LMFDB - Embedded newform 880.2.cm.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(17,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))

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

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

chi := DirichletCharacter("880.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, 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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	880.17
Dual form			880.2.cm.a.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98021 + 0.313634i) q^{3} +(-0.867371 - 2.06099i) q^{5} +(-0.282837 + 1.78576i) q^{7} +(0.969677 - 0.315067i) q^{9} +O(q^{10})$	\(q+(-1.98021 + 0.313634i) q^{3} +(-0.867371 - 2.06099i) q^{5} +(-0.282837 + 1.78576i) q^{7} +(0.969677 - 0.315067i) q^{9} +(-1.72268 - 2.83415i) q^{11} +(-1.02411 + 2.00993i) q^{13} +(2.36397 + 3.80914i) q^{15} +(1.52724 + 2.99738i) q^{17} +(-1.05647 - 0.767569i) q^{19} -3.62488i q^{21} +(3.16488 - 3.16488i) q^{23} +(-3.49534 + 3.57528i) q^{25} +(3.53776 - 1.80258i) q^{27} +(2.37569 - 1.72604i) q^{29} +(1.23925 + 3.81401i) q^{31} +(4.30014 + 5.07190i) q^{33} +(3.92576 - 0.965994i) q^{35} +(3.16942 + 0.501987i) q^{37} +(1.39757 - 4.30127i) q^{39} +(0.766287 - 1.05470i) q^{41} +(4.55431 + 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} +(1.20824 + 7.62854i) q^{47} +(3.54845 + 1.15296i) q^{49} +(-3.96433 - 5.45644i) q^{51} +(5.67482 + 2.89146i) q^{53} +(-4.34694 + 6.00867i) q^{55} +(2.33276 + 1.18860i) q^{57} +(7.28135 + 10.0219i) q^{59} +(-8.85435 - 2.87695i) q^{61} +(0.288374 + 1.82072i) q^{63} +(5.03072 + 0.367324i) q^{65} +(2.46236 + 2.46236i) q^{67} +(-5.27449 + 7.25972i) q^{69} +(2.09243 - 6.43984i) q^{71} +(9.32763 + 1.47735i) q^{73} +(5.80015 - 8.17604i) q^{75} +(5.54835 - 2.27469i) q^{77} +(0.353860 + 1.08907i) q^{79} +(-8.91472 + 6.47692i) q^{81} +(9.32422 - 4.75092i) q^{83} +(4.85288 - 5.74747i) q^{85} +(-4.16301 + 4.16301i) q^{87} +3.85743i q^{89} +(-3.29960 - 2.39730i) q^{91} +(-3.65016 - 7.16385i) q^{93} +(-0.665600 + 2.84313i) q^{95} +(0.353228 - 0.693249i) q^{97} +(-2.56339 - 2.20545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 2 q^{5}+O(q^{10}) $ 32 * q + 4 * q^3 - 2 * q^5	$ 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53} + 64 q^{55} + 30 q^{57} - 60 q^{61} + 30 q^{63} + 8 q^{67} - 24 q^{71} + 50 q^{73} - 34 q^{75} + 70 q^{77} - 12 q^{81} - 90 q^{83} + 30 q^{85} - 20 q^{91} - 8 q^{93} + 40 q^{95} - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$	$1$

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
$3$	−1.98021	+	0.313634i	−1.14327	+	0.181076i	−0.699208	−	0.714918i	$-0.746464\pi$
$3$	−1.98021	+	0.313634i	−1.14327	+	0.181076i	−0.444064	+	0.895995i	$0.646464\pi$
$4$		0			0
$5$	−0.867371	−	2.06099i	−0.387900	−	0.921701i
$5$	−0.867371	−	2.06099i	−0.387900	−	0.921701i
$6$		0			0
$7$	−0.282837	+	1.78576i	−0.106902	+	0.674955i	0.874793	+	0.484497i	$0.160997\pi$
$7$	−0.282837	+	1.78576i	−0.106902	+	0.674955i	−0.981695	+	0.190458i	$0.939003\pi$
$8$		0			0
$9$	0.969677	−	0.315067i	0.323226	−	0.105022i
$10$		0			0
$11$	−1.72268	−	2.83415i	−0.519407	−	0.854527i
$11$	−1.72268	−	2.83415i	−0.519407	−	0.854527i
$12$		0			0
$13$	−1.02411	+	2.00993i	−0.284037	+	0.557454i	−0.988307	−	0.152478i	$-0.951275\pi$
$13$	−1.02411	+	2.00993i	−0.284037	+	0.557454i	0.704270	+	0.709933i	$0.251275\pi$
$14$		0			0
$15$	2.36397	+	3.80914i	0.610374	+	0.983516i
$16$		0			0
$17$	1.52724	+	2.99738i	0.370411	+	0.726972i	0.998698	−	0.0510094i	$-0.0162439\pi$
$17$	1.52724	+	2.99738i	0.370411	+	0.726972i	−0.628288	+	0.777981i	$0.716244\pi$
$18$		0			0
$19$	−1.05647	−	0.767569i	−0.242370	−	0.176092i	0.459968	−	0.887935i	$-0.347861\pi$
$19$	−1.05647	−	0.767569i	−0.242370	−	0.176092i	−0.702339	+	0.711843i	$0.747861\pi$
$20$		0			0
$21$		−	3.62488i		−	0.791014i
$22$		0			0
$23$	3.16488	−	3.16488i	0.659922	−	0.659922i	−0.295439	−	0.955362i	$-0.595466\pi$
$23$	3.16488	−	3.16488i	0.659922	−	0.659922i	0.955362	+	0.295439i	$0.0954660\pi$
$24$		0			0
$25$	−3.49534	+	3.57528i	−0.699067	+	0.715056i
$26$		0			0
$27$	3.53776	−	1.80258i	0.680843	−	0.346907i
$28$		0			0
$29$	2.37569	−	1.72604i	0.441154	−	0.320517i	−0.344939	−	0.938625i	$-0.612100\pi$
$29$	2.37569	−	1.72604i	0.441154	−	0.320517i	0.786093	+	0.618108i	$0.212100\pi$
$30$		0			0
$31$	1.23925	+	3.81401i	0.222575	+	0.685016i	0.998529	+	0.0542261i	$0.0172692\pi$
$31$	1.23925	+	3.81401i	0.222575	+	0.685016i	−0.775953	+	0.630790i	$0.782731\pi$
$32$		0			0
$33$	4.30014	+	5.07190i	0.748558	+	0.882905i
$34$		0			0
$35$	3.92576	−	0.965994i	0.663574	−	0.163283i
$36$		0			0
$37$	3.16942	+	0.501987i	0.521050	+	0.0825262i	0.411419	−	0.911446i	$-0.365033\pi$
$37$	3.16942	+	0.501987i	0.521050	+	0.0825262i	0.109631	+	0.993972i	$0.465033\pi$
$38$		0			0
$39$	1.39757	−	4.30127i	0.223790	−	0.688754i
$40$		0			0
$41$	0.766287	−	1.05470i	0.119674	−	0.164717i	−0.744977	−	0.667090i	$-0.767540\pi$
$41$	0.766287	−	1.05470i	0.119674	−	0.164717i	0.864651	+	0.502373i	$0.167540\pi$
$42$		0			0
$43$	4.55431	+	4.55431i	0.694526	+	0.694526i	0.963224	−	0.268698i	$-0.0865935\pi$
$43$	4.55431	+	4.55431i	0.694526	+	0.694526i	−0.268698	+	0.963224i	$0.586593\pi$
$44$		0			0
$45$	−1.49042	−	1.72521i	−0.222178	−	0.257179i
$46$		0			0
$47$	1.20824	+	7.62854i	0.176240	+	1.11274i	0.904198	+	0.427114i	$0.140470\pi$
$47$	1.20824	+	7.62854i	0.176240	+	1.11274i	−0.727957	+	0.685622i	$0.759530\pi$
$48$		0			0
$49$	3.54845	+	1.15296i	0.506921	+	0.164709i
$50$		0			0
$51$	−3.96433	−	5.45644i	−0.555118	−	0.764054i
$52$		0			0
$53$	5.67482	+	2.89146i	0.779496	+	0.397173i	0.798001	−	0.602656i	$-0.205891\pi$
$53$	5.67482	+	2.89146i	0.779496	+	0.397173i	−0.0185052	+	0.999829i	$0.505891\pi$
$54$		0			0
$55$	−4.34694	+	6.00867i	−0.586141	+	0.810209i
$56$		0			0
$57$	2.33276	+	1.18860i	0.308981	+	0.157434i
$58$		0			0
$59$	7.28135	+	10.0219i	0.947952	+	1.30474i	0.952431	+	0.304753i	$0.0985740\pi$
$59$	7.28135	+	10.0219i	0.947952	+	1.30474i	−0.00447977	+	0.999990i	$0.501426\pi$
$60$		0			0
$61$	−8.85435	−	2.87695i	−1.13368	−	0.368356i	−0.318709	−	0.947853i	$-0.603249\pi$
$61$	−8.85435	−	2.87695i	−1.13368	−	0.368356i	−0.814975	+	0.579496i	$0.803249\pi$
$62$		0			0
$63$	0.288374	+	1.82072i	0.0363318	+	0.229390i
$64$		0			0
$65$	5.03072	+	0.367324i	0.623984	+	0.0455609i
$66$		0			0
$67$	2.46236	+	2.46236i	0.300825	+	0.300825i	0.841336	−	0.540512i	$-0.181769\pi$
