LMFDB - Embedded newform 592.2.be.b.415.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.1234538496.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 24x^{6} - 58x^{5} + 167x^{4} - 242x^{3} + 394x^{2} - 282x + 241 $ x^8 - 4x^7 + 24x^6 - 58x^5 + 167x^4 - 242x^3 + 394x^2 - 282*x + 241
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			415.2
Root			$0.500000 + 2.70591i$ of defining polynomial
Character	$\chi$	$=$	592.415
Dual form			592.2.be.b.495.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 0.633975i) q^{3} +(1.78597 - 0.478548i) q^{5} +(-4.49187 - 2.59338i) q^{7} +(1.23205 + 2.13397i) q^{9} +O(q^{10})$	\(q+(0.366025 - 0.633975i) q^{3} +(1.78597 - 0.478548i) q^{5} +(-4.49187 - 2.59338i) q^{7} +(1.23205 + 2.13397i) q^{9} +5.30398 q^{11} +(-0.366025 + 0.0980762i) q^{13} +(0.350322 - 1.30742i) q^{15} +(1.74881 - 6.52665i) q^{17} +(-0.978548 - 3.65199i) q^{19} +(-3.28828 + 1.89849i) q^{21} +(1.16012 - 1.16012i) q^{23} +(-1.36946 + 0.790658i) q^{25} +4.00000 q^{27} +(4.77152 - 4.77152i) q^{29} +(-4.12816 - 4.12816i) q^{31} +(1.94139 - 3.36259i) q^{33} +(-9.26339 - 2.48212i) q^{35} +(-4.66532 + 3.90318i) q^{37} +(-0.0717968 + 0.267949i) q^{39} +(1.50000 + 0.866025i) q^{41} +(-2.24538 + 2.24538i) q^{43} +(3.22161 + 3.22161i) q^{45} +1.91882i q^{47} +(9.95128 + 17.2361i) q^{49} +(-3.49762 - 3.49762i) q^{51} +(3.18677 + 5.51964i) q^{53} +(9.47273 - 2.53821i) q^{55} +(-2.67344 - 0.716347i) q^{57} +(-1.05861 - 0.283653i) q^{59} +(-3.01101 - 11.2372i) q^{61} -12.7807i q^{63} +(-0.606775 + 0.350322i) q^{65} +(-0.348008 + 0.602768i) q^{67} +(-0.310853 - 1.16012i) q^{69} +(10.9669 + 6.33175i) q^{71} -8.09158i q^{73} +1.15760i q^{75} +(-23.8248 - 13.7553i) q^{77} +(3.22736 + 12.0447i) q^{79} +(-2.23205 + 3.86603i) q^{81} +(-8.26451 + 4.77152i) q^{83} -12.4933i q^{85} +(-1.27852 - 4.77152i) q^{87} +(16.7100 + 4.47743i) q^{89} +(1.89849 + 0.508699i) q^{91} +(-4.12816 + 1.10614i) q^{93} +(-3.49531 - 6.05405i) q^{95} +(0.873031 + 0.873031i) q^{97} +(6.53478 + 11.3186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 2 q^{5} - 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 2 * q^5 - 6 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} + 2 q^{5} - 6 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} + 8 q^{17} - 2 q^{19} + 20 q^{23} - 36 q^{25} + 32 q^{27} + 4 q^{29} + 4 q^{31} + 16 q^{33} - 10 q^{35} + 6 q^{37} - 56 q^{39} + 12 q^{41} + 20 q^{43} - 4 q^{45} + 24 q^{49} - 16 q^{51} - 12 q^{53} + 26 q^{55} - 8 q^{57} - 8 q^{59} - 14 q^{61} + 12 q^{65} - 22 q^{67} - 28 q^{69} - 6 q^{71} - 60 q^{77} + 14 q^{79} - 4 q^{81} - 48 q^{83} + 40 q^{87} + 16 q^{89} + 4 q^{91} + 4 q^{93} - 30 q^{95} - 16 q^{97} + 34 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 2 * q^5 - 6 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 + 8 * q^17 - 2 * q^19 + 20 * q^23 - 36 * q^25 + 32 * q^27 + 4 * q^29 + 4 * q^31 + 16 * q^33 - 10 * q^35 + 6 * q^37 - 56 * q^39 + 12 * q^41 + 20 * q^43 - 4 * q^45 + 24 * q^49 - 16 * q^51 - 12 * q^53 + 26 * q^55 - 8 * q^57 - 8 * q^59 - 14 * q^61 + 12 * q^65 - 22 * q^67 - 28 * q^69 - 6 * q^71 - 60 * q^77 + 14 * q^79 - 4 * q^81 - 48 * q^83 + 40 * q^87 + 16 * q^89 + 4 * q^91 + 4 * q^93 - 30 * q^95 - 16 * q^97 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	−0.740805	−	0.671721i	$-0.765556\pi$
$3$	0.366025	−	0.633975i	0.211325	−	0.366025i	0.952129	+	0.305695i	$0.0988889\pi$
$4$		0			0
$5$	1.78597	−	0.478548i	0.798708	−	0.214013i	0.163692	−	0.986512i	$-0.447660\pi$
$5$	1.78597	−	0.478548i	0.798708	−	0.214013i	0.635017	+	0.772498i	$0.280993\pi$
$6$		0			0
$7$	−4.49187	−	2.59338i	−1.69777	−	0.980207i	−0.947872	−	0.318652i	$-0.896770\pi$
$7$	−4.49187	−	2.59338i	−1.69777	−	0.980207i	−0.749897	−	0.661555i	$-0.769897\pi$
$8$		0			0
$9$	1.23205	+	2.13397i	0.410684	+	0.711325i
$10$		0			0
$11$	5.30398			1.59921			0.799606	−	0.600526i	$-0.205042\pi$
$11$	5.30398			1.59921			0.799606	+	0.600526i	$0.205042\pi$
$12$		0			0
$13$	−0.366025	+	0.0980762i	−0.101517	+	0.0272014i	−0.309220	−	0.950991i	$-0.600068\pi$
$13$	−0.366025	+	0.0980762i	−0.101517	+	0.0272014i	0.207703	+	0.978192i	$0.433401\pi$
$14$		0			0
$15$	0.350322	−	1.30742i	0.0904526	−	0.337574i
$16$		0			0
$17$	1.74881	−	6.52665i	0.424149	−	1.58295i	−0.341626	−	0.939836i	$-0.610978\pi$
$17$	1.74881	−	6.52665i	0.424149	−	1.58295i	0.765775	−	0.643109i	$-0.222356\pi$
$18$		0			0
$19$	−0.978548	−	3.65199i	−0.224494	−	0.837824i	−0.982606	−	0.185700i	$-0.940545\pi$
$19$	−0.978548	−	3.65199i	−0.224494	−	0.837824i	0.758112	−	0.652124i	$-0.226122\pi$
$20$		0			0
$21$	−3.28828	+	1.89849i	−0.717561	+	0.414284i
$22$		0			0
$23$	1.16012	−	1.16012i	0.241901	−	0.241901i	−0.575735	−	0.817636i	$-0.695284\pi$
$23$	1.16012	−	1.16012i	0.241901	−	0.241901i	0.817636	+	0.575735i	$0.195284\pi$
$24$		0			0
$25$	−1.36946	+	0.790658i	−0.273892	+	0.158132i
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	4.77152	−	4.77152i	0.886049	−	0.886049i	−0.108092	−	0.994141i	$-0.534474\pi$
$29$	4.77152	−	4.77152i	0.886049	−	0.886049i	0.994141	+	0.108092i	$0.0344741\pi$
$30$		0			0
$31$	−4.12816	−	4.12816i	−0.741440	−	0.741440i	0.231415	−	0.972855i	$-0.425664\pi$
$31$	−4.12816	−	4.12816i	−0.741440	−	0.741440i	−0.972855	+	0.231415i	$0.925664\pi$
$32$		0			0
$33$	1.94139	−	3.36259i	0.337953	−	0.585352i
$34$		0			0
$35$	−9.26339	−	2.48212i	−1.56580	−	0.419555i
$36$		0			0
$37$	−4.66532	+	3.90318i	−0.766973	+	0.641679i
$37$	−4.66532	+	3.90318i	−0.766973	+	0.641679i
$38$		0			0
$39$	−0.0717968	+	0.267949i	−0.0114967	+	0.0429062i
$40$		0			0
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	0.612536	−	0.790443i	$-0.290149\pi$
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	−0.378275	+	0.925693i	$0.623483\pi$
$42$		0			0
$43$	−2.24538	+	2.24538i	−0.342417	+	0.342417i	−0.857275	−	0.514859i	$-0.827844\pi$
$43$	−2.24538	+	2.24538i	−0.342417	+	0.342417i	0.514859	+	0.857275i	$0.327844\pi$
$44$		0			0
$45$	3.22161	+	3.22161i	0.480249	+	0.480249i
$46$		0			0
$47$			1.91882i			0.279889i	0.990159	+	0.139944i	$0.0446923\pi$
$47$			1.91882i			0.279889i	−0.990159	+	0.139944i	$0.955308\pi$
$48$		0			0
$49$	9.95128	+	17.2361i	1.42161	+	2.46230i
$50$		0			0
$51$	−3.49762	−	3.49762i	−0.489765	−	0.489765i
$52$		0			0
$53$	3.18677	+	5.51964i	0.437736	+	0.758181i	0.997515	−	0.0704610i	$-0.0224470\pi$
$53$	3.18677	+	5.51964i	0.437736	+	0.758181i	−0.559778	+	0.828642i	$0.689114\pi$
$54$		0			0
$55$	9.47273	−	2.53821i	1.27730	−	0.342252i
$56$		0			0
$57$	−2.67344	−	0.716347i	−0.354106	−	0.0948825i
$58$		0			0
$59$	−1.05861	−	0.283653i	−0.137819	−	0.0369285i	0.189250	−	0.981929i	$-0.439394\pi$
$59$	−1.05861	−	0.283653i	−0.137819	−	0.0369285i	−0.327069	+	0.945000i	$0.606061\pi$
$60$		0			0
$61$	−3.01101	−	11.2372i	−0.385521	−	1.43878i	−0.837345	−	0.546675i	$-0.815893\pi$
$61$	−3.01101	−	11.2372i	−0.385521	−	1.43878i	0.451824	−	0.892107i	$-0.350773\pi$
