670	−0.726674	−0.363337	+	0.931658i	$0.618363\pi$
$110$	−3.77574	−0.360003
$111$	−20.0005	−1.89837
$112$	−31.9163	−3.01580
$113$	10.8606	1.02168	0.510842	−	0.859675i	$-0.329334\pi$
$113$	10.8606	1.02168	0.510842	+	0.859675i	$0.329334\pi$
$114$	20.4368	1.91408
$115$	1.25547	0.117073
$116$	−12.8992	−1.19766
$117$	−0.101236	−0.00935924
$118$	20.9128	1.92518
$119$	13.3526	1.22403
$120$	10.2702	0.937541
$121$	−8.75371	−0.795792
$122$	−4.34722	−0.393579
$123$	−2.59198	−0.233711
$124$	−28.6164	−2.56983
$125$	1.00000	0.0894427
$126$	0.236560	0.0210744
$127$	14.5290	1.28924	0.644619	−	0.764504i	$-0.277016\pi$
$127$	14.5290	1.28924	0.644619	+	0.764504i	$0.277016\pi$
$128$	14.7411	1.30294
$129$	−15.6666	−1.37937
$130$	13.9825	1.22634
$131$	−6.76961	−0.591463	−0.295732	−	0.955271i	$-0.595563\pi$
$131$	−6.76961	−0.591463	−0.295732	+	0.955271i	$0.595563\pi$
$132$	−11.3177	−0.985075
$133$	−24.0391	−2.08445
$134$	36.8058	3.17954
$135$	5.18024	0.445844
$136$	15.3327	1.31477
$137$	−18.6539	−1.59371	−0.796857	−	0.604168i	$-0.793506\pi$
$137$	−18.6539	−1.59371	−0.796857	+	0.604168i	$0.793506\pi$
$138$	5.49481	0.467749
$139$	−17.7056	−1.50177	−0.750884	−	0.660434i	$-0.770372\pi$
$139$	−17.7056	−1.50177	−0.750884	+	0.660434i	$0.770372\pi$
$140$	−22.3768	−1.89119
$141$	3.72594	0.313781
$142$	−5.55563	−0.466218
$143$	−8.31852	−0.695630
$144$	0.113079	0.00942321
$145$	−2.96767	−0.246452
$146$	28.0264	2.31948
$147$	−33.8836	−2.79467
$148$	50.0393	4.11321
$149$	5.93816	0.486473	0.243237	−	0.969967i	$-0.421791\pi$
$149$	5.93816	0.486473	0.243237	+	0.969967i	$0.421791\pi$
$150$	4.37670	0.357356
$151$	−5.81861	−0.473512	−0.236756	−	0.971569i	$-0.576084\pi$
$151$	−5.81861	−0.473512	−0.236756	+	0.971569i	$0.576084\pi$
$152$	−27.6039	−2.23897
$153$	−0.0473081	−0.00382463
$154$	19.4381	1.56637
$155$	−6.58366	−0.528812
$156$	41.9119	3.35564
$157$	1.97300	0.157463	0.0787313	−	0.996896i	$-0.474913\pi$
$157$	1.97300	0.157463	0.0787313	+	0.996896i	$0.474913\pi$
$158$	0.296415	0.0235815
$159$	14.5789	1.15619
$160$	−3.79500	−0.300021
$161$	−6.46335	−0.509383
$162$	22.8102	1.79214
$163$	−15.7510	−1.23371	−0.616855	−	0.787077i	$-0.711594\pi$
$163$	−15.7510	−1.23371	−0.616855	+	0.787077i	$0.711594\pi$
$164$	6.48488	0.506384
$165$	−2.60381	−0.202706
$166$	23.7561	1.84383
$167$	−11.4177	−0.883528	−0.441764	−	0.897131i	$-0.645647\pi$
$167$	−11.4177	−0.883528	−0.441764	+	0.897131i	$0.645647\pi$
$168$	−52.8728	−4.07922
$169$	17.8054	1.36965
$170$	6.53409	0.501142
$171$	0.0851699	0.00651310
$172$	39.1963	2.98869
$173$	12.4032	0.942996	0.471498	−	0.881867i	$-0.343714\pi$
$173$	12.4032	0.942996	0.471498	+	0.881867i	$0.343714\pi$
$174$	−12.9886	−0.984663
$175$	−5.14815	−0.389164
$176$	9.29165	0.700384
$177$	14.4218	1.08401
$178$	45.2369	3.39065
$179$	11.0424	0.825348	0.412674	−	0.910879i	$-0.364595\pi$
$179$	11.0424	0.825348	0.412674	+	0.910879i	$0.364595\pi$
$180$	0.0792806	0.00590922
$181$	−15.3615	−1.14181	−0.570905	−	0.821016i	$-0.693407\pi$
$181$	−15.3615	−1.14181	−0.570905	+	0.821016i	$0.693407\pi$
$182$	−71.9838	−5.33579
$183$	−2.99791	−0.221612
$184$	−7.42181	−0.547143
$185$	11.5124	0.846406
$186$	−28.8147	−2.11280
$187$	−3.88730	−0.284267
$188$	−9.32194	−0.679872
$189$	−26.6687	−1.93986
$190$	−11.7635	−0.853413
$191$	−7.97570	−0.577101	−0.288551	−	0.957465i	$-0.593173\pi$
$191$	−7.97570	−0.577101	−0.288551	+	0.957465i	$0.593173\pi$
$192$	4.93150	0.355900
$193$	0.286972	0.0206567	0.0103283	−	0.999947i	$-0.496712\pi$
$193$	0.286972	0.0206567	0.0103283	+	0.999947i	$0.496712\pi$
$194$	38.6589	2.77555
$195$	9.64252	0.690515
$196$	84.7733	6.05524
$197$	12.5769	0.896069	0.448034	−	0.894016i	$-0.352124\pi$
$197$	12.5769	0.896069	0.448034	+	0.894016i	$0.352124\pi$
$198$	−0.0688687	−0.00489428
$199$	−4.64955	−0.329598	−0.164799	−	0.986327i	$-0.552698\pi$
$199$	−4.64955	−0.329598	−0.164799	+	0.986327i	$0.552698\pi$
$200$	−5.91158	−0.418012
$201$	25.3819	1.79030
$202$	7.78179	0.547525
$203$	15.2780	1.07231
$204$	19.5857	1.37127
$205$	1.49195	0.104202
$206$	25.3103	1.76345
$207$	0.0228995	0.00159162
$208$	−34.4092	−2.38585
$209$	6.99840	0.484089
$210$	−22.5319	−1.55485
$211$	26.9726	1.85687	0.928434	−	0.371497i	$-0.121155\pi$
$211$	26.9726	1.85687	0.928434	+	0.371497i	$0.121155\pi$
$212$	−36.4751	−2.50512
$213$	−3.83125	−0.262513
$214$	−16.7719	−1.14650
$215$	9.01775	0.615006
$216$	−30.6234	−2.08366
$217$	33.8937	2.30085
$218$	19.1127	1.29448
$219$	19.3274	1.30603
$220$	6.51448	0.439206
$221$	14.3956	0.968351
$222$	50.3861	3.38170
$223$	25.5584	1.71152	0.855760	−	0.517373i	$-0.173090\pi$
$223$	25.5584	1.71152	0.855760	+	0.517373i	$0.173090\pi$
