LMFDB - Embedded newform 900.2.bj.f.523.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.14
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.f.487.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.152118 - 1.40601i) q^{2} +(-1.95372 + 0.427760i) q^{4} +(-1.07461 + 1.96092i) q^{5} +(-0.868967 - 0.868967i) q^{7} +(0.898631 + 2.68188i) q^{8} +(2.92054 + 1.21262i) q^{10} +(2.63624 + 3.62847i) q^{11} +(-0.530391 - 3.34876i) q^{13} +(-1.08959 + 1.35396i) q^{14} +(3.63404 - 1.67145i) q^{16} +(-5.52269 - 2.81395i) q^{17} +(-1.47067 - 4.52625i) q^{19} +(1.26069 - 4.29076i) q^{20} +(4.70064 - 4.25853i) q^{22} +(0.748674 - 4.72694i) q^{23} +(-2.69041 - 4.21446i) q^{25} +(-4.62770 + 1.25514i) q^{26} +(2.06943 + 1.32601i) q^{28} +(-2.21880 - 0.720931i) q^{29} +(9.32059 - 3.02844i) q^{31} +(-2.90287 - 4.85524i) q^{32} +(-3.11633 + 8.19300i) q^{34} +(2.63778 - 0.770171i) q^{35} +(-8.45865 + 1.33972i) q^{37} +(-6.14023 + 2.75630i) q^{38} +(-6.22463 - 1.11984i) q^{40} +(-2.25676 - 1.63963i) q^{41} +(-5.74249 + 5.74249i) q^{43} +(-6.70259 - 5.96134i) q^{44} +(-6.76001 - 0.333587i) q^{46} +(4.24551 - 2.16319i) q^{47} -5.48979i q^{49} +(-5.51631 + 4.42384i) q^{50} +(2.46870 + 6.31566i) q^{52} +(-0.643686 + 0.327974i) q^{53} +(-9.94808 + 1.27025i) q^{55} +(1.54958 - 3.11134i) q^{56} +(-0.676115 + 3.22932i) q^{58} +(-0.305784 - 0.222165i) q^{59} +(2.68715 - 1.95233i) q^{61} +(-5.67585 - 12.6441i) q^{62} +(-6.38493 + 4.82003i) q^{64} +(7.13661 + 2.55857i) q^{65} +(3.01843 - 5.92399i) q^{67} +(11.9935 + 3.13529i) q^{68} +(-1.48412 - 3.59158i) q^{70} +(-4.75445 - 1.54481i) q^{71} +(3.39138 + 0.537142i) q^{73} +(3.17037 + 11.6891i) q^{74} +(4.80942 + 8.21394i) q^{76} +(0.862218 - 5.44383i) q^{77} +(0.521056 - 1.60364i) q^{79} +(-0.627622 + 8.92222i) q^{80} +(-1.96204 + 3.42244i) q^{82} +(-13.5881 - 6.92350i) q^{83} +(11.4527 - 7.80563i) q^{85} +(8.94753 + 7.20045i) q^{86} +(-7.36211 + 10.3307i) q^{88} +(0.948617 + 1.30566i) q^{89} +(-2.44907 + 3.37085i) q^{91} +(0.559295 + 9.55537i) q^{92} +(-3.68729 - 5.64016i) q^{94} +(10.4560 + 1.98011i) q^{95} +(-5.55806 - 10.9083i) q^{97} +(-7.71870 + 0.835099i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.152118	−	1.40601i	−0.107564	−	0.994198i
$2$	−0.152118	−	1.40601i	−0.107564	−	0.994198i
$3$		0			0
$3$		0			0
$4$	−1.95372	+	0.427760i	−0.976860	+	0.213880i
$5$	−1.07461	+	1.96092i	−0.480582	+	0.876950i
$5$	−1.07461	+	1.96092i	−0.480582	+	0.876950i
$6$		0			0
$7$	−0.868967	−	0.868967i	−0.328439	−	0.328439i	0.523554	−	0.851993i	$-0.324606\pi$
$7$	−0.868967	−	0.868967i	−0.328439	−	0.328439i	−0.851993	+	0.523554i	$0.824606\pi$
$8$	0.898631	+	2.68188i	0.317714	+	0.948187i
$9$		0			0
$10$	2.92054	+	1.21262i	0.923555	+	0.383465i
$11$	2.63624	+	3.62847i	0.794856	+	1.09403i	0.993486	+	0.113951i	$0.0363507\pi$
$11$	2.63624	+	3.62847i	0.794856	+	1.09403i	−0.198630	+	0.980075i	$0.563649\pi$
$12$		0			0
$13$	−0.530391	−	3.34876i	−0.147104	−	0.928778i	−0.945258	−	0.326325i	$-0.894190\pi$
$13$	−0.530391	−	3.34876i	−0.147104	−	0.928778i	0.798154	−	0.602454i	$-0.205810\pi$
$14$	−1.08959	+	1.35396i	−0.291205	+	0.361861i
$15$		0			0
$16$	3.63404	−	1.67145i	0.908511	−	0.417861i
$17$	−5.52269	−	2.81395i	−1.33945	−	0.682483i	−0.370288	−	0.928917i	$-0.620741\pi$
$17$	−5.52269	−	2.81395i	−1.33945	−	0.682483i	−0.969160	+	0.246434i	$0.920741\pi$
$18$		0			0
$19$	−1.47067	−	4.52625i	−0.337394	−	1.03839i	−0.965531	−	0.260290i	$-0.916182\pi$
$19$	−1.47067	−	4.52625i	−0.337394	−	1.03839i	0.628136	−	0.778103i	$-0.283818\pi$
$20$	1.26069	−	4.29076i	0.281899	−	0.959444i
$21$		0			0
$22$	4.70064	−	4.25853i	1.00218	−	0.907922i
$23$	0.748674	−	4.72694i	0.156109	−	0.985635i	−0.777900	−	0.628388i	$-0.783715\pi$
$23$	0.748674	−	4.72694i	0.156109	−	0.985635i	0.934010	−	0.357248i	$-0.116285\pi$
$24$		0			0
$25$	−2.69041	−	4.21446i	−0.538082	−	0.842892i
$26$	−4.62770	+	1.25514i	−0.907567	+	0.246154i
$27$		0			0
$28$	2.06943	+	1.32601i	0.391085	+	0.250592i
$29$	−2.21880	−	0.720931i	−0.412020	−	0.133874i	0.0956700	−	0.995413i	$-0.469501\pi$
$29$	−2.21880	−	0.720931i	−0.412020	−	0.133874i	−0.507690	+	0.861540i	$0.669501\pi$
$30$		0			0
$31$	9.32059	−	3.02844i	1.67403	−	0.543925i	0.690289	−	0.723533i	$-0.257483\pi$
$31$	9.32059	−	3.02844i	1.67403	−	0.543925i	0.983738	+	0.179609i	$0.0574832\pi$
$32$	−2.90287	−	4.85524i	−0.513160	−	0.858293i
$33$		0			0
$34$	−3.11633	+	8.19300i	−0.534447	+	1.40509i
$35$	2.63778	−	0.770171i	0.445866	−	0.130183i
$36$		0			0
$37$	−8.45865	+	1.33972i	−1.39059	+	0.220248i	−0.806402	−	0.591368i	$-0.798588\pi$
$37$	−8.45865	+	1.33972i	−1.39059	+	0.220248i	−0.584191	+	0.811616i	$0.698588\pi$
$38$	−6.14023	+	2.75630i	−0.996077	+	0.447131i
$39$		0			0
$40$	−6.22463	−	1.11984i	−0.984200	−	0.177062i
$41$	−2.25676	−	1.63963i	−0.352447	−	0.256067i	0.397448	−	0.917625i	$-0.369896\pi$
$41$	−2.25676	−	1.63963i	−0.352447	−	0.256067i	−0.749895	+	0.661557i	$0.769896\pi$
$42$		0			0
$43$	−5.74249	+	5.74249i	−0.875722	+	0.875722i	−0.993089	−	0.117367i	$-0.962555\pi$
$43$	−5.74249	+	5.74249i	−0.875722	+	0.875722i	0.117367	+	0.993089i	$0.462555\pi$
$44$	−6.70259	−	5.96134i	−1.01045	−	0.898706i
$45$		0			0
$46$	−6.76001	−	0.333587i	−0.996708	−	0.0491847i
$47$	4.24551	−	2.16319i	0.619271	−	0.315534i	−0.116061	−	0.993242i	$-0.537027\pi$
$47$	4.24551	−	2.16319i	0.619271	−	0.315534i	0.735331	+	0.677708i	$0.237027\pi$
$48$		0			0
$49$		−	5.48979i		−	0.784256i
$50$	−5.51631	+	4.42384i	−0.780124	+	0.625625i
$51$		0			0
$52$	2.46870	+	6.31566i	0.342347	+	0.875824i
$53$	−0.643686	+	0.327974i	−0.0884171	+	0.0450507i	−0.497640	−	0.867384i	$-0.665800\pi$
$53$	−0.643686	+	0.327974i	−0.0884171	+	0.0450507i	0.409223	+	0.912434i	$0.365800\pi$
$54$		0			0
$55$	−9.94808	+	1.27025i	−1.34140	+	0.171280i
$56$	1.54958	−	3.11134i	0.207072	−	0.415771i
$57$		0			0
$58$	−0.676115	+	3.22932i	−0.0887783	+	0.424030i
$59$	−0.305784	−	0.222165i	−0.0398097	−	0.0289234i	0.567702	−	0.823234i	$-0.307832\pi$
$59$	−0.305784	−	0.222165i	−0.0398097	−	0.0289234i	−0.607512	+	0.794310i	$0.707832\pi$
$60$		0			0
$61$	2.68715	−	1.95233i	0.344054	−	0.249970i	−0.402316	−	0.915501i	$-0.631795\pi$
$61$	2.68715	−	1.95233i	0.344054	−	0.249970i	0.746370	+	0.665531i	$0.231795\pi$
$62$	−5.67585	−	12.6441i	−0.720834	−	1.60581i
$63$		0			0
$64$	−6.38493	+	4.82003i	−0.798116	+	0.602504i
$65$	7.13661	+	2.55857i	0.885188	+	0.317351i
$66$		0			0
$67$	3.01843	−	5.92399i	0.368759	−	0.723731i	−0.629835	−	0.776729i	$-0.716878\pi$
$67$	3.01843	−	5.92399i	0.368759	−	0.723731i	0.998595	+	0.0529977i	$0.0168776\pi$
$68$	11.9935	+	3.13529i	1.45442	+	0.380209i
$69$		0			0
$70$	−1.48412	−	3.59158i	−0.177386	−	0.429276i
$71$	−4.75445	−	1.54481i	−0.564249	−	0.183336i	0.0129832	−	0.999916i	$-0.495867\pi$
$71$	−4.75445	−	1.54481i	−0.564249	−	0.183336i	−0.577232	+	0.816580i	$0.695867\pi$
$72$		0			0
$73$	3.39138	+	0.537142i	0.396931	+	0.0628677i	0.351709	−	0.936109i	$-0.385601\pi$
$73$	3.39138	+	0.537142i	0.396931	+	0.0628677i	0.0452218	+	0.998977i	$0.485601\pi$
$74$	3.17037	+	11.6891i	0.368548	+	1.35883i
$75$		0			0
$76$	4.80942	+	8.21394i	0.551678	+	0.942203i
$77$	0.862218	−	5.44383i	0.0982588	−	0.620382i
$78$		0			0
$79$	0.521056	−	1.60364i	0.0586234	−	0.180424i	−0.917457	−	0.397836i	$-0.869761\pi$
$79$	0.521056	−	1.60364i	0.0586234	−	0.180424i	0.976080	+	0.217412i	$0.0697614\pi$
$80$	−0.627622	+	8.92222i	−0.0701703	+	0.997535i
$81$		0			0
$82$	−1.96204	+	3.42244i	−0.216671	+	0.377945i
$83$	−13.5881	−	6.92350i	−1.49149	−	0.759953i	−0.497300	−	0.867578i	$-0.665675\pi$