$62$		0			0
$63$		−	12.7807i		−	1.61022i
$64$		0			0
$65$	−0.606775	+	0.350322i	−0.0752612	+	0.0434520i
$66$		0			0
$67$	−0.348008	+	0.602768i	−0.0425160	+	0.0736399i	−0.886500	−	0.462728i	$-0.846871\pi$
$67$	−0.348008	+	0.602768i	−0.0425160	+	0.0736399i	0.843984	+	0.536368i	$0.180204\pi$
$68$		0			0
$69$	−0.310853	−	1.16012i	−0.0374223	−	0.139662i
$70$		0			0
$71$	10.9669	+	6.33175i	1.30153	+	0.751441i	0.980667	−	0.195683i	$-0.0626925\pi$
$71$	10.9669	+	6.33175i	1.30153	+	0.751441i	0.320867	+	0.947124i	$0.396026\pi$
$72$		0			0
$73$		−	8.09158i		−	0.947047i	−0.880781	−	0.473524i	$-0.842982\pi$
$73$		−	8.09158i		−	0.947047i	0.880781	−	0.473524i	$-0.157018\pi$
$74$		0			0
$75$			1.15760i			0.133669i
$76$		0			0
$77$	−23.8248	−	13.7553i	−2.71509	−	1.56756i
$78$		0			0
$79$	3.22736	+	12.0447i	0.363106	+	1.35513i	0.869970	+	0.493105i	$0.164138\pi$
$79$	3.22736	+	12.0447i	0.363106	+	1.35513i	−0.506864	+	0.862026i	$0.669195\pi$
$80$		0			0
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$		0			0
$83$	−8.26451	+	4.77152i	−0.907148	+	0.523742i	−0.879513	−	0.475876i	$-0.842131\pi$
$83$	−8.26451	+	4.77152i	−0.907148	+	0.523742i	−0.0276358	+	0.999618i	$0.508798\pi$
$84$		0			0
$85$		−	12.4933i		−	1.35508i
$86$		0			0
$87$	−1.27852	−	4.77152i	−0.137072	−	0.511561i
$88$		0			0
$89$	16.7100	+	4.47743i	1.77125	+	0.474606i	0.988945	−	0.148283i	$-0.0473748\pi$
$89$	16.7100	+	4.47743i	1.77125	+	0.474606i	0.782310	+	0.622890i	$0.214041\pi$
$90$		0			0
$91$	1.89849	+	0.508699i	0.199016	+	0.0533261i
$92$		0			0
$93$	−4.12816	+	1.10614i	−0.428070	+	0.114701i
$94$		0			0
$95$	−3.49531	−	6.05405i	−0.358611	−	0.621133i
$96$		0			0
$97$	0.873031	+	0.873031i	0.0886428	+	0.0886428i	0.750038	−	0.661395i	$-0.230035\pi$
$97$	0.873031	+	0.873031i	0.0886428	+	0.0886428i	−0.661395	+	0.750038i	$0.730035\pi$
$98$		0			0
$99$	6.53478	+	11.3186i	0.656770	+	1.13756i
$100$		0			0
$101$			4.91882i			0.489441i	0.969594	+	0.244720i	$0.0786962\pi$
$101$			4.91882i			0.489441i	−0.969594	+	0.244720i	$0.921304\pi$
$102$		0			0
$103$	7.62116	+	7.62116i	0.750935	+	0.750935i	0.974654	−	0.223719i	$-0.0718198\pi$
$103$	7.62116	+	7.62116i	0.750935	+	0.750935i	−0.223719	+	0.974654i	$0.571820\pi$
$104$		0			0
$105$	−4.96424	+	4.96424i	−0.484460	+	0.484460i
$106$		0			0
$107$	4.18139	+	2.41413i	0.404230	+	0.233382i	0.688308	−	0.725419i	$-0.258354\pi$
$107$	4.18139	+	2.41413i	0.404230	+	0.233382i	−0.284077	+	0.958801i	$0.591687\pi$
$108$		0			0
$109$	−1.59695	+	5.95992i	−0.152961	+	0.570856i	0.846311	+	0.532689i	$0.178819\pi$
$109$	−1.59695	+	5.95992i	−0.152961	+	0.570856i	−0.999271	+	0.0381671i	$0.987848\pi$
$110$		0			0
$111$	0.766893	+	4.38636i	0.0727903	+	0.416334i
$112$		0			0
$113$	−6.86653	−	1.83988i	−0.645949	−	0.173081i	−0.0790524	−	0.996870i	$-0.525189\pi$
$113$	−6.86653	−	1.83988i	−0.645949	−	0.173081i	−0.566897	+	0.823789i	$0.691856\pi$
$114$		0			0
$115$	1.51676	−	2.62710i	0.141439	−	0.244979i
$116$		0			0
$117$	−0.660254	−	0.660254i	−0.0610405	−	0.0610405i
$118$		0			0
$119$	−24.7815	+	24.7815i	−2.27172	+	2.27172i
$120$		0			0
$121$	17.1322			1.55748
$122$		0			0
$123$	1.09808	−	0.633975i	0.0990102	−	0.0571636i
$124$		0			0
$125$	−8.60453	+	8.60453i	−0.769613	+	0.769613i
$126$		0			0
$127$	−14.6271	+	8.44496i	−1.29795	+	0.749369i	−0.980049	−	0.198756i	$-0.936310\pi$
$127$	−14.6271	+	8.44496i	−1.29795	+	0.749369i	−0.317897	+	0.948125i	$0.602977\pi$
$128$		0			0
$129$	0.601647	+	2.24538i	0.0529720	+	0.197694i
$130$		0			0
$131$	−2.57537	+	9.61140i	−0.225011	+	0.839752i	0.757389	+	0.652964i	$0.226475\pi$
$131$	−2.57537	+	9.61140i	−0.225011	+	0.839752i	−0.982400	+	0.186788i	$0.940192\pi$
$132$		0			0
$133$	−5.07550	+	18.9420i	−0.440102	+	1.64248i
$134$		0			0
$135$	7.14386	−	1.91419i	0.614846	−	0.164747i
$136$		0			0
$137$	−5.49075			−0.469107			−0.234553	−	0.972103i	$-0.575363\pi$
$137$	−5.49075			−0.469107			−0.234553	+	0.972103i	$0.575363\pi$
$138$		0			0
$139$	9.50357	+	16.4607i	0.806082	+	1.39618i	0.915558	+	0.402186i	$0.131750\pi$
$139$	9.50357	+	16.4607i	0.806082	+	1.39618i	−0.109476	+	0.993989i	$0.534917\pi$
$140$		0			0
$141$	1.21648	+	0.702337i	0.102446	+	0.0591474i
$142$		0			0
$143$	−1.94139	+	0.520195i	−0.162347	+	0.0435009i
$144$		0			0
$145$	6.23837	−	10.8052i	0.518068	−	0.897321i
$146$		0			0
$147$	14.5697			1.20169
$148$		0			0
$149$	−15.3689			−1.25907			−0.629535	−	0.776972i	$-0.716755\pi$
$149$	−15.3689			−1.25907			−0.629535	+	0.776972i	$0.716755\pi$
$150$		0			0
$151$	6.66062	−	11.5365i	0.542034	−	0.938830i	−0.456753	−	0.889593i	$-0.650988\pi$
$151$	6.66062	−	11.5365i	0.542034	−	0.938830i	0.998787	−	0.0492368i	$-0.0156789\pi$
$152$		0			0
$153$	16.0823	−	4.30925i	1.30018	−	0.348382i
$154$		0			0
$155$	−9.34828	−	5.39723i	−0.750872	−	0.433516i
$156$		0			0
$157$	−7.67814	−	13.2989i	−0.612782	−	1.06137i	−0.990769	−	0.135559i	$-0.956717\pi$
$157$	−7.67814	−	13.2989i	−0.612782	−	1.06137i	0.377987	−	0.925811i	$-0.376616\pi$
$158$		0			0
$159$	4.66575			0.370018
$160$		0			0
$161$	−8.21974	+	2.20247i	−0.647806	+	0.173579i
$162$		0			0
$163$	1.37429	−	5.12891i	0.107643	−	0.401727i	−0.890989	−	0.454025i	$-0.849988\pi$
$163$	1.37429	−	5.12891i	0.107643	−	0.401727i	0.998632	+	0.0522975i	$0.0166544\pi$
$164$		0			0
$165$	1.85810	−	6.93452i	0.144653	−	0.539852i
$166$		0			0
$167$	1.31969	+	4.92514i	0.102120	+	0.381119i	0.998003	−	0.0631731i	$-0.0201220\pi$
$167$	1.31969	+	4.92514i	0.102120	+	0.381119i	−0.895882	+	0.444292i	$0.853455\pi$
$168$		0			0
$169$	−11.1340	+	6.42820i	−0.856460	+	0.494477i
$170$		0			0
$171$	6.58764	−	6.58764i	0.503769	−	0.503769i
$172$		0			0
$173$	−0.0542857	+	0.0313419i	−0.00412727	+	0.00238288i	−0.502062	−	0.864832i	$-0.667425\pi$
$173$	−0.0542857	+	0.0313419i	−0.00412727	+	0.00238288i	0.497935	+	0.867214i	$0.334092\pi$
$174$		0			0
$175$	8.20192			0.620007
$176$		0			0
$177$	−0.567306	+	0.567306i	−0.0426413	+	0.0426413i
$178$		0			0
$179$	2.06017	+	2.06017i	0.153984	+	0.153984i	0.779895	−	0.625911i	$-0.215273\pi$
$179$	2.06017	+	2.06017i	0.153984	+	0.153984i	−0.625911	+	0.779895i	$0.715273\pi$
$180$		0			0
$181$	8.40369	−	14.5556i	0.624641	−	1.08191i	−0.363969	−	0.931411i	$-0.618579\pi$
$181$	8.40369	−	14.5556i	0.624641	−	1.08191i	0.988610	−	0.150499i	$-0.0480881\pi$
$182$		0			0
$183$	−8.22624	−	2.20421i	−0.608101	−	0.162940i
$184$		0			0
$185$	−6.46424	+	9.20353i	−0.475260	+	0.676657i
$186$		0			0
$187$	9.27566	−	34.6172i	0.678304	−	2.53146i
$188$		0			0
$189$	−17.9675	−	10.3735i	−1.30694	−	0.754564i
$190$		0			0
$191$	−1.65774	+	1.65774i	−0.119950	+	0.119950i	−0.764534	−	0.644584i	$-0.777031\pi$
$191$	−1.65774	+	1.65774i	−0.119950	+	0.119950i	0.644584	+	0.764534i	$0.277031\pi$
$192$		0			0
$193$	5.46447	+	5.46447i	0.393341	+	0.393341i	0.875877	−	0.482535i	$-0.160284\pi$
$193$	5.46447	+	5.46447i	0.393341	+	0.393341i	−0.482535	+	0.875877i	$0.660284\pi$
