LMFDB - Embedded newform 5610.2.a.ci.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.18569692.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 23x^{3} - 32x^{2} + 26x - 4 $ x^5 - 23x^3 - 32x^2 + 26*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$5.30430$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +4.28107 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +4.28107 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.90919 q^{13} +4.28107 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.90919 q^{19} +1.00000 q^{20} -4.28107 q^{21} +1.00000 q^{22} +7.75504 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.90919 q^{26} -1.00000 q^{27} +4.28107 q^{28} -2.19026 q^{29} -1.00000 q^{30} +4.85355 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +4.28107 q^{35} +1.00000 q^{36} -8.69940 q^{37} -1.90919 q^{38} +1.90919 q^{39} +1.00000 q^{40} -1.47397 q^{41} -4.28107 q^{42} +11.4362 q^{43} +1.00000 q^{44} +1.00000 q^{45} +7.75504 q^{46} -1.47397 q^{47} -1.00000 q^{48} +11.3275 q^{49} +1.00000 q^{50} +1.00000 q^{51} -1.90919 q^{52} +1.77192 q^{53} -1.00000 q^{54} +1.00000 q^{55} +4.28107 q^{56} +1.90919 q^{57} -2.19026 q^{58} +14.4270 q^{59} -1.00000 q^{60} -3.22543 q^{61} +4.85355 q^{62} +4.28107 q^{63} +1.00000 q^{64} -1.90919 q^{65} -1.00000 q^{66} +7.95565 q^{67} -1.00000 q^{68} -7.75504 q^{69} +4.28107 q^{70} +14.6086 q^{71} +1.00000 q^{72} +0.228078 q^{73} -8.69940 q^{74} -1.00000 q^{75} -1.90919 q^{76} +4.28107 q^{77} +1.90919 q^{78} -7.13462 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.47397 q^{82} -15.9918 q^{83} -4.28107 q^{84} -1.00000 q^{85} +11.4362 q^{86} +2.19026 q^{87} +1.00000 q^{88} -10.3805 q^{89} +1.00000 q^{90} -8.17337 q^{91} +7.75504 q^{92} -4.85355 q^{93} -1.47397 q^{94} -1.90919 q^{95} -1.00000 q^{96} -1.03517 q^{97} +11.3275 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - q^{13} + 2 q^{14} - 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} - q^{19} + 5 q^{20} - 2 q^{21} + 5 q^{22} - 5 q^{24} + 5 q^{25} - q^{26} - 5 q^{27} + 2 q^{28} + 17 q^{29} - 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + q^{37} - q^{38} + q^{39} + 5 q^{40} + 12 q^{41} - 2 q^{42} + 7 q^{43} + 5 q^{44} + 5 q^{45} + 12 q^{47} - 5 q^{48} + 23 q^{49} + 5 q^{50} + 5 q^{51} - q^{52} + 6 q^{53} - 5 q^{54} + 5 q^{55} + 2 q^{56} + q^{57} + 17 q^{58} + 2 q^{59} - 5 q^{60} + 9 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} - q^{65} - 5 q^{66} + 17 q^{67} - 5 q^{68} + 2 q^{70} + 20 q^{71} + 5 q^{72} + 4 q^{73} + q^{74} - 5 q^{75} - q^{76} + 2 q^{77} + q^{78} - 2 q^{79} + 5 q^{80} + 5 q^{81} + 12 q^{82} + q^{83} - 2 q^{84} - 5 q^{85} + 7 q^{86} - 17 q^{87} + 5 q^{88} + 4 q^{89} + 5 q^{90} + 23 q^{91} - 10 q^{93} + 12 q^{94} - q^{95} - 5 q^{96} - 8 q^{97} + 23 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9 + 5 * q^10 + 5 * q^11 - 5 * q^12 - q^13 + 2 * q^14 - 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 - q^19 + 5 * q^20 - 2 * q^21 + 5 * q^22 - 5 * q^24 + 5 * q^25 - q^26 - 5 * q^27 + 2 * q^28 + 17 * q^29 - 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + q^37 - q^38 + q^39 + 5 * q^40 + 12 * q^41 - 2 * q^42 + 7 * q^43 + 5 * q^44 + 5 * q^45 + 12 * q^47 - 5 * q^48 + 23 * q^49 + 5 * q^50 + 5 * q^51 - q^52 + 6 * q^53 - 5 * q^54 + 5 * q^55 + 2 * q^56 + q^57 + 17 * q^58 + 2 * q^59 - 5 * q^60 + 9 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 - q^65 - 5 * q^66 + 17 * q^67 - 5 * q^68 + 2 * q^70 + 20 * q^71 + 5 * q^72 + 4 * q^73 + q^74 - 5 * q^75 - q^76 + 2 * q^77 + q^78 - 2 * q^79 + 5 * q^80 + 5 * q^81 + 12 * q^82 + q^83 - 2 * q^84 - 5 * q^85 + 7 * q^86 - 17 * q^87 + 5 * q^88 + 4 * q^89 + 5 * q^90 + 23 * q^91 - 10 * q^93 + 12 * q^94 - q^95 - 5 * q^96 - 8 * q^97 + 23 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	4.28107	1.61809	0.809045	−	0.587746i	$-0.199985\pi$
$7$	4.28107	1.61809	0.809045	+	0.587746i	$0.199985\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−1.90919	−0.529514	−0.264757	−	0.964315i	$-0.585292\pi$
$13$	−1.90919	−0.529514	−0.264757	+	0.964315i	$0.585292\pi$
$14$	4.28107	1.14416
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−1.90919	−0.437998	−0.218999	−	0.975725i	$-0.570279\pi$
$19$	−1.90919	−0.437998	−0.218999	+	0.975725i	$0.570279\pi$
$20$	1.00000	0.223607
$21$	−4.28107	−0.934205
$22$	1.00000	0.213201
$23$	7.75504	1.61704	0.808519	−	0.588471i	$-0.200270\pi$
$23$	7.75504	1.61704	0.808519	+	0.588471i	$0.200270\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.90919	−0.374423
$27$	−1.00000	−0.192450
$28$	4.28107	0.809045
$29$	−2.19026	−0.406720	−0.203360	−	0.979104i	$-0.565186\pi$
$29$	−2.19026	−0.406720	−0.203360	+	0.979104i	$0.565186\pi$
$30$	−1.00000	−0.182574
$31$	4.85355	0.871724	0.435862	−	0.900014i	$-0.356444\pi$
$31$	4.85355	0.871724	0.435862	+	0.900014i	$0.356444\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	4.28107	0.723632
$36$	1.00000	0.166667
$37$	−8.69940	−1.43017	−0.715086	−	0.699036i	$-0.753613\pi$
$37$	−8.69940	−1.43017	−0.715086	+	0.699036i	$0.753613\pi$
$38$	−1.90919	−0.309712
$39$	1.90919	0.305715
$40$	1.00000	0.158114
$41$	−1.47397	−0.230196	−0.115098	−	0.993354i	$-0.536718\pi$
$41$	−1.47397	−0.230196	−0.115098	+	0.993354i	$0.536718\pi$
$42$	−4.28107	−0.660583
$43$	11.4362	1.74400	0.871998	−	0.489509i	$-0.162824\pi$
$43$	11.4362	1.74400	0.871998	+	0.489509i	$0.162824\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	7.75504	1.14342
$47$	−1.47397	−0.215001	−0.107500	−	0.994205i	$-0.534285\pi$
$47$	−1.47397	−0.215001	−0.107500	+	0.994205i	$0.534285\pi$
$48$	−1.00000	−0.144338
$49$	11.3275	1.61822
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−1.90919	−0.264757
$53$	1.77192	0.243392	0.121696	−	0.992567i	$-0.461167\pi$
$53$	1.77192	0.243392	0.121696	+	0.992567i	$0.461167\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	4.28107	0.572081
$57$	1.90919	0.252879
$58$	−2.19026	−0.287595
