LMFDB - Embedded newform 525.3.e.c.349.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(349,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("525.349");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.e (of order $2$, degree $1$, not 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.10
Character	$\chi$	$=$	525.349
Dual form			525.3.e.c.349.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.50369i q^{2} -1.73205 q^{3} -8.27584 q^{4} -6.06857i q^{6} +(2.03600 - 6.69736i) q^{7} -14.9812i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+3.50369i q^{2} -1.73205 q^{3} -8.27584 q^{4} -6.06857i q^{6} +(2.03600 - 6.69736i) q^{7} -14.9812i q^{8} +3.00000 q^{9} -2.03112 q^{11} +14.3342 q^{12} +18.0174 q^{13} +(23.4655 + 7.13352i) q^{14} +19.3861 q^{16} +1.07289 q^{17} +10.5111i q^{18} +28.7852i q^{19} +(-3.52646 + 11.6002i) q^{21} -7.11640i q^{22} -24.8710i q^{23} +25.9482i q^{24} +63.1275i q^{26} -5.19615 q^{27} +(-16.8496 + 55.4263i) q^{28} +38.4300 q^{29} +44.0899i q^{31} +7.99812i q^{32} +3.51800 q^{33} +3.75906i q^{34} -24.8275 q^{36} +37.2832i q^{37} -100.855 q^{38} -31.2071 q^{39} -49.9206i q^{41} +(-40.6434 - 12.3556i) q^{42} +9.58871i q^{43} +16.8092 q^{44} +87.1402 q^{46} +55.6978 q^{47} -33.5777 q^{48} +(-40.7094 - 27.2717i) q^{49} -1.85829 q^{51} -149.109 q^{52} -57.4656i q^{53} -18.2057i q^{54} +(-100.335 - 30.5018i) q^{56} -49.8575i q^{57} +134.647i q^{58} +101.697i q^{59} +31.9530i q^{61} -154.477 q^{62} +(6.10801 - 20.0921i) q^{63} +49.5215 q^{64} +12.3260i q^{66} +95.7318i q^{67} -8.87902 q^{68} +43.0778i q^{69} -25.8039 q^{71} -44.9436i q^{72} +95.6803 q^{73} -130.629 q^{74} -238.222i q^{76} +(-4.13536 + 13.6031i) q^{77} -109.340i q^{78} -28.1212 q^{79} +9.00000 q^{81} +174.906 q^{82} +103.374 q^{83} +(29.1844 - 96.0012i) q^{84} -33.5959 q^{86} -66.5628 q^{87} +30.4286i q^{88} +29.3629i q^{89} +(36.6835 - 120.669i) q^{91} +205.828i q^{92} -76.3659i q^{93} +195.148i q^{94} -13.8531i q^{96} -67.6473 q^{97} +(95.5515 - 142.633i) q^{98} -6.09335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 88 q^{4} + 72 q^{9}+O(q^{10}) $ 24 * q - 88 * q^4 + 72 * q^9	$ 24 q - 88 q^{4} + 72 q^{9} - 32 q^{11} + 80 q^{14} + 184 q^{16} + 72 q^{21} - 208 q^{29} - 264 q^{36} + 48 q^{39} - 384 q^{44} + 400 q^{46} - 120 q^{49} + 48 q^{51} - 736 q^{56} + 40 q^{64} + 64 q^{71} - 368 q^{74} - 240 q^{79} + 216 q^{81} - 216 q^{84} + 800 q^{86} + 48 q^{91} - 96 q^{99}+O(q^{100}) $ 24 * q - 88 * q^4 + 72 * q^9 - 32 * q^11 + 80 * q^14 + 184 * q^16 + 72 * q^21 - 208 * q^29 - 264 * q^36 + 48 * q^39 - 384 * q^44 + 400 * q^46 - 120 * q^49 + 48 * q^51 - 736 * q^56 + 40 * q^64 + 64 * q^71 - 368 * q^74 - 240 * q^79 + 216 * q^81 - 216 * q^84 + 800 * q^86 + 48 * q^91 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			3.50369i			1.75184i	0.482452	+	0.875922i	$0.339746\pi$
$2$			3.50369i			1.75184i	−0.482452	+	0.875922i	$0.660254\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−8.27584			−2.06896
$5$		0			0
$5$		0			0
$6$		−	6.06857i		−	1.01143i
$7$	2.03600	−	6.69736i	0.290857	−	0.956766i
$7$	2.03600	−	6.69736i	0.290857	−	0.956766i
$8$		−	14.9812i		−	1.87265i
$9$	3.00000			0.333333
$10$		0			0
$11$	−2.03112			−0.184647			−0.0923235	−	0.995729i	$-0.529429\pi$
$11$	−2.03112			−0.184647			−0.0923235	+	0.995729i	$0.529429\pi$
$12$	14.3342			1.19451
$13$	18.0174			1.38596			0.692978	−	0.720958i	$-0.256298\pi$
$13$	18.0174			1.38596			0.692978	+	0.720958i	$0.256298\pi$
$14$	23.4655	+	7.13352i	1.67611	+	0.509537i
$15$		0			0
$16$	19.3861			1.21163
$17$	1.07289			0.0631109			0.0315555	−	0.999502i	$-0.489954\pi$
$17$	1.07289			0.0631109			0.0315555	+	0.999502i	$0.489954\pi$
$18$			10.5111i			0.583948i
$19$			28.7852i			1.51501i	0.652828	+	0.757506i	$0.273583\pi$
$19$			28.7852i			1.51501i	−0.652828	+	0.757506i	$0.726417\pi$
$20$		0			0
$21$	−3.52646	+	11.6002i	−0.167927	+	0.552389i
$22$		−	7.11640i		−	0.323473i
$23$		−	24.8710i		−	1.08135i	−0.841232	−	0.540674i	$-0.818169\pi$
$23$		−	24.8710i		−	1.08135i	0.841232	−	0.540674i	$-0.181831\pi$
$24$			25.9482i			1.08117i
$25$		0			0
$26$			63.1275i			2.42798i
$27$	−5.19615			−0.192450
$28$	−16.8496	+	55.4263i	−0.601772	+	1.97951i
$29$	38.4300			1.32517			0.662587	−	0.748985i	$-0.269458\pi$
$29$	38.4300			1.32517			0.662587	+	0.748985i	$0.269458\pi$
$30$		0			0
$31$			44.0899i			1.42225i	0.703064	+	0.711127i	$0.251815\pi$
$31$			44.0899i			1.42225i	−0.703064	+	0.711127i	$0.748185\pi$
$32$			7.99812i			0.249941i
$33$	3.51800			0.106606
$34$			3.75906i			0.110561i
$35$		0			0
$36$	−24.8275			−0.689653
$37$			37.2832i			1.00765i	0.863804	+	0.503827i	$0.168075\pi$
$37$			37.2832i			1.00765i	−0.863804	+	0.503827i	$0.831925\pi$
$38$	−100.855			−2.65407
$39$	−31.2071			−0.800182
$40$		0			0
$41$		−	49.9206i		−	1.21758i	−0.793333	−	0.608788i	$-0.791656\pi$
$41$		−	49.9206i		−	1.21758i	0.793333	−	0.608788i	$-0.208344\pi$
$42$	−40.6434	−	12.3556i	−0.967700	−	0.294181i
$43$			9.58871i			0.222993i	0.993765	+	0.111497i	$0.0355644\pi$
$43$			9.58871i			0.222993i	−0.993765	+	0.111497i	$0.964436\pi$
$44$	16.8092			0.382027
$45$		0			0
$46$	87.1402			1.89435
$47$	55.6978			1.18506			0.592529	−	0.805549i	$-0.298129\pi$
$47$	55.6978			1.18506			0.592529	+	0.805549i	$0.298129\pi$
$48$	−33.5777			−0.699536
$49$	−40.7094	−	27.2717i	−0.830804	−	0.556565i
$50$		0			0
$51$	−1.85829			−0.0364371
$52$	−149.109			−2.86749
$53$		−	57.4656i		−	1.08426i	−0.840296	−	0.542128i	$-0.817619\pi$
$53$		−	57.4656i		−	1.08426i	0.840296	−	0.542128i	$-0.182381\pi$
$54$		−	18.2057i		−	0.337143i
$55$		0			0
$56$	−100.335	−	30.5018i	−1.79169	−	0.544674i
$57$		−	49.8575i		−	0.874693i
$58$			134.647i			2.32150i
$59$			101.697i			1.72368i	0.507178	+	0.861841i	$0.330689\pi$
$59$			101.697i			1.72368i	−0.507178	+	0.861841i	$0.669311\pi$
$60$		0			0
$61$			31.9530i			0.523819i	0.965092	+	0.261910i	$0.0843523\pi$
$61$			31.9530i			0.523819i	−0.965092	+	0.261910i	$0.915648\pi$
$62$	−154.477			−2.49157
$63$	6.10801	−	20.0921i	0.0969525	−	0.318922i
$64$	49.5215			0.773774
$65$		0			0
$66$			12.3260i			0.186757i
$67$			95.7318i			1.42883i	0.699721	+	0.714416i	$0.253308\pi$
$67$			95.7318i			1.42883i	−0.699721	+	0.714416i	$0.746692\pi$
$68$	−8.87902			−0.130574
$69$			43.0778i			0.624316i
$70$		0			0
