LMFDB - Embedded newform 1148.2.n.c.57.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 12 x^{14} - 19 x^{13} + 49 x^{12} - 91 x^{11} + 269 x^{10} - 367 x^{9} + 1058 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 12x^14 - 19x^13 + 49x^12 - 91x^11 + 269x^10 - 367x^9 + 1058x^8 - 1675x^7 + 2755x^6 - 2800x^5 + 4032x^4 - 2186x^3 + 2189x^2 + 76*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.3
Root			$-0.0169945 - 0.0123472i$ of defining polynomial
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.c.141.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0210063 q^{3} +(0.567750 + 0.412494i) q^{5} +(-0.309017 - 0.951057i) q^{7} -2.99956 q^{9} +O(q^{10})$	\(q+0.0210063 q^{3} +(0.567750 + 0.412494i) q^{5} +(-0.309017 - 0.951057i) q^{7} -2.99956 q^{9} +(-0.883310 + 0.641762i) q^{11} +(0.0516606 - 0.158995i) q^{13} +(0.0119263 + 0.00866500i) q^{15} +(6.53112 - 4.74513i) q^{17} +(0.882282 + 2.71539i) q^{19} +(-0.00649132 - 0.0199782i) q^{21} +(2.42691 - 7.46928i) q^{23} +(-1.39290 - 4.28690i) q^{25} -0.126029 q^{27} +(6.32180 + 4.59306i) q^{29} +(2.27513 - 1.65298i) q^{31} +(-0.0185551 + 0.0134811i) q^{33} +(0.216861 - 0.667430i) q^{35} +(1.30184 + 0.945845i) q^{37} +(0.00108520 - 0.00333990i) q^{39} +(5.44065 - 3.37630i) q^{41} +(1.79969 - 5.53886i) q^{43} +(-1.70300 - 1.23730i) q^{45} +(0.776051 - 2.38844i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(0.137195 - 0.0996779i) q^{51} +(-7.52425 - 5.46668i) q^{53} -0.766222 q^{55} +(0.0185335 + 0.0570403i) q^{57} +(-4.17834 + 12.8596i) q^{59} +(-1.82216 - 5.60804i) q^{61} +(0.926915 + 2.85275i) q^{63} +(0.0949148 - 0.0689596i) q^{65} +(3.24342 + 2.35648i) q^{67} +(0.0509806 - 0.156902i) q^{69} +(-5.46740 + 3.97230i) q^{71} +11.6708 q^{73} +(-0.0292597 - 0.0900520i) q^{75} +(0.883310 + 0.641762i) q^{77} +3.45167 q^{79} +8.99603 q^{81} -4.51716 q^{83} +5.66538 q^{85} +(0.132798 + 0.0964833i) q^{87} +(-3.96880 - 12.2147i) q^{89} -0.167177 q^{91} +(0.0477923 - 0.0347231i) q^{93} +(-0.619166 + 1.90560i) q^{95} +(-0.661455 - 0.480575i) q^{97} +(2.64954 - 1.92500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	$ 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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			0
$2$		0			0
$3$	0.0210063			0.0121280			0.00606401	−	0.999982i	$-0.498070\pi$
$3$	0.0210063			0.0121280			0.00606401	+	0.999982i	$0.498070\pi$
$4$		0			0
$5$	0.567750	+	0.412494i	0.253905	+	0.184473i	0.707456	−	0.706758i	$-0.249843\pi$
$5$	0.567750	+	0.412494i	0.253905	+	0.184473i	−0.453550	+	0.891231i	$0.649843\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$		0			0
$9$	−2.99956			−0.999853
$10$		0			0
$11$	−0.883310	+	0.641762i	−0.266328	+	0.193499i	−0.712932	−	0.701233i	$-0.752633\pi$
$11$	−0.883310	+	0.641762i	−0.266328	+	0.193499i	0.446604	+	0.894732i	$0.352633\pi$
$12$		0			0
$13$	0.0516606	−	0.158995i	0.0143281	−	0.0440972i	−0.943637	−	0.330983i	$-0.892620\pi$
$13$	0.0516606	−	0.158995i	0.0143281	−	0.0440972i	0.957965	+	0.286885i	$0.0926199\pi$
$14$		0			0
$15$	0.0119263	+	0.00866500i	0.00307937	+	0.00223729i
$16$		0			0
$17$	6.53112	−	4.74513i	1.58403	−	1.15086i	0.672141	−	0.740423i	$-0.265375\pi$
$17$	6.53112	−	4.74513i	1.58403	−	1.15086i	0.911887	−	0.410441i	$-0.134625\pi$
$18$		0			0
$19$	0.882282	+	2.71539i	0.202409	+	0.622952i	0.999810	+	0.0195016i	$0.00620795\pi$
$19$	0.882282	+	2.71539i	0.202409	+	0.622952i	−0.797400	+	0.603451i	$0.793792\pi$
$20$		0			0
$21$	−0.00649132	−	0.0199782i	−0.00141652	−	0.00435960i
$22$		0			0
$23$	2.42691	−	7.46928i	0.506047	−	1.55745i	−0.292957	−	0.956126i	$-0.594639\pi$
$23$	2.42691	−	7.46928i	0.506047	−	1.55745i	0.799004	−	0.601326i	$-0.205361\pi$
$24$		0			0
$25$	−1.39290	−	4.28690i	−0.278579	−	0.857379i
$26$		0			0
$27$	−0.126029			−0.0242543
$28$		0			0
$29$	6.32180	+	4.59306i	1.17393	+	0.852909i	0.991474	−	0.130305i	$-0.0415957\pi$
$29$	6.32180	+	4.59306i	1.17393	+	0.852909i	0.182455	+	0.983214i	$0.441596\pi$
$30$		0			0
$31$	2.27513	−	1.65298i	0.408626	−	0.296884i	−0.364419	−	0.931235i	$-0.618732\pi$
$31$	2.27513	−	1.65298i	0.408626	−	0.296884i	0.773045	+	0.634351i	$0.218732\pi$
$32$		0			0
$33$	−0.0185551	+	0.0134811i	−0.00323003	+	0.00234675i
$34$		0			0
$35$	0.216861	−	0.667430i	0.0366562	−	0.112816i
$36$		0			0
$37$	1.30184	+	0.945845i	0.214022	+	0.155496i	0.689631	−	0.724161i	$-0.257773\pi$
$37$	1.30184	+	0.945845i	0.214022	+	0.155496i	−0.475610	+	0.879656i	$0.657773\pi$
$38$		0			0
$39$	0.00108520	−	0.00333990i	0.000173771	−	0.000534812i
$40$		0			0
$41$	5.44065	−	3.37630i	0.849686	−	0.527289i
$41$	5.44065	−	3.37630i	0.849686	−	0.527289i
$42$		0			0
$43$	1.79969	−	5.53886i	0.274449	−	0.844669i	−0.714915	−	0.699211i	$-0.753535\pi$
$43$	1.79969	−	5.53886i	0.274449	−	0.844669i	0.989365	−	0.145457i	$-0.0464653\pi$
$44$		0			0
$45$	−1.70300	−	1.23730i	−0.253868	−	0.184446i
$46$		0			0
$47$	0.776051	−	2.38844i	0.113199	−	0.348390i	−0.878368	−	0.477984i	$-0.841368\pi$
$47$	0.776051	−	2.38844i	0.113199	−	0.348390i	0.991567	+	0.129594i	$0.0413676\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	0.137195	−	0.0996779i	0.0192111	−	0.0139577i
$52$		0			0
$53$	−7.52425	−	5.46668i	−1.03353	−	0.750907i	−0.0645216	−	0.997916i	$-0.520552\pi$
$53$	−7.52425	−	5.46668i	−1.03353	−	0.750907i	−0.969013	+	0.247009i	$0.920552\pi$
$54$		0			0
$55$	−0.766222			−0.103317
$56$		0			0
$57$	0.0185335	+	0.0570403i	0.00245483	+	0.00755518i
$58$		0			0
$59$	−4.17834	+	12.8596i	−0.543973	+	1.67418i	0.179446	+	0.983768i	$0.442570\pi$
$59$	−4.17834	+	12.8596i	−0.543973	+	1.67418i	−0.723419	+	0.690409i	$0.757430\pi$
$60$		0			0
$61$	−1.82216	−	5.60804i	−0.233304	−	0.718036i	−0.997342	−	0.0728647i	$-0.976786\pi$
$61$	−1.82216	−	5.60804i	−0.233304	−	0.718036i	0.764038	−	0.645172i	$-0.223214\pi$
$62$		0			0
$63$	0.926915	+	2.85275i	0.116780	+	0.359413i
$64$		0			0
$65$	0.0949148	−	0.0689596i	0.0117727	−	0.00855339i
$66$		0			0
$67$	3.24342	+	2.35648i	0.396246	+	0.287890i	0.768010	−	0.640437i	$-0.221247\pi$
$67$	3.24342	+	2.35648i	0.396246	+	0.287890i	−0.371764	+	0.928327i	$0.621247\pi$
$68$		0			0
$69$	0.0509806	−	0.156902i	0.00613734	−	0.0188888i
$70$		0			0
$71$	−5.46740	+	3.97230i	−0.648861	+	0.471425i	−0.862883	−	0.505404i	$-0.831344\pi$
$71$	−5.46740	+	3.97230i	−0.648861	+	0.471425i	0.214022	+	0.976829i	$0.431344\pi$
$72$		0			0
$73$	11.6708			1.36596			0.682982	−	0.730435i	$-0.260683\pi$
$73$	11.6708			1.36596			0.682982	+	0.730435i	$0.260683\pi$
$74$		0			0
$75$	−0.0292597	−	0.0900520i	−0.00337862	−	0.0103983i
$76$		0			0
$77$	0.883310	+	0.641762i	0.100662	+	0.0731356i
$78$		0			0
$79$	3.45167			0.388344			0.194172	−	0.980968i	$-0.437798\pi$
$79$	3.45167			0.388344			0.194172	+	0.980968i	$0.437798\pi$