$67$	2.46236	+	2.46236i	0.300825	+	0.300825i	−0.540512	+	0.841336i	$0.681769\pi$
$68$		0			0
$69$	−5.27449	+	7.25972i	−0.634974	+	0.873967i
$70$		0			0
$71$	2.09243	−	6.43984i	0.248326	−	0.764268i	−0.746746	−	0.665110i	$-0.768385\pi$
$71$	2.09243	−	6.43984i	0.248326	−	0.764268i	0.995072	−	0.0991588i	$-0.0316152\pi$
$72$		0			0
$73$	9.32763	+	1.47735i	1.09172	+	0.172911i	0.676232	−	0.736689i	$-0.263612\pi$
$73$	9.32763	+	1.47735i	1.09172	+	0.172911i	0.415485	+	0.909600i	$0.363612\pi$
$74$		0			0
$75$	5.80015	−	8.17604i	0.669744	−	0.944088i
$76$		0			0
$77$	5.54835	−	2.27469i	0.632293	−	0.259225i
$78$		0			0
$79$	0.353860	+	1.08907i	0.0398123	+	0.122530i	0.968987	−	0.247110i	$-0.0794810\pi$
$79$	0.353860	+	1.08907i	0.0398123	+	0.122530i	−0.929175	+	0.369640i	$0.879481\pi$
$80$		0			0
$81$	−8.91472	+	6.47692i	−0.990524	+	0.719658i
$82$		0			0
$83$	9.32422	−	4.75092i	1.02347	−	0.521482i	0.140086	−	0.990139i	$-0.455262\pi$
$83$	9.32422	−	4.75092i	1.02347	−	0.521482i	0.883380	+	0.468658i	$0.155262\pi$
$84$		0			0
$85$	4.85288	−	5.74747i	0.526369	−	0.623400i
$86$		0			0
$87$	−4.16301	+	4.16301i	−0.446321	+	0.446321i
$88$		0			0
$89$			3.85743i			0.408887i	0.978878	+	0.204443i	$0.0655384\pi$
$89$			3.85743i			0.408887i	−0.978878	+	0.204443i	$0.934462\pi$
$90$		0			0
$91$	−3.29960	−	2.39730i	−0.345892	−	0.251305i
$92$		0			0
$93$	−3.65016	−	7.16385i	−0.378504	−	0.742857i
$94$		0			0
$95$	−0.665600	+	2.84313i	−0.0682891	+	0.291699i
$96$		0			0
$97$	0.353228	−	0.693249i	0.0358649	−	0.0703888i	−0.872379	−	0.488831i	$-0.837424\pi$
$97$	0.353228	−	0.693249i	0.0358649	−	0.0703888i	0.908244	+	0.418442i	$0.137424\pi$
$98$		0			0
$99$	−2.56339	−	2.20545i	−0.257630	−	0.221656i
$100$		0			0
$101$	9.28960	−	3.01837i	0.924350	−	0.300339i	0.192100	−	0.981375i	$-0.438470\pi$
$101$	9.28960	−	3.01837i	0.924350	−	0.300339i	0.732250	+	0.681036i	$0.238470\pi$
$102$		0			0
$103$	−0.730841	+	4.61435i	−0.0720119	+	0.454665i	0.925164	+	0.379567i	$0.123927\pi$
$103$	−0.730841	+	4.61435i	−0.0720119	+	0.454665i	−0.997176	+	0.0750982i	$0.976073\pi$
$104$		0			0
$105$	−7.47084	+	3.14412i	−0.729079	+	0.306834i
$106$		0			0
$107$	−15.1133	+	2.39372i	−1.46106	+	0.231410i	−0.835813	−	0.549015i	$-0.815003\pi$
$107$	−15.1133	+	2.39372i	−1.46106	+	0.231410i	−0.625250	+	0.780424i	$0.715003\pi$
$108$		0			0
$109$	−17.8837			−1.71295			−0.856476	−	0.516187i	$-0.827351\pi$
$109$	−17.8837			−1.71295			−0.856476	+	0.516187i	$0.827351\pi$
$110$		0			0
$111$	−6.43355			−0.610646
$112$		0			0
$113$	7.37759	−	1.16850i	0.694025	−	0.109923i	0.200551	−	0.979683i	$-0.435727\pi$
$113$	7.37759	−	1.16850i	0.694025	−	0.109923i	0.493474	+	0.869760i	$0.335727\pi$
$114$		0			0
$115$	−9.26789	−	3.77765i	−0.864235	−	0.352268i
$116$		0			0
$117$	−0.359793	+	2.27165i	−0.0332629	+	0.210014i
$118$		0			0
$119$	−5.78457	+	1.87952i	−0.530271	+	0.172295i
$120$		0			0
$121$	−5.06477	+	9.76464i	−0.460433	+	0.887694i
$122$		0			0
$123$	−1.18662	+	2.32886i	−0.106994	+	0.209987i
$124$		0			0
$125$	10.4004	+	4.10275i	0.930236	+	0.366961i
$126$		0			0
$127$	0.0936079	+	0.183716i	0.00830635	+	0.0163021i	0.895122	−	0.445820i	$-0.147088\pi$
$127$	0.0936079	+	0.183716i	0.00830635	+	0.0163021i	−0.886816	+	0.462123i	$0.847088\pi$
$128$		0			0
$129$	−10.4469	−	7.59009i	−0.919794	−	0.668270i
$130$		0			0
$131$			0.551708i			0.0482029i	0.999710	+	0.0241015i	$0.00767248\pi$
$131$			0.551708i			0.0482029i	−0.999710	+	0.0241015i	$0.992328\pi$
$132$		0			0
$133$	1.66950	−	1.66950i	0.144764	−	0.144764i
$134$		0			0
$135$	−6.78365	−	5.72778i	−0.583843	−	0.492969i
$136$		0			0
$137$	−13.7896	+	7.02615i	−1.17812	+	0.600284i	−0.929682	−	0.368362i	$-0.879919\pi$
$137$	−13.7896	+	7.02615i	−1.17812	+	0.600284i	−0.248442	+	0.968647i	$0.579919\pi$
$138$		0			0
$139$	1.15101	−	0.836256i	0.0976272	−	0.0709303i	−0.537901	−	0.843008i	$-0.680782\pi$
$139$	1.15101	−	0.836256i	0.0976272	−	0.0709303i	0.635528	+	0.772078i	$0.280782\pi$
$140$		0			0
$141$	−4.78513	−	14.7271i	−0.402981	−	1.24025i
$142$		0			0
$143$	7.46065	−	0.559982i	0.623891	−	0.0468280i
$144$		0			0
$145$	−5.61795	−	3.39915i	−0.466545	−	0.282284i
$146$		0			0
$147$	−7.38826	−	1.17019i	−0.609373	−	0.0965153i
$148$		0			0
$149$	7.35615	−	22.6399i	0.602639	−	1.85473i	0.0903702	−	0.995908i	$-0.471195\pi$
$149$	7.35615	−	22.6399i	0.602639	−	1.85473i	0.512269	−	0.858825i	$-0.328805\pi$
$150$		0			0
$151$	8.45592	−	11.6386i	0.688133	−	0.947134i	−0.311862	−	0.950127i	$-0.600953\pi$
$151$	8.45592	−	11.6386i	0.688133	−	0.947134i	0.999996	+	0.00299311i	$0.000952737\pi$
$152$		0			0
$153$	2.42531	+	2.42531i	0.196075	+	0.196075i
$154$		0			0
$155$	6.78574	−	5.86223i	0.545044	−	0.470866i
$156$		0			0
$157$	2.11091	+	13.3277i	0.168469	+	1.06367i	0.916508	+	0.400016i	$0.130995\pi$
$157$	2.11091	+	13.3277i	0.168469	+	1.06367i	−0.748040	+	0.663654i	$0.769005\pi$
$158$		0			0
$159$	−12.1442	−	3.94588i	−0.963095	−	0.312928i
$160$		0			0
$161$	4.75657	+	6.54686i	0.374870	+	0.515965i
$162$		0			0
$163$	−0.956239	−	0.487228i	−0.0748984	−	0.0381626i	0.416140	−	0.909300i	$-0.363383\pi$
$163$	−0.956239	−	0.487228i	−0.0748984	−	0.0381626i	−0.491039	+	0.871138i	$0.663383\pi$
$164$		0			0
$165$	6.72331	−	13.2617i	0.523409	−	1.03243i
$166$		0			0
$167$	1.68563	+	0.858874i	0.130438	+	0.0664616i	0.517992	−	0.855386i	$-0.326680\pi$
$167$	1.68563	+	0.858874i	0.130438	+	0.0664616i	−0.387554	+	0.921847i	$0.626680\pi$
$168$		0			0
$169$	4.65019	+	6.40044i	0.357707	+	0.492342i
$170$		0			0
$171$	−1.26627	−	0.411435i	−0.0968339	−	0.0314633i
$172$		0			0
$173$	−2.96401	−	18.7140i	−0.225350	−	1.42280i	−0.797830	−	0.602883i	$-0.794019\pi$
$173$	−2.96401	−	18.7140i	−0.225350	−	1.42280i	0.572480	−	0.819919i	$-0.305981\pi$
$174$		0			0
$175$	−5.39599	−	7.25306i	−0.407898	−	0.548280i
$176$		0			0
$177$	−17.5618	−	17.5618i	−1.32002	−	1.32002i
$178$		0			0
$179$	−9.62961	+	13.2540i	−0.719751	+	0.990652i	0.279781	+	0.960064i	$0.409738\pi$
$179$	−9.62961	+	13.2540i	−0.719751	+	0.990652i	−0.999532	+	0.0305880i	$0.990262\pi$
$180$		0			0
$181$	4.59306	−	14.1360i	0.341400	−	1.05072i	−0.622084	−	0.782951i	$-0.713714\pi$
$181$	4.59306	−	14.1360i	0.341400	−	1.05072i	0.963483	−	0.267769i	$-0.0862864\pi$
$182$		0			0
$183$	18.4357	+	2.91994i	1.36281	+	0.215848i
$184$		0			0
$185$	−1.71448	−	6.96755i	−0.126051	−	0.512265i
$186$		0			0
$187$	5.86407	−	9.49195i	0.428823	−	0.694120i
$188$		0			0
$189$	2.21837	+	6.82744i	0.161363	+	0.496623i
