LMFDB - Embedded newform 1710.2.c.d.1709.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1709,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("1710.1709");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1709.9
Character	$\chi$	$=$	1710.1709
Dual form			1710.2.c.d.1709.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.586990 - 2.15765i) q^{5} -3.03449i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.586990 - 2.15765i) q^{5} -3.03449i q^{7} +1.00000i q^{8} +(-2.15765 - 0.586990i) q^{10} -2.90108i q^{11} -1.78122 q^{13} -3.03449 q^{14} +1.00000 q^{16} +1.79113 q^{17} +(-3.39593 + 2.73270i) q^{19} +(-0.586990 + 2.15765i) q^{20} -2.90108 q^{22} -5.93022 q^{23} +(-4.31088 - 2.53304i) q^{25} +1.78122i q^{26} +3.03449i q^{28} +4.19330 q^{29} -9.66480i q^{31} -1.00000i q^{32} -1.79113i q^{34} +(-6.54736 - 1.78122i) q^{35} -2.75577 q^{37} +(2.73270 + 3.39593i) q^{38} +(2.15765 + 0.586990i) q^{40} +7.22779 q^{41} +5.85355i q^{43} +2.90108i q^{44} +5.93022i q^{46} +4.29142 q^{47} -2.20814 q^{49} +(-2.53304 + 4.31088i) q^{50} +1.78122 q^{52} +13.4136i q^{53} +(-6.25951 - 1.70291i) q^{55} +3.03449 q^{56} -4.19330i q^{58} +6.22488 q^{59} -4.10275 q^{61} -9.66480 q^{62} -1.00000 q^{64} +(-1.04556 + 3.84324i) q^{65} -9.97215 q^{67} -1.79113 q^{68} +(-1.78122 + 6.54736i) q^{70} +10.9196 q^{71} -7.59911i q^{73} +2.75577i q^{74} +(3.39593 - 2.73270i) q^{76} -8.80331 q^{77} -2.50029i q^{79} +(0.586990 - 2.15765i) q^{80} -7.22779i q^{82} -15.1302 q^{83} +(1.05137 - 3.86462i) q^{85} +5.85355 q^{86} +2.90108 q^{88} -17.3599 q^{89} +5.40509i q^{91} +5.93022 q^{92} -4.29142i q^{94} +(3.90282 + 8.93129i) q^{95} -3.94829 q^{97} +2.20814i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4}+O(q^{10}) $ 24 * q - 24 * q^4	$ 24 q - 24 q^{4} + 24 q^{16} - 56 q^{19} - 8 q^{25} - 104 q^{49} - 128 q^{55} + 48 q^{61} - 24 q^{64} + 56 q^{76} - 48 q^{85}+O(q^{100}) $ 24 * q - 24 * q^4 + 24 * q^16 - 56 * q^19 - 8 * q^25 - 104 * q^49 - 128 * q^55 + 48 * q^61 - 24 * q^64 + 56 * q^76 - 48 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.586990	−	2.15765i	0.262510	−	0.964929i
$5$	0.586990	−	2.15765i	0.262510	−	0.964929i
$6$		0			0
$7$		−	3.03449i		−	1.14693i	−0.819230	−	0.573465i	$-0.805599\pi$
$7$		−	3.03449i		−	1.14693i	0.819230	−	0.573465i	$-0.194401\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.15765	−	0.586990i	−0.682308	−	0.185623i
$11$		−	2.90108i		−	0.874709i	−0.899289	−	0.437354i	$-0.855916\pi$
$11$		−	2.90108i		−	0.874709i	0.899289	−	0.437354i	$-0.144084\pi$
$12$		0			0
$13$	−1.78122			−0.494021			−0.247010	−	0.969013i	$-0.579448\pi$
$13$	−1.78122			−0.494021			−0.247010	+	0.969013i	$0.579448\pi$
$14$	−3.03449			−0.811002
$15$		0			0
$16$	1.00000			0.250000
$17$	1.79113			0.434412			0.217206	−	0.976126i	$-0.430306\pi$
$17$	1.79113			0.434412			0.217206	+	0.976126i	$0.430306\pi$
$18$		0			0
$19$	−3.39593	+	2.73270i	−0.779080	+	0.626924i
$19$	−3.39593	+	2.73270i	−0.779080	+	0.626924i
$20$	−0.586990	+	2.15765i	−0.131255	+	0.482465i
$21$		0			0
$22$	−2.90108			−0.618513
$23$	−5.93022			−1.23654			−0.618268	−	0.785968i	$-0.712165\pi$
$23$	−5.93022			−1.23654			−0.618268	+	0.785968i	$0.712165\pi$
$24$		0			0
$25$	−4.31088	−	2.53304i	−0.862177	−	0.506607i
$26$			1.78122i			0.349325i
$27$		0			0
$28$			3.03449i			0.573465i
$29$	4.19330			0.778675			0.389338	−	0.921095i	$-0.372704\pi$
$29$	4.19330			0.778675			0.389338	+	0.921095i	$0.372704\pi$
$30$		0			0
$31$		−	9.66480i		−	1.73585i	−0.496696	−	0.867925i	$-0.665454\pi$
$31$		−	9.66480i		−	1.73585i	0.496696	−	0.867925i	$-0.334546\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		−	1.79113i		−	0.307176i
$35$	−6.54736	−	1.78122i	−1.10671	−	0.301081i
$36$		0			0
$37$	−2.75577			−0.453046			−0.226523	−	0.974006i	$-0.572736\pi$
$37$	−2.75577			−0.453046			−0.226523	+	0.974006i	$0.572736\pi$
$38$	2.73270	+	3.39593i	0.443302	+	0.550893i
$39$		0			0
$40$	2.15765	+	0.586990i	0.341154	+	0.0928113i
$41$	7.22779			1.12879			0.564395	−	0.825505i	$-0.309109\pi$
$41$	7.22779			1.12879			0.564395	+	0.825505i	$0.309109\pi$
$42$		0			0
$43$			5.85355i			0.892659i	0.894869	+	0.446329i	$0.147269\pi$
$43$			5.85355i			0.892659i	−0.894869	+	0.446329i	$0.852731\pi$
$44$			2.90108i			0.437354i
$45$		0			0
$46$			5.93022i			0.874363i
$47$	4.29142			0.625968			0.312984	−	0.949758i	$-0.398671\pi$
$47$	4.29142			0.625968			0.312984	+	0.949758i	$0.398671\pi$
$48$		0			0
$49$	−2.20814			−0.315448
$50$	−2.53304	+	4.31088i	−0.358225	+	0.609651i
$51$		0			0
$52$	1.78122			0.247010
$53$			13.4136i			1.84250i	0.388966	+	0.921252i	$0.372832\pi$
$53$			13.4136i			1.84250i	−0.388966	+	0.921252i	$0.627168\pi$
$54$		0			0
$55$	−6.25951	−	1.70291i	−0.844032	−	0.229620i
$56$	3.03449			0.405501
$57$		0			0
$58$		−	4.19330i		−	0.550607i
$59$	6.22488			0.810410			0.405205	−	0.914226i	$-0.367200\pi$
$59$	6.22488			0.810410			0.405205	+	0.914226i	$0.367200\pi$
$60$		0			0
$61$	−4.10275			−0.525303			−0.262652	−	0.964891i	$-0.584597\pi$
$61$	−4.10275			−0.525303			−0.262652	+	0.964891i	$0.584597\pi$
$62$	−9.66480			−1.22743
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.04556	+	3.84324i	−0.129685	+	0.476695i
$66$		0			0
$67$	−9.97215			−1.21829			−0.609146	−	0.793058i	$-0.708488\pi$
$67$	−9.97215			−1.21829			−0.609146	+	0.793058i	$0.708488\pi$
$68$	−1.79113			−0.217206
$69$		0			0
$70$	−1.78122	+	6.54736i	−0.212896	+	0.782559i
$71$	10.9196			1.29592			0.647961	−	0.761674i	$-0.275622\pi$
$71$	10.9196			1.29592			0.647961	+	0.761674i	$0.275622\pi$
$72$		0			0
$73$		−	7.59911i		−	0.889408i	−0.895677	−	0.444704i	$-0.853309\pi$
$73$		−	7.59911i		−	0.889408i	0.895677	−	0.444704i	$-0.146691\pi$
$74$			2.75577i			0.320352i
$75$		0			0
$76$	3.39593	−	2.73270i	0.389540	−	0.313462i
$77$	−8.80331			−1.00323
$78$		0			0
$79$		−	2.50029i		−	0.281305i	−0.990059	−	0.140652i	$-0.955080\pi$
$79$		−	2.50029i		−	0.281305i	0.990059	−	0.140652i	$-0.0449200\pi$
$80$	0.586990	−	2.15765i	0.0656275	−	0.241232i
