LMFDB - Embedded newform 900.3.f.f.199.14

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} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 12x^12 + 25x^10 + 53x^8 + 100x^6 + 192x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{28} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.14
Root			$0.120653 + 1.40906i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.f.199.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08539 + 1.67986i) q^{2} +(-1.64388 + 3.64660i) q^{4} +0.596540 q^{7} +(-7.91002 + 1.19648i) q^{8} +O(q^{10})$	\(q+(1.08539 + 1.67986i) q^{2} +(-1.64388 + 3.64660i) q^{4} +0.596540 q^{7} +(-7.91002 + 1.19648i) q^{8} -9.27963i q^{11} -23.5117i q^{13} +(0.647476 + 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} +3.97751i q^{17} +7.04756i q^{19} +(15.5885 - 10.0720i) q^{22} +32.0793 q^{23} +(39.4964 - 25.5192i) q^{26} +(-0.980637 + 2.17534i) q^{28} +35.6734 q^{29} -59.2585i q^{31} +(8.64000 - 30.8115i) q^{32} +(-6.68167 + 4.31713i) q^{34} +5.38761i q^{37} +(-11.8389 + 7.64932i) q^{38} -40.0791 q^{41} -36.1157 q^{43} +(33.8391 + 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131 q^{47} -48.6441 q^{49} +(85.7376 + 38.6503i) q^{52} +2.55123i q^{53} +(-4.71864 + 0.713748i) q^{56} +(38.7194 + 59.9265i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(99.5461 - 64.3183i) q^{62} +(61.1369 - 18.9284i) q^{64} +69.7379 q^{67} +(-14.5044 - 6.53853i) q^{68} +59.2170i q^{71} -83.0019i q^{73} +(-9.05044 + 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} -5.53566i q^{77} -65.8705i q^{79} +(-43.5013 - 67.3274i) q^{82} +129.909 q^{83} +(-39.1995 - 60.6695i) q^{86} +(11.1029 + 73.4020i) q^{88} -130.466 q^{89} -14.0256i q^{91} +(-52.7344 + 116.980i) q^{92} +(80.3327 + 124.332i) q^{94} -93.1113i q^{97} +(-52.7977 - 81.7155i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4}+O(q^{10}) $ 16 * q - 20 * q^4	$ 16 q - 20 q^{4} - 40 q^{14} + 68 q^{16} + 72 q^{26} + 128 q^{29} + 184 q^{34} + 32 q^{41} + 344 q^{44} + 304 q^{46} + 112 q^{49} - 232 q^{56} - 352 q^{61} + 220 q^{64} + 264 q^{74} - 48 q^{76} + 400 q^{86} + 160 q^{89} + 192 q^{94}+O(q^{100}) $ 16 * q - 20 * q^4 - 40 * q^14 + 68 * q^16 + 72 * q^26 + 128 * q^29 + 184 * q^34 + 32 * q^41 + 344 * q^44 + 304 * q^46 + 112 * q^49 - 232 * q^56 - 352 * q^61 + 220 * q^64 + 264 * q^74 - 48 * q^76 + 400 * q^86 + 160 * q^89 + 192 * 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 $

$2$	1.08539	+	1.67986i	0.542693	+	0.839931i
$2$	1.08539	+	1.67986i	0.542693	+	0.839931i
$3$		0			0
$3$		0			0
$4$	−1.64388	+	3.64660i	−0.410969	+	0.911649i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.596540			0.0852199			0.0426100	−	0.999092i	$-0.486433\pi$
$7$	0.596540			0.0852199			0.0426100	+	0.999092i	$0.486433\pi$
$8$	−7.91002	+	1.19648i	−0.988753	+	0.149560i
$9$		0			0
$10$		0			0
$11$		−	9.27963i		−	0.843602i	−0.906688	−	0.421801i	$-0.861398\pi$
$11$		−	9.27963i		−	0.843602i	0.906688	−	0.421801i	$-0.138602\pi$
$12$		0			0
$13$		−	23.5117i		−	1.80859i	−0.426907	−	0.904295i	$-0.640397\pi$
$13$		−	23.5117i		−	1.80859i	0.426907	−	0.904295i	$-0.359603\pi$
$14$	0.647476	+	1.00210i	0.0462483	+	0.0715789i
$15$		0			0
$16$	−10.5953	−	11.9891i	−0.662209	−	0.749319i
$17$			3.97751i			0.233971i	0.993134	+	0.116986i	$0.0373231\pi$
$17$			3.97751i			0.233971i	−0.993134	+	0.116986i	$0.962677\pi$
$18$		0			0
$19$			7.04756i			0.370924i	0.982651	+	0.185462i	$0.0593782\pi$
$19$			7.04756i			0.370924i	−0.982651	+	0.185462i	$0.940622\pi$
$20$		0			0
$21$		0			0
$22$	15.5885	−	10.0720i	0.708568	−	0.457817i
$23$	32.0793			1.39475			0.697376	−	0.716705i	$-0.254351\pi$
$23$	32.0793			1.39475			0.697376	+	0.716705i	$0.254351\pi$
$24$		0			0
$25$		0			0
$26$	39.4964	−	25.5192i	1.51909	−	0.981509i
$27$		0			0
$28$	−0.980637	+	2.17534i	−0.0350227	+	0.0776907i
$29$	35.6734			1.23012			0.615059	−	0.788481i	$-0.289132\pi$
$29$	35.6734			1.23012			0.615059	+	0.788481i	$0.289132\pi$
$30$		0			0
$31$		−	59.2585i		−	1.91156i	−0.294076	−	0.955782i	$-0.595012\pi$
$31$		−	59.2585i		−	1.91156i	0.294076	−	0.955782i	$-0.404988\pi$
$32$	8.64000	−	30.8115i	0.270000	−	0.962860i
$33$		0			0
$34$	−6.68167	+	4.31713i	−0.196520	+	0.126974i
$35$		0			0
$36$		0			0
$37$			5.38761i			0.145611i	0.997346	+	0.0728055i	$0.0231952\pi$
$37$			5.38761i			0.145611i	−0.997346	+	0.0728055i	$0.976805\pi$
$38$	−11.8389	+	7.64932i	−0.311551	+	0.201298i
$39$		0			0
$40$		0			0
$41$	−40.0791			−0.977539			−0.488769	−	0.872413i	$-0.662554\pi$
$41$	−40.0791			−0.977539			−0.488769	+	0.872413i	$0.662554\pi$
$42$		0			0
$43$	−36.1157			−0.839901			−0.419950	−	0.907547i	$-0.637953\pi$
$43$	−36.1157			−0.839901			−0.419950	+	0.907547i	$0.637953\pi$
$44$	33.8391	+	15.2545i	0.769070	+	0.346694i
$45$		0			0
$46$	34.8184	+	53.8888i	0.756922	+	1.17150i
$47$	74.0131			1.57475			0.787373	−	0.616477i	$-0.211441\pi$
$47$	74.0131			1.57475			0.787373	+	0.616477i	$0.211441\pi$
$48$		0			0
$49$	−48.6441			−0.992738
$50$		0			0
$51$		0			0
$52$	85.7376	+	38.6503i	1.64880	+	0.743275i
$53$			2.55123i			0.0481364i	0.999710	+	0.0240682i	$0.00766189\pi$
$53$			2.55123i			0.0481364i	−0.999710	+	0.0240682i	$0.992338\pi$
$54$		0			0
$55$		0			0
$56$	−4.71864	+	0.713748i	−0.0842614	+	0.0127455i
$57$		0			0
$58$	38.7194	+	59.9265i	0.667576	+	1.03321i
$59$			36.4026i			0.616993i	0.951225	+	0.308497i	$0.0998259\pi$
$59$			36.4026i			0.616993i	−0.951225	+	0.308497i	$0.900174\pi$
$60$		0			0
$61$	−8.73223			−0.143151			−0.0715757	−	0.997435i	$-0.522803\pi$
$61$	−8.73223			−0.143151			−0.0715757	+	0.997435i	$0.522803\pi$
$62$	99.5461	−	64.3183i	1.60558	−	1.03739i
$63$		0			0
$64$	61.1369	−	18.9284i	0.955264	−	0.295756i
$65$		0			0
$66$		0			0
$67$	69.7379			1.04086			0.520432	−	0.853903i	$-0.325771\pi$
$67$	69.7379			1.04086			0.520432	+	0.853903i	$0.325771\pi$
$68$	−14.5044	−	6.53853i	−0.213300	−	0.0961548i
$69$		0			0
$70$		0			0
$71$			59.2170i			0.834043i	0.908897	+	0.417021i	$0.136926\pi$
$71$			59.2170i			0.834043i	−0.908897	+	0.417021i	$0.863074\pi$
$72$		0			0
$73$		−	83.0019i		−	1.13701i	−0.822679	−	0.568506i	$-0.807522\pi$
$73$		−	83.0019i		−	1.13701i	0.822679	−	0.568506i	$-0.192478\pi$