$194$		0			0
$195$			0.512906i			0.0367300i
$196$		0			0
$197$	4.46916	+	7.74082i	0.318415	+	0.551511i	0.980157	−	0.198220i	$-0.0635162\pi$
$197$	4.46916	+	7.74082i	0.318415	+	0.551511i	−0.661743	+	0.749731i	$0.730183\pi$
$198$		0			0
$199$	−0.771890	−	0.771890i	−0.0547178	−	0.0547178i	0.679218	−	0.733936i	$-0.262319\pi$
$199$	−0.771890	−	0.771890i	−0.0547178	−	0.0547178i	−0.733936	+	0.679218i	$0.762319\pi$
$200$		0			0
$201$	0.254760	+	0.441257i	0.0179694	+	0.0311239i
$202$		0			0
$203$	−33.8074	+	9.05868i	−2.37282	+	0.635795i
$204$		0			0
$205$	3.09338	+	0.828870i	0.216051	+	0.0578908i
$206$		0			0
$207$	3.90499	+	1.04634i	0.271415	+	0.0727255i
$208$		0			0
$209$	−5.19020	−	19.3701i	−0.359014	−	1.33986i
$210$		0			0
$211$			9.48137i			0.652724i	0.945245	+	0.326362i	$0.105823\pi$
$211$			9.48137i			0.652724i	−0.945245	+	0.326362i	$0.894177\pi$
$212$		0			0
$213$	8.02834	−	4.63517i	0.550093	−	0.317596i
$214$		0			0
$215$	−2.93564	+	5.08469i	−0.200209	+	0.346773i
$216$		0			0
$217$	7.83727	+	29.2491i	0.532028	+	1.98556i
$218$		0			0
$219$	−5.12985	−	2.96172i	−0.346643	−	0.200135i
$220$		0			0
$221$			2.56044i			0.172234i
$222$		0			0
$223$		−	14.3540i		−	0.961217i	−0.876935	−	0.480608i	$-0.840416\pi$
$223$		−	14.3540i		−	0.961217i	0.876935	−	0.480608i	$-0.159584\pi$
$224$		0			0
$225$	−3.37449	−	1.94826i	−0.224966	−	0.129884i
$226$		0			0
$227$	−2.67919	−	9.99888i	−0.177824	−	0.663649i	−0.996053	−	0.0887567i	$-0.971711\pi$
$227$	−2.67919	−	9.99888i	−0.177824	−	0.663649i	0.818229	−	0.574892i	$-0.194956\pi$
$228$		0			0
$229$	−2.92695	+	5.06962i	−0.193418	+	0.335010i	−0.946381	−	0.323053i	$-0.895291\pi$
$229$	−2.92695	+	5.06962i	−0.193418	+	0.335010i	0.752963	+	0.658063i	$0.228624\pi$
$230$		0			0
$231$	−17.4410	+	10.0696i	−1.14753	+	0.662528i
$232$		0			0
$233$		−	11.8550i		−	0.776649i	−0.921523	−	0.388325i	$-0.873054\pi$
$233$		−	11.8550i		−	0.776649i	0.921523	−	0.388325i	$-0.126946\pi$
$234$		0			0
$235$	0.918247	+	3.42695i	0.0598999	+	0.223549i
$236$		0			0
$237$	8.81731	+	2.36259i	0.572746	+	0.153467i
$238$		0			0
$239$	20.4373	+	5.47617i	1.32198	+	0.354224i	0.849720	−	0.527234i	$-0.176771\pi$
$239$	20.4373	+	5.47617i	1.32198	+	0.354224i	0.472262	+	0.881458i	$0.343438\pi$
$240$		0			0
$241$	−14.4651	+	3.87592i	−0.931780	+	0.249670i	−0.692613	−	0.721309i	$-0.743541\pi$
$241$	−14.4651	+	3.87592i	−0.931780	+	0.249670i	−0.239166	+	0.970979i	$0.576874\pi$
$242$		0			0
$243$	7.63397	+	13.2224i	0.489720	+	0.848219i
$244$		0			0
$245$	26.0210	+	26.0210i	1.66242	+	1.66242i
$246$		0			0
$247$	0.716347	+	1.24075i	0.0455801	+	0.0789470i
$248$		0			0
$249$			6.98599i			0.442719i
$250$		0			0
$251$	−10.9706	−	10.9706i	−0.692455	−	0.692455i	0.270316	−	0.962772i	$-0.412872\pi$
$251$	−10.9706	−	10.9706i	−0.692455	−	0.692455i	−0.962772	+	0.270316i	$0.912872\pi$
$252$		0			0
$253$	6.15325	−	6.15325i	0.386851	−	0.386851i
$254$		0			0
$255$	−7.92041	−	4.57285i	−0.495996	−	0.286363i
$256$		0			0
$257$	3.99038	−	14.8923i	0.248913	−	0.928956i	−0.722463	−	0.691410i	$-0.756990\pi$
$257$	3.99038	−	14.8923i	0.248913	−	0.928956i	0.971376	−	0.237547i	$-0.0763433\pi$
$258$		0			0
$259$	31.0785	−	5.43364i	1.93112	−	0.337630i
$260$		0			0
$261$	16.0611	+	4.30355i	0.994154	+	0.266383i
$262$		0			0
$263$	0.741435	−	1.28420i	0.0457188	−	0.0791873i	−0.842260	−	0.539071i	$-0.818776\pi$
$263$	0.741435	−	1.28420i	0.0457188	−	0.0791873i	0.887979	+	0.459883i	$0.152109\pi$
$264$		0			0
$265$	8.33288	+	8.33288i	0.511885	+	0.511885i
$266$		0			0
$267$	8.95485	−	8.95485i	0.548028	−	0.548028i
$268$		0			0
$269$	−5.10559			−0.311293			−0.155647	−	0.987813i	$-0.549746\pi$
$269$	−5.10559			−0.311293			−0.155647	+	0.987813i	$0.549746\pi$
$270$		0			0
$271$	−3.12741	+	1.80561i	−0.189977	+	0.109683i	−0.591972	−	0.805959i	$-0.701650\pi$
$271$	−3.12741	+	1.80561i	−0.189977	+	0.109683i	0.401995	+	0.915642i	$0.368317\pi$
$272$		0			0
$273$	1.01740	−	1.01740i	0.0615757	−	0.0615757i
$274$		0			0
$275$	−7.26359	+	4.19364i	−0.438011	+	0.252886i
$276$		0			0
$277$	−0.593520	−	2.21505i	−0.0356611	−	0.133089i	0.945800	−	0.324749i	$-0.105280\pi$
$277$	−0.593520	−	2.21505i	−0.0356611	−	0.133089i	−0.981461	+	0.191660i	$0.938613\pi$
$278$		0			0
$279$	3.72329	−	13.8955i	0.222907	−	0.831901i
$280$		0			0
$281$	6.48718	−	24.2105i	0.386993	−	1.44428i	−0.448009	−	0.894029i	$-0.647867\pi$
$281$	6.48718	−	24.2105i	0.386993	−	1.44428i	0.835002	−	0.550248i	$-0.185467\pi$
$282$		0			0
$283$	−5.49632	+	1.47273i	−0.326722	+	0.0875450i	−0.418452	−	0.908239i	$-0.637427\pi$
$283$	−5.49632	+	1.47273i	−0.326722	+	0.0875450i	0.0917296	+	0.995784i	$0.470760\pi$
$284$		0			0
$285$	−5.11749			−0.303134
$286$		0			0
$287$	−4.49187	−	7.78015i	−0.265147	−	0.459248i
$288$		0			0
$289$	−24.8164	−	14.3277i	−1.45979	−	0.842809i
$290$		0			0
$291$	0.873031	−	0.233928i	0.0511780	−	0.0137131i
$292$		0			0
$293$	−2.75932	+	4.77928i	−0.161201	+	0.279208i	−0.935300	−	0.353857i	$-0.884870\pi$
$293$	−2.75932	+	4.77928i	−0.161201	+	0.279208i	0.774099	+	0.633065i	$0.218203\pi$
$294$		0			0
$295$	−2.02638			−0.117980
$296$		0			0
$297$	21.2159			1.23107
$298$		0			0
$299$	−0.310853	+	0.538413i	−0.0179771	+	0.0311372i
$300$		0			0
$301$	15.9091	−	4.26282i	0.916983	−	0.245705i
$302$		0			0
$303$	3.11841	+	1.80041i	0.179148	+	0.103431i
$304$		0			0
$305$	−10.7551	−	18.6284i	−0.615837	−	1.06666i
$306$		0			0
$307$	−14.9003			−0.850406			−0.425203	−	0.905098i	$-0.639797\pi$
$307$	−14.9003			−0.850406			−0.425203	+	0.905098i	$0.639797\pi$
$308$		0			0
$309$	7.62116	−	2.04208i	0.433552	−	0.116170i
$310$		0			0
$311$	−0.352635	+	1.31605i	−0.0199961	+	0.0746264i	−0.975203	−	0.221313i	$-0.928966\pi$
$311$	−0.352635	+	1.31605i	−0.0199961	+	0.0746264i	0.955207	+	0.295939i	$0.0956325\pi$
$312$		0			0
$313$	−7.27958	+	27.1678i	−0.411466	+	1.53561i	0.380344	+	0.924845i	$0.375806\pi$
$313$	−7.27958	+	27.1678i	−0.411466	+	1.53561i	−0.791810	+	0.610768i	$0.790861\pi$
$314$		0			0
$315$	−6.11619	−	22.8259i	−0.344608	−	1.28610i
$316$		0			0
$317$	19.3892	−	11.1943i	1.08900	−	0.628737i	0.155693	−	0.987805i	$-0.450239\pi$
$317$	19.3892	−	11.1943i	1.08900	−	0.628737i	0.933311	+	0.359068i	$0.116906\pi$
$318$		0			0
$319$	25.3081	−	25.3081i	1.41698	−	1.41698i
$320$		0			0
$321$	3.06099	−	1.76726i	0.170848	−	0.0986390i
$322$		0			0
$323$	−25.5466			−1.42145
$324$		0			0
$325$	0.423712	−	0.423712i	0.0235033	−	0.0235033i
$326$		0			0
$327$	3.19391	+	3.19391i	0.176624	+	0.176624i
$328$		0			0
$329$	4.97624	−	8.61909i	0.274349	−	0.475186i
$330$		0			0
$331$	−23.2908	−	6.24075i	−1.28018	−	0.343023i	−0.446256	−	0.894905i	$-0.647243\pi$
$331$	−23.2908	−	6.24075i	−1.28018	−	0.343023i	−0.833922	+	0.551883i	$0.813910\pi$
$332$		0			0
$333$	−14.0772	−	5.14675i	−0.771426	−	0.282040i
$334$		0			0
$335$	−0.333078	+	1.24306i	−0.0181980	+	0.0679158i
$336$		0			0