$81$		0			0
$82$		−	7.22779i		−	0.798176i
$83$	−15.1302			−1.66076			−0.830378	−	0.557201i	$-0.811875\pi$
$83$	−15.1302			−1.66076			−0.830378	+	0.557201i	$0.811875\pi$
$84$		0			0
$85$	1.05137	−	3.86462i	0.114038	−	0.419177i
$86$	5.85355			0.631205
$87$		0			0
$88$	2.90108			0.309256
$89$	−17.3599			−1.84015			−0.920075	−	0.391743i	$-0.871872\pi$
$89$	−17.3599			−1.84015			−0.920075	+	0.391743i	$0.871872\pi$
$90$		0			0
$91$			5.40509i			0.566607i
$92$	5.93022			0.618268
$93$		0			0
$94$		−	4.29142i		−	0.442626i
$95$	3.90282	+	8.93129i	0.400421	+	0.916331i
$96$		0			0
$97$	−3.94829			−0.400888			−0.200444	−	0.979705i	$-0.564239\pi$
$97$	−3.94829			−0.400888			−0.200444	+	0.979705i	$0.564239\pi$
$98$			2.20814i			0.223055i
$99$		0			0
$100$	4.31088	+	2.53304i	0.431088	+	0.253304i
$101$		−	1.11986i		−	0.111431i	−0.998447	−	0.0557153i	$-0.982256\pi$
$101$		−	1.11986i		−	0.111431i	0.998447	−	0.0557153i	$-0.0177439\pi$
$102$		0			0
$103$	−3.26808			−0.322014			−0.161007	−	0.986953i	$-0.551474\pi$
$103$	−3.26808			−0.322014			−0.161007	+	0.986953i	$0.551474\pi$
$104$		−	1.78122i		−	0.174663i
$105$		0			0
$106$	13.4136			1.30285
$107$			5.03804i			0.487046i	0.969895	+	0.243523i	$0.0783031\pi$
$107$			5.03804i			0.487046i	−0.969895	+	0.243523i	$0.921697\pi$
$108$		0			0
$109$		−	4.90856i		−	0.470155i	−0.971977	−	0.235078i	$-0.924466\pi$
$109$		−	4.90856i		−	0.470155i	0.971977	−	0.235078i	$-0.0755344\pi$
$110$	−1.70291	+	6.25951i	−0.162366	+	0.596821i
$111$		0			0
$112$		−	3.03449i		−	0.286732i
$113$			4.62177i			0.434780i	0.976085	+	0.217390i	$0.0697543\pi$
$113$			4.62177i			0.434780i	−0.976085	+	0.217390i	$0.930246\pi$
$114$		0			0
$115$	−3.48098	+	12.7953i	−0.324603	+	1.19317i
$116$	−4.19330			−0.389338
$117$		0			0
$118$		−	6.22488i		−	0.573046i
$119$		−	5.43516i		−	0.498240i
$120$		0			0
$121$	2.58373			0.234884
$122$			4.10275i			0.371445i
$123$		0			0
$124$			9.66480i			0.867925i
$125$	−7.99585	+	7.81450i	−0.715170	+	0.698950i
$126$		0			0
$127$	−19.2641			−1.70941			−0.854706	−	0.519113i	$-0.826263\pi$
$127$	−19.2641			−1.70941			−0.854706	+	0.519113i	$0.826263\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	3.84324	+	1.04556i	0.337074	+	0.0917014i
$131$		−	12.5062i		−	1.09267i	−0.837565	−	0.546337i	$-0.816022\pi$
$131$		−	12.5062i		−	1.09267i	0.837565	−	0.546337i	$-0.183978\pi$
$132$		0			0
$133$	8.29235	+	10.3049i	0.719038	+	0.893550i
$134$			9.97215i			0.861462i
$135$		0			0
$136$			1.79113i			0.153588i
$137$	4.44375			0.379655			0.189828	−	0.981817i	$-0.439207\pi$
$137$	4.44375			0.379655			0.189828	+	0.981817i	$0.439207\pi$
$138$		0			0
$139$	2.89461			0.245518			0.122759	−	0.992437i	$-0.460826\pi$
$139$	2.89461			0.245518			0.122759	+	0.992437i	$0.460826\pi$
$140$	6.54736	+	1.78122i	0.553353	+	0.150540i
$141$		0			0
$142$		−	10.9196i		−	0.916355i
$143$			5.16745i			0.432124i
$144$		0			0
$145$	2.46142	−	9.04765i	0.204410	−	0.751367i
$146$	−7.59911			−0.628907
$147$		0			0
$148$	2.75577			0.226523
$149$		−	4.68230i		−	0.383589i	−0.981435	−	0.191794i	$-0.938569\pi$
$149$		−	4.68230i		−	0.383589i	0.981435	−	0.191794i	$-0.0614307\pi$
$150$		0			0
$151$		−	9.36014i		−	0.761717i	−0.924633	−	0.380859i	$-0.875628\pi$
$151$		−	9.36014i		−	0.761717i	0.924633	−	0.380859i	$-0.124372\pi$
$152$	−2.73270	−	3.39593i	−0.221651	−	0.275446i
$153$		0			0
$154$			8.80331i			0.709391i
$155$	−20.8532	−	5.67314i	−1.67497	−	0.455678i
$156$		0			0
$157$		−	15.8298i		−	1.26336i	−0.775231	−	0.631678i	$-0.782366\pi$
$157$		−	15.8298i		−	1.26336i	0.775231	−	0.631678i	$-0.217634\pi$
$158$	−2.50029			−0.198913
$159$		0			0
$160$	−2.15765	−	0.586990i	−0.170577	−	0.0464057i
$161$			17.9952i			1.41822i
$162$		0			0
$163$		−	13.6681i		−	1.07057i	−0.844672	−	0.535284i	$-0.820205\pi$
$163$		−	13.6681i		−	1.07057i	0.844672	−	0.535284i	$-0.179795\pi$
$164$	−7.22779			−0.564395
$165$		0			0
$166$			15.1302i			1.17433i
$167$			9.93265i			0.768612i	0.923206	+	0.384306i	$0.125559\pi$
$167$			9.93265i			0.768612i	−0.923206	+	0.384306i	$0.874441\pi$
$168$		0			0
$169$	−9.82727			−0.755944
$170$	−3.86462	−	1.05137i	−0.296403	−	0.0806367i
$171$		0			0
$172$		−	5.85355i		−	0.446329i
$173$		−	12.0354i		−	0.915035i	−0.889201	−	0.457517i	$-0.848739\pi$
$173$		−	12.0354i		−	0.915035i	0.889201	−	0.457517i	$-0.151261\pi$
$174$		0			0
$175$	−7.68648	+	13.0813i	−0.581043	+	0.988856i
$176$		−	2.90108i		−	0.218677i
$177$		0			0
$178$			17.3599i			1.30118i
$179$	18.2775			1.36613			0.683064	−	0.730359i	$-0.260647\pi$
$179$	18.2775			1.36613			0.683064	+	0.730359i	$0.260647\pi$
$180$		0			0
$181$			23.6288i			1.75632i	0.478369	+	0.878159i	$0.341228\pi$
$181$			23.6288i			1.75632i	−0.478369	+	0.878159i	$0.658772\pi$
$182$	5.40509			0.400652
$183$		0			0
$184$		−	5.93022i		−	0.437181i
$185$	−1.61761	+	5.94599i	−0.118929	+	0.437158i
$186$		0			0
$187$		−	5.19621i		−	0.379984i
$188$	−4.29142			−0.312984
$189$		0			0
$190$	8.93129	−	3.90282i	0.647944	−	0.283141i
$191$		−	16.3630i		−	1.18399i	−0.805943	−	0.591993i	$-0.798341\pi$
$191$		−	16.3630i		−	1.18399i	0.805943	−	0.591993i	$-0.201659\pi$
$192$		0			0
$193$	−1.10101			−0.0792524			−0.0396262	−	0.999215i	$-0.512617\pi$
$193$	−1.10101			−0.0792524			−0.0396262	+	0.999215i	$0.512617\pi$
$194$			3.94829i			0.283471i
$195$		0			0
$196$	2.20814			0.157724
$197$	27.5475			1.96268			0.981338	−	0.192292i	$-0.0615921\pi$
$197$	27.5475			1.96268			0.981338	+	0.192292i	$0.0615921\pi$
$198$		0			0
$199$	−2.62177			−0.185852			−0.0929262	−	0.995673i	$-0.529622\pi$
$199$	−2.62177			−0.185852			−0.0929262	+	0.995673i	$0.529622\pi$
$200$	2.53304	−	4.31088i	0.179113	−	0.304826i
$201$		0			0
$202$	−1.11986			−0.0787934
$203$		−	12.7245i		−	0.893086i
$204$		0			0
$205$	4.24264	−	15.5950i	0.296319	−	1.08920i
$206$			3.26808i			0.227698i
$207$		0			0
$208$	−1.78122			−0.123505
$209$	7.92778	+	9.85187i	0.548376	+	0.681468i
$210$		0			0
$211$			8.64315i			0.595019i	0.954719	+	0.297509i	$0.0961560\pi$
