LMFDB - Embedded newform 4730.2.a.v.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.220036.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - 2x - 1 $ x^5 - 2x^4 - 5x^3 + 11x^2 - 2x - 1
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			$0.493132$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.493132 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.493132 q^{6} +2.43893 q^{7} +1.00000 q^{8} -2.75682 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.493132 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.493132 q^{6} +2.43893 q^{7} +1.00000 q^{8} -2.75682 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.493132 q^{12} -3.83887 q^{13} +2.43893 q^{14} -0.493132 q^{15} +1.00000 q^{16} -2.42956 q^{17} -2.75682 q^{18} -5.39208 q^{19} -1.00000 q^{20} +1.20272 q^{21} +1.00000 q^{22} -0.133655 q^{23} +0.493132 q^{24} +1.00000 q^{25} -3.83887 q^{26} -2.83887 q^{27} +2.43893 q^{28} -4.69585 q^{29} -0.493132 q^{30} +7.17201 q^{31} +1.00000 q^{32} +0.493132 q^{33} -2.42956 q^{34} -2.43893 q^{35} -2.75682 q^{36} -1.99563 q^{37} -5.39208 q^{38} -1.89307 q^{39} -1.00000 q^{40} -2.17987 q^{41} +1.20272 q^{42} -1.00000 q^{43} +1.00000 q^{44} +2.75682 q^{45} -0.133655 q^{46} +1.86172 q^{47} +0.493132 q^{48} -1.05160 q^{49} +1.00000 q^{50} -1.19810 q^{51} -3.83887 q^{52} -1.84799 q^{53} -2.83887 q^{54} -1.00000 q^{55} +2.43893 q^{56} -2.65901 q^{57} -4.69585 q^{58} -11.2330 q^{59} -0.493132 q^{60} +2.06007 q^{61} +7.17201 q^{62} -6.72370 q^{63} +1.00000 q^{64} +3.83887 q^{65} +0.493132 q^{66} -9.78170 q^{67} -2.42956 q^{68} -0.0659097 q^{69} -2.43893 q^{70} -14.0900 q^{71} -2.75682 q^{72} -7.59682 q^{73} -1.99563 q^{74} +0.493132 q^{75} -5.39208 q^{76} +2.43893 q^{77} -1.89307 q^{78} -4.48579 q^{79} -1.00000 q^{80} +6.87052 q^{81} -2.17987 q^{82} +2.77004 q^{83} +1.20272 q^{84} +2.42956 q^{85} -1.00000 q^{86} -2.31567 q^{87} +1.00000 q^{88} -1.73631 q^{89} +2.75682 q^{90} -9.36276 q^{91} -0.133655 q^{92} +3.53675 q^{93} +1.86172 q^{94} +5.39208 q^{95} +0.493132 q^{96} -7.15262 q^{97} -1.05160 q^{98} -2.75682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9} - 5 q^{10} + 5 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{14} - 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 5 q^{20} + 2 q^{21} + 5 q^{22} - 6 q^{23} + 2 q^{24} + 5 q^{25} - 12 q^{26} - 7 q^{27} - 6 q^{28} - 19 q^{29} - 2 q^{30} - 7 q^{31} + 5 q^{32} + 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} - q^{37} - 4 q^{38} - 20 q^{39} - 5 q^{40} - 2 q^{41} + 2 q^{42} - 5 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} - 5 q^{49} + 5 q^{50} - 5 q^{51} - 12 q^{52} - 6 q^{53} - 7 q^{54} - 5 q^{55} - 6 q^{56} - 15 q^{57} - 19 q^{58} - 5 q^{59} - 2 q^{60} - 5 q^{61} - 7 q^{62} - 17 q^{63} + 5 q^{64} + 12 q^{65} + 2 q^{66} - 20 q^{67} - 2 q^{68} - 40 q^{69} + 6 q^{70} - 22 q^{71} - q^{72} + 10 q^{73} - q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 20 q^{78} - 9 q^{79} - 5 q^{80} - 15 q^{81} - 2 q^{82} - 19 q^{83} + 2 q^{84} + 2 q^{85} - 5 q^{86} + 15 q^{87} + 5 q^{88} - 21 q^{89} + q^{90} + 10 q^{91} - 6 q^{92} - 15 q^{93} + 7 q^{94} + 4 q^{95} + 2 q^{96} + 10 q^{97} - 5 q^{98} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9 - 5 * q^10 + 5 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^14 - 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 - 4 * q^19 - 5 * q^20 + 2 * q^21 + 5 * q^22 - 6 * q^23 + 2 * q^24 + 5 * q^25 - 12 * q^26 - 7 * q^27 - 6 * q^28 - 19 * q^29 - 2 * q^30 - 7 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 - q^37 - 4 * q^38 - 20 * q^39 - 5 * q^40 - 2 * q^41 + 2 * q^42 - 5 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 - 5 * q^49 + 5 * q^50 - 5 * q^51 - 12 * q^52 - 6 * q^53 - 7 * q^54 - 5 * q^55 - 6 * q^56 - 15 * q^57 - 19 * q^58 - 5 * q^59 - 2 * q^60 - 5 * q^61 - 7 * q^62 - 17 * q^63 + 5 * q^64 + 12 * q^65 + 2 * q^66 - 20 * q^67 - 2 * q^68 - 40 * q^69 + 6 * q^70 - 22 * q^71 - q^72 + 10 * q^73 - q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 20 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 - 2 * q^82 - 19 * q^83 + 2 * q^84 + 2 * q^85 - 5 * q^86 + 15 * q^87 + 5 * q^88 - 21 * q^89 + q^90 + 10 * q^91 - 6 * q^92 - 15 * q^93 + 7 * q^94 + 4 * q^95 + 2 * q^96 + 10 * q^97 - 5 * q^98 - 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
$3$	0.493132	0.284710	0.142355	−	0.989816i	$-0.454533\pi$
$3$	0.493132	0.284710	0.142355	+	0.989816i	$0.454533\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.493132	0.201320
$7$	2.43893	0.921830	0.460915	−	0.887444i	$-0.347521\pi$
$7$	2.43893	0.921830	0.460915	+	0.887444i	$0.347521\pi$
$8$	1.00000	0.353553
$9$	−2.75682	−0.918940
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.493132	0.142355
$13$	−3.83887	−1.06471	−0.532356	−	0.846521i	$-0.678693\pi$
$13$	−3.83887	−1.06471	−0.532356	+	0.846521i	$0.678693\pi$
$14$	2.43893	0.651832
$15$	−0.493132	−0.127326
$16$	1.00000	0.250000
$17$	−2.42956	−0.589256	−0.294628	−	0.955612i	$-0.595196\pi$
$17$	−2.42956	−0.589256	−0.294628	+	0.955612i	$0.595196\pi$
$18$	−2.75682	−0.649789
$19$	−5.39208	−1.23703	−0.618514	−	0.785774i	$-0.712265\pi$
$19$	−5.39208	−1.23703	−0.618514	+	0.785774i	$0.712265\pi$
$20$	−1.00000	−0.223607
$21$	1.20272	0.262454
$22$	1.00000	0.213201
$23$	−0.133655	−0.0278690	−0.0139345	−	0.999903i	$-0.504436\pi$
$23$	−0.133655	−0.0278690	−0.0139345	+	0.999903i	$0.504436\pi$
$24$	0.493132	0.100660
$25$	1.00000	0.200000
$26$	−3.83887	−0.752865
$27$	−2.83887	−0.546341
$28$	2.43893	0.460915
$29$	−4.69585	−0.871997	−0.435999	−	0.899947i	$-0.643605\pi$
$29$	−4.69585	−0.871997	−0.435999	+	0.899947i	$0.643605\pi$
$30$	−0.493132	−0.0900332
$31$	7.17201	1.28813	0.644065	−	0.764971i	$-0.277247\pi$
$31$	7.17201	1.28813	0.644065	+	0.764971i	$0.277247\pi$
$32$	1.00000	0.176777
$33$	0.493132	0.0858433
$34$	−2.42956	−0.416667
$35$	−2.43893	−0.412255
$36$	−2.75682	−0.459470
$37$	−1.99563	−0.328080	−0.164040	−	0.986454i	$-0.552453\pi$
$37$	−1.99563	−0.328080	−0.164040	+	0.986454i	$0.552453\pi$
$38$	−5.39208	−0.874711
$39$	−1.89307	−0.303134
$40$	−1.00000	−0.158114
