LMFDB - Embedded newform 8030.2.a.v.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.216637.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + x - 2 $ x^5 - 2x^4 - 4x^3 + 7*x^2 + x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.85769$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.34993 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34993 q^{6} +1.63877 q^{7} +1.00000 q^{8} -1.17768 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.34993 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34993 q^{6} +1.63877 q^{7} +1.00000 q^{8} -1.17768 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.34993 q^{12} +2.32855 q^{13} +1.63877 q^{14} -1.34993 q^{15} +1.00000 q^{16} -4.38296 q^{17} -1.17768 q^{18} -2.37005 q^{19} +1.00000 q^{20} -2.21223 q^{21} +1.00000 q^{22} -3.15321 q^{23} -1.34993 q^{24} +1.00000 q^{25} +2.32855 q^{26} +5.63959 q^{27} +1.63877 q^{28} -6.28423 q^{29} -1.34993 q^{30} -2.49024 q^{31} +1.00000 q^{32} -1.34993 q^{33} -4.38296 q^{34} +1.63877 q^{35} -1.17768 q^{36} +6.14192 q^{37} -2.37005 q^{38} -3.14339 q^{39} +1.00000 q^{40} -12.1951 q^{41} -2.21223 q^{42} +7.75536 q^{43} +1.00000 q^{44} -1.17768 q^{45} -3.15321 q^{46} -4.50542 q^{47} -1.34993 q^{48} -4.31443 q^{49} +1.00000 q^{50} +5.91671 q^{51} +2.32855 q^{52} -7.19906 q^{53} +5.63959 q^{54} +1.00000 q^{55} +1.63877 q^{56} +3.19941 q^{57} -6.28423 q^{58} +6.79507 q^{59} -1.34993 q^{60} -7.93430 q^{61} -2.49024 q^{62} -1.92995 q^{63} +1.00000 q^{64} +2.32855 q^{65} -1.34993 q^{66} -13.8825 q^{67} -4.38296 q^{68} +4.25663 q^{69} +1.63877 q^{70} -7.90662 q^{71} -1.17768 q^{72} +1.00000 q^{73} +6.14192 q^{74} -1.34993 q^{75} -2.37005 q^{76} +1.63877 q^{77} -3.14339 q^{78} +6.82527 q^{79} +1.00000 q^{80} -4.08003 q^{81} -12.1951 q^{82} +0.433489 q^{83} -2.21223 q^{84} -4.38296 q^{85} +7.75536 q^{86} +8.48329 q^{87} +1.00000 q^{88} +9.07813 q^{89} -1.17768 q^{90} +3.81597 q^{91} -3.15321 q^{92} +3.36165 q^{93} -4.50542 q^{94} -2.37005 q^{95} -1.34993 q^{96} -0.217397 q^{97} -4.31443 q^{98} -1.17768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - 7 q^{13} - 8 q^{14} - 5 q^{15} + 5 q^{16} - 3 q^{17} + 4 q^{18} + 4 q^{19} + 5 q^{20} - 3 q^{21} + 5 q^{22} - 3 q^{23} - 5 q^{24} + 5 q^{25} - 7 q^{26} - 11 q^{27} - 8 q^{28} - 12 q^{29} - 5 q^{30} - q^{31} + 5 q^{32} - 5 q^{33} - 3 q^{34} - 8 q^{35} + 4 q^{36} + 4 q^{38} + 8 q^{39} + 5 q^{40} + q^{41} - 3 q^{42} + 5 q^{44} + 4 q^{45} - 3 q^{46} - 17 q^{47} - 5 q^{48} + 13 q^{49} + 5 q^{50} + 23 q^{51} - 7 q^{52} - 43 q^{53} - 11 q^{54} + 5 q^{55} - 8 q^{56} - 29 q^{57} - 12 q^{58} - 9 q^{59} - 5 q^{60} - 22 q^{61} - q^{62} + 25 q^{63} + 5 q^{64} - 7 q^{65} - 5 q^{66} - 9 q^{67} - 3 q^{68} + q^{69} - 8 q^{70} - 34 q^{71} + 4 q^{72} + 5 q^{73} - 5 q^{75} + 4 q^{76} - 8 q^{77} + 8 q^{78} - 24 q^{79} + 5 q^{80} + 25 q^{81} + q^{82} - 5 q^{83} - 3 q^{84} - 3 q^{85} + 30 q^{87} + 5 q^{88} + 58 q^{89} + 4 q^{90} - 9 q^{91} - 3 q^{92} - 32 q^{93} - 17 q^{94} + 4 q^{95} - 5 q^{96} + 13 q^{97} + 13 q^{98} + 4 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + 5 * q^11 - 5 * q^12 - 7 * q^13 - 8 * q^14 - 5 * q^15 + 5 * q^16 - 3 * q^17 + 4 * q^18 + 4 * q^19 + 5 * q^20 - 3 * q^21 + 5 * q^22 - 3 * q^23 - 5 * q^24 + 5 * q^25 - 7 * q^26 - 11 * q^27 - 8 * q^28 - 12 * q^29 - 5 * q^30 - q^31 + 5 * q^32 - 5 * q^33 - 3 * q^34 - 8 * q^35 + 4 * q^36 + 4 * q^38 + 8 * q^39 + 5 * q^40 + q^41 - 3 * q^42 + 5 * q^44 + 4 * q^45 - 3 * q^46 - 17 * q^47 - 5 * q^48 + 13 * q^49 + 5 * q^50 + 23 * q^51 - 7 * q^52 - 43 * q^53 - 11 * q^54 + 5 * q^55 - 8 * q^56 - 29 * q^57 - 12 * q^58 - 9 * q^59 - 5 * q^60 - 22 * q^61 - q^62 + 25 * q^63 + 5 * q^64 - 7 * q^65 - 5 * q^66 - 9 * q^67 - 3 * q^68 + q^69 - 8 * q^70 - 34 * q^71 + 4 * q^72 + 5 * q^73 - 5 * q^75 + 4 * q^76 - 8 * q^77 + 8 * q^78 - 24 * q^79 + 5 * q^80 + 25 * q^81 + q^82 - 5 * q^83 - 3 * q^84 - 3 * q^85 + 30 * q^87 + 5 * q^88 + 58 * q^89 + 4 * q^90 - 9 * q^91 - 3 * q^92 - 32 * q^93 - 17 * q^94 + 4 * q^95 - 5 * q^96 + 13 * q^97 + 13 * q^98 + 4 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.34993	−0.779384	−0.389692	−	0.920945i	$-0.627419\pi$
$3$	−1.34993	−0.779384	−0.389692	+	0.920945i	$0.627419\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.34993	−0.551108
$7$	1.63877	0.619397	0.309699	−	0.950835i	$-0.399772\pi$
$7$	1.63877	0.619397	0.309699	+	0.950835i	$0.399772\pi$
$8$	1.00000	0.353553
$9$	−1.17768	−0.392560
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.34993	−0.389692
$13$	2.32855	0.645825	0.322912	−	0.946429i	$-0.395338\pi$
$13$	2.32855	0.645825	0.322912	+	0.946429i	$0.395338\pi$
$14$	1.63877	0.437980
$15$	−1.34993	−0.348551
$16$	1.00000	0.250000
$17$	−4.38296	−1.06302	−0.531512	−	0.847051i	$-0.678376\pi$
$17$	−4.38296	−1.06302	−0.531512	+	0.847051i	$0.678376\pi$
$18$	−1.17768	−0.277582
$19$	−2.37005	−0.543727	−0.271864	−	0.962336i	$-0.587640\pi$
$19$	−2.37005	−0.543727	−0.271864	+	0.962336i	$0.587640\pi$
$20$	1.00000	0.223607
$21$	−2.21223	−0.482748
$22$	1.00000	0.213201
$23$	−3.15321	−0.657490	−0.328745	−	0.944419i	$-0.606626\pi$
$23$	−3.15321	−0.657490	−0.328745	+	0.944419i	$0.606626\pi$
$24$	−1.34993	−0.275554
$25$	1.00000	0.200000
$26$	2.32855	0.456667
$27$	5.63959	1.08534
$28$	1.63877	0.309699
$29$	−6.28423	−1.16695	−0.583476	−	0.812130i	$-0.698308\pi$
$29$	−6.28423	−1.16695	−0.583476	+	0.812130i	$0.698308\pi$
$30$	−1.34993	−0.246463
$31$	−2.49024	−0.447260	−0.223630	−	0.974674i	$-0.571791\pi$
$31$	−2.49024	−0.447260	−0.223630	+	0.974674i	$0.571791\pi$
$32$	1.00000	0.176777
$33$	−1.34993	−0.234993
$34$	−4.38296	−0.751672
$35$	1.63877	0.277003
$36$	−1.17768	−0.196280
$37$	6.14192	1.00972	0.504862	−	0.863200i	$-0.331543\pi$
$37$	6.14192	1.00972	0.504862	+	0.863200i	$0.331543\pi$
$38$	−2.37005	−0.384473
$39$	−3.14339	−0.503346
$40$	1.00000	0.158114
$41$	−12.1951	−1.90455	−0.952275	−	0.305243i	$-0.901262\pi$
$41$	−12.1951	−1.90455	−0.952275	+	0.305243i	$0.901262\pi$
$42$	−2.21223	−0.341355
$43$	7.75536	1.18268	0.591340	−	0.806422i	$-0.298599\pi$
