LMFDB - Embedded newform 880.2.bo.k.641.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
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} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.3
Root			$0.507132 + 1.56079i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.k.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.507132 + 1.56079i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.04337 + 3.21117i) q^{7} +(0.248161 - 0.180299i) q^{9} +O(q^{10})$	\(q+(0.507132 + 1.56079i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.04337 + 3.21117i) q^{7} +(0.248161 - 0.180299i) q^{9} +(-3.04773 - 1.30817i) q^{11} +(-3.81111 + 2.76894i) q^{13} +(0.507132 - 1.56079i) q^{15} +(-6.11288 - 4.44127i) q^{17} +(0.689025 + 2.12060i) q^{19} -5.54110 q^{21} +0.0373449 q^{23} +(0.309017 + 0.951057i) q^{25} +(4.39033 + 3.18976i) q^{27} +(1.96680 - 6.05318i) q^{29} +(-0.282197 + 0.205028i) q^{31} +(0.496182 - 5.42030i) q^{33} +(2.73159 - 1.98461i) q^{35} +(-2.04989 + 6.30890i) q^{37} +(-6.25447 - 4.54414i) q^{39} +(-0.609134 - 1.87472i) q^{41} -12.1934 q^{43} -0.306743 q^{45} +(1.96818 + 6.05743i) q^{47} +(-3.55987 - 2.58640i) q^{49} +(3.83186 - 11.7932i) q^{51} +(-7.33459 + 5.32889i) q^{53} +(1.69674 + 2.84975i) q^{55} +(-2.96039 + 2.15085i) q^{57} +(0.959323 - 2.95249i) q^{59} +(9.45447 + 6.86907i) q^{61} +(0.320048 + 0.985006i) q^{63} +4.71080 q^{65} -7.94556 q^{67} +(0.0189388 + 0.0582877i) q^{69} +(0.193262 + 0.140413i) q^{71} +(4.12771 - 12.7038i) q^{73} +(-1.32769 + 0.964623i) q^{75} +(7.38069 - 8.42188i) q^{77} +(-5.73224 + 4.16471i) q^{79} +(-2.46771 + 7.59483i) q^{81} +(-9.72451 - 7.06527i) q^{83} +(2.33491 + 7.18612i) q^{85} +10.4452 q^{87} +1.87036 q^{89} +(-4.91512 - 15.1272i) q^{91} +(-0.463118 - 0.336475i) q^{93} +(0.689025 - 2.12060i) q^{95} +(12.7721 - 9.27950i) q^{97} +(-0.992190 + 0.224867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9}+O(q^{10}) $ 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9	$ 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37} - 3 q^{39} - 11 q^{41} + 16 q^{43} + 38 q^{45} + 10 q^{47} + 4 q^{49} - 26 q^{51} - 9 q^{53} - 3 q^{55} - 50 q^{57} + 60 q^{59} + 30 q^{61} - 52 q^{63} + 24 q^{65} + 4 q^{67} + 41 q^{69} + 10 q^{71} + q^{73} - 2 q^{75} - 4 q^{77} - 19 q^{79} - 31 q^{81} - 64 q^{83} - 11 q^{85} - 30 q^{87} + 24 q^{89} + 9 q^{91} + 45 q^{93} + 2 q^{95} - 3 q^{97} + 10 q^{99}+O(q^{100}) $ 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.507132	+	1.56079i	0.292793	+	0.901124i	0.983954	+	0.178423i	$0.0570996\pi$
$3$	0.507132	+	1.56079i	0.292793	+	0.901124i	−0.691161	+	0.722701i	$0.742900\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−1.04337	+	3.21117i	−0.394358	+	1.21371i	0.535103	+	0.844787i	$0.320273\pi$
$7$	−1.04337	+	3.21117i	−0.394358	+	1.21371i	−0.929461	+	0.368922i	$0.879727\pi$
$8$		0			0
$9$	0.248161	−	0.180299i	0.0827202	−	0.0600998i
$10$		0			0
$11$	−3.04773	−	1.30817i	−0.918926	−	0.394429i
$11$	−3.04773	−	1.30817i	−0.918926	−	0.394429i
$12$		0			0
$13$	−3.81111	+	2.76894i	−1.05701	+	0.767965i	−0.973533	−	0.228545i	$-0.926603\pi$
$13$	−3.81111	+	2.76894i	−1.05701	+	0.767965i	−0.0834794	+	0.996510i	$0.526603\pi$
$14$		0			0
$15$	0.507132	−	1.56079i	0.130941	−	0.402995i
$16$		0			0
$17$	−6.11288	−	4.44127i	−1.48259	−	1.07717i	−0.976711	−	0.214561i	$-0.931168\pi$
$17$	−6.11288	−	4.44127i	−1.48259	−	1.07717i	−0.505880	−	0.862604i	$-0.668832\pi$
$18$		0			0
$19$	0.689025	+	2.12060i	0.158073	+	0.486500i	0.998459	−	0.0554888i	$-0.0176717\pi$
$19$	0.689025	+	2.12060i	0.158073	+	0.486500i	−0.840386	+	0.541988i	$0.817672\pi$
$20$		0			0
$21$	−5.54110			−1.20917
$22$		0			0
$23$	0.0373449			0.00778696			0.00389348	−	0.999992i	$-0.498761\pi$
$23$	0.0373449			0.00778696			0.00389348	+	0.999992i	$0.498761\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	4.39033	+	3.18976i	0.844919	+	0.613870i
$28$		0			0
$29$	1.96680	−	6.05318i	0.365225	−	1.12405i	−0.584615	−	0.811311i	$-0.698754\pi$
$29$	1.96680	−	6.05318i	0.365225	−	1.12405i	0.949840	−	0.312736i	$-0.101246\pi$
$30$		0			0
$31$	−0.282197	+	0.205028i	−0.0506841	+	0.0368242i	−0.612839	−	0.790208i	$-0.709973\pi$
$31$	−0.282197	+	0.205028i	−0.0506841	+	0.0368242i	0.562155	+	0.827032i	$0.309973\pi$
$32$		0			0
$33$	0.496182	−	5.42030i	0.0863741	−	0.943553i
$34$		0			0
$35$	2.73159	−	1.98461i	0.461722	−	0.335461i
$36$		0			0
$37$	−2.04989	+	6.30890i	−0.336999	+	1.03718i	0.628730	+	0.777624i	$0.283575\pi$
$37$	−2.04989	+	6.30890i	−0.336999	+	1.03718i	−0.965729	+	0.259553i	$0.916425\pi$
$38$		0			0
$39$	−6.25447	−	4.54414i	−1.00152	−	0.727645i
$40$		0			0
$41$	−0.609134	−	1.87472i	−0.0951307	−	0.292782i	0.892157	−	0.451725i	$-0.149191\pi$
$41$	−0.609134	−	1.87472i	−0.0951307	−	0.292782i	−0.987288	+	0.158943i	$0.949191\pi$
$42$		0			0
$43$	−12.1934			−1.85948			−0.929739	−	0.368218i	$-0.879968\pi$
$43$	−12.1934			−1.85948			−0.929739	+	0.368218i	$0.879968\pi$
$44$		0			0
$45$	−0.306743			−0.0457266
$46$		0			0
$47$	1.96818	+	6.05743i	0.287088	+	0.883566i	0.985765	+	0.168129i	$0.0537725\pi$
$47$	1.96818	+	6.05743i	0.287088	+	0.883566i	−0.698677	+	0.715437i	$0.746228\pi$
$48$		0			0
$49$	−3.55987	−	2.58640i	−0.508553	−	0.369486i
$50$		0			0
$51$	3.83186	−	11.7932i	0.536567	−	1.65138i
$52$		0			0
$53$	−7.33459	+	5.32889i	−1.00748	+	0.731980i	−0.963680	−	0.267060i	$-0.913948\pi$
$53$	−7.33459	+	5.32889i	−1.00748	+	0.731980i	−0.0438038	+	0.999040i	$0.513948\pi$
$54$		0			0
$55$	1.69674	+	2.84975i	0.228789	+	0.384260i
$56$		0			0
$57$	−2.96039	+	2.15085i	−0.392114	+	0.284887i
$58$		0			0
$59$	0.959323	−	2.95249i	0.124893	−	0.384382i	−0.868988	−	0.494832i	$-0.835229\pi$
$59$	0.959323	−	2.95249i	0.124893	−	0.384382i	0.993882	+	0.110451i	$0.0352294\pi$
$60$		0			0
$61$	9.45447	+	6.86907i	1.21052	+	0.879495i	0.995278	−	0.0970656i	$-0.0309457\pi$
$61$	9.45447	+	6.86907i	1.21052	+	0.879495i	0.215243	+	0.976561i	$0.430946\pi$
$62$		0			0
$63$	0.320048	+	0.985006i	0.0403222	+	0.124099i
$64$		0			0
$65$	4.71080			0.584302
$66$		0			0
$67$	−7.94556			−0.970704			−0.485352	−	0.874319i	$-0.661309\pi$
$67$	−7.94556			−0.970704			−0.485352	+	0.874319i	$0.661309\pi$
$68$		0			0
$69$	0.0189388	+	0.0582877i	0.00227997	+	0.00701702i
$70$		0			0
$71$	0.193262	+	0.140413i	0.0229359	+	0.0166639i	0.599194	−	0.800604i	$-0.295488\pi$
$71$	0.193262	+	0.140413i	0.0229359	+	0.0166639i	−0.576258	+	0.817268i	$0.695488\pi$
$72$		0			0
$73$	4.12771	−	12.7038i	0.483111	−	1.48686i	−0.351586	−	0.936156i	$-0.614358\pi$
$73$	4.12771	−	12.7038i	0.483111	−	1.48686i	0.834698	−	0.550709i	$-0.185642\pi$
$74$		0			0
$75$	−1.32769	+	0.964623i	−0.153308	+	0.111385i
$76$		0			0
$77$	7.38069	−	8.42188i	0.841107	−	0.959763i
$78$		0			0