$337$	18.0187	+	10.4031i	0.981542	+	0.566694i	0.902735	−	0.430196i	$-0.141556\pi$
$337$	18.0187	+	10.4031i	0.981542	+	0.566694i	0.0788070	+	0.996890i	$0.474889\pi$
$338$		0			0
$339$	−3.67976	+	3.67976i	−0.199857	+	0.199857i
$340$		0			0
$341$	−21.8957	−	21.8957i	−1.18572	−	1.18572i
$342$		0			0
$343$		−	66.9226i		−	3.61348i
$344$		0			0
$345$	−1.11035	−	1.92317i	−0.0597790	−	0.103540i
$346$		0			0
$347$	20.6729	+	20.6729i	1.10978	+	1.10978i	0.993179	+	0.116600i	$0.0371996\pi$
$347$	20.6729	+	20.6729i	1.10978	+	1.10978i	0.116600	+	0.993179i	$0.462800\pi$
$348$		0			0
$349$	2.57319	+	4.45690i	0.137740	+	0.238572i	0.926641	−	0.375948i	$-0.122683\pi$
$349$	2.57319	+	4.45690i	0.137740	+	0.238572i	−0.788901	+	0.614520i	$0.789350\pi$
$350$		0			0
$351$	−1.46410	+	0.392305i	−0.0781480	+	0.0209397i
$352$		0			0
$353$	11.5360	+	3.09107i	0.614001	+	0.164521i	0.552399	−	0.833580i	$-0.313712\pi$
$353$	11.5360	+	3.09107i	0.614001	+	0.164521i	0.0616019	+	0.998101i	$0.480379\pi$
$354$		0			0
$355$	22.6166	+	6.06010i	1.20036	+	0.321637i
$356$		0			0
$357$	6.64020	+	24.7815i	0.351436	+	1.31158i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	4.07500	−	2.35270i	0.214474	−	0.123826i
$362$		0			0
$363$	6.27083	−	10.8614i	0.329133	−	0.570076i
$364$		0			0
$365$	−3.87221	−	14.4513i	−0.202681	−	0.756415i
$366$		0			0
$367$	9.97166	+	5.75714i	0.520516	+	0.300520i	0.737146	−	0.675734i	$-0.236173\pi$
$367$	9.97166	+	5.75714i	0.520516	+	0.300520i	−0.216630	+	0.976254i	$0.569506\pi$
$368$		0			0
$369$			4.26795i			0.222181i
$370$		0			0
$371$		−	33.0581i		−	1.71629i
$372$		0			0
$373$	26.5225	+	15.3128i	1.37328	+	0.792864i	0.991340	−	0.131322i	$-0.0419223\pi$
$373$	26.5225	+	15.3128i	1.37328	+	0.792864i	0.381941	+	0.924187i	$0.375256\pi$
$374$		0			0
$375$	2.30558	+	8.60453i	0.119059	+	0.444336i
$376$		0			0
$377$	−1.27852	+	2.21447i	−0.0658474	+	0.114051i
$378$		0			0
$379$	−6.81174	+	3.93276i	−0.349896	+	0.202012i	−0.664639	−	0.747164i	$-0.731415\pi$
$379$	−6.81174	+	3.93276i	−0.349896	+	0.202012i	0.314744	+	0.949177i	$0.398081\pi$
$380$		0			0
$381$			12.3643i			0.633441i
$382$		0			0
$383$	−3.32081	−	12.3934i	−0.169685	−	0.633275i	−0.997396	−	0.0721193i	$-0.977024\pi$
$383$	−3.32081	−	12.3934i	−0.169685	−	0.633275i	0.827711	−	0.561155i	$-0.189643\pi$
$384$		0			0
$385$	−49.1329	−	13.1651i	−2.50404	−	0.670956i
$386$		0			0
$387$	−7.55799	−	2.02516i	−0.384194	−	0.102945i
$388$		0			0
$389$	1.74119	−	0.466550i	0.0882818	−	0.0236550i	−0.214408	−	0.976744i	$-0.568782\pi$
$389$	1.74119	−	0.466550i	0.0882818	−	0.0236550i	0.302690	+	0.953089i	$0.402115\pi$
$390$		0			0
$391$	−5.54286	−	9.60051i	−0.280314	−	0.485519i
$392$		0			0
$393$	5.15073	+	5.15073i	0.259820	+	0.259820i
$394$		0			0
$395$	11.5279	+	19.9669i	0.580032	+	1.00464i
$396$		0			0
$397$		−	2.66937i		−	0.133972i	−0.997754	−	0.0669858i	$-0.978662\pi$
$397$		−	2.66937i		−	0.133972i	0.997754	−	0.0669858i	$-0.0213382\pi$
$398$		0			0
$399$	10.1510	+	10.1510i	0.508186	+	0.508186i
$400$		0			0
$401$	20.3992	−	20.3992i	1.01869	−	1.01869i	0.0188641	−	0.999822i	$-0.493995\pi$
$401$	20.3992	−	20.3992i	1.01869	−	1.01869i	0.999822	−	0.0188641i	$-0.00600499\pi$
$402$		0			0
$403$	1.91589	+	1.10614i	0.0954371	+	0.0551006i
$404$		0			0
$405$	−2.13629	+	7.97273i	−0.106153	+	0.396168i
$406$		0			0
$407$	−24.7448	+	20.7024i	−1.22655	+	1.02618i
$408$		0			0
$409$	−17.6864	−	4.73906i	−0.874536	−	0.234331i	−0.206488	−	0.978449i	$-0.566203\pi$
$409$	−17.6864	−	4.73906i	−0.874536	−	0.234331i	−0.668048	+	0.744118i	$0.732870\pi$
$410$		0			0
$411$	−2.00975	+	3.48100i	−0.0991339	+	0.171705i
$412$		0			0
$413$	4.01951	+	4.01951i	0.197787	+	0.197787i
$414$		0			0
$415$	−12.4767	+	12.4767i	−0.612459	+	0.612459i
$416$		0			0
$417$	13.9142			0.681381
$418$		0			0
$419$	22.6159	−	13.0573i	1.10486	−	0.637891i	0.167367	−	0.985895i	$-0.446474\pi$
$419$	22.6159	−	13.0573i	1.10486	−	0.637891i	0.937493	+	0.348004i	$0.113140\pi$
$420$		0			0
$421$	−0.790288	+	0.790288i	−0.0385163	+	0.0385163i	−0.726103	−	0.687586i	$-0.758670\pi$
$421$	−0.790288	+	0.790288i	−0.0385163	+	0.0385163i	0.687586	+	0.726103i	$0.258670\pi$
$422$		0			0
$423$	−4.09471	+	2.36408i	−0.199092	+	0.114946i
$424$		0			0
$425$	2.76542	+	10.3207i	0.134143	+	0.500627i
$426$		0			0
$427$	−15.6174	+	58.2850i	−0.755780	+	2.82061i
$428$		0			0
$429$	−0.380809	+	1.42120i	−0.0183856	+	0.0686161i
$430$		0			0
$431$	19.5704	−	5.24388i	0.942675	−	0.252589i	0.245424	−	0.969416i	$-0.421073\pi$
$431$	19.5704	−	5.24388i	0.942675	−	0.252589i	0.697251	+	0.716827i	$0.254406\pi$
$432$		0			0
$433$	12.3155			0.591844			0.295922	−	0.955212i	$-0.404373\pi$
$433$	12.3155			0.591844			0.295922	+	0.955212i	$0.404373\pi$
$434$		0			0
$435$	−4.56680	−	7.90994i	−0.218961	−	0.379252i
$436$		0			0
$437$	−5.37197	−	3.10151i	−0.256976	−	0.148365i
$438$		0			0
$439$	−24.2751	+	6.50449i	−1.15859	+	0.310442i	−0.786401	−	0.617716i	$-0.788058\pi$
$439$	−24.2751	+	6.50449i	−1.15859	+	0.310442i	−0.372186	+	0.928158i	$0.621391\pi$
$440$		0			0
$441$	−24.5210	+	42.4716i	−1.16767	+	2.02246i
$442$		0			0
$443$	−18.1579			−0.862707			−0.431353	−	0.902183i	$-0.641964\pi$
$443$	−18.1579			−0.862707			−0.431353	+	0.902183i	$0.641964\pi$
$444$		0			0
$445$	31.9861			1.51629
$446$		0			0
$447$	−5.62541	+	9.74350i	−0.266073	+	0.460852i
$448$		0			0
$449$	−29.4755	+	7.89794i	−1.39104	+	0.372727i	−0.875117	−	0.483911i	$-0.839216\pi$
$449$	−29.4755	+	7.89794i	−1.39104	+	0.372727i	−0.515918	+	0.856638i	$0.672549\pi$
$450$		0			0
$451$	7.95597	+	4.59338i	0.374632	+	0.216294i
$452$		0			0
$453$	−4.87592	−	8.44533i	−0.229090	−	0.396796i
$454$		0			0
$455$	3.63407			0.170368
$456$		0			0
$457$	12.7291	−	3.41076i	0.595443	−	0.159549i	0.0515035	−	0.998673i	$-0.483599\pi$
$457$	12.7291	−	3.41076i	0.595443	−	0.159549i	0.543940	+	0.839124i	$0.316932\pi$
$458$		0			0
$459$	6.99524	−	26.1066i	0.326510	−	1.21855i
$460$		0			0
$461$	−5.46923	+	20.4114i	−0.254727	+	0.950656i	0.713514	+	0.700640i	$0.247102\pi$
$461$	−5.46923	+	20.4114i	−0.254727	+	0.950656i	−0.968242	+	0.250015i	$0.919564\pi$
$462$		0			0
$463$	3.73262	+	13.9303i	0.173470	+	0.647398i	0.996807	+	0.0798457i	$0.0254427\pi$
$463$	3.73262	+	13.9303i	0.173470	+	0.647398i	−0.823338	+	0.567552i	$0.807891\pi$
$464$		0			0
$465$	−6.84342	+	3.95105i	−0.317356	+	0.183225i
$466$		0			0
$467$	−10.1157	+	10.1157i	−0.468099	+	0.468099i	−0.901298	−	0.433199i	$-0.857385\pi$
$467$	−10.1157	+	10.1157i	−0.468099	+	0.468099i	0.433199	+	0.901298i	$0.357385\pi$
$468$		0			0
$469$	3.12642	−	1.80504i	0.144365	−	0.0833490i
$470$		0			0
$471$	−11.2416			−0.517984
$472$		0			0
$473$	−11.9094	+	11.9094i	−0.547596	+	0.547596i
$474$		0			0
$475$	4.22756	+	4.22756i	0.193974	+	0.193974i
$476$		0			0
$477$	−7.85252	+	13.6010i	−0.359542	+	0.622745i
$478$		0			0
$479$	4.16745	+	1.11666i	0.190416	+	0.0510217i	0.352767	−	0.935711i	$-0.385241\pi$