$83$	−13.5881	−	6.92350i	−1.49149	−	0.759953i	−0.994192	+	0.107625i	$0.965675\pi$
$84$		0			0
$85$	11.4527	−	7.80563i	1.24222	−	0.846640i
$86$	8.94753	+	7.20045i	0.964837	+	0.776445i
$87$		0			0
$88$	−7.36211	+	10.3307i	−0.784804	+	1.10126i
$89$	0.948617	+	1.30566i	0.100553	+	0.138400i	0.856329	−	0.516431i	$-0.172740\pi$
$89$	0.948617	+	1.30566i	0.100553	+	0.138400i	−0.755775	+	0.654831i	$0.772740\pi$
$90$		0			0
$91$	−2.44907	+	3.37085i	−0.256732	+	0.353361i
$92$	0.559295	+	9.55537i	0.0583106	+	0.996216i
$93$		0			0
$94$	−3.68729	−	5.64016i	−0.380315	−	0.581738i
$95$	10.4560	+	1.98011i	1.07276	+	0.203155i
$96$		0			0
$97$	−5.55806	−	10.9083i	−0.564336	−	1.10757i	−0.980175	−	0.198133i	$-0.936512\pi$
$97$	−5.55806	−	10.9083i	−0.564336	−	1.10757i	0.415840	−	0.909438i	$-0.363488\pi$
$98$	−7.71870	+	0.835099i	−0.779706	+	0.0843577i
$99$		0			0
$100$	7.05909	+	7.08303i	0.705909	+	0.708303i
$101$	7.90808			0.786884			0.393442	−	0.919350i	$-0.371284\pi$
$101$	7.90808			0.786884			0.393442	+	0.919350i	$0.371284\pi$
$102$		0			0
$103$	7.63035	+	14.9754i	0.751841	+	1.47557i	0.875485	+	0.483245i	$0.160542\pi$
$103$	7.63035	+	14.9754i	0.751841	+	1.47557i	−0.123644	+	0.992327i	$0.539458\pi$
$104$	8.50433	−	4.43174i	0.833918	−	0.434568i
$105$		0			0
$106$	0.559051	+	0.855137i	0.0542999	+	0.0830582i
$107$	−0.756931	−	0.756931i	−0.0731753	−	0.0731753i	0.669572	−	0.742747i	$-0.266478\pi$
$107$	−0.756931	−	0.756931i	−0.0731753	−	0.0731753i	−0.742747	+	0.669572i	$0.766478\pi$
$108$		0			0
$109$	−3.37095	+	4.63972i	−0.322879	+	0.444404i	−0.939343	−	0.342978i	$-0.888564\pi$
$109$	−3.37095	+	4.63972i	−0.322879	+	0.444404i	0.616465	+	0.787383i	$0.288564\pi$
$110$	3.29927	+	13.7939i	0.314573	+	1.31519i
$111$		0			0
$112$	−4.61029	−	1.70543i	−0.435632	−	0.161148i
$113$	−2.86561	−	18.0927i	−0.269574	−	1.70202i	−0.636095	−	0.771611i	$-0.719451\pi$
$113$	−2.86561	−	18.0927i	−0.269574	−	1.70202i	0.366522	−	0.930410i	$-0.380549\pi$
$114$		0			0
$115$	8.46461	+	6.54772i	0.789329	+	0.610578i
$116$	4.64329	+	0.459385i	0.431119	+	0.0426529i
$117$		0			0
$118$	−0.265851	+	0.463730i	−0.0244735	+	0.0426898i
$119$	2.35380	+	7.24426i	0.215773	+	0.664080i
$120$		0			0
$121$	−2.81687	+	8.66943i	−0.256079	+	0.788130i
$122$	−3.15375	−	3.48117i	−0.285527	−	0.315170i
$123$		0			0
$124$	−16.9144	+	9.90370i	−1.51896	+	0.889379i
$125$	11.1554	−	0.746764i	0.997767	−	0.0667926i
$126$		0			0
$127$	2.29897	+	0.364120i	0.204000	+	0.0323105i	0.257598	−	0.966252i	$-0.417069\pi$
$127$	2.29897	+	0.364120i	0.204000	+	0.0323105i	−0.0535979	+	0.998563i	$0.517069\pi$
$128$	7.74827	+	8.24404i	0.684857	+	0.728678i
$129$		0			0
$130$	2.51176	−	10.4233i	0.220296	−	0.914188i
$131$	−21.3803	+	6.94688i	−1.86801	+	0.606952i	−0.875746	+	0.482772i	$0.839630\pi$
$131$	−21.3803	+	6.94688i	−1.86801	+	0.606952i	−0.992260	+	0.124180i	$0.960370\pi$
$132$		0			0
$133$	−2.65520	+	5.21113i	−0.230235	+	0.451862i
$134$	−8.78834	−	3.34278i	−0.759197	−	0.288773i
$135$		0			0
$136$	2.58381	−	17.3399i	0.221560	−	1.48688i
$137$	−20.2164	+	3.20196i	−1.72720	+	0.273562i	−0.939514	−	0.342510i	$-0.888723\pi$
$137$	−20.2164	+	3.20196i	−1.72720	+	0.273562i	−0.787690	+	0.616072i	$0.788723\pi$
$138$		0			0
$139$	7.81703	−	5.67941i	0.663032	−	0.481721i	−0.204653	−	0.978834i	$-0.565607\pi$
$139$	7.81703	−	5.67941i	0.663032	−	0.481721i	0.867686	+	0.497114i	$0.165607\pi$
$140$	−4.82403	+	2.63303i	−0.407705	+	0.222532i
$141$		0			0
$142$	−1.44878	+	6.91978i	−0.121579	+	0.580695i
$143$	10.7526	−	10.7526i	0.899181	−	0.899181i
$144$		0			0
$145$	3.79804	−	3.57616i	0.315410	−	0.296984i
$146$	0.239335	−	4.85002i	0.0198075	−	0.401391i
$147$		0			0
$148$	15.9528	−	6.23570i	1.31131	−	0.512572i
$149$			8.40173i			0.688296i	0.938915	+	0.344148i	$0.111832\pi$
$149$			8.40173i			0.688296i	−0.938915	+	0.344148i	$0.888168\pi$
$150$		0			0
$151$		−	0.959977i		−	0.0781219i	−0.999237	−	0.0390609i	$-0.987563\pi$
$151$		−	0.959977i		−	0.0781219i	0.999237	−	0.0390609i	$-0.0124366\pi$
$152$	10.8173	−	8.01158i	0.877396	−	0.649825i
$153$		0			0
$154$	−7.78523	−	0.384179i	−0.627352	−	0.0309580i
$155$	−4.07750	+	21.5313i	−0.327513	+	1.72944i
$156$		0			0
$157$	8.31117	−	8.31117i	0.663303	−	0.663303i	−0.292854	−	0.956157i	$-0.594605\pi$
$157$	8.31117	−	8.31117i	0.663303	−	0.663303i	0.956157	+	0.292854i	$0.0946049\pi$
$158$	−2.33400	−	0.488665i	−0.185683	−	0.0388761i
$159$		0			0
$160$	12.6402	−	0.474792i	0.999295	−	0.0375356i
$161$	−4.75813	+	3.45698i	−0.374993	+	0.272448i
$162$		0			0
$163$	22.0465	−	3.49183i	1.72682	−	0.273501i	0.787442	−	0.616389i	$-0.211405\pi$
$163$	22.0465	−	3.49183i	1.72682	−	0.273501i	0.939376	+	0.342888i	$0.111405\pi$
$164$	5.11044	+	2.23803i	0.399059	+	0.174761i
$165$		0			0
$166$	−7.66750	+	20.1582i	−0.595113	+	1.56458i
$167$	0.816203	−	1.60189i	0.0631597	−	0.123958i	−0.857268	−	0.514870i	$-0.827840\pi$
$167$	0.816203	−	1.60189i	0.0631597	−	0.123958i	0.920428	+	0.390912i	$0.127840\pi$
$168$		0			0
$169$	1.43087	−	0.464917i	0.110067	−	0.0357628i
$170$	−12.7170	−	14.9152i	−0.975346	−	1.14394i
$171$		0			0
$172$	8.76282	−	13.6756i	0.668158	−	1.04276i
$173$	8.78515	+	1.39143i	0.667923	+	0.105789i	0.481182	−	0.876621i	$-0.340208\pi$
$173$	8.78515	+	1.39143i	0.667923	+	0.105789i	0.186741	+	0.982409i	$0.440208\pi$
$174$		0			0
$175$	−1.32435	+	6.00011i	−0.100111	+	0.453565i
$176$	15.6450	+	8.77970i	1.17929	+	0.661795i
$177$		0			0
$178$	1.69147	−	1.53238i	0.126781	−	0.114857i
$179$	−2.58378	+	7.95205i	−0.193120	+	0.594364i	0.806873	+	0.590725i	$0.201158\pi$
$179$	−2.58378	+	7.95205i	−0.193120	+	0.594364i	−0.999993	+	0.00363866i	$0.998842\pi$
$180$		0			0
$181$	6.98134	+	21.4863i	0.518919	+	1.59707i	0.776037	+	0.630688i	$0.217227\pi$
$181$	6.98134	+	21.4863i	0.518919	+	1.59707i	−0.257118	+	0.966380i	$0.582773\pi$
$182$	5.11200	+	2.93064i	0.378926	+	0.217234i
$183$		0			0
$184$	13.3499	−	2.23992i	0.984164	−	0.165129i
$185$	6.46270	−	18.0264i	0.475147	−	1.32533i
$186$		0			0
$187$	−4.34879	−	27.4572i	−0.318015	−	2.00787i
$188$	−7.36920	+	6.04233i	−0.537454	+	0.440682i
$189$		0			0
$190$	1.19350	−	15.0025i	0.0865854	−	1.08839i
$191$	3.77520	−	5.19612i	0.273164	−	0.375978i	−0.650291	−	0.759686i	$-0.725353\pi$
$191$	3.77520	−	5.19612i	0.273164	−	0.375978i	0.923455	+	0.383707i	$0.125353\pi$
$192$		0			0
$193$	−11.6325	−	11.6325i	−0.837323	−	0.837323i	0.151183	−	0.988506i	$-0.451692\pi$
$193$	−11.6325	−	11.6325i	−0.837323	−	0.837323i	−0.988506	+	0.151183i	$0.951692\pi$
$194$	−14.4917	+	9.47404i	−1.04044	+	0.680196i
$195$		0			0
$196$	2.34831	+	10.7255i	0.167737	+	0.766108i
$197$	0.611842	+	1.20081i	0.0435919	+	0.0855540i	0.911775	−	0.410690i	$-0.134712\pi$
$197$	0.611842	+	1.20081i	0.0435919	+	0.0855540i	−0.868183	+	0.496244i	$0.834712\pi$
$198$		0			0
$199$	−20.5955			−1.45997			−0.729987	−	0.683461i	$-0.760474\pi$
$199$	−20.5955			−1.45997			−0.729987	+	0.683461i	$0.760474\pi$
$200$	8.88498	−	11.0026i	0.628263	−	0.778001i
$201$		0			0
$202$	−1.20297	−	11.1188i	−0.0846403	−	0.782318i
$203$	1.30160	+	2.55453i	0.0913542	+	0.179293i
$204$		0			0
$205$	5.64033	−	2.66335i	0.393938	−	0.186017i
$206$	19.8948	−	13.0064i	1.38614	−	0.906197i
$207$		0			0
$208$	−7.52473	−	11.2830i	−0.521746	−	0.782336i
$209$	12.5463	−	17.2686i	0.867849	−	1.19449i
$210$		0			0
$211$	3.36303	+	4.62882i	0.231521	+	0.318661i	0.908933	−	0.416943i	$-0.136899\pi$
$211$	3.36303	+	4.62882i	0.231521	+	0.318661i	−0.677412	+	0.735604i	$0.736899\pi$
$212$	1.11729	−	0.916113i	0.0767356	−	0.0629189i
$213$		0			0
$214$	−0.949108	+	1.17939i	−0.0648797	+	0.0806218i
$215$	−5.08961	−	17.4315i	−0.347108	−	1.18882i