$211$			8.64315i			0.595019i	−0.954719	+	0.297509i	$0.903844\pi$
$212$		−	13.4136i		−	0.921252i
$213$		0			0
$214$	5.03804			0.344393
$215$	12.6299	+	3.43598i	0.861353	+	0.234332i
$216$		0			0
$217$	−29.3277			−1.99090
$218$	−4.90856			−0.332450
$219$		0			0
$220$	6.25951	+	1.70291i	0.422016	+	0.114810i
$221$	−3.19039			−0.214609
$222$		0			0
$223$	29.1599			1.95269			0.976344	−	0.216223i	$-0.0693737\pi$
$223$	29.1599			1.95269			0.976344	+	0.216223i	$0.0693737\pi$
$224$	−3.03449			−0.202750
$225$		0			0
$226$	4.62177			0.307436
$227$		−	21.7892i		−	1.44620i	−0.690743	−	0.723101i	$-0.742716\pi$
$227$		−	21.7892i		−	1.44620i	0.690743	−	0.723101i	$-0.257284\pi$
$228$		0			0
$229$	15.0380			0.993742			0.496871	−	0.867824i	$-0.334482\pi$
$229$	15.0380			0.993742			0.496871	+	0.867824i	$0.334482\pi$
$230$	12.7953	+	3.48098i	0.843698	+	0.229529i
$231$		0			0
$232$			4.19330i			0.275303i
$233$	5.37338			0.352022			0.176011	−	0.984388i	$-0.443681\pi$
$233$	5.37338			0.352022			0.176011	+	0.984388i	$0.443681\pi$
$234$		0			0
$235$	2.51902	−	9.25937i	0.164323	−	0.604015i
$236$	−6.22488			−0.405205
$237$		0			0
$238$	−5.43516			−0.352309
$239$		−	7.36542i		−	0.476429i	−0.971213	−	0.238215i	$-0.923438\pi$
$239$		−	7.36542i		−	0.476429i	0.971213	−	0.238215i	$-0.0765622\pi$
$240$		0			0
$241$		−	2.75247i		−	0.177302i	−0.996063	−	0.0886509i	$-0.971744\pi$
$241$		−	2.75247i		−	0.177302i	0.996063	−	0.0886509i	$-0.0282556\pi$
$242$		−	2.58373i		−	0.166088i
$243$		0			0
$244$	4.10275			0.262652
$245$	−1.29615	+	4.76438i	−0.0828083	+	0.304385i
$246$		0			0
$247$	6.04889	−	4.86753i	0.384882	−	0.309714i
$248$	9.66480			0.613715
$249$		0			0
$250$	7.81450	+	7.99585i	0.494232	+	0.505702i
$251$		−	20.0170i		−	1.26346i	−0.775189	−	0.631729i	$-0.782345\pi$
$251$		−	20.0170i		−	1.26346i	0.775189	−	0.631729i	$-0.217655\pi$
$252$		0			0
$253$			17.2040i			1.08161i
$254$			19.2641i			1.20874i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	11.0380i		−	0.688534i	−0.938872	−	0.344267i	$-0.888127\pi$
$257$		−	11.0380i		−	0.688534i	0.938872	−	0.344267i	$-0.111873\pi$
$258$		0			0
$259$			8.36237i			0.519612i
$260$	1.04556	−	3.84324i	0.0648427	−	0.238348i
$261$		0			0
$262$	−12.5062			−0.772637
$263$	12.1651			0.750132			0.375066	−	0.926998i	$-0.377620\pi$
$263$	12.1651			0.750132			0.375066	+	0.926998i	$0.377620\pi$
$264$		0			0
$265$	28.9419	+	7.87367i	1.77789	+	0.483676i
$266$	10.3049	−	8.29235i	0.631835	−	0.508437i
$267$		0			0
$268$	9.97215			0.609146
$269$	0.430855			0.0262697			0.0131348	−	0.999914i	$-0.495819\pi$
$269$	0.430855			0.0262697			0.0131348	+	0.999914i	$0.495819\pi$
$270$		0			0
$271$	−20.1788			−1.22578			−0.612888	−	0.790169i	$-0.709992\pi$
$271$	−20.1788			−1.22578			−0.612888	+	0.790169i	$0.709992\pi$
$272$	1.79113			0.108603
$273$		0			0
$274$		−	4.44375i		−	0.268457i
$275$	−7.34854	+	12.5062i	−0.443134	+	0.754154i
$276$		0			0
$277$			4.78004i			0.287205i	0.989635	+	0.143603i	$0.0458687\pi$
$277$			4.78004i			0.287205i	−0.989635	+	0.143603i	$0.954131\pi$
$278$		−	2.89461i		−	0.173607i
$279$		0			0
$280$	1.78122	−	6.54736i	0.106448	−	0.391280i
$281$	−7.31308			−0.436262			−0.218131	−	0.975920i	$-0.569996\pi$
$281$	−7.31308			−0.436262			−0.218131	+	0.975920i	$0.569996\pi$
$282$		0			0
$283$			19.4364i			1.15537i	0.816259	+	0.577686i	$0.196044\pi$
$283$			19.4364i			1.15537i	−0.816259	+	0.577686i	$0.803956\pi$
$284$	−10.9196			−0.647961
$285$		0			0
$286$	5.16745			0.305558
$287$		−	21.9327i		−	1.29464i
$288$		0			0
$289$	−13.7919			−0.811286
$290$	−9.04765	−	2.46142i	−0.531296	−	0.144540i
$291$		0			0
$292$			7.59911i			0.444704i
$293$			24.7245i			1.44442i	0.691673	+	0.722211i	$0.256874\pi$
$293$			24.7245i			1.44442i	−0.691673	+	0.722211i	$0.743126\pi$
$294$		0			0
$295$	3.65394	−	13.4311i	0.212741	−	0.781988i
$296$		−	2.75577i		−	0.160176i
$297$		0			0
$298$	−4.68230			−0.271238
$299$	10.5630			0.610874
$300$		0			0
$301$	17.7626			1.02382
$302$	−9.36014			−0.538616
$303$		0			0
$304$	−3.39593	+	2.73270i	−0.194770	+	0.156731i
$305$	−2.40827	+	8.85228i	−0.137897	+	0.506880i
$306$		0			0
$307$	1.48687			0.0848600			0.0424300	−	0.999099i	$-0.486490\pi$
$307$	1.48687			0.0848600			0.0424300	+	0.999099i	$0.486490\pi$
$308$	8.80331			0.501615
$309$		0			0
$310$	−5.67314	+	20.8532i	−0.322213	+	1.18438i
$311$		−	2.80957i		−	0.159316i	−0.996822	−	0.0796581i	$-0.974617\pi$
$311$		−	2.80957i		−	0.159316i	0.996822	−	0.0796581i	$-0.0253829\pi$
$312$		0			0
$313$			17.9467i			1.01441i	0.861827	+	0.507203i	$0.169321\pi$
$313$			17.9467i			1.01441i	−0.861827	+	0.507203i	$0.830679\pi$
$314$	−15.8298			−0.893328
$315$		0			0
$316$			2.50029i			0.140652i
$317$		−	25.2702i		−	1.41932i	−0.704546	−	0.709658i	$-0.748849\pi$
$317$		−	25.2702i		−	1.41932i	0.704546	−	0.709658i	$-0.251151\pi$
$318$		0			0
$319$		−	12.1651i		−	0.681114i
$320$	−0.586990	+	2.15765i	−0.0328138	+	0.120616i
$321$		0			0
$322$	17.9952			1.00283
$323$	−6.08255	+	4.89461i	−0.338442	+	0.272344i
$324$		0			0
$325$	7.67862	+	4.51189i	0.425933	+	0.250274i
$326$	−13.6681			−0.757006
$327$		0			0
$328$			7.22779i			0.399088i
$329$		−	13.0223i		−	0.717941i
$330$		0			0
$331$		−	1.69911i		−	0.0933915i	−0.998909	−	0.0466957i	$-0.985131\pi$
$331$		−	1.69911i		−	0.0933915i	0.998909	−	0.0466957i	$-0.0148691\pi$
$332$	15.1302			0.830378
$333$		0			0
$334$	9.93265			0.543491
$335$	−5.85355	+	21.5164i	−0.319814	+	1.17557i
$336$		0			0
$337$	16.1225			0.878246			0.439123	−	0.898427i	$-0.355289\pi$
$337$	16.1225			0.878246			0.439123	+	0.898427i	$0.355289\pi$
$338$			9.82727i			0.534533i
$339$		0			0
$340$	−1.05137	+	3.86462i	−0.0570188	+	0.209588i
$341$	−28.0384			−1.51836
$342$		0			0
$343$		−	14.5409i		−	0.785133i
$344$	−5.85355			−0.315603
$345$		0			0
$346$	−12.0354			−0.647027
$347$	9.01595			0.484001			0.242001	−	0.970276i	$-0.422196\pi$
$347$	9.01595			0.484001			0.242001	+	0.970276i	$0.422196\pi$
$348$		0			0
$349$	36.5137			1.95454			0.977268	−	0.212008i	$-0.0680003\pi$