$479$	4.16745	+	1.11666i	0.190416	+	0.0510217i	−0.162351	+	0.986733i	$0.551908\pi$
$480$		0			0
$481$	1.32482	−	1.88622i	0.0604064	−	0.0860042i
$482$		0			0
$483$	−1.61232	+	6.01727i	−0.0733632	+	0.273795i
$484$		0			0
$485$	1.97699	+	1.14142i	0.0897705	+	0.0518290i
$486$		0			0
$487$	15.4720	−	15.4720i	0.701102	−	0.701102i	−0.263545	−	0.964647i	$-0.584892\pi$
$487$	15.4720	−	15.4720i	0.701102	−	0.701102i	0.964647	+	0.263545i	$0.0848916\pi$
$488$		0			0
$489$	−2.74858	−	2.74858i	−0.124295	−	0.124295i
$490$		0			0
$491$		−	17.7916i		−	0.802924i	−0.915876	−	0.401462i	$-0.868502\pi$
$491$		−	17.7916i		−	0.802924i	0.915876	−	0.401462i	$-0.131498\pi$
$492$		0			0
$493$	−22.7976	−	39.4865i	−1.02675	−	1.77838i
$494$		0			0
$495$	17.0874	+	17.0874i	0.768020	+	0.768020i
$496$		0			0
$497$	−32.8413	−	56.8829i	−1.47314	−	2.55155i
$498$		0			0
$499$	5.23181	−	1.40186i	0.234208	−	0.0627558i	−0.139806	−	0.990179i	$-0.544648\pi$
$499$	5.23181	−	1.40186i	0.234208	−	0.0627558i	0.374014	+	0.927423i	$0.377981\pi$
$500$		0			0
$501$	3.60545	+	0.966078i	0.161080	+	0.0431612i
$502$		0			0
$503$	19.8876	+	5.32887i	0.886745	+	0.237603i	0.673315	−	0.739356i	$-0.264870\pi$
$503$	19.8876	+	5.32887i	0.886745	+	0.237603i	0.213430	+	0.976958i	$0.431537\pi$
$504$		0			0
$505$	2.35389	+	8.78484i	0.104747	+	0.390920i
$506$		0			0
$507$			9.41154i			0.417981i
$508$		0			0
$509$	−29.7895	+	17.1990i	−1.32040	+	0.762331i	−0.983792	−	0.179315i	$-0.942612\pi$
$509$	−29.7895	+	17.1990i	−1.32040	+	0.762331i	−0.336604	+	0.941646i	$0.609278\pi$
$510$		0			0
$511$	−20.9846	+	36.3463i	−0.928303	+	1.60787i
$512$		0			0
$513$	−3.91419	−	14.6080i	−0.172816	−	0.644957i
$514$		0			0
$515$	17.2582	+	9.96404i	0.760488	+	0.439068i
$516$		0			0
$517$			10.1774i			0.447601i
$518$		0			0
$519$			0.0458877i			0.00201425i
$520$		0			0
$521$	−8.43232	−	4.86840i	−0.369427	−	0.213289i	0.303781	−	0.952742i	$-0.401751\pi$
$521$	−8.43232	−	4.86840i	−0.369427	−	0.213289i	−0.673208	+	0.739453i	$0.735084\pi$
$522$		0			0
$523$	−9.52097	−	35.5327i	−0.416323	−	1.55374i	−0.782171	−	0.623064i	$-0.785888\pi$
$523$	−9.52097	−	35.5327i	−0.416323	−	1.55374i	0.365848	−	0.930674i	$-0.380779\pi$
$524$		0			0
$525$	3.00211	−	5.19981i	0.131023	−	0.226938i
$526$		0			0
$527$	−34.1624	+	19.7237i	−1.48814	+	0.859177i
$528$		0			0
$529$			20.3083i			0.882967i
$530$		0			0
$531$	−0.698950	−	2.60852i	−0.0303318	−	0.113200i
$532$		0			0
$533$	−0.633975	−	0.169873i	−0.0274605	−	0.00735802i
$534$		0			0
$535$	8.62310	+	2.31055i	0.372809	+	0.0998939i
$536$		0			0
$537$	2.06017	−	0.552021i	0.0889029	−	0.0238215i
$538$		0			0
$539$	52.7814	+	91.4201i	2.27346	+	3.93774i
$540$		0			0
$541$	−16.9568	−	16.9568i	−0.729029	−	0.729029i	0.241397	−	0.970426i	$-0.422394\pi$
$541$	−16.9568	−	16.9568i	−0.729029	−	0.729029i	−0.970426	+	0.241397i	$0.922394\pi$
$542$		0			0
$543$	−6.15193	−	10.6554i	−0.264004	−	0.457269i
$544$		0			0
$545$			11.4084i			0.488683i
$546$		0			0
$547$	−28.7628	−	28.7628i	−1.22981	−	1.22981i	−0.964036	−	0.265771i	$-0.914373\pi$
$547$	−28.7628	−	28.7628i	−1.22981	−	1.22981i	−0.265771	−	0.964036i	$-0.585627\pi$
$548$		0			0
$549$	20.2703	−	20.2703i	0.865115	−	0.865115i
$550$		0			0
$551$	−22.0947	−	12.7564i	−0.941266	−	0.543440i
$552$		0			0
$553$	16.7396	−	62.4729i	0.711839	−	2.65662i
$554$		0			0
$555$	3.46873	+	7.46689i	0.147239	+	0.316952i
$556$		0			0
$557$	36.2582	+	9.71536i	1.53631	+	0.411653i	0.925071	−	0.379793i	$-0.124005\pi$
$557$	36.2582	+	9.71536i	1.53631	+	0.411653i	0.611239	+	0.791446i	$0.290672\pi$
$558$		0			0
$559$	0.601647	−	1.04208i	0.0254469	−	0.0440754i
$560$		0			0
$561$	−18.5513	−	18.5513i	−0.783237	−	0.783237i
$562$		0			0
$563$	16.3316	−	16.3316i	0.688297	−	0.688297i	−0.273559	−	0.961855i	$-0.588201\pi$
$563$	16.3316	−	16.3316i	0.688297	−	0.688297i	0.961855	+	0.273559i	$0.0882007\pi$
$564$		0			0
$565$	−13.1439			−0.552967
$566$		0			0
$567$	20.0522	−	11.5771i	0.842112	−	0.486194i
$568$		0			0
$569$	−13.6076	+	13.6076i	−0.570460	+	0.570460i	−0.932257	−	0.361797i	$-0.882163\pi$
$569$	−13.6076	+	13.6076i	−0.570460	+	0.570460i	0.361797	+	0.932257i	$0.382163\pi$
$570$		0			0
$571$	29.4649	−	17.0116i	1.23307	−	0.711913i	0.265401	−	0.964138i	$-0.414496\pi$
$571$	29.4649	−	17.0116i	1.23307	−	0.711913i	0.967668	+	0.252225i	$0.0811625\pi$
$572$		0			0
$573$	0.444190	+	1.65774i	0.0185563	+	0.0692531i
$574$		0			0
$575$	−0.671479	+	2.50599i	−0.0280026	+	0.104507i
$576$		0			0
$577$	−6.97743	+	26.0401i	−0.290474	+	1.08406i	0.654272	+	0.756260i	$0.272975\pi$
$577$	−6.97743	+	26.0401i	−0.290474	+	1.08406i	−0.944746	+	0.327804i	$0.893691\pi$
$578$		0			0
$579$	5.46447	−	1.46420i	0.227096	−	0.0608501i
$580$		0			0
$581$	49.4975			2.05350
$582$		0			0
$583$	16.9026	+	29.2761i	0.700033	+	1.21249i
$584$		0			0
$585$	−1.49515	−	0.863228i	−0.0618170	−	0.0356901i
$586$		0			0
$587$	34.5170	−	9.24881i	1.42467	−	0.381739i	0.537532	−	0.843243i	$-0.319357\pi$
$587$	34.5170	−	9.24881i	1.42467	−	0.381739i	0.887138	+	0.461504i	$0.152690\pi$
$588$		0			0
$589$	−11.0364	+	19.1156i	−0.454747	+	0.787645i
$590$		0			0
$591$	6.54331			0.269156
$592$		0			0
$593$	−29.4138			−1.20788			−0.603941	−	0.797029i	$-0.706404\pi$
$593$	−29.4138			−1.20788			−0.603941	+	0.797029i	$0.706404\pi$
$594$		0			0
$595$	−32.3998	+	56.1182i	−1.32826	+	2.30062i
$596$		0			0
$597$	−0.771890	+	0.206827i	−0.0315914	+	0.00846488i
$598$		0			0
$599$	18.3586	+	10.5993i	0.750111	+	0.433077i	0.825734	−	0.564059i	$-0.190761\pi$
$599$	18.3586	+	10.5993i	0.750111	+	0.433077i	−0.0756228	+	0.997136i	$0.524094\pi$
$600$		0			0
$601$	3.57244	+	6.18764i	0.145723	+	0.252399i	0.929642	−	0.368463i	$-0.120116\pi$
$601$	3.57244	+	6.18764i	0.145723	+	0.252399i	−0.783920	+	0.620862i	$0.786783\pi$
$602$		0			0
$603$	−1.71506			−0.0698425
$604$		0			0
$605$	30.5976	−	8.19860i	1.24397	−	0.333321i
$606$		0			0
$607$	−3.94791	+	14.7338i	−0.160241	+	0.598027i	0.838359	+	0.545119i	$0.183516\pi$
$607$	−3.94791	+	14.7338i	−0.160241	+	0.598027i	−0.998599	+	0.0529078i	$0.983151\pi$
$608$		0			0
$609$	−6.63141	+	24.7488i	−0.268718	+	1.00287i
$610$		0			0
$611$	−0.188191	−	0.702337i	−0.00761337	−	0.0284135i
$612$		0			0
$613$	−9.38761	+	5.41994i	−0.379162	+	0.218909i	−0.677454	−	0.735565i	$-0.736917\pi$
$613$	−9.38761	+	5.41994i	−0.379162	+	0.218909i	0.298292	+	0.954475i	$0.403583\pi$
$614$		0			0
$615$	1.65774	−	1.65774i	0.0668465	−	0.0668465i
$616$		0			0
$617$	−0.618362	+	0.357012i	−0.0248943	+	0.0143727i	−0.512396	−	0.858750i	$-0.671242\pi$
$617$	−0.618362	+	0.357012i	−0.0248943	+	0.0143727i	0.487501	+	0.873122i	$0.337908\pi$
$618$		0			0
$619$	−5.94372			−0.238898			−0.119449	−	0.992840i	$-0.538113\pi$
$619$	−5.94372			−0.238898			−0.119449	+	0.992840i	$0.538113\pi$
$620$		0			0
$621$	4.64047	−	4.64047i	0.186216	−	0.186216i
$622$		0			0
$623$	−63.4474	−	63.4474i	−2.54197	−	2.54197i