$59$	14.4270	1.87823	0.939116	−	0.343600i	$-0.111647\pi$
$59$	14.4270	1.87823	0.939116	+	0.343600i	$0.111647\pi$
$60$	−1.00000	−0.129099
$61$	−3.22543	−0.412974	−0.206487	−	0.978449i	$-0.566203\pi$
$61$	−3.22543	−0.412974	−0.206487	+	0.978449i	$0.566203\pi$
$62$	4.85355	0.616402
$63$	4.28107	0.539364
$64$	1.00000	0.125000
$65$	−1.90919	−0.236806
$66$	−1.00000	−0.123091
$67$	7.95565	0.971937	0.485969	−	0.873976i	$-0.338467\pi$
$67$	7.95565	0.971937	0.485969	+	0.873976i	$0.338467\pi$
$68$	−1.00000	−0.121268
$69$	−7.75504	−0.933597
$70$	4.28107	0.511685
$71$	14.6086	1.73372	0.866860	−	0.498551i	$-0.166134\pi$
$71$	14.6086	1.73372	0.866860	+	0.498551i	$0.166134\pi$
$72$	1.00000	0.117851
$73$	0.228078	0.0266945	0.0133472	−	0.999911i	$-0.495751\pi$
$73$	0.228078	0.0266945	0.0133472	+	0.999911i	$0.495751\pi$
$74$	−8.69940	−1.01128
$75$	−1.00000	−0.115470
$76$	−1.90919	−0.218999
$77$	4.28107	0.487873
$78$	1.90919	0.216173
$79$	−7.13462	−0.802707	−0.401354	−	0.915923i	$-0.631460\pi$
$79$	−7.13462	−0.802707	−0.401354	+	0.915923i	$0.631460\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.47397	−0.162773
$83$	−15.9918	−1.75532	−0.877662	−	0.479281i	$-0.840897\pi$
$83$	−15.9918	−1.75532	−0.877662	+	0.479281i	$0.840897\pi$
$84$	−4.28107	−0.467103
$85$	−1.00000	−0.108465
$86$	11.4362	1.23319
$87$	2.19026	0.234820
$88$	1.00000	0.106600
$89$	−10.3805	−1.10033	−0.550166	−	0.835055i	$-0.685436\pi$
$89$	−10.3805	−1.10033	−0.550166	+	0.835055i	$0.685436\pi$
$90$	1.00000	0.105409
$91$	−8.17337	−0.856802
$92$	7.75504	0.808519
$93$	−4.85355	−0.503290
$94$	−1.47397	−0.152029
$95$	−1.90919	−0.195879
$96$	−1.00000	−0.102062
$97$	−1.03517	−0.105106	−0.0525529	−	0.998618i	$-0.516736\pi$
$97$	−1.03517	−0.105106	−0.0525529	+	0.998618i	$0.516736\pi$
$98$	11.3275	1.14425
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−13.8545	−1.37857	−0.689286	−	0.724489i	$-0.742076\pi$
$101$	−13.8545	−1.37857	−0.689286	+	0.724489i	$0.742076\pi$
$102$	1.00000	0.0990148
$103$	−10.0530	−0.990550	−0.495275	−	0.868736i	$-0.664933\pi$
$103$	−10.0530	−0.990550	−0.495275	+	0.868736i	$0.664933\pi$
$104$	−1.90919	−0.187212
$105$	−4.28107	−0.417789
$106$	1.77192	0.172104
$107$	−10.8092	−1.04497	−0.522483	−	0.852650i	$-0.674994\pi$
$107$	−10.8092	−1.04497	−0.522483	+	0.852650i	$0.674994\pi$
$108$	−1.00000	−0.0962250
$109$	2.48168	0.237702	0.118851	−	0.992912i	$-0.462079\pi$
$109$	2.48168	0.237702	0.118851	+	0.992912i	$0.462079\pi$
$110$	1.00000	0.0953463
$111$	8.69940	0.825711
$112$	4.28107	0.404523
$113$	13.4092	1.26143	0.630714	−	0.776016i	$-0.282762\pi$
$113$	13.4092	1.26143	0.630714	+	0.776016i	$0.282762\pi$
$114$	1.90919	0.178812
$115$	7.75504	0.723161
$116$	−2.19026	−0.203360
$117$	−1.90919	−0.176505
$118$	14.4270	1.32811
$119$	−4.28107	−0.392445
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−3.22543	−0.292017
$123$	1.47397	0.132904
$124$	4.85355	0.435862
$125$	1.00000	0.0894427
$126$	4.28107	0.381388
$127$	18.1290	1.60869	0.804345	−	0.594162i	$-0.202516\pi$
$127$	18.1290	1.60869	0.804345	+	0.594162i	$0.202516\pi$
$128$	1.00000	0.0883883
$129$	−11.4362	−1.00690
$130$	−1.90919	−0.167447
$131$	−11.7172	−1.02374	−0.511869	−	0.859064i	$-0.671047\pi$
$131$	−11.7172	−1.02374	−0.511869	+	0.859064i	$0.671047\pi$
$132$	−1.00000	−0.0870388
$133$	−8.17337	−0.708721
$134$	7.95565	0.687263
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	11.1826	0.955390	0.477695	−	0.878526i	$-0.341472\pi$
$137$	11.1826	0.955390	0.477695	+	0.878526i	$0.341472\pi$
$138$	−7.75504	−0.660153
$139$	−15.5530	−1.31918	−0.659592	−	0.751624i	$-0.729271\pi$
$139$	−15.5530	−1.31918	−0.659592	+	0.751624i	$0.729271\pi$
$140$	4.28107	0.361816
$141$	1.47397	0.124131
$142$	14.6086	1.22593
$143$	−1.90919	−0.159655
$144$	1.00000	0.0833333
$145$	−2.19026	−0.181891
$146$	0.228078	0.0188758
$147$	−11.3275	−0.934279
$148$	−8.69940	−0.715086
$149$	4.24854	0.348054	0.174027	−	0.984741i	$-0.444322\pi$
$149$	4.24854	0.348054	0.174027	+	0.984741i	$0.444322\pi$
$150$	−1.00000	−0.0816497
$151$	6.42486	0.522848	0.261424	−	0.965224i	$-0.415808\pi$
$151$	6.42486	0.522848	0.261424	+	0.965224i	$0.415808\pi$
$152$	−1.90919	−0.154856
$153$	−1.00000	−0.0808452
$154$	4.28107	0.344978
$155$	4.85355	0.389847
$156$	1.90919	0.152858
$157$	15.1811	1.21158	0.605791	−	0.795624i	$-0.292857\pi$
$157$	15.1811	1.21158	0.605791	+	0.795624i	$0.292857\pi$
$158$	−7.13462	−0.567600
$159$	−1.77192	−0.140523
$160$	1.00000	0.0790569
$161$	33.1998	2.61651
$162$	1.00000	0.0785674
$163$	−13.3897	−1.04876	−0.524381	−	0.851484i	$-0.675703\pi$
$163$	−13.3897	−1.04876	−0.524381	+	0.851484i	$0.675703\pi$
$164$	−1.47397	−0.115098
$165$	−1.00000	−0.0778499
$166$	−15.9918	−1.24120
$167$	24.3053	1.88080	0.940402	−	0.340065i	$-0.110449\pi$
$167$	24.3053	1.88080	0.940402	+	0.340065i	$0.110449\pi$
$168$	−4.28107	−0.330291
$169$	−9.35499	−0.719615
$170$	−1.00000	−0.0766965
$171$	−1.90919	−0.145999
$172$	11.4362	0.871998
$173$	15.6473	1.18965	0.594823	−	0.803857i	$-0.297222\pi$
$173$	15.6473	1.18965	0.594823	+	0.803857i	$0.297222\pi$
$174$	2.19026	0.166043
$175$	4.28107	0.323618
$176$	1.00000	0.0753778
$177$	−14.4270	−1.08440
$178$	−10.3805	−0.778052
$179$	8.23819	0.615751	0.307876	−	0.951427i	$-0.400382\pi$
$179$	8.23819	0.615751	0.307876	+	0.951427i	$0.400382\pi$
$180$	1.00000	0.0745356
$181$	18.0086	1.33857	0.669286	−	0.743005i	$-0.266600\pi$
$181$	18.0086	1.33857	0.669286	+	0.743005i	$0.266600\pi$
$182$	−8.17337	−0.605851
$183$	3.22543	0.238431
$184$	7.75504	0.571709
$185$	−8.69940	−0.639593
$186$	−4.85355	−0.355880
$187$	−1.00000	−0.0731272
$188$	−1.47397	−0.107500
$189$	−4.28107	−0.311402
$190$	−1.90919	−0.138507
$191$	−13.0269	−0.942595	−0.471298	−	0.881974i	$-0.656214\pi$
$191$	−13.0269	−0.942595	−0.471298	+	0.881974i	$0.656214\pi$
$192$	−1.00000	−0.0721688
$193$	−23.9370	−1.72303	−0.861513	−	0.507735i	$-0.830483\pi$
$193$	−23.9370	−1.72303	−0.861513	+	0.507735i	$0.830483\pi$
