LMFDB - Embedded newform 585.2.c.c.469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 90x^{6} + 208x^{4} + 169x^{2} + 16 $ x^10 + 16x^8 + 90x^6 + 208x^4 + 169x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.2
Root			$-2.26036i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.c.469.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26036i q^{2} -3.10922 q^{4} +(2.23266 - 0.123438i) q^{5} +4.96953i q^{7} +2.50723i q^{8} +O(q^{10})$	\(q-2.26036i q^{2} -3.10922 q^{4} +(2.23266 - 0.123438i) q^{5} +4.96953i q^{7} +2.50723i q^{8} +(-0.279015 - 5.04661i) q^{10} +3.21640 q^{11} -1.00000i q^{13} +11.2329 q^{14} -0.551191 q^{16} +0.448809i q^{17} +7.23291 q^{19} +(-6.94183 + 0.383797i) q^{20} -7.27022i q^{22} -6.26338i q^{23} +(4.96953 - 0.551191i) q^{25} -2.26036 q^{26} -15.4513i q^{28} -2.21844 q^{29} +2.19148 q^{31} +6.26036i q^{32} +1.01447 q^{34} +(0.613429 + 11.0953i) q^{35} +8.26338i q^{37} -16.3490i q^{38} +(0.309489 + 5.59780i) q^{40} -1.79807 q^{41} -6.21844i q^{43} -10.0005 q^{44} -14.1575 q^{46} -1.66521i q^{47} -17.6962 q^{49} +(-1.24589 - 11.2329i) q^{50} +3.10922i q^{52} +1.16100i q^{53} +(7.18113 - 0.397027i) q^{55} -12.4598 q^{56} +5.01447i q^{58} -5.88365 q^{59} -1.76963 q^{61} -4.95352i q^{62} +13.0483 q^{64} +(-0.123438 - 2.23266i) q^{65} -2.73916i q^{67} -1.39545i q^{68} +(25.0792 - 1.38657i) q^{70} -4.11402 q^{71} +10.4369i q^{73} +18.6782 q^{74} -22.4887 q^{76} +15.9840i q^{77} -1.05336 q^{79} +(-1.23062 + 0.0680380i) q^{80} +4.06428i q^{82} -5.77601i q^{83} +(0.0554002 + 1.00204i) q^{85} -14.0559 q^{86} +8.06428i q^{88} +11.1326 q^{89} +4.96953 q^{91} +19.4742i q^{92} -3.76398 q^{94} +(16.1486 - 0.892818i) q^{95} -8.37418i q^{97} +39.9997i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) $ 10 * q - 12 * q^4 + 2 * q^5	$ 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) $ 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	2.26036i		−	1.59831i	−0.601122	−	0.799157i	$-0.705279\pi$
$2$		−	2.26036i		−	1.59831i	0.601122	−	0.799157i	$-0.294721\pi$
$3$		0			0
$3$		0			0
$4$	−3.10922			−1.55461
$5$	2.23266	−	0.123438i	0.998475	−	0.0552033i
$5$	2.23266	−	0.123438i	0.998475	−	0.0552033i
$6$		0			0
$7$			4.96953i			1.87830i	0.343501	+	0.939152i	$0.388387\pi$
$7$			4.96953i			1.87830i	−0.343501	+	0.939152i	$0.611613\pi$
$8$			2.50723i			0.886441i
$9$		0			0
$10$	−0.279015	−	5.04661i	−0.0882322	−	1.59588i
$11$	3.21640			0.969782			0.484891	−	0.874575i	$-0.338859\pi$
$11$	3.21640			0.969782			0.484891	+	0.874575i	$0.338859\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	11.2329			3.00212
$15$		0			0
$16$	−0.551191			−0.137798
$17$			0.448809i			0.108852i	0.998518	+	0.0544261i	$0.0173329\pi$
$17$			0.448809i			0.108852i	−0.998518	+	0.0544261i	$0.982667\pi$
$18$		0			0
$19$	7.23291			1.65934			0.829672	−	0.558252i	$-0.188528\pi$
$19$	7.23291			1.65934			0.829672	+	0.558252i	$0.188528\pi$
$20$	−6.94183	+	0.383797i	−1.55224	+	0.0858195i
$21$		0			0
$22$		−	7.27022i		−	1.55002i
$23$		−	6.26338i		−	1.30601i	−0.757355	−	0.653003i	$-0.773509\pi$
$23$		−	6.26338i		−	1.30601i	0.757355	−	0.653003i	$-0.226491\pi$
$24$		0			0
$25$	4.96953	−	0.551191i	0.993905	−	0.110238i
$26$	−2.26036			−0.443293
$27$		0			0
$28$		−	15.4513i		−	2.92003i
$29$	−2.21844			−0.411954			−0.205977	−	0.978557i	$-0.566037\pi$
$29$	−2.21844			−0.411954			−0.205977	+	0.978557i	$0.566037\pi$
$30$		0			0
$31$	2.19148			0.393601			0.196800	−	0.980444i	$-0.436945\pi$
$31$	2.19148			0.393601			0.196800	+	0.980444i	$0.436945\pi$
$32$			6.26036i			1.10669i
$33$		0			0
$34$	1.01447			0.173980
$35$	0.613429	+	11.0953i	0.103689	+	1.87544i
$36$		0			0
$37$			8.26338i			1.35849i	0.733911	+	0.679246i	$0.237693\pi$
$37$			8.26338i			1.35849i	−0.733911	+	0.679246i	$0.762307\pi$
$38$		−	16.3490i		−	2.65215i
$39$		0			0
$40$	0.309489	+	5.59780i	0.0489344	+	0.885090i
$41$	−1.79807			−0.280811			−0.140405	−	0.990094i	$-0.544841\pi$
$41$	−1.79807			−0.280811			−0.140405	+	0.990094i	$0.544841\pi$
$42$		0			0
$43$		−	6.21844i		−	0.948303i	−0.880443	−	0.474152i	$-0.842755\pi$
$43$		−	6.21844i		−	0.948303i	0.880443	−	0.474152i	$-0.157245\pi$
$44$	−10.0005			−1.50763
$45$		0			0
$46$	−14.1575			−2.08741
$47$		−	1.66521i		−	0.242896i	−0.992598	−	0.121448i	$-0.961246\pi$
$47$		−	1.66521i		−	0.242896i	0.992598	−	0.121448i	$-0.0387538\pi$
$48$		0			0
$49$	−17.6962			−2.52803
$50$	−1.24589	−	11.2329i	−0.176195	−	1.58857i
$51$		0			0
$52$			3.10922i			0.431171i
$53$			1.16100i			0.159476i	0.996816	+	0.0797380i	$0.0254084\pi$
$53$			1.16100i			0.159476i	−0.996816	+	0.0797380i	$0.974592\pi$
$54$		0			0
$55$	7.18113	−	0.397027i	0.968303	−	0.0535351i
$56$	−12.4598			−1.66501
$57$		0			0
$58$			5.01447i			0.658432i
$59$	−5.88365			−0.765986			−0.382993	−	0.923751i	$-0.625107\pi$
$59$	−5.88365			−0.765986			−0.382993	+	0.923751i	$0.625107\pi$
$60$		0			0
$61$	−1.76963			−0.226578			−0.113289	−	0.993562i	$-0.536139\pi$
$61$	−1.76963			−0.226578			−0.113289	+	0.993562i	$0.536139\pi$
$62$		−	4.95352i		−	0.629098i
$63$		0			0
$64$	13.0483			1.63103
$65$	−0.123438	−	2.23266i	−0.0153106	−	0.276927i
$66$		0			0
$67$		−	2.73916i		−	0.334641i	−0.985903	−	0.167321i	$-0.946488\pi$
$67$		−	2.73916i		−	0.334641i	0.985903	−	0.167321i	$-0.0535115\pi$
$68$		−	1.39545i		−	0.169223i
$69$		0			0
$70$	25.0792	−	1.38657i	2.99754	−	0.165727i
$71$	−4.11402			−0.488244			−0.244122	−	0.969744i	$-0.578500\pi$
$71$	−4.11402			−0.488244			−0.244122	+	0.969744i	$0.578500\pi$
$72$		0			0
$73$			10.4369i			1.22154i	0.791806	+	0.610772i	$0.209141\pi$
$73$			10.4369i			1.22154i	−0.791806	+	0.610772i	$0.790859\pi$
$74$	18.6782			2.17130
$75$		0			0
$76$	−22.4887			−2.57963
$77$			15.9840i			1.82155i
$78$		0			0
$79$	−1.05336			−0.118513			−0.0592563	−	0.998243i	$-0.518873\pi$
$79$	−1.05336			−0.118513			−0.0592563	+	0.998243i	$0.518873\pi$
$80$	−1.23062	+	0.0680380i	−0.137588	+	0.00760688i