$216$		0			0
$217$	−10.7309	−	5.46767i	−0.728461	−	0.371170i
$218$	7.03627	+	4.03380i	0.476556	+	0.273204i
$219$		0			0
$220$	18.8924	−	6.73710i	1.27373	−	0.454215i
$221$	−6.49405	+	19.9866i	−0.436837	+	1.34445i
$222$		0			0
$223$	0.323229	−	2.04079i	0.0216450	−	0.136661i	−0.974499	−	0.224390i	$-0.927961\pi$
$223$	0.323229	−	2.04079i	0.0216450	−	0.136661i	0.996144	+	0.0877290i	$0.0279609\pi$
$224$	−1.69654	+	6.74154i	−0.113355	+	0.450438i
$225$		0			0
$226$	−25.0026	+	6.78130i	−1.66315	+	0.451086i
$227$	21.4739	+	3.40114i	1.42528	+	0.225741i	0.820952	−	0.570998i	$-0.193443\pi$
$227$	21.4739	+	3.40114i	1.42528	+	0.225741i	0.604323	+	0.796739i	$0.293443\pi$
$228$		0			0
$229$	−9.11712	−	2.96233i	−0.602476	−	0.195756i	−0.00813172	−	0.999967i	$-0.502588\pi$
$229$	−9.11712	−	2.96233i	−0.602476	−	0.195756i	−0.594345	+	0.804211i	$0.702588\pi$
$230$	7.91853	−	12.8974i	0.522132	−	0.850426i
$231$		0			0
$232$	−0.0604311	−	6.59839i	−0.00396749	−	0.433206i
$233$	−3.34038	+	6.55586i	−0.218835	+	0.429488i	−0.974159	−	0.225864i	$-0.927480\pi$
$233$	−3.34038	+	6.55586i	−0.218835	+	0.429488i	0.755324	+	0.655352i	$0.227480\pi$
$234$		0			0
$235$	−0.320430	+	10.6497i	−0.0209025	+	0.694709i
$236$	0.692450	+	0.303246i	0.0450746	+	0.0197397i
$237$		0			0
$238$	9.82743	−	4.41145i	0.637018	−	0.285952i
$239$	−9.18160	+	6.67082i	−0.593908	+	0.431500i	−0.843711	−	0.536797i	$-0.819634\pi$
$239$	−9.18160	+	6.67082i	−0.593908	+	0.431500i	0.249803	+	0.968297i	$0.419634\pi$
$240$		0			0
$241$	−4.36910	−	3.17434i	−0.281438	−	0.204477i	0.438106	−	0.898923i	$-0.355649\pi$
$241$	−4.36910	−	3.17434i	−0.281438	−	0.204477i	−0.719545	+	0.694446i	$0.755649\pi$
$242$	12.6178	+	2.64176i	0.811102	+	0.169819i
$243$		0			0
$244$	−4.41481	+	4.96375i	−0.282629	+	0.317772i
$245$	10.7650	+	5.89941i	0.687753	+	0.376899i
$246$		0			0
$247$	−14.3773	+	7.32560i	−0.914805	+	0.466117i
$248$	16.4977	+	22.2752i	1.04760	+	1.41448i
$249$		0			0
$250$	−2.74689	−	15.5710i	−0.173729	−	0.984794i
$251$		−	12.4891i		−	0.788307i	−0.919045	−	0.394153i	$-0.871038\pi$
$251$		−	12.4891i		−	0.788307i	0.919045	−	0.394153i	$-0.128962\pi$
$252$		0			0
$253$	19.1253	−	9.74480i	1.20239	−	0.612651i
$254$	0.162241	−	3.28775i	0.0101799	−	0.206292i
$255$		0			0
$256$	10.4125	−	12.1482i	0.650784	−	0.759263i
$257$	−12.3554	+	12.3554i	−0.770711	+	0.770711i	−0.978231	−	0.207520i	$-0.933461\pi$
$257$	−12.3554	+	12.3554i	−0.770711	+	0.770711i	0.207520	+	0.978231i	$0.433461\pi$
$258$		0			0
$259$	8.51446	+	6.18612i	0.529063	+	0.384387i
$260$	−15.0374	−	1.94597i	−0.932579	−	0.120684i
$261$		0			0
$262$	13.0197	+	29.0041i	0.804361	+	1.79188i
$263$	6.03239	−	0.955437i	0.371973	−	0.0589148i	0.0323506	−	0.999477i	$-0.489701\pi$
$263$	6.03239	−	0.955437i	0.371973	−	0.0589148i	0.339623	+	0.940562i	$0.389701\pi$
$264$		0			0
$265$	0.0485822	−	1.61466i	0.00298438	−	0.0991879i
$266$	7.73079	+	2.94053i	0.474005	+	0.180295i
$267$		0			0
$268$	−3.36311	+	12.8650i	−0.205435	+	0.785854i
$269$	15.3432	−	4.98530i	0.935490	−	0.303959i	0.198684	−	0.980064i	$-0.436333\pi$
$269$	15.3432	−	4.98530i	0.935490	−	0.303959i	0.736806	+	0.676105i	$0.236333\pi$
$270$		0			0
$271$	−13.5467	−	4.40159i	−0.822904	−	0.267378i	−0.132850	−	0.991136i	$-0.542413\pi$
$271$	−13.5467	−	4.40159i	−0.822904	−	0.267378i	−0.690053	+	0.723758i	$0.742413\pi$
$272$	−24.7730	−	0.995146i	−1.50209	−	0.0603396i
$273$		0			0
$274$	7.57728	+	27.9374i	0.457760	+	1.68776i
$275$	8.19949	−	20.8724i	0.494448	−	1.25865i
$276$		0			0
$277$	−2.25919	+	14.2640i	−0.135742	+	0.857040i	0.822016	+	0.569464i	$0.192849\pi$
$277$	−2.25919	+	14.2640i	−0.135742	+	0.857040i	−0.957758	+	0.287576i	$0.907151\pi$
$278$	−9.17441	−	10.1269i	−0.550244	−	0.607369i
$279$		0			0
$280$	4.43589	+	6.38210i	0.265095	+	0.381403i
$281$	0.729043	+	2.24376i	0.0434911	+	0.133852i	0.970444	−	0.241325i	$-0.0775820\pi$
$281$	0.729043	+	2.24376i	0.0434911	+	0.133852i	−0.926953	+	0.375177i	$0.877582\pi$
$282$		0			0
$283$	−12.0621	−	6.14594i	−0.717016	−	0.365338i	0.0571112	−	0.998368i	$-0.481811\pi$
$283$	−12.0621	−	6.14594i	−0.717016	−	0.365338i	−0.774127	+	0.633030i	$0.781811\pi$
$284$	9.94966	+	0.984372i	0.590404	+	0.0584117i
$285$		0			0
$286$	−16.7540	−	13.4826i	−0.990683	−	0.797245i
$287$	0.536263	+	3.38583i	0.0316546	+	0.199859i
$288$		0			0
$289$	12.5894	+	17.3278i	0.740553	+	1.01928i
$290$	−5.60587	−	4.79607i	−0.329188	−	0.281635i
$291$		0			0
$292$	−6.85558	+	0.401271i	−0.401192	+	0.0234826i
$293$	−13.5220	−	13.5220i	−0.789964	−	0.789964i	0.191524	−	0.981488i	$-0.438657\pi$
$293$	−13.5220	−	13.5220i	−0.789964	−	0.789964i	−0.981488	+	0.191524i	$0.938657\pi$
$294$		0			0
$295$	0.764247	−	0.360876i	0.0444962	−	0.0210110i
$296$	−11.1942	−	21.4811i	−0.650647	−	1.24857i
$297$		0			0
$298$	11.8129	−	1.27806i	0.684303	−	0.0740359i
$299$	−16.2265			−0.938401
$300$		0			0
$301$	9.98007			0.575242
$302$	−1.34974	+	0.146030i	−0.0776686	+	0.00840310i
$303$		0			0
$304$	−12.9099	−	13.9905i	−0.740431	−	0.802407i
$305$	0.940711	+	7.36728i	0.0538650	+	0.421849i
$306$		0			0
$307$	11.3516	+	11.3516i	0.647873	+	0.647873i	0.952479	−	0.304606i	$-0.0985247\pi$
$307$	11.3516	+	11.3516i	0.647873	+	0.647873i	−0.304606	+	0.952479i	$0.598525\pi$
$308$	0.644118	+	11.0045i	0.0367020	+	0.627042i
$309$		0			0
$310$	30.8935	+	2.45768i	1.75463	+	0.139587i
$311$	7.06216	+	9.72023i	0.400458	+	0.551183i	0.960859	−	0.277038i	$-0.0893528\pi$
$311$	7.06216	+	9.72023i	0.400458	+	0.551183i	−0.560401	+	0.828222i	$0.689353\pi$
$312$		0			0
$313$	0.0322523	+	0.203633i	0.00182301	+	0.0115100i	0.988583	−	0.150677i	$-0.0481453\pi$
$313$	0.0322523	+	0.203633i	0.00182301	+	0.0115100i	−0.986760	+	0.162187i	$0.948145\pi$
$314$	−12.9499	−	10.4213i	−0.730803	−	0.588108i
$315$		0			0
$316$	−0.332023	+	3.35596i	−0.0186777	+	0.188787i
$317$	0.800165	+	0.407705i	0.0449418	+	0.0228990i	0.476317	−	0.879274i	$-0.341971\pi$
$317$	0.800165	+	0.407705i	0.0449418	+	0.0228990i	−0.431375	+	0.902173i	$0.641971\pi$
$318$		0			0
$319$	−3.23340	−	9.95139i	−0.181036	−	0.557171i
$320$	−2.59037	−	17.7000i	−0.144806	−	0.989460i
$321$		0			0
$322$	5.58435	+	6.16410i	0.311203	+	0.343512i
$323$	−4.61460	+	29.1354i	−0.256763	+	1.62114i
$324$		0			0
$325$	−12.6862	+	11.2449i	−0.703706	+	0.623752i
$326$	−8.26323	−	30.4665i	−0.457658	−	1.68738i
$327$		0			0
$328$	2.36930	−	7.52577i	0.130823	−	0.415541i
$329$	−5.56895	−	1.80946i	−0.307026	−	0.0997588i
$330$		0			0
$331$	−8.52303	+	2.76930i	−0.468468	+	0.152214i	−0.533732	−	0.845654i	$-0.679211\pi$
$331$	−8.52303	+	2.76930i	−0.468468	+	0.152214i	0.0652642	+	0.997868i	$0.479211\pi$
$332$	29.5090	+	7.71413i	1.61952	+	0.423368i
$333$		0			0
$334$	−2.37643	−	0.903912i	−0.130032	−	0.0494599i
$335$	8.37284	+	12.2849i	0.457457	+	0.671195i
$336$		0			0
$337$	−7.67391	+	1.21543i	−0.418024	+	0.0662085i	−0.361904	−	0.932215i	$-0.617873\pi$
$337$	−7.67391	+	1.21543i	−0.418024	+	0.0662085i	−0.0561205	+	0.998424i	$0.517873\pi$
$338$	−0.871339	−	1.94109i	−0.0473946	−	0.105581i
$339$		0			0
$340$	−19.0364	+	20.1490i	−1.03239	+	1.09273i
$341$	35.5599	+	25.8358i	1.92568	+	1.39909i
$342$		0			0
$343$	−10.8532	+	10.8532i	−0.586019	+	0.586019i
$344$	−20.5610	−	10.2403i	−1.10858	−	0.552119i
$345$		0			0
$346$	0.619981	−	12.5637i	0.0333304	−	0.675427i
$347$	19.3079	−	9.83786i	1.03650	−	0.528124i	0.148956	−	0.988844i	$-0.452409\pi$
$347$	19.3079	−	9.83786i	1.03650	−	0.528124i	0.887546	+	0.460720i	$0.152409\pi$
$348$		0			0
$349$			23.0418i			1.23340i	0.787198	+	0.616701i	$0.211531\pi$
$349$			23.0418i			1.23340i	−0.787198	+	0.616701i	$0.788469\pi$