$79$	−5.73224	+	4.16471i	−0.644927	+	0.468567i	−0.861539	−	0.507691i	$-0.830499\pi$
$79$	−5.73224	+	4.16471i	−0.644927	+	0.468567i	0.216612	+	0.976258i	$0.430499\pi$
$80$		0			0
$81$	−2.46771	+	7.59483i	−0.274190	+	0.843870i
$82$		0			0
$83$	−9.72451	−	7.06527i	−1.06740	−	0.775514i	−0.0919597	−	0.995763i	$-0.529313\pi$
$83$	−9.72451	−	7.06527i	−1.06740	−	0.775514i	−0.975444	+	0.220249i	$0.929313\pi$
$84$		0			0
$85$	2.33491	+	7.18612i	0.253257	+	0.779444i
$86$		0			0
$87$	10.4452			1.11984
$88$		0			0
$89$	1.87036			0.198258			0.0991288	−	0.995075i	$-0.468394\pi$
$89$	1.87036			0.198258			0.0991288	+	0.995075i	$0.468394\pi$
$90$		0			0
$91$	−4.91512	−	15.1272i	−0.515244	−	1.58576i
$92$		0			0
$93$	−0.463118	−	0.336475i	−0.0480231	−	0.0348908i
$94$		0			0
$95$	0.689025	−	2.12060i	0.0706925	−	0.217569i
$96$		0			0
$97$	12.7721	−	9.27950i	1.29681	−	0.942191i	0.296895	−	0.954910i	$-0.404049\pi$
$97$	12.7721	−	9.27950i	1.29681	−	0.942191i	0.999919	+	0.0127192i	$0.00404877\pi$
$98$		0			0
$99$	−0.992190	+	0.224867i	−0.0997189	+	0.0226000i
$100$		0			0
$101$	−11.3337	+	8.23442i	−1.12775	+	0.819355i	−0.985365	−	0.170457i	$-0.945476\pi$
$101$	−11.3337	+	8.23442i	−1.12775	+	0.819355i	−0.142380	+	0.989812i	$0.545476\pi$
$102$		0			0
$103$	−0.363149	+	1.11766i	−0.0357821	+	0.110126i	−0.967352	−	0.253436i	$-0.918439\pi$
$103$	−0.363149	+	1.11766i	−0.0357821	+	0.110126i	0.931570	+	0.363562i	$0.118439\pi$
$104$		0			0
$105$	4.48284	+	3.25698i	0.437481	+	0.317848i
$106$		0			0
$107$	5.95116	+	18.3158i	0.575321	+	1.77066i	0.635084	+	0.772443i	$0.280965\pi$
$107$	5.95116	+	18.3158i	0.575321	+	1.77066i	−0.0597635	+	0.998213i	$0.519035\pi$
$108$		0			0
$109$	2.43185			0.232929			0.116464	−	0.993195i	$-0.462844\pi$
$109$	2.43185			0.232929			0.116464	+	0.993195i	$0.462844\pi$
$110$		0			0
$111$	−10.8864			−1.03330
$112$		0			0
$113$	3.20288	+	9.85746i	0.301302	+	0.927312i	0.981031	+	0.193849i	$0.0620971\pi$
$113$	3.20288	+	9.85746i	0.301302	+	0.927312i	−0.679730	+	0.733463i	$0.737903\pi$
$114$		0			0
$115$	−0.0302127	−	0.0219508i	−0.00281735	−	0.00204692i
$116$		0			0
$117$	−0.446531	+	1.37428i	−0.0412818	+	0.127052i
$118$		0			0
$119$	20.6397	−	14.9956i	1.89204	−	1.37464i
$120$		0			0
$121$	7.57737	+	7.97392i	0.688852	+	0.724902i
$122$		0			0
$123$	2.61714	−	1.90146i	0.235980	−	0.171449i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−1.57269	−	1.14263i	−0.139554	−	0.101392i	0.515818	−	0.856698i	$-0.327488\pi$
$127$	−1.57269	−	1.14263i	−0.139554	−	0.101392i	−0.655372	+	0.755306i	$0.727488\pi$
$128$		0			0
$129$	−6.18368	−	19.0314i	−0.544442	−	1.67562i
$130$		0			0
$131$	−8.69173			−0.759400			−0.379700	−	0.925110i	$-0.623973\pi$
$131$	−8.69173			−0.759400			−0.379700	+	0.925110i	$0.623973\pi$
$132$		0			0
$133$	−7.52853			−0.652806
$134$		0			0
$135$	−1.67696	−	5.16114i	−0.144329	−	0.444200i
$136$		0			0
$137$	14.3484	+	10.4248i	1.22587	+	0.890647i	0.996574	−	0.0827100i	$-0.0263575\pi$
$137$	14.3484	+	10.4248i	1.22587	+	0.890647i	0.229296	+	0.973357i	$0.426358\pi$
$138$		0			0
$139$	−0.993953	+	3.05907i	−0.0843060	+	0.259467i	−0.984319	−	0.176395i	$-0.943556\pi$
$139$	−0.993953	+	3.05907i	−0.0843060	+	0.259467i	0.900014	+	0.435862i	$0.143556\pi$
$140$		0			0
$141$	−8.45626	+	6.14383i	−0.712145	+	0.517404i
$142$		0			0
$143$	15.2375	−	3.45339i	1.27422	−	0.288787i
$144$		0			0
$145$	−5.14914	+	3.74107i	−0.427613	+	0.310679i
$146$		0			0
$147$	2.23151	−	6.86787i	0.184052	−	0.566452i
$148$		0			0
$149$	−2.65448	−	1.92859i	−0.217464	−	0.157996i	0.473721	−	0.880675i	$-0.342911\pi$
$149$	−2.65448	−	1.92859i	−0.217464	−	0.157996i	−0.691184	+	0.722679i	$0.742911\pi$
$150$		0			0
$151$	6.84986	+	21.0817i	0.557434	+	1.71561i	0.689428	+	0.724355i	$0.257862\pi$
$151$	6.84986	+	21.0817i	0.557434	+	1.71561i	−0.131994	+	0.991251i	$0.542138\pi$
$152$		0			0
$153$	−2.31773			−0.187378
$154$		0			0
$155$	0.348815			0.0280175
$156$		0			0
$157$	3.57071	+	10.9895i	0.284974	+	0.877060i	0.986406	+	0.164324i	$0.0525442\pi$
$157$	3.57071	+	10.9895i	0.284974	+	0.877060i	−0.701433	+	0.712736i	$0.747456\pi$
$158$		0			0
$159$	−12.0369	−	8.74532i	−0.954589	−	0.693549i
$160$		0			0
$161$	−0.0389647	+	0.119921i	−0.00307085	+	0.00945110i
$162$		0			0
$163$	4.29825	−	3.12286i	0.336665	−	0.244602i	−0.406588	−	0.913612i	$-0.633282\pi$
$163$	4.29825	−	3.12286i	0.336665	−	0.244602i	0.743253	+	0.669010i	$0.233282\pi$
$164$		0			0
$165$	−3.58739	+	4.09346i	−0.279278	+	0.318676i
$166$		0			0
$167$	−1.11886	+	0.812900i	−0.0865800	+	0.0629041i	−0.630233	−	0.776406i	$-0.717041\pi$
$167$	−1.11886	+	0.812900i	−0.0865800	+	0.0629041i	0.543653	+	0.839310i	$0.317041\pi$
$168$		0			0
$169$	2.84036	−	8.74173i	0.218489	−	0.672441i
$170$		0			0
$171$	0.553332	+	0.402019i	0.0423144	+	0.0307432i
$172$		0			0
$173$	−0.168768	−	0.519413i	−0.0128312	−	0.0394903i	0.944436	−	0.328696i	$-0.106609\pi$
$173$	−0.168768	−	0.519413i	−0.0128312	−	0.0394903i	−0.957267	+	0.289205i	$0.906609\pi$
$174$		0			0
$175$	−3.37642			−0.255234
$176$		0			0
$177$	5.09473			0.382944
$178$		0			0
$179$	6.45204	+	19.8573i	0.482248	+	1.48421i	0.835928	+	0.548840i	$0.184930\pi$
$179$	6.45204	+	19.8573i	0.482248	+	1.48421i	−0.353680	+	0.935366i	$0.615070\pi$
$180$		0			0
$181$	2.65261	+	1.92723i	0.197167	+	0.143250i	0.681988	−	0.731363i	$-0.261115\pi$
$181$	2.65261	+	1.92723i	0.197167	+	0.143250i	−0.484822	+	0.874613i	$0.661115\pi$
$182$		0			0
$183$	−5.92653	+	18.2400i	−0.438102	+	1.34834i
$184$		0			0
$185$	5.36667	−	3.89912i	0.394566	−	0.286669i
$186$		0			0
$187$	12.8205	+	21.5325i	0.937527	+	1.57461i
$188$		0			0
$189$	−14.8236	+	10.7700i	−1.07826	+	0.783401i
$190$		0			0
$191$	2.21356	−	6.81264i	0.160168	−	0.492946i	−0.838480	−	0.544932i	$-0.816555\pi$
$191$	2.21356	−	6.81264i	0.160168	−	0.492946i	0.998648	+	0.0519867i	$0.0165554\pi$
$192$		0			0
$193$	−6.88742	−	5.00400i	−0.495767	−	0.360196i	0.311631	−	0.950203i	$-0.399125\pi$
$193$	−6.88742	−	5.00400i	−0.495767	−	0.360196i	−0.807398	+	0.590007i	$0.799125\pi$
$194$		0			0
$195$	2.38900	+	7.35258i	0.171080	+	0.526529i
$196$		0			0
$197$	17.4391			1.24248			0.621242	−	0.783619i	$-0.286628\pi$
$197$	17.4391			1.24248			0.621242	+	0.783619i	$0.286628\pi$
$198$		0			0
$199$	−11.9860			−0.849668			−0.424834	−	0.905271i	$-0.639668\pi$
$199$	−11.9860			−0.849668			−0.424834	+	0.905271i	$0.639668\pi$
$200$		0			0
$201$	−4.02945	−	12.4014i	−0.284215	−	0.874725i
$202$		0			0
$203$	17.3857	+	12.6314i	1.22024	+	0.886553i
$204$		0			0
$205$	−0.609134	+	1.87472i	−0.0425438	+	0.130936i
$206$		0			0
$207$	0.00926755	−	0.00673327i	0.000644139	−	0.000467994i
$208$		0			0
$209$	0.674147	−	7.36440i	0.0466317	−	0.509406i
$210$		0			0
$211$	−1.72765	+	1.25521i	−0.118936	+	0.0864122i	−0.645663	−	0.763622i	$-0.723419\pi$
