LMFDB - Embedded newform 1148.2.n.c.953.1

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			953.1
Root			$-0.567301 - 1.74597i$ of defining polynomial
Character	$\chi$	$=$	1148.953
Dual form			1148.2.n.c.365.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83583 q^{3} +(-0.827871 - 2.54793i) q^{5} +(0.809017 - 0.587785i) q^{7} +0.370254 q^{9} +O(q^{10})$	\(q-1.83583 q^{3} +(-0.827871 - 2.54793i) q^{5} +(0.809017 - 0.587785i) q^{7} +0.370254 q^{9} +(1.94954 - 6.00008i) q^{11} +(0.351849 + 0.255633i) q^{13} +(1.51983 + 4.67755i) q^{15} +(0.180162 - 0.554482i) q^{17} +(-2.50151 + 1.81746i) q^{19} +(-1.48521 + 1.07907i) q^{21} +(1.79954 + 1.30744i) q^{23} +(-1.76147 + 1.27978i) q^{25} +4.82775 q^{27} +(-3.02275 - 9.30307i) q^{29} +(-0.0253864 + 0.0781312i) q^{31} +(-3.57902 + 11.0151i) q^{33} +(-2.16740 - 1.57471i) q^{35} +(3.69772 + 11.3804i) q^{37} +(-0.645933 - 0.469298i) q^{39} +(-1.88183 + 6.12035i) q^{41} +(-8.95206 - 6.50405i) q^{43} +(-0.306523 - 0.943380i) q^{45} +(-6.20261 - 4.50646i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.330746 + 1.01793i) q^{51} +(0.110542 + 0.340212i) q^{53} -16.9017 q^{55} +(4.59234 - 3.33653i) q^{57} +(-0.818866 - 0.594941i) q^{59} +(-9.84501 + 7.15282i) q^{61} +(0.299542 - 0.217630i) q^{63} +(0.360049 - 1.10812i) q^{65} +(-4.33273 - 13.3348i) q^{67} +(-3.30364 - 2.40024i) q^{69} +(0.898027 - 2.76384i) q^{71} -0.150047 q^{73} +(3.23376 - 2.34946i) q^{75} +(-1.94954 - 6.00008i) q^{77} +3.22512 q^{79} -9.97367 q^{81} -5.55513 q^{83} -1.56193 q^{85} +(5.54924 + 17.0788i) q^{87} +(-12.6415 + 9.18459i) q^{89} +0.434909 q^{91} +(0.0466049 - 0.143435i) q^{93} +(6.70167 + 4.86905i) q^{95} +(3.68068 + 11.3280i) q^{97} +(0.721827 - 2.22155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

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

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
$3$	−1.83583			−1.05991			−0.529957	−	0.848024i	$-0.677792\pi$
$3$	−1.83583			−1.05991			−0.529957	+	0.848024i	$0.677792\pi$
$4$		0			0
$5$	−0.827871	−	2.54793i	−0.370235	−	1.13947i	−0.946637	−	0.322301i	$-0.895544\pi$
$5$	−0.827871	−	2.54793i	−0.370235	−	1.13947i	0.576402	−	0.817166i	$-0.304456\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$		0			0
$9$	0.370254			0.123418
$10$		0			0
$11$	1.94954	−	6.00008i	0.587810	−	1.80909i	0.000128806	−	1.00000i	$-0.499959\pi$
$11$	1.94954	−	6.00008i	0.587810	−	1.80909i	0.587681	−	0.809093i	$-0.300041\pi$
$12$		0			0
$13$	0.351849	+	0.255633i	0.0975853	+	0.0708998i	0.635508	−	0.772094i	$-0.280791\pi$
$13$	0.351849	+	0.255633i	0.0975853	+	0.0708998i	−0.537923	+	0.842994i	$0.680791\pi$
$14$		0			0
$15$	1.51983	+	4.67755i	0.392418	+	1.20774i
$16$		0			0
$17$	0.180162	−	0.554482i	0.0436957	−	0.134482i	−0.926829	−	0.375484i	$-0.877476\pi$
$17$	0.180162	−	0.554482i	0.0436957	−	0.134482i	0.970524	+	0.241003i	$0.0774763\pi$
$18$		0			0
$19$	−2.50151	+	1.81746i	−0.573886	+	0.416953i	−0.836515	−	0.547944i	$-0.815411\pi$
$19$	−2.50151	+	1.81746i	−0.573886	+	0.416953i	0.262629	+	0.964897i	$0.415411\pi$
$20$		0			0
$21$	−1.48521	+	1.07907i	−0.324100	+	0.235473i
$22$		0			0
$23$	1.79954	+	1.30744i	0.375230	+	0.272621i	0.759376	−	0.650651i	$-0.225504\pi$
$23$	1.79954	+	1.30744i	0.375230	+	0.272621i	−0.384146	+	0.923272i	$0.625504\pi$
$24$		0			0
$25$	−1.76147	+	1.27978i	−0.352294	+	0.255957i
$26$		0			0
$27$	4.82775			0.929102
$28$		0			0
$29$	−3.02275	−	9.30307i	−0.561311	−	1.72754i	−0.678666	−	0.734447i	$-0.737442\pi$
$29$	−3.02275	−	9.30307i	−0.561311	−	1.72754i	0.117355	−	0.993090i	$-0.462558\pi$
$30$		0			0
$31$	−0.0253864	+	0.0781312i	−0.00455952	+	0.0140328i	−0.953310	−	0.301992i	$-0.902348\pi$
$31$	−0.0253864	+	0.0781312i	−0.00455952	+	0.0140328i	0.948751	+	0.316025i	$0.102348\pi$
$32$		0			0
$33$	−3.57902	+	11.0151i	−0.623028	+	1.91748i
$34$		0			0
$35$	−2.16740	−	1.57471i	−0.366357	−	0.266174i
$36$		0			0
$37$	3.69772	+	11.3804i	0.607901	+	1.87093i	0.475466	+	0.879734i	$0.342280\pi$
$37$	3.69772	+	11.3804i	0.607901	+	1.87093i	0.132435	+	0.991192i	$0.457720\pi$
$38$		0			0
$39$	−0.645933	−	0.469298i	−0.103432	−	0.0751477i
$40$		0			0
$41$	−1.88183	+	6.12035i	−0.293892	+	0.955839i
$41$	−1.88183	+	6.12035i	−0.293892	+	0.955839i
$42$		0			0
$43$	−8.95206	−	6.50405i	−1.36518	−	0.991859i	−0.998097	−	0.0616697i	$-0.980357\pi$
$43$	−8.95206	−	6.50405i	−1.36518	−	0.991859i	−0.367080	−	0.930189i	$-0.619643\pi$
$44$		0			0
$45$	−0.306523	−	0.943380i	−0.0456937	−	0.140631i
$46$		0			0
$47$	−6.20261	−	4.50646i	−0.904744	−	0.657335i	0.0349365	−	0.999390i	$-0.488877\pi$
$47$	−6.20261	−	4.50646i	−0.904744	−	0.657335i	−0.939680	+	0.342055i	$0.888877\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$		0			0
$51$	−0.330746	+	1.01793i	−0.0463137	+	0.142539i
$52$		0			0
$53$	0.110542	+	0.340212i	0.0151841	+	0.0467318i	0.958361	−	0.285558i	$-0.0921789\pi$
$53$	0.110542	+	0.340212i	0.0151841	+	0.0467318i	−0.943177	+	0.332290i	$0.892179\pi$
$54$		0			0
$55$	−16.9017			−2.27903
$56$		0			0
$57$	4.59234	−	3.33653i	0.608270	−	0.441934i
$58$		0			0
$59$	−0.818866	−	0.594941i	−0.106607	−	0.0774547i	0.533204	−	0.845986i	$-0.320988\pi$
$59$	−0.818866	−	0.594941i	−0.106607	−	0.0774547i	−0.639812	+	0.768532i	$0.720988\pi$
$60$		0			0
$61$	−9.84501	+	7.15282i	−1.26052	+	0.915825i	−0.998783	−	0.0493132i	$-0.984297\pi$
$61$	−9.84501	+	7.15282i	−1.26052	+	0.915825i	−0.261741	+	0.965138i	$0.584297\pi$
$62$		0			0
$63$	0.299542	−	0.217630i	0.0377387	−	0.0274188i
$64$		0			0
$65$	0.360049	−	1.10812i	0.0446585	−	0.137445i
$66$		0			0
$67$	−4.33273	−	13.3348i	−0.529327	−	1.62910i	−0.755598	−	0.655036i	$-0.772653\pi$
$67$	−4.33273	−	13.3348i	−0.529327	−	1.62910i	0.226271	−	0.974064i	$-0.427347\pi$
$68$		0			0
$69$	−3.30364	−	2.40024i	−0.397712	−	0.288955i
$70$		0			0
$71$	0.898027	−	2.76384i	0.106576	−	0.328008i	−0.883521	−	0.468392i	$-0.844834\pi$
$71$	0.898027	−	2.76384i	0.106576	−	0.328008i	0.990097	+	0.140384i	$0.0448336\pi$
$72$		0			0
$73$	−0.150047			−0.0175617			−0.00878083	−	0.999961i	$-0.502795\pi$
$73$	−0.150047			−0.0175617			−0.00878083	+	0.999961i	$0.502795\pi$
$74$		0			0
$75$	3.23376	−	2.34946i	0.373402	−	0.271292i
$76$		0			0
$77$	−1.94954	−	6.00008i	−0.222171	−	0.683773i
$78$		0			0
$79$	3.22512			0.362854			0.181427	−	0.983404i	$-0.441928\pi$
$79$	3.22512			0.362854			0.181427	+	0.983404i	$0.441928\pi$
$80$		0			0
$81$	−9.97367			−1.10819
$82$		0			0
$83$	−5.55513			−0.609755			−0.304878	−	0.952392i	$-0.598616\pi$
