LMFDB - Embedded newform 900.3.f.h.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(199,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("900.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.f (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 14x^13 + 23x^12 - 26x^11 + 18x^10 - 10x^9 + 9x^8 - 20x^7 + 72x^6 - 208x^5 + 368x^4 - 448x^3 + 512x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$-0.637499 + 1.26238i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.h.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49110 + 1.33290i) q^{2} +(0.446749 - 3.97497i) q^{4} +6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +O(q^{10})$	\(q+(-1.49110 + 1.33290i) q^{2} +(0.446749 - 3.97497i) q^{4} +6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +2.26696i q^{11} -14.8772i q^{13} +(-9.79404 + 8.75495i) q^{14} +(-15.6008 - 3.55163i) q^{16} +26.8250i q^{17} +10.8680i q^{19} +(-3.02164 - 3.38027i) q^{22} +36.4610 q^{23} +(19.8298 + 22.1834i) q^{26} +(2.93440 - 26.1090i) q^{28} -35.2510 q^{29} +23.8330i q^{31} +(27.9963 - 15.4985i) q^{32} +(-35.7550 - 39.9987i) q^{34} -54.7495i q^{37} +(-14.4860 - 16.2053i) q^{38} +23.8298 q^{41} +56.2515 q^{43} +(9.01112 + 1.01276i) q^{44} +(-54.3670 + 48.5989i) q^{46} -51.4177 q^{47} -5.85689 q^{49} +(-59.1364 - 6.64636i) q^{52} -30.6465i q^{53} +(30.4252 + 42.8423i) q^{56} +(52.5627 - 46.9861i) q^{58} +6.92483i q^{59} +107.426 q^{61} +(-31.7671 - 35.5374i) q^{62} +(-21.0873 + 60.4262i) q^{64} +111.444 q^{67} +(106.629 + 11.9840i) q^{68} -31.3190i q^{71} +110.909i q^{73} +(72.9757 + 81.6369i) q^{74} +(43.2002 + 4.85528i) q^{76} +14.8902i q^{77} +59.0065i q^{79} +(-35.5326 + 31.7628i) q^{82} +142.416 q^{83} +(-83.8765 + 74.9776i) q^{86} +(-14.7864 + 10.5008i) q^{88} +7.14798 q^{89} -97.7185i q^{91} +(16.2889 - 144.932i) q^{92} +(76.6689 - 68.5347i) q^{94} +126.308i q^{97} +(8.73319 - 7.80665i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4}+O(q^{10}) $ 16 * q + 16 * q^4	$ 16 q + 16 q^{4} + 44 q^{14} + 80 q^{16} + 132 q^{26} - 64 q^{29} - 248 q^{34} + 32 q^{41} + 80 q^{44} - 152 q^{46} - 32 q^{49} + 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{74} + 240 q^{76} - 428 q^{86} + 256 q^{89} - 24 q^{94}+O(q^{100}) $ 16 * q + 16 * q^4 + 44 * q^14 + 80 * q^16 + 132 * q^26 - 64 * q^29 - 248 * q^34 + 32 * q^41 + 80 * q^44 - 152 * q^46 - 32 * q^49 + 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^74 + 240 * q^76 - 428 * q^86 + 256 * q^89 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.49110	+	1.33290i	−0.745549	+	0.666451i
$2$	−1.49110	+	1.33290i	−0.745549	+	0.666451i
$3$		0			0
$3$		0			0
$4$	0.446749	−	3.97497i	0.111687	−	0.993743i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	6.56834			0.938335			0.469167	−	0.883109i	$-0.344554\pi$
$7$	6.56834			0.938335			0.469167	+	0.883109i	$0.344554\pi$
$8$	4.63210	+	6.52255i	0.579013	+	0.815319i
$9$		0			0
$10$		0			0
$11$			2.26696i			0.206088i	0.994677	+	0.103044i	$0.0328582\pi$
$11$			2.26696i			0.206088i	−0.994677	+	0.103044i	$0.967142\pi$
$12$		0			0
$13$		−	14.8772i		−	1.14440i	−0.820114	−	0.572200i	$-0.806090\pi$
$13$		−	14.8772i		−	1.14440i	0.820114	−	0.572200i	$-0.193910\pi$
$14$	−9.79404	+	8.75495i	−0.699575	+	0.625354i
$15$		0			0
$16$	−15.6008	−	3.55163i	−0.975052	−	0.221977i
$17$			26.8250i			1.57794i	0.614432	+	0.788969i	$0.289385\pi$
$17$			26.8250i			1.57794i	−0.614432	+	0.788969i	$0.710615\pi$
$18$		0			0
$19$			10.8680i			0.572002i	0.958229	+	0.286001i	$0.0923260\pi$
$19$			10.8680i			0.572002i	−0.958229	+	0.286001i	$0.907674\pi$
$20$		0			0
$21$		0			0
$22$	−3.02164	−	3.38027i	−0.137347	−	0.153648i
$23$	36.4610			1.58526			0.792631	−	0.609702i	$-0.208711\pi$
$23$	36.4610			1.58526			0.792631	+	0.609702i	$0.208711\pi$
$24$		0			0
$25$		0			0
$26$	19.8298	+	22.1834i	0.762685	+	0.853206i
$27$		0			0
$28$	2.93440	−	26.1090i	0.104800	−	0.932464i
$29$	−35.2510			−1.21555			−0.607775	−	0.794109i	$-0.707938\pi$
$29$	−35.2510			−1.21555			−0.607775	+	0.794109i	$0.707938\pi$
$30$		0			0
$31$			23.8330i			0.768808i	0.923165	+	0.384404i	$0.125593\pi$
$31$			23.8330i			0.768808i	−0.923165	+	0.384404i	$0.874407\pi$
$32$	27.9963	−	15.4985i	0.874886	−	0.484329i
$33$		0			0
$34$	−35.7550	−	39.9987i	−1.05162	−	1.17643i
$35$		0			0
$36$		0			0
$37$		−	54.7495i		−	1.47972i	−0.672763	−	0.739858i	$-0.734893\pi$
$37$		−	54.7495i		−	1.47972i	0.672763	−	0.739858i	$-0.265107\pi$
$38$	−14.4860	−	16.2053i	−0.381211	−	0.426455i
$39$		0			0
$40$		0			0
$41$	23.8298			0.581215			0.290608	−	0.956842i	$-0.406143\pi$
$41$	23.8298			0.581215			0.290608	+	0.956842i	$0.406143\pi$
$42$		0			0
$43$	56.2515			1.30817			0.654087	−	0.756420i	$-0.273053\pi$
$43$	56.2515			1.30817			0.654087	+	0.756420i	$0.273053\pi$
$44$	9.01112	+	1.01276i	0.204798	+	0.0230173i
$45$		0			0
$46$	−54.3670	+	48.5989i	−1.18189	+	1.05650i
$47$	−51.4177			−1.09399			−0.546997	−	0.837135i	$-0.684229\pi$
$47$	−51.4177			−1.09399			−0.546997	+	0.837135i	$0.684229\pi$
$48$		0			0
$49$	−5.85689			−0.119528
$50$		0			0
$51$		0			0
$52$	−59.1364	−	6.64636i	−1.13724	−	0.127815i
$53$		−	30.6465i		−	0.578236i	−0.957293	−	0.289118i	$-0.906638\pi$
$53$		−	30.6465i		−	0.578236i	0.957293	−	0.289118i	$-0.0933620\pi$
$54$		0			0
$55$		0			0
$56$	30.4252	+	42.8423i	0.543308	+	0.765042i
$57$		0			0
$58$	52.5627	−	46.9861i	0.906253	−	0.810105i
$59$			6.92483i			0.117370i	0.998277	+	0.0586850i	$0.0186908\pi$
$59$			6.92483i			0.117370i	−0.998277	+	0.0586850i	$0.981309\pi$
$60$		0			0
$61$	107.426			1.76107			0.880537	−	0.473977i	$-0.157182\pi$
$61$	107.426			1.76107			0.880537	+	0.473977i	$0.157182\pi$
$62$	−31.7671	−	35.5374i	−0.512372	−	0.573184i
$63$		0			0
$64$	−21.0873	+	60.4262i	−0.329489	+	0.944160i
$65$		0			0
$66$		0			0
$67$	111.444			1.66334			0.831670	−	0.555271i	$-0.187385\pi$
$67$	111.444			1.66334			0.831670	+	0.555271i	$0.187385\pi$
$68$	106.629	+	11.9840i	1.56807	+	0.176235i
$69$		0			0
$70$		0			0
$71$		−	31.3190i		−	0.441113i	−0.975374	−	0.220556i	$-0.929213\pi$
$71$		−	31.3190i		−	0.441113i	0.975374	−	0.220556i	$-0.0707873\pi$
$72$		0			0
