LMFDB - Embedded newform 4022.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.89591 q^{3} +1.00000 q^{4} -0.0804536 q^{5} +2.89591 q^{6} +2.75347 q^{7} -1.00000 q^{8} +5.38632 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.89591 q^{3} +1.00000 q^{4} -0.0804536 q^{5} +2.89591 q^{6} +2.75347 q^{7} -1.00000 q^{8} +5.38632 q^{9} +0.0804536 q^{10} +1.67842 q^{11} -2.89591 q^{12} -5.39948 q^{13} -2.75347 q^{14} +0.232987 q^{15} +1.00000 q^{16} +7.39748 q^{17} -5.38632 q^{18} +3.47125 q^{19} -0.0804536 q^{20} -7.97380 q^{21} -1.67842 q^{22} +0.325508 q^{23} +2.89591 q^{24} -4.99353 q^{25} +5.39948 q^{26} -6.91058 q^{27} +2.75347 q^{28} +9.31615 q^{29} -0.232987 q^{30} +0.749494 q^{31} -1.00000 q^{32} -4.86056 q^{33} -7.39748 q^{34} -0.221526 q^{35} +5.38632 q^{36} +10.4374 q^{37} -3.47125 q^{38} +15.6364 q^{39} +0.0804536 q^{40} -9.26947 q^{41} +7.97380 q^{42} +4.99940 q^{43} +1.67842 q^{44} -0.433349 q^{45} -0.325508 q^{46} +7.03523 q^{47} -2.89591 q^{48} +0.581578 q^{49} +4.99353 q^{50} -21.4225 q^{51} -5.39948 q^{52} +1.56470 q^{53} +6.91058 q^{54} -0.135035 q^{55} -2.75347 q^{56} -10.0524 q^{57} -9.31615 q^{58} -4.79524 q^{59} +0.232987 q^{60} +13.4583 q^{61} -0.749494 q^{62} +14.8310 q^{63} +1.00000 q^{64} +0.434408 q^{65} +4.86056 q^{66} +10.5250 q^{67} +7.39748 q^{68} -0.942644 q^{69} +0.221526 q^{70} -16.8115 q^{71} -5.38632 q^{72} +2.57597 q^{73} -10.4374 q^{74} +14.4608 q^{75} +3.47125 q^{76} +4.62147 q^{77} -15.6364 q^{78} -15.0477 q^{79} -0.0804536 q^{80} +3.85348 q^{81} +9.26947 q^{82} +3.03184 q^{83} -7.97380 q^{84} -0.595154 q^{85} -4.99940 q^{86} -26.9788 q^{87} -1.67842 q^{88} +12.8566 q^{89} +0.433349 q^{90} -14.8673 q^{91} +0.325508 q^{92} -2.17047 q^{93} -7.03523 q^{94} -0.279275 q^{95} +2.89591 q^{96} -10.5877 q^{97} -0.581578 q^{98} +9.04050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * 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
$3$	−2.89591	−1.67196	−0.835978	−	0.548762i	$-0.815099\pi$
$3$	−2.89591	−1.67196	−0.835978	+	0.548762i	$0.815099\pi$
$4$	1.00000	0.500000
$5$	−0.0804536	−0.0359799	−0.0179900	−	0.999838i	$-0.505727\pi$
$5$	−0.0804536	−0.0359799	−0.0179900	+	0.999838i	$0.505727\pi$
$6$	2.89591	1.18225
$7$	2.75347	1.04071	0.520356	−	0.853949i	$-0.325799\pi$
$7$	2.75347	1.04071	0.520356	+	0.853949i	$0.325799\pi$
$8$	−1.00000	−0.353553
$9$	5.38632	1.79544
$10$	0.0804536	0.0254417
$11$	1.67842	0.506062	0.253031	−	0.967458i	$-0.418573\pi$
$11$	1.67842	0.506062	0.253031	+	0.967458i	$0.418573\pi$
$12$	−2.89591	−0.835978
$13$	−5.39948	−1.49755	−0.748773	−	0.662826i	$-0.769357\pi$
$13$	−5.39948	−1.49755	−0.748773	+	0.662826i	$0.769357\pi$
$14$	−2.75347	−0.735895
$15$	0.232987	0.0601569
$16$	1.00000	0.250000
$17$	7.39748	1.79415	0.897076	−	0.441876i	$-0.145687\pi$
$17$	7.39748	1.79415	0.897076	+	0.441876i	$0.145687\pi$
$18$	−5.38632	−1.26957
$19$	3.47125	0.796360	0.398180	−	0.917307i	$-0.369642\pi$
$19$	3.47125	0.796360	0.398180	+	0.917307i	$0.369642\pi$
$20$	−0.0804536	−0.0179900
$21$	−7.97380	−1.74003
$22$	−1.67842	−0.357840
$23$	0.325508	0.0678732	0.0339366	−	0.999424i	$-0.489196\pi$
$23$	0.325508	0.0678732	0.0339366	+	0.999424i	$0.489196\pi$
$24$	2.89591	0.591126
$25$	−4.99353	−0.998705
$26$	5.39948	1.05893
$27$	−6.91058	−1.32994
$28$	2.75347	0.520356
$29$	9.31615	1.72997	0.864983	−	0.501801i	$-0.167329\pi$
$29$	9.31615	1.72997	0.864983	+	0.501801i	$0.167329\pi$
$30$	−0.232987	−0.0425374
$31$	0.749494	0.134613	0.0673065	−	0.997732i	$-0.478559\pi$
$31$	0.749494	0.134613	0.0673065	+	0.997732i	$0.478559\pi$
$32$	−1.00000	−0.176777
$33$	−4.86056	−0.846114
$34$	−7.39748	−1.26866
$35$	−0.221526	−0.0374448
$36$	5.38632	0.897720
$37$	10.4374	1.71590	0.857948	−	0.513737i	$-0.171739\pi$
$37$	10.4374	1.71590	0.857948	+	0.513737i	$0.171739\pi$
$38$	−3.47125	−0.563112
$39$	15.6364	2.50383
$40$	0.0804536	0.0127208
$41$	−9.26947	−1.44765	−0.723824	−	0.689984i	$-0.757617\pi$
$41$	−9.26947	−1.44765	−0.723824	+	0.689984i	$0.757617\pi$
$42$	7.97380	1.23038
$43$	4.99940	0.762401	0.381201	−	0.924492i	$-0.375511\pi$
$43$	4.99940	0.762401	0.381201	+	0.924492i	$0.375511\pi$
$44$	1.67842	0.253031
$45$	−0.433349	−0.0645998
$46$	−0.325508	−0.0479936
$47$	7.03523	1.02619	0.513097	−	0.858331i	$-0.328498\pi$
$47$	7.03523	1.02619	0.513097	+	0.858331i	$0.328498\pi$
$48$	−2.89591	−0.417989
$49$	0.581578	0.0830825
$50$	4.99353	0.706191
$51$	−21.4225	−2.99974
$52$	−5.39948	−0.748773
$53$	1.56470	0.214928	0.107464	−	0.994209i	$-0.465727\pi$
$53$	1.56470	0.214928	0.107464	+	0.994209i	$0.465727\pi$
$54$	6.91058	0.940410
$55$	−0.135035	−0.0182081
$56$	−2.75347	−0.367947
$57$	−10.0524	−1.33148
$58$	−9.31615	−1.22327
$59$	−4.79524	−0.624287	−0.312143	−	0.950035i	$-0.601047\pi$
$59$	−4.79524	−0.624287	−0.312143	+	0.950035i	$0.601047\pi$
$60$	0.232987	0.0300785
$61$	13.4583	1.72315	0.861577	−	0.507628i	$-0.169477\pi$
$61$	13.4583	1.72315	0.861577	+	0.507628i	$0.169477\pi$
$62$	−0.749494	−0.0951858
$63$	14.8310	1.86854
$64$	1.00000	0.125000
$65$	0.434408	0.0538816
$66$	4.86056	0.598293
$67$	10.5250	1.28583	0.642914	−	0.765938i	$-0.277725\pi$
$67$	10.5250	1.28583	0.642914	+	0.765938i	$0.277725\pi$
$68$	7.39748	0.897076
$69$	−0.942644	−0.113481
$70$	0.221526	0.0264775
$71$	−16.8115	−1.99516	−0.997579	−	0.0695467i	$-0.977845\pi$
$71$	−16.8115	−1.99516	−0.997579	+	0.0695467i	$0.977845\pi$
$72$	−5.38632	−0.634784
$73$	2.57597	0.301494	0.150747	−	0.988572i	$-0.451832\pi$
$73$	2.57597	0.301494	0.150747	+	0.988572i	$0.451832\pi$
$74$	−10.4374	−1.21332
$75$	14.4608	1.66979
$76$	3.47125	0.398180