$349$	36.5137			1.95454			0.977268	+	0.212008i	$0.0680003\pi$
$350$	13.0813	+	7.68648i	0.699227	+	0.410859i
$351$		0			0
$352$	−2.90108			−0.154628
$353$	12.5379			0.667325			0.333662	−	0.942693i	$-0.391715\pi$
$353$	12.5379			0.667325			0.333662	+	0.942693i	$0.391715\pi$
$354$		0			0
$355$	6.40972	−	23.5607i	0.340192	−	1.25047i
$356$	17.3599			0.920075
$357$		0			0
$358$		−	18.2775i		−	0.965998i
$359$		−	16.1413i		−	0.851906i	−0.904745	−	0.425953i	$-0.859939\pi$
$359$		−	16.1413i		−	0.851906i	0.904745	−	0.425953i	$-0.140061\pi$
$360$		0			0
$361$	4.06471	−	18.5601i	0.213932	−	0.976849i
$362$	23.6288			1.24190
$363$		0			0
$364$		−	5.40509i		−	0.283304i
$365$	−16.3962	−	4.46060i	−0.858216	−	0.233479i
$366$		0			0
$367$		−	19.5812i		−	1.02213i	−0.859542	−	0.511065i	$-0.829251\pi$
$367$		−	19.5812i		−	1.02213i	0.859542	−	0.511065i	$-0.170749\pi$
$368$	−5.93022			−0.309134
$369$		0			0
$370$	5.94599	+	1.61761i	0.309117	+	0.0840956i
$371$	40.7036			2.11322
$372$		0			0
$373$	15.2394			0.789067			0.394533	−	0.918882i	$-0.370906\pi$
$373$	15.2394			0.789067			0.394533	+	0.918882i	$0.370906\pi$
$374$	−5.19621			−0.268689
$375$		0			0
$376$			4.29142i			0.221313i
$377$	−7.46917			−0.384682
$378$		0			0
$379$		−	30.0160i		−	1.54182i	−0.636944	−	0.770910i	$-0.719802\pi$
$379$		−	30.0160i		−	1.54182i	0.636944	−	0.770910i	$-0.280198\pi$
$380$	−3.90282	−	8.93129i	−0.200211	−	0.458166i
$381$		0			0
$382$	−16.3630			−0.837204
$383$		−	28.2055i		−	1.44123i	−0.693334	−	0.720617i	$-0.743859\pi$
$383$		−	28.2055i		−	1.44123i	0.693334	−	0.720617i	$-0.256141\pi$
$384$		0			0
$385$	−5.16745	+	18.9944i	−0.263358	+	0.968046i
$386$			1.10101i			0.0560399i
$387$		0			0
$388$	3.94829			0.200444
$389$		−	3.21428i		−	0.162971i	−0.996675	−	0.0814854i	$-0.974034\pi$
$389$		−	3.21428i		−	0.162971i	0.996675	−	0.0814854i	$-0.0259664\pi$
$390$		0			0
$391$	−10.6218			−0.537166
$392$		−	2.20814i		−	0.111528i
$393$		0			0
$394$		−	27.5475i		−	1.38782i
$395$	−5.39475	−	1.46765i	−0.271439	−	0.0738453i
$396$		0			0
$397$		−	17.4901i		−	0.877801i	−0.898536	−	0.438901i	$-0.855368\pi$
$397$		−	17.4901i		−	0.877801i	0.898536	−	0.438901i	$-0.144632\pi$
$398$			2.62177i			0.131417i
$399$		0			0
$400$	−4.31088	−	2.53304i	−0.215544	−	0.126652i
$401$	−6.13958			−0.306596			−0.153298	−	0.988180i	$-0.548989\pi$
$401$	−6.13958			−0.306596			−0.153298	+	0.988180i	$0.548989\pi$
$402$		0			0
$403$			17.2151i			0.857545i
$404$			1.11986i			0.0557153i
$405$		0			0
$406$	−12.7245			−0.631507
$407$			7.99472i			0.396284i
$408$		0			0
$409$			10.0012i			0.494526i	0.968948	+	0.247263i	$0.0795311\pi$
$409$			10.0012i			0.494526i	−0.968948	+	0.247263i	$0.920469\pi$
$410$	−15.5950	−	4.24264i	−0.770183	−	0.209529i
$411$		0			0
$412$	3.26808			0.161007
$413$		−	18.8893i		−	0.929483i
$414$		0			0
$415$	−8.88128	+	32.6456i	−0.435965	+	1.60251i
$416$			1.78122i			0.0873313i
$417$		0			0
$418$	9.85187	−	7.92778i	0.481871	−	0.387761i
$419$		−	20.9915i		−	1.02550i	−0.858537	−	0.512751i	$-0.828626\pi$
$419$		−	20.9915i		−	1.02550i	0.858537	−	0.512751i	$-0.171374\pi$
$420$		0			0
$421$			15.6553i			0.762994i	0.924370	+	0.381497i	$0.124591\pi$
$421$			15.6553i			0.762994i	−0.924370	+	0.381497i	$0.875409\pi$
$422$	8.64315			0.420742
$423$		0			0
$424$	−13.4136			−0.651424
$425$	−7.72134	−	4.53699i	−0.374540	−	0.220076i
$426$		0			0
$427$			12.4498i			0.602486i
$428$		−	5.03804i		−	0.243523i
$429$		0			0
$430$	3.43598	−	12.6299i	0.165698	−	0.609068i
$431$	0.430855			0.0207535			0.0103768	−	0.999946i	$-0.496697\pi$
$431$	0.430855			0.0207535			0.0103768	+	0.999946i	$0.496697\pi$
$432$		0			0
$433$	−34.8894			−1.67668			−0.838338	−	0.545151i	$-0.816472\pi$
$433$	−34.8894			−1.67668			−0.838338	+	0.545151i	$0.816472\pi$
$434$			29.3277i			1.40778i
$435$		0			0
$436$			4.90856i			0.235078i
$437$	20.1386	−	16.2055i	0.963360	−	0.775214i
$438$		0			0
$439$			15.8997i			0.758850i	0.925222	+	0.379425i	$0.123878\pi$
$439$			15.8997i			0.758850i	−0.925222	+	0.379425i	$0.876122\pi$
$440$	1.70291	−	6.25951i	0.0811829	−	0.298410i
$441$		0			0
$442$			3.19039i			0.151751i
$443$	−7.47699			−0.355243			−0.177621	−	0.984099i	$-0.556840\pi$
$443$	−7.47699			−0.355243			−0.177621	+	0.984099i	$0.556840\pi$
$444$		0			0
$445$	−10.1901	+	37.4566i	−0.483058	+	1.77561i
$446$		−	29.1599i		−	1.38076i
$447$		0			0
$448$			3.03449i			0.143366i
$449$	−17.7055			−0.835574			−0.417787	−	0.908545i	$-0.637194\pi$
$449$	−17.7055			−0.835574			−0.417787	+	0.908545i	$0.637194\pi$
$450$		0			0
$451$		−	20.9684i		−	0.987363i
$452$		−	4.62177i		−	0.217390i
$453$		0			0
$454$	−21.7892			−1.02262
$455$	11.6623	+	3.17273i	0.546736	+	0.148740i
$456$		0			0
$457$			14.7674i			0.690788i	0.938458	+	0.345394i	$0.112255\pi$
$457$			14.7674i			0.690788i	−0.938458	+	0.345394i	$0.887745\pi$
$458$		−	15.0380i		−	0.702682i
$459$		0			0
$460$	3.48098	−	12.7953i	0.162301	−	0.596585i
$461$		−	3.54358i		−	0.165041i	−0.996589	−	0.0825205i	$-0.973703\pi$
$461$		−	3.54358i		−	0.165041i	0.996589	−	0.0825205i	$-0.0262970\pi$
$462$		0			0
$463$		−	23.7855i		−	1.10541i	−0.833378	−	0.552704i	$-0.813596\pi$
$463$		−	23.7855i		−	1.10541i	0.833378	−	0.552704i	$-0.186404\pi$
$464$	4.19330			0.194669
$465$		0			0
$466$		−	5.37338i		−	0.248917i
$467$	29.9479			1.38582			0.692912	−	0.721022i	$-0.256327\pi$
$467$	29.9479			1.38582			0.692912	+	0.721022i	$0.256327\pi$
$468$		0			0
$469$			30.2604i			1.39730i
$470$	−9.25937	−	2.51902i	−0.427103	−	0.116194i
$471$		0			0
$472$			6.22488i			0.286523i
$473$	16.9816			0.780817
$474$		0			0
$475$	21.5615	−	3.17833i	0.989309	−	0.145832i
$476$			5.43516i			0.249120i
$477$		0			0
$478$	−7.36542			−0.336886
$479$		−	9.52876i		−	0.435380i	−0.976018	−	0.217690i	$-0.930148\pi$
$479$		−	9.52876i		−	0.435380i	0.976018	−	0.217690i	$-0.0698522\pi$
$480$		0			0
$481$	4.90863			0.223814
$482$	−2.75247			−0.125371
$483$		0			0
$484$	−2.58373			−0.117442
$485$	−2.31761	+	8.51902i	−0.105237	+	0.386829i
$486$		0			0