$73$			110.909i			1.51930i	0.650330	+	0.759652i	$0.274631\pi$
$73$			110.909i			1.51930i	−0.650330	+	0.759652i	$0.725369\pi$
$74$	72.9757	+	81.6369i	0.986158	+	1.10320i
$75$		0			0
$76$	43.2002	+	4.85528i	0.568423	+	0.0638853i
$77$			14.8902i			0.193379i
$78$		0			0
$79$			59.0065i			0.746917i	0.927647	+	0.373459i	$0.121828\pi$
$79$			59.0065i			0.746917i	−0.927647	+	0.373459i	$0.878172\pi$
$80$		0			0
$81$		0			0
$82$	−35.5326	+	31.7628i	−0.433325	+	0.387351i
$83$	142.416			1.71586			0.857930	−	0.513767i	$-0.171751\pi$
$83$	142.416			1.71586			0.857930	+	0.513767i	$0.171751\pi$
$84$		0			0
$85$		0			0
$86$	−83.8765	+	74.9776i	−0.975308	+	0.871833i
$87$		0			0
$88$	−14.7864	+	10.5008i	−0.168027	+	0.119327i
$89$	7.14798			0.0803144			0.0401572	−	0.999193i	$-0.487214\pi$
$89$	7.14798			0.0803144			0.0401572	+	0.999193i	$0.487214\pi$
$90$		0			0
$91$		−	97.7185i		−	1.07383i
$92$	16.2889	−	144.932i	0.177053	−	1.57534i
$93$		0			0
$94$	76.6689	−	68.5347i	0.815626	−	0.729093i
$95$		0			0
$96$		0			0
$97$			126.308i			1.30214i	0.759017	+	0.651070i	$0.225680\pi$
$97$			126.308i			1.30214i	−0.759017	+	0.651070i	$0.774320\pi$
$98$	8.73319	−	7.80665i	0.0891142	−	0.0796597i
$99$		0			0
$100$		0			0
$101$	−86.7133			−0.858547			−0.429274	−	0.903174i	$-0.641230\pi$
$101$	−86.7133			−0.858547			−0.429274	+	0.903174i	$0.641230\pi$
$102$		0			0
$103$	21.9281			0.212895			0.106447	−	0.994318i	$-0.466052\pi$
$103$	21.9281			0.212895			0.106447	+	0.994318i	$0.466052\pi$
$104$	97.0372	−	68.9126i	0.933050	−	0.662622i
$105$		0			0
$106$	40.8488	+	45.6970i	0.385366	+	0.431104i
$107$	−7.17725			−0.0670771			−0.0335385	−	0.999437i	$-0.510678\pi$
$107$	−7.17725			−0.0670771			−0.0335385	+	0.999437i	$0.510678\pi$
$108$		0			0
$109$	−25.4256			−0.233262			−0.116631	−	0.993175i	$-0.537210\pi$
$109$	−25.4256			−0.233262			−0.116631	+	0.993175i	$0.537210\pi$
$110$		0			0
$111$		0			0
$112$	−102.472	−	23.3283i	−0.914925	−	0.208288i
$113$			78.3588i			0.693441i	0.937968	+	0.346720i	$0.112705\pi$
$113$			78.3588i			0.693441i	−0.937968	+	0.346720i	$0.887295\pi$
$114$		0			0
$115$		0			0
$116$	−15.7483	+	140.122i	−0.135761	+	1.20795i
$117$		0			0
$118$	−9.23012	−	10.3256i	−0.0782214	−	0.0875052i
$119$			176.196i			1.48063i
$120$		0			0
$121$	115.861			0.957528
$122$	−160.182	+	143.188i	−1.31297	+	1.17367i
$123$		0			0
$124$	94.7357	+	10.6474i	0.763997	+	0.0858659i
$125$		0			0
$126$		0			0
$127$	−71.6077			−0.563840			−0.281920	−	0.959438i	$-0.590971\pi$
$127$	−71.6077			−0.563840			−0.281920	+	0.959438i	$0.590971\pi$
$128$	−49.0990	−	118.209i	−0.383586	−	0.923505i
$129$		0			0
$130$		0			0
$131$			103.978i			0.793728i	0.917877	+	0.396864i	$0.129902\pi$
$131$			103.978i			0.793728i	−0.917877	+	0.396864i	$0.870098\pi$
$132$		0			0
$133$			71.3850i			0.536729i
$134$	−166.174	+	148.543i	−1.24010	+	1.10853i
$135$		0			0
$136$	−174.967	+	124.256i	−1.28652	+	0.913647i
$137$			7.16645i			0.0523099i	0.999658	+	0.0261549i	$0.00832633\pi$
$137$			7.16645i			0.0523099i	−0.999658	+	0.0261549i	$0.991674\pi$
$138$		0			0
$139$			146.909i			1.05690i	0.848965	+	0.528449i	$0.177226\pi$
$139$			146.909i			1.05690i	−0.848965	+	0.528449i	$0.822774\pi$
$140$		0			0
$141$		0			0
$142$	41.7451	+	46.6997i	0.293980	+	0.328871i
$143$	33.7261			0.235847
$144$		0			0
$145$		0			0
$146$	−147.831	−	165.376i	−1.01254	−	1.13272i
$147$		0			0
$148$	−217.628	−	24.4593i	−1.47046	−	0.165265i
$149$	79.6054			0.534265			0.267132	−	0.963660i	$-0.413924\pi$
$149$	79.6054			0.534265			0.267132	+	0.963660i	$0.413924\pi$
$150$		0			0
$151$		−	182.722i		−	1.21008i	−0.796196	−	0.605039i	$-0.793158\pi$
$151$		−	182.722i		−	1.21008i	0.796196	−	0.605039i	$-0.206842\pi$
$152$	−70.8873	+	50.3418i	−0.466364	+	0.331196i
$153$		0			0
$154$	−19.8472	−	22.2027i	−0.128878	−	0.144174i
$155$		0			0
$156$		0			0
$157$			212.182i			1.35148i	0.737141	+	0.675739i	$0.236175\pi$
$157$			212.182i			1.35148i	−0.737141	+	0.675739i	$0.763825\pi$
$158$	−78.6498	−	87.9844i	−0.497783	−	0.556864i
$159$		0			0
$160$		0			0
$161$	239.488			1.48751
$162$		0			0
$163$	243.400			1.49325			0.746626	−	0.665244i	$-0.231673\pi$
$163$	243.400			1.49325			0.746626	+	0.665244i	$0.231673\pi$
$164$	10.6459	−	94.7229i	0.0649143	−	0.577579i
$165$		0			0
$166$	−212.357	+	189.827i	−1.27926	+	1.14354i
$167$	211.395			1.26584			0.632919	−	0.774218i	$-0.281857\pi$
$167$	211.395			1.26584			0.632919	+	0.774218i	$0.281857\pi$
$168$		0			0
$169$	−52.3307			−0.309649
$170$		0			0
$171$		0			0
$172$	25.1303	−	223.598i	0.146106	−	1.29999i
$173$		−	22.3138i		−	0.128982i	−0.997918	−	0.0644909i	$-0.979458\pi$
$173$		−	22.3138i		−	0.128982i	0.997918	−	0.0644909i	$-0.0205423\pi$
$174$		0			0
$175$		0			0
$176$	8.05141	−	35.3665i	0.0457467	−	0.200946i
$177$		0			0
$178$	−10.6583	+	9.52755i	−0.0598783	+	0.0535255i
$179$		−	94.5219i		−	0.528055i	−0.964515	−	0.264028i	$-0.914949\pi$
$179$		−	94.5219i		−	0.528055i	0.964515	−	0.264028i	$-0.0850510\pi$
$180$		0			0
$181$	−80.6179			−0.445403			−0.222702	−	0.974887i	$-0.571488\pi$
$181$	−80.6179			−0.445403			−0.222702	+	0.974887i	$0.571488\pi$
$182$	130.249	+	145.708i	0.715654	+	0.800592i
$183$		0			0
$184$	168.891	+	237.819i	0.917887	+	1.29249i
$185$		0			0
$186$		0			0
$187$	−60.8112			−0.325194
$188$	−22.9708	+	204.384i	−0.122185	+	1.08715i
$189$		0			0
$190$		0			0
$191$		−	330.540i		−	1.73058i	−0.501275	−	0.865288i	$-0.667135\pi$
$191$		−	330.540i		−	1.73058i	0.501275	−	0.865288i	$-0.332865\pi$
$192$		0			0
$193$		−	103.609i		−	0.536836i	−0.963303	−	0.268418i	$-0.913499\pi$
$193$		−	103.609i		−	0.536836i	0.963303	−	0.268418i	$-0.0865008\pi$
$194$	−168.356	−	188.337i	−0.867812	−	0.970810i
$195$		0			0
$196$	−2.61656	+	23.2810i	−0.0133498	+	0.118780i
$197$			160.633i			0.815394i	0.913117	+	0.407697i	$0.133668\pi$
$197$			160.633i			0.815394i	−0.913117	+	0.407697i	$0.866332\pi$
$198$		0			0
$199$		−	27.5518i		−	0.138451i	−0.997601	−	0.0692255i	$-0.977947\pi$
$199$		−	27.5518i		−	0.138451i	0.997601	−	0.0692255i	$-0.0220528\pi$
$200$		0			0
$201$		0			0
$202$	129.298	−	115.580i	0.640089	−	0.572179i
$203$	−231.540			−1.14059
$204$		0			0
$205$		0			0