$41$	−2.17987	−0.340438	−0.170219	−	0.985406i	$-0.554447\pi$
$41$	−2.17987	−0.340438	−0.170219	+	0.985406i	$0.554447\pi$
$42$	1.20272	0.185583
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	2.75682	0.410963
$46$	−0.133655	−0.0197064
$47$	1.86172	0.271560	0.135780	−	0.990739i	$-0.456646\pi$
$47$	1.86172	0.271560	0.135780	+	0.990739i	$0.456646\pi$
$48$	0.493132	0.0711775
$49$	−1.05160	−0.150229
$50$	1.00000	0.141421
$51$	−1.19810	−0.167767
$52$	−3.83887	−0.532356
$53$	−1.84799	−0.253841	−0.126920	−	0.991913i	$-0.540509\pi$
$53$	−1.84799	−0.253841	−0.126920	+	0.991913i	$0.540509\pi$
$54$	−2.83887	−0.386322
$55$	−1.00000	−0.134840
$56$	2.43893	0.325916
$57$	−2.65901	−0.352194
$58$	−4.69585	−0.616595
$59$	−11.2330	−1.46241	−0.731205	−	0.682158i	$-0.761042\pi$
$59$	−11.2330	−1.46241	−0.731205	+	0.682158i	$0.761042\pi$
$60$	−0.493132	−0.0636631
$61$	2.06007	0.263766	0.131883	−	0.991265i	$-0.457898\pi$
$61$	2.06007	0.263766	0.131883	+	0.991265i	$0.457898\pi$
$62$	7.17201	0.910846
$63$	−6.72370	−0.847107
$64$	1.00000	0.125000
$65$	3.83887	0.476154
$66$	0.493132	0.0607004
$67$	−9.78170	−1.19502	−0.597512	−	0.801860i	$-0.703844\pi$
$67$	−9.78170	−1.19502	−0.597512	+	0.801860i	$0.703844\pi$
$68$	−2.42956	−0.294628
$69$	−0.0659097	−0.00793460
$70$	−2.43893	−0.291508
$71$	−14.0900	−1.67217	−0.836085	−	0.548600i	$-0.815161\pi$
$71$	−14.0900	−1.67217	−0.836085	+	0.548600i	$0.815161\pi$
$72$	−2.75682	−0.324894
$73$	−7.59682	−0.889141	−0.444570	−	0.895744i	$-0.646644\pi$
$73$	−7.59682	−0.889141	−0.444570	+	0.895744i	$0.646644\pi$
$74$	−1.99563	−0.231988
$75$	0.493132	0.0569420
$76$	−5.39208	−0.618514
$77$	2.43893	0.277942
$78$	−1.89307	−0.214348
$79$	−4.48579	−0.504691	−0.252345	−	0.967637i	$-0.581202\pi$
$79$	−4.48579	−0.504691	−0.252345	+	0.967637i	$0.581202\pi$
$80$	−1.00000	−0.111803
$81$	6.87052	0.763391
$82$	−2.17987	−0.240726
$83$	2.77004	0.304052	0.152026	−	0.988377i	$-0.451420\pi$
$83$	2.77004	0.304052	0.152026	+	0.988377i	$0.451420\pi$
$84$	1.20272	0.131227
$85$	2.42956	0.263523
$86$	−1.00000	−0.107833
$87$	−2.31567	−0.248266
$88$	1.00000	0.106600
$89$	−1.73631	−0.184049	−0.0920243	−	0.995757i	$-0.529334\pi$
$89$	−1.73631	−0.184049	−0.0920243	+	0.995757i	$0.529334\pi$
$90$	2.75682	0.290594
$91$	−9.36276	−0.981484
$92$	−0.133655	−0.0139345
$93$	3.53675	0.366744
$94$	1.86172	0.192022
$95$	5.39208	0.553216
$96$	0.493132	0.0503301
$97$	−7.15262	−0.726239	−0.363119	−	0.931743i	$-0.618288\pi$
$97$	−7.15262	−0.726239	−0.363119	+	0.931743i	$0.618288\pi$
$98$	−1.05160	−0.106228
$99$	−2.75682	−0.277071
$100$	1.00000	0.100000
$101$	19.9230	1.98241	0.991206	−	0.132329i	$-0.0422455\pi$
$101$	19.9230	1.98241	0.991206	+	0.132329i	$0.0422455\pi$
$102$	−1.19810	−0.118629
$103$	−4.42222	−0.435734	−0.217867	−	0.975978i	$-0.569910\pi$
$103$	−4.42222	−0.435734	−0.217867	+	0.975978i	$0.569910\pi$
$104$	−3.83887	−0.376432
$105$	−1.20272	−0.117373
$106$	−1.84799	−0.179493
$107$	9.63703	0.931647	0.465823	−	0.884878i	$-0.345758\pi$
$107$	9.63703	0.931647	0.465823	+	0.884878i	$0.345758\pi$
$108$	−2.83887	−0.273171
$109$	−0.631025	−0.0604412	−0.0302206	−	0.999543i	$-0.509621\pi$
$109$	−0.631025	−0.0604412	−0.0302206	+	0.999543i	$0.509621\pi$
$110$	−1.00000	−0.0953463
$111$	−0.984111	−0.0934077
$112$	2.43893	0.230458
$113$	13.3558	1.25641	0.628204	−	0.778049i	$-0.283790\pi$
$113$	13.3558	1.25641	0.628204	+	0.778049i	$0.283790\pi$
$114$	−2.65901	−0.249039
$115$	0.133655	0.0124634
$116$	−4.69585	−0.435999
$117$	10.5831	0.978407
$118$	−11.2330	−1.03408
$119$	−5.92555	−0.543194
$120$	−0.493132	−0.0450166
$121$	1.00000	0.0909091
$122$	2.06007	0.186510
$123$	−1.07496	−0.0969260
$124$	7.17201	0.644065
$125$	−1.00000	−0.0894427
$126$	−6.72370	−0.598995
$127$	−10.3425	−0.917749	−0.458874	−	0.888501i	$-0.651747\pi$
$127$	−10.3425	−0.917749	−0.458874	+	0.888501i	$0.651747\pi$
$128$	1.00000	0.0883883
$129$	−0.493132	−0.0434179
$130$	3.83887	0.336691
$131$	9.25665	0.808758	0.404379	−	0.914592i	$-0.367488\pi$
$131$	9.25665	0.808758	0.404379	+	0.914592i	$0.367488\pi$
$132$	0.493132	0.0429216
$133$	−13.1509	−1.14033
$134$	−9.78170	−0.845010
$135$	2.83887	0.244331
$136$	−2.42956	−0.208333
$137$	−7.02696	−0.600353	−0.300177	−	0.953884i	$-0.597046\pi$
$137$	−7.02696	−0.600353	−0.300177	+	0.953884i	$0.597046\pi$
$138$	−0.0659097	−0.00561061
$139$	−8.09522	−0.686627	−0.343314	−	0.939221i	$-0.611549\pi$
$139$	−8.09522	−0.686627	−0.343314	+	0.939221i	$0.611549\pi$
$140$	−2.43893	−0.206128
$141$	0.918076	0.0773160
$142$	−14.0900	−1.18240
$143$	−3.83887	−0.321023
$144$	−2.75682	−0.229735
$145$	4.69585	0.389969
$146$	−7.59682	−0.628717
$147$	−0.518579	−0.0427717
$148$	−1.99563	−0.164040
$149$	3.00164	0.245904	0.122952	−	0.992413i	$-0.460764\pi$
$149$	3.00164	0.245904	0.122952	+	0.992413i	$0.460764\pi$
$150$	0.493132	0.0402641
$151$	5.61184	0.456685	0.228342	−	0.973581i	$-0.426669\pi$
$151$	5.61184	0.456685	0.228342	+	0.973581i	$0.426669\pi$
$152$	−5.39208	−0.437355
$153$	6.69787	0.541491
$154$	2.43893	0.196535
$155$	−7.17201	−0.576069
$156$	−1.89307	−0.151567
$157$	−2.68116	−0.213980	−0.106990	−	0.994260i	$-0.534121\pi$
$157$	−2.68116	−0.213980	−0.106990	+	0.994260i	$0.534121\pi$
$158$	−4.48579	−0.356870
$159$	−0.911303	−0.0722710
$160$	−1.00000	−0.0790569
$161$	−0.325976	−0.0256905
$162$	6.87052	0.539799
$163$	15.8023	1.23773	0.618867	−	0.785496i	$-0.287592\pi$
$163$	15.8023	1.23773	0.618867	+	0.785496i	$0.287592\pi$
$164$	−2.17987	−0.170219
$165$	−0.493132	−0.0383903
$166$	2.77004	0.214997
$167$	−7.32941	−0.567167	−0.283583	−	0.958948i	$-0.591523\pi$
$167$	−7.32941	−0.567167	−0.283583	+	0.958948i	$0.591523\pi$
$168$	1.20272	0.0927916
$169$	1.73695	0.133611
$170$	2.42956	0.186339
$171$	14.8650	1.13675
$172$	−1.00000	−0.0762493
$173$	23.6156	1.79546	0.897729	−	0.440548i	$-0.145216\pi$
$173$	23.6156	1.79546	0.897729	+	0.440548i	$0.145216\pi$
$174$	−2.31567	−0.175551
$175$	2.43893	0.184366
$176$	1.00000	0.0753778
$177$	−5.53934	−0.416362
$178$	−1.73631	−0.130142
$179$	0.944103	0.0705656	0.0352828	−	0.999377i	$-0.488767\pi$
$179$	0.944103	0.0705656	0.0352828	+	0.999377i	$0.488767\pi$
$180$	2.75682	0.205481