$80$		0			0
$81$	8.99603			0.999559
$82$		0			0
$83$	−4.51716			−0.495823			−0.247912	−	0.968783i	$-0.579744\pi$
$83$	−4.51716			−0.495823			−0.247912	+	0.968783i	$0.579744\pi$
$84$		0			0
$85$	5.66538			0.614497
$86$		0			0
$87$	0.132798	+	0.0964833i	0.0142374	+	0.0103441i
$88$		0			0
$89$	−3.96880	−	12.2147i	−0.420692	−	1.29476i	−0.907059	−	0.421003i	$-0.861678\pi$
$89$	−3.96880	−	12.2147i	−0.420692	−	1.29476i	0.486367	−	0.873755i	$-0.338322\pi$
$90$		0			0
$91$	−0.167177			−0.0175249
$92$		0			0
$93$	0.0477923	−	0.0347231i	0.00495583	−	0.00360062i
$94$		0			0
$95$	−0.619166	+	1.90560i	−0.0635251	+	0.195510i
$96$		0			0
$97$	−0.661455	−	0.480575i	−0.0671606	−	0.0487950i	0.553698	−	0.832717i	$-0.313216\pi$
$97$	−0.661455	−	0.480575i	−0.0671606	−	0.0487950i	−0.620859	+	0.783922i	$0.713216\pi$
$98$		0			0
$99$	2.64954	−	1.92500i	0.266289	−	0.193470i
$100$		0			0
$101$	2.72252	+	8.37905i	0.270901	+	0.833747i	0.990275	+	0.139124i	$0.0444287\pi$
$101$	2.72252	+	8.37905i	0.270901	+	0.833747i	−0.719374	+	0.694623i	$0.755571\pi$
$102$		0			0
$103$	−4.63309	−	14.2592i	−0.456512	−	1.40500i	−0.869351	−	0.494195i	$-0.835463\pi$
$103$	−4.63309	−	14.2592i	−0.456512	−	1.40500i	0.412840	−	0.910804i	$-0.364537\pi$
$104$		0			0
$105$	0.00455546	−	0.0140203i	0.000444567	−	0.00136824i
$106$		0			0
$107$	−3.30156	−	10.1612i	−0.319174	−	0.982318i	−0.974002	−	0.226539i	$-0.927259\pi$
$107$	−3.30156	−	10.1612i	−0.319174	−	0.982318i	0.654828	−	0.755778i	$-0.272741\pi$
$108$		0			0
$109$	11.5865			1.10979			0.554893	−	0.831921i	$-0.312759\pi$
$109$	11.5865			1.10979			0.554893	+	0.831921i	$0.312759\pi$
$110$		0			0
$111$	0.0273470	+	0.0198687i	0.00259566	+	0.00188586i
$112$		0			0
$113$	5.25713	−	3.81953i	0.494550	−	0.359311i	−0.312382	−	0.949957i	$-0.601127\pi$
$113$	5.25713	−	3.81953i	0.494550	−	0.359311i	0.806931	+	0.590645i	$0.201127\pi$
$114$		0			0
$115$	4.45891	−	3.23959i	0.415796	−	0.302093i
$116$		0			0
$117$	−0.154959	+	0.476914i	−0.0143260	+	0.0440908i
$118$		0			0
$119$	−6.53112	−	4.74513i	−0.598706	−	0.434986i
$120$		0			0
$121$	−3.03081	+	9.32787i	−0.275528	+	0.847988i
$122$		0			0
$123$	0.114288	−	0.0709236i	0.0103050	−	0.00639497i
$124$		0			0
$125$	2.06181	−	6.34560i	0.184414	−	0.567567i
$126$		0			0
$127$	10.2215	+	7.42633i	0.907009	+	0.658980i	0.940257	−	0.340467i	$-0.110585\pi$
$127$	10.2215	+	7.42633i	0.907009	+	0.658980i	−0.0332479	+	0.999447i	$0.510585\pi$
$128$		0			0
$129$	0.0378048	−	0.116351i	0.00332853	−	0.0102442i
$130$		0			0
$131$	−15.6235	+	11.3512i	−1.36503	+	0.991755i	−0.366927	+	0.930250i	$0.619590\pi$
$131$	−15.6235	+	11.3512i	−1.36503	+	0.991755i	−0.998107	+	0.0615058i	$0.980410\pi$
$132$		0			0
$133$	2.30985	−	1.67820i	0.200289	−	0.145518i
$134$		0			0
$135$	−0.0715528	−	0.0519862i	−0.00615829	−	0.00447426i
$136$		0			0
$137$	−0.338753			−0.0289416			−0.0144708	−	0.999895i	$-0.504606\pi$
$137$	−0.338753			−0.0289416			−0.0144708	+	0.999895i	$0.504606\pi$
$138$		0			0
$139$	−3.86843	−	11.9058i	−0.328116	−	1.00984i	−0.970014	−	0.243048i	$-0.921853\pi$
$139$	−3.86843	−	11.9058i	−0.328116	−	1.00984i	0.641898	−	0.766790i	$-0.278147\pi$
$140$		0			0
$141$	0.0163020	−	0.0501724i	0.00137288	−	0.00422528i
$142$		0			0
$143$	0.0564046	+	0.173595i	0.00471679	+	0.0145168i
$144$		0			0
$145$	1.69459	+	5.21541i	0.140728	+	0.433116i
$146$		0			0
$147$	−0.0169945	+	0.0123472i	−0.00140168	+	0.00101838i
$148$		0			0
$149$	14.8575	+	10.7946i	1.21718	+	0.884331i	0.995863	−	0.0908715i	$-0.0289652\pi$
$149$	14.8575	+	10.7946i	1.21718	+	0.884331i	0.221315	+	0.975202i	$0.428965\pi$
$150$		0			0
$151$	−3.22956	+	9.93955i	−0.262818	+	0.808870i	0.729370	+	0.684119i	$0.239813\pi$
$151$	−3.22956	+	9.93955i	−0.262818	+	0.808870i	−0.992188	+	0.124751i	$0.960187\pi$
$152$		0			0
$153$	−19.5905	+	14.2333i	−1.58380	+	1.15069i
$154$		0			0
$155$	1.97355			0.158520
$156$		0			0
$157$	−3.62646	−	11.1611i	−0.289423	−	0.890752i	−0.985038	−	0.172337i	$-0.944868\pi$
$157$	−3.62646	−	11.1611i	−0.289423	−	0.890752i	0.695615	−	0.718415i	$-0.255132\pi$
$158$		0			0
$159$	−0.158057	−	0.114835i	−0.0125347	−	0.00910701i
$160$		0			0
$161$	−7.85366			−0.618955
$162$		0			0
$163$	−19.4105			−1.52035			−0.760176	−	0.649718i	$-0.774887\pi$
$163$	−19.4105			−1.52035			−0.760176	+	0.649718i	$0.774887\pi$
$164$		0			0
$165$	−0.0160955			−0.00125303
$166$		0			0
$167$	−17.7859			−1.37631			−0.688156	−	0.725563i	$-0.741579\pi$
$167$	−17.7859			−1.37631			−0.688156	+	0.725563i	$0.741579\pi$
$168$		0			0
$169$	10.4946	+	7.62478i	0.807278	+	0.586522i
$170$		0			0
$171$	−2.64646	−	8.14496i	−0.202380	−	0.622861i
$172$		0			0
$173$	3.76639			0.286353			0.143177	−	0.989697i	$-0.454268\pi$
$173$	3.76639			0.286353			0.143177	+	0.989697i	$0.454268\pi$
$174$		0			0
$175$	−3.64665	+	2.64945i	−0.275661	+	0.200279i
$176$		0			0
$177$	−0.0877716	+	0.270133i	−0.00659732	+	0.0203045i
$178$		0			0
$179$	5.92794	+	4.30690i	0.443075	+	0.321913i	0.786856	−	0.617137i	$-0.211708\pi$
$179$	5.92794	+	4.30690i	0.443075	+	0.321913i	−0.343780	+	0.939050i	$0.611708\pi$
$180$		0			0
$181$	7.87092	−	5.71856i	0.585041	−	0.425057i	−0.255497	−	0.966810i	$-0.582239\pi$
$181$	7.87092	−	5.71856i	0.585041	−	0.425057i	0.840538	+	0.541753i	$0.182239\pi$
$182$		0			0
$183$	−0.0382770	−	0.117804i	−0.00282952	−	0.00870836i
$184$		0			0
$185$	0.348966	+	1.07401i	0.0256565	+	0.0789625i
$186$		0			0
$187$	−2.72375	+	8.38284i	−0.199180	+	0.613014i
$188$		0			0
$189$	0.0389450	+	0.119860i	0.00283283	+	0.00871857i
$190$		0			0
$191$	−16.7539			−1.21227			−0.606134	−	0.795362i	$-0.707281\pi$
$191$	−16.7539			−1.21227			−0.606134	+	0.795362i	$0.707281\pi$
$192$		0			0
$193$	1.33764	+	0.971851i	0.0962853	+	0.0699554i	0.634886	−	0.772606i	$-0.281047\pi$
$193$	1.33764	+	0.971851i	0.0962853	+	0.0699554i	−0.538601	+	0.842561i	$0.681047\pi$
$194$		0			0
$195$	0.00199381	−	0.00144859i	0.000142780	−	0.000103736i
$196$		0			0
$197$	−2.60652	+	1.89375i	−0.185707	+	0.134924i	−0.676754	−	0.736209i	$-0.736614\pi$
$197$	−2.60652	+	1.89375i	−0.185707	+	0.134924i	0.491048	+	0.871133i	$0.336614\pi$
$198$		0			0
$199$	2.65665	−	8.17633i	0.188325	−	0.579605i	−0.811665	−	0.584124i	$-0.801438\pi$
$199$	2.65665	−	8.17633i	0.188325	−	0.579605i	0.999990	+	0.00451866i	$0.00143834\pi$
$200$		0			0
$201$	0.0681323	+	0.0495010i	0.00480568	+	0.00349153i
$202$		0			0
$203$	2.41471	−	7.43172i	0.169480	−	0.521605i
$204$		0			0
$205$	4.48163	+	0.327345i	0.313011	+	0.0228627i
$206$		0			0
$207$	−7.27967	+	22.4045i	−0.505972	+	1.55722i
$208$		0			0
$209$	−2.52196	−	1.83231i	−0.174448	−	0.126744i
$210$		0			0
$211$	0.938897	−	2.88963i	0.0646363	−	0.198930i	−0.913523	−	0.406787i	$-0.866649\pi$