$224$	19.5372	1.30539
$225$	0.0182398	0.00121599
$226$	−27.3606	−1.82000
$227$	−23.0291	−1.52849	−0.764247	−	0.644923i	$-0.776889\pi$
$227$	−23.0291	−1.52849	−0.764247	+	0.644923i	$0.776889\pi$
$228$	−35.2606	−2.33519
$229$	2.84890	0.188261	0.0941304	−	0.995560i	$-0.469993\pi$
$229$	2.84890	0.188261	0.0941304	+	0.995560i	$0.469993\pi$
$230$	−3.16283	−0.208551
$231$	13.4048	0.881972
$232$	17.5436	1.15180
$233$	28.5323	1.86921	0.934605	−	0.355686i	$-0.115753\pi$
$233$	28.5323	1.86921	0.934605	+	0.355686i	$0.115753\pi$
$234$	0.255037	0.0166723
$235$	−2.14466	−0.139902
$236$	−36.0819	−2.34873
$237$	0.204412	0.0132780
$238$	−33.6385	−2.18046
$239$	3.50969	0.227023	0.113511	−	0.993537i	$-0.463790\pi$
$239$	3.50969	0.227023	0.113511	+	0.993537i	$0.463790\pi$
$240$	−10.7705	−0.695235
$241$	22.8121	1.46945	0.734727	−	0.678363i	$-0.237310\pi$
$241$	22.8121	1.46945	0.734727	+	0.678363i	$0.237310\pi$
$242$	22.0527	1.41760
$243$	0.189551	0.0121597
$244$	7.50047	0.480169
$245$	19.5035	1.24603
$246$	6.52982	0.416326
$247$	−25.9167	−1.64904
$248$	38.9199	2.47141
$249$	16.3826	1.03821
$250$	−2.51924	−0.159331
$251$	−27.8012	−1.75480	−0.877398	−	0.479763i	$-0.840723\pi$
$251$	−27.8012	−1.75480	−0.877398	+	0.479763i	$0.840723\pi$
$252$	−0.408149	−0.0257109
$253$	1.88165	0.118298
$254$	−36.6020	−2.29661
$255$	4.50601	0.282177
$256$	−31.4592	−1.96620
$257$	−16.1111	−1.00498	−0.502491	−	0.864583i	$-0.667583\pi$
$257$	−16.1111	−1.00498	−0.502491	+	0.864583i	$0.667583\pi$
$258$	39.4680	2.45717
$259$	−59.2674	−3.68270
$260$	−24.1246	−1.49615
$261$	−0.0541297	−0.00335054
$262$	17.0543	1.05362
$263$	−7.69079	−0.474234	−0.237117	−	0.971481i	$-0.576203\pi$
$263$	−7.69079	−0.474234	−0.237117	+	0.971481i	$0.576203\pi$
$264$	15.3926	0.947351
$265$	−8.39169	−0.515497
$266$	60.5602	3.71318
$267$	31.1961	1.90917
$268$	−63.5029	−3.87906
$269$	3.64349	0.222147	0.111074	−	0.993812i	$-0.464571\pi$
$269$	3.64349	0.222147	0.111074	+	0.993812i	$0.464571\pi$
$270$	−13.0503	−0.794214
$271$	−20.5532	−1.24852	−0.624259	−	0.781218i	$-0.714599\pi$
$271$	−20.5532	−1.24852	−0.624259	+	0.781218i	$0.714599\pi$
$272$	−16.0796	−0.974970
$273$	−49.6412	−3.00442
$274$	46.9938	2.83900
$275$	1.49876	0.0903787
$276$	−9.48047	−0.570657
$277$	16.1849	0.972456	0.486228	−	0.873832i	$-0.338373\pi$
$277$	16.1849	0.972456	0.486228	+	0.873832i	$0.338373\pi$
$278$	44.6047	2.67521
$279$	−0.120085	−0.00718927
$280$	30.4337	1.81876
$281$	10.0276	0.598196	0.299098	−	0.954222i	$-0.403314\pi$
$281$	10.0276	0.598196	0.299098	+	0.954222i	$0.403314\pi$
$282$	−9.38655	−0.558961
$283$	3.50549	0.208380	0.104190	−	0.994557i	$-0.466775\pi$
$283$	3.50549	0.208380	0.104190	+	0.994557i	$0.466775\pi$
$284$	9.58541	0.568789
$285$	−8.11228	−0.480530
$286$	20.9564	1.23918
$287$	−7.68079	−0.453383
$288$	−0.0692200	−0.00407883
$289$	−10.2729	−0.604286
$290$	7.47628	0.439022
$291$	26.6598	1.56282
$292$	−48.3553	−2.82978
$293$	−1.20570	−0.0704380	−0.0352190	−	0.999380i	$-0.511213\pi$
$293$	−1.20570	−0.0704380	−0.0352190	+	0.999380i	$0.511213\pi$
$294$	85.3609	4.97835
$295$	−8.30122	−0.483316
$296$	−68.0563	−3.95569
$297$	7.76394	0.450509
$298$	−14.9597	−0.866590
$299$	−6.96819	−0.402981
$300$	−7.55134	−0.435977
$301$	−46.4248	−2.67588
$302$	14.6585	0.843500
$303$	5.36645	0.308294
$304$	28.9485	1.66031
$305$	1.72561	0.0988079
$306$	0.119180	0.00681309
$307$	−20.9436	−1.19532	−0.597659	−	0.801751i	$-0.703902\pi$
$307$	−20.9436	−1.19532	−0.597659	+	0.801751i	$0.703902\pi$
$308$	−33.5375	−1.91098
$309$	17.4544	0.992944
$310$	16.5858	0.942011
$311$	−30.0309	−1.70290	−0.851449	−	0.524437i	$-0.824276\pi$
$311$	−30.0309	−1.70290	−0.851449	+	0.524437i	$0.824276\pi$
$312$	−57.0026	−3.22713
$313$	−2.14851	−0.121441	−0.0607204	−	0.998155i	$-0.519340\pi$
$313$	−2.14851	−0.121441	−0.0607204	+	0.998155i	$0.519340\pi$
$314$	−4.97046	−0.280500
$315$	−0.0939012	−0.00529073
$316$	−0.511419	−0.0287696
$317$	−6.34033	−0.356108	−0.178054	−	0.984021i	$-0.556980\pi$
$317$	−6.34033	−0.356108	−0.178054	+	0.984021i	$0.556980\pi$
$318$	−36.7279	−2.05960
$319$	−4.44783	−0.249031
$320$	−2.83859	−0.158682
$321$	−11.5662	−0.645560
$322$	16.2827	0.907401
$323$	−12.1110	−0.673877
$324$	−39.3556	−2.18642
$325$	−5.55026	−0.307873
$326$	39.6805	2.19770
$327$	13.1804	0.728880
$328$	−8.81979	−0.486992
$329$	11.0411	0.608713
$330$	6.55962	0.361095
$331$	−9.37810	−0.515467	−0.257733	−	0.966216i	$-0.582976\pi$
$331$	−9.37810	−0.515467	−0.257733	+	0.966216i	$0.582976\pi$
$332$	−40.9877	−2.24949
$333$	0.209983	0.0115070
$334$	28.7639	1.57389
$335$	−14.6099	−0.798223
$336$	55.4484	3.02496
$337$	7.94442	0.432760	0.216380	−	0.976309i	$-0.430575\pi$