$181$	13.1662	0.978634	0.489317	−	0.872106i	$-0.337246\pi$
$181$	13.1662	0.978634	0.489317	+	0.872106i	$0.337246\pi$
$182$	−9.36276	−0.694014
$183$	1.01589	0.0750967
$184$	−0.133655	−0.00985320
$185$	1.99563	0.146722
$186$	3.53675	0.259327
$187$	−2.42956	−0.177667
$188$	1.86172	0.135780
$189$	−6.92382	−0.503634
$190$	5.39208	0.391183
$191$	−23.2131	−1.67964	−0.839820	−	0.542865i	$-0.817339\pi$
$191$	−23.2131	−1.67964	−0.839820	+	0.542865i	$0.817339\pi$
$192$	0.493132	0.0355887
$193$	−9.03553	−0.650391	−0.325196	−	0.945647i	$-0.605430\pi$
$193$	−9.03553	−0.650391	−0.325196	+	0.945647i	$0.605430\pi$
$194$	−7.15262	−0.513528
$195$	1.89307	0.135566
$196$	−1.05160	−0.0751145
$197$	0.403179	0.0287253	0.0143627	−	0.999897i	$-0.495428\pi$
$197$	0.403179	0.0287253	0.0143627	+	0.999897i	$0.495428\pi$
$198$	−2.75682	−0.195919
$199$	3.69964	0.262261	0.131130	−	0.991365i	$-0.458139\pi$
$199$	3.69964	0.262261	0.131130	+	0.991365i	$0.458139\pi$
$200$	1.00000	0.0707107
$201$	−4.82367	−0.340235
$202$	19.9230	1.40178
$203$	−11.4529	−0.803833
$204$	−1.19810	−0.0838835
$205$	2.17987	0.152248
$206$	−4.42222	−0.308111
$207$	0.368464	0.0256100
$208$	−3.83887	−0.266178
$209$	−5.39208	−0.372978
$210$	−1.20272	−0.0829953
$211$	−6.07047	−0.417908	−0.208954	−	0.977925i	$-0.567006\pi$
$211$	−6.07047	−0.417908	−0.208954	+	0.977925i	$0.567006\pi$
$212$	−1.84799	−0.126920
$213$	−6.94821	−0.476083
$214$	9.63703	0.658774
$215$	1.00000	0.0681994
$216$	−2.83887	−0.193161
$217$	17.4920	1.18744
$218$	−0.631025	−0.0427384
$219$	−3.74624	−0.253147
$220$	−1.00000	−0.0674200
$221$	9.32679	0.627388
$222$	−0.984111	−0.0660492
$223$	−4.11643	−0.275656	−0.137828	−	0.990456i	$-0.544012\pi$
$223$	−4.11643	−0.275656	−0.137828	+	0.990456i	$0.544012\pi$
$224$	2.43893	0.162958
$225$	−2.75682	−0.183788
$226$	13.3558	0.888414
$227$	−14.9358	−0.991326	−0.495663	−	0.868515i	$-0.665075\pi$
$227$	−14.9358	−0.991326	−0.495663	+	0.868515i	$0.665075\pi$
$228$	−2.65901	−0.176097
$229$	−5.20012	−0.343634	−0.171817	−	0.985129i	$-0.554964\pi$
$229$	−5.20012	−0.343634	−0.171817	+	0.985129i	$0.554964\pi$
$230$	0.133655	0.00881297
$231$	1.20272	0.0791329
$232$	−4.69585	−0.308298
$233$	−8.41056	−0.550994	−0.275497	−	0.961302i	$-0.588842\pi$
$233$	−8.41056	−0.550994	−0.275497	+	0.961302i	$0.588842\pi$
$234$	10.5831	0.691838
$235$	−1.86172	−0.121446
$236$	−11.2330	−0.731205
$237$	−2.21209	−0.143690
$238$	−5.92555	−0.384096
$239$	−4.35373	−0.281619	−0.140810	−	0.990037i	$-0.544971\pi$
$239$	−4.35373	−0.281619	−0.140810	+	0.990037i	$0.544971\pi$
$240$	−0.493132	−0.0318315
$241$	−20.7851	−1.33889	−0.669443	−	0.742863i	$-0.733467\pi$
$241$	−20.7851	−1.33889	−0.669443	+	0.742863i	$0.733467\pi$
$242$	1.00000	0.0642824
$243$	11.9047	0.763687
$244$	2.06007	0.131883
$245$	1.05160	0.0671844
$246$	−1.07496	−0.0685371
$247$	20.6995	1.31708
$248$	7.17201	0.455423
$249$	1.36600	0.0865665
$250$	−1.00000	−0.0632456
$251$	20.3948	1.28731	0.643654	−	0.765317i	$-0.277418\pi$
$251$	20.3948	1.28731	0.643654	+	0.765317i	$0.277418\pi$
$252$	−6.72370	−0.423553
$253$	−0.133655	−0.00840283
$254$	−10.3425	−0.648946
$255$	1.19810	0.0750277
$256$	1.00000	0.0625000
$257$	−28.6666	−1.78817	−0.894086	−	0.447896i	$-0.852173\pi$
$257$	−28.6666	−1.78817	−0.894086	+	0.447896i	$0.852173\pi$
$258$	−0.493132	−0.0307011
$259$	−4.86722	−0.302434
$260$	3.83887	0.238077
$261$	12.9456	0.801313
$262$	9.25665	0.571878
$263$	−8.25172	−0.508823	−0.254411	−	0.967096i	$-0.581882\pi$
$263$	−8.25172	−0.508823	−0.254411	+	0.967096i	$0.581882\pi$
$264$	0.493132	0.0303502
$265$	1.84799	0.113521
$266$	−13.1509	−0.806335
$267$	−0.856231	−0.0524005
$268$	−9.78170	−0.597512
$269$	25.5049	1.55506	0.777532	−	0.628843i	$-0.216471\pi$
$269$	25.5049	1.55506	0.777532	+	0.628843i	$0.216471\pi$
$270$	2.83887	0.172768
$271$	10.3575	0.629174	0.314587	−	0.949229i	$-0.398134\pi$
$271$	10.3575	0.629174	0.314587	+	0.949229i	$0.398134\pi$
$272$	−2.42956	−0.147314
$273$	−4.61708	−0.279438
$274$	−7.02696	−0.424514
$275$	1.00000	0.0603023
$276$	−0.0659097	−0.00396730
$277$	−5.33853	−0.320761	−0.160380	−	0.987055i	$-0.551272\pi$
$277$	−5.33853	−0.320761	−0.160380	+	0.987055i	$0.551272\pi$
$278$	−8.09522	−0.485519
$279$	−19.7719	−1.18371
$280$	−2.43893	−0.145754
$281$	−11.6368	−0.694191	−0.347096	−	0.937830i	$-0.612832\pi$
$281$	−11.6368	−0.694191	−0.347096	+	0.937830i	$0.612832\pi$
$282$	0.918076	0.0546706
$283$	−2.75043	−0.163496	−0.0817480	−	0.996653i	$-0.526050\pi$
$283$	−2.75043	−0.163496	−0.0817480	+	0.996653i	$0.526050\pi$
$284$	−14.0900	−0.836085
$285$	2.65901	0.157506
$286$	−3.83887	−0.226997
$287$	−5.31655	−0.313826
$288$	−2.75682	−0.162447
$289$	−11.0972	−0.652777
$290$	4.69585	0.275750
$291$	−3.52719	−0.206767
$292$	−7.59682	−0.444570
$293$	5.88585	0.343855	0.171927	−	0.985110i	$-0.445001\pi$
$293$	5.88585	0.343855	0.171927	+	0.985110i	$0.445001\pi$
$294$	−0.518579	−0.0302441
$295$	11.2330	0.654009
$296$	−1.99563	−0.115994
$297$	−2.83887	−0.164728
$298$	3.00164	0.173880
$299$	0.513086	0.0296725
$300$	0.493132	0.0284710
$301$	−2.43893	−0.140578
$302$	5.61184	0.322925
$303$	9.82467	0.564412
$304$	−5.39208	−0.309257
$305$	−2.06007	−0.117960
$306$	6.69787	0.382892
$307$	−6.66919	−0.380631	−0.190316	−	0.981723i	$-0.560951\pi$
$307$	−6.66919	−0.380631	−0.190316	+	0.981723i	$0.560951\pi$
$308$	2.43893	0.138971
$309$	−2.18074	−0.124058
$310$	−7.17201	−0.407343
$311$	10.0149	0.567895	0.283947	−	0.958840i	$-0.408356\pi$
$311$	10.0149	0.567895	0.283947	+	0.958840i	$0.408356\pi$
$312$	−1.89307	−0.107174
$313$	3.39719	0.192021	0.0960103	−	0.995380i	$-0.469392\pi$
$313$	3.39719	0.192021	0.0960103	+	0.995380i	$0.469392\pi$
$314$	−2.68116	−0.151307
$315$	6.72370	0.378838
$316$	−4.48579	−0.252345
$317$	−1.12339	−0.0630958	−0.0315479	−	0.999502i	$-0.510044\pi$
$317$	−1.12339	−0.0630958	−0.0315479	+	0.999502i	$0.510044\pi$
$318$	−0.911303	−0.0511033
$319$	−4.69585	−0.262917
$320$	−1.00000	−0.0559017
$321$	4.75233	0.265249
$322$	−0.325976	−0.0181659
$323$	13.1004	0.728926
$324$	6.87052	0.381696
$325$	−3.83887	−0.212942
$326$	15.8023	0.875210
$327$	−0.311179	−0.0172082