$74$	−9.05044	+	5.84763i	−0.122303	+	0.0790220i
$75$		0			0
$76$	−25.6996	−	11.5853i	−0.338153	−	0.152438i
$77$		−	5.53566i		−	0.0718917i
$78$		0			0
$79$		−	65.8705i		−	0.833804i	−0.908951	−	0.416902i	$-0.863116\pi$
$79$		−	65.8705i		−	0.833804i	0.908951	−	0.416902i	$-0.136884\pi$
$80$		0			0
$81$		0			0
$82$	−43.5013	−	67.3274i	−0.530503	−	0.821065i
$83$	129.909			1.56517			0.782586	−	0.622542i	$-0.213900\pi$
$83$	129.909			1.56517			0.782586	+	0.622542i	$0.213900\pi$
$84$		0			0
$85$		0			0
$86$	−39.1995	−	60.6695i	−0.455808	−	0.705459i
$87$		0			0
$88$	11.1029	+	73.4020i	0.126169	+	0.834114i
$89$	−130.466			−1.46591			−0.732956	−	0.680277i	$-0.761860\pi$
$89$	−130.466			−1.46591			−0.732956	+	0.680277i	$0.761860\pi$
$90$		0			0
$91$		−	14.0256i		−	0.154128i
$92$	−52.7344	+	116.980i	−0.573200	+	1.27152i
$93$		0			0
$94$	80.3327	+	124.332i	0.854603	+	1.32268i
$95$		0			0
$96$		0			0
$97$		−	93.1113i		−	0.959911i	−0.877293	−	0.479955i	$-0.840653\pi$
$97$		−	93.1113i		−	0.959911i	0.877293	−	0.479955i	$-0.159347\pi$
$98$	−52.7977	−	81.7155i	−0.538752	−	0.833831i
$99$		0			0
$100$		0			0
$101$	3.66081			0.0362457			0.0181228	−	0.999836i	$-0.494231\pi$
$101$	3.66081			0.0362457			0.0181228	+	0.999836i	$0.494231\pi$
$102$		0			0
$103$	151.417			1.47007			0.735033	−	0.678032i	$-0.237167\pi$
$103$	151.417			1.47007			0.735033	+	0.678032i	$0.237167\pi$
$104$	28.1313	+	185.978i	0.270493	+	1.78825i
$105$		0			0
$106$	−4.28571	+	2.76907i	−0.0404313	+	0.0261233i
$107$	82.8092			0.773918			0.386959	−	0.922097i	$-0.373526\pi$
$107$	82.8092			0.773918			0.386959	+	0.922097i	$0.373526\pi$
$108$		0			0
$109$	7.36835			0.0675996			0.0337998	−	0.999429i	$-0.489239\pi$
$109$	7.36835			0.0675996			0.0337998	+	0.999429i	$0.489239\pi$
$110$		0			0
$111$		0			0
$112$	−6.32054	−	7.15197i	−0.0564334	−	0.0638569i
$113$		−	65.0370i		−	0.575549i	−0.957698	−	0.287774i	$-0.907085\pi$
$113$		−	65.0370i		−	0.575549i	0.957698	−	0.287774i	$-0.0929153\pi$
$114$		0			0
$115$		0			0
$116$	−58.6427	+	130.087i	−0.505540	+	1.12144i
$117$		0			0
$118$	−61.1514	+	39.5109i	−0.518232	+	0.334838i
$119$			2.37274i			0.0199390i
$120$		0			0
$121$	34.8885			0.288335
$122$	−9.47784	−	14.6689i	−0.0776872	−	0.120237i
$123$		0			0
$124$	216.092	+	97.4136i	1.74268	+	0.785593i
$125$		0			0
$126$		0			0
$127$	−139.469			−1.09818			−0.549091	−	0.835763i	$-0.685026\pi$
$127$	−139.469			−1.09818			−0.549091	+	0.835763i	$0.685026\pi$
$128$	98.1542	+	82.1569i	0.766829	+	0.641851i
$129$		0			0
$130$		0			0
$131$		−	63.4856i		−	0.484623i	−0.970198	−	0.242312i	$-0.922094\pi$
$131$		−	63.4856i		−	0.484623i	0.970198	−	0.242312i	$-0.0779056\pi$
$132$		0			0
$133$			4.20415i			0.0316101i
$134$	75.6925	+	117.150i	0.564870	+	0.874254i
$135$		0			0
$136$	−4.75901	−	31.4622i	−0.0349927	−	0.231340i
$137$		−	138.157i		−	1.00845i	−0.863573	−	0.504223i	$-0.831779\pi$
$137$		−	138.157i		−	1.00845i	0.863573	−	0.504223i	$-0.168221\pi$
$138$		0			0
$139$			29.9578i			0.215523i	0.994177	+	0.107762i	$0.0343684\pi$
$139$			29.9578i			0.215523i	−0.994177	+	0.107762i	$0.965632\pi$
$140$		0			0
$141$		0			0
$142$	−99.4765	+	64.2733i	−0.700539	+	0.452629i
$143$	−218.180			−1.52573
$144$		0			0
$145$		0			0
$146$	139.432	−	90.0891i	0.955012	−	0.617048i
$147$		0			0
$148$	−19.6464	−	8.85655i	−0.132746	−	0.0598416i
$149$	−47.3823			−0.318002			−0.159001	−	0.987278i	$-0.550827\pi$
$149$	−47.3823			−0.318002			−0.159001	+	0.987278i	$0.550827\pi$
$150$		0			0
$151$			109.604i			0.725852i	0.931818	+	0.362926i	$0.118222\pi$
$151$			109.604i			0.725852i	−0.931818	+	0.362926i	$0.881778\pi$
$152$	−8.43227	−	55.7463i	−0.0554755	−	0.366752i
$153$		0			0
$154$	9.29915	−	6.00833i	0.0603841	−	0.0390151i
$155$		0			0
$156$		0			0
$157$			177.588i			1.13113i	0.824703	+	0.565566i	$0.191342\pi$
$157$			177.588i			1.13113i	−0.824703	+	0.565566i	$0.808658\pi$
$158$	110.653	−	71.4950i	0.700338	−	0.452500i
$159$		0			0
$160$		0			0
$161$	19.1366			0.118861
$162$		0			0
$163$	96.8778			0.594342			0.297171	−	0.954824i	$-0.403957\pi$
$163$	96.8778			0.594342			0.297171	+	0.954824i	$0.403957\pi$
$164$	65.8850	−	146.152i	0.401738	−	0.891173i
$165$		0			0
$166$	141.002	+	218.230i	0.849408	+	1.31464i
$167$	−152.605			−0.913801			−0.456901	−	0.889518i	$-0.651040\pi$
$167$	−152.605			−0.913801			−0.456901	+	0.889518i	$0.651040\pi$
$168$		0			0
$169$	−383.799			−2.27100
$170$		0			0
$171$		0			0
$172$	59.3698	−	131.700i	0.345173	−	0.765695i
$173$		−	155.773i		−	0.900422i	−0.892922	−	0.450211i	$-0.851349\pi$
$173$		−	155.773i		−	0.900422i	0.892922	−	0.450211i	$-0.148651\pi$
$174$		0			0
$175$		0			0
$176$	−111.254	+	98.3209i	−0.632127	+	0.558641i
$177$		0			0
$178$	−141.606	−	219.165i	−0.795540	−	1.23126i
$179$		−	126.001i		−	0.703915i	−0.936016	−	0.351957i	$-0.885516\pi$
$179$		−	126.001i		−	0.703915i	0.936016	−	0.351957i	$-0.114484\pi$
$180$		0			0
$181$	−346.725			−1.91561			−0.957803	−	0.287424i	$-0.907201\pi$
$181$	−346.725			−1.91561			−0.957803	+	0.287424i	$0.907201\pi$
$182$	23.5612	−	15.2232i	0.129457	−	0.0836442i
$183$		0			0
$184$	−253.748	+	38.3823i	−1.37906	+	0.208599i
$185$		0			0
$186$		0			0
$187$	36.9098			0.197379
$188$	−121.668	+	269.896i	−0.647171	+	1.43562i
$189$		0			0
$190$		0			0
$191$		−	133.159i		−	0.697167i	−0.937278	−	0.348584i	$-0.886663\pi$
$191$		−	133.159i		−	0.697167i	0.937278	−	0.348584i	$-0.113337\pi$
$192$		0			0
$193$		−	136.246i		−	0.705940i	−0.935635	−	0.352970i	$-0.885172\pi$
$193$		−	136.246i		−	0.705940i	0.935635	−	0.352970i	$-0.114828\pi$
$194$	156.414	−	101.062i	0.806259	−	0.520937i
$195$		0			0
$196$	79.9649	−	177.386i	0.407984	−	0.905029i
$197$			74.8945i			0.380175i	0.981767	+	0.190087i	$0.0608772\pi$
$197$			74.8945i			0.380175i	−0.981767	+	0.190087i	$0.939123\pi$
$198$		0			0
$199$		−	251.605i		−	1.26434i	−0.774828	−	0.632172i	$-0.782164\pi$
$199$		−	251.605i		−	1.26434i	0.774828	−	0.632172i	$-0.217836\pi$
$200$		0			0
$201$		0			0
$202$	3.97339	+	6.14966i	0.0196703	+	0.0304439i
$203$	21.2806			0.104831
$204$		0			0
$205$		0			0
$206$	164.346	+	254.359i	0.797794	+	1.23475i
$207$		0			0
$208$	−281.884	+	249.114i	−1.35521	+	1.19767i
