LMFDB - Embedded newform 8030.2.a.v.1.5

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			1.5
Root			$1.37067$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.69782 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.69782 q^{6} -2.28220 q^{7} +1.00000 q^{8} -0.117414 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.69782 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.69782 q^{6} -2.28220 q^{7} +1.00000 q^{8} -0.117414 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.69782 q^{12} -6.39949 q^{13} -2.28220 q^{14} +1.69782 q^{15} +1.00000 q^{16} +5.54969 q^{17} -0.117414 q^{18} -6.89973 q^{19} +1.00000 q^{20} -3.87476 q^{21} +1.00000 q^{22} +1.91828 q^{23} +1.69782 q^{24} +1.00000 q^{25} -6.39949 q^{26} -5.29280 q^{27} -2.28220 q^{28} +2.52763 q^{29} +1.69782 q^{30} -8.83332 q^{31} +1.00000 q^{32} +1.69782 q^{33} +5.54969 q^{34} -2.28220 q^{35} -0.117414 q^{36} -5.89830 q^{37} -6.89973 q^{38} -10.8652 q^{39} +1.00000 q^{40} -0.847370 q^{41} -3.87476 q^{42} +4.94865 q^{43} +1.00000 q^{44} -0.117414 q^{45} +1.91828 q^{46} -1.72853 q^{47} +1.69782 q^{48} -1.79157 q^{49} +1.00000 q^{50} +9.42237 q^{51} -6.39949 q^{52} -11.8191 q^{53} -5.29280 q^{54} +1.00000 q^{55} -2.28220 q^{56} -11.7145 q^{57} +2.52763 q^{58} -3.86645 q^{59} +1.69782 q^{60} -2.17019 q^{61} -8.83332 q^{62} +0.267961 q^{63} +1.00000 q^{64} -6.39949 q^{65} +1.69782 q^{66} +4.86854 q^{67} +5.54969 q^{68} +3.25689 q^{69} -2.28220 q^{70} -12.7007 q^{71} -0.117414 q^{72} +1.00000 q^{73} -5.89830 q^{74} +1.69782 q^{75} -6.89973 q^{76} -2.28220 q^{77} -10.8652 q^{78} +2.45274 q^{79} +1.00000 q^{80} -8.63397 q^{81} -0.847370 q^{82} +5.38491 q^{83} -3.87476 q^{84} +5.54969 q^{85} +4.94865 q^{86} +4.29145 q^{87} +1.00000 q^{88} +16.1501 q^{89} -0.117414 q^{90} +14.6049 q^{91} +1.91828 q^{92} -14.9974 q^{93} -1.72853 q^{94} -6.89973 q^{95} +1.69782 q^{96} +8.69769 q^{97} -1.79157 q^{98} -0.117414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.69782	0.980236	0.490118	−	0.871656i	$-0.336954\pi$
$3$	1.69782	0.980236	0.490118	+	0.871656i	$0.336954\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.69782	0.693131
$7$	−2.28220	−0.862590	−0.431295	−	0.902211i	$-0.641943\pi$
$7$	−2.28220	−0.862590	−0.431295	+	0.902211i	$0.641943\pi$
$8$	1.00000	0.353553
$9$	−0.117414	−0.0391379
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.69782	0.490118
$13$	−6.39949	−1.77490	−0.887449	−	0.460906i	$-0.847525\pi$
$13$	−6.39949	−1.77490	−0.887449	+	0.460906i	$0.847525\pi$
$14$	−2.28220	−0.609943
$15$	1.69782	0.438375
$16$	1.00000	0.250000
$17$	5.54969	1.34600	0.672999	−	0.739643i	$-0.265006\pi$
$17$	5.54969	1.34600	0.672999	+	0.739643i	$0.265006\pi$
$18$	−0.117414	−0.0276747
$19$	−6.89973	−1.58291	−0.791453	−	0.611230i	$-0.790675\pi$
$19$	−6.89973	−1.58291	−0.791453	+	0.611230i	$0.790675\pi$
$20$	1.00000	0.223607
$21$	−3.87476	−0.845542
$22$	1.00000	0.213201
$23$	1.91828	0.399989	0.199995	−	0.979797i	$-0.435908\pi$
$23$	1.91828	0.399989	0.199995	+	0.979797i	$0.435908\pi$
$24$	1.69782	0.346566
$25$	1.00000	0.200000
$26$	−6.39949	−1.25504
$27$	−5.29280	−1.01860
$28$	−2.28220	−0.431295
$29$	2.52763	0.469369	0.234684	−	0.972072i	$-0.424594\pi$
$29$	2.52763	0.469369	0.234684	+	0.972072i	$0.424594\pi$
$30$	1.69782	0.309978
$31$	−8.83332	−1.58651	−0.793256	−	0.608889i	$-0.791616\pi$
$31$	−8.83332	−1.58651	−0.793256	+	0.608889i	$0.791616\pi$
$32$	1.00000	0.176777
$33$	1.69782	0.295552
$34$	5.54969	0.951765
$35$	−2.28220	−0.385762
$36$	−0.117414	−0.0195689
$37$	−5.89830	−0.969674	−0.484837	−	0.874604i	$-0.661121\pi$
$37$	−5.89830	−0.969674	−0.484837	+	0.874604i	$0.661121\pi$
$38$	−6.89973	−1.11928
$39$	−10.8652	−1.73982
$40$	1.00000	0.158114
$41$	−0.847370	−0.132337	−0.0661685	−	0.997808i	$-0.521077\pi$
$41$	−0.847370	−0.132337	−0.0661685	+	0.997808i	$0.521077\pi$
$42$	−3.87476	−0.597888
$43$	4.94865	0.754662	0.377331	−	0.926078i	$-0.376842\pi$
$43$	4.94865	0.754662	0.377331	+	0.926078i	$0.376842\pi$
$44$	1.00000	0.150756
$45$	−0.117414	−0.0175030
$46$	1.91828	0.282835
$47$	−1.72853	−0.252132	−0.126066	−	0.992022i	$-0.540235\pi$
$47$	−1.72853	−0.252132	−0.126066	+	0.992022i	$0.540235\pi$
$48$	1.69782	0.245059
$49$	−1.79157	−0.255938
$50$	1.00000	0.141421
$51$	9.42237	1.31940
$52$	−6.39949	−0.887449
$53$	−11.8191	−1.62348	−0.811738	−	0.584022i	$-0.801478\pi$
$53$	−11.8191	−1.62348	−0.811738	+	0.584022i	$0.801478\pi$
$54$	−5.29280	−0.720259
$55$	1.00000	0.134840
$56$	−2.28220	−0.304972
$57$	−11.7145	−1.55162
$58$	2.52763	0.331894
$59$	−3.86645	−0.503369	−0.251685	−	0.967809i	$-0.580985\pi$
$59$	−3.86645	−0.503369	−0.251685	+	0.967809i	$0.580985\pi$
$60$	1.69782	0.219187
$61$	−2.17019	−0.277864	−0.138932	−	0.990302i	$-0.544367\pi$
$61$	−2.17019	−0.277864	−0.138932	+	0.990302i	$0.544367\pi$
$62$	−8.83332	−1.12183
$63$	0.267961	0.0337599
$64$	1.00000	0.125000
$65$	−6.39949	−0.793759
$66$	1.69782	0.208987
$67$	4.86854	0.594786	0.297393	−	0.954755i	$-0.403883\pi$
$67$	4.86854	0.594786	0.297393	+	0.954755i	$0.403883\pi$
$68$	5.54969	0.672999
$69$	3.25689	0.392084
$70$	−2.28220	−0.272775
$71$	−12.7007	−1.50730	−0.753649	−	0.657277i	$-0.771708\pi$
$71$	−12.7007	−1.50730	−0.753649	+	0.657277i	$0.771708\pi$
$72$	−0.117414	−0.0138373
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−5.89830	−0.685663
$75$	1.69782	0.196047
$76$	−6.89973	−0.791453
$77$	−2.28220	−0.260081
$78$	−10.8652	−1.23024
$79$	2.45274	0.275955	0.137977	−	0.990435i	$-0.455940\pi$
$79$	2.45274	0.275955	0.137977	+	0.990435i	$0.455940\pi$