$83$	−5.55513			−0.609755			−0.304878	+	0.952392i	$0.598616\pi$
$84$		0			0
$85$	−1.56193			−0.169415
$86$		0			0
$87$	5.54924	+	17.0788i	0.594941	+	1.83104i
$88$		0			0
$89$	−12.6415	+	9.18459i	−1.34000	+	0.973565i	−0.340553	+	0.940225i	$0.610614\pi$
$89$	−12.6415	+	9.18459i	−1.34000	+	0.973565i	−0.999444	+	0.0333393i	$0.989386\pi$
$90$		0			0
$91$	0.434909			0.0455908
$92$		0			0
$93$	0.0466049	−	0.143435i	0.00483270	−	0.0148735i
$94$		0			0
$95$	6.70167	+	4.86905i	0.687577	+	0.499554i
$96$		0			0
$97$	3.68068	+	11.3280i	0.373716	+	1.15018i	0.944341	+	0.328969i	$0.106701\pi$
$97$	3.68068	+	11.3280i	0.373716	+	1.15018i	−0.570625	+	0.821211i	$0.693299\pi$
$98$		0			0
$99$	0.721827	−	2.22155i	0.0725463	−	0.223275i
$100$		0			0
$101$	1.32446	−	0.962274i	0.131788	−	0.0957499i	−0.519938	−	0.854204i	$-0.674045\pi$
$101$	1.32446	−	0.962274i	0.131788	−	0.0957499i	0.651727	+	0.758454i	$0.274045\pi$
$102$		0			0
$103$	−3.35147	+	2.43498i	−0.330230	+	0.239926i	−0.740528	−	0.672025i	$-0.765425\pi$
$103$	−3.35147	+	2.43498i	−0.330230	+	0.239926i	0.410298	+	0.911951i	$0.365425\pi$
$104$		0			0
$105$	3.97896	+	2.89088i	0.388307	+	0.282121i
$106$		0			0
$107$	4.50605	−	3.27383i	0.435616	−	0.316494i	−0.348275	−	0.937393i	$-0.613232\pi$
$107$	4.50605	−	3.27383i	0.435616	−	0.316494i	0.783891	+	0.620899i	$0.213232\pi$
$108$		0			0
$109$	4.10375			0.393068			0.196534	−	0.980497i	$-0.437031\pi$
$109$	4.10375			0.393068			0.196534	+	0.980497i	$0.437031\pi$
$110$		0			0
$111$	−6.78836	−	20.8924i	−0.644323	−	1.98302i
$112$		0			0
$113$	−2.99768	+	9.22592i	−0.281998	+	0.867901i	0.705284	+	0.708925i	$0.250819\pi$
$113$	−2.99768	+	9.22592i	−0.281998	+	0.867901i	−0.987282	+	0.158976i	$0.949181\pi$
$114$		0			0
$115$	1.84148	−	5.66750i	0.171719	−	0.528497i
$116$		0			0
$117$	0.130273	+	0.0946492i	0.0120438	+	0.00875032i
$118$		0			0
$119$	−0.180162	−	0.554482i	−0.0165154	−	0.0508293i
$120$		0			0
$121$	−23.3011	−	16.9292i	−2.11828	−	1.53902i
$122$		0			0
$123$	3.45470	−	11.2359i	0.311500	−	1.01311i
$124$		0			0
$125$	−6.11791	−	4.44492i	−0.547202	−	0.397566i
$126$		0			0
$127$	3.03157	+	9.33020i	0.269008	+	0.827922i	0.990743	+	0.135752i	$0.0433450\pi$
$127$	3.03157	+	9.33020i	0.269008	+	0.827922i	−0.721735	+	0.692170i	$0.756655\pi$
$128$		0			0
$129$	16.4344	+	11.9403i	1.44697	+	1.05129i
$130$		0			0
$131$	5.72067	−	17.6064i	0.499817	−	1.53828i	−0.309495	−	0.950901i	$-0.600160\pi$
$131$	5.72067	−	17.6064i	0.499817	−	1.53828i	0.809312	−	0.587378i	$-0.199840\pi$
$132$		0			0
$133$	−0.955493	+	2.94070i	−0.0828517	+	0.254991i
$134$		0			0
$135$	−3.99676	−	12.3008i	−0.343986	−	1.05868i
$136$		0			0
$137$	19.0052			1.62373			0.811863	−	0.583848i	$-0.198454\pi$
$137$	19.0052			1.62373			0.811863	+	0.583848i	$0.198454\pi$
$138$		0			0
$139$	4.90355	−	3.56263i	0.415913	−	0.302179i	−0.360078	−	0.932922i	$-0.617250\pi$
$139$	4.90355	−	3.56263i	0.415913	−	0.302179i	0.775991	+	0.630743i	$0.217250\pi$
$140$		0			0
$141$	11.3869	+	8.27307i	0.958950	+	0.696718i
$142$		0			0
$143$	2.21976	−	1.61275i	0.185626	−	0.134865i
$144$		0			0
$145$	−21.2011	+	15.4035i	−1.76065	+	1.27919i
$146$		0			0
$147$	−0.567301	+	1.74597i	−0.0467902	+	0.144005i
$148$		0			0
$149$	3.23919	+	9.96919i	0.265365	+	0.816708i	0.991609	+	0.129272i	$0.0412640\pi$
$149$	3.23919	+	9.96919i	0.265365	+	0.816708i	−0.726245	+	0.687436i	$0.758736\pi$
$150$		0			0
$151$	−9.73946	−	7.07614i	−0.792586	−	0.575848i	0.116144	−	0.993232i	$-0.462947\pi$
$151$	−9.73946	−	7.07614i	−0.792586	−	0.575848i	−0.908730	+	0.417385i	$0.862947\pi$
$152$		0			0
$153$	0.0667057	−	0.205299i	0.00539284	−	0.0165975i
$154$		0			0
$155$	0.220089			0.0176780
$156$		0			0
$157$	9.97256	−	7.24549i	0.795897	−	0.578253i	−0.113811	−	0.993502i	$-0.536306\pi$
$157$	9.97256	−	7.24549i	0.795897	−	0.578253i	0.909707	+	0.415250i	$0.136306\pi$
$158$		0			0
$159$	−0.202935	−	0.624571i	−0.0160938	−	0.0495317i
$160$		0			0
$161$	2.22436			0.175304
$162$		0			0
$163$	−6.81179			−0.533541			−0.266770	−	0.963760i	$-0.585957\pi$
$163$	−6.81179			−0.533541			−0.266770	+	0.963760i	$0.585957\pi$
$164$		0			0
$165$	31.0286			2.41558
$166$		0			0
$167$	2.89739			0.224207			0.112104	−	0.993697i	$-0.464241\pi$
$167$	2.89739			0.224207			0.112104	+	0.993697i	$0.464241\pi$
$168$		0			0
$169$	−3.95877	−	12.1838i	−0.304521	−	0.937219i
$170$		0			0
$171$	−0.926195	+	0.672920i	−0.0708279	+	0.0514595i
$172$		0			0
$173$	10.6572			0.810249			0.405124	−	0.914262i	$-0.367228\pi$
$173$	10.6572			0.810249			0.405124	+	0.914262i	$0.367228\pi$
$174$		0			0
$175$	−0.672823	+	2.07074i	−0.0508606	+	0.156533i
$176$		0			0
$177$	1.50329	+	1.09221i	0.112995	+	0.0820953i
$178$		0			0
$179$	7.35510	+	22.6367i	0.549746	+	1.69194i	0.709430	+	0.704776i	$0.248953\pi$
$179$	7.35510	+	22.6367i	0.549746	+	1.69194i	−0.159684	+	0.987168i	$0.551047\pi$
$180$		0			0
$181$	−5.62884	+	17.3238i	−0.418388	+	1.28767i	0.490796	+	0.871274i	$0.336706\pi$
$181$	−5.62884	+	17.3238i	−0.418388	+	1.28767i	−0.909185	+	0.416393i	$0.863294\pi$
$182$		0			0
$183$	18.0737	−	13.1313i	1.33605	−	0.970696i
$184$		0			0
$185$	25.9352	−	18.8430i	1.90679	−	1.38537i
$186$		0			0
$187$	−2.97570	−	2.16197i	−0.217605	−	0.158099i
$188$		0			0
$189$	3.90573	−	2.83768i	0.284100	−	0.206411i
$190$		0			0
$191$	−11.7683			−0.851526			−0.425763	−	0.904835i	$-0.639994\pi$
$191$	−11.7683			−0.851526			−0.425763	+	0.904835i	$0.639994\pi$
$192$		0			0
$193$	−1.76065	−	5.41871i	−0.126734	−	0.390047i	0.867479	−	0.497474i	$-0.165739\pi$
$193$	−1.76065	−	5.41871i	−0.126734	−	0.390047i	−0.994213	+	0.107427i	$0.965739\pi$
$194$		0			0
$195$	−0.660986	+	2.03431i	−0.0473342	+	0.145680i
$196$		0			0
$197$	7.05012	−	21.6980i	0.502300	−	1.54592i	−0.302962	−	0.953003i	$-0.597976\pi$
$197$	7.05012	−	21.6980i	0.502300	−	1.54592i	0.805262	−	0.592919i	$-0.202024\pi$
$198$		0			0
$199$	−3.63084	−	2.63796i	−0.257384	−	0.187000i	0.451609	−	0.892216i	$-0.350850\pi$
$199$	−3.63084	−	2.63796i	−0.257384	−	0.187000i	−0.708993	+	0.705216i	$0.750850\pi$
$200$		0			0
$201$	7.95413	+	24.4803i	0.561041	+	1.72671i
$202$		0			0
$203$	−7.91367	−	5.74961i	−0.555430	−	0.403544i
$204$		0			0
$205$	17.1521	−	0.272115i	1.19796	−	0.0190053i
$206$		0			0
$207$	0.666288	+	0.484086i	0.0463102	+	0.0336463i
$208$		0			0
$209$	6.02807	+	18.5525i	0.416970	+	1.28330i
$210$		0			0
$211$	14.0611	+	10.2160i	0.968003	+	0.703295i	0.954996	−	0.296620i	$-0.0958595\pi$