$350$	8.63766	+	0.949319i	0.461702	+	0.0507432i
$351$		0			0
$352$	9.96444	−	23.3326i	0.531106	−	1.24363i
$353$	13.7543	−	7.00816i	0.732066	−	0.373006i	−0.0478797	−	0.998853i	$-0.515246\pi$
$353$	13.7543	−	7.00816i	0.732066	−	0.373006i	0.779946	+	0.625847i	$0.215246\pi$
$354$		0			0
$355$	8.13844	−	7.66301i	0.431944	−	0.406710i
$356$	−2.41184	−	2.14511i	−0.127827	−	0.113691i
$357$		0			0
$358$	11.5737	+	2.42316i	0.611688	+	0.128068i
$359$	18.1516	+	13.1879i	0.958007	+	0.696033i	0.952687	−	0.303953i	$-0.0983065\pi$
$359$	18.1516	+	13.1879i	0.958007	+	0.696033i	0.00532016	+	0.999986i	$0.498307\pi$
$360$		0			0
$361$	−2.95276	+	2.14531i	−0.155409	+	0.112911i
$362$	29.1480	−	13.0843i	1.53198	−	0.687695i
$363$		0			0
$364$	3.34288	−	7.63332i	0.175214	−	0.400094i
$365$	−4.69772	+	6.07301i	−0.245890	+	0.317876i
$366$		0			0
$367$	−7.37062	+	14.4657i	−0.384743	+	0.755101i	−0.999433	−	0.0336676i	$-0.989281\pi$
$367$	−7.37062	+	14.4657i	−0.384743	+	0.755101i	0.614690	+	0.788769i	$0.289281\pi$
$368$	−5.18011	−	18.4293i	−0.270032	−	0.960692i
$369$		0			0
$370$	−26.3284	−	6.34446i	−1.36875	−	0.329833i
$371$	0.844341	+	0.274343i	0.0438360	+	0.0142432i
$372$		0			0
$373$	8.67472	+	1.37394i	0.449160	+	0.0711400i	0.376917	−	0.926247i	$-0.376984\pi$
$373$	8.67472	+	1.37394i	0.449160	+	0.0711400i	0.0722432	+	0.997387i	$0.476984\pi$
$374$	−37.9435	+	10.2912i	−1.96201	+	0.532144i
$375$		0			0
$376$	9.61656	+	9.44201i	0.495936	+	0.486935i
$377$	−1.23739	+	7.81259i	−0.0637290	+	0.402369i
$378$		0			0
$379$	4.77015	−	14.6810i	0.245026	−	0.754112i	−0.750606	−	0.660750i	$-0.770238\pi$
$379$	4.77015	−	14.6810i	0.245026	−	0.754112i	0.995632	−	0.0933626i	$-0.0297616\pi$
$380$	−21.2751	+	0.604084i	−1.09139	+	0.0309888i
$381$		0			0
$382$	−7.88007	−	4.51754i	−0.403180	−	0.231138i
$383$	19.5086	+	9.94011i	0.996841	+	0.507916i	0.874735	−	0.484601i	$-0.161035\pi$
$383$	19.5086	+	9.94011i	0.996841	+	0.507916i	0.122106	+	0.992517i	$0.461035\pi$
$384$		0			0
$385$	9.74836	+	7.54075i	0.496822	+	0.384312i
$386$	−14.5858	+	18.1249i	−0.742399	+	0.922531i
$387$		0			0
$388$	15.5250	+	18.9343i	0.788164	+	0.961242i
$389$	−19.3223	−	26.5948i	−0.979678	−	1.34841i	−0.937002	−	0.349323i	$-0.886412\pi$
$389$	−19.3223	−	26.5948i	−0.979678	−	1.34841i	−0.0426759	−	0.999089i	$-0.513588\pi$
$390$		0			0
$391$	−17.4361	+	23.9987i	−0.881779	+	1.21367i
$392$	14.7229	−	4.93330i	0.743621	−	0.249169i
$393$		0			0
$394$	1.59527	−	1.04292i	0.0803687	−	0.0525415i
$395$	2.58468	+	2.74505i	0.130050	+	0.138118i
$396$		0			0
$397$	−4.68709	−	9.19893i	−0.235238	−	0.461681i	0.742965	−	0.669330i	$-0.233419\pi$
$397$	−4.68709	−	9.19893i	−0.235238	−	0.461681i	−0.978203	+	0.207649i	$0.933419\pi$
$398$	3.13295	+	28.9574i	0.157041	+	1.45150i
$399$		0			0
$400$	−16.8213	−	10.8187i	−0.841066	−	0.540933i
$401$	−19.3269			−0.965137			−0.482569	−	0.875858i	$-0.660296\pi$
$401$	−19.3269			−0.965137			−0.482569	+	0.875858i	$0.660296\pi$
$402$		0			0
$403$	−15.0851	−	29.6061i	−0.751442	−	1.47479i
$404$	−15.4502	+	3.38276i	−0.768675	+	0.168299i
$405$		0			0
$406$	3.39369	−	2.21865i	0.168426	−	0.110110i
$407$	−27.1602	−	27.1602i	−1.34628	−	1.34628i
$408$		0			0
$409$	20.5429	−	28.2749i	1.01578	−	1.39810i	0.100661	−	0.994921i	$-0.467904\pi$
$409$	20.5429	−	28.2749i	1.01578	−	1.39810i	0.915120	−	0.403182i	$-0.132096\pi$
$410$	−4.60269	−	7.52520i	−0.227311	−	0.371643i
$411$		0			0
$412$	−21.3135	−	25.9938i	−1.05004	−	1.28062i
$413$	0.0726621	+	0.458770i	0.00357547	+	0.0225746i
$414$		0			0
$415$	28.1784	−	19.2052i	1.38322	−	0.942744i
$416$	−14.7194	+	12.2962i	−0.721676	+	0.602870i
$417$		0			0
$418$	−26.1883	−	15.0134i	−1.28091	−	0.734329i
$419$	−5.52699	−	17.0103i	−0.270011	−	0.831010i	−0.990496	−	0.137539i	$-0.956081\pi$
$419$	−5.52699	−	17.0103i	−0.270011	−	0.831010i	0.720485	−	0.693471i	$-0.243919\pi$
$420$		0			0
$421$	−11.1963	+	34.4588i	−0.545676	+	1.67942i	0.173703	+	0.984798i	$0.444427\pi$
$421$	−11.1963	+	34.4588i	−0.545676	+	1.67942i	−0.719378	+	0.694619i	$0.755573\pi$
$422$	5.99658	−	5.43258i	0.291909	−	0.264454i
$423$		0			0
$424$	−1.45802	−	1.43156i	−0.0708078	−	0.0695226i
$425$	2.99902	+	30.8458i	0.145474	+	1.49624i
$426$		0			0
$427$	−4.03155	−	0.638535i	−0.195100	−	0.0309009i
$428$	1.80262	+	1.15505i	0.0871327	+	0.0558313i
$429$		0			0
$430$	−23.7347	+	9.80769i	−1.14459	+	0.472969i
$431$	−32.9891	+	10.7188i	−1.58903	+	0.516307i	−0.964362	−	0.264586i	$-0.914765\pi$
$431$	−32.9891	+	10.7188i	−1.58903	+	0.516307i	−0.624666	+	0.780892i	$0.714765\pi$
$432$		0			0
$433$	−0.342596	+	0.672382i	−0.0164641	+	0.0323126i	−0.899092	−	0.437760i	$-0.855772\pi$
$433$	−0.342596	+	0.672382i	−0.0164641	+	0.0323126i	0.882628	+	0.470072i	$0.155772\pi$
$434$	−6.05522	+	15.9195i	−0.290660	+	0.764159i
$435$		0			0
$436$	4.60121	−	10.5067i	0.220358	−	0.503178i
$437$	−22.4964	+	3.56308i	−1.07615	+	0.170445i
$438$		0			0
$439$	−6.65831	+	4.83755i	−0.317784	+	0.230883i	−0.735229	−	0.677819i	$-0.762925\pi$
$439$	−6.65831	+	4.83755i	−0.317784	+	0.230883i	0.417445	+	0.908702i	$0.362925\pi$
$440$	−12.3463	−	25.5380i	−0.588587	−	1.21748i
$441$		0			0
$442$	29.0892	+	6.09035i	1.38363	+	0.289689i
$443$	−5.05289	+	5.05289i	−0.240070	+	0.240070i	−0.816879	−	0.576809i	$-0.804298\pi$
$443$	−5.05289	+	5.05289i	−0.240070	+	0.240070i	0.576809	+	0.816879i	$0.304298\pi$
$444$		0			0
$445$	−3.57969	+	0.457083i	−0.169694	+	0.0216678i
$446$	−2.91854	−	0.144021i	−0.138197	−	0.00681961i
$447$		0			0
$448$	9.73674	+	1.35984i	0.460018	+	0.0642464i
$449$			3.96534i			0.187136i	0.995613	+	0.0935679i	$0.0298272\pi$
$449$			3.96534i			0.187136i	−0.995613	+	0.0935679i	$0.970173\pi$
$450$		0			0
$451$		−	12.5110i		−	0.589122i
$452$	13.3379	+	34.1223i	0.627363	+	1.60498i
$453$		0			0
$454$	1.51545	−	30.7099i	0.0711234	−	1.44129i
$455$	−3.97817	−	8.42479i	−0.186500	−	0.394960i
$456$		0			0
$457$	−28.6276	+	28.6276i	−1.33914	+	1.33914i	−0.442252	+	0.896891i	$0.645820\pi$
$457$	−28.6276	+	28.6276i	−1.33914	+	1.33914i	−0.896891	+	0.442252i	$0.854180\pi$
$458$	−2.77818	+	13.2694i	−0.129816	+	0.620037i
$459$		0			0
$460$	−19.3383	−	9.17160i	−0.901655	−	0.427628i
$461$	−19.5894	+	14.2325i	−0.912367	+	0.662874i	−0.941613	−	0.336699i	$-0.890690\pi$
$461$	−19.5894	+	14.2325i	−0.912367	+	0.662874i	0.0292451	+	0.999572i	$0.490690\pi$
$462$		0			0
$463$	−2.56198	+	0.405779i	−0.119066	+	0.0188581i	−0.215683	−	0.976463i	$-0.569198\pi$
$463$	−2.56198	+	0.405779i	−0.119066	+	0.0188581i	0.0966173	+	0.995322i	$0.469198\pi$
$464$	−9.26820	+	1.08870i	−0.430266	+	0.0505418i
$465$		0			0
$466$	9.72572	+	3.69933i	0.450535	+	0.171368i
$467$	−15.4035	+	30.2311i	−0.712789	+	1.39893i	0.195550	+	0.980694i	$0.437351\pi$
$467$	−15.4035	+	30.2311i	−0.712789	+	1.39893i	−0.908339	+	0.418234i	$0.862649\pi$
$468$		0			0
$469$	−7.77067	+	2.52484i	−0.358816	+	0.116586i
$470$	15.0223	−	1.16949i	0.692927	−	0.0539444i
$471$		0			0
$472$	0.321033	−	1.01972i	0.0147767	−	0.0469364i
$473$	−35.9751	−	5.69789i	−1.65414	−	0.261989i
$474$		0			0
$475$	−15.1190	+	18.3756i	−0.693708	+	0.843128i
$476$	−7.69747	−	13.1464i	−0.352813	−	0.602564i
$477$		0			0
$478$	10.7759	+	11.8947i	0.492879	+	0.544049i
$479$	9.51698	−	29.2903i	0.434842	−	1.33831i	−0.458406	−	0.888743i	$-0.651579\pi$
$479$	9.51698	−	29.2903i	0.434842	−	1.33831i	0.893248	−	0.449564i	$-0.148421\pi$
$480$		0			0
$481$	8.97279	+	27.6154i	0.409124	+	1.25915i
$482$	−3.79852	+	6.62587i	−0.173018	+	0.301800i
$483$		0			0
$484$	1.79494	−	18.1426i	0.0815881	−	0.824662i
$485$	27.3631	+	0.823305i	1.24249	+	0.0373843i
$486$		0			0