$80$	1.00000	0.111803
$81$	−8.63397	−0.959330
$82$	−0.847370	−0.0935763
$83$	5.38491	0.591070	0.295535	−	0.955332i	$-0.404502\pi$
$83$	5.38491	0.591070	0.295535	+	0.955332i	$0.404502\pi$
$84$	−3.87476	−0.422771
$85$	5.54969	0.601949
$86$	4.94865	0.533627
$87$	4.29145	0.460092
$88$	1.00000	0.106600
$89$	16.1501	1.71191	0.855953	−	0.517054i	$-0.172971\pi$
$89$	16.1501	1.71191	0.855953	+	0.517054i	$0.172971\pi$
$90$	−0.117414	−0.0123765
$91$	14.6049	1.53101
$92$	1.91828	0.199995
$93$	−14.9974	−1.55515
$94$	−1.72853	−0.178284
$95$	−6.89973	−0.707897
$96$	1.69782	0.173283
$97$	8.69769	0.883117	0.441558	−	0.897233i	$-0.354426\pi$
$97$	8.69769	0.883117	0.441558	+	0.897233i	$0.354426\pi$
$98$	−1.79157	−0.180976
$99$	−0.117414	−0.0118005
$100$	1.00000	0.100000
$101$	−17.1066	−1.70217	−0.851086	−	0.525026i	$-0.824055\pi$
$101$	−17.1066	−1.70217	−0.851086	+	0.525026i	$0.824055\pi$
$102$	9.42237	0.932954
$103$	3.12482	0.307898	0.153949	−	0.988079i	$-0.450801\pi$
$103$	3.12482	0.307898	0.153949	+	0.988079i	$0.450801\pi$
$104$	−6.39949	−0.627521
$105$	−3.87476	−0.378138
$106$	−11.8191	−1.14797
$107$	15.3641	1.48531	0.742654	−	0.669675i	$-0.233567\pi$
$107$	15.3641	1.48531	0.742654	+	0.669675i	$0.233567\pi$
$108$	−5.29280	−0.509300
$109$	0.203512	0.0194929	0.00974646	−	0.999953i	$-0.496898\pi$
$109$	0.203512	0.0194929	0.00974646	+	0.999953i	$0.496898\pi$
$110$	1.00000	0.0953463
$111$	−10.0142	−0.950509
$112$	−2.28220	−0.215648
$113$	−9.09411	−0.855502	−0.427751	−	0.903897i	$-0.640694\pi$
$113$	−9.09411	−0.855502	−0.427751	+	0.903897i	$0.640694\pi$
$114$	−11.7145	−1.09716
$115$	1.91828	0.178881
$116$	2.52763	0.234684
$117$	0.751387	0.0694657
$118$	−3.86645	−0.355936
$119$	−12.6655	−1.16105
$120$	1.69782	0.154989
$121$	1.00000	0.0909091
$122$	−2.17019	−0.196480
$123$	−1.43868	−0.129721
$124$	−8.83332	−0.793256
$125$	1.00000	0.0894427
$126$	0.267961	0.0238719
$127$	−15.7282	−1.39565	−0.697826	−	0.716268i	$-0.745849\pi$
$127$	−15.7282	−1.39565	−0.697826	+	0.716268i	$0.745849\pi$
$128$	1.00000	0.0883883
$129$	8.40191	0.739747
$130$	−6.39949	−0.561272
$131$	11.4147	0.997304	0.498652	−	0.866802i	$-0.333829\pi$
$131$	11.4147	0.997304	0.498652	+	0.866802i	$0.333829\pi$
$132$	1.69782	0.147776
$133$	15.7465	1.36540
$134$	4.86854	0.420578
$135$	−5.29280	−0.455532
$136$	5.54969	0.475882
$137$	−14.3619	−1.22702	−0.613512	−	0.789685i	$-0.710244\pi$
$137$	−14.3619	−1.22702	−0.613512	+	0.789685i	$0.710244\pi$
$138$	3.25689	0.277245
$139$	−21.3824	−1.81363	−0.906816	−	0.421527i	$-0.861494\pi$
$139$	−21.3824	−1.81363	−0.906816	+	0.421527i	$0.861494\pi$
$140$	−2.28220	−0.192881
$141$	−2.93473	−0.247149
$142$	−12.7007	−1.06582
$143$	−6.39949	−0.535152
$144$	−0.117414	−0.00978447
$145$	2.52763	0.209908
$146$	1.00000	0.0827606
$147$	−3.04175	−0.250880
$148$	−5.89830	−0.484837
$149$	12.4998	1.02403	0.512013	−	0.858978i	$-0.328900\pi$
$149$	12.4998	1.02403	0.512013	+	0.858978i	$0.328900\pi$
$150$	1.69782	0.138626
$151$	−12.8229	−1.04352	−0.521758	−	0.853094i	$-0.674724\pi$
$151$	−12.8229	−1.04352	−0.521758	+	0.853094i	$0.674724\pi$
$152$	−6.89973	−0.559642
$153$	−0.651610	−0.0526795
$154$	−2.28220	−0.183905
$155$	−8.83332	−0.709509
$156$	−10.8652	−0.869909
$157$	−4.56867	−0.364619	−0.182310	−	0.983241i	$-0.558357\pi$
$157$	−4.56867	−0.364619	−0.182310	+	0.983241i	$0.558357\pi$
$158$	2.45274	0.195130
$159$	−20.0667	−1.59139
$160$	1.00000	0.0790569
$161$	−4.37790	−0.345027
$162$	−8.63397	−0.678349
$163$	12.1580	0.952285	0.476143	−	0.879368i	$-0.342035\pi$
$163$	12.1580	0.952285	0.476143	+	0.879368i	$0.342035\pi$
$164$	−0.847370	−0.0661685
$165$	1.69782	0.132175
$166$	5.38491	0.417950
$167$	−6.75955	−0.523070	−0.261535	−	0.965194i	$-0.584229\pi$
$167$	−6.75955	−0.523070	−0.261535	+	0.965194i	$0.584229\pi$
$168$	−3.87476	−0.298944
$169$	27.9534	2.15026
$170$	5.54969	0.425642
$171$	0.810122	0.0619516
$172$	4.94865	0.377331
$173$	7.68722	0.584448	0.292224	−	0.956350i	$-0.405605\pi$
$173$	7.68722	0.584448	0.292224	+	0.956350i	$0.405605\pi$
$174$	4.29145	0.325334
$175$	−2.28220	−0.172518
$176$	1.00000	0.0753778
$177$	−6.56454	−0.493421
$178$	16.1501	1.21050
$179$	14.3457	1.07225	0.536125	−	0.844139i	$-0.319888\pi$
$179$	14.3457	1.07225	0.536125	+	0.844139i	$0.319888\pi$
$180$	−0.117414	−0.00875149
$181$	16.1536	1.20069	0.600345	−	0.799741i	$-0.295030\pi$
$181$	16.1536	1.20069	0.600345	+	0.799741i	$0.295030\pi$
$182$	14.6049	1.08259
$183$	−3.68459	−0.272373
$184$	1.91828	0.141418
$185$	−5.89830	−0.433652
$186$	−14.9974	−1.09966
$187$	5.54969	0.405834
$188$	−1.72853	−0.126066
$189$	12.0792	0.878635
$190$	−6.89973	−0.500559
$191$	−26.3257	−1.90486	−0.952432	−	0.304753i	$-0.901426\pi$
$191$	−26.3257	−1.90486	−0.952432	+	0.304753i	$0.901426\pi$
$192$	1.69782	0.122529
$193$	15.2044	1.09444	0.547218	−	0.836990i	$-0.315687\pi$
$193$	15.2044	1.09444	0.547218	+	0.836990i	$0.315687\pi$
$194$	8.69769	0.624458
$195$	−10.8652	−0.778071
$196$	−1.79157	−0.127969
$197$	13.1695	0.938286	0.469143	−	0.883122i	$-0.344563\pi$
$197$	13.1695	0.938286	0.469143	+	0.883122i	$0.344563\pi$
$198$	−0.117414	−0.00834422
$199$	−4.35643	−0.308819	−0.154410	−	0.988007i	$-0.549348\pi$
$199$	−4.35643	−0.308819	−0.154410	+	0.988007i	$0.549348\pi$
$200$	1.00000	0.0707107
$201$	8.26589	0.583031
$202$	−17.1066	−1.20362
$203$	−5.76855	−0.404873
$204$	9.42237	0.659698
$205$	−0.847370	−0.0591829
$206$	3.12482	0.217717
$207$	−0.225232	−0.0156547
$208$	−6.39949	−0.443725
$209$	−6.89973	−0.477264
$210$	−3.87476	−0.267384