$190$		0			0
$191$	−1.54488	+	1.12242i	−0.111784	+	0.0812156i	−0.642273	−	0.766476i	$-0.722008\pi$
$191$	−1.54488	+	1.12242i	−0.111784	+	0.0812156i	0.530489	+	0.847692i	$0.322008\pi$
$192$		0			0
$193$	10.1423	−	5.16774i	0.730056	−	0.371982i	−0.0491153	−	0.998793i	$-0.515640\pi$
$193$	10.1423	−	5.16774i	0.730056	−	0.371982i	0.779171	+	0.626811i	$0.215640\pi$
$194$		0			0
$195$	−10.0771	+	0.850427i	−0.721634	+	0.0609004i
$196$		0			0
$197$	−13.8092	+	13.8092i	−0.983863	+	0.983863i	−0.999872	−	0.0160086i	$-0.994904\pi$
$197$	−13.8092	+	13.8092i	−0.983863	+	0.983863i	0.0160086	+	0.999872i	$0.494904\pi$
$198$		0			0
$199$		−	22.3508i		−	1.58441i	−0.610258	−	0.792203i	$-0.708934\pi$
$199$		−	22.3508i		−	1.58441i	0.610258	−	0.792203i	$-0.291066\pi$
$200$		0			0
$201$	−5.64825	−	4.10369i	−0.398397	−	0.289452i
$202$		0			0
$203$	2.41036	+	4.73060i	0.169174	+	0.332023i
$204$		0			0
$205$	−2.83839	−	0.664489i	−0.198242	−	0.0464099i
$206$		0			0
$207$	2.07176	−	4.06606i	0.143997	−	0.282610i
$208$		0			0
$209$	−0.355449	+	4.31646i	−0.0245869	+	0.298576i
$210$		0			0
$211$	0.358113	−	0.116358i	0.0246535	−	0.00801042i	−0.296664	−	0.954982i	$-0.595874\pi$
$211$	0.358113	−	0.116358i	0.0246535	−	0.00801042i	0.321318	+	0.946971i	$0.395874\pi$
$212$		0			0
$213$	−2.12369	+	13.4085i	−0.145513	+	0.918733i
$214$		0			0
$215$	5.43610	−	13.3367i	0.370739	−	0.909552i
$216$		0			0
$217$	−7.16142	+	1.13426i	−0.486149	+	0.0769984i
$218$		0			0
$219$	−18.9340			−1.27944
$220$		0			0
$221$	−7.58859			−0.510464
$222$		0			0
$223$	−7.51570	+	1.19037i	−0.503289	+	0.0797131i	−0.402916	−	0.915237i	$-0.632003\pi$
$223$	−7.51570	+	1.19037i	−0.503289	+	0.0797131i	−0.100372	+	0.994950i	$0.532003\pi$
$224$		0			0
$225$	−2.26289	+	4.56813i	−0.150860	+	0.304542i
$226$		0			0
$227$	−1.28318	+	8.10167i	−0.0851676	+	0.537727i	0.907806	+	0.419390i	$0.137756\pi$
$227$	−1.28318	+	8.10167i	−0.0851676	+	0.537727i	−0.992974	+	0.118336i	$0.962244\pi$
$228$		0			0
$229$	−7.21772	+	2.34518i	−0.476960	+	0.154974i	−0.537624	−	0.843184i	$-0.680678\pi$
$229$	−7.21772	+	2.34518i	−0.476960	+	0.154974i	0.0606641	+	0.998158i	$0.480678\pi$
$230$		0			0
$231$	−10.2734	+	6.24450i	−0.675943	+	0.410858i
$232$		0			0
$233$	−11.9023	+	23.3597i	−0.779749	+	1.53034i	0.0666396	+	0.997777i	$0.478772\pi$
$233$	−11.9023	+	23.3597i	−0.779749	+	1.53034i	−0.846388	+	0.532566i	$0.821228\pi$
$234$		0			0
$235$	14.6743	−	9.10694i	0.957247	−	0.594071i
$236$		0			0
$237$	−1.04228	−	2.04560i	−0.0677036	−	0.132876i
$238$		0			0
$239$	−1.84133	−	1.33781i	−0.119106	−	0.0865356i	0.526638	−	0.850090i	$-0.323452\pi$
$239$	−1.84133	−	1.33781i	−0.119106	−	0.0865356i	−0.645744	+	0.763554i	$0.723452\pi$
$240$		0			0
$241$			6.29531i			0.405517i	0.979229	+	0.202758i	$0.0649906\pi$
$241$			6.29531i			0.405517i	−0.979229	+	0.202758i	$0.935009\pi$
$242$		0			0
$243$	7.19883	−	7.19883i	0.461805	−	0.461805i
$244$		0			0
$245$	−0.701583	−	8.31335i	−0.0448225	−	0.531120i
$246$		0			0
$247$	2.62470	−	1.33735i	0.167006	−	0.0850936i
$248$		0			0
$249$	−16.9738	+	12.3322i	−1.07567	+	0.781521i
$250$		0			0
$251$	8.21826	+	25.2932i	0.518732	+	1.59649i	0.776387	+	0.630256i	$0.217050\pi$
$251$	8.21826	+	25.2932i	0.518732	+	1.59649i	−0.257655	+	0.966237i	$0.582950\pi$
$252$		0			0
$253$	−14.4218	−	3.51766i	−0.906690	−	0.221153i
$254$		0			0
$255$	−7.80710	+	12.9032i	−0.488899	+	0.808029i
$256$		0			0
$257$	19.5307	+	3.09337i	1.21829	+	0.192959i	0.732287	−	0.680996i	$-0.238453\pi$
$257$	19.5307	+	3.09337i	1.21829	+	0.192959i	0.486007	+	0.873955i	$0.338453\pi$
$258$		0			0
$259$	−1.79286	+	5.51786i	−0.111403	+	0.342863i
$260$		0			0
$261$	1.75983	−	2.42220i	0.108931	−	0.149931i
$262$		0			0
$263$	−5.91748	−	5.91748i	−0.364888	−	0.364888i	0.500721	−	0.865609i	$-0.333068\pi$
$263$	−5.91748	−	5.91748i	−0.364888	−	0.364888i	−0.865609	+	0.500721i	$0.833068\pi$
$264$		0			0
$265$	1.03710	−	14.2037i	0.0637085	−	0.872526i
$266$		0			0
$267$	−1.20982	−	7.63850i	−0.0740398	−	0.467469i
$268$		0			0
$269$	9.23539	+	3.00076i	0.563092	+	0.182960i	0.576712	−	0.816948i	$-0.304336\pi$
$269$	9.23539	+	3.00076i	0.563092	+	0.182960i	−0.0136201	+	0.999907i	$0.504336\pi$
$270$		0			0
$271$	−1.79360	−	2.46868i	−0.108954	−	0.149962i	0.751058	−	0.660236i	$-0.229544\pi$
$271$	−1.79360	−	2.46868i	−0.108954	−	0.149962i	−0.860012	+	0.510274i	$0.829544\pi$
$272$		0			0
$273$	7.28576	+	3.71228i	0.440954	+	0.224677i
$274$		0			0
$275$	16.1542	+	3.74724i	0.974135	+	0.225967i
$276$		0			0
$277$	−2.12073	−	1.08057i	−0.127422	−	0.0649249i	0.389117	−	0.921188i	$-0.372780\pi$
$277$	−2.12073	−	1.08057i	−0.127422	−	0.0649249i	−0.516540	+	0.856263i	$0.672780\pi$
$278$		0			0
$279$	2.40334	+	3.30791i	0.143884	+	0.198039i
$280$		0			0
$281$	26.8503	+	8.72419i	1.60175	+	0.520442i	0.967541	−	0.252716i	$-0.0813238\pi$
$281$	26.8503	+	8.72419i	1.60175	+	0.520442i	0.634214	+	0.773157i	$0.281324\pi$
$282$		0			0
$283$	2.66149	+	16.8040i	0.158209	+	0.998893i	0.931209	+	0.364486i	$0.118755\pi$
$283$	2.66149	+	16.8040i	0.158209	+	0.998893i	−0.773000	+	0.634406i	$0.781245\pi$
$284$		0			0
$285$	0.426322	−	5.83874i	0.0252532	−	0.345857i
$286$		0			0
$287$	1.66672	+	1.66672i	0.0983831	+	0.0983831i
$288$		0			0
$289$	3.34052	−	4.59783i	0.196501	−	0.270461i
$290$		0			0
$291$	−0.482038	+	1.48356i	−0.0282576	+	0.0869678i
$292$		0			0
$293$	10.5533	+	1.67148i	0.616533	+	0.0976492i	0.456886	−	0.889525i	$-0.348965\pi$
$293$	10.5533	+	1.67148i	0.616533	+	0.0976492i	0.159646	+	0.987174i	$0.448965\pi$
$294$		0			0
$295$	14.3394	−	23.6995i	0.834873	−	1.37984i
$296$		0			0
$297$	−11.2032	−	6.92127i	−0.650076	−	0.401613i
$298$		0			0
$299$	3.12000	+	9.60236i	0.180434	+	0.555319i
$300$		0			0
$301$	−9.42104	+	6.84479i	−0.543020	+	0.394527i
$302$		0			0
$303$	−17.4487	+	8.89053i	−1.00240	+	0.510748i
$304$		0			0
$305$	1.75064	+	20.7441i	0.100241	+	1.18780i
$306$		0			0
$307$	−22.9923	+	22.9923i	−1.31224	+	1.31224i	−0.392474	+	0.919763i	$0.628381\pi$
$307$	−22.9923	+	22.9923i	−1.31224	+	1.31224i	−0.919763	+	0.392474i	$0.871619\pi$
$308$		0			0
$309$		−	9.36657i		−	0.532846i
$310$		0			0
$311$	11.2361	+	8.16354i	0.637143	+	0.462912i	0.858868	−	0.512198i	$-0.171168\pi$
$311$	11.2361	+	8.16354i	0.637143	+	0.462912i	−0.221724	+	0.975109i	$0.571168\pi$
$312$		0			0
$313$	7.89399	+	15.4928i	0.446195	+	0.875707i	0.999098	+	0.0424612i	$0.0135199\pi$
$313$	7.89399	+	15.4928i	0.446195	+	0.875707i	−0.552903	+	0.833245i	$0.686480\pi$