$209$	65.3987			0.312913
$210$		0			0
$211$			228.203i			1.08153i	0.841173	+	0.540766i	$0.181865\pi$
$211$			228.203i			1.08153i	−0.841173	+	0.540766i	$0.818135\pi$
$212$	−9.30331	−	4.19390i	−0.0438835	−	0.0197826i
$213$		0			0
$214$	89.8799	+	139.108i	0.420000	+	0.650038i
$215$		0			0
$216$		0			0
$217$		−	35.3500i		−	0.162903i
$218$	7.99751	+	12.3778i	0.0366858	+	0.0567790i
$219$		0			0
$220$		0			0
$221$	93.5179			0.423158
$222$		0			0
$223$	85.9549			0.385448			0.192724	−	0.981253i	$-0.438268\pi$
$223$	85.9549			0.385448			0.192724	+	0.981253i	$0.438268\pi$
$224$	5.15410	−	18.3803i	0.0230094	−	0.0820549i
$225$		0			0
$226$	109.253	−	70.5902i	0.483421	−	0.312346i
$227$	−282.357			−1.24386			−0.621932	−	0.783071i	$-0.713652\pi$
$227$	−282.357			−1.24386			−0.621932	+	0.783071i	$0.713652\pi$
$228$		0			0
$229$	−138.263			−0.603768			−0.301884	−	0.953345i	$-0.597615\pi$
$229$	−138.263			−0.603768			−0.301884	+	0.953345i	$0.597615\pi$
$230$		0			0
$231$		0			0
$232$	−282.178	+	42.6826i	−1.21628	+	0.183977i
$233$			0.522939i			0.00224438i	0.999999	+	0.00112219i	$0.000357204\pi$
$233$			0.522939i			0.00224438i	−0.999999	+	0.00112219i	$0.999643\pi$
$234$		0			0
$235$		0			0
$236$	−132.746	−	59.8413i	−0.562482	−	0.253565i
$237$		0			0
$238$	−3.98588	+	2.57534i	−0.0167474	+	0.0108208i
$239$			73.6928i			0.308338i	0.988044	+	0.154169i	$0.0492700\pi$
$239$			73.6928i			0.308338i	−0.988044	+	0.154169i	$0.950730\pi$
$240$		0			0
$241$	31.3705			0.130168			0.0650840	−	0.997880i	$-0.479268\pi$
$241$	31.3705			0.130168			0.0650840	+	0.997880i	$0.479268\pi$
$242$	37.8675	+	58.6080i	0.156477	+	0.242182i
$243$		0			0
$244$	14.3547	−	31.8429i	0.0588307	−	0.130504i
$245$		0			0
$246$		0			0
$247$	165.700			0.670850
$248$	70.9016	+	468.736i	0.285894	+	1.89006i
$249$		0			0
$250$		0			0
$251$		−	78.7478i		−	0.313736i	−0.987620	−	0.156868i	$-0.949860\pi$
$251$		−	78.7478i		−	0.313736i	0.987620	−	0.156868i	$-0.0501398\pi$
$252$		0			0
$253$		−	297.684i		−	1.17662i
$254$	−151.378	−	234.289i	−0.595975	−	0.922397i
$255$		0			0
$256$	−31.4772	+	254.057i	−0.122958	+	0.992412i
$257$			243.954i			0.949236i	0.880192	+	0.474618i	$0.157414\pi$
$257$			243.954i			0.949236i	−0.880192	+	0.474618i	$0.842586\pi$
$258$		0			0
$259$			3.21392i			0.0124090i
$260$		0			0
$261$		0			0
$262$	106.647	−	68.9064i	0.407050	−	0.263002i
$263$	102.737			0.390635			0.195317	−	0.980740i	$-0.437426\pi$
$263$	102.737			0.390635			0.195317	+	0.980740i	$0.437426\pi$
$264$		0			0
$265$		0			0
$266$	−7.06239	+	4.56312i	−0.0265503	+	0.0171546i
$267$		0			0
$268$	−114.640	+	254.306i	−0.427763	+	0.948903i
$269$	−123.646			−0.459651			−0.229825	−	0.973232i	$-0.573816\pi$
$269$	−123.646			−0.459651			−0.229825	+	0.973232i	$0.573816\pi$
$270$		0			0
$271$		−	332.371i		−	1.22646i	−0.789904	−	0.613230i	$-0.789870\pi$
$271$		−	332.371i		−	1.22646i	0.789904	−	0.613230i	$-0.210130\pi$
$272$	47.6868	−	42.1431i	0.175319	−	0.154938i
$273$		0			0
$274$	232.085	−	149.954i	0.847026	−	0.547277i
$275$		0			0
$276$		0			0
$277$			125.916i			0.454571i	0.973828	+	0.227286i	$0.0729851\pi$
$277$			125.916i			0.454571i	−0.973828	+	0.227286i	$0.927015\pi$
$278$	−50.3249	+	32.5157i	−0.181025	+	0.116963i
$279$		0			0
$280$		0			0
$281$	−52.5628			−0.187056			−0.0935281	−	0.995617i	$-0.529814\pi$
$281$	−52.5628			−0.187056			−0.0935281	+	0.995617i	$0.529814\pi$
$282$		0			0
$283$	199.288			0.704199			0.352100	−	0.935963i	$-0.385468\pi$
$283$	199.288			0.704199			0.352100	+	0.935963i	$0.385468\pi$
$284$	−215.941	−	97.3454i	−0.760355	−	0.342766i
$285$		0			0
$286$	−236.809	−	366.512i	−0.828004	−	1.28151i
$287$	−23.9088			−0.0833058
$288$		0			0
$289$	273.179			0.945258
$290$		0			0
$291$		0			0
$292$	302.674	+	136.445i	1.03656	+	0.467276i
$293$		−	102.161i		−	0.348672i	−0.984686	−	0.174336i	$-0.944222\pi$
$293$		−	102.161i		−	0.348672i	0.984686	−	0.174336i	$-0.0557779\pi$
$294$		0			0
$295$		0			0
$296$	−6.44617	−	42.6161i	−0.0217776	−	0.143973i
$297$		0			0
$298$	−51.4281	−	79.5957i	−0.172577	−	0.267100i
$299$		−	754.238i		−	2.52254i
$300$		0			0
$301$	−21.5445			−0.0715763
$302$	−184.119	+	118.962i	−0.609666	+	0.393915i
$303$		0			0
$304$	84.4939	−	74.6713i	0.277941	−	0.245629i
$305$		0			0
$306$		0			0
$307$	−328.391			−1.06968			−0.534839	−	0.844954i	$-0.679628\pi$
$307$	−328.391			−1.06968			−0.534839	+	0.844954i	$0.679628\pi$
$308$	20.1863	+	9.09994i	0.0655401	+	0.0295453i
$309$		0			0
$310$		0			0
$311$			95.4377i			0.306874i	0.988158	+	0.153437i	$0.0490342\pi$
$311$			95.4377i			0.306874i	−0.988158	+	0.153437i	$0.950966\pi$
$312$		0			0
$313$			550.408i			1.75849i	0.476368	+	0.879246i	$0.341953\pi$
$313$			550.408i			1.75849i	−0.476368	+	0.879246i	$0.658047\pi$
$314$	−298.323	+	192.751i	−0.950073	+	0.613858i
$315$		0			0
$316$	240.203	+	108.283i	0.760137	+	0.342668i
$317$			439.394i			1.38610i	0.720889	+	0.693051i	$0.243734\pi$
$317$			439.394i			1.38610i	−0.720889	+	0.693051i	$0.756266\pi$
$318$		0			0
$319$		−	331.036i		−	1.03773i
$320$		0			0
$321$		0			0
$322$	20.7706	+	32.1468i	0.0645048	+	0.0998348i
$323$	−28.0317			−0.0867855
$324$		0			0
$325$		0			0
$326$	105.150	+	162.741i	0.322545	+	0.499206i
$327$		0			0
$328$	317.026	−	47.9539i	0.966544	−	0.146201i
$329$	44.1517			0.134200
$330$		0			0
$331$		−	479.922i		−	1.44992i	−0.688794	−	0.724958i	$-0.741859\pi$
$331$		−	479.922i		−	1.44992i	0.688794	−	0.724958i	$-0.258141\pi$
$332$	−213.555	+	473.727i	−0.643237	+	1.42689i
$333$		0			0
$334$	−165.635	−	256.355i	−0.495913	−	0.767530i
$335$		0			0
$336$		0			0
$337$		−	58.8437i		−	0.174610i	−0.996182	−	0.0873052i	$-0.972174\pi$
$337$		−	58.8437i		−	0.174610i	0.996182	−	0.0873052i	$-0.0278255\pi$
$338$	−416.570	−	644.730i	−1.23246	−	1.90748i
$339$		0			0
$340$		0			0
$341$	−549.897			−1.61260
$342$		0			0
$343$	−58.2486			−0.169821
$344$	285.676	−	43.2118i	0.830454	−	0.125616i
$345$		0			0
$346$	261.677	−	169.074i	0.756293	−	0.488653i
$347$	−12.1484			−0.0350099			−0.0175049	−	0.999847i	$-0.505572\pi$
$347$	−12.1484			−0.0350099			−0.0175049	+	0.999847i	$0.505572\pi$
$348$		0			0
$349$	30.9277			0.0886180			0.0443090	−	0.999018i	$-0.485891\pi$