$337$	7.94442	0.432760	0.216380	+	0.976309i	$0.430575\pi$
$338$	−44.8562	−2.43985
$339$	−18.8683	−1.02478
$340$	−11.2736	−0.611397
$341$	−9.86733	−0.534346
$342$	−0.214563	−0.0116023
$343$	−64.3699	−3.47565
$344$	−53.3092	−2.87424
$345$	−2.18114	−0.117428
$346$	−31.2466	−1.67983
$347$	−7.27951	−0.390785	−0.195392	−	0.980725i	$-0.562598\pi$
$347$	−7.27951	−0.390785	−0.195392	+	0.980725i	$0.562598\pi$
$348$	22.4099	1.20130
$349$	3.79150	0.202954	0.101477	−	0.994838i	$-0.467643\pi$
$349$	3.79150	0.202954	0.101477	+	0.994838i	$0.467643\pi$
$350$	12.9694	0.693246
$351$	−28.7517	−1.53465
$352$	−5.68780	−0.303161
$353$	9.49982	0.505624	0.252812	−	0.967515i	$-0.418645\pi$
$353$	9.49982	0.505624	0.252812	+	0.967515i	$0.418645\pi$
$354$	−36.3319	−1.93102
$355$	2.20528	0.117044
$356$	−78.0495	−4.13661
$357$	−23.1976	−1.22775
$358$	−27.8185	−1.47025
$359$	14.4756	0.763993	0.381997	−	0.924164i	$-0.375237\pi$
$359$	14.4756	0.763993	0.381997	+	0.924164i	$0.375237\pi$
$360$	−0.107826	−0.00568293
$361$	2.80381	0.147569
$362$	38.6993	2.03399
$363$	15.2079	0.798208
$364$	124.197	6.50971
$365$	−11.1249	−0.582305
$366$	7.55246	0.394773
$367$	−35.8718	−1.87249	−0.936247	−	0.351344i	$-0.885725\pi$
$367$	−35.8718	−1.87249	−0.936247	+	0.351344i	$0.885725\pi$
$368$	7.78335	0.405735
$369$	0.0272129	0.00141665
$370$	−29.0024	−1.50776
$371$	43.2017	2.24292
$372$	49.7154	2.57763
$373$	12.9922	0.672713	0.336356	−	0.941735i	$-0.390805\pi$
$373$	12.9922	0.672713	0.336356	+	0.941735i	$0.390805\pi$
$374$	9.79304	0.506386
$375$	−1.73731	−0.0897142
$376$	12.6784	0.653837
$377$	16.4714	0.848318
$378$	67.1848	3.45561
$379$	6.22008	0.319504	0.159752	−	0.987157i	$-0.448931\pi$
$379$	6.22008	0.319504	0.159752	+	0.987157i	$0.448931\pi$
$380$	20.2961	1.04117
$381$	−25.2413	−1.29315
$382$	20.0927	1.02803
$383$	35.2079	1.79904	0.899520	−	0.436880i	$-0.143916\pi$
$383$	35.2079	1.79904	0.899520	+	0.436880i	$0.143916\pi$
$384$	−25.6098	−1.30689
$385$	−7.71585	−0.393236
$386$	−0.722951	−0.0367972
$387$	0.164482	0.00836109
$388$	−66.7001	−3.38619
$389$	7.63794	0.387259	0.193629	−	0.981075i	$-0.437974\pi$
$389$	7.63794	0.387259	0.193629	+	0.981075i	$0.437974\pi$
$390$	−24.2918	−1.23006
$391$	−3.25628	−0.164677
$392$	−115.296	−5.82335
$393$	11.7609	0.593259
$394$	−31.6843	−1.59623
$395$	−0.117660	−0.00592013
$396$	0.118823	0.00597106
$397$	−1.51998	−0.0762854	−0.0381427	−	0.999272i	$-0.512144\pi$
$397$	−1.51998	−0.0762854	−0.0381427	+	0.999272i	$0.512144\pi$
$398$	11.7133	0.587137
$399$	41.7633	2.09078
$400$	6.19955	0.309978
$401$	27.8375	1.39014	0.695070	−	0.718942i	$-0.255373\pi$
$401$	27.8375	1.39014	0.695070	+	0.718942i	$0.255373\pi$
$402$	−63.9430	−3.18919
$403$	36.5411	1.82024
$404$	−13.4263	−0.667984
$405$	−9.05439	−0.449916
$406$	−38.4890	−1.91018
$407$	17.2543	0.855263
$408$	−26.6377	−1.31876
$409$	14.9561	0.739530	0.369765	−	0.929125i	$-0.379438\pi$
$409$	14.9561	0.739530	0.369765	+	0.929125i	$0.379438\pi$
$410$	−3.75858	−0.185623
$411$	32.4077	1.59855
$412$	−43.6691	−2.15142
$413$	42.7360	2.10290
$414$	−0.0576893	−0.00283528
$415$	−9.42988	−0.462894
$416$	21.0633	1.03271
$417$	30.7601	1.50633
$418$	−17.6307	−0.862343
$419$	−39.1182	−1.91105	−0.955524	−	0.294914i	$-0.904709\pi$
$419$	−39.1182	−1.91105	−0.955524	+	0.294914i	$0.904709\pi$
$420$	38.8754	1.89693
$421$	16.5435	0.806279	0.403139	−	0.915139i	$-0.367919\pi$
$421$	16.5435	0.806279	0.403139	+	0.915139i	$0.367919\pi$
$422$	−67.9504	−3.30777
$423$	−0.0391182	−0.00190199
$424$	49.6081	2.40918
$425$	−2.59367	−0.125812
$426$	9.65184	0.467633
$427$	−8.88369	−0.429912
$428$	28.9374	1.39874
$429$	14.4518	0.697741
$430$	−22.7179	−1.09555
$431$	−21.5105	−1.03612	−0.518061	−	0.855343i	$-0.673346\pi$
$431$	−21.5105	−1.03612	−0.518061	+	0.855343i	$0.673346\pi$
$432$	32.1152	1.54514
$433$	0.853375	0.0410106	0.0205053	−	0.999790i	$-0.493473\pi$
$433$	0.853375	0.0410106	0.0205053	+	0.999790i	$0.493473\pi$
$434$	−85.3864	−4.09868
$435$	5.15576	0.247200
$436$	−32.9761	−1.57927
$437$	5.86236	0.280435
$438$	−48.6905	−2.32652
$439$	8.42789	0.402241	0.201121	−	0.979566i	$-0.435542\pi$
$439$	8.42789	0.402241	0.201121	+	0.979566i	$0.435542\pi$
$440$	−8.86005	−0.422386
$441$	0.355739	0.0169400
$442$	−36.2659	−1.72499
$443$	10.4539	0.496679	0.248340	−	0.968673i	$-0.420115\pi$
$443$	10.4539	0.496679	0.248340	+	0.968673i	$0.420115\pi$
$444$	−86.9338	−4.12569
$445$	−17.9566	−0.851222
$446$	−64.3879	−3.04885
$447$	−10.3164	−0.487950
$448$	14.6135	0.690422
$449$	7.84557	0.370255	0.185128	−	0.982714i	$-0.440730\pi$
$449$	7.84557	0.370255	0.185128	+	0.982714i	$0.440730\pi$
$450$	−0.0459504	−0.00216612