$43$	7.75536	1.18268	0.591340	+	0.806422i	$0.298599\pi$
$44$	1.00000	0.150756
$45$	−1.17768	−0.175558
$46$	−3.15321	−0.464916
$47$	−4.50542	−0.657182	−0.328591	−	0.944472i	$-0.606574\pi$
$47$	−4.50542	−0.657182	−0.328591	+	0.944472i	$0.606574\pi$
$48$	−1.34993	−0.194846
$49$	−4.31443	−0.616347
$50$	1.00000	0.141421
$51$	5.91671	0.828505
$52$	2.32855	0.322912
$53$	−7.19906	−0.988867	−0.494433	−	0.869215i	$-0.664624\pi$
$53$	−7.19906	−0.988867	−0.494433	+	0.869215i	$0.664624\pi$
$54$	5.63959	0.767451
$55$	1.00000	0.134840
$56$	1.63877	0.218990
$57$	3.19941	0.423773
$58$	−6.28423	−0.825160
$59$	6.79507	0.884643	0.442321	−	0.896857i	$-0.354155\pi$
$59$	6.79507	0.884643	0.442321	+	0.896857i	$0.354155\pi$
$60$	−1.34993	−0.174276
$61$	−7.93430	−1.01588	−0.507941	−	0.861392i	$-0.669593\pi$
$61$	−7.93430	−1.01588	−0.507941	+	0.861392i	$0.669593\pi$
$62$	−2.49024	−0.316260
$63$	−1.92995	−0.243151
$64$	1.00000	0.125000
$65$	2.32855	0.288822
$66$	−1.34993	−0.166165
$67$	−13.8825	−1.69602	−0.848009	−	0.529982i	$-0.822199\pi$
$67$	−13.8825	−1.69602	−0.848009	+	0.529982i	$0.822199\pi$
$68$	−4.38296	−0.531512
$69$	4.25663	0.512438
$70$	1.63877	0.195871
$71$	−7.90662	−0.938343	−0.469172	−	0.883107i	$-0.655447\pi$
$71$	−7.90662	−0.938343	−0.469172	+	0.883107i	$0.655447\pi$
$72$	−1.17768	−0.138791
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	6.14192	0.713983
$75$	−1.34993	−0.155877
$76$	−2.37005	−0.271864
$77$	1.63877	0.186755
$78$	−3.14339	−0.355919
$79$	6.82527	0.767903	0.383952	−	0.923353i	$-0.374563\pi$
$79$	6.82527	0.767903	0.383952	+	0.923353i	$0.374563\pi$
$80$	1.00000	0.111803
$81$	−4.08003	−0.453336
$82$	−12.1951	−1.34672
$83$	0.433489	0.0475816	0.0237908	−	0.999717i	$-0.492426\pi$
$83$	0.433489	0.0475816	0.0237908	+	0.999717i	$0.492426\pi$
$84$	−2.21223	−0.241374
$85$	−4.38296	−0.475399
$86$	7.75536	0.836281
$87$	8.48329	0.909504
$88$	1.00000	0.106600
$89$	9.07813	0.962280	0.481140	−	0.876644i	$-0.340223\pi$
$89$	9.07813	0.962280	0.481140	+	0.876644i	$0.340223\pi$
$90$	−1.17768	−0.124138
$91$	3.81597	0.400022
$92$	−3.15321	−0.328745
$93$	3.36165	0.348587
$94$	−4.50542	−0.464698
$95$	−2.37005	−0.243162
$96$	−1.34993	−0.137777
$97$	−0.217397	−0.0220733	−0.0110367	−	0.999939i	$-0.503513\pi$
$97$	−0.217397	−0.0220733	−0.0110367	+	0.999939i	$0.503513\pi$
$98$	−4.31443	−0.435823
$99$	−1.17768	−0.118361
$100$	1.00000	0.100000
$101$	−1.25916	−0.125291	−0.0626454	−	0.998036i	$-0.519954\pi$
$101$	−1.25916	−0.125291	−0.0626454	+	0.998036i	$0.519954\pi$
$102$	5.91671	0.585841
$103$	−15.7939	−1.55622	−0.778108	−	0.628131i	$-0.783820\pi$
$103$	−15.7939	−1.55622	−0.778108	+	0.628131i	$0.783820\pi$
$104$	2.32855	0.228333
$105$	−2.21223	−0.215892
$106$	−7.19906	−0.699235
$107$	13.1767	1.27384	0.636921	−	0.770929i	$-0.280208\pi$
$107$	13.1767	1.27384	0.636921	+	0.770929i	$0.280208\pi$
$108$	5.63959	0.542670
$109$	−17.7647	−1.70155	−0.850773	−	0.525533i	$-0.823866\pi$
$109$	−17.7647	−1.70155	−0.850773	+	0.525533i	$0.823866\pi$
$110$	1.00000	0.0953463
$111$	−8.29118	−0.786964
$112$	1.63877	0.154849
$113$	15.6492	1.47215	0.736077	−	0.676898i	$-0.236676\pi$
$113$	15.6492	1.47215	0.736077	+	0.676898i	$0.236676\pi$
$114$	3.19941	0.299652
$115$	−3.15321	−0.294039
$116$	−6.28423	−0.583476
$117$	−2.74229	−0.253525
$118$	6.79507	0.625537
$119$	−7.18267	−0.658434
$120$	−1.34993	−0.123231
$121$	1.00000	0.0909091
$122$	−7.93430	−0.718337
$123$	16.4625	1.48438
$124$	−2.49024	−0.223630
$125$	1.00000	0.0894427
$126$	−1.92995	−0.171933
$127$	−20.5586	−1.82428	−0.912142	−	0.409874i	$-0.865573\pi$
$127$	−20.5586	−1.82428	−0.912142	+	0.409874i	$0.865573\pi$
$128$	1.00000	0.0883883
$129$	−10.4692	−0.921763
$130$	2.32855	0.204228
$131$	13.1741	1.15102	0.575512	−	0.817793i	$-0.304803\pi$
$131$	13.1741	1.15102	0.575512	+	0.817793i	$0.304803\pi$
$132$	−1.34993	−0.117497
$133$	−3.88397	−0.336783
$134$	−13.8825	−1.19927
$135$	5.63959	0.485379
$136$	−4.38296	−0.375836
$137$	18.4466	1.57600	0.788000	−	0.615675i	$-0.211116\pi$
$137$	18.4466	1.57600	0.788000	+	0.615675i	$0.211116\pi$
$138$	4.25663	0.362348
$139$	−3.93930	−0.334127	−0.167063	−	0.985946i	$-0.553428\pi$
$139$	−3.93930	−0.334127	−0.167063	+	0.985946i	$0.553428\pi$
$140$	1.63877	0.138501
$141$	6.08201	0.512198
$142$	−7.90662	−0.663509
$143$	2.32855	0.194723
$144$	−1.17768	−0.0981400
$145$	−6.28423	−0.521877
$146$	1.00000	0.0827606
$147$	5.82419	0.480371
$148$	6.14192	0.504862
$149$	−3.88302	−0.318109	−0.159055	−	0.987270i	$-0.550845\pi$
$149$	−3.88302	−0.318109	−0.159055	+	0.987270i	$0.550845\pi$
$150$	−1.34993	−0.110222
$151$	−5.57037	−0.453310	−0.226655	−	0.973975i	$-0.572779\pi$
$151$	−5.57037	−0.453310	−0.226655	+	0.973975i	$0.572779\pi$
$152$	−2.37005	−0.192237
$153$	5.16173	0.417301
$154$	1.63877	0.132056
$155$	−2.49024	−0.200021
$156$	−3.14339	−0.251673
$157$	−14.6754	−1.17122	−0.585612	−	0.810591i	$-0.699146\pi$
$157$	−14.6754	−1.17122	−0.585612	+	0.810591i	$0.699146\pi$
$158$	6.82527	0.542990
$159$	9.71825	0.770707
$160$	1.00000	0.0790569
$161$	−5.16739	−0.407248
$162$	−4.08003	−0.320557
$163$	−6.49620	−0.508821	−0.254411	−	0.967096i	$-0.581882\pi$
$163$	−6.49620	−0.508821	−0.254411	+	0.967096i	$0.581882\pi$
$164$	−12.1951	−0.952275
$165$	−1.34993	−0.105092
$166$	0.433489	0.0336453
$167$	−1.81458	−0.140416	−0.0702081	−	0.997532i	$-0.522366\pi$
$167$	−1.81458	−0.140416	−0.0702081	+	0.997532i	$0.522366\pi$
$168$	−2.21223	−0.170677
$169$	−7.57784	−0.582911
$170$	−4.38296	−0.336158
$171$	2.79116	0.213446
$172$	7.75536	0.591340
$173$	11.6509	0.885800	0.442900	−	0.896571i	$-0.353950\pi$
$173$	11.6509	0.885800	0.442900	+	0.896571i	$0.353950\pi$
$174$	8.48329	0.643116
$175$	1.63877	0.123879
$176$	1.00000	0.0753778
$177$	−9.17289	−0.689477
$178$	9.07813	0.680434
$179$	18.5675	1.38780	0.693899	−	0.720073i	$-0.255892\pi$
$179$	18.5675	1.38780	0.693899	+	0.720073i	$0.255892\pi$
$180$	−1.17768	−0.0877791
$181$	−8.26472	−0.614312	−0.307156	−	0.951659i	$-0.599377\pi$
$181$	−8.26472	−0.614312	−0.307156	+	0.951659i	$0.599377\pi$