$624$		0			0
$625$	−7.29643	+	12.6378i	−0.291857	+	0.505511i
$626$		0			0
$627$	−14.1799	−	3.79949i	−0.566291	−	0.151737i
$628$		0			0
$629$	17.3159	+	37.2748i	0.690432	+	1.48624i
$630$		0			0
$631$	−4.60916	+	17.2016i	−0.183488	+	0.684785i	0.811462	+	0.584406i	$0.198672\pi$
$631$	−4.60916	+	17.2016i	−0.183488	+	0.684785i	−0.994949	+	0.100380i	$0.967994\pi$
$632$		0			0
$633$	6.01095	+	3.47042i	0.238914	+	0.137937i
$634$		0			0
$635$	−22.0822	+	22.0822i	−0.876305	+	0.876305i
$636$		0			0
$637$	−5.33288	−	5.33288i	−0.211296	−	0.211296i
$638$		0			0
$639$			31.2042i			1.23442i
$640$		0			0
$641$	−9.76914	−	16.9206i	−0.385858	−	0.668325i	0.606030	−	0.795442i	$-0.292761\pi$
$641$	−9.76914	−	16.9206i	−0.385858	−	0.668325i	−0.991888	+	0.127116i	$0.959428\pi$
$642$		0			0
$643$	16.8884	+	16.8884i	0.666012	+	0.666012i	0.956790	−	0.290778i	$-0.0939142\pi$
$643$	16.8884	+	16.8884i	0.666012	+	0.666012i	−0.290778	+	0.956790i	$0.593914\pi$
$644$		0			0
$645$	2.14904	+	3.72225i	0.0846184	+	0.146563i
$646$		0			0
$647$	15.5358	−	4.16280i	0.610775	−	0.163657i	0.0598443	−	0.998208i	$-0.480940\pi$
$647$	15.5358	−	4.16280i	0.610775	−	0.163657i	0.550931	+	0.834551i	$0.314273\pi$
$648$		0			0
$649$	−5.61484	−	1.50449i	−0.220402	−	0.0590564i
$650$		0			0
$651$	21.4118	+	5.73728i	0.839195	+	0.224862i
$652$		0			0
$653$	11.7477	+	43.8430i	0.459723	+	1.71571i	0.673820	+	0.738896i	$0.264652\pi$
$653$	11.7477	+	43.8430i	0.459723	+	1.71571i	−0.214097	+	0.976812i	$0.568681\pi$
$654$		0			0
$655$			18.3981i			0.718872i
$656$		0			0
$657$	17.2672	−	9.96923i	0.673658	−	0.388937i
$658$		0			0
$659$	−15.4369	+	26.7375i	−0.601336	+	1.04155i	0.391283	+	0.920271i	$0.372031\pi$
$659$	−15.4369	+	26.7375i	−0.601336	+	1.04155i	−0.992619	+	0.121275i	$0.961302\pi$
$660$		0			0
$661$	5.19315	+	19.3811i	0.201990	+	0.753838i	0.990346	+	0.138618i	$0.0442661\pi$
$661$	5.19315	+	19.3811i	0.201990	+	0.753838i	−0.788356	+	0.615220i	$0.789067\pi$
$662$		0			0
$663$	1.62325	+	0.937185i	0.0630419	+	0.0363972i
$664$		0			0
$665$			36.2587i			1.40605i
$666$		0			0
$667$		−	11.0711i		−	0.428673i
$668$		0			0
$669$	−9.10009	−	5.25394i	−0.351830	−	0.203129i
$670$		0			0
$671$	−15.9704	−	59.6022i	−0.616529	−	2.30092i
$672$		0			0
$673$	11.0389	−	19.1200i	0.425519	−	0.737021i	−0.570950	−	0.820985i	$-0.693425\pi$
$673$	11.0389	−	19.1200i	0.425519	−	0.737021i	0.996469	+	0.0839644i	$0.0267582\pi$
$674$		0			0
$675$	−5.47784	+	3.16263i	−0.210842	+	0.121730i
$676$		0			0
$677$			38.5872i			1.48303i	0.670938	+	0.741514i	$0.265892\pi$
$677$			38.5872i			1.48303i	−0.670938	+	0.741514i	$0.734108\pi$
$678$		0			0
$679$	−1.65744	−	6.18565i	−0.0636067	−	0.237383i
$680$		0			0
$681$	−7.31969	−	1.96130i	−0.280491	−	0.0751573i
$682$		0			0
$683$	−40.7991	−	10.9321i	−1.56113	−	0.418304i	−0.628111	−	0.778124i	$-0.716172\pi$
$683$	−40.7991	−	10.9321i	−1.56113	−	0.418304i	−0.933022	+	0.359819i	$0.882838\pi$
$684$		0			0
$685$	−9.80630	+	2.62759i	−0.374679	+	0.100395i
$686$		0			0
$687$	2.14267	+	3.71122i	0.0817481	+	0.141592i
$688$		0			0
$689$	−1.70778	−	1.70778i	−0.0650614	−	0.0650614i
$690$		0			0
$691$	−11.6022	−	20.0956i	−0.441369	−	0.764474i	0.556422	−	0.830900i	$-0.312174\pi$
$691$	−11.6022	−	20.0956i	−0.441369	−	0.764474i	−0.997791	+	0.0664259i	$0.978840\pi$
$692$		0			0
$693$		−	67.7887i		−	2.57508i
$694$		0			0
$695$	24.8503	+	24.8503i	0.942625	+	0.942625i
$696$		0			0
$697$	8.27546	−	8.27546i	0.313455	−	0.313455i
$698$		0			0
$699$	−7.51579	−	4.33924i	−0.284273	−	0.164125i
$700$		0			0
$701$	9.62840	−	35.9337i	0.363659	−	1.35720i	−0.505569	−	0.862786i	$-0.668718\pi$
$701$	9.62840	−	35.9337i	0.363659	−	1.35720i	0.869229	−	0.494410i	$-0.164616\pi$
$702$		0			0
$703$	18.8196	+	13.2182i	0.709795	+	0.498536i
$704$		0			0
$705$	2.50870	+	0.672204i	0.0944831	+	0.0253167i
$706$		0			0
$707$	12.7564	−	22.0947i	0.479753	−	0.830957i
$708$		0			0
$709$	−23.4940	−	23.4940i	−0.882336	−	0.882336i	0.111436	−	0.993772i	$-0.464455\pi$
$709$	−23.4940	−	23.4940i	−0.882336	−	0.882336i	−0.993772	+	0.111436i	$0.964455\pi$
$710$		0			0
$711$	−21.7267	+	21.7267i	−0.814817	+	0.814817i
$712$		0			0
$713$	−9.57831			−0.358711
$714$		0			0
$715$	−3.21832	+	1.85810i	−0.120358	+	0.0694890i
$716$		0			0
$717$	10.9523	−	10.9523i	0.409023	−	0.409023i
$718$		0			0
$719$	−9.63786	+	5.56442i	−0.359432	+	0.207518i	−0.668831	−	0.743414i	$-0.733205\pi$
$719$	−9.63786	+	5.56442i	−0.359432	+	0.207518i	0.309400	+	0.950932i	$0.399872\pi$
$720$		0			0
$721$	−14.4687	−	53.9978i	−0.538842	−	2.01098i
$722$		0			0
$723$	−2.83737	+	10.5892i	−0.105523	+	0.393817i
$724$		0			0
$725$	−2.76177	+	10.3070i	−0.102569	+	0.382794i
$726$		0			0
$727$	48.1739	−	12.9081i	1.78667	−	0.478737i	0.794896	−	0.606745i	$-0.207525\pi$
$727$	48.1739	−	12.9081i	1.78667	−	0.478737i	0.991773	+	0.128009i	$0.0408586\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	10.7280	+	18.5815i	0.396791	+	0.687262i
$732$		0			0
$733$	−15.3626	−	8.86960i	−0.567430	−	0.327606i	0.188692	−	0.982036i	$-0.439575\pi$
$733$	−15.3626	−	8.86960i	−0.567430	−	0.327606i	−0.756122	+	0.654430i	$0.772909\pi$
$734$		0			0
$735$	26.0210	−	6.97230i	0.959798	−	0.257177i
$736$		0			0
$737$	−1.84583	+	3.19707i	−0.0679921	+	0.117766i
$738$		0			0
$739$	−31.0406			−1.14185			−0.570923	−	0.821004i	$-0.693415\pi$
$739$	−31.0406			−1.14185			−0.570923	+	0.821004i	$0.693415\pi$
$740$		0			0
$741$	1.04880			0.0385288
$742$		0			0
$743$	4.96628	−	8.60185i	0.182195	−	0.315571i	−0.760433	−	0.649417i	$-0.775013\pi$
$743$	4.96628	−	8.60185i	0.182195	−	0.315571i	0.942628	+	0.333846i	$0.108346\pi$
$744$		0			0
$745$	−27.4484	+	7.35476i	−1.00563	+	0.269458i
$746$		0			0
$747$	−20.3646	−	11.7575i	−0.745102	−	0.430185i
$748$		0			0
$749$	−12.5215	−	21.6879i	−0.457526	−	0.792459i
$750$		0			0
$751$	4.96498			0.181175			0.0905873	−	0.995889i	$-0.471126\pi$
$751$	4.96498			0.181175			0.0905873	+	0.995889i	$0.471126\pi$
$752$		0			0
$753$	−10.9706	+	2.93955i	−0.399789	+	0.107123i
$754$		0			0
$755$	6.37486	−	23.7913i	0.232005	−	0.865854i
$756$		0			0
$757$	−6.41476	+	23.9402i	−0.233149	+	0.870122i	0.745826	+	0.666141i	$0.232055\pi$
$757$	−6.41476	+	23.9402i	−0.233149	+	0.870122i	−0.978975	+	0.203982i	$0.934612\pi$
$758$		0			0
$759$	−1.64876	−	6.15325i	−0.0598461	−	0.223349i
$760$		0			0
$761$	−28.1662	+	16.2618i	−1.02102	+	0.589489i	−0.914400	−	0.404811i	$-0.867337\pi$
$761$	−28.1662	+	16.2618i	−1.02102	+	0.589489i	−0.106624	+	0.994299i	$0.534004\pi$
$762$		0			0
$763$	22.6297	−	22.6297i	0.819249	−	0.819249i
$764$		0			0
$765$	26.6603	−	15.3923i	0.963906	−	0.556511i
$766$		0			0
$767$	0.415297			0.0149955
$768$		0			0
$769$	−4.19038	+	4.19038i	−0.151109	+	0.151109i	−0.778613	−	0.627504i	$-0.784077\pi$
$769$	−4.19038	+	4.19038i	−0.151109	+	0.151109i	0.627504	+	0.778613i	$0.284077\pi$
$770$		0			0
$771$	−7.98076	−	7.98076i	−0.287420	−	0.287420i