$71$	−25.8039			−0.363435			−0.181718	−	0.983351i	$-0.558166\pi$
$71$	−25.8039			−0.363435			−0.181718	+	0.983351i	$0.558166\pi$
$72$		−	44.9436i		−	0.624217i
$73$	95.6803			1.31069			0.655345	−	0.755330i	$-0.272523\pi$
$73$	95.6803			1.31069			0.655345	+	0.755330i	$0.272523\pi$
$74$	−130.629			−1.76525
$75$		0			0
$76$		−	238.222i		−	3.13450i
$77$	−4.13536	+	13.6031i	−0.0537059	+	0.176664i
$78$		−	109.340i		−	1.40180i
$79$	−28.1212			−0.355965			−0.177982	−	0.984034i	$-0.556957\pi$
$79$	−28.1212			−0.355965			−0.177982	+	0.984034i	$0.556957\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	174.906			2.13301
$83$	103.374			1.24547			0.622733	−	0.782435i	$-0.286022\pi$
$83$	103.374			1.24547			0.622733	+	0.782435i	$0.286022\pi$
$84$	29.1844	−	96.0012i	0.347433	−	1.14287i
$85$		0			0
$86$	−33.5959			−0.390650
$87$	−66.5628			−0.765090
$88$			30.4286i			0.345779i
$89$			29.3629i			0.329920i	0.986300	+	0.164960i	$0.0527496\pi$
$89$			29.3629i			0.329920i	−0.986300	+	0.164960i	$0.947250\pi$
$90$		0			0
$91$	36.6835	−	120.669i	0.403116	−	1.32604i
$92$			205.828i			2.23726i
$93$		−	76.3659i		−	0.821138i
$94$			195.148i			2.07604i
$95$		0			0
$96$		−	13.8531i		−	0.144304i
$97$	−67.6473			−0.697395			−0.348697	−	0.937235i	$-0.613376\pi$
$97$	−67.6473			−0.697395			−0.348697	+	0.937235i	$0.613376\pi$
$98$	95.5515	−	142.633i	0.975016	−	1.45544i
$99$	−6.09335			−0.0615490
$100$		0			0
$101$		−	73.3301i		−	0.726040i	−0.931781	−	0.363020i	$-0.881746\pi$
$101$		−	73.3301i		−	0.726040i	0.931781	−	0.363020i	$-0.118254\pi$
$102$		−	6.51088i		−	0.0638321i
$103$	57.3431			0.556729			0.278365	−	0.960476i	$-0.410208\pi$
$103$	57.3431			0.556729			0.278365	+	0.960476i	$0.410208\pi$
$104$		−	269.923i		−	2.59541i
$105$		0			0
$106$	201.342			1.89945
$107$		−	39.8399i		−	0.372336i	−0.982518	−	0.186168i	$-0.940393\pi$
$107$		−	39.8399i		−	0.372336i	0.982518	−	0.186168i	$-0.0596068\pi$
$108$	43.0025			0.398171
$109$	185.052			1.69773			0.848863	−	0.528613i	$-0.177288\pi$
$109$	185.052			1.69773			0.848863	+	0.528613i	$0.177288\pi$
$110$		0			0
$111$		−	64.5764i		−	0.581770i
$112$	39.4702	−	129.836i	0.352412	−	1.15925i
$113$			120.716i			1.06829i	0.845394	+	0.534143i	$0.179366\pi$
$113$			120.716i			1.06829i	−0.845394	+	0.534143i	$0.820634\pi$
$114$	174.685			1.53233
$115$		0			0
$116$	−318.041			−2.74173
$117$	54.0523			0.461986
$118$	−356.316			−3.01962
$119$	2.18440	−	7.18551i	0.0183563	−	0.0603824i
$120$		0			0
$121$	−116.875			−0.965906
$122$	−111.953			−0.917650
$123$			86.4651i			0.702968i
$124$		−	364.880i		−	2.94258i
$125$		0			0
$126$	70.3964	+	21.4006i	0.558702	+	0.169846i
$127$		−	83.5096i		−	0.657556i	−0.944407	−	0.328778i	$-0.893363\pi$
$127$		−	83.5096i		−	0.657556i	0.944407	−	0.328778i	$-0.106637\pi$
$128$			205.501i			1.60547i
$129$		−	16.6081i		−	0.128745i
$130$		0			0
$131$			198.248i			1.51334i	0.653796	+	0.756671i	$0.273175\pi$
$131$			198.248i			1.51334i	−0.653796	+	0.756671i	$0.726825\pi$
$132$	−29.1144			−0.220563
$133$	192.785	+	58.6068i	1.44951	+	0.440653i
$134$	−335.414			−2.50309
$135$		0			0
$136$		−	16.0731i		−	0.118185i
$137$		−	24.1635i		−	0.176376i	−0.996104	−	0.0881880i	$-0.971892\pi$
$137$		−	24.1635i		−	0.176376i	0.996104	−	0.0881880i	$-0.0281076\pi$
$138$	−150.931			−1.09371
$139$			61.6370i			0.443432i	0.975111	+	0.221716i	$0.0711658\pi$
$139$			61.6370i			0.443432i	−0.975111	+	0.221716i	$0.928834\pi$
$140$		0			0
$141$	−96.4714			−0.684194
$142$		−	90.4088i		−	0.636682i
$143$	−36.5955			−0.255913
$144$	58.1583			0.403877
$145$		0			0
$146$			335.234i			2.29612i
$147$	70.5107	+	47.2360i	0.479665	+	0.321333i
$148$		−	308.550i		−	2.08480i
$149$	28.8271			0.193470			0.0967351	−	0.995310i	$-0.469160\pi$
$149$	28.8271			0.193470			0.0967351	+	0.995310i	$0.469160\pi$
$150$		0			0
$151$	248.311			1.64445			0.822223	−	0.569166i	$-0.192734\pi$
$151$	248.311			1.64445			0.822223	+	0.569166i	$0.192734\pi$
$152$	431.237			2.83709
$153$	3.21866			0.0210370
$154$	−47.6611	−	14.4890i	−0.309488	−	0.0940844i
$155$		0			0
$156$	258.265			1.65554
$157$	41.3848			0.263597			0.131799	−	0.991277i	$-0.457925\pi$
$157$	41.3848			0.263597			0.131799	+	0.991277i	$0.457925\pi$
$158$		−	98.5280i		−	0.623595i
$159$			99.5334i			0.625996i
$160$		0			0
$161$	−166.570	−	50.6374i	−1.03460	−	0.314518i
$162$			31.5332i			0.194649i
$163$			51.8103i			0.317855i	0.987290	+	0.158927i	$0.0508036\pi$
$163$			51.8103i			0.317855i	−0.987290	+	0.158927i	$0.949196\pi$
$164$			413.135i			2.51912i
$165$		0			0
$166$			362.189i			2.18186i
$167$	41.9711			0.251324			0.125662	−	0.992073i	$-0.459895\pi$
$167$	41.9711			0.251324			0.125662	+	0.992073i	$0.459895\pi$
$168$	173.785	+	52.8306i	1.03443	+	0.314468i
$169$	155.628			0.920876
$170$		0			0
$171$			86.3557i			0.505004i
$172$		−	79.3546i		−	0.461364i
$173$	98.0199			0.566589			0.283295	−	0.959033i	$-0.408573\pi$
$173$	98.0199			0.566589			0.283295	+	0.959033i	$0.408573\pi$
$174$		−	233.215i		−	1.34032i
$175$		0			0
$176$	−39.3754			−0.223724
$177$		−	176.145i		−	0.995168i
$178$	−102.879			−0.577969
$179$	−68.5830			−0.383145			−0.191573	−	0.981478i	$-0.561359\pi$
$179$	−68.5830			−0.383145			−0.191573	+	0.981478i	$0.561359\pi$
$180$		0			0
$181$			105.124i			0.580798i	0.956906	+	0.290399i	$0.0937880\pi$
$181$			105.124i			0.580798i	−0.956906	+	0.290399i	$0.906212\pi$
$182$	422.788	+	128.528i	2.32301	+	0.706196i
$183$		−	55.3442i		−	0.302427i
$184$	−372.597			−2.02499
$185$		0			0
$186$	267.562			1.43851
$187$	−2.17916			−0.0116532
$188$	−460.946			−2.45184
$189$	−10.5794	+	34.8005i	−0.0559755	+	0.184130i
$190$		0			0
$191$	229.803			1.20316			0.601579	−	0.798813i	$-0.294539\pi$
$191$	229.803			1.20316			0.601579	+	0.798813i	$0.294539\pi$
$192$	−85.7738			−0.446739
$193$		−	111.530i		−	0.577877i	−0.957348	−	0.288939i	$-0.906698\pi$
$193$		−	111.530i		−	0.577877i	0.957348	−	0.288939i	$-0.0933023\pi$
$194$		−	237.015i		−	1.22173i
$195$		0			0
$196$	336.904	+	225.696i	1.71890	+	1.15151i
$197$		−	172.865i		−	0.877486i	−0.898613	−	0.438743i	$-0.855424\pi$
$197$		−	172.865i		−	0.877486i	0.898613	−	0.438743i	$-0.144576\pi$
$198$		−	21.3492i		−	0.107824i
$199$			117.944i			0.592685i	0.955082	+	0.296343i	$0.0957670\pi$
$199$			117.944i			0.592685i	−0.955082	+	0.296343i	$0.904233\pi$
$200$		0			0
$201$		−	165.812i		−	0.824937i