$81$		0			0
$82$			4.06428i			0.448824i
$83$		−	5.77601i		−	0.634000i	−0.948426	−	0.317000i	$-0.897325\pi$
$83$		−	5.77601i		−	0.634000i	0.948426	−	0.317000i	$-0.102675\pi$
$84$		0			0
$85$	0.0554002	+	1.00204i	0.00600900	+	0.108686i
$86$	−14.0559			−1.51569
$87$		0			0
$88$			8.06428i			0.859655i
$89$	11.1326			1.18005			0.590025	−	0.807385i	$-0.299118\pi$
$89$	11.1326			1.18005			0.590025	+	0.807385i	$0.299118\pi$
$90$		0			0
$91$	4.96953			0.520948
$92$			19.4742i			2.03033i
$93$		0			0
$94$	−3.76398			−0.388224
$95$	16.1486	−	0.892818i	1.65681	−	0.0916012i
$96$		0			0
$97$		−	8.37418i		−	0.850270i	−0.905130	−	0.425135i	$-0.860227\pi$
$97$		−	8.37418i		−	0.850270i	0.905130	−	0.425135i	$-0.139773\pi$
$98$			39.9997i			4.04058i
$99$		0			0
$100$	−15.4513	+	1.71377i	−1.54513	+	0.171377i
$101$	−5.50625			−0.547892			−0.273946	−	0.961745i	$-0.588329\pi$
$101$	−5.50625			−0.547892			−0.273946	+	0.961745i	$0.588329\pi$
$102$		0			0
$103$			1.32082i			0.130144i	0.997881	+	0.0650722i	$0.0207278\pi$
$103$			1.32082i			0.130144i	−0.997881	+	0.0650722i	$0.979272\pi$
$104$	2.50723			0.245855
$105$		0			0
$106$	2.62428			0.254893
$107$			7.49024i			0.724109i	0.932157	+	0.362055i	$0.117925\pi$
$107$			7.49024i			0.724109i	−0.932157	+	0.362055i	$0.882075\pi$
$108$		0			0
$109$	−14.0330			−1.34412			−0.672060	−	0.740497i	$-0.734590\pi$
$109$	−14.0330			−1.34412			−0.672060	+	0.740497i	$0.734590\pi$
$110$	−0.897423	−	16.2319i	−0.0855660	−	1.54765i
$111$		0			0
$112$		−	2.73916i		−	0.258826i
$113$		−	11.2269i		−	1.05613i	−0.849203	−	0.528067i	$-0.822917\pi$
$113$		−	11.2269i		−	1.05613i	0.849203	−	0.528067i	$-0.177083\pi$
$114$		0			0
$115$	−0.773141	−	13.9840i	−0.0720958	−	1.30401i
$116$	6.89762			0.640428
$117$		0			0
$118$			13.2992i			1.22429i
$119$	−2.23037			−0.204458
$120$		0			0
$121$	−0.654755			−0.0595232
$122$			4.00000i			0.362143i
$123$		0			0
$124$	−6.81378			−0.611896
$125$	11.0272	−	1.84405i	0.986304	−	0.164937i
$126$		0			0
$127$		−	1.50217i		−	0.133296i	−0.997777	−	0.0666481i	$-0.978770\pi$
$127$		−	1.50217i		−	0.133296i	0.997777	−	0.0666481i	$-0.0212305\pi$
$128$		−	16.9731i		−	1.50022i
$129$		0			0
$130$	−5.04661	+	0.279015i	−0.442617	+	0.0244712i
$131$	−12.5477			−1.09630			−0.548148	−	0.836381i	$-0.684667\pi$
$131$	−12.5477			−1.09630			−0.548148	+	0.836381i	$0.684667\pi$
$132$		0			0
$133$			35.9441i			3.11675i
$134$	−6.19148			−0.534862
$135$		0			0
$136$	−1.12527			−0.0964911
$137$			10.6797i			0.912427i	0.889870	+	0.456213i	$0.150795\pi$
$137$			10.6797i			0.912427i	−0.889870	+	0.456213i	$0.849205\pi$
$138$		0			0
$139$	20.6962			1.75543			0.877714	−	0.479185i	$-0.159068\pi$
$139$	20.6962			1.75543			0.877714	+	0.479185i	$0.159068\pi$
$140$	−1.90729	−	34.4976i	−0.161195	−	2.91558i
$141$		0			0
$142$			9.29916i			0.780368i
$143$		−	3.21640i		−	0.268969i
$144$		0			0
$145$	−4.95302	+	0.273840i	−0.411326	+	0.0227412i
$146$	23.5911			1.95241
$147$		0			0
$148$		−	25.6927i		−	2.11193i
$149$	−10.3457			−0.847557			−0.423778	−	0.905766i	$-0.639296\pi$
$149$	−10.3457			−0.847557			−0.423778	+	0.905766i	$0.639296\pi$
$150$		0			0
$151$	9.34779			0.760712			0.380356	−	0.924840i	$-0.375801\pi$
$151$	9.34779			0.760712			0.380356	+	0.924840i	$0.375801\pi$
$152$			18.1346i			1.47091i
$153$		0			0
$154$	36.1296			2.91140
$155$	4.89282	−	0.270512i	0.393001	−	0.0217280i
$156$		0			0
$157$			0.987506i			0.0788115i	0.999223	+	0.0394058i	$0.0125465\pi$
$157$			0.987506i			0.0788115i	−0.999223	+	0.0394058i	$0.987454\pi$
$158$			2.38098i			0.189420i
$159$		0			0
$160$	0.772768	+	13.9772i	0.0610926	+	1.10500i
$161$	31.1260			2.45308
$162$		0			0
$163$		−	11.0635i		−	0.866559i	−0.901260	−	0.433280i	$-0.857356\pi$
$163$		−	11.0635i		−	0.866559i	0.901260	−	0.433280i	$-0.142644\pi$
$164$	5.59059			0.436551
$165$		0			0
$166$	−13.0559			−1.01333
$167$		−	19.6373i		−	1.51958i	−0.650170	−	0.759789i	$-0.725302\pi$
$167$		−	19.6373i		−	1.51958i	0.650170	−	0.759789i	$-0.274698\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	2.26496	−	0.125224i	0.173715	−	0.00960427i
$171$		0			0
$172$			19.3345i			1.47424i
$173$			15.4783i			1.17679i	0.808572	+	0.588397i	$0.200241\pi$
$173$			15.4783i			1.17679i	−0.808572	+	0.588397i	$0.799759\pi$
$174$		0			0
$175$	2.73916	+	24.6962i	0.207061	+	1.86686i
$176$	−1.77285			−0.133634
$177$		0			0
$178$		−	25.1636i		−	1.88609i
$179$	−3.10238			−0.231883			−0.115941	−	0.993256i	$-0.536988\pi$
$179$	−3.10238			−0.231883			−0.115941	+	0.993256i	$0.536988\pi$
$180$		0			0
$181$	12.8111			0.952239			0.476119	−	0.879381i	$-0.342043\pi$
$181$	12.8111			0.952239			0.476119	+	0.879381i	$0.342043\pi$
$182$		−	11.2329i		−	0.832639i
$183$		0			0
$184$	15.7038			1.15770
$185$	1.02002	+	18.4493i	0.0749932	+	1.35642i
$186$		0			0
$187$			1.44355i			0.105563i
$188$			5.17751i			0.377609i
$189$		0			0
$190$	−2.01809	−	36.5017i	−0.146407	−	2.64811i
$191$	−15.1780			−1.09824			−0.549121	−	0.835743i	$-0.685037\pi$
$191$	−15.1780			−1.09824			−0.549121	+	0.835743i	$0.685037\pi$
$192$		0			0
$193$			0.173496i			0.0124885i	0.999981	+	0.00624427i	$0.00198763\pi$
$193$			0.173496i			0.0124885i	−0.999981	+	0.00624427i	$0.998012\pi$
$194$	−18.9287			−1.35900
$195$		0			0
$196$	55.0213			3.93010
$197$			4.27989i			0.304930i	0.988309	+	0.152465i	$0.0487211\pi$
$197$			4.27989i			0.304930i	−0.988309	+	0.152465i	$0.951279\pi$
$198$		0			0
$199$	−16.6843			−1.18272			−0.591358	−	0.806409i	$-0.701408\pi$
$199$	−16.6843			−1.18272			−0.591358	+	0.806409i	$0.701408\pi$
$200$	1.38196	+	12.4598i	0.0977197	+	0.881039i
$201$		0			0
$202$			12.4461i			0.875704i
$203$		−	11.0246i		−	0.773775i
$204$		0			0
$205$	−4.01447	+	0.221950i	−0.280383	+	0.0155017i
$206$	2.98553			0.208012
$207$		0			0
$208$			0.551191i			0.0382182i
$209$	23.2639			1.60920
$210$		0			0
$211$	−24.3013			−1.67297			−0.836485	−	0.547989i	$-0.815394\pi$