$487$	−4.00267	−	25.2719i	−0.181378	−	1.14518i	−0.895469	−	0.445124i	$-0.853159\pi$
$487$	−4.00267	−	25.2719i	−0.181378	−	1.14518i	0.714090	−	0.700053i	$-0.246841\pi$
$488$	7.65065	+	5.45218i	0.346329	+	0.246809i
$489$		0			0
$490$	6.65705	−	16.0331i	0.300735	−	0.724304i
$491$	21.3712	−	29.4149i	0.964467	−	1.32748i	0.0196748	−	0.999806i	$-0.493737\pi$
$491$	21.3712	−	29.4149i	0.964467	−	1.32748i	0.944793	−	0.327669i	$-0.106263\pi$
$492$		0			0
$493$	10.2251	+	10.2251i	0.460513	+	0.460513i
$494$	12.4869	+	19.1002i	0.561812	+	0.859360i
$495$		0			0
$496$	28.8096	−	26.5844i	1.29359	−	1.19367i
$497$	2.78906	+	5.47385i	0.125107	+	0.245536i
$498$		0			0
$499$	21.4166			0.958738			0.479369	−	0.877613i	$-0.340866\pi$
$499$	21.4166			0.958738			0.479369	+	0.877613i	$0.340866\pi$
$500$	−21.4750	+	6.23079i	−0.960393	+	0.278649i
$501$		0			0
$502$	−17.5598	+	1.89983i	−0.783733	+	0.0847934i
$503$	−2.54246	−	4.98985i	−0.113362	−	0.222486i	0.827354	−	0.561681i	$-0.189845\pi$
$503$	−2.54246	−	4.98985i	−0.113362	−	0.222486i	−0.940716	+	0.339195i	$0.889845\pi$
$504$		0			0
$505$	−8.49813	+	15.5071i	−0.378162	+	0.690058i
$506$	−16.6106	−	25.4079i	−0.738430	−	1.12952i
$507$		0			0
$508$	−4.64729	+	0.272015i	−0.206190	+	0.0120687i
$509$	14.8244	−	20.4041i	0.657082	−	0.904395i	−0.342299	−	0.939591i	$-0.611205\pi$
$509$	14.8244	−	20.4041i	0.657082	−	0.904395i	0.999380	+	0.0351958i	$0.0112055\pi$
$510$		0			0
$511$	−2.48024	−	3.41376i	−0.109719	−	0.151016i
$512$	−18.6644	−	12.7922i	−0.824859	−	0.565339i
$513$		0			0
$514$	19.2513	+	15.4924i	0.849140	+	0.683339i
$515$	−37.5653	−	1.13027i	−1.65532	−	0.0498056i
$516$		0			0
$517$	19.0413	+	9.70200i	0.837433	+	0.426694i
$518$	7.40253	−	12.9124i	0.325248	−	0.567339i
$519$		0			0
$520$	−0.448582	+	21.4387i	−0.0196716	+	0.940150i
$521$	−10.5745	+	32.5450i	−0.463278	+	1.42582i	0.397858	+	0.917447i	$0.369754\pi$
$521$	−10.5745	+	32.5450i	−0.463278	+	1.42582i	−0.861136	+	0.508375i	$0.830246\pi$
$522$		0			0
$523$	−2.99899	+	18.9349i	−0.131137	+	0.827966i	0.831174	+	0.556013i	$0.187669\pi$
$523$	−2.99899	+	18.9349i	−0.131137	+	0.827966i	−0.962311	+	0.271953i	$0.912331\pi$
$524$	38.7995	−	22.7179i	1.69497	−	0.992436i
$525$		0			0
$526$	−2.26099	−	8.33625i	−0.0985839	−	0.363478i
$527$	−59.9966	−	9.50252i	−2.61349	−	0.413936i
$528$		0			0
$529$	0.0908487	+	0.0295185i	0.00394994	+	0.00128341i
$530$	−2.27762	+	0.177313i	−0.0989334	+	0.00770198i
$531$		0			0
$532$	2.95841	−	11.3169i	0.128263	−	0.490648i
$533$	−4.29376	+	8.42699i	−0.185984	+	0.365013i
$534$		0			0
$535$	2.29769	−	0.670873i	0.0993378	−	0.0290044i
$536$	18.5999	+	2.77156i	0.803392	+	0.119713i
$537$		0			0
$538$	−9.34335	−	20.8143i	−0.402820	−	0.897367i
$539$	19.9196	−	14.4724i	0.857996	−	0.623371i
$540$		0			0
$541$	−29.5454	−	21.4660i	−1.27026	−	0.922895i	−0.271043	−	0.962567i	$-0.587369\pi$
$541$	−29.5454	−	21.4660i	−1.27026	−	0.922895i	−0.999213	+	0.0396722i	$0.987369\pi$
$542$	−4.12797	+	19.7164i	−0.177312	+	0.846890i
$543$		0			0
$544$	2.36925	+	34.9825i	0.101581	+	1.49986i
$545$	−5.47564	−	11.5961i	−0.234551	−	0.496721i
$546$		0			0
$547$	−3.73686	+	1.90403i	−0.159777	+	0.0814103i	−0.532050	−	0.846713i	$-0.678578\pi$
$547$	−3.73686	+	1.90403i	−0.159777	+	0.0814103i	0.372274	+	0.928123i	$0.378578\pi$
$548$	38.1275	−	14.9035i	1.62873	−	0.636646i
$549$		0			0
$550$	−30.5941	−	8.35347i	−1.30454	−	0.356193i
$551$			11.1031i			0.473007i
$552$		0			0
$553$	−1.84629	+	0.940734i	−0.0785124	+	0.0400041i
$554$	20.3990	+	1.00663i	0.866668	+	0.0427676i
$555$		0			0
$556$	−12.8429	+	14.4398i	−0.544659	+	0.612383i
$557$	9.53036	−	9.53036i	0.403814	−	0.403814i	−0.475761	−	0.879575i	$-0.657827\pi$
$557$	9.53036	−	9.53036i	0.403814	−	0.403814i	0.879575	+	0.475761i	$0.157827\pi$
$558$		0			0
$559$	22.2760	+	16.1845i	0.942174	+	0.684529i
$560$	8.29850	−	7.20774i	0.350676	−	0.304582i
$561$		0			0
$562$	3.04385	−	1.36636i	0.128397	−	0.0576364i
$563$	7.44681	−	1.17946i	0.313846	−	0.0497083i	0.00247542	−	0.999997i	$-0.499212\pi$
$563$	7.44681	−	1.17946i	0.313846	−	0.0497083i	0.311370	+	0.950289i	$0.399212\pi$
$564$		0			0
$565$	38.5578	+	13.8235i	1.62214	+	0.581557i
$566$	−6.80638	+	17.8943i	−0.286093	+	0.752153i
$567$		0			0
$568$	−0.129492	−	14.1391i	−0.00543336	−	0.593261i
$569$	−19.9781	+	6.49127i	−0.837524	+	0.272128i	−0.696211	−	0.717837i	$-0.745132\pi$
$569$	−19.9781	+	6.49127i	−0.837524	+	0.272128i	−0.141313	+	0.989965i	$0.545132\pi$
$570$		0			0
$571$	−16.6846	−	5.42116i	−0.698230	−	0.226869i	−0.0616706	−	0.998097i	$-0.519643\pi$
$571$	−16.6846	−	5.42116i	−0.698230	−	0.226869i	−0.636559	+	0.771228i	$0.719643\pi$
$572$	−16.4081	+	25.6072i	−0.686057	+	1.07069i
$573$		0			0
$574$	4.67894	−	1.26904i	0.195295	−	0.0529687i
$575$	−21.9357	+	9.56216i	−0.914784	+	0.398770i
$576$		0			0
$577$	0.710623	−	4.48670i	0.0295836	−	0.186784i	−0.968471	−	0.249125i	$-0.919857\pi$
$577$	0.710623	−	4.48670i	0.0295836	−	0.186784i	0.998055	+	0.0623417i	$0.0198569\pi$
$578$	22.4480	−	20.3367i	0.933713	−	0.845894i
$579$		0			0
$580$	−5.89057	+	8.61147i	−0.244592	+	0.357572i
$581$	5.79135	+	17.8239i	0.240266	+	0.739462i
$582$		0			0
$583$	−2.88696	−	1.47098i	−0.119566	−	0.0609217i
$584$	1.60705	+	9.57796i	0.0665002	+	0.396339i
$585$		0			0
$586$	−16.9551	+	21.0690i	−0.700409	+	0.870352i
$587$	0.853147	+	5.38656i	0.0352131	+	0.222327i	0.999019	−	0.0442770i	$-0.0140984\pi$
$587$	0.853147	+	5.38656i	0.0352131	+	0.222327i	−0.963806	+	0.266604i	$0.914098\pi$
$588$		0			0
$589$	−27.4150	−	37.7335i	−1.12962	−	1.55478i
$590$	−0.623651	−	1.01964i	−0.0256753	−	0.0419780i
$591$		0			0
$592$	−28.4998	+	19.0068i	−1.17134	+	0.781173i
$593$	−10.2013	−	10.2013i	−0.418916	−	0.418916i	0.465914	−	0.884830i	$-0.345726\pi$
$593$	−10.2013	−	10.2013i	−0.418916	−	0.418916i	−0.884830	+	0.465914i	$0.845726\pi$
$594$		0			0
$595$	−16.7348	−	3.16916i	−0.686062	−	0.129923i
$596$	−3.59392	−	16.4146i	−0.147213	−	0.672369i
$597$		0			0
$598$	2.46835	+	22.8146i	0.100938	+	0.932957i
$599$	16.3953			0.669893			0.334947	−	0.942237i	$-0.391282\pi$
$599$	16.3953			0.669893			0.334947	+	0.942237i	$0.391282\pi$
$600$		0			0
$601$	−12.3492			−0.503736			−0.251868	−	0.967762i	$-0.581045\pi$
$601$	−12.3492			−0.503736			−0.251868	+	0.967762i	$0.581045\pi$
$602$	−1.51815	−	14.0321i	−0.0618753	−	0.571904i
$603$		0			0
$604$	0.410640	+	1.87553i	0.0167087	+	0.0763141i
$605$	−13.9730	−	14.8399i	−0.568083	−	0.603329i
$606$		0			0
$607$	29.6207	+	29.6207i	1.20227	+	1.20227i	0.973476	+	0.228791i	$0.0734771\pi$
$607$	29.6207	+	29.6207i	1.20227	+	1.20227i	0.228791	+	0.973476i	$0.426523\pi$
$608$	−17.7069	+	20.2796i	−0.718108	+	0.822445i
$609$		0			0
$610$	10.2154	−	2.44335i	0.413608	−	0.0989282i
$611$	−9.49579	−	13.0698i	−0.384159	−	0.528749i
$612$		0			0
$613$	−0.513499	−	3.24210i	−0.0207400	−	0.130947i	0.975146	−	0.221564i	$-0.0711162\pi$
$613$	−0.513499	−	3.24210i	−0.0207400	−	0.130947i	−0.995886	+	0.0906167i	$0.971116\pi$
$614$	14.2337	−	17.6873i	0.574426	−	0.713802i
$615$		0			0
$616$	15.3745	−	2.57963i	0.619456	−	0.103936i
$617$	−18.7804	−	9.56911i	−0.756072	−	0.385238i	0.0330668	−	0.999453i	$-0.489473\pi$
$617$	−18.7804	−	9.56911i	−0.756072	−	0.385238i	−0.789138	+	0.614215i	$0.789473\pi$
$618$		0			0
$619$	6.78934	+	20.8954i	0.272887	+	0.839859i	0.989771	+	0.142667i	$0.0455677\pi$
$619$	6.78934	+	20.8954i	0.272887	+	0.839859i	−0.716884	+	0.697192i	$0.754432\pi$
$620$	−1.24395	−	43.8104i	−0.0499581	−	1.75947i
$621$		0			0
$622$	12.5924	−	11.4081i	0.504911	−	0.457422i
$623$	0.310258	−	1.95889i	0.0124302	−	0.0784813i
$624$		0			0