$211$	14.0611	+	10.2160i	0.968003	+	0.703295i	0.0130075	+	0.999915i	$0.495859\pi$
$212$		0			0
$213$	−1.64862	+	5.07393i	−0.112962	+	0.347660i
$214$		0			0
$215$	−9.16069	+	28.1937i	−0.624754	+	1.92280i
$216$		0			0
$217$	0.0253864	+	0.0781312i	0.00172334	+	0.00530389i
$218$		0			0
$219$	0.275460			0.0186139
$220$		0			0
$221$	0.205134	−	0.149038i	0.0137988	−	0.0100254i
$222$		0			0
$223$	−13.0532	−	9.48369i	−0.874105	−	0.635075i	0.0575802	−	0.998341i	$-0.481662\pi$
$223$	−13.0532	−	9.48369i	−0.874105	−	0.635075i	−0.931685	+	0.363266i	$0.881662\pi$
$224$		0			0
$225$	−0.652192	+	0.473845i	−0.0434795	+	0.0315897i
$226$		0			0
$227$	1.43908	−	1.04555i	0.0955150	−	0.0693957i	−0.539003	−	0.842304i	$-0.681199\pi$
$227$	1.43908	−	1.04555i	0.0955150	−	0.0693957i	0.634518	+	0.772908i	$0.281199\pi$
$228$		0			0
$229$	−0.383958	+	1.18170i	−0.0253727	+	0.0780891i	−0.962941	−	0.269712i	$-0.913072\pi$
$229$	−0.383958	+	1.18170i	−0.0253727	+	0.0780891i	0.937568	+	0.347801i	$0.113072\pi$
$230$		0			0
$231$	3.57902	+	11.0151i	0.235482	+	0.724740i
$232$		0			0
$233$	5.12757	+	3.72540i	0.335919	+	0.244059i	0.742938	−	0.669360i	$-0.233432\pi$
$233$	5.12757	+	3.72540i	0.335919	+	0.244059i	−0.407019	+	0.913420i	$0.633432\pi$
$234$		0			0
$235$	−6.34716	+	19.5346i	−0.414043	+	1.27429i
$236$		0			0
$237$	−5.92076			−0.384594
$238$		0			0
$239$	−1.91983	+	1.39483i	−0.124183	+	0.0902244i	−0.648143	−	0.761519i	$-0.724454\pi$
$239$	−1.91983	+	1.39483i	−0.124183	+	0.0902244i	0.523960	+	0.851743i	$0.324454\pi$
$240$		0			0
$241$	5.86479	+	18.0500i	0.377784	+	1.16270i	0.941581	+	0.336786i	$0.109340\pi$
$241$	5.86479	+	18.0500i	0.377784	+	1.16270i	−0.563797	+	0.825913i	$0.690660\pi$
$242$		0			0
$243$	3.82666			0.245480
$244$		0			0
$245$	−2.67905			−0.171158
$246$		0			0
$247$	−1.34476			−0.0855647
$248$		0			0
$249$	10.1983			0.646288
$250$		0			0
$251$	5.98554	+	18.4216i	0.377804	+	1.16276i	0.941567	+	0.336824i	$0.109353\pi$
$251$	5.98554	+	18.4216i	0.377804	+	1.16276i	−0.563764	+	0.825936i	$0.690647\pi$
$252$		0			0
$253$	11.3531	−	8.24848i	0.713761	−	0.518577i
$254$		0			0
$255$	2.86743			0.179565
$256$		0			0
$257$	−4.80418	+	14.7857i	−0.299676	+	0.922309i	0.681934	+	0.731414i	$0.261139\pi$
$257$	−4.80418	+	14.7857i	−0.299676	+	0.922309i	−0.981610	+	0.190895i	$0.938861\pi$
$258$		0			0
$259$	9.68075	+	7.03347i	0.601532	+	0.437039i
$260$		0			0
$261$	−1.11919	−	3.44450i	−0.0692759	−	0.213209i
$262$		0			0
$263$	3.80421	−	11.7082i	0.234578	−	0.721956i	−0.762600	−	0.646871i	$-0.776077\pi$
$263$	3.80421	−	11.7082i	0.234578	−	0.721956i	0.997177	−	0.0750848i	$-0.0239227\pi$
$264$		0			0
$265$	0.775322	−	0.563304i	0.0476276	−	0.0346035i
$266$		0			0
$267$	23.2076	−	16.8613i	1.42028	−	1.03190i
$268$		0			0
$269$	−17.6089	−	12.7936i	−1.07364	−	0.780042i	−0.0970730	−	0.995277i	$-0.530948\pi$
$269$	−17.6089	−	12.7936i	−1.07364	−	0.780042i	−0.976562	+	0.215236i	$0.930948\pi$
$270$		0			0
$271$	17.2248	−	12.5145i	1.04633	−	0.760205i	0.0748204	−	0.997197i	$-0.476162\pi$
$271$	17.2248	−	12.5145i	1.04633	−	0.760205i	0.971512	+	0.236992i	$0.0761616\pi$
$272$		0			0
$273$	−0.798417			−0.0483224
$274$		0			0
$275$	4.24474	+	13.0640i	0.255968	+	0.787787i
$276$		0			0
$277$	6.64220	−	20.4426i	0.399091	−	1.22828i	−0.526638	−	0.850089i	$-0.676548\pi$
$277$	6.64220	−	20.4426i	0.399091	−	1.22828i	0.925729	−	0.378187i	$-0.123452\pi$
$278$		0			0
$279$	−0.00939940	+	0.0289284i	−0.000562727	+	0.00173190i
$280$		0			0
$281$	−10.8258	−	7.86544i	−0.645816	−	0.469213i	0.216027	−	0.976387i	$-0.430690\pi$
$281$	−10.8258	−	7.86544i	−0.645816	−	0.469213i	−0.861843	+	0.507175i	$0.830690\pi$
$282$		0			0
$283$	−3.03057	−	9.32715i	−0.180149	−	0.554441i	0.819682	−	0.572818i	$-0.194150\pi$
$283$	−3.03057	−	9.32715i	−0.180149	−	0.554441i	−0.999831	+	0.0183772i	$0.994150\pi$
$284$		0			0
$285$	−12.3031	−	8.93873i	−0.728773	−	0.529484i
$286$		0			0
$287$	2.07503	+	6.05758i	0.122485	+	0.357568i
$288$		0			0
$289$	13.4783	+	9.79256i	0.792841	+	0.576033i
$290$		0			0
$291$	−6.75708	−	20.7962i	−0.396107	−	1.21909i
$292$		0			0
$293$	4.34987	+	3.16037i	0.254122	+	0.184631i	0.707552	−	0.706661i	$-0.249800\pi$
$293$	4.34987	+	3.16037i	0.254122	+	0.184631i	−0.453429	+	0.891292i	$0.649800\pi$
$294$		0			0
$295$	−0.837950	+	2.57894i	−0.0487873	+	0.150152i
$296$		0			0
$297$	9.41192	−	28.9669i	0.546135	−	1.68083i
$298$		0			0
$299$	0.298941	+	0.920045i	0.0172882	+	0.0532076i
$300$		0			0
$301$	−11.0654			−0.637797
$302$		0			0
$303$	−2.43147	+	1.76657i	−0.139684	+	0.101487i
$304$		0			0
$305$	26.3753	+	19.1628i	1.51024	+	1.09726i
$306$		0			0
$307$	21.2518	−	15.4403i	1.21290	−	0.881226i	0.217413	−	0.976080i	$-0.430238\pi$
$307$	21.2518	−	15.4403i	1.21290	−	0.881226i	0.995491	+	0.0948533i	$0.0302382\pi$
$308$		0			0
$309$	6.15271	−	4.47021i	0.350015	−	0.254301i
$310$		0			0
$311$	8.29843	−	25.5400i	0.470561	−	1.44824i	−0.381291	−	0.924455i	$-0.624520\pi$
$311$	8.29843	−	25.5400i	0.470561	−	1.44824i	0.851852	−	0.523783i	$-0.175480\pi$
$312$		0			0
$313$	−8.26792	−	25.4460i	−0.467330	−	1.43830i	−0.856028	−	0.516930i	$-0.827075\pi$
$313$	−8.26792	−	25.4460i	−0.467330	−	1.43830i	0.388697	−	0.921365i	$-0.372925\pi$
$314$		0			0
$315$	−0.802487	−	0.583041i	−0.0452150	−	0.0328506i
$316$		0			0
$317$	2.25839	−	6.95061i	0.126844	−	0.390385i	−0.867389	−	0.497631i	$-0.834203\pi$
$317$	2.25839	−	6.95061i	0.126844	−	0.390385i	0.994233	+	0.107246i	$0.0342033\pi$
$318$		0			0
$319$	−61.7122			−3.45522
$320$		0			0
$321$	−8.27231	+	6.01019i	−0.461716	+	0.335456i
$322$		0			0
$323$	0.557068	+	1.71448i	0.0309961	+	0.0953962i
$324$		0			0
$325$	−0.946927			−0.0525261
$326$		0			0
$327$	−7.53376			−0.416618
$328$		0			0
$329$	−7.66685			−0.422687
$330$		0			0
$331$	1.54130			0.0847173			0.0423587	−	0.999102i	$-0.486513\pi$
$331$	1.54130			0.0847173			0.0423587	+	0.999102i	$0.486513\pi$
$332$		0			0
$333$	1.36909	+	4.21364i	0.0750259	+	0.230906i
$334$		0			0
$335$	−30.3890	+	22.0789i	−1.66033	+	1.20630i
$336$		0			0
$337$	27.5616			1.50138			0.750688	−	0.660657i	$-0.229722\pi$
$337$	27.5616			1.50138			0.750688	+	0.660657i	$0.229722\pi$
$338$		0			0
$339$	5.50322	−	16.9372i	0.298894	−	0.919901i
$340$		0			0
$341$	0.419302	+	0.304640i	0.0227064	+	0.0164972i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$		0			0
$345$	−3.38064	+	10.4045i	−0.182007	+	0.560161i
$346$		0			0
$347$	9.20934	−	6.69098i	0.494383	−	0.359190i	−0.312484	−	0.949923i	$-0.601161\pi$