$328$	−2.17987	−0.120363
$329$	4.54062	0.250333
$330$	−0.493132	−0.0271460
$331$	−28.5681	−1.57025	−0.785123	−	0.619340i	$-0.787400\pi$
$331$	−28.5681	−1.57025	−0.785123	+	0.619340i	$0.787400\pi$
$332$	2.77004	0.152026
$333$	5.50160	0.301486
$334$	−7.32941	−0.401047
$335$	9.78170	0.534431
$336$	1.20272	0.0656136
$337$	0.302192	0.0164614	0.00823072	−	0.999966i	$-0.497380\pi$
$337$	0.302192	0.0164614	0.00823072	+	0.999966i	$0.497380\pi$
$338$	1.73695	0.0944775
$339$	6.58617	0.357712
$340$	2.42956	0.131762
$341$	7.17201	0.388386
$342$	14.8650	0.803807
$343$	−19.6373	−1.06032
$344$	−1.00000	−0.0539164
$345$	0.0659097	0.00354846
$346$	23.6156	1.26958
$347$	−12.9705	−0.696295	−0.348148	−	0.937440i	$-0.613189\pi$
$347$	−12.9705	−0.696295	−0.348148	+	0.937440i	$0.613189\pi$
$348$	−2.31567	−0.124133
$349$	17.0303	0.911611	0.455806	−	0.890079i	$-0.349351\pi$
$349$	17.0303	0.911611	0.455806	+	0.890079i	$0.349351\pi$
$350$	2.43893	0.130366
$351$	10.8981	0.581696
$352$	1.00000	0.0533002
$353$	−31.1974	−1.66047	−0.830235	−	0.557414i	$-0.811794\pi$
$353$	−31.1974	−1.66047	−0.830235	+	0.557414i	$0.811794\pi$
$354$	−5.53934	−0.294413
$355$	14.0900	0.747817
$356$	−1.73631	−0.0920243
$357$	−2.92208	−0.154653
$358$	0.944103	0.0498974
$359$	6.16662	0.325462	0.162731	−	0.986671i	$-0.447970\pi$
$359$	6.16662	0.325462	0.162731	+	0.986671i	$0.447970\pi$
$360$	2.75682	0.145297
$361$	10.0745	0.530238
$362$	13.1662	0.691999
$363$	0.493132	0.0258827
$364$	−9.36276	−0.490742
$365$	7.59682	0.397636
$366$	1.01589	0.0531014
$367$	−9.14769	−0.477506	−0.238753	−	0.971080i	$-0.576739\pi$
$367$	−9.14769	−0.477506	−0.238753	+	0.971080i	$0.576739\pi$
$368$	−0.133655	−0.00696726
$369$	6.00950	0.312842
$370$	1.99563	0.103748
$371$	−4.50712	−0.233998
$372$	3.53675	0.183372
$373$	9.19804	0.476256	0.238128	−	0.971234i	$-0.423466\pi$
$373$	9.19804	0.476256	0.238128	+	0.971234i	$0.423466\pi$
$374$	−2.42956	−0.125630
$375$	−0.493132	−0.0254652
$376$	1.86172	0.0960111
$377$	18.0268	0.928426
$378$	−6.92382	−0.356123
$379$	21.6761	1.11343	0.556714	−	0.830704i	$-0.312062\pi$
$379$	21.6761	1.11343	0.556714	+	0.830704i	$0.312062\pi$
$380$	5.39208	0.276608
$381$	−5.10022	−0.261292
$382$	−23.2131	−1.18768
$383$	7.80695	0.398917	0.199458	−	0.979906i	$-0.436082\pi$
$383$	7.80695	0.398917	0.199458	+	0.979906i	$0.436082\pi$
$384$	0.493132	0.0251650
$385$	−2.43893	−0.124300
$386$	−9.03553	−0.459896
$387$	2.75682	0.140137
$388$	−7.15262	−0.363119
$389$	−6.15253	−0.311945	−0.155973	−	0.987761i	$-0.549851\pi$
$389$	−6.15253	−0.311945	−0.155973	+	0.987761i	$0.549851\pi$
$390$	1.89307	0.0958594
$391$	0.324724	0.0164220
$392$	−1.05160	−0.0531140
$393$	4.56475	0.230261
$394$	0.403179	0.0203119
$395$	4.48579	0.225704
$396$	−2.75682	−0.138535
$397$	24.2313	1.21614	0.608068	−	0.793885i	$-0.291945\pi$
$397$	24.2313	1.21614	0.608068	+	0.793885i	$0.291945\pi$
$398$	3.69964	0.185446
$399$	−6.48514	−0.324663
$400$	1.00000	0.0500000
$401$	−20.7721	−1.03731	−0.518654	−	0.854984i	$-0.673567\pi$
$401$	−20.7721	−1.03731	−0.518654	+	0.854984i	$0.673567\pi$
$402$	−4.82367	−0.240583
$403$	−27.5324	−1.37149
$404$	19.9230	0.991206
$405$	−6.87052	−0.341399
$406$	−11.4529	−0.568396
$407$	−1.99563	−0.0989199
$408$	−1.19810	−0.0593146
$409$	21.7502	1.07548	0.537740	−	0.843111i	$-0.319278\pi$
$409$	21.7502	1.07548	0.537740	+	0.843111i	$0.319278\pi$
$410$	2.17987	0.107656
$411$	−3.46522	−0.170927
$412$	−4.42222	−0.217867
$413$	−27.3965	−1.34809
$414$	0.368464	0.0181090
$415$	−2.77004	−0.135976
$416$	−3.83887	−0.188216
$417$	−3.99201	−0.195490
$418$	−5.39208	−0.263735
$419$	6.40222	0.312769	0.156384	−	0.987696i	$-0.450016\pi$
$419$	6.40222	0.312769	0.156384	+	0.987696i	$0.450016\pi$
$420$	−1.20272	−0.0586866
$421$	10.6420	0.518661	0.259330	−	0.965789i	$-0.416498\pi$
$421$	10.6420	0.518661	0.259330	+	0.965789i	$0.416498\pi$
$422$	−6.07047	−0.295506
$423$	−5.13244	−0.249548
$424$	−1.84799	−0.0897463
$425$	−2.42956	−0.117851
$426$	−6.94821	−0.336642
$427$	5.02439	0.243147
$428$	9.63703	0.465823
$429$	−1.89307	−0.0913984
$430$	1.00000	0.0482243
$431$	−0.845010	−0.0407027	−0.0203514	−	0.999793i	$-0.506478\pi$
$431$	−0.845010	−0.0407027	−0.0203514	+	0.999793i	$0.506478\pi$
$432$	−2.83887	−0.136585
$433$	23.6708	1.13754	0.568772	−	0.822495i	$-0.307419\pi$
$433$	23.6708	1.13754	0.568772	+	0.822495i	$0.307419\pi$
$434$	17.4920	0.839645
$435$	2.31567	0.111028
$436$	−0.631025	−0.0302206
$437$	0.720680	0.0344748
$438$	−3.74624	−0.179002
$439$	−13.1707	−0.628605	−0.314303	−	0.949323i	$-0.601771\pi$
$439$	−13.1707	−0.628605	−0.314303	+	0.949323i	$0.601771\pi$
$440$	−1.00000	−0.0476731
$441$	2.89908	0.138051
$442$	9.32679	0.443630
$443$	20.5096	0.974442	0.487221	−	0.873279i	$-0.338011\pi$
$443$	20.5096	0.974442	0.487221	+	0.873279i	$0.338011\pi$
$444$	−0.984111	−0.0467038
$445$	1.73631	0.0823091
$446$	−4.11643	−0.194918
$447$	1.48020	0.0700113
$448$	2.43893	0.115229
$449$	19.9943	0.943589	0.471794	−	0.881709i	$-0.343606\pi$
$449$	19.9943	0.943589	0.471794	+	0.881709i	$0.343606\pi$
$450$	−2.75682	−0.129958
$451$	−2.17987	−0.102646
$452$	13.3558	0.628204
$453$	2.76738	0.130023
$454$	−14.9358	−0.700973
$455$	9.36276	0.438933
$456$	−2.65901	−0.124519
$457$	33.7511	1.57881	0.789405	−	0.613873i	$-0.210389\pi$
$457$	33.7511	1.57881	0.789405	+	0.613873i	$0.210389\pi$
$458$	−5.20012	−0.242986
$459$	6.89723	0.321935
$460$	0.133655	0.00623171
$461$	−15.2380	−0.709705	−0.354853	−	0.934922i	$-0.615469\pi$
$461$	−15.2380	−0.709705	−0.354853	+	0.934922i	$0.615469\pi$
$462$	1.20272	0.0559554
$463$	−16.8651	−0.783787	−0.391893	−	0.920011i	$-0.628180\pi$
$463$	−16.8651	−0.783787	−0.391893	+	0.920011i	$0.628180\pi$
$464$	−4.69585	−0.217999
$465$	−3.53675	−0.164013
$466$	−8.41056	−0.389612
$467$	26.8405	1.24203	0.621015	−	0.783798i	$-0.286720\pi$
$467$	26.8405	1.24203	0.621015	+	0.783798i	$0.286720\pi$
$468$	10.5831	0.489203
$469$	−23.8569	−1.10161
$470$	−1.86172	−0.0858749
$471$	−1.32217	−0.0609222
$472$	−11.2330	−0.517040
$473$	−1.00000	−0.0459800
$474$	−2.21209	−0.101604
$475$	−5.39208	−0.247406
$476$	−5.92555	−0.271597
$477$	5.09457	0.233264
$478$	−4.35373	−0.199135