$211$	−12.6080	−0.867969	−0.433985	−	0.900920i	$-0.642893\pi$
$211$	−12.6080	−0.867969	−0.433985	+	0.900920i	$0.642893\pi$
$212$	−11.8191	−0.811738
$213$	−21.5635	−1.47751
$214$	15.3641	1.05027
$215$	4.94865	0.337495
$216$	−5.29280	−0.360130
$217$	20.1594	1.36851
$218$	0.203512	0.0137836
$219$	1.69782	0.114728
$220$	1.00000	0.0674200
$221$	−35.5152	−2.38901
$222$	−10.0142	−0.672112
$223$	4.86395	0.325714	0.162857	−	0.986650i	$-0.447929\pi$
$223$	4.86395	0.325714	0.162857	+	0.986650i	$0.447929\pi$
$224$	−2.28220	−0.152486
$225$	−0.117414	−0.00782757
$226$	−9.09411	−0.604931
$227$	−27.7929	−1.84468	−0.922339	−	0.386381i	$-0.873725\pi$
$227$	−27.7929	−1.84468	−0.922339	+	0.386381i	$0.873725\pi$
$228$	−11.7145	−0.775810
$229$	8.87680	0.586595	0.293298	−	0.956021i	$-0.405247\pi$
$229$	8.87680	0.586595	0.293298	+	0.956021i	$0.405247\pi$
$230$	1.91828	0.126488
$231$	−3.87476	−0.254940
$232$	2.52763	0.165947
$233$	12.4762	0.817340	0.408670	−	0.912682i	$-0.365993\pi$
$233$	12.4762	0.817340	0.408670	+	0.912682i	$0.365993\pi$
$234$	0.751387	0.0491197
$235$	−1.72853	−0.112757
$236$	−3.86645	−0.251685
$237$	4.16431	0.270501
$238$	−12.6655	−0.820983
$239$	−23.0955	−1.49392	−0.746960	−	0.664868i	$-0.768488\pi$
$239$	−23.0955	−1.49392	−0.746960	+	0.664868i	$0.768488\pi$
$240$	1.69782	0.109594
$241$	−7.44780	−0.479755	−0.239878	−	0.970803i	$-0.577107\pi$
$241$	−7.44780	−0.479755	−0.239878	+	0.970803i	$0.577107\pi$
$242$	1.00000	0.0642824
$243$	1.21949	0.0782302
$244$	−2.17019	−0.138932
$245$	−1.79157	−0.114459
$246$	−1.43868	−0.0917269
$247$	44.1547	2.80950
$248$	−8.83332	−0.560916
$249$	9.14259	0.579388
$250$	1.00000	0.0632456
$251$	−28.3341	−1.78843	−0.894217	−	0.447633i	$-0.852267\pi$
$251$	−28.3341	−1.78843	−0.894217	+	0.447633i	$0.852267\pi$
$252$	0.267961	0.0168800
$253$	1.91828	0.120601
$254$	−15.7282	−0.986874
$255$	9.42237	0.590052
$256$	1.00000	0.0625000
$257$	−14.1466	−0.882443	−0.441221	−	0.897398i	$-0.645455\pi$
$257$	−14.1466	−0.882443	−0.441221	+	0.897398i	$0.645455\pi$
$258$	8.40191	0.523080
$259$	13.4611	0.836432
$260$	−6.39949	−0.396879
$261$	−0.296778	−0.0183701
$262$	11.4147	0.705201
$263$	−21.5878	−1.33116	−0.665579	−	0.746327i	$-0.731815\pi$
$263$	−21.5878	−1.33116	−0.665579	+	0.746327i	$0.731815\pi$
$264$	1.69782	0.104493
$265$	−11.8191	−0.726040
$266$	15.7465	0.965483
$267$	27.4199	1.67807
$268$	4.86854	0.297393
$269$	7.90898	0.482219	0.241110	−	0.970498i	$-0.422489\pi$
$269$	7.90898	0.482219	0.241110	+	0.970498i	$0.422489\pi$
$270$	−5.29280	−0.322110
$271$	22.3186	1.35576	0.677879	−	0.735173i	$-0.262899\pi$
$271$	22.3186	1.35576	0.677879	+	0.735173i	$0.262899\pi$
$272$	5.54969	0.336500
$273$	24.7965	1.50075
$274$	−14.3619	−0.867637
$275$	1.00000	0.0603023
$276$	3.25689	0.196042
$277$	−30.7234	−1.84599	−0.922994	−	0.384814i	$-0.874266\pi$
$277$	−30.7234	−1.84599	−0.922994	+	0.384814i	$0.874266\pi$
$278$	−21.3824	−1.28243
$279$	1.03715	0.0620927
$280$	−2.28220	−0.136387
$281$	5.86126	0.349653	0.174827	−	0.984599i	$-0.444064\pi$
$281$	5.86126	0.349653	0.174827	+	0.984599i	$0.444064\pi$
$282$	−2.93473	−0.174761
$283$	26.4004	1.56934	0.784671	−	0.619913i	$-0.212832\pi$
$283$	26.4004	1.56934	0.784671	+	0.619913i	$0.212832\pi$
$284$	−12.7007	−0.753649
$285$	−11.7145	−0.693906
$286$	−6.39949	−0.378410
$287$	1.93387	0.114153
$288$	−0.117414	−0.00691866
$289$	13.7991	0.811712
$290$	2.52763	0.148427
$291$	14.7671	0.865663
$292$	1.00000	0.0585206
$293$	19.7245	1.15232	0.576159	−	0.817338i	$-0.304551\pi$
$293$	19.7245	1.15232	0.576159	+	0.817338i	$0.304551\pi$
$294$	−3.04175	−0.177399
$295$	−3.86645	−0.225114
$296$	−5.89830	−0.342832
$297$	−5.29280	−0.307119
$298$	12.4998	0.724095
$299$	−12.2760	−0.709940
$300$	1.69782	0.0980236
$301$	−11.2938	−0.650964
$302$	−12.8229	−0.737877
$303$	−29.0439	−1.66853
$304$	−6.89973	−0.395726
$305$	−2.17019	−0.124265
$306$	−0.651610	−0.0372500
$307$	2.13294	0.121733	0.0608666	−	0.998146i	$-0.480614\pi$
$307$	2.13294	0.121733	0.0608666	+	0.998146i	$0.480614\pi$
$308$	−2.28220	−0.130040
$309$	5.30538	0.301812
$310$	−8.83332	−0.501699
$311$	21.6432	1.22727	0.613637	−	0.789588i	$-0.289706\pi$
$311$	21.6432	1.22727	0.613637	+	0.789588i	$0.289706\pi$
$312$	−10.8652	−0.615119
$313$	−20.2440	−1.14426	−0.572130	−	0.820163i	$-0.693883\pi$
$313$	−20.2440	−1.14426	−0.572130	+	0.820163i	$0.693883\pi$
$314$	−4.56867	−0.257825
$315$	0.267961	0.0150979
$316$	2.45274	0.137977
$317$	−27.2831	−1.53237	−0.766187	−	0.642618i	$-0.777848\pi$
$317$	−27.2831	−1.53237	−0.766187	+	0.642618i	$0.777848\pi$
$318$	−20.0667	−1.12528
$319$	2.52763	0.141520
$320$	1.00000	0.0559017
$321$	26.0855	1.45595
$322$	−4.37790	−0.243971
$323$	−38.2914	−2.13059
$324$	−8.63397	−0.479665
$325$	−6.39949	−0.354980
$326$	12.1580	0.673367
$327$	0.345526	0.0191077
$328$	−0.847370	−0.0467882
$329$	3.94485	0.217486
$330$	1.69782	0.0934618
$331$	28.3061	1.55584	0.777922	−	0.628361i	$-0.216274\pi$
$331$	28.3061	1.55584	0.777922	+	0.628361i	$0.216274\pi$
$332$	5.38491	0.295535
$333$	0.692541	0.0379510
$334$	−6.75955	−0.369866
$335$	4.86854	0.265997
$336$	−3.87476	−0.211385
$337$	5.66151	0.308402	0.154201	−	0.988039i	$-0.450720\pi$
$337$	5.66151	0.308402	0.154201	+	0.988039i	$0.450720\pi$
$338$	27.9534	1.52047
$339$	−15.4401	−0.838594
$340$	5.54969	0.300974
$341$	−8.83332	−0.478351
$342$	0.810122	0.0438064
$343$	20.0641	1.08336
$344$	4.94865	0.266813
$345$	3.25689	0.175345
$346$	7.68722	0.413267
$347$	−19.6793	−1.05644	−0.528220	−	0.849107i	$-0.677140\pi$
$347$	−19.6793	−1.05644	−0.528220	+	0.849107i	$0.677140\pi$