$211$	−1.72765	+	1.25521i	−0.118936	+	0.0864122i	0.526727	+	0.850035i	$0.323419\pi$
$212$		0			0
$213$	−0.121146	+	0.372849i	−0.00830079	+	0.0255472i
$214$		0			0
$215$	9.86468	+	7.16711i	0.672766	+	0.488793i
$216$		0			0
$217$	−0.363944	−	1.12010i	−0.0247061	−	0.0760376i
$218$		0			0
$219$	21.9212			1.48130
$220$		0			0
$221$	35.5945			2.39434
$222$		0			0
$223$	−5.21671	−	16.0554i	−0.349337	−	1.07515i	−0.959221	−	0.282657i	$-0.908784\pi$
$223$	−5.21671	−	16.0554i	−0.349337	−	1.07515i	0.609884	−	0.792491i	$-0.291216\pi$
$224$		0			0
$225$	0.248161	+	0.180299i	0.0165440	+	0.0120200i
$226$		0			0
$227$	−2.32601	+	7.15873i	−0.154383	+	0.475141i	−0.998098	−	0.0616499i	$-0.980364\pi$
$227$	−2.32601	+	7.15873i	−0.154383	+	0.475141i	0.843715	+	0.536791i	$0.180364\pi$
$228$		0			0
$229$	−6.21977	+	4.51893i	−0.411014	+	0.298619i	−0.774012	−	0.633171i	$-0.781753\pi$
$229$	−6.21977	+	4.51893i	−0.411014	+	0.298619i	0.362998	+	0.931790i	$0.381753\pi$
$230$		0			0
$231$	16.8878	+	7.24871i	1.11114	+	0.476930i
$232$		0			0
$233$	5.01615	−	3.64444i	0.328619	−	0.238755i	−0.411226	−	0.911534i	$-0.634899\pi$
$233$	5.01615	−	3.64444i	0.328619	−	0.238755i	0.739844	+	0.672778i	$0.234899\pi$
$234$		0			0
$235$	1.96818	−	6.05743i	0.128390	−	0.395143i
$236$		0			0
$237$	−9.40725	−	6.83477i	−0.611067	−	0.443966i
$238$		0			0
$239$	−3.09863	−	9.53659i	−0.200433	−	0.616871i	−0.999870	−	0.0161202i	$-0.994869\pi$
$239$	−3.09863	−	9.53659i	−0.200433	−	0.616871i	0.799437	−	0.600750i	$-0.205131\pi$
$240$		0			0
$241$	−3.46869			−0.223438			−0.111719	−	0.993740i	$-0.535636\pi$
$241$	−3.46869			−0.223438			−0.111719	+	0.993740i	$0.535636\pi$
$242$		0			0
$243$	3.17482			0.203665
$244$		0			0
$245$	1.35975	+	4.18488i	0.0868713	+	0.267362i
$246$		0			0
$247$	−8.49777	−	6.17399i	−0.540700	−	0.392842i
$248$		0			0
$249$	6.09581	−	18.7610i	0.386306	−	1.18893i
$250$		0			0
$251$	18.2313	−	13.2458i	1.15075	−	0.836066i	0.162167	−	0.986763i	$-0.448152\pi$
$251$	18.2313	−	13.2458i	1.15075	−	0.836066i	0.988580	+	0.150697i	$0.0481518\pi$
$252$		0			0
$253$	−0.113817	−	0.0488536i	−0.00715564	−	0.00307140i
$254$		0			0
$255$	−10.0319	+	7.28862i	−0.628224	+	0.456431i
$256$		0			0
$257$	−0.0692136	+	0.213017i	−0.00431742	+	0.0132877i	−0.953192	−	0.302366i	$-0.902224\pi$
$257$	−0.0692136	+	0.213017i	−0.00431742	+	0.0132877i	0.948875	+	0.315653i	$0.102224\pi$
$258$		0			0
$259$	−18.1202	−	13.1651i	−1.12593	−	0.818038i
$260$		0			0
$261$	−0.603302	−	1.85677i	−0.0373435	−	0.114931i
$262$		0			0
$263$	7.31270			0.450921			0.225460	−	0.974252i	$-0.427611\pi$
$263$	7.31270			0.450921			0.225460	+	0.974252i	$0.427611\pi$
$264$		0			0
$265$	9.06605			0.556923
$266$		0			0
$267$	0.948519	+	2.91924i	0.0580484	+	0.178655i
$268$		0			0
$269$	−22.5295	−	16.3686i	−1.37365	−	0.998014i	−0.997442	−	0.0714778i	$-0.977228\pi$
$269$	−22.5295	−	16.3686i	−1.37365	−	0.998014i	−0.376206	−	0.926536i	$-0.622772\pi$
$270$		0			0
$271$	6.53606	−	20.1159i	0.397037	−	1.22195i	−0.530326	−	0.847794i	$-0.677931\pi$
$271$	6.53606	−	20.1159i	0.397037	−	1.22195i	0.927364	−	0.374161i	$-0.122069\pi$
$272$		0			0
$273$	21.1178	−	15.3430i	1.27811	−	0.928598i
$274$		0			0
$275$	0.302344	−	3.30282i	0.0182320	−	0.199167i
$276$		0			0
$277$	−2.68126	+	1.94805i	−0.161101	+	0.117047i	−0.665415	−	0.746473i	$-0.731745\pi$
$277$	−2.68126	+	1.94805i	−0.161101	+	0.117047i	0.504314	+	0.863520i	$0.331745\pi$
$278$		0			0
$279$	−0.0330638	+	0.101760i	−0.00197948	+	0.00609221i
$280$		0			0
$281$	−13.3429	−	9.69419i	−0.795971	−	0.578307i	0.113758	−	0.993508i	$-0.463711\pi$
$281$	−13.3429	−	9.69419i	−0.795971	−	0.578307i	−0.909730	+	0.415201i	$0.863711\pi$
$282$		0			0
$283$	−2.72185	−	8.37700i	−0.161797	−	0.497961i	0.836989	−	0.547220i	$-0.184314\pi$
$283$	−2.72185	−	8.37700i	−0.161797	−	0.497961i	−0.998786	+	0.0492591i	$0.984314\pi$
$284$		0			0
$285$	3.65925			0.216755
$286$		0			0
$287$	6.65561			0.392868
$288$		0			0
$289$	12.3891	+	38.1299i	0.728773	+	2.24293i
$290$		0			0
$291$	20.9605	+	15.2287i	1.22873	+	0.892724i
$292$		0			0
$293$	2.00266	−	6.16355i	0.116997	−	0.360079i	−0.875362	−	0.483469i	$-0.839377\pi$
$293$	2.00266	−	6.16355i	0.116997	−	0.360079i	0.992358	+	0.123390i	$0.0393766\pi$
$294$		0			0
$295$	−2.51154	+	1.82474i	−0.146228	+	0.106241i
$296$		0			0
$297$	−9.20780	−	15.4648i	−0.534291	−	0.897362i
$298$		0			0
$299$	−0.142326	+	0.103406i	−0.00823092	+	0.00598011i
$300$		0			0
$301$	12.7223	−	39.1552i	0.733300	−	2.25687i
$302$		0			0
$303$	−18.5999	−	13.5136i	−1.06854	−	0.776337i
$304$		0			0
$305$	−3.61129	−	11.1144i	−0.206782	−	0.636409i
$306$		0			0
$307$	25.9368			1.48029			0.740145	−	0.672447i	$-0.234757\pi$
$307$	25.9368			1.48029			0.740145	+	0.672447i	$0.234757\pi$
$308$		0			0
$309$	−1.92860			−0.109714
$310$		0			0
$311$	2.50315	+	7.70391i	0.141941	+	0.436849i	0.996605	−	0.0823324i	$-0.0262369\pi$
$311$	2.50315	+	7.70391i	0.141941	+	0.436849i	−0.854664	+	0.519181i	$0.826237\pi$
$312$		0			0
$313$	3.47852	+	2.52729i	0.196618	+	0.142851i	0.681738	−	0.731596i	$-0.261224\pi$
$313$	3.47852	+	2.52729i	0.196618	+	0.142851i	−0.485121	+	0.874447i	$0.661224\pi$
$314$		0			0
$315$	0.320048	−	0.985006i	0.0180326	−	0.0554988i
$316$		0			0
$317$	−24.5447	+	17.8328i	−1.37857	+	1.00159i	−0.381556	+	0.924346i	$0.624612\pi$
$317$	−24.5447	+	17.8328i	−1.37857	+	1.00159i	−0.997012	+	0.0772425i	$0.975388\pi$
$318$		0			0
$319$	−13.9129	+	15.8756i	−0.778971	+	0.888861i
$320$		0			0
$321$	−25.5691	+	18.5771i	−1.42713	+	1.03687i
$322$		0			0
$323$	5.20623	−	16.0231i	0.289682	−	0.891551i
$324$		0			0
$325$	−3.81111	−	2.76894i	−0.211403	−	0.153593i
$326$		0			0
$327$	1.23327	+	3.79561i	0.0681998	+	0.209898i
$328$		0			0
$329$	−21.5050			−1.18561
$330$		0			0
$331$	−17.1659			−0.943526			−0.471763	−	0.881726i	$-0.656382\pi$
$331$	−17.1659			−0.943526			−0.471763	+	0.881726i	$0.656382\pi$
$332$		0			0
$333$	0.628789	+	1.93521i	0.0344574	+	0.106049i
$334$		0			0
$335$	6.42809	+	4.67028i	0.351204	+	0.255165i
$336$		0			0
$337$	−7.12473	+	21.9277i	−0.388109	+	1.19448i	0.546091	+	0.837726i	$0.316115\pi$
$337$	−7.12473	+	21.9277i	−0.388109	+	1.19448i	−0.934200	+	0.356750i	$0.883885\pi$
$338$		0			0
$339$	−13.7612	+	9.99807i	−0.747404	+	0.543021i
$340$		0			0
$341$	1.12827	−	0.255709i	0.0610995	−	0.0138474i
$342$		0			0
$343$	−7.10145	+	5.15951i	−0.383442	+	0.278587i
$344$		0			0
$345$	0.0189388	−	0.0582877i	0.00101963	−	0.00313810i
$346$		0			0
$347$	6.35578	+	4.61775i	0.341196	+	0.247894i	0.745166	−	0.666879i	$-0.232370\pi$
$347$	6.35578	+	4.61775i	0.341196	+	0.247894i	−0.403970	+	0.914772i	$0.632370\pi$
$348$		0			0
$349$	9.00062	+	27.7011i	0.481792	+	1.48280i	0.836574	+	0.547855i	$0.184555\pi$
$349$	9.00062	+	27.7011i	0.481792	+	1.48280i	−0.354781	+	0.934949i	$0.615445\pi$