$206$	−32.6970	+	29.2280i	−0.158723	+	0.141884i
$207$		0			0
$208$	−52.8382	+	232.097i	−0.254030	+	1.11585i
$209$	−24.6374			−0.117883
$210$		0			0
$211$		−	269.808i		−	1.27871i	−0.768911	−	0.639355i	$-0.779201\pi$
$211$		−	269.808i		−	1.27871i	0.768911	−	0.639355i	$-0.220799\pi$
$212$	−121.819	−	13.6913i	−0.574618	−	0.0645816i
$213$		0			0
$214$	10.7020	−	9.56656i	0.0500093	−	0.0447036i
$215$		0			0
$216$		0			0
$217$			156.544i			0.721399i
$218$	37.9120	−	33.8898i	0.173908	−	0.155458i
$219$		0			0
$220$		0			0
$221$	399.080			1.80579
$222$		0			0
$223$	−41.3345			−0.185356			−0.0926782	−	0.995696i	$-0.529543\pi$
$223$	−41.3345			−0.185356			−0.0926782	+	0.995696i	$0.529543\pi$
$224$	183.890	−	101.800i	0.820935	−	0.454463i
$225$		0			0
$226$	−104.445	−	116.841i	−0.462144	−	0.516994i
$227$	149.837			0.660076			0.330038	−	0.943968i	$-0.392939\pi$
$227$	149.837			0.660076			0.330038	+	0.943968i	$0.392939\pi$
$228$		0			0
$229$	61.6770			0.269332			0.134666	−	0.990891i	$-0.457004\pi$
$229$	61.6770			0.269332			0.134666	+	0.990891i	$0.457004\pi$
$230$		0			0
$231$		0			0
$232$	−163.286	−	229.926i	−0.703819	−	0.991061i
$233$			405.585i			1.74071i	0.492425	+	0.870355i	$0.336110\pi$
$233$			405.585i			1.74071i	−0.492425	+	0.870355i	$0.663890\pi$
$234$		0			0
$235$		0			0
$236$	27.5260	+	3.09366i	0.116636	+	0.0131087i
$237$		0			0
$238$	−234.851	−	262.725i	−0.986770	−	1.10389i
$239$			267.769i			1.12037i	0.828367	+	0.560185i	$0.189270\pi$
$239$			267.769i			1.12037i	−0.828367	+	0.560185i	$0.810730\pi$
$240$		0			0
$241$	−89.5377			−0.371526			−0.185763	−	0.982595i	$-0.559476\pi$
$241$	−89.5377			−0.371526			−0.185763	+	0.982595i	$0.559476\pi$
$242$	−172.760	+	154.431i	−0.713884	+	0.638145i
$243$		0			0
$244$	47.9922	−	427.014i	0.196689	−	1.75006i
$245$		0			0
$246$		0			0
$247$	161.686			0.654598
$248$	−155.452	+	110.397i	−0.626823	+	0.445149i
$249$		0			0
$250$		0			0
$251$			227.844i			0.907745i	0.891067	+	0.453873i	$0.149958\pi$
$251$			227.844i			0.907745i	−0.891067	+	0.453873i	$0.850042\pi$
$252$		0			0
$253$			82.6559i			0.326703i
$254$	106.774	−	95.4460i	0.420371	−	0.375772i
$255$		0			0
$256$	230.772	+	110.817i	0.901453	+	0.432878i
$257$		−	442.129i		−	1.72035i	−0.510003	−	0.860173i	$-0.670356\pi$
$257$		−	442.129i		−	1.72035i	0.510003	−	0.860173i	$-0.329644\pi$
$258$		0			0
$259$		−	359.614i		−	1.38847i
$260$		0			0
$261$		0			0
$262$	−138.593	−	155.042i	−0.528981	−	0.591763i
$263$	−34.1556			−0.129869			−0.0649346	−	0.997890i	$-0.520684\pi$
$263$	−34.1556			−0.129869			−0.0649346	+	0.997890i	$0.520684\pi$
$264$		0			0
$265$		0			0
$266$	−95.1491	−	106.442i	−0.357703	−	0.400158i
$267$		0			0
$268$	49.7873	−	442.986i	0.185774	−	1.65293i
$269$	−9.96085			−0.0370292			−0.0185146	−	0.999829i	$-0.505894\pi$
$269$	−9.96085			−0.0370292			−0.0185146	+	0.999829i	$0.505894\pi$
$270$		0			0
$271$			56.5791i			0.208779i	0.994536	+	0.104390i	$0.0332889\pi$
$271$			56.5791i			0.208779i	−0.994536	+	0.104390i	$0.966711\pi$
$272$	95.2723	−	418.492i	0.350266	−	1.53857i
$273$		0			0
$274$	−9.55218	−	10.6859i	−0.0348620	−	0.0389996i
$275$		0			0
$276$		0			0
$277$		−	103.794i		−	0.374708i	−0.982292	−	0.187354i	$-0.940009\pi$
$277$		−	103.794i		−	0.374708i	0.982292	−	0.187354i	$-0.0599911\pi$
$278$	−195.815	−	219.056i	−0.704370	−	0.787969i
$279$		0			0
$280$		0			0
$281$	−393.069			−1.39882			−0.699411	−	0.714720i	$-0.746554\pi$
$281$	−393.069			−1.39882			−0.699411	+	0.714720i	$0.746554\pi$
$282$		0			0
$283$	−114.027			−0.402923			−0.201462	−	0.979496i	$-0.564569\pi$
$283$	−114.027			−0.402923			−0.201462	+	0.979496i	$0.564569\pi$
$284$	−124.492	−	13.9917i	−0.438353	−	0.0492666i
$285$		0			0
$286$	−50.2889	+	44.9535i	−0.175835	+	0.157180i
$287$	156.522			0.545374
$288$		0			0
$289$	−430.579			−1.48989
$290$		0			0
$291$		0			0
$292$	440.861	+	49.5485i	1.50980	+	0.169687i
$293$		−	126.796i		−	0.432750i	−0.976310	−	0.216375i	$-0.930577\pi$
$293$		−	126.796i		−	0.432750i	0.976310	−	0.216375i	$-0.0694234\pi$
$294$		0			0
$295$		0			0
$296$	357.106	−	253.605i	1.20644	−	0.856775i
$297$		0			0
$298$	−118.700	+	106.106i	−0.398321	+	0.356061i
$299$		−	542.438i		−	1.81417i
$300$		0			0
$301$	369.479			1.22750
$302$	243.550	+	272.456i	0.806457	+	0.902172i
$303$		0			0
$304$	38.5992	−	169.550i	0.126971	−	0.557732i
$305$		0			0
$306$		0			0
$307$	408.420			1.33036			0.665180	−	0.746683i	$-0.268355\pi$
$307$	408.420			1.33036			0.665180	+	0.746683i	$0.268355\pi$
$308$	59.1881	+	6.65217i	0.192169	+	0.0215980i
$309$		0			0
$310$		0			0
$311$		−	472.495i		−	1.51928i	−0.650345	−	0.759639i	$-0.725376\pi$
$311$		−	472.495i		−	1.51928i	0.650345	−	0.759639i	$-0.274624\pi$
$312$		0			0
$313$			54.6519i			0.174607i	0.996182	+	0.0873033i	$0.0278249\pi$
$313$			54.6519i			0.174607i	−0.996182	+	0.0873033i	$0.972175\pi$
$314$	−282.818	−	316.384i	−0.900693	−	1.00759i
$315$		0			0
$316$	234.549	+	26.3611i	0.742244	+	0.0834211i
$317$		−	63.3734i		−	0.199916i	−0.994992	−	0.0999581i	$-0.968129\pi$
$317$		−	63.3734i		−	0.199916i	0.994992	−	0.0999581i	$-0.0318709\pi$
$318$		0			0
$319$		−	79.9127i		−	0.250510i
$320$		0			0
$321$		0			0
$322$	−357.101	+	319.215i	−1.10901	+	0.991349i
$323$	−291.535			−0.902584
$324$		0			0
$325$		0			0
$326$	−362.933	+	324.428i	−1.11329	+	0.995179i
$327$		0			0
$328$	110.382	+	155.431i	0.336531	+	0.473876i
$329$	−337.729			−1.02653
$330$		0			0
$331$		−	431.595i		−	1.30391i	−0.758257	−	0.651955i	$-0.773949\pi$
$331$		−	431.595i		−	1.30391i	0.758257	−	0.651955i	$-0.226051\pi$
$332$	63.6243	−	566.101i	0.191639	−	1.70512i
$333$		0			0
$334$	−315.211	+	281.768i	−0.943744	+	0.843618i
$335$		0			0
$336$		0			0
$337$		−	486.091i		−	1.44241i	−0.692723	−	0.721203i	$-0.743589\pi$
$337$		−	486.091i		−	1.44241i	0.692723	−	0.721203i	$-0.256411\pi$
$338$	78.0303	−	69.7517i	0.230859	−	0.206366i
$339$		0			0
$340$		0			0
$341$	−54.0286			−0.158442
$342$		0			0
$343$	−360.319			−1.05049
$344$	260.562	+	366.903i	0.757449	+	1.06658i
$345$		0			0
$346$	29.7422	+	33.2721i	0.0859600	+	0.0961623i
$347$	−294.297			−0.848119			−0.424060	−	0.905634i	$-0.639395\pi$