$77$	4.62147	0.526665
$78$	−15.6364	−1.77048
$79$	−15.0477	−1.69300	−0.846498	−	0.532392i	$-0.821293\pi$
$79$	−15.0477	−1.69300	−0.846498	+	0.532392i	$0.821293\pi$
$80$	−0.0804536	−0.00899499
$81$	3.85348	0.428164
$82$	9.26947	1.02364
$83$	3.03184	0.332788	0.166394	−	0.986059i	$-0.446788\pi$
$83$	3.03184	0.332788	0.166394	+	0.986059i	$0.446788\pi$
$84$	−7.97380	−0.870013
$85$	−0.595154	−0.0645535
$86$	−4.99940	−0.539099
$87$	−26.9788	−2.89243
$88$	−1.67842	−0.178920
$89$	12.8566	1.36280	0.681400	−	0.731911i	$-0.261371\pi$
$89$	12.8566	1.36280	0.681400	+	0.731911i	$0.261371\pi$
$90$	0.433349	0.0456790
$91$	−14.8673	−1.55852
$92$	0.325508	0.0339366
$93$	−2.17047	−0.225067
$94$	−7.03523	−0.725628
$95$	−0.279275	−0.0286530
$96$	2.89591	0.295563
$97$	−10.5877	−1.07501	−0.537507	−	0.843259i	$-0.680634\pi$
$97$	−10.5877	−1.07501	−0.537507	+	0.843259i	$0.680634\pi$
$98$	−0.581578	−0.0587482
$99$	9.04050	0.908604
$100$	−4.99353	−0.499353
$101$	−9.83016	−0.978138	−0.489069	−	0.872245i	$-0.662663\pi$
$101$	−9.83016	−0.978138	−0.489069	+	0.872245i	$0.662663\pi$
$102$	21.4225	2.12114
$103$	7.38158	0.727328	0.363664	−	0.931530i	$-0.381526\pi$
$103$	7.38158	0.727328	0.363664	+	0.931530i	$0.381526\pi$
$104$	5.39948	0.529463
$105$	0.641521	0.0626061
$106$	−1.56470	−0.151977
$107$	−2.93582	−0.283816	−0.141908	−	0.989880i	$-0.545324\pi$
$107$	−2.93582	−0.283816	−0.141908	+	0.989880i	$0.545324\pi$
$108$	−6.91058	−0.664970
$109$	−8.37114	−0.801810	−0.400905	−	0.916120i	$-0.631304\pi$
$109$	−8.37114	−0.801810	−0.400905	+	0.916120i	$0.631304\pi$
$110$	0.135035	0.0128751
$111$	−30.2258	−2.86890
$112$	2.75347	0.260178
$113$	4.20537	0.395608	0.197804	−	0.980242i	$-0.436619\pi$
$113$	4.20537	0.395608	0.197804	+	0.980242i	$0.436619\pi$
$114$	10.0524	0.941498
$115$	−0.0261883	−0.00244207
$116$	9.31615	0.864983
$117$	−29.0833	−2.68875
$118$	4.79524	0.441437
$119$	20.3687	1.86720
$120$	−0.232987	−0.0212687
$121$	−8.18291	−0.743901
$122$	−13.4583	−1.21845
$123$	26.8436	2.42041
$124$	0.749494	0.0673065
$125$	0.804015	0.0719133
$126$	−14.8310	−1.32125
$127$	−1.42572	−0.126512	−0.0632559	−	0.997997i	$-0.520148\pi$
$127$	−1.42572	−0.126512	−0.0632559	+	0.997997i	$0.520148\pi$
$128$	−1.00000	−0.0883883
$129$	−14.4778	−1.27470
$130$	−0.434408	−0.0381001
$131$	4.42791	0.386869	0.193434	−	0.981113i	$-0.438037\pi$
$131$	4.42791	0.386869	0.193434	+	0.981113i	$0.438037\pi$
$132$	−4.86056	−0.423057
$133$	9.55798	0.828782
$134$	−10.5250	−0.909217
$135$	0.555981	0.0478512
$136$	−7.39748	−0.634328
$137$	−7.33790	−0.626919	−0.313460	−	0.949602i	$-0.601488\pi$
$137$	−7.33790	−0.626919	−0.313460	+	0.949602i	$0.601488\pi$
$138$	0.942644	0.0802432
$139$	−5.73361	−0.486318	−0.243159	−	0.969986i	$-0.578184\pi$
$139$	−5.73361	−0.486318	−0.243159	+	0.969986i	$0.578184\pi$
$140$	−0.221526	−0.0187224
$141$	−20.3734	−1.71575
$142$	16.8115	1.41079
$143$	−9.06259	−0.757852
$144$	5.38632	0.448860
$145$	−0.749518	−0.0622441
$146$	−2.57597	−0.213189
$147$	−1.68420	−0.138910
$148$	10.4374	0.857948
$149$	−21.4852	−1.76013	−0.880067	−	0.474849i	$-0.842503\pi$
$149$	−21.4852	−1.76013	−0.880067	+	0.474849i	$0.842503\pi$
$150$	−14.4608	−1.18072
$151$	−9.43073	−0.767462	−0.383731	−	0.923445i	$-0.625361\pi$
$151$	−9.43073	−0.767462	−0.383731	+	0.923445i	$0.625361\pi$
$152$	−3.47125	−0.281556
$153$	39.8452	3.22129
$154$	−4.62147	−0.372409
$155$	−0.0602995	−0.00484337
$156$	15.6364	1.25192
$157$	3.84632	0.306970	0.153485	−	0.988151i	$-0.450950\pi$
$157$	3.84632	0.306970	0.153485	+	0.988151i	$0.450950\pi$
$158$	15.0477	1.19713
$159$	−4.53124	−0.359351
$160$	0.0804536	0.00636042
$161$	0.896276	0.0706365
$162$	−3.85348	−0.302758
$163$	10.1275	0.793248	0.396624	−	0.917981i	$-0.370182\pi$
$163$	10.1275	0.793248	0.396624	+	0.917981i	$0.370182\pi$
$164$	−9.26947	−0.723824
$165$	0.391049	0.0304431
$166$	−3.03184	−0.235316
$167$	−1.82406	−0.141150	−0.0705750	−	0.997506i	$-0.522483\pi$
$167$	−1.82406	−0.141150	−0.0705750	+	0.997506i	$0.522483\pi$
$168$	7.97380	0.615192
$169$	16.1544	1.24265
$170$	0.595154	0.0456462
$171$	18.6973	1.42982
$172$	4.99940	0.381201
$173$	23.5949	1.79389	0.896944	−	0.442145i	$-0.145782\pi$
$173$	23.5949	1.79389	0.896944	+	0.442145i	$0.145782\pi$
$174$	26.9788	2.04526
$175$	−13.7495	−1.03937
$176$	1.67842	0.126516
$177$	13.8866	1.04378
$178$	−12.8566	−0.963645
$179$	−15.0324	−1.12358	−0.561789	−	0.827281i	$-0.689887\pi$
$179$	−15.0324	−1.12358	−0.561789	+	0.827281i	$0.689887\pi$
$180$	−0.433349	−0.0322999
$181$	14.9010	1.10759	0.553793	−	0.832654i	$-0.313180\pi$
$181$	14.9010	1.10759	0.553793	+	0.832654i	$0.313180\pi$
$182$	14.8673	1.10204
$183$	−38.9740	−2.88104
$184$	−0.325508	−0.0239968
$185$	−0.839725	−0.0617378
$186$	2.17047	0.159147
$187$	12.4161	0.907952
$188$	7.03523	0.513097
$189$	−19.0280	−1.38409
$190$	0.279275	0.0202607
$191$	−8.77826	−0.635173	−0.317586	−	0.948229i	$-0.602872\pi$
$191$	−8.77826	−0.635173	−0.317586	+	0.948229i	$0.602872\pi$
$192$	−2.89591	−0.208995
$193$	26.3273	1.89508	0.947539	−	0.319641i	$-0.103562\pi$
$193$	26.3273	1.89508	0.947539	+	0.319641i	$0.103562\pi$
$194$	10.5877	0.760150
$195$	−1.25801	−0.0900878
$196$	0.581578	0.0415413
$197$	9.28411	0.661465	0.330733	−	0.943724i	$-0.392704\pi$
$197$	9.28411	0.661465	0.330733	+	0.943724i	$0.392704\pi$
$198$	−9.04050	−0.642480
$199$	9.49950	0.673402	0.336701	−	0.941612i	$-0.390689\pi$
$199$	9.49950	0.673402	0.336701	+	0.941612i	$0.390689\pi$
$200$	4.99353	0.353096
$201$	−30.4794	−2.14985
$202$	9.83016	0.691648
$203$	25.6517	1.80040
$204$	−21.4225	−1.49987