$182$	3.81597	0.282858
$183$	10.7108	0.791763
$184$	−3.15321	−0.232458
$185$	6.14192	0.451563
$186$	3.36165	0.246488
$187$	−4.38296	−0.320514
$188$	−4.50542	−0.328591
$189$	9.24199	0.672256
$190$	−2.37005	−0.171942
$191$	−23.5788	−1.70610	−0.853049	−	0.521830i	$-0.825249\pi$
$191$	−23.5788	−1.70610	−0.853049	+	0.521830i	$0.825249\pi$
$192$	−1.34993	−0.0974230
$193$	−8.60509	−0.619408	−0.309704	−	0.950833i	$-0.600230\pi$
$193$	−8.60509	−0.619408	−0.309704	+	0.950833i	$0.600230\pi$
$194$	−0.217397	−0.0156082
$195$	−3.14339	−0.225103
$196$	−4.31443	−0.308174
$197$	16.4818	1.17428	0.587141	−	0.809485i	$-0.300254\pi$
$197$	16.4818	1.17428	0.587141	+	0.809485i	$0.300254\pi$
$198$	−1.17768	−0.0836941
$199$	−2.85113	−0.202112	−0.101056	−	0.994881i	$-0.532222\pi$
$199$	−2.85113	−0.202112	−0.101056	+	0.994881i	$0.532222\pi$
$200$	1.00000	0.0707107
$201$	18.7405	1.32185
$202$	−1.25916	−0.0885940
$203$	−10.2984	−0.722807
$204$	5.91671	0.414252
$205$	−12.1951	−0.851740
$206$	−15.7939	−1.10041
$207$	3.71348	0.258105
$208$	2.32855	0.161456
$209$	−2.37005	−0.163940
$210$	−2.21223	−0.152658
$211$	10.8274	0.745389	0.372694	−	0.927954i	$-0.378434\pi$
$211$	10.8274	0.745389	0.372694	+	0.927954i	$0.378434\pi$
$212$	−7.19906	−0.494433
$213$	10.6734	0.731330
$214$	13.1767	0.900743
$215$	7.75536	0.528911
$216$	5.63959	0.383725
$217$	−4.08093	−0.277031
$218$	−17.7647	−1.20317
$219$	−1.34993	−0.0912200
$220$	1.00000	0.0674200
$221$	−10.2060	−0.686527
$222$	−8.29118	−0.556467
$223$	−18.2893	−1.22474	−0.612370	−	0.790571i	$-0.709784\pi$
$223$	−18.2893	−1.22474	−0.612370	+	0.790571i	$0.709784\pi$
$224$	1.63877	0.109495
$225$	−1.17768	−0.0785120
$226$	15.6492	1.04097
$227$	−3.69859	−0.245484	−0.122742	−	0.992439i	$-0.539169\pi$
$227$	−3.69859	−0.245484	−0.122742	+	0.992439i	$0.539169\pi$
$228$	3.19941	0.211886
$229$	15.8922	1.05018	0.525092	−	0.851045i	$-0.324031\pi$
$229$	15.8922	1.05018	0.525092	+	0.851045i	$0.324031\pi$
$230$	−3.15321	−0.207917
$231$	−2.21223	−0.145554
$232$	−6.28423	−0.412580
$233$	0.603663	0.0395473	0.0197736	−	0.999804i	$-0.493705\pi$
$233$	0.603663	0.0395473	0.0197736	+	0.999804i	$0.493705\pi$
$234$	−2.74229	−0.179269
$235$	−4.50542	−0.293901
$236$	6.79507	0.442321
$237$	−9.21366	−0.598492
$238$	−7.18267	−0.465583
$239$	16.7721	1.08490	0.542448	−	0.840089i	$-0.317498\pi$
$239$	16.7721	1.08490	0.542448	+	0.840089i	$0.317498\pi$
$240$	−1.34993	−0.0871378
$241$	−4.88877	−0.314913	−0.157457	−	0.987526i	$-0.550329\pi$
$241$	−4.88877	−0.314913	−0.157457	+	0.987526i	$0.550329\pi$
$242$	1.00000	0.0642824
$243$	−11.4110	−0.732016
$244$	−7.93430	−0.507941
$245$	−4.31443	−0.275639
$246$	16.4625	1.04961
$247$	−5.51880	−0.351153
$248$	−2.49024	−0.158130
$249$	−0.585181	−0.0370843
$250$	1.00000	0.0632456
$251$	12.0454	0.760300	0.380150	−	0.924925i	$-0.375872\pi$
$251$	12.0454	0.760300	0.380150	+	0.924925i	$0.375872\pi$
$252$	−1.92995	−0.121575
$253$	−3.15321	−0.198241
$254$	−20.5586	−1.28996
$255$	5.91671	0.370518
$256$	1.00000	0.0625000
$257$	17.6275	1.09957	0.549787	−	0.835305i	$-0.314709\pi$
$257$	17.6275	1.09957	0.549787	+	0.835305i	$0.314709\pi$
$258$	−10.4692	−0.651785
$259$	10.0652	0.625421
$260$	2.32855	0.144411
$261$	7.40081	0.458099
$262$	13.1741	0.813897
$263$	−14.2682	−0.879817	−0.439908	−	0.898043i	$-0.644989\pi$
$263$	−14.2682	−0.879817	−0.439908	+	0.898043i	$0.644989\pi$
$264$	−1.34993	−0.0830826
$265$	−7.19906	−0.442235
$266$	−3.88397	−0.238142
$267$	−12.2549	−0.749986
$268$	−13.8825	−0.848009
$269$	11.4921	0.700686	0.350343	−	0.936621i	$-0.386065\pi$
$269$	11.4921	0.700686	0.350343	+	0.936621i	$0.386065\pi$
$270$	5.63959	0.343214
$271$	−13.3981	−0.813878	−0.406939	−	0.913455i	$-0.633404\pi$
$271$	−13.3981	−0.813878	−0.406939	+	0.913455i	$0.633404\pi$
$272$	−4.38296	−0.265756
$273$	−5.15130	−0.311771
$274$	18.4466	1.11440
$275$	1.00000	0.0603023
$276$	4.25663	0.256219
$277$	8.84340	0.531348	0.265674	−	0.964063i	$-0.414405\pi$
$277$	8.84340	0.531348	0.265674	+	0.964063i	$0.414405\pi$
$278$	−3.93930	−0.236263
$279$	2.93270	0.175576
$280$	1.63877	0.0979353
$281$	12.9565	0.772920	0.386460	−	0.922306i	$-0.373698\pi$
$281$	12.9565	0.772920	0.386460	+	0.922306i	$0.373698\pi$
$282$	6.08201	0.362178
$283$	−18.0331	−1.07195	−0.535977	−	0.844233i	$-0.680057\pi$
$283$	−18.0331	−1.07195	−0.535977	+	0.844233i	$0.680057\pi$
$284$	−7.90662	−0.469172
$285$	3.19941	0.189517
$286$	2.32855	0.137690
$287$	−19.9849	−1.17967
$288$	−1.17768	−0.0693955
$289$	2.21036	0.130021
$290$	−6.28423	−0.369023
$291$	0.293471	0.0172036
$292$	1.00000	0.0585206
$293$	−31.6286	−1.84776	−0.923880	−	0.382682i	$-0.875000\pi$
$293$	−31.6286	−1.84776	−0.923880	+	0.382682i	$0.875000\pi$
$294$	5.82419	0.339674
$295$	6.79507	0.395624
$296$	6.14192	0.356992
$297$	5.63959	0.327242
$298$	−3.88302	−0.224937
$299$	−7.34243	−0.424624
$300$	−1.34993	−0.0779384
$301$	12.7092	0.732549
$302$	−5.57037	−0.320539
$303$	1.69978	0.0976497
$304$	−2.37005	−0.135932
$305$	−7.93430	−0.454316
$306$	5.16173	0.295076
$307$	11.6271	0.663593	0.331797	−	0.943351i	$-0.392345\pi$
$307$	11.6271	0.663593	0.331797	+	0.943351i	$0.392345\pi$
$308$	1.63877	0.0933776
$309$	21.3207	1.21289
$310$	−2.49024	−0.141436
$311$	−9.61718	−0.545340	−0.272670	−	0.962108i	$-0.587907\pi$
$311$	−9.61718	−0.545340	−0.272670	+	0.962108i	$0.587907\pi$
$312$	−3.14339	−0.177960
$313$	−12.4255	−0.702333	−0.351167	−	0.936313i	$-0.614215\pi$
$313$	−12.4255	−0.702333	−0.351167	+	0.936313i	$0.614215\pi$
$314$	−14.6754	−0.828181
$315$	−1.92995	−0.108740
$316$	6.82527	0.383952
$317$	12.3433	0.693267	0.346634	−	0.938001i	$-0.387325\pi$
$317$	12.3433	0.693267	0.346634	+	0.938001i	$0.387325\pi$
$318$	9.71825	0.544972
$319$	−6.28423	−0.351849
$320$	1.00000	0.0559017
$321$	−17.7877	−0.992813
$322$	−5.16739	−0.287968
$323$	10.3879	0.577996
$324$	−4.08003	−0.226668
$325$	2.32855	0.129165
$326$	−6.49620	−0.359791
$327$	23.9811	1.32616
$328$	−12.1951	−0.673360
$329$	−7.38334	−0.407057
$330$	−1.34993	−0.0743114
$331$	21.1198	1.16085	0.580425	−	0.814314i	$-0.302887\pi$