$314$		0			0
$315$	3.50236	−	2.17358i	0.197336	−	0.122467i
$316$		0			0
$317$	−7.33513	+	14.3960i	−0.411982	+	0.808560i	−1.00000		0.000287853i	$-0.999908\pi$
$317$	−7.33513	+	14.3960i	−0.411982	+	0.808560i	0.588018	+	0.808848i	$0.299908\pi$
$318$		0			0
$319$	−8.98439	−	3.75964i	−0.503029	−	0.210500i
$320$		0			0
$321$	29.1768	−	9.48011i	1.62849	−	0.529128i
$322$		0			0
$323$	0.687214	−	4.33890i	0.0382376	−	0.241423i
$324$		0			0
$325$	−3.60645	−	10.6869i	−0.200050	−	0.592800i
$326$		0			0
$327$	35.4135	−	5.60894i	1.95837	−	0.310175i
$328$		0			0
$329$	−13.9645			−0.769887
$330$		0			0
$331$	−14.6837			−0.807090			−0.403545	−	0.914960i	$-0.632222\pi$
$331$	−14.6837			−0.807090			−0.403545	+	0.914960i	$0.632222\pi$
$332$		0			0
$333$	3.23148	−	0.511816i	0.177084	−	0.0280473i
$334$		0			0
$335$	2.93911	−	7.21066i	0.160581	−	0.393961i
$336$		0			0
$337$	2.11047	−	13.3250i	0.114965	−	0.725859i	−0.861109	−	0.508420i	$-0.830230\pi$
$337$	2.11047	−	13.3250i	0.114965	−	0.725859i	0.976074	−	0.217439i	$-0.0697703\pi$
$338$		0			0
$339$	−14.2427	+	4.62772i	−0.773555	+	0.251343i
$340$		0			0
$341$	8.67464	−	10.0825i	0.469758	−	0.545999i
$342$		0			0
$343$	−8.80832	+	17.2873i	−0.475604	+	0.933426i
$344$		0			0
$345$	19.5371	+	4.57380i	1.05184	+	0.246245i
$346$		0			0
$347$	−5.55495	−	10.9022i	−0.298205	−	0.585261i	0.692479	−	0.721438i	$-0.256518\pi$
$347$	−5.55495	−	10.9022i	−0.298205	−	0.585261i	−0.990685	+	0.136177i	$0.956518\pi$
$348$		0			0
$349$	16.4807	+	11.9739i	0.882193	+	0.640951i	0.933831	−	0.357715i	$-0.116444\pi$
$349$	16.4807	+	11.9739i	0.882193	+	0.640951i	−0.0516378	+	0.998666i	$0.516444\pi$
$350$		0			0
$351$			8.95670i			0.478073i
$352$		0			0
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	−0.237495	−	0.971389i	$-0.576326\pi$
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	0.971389	+	0.237495i	$0.0763264\pi$
$354$		0			0
$355$	−15.0873	+	1.27326i	−0.800753	+	0.0675774i
$356$		0			0
$357$	10.8652	−	5.53607i	0.575045	−	0.293000i
$358$		0			0
$359$	13.3648	−	9.71011i	0.705368	−	0.512480i	−0.176308	−	0.984335i	$-0.556415\pi$
$359$	13.3648	−	9.71011i	0.705368	−	0.512480i	0.881676	+	0.471855i	$0.156415\pi$
$360$		0			0
$361$	−5.34436	−	16.4483i	−0.281282	−	0.865697i
$362$		0			0
$363$	6.96676	−	20.9245i	0.365660	−	1.09825i
$364$		0			0
$365$	−5.04571	−	20.5055i	−0.264105	−	1.07331i
$366$		0			0
$367$	6.36207	+	1.00765i	0.332097	+	0.0525990i	0.320256	−	0.947331i	$-0.396231\pi$
$367$	6.36207	+	1.00765i	0.332097	+	0.0525990i	0.0118406	+	0.999930i	$0.496231\pi$
$368$		0			0
$369$	0.410749	−	1.26415i	0.0213827	−	0.0658092i
$370$		0			0
$371$	−6.76851	+	9.31606i	−0.351404	+	0.483666i
$372$		0			0
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	0.410021	−	0.912076i	$-0.365522\pi$
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	−0.912076	+	0.410021i	$0.865522\pi$
$374$		0			0
$375$	−21.8816	−	4.86238i	−1.12996	−	0.251092i
$376$		0			0
$377$	1.03625	+	6.54262i	0.0533696	+	0.336962i
$378$		0			0
$379$	20.4487	+	6.64419i	1.05038	+	0.341289i	0.782818	−	0.622251i	$-0.213782\pi$
$379$	20.4487	+	6.64419i	1.05038	+	0.341289i	0.267563	+	0.963540i	$0.413782\pi$
$380$		0			0
$381$	−0.242982	−	0.334436i	−0.0124484	−	0.0171337i
$382$		0			0
$383$	−0.270362	−	0.137756i	−0.0138148	−	0.00703902i	0.447069	−	0.894499i	$-0.352468\pi$
$383$	−0.270362	−	0.137756i	−0.0138148	−	0.00703902i	−0.460884	+	0.887460i	$0.652468\pi$
$384$		0			0
$385$	−9.50058	−	9.46207i	−0.484194	−	0.482232i
$386$		0			0
$387$	5.85112	+	2.98130i	0.297429	+	0.151548i
$388$		0			0
$389$	−2.11680	−	2.91353i	−0.107326	−	0.147722i	0.751975	−	0.659191i	$-0.229101\pi$
$389$	−2.11680	−	2.91353i	−0.107326	−	0.147722i	−0.859301	+	0.511470i	$0.829101\pi$
$390$		0			0
$391$	14.3199	+	4.65281i	0.724187	+	0.235303i
$392$		0			0
$393$	−0.173034	−	1.09249i	−0.00872842	−	0.0551091i
$394$		0			0
$395$	1.93763	−	1.67393i	0.0974927	−	0.0842244i
$396$		0			0
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.992731	+	0.120357i	$0.0384039\pi$
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.120357	+	0.992731i	$0.461596\pi$
$398$		0			0
$399$	−2.78235	+	3.82957i	−0.139292	+	0.191718i
$400$		0			0
$401$	−3.08934	+	9.50802i	−0.154274	+	0.474808i	−0.998087	−	0.0618306i	$-0.980306\pi$
$401$	−3.08934	+	9.50802i	−0.154274	+	0.474808i	0.843812	+	0.536639i	$0.180306\pi$
$402$		0			0
$403$	−8.93502	−	1.41517i	−0.445085	−	0.0704945i
$404$		0			0
$405$	21.0812	+	12.7552i	1.04753	+	0.633812i
$406$		0			0
$407$	−4.03719	−	9.84737i	−0.200116	−	0.488116i
$408$		0			0
$409$	9.39140	+	28.9037i	0.464375	+	1.42920i	0.859767	+	0.510686i	$0.170609\pi$
$409$	9.39140	+	28.9037i	0.464375	+	1.42920i	−0.395393	+	0.918512i	$0.629391\pi$
$410$		0			0
$411$	25.1026	−	18.2381i	1.23822	−	0.899619i
$412$		0			0
$413$	−19.9562	+	10.1682i	−0.981981	+	0.500344i
$414$		0			0
$415$	−17.8791	−	15.0963i	−0.877653	−	0.741047i
$416$		0			0
$417$	−2.01695	+	2.01695i	−0.0987706	+	0.0987706i
$418$		0			0
$419$			7.48185i			0.365512i	0.983158	+	0.182756i	$0.0585019\pi$
$419$			7.48185i			0.365512i	−0.983158	+	0.182756i	$0.941498\pi$
$420$		0			0
$421$	−16.5226	−	12.0043i	−0.805260	−	0.585056i	0.107192	−	0.994238i	$-0.465814\pi$
$421$	−16.5226	−	12.0043i	−0.805260	−	0.585056i	−0.912453	+	0.409182i	$0.865814\pi$
$422$		0			0
$423$	3.57511	+	7.01654i	0.173828	+	0.341156i
$424$		0			0
$425$	−16.0547	−	5.01654i	−0.778767	−	0.243338i
$426$		0			0
$427$	7.64189	−	14.9981i	0.369817	−	0.725807i
$428$		0			0
$429$	−14.5980	+	3.44879i	−0.704797	+	0.166509i
$430$		0			0
$431$	32.0182	−	10.4034i	1.54226	−	0.501112i	0.590264	−	0.807210i	$-0.299024\pi$
$431$	32.0182	−	10.4034i	1.54226	−	0.501112i	0.952000	+	0.306098i	$0.0990236\pi$
$432$		0			0
$433$	1.81451	−	11.4564i	0.0871997	−	0.550557i	−0.904952	−	0.425514i	$-0.860093\pi$
$433$	1.81451	−	11.4564i	0.0871997	−	0.550557i	0.992151	−	0.125043i	$-0.0399068\pi$
$434$		0			0
$435$	12.1908	+	4.96903i	0.584503	+	0.238247i
$436$		0			0
$437$	−5.77285	+	0.914330i	−0.276153	+	0.0437383i
$438$		0			0
$439$	−10.7242			−0.511837			−0.255918	−	0.966698i	$-0.582378\pi$
$439$	−10.7242			−0.511837			−0.255918	+	0.966698i	$0.582378\pi$
$440$		0			0
$441$	3.80411			0.181148
$442$		0			0
$443$	39.8371	−	6.30958i	1.89272	−	0.299777i	0.901580	−	0.432612i	$-0.142408\pi$
$443$	39.8371	−	6.30958i	1.89272	−	0.299777i	0.991138	+	0.132835i	$0.0424079\pi$
$444$		0			0