$348$	4.29145	0.230046
$349$	14.2523	0.762909	0.381454	−	0.924388i	$-0.375423\pi$
$349$	14.2523	0.762909	0.381454	+	0.924388i	$0.375423\pi$
$350$	−2.28220	−0.121989
$351$	33.8712	1.80791
$352$	1.00000	0.0533002
$353$	−10.2037	−0.543087	−0.271543	−	0.962426i	$-0.587534\pi$
$353$	−10.2037	−0.543087	−0.271543	+	0.962426i	$0.587534\pi$
$354$	−6.56454	−0.348901
$355$	−12.7007	−0.674084
$356$	16.1501	0.855953
$357$	−21.5037	−1.13810
$358$	14.3457	0.758195
$359$	30.6291	1.61654	0.808272	−	0.588809i	$-0.200403\pi$
$359$	30.6291	1.61654	0.808272	+	0.588809i	$0.200403\pi$
$360$	−0.117414	−0.00618824
$361$	28.6062	1.50559
$362$	16.1536	0.849016
$363$	1.69782	0.0891123
$364$	14.6049	0.765505
$365$	1.00000	0.0523424
$366$	−3.68459	−0.192596
$367$	−23.6884	−1.23652	−0.618262	−	0.785972i	$-0.712163\pi$
$367$	−23.6884	−1.23652	−0.618262	+	0.785972i	$0.712163\pi$
$368$	1.91828	0.0999973
$369$	0.0994928	0.00517939
$370$	−5.89830	−0.306638
$371$	26.9735	1.40039
$372$	−14.9974	−0.777577
$373$	14.8555	0.769187	0.384594	−	0.923086i	$-0.374342\pi$
$373$	14.8555	0.769187	0.384594	+	0.923086i	$0.374342\pi$
$374$	5.54969	0.286968
$375$	1.69782	0.0876750
$376$	−1.72853	−0.0891421
$377$	−16.1755	−0.833082
$378$	12.0792	0.621288
$379$	2.41537	0.124069	0.0620347	−	0.998074i	$-0.480241\pi$
$379$	2.41537	0.124069	0.0620347	+	0.998074i	$0.480241\pi$
$380$	−6.89973	−0.353948
$381$	−26.7036	−1.36807
$382$	−26.3257	−1.34694
$383$	4.84648	0.247644	0.123822	−	0.992304i	$-0.460485\pi$
$383$	4.84648	0.247644	0.123822	+	0.992304i	$0.460485\pi$
$384$	1.69782	0.0866414
$385$	−2.28220	−0.116312
$386$	15.2044	0.773883
$387$	−0.581039	−0.0295359
$388$	8.69769	0.441558
$389$	11.9323	0.604991	0.302496	−	0.953151i	$-0.402180\pi$
$389$	11.9323	0.604991	0.302496	+	0.953151i	$0.402180\pi$
$390$	−10.8652	−0.550179
$391$	10.6459	0.538385
$392$	−1.79157	−0.0904878
$393$	19.3800	0.977593
$394$	13.1695	0.663468
$395$	2.45274	0.123411
$396$	−0.117414	−0.00590026
$397$	−16.7491	−0.840613	−0.420307	−	0.907382i	$-0.638077\pi$
$397$	−16.7491	−0.840613	−0.420307	+	0.907382i	$0.638077\pi$
$398$	−4.35643	−0.218368
$399$	26.7348	1.33841
$400$	1.00000	0.0500000
$401$	22.6458	1.13088	0.565440	−	0.824790i	$-0.308706\pi$
$401$	22.6458	1.13088	0.565440	+	0.824790i	$0.308706\pi$
$402$	8.26589	0.412265
$403$	56.5287	2.81590
$404$	−17.1066	−0.851086
$405$	−8.63397	−0.429026
$406$	−5.76855	−0.286288
$407$	−5.89830	−0.292368
$408$	9.42237	0.466477
$409$	−23.6120	−1.16754	−0.583769	−	0.811920i	$-0.698423\pi$
$409$	−23.6120	−1.16754	−0.583769	+	0.811920i	$0.698423\pi$
$410$	−0.847370	−0.0418486
$411$	−24.3840	−1.20277
$412$	3.12482	0.153949
$413$	8.82402	0.434202
$414$	−0.225232	−0.0110696
$415$	5.38491	0.264335
$416$	−6.39949	−0.313761
$417$	−36.3034	−1.77779
$418$	−6.89973	−0.337477
$419$	−27.0681	−1.32236	−0.661181	−	0.750227i	$-0.729944\pi$
$419$	−27.0681	−1.32236	−0.661181	+	0.750227i	$0.729944\pi$
$420$	−3.87476	−0.189069
$421$	17.5050	0.853140	0.426570	−	0.904455i	$-0.359722\pi$
$421$	17.5050	0.853140	0.426570	+	0.904455i	$0.359722\pi$
$422$	−12.6080	−0.613747
$423$	0.202953	0.00986790
$424$	−11.8191	−0.573985
$425$	5.54969	0.269200
$426$	−21.5635	−1.04476
$427$	4.95281	0.239683
$428$	15.3641	0.742654
$429$	−10.8652	−0.524575
$430$	4.94865	0.238645
$431$	26.2133	1.26265	0.631324	−	0.775519i	$-0.282512\pi$
$431$	26.2133	1.26265	0.631324	+	0.775519i	$0.282512\pi$
$432$	−5.29280	−0.254650
$433$	−15.5052	−0.745133	−0.372567	−	0.928005i	$-0.621522\pi$
$433$	−15.5052	−0.745133	−0.372567	+	0.928005i	$0.621522\pi$
$434$	20.1594	0.967682
$435$	4.29145	0.205759
$436$	0.203512	0.00974646
$437$	−13.2356	−0.633145
$438$	1.69782	0.0811249
$439$	36.3678	1.73574	0.867871	−	0.496789i	$-0.165488\pi$
$439$	36.3678	1.73574	0.867871	+	0.496789i	$0.165488\pi$
$440$	1.00000	0.0476731
$441$	0.210354	0.0100169
$442$	−35.5152	−1.68929
$443$	−12.2924	−0.584030	−0.292015	−	0.956414i	$-0.594326\pi$
$443$	−12.2924	−0.584030	−0.292015	+	0.956414i	$0.594326\pi$
$444$	−10.0142	−0.475255
$445$	16.1501	0.765587
$446$	4.86395	0.230315
$447$	21.2224	1.00379
$448$	−2.28220	−0.107824
$449$	−33.1595	−1.56489	−0.782447	−	0.622717i	$-0.786029\pi$
$449$	−33.1595	−1.56489	−0.782447	+	0.622717i	$0.786029\pi$
$450$	−0.117414	−0.00553493
$451$	−0.847370	−0.0399011
$452$	−9.09411	−0.427751
$453$	−21.7710	−1.02289
$454$	−27.7929	−1.30438
$455$	14.6049	0.684688
$456$	−11.7145	−0.548581
$457$	4.22225	0.197509	0.0987543	−	0.995112i	$-0.468514\pi$
$457$	4.22225	0.197509	0.0987543	+	0.995112i	$0.468514\pi$
$458$	8.87680	0.414785
$459$	−29.3734	−1.37103
$460$	1.91828	0.0894403
$461$	0.153285	0.00713922	0.00356961	−	0.999994i	$-0.498864\pi$
$461$	0.153285	0.00713922	0.00356961	+	0.999994i	$0.498864\pi$
$462$	−3.87476	−0.180270
$463$	8.77472	0.407796	0.203898	−	0.978992i	$-0.434639\pi$
$463$	8.77472	0.407796	0.203898	+	0.978992i	$0.434639\pi$
$464$	2.52763	0.117342
$465$	−14.9974	−0.695486
$466$	12.4762	0.577947
$467$	22.8052	1.05530	0.527650	−	0.849462i	$-0.323073\pi$
$467$	22.8052	1.05530	0.527650	+	0.849462i	$0.323073\pi$
$468$	0.751387	0.0347329
$469$	−11.1110	−0.513057
$470$	−1.72853	−0.0797311
$471$	−7.75677	−0.357413
$472$	−3.86645	−0.177968
$473$	4.94865	0.227539
$474$	4.16431	0.191273
$475$	−6.89973	−0.316581
$476$	−12.6655	−0.580523
$477$	1.38772	0.0635394
$478$	−23.0955	−1.05636
$479$	31.7755	1.45186	0.725930	−	0.687769i	$-0.241410\pi$
$479$	31.7755	1.45186	0.725930	+	0.687769i	$0.241410\pi$
$480$	1.69782	0.0774944
$481$	37.7461	1.72107
$482$	−7.44780	−0.339238