$487$	−11.7534			−0.532596			−0.266298	−	0.963891i	$-0.585800\pi$
$487$	−11.7534			−0.532596			−0.266298	+	0.963891i	$0.585800\pi$
$488$		−	4.10275i		−	0.185723i
$489$		0			0
$490$	4.76438	+	1.29615i	0.215233	+	0.0585543i
$491$			9.05139i			0.408484i	0.978920	+	0.204242i	$0.0654729\pi$
$491$			9.05139i			0.408484i	−0.978920	+	0.204242i	$0.934527\pi$
$492$		0			0
$493$	7.51073			0.338266
$494$	−4.86753	−	6.04889i	−0.219001	−	0.272152i
$495$		0			0
$496$		−	9.66480i		−	0.433962i
$497$		−	33.1355i		−	1.48633i
$498$		0			0
$499$	−40.4464			−1.81063			−0.905315	−	0.424741i	$-0.860365\pi$
$499$	−40.4464			−1.81063			−0.905315	+	0.424741i	$0.860365\pi$
$500$	7.99585	−	7.81450i	0.357585	−	0.349475i
$501$		0			0
$502$	−20.0170			−0.893400
$503$	3.98676			0.177761			0.0888804	−	0.996042i	$-0.471671\pi$
$503$	3.98676			0.177761			0.0888804	+	0.996042i	$0.471671\pi$
$504$		0			0
$505$	−2.41627	−	0.657350i	−0.107523	−	0.0292517i
$506$	17.2040			0.764813
$507$		0			0
$508$	19.2641			0.854706
$509$	31.3589			1.38996			0.694979	−	0.719030i	$-0.255414\pi$
$509$	31.3589			1.38996			0.694979	+	0.719030i	$0.255414\pi$
$510$		0			0
$511$	−23.0594			−1.02009
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−11.0380			−0.486867
$515$	−1.91833	+	7.05137i	−0.0845319	+	0.310721i
$516$		0			0
$517$		−	12.4498i		−	0.547540i
$518$	8.36237			0.367421
$519$		0			0
$520$	−3.84324	−	1.04556i	−0.168537	−	0.0458507i
$521$	−4.99547			−0.218856			−0.109428	−	0.993995i	$-0.534902\pi$
$521$	−4.99547			−0.218856			−0.109428	+	0.993995i	$0.534902\pi$
$522$		0			0
$523$	−18.8934			−0.826149			−0.413074	−	0.910697i	$-0.635545\pi$
$523$	−18.8934			−0.826149			−0.413074	+	0.910697i	$0.635545\pi$
$524$			12.5062i			0.546337i
$525$		0			0
$526$		−	12.1651i		−	0.530423i
$527$		−	17.3109i		−	0.754074i
$528$		0			0
$529$	12.1675			0.529020
$530$	7.87367	−	28.9419i	0.342010	−	1.25716i
$531$		0			0
$532$	−8.29235	−	10.3049i	−0.359519	−	0.446775i
$533$	−12.8743			−0.557646
$534$		0			0
$535$	10.8703	+	2.95728i	0.469965	+	0.127854i
$536$		−	9.97215i		−	0.430731i
$537$		0			0
$538$		−	0.430855i		−	0.0185755i
$539$			6.40598i			0.275925i
$540$		0			0
$541$	36.1736			1.55522			0.777611	−	0.628745i	$-0.216431\pi$
$541$	36.1736			1.55522			0.777611	+	0.628745i	$0.216431\pi$
$542$			20.1788i			0.866755i
$543$		0			0
$544$		−	1.79113i		−	0.0767939i
$545$	−10.5910	−	2.88128i	−0.453667	−	0.123420i
$546$		0			0
$547$	−21.4312			−0.916330			−0.458165	−	0.888867i	$-0.651493\pi$
$547$	−21.4312			−0.916330			−0.458165	+	0.888867i	$0.651493\pi$
$548$	−4.44375			−0.189828
$549$		0			0
$550$	12.5062	+	7.34854i	0.533267	+	0.313343i
$551$	−14.2401	+	11.4590i	−0.606651	+	0.488171i
$552$		0			0
$553$	−7.58711			−0.322637
$554$	4.78004			0.203085
$555$		0			0
$556$	−2.89461			−0.122759
$557$	−33.3778			−1.41426			−0.707132	−	0.707081i	$-0.750011\pi$
$557$	−33.3778			−1.41426			−0.707132	+	0.707081i	$0.750011\pi$
$558$		0			0
$559$		−	10.4265i		−	0.440992i
$560$	−6.54736	−	1.78122i	−0.276677	−	0.0752702i
$561$		0			0
$562$			7.31308i			0.308484i
$563$		−	35.3463i		−	1.48967i	−0.667250	−	0.744834i	$-0.732529\pi$
$563$		−	35.3463i		−	1.48967i	0.667250	−	0.744834i	$-0.267471\pi$
$564$		0			0
$565$	9.97215	+	2.71293i	0.419531	+	0.114134i
$566$	19.4364			0.816971
$567$		0			0
$568$			10.9196i			0.458177i
$569$	34.2522			1.43593			0.717963	−	0.696081i	$-0.245075\pi$
$569$	34.2522			1.43593			0.717963	+	0.696081i	$0.245075\pi$
$570$		0			0
$571$	−23.9681			−1.00303			−0.501516	−	0.865148i	$-0.667224\pi$
$571$	−23.9681			−1.00303			−0.501516	+	0.865148i	$0.667224\pi$
$572$		−	5.16745i		−	0.216062i
$573$		0			0
$574$	−21.9327			−0.915451
$575$	25.5645	+	15.0215i	1.06611	+	0.626438i
$576$		0			0
$577$		−	30.0104i		−	1.24935i	−0.780885	−	0.624675i	$-0.785231\pi$
$577$		−	30.0104i		−	1.24935i	0.780885	−	0.624675i	$-0.214769\pi$
$578$			13.7919i			0.573666i
$579$		0			0
$580$	−2.46142	+	9.04765i	−0.102205	+	0.375683i
$581$			45.9125i			1.90477i
$582$		0			0
$583$	38.9140			1.61165
$584$	7.59911			0.314453
$585$		0			0
$586$	24.7245			1.02136
$587$	2.03548			0.0840130			0.0420065	−	0.999117i	$-0.486625\pi$
$587$	2.03548			0.0840130			0.0420065	+	0.999117i	$0.486625\pi$
$588$		0			0
$589$	26.4110	+	32.8210i	1.08825	+	1.35237i
$590$	−13.4311	−	3.65394i	−0.552949	−	0.150430i
$591$		0			0
$592$	−2.75577			−0.113262
$593$	−18.9568			−0.778463			−0.389231	−	0.921140i	$-0.627259\pi$
$593$	−18.9568			−0.778463			−0.389231	+	0.921140i	$0.627259\pi$
$594$		0			0
$595$	−11.7272	−	3.19039i	−0.480767	−	0.130793i
$596$			4.68230i			0.191794i
$597$		0			0
$598$		−	10.5630i		−	0.431953i
$599$	−37.6838			−1.53972			−0.769858	−	0.638215i	$-0.779673\pi$
$599$	−37.6838			−1.53972			−0.769858	+	0.638215i	$0.779673\pi$
$600$		0			0
$601$		−	11.9446i		−	0.487231i	−0.969872	−	0.243616i	$-0.921666\pi$
$601$		−	11.9446i		−	0.487231i	0.969872	−	0.243616i	$-0.0783335\pi$
$602$		−	17.7626i		−	0.723948i
$603$		0			0
$604$			9.36014i			0.380859i
$605$	1.51662	−	5.57477i	0.0616595	−	0.226647i
$606$		0			0
$607$	11.3675			0.461393			0.230696	−	0.973026i	$-0.425900\pi$
$607$	11.3675			0.461393			0.230696	+	0.973026i	$0.425900\pi$
$608$	2.73270	+	3.39593i	0.110826	+	0.137723i
$609$		0			0
$610$	8.85228	+	2.40827i	0.358419	+	0.0975081i
$611$	−7.64395			−0.309241
$612$		0			0
$613$		−	28.9369i		−	1.16875i	−0.811483	−	0.584375i	$-0.801340\pi$
$613$		−	28.9369i		−	1.16875i	0.811483	−	0.584375i	$-0.198660\pi$
$614$		−	1.48687i		−	0.0600051i
$615$		0			0
$616$		−	8.80331i		−	0.354695i
$617$	17.4178			0.701216			0.350608	−	0.936522i	$-0.385975\pi$
$617$	17.4178			0.701216			0.350608	+	0.936522i	$0.385975\pi$
$618$		0			0
$619$	17.3782			0.698490			0.349245	−	0.937031i	$-0.386438\pi$
$619$	17.3782			0.698490			0.349245	+	0.937031i	$0.386438\pi$
$620$	20.8532	+	5.67314i	0.837486	+	0.227839i
$621$		0			0
$622$	−2.80957			−0.112654
$623$			52.6786i			2.11052i
$624$		0			0
$625$	12.1675	+	21.8393i	0.486698	+	0.873570i
$626$	17.9467			0.717294
$627$		0			0