$625$	−10.5234	+	22.6773i	−0.420935	+	0.907091i
$626$	0.281404	−	0.0763234i	0.0112472	−	0.00305050i
$627$		0			0
$628$	−12.6825	+	19.7929i	−0.506087	+	0.789822i
$629$	50.4844	+	16.4034i	2.01294	+	0.654045i
$630$		0			0
$631$	41.0489	−	13.3376i	1.63413	−	0.530962i	0.658916	−	0.752217i	$-0.271015\pi$
$631$	41.0489	−	13.3376i	1.63413	−	0.530962i	0.975216	+	0.221255i	$0.0710153\pi$
$632$	4.76901	−	0.0436768i	0.189701	−	0.00173737i
$633$		0			0
$634$	0.451516	−	1.18706i	0.0179320	−	0.0471441i
$635$	−3.18451	+	4.11680i	−0.126373	+	0.163370i
$636$		0			0
$637$	−18.3840	+	2.91174i	−0.728400	+	0.115367i
$638$	−13.4999	+	6.05998i	−0.534466	+	0.239917i
$639$		0			0
$640$	−24.4923	+	6.33458i	−0.968143	+	0.250396i
$641$	−23.0054	−	16.7144i	−0.908660	−	0.660180i	0.0320157	−	0.999487i	$-0.489807\pi$
$641$	−23.0054	−	16.7144i	−0.908660	−	0.660180i	−0.940676	+	0.339307i	$0.889807\pi$
$642$		0			0
$643$	31.2213	−	31.2213i	1.23125	−	1.23125i	0.267763	−	0.963485i	$-0.413716\pi$
$643$	31.2213	−	31.2213i	1.23125	−	1.23125i	0.963485	−	0.267763i	$-0.0862843\pi$
$644$	7.81729	−	8.78931i	0.308044	−	0.346347i
$645$		0			0
$646$	41.6667	+	2.05613i	1.63935	+	0.0808974i
$647$	32.1671	−	16.3899i	1.26462	−	0.644355i	0.312452	−	0.949934i	$-0.398850\pi$
$647$	32.1671	−	16.3899i	1.26462	−	0.644355i	0.952167	+	0.305578i	$0.0988498\pi$
$648$		0			0
$649$		−	1.69521i		−	0.0665428i
$650$	17.7402	+	16.1264i	0.695827	+	0.632530i
$651$		0			0
$652$	−41.5791	+	16.2527i	−1.62836	+	0.636504i
$653$	34.2761	−	17.4646i	1.34133	−	0.683441i	0.371775	−	0.928323i	$-0.378749\pi$
$653$	34.2761	−	17.4646i	1.34133	−	0.683441i	0.969553	+	0.244882i	$0.0787492\pi$
$654$		0			0
$655$	9.35329	−	49.3903i	0.365463	−	1.92984i
$656$	−10.9417	−	2.18644i	−0.427202	−	0.0853662i
$657$		0			0
$658$	−1.69698	+	8.10524i	−0.0661551	+	0.315975i
$659$	9.74331	+	7.07893i	0.379545	+	0.275756i	0.761158	−	0.648566i	$-0.224631\pi$
$659$	9.74331	+	7.07893i	0.379545	+	0.275756i	−0.381613	+	0.924322i	$0.624631\pi$
$660$		0			0
$661$	31.6245	−	22.9765i	1.23005	−	0.893683i	0.233155	−	0.972440i	$-0.425095\pi$
$661$	31.6245	−	22.9765i	1.23005	−	0.893683i	0.996894	+	0.0787568i	$0.0250951\pi$
$662$	5.19017	+	11.5622i	0.201722	+	0.449377i
$663$		0			0
$664$	6.35726	−	42.6634i	0.246710	−	1.65566i
$665$	−7.36528	−	10.8066i	−0.285613	−	0.419061i
$666$		0			0
$667$	−5.06895	+	9.94838i	−0.196271	+	0.385203i
$668$	−0.909409	+	3.47878i	−0.0351861	+	0.134598i
$669$		0			0
$670$	15.9990	−	13.6410i	0.618095	−	0.526999i
$671$	14.1679	+	4.60344i	0.546947	+	0.177714i
$672$		0			0
$673$	−34.7952	−	5.51101i	−1.34126	−	0.212434i	−0.555781	−	0.831329i	$-0.687581\pi$
$673$	−34.7952	−	5.51101i	−1.34126	−	0.212434i	−0.785474	+	0.618895i	$0.787581\pi$
$674$	2.87624	+	10.6047i	0.110789	+	0.408477i
$675$		0			0
$676$	−2.59664	+	1.52039i	−0.0998708	+	0.0584763i
$677$	−3.20219	+	20.2178i	−0.123070	+	0.777035i	0.846530	+	0.532341i	$0.178687\pi$
$677$	−3.20219	+	20.2178i	−0.123070	+	0.777035i	−0.969600	+	0.244694i	$0.921313\pi$
$678$		0			0
$679$	−4.64919	+	14.3087i	−0.178419	+	0.549119i
$680$	31.2255	+	23.7003i	1.19744	+	0.908865i
$681$		0			0
$682$	30.9160	−	53.9277i	1.18384	−	2.06500i
$683$	−0.181468	−	0.0924627i	−0.00694369	−	0.00353799i	0.450515	−	0.892769i	$-0.351240\pi$
$683$	−0.181468	−	0.0924627i	−0.00694369	−	0.00353799i	−0.457459	+	0.889231i	$0.651240\pi$
$684$		0			0
$685$	15.4460	−	43.0836i	0.590162	−	1.64614i
$686$	16.9107	+	13.6087i	0.645653	+	0.519584i
$687$		0			0
$688$	−11.2702	+	30.4667i	−0.429673	+	1.16153i
$689$	1.43971	+	1.98159i	0.0548487	+	0.0754927i
$690$		0			0
$691$	−11.4692	+	15.7860i	−0.436309	+	0.600528i	−0.969387	−	0.245538i	$-0.921035\pi$
$691$	−11.4692	+	15.7860i	−0.436309	+	0.600528i	0.533078	+	0.846066i	$0.321035\pi$
$692$	−17.7589	+	1.03947i	−0.675093	+	0.0395146i
$693$		0			0
$694$	−16.7692	−	25.6505i	−0.636550	−	0.973681i
$695$	2.73657	+	21.4317i	0.103804	+	0.812952i
$696$		0			0
$697$	7.84953	+	15.4056i	0.297322	+	0.583528i
$698$	32.3970	−	3.50509i	1.22625	−	0.132670i
$699$		0			0
$700$	0.0208031	−	12.2890i	0.000786285	−	0.464482i
$701$	10.3544			0.391080			0.195540	−	0.980696i	$-0.437354\pi$
$701$	10.3544			0.391080			0.195540	+	0.980696i	$0.437354\pi$
$702$		0			0
$703$	18.5038	+	36.3157i	0.697883	+	1.36967i
$704$	−34.3216	−	10.4608i	−1.29354	−	0.394255i
$705$		0			0
$706$	−11.9458	−	18.2726i	−0.449586	−	0.687697i
$707$	−6.87186	−	6.87186i	−0.258443	−	0.258443i
$708$		0			0
$709$	15.3330	−	21.1040i	0.575841	−	0.792578i	−0.417390	−	0.908727i	$-0.637055\pi$
$709$	15.3330	−	21.1040i	0.575841	−	0.792578i	0.993232	+	0.116150i	$0.0370552\pi$
$710$	−12.0123	−	10.2770i	−0.450812	−	0.385690i
$711$		0			0
$712$	−2.64916	+	3.71738i	−0.0992815	+	0.139315i
$713$	−7.33719	−	46.3252i	−0.274780	−	1.73489i
$714$		0			0
$715$	9.53013	+	32.6400i	0.356407	+	1.22067i
$716$	1.64641	−	16.6413i	0.0615293	−	0.621915i
$717$		0			0
$718$	15.7812	−	27.5275i	0.588948	−	1.02732i
$719$	0.0165289	+	0.0508707i	0.000616424	+	0.00189716i	0.951364	−	0.308068i	$-0.0996825\pi$
$719$	0.0165289	+	0.0508707i	0.000616424	+	0.00189716i	−0.950748	+	0.309965i	$0.899683\pi$
$720$		0			0
$721$	6.38261	−	19.6437i	0.237701	−	0.731568i
$722$	3.46549	+	3.82527i	0.128972	+	0.142362i
$723$		0			0
$724$	−22.8306	−	38.9920i	−0.848491	−	1.44913i
$725$	2.93114	+	11.2906i	0.108860	+	0.419324i
$726$		0			0
$727$	30.0813	+	4.76440i	1.11565	+	0.176702i	0.686922	−	0.726731i	$-0.258961\pi$
$727$	30.0813	+	4.76440i	1.11565	+	0.176702i	0.428730	+	0.903433i	$0.358961\pi$
$728$	−11.2410	−	3.53895i	−0.416620	−	0.131162i
$729$		0			0
$730$	9.25331	+	5.68121i	0.342480	+	0.210271i
$731$	47.8731	−	15.5549i	1.77065	−	0.575319i
$732$		0			0
$733$	1.86449	−	3.65926i	0.0688664	−	0.135158i	−0.854007	−	0.520262i	$-0.825834\pi$
$733$	1.86449	−	3.65926i	0.0688664	−	0.135158i	0.922873	+	0.385104i	$0.125834\pi$
$734$	21.4601	+	8.16266i	0.792105	+	0.301289i
$735$		0			0
$736$	−25.1237	+	10.0867i	−0.926073	+	0.371801i
$737$	29.4523	−	4.66479i	1.08489	−	0.171830i
$738$		0			0
$739$	−37.0386	+	26.9101i	−1.36249	+	0.989905i	−0.364205	+	0.931319i	$0.618659\pi$
$739$	−37.0386	+	26.9101i	−1.36249	+	0.989905i	−0.998282	+	0.0585867i	$0.981341\pi$
$740$	−4.91533	+	37.9830i	−0.180691	+	1.39628i
$741$		0			0
$742$	0.257289	−	1.22888i	0.00944537	−	0.0451137i
$743$	20.4738	−	20.4738i	0.751110	−	0.751110i	−0.223576	−	0.974686i	$-0.571773\pi$
$743$	20.4738	−	20.4738i	0.751110	−	0.751110i	0.974686	+	0.223576i	$0.0717732\pi$
$744$		0			0
$745$	−16.4751	−	9.02861i	−0.603601	−	0.330783i
$746$	0.612188	−	12.4057i	0.0224138	−	0.454206i
$747$		0			0
$748$	20.2414	+	51.7834i	0.740098	+	1.89339i
$749$			1.31550i			0.0480672i
$750$		0			0
$751$		−	11.0553i		−	0.403414i	−0.979446	−	0.201707i	$-0.935351\pi$
$751$		−	11.0553i		−	0.403414i	0.979446	−	0.201707i	$-0.0646489\pi$
$752$	11.8127	−	14.9573i	0.430765	−	0.545435i
$753$		0			0
$754$	11.1728	+	0.551346i	0.406889	+	0.0200788i
$755$	1.88244	+	1.03160i	0.0685090	+	0.0375439i
$756$		0			0
$757$	13.0048	−	13.0048i	0.472669	−	0.472669i	−0.430109	−	0.902777i	$-0.641525\pi$
$757$	13.0048	−	13.0048i	0.472669	−	0.472669i	0.902777	+	0.430109i	$0.141525\pi$
$758$	−21.3672	−	4.47362i	−0.776093	−	0.162489i
$759$		0			0
$760$	4.08569	+	29.8211i	0.148203	+	1.08173i
$761$	43.5067	−	31.6095i	1.57712	−	1.14584i	0.657209	−	0.753709i	$-0.271737\pi$
$761$	43.5067	−	31.6095i	1.57712	−	1.14584i	0.919908	−	0.392134i	$-0.128263\pi$
$762$		0			0
$763$	6.96101	−	1.10252i	0.252005	−	0.0399137i
$764$	−5.15300	+	11.7667i	−0.186429	+	0.425702i
$765$		0			0
$766$	11.0083	−	28.9413i	0.397745	−	1.04569i