$211$	0.938897	−	2.88963i	0.0646363	−	0.198930i	0.978159	+	0.207857i	$0.0666490\pi$
$212$		0			0
$213$	−0.114850	+	0.0834435i	−0.00786940	+	0.00571745i
$214$		0			0
$215$	3.30652	−	2.40233i	0.225503	−	0.163837i
$216$		0			0
$217$	−2.27513	−	1.65298i	−0.154446	−	0.112212i
$218$		0			0
$219$	0.245161			0.0165664
$220$		0			0
$221$	−0.417051	−	1.28355i	−0.0280539	−	0.0863409i
$222$		0			0
$223$	−1.99907	+	6.15251i	−0.133868	+	0.412003i	−0.995412	−	0.0956795i	$-0.969498\pi$
$223$	−1.99907	+	6.15251i	−0.133868	+	0.412003i	0.861544	+	0.507682i	$0.169498\pi$
$224$		0			0
$225$	4.17808	+	12.8588i	0.278538	+	0.857253i
$226$		0			0
$227$	8.27508	+	25.4681i	0.549236	+	1.69038i	0.710699	+	0.703496i	$0.248379\pi$
$227$	8.27508	+	25.4681i	0.549236	+	1.69038i	−0.161463	+	0.986879i	$0.551621\pi$
$228$		0			0
$229$	−9.99575	+	7.26234i	−0.660538	+	0.479909i	−0.866844	−	0.498579i	$-0.833856\pi$
$229$	−9.99575	+	7.26234i	−0.660538	+	0.479909i	0.206307	+	0.978487i	$0.433856\pi$
$230$		0			0
$231$	0.0185551	+	0.0134811i	0.00122084	+	0.000886989i
$232$		0			0
$233$	−5.46347	+	16.8148i	−0.357924	+	1.10158i	0.596371	+	0.802709i	$0.296609\pi$
$233$	−5.46347	+	16.8148i	−0.357924	+	1.10158i	−0.954295	+	0.298867i	$0.903391\pi$
$234$		0			0
$235$	1.42582	−	1.03592i	0.0930103	−	0.0675760i
$236$		0			0
$237$	0.0725070			0.00470984
$238$		0			0
$239$	5.60665	+	17.2555i	0.362664	+	1.11617i	0.951431	+	0.307862i	$0.0996136\pi$
$239$	5.60665	+	17.2555i	0.362664	+	1.11617i	−0.588767	+	0.808303i	$0.700386\pi$
$240$		0			0
$241$	−3.11806	−	2.26540i	−0.200852	−	0.145927i	0.482813	−	0.875723i	$-0.339615\pi$
$241$	−3.11806	−	2.26540i	−0.200852	−	0.145927i	−0.683665	+	0.729796i	$0.739615\pi$
$242$		0			0
$243$	0.567060			0.0363769
$244$		0			0
$245$	−0.701777			−0.0448349
$246$		0			0
$247$	0.477312			0.0303706
$248$		0			0
$249$	−0.0948891			−0.00601335
$250$		0			0
$251$	−12.1963	−	8.86114i	−0.769825	−	0.559310i	0.132083	−	0.991239i	$-0.457833\pi$
$251$	−12.1963	−	8.86114i	−0.769825	−	0.559310i	−0.901908	+	0.431928i	$0.857833\pi$
$252$		0			0
$253$	2.64978	+	8.15518i	0.166590	+	0.512712i
$254$		0			0
$255$	0.119009			0.00745263
$256$		0			0
$257$	−3.43578	+	2.49624i	−0.214318	+	0.155711i	−0.689765	−	0.724033i	$-0.742286\pi$
$257$	−3.43578	+	2.49624i	−0.214318	+	0.155711i	0.475447	+	0.879744i	$0.342286\pi$
$258$		0			0
$259$	0.497260	−	1.53041i	0.0308982	−	0.0950950i
$260$		0			0
$261$	−18.9626	−	13.7771i	−1.17376	−	0.852784i
$262$		0			0
$263$	11.5393	−	8.38382i	0.711546	−	0.516969i	−0.172126	−	0.985075i	$-0.555064\pi$
$263$	11.5393	−	8.38382i	0.711546	−	0.516969i	0.883672	+	0.468106i	$0.155064\pi$
$264$		0			0
$265$	−2.01691	−	6.20742i	−0.123898	−	0.381319i
$266$		0			0
$267$	−0.0833700	−	0.256587i	−0.00510216	−	0.0157028i
$268$		0			0
$269$	−7.14681	+	21.9956i	−0.435749	+	1.34110i	0.456569	+	0.889688i	$0.349078\pi$
$269$	−7.14681	+	21.9956i	−0.435749	+	1.34110i	−0.892317	+	0.451408i	$0.850922\pi$
$270$		0			0
$271$	3.61210	+	11.1169i	0.219419	+	0.675303i	0.998810	+	0.0487650i	$0.0155285\pi$
$271$	3.61210	+	11.1169i	0.219419	+	0.675303i	−0.779391	+	0.626538i	$0.784471\pi$
$272$		0			0
$273$	−0.00351178			−0.000212543
$274$		0			0
$275$	3.98153	+	2.89275i	0.240095	+	0.174439i
$276$		0			0
$277$	1.25179	−	0.909481i	0.0752130	−	0.0546454i	−0.549543	−	0.835465i	$-0.685198\pi$
$277$	1.25179	−	0.909481i	0.0752130	−	0.0546454i	0.624756	+	0.780820i	$0.285198\pi$
$278$		0			0
$279$	−6.82440	+	4.95822i	−0.408566	+	0.296841i
$280$		0			0
$281$	−1.69955	+	5.23069i	−0.101387	+	0.312037i	−0.988865	−	0.148812i	$-0.952455\pi$
$281$	−1.69955	+	5.23069i	−0.101387	+	0.312037i	0.887479	+	0.460849i	$0.152455\pi$
$282$		0			0
$283$	−15.5184	−	11.2748i	−0.922472	−	0.670215i	0.0216658	−	0.999765i	$-0.493103\pi$
$283$	−15.5184	−	11.2748i	−0.922472	−	0.670215i	−0.944138	+	0.329550i	$0.893103\pi$
$284$		0			0
$285$	−0.0130064	+	0.0400296i	−0.000770433	+	0.00237115i
$286$		0			0
$287$	−4.89230	−	4.13103i	−0.288783	−	0.243847i
$288$		0			0
$289$	14.8859	−	45.8141i	0.875641	−	2.69495i
$290$		0			0
$291$	−0.0138948	−	0.0100951i	−0.000814525	−	0.000591787i
$292$		0			0
$293$	−0.650578	+	2.00227i	−0.0380072	+	0.116974i	−0.968260	−	0.249945i	$-0.919587\pi$
$293$	−0.650578	+	2.00227i	−0.0380072	+	0.116974i	0.930253	+	0.366919i	$0.119587\pi$
$294$		0			0
$295$	−7.67676	+	5.57749i	−0.446958	+	0.324734i
$296$		0			0
$297$	0.111322	−	0.0808805i	0.00645958	−	0.00469316i
$298$		0			0
$299$	−1.06220	−	0.771734i	−0.0614286	−	0.0446305i
$300$		0			0
$301$	−5.82390			−0.335684
$302$		0			0
$303$	0.0571902	+	0.176013i	0.00328549	+	0.0101117i
$304$		0			0
$305$	1.27875	−	3.93560i	0.0732212	−	0.225352i
$306$		0			0
$307$	6.12884	+	18.8626i	0.349791	+	1.07655i	0.958968	+	0.283513i	$0.0914999\pi$
$307$	6.12884	+	18.8626i	0.349791	+	1.07655i	−0.609177	+	0.793034i	$0.708500\pi$
$308$		0			0
$309$	−0.0973242	−	0.299533i	−0.00553658	−	0.0170398i
$310$		0			0
$311$	7.63976	−	5.55061i	0.433211	−	0.314746i	−0.349721	−	0.936854i	$-0.613723\pi$
$311$	7.63976	−	5.55061i	0.433211	−	0.314746i	0.782932	+	0.622108i	$0.213723\pi$
$312$		0			0
$313$	−23.2332	−	16.8799i	−1.31322	−	0.954109i	−0.999990	−	0.00443156i	$-0.998589\pi$
$313$	−23.2332	−	16.8799i	−1.31322	−	0.954109i	−0.313229	−	0.949678i	$-0.601411\pi$
$314$		0			0
$315$	−0.650488	+	2.00200i	−0.0366508	+	0.112800i
$316$		0			0
$317$	2.12173	−	1.54152i	0.119168	−	0.0865806i	−0.526605	−	0.850110i	$-0.676535\pi$
$317$	2.12173	−	1.54152i	0.119168	−	0.0865806i	0.645773	+	0.763530i	$0.276535\pi$
$318$		0			0
$319$	−8.53175			−0.477686
$320$		0			0
$321$	−0.0693538	−	0.213449i	−0.00387095	−	0.0119136i
$322$		0			0
$323$	18.6472	+	13.5480i	1.03756	+	0.753828i
$324$		0			0
$325$	−0.753552			−0.0417996
$326$		0			0
$327$	0.243390			0.0134595
$328$		0			0
$329$	−2.51136			−0.138455
$330$		0			0
$331$	−22.0840			−1.21385			−0.606923	−	0.794761i	$-0.707596\pi$
$331$	−22.0840			−1.21385			−0.606923	+	0.794761i	$0.707596\pi$
$332$		0			0
$333$	−3.90496	−	2.83712i	−0.213990	−	0.155473i
$334$		0			0
$335$	0.869414	+	2.67578i	0.0475012	+	0.146194i
$336$		0			0
$337$	25.0025			1.36197			0.680986	−	0.732296i	$-0.261551\pi$
$337$	25.0025			1.36197			0.680986	+	0.732296i	$0.261551\pi$
$338$		0			0
$339$	0.110433	−	0.0802344i	0.00599791	−	0.00435773i
$340$		0			0
$341$	−0.948827	+	2.92019i	−0.0513819	+	0.158137i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$		0			0
$345$	0.0936655	−	0.0680520i	0.00504278	−	0.00366379i
$346$		0			0
$347$	−5.90724	−	18.1806i	−0.317117	−	0.975986i	−0.974874	−	0.222756i	$-0.928495\pi$
$347$	−5.90724	−	18.1806i	−0.317117	−	0.975986i	0.657757	−	0.753230i	$-0.271505\pi$
$348$		0			0
$349$	4.57040	+	14.0662i	0.244648	+	0.752948i	0.995694	+	0.0926990i	$0.0295494\pi$