$194$	−1.03517	−0.0743210
$195$	1.90919	0.136720
$196$	11.3275	0.809109
$197$	7.95565	0.566817	0.283408	−	0.958999i	$-0.408535\pi$
$197$	7.95565	0.566817	0.283408	+	0.958999i	$0.408535\pi$
$198$	1.00000	0.0710669
$199$	−19.6420	−1.39239	−0.696194	−	0.717854i	$-0.745125\pi$
$199$	−19.6420	−1.39239	−0.696194	+	0.717854i	$0.745125\pi$
$200$	1.00000	0.0707107
$201$	−7.95565	−0.561148
$202$	−13.8545	−0.974798
$203$	−9.37663	−0.658111
$204$	1.00000	0.0700140
$205$	−1.47397	−0.102947
$206$	−10.0530	−0.700425
$207$	7.75504	0.539012
$208$	−1.90919	−0.132379
$209$	−1.90919	−0.132061
$210$	−4.28107	−0.295422
$211$	1.28371	0.0883746	0.0441873	−	0.999023i	$-0.485930\pi$
$211$	1.28371	0.0883746	0.0441873	+	0.999023i	$0.485930\pi$
$212$	1.77192	0.121696
$213$	−14.6086	−1.00096
$214$	−10.8092	−0.738902
$215$	11.4362	0.779939
$216$	−1.00000	−0.0680414
$217$	20.7784	1.41053
$218$	2.48168	0.168080
$219$	−0.228078	−0.0154121
$220$	1.00000	0.0674200
$221$	1.90919	0.128426
$222$	8.69940	0.583866
$223$	−7.37958	−0.494173	−0.247087	−	0.968993i	$-0.579473\pi$
$223$	−7.37958	−0.494173	−0.247087	+	0.968993i	$0.579473\pi$
$224$	4.28107	0.286041
$225$	1.00000	0.0666667
$226$	13.4092	0.891964
$227$	−1.66423	−0.110459	−0.0552294	−	0.998474i	$-0.517589\pi$
$227$	−1.66423	−0.110459	−0.0552294	+	0.998474i	$0.517589\pi$
$228$	1.90919	0.126439
$229$	−9.15509	−0.604985	−0.302493	−	0.953152i	$-0.597819\pi$
$229$	−9.15509	−0.604985	−0.302493	+	0.953152i	$0.597819\pi$
$230$	7.75504	0.511352
$231$	−4.28107	−0.281673
$232$	−2.19026	−0.143797
$233$	4.15415	0.272148	0.136074	−	0.990699i	$-0.456552\pi$
$233$	4.15415	0.272148	0.136074	+	0.990699i	$0.456552\pi$
$234$	−1.90919	−0.124808
$235$	−1.47397	−0.0961513
$236$	14.4270	0.939116
$237$	7.13462	0.463443
$238$	−4.28107	−0.277500
$239$	5.70711	0.369162	0.184581	−	0.982817i	$-0.440907\pi$
$239$	5.70711	0.369162	0.184581	+	0.982817i	$0.440907\pi$
$240$	−1.00000	−0.0645497
$241$	−1.19291	−0.0768418	−0.0384209	−	0.999262i	$-0.512233\pi$
$241$	−1.19291	−0.0768418	−0.0384209	+	0.999262i	$0.512233\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−3.22543	−0.206487
$245$	11.3275	0.723689
$246$	1.47397	0.0939770
$247$	3.64501	0.231926
$248$	4.85355	0.308201
$249$	15.9918	1.01344
$250$	1.00000	0.0632456
$251$	22.9087	1.44598	0.722991	−	0.690858i	$-0.242767\pi$
$251$	22.9087	1.44598	0.722991	+	0.690858i	$0.242767\pi$
$252$	4.28107	0.269682
$253$	7.75504	0.487555
$254$	18.1290	1.13752
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	21.0630	1.31388	0.656938	−	0.753945i	$-0.271851\pi$
$257$	21.0630	1.31388	0.656938	+	0.753945i	$0.271851\pi$
$258$	−11.4362	−0.711984
$259$	−37.2427	−2.31415
$260$	−1.90919	−0.118403
$261$	−2.19026	−0.135573
$262$	−11.7172	−0.723892
$263$	−29.8376	−1.83987	−0.919933	−	0.392076i	$-0.871757\pi$
$263$	−29.8376	−1.83987	−0.919933	+	0.392076i	$0.871757\pi$
$264$	−1.00000	−0.0615457
$265$	1.77192	0.108848
$266$	−8.17337	−0.501142
$267$	10.3805	0.635277
$268$	7.95565	0.485969
$269$	31.0231	1.89151	0.945756	−	0.324878i	$-0.105323\pi$
$269$	31.0231	1.89151	0.945756	+	0.324878i	$0.105323\pi$
$270$	−1.00000	−0.0608581
$271$	21.3145	1.29476	0.647382	−	0.762165i	$-0.275864\pi$
$271$	21.3145	1.29476	0.647382	+	0.762165i	$0.275864\pi$
$272$	−1.00000	−0.0606339
$273$	8.17337	0.494675
$274$	11.1826	0.675563
$275$	1.00000	0.0603023
$276$	−7.75504	−0.466798
$277$	−30.6723	−1.84292	−0.921461	−	0.388471i	$-0.873003\pi$
$277$	−30.6723	−1.84292	−0.921461	+	0.388471i	$0.873003\pi$
$278$	−15.5530	−0.932804
$279$	4.85355	0.290575
$280$	4.28107	0.255843
$281$	8.15415	0.486436	0.243218	−	0.969972i	$-0.421797\pi$
$281$	8.15415	0.486436	0.243218	+	0.969972i	$0.421797\pi$
$282$	1.47397	0.0877737
$283$	−19.7846	−1.17607	−0.588037	−	0.808834i	$-0.700099\pi$
$283$	−19.7846	−1.17607	−0.588037	+	0.808834i	$0.700099\pi$
$284$	14.6086	0.866860
$285$	1.90919	0.113091
$286$	−1.90919	−0.112893
$287$	−6.31017	−0.372478
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−2.19026	−0.128616
$291$	1.03517	0.0606828
$292$	0.228078	0.0133472
$293$	−26.6122	−1.55470	−0.777350	−	0.629069i	$-0.783436\pi$
$293$	−26.6122	−1.55470	−0.777350	+	0.629069i	$0.783436\pi$
$294$	−11.3275	−0.660635
$295$	14.4270	0.839971
$296$	−8.69940	−0.505642
$297$	−1.00000	−0.0580259
$298$	4.24854	0.246112
$299$	−14.8058	−0.856244
$300$	−1.00000	−0.0577350
$301$	48.9589	2.82194
$302$	6.42486	0.369709
$303$	13.8545	0.795919
$304$	−1.90919	−0.109500
$305$	−3.22543	−0.184687
$306$	−1.00000	−0.0571662
$307$	−22.8075	−1.30169	−0.650846	−	0.759210i	$-0.725586\pi$
$307$	−22.8075	−1.30169	−0.650846	+	0.759210i	$0.725586\pi$
$308$	4.28107	0.243936
$309$	10.0530	0.571895
$310$	4.85355	0.275663
$311$	4.62695	0.262370	0.131185	−	0.991358i	$-0.458122\pi$
$311$	4.62695	0.262370	0.131185	+	0.991358i	$0.458122\pi$
$312$	1.90919	0.108087
$313$	11.6199	0.656794	0.328397	−	0.944540i	$-0.393492\pi$
$313$	11.6199	0.656794	0.328397	+	0.944540i	$0.393492\pi$
$314$	15.1811	0.856718
$315$	4.28107	0.241211
$316$	−7.13462	−0.401354
$317$	−33.4435	−1.87838	−0.939188	−	0.343403i	$-0.888420\pi$
$317$	−33.4435	−1.87838	−0.939188	+	0.343403i	$0.888420\pi$
$318$	−1.77192	−0.0993645
$319$	−2.19026	−0.122631
$320$	1.00000	0.0559017
$321$	10.8092	0.603311
$322$	33.1998	1.85015
$323$	1.90919	0.106230
$324$	1.00000	0.0555556
$325$	−1.90919	−0.105903
$326$	−13.3897	−0.741586
$327$	−2.48168	−0.137237
$328$	−1.47397	−0.0813865
$329$	−6.31017	−0.347891
$330$	−1.00000	−0.0550482
$331$	26.6825	1.46660	0.733302	−	0.679903i	$-0.237978\pi$
$331$	26.6825	1.46660	0.733302	+	0.679903i	$0.237978\pi$
$332$	−15.9918	−0.877662
$333$	−8.69940	−0.476724
$334$	24.3053	1.32993
$335$	7.95565	0.434664
$336$	−4.28107	−0.233551
$337$	10.6269	0.578887	0.289443	−	0.957195i	$-0.406530\pi$
$337$	10.6269	0.578887	0.289443	+	0.957195i	$0.406530\pi$
$338$	−9.35499	−0.508844
$339$	−13.4092	−0.728285