$205$	0.745762	0.0520863
$206$	−7.38158	−0.514299
$207$	1.75329	0.121862
$208$	−5.39948	−0.374387
$209$	5.82621	0.403008
$210$	−0.641521	−0.0442692
$211$	−17.9396	−1.23501	−0.617507	−	0.786566i	$-0.711857\pi$
$211$	−17.9396	−1.23501	−0.617507	+	0.786566i	$0.711857\pi$
$212$	1.56470	0.107464
$213$	48.6846	3.33582
$214$	2.93582	0.200688
$215$	−0.402220	−0.0274312
$216$	6.91058	0.470205
$217$	2.06371	0.140094
$218$	8.37114	0.566965
$219$	−7.45978	−0.504085
$220$	−0.135035	−0.00910405
$221$	−39.9425	−2.68683
$222$	30.2258	2.02862
$223$	−15.3487	−1.02783	−0.513913	−	0.857842i	$-0.671805\pi$
$223$	−15.3487	−1.02783	−0.513913	+	0.857842i	$0.671805\pi$
$224$	−2.75347	−0.183974
$225$	−26.8967	−1.79312
$226$	−4.20537	−0.279737
$227$	−10.6505	−0.706900	−0.353450	−	0.935453i	$-0.614991\pi$
$227$	−10.6505	−0.706900	−0.353450	+	0.935453i	$0.614991\pi$
$228$	−10.0524	−0.665740
$229$	20.7422	1.37068	0.685340	−	0.728223i	$-0.259654\pi$
$229$	20.7422	1.37068	0.685340	+	0.728223i	$0.259654\pi$
$230$	0.0261883	0.00172681
$231$	−13.3834	−0.880562
$232$	−9.31615	−0.611635
$233$	−11.8308	−0.775064	−0.387532	−	0.921856i	$-0.626672\pi$
$233$	−11.8308	−0.775064	−0.387532	+	0.921856i	$0.626672\pi$
$234$	29.0833	1.90124
$235$	−0.566009	−0.0369224
$236$	−4.79524	−0.312143
$237$	43.5768	2.83062
$238$	−20.3687	−1.32031
$239$	−4.40707	−0.285070	−0.142535	−	0.989790i	$-0.545525\pi$
$239$	−4.40707	−0.285070	−0.142535	+	0.989790i	$0.545525\pi$
$240$	0.232987	0.0150392
$241$	−2.79206	−0.179852	−0.0899261	−	0.995948i	$-0.528663\pi$
$241$	−2.79206	−0.179852	−0.0899261	+	0.995948i	$0.528663\pi$
$242$	8.18291	0.526017
$243$	9.57239	0.614069
$244$	13.4583	0.861577
$245$	−0.0467900	−0.00298930
$246$	−26.8436	−1.71149
$247$	−18.7430	−1.19259
$248$	−0.749494	−0.0475929
$249$	−8.77995	−0.556407
$250$	−0.804015	−0.0508504
$251$	22.0755	1.39340	0.696698	−	0.717365i	$-0.254652\pi$
$251$	22.0755	1.39340	0.696698	+	0.717365i	$0.254652\pi$
$252$	14.8310	0.934268
$253$	0.546339	0.0343481
$254$	1.42572	0.0894574
$255$	1.72351	0.107931
$256$	1.00000	0.0625000
$257$	2.47845	0.154601	0.0773007	−	0.997008i	$-0.475370\pi$
$257$	2.47845	0.154601	0.0773007	+	0.997008i	$0.475370\pi$
$258$	14.4778	0.901350
$259$	28.7390	1.78575
$260$	0.434408	0.0269408
$261$	50.1798	3.10605
$262$	−4.42791	−0.273557
$263$	2.05744	0.126867	0.0634336	−	0.997986i	$-0.479795\pi$
$263$	2.05744	0.126867	0.0634336	+	0.997986i	$0.479795\pi$
$264$	4.86056	0.299147
$265$	−0.125886	−0.00773310
$266$	−9.55798	−0.586037
$267$	−37.2317	−2.27854
$268$	10.5250	0.642914
$269$	19.3606	1.18044	0.590218	−	0.807244i	$-0.299042\pi$
$269$	19.3606	1.18044	0.590218	+	0.807244i	$0.299042\pi$
$270$	−0.555981	−0.0338359
$271$	29.1562	1.77111	0.885557	−	0.464531i	$-0.153777\pi$
$271$	29.1562	1.77111	0.885557	+	0.464531i	$0.153777\pi$
$272$	7.39748	0.448538
$273$	43.0544	2.60577
$274$	7.33790	0.443299
$275$	−8.38123	−0.505407
$276$	−0.942644	−0.0567405
$277$	−3.73558	−0.224449	−0.112225	−	0.993683i	$-0.535798\pi$
$277$	−3.73558	−0.224449	−0.112225	+	0.993683i	$0.535798\pi$
$278$	5.73361	0.343879
$279$	4.03701	0.241690
$280$	0.221526	0.0132387
$281$	25.5119	1.52191	0.760955	−	0.648804i	$-0.224731\pi$
$281$	25.5119	1.52191	0.760955	+	0.648804i	$0.224731\pi$
$282$	20.3734	1.21322
$283$	17.1330	1.01845	0.509226	−	0.860633i	$-0.329932\pi$
$283$	17.1330	1.01845	0.509226	+	0.860633i	$0.329932\pi$
$284$	−16.8115	−0.997579
$285$	0.808756	0.0479066
$286$	9.06259	0.535882
$287$	−25.5232	−1.50659
$288$	−5.38632	−0.317392
$289$	37.7227	2.21898
$290$	0.749518	0.0440132
$291$	30.6610	1.79738
$292$	2.57597	0.150747
$293$	−23.1053	−1.34983	−0.674913	−	0.737897i	$-0.735819\pi$
$293$	−23.1053	−1.34983	−0.674913	+	0.737897i	$0.735819\pi$
$294$	1.68420	0.0982245
$295$	0.385794	0.0224618
$296$	−10.4374	−0.606661
$297$	−11.5988	−0.673033
$298$	21.4852	1.24460
$299$	−1.75758	−0.101643
$300$	14.4608	0.834896
$301$	13.7657	0.793440
$302$	9.43073	0.542678
$303$	28.4673	1.63540
$304$	3.47125	0.199090
$305$	−1.08277	−0.0619990
$306$	−39.8452	−2.27780
$307$	4.04232	0.230707	0.115354	−	0.993324i	$-0.463200\pi$
$307$	4.04232	0.230707	0.115354	+	0.993324i	$0.463200\pi$
$308$	4.62147	0.263333
$309$	−21.3764	−1.21606
$310$	0.0602995	0.00342478
$311$	−15.5798	−0.883448	−0.441724	−	0.897151i	$-0.645633\pi$
$311$	−15.5798	−0.883448	−0.441724	+	0.897151i	$0.645633\pi$
$312$	−15.6364	−0.885239
$313$	34.0667	1.92556	0.962782	−	0.270281i	$-0.0871165\pi$
$313$	34.0667	1.92556	0.962782	+	0.270281i	$0.0871165\pi$
$314$	−3.84632	−0.217060
$315$	−1.19321	−0.0672298
$316$	−15.0477	−0.846498
$317$	8.65790	0.486276	0.243138	−	0.969992i	$-0.421823\pi$
$317$	8.65790	0.486276	0.243138	+	0.969992i	$0.421823\pi$
$318$	4.53124	0.254099
$319$	15.6364	0.875470
$320$	−0.0804536	−0.00449749
$321$	8.50188	0.474529
$322$	−0.896276	−0.0499475
$323$	25.6785	1.42879
$324$	3.85348	0.214082
$325$	26.9625	1.49561
$326$	−10.1275	−0.560911
$327$	24.2421	1.34059
$328$	9.26947	0.511821
$329$	19.3713	1.06797
$330$	−0.391049	−0.0215266
$331$	34.8527	1.91568	0.957840	−	0.287303i	$-0.0927587\pi$
$331$	34.8527	1.91568	0.957840	+	0.287303i	$0.0927587\pi$
$332$	3.03184	0.166394
$333$	56.2191	3.08079
$334$	1.82406	0.0998082
$335$	−0.846770	−0.0462640
$336$	−7.97380	−0.435007
$337$	20.8768	1.13723	0.568615	−	0.822604i	$-0.307479\pi$
$337$	20.8768	1.13723	0.568615	+	0.822604i	$0.307479\pi$
$338$	−16.1544	−0.878683
$339$	−12.1784	−0.661440
$340$	−0.595154	−0.0322767
$341$	1.25796	0.0681226
$342$	−18.6973	−1.01103
$343$	−17.6729	−0.954247
$344$	−4.99940	−0.269549