$349$	4.57040	+	14.0662i	0.244648	+	0.752948i	−0.751046	+	0.660249i	$0.770451\pi$
$350$		0			0
$351$	−0.00651072	+	0.0200379i	−0.000347516	+	0.00106955i
$352$		0			0
$353$	8.78475	+	27.0367i	0.467565	+	1.43902i	0.855728	+	0.517426i	$0.173110\pi$
$353$	8.78475	+	27.0367i	0.467565	+	1.43902i	−0.388163	+	0.921591i	$0.626890\pi$
$354$		0			0
$355$	−4.74267			−0.251715
$356$		0			0
$357$	−0.137195	−	0.0996779i	−0.00726112	−	0.00527551i
$358$		0			0
$359$	0.242631	−	0.176282i	0.0128056	−	0.00930380i	−0.581364	−	0.813644i	$-0.697481\pi$
$359$	0.242631	−	0.176282i	0.0128056	−	0.00930380i	0.594170	+	0.804340i	$0.297481\pi$
$360$		0			0
$361$	8.77642	−	6.37645i	0.461917	−	0.335602i
$362$		0			0
$363$	−0.0636662	+	0.195944i	−0.00334161	+	0.0102844i
$364$		0			0
$365$	6.62610	+	4.81414i	0.346826	+	0.251984i
$366$		0			0
$367$	−5.24201	+	16.1332i	−0.273631	+	0.842148i	0.715948	+	0.698154i	$0.245995\pi$
$367$	−5.24201	+	16.1332i	−0.273631	+	0.842148i	−0.989578	+	0.143995i	$0.954005\pi$
$368$		0			0
$369$	−16.3195	+	10.1274i	−0.849561	+	0.527211i
$370$		0			0
$371$	−2.87401	+	8.84528i	−0.149211	+	0.459224i
$372$		0			0
$373$	17.1527	+	12.4622i	0.888135	+	0.645268i	0.935391	−	0.353615i	$-0.115048\pi$
$373$	17.1527	+	12.4622i	0.888135	+	0.645268i	−0.0472563	+	0.998883i	$0.515048\pi$
$374$		0			0
$375$	0.0433111	−	0.133298i	0.00223657	−	0.00688347i
$376$		0			0
$377$	1.05686	−	0.767854i	0.0544311	−	0.0395465i
$378$		0			0
$379$	24.9147	−	18.1016i	1.27978	−	0.929815i	0.280235	−	0.959931i	$-0.409588\pi$
$379$	24.9147	−	18.1016i	1.27978	−	0.929815i	0.999546	+	0.0301160i	$0.00958767\pi$
$380$		0			0
$381$	0.214716	+	0.156000i	0.0110002	+	0.00799212i
$382$		0			0
$383$	−6.97915			−0.356618			−0.178309	−	0.983975i	$-0.557063\pi$
$383$	−6.97915			−0.356618			−0.178309	+	0.983975i	$0.557063\pi$
$384$		0			0
$385$	0.236776	+	0.728720i	0.0120672	+	0.0371390i
$386$		0			0
$387$	−5.39826	+	16.6141i	−0.274409	+	0.844544i
$388$		0			0
$389$	9.02294	+	27.7697i	0.457481	+	1.40798i	0.868197	+	0.496219i	$0.165279\pi$
$389$	9.02294	+	27.7697i	0.457481	+	1.40798i	−0.410716	+	0.911763i	$0.634721\pi$
$390$		0			0
$391$	−19.5922	−	60.2987i	−0.990823	−	3.04944i
$392$		0			0
$393$	−0.328193	+	0.238446i	−0.0165552	+	0.0120280i
$394$		0			0
$395$	1.95969	+	1.42380i	0.0986025	+	0.0716389i
$396$		0			0
$397$	10.4611	−	32.1959i	0.525026	−	1.61586i	−0.239239	−	0.970961i	$-0.576898\pi$
$397$	10.4611	−	32.1959i	0.525026	−	1.61586i	0.764265	−	0.644903i	$-0.223102\pi$
$398$		0			0
$399$	0.0485214	−	0.0352529i	0.00242911	−	0.00176485i
$400$		0			0
$401$	−35.2484			−1.76022			−0.880111	−	0.474767i	$-0.842532\pi$
$401$	−35.2484			−1.76022			−0.880111	+	0.474767i	$0.842532\pi$
$402$		0			0
$403$	−0.145281	−	0.447129i	−0.00723696	−	0.0222731i
$404$		0			0
$405$	5.10749	+	3.71081i	0.253793	+	0.184392i
$406$		0			0
$407$	−1.75694			−0.0870882
$408$		0			0
$409$	9.72462			0.480851			0.240426	−	0.970668i	$-0.422713\pi$
$409$	9.72462			0.480851			0.240426	+	0.970668i	$0.422713\pi$
$410$		0			0
$411$	−0.00711595			−0.000351004
$412$		0			0
$413$	13.5214			0.665344
$414$		0			0
$415$	−2.56462	−	1.86330i	−0.125892	−	0.0914660i
$416$		0			0
$417$	−0.0812616	−	0.250097i	−0.00397940	−	0.0122473i
$418$		0			0
$419$	−19.4931			−0.952300			−0.476150	−	0.879364i	$-0.657968\pi$
$419$	−19.4931			−0.952300			−0.476150	+	0.879364i	$0.657968\pi$
$420$		0			0
$421$	7.12717	−	5.17820i	0.347357	−	0.252370i	−0.400402	−	0.916339i	$-0.631130\pi$
$421$	7.12717	−	5.17820i	0.347357	−	0.252370i	0.747760	+	0.663970i	$0.231130\pi$
$422$		0			0
$423$	−2.32781	+	7.16427i	−0.113182	+	0.348339i
$424$		0			0
$425$	−29.4391	−	21.3887i	−1.42800	−	1.03751i
$426$		0			0
$427$	−4.77049	+	3.46596i	−0.230860	+	0.167730i
$428$		0			0
$429$	0.00118485	+	0.00364661i	5.72053e−5	+	0.000176060i
$430$		0			0
$431$	0.0616941	+	0.189875i	0.00297170	+	0.00914595i	0.952531	−	0.304440i	$-0.0984695\pi$
$431$	0.0616941	+	0.189875i	0.00297170	+	0.00914595i	−0.949560	+	0.313586i	$0.898469\pi$
$432$		0			0
$433$	−3.13978	+	9.66326i	−0.150888	+	0.464387i	−0.997721	−	0.0674726i	$-0.978506\pi$
$433$	−3.13978	+	9.66326i	−0.150888	+	0.464387i	0.846833	+	0.531859i	$0.178506\pi$
$434$		0			0
$435$	0.0355971	+	0.109557i	0.00170675	+	0.00525284i
$436$		0			0
$437$	22.4232			1.07265
$438$		0			0
$439$	−18.0724	−	13.1304i	−0.862550	−	0.626679i	0.0660276	−	0.997818i	$-0.478967\pi$
$439$	−18.0724	−	13.1304i	−0.862550	−	0.626679i	−0.928577	+	0.371139i	$0.878967\pi$
$440$		0			0
$441$	2.42669	−	1.76310i	0.115557	−	0.0839570i
$442$		0			0
$443$	−25.4565	+	18.4953i	−1.20948	+	0.878736i	−0.995183	−	0.0980333i	$-0.968745\pi$
$443$	−25.4565	+	18.4953i	−1.20948	+	0.878736i	−0.214293	+	0.976769i	$0.568745\pi$
$444$		0			0
$445$	2.78522	−	8.57201i	0.132032	−	0.406352i
$446$		0			0
$447$	0.312103	+	0.226756i	0.0147619	+	0.0107252i
$448$		0			0
$449$	11.2257	−	34.5491i	0.529773	−	1.63047i	−0.224907	−	0.974380i	$-0.572208\pi$
$449$	11.2257	−	34.5491i	0.529773	−	1.63047i	0.754680	−	0.656093i	$-0.227792\pi$
$450$		0			0
$451$	−2.63900	+	6.47391i	−0.124265	+	0.304845i
$452$		0			0
$453$	−0.0678412	+	0.208794i	−0.00318746	+	0.00980998i
$454$		0			0
$455$	−0.0949148	−	0.0689596i	−0.00444967	−	0.00323288i
$456$		0			0
$457$	6.86607	−	21.1316i	0.321181	−	0.988494i	−0.651954	−	0.758259i	$-0.726050\pi$
$457$	6.86607	−	21.1316i	0.321181	−	0.988494i	0.973135	−	0.230235i	$-0.0739496\pi$
$458$		0			0
$459$	−0.823109	+	0.598023i	−0.0384194	+	0.0279133i
$460$		0			0
$461$	−14.4292	+	10.4834i	−0.672035	+	0.488262i	−0.870706	−	0.491804i	$-0.836338\pi$
$461$	−14.4292	+	10.4834i	−0.672035	+	0.488262i	0.198671	+	0.980066i	$0.436338\pi$
$462$		0			0
$463$	30.9974	+	22.5209i	1.44057	+	1.04664i	0.987923	+	0.154947i	$0.0495206\pi$
$463$	30.9974	+	22.5209i	1.44057	+	1.04664i	0.452648	+	0.891689i	$0.350479\pi$
$464$		0			0
$465$	0.0414571			0.00192253
$466$		0			0
$467$	−1.91961	−	5.90796i	−0.0888291	−	0.273388i	0.896767	−	0.442502i	$-0.145909\pi$
$467$	−1.91961	−	5.90796i	−0.0888291	−	0.273388i	−0.985596	+	0.169115i	$0.945909\pi$
$468$		0			0
$469$	1.23887	−	3.81286i	0.0572059	−	0.176062i
$470$		0			0
$471$	−0.0761786	−	0.234454i	−0.00351013	−	0.0108031i
$472$		0			0
$473$	1.96495	+	6.04750i	0.0903486	+	0.278064i
$474$		0			0
$475$	10.4116	−	7.56450i	0.477719	−	0.347083i
$476$		0			0
$477$	22.5694	+	16.3976i	1.03338	+	0.750796i
$478$		0			0
$479$	7.80810	−	24.0309i	0.356761	−	1.09800i	−0.598220	−	0.801332i	$-0.704125\pi$
$479$	7.80810	−	24.0309i	0.356761	−	1.09800i	0.954981	−	0.296666i	$-0.0958748\pi$
$480$		0			0
$481$	0.217638	−	0.158124i	0.00992346	−	0.00720981i
$482$		0			0
$483$	−0.164977			−0.00750670
$484$		0			0