$202$	256.926			1.27191
$203$	78.2437	−	257.380i	0.385437	−	1.26788i
$204$	15.3789			0.0753869
$205$		0			0
$206$			200.912i			0.975303i
$207$		−	74.6130i		−	0.360449i
$208$	349.288			1.67927
$209$		−	58.4662i		−	0.279742i
$210$		0			0
$211$	−391.940			−1.85754			−0.928769	−	0.370660i	$-0.879131\pi$
$211$	−391.940			−1.85754			−0.928769	+	0.370660i	$0.879131\pi$
$212$			475.576i			2.24328i
$213$	44.6936			0.209829
$214$	139.587			0.652274
$215$		0			0
$216$			77.8446i			0.360392i
$217$	295.286	+	89.7670i	1.36076	+	0.413673i
$218$			648.365i			2.97415i
$219$	−165.723			−0.756727
$220$		0			0
$221$	19.3306			0.0874690
$222$	226.256			1.01917
$223$	96.2512			0.431620			0.215810	−	0.976435i	$-0.430761\pi$
$223$	96.2512			0.431620			0.215810	+	0.976435i	$0.430761\pi$
$224$	53.5663	+	16.2842i	0.239135	+	0.0726972i
$225$		0			0
$226$	−422.952			−1.87147
$227$	−91.6962			−0.403948			−0.201974	−	0.979391i	$-0.564736\pi$
$227$	−91.6962			−0.403948			−0.201974	+	0.979391i	$0.564736\pi$
$228$			412.612i			1.80970i
$229$		−	323.972i		−	1.41472i	−0.706852	−	0.707361i	$-0.749885\pi$
$229$		−	323.972i		−	1.41472i	0.706852	−	0.707361i	$-0.250115\pi$
$230$		0			0
$231$	7.16265	−	23.5613i	0.0310071	−	0.101997i
$232$		−	575.728i		−	2.48159i
$233$		−	182.918i		−	0.785055i	−0.919740	−	0.392528i	$-0.871601\pi$
$233$		−	182.918i		−	0.785055i	0.919740	−	0.392528i	$-0.128399\pi$
$234$			189.382i			0.809327i
$235$		0			0
$236$		−	841.630i		−	3.56623i
$237$	48.7074			0.205516
$238$	25.1758	+	7.65345i	0.105781	+	0.0321573i
$239$	42.9240			0.179598			0.0897992	−	0.995960i	$-0.471377\pi$
$239$	42.9240			0.179598			0.0897992	+	0.995960i	$0.471377\pi$
$240$		0			0
$241$		−	99.8942i		−	0.414499i	−0.978288	−	0.207249i	$-0.933549\pi$
$241$		−	99.8942i		−	0.414499i	0.978288	−	0.207249i	$-0.0664511\pi$
$242$		−	409.492i		−	1.69212i
$243$	−15.5885			−0.0641500
$244$		−	264.438i		−	1.08376i
$245$		0			0
$246$	−302.947			−1.23149
$247$			518.636i			2.09974i
$248$	660.519			2.66338
$249$	−179.048			−0.719070
$250$		0			0
$251$		−	404.945i		−	1.61333i	−0.591011	−	0.806663i	$-0.701271\pi$
$251$		−	404.945i		−	1.61333i	0.591011	−	0.806663i	$-0.298729\pi$
$252$	−50.5489	+	166.279i	−0.200591	+	0.659837i
$253$			50.5159i			0.199668i
$254$	292.592			1.15194
$255$		0			0
$256$	−521.924			−2.03876
$257$	−102.697			−0.399600			−0.199800	−	0.979837i	$-0.564029\pi$
$257$	−102.697			−0.399600			−0.199800	+	0.979837i	$0.564029\pi$
$258$	58.1897			0.225542
$259$	249.699	+	75.9087i	0.964090	+	0.293084i
$260$		0			0
$261$	115.290			0.441725
$262$	−694.598			−2.65114
$263$		−	281.479i		−	1.07026i	−0.844769	−	0.535132i	$-0.820262\pi$
$263$		−	281.479i		−	1.07026i	0.844769	−	0.535132i	$-0.179738\pi$
$264$		−	52.7038i		−	0.199636i
$265$		0			0
$266$	−205.340	+	675.460i	−0.771955	+	2.53932i
$267$		−	50.8581i		−	0.190480i
$268$		−	792.260i		−	2.95620i
$269$			176.412i			0.655808i	0.944711	+	0.327904i	$0.106342\pi$
$269$			176.412i			0.655808i	−0.944711	+	0.327904i	$0.893658\pi$
$270$		0			0
$271$		−	306.041i		−	1.12930i	−0.825330	−	0.564651i	$-0.809011\pi$
$271$		−	306.041i		−	1.12930i	0.825330	−	0.564651i	$-0.190989\pi$
$272$	20.7991			0.0764672
$273$	−63.5378	+	209.005i	−0.232739	+	0.765588i
$274$	84.6614			0.308983
$275$		0			0
$276$		−	356.505i		−	1.29169i
$277$			43.7993i			0.158120i	0.996870	+	0.0790601i	$0.0251919\pi$
$277$			43.7993i			0.158120i	−0.996870	+	0.0790601i	$0.974808\pi$
$278$	−215.957			−0.776824
$279$			132.270i			0.474084i
$280$		0			0
$281$	499.502			1.77759			0.888794	−	0.458307i	$-0.151544\pi$
$281$	499.502			1.77759			0.888794	+	0.458307i	$0.151544\pi$
$282$		−	338.006i		−	1.19860i
$283$	−122.672			−0.433470			−0.216735	−	0.976231i	$-0.569541\pi$
$283$	−122.672			−0.433470			−0.216735	+	0.976231i	$0.569541\pi$
$284$	213.549			0.751932
$285$		0			0
$286$		−	128.219i		−	0.448319i
$287$	−334.337	−	101.639i	−1.16494	−	0.354141i
$288$			23.9944i			0.0833137i
$289$	−287.849			−0.996017
$290$		0			0
$291$	117.169			0.402641
$292$	−791.835			−2.71176
$293$	123.871			0.422769			0.211385	−	0.977403i	$-0.432203\pi$
$293$	123.871			0.422769			0.211385	+	0.977403i	$0.432203\pi$
$294$	−165.500	+	247.048i	−0.562926	+	0.840298i
$295$		0			0
$296$	558.547			1.88698
$297$	10.5540			0.0355353
$298$			101.001i			0.338930i
$299$		−	448.112i		−	1.49870i
$300$		0			0
$301$	64.2191	+	19.5226i	0.213352	+	0.0648593i
$302$			870.006i			2.88081i
$303$			127.011i			0.419180i
$304$			558.034i			1.83564i
$305$		0			0
$306$			11.2772i			0.0368535i
$307$	225.577			0.734778			0.367389	−	0.930067i	$-0.380252\pi$
$307$	225.577			0.734778			0.367389	+	0.930067i	$0.380252\pi$
$308$	34.2235	−	112.577i	0.111115	−	0.365511i
$309$	−99.3211			−0.321428
$310$		0			0
$311$		−	52.9648i		−	0.170305i	−0.996368	−	0.0851525i	$-0.972862\pi$
$311$		−	52.9648i		−	0.170305i	0.996368	−	0.0851525i	$-0.0271377\pi$
$312$			467.520i			1.49846i
$313$	−374.563			−1.19669			−0.598343	−	0.801240i	$-0.704174\pi$
$313$	−374.563			−1.19669			−0.598343	+	0.801240i	$0.704174\pi$
$314$			144.999i			0.461782i
$315$		0			0
$316$	232.727			0.736477
$317$			12.0550i			0.0380283i	0.999819	+	0.0190142i	$0.00605276\pi$
$317$			12.0550i			0.0380283i	−0.999819	+	0.0190142i	$0.993947\pi$
$318$	−348.734			−1.09665
$319$	−78.0559			−0.244689
$320$		0			0
$321$			69.0048i			0.214968i
$322$	177.418	−	583.610i	0.550987	−	1.81245i
$323$			30.8833i			0.0956138i
$324$	−74.4825			−0.229884
$325$		0			0
$326$	−181.527			−0.556832
$327$	−320.520			−0.980183
$328$	−747.871			−2.28009
$329$	113.401	−	373.028i	0.344683	−	1.13382i
$330$		0			0
$331$	−376.184			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$331$	−376.184			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$332$	−855.503			−2.57682
$333$			111.850i			0.335885i
$334$			147.054i			0.440281i
$335$		0			0
$336$	−68.3643	+	224.882i	−0.203465	+	0.669293i
$337$		−	108.973i		−	0.323363i	−0.986843	−	0.161682i	$-0.948308\pi$
$337$		−	108.973i		−	0.323363i	0.986843	−	0.161682i	$-0.0516917\pi$
$338$			545.272i			1.61323i
$339$		−	209.087i		−	0.616775i
$340$		0			0
$341$		−	89.5516i		−	0.262615i
$342$	−302.564			−0.884689
$343$	−265.533	+	217.120i	−0.774148	+	0.633004i
$344$	143.650			0.417588
$345$		0			0
$346$			343.431i			0.992576i