$350$		0			0
$351$	−25.5643			−1.36452
$352$		0			0
$353$	27.0092			1.43756			0.718778	−	0.695240i	$-0.244702\pi$
$353$	27.0092			1.43756			0.718778	+	0.695240i	$0.244702\pi$
$354$		0			0
$355$	−0.0738194	−	0.227193i	−0.00391793	−	0.0120581i
$356$		0			0
$357$	33.8721	+	24.6095i	1.79270	+	1.30247i
$358$		0			0
$359$	−1.04293	+	3.20979i	−0.0550435	+	0.169406i	−0.974799	−	0.223086i	$-0.928387\pi$
$359$	−1.04293	+	3.20979i	−0.0550435	+	0.169406i	0.919755	+	0.392492i	$0.128387\pi$
$360$		0			0
$361$	11.3491	−	8.24562i	0.597322	−	0.433980i
$362$		0			0
$363$	−8.60291	+	15.8705i	−0.451536	+	0.832987i
$364$		0			0
$365$	−10.8065	+	7.85136i	−0.565637	+	0.410959i
$366$		0			0
$367$	7.52499	−	23.1595i	0.392801	−	1.20892i	−0.537860	−	0.843034i	$-0.680767\pi$
$367$	7.52499	−	23.1595i	0.392801	−	1.20892i	0.930661	−	0.365883i	$-0.119233\pi$
$368$		0			0
$369$	−0.489174	−	0.355406i	−0.0254654	−	0.0185017i
$370$		0			0
$371$	−9.45927	−	29.1126i	−0.491101	−	1.51145i
$372$		0			0
$373$	−31.6078			−1.63659			−0.818296	−	0.574797i	$-0.805081\pi$
$373$	−31.6078			−1.63659			−0.818296	+	0.574797i	$0.805081\pi$
$374$		0			0
$375$	1.64111			0.0847468
$376$		0			0
$377$	9.26518	+	28.5153i	0.477181	+	1.46861i
$378$		0			0
$379$	−14.6414	−	10.6376i	−0.752080	−	0.546418i	0.144391	−	0.989521i	$-0.453878\pi$
$379$	−14.6414	−	10.6376i	−0.752080	−	0.546418i	−0.896471	+	0.443102i	$0.853878\pi$
$380$		0			0
$381$	0.985842	−	3.03411i	0.0505062	−	0.155442i
$382$		0			0
$383$	8.27421	−	6.01157i	0.422792	−	0.307177i	−0.355968	−	0.934498i	$-0.615849\pi$
$383$	8.27421	−	6.01157i	0.422792	−	0.307177i	0.778760	+	0.627321i	$0.215849\pi$
$384$		0			0
$385$	−10.9214	+	2.47519i	−0.556604	+	0.126147i
$386$		0			0
$387$	−3.02593	+	2.19846i	−0.153816	+	0.111754i
$388$		0			0
$389$	2.17892	−	6.70602i	0.110475	−	0.340009i	−0.880501	−	0.474044i	$-0.842794\pi$
$389$	2.17892	−	6.70602i	0.110475	−	0.340009i	0.990977	+	0.134036i	$0.0427937\pi$
$390$		0			0
$391$	−0.228285	−	0.165859i	−0.0115449	−	0.00838784i
$392$		0			0
$393$	−4.40786	−	13.5660i	−0.222347	−	0.684314i
$394$		0			0
$395$	7.08543			0.356507
$396$		0			0
$397$	0.319352			0.0160278			0.00801391	−	0.999968i	$-0.497449\pi$
$397$	0.319352			0.0160278			0.00801391	+	0.999968i	$0.497449\pi$
$398$		0			0
$399$	−3.81796	−	11.7505i	−0.191137	−	0.588259i
$400$		0			0
$401$	−12.7874	−	9.29059i	−0.638572	−	0.463950i	0.220787	−	0.975322i	$-0.429137\pi$
$401$	−12.7874	−	9.29059i	−0.638572	−	0.463950i	−0.859359	+	0.511372i	$0.829137\pi$
$402$		0			0
$403$	0.507776	−	1.56277i	0.0252941	−	0.0778472i
$404$		0			0
$405$	6.46055	−	4.69386i	0.321027	−	0.233240i
$406$		0			0
$407$	14.5006	−	16.5462i	0.718770	−	0.820167i
$408$		0			0
$409$	−1.44204	+	1.04770i	−0.0713041	+	0.0518055i	−0.622866	−	0.782328i	$-0.714032\pi$
$409$	−1.44204	+	1.04770i	−0.0713041	+	0.0518055i	0.551562	+	0.834134i	$0.314032\pi$
$410$		0			0
$411$	−8.99432	+	27.6817i	−0.443657	+	1.36544i
$412$		0			0
$413$	8.48003	+	6.16110i	0.417275	+	0.303168i
$414$		0			0
$415$	3.71443	+	11.4318i	0.182334	+	0.561167i
$416$		0			0
$417$	−5.27864			−0.258496
$418$		0			0
$419$	−30.3772			−1.48402			−0.742012	−	0.670386i	$-0.766128\pi$
$419$	−30.3772			−1.48402			−0.742012	+	0.670386i	$0.766128\pi$
$420$		0			0
$421$	−1.80598	−	5.55823i	−0.0880180	−	0.270892i	0.897353	−	0.441313i	$-0.145487\pi$
$421$	−1.80598	−	5.55823i	−0.0880180	−	0.270892i	−0.985371	+	0.170421i	$0.945487\pi$
$422$		0			0
$423$	1.58057	+	1.14835i	0.0768501	+	0.0558349i
$424$		0			0
$425$	2.33491	−	7.18612i	0.113260	−	0.348578i
$426$		0			0
$427$	−31.9223	+	23.1929i	−1.54483	+	1.12238i
$428$		0			0
$429$	13.1175	+	22.0313i	0.633317	+	1.06368i
$430$		0			0
$431$	−10.9362	+	7.94558i	−0.526776	+	0.382725i	−0.819150	−	0.573579i	$-0.805555\pi$
$431$	−10.9362	+	7.94558i	−0.526776	+	0.382725i	0.292374	+	0.956304i	$0.405555\pi$
$432$		0			0
$433$	2.55849	−	7.87422i	0.122953	−	0.378411i	−0.870569	−	0.492046i	$-0.836249\pi$
$433$	2.55849	−	7.87422i	0.122953	−	0.378411i	0.993523	+	0.113635i	$0.0362493\pi$
$434$		0			0
$435$	−8.45033	−	6.13952i	−0.405162	−	0.294368i
$436$		0			0
$437$	0.0257316	+	0.0791938i	0.00123091	+	0.00378835i
$438$		0			0
$439$	−16.1631			−0.771420			−0.385710	−	0.922620i	$-0.626044\pi$
$439$	−16.1631			−0.771420			−0.385710	+	0.922620i	$0.626044\pi$
$440$		0			0
$441$	−1.34975			−0.0642736
$442$		0			0
$443$	−4.67176	−	14.3782i	−0.221962	−	0.683129i	−0.998586	−	0.0531645i	$-0.983069\pi$
$443$	−4.67176	−	14.3782i	−0.221962	−	0.683129i	0.776624	−	0.629965i	$-0.216931\pi$
$444$		0			0
$445$	−1.51315	−	1.09937i	−0.0717302	−	0.0521151i
$446$		0			0
$447$	1.66396	−	5.12115i	0.0787027	−	0.242222i
$448$		0			0
$449$	−12.6035	+	9.15696i	−0.594795	+	0.432144i	−0.844027	−	0.536300i	$-0.819822\pi$
$449$	−12.6035	+	9.15696i	−0.594795	+	0.432144i	0.249233	+	0.968444i	$0.419822\pi$
$450$		0			0
$451$	−0.595981	+	6.51051i	−0.0280636	+	0.306568i
$452$		0			0
$453$	−29.4304	+	21.3824i	−1.38276	+	1.00463i
$454$		0			0
$455$	−4.91512	+	15.1272i	−0.230424	+	0.709173i
$456$		0			0
$457$	−1.36973	−	0.995165i	−0.0640731	−	0.0465518i	0.555288	−	0.831658i	$-0.312608\pi$
$457$	−1.36973	−	0.995165i	−0.0640731	−	0.0465518i	−0.619361	+	0.785107i	$0.712608\pi$
$458$		0			0
$459$	−12.6710	−	38.9972i	−0.591430	−	1.82023i
$460$		0			0
$461$	22.1699			1.03256			0.516279	−	0.856421i	$-0.327317\pi$
$461$	22.1699			1.03256			0.516279	+	0.856421i	$0.327317\pi$
$462$		0			0
$463$	−26.9423			−1.25211			−0.626057	−	0.779777i	$-0.715332\pi$
$463$	−26.9423			−1.25211			−0.626057	+	0.779777i	$0.715332\pi$
$464$		0			0
$465$	0.176895	+	0.544428i	0.00820332	+	0.0252472i
$466$		0			0
$467$	−33.7398	−	24.5134i	−1.56129	−	1.13434i	−0.934942	−	0.354800i	$-0.884549\pi$
$467$	−33.7398	−	24.5134i	−1.56129	−	1.13434i	−0.626348	−	0.779543i	$-0.715451\pi$
$468$		0			0
$469$	8.29018	−	25.5145i	0.382805	−	1.17815i
$470$		0			0
$471$	−15.3415	+	11.1463i	−0.706901	+	0.513594i
$472$		0			0
$473$	37.1623	+	15.9511i	1.70872	+	0.733432i
$474$		0			0
$475$	−1.80389	+	1.31060i	−0.0827682	+	0.0601346i
$476$		0			0
$477$	−0.859361	+	2.64484i	−0.0393475	+	0.121099i
$478$		0			0
$479$	3.41417	+	2.48054i	0.155998	+	0.113339i	0.663046	−	0.748579i	$-0.269263\pi$
$479$	3.41417	+	2.48054i	0.155998	+	0.113339i	−0.507048	+	0.861918i	$0.669263\pi$
$480$		0			0
$481$	−9.65660	−	29.7199i	−0.440303	−	1.35511i
$482$		0			0
$483$	−0.206932			−0.00941573
$484$		0			0
$485$	−15.7872			−0.716861
$486$		0			0
$487$	−0.267675	−	0.823818i	−0.0121295	−	0.0373308i	0.944809	−	0.327623i	$-0.106248\pi$
$487$	−0.267675	−	0.823818i	−0.0121295	−	0.0373308i	−0.956938	+	0.290292i	$0.906248\pi$
$488$		0			0
$489$	7.05393	+	5.12498i	0.318990	+	0.231760i
$490$		0			0