$485$	−0.177306	−	0.545693i	−0.00805107	−	0.0247786i
$486$		0			0
$487$	34.7020	+	25.2125i	1.57250	+	1.14249i	0.924716	+	0.380658i	$0.124303\pi$
$487$	34.7020	+	25.2125i	1.57250	+	1.14249i	0.647780	+	0.761827i	$0.275697\pi$
$488$		0			0
$489$	−0.407744			−0.0184388
$490$		0			0
$491$	−10.1781			−0.459333			−0.229667	−	0.973269i	$-0.573764\pi$
$491$	−10.1781			−0.459333			−0.229667	+	0.973269i	$0.573764\pi$
$492$		0			0
$493$	63.0831			2.84112
$494$		0			0
$495$	2.29833			0.103302
$496$		0			0
$497$	5.46740	+	3.97230i	0.245247	+	0.178182i
$498$		0			0
$499$	13.6260	+	41.9366i	0.609985	+	1.87734i	0.457988	+	0.888958i	$0.348570\pi$
$499$	13.6260	+	41.9366i	0.609985	+	1.87734i	0.151996	+	0.988381i	$0.451430\pi$
$500$		0			0
$501$	−0.373616			−0.0166919
$502$		0			0
$503$	14.2267	−	10.3363i	0.634339	−	0.460875i	−0.223561	−	0.974690i	$-0.571768\pi$
$503$	14.2267	−	10.3363i	0.634339	−	0.460875i	0.857901	+	0.513815i	$0.171768\pi$
$504$		0			0
$505$	−1.91060	+	5.88023i	−0.0850207	+	0.261667i
$506$		0			0
$507$	0.220453	+	0.160169i	0.00979068	+	0.00711334i
$508$		0			0
$509$	5.86919	−	4.26421i	0.260147	−	0.189008i	−0.450065	−	0.892996i	$-0.648599\pi$
$509$	5.86919	−	4.26421i	0.260147	−	0.189008i	0.710212	+	0.703988i	$0.248599\pi$
$510$		0			0
$511$	−3.60648	−	11.0996i	−0.159541	−	0.491017i
$512$		0			0
$513$	−0.111193	−	0.342217i	−0.00490929	−	0.0151092i
$514$		0			0
$515$	3.25140	−	10.0068i	0.143274	−	0.440951i
$516$		0			0
$517$	0.847317	+	2.60777i	0.0372649	+	0.114690i
$518$		0			0
$519$	0.0791180			0.00347290
$520$		0			0
$521$	−16.5849	−	12.0496i	−0.726598	−	0.527904i	0.161887	−	0.986809i	$-0.448242\pi$
$521$	−16.5849	−	12.0496i	−0.726598	−	0.527904i	−0.888485	+	0.458905i	$0.848242\pi$
$522$		0			0
$523$	5.37714	−	3.90672i	0.235126	−	0.170829i	−0.463983	−	0.885844i	$-0.653580\pi$
$523$	5.37714	−	3.90672i	0.235126	−	0.170829i	0.699109	+	0.715015i	$0.253580\pi$
$524$		0			0
$525$	−0.0766028	+	0.0556552i	−0.00334322	+	0.00242899i
$526$		0			0
$527$	7.01555	−	21.5916i	0.305602	−	0.940547i
$528$		0			0
$529$	−31.2928	−	22.7355i	−1.36056	−	0.988501i
$530$		0			0
$531$	12.5332	−	38.5731i	0.543893	−	1.67393i
$532$		0			0
$533$	−0.255747	−	1.03946i	−0.0110776	−	0.0450238i
$534$		0			0
$535$	2.31696	−	7.13088i	0.100171	−	0.308295i
$536$		0			0
$537$	0.124524	+	0.0904723i	0.00537362	+	0.00390417i
$538$		0			0
$539$	0.337394	−	1.03839i	0.0145326	−	0.0447267i
$540$		0			0
$541$	33.7689	−	24.5345i	1.45184	−	1.05482i	0.466440	−	0.884553i	$-0.345537\pi$
$541$	33.7689	−	24.5345i	1.45184	−	1.05482i	0.985398	−	0.170268i	$-0.0544635\pi$
$542$		0			0
$543$	0.165339	−	0.120126i	0.00709538	−	0.00515510i
$544$		0			0
$545$	6.57824	+	4.77937i	0.281781	+	0.204726i
$546$		0			0
$547$	11.5951			0.495770			0.247885	−	0.968790i	$-0.420265\pi$
$547$	11.5951			0.495770			0.247885	+	0.968790i	$0.420265\pi$
$548$		0			0
$549$	5.46569	+	16.8217i	0.233270	+	0.717931i
$550$		0			0
$551$	−6.89431	+	21.2185i	−0.293707	+	0.903938i
$552$		0			0
$553$	−1.06663	−	3.28274i	−0.0453575	−	0.139596i
$554$		0			0
$555$	0.00733049	+	0.0225609i	0.000311162	+	0.000957659i
$556$		0			0
$557$	−20.8267	+	15.1315i	−0.882454	+	0.641141i	−0.933900	−	0.357535i	$-0.883617\pi$
$557$	−20.8267	+	15.1315i	−0.882454	+	0.641141i	0.0514453	+	0.998676i	$0.483617\pi$
$558$		0			0
$559$	−0.787678	−	0.572281i	−0.0333152	−	0.0242049i
$560$		0			0
$561$	−0.0572160	+	0.176093i	−0.00241566	+	0.00743465i
$562$		0			0
$563$	20.9807	−	15.2434i	0.884231	−	0.642431i	−0.0501368	−	0.998742i	$-0.515966\pi$
$563$	20.9807	−	15.2434i	0.884231	−	0.642431i	0.934367	+	0.356311i	$0.115966\pi$
$564$		0			0
$565$	4.56027			0.191852
$566$		0			0
$567$	−2.77993	−	8.55573i	−0.116746	−	0.359307i
$568$		0			0
$569$	−23.2352	−	16.8814i	−0.974072	−	0.707705i	−0.0176960	−	0.999843i	$-0.505633\pi$
$569$	−23.2352	−	16.8814i	−0.974072	−	0.707705i	−0.956376	+	0.292139i	$0.905633\pi$
$570$		0			0
$571$	3.74584			0.156758			0.0783792	−	0.996924i	$-0.475026\pi$
$571$	3.74584			0.156758			0.0783792	+	0.996924i	$0.475026\pi$
$572$		0			0
$573$	−0.351938			−0.0147024
$574$		0			0
$575$	−35.4004			−1.47630
$576$		0			0
$577$	−36.6243			−1.52469			−0.762344	−	0.647172i	$-0.775952\pi$
$577$	−36.6243			−1.52469			−0.762344	+	0.647172i	$0.775952\pi$
$578$		0			0
$579$	0.0280989	+	0.0204150i	0.00116775	+	0.000848420i
$580$		0			0
$581$	1.39588	+	4.29608i	0.0579109	+	0.178231i
$582$		0			0
$583$	10.1545			0.420558
$584$		0			0
$585$	−0.284702	+	0.206848i	−0.0117710	+	0.00855213i
$586$		0			0
$587$	−4.10327	+	12.6286i	−0.169360	+	0.521237i	−0.999331	−	0.0365695i	$-0.988357\pi$
$587$	−4.10327	+	12.6286i	−0.169360	+	0.521237i	0.829971	+	0.557807i	$0.188357\pi$
$588$		0			0
$589$	6.49580	+	4.71947i	0.267655	+	0.194462i
$590$		0			0
$591$	−0.0547535	+	0.0397807i	−0.00225226	+	0.00163636i
$592$		0			0
$593$	−6.84445	−	21.0650i	−0.281068	−	0.865038i	−0.987550	−	0.157307i	$-0.949719\pi$
$593$	−6.84445	−	21.0650i	−0.281068	−	0.865038i	0.706482	−	0.707731i	$-0.250281\pi$
$594$		0			0
$595$	−1.75070	−	5.38810i	−0.0717717	−	0.220890i
$596$		0			0
$597$	0.0558065	−	0.171755i	0.00228401	−	0.00702946i
$598$		0			0
$599$	11.7304	+	36.1024i	0.479291	+	1.47510i	0.840083	+	0.542458i	$0.182506\pi$
$599$	11.7304	+	36.1024i	0.479291	+	1.47510i	−0.360792	+	0.932646i	$0.617494\pi$
$600$		0			0
$601$	24.1576			0.985408			0.492704	−	0.870197i	$-0.336009\pi$
$601$	24.1576			0.985408			0.492704	+	0.870197i	$0.336009\pi$
$602$		0			0
$603$	−9.72882	−	7.06840i	−0.396188	−	0.287847i
$604$		0			0
$605$	−5.56844	+	4.04571i	−0.226389	+	0.164481i
$606$		0			0
$607$	15.1591	−	11.0137i	0.615289	−	0.447034i	−0.235984	−	0.971757i	$-0.575831\pi$
$607$	15.1591	−	11.0137i	0.615289	−	0.447034i	0.851273	+	0.524723i	$0.175831\pi$
$608$		0			0
$609$	0.0507243	−	0.156113i	0.00205545	−	0.00632603i
$610$		0			0
$611$	−0.339659	−	0.246776i	−0.0137411	−	0.00998350i
$612$		0			0
$613$	5.52064	−	16.9908i	0.222976	−	0.686251i	−0.775514	−	0.631330i	$-0.782509\pi$
$613$	5.52064	−	16.9908i	0.222976	−	0.686251i	0.998491	−	0.0549207i	$-0.0174906\pi$
$614$		0			0
$615$	0.0941426	+	0.00687631i	0.00379620	+	0.000277280i
$616$		0			0
$617$	0.659596	−	2.03003i	0.0265544	−	0.0817259i	−0.936901	−	0.349595i	$-0.886319\pi$
$617$	0.659596	−	2.03003i	0.0265544	−	0.0817259i	0.963455	+	0.267869i	$0.0863193\pi$
$618$		0			0
$619$	−30.2077	−	21.9472i	−1.21415	−	0.882132i	−0.218549	−	0.975826i	$-0.570132\pi$
$619$	−30.2077	−	21.9472i	−1.21415	−	0.882132i	−0.995601	+	0.0936942i	$0.970132\pi$
$620$		0			0
$621$	−0.305861	+	0.941344i	−0.0122738	+	0.0377748i
$622$		0			0
$623$	−10.3905	+	7.54911i	−0.416285	+	0.302449i
$624$		0			0
$625$	−14.4451	+	10.4950i	−0.577806	+	0.419800i
$626$		0			0
$627$	−0.0529771	−	0.0384902i	−0.00211570	−	0.00153715i