$445$	7.95012	−	3.34582i	0.376872	−	0.158607i
$446$		0			0
$447$	−7.46605	+	47.1388i	−0.353132	+	2.22959i
$448$		0			0
$449$	−3.46337	+	1.12532i	−0.163447	+	0.0531070i	−0.389597	−	0.920985i	$-0.627386\pi$
$449$	−3.46337	+	1.12532i	−0.163447	+	0.0531070i	0.226151	+	0.974092i	$0.427386\pi$
$450$		0			0
$451$	−4.30925	−	0.354856i	−0.202915	−	0.0167095i
$452$		0			0
$453$	−13.0942	+	25.6988i	−0.615220	+	1.20744i
$454$		0			0
$455$	−2.07883	+	8.87978i	−0.0974569	+	0.416291i
$456$		0			0
$457$	−8.21391	−	16.1207i	−0.384230	−	0.754094i	0.615182	−	0.788385i	$-0.289083\pi$
$457$	−8.21391	−	16.1207i	−0.384230	−	0.754094i	−0.999412	+	0.0342910i	$0.989083\pi$
$458$		0			0
$459$	10.8060	+	7.85105i	0.504383	+	0.366456i
$460$		0			0
$461$			35.5884i			1.65751i	0.559608	+	0.828757i	$0.310952\pi$
$461$			35.5884i			1.65751i	−0.559608	+	0.828757i	$0.689048\pi$
$462$		0			0
$463$	4.46802	−	4.46802i	0.207647	−	0.207647i	−0.595620	−	0.803266i	$-0.703093\pi$
$463$	4.46802	−	4.46802i	0.207647	−	0.207647i	0.803266	+	0.595620i	$0.203093\pi$
$464$		0			0
$465$	−11.5986	+	13.7367i	−0.537870	+	0.637022i
$466$		0			0
$467$	7.70967	−	3.92827i	0.356761	−	0.181779i	−0.266419	−	0.963857i	$-0.585840\pi$
$467$	7.70967	−	3.92827i	0.356761	−	0.181779i	0.623180	+	0.782079i	$0.285840\pi$
$468$		0			0
$469$	−5.09363	+	3.70074i	−0.235202	+	0.170884i
$470$		0			0
$471$	−8.36006	−	25.7296i	−0.385211	−	1.18556i
$472$		0			0
$473$	5.06198	−	20.7532i	0.232750	−	0.954233i
$474$		0			0
$475$	6.43698	−	1.09426i	0.295349	−	0.0502080i
$476$		0			0
$477$	6.41374	+	1.01584i	0.293665	+	0.0465120i
$478$		0			0
$479$	4.75378	−	14.6306i	0.217206	−	0.668490i	−0.781784	−	0.623549i	$-0.785690\pi$
$479$	4.75378	−	14.6306i	0.217206	−	0.668490i	0.998990	−	0.0449410i	$-0.0143100\pi$
$480$		0			0
$481$	−4.25480	+	5.85623i	−0.194002	+	0.267021i
$482$		0			0
$483$	−11.4723	−	11.4723i	−0.522008	−	0.522008i
$484$		0			0
$485$	−1.73516	−	0.126694i	−0.0787894	−	0.00575290i
$486$		0			0
$487$	0.930218	+	5.87316i	0.0421522	+	0.266138i	0.999759	−	0.0219390i	$-0.00698396\pi$
$487$	0.930218	+	5.87316i	0.0421522	+	0.266138i	−0.957607	+	0.288077i	$0.906984\pi$
$488$		0			0
$489$	2.04636	+	0.664903i	0.0925396	+	0.0300679i
$490$		0			0
$491$	−24.0702	−	33.1298i	−1.08627	−	1.49513i	−0.852422	−	0.522855i	$-0.824867\pi$
$491$	−24.0702	−	33.1298i	−1.08627	−	1.49513i	−0.233851	−	0.972272i	$-0.575133\pi$
$492$		0			0
$493$	8.80185	+	4.48477i	0.396415	+	0.201984i
$494$		0			0
$495$	−2.32199	+	7.19605i	−0.104366	+	0.323438i
$496$		0			0
$497$	10.9082	+	5.55801i	0.489300	+	0.249311i
$498$		0			0
$499$	13.6289	+	18.7585i	0.610111	+	0.839746i	0.996587	−	0.0825534i	$-0.0263075\pi$
$499$	13.6289	+	18.7585i	0.610111	+	0.839746i	−0.386475	+	0.922300i	$0.626308\pi$
$500$		0			0
$501$	−3.60727	−	1.17207i	−0.161161	−	0.0523644i
$502$		0			0
$503$	−0.523026	−	3.30226i	−0.0233206	−	0.147240i	0.973280	−	0.229619i	$-0.0737482\pi$
$503$	−0.523026	−	3.30226i	−0.0233206	−	0.147240i	−0.996601	+	0.0823791i	$0.973748\pi$
$504$		0			0
$505$	−14.2784	−	16.5277i	−0.635379	−	0.735473i
$506$		0			0
$507$	−11.2157	−	11.2157i	−0.498108	−	0.498108i
$508$		0			0
$509$	13.0172	−	17.9166i	0.576977	−	0.794141i	−0.416383	−	0.909189i	$-0.636702\pi$
$509$	13.0172	−	17.9166i	0.576977	−	0.794141i	0.993360	+	0.115049i	$0.0367024\pi$
$510$		0			0
$511$	−5.27640	+	16.2391i	−0.233414	+	0.718375i
$512$		0			0
$513$	−5.12114	−	0.811108i	−0.226104	−	0.0358113i
$514$		0			0
$515$	10.1440	−	2.49610i	0.446999	−	0.109991i
$516$		0			0
$517$	19.5390	−	16.5658i	0.859323	−	0.728565i
$518$		0			0
$519$	11.7387	+	36.1280i	0.515272	+	1.58584i
$520$		0			0
$521$	8.59679	−	6.24594i	0.376632	−	0.273639i	−0.383323	−	0.923614i	$-0.625221\pi$
$521$	8.59679	−	6.24594i	0.376632	−	0.273639i	0.759956	+	0.649975i	$0.225221\pi$
$522$		0			0
$523$	−38.5151	+	19.6244i	−1.68415	+	0.858116i	−0.693694	+	0.720269i	$0.744018\pi$
$523$	−38.5151	+	19.6244i	−1.68415	+	0.858116i	−0.990454	+	0.137847i	$0.955982\pi$
$524$		0			0
$525$	12.9600	+	12.6702i	0.565619	+	0.552972i
$526$		0			0
$527$	−9.53941	+	9.53941i	−0.415543	+	0.415543i
$528$		0			0
$529$			2.96712i			0.129005i
$530$		0			0
$531$	10.2181	+	7.42391i	0.443429	+	0.322170i
$532$		0			0
$533$	1.33512	+	2.62032i	0.0578304	+	0.113499i
$534$		0			0
$535$	18.0423	+	29.0722i	0.780037	+	1.25690i
$536$		0			0
$537$	14.9117	−	29.2658i	0.643487	−	1.26291i
$538$		0			0
$539$	−2.84517	−	12.0430i	−0.122550	−	0.518728i
$540$		0			0
$541$	−20.0780	+	6.52373i	−0.863220	+	0.280477i	−0.706973	−	0.707241i	$-0.749940\pi$
$541$	−20.0780	+	6.52373i	−0.863220	+	0.280477i	−0.156247	+	0.987718i	$0.549940\pi$
$542$		0			0
$543$	−4.66168	+	29.4327i	−0.200052	+	1.26308i
$544$		0			0
$545$	15.5118	+	36.8582i	0.664454	+	1.57883i
$546$		0			0
$547$	1.37675	−	0.218056i	0.0588658	−	0.00932342i	−0.126932	−	0.991911i	$-0.540513\pi$
$547$	1.37675	−	0.218056i	0.0588658	−	0.00932342i	0.185798	+	0.982588i	$0.440513\pi$
$548$		0			0
$549$	−9.49230			−0.405121
$550$		0			0
$551$	−3.83469			−0.163363
$552$		0			0
$553$	−2.04490	+	0.323881i	−0.0869581	+	0.0137728i
$554$		0			0
$555$	5.58027	+	13.2595i	0.236869	+	0.562833i
$556$		0			0
$557$	0.599510	−	3.78516i	0.0254021	−	0.160382i	−0.971727	−	0.236109i	$-0.924128\pi$
$557$	0.599510	−	3.78516i	0.0254021	−	0.160382i	0.997129	+	0.0757269i	$0.0241277\pi$
$558$		0			0
$559$	−13.8180	+	4.48973i	−0.584438	+	0.189895i
$560$		0			0
$561$	−8.63507	+	20.6352i	−0.364573	+	0.871218i
$562$		0			0
$563$	1.10871	−	2.17596i	0.0467264	−	0.0917058i	−0.866463	−	0.499242i	$-0.833612\pi$
$563$	1.10871	−	2.17596i	0.0467264	−	0.0917058i	0.913189	+	0.407536i	$0.133612\pi$
$564$		0			0
$565$	−8.80736	−	14.1916i	−0.370529	−	0.597045i
$566$		0			0
$567$	−9.04483	−	17.7515i	−0.379847	−	0.745492i
$568$		0			0
$569$	5.21403	+	3.78822i	0.218584	+	0.158810i	0.691689	−	0.722196i	$-0.256867\pi$
$569$	5.21403	+	3.78822i	0.218584	+	0.158810i	−0.473105	+	0.881006i	$0.656867\pi$
$570$		0			0
$571$		−	13.2864i		−	0.556019i	−0.960578	−	0.278009i	$-0.910325\pi$
$571$		−	13.2864i		−	0.556019i	0.960578	−	0.278009i	$-0.0896747\pi$
$572$		0			0
$573$	2.70715	−	2.70715i	0.113093	−	0.113093i
$574$		0			0
$575$	0.253012	+	22.3776i	0.0105513	+	0.933211i
$576$		0			0
$577$	16.6874	−	8.50263i	0.694704	−	0.353969i	−0.0707197	−	0.997496i	$-0.522530\pi$
$577$	16.6874	−	8.50263i	0.694704	−	0.353969i	0.765423	+	0.643527i	$0.222530\pi$
$578$		0			0
$579$	−18.4630	+	13.4141i	−0.767295	+	0.557473i