$479$	−9.55657	−0.436651	−0.218325	−	0.975876i	$-0.570059\pi$
$479$	−9.55657	−0.436651	−0.218325	+	0.975876i	$0.570059\pi$
$480$	−0.493132	−0.0225083
$481$	7.66098	0.349311
$482$	−20.7851	−0.946735
$483$	−0.160749	−0.00731435
$484$	1.00000	0.0454545
$485$	7.15262	0.324784
$486$	11.9047	0.540008
$487$	−3.71580	−0.168379	−0.0841894	−	0.996450i	$-0.526830\pi$
$487$	−3.71580	−0.168379	−0.0841894	+	0.996450i	$0.526830\pi$
$488$	2.06007	0.0932552
$489$	7.79264	0.352395
$490$	1.05160	0.0475066
$491$	−5.59435	−0.252470	−0.126235	−	0.992000i	$-0.540289\pi$
$491$	−5.59435	−0.252470	−0.126235	+	0.992000i	$0.540289\pi$
$492$	−1.07496	−0.0484630
$493$	11.4089	0.513829
$494$	20.6995	0.931315
$495$	2.75682	0.123910
$496$	7.17201	0.322033
$497$	−34.3645	−1.54146
$498$	1.36600	0.0612118
$499$	−27.7888	−1.24400	−0.622000	−	0.783018i	$-0.713679\pi$
$499$	−27.7888	−1.24400	−0.622000	+	0.783018i	$0.713679\pi$
$500$	−1.00000	−0.0447214
$501$	−3.61437	−0.161478
$502$	20.3948	0.910264
$503$	−21.9071	−0.976789	−0.488395	−	0.872623i	$-0.662417\pi$
$503$	−21.9071	−0.976789	−0.488395	+	0.872623i	$0.662417\pi$
$504$	−6.72370	−0.299498
$505$	−19.9230	−0.886561
$506$	−0.133655	−0.00594170
$507$	0.856545	0.0380405
$508$	−10.3425	−0.458874
$509$	20.0777	0.889929	0.444965	−	0.895548i	$-0.353216\pi$
$509$	20.0777	0.889929	0.444965	+	0.895548i	$0.353216\pi$
$510$	1.19810	0.0530526
$511$	−18.5281	−0.819637
$512$	1.00000	0.0441942
$513$	15.3074	0.675840
$514$	−28.6666	−1.26443
$515$	4.42222	0.194866
$516$	−0.493132	−0.0217089
$517$	1.86172	0.0818785
$518$	−4.86722	−0.213853
$519$	11.6456	0.511185
$520$	3.83887	0.168346
$521$	5.31154	0.232703	0.116351	−	0.993208i	$-0.462880\pi$
$521$	5.31154	0.232703	0.116351	+	0.993208i	$0.462880\pi$
$522$	12.9456	0.566614
$523$	19.4977	0.852577	0.426288	−	0.904587i	$-0.359821\pi$
$523$	19.4977	0.852577	0.426288	+	0.904587i	$0.359821\pi$
$524$	9.25665	0.404379
$525$	1.20272	0.0524909
$526$	−8.25172	−0.359792
$527$	−17.4248	−0.759038
$528$	0.493132	0.0214608
$529$	−22.9821	−0.999223
$530$	1.84799	0.0802715
$531$	30.9673	1.34387
$532$	−13.1509	−0.570165
$533$	8.36823	0.362468
$534$	−0.856231	−0.0370527
$535$	−9.63703	−0.416645
$536$	−9.78170	−0.422505
$537$	0.465568	0.0200907
$538$	25.5049	1.09960
$539$	−1.05160	−0.0452957
$540$	2.83887	0.122166
$541$	5.36627	0.230714	0.115357	−	0.993324i	$-0.463199\pi$
$541$	5.36627	0.230714	0.115357	+	0.993324i	$0.463199\pi$
$542$	10.3575	0.444893
$543$	6.49266	0.278627
$544$	−2.42956	−0.104167
$545$	0.631025	0.0270301
$546$	−4.61708	−0.197593
$547$	15.2159	0.650586	0.325293	−	0.945613i	$-0.394537\pi$
$547$	15.2159	0.650586	0.325293	+	0.945613i	$0.394537\pi$
$548$	−7.02696	−0.300177
$549$	−5.67926	−0.242385
$550$	1.00000	0.0426401
$551$	25.3204	1.07868
$552$	−0.0659097	−0.00280530
$553$	−10.9405	−0.465239
$554$	−5.33853	−0.226812
$555$	0.984111	0.0417732
$556$	−8.09522	−0.343314
$557$	16.8227	0.712799	0.356400	−	0.934334i	$-0.384004\pi$
$557$	16.8227	0.712799	0.356400	+	0.934334i	$0.384004\pi$
$558$	−19.7719	−0.837013
$559$	3.83887	0.162367
$560$	−2.43893	−0.103064
$561$	−1.19810	−0.0505837
$562$	−11.6368	−0.490867
$563$	26.1290	1.10120	0.550602	−	0.834768i	$-0.314398\pi$
$563$	26.1290	1.10120	0.550602	+	0.834768i	$0.314398\pi$
$564$	0.918076	0.0386580
$565$	−13.3558	−0.561883
$566$	−2.75043	−0.115609
$567$	16.7567	0.703717
$568$	−14.0900	−0.591201
$569$	18.1419	0.760547	0.380273	−	0.924874i	$-0.375830\pi$
$569$	18.1419	0.760547	0.380273	+	0.924874i	$0.375830\pi$
$570$	2.65901	0.111374
$571$	28.8837	1.20874	0.604372	−	0.796702i	$-0.293424\pi$
$571$	28.8837	1.20874	0.604372	+	0.796702i	$0.293424\pi$
$572$	−3.83887	−0.160511
$573$	−11.4471	−0.478210
$574$	−5.31655	−0.221908
$575$	−0.133655	−0.00557381
$576$	−2.75682	−0.114868
$577$	6.66816	0.277599	0.138800	−	0.990320i	$-0.455676\pi$
$577$	6.66816	0.277599	0.138800	+	0.990320i	$0.455676\pi$
$578$	−11.0972	−0.461583
$579$	−4.45571	−0.185173
$580$	4.69585	0.194985
$581$	6.75595	0.280284
$582$	−3.52719	−0.146207
$583$	−1.84799	−0.0765359
$584$	−7.59682	−0.314359
$585$	−10.5831	−0.437557
$586$	5.88585	0.243142
$587$	−29.0525	−1.19913	−0.599563	−	0.800328i	$-0.704659\pi$
$587$	−29.0525	−1.19913	−0.599563	+	0.800328i	$0.704659\pi$
$588$	−0.518579	−0.0213858
$589$	−38.6720	−1.59345
$590$	11.2330	0.462454
$591$	0.198821	0.00817838
$592$	−1.99563	−0.0820200
$593$	30.2703	1.24305	0.621527	−	0.783393i	$-0.286513\pi$
$593$	30.2703	1.24305	0.621527	+	0.783393i	$0.286513\pi$
$594$	−2.83887	−0.116480
$595$	5.92555	0.242924
$596$	3.00164	0.122952
$597$	1.82441	0.0746683
$598$	0.513086	0.0209816
$599$	17.9132	0.731915	0.365958	−	0.930632i	$-0.380742\pi$
$599$	17.9132	0.731915	0.365958	+	0.930632i	$0.380742\pi$
$600$	0.493132	0.0201320
$601$	26.0464	1.06245	0.531227	−	0.847229i	$-0.321731\pi$
$601$	26.0464	1.06245	0.531227	+	0.847229i	$0.321731\pi$
$602$	−2.43893	−0.0994035
$603$	26.9664	1.09816
$604$	5.61184	0.228342
$605$	−1.00000	−0.0406558
$606$	9.82467	0.399100
$607$	7.29038	0.295908	0.147954	−	0.988994i	$-0.452731\pi$
$607$	7.29038	0.295908	0.147954	+	0.988994i	$0.452731\pi$
$608$	−5.39208	−0.218678
$609$	−5.64777	−0.228859
$610$	−2.06007	−0.0834100
$611$	−7.14692	−0.289134
$612$	6.69787	0.270745
$613$	−19.5859	−0.791066	−0.395533	−	0.918452i	$-0.629440\pi$
$613$	−19.5859	−0.791066	−0.395533	+	0.918452i	$0.629440\pi$
$614$	−6.66919	−0.269147
$615$	1.07496	0.0433466
$616$	2.43893	0.0982674
$617$	24.3231	0.979210	0.489605	−	0.871944i	$-0.337141\pi$
$617$	24.3231	0.979210	0.489605	+	0.871944i	$0.337141\pi$
$618$	−2.18074	−0.0877222
$619$	−25.9105	−1.04143	−0.520716	−	0.853730i	$-0.674335\pi$
$619$	−25.9105	−1.04143	−0.520716	+	0.853730i	$0.674335\pi$
$620$	−7.17201	−0.288035
$621$	0.379430	0.0152260
$622$	10.0149	0.401562
$623$	−4.23475	−0.169662
$624$	−1.89307	−0.0757835
$625$	1.00000	0.0400000
$626$	3.39719	0.135779
$627$	−2.65901	−0.106191
$628$	−2.68116	−0.106990
$629$	4.84852	0.193323
$630$	6.72370	0.267879
$631$	−10.8803	−0.433139	−0.216570	−	0.976267i	$-0.569487\pi$
$631$	−10.8803	−0.433139	−0.216570	+	0.976267i	$0.569487\pi$
$632$	−4.48579	−0.178435