$345$	0.0758391	0.00408304
$346$	−23.5949	−1.26847
$347$	−32.7247	−1.75675	−0.878376	−	0.477970i	$-0.841373\pi$
$347$	−32.7247	−1.75675	−0.878376	+	0.477970i	$0.841373\pi$
$348$	−26.9788	−1.44621
$349$	30.6997	1.64332	0.821658	−	0.569980i	$-0.193049\pi$
$349$	30.6997	1.64332	0.821658	+	0.569980i	$0.193049\pi$
$350$	13.7495	0.734942
$351$	37.3135	1.99165
$352$	−1.67842	−0.0894600
$353$	−1.11994	−0.0596086	−0.0298043	−	0.999556i	$-0.509488\pi$
$353$	−1.11994	−0.0596086	−0.0298043	+	0.999556i	$0.509488\pi$
$354$	−13.8866	−0.738064
$355$	1.35255	0.0717857
$356$	12.8566	0.681400
$357$	−58.9860	−3.12187
$358$	15.0324	0.794489
$359$	10.9729	0.579127	0.289564	−	0.957159i	$-0.406490\pi$
$359$	10.9729	0.579127	0.289564	+	0.957159i	$0.406490\pi$
$360$	0.433349	0.0228395
$361$	−6.95041	−0.365811
$362$	−14.9010	−0.783182
$363$	23.6970	1.24377
$364$	−14.8673	−0.779258
$365$	−0.207246	−0.0108477
$366$	38.9740	2.03720
$367$	7.41123	0.386863	0.193432	−	0.981114i	$-0.438038\pi$
$367$	7.41123	0.386863	0.193432	+	0.981114i	$0.438038\pi$
$368$	0.325508	0.0169683
$369$	−49.9283	−2.59917
$370$	0.839725	0.0436552
$371$	4.30835	0.223678
$372$	−2.17047	−0.112534
$373$	−5.92175	−0.306616	−0.153308	−	0.988178i	$-0.548993\pi$
$373$	−5.92175	−0.306616	−0.153308	+	0.988178i	$0.548993\pi$
$374$	−12.4161	−0.642019
$375$	−2.32836	−0.120236
$376$	−7.03523	−0.362814
$377$	−50.3024	−2.59070
$378$	19.0280	0.978697
$379$	−3.70256	−0.190188	−0.0950939	−	0.995468i	$-0.530315\pi$
$379$	−3.70256	−0.190188	−0.0950939	+	0.995468i	$0.530315\pi$
$380$	−0.279275	−0.0143265
$381$	4.12875	0.211522
$382$	8.77826	0.449135
$383$	−24.4675	−1.25023	−0.625114	−	0.780533i	$-0.714948\pi$
$383$	−24.4675	−1.25023	−0.625114	+	0.780533i	$0.714948\pi$
$384$	2.89591	0.147782
$385$	−0.371814	−0.0189494
$386$	−26.3273	−1.34002
$387$	26.9284	1.36885
$388$	−10.5877	−0.537507
$389$	6.21168	0.314945	0.157472	−	0.987523i	$-0.449666\pi$
$389$	6.21168	0.314945	0.157472	+	0.987523i	$0.449666\pi$
$390$	1.25801	0.0637017
$391$	2.40794	0.121775
$392$	−0.581578	−0.0293741
$393$	−12.8229	−0.646828
$394$	−9.28411	−0.467727
$395$	1.21064	0.0609139
$396$	9.04050	0.454302
$397$	26.5473	1.33237	0.666184	−	0.745787i	$-0.267926\pi$
$397$	26.5473	1.33237	0.666184	+	0.745787i	$0.267926\pi$
$398$	−9.49950	−0.476167
$399$	−27.6791	−1.38569
$400$	−4.99353	−0.249676
$401$	−14.7113	−0.734645	−0.367322	−	0.930094i	$-0.619725\pi$
$401$	−14.7113	−0.734645	−0.367322	+	0.930094i	$0.619725\pi$
$402$	30.4794	1.52017
$403$	−4.04688	−0.201589
$404$	−9.83016	−0.489069
$405$	−0.310026	−0.0154053
$406$	−25.6517	−1.27307
$407$	17.5183	0.868350
$408$	21.4225	1.06057
$409$	29.5820	1.46274	0.731369	−	0.681982i	$-0.238882\pi$
$409$	29.5820	1.46274	0.731369	+	0.681982i	$0.238882\pi$
$410$	−0.745762	−0.0368306
$411$	21.2499	1.04818
$412$	7.38158	0.363664
$413$	−13.2035	−0.649703
$414$	−1.75329	−0.0861696
$415$	−0.243922	−0.0119737
$416$	5.39948	0.264731
$417$	16.6040	0.813103
$418$	−5.82621	−0.284969
$419$	−20.3766	−0.995461	−0.497730	−	0.867332i	$-0.665833\pi$
$419$	−20.3766	−0.995461	−0.497730	+	0.867332i	$0.665833\pi$
$420$	0.641521	0.0313030
$421$	−2.62633	−0.128000	−0.0639998	−	0.997950i	$-0.520386\pi$
$421$	−2.62633	−0.128000	−0.0639998	+	0.997950i	$0.520386\pi$
$422$	17.9396	0.873286
$423$	37.8940	1.84247
$424$	−1.56470	−0.0759886
$425$	−36.9395	−1.79183
$426$	−48.6846	−2.35878
$427$	37.0569	1.79331
$428$	−2.93582	−0.141908
$429$	26.2445	1.26710
$430$	0.402220	0.0193968
$431$	−12.6168	−0.607730	−0.303865	−	0.952715i	$-0.598277\pi$
$431$	−12.6168	−0.607730	−0.303865	+	0.952715i	$0.598277\pi$
$432$	−6.91058	−0.332485
$433$	−8.90812	−0.428097	−0.214049	−	0.976823i	$-0.568665\pi$
$433$	−8.90812	−0.428097	−0.214049	+	0.976823i	$0.568665\pi$
$434$	−2.06371	−0.0990611
$435$	2.17054	0.104069
$436$	−8.37114	−0.400905
$437$	1.12992	0.0540515
$438$	7.45978	0.356442
$439$	−21.9601	−1.04810	−0.524049	−	0.851688i	$-0.675579\pi$
$439$	−21.9601	−1.04810	−0.524049	+	0.851688i	$0.675579\pi$
$440$	0.135035	0.00643753
$441$	3.13256	0.149170
$442$	39.9425	1.89987
$443$	−10.6914	−0.507962	−0.253981	−	0.967209i	$-0.581740\pi$
$443$	−10.6914	−0.507962	−0.253981	+	0.967209i	$0.581740\pi$
$444$	−30.2258	−1.43445
$445$	−1.03436	−0.0490335
$446$	15.3487	0.726783
$447$	62.2193	2.94287
$448$	2.75347	0.130089
$449$	0.978741	0.0461896	0.0230948	−	0.999733i	$-0.492648\pi$
$449$	0.978741	0.0461896	0.0230948	+	0.999733i	$0.492648\pi$
$450$	26.8967	1.26792
$451$	−15.5581	−0.732600
$452$	4.20537	0.197804
$453$	27.3106	1.28316
$454$	10.6505	0.499854
$455$	1.19613	0.0560753
$456$	10.0524	0.470749
$457$	−6.99329	−0.327132	−0.163566	−	0.986532i	$-0.552300\pi$
$457$	−6.99329	−0.327132	−0.163566	+	0.986532i	$0.552300\pi$
$458$	−20.7422	−0.969217
$459$	−51.1208	−2.38612
$460$	−0.0261883	−0.00122104
$461$	14.0202	0.652987	0.326494	−	0.945199i	$-0.394133\pi$
$461$	14.0202	0.652987	0.326494	+	0.945199i	$0.394133\pi$
$462$	13.3834	0.622651
$463$	−37.4441	−1.74017	−0.870087	−	0.492898i	$-0.835938\pi$
$463$	−37.4441	−1.74017	−0.870087	+	0.492898i	$0.835938\pi$
$464$	9.31615	0.432491
$465$	0.174622	0.00809791
$466$	11.8308	0.548053
$467$	11.6957	0.541214	0.270607	−	0.962690i	$-0.412776\pi$
$467$	11.6957	0.541214	0.270607	+	0.962690i	$0.412776\pi$
$468$	−29.0833	−1.34438
$469$	28.9801	1.33818
$470$	0.566009	0.0261081
$471$	−11.1386	−0.513240
$472$	4.79524	0.220719
$473$	8.39108	0.385822
$474$	−43.5768	−2.00155
$475$	−17.3338	−0.795329
$476$	20.3687	0.933598
$477$	8.42798	0.385891
$478$	4.40707	0.201575
$479$	−11.7966	−0.539002	−0.269501	−	0.963000i	$-0.586859\pi$