$580$		0			0
$581$	5.84679	+	17.9946i	0.242566	+	0.746540i
$582$		0			0
$583$	−1.58105	−	21.0643i	−0.0654803	−	0.872395i
$584$		0			0
$585$	4.99391	−	1.22883i	0.206473	−	0.0508059i
$586$		0			0
$587$	8.32531	+	1.31860i	0.343622	+	0.0544244i	0.325861	−	0.945418i	$-0.394346\pi$
$587$	8.32531	+	1.31860i	0.343622	+	0.0544244i	0.0177617	+	0.999842i	$0.494346\pi$
$588$		0			0
$589$	1.61829	−	4.98059i	0.0666805	−	0.205221i
$590$		0			0
$591$	23.0140	−	31.6760i	0.946669	−	1.30298i
$592$		0			0
$593$	−4.37233	−	4.37233i	−0.179550	−	0.179550i	0.611610	−	0.791160i	$-0.290522\pi$
$593$	−4.37233	−	4.37233i	−0.179550	−	0.179550i	−0.791160	+	0.611610i	$0.790522\pi$
$594$		0			0
$595$	8.89103	+	10.2917i	0.364497	+	0.421918i
$596$		0			0
$597$	7.00996	+	44.2592i	0.286899	+	1.81141i
$598$		0			0
$599$	34.7989	+	11.3068i	1.42184	+	0.461985i	0.916187	−	0.400750i	$-0.131250\pi$
$599$	34.7989	+	11.3068i	1.42184	+	0.461985i	0.505656	+	0.862735i	$0.331250\pi$
$600$		0			0
$601$	6.33088	+	8.71371i	0.258242	+	0.355440i	0.918376	−	0.395708i	$-0.129501\pi$
$601$	6.33088	+	8.71371i	0.258242	+	0.355440i	−0.660134	+	0.751147i	$0.729501\pi$
$602$		0			0
$603$	3.16350	+	1.61188i	0.128828	+	0.0656410i
$604$		0			0
$605$	24.5178	+	1.96886i	0.996791	+	0.0800455i
$606$		0			0
$607$	−29.4880	−	15.0249i	−1.19688	−	0.609842i	−0.262092	−	0.965043i	$-0.584412\pi$
$607$	−29.4880	−	15.0249i	−1.19688	−	0.609842i	−0.934790	+	0.355201i	$0.884412\pi$
$608$		0			0
$609$	−6.25669	−	8.61159i	−0.253534	−	0.348959i
$610$		0			0
$611$	−16.5702	−	5.38398i	−0.670359	−	0.217813i
$612$		0			0
$613$	3.38501	+	21.3721i	0.136719	+	0.863213i	0.956754	+	0.290898i	$0.0939542\pi$
$613$	3.38501	+	21.3721i	0.136719	+	0.863213i	−0.820034	+	0.572314i	$0.806046\pi$
$614$		0			0
$615$	5.82899	+	0.425611i	0.235048	+	0.0171623i
$616$		0			0
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	0.0616431	−	0.998098i	$-0.480366\pi$
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	−0.998098	+	0.0616431i	$0.980366\pi$
$618$		0			0
$619$	24.3484	−	33.5126i	0.978643	−	1.34699i	0.0410856	−	0.999156i	$-0.486918\pi$
$619$	24.3484	−	33.5126i	0.978643	−	1.34699i	0.937557	−	0.347831i	$-0.113082\pi$
$620$		0			0
$621$	5.49164	−	16.9015i	0.220372	−	0.678235i
$622$		0			0
$623$	−6.88845	−	1.09102i	−0.275980	−	0.0437109i
$624$		0			0
$625$	−0.565252	−	24.9936i	−0.0226101	−	0.999744i
$626$		0			0
$627$	−0.649924	−	8.65895i	−0.0259555	−	0.345805i
$628$		0			0
$629$	3.33583	+	10.2666i	0.133008	+	0.409357i
$630$		0			0
$631$	−25.4513	+	18.4915i	−1.01320	+	0.736134i	−0.964878	−	0.262697i	$-0.915388\pi$
$631$	−25.4513	+	18.4915i	−1.01320	+	0.736134i	−0.0483238	+	0.998832i	$0.515388\pi$
$632$		0			0
$633$	−0.672644	+	0.342729i	−0.0267352	+	0.0136223i
$634$		0			0
$635$	0.297443	−	0.352274i	0.0118037	−	0.0139796i
$636$		0			0
$637$	−5.95137	+	5.95137i	−0.235802	+	0.235802i
$638$		0			0
$639$		−	6.90382i		−	0.273111i
$640$		0			0
$641$	−16.6022	−	12.0622i	−0.655749	−	0.476430i	0.209476	−	0.977814i	$-0.432824\pi$
$641$	−16.6022	−	12.0622i	−0.655749	−	0.476430i	−0.865225	+	0.501384i	$0.832824\pi$
$642$		0			0
$643$	8.00058	+	15.7020i	0.315512	+	0.619228i	0.993239	−	0.116086i	$-0.0370348\pi$
$643$	8.00058	+	15.7020i	0.315512	+	0.619228i	−0.677727	+	0.735314i	$0.737035\pi$
$644$		0			0
$645$	−6.58177	+	28.1143i	−0.259157	+	1.10700i
$646$		0			0
$647$	2.61567	−	5.13354i	0.102833	−	0.201820i	−0.833857	−	0.551980i	$-0.813873\pi$
$647$	2.61567	−	5.13354i	0.102833	−	0.201820i	0.936690	+	0.350159i	$0.113873\pi$
$648$		0			0
$649$	15.8602	−	37.9010i	0.622566	−	1.48774i
$650$		0			0
$651$	13.8253	−	4.49212i	0.541858	−	0.176060i
$652$		0			0
$653$	0.912669	−	5.76236i	0.0357155	−	0.225499i	−0.963374	−	0.268161i	$-0.913584\pi$
$653$	0.912669	−	5.76236i	0.0357155	−	0.225499i	0.999090	+	0.0426625i	$0.0135840\pi$
$654$		0			0
$655$	1.13706	−	0.478535i	0.0444287	−	0.0186979i
$656$		0			0
$657$	9.51025	−	1.50628i	0.371030	−	0.0587654i
$658$		0			0
$659$	−5.21347			−0.203088			−0.101544	−	0.994831i	$-0.532378\pi$
$659$	−5.21347			−0.203088			−0.101544	+	0.994831i	$0.532378\pi$
$660$		0			0
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$		0			0
$663$	15.0270	−	2.38004i	0.583599	−	0.0924330i
$664$		0			0
$665$	−4.88890	−	1.99275i	−0.189584	−	0.0772754i
$666$		0			0
$667$	2.05606	−	12.9815i	0.0796110	−	0.502644i
$668$		0			0
$669$	14.5093	−	4.71435i	0.560962	−	0.182267i
$670$		0			0
$671$	7.09949	+	30.0506i	0.274073	+	1.16009i
$672$		0			0
$673$	−0.253956	+	0.498417i	−0.00978930	+	0.0192126i	−0.895849	−	0.444358i	$-0.853432\pi$
$673$	−0.253956	+	0.498417i	−0.00978930	+	0.0192126i	0.886060	+	0.463570i	$0.153432\pi$
$674$		0			0
$675$	−5.92094	+	18.9491i	−0.227897	+	0.729352i
$676$		0			0
$677$	−13.2166	−	25.9390i	−0.507955	−	0.996918i	−0.992511	−	0.122157i	$-0.961019\pi$
$677$	−13.2166	−	25.9390i	−0.507955	−	0.996918i	0.484556	−	0.874760i	$-0.338981\pi$
$678$		0			0
$679$	1.13807	+	0.826858i	0.0436752	+	0.0317319i
$680$		0			0
$681$		−	16.4454i		−	0.630190i
$682$		0			0
$683$	−5.43554	+	5.43554i	−0.207985	+	0.207985i	−0.803411	−	0.595425i	$-0.796984\pi$
$683$	−5.43554	+	5.43554i	−0.207985	+	0.207985i	0.595425	+	0.803411i	$0.296984\pi$
$684$		0			0
$685$	26.4415	+	22.3259i	1.01028	+	0.853029i
$686$		0			0
$687$	13.5570	−	6.90765i	0.517233	−	0.263543i
$688$		0			0
$689$	−11.6233	+	8.44481i	−0.442812	+	0.321722i
$690$		0			0
$691$	2.91716	+	8.97809i	0.110974	+	0.341542i	0.991086	−	0.133223i	$-0.0425328\pi$
$691$	2.91716	+	8.97809i	0.110974	+	0.341542i	−0.880112	+	0.474766i	$0.842533\pi$
$692$		0			0
$693$	4.66342	−	3.95382i	0.177149	−	0.150193i
$694$		0			0
$695$	−2.72186	−	1.64687i	−0.103246	−	0.0624693i
$696$		0			0
$697$	4.33166	+	0.686067i	0.164073	+	0.0259866i
$698$		0			0
$699$	16.2427	−	49.9899i	0.614356	−	1.89079i
$700$		0			0
$701$	−11.5843	+	15.9445i	−0.437535	+	0.602215i	−0.969662	−	0.244449i	$-0.921393\pi$
$701$	−11.5843	+	15.9445i	−0.437535	+	0.602215i	0.532127	+	0.846664i	$0.321393\pi$
$702$		0			0
$703$	−2.96308	−	2.96308i	−0.111755	−	0.111755i
$704$		0			0
$705$	−26.2019	+	22.6360i	−0.986822	+	0.852520i
$706$		0			0
$707$	2.76266	+	17.4427i	0.103900	+	0.656001i
$708$		0			0
$709$	42.2836	+	13.7388i	1.58799	+	0.515970i	0.964100	−	0.265540i	$-0.0855503\pi$
$709$	42.2836	+	13.7388i	1.58799	+	0.515970i	0.623893	+	0.781510i	$0.285550\pi$
$710$		0			0
$711$	0.686259	+	0.944555i	0.0257367	+	0.0354236i
$712$		0			0