$451$	2.23608	0.105293
$452$	47.2066	2.22041
$453$	10.1087	0.474949
$454$	58.0158	2.72282
$455$	28.5736	1.33955
$456$	47.9564	2.24577
$457$	−32.9157	−1.53973	−0.769866	−	0.638205i	$-0.779677\pi$
$457$	−32.9157	−1.53973	−0.769866	+	0.638205i	$0.779677\pi$
$458$	−7.17708	−0.335363
$459$	−13.4358	−0.627132
$460$	5.45699	0.254433
$461$	10.5433	0.491050	0.245525	−	0.969390i	$-0.421040\pi$
$461$	10.5433	0.491050	0.245525	+	0.969390i	$0.421040\pi$
$462$	−33.7700	−1.57112
$463$	−15.1692	−0.704975	−0.352487	−	0.935817i	$-0.614664\pi$
$463$	−15.1692	−0.704975	−0.352487	+	0.935817i	$0.614664\pi$
$464$	−18.3982	−0.854116
$465$	11.4378	0.530417
$466$	−71.8796	−3.32976
$467$	−7.23586	−0.334836	−0.167418	−	0.985886i	$-0.553543\pi$
$467$	−7.23586	−0.334836	−0.167418	+	0.985886i	$0.553543\pi$
$468$	−0.440028	−0.0203403
$469$	75.2139	3.47306
$470$	5.40293	0.249218
$471$	−3.42771	−0.157941
$472$	49.0734	2.25879
$473$	13.5155	0.621442
$474$	−0.514964	−0.0236531
$475$	4.66946	0.214249
$476$	58.0382	2.66018
$477$	−0.153063	−0.00700825
$478$	−8.84174	−0.404412
$479$	−14.8903	−0.680355	−0.340178	−	0.940361i	$-0.610487\pi$
$479$	−14.8903	−0.680355	−0.340178	+	0.940361i	$0.610487\pi$
$480$	6.59309	0.300932
$481$	−63.8967	−2.91344
$482$	−57.4691	−2.61764
$483$	11.2288	0.510929
$484$	−38.0487	−1.72948
$485$	−15.3455	−0.696801
$486$	−0.477524	−0.0216609
$487$	3.47978	0.157684	0.0788420	−	0.996887i	$-0.474878\pi$
$487$	3.47978	0.157684	0.0788420	+	0.996887i	$0.474878\pi$
$488$	−10.2011	−0.461780
$489$	27.3643	1.23746
$490$	−49.1340	−2.21965
$491$	7.96411	0.359415	0.179708	−	0.983720i	$-0.442485\pi$
$491$	7.96411	0.359415	0.179708	+	0.983720i	$0.442485\pi$
$492$	−11.2662	−0.507921
$493$	7.69717	0.346663
$494$	65.2904	2.93756
$495$	0.0273371	0.00122871
$496$	−40.8158	−1.83268
$497$	−11.3531	−0.509257
$498$	−41.2717	−1.84943
$499$	−32.5746	−1.45824	−0.729120	−	0.684386i	$-0.760070\pi$
$499$	−32.5746	−1.45824	−0.729120	+	0.684386i	$0.760070\pi$
$500$	4.34657	0.194385
$501$	19.8361	0.886209
$502$	70.0379	3.12595
$503$	34.9807	1.55971	0.779856	−	0.625959i	$-0.215292\pi$
$503$	34.9807	1.55971	0.779856	+	0.625959i	$0.215292\pi$
$504$	0.555105	0.0247263
$505$	−3.08894	−0.137456
$506$	−4.74033	−0.210733
$507$	−30.9335	−1.37381
$508$	63.1512	2.80188
$509$	−36.7736	−1.62996	−0.814980	−	0.579490i	$-0.803252\pi$
$509$	−36.7736	−1.62996	−0.814980	+	0.579490i	$0.803252\pi$
$510$	−11.3517	−0.502663
$511$	57.2728	2.53360
$512$	49.7710	2.19959
$513$	24.1889	1.06797
$514$	40.5877	1.79025
$515$	−10.0468	−0.442714
$516$	−68.0961	−2.99776
$517$	−3.21434	−0.141366
$518$	149.309	6.56026
$519$	−21.5481	−0.945858
$520$	32.8108	1.43885
$521$	42.0157	1.84074	0.920370	−	0.391049i	$-0.127888\pi$
$521$	42.0157	1.84074	0.920370	+	0.391049i	$0.127888\pi$
$522$	0.136366	0.00596856
$523$	−18.3141	−0.800818	−0.400409	−	0.916336i	$-0.631132\pi$
$523$	−18.3141	−0.800818	−0.400409	+	0.916336i	$0.631132\pi$
$524$	−29.4246	−1.28542
$525$	8.94393	0.390345
$526$	19.3749	0.844788
$527$	17.0759	0.743837
$528$	−16.1425	−0.702510
$529$	−21.4238	−0.931469
$530$	21.1407	0.918292
$531$	−0.151413	−0.00657075
$532$	−104.488	−4.53011
$533$	−8.28072	−0.358678
$534$	−78.5904	−3.40094
$535$	6.65751	0.287829
$536$	86.3675	3.73051
$537$	−19.1841	−0.827853
$538$	−9.17882	−0.395727
$539$	29.2311	1.25907
$540$	22.5163	0.968946
$541$	−29.0873	−1.25056	−0.625280	−	0.780400i	$-0.715015\pi$
$541$	−29.0873	−1.25056	−0.625280	+	0.780400i	$0.715015\pi$
$542$	51.7784	2.22407
$543$	26.6876	1.14528
$544$	9.84300	0.422015
$545$	−7.58670	−0.324979
$546$	125.058	5.35199
$547$	−17.6482	−0.754584	−0.377292	−	0.926094i	$-0.623145\pi$
$547$	−17.6482	−0.754584	−0.377292	+	0.926094i	$0.623145\pi$
$548$	−81.0808	−3.46360
$549$	0.0314747	0.00134331
$550$	−3.77574	−0.160998
$551$	−13.8574	−0.590345
$552$	12.8940	0.548804
$553$	0.605734	0.0257584
$554$	−40.7736	−1.73231
$555$	−20.0005	−0.848975
$556$	−76.9587	−3.26377
$557$	22.6676	0.960458	0.480229	−	0.877143i	$-0.340554\pi$
$557$	22.6676	0.960458	0.480229	+	0.877143i	$0.340554\pi$
$558$	0.302522	0.0128068
$559$	−50.0509	−2.11693
$560$	−31.9163	−1.34871
$561$	6.75344	0.285130
$562$	−25.2619	−1.06561
$563$	36.9122	1.55566	0.777832	−	0.628473i	$-0.216320\pi$
$563$	36.9122	1.55566	0.777832	+	0.628473i	$0.216320\pi$
$564$	16.1951	0.681936
$565$	10.8606	0.456911
$566$	−8.83116	−0.371202
$567$	46.6134	1.95758
$568$	−13.0367	−0.547007
$569$	35.7955	1.50062	0.750312	−	0.661084i	$-0.229903\pi$
$569$	35.7955	1.50062	0.750312	+	0.661084i	$0.229903\pi$
$570$	20.4368	0.856003
$571$	5.31789	0.222547	0.111273	−	0.993790i	$-0.464507\pi$