$331$	21.1198	1.16085	0.580425	+	0.814314i	$0.302887\pi$
$332$	0.433489	0.0237908
$333$	−7.23322	−0.396378
$334$	−1.81458	−0.0992892
$335$	−13.8825	−0.758482
$336$	−2.21223	−0.120687
$337$	5.45762	0.297296	0.148648	−	0.988890i	$-0.452508\pi$
$337$	5.45762	0.297296	0.148648	+	0.988890i	$0.452508\pi$
$338$	−7.57784	−0.412180
$339$	−21.1254	−1.14737
$340$	−4.38296	−0.237699
$341$	−2.49024	−0.134854
$342$	2.79116	0.150929
$343$	−18.5418	−1.00116
$344$	7.75536	0.418141
$345$	4.25663	0.229169
$346$	11.6509	0.626355
$347$	−0.405949	−0.0217925	−0.0108962	−	0.999941i	$-0.503468\pi$
$347$	−0.405949	−0.0217925	−0.0108962	+	0.999941i	$0.503468\pi$
$348$	8.48329	0.454752
$349$	10.8499	0.580780	0.290390	−	0.956908i	$-0.406215\pi$
$349$	10.8499	0.580780	0.290390	+	0.956908i	$0.406215\pi$
$350$	1.63877	0.0875960
$351$	13.1321	0.700939
$352$	1.00000	0.0533002
$353$	−14.1787	−0.754658	−0.377329	−	0.926079i	$-0.623157\pi$
$353$	−14.1787	−0.754658	−0.377329	+	0.926079i	$0.623157\pi$
$354$	−9.17289	−0.487534
$355$	−7.90662	−0.419640
$356$	9.07813	0.481140
$357$	9.69612	0.513173
$358$	18.5675	0.981321
$359$	9.93835	0.524526	0.262263	−	0.964996i	$-0.415531\pi$
$359$	9.93835	0.524526	0.262263	+	0.964996i	$0.415531\pi$
$360$	−1.17768	−0.0620692
$361$	−13.3828	−0.704360
$362$	−8.26472	−0.434384
$363$	−1.34993	−0.0708531
$364$	3.81597	0.200011
$365$	1.00000	0.0523424
$366$	10.7108	0.559861
$367$	−23.4279	−1.22293	−0.611464	−	0.791272i	$-0.709419\pi$
$367$	−23.4279	−1.22293	−0.611464	+	0.791272i	$0.709419\pi$
$368$	−3.15321	−0.164373
$369$	14.3619	0.747650
$370$	6.14192	0.319303
$371$	−11.7976	−0.612501
$372$	3.36165	0.174294
$373$	6.70006	0.346916	0.173458	−	0.984841i	$-0.444506\pi$
$373$	6.70006	0.346916	0.173458	+	0.984841i	$0.444506\pi$
$374$	−4.38296	−0.226638
$375$	−1.34993	−0.0697102
$376$	−4.50542	−0.232349
$377$	−14.6332	−0.753646
$378$	9.24199	0.475357
$379$	−28.1927	−1.44816	−0.724081	−	0.689715i	$-0.757736\pi$
$379$	−28.1927	−1.44816	−0.724081	+	0.689715i	$0.757736\pi$
$380$	−2.37005	−0.121581
$381$	27.7528	1.42182
$382$	−23.5788	−1.20639
$383$	−8.20081	−0.419042	−0.209521	−	0.977804i	$-0.567190\pi$
$383$	−8.20081	−0.419042	−0.209521	+	0.977804i	$0.567190\pi$
$384$	−1.34993	−0.0688885
$385$	1.63877	0.0835195
$386$	−8.60509	−0.437987
$387$	−9.13333	−0.464273
$388$	−0.217397	−0.0110367
$389$	8.47568	0.429734	0.214867	−	0.976643i	$-0.431068\pi$
$389$	8.47568	0.429734	0.214867	+	0.976643i	$0.431068\pi$
$390$	−3.14339	−0.159172
$391$	13.8204	0.698928
$392$	−4.31443	−0.217912
$393$	−17.7841	−0.897091
$394$	16.4818	0.830342
$395$	6.82527	0.343417
$396$	−1.17768	−0.0591807
$397$	7.15717	0.359208	0.179604	−	0.983739i	$-0.442518\pi$
$397$	7.15717	0.359208	0.179604	+	0.983739i	$0.442518\pi$
$398$	−2.85113	−0.142914
$399$	5.24310	0.262483
$400$	1.00000	0.0500000
$401$	−26.6785	−1.33226	−0.666131	−	0.745835i	$-0.732051\pi$
$401$	−26.6785	−1.33226	−0.666131	+	0.745835i	$0.732051\pi$
$402$	18.7405	0.934689
$403$	−5.79865	−0.288851
$404$	−1.25916	−0.0626454
$405$	−4.08003	−0.202738
$406$	−10.2984	−0.511101
$407$	6.14192	0.304444
$408$	5.91671	0.292921
$409$	26.4527	1.30800	0.654001	−	0.756494i	$-0.273089\pi$
$409$	26.4527	1.30800	0.654001	+	0.756494i	$0.273089\pi$
$410$	−12.1951	−0.602271
$411$	−24.9017	−1.22831
$412$	−15.7939	−0.778108
$413$	11.1356	0.547945
$414$	3.71348	0.182507
$415$	0.433489	0.0212791
$416$	2.32855	0.114167
$417$	5.31779	0.260413
$418$	−2.37005	−0.115923
$419$	−33.0541	−1.61480	−0.807399	−	0.590006i	$-0.799125\pi$
$419$	−33.0541	−1.61480	−0.807399	+	0.590006i	$0.799125\pi$
$420$	−2.21223	−0.107946
$421$	−37.2935	−1.81757	−0.908787	−	0.417261i	$-0.862990\pi$
$421$	−37.2935	−1.81757	−0.908787	+	0.417261i	$0.862990\pi$
$422$	10.8274	0.527070
$423$	5.30594	0.257984
$424$	−7.19906	−0.349617
$425$	−4.38296	−0.212605
$426$	10.6734	0.517129
$427$	−13.0025	−0.629235
$428$	13.1767	0.636921
$429$	−3.14339	−0.151764
$430$	7.75536	0.373996
$431$	−39.9287	−1.92330	−0.961650	−	0.274280i	$-0.911560\pi$
$431$	−39.9287	−1.92330	−0.961650	+	0.274280i	$0.911560\pi$
$432$	5.63959	0.271335
$433$	−9.86773	−0.474213	−0.237106	−	0.971484i	$-0.576199\pi$
$433$	−9.86773	−0.474213	−0.237106	+	0.971484i	$0.576199\pi$
$434$	−4.08093	−0.195891
$435$	8.48329	0.406743
$436$	−17.7647	−0.850773
$437$	7.47328	0.357496
$438$	−1.34993	−0.0645023
$439$	14.1876	0.677138	0.338569	−	0.940942i	$-0.390057\pi$
$439$	14.1876	0.677138	0.338569	+	0.940942i	$0.390057\pi$
$440$	1.00000	0.0476731
$441$	5.08102	0.241953
$442$	−10.2060	−0.485448
$443$	−20.1810	−0.958829	−0.479414	−	0.877589i	$-0.659151\pi$
$443$	−20.1810	−0.958829	−0.479414	+	0.877589i	$0.659151\pi$
$444$	−8.29118	−0.393482
$445$	9.07813	0.430345
$446$	−18.2893	−0.866022
$447$	5.24182	0.247930
$448$	1.63877	0.0774246
$449$	20.0327	0.945403	0.472701	−	0.881223i	$-0.343279\pi$
$449$	20.0327	0.945403	0.472701	+	0.881223i	$0.343279\pi$
$450$	−1.17768	−0.0555164
$451$	−12.1951	−0.574243
$452$	15.6492	0.736077
$453$	7.51963	0.353303
$454$	−3.69859	−0.173583
$455$	3.81597	0.178895
$456$	3.19941	0.149826
$457$	−20.6049	−0.963856	−0.481928	−	0.876211i	$-0.660063\pi$
$457$	−20.6049	−0.963856	−0.481928	+	0.876211i	$0.660063\pi$
$458$	15.8922	0.742593
$459$	−24.7181	−1.15374
$460$	−3.15321	−0.147019
$461$	−26.7945	−1.24794	−0.623972	−	0.781447i	$-0.714482\pi$
$461$	−26.7945	−1.24794	−0.623972	+	0.781447i	$0.714482\pi$
$462$	−2.21223	−0.102922
$463$	−33.5988	−1.56147	−0.780733	−	0.624865i	$-0.785154\pi$
$463$	−33.5988	−1.56147	−0.780733	+	0.624865i	$0.785154\pi$
$464$	−6.28423	−0.291738
$465$	3.36165	0.155893
$466$	0.603663	0.0279641
$467$	−18.9194	−0.875486	−0.437743	−	0.899100i	$-0.644222\pi$
$467$	−18.9194	−0.875486	−0.437743	+	0.899100i	$0.644222\pi$
$468$	−2.74229	−0.126763
$469$	−22.7502	−1.05051
$470$	−4.50542	−0.207819
$471$	19.8108	0.912834
$472$	6.79507	0.312769
$473$	7.75536	0.356592
$474$	−9.21366	−0.423198
$475$	−2.37005	−0.108745
$476$	−7.18267	−0.329217
$477$	8.47819	0.388190
$478$	16.7721	0.767137