$211$	−24.3013			−1.67297			−0.836485	+	0.547989i	$0.815394\pi$
$212$		−	3.60981i		−	0.247923i
$213$		0			0
$214$	16.9306			1.15735
$215$	−0.767593	−	13.8837i	−0.0523494	−	0.946857i
$216$		0			0
$217$			10.8906i			0.739302i
$218$			31.7196i			2.14833i
$219$		0			0
$220$	−22.3277	+	1.23444i	−1.50533	+	0.0832262i
$221$	0.448809			0.0301902
$222$		0			0
$223$		−	0.821018i		−	0.0549794i	−0.999622	−	0.0274897i	$-0.991249\pi$
$223$		−	0.821018i		−	0.0549794i	0.999622	−	0.0274897i	$-0.00875135\pi$
$224$	−31.1110			−2.07869
$225$		0			0
$226$	−25.3767			−1.68803
$227$		−	6.24591i		−	0.414555i	−0.978282	−	0.207278i	$-0.933540\pi$
$227$		−	6.24591i		−	0.414555i	0.978282	−	0.207278i	$-0.0664604\pi$
$228$		0			0
$229$	−20.5766			−1.35974			−0.679871	−	0.733332i	$-0.737964\pi$
$229$	−20.5766			−1.35974			−0.679871	+	0.733332i	$0.737964\pi$
$230$	−31.6088	+	1.74758i	−2.08423	+	0.115232i
$231$		0			0
$232$		−	5.56215i		−	0.365173i
$233$			5.19402i			0.340271i	0.985421	+	0.170136i	$0.0544206\pi$
$233$			5.19402i			0.340271i	−0.985421	+	0.170136i	$0.945579\pi$
$234$		0			0
$235$	−0.205551	−	3.71785i	−0.0134087	−	0.242526i
$236$	18.2936			1.19081
$237$		0			0
$238$			5.04143i			0.326788i
$239$	−12.3229			−0.797100			−0.398550	−	0.917147i	$-0.630486\pi$
$239$	−12.3229			−0.797100			−0.398550	+	0.917147i	$0.630486\pi$
$240$		0			0
$241$	−2.41597			−0.155626			−0.0778131	−	0.996968i	$-0.524794\pi$
$241$	−2.41597			−0.155626			−0.0778131	+	0.996968i	$0.524794\pi$
$242$			1.47998i			0.0951368i
$243$		0			0
$244$	5.50217			0.352240
$245$	−39.5095	+	2.18439i	−2.52417	+	0.139555i
$246$		0			0
$247$		−	7.23291i		−	0.460219i
$248$			5.49455i			0.348904i
$249$		0			0
$250$	−4.16821	−	24.9255i	−0.263621	−	1.57642i
$251$	−21.6428			−1.36608			−0.683042	−	0.730380i	$-0.739343\pi$
$251$	−21.6428			−1.36608			−0.683042	+	0.730380i	$0.739343\pi$
$252$		0			0
$253$		−	20.1456i		−	1.26654i
$254$	−3.39545			−0.213049
$255$		0			0
$256$	−12.2686			−0.766790
$257$		−	16.9027i		−	1.05436i	−0.849753	−	0.527181i	$-0.823249\pi$
$257$		−	16.9027i		−	1.05436i	0.849753	−	0.527181i	$-0.176751\pi$
$258$		0			0
$259$	−41.0651			−2.55166
$260$	0.383797	+	6.94183i	0.0238021	+	0.430514i
$261$		0			0
$262$			28.3623i			1.75223i
$263$			20.1864i			1.24475i	0.782720	+	0.622374i	$0.213832\pi$
$263$			20.1864i			1.24475i	−0.782720	+	0.622374i	$0.786168\pi$
$264$		0			0
$265$	0.143312	+	2.59212i	0.00880359	+	0.159233i
$266$	81.2466			4.98155
$267$		0			0
$268$			8.51664i			0.520237i
$269$	−29.6277			−1.80643			−0.903215	−	0.429188i	$-0.858800\pi$
$269$	−29.6277			−1.80643			−0.903215	+	0.429188i	$0.858800\pi$
$270$		0			0
$271$	22.2703			1.35282			0.676411	−	0.736524i	$-0.263534\pi$
$271$	22.2703			1.35282			0.676411	+	0.736524i	$0.263534\pi$
$272$		−	0.247380i		−	0.0149996i
$273$		0			0
$274$	24.1399			1.45835
$275$	15.9840	−	1.77285i	0.963871	−	0.106907i
$276$		0			0
$277$		−	1.88512i		−	0.113266i	−0.998395	−	0.0566331i	$-0.981963\pi$
$277$		−	1.88512i		−	0.113266i	0.998395	−	0.0566331i	$-0.0180365\pi$
$278$		−	46.7808i		−	2.80573i
$279$		0			0
$280$	−27.8184	+	1.53801i	−1.66247	+	0.0919138i
$281$	8.84827			0.527843			0.263922	−	0.964544i	$-0.414984\pi$
$281$	8.84827			0.527843			0.263922	+	0.964544i	$0.414984\pi$
$282$		0			0
$283$			24.0219i			1.42795i	0.700169	+	0.713977i	$0.253108\pi$
$283$			24.0219i			1.42795i	−0.700169	+	0.713977i	$0.746892\pi$
$284$	12.7914			0.759030
$285$		0			0
$286$	−7.27022			−0.429897
$287$		−	8.93554i		−	0.527448i
$288$		0			0
$289$	16.7986			0.988151
$290$	0.618977	+	11.1956i	0.0363476	+	0.657428i
$291$		0			0
$292$		−	32.4506i		−	1.89903i
$293$		−	22.6019i		−	1.32042i	−0.751082	−	0.660208i	$-0.770468\pi$
$293$		−	22.6019i		−	1.32042i	0.751082	−	0.660208i	$-0.229532\pi$
$294$		0			0
$295$	−13.1362	+	0.726268i	−0.764818	+	0.0422849i
$296$	−20.7182			−1.20422
$297$		0			0
$298$			23.3851i			1.35466i
$299$	−6.26338			−0.362221
$300$		0			0
$301$	30.9027			1.78120
$302$		−	21.1293i		−	1.21586i
$303$		0			0
$304$	−3.98671			−0.228654
$305$	−3.95098	+	0.218440i	−0.226233	+	0.0125078i
$306$		0			0
$307$		−	2.90858i		−	0.166001i	−0.996549	−	0.0830007i	$-0.973550\pi$
$307$		−	2.90858i		−	0.166001i	0.996549	−	0.0830007i	$-0.0264504\pi$
$308$		−	49.6978i		−	2.83179i
$309$		0			0
$310$	−0.611454	−	11.0595i	−0.0347283	−	0.628139i
$311$	−7.13290			−0.404469			−0.202235	−	0.979337i	$-0.564820\pi$
$311$	−7.13290			−0.404469			−0.202235	+	0.979337i	$0.564820\pi$
$312$		0			0
$313$		−	26.8418i		−	1.51719i	−0.651565	−	0.758593i	$-0.725887\pi$
$313$		−	26.8418i		−	1.51719i	0.651565	−	0.758593i	$-0.274113\pi$
$314$	2.23212			0.125966
$315$		0			0
$316$	3.27514			0.184241
$317$			8.19000i			0.459996i	0.973191	+	0.229998i	$0.0738720\pi$
$317$			8.19000i			0.459996i	−0.973191	+	0.229998i	$0.926128\pi$
$318$		0			0
$319$	−7.13540			−0.399505
$320$	29.1323	−	1.61066i	1.62855	−	0.0900384i
$321$		0			0
$322$		−	70.3560i		−	3.92079i
$323$			3.24620i			0.180623i
$324$		0			0
$325$	−0.551191	−	4.96953i	−0.0305746	−	0.275660i
$326$	−25.0074			−1.38503
$327$		0			0
$328$		−	4.50818i		−	0.248922i
$329$	8.27531			0.456233
$330$		0			0
$331$	−4.75599			−0.261413			−0.130707	−	0.991421i	$-0.541725\pi$
$331$	−4.75599			−0.261413			−0.130707	+	0.991421i	$0.541725\pi$
$332$			17.9589i			0.985622i
$333$		0			0
$334$	−44.3873			−2.42876
$335$	−0.338117	−	6.11560i	−0.0184733	−	0.334131i
$336$		0			0
$337$			4.54361i			0.247506i	0.992313	+	0.123753i	$0.0394930\pi$
$337$			4.54361i			0.247506i	−0.992313	+	0.123753i	$0.960507\pi$
$338$			2.26036i			0.122947i
$339$		0			0
$340$	−0.172251	−	3.11556i	−0.00934165	−	0.168965i
$341$	7.04867			0.381707
$342$		0			0
$343$		−	53.1550i		−	2.87010i
$344$	15.5911			0.840615
$345$		0			0
$346$	34.9865			1.88089
$347$			33.2648i			1.78575i	0.450307	+	0.892874i	$0.351314\pi$
$347$			33.2648i			1.78575i	−0.450307	+	0.892874i	$0.648686\pi$