$628$		0			0
$629$	12.9907			0.517971
$630$		0			0
$631$	−2.80320	−	8.62736i	−0.111594	−	0.343450i	0.879628	−	0.475663i	$-0.157792\pi$
$631$	−2.80320	−	8.62736i	−0.111594	−	0.343450i	−0.991221	+	0.132213i	$0.957792\pi$
$632$		0			0
$633$	0.0197228	−	0.0607005i	0.000783910	−	0.00241263i
$634$		0			0
$635$	2.73992	+	8.43260i	0.108730	+	0.334637i
$636$		0			0
$637$	0.0516606	+	0.158995i	0.00204687	+	0.00629961i
$638$		0			0
$639$	16.3998	−	11.9151i	0.648766	−	0.471356i
$640$		0			0
$641$	−15.2407	−	11.0730i	−0.601972	−	0.437358i	0.244607	−	0.969622i	$-0.421341\pi$
$641$	−15.2407	−	11.0730i	−0.601972	−	0.437358i	−0.846578	+	0.532264i	$0.821341\pi$
$642$		0			0
$643$	−1.09984	+	3.38495i	−0.0433734	+	0.133490i	−0.970398	−	0.241510i	$-0.922357\pi$
$643$	−1.09984	+	3.38495i	−0.0433734	+	0.133490i	0.927025	+	0.375000i	$0.122357\pi$
$644$		0			0
$645$	0.0694579	−	0.0504641i	0.00273490	−	0.00198702i
$646$		0			0
$647$	31.4411			1.23608			0.618039	−	0.786147i	$-0.287927\pi$
$647$	31.4411			1.23608			0.618039	+	0.786147i	$0.287927\pi$
$648$		0			0
$649$	−4.56204	−	14.0405i	−0.179076	−	0.551138i
$650$		0			0
$651$	−0.0477923	−	0.0347231i	−0.00187313	−	0.00136091i
$652$		0			0
$653$	−39.8918			−1.56108			−0.780542	−	0.625103i	$-0.785057\pi$
$653$	−39.8918			−1.56108			−0.780542	+	0.625103i	$0.785057\pi$
$654$		0			0
$655$	−13.5525			−0.529542
$656$		0			0
$657$	−35.0073			−1.36576
$658$		0			0
$659$	50.1185			1.95234			0.976170	−	0.217007i	$-0.0696296\pi$
$659$	50.1185			1.95234			0.976170	+	0.217007i	$0.0696296\pi$
$660$		0			0
$661$	23.0775	+	16.7668i	0.897611	+	0.652153i	0.937851	−	0.347037i	$-0.112812\pi$
$661$	23.0775	+	16.7668i	0.897611	+	0.652153i	−0.0402403	+	0.999190i	$0.512812\pi$
$662$		0			0
$663$	−0.00876071	−	0.0269627i	−0.000340238	−	0.00104714i
$664$		0			0
$665$	2.00366			0.0776987
$666$		0			0
$667$	49.6493	−	36.0723i	1.92243	−	1.39673i
$668$		0			0
$669$	−0.0419932	+	0.129242i	−0.00162355	+	0.00499678i
$670$		0			0
$671$	5.20856	+	3.78424i	0.201074	+	0.146089i
$672$		0			0
$673$	−14.2452	+	10.3498i	−0.549114	+	0.398954i	−0.827459	−	0.561527i	$-0.810214\pi$
$673$	−14.2452	+	10.3498i	−0.549114	+	0.398954i	0.278345	+	0.960481i	$0.410214\pi$
$674$		0			0
$675$	0.175545	+	0.540272i	0.00675673	+	0.0207951i
$676$		0			0
$677$	2.49267	+	7.67165i	0.0958011	+	0.294846i	0.987462	−	0.157859i	$-0.0504592\pi$
$677$	2.49267	+	7.67165i	0.0958011	+	0.294846i	−0.891661	+	0.452705i	$0.850459\pi$
$678$		0			0
$679$	−0.252653	+	0.777587i	−0.00969595	+	0.0298411i
$680$		0			0
$681$	0.173829	+	0.534991i	0.00666115	+	0.0205009i
$682$		0			0
$683$	39.9016			1.52679			0.763396	−	0.645931i	$-0.223531\pi$
$683$	39.9016			1.52679			0.763396	+	0.645931i	$0.223531\pi$
$684$		0			0
$685$	−0.192327	−	0.139734i	−0.00734843	−	0.00533894i
$686$		0			0
$687$	−0.209974	+	0.152555i	−0.00801101	+	0.00582034i
$688$		0			0
$689$	−1.25788	+	0.913904i	−0.0479215	+	0.0348170i
$690$		0			0
$691$	6.66964	−	20.5270i	0.253725	−	0.780886i	−0.740353	−	0.672218i	$-0.765342\pi$
$691$	6.66964	−	20.5270i	0.253725	−	0.780886i	0.994078	−	0.108667i	$-0.0346584\pi$
$692$		0			0
$693$	−2.64954	−	1.92500i	−0.100648	−	0.0731248i
$694$		0			0
$695$	2.71478	−	8.35523i	0.102977	−	0.316932i
$696$		0			0
$697$	19.5125	−	47.8676i	0.739089	−	1.81311i
$698$		0			0
$699$	−0.114768	+	0.353218i	−0.00434091	+	0.0133599i
$700$		0			0
$701$	36.9488	+	26.8449i	1.39554	+	1.01392i	0.995232	+	0.0975353i	$0.0310959\pi$
$701$	36.9488	+	26.8449i	1.39554	+	1.01392i	0.400305	+	0.916382i	$0.368904\pi$
$702$		0			0
$703$	−1.41974	+	4.36951i	−0.0535465	+	0.164799i
$704$		0			0
$705$	0.0299513	−	0.0217609i	0.00112803	−	0.000819562i
$706$		0			0
$707$	7.12765	−	5.17854i	0.268063	−	0.194759i
$708$		0			0
$709$	17.2363	+	12.5229i	0.647323	+	0.470307i	0.862358	−	0.506299i	$-0.168987\pi$
$709$	17.2363	+	12.5229i	0.647323	+	0.470307i	−0.215035	+	0.976606i	$0.568987\pi$
$710$		0			0
$711$	−10.3535			−0.388286
$712$		0			0
$713$	−6.82502	−	21.0053i	−0.255599	−	0.786653i
$714$		0			0
$715$	−0.0395835	+	0.121825i	−0.00148034	+	0.00455601i
$716$		0			0
$717$	0.117775	+	0.362475i	0.00439840	+	0.0135369i
$718$		0			0
$719$	12.6798	+	39.0245i	0.472878	+	1.45537i	0.848799	+	0.528716i	$0.177326\pi$
$719$	12.6798	+	39.0245i	0.472878	+	1.45537i	−0.375921	+	0.926652i	$0.622674\pi$
$720$		0			0
$721$	−12.1296	+	8.81266i	−0.451729	+	0.328200i
$722$		0			0
$723$	−0.0654989	−	0.0475878i	−0.00243593	−	0.00176981i
$724$		0			0
$725$	10.8843	−	33.4985i	0.404234	−	1.24410i
$726$		0			0
$727$	5.18726	−	3.76877i	0.192385	−	0.139776i	−0.487423	−	0.873166i	$-0.662063\pi$
$727$	5.18726	−	3.76877i	0.192385	−	0.139776i	0.679808	+	0.733390i	$0.262063\pi$
$728$		0			0
$729$	−26.9762			−0.999118
$730$		0			0
$731$	−14.5287	−	44.7147i	−0.537363	−	1.65383i
$732$		0			0
$733$	27.8130	+	20.2073i	1.02730	+	0.746374i	0.967766	−	0.251852i	$-0.0810396\pi$
$733$	27.8130	+	20.2073i	1.02730	+	0.746374i	0.0595306	+	0.998226i	$0.481040\pi$
$734$		0			0
$735$	−0.0147418			−0.000543759
$736$		0			0
$737$	−4.37724			−0.161238
$738$		0			0
$739$	−15.6285			−0.574905			−0.287453	−	0.957795i	$-0.592808\pi$
$739$	−15.6285			−0.574905			−0.287453	+	0.957795i	$0.592808\pi$
$740$		0			0
$741$	0.0100266			0.000368335
$742$		0			0
$743$	−1.17188	−	0.851418i	−0.0429920	−	0.0312355i	0.566082	−	0.824349i	$-0.308459\pi$
$743$	−1.17188	−	0.851418i	−0.0429920	−	0.0312355i	−0.609074	+	0.793114i	$0.708459\pi$
$744$		0			0
$745$	3.98264	+	12.2573i	0.145913	+	0.449073i
$746$		0			0
$747$	13.5495			0.495750
$748$		0			0
$749$	−8.64361	+	6.27995i	−0.315831	+	0.229464i
$750$		0			0
$751$	2.61604	−	8.05134i	0.0954606	−	0.293798i	−0.891913	−	0.452207i	$-0.850637\pi$
$751$	2.61604	−	8.05134i	0.0954606	−	0.293798i	0.987373	+	0.158410i	$0.0506367\pi$
$752$		0			0
$753$	−0.256200	−	0.186140i	−0.00933645	−	0.00678333i
$754$		0			0
$755$	−5.93359	+	4.31101i	−0.215945	+	0.156894i
$756$		0			0
$757$	4.33257	+	13.3343i	0.157470	+	0.484642i	0.998403	−	0.0564970i	$-0.0179931\pi$
$757$	4.33257	+	13.3343i	0.157470	+	0.484642i	−0.840933	+	0.541139i	$0.817993\pi$
$758$		0			0
$759$	0.0556622	+	0.171311i	0.00202041	+	0.00621818i
$760$		0			0
$761$	−2.18485	+	6.72427i	−0.0792006	+	0.243754i	−0.982815	−	0.184592i	$-0.940904\pi$
$761$	−2.18485	+	6.72427i	−0.0792006	+	0.243754i	0.903615	+	0.428346i	$0.140904\pi$
$762$		0			0
$763$	−3.58043	−	11.0194i	−0.129620	−	0.398930i
$764$		0			0
$765$	−16.9936			−0.614406
$766$		0			0
$767$	1.82875	+	1.32867i	0.0660325	+	0.0479754i
$768$		0			0
$769$	−21.7945	+	15.8346i	−0.785930	+	0.571012i	−0.906753	−	0.421662i	$-0.861447\pi$
$769$	−21.7945	+	15.8346i	−0.785930	+	0.571012i	0.120823	+	0.992674i	$0.461447\pi$