$633$	−2.99354	−0.118983
$634$	−1.12339	−0.0446155
$635$	10.3425	0.410430
$636$	−0.911303	−0.0361355
$637$	4.03697	0.159951
$638$	−4.69585	−0.185910
$639$	38.8435	1.53662
$640$	−1.00000	−0.0395285
$641$	−34.7434	−1.37228	−0.686142	−	0.727468i	$-0.740697\pi$
$641$	−34.7434	−1.37228	−0.686142	+	0.727468i	$0.740697\pi$
$642$	4.75233	0.187559
$643$	13.5823	0.535632	0.267816	−	0.963470i	$-0.413698\pi$
$643$	13.5823	0.535632	0.267816	+	0.963470i	$0.413698\pi$
$644$	−0.325976	−0.0128453
$645$	0.493132	0.0194171
$646$	13.1004	0.515429
$647$	41.4972	1.63142	0.815712	−	0.578458i	$-0.196345\pi$
$647$	41.4972	1.63142	0.815712	+	0.578458i	$0.196345\pi$
$648$	6.87052	0.269900
$649$	−11.2330	−0.440933
$650$	−3.83887	−0.150573
$651$	8.62589	0.338075
$652$	15.8023	0.618867
$653$	37.8591	1.48154	0.740771	−	0.671758i	$-0.234461\pi$
$653$	37.8591	1.48154	0.740771	+	0.671758i	$0.234461\pi$
$654$	−0.311179	−0.0121681
$655$	−9.25665	−0.361687
$656$	−2.17987	−0.0851094
$657$	20.9431	0.817067
$658$	4.54062	0.177012
$659$	34.1831	1.33158	0.665792	−	0.746138i	$-0.268094\pi$
$659$	34.1831	1.33158	0.665792	+	0.746138i	$0.268094\pi$
$660$	−0.493132	−0.0191951
$661$	31.1252	1.21063	0.605316	−	0.795986i	$-0.293047\pi$
$661$	31.1252	1.21063	0.605316	+	0.795986i	$0.293047\pi$
$662$	−28.5681	−1.11033
$663$	4.59934	0.178624
$664$	2.77004	0.107498
$665$	13.1509	0.509971
$666$	5.50160	0.213183
$667$	0.627625	0.0243017
$668$	−7.32941	−0.283583
$669$	−2.02994	−0.0784821
$670$	9.78170	0.377900
$671$	2.06007	0.0795283
$672$	1.20272	0.0463958
$673$	−7.23971	−0.279070	−0.139535	−	0.990217i	$-0.544561\pi$
$673$	−7.23971	−0.279070	−0.139535	+	0.990217i	$0.544561\pi$
$674$	0.302192	0.0116400
$675$	−2.83887	−0.109268
$676$	1.73695	0.0668057
$677$	−2.01337	−0.0773802	−0.0386901	−	0.999251i	$-0.512319\pi$
$677$	−2.01337	−0.0773802	−0.0386901	+	0.999251i	$0.512319\pi$
$678$	6.58617	0.252940
$679$	−17.4448	−0.669469
$680$	2.42956	0.0931695
$681$	−7.36534	−0.282240
$682$	7.17201	0.274630
$683$	−17.8679	−0.683698	−0.341849	−	0.939755i	$-0.611053\pi$
$683$	−17.8679	−0.683698	−0.341849	+	0.939755i	$0.611053\pi$
$684$	14.8650	0.568377
$685$	7.02696	0.268486
$686$	−19.6373	−0.749757
$687$	−2.56435	−0.0978359
$688$	−1.00000	−0.0381246
$689$	7.09419	0.270267
$690$	0.0659097	0.00250914
$691$	1.10840	0.0421657	0.0210828	−	0.999778i	$-0.493289\pi$
$691$	1.10840	0.0421657	0.0210828	+	0.999778i	$0.493289\pi$
$692$	23.6156	0.897729
$693$	−6.72370	−0.255412
$694$	−12.9705	−0.492355
$695$	8.09522	0.307069
$696$	−2.31567	−0.0877754
$697$	5.29612	0.200605
$698$	17.0303	0.644606
$699$	−4.14752	−0.156874
$700$	2.43893	0.0921830
$701$	24.0646	0.908908	0.454454	−	0.890770i	$-0.349834\pi$
$701$	24.0646	0.908908	0.454454	+	0.890770i	$0.349834\pi$
$702$	10.8981	0.411321
$703$	10.7606	0.405844
$704$	1.00000	0.0376889
$705$	−0.918076	−0.0345767
$706$	−31.1974	−1.17413
$707$	48.5909	1.82745
$708$	−5.53934	−0.208181
$709$	−27.7073	−1.04057	−0.520285	−	0.853993i	$-0.674174\pi$
$709$	−27.7073	−1.04057	−0.520285	+	0.853993i	$0.674174\pi$
$710$	14.0900	0.528787
$711$	12.3665	0.463780
$712$	−1.73631	−0.0650710
$713$	−0.958576	−0.0358990
$714$	−2.92208	−0.109356
$715$	3.83887	0.143566
$716$	0.944103	0.0352828
$717$	−2.14696	−0.0801798
$718$	6.16662	0.230136
$719$	−40.2018	−1.49928	−0.749638	−	0.661849i	$-0.769772\pi$
$719$	−40.2018	−1.49928	−0.749638	+	0.661849i	$0.769772\pi$
$720$	2.75682	0.102741
$721$	−10.7855	−0.401673
$722$	10.0745	0.374935
$723$	−10.2498	−0.381194
$724$	13.1662	0.489317
$725$	−4.69585	−0.174399
$726$	0.493132	0.0183018
$727$	15.8480	0.587768	0.293884	−	0.955841i	$-0.405052\pi$
$727$	15.8480	0.587768	0.293884	+	0.955841i	$0.405052\pi$
$728$	−9.36276	−0.347007
$729$	−14.7410	−0.545962
$730$	7.59682	0.281171
$731$	2.42956	0.0898607
$732$	1.01589	0.0375483
$733$	−43.1764	−1.59476	−0.797379	−	0.603479i	$-0.793781\pi$
$733$	−43.1764	−1.59476	−0.797379	+	0.603479i	$0.793781\pi$
$734$	−9.14769	−0.337648
$735$	0.518579	0.0191281
$736$	−0.133655	−0.00492660
$737$	−9.78170	−0.360313
$738$	6.00950	0.221213
$739$	−10.6826	−0.392966	−0.196483	−	0.980507i	$-0.562952\pi$
$739$	−10.6826	−0.392966	−0.196483	+	0.980507i	$0.562952\pi$
$740$	1.99563	0.0733609
$741$	10.2076	0.374985
$742$	−4.50712	−0.165462
$743$	4.01700	0.147369	0.0736846	−	0.997282i	$-0.476524\pi$
$743$	4.01700	0.147369	0.0736846	+	0.997282i	$0.476524\pi$
$744$	3.53675	0.129663
$745$	−3.00164	−0.109972
$746$	9.19804	0.336764
$747$	−7.63651	−0.279405
$748$	−2.42956	−0.0888337
$749$	23.5041	0.858820
$750$	−0.493132	−0.0180066
$751$	−35.1779	−1.28366	−0.641829	−	0.766848i	$-0.721824\pi$
$751$	−35.1779	−1.28366	−0.641829	+	0.766848i	$0.721824\pi$
$752$	1.86172	0.0678901
$753$	10.0573	0.366509
$754$	18.0268	0.656496
$755$	−5.61184	−0.204236
$756$	−6.92382	−0.251817
$757$	−15.7914	−0.573949	−0.286974	−	0.957938i	$-0.592649\pi$
$757$	−15.7914	−0.573949	−0.286974	+	0.957938i	$0.592649\pi$
$758$	21.6761	0.787313
$759$	−0.0659097	−0.00239237
$760$	5.39208	0.195591
$761$	−12.1696	−0.441148	−0.220574	−	0.975370i	$-0.570793\pi$
$761$	−12.1696	−0.441148	−0.220574	+	0.975370i	$0.570793\pi$
$762$	−5.10022	−0.184761
$763$	−1.53903	−0.0557166
$764$	−23.2131	−0.839820
$765$	−6.69787	−0.242162
$766$	7.80695	0.282077
$767$	43.1220	1.55704
$768$	0.493132	0.0177944
$769$	2.10027	0.0757376	0.0378688	−	0.999283i	$-0.487943\pi$
$769$	2.10027	0.0757376	0.0378688	+	0.999283i	$0.487943\pi$
$770$	−2.43893	−0.0878931
$771$	−14.1364	−0.509110
$772$	−9.03553	−0.325196
$773$	13.2689	0.477250	0.238625	−	0.971112i	$-0.423303\pi$
$773$	13.2689	0.477250	0.238625	+	0.971112i	$0.423303\pi$
$774$	2.75682	0.0990919
$775$	7.17201	0.257626
$776$	−7.15262	−0.256764
$777$	−2.40018	−0.0861060
$778$	−6.15253	−0.220579
$779$	11.7540	0.421131
$780$	1.89307	0.0677828
$781$	−14.0900	−0.504178
$782$	0.324724	0.0116121
$783$	13.3309	0.476408
$784$	−1.05160	−0.0375572
$785$	2.68116	0.0956947
$786$	4.56475	0.162819
$787$	−4.68117	−0.166866	−0.0834329	−	0.996513i	$-0.526588\pi$
$787$	−4.68117	−0.166866	−0.0834329	+	0.996513i	$0.526588\pi$
$788$	0.403179	0.0143627
$789$	−4.06919	−0.144867