$340$	−1.00000	−0.0542326
$341$	4.85355	0.262835
$342$	−1.90919	−0.103237
$343$	18.5264	1.00033
$344$	11.4362	0.616596
$345$	−7.75504	−0.417517
$346$	15.6473	0.841206
$347$	28.3467	1.52173	0.760866	−	0.648908i	$-0.224774\pi$
$347$	28.3467	1.52173	0.760866	+	0.648908i	$0.224774\pi$
$348$	2.19026	0.117410
$349$	−7.88320	−0.421978	−0.210989	−	0.977488i	$-0.567668\pi$
$349$	−7.88320	−0.421978	−0.210989	+	0.977488i	$0.567668\pi$
$350$	4.28107	0.228833
$351$	1.90919	0.101905
$352$	1.00000	0.0533002
$353$	36.1252	1.92275	0.961375	−	0.275242i	$-0.0887579\pi$
$353$	36.1252	1.92275	0.961375	+	0.275242i	$0.0887579\pi$
$354$	−14.4270	−0.766785
$355$	14.6086	0.775344
$356$	−10.3805	−0.550166
$357$	4.28107	0.226578
$358$	8.23819	0.435402
$359$	18.8314	0.993882	0.496941	−	0.867784i	$-0.334457\pi$
$359$	18.8314	0.993882	0.496941	+	0.867784i	$0.334457\pi$
$360$	1.00000	0.0527046
$361$	−15.3550	−0.808157
$362$	18.0086	0.946513
$363$	−1.00000	−0.0524864
$364$	−8.17337	−0.428401
$365$	0.228078	0.0119381
$366$	3.22543	0.168596
$367$	−2.18162	−0.113880	−0.0569398	−	0.998378i	$-0.518134\pi$
$367$	−2.18162	−0.113880	−0.0569398	+	0.998378i	$0.518134\pi$
$368$	7.75504	0.404259
$369$	−1.47397	−0.0767319
$370$	−8.69940	−0.452260
$371$	7.58572	0.393831
$372$	−4.85355	−0.251645
$373$	29.4110	1.52284	0.761422	−	0.648256i	$-0.224501\pi$
$373$	29.4110	1.52284	0.761422	+	0.648256i	$0.224501\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	−1.47397	−0.0760143
$377$	4.18162	0.215364
$378$	−4.28107	−0.220194
$379$	5.49997	0.282514	0.141257	−	0.989973i	$-0.454886\pi$
$379$	5.49997	0.282514	0.141257	+	0.989973i	$0.454886\pi$
$380$	−1.90919	−0.0979394
$381$	−18.1290	−0.928778
$382$	−13.0269	−0.666515
$383$	−14.5260	−0.742245	−0.371123	−	0.928584i	$-0.621027\pi$
$383$	−14.5260	−0.742245	−0.371123	+	0.928584i	$0.621027\pi$
$384$	−1.00000	−0.0510310
$385$	4.28107	0.218183
$386$	−23.9370	−1.21836
$387$	11.4362	0.581332
$388$	−1.03517	−0.0525529
$389$	6.57249	0.333238	0.166619	−	0.986021i	$-0.446715\pi$
$389$	6.57249	0.333238	0.166619	+	0.986021i	$0.446715\pi$
$390$	1.90919	0.0966756
$391$	−7.75504	−0.392189
$392$	11.3275	0.572126
$393$	11.7172	0.591055
$394$	7.95565	0.400800
$395$	−7.13462	−0.358982
$396$	1.00000	0.0502519
$397$	2.07517	0.104150	0.0520749	−	0.998643i	$-0.483417\pi$
$397$	2.07517	0.104150	0.0520749	+	0.998643i	$0.483417\pi$
$398$	−19.6420	−0.984567
$399$	8.17337	0.409180
$400$	1.00000	0.0500000
$401$	−4.73192	−0.236301	−0.118150	−	0.992996i	$-0.537697\pi$
$401$	−4.73192	−0.236301	−0.118150	+	0.992996i	$0.537697\pi$
$402$	−7.95565	−0.396792
$403$	−9.26636	−0.461590
$404$	−13.8545	−0.689286
$405$	1.00000	0.0496904
$406$	−9.37663	−0.465355
$407$	−8.69940	−0.431213
$408$	1.00000	0.0495074
$409$	−24.5568	−1.21426	−0.607129	−	0.794604i	$-0.707679\pi$
$409$	−24.5568	−1.21426	−0.607129	+	0.794604i	$0.707679\pi$
$410$	−1.47397	−0.0727943
$411$	−11.1826	−0.551595
$412$	−10.0530	−0.495275
$413$	61.7628	3.03915
$414$	7.75504	0.381139
$415$	−15.9918	−0.785004
$416$	−1.90919	−0.0936058
$417$	15.5530	0.761631
$418$	−1.90919	−0.0933816
$419$	17.4826	0.854081	0.427041	−	0.904232i	$-0.359556\pi$
$419$	17.4826	0.854081	0.427041	+	0.904232i	$0.359556\pi$
$420$	−4.28107	−0.208895
$421$	16.9735	0.827236	0.413618	−	0.910450i	$-0.364265\pi$
$421$	16.9735	0.827236	0.413618	+	0.910450i	$0.364265\pi$
$422$	1.28371	0.0624903
$423$	−1.47397	−0.0716670
$424$	1.77192	0.0860522
$425$	−1.00000	−0.0485071
$426$	−14.6086	−0.707789
$427$	−13.8083	−0.668229
$428$	−10.8092	−0.522483
$429$	1.90919	0.0921766
$430$	11.4362	0.551500
$431$	31.6642	1.52521	0.762606	−	0.646863i	$-0.223920\pi$
$431$	31.6642	1.52521	0.762606	+	0.646863i	$0.223920\pi$
$432$	−1.00000	−0.0481125
$433$	−25.7846	−1.23913	−0.619565	−	0.784946i	$-0.712691\pi$
$433$	−25.7846	−1.23913	−0.619565	+	0.784946i	$0.712691\pi$
$434$	20.7784	0.997394
$435$	2.19026	0.105015
$436$	2.48168	0.118851
$437$	−14.8058	−0.708260
$438$	−0.228078	−0.0108980
$439$	26.0069	1.24124	0.620621	−	0.784110i	$-0.286880\pi$
$439$	26.0069	1.24124	0.620621	+	0.784110i	$0.286880\pi$
$440$	1.00000	0.0476731
$441$	11.3275	0.539406
$442$	1.90919	0.0908109
$443$	1.07338	0.0509980	0.0254990	−	0.999675i	$-0.491883\pi$
$443$	1.07338	0.0509980	0.0254990	+	0.999675i	$0.491883\pi$
$444$	8.69940	0.412855
$445$	−10.3805	−0.492084
$446$	−7.37958	−0.349433
$447$	−4.24854	−0.200949
$448$	4.28107	0.202261
$449$	−35.5155	−1.67608	−0.838041	−	0.545608i	$-0.816299\pi$
$449$	−35.5155	−1.67608	−0.838041	+	0.545608i	$0.816299\pi$
$450$	1.00000	0.0471405
$451$	−1.47397	−0.0694066
$452$	13.4092	0.630714
$453$	−6.42486	−0.301866
$454$	−1.66423	−0.0781061
$455$	−8.17337	−0.383174
$456$	1.90919	0.0894061
$457$	20.5313	0.960414	0.480207	−	0.877155i	$-0.340562\pi$
$457$	20.5313	0.960414	0.480207	+	0.877155i	$0.340562\pi$
$458$	−9.15509	−0.427789
$459$	1.00000	0.0466760
$460$	7.75504	0.361580
$461$	−40.1237	−1.86875	−0.934374	−	0.356294i	$-0.884040\pi$
$461$	−40.1237	−1.86875	−0.934374	+	0.356294i	$0.884040\pi$
$462$	−4.28107	−0.199173
$463$	−20.0805	−0.933218	−0.466609	−	0.884464i	$-0.654524\pi$
$463$	−20.0805	−0.933218	−0.466609	+	0.884464i	$0.654524\pi$
$464$	−2.19026	−0.101680
$465$	−4.85355	−0.225078
$466$	4.15415	0.192437
$467$	−21.2121	−0.981580	−0.490790	−	0.871278i	$-0.663292\pi$
$467$	−21.2121	−0.981580	−0.490790	+	0.871278i	$0.663292\pi$
$468$	−1.90919	−0.0882524
$469$	34.0587	1.57268
$470$	−1.47397	−0.0679892
$471$	−15.1811	−0.699507
$472$	14.4270	0.664055
$473$	11.4362	0.525835
$474$	7.13462	0.327704
$475$	−1.90919	−0.0875997
$476$	−4.28107	−0.196222
$477$	1.77192	0.0811308
$478$	5.70711	0.261037
$479$	25.9590	1.18610	0.593048	−	0.805167i	$-0.297924\pi$
$479$	25.9590	1.18610	0.593048	+	0.805167i	$0.297924\pi$
$480$	−1.00000	−0.0456435
$481$	16.6088	0.757297
$482$	−1.19291	−0.0543354
$483$	−33.1998	−1.51064
$484$	1.00000	0.0454545
$485$	−1.03517	−0.0470047
$486$	−1.00000	−0.0453609