$347$		−	206.351i		−	0.594671i	−0.954773	−	0.297335i	$-0.903902\pi$
$347$		−	206.351i		−	0.594671i	0.954773	−	0.297335i	$-0.0960979\pi$
$348$	550.863			1.58294
$349$		−	373.475i		−	1.07013i	−0.844811	−	0.535064i	$-0.820287\pi$
$349$		−	373.475i		−	1.07013i	0.844811	−	0.535064i	$-0.179713\pi$
$350$		0			0
$351$	−93.6213			−0.266727
$352$		−	16.2451i		−	0.0461509i
$353$	−646.142			−1.83043			−0.915216	−	0.402964i	$-0.867980\pi$
$353$	−646.142			−1.83043			−0.915216	+	0.402964i	$0.867980\pi$
$354$	617.157			1.74338
$355$		0			0
$356$		−	243.003i		−	0.682592i
$357$	−3.78349	+	12.4457i	−0.0105980	+	0.0348618i
$358$		−	240.294i		−	0.671211i
$359$	−175.261			−0.488192			−0.244096	−	0.969751i	$-0.578491\pi$
$359$	−175.261			−0.488192			−0.244096	+	0.969751i	$0.578491\pi$
$360$		0			0
$361$	−467.590			−1.29526
$362$	−368.323			−1.01747
$363$	202.433			0.557666
$364$	−303.587	+	998.640i	−0.834030	+	2.74352i
$365$		0			0
$366$	193.909			0.529805
$367$	−106.477			−0.290127			−0.145063	−	0.989422i	$-0.546339\pi$
$367$	−106.477			−0.290127			−0.145063	+	0.989422i	$0.546339\pi$
$368$		−	482.152i		−	1.31020i
$369$		−	149.762i		−	0.405859i
$370$		0			0
$371$	−384.868	−	117.000i	−1.03738	−	0.315364i
$372$			631.991i			1.69890i
$373$		−	223.324i		−	0.598723i	−0.954140	−	0.299362i	$-0.903226\pi$
$373$		−	223.324i		−	0.598723i	0.954140	−	0.299362i	$-0.0967737\pi$
$374$		−	7.63508i		−	0.0204147i
$375$		0			0
$376$		−	834.419i		−	2.21920i
$377$	692.411			1.83663
$378$	−121.930	−	37.0668i	−0.322567	−	0.0980604i
$379$	−119.075			−0.314183			−0.157092	−	0.987584i	$-0.550212\pi$
$379$	−119.075			−0.314183			−0.157092	+	0.987584i	$0.550212\pi$
$380$		0			0
$381$			144.643i			0.379640i
$382$			805.159i			2.10775i
$383$	−494.637			−1.29148			−0.645740	−	0.763557i	$-0.723451\pi$
$383$	−494.637			−1.29148			−0.645740	+	0.763557i	$0.723451\pi$
$384$		−	355.937i		−	0.926920i
$385$		0			0
$386$	390.767			1.01235
$387$			28.7661i			0.0743311i
$388$	559.838			1.44288
$389$	270.578			0.695574			0.347787	−	0.937574i	$-0.386933\pi$
$389$	270.578			0.695574			0.347787	+	0.937574i	$0.386933\pi$
$390$		0			0
$391$		−	26.6837i		−	0.0682448i
$392$	−408.563	+	609.875i	−1.04225	+	1.55580i
$393$		−	343.375i		−	0.873728i
$394$	605.664			1.53722
$395$		0			0
$396$	50.4276			0.127342
$397$	−37.1881			−0.0936727			−0.0468364	−	0.998903i	$-0.514914\pi$
$397$	−37.1881			−0.0936727			−0.0468364	+	0.998903i	$0.514914\pi$
$398$	−413.240			−1.03829
$399$	−333.914	−	101.510i	−0.836877	−	0.254411i
$400$		0			0
$401$	−36.7102			−0.0915467			−0.0457733	−	0.998952i	$-0.514575\pi$
$401$	−36.7102			−0.0915467			−0.0457733	+	0.998952i	$0.514575\pi$
$402$	580.955			1.44516
$403$			794.386i			1.97118i
$404$			606.868i			1.50215i
$405$		0			0
$406$	901.780	+	274.141i	2.22113	+	0.675225i
$407$		−	75.7266i		−	0.186060i
$408$			27.8394i			0.0682339i
$409$		−	495.325i		−	1.21106i	−0.795821	−	0.605532i	$-0.792960\pi$
$409$		−	495.325i		−	1.21106i	0.795821	−	0.605532i	$-0.207040\pi$
$410$		0			0
$411$			41.8524i			0.101831i
$412$	−474.562			−1.15185
$413$	681.104	+	207.056i	1.64916	+	0.501346i
$414$	261.421			0.631451
$415$		0			0
$416$			144.106i			0.346408i
$417$		−	106.758i		−	0.256016i
$418$	204.847			0.490065
$419$			269.297i			0.642713i	0.946958	+	0.321357i	$0.104139\pi$
$419$			269.297i			0.642713i	−0.946958	+	0.321357i	$0.895861\pi$
$420$		0			0
$421$	756.722			1.79744			0.898719	−	0.438524i	$-0.144499\pi$
$421$	756.722			1.79744			0.898719	+	0.438524i	$0.144499\pi$
$422$		−	1373.24i		−	3.25412i
$423$	167.093			0.395020
$424$	−860.904			−2.03043
$425$		0			0
$426$			156.593i			0.367588i
$427$	214.001	+	65.0563i	0.501173	+	0.152357i
$428$			329.709i			0.770347i
$429$	63.3853			0.147751
$430$		0			0
$431$	185.182			0.429657			0.214828	−	0.976652i	$-0.431081\pi$
$431$	185.182			0.429657			0.214828	+	0.976652i	$0.431081\pi$
$432$	−100.733			−0.233179
$433$	642.846			1.48463			0.742317	−	0.670049i	$-0.233727\pi$
$433$	642.846			1.48463			0.742317	+	0.670049i	$0.233727\pi$
$434$	−314.516	+	1034.59i	−0.724691	+	2.38385i
$435$		0			0
$436$	−1531.46			−3.51253
$437$	715.918			1.63826
$438$		−	580.643i		−	1.32567i
$439$			464.239i			1.05749i	0.848780	+	0.528745i	$0.177337\pi$
$439$			464.239i			1.05749i	−0.848780	+	0.528745i	$0.822663\pi$
$440$		0			0
$441$	−122.128	−	81.8151i	−0.276935	−	0.185522i
$442$			67.7286i			0.153232i
$443$			115.228i			0.260109i	0.991507	+	0.130054i	$0.0415152\pi$
$443$			115.228i			0.260109i	−0.991507	+	0.130054i	$0.958485\pi$
$444$			534.424i			1.20366i
$445$		0			0
$446$			337.234i			0.756130i
$447$	−49.9299			−0.111700
$448$	100.826	−	331.664i	0.225058	−	0.740321i
$449$	−333.955			−0.743774			−0.371887	−	0.928278i	$-0.621289\pi$
$449$	−333.955			−0.743774			−0.371887	+	0.928278i	$0.621289\pi$
$450$		0			0
$451$			101.395i			0.224822i
$452$		−	999.028i		−	2.21024i
$453$	−430.088			−0.949421
$454$		−	321.275i		−	0.707654i
$455$		0			0
$456$	−746.925			−1.63799
$457$			354.152i			0.774949i	0.921880	+	0.387474i	$0.126652\pi$
$457$			354.152i			0.774949i	−0.921880	+	0.387474i	$0.873348\pi$
$458$	1135.10			2.47837
$459$	−5.57488			−0.0121457
$460$		0			0
$461$		−	128.906i		−	0.279623i	−0.990178	−	0.139811i	$-0.955350\pi$
$461$		−	128.906i		−	0.279623i	0.990178	−	0.139811i	$-0.0446497\pi$
$462$	82.5515	+	25.0957i	0.178683	+	0.0543197i
$463$			302.175i			0.652645i	0.945259	+	0.326322i	$0.105810\pi$
$463$			302.175i			0.652645i	−0.945259	+	0.326322i	$0.894190\pi$
$464$	745.009			1.60562
$465$		0			0
$466$	640.887			1.37530
$467$	−808.227			−1.73068			−0.865339	−	0.501186i	$-0.832897\pi$
$467$	−808.227			−1.73068			−0.865339	+	0.501186i	$0.832897\pi$
$468$	−447.328			−0.955829
$469$	641.151	+	194.910i	1.36706	+	0.415587i
$470$		0			0
$471$	−71.6805			−0.152188
$472$	1523.55			3.22785
$473$		−	19.4758i		−	0.0411750i
$474$			170.656i			0.360033i
$475$		0			0
$476$	−18.0777	+	59.4661i	−0.0379784	+	0.124929i
$477$		−	172.397i		−	0.361419i
$478$			150.392i			0.314628i
$479$			48.8836i			0.102053i	0.998697	+	0.0510267i	$0.0162494\pi$
$479$			48.8836i			0.102053i	−0.998697	+	0.0510267i	$0.983751\pi$
$480$		0			0
$481$			671.748i			1.39657i
$482$	349.998			0.726137
$483$	288.508	+	87.7066i	0.597325	+	0.181587i
$484$	967.235			1.99842
$485$		0			0
$486$		−	54.6171i		−	0.112381i