$767$	−0.581792	+	1.14183i	−0.0210073	+	0.0412291i
$768$		0			0
$769$	−0.181257	+	0.0588941i	−0.00653631	+	0.00212377i	−0.312283	−	0.949989i	$-0.601094\pi$
$769$	−0.181257	+	0.0588941i	−0.00653631	+	0.00212377i	0.305747	+	0.952113i	$0.401094\pi$
$770$	9.11945	−	14.8534i	0.328642	−	0.535278i
$771$		0			0
$772$	27.7025	+	17.7507i	0.997034	+	0.638861i
$773$	19.0875	+	3.02316i	0.686528	+	0.108735i	0.489947	−	0.871752i	$-0.337016\pi$
$773$	19.0875	+	3.02316i	0.686528	+	0.108735i	0.196581	+	0.980488i	$0.437016\pi$
$774$		0			0
$775$	−37.8395	−	31.1335i	−1.35923	−	1.11835i
$776$	24.2601	−	24.7086i	0.870887	−	0.886986i
$777$		0			0
$778$	−34.4533	+	31.2129i	−1.23521	+	1.11903i
$779$	−4.10244	+	12.6260i	−0.146985	+	0.452374i
$780$		0			0
$781$	−6.92855	−	21.3239i	−0.247923	−	0.763028i
$782$	36.3947	+	20.8646i	1.30147	+	0.746117i
$783$		0			0
$784$	−9.17589	−	19.9501i	−0.327710	−	0.712505i
$785$	7.36624	+	25.2288i	0.262912	+	0.900455i
$786$		0			0
$787$	−1.63251	−	10.3073i	−0.0581927	−	0.367414i	−0.999550	−	0.0300023i	$-0.990449\pi$
$787$	−1.63251	−	10.3073i	−0.0581927	−	0.367414i	0.941357	−	0.337412i	$-0.109551\pi$
$788$	−1.70902	−	2.08432i	−0.0608815	−	0.0742508i
$789$		0			0
$790$	3.46638	−	4.05166i	0.123328	−	0.144152i
$791$	−13.2319	+	18.2121i	−0.470471	+	0.647548i
$792$		0			0
$793$	−7.96311	−	7.96311i	−0.282778	−	0.282778i
$794$	−12.2208	+	7.98941i	−0.433699	+	0.283534i
$795$		0			0
$796$	40.2378	−	8.80991i	1.42619	−	0.312259i
$797$	−9.74336	−	19.1224i	−0.345127	−	0.677351i	0.651567	−	0.758591i	$-0.274112\pi$
$797$	−9.74336	−	19.1224i	−0.345127	−	0.677351i	−0.996695	+	0.0812404i	$0.974112\pi$
$798$		0			0
$799$	−29.5337			−1.04483
$800$	−12.6523	+	25.2966i	−0.447326	+	0.894371i
$801$		0			0
$802$	2.93997	+	27.1737i	0.103814	+	0.959538i
$803$	6.99149	+	13.7216i	0.246724	+	0.484224i
$804$		0			0
$805$	−1.66572	−	13.0452i	−0.0587088	−	0.459784i
$806$	−39.3318	+	25.7134i	−1.38540	+	0.905716i
$807$		0			0
$808$	7.10644	+	21.2085i	0.250004	+	0.746113i
$809$	20.9545	−	28.8414i	0.736720	−	1.01401i	−0.262081	−	0.965046i	$-0.584409\pi$
$809$	20.9545	−	28.8414i	0.736720	−	1.01401i	0.998801	−	0.0489622i	$-0.0155914\pi$
$810$		0			0
$811$	−3.52375	−	4.85003i	−0.123736	−	0.170308i	0.742655	−	0.669674i	$-0.233566\pi$
$811$	−3.52375	−	4.85003i	−0.123736	−	0.170308i	−0.866391	+	0.499366i	$0.833566\pi$
$812$	−3.63568	−	4.43406i	−0.127587	−	0.155605i
$813$		0			0
$814$	−34.0559	+	42.3190i	−1.19366	+	1.48328i
$815$	−16.8443	+	46.9839i	−0.590031	+	1.64577i
$816$		0			0
$817$	34.4373	+	17.5467i	1.20481	+	0.613880i
$818$	−42.8797	−	24.5824i	−1.49925	−	0.859502i
$819$		0			0
$820$	−9.88035	+	7.61615i	−0.345037	+	0.265968i
$821$	3.94578	−	12.1439i	0.137709	−	0.423824i	−0.858293	−	0.513160i	$-0.828475\pi$
$821$	3.94578	−	12.1439i	0.137709	−	0.423824i	0.996002	+	0.0893362i	$0.0284746\pi$
$822$		0			0
$823$	7.94099	−	50.1375i	0.276806	−	1.74768i	−0.321956	−	0.946755i	$-0.604340\pi$
$823$	7.94099	−	50.1375i	0.276806	−	1.74768i	0.598761	−	0.800927i	$-0.295660\pi$
$824$	−33.3053	+	33.9210i	−1.16025	+	1.18170i
$825$		0			0
$826$	0.633982	−	0.171951i	0.0220590	−	0.00598294i
$827$	−12.9219	−	2.04663i	−0.449339	−	0.0711683i	−0.0723358	−	0.997380i	$-0.523045\pi$
$827$	−12.9219	−	2.04663i	−0.449339	−	0.0711683i	−0.377003	+	0.926212i	$0.623045\pi$
$828$		0			0
$829$	29.1547	+	9.47295i	1.01259	+	0.329009i	0.767884	−	0.640589i	$-0.221310\pi$
$829$	29.1547	+	9.47295i	1.01259	+	0.329009i	0.244702	+	0.969598i	$0.421310\pi$
$830$	−31.2891	−	36.6977i	−1.08606	−	1.27379i
$831$		0			0
$832$	19.5276	+	18.8251i	0.676999	+	0.652642i
$833$	−15.4480	+	30.3184i	−0.535241	+	1.05047i
$834$		0			0
$835$	2.26407	+	3.32192i	0.0783515	+	0.114960i
$836$	−17.1253	+	39.1048i	−0.592289	+	1.35247i
$837$		0			0
$838$	−23.0759	+	10.3586i	−0.797145	+	0.357832i
$839$	39.5519	−	28.7361i	1.36548	−	0.992081i	0.367408	−	0.930060i	$-0.380245\pi$
$839$	39.5519	−	28.7361i	1.36548	−	0.992081i	0.998075	−	0.0620209i	$-0.0197546\pi$
$840$		0			0
$841$	−19.0582	−	13.8466i	−0.657178	−	0.477468i
$842$	50.1525	+	10.5003i	1.72837	+	0.361865i
$843$		0			0
$844$	−8.55044	−	7.60484i	−0.294318	−	0.261769i
$845$	−0.625965	+	3.30542i	−0.0215338	+	0.113710i
$846$		0			0
$847$	9.98121	−	5.08568i	0.342958	−	0.174746i
$848$	−1.79099	+	2.26776i	−0.0615029	+	0.0778752i
$849$		0			0
$850$	42.9133	−	8.90887i	1.47191	−	0.305572i
$851$			40.9865i			1.40500i
$852$		0			0
$853$	−7.99542	+	4.07387i	−0.273758	+	0.139487i	−0.585480	−	0.810687i	$-0.699094\pi$
$853$	−7.99542	+	4.07387i	−0.273758	+	0.139487i	0.311722	+	0.950173i	$0.399094\pi$
$854$	−0.284512	+	5.76553i	−0.00973581	+	0.197292i
$855$		0			0
$856$	1.34979	−	2.71020i	0.0461350	−	0.0926326i
$857$	0.588621	−	0.588621i	0.0201069	−	0.0201069i	−0.696982	−	0.717089i	$-0.745474\pi$
$857$	0.588621	−	0.588621i	0.0201069	−	0.0201069i	0.717089	+	0.696982i	$0.245474\pi$
$858$		0			0
$859$	8.15543	+	5.92527i	0.278260	+	0.202168i	0.718158	−	0.695880i	$-0.244985\pi$
$859$	8.15543	+	5.92527i	0.278260	+	0.202168i	−0.439898	+	0.898048i	$0.644985\pi$
$860$	17.4002	+	31.8792i	0.593341	+	1.08707i
$861$		0			0
$862$	20.0890	+	44.7524i	0.684233	+	1.52427i
$863$	−28.6065	+	4.53083i	−0.973777	+	0.154231i	−0.622995	−	0.782226i	$-0.714084\pi$
$863$	−28.6065	+	4.53083i	−0.973777	+	0.154231i	−0.350782	+	0.936457i	$0.614084\pi$
$864$		0			0
$865$	−12.1691	+	15.7317i	−0.413763	+	0.534895i
$866$	0.997490	+	0.379411i	0.0338961	+	0.0128929i
$867$		0			0
$868$	23.3040	+	6.09205i	0.790990	+	0.206777i
$869$	7.19241	−	2.33696i	0.243986	−	0.0792758i
$870$		0			0
$871$	−21.4390	−	6.96594i	−0.726432	−	0.236032i
$872$	−15.4724	−	4.87109i	−0.523961	−	0.164956i
$873$		0			0
$874$	8.43183	+	31.0881i	0.285211	+	1.05157i
$875$	−10.3426	−	9.04474i	−0.349642	−	0.305768i
$876$		0			0
$877$	−2.86266	+	18.0741i	−0.0966652	+	0.610320i	0.891032	+	0.453941i	$0.149982\pi$
$877$	−2.86266	+	18.0741i	−0.0966652	+	0.610320i	−0.987697	+	0.156379i	$0.950018\pi$
$878$	7.81448	+	8.62576i	0.263726	+	0.291105i
$879$		0			0
$880$	−34.0286	+	21.2438i	−1.14710	+	0.716129i
$881$	4.26429	+	13.1241i	0.143668	+	0.442164i	0.996837	−	0.0794700i	$-0.0253228\pi$
$881$	4.26429	+	13.1241i	0.143668	+	0.442164i	−0.853170	+	0.521634i	$0.825323\pi$
$882$		0			0
$883$	−30.1105	−	15.3421i	−1.01330	−	0.516301i	−0.133198	−	0.991089i	$-0.542525\pi$
$883$	−30.1105	−	15.3421i	−1.01330	−	0.516301i	−0.880100	+	0.474788i	$0.842525\pi$
$884$	4.13808	−	41.8262i	0.139179	−	1.40677i
$885$		0			0
$886$	7.87304	+	6.33577i	0.264500	+	0.212854i
$887$	4.87731	+	30.7941i	0.163764	+	1.03397i	0.923462	+	0.383689i	$0.125347\pi$
$887$	4.87731	+	30.7941i	0.163764	+	1.03397i	−0.759698	+	0.650276i	$0.774653\pi$
$888$		0			0
$889$	−1.68132	−	2.31413i	−0.0563895	−	0.0776136i
$890$	1.18720	+	4.96354i	0.0397950	+	0.166378i
$891$		0			0
$892$	0.241468	+	4.12540i	0.00808494	+	0.138128i
$893$	−16.0349	−	16.0349i	−0.536587	−	0.536587i
$894$		0			0
$895$	−12.8168	−	13.6120i	−0.428417	−	0.454997i
$896$	0.430810	−	13.8968i	0.0143924	−	0.464259i
$897$		0			0
$898$	5.57530	−	0.603201i	0.186050	−	0.0201291i
$899$	−22.8638			−0.762551
$900$		0			0
$901$	4.47778			0.149176
$902$	−17.5906	+	1.90316i	−0.585704	+	0.0633683i
$903$		0			0
$904$	45.9473	−	23.9439i	1.52819	−	0.796361i
$905$	−49.6352	−	9.39968i	−1.64993	−	0.312456i
$906$		0			0
$907$	6.58434	+	6.58434i	0.218629	+	0.218629i	0.807921	−	0.589291i	$-0.200593\pi$
$907$	6.58434	+	6.58434i	0.218629	+	0.218629i	−0.589291	+	0.807921i	$0.700593\pi$
$908$	−43.4089	+	2.54081i	−1.44058	+	0.0843199i
$909$		0			0
$910$	−11.2402	+	6.87491i	−0.372608	+	0.227901i