$483$	−7.43288	−0.338208
$484$	1.00000	0.0454545
$485$	8.69769	0.394942
$486$	1.21949	0.0553171
$487$	−32.8248	−1.48743	−0.743716	−	0.668496i	$-0.766939\pi$
$487$	−32.8248	−1.48743	−0.743716	+	0.668496i	$0.766939\pi$
$488$	−2.17019	−0.0982399
$489$	20.6420	0.933464
$490$	−1.79157	−0.0809347
$491$	−2.51850	−0.113658	−0.0568292	−	0.998384i	$-0.518099\pi$
$491$	−2.51850	−0.113658	−0.0568292	+	0.998384i	$0.518099\pi$
$492$	−1.43868	−0.0648607
$493$	14.0276	0.631770
$494$	44.1547	1.98661
$495$	−0.117414	−0.00527735
$496$	−8.83332	−0.396628
$497$	28.9856	1.30018
$498$	9.14259	0.409689
$499$	−41.0134	−1.83601	−0.918005	−	0.396568i	$-0.870201\pi$
$499$	−41.0134	−1.83601	−0.918005	+	0.396568i	$0.870201\pi$
$500$	1.00000	0.0447214
$501$	−11.4765	−0.512732
$502$	−28.3341	−1.26461
$503$	−11.4292	−0.509605	−0.254802	−	0.966993i	$-0.582010\pi$
$503$	−11.4292	−0.509605	−0.254802	+	0.966993i	$0.582010\pi$
$504$	0.267961	0.0119359
$505$	−17.1066	−0.761234
$506$	1.91828	0.0852780
$507$	47.4598	2.10777
$508$	−15.7282	−0.697826
$509$	−23.3517	−1.03505	−0.517524	−	0.855669i	$-0.673146\pi$
$509$	−23.3517	−1.03505	−0.517524	+	0.855669i	$0.673146\pi$
$510$	9.42237	0.417230
$511$	−2.28220	−0.100959
$512$	1.00000	0.0441942
$513$	36.5189	1.61235
$514$	−14.1466	−0.623981
$515$	3.12482	0.137696
$516$	8.40191	0.369873
$517$	−1.72853	−0.0760206
$518$	13.4611	0.591446
$519$	13.0515	0.572897
$520$	−6.39949	−0.280636
$521$	7.23523	0.316981	0.158490	−	0.987361i	$-0.449337\pi$
$521$	7.23523	0.316981	0.158490	+	0.987361i	$0.449337\pi$
$522$	−0.296778	−0.0129896
$523$	−7.59444	−0.332082	−0.166041	−	0.986119i	$-0.553098\pi$
$523$	−7.59444	−0.332082	−0.166041	+	0.986119i	$0.553098\pi$
$524$	11.4147	0.498652
$525$	−3.87476	−0.169108
$526$	−21.5878	−0.941271
$527$	−49.0222	−2.13544
$528$	1.69782	0.0738880
$529$	−19.3202	−0.840009
$530$	−11.8191	−0.513388
$531$	0.453974	0.0197008
$532$	15.7465	0.682699
$533$	5.42273	0.234885
$534$	27.4199	1.18658
$535$	15.3641	0.664250
$536$	4.86854	0.210289
$537$	24.3564	1.05106
$538$	7.90898	0.340980
$539$	−1.79157	−0.0771682
$540$	−5.29280	−0.227766
$541$	18.3912	0.790701	0.395350	−	0.918530i	$-0.370623\pi$
$541$	18.3912	0.790701	0.395350	+	0.918530i	$0.370623\pi$
$542$	22.3186	0.958666
$543$	27.4259	1.17696
$544$	5.54969	0.237941
$545$	0.203512	0.00871750
$546$	24.7965	1.06119
$547$	24.7893	1.05992	0.529958	−	0.848024i	$-0.322208\pi$
$547$	24.7893	1.05992	0.529958	+	0.848024i	$0.322208\pi$
$548$	−14.3619	−0.613512
$549$	0.254810	0.0108750
$550$	1.00000	0.0426401
$551$	−17.4399	−0.742967
$552$	3.25689	0.138623
$553$	−5.59764	−0.238036
$554$	−30.7234	−1.30531
$555$	−10.0142	−0.425081
$556$	−21.3824	−0.906816
$557$	−16.1764	−0.685417	−0.342708	−	0.939442i	$-0.611344\pi$
$557$	−16.1764	−0.685417	−0.342708	+	0.939442i	$0.611344\pi$
$558$	1.03715	0.0439061
$559$	−31.6688	−1.33945
$560$	−2.28220	−0.0964405
$561$	9.42237	0.397813
$562$	5.86126	0.247242
$563$	33.8009	1.42454	0.712269	−	0.701907i	$-0.247668\pi$
$563$	33.8009	1.42454	0.712269	+	0.701907i	$0.247668\pi$
$564$	−2.93473	−0.123574
$565$	−9.09411	−0.382592
$566$	26.4004	1.10969
$567$	19.7044	0.827509
$568$	−12.7007	−0.532910
$569$	26.1355	1.09566	0.547828	−	0.836591i	$-0.315455\pi$
$569$	26.1355	1.09566	0.547828	+	0.836591i	$0.315455\pi$
$570$	−11.7145	−0.490666
$571$	27.8519	1.16556	0.582782	−	0.812628i	$-0.301964\pi$
$571$	27.8519	1.16556	0.582782	+	0.812628i	$0.301964\pi$
$572$	−6.39949	−0.267576
$573$	−44.6963	−1.86721
$574$	1.93387	0.0807180
$575$	1.91828	0.0799978
$576$	−0.117414	−0.00489223
$577$	25.5038	1.06174	0.530868	−	0.847454i	$-0.321866\pi$
$577$	25.5038	1.06174	0.530868	+	0.847454i	$0.321866\pi$
$578$	13.7991	0.573967
$579$	25.8143	1.07281
$580$	2.52763	0.104954
$581$	−12.2894	−0.509852
$582$	14.7671	0.612116
$583$	−11.8191	−0.489496
$584$	1.00000	0.0413803
$585$	0.751387	0.0310660
$586$	19.7245	0.814811
$587$	−42.8312	−1.76783	−0.883916	−	0.467645i	$-0.845102\pi$
$587$	−42.8312	−1.76783	−0.883916	+	0.467645i	$0.845102\pi$
$588$	−3.04175	−0.125440
$589$	60.9475	2.51130
$590$	−3.86645	−0.159179
$591$	22.3594	0.919741
$592$	−5.89830	−0.242419
$593$	11.3436	0.465824	0.232912	−	0.972498i	$-0.425175\pi$
$593$	11.3436	0.465824	0.232912	+	0.972498i	$0.425175\pi$
$594$	−5.29280	−0.217166
$595$	−12.6655	−0.519235
$596$	12.4998	0.512013
$597$	−7.39643	−0.302716
$598$	−12.2760	−0.502004
$599$	41.6862	1.70325	0.851626	−	0.524150i	$-0.175617\pi$
$599$	41.6862	1.70325	0.851626	+	0.524150i	$0.175617\pi$
$600$	1.69782	0.0693131
$601$	−23.0400	−0.939822	−0.469911	−	0.882714i	$-0.655714\pi$
$601$	−23.0400	−0.939822	−0.469911	+	0.882714i	$0.655714\pi$
$602$	−11.2938	−0.460301
$603$	−0.571632	−0.0232787
$604$	−12.8229	−0.521758
$605$	1.00000	0.0406558
$606$	−29.0439	−1.17983
$607$	25.0568	1.01703	0.508513	−	0.861054i	$-0.330195\pi$
$607$	25.0568	1.01703	0.508513	+	0.861054i	$0.330195\pi$
$608$	−6.89973	−0.279821
$609$	−9.79395	−0.396871
$610$	−2.17019	−0.0878684
$611$	11.0617	0.447508
$612$	−0.651610	−0.0263398
$613$	−19.2595	−0.777885	−0.388943	−	0.921262i	$-0.627160\pi$
$613$	−19.2595	−0.777885	−0.388943	+	0.921262i	$0.627160\pi$
$614$	2.13294	0.0860783
$615$	−1.43868	−0.0580132
$616$	−2.28220	−0.0919524
$617$	25.8452	1.04049	0.520245	−	0.854017i	$-0.325841\pi$
$617$	25.8452	1.04049	0.520245	+	0.854017i	$0.325841\pi$
$618$	5.30538	0.213414
$619$	−28.7345	−1.15494	−0.577468	−	0.816413i	$-0.695959\pi$
$619$	−28.7345	−1.15494	−0.577468	+	0.816413i	$0.695959\pi$
$620$	−8.83332	−0.354755
$621$	−10.1531	−0.407429
$622$	21.6432	0.867813