$348$		0			0
$349$	−19.6460			−1.05163			−0.525813	−	0.850600i	$-0.676239\pi$
$349$	−19.6460			−1.05163			−0.525813	+	0.850600i	$0.676239\pi$
$350$	55.8222	−	6.19148i	2.98382	−	0.330948i
$351$		0			0
$352$			20.1358i			1.07324i
$353$			12.1609i			0.647262i	0.946183	+	0.323631i	$0.104904\pi$
$353$			12.1609i			0.647262i	−0.946183	+	0.323631i	$0.895096\pi$
$354$		0			0
$355$	−9.18520	+	0.507827i	−0.487500	+	0.0269527i
$356$	−34.6136			−1.83452
$357$		0			0
$358$			7.01249i			0.370622i
$359$	−23.5378			−1.24228			−0.621139	−	0.783701i	$-0.713330\pi$
$359$	−23.5378			−1.24228			−0.621139	+	0.783701i	$0.713330\pi$
$360$		0			0
$361$	33.3150			1.75342
$362$		−	28.9576i		−	1.52198i
$363$		0			0
$364$	−15.4513			−0.809871
$365$	1.28831	+	23.3020i	0.0674332	+	1.21968i
$366$		0			0
$367$		−	12.5944i		−	0.657421i	−0.944431	−	0.328710i	$-0.893386\pi$
$367$		−	12.5944i		−	0.657421i	0.944431	−	0.328710i	$-0.106614\pi$
$368$			3.45232i			0.179965i
$369$		0			0
$370$	41.7021	−	2.30561i	2.16799	−	0.119863i
$371$	−5.76963			−0.299544
$372$		0			0
$373$		−	10.6585i		−	0.551875i	−0.961176	−	0.275938i	$-0.911012\pi$
$373$		−	10.6585i		−	0.551875i	0.961176	−	0.275938i	$-0.0889883\pi$
$374$	3.26294			0.168723
$375$		0			0
$376$	4.17508			0.215313
$377$			2.21844i			0.114255i
$378$		0			0
$379$	22.5065			1.15608			0.578040	−	0.816009i	$-0.303818\pi$
$379$	22.5065			1.15608			0.578040	+	0.816009i	$0.303818\pi$
$380$	−50.2096	+	2.77597i	−2.57570	+	0.142404i
$381$		0			0
$382$			34.3077i			1.75534i
$383$		−	6.22399i		−	0.318031i	−0.987276	−	0.159015i	$-0.949168\pi$
$383$		−	6.22399i		−	0.318031i	0.987276	−	0.159015i	$-0.0508320\pi$
$384$		0			0
$385$	1.97304	+	35.6868i	0.100555	+	1.81877i
$386$	0.392164			0.0199606
$387$		0			0
$388$			26.0372i			1.32184i
$389$	−6.49059			−0.329086			−0.164543	−	0.986370i	$-0.552615\pi$
$389$	−6.49059			−0.329086			−0.164543	+	0.986370i	$0.552615\pi$
$390$		0			0
$391$	2.81106			0.142162
$392$		−	44.3685i		−	2.24095i
$393$		0			0
$394$	9.67409			0.487374
$395$	−2.35180	+	0.130025i	−0.118332	+	0.00654228i
$396$		0			0
$397$			13.0832i			0.656628i	0.944569	+	0.328314i	$0.106480\pi$
$397$			13.0832i			0.656628i	−0.944569	+	0.328314i	$0.893520\pi$
$398$			37.7124i			1.89035i
$399$		0			0
$400$	−2.73916	+	0.303811i	−0.136958	+	0.0151906i
$401$	−24.2326			−1.21012			−0.605060	−	0.796180i	$-0.706851\pi$
$401$	−24.2326			−1.21012			−0.605060	+	0.796180i	$0.706851\pi$
$402$		0			0
$403$		−	2.19148i		−	0.109165i
$404$	17.1201			0.851758
$405$		0			0
$406$	−24.9195			−1.23674
$407$			26.5784i			1.31744i
$408$		0			0
$409$	−2.52576			−0.124891			−0.0624454	−	0.998048i	$-0.519890\pi$
$409$	−2.52576			−0.124891			−0.0624454	+	0.998048i	$0.519890\pi$
$410$	0.501687	+	9.07414i	0.0247766	+	0.448140i
$411$		0			0
$412$		−	4.10673i		−	0.202324i
$413$		−	29.2390i		−	1.43876i
$414$		0			0
$415$	−0.712981	−	12.8959i	−0.0349988	−	0.633033i
$416$	6.26036			0.306939
$417$		0			0
$418$		−	52.5849i		−	2.57201i
$419$	29.1917			1.42611			0.713054	−	0.701109i	$-0.247312\pi$
$419$	29.1917			1.42611			0.713054	+	0.701109i	$0.247312\pi$
$420$		0			0
$421$	−22.3719			−1.09034			−0.545169	−	0.838326i	$-0.683534\pi$
$421$	−22.3719			−1.09034			−0.545169	+	0.838326i	$0.683534\pi$
$422$			54.9297i			2.67393i
$423$		0			0
$424$	−2.91091			−0.141366
$425$	0.247380	+	2.23037i	0.0119997	+	0.108189i
$426$		0			0
$427$		−	8.79423i		−	0.425582i
$428$		−	23.2888i		−	1.12571i
$429$		0			0
$430$	−31.3820	+	1.73504i	−1.51338	+	0.0836709i
$431$	26.6111			1.28181			0.640906	−	0.767619i	$-0.278559\pi$
$431$	26.6111			1.28181			0.640906	+	0.767619i	$0.278559\pi$
$432$		0			0
$433$			10.4369i			0.501564i	0.968044	+	0.250782i	$0.0806878\pi$
$433$			10.4369i			0.501564i	−0.968044	+	0.250782i	$0.919312\pi$
$434$	24.6167			1.18164
$435$		0			0
$436$	43.6317			2.08958
$437$		−	45.3025i		−	2.16711i
$438$		0			0
$439$	28.0916			1.34074			0.670370	−	0.742027i	$-0.266135\pi$
$439$	28.0916			1.34074			0.670370	+	0.742027i	$0.266135\pi$
$440$	0.995440	+	18.0048i	0.0474557	+	0.858344i
$441$		0			0
$442$		−	1.01447i		−	0.0482534i
$443$		−	28.9146i		−	1.37378i	−0.726764	−	0.686888i	$-0.758976\pi$
$443$		−	28.9146i		−	1.37378i	0.726764	−	0.686888i	$-0.241024\pi$
$444$		0			0
$445$	24.8552	−	1.37418i	1.17825	−	0.0651426i
$446$	−1.85579			−0.0878744
$447$		0			0
$448$			64.8437i			3.06358i
$449$	27.9652			1.31976			0.659879	−	0.751372i	$-0.270608\pi$
$449$	27.9652			1.31976			0.659879	+	0.751372i	$0.270608\pi$
$450$		0			0
$451$	−5.78331			−0.272325
$452$			34.9068i			1.64188i
$453$		0			0
$454$	−14.1180			−0.662590
$455$	11.0953	−	0.613429i	0.520154	−	0.0287580i
$456$		0			0
$457$			28.7251i			1.34370i	0.740685	+	0.671852i	$0.234501\pi$
$457$			28.7251i			1.34370i	−0.740685	+	0.671852i	$0.765499\pi$
$458$			46.5105i			2.17329i
$459$		0			0
$460$	2.40387	+	43.4793i	0.112081	+	2.02723i
$461$	−5.81017			−0.270607			−0.135303	−	0.990804i	$-0.543201\pi$
$461$	−5.81017			−0.270607			−0.135303	+	0.990804i	$0.543201\pi$
$462$		0			0
$463$		−	27.1743i		−	1.26290i	−0.775418	−	0.631448i	$-0.782461\pi$
$463$		−	27.1743i		−	1.26290i	0.775418	−	0.631448i	$-0.217539\pi$
$464$	1.22278			0.0567663
$465$		0			0
$466$	11.7403			0.543861
$467$			23.1290i			1.07028i	0.844763	+	0.535141i	$0.179742\pi$
$467$			23.1290i			1.07028i	−0.844763	+	0.535141i	$0.820258\pi$
$468$		0			0
$469$	13.6123			0.628558
$470$	−8.40367	+	0.464618i	−0.387632	+	0.0214313i
$471$		0			0
$472$		−	14.7517i		−	0.679002i
$473$		−	20.0010i		−	0.919647i
$474$		0			0
$475$	35.9441	−	3.98671i	1.64923	−	0.182923i
$476$	6.93471			0.317852
$477$		0			0
$478$			27.8541i			1.27402i
$479$	23.3243			1.06571			0.532856	−	0.846206i	$-0.321119\pi$
$479$	23.3243			1.06571			0.532856	+	0.846206i	$0.321119\pi$
$480$		0			0
$481$	8.26338			0.376778
$482$			5.46095i			0.248740i
$483$		0			0
$484$	2.03578			0.0925354