$628$			15.8298i			0.631678i
$629$	−4.93594			−0.196809
$630$		0			0
$631$	12.5190			0.498374			0.249187	−	0.968455i	$-0.419837\pi$
$631$	12.5190			0.498374			0.249187	+	0.968455i	$0.419837\pi$
$632$	2.50029			0.0994563
$633$		0			0
$634$	−25.2702			−1.00361
$635$	−11.3078	+	41.5651i	−0.448738	+	1.64946i
$636$		0			0
$637$	3.93317			0.155838
$638$	−12.1651			−0.481621
$639$		0			0
$640$	2.15765	+	0.586990i	0.0852885	+	0.0232028i
$641$	−37.1418			−1.46701			−0.733507	−	0.679682i	$-0.762118\pi$
$641$	−37.1418			−1.46701			−0.733507	+	0.679682i	$0.762118\pi$
$642$		0			0
$643$			40.1315i			1.58263i	0.611408	+	0.791316i	$0.290604\pi$
$643$			40.1315i			1.58263i	−0.611408	+	0.791316i	$0.709396\pi$
$644$		−	17.9952i		−	0.709110i
$645$		0			0
$646$	4.89461	+	6.08255i	0.192576	+	0.239315i
$647$	−11.6400			−0.457614			−0.228807	−	0.973472i	$-0.573482\pi$
$647$	−11.6400			−0.457614			−0.228807	+	0.973472i	$0.573482\pi$
$648$		0			0
$649$		−	18.0589i		−	0.708873i
$650$	4.51189	−	7.67862i	0.176971	−	0.301180i
$651$		0			0
$652$			13.6681i			0.535284i
$653$	26.3132			1.02971			0.514857	−	0.857276i	$-0.327845\pi$
$653$	26.3132			1.02971			0.514857	+	0.857276i	$0.327845\pi$
$654$		0			0
$655$	−26.9840	−	7.34103i	−1.05435	−	0.286838i
$656$	7.22779			0.282198
$657$		0			0
$658$	−13.0223			−0.507661
$659$	−2.07642			−0.0808858			−0.0404429	−	0.999182i	$-0.512877\pi$
$659$	−2.07642			−0.0808858			−0.0404429	+	0.999182i	$0.512877\pi$
$660$		0			0
$661$			9.42045i			0.366413i	0.983074	+	0.183207i	$0.0586477\pi$
$661$			9.42045i			0.366413i	−0.983074	+	0.183207i	$0.941352\pi$
$662$	−1.69911			−0.0660378
$663$		0			0
$664$		−	15.1302i		−	0.587166i
$665$	27.1019	−	11.8431i	1.05097	−	0.459255i
$666$		0			0
$667$	−24.8671			−0.962860
$668$		−	9.93265i		−	0.384306i
$669$		0			0
$670$	21.5164	+	5.85355i	0.831250	+	0.226143i
$671$			11.9024i			0.459487i
$672$		0			0
$673$	18.5338			0.714426			0.357213	−	0.934023i	$-0.383727\pi$
$673$	18.5338			0.714426			0.357213	+	0.934023i	$0.383727\pi$
$674$		−	16.1225i		−	0.621014i
$675$		0			0
$676$	9.82727			0.377972
$677$			27.5518i			1.05890i	0.848341	+	0.529451i	$0.177602\pi$
$677$			27.5518i			1.05890i	−0.848341	+	0.529451i	$0.822398\pi$
$678$		0			0
$679$			11.9811i			0.459791i
$680$	3.86462	+	1.05137i	0.148201	+	0.0403184i
$681$		0			0
$682$			28.0384i			1.07364i
$683$			6.30825i			0.241378i	0.992690	+	0.120689i	$0.0385104\pi$
$683$			6.30825i			0.241378i	−0.992690	+	0.120689i	$0.961490\pi$
$684$		0			0
$685$	2.60844	−	9.58804i	0.0996633	−	0.366340i
$686$	−14.5409			−0.555173
$687$		0			0
$688$			5.85355i			0.223165i
$689$		−	23.8926i		−	0.910235i
$690$		0			0
$691$	26.0975			0.992795			0.496397	−	0.868095i	$-0.334656\pi$
$691$	26.0975			0.992795			0.496397	+	0.868095i	$0.334656\pi$
$692$			12.0354i			0.457517i
$693$		0			0
$694$		−	9.01595i		−	0.342241i
$695$	1.69911	−	6.24555i	0.0644509	−	0.236907i
$696$		0			0
$697$	12.9459			0.490360
$698$		−	36.5137i		−	1.38207i
$699$		0			0
$700$	7.68648	−	13.0813i	0.290521	−	0.494428i
$701$			39.8697i			1.50586i	0.658101	+	0.752930i	$0.271360\pi$
$701$			39.8697i			1.50586i	−0.658101	+	0.752930i	$0.728640\pi$
$702$		0			0
$703$	9.35842	−	7.53070i	0.352959	−	0.284026i
$704$			2.90108i			0.109339i
$705$		0			0
$706$		−	12.5379i		−	0.471870i
$707$	−3.39822			−0.127803
$708$		0			0
$709$	33.6865			1.26512			0.632561	−	0.774510i	$-0.282004\pi$
$709$	33.6865			1.26512			0.632561	+	0.774510i	$0.282004\pi$
$710$	−23.5607	−	6.40972i	−0.884218	−	0.240552i
$711$		0			0
$712$		−	17.3599i		−	0.650591i
$713$			57.3143i			2.14644i
$714$		0			0
$715$	11.1495	+	3.03325i	0.416969	+	0.113437i
$716$	−18.2775			−0.683064
$717$		0			0
$718$	−16.1413			−0.602389
$719$			28.9230i			1.07865i	0.842099	+	0.539324i	$0.181320\pi$
$719$			28.9230i			1.07865i	−0.842099	+	0.539324i	$0.818680\pi$
$720$		0			0
$721$			9.91697i			0.369327i
$722$	−18.5601	−	4.06471i	−0.690736	−	0.151273i
$723$		0			0
$724$		−	23.6288i		−	0.878159i
$725$	−18.0768	−	10.6218i	−0.671356	−	0.394483i
$726$		0			0
$727$		−	0.371322i		−	0.0137716i	−0.999976	−	0.00688579i	$-0.997808\pi$
$727$		−	0.371322i		−	0.0137716i	0.999976	−	0.00688579i	$-0.00219183\pi$
$728$	−5.40509			−0.200326
$729$		0			0
$730$	−4.46060	+	16.3962i	−0.165094	+	0.606850i
$731$			10.4845i			0.387782i
$732$		0			0
$733$			13.2519i			0.489471i	0.969590	+	0.244736i	$0.0787012\pi$
$733$			13.2519i			0.489471i	−0.969590	+	0.244736i	$0.921299\pi$
$734$	−19.5812			−0.722754
$735$		0			0
$736$			5.93022i			0.218591i
$737$			28.9300i			1.06565i
$738$		0			0
$739$	−14.3135			−0.526531			−0.263266	−	0.964723i	$-0.584800\pi$
$739$	−14.3135			−0.526531			−0.263266	+	0.964723i	$0.584800\pi$
$740$	1.61761	−	5.94599i	0.0594646	−	0.218579i
$741$		0			0
$742$		−	40.7036i		−	1.49427i
$743$		−	0.818528i		−	0.0300289i	−0.999887	−	0.0150144i	$-0.995221\pi$
$743$		−	0.818528i		−	0.0300289i	0.999887	−	0.0150144i	$-0.00477942\pi$
$744$		0			0
$745$	−10.1027	−	2.74846i	−0.370136	−	0.100696i
$746$		−	15.2394i		−	0.557955i
$747$		0			0
$748$			5.19621i			0.189992i
$749$	15.2879			0.558607
$750$		0			0
$751$		−	33.5063i		−	1.22266i	−0.791375	−	0.611331i	$-0.790634\pi$
$751$		−	33.5063i		−	1.22266i	0.791375	−	0.611331i	$-0.209366\pi$
$752$	4.29142			0.156492
$753$		0			0
$754$			7.46917i			0.272011i
$755$	−20.1959	−	5.49431i	−0.735003	−	0.199958i
$756$		0			0
$757$		−	45.3130i		−	1.64693i	−0.567368	−	0.823465i	$-0.692038\pi$
$757$		−	45.3130i		−	1.64693i	0.567368	−	0.823465i	$-0.307962\pi$
$758$	−30.0160			−1.09023
$759$		0			0
$760$	−8.93129	+	3.90282i	−0.323972	+	0.141570i
$761$			9.60888i			0.348322i	0.984717	+	0.174161i	$0.0557212\pi$
$761$			9.60888i			0.348322i	−0.984717	+	0.174161i	$0.944279\pi$
$762$		0			0
$763$	−14.8950			−0.539235
$764$			16.3630i			0.591993i
$765$		0			0
$766$	−28.2055			−1.01911
$767$	−11.0879			−0.400359
$768$		0			0
$769$	39.6191			1.42870			0.714351	−	0.699787i	$-0.246722\pi$
$769$	39.6191			1.42870			0.714351	+	0.699787i	$0.246722\pi$