$491$	−8.05770	+	24.7990i	−0.363639	+	1.11917i	0.587190	+	0.809449i	$0.300234\pi$
$491$	−8.05770	+	24.7990i	−0.363639	+	1.11917i	−0.950829	+	0.309716i	$0.899766\pi$
$492$		0			0
$493$	−38.9066	+	28.2673i	−1.75226	+	1.27309i
$494$		0			0
$495$	0.934872	+	0.401273i	0.0420194	+	0.0180359i
$496$		0			0
$497$	−0.652534	+	0.474093i	−0.0292701	+	0.0212660i
$498$		0			0
$499$	3.30420	−	10.1693i	0.147916	−	0.455239i	−0.849458	−	0.527656i	$-0.823071\pi$
$499$	3.30420	−	10.1693i	0.147916	−	0.455239i	0.997374	+	0.0724167i	$0.0230711\pi$
$500$		0			0
$501$	−1.83618	−	1.33406i	−0.0820344	−	0.0596015i
$502$		0			0
$503$	−8.28523	−	25.4993i	−0.369420	−	1.13696i	−0.947167	−	0.320742i	$-0.896068\pi$
$503$	−8.28523	−	25.4993i	−0.369420	−	1.13696i	0.577746	−	0.816216i	$-0.303932\pi$
$504$		0			0
$505$	14.0092			0.623402
$506$		0			0
$507$	15.0845			0.669925
$508$		0			0
$509$	−7.27313	−	22.3844i	−0.322376	−	0.992171i	−0.972611	−	0.232438i	$-0.925330\pi$
$509$	−7.27313	−	22.3844i	−0.322376	−	0.992171i	0.650236	−	0.759733i	$-0.274670\pi$
$510$		0			0
$511$	36.4873	+	26.5095i	1.61410	+	1.17271i
$512$		0			0
$513$	−3.73916	+	11.5080i	−0.165088	+	0.508089i
$514$		0			0
$515$	0.950736	−	0.690750i	0.0418944	−	0.0304381i
$516$		0			0
$517$	1.92568	−	21.0361i	0.0846912	−	0.925168i
$518$		0			0
$519$	0.725109	−	0.526822i	0.0318287	−	0.0231249i
$520$		0			0
$521$	2.84549	−	8.75752i	0.124663	−	0.383674i	−0.869176	−	0.494502i	$-0.835350\pi$
$521$	2.84549	−	8.75752i	0.124663	−	0.383674i	0.993840	+	0.110828i	$0.0353504\pi$
$522$		0			0
$523$	28.6174	+	20.7918i	1.25135	+	0.909161i	0.998300	−	0.0582920i	$-0.0185654\pi$
$523$	28.6174	+	20.7918i	1.25135	+	0.909161i	0.253053	+	0.967453i	$0.418565\pi$
$524$		0			0
$525$	−1.71229	−	5.26990i	−0.0747306	−	0.229997i
$526$		0			0
$527$	2.63562			0.114810
$528$		0			0
$529$	−22.9986			−0.999939
$530$		0			0
$531$	−0.294266	−	0.905658i	−0.0127701	−	0.0393022i
$532$		0			0
$533$	7.51246	+	5.45812i	0.325401	+	0.236418i
$534$		0			0
$535$	5.95116	−	18.3158i	0.257291	−	0.791861i
$536$		0			0
$537$	−27.7211	+	20.1406i	−1.19625	+	0.869130i
$538$		0			0
$539$	7.46609	+	12.5396i	0.321587	+	0.540118i
$540$		0			0
$541$	−3.05682	+	2.22091i	−0.131423	+	0.0954842i	−0.651555	−	0.758602i	$-0.725883\pi$
$541$	−3.05682	+	2.22091i	−0.131423	+	0.0954842i	0.520132	+	0.854086i	$0.325883\pi$
$542$		0			0
$543$	−1.66279	+	5.11753i	−0.0713570	+	0.219614i
$544$		0			0
$545$	−1.96740	−	1.42940i	−0.0842743	−	0.0612289i
$546$		0			0
$547$	−8.30057	−	25.5465i	−0.354907	−	1.09229i	−0.956063	−	0.293160i	$-0.905293\pi$
$547$	−8.30057	−	25.5465i	−0.354907	−	1.09229i	0.601157	−	0.799131i	$-0.294707\pi$
$548$		0			0
$549$	3.58472			0.152992
$550$		0			0
$551$	14.1916			0.604581
$552$		0			0
$553$	−7.39275	−	22.7525i	−0.314372	−	0.967536i
$554$		0			0
$555$	8.80732	+	6.39889i	0.373850	+	0.271618i
$556$		0			0
$557$	8.80804	−	27.1084i	0.373209	−	1.14862i	−0.571470	−	0.820623i	$-0.693627\pi$
$557$	8.80804	−	27.1084i	0.373209	−	1.14862i	0.944679	−	0.327996i	$-0.106373\pi$
$558$		0			0
$559$	46.4705	−	33.7628i	1.96549	−	1.42801i
$560$		0			0
$561$	−27.1061	+	30.9299i	−1.14442	+	1.30586i
$562$		0			0
$563$	−12.6157	+	9.16582i	−0.531687	+	0.386293i	−0.820988	−	0.570945i	$-0.806577\pi$
$563$	−12.6157	+	9.16582i	−0.531687	+	0.386293i	0.289302	+	0.957238i	$0.406577\pi$
$564$		0			0
$565$	3.20288	−	9.85746i	0.134746	−	0.414706i
$566$		0			0
$567$	−21.8136	−	15.8485i	−0.916083	−	0.665574i
$568$		0			0
$569$	4.11740	+	12.6720i	0.172610	+	0.531240i	0.999516	−	0.0311005i	$-0.00990119\pi$
$569$	4.11740	+	12.6720i	0.172610	+	0.531240i	−0.826906	+	0.562340i	$0.809901\pi$
$570$		0			0
$571$	9.29818			0.389117			0.194558	−	0.980891i	$-0.437673\pi$
$571$	9.29818			0.389117			0.194558	+	0.980891i	$0.437673\pi$
$572$		0			0
$573$	11.7557			0.491101
$574$		0			0
$575$	0.0115402	+	0.0355172i	0.000481261	+	0.00148117i
$576$		0			0
$577$	2.10665	+	1.53057i	0.0877009	+	0.0637184i	0.630772	−	0.775969i	$-0.282738\pi$
$577$	2.10665	+	1.53057i	0.0877009	+	0.0637184i	−0.543071	+	0.839687i	$0.682738\pi$
$578$		0			0
$579$	4.31738	−	13.2875i	0.179424	−	0.552211i
$580$		0			0
$581$	32.8341	−	23.8553i	1.36219	−	0.989687i
$582$		0			0
$583$	29.3250	−	6.64614i	1.21452	−	0.275255i
$584$		0			0
$585$	1.16903	−	0.849353i	0.0483336	−	0.0351164i
$586$		0			0
$587$	12.0626	−	37.1249i	0.497878	−	1.53231i	−0.314546	−	0.949242i	$-0.601852\pi$
$587$	12.0626	−	37.1249i	0.497878	−	1.53231i	0.812423	−	0.583068i	$-0.198148\pi$
$588$		0			0
$589$	−0.629224	−	0.457158i	−0.0259267	−	0.0188369i
$590$		0			0
$591$	8.84392	+	27.2188i	0.363790	+	1.11963i
$592$		0			0
$593$	−13.6184			−0.559241			−0.279620	−	0.960111i	$-0.590209\pi$
$593$	−13.6184			−0.559241			−0.279620	+	0.960111i	$0.590209\pi$
$594$		0			0
$595$	−25.5120			−1.04589
$596$		0			0
$597$	−6.07851	−	18.7077i	−0.248777	−	0.765656i
$598$		0			0
$599$	36.9382	+	26.8372i	1.50925	+	1.09654i	0.966506	+	0.256643i	$0.0826164\pi$
$599$	36.9382	+	26.8372i	1.50925	+	1.09654i	0.542749	+	0.839895i	$0.317384\pi$
$600$		0			0
$601$	−8.60273	+	26.4765i	−0.350913	+	1.08000i	0.607429	+	0.794374i	$0.292201\pi$
$601$	−8.60273	+	26.4765i	−0.350913	+	1.08000i	−0.958342	+	0.285624i	$0.907799\pi$
$602$		0			0
$603$	−1.97177	+	1.43258i	−0.0802969	+	0.0583391i
$604$		0			0
$605$	−1.44327	−	10.9049i	−0.0586771	−	0.443347i
$606$		0			0
$607$	−32.0144	+	23.2599i	−1.29943	+	0.944088i	−0.999950	−	0.0100154i	$-0.996812\pi$
$607$	−32.0144	+	23.2599i	−1.29943	+	0.944088i	−0.299476	+	0.954104i	$0.596812\pi$
$608$		0			0
$609$	−10.8982	+	33.5413i	−0.441618	+	1.35916i
$610$		0			0
$611$	−24.2736	−	17.6358i	−0.982004	−	0.713467i
$612$		0			0
$613$	−9.07646	−	27.9345i	−0.366595	−	1.12826i	−0.948976	−	0.315347i	$-0.897879\pi$
$613$	−9.07646	−	27.9345i	−0.366595	−	1.12826i	0.582382	−	0.812916i	$-0.302121\pi$
$614$		0			0
$615$	−3.23496			−0.130446
$616$		0			0
$617$	−39.4548			−1.58839			−0.794196	−	0.607662i	$-0.792107\pi$
$617$	−39.4548			−1.58839			−0.794196	+	0.607662i	$0.792107\pi$
$618$		0			0
$619$	11.2194	+	34.5299i	0.450948	+	1.38787i	0.875828	+	0.482624i	$0.160316\pi$
$619$	11.2194	+	34.5299i	0.450948	+	1.38787i	−0.424880	+	0.905250i	$0.639684\pi$
$620$		0			0
$621$	0.163957	+	0.119121i	0.00657935	+	0.00478018i
$622$		0			0
$623$	−1.95148	+	6.00604i	−0.0781844	+	0.240627i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	11.8362	−	2.68252i	0.472691	−	0.107129i
$628$		0			0
$629$	40.5502	−	29.4615i	1.61684	−	1.17470i
$630$		0			0
$631$	−3.45261	+	10.6261i	−0.137446	+	0.423017i	−0.995963	−	0.0897701i	$-0.971387\pi$
$631$	−3.45261	+	10.6261i	−0.137446	+	0.423017i	0.858516	+	0.512787i	$0.171387\pi$
$632$		0			0
$633$	−2.83527	−	2.05994i	−0.112692	−	0.0818754i
$634$		0			0
$635$	0.600715	+	1.84881i	0.0238386	+	0.0733678i