$487$			334.433i			0.686720i	0.939204	+	0.343360i	$0.111565\pi$
$487$			334.433i			0.686720i	−0.939204	+	0.343360i	$0.888435\pi$
$488$	478.694			0.980930
$489$		−	89.7381i		−	0.183514i
$490$		0			0
$491$	−549.151			−1.11843			−0.559217	−	0.829021i	$-0.688898\pi$
$491$	−549.151			−1.11843			−0.559217	+	0.829021i	$0.688898\pi$
$492$		−	715.571i		−	1.45441i
$493$	41.2310			0.0836329
$494$	−1817.14			−3.67842
$495$		0			0
$496$			854.731i			1.72325i
$497$	−52.5368	+	172.818i	−0.105708	+	0.347722i
$498$		−	627.330i		−	1.25970i
$499$	462.450			0.926754			0.463377	−	0.886161i	$-0.346638\pi$
$499$	462.450			0.926754			0.463377	+	0.886161i	$0.346638\pi$
$500$		0			0
$501$	−72.6961			−0.145102
$502$	1418.80			2.82630
$503$	−676.817			−1.34556			−0.672781	−	0.739842i	$-0.734900\pi$
$503$	−676.817			−1.34556			−0.672781	+	0.739842i	$0.734900\pi$
$504$	−301.004	−	91.5053i	−0.597229	−	0.181558i
$505$		0			0
$506$	−176.992			−0.349786
$507$	−269.556			−0.531668
$508$			691.112i			1.36046i
$509$			31.5959i			0.0620744i	0.999518	+	0.0310372i	$0.00988104\pi$
$509$			31.5959i			0.0620744i	−0.999518	+	0.0310372i	$0.990119\pi$
$510$		0			0
$511$	194.805	−	640.806i	0.381224	−	1.25402i
$512$		−	1006.66i		−	1.96613i
$513$		−	149.572i		−	0.291564i
$514$		−	359.819i		−	0.700036i
$515$		0			0
$516$			137.446i			0.266369i
$517$	−113.129			−0.218817
$518$	−265.961	+	874.869i	−0.513437	+	1.68894i
$519$	−169.775			−0.327120
$520$		0			0
$521$			793.420i			1.52288i	0.648236	+	0.761440i	$0.275507\pi$
$521$			793.420i			1.52288i	−0.648236	+	0.761440i	$0.724493\pi$
$522$			403.941i			0.773833i
$523$	−593.508			−1.13481			−0.567407	−	0.823438i	$-0.692053\pi$
$523$	−593.508			−1.13481			−0.567407	+	0.823438i	$0.692053\pi$
$524$		−	1640.67i		−	3.13104i
$525$		0			0
$526$	986.216			1.87494
$527$			47.3034i			0.0897597i
$528$	68.2003			0.129167
$529$	−89.5666			−0.169313
$530$		0			0
$531$			305.092i			0.574561i
$532$	−1595.46	−	485.020i	−2.99898	−	0.911692i
$533$		−	899.442i		−	1.68751i
$534$	178.191			0.333691
$535$		0			0
$536$	1434.18			2.67570
$537$	118.789			0.221209
$538$	−618.094			−1.14887
$539$	82.6855	+	55.3920i	0.153405	+	0.102768i
$540$		0			0
$541$	217.690			0.402385			0.201192	−	0.979552i	$-0.435518\pi$
$541$	217.690			0.402385			0.201192	+	0.979552i	$0.435518\pi$
$542$	1072.27			1.97836
$543$		−	182.081i		−	0.335324i
$544$			8.58106i			0.0157740i
$545$		0			0
$546$	−732.290	−	222.617i	−1.34119	−	0.407723i
$547$		−	137.891i		−	0.252085i	−0.992025	−	0.126043i	$-0.959772\pi$
$547$		−	137.891i		−	0.252085i	0.992025	−	0.126043i	$-0.0402276\pi$
$548$			199.973i			0.364915i
$549$			95.8589i			0.174606i
$550$		0			0
$551$			1106.22i			2.00766i
$552$	645.358			1.16913
$553$	−57.2549	+	188.338i	−0.103535	+	0.340575i
$554$	−153.459			−0.277002
$555$		0			0
$556$		−	510.098i		−	0.917442i
$557$		−	316.337i		−	0.567930i	−0.958835	−	0.283965i	$-0.908350\pi$
$557$		−	316.337i		−	0.567930i	0.958835	−	0.283965i	$-0.0916500\pi$
$558$	−463.431			−0.830522
$559$			172.764i			0.309059i
$560$		0			0
$561$	3.77441			0.00672800
$562$			1750.10i			3.11406i
$563$	151.482			0.269063			0.134531	−	0.990909i	$-0.457047\pi$
$563$	151.482			0.269063			0.134531	+	0.990909i	$0.457047\pi$
$564$	798.381			1.41557
$565$		0			0
$566$		−	429.804i		−	0.759371i
$567$	18.3240	−	60.2763i	0.0323175	−	0.106307i
$568$			386.573i			0.680586i
$569$	213.993			0.376086			0.188043	−	0.982161i	$-0.439786\pi$
$569$	213.993			0.376086			0.188043	+	0.982161i	$0.439786\pi$
$570$		0			0
$571$	−204.492			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$571$	−204.492			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$572$	302.858			0.529473
$573$	−398.031			−0.694643
$574$	356.110	−	1171.41i	0.620400	−	2.04079i
$575$		0			0
$576$	148.565			0.257925
$577$	957.823			1.66001			0.830003	−	0.557759i	$-0.188339\pi$
$577$	957.823			1.66001			0.830003	+	0.557759i	$0.188339\pi$
$578$		−	1008.53i		−	1.74487i
$579$			193.176i			0.333638i
$580$		0			0
$581$	210.469	−	692.331i	0.362253	−	1.19162i
$582$			410.522i			0.705364i
$583$			116.719i			0.200205i
$584$		−	1433.41i		−	2.45446i
$585$		0			0
$586$			434.007i			0.740626i
$587$	−981.279			−1.67168			−0.835842	−	0.548969i	$-0.815020\pi$
$587$	−981.279			−1.67168			−0.835842	+	0.548969i	$0.815020\pi$
$588$	−583.535	−	390.917i	−0.992407	−	0.664825i
$589$	−1269.14			−2.15473
$590$		0			0
$591$			299.410i			0.506617i
$592$			722.777i			1.22091i
$593$	−708.384			−1.19458			−0.597288	−	0.802026i	$-0.703755\pi$
$593$	−708.384			−1.19458			−0.597288	+	0.802026i	$0.703755\pi$
$594$			36.9779i			0.0622523i
$595$		0			0
$596$	−238.568			−0.400282
$597$		−	204.286i		−	0.342187i
$598$	1570.04			2.62549
$599$	928.994			1.55091			0.775454	−	0.631404i	$-0.217521\pi$
$599$	928.994			1.55091			0.775454	+	0.631404i	$0.217521\pi$
$600$		0			0
$601$		−	466.882i		−	0.776842i	−0.921482	−	0.388421i	$-0.873021\pi$
$601$		−	466.882i		−	0.776842i	0.921482	−	0.388421i	$-0.126979\pi$
$602$	−68.4012	+	225.004i	−0.113623	+	0.373760i
$603$			287.195i			0.476277i
$604$	−2054.98			−3.40229
$605$		0			0
$606$	−445.009			−0.734338
$607$	−988.757			−1.62892			−0.814462	−	0.580216i	$-0.802968\pi$
$607$	−988.757			−1.62892			−0.814462	+	0.580216i	$0.802968\pi$
$608$	−230.228			−0.378664
$609$	−135.522	+	445.795i	−0.222532	+	0.732012i
$610$		0			0
$611$	1003.53			1.64244
$612$	−26.6371			−0.0435246
$613$		−	469.962i		−	0.766660i	−0.923612	−	0.383330i	$-0.874777\pi$
$613$		−	469.962i		−	0.766660i	0.923612	−	0.383330i	$-0.125223\pi$
$614$			790.351i			1.28722i
$615$		0			0
$616$	203.791	+	61.9526i	0.330830	+	0.100572i
$617$			1081.72i			1.75320i	0.481223	+	0.876598i	$0.340193\pi$
$617$			1081.72i			1.75320i	−0.481223	+	0.876598i	$0.659807\pi$
$618$		−	347.990i		−	0.563091i
$619$			553.956i			0.894921i	0.894304	+	0.447461i	$0.147672\pi$
$619$			553.956i			0.894921i	−0.894304	+	0.447461i	$0.852328\pi$
$620$		0			0
$621$			129.234i			0.208105i
$622$	185.572			0.298348
$623$	196.654	+	59.7829i	0.315657	+	0.0959598i
$624$	−604.985			−0.969527
$625$		0			0
$626$		−	1312.35i		−	2.09641i
$627$			101.266i			0.161509i
$628$	−342.494			−0.545372
$629$			40.0006i			0.0635940i
$630$		0			0
$631$	−77.8822			−0.123427			−0.0617133	−	0.998094i	$-0.519656\pi$
$631$	−77.8822			−0.123427			−0.0617133	+	0.998094i	$0.519656\pi$