$347$	−294.297			−0.848119			−0.424060	+	0.905634i	$0.639395\pi$
$348$		0			0
$349$	−83.0428			−0.237945			−0.118972	−	0.992898i	$-0.537960\pi$
$349$	−83.0428			−0.237945			−0.118972	+	0.992898i	$0.537960\pi$
$350$		0			0
$351$		0			0
$352$	35.1346	+	63.4667i	0.0998143	+	0.180303i
$353$		−	570.733i		−	1.61681i	−0.588628	−	0.808404i	$-0.700332\pi$
$353$		−	570.733i		−	1.61681i	0.588628	−	0.808404i	$-0.299668\pi$
$354$		0			0
$355$		0			0
$356$	3.19335	−	28.4130i	0.00897008	−	0.0798119i
$357$		0			0
$358$	125.988	+	140.941i	0.351923	+	0.393691i
$359$		−	558.265i		−	1.55506i	−0.628848	−	0.777528i	$-0.716473\pi$
$359$		−	558.265i		−	1.55506i	0.628848	−	0.777528i	$-0.283527\pi$
$360$		0			0
$361$	242.886			0.672814
$362$	120.209	−	107.456i	0.332070	−	0.296839i
$363$		0			0
$364$	−388.428	−	43.6556i	−1.06711	−	0.119933i
$365$		0			0
$366$		0			0
$367$	−446.467			−1.21653			−0.608265	−	0.793734i	$-0.708134\pi$
$367$	−446.467			−1.21653			−0.608265	+	0.793734i	$0.708134\pi$
$368$	−568.822	−	129.496i	−1.54571	−	0.351891i
$369$		0			0
$370$		0			0
$371$		−	201.297i		−	0.542579i
$372$		0			0
$373$			112.924i			0.302744i	0.988477	+	0.151372i	$0.0483692\pi$
$373$			112.924i			0.302744i	−0.988477	+	0.151372i	$0.951631\pi$
$374$	90.6755	−	81.0554i	0.242448	−	0.216726i
$375$		0			0
$376$	−238.172	−	335.375i	−0.633436	−	0.891954i
$377$			524.435i			1.39108i
$378$		0			0
$379$			321.457i			0.848173i	0.905622	+	0.424086i	$0.139405\pi$
$379$			321.457i			0.848173i	−0.905622	+	0.424086i	$0.860595\pi$
$380$		0			0
$381$		0			0
$382$	440.577	+	492.868i	1.15334	+	1.29023i
$383$	−89.2269			−0.232968			−0.116484	−	0.993193i	$-0.537162\pi$
$383$	−89.2269			−0.232968			−0.116484	+	0.993193i	$0.537162\pi$
$384$		0			0
$385$		0			0
$386$	138.101	+	154.492i	0.357775	+	0.400238i
$387$		0			0
$388$	502.069	+	56.4278i	1.29399	+	0.145432i
$389$	260.714			0.670217			0.335108	−	0.942180i	$-0.391227\pi$
$389$	260.714			0.670217			0.335108	+	0.942180i	$0.391227\pi$
$390$		0			0
$391$			978.066i			2.50145i
$392$	−27.1297	−	38.2018i	−0.0692084	−	0.0974536i
$393$		0			0
$394$	−214.107	−	239.519i	−0.543420	−	0.607916i
$395$		0			0
$396$		0			0
$397$			112.607i			0.283644i	0.989892	+	0.141822i	$0.0452960\pi$
$397$			112.607i			0.283644i	−0.989892	+	0.141822i	$0.954704\pi$
$398$	36.7238	+	41.0824i	0.0922708	+	0.103222i
$399$		0			0
$400$		0			0
$401$	−577.513			−1.44018			−0.720091	−	0.693880i	$-0.755900\pi$
$401$	−577.513			−1.44018			−0.720091	+	0.693880i	$0.755900\pi$
$402$		0			0
$403$	354.569			0.879823
$404$	−38.7390	+	344.683i	−0.0958887	+	0.853176i
$405$		0			0
$406$	345.250	−	308.621i	0.850368	−	0.760149i
$407$	124.115			0.304951
$408$		0			0
$409$	276.255			0.675441			0.337721	−	0.941246i	$-0.390344\pi$
$409$	276.255			0.675441			0.337721	+	0.941246i	$0.390344\pi$
$410$		0			0
$411$		0			0
$412$	9.79636	−	87.1638i	0.0237776	−	0.211563i
$413$			45.4847i			0.110132i
$414$		0			0
$415$		0			0
$416$	−230.575	−	416.507i	−0.554266	−	1.00122i
$417$		0			0
$418$	36.7369	−	32.8393i	0.0878872	−	0.0785629i
$419$			247.520i			0.590739i	0.955383	+	0.295370i	$0.0954428\pi$
$419$			247.520i			0.590739i	−0.955383	+	0.295370i	$0.904557\pi$
$420$		0			0
$421$	−77.7303			−0.184632			−0.0923162	−	0.995730i	$-0.529427\pi$
$421$	−77.7303			−0.184632			−0.0923162	+	0.995730i	$0.529427\pi$
$422$	359.627	+	402.310i	0.852197	+	0.953342i
$423$		0			0
$424$	199.893	−	141.958i	0.471447	−	0.334806i
$425$		0			0
$426$		0			0
$427$	705.608			1.65248
$428$	−3.20643	+	28.5294i	−0.00749165	+	0.0666574i
$429$		0			0
$430$		0			0
$431$			317.184i			0.735926i	0.929840	+	0.367963i	$0.119945\pi$
$431$			317.184i			0.735926i	−0.929840	+	0.367963i	$0.880055\pi$
$432$		0			0
$433$			82.9688i			0.191614i	0.995400	+	0.0958069i	$0.0305431\pi$
$433$			82.9688i			0.191614i	−0.995400	+	0.0958069i	$0.969457\pi$
$434$	−208.657	−	233.422i	−0.480777	−	0.537838i
$435$		0			0
$436$	−11.3588	+	101.066i	−0.0260524	+	0.231803i
$437$			396.260i			0.906773i
$438$		0			0
$439$		−	117.621i		−	0.267930i	−0.990986	−	0.133965i	$-0.957229\pi$
$439$		−	117.621i		−	0.267930i	0.990986	−	0.133965i	$-0.0427709\pi$
$440$		0			0
$441$		0			0
$442$	−595.068	+	531.934i	−1.34631	+	1.20347i
$443$	−35.1780			−0.0794086			−0.0397043	−	0.999211i	$-0.512642\pi$
$443$	−35.1780			−0.0794086			−0.0397043	+	0.999211i	$0.512642\pi$
$444$		0			0
$445$		0			0
$446$	61.6337	−	55.0948i	0.138192	−	0.123531i
$447$		0			0
$448$	−138.508	+	396.900i	−0.309171	+	0.885938i
$449$	−67.4253			−0.150168			−0.0750838	−	0.997177i	$-0.523922\pi$
$449$	−67.4253			−0.150168			−0.0750838	+	0.997177i	$0.523922\pi$
$450$		0			0
$451$			54.0214i			0.119781i
$452$	311.474	+	35.0067i	0.689102	+	0.0774484i
$453$		0			0
$454$	−223.422	+	199.718i	−0.492119	+	0.439908i
$455$		0			0
$456$		0			0
$457$		−	204.153i		−	0.446724i	−0.974736	−	0.223362i	$-0.928297\pi$
$457$		−	204.153i		−	0.446724i	0.974736	−	0.223362i	$-0.0717032\pi$
$458$	−91.9665	+	82.2094i	−0.200800	+	0.179496i
$459$		0			0
$460$		0			0
$461$	−125.762			−0.272802			−0.136401	−	0.990654i	$-0.543554\pi$
$461$	−125.762			−0.272802			−0.136401	+	0.990654i	$0.543554\pi$
$462$		0			0
$463$	−553.629			−1.19574			−0.597871	−	0.801592i	$-0.703987\pi$
$463$	−553.629			−1.19574			−0.597871	+	0.801592i	$0.703987\pi$
$464$	549.944	+	125.198i	1.18523	+	0.269824i
$465$		0			0
$466$	−540.605	−	604.768i	−1.16010	−	1.29778i
$467$	−625.772			−1.33998			−0.669991	−	0.742369i	$-0.733702\pi$
$467$	−625.772			−1.33998			−0.669991	+	0.742369i	$0.733702\pi$
$468$		0			0
$469$	732.000			1.56077
$470$		0			0
$471$		0			0
$472$	−45.1676	+	32.0765i	−0.0956940	+	0.0679588i
$473$			127.520i			0.269598i
$474$		0			0
$475$		0			0
$476$	700.373	+	78.7151i	1.47137	+	0.165368i
$477$		0			0
$478$	−356.909	−	399.269i	−0.746672	−	0.835291i
$479$			488.207i			1.01922i	0.860405	+	0.509610i	$0.170210\pi$
$479$			488.207i			1.01922i	−0.860405	+	0.509610i	$0.829790\pi$
$480$		0			0
$481$	−814.519			−1.69339
$482$	133.509	−	119.345i	0.276991	−	0.247604i
$483$		0			0
$484$	51.7607	−	460.544i	0.106944	−	0.951537i
$485$		0			0
$486$		0			0
$487$	−609.476			−1.25149			−0.625746	−	0.780027i	$-0.715205\pi$