$636$		0			0
$637$	20.7287			0.821299
$638$		0			0
$639$	0.0732763			0.00289877
$640$		0			0
$641$	7.59555	+	23.3767i	0.300006	+	0.923324i	0.981494	+	0.191495i	$0.0613334\pi$
$641$	7.59555	+	23.3767i	0.300006	+	0.923324i	−0.681487	+	0.731830i	$0.738667\pi$
$642$		0			0
$643$	−5.39099	−	3.91678i	−0.212600	−	0.154463i	0.476389	−	0.879234i	$-0.341945\pi$
$643$	−5.39099	−	3.91678i	−0.212600	−	0.154463i	−0.688989	+	0.724772i	$0.741945\pi$
$644$		0			0
$645$	−6.18368	+	19.0314i	−0.243482	+	0.749361i
$646$		0			0
$647$	−1.03955	+	0.755276i	−0.0408688	+	0.0296930i	−0.608032	−	0.793912i	$-0.708041\pi$
$647$	−1.03955	+	0.755276i	−0.0408688	+	0.0296930i	0.567163	+	0.823605i	$0.308041\pi$
$648$		0			0
$649$	−6.78613	+	7.74345i	−0.266379	+	0.303957i
$650$		0			0
$651$	1.56368	−	1.13608i	0.0612856	−	0.0445266i
$652$		0			0
$653$	4.39744	−	13.5339i	0.172085	−	0.529624i	−0.827403	−	0.561608i	$-0.810183\pi$
$653$	4.39744	−	13.5339i	0.172085	−	0.529624i	0.999488	+	0.0319847i	$0.0101828\pi$
$654$		0			0
$655$	7.03176	+	5.10887i	0.274753	+	0.199620i
$656$		0			0
$657$	−1.26615	−	3.89680i	−0.0493971	−	0.152029i
$658$		0			0
$659$	9.89307			0.385379			0.192690	−	0.981260i	$-0.438279\pi$
$659$	9.89307			0.385379			0.192690	+	0.981260i	$0.438279\pi$
$660$		0			0
$661$	−37.1307			−1.44422			−0.722108	−	0.691781i	$-0.756827\pi$
$661$	−37.1307			−1.44422			−0.722108	+	0.691781i	$0.756827\pi$
$662$		0			0
$663$	18.0511	+	55.5556i	0.701046	+	2.15760i
$664$		0			0
$665$	6.09071	+	4.42516i	0.236187	+	0.171600i
$666$		0			0
$667$	0.0734499	−	0.226056i	0.00284399	−	0.00875291i
$668$		0			0
$669$	22.4136	−	16.2844i	0.866558	−	0.629591i
$670$		0			0
$671$	−19.8288	−	33.3032i	−0.765482	−	1.28566i
$672$		0			0
$673$	31.2042	−	22.6711i	1.20283	−	0.873908i	0.208271	−	0.978071i	$-0.433216\pi$
$673$	31.2042	−	22.6711i	1.20283	−	0.873908i	0.994560	+	0.104163i	$0.0332162\pi$
$674$		0			0
$675$	−1.67696	+	5.16114i	−0.0645461	+	0.198652i
$676$		0			0
$677$	−11.9958	−	8.71549i	−0.461038	−	0.334964i	0.332900	−	0.942962i	$-0.391973\pi$
$677$	−11.9958	−	8.71549i	−0.461038	−	0.334964i	−0.793938	+	0.607998i	$0.791973\pi$
$678$		0			0
$679$	16.4720	+	50.6955i	0.632136	+	1.94551i
$680$		0			0
$681$	−12.3529			−0.473364
$682$		0			0
$683$	19.6477			0.751796			0.375898	−	0.926661i	$-0.377334\pi$
$683$	19.6477			0.751796			0.375898	+	0.926661i	$0.377334\pi$
$684$		0			0
$685$	−5.48062	−	16.8676i	−0.209404	−	0.644478i
$686$		0			0
$687$	−10.2074	−	7.41608i	−0.389435	−	0.282941i
$688$		0			0
$689$	13.1976	−	40.6180i	0.502788	−	1.54742i
$690$		0			0
$691$	−5.59351	+	4.06392i	−0.212787	+	0.154599i	−0.689074	−	0.724691i	$-0.741982\pi$
$691$	−5.59351	+	4.06392i	−0.212787	+	0.154599i	0.476287	+	0.879290i	$0.341982\pi$
$692$		0			0
$693$	0.313137	−	3.42071i	0.0118951	−	0.129942i
$694$		0			0
$695$	2.60220	−	1.89061i	0.0987071	−	0.0717149i
$696$		0			0
$697$	−4.60258	+	14.1653i	−0.174335	+	0.536548i
$698$		0			0
$699$	8.23207	+	5.98095i	0.311365	+	0.226220i
$700$		0			0
$701$	−13.8041	−	42.4847i	−0.521374	−	1.60462i	−0.771377	−	0.636379i	$-0.780432\pi$
$701$	−13.8041	−	42.4847i	−0.521374	−	1.60462i	0.250003	−	0.968245i	$-0.419568\pi$
$702$		0			0
$703$	−14.7911			−0.557857
$704$		0			0
$705$	10.4525			0.393664
$706$		0			0
$707$	−14.6168	−	44.9860i	−0.549723	−	1.69187i
$708$		0			0
$709$	41.7225	+	30.3132i	1.56692	+	1.13844i	0.930030	+	0.367483i	$0.119780\pi$
$709$	41.7225	+	30.3132i	1.56692	+	1.13844i	0.636892	+	0.770953i	$0.280220\pi$
$710$		0			0
$711$	−0.671621	+	2.06704i	−0.0251877	+	0.0775199i
$712$		0			0
$713$	−0.0105386	+	0.00765677i	−0.000394675	+	0.000286748i
$714$		0			0
$715$	−14.3573	−	6.16253i	−0.536931	−	0.230466i
$716$		0			0
$717$	13.3132	−	9.67262i	0.497191	−	0.361231i
$718$		0			0
$719$	−1.82464	+	5.61567i	−0.0680476	+	0.209429i	−0.979298	−	0.202424i	$-0.935118\pi$
$719$	−1.82464	+	5.61567i	−0.0680476	+	0.209429i	0.911250	+	0.411853i	$0.135118\pi$
$720$		0			0
$721$	−3.21009	−	2.33227i	−0.119550	−	0.0868581i
$722$		0			0
$723$	−1.75908	−	5.41390i	−0.0654210	−	0.201345i
$724$		0			0
$725$	6.36469			0.236379
$726$		0			0
$727$	13.5653			0.503107			0.251554	−	0.967843i	$-0.419059\pi$
$727$	13.5653			0.503107			0.251554	+	0.967843i	$0.419059\pi$
$728$		0			0
$729$	9.01319	+	27.7397i	0.333822	+	1.02740i
$730$		0			0
$731$	74.5369	+	54.1542i	2.75685	+	2.00297i
$732$		0			0
$733$	−9.88074	+	30.4098i	−0.364953	+	1.12321i	0.585057	+	0.810992i	$0.301072\pi$
$733$	−9.88074	+	30.4098i	−0.364953	+	1.12321i	−0.950010	+	0.312219i	$0.898928\pi$
$734$		0			0
$735$	−5.84216	+	4.24458i	−0.215491	+	0.156564i
$736$		0			0
$737$	24.2159	+	10.3942i	0.892006	+	0.382874i
$738$		0			0
$739$	29.5737	−	21.4865i	1.08789	−	0.790395i	0.108845	−	0.994059i	$-0.465285\pi$
$739$	29.5737	−	21.4865i	1.08789	−	0.790395i	0.979041	+	0.203664i	$0.0652849\pi$
$740$		0			0
$741$	5.32682	−	16.3943i	0.195686	−	0.602259i
$742$		0			0
$743$	−22.3681	−	16.2514i	−0.820605	−	0.596204i	0.0962809	−	0.995354i	$-0.469305\pi$
$743$	−22.3681	−	16.2514i	−0.820605	−	0.596204i	−0.916886	+	0.399150i	$0.869305\pi$
$744$		0			0
$745$	1.01392	+	3.12053i	0.0371472	+	0.114327i
$746$		0			0
$747$	−3.68710			−0.134904
$748$		0			0
$749$	−65.0245			−2.37594
$750$		0			0
$751$	−0.618078	−	1.90225i	−0.0225540	−	0.0694141i	0.939146	−	0.343518i	$-0.111619\pi$
$751$	−0.618078	−	1.90225i	−0.0225540	−	0.0694141i	−0.961700	+	0.274104i	$0.911619\pi$
$752$		0			0
$753$	29.9196	+	21.7378i	1.09033	+	0.792171i
$754$		0			0
$755$	6.84986	−	21.0817i	0.249292	−	0.767242i
$756$		0			0
$757$	12.9917	−	9.43901i	0.472191	−	0.343067i	−0.326104	−	0.945334i	$-0.605736\pi$
$757$	12.9917	−	9.43901i	0.472191	−	0.343067i	0.798294	+	0.602267i	$0.205736\pi$
$758$		0			0
$759$	0.0185299	−	0.202421i	0.000672592	−	0.00734741i
$760$		0			0
$761$	0.747240	−	0.542902i	0.0270874	−	0.0196802i	−0.574159	−	0.818744i	$-0.694671\pi$
$761$	0.747240	−	0.542902i	0.0270874	−	0.0196802i	0.601247	+	0.799064i	$0.294671\pi$
$762$		0			0
$763$	−2.53732	+	7.80907i	−0.0918572	+	0.282707i
$764$		0			0
$765$	1.87508	+	1.36233i	0.0677938	+	0.0492551i
$766$		0			0
$767$	4.51917	+	13.9086i	0.163178	+	0.502210i
$768$		0			0
$769$	−20.5251			−0.740153			−0.370076	−	0.929001i	$-0.620669\pi$
$769$	−20.5251			−0.740153			−0.370076	+	0.929001i	$0.620669\pi$
$770$		0			0
$771$	−0.367576			−0.0132379
$772$		0			0
$773$	0.565077	+	1.73913i	0.0203244	+	0.0625521i	0.960704	−	0.277574i	$-0.0895303\pi$
$773$	0.565077	+	1.73913i	0.0203244	+	0.0625521i	−0.940380	+	0.340126i	$0.889530\pi$
$774$		0			0
$775$	−0.282197	−	0.205028i	−0.0101368	−	0.00736483i
$776$		0			0
$777$	11.3586	−	34.9582i	0.407488	−	1.25412i
$778$		0			0
$779$	3.55583	−	2.58346i	0.127401	−	0.0925621i
$780$		0			0
$781$	−0.405326	−	0.680761i	−0.0145037	−	0.0243595i