$790$	4.48579	0.159597
$791$	32.5739	1.15819
$792$	−2.75682	−0.0979594
$793$	−7.90837	−0.280834
$794$	24.2313	0.859937
$795$	0.911303	0.0323206
$796$	3.69964	0.131130
$797$	1.77538	0.0628874	0.0314437	−	0.999506i	$-0.489990\pi$
$797$	1.77538	0.0628874	0.0314437	+	0.999506i	$0.489990\pi$
$798$	−6.48514	−0.229572
$799$	−4.52318	−0.160019
$800$	1.00000	0.0353553
$801$	4.78670	0.169130
$802$	−20.7721	−0.733487
$803$	−7.59682	−0.268086
$804$	−4.82367	−0.170118
$805$	0.325976	0.0114892
$806$	−27.5324	−0.969788
$807$	12.5773	0.442742
$808$	19.9230	0.700888
$809$	−33.5159	−1.17836	−0.589179	−	0.808003i	$-0.700549\pi$
$809$	−33.5159	−1.17836	−0.589179	+	0.808003i	$0.700549\pi$
$810$	−6.87052	−0.241406
$811$	−4.25533	−0.149425	−0.0747124	−	0.997205i	$-0.523804\pi$
$811$	−4.25533	−0.149425	−0.0747124	+	0.997205i	$0.523804\pi$
$812$	−11.4529	−0.401917
$813$	5.10762	0.179132
$814$	−1.99563	−0.0699469
$815$	−15.8023	−0.553531
$816$	−1.19810	−0.0419418
$817$	5.39208	0.188645
$818$	21.7502	0.760479
$819$	25.8114	0.901925
$820$	2.17987	0.0761242
$821$	8.01533	0.279737	0.139868	−	0.990170i	$-0.455332\pi$
$821$	8.01533	0.279737	0.139868	+	0.990170i	$0.455332\pi$
$822$	−3.46522	−0.120863
$823$	34.0353	1.18640	0.593199	−	0.805056i	$-0.297865\pi$
$823$	34.0353	1.18640	0.593199	+	0.805056i	$0.297865\pi$
$824$	−4.42222	−0.154055
$825$	0.493132	0.0171687
$826$	−27.3965	−0.953246
$827$	6.73288	0.234125	0.117063	−	0.993125i	$-0.462652\pi$
$827$	6.73288	0.234125	0.117063	+	0.993125i	$0.462652\pi$
$828$	0.368464	0.0128050
$829$	−26.1780	−0.909199	−0.454599	−	0.890696i	$-0.650218\pi$
$829$	−26.1780	−0.909199	−0.454599	+	0.890696i	$0.650218\pi$
$830$	−2.77004	−0.0961495
$831$	−2.63260	−0.0913238
$832$	−3.83887	−0.133089
$833$	2.55494	0.0885233
$834$	−3.99201	−0.138232
$835$	7.32941	0.253645
$836$	−5.39208	−0.186489
$837$	−20.3604	−0.703759
$838$	6.40222	0.221161
$839$	−3.28798	−0.113514	−0.0567569	−	0.998388i	$-0.518076\pi$
$839$	−3.28798	−0.113514	−0.0567569	+	0.998388i	$0.518076\pi$
$840$	−1.20272	−0.0414977
$841$	−6.94901	−0.239621
$842$	10.6420	0.366749
$843$	−5.73846	−0.197643
$844$	−6.07047	−0.208954
$845$	−1.73695	−0.0597528
$846$	−5.13244	−0.176457
$847$	2.43893	0.0838028
$848$	−1.84799	−0.0634602
$849$	−1.35633	−0.0465490
$850$	−2.42956	−0.0833334
$851$	0.266727	0.00914328
$852$	−6.94821	−0.238042
$853$	−22.9962	−0.787374	−0.393687	−	0.919245i	$-0.628801\pi$
$853$	−22.9962	−0.787374	−0.393687	+	0.919245i	$0.628801\pi$
$854$	5.02439	0.171931
$855$	−14.8650	−0.508372
$856$	9.63703	0.329387
$857$	55.4983	1.89579	0.947893	−	0.318589i	$-0.103209\pi$
$857$	55.4983	1.89579	0.947893	+	0.318589i	$0.103209\pi$
$858$	−1.89307	−0.0646284
$859$	31.5251	1.07562	0.537812	−	0.843065i	$-0.319251\pi$
$859$	31.5251	1.07562	0.537812	+	0.843065i	$0.319251\pi$
$860$	1.00000	0.0340997
$861$	−2.62176	−0.0893493
$862$	−0.845010	−0.0287812
$863$	54.7516	1.86377	0.931883	−	0.362760i	$-0.118165\pi$
$863$	54.7516	1.86377	0.931883	+	0.362760i	$0.118165\pi$
$864$	−2.83887	−0.0965804
$865$	−23.6156	−0.802953
$866$	23.6708	0.804365
$867$	−5.47239	−0.185852
$868$	17.4920	0.593719
$869$	−4.48579	−0.152170
$870$	2.31567	0.0785087
$871$	37.5507	1.27236
$872$	−0.631025	−0.0213692
$873$	19.7185	0.667370
$874$	0.720680	0.0243774
$875$	−2.43893	−0.0824510
$876$	−3.74624	−0.126574
$877$	−24.9453	−0.842344	−0.421172	−	0.906981i	$-0.638381\pi$
$877$	−24.9453	−0.842344	−0.421172	+	0.906981i	$0.638381\pi$
$878$	−13.1707	−0.444491
$879$	2.90250	0.0978989
$880$	−1.00000	−0.0337100
$881$	25.9439	0.874072	0.437036	−	0.899444i	$-0.356028\pi$
$881$	25.9439	0.874072	0.437036	+	0.899444i	$0.356028\pi$
$882$	2.89908	0.0976171
$883$	−7.68373	−0.258578	−0.129289	−	0.991607i	$-0.541269\pi$
$883$	−7.68373	−0.258578	−0.129289	+	0.991607i	$0.541269\pi$
$884$	9.32679	0.313694
$885$	5.53934	0.186203
$886$	20.5096	0.689034
$887$	36.7490	1.23391	0.616956	−	0.786998i	$-0.288366\pi$
$887$	36.7490	1.23391	0.616956	+	0.786998i	$0.288366\pi$
$888$	−0.984111	−0.0330246
$889$	−25.2247	−0.846008
$890$	1.73631	0.0582013
$891$	6.87052	0.230171
$892$	−4.11643	−0.137828
$893$	−10.0386	−0.335928
$894$	1.48020	0.0495054
$895$	−0.944103	−0.0315579
$896$	2.43893	0.0814791
$897$	0.253019	0.00844806
$898$	19.9943	0.667218
$899$	−33.6787	−1.12325
$900$	−2.75682	−0.0918940
$901$	4.48981	0.149577
$902$	−2.17987	−0.0725816
$903$	−1.20272	−0.0400239
$904$	13.3558	0.444207
$905$	−13.1662	−0.437658
$906$	2.76738	0.0919399
$907$	22.2320	0.738200	0.369100	−	0.929390i	$-0.379666\pi$
$907$	22.2320	0.738200	0.369100	+	0.929390i	$0.379666\pi$
$908$	−14.9358	−0.495663
$909$	−54.9241	−1.82172
$910$	9.36276	0.310372
$911$	35.5627	1.17825	0.589123	−	0.808043i	$-0.299473\pi$
$911$	35.5627	1.17825	0.589123	+	0.808043i	$0.299473\pi$
$912$	−2.65901	−0.0880485
$913$	2.77004	0.0916750
$914$	33.7511	1.11639
$915$	−1.01589	−0.0335843
$916$	−5.20012	−0.171817
$917$	22.5764	0.745537
$918$	6.89723	0.227642
$919$	−25.2577	−0.833176	−0.416588	−	0.909095i	$-0.636774\pi$
$919$	−25.2577	−0.833176	−0.416588	+	0.909095i	$0.636774\pi$
$920$	0.133655	0.00440648
$921$	−3.28879	−0.108369
$922$	−15.2380	−0.501838
$923$	54.0895	1.78038
$924$	1.20272	0.0395665
$925$	−1.99563	−0.0656160
$926$	−16.8651	−0.554221
$927$	12.1913	0.400414
$928$	−4.69585	−0.154149
$929$	−23.3678	−0.766673	−0.383337	−	0.923609i	$-0.625225\pi$
$929$	−23.3678	−0.766673	−0.383337	+	0.923609i	$0.625225\pi$
$930$	−3.53675	−0.115974
$931$	5.67033	0.185837
$932$	−8.41056	−0.275497
$933$	4.93869	0.161685
$934$	26.8405	0.878248
$935$	2.42956	0.0794552
$936$	10.5831	0.345919
$937$	−33.4999	−1.09440	−0.547198	−	0.837003i	$-0.684305\pi$
$937$	−33.4999	−1.09440	−0.547198	+	0.837003i	$0.684305\pi$
$938$	−23.8569	−0.778956
$939$	1.67526	0.0546702
$940$	−1.86172	−0.0607228
$941$	−8.40440	−0.273975	−0.136988	−	0.990573i	$-0.543742\pi$
$941$	−8.40440	−0.273975	−0.136988	+	0.990573i	$0.543742\pi$
$942$	−1.32217	−0.0430785
$943$	0.291350	0.00948768
$944$	−11.2330	−0.365602
$945$	6.92382	0.225232
$946$	−1.00000	−0.0325128
$947$	43.7899	1.42298	0.711491	−	0.702696i	$-0.248020\pi$
$947$	43.7899	1.42298	0.711491	+	0.702696i	$0.248020\pi$