$347$	9.20934	−	6.69098i	0.494383	−	0.359190i	0.806867	+	0.590733i	$0.201161\pi$
$348$		0			0
$349$	0.927709	−	0.674020i	0.0496591	−	0.0360794i	−0.562679	−	0.826676i	$-0.690229\pi$
$349$	0.927709	−	0.674020i	0.0496591	−	0.0360794i	0.612338	+	0.790596i	$0.290229\pi$
$350$		0			0
$351$	1.69864	+	1.23413i	0.0906666	+	0.0658732i
$352$		0			0
$353$	−6.70816	+	4.87377i	−0.357039	+	0.259404i	−0.751816	−	0.659373i	$-0.770822\pi$
$353$	−6.70816	+	4.87377i	−0.357039	+	0.259404i	0.394777	+	0.918777i	$0.370822\pi$
$354$		0			0
$355$	−7.78552			−0.413213
$356$		0			0
$357$	0.330746	+	1.01793i	0.0175049	+	0.0538747i
$358$		0			0
$359$	1.33326	−	4.10337i	0.0703670	−	0.216567i	−0.909689	−	0.415291i	$-0.863680\pi$
$359$	1.33326	−	4.10337i	0.0703670	−	0.216567i	0.980056	+	0.198724i	$0.0636797\pi$
$360$		0			0
$361$	−2.91690	+	8.97730i	−0.153521	+	0.472489i
$362$		0			0
$363$	42.7767	+	31.0791i	2.24519	+	1.63123i
$364$		0			0
$365$	0.124220	+	0.382309i	0.00650195	+	0.0200109i
$366$		0			0
$367$	−20.7024	−	15.0412i	−1.08066	−	0.785143i	−0.102859	−	0.994696i	$-0.532799\pi$
$367$	−20.7024	−	15.0412i	−1.08066	−	0.785143i	−0.977797	+	0.209553i	$0.932799\pi$
$368$		0			0
$369$	−0.696753	+	2.26609i	−0.0362715	+	0.117968i
$370$		0			0
$371$	0.289402	+	0.210263i	0.0150250	+	0.0109163i
$372$		0			0
$373$	−2.16477	−	6.66249i	−0.112088	−	0.344971i	0.879241	−	0.476378i	$-0.158051\pi$
$373$	−2.16477	−	6.66249i	−0.112088	−	0.344971i	−0.991328	+	0.131407i	$0.958051\pi$
$374$		0			0
$375$	11.2314	+	8.16010i	0.579988	+	0.421386i
$376$		0			0
$377$	1.31462	−	4.04599i	0.0677064	−	0.208379i
$378$		0			0
$379$	−4.18871	+	12.8915i	−0.215159	+	0.662193i	0.783983	+	0.620783i	$0.213185\pi$
$379$	−4.18871	+	12.8915i	−0.215159	+	0.662193i	−0.999142	+	0.0414102i	$0.986815\pi$
$380$		0			0
$381$	−5.56543	−	17.1286i	−0.285125	−	0.877526i
$382$		0			0
$383$	7.82662			0.399922			0.199961	−	0.979804i	$-0.435918\pi$
$383$	7.82662			0.399922			0.199961	+	0.979804i	$0.435918\pi$
$384$		0			0
$385$	−13.6738	+	9.93459i	−0.696881	+	0.506314i
$386$		0			0
$387$	−3.31454	−	2.40815i	−0.168487	−	0.122413i
$388$		0			0
$389$	13.9014	−	10.1000i	0.704830	−	0.512089i	−0.176672	−	0.984270i	$-0.556533\pi$
$389$	13.9014	−	10.1000i	0.704830	−	0.512089i	0.881502	+	0.472181i	$0.156533\pi$
$390$		0			0
$391$	1.04916	−	0.762261i	0.0530584	−	0.0385492i
$392$		0			0
$393$	−10.5022	+	32.3223i	−0.529763	+	1.63044i
$394$		0			0
$395$	−2.66998	−	8.21737i	−0.134341	−	0.413461i
$396$		0			0
$397$	−25.9460	−	18.8509i	−1.30219	−	0.946098i	−0.302218	−	0.953239i	$-0.597727\pi$
$397$	−25.9460	−	18.8509i	−1.30219	−	0.946098i	−0.999975	+	0.00714087i	$0.997727\pi$
$398$		0			0
$399$	1.75412	−	5.39862i	0.0878157	−	0.270269i
$400$		0			0
$401$	−15.8996			−0.793987			−0.396994	−	0.917821i	$-0.629946\pi$
$401$	−15.8996			−0.793987			−0.396994	+	0.917821i	$0.629946\pi$
$402$		0			0
$403$	−0.0289051	+	0.0210008i	−0.00143986	+	0.00104612i
$404$		0			0
$405$	8.25692	+	25.4122i	0.410290	+	1.26274i
$406$		0			0
$407$	75.4922			3.74201
$408$		0			0
$409$	−25.9715			−1.28421			−0.642105	−	0.766617i	$-0.721939\pi$
$409$	−25.9715			−1.28421			−0.642105	+	0.766617i	$0.721939\pi$
$410$		0			0
$411$	−34.8903			−1.72101
$412$		0			0
$413$	−1.01217			−0.0498058
$414$		0			0
$415$	4.59894	+	14.1541i	0.225753	+	0.694796i
$416$		0			0
$417$	−9.00205	+	6.54037i	−0.440832	+	0.320283i
$418$		0			0
$419$	−35.1970			−1.71949			−0.859743	−	0.510726i	$-0.829377\pi$
$419$	−35.1970			−1.71949			−0.859743	+	0.510726i	$0.829377\pi$
$420$		0			0
$421$	−5.25491	+	16.1730i	−0.256109	+	0.788222i	0.737500	+	0.675347i	$0.236006\pi$
$421$	−5.25491	+	16.1730i	−0.256109	+	0.788222i	−0.993609	+	0.112875i	$0.963994\pi$
$422$		0			0
$423$	−2.29654	−	1.66853i	−0.111662	−	0.0811269i
$424$		0			0
$425$	0.392267	+	1.20727i	0.0190277	+	0.0585613i
$426$		0			0
$427$	−3.76046	+	11.5735i	−0.181981	+	0.560081i
$428$		0			0
$429$	−4.07510	+	2.96073i	−0.196748	+	0.142945i
$430$		0			0
$431$	−10.1754	+	7.39286i	−0.490131	+	0.356101i	−0.805235	−	0.592956i	$-0.797961\pi$
$431$	−10.1754	+	7.39286i	−0.490131	+	0.356101i	0.315103	+	0.949057i	$0.397961\pi$
$432$		0			0
$433$	−26.5432	−	19.2848i	−1.27559	−	0.926767i	−0.276175	−	0.961107i	$-0.589067\pi$
$433$	−26.5432	−	19.2848i	−1.27559	−	0.926767i	−0.999410	+	0.0343406i	$0.989067\pi$
$434$		0			0
$435$	38.9215	−	28.2781i	1.86614	−	1.35583i
$436$		0			0
$437$	−6.87780			−0.329010
$438$		0			0
$439$	−3.38626	−	10.4218i	−0.161617	−	0.497407i	0.837154	−	0.546967i	$-0.184218\pi$
$439$	−3.38626	−	10.4218i	−0.161617	−	0.497407i	−0.998771	+	0.0495607i	$0.984218\pi$
$440$		0			0
$441$	0.114415	−	0.352133i	0.00544832	−	0.0167682i
$442$		0			0
$443$	−7.88972	+	24.2821i	−0.374852	+	1.15368i	0.568726	+	0.822527i	$0.307436\pi$
$443$	−7.88972	+	24.2821i	−0.374852	+	1.15368i	−0.943578	+	0.331149i	$0.892564\pi$
$444$		0			0
$445$	33.8672	+	24.6060i	1.60546	+	1.16643i
$446$		0			0
$447$	−5.94658	−	18.3017i	−0.281264	−	0.865640i
$448$		0			0
$449$	−30.0247	−	21.8142i	−1.41695	−	1.02948i	−0.992265	−	0.124138i	$-0.960383\pi$
$449$	−30.0247	−	21.8142i	−1.41695	−	1.02948i	−0.424689	−	0.905339i	$-0.639617\pi$
$450$		0			0
$451$	33.0539	+	23.2230i	1.55645	+	1.09353i
$452$		0			0
$453$	17.8800	+	12.9905i	0.840074	+	0.610349i
$454$		0			0
$455$	−0.360049	−	1.10812i	−0.0168793	−	0.0519493i
$456$		0			0
$457$	−18.4289	−	13.3894i	−0.862069	−	0.626330i	0.0663781	−	0.997795i	$-0.478856\pi$
$457$	−18.4289	−	13.3894i	−0.862069	−	0.626330i	−0.928447	+	0.371465i	$0.878856\pi$
$458$		0			0
$459$	0.869778	−	2.67690i	0.0405978	−	0.124947i
$460$		0			0
$461$	7.50108	−	23.0860i	0.349360	−	1.07522i	−0.609848	−	0.792519i	$-0.708769\pi$
$461$	7.50108	−	23.0860i	0.349360	−	1.07522i	0.959208	−	0.282702i	$-0.0912307\pi$
$462$		0			0
$463$	−1.27713	−	3.93059i	−0.0593531	−	0.182670i	0.916984	−	0.398924i	$-0.130616\pi$
$463$	−1.27713	−	3.93059i	−0.0593531	−	0.182670i	−0.976337	+	0.216254i	$0.930616\pi$
$464$		0			0
$465$	−0.404045			−0.0187371
$466$		0			0
$467$	29.6180	−	21.5187i	1.37056	−	0.995767i	0.372862	−	0.927887i	$-0.378377\pi$
$467$	29.6180	−	21.5187i	1.37056	−	0.995767i	0.997693	−	0.0678800i	$-0.0216235\pi$
$468$		0			0
$469$	−11.3432	−	8.24134i	−0.523781	−	0.380550i
$470$		0			0
$471$	−18.3079	+	13.3014i	−0.843582	+	0.612898i
$472$		0			0
$473$	−56.4773	+	41.0332i	−2.59683	+	1.88671i
$474$		0			0
$475$	2.08039	−	6.40280i	0.0954550	−	0.293780i
$476$		0			0
$477$	0.0409285	+	0.125965i	0.00187399	+	0.00576754i