$571$	5.31789	0.222547	0.111273	+	0.993790i	$0.464507\pi$
$572$	−36.1571	−1.51180
$573$	13.8562	0.578853
$574$	19.3498	0.807644
$575$	1.25547	0.0523567
$576$	−0.0517752	−0.00215730
$577$	18.0746	0.752457	0.376229	−	0.926527i	$-0.377221\pi$
$577$	18.0746	0.752457	0.376229	+	0.926527i	$0.377221\pi$
$578$	25.8798	1.07646
$579$	−0.498558	−0.0207194
$580$	−12.8992	−0.535610
$581$	48.5465	2.01405
$582$	−67.1624	−2.78397
$583$	−12.5771	−0.520892
$584$	65.7659	2.72141
$585$	−0.101236	−0.00418558
$586$	3.03746	0.125476
$587$	15.3696	0.634372	0.317186	−	0.948363i	$-0.397262\pi$
$587$	15.3696	0.634372	0.317186	+	0.948363i	$0.397262\pi$
$588$	−147.277	−6.07362
$589$	−30.7421	−1.26671
$590$	20.9128	0.860966
$591$	−21.8500	−0.898789
$592$	71.3715	2.93335
$593$	27.6247	1.13441	0.567205	−	0.823576i	$-0.308025\pi$
$593$	27.6247	1.13441	0.567205	+	0.823576i	$0.308025\pi$
$594$	−19.5592	−0.802525
$595$	13.3526	0.547405
$596$	25.8107	1.05725
$597$	8.07771	0.330599
$598$	17.5545	0.717859
$599$	3.05798	0.124946	0.0624728	−	0.998047i	$-0.480101\pi$
$599$	3.05798	0.124946	0.0624728	+	0.998047i	$0.480101\pi$
$600$	10.2702	0.419281
$601$	9.55225	0.389644	0.194822	−	0.980839i	$-0.437587\pi$
$601$	9.55225	0.389644	0.194822	+	0.980839i	$0.437587\pi$
$602$	116.955	4.76674
$603$	−0.266481	−0.0108519
$604$	−25.2910	−1.02908
$605$	−8.75371	−0.355889
$606$	−13.5194	−0.549187
$607$	19.0675	0.773927	0.386963	−	0.922095i	$-0.373524\pi$
$607$	19.0675	0.773927	0.386963	+	0.922095i	$0.373524\pi$
$608$	−17.7206	−0.718665
$609$	−26.5426	−1.07556
$610$	−4.34722	−0.176014
$611$	11.9035	0.481562
$612$	−0.205628	−0.00831202
$613$	−19.6124	−0.792137	−0.396068	−	0.918221i	$-0.629626\pi$
$613$	−19.6124	−0.792137	−0.396068	+	0.918221i	$0.629626\pi$
$614$	52.7621	2.12930
$615$	−2.59198	−0.104519
$616$	45.6129	1.83780
$617$	−19.8107	−0.797549	−0.398775	−	0.917049i	$-0.630564\pi$
$617$	−19.8107	−0.797549	−0.398775	+	0.917049i	$0.630564\pi$
$618$	−43.9717	−1.76880
$619$	15.2080	0.611260	0.305630	−	0.952150i	$-0.401133\pi$
$619$	15.2080	0.611260	0.305630	+	0.952150i	$0.401133\pi$
$620$	−28.6164	−1.14926
$621$	6.50363	0.260982
$622$	75.6552	3.03350
$623$	92.4431	3.70365
$624$	59.7793	2.39309
$625$	1.00000	0.0400000
$626$	5.41260	0.216331
$627$	−12.1584	−0.485559
$628$	8.57579	0.342211
$629$	−29.8593	−1.19057
$630$	0.236560	0.00942477
$631$	43.5896	1.73527	0.867637	−	0.497198i	$-0.165638\pi$
$631$	43.5896	1.73527	0.867637	+	0.497198i	$0.165638\pi$
$632$	0.695559	0.0276678
$633$	−46.8597	−1.86250
$634$	15.9728	0.634361
$635$	14.5290	0.576564
$636$	63.3684	2.51272
$637$	−108.249	−4.28900
$638$	11.2052	0.443616
$639$	0.0402238	0.00159123
$640$	14.7411	0.582693
$641$	−6.85324	−0.270687	−0.135343	−	0.990799i	$-0.543214\pi$
$641$	−6.85324	−0.270687	−0.135343	+	0.990799i	$0.543214\pi$
$642$	29.1379	1.14998
$643$	−45.2395	−1.78407	−0.892035	−	0.451966i	$-0.850723\pi$
$643$	−45.2395	−1.78407	−0.892035	+	0.451966i	$0.850723\pi$
$644$	−28.0934	−1.10704
$645$	−15.6666	−0.616873
$646$	30.5106	1.20043
$647$	−5.24149	−0.206064	−0.103032	−	0.994678i	$-0.532854\pi$
$647$	−5.24149	−0.206064	−0.103032	+	0.994678i	$0.532854\pi$
$648$	53.5258	2.10269
$649$	−12.4416	−0.488374
$650$	13.9825	0.548437
$651$	−58.8838	−2.30784
$652$	−68.4627	−2.68121
$653$	25.3428	0.991739	0.495869	−	0.868397i	$-0.334850\pi$
$653$	25.3428	0.991739	0.495869	+	0.868397i	$0.334850\pi$
$654$	−33.2047	−1.29841
$655$	−6.76961	−0.264510
$656$	9.24943	0.361130
$657$	−0.202916	−0.00791652
$658$	−27.8151	−1.08435
$659$	−7.73809	−0.301433	−0.150717	−	0.988577i	$-0.548158\pi$
$659$	−7.73809	−0.301433	−0.150717	+	0.988577i	$0.548158\pi$
$660$	−11.3177	−0.440539
$661$	−31.9013	−1.24082	−0.620409	−	0.784279i	$-0.713033\pi$
$661$	−31.9013	−1.24082	−0.620409	+	0.784279i	$0.713033\pi$
$662$	23.6257	0.918239
$663$	−25.0096	−0.971291
$664$	55.7455	2.16334
$665$	−24.0391	−0.932195
$666$	−0.528998	−0.0204983
$667$	−3.72582	−0.144264
$668$	−49.6278	−1.92016
$669$	−44.4029	−1.71672
$670$	36.8058	1.42193
$671$	2.58627	0.0998419
$672$	−33.9422	−1.30935
$673$	−38.1816	−1.47179	−0.735896	−	0.677094i	$-0.763239\pi$
$673$	−38.1816	−1.47179	−0.735896	+	0.677094i	$0.763239\pi$
$674$	−20.0139	−0.770906
$675$	5.18024	0.199387
$676$	77.3926	2.97664
$677$	34.4757	1.32501	0.662505	−	0.749057i	$-0.269493\pi$
$677$	34.4757	1.32501	0.662505	+	0.749057i	$0.269493\pi$
$678$	47.5338	1.82552
$679$	79.0008	3.03177
$680$	15.3327	0.587983
$681$	40.0086	1.53313
$682$	24.8582	0.951869
$683$	13.7480	0.526053	0.263027	−	0.964789i	$-0.415279\pi$
$683$	13.7480	0.526053	0.263027	+	0.964789i	$0.415279\pi$
$684$	0.370197	0.0141548
$685$	−18.6539	−0.712731
$686$	162.163	6.19142