$349$	30.9277			0.0886180			0.0443090	+	0.999018i	$0.485891\pi$
$350$		0			0
$351$		0			0
$352$	−285.919	−	80.1760i	−0.812271	−	0.227773i
$353$			288.065i			0.816048i	0.912971	+	0.408024i	$0.133782\pi$
$353$			288.065i			0.816048i	−0.912971	+	0.408024i	$0.866218\pi$
$354$		0			0
$355$		0			0
$356$	214.470	−	475.757i	0.602444	−	1.33640i
$357$		0			0
$358$	211.664	−	136.759i	0.591240	−	0.382010i
$359$			663.911i			1.84933i	0.380776	+	0.924667i	$0.375657\pi$
$359$			663.911i			1.84933i	−0.380776	+	0.924667i	$0.624343\pi$
$360$		0			0
$361$	311.332			0.862415
$362$	−376.330	−	582.450i	−1.03959	−	1.60898i
$363$		0			0
$364$	51.1459	+	23.0564i	0.140511	+	0.0633418i
$365$		0			0
$366$		0			0
$367$	6.08529			0.0165812			0.00829059	−	0.999966i	$-0.497361\pi$
$367$	6.08529			0.0165812			0.00829059	+	0.999966i	$0.497361\pi$
$368$	−339.891	−	384.602i	−0.923618	−	1.04511i
$369$		0			0
$370$		0			0
$371$			1.52191i			0.00410218i
$372$		0			0
$373$		−	204.741i		−	0.548903i	−0.961601	−	0.274451i	$-0.911504\pi$
$373$		−	204.741i		−	0.548903i	0.961601	−	0.274451i	$-0.0884963\pi$
$374$	40.0614	+	62.0034i	0.107116	+	0.165784i
$375$		0			0
$376$	−585.445	+	88.5552i	−1.55703	+	0.235519i
$377$		−	838.742i		−	2.22478i
$378$		0			0
$379$			402.331i			1.06156i	0.847510	+	0.530780i	$0.178101\pi$
$379$			402.331i			1.06156i	−0.847510	+	0.530780i	$0.821899\pi$
$380$		0			0
$381$		0			0
$382$	223.689	−	144.529i	0.585573	−	0.378348i
$383$	−331.751			−0.866191			−0.433096	−	0.901348i	$-0.642579\pi$
$383$	−331.751			−0.866191			−0.433096	+	0.901348i	$0.642579\pi$
$384$		0			0
$385$		0			0
$386$	228.875	−	147.880i	0.592941	−	0.383109i
$387$		0			0
$388$	339.540	+	153.063i	0.875102	+	0.394493i
$389$	−623.310			−1.60234			−0.801169	−	0.598438i	$-0.795788\pi$
$389$	−623.310			−1.60234			−0.801169	+	0.598438i	$0.795788\pi$
$390$		0			0
$391$			127.596i			0.326332i
$392$	384.776	−	58.2018i	0.981572	−	0.148474i
$393$		0			0
$394$	−125.812	+	81.2894i	−0.319321	+	0.206318i
$395$		0			0
$396$		0			0
$397$			355.449i			0.895338i	0.894199	+	0.447669i	$0.147746\pi$
$397$			355.449i			0.895338i	−0.894199	+	0.447669i	$0.852254\pi$
$398$	422.661	−	273.088i	1.06196	−	0.686151i
$399$		0			0
$400$		0			0
$401$	542.927			1.35393			0.676966	−	0.736014i	$-0.263294\pi$
$401$	542.927			1.35393			0.676966	+	0.736014i	$0.263294\pi$
$402$		0			0
$403$	−1393.27			−3.45724
$404$	−6.01792	+	13.3495i	−0.0148958	+	0.0330433i
$405$		0			0
$406$	23.0977	+	35.7485i	0.0568908	+	0.0880505i
$407$	49.9950			0.122838
$408$		0			0
$409$	108.497			0.265273			0.132636	−	0.991165i	$-0.457656\pi$
$409$	108.497			0.265273			0.132636	+	0.991165i	$0.457656\pi$
$410$		0			0
$411$		0			0
$412$	−248.910	+	552.156i	−0.604151	+	1.34018i
$413$			21.7156i			0.0525801i
$414$		0			0
$415$		0			0
$416$	−724.431	−	203.141i	−1.74142	−	0.488320i
$417$		0			0
$418$	70.9828	+	109.861i	0.169815	+	0.262825i
$419$		−	172.176i		−	0.410921i	−0.978665	−	0.205460i	$-0.934131\pi$
$419$		−	172.176i		−	0.410921i	0.978665	−	0.205460i	$-0.0658691\pi$
$420$		0			0
$421$	478.522			1.13663			0.568316	−	0.822810i	$-0.307595\pi$
$421$	478.522			1.13663			0.568316	+	0.822810i	$0.307595\pi$
$422$	−383.350	+	247.688i	−0.908412	+	0.586940i
$423$		0			0
$424$	−3.05250	−	20.1803i	−0.00719929	−	0.0475950i
$425$		0			0
$426$		0			0
$427$	−5.20912			−0.0121993
$428$	−136.128	+	301.972i	−0.318056	+	0.705541i
$429$		0			0
$430$		0			0
$431$			290.722i			0.674530i	0.941410	+	0.337265i	$0.109502\pi$
$431$			290.722i			0.674530i	−0.941410	+	0.337265i	$0.890498\pi$
$432$		0			0
$433$			53.7726i			0.124186i	0.998070	+	0.0620931i	$0.0197776\pi$
$433$			53.7726i			0.124186i	−0.998070	+	0.0620931i	$0.980222\pi$
$434$	59.3832	−	38.3684i	0.136828	−	0.0884065i
$435$		0			0
$436$	−12.1127	+	26.8694i	−0.0277813	+	0.0616271i
$437$			226.081i			0.517347i
$438$		0			0
$439$		−	328.657i		−	0.748650i	−0.927298	−	0.374325i	$-0.877874\pi$
$439$		−	328.657i		−	0.748650i	0.927298	−	0.374325i	$-0.122126\pi$
$440$		0			0
$441$		0			0
$442$	101.503	+	157.097i	0.229645	+	0.355424i
$443$	428.910			0.968194			0.484097	−	0.875014i	$-0.339148\pi$
$443$	428.910			0.968194			0.484097	+	0.875014i	$0.339148\pi$
$444$		0			0
$445$		0			0
$446$	93.2942	+	144.392i	0.209180	+	0.323750i
$447$		0			0
$448$	36.4706	−	11.2915i	0.0814075	−	0.0252043i
$449$	409.229			0.911423			0.455711	−	0.890128i	$-0.349385\pi$
$449$	409.229			0.911423			0.455711	+	0.890128i	$0.349385\pi$
$450$		0			0
$451$			371.919i			0.824654i
$452$	237.164	+	106.913i	0.524698	+	0.236533i
$453$		0			0
$454$	−306.466	−	474.321i	−0.675036	−	1.04476i
$455$		0			0
$456$		0			0
$457$		−	768.561i		−	1.68175i	−0.541228	−	0.840876i	$-0.682040\pi$
$457$		−	768.561i		−	1.68175i	0.541228	−	0.840876i	$-0.317960\pi$
$458$	−150.068	−	232.262i	−0.327660	−	0.507123i
$459$		0			0
$460$		0			0
$461$	316.563			0.686687			0.343343	−	0.939210i	$-0.388441\pi$
$461$	316.563			0.686687			0.343343	+	0.939210i	$0.388441\pi$
$462$		0			0
$463$	491.208			1.06093			0.530463	−	0.847708i	$-0.322018\pi$
$463$	491.208			1.06093			0.530463	+	0.847708i	$0.322018\pi$
$464$	−377.972	−	427.692i	−0.814596	−	0.921751i
$465$		0			0
$466$	−0.878466	+	0.567591i	−0.00188512	+	0.00121801i
$467$	410.393			0.878785			0.439393	−	0.898295i	$-0.355194\pi$
$467$	410.393			0.878785			0.439393	+	0.898295i	$0.355194\pi$
$468$		0			0
$469$	41.6014			0.0887024
$470$		0			0
$471$		0			0
$472$	−43.5550	−	287.945i	−0.0922776	−	0.610054i
$473$			335.141i			0.708542i
$474$		0			0
$475$		0			0
$476$	−8.65243	−	3.90049i	−0.0181774	−	0.00819431i
$477$		0			0
$478$	−123.794	+	79.9851i	−0.258983	+	0.167333i
$479$		−	198.918i		−	0.415277i	−0.978206	−	0.207638i	$-0.933422\pi$
$479$		−	198.918i		−	0.415277i	0.978206	−	0.207638i	$-0.0665778\pi$
$480$		0			0
$481$	126.672			0.263351
$482$	34.0491	+	52.6981i	0.0706413	+	0.109332i
$483$		0			0
$484$	−57.3524	+	127.224i	−0.118497	+	0.262860i
$485$		0			0
$486$		0			0
$487$	204.762			0.420456			0.210228	−	0.977652i	$-0.432579\pi$
$487$	204.762			0.420456			0.210228	+	0.977652i	$0.432579\pi$
$488$	69.0721	−	10.4479i	0.141541	−	0.0214097i
$489$		0			0
$490$		0			0