$713$	15.9929	+	8.14881i	0.598940	+	0.305175i
$714$		0			0
$715$	−7.62526	−	14.8906i	−0.285169	−	0.556876i
$716$		0			0
$717$	4.06580	+	2.07163i	0.151840	+	0.0773664i
$718$		0			0
$719$	−14.1002	−	19.4073i	−0.525850	−	0.723770i	0.460641	−	0.887587i	$-0.347620\pi$
$719$	−14.1002	−	19.4073i	−0.525850	−	0.723770i	−0.986491	+	0.163816i	$0.947620\pi$
$720$		0			0
$721$	−8.03342	−	2.61022i	−0.299180	−	0.0972095i
$722$		0			0
$723$	−1.97442	−	12.4660i	−0.0734296	−	0.463616i
$724$		0			0
$725$	−2.13276	+	14.5268i	−0.0792087	+	0.539513i
$726$		0			0
$727$	17.6187	+	17.6187i	0.653441	+	0.653441i	0.953820	−	0.300379i	$-0.0971131\pi$
$727$	17.6187	+	17.6187i	0.653441	+	0.653441i	−0.300379	+	0.953820i	$0.597113\pi$
$728$		0			0
$729$	7.43339	−	10.2312i	0.275311	−	0.378933i
$730$		0			0
$731$	−6.69547	+	20.6065i	−0.247641	+	0.762161i
$732$		0			0
$733$	0.0534353	+	0.00846331i	0.00197368	+	0.000312600i	0.157421	−	0.987532i	$-0.449682\pi$
$733$	0.0534353	+	0.00846331i	0.00197368	+	0.000312600i	−0.155448	+	0.987844i	$0.549682\pi$
$734$		0			0
$735$	3.99662	+	16.2421i	0.147418	+	0.599099i
$736$		0			0
$737$	2.73683	−	11.2205i	0.100813	−	0.413313i
$738$		0			0
$739$	−5.95011	−	18.3126i	−0.218878	−	0.673638i	−0.998855	−	0.0478303i	$-0.984769\pi$
$739$	−5.95011	−	18.3126i	−0.218878	−	0.673638i	0.779977	−	0.625808i	$-0.215231\pi$
$740$		0			0
$741$	−4.77800	+	3.47142i	−0.175524	+	0.127526i
$742$		0			0
$743$	6.63666	−	3.38155i	0.243475	−	0.124057i	−0.327995	−	0.944679i	$-0.606373\pi$
$743$	6.63666	−	3.38155i	0.243475	−	0.124057i	0.571471	+	0.820622i	$0.306373\pi$
$744$		0			0
$745$	−53.0411	+	4.47626i	−1.94327	+	0.163997i
$746$		0			0
$747$	7.54462	−	7.54462i	0.276043	−	0.276043i
$748$		0			0
$749$		−	27.6659i		−	1.01089i
$750$		0			0
$751$	−24.3907	−	17.7209i	−0.890031	−	0.646645i	0.0458552	−	0.998948i	$-0.485399\pi$
$751$	−24.3907	−	17.7209i	−0.890031	−	0.646645i	−0.935886	+	0.352303i	$0.885399\pi$
$752$		0			0
$753$	−24.2066	−	47.5082i	−0.882139	−	1.73130i
$754$		0			0
$755$	−31.3214	−	7.33259i	−1.13990	−	0.266860i
$756$		0			0
$757$	−20.2037	+	39.6521i	−0.734318	+	1.44118i	0.156905	+	0.987614i	$0.449848\pi$
$757$	−20.2037	+	39.6521i	−0.734318	+	1.44118i	−0.891223	+	0.453566i	$0.850152\pi$
$758$		0			0
$759$	29.6613	+	2.44254i	1.07664	+	0.0886584i
$760$		0			0
$761$	44.8060	−	14.5584i	1.62422	−	0.527740i	0.651285	−	0.758833i	$-0.274230\pi$
$761$	44.8060	−	14.5584i	1.62422	−	0.527740i	0.972932	+	0.231093i	$0.0742301\pi$
$762$		0			0
$763$	5.05818	−	31.9361i	0.183118	−	1.15616i
$764$		0			0
$765$	2.89489	−	7.10217i	0.104665	−	0.256779i
$766$		0			0
$767$	−27.6003	+	4.37145i	−0.996588	+	0.157844i
$768$		0			0
$769$	−29.7849			−1.07407			−0.537036	−	0.843559i	$-0.680456\pi$
$769$	−29.7849			−1.07407			−0.537036	+	0.843559i	$0.680456\pi$
$770$		0			0
$771$	−39.6451			−1.42778
$772$		0			0
$773$	−7.03566	+	1.11434i	−0.253055	+	0.0400800i	−0.281673	−	0.959510i	$-0.590889\pi$
$773$	−7.03566	+	1.11434i	−0.253055	+	0.0400800i	0.0286180	+	0.999590i	$0.490889\pi$
$774$		0			0
$775$	−17.9677	−	8.90059i	−0.645420	−	0.319719i
$776$		0			0
$777$	1.81965	−	11.4888i	0.0652794	−	0.412158i
$778$		0			0
$779$	−1.61912	+	0.526083i	−0.0580108	+	0.0188489i
$780$		0			0
$781$	−21.8560	+	5.16351i	−0.782070	+	0.184765i
$782$		0			0
$783$	5.29330	−	10.3887i	0.189167	−	0.371261i
$784$		0			0
$785$	25.6374	−	15.9106i	0.915037	−	0.567875i
$786$		0			0
$787$	13.1008	+	25.7117i	0.466992	+	0.916524i	0.997622	+	0.0689202i	$0.0219554\pi$
$787$	13.1008	+	25.7117i	0.466992	+	0.916524i	−0.530630	+	0.847604i	$0.678045\pi$
$788$		0			0
$789$	13.5737	+	9.86191i	0.483238	+	0.351093i
$790$		0			0
$791$			13.5051i			0.480187i
$792$		0			0
$793$	14.8503	−	14.8503i	0.527350	−	0.527350i
$794$		0			0
$795$	2.40109	+	28.4515i	0.0851578	+	1.00907i
$796$		0			0
$797$	−27.5666	+	14.0459i	−0.976460	+	0.497531i	−0.867997	−	0.496569i	$-0.834593\pi$
$797$	−27.5666	+	14.0459i	−0.976460	+	0.497531i	−0.108463	+	0.994100i	$0.534593\pi$
$798$		0			0
$799$	−21.0204	+	15.2722i	−0.743647	+	0.540291i
$800$		0			0
$801$	1.21535	+	3.74046i	0.0429423	+	0.132163i
$802$		0			0
$803$	−11.8815	−	28.9809i	−0.419288	−	1.02271i
$804$		0			0
$805$	9.36728	−	15.4818i	0.330153	−	0.545661i
$806$		0			0
$807$	−19.2291	−	3.04559i	−0.676897	−	0.107210i
$808$		0			0
$809$	−6.07857	+	18.7079i	−0.213711	+	0.657735i	0.785531	+	0.618822i	$0.212390\pi$
$809$	−6.07857	+	18.7079i	−0.213711	+	0.657735i	−0.999243	+	0.0389136i	$0.987610\pi$
$810$		0			0
$811$	−24.8398	+	34.1891i	−0.872243	+	1.20054i	0.106266	+	0.994338i	$0.466110\pi$
$811$	−24.8398	+	34.1891i	−0.872243	+	1.20054i	−0.978509	+	0.206202i	$0.933890\pi$
$812$		0			0
$813$	4.32597	+	4.32597i	0.151718	+	0.151718i
$814$		0			0
$815$	−0.174757	+	2.39340i	−0.00612147	+	0.0838373i
$816$		0			0
$817$	−1.31574	−	8.30723i	−0.0460318	−	0.290633i
$818$		0			0
$819$	−3.95486	−	1.28501i	−0.138194	−	0.0449019i
$820$		0			0
$821$	−31.2544	−	43.0180i	−1.09079	−	1.50134i	−0.847061	−	0.531496i	$-0.821630\pi$
$821$	−31.2544	−	43.0180i	−1.09079	−	1.50134i	−0.243726	−	0.969844i	$-0.578370\pi$
$822$		0			0
$823$	1.24781	+	0.635792i	0.0434960	+	0.0221623i	0.475603	−	0.879660i	$-0.342230\pi$
$823$	1.24781	+	0.635792i	0.0434960	+	0.0221623i	−0.432107	+	0.901822i	$0.642230\pi$
$824$		0			0
$825$	−33.1639	−	2.35380i	−1.15462	−	0.0819489i
$826$		0			0
$827$	15.4022	+	7.84783i	0.535588	+	0.272896i	0.700794	−	0.713363i	$-0.252829\pi$
$827$	15.4022	+	7.84783i	0.535588	+	0.272896i	−0.165206	+	0.986259i	$0.552829\pi$
$828$		0			0
$829$	−21.0969	−	29.0374i	−0.732727	−	1.00851i	−0.999004	−	0.0446158i	$-0.985794\pi$
$829$	−21.0969	−	29.0374i	−0.732727	−	1.00851i	0.266277	−	0.963897i	$-0.414206\pi$
$830$		0			0
$831$	4.53838	+	1.47461i	0.157435	+	0.0511536i
$832$		0			0
$833$	1.96348	+	12.3969i	0.0680304	+	0.429527i
$834$		0			0
$835$	0.308058	−	4.21903i	0.0106608	−	0.146006i
$836$		0			0
$837$	11.2592	+	11.2592i	0.389176	+	0.389176i
$838$		0			0
$839$	2.91587	−	4.01335i	0.100667	−	0.138556i	−0.755712	−	0.654904i	$-0.772709\pi$
$839$	2.91587	−	4.01335i	0.100667	−	0.138556i	0.856379	+	0.516348i	$0.172709\pi$
$840$		0			0
$841$	−6.29681	+	19.3796i	−0.217131	+	0.668261i
$842$		0			0
$843$	−55.9053	−	8.85453i	−1.92548	−	0.304966i
$844$		0			0
$845$	9.15778	−	15.1355i	0.315037	−	0.520678i
$846$		0			0
$847$	−16.0048	−	11.8063i	−0.549932	−	0.405668i
$848$		0			0
$849$	−10.5406	−	32.4406i	−0.361752	−	1.11336i
$850$		0			0