$687$	−4.94942	−0.188832
$688$	55.9061	2.13140
$689$	46.5761	1.77441
$690$	5.49481	0.209184
$691$	−0.759840	−0.0289057	−0.0144528	−	0.999896i	$-0.504601\pi$
$691$	−0.759840	−0.0289057	−0.0144528	+	0.999896i	$0.504601\pi$
$692$	53.9113	2.04940
$693$	−0.140735	−0.00534610
$694$	18.3388	0.696133
$695$	−17.7056	−0.671611
$696$	−30.4787	−1.15529
$697$	−3.86964	−0.146573
$698$	−9.55170	−0.361537
$699$	−49.5693	−1.87488
$700$	−22.3768	−0.845765
$701$	9.20642	0.347722	0.173861	−	0.984770i	$-0.444376\pi$
$701$	9.20642	0.347722	0.173861	+	0.984770i	$0.444376\pi$
$702$	72.4324	2.73378
$703$	53.7565	2.02746
$704$	−4.25436	−0.160342
$705$	3.72594	0.140327
$706$	−23.9323	−0.900705
$707$	15.9024	0.598070
$708$	62.6854	2.35586
$709$	7.88236	0.296028	0.148014	−	0.988985i	$-0.452712\pi$
$709$	7.88236	0.296028	0.148014	+	0.988985i	$0.452712\pi$
$710$	−5.55563	−0.208499
$711$	−0.00214610	−8.04850e−5 0
$712$	106.152	3.97820
$713$	−8.26558	−0.309549
$714$	58.4404	2.18708
$715$	−8.31852	−0.311095
$716$	47.9966	1.79372
$717$	−6.09740	−0.227712
$718$	−36.4675	−1.36096
$719$	43.4286	1.61961	0.809807	−	0.586696i	$-0.199572\pi$
$719$	43.4286	1.61961	0.809807	+	0.586696i	$0.199572\pi$
$720$	0.113079	0.00421419
$721$	51.7224	1.92624
$722$	−7.06348	−0.262876
$723$	−39.6316	−1.47391
$724$	−66.7698	−2.48148
$725$	−2.96767	−0.110217
$726$	−38.3124	−1.42191
$727$	10.4078	0.386003	0.193002	−	0.981198i	$-0.438178\pi$
$727$	10.4078	0.386003	0.193002	+	0.981198i	$0.438178\pi$
$728$	−168.915	−6.26042
$729$	26.8339	0.993846
$730$	28.0264	1.03730
$731$	−23.3891	−0.865078
$732$	−13.0306	−0.481626
$733$	−16.8278	−0.621547	−0.310774	−	0.950484i	$-0.600588\pi$
$733$	−16.8278	−0.621547	−0.310774	+	0.950484i	$0.600588\pi$
$734$	90.3697	3.33561
$735$	−33.8836	−1.24981
$736$	−4.76451	−0.175622
$737$	−21.8967	−0.806576
$738$	−0.0685558	−0.00252357
$739$	−22.1330	−0.814177	−0.407088	−	0.913389i	$-0.633456\pi$
$739$	−22.1330	−0.814177	−0.407088	+	0.913389i	$0.633456\pi$
$740$	50.0393	1.83948
$741$	45.0253	1.65405
$742$	−108.835	−3.99547
$743$	−6.93513	−0.254425	−0.127213	−	0.991875i	$-0.540603\pi$
$743$	−6.93513	−0.254425	−0.127213	+	0.991875i	$0.540603\pi$
$744$	−67.6158	−2.47891
$745$	5.93816	0.217557
$746$	−32.7306	−1.19835
$747$	−0.171999	−0.00629311
$748$	−16.8964	−0.617795
$749$	−34.2739	−1.25234
$750$	4.37670	0.159814
$751$	−3.76795	−0.137495	−0.0687473	−	0.997634i	$-0.521900\pi$
$751$	−3.76795	−0.137495	−0.0687473	+	0.997634i	$0.521900\pi$
$752$	−13.2960	−0.484854
$753$	48.2993	1.76012
$754$	−41.4953	−1.51117
$755$	−5.81861	−0.211761
$756$	−115.917	−4.21587
$757$	31.8436	1.15738	0.578688	−	0.815549i	$-0.303565\pi$
$757$	31.8436	1.15738	0.578688	+	0.815549i	$0.303565\pi$
$758$	−15.6699	−0.569156
$759$	−3.26900	−0.118657
$760$	−27.6039	−1.00130
$761$	31.1249	1.12828	0.564139	−	0.825680i	$-0.309208\pi$
$761$	31.1249	1.12828	0.564139	+	0.825680i	$0.309208\pi$
$762$	63.5889	2.30358
$763$	39.0575	1.41398
$764$	−34.6669	−1.25421
$765$	−0.0473081	−0.00171043
$766$	−88.6972	−3.20476
$767$	46.0740	1.66364
$768$	54.6543	1.97217
$769$	25.9026	0.934070	0.467035	−	0.884239i	$-0.345322\pi$
$769$	25.9026	0.934070	0.467035	+	0.884239i	$0.345322\pi$
$770$	19.4381	0.700500
$771$	27.9899	1.00803
$772$	1.24734	0.0448929
$773$	18.3208	0.658953	0.329476	−	0.944164i	$-0.393128\pi$
$773$	18.3208	0.658953	0.329476	+	0.944164i	$0.393128\pi$
$774$	−0.414370	−0.0148942
$775$	−6.58366	−0.236492
$776$	90.7159	3.25651
$777$	102.966	3.69388
$778$	−19.2418	−0.689852
$779$	6.96660	0.249604
$780$	41.9119	1.50069
$781$	3.30519	0.118269
$782$	8.20335	0.293351
$783$	−15.3732	−0.549395
$784$	120.913	4.31832
$785$	1.97300	0.0704194
$786$	−29.6285	−1.05681
$787$	−1.36139	−0.0485285	−0.0242642	−	0.999706i	$-0.507724\pi$
$787$	−1.36139	−0.0485285	−0.0242642	+	0.999706i	$0.507724\pi$
$788$	54.6665	1.94741
$789$	13.3613	0.475674
$790$	0.296415	0.0105460
$791$	−55.9123	−1.98801
$792$	−0.161605	−0.00574240
$793$	−9.57757	−0.340109
$794$	3.82919	0.135893
$795$	14.5789	0.517062
$796$	−20.2096	−0.716311
$797$	−0.955825	−0.0338571	−0.0169285	−	0.999857i	$-0.505389\pi$
$797$	−0.955825	−0.0338571	−0.0169285	+	0.999857i	$0.505389\pi$
$798$	−105.212	−3.72446
$799$	5.56256	0.196789
$800$	−3.79500	−0.134174
$801$	−0.327524	−0.0115725
$802$	−70.1295	−2.47636
$803$	−16.6736	−0.588399
$804$	110.324	3.89083
$805$	−6.46335	−0.227803
$806$	−92.0557	−3.24252
$807$	−6.32986	−0.222822
$808$	18.2605	0.642404
$809$	−15.4375	−0.542752	−0.271376	−	0.962473i	$-0.587479\pi$
$809$	−15.4375	−0.542752	−0.271376	+	0.962473i	$0.587479\pi$
$810$	22.8102	0.801468
$811$	−11.7026	−0.410934	−0.205467	−	0.978664i	$-0.565871\pi$