$491$			788.598i			1.60611i	0.595908	+	0.803053i	$0.296792\pi$
$491$			788.598i			1.60611i	−0.595908	+	0.803053i	$0.703208\pi$
$492$		0			0
$493$			141.891i			0.287812i
$494$	179.848	+	278.353i	0.364066	+	0.563468i
$495$		0			0
$496$	−710.456	+	627.864i	−1.43237	+	1.26586i
$497$			35.3253i			0.0710771i
$498$		0			0
$499$			740.385i			1.48374i	0.670545	+	0.741869i	$0.266060\pi$
$499$			740.385i			1.48374i	−0.670545	+	0.741869i	$0.733940\pi$
$500$		0			0
$501$		0			0
$502$	132.285	−	85.4717i	0.263517	−	0.170262i
$503$	−70.8800			−0.140914			−0.0704572	−	0.997515i	$-0.522446\pi$
$503$	−70.8800			−0.140914			−0.0704572	+	0.997515i	$0.522446\pi$
$504$		0			0
$505$		0			0
$506$	500.068	−	323.102i	0.988277	−	0.638541i
$507$		0			0
$508$	229.270	−	508.588i	0.451318	−	1.00116i
$509$	522.642			1.02680			0.513400	−	0.858149i	$-0.328386\pi$
$509$	522.642			1.02680			0.513400	+	0.858149i	$0.328386\pi$
$510$		0			0
$511$		−	49.5139i		−	0.0968961i
$512$	−460.946	+	222.873i	−0.900286	+	0.435299i
$513$		0			0
$514$	−409.809	+	264.784i	−0.797293	+	0.515144i
$515$		0			0
$516$		0			0
$517$		−	686.813i		−	1.32846i
$518$	−5.39894	+	3.48834i	−0.0104227	+	0.00673425i
$519$		0			0
$520$		0			0
$521$	−304.082			−0.583650			−0.291825	−	0.956472i	$-0.594262\pi$
$521$	−304.082			−0.583650			−0.291825	+	0.956472i	$0.594262\pi$
$522$		0			0
$523$	−174.416			−0.333491			−0.166746	−	0.986000i	$-0.553326\pi$
$523$	−174.416			−0.333491			−0.166746	+	0.986000i	$0.553326\pi$
$524$	231.507	+	104.362i	0.441806	+	0.199165i
$525$		0			0
$526$	111.509	+	172.584i	0.211995	+	0.328106i
$527$	235.701			0.447251
$528$		0			0
$529$	500.081			0.945333
$530$		0			0
$531$		0			0
$532$	−15.3308	−	6.91109i	−0.0288174	−	0.0129908i
$533$			942.327i			1.76797i
$534$		0			0
$535$		0			0
$536$	−551.628	+	83.4401i	−1.02916	+	0.155672i
$537$		0			0
$538$	−134.204	−	207.708i	−0.249449	−	0.386075i
$539$			451.399i			0.837476i
$540$		0			0
$541$	−262.199			−0.484655			−0.242328	−	0.970194i	$-0.577911\pi$
$541$	−262.199			−0.484655			−0.242328	+	0.970194i	$0.577911\pi$
$542$	558.337	−	360.750i	1.03014	−	0.665591i
$543$		0			0
$544$	122.553	+	34.3657i	0.225281	+	0.0631722i
$545$		0			0
$546$		0			0
$547$	−146.179			−0.267237			−0.133619	−	0.991033i	$-0.542660\pi$
$547$	−146.179			−0.267237			−0.133619	+	0.991033i	$0.542660\pi$
$548$	503.804	+	227.113i	0.919350	+	0.414440i
$549$		0			0
$550$		0			0
$551$			251.411i			0.456281i
$552$		0			0
$553$		−	39.2944i		−	0.0710568i
$554$	−211.522	+	136.668i	−0.381809	+	0.246693i
$555$		0			0
$556$	−109.244	−	49.2468i	−0.196482	−	0.0885734i
$557$			187.700i			0.336984i	0.985703	+	0.168492i	$0.0538898\pi$
$557$			187.700i			0.336984i	−0.985703	+	0.168492i	$0.946110\pi$
$558$		0			0
$559$			849.142i			1.51904i
$560$		0			0
$561$		0			0
$562$	−57.0509	−	88.2982i	−0.101514	−	0.157114i
$563$	447.848			0.795467			0.397734	−	0.917501i	$-0.369797\pi$
$563$	447.848			0.795467			0.397734	+	0.917501i	$0.369797\pi$
$564$		0			0
$565$		0			0
$566$	216.305	+	334.777i	0.382164	+	0.591479i
$567$		0			0
$568$	−70.8520	−	468.408i	−0.124740	−	0.824662i
$569$	1078.91			1.89615			0.948077	−	0.318042i	$-0.103025\pi$
$569$	1078.91			1.89615			0.948077	+	0.318042i	$0.103025\pi$
$570$		0			0
$571$			936.324i			1.63980i	0.572509	+	0.819899i	$0.305970\pi$
$571$			936.324i			1.63980i	−0.572509	+	0.819899i	$0.694030\pi$
$572$	358.660	−	795.613i	0.627028	−	1.39093i
$573$		0			0
$574$	−25.9502	−	40.1634i	−0.0452095	−	0.0699711i
$575$		0			0
$576$		0			0
$577$			544.832i			0.944250i	0.881532	+	0.472125i	$0.156513\pi$
$577$			544.832i			0.944250i	−0.881532	+	0.472125i	$0.843487\pi$
$578$	296.505	+	458.904i	0.512985	+	0.793951i
$579$		0			0
$580$		0			0
$581$	77.4960			0.133384
$582$		0			0
$583$	23.6745			0.0406080
$584$	99.3101	+	656.547i	0.170052	+	1.12422i
$585$		0			0
$586$	171.616	−	110.884i	0.292861	−	0.189222i
$587$	−337.889			−0.575619			−0.287810	−	0.957688i	$-0.592927\pi$
$587$	−337.889			−0.575619			−0.287810	+	0.957688i	$0.592927\pi$
$588$		0			0
$589$	417.628			0.709045
$590$		0			0
$591$		0			0
$592$	64.5926	−	57.0836i	0.109109	−	0.0964249i
$593$		−	567.269i		−	0.956608i	−0.878194	−	0.478304i	$-0.841252\pi$
$593$		−	567.269i		−	0.956608i	0.878194	−	0.478304i	$-0.158748\pi$
$594$		0			0
$595$		0			0
$596$	77.8906	−	172.784i	0.130689	−	0.289906i
$597$		0			0
$598$	1267.02	−	818.640i	2.11876	−	1.36896i
$599$			762.966i			1.27373i	0.770974	+	0.636867i	$0.219770\pi$
$599$			762.966i			1.27373i	−0.770974	+	0.636867i	$0.780230\pi$
$600$		0			0
$601$	−790.102			−1.31464			−0.657322	−	0.753609i	$-0.728311\pi$
$601$	−790.102			−1.31464			−0.657322	+	0.753609i	$0.728311\pi$
$602$	−23.3841	−	36.1917i	−0.0388440	−	0.0601192i
$603$		0			0
$604$	−399.680	−	180.175i	−0.661722	−	0.298302i
$605$		0			0
$606$		0			0
$607$	−522.994			−0.861605			−0.430802	−	0.902446i	$-0.641769\pi$
$607$	−522.994			−0.861605			−0.430802	+	0.902446i	$0.641769\pi$
$608$	217.146	+	60.8909i	0.357148	+	0.100150i
$609$		0			0
$610$		0			0
$611$		−	1740.17i		−	2.84807i
$612$		0			0
$613$			1026.91i			1.67522i	0.546270	+	0.837609i	$0.316047\pi$
$613$			1026.91i			1.67522i	−0.546270	+	0.837609i	$0.683953\pi$
$614$	−356.431	−	551.652i	−0.580506	−	0.898455i
$615$		0			0
$616$	6.62332	+	43.7872i	0.0107521	+	0.0710831i
$617$		−	479.223i		−	0.776698i	−0.921512	−	0.388349i	$-0.873046\pi$
$617$		−	479.223i		−	0.776698i	0.921512	−	0.388349i	$-0.126954\pi$
$618$		0			0
$619$			507.654i			0.820119i	0.912059	+	0.410059i	$0.134492\pi$
$619$			507.654i			0.820119i	−0.912059	+	0.410059i	$0.865508\pi$
$620$		0			0
$621$		0			0
$622$	−160.322	+	103.587i	−0.257753	+	0.166538i
$623$	−77.8282			−0.124925
$624$		0			0
$625$		0			0
$626$	−924.609	+	597.405i	−1.47701	+	0.954321i
$627$		0			0
$628$	−647.591	−	291.932i	−1.03120	−	0.464860i
$629$	−21.4293			−0.0340688
$630$		0			0
$631$		−	460.186i		−	0.729297i	−0.931145	−	0.364648i	$-0.881189\pi$
$631$		−	460.186i		−	0.729297i	0.931145	−	0.364648i	$-0.118811\pi$
$632$	78.8128	+	521.037i	0.124704	+	0.824426i
$633$		0			0
$634$	−738.122	+	476.912i	−1.16423	+	0.752228i
$635$		0			0
$636$		0			0
$637$			1143.71i			1.79546i
$638$	556.095	−	359.302i	0.871622	−	0.563169i