$479$	−20.3307	−0.928933	−0.464467	−	0.885591i	$-0.653754\pi$
$479$	−20.3307	−0.928933	−0.464467	+	0.885591i	$0.653754\pi$
$480$	−1.34993	−0.0616157
$481$	14.3018	0.652105
$482$	−4.88877	−0.222677
$483$	6.97564	0.317402
$484$	1.00000	0.0454545
$485$	−0.217397	−0.00987148
$486$	−11.4110	−0.517614
$487$	−23.4277	−1.06161	−0.530805	−	0.847494i	$-0.678110\pi$
$487$	−23.4277	−1.06161	−0.530805	+	0.847494i	$0.678110\pi$
$488$	−7.93430	−0.359169
$489$	8.76943	0.396567
$490$	−4.31443	−0.194906
$491$	8.53882	0.385352	0.192676	−	0.981262i	$-0.438283\pi$
$491$	8.53882	0.385352	0.192676	+	0.981262i	$0.438283\pi$
$492$	16.4625	0.742188
$493$	27.5435	1.24050
$494$	−5.51880	−0.248302
$495$	−1.17768	−0.0529328
$496$	−2.49024	−0.111815
$497$	−12.9571	−0.581207
$498$	−0.585181	−0.0262226
$499$	36.6913	1.64253	0.821265	−	0.570547i	$-0.193269\pi$
$499$	36.6913	1.64253	0.821265	+	0.570547i	$0.193269\pi$
$500$	1.00000	0.0447214
$501$	2.44956	0.109438
$502$	12.0454	0.537613
$503$	−9.41204	−0.419662	−0.209831	−	0.977738i	$-0.567291\pi$
$503$	−9.41204	−0.419662	−0.209831	+	0.977738i	$0.567291\pi$
$504$	−1.92995	−0.0859667
$505$	−1.25916	−0.0560318
$506$	−3.15321	−0.140177
$507$	10.2296	0.454311
$508$	−20.5586	−0.912142
$509$	29.7801	1.31998	0.659991	−	0.751274i	$-0.270560\pi$
$509$	29.7801	1.31998	0.659991	+	0.751274i	$0.270560\pi$
$510$	5.91671	0.261996
$511$	1.63877	0.0724949
$512$	1.00000	0.0441942
$513$	−13.3661	−0.590129
$514$	17.6275	0.777517
$515$	−15.7939	−0.695961
$516$	−10.4692	−0.460881
$517$	−4.50542	−0.198148
$518$	10.0652	0.442239
$519$	−15.7279	−0.690379
$520$	2.32855	0.102114
$521$	−4.88227	−0.213896	−0.106948	−	0.994265i	$-0.534108\pi$
$521$	−4.88227	−0.213896	−0.106948	+	0.994265i	$0.534108\pi$
$522$	7.40081	0.323925
$523$	26.7387	1.16920	0.584602	−	0.811320i	$-0.301251\pi$
$523$	26.7387	1.16920	0.584602	+	0.811320i	$0.301251\pi$
$524$	13.1741	0.575512
$525$	−2.21223	−0.0965497
$526$	−14.2682	−0.622124
$527$	10.9146	0.475448
$528$	−1.34993	−0.0587483
$529$	−13.0572	−0.567706
$530$	−7.19906	−0.312707
$531$	−8.00242	−0.347276
$532$	−3.88397	−0.168392
$533$	−28.3969	−1.23000
$534$	−12.2549	−0.530320
$535$	13.1767	0.569680
$536$	−13.8825	−0.599633
$537$	−25.0648	−1.08163
$538$	11.4921	0.495460
$539$	−4.31443	−0.185836
$540$	5.63959	0.242689
$541$	1.57643	0.0677760	0.0338880	−	0.999426i	$-0.489211\pi$
$541$	1.57643	0.0677760	0.0338880	+	0.999426i	$0.489211\pi$
$542$	−13.3981	−0.575499
$543$	11.1568	0.478785
$544$	−4.38296	−0.187918
$545$	−17.7647	−0.760955
$546$	−5.15130	−0.220455
$547$	18.0414	0.771396	0.385698	−	0.922625i	$-0.373961\pi$
$547$	18.0414	0.771396	0.385698	+	0.922625i	$0.373961\pi$
$548$	18.4466	0.788000
$549$	9.34406	0.398795
$550$	1.00000	0.0426401
$551$	14.8940	0.634504
$552$	4.25663	0.181174
$553$	11.1851	0.475637
$554$	8.84340	0.375720
$555$	−8.29118	−0.351941
$556$	−3.93930	−0.167063
$557$	37.1473	1.57398	0.786990	−	0.616965i	$-0.211638\pi$
$557$	37.1473	1.57398	0.786990	+	0.616965i	$0.211638\pi$
$558$	2.93270	0.124151
$559$	18.0588	0.763804
$560$	1.63877	0.0692507
$561$	5.91671	0.249804
$562$	12.9565	0.546537
$563$	36.8350	1.55241	0.776206	−	0.630479i	$-0.217142\pi$
$563$	36.8350	1.55241	0.776206	+	0.630479i	$0.217142\pi$
$564$	6.08201	0.256099
$565$	15.6492	0.658367
$566$	−18.0331	−0.757986
$567$	−6.68623	−0.280795
$568$	−7.90662	−0.331755
$569$	−11.9791	−0.502190	−0.251095	−	0.967962i	$-0.580791\pi$
$569$	−11.9791	−0.502190	−0.251095	+	0.967962i	$0.580791\pi$
$570$	3.19941	0.134009
$571$	−9.26932	−0.387909	−0.193955	−	0.981011i	$-0.562131\pi$
$571$	−9.26932	−0.387909	−0.193955	+	0.981011i	$0.562131\pi$
$572$	2.32855	0.0973617
$573$	31.8297	1.32971
$574$	−19.9849	−0.834154
$575$	−3.15321	−0.131498
$576$	−1.17768	−0.0490700
$577$	12.3558	0.514377	0.257188	−	0.966361i	$-0.417204\pi$
$577$	12.3558	0.514377	0.257188	+	0.966361i	$0.417204\pi$
$578$	2.21036	0.0919387
$579$	11.6163	0.482757
$580$	−6.28423	−0.260938
$581$	0.710389	0.0294719
$582$	0.293471	0.0121648
$583$	−7.19906	−0.298155
$584$	1.00000	0.0413803
$585$	−2.74229	−0.113380
$586$	−31.6286	−1.30656
$587$	1.73455	0.0715927	0.0357964	−	0.999359i	$-0.488603\pi$
$587$	1.73455	0.0715927	0.0357964	+	0.999359i	$0.488603\pi$
$588$	5.82419	0.240186
$589$	5.90199	0.243187
$590$	6.79507	0.279749
$591$	−22.2494	−0.915216
$592$	6.14192	0.252431
$593$	−31.8233	−1.30683	−0.653413	−	0.757002i	$-0.726663\pi$
$593$	−31.8233	−1.30683	−0.653413	+	0.757002i	$0.726663\pi$
$594$	5.63959	0.231395
$595$	−7.18267	−0.294461
$596$	−3.88302	−0.159055
$597$	3.84884	0.157523
$598$	−7.34243	−0.300254
$599$	33.0672	1.35109	0.675545	−	0.737319i	$-0.263908\pi$
$599$	33.0672	1.35109	0.675545	+	0.737319i	$0.263908\pi$
$600$	−1.34993	−0.0551108
$601$	−11.6963	−0.477102	−0.238551	−	0.971130i	$-0.576672\pi$
$601$	−11.6963	−0.477102	−0.238551	+	0.971130i	$0.576672\pi$
$602$	12.7092	0.517990
$603$	16.3492	0.665789
$604$	−5.57037	−0.226655
$605$	1.00000	0.0406558
$606$	1.69978	0.0690488
$607$	−11.0290	−0.447655	−0.223828	−	0.974629i	$-0.571855\pi$
$607$	−11.0290	−0.447655	−0.223828	+	0.974629i	$0.571855\pi$
$608$	−2.37005	−0.0961183
$609$	13.9022	0.563344
$610$	−7.93430	−0.321250
$611$	−10.4911	−0.424425
$612$	5.16173	0.208651
$613$	−19.8750	−0.802742	−0.401371	−	0.915916i	$-0.631466\pi$
$613$	−19.8750	−0.802742	−0.401371	+	0.915916i	$0.631466\pi$
$614$	11.6271	0.469231
$615$	16.4625	0.663833
$616$	1.63877	0.0660279
$617$	31.8136	1.28077	0.640384	−	0.768055i	$-0.278775\pi$
$617$	31.8136	1.28077	0.640384	+	0.768055i	$0.278775\pi$
$618$	21.3207	0.857642
$619$	43.8941	1.76425	0.882126	−	0.471014i	$-0.156112\pi$
$619$	43.8941	1.76425	0.882126	+	0.471014i	$0.156112\pi$
$620$	−2.49024	−0.100010
$621$	−17.7828	−0.713600
$622$	−9.61718	−0.385614
$623$	14.8770	0.596033
$624$	−3.14339	−0.125836
$625$	1.00000	0.0400000
$626$	−12.4255	−0.496625
$627$	3.19941	0.127772
$628$	−14.6754	−0.585612
$629$	−26.9198	−1.07336
$630$	−1.92995	−0.0768910
$631$	−18.6611	−0.742886	−0.371443	−	0.928456i	$-0.621137\pi$
$631$	−18.6611	−0.742886	−0.371443	+	0.928456i	$0.621137\pi$