$479$	−11.7966	−0.539002	−0.269501	+	0.963000i	$0.586859\pi$
$480$	−0.232987	−0.0106343
$481$	−56.3564	−2.56963
$482$	2.79206	0.127175
$483$	−2.59554	−0.118101
$484$	−8.18291	−0.371951
$485$	0.851816	0.0386790
$486$	−9.57239	−0.434212
$487$	12.5206	0.567362	0.283681	−	0.958919i	$-0.408444\pi$
$487$	12.5206	0.567362	0.283681	+	0.958919i	$0.408444\pi$
$488$	−13.4583	−0.609227
$489$	−29.3284	−1.32628
$490$	0.0467900	0.00211376
$491$	36.0348	1.62623	0.813113	−	0.582106i	$-0.197771\pi$
$491$	36.0348	1.62623	0.813113	+	0.582106i	$0.197771\pi$
$492$	26.8436	1.21020
$493$	68.9160	3.10382
$494$	18.7430	0.843286
$495$	−0.727341	−0.0326915
$496$	0.749494	0.0336533
$497$	−46.2899	−2.07639
$498$	8.77995	0.393439
$499$	−11.2115	−0.501896	−0.250948	−	0.968001i	$-0.580742\pi$
$499$	−11.2115	−0.501896	−0.250948	+	0.968001i	$0.580742\pi$
$500$	0.804015	0.0359567
$501$	5.28232	0.235997
$502$	−22.0755	−0.985280
$503$	10.8418	0.483410	0.241705	−	0.970350i	$-0.422293\pi$
$503$	10.8418	0.483410	0.241705	+	0.970350i	$0.422293\pi$
$504$	−14.8310	−0.660627
$505$	0.790872	0.0351933
$506$	−0.546339	−0.0242877
$507$	−46.7817	−2.07765
$508$	−1.42572	−0.0632559
$509$	−15.6462	−0.693507	−0.346754	−	0.937956i	$-0.612716\pi$
$509$	−15.6462	−0.693507	−0.346754	+	0.937956i	$0.612716\pi$
$510$	−1.72351	−0.0763185
$511$	7.09284	0.313769
$512$	−1.00000	−0.0441942
$513$	−23.9884	−1.05911
$514$	−2.47845	−0.109320
$515$	−0.593875	−0.0261692
$516$	−14.4778	−0.637351
$517$	11.8081	0.519318
$518$	−28.7390	−1.26272
$519$	−68.3288	−2.99930
$520$	−0.434408	−0.0190500
$521$	14.2179	0.622898	0.311449	−	0.950263i	$-0.399186\pi$
$521$	14.2179	0.622898	0.311449	+	0.950263i	$0.399186\pi$
$522$	−50.1798	−2.19631
$523$	−21.9773	−0.961002	−0.480501	−	0.876994i	$-0.659545\pi$
$523$	−21.9773	−0.961002	−0.480501	+	0.876994i	$0.659545\pi$
$524$	4.42791	0.193434
$525$	39.8174	1.73777
$526$	−2.05744	−0.0897087
$527$	5.54436	0.241516
$528$	−4.86056	−0.211529
$529$	−22.8940	−0.995393
$530$	0.125886	0.00546813
$531$	−25.8287	−1.12087
$532$	9.55798	0.414391
$533$	50.0503	2.16792
$534$	37.2317	1.61117
$535$	0.236197	0.0102117
$536$	−10.5250	−0.454609
$537$	43.5327	1.87857
$538$	−19.3606	−0.834694
$539$	0.976131	0.0420449
$540$	0.555981	0.0239256
$541$	14.0421	0.603717	0.301858	−	0.953353i	$-0.402393\pi$
$541$	14.0421	0.603717	0.301858	+	0.953353i	$0.402393\pi$
$542$	−29.1562	−1.25237
$543$	−43.1522	−1.85184
$544$	−7.39748	−0.317164
$545$	0.673489	0.0288491
$546$	−43.0544	−1.84256
$547$	−22.4330	−0.959165	−0.479583	−	0.877497i	$-0.659212\pi$
$547$	−22.4330	−0.959165	−0.479583	+	0.877497i	$0.659212\pi$
$548$	−7.33790	−0.313460
$549$	72.4905	3.09382
$550$	8.38123	0.357377
$551$	32.3387	1.37768
$552$	0.942644	0.0401216
$553$	−41.4333	−1.76192
$554$	3.73558	0.158710
$555$	2.43177	0.103223
$556$	−5.73361	−0.243159
$557$	7.97566	0.337940	0.168970	−	0.985621i	$-0.445956\pi$
$557$	7.97566	0.337940	0.168970	+	0.985621i	$0.445956\pi$
$558$	−4.03701	−0.170900
$559$	−26.9942	−1.14173
$560$	−0.221526	−0.00936120
$561$	−35.9559	−1.51806
$562$	−25.5119	−1.07615
$563$	15.4330	0.650422	0.325211	−	0.945642i	$-0.394565\pi$
$563$	15.4330	0.650422	0.325211	+	0.945642i	$0.394565\pi$
$564$	−20.3734	−0.857875
$565$	−0.338337	−0.0142340
$566$	−17.1330	−0.720155
$567$	10.6104	0.445596
$568$	16.8115	0.705395
$569$	33.1113	1.38810	0.694048	−	0.719928i	$-0.255825\pi$
$569$	33.1113	1.38810	0.694048	+	0.719928i	$0.255825\pi$
$570$	−0.808756	−0.0338751
$571$	−24.6819	−1.03291	−0.516453	−	0.856315i	$-0.672748\pi$
$571$	−24.6819	−1.03291	−0.516453	+	0.856315i	$0.672748\pi$
$572$	−9.06259	−0.378926
$573$	25.4211	1.06198
$574$	25.5232	1.06532
$575$	−1.62543	−0.0677853
$576$	5.38632	0.224430
$577$	19.1560	0.797473	0.398737	−	0.917066i	$-0.369449\pi$
$577$	19.1560	0.797473	0.398737	+	0.917066i	$0.369449\pi$
$578$	−37.7227	−1.56906
$579$	−76.2415	−3.16849
$580$	−0.749518	−0.0311220
$581$	8.34807	0.346336
$582$	−30.6610	−1.27094
$583$	2.62622	0.108767
$584$	−2.57597	−0.106594
$585$	2.33986	0.0967413
$586$	23.1053	0.954471
$587$	−18.6059	−0.767949	−0.383974	−	0.923344i	$-0.625445\pi$
$587$	−18.6059	−0.767949	−0.383974	+	0.923344i	$0.625445\pi$
$588$	−1.68420	−0.0694552
$589$	2.60168	0.107200
$590$	−0.385794	−0.0158829
$591$	−26.8860	−1.10594
$592$	10.4374	0.428974
$593$	−18.9779	−0.779330	−0.389665	−	0.920957i	$-0.627409\pi$
$593$	−18.9779	−0.779330	−0.389665	+	0.920957i	$0.627409\pi$
$594$	11.5988	0.475906
$595$	−1.63874	−0.0671816
$596$	−21.4852	−0.880067
$597$	−27.5097	−1.12590
$598$	1.75758	0.0718726
$599$	−18.3664	−0.750429	−0.375215	−	0.926938i	$-0.622431\pi$
$599$	−18.3664	−0.750429	−0.375215	+	0.926938i	$0.622431\pi$
$600$	−14.4608	−0.590361
$601$	−4.87235	−0.198747	−0.0993736	−	0.995050i	$-0.531684\pi$
$601$	−4.87235	−0.198747	−0.0993736	+	0.995050i	$0.531684\pi$
$602$	−13.7657	−0.561047
$603$	56.6908	2.30863
$604$	−9.43073	−0.383731
$605$	0.658345	0.0267655
$606$	−28.4673	−1.15641
$607$	27.1162	1.10061	0.550305	−	0.834963i	$-0.314511\pi$
$607$	27.1162	1.10061	0.550305	+	0.834963i	$0.314511\pi$
$608$	−3.47125	−0.140778
$609$	−74.2851	−3.01019
$610$	1.08277	0.0438399
$611$	−37.9866	−1.53677
$612$	39.8452	1.61065
$613$	37.0949	1.49825	0.749125	−	0.662428i	$-0.230474\pi$
$613$	37.0949	1.49825	0.749125	+	0.662428i	$0.230474\pi$
$614$	−4.04232	−0.163135
$615$	−2.15966	−0.0870861
$616$	−4.62147	−0.186204
$617$	−49.0182	−1.97340	−0.986699	−	0.162557i	$-0.948026\pi$
$617$	−49.0182	−1.97340	−0.986699	+	0.162557i	$0.948026\pi$
$618$	21.3764	0.859886