$478$		0			0
$479$	23.0108	+	16.7183i	1.05139	+	0.763880i	0.972476	−	0.233001i	$-0.0748546\pi$
$479$	23.0108	+	16.7183i	1.05139	+	0.763880i	0.0789143	+	0.996881i	$0.474855\pi$
$480$		0			0
$481$	−1.60817	+	4.94944i	−0.0733262	+	0.225675i
$482$		0			0
$483$	−4.08353			−0.185807
$484$		0			0
$485$	25.8157	−	18.7562i	1.17223	−	0.851675i
$486$		0			0
$487$	−3.38460	−	10.4167i	−0.153371	−	0.472026i	0.844621	−	0.535364i	$-0.179826\pi$
$487$	−3.38460	−	10.4167i	−0.153371	−	0.472026i	−0.997992	+	0.0633375i	$0.979826\pi$
$488$		0			0
$489$	12.5053			0.565508
$490$		0			0
$491$	−19.1158			−0.862685			−0.431343	−	0.902188i	$-0.641960\pi$
$491$	−19.1158			−0.862685			−0.431343	+	0.902188i	$0.641960\pi$
$492$		0			0
$493$	−5.70297			−0.256849
$494$		0			0
$495$	−6.25794			−0.281273
$496$		0			0
$497$	−0.898027	−	2.76384i	−0.0402820	−	0.123975i
$498$		0			0
$499$	10.8290	−	7.86772i	0.484772	−	0.352207i	−0.318398	−	0.947957i	$-0.603145\pi$
$499$	10.8290	−	7.86772i	0.484772	−	0.352207i	0.803170	+	0.595750i	$0.203145\pi$
$500$		0			0
$501$	−5.31911			−0.237640
$502$		0			0
$503$	−0.422846	+	1.30139i	−0.0188538	+	0.0580260i	−0.960041	−	0.279860i	$-0.909712\pi$
$503$	−0.422846	+	1.30139i	−0.0188538	+	0.0580260i	0.941187	+	0.337886i	$0.109712\pi$
$504$		0			0
$505$	−3.54828	−	2.57798i	−0.157897	−	0.114719i
$506$		0			0
$507$	7.26761	+	22.3674i	0.322766	+	0.993372i
$508$		0			0
$509$	6.65470	−	20.4810i	0.294964	−	0.907806i	−0.688269	−	0.725455i	$-0.741629\pi$
$509$	6.65470	−	20.4810i	0.294964	−	0.907806i	0.983233	−	0.182351i	$-0.0583708\pi$
$510$		0			0
$511$	−0.121391	+	0.0881954i	−0.00537000	+	0.00390153i
$512$		0			0
$513$	−12.0767	+	8.77423i	−0.533199	+	0.387392i
$514$		0			0
$515$	8.97875	+	6.52344i	0.395651	+	0.287457i
$516$		0			0
$517$	−39.1314	+	28.4306i	−1.72100	+	1.25038i
$518$		0			0
$519$	−19.5647			−0.858794
$520$		0			0
$521$	−1.77130	−	5.45149i	−0.0776020	−	0.238834i	0.904729	−	0.425988i	$-0.140074\pi$
$521$	−1.77130	−	5.45149i	−0.0776020	−	0.238834i	−0.982331	+	0.187154i	$0.940074\pi$
$522$		0			0
$523$	−9.86737	+	30.3686i	−0.431470	+	1.32793i	0.465191	+	0.885210i	$0.345986\pi$
$523$	−9.86737	+	30.3686i	−0.431470	+	1.32793i	−0.896661	+	0.442717i	$0.854014\pi$
$524$		0			0
$525$	1.23518	−	3.80151i	0.0539079	−	0.165911i
$526$		0			0
$527$	0.0387486	+	0.0281525i	0.00168792	+	0.00122634i
$528$		0			0
$529$	−5.57845	−	17.1687i	−0.242541	−	0.746465i
$530$		0			0
$531$	−0.303188	−	0.220279i	−0.0131573	−	0.00955931i
$532$		0			0
$533$	−2.22668	+	1.67238i	−0.0964483	+	0.0724389i
$534$		0			0
$535$	−12.0719	−	8.77076i	−0.521914	−	0.379193i
$536$		0			0
$537$	−13.5027	−	41.5570i	−0.582684	−	1.79332i
$538$		0			0
$539$	−5.10397	−	3.70825i	−0.219844	−	0.159726i
$540$		0			0
$541$	−3.21518	+	9.89530i	−0.138231	+	0.425432i	−0.996079	−	0.0884724i	$-0.971801\pi$
$541$	−3.21518	+	9.89530i	−0.138231	+	0.425432i	0.857847	+	0.513905i	$0.171801\pi$
$542$		0			0
$543$	10.3336	−	31.8035i	0.443456	−	1.36482i
$544$		0			0
$545$	−3.39738	−	10.4560i	−0.145528	−	0.447888i
$546$		0			0
$547$	16.7444			0.715939			0.357969	−	0.933733i	$-0.383469\pi$
$547$	16.7444			0.715939			0.357969	+	0.933733i	$0.383469\pi$
$548$		0			0
$549$	−3.64516	+	2.64836i	−0.155571	+	0.113029i
$550$		0			0
$551$	24.4694	+	17.7780i	1.04243	+	0.757370i
$552$		0			0
$553$	2.60918	−	1.89568i	0.110953	−	0.0806124i
$554$		0			0
$555$	−47.6125	+	34.5925i	−2.02104	+	1.46837i
$556$		0			0
$557$	5.64211	−	17.3646i	0.239064	−	0.735763i	−0.757493	−	0.652844i	$-0.773576\pi$
$557$	5.64211	−	17.3646i	0.239064	−	0.735763i	0.996556	−	0.0829188i	$-0.0264242\pi$
$558$		0			0
$559$	−1.48712	−	4.57689i	−0.0628985	−	0.193582i
$560$		0			0
$561$	5.46287	+	3.96901i	0.230643	+	0.167572i
$562$		0			0
$563$	10.8634	−	33.4340i	0.457836	−	1.40907i	−0.409937	−	0.912114i	$-0.634449\pi$
$563$	10.8634	−	33.4340i	0.457836	−	1.40907i	0.867773	−	0.496961i	$-0.165551\pi$
$564$		0			0
$565$	25.9886			1.09335
$566$		0			0
$567$	−8.06887	+	5.86238i	−0.338861	+	0.246197i
$568$		0			0
$569$	−13.0886	−	40.2827i	−0.548704	−	1.68874i	−0.712016	−	0.702163i	$-0.752218\pi$
$569$	−13.0886	−	40.2827i	−0.548704	−	1.68874i	0.163312	−	0.986574i	$-0.447782\pi$
$570$		0			0
$571$	−21.4671			−0.898371			−0.449185	−	0.893439i	$-0.648286\pi$
$571$	−21.4671			−0.898371			−0.449185	+	0.893439i	$0.648286\pi$
$572$		0			0
$573$	21.6046			0.902544
$574$		0			0
$575$	−4.84309			−0.201971
$576$		0			0
$577$	24.1597			1.00578			0.502892	−	0.864349i	$-0.332269\pi$
$577$	24.1597			1.00578			0.502892	+	0.864349i	$0.332269\pi$
$578$		0			0
$579$	3.23224	+	9.94780i	0.134327	+	0.413417i
$580$		0			0
$581$	−4.49420	+	3.26523i	−0.186451	+	0.135464i
$582$		0			0
$583$	2.25681			0.0934674
$584$		0			0
$585$	0.133309	−	0.410284i	0.00551167	−	0.0169632i
$586$		0			0
$587$	−3.47692	−	2.52613i	−0.143508	−	0.104264i	0.513715	−	0.857961i	$-0.328269\pi$
$587$	−3.47692	−	2.52613i	−0.143508	−	0.104264i	−0.657223	+	0.753696i	$0.728269\pi$
$588$		0			0
$589$	−0.0784956	−	0.241585i	−0.00323436	−	0.00995432i
$590$		0			0
$591$	−12.9428	+	39.8338i	−0.532395	+	1.63854i
$592$		0			0
$593$	−1.87230	+	1.36030i	−0.0768861	+	0.0558610i	−0.625564	−	0.780173i	$-0.715131\pi$
$593$	−1.87230	+	1.36030i	−0.0768861	+	0.0558610i	0.548678	+	0.836034i	$0.315131\pi$
$594$		0			0
$595$	−1.26363	+	0.918079i	−0.0518037	+	0.0376376i
$596$		0			0
$597$	6.66559	+	4.84283i	0.272804	+	0.198204i
$598$		0			0
$599$	−6.49217	+	4.71684i	−0.265263	+	0.192725i	−0.712464	−	0.701709i	$-0.752421\pi$
$599$	−6.49217	+	4.71684i	−0.265263	+	0.192725i	0.447201	+	0.894433i	$0.352421\pi$
$600$		0			0
$601$	20.8059			0.848692			0.424346	−	0.905500i	$-0.360504\pi$
$601$	20.8059			0.848692			0.424346	+	0.905500i	$0.360504\pi$
$602$		0			0
$603$	−1.60421	−	4.93725i	−0.0653285	−	0.201060i
$604$		0			0
$605$	−23.8441	+	73.3846i	−0.969401	+	2.98351i
$606$		0			0
$607$	−6.52013	+	20.0669i	−0.264644	+	0.814490i	0.727132	+	0.686498i	$0.240853\pi$
$607$	−6.52013	+	20.0669i	−0.264644	+	0.814490i	−0.991775	+	0.127991i	$0.959147\pi$
$608$		0			0
$609$	14.5281	+	10.5553i	0.588709	+	0.427722i
$610$		0			0
$611$	−1.03038	−	3.17118i	−0.0416847	−	0.128292i
$612$		0			0
$613$	30.5215	+	22.1752i	1.23275	+	0.895646i	0.997093	−	0.0761902i	$-0.0242756\pi$
$613$	30.5215	+	22.1752i	1.23275	+	0.895646i	0.235658	+	0.971836i	$0.424276\pi$
$614$		0			0
$615$	−31.4883	+	0.499555i	−1.26973	+	0.0201440i
$616$		0			0