$485$	−1.03369	−	18.6967i	−0.0469376	−	0.848973i
$486$		0			0
$487$			7.23466i			0.327834i	0.986474	+	0.163917i	$0.0524129\pi$
$487$			7.23466i			0.327834i	−0.986474	+	0.163917i	$0.947587\pi$
$488$		−	4.43688i		−	0.200848i
$489$		0			0
$490$	4.93750	+	89.3057i	0.223053	+	4.03442i
$491$	42.9453			1.93809			0.969047	−	0.246874i	$-0.0794035\pi$
$491$	42.9453			1.93809			0.969047	+	0.246874i	$0.0794035\pi$
$492$		0			0
$493$		−	0.995656i		−	0.0448421i
$494$	−16.3490			−0.735575
$495$		0			0
$496$	−1.20792			−0.0542373
$497$		−	20.4447i		−	0.917072i
$498$		0			0
$499$	18.0487			0.807969			0.403985	−	0.914766i	$-0.367625\pi$
$499$	18.0487			0.807969			0.403985	+	0.914766i	$0.367625\pi$
$500$	−34.2860	+	5.73356i	−1.53332	+	0.256412i
$501$		0			0
$502$			48.9205i			2.18343i
$503$		−	10.3252i		−	0.460376i	−0.973146	−	0.230188i	$-0.926066\pi$
$503$		−	10.3252i		−	0.460376i	0.973146	−	0.230188i	$-0.0739342\pi$
$504$		0			0
$505$	−12.2936	+	0.679681i	−0.547057	+	0.0302454i
$506$	−45.5362			−2.02433
$507$		0			0
$508$			4.67058i			0.207224i
$509$	−8.57786			−0.380207			−0.190104	−	0.981764i	$-0.560882\pi$
$509$	−8.57786			−0.380207			−0.190104	+	0.981764i	$0.560882\pi$
$510$		0			0
$511$	−51.8663			−2.29443
$512$		−	6.21458i		−	0.274648i
$513$		0			0
$514$	−38.2062			−1.68520
$515$	0.163040	+	2.94894i	0.00718440	+	0.129946i
$516$		0			0
$517$		−	5.35599i		−	0.235556i
$518$			92.8218i			4.07836i
$519$		0			0
$520$	5.59780	−	0.309489i	0.245480	−	0.0135720i
$521$	−8.44706			−0.370072			−0.185036	−	0.982732i	$-0.559240\pi$
$521$	−8.44706			−0.370072			−0.185036	+	0.982732i	$0.559240\pi$
$522$		0			0
$523$		−	31.5650i		−	1.38024i	−0.723694	−	0.690121i	$-0.757557\pi$
$523$		−	31.5650i		−	1.38024i	0.723694	−	0.690121i	$-0.242443\pi$
$524$	39.0135			1.70431
$525$		0			0
$526$	45.6286			1.98950
$527$			0.983555i			0.0428443i
$528$		0			0
$529$	−16.2300			−0.705651
$530$	5.85912	−	0.323937i	0.254504	−	0.0140709i
$531$		0			0
$532$		−	111.758i		−	4.84533i
$533$			1.79807i			0.0778829i
$534$		0			0
$535$	0.924582	+	16.7232i	0.0399732	+	0.723005i
$536$	6.86771			0.296640
$537$		0			0
$538$			66.9691i			2.88724i
$539$	−56.9181			−2.45163
$540$		0			0
$541$	24.7478			1.06399			0.531995	−	0.846747i	$-0.321442\pi$
$541$	24.7478			1.06399			0.531995	+	0.846747i	$0.321442\pi$
$542$		−	50.3388i		−	2.16224i
$543$		0			0
$544$	−2.80971			−0.120465
$545$	−31.3309	+	1.73221i	−1.34207	+	0.0741997i
$546$		0			0
$547$		−	25.9207i		−	1.10829i	−0.832420	−	0.554145i	$-0.813045\pi$
$547$		−	25.9207i		−	1.10829i	0.832420	−	0.554145i	$-0.186955\pi$
$548$		−	33.2055i		−	1.41847i
$549$		0			0
$550$	−4.00728	−	36.1296i	−0.170871	−	1.54057i
$551$	−16.0458			−0.683573
$552$		0			0
$553$		−	5.23471i		−	0.222603i
$554$	−4.26106			−0.181035
$555$		0			0
$556$	−64.3490			−2.72901
$557$			35.3538i			1.49799i	0.662577	+	0.748993i	$0.269463\pi$
$557$			35.3538i			1.49799i	−0.662577	+	0.748993i	$0.730537\pi$
$558$		0			0
$559$	−6.21844			−0.263012
$560$	−0.338117	−	6.11560i	−0.0142880	−	0.258431i
$561$		0			0
$562$		−	20.0003i		−	0.843660i
$563$		−	22.3919i		−	0.943708i	−0.881677	−	0.471854i	$-0.843585\pi$
$563$		−	22.3919i		−	0.943708i	0.881677	−	0.471854i	$-0.156415\pi$
$564$		0			0
$565$	−1.38582	−	25.0657i	−0.0583020	−	1.05452i
$566$	54.2981			2.28232
$567$		0			0
$568$		−	10.3148i		−	0.432800i
$569$	41.1034			1.72314			0.861572	−	0.507636i	$-0.169480\pi$
$569$	41.1034			1.72314			0.861572	+	0.507636i	$0.169480\pi$
$570$		0			0
$571$	28.3848			1.18787			0.593933	−	0.804514i	$-0.297574\pi$
$571$	28.3848			1.18787			0.593933	+	0.804514i	$0.297574\pi$
$572$			10.0005i			0.418142i
$573$		0			0
$574$	−20.1975			−0.843028
$575$	−3.45232	−	31.1260i	−0.143972	−	1.29805i
$576$		0			0
$577$		−	5.44592i		−	0.226716i	−0.993554	−	0.113358i	$-0.963839\pi$
$577$		−	5.44592i		−	0.226716i	0.993554	−	0.113358i	$-0.0361608\pi$
$578$		−	37.9708i		−	1.57938i
$579$		0			0
$580$	15.4000	−	0.851430i	0.639451	−	0.0353537i
$581$	28.7040			1.19084
$582$		0			0
$583$			3.73425i			0.154657i
$584$	−26.1677			−1.08283
$585$		0			0
$586$	−51.0884			−2.11044
$587$		−	18.7717i		−	0.774790i	−0.921914	−	0.387395i	$-0.873375\pi$
$587$		−	18.7717i		−	0.774790i	0.921914	−	0.387395i	$-0.126625\pi$
$588$		0			0
$589$	15.8508			0.653119
$590$	1.64162	+	29.6925i	0.0675846	+	1.22242i
$591$		0			0
$592$		−	4.55470i		−	0.187197i
$593$			39.9300i			1.63973i	0.572559	+	0.819863i	$0.305951\pi$
$593$			39.9300i			1.63973i	−0.572559	+	0.819863i	$0.694049\pi$
$594$		0			0
$595$	−4.97965	+	0.275313i	−0.204146	+	0.0112867i
$596$	32.1672			1.31762
$597$		0			0
$598$			14.1575i			0.578943i
$599$	36.7310			1.50079			0.750393	−	0.660992i	$-0.229864\pi$
$599$	36.7310			1.50079			0.750393	+	0.660992i	$0.229864\pi$
$600$		0			0
$601$	−25.7376			−1.04986			−0.524930	−	0.851146i	$-0.675908\pi$
$601$	−25.7376			−1.04986			−0.524930	+	0.851146i	$0.675908\pi$
$602$		−	69.8512i		−	2.84692i
$603$		0			0
$604$	−29.0643			−1.18261
$605$	−1.46184	+	0.0808218i	−0.0594324	+	0.00328587i
$606$		0			0
$607$		−	3.95975i		−	0.160721i	−0.996766	−	0.0803606i	$-0.974393\pi$
$607$		−	3.95975i		−	0.160721i	0.996766	−	0.0803606i	$-0.0256072\pi$
$608$			45.2806i			1.83637i
$609$		0			0
$610$	0.493753	+	8.93063i	0.0199915	+	0.361591i
$611$	−1.66521			−0.0673673
$612$		0			0
$613$			14.0707i			0.568311i	0.958778	+	0.284156i	$0.0917132\pi$
$613$			14.0707i			0.568311i	−0.958778	+	0.284156i	$0.908287\pi$
$614$	−6.57443			−0.265322
$615$		0			0
$616$	−40.0756			−1.61469
$617$		−	31.6852i		−	1.27560i	−0.770204	−	0.637798i	$-0.779845\pi$
$617$		−	31.6852i		−	1.27560i	0.770204	−	0.637798i	$-0.220155\pi$
$618$		0			0
$619$	−12.4566			−0.500673			−0.250337	−	0.968159i	$-0.580541\pi$
$619$	−12.4566			−0.500673			−0.250337	+	0.968159i	$0.580541\pi$
$620$	−15.2128	+	0.841081i	−0.610963	+	0.0337786i
$621$		0			0
$622$			16.1229i			0.646469i
$623$			55.3236i			2.21649i
$624$		0			0