$619$	8.42188	0.338504	0.169252	−	0.985573i	$-0.445865\pi$
$619$	8.42188	0.338504	0.169252	+	0.985573i	$0.445865\pi$
$620$	−0.0602995	−0.00242169
$621$	−2.24945	−0.0902673
$622$	15.5798	0.624692
$623$	35.4003	1.41828
$624$	15.6364	0.625958
$625$	24.9030	0.996118
$626$	−34.0667	−1.36158
$627$	−16.8722	−0.673811
$628$	3.84632	0.153485
$629$	77.2103	3.07858
$630$	1.19321	0.0475387
$631$	30.9932	1.23382	0.616909	−	0.787034i	$-0.288385\pi$
$631$	30.9932	1.23382	0.616909	+	0.787034i	$0.288385\pi$
$632$	15.0477	0.598564
$633$	51.9516	2.06489
$634$	−8.65790	−0.343849
$635$	0.114704	0.00455189
$636$	−4.53124	−0.179675
$637$	−3.14022	−0.124420
$638$	−15.6364	−0.619051
$639$	−90.5521	−3.58218
$640$	0.0804536	0.00318021
$641$	33.3057	1.31550	0.657748	−	0.753238i	$-0.271509\pi$
$641$	33.3057	1.31550	0.657748	+	0.753238i	$0.271509\pi$
$642$	−8.50188	−0.335542
$643$	11.8105	0.465761	0.232880	−	0.972505i	$-0.425185\pi$
$643$	11.8105	0.465761	0.232880	+	0.972505i	$0.425185\pi$
$644$	0.896276	0.0353182
$645$	1.16479	0.0458637
$646$	−25.6785	−1.01031
$647$	22.7812	0.895621	0.447810	−	0.894129i	$-0.352204\pi$
$647$	22.7812	0.895621	0.447810	+	0.894129i	$0.352204\pi$
$648$	−3.85348	−0.151379
$649$	−8.04841	−0.315928
$650$	−26.9625	−1.05755
$651$	−5.97632	−0.234230
$652$	10.1275	0.396624
$653$	−2.34812	−0.0918889	−0.0459444	−	0.998944i	$-0.514630\pi$
$653$	−2.34812	−0.0918889	−0.0459444	+	0.998944i	$0.514630\pi$
$654$	−24.2421	−0.947942
$655$	−0.356242	−0.0139195
$656$	−9.26947	−0.361912
$657$	13.8750	0.541315
$658$	−19.3713	−0.755170
$659$	−11.8686	−0.462336	−0.231168	−	0.972914i	$-0.574255\pi$
$659$	−11.8686	−0.462336	−0.231168	+	0.972914i	$0.574255\pi$
$660$	0.391049	0.0152216
$661$	18.2643	0.710398	0.355199	−	0.934791i	$-0.384413\pi$
$661$	18.2643	0.710398	0.355199	+	0.934791i	$0.384413\pi$
$662$	−34.8527	−1.35459
$663$	115.670	4.49226
$664$	−3.03184	−0.117658
$665$	−0.768974	−0.0298195
$666$	−56.2191	−2.17844
$667$	3.03248	0.117418
$668$	−1.82406	−0.0705750
$669$	44.4486	1.71848
$670$	0.846770	0.0327136
$671$	22.5886	0.872023
$672$	7.97380	0.307596
$673$	12.5127	0.482328	0.241164	−	0.970484i	$-0.422471\pi$
$673$	12.5127	0.482328	0.241164	+	0.970484i	$0.422471\pi$
$674$	−20.8768	−0.804144
$675$	34.5081	1.32822
$676$	16.1544	0.621323
$677$	6.16899	0.237094	0.118547	−	0.992948i	$-0.462176\pi$
$677$	6.16899	0.237094	0.118547	+	0.992948i	$0.462176\pi$
$678$	12.1784	0.467709
$679$	−29.1528	−1.11878
$680$	0.595154	0.0228231
$681$	30.8430	1.18191
$682$	−1.25796	−0.0481699
$683$	21.3021	0.815103	0.407551	−	0.913182i	$-0.366383\pi$
$683$	21.3021	0.815103	0.407551	+	0.913182i	$0.366383\pi$
$684$	18.6973	0.714908
$685$	0.590361	0.0225565
$686$	17.6729	0.674755
$687$	−60.0675	−2.29172
$688$	4.99940	0.190600
$689$	−8.44857	−0.321865
$690$	−0.0758391	−0.00288715
$691$	−32.0000	−1.21734	−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000	−1.21734	−0.608669	+	0.793424i	$0.708296\pi$
$692$	23.5949	0.896944
$693$	24.8927	0.945596
$694$	32.7247	1.24221
$695$	0.461289	0.0174977
$696$	26.9788	1.02263
$697$	−68.5707	−2.59730
$698$	−30.6997	−1.16200
$699$	34.2611	1.29587
$700$	−13.7495	−0.519683
$701$	2.33569	0.0882177	0.0441089	−	0.999027i	$-0.485955\pi$
$701$	2.33569	0.0882177	0.0441089	+	0.999027i	$0.485955\pi$
$702$	−37.3135	−1.40831
$703$	36.2308	1.36647
$704$	1.67842	0.0632578
$705$	1.63911	0.0617326
$706$	1.11994	0.0421497
$707$	−27.0670	−1.01796
$708$	13.8866	0.521890
$709$	39.5337	1.48472	0.742360	−	0.670001i	$-0.233706\pi$
$709$	39.5337	1.48472	0.742360	+	0.670001i	$0.233706\pi$
$710$	−1.35255	−0.0507601
$711$	−81.0516	−3.03967
$712$	−12.8566	−0.481823
$713$	0.243967	0.00913662
$714$	58.9860	2.20750
$715$	0.729118	0.0272675
$716$	−15.0324	−0.561789
$717$	12.7625	0.476625
$718$	−10.9729	−0.409505
$719$	15.1176	0.563791	0.281896	−	0.959445i	$-0.409037\pi$
$719$	15.1176	0.563791	0.281896	+	0.959445i	$0.409037\pi$
$720$	−0.433349	−0.0161500
$721$	20.3249	0.756940
$722$	6.95041	0.258667
$723$	8.08555	0.300705
$724$	14.9010	0.553793
$725$	−46.5204	−1.72773
$726$	−23.6970	−0.879479
$727$	26.4390	0.980567	0.490283	−	0.871563i	$-0.336893\pi$
$727$	26.4390	0.980567	0.490283	+	0.871563i	$0.336893\pi$
$728$	14.8673	0.551018
$729$	−39.2812	−1.45486
$730$	0.207246	0.00767051
$731$	36.9829	1.36786
$732$	−38.9740	−1.44052
$733$	−38.5189	−1.42273	−0.711364	−	0.702824i	$-0.751922\pi$
$733$	−38.5189	−1.42273	−0.711364	+	0.702824i	$0.751922\pi$
$734$	−7.41123	−0.273554
$735$	0.135500	0.00499799
$736$	−0.325508	−0.0119984
$737$	17.6653	0.650709
$738$	49.9283	1.83789
$739$	37.0039	1.36121	0.680606	−	0.732650i	$-0.261717\pi$
$739$	37.0039	1.36121	0.680606	+	0.732650i	$0.261717\pi$
$740$	−0.839725	−0.0308689
$741$	54.2780	1.99395
$742$	−4.30835	−0.158165
$743$	36.1965	1.32792	0.663960	−	0.747768i	$-0.268874\pi$
$743$	36.1965	1.32792	0.663960	+	0.747768i	$0.268874\pi$
$744$	2.17047	0.0795733
$745$	1.72856	0.0633296
$746$	5.92175	0.216811
$747$	16.3305	0.597500
$748$	12.4161	0.453976
$749$	−8.08368	−0.295371
$750$	2.32836	0.0850197
$751$	−41.1281	−1.50078	−0.750392	−	0.660993i	$-0.770135\pi$
$751$	−41.1281	−1.50078	−0.750392	+	0.660993i	$0.770135\pi$
$752$	7.03523	0.256548
$753$	−63.9289	−2.32970
$754$	50.3024	1.83190
$755$	0.758736	0.0276132
$756$	−19.0280	−0.692043
$757$	−30.8573	−1.12153	−0.560763	−	0.827976i	$-0.689492\pi$
$757$	−30.8573	−1.12153	−0.560763	+	0.827976i	$0.689492\pi$
$758$	3.70256	0.134483
$759$	−1.58215	−0.0574285
$760$	0.279275	0.0101304
$761$	−10.2352	−0.371026	−0.185513	−	0.982642i	$-0.559395\pi$