$772$		0			0
$773$	−5.84920	+	10.1311i	−0.210381	+	0.364391i	−0.951834	−	0.306614i	$-0.900804\pi$
$773$	−5.84920	+	10.1311i	−0.210381	+	0.364391i	0.741453	+	0.671005i	$0.234137\pi$
$774$		0			0
$775$	8.91732	+	2.38939i	0.320319	+	0.0858293i
$776$		0			0
$777$	7.93072	−	21.6918i	0.284513	−	0.778189i
$778$		0			0
$779$	1.69490	−	6.32543i	0.0607259	−	0.226632i
$780$		0			0
$781$	58.1684	+	33.5835i	2.08143	+	1.20171i
$782$		0			0
$783$	19.0861	−	19.0861i	0.682081	−	0.682081i
$784$		0			0
$785$	−20.0771	−	20.0771i	−0.716581	−	0.716581i
$786$		0			0
$787$		−	29.4944i		−	1.05136i	−0.850682	−	0.525681i	$-0.823811\pi$
$787$		−	29.4944i		−	1.05136i	0.850682	−	0.525681i	$-0.176189\pi$
$788$		0			0
$789$	−0.542768	−	0.940102i	−0.0193231	−	0.0334685i
$790$		0			0
$791$	26.0721	+	26.0721i	0.927016	+	0.927016i
$792$		0			0
$793$	2.20421	+	3.81781i	0.0782739	+	0.135574i
$794$		0			0
$795$	8.33288	−	2.23279i	0.295537	−	0.0791888i
$796$		0			0
$797$	−30.5663	−	8.19020i	−1.08271	−	0.290112i	−0.327006	−	0.945022i	$-0.606040\pi$
$797$	−30.5663	−	8.19020i	−1.08271	−	0.290112i	−0.755706	+	0.654910i	$0.772706\pi$
$798$		0			0
$799$	12.5235	+	3.35565i	0.443048	+	0.118714i
$800$		0			0
$801$	11.0328	+	41.1751i	0.389826	+	1.45485i
$802$		0			0
$803$		−	42.9176i		−	1.51453i
$804$		0			0
$805$	−13.6262	+	7.86708i	−0.480260	+	0.277278i
$806$		0			0
$807$	−1.86877	+	3.23681i	−0.0657840	+	0.113941i
$808$		0			0
$809$	−4.23348	−	15.7996i	−0.148841	−	0.555483i	−0.999554	−	0.0298525i	$-0.990496\pi$
$809$	−4.23348	−	15.7996i	−0.148841	−	0.555483i	0.850713	−	0.525630i	$-0.176170\pi$
$810$		0			0
$811$	−17.8893	−	10.3284i	−0.628178	−	0.362679i	0.151868	−	0.988401i	$-0.451471\pi$
$811$	−17.8893	−	10.3284i	−0.628178	−	0.362679i	−0.780046	+	0.625722i	$0.784804\pi$
$812$		0			0
$813$			2.64360i			0.0927150i
$814$		0			0
$815$		−	9.81773i		−	0.343900i
$816$		0			0
$817$	10.3973	+	6.00288i	0.363756	+	0.210014i
$818$		0			0
$819$	1.25349	+	4.67807i	0.0438003	+	0.163465i
$820$		0			0
$821$	−17.1630	+	29.7272i	−0.598993	+	1.03749i	0.393977	+	0.919120i	$0.371099\pi$
$821$	−17.1630	+	29.7272i	−0.598993	+	1.03749i	−0.992970	+	0.118366i	$0.962234\pi$
$822$		0			0
$823$	−14.7478	+	8.51465i	−0.514076	+	0.296802i	−0.734508	−	0.678600i	$-0.762587\pi$
$823$	−14.7478	+	8.51465i	−0.514076	+	0.296802i	0.220431	+	0.975402i	$0.429253\pi$
$824$		0			0
$825$			6.13991i			0.213764i
$826$		0			0
$827$	−4.70458	−	17.5577i	−0.163594	−	0.610542i	−0.998215	−	0.0597176i	$-0.980980\pi$
$827$	−4.70458	−	17.5577i	−0.163594	−	0.610542i	0.834621	−	0.550825i	$-0.185687\pi$
$828$		0			0
$829$	10.8129	+	2.89730i	0.375546	+	0.100627i	0.441655	−	0.897185i	$-0.354392\pi$
$829$	10.8129	+	2.89730i	0.375546	+	0.100627i	−0.0661084	+	0.997812i	$0.521058\pi$
$830$		0			0
$831$	−1.62153	−	0.434487i	−0.0562501	−	0.0150722i
$832$		0			0
$833$	129.897	−	34.8058i	4.50067	−	1.20595i
$834$		0			0
$835$	4.71383	+	8.16460i	0.163129	+	0.282548i
$836$		0			0
$837$	−16.5126	−	16.5126i	−0.570760	−	0.570760i
$838$		0			0
$839$	−5.71699	−	9.90211i	−0.197372	−	0.341859i	0.750303	−	0.661094i	$-0.229907\pi$
$839$	−5.71699	−	9.90211i	−0.197372	−	0.341859i	−0.947676	+	0.319235i	$0.896574\pi$
$840$		0			0
$841$		−	16.5348i		−	0.570165i
$842$		0			0
$843$	−12.9744	−	12.9744i	−0.446861	−	0.446861i
$844$		0			0
$845$	−16.8087	+	16.8087i	−0.578237	+	0.578237i
$846$		0			0
$847$	−76.9558	−	44.4305i	−2.64423	−	1.52665i
$848$		0			0
$849$	−1.07812	+	4.02359i	−0.0370009	+	0.138089i
$850$		0			0
$851$	−0.884167	+	9.94047i	−0.0303089	+	0.340755i
$852$		0			0
$853$	39.6326	+	10.6195i	1.35699	+	0.363606i	0.862712	−	0.505695i	$-0.168764\pi$
$853$	39.6326	+	10.6195i	1.35699	+	0.363606i	0.494283	+	0.869301i	$0.335431\pi$
$854$		0			0
$855$	8.61279	−	14.9178i	0.294551	−	0.510178i
$856$		0			0
$857$	21.0215	+	21.0215i	0.718082	+	0.718082i	0.968212	−	0.250131i	$-0.0804736\pi$
$857$	21.0215	+	21.0215i	0.718082	+	0.718082i	−0.250131	+	0.968212i	$0.580474\pi$
$858$		0			0
$859$	−27.0632	+	27.0632i	−0.923386	+	0.923386i	−0.997267	−	0.0738814i	$-0.976461\pi$
$859$	−27.0632	+	27.0632i	−0.923386	+	0.923386i	0.0738814	+	0.997267i	$0.476461\pi$
$860$		0			0
$861$	−6.57656			−0.224129
$862$		0			0
$863$	−16.9825	+	9.80486i	−0.578092	+	0.333761i	−0.760375	−	0.649485i	$-0.774985\pi$
$863$	−16.9825	+	9.80486i	−0.578092	+	0.333761i	0.182283	+	0.983246i	$0.441651\pi$
$864$		0			0
$865$	−0.0819539	+	0.0819539i	−0.00278652	+	0.00278652i
$866$		0			0
$867$	−18.1669	+	10.4886i	−0.616979	+	0.356213i
$868$		0			0
$869$	17.1179	+	63.8847i	0.580684	+	2.16714i
$870$		0			0
$871$	0.0682627	−	0.254760i	0.00231299	−	0.00863221i
$872$		0			0
$873$	−0.787407	+	2.93864i	−0.0266497	+	0.0994580i
$874$		0			0
$875$	60.9653	−	16.3356i	2.06100	−	0.552244i
$876$		0			0
$877$	−37.0910			−1.25247			−0.626237	−	0.779633i	$-0.715406\pi$
$877$	−37.0910			−1.25247			−0.626237	+	0.779633i	$0.715406\pi$
$878$		0			0
$879$	2.01996	+	3.49867i	0.0681316	+	0.118007i
$880$		0			0
$881$	27.5790	+	15.9228i	0.929161	+	0.536451i	0.886546	−	0.462640i	$-0.153098\pi$
$881$	27.5790	+	15.9228i	0.929161	+	0.536451i	0.0426149	+	0.999092i	$0.486431\pi$
$882$		0			0
$883$	−29.5772	+	7.92519i	−0.995352	+	0.266704i	−0.719497	−	0.694495i	$-0.755628\pi$
$883$	−29.5772	+	7.92519i	−0.995352	+	0.266704i	−0.275855	+	0.961199i	$0.588961\pi$
$884$		0			0
$885$	−0.741706	+	1.28467i	−0.0249322	+	0.0431838i
$886$		0			0
$887$	−10.3513			−0.347562			−0.173781	−	0.984784i	$-0.555599\pi$
$887$	−10.3513			−0.347562			−0.173781	+	0.984784i	$0.555599\pi$
$888$		0			0
$889$	87.6041			2.93815
$890$		0			0
$891$	−11.8388	+	20.5053i	−0.396613	+	0.686955i
$892$		0			0
$893$	7.00751	−	1.87766i	0.234497	−	0.0628334i
$894$		0			0
$895$	4.66528	+	2.69350i	0.155943	+	0.0900339i
$896$		0			0
$897$	0.227560	+	0.394146i	0.00759801	+	0.0131601i
$898$		0			0
$899$	−39.3952			−1.31390
$900$		0			0
$901$	41.5978	−	11.1461i	1.38583	−	0.371331i
$902$		0			0
$903$	3.12060	−	11.6462i	0.103847	−	0.387563i
$904$		0			0
$905$	8.04314	−	30.0174i	0.267363	−	0.997812i
$906$		0			0
$907$	−15.2914	−	57.0682i	−0.507741	−	1.89492i	−0.441847	−	0.897090i	$-0.645677\pi$
$907$	−15.2914	−	57.0682i	−0.507741	−	1.89492i	−0.0658942	−	0.997827i	$-0.520990\pi$
$908$		0			0
$909$	−10.4966	+	6.06024i	−0.348151	+	0.201005i
$910$		0			0
$911$	32.8261	−	32.8261i	1.08758	−	1.08758i	0.0918013	−	0.995777i	$-0.470738\pi$
$911$	32.8261	−	32.8261i	1.08758	−	1.08758i	0.995777	−	0.0918013i	$-0.0292624\pi$
$912$		0			0
$913$	−43.8348	+	25.3081i	−1.45072	+	0.837575i
$914$		0			0
$915$	−15.7466			−0.520567
$916$		0			0
$917$	36.4943	−	36.4943i	1.20515	−	1.20515i
$918$		0			0
$919$	−9.53053	−	9.53053i	−0.314383	−	0.314383i	0.532222	−	0.846605i	$-0.321357\pi$
$919$	−9.53053	−	9.53053i	−0.314383	−	0.314383i	−0.846605	+	0.532222i	$0.821357\pi$
$920$		0			0
$921$	−5.45390	+	9.44643i	−0.179712	+	0.311270i