$487$	−609.476			−1.25149			−0.625746	+	0.780027i	$0.715205\pi$
$488$	497.606	+	700.689i	1.01968	+	1.43584i
$489$		0			0
$490$		0			0
$491$			689.074i			1.40341i	0.712468	+	0.701705i	$0.247578\pi$
$491$			689.074i			1.40341i	−0.712468	+	0.701705i	$0.752422\pi$
$492$		0			0
$493$		−	945.606i		−	1.91806i
$494$	−241.089	+	215.511i	−0.488035	+	0.436257i
$495$		0			0
$496$	84.6461	−	371.815i	0.170657	−	0.749627i
$497$		−	205.714i		−	0.413911i
$498$		0			0
$499$			700.401i			1.40361i	0.712370	+	0.701804i	$0.247622\pi$
$499$			700.401i			1.40361i	−0.712370	+	0.701804i	$0.752378\pi$
$500$		0			0
$501$		0			0
$502$	−303.694	−	339.738i	−0.604967	−	0.676769i
$503$	943.945			1.87663			0.938315	−	0.345782i	$-0.112386\pi$
$503$	943.945			1.87663			0.938315	+	0.345782i	$0.112386\pi$
$504$		0			0
$505$		0			0
$506$	−110.172	−	123.248i	−0.217731	−	0.243573i
$507$		0			0
$508$	−31.9906	+	284.639i	−0.0629737	+	0.560313i
$509$	−357.147			−0.701665			−0.350832	−	0.936438i	$-0.614101\pi$
$509$	−357.147			−0.701665			−0.350832	+	0.936438i	$0.614101\pi$
$510$		0			0
$511$			728.489i			1.42562i
$512$	−491.811	+	142.358i	−0.960569	+	0.278042i
$513$		0			0
$514$	589.314	+	659.258i	1.14653	+	1.28260i
$515$		0			0
$516$		0			0
$517$		−	116.562i		−	0.225459i
$518$	479.329	+	536.219i	0.925346	+	1.03517i
$519$		0			0
$520$		0			0
$521$	88.8415			0.170521			0.0852605	−	0.996359i	$-0.472828\pi$
$521$	88.8415			0.170521			0.0852605	+	0.996359i	$0.472828\pi$
$522$		0			0
$523$	−220.427			−0.421467			−0.210734	−	0.977544i	$-0.567585\pi$
$523$	−220.427			−0.421467			−0.210734	+	0.977544i	$0.567585\pi$
$524$	413.311	+	46.4522i	0.788762	+	0.0886492i
$525$		0			0
$526$	50.9294	−	45.5261i	0.0968239	−	0.0865514i
$527$	−639.320			−1.21313
$528$		0			0
$529$	800.407			1.51306
$530$		0			0
$531$		0			0
$532$	283.753	+	31.8911i	0.533371	+	0.0599457i
$533$		−	354.521i		−	0.665142i
$534$		0			0
$535$		0			0
$536$	516.219	+	726.897i	0.963094	+	1.35615i
$537$		0			0
$538$	14.8526	−	13.2768i	0.0276071	−	0.0246781i
$539$		−	13.2774i		−	0.0246333i
$540$		0			0
$541$	−411.560			−0.760740			−0.380370	−	0.924834i	$-0.624203\pi$
$541$	−411.560			−0.760740			−0.380370	+	0.924834i	$0.624203\pi$
$542$	−75.4144	−	84.3651i	−0.139141	−	0.155655i
$543$		0			0
$544$	415.748	+	751.001i	0.764242	+	1.38052i
$545$		0			0
$546$		0			0
$547$	−851.537			−1.55674			−0.778370	−	0.627806i	$-0.783953\pi$
$547$	−851.537			−1.55674			−0.778370	+	0.627806i	$0.783953\pi$
$548$	28.4865	+	3.20160i	0.0519826	+	0.00584234i
$549$		0			0
$550$		0			0
$551$		−	383.109i		−	0.695297i
$552$		0			0
$553$			387.575i			0.700858i
$554$	138.347	+	154.767i	0.249724	+	0.279363i
$555$		0			0
$556$	583.959	+	65.6313i	1.05029	+	0.118042i
$557$		−	211.553i		−	0.379808i	−0.981803	−	0.189904i	$-0.939182\pi$
$557$		−	211.553i		−	0.379808i	0.981803	−	0.189904i	$-0.0608177\pi$
$558$		0			0
$559$		−	836.864i		−	1.49707i
$560$		0			0
$561$		0			0
$562$	586.104	−	523.922i	1.04289	−	0.932246i
$563$	−404.044			−0.717663			−0.358832	−	0.933402i	$-0.616825\pi$
$563$	−404.044			−0.717663			−0.358832	+	0.933402i	$0.616825\pi$
$564$		0			0
$565$		0			0
$566$	170.026	−	151.987i	0.300399	−	0.268529i
$567$		0			0
$568$	204.280	−	145.073i	0.359647	−	0.255410i
$569$	230.465			0.405036			0.202518	−	0.979279i	$-0.435088\pi$
$569$	230.465			0.405036			0.202518	+	0.979279i	$0.435088\pi$
$570$		0			0
$571$			351.234i			0.615121i	0.951529	+	0.307560i	$0.0995126\pi$
$571$			351.234i			0.615121i	−0.951529	+	0.307560i	$0.900487\pi$
$572$	15.0671	−	134.060i	0.0263410	−	0.234371i
$573$		0			0
$574$	−233.390	+	208.629i	−0.406603	+	0.363465i
$575$		0			0
$576$		0			0
$577$		−	638.575i		−	1.10672i	−0.832944	−	0.553358i	$-0.813346\pi$
$577$		−	638.575i		−	1.10672i	0.832944	−	0.553358i	$-0.186654\pi$
$578$	642.035	−	573.919i	1.11079	−	0.992939i
$579$		0			0
$580$		0			0
$581$	935.439			1.61005
$582$		0			0
$583$	69.4746			0.119167
$584$	−723.410	+	513.742i	−1.23872	+	0.879696i
$585$		0			0
$586$	169.006	+	189.065i	0.288407	+	0.322637i
$587$	−105.047			−0.178956			−0.0894779	−	0.995989i	$-0.528520\pi$
$587$	−105.047			−0.178956			−0.0894779	+	0.995989i	$0.528520\pi$
$588$		0			0
$589$	−259.018			−0.439759
$590$		0			0
$591$		0			0
$592$	−194.450	+	854.138i	−0.328463	+	1.44280i
$593$			990.175i			1.66977i	0.550422	+	0.834886i	$0.314467\pi$
$593$			990.175i			1.66977i	−0.550422	+	0.834886i	$0.685533\pi$
$594$		0			0
$595$		0			0
$596$	35.5636	−	316.429i	0.0596705	−	0.530922i
$597$		0			0
$598$	723.016	+	808.828i	1.20906	+	1.35255i
$599$			78.0745i			0.130341i	0.997874	+	0.0651707i	$0.0207592\pi$
$599$			78.0745i			0.130341i	−0.997874	+	0.0651707i	$0.979241\pi$
$600$		0			0
$601$	−616.498			−1.02579			−0.512893	−	0.858452i	$-0.671426\pi$
$601$	−616.498			−1.02579			−0.512893	+	0.858452i	$0.671426\pi$
$602$	−550.929	+	492.479i	−0.915165	+	0.818071i
$603$		0			0
$604$	−726.314	−	81.6306i	−1.20251	−	0.135150i
$605$		0			0
$606$		0			0
$607$	226.520			0.373179			0.186590	−	0.982438i	$-0.440257\pi$
$607$	226.520			0.373179			0.186590	+	0.982438i	$0.440257\pi$
$608$	168.439	+	304.265i	0.277037	+	0.500436i
$609$		0			0
$610$		0			0
$611$			764.951i			1.25197i
$612$		0			0
$613$		−	732.519i		−	1.19497i	−0.801879	−	0.597487i	$-0.796166\pi$
$613$		−	732.519i		−	1.19497i	0.801879	−	0.597487i	$-0.203834\pi$
$614$	−608.995	+	544.384i	−0.991848	+	0.886619i
$615$		0			0
$616$	−97.1220	+	68.9729i	−0.157666	+	0.111969i
$617$		−	350.585i		−	0.568209i	−0.958793	−	0.284105i	$-0.908304\pi$
$617$		−	350.585i		−	0.568209i	0.958793	−	0.284105i	$-0.0916963\pi$
$618$		0			0
$619$		−	237.923i		−	0.384367i	−0.981359	−	0.192184i	$-0.938443\pi$
$619$		−	237.923i		−	0.384367i	0.981359	−	0.192184i	$-0.0615569\pi$
$620$		0			0
$621$		0			0
$622$	629.790	+	704.537i	1.01252	+	1.13270i
$623$	46.9504			0.0753617
$624$		0			0
$625$		0			0
$626$	−72.8455	−	81.4913i	−0.116367	−	0.130178i
$627$		0			0
$628$	843.417	+	94.7920i	1.34302	+	0.150943i
$629$	1468.65			2.33490
$630$		0			0
$631$		−	200.923i		−	0.318419i	−0.987245	−	0.159210i	$-0.949105\pi$
$631$		−	200.923i		−	0.318419i	0.987245	−	0.159210i	$-0.0508946\pi$