$911$	−16.5700	−	22.8067i	−0.548990	−	0.755620i	0.440885	−	0.897564i	$-0.354665\pi$
$911$	−16.5700	−	22.8067i	−0.548990	−	0.755620i	−0.989875	+	0.141944i	$0.954665\pi$
$912$		0			0
$913$	−10.6999	−	67.5562i	−0.354113	−	2.23578i
$914$	44.6054	+	35.8959i	1.47542	+	1.18733i
$915$		0			0
$916$	19.0795	+	1.88763i	0.630403	+	0.0623691i
$917$	24.6154	+	12.5422i	0.812872	+	0.414179i
$918$		0			0
$919$	8.14444	+	25.0660i	0.268660	+	0.826852i	0.990827	+	0.135133i	$0.0431461\pi$
$919$	8.14444	+	25.0660i	0.268660	+	0.826852i	−0.722167	+	0.691719i	$0.756854\pi$
$920$	−9.95362	+	28.5850i	−0.328161	+	0.942421i
$921$		0			0
$922$	22.9909	+	25.3778i	0.757166	+	0.835773i
$923$	−2.65149	+	16.7408i	−0.0872748	+	0.551032i
$924$		0			0
$925$	28.4034	+	32.0443i	0.933899	+	1.05361i
$926$	0.960253	+	3.54045i	0.0315559	+	0.116346i
$927$		0			0
$928$	2.94059	+	12.8656i	0.0965297	+	0.422333i
$929$	−7.31939	−	2.37821i	−0.240141	−	0.0780266i	0.186474	−	0.982460i	$-0.440294\pi$
$929$	−7.31939	−	2.37821i	−0.240141	−	0.0780266i	−0.426615	+	0.904433i	$0.640294\pi$
$930$		0			0
$931$	−24.8482	+	8.07366i	−0.814366	+	0.264604i
$932$	3.72183	−	14.2372i	0.121913	−	0.466354i
$933$		0			0
$934$	44.8483	+	17.0588i	1.46748	+	0.558180i
$935$	58.5145	+	20.9782i	1.91363	+	0.686061i
$936$		0			0
$937$	41.5344	−	6.57840i	1.35687	−	0.214907i	0.564744	−	0.825266i	$-0.308975\pi$
$937$	41.5344	−	6.57840i	1.35687	−	0.214907i	0.792125	+	0.610359i	$0.208975\pi$
$938$	4.73201	+	10.5416i	0.154506	+	0.344194i
$939$		0			0
$940$	−3.92948	−	20.9436i	−0.128165	−	0.683104i
$941$	−41.1994	−	29.9331i	−1.34306	−	0.975792i	−0.999325	−	0.0367262i	$-0.988307\pi$
$941$	−41.1994	−	29.9331i	−1.34306	−	0.975792i	−0.343737	−	0.939066i	$-0.611693\pi$
$942$		0			0
$943$	−9.44001	+	9.44001i	−0.307409	+	0.307409i
$944$	−1.48257	−	0.296256i	−0.0482535	−	0.00964232i
$945$		0			0
$946$	−2.53881	+	51.4480i	−0.0825439	+	1.67272i
$947$	−9.51643	+	4.84886i	−0.309242	+	0.157567i	−0.601724	−	0.798704i	$-0.705519\pi$
$947$	−9.51643	+	4.84886i	−0.309242	+	0.157567i	0.292481	+	0.956271i	$0.405519\pi$
$948$		0			0
$949$		−	11.6418i		−	0.377909i
$950$	28.1361	+	18.4622i	0.912855	+	0.598993i
$951$		0			0
$952$	−17.3130	+	12.8225i	−0.561118	+	0.415580i
$953$	−9.54986	+	4.86590i	−0.309350	+	0.157622i	−0.601773	−	0.798667i	$-0.705539\pi$
$953$	−9.54986	+	4.86590i	−0.309350	+	0.157622i	0.292422	+	0.956289i	$0.405539\pi$
$954$		0			0
$955$	6.13229	+	12.9867i	0.198436	+	0.420240i
$956$	15.0848	−	16.9604i	0.487876	−	0.548540i
$957$		0			0
$958$	−42.6301	−	8.92537i	−1.37732	−	0.288366i
$959$	20.3498	+	14.7850i	0.657129	+	0.477432i
$960$		0			0
$961$	52.6224	−	38.2324i	1.69750	−	1.23330i
$962$	37.4626	−	16.8166i	1.20784	−	0.542190i
$963$		0			0
$964$	9.89385	+	4.33284i	0.318659	+	0.139551i
$965$	35.3107	−	10.3099i	1.13669	−	0.331888i
$966$		0			0
$967$	9.81345	−	19.2600i	0.315579	−	0.619359i	−0.677669	−	0.735367i	$-0.737010\pi$
$967$	9.81345	−	19.2600i	0.315579	−	0.619359i	0.993248	+	0.116008i	$0.0370098\pi$
$968$	−25.7817	+	0.236120i	−0.828654	+	0.00758918i
$969$		0			0
$970$	−3.00486	−	38.5980i	−0.0964801	−	1.23931i
$971$	32.1098	+	10.4331i	1.03045	+	0.334815i	0.774970	−	0.631998i	$-0.217765\pi$
$971$	32.1098	+	10.4331i	1.03045	+	0.334815i	0.255484	+	0.966813i	$0.417765\pi$
$972$		0			0
$973$	−11.7280	−	1.85753i	−0.375981	−	0.0595496i
$974$	−34.9236	+	9.47211i	−1.11902	+	0.303506i
$975$		0			0
$976$	6.50200	−	11.5863i	0.208124	−	0.370867i
$977$	3.21252	−	20.2830i	0.102777	−	0.648911i	−0.881487	−	0.472209i	$-0.843457\pi$
$977$	3.21252	−	20.2830i	0.102777	−	0.648911i	0.984264	−	0.176703i	$-0.0565431\pi$
$978$		0			0
$979$	−2.23677	+	6.88406i	−0.0714874	+	0.220016i
$980$	−23.5554	−	6.92093i	−0.752450	−	0.221081i
$981$		0			0
$982$	−44.6085	−	25.5735i	−1.42352	−	0.816083i
$983$	−9.38458	−	4.78168i	−0.299322	−	0.152512i	0.297880	−	0.954603i	$-0.403721\pi$
$983$	−9.38458	−	4.78168i	−0.299322	−	0.152512i	−0.597201	+	0.802092i	$0.703721\pi$
$984$		0			0
$985$	−3.01218	−	0.0906309i	−0.0959760	−	0.00288774i
$986$	12.8211	−	15.9319i	0.408307	−	0.507376i
$987$		0			0
$988$	24.9556	−	20.4622i	0.793944	−	0.650989i
$989$	22.8452	+	31.4437i	0.726434	+	0.999851i
$990$		0			0
$991$	32.0318	−	44.0880i	1.01752	−	1.40050i	0.103598	−	0.994619i	$-0.466964\pi$
$991$	32.0318	−	44.0880i	1.01752	−	1.40050i	0.913925	−	0.405882i	$-0.133036\pi$
$992$	−41.7603	−	36.4625i	−1.32589	−	1.15769i
$993$		0			0
$994$	7.27201	−	4.75412i	0.230654	−	0.150792i
$995$	22.1322	−	40.3860i	0.701637	−	1.28032i
$996$		0			0
$997$	−25.1191	−	49.2990i	−0.795529	−	1.56131i	−0.827262	−	0.561817i	$-0.810102\pi$
$997$	−25.1191	−	49.2990i	−0.795529	−	1.56131i	0.0317326	−	0.999496i	$-0.489898\pi$
$998$	−3.25786	−	30.1119i	−0.103126	−	0.953175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.523.14		240
3.2	odd	2		300.2.w.a.223.17	yes	240
4.3	odd	2	inner	900.2.bj.f.523.19		240
12.11	even	2		300.2.w.a.223.12	yes	240
25.12	odd	20	inner	900.2.bj.f.487.19		240
75.62	even	20		300.2.w.a.187.12	✓	240
100.87	even	20	inner	900.2.bj.f.487.14		240
300.287	odd	20		300.2.w.a.187.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.12	✓	240	75.62	even	20
300.2.w.a.187.17	yes	240	300.287	odd	20
300.2.w.a.223.12	yes	240	12.11	even	2
300.2.w.a.223.17	yes	240	3.2	odd	2
900.2.bj.f.487.14		240	100.87	even	20	inner
900.2.bj.f.487.19		240	25.12	odd	20	inner
900.2.bj.f.523.14		240	1.1	even	1	trivial
900.2.bj.f.523.19		240	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.152118 - 1.40601i) q^{2} +(-1.95372 + 0.427760i) q^{4} +(-1.07461 + 1.96092i) q^{5} +(-0.868967 - 0.868967i) q^{7} +(0.898631 + 2.68188i) q^{8} +(2.92054 + 1.21262i) q^{10} +(2.63624 + 3.62847i) q^{11} +(-0.530391 - 3.34876i) q^{13} +(-1.08959 + 1.35396i) q^{14} +(3.63404 - 1.67145i) q^{16} +(-5.52269 - 2.81395i) q^{17} +(-1.47067 - 4.52625i) q^{19} +(1.26069 - 4.29076i) q^{20} +(4.70064 - 4.25853i) q^{22} +(0.748674 - 4.72694i) q^{23} +(-2.69041 - 4.21446i) q^{25} +(-4.62770 + 1.25514i) q^{26} +(2.06943 + 1.32601i) q^{28} +(-2.21880 - 0.720931i) q^{29} +(9.32059 - 3.02844i) q^{31} +(-2.90287 - 4.85524i) q^{32} +(-3.11633 + 8.19300i) q^{34} +(2.63778 - 0.770171i) q^{35} +(-8.45865 + 1.33972i) q^{37} +(-6.14023 + 2.75630i) q^{38} +(-6.22463 - 1.11984i) q^{40} +(-2.25676 - 1.63963i) q^{41} +(-5.74249 + 5.74249i) q^{43} +(-6.70259 - 5.96134i) q^{44} +(-6.76001 - 0.333587i) q^{46} +(4.24551 - 2.16319i) q^{47} -5.48979i q^{49} +(-5.51631 + 4.42384i) q^{50} +(2.46870 + 6.31566i) q^{52} +(-0.643686 + 0.327974i) q^{53} +(-9.94808 + 1.27025i) q^{55} +(1.54958 - 3.11134i) q^{56} +(-0.676115 + 3.22932i) q^{58} +(-0.305784 - 0.222165i) q^{59} +(2.68715 - 1.95233i) q^{61} +(-5.67585 - 12.6441i) q^{62} +(-6.38493 + 4.82003i) q^{64} +(7.13661 + 2.55857i) q^{65} +(3.01843 - 5.92399i) q^{67} +(11.9935 + 3.13529i) q^{68} +(-1.48412 - 3.59158i) q^{70} +(-4.75445 - 1.54481i) q^{71} +(3.39138 + 0.537142i) q^{73} +(3.17037 + 11.6891i) q^{74} +(4.80942 + 8.21394i) q^{76} +(0.862218 - 5.44383i) q^{77} +(0.521056 - 1.60364i) q^{79} +(-0.627622 + 8.92222i) q^{80} +(-1.96204 + 3.42244i) q^{82} +(-13.5881 - 6.92350i) q^{83} +(11.4527 - 7.80563i) q^{85} +(8.94753 + 7.20045i) q^{86} +(-7.36211 + 10.3307i) q^{88} +(0.948617 + 1.30566i) q^{89} +(-2.44907 + 3.37085i) q^{91} +(0.559295 + 9.55537i) q^{92} +(-3.68729 - 5.64016i) q^{94} +(10.4560 + 1.98011i) q^{95} +(-5.55806 - 10.9083i) q^{97} +(-7.71870 + 0.835099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

L-functions

Modular forms

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