$632$	6.82527	0.271495
$633$	−14.6163	−0.580944
$634$	12.3433	0.490214
$635$	−20.5586	−0.815845
$636$	9.71825	0.385354
$637$	−10.0464	−0.398052
$638$	−6.28423	−0.248795
$639$	9.31148	0.368356
$640$	1.00000	0.0395285
$641$	22.1616	0.875329	0.437665	−	0.899138i	$-0.355806\pi$
$641$	22.1616	0.875329	0.437665	+	0.899138i	$0.355806\pi$
$642$	−17.7877	−0.702025
$643$	7.12714	0.281067	0.140533	−	0.990076i	$-0.455118\pi$
$643$	7.12714	0.281067	0.140533	+	0.990076i	$0.455118\pi$
$644$	−5.16739	−0.203624
$645$	−10.4692	−0.412225
$646$	10.3879	0.408705
$647$	6.29172	0.247353	0.123677	−	0.992323i	$-0.460531\pi$
$647$	6.29172	0.247353	0.123677	+	0.992323i	$0.460531\pi$
$648$	−4.08003	−0.160279
$649$	6.79507	0.266730
$650$	2.32855	0.0913334
$651$	5.50898	0.215914
$652$	−6.49620	−0.254411
$653$	44.5733	1.74429	0.872144	−	0.489249i	$-0.162729\pi$
$653$	44.5733	1.74429	0.872144	+	0.489249i	$0.162729\pi$
$654$	23.9811	0.937736
$655$	13.1741	0.514754
$656$	−12.1951	−0.476137
$657$	−1.17768	−0.0459457
$658$	−7.38334	−0.287833
$659$	−48.3958	−1.88523	−0.942616	−	0.333879i	$-0.891642\pi$
$659$	−48.3958	−1.88523	−0.942616	+	0.333879i	$0.891642\pi$
$660$	−1.34993	−0.0525461
$661$	−18.5463	−0.721368	−0.360684	−	0.932688i	$-0.617457\pi$
$661$	−18.5463	−0.721368	−0.360684	+	0.932688i	$0.617457\pi$
$662$	21.1198	0.820844
$663$	13.7774	0.535069
$664$	0.433489	0.0168226
$665$	−3.88397	−0.150614
$666$	−7.23322	−0.280281
$667$	19.8155	0.767260
$668$	−1.81458	−0.0702081
$669$	24.6893	0.954543
$670$	−13.8825	−0.536328
$671$	−7.93430	−0.306300
$672$	−2.21223	−0.0853386
$673$	−14.3681	−0.553850	−0.276925	−	0.960892i	$-0.589315\pi$
$673$	−14.3681	−0.553850	−0.276925	+	0.960892i	$0.589315\pi$
$674$	5.45762	0.210220
$675$	5.63959	0.217068
$676$	−7.57784	−0.291455
$677$	8.59685	0.330404	0.165202	−	0.986260i	$-0.447172\pi$
$677$	8.59685	0.330404	0.165202	+	0.986260i	$0.447172\pi$
$678$	−21.1254	−0.811315
$679$	−0.356264	−0.0136721
$680$	−4.38296	−0.168079
$681$	4.99284	0.191326
$682$	−2.49024	−0.0953561
$683$	−19.2474	−0.736481	−0.368241	−	0.929731i	$-0.620040\pi$
$683$	−19.2474	−0.736481	−0.368241	+	0.929731i	$0.620040\pi$
$684$	2.79116	0.106723
$685$	18.4466	0.704809
$686$	−18.5418	−0.707928
$687$	−21.4534	−0.818497
$688$	7.75536	0.295670
$689$	−16.7634	−0.638635
$690$	4.25663	0.162047
$691$	2.63703	0.100318	0.0501588	−	0.998741i	$-0.484027\pi$
$691$	2.63703	0.100318	0.0501588	+	0.998741i	$0.484027\pi$
$692$	11.6509	0.442900
$693$	−1.92995	−0.0733127
$694$	−0.405949	−0.0154096
$695$	−3.93930	−0.149426
$696$	8.48329	0.321558
$697$	53.4505	2.02458
$698$	10.8499	0.410674
$699$	−0.814905	−0.0308225
$700$	1.63877	0.0619397
$701$	45.5628	1.72088	0.860442	−	0.509549i	$-0.170188\pi$
$701$	45.5628	1.72088	0.860442	+	0.509549i	$0.170188\pi$
$702$	13.1321	0.495639
$703$	−14.5567	−0.549015
$704$	1.00000	0.0376889
$705$	6.08201	0.229062
$706$	−14.1787	−0.533624
$707$	−2.06347	−0.0776048
$708$	−9.17289	−0.344738
$709$	−18.4304	−0.692170	−0.346085	−	0.938203i	$-0.612489\pi$
$709$	−18.4304	−0.692170	−0.346085	+	0.938203i	$0.612489\pi$
$710$	−7.90662	−0.296730
$711$	−8.03799	−0.301448
$712$	9.07813	0.340217
$713$	7.85225	0.294069
$714$	9.69612	0.362868
$715$	2.32855	0.0870830
$716$	18.5675	0.693899
$717$	−22.6412	−0.845551
$718$	9.93835	0.370896
$719$	16.2326	0.605374	0.302687	−	0.953090i	$-0.402116\pi$
$719$	16.2326	0.605374	0.302687	+	0.953090i	$0.402116\pi$
$720$	−1.17768	−0.0438896
$721$	−25.8825	−0.963915
$722$	−13.3828	−0.498058
$723$	6.59951	0.245439
$724$	−8.26472	−0.307156
$725$	−6.28423	−0.233390
$726$	−1.34993	−0.0501007
$727$	−8.25174	−0.306040	−0.153020	−	0.988223i	$-0.548900\pi$
$727$	−8.25174	−0.306040	−0.153020	+	0.988223i	$0.548900\pi$
$728$	3.81597	0.141429
$729$	27.6442	1.02386
$730$	1.00000	0.0370117
$731$	−33.9914	−1.25722
$732$	10.7108	0.395881
$733$	−49.0717	−1.81251	−0.906253	−	0.422737i	$-0.861069\pi$
$733$	−49.0717	−1.81251	−0.906253	+	0.422737i	$0.861069\pi$
$734$	−23.4279	−0.864741
$735$	5.82419	0.214829
$736$	−3.15321	−0.116229
$737$	−13.8825	−0.511369
$738$	14.3619	0.528668
$739$	39.6053	1.45690	0.728452	−	0.685097i	$-0.240240\pi$
$739$	39.6053	1.45690	0.728452	+	0.685097i	$0.240240\pi$
$740$	6.14192	0.225781
$741$	7.45000	0.273683
$742$	−11.7976	−0.433104
$743$	−24.8274	−0.910831	−0.455415	−	0.890279i	$-0.650509\pi$
$743$	−24.8274	−0.910831	−0.455415	+	0.890279i	$0.650509\pi$
$744$	3.36165	0.123244
$745$	−3.88302	−0.142263
$746$	6.70006	0.245306
$747$	−0.510511	−0.0186786
$748$	−4.38296	−0.160257
$749$	21.5936	0.789014
$750$	−1.34993	−0.0492926
$751$	2.29084	0.0835938	0.0417969	−	0.999126i	$-0.486692\pi$
$751$	2.29084	0.0835938	0.0417969	+	0.999126i	$0.486692\pi$
$752$	−4.50542	−0.164296
$753$	−16.2605	−0.592566
$754$	−14.6332	−0.532908
$755$	−5.57037	−0.202727
$756$	9.24199	0.336128
$757$	6.46738	0.235061	0.117531	−	0.993069i	$-0.462502\pi$
$757$	6.46738	0.235061	0.117531	+	0.993069i	$0.462502\pi$
$758$	−28.1927	−1.02401
$759$	4.25663	0.154506
$760$	−2.37005	−0.0859709
$761$	13.7171	0.497245	0.248622	−	0.968600i	$-0.420022\pi$
$761$	13.7171	0.497245	0.248622	+	0.968600i	$0.420022\pi$
$762$	27.7528	1.00538
$763$	−29.1122	−1.05393
$764$	−23.5788	−0.853049
$765$	5.16173	0.186623
$766$	−8.20081	−0.296307
$767$	15.8227	0.571324
$768$	−1.34993	−0.0487115
$769$	18.9867	0.684679	0.342339	−	0.939576i	$-0.388781\pi$
$769$	18.9867	0.684679	0.342339	+	0.939576i	$0.388781\pi$
$770$	1.63877	0.0590572
$771$	−23.7960	−0.856991
$772$	−8.60509	−0.309704
$773$	42.1697	1.51674	0.758369	−	0.651825i	$-0.225996\pi$
$773$	42.1697	1.51674	0.758369	+	0.651825i	$0.225996\pi$
$774$	−9.13333	−0.328291
$775$	−2.49024	−0.0894520
$776$	−0.217397	−0.00780409
$777$	−13.5873	−0.487443
$778$	8.47568	0.303868
$779$	28.9030	1.03556
$780$	−3.14339	−0.112551
$781$	−7.90662	−0.282921
$782$	13.8204	0.494217
$783$	−35.4405	−1.26654
$784$	−4.31443	−0.154087
$785$	−14.6754	−0.523787
$786$	−17.7841	−0.634339
$787$	−4.14637	−0.147802	−0.0739010	−	0.997266i	$-0.523545\pi$
$787$	−4.14637	−0.147802	−0.0739010	+	0.997266i	$0.523545\pi$