$782$		0			0
$783$	27.9431	−	20.3018i	0.998604	−	0.725528i
$784$		0			0
$785$	3.57071	−	10.9895i	0.127444	−	0.392233i
$786$		0			0
$787$	32.2876	+	23.4583i	1.15093	+	0.836199i	0.988604	−	0.150538i	$-0.0481006\pi$
$787$	32.2876	+	23.4583i	1.15093	+	0.836199i	0.162325	+	0.986737i	$0.448101\pi$
$788$		0			0
$789$	3.70851	+	11.4136i	0.132026	+	0.406335i
$790$		0			0
$791$	−34.9958			−1.24431
$792$		0			0
$793$	−55.0521			−1.95496
$794$		0			0
$795$	4.59769	+	14.1502i	0.163063	+	0.501857i
$796$		0			0
$797$	25.7463	+	18.7058i	0.911981	+	0.662593i	0.941515	−	0.336971i	$-0.109402\pi$
$797$	25.7463	+	18.7058i	0.911981	+	0.662593i	−0.0295339	+	0.999564i	$0.509402\pi$
$798$		0			0
$799$	14.8714	−	45.7695i	0.526113	−	1.61921i
$800$		0			0
$801$	0.464149	−	0.337224i	0.0163999	−	0.0119152i
$802$		0			0
$803$	−29.1989	+	33.3180i	−1.03041	+	1.17577i
$804$		0			0
$805$	0.102011	−	0.0741153i	0.00359541	−	0.00261222i
$806$		0			0
$807$	14.1226	−	43.4650i	0.497140	−	1.53004i
$808$		0			0
$809$	39.6884	+	28.8353i	1.39537	+	1.01380i	0.995252	+	0.0973311i	$0.0310306\pi$
$809$	39.6884	+	28.8353i	1.39537	+	1.01380i	0.400117	+	0.916464i	$0.368969\pi$
$810$		0			0
$811$	−9.07746	−	27.9376i	−0.318753	−	0.981020i	−0.974182	−	0.225764i	$-0.927512\pi$
$811$	−9.07746	−	27.9376i	−0.318753	−	0.981020i	0.655429	−	0.755257i	$-0.272488\pi$
$812$		0			0
$813$	34.7114			1.21738
$814$		0			0
$815$	−5.31293			−0.186104
$816$		0			0
$817$	−8.40158	−	25.8574i	−0.293934	−	0.904636i
$818$		0			0
$819$	−3.94716	−	2.86778i	−0.137925	−	0.100208i
$820$		0			0
$821$	−5.67029	+	17.4514i	−0.197895	+	0.609057i	0.802036	+	0.597276i	$0.203750\pi$
$821$	−5.67029	+	17.4514i	−0.197895	+	0.609057i	−0.999931	+	0.0117813i	$0.996250\pi$
$822$		0			0
$823$	−10.8259	+	7.86549i	−0.377368	+	0.274174i	−0.760260	−	0.649619i	$-0.774928\pi$
$823$	−10.8259	+	7.86549i	−0.377368	+	0.274174i	0.382892	+	0.923793i	$0.374928\pi$
$824$		0			0
$825$	5.30834	−	1.20307i	0.184813	−	0.0418854i
$826$		0			0
$827$	−9.68590	+	7.03722i	−0.336812	+	0.244708i	−0.743315	−	0.668941i	$-0.766748\pi$
$827$	−9.68590	+	7.03722i	−0.336812	+	0.244708i	0.406504	+	0.913649i	$0.366748\pi$
$828$		0			0
$829$	4.66231	−	14.3491i	0.161929	−	0.498365i	−0.836868	−	0.547405i	$-0.815616\pi$
$829$	4.66231	−	14.3491i	0.161929	−	0.498365i	0.998797	+	0.0490392i	$0.0156159\pi$
$830$		0			0
$831$	−4.40026	−	3.19697i	−0.152643	−	0.110902i
$832$		0			0
$833$	10.2742	+	31.6207i	0.355979	+	1.09559i
$834$		0			0
$835$	1.38299			0.0478603
$836$		0			0
$837$	−1.89293			−0.0654292
$838$		0			0
$839$	15.6167	+	48.0633i	0.539149	+	1.65933i	0.734510	+	0.678598i	$0.237412\pi$
$839$	15.6167	+	48.0633i	0.539149	+	1.65933i	−0.195361	+	0.980731i	$0.562588\pi$
$840$		0			0
$841$	−9.31118	−	6.76497i	−0.321075	−	0.233275i
$842$		0			0
$843$	8.36400	−	25.7418i	0.288072	−	0.886593i
$844$		0			0
$845$	−7.43616	+	5.40269i	−0.255812	+	0.185858i
$846$		0			0
$847$	−33.5117	+	16.0125i	−1.15147	+	0.550194i
$848$		0			0
$849$	11.6944	−	8.49650i	0.401352	−	0.291599i
$850$		0			0
$851$	−0.0765529	+	0.235606i	−0.00262420	+	0.00807645i
$852$		0			0
$853$	−32.0750	−	23.3039i	−1.09823	−	0.797909i	−0.117458	−	0.993078i	$-0.537475\pi$
$853$	−32.0750	−	23.3039i	−1.09823	−	0.797909i	−0.980770	+	0.195168i	$0.937475\pi$
$854$		0			0
$855$	−0.211354	−	0.650481i	−0.00722815	−	0.0222460i
$856$		0			0
$857$	−29.8795			−1.02067			−0.510333	−	0.859977i	$-0.670478\pi$
$857$	−29.8795			−1.02067			−0.510333	+	0.859977i	$0.670478\pi$
$858$		0			0
$859$	17.4024			0.593762			0.296881	−	0.954915i	$-0.404054\pi$
$859$	17.4024			0.593762			0.296881	+	0.954915i	$0.404054\pi$
$860$		0			0
$861$	3.37527	+	10.3880i	0.115029	+	0.354023i
$862$		0			0
$863$	−27.4852	−	19.9692i	−0.935609	−	0.679760i	0.0117509	−	0.999931i	$-0.496259\pi$
$863$	−27.4852	−	19.9692i	−0.935609	−	0.679760i	−0.947360	+	0.320171i	$0.896259\pi$
$864$		0			0
$865$	−0.168768	+	0.519413i	−0.00573827	+	0.0176606i
$866$		0			0
$867$	−53.2299	+	38.6738i	−1.80778	+	1.31343i
$868$		0			0
$869$	22.9185	−	5.19419i	0.777457	−	0.176201i
$870$		0			0
$871$	30.2814	−	22.0007i	1.02605	−	0.745467i
$872$		0			0
$873$	1.49645	−	4.60561i	0.0506473	−	0.155876i
$874$		0			0
$875$	2.73159	+	1.98461i	0.0923444	+	0.0670922i
$876$		0			0
$877$	17.7373	+	54.5899i	0.598947	+	1.84337i	0.534007	+	0.845480i	$0.320685\pi$
$877$	17.7373	+	54.5899i	0.598947	+	1.84337i	0.0649395	+	0.997889i	$0.479315\pi$
$878$		0			0
$879$	10.6356			0.358731
$880$		0			0
$881$	23.3382			0.786285			0.393142	−	0.919478i	$-0.371388\pi$
$881$	23.3382			0.786285			0.393142	+	0.919478i	$0.371388\pi$
$882$		0			0
$883$	10.9075	+	33.5697i	0.367066	+	1.12971i	0.948677	+	0.316245i	$0.102422\pi$
$883$	10.9075	+	33.5697i	0.367066	+	1.12971i	−0.581612	+	0.813466i	$0.697578\pi$
$884$		0			0
$885$	−4.12172	−	2.99461i	−0.138550	−	0.100663i
$886$		0			0
$887$	−10.7379	+	33.0479i	−0.360544	+	1.10964i	0.592181	+	0.805805i	$0.298267\pi$
$887$	−10.7379	+	33.0479i	−0.360544	+	1.10964i	−0.952725	+	0.303835i	$0.901733\pi$
$888$		0			0
$889$	5.31008	−	3.85800i	0.178094	−	0.129393i
$890$		0			0
$891$	17.4563	−	19.9188i	0.584807	−	0.667306i
$892$		0			0
$893$	−11.4893	+	8.34744i	−0.384474	+	0.279336i
$894$		0			0
$895$	6.45204	−	19.8573i	0.215668	−	0.663757i
$896$		0			0
$897$	−0.233573	−	0.169701i	−0.00779878	−	0.00566614i
$898$		0			0
$899$	0.686048	+	2.11144i	0.0228810	+	0.0704204i
$900$		0			0
$901$	68.5025			2.28215
$902$		0			0
$903$	67.5649			2.24842
$904$		0			0
$905$	−1.01321	−	3.11832i	−0.0336801	−	0.103657i
$906$		0			0
$907$	31.7234	+	23.0484i	1.05336	+	0.765310i	0.972848	−	0.231444i	$-0.0743450\pi$
$907$	31.7234	+	23.0484i	1.05336	+	0.765310i	0.0805104	+	0.996754i	$0.474345\pi$
$908$		0			0
$909$	−1.32792	+	4.08692i	−0.0440443	+	0.135554i
$910$		0			0
$911$	−3.80478	+	2.76434i	−0.126058	+	0.0915865i	−0.649028	−	0.760765i	$-0.724824\pi$
$911$	−3.80478	+	2.76434i	−0.126058	+	0.0915865i	0.522970	+	0.852351i	$0.324824\pi$
$912$		0			0
$913$	20.3951	+	34.2544i	0.674980	+	1.13366i
$914$		0			0
$915$	15.5159	−	11.2729i	0.512939	−	0.372672i
$916$		0			0
$917$	9.06871	−	27.9106i	0.299475	−	0.921690i
$918$		0			0
$919$	11.2154	+	8.14847i	0.369962	+	0.268793i	0.757195	−	0.653189i	$-0.226569\pi$
$919$	11.2154	+	8.14847i	0.369962	+	0.268793i	−0.387233	+	0.921982i	$0.626569\pi$
$920$		0			0
$921$	13.1534	+	40.4819i	0.433418	+	1.33392i
$922$		0			0
$923$	−1.12534			−0.0370409
$924$		0			0
$925$	−6.63357			−0.218110
$926$		0			0
$927$	0.111394	+	0.342834i	0.00365864	+	0.0112601i
$928$		0			0
$929$	0.847872	+	0.616015i	0.0278178	+	0.0202108i	0.601607	−	0.798792i	$-0.294527\pi$
$929$	0.847872	+	0.616015i	0.0278178	+	0.0202108i	−0.573789	+	0.819003i	$0.694527\pi$
$930$		0			0