$770$		0			0
$771$	−0.0721731	+	0.0524368i	−0.00259925	+	0.00188847i
$772$		0			0
$773$	14.2193	−	43.7626i	0.511434	−	1.57403i	−0.278245	−	0.960510i	$-0.589753\pi$
$773$	14.2193	−	43.7626i	0.511434	−	1.57403i	0.789678	−	0.613521i	$-0.210247\pi$
$774$		0			0
$775$	−10.2552	−	7.45083i	−0.368377	−	0.267642i
$776$		0			0
$777$	0.0104456	−	0.0321483i	0.000374734	−	0.00115331i
$778$		0			0
$779$	13.9681	+	11.7946i	0.500460	+	0.422586i
$780$		0			0
$781$	2.28014	−	7.01754i	0.0815897	−	0.251107i
$782$		0			0
$783$	−0.796729	−	0.578857i	−0.0284728	−	0.0206867i
$784$		0			0
$785$	2.54497	−	7.83260i	0.0908338	−	0.279558i
$786$		0			0
$787$	−6.95424	+	5.05255i	−0.247892	+	0.180104i	−0.704792	−	0.709414i	$-0.748960\pi$
$787$	−6.95424	+	5.05255i	−0.247892	+	0.180104i	0.456900	+	0.889518i	$0.348960\pi$
$788$		0			0
$789$	0.242399	−	0.176113i	0.00862965	−	0.00626980i
$790$		0			0
$791$	−5.25713	−	3.81953i	−0.186922	−	0.135807i
$792$		0			0
$793$	−0.985784			−0.0350062
$794$		0			0
$795$	−0.0423680	−	0.130395i	−0.00150264	−	0.00462464i
$796$		0			0
$797$	−3.43552	+	10.5734i	−0.121692	+	0.374530i	−0.993284	−	0.115702i	$-0.963088\pi$
$797$	−3.43552	+	10.5734i	−0.121692	+	0.374530i	0.871592	+	0.490233i	$0.163088\pi$
$798$		0			0
$799$	−6.26499	−	19.2817i	−0.221639	−	0.682136i
$800$		0			0
$801$	11.9047	+	36.6388i	0.420630	+	1.29457i
$802$		0			0
$803$	−10.3089	+	7.48988i	−0.363794	+	0.264312i
$804$		0			0
$805$	−4.45891	−	3.23959i	−0.157156	−	0.114181i
$806$		0			0
$807$	−0.150128	+	0.462048i	−0.00528477	+	0.0162648i
$808$		0			0
$809$	−24.5755	+	17.8551i	−0.864028	+	0.627753i	−0.928978	−	0.370136i	$-0.879311\pi$
$809$	−24.5755	+	17.8551i	−0.864028	+	0.627753i	0.0649501	+	0.997889i	$0.479311\pi$
$810$		0			0
$811$	−20.3412			−0.714278			−0.357139	−	0.934051i	$-0.616248\pi$
$811$	−20.3412			−0.714278			−0.357139	+	0.934051i	$0.616248\pi$
$812$		0			0
$813$	0.0758769	+	0.233525i	0.00266112	+	0.00819008i
$814$		0			0
$815$	−11.0203	−	8.00674i	−0.386025	−	0.280464i
$816$		0			0
$817$	16.6280			0.581739
$818$		0			0
$819$	0.501458			0.0175223
$820$		0			0
$821$	−25.6563			−0.895413			−0.447706	−	0.894181i	$-0.647759\pi$
$821$	−25.6563			−0.895413			−0.447706	+	0.894181i	$0.647759\pi$
$822$		0			0
$823$	9.63142			0.335730			0.167865	−	0.985810i	$-0.446313\pi$
$823$	9.63142			0.335730			0.167865	+	0.985810i	$0.446313\pi$
$824$		0			0
$825$	0.0836373	+	0.0607660i	0.00291188	+	0.00211560i
$826$		0			0
$827$	2.78227	+	8.56293i	0.0967489	+	0.297762i	0.987706	−	0.156326i	$-0.0499650\pi$
$827$	2.78227	+	8.56293i	0.0967489	+	0.297762i	−0.890957	+	0.454088i	$0.849965\pi$
$828$		0			0
$829$	−32.8982			−1.14260			−0.571301	−	0.820741i	$-0.693561\pi$
$829$	−32.8982			−1.14260			−0.571301	+	0.820741i	$0.693561\pi$
$830$		0			0
$831$	0.0262956	−	0.0191049i	0.000912185	−	0.000662741i
$832$		0			0
$833$	−2.49466	+	7.67779i	−0.0864350	+	0.266020i
$834$		0			0
$835$	−10.0979	−	7.33657i	−0.349453	−	0.253892i
$836$		0			0
$837$	−0.286732	+	0.208323i	−0.00991092	+	0.00720071i
$838$		0			0
$839$	10.4679	+	32.2167i	0.361391	+	1.11225i	0.952211	+	0.305442i	$0.0988043\pi$
$839$	10.4679	+	32.2167i	0.361391	+	1.11225i	−0.590820	+	0.806803i	$0.701196\pi$
$840$		0			0
$841$	9.90749	+	30.4921i	0.341637	+	1.05145i
$842$		0			0
$843$	−0.0357014	+	0.109878i	−0.00122962	+	0.00378439i
$844$		0			0
$845$	2.81313	+	8.65794i	0.0967747	+	0.297842i
$846$		0			0
$847$	9.80791			0.337004
$848$		0			0
$849$	−0.325985	−	0.236842i	−0.0111878	−	0.00812838i
$850$		0			0
$851$	10.2242	−	7.42834i	0.350482	−	0.254640i
$852$		0			0
$853$	2.16276	−	1.57134i	0.0740515	−	0.0538015i	−0.550144	−	0.835070i	$-0.685427\pi$
$853$	2.16276	−	1.57134i	0.0740515	−	0.0538015i	0.624195	+	0.781269i	$0.285427\pi$
$854$		0			0
$855$	1.85722	−	5.71595i	0.0635157	−	0.195481i
$856$		0			0
$857$	3.22093	+	2.34014i	0.110025	+	0.0799376i	0.641437	−	0.767176i	$-0.278339\pi$
$857$	3.22093	+	2.34014i	0.110025	+	0.0799376i	−0.531412	+	0.847113i	$0.678339\pi$
$858$		0			0
$859$	−6.31736	+	19.4428i	−0.215545	+	0.663381i	0.783569	+	0.621305i	$0.213397\pi$
$859$	−6.31736	+	19.4428i	−0.215545	+	0.663381i	−0.999114	+	0.0420759i	$0.986603\pi$
$860$		0			0
$861$	−0.102769	−	0.0867778i	−0.00350237	−	0.00295738i
$862$		0			0
$863$	2.38706	−	7.34662i	0.0812565	−	0.250082i	−0.902172	−	0.431375i	$-0.858028\pi$
$863$	2.38706	−	7.34662i	0.0812565	−	0.250082i	0.983429	+	0.181294i	$0.0580284\pi$
$864$		0			0
$865$	2.13837	+	1.55361i	0.0727066	+	0.0528245i
$866$		0			0
$867$	0.312698	−	0.962386i	0.0106198	−	0.0326844i
$868$		0			0
$869$	−3.04890	+	2.21515i	−0.103427	+	0.0751439i
$870$		0			0
$871$	0.542225	−	0.393949i	0.0183726	−	0.0133485i
$872$		0			0
$873$	1.98407	+	1.44151i	0.0671507	+	0.0487878i
$874$		0			0
$875$	−6.67215			−0.225560
$876$		0			0
$877$	6.18491	+	19.0352i	0.208850	+	0.642773i	0.999533	+	0.0305483i	$0.00972535\pi$
$877$	6.18491	+	19.0352i	0.208850	+	0.642773i	−0.790684	+	0.612225i	$0.790275\pi$
$878$		0			0
$879$	−0.0136663	+	0.0420605i	−0.000460952	+	0.00141866i
$880$		0			0
$881$	−5.47888	−	16.8623i	−0.184588	−	0.568104i	0.815353	−	0.578964i	$-0.196543\pi$
$881$	−5.47888	−	16.8623i	−0.184588	−	0.568104i	−0.999941	+	0.0108602i	$0.996543\pi$
$882$		0			0
$883$	−12.9008	−	39.7045i	−0.434146	−	1.33616i	−0.893959	−	0.448148i	$-0.852084\pi$
$883$	−12.9008	−	39.7045i	−0.434146	−	1.33616i	0.459813	−	0.888016i	$-0.347916\pi$
$884$		0			0
$885$	−0.161261	+	0.117163i	−0.00542072	+	0.00393838i
$886$		0			0
$887$	23.0816	+	16.7698i	0.775005	+	0.563074i	0.903476	−	0.428639i	$-0.141007\pi$
$887$	23.0816	+	16.7698i	0.775005	+	0.563074i	−0.128471	+	0.991713i	$0.541007\pi$
$888$		0			0
$889$	3.90425	−	12.0161i	0.130944	−	0.403006i
$890$		0			0
$891$	−7.94628	+	5.77331i	−0.266210	+	0.193413i
$892$		0			0
$893$	7.17023			0.239943
$894$		0			0
$895$	1.58902	+	4.89049i	0.0531149	+	0.163471i
$896$		0			0
$897$	−0.0223129	−	0.0162113i	−0.000745008	−	0.000541280i
$898$		0			0
$899$	21.9752			0.732913
$900$		0			0
$901$	−75.0819			−2.50134
$902$		0			0
$903$	−0.122339			−0.00407118
$904$		0			0
$905$	6.82758			0.226957
$906$		0			0
$907$	30.7821	+	22.3645i	1.02210	+	0.742602i	0.966713	−	0.255863i	$-0.0823594\pi$
$907$	30.7821	+	22.3645i	1.02210	+	0.742602i	0.0553911	+	0.998465i	$0.482359\pi$
$908$		0			0
$909$	−8.16636	−	25.1335i	−0.270861	−	0.833624i
$910$		0			0
$911$	−9.31754			−0.308704			−0.154352	−	0.988016i	$-0.549329\pi$
$911$	−9.31754			−0.308704			−0.154352	+	0.988016i	$0.549329\pi$
$912$		0			0
$913$	3.99005	−	2.89894i	0.132052	−	0.0959410i
$914$		0			0
$915$	0.0268619	−	0.0826725i	0.000888028	−	0.00273307i
$916$		0			0
$917$	15.6235	+	11.3512i	0.515934	+	0.374848i
$918$		0			0