$623$	−36.8577	−1.47667
$624$	−10.8652	−0.434955
$625$	1.00000	0.0400000
$626$	−20.2440	−0.809113
$627$	−11.7145	−0.467831
$628$	−4.56867	−0.182310
$629$	−32.7337	−1.30518
$630$	0.267961	0.0106758
$631$	−3.01168	−0.119893	−0.0599466	−	0.998202i	$-0.519093\pi$
$631$	−3.01168	−0.119893	−0.0599466	+	0.998202i	$0.519093\pi$
$632$	2.45274	0.0975648
$633$	−21.4061	−0.850814
$634$	−27.2831	−1.08355
$635$	−15.7282	−0.624154
$636$	−20.0667	−0.795695
$637$	11.4651	0.454264
$638$	2.52763	0.100070
$639$	1.49124	0.0589924
$640$	1.00000	0.0395285
$641$	5.17629	0.204451	0.102226	−	0.994761i	$-0.467404\pi$
$641$	5.17629	0.204451	0.102226	+	0.994761i	$0.467404\pi$
$642$	26.0855	1.02951
$643$	−25.4813	−1.00488	−0.502442	−	0.864611i	$-0.667565\pi$
$643$	−25.4813	−1.00488	−0.502442	+	0.864611i	$0.667565\pi$
$644$	−4.37790	−0.172513
$645$	8.40191	0.330825
$646$	−38.2914	−1.50655
$647$	2.73178	0.107397	0.0536987	−	0.998557i	$-0.482899\pi$
$647$	2.73178	0.107397	0.0536987	+	0.998557i	$0.482899\pi$
$648$	−8.63397	−0.339175
$649$	−3.86645	−0.151772
$650$	−6.39949	−0.251009
$651$	34.2270	1.34146
$652$	12.1580	0.476143
$653$	18.9988	0.743480	0.371740	−	0.928337i	$-0.378761\pi$
$653$	18.9988	0.743480	0.371740	+	0.928337i	$0.378761\pi$
$654$	0.345526	0.0135111
$655$	11.4147	0.446008
$656$	−0.847370	−0.0330842
$657$	−0.117414	−0.00458074
$658$	3.94485	0.153786
$659$	−3.32995	−0.129717	−0.0648583	−	0.997894i	$-0.520660\pi$
$659$	−3.32995	−0.129717	−0.0648583	+	0.997894i	$0.520660\pi$
$660$	1.69782	0.0660875
$661$	18.6307	0.724652	0.362326	−	0.932051i	$-0.381983\pi$
$661$	18.6307	0.724652	0.362326	+	0.932051i	$0.381983\pi$
$662$	28.3061	1.10015
$663$	−60.2983	−2.34179
$664$	5.38491	0.208975
$665$	15.7465	0.610625
$666$	0.692541	0.0268354
$667$	4.84870	0.187742
$668$	−6.75955	−0.261535
$669$	8.25811	0.319277
$670$	4.86854	0.188088
$671$	−2.17019	−0.0837792
$672$	−3.87476	−0.149472
$673$	24.1169	0.929637	0.464819	−	0.885406i	$-0.346120\pi$
$673$	24.1169	0.929637	0.464819	+	0.885406i	$0.346120\pi$
$674$	5.66151	0.218073
$675$	−5.29280	−0.203720
$676$	27.9534	1.07513
$677$	−31.2586	−1.20137	−0.600683	−	0.799487i	$-0.705105\pi$
$677$	−31.2586	−1.20137	−0.600683	+	0.799487i	$0.705105\pi$
$678$	−15.4401	−0.592975
$679$	−19.8499	−0.761768
$680$	5.54969	0.212821
$681$	−47.1873	−1.80822
$682$	−8.83332	−0.338245
$683$	29.3531	1.12317	0.561583	−	0.827420i	$-0.310192\pi$
$683$	29.3531	1.12317	0.561583	+	0.827420i	$0.310192\pi$
$684$	0.810122	0.0309758
$685$	−14.3619	−0.548742
$686$	20.0641	0.766051
$687$	15.0712	0.575002
$688$	4.94865	0.188666
$689$	75.6361	2.88150
$690$	3.25689	0.123988
$691$	−32.5508	−1.23829	−0.619145	−	0.785277i	$-0.712521\pi$
$691$	−32.5508	−1.23829	−0.619145	+	0.785277i	$0.712521\pi$
$692$	7.68722	0.292224
$693$	0.267961	0.0101790
$694$	−19.6793	−0.747016
$695$	−21.3824	−0.811081
$696$	4.29145	0.162667
$697$	−4.70264	−0.178125
$698$	14.2523	0.539458
$699$	21.1822	0.801186
$700$	−2.28220	−0.0862590
$701$	−1.40006	−0.0528796	−0.0264398	−	0.999650i	$-0.508417\pi$
$701$	−1.40006	−0.0528796	−0.0264398	+	0.999650i	$0.508417\pi$
$702$	33.8712	1.27839
$703$	40.6966	1.53490
$704$	1.00000	0.0376889
$705$	−2.93473	−0.110528
$706$	−10.2037	−0.384020
$707$	39.0407	1.46828
$708$	−6.56454	−0.246710
$709$	−4.16647	−0.156475	−0.0782374	−	0.996935i	$-0.524929\pi$
$709$	−4.16647	−0.156475	−0.0782374	+	0.996935i	$0.524929\pi$
$710$	−12.7007	−0.476650
$711$	−0.287985	−0.0108003
$712$	16.1501	0.605250
$713$	−16.9448	−0.634587
$714$	−21.5037	−0.804757
$715$	−6.39949	−0.239327
$716$	14.3457	0.536125
$717$	−39.2119	−1.46439
$718$	30.6291	1.14307
$719$	−39.3510	−1.46755	−0.733773	−	0.679395i	$-0.762242\pi$
$719$	−39.3510	−1.46755	−0.733773	+	0.679395i	$0.762242\pi$
$720$	−0.117414	−0.00437575
$721$	−7.13146	−0.265590
$722$	28.6062	1.06461
$723$	−12.6450	−0.470273
$724$	16.1536	0.600345
$725$	2.52763	0.0938738
$726$	1.69782	0.0630119
$727$	−1.04179	−0.0386379	−0.0193189	−	0.999813i	$-0.506150\pi$
$727$	−1.04179	−0.0386379	−0.0193189	+	0.999813i	$0.506150\pi$
$728$	14.6049	0.541294
$729$	27.9724	1.03601
$730$	1.00000	0.0370117
$731$	27.4635	1.01577
$732$	−3.68459	−0.136186
$733$	32.0253	1.18288	0.591441	−	0.806348i	$-0.298559\pi$
$733$	32.0253	1.18288	0.591441	+	0.806348i	$0.298559\pi$
$734$	−23.6884	−0.874354
$735$	−3.04175	−0.112197
$736$	1.91828	0.0707088
$737$	4.86854	0.179335
$738$	0.0994928	0.00366238
$739$	2.65242	0.0975708	0.0487854	−	0.998809i	$-0.484465\pi$
$739$	2.65242	0.0975708	0.0487854	+	0.998809i	$0.484465\pi$
$740$	−5.89830	−0.216826
$741$	74.9667	2.75397
$742$	26.9735	0.990228
$743$	19.4924	0.715107	0.357553	−	0.933893i	$-0.383611\pi$
$743$	19.4924	0.715107	0.357553	+	0.933893i	$0.383611\pi$
$744$	−14.9974	−0.549830
$745$	12.4998	0.457958
$746$	14.8555	0.543897
$747$	−0.632261	−0.0231332
$748$	5.54969	0.202917
$749$	−35.0640	−1.28121
$750$	1.69782	0.0619956
$751$	44.1893	1.61249	0.806245	−	0.591582i	$-0.201496\pi$
$751$	44.1893	1.61249	0.806245	+	0.591582i	$0.201496\pi$
$752$	−1.72853	−0.0630330
$753$	−48.1062	−1.75309
$754$	−16.1755	−0.589078
$755$	−12.8229	−0.466674
$756$	12.0792	0.439317
$757$	−12.6318	−0.459111	−0.229555	−	0.973296i	$-0.573727\pi$
$757$	−12.6318	−0.459111	−0.229555	+	0.973296i	$0.573727\pi$
$758$	2.41537	0.0877303
$759$	3.25689	0.118218
$760$	−6.89973	−0.250279
$761$	−27.0710	−0.981324	−0.490662	−	0.871350i	$-0.663245\pi$
$761$	−27.0710	−0.981324	−0.490662	+	0.871350i	$0.663245\pi$
$762$	−26.7036	−0.967369
$763$	−0.464455	−0.0168144
$764$	−26.3257	−0.952432