$632$			421.290i			0.666597i
$633$	678.861			1.07245
$634$	−42.2369			−0.0666197
$635$		0			0
$636$		−	823.722i		−	1.29516i
$637$	−733.479	−	491.366i	−1.15146	−	0.771375i
$638$		−	273.484i		−	0.428658i
$639$	−77.4117			−0.121145
$640$		0			0
$641$	−360.619			−0.562589			−0.281294	−	0.959622i	$-0.590764\pi$
$641$	−360.619			−0.562589			−0.281294	+	0.959622i	$0.590764\pi$
$642$	−241.771			−0.376591
$643$	793.158			1.23353			0.616764	−	0.787148i	$-0.288443\pi$
$643$	793.158			1.23353			0.616764	+	0.787148i	$0.288443\pi$
$644$	1378.51	+	419.067i	2.14054	+	0.650725i
$645$		0			0
$646$	−108.205			−0.167501
$647$	405.244			0.626344			0.313172	−	0.949696i	$-0.398608\pi$
$647$	405.244			0.626344			0.313172	+	0.949696i	$0.398608\pi$
$648$		−	134.831i		−	0.208072i
$649$		−	206.559i		−	0.318273i
$650$		0			0
$651$	−511.450	−	155.481i	−0.785638	−	0.238834i
$652$		−	428.774i		−	0.657629i
$653$		−	493.508i		−	0.755755i	−0.925856	−	0.377877i	$-0.876654\pi$
$653$		−	493.508i		−	0.755755i	0.925856	−	0.377877i	$-0.123346\pi$
$654$		−	1123.00i		−	1.71713i
$655$		0			0
$656$		−	967.767i		−	1.47526i
$657$	287.041			0.436896
$658$	1306.97	+	397.321i	1.98628	+	0.603831i
$659$	1120.88			1.70088			0.850441	−	0.526070i	$-0.176335\pi$
$659$	1120.88			1.70088			0.850441	+	0.526070i	$0.176335\pi$
$660$		0			0
$661$			1134.48i			1.71631i	0.513393	+	0.858154i	$0.328388\pi$
$661$			1134.48i			1.71631i	−0.513393	+	0.858154i	$0.671612\pi$
$662$		−	1318.03i		−	1.99098i
$663$	−33.4817			−0.0505002
$664$		−	1548.66i		−	2.33232i
$665$		0			0
$666$	−391.887			−0.588418
$667$		−	955.794i		−	1.43297i
$668$	−347.346			−0.519979
$669$	−166.712			−0.249196
$670$		0			0
$671$		−	64.9002i		−	0.0967216i
$672$	−92.7796	−	28.2050i	−0.138065	−	0.0419718i
$673$			763.267i			1.13413i	0.823674	+	0.567063i	$0.191920\pi$
$673$			763.267i			1.13413i	−0.823674	+	0.567063i	$0.808080\pi$
$674$	381.809			0.566482
$675$		0			0
$676$	−1287.95			−1.90525
$677$	456.611			0.674463			0.337232	−	0.941422i	$-0.390509\pi$
$677$	456.611			0.674463			0.337232	+	0.941422i	$0.390509\pi$
$678$	732.575			1.08049
$679$	−137.730	+	453.058i	−0.202842	+	0.667244i
$680$		0			0
$681$	158.822			0.233219
$682$	313.761			0.460060
$683$			219.276i			0.321049i	0.987032	+	0.160524i	$0.0513185\pi$
$683$			219.276i			0.321049i	−0.987032	+	0.160524i	$0.948681\pi$
$684$		−	714.666i		−	1.04483i
$685$		0			0
$686$	−760.722	−	930.345i	−1.10892	−	1.35619i
$687$			561.135i			0.816791i
$688$			185.888i			0.270186i
$689$		−	1035.38i		−	1.50273i
$690$		0			0
$691$			396.801i			0.574242i	0.957894	+	0.287121i	$0.0926982\pi$
$691$			396.801i			0.574242i	−0.957894	+	0.287121i	$0.907302\pi$
$692$	−811.197			−1.17225
$693$	−12.4061	+	40.8094i	−0.0179020	+	0.0588880i
$694$	722.989			1.04177
$695$		0			0
$696$			997.190i			1.43274i
$697$		−	53.5591i		−	0.0768424i
$698$	1308.54			1.87470
$699$			316.823i			0.453252i
$700$		0			0
$701$	−493.156			−0.703503			−0.351752	−	0.936093i	$-0.614414\pi$
$701$	−493.156			−0.703503			−0.351752	+	0.936093i	$0.614414\pi$
$702$		−	328.020i		−	0.467265i
$703$	−1073.21			−1.52661
$704$	−100.584			−0.142875
$705$		0			0
$706$		−	2263.88i		−	3.20663i
$707$	−491.118	−	149.300i	−0.694651	−	0.211174i
$708$			1457.75i			2.05896i
$709$	−859.326			−1.21202			−0.606012	−	0.795455i	$-0.707232\pi$
$709$	−859.326			−1.21202			−0.606012	+	0.795455i	$0.707232\pi$
$710$		0			0
$711$	−84.3637			−0.118655
$712$	439.892			0.617825
$713$	1096.56			1.53795
$714$	−43.6057	−	13.2562i	−0.0610724	−	0.0185661i
$715$		0			0
$716$	567.582			0.792712
$717$	−74.3466			−0.103691
$718$		−	614.060i		−	0.855237i
$719$			385.539i			0.536216i	0.963389	+	0.268108i	$0.0863983\pi$
$719$			385.539i			0.536216i	−0.963389	+	0.268108i	$0.913602\pi$
$720$		0			0
$721$	116.751	−	384.048i	0.161929	−	0.532660i
$722$		−	1638.29i		−	2.26910i
$723$			173.022i			0.239311i
$724$		−	869.992i		−	1.20165i
$725$		0			0
$726$			709.261i			0.976944i
$727$	114.722			0.157802			0.0789012	−	0.996882i	$-0.474859\pi$
$727$	114.722			0.157802			0.0789012	+	0.996882i	$0.474859\pi$
$728$	−1807.77	−	549.563i	−2.48320	−	0.754895i
$729$	27.0000			0.0370370
$730$		0			0
$731$			10.2876i			0.0140733i
$732$			458.019i			0.625710i
$733$	−140.433			−0.191586			−0.0957932	−	0.995401i	$-0.530539\pi$
$733$	−140.433			−0.191586			−0.0957932	+	0.995401i	$0.530539\pi$
$734$		−	373.061i		−	0.508257i
$735$		0			0
$736$	198.921			0.270273
$737$		−	194.442i		−	0.263830i
$738$	524.719			0.711002
$739$	50.8609			0.0688239			0.0344120	−	0.999408i	$-0.489044\pi$
$739$	50.8609			0.0688239			0.0344120	+	0.999408i	$0.489044\pi$
$740$		0			0
$741$		−	898.304i		−	1.21229i
$742$	409.932	−	1348.46i	0.552469	−	1.81733i
$743$		−	930.694i		−	1.25262i	−0.779575	−	0.626309i	$-0.784565\pi$
$743$		−	930.694i		−	1.25262i	0.779575	−	0.626309i	$-0.215435\pi$
$744$	−1144.05			−1.53770
$745$		0			0
$746$	782.457			1.04887
$747$	310.121			0.415155
$748$	18.0343			0.0241101
$749$	−266.822	−	81.1142i	−0.356238	−	0.108297i
$750$		0			0
$751$	−446.702			−0.594809			−0.297404	−	0.954752i	$-0.596121\pi$
$751$	−446.702			−0.594809			−0.297404	+	0.954752i	$0.596121\pi$
$752$	1079.76			1.43586
$753$			701.385i			0.931455i
$754$			2425.99i			3.21750i
$755$		0			0
$756$	87.5532	−	288.003i	0.115811	−	0.380957i
$757$			27.2042i			0.0359369i	0.999839	+	0.0179684i	$0.00571984\pi$
$757$			27.2042i			0.0359369i	−0.999839	+	0.0179684i	$0.994280\pi$
$758$		−	417.203i		−	0.550400i
$759$		−	87.4961i		−	0.115278i
$760$		0			0
$761$			333.536i			0.438287i	0.975693	+	0.219143i	$0.0703262\pi$
$761$			333.536i			0.438287i	−0.975693	+	0.219143i	$0.929674\pi$
$762$	−506.784			−0.665070
$763$	376.767	−	1239.36i	0.493796	−	1.62433i
$764$	−1901.81			−2.48928
$765$		0			0
$766$		−	1733.05i		−	2.26247i
$767$			1832.32i			2.38895i
$768$	903.998			1.17708
$769$			56.3903i			0.0733294i	0.999328	+	0.0366647i	$0.0116734\pi$
$769$			56.3903i			0.0733294i	−0.999328	+	0.0366647i	$0.988327\pi$
$770$		0			0
$771$	177.877			0.230709
$772$			923.006i			1.19560i
$773$	−296.398			−0.383438			−0.191719	−	0.981450i	$-0.561406\pi$
$773$	−296.398			−0.383438			−0.191719	+	0.981450i	$0.561406\pi$
$774$	−100.788			−0.130217
$775$		0			0
$776$			1013.44i			1.30598i
$777$	−432.492	−	131.478i	−0.556618	−	0.169212i
$778$			948.022i			1.21854i