$919$	6.15602	−	4.47261i	0.203068	−	0.147538i	−0.481604	−	0.876389i	$-0.659945\pi$
$919$	6.15602	−	4.47261i	0.203068	−	0.147538i	0.684672	+	0.728851i	$0.259945\pi$
$920$		0			0
$921$	0.128745	+	0.396235i	0.00424228	+	0.0130564i
$922$		0			0
$923$	0.349126	+	1.07450i	0.0114916	+	0.0353676i
$924$		0			0
$925$	2.24140	−	6.89833i	0.0736969	−	0.226816i
$926$		0			0
$927$	13.8972	+	42.7712i	0.456445	+	1.40479i
$928$		0			0
$929$	26.0486			0.854626			0.427313	−	0.904104i	$-0.359460\pi$
$929$	26.0486			0.854626			0.427313	+	0.904104i	$0.359460\pi$
$930$		0			0
$931$	−2.30985	−	1.67820i	−0.0757021	−	0.0550008i
$932$		0			0
$933$	0.160483	−	0.116598i	0.00525399	−	0.00381725i
$934$		0			0
$935$	−5.00429	+	3.63583i	−0.163658	+	0.118904i
$936$		0			0
$937$	−5.68685	+	17.5023i	−0.185781	+	0.571776i	−0.999961	−	0.00883724i	$-0.997187\pi$
$937$	−5.68685	+	17.5023i	−0.185781	+	0.571776i	0.814180	+	0.580613i	$0.197187\pi$
$938$		0			0
$939$	−0.488045	−	0.354585i	−0.0159267	−	0.0115715i
$940$		0			0
$941$	−9.15801	+	28.1854i	−0.298542	+	0.918819i	0.683466	+	0.729982i	$0.260472\pi$
$941$	−9.15801	+	28.1854i	−0.298542	+	0.918819i	−0.982008	+	0.188837i	$0.939528\pi$
$942$		0			0
$943$	−12.0145	−	48.8317i	−0.391246	−	1.59018i
$944$		0			0
$945$	−0.0273307	+	0.0841154i	−0.000889069	+	0.00273627i
$946$		0			0
$947$	32.1238	+	23.3393i	1.04388	+	0.758426i	0.971040	−	0.238917i	$-0.0767924\pi$
$947$	32.1238	+	23.3393i	1.04388	+	0.758426i	0.0728443	+	0.997343i	$0.476792\pi$
$948$		0			0
$949$	0.602920	−	1.85560i	0.0195716	−	0.0602353i
$950$		0			0
$951$	0.0445697	−	0.0323818i	0.00144527	−	0.00105005i
$952$		0			0
$953$	−42.0198	+	30.5292i	−1.36115	+	0.988937i	−0.362784	+	0.931873i	$0.618174\pi$
$953$	−42.0198	+	30.5292i	−1.36115	+	0.988937i	−0.998371	+	0.0570636i	$0.981826\pi$
$954$		0			0
$955$	−9.51202	−	6.91089i	−0.307802	−	0.223631i
$956$		0			0
$957$	−0.179221			−0.00579339
$958$		0			0
$959$	0.104680	+	0.322173i	0.00338030	+	0.0104035i
$960$		0			0
$961$	−7.13564	+	21.9612i	−0.230182	+	0.708427i
$962$		0			0
$963$	9.90324	+	30.4790i	0.319127	+	0.982173i
$964$		0			0
$965$	0.358561	+	1.10354i	0.0115425	+	0.0355241i
$966$		0			0
$967$	1.76452	−	1.28200i	0.0567431	−	0.0412262i	−0.559052	−	0.829132i	$-0.688835\pi$
$967$	1.76452	−	1.28200i	0.0567431	−	0.0412262i	0.615795	+	0.787906i	$0.288835\pi$
$968$		0			0
$969$	0.391709	+	0.284593i	0.0125835	+	0.00914244i
$970$		0			0
$971$	7.06742	−	21.7513i	0.226804	−	0.698032i	−0.771299	−	0.636473i	$-0.780393\pi$
$971$	7.06742	−	21.7513i	0.226804	−	0.698032i	0.998103	−	0.0615593i	$-0.0196073\pi$
$972$		0			0
$973$	−10.1277	+	7.35819i	−0.324679	+	0.235893i
$974$		0			0
$975$	−0.0158294			−0.000506946
$976$		0			0
$977$	3.48826	+	10.7358i	0.111599	+	0.343467i	0.991223	−	0.132204i	$-0.0422053\pi$
$977$	3.48826	+	10.7358i	0.111599	+	0.343467i	−0.879623	+	0.475671i	$0.842205\pi$
$978$		0			0
$979$	11.3446	+	8.24235i	0.362576	+	0.263427i
$980$		0			0
$981$	−34.7544			−1.10962
$982$		0			0
$983$	−61.5039			−1.96167			−0.980835	−	0.194841i	$-0.937581\pi$
$983$	−61.5039			−1.96167			−0.980835	+	0.194841i	$0.937581\pi$
$984$		0			0
$985$	−2.26101			−0.0720418
$986$		0			0
$987$	−0.0527544			−0.00167919
$988$		0			0
$989$	−37.0036	−	26.8847i	−1.17665	−	0.854883i
$990$		0			0
$991$	12.1888	+	37.5134i	0.387191	+	1.19165i	0.934878	+	0.354968i	$0.115508\pi$
$991$	12.1888	+	37.5134i	0.387191	+	1.19165i	−0.547687	+	0.836683i	$0.684492\pi$
$992$		0			0
$993$	−0.463904			−0.0147215
$994$		0			0
$995$	4.88101	−	3.54626i	0.154738	−	0.112424i
$996$		0			0
$997$	−5.74899	+	17.6936i	−0.182072	+	0.560361i	−0.999886	−	0.0151225i	$-0.995186\pi$
$997$	−5.74899	+	17.6936i	−0.182072	+	0.560361i	0.817813	+	0.575484i	$0.195186\pi$
$998$		0			0
$999$	−0.164070	−	0.119204i	−0.00519094	−	0.00377144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.c.57.3	✓	16
41.18	even	5	inner	1148.2.n.c.141.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.c.57.3	✓	16	1.1	even	1	trivial
1148.2.n.c.141.3	yes	16	41.18	even	5	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.0210063 q^{3} +(0.567750 + 0.412494i) q^{5} +(-0.309017 - 0.951057i) q^{7} -2.99956 q^{9} +O(q^{10})\)	\(q+0.0210063 q^{3} +(0.567750 + 0.412494i) q^{5} +(-0.309017 - 0.951057i) q^{7} -2.99956 q^{9} +(-0.883310 + 0.641762i) q^{11} +(0.0516606 - 0.158995i) q^{13} +(0.0119263 + 0.00866500i) q^{15} +(6.53112 - 4.74513i) q^{17} +(0.882282 + 2.71539i) q^{19} +(-0.00649132 - 0.0199782i) q^{21} +(2.42691 - 7.46928i) q^{23} +(-1.39290 - 4.28690i) q^{25} -0.126029 q^{27} +(6.32180 + 4.59306i) q^{29} +(2.27513 - 1.65298i) q^{31} +(-0.0185551 + 0.0134811i) q^{33} +(0.216861 - 0.667430i) q^{35} +(1.30184 + 0.945845i) q^{37} +(0.00108520 - 0.00333990i) q^{39} +(5.44065 - 3.37630i) q^{41} +(1.79969 - 5.53886i) q^{43} +(-1.70300 - 1.23730i) q^{45} +(0.776051 - 2.38844i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(0.137195 - 0.0996779i) q^{51} +(-7.52425 - 5.46668i) q^{53} -0.766222 q^{55} +(0.0185335 + 0.0570403i) q^{57} +(-4.17834 + 12.8596i) q^{59} +(-1.82216 - 5.60804i) q^{61} +(0.926915 + 2.85275i) q^{63} +(0.0949148 - 0.0689596i) q^{65} +(3.24342 + 2.35648i) q^{67} +(0.0509806 - 0.156902i) q^{69} +(-5.46740 + 3.97230i) q^{71} +11.6708 q^{73} +(-0.0292597 - 0.0900520i) q^{75} +(0.883310 + 0.641762i) q^{77} +3.45167 q^{79} +8.99603 q^{81} -4.51716 q^{83} +5.66538 q^{85} +(0.132798 + 0.0964833i) q^{87} +(-3.96880 - 12.2147i) q^{89} -0.167177 q^{91} +(0.0477923 - 0.0347231i) q^{93} +(-0.619166 + 1.90560i) q^{95} +(-0.661455 - 0.480575i) q^{97} +(2.64954 - 1.92500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - q^{17} + 15 q^{19} + 2 q^{21} + 27 q^{23} - 3 q^{25} + 28 q^{27} - q^{29} - 14 q^{31} - 13 q^{33} - 12 q^{35} - 16 q^{37} + 10 q^{39} + 26 q^{41} + 5 q^{43} - 9 q^{45} - 14 q^{47} - 4 q^{49} + 4 q^{51} - 20 q^{53} + 10 q^{55} - 13 q^{57} - 47 q^{61} + 3 q^{63} - 29 q^{65} - 27 q^{67} + 15 q^{69} - 11 q^{71} + 70 q^{73} + 14 q^{75} + q^{77} + 30 q^{79} - 72 q^{81} - 78 q^{83} + 72 q^{85} + 21 q^{87} + 17 q^{89} - 24 q^{91} - 7 q^{93} + 27 q^{95} - 17 q^{97} + 13 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 13 * q^5 + 4 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - q^17 + 15 * q^19 + 2 * q^21 + 27 * q^23 - 3 * q^25 + 28 * q^27 - q^29 - 14 * q^31 - 13 * q^33 - 12 * q^35 - 16 * q^37 + 10 * q^39 + 26 * q^41 + 5 * q^43 - 9 * q^45 - 14 * q^47 - 4 * q^49 + 4 * q^51 - 20 * q^53 + 10 * q^55 - 13 * q^57 - 47 * q^61 + 3 * q^63 - 29 * q^65 - 27 * q^67 + 15 * q^69 - 11 * q^71 + 70 * q^73 + 14 * q^75 + q^77 + 30 * q^79 - 72 * q^81 - 78 * q^83 + 72 * q^85 + 21 * q^87 + 17 * q^89 - 24 * q^91 - 7 * q^93 + 27 * q^95 - 17 * q^97 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more