$761$	−10.2352	−0.371026	−0.185513	+	0.982642i	$0.559395\pi$
$762$	−4.12875	−0.149569
$763$	−23.0497	−0.834454
$764$	−8.77826	−0.317586
$765$	−3.20569	−0.115902
$766$	24.4675	0.884045
$767$	25.8918	0.934898
$768$	−2.89591	−0.104497
$769$	37.0723	1.33686	0.668431	−	0.743774i	$-0.266966\pi$
$769$	37.0723	1.33686	0.668431	+	0.743774i	$0.266966\pi$
$770$	0.371814	0.0133992
$771$	−7.17738	−0.258487
$772$	26.3273	0.947539
$773$	−13.9451	−0.501569	−0.250784	−	0.968043i	$-0.580689\pi$
$773$	−13.9451	−0.501569	−0.250784	+	0.968043i	$0.580689\pi$
$774$	−26.9284	−0.967920
$775$	−3.74262	−0.134439
$776$	10.5877	0.380075
$777$	−83.2256	−2.98570
$778$	−6.21168	−0.222699
$779$	−32.1767	−1.15285
$780$	−1.25801	−0.0450439
$781$	−28.2167	−1.00967
$782$	−2.40794	−0.0861078
$783$	−64.3800	−2.30075
$784$	0.581578	0.0207706
$785$	−0.309450	−0.0110448
$786$	12.8229	0.457376
$787$	−51.9276	−1.85102	−0.925509	−	0.378726i	$-0.876362\pi$
$787$	−51.9276	−1.85102	−0.925509	+	0.378726i	$0.876362\pi$
$788$	9.28411	0.330733
$789$	−5.95817	−0.212117
$790$	−1.21064	−0.0430726
$791$	11.5794	0.411714
$792$	−9.04050	−0.321240
$793$	−72.6676	−2.58050
$794$	−26.5473	−0.942127
$795$	0.364554	0.0129294
$796$	9.49950	0.336701
$797$	−43.0450	−1.52473	−0.762367	−	0.647145i	$-0.775963\pi$
$797$	−43.0450	−1.52473	−0.762367	+	0.647145i	$0.775963\pi$
$798$	27.6791	0.979829
$799$	52.0429	1.84115
$800$	4.99353	0.176548
$801$	69.2499	2.44683
$802$	14.7113	0.519472
$803$	4.32355	0.152575
$804$	−30.4794	−1.07492
$805$	−0.0721087	−0.00254150
$806$	4.04688	0.142545
$807$	−56.0666	−1.97364
$808$	9.83016	0.345824
$809$	11.4781	0.403547	0.201774	−	0.979432i	$-0.435329\pi$
$809$	11.4781	0.403547	0.201774	+	0.979432i	$0.435329\pi$
$810$	0.310026	0.0108932
$811$	40.2947	1.41494	0.707469	−	0.706745i	$-0.249837\pi$
$811$	40.2947	1.41494	0.707469	+	0.706745i	$0.249837\pi$
$812$	25.6517	0.900198
$813$	−84.4339	−2.96122
$814$	−17.5183	−0.614016
$815$	−0.814795	−0.0285410
$816$	−21.4225	−0.749936
$817$	17.3542	0.607146
$818$	−29.5820	−1.03431
$819$	−80.0800	−2.79822
$820$	0.745762	0.0260432
$821$	−32.3851	−1.13025	−0.565124	−	0.825006i	$-0.691172\pi$
$821$	−32.3851	−1.13025	−0.565124	+	0.825006i	$0.691172\pi$
$822$	−21.2499	−0.741177
$823$	26.4088	0.920554	0.460277	−	0.887775i	$-0.347750\pi$
$823$	26.4088	0.920554	0.460277	+	0.887775i	$0.347750\pi$
$824$	−7.38158	−0.257149
$825$	24.2713	0.845019
$826$	13.2035	0.459409
$827$	15.6164	0.543037	0.271518	−	0.962433i	$-0.412474\pi$
$827$	15.6164	0.543037	0.271518	+	0.962433i	$0.412474\pi$
$828$	1.75329	0.0609311
$829$	29.2870	1.01718	0.508590	−	0.861009i	$-0.330167\pi$
$829$	29.2870	1.01718	0.508590	+	0.861009i	$0.330167\pi$
$830$	0.243922	0.00846667
$831$	10.8179	0.375269
$832$	−5.39948	−0.187193
$833$	4.30221	0.149063
$834$	−16.6040	−0.574951
$835$	0.146752	0.00507857
$836$	5.82621	0.201504
$837$	−5.17943	−0.179027
$838$	20.3766	0.703897
$839$	−32.8755	−1.13499	−0.567494	−	0.823378i	$-0.692087\pi$
$839$	−32.8755	−1.13499	−0.567494	+	0.823378i	$0.692087\pi$
$840$	−0.641521	−0.0221346
$841$	57.7907	1.99278
$842$	2.62633	0.0905094
$843$	−73.8802	−2.54457
$844$	−17.9396	−0.617507
$845$	−1.29968	−0.0447103
$846$	−37.8940	−1.30282
$847$	−22.5314	−0.774187
$848$	1.56470	0.0537320
$849$	−49.6158	−1.70281
$850$	36.9395	1.26701
$851$	3.39746	0.116463
$852$	48.6846	1.66791
$853$	−11.4892	−0.393384	−0.196692	−	0.980465i	$-0.563020\pi$
$853$	−11.4892	−0.393384	−0.196692	+	0.980465i	$0.563020\pi$
$854$	−37.0569	−1.26806
$855$	−1.50426	−0.0514447
$856$	2.93582	0.100344
$857$	41.2035	1.40748	0.703742	−	0.710455i	$-0.251511\pi$
$857$	41.2035	1.40748	0.703742	+	0.710455i	$0.251511\pi$
$858$	−26.2445	−0.895972
$859$	30.4505	1.03896	0.519480	−	0.854483i	$-0.326126\pi$
$859$	30.4505	1.03896	0.519480	+	0.854483i	$0.326126\pi$
$860$	−0.402220	−0.0137156
$861$	73.9129	2.51895
$862$	12.6168	0.429730
$863$	57.4513	1.95566	0.977832	−	0.209391i	$-0.0671481\pi$
$863$	57.4513	1.95566	0.977832	+	0.209391i	$0.0671481\pi$
$864$	6.91058	0.235103
$865$	−1.89830	−0.0645440
$866$	8.90812	0.302710
$867$	−109.242	−3.71004
$868$	2.06371	0.0700468
$869$	−25.2563	−0.856761
$870$	−2.17054	−0.0735882
$871$	−56.8293	−1.92559
$872$	8.37114	0.283483
$873$	−57.0285	−1.93012
$874$	−1.12992	−0.0382202
$875$	2.21383	0.0748411
$876$	−7.45978	−0.252043
$877$	−6.64531	−0.224396	−0.112198	−	0.993686i	$-0.535789\pi$
$877$	−6.64531	−0.224396	−0.112198	+	0.993686i	$0.535789\pi$
$878$	21.9601	0.741117
$879$	66.9110	2.25685
$880$	−0.135035	−0.00455202
$881$	−35.4650	−1.19485	−0.597423	−	0.801926i	$-0.703809\pi$
$881$	−35.4650	−1.19485	−0.597423	+	0.801926i	$0.703809\pi$
$882$	−3.13256	−0.105479
$883$	1.30451	0.0439001	0.0219501	−	0.999759i	$-0.493013\pi$
$883$	1.30451	0.0439001	0.0219501	+	0.999759i	$0.493013\pi$
$884$	−39.9425	−1.34341
$885$	−1.11723	−0.0375552
$886$	10.6914	0.359183
$887$	−4.93724	−0.165776	−0.0828881	−	0.996559i	$-0.526414\pi$
$887$	−4.93724	−0.165776	−0.0828881	+	0.996559i	$0.526414\pi$
$888$	30.2258	1.01431
$889$	−3.92566	−0.131662
$890$	1.03436	0.0346719
$891$	6.46775	0.216678
$892$	−15.3487	−0.513913
$893$	24.4210	0.817219
$894$	−62.2193	−2.08092
$895$	1.20941	0.0404263
$896$	−2.75347	−0.0919869
$897$	5.08979	0.169943
$898$	−0.978741	−0.0326610
$899$	6.98240	0.232876
$900$	−26.8967	−0.896558
$901$	11.5748	0.385614
$902$	15.5581	0.518027
$903$	−39.8642	−1.32660
$904$	−4.20537	−0.139869
$905$	−1.19884	−0.0398509
$906$	−27.3106	−0.907333
$907$	−12.8622	−0.427084	−0.213542	−	0.976934i	$-0.568500\pi$
$907$	−12.8622	−0.427084	−0.213542	+	0.976934i	$0.568500\pi$