$639$		0			0
$640$		0			0
$641$	−250.774			−0.391223			−0.195612	−	0.980681i	$-0.562669\pi$
$641$	−250.774			−0.391223			−0.195612	+	0.980681i	$0.562669\pi$
$642$		0			0
$643$	590.355			0.918126			0.459063	−	0.888404i	$-0.348185\pi$
$643$	590.355			0.918126			0.459063	+	0.888404i	$0.348185\pi$
$644$	−31.4581	+	69.7834i	−0.0488480	+	0.108359i
$645$		0			0
$646$	−30.4252	−	47.0894i	−0.0470979	−	0.0728939i
$647$	319.341			0.493572			0.246786	−	0.969070i	$-0.420626\pi$
$647$	319.341			0.493572			0.246786	+	0.969070i	$0.420626\pi$
$648$		0			0
$649$	337.803			0.520497
$650$		0			0
$651$		0			0
$652$	−159.255	+	353.274i	−0.244256	+	0.541832i
$653$		−	88.5949i		−	0.135674i	−0.997696	−	0.0678369i	$-0.978390\pi$
$653$		−	88.5949i		−	0.135674i	0.997696	−	0.0678369i	$-0.0216097\pi$
$654$		0			0
$655$		0			0
$656$	424.652	+	480.512i	0.647335	+	0.732488i
$657$		0			0
$658$	47.9216	+	74.1688i	0.0728292	+	0.112719i
$659$			758.423i			1.15087i	0.817847	+	0.575435i	$0.195167\pi$
$659$			758.423i			1.15087i	−0.817847	+	0.575435i	$0.804833\pi$
$660$		0			0
$661$	527.327			0.797771			0.398885	−	0.917001i	$-0.369397\pi$
$661$	527.327			0.797771			0.398885	+	0.917001i	$0.369397\pi$
$662$	806.203	−	520.900i	1.21783	−	0.786859i
$663$		0			0
$664$	−1027.59	+	155.434i	−1.54757	+	0.234087i
$665$		0			0
$666$		0			0
$667$	1144.38			1.71571
$668$	250.863	−	556.488i	0.375544	−	0.833066i
$669$		0			0
$670$		0			0
$671$			81.0318i			0.120763i
$672$		0			0
$673$			120.657i			0.179283i	0.995974	+	0.0896415i	$0.0285721\pi$
$673$			120.657i			0.179283i	−0.995974	+	0.0896415i	$0.971428\pi$
$674$	98.8493	−	63.8681i	0.146661	−	0.0947598i
$675$		0			0
$676$	630.918	−	1399.56i	0.933311	−	2.07036i
$677$		−	219.196i		−	0.323776i	−0.986809	−	0.161888i	$-0.948242\pi$
$677$		−	219.196i		−	0.323776i	0.986809	−	0.161888i	$-0.0517583\pi$
$678$		0			0
$679$		−	55.5446i		−	0.0818035i
$680$		0			0
$681$		0			0
$682$	−596.850	−	923.751i	−0.875146	−	1.35447i
$683$	−205.502			−0.300881			−0.150441	−	0.988619i	$-0.548069\pi$
$683$	−205.502			−0.300881			−0.150441	+	0.988619i	$0.548069\pi$
$684$		0			0
$685$		0			0
$686$	−63.2222	−	97.8496i	−0.0921606	−	0.142638i
$687$		0			0
$688$	382.659	+	432.995i	0.556190	+	0.629354i
$689$	59.9837			0.0870591
$690$		0			0
$691$		−	109.536i		−	0.158519i	−0.996854	−	0.0792593i	$-0.974744\pi$
$691$		−	109.536i		−	0.158519i	0.996854	−	0.0792593i	$-0.0252555\pi$
$692$	568.042	+	256.071i	0.820869	+	0.370045i
$693$		0			0
$694$	−13.1857	−	20.4077i	−0.0189996	−	0.0294059i
$695$		0			0
$696$		0			0
$697$		−	159.415i		−	0.228716i
$698$	33.5685	+	51.9543i	0.0480924	+	0.0744331i
$699$		0			0
$700$		0			0
$701$	−168.847			−0.240865			−0.120433	−	0.992721i	$-0.538428\pi$
$701$	−168.847			−0.240865			−0.120433	+	0.992721i	$0.538428\pi$
$702$		0			0
$703$	−37.9695			−0.0540106
$704$	−175.648	−	567.327i	−0.249500	−	0.805863i
$705$		0			0
$706$	−483.909	+	312.661i	−0.685424	+	0.442863i
$707$	2.18382			0.00308885
$708$		0			0
$709$	554.846			0.782576			0.391288	−	0.920268i	$-0.372030\pi$
$709$	554.846			0.782576			0.391288	+	0.920268i	$0.372030\pi$
$710$		0			0
$711$		0			0
$712$	1031.99	−	156.100i	1.44942	−	0.219242i
$713$		−	1900.97i		−	2.66616i
$714$		0			0
$715$		0			0
$716$	459.474	+	207.130i	0.641723	+	0.289287i
$717$		0			0
$718$	−1115.28	+	720.600i	−1.55331	+	1.00362i
$719$			377.485i			0.525014i	0.964930	+	0.262507i	$0.0845494\pi$
$719$			377.485i			0.525014i	−0.964930	+	0.262507i	$0.915451\pi$
$720$		0			0
$721$	90.3261			0.125279
$722$	337.915	+	522.995i	0.468027	+	0.724369i
$723$		0			0
$724$	569.972	−	1264.37i	0.787255	−	1.74636i
$725$		0			0
$726$		0			0
$727$	173.183			0.238216			0.119108	−	0.992881i	$-0.461997\pi$
$727$	173.183			0.238216			0.119108	+	0.992881i	$0.461997\pi$
$728$	16.7814	+	110.943i	0.0230514	+	0.152394i
$729$		0			0
$730$		0			0
$731$		−	143.651i		−	0.196513i
$732$		0			0
$733$			278.722i			0.380249i	0.981760	+	0.190124i	$0.0608891\pi$
$733$			278.722i			0.380249i	−0.981760	+	0.190124i	$0.939111\pi$
$734$	6.60489	+	10.2225i	0.00899849	+	0.0139270i
$735$		0			0
$736$	277.165	−	988.412i	0.376583	−	1.34295i
$737$		−	647.142i		−	0.878075i
$738$		0			0
$739$		−	521.363i		−	0.705498i	−0.935718	−	0.352749i	$-0.885247\pi$
$739$		−	521.363i		−	0.705498i	0.935718	−	0.352749i	$-0.114753\pi$
$740$		0			0
$741$		0			0
$742$	−2.55660	+	1.65186i	−0.00344555	+	0.00222622i
$743$	−1277.93			−1.71996			−0.859981	−	0.510326i	$-0.829525\pi$
$743$	−1277.93			−1.71996			−0.859981	+	0.510326i	$0.829525\pi$
$744$		0			0
$745$		0			0
$746$	343.936	−	222.223i	0.461041	−	0.297886i
$747$		0			0
$748$	−60.6751	+	134.595i	−0.0811164	+	0.179940i
$749$	49.3989			0.0659532
$750$		0			0
$751$			1165.31i			1.55168i	0.630930	+	0.775840i	$0.282673\pi$
$751$			1165.31i			1.55168i	−0.630930	+	0.775840i	$0.717327\pi$
$752$	−784.194	−	887.350i	−1.04281	−	1.17999i
$753$		0			0
$754$	1408.97	−	910.359i	1.86866	−	1.20737i
$755$		0			0
$756$		0			0
$757$		−	1063.75i		−	1.40522i	−0.711574	−	0.702611i	$-0.752017\pi$
$757$		−	1063.75i		−	1.40522i	0.711574	−	0.702611i	$-0.247983\pi$
$758$	−675.861	+	436.685i	−0.891638	+	0.576101i
$759$		0			0
$760$		0			0
$761$	677.847			0.890732			0.445366	−	0.895349i	$-0.353074\pi$
$761$	677.847			0.890732			0.445366	+	0.895349i	$0.353074\pi$
$762$		0			0
$763$	4.39551			0.00576083
$764$	485.577	+	218.897i	0.635572	+	0.286514i
$765$		0			0
$766$	−360.078	−	557.296i	−0.470076	−	0.727541i
$767$	855.887			1.11589
$768$		0			0
$769$	1289.59			1.67697			0.838486	−	0.544922i	$-0.183441\pi$
$769$	1289.59			1.67697			0.838486	+	0.544922i	$0.183441\pi$
$770$		0			0
$771$		0			0
$772$	496.836	+	223.972i	0.643570	+	0.290119i
$773$			750.339i			0.970684i	0.874324	+	0.485342i	$0.161305\pi$
$773$			750.339i			0.970684i	−0.874324	+	0.485342i	$0.838695\pi$
$774$		0			0
$775$		0			0
$776$	111.406	+	736.513i	0.143564	+	0.949114i
$777$		0			0
$778$	−676.532	−	1047.07i	−0.869578	−	1.34585i
$779$		−	282.460i		−	0.362593i
$780$		0			0
$781$	549.512			0.703600
$782$	−214.343	+	138.491i	−0.274096	+	0.177098i
$783$		0			0
$784$	515.402	+	583.200i	0.657400	+	0.743877i
$785$		0			0
$786$		0			0