$617$	29.1464	+	21.1761i	1.17339	+	0.852519i	0.991411	−	0.130784i	$-0.0417493\pi$
$617$	29.1464	+	21.1761i	1.17339	+	0.852519i	0.181980	+	0.983302i	$0.441749\pi$
$618$		0			0
$619$	−3.13576	−	9.65087i	−0.126037	−	0.387901i	0.868052	−	0.496474i	$-0.165372\pi$
$619$	−3.13576	−	9.65087i	−0.126037	−	0.387901i	−0.994089	+	0.108573i	$0.965372\pi$
$620$		0			0
$621$	8.68774	+	6.31202i	0.348627	+	0.253292i
$622$		0			0
$623$	−4.82863	+	14.8610i	−0.193455	+	0.595393i
$624$		0			0
$625$	−9.62460	+	29.6215i	−0.384984	+	1.18486i
$626$		0			0
$627$	−11.0665	−	34.0591i	−0.441953	−	1.36019i
$628$		0			0
$629$	6.97641			0.278168
$630$		0			0
$631$	14.6021	−	10.6090i	0.581300	−	0.422339i	−0.257892	−	0.966174i	$-0.583028\pi$
$631$	14.6021	−	10.6090i	0.581300	−	0.422339i	0.839193	+	0.543834i	$0.183028\pi$
$632$		0			0
$633$	−25.8136	−	18.7547i	−1.02600	−	0.745433i
$634$		0			0
$635$	21.2629	−	15.4484i	0.843793	−	0.613052i
$636$		0			0
$637$	0.351849	−	0.255633i	0.0139408	−	0.0101285i
$638$		0			0
$639$	0.332498	−	1.02332i	0.0131534	−	0.0404821i
$640$		0			0
$641$	5.21592	+	16.0530i	0.206017	+	0.634054i	0.999670	+	0.0256838i	$0.00817630\pi$
$641$	5.21592	+	16.0530i	0.206017	+	0.634054i	−0.793654	+	0.608370i	$0.791824\pi$
$642$		0			0
$643$	−25.7700	−	18.7230i	−1.01627	−	0.738363i	−0.0507548	−	0.998711i	$-0.516163\pi$
$643$	−25.7700	−	18.7230i	−1.01627	−	0.738363i	−0.965515	+	0.260348i	$0.916163\pi$
$644$		0			0
$645$	16.8174	−	51.7587i	0.662186	−	2.03800i
$646$		0			0
$647$	39.4779			1.55204			0.776018	−	0.630710i	$-0.217236\pi$
$647$	39.4779			1.55204			0.776018	+	0.630710i	$0.217236\pi$
$648$		0			0
$649$	−5.16611	+	3.75340i	−0.202788	+	0.147334i
$650$		0			0
$651$	−0.0466049	−	0.143435i	−0.00182659	−	0.00562167i
$652$		0			0
$653$	−5.46357			−0.213806			−0.106903	−	0.994269i	$-0.534093\pi$
$653$	−5.46357			−0.213806			−0.106903	+	0.994269i	$0.534093\pi$
$654$		0			0
$655$	−49.5958			−1.93787
$656$		0			0
$657$	−0.0555555			−0.00216743
$658$		0			0
$659$	3.08187			0.120053			0.0600263	−	0.998197i	$-0.480882\pi$
$659$	3.08187			0.120053			0.0600263	+	0.998197i	$0.480882\pi$
$660$		0			0
$661$	−5.92435	−	18.2333i	−0.230430	−	0.709192i	−0.997695	−	0.0678609i	$-0.978383\pi$
$661$	−5.92435	−	18.2333i	−0.230430	−	0.709192i	0.767264	−	0.641331i	$-0.221617\pi$
$662$		0			0
$663$	−0.376590	+	0.273608i	−0.0146255	+	0.0106261i
$664$		0			0
$665$	8.28372			0.321229
$666$		0			0
$667$	6.72367	−	20.6933i	0.260342	−	0.801249i
$668$		0			0
$669$	23.9633	+	17.4104i	0.926476	+	0.673125i
$670$		0			0
$671$	23.7242	+	73.0156i	0.915863	+	2.81874i
$672$		0			0
$673$	9.28368	−	28.5722i	0.357860	−	1.10138i	−0.596473	−	0.802633i	$-0.703432\pi$
$673$	9.28368	−	28.5722i	0.357860	−	1.10138i	0.954333	−	0.298745i	$-0.0965681\pi$
$674$		0			0
$675$	−8.50396	+	6.17849i	−0.327317	+	0.237810i
$676$		0			0
$677$	−14.4053	+	10.4661i	−0.553640	+	0.402243i	−0.829126	−	0.559062i	$-0.811161\pi$
$677$	−14.4053	+	10.4661i	−0.553640	+	0.402243i	0.275486	+	0.961305i	$0.411161\pi$
$678$		0			0
$679$	9.63614	+	7.00106i	0.369801	+	0.268676i
$680$		0			0
$681$	−2.64190	+	1.91945i	−0.101238	+	0.0735535i
$682$		0			0
$683$	−3.81019			−0.145793			−0.0728964	−	0.997340i	$-0.523224\pi$
$683$	−3.81019			−0.145793			−0.0728964	+	0.997340i	$0.523224\pi$
$684$		0			0
$685$	−15.7339	−	48.4239i	−0.601161	−	1.85018i
$686$		0			0
$687$	0.704880	−	2.16940i	0.0268929	−	0.0827677i
$688$		0			0
$689$	−0.0480756	+	0.147961i	−0.00183153	+	0.00563688i
$690$		0			0
$691$	−17.9186	−	13.0186i	−0.681656	−	0.495252i	0.192251	−	0.981346i	$-0.438421\pi$
$691$	−17.9186	−	13.0186i	−0.681656	−	0.495252i	−0.873907	+	0.486094i	$0.838421\pi$
$692$		0			0
$693$	−0.721827	−	2.22155i	−0.0274199	−	0.0843899i
$694$		0			0
$695$	−13.1368	−	9.54447i	−0.498309	−	0.362042i
$696$		0			0
$697$	3.05459	+	2.14609i	0.115701	+	0.0812891i
$698$		0			0
$699$	−9.41333	−	6.83918i	−0.356045	−	0.258682i
$700$		0			0
$701$	−8.41281	−	25.8920i	−0.317747	−	0.977926i	−0.974609	−	0.223915i	$-0.928116\pi$
$701$	−8.41281	−	25.8920i	−0.317747	−	0.977926i	0.656861	−	0.754011i	$-0.271884\pi$
$702$		0			0
$703$	−29.9333	−	21.7478i	−1.12895	−	0.820233i
$704$		0			0
$705$	11.6523	−	35.8620i	0.438850	−	1.35064i
$706$		0			0
$707$	0.505898	−	1.55699i	0.0190262	−	0.0585567i
$708$		0			0
$709$	−2.71924	−	8.36897i	−0.102123	−	0.314303i	0.886921	−	0.461921i	$-0.152840\pi$
$709$	−2.71924	−	8.36897i	−0.102123	−	0.314303i	−0.989045	+	0.147617i	$0.952840\pi$
$710$		0			0
$711$	1.19411			0.0447828
$712$		0			0
$713$	−0.147836	+	0.107409i	−0.00553650	+	0.00402250i
$714$		0			0
$715$	−5.94685	−	4.32064i	−0.222400	−	0.161583i
$716$		0			0
$717$	3.52446	−	2.56067i	0.131624	−	0.0956301i
$718$		0			0
$719$	19.8842	−	14.4467i	0.741556	−	0.538772i	−0.151642	−	0.988436i	$-0.548456\pi$
$719$	19.8842	−	14.4467i	0.741556	−	0.538772i	0.893198	+	0.449663i	$0.148456\pi$
$720$		0			0
$721$	−1.28015	+	3.93989i	−0.0476752	+	0.146729i
$722$		0			0
$723$	−10.7667	−	33.1366i	−0.400419	−	1.23236i
$724$		0			0
$725$	17.2304	+	12.5186i	0.639922	+	0.464930i
$726$		0			0
$727$	−0.406974	+	1.25254i	−0.0150938	+	0.0464541i	−0.958320	−	0.285698i	$-0.907775\pi$
$727$	−0.406974	+	1.25254i	−0.0150938	+	0.0464541i	0.943226	+	0.332152i	$0.107775\pi$
$728$		0			0
$729$	22.8959			0.847998
$730$		0			0
$731$	−5.21920	+	3.79197i	−0.193039	+	0.140251i
$732$		0			0
$733$	13.2028	+	40.6342i	0.487658	+	1.50086i	0.828094	+	0.560589i	$0.189425\pi$
$733$	13.2028	+	40.6342i	0.487658	+	1.50086i	−0.340436	+	0.940268i	$0.610575\pi$
$734$		0			0
$735$	4.91826			0.181413
$736$		0			0
$737$	−88.4565			−3.25834
$738$		0			0
$739$	−11.3342			−0.416934			−0.208467	−	0.978029i	$-0.566847\pi$
$739$	−11.3342			−0.416934			−0.208467	+	0.978029i	$0.566847\pi$
$740$		0			0
$741$	2.46874			0.0906913
$742$		0			0
$743$	−8.16002	−	25.1140i	−0.299362	−	0.921342i	−0.981721	−	0.190325i	$-0.939046\pi$
$743$	−8.16002	−	25.1140i	−0.299362	−	0.921342i	0.682359	−	0.731017i	$-0.260954\pi$
$744$		0			0
$745$	22.7191	−	16.5064i	0.832365	−	0.604748i
$746$		0			0
$747$	−2.05681			−0.0752548
$748$		0			0
$749$	1.72116	−	5.29718i	0.0628897	−	0.193555i
$750$		0			0
$751$	14.4805	+	10.5207i	0.528403	+	0.383907i	0.819760	−	0.572707i	$-0.194107\pi$
$751$	14.4805	+	10.5207i	0.528403	+	0.383907i	−0.291357	+	0.956614i	$0.594107\pi$
$752$		0			0
$753$	−10.9884	−	33.8188i	−0.400440	−	1.23243i
$754$		0			0
$755$	−9.96645	+	30.6736i	−0.362716	+	1.11633i
$756$		0			0
$757$	−3.35280	+	2.43595i	−0.121860	+	0.0885362i	−0.647046	−	0.762451i	$-0.723996\pi$