$487$	−22.9426	−1.03963	−0.519815	−	0.854279i	$-0.673999\pi$
$487$	−22.9426	−1.03963	−0.519815	+	0.854279i	$0.673999\pi$
$488$	−3.22543	−0.146008
$489$	13.3897	0.605503
$490$	11.3275	0.511725
$491$	−2.23314	−0.100780	−0.0503900	−	0.998730i	$-0.516046\pi$
$491$	−2.23314	−0.100780	−0.0503900	+	0.998730i	$0.516046\pi$
$492$	1.47397	0.0664518
$493$	2.19026	0.0986442
$494$	3.64501	0.163997
$495$	1.00000	0.0449467
$496$	4.85355	0.217931
$497$	62.5403	2.80532
$498$	15.9918	0.716608
$499$	−24.0722	−1.07762	−0.538810	−	0.842427i	$-0.681126\pi$
$499$	−24.0722	−1.07762	−0.538810	+	0.842427i	$0.681126\pi$
$500$	1.00000	0.0447214
$501$	−24.3053	−1.08588
$502$	22.9087	1.02246
$503$	−35.4687	−1.58147	−0.790735	−	0.612159i	$-0.790301\pi$
$503$	−35.4687	−1.58147	−0.790735	+	0.612159i	$0.790301\pi$
$504$	4.28107	0.190694
$505$	−13.8545	−0.616517
$506$	7.75504	0.344753
$507$	9.35499	0.415470
$508$	18.1290	0.804345
$509$	−33.4110	−1.48092	−0.740459	−	0.672102i	$-0.765392\pi$
$509$	−33.4110	−1.48092	−0.740459	+	0.672102i	$0.765392\pi$
$510$	1.00000	0.0442807
$511$	0.976415	0.0431941
$512$	1.00000	0.0441942
$513$	1.90919	0.0842928
$514$	21.0630	0.929050
$515$	−10.0530	−0.442988
$516$	−11.4362	−0.503448
$517$	−1.47397	−0.0648252
$518$	−37.2427	−1.63635
$519$	−15.6473	−0.686842
$520$	−1.90919	−0.0837236
$521$	27.7637	1.21635	0.608174	−	0.793803i	$-0.291902\pi$
$521$	27.7637	1.21635	0.608174	+	0.793803i	$0.291902\pi$
$522$	−2.19026	−0.0958649
$523$	−5.34559	−0.233746	−0.116873	−	0.993147i	$-0.537287\pi$
$523$	−5.34559	−0.233746	−0.116873	+	0.993147i	$0.537287\pi$
$524$	−11.7172	−0.511869
$525$	−4.28107	−0.186841
$526$	−29.8376	−1.30098
$527$	−4.85355	−0.211424
$528$	−1.00000	−0.0435194
$529$	37.1406	1.61481
$530$	1.77192	0.0769674
$531$	14.4270	0.626077
$532$	−8.17337	−0.354361
$533$	2.81409	0.121892
$534$	10.3805	0.449209
$535$	−10.8092	−0.467323
$536$	7.95565	0.343632
$537$	−8.23819	−0.355504
$538$	31.0231	1.33750
$539$	11.3275	0.487911
$540$	−1.00000	−0.0430331
$541$	−28.5091	−1.22570	−0.612850	−	0.790199i	$-0.709977\pi$
$541$	−28.5091	−1.22570	−0.612850	+	0.790199i	$0.709977\pi$
$542$	21.3145	0.915537
$543$	−18.0086	−0.772825
$544$	−1.00000	−0.0428746
$545$	2.48168	0.106303
$546$	8.17337	0.349788
$547$	18.5693	0.793966	0.396983	−	0.917826i	$-0.370057\pi$
$547$	18.5693	0.793966	0.396983	+	0.917826i	$0.370057\pi$
$548$	11.1826	0.477695
$549$	−3.22543	−0.137658
$550$	1.00000	0.0426401
$551$	4.18162	0.178143
$552$	−7.75504	−0.330076
$553$	−30.5438	−1.29885
$554$	−30.6723	−1.30314
$555$	8.69940	0.369269
$556$	−15.5530	−0.659592
$557$	10.9754	0.465043	0.232521	−	0.972591i	$-0.425302\pi$
$557$	10.9754	0.465043	0.232521	+	0.972591i	$0.425302\pi$
$558$	4.85355	0.205467
$559$	−21.8338	−0.923471
$560$	4.28107	0.180908
$561$	1.00000	0.0422200
$562$	8.15415	0.343962
$563$	−13.5409	−0.570681	−0.285340	−	0.958426i	$-0.592107\pi$
$563$	−13.5409	−0.570681	−0.285340	+	0.958426i	$0.592107\pi$
$564$	1.47397	0.0620654
$565$	13.4092	0.564127
$566$	−19.7846	−0.831609
$567$	4.28107	0.179788
$568$	14.6086	0.612963
$569$	−29.0804	−1.21911	−0.609557	−	0.792743i	$-0.708652\pi$
$569$	−29.0804	−1.21911	−0.609557	+	0.792743i	$0.708652\pi$
$570$	1.90919	0.0799672
$571$	−16.1816	−0.677180	−0.338590	−	0.940934i	$-0.609950\pi$
$571$	−16.1816	−0.677180	−0.338590	+	0.940934i	$0.609950\pi$
$572$	−1.90919	−0.0798273
$573$	13.0269	0.544208
$574$	−6.31017	−0.263381
$575$	7.75504	0.323407
$576$	1.00000	0.0416667
$577$	10.4562	0.435295	0.217648	−	0.976027i	$-0.430162\pi$
$577$	10.4562	0.435295	0.217648	+	0.976027i	$0.430162\pi$
$578$	1.00000	0.0415945
$579$	23.9370	0.994790
$580$	−2.19026	−0.0909455
$581$	−68.4618	−2.84027
$582$	1.03517	0.0429092
$583$	1.77192	0.0733855
$584$	0.228078	0.00943792
$585$	−1.90919	−0.0789353
$586$	−26.6122	−1.09934
$587$	19.2776	0.795671	0.397835	−	0.917457i	$-0.369762\pi$
$587$	19.2776	0.795671	0.397835	+	0.917457i	$0.369762\pi$
$588$	−11.3275	−0.467139
$589$	−9.26636	−0.381814
$590$	14.4270	0.593949
$591$	−7.95565	−0.327252
$592$	−8.69940	−0.357543
$593$	0.947943	0.0389274	0.0194637	−	0.999811i	$-0.493804\pi$
$593$	0.947943	0.0389274	0.0194637	+	0.999811i	$0.493804\pi$
$594$	−1.00000	−0.0410305
$595$	−4.28107	−0.175507
$596$	4.24854	0.174027
$597$	19.6420	0.803895
$598$	−14.8058	−0.605456
$599$	38.1429	1.55848	0.779239	−	0.626727i	$-0.215606\pi$
$599$	38.1429	1.55848	0.779239	+	0.626727i	$0.215606\pi$
$600$	−1.00000	−0.0408248
$601$	47.4678	1.93625	0.968126	−	0.250462i	$-0.0805826\pi$
$601$	47.4678	1.93625	0.968126	+	0.250462i	$0.0805826\pi$
$602$	48.9589	1.99542
$603$	7.95565	0.323979
$604$	6.42486	0.261424
$605$	1.00000	0.0406558
$606$	13.8545	0.562800
$607$	29.3075	1.18956	0.594778	−	0.803890i	$-0.297240\pi$
$607$	29.3075	1.18956	0.594778	+	0.803890i	$0.297240\pi$
$608$	−1.90919	−0.0774279
$609$	9.37663	0.379960
$610$	−3.22543	−0.130594
$611$	2.81409	0.113846
$612$	−1.00000	−0.0404226
$613$	−27.2825	−1.10193	−0.550964	−	0.834529i	$-0.685740\pi$
$613$	−27.2825	−1.10193	−0.550964	+	0.834529i	$0.685740\pi$
$614$	−22.8075	−0.920435
$615$	1.47397	0.0594363
$616$	4.28107	0.172489
$617$	−3.11921	−0.125575	−0.0627873	−	0.998027i	$-0.519999\pi$
$617$	−3.11921	−0.125575	−0.0627873	+	0.998027i	$0.519999\pi$
$618$	10.0530	0.404390
$619$	−32.8753	−1.32137	−0.660684	−	0.750664i	$-0.729734\pi$
$619$	−32.8753	−1.32137	−0.660684	+	0.750664i	$0.729734\pi$
$620$	4.85355	0.194923
$621$	−7.75504	−0.311199
$622$	4.62695	0.185524
$623$	−44.4397	−1.78044
$624$	1.90919	0.0764288
$625$	1.00000	0.0400000
$626$	11.6199	0.464424
$627$	1.90919	0.0762457
$628$	15.1811	0.605791
$629$	8.69940	0.346868
$630$	4.28107	0.170562
$631$	−4.67576	−0.186139	−0.0930696	−	0.995660i	$-0.529668\pi$
$631$	−4.67576	−0.186139	−0.0930696	+	0.995660i	$0.529668\pi$
$632$	−7.13462	−0.283800
$633$	−1.28371	−0.0510231
$634$	−33.4435	−1.32821
$635$	18.1290	0.719428
$636$	−1.77192	−0.0702613
$637$	−21.6264	−0.856869