$787$	825.185			1.04852			0.524260	−	0.851558i	$-0.324342\pi$
$787$	825.185			1.04852			0.524260	+	0.851558i	$0.324342\pi$
$788$	−273.110	−	123.117i	−0.346586	−	0.156240i
$789$		0			0
$790$		0			0
$791$		−	38.7971i		−	0.0490482i
$792$		0			0
$793$			205.309i			0.258902i
$794$	−597.106	+	385.799i	−0.752022	+	0.485893i
$795$		0			0
$796$	917.500	+	413.606i	1.15264	+	0.519606i
$797$			1113.70i			1.39737i	0.715430	+	0.698684i	$0.246231\pi$
$797$			1113.70i			1.39737i	−0.715430	+	0.698684i	$0.753769\pi$
$798$		0			0
$799$			294.388i			0.368445i
$800$		0			0
$801$		0			0
$802$	589.285	+	912.043i	0.734770	+	1.13721i
$803$	−770.226			−0.959186
$804$		0			0
$805$		0			0
$806$	−1512.23	−	2340.50i	−1.87622	−	2.90384i
$807$		0			0
$808$	−28.9571	+	4.38009i	−0.0358380	+	0.00542090i
$809$	−1049.54			−1.29733			−0.648664	−	0.761075i	$-0.724672\pi$
$809$	−1049.54			−1.29733			−0.648664	+	0.761075i	$0.724672\pi$
$810$		0			0
$811$		−	424.482i		−	0.523406i	−0.965148	−	0.261703i	$-0.915716\pi$
$811$		−	424.482i		−	0.523406i	0.965148	−	0.261703i	$-0.0842841\pi$
$812$	−34.9827	+	77.6018i	−0.0430821	+	0.0955688i
$813$		0			0
$814$	54.2638	+	83.9847i	0.0666632	+	0.103175i
$815$		0			0
$816$		0			0
$817$		−	254.528i		−	0.311540i
$818$	117.761	+	182.259i	0.143962	+	0.222811i
$819$		0			0
$820$		0			0
$821$	1257.98			1.53225			0.766126	−	0.642690i	$-0.222182\pi$
$821$	1257.98			1.53225			0.766126	+	0.642690i	$0.222182\pi$
$822$		0			0
$823$	729.181			0.886004			0.443002	−	0.896521i	$-0.353913\pi$
$823$	729.181			0.886004			0.443002	+	0.896521i	$0.353913\pi$
$824$	−1197.71	+	181.167i	−1.45353	+	0.219863i
$825$		0			0
$826$	−36.4792	+	23.5698i	−0.0441637	+	0.0285349i
$827$	−72.5882			−0.0877729			−0.0438865	−	0.999037i	$-0.513974\pi$
$827$	−72.5882			−0.0877729			−0.0438865	+	0.999037i	$0.513974\pi$
$828$		0			0
$829$	−900.257			−1.08596			−0.542978	−	0.839747i	$-0.682703\pi$
$829$	−900.257			−1.08596			−0.542978	+	0.839747i	$0.682703\pi$
$830$		0			0
$831$		0			0
$832$	−445.038	−	1437.43i	−0.534901	−	1.72768i
$833$		−	193.482i		−	0.232272i
$834$		0			0
$835$		0			0
$836$	−107.507	+	238.483i	−0.128597	+	0.285266i
$837$		0			0
$838$	289.232	−	186.877i	0.345145	−	0.223004i
$839$		−	71.4721i		−	0.0851872i	−0.999092	−	0.0425936i	$-0.986438\pi$
$839$		−	71.4721i		−	0.0851872i	0.999092	−	0.0425936i	$-0.0135621\pi$
$840$		0			0
$841$	431.594			0.513191
$842$	519.381	+	803.851i	0.616842	+	0.954693i
$843$		0			0
$844$	−832.165	−	375.138i	−0.985978	−	0.444476i
$845$		0			0
$846$		0			0
$847$	20.8124			0.0245719
$848$	30.5870	−	27.0312i	0.0360695	−	0.0318764i
$849$		0			0
$850$		0			0
$851$			172.831i			0.203091i
$852$		0			0
$853$			882.349i			1.03441i	0.855862	+	0.517203i	$0.173027\pi$
$853$			882.349i			1.03441i	−0.855862	+	0.517203i	$0.826973\pi$
$854$	−5.65391	−	8.75061i	−0.00662050	−	0.0102466i
$855$		0			0
$856$	−655.022	+	99.0796i	−0.765213	+	0.115747i
$857$		−	370.111i		−	0.431868i	−0.976408	−	0.215934i	$-0.930720\pi$
$857$		−	370.111i		−	0.431868i	0.976408	−	0.215934i	$-0.0692796\pi$
$858$		0			0
$859$		−	1039.00i		−	1.20955i	−0.796397	−	0.604774i	$-0.793264\pi$
$859$		−	1039.00i		−	1.20955i	0.796397	−	0.604774i	$-0.206736\pi$
$860$		0			0
$861$		0			0
$862$	−488.373	+	315.546i	−0.566558	+	0.366062i
$863$	−72.0666			−0.0835071			−0.0417535	−	0.999128i	$-0.513294\pi$
$863$	−72.0666			−0.0835071			−0.0417535	+	0.999128i	$0.513294\pi$
$864$		0			0
$865$		0			0
$866$	−90.3306	+	58.3640i	−0.104308	+	0.0673950i
$867$		0			0
$868$	128.907	+	58.1110i	0.148511	+	0.0669482i
$869$	−611.254			−0.703399
$870$		0			0
$871$		−	1639.66i		−	1.88250i
$872$	−58.2838	+	8.81609i	−0.0668393	+	0.0101102i
$873$		0			0
$874$	−379.785	+	245.385i	−0.434536	+	0.280761i
$875$		0			0
$876$		0			0
$877$		−	14.4444i		−	0.0164703i	−0.999966	−	0.00823514i	$-0.997379\pi$
$877$		−	14.4444i		−	0.0164703i	0.999966	−	0.00823514i	$-0.00262136\pi$
$878$	552.099	−	356.720i	0.628815	−	0.406287i
$879$		0			0
$880$		0			0
$881$	−1589.22			−1.80388			−0.901942	−	0.431858i	$-0.857858\pi$
$881$	−1589.22			−1.80388			−0.901942	+	0.431858i	$0.857858\pi$
$882$		0			0
$883$	−495.149			−0.560758			−0.280379	−	0.959889i	$-0.590460\pi$
$883$	−495.149			−0.560758			−0.280379	+	0.959889i	$0.590460\pi$
$884$	−153.732	+	341.022i	−0.173905	+	0.385772i
$885$		0			0
$886$	465.533	+	720.510i	0.525432	+	0.813216i
$887$	−1384.20			−1.56054			−0.780272	−	0.625440i	$-0.784919\pi$
$887$	−1384.20			−1.56054			−0.780272	+	0.625440i	$0.784919\pi$
$888$		0			0
$889$	−83.1988			−0.0935870
$890$		0			0
$891$		0			0
$892$	−141.299	+	313.443i	−0.158407	+	0.351393i
$893$			521.611i			0.584111i
$894$		0			0
$895$		0			0
$896$	58.5528	+	49.0099i	0.0653491	+	0.0546985i
$897$		0			0
$898$	444.171	+	687.448i	0.494623	+	0.765533i
$899$		−	2113.95i		−	2.35145i
$900$		0			0
$901$	−10.1475			−0.0112625
$902$	−624.773	+	403.676i	−0.692653	+	0.447534i
$903$		0			0
$904$	77.8155	+	514.444i	0.0860791	+	0.569075i
$905$		0			0
$906$		0			0
$907$	−957.750			−1.05595			−0.527977	−	0.849259i	$-0.677049\pi$
$907$	−957.750			−1.05595			−0.527977	+	0.849259i	$0.677049\pi$
$908$	464.160	−	1029.64i	0.511189	−	1.13397i
$909$		0			0
$910$		0			0
$911$		−	704.979i		−	0.773852i	−0.922111	−	0.386926i	$-0.873537\pi$
$911$		−	704.979i		−	0.773852i	0.922111	−	0.386926i	$-0.126463\pi$
$912$		0			0
$913$		−	1205.51i		−	1.32038i
$914$	1291.08	−	834.185i	1.41256	−	0.912675i
$915$		0			0
$916$	227.287	−	504.189i	0.248130	−	0.550424i
$917$		−	37.8717i		−	0.0412996i
$918$		0			0
$919$		−	607.048i		−	0.660553i	−0.943884	−	0.330277i	$-0.892858\pi$
$919$		−	607.048i		−	0.660553i	0.943884	−	0.330277i	$-0.107142\pi$
$920$		0			0
$921$		0			0
$922$	343.593	+	531.782i	0.372660	+	0.576770i
$923$	1392.29			1.50844
$924$		0			0
$925$		0			0
$926$	533.151	+	825.163i	0.575757	+	0.891104i
$927$		0			0
$928$	308.219	−	1099.15i	0.332132	−	1.18443i
$929$	1011.21			1.08849			0.544247	−	0.838925i	$-0.316815\pi$
$929$	1011.21			1.08849			0.544247	+	0.838925i	$0.316815\pi$
$930$		0			0
$931$		−	342.822i		−	0.368230i
$932$	−1.90695	−	0.859647i	−0.00204608	−	0.000922368i
$933$		0			0
$934$	445.434	+	689.403i	0.476910	+	0.738119i