$632$	−384.873	+	273.324i	−0.608976	+	0.432475i
$633$		0			0
$634$	84.4705	+	94.4960i	0.133234	+	0.149047i
$635$		0			0
$636$		0			0
$637$			87.1340i			0.136788i
$638$	106.516	+	119.158i	0.166953	+	0.186768i
$639$		0			0
$640$		0			0
$641$	−216.861			−0.338316			−0.169158	−	0.985589i	$-0.554105\pi$
$641$	−216.861			−0.338316			−0.169158	+	0.985589i	$0.554105\pi$
$642$		0			0
$643$	−37.5349			−0.0583746			−0.0291873	−	0.999574i	$-0.509292\pi$
$643$	−37.5349			−0.0583746			−0.0291873	+	0.999574i	$0.509292\pi$
$644$	106.991	−	951.960i	0.166135	−	1.47820i
$645$		0			0
$646$	434.707	−	388.587i	0.672921	−	0.601528i
$647$	1192.56			1.84321			0.921607	−	0.388125i	$-0.126877\pi$
$647$	1192.56			1.84321			0.921607	+	0.388125i	$0.126877\pi$
$648$		0			0
$649$	−15.6984			−0.0241885
$650$		0			0
$651$		0			0
$652$	108.739	−	967.509i	0.166777	−	1.48391i
$653$		−	1087.78i		−	1.66582i	−0.553412	−	0.832908i	$-0.686675\pi$
$653$		−	1087.78i		−	1.66582i	0.553412	−	0.832908i	$-0.313325\pi$
$654$		0			0
$655$		0			0
$656$	−371.765	−	84.6347i	−0.566715	−	0.129016i
$657$		0			0
$658$	503.587	−	450.160i	0.765330	−	0.684133i
$659$			852.957i			1.29432i	0.762354	+	0.647160i	$0.224044\pi$
$659$			852.957i			1.29432i	−0.762354	+	0.647160i	$0.775956\pi$
$660$		0			0
$661$	−504.933			−0.763892			−0.381946	−	0.924185i	$-0.624746\pi$
$661$	−504.933			−0.763892			−0.381946	+	0.924185i	$0.624746\pi$
$662$	575.273	+	643.550i	0.868992	+	0.972130i
$663$		0			0
$664$	659.687	+	928.917i	0.993504	+	1.39897i
$665$		0			0
$666$		0			0
$667$	−1285.29			−1.92697
$668$	94.4403	−	840.289i	0.141378	−	1.25792i
$669$		0			0
$670$		0			0
$671$			243.530i			0.362936i
$672$		0			0
$673$			902.689i			1.34129i	0.741778	+	0.670646i	$0.233983\pi$
$673$			902.689i			1.34129i	−0.741778	+	0.670646i	$0.766017\pi$
$674$	647.911	+	724.810i	0.961293	+	1.07539i
$675$		0			0
$676$	−23.3787	+	208.013i	−0.0345838	+	0.307712i
$677$		−	930.750i		−	1.37482i	−0.726272	−	0.687408i	$-0.758748\pi$
$677$		−	930.750i		−	1.37482i	0.726272	−	0.687408i	$-0.241252\pi$
$678$		0			0
$679$			829.632i			1.22184i
$680$		0			0
$681$		0			0
$682$	80.5620	−	72.0148i	0.118126	−	0.105594i
$683$	64.9023			0.0950253			0.0475127	−	0.998871i	$-0.484871\pi$
$683$	64.9023			0.0950253			0.0475127	+	0.998871i	$0.484871\pi$
$684$		0			0
$685$		0			0
$686$	537.271	−	480.269i	0.783193	−	0.700101i
$687$		0			0
$688$	−877.570	−	199.784i	−1.27554	−	0.290384i
$689$	−455.934			−0.661733
$690$		0			0
$691$		−	348.329i		−	0.504094i	−0.967715	−	0.252047i	$-0.918896\pi$
$691$		−	348.329i		−	0.504094i	0.967715	−	0.252047i	$-0.0811038\pi$
$692$	−88.6970	−	9.96868i	−0.128175	−	0.0144056i
$693$		0			0
$694$	438.826	−	392.269i	0.632315	−	0.565230i
$695$		0			0
$696$		0			0
$697$			639.234i			0.917122i
$698$	123.825	−	110.688i	0.177400	−	0.158579i
$699$		0			0
$700$		0			0
$701$	−815.159			−1.16285			−0.581426	−	0.813600i	$-0.697505\pi$
$701$	−815.159			−1.16285			−0.581426	+	0.813600i	$0.697505\pi$
$702$		0			0
$703$	595.020			0.846401
$704$	−136.984	−	47.8041i	−0.194580	−	0.0679036i
$705$		0			0
$706$	760.731	+	851.020i	1.07752	+	1.20541i
$707$	−569.562			−0.805605
$708$		0			0
$709$	−1300.08			−1.83368			−0.916839	−	0.399257i	$-0.869268\pi$
$709$	−1300.08			−1.83368			−0.916839	+	0.399257i	$0.869268\pi$
$710$		0			0
$711$		0			0
$712$	33.1102	+	46.6230i	0.0465030	+	0.0654818i
$713$			868.977i			1.21876i
$714$		0			0
$715$		0			0
$716$	−375.722	−	42.2275i	−0.524751	−	0.0589770i
$717$		0			0
$718$	744.112	+	832.428i	1.03637	+	1.15937i
$719$		−	782.612i		−	1.08847i	−0.838932	−	0.544237i	$-0.816819\pi$
$719$		−	782.612i		−	1.08847i	0.838932	−	0.544237i	$-0.183181\pi$
$720$		0			0
$721$	144.031			0.199766
$722$	−362.167	+	323.743i	−0.501616	+	0.448397i
$723$		0			0
$724$	−36.0160	+	320.454i	−0.0497458	+	0.442616i
$725$		0			0
$726$		0			0
$727$	−850.638			−1.17007			−0.585033	−	0.811009i	$-0.698919\pi$
$727$	−850.638			−1.17007			−0.585033	+	0.811009i	$0.698919\pi$
$728$	637.373	−	452.642i	0.875513	−	0.621761i
$729$		0			0
$730$		0			0
$731$			1508.94i			2.06422i
$732$		0			0
$733$		−	365.781i		−	0.499019i	−0.968372	−	0.249510i	$-0.919731\pi$
$733$		−	365.781i		−	0.499019i	0.968372	−	0.249510i	$-0.0802694\pi$
$734$	665.726	−	595.096i	0.906984	−	0.810758i
$735$		0			0
$736$	1020.78	−	565.093i	1.38692	−	0.767789i
$737$			252.639i			0.342794i
$738$		0			0
$739$		−	727.328i		−	0.984205i	−0.870537	−	0.492103i	$-0.836228\pi$
$739$		−	727.328i		−	0.984205i	0.870537	−	0.492103i	$-0.163772\pi$
$740$		0			0
$741$		0			0
$742$	268.309	+	300.153i	0.361602	+	0.404519i
$743$	481.526			0.648083			0.324041	−	0.946043i	$-0.394958\pi$
$743$	481.526			0.648083			0.324041	+	0.946043i	$0.394958\pi$
$744$		0			0
$745$		0			0
$746$	−150.516	−	168.380i	−0.201764	−	0.225711i
$747$		0			0
$748$	−27.1673	+	241.723i	−0.0363200	+	0.323159i
$749$	−47.1426			−0.0629408
$750$		0			0
$751$			1316.30i			1.75273i	0.481647	+	0.876365i	$0.340039\pi$
$751$			1316.30i			1.75273i	−0.481647	+	0.876365i	$0.659961\pi$
$752$	802.159	+	182.617i	1.06670	+	0.242841i
$753$		0			0
$754$	−699.021	−	781.985i	−0.927083	−	1.03711i
$755$		0			0
$756$		0			0
$757$			483.813i			0.639118i	0.947566	+	0.319559i	$0.103535\pi$
$757$			483.813i			0.639118i	−0.947566	+	0.319559i	$0.896465\pi$
$758$	−428.471	−	479.325i	−0.565265	−	0.632354i
$759$		0			0
$760$		0			0
$761$	−1027.03			−1.34958			−0.674789	−	0.738011i	$-0.735765\pi$
$761$	−1027.03			−1.34958			−0.674789	+	0.738011i	$0.735765\pi$
$762$		0			0
$763$	−167.004			−0.218878
$764$	−1313.89	−	147.668i	−1.71975	−	0.193283i
$765$		0			0
$766$	133.046	−	118.931i	0.173689	−	0.155262i
$767$	103.022			0.134318
$768$		0			0
$769$	−1024.79			−1.33263			−0.666314	−	0.745671i	$-0.732129\pi$
$769$	−1024.79			−1.33263			−0.666314	+	0.745671i	$0.732129\pi$
$770$		0			0
$771$		0			0
$772$	−411.844	−	46.2873i	−0.533477	−	0.0599577i
$773$		−	1092.74i		−	1.41364i	−0.707395	−	0.706819i	$-0.750130\pi$
$773$		−	1092.74i		−	1.41364i	0.707395	−	0.706819i	$-0.249870\pi$
$774$		0			0
$775$		0			0
$776$	−823.848	+	585.070i	−1.06166	+	0.753956i