$765$	−0.651610	−0.0235590
$766$	4.84648	0.175111
$767$	24.7433	0.893430
$768$	1.69782	0.0612647
$769$	−10.1122	−0.364655	−0.182328	−	0.983238i	$-0.558363\pi$
$769$	−10.1122	−0.364655	−0.182328	+	0.983238i	$0.558363\pi$
$770$	−2.28220	−0.0822448
$771$	−24.0184	−0.865002
$772$	15.2044	0.547218
$773$	9.17399	0.329965	0.164983	−	0.986296i	$-0.447243\pi$
$773$	9.17399	0.329965	0.164983	+	0.986296i	$0.447243\pi$
$774$	−0.581039	−0.0208850
$775$	−8.83332	−0.317302
$776$	8.69769	0.312229
$777$	22.8545	0.819900
$778$	11.9323	0.427793
$779$	5.84662	0.209477
$780$	−10.8652	−0.389035
$781$	−12.7007	−0.454467
$782$	10.6459	0.380696
$783$	−13.3782	−0.478099
$784$	−1.79157	−0.0639845
$785$	−4.56867	−0.163063
$786$	19.3800	0.691263
$787$	21.8573	0.779130	0.389565	−	0.920999i	$-0.372625\pi$
$787$	21.8573	0.779130	0.389565	+	0.920999i	$0.372625\pi$
$788$	13.1695	0.469143
$789$	−36.6521	−1.30485
$790$	2.45274	0.0872646
$791$	20.7546	0.737948
$792$	−0.117414	−0.00417211
$793$	13.8881	0.493181
$794$	−16.7491	−0.594403
$795$	−20.0667	−0.711691
$796$	−4.35643	−0.154410
$797$	−38.3171	−1.35726	−0.678631	−	0.734479i	$-0.737426\pi$
$797$	−38.3171	−1.35726	−0.678631	+	0.734479i	$0.737426\pi$
$798$	26.7348	0.946401
$799$	−9.59281	−0.339369
$800$	1.00000	0.0353553
$801$	−1.89624	−0.0670003
$802$	22.6458	0.799653
$803$	1.00000	0.0352892
$804$	8.26589	0.291515
$805$	−4.37790	−0.154301
$806$	56.5287	1.99114
$807$	13.4280	0.472688
$808$	−17.1066	−0.601809
$809$	−22.6567	−0.796567	−0.398284	−	0.917262i	$-0.630394\pi$
$809$	−22.6567	−0.796567	−0.398284	+	0.917262i	$0.630394\pi$
$810$	−8.63397	−0.303367
$811$	−3.71821	−0.130564	−0.0652821	−	0.997867i	$-0.520795\pi$
$811$	−3.71821	−0.130564	−0.0652821	+	0.997867i	$0.520795\pi$
$812$	−5.76855	−0.202436
$813$	37.8929	1.32896
$814$	−5.89830	−0.206735
$815$	12.1580	0.425875
$816$	9.42237	0.329849
$817$	−34.1443	−1.19456
$818$	−23.6120	−0.825574
$819$	−1.71481	−0.0599205
$820$	−0.847370	−0.0295914
$821$	−13.3545	−0.466075	−0.233038	−	0.972468i	$-0.574867\pi$
$821$	−13.3545	−0.466075	−0.233038	+	0.972468i	$0.574867\pi$
$822$	−24.3840	−0.850489
$823$	−19.0422	−0.663768	−0.331884	−	0.943320i	$-0.607684\pi$
$823$	−19.0422	−0.663768	−0.331884	+	0.943320i	$0.607684\pi$
$824$	3.12482	0.108858
$825$	1.69782	0.0591104
$826$	8.82402	0.307027
$827$	6.57515	0.228640	0.114320	−	0.993444i	$-0.463531\pi$
$827$	6.57515	0.228640	0.114320	+	0.993444i	$0.463531\pi$
$828$	−0.225232	−0.00782736
$829$	−16.1975	−0.562561	−0.281281	−	0.959626i	$-0.590759\pi$
$829$	−16.1975	−0.562561	−0.281281	+	0.959626i	$0.590759\pi$
$830$	5.38491	0.186913
$831$	−52.1627	−1.80950
$832$	−6.39949	−0.221862
$833$	−9.94264	−0.344492
$834$	−36.3034	−1.25709
$835$	−6.75955	−0.233924
$836$	−6.89973	−0.238632
$837$	46.7530	1.61602
$838$	−27.0681	−0.935051
$839$	26.6254	0.919211	0.459606	−	0.888123i	$-0.347991\pi$
$839$	26.6254	0.919211	0.459606	+	0.888123i	$0.347991\pi$
$840$	−3.87476	−0.133692
$841$	−22.6111	−0.779693
$842$	17.5050	0.603261
$843$	9.95135	0.342743
$844$	−12.6080	−0.433985
$845$	27.9534	0.961627
$846$	0.202953	0.00697766
$847$	−2.28220	−0.0784173
$848$	−11.8191	−0.405869
$849$	44.8231	1.53832
$850$	5.54969	0.190353
$851$	−11.3146	−0.387859
$852$	−21.5635	−0.738754
$853$	−10.6897	−0.366009	−0.183005	−	0.983112i	$-0.558582\pi$
$853$	−10.6897	−0.366009	−0.183005	+	0.983112i	$0.558582\pi$
$854$	4.95281	0.169482
$855$	0.810122	0.0277056
$856$	15.3641	0.525136
$857$	−1.72005	−0.0587558	−0.0293779	−	0.999568i	$-0.509353\pi$
$857$	−1.72005	−0.0587558	−0.0293779	+	0.999568i	$0.509353\pi$
$858$	−10.8652	−0.370931
$859$	−16.6416	−0.567804	−0.283902	−	0.958853i	$-0.591629\pi$
$859$	−16.6416	−0.567804	−0.283902	+	0.958853i	$0.591629\pi$
$860$	4.94865	0.168748
$861$	3.28335	0.111896
$862$	26.2133	0.892828
$863$	−23.5974	−0.803265	−0.401633	−	0.915801i	$-0.631557\pi$
$863$	−23.5974	−0.803265	−0.401633	+	0.915801i	$0.631557\pi$
$864$	−5.29280	−0.180065
$865$	7.68722	0.261373
$866$	−15.5052	−0.526889
$867$	23.4284	0.795669
$868$	20.1594	0.684255
$869$	2.45274	0.0832035
$870$	4.29145	0.145494
$871$	−31.1561	−1.05569
$872$	0.203512	0.00689179
$873$	−1.02123	−0.0345633
$874$	−13.2356	−0.447701
$875$	−2.28220	−0.0771524
$876$	1.69782	0.0573640
$877$	40.0228	1.35147	0.675737	−	0.737143i	$-0.263825\pi$
$877$	40.0228	1.35147	0.675737	+	0.737143i	$0.263825\pi$
$878$	36.3678	1.22736
$879$	33.4886	1.12954
$880$	1.00000	0.0337100
$881$	−9.33823	−0.314613	−0.157306	−	0.987550i	$-0.550281\pi$
$881$	−9.33823	−0.314613	−0.157306	+	0.987550i	$0.550281\pi$
$882$	0.210354	0.00708300
$883$	−28.7642	−0.967991	−0.483996	−	0.875070i	$-0.660815\pi$
$883$	−28.7642	−0.967991	−0.483996	+	0.875070i	$0.660815\pi$
$884$	−35.5152	−1.19451
$885$	−6.56454	−0.220664
$886$	−12.2924	−0.412972
$887$	−33.3761	−1.12066	−0.560330	−	0.828270i	$-0.689326\pi$
$887$	−33.3761	−1.12066	−0.560330	+	0.828270i	$0.689326\pi$
$888$	−10.0142	−0.336056
$889$	35.8949	1.20387
$890$	16.1501	0.541352
$891$	−8.63397	−0.289249
$892$	4.86395	0.162857
$893$	11.9264	0.399101
$894$	21.2224	0.709784
$895$	14.3457	0.479524
$896$	−2.28220	−0.0762429
$897$	−20.8424	−0.695909
$898$	−33.1595	−1.10655
$899$	−22.3274	−0.744659
$900$	−0.117414	−0.00391379
$901$	−65.5923	−2.18520
$902$	−0.847370	−0.0282143
$903$	−19.1748	−0.638098
$904$	−9.09411	−0.302466
$905$	16.1536	0.536965
$906$	−21.7710	−0.723293
$907$	−51.8002	−1.72000	−0.859998	−	0.510298i	$-0.829535\pi$
$907$	−51.8002	−1.72000	−0.859998	+	0.510298i	$0.829535\pi$
$908$	−27.7929	−0.922339
$909$	2.00855	0.0666194