$779$	1436.98			1.84464
$780$		0			0
$781$	52.4107			0.0671072
$782$	93.4915			0.119554
$783$	−199.688			−0.255030
$784$	−789.197	−	528.692i	−1.00663	−	0.674352i
$785$		0			0
$786$	1203.08			1.53064
$787$	−226.427			−0.287709			−0.143854	−	0.989599i	$-0.545950\pi$
$787$	−226.427			−0.287709			−0.143854	+	0.989599i	$0.545950\pi$
$788$			1430.60i			1.81548i
$789$			487.537i			0.617917i
$790$		0			0
$791$	808.481	+	245.779i	1.02210	+	0.310719i
$792$			91.2857i			0.115260i
$793$			575.711i			0.725991i
$794$		−	130.295i		−	0.164100i
$795$		0			0
$796$		−	976.088i		−	1.22624i
$797$	305.282			0.383038			0.191519	−	0.981489i	$-0.438659\pi$
$797$	305.282			0.383038			0.191519	+	0.981489i	$0.438659\pi$
$798$	355.659	−	1169.93i	0.445688	−	1.46608i
$799$	59.7573			0.0747901
$800$		0			0
$801$			88.0887i			0.109973i
$802$		−	128.621i		−	0.160375i
$803$	−194.338			−0.242015
$804$			1372.24i			1.70676i
$805$		0			0
$806$	−2783.28			−3.45320
$807$		−	305.555i		−	0.378631i
$808$	−1098.57			−1.35962
$809$	−592.651			−0.732573			−0.366286	−	0.930502i	$-0.619371\pi$
$809$	−592.651			−0.732573			−0.366286	+	0.930502i	$0.619371\pi$
$810$		0			0
$811$			731.348i			0.901785i	0.892578	+	0.450893i	$0.148894\pi$
$811$			731.348i			0.901785i	−0.892578	+	0.450893i	$0.851106\pi$
$812$	−647.532	+	2130.04i	−0.797453	+	2.62320i
$813$			530.078i			0.652003i
$814$	265.322			0.325949
$815$		0			0
$816$	−36.0251			−0.0441484
$817$	−276.013			−0.337838
$818$	1735.47			2.12160
$819$	110.051	−	362.008i	0.134372	−	0.442012i
$820$		0			0
$821$	268.560			0.327114			0.163557	−	0.986534i	$-0.447703\pi$
$821$	268.560			0.327114			0.163557	+	0.986534i	$0.447703\pi$
$822$	−146.638			−0.178392
$823$		−	1213.35i		−	1.47430i	−0.675728	−	0.737151i	$-0.736170\pi$
$823$		−	1213.35i		−	1.47430i	0.675728	−	0.737151i	$-0.263830\pi$
$824$		−	859.068i		−	1.04256i
$825$		0			0
$826$	−725.459	+	2386.37i	−0.878280	+	2.88907i
$827$		−	1238.49i		−	1.49757i	−0.662813	−	0.748785i	$-0.730637\pi$
$827$		−	1238.49i		−	1.49757i	0.662813	−	0.748785i	$-0.269363\pi$
$828$			617.485i			0.745755i
$829$			873.056i			1.05314i	0.850131	+	0.526572i	$0.176523\pi$
$829$			873.056i			1.05314i	−0.850131	+	0.526572i	$0.823477\pi$
$830$		0			0
$831$		−	75.8626i		−	0.0912908i
$832$	892.251			1.07242
$833$	−43.6765	−	29.2594i	−0.0524328	−	0.0351253i
$834$	374.048			0.448499
$835$		0			0
$836$			483.856i			0.578776i
$837$		−	229.098i		−	0.273713i
$838$	−943.532			−1.12593
$839$			100.572i			0.119871i	0.998202	+	0.0599355i	$0.0190895\pi$
$839$			100.572i			0.119871i	−0.998202	+	0.0599355i	$0.980910\pi$
$840$		0			0
$841$	635.869			0.756086
$842$			2651.32i			3.14883i
$843$	−865.163			−1.02629
$844$	3243.63			3.84317
$845$		0			0
$846$			585.443i			0.692013i
$847$	−237.957	+	782.752i	−0.280941	+	0.924146i
$848$		−	1114.03i		−	1.31372i
$849$	212.474			0.250264
$850$		0			0
$851$	927.271			1.08963
$852$	−369.877			−0.434128
$853$	1162.30			1.36260			0.681302	−	0.732003i	$-0.261414\pi$
$853$	1162.30			1.36260			0.681302	+	0.732003i	$0.261414\pi$
$854$	−227.937	+	749.792i	−0.266905	+	0.877977i
$855$		0			0
$856$	−596.850			−0.697254
$857$	87.8213			0.102475			0.0512376	−	0.998686i	$-0.483683\pi$
$857$	87.8213			0.102475			0.0512376	+	0.998686i	$0.483683\pi$
$858$			222.082i			0.258837i
$859$			200.580i			0.233504i	0.993161	+	0.116752i	$0.0372482\pi$
$859$			200.580i			0.233504i	−0.993161	+	0.116752i	$0.962752\pi$
$860$		0			0
$861$	579.088	+	176.043i	0.672576	+	0.204464i
$862$			648.820i			0.752691i
$863$			617.914i			0.716007i	0.933720	+	0.358004i	$0.116542\pi$
$863$			617.914i			0.716007i	−0.933720	+	0.358004i	$0.883458\pi$
$864$		−	41.5594i		−	0.0481012i
$865$		0			0
$866$			2252.33i			2.60085i
$867$	498.569			0.575051
$868$	−2443.74	−	742.897i	−2.81537	−	0.855872i
$869$	57.1175			0.0657278
$870$		0			0
$871$			1724.84i			1.98030i
$872$		−	2772.30i		−	3.17925i
$873$	−202.942			−0.232465
$874$			2508.35i			2.86997i
$875$		0			0
$876$	1371.50			1.56564
$877$		−	638.649i		−	0.728220i	−0.931356	−	0.364110i	$-0.881373\pi$
$877$		−	638.649i		−	0.728220i	0.931356	−	0.364110i	$-0.118627\pi$
$878$	−1626.55			−1.85256
$879$	−214.551			−0.244086
$880$		0			0
$881$			148.009i			0.168001i	0.996466	+	0.0840003i	$0.0267697\pi$
$881$			148.009i			0.168001i	−0.996466	+	0.0840003i	$0.973230\pi$
$882$	286.655	−	427.899i	0.325005	−	0.485146i
$883$			784.505i			0.888454i	0.895914	+	0.444227i	$0.146522\pi$
$883$			784.505i			0.888454i	−0.895914	+	0.444227i	$0.853478\pi$
$884$	−159.977			−0.180970
$885$		0			0
$886$	−403.724			−0.455670
$887$	−1466.40			−1.65321			−0.826605	−	0.562783i	$-0.809731\pi$
$887$	−1466.40			−1.65321			−0.826605	+	0.562783i	$0.809731\pi$
$888$	−967.433			−1.08945
$889$	−559.294	−	170.026i	−0.629127	−	0.191255i
$890$		0			0
$891$	−18.2800			−0.0205163
$892$	−796.559			−0.893003
$893$			1603.27i			1.79538i
$894$		−	174.939i		−	0.195681i
$895$		0			0
$896$	1376.31	+	418.400i	1.53606	+	0.466964i
$897$			776.152i			0.865276i
$898$		−	1170.07i		−	1.30298i
$899$			1694.38i			1.88473i
$900$		0			0
$901$		−	61.6540i		−	0.0684284i
$902$	−355.255			−0.393853
$903$	−111.231	−	33.8142i	−0.123179	−	0.0374465i
$904$	1808.48			2.00053
$905$		0			0
$906$		−	1506.89i		−	1.66324i
$907$			488.454i			0.538538i	0.963065	+	0.269269i	$0.0867821\pi$
$907$			488.454i			0.538538i	−0.963065	+	0.269269i	$0.913218\pi$
$908$	758.863			0.835752
$909$		−	219.990i		−	0.242013i
$910$		0			0
$911$	1329.44			1.45932			0.729658	−	0.683812i	$-0.239679\pi$
$911$	1329.44			1.45932			0.729658	+	0.683812i	$0.239679\pi$
$912$		−	966.543i		−	1.05981i
$913$	−209.964			−0.229971
$914$	−1240.84			−1.35759
$915$		0			0
$916$			2681.14i			2.92700i
$917$	1327.74	+	403.633i	1.44791	+	0.440167i
$918$		−	19.5326i		−	0.0212774i
$919$	−1369.52			−1.49023			−0.745113	−	0.666938i	$-0.767605\pi$
$919$	−1369.52			−1.49023			−0.745113	+	0.666938i	$0.767605\pi$
$920$		0			0
$921$	−390.710			−0.424224
$922$	451.647			0.489856
$923$	−464.920			−0.503705
$924$	−59.2769	+	194.989i	−0.0641525	+	0.211028i
$925$		0			0
$926$	−1058.73			−1.14333
$927$	172.029			0.185576
$928$			307.368i			0.331216i
$929$		−	909.289i		−	0.978783i	−0.872064	−	0.489391i	$-0.837219\pi$
$929$		−	909.289i		−	0.978783i	0.872064	−	0.489391i	$-0.162781\pi$
$930$		0			0