$788$	16.4818	0.587141
$789$	19.2612	0.685715
$790$	6.82527	0.242832
$791$	25.6455	0.911848
$792$	−1.17768	−0.0418471
$793$	−18.4754	−0.656082
$794$	7.15717	0.253998
$795$	9.71825	0.344671
$796$	−2.85113	−0.101056
$797$	−31.6039	−1.11947	−0.559734	−	0.828672i	$-0.689097\pi$
$797$	−31.6039	−1.11947	−0.559734	+	0.828672i	$0.689097\pi$
$798$	5.24310	0.185604
$799$	19.7471	0.698601
$800$	1.00000	0.0353553
$801$	−10.6911	−0.377753
$802$	−26.6785	−0.942051
$803$	1.00000	0.0352892
$804$	18.7405	0.660925
$805$	−5.16739	−0.182127
$806$	−5.79865	−0.204249
$807$	−15.5136	−0.546104
$808$	−1.25916	−0.0442970
$809$	17.3614	0.610396	0.305198	−	0.952289i	$-0.401277\pi$
$809$	17.3614	0.610396	0.305198	+	0.952289i	$0.401277\pi$
$810$	−4.08003	−0.143358
$811$	52.5389	1.84489	0.922445	−	0.386129i	$-0.126188\pi$
$811$	52.5389	1.84489	0.922445	+	0.386129i	$0.126188\pi$
$812$	−10.2984	−0.361403
$813$	18.0866	0.634324
$814$	6.14192	0.215274
$815$	−6.49620	−0.227552
$816$	5.91671	0.207126
$817$	−18.3806	−0.643056
$818$	26.4527	0.924897
$819$	−4.49399	−0.157033
$820$	−12.1951	−0.425870
$821$	15.5510	0.542734	0.271367	−	0.962476i	$-0.412524\pi$
$821$	15.5510	0.542734	0.271367	+	0.962476i	$0.412524\pi$
$822$	−24.9017	−0.868547
$823$	50.0018	1.74295	0.871477	−	0.490436i	$-0.163162\pi$
$823$	50.0018	1.74295	0.871477	+	0.490436i	$0.163162\pi$
$824$	−15.7939	−0.550205
$825$	−1.34993	−0.0469986
$826$	11.1356	0.387456
$827$	−34.2509	−1.19102	−0.595511	−	0.803347i	$-0.703050\pi$
$827$	−34.2509	−1.19102	−0.595511	+	0.803347i	$0.703050\pi$
$828$	3.71348	0.129052
$829$	−7.66697	−0.266285	−0.133142	−	0.991097i	$-0.542507\pi$
$829$	−7.66697	−0.266285	−0.133142	+	0.991097i	$0.542507\pi$
$830$	0.433489	0.0150466
$831$	−11.9380	−0.414124
$832$	2.32855	0.0807281
$833$	18.9100	0.655192
$834$	5.31779	0.184140
$835$	−1.81458	−0.0627960
$836$	−2.37005	−0.0819700
$837$	−14.0439	−0.485429
$838$	−33.0541	−1.14183
$839$	14.4345	0.498334	0.249167	−	0.968461i	$-0.419843\pi$
$839$	14.4345	0.498334	0.249167	+	0.968461i	$0.419843\pi$
$840$	−2.21223	−0.0763292
$841$	10.4915	0.361777
$842$	−37.2935	−1.28522
$843$	−17.4904	−0.602401
$844$	10.8274	0.372694
$845$	−7.57784	−0.260686
$846$	5.30594	0.182422
$847$	1.63877	0.0563088
$848$	−7.19906	−0.247217
$849$	24.3434	0.835464
$850$	−4.38296	−0.150334
$851$	−19.3668	−0.663885
$852$	10.6734	0.365665
$853$	−31.7280	−1.08635	−0.543174	−	0.839620i	$-0.682778\pi$
$853$	−31.7280	−1.08635	−0.543174	+	0.839620i	$0.682778\pi$
$854$	−13.0025	−0.444936
$855$	2.79116	0.0954558
$856$	13.1767	0.450371
$857$	−6.39803	−0.218553	−0.109276	−	0.994011i	$-0.534853\pi$
$857$	−6.39803	−0.218553	−0.109276	+	0.994011i	$0.534853\pi$
$858$	−3.14339	−0.107314
$859$	11.2292	0.383136	0.191568	−	0.981479i	$-0.438643\pi$
$859$	11.2292	0.383136	0.191568	+	0.981479i	$0.438643\pi$
$860$	7.75536	0.264455
$861$	26.9783	0.919418
$862$	−39.9287	−1.35998
$863$	27.2736	0.928405	0.464203	−	0.885729i	$-0.346341\pi$
$863$	27.2736	0.928405	0.464203	+	0.885729i	$0.346341\pi$
$864$	5.63959	0.191863
$865$	11.6509	0.396142
$866$	−9.86773	−0.335319
$867$	−2.98383	−0.101336
$868$	−4.08093	−0.138516
$869$	6.82527	0.231532
$870$	8.48329	0.287610
$871$	−32.3262	−1.09533
$872$	−17.7647	−0.601587
$873$	0.256024	0.00866510
$874$	7.47328	0.252788
$875$	1.63877	0.0554006
$876$	−1.34993	−0.0456100
$877$	27.1934	0.918255	0.459128	−	0.888370i	$-0.348162\pi$
$877$	27.1934	0.918255	0.459128	+	0.888370i	$0.348162\pi$
$878$	14.1876	0.478809
$879$	42.6964	1.44012
$880$	1.00000	0.0337100
$881$	26.5221	0.893554	0.446777	−	0.894645i	$-0.352572\pi$
$881$	26.5221	0.893554	0.446777	+	0.894645i	$0.352572\pi$
$882$	5.08102	0.171087
$883$	23.3653	0.786306	0.393153	−	0.919473i	$-0.371384\pi$
$883$	23.3653	0.786306	0.393153	+	0.919473i	$0.371384\pi$
$884$	−10.2060	−0.343264
$885$	−9.17289	−0.308343
$886$	−20.1810	−0.677994
$887$	−22.1497	−0.743715	−0.371858	−	0.928290i	$-0.621279\pi$
$887$	−22.1497	−0.743715	−0.371858	+	0.928290i	$0.621279\pi$
$888$	−8.29118	−0.278234
$889$	−33.6909	−1.12996
$890$	9.07813	0.304300
$891$	−4.08003	−0.136686
$892$	−18.2893	−0.612370
$893$	10.6781	0.357328
$894$	5.24182	0.175313
$895$	18.5675	0.620642
$896$	1.63877	0.0547475
$897$	9.91179	0.330945
$898$	20.0327	0.668501
$899$	15.6492	0.521931
$900$	−1.17768	−0.0392560
$901$	31.5532	1.05119
$902$	−12.1951	−0.406051
$903$	−17.1566	−0.570937
$904$	15.6492	0.520485
$905$	−8.26472	−0.274729
$906$	7.51963	0.249823
$907$	46.0564	1.52928	0.764638	−	0.644459i	$-0.222918\pi$
$907$	46.0564	1.52928	0.764638	+	0.644459i	$0.222918\pi$
$908$	−3.69859	−0.122742
$909$	1.48289	0.0491842
$910$	3.81597	0.126498
$911$	38.6332	1.27998	0.639988	−	0.768385i	$-0.278939\pi$
$911$	38.6332	1.27998	0.639988	+	0.768385i	$0.278939\pi$
$912$	3.19941	0.105943
$913$	0.433489	0.0143464
$914$	−20.6049	−0.681549
$915$	10.7108	0.354087
$916$	15.8922	0.525092
$917$	21.5893	0.712941
$918$	−24.7181	−0.815819
$919$	−24.9571	−0.823258	−0.411629	−	0.911351i	$-0.635040\pi$
$919$	−24.9571	−0.823258	−0.411629	+	0.911351i	$0.635040\pi$
$920$	−3.15321	−0.103958
$921$	−15.6958	−0.517194
$922$	−26.7945	−0.882429
$923$	−18.4110	−0.606005
$924$	−2.21223	−0.0727770
$925$	6.14192	0.201945
$926$	−33.5988	−1.10412
$927$	18.6001	0.610908
$928$	−6.28423	−0.206290
$929$	35.5379	1.16596	0.582980	−	0.812487i	$-0.301887\pi$
$929$	35.5379	1.16596	0.582980	+	0.812487i	$0.301887\pi$
$930$	3.36165	0.110233
$931$	10.2254	0.335125
$932$	0.603663	0.0197736
$933$	12.9825	0.425029
$934$	−18.9194	−0.619062
$935$	−4.38296	−0.143338
$936$	−2.74229	−0.0896346
$937$	34.1068	1.11422	0.557111	−	0.830438i	$-0.311910\pi$
$937$	34.1068	1.11422	0.557111	+	0.830438i	$0.311910\pi$
$938$	−22.7502	−0.742822
$939$	16.7737	0.547387
$940$	−4.50542	−0.146950
$941$	−19.6792	−0.641522	−0.320761	−	0.947160i	$-0.603939\pi$
$941$	−19.6792	−0.641522	−0.320761	+	0.947160i	$0.603939\pi$
$942$	19.8108	0.645471
$943$	38.4536	1.25222
$944$	6.79507	0.221161
$945$	9.24199	0.300642
$946$	7.75536	0.252148