$948$	−2.21209	−0.0718452
$949$	29.1632	0.946679
$950$	−5.39208	−0.174942
$951$	−0.553979	−0.0179640
$952$	−5.92555	−0.192048
$953$	43.6351	1.41348	0.706740	−	0.707474i	$-0.250165\pi$
$953$	43.6351	1.41348	0.706740	+	0.707474i	$0.250165\pi$
$954$	5.09457	0.164943
$955$	23.2131	0.751158
$956$	−4.35373	−0.140810
$957$	−2.31567	−0.0748551
$958$	−9.55657	−0.308759
$959$	−17.1383	−0.553424
$960$	−0.493132	−0.0159158
$961$	20.4377	0.659280
$962$	7.66098	0.247000
$963$	−26.5676	−0.856128
$964$	−20.7851	−0.669443
$965$	9.03553	0.290864
$966$	−0.160749	−0.00517203
$967$	29.4599	0.947368	0.473684	−	0.880695i	$-0.342924\pi$
$967$	29.4599	0.947368	0.473684	+	0.880695i	$0.342924\pi$
$968$	1.00000	0.0321412
$969$	6.46023	0.207533
$970$	7.15262	0.229657
$971$	−31.6517	−1.01575	−0.507876	−	0.861430i	$-0.669569\pi$
$971$	−31.6517	−1.01575	−0.507876	+	0.861430i	$0.669569\pi$
$972$	11.9047	0.381843
$973$	−19.7437	−0.632954
$974$	−3.71580	−0.119062
$975$	−1.89307	−0.0606268
$976$	2.06007	0.0659414
$977$	−52.3496	−1.67481	−0.837406	−	0.546582i	$-0.815929\pi$
$977$	−52.3496	−1.67481	−0.837406	+	0.546582i	$0.815929\pi$
$978$	7.79264	0.249181
$979$	−1.73631	−0.0554928
$980$	1.05160	0.0335922
$981$	1.73962	0.0555419
$982$	−5.59435	−0.178523
$983$	−8.29876	−0.264689	−0.132345	−	0.991204i	$-0.542251\pi$
$983$	−8.29876	−0.264689	−0.132345	+	0.991204i	$0.542251\pi$
$984$	−1.07496	−0.0342685
$985$	−0.403179	−0.0128464
$986$	11.4089	0.363332
$987$	2.23913	0.0712722
$988$	20.6995	0.658539
$989$	0.133655	0.00424999
$990$	2.75682	0.0876175
$991$	−41.3845	−1.31462	−0.657312	−	0.753619i	$-0.728306\pi$
$991$	−41.3845	−1.31462	−0.657312	+	0.753619i	$0.728306\pi$
$992$	7.17201	0.227711
$993$	−14.0879	−0.447065
$994$	−34.3645	−1.08997
$995$	−3.69964	−0.117287
$996$	1.36600	0.0432833
$997$	−14.0252	−0.444182	−0.222091	−	0.975026i	$-0.571288\pi$
$997$	−14.0252	−0.444182	−0.222091	+	0.975026i	$0.571288\pi$
$998$	−27.7888	−0.879640
$999$	5.66535	0.179244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.v.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.493132 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.493132 q^{6} +2.43893 q^{7} +1.00000 q^{8} -2.75682 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.493132 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.493132 q^{6} +2.43893 q^{7} +1.00000 q^{8} -2.75682 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.493132 q^{12} -3.83887 q^{13} +2.43893 q^{14} -0.493132 q^{15} +1.00000 q^{16} -2.42956 q^{17} -2.75682 q^{18} -5.39208 q^{19} -1.00000 q^{20} +1.20272 q^{21} +1.00000 q^{22} -0.133655 q^{23} +0.493132 q^{24} +1.00000 q^{25} -3.83887 q^{26} -2.83887 q^{27} +2.43893 q^{28} -4.69585 q^{29} -0.493132 q^{30} +7.17201 q^{31} +1.00000 q^{32} +0.493132 q^{33} -2.42956 q^{34} -2.43893 q^{35} -2.75682 q^{36} -1.99563 q^{37} -5.39208 q^{38} -1.89307 q^{39} -1.00000 q^{40} -2.17987 q^{41} +1.20272 q^{42} -1.00000 q^{43} +1.00000 q^{44} +2.75682 q^{45} -0.133655 q^{46} +1.86172 q^{47} +0.493132 q^{48} -1.05160 q^{49} +1.00000 q^{50} -1.19810 q^{51} -3.83887 q^{52} -1.84799 q^{53} -2.83887 q^{54} -1.00000 q^{55} +2.43893 q^{56} -2.65901 q^{57} -4.69585 q^{58} -11.2330 q^{59} -0.493132 q^{60} +2.06007 q^{61} +7.17201 q^{62} -6.72370 q^{63} +1.00000 q^{64} +3.83887 q^{65} +0.493132 q^{66} -9.78170 q^{67} -2.42956 q^{68} -0.0659097 q^{69} -2.43893 q^{70} -14.0900 q^{71} -2.75682 q^{72} -7.59682 q^{73} -1.99563 q^{74} +0.493132 q^{75} -5.39208 q^{76} +2.43893 q^{77} -1.89307 q^{78} -4.48579 q^{79} -1.00000 q^{80} +6.87052 q^{81} -2.17987 q^{82} +2.77004 q^{83} +1.20272 q^{84} +2.42956 q^{85} -1.00000 q^{86} -2.31567 q^{87} +1.00000 q^{88} -1.73631 q^{89} +2.75682 q^{90} -9.36276 q^{91} -0.133655 q^{92} +3.53675 q^{93} +1.86172 q^{94} +5.39208 q^{95} +0.493132 q^{96} -7.15262 q^{97} -1.05160 q^{98} -2.75682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9} - 5 q^{10} + 5 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{14} - 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 5 q^{20} + 2 q^{21} + 5 q^{22} - 6 q^{23} + 2 q^{24} + 5 q^{25} - 12 q^{26} - 7 q^{27} - 6 q^{28} - 19 q^{29} - 2 q^{30} - 7 q^{31} + 5 q^{32} + 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} - q^{37} - 4 q^{38} - 20 q^{39} - 5 q^{40} - 2 q^{41} + 2 q^{42} - 5 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} - 5 q^{49} + 5 q^{50} - 5 q^{51} - 12 q^{52} - 6 q^{53} - 7 q^{54} - 5 q^{55} - 6 q^{56} - 15 q^{57} - 19 q^{58} - 5 q^{59} - 2 q^{60} - 5 q^{61} - 7 q^{62} - 17 q^{63} + 5 q^{64} + 12 q^{65} + 2 q^{66} - 20 q^{67} - 2 q^{68} - 40 q^{69} + 6 q^{70} - 22 q^{71} - q^{72} + 10 q^{73} - q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 20 q^{78} - 9 q^{79} - 5 q^{80} - 15 q^{81} - 2 q^{82} - 19 q^{83} + 2 q^{84} + 2 q^{85} - 5 q^{86} + 15 q^{87} + 5 q^{88} - 21 q^{89} + q^{90} + 10 q^{91} - 6 q^{92} - 15 q^{93} + 7 q^{94} + 4 q^{95} + 2 q^{96} + 10 q^{97} - 5 q^{98} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9 - 5 * q^10 + 5 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^14 - 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 - 4 * q^19 - 5 * q^20 + 2 * q^21 + 5 * q^22 - 6 * q^23 + 2 * q^24 + 5 * q^25 - 12 * q^26 - 7 * q^27 - 6 * q^28 - 19 * q^29 - 2 * q^30 - 7 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 - q^37 - 4 * q^38 - 20 * q^39 - 5 * q^40 - 2 * q^41 + 2 * q^42 - 5 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 - 5 * q^49 + 5 * q^50 - 5 * q^51 - 12 * q^52 - 6 * q^53 - 7 * q^54 - 5 * q^55 - 6 * q^56 - 15 * q^57 - 19 * q^58 - 5 * q^59 - 2 * q^60 - 5 * q^61 - 7 * q^62 - 17 * q^63 + 5 * q^64 + 12 * q^65 + 2 * q^66 - 20 * q^67 - 2 * q^68 - 40 * q^69 + 6 * q^70 - 22 * q^71 - q^72 + 10 * q^73 - q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 20 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 - 2 * q^82 - 19 * q^83 + 2 * q^84 + 2 * q^85 - 5 * q^86 + 15 * q^87 + 5 * q^88 - 21 * q^89 + q^90 + 10 * q^91 - 6 * q^92 - 15 * q^93 + 7 * q^94 + 4 * q^95 + 2 * q^96 + 10 * q^97 - 5 * q^98 - q^99

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