$625$	24.3924	−	5.47831i	0.975695	−	0.219133i
$626$	−60.6720			−2.42494
$627$		0			0
$628$		−	3.07037i		−	0.122521i
$629$	−3.70868			−0.147875
$630$		0			0
$631$	−14.8500			−0.591167			−0.295584	−	0.955317i	$-0.595514\pi$
$631$	−14.8500			−0.591167			−0.295584	+	0.955317i	$0.595514\pi$
$632$		−	2.64103i		−	0.105054i
$633$		0			0
$634$	18.5123			0.735219
$635$	−0.185425	−	3.35384i	−0.00735838	−	0.133093i
$636$		0			0
$637$			17.6962i			0.701149i
$638$			16.1286i			0.638536i
$639$		0			0
$640$	−2.09512	−	37.8950i	−0.0828170	−	1.49793i
$641$	−13.2878			−0.524837			−0.262418	−	0.964954i	$-0.584520\pi$
$641$	−13.2878			−0.524837			−0.262418	+	0.964954i	$0.584520\pi$
$642$		0			0
$643$			18.7409i			0.739069i	0.929217	+	0.369535i	$0.120483\pi$
$643$			18.7409i			0.739069i	−0.929217	+	0.369535i	$0.879517\pi$
$644$	−96.7777			−3.81358
$645$		0			0
$646$	7.33757			0.288693
$647$			30.9106i			1.21522i	0.794236	+	0.607610i	$0.207871\pi$
$647$			30.9106i			1.21522i	−0.794236	+	0.607610i	$0.792129\pi$
$648$		0			0
$649$	−18.9242			−0.742840
$650$	−11.2329	+	1.24589i	−0.440591	+	0.0488678i
$651$		0			0
$652$			34.3988i			1.34716i
$653$			1.99040i			0.0778903i	0.999241	+	0.0389452i	$0.0123998\pi$
$653$			1.99040i			0.0778903i	−0.999241	+	0.0389452i	$0.987600\pi$
$654$		0			0
$655$	−28.0147	+	1.54886i	−1.09462	+	0.0605191i
$656$	0.991078			0.0386951
$657$		0			0
$658$		−	18.7052i		−	0.729204i
$659$	38.5954			1.50346			0.751731	−	0.659470i	$-0.229219\pi$
$659$	38.5954			1.50346			0.751731	+	0.659470i	$0.229219\pi$
$660$		0			0
$661$	−10.3150			−0.401206			−0.200603	−	0.979673i	$-0.564290\pi$
$661$	−10.3150			−0.401206			−0.200603	+	0.979673i	$0.564290\pi$
$662$			10.7503i			0.417820i
$663$		0			0
$664$	14.4818			0.562004
$665$	4.43688	+	80.2510i	0.172055	+	3.11200i
$666$		0			0
$667$			13.8949i			0.538014i
$668$			61.0566i			2.36235i
$669$		0			0
$670$	−13.8235	+	0.764265i	−0.534046	+	0.0295261i
$671$	−5.69185			−0.219731
$672$		0			0
$673$			19.1024i			0.736343i	0.929758	+	0.368171i	$0.120016\pi$
$673$			19.1024i			0.736343i	−0.929758	+	0.368171i	$0.879984\pi$
$674$	10.2702			0.395592
$675$		0			0
$676$	3.10922			0.119585
$677$		−	18.2482i		−	0.701336i	−0.936500	−	0.350668i	$-0.885955\pi$
$677$		−	18.2482i		−	0.701336i	0.936500	−	0.350668i	$-0.114045\pi$
$678$		0			0
$679$	41.6157			1.59706
$680$	−2.51234	+	0.138901i	−0.0963440	+	0.00532662i
$681$		0			0
$682$		−	15.9325i		−	0.610088i
$683$		−	45.2264i		−	1.73054i	−0.501306	−	0.865270i	$-0.667147\pi$
$683$		−	45.2264i		−	1.73054i	0.501306	−	0.865270i	$-0.332853\pi$
$684$		0			0
$685$	1.31828	+	23.8441i	0.0503689	+	0.911035i
$686$	−120.149			−4.58732
$687$		0			0
$688$			3.42755i			0.130674i
$689$	1.16100			0.0442307
$690$		0			0
$691$	12.4293			0.472831			0.236416	−	0.971652i	$-0.424027\pi$
$691$	12.4293			0.472831			0.236416	+	0.971652i	$0.424027\pi$
$692$		−	48.1255i		−	1.82946i
$693$		0			0
$694$	75.1903			2.85419
$695$	46.2075	−	2.55470i	1.75275	−	0.0969053i
$696$		0			0
$697$		−	0.806989i		−	0.0305669i
$698$			44.4070i			1.68083i
$699$		0			0
$700$	−8.51664	−	76.7859i	−0.321899	−	2.90223i
$701$	30.9611			1.16939			0.584693	−	0.811254i	$-0.301215\pi$
$701$	30.9611			1.16939			0.584693	+	0.811254i	$0.301215\pi$
$702$		0			0
$703$			59.7683i			2.25420i
$704$	41.9685			1.58175
$705$		0			0
$706$	27.4881			1.03453
$707$		−	27.3634i		−	1.02911i
$708$		0			0
$709$	−2.20069			−0.0826486			−0.0413243	−	0.999146i	$-0.513158\pi$
$709$	−2.20069			−0.0826486			−0.0413243	+	0.999146i	$0.513158\pi$
$710$	1.14787	+	20.7619i	0.0430789	+	0.779178i
$711$		0			0
$712$			27.9120i			1.04604i
$713$		−	13.7261i		−	0.514045i
$714$		0			0
$715$	−0.397027	−	7.18113i	−0.0148480	−	0.268559i
$716$	9.64599			0.360487
$717$		0			0
$718$			53.2038i			1.98555i
$719$	−44.5913			−1.66297			−0.831487	−	0.555543i	$-0.812510\pi$
$719$	−44.5913			−1.66297			−0.831487	+	0.555543i	$0.812510\pi$
$720$		0			0
$721$	−6.56386			−0.244451
$722$		−	75.3038i		−	2.80252i
$723$		0			0
$724$	−39.8324			−1.48036
$725$	−11.0246	+	1.22278i	−0.409443	+	0.0454130i
$726$		0			0
$727$			34.7808i			1.28995i	0.764204	+	0.644974i	$0.223132\pi$
$727$			34.7808i			1.28995i	−0.764204	+	0.644974i	$0.776868\pi$
$728$			12.4598i			0.461790i
$729$		0			0
$730$	52.6708	−	2.91204i	1.94944	−	0.107780i
$731$	2.79089			0.103225
$732$		0			0
$733$		−	31.0158i		−	1.14560i	−0.819697	−	0.572798i	$-0.805858\pi$
$733$		−	31.0158i		−	1.14560i	0.819697	−	0.572798i	$-0.194142\pi$
$734$	−28.4678			−1.05077
$735$		0			0
$736$	39.2110			1.44534
$737$		−	8.81023i		−	0.324529i
$738$		0			0
$739$	−37.9029			−1.39428			−0.697141	−	0.716934i	$-0.745545\pi$
$739$	−37.9029			−1.39428			−0.697141	+	0.716934i	$0.745545\pi$
$740$	−3.17146	−	57.3630i	−0.116585	−	2.10870i
$741$		0			0
$742$			13.0414i			0.478766i
$743$		−	14.6939i		−	0.539066i	−0.962991	−	0.269533i	$-0.913131\pi$
$743$		−	14.6939i		−	0.539066i	0.962991	−	0.269533i	$-0.0868694\pi$
$744$		0			0
$745$	−23.0985	+	1.27706i	−0.846264	+	0.0467879i
$746$	−24.0920			−0.882070
$747$		0			0
$748$		−	4.48832i		−	0.164109i
$749$	−37.2230			−1.36010
$750$		0			0
$751$	−32.5622			−1.18821			−0.594106	−	0.804387i	$-0.702494\pi$
$751$	−32.5622			−1.18821			−0.594106	+	0.804387i	$0.702494\pi$
$752$			0.917849i			0.0334705i
$753$		0			0
$754$	5.01447			0.182616
$755$	20.8704	−	1.15387i	0.759552	−	0.0419938i
$756$		0			0
$757$			15.2365i			0.553779i	0.960902	+	0.276889i	$0.0893035\pi$
$757$			15.2365i			0.553779i	−0.960902	+	0.276889i	$0.910696\pi$
$758$		−	50.8727i		−	1.84778i
$759$		0			0
$760$	2.23850	+	40.4884i	0.0811991	+	1.46867i
$761$	−51.5327			−1.86806			−0.934030	−	0.357194i	$-0.883734\pi$
$761$	−51.5327			−1.86806			−0.934030	+	0.357194i	$0.883734\pi$
$762$		0			0
$763$		−	69.7374i		−	2.52466i
$764$	47.1918			1.70734
$765$		0			0
$766$	−14.0684			−0.508314
$767$			5.88365i			0.212446i
$768$		0			0