$757$	−3.35280	+	2.43595i	−0.121860	+	0.0885362i	0.525186	+	0.850987i	$0.323996\pi$
$758$		0			0
$759$	−20.8422	+	15.1428i	−0.756525	+	0.549648i
$760$		0			0
$761$	0.788403	+	0.572808i	0.0285796	+	0.0207643i	0.601983	−	0.798509i	$-0.294377\pi$
$761$	0.788403	+	0.572808i	0.0285796	+	0.0207643i	−0.573404	+	0.819273i	$0.694377\pi$
$762$		0			0
$763$	3.32000	−	2.41212i	0.120192	−	0.0873247i
$764$		0			0
$765$	−0.578311			−0.0209089
$766$		0			0
$767$	−0.136030	−	0.418658i	−0.00491177	−	0.0151169i
$768$		0			0
$769$	−13.3061	+	40.9519i	−0.479829	+	1.47676i	0.359502	+	0.933144i	$0.382946\pi$
$769$	−13.3061	+	40.9519i	−0.479829	+	1.47676i	−0.839332	+	0.543619i	$0.817054\pi$
$770$		0			0
$771$	8.81963	−	27.1440i	0.317631	−	0.977568i
$772$		0			0
$773$	33.4070	+	24.2716i	1.20157	+	0.872990i	0.994438	−	0.105324i	$-0.0335878\pi$
$773$	33.4070	+	24.2716i	1.20157	+	0.872990i	0.207130	+	0.978314i	$0.433588\pi$
$774$		0			0
$775$	−0.0552737	−	0.170115i	−0.00198549	−	0.00611071i
$776$		0			0
$777$	−17.7722	−	12.9122i	−0.637573	−	0.463224i
$778$		0			0
$779$	−6.41606	−	18.7303i	−0.229879	−	0.671082i
$780$		0			0
$781$	−14.8325	−	10.7765i	−0.530750	−	0.385612i
$782$		0			0
$783$	−14.5931	−	44.9129i	−0.521515	−	1.60506i
$784$		0			0
$785$	−26.7170	−	19.4110i	−0.953569	−	0.692809i
$786$		0			0
$787$	−8.22149	+	25.3032i	−0.293065	+	0.901960i	0.690800	+	0.723046i	$0.257258\pi$
$787$	−8.22149	+	25.3032i	−0.293065	+	0.901960i	−0.983865	+	0.178914i	$0.942742\pi$
$788$		0			0
$789$	−6.98386	+	21.4941i	−0.248632	+	0.765211i
$790$		0			0
$791$	2.99768	+	9.22592i	0.106585	+	0.328036i
$792$		0			0
$793$	−5.29245			−0.187940
$794$		0			0
$795$	−1.42336	+	1.03413i	−0.0504812	+	0.0366767i
$796$		0			0
$797$	−4.66389	−	3.38851i	−0.165203	−	0.120027i	0.502112	−	0.864803i	$-0.332557\pi$
$797$	−4.66389	−	3.38851i	−0.165203	−	0.120027i	−0.667315	+	0.744775i	$0.732557\pi$
$798$		0			0
$799$	−3.61622	+	2.62734i	−0.127933	+	0.0929486i
$800$		0			0
$801$	−4.68057	+	3.40063i	−0.165380	+	0.120155i
$802$		0			0
$803$	−0.292523	+	0.900294i	−0.0103229	+	0.0317707i
$804$		0			0
$805$	−1.84148	−	5.66750i	−0.0649037	−	0.199753i
$806$		0			0
$807$	32.3269	+	23.4869i	1.13796	+	0.826777i
$808$		0			0
$809$	−10.6405	+	32.7480i	−0.374099	+	1.15136i	0.569985	+	0.821655i	$0.306949\pi$
$809$	−10.6405	+	32.7480i	−0.374099	+	1.15136i	−0.944084	+	0.329704i	$0.893051\pi$
$810$		0			0
$811$	−8.86744			−0.311378			−0.155689	−	0.987806i	$-0.549760\pi$
$811$	−8.86744			−0.311378			−0.155689	+	0.987806i	$0.549760\pi$
$812$		0			0
$813$	−31.6217	+	22.9745i	−1.10902	+	0.805752i
$814$		0			0
$815$	5.63929	+	17.3559i	0.197536	+	0.607952i
$816$		0			0
$817$	34.2145			1.19701
$818$		0			0
$819$	0.161027			0.00562673
$820$		0			0
$821$	−13.7601			−0.480232			−0.240116	−	0.970744i	$-0.577186\pi$
$821$	−13.7601			−0.480232			−0.240116	+	0.970744i	$0.577186\pi$
$822$		0			0
$823$	17.5236			0.610834			0.305417	−	0.952219i	$-0.401204\pi$
$823$	17.5236			0.610834			0.305417	+	0.952219i	$0.401204\pi$
$824$		0			0
$825$	−7.79261	−	23.9832i	−0.271304	−	0.834987i
$826$		0			0
$827$	19.4972	−	14.1655i	0.677984	−	0.492584i	−0.194704	−	0.980862i	$-0.562375\pi$
$827$	19.4972	−	14.1655i	0.677984	−	0.492584i	0.872688	+	0.488278i	$0.162375\pi$
$828$		0			0
$829$	17.8679			0.620576			0.310288	−	0.950643i	$-0.399574\pi$
$829$	17.8679			0.620576			0.310288	+	0.950643i	$0.399574\pi$
$830$		0			0
$831$	−12.1939	+	37.5290i	−0.423002	+	1.30187i
$832$		0			0
$833$	−0.471670	−	0.342689i	−0.0163424	−	0.0118735i
$834$		0			0
$835$	−2.39867	−	7.38234i	−0.0830094	−	0.255477i
$836$		0			0
$837$	−0.122559	+	0.377198i	−0.00423626	+	0.0130379i
$838$		0			0
$839$	42.2728	−	30.7130i	1.45942	−	1.06033i	0.475906	−	0.879496i	$-0.342120\pi$
$839$	42.2728	−	30.7130i	1.45942	−	1.06033i	0.983514	−	0.180835i	$-0.0578799\pi$
$840$		0			0
$841$	−53.9486	+	39.1960i	−1.86030	+	1.35159i
$842$		0			0
$843$	19.8744	+	14.4396i	0.684509	+	0.497325i
$844$		0			0
$845$	−27.7662	+	20.1733i	−0.955186	+	0.693983i
$846$		0			0
$847$	−28.8017			−0.989638
$848$		0			0
$849$	5.56360	+	17.1230i	0.190942	+	0.587660i
$850$		0			0
$851$	−8.22504	+	25.3141i	−0.281951	+	0.867755i
$852$		0			0
$853$	10.6910	−	32.9035i	0.366052	−	1.12659i	−0.583267	−	0.812281i	$-0.698226\pi$
$853$	10.6910	−	32.9035i	0.366052	−	1.12659i	0.949319	−	0.314313i	$-0.101774\pi$
$854$		0			0
$855$	2.48132	+	1.80279i	0.0848594	+	0.0616540i
$856$		0			0
$857$	0.737371	+	2.26939i	0.0251881	+	0.0775210i	0.962860	−	0.270000i	$-0.0870236\pi$
$857$	0.737371	+	2.26939i	0.0251881	+	0.0775210i	−0.937672	+	0.347521i	$0.887024\pi$
$858$		0			0
$859$	2.82140	+	2.04987i	0.0962649	+	0.0699405i	0.634876	−	0.772614i	$-0.281051\pi$
$859$	2.82140	+	2.04987i	0.0962649	+	0.0699405i	−0.538612	+	0.842554i	$0.681051\pi$
$860$		0			0
$861$	−3.80938	−	11.1207i	−0.129823	−	0.378991i
$862$		0			0
$863$	40.2324	+	29.2306i	1.36953	+	0.995021i	0.997774	+	0.0666897i	$0.0212438\pi$
$863$	40.2324	+	29.2306i	1.36953	+	0.995021i	0.371755	+	0.928331i	$0.378756\pi$
$864$		0			0
$865$	−8.82276	−	27.1537i	−0.299983	−	0.923252i
$866$		0			0
$867$	−24.7438	−	17.9774i	−0.840343	−	0.610545i
$868$		0			0
$869$	6.28751	−	19.3510i	0.213289	−	0.656437i
$870$		0			0
$871$	1.88434	−	5.79941i	0.0638485	−	0.196505i
$872$		0			0
$873$	1.36279	+	4.19422i	0.0461233	+	0.141953i
$874$		0			0
$875$	−7.56215			−0.255647
$876$		0			0
$877$	4.10559	−	2.98289i	0.138636	−	0.100725i	−0.516306	−	0.856404i	$-0.672693\pi$
$877$	4.10559	−	2.98289i	0.138636	−	0.100725i	0.654942	+	0.755679i	$0.272693\pi$
$878$		0			0
$879$	−7.98561	−	5.80188i	−0.269348	−	0.195693i
$880$		0			0
$881$	11.3600	−	8.25351i	0.382728	−	0.278068i	−0.379741	−	0.925093i	$-0.623987\pi$
$881$	11.3600	−	8.25351i	0.382728	−	0.278068i	0.762469	+	0.647025i	$0.223987\pi$
$882$		0			0
$883$	−29.1041	+	21.1454i	−0.979433	+	0.711599i	−0.957582	−	0.288162i	$-0.906956\pi$
$883$	−29.1041	+	21.1454i	−0.979433	+	0.711599i	−0.0218509	+	0.999761i	$0.506956\pi$
$884$		0			0
$885$	1.53833	−	4.73449i	0.0517104	−	0.159148i
$886$		0			0
$887$	−5.05829	−	15.5678i	−0.169841	−	0.522716i	0.829520	−	0.558478i	$-0.188614\pi$
$887$	−5.05829	−	15.5678i	−0.169841	−	0.522716i	−0.999360	+	0.0357616i	$0.988614\pi$
$888$		0			0
$889$	7.93674	+	5.76638i	0.266190	+	0.193398i
$890$		0			0
$891$	−19.4441	+	59.8429i	−0.651403	+	2.00481i
$892$		0			0
$893$	23.7062			0.793298
$894$		0			0
$895$	51.5875	−	37.4805i	1.72438	−	1.25284i