$638$	−2.19026	−0.0867131
$639$	14.6086	0.577907
$640$	1.00000	0.0395285
$641$	−13.4154	−0.529878	−0.264939	−	0.964265i	$-0.585352\pi$
$641$	−13.4154	−0.529878	−0.264939	+	0.964265i	$0.585352\pi$
$642$	10.8092	0.426605
$643$	12.8039	0.504937	0.252468	−	0.967605i	$-0.418758\pi$
$643$	12.8039	0.504937	0.252468	+	0.967605i	$0.418758\pi$
$644$	33.1998	1.30826
$645$	−11.4362	−0.450298
$646$	1.90919	0.0751161
$647$	−28.7095	−1.12869	−0.564344	−	0.825540i	$-0.690871\pi$
$647$	−28.7095	−1.12869	−0.564344	+	0.825540i	$0.690871\pi$
$648$	1.00000	0.0392837
$649$	14.4270	0.566308
$650$	−1.90919	−0.0748846
$651$	−20.7784	−0.814369
$652$	−13.3897	−0.524381
$653$	11.3010	0.442242	0.221121	−	0.975246i	$-0.429028\pi$
$653$	11.3010	0.442242	0.221121	+	0.975246i	$0.429028\pi$
$654$	−2.48168	−0.0970413
$655$	−11.7172	−0.457830
$656$	−1.47397	−0.0575489
$657$	0.228078	0.00889815
$658$	−6.31017	−0.245996
$659$	−13.6594	−0.532095	−0.266047	−	0.963960i	$-0.585718\pi$
$659$	−13.6594	−0.532095	−0.266047	+	0.963960i	$0.585718\pi$
$660$	−1.00000	−0.0389249
$661$	18.6426	0.725113	0.362556	−	0.931962i	$-0.381904\pi$
$661$	18.6426	0.725113	0.362556	+	0.931962i	$0.381904\pi$
$662$	26.6825	1.03705
$663$	−1.90919	−0.0741468
$664$	−15.9918	−0.620600
$665$	−8.17337	−0.316950
$666$	−8.69940	−0.337095
$667$	−16.9855	−0.657682
$668$	24.3053	0.940402
$669$	7.37958	0.285311
$670$	7.95565	0.307354
$671$	−3.22543	−0.124516
$672$	−4.28107	−0.165146
$673$	−26.8677	−1.03567	−0.517837	−	0.855479i	$-0.673263\pi$
$673$	−26.8677	−1.03567	−0.517837	+	0.855479i	$0.673263\pi$
$674$	10.6269	0.409335
$675$	−1.00000	−0.0384900
$676$	−9.35499	−0.359807
$677$	−36.7431	−1.41215	−0.706077	−	0.708135i	$-0.749537\pi$
$677$	−36.7431	−1.41215	−0.706077	+	0.708135i	$0.749537\pi$
$678$	−13.4092	−0.514976
$679$	−4.43164	−0.170071
$680$	−1.00000	−0.0383482
$681$	1.66423	0.0637734
$682$	4.85355	0.185852
$683$	21.0640	0.805993	0.402996	−	0.915202i	$-0.367969\pi$
$683$	21.0640	0.805993	0.402996	+	0.915202i	$0.367969\pi$
$684$	−1.90919	−0.0729997
$685$	11.1826	0.427263
$686$	18.5264	0.707342
$687$	9.15509	0.349288
$688$	11.4362	0.435999
$689$	−3.38294	−0.128880
$690$	−7.75504	−0.295229
$691$	−4.18986	−0.159390	−0.0796950	−	0.996819i	$-0.525395\pi$
$691$	−4.18986	−0.159390	−0.0796950	+	0.996819i	$0.525395\pi$
$692$	15.6473	0.594823
$693$	4.28107	0.162624
$694$	28.3467	1.07603
$695$	−15.5530	−0.589957
$696$	2.19026	0.0830215
$697$	1.47397	0.0558307
$698$	−7.88320	−0.298383
$699$	−4.15415	−0.157125
$700$	4.28107	0.161809
$701$	−29.8338	−1.12681	−0.563403	−	0.826182i	$-0.690508\pi$
$701$	−29.8338	−1.12681	−0.563403	+	0.826182i	$0.690508\pi$
$702$	1.90919	0.0720578
$703$	16.6088	0.626413
$704$	1.00000	0.0376889
$705$	1.47397	0.0555130
$706$	36.1252	1.35959
$707$	−59.3120	−2.23066
$708$	−14.4270	−0.542199
$709$	−30.0900	−1.13005	−0.565026	−	0.825073i	$-0.691134\pi$
$709$	−30.0900	−1.13005	−0.565026	+	0.825073i	$0.691134\pi$
$710$	14.6086	0.548251
$711$	−7.13462	−0.267569
$712$	−10.3805	−0.389026
$713$	37.6395	1.40961
$714$	4.28107	0.160215
$715$	−1.90919	−0.0713997
$716$	8.23819	0.307876
$717$	−5.70711	−0.213136
$718$	18.8314	0.702781
$719$	−38.6808	−1.44255	−0.721275	−	0.692649i	$-0.756444\pi$
$719$	−38.6808	−1.44255	−0.721275	+	0.692649i	$0.756444\pi$
$720$	1.00000	0.0372678
$721$	−43.0375	−1.60280
$722$	−15.3550	−0.571454
$723$	1.19291	0.0443646
$724$	18.0086	0.669286
$725$	−2.19026	−0.0813441
$726$	−1.00000	−0.0371135
$727$	−37.6199	−1.39524	−0.697622	−	0.716466i	$-0.745758\pi$
$727$	−37.6199	−1.39524	−0.697622	+	0.716466i	$0.745758\pi$
$728$	−8.17337	−0.302925
$729$	1.00000	0.0370370
$730$	0.228078	0.00844153
$731$	−11.4362	−0.422981
$732$	3.22543	0.119215
$733$	−9.63465	−0.355864	−0.177932	−	0.984043i	$-0.556941\pi$
$733$	−9.63465	−0.355864	−0.177932	+	0.984043i	$0.556941\pi$
$734$	−2.18162	−0.0805250
$735$	−11.3275	−0.417822
$736$	7.75504	0.285854
$737$	7.95565	0.293050
$738$	−1.47397	−0.0542576
$739$	25.2478	0.928754	0.464377	−	0.885638i	$-0.346278\pi$
$739$	25.2478	0.928754	0.464377	+	0.885638i	$0.346278\pi$
$740$	−8.69940	−0.319796
$741$	−3.64501	−0.133903
$742$	7.58572	0.278480
$743$	−18.7799	−0.688966	−0.344483	−	0.938793i	$-0.611946\pi$
$743$	−18.7799	−0.688966	−0.344483	+	0.938793i	$0.611946\pi$
$744$	−4.85355	−0.177940
$745$	4.24854	0.155655
$746$	29.4110	1.07681
$747$	−15.9918	−0.585108
$748$	−1.00000	−0.0365636
$749$	−46.2749	−1.69085
$750$	−1.00000	−0.0365148
$751$	−42.0105	−1.53298	−0.766492	−	0.642253i	$-0.778000\pi$
$751$	−42.0105	−1.53298	−0.766492	+	0.642253i	$0.778000\pi$
$752$	−1.47397	−0.0537502
$753$	−22.9087	−0.834838
$754$	4.18162	0.152286
$755$	6.42486	0.233825
$756$	−4.28107	−0.155701
$757$	−38.2399	−1.38985	−0.694926	−	0.719081i	$-0.744563\pi$
$757$	−38.2399	−1.38985	−0.694926	+	0.719081i	$0.744563\pi$
$758$	5.49997	0.199768
$759$	−7.75504	−0.281490
$760$	−1.90919	−0.0692536
$761$	30.2163	1.09534	0.547669	−	0.836695i	$-0.315515\pi$
$761$	30.2163	1.09534	0.547669	+	0.836695i	$0.315515\pi$
$762$	−18.1290	−0.656745
$763$	10.6242	0.384623
$764$	−13.0269	−0.471298
$765$	−1.00000	−0.0361551
$766$	−14.5260	−0.524847
$767$	−27.5438	−0.994551
$768$	−1.00000	−0.0360844
$769$	−40.6160	−1.46465	−0.732325	−	0.680955i	$-0.761565\pi$
$769$	−40.6160	−1.46465	−0.732325	+	0.680955i	$0.761565\pi$
$770$	4.28107	0.154279
$771$	−21.0630	−0.758566
$772$	−23.9370	−0.861513
$773$	−52.1009	−1.87394	−0.936970	−	0.349411i	$-0.886382\pi$
$773$	−52.1009	−1.87394	−0.936970	+	0.349411i	$0.886382\pi$
$774$	11.4362	0.411064
$775$	4.85355	0.174345
$776$	−1.03517	−0.0371605
$777$	37.2427	1.33607
$778$	6.57249	0.235635
$779$	2.81409	0.100825
$780$	1.90919	0.0683600
$781$	14.6086	0.522736
$782$	−7.75504	−0.277320
$783$	2.19026	0.0782734
$784$	11.3275	0.404554
$785$	15.1811	0.541836
$786$	11.7172	0.417939
$787$	−22.9397	−0.817712	−0.408856	−	0.912599i	$-0.634072\pi$
$787$	−22.9397	−0.817712	−0.408856	+	0.912599i	$0.634072\pi$