$908$	−10.6505	−0.353450
$909$	−52.9484	−1.75619
$910$	−1.19613	−0.0396512
$911$	−31.8417	−1.05496	−0.527481	−	0.849567i	$-0.676863\pi$
$911$	−31.8417	−1.05496	−0.527481	+	0.849567i	$0.676863\pi$
$912$	−10.0524	−0.332870
$913$	5.08870	0.168411
$914$	6.99329	0.231317
$915$	3.13560	0.103660
$916$	20.7422	0.685340
$917$	12.1921	0.402619
$918$	51.1208	1.68724
$919$	−35.5188	−1.17166	−0.585828	−	0.810435i	$-0.699231\pi$
$919$	−35.5188	−1.17166	−0.585828	+	0.810435i	$0.699231\pi$
$920$	0.0261883	0.000863403 0
$921$	−11.7062	−0.385733
$922$	−14.0202	−0.461732
$923$	90.7734	2.98784
$924$	−13.3834	−0.440281
$925$	−52.1194	−1.71367
$926$	37.4441	1.23049
$927$	39.7595	1.30587
$928$	−9.31615	−0.305818
$929$	−37.9572	−1.24534	−0.622668	−	0.782486i	$-0.713951\pi$
$929$	−37.9572	−1.24534	−0.622668	+	0.782486i	$0.713951\pi$
$930$	−0.174622	−0.00572609
$931$	2.01880	0.0661636
$932$	−11.8308	−0.387532
$933$	45.1177	1.47709
$934$	−11.6957	−0.382696
$935$	−0.998917	−0.0326681
$936$	29.0833	0.950618
$937$	29.9080	0.977053	0.488527	−	0.872549i	$-0.337535\pi$
$937$	29.9080	0.977053	0.488527	+	0.872549i	$0.337535\pi$
$938$	−28.9801	−0.946234
$939$	−98.6542	−3.21946
$940$	−0.566009	−0.0184612
$941$	−5.48759	−0.178890	−0.0894452	−	0.995992i	$-0.528509\pi$
$941$	−5.48759	−0.178890	−0.0894452	+	0.995992i	$0.528509\pi$
$942$	11.1386	0.362916
$943$	−3.01729	−0.0982565
$944$	−4.79524	−0.156072
$945$	1.53087	0.0497993
$946$	−8.39108	−0.272818
$947$	−18.2017	−0.591475	−0.295738	−	0.955269i	$-0.595565\pi$
$947$	−18.2017	−0.591475	−0.295738	+	0.955269i	$0.595565\pi$
$948$	43.5768	1.41531
$949$	−13.9089	−0.451502
$950$	17.3338	0.562383
$951$	−25.0725	−0.813033
$952$	−20.3687	−0.660154
$953$	18.2412	0.590892	0.295446	−	0.955359i	$-0.404532\pi$
$953$	18.2412	0.590892	0.295446	+	0.955359i	$0.404532\pi$
$954$	−8.42798	−0.272866
$955$	0.706243	0.0228535
$956$	−4.40707	−0.142535
$957$	−45.2817	−1.46375
$958$	11.7966	0.381132
$959$	−20.2047	−0.652443
$960$	0.232987	0.00751961
$961$	−30.4383	−0.981879
$962$	56.3564	1.81700
$963$	−15.8133	−0.509575
$964$	−2.79206	−0.0899261
$965$	−2.11812	−0.0681848
$966$	2.59554	0.0835101
$967$	40.2666	1.29488	0.647442	−	0.762114i	$-0.275839\pi$
$967$	40.2666	1.29488	0.647442	+	0.762114i	$0.275839\pi$
$968$	8.18291	0.263009
$969$	−74.3628	−2.38888
$970$	−0.851816	−0.0273502
$971$	−26.8118	−0.860431	−0.430216	−	0.902726i	$-0.641562\pi$
$971$	−26.8118	−0.860431	−0.430216	+	0.902726i	$0.641562\pi$
$972$	9.57239	0.307035
$973$	−15.7873	−0.506117
$974$	−12.5206	−0.401186
$975$	−78.0810	−2.50059
$976$	13.4583	0.430788
$977$	29.0495	0.929374	0.464687	−	0.885475i	$-0.346167\pi$
$977$	29.0495	0.929374	0.464687	+	0.885475i	$0.346167\pi$
$978$	29.3284	0.937819
$979$	21.5788	0.689662
$980$	−0.0467900	−0.00149465
$981$	−45.0896	−1.43960
$982$	−36.0348	−1.14992
$983$	−7.08575	−0.226000	−0.113000	−	0.993595i	$-0.536046\pi$
$983$	−7.08575	−0.226000	−0.113000	+	0.993595i	$0.536046\pi$
$984$	−26.8436	−0.855743
$985$	−0.746940	−0.0237995
$986$	−68.9160	−2.19473
$987$	−56.0975	−1.78560
$988$	−18.7430	−0.596293
$989$	1.62735	0.0517466
$990$	0.727341	0.0231164
$991$	−21.0386	−0.668312	−0.334156	−	0.942518i	$-0.608451\pi$
$991$	−21.0386	−0.668312	−0.334156	+	0.942518i	$0.608451\pi$
$992$	−0.749494	−0.0237965
$993$	−100.931	−3.20293
$994$	46.2899	1.46823
$995$	−0.764269	−0.0242290
$996$	−8.77995	−0.278203
$997$	35.2391	1.11603	0.558017	−	0.829829i	$-0.311562\pi$
$997$	35.2391	1.11603	0.558017	+	0.829829i	$0.311562\pi$
$998$	11.2115	0.354894
$999$	−72.1283	−2.28204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.4	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.4	✓	46	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.89591 q^{3} +1.00000 q^{4} -0.0804536 q^{5} +2.89591 q^{6} +2.75347 q^{7} -1.00000 q^{8} +5.38632 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.89591 q^{3} +1.00000 q^{4} -0.0804536 q^{5} +2.89591 q^{6} +2.75347 q^{7} -1.00000 q^{8} +5.38632 q^{9} +0.0804536 q^{10} +1.67842 q^{11} -2.89591 q^{12} -5.39948 q^{13} -2.75347 q^{14} +0.232987 q^{15} +1.00000 q^{16} +7.39748 q^{17} -5.38632 q^{18} +3.47125 q^{19} -0.0804536 q^{20} -7.97380 q^{21} -1.67842 q^{22} +0.325508 q^{23} +2.89591 q^{24} -4.99353 q^{25} +5.39948 q^{26} -6.91058 q^{27} +2.75347 q^{28} +9.31615 q^{29} -0.232987 q^{30} +0.749494 q^{31} -1.00000 q^{32} -4.86056 q^{33} -7.39748 q^{34} -0.221526 q^{35} +5.38632 q^{36} +10.4374 q^{37} -3.47125 q^{38} +15.6364 q^{39} +0.0804536 q^{40} -9.26947 q^{41} +7.97380 q^{42} +4.99940 q^{43} +1.67842 q^{44} -0.433349 q^{45} -0.325508 q^{46} +7.03523 q^{47} -2.89591 q^{48} +0.581578 q^{49} +4.99353 q^{50} -21.4225 q^{51} -5.39948 q^{52} +1.56470 q^{53} +6.91058 q^{54} -0.135035 q^{55} -2.75347 q^{56} -10.0524 q^{57} -9.31615 q^{58} -4.79524 q^{59} +0.232987 q^{60} +13.4583 q^{61} -0.749494 q^{62} +14.8310 q^{63} +1.00000 q^{64} +0.434408 q^{65} +4.86056 q^{66} +10.5250 q^{67} +7.39748 q^{68} -0.942644 q^{69} +0.221526 q^{70} -16.8115 q^{71} -5.38632 q^{72} +2.57597 q^{73} -10.4374 q^{74} +14.4608 q^{75} +3.47125 q^{76} +4.62147 q^{77} -15.6364 q^{78} -15.0477 q^{79} -0.0804536 q^{80} +3.85348 q^{81} +9.26947 q^{82} +3.03184 q^{83} -7.97380 q^{84} -0.595154 q^{85} -4.99940 q^{86} -26.9788 q^{87} -1.67842 q^{88} +12.8566 q^{89} +0.433349 q^{90} -14.8673 q^{91} +0.325508 q^{92} -2.17047 q^{93} -7.03523 q^{94} -0.279275 q^{95} +2.89591 q^{96} -10.5877 q^{97} -0.581578 q^{98} +9.04050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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