$931$	3.03188	−	9.33117i	0.0993659	−	0.305817i
$932$		0			0
$933$	−10.7548	+	7.81381i	−0.352096	+	0.255813i
$934$		0			0
$935$	2.28449	−	24.9558i	0.0747109	−	0.816143i
$936$		0			0
$937$	−34.7240	+	25.2285i	−1.13438	+	0.824178i	−0.986327	−	0.164801i	$-0.947302\pi$
$937$	−34.7240	+	25.2285i	−1.13438	+	0.824178i	−0.148057	+	0.988979i	$0.547302\pi$
$938$		0			0
$939$	−2.18051	+	6.71092i	−0.0711582	+	0.219003i
$940$		0			0
$941$	36.5611	+	26.5632i	1.19186	+	0.865935i	0.993459	−	0.114186i	$-0.0364260\pi$
$941$	36.5611	+	26.5632i	1.19186	+	0.865935i	0.198398	+	0.980121i	$0.436426\pi$
$942$		0			0
$943$	−0.0227481	−	0.0700114i	−0.000740779	−	0.00227988i
$944$		0			0
$945$	18.3230			0.596047
$946$		0			0
$947$	−7.77351			−0.252605			−0.126303	−	0.991992i	$-0.540311\pi$
$947$	−7.77351			−0.252605			−0.126303	+	0.991992i	$0.540311\pi$
$948$		0			0
$949$	19.4448	+	59.8449i	0.631204	+	1.94265i
$950$		0			0
$951$	−40.2807	−	29.2656i	−1.30619	−	0.949003i
$952$		0			0
$953$	−14.7986	+	45.5455i	−0.479374	+	1.47536i	0.360592	+	0.932724i	$0.382575\pi$
$953$	−14.7986	+	45.5455i	−0.479374	+	1.47536i	−0.839966	+	0.542639i	$0.817425\pi$
$954$		0			0
$955$	−5.79518	+	4.21045i	−0.187528	+	0.136247i
$956$		0			0
$957$	−31.8341	−	13.6641i	−1.02905	−	0.441698i
$958$		0			0
$959$	−48.4464	+	35.1984i	−1.56442	+	1.13662i
$960$		0			0
$961$	−9.54193	+	29.3670i	−0.307804	+	0.947324i
$962$		0			0
$963$	4.77917	+	3.47227i	0.154007	+	0.111892i
$964$		0			0
$965$	2.63076	+	8.09665i	0.0846872	+	0.260640i
$966$		0			0
$967$	47.3661			1.52319			0.761596	−	0.648053i	$-0.224416\pi$
$967$	47.3661			1.52319			0.761596	+	0.648053i	$0.224416\pi$
$968$		0			0
$969$	27.6490			0.888215
$970$		0			0
$971$	−7.48866	−	23.0477i	−0.240322	−	0.739636i	−0.996371	−	0.0851204i	$-0.972872\pi$
$971$	−7.48866	−	23.0477i	−0.240322	−	0.739636i	0.756048	−	0.654516i	$-0.227128\pi$
$972$		0			0
$973$	−8.78614	−	6.38350i	−0.281671	−	0.204646i
$974$		0			0
$975$	2.38900	−	7.35258i	0.0765091	−	0.235471i
$976$		0			0
$977$	4.32368	−	3.14134i	0.138327	−	0.100500i	−0.516470	−	0.856305i	$-0.672754\pi$
$977$	4.32368	−	3.14134i	0.138327	−	0.100500i	0.654797	+	0.755805i	$0.272754\pi$
$978$		0			0
$979$	−5.70035	−	2.44675i	−0.182184	−	0.0781985i
$980$		0			0
$981$	0.603488	−	0.438460i	0.0192679	−	0.0139989i
$982$		0			0
$983$	0.265704	−	0.817754i	0.00847465	−	0.0260823i	−0.946730	−	0.322029i	$-0.895635\pi$
$983$	0.265704	−	0.817754i	0.00847465	−	0.0260823i	0.955204	+	0.295947i	$0.0956351\pi$
$984$		0			0
$985$	−14.1085	−	10.2504i	−0.449535	−	0.326606i
$986$		0			0
$987$	−10.9059	−	33.5648i	−0.347137	−	1.06838i
$988$		0			0
$989$	−0.455363			−0.0144797
$990$		0			0
$991$	12.5007			0.397097			0.198548	−	0.980091i	$-0.436377\pi$
$991$	12.5007			0.397097			0.198548	+	0.980091i	$0.436377\pi$
$992$		0			0
$993$	−8.70540	−	26.7925i	−0.276258	−	0.850234i
$994$		0			0
$995$	9.69691	+	7.04522i	0.307413	+	0.223348i
$996$		0			0
$997$	10.0091	−	30.8050i	0.316993	−	0.975603i	−0.657934	−	0.753076i	$-0.728569\pi$
$997$	10.0091	−	30.8050i	0.316993	−	0.975603i	0.974926	−	0.222527i	$-0.0714306\pi$
$998$		0			0
$999$	−29.1236	+	21.1595i	−0.921429	+	0.669457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.k.641.3		16
4.3	odd	2		440.2.y.d.201.2	yes	16
11.2	odd	10		9680.2.a.de.1.6		8
11.4	even	5	inner	880.2.bo.k.81.3		16
11.9	even	5		9680.2.a.df.1.6		8
44.15	odd	10		440.2.y.d.81.2	✓	16
44.31	odd	10		4840.2.a.bg.1.3		8
44.35	even	10		4840.2.a.bh.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.81.2	✓	16	44.15	odd	10
440.2.y.d.201.2	yes	16	4.3	odd	2
880.2.bo.k.81.3		16	11.4	even	5	inner
880.2.bo.k.641.3		16	1.1	even	1	trivial
4840.2.a.bg.1.3		8	44.31	odd	10
4840.2.a.bh.1.3		8	44.35	even	10
9680.2.a.de.1.6		8	11.2	odd	10
9680.2.a.df.1.6		8	11.9	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.507132 + 1.56079i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.04337 + 3.21117i) q^{7} +(0.248161 - 0.180299i) q^{9} +O(q^{10})\)	\(q+(0.507132 + 1.56079i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-1.04337 + 3.21117i) q^{7} +(0.248161 - 0.180299i) q^{9} +(-3.04773 - 1.30817i) q^{11} +(-3.81111 + 2.76894i) q^{13} +(0.507132 - 1.56079i) q^{15} +(-6.11288 - 4.44127i) q^{17} +(0.689025 + 2.12060i) q^{19} -5.54110 q^{21} +0.0373449 q^{23} +(0.309017 + 0.951057i) q^{25} +(4.39033 + 3.18976i) q^{27} +(1.96680 - 6.05318i) q^{29} +(-0.282197 + 0.205028i) q^{31} +(0.496182 - 5.42030i) q^{33} +(2.73159 - 1.98461i) q^{35} +(-2.04989 + 6.30890i) q^{37} +(-6.25447 - 4.54414i) q^{39} +(-0.609134 - 1.87472i) q^{41} -12.1934 q^{43} -0.306743 q^{45} +(1.96818 + 6.05743i) q^{47} +(-3.55987 - 2.58640i) q^{49} +(3.83186 - 11.7932i) q^{51} +(-7.33459 + 5.32889i) q^{53} +(1.69674 + 2.84975i) q^{55} +(-2.96039 + 2.15085i) q^{57} +(0.959323 - 2.95249i) q^{59} +(9.45447 + 6.86907i) q^{61} +(0.320048 + 0.985006i) q^{63} +4.71080 q^{65} -7.94556 q^{67} +(0.0189388 + 0.0582877i) q^{69} +(0.193262 + 0.140413i) q^{71} +(4.12771 - 12.7038i) q^{73} +(-1.32769 + 0.964623i) q^{75} +(7.38069 - 8.42188i) q^{77} +(-5.73224 + 4.16471i) q^{79} +(-2.46771 + 7.59483i) q^{81} +(-9.72451 - 7.06527i) q^{83} +(2.33491 + 7.18612i) q^{85} +10.4452 q^{87} +1.87036 q^{89} +(-4.91512 - 15.1272i) q^{91} +(-0.463118 - 0.336475i) q^{93} +(0.689025 - 2.12060i) q^{95} +(12.7721 - 9.27950i) q^{97} +(-0.992190 + 0.224867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9}+O(q^{10}) \) 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9	\( 16 q + 3 q^{3} - 4 q^{5} - 8 q^{7} - 7 q^{9} + 7 q^{11} - 11 q^{13} + 3 q^{15} + 9 q^{17} + 2 q^{19} + 12 q^{21} - 20 q^{23} - 4 q^{25} + 9 q^{27} + q^{29} + 2 q^{31} - 32 q^{33} + 2 q^{35} - 16 q^{37} - 3 q^{39} - 11 q^{41} + 16 q^{43} + 38 q^{45} + 10 q^{47} + 4 q^{49} - 26 q^{51} - 9 q^{53} - 3 q^{55} - 50 q^{57} + 60 q^{59} + 30 q^{61} - 52 q^{63} + 24 q^{65} + 4 q^{67} + 41 q^{69} + 10 q^{71} + q^{73} - 2 q^{75} - 4 q^{77} - 19 q^{79} - 31 q^{81} - 64 q^{83} - 11 q^{85} - 30 q^{87} + 24 q^{89} + 9 q^{91} + 45 q^{93} + 2 q^{95} - 3 q^{97} + 10 q^{99}+O(q^{100}) \) 16 * q + 3 * q^3 - 4 * q^5 - 8 * q^7 - 7 * q^9 + 7 * q^11 - 11 * q^13 + 3 * q^15 + 9 * q^17 + 2 * q^19 + 12 * q^21 - 20 * q^23 - 4 * q^25 + 9 * q^27 + q^29 + 2 * q^31 - 32 * q^33 + 2 * q^35 - 16 * q^37 - 3 * q^39 - 11 * q^41 + 16 * q^43 + 38 * q^45 + 10 * q^47 + 4 * q^49 - 26 * q^51 - 9 * q^53 - 3 * q^55 - 50 * q^57 + 60 * q^59 + 30 * q^61 - 52 * q^63 + 24 * q^65 + 4 * q^67 + 41 * q^69 + 10 * q^71 + q^73 - 2 * q^75 - 4 * q^77 - 19 * q^79 - 31 * q^81 - 64 * q^83 - 11 * q^85 - 30 * q^87 + 24 * q^89 + 9 * q^91 + 45 * q^93 + 2 * q^95 - 3 * q^97 + 10 * q^99

Introduction

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Modular forms

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