$788$	7.95565	0.283408
$789$	29.8376	1.06225
$790$	−7.13462	−0.253838
$791$	57.4055	2.04110
$792$	1.00000	0.0355335
$793$	6.15796	0.218676
$794$	2.07517	0.0736451
$795$	−1.77192	−0.0628436
$796$	−19.6420	−0.696194
$797$	−5.44821	−0.192985	−0.0964927	−	0.995334i	$-0.530762\pi$
$797$	−5.44821	−0.192985	−0.0964927	+	0.995334i	$0.530762\pi$
$798$	8.17337	0.289334
$799$	1.47397	0.0521454
$800$	1.00000	0.0353553
$801$	−10.3805	−0.366777
$802$	−4.73192	−0.167090
$803$	0.228078	0.00804868
$804$	−7.95565	−0.280574
$805$	33.1998	1.17014
$806$	−9.26636	−0.326394
$807$	−31.0231	−1.09206
$808$	−13.8545	−0.487399
$809$	15.3627	0.540124	0.270062	−	0.962843i	$-0.412956\pi$
$809$	15.3627	0.540124	0.270062	+	0.962843i	$0.412956\pi$
$810$	1.00000	0.0351364
$811$	15.5751	0.546916	0.273458	−	0.961884i	$-0.411832\pi$
$811$	15.5751	0.546916	0.273458	+	0.961884i	$0.411832\pi$
$812$	−9.37663	−0.329055
$813$	−21.3145	−0.747533
$814$	−8.69940	−0.304914
$815$	−13.3897	−0.469020
$816$	1.00000	0.0350070
$817$	−21.8338	−0.763868
$818$	−24.5568	−0.858610
$819$	−8.17337	−0.285601
$820$	−1.47397	−0.0514733
$821$	20.8227	0.726718	0.363359	−	0.931649i	$-0.381630\pi$
$821$	20.8227	0.726718	0.363359	+	0.931649i	$0.381630\pi$
$822$	−11.1826	−0.390036
$823$	−23.4875	−0.818723	−0.409361	−	0.912372i	$-0.634248\pi$
$823$	−23.4875	−0.818723	−0.409361	+	0.912372i	$0.634248\pi$
$824$	−10.0530	−0.350212
$825$	−1.00000	−0.0348155
$826$	61.7628	2.14900
$827$	6.12038	0.212827	0.106413	−	0.994322i	$-0.466063\pi$
$827$	6.12038	0.212827	0.106413	+	0.994322i	$0.466063\pi$
$828$	7.75504	0.269506
$829$	11.1325	0.386648	0.193324	−	0.981135i	$-0.438073\pi$
$829$	11.1325	0.386648	0.193324	+	0.981135i	$0.438073\pi$
$830$	−15.9918	−0.555082
$831$	30.6723	1.06401
$832$	−1.90919	−0.0661893
$833$	−11.3275	−0.392475
$834$	15.5530	0.538555
$835$	24.3053	0.841121
$836$	−1.90919	−0.0660307
$837$	−4.85355	−0.167763
$838$	17.4826	0.603927
$839$	−1.32977	−0.0459086	−0.0229543	−	0.999737i	$-0.507307\pi$
$839$	−1.32977	−0.0459086	−0.0229543	+	0.999737i	$0.507307\pi$
$840$	−4.28107	−0.147711
$841$	−24.2028	−0.834578
$842$	16.9735	0.584944
$843$	−8.15415	−0.280844
$844$	1.28371	0.0441873
$845$	−9.35499	−0.321821
$846$	−1.47397	−0.0506762
$847$	4.28107	0.147099
$848$	1.77192	0.0608481
$849$	19.7846	0.679006
$850$	−1.00000	−0.0342997
$851$	−67.4642	−2.31264
$852$	−14.6086	−0.500482
$853$	−0.315060	−0.0107874	−0.00539372	−	0.999985i	$-0.501717\pi$
$853$	−0.315060	−0.0107874	−0.00539372	+	0.999985i	$0.501717\pi$
$854$	−13.8083	−0.472509
$855$	−1.90919	−0.0652930
$856$	−10.8092	−0.369451
$857$	11.3092	0.386316	0.193158	−	0.981168i	$-0.438127\pi$
$857$	11.3092	0.386316	0.193158	+	0.981168i	$0.438127\pi$
$858$	1.90919	0.0651787
$859$	−2.13344	−0.0727921	−0.0363960	−	0.999337i	$-0.511588\pi$
$859$	−2.13344	−0.0727921	−0.0363960	+	0.999337i	$0.511588\pi$
$860$	11.4362	0.389970
$861$	6.31017	0.215050
$862$	31.6642	1.07849
$863$	38.7799	1.32008	0.660041	−	0.751230i	$-0.270539\pi$
$863$	38.7799	1.32008	0.660041	+	0.751230i	$0.270539\pi$
$864$	−1.00000	−0.0340207
$865$	15.6473	0.532026
$866$	−25.7846	−0.876197
$867$	−1.00000	−0.0339618
$868$	20.7784	0.705264
$869$	−7.13462	−0.242025
$870$	2.19026	0.0742567
$871$	−15.1889	−0.514655
$872$	2.48168	0.0840402
$873$	−1.03517	−0.0350353
$874$	−14.8058	−0.500815
$875$	4.28107	0.144726
$876$	−0.228078	−0.00770603
$877$	30.6223	1.03404	0.517021	−	0.855973i	$-0.327041\pi$
$877$	30.6223	1.03404	0.517021	+	0.855973i	$0.327041\pi$
$878$	26.0069	0.877691
$879$	26.6122	0.897606
$880$	1.00000	0.0337100
$881$	31.5196	1.06192	0.530960	−	0.847397i	$-0.321831\pi$
$881$	31.5196	1.06192	0.530960	+	0.847397i	$0.321831\pi$
$882$	11.3275	0.381418
$883$	−55.8545	−1.87965	−0.939827	−	0.341652i	$-0.889014\pi$
$883$	−55.8545	−1.87965	−0.939827	+	0.341652i	$0.889014\pi$
$884$	1.90919	0.0642130
$885$	−14.4270	−0.484957
$886$	1.07338	0.0360611
$887$	−34.7591	−1.16710	−0.583549	−	0.812078i	$-0.698336\pi$
$887$	−34.7591	−1.16710	−0.583549	+	0.812078i	$0.698336\pi$
$888$	8.69940	0.291933
$889$	77.6115	2.60301
$890$	−10.3805	−0.347956
$891$	1.00000	0.0335013
$892$	−7.37958	−0.247087
$893$	2.81409	0.0941700
$894$	−4.24854	−0.142093
$895$	8.23819	0.275372
$896$	4.28107	0.143020
$897$	14.8058	0.494353
$898$	−35.5155	−1.18517
$899$	−10.6305	−0.354548
$900$	1.00000	0.0333333
$901$	−1.77192	−0.0590313
$902$	−1.47397	−0.0490779
$903$	−48.9589	−1.62925
$904$	13.4092	0.445982
$905$	18.0086	0.598627
$906$	−6.42486	−0.213452
$907$	−2.68252	−0.0890715	−0.0445357	−	0.999008i	$-0.514181\pi$
$907$	−2.68252	−0.0890715	−0.0445357	+	0.999008i	$0.514181\pi$
$908$	−1.66423	−0.0552294
$909$	−13.8545	−0.459524
$910$	−8.17337	−0.270945
$911$	34.1394	1.13109	0.565544	−	0.824718i	$-0.308666\pi$
$911$	34.1394	1.13109	0.565544	+	0.824718i	$0.308666\pi$
$912$	1.90919	0.0632196
$913$	−15.9918	−0.529250
$914$	20.5313	0.679115
$915$	3.22543	0.106629
$916$	−9.15509	−0.302493
$917$	−50.1622	−1.65650
$918$	1.00000	0.0330049
$919$	−18.6286	−0.614502	−0.307251	−	0.951628i	$-0.599409\pi$
$919$	−18.6286	−0.614502	−0.307251	+	0.951628i	$0.599409\pi$
$920$	7.75504	0.255676
$921$	22.8075	0.751532
$922$	−40.1237	−1.32140
$923$	−27.8906	−0.918030
$924$	−4.28107	−0.140837
$925$	−8.69940	−0.286035
$926$	−20.0805	−0.659885
$927$	−10.0530	−0.330183
$928$	−2.19026	−0.0718987
$929$	43.6799	1.43309	0.716545	−	0.697541i	$-0.245722\pi$
$929$	43.6799	1.43309	0.716545	+	0.697541i	$0.245722\pi$
$930$	−4.85355	−0.159154
$931$	−21.6264	−0.708777
$932$	4.15415	0.136074
$933$	−4.62695	−0.151479
$934$	−21.2121	−0.694082
$935$	−1.00000	−0.0327035
$936$	−1.90919	−0.0624039
$937$	−4.50003	−0.147010	−0.0735049	−	0.997295i	$-0.523418\pi$
$937$	−4.50003	−0.147010	−0.0735049	+	0.997295i	$0.523418\pi$
$938$	34.0587	1.11205
$939$	−11.6199	−0.379200
$940$	−1.47397	−0.0480757
$941$	−11.9195	−0.388566	−0.194283	−	0.980946i	$-0.562238\pi$