$896$		0			0
$897$	−0.548803	−	1.68904i	−0.0183240	−	0.0563954i
$898$		0			0
$899$	0.803596			0.0268014
$900$		0			0
$901$	0.208557			0.00694804
$902$		0			0
$903$	20.3141			0.676010
$904$		0			0
$905$	48.7997			1.62216
$906$		0			0
$907$	−9.22030	−	28.3772i	−0.306155	−	0.942248i	−0.979244	−	0.202686i	$-0.935033\pi$
$907$	−9.22030	−	28.3772i	−0.306155	−	0.942248i	0.673089	−	0.739562i	$-0.264967\pi$
$908$		0			0
$909$	0.490386	−	0.356286i	0.0162651	−	0.0118173i
$910$		0			0
$911$	7.12087			0.235925			0.117962	−	0.993018i	$-0.462364\pi$
$911$	7.12087			0.235925			0.117962	+	0.993018i	$0.462364\pi$
$912$		0			0
$913$	−10.8300	+	33.3313i	−0.358420	+	1.10310i
$914$		0			0
$915$	−48.4204	−	35.1795i	−1.60073	−	1.16300i
$916$		0			0
$917$	−5.72067	−	17.6064i	−0.188913	−	0.581415i
$918$		0			0
$919$	−1.82292	+	5.61038i	−0.0601326	+	0.185069i	−0.976610	−	0.215016i	$-0.931020\pi$
$919$	−1.82292	+	5.61038i	−0.0601326	+	0.185069i	0.916478	+	0.400085i	$0.131020\pi$
$920$		0			0
$921$	−39.0146	+	28.3458i	−1.28557	+	0.934024i
$922$		0			0
$923$	1.02250	−	0.742889i	0.0336560	−	0.0244525i
$924$		0			0
$925$	−21.0779	−	15.3140i	−0.693037	−	0.503521i
$926$		0			0
$927$	−1.24090	+	0.901563i	−0.0407563	+	0.0296112i
$928$		0			0
$929$	41.1164			1.34899			0.674493	−	0.738281i	$-0.264362\pi$
$929$	41.1164			1.34899			0.674493	+	0.738281i	$0.264362\pi$
$930$		0			0
$931$	0.955493	+	2.94070i	0.0313150	+	0.0963777i
$932$		0			0
$933$	−15.2345	+	46.8869i	−0.498754	+	1.53501i
$934$		0			0
$935$	−3.04505	+	9.37171i	−0.0995839	+	0.306488i
$936$		0			0
$937$	7.07081	+	5.13724i	0.230993	+	0.167826i	0.697261	−	0.716817i	$-0.254402\pi$
$937$	7.07081	+	5.13724i	0.230993	+	0.167826i	−0.466268	+	0.884644i	$0.654402\pi$
$938$		0			0
$939$	15.1785	+	46.7145i	0.495330	+	1.52447i
$940$		0			0
$941$	−8.33148	−	6.05318i	−0.271599	−	0.197328i	0.443646	−	0.896202i	$-0.353685\pi$
$941$	−8.33148	−	6.05318i	−0.271599	−	0.197328i	−0.715245	+	0.698874i	$0.753685\pi$
$942$		0			0
$943$	−11.3884	+	8.55345i	−0.370859	+	0.278539i
$944$		0			0
$945$	−10.4637	−	7.60229i	−0.340383	−	0.247302i
$946$		0			0
$947$	−3.92849	−	12.0907i	−0.127659	−	0.392893i	0.866717	−	0.498800i	$-0.166226\pi$
$947$	−3.92849	−	12.0907i	−0.127659	−	0.392893i	−0.994376	+	0.105906i	$0.966226\pi$
$948$		0			0
$949$	−0.0527938	−	0.0383570i	−0.00171376	−	0.00124512i
$950$		0			0
$951$	−4.14601	+	12.7601i	−0.134444	+	0.413775i
$952$		0			0
$953$	−9.45130	+	29.0881i	−0.306158	+	0.942256i	0.673085	+	0.739565i	$0.264969\pi$
$953$	−9.45130	+	29.0881i	−0.306158	+	0.942256i	−0.979243	+	0.202691i	$0.935031\pi$
$954$		0			0
$955$	9.74266	+	29.9848i	0.315265	+	0.970286i
$956$		0			0
$957$	113.293			3.66224
$958$		0			0
$959$	15.3756	−	11.1710i	0.496502	−	0.360730i
$960$		0			0
$961$	25.0741	+	18.2174i	0.808841	+	0.587657i
$962$		0			0
$963$	1.66838	−	1.21215i	0.0537629	−	0.0390610i
$964$		0			0
$965$	−12.3489	+	8.97199i	−0.397525	+	0.288819i
$966$		0			0
$967$	9.01878	−	27.7570i	0.290025	−	0.892604i	−0.694823	−	0.719181i	$-0.744517\pi$
$967$	9.01878	−	27.7570i	0.290025	−	0.892604i	0.984847	−	0.173423i	$-0.0554827\pi$
$968$		0			0
$969$	−1.02268	−	3.14749i	−0.0328532	−	0.101112i
$970$		0			0
$971$	−25.0124	−	18.1726i	−0.802686	−	0.583186i	0.109015	−	0.994040i	$-0.465230\pi$
$971$	−25.0124	−	18.1726i	−0.802686	−	0.583186i	−0.911701	+	0.410854i	$0.865230\pi$
$972$		0			0
$973$	1.87299	−	5.76446i	0.0600452	−	0.184800i
$974$		0			0
$975$	1.73839			0.0556731
$976$		0			0
$977$	25.2044	−	18.3121i	0.806360	−	0.585855i	−0.106413	−	0.994322i	$-0.533937\pi$
$977$	25.2044	−	18.3121i	0.806360	−	0.585855i	0.912773	+	0.408467i	$0.133937\pi$
$978$		0			0
$979$	30.4631	+	93.7558i	0.973605	+	2.99645i
$980$		0			0
$981$	1.51943			0.0485116
$982$		0			0
$983$	46.2009			1.47358			0.736790	−	0.676122i	$-0.236341\pi$
$983$	46.2009			1.47358			0.736790	+	0.676122i	$0.236341\pi$
$984$		0			0
$985$	−61.1216			−1.94750
$986$		0			0
$987$	14.0750			0.448012
$988$		0			0
$989$	−7.60593	−	23.4086i	−0.241854	−	0.744351i
$990$		0			0
$991$	13.7266	−	9.97297i	0.436040	−	0.316802i	−0.348019	−	0.937487i	$-0.613146\pi$
$991$	13.7266	−	9.97297i	0.436040	−	0.316802i	0.784060	+	0.620686i	$0.213146\pi$
$992$		0			0
$993$	−2.82955			−0.0897931
$994$		0			0
$995$	−3.71546	+	11.4350i	−0.117788	+	0.362514i
$996$		0			0
$997$	13.9542	+	10.1383i	0.441933	+	0.321083i	0.786402	−	0.617715i	$-0.211941\pi$
$997$	13.9542	+	10.1383i	0.441933	+	0.321083i	−0.344470	+	0.938797i	$0.611941\pi$
$998$		0			0
$999$	17.8517	+	54.9418i	0.564802	+	1.73828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.c.953.1	yes	16
41.37	even	5	inner	1148.2.n.c.365.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.c.365.1	✓	16	41.37	even	5	inner
1148.2.n.c.953.1	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.83583 q^{3} +(-0.827871 - 2.54793i) q^{5} +(0.809017 - 0.587785i) q^{7} +0.370254 q^{9} +O(q^{10})\)	\(q-1.83583 q^{3} +(-0.827871 - 2.54793i) q^{5} +(0.809017 - 0.587785i) q^{7} +0.370254 q^{9} +(1.94954 - 6.00008i) q^{11} +(0.351849 + 0.255633i) q^{13} +(1.51983 + 4.67755i) q^{15} +(0.180162 - 0.554482i) q^{17} +(-2.50151 + 1.81746i) q^{19} +(-1.48521 + 1.07907i) q^{21} +(1.79954 + 1.30744i) q^{23} +(-1.76147 + 1.27978i) q^{25} +4.82775 q^{27} +(-3.02275 - 9.30307i) q^{29} +(-0.0253864 + 0.0781312i) q^{31} +(-3.57902 + 11.0151i) q^{33} +(-2.16740 - 1.57471i) q^{35} +(3.69772 + 11.3804i) q^{37} +(-0.645933 - 0.469298i) q^{39} +(-1.88183 + 6.12035i) q^{41} +(-8.95206 - 6.50405i) q^{43} +(-0.306523 - 0.943380i) q^{45} +(-6.20261 - 4.50646i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.330746 + 1.01793i) q^{51} +(0.110542 + 0.340212i) q^{53} -16.9017 q^{55} +(4.59234 - 3.33653i) q^{57} +(-0.818866 - 0.594941i) q^{59} +(-9.84501 + 7.15282i) q^{61} +(0.299542 - 0.217630i) q^{63} +(0.360049 - 1.10812i) q^{65} +(-4.33273 - 13.3348i) q^{67} +(-3.30364 - 2.40024i) q^{69} +(0.898027 - 2.76384i) q^{71} -0.150047 q^{73} +(3.23376 - 2.34946i) q^{75} +(-1.94954 - 6.00008i) q^{77} +3.22512 q^{79} -9.97367 q^{81} -5.55513 q^{83} -1.56193 q^{85} +(5.54924 + 17.0788i) q^{87} +(-12.6415 + 9.18459i) q^{89} +0.434909 q^{91} +(0.0466049 - 0.143435i) q^{93} +(6.70167 + 4.86905i) q^{95} +(3.68068 + 11.3280i) q^{97} +(0.721827 - 2.22155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 13 q^{5} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 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