$769$	−28.7148			−1.03548			−0.517741	−	0.855538i	$-0.673227\pi$
$769$	−28.7148			−1.03548			−0.517741	+	0.855538i	$0.673227\pi$
$770$	80.6650	−	4.45977i	2.90696	−	0.160719i
$771$		0			0
$772$		−	0.539439i		−	0.0194148i
$773$			34.5120i			1.24131i	0.784084	+	0.620655i	$0.213133\pi$
$773$			34.5120i			1.24131i	−0.784084	+	0.620655i	$0.786867\pi$
$774$		0			0
$775$	10.8906	−	1.20792i	0.391202	−	0.0433898i
$776$	20.9960			0.753714
$777$		0			0
$778$			14.6711i			0.525983i
$779$	−13.0053			−0.465962
$780$		0			0
$781$	−13.2323			−0.473491
$782$		−	6.35401i		−	0.227219i
$783$		0			0
$784$	9.75398			0.348356
$785$	0.121896	+	2.20476i	0.00435065	+	0.0786914i
$786$		0			0
$787$		−	34.2046i		−	1.21926i	−0.792685	−	0.609631i	$-0.791318\pi$
$787$		−	34.2046i		−	1.21926i	0.792685	−	0.609631i	$-0.208682\pi$
$788$		−	13.3071i		−	0.474047i
$789$		0			0
$790$	0.293904	+	5.31591i	0.0104566	+	0.189132i
$791$	55.7922			1.98374
$792$		0			0
$793$			1.76963i			0.0628414i
$794$	29.5728			1.04950
$795$		0			0
$796$	51.8750			1.83866
$797$			42.9365i			1.52089i	0.649402	+	0.760445i	$0.275019\pi$
$797$			42.9365i			1.52089i	−0.649402	+	0.760445i	$0.724981\pi$
$798$		0			0
$799$	0.747362			0.0264398
$800$	3.45065	+	31.1110i	0.121999	+	1.09994i
$801$		0			0
$802$			54.7744i			1.93415i
$803$			33.5692i			1.18463i
$804$		0			0
$805$	69.4938	−	3.84214i	2.44934	−	0.135418i
$806$	−4.95352			−0.174480
$807$		0			0
$808$		−	13.8055i		−	0.485674i
$809$	−8.42320			−0.296144			−0.148072	−	0.988977i	$-0.547307\pi$
$809$	−8.42320			−0.296144			−0.148072	+	0.988977i	$0.547307\pi$
$810$		0			0
$811$	39.8090			1.39788			0.698941	−	0.715180i	$-0.253655\pi$
$811$	39.8090			1.39788			0.698941	+	0.715180i	$0.253655\pi$
$812$			34.2779i			1.20292i
$813$		0			0
$814$	60.0766			2.10569
$815$	−1.36566	−	24.7010i	−0.0478369	−	0.865238i
$816$		0			0
$817$		−	44.9774i		−	1.57356i
$818$			5.70913i			0.199615i
$819$		0			0
$820$	12.4819	−	0.690092i	0.435886	−	0.0240991i
$821$	29.3494			1.02430			0.512151	−	0.858895i	$-0.328849\pi$
$821$	29.3494			1.02430			0.512151	+	0.858895i	$0.328849\pi$
$822$		0			0
$823$		−	4.65419i		−	0.162235i	−0.996705	−	0.0811174i	$-0.974151\pi$
$823$		−	4.65419i		−	0.162235i	0.996705	−	0.0811174i	$-0.0258489\pi$
$824$	−3.31161			−0.115365
$825$		0			0
$826$	−66.0905			−2.29958
$827$		−	53.8430i		−	1.87231i	−0.351593	−	0.936153i	$-0.614360\pi$
$827$		−	53.8430i		−	1.87231i	0.351593	−	0.936153i	$-0.385640\pi$
$828$		0			0
$829$	4.58070			0.159094			0.0795471	−	0.996831i	$-0.474653\pi$
$829$	4.58070			0.159094			0.0795471	+	0.996831i	$0.474653\pi$
$830$	−29.1493	+	1.61159i	−1.01179	+	0.0559392i
$831$		0			0
$832$		−	13.0483i		−	0.452367i
$833$		−	7.94221i		−	0.275181i
$834$		0			0
$835$	−2.42399	−	43.8433i	−0.0838857	−	1.51726i
$836$	−72.3327			−2.50168
$837$		0			0
$838$		−	65.9837i		−	2.27937i
$839$	21.2754			0.734509			0.367254	−	0.930121i	$-0.380298\pi$
$839$	21.2754			0.734509			0.367254	+	0.930121i	$0.380298\pi$
$840$		0			0
$841$	−24.0785			−0.830294
$842$			50.5684i			1.74270i
$843$		0			0
$844$	75.5581			2.60082
$845$	−2.23266	+	0.123438i	−0.0768058	+	0.00424640i
$846$		0			0
$847$		−	3.25382i		−	0.111803i
$848$		−	0.639934i		−	0.0219754i
$849$		0			0
$850$	5.04143	−	0.559166i	0.172920	−	0.0191792i
$851$	51.7567			1.77420
$852$		0			0
$853$		−	15.5689i		−	0.533070i	−0.963825	−	0.266535i	$-0.914121\pi$
$853$		−	15.5689i		−	0.533070i	0.963825	−	0.266535i	$-0.0858789\pi$
$854$	−19.8781			−0.680215
$855$		0			0
$856$	−18.7798			−0.641880
$857$		−	18.5524i		−	0.633737i	−0.948469	−	0.316869i	$-0.897369\pi$
$857$		−	18.5524i		−	0.633737i	0.948469	−	0.316869i	$-0.102631\pi$
$858$		0			0
$859$	26.2980			0.897275			0.448638	−	0.893714i	$-0.351909\pi$
$859$	26.2980			0.897275			0.448638	+	0.893714i	$0.351909\pi$
$860$	2.38662	+	43.1673i	0.0813829	+	1.47199i
$861$		0			0
$862$		−	60.1506i		−	2.04874i
$863$			0.537842i			0.0183083i	0.999958	+	0.00915417i	$0.00291390\pi$
$863$			0.537842i			0.0183083i	−0.999958	+	0.00915417i	$0.997086\pi$
$864$		0			0
$865$	1.91062	+	34.5578i	0.0649629	+	1.17500i
$866$	23.5911			0.801658
$867$		0			0
$868$		−	33.8613i		−	1.14933i
$869$	−3.38804			−0.114931
$870$		0			0
$871$	−2.73916			−0.0928128
$872$		−	35.1841i		−	1.19148i
$873$		0			0
$874$	−102.400			−3.46373
$875$	9.16406	+	54.8000i	0.309802	+	1.85258i
$876$		0			0
$877$		−	49.9065i		−	1.68522i	−0.538523	−	0.842611i	$-0.681018\pi$
$877$		−	49.9065i		−	1.68522i	0.538523	−	0.842611i	$-0.318982\pi$
$878$		−	63.4972i		−	2.14293i
$879$		0			0
$880$	−3.95817	+	0.218838i	−0.133430	+	0.00737702i
$881$	−41.0327			−1.38243			−0.691213	−	0.722651i	$-0.742924\pi$
$881$	−41.0327			−1.38243			−0.691213	+	0.722651i	$0.742924\pi$
$882$		0			0
$883$			6.59753i			0.222025i	0.993819	+	0.111012i	$0.0354093\pi$
$883$			6.59753i			0.222025i	−0.993819	+	0.111012i	$0.964591\pi$
$884$	−1.39545			−0.0469339
$885$		0			0
$886$	−65.3574			−2.19573
$887$			9.02521i			0.303037i	0.988454	+	0.151519i	$0.0484163\pi$
$887$			9.02521i			0.303037i	−0.988454	+	0.151519i	$0.951584\pi$
$888$		0			0
$889$	7.46508			0.250371
$890$	−3.10615	−	56.1817i	−0.104118	−	1.88321i
$891$		0			0
$892$			2.55273i			0.0854716i
$893$		−	12.0443i		−	0.403048i
$894$		0			0
$895$	−6.92656	+	0.382952i	−0.231529	+	0.0128007i
$896$	84.3480			2.81787
$897$		0			0
$898$		−	63.2113i		−	2.10939i
$899$	−4.86166			−0.162145
$900$		0			0
$901$	−0.521069			−0.0173593
$902$			13.0723i			0.435262i
$903$		0			0
$904$	28.1484			0.936201
$905$	28.6027	−	1.58138i	0.950787	−	0.0525667i
$906$		0			0
$907$		−	15.5850i		−	0.517493i	−0.965945	−	0.258746i	$-0.916691\pi$
$907$		−	15.5850i		−	0.517493i	0.965945	−	0.258746i	$-0.0833094\pi$
$908$			19.4199i			0.644472i
$909$		0			0
$910$	−1.38657	−	25.0792i	−0.0459644	−	0.831369i
$911$	−2.86303			−0.0948564			−0.0474282	−	0.998875i	$-0.515103\pi$
$911$	−2.86303			−0.0948564			−0.0474282	+	0.998875i	$0.515103\pi$