$941$	−11.9195	−0.388566	−0.194283	+	0.980946i	$0.562238\pi$
$942$	−15.1811	−0.494626
$943$	−11.4307	−0.372235
$944$	14.4270	0.469558
$945$	−4.28107	−0.139263
$946$	11.4362	0.371821
$947$	−14.7794	−0.480265	−0.240133	−	0.970740i	$-0.577191\pi$
$947$	−14.7794	−0.480265	−0.240133	+	0.970740i	$0.577191\pi$
$948$	7.13462	0.231722
$949$	−0.435444	−0.0141351
$950$	−1.90919	−0.0619423
$951$	33.4435	1.08448
$952$	−4.28107	−0.138750
$953$	−32.9999	−1.06897	−0.534486	−	0.845177i	$-0.679495\pi$
$953$	−32.9999	−1.06897	−0.534486	+	0.845177i	$0.679495\pi$
$954$	1.77192	0.0573681
$955$	−13.0269	−0.421541
$956$	5.70711	0.184581
$957$	2.19026	0.0708009
$958$	25.9590	0.838697
$959$	47.8732	1.54591
$960$	−1.00000	−0.0322749
$961$	−7.44302	−0.240097
$962$	16.6088	0.535490
$963$	−10.8092	−0.348322
$964$	−1.19291	−0.0384209
$965$	−23.9370	−0.770561
$966$	−33.1998	−1.06819
$967$	11.6883	0.375870	0.187935	−	0.982181i	$-0.439821\pi$
$967$	11.6883	0.375870	0.187935	+	0.982181i	$0.439821\pi$
$968$	1.00000	0.0321412
$969$	−1.90919	−0.0613320
$970$	−1.03517	−0.0332374
$971$	12.4371	0.399125	0.199562	−	0.979885i	$-0.436048\pi$
$971$	12.4371	0.399125	0.199562	+	0.979885i	$0.436048\pi$
$972$	−1.00000	−0.0320750
$973$	−66.5832	−2.13456
$974$	−22.9426	−0.735130
$975$	1.90919	0.0611430
$976$	−3.22543	−0.103243
$977$	18.5408	0.593174	0.296587	−	0.955006i	$-0.404152\pi$
$977$	18.5408	0.593174	0.296587	+	0.955006i	$0.404152\pi$
$978$	13.3897	0.428155
$979$	−10.3805	−0.331763
$980$	11.3275	0.361845
$981$	2.48168	0.0792339
$982$	−2.23314	−0.0712622
$983$	−17.4497	−0.556558	−0.278279	−	0.960500i	$-0.589764\pi$
$983$	−17.4497	−0.556558	−0.278279	+	0.960500i	$0.589764\pi$
$984$	1.47397	0.0469885
$985$	7.95565	0.253488
$986$	2.19026	0.0697520
$987$	6.31017	0.200855
$988$	3.64501	0.115963
$989$	88.6878	2.82011
$990$	1.00000	0.0317821
$991$	15.9282	0.505975	0.252988	−	0.967469i	$-0.418587\pi$
$991$	15.9282	0.505975	0.252988	+	0.967469i	$0.418587\pi$
$992$	4.85355	0.154100
$993$	−26.6825	−0.846744
$994$	62.5403	1.98366
$995$	−19.6420	−0.622695
$996$	15.9918	0.506718
$997$	14.5163	0.459736	0.229868	−	0.973222i	$-0.426171\pi$
$997$	14.5163	0.459736	0.229868	+	0.973222i	$0.426171\pi$
$998$	−24.0722	−0.761992
$999$	8.69940	0.275237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ci.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ci.1.5	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +4.28107 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +4.28107 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.90919 q^{13} +4.28107 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.90919 q^{19} +1.00000 q^{20} -4.28107 q^{21} +1.00000 q^{22} +7.75504 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.90919 q^{26} -1.00000 q^{27} +4.28107 q^{28} -2.19026 q^{29} -1.00000 q^{30} +4.85355 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +4.28107 q^{35} +1.00000 q^{36} -8.69940 q^{37} -1.90919 q^{38} +1.90919 q^{39} +1.00000 q^{40} -1.47397 q^{41} -4.28107 q^{42} +11.4362 q^{43} +1.00000 q^{44} +1.00000 q^{45} +7.75504 q^{46} -1.47397 q^{47} -1.00000 q^{48} +11.3275 q^{49} +1.00000 q^{50} +1.00000 q^{51} -1.90919 q^{52} +1.77192 q^{53} -1.00000 q^{54} +1.00000 q^{55} +4.28107 q^{56} +1.90919 q^{57} -2.19026 q^{58} +14.4270 q^{59} -1.00000 q^{60} -3.22543 q^{61} +4.85355 q^{62} +4.28107 q^{63} +1.00000 q^{64} -1.90919 q^{65} -1.00000 q^{66} +7.95565 q^{67} -1.00000 q^{68} -7.75504 q^{69} +4.28107 q^{70} +14.6086 q^{71} +1.00000 q^{72} +0.228078 q^{73} -8.69940 q^{74} -1.00000 q^{75} -1.90919 q^{76} +4.28107 q^{77} +1.90919 q^{78} -7.13462 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.47397 q^{82} -15.9918 q^{83} -4.28107 q^{84} -1.00000 q^{85} +11.4362 q^{86} +2.19026 q^{87} +1.00000 q^{88} -10.3805 q^{89} +1.00000 q^{90} -8.17337 q^{91} +7.75504 q^{92} -4.85355 q^{93} -1.47397 q^{94} -1.90919 q^{95} -1.00000 q^{96} -1.03517 q^{97} +11.3275 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - q^{13} + 2 q^{14} - 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} - q^{19} + 5 q^{20} - 2 q^{21} + 5 q^{22} - 5 q^{24} + 5 q^{25} - q^{26} - 5 q^{27} + 2 q^{28} + 17 q^{29} - 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + q^{37} - q^{38} + q^{39} + 5 q^{40} + 12 q^{41} - 2 q^{42} + 7 q^{43} + 5 q^{44} + 5 q^{45} + 12 q^{47} - 5 q^{48} + 23 q^{49} + 5 q^{50} + 5 q^{51} - q^{52} + 6 q^{53} - 5 q^{54} + 5 q^{55} + 2 q^{56} + q^{57} + 17 q^{58} + 2 q^{59} - 5 q^{60} + 9 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} - q^{65} - 5 q^{66} + 17 q^{67} - 5 q^{68} + 2 q^{70} + 20 q^{71} + 5 q^{72} + 4 q^{73} + q^{74} - 5 q^{75} - q^{76} + 2 q^{77} + q^{78} - 2 q^{79} + 5 q^{80} + 5 q^{81} + 12 q^{82} + q^{83} - 2 q^{84} - 5 q^{85} + 7 q^{86} - 17 q^{87} + 5 q^{88} + 4 q^{89} + 5 q^{90} + 23 q^{91} - 10 q^{93} + 12 q^{94} - q^{95} - 5 q^{96} - 8 q^{97} + 23 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9 + 5 * q^10 + 5 * q^11 - 5 * q^12 - q^13 + 2 * q^14 - 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 - q^19 + 5 * q^20 - 2 * q^21 + 5 * q^22 - 5 * q^24 + 5 * q^25 - q^26 - 5 * q^27 + 2 * q^28 + 17 * q^29 - 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + q^37 - q^38 + q^39 + 5 * q^40 + 12 * q^41 - 2 * q^42 + 7 * q^43 + 5 * q^44 + 5 * q^45 + 12 * q^47 - 5 * q^48 + 23 * q^49 + 5 * q^50 + 5 * q^51 - q^52 + 6 * q^53 - 5 * q^54 + 5 * q^55 + 2 * q^56 + q^57 + 17 * q^58 + 2 * q^59 - 5 * q^60 + 9 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 - q^65 - 5 * q^66 + 17 * q^67 - 5 * q^68 + 2 * q^70 + 20 * q^71 + 5 * q^72 + 4 * q^73 + q^74 - 5 * q^75 - q^76 + 2 * q^77 + q^78 - 2 * q^79 + 5 * q^80 + 5 * q^81 + 12 * q^82 + q^83 - 2 * q^84 - 5 * q^85 + 7 * q^86 - 17 * q^87 + 5 * q^88 + 4 * q^89 + 5 * q^90 + 23 * q^91 - 10 * q^93 + 12 * q^94 - q^95 - 5 * q^96 - 8 * q^97 + 23 * q^98 + 5 * q^99

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