$935$		0			0
$936$		0			0
$937$			363.105i			0.387519i	0.981049	+	0.193760i	$0.0620682\pi$
$937$			363.105i			0.387519i	−0.981049	+	0.193760i	$0.937932\pi$
$938$	45.1536	+	69.8846i	0.0481381	+	0.0745039i
$939$		0			0
$940$		0			0
$941$	1106.51			1.17588			0.587942	−	0.808903i	$-0.299939\pi$
$941$	1106.51			1.17588			0.587942	+	0.808903i	$0.299939\pi$
$942$		0			0
$943$	−1285.71			−1.36342
$944$	436.435	−	385.698i	0.462325	−	0.408579i
$945$		0			0
$946$	−562.990	+	363.757i	−0.595127	+	0.384521i
$947$	553.561			0.584541			0.292271	−	0.956336i	$-0.405589\pi$
$947$	553.561			0.584541			0.292271	+	0.956336i	$0.405589\pi$
$948$		0			0
$949$	−1951.51			−2.05639
$950$		0			0
$951$		0			0
$952$	−2.83894	−	18.7684i	−0.00298208	−	0.0197147i
$953$			1674.84i			1.75744i	0.477342	+	0.878718i	$0.341600\pi$
$953$			1674.84i			1.75744i	−0.477342	+	0.878718i	$0.658400\pi$
$954$		0			0
$955$		0			0
$956$	−268.728	−	121.142i	−0.281096	−	0.126717i
$957$		0			0
$958$	334.154	−	215.902i	0.348804	−	0.225368i
$959$		−	82.4162i		−	0.0859398i
$960$		0			0
$961$	−2550.57			−2.65408
$962$	137.488	+	212.791i	0.142919	+	0.221196i
$963$		0			0
$964$	−51.5692	+	114.396i	−0.0534950	+	0.118668i
$965$		0			0
$966$		0			0
$967$	786.720			0.813568			0.406784	−	0.913524i	$-0.366650\pi$
$967$	786.720			0.813568			0.406784	+	0.913524i	$0.366650\pi$
$968$	−275.969	+	41.7435i	−0.285092	+	0.0431234i
$969$		0			0
$970$		0			0
$971$			1289.75i			1.32827i	0.747612	+	0.664135i	$0.231200\pi$
$971$			1289.75i			1.32827i	−0.747612	+	0.664135i	$0.768800\pi$
$972$		0			0
$973$			17.8710i			0.0183669i
$974$	222.246	+	343.972i	0.228178	+	0.353154i
$975$		0			0
$976$	92.5210	+	104.692i	0.0947961	+	0.107266i
$977$			495.847i			0.507520i	0.967267	+	0.253760i	$0.0816674\pi$
$977$			495.847i			0.507520i	−0.967267	+	0.253760i	$0.918333\pi$
$978$		0			0
$979$			1210.68i			1.23665i
$980$		0			0
$981$		0			0
$982$	−1324.74	+	855.933i	−1.34902	+	0.871622i
$983$	967.035			0.983759			0.491880	−	0.870663i	$-0.336310\pi$
$983$	967.035			0.983759			0.491880	+	0.870663i	$0.336310\pi$
$984$		0			0
$985$		0			0
$986$	−238.358	+	154.007i	−0.241742	+	0.156194i
$987$		0			0
$988$	−272.390	+	604.241i	−0.275698	+	0.611580i
$989$	−1158.57			−1.17145
$990$		0			0
$991$			1203.68i			1.21461i	0.794469	+	0.607305i	$0.207749\pi$
$991$			1203.68i			1.21461i	−0.794469	+	0.607305i	$0.792251\pi$
$992$	−1825.84	−	511.994i	−1.84057	−	0.516123i
$993$		0			0
$994$	−59.3417	+	38.3416i	−0.0596999	+	0.0385730i
$995$		0			0
$996$		0			0
$997$			1274.55i			1.27838i	0.769047	+	0.639192i	$0.220731\pi$
$997$			1274.55i			1.27838i	−0.769047	+	0.639192i	$0.779269\pi$
$998$	−1243.74	+	803.603i	−1.24624	+	0.805214i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.f.199.14		16
3.2	odd	2		300.3.f.b.199.3		16
4.3	odd	2	inner	900.3.f.f.199.4		16
5.2	odd	4		180.3.c.b.91.4		8
5.3	odd	4		900.3.c.u.451.5		8
5.4	even	2	inner	900.3.f.f.199.3		16
12.11	even	2		300.3.f.b.199.13		16
15.2	even	4		60.3.c.a.31.5	✓	8
15.8	even	4		300.3.c.d.151.4		8
15.14	odd	2		300.3.f.b.199.14		16
20.3	even	4		900.3.c.u.451.6		8
20.7	even	4		180.3.c.b.91.3		8
20.19	odd	2	inner	900.3.f.f.199.13		16
40.27	even	4		2880.3.e.j.2431.6		8
40.37	odd	4		2880.3.e.j.2431.7		8
60.23	odd	4		300.3.c.d.151.3		8
60.47	odd	4		60.3.c.a.31.6	yes	8
60.59	even	2		300.3.f.b.199.4		16
120.77	even	4		960.3.e.c.511.1		8
120.107	odd	4		960.3.e.c.511.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.5	✓	8	15.2	even	4
60.3.c.a.31.6	yes	8	60.47	odd	4
180.3.c.b.91.3		8	20.7	even	4
180.3.c.b.91.4		8	5.2	odd	4
300.3.c.d.151.3		8	60.23	odd	4
300.3.c.d.151.4		8	15.8	even	4
300.3.f.b.199.3		16	3.2	odd	2
300.3.f.b.199.4		16	60.59	even	2
300.3.f.b.199.13		16	12.11	even	2
300.3.f.b.199.14		16	15.14	odd	2
900.3.c.u.451.5		8	5.3	odd	4
900.3.c.u.451.6		8	20.3	even	4
900.3.f.f.199.3		16	5.4	even	2	inner
900.3.f.f.199.4		16	4.3	odd	2	inner
900.3.f.f.199.13		16	20.19	odd	2	inner
900.3.f.f.199.14		16	1.1	even	1	trivial
960.3.e.c.511.1		8	120.77	even	4
960.3.e.c.511.6		8	120.107	odd	4
2880.3.e.j.2431.6		8	40.27	even	4
2880.3.e.j.2431.7		8	40.37	odd	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.08539 + 1.67986i) q^{2} +(-1.64388 + 3.64660i) q^{4} +0.596540 q^{7} +(-7.91002 + 1.19648i) q^{8} +O(q^{10})\)	\(q+(1.08539 + 1.67986i) q^{2} +(-1.64388 + 3.64660i) q^{4} +0.596540 q^{7} +(-7.91002 + 1.19648i) q^{8} -9.27963i q^{11} -23.5117i q^{13} +(0.647476 + 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} +3.97751i q^{17} +7.04756i q^{19} +(15.5885 - 10.0720i) q^{22} +32.0793 q^{23} +(39.4964 - 25.5192i) q^{26} +(-0.980637 + 2.17534i) q^{28} +35.6734 q^{29} -59.2585i q^{31} +(8.64000 - 30.8115i) q^{32} +(-6.68167 + 4.31713i) q^{34} +5.38761i q^{37} +(-11.8389 + 7.64932i) q^{38} -40.0791 q^{41} -36.1157 q^{43} +(33.8391 + 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131 q^{47} -48.6441 q^{49} +(85.7376 + 38.6503i) q^{52} +2.55123i q^{53} +(-4.71864 + 0.713748i) q^{56} +(38.7194 + 59.9265i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(99.5461 - 64.3183i) q^{62} +(61.1369 - 18.9284i) q^{64} +69.7379 q^{67} +(-14.5044 - 6.53853i) q^{68} +59.2170i q^{71} -83.0019i q^{73} +(-9.05044 + 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} -5.53566i q^{77} -65.8705i q^{79} +(-43.5013 - 67.3274i) q^{82} +129.909 q^{83} +(-39.1995 - 60.6695i) q^{86} +(11.1029 + 73.4020i) q^{88} -130.466 q^{89} -14.0256i q^{91} +(-52.7344 + 116.980i) q^{92} +(80.3327 + 124.332i) q^{94} -93.1113i q^{97} +(-52.7977 - 81.7155i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4}+O(q^{10}) \) 16 * q - 20 * q^4	\( 16 q - 20 q^{4} - 40 q^{14} + 68 q^{16} + 72 q^{26} + 128 q^{29} + 184 q^{34} + 32 q^{41} + 344 q^{44} + 304 q^{46} + 112 q^{49} - 232 q^{56} - 352 q^{61} + 220 q^{64} + 264 q^{74} - 48 q^{76} + 400 q^{86} + 160 q^{89} + 192 q^{94}+O(q^{100}) \) 16 * q - 20 * q^4 - 40 * q^14 + 68 * q^16 + 72 * q^26 + 128 * q^29 + 184 * q^34 + 32 * q^41 + 344 * q^44 + 304 * q^46 + 112 * q^49 - 232 * q^56 - 352 * q^61 + 220 * q^64 + 264 * q^74 - 48 * q^76 + 400 * q^86 + 160 * q^89 + 192 * q^94

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