$777$		0			0
$778$	−388.751	+	347.506i	−0.499679	+	0.446666i
$779$			258.983i			0.332456i
$780$		0			0
$781$	70.9991			0.0909079
$782$	−1303.66	−	1458.39i	−1.66709	−	1.86495i
$783$		0			0
$784$	91.3723	+	20.8015i	0.116546	+	0.0265325i
$785$		0			0
$786$		0			0
$787$	1385.63			1.76064			0.880322	−	0.474376i	$-0.157326\pi$
$787$	1385.63			1.76064			0.880322	+	0.474376i	$0.157326\pi$
$788$	638.511	+	71.7624i	0.810293	+	0.0910691i
$789$		0			0
$790$		0			0
$791$			514.688i			0.650680i
$792$		0			0
$793$		−	1598.19i		−	2.01537i
$794$	−150.093	−	167.907i	−0.189034	−	0.211470i
$795$		0			0
$796$	−109.518	−	12.3087i	−0.137585	−	0.0154632i
$797$			98.5251i			0.123620i	0.998088	+	0.0618100i	$0.0196873\pi$
$797$			98.5251i			0.123620i	−0.998088	+	0.0618100i	$0.980313\pi$
$798$		0			0
$799$		−	1379.28i		−	1.72626i
$800$		0			0
$801$		0			0
$802$	861.128	−	769.767i	1.07373	−	0.959810i
$803$	−251.427			−0.313110
$804$		0			0
$805$		0			0
$806$	−528.697	+	472.605i	−0.655951	+	0.586358i
$807$		0			0
$808$	−401.665	−	565.592i	−0.497110	−	0.699990i
$809$	−212.100			−0.262176			−0.131088	−	0.991371i	$-0.541847\pi$
$809$	−212.100			−0.262176			−0.131088	+	0.991371i	$0.541847\pi$
$810$		0			0
$811$			485.409i			0.598531i	0.954170	+	0.299266i	$0.0967417\pi$
$811$			485.409i			0.598531i	−0.954170	+	0.299266i	$0.903258\pi$
$812$	−103.440	+	920.367i	−0.127390	+	1.13346i
$813$		0			0
$814$	−185.068	+	165.433i	−0.227356	+	0.203235i
$815$		0			0
$816$		0			0
$817$			611.343i			0.748278i
$818$	−411.924	+	368.221i	−0.503575	+	0.450148i
$819$		0			0
$820$		0			0
$821$	862.231			1.05022			0.525110	−	0.851034i	$-0.324024\pi$
$821$	862.231			1.05022			0.525110	+	0.851034i	$0.324024\pi$
$822$		0			0
$823$	−485.042			−0.589358			−0.294679	−	0.955596i	$-0.595213\pi$
$823$	−485.042			−0.589358			−0.294679	+	0.955596i	$0.595213\pi$
$824$	101.573	+	143.027i	0.123269	+	0.173577i
$825$		0			0
$826$	−60.6266	−	67.8221i	−0.0733978	−	0.0821091i
$827$	590.547			0.714084			0.357042	−	0.934088i	$-0.383785\pi$
$827$	590.547			0.714084			0.357042	+	0.934088i	$0.383785\pi$
$828$		0			0
$829$	1071.30			1.29228			0.646139	−	0.763220i	$-0.276383\pi$
$829$	1071.30			1.29228			0.646139	+	0.763220i	$0.276383\pi$
$830$		0			0
$831$		0			0
$832$	898.972	+	313.719i	1.08050	+	0.377067i
$833$		−	157.111i		−	0.188608i
$834$		0			0
$835$		0			0
$836$	−11.0067	+	97.9332i	−0.0131660	+	0.117145i
$837$		0			0
$838$	−329.919	−	369.076i	−0.393698	−	0.440425i
$839$			783.581i			0.933946i	0.884272	+	0.466973i	$0.154655\pi$
$839$			783.581i			0.933946i	−0.884272	+	0.466973i	$0.845345\pi$
$840$		0			0
$841$	401.631			0.477564
$842$	115.903	−	103.607i	0.137653	−	0.123048i
$843$		0			0
$844$	−1072.48	−	120.536i	−1.27071	−	0.142816i
$845$		0			0
$846$		0			0
$847$	761.014			0.898481
$848$	−108.845	+	478.111i	−0.128355	+	0.563810i
$849$		0			0
$850$		0			0
$851$		−	1996.22i		−	2.34574i
$852$		0			0
$853$			104.807i			0.122868i	0.998111	+	0.0614341i	$0.0195674\pi$
$853$			104.807i			0.122868i	−0.998111	+	0.0614341i	$0.980433\pi$
$854$	−1052.13	+	940.506i	−1.23200	+	1.10129i
$855$		0			0
$856$	−33.2457	−	46.8140i	−0.0388385	−	0.0546892i
$857$		−	1163.30i		−	1.35741i	−0.734411	−	0.678705i	$-0.762542\pi$
$857$		−	1163.30i		−	1.35741i	0.734411	−	0.678705i	$-0.237458\pi$
$858$		0			0
$859$			337.818i			0.393269i	0.980477	+	0.196634i	$0.0630012\pi$
$859$			337.818i			0.393269i	−0.980477	+	0.196634i	$0.936999\pi$
$860$		0			0
$861$		0			0
$862$	−422.775	−	472.953i	−0.490458	−	0.548669i
$863$	−199.699			−0.231400			−0.115700	−	0.993284i	$-0.536911\pi$
$863$	−199.699			−0.231400			−0.115700	+	0.993284i	$0.536911\pi$
$864$		0			0
$865$		0			0
$866$	−110.589	−	123.715i	−0.127701	−	0.142858i
$867$		0			0
$868$	622.256	+	69.9356i	0.716885	+	0.0805710i
$869$	−133.766			−0.153930
$870$		0			0
$871$		−	1657.97i		−	1.90352i
$872$	−117.774	−	165.840i	−0.135062	−	0.190183i
$873$		0			0
$874$	−528.175	−	590.862i	−0.604319	−	0.676044i
$875$		0			0
$876$		0			0
$877$		−	1032.82i		−	1.17767i	−0.808252	−	0.588836i	$-0.799586\pi$
$877$		−	1032.82i		−	1.17767i	0.808252	−	0.588836i	$-0.200414\pi$
$878$	156.777	+	175.385i	0.178562	+	0.199755i
$879$		0			0
$880$		0			0
$881$	585.412			0.664486			0.332243	−	0.943194i	$-0.392195\pi$
$881$	585.412			0.664486			0.332243	+	0.943194i	$0.392195\pi$
$882$		0			0
$883$	536.231			0.607283			0.303641	−	0.952786i	$-0.401797\pi$
$883$	536.231			0.607283			0.303641	+	0.952786i	$0.401797\pi$
$884$	178.288	−	1586.33i	0.201684	−	1.79449i
$885$		0			0
$886$	52.4539	−	46.8888i	0.0592030	−	0.0529219i
$887$	−173.466			−0.195564			−0.0977822	−	0.995208i	$-0.531175\pi$
$887$	−173.466			−0.195564			−0.0977822	+	0.995208i	$0.531175\pi$
$888$		0			0
$889$	−470.344			−0.529071
$890$		0			0
$891$		0			0
$892$	−18.4661	+	164.303i	−0.0207019	+	0.184197i
$893$		−	558.810i		−	0.625767i
$894$		0			0
$895$		0			0
$896$	−322.499	−	776.435i	−0.359932	−	0.866557i
$897$		0			0
$898$	100.538	−	89.8712i	0.111957	−	0.100079i
$899$		−	840.138i		−	0.934525i
$900$		0			0
$901$	822.092			0.912421
$902$	−72.0051	−	80.5512i	−0.0798283	−	0.0893028i
$903$		0			0
$904$	−511.099	+	362.966i	−0.565375	+	0.401511i
$905$		0			0
$906$		0			0
$907$	−817.237			−0.901033			−0.450516	−	0.892768i	$-0.648760\pi$
$907$	−817.237			−0.901033			−0.450516	+	0.892768i	$0.648760\pi$
$908$	66.9395	−	595.599i	0.0737220	−	0.655946i
$909$		0			0
$910$		0			0
$911$			227.911i			0.250177i	0.992146	+	0.125088i	$0.0399215\pi$
$911$			227.911i			0.250177i	−0.992146	+	0.125088i	$0.960079\pi$
$912$		0			0
$913$			322.853i			0.353617i
$914$	272.115	+	304.412i	0.297719	+	0.333055i
$915$		0			0
$916$	27.5541	−	245.165i	0.0300809	−	0.267647i
$917$			682.966i			0.744783i
$918$		0			0
$919$			669.088i			0.728061i	0.931387	+	0.364031i	$0.118600\pi$
$919$			669.088i			0.728061i	−0.931387	+	0.364031i	$0.881400\pi$
$920$		0			0
$921$		0			0
$922$	187.523	−	167.628i	0.203387	−	0.181809i
$923$	−465.939			−0.504809
$924$		0			0
$925$		0			0
$926$	825.515	−	737.933i	0.891485	−	0.796904i
$927$		0			0
$928$	−986.898	+	546.339i	−1.06347	+	0.588727i
$929$	−1192.84			−1.28400			−0.642000	−	0.766705i	$-0.721895\pi$