$770$	18.9944	+	5.16745i	0.684512	+	0.186222i
$771$		0			0
$772$	1.10101			0.0396262
$773$		−	12.3436i		−	0.443970i	−0.975050	−	0.221985i	$-0.928746\pi$
$773$		−	12.3436i		−	0.443970i	0.975050	−	0.221985i	$-0.0712536\pi$
$774$		0			0
$775$	−24.4813	+	41.6638i	−0.879394	+	1.49661i
$776$		−	3.94829i		−	0.141735i
$777$		0			0
$778$	−3.21428			−0.115238
$779$	−24.5451	+	19.7514i	−0.879418	+	0.707666i
$780$		0			0
$781$		−	31.6787i		−	1.13355i
$782$			10.6218i			0.379834i
$783$		0			0
$784$	−2.20814			−0.0788620
$785$	−34.1551	−	9.29194i	−1.21905	−	0.331644i
$786$		0			0
$787$	−46.4248			−1.65486			−0.827432	−	0.561566i	$-0.810199\pi$
$787$	−46.4248			−1.65486			−0.827432	+	0.561566i	$0.810199\pi$
$788$	−27.5475			−0.981338
$789$		0			0
$790$	−1.46765	+	5.39475i	−0.0522165	+	0.191936i
$791$	14.0247			0.498662
$792$		0			0
$793$	7.30788			0.259511
$794$	−17.4901			−0.620699
$795$		0			0
$796$	2.62177			0.0929262
$797$			6.83255i			0.242021i	0.992651	+	0.121011i	$0.0386135\pi$
$797$			6.83255i			0.242021i	−0.992651	+	0.121011i	$0.961387\pi$
$798$		0			0
$799$	7.68648			0.271928
$800$	−2.53304	+	4.31088i	−0.0895564	+	0.152413i
$801$		0			0
$802$			6.13958i			0.216796i
$803$	−22.0456			−0.777973
$804$		0			0
$805$	38.8273	+	10.5630i	1.36848	+	0.372297i
$806$	17.2151			0.606376
$807$		0			0
$808$	1.11986			0.0393967
$809$		−	0.332058i		−	0.0116745i	−0.999983	−	0.00583727i	$-0.998142\pi$
$809$		−	0.332058i		−	0.0116745i	0.999983	−	0.00583727i	$-0.00185807\pi$
$810$		0			0
$811$			16.1280i			0.566330i	0.959071	+	0.283165i	$0.0913843\pi$
$811$			16.1280i			0.566330i	−0.959071	+	0.283165i	$0.908616\pi$
$812$			12.7245i			0.446543i
$813$		0			0
$814$	7.99472			0.280215
$815$	−29.4909	−	8.02304i	−1.03302	−	0.281035i
$816$		0			0
$817$	−15.9960	−	19.8783i	−0.559629	−	0.695453i
$818$	10.0012			0.349683
$819$		0			0
$820$	−4.24264	+	15.5950i	−0.148159	+	0.544602i
$821$		−	28.9230i		−	1.00942i	−0.863289	−	0.504710i	$-0.831599\pi$
$821$		−	28.9230i		−	1.00942i	0.863289	−	0.504710i	$-0.168401\pi$
$822$		0			0
$823$		−	10.0726i		−	0.351109i	−0.984470	−	0.175555i	$-0.943828\pi$
$823$		−	10.0726i		−	0.351109i	0.984470	−	0.175555i	$-0.0561719\pi$
$824$		−	3.26808i		−	0.113849i
$825$		0			0
$826$	−18.8893			−0.657244
$827$			48.7245i			1.69432i	0.531340	+	0.847159i	$0.321689\pi$
$827$			48.7245i			1.69432i	−0.531340	+	0.847159i	$0.678311\pi$
$828$		0			0
$829$			51.7253i			1.79649i	0.439490	+	0.898247i	$0.355159\pi$
$829$			51.7253i			1.79649i	−0.439490	+	0.898247i	$0.644841\pi$
$830$	32.6456	+	8.88128i	1.13315	+	0.308274i
$831$		0			0
$832$	1.78122			0.0617526
$833$	−3.95505			−0.137034
$834$		0			0
$835$	21.4312	+	5.83037i	0.741656	+	0.201768i
$836$	−7.92778	−	9.85187i	−0.274188	−	0.340734i
$837$		0			0
$838$	−20.9915			−0.725140
$839$	35.9830			1.24227			0.621136	−	0.783703i	$-0.286671\pi$
$839$	35.9830			1.24227			0.621136	+	0.783703i	$0.286671\pi$
$840$		0			0
$841$	−11.4163			−0.393665
$842$	15.6553			0.539518
$843$		0			0
$844$		−	8.64315i		−	0.297509i
$845$	−5.76851	+	21.2038i	−0.198443	+	0.729432i
$846$		0			0
$847$		−	7.84030i		−	0.269396i
$848$			13.4136i			0.460626i
$849$		0			0
$850$	−4.53699	+	7.72134i	−0.155617	+	0.264840i
$851$	16.3423			0.560208
$852$		0			0
$853$		−	43.9645i		−	1.50532i	−0.658411	−	0.752659i	$-0.728771\pi$
$853$		−	43.9645i		−	1.50532i	0.658411	−	0.752659i	$-0.271229\pi$
$854$	12.4498			0.426022
$855$		0			0
$856$	−5.03804			−0.172197
$857$			0.308245i			0.0105295i	0.999986	+	0.00526473i	$0.00167582\pi$
$857$			0.308245i			0.0105295i	−0.999986	+	0.00526473i	$0.998324\pi$
$858$		0			0
$859$	−8.75118			−0.298586			−0.149293	−	0.988793i	$-0.547700\pi$
$859$	−8.75118			−0.298586			−0.149293	+	0.988793i	$0.547700\pi$
$860$	−12.6299	−	3.43598i	−0.430676	−	0.117166i
$861$		0			0
$862$		−	0.430855i		−	0.0146750i
$863$			50.4110i			1.71601i	0.513641	+	0.858005i	$0.328296\pi$
$863$			50.4110i			1.71601i	−0.513641	+	0.858005i	$0.671704\pi$
$864$		0			0
$865$	−25.9682	−	7.06466i	−0.882944	−	0.240206i
$866$			34.8894i			1.18559i
$867$		0			0
$868$	29.3277			0.995449
$869$	−7.25355			−0.246060
$870$		0			0
$871$	17.7626			0.601861
$872$	4.90856			0.166225
$873$		0			0
$874$	−16.2055	−	20.1386i	−0.548159	−	0.681199i
$875$	23.7130	+	24.2633i	0.801647	+	0.820250i
$876$		0			0
$877$	28.6475			0.967359			0.483679	−	0.875245i	$-0.339300\pi$
$877$	28.6475			0.967359			0.483679	+	0.875245i	$0.339300\pi$
$878$	15.8997			0.536588
$879$		0			0
$880$	−6.25951	−	1.70291i	−0.211008	−	0.0574050i
$881$			48.3201i			1.62794i	0.580904	+	0.813972i	$0.302699\pi$
$881$			48.3201i			1.62794i	−0.580904	+	0.813972i	$0.697301\pi$
$882$		0			0
$883$		−	38.1257i		−	1.28303i	−0.767110	−	0.641516i	$-0.778306\pi$
$883$		−	38.1257i		−	1.28303i	0.767110	−	0.641516i	$-0.221694\pi$
$884$	3.19039			0.107304
$885$		0			0
$886$			7.47699i			0.251195i
$887$		−	25.3056i		−	0.849679i	−0.905269	−	0.424840i	$-0.860331\pi$
$887$		−	25.3056i		−	0.849679i	0.905269	−	0.424840i	$-0.139669\pi$
$888$		0			0
$889$			58.4567i			1.96058i
$890$	37.4566	+	10.1901i	1.25555	+	0.341573i
$891$		0			0
$892$	−29.1599			−0.976344
$893$	−14.5734	+	11.7272i	−0.487679	+	0.392434i
$894$		0			0
$895$	10.7287	−	39.4365i	0.358622	−	1.31822i
$896$	3.03449			0.101375
$897$		0			0
$898$			17.7055i			0.590840i
$899$		−	40.5274i		−	1.35166i
$900$		0			0
$901$			24.0255i			0.800406i
$902$	−20.9684			−0.698171
$903$		0			0
$904$	−4.62177			−0.153718
$905$	50.9827	+	13.8699i	1.69472	+	0.461051i
$906$		0			0
$907$	9.84570			0.326921			0.163460	−	0.986550i	$-0.447734\pi$
$907$	9.84570			0.326921			0.163460	+	0.986550i	$0.447734\pi$
$908$			21.7892i			0.723101i
$909$		0			0
$910$	3.17273	−	11.6623i	0.105175	−	0.386601i
$911$	−0.215427			−0.00713743			−0.00356871	−	0.999994i	$-0.501136\pi$
$911$	−0.215427			−0.00713743			−0.00356871	+	0.999994i	$0.501136\pi$
$912$		0			0
$913$			43.8939i			1.45268i
$914$	14.7674			0.488461
$915$		0			0
$916$	−15.0380			−0.496871