$922$		0			0
$923$	−4.63517	−	1.24199i	−0.152568	−	0.0408806i
$924$		0			0
$925$	3.30288	−	9.03392i	0.108598	−	0.297034i
$926$		0			0
$927$	−6.87370	+	25.6530i	−0.225762	+	0.842555i
$928$		0			0
$929$	−7.09094	−	4.09396i	−0.232646	−	0.134318i	0.379146	−	0.925337i	$-0.376218\pi$
$929$	−7.09094	−	4.09396i	−0.232646	−	0.134318i	−0.611792	+	0.791019i	$0.709551\pi$
$930$		0			0
$931$	53.2084	−	53.2084i	1.74383	−	1.74383i
$932$		0			0
$933$	0.705270	+	0.705270i	0.0230895	+	0.0230895i
$934$		0			0
$935$		−	66.2641i		−	2.16707i
$936$		0			0
$937$	3.23392	+	5.60132i	0.105648	+	0.182987i	0.914003	−	0.405708i	$-0.132975\pi$
$937$	3.23392	+	5.60132i	0.105648	+	0.182987i	−0.808355	+	0.588695i	$0.799642\pi$
$938$		0			0
$939$	14.5592	+	14.5592i	0.475120	+	0.475120i
$940$		0			0
$941$	−19.6217	−	33.9858i	−0.639650	−	1.10791i	−0.985510	−	0.169620i	$-0.945746\pi$
$941$	−19.6217	−	33.9858i	−0.639650	−	1.10791i	0.345859	−	0.938286i	$-0.387587\pi$
$942$		0			0
$943$	2.74487	−	0.735486i	0.0893853	−	0.0239507i
$944$		0			0
$945$	−37.0536	−	9.92847i	−1.20535	−	0.322973i
$946$		0			0
$947$	18.3463	+	4.91589i	0.596176	+	0.159745i	0.544274	−	0.838907i	$-0.316805\pi$
$947$	18.3463	+	4.91589i	0.596176	+	0.159745i	0.0519016	+	0.998652i	$0.483472\pi$
$948$		0			0
$949$	0.793591	+	2.96172i	0.0257611	+	0.0961416i
$950$		0			0
$951$		−	16.3897i		−	0.531471i
$952$		0			0
$953$	−5.88159	+	3.39574i	−0.190524	+	0.109999i	−0.592228	−	0.805771i	$-0.701751\pi$
$953$	−5.88159	+	3.39574i	−0.190524	+	0.109999i	0.401704	+	0.915770i	$0.368418\pi$
$954$		0			0
$955$	−2.16736	+	3.75398i	−0.0701341	+	0.121476i
$956$		0			0
$957$	−6.78127	−	25.3081i	−0.219207	−	0.818093i
$958$		0			0
$959$	24.6638	+	14.2396i	0.796434	+	0.459822i
$960$		0			0
$961$			3.08342i			0.0994653i
$962$		0			0
$963$			11.8973i			0.383385i
$964$		0			0
$965$	12.3744	+	7.14435i	0.398345	+	0.229985i
$966$		0			0
$967$	5.63347	+	21.0244i	0.181160	+	0.676099i	0.995420	+	0.0955986i	$0.0304765\pi$
$967$	5.63347	+	21.0244i	0.181160	+	0.676099i	−0.814260	+	0.580501i	$0.802857\pi$
$968$		0			0
$969$	−9.35069	+	16.1959i	−0.300388	+	0.520286i
$970$		0			0
$971$	−9.82170	+	5.67056i	−0.315193	+	0.181977i	−0.649248	−	0.760577i	$-0.724916\pi$
$971$	−9.82170	+	5.67056i	−0.315193	+	0.181977i	0.334055	+	0.942554i	$0.391583\pi$
$972$		0			0
$973$		−	98.5856i		−	3.16051i
$974$		0			0
$975$	−0.113533	−	0.423712i	−0.00363598	−	0.0135697i
$976$		0			0
$977$	13.0071	+	3.48525i	0.416135	+	0.111503i	0.460811	−	0.887498i	$-0.347559\pi$
$977$	13.0071	+	3.48525i	0.416135	+	0.111503i	−0.0446754	+	0.999002i	$0.514225\pi$
$978$		0			0
$979$	88.6295	+	23.7482i	2.83261	+	0.758996i
$980$		0			0
$981$	−14.6858	+	3.93506i	−0.468883	+	0.125637i
$982$		0			0
$983$	−2.80003	−	4.84980i	−0.0893071	−	0.154685i	0.817911	−	0.575344i	$-0.195132\pi$
$983$	−2.80003	−	4.84980i	−0.0893071	−	0.154685i	−0.907218	+	0.420660i	$0.861799\pi$
$984$		0			0
$985$	11.6861	+	11.6861i	0.372351	+	0.372351i
$986$		0			0
$987$	−3.64286	−	6.30961i	−0.115953	−	0.200837i
$988$		0			0
$989$			5.20980i			0.165662i
$990$		0			0
$991$	−16.6980	−	16.6980i	−0.530429	−	0.530429i	0.390271	−	0.920700i	$-0.372381\pi$
$991$	−16.6980	−	16.6980i	−0.530429	−	0.530429i	−0.920700	+	0.390271i	$0.872381\pi$
$992$		0			0
$993$	−12.4815	+	12.4815i	−0.396088	+	0.396088i
$994$		0			0
$995$	−1.74796	−	1.00918i	−0.0554139	−	0.0319932i
$996$		0			0
$997$	5.34400	−	19.9441i	0.169246	−	0.631636i	−0.828214	−	0.560412i	$-0.810643\pi$
$997$	5.34400	−	19.9441i	0.169246	−	0.631636i	0.997460	−	0.0712238i	$-0.0226904\pi$
$998$		0			0
$999$	−18.6613	+	15.6127i	−0.590416	+	0.493965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.b.415.2	✓	8
4.3	odd	2		592.2.be.c.415.2	yes	8
37.14	odd	12		592.2.be.c.495.2	yes	8
148.51	even	12	inner	592.2.be.b.495.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.b.415.2	✓	8	1.1	even	1	trivial
592.2.be.b.495.2	yes	8	148.51	even	12	inner
592.2.be.c.415.2	yes	8	4.3	odd	2
592.2.be.c.495.2	yes	8	37.14	odd	12

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 0.633975i) q^{3} +(1.78597 - 0.478548i) q^{5} +(-4.49187 - 2.59338i) q^{7} +(1.23205 + 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 0.633975i) q^{3} +(1.78597 - 0.478548i) q^{5} +(-4.49187 - 2.59338i) q^{7} +(1.23205 + 2.13397i) q^{9} +5.30398 q^{11} +(-0.366025 + 0.0980762i) q^{13} +(0.350322 - 1.30742i) q^{15} +(1.74881 - 6.52665i) q^{17} +(-0.978548 - 3.65199i) q^{19} +(-3.28828 + 1.89849i) q^{21} +(1.16012 - 1.16012i) q^{23} +(-1.36946 + 0.790658i) q^{25} +4.00000 q^{27} +(4.77152 - 4.77152i) q^{29} +(-4.12816 - 4.12816i) q^{31} +(1.94139 - 3.36259i) q^{33} +(-9.26339 - 2.48212i) q^{35} +(-4.66532 + 3.90318i) q^{37} +(-0.0717968 + 0.267949i) q^{39} +(1.50000 + 0.866025i) q^{41} +(-2.24538 + 2.24538i) q^{43} +(3.22161 + 3.22161i) q^{45} +1.91882i q^{47} +(9.95128 + 17.2361i) q^{49} +(-3.49762 - 3.49762i) q^{51} +(3.18677 + 5.51964i) q^{53} +(9.47273 - 2.53821i) q^{55} +(-2.67344 - 0.716347i) q^{57} +(-1.05861 - 0.283653i) q^{59} +(-3.01101 - 11.2372i) q^{61} -12.7807i q^{63} +(-0.606775 + 0.350322i) q^{65} +(-0.348008 + 0.602768i) q^{67} +(-0.310853 - 1.16012i) q^{69} +(10.9669 + 6.33175i) q^{71} -8.09158i q^{73} +1.15760i q^{75} +(-23.8248 - 13.7553i) q^{77} +(3.22736 + 12.0447i) q^{79} +(-2.23205 + 3.86603i) q^{81} +(-8.26451 + 4.77152i) q^{83} -12.4933i q^{85} +(-1.27852 - 4.77152i) q^{87} +(16.7100 + 4.47743i) q^{89} +(1.89849 + 0.508699i) q^{91} +(-4.12816 + 1.10614i) q^{93} +(-3.49531 - 6.05405i) q^{95} +(0.873031 + 0.873031i) q^{97} +(6.53478 + 11.3186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 2 q^{5} - 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 2 * q^5 - 6 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} + 2 q^{5} - 6 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} + 8 q^{17} - 2 q^{19} + 20 q^{23} - 36 q^{25} + 32 q^{27} + 4 q^{29} + 4 q^{31} + 16 q^{33} - 10 q^{35} + 6 q^{37} - 56 q^{39} + 12 q^{41} + 20 q^{43} - 4 q^{45} + 24 q^{49} - 16 q^{51} - 12 q^{53} + 26 q^{55} - 8 q^{57} - 8 q^{59} - 14 q^{61} + 12 q^{65} - 22 q^{67} - 28 q^{69} - 6 q^{71} - 60 q^{77} + 14 q^{79} - 4 q^{81} - 48 q^{83} + 40 q^{87} + 16 q^{89} + 4 q^{91} + 4 q^{93} - 30 q^{95} - 16 q^{97} + 34 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 2 * q^5 - 6 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 + 8 * q^17 - 2 * q^19 + 20 * q^23 - 36 * q^25 + 32 * q^27 + 4 * q^29 + 4 * q^31 + 16 * q^33 - 10 * q^35 + 6 * q^37 - 56 * q^39 + 12 * q^41 + 20 * q^43 - 4 * q^45 + 24 * q^49 - 16 * q^51 - 12 * q^53 + 26 * q^55 - 8 * q^57 - 8 * q^59 - 14 * q^61 + 12 * q^65 - 22 * q^67 - 28 * q^69 - 6 * q^71 - 60 * q^77 + 14 * q^79 - 4 * q^81 - 48 * q^83 + 40 * q^87 + 16 * q^89 + 4 * q^91 + 4 * q^93 - 30 * q^95 - 16 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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