$931$	785.022	−	1171.83i	0.843203	−	1.25868i
$932$			1513.80i			1.62425i
$933$			91.7378i			0.0983256i
$934$		−	2831.78i		−	3.03188i
$935$		0			0
$936$		−	809.768i		−	0.865137i
$937$	−184.883			−0.197313			−0.0986566	−	0.995122i	$-0.531455\pi$
$937$	−184.883			−0.197313			−0.0986566	+	0.995122i	$0.531455\pi$
$938$	−682.904	+	2246.39i	−0.728043	+	2.39487i
$939$	648.762			0.690907
$940$		0			0
$941$			884.454i			0.939909i	0.882691	+	0.469955i	$0.155730\pi$
$941$			884.454i			0.939909i	−0.882691	+	0.469955i	$0.844270\pi$
$942$		−	251.146i		−	0.266610i
$943$	−1241.58			−1.31662
$944$			1971.51i			2.08847i
$945$		0			0
$946$	68.2371			0.0721322
$947$		−	651.331i		−	0.687784i	−0.939009	−	0.343892i	$-0.888255\pi$
$947$		−	651.331i		−	0.687784i	0.939009	−	0.343892i	$-0.111745\pi$
$948$	−403.094			−0.425205
$949$	1723.91			1.81656
$950$		0			0
$951$		−	20.8798i		−	0.0219557i
$952$	−107.647	−	32.7249i	−0.113075	−	0.0343749i
$953$		−	1622.61i		−	1.70263i	−0.524654	−	0.851316i	$-0.675805\pi$
$953$		−	1622.61i		−	1.70263i	0.524654	−	0.851316i	$-0.324195\pi$
$954$	604.025			0.633150
$955$		0			0
$956$	−355.232			−0.371582
$957$	135.197			0.141271
$958$	−171.273			−0.178782
$959$	−161.832	−	49.1970i	−0.168751	−	0.0513003i
$960$		0			0
$961$	−982.915			−1.02280
$962$	−2353.60			−2.44657
$963$		−	119.520i		−	0.124112i
$964$			826.708i			0.857581i
$965$		0			0
$966$	−307.297	+	1010.84i	−0.318112	+	1.04642i
$967$		−	1491.24i		−	1.54213i	−0.636754	−	0.771067i	$-0.719724\pi$
$967$		−	1491.24i		−	1.54213i	0.636754	−	0.771067i	$-0.280276\pi$
$968$			1750.92i			1.80880i
$969$		−	53.4914i		−	0.0552027i
$970$		0			0
$971$		−	1739.36i		−	1.79130i	−0.444756	−	0.895652i	$-0.646709\pi$
$971$		−	1739.36i		−	1.79130i	0.444756	−	0.895652i	$-0.353291\pi$
$972$	129.008			0.132724
$973$	412.806	+	125.493i	0.424261	+	0.128975i
$974$	−1171.75			−1.20303
$975$		0			0
$976$			619.444i			0.634676i
$977$		−	62.8973i		−	0.0643780i	−0.999482	−	0.0321890i	$-0.989752\pi$
$977$		−	62.8973i		−	0.0643780i	0.999482	−	0.0321890i	$-0.0102478\pi$
$978$	314.414			0.321487
$979$		−	59.6395i		−	0.0609188i
$980$		0			0
$981$	555.156			0.565909
$982$		−	1924.06i		−	1.95932i
$983$	1214.68			1.23569			0.617846	−	0.786299i	$-0.288006\pi$
$983$	1214.68			1.23569			0.617846	+	0.786299i	$0.288006\pi$
$984$	1295.35			1.31641
$985$		0			0
$986$			144.461i			0.146512i
$987$	−196.416	+	646.104i	−0.199003	+	0.654614i
$988$		−	4292.15i		−	4.34428i
$989$	238.481			0.241133
$990$		0			0
$991$	114.216			0.115253			0.0576266	−	0.998338i	$-0.481647\pi$
$991$	114.216			0.115253			0.0576266	+	0.998338i	$0.481647\pi$
$992$	−352.636			−0.355480
$993$	651.570			0.656163
$994$	−605.501	−	184.072i	−0.609156	−	0.185184i
$995$		0			0
$996$	1481.78			1.48773
$997$	178.000			0.178536			0.0892678	−	0.996008i	$-0.471547\pi$
$997$	178.000			0.178536			0.0892678	+	0.996008i	$0.471547\pi$
$998$			1620.28i			1.62353i
$999$		−	193.729i		−	0.193923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.e.c.349.10		24
5.2	odd	4		525.3.h.d.76.2		12
5.3	odd	4		105.3.h.a.76.11	✓	12
5.4	even	2	inner	525.3.e.c.349.23		24
7.6	odd	2	inner	525.3.e.c.349.24		24
15.8	even	4		315.3.h.d.181.1		12
20.3	even	4		1680.3.s.c.1441.12		12
35.13	even	4		105.3.h.a.76.12	yes	12
35.27	even	4		525.3.h.d.76.1		12
35.34	odd	2	inner	525.3.e.c.349.9		24
105.83	odd	4		315.3.h.d.181.2		12
140.83	odd	4		1680.3.s.c.1441.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.11	✓	12	5.3	odd	4
105.3.h.a.76.12	yes	12	35.13	even	4
315.3.h.d.181.1		12	15.8	even	4
315.3.h.d.181.2		12	105.83	odd	4
525.3.e.c.349.9		24	35.34	odd	2	inner
525.3.e.c.349.10		24	1.1	even	1	trivial
525.3.e.c.349.23		24	5.4	even	2	inner
525.3.e.c.349.24		24	7.6	odd	2	inner
525.3.h.d.76.1		12	35.27	even	4
525.3.h.d.76.2		12	5.2	odd	4
1680.3.s.c.1441.3		12	140.83	odd	4
1680.3.s.c.1441.12		12	20.3	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.50369i q^{2} -1.73205 q^{3} -8.27584 q^{4} -6.06857i q^{6} +(2.03600 - 6.69736i) q^{7} -14.9812i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+3.50369i q^{2} -1.73205 q^{3} -8.27584 q^{4} -6.06857i q^{6} +(2.03600 - 6.69736i) q^{7} -14.9812i q^{8} +3.00000 q^{9} -2.03112 q^{11} +14.3342 q^{12} +18.0174 q^{13} +(23.4655 + 7.13352i) q^{14} +19.3861 q^{16} +1.07289 q^{17} +10.5111i q^{18} +28.7852i q^{19} +(-3.52646 + 11.6002i) q^{21} -7.11640i q^{22} -24.8710i q^{23} +25.9482i q^{24} +63.1275i q^{26} -5.19615 q^{27} +(-16.8496 + 55.4263i) q^{28} +38.4300 q^{29} +44.0899i q^{31} +7.99812i q^{32} +3.51800 q^{33} +3.75906i q^{34} -24.8275 q^{36} +37.2832i q^{37} -100.855 q^{38} -31.2071 q^{39} -49.9206i q^{41} +(-40.6434 - 12.3556i) q^{42} +9.58871i q^{43} +16.8092 q^{44} +87.1402 q^{46} +55.6978 q^{47} -33.5777 q^{48} +(-40.7094 - 27.2717i) q^{49} -1.85829 q^{51} -149.109 q^{52} -57.4656i q^{53} -18.2057i q^{54} +(-100.335 - 30.5018i) q^{56} -49.8575i q^{57} +134.647i q^{58} +101.697i q^{59} +31.9530i q^{61} -154.477 q^{62} +(6.10801 - 20.0921i) q^{63} +49.5215 q^{64} +12.3260i q^{66} +95.7318i q^{67} -8.87902 q^{68} +43.0778i q^{69} -25.8039 q^{71} -44.9436i q^{72} +95.6803 q^{73} -130.629 q^{74} -238.222i q^{76} +(-4.13536 + 13.6031i) q^{77} -109.340i q^{78} -28.1212 q^{79} +9.00000 q^{81} +174.906 q^{82} +103.374 q^{83} +(29.1844 - 96.0012i) q^{84} -33.5959 q^{86} -66.5628 q^{87} +30.4286i q^{88} +29.3629i q^{89} +(36.6835 - 120.669i) q^{91} +205.828i q^{92} -76.3659i q^{93} +195.148i q^{94} -13.8531i q^{96} -67.6473 q^{97} +(95.5515 - 142.633i) q^{98} -6.09335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 88 q^{4} + 72 q^{9}+O(q^{10}) \) 24 * q - 88 * q^4 + 72 * q^9	\( 24 q - 88 q^{4} + 72 q^{9} - 32 q^{11} + 80 q^{14} + 184 q^{16} + 72 q^{21} - 208 q^{29} - 264 q^{36} + 48 q^{39} - 384 q^{44} + 400 q^{46} - 120 q^{49} + 48 q^{51} - 736 q^{56} + 40 q^{64} + 64 q^{71} - 368 q^{74} - 240 q^{79} + 216 q^{81} - 216 q^{84} + 800 q^{86} + 48 q^{91} - 96 q^{99}+O(q^{100}) \) 24 * q - 88 * q^4 + 72 * q^9 - 32 * q^11 + 80 * q^14 + 184 * q^16 + 72 * q^21 - 208 * q^29 - 264 * q^36 + 48 * q^39 - 384 * q^44 + 400 * q^46 - 120 * q^49 + 48 * q^51 - 736 * q^56 + 40 * q^64 + 64 * q^71 - 368 * q^74 - 240 * q^79 + 216 * q^81 - 216 * q^84 + 800 * q^86 + 48 * q^91 - 96 * q^99

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