$917$	−37.9500			−1.25322
$918$		0			0
$919$	55.9628			1.84604			0.923021	−	0.384750i	$-0.125712\pi$
$919$	55.9628			1.84604			0.923021	+	0.384750i	$0.125712\pi$
$920$	−12.7953	−	3.48098i	−0.421849	−	0.114764i
$921$		0			0
$922$	−3.54358			−0.116702
$923$	−19.4502			−0.640212
$924$		0			0
$925$	11.8798	+	6.98047i	0.390606	+	0.229517i
$926$	−23.7855			−0.781641
$927$		0			0
$928$		−	4.19330i		−	0.137652i
$929$			22.9718i			0.753681i	0.926278	+	0.376841i	$0.122990\pi$
$929$			22.9718i			0.753681i	−0.926278	+	0.376841i	$0.877010\pi$
$930$		0			0
$931$	7.49868	−	6.03417i	0.245759	−	0.197762i
$932$	−5.37338			−0.176011
$933$		0			0
$934$		−	29.9479i		−	0.979926i
$935$	−11.2116	−	3.05012i	−0.366658	−	0.0997497i
$936$		0			0
$937$		−	0.215427i		−	0.00703771i	−0.999994	−	0.00351885i	$-0.998880\pi$
$937$		−	0.215427i		−	0.00703771i	0.999994	−	0.00351885i	$-0.00112009\pi$
$938$	30.2604			0.988037
$939$		0			0
$940$	−2.51902	+	9.25937i	−0.0821614	+	0.302007i
$941$	−49.4762			−1.61288			−0.806438	−	0.591318i	$-0.798608\pi$
$941$	−49.4762			−1.61288			−0.806438	+	0.591318i	$0.798608\pi$
$942$		0			0
$943$	−42.8623			−1.39579
$944$	6.22488			0.202602
$945$		0			0
$946$		−	16.9816i		−	0.552121i
$947$	14.9462			0.485685			0.242843	−	0.970066i	$-0.421920\pi$
$947$	14.9462			0.485685			0.242843	+	0.970066i	$0.421920\pi$
$948$		0			0
$949$			13.5357i			0.439386i
$950$	−3.17833	−	21.5615i	−0.103119	−	0.699547i
$951$		0			0
$952$	5.43516			0.176155
$953$			4.62177i			0.149714i	0.997194	+	0.0748569i	$0.0238500\pi$
$953$			4.62177i			0.149714i	−0.997194	+	0.0748569i	$0.976150\pi$
$954$		0			0
$955$	−35.3056	−	9.60493i	−1.14246	−	0.310808i
$956$			7.36542i			0.238215i
$957$		0			0
$958$	−9.52876			−0.307860
$959$		−	13.4845i		−	0.435438i
$960$		0			0
$961$	−62.4084			−2.01317
$962$		−	4.90863i		−	0.158261i
$963$		0			0
$964$			2.75247i			0.0886509i
$965$	−0.646282	+	2.37559i	−0.0208046	+	0.0764730i
$966$		0			0
$967$			1.94629i			0.0625884i	0.999510	+	0.0312942i	$0.00996287\pi$
$967$			1.94629i			0.0625884i	−0.999510	+	0.0312942i	$0.990037\pi$
$968$			2.58373i			0.0830441i
$969$		0			0
$970$	8.51902	+	2.31761i	0.273529	+	0.0744139i
$971$	−8.97334			−0.287968			−0.143984	−	0.989580i	$-0.545991\pi$
$971$	−8.97334			−0.287968			−0.143984	+	0.989580i	$0.545991\pi$
$972$		0			0
$973$		−	8.78367i		−	0.281592i
$974$			11.7534i			0.376602i
$975$		0			0
$976$	−4.10275			−0.131326
$977$			49.7573i			1.59188i	0.605378	+	0.795938i	$0.293022\pi$
$977$			49.7573i			1.59188i	−0.605378	+	0.795938i	$0.706978\pi$
$978$		0			0
$979$			50.3626i			1.60959i
$980$	1.29615	−	4.76438i	0.0414041	−	0.152193i
$981$		0			0
$982$	9.05139			0.288842
$983$		−	44.7546i		−	1.42745i	−0.700425	−	0.713726i	$-0.747006\pi$
$983$		−	44.7546i		−	1.42745i	0.700425	−	0.713726i	$-0.252994\pi$
$984$		0			0
$985$	16.1701	−	59.4377i	0.515222	−	1.89384i
$986$		−	7.51073i		−	0.239190i
$987$		0			0
$988$	−6.04889	+	4.86753i	−0.192441	+	0.154857i
$989$		−	34.7128i		−	1.10380i
$990$		0			0
$991$			36.6476i			1.16415i	0.813135	+	0.582075i	$0.197759\pi$
$991$			36.6476i			1.16415i	−0.813135	+	0.582075i	$0.802241\pi$
$992$	−9.66480			−0.306858
$993$		0			0
$994$	−33.1355			−1.05099
$995$	−1.53895	+	5.65685i	−0.0487881	+	0.179334i
$996$		0			0
$997$			24.7325i			0.783288i	0.920117	+	0.391644i	$0.128093\pi$
$997$			24.7325i			0.783288i	−0.920117	+	0.391644i	$0.871907\pi$
$998$			40.4464i			1.28031i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.c.d.1709.9	✓	24
3.2	odd	2	inner	1710.2.c.d.1709.20	yes	24
5.4	even	2	inner	1710.2.c.d.1709.19	yes	24
15.14	odd	2	inner	1710.2.c.d.1709.10	yes	24
19.18	odd	2	inner	1710.2.c.d.1709.11	yes	24
57.56	even	2	inner	1710.2.c.d.1709.18	yes	24
95.94	odd	2	inner	1710.2.c.d.1709.17	yes	24
285.284	even	2	inner	1710.2.c.d.1709.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.c.d.1709.9	✓	24	1.1	even	1	trivial
1710.2.c.d.1709.10	yes	24	15.14	odd	2	inner
1710.2.c.d.1709.11	yes	24	19.18	odd	2	inner
1710.2.c.d.1709.12	yes	24	285.284	even	2	inner
1710.2.c.d.1709.17	yes	24	95.94	odd	2	inner
1710.2.c.d.1709.18	yes	24	57.56	even	2	inner
1710.2.c.d.1709.19	yes	24	5.4	even	2	inner
1710.2.c.d.1709.20	yes	24	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.586990 - 2.15765i) q^{5} -3.03449i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.586990 - 2.15765i) q^{5} -3.03449i q^{7} +1.00000i q^{8} +(-2.15765 - 0.586990i) q^{10} -2.90108i q^{11} -1.78122 q^{13} -3.03449 q^{14} +1.00000 q^{16} +1.79113 q^{17} +(-3.39593 + 2.73270i) q^{19} +(-0.586990 + 2.15765i) q^{20} -2.90108 q^{22} -5.93022 q^{23} +(-4.31088 - 2.53304i) q^{25} +1.78122i q^{26} +3.03449i q^{28} +4.19330 q^{29} -9.66480i q^{31} -1.00000i q^{32} -1.79113i q^{34} +(-6.54736 - 1.78122i) q^{35} -2.75577 q^{37} +(2.73270 + 3.39593i) q^{38} +(2.15765 + 0.586990i) q^{40} +7.22779 q^{41} +5.85355i q^{43} +2.90108i q^{44} +5.93022i q^{46} +4.29142 q^{47} -2.20814 q^{49} +(-2.53304 + 4.31088i) q^{50} +1.78122 q^{52} +13.4136i q^{53} +(-6.25951 - 1.70291i) q^{55} +3.03449 q^{56} -4.19330i q^{58} +6.22488 q^{59} -4.10275 q^{61} -9.66480 q^{62} -1.00000 q^{64} +(-1.04556 + 3.84324i) q^{65} -9.97215 q^{67} -1.79113 q^{68} +(-1.78122 + 6.54736i) q^{70} +10.9196 q^{71} -7.59911i q^{73} +2.75577i q^{74} +(3.39593 - 2.73270i) q^{76} -8.80331 q^{77} -2.50029i q^{79} +(0.586990 - 2.15765i) q^{80} -7.22779i q^{82} -15.1302 q^{83} +(1.05137 - 3.86462i) q^{85} +5.85355 q^{86} +2.90108 q^{88} -17.3599 q^{89} +5.40509i q^{91} +5.93022 q^{92} -4.29142i q^{94} +(3.90282 + 8.93129i) q^{95} -3.94829 q^{97} +2.20814i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4}+O(q^{10}) \) 24 * q - 24 * q^4	\( 24 q - 24 q^{4} + 24 q^{16} - 56 q^{19} - 8 q^{25} - 104 q^{49} - 128 q^{55} + 48 q^{61} - 24 q^{64} + 56 q^{76} - 48 q^{85}+O(q^{100}) \) 24 * q - 24 * q^4 + 24 * q^16 - 56 * q^19 - 8 * q^25 - 104 * q^49 - 128 * q^55 + 48 * q^61 - 24 * q^64 + 56 * q^76 - 48 * q^85

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