$910$	14.6049	0.484148
$911$	50.6628	1.67853	0.839266	−	0.543721i	$-0.182985\pi$
$911$	50.6628	1.67853	0.839266	+	0.543721i	$0.182985\pi$
$912$	−11.7145	−0.387905
$913$	5.38491	0.178214
$914$	4.22225	0.139660
$915$	−3.68459	−0.121809
$916$	8.87680	0.293298
$917$	−26.0506	−0.860265
$918$	−29.3734	−0.969468
$919$	8.30562	0.273977	0.136989	−	0.990573i	$-0.456258\pi$
$919$	8.30562	0.273977	0.136989	+	0.990573i	$0.456258\pi$
$920$	1.91828	0.0632439
$921$	3.62134	0.119327
$922$	0.153285	0.00504819
$923$	81.2781	2.67530
$924$	−3.87476	−0.127470
$925$	−5.89830	−0.193935
$926$	8.77472	0.288355
$927$	−0.366896	−0.0120505
$928$	2.52763	0.0829735
$929$	45.2907	1.48594	0.742970	−	0.669325i	$-0.233417\pi$
$929$	45.2907	1.48594	0.742970	+	0.669325i	$0.233417\pi$
$930$	−14.9974	−0.491783
$931$	12.3613	0.405126
$932$	12.4762	0.408670
$933$	36.7462	1.20302
$934$	22.8052	0.746210
$935$	5.54969	0.181494
$936$	0.751387	0.0245598
$937$	−48.6226	−1.58843	−0.794216	−	0.607636i	$-0.792118\pi$
$937$	−48.6226	−1.58843	−0.794216	+	0.607636i	$0.792118\pi$
$938$	−11.1110	−0.362786
$939$	−34.3707	−1.12164
$940$	−1.72853	−0.0563784
$941$	55.2368	1.80067	0.900334	−	0.435200i	$-0.143322\pi$
$941$	55.2368	1.80067	0.900334	+	0.435200i	$0.143322\pi$
$942$	−7.75677	−0.252729
$943$	−1.62549	−0.0529334
$944$	−3.86645	−0.125842
$945$	12.0792	0.392937
$946$	4.94865	0.160895
$947$	2.77973	0.0903291	0.0451645	−	0.998980i	$-0.485619\pi$
$947$	2.77973	0.0903291	0.0451645	+	0.998980i	$0.485619\pi$
$948$	4.16431	0.135250
$949$	−6.39949	−0.207736
$950$	−6.89973	−0.223857
$951$	−46.3218	−1.50209
$952$	−12.6655	−0.410491
$953$	37.3578	1.21014	0.605069	−	0.796173i	$-0.293146\pi$
$953$	37.3578	1.21014	0.605069	+	0.796173i	$0.293146\pi$
$954$	1.38772	0.0449291
$955$	−26.3257	−0.851881
$956$	−23.0955	−0.746960
$957$	4.29145	0.138723
$958$	31.7755	1.02662
$959$	32.7768	1.05842
$960$	1.69782	0.0547968
$961$	47.0275	1.51702
$962$	37.7461	1.21698
$963$	−1.80396	−0.0581318
$964$	−7.44780	−0.239878
$965$	15.2044	0.489447
$966$	−7.43288	−0.239149
$967$	−6.58995	−0.211918	−0.105959	−	0.994370i	$-0.533791\pi$
$967$	−6.58995	−0.211918	−0.105959	+	0.994370i	$0.533791\pi$
$968$	1.00000	0.0321412
$969$	−65.0118	−2.08848
$970$	8.69769	0.279266
$971$	3.92155	0.125849	0.0629243	−	0.998018i	$-0.479957\pi$
$971$	3.92155	0.125849	0.0629243	+	0.998018i	$0.479957\pi$
$972$	1.21949	0.0391151
$973$	48.7989	1.56442
$974$	−32.8248	−1.05177
$975$	−10.8652	−0.347964
$976$	−2.17019	−0.0694661
$977$	−22.6860	−0.725791	−0.362895	−	0.931830i	$-0.618212\pi$
$977$	−22.6860	−0.725791	−0.362895	+	0.931830i	$0.618212\pi$
$978$	20.6420	0.660059
$979$	16.1501	0.516159
$980$	−1.79157	−0.0572295
$981$	−0.0238951	−0.000762911 0
$982$	−2.51850	−0.0803686
$983$	7.67985	0.244949	0.122475	−	0.992472i	$-0.460917\pi$
$983$	7.67985	0.244949	0.122475	+	0.992472i	$0.460917\pi$
$984$	−1.43868	−0.0458634
$985$	13.1695	0.419614
$986$	14.0276	0.446729
$987$	6.69763	0.213188
$988$	44.1547	1.40475
$989$	9.49290	0.301857
$990$	−0.117414	−0.00373165
$991$	−54.2597	−1.72362	−0.861808	−	0.507235i	$-0.830668\pi$
$991$	−54.2597	−1.72362	−0.861808	+	0.507235i	$0.830668\pi$
$992$	−8.83332	−0.280458
$993$	48.0586	1.52509
$994$	28.9856	0.919367
$995$	−4.35643	−0.138108
$996$	9.14259	0.289694
$997$	14.9957	0.474919	0.237459	−	0.971397i	$-0.423685\pi$
$997$	14.9957	0.474919	0.237459	+	0.971397i	$0.423685\pi$
$998$	−41.0134	−1.29826
$999$	31.2185	0.987710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.v.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.v.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.69782 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.69782 q^{6} -2.28220 q^{7} +1.00000 q^{8} -0.117414 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.69782 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.69782 q^{6} -2.28220 q^{7} +1.00000 q^{8} -0.117414 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.69782 q^{12} -6.39949 q^{13} -2.28220 q^{14} +1.69782 q^{15} +1.00000 q^{16} +5.54969 q^{17} -0.117414 q^{18} -6.89973 q^{19} +1.00000 q^{20} -3.87476 q^{21} +1.00000 q^{22} +1.91828 q^{23} +1.69782 q^{24} +1.00000 q^{25} -6.39949 q^{26} -5.29280 q^{27} -2.28220 q^{28} +2.52763 q^{29} +1.69782 q^{30} -8.83332 q^{31} +1.00000 q^{32} +1.69782 q^{33} +5.54969 q^{34} -2.28220 q^{35} -0.117414 q^{36} -5.89830 q^{37} -6.89973 q^{38} -10.8652 q^{39} +1.00000 q^{40} -0.847370 q^{41} -3.87476 q^{42} +4.94865 q^{43} +1.00000 q^{44} -0.117414 q^{45} +1.91828 q^{46} -1.72853 q^{47} +1.69782 q^{48} -1.79157 q^{49} +1.00000 q^{50} +9.42237 q^{51} -6.39949 q^{52} -11.8191 q^{53} -5.29280 q^{54} +1.00000 q^{55} -2.28220 q^{56} -11.7145 q^{57} +2.52763 q^{58} -3.86645 q^{59} +1.69782 q^{60} -2.17019 q^{61} -8.83332 q^{62} +0.267961 q^{63} +1.00000 q^{64} -6.39949 q^{65} +1.69782 q^{66} +4.86854 q^{67} +5.54969 q^{68} +3.25689 q^{69} -2.28220 q^{70} -12.7007 q^{71} -0.117414 q^{72} +1.00000 q^{73} -5.89830 q^{74} +1.69782 q^{75} -6.89973 q^{76} -2.28220 q^{77} -10.8652 q^{78} +2.45274 q^{79} +1.00000 q^{80} -8.63397 q^{81} -0.847370 q^{82} +5.38491 q^{83} -3.87476 q^{84} +5.54969 q^{85} +4.94865 q^{86} +4.29145 q^{87} +1.00000 q^{88} +16.1501 q^{89} -0.117414 q^{90} +14.6049 q^{91} +1.91828 q^{92} -14.9974 q^{93} -1.72853 q^{94} -6.89973 q^{95} +1.69782 q^{96} +8.69769 q^{97} -1.79157 q^{98} -0.117414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 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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