$929$	−1192.84			−1.28400			−0.642000	+	0.766705i	$0.721895\pi$
$930$		0			0
$931$		−	63.6528i		−	0.0683704i
$932$	1612.19	+	181.195i	1.72982	+	0.194415i
$933$		0			0
$934$	933.088	−	834.092i	0.999023	−	0.893032i
$935$		0			0
$936$		0			0
$937$		−	530.621i		−	0.566298i	−0.959076	−	0.283149i	$-0.908621\pi$
$937$		−	530.621i		−	0.566298i	0.959076	−	0.283149i	$-0.0913790\pi$
$938$	−1091.48	+	975.684i	−1.16363	+	1.04018i
$939$		0			0
$940$		0			0
$941$	507.433			0.539248			0.269624	−	0.962966i	$-0.413101\pi$
$941$	507.433			0.539248			0.269624	+	0.962966i	$0.413101\pi$
$942$		0			0
$943$	868.860			0.921378
$944$	24.5944	−	108.033i	0.0260534	−	0.114442i
$945$		0			0
$946$	−169.972	−	190.145i	−0.179674	−	0.200999i
$947$	−453.872			−0.479274			−0.239637	−	0.970863i	$-0.577028\pi$
$947$	−453.872			−0.479274			−0.239637	+	0.970863i	$0.577028\pi$
$948$		0			0
$949$	1650.02			1.73869
$950$		0			0
$951$		0			0
$952$	−1149.24	+	816.155i	−1.20719	+	0.857306i
$953$			1220.52i			1.28071i	0.768078	+	0.640356i	$0.221213\pi$
$953$			1220.52i			1.28071i	−0.768078	+	0.640356i	$0.778787\pi$
$954$		0			0
$955$		0			0
$956$	1064.37	+	119.625i	1.11336	+	0.125131i
$957$		0			0
$958$	−650.731	−	727.964i	−0.679260	−	0.759879i
$959$			47.0717i			0.0490842i
$960$		0			0
$961$	392.986			0.408935
$962$	1214.53	−	1085.67i	1.26250	−	1.12856i
$963$		0			0
$964$	−40.0008	+	355.910i	−0.0414946	+	0.369201i
$965$		0			0
$966$		0			0
$967$	292.088			0.302056			0.151028	−	0.988530i	$-0.451742\pi$
$967$	292.088			0.302056			0.151028	+	0.988530i	$0.451742\pi$
$968$	536.679	+	755.708i	0.554421	+	0.780690i
$969$		0			0
$970$		0			0
$971$		−	1097.69i		−	1.13047i	−0.824928	−	0.565237i	$-0.808785\pi$
$971$		−	1097.69i		−	1.13047i	0.824928	−	0.565237i	$-0.191215\pi$
$972$		0			0
$973$			964.947i			0.991724i
$974$	908.789	−	812.372i	0.933048	−	0.834057i
$975$		0			0
$976$	−1675.93	−	381.536i	−1.71714	−	0.390918i
$977$		−	338.550i		−	0.346520i	−0.984876	−	0.173260i	$-0.944570\pi$
$977$		−	338.550i		−	0.346520i	0.984876	−	0.173260i	$-0.0554301\pi$
$978$		0			0
$979$			16.2042i			0.0165518i
$980$		0			0
$981$		0			0
$982$	−918.468	−	1027.48i	−0.935304	−	1.04631i
$983$	−346.346			−0.352336			−0.176168	−	0.984360i	$-0.556370\pi$
$983$	−346.346			−0.352336			−0.176168	+	0.984360i	$0.556370\pi$
$984$		0			0
$985$		0			0
$986$	1260.40	+	1409.99i	1.27830	+	1.43001i
$987$		0			0
$988$	72.2329	−	642.697i	0.0731102	−	0.650503i
$989$	2050.99			2.07380
$990$		0			0
$991$		−	242.030i		−	0.244228i	−0.992516	−	0.122114i	$-0.961033\pi$
$991$		−	242.030i		−	0.244228i	0.992516	−	0.122114i	$-0.0389673\pi$
$992$	369.377	+	667.238i	0.372356	+	0.672619i
$993$		0			0
$994$	274.196	+	306.740i	0.275851	+	0.308591i
$995$		0			0
$996$		0			0
$997$		−	178.452i		−	0.178989i	−0.995987	−	0.0894946i	$-0.971475\pi$
$997$		−	178.452i		−	0.178989i	0.995987	−	0.0894946i	$-0.0285252\pi$
$998$	−933.565	−	1044.37i	−0.935436	−	1.04646i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.h.199.6		16
3.2	odd	2		300.3.f.c.199.11		16
4.3	odd	2	inner	900.3.f.h.199.12		16
5.2	odd	4		900.3.c.t.451.1		8
5.3	odd	4		900.3.c.n.451.8		8
5.4	even	2	inner	900.3.f.h.199.11		16
12.11	even	2		300.3.f.c.199.5		16
15.2	even	4		300.3.c.e.151.8	yes	8
15.8	even	4		300.3.c.g.151.1	yes	8
15.14	odd	2		300.3.f.c.199.6		16
20.3	even	4		900.3.c.n.451.7		8
20.7	even	4		900.3.c.t.451.2		8
20.19	odd	2	inner	900.3.f.h.199.5		16
60.23	odd	4		300.3.c.g.151.2	yes	8
60.47	odd	4		300.3.c.e.151.7	✓	8
60.59	even	2		300.3.f.c.199.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.7	✓	8	60.47	odd	4
300.3.c.e.151.8	yes	8	15.2	even	4
300.3.c.g.151.1	yes	8	15.8	even	4
300.3.c.g.151.2	yes	8	60.23	odd	4
300.3.f.c.199.5		16	12.11	even	2
300.3.f.c.199.6		16	15.14	odd	2
300.3.f.c.199.11		16	3.2	odd	2
300.3.f.c.199.12		16	60.59	even	2
900.3.c.n.451.7		8	20.3	even	4
900.3.c.n.451.8		8	5.3	odd	4
900.3.c.t.451.1		8	5.2	odd	4
900.3.c.t.451.2		8	20.7	even	4
900.3.f.h.199.5		16	20.19	odd	2	inner
900.3.f.h.199.6		16	1.1	even	1	trivial
900.3.f.h.199.11		16	5.4	even	2	inner
900.3.f.h.199.12		16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.49110 + 1.33290i) q^{2} +(0.446749 - 3.97497i) q^{4} +6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +O(q^{10})\)	\(q+(-1.49110 + 1.33290i) q^{2} +(0.446749 - 3.97497i) q^{4} +6.56834 q^{7} +(4.63210 + 6.52255i) q^{8} +2.26696i q^{11} -14.8772i q^{13} +(-9.79404 + 8.75495i) q^{14} +(-15.6008 - 3.55163i) q^{16} +26.8250i q^{17} +10.8680i q^{19} +(-3.02164 - 3.38027i) q^{22} +36.4610 q^{23} +(19.8298 + 22.1834i) q^{26} +(2.93440 - 26.1090i) q^{28} -35.2510 q^{29} +23.8330i q^{31} +(27.9963 - 15.4985i) q^{32} +(-35.7550 - 39.9987i) q^{34} -54.7495i q^{37} +(-14.4860 - 16.2053i) q^{38} +23.8298 q^{41} +56.2515 q^{43} +(9.01112 + 1.01276i) q^{44} +(-54.3670 + 48.5989i) q^{46} -51.4177 q^{47} -5.85689 q^{49} +(-59.1364 - 6.64636i) q^{52} -30.6465i q^{53} +(30.4252 + 42.8423i) q^{56} +(52.5627 - 46.9861i) q^{58} +6.92483i q^{59} +107.426 q^{61} +(-31.7671 - 35.5374i) q^{62} +(-21.0873 + 60.4262i) q^{64} +111.444 q^{67} +(106.629 + 11.9840i) q^{68} -31.3190i q^{71} +110.909i q^{73} +(72.9757 + 81.6369i) q^{74} +(43.2002 + 4.85528i) q^{76} +14.8902i q^{77} +59.0065i q^{79} +(-35.5326 + 31.7628i) q^{82} +142.416 q^{83} +(-83.8765 + 74.9776i) q^{86} +(-14.7864 + 10.5008i) q^{88} +7.14798 q^{89} -97.7185i q^{91} +(16.2889 - 144.932i) q^{92} +(76.6689 - 68.5347i) q^{94} +126.308i q^{97} +(8.73319 - 7.80665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4}+O(q^{10}) \) 16 * q + 16 * q^4	\( 16 q + 16 q^{4} + 44 q^{14} + 80 q^{16} + 132 q^{26} - 64 q^{29} - 248 q^{34} + 32 q^{41} + 80 q^{44} - 152 q^{46} - 32 q^{49} + 344 q^{56} + 272 q^{61} - 32 q^{64} - 216 q^{74} + 240 q^{76} - 428 q^{86} + 256 q^{89} - 24 q^{94}+O(q^{100}) \) 16 * q + 16 * q^4 + 44 * q^14 + 80 * q^16 + 132 * q^26 - 64 * q^29 - 248 * q^34 + 32 * q^41 + 80 * q^44 - 152 * q^46 - 32 * q^49 + 344 * q^56 + 272 * q^61 - 32 * q^64 - 216 * q^74 + 240 * q^76 - 428 * q^86 + 256 * q^89 - 24 * q^94

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