$947$	−37.9367	−1.23278	−0.616388	−	0.787443i	$-0.711405\pi$
$947$	−37.9367	−1.23278	−0.616388	+	0.787443i	$0.711405\pi$
$948$	−9.21366	−0.299246
$949$	2.32855	0.0755881
$950$	−2.37005	−0.0768947
$951$	−16.6626	−0.540322
$952$	−7.18267	−0.232792
$953$	16.7975	0.544124	0.272062	−	0.962280i	$-0.412294\pi$
$953$	16.7975	0.544124	0.272062	+	0.962280i	$0.412294\pi$
$954$	8.47819	0.274492
$955$	−23.5788	−0.762991
$956$	16.7721	0.542448
$957$	8.48329	0.274226
$958$	−20.3307	−0.656855
$959$	30.2298	0.976170
$960$	−1.34993	−0.0435689
$961$	−24.7987	−0.799959
$962$	14.3018	0.461108
$963$	−15.5180	−0.500060
$964$	−4.88877	−0.157457
$965$	−8.60509	−0.277008
$966$	6.97564	0.224437
$967$	−38.4053	−1.23503	−0.617516	−	0.786559i	$-0.711861\pi$
$967$	−38.4053	−1.23503	−0.617516	+	0.786559i	$0.711861\pi$
$968$	1.00000	0.0321412
$969$	−14.0229	−0.450481
$970$	−0.217397	−0.00698019
$971$	−59.4036	−1.90635	−0.953177	−	0.302414i	$-0.902207\pi$
$971$	−59.4036	−1.90635	−0.953177	+	0.302414i	$0.902207\pi$
$972$	−11.4110	−0.366008
$973$	−6.45561	−0.206957
$974$	−23.4277	−0.750671
$975$	−3.14339	−0.100669
$976$	−7.93430	−0.253971
$977$	35.7854	1.14488	0.572439	−	0.819947i	$-0.305997\pi$
$977$	35.7854	1.14488	0.572439	+	0.819947i	$0.305997\pi$
$978$	8.76943	0.280416
$979$	9.07813	0.290138
$980$	−4.31443	−0.137819
$981$	20.9211	0.667959
$982$	8.53882	0.272485
$983$	−28.4780	−0.908306	−0.454153	−	0.890924i	$-0.650058\pi$
$983$	−28.4780	−0.908306	−0.454153	+	0.890924i	$0.650058\pi$
$984$	16.4625	0.524806
$985$	16.4818	0.525155
$986$	27.5435	0.877165
$987$	9.96702	0.317254
$988$	−5.51880	−0.175576
$989$	−24.4543	−0.777601
$990$	−1.17768	−0.0374291
$991$	−52.2287	−1.65910	−0.829549	−	0.558433i	$-0.811403\pi$
$991$	−52.2287	−1.65910	−0.829549	+	0.558433i	$0.811403\pi$
$992$	−2.49024	−0.0790651
$993$	−28.5103	−0.904748
$994$	−12.9571	−0.410976
$995$	−2.85113	−0.0903870
$996$	−0.585181	−0.0185422
$997$	−55.4519	−1.75618	−0.878089	−	0.478497i	$-0.841182\pi$
$997$	−55.4519	−1.75618	−0.878089	+	0.478497i	$0.841182\pi$
$998$	36.6913	1.16144
$999$	34.6379	1.09589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.v.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.v.1.3	✓	5	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.34993 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34993 q^{6} +1.63877 q^{7} +1.00000 q^{8} -1.17768 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.34993 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34993 q^{6} +1.63877 q^{7} +1.00000 q^{8} -1.17768 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.34993 q^{12} +2.32855 q^{13} +1.63877 q^{14} -1.34993 q^{15} +1.00000 q^{16} -4.38296 q^{17} -1.17768 q^{18} -2.37005 q^{19} +1.00000 q^{20} -2.21223 q^{21} +1.00000 q^{22} -3.15321 q^{23} -1.34993 q^{24} +1.00000 q^{25} +2.32855 q^{26} +5.63959 q^{27} +1.63877 q^{28} -6.28423 q^{29} -1.34993 q^{30} -2.49024 q^{31} +1.00000 q^{32} -1.34993 q^{33} -4.38296 q^{34} +1.63877 q^{35} -1.17768 q^{36} +6.14192 q^{37} -2.37005 q^{38} -3.14339 q^{39} +1.00000 q^{40} -12.1951 q^{41} -2.21223 q^{42} +7.75536 q^{43} +1.00000 q^{44} -1.17768 q^{45} -3.15321 q^{46} -4.50542 q^{47} -1.34993 q^{48} -4.31443 q^{49} +1.00000 q^{50} +5.91671 q^{51} +2.32855 q^{52} -7.19906 q^{53} +5.63959 q^{54} +1.00000 q^{55} +1.63877 q^{56} +3.19941 q^{57} -6.28423 q^{58} +6.79507 q^{59} -1.34993 q^{60} -7.93430 q^{61} -2.49024 q^{62} -1.92995 q^{63} +1.00000 q^{64} +2.32855 q^{65} -1.34993 q^{66} -13.8825 q^{67} -4.38296 q^{68} +4.25663 q^{69} +1.63877 q^{70} -7.90662 q^{71} -1.17768 q^{72} +1.00000 q^{73} +6.14192 q^{74} -1.34993 q^{75} -2.37005 q^{76} +1.63877 q^{77} -3.14339 q^{78} +6.82527 q^{79} +1.00000 q^{80} -4.08003 q^{81} -12.1951 q^{82} +0.433489 q^{83} -2.21223 q^{84} -4.38296 q^{85} +7.75536 q^{86} +8.48329 q^{87} +1.00000 q^{88} +9.07813 q^{89} -1.17768 q^{90} +3.81597 q^{91} -3.15321 q^{92} +3.36165 q^{93} -4.50542 q^{94} -2.37005 q^{95} -1.34993 q^{96} -0.217397 q^{97} -4.31443 q^{98} -1.17768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - 7 q^{13} - 8 q^{14} - 5 q^{15} + 5 q^{16} - 3 q^{17} + 4 q^{18} + 4 q^{19} + 5 q^{20} - 3 q^{21} + 5 q^{22} - 3 q^{23} - 5 q^{24} + 5 q^{25} - 7 q^{26} - 11 q^{27} - 8 q^{28} - 12 q^{29} - 5 q^{30} - q^{31} + 5 q^{32} - 5 q^{33} - 3 q^{34} - 8 q^{35} + 4 q^{36} + 4 q^{38} + 8 q^{39} + 5 q^{40} + q^{41} - 3 q^{42} + 5 q^{44} + 4 q^{45} - 3 q^{46} - 17 q^{47} - 5 q^{48} + 13 q^{49} + 5 q^{50} + 23 q^{51} - 7 q^{52} - 43 q^{53} - 11 q^{54} + 5 q^{55} - 8 q^{56} - 29 q^{57} - 12 q^{58} - 9 q^{59} - 5 q^{60} - 22 q^{61} - q^{62} + 25 q^{63} + 5 q^{64} - 7 q^{65} - 5 q^{66} - 9 q^{67} - 3 q^{68} + q^{69} - 8 q^{70} - 34 q^{71} + 4 q^{72} + 5 q^{73} - 5 q^{75} + 4 q^{76} - 8 q^{77} + 8 q^{78} - 24 q^{79} + 5 q^{80} + 25 q^{81} + q^{82} - 5 q^{83} - 3 q^{84} - 3 q^{85} + 30 q^{87} + 5 q^{88} + 58 q^{89} + 4 q^{90} - 9 q^{91} - 3 q^{92} - 32 q^{93} - 17 q^{94} + 4 q^{95} - 5 q^{96} + 13 q^{97} + 13 q^{98} + 4 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + 5 * q^11 - 5 * q^12 - 7 * q^13 - 8 * q^14 - 5 * q^15 + 5 * q^16 - 3 * q^17 + 4 * q^18 + 4 * q^19 + 5 * q^20 - 3 * q^21 + 5 * q^22 - 3 * q^23 - 5 * q^24 + 5 * q^25 - 7 * q^26 - 11 * q^27 - 8 * q^28 - 12 * q^29 - 5 * q^30 - q^31 + 5 * q^32 - 5 * q^33 - 3 * q^34 - 8 * q^35 + 4 * q^36 + 4 * q^38 + 8 * q^39 + 5 * q^40 + q^41 - 3 * q^42 + 5 * q^44 + 4 * q^45 - 3 * q^46 - 17 * q^47 - 5 * q^48 + 13 * q^49 + 5 * q^50 + 23 * q^51 - 7 * q^52 - 43 * q^53 - 11 * q^54 + 5 * q^55 - 8 * q^56 - 29 * q^57 - 12 * q^58 - 9 * q^59 - 5 * q^60 - 22 * q^61 - q^62 + 25 * q^63 + 5 * q^64 - 7 * q^65 - 5 * q^66 - 9 * q^67 - 3 * q^68 + q^69 - 8 * q^70 - 34 * q^71 + 4 * q^72 + 5 * q^73 - 5 * q^75 + 4 * q^76 - 8 * q^77 + 8 * q^78 - 24 * q^79 + 5 * q^80 + 25 * q^81 + q^82 - 5 * q^83 - 3 * q^84 - 3 * q^85 + 30 * q^87 + 5 * q^88 + 58 * q^89 + 4 * q^90 - 9 * q^91 - 3 * q^92 - 32 * q^93 - 17 * q^94 + 4 * q^95 - 5 * q^96 + 13 * q^97 + 13 * q^98 + 4 * q^99

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