$811$	−11.7026	−0.410934	−0.205467	+	0.978664i	$0.565871\pi$
$812$	66.4070	2.33043
$813$	35.7072	1.25231
$814$	−43.4677	−1.52354
$815$	−15.7510	−0.551732
$816$	27.9353	0.977930
$817$	42.1080	1.47317
$818$	−37.6779	−1.31738
$819$	0.521177	0.0182114
$820$	6.48488	0.226462
$821$	1.73635	0.0605991	0.0302996	−	0.999541i	$-0.490354\pi$
$821$	1.73635	0.0605991	0.0302996	+	0.999541i	$0.490354\pi$
$822$	−81.6427	−2.84762
$823$	−42.1245	−1.46837	−0.734184	−	0.678950i	$-0.762435\pi$
$823$	−42.1245	−1.46837	−0.734184	+	0.678950i	$0.762435\pi$
$824$	59.3924	2.06903
$825$	−2.60381	−0.0906530
$826$	−107.662	−3.74605
$827$	21.4627	0.746330	0.373165	−	0.927765i	$-0.378273\pi$
$827$	21.4627	0.746330	0.373165	+	0.927765i	$0.378273\pi$
$828$	0.0995343	0.00345906
$829$	−21.4225	−0.744034	−0.372017	−	0.928226i	$-0.621334\pi$
$829$	−21.4225	−0.744034	−0.372017	+	0.928226i	$0.621334\pi$
$830$	23.7561	0.824587
$831$	−28.1181	−0.975407
$832$	15.7549	0.546203
$833$	−50.5857	−1.75269
$834$	−77.4920	−2.68333
$835$	−11.4177	−0.395126
$836$	30.4191	1.05206
$837$	−34.1049	−1.17884
$838$	98.5481	3.40429
$839$	−44.3450	−1.53096	−0.765479	−	0.643461i	$-0.777498\pi$
$839$	−44.3450	−1.53096	−0.765479	+	0.643461i	$0.777498\pi$
$840$	−52.8728	−1.82428
$841$	−20.1929	−0.696308
$842$	−41.6769	−1.43628
$843$	−17.4210	−0.600012
$844$	117.238	4.03551
$845$	17.8054	0.612526
$846$	0.0985482	0.00338816
$847$	45.0655	1.54847
$848$	−52.0247	−1.78654
$849$	−6.09011	−0.209012
$850$	6.53409	0.224117
$851$	14.4534	0.495457
$852$	−16.6528	−0.570516
$853$	−11.6413	−0.398591	−0.199296	−	0.979939i	$-0.563865\pi$
$853$	−11.6413	−0.398591	−0.199296	+	0.979939i	$0.563865\pi$
$854$	22.3801	0.765833
$855$	0.0851699	0.00291275
$856$	−39.3564	−1.34518
$857$	37.9736	1.29715	0.648576	−	0.761150i	$-0.275365\pi$
$857$	37.9736	1.29715	0.648576	+	0.761150i	$0.275365\pi$
$858$	−36.4076	−1.24294
$859$	−50.5332	−1.72417	−0.862086	−	0.506762i	$-0.830842\pi$
$859$	−50.5332	−1.72417	−0.862086	+	0.506762i	$0.830842\pi$
$860$	39.1963	1.33658
$861$	13.3439	0.454759
$862$	54.1900	1.84572
$863$	40.6994	1.38542	0.692711	−	0.721215i	$-0.256416\pi$
$863$	40.6994	1.38542	0.692711	+	0.721215i	$0.256416\pi$
$864$	−19.6590	−0.668813
$865$	12.4032	0.421720
$866$	−2.14986	−0.0730551
$867$	17.8471	0.606120
$868$	147.321	5.00041
$869$	−0.176345	−0.00598209
$870$	−12.9886	−0.440355
$871$	81.0887	2.74759
$872$	44.8494	1.51879
$873$	−0.279898	−0.00947311
$874$	−14.7687	−0.499558
$875$	−5.14815	−0.174039
$876$	84.0081	2.83837
$877$	−4.56054	−0.153999	−0.0769993	−	0.997031i	$-0.524534\pi$
$877$	−4.56054	−0.153999	−0.0769993	+	0.997031i	$0.524534\pi$
$878$	−21.2319	−0.716542
$879$	2.09468	0.0706518
$880$	9.29165	0.313221
$881$	−14.3939	−0.484942	−0.242471	−	0.970159i	$-0.577958\pi$
$881$	−14.3939	−0.484942	−0.242471	+	0.970159i	$0.577958\pi$
$882$	−0.896193	−0.0301764
$883$	56.8544	1.91330	0.956651	−	0.291238i	$-0.0940671\pi$
$883$	56.8544	1.91330	0.956651	+	0.291238i	$0.0940671\pi$
$884$	62.5714	2.10451
$885$	14.4218	0.484783
$886$	−26.3359	−0.884771
$887$	−49.9388	−1.67678	−0.838391	−	0.545069i	$-0.816503\pi$
$887$	−49.9388	−1.67678	−0.838391	+	0.545069i	$0.816503\pi$
$888$	118.235	3.96770
$889$	−74.7974	−2.50862
$890$	45.2369	1.51634
$891$	−13.5704	−0.454624
$892$	111.092	3.71962
$893$	−10.0144	−0.335120
$894$	25.9895	0.869220
$895$	11.0424	0.369107
$896$	−75.8894	−2.53529
$897$	12.1059	0.404204
$898$	−19.7649	−0.659563
$899$	19.5381	0.651633
$900$	0.0792806	0.00264269
$901$	21.7653	0.725107
$902$	−5.63322	−0.187566
$903$	80.6542	2.68400
$904$	−64.2036	−2.13538
$905$	−15.3615	−0.510633
$906$	−25.4663	−0.846061
$907$	−47.9971	−1.59372	−0.796859	−	0.604165i	$-0.793507\pi$
$907$	−47.9971	−1.59372	−0.796859	+	0.604165i	$0.793507\pi$
$908$	−100.098	−3.32186
$909$	−0.0563417	−0.00186873
$910$	−71.9838	−2.38624
$911$	−16.0865	−0.532970	−0.266485	−	0.963839i	$-0.585862\pi$
$911$	−16.0865	−0.532970	−0.266485	+	0.963839i	$0.585862\pi$
$912$	−50.2925	−1.66535
$913$	−14.1331	−0.467738
$914$	82.9226	2.74284
$915$	−2.99791	−0.0991078
$916$	12.3830	0.409145
$917$	34.8510	1.15088
$918$	33.8481	1.11715
$919$	−16.7174	−0.551456	−0.275728	−	0.961236i	$-0.588919\pi$
$919$	−16.7174	−0.551456	−0.275728	+	0.961236i	$0.588919\pi$
$920$	−7.42181	−0.244690
$921$	36.3856	1.19895
$922$	−26.5611	−0.874742
$923$	−12.2399	−0.402881
$924$	58.2650	1.91678
$925$	11.5124	0.378524
$926$	38.2150	1.25582
$927$	−0.183251	−0.00601876
$928$	11.2623	0.369703
$929$	13.0869	0.429368	0.214684	−	0.976684i	$-0.431128\pi$
$929$	13.0869	0.429368	0.214684	+	0.976684i	$0.431128\pi$
$930$	−28.8147	−0.944871