$912$		0			0
$913$		−	18.5780i		−	0.614841i
$914$	64.9291			2.14766
$915$		0			0
$916$	63.9772			2.11387
$917$		−	62.3560i		−	2.05918i
$918$		0			0
$919$	53.0874			1.75119			0.875596	−	0.483045i	$-0.160469\pi$
$919$	53.0874			1.75119			0.875596	+	0.483045i	$0.160469\pi$
$920$	35.0612	−	1.93845i	1.15593	−	0.0639087i
$921$		0			0
$922$			13.1331i			0.432514i
$923$			4.11402i			0.135415i
$924$		0			0
$925$	4.55470	+	41.0651i	0.149758	+	1.35021i
$926$	−61.4236			−2.01851
$927$		0			0
$928$		−	13.8882i		−	0.455903i
$929$	25.0925			0.823259			0.411630	−	0.911351i	$-0.364960\pi$
$929$	25.0925			0.823259			0.411630	+	0.911351i	$0.364960\pi$
$930$		0			0
$931$	−127.995			−4.19486
$932$		−	16.1493i		−	0.528989i
$933$		0			0
$934$	52.2798			1.71065
$935$	0.178189	+	3.22296i	0.00582742	+	0.105402i
$936$		0			0
$937$		−	54.5029i		−	1.78053i	−0.455441	−	0.890266i	$-0.650518\pi$
$937$		−	54.5029i		−	1.78053i	0.455441	−	0.890266i	$-0.349482\pi$
$938$		−	30.7687i		−	1.00463i
$939$		0			0
$940$	0.639103	+	11.5596i	0.0208452	+	0.377033i
$941$	−32.3538			−1.05470			−0.527351	−	0.849647i	$-0.676815\pi$
$941$	−32.3538			−1.05470			−0.527351	+	0.849647i	$0.676815\pi$
$942$		0			0
$943$			11.2620i			0.366741i
$944$	3.24301			0.105551
$945$		0			0
$946$	−45.2094			−1.46989
$947$			36.3069i			1.17981i	0.807471	+	0.589907i	$0.200836\pi$
$947$			36.3069i			1.17981i	−0.807471	+	0.589907i	$0.799164\pi$
$948$		0			0
$949$	10.4369			0.338795
$950$	−9.01140	−	81.2466i	−0.292368	−	2.63599i
$951$		0			0
$952$		−	5.59206i		−	0.181240i
$953$			13.3176i			0.431399i	0.976460	+	0.215699i	$0.0692031\pi$
$953$			13.3176i			0.431399i	−0.976460	+	0.215699i	$0.930797\pi$
$954$		0			0
$955$	−33.8873	+	1.87355i	−1.09657	+	0.0606266i
$956$	38.3145			1.23918
$957$		0			0
$958$		−	52.7212i		−	1.70334i
$959$	−53.0730			−1.71382
$960$		0			0
$961$	−26.1974			−0.845078
$962$		−	18.6782i		−	0.602210i
$963$		0			0
$964$	7.51177			0.241938
$965$	0.0214161	+	0.387358i	0.000689408	+	0.0124695i
$966$		0			0
$967$			46.9352i			1.50933i	0.656108	+	0.754667i	$0.272202\pi$
$967$			46.9352i			1.50933i	−0.656108	+	0.754667i	$0.727798\pi$
$968$		−	1.64162i		−	0.0527638i
$969$		0			0
$970$	−42.2612	+	2.33652i	−1.35693	+	0.0750211i
$971$	22.5340			0.723151			0.361575	−	0.932343i	$-0.382239\pi$
$971$	22.5340			0.723151			0.361575	+	0.932343i	$0.382239\pi$
$972$		0			0
$973$			102.850i			3.29723i
$974$	16.3529			0.523981
$975$		0			0
$976$	0.975404			0.0312219
$977$			59.9345i			1.91747i	0.284296	+	0.958737i	$0.408240\pi$
$977$			59.9345i			1.91747i	−0.284296	+	0.958737i	$0.591760\pi$
$978$		0			0
$979$	35.8068			1.14439
$980$	122.844	−	6.79174i	3.92410	−	0.216954i
$981$		0			0
$982$		−	97.0718i		−	3.09769i
$983$		−	52.0879i		−	1.66135i	−0.556760	−	0.830673i	$-0.687956\pi$
$983$		−	52.0879i		−	1.66135i	0.556760	−	0.830673i	$-0.312044\pi$
$984$		0			0
$985$	0.528302	+	9.55553i	0.0168331	+	0.304465i
$986$	−2.25054			−0.0716718
$987$		0			0
$988$			22.4887i			0.715461i
$989$	−38.9485			−1.23849
$990$		0			0
$991$	18.6973			0.593940			0.296970	−	0.954887i	$-0.404024\pi$
$991$	18.6973			0.593940			0.296970	+	0.954887i	$0.404024\pi$
$992$			13.7194i			0.435592i
$993$		0			0
$994$	−46.2124			−1.46577
$995$	−37.2503	+	2.05948i	−1.18091	+	0.0652898i
$996$		0			0
$997$			18.9805i			0.601118i	0.953763	+	0.300559i	$0.0971732\pi$
$997$			18.9805i			0.601118i	−0.953763	+	0.300559i	$0.902827\pi$
$998$		−	40.7965i		−	1.29139i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.c.469.2		10
3.2	odd	2		195.2.c.b.79.9	yes	10
5.2	odd	4		2925.2.a.bl.1.5		5
5.3	odd	4		2925.2.a.bm.1.1		5
5.4	even	2	inner	585.2.c.c.469.9		10
12.11	even	2		3120.2.l.p.1249.6		10
15.2	even	4		975.2.a.r.1.1		5
15.8	even	4		975.2.a.s.1.5		5
15.14	odd	2		195.2.c.b.79.2	✓	10
60.59	even	2		3120.2.l.p.1249.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.c.b.79.2	✓	10	15.14	odd	2
195.2.c.b.79.9	yes	10	3.2	odd	2
585.2.c.c.469.2		10	1.1	even	1	trivial
585.2.c.c.469.9		10	5.4	even	2	inner
975.2.a.r.1.1		5	15.2	even	4
975.2.a.s.1.5		5	15.8	even	4
2925.2.a.bl.1.5		5	5.2	odd	4
2925.2.a.bm.1.1		5	5.3	odd	4
3120.2.l.p.1249.1		10	60.59	even	2
3120.2.l.p.1249.6		10	12.11	even	2

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.26036i q^{2} -3.10922 q^{4} +(2.23266 - 0.123438i) q^{5} +4.96953i q^{7} +2.50723i q^{8} +O(q^{10})\)	\(q-2.26036i q^{2} -3.10922 q^{4} +(2.23266 - 0.123438i) q^{5} +4.96953i q^{7} +2.50723i q^{8} +(-0.279015 - 5.04661i) q^{10} +3.21640 q^{11} -1.00000i q^{13} +11.2329 q^{14} -0.551191 q^{16} +0.448809i q^{17} +7.23291 q^{19} +(-6.94183 + 0.383797i) q^{20} -7.27022i q^{22} -6.26338i q^{23} +(4.96953 - 0.551191i) q^{25} -2.26036 q^{26} -15.4513i q^{28} -2.21844 q^{29} +2.19148 q^{31} +6.26036i q^{32} +1.01447 q^{34} +(0.613429 + 11.0953i) q^{35} +8.26338i q^{37} -16.3490i q^{38} +(0.309489 + 5.59780i) q^{40} -1.79807 q^{41} -6.21844i q^{43} -10.0005 q^{44} -14.1575 q^{46} -1.66521i q^{47} -17.6962 q^{49} +(-1.24589 - 11.2329i) q^{50} +3.10922i q^{52} +1.16100i q^{53} +(7.18113 - 0.397027i) q^{55} -12.4598 q^{56} +5.01447i q^{58} -5.88365 q^{59} -1.76963 q^{61} -4.95352i q^{62} +13.0483 q^{64} +(-0.123438 - 2.23266i) q^{65} -2.73916i q^{67} -1.39545i q^{68} +(25.0792 - 1.38657i) q^{70} -4.11402 q^{71} +10.4369i q^{73} +18.6782 q^{74} -22.4887 q^{76} +15.9840i q^{77} -1.05336 q^{79} +(-1.23062 + 0.0680380i) q^{80} +4.06428i q^{82} -5.77601i q^{83} +(0.0554002 + 1.00204i) q^{85} -14.0559 q^{86} +8.06428i q^{88} +11.1326 q^{89} +4.96953 q^{91} +19.4742i q^{92} -3.76398 q^{94} +(16.1486 - 0.892818i) q^{95} -8.37418i q^{97} +39.9997i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) \) 10 * q - 12 * q^4 + 2 * q^5	\( 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) \) 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

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