$931$	91.0707	2.98472
$932$	124.018	4.06233
$933$	52.1730	1.70807
$934$	18.2289	0.596467
$935$	−3.88730	−0.127128
$936$	0.598463	0.0195614
$937$	23.2606	0.759891	0.379945	−	0.925009i	$-0.375943\pi$
$937$	23.2606	0.759891	0.379945	+	0.925009i	$0.375943\pi$
$938$	−189.482	−6.18681
$939$	3.73262	0.121809
$940$	−9.32194	−0.304048
$941$	−5.97362	−0.194734	−0.0973672	−	0.995249i	$-0.531042\pi$
$941$	−5.97362	−0.194734	−0.0973672	+	0.995249i	$0.531042\pi$
$942$	8.63523	0.281351
$943$	1.87310	0.0609965
$944$	−51.4639	−1.67501
$945$	−26.6687	−0.867531
$946$	−34.0487	−1.10702
$947$	12.6464	0.410953	0.205477	−	0.978662i	$-0.434126\pi$
$947$	12.6464	0.410953	0.205477	+	0.978662i	$0.434126\pi$
$948$	0.888493	0.0288569
$949$	61.7463	2.00437
$950$	−11.7635	−0.381658
$951$	11.0151	0.357189
$952$	−78.9352	−2.55830
$953$	−25.2773	−0.818812	−0.409406	−	0.912352i	$-0.634264\pi$
$953$	−25.2773	−0.818812	−0.409406	+	0.912352i	$0.634264\pi$
$954$	0.385601	0.0124843
$955$	−7.97570	−0.258087
$956$	15.2551	0.493385
$957$	7.72725	0.249787
$958$	37.5123	1.21197
$959$	96.0334	3.10108
$960$	4.93150	0.159163
$961$	12.3446	0.398212
$962$	160.971	5.18992
$963$	0.121432	0.00391308
$964$	99.1543	3.19355
$965$	0.286972	0.00923794
$966$	−28.2881	−0.910156
$967$	19.2151	0.617915	0.308957	−	0.951076i	$-0.400020\pi$
$967$	19.2151	0.617915	0.308957	+	0.951076i	$0.400020\pi$
$968$	51.7483	1.66325
$969$	21.0406	0.675922
$970$	38.6589	1.24126
$971$	19.0233	0.610485	0.305243	−	0.952275i	$-0.401262\pi$
$971$	19.0233	0.610485	0.305243	+	0.952275i	$0.401262\pi$
$972$	0.823896	0.0264265
$973$	91.1511	2.92217
$974$	−8.76640	−0.280894
$975$	9.64252	0.308808
$976$	10.6980	0.342434
$977$	−20.3813	−0.652057	−0.326028	−	0.945360i	$-0.605711\pi$
$977$	−20.3813	−0.652057	−0.326028	+	0.945360i	$0.605711\pi$
$978$	−68.9372	−2.20437
$979$	−26.9126	−0.860130
$980$	84.7733	2.70798
$981$	−0.138380	−0.00441813
$982$	−20.0635	−0.640252
$983$	−1.48484	−0.0473592	−0.0236796	−	0.999720i	$-0.507538\pi$
$983$	−1.48484	−0.0473592	−0.0236796	+	0.999720i	$0.507538\pi$
$984$	15.3227	0.488470
$985$	12.5769	0.400734
$986$	−19.3910	−0.617536
$987$	−19.1817	−0.610561
$988$	−112.649	−3.58384
$989$	11.3215	0.360003
$990$	−0.0688687	−0.00218879
$991$	−29.5152	−0.937582	−0.468791	−	0.883309i	$-0.655310\pi$
$991$	−29.5152	−0.937582	−0.468791	+	0.883309i	$0.655310\pi$
$992$	24.9850	0.793274
$993$	16.2926	0.517032
$994$	28.6012	0.907176
$995$	−4.64955	−0.147401
$996$	71.2082	2.25632
$997$	−33.6203	−1.06476	−0.532382	−	0.846504i	$-0.678703\pi$
$997$	−33.6203	−1.06476	−0.532382	+	0.846504i	$0.678703\pi$
$998$	82.0633	2.59767
$999$	59.6368	1.88682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.12	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.12	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51924 q^{2} -1.73731 q^{3} +4.34657 q^{4} +1.00000 q^{5} +4.37670 q^{6} -5.14815 q^{7} -5.91158 q^{8} +0.0182398 q^{9} +O(q^{10})\)	\(q-2.51924 q^{2} -1.73731 q^{3} +4.34657 q^{4} +1.00000 q^{5} +4.37670 q^{6} -5.14815 q^{7} -5.91158 q^{8} +0.0182398 q^{9} -2.51924 q^{10} +1.49876 q^{11} -7.55134 q^{12} -5.55026 q^{13} +12.9694 q^{14} -1.73731 q^{15} +6.19955 q^{16} -2.59367 q^{17} -0.0459504 q^{18} +4.66946 q^{19} +4.34657 q^{20} +8.94393 q^{21} -3.77574 q^{22} +1.25547 q^{23} +10.2702 q^{24} +1.00000 q^{25} +13.9825 q^{26} +5.18024 q^{27} -22.3768 q^{28} -2.96767 q^{29} +4.37670 q^{30} -6.58366 q^{31} -3.79500 q^{32} -2.60381 q^{33} +6.53409 q^{34} -5.14815 q^{35} +0.0792806 q^{36} +11.5124 q^{37} -11.7635 q^{38} +9.64252 q^{39} -5.91158 q^{40} +1.49195 q^{41} -22.5319 q^{42} +9.01775 q^{43} +6.51448 q^{44} +0.0182398 q^{45} -3.16283 q^{46} -2.14466 q^{47} -10.7705 q^{48} +19.5035 q^{49} -2.51924 q^{50} +4.50601 q^{51} -24.1246 q^{52} -8.39169 q^{53} -13.0503 q^{54} +1.49876 q^{55} +30.4337 q^{56} -8.11228 q^{57} +7.47628 q^{58} -8.30122 q^{59} -7.55134 q^{60} +1.72561 q^{61} +16.5858 q^{62} -0.0939012 q^{63} -2.83859 q^{64} -5.55026 q^{65} +6.55962 q^{66} -14.6099 q^{67} -11.2736 q^{68} -2.18114 q^{69} +12.9694 q^{70} +2.20528 q^{71} -0.107826 q^{72} -11.1249 q^{73} -29.0024 q^{74} -1.73731 q^{75} +20.2961 q^{76} -7.71585 q^{77} -24.2918 q^{78} -0.117660 q^{79} +6.19955 q^{80} -9.05439 q^{81} -3.75858 q^{82} -9.42988 q^{83} +38.8754 q^{84} -2.59367 q^{85} -22.7179 q^{86} +5.15576 q^{87} -8.86005 q^{88} -17.9566 q^{89} -0.0459504 q^{90} +28.5736 q^{91} +5.45699 q^{92} +11.4378 q^{93} +5.40293 q^{94} +4.66946 q^{95} +6.59309 q^{96} -15.3455 q^{97} -49.1340 q^{98} +0.0273371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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