$851$	11.6196	−	8.44211i	0.398313	−	0.289392i
$852$		0			0
$853$	−23.6804	+	12.0658i	−0.810803	+	0.413125i	−0.809678	−	0.586875i	$-0.800358\pi$
$853$	−23.6804	+	12.0658i	−0.810803	+	0.413125i	−0.00112492	+	0.999999i	$0.500358\pi$
$854$		0			0
$855$	0.250361	+	2.96663i	0.00856216	+	0.101457i
$856$		0			0
$857$	1.04396	−	1.04396i	0.0356609	−	0.0356609i	−0.689051	−	0.724712i	$-0.741973\pi$
$857$	1.04396	−	1.04396i	0.0356609	−	0.0356609i	0.724712	+	0.689051i	$0.241973\pi$
$858$		0			0
$859$		−	13.9402i		−	0.475633i	−0.971310	−	0.237816i	$-0.923568\pi$
$859$		−	13.9402i		−	0.475633i	0.971310	−	0.237816i	$-0.0764316\pi$
$860$		0			0
$861$	−3.82318	−	2.77770i	−0.130294	−	0.0946638i
$862$		0			0
$863$	−23.2938	−	45.7166i	−0.792929	−	1.55621i	−0.830567	−	0.556919i	$-0.811983\pi$
$863$	−23.2938	−	45.7166i	−0.792929	−	1.55621i	0.0376382	−	0.999291i	$-0.488017\pi$
$864$		0			0
$865$	−35.9985	+	22.3408i	−1.22399	+	0.759610i
$866$		0			0
$867$	−5.17288	+	10.1524i	−0.175680	+	0.344792i
$868$		0			0
$869$	2.47699	−	2.87900i	0.0840262	−	0.0976635i
$870$		0			0
$871$	−7.47089	+	2.42744i	−0.253141	+	0.0822507i
$872$		0			0
$873$	0.124097	−	0.783518i	0.00420005	−	0.0265181i
$874$		0			0
$875$	−10.2681	+	17.4122i	−0.347126	+	0.588638i
$876$		0			0
$877$	−6.59105	+	1.04392i	−0.222564	+	0.0352507i	−0.266720	−	0.963774i	$-0.585940\pi$
$877$	−6.59105	+	1.04392i	−0.222564	+	0.0352507i	0.0441563	+	0.999025i	$0.485940\pi$
$878$		0			0
$879$	−21.4220			−0.722546
$880$		0			0
$881$	−14.4573			−0.487080			−0.243540	−	0.969891i	$-0.578309\pi$
$881$	−14.4573			−0.487080			−0.243540	+	0.969891i	$0.578309\pi$
$882$		0			0
$883$	10.3324	−	1.63650i	0.347714	−	0.0550725i	0.0198651	−	0.999803i	$-0.493676\pi$
$883$	10.3324	−	1.63650i	0.347714	−	0.0550725i	0.327849	+	0.944730i	$0.393676\pi$
$884$		0			0
$885$	−20.9620	+	51.4272i	−0.704631	+	1.72871i
$886$		0			0
$887$	1.54605	−	9.76140i	0.0519114	−	0.327756i	−0.948042	−	0.318144i	$-0.896940\pi$
$887$	1.54605	−	9.76140i	0.0519114	−	0.327756i	0.999954	−	0.00961170i	$-0.00305955\pi$
$888$		0			0
$889$	−0.354548	+	0.115200i	−0.0118912	+	0.00386368i
$890$		0			0
$891$	33.7137	+	14.1080i	1.12945	+	0.472635i
$892$		0			0
$893$	4.57896	−	8.98671i	0.153229	−	0.300729i
$894$		0			0
$895$	35.6688	+	8.35035i	1.19228	+	0.279121i
$896$		0			0
$897$	−9.18986	−	18.0361i	−0.306840	−	0.602208i
$898$		0			0
$899$	9.52719	+	6.92191i	0.317750	+	0.230859i
$900$		0			0
$901$			21.4256i			0.713789i
$902$		0			0
$903$	16.5088	−	16.5088i	0.549380	−	0.549380i
$904$		0			0
$905$	−33.1180	+	2.79490i	−1.10088	+	0.0929057i
$906$		0			0
$907$	10.3100	−	5.25319i	0.342337	−	0.174429i	−0.274366	−	0.961625i	$-0.588468\pi$
$907$	10.3100	−	5.25319i	0.342337	−	0.174429i	0.616703	+	0.787196i	$0.288468\pi$
$908$		0			0
$909$	8.05692	−	5.85370i	0.267231	−	0.194155i
$910$		0			0
$911$	2.69510	+	8.29465i	0.0892925	+	0.274814i	0.985724	−	0.168368i	$-0.0538496\pi$
$911$	2.69510	+	8.29465i	0.0892925	+	0.274814i	−0.896432	+	0.443182i	$0.853850\pi$
$912$		0			0
$913$	−29.5274	−	18.2419i	−0.977215	−	0.603718i
$914$		0			0
$915$	−9.97268	−	40.5285i	−0.329687	−	1.33983i
$916$		0			0
$917$	−0.985219	−	0.156043i	−0.0325348	−	0.00515301i
$918$		0			0
$919$	1.78507	−	5.49388i	0.0588840	−	0.181226i	−0.917288	−	0.398224i	$-0.869627\pi$
$919$	1.78507	−	5.49388i	0.0588840	−	0.181226i	0.976172	+	0.216998i	$0.0696265\pi$
$920$		0			0
$921$	38.3182	−	52.7405i	1.26263	−	1.73786i
$922$		0			0
$923$	10.8007	+	10.8007i	0.355511	+	0.355511i
$924$		0			0
$925$	−12.8729	+	9.57696i	−0.423260	+	0.314889i
$926$		0			0
$927$	0.745150	+	4.70469i	0.0244739	+	0.154522i
$928$		0			0
$929$	17.2514	+	5.60532i	0.566000	+	0.183905i	0.578019	−	0.816023i	$-0.303826\pi$
$929$	17.2514	+	5.60532i	0.566000	+	0.183905i	−0.0120191	+	0.999928i	$0.503826\pi$
$930$		0			0
$931$	−2.86384	−	3.94174i	−0.0938587	−	0.129185i
$932$		0			0
$933$	−24.8102	−	12.6414i	−0.812251	−	0.413862i
$934$		0			0
$935$	−24.6491	−	3.85274i	−0.806112	−	0.125998i
$936$		0			0
$937$	−28.6359	−	14.5907i	−0.935496	−	0.476659i	−0.0813459	−	0.996686i	$-0.525922\pi$
$937$	−28.6359	−	14.5907i	−0.935496	−	0.476659i	−0.854150	+	0.520027i	$0.825922\pi$
$938$		0			0
$939$	−20.4908	−	28.2032i	−0.668692	−	0.920376i
$940$		0			0
$941$	−4.95612	−	1.61034i	−0.161565	−	0.0524956i	0.227118	−	0.973867i	$-0.427070\pi$
$941$	−4.95612	−	1.61034i	−0.161565	−	0.0524956i	−0.388683	+	0.921372i	$0.627070\pi$
$942$		0			0
$943$	−0.912803	−	5.76321i	−0.0297250	−	0.187676i
$944$		0			0
$945$	12.1471	−	10.4940i	0.395146	−	0.341368i
$946$		0			0
$947$	0.545091	+	0.545091i	0.0177131	+	0.0177131i	0.715908	−	0.698195i	$-0.246013\pi$
$947$	0.545091	+	0.545091i	0.0177131	+	0.0177131i	−0.698195	+	0.715908i	$0.746013\pi$
$948$		0			0
$949$	−12.5219	+	17.2349i	−0.406478	+	0.559469i
$950$		0			0
$951$	10.0100	−	30.8076i	0.324596	−	0.999004i
$952$		0			0
$953$	−13.4139	−	2.12456i	−0.434519	−	0.0688211i	−0.0646568	−	0.997908i	$-0.520595\pi$
$953$	−13.4139	−	2.12456i	−0.434519	−	0.0688211i	−0.369863	+	0.929086i	$0.620595\pi$
$954$		0			0
$955$	3.65328	+	2.21042i	0.118217	+	0.0715277i
$956$		0			0
$957$	18.9701	+	4.62705i	0.613216	+	0.149571i
$958$		0			0
$959$	−8.64682	−	26.6122i	−0.279221	−	0.859352i
$960$		0			0
$961$	12.0686	−	8.76834i	0.389309	−	0.282850i
$962$		0			0
$963$	−13.9009	+	7.08285i	−0.447950	+	0.228242i
$964$		0			0
$965$	−19.4477	−	16.4207i	−0.626045	−	0.528602i
$966$		0			0
$967$	28.7882	−	28.7882i	0.925767	−	0.925767i	−0.0716619	−	0.997429i	$-0.522830\pi$
$967$	28.7882	−	28.7882i	0.925767	−	0.925767i	0.997429	+	0.0716619i	$0.0228303\pi$
$968$		0			0
$969$			8.80745i			0.282936i
$970$		0			0
$971$	−23.7651	−	17.2663i	−0.762657	−	0.554103i	0.137067	−	0.990562i	$-0.456232\pi$
$971$	−23.7651	−	17.2663i	−0.762657	−	0.554103i	−0.899724	+	0.436459i	$0.856232\pi$
$972$		0			0
$973$	1.16781	+	2.29195i	0.0374382	+	0.0734765i
$974$		0			0
$975$	10.4933	+	20.0311i	0.336054	+	0.641508i
$976$		0			0
$977$	10.6212	−	20.8453i	0.339803	−	0.666901i	−0.656357	−	0.754450i	$-0.727904\pi$
$977$	10.6212	−	20.8453i	0.339803	−	0.666901i	0.996160	+	0.0875496i	$0.0279036\pi$
$978$		0			0
$979$	10.9325	−	6.64511i	0.349405	−	0.212379i
$980$		0			0
$981$	−17.3414	+	5.63458i	−0.553670	+	0.179898i
$982$		0			0
$983$	3.26285	−	20.6008i	0.104069	−	0.657064i	−0.879413	−	0.476059i	$-0.842065\pi$
$983$	3.26285	−	20.6008i	0.104069	−	0.657064i	0.983482	−	0.181005i	$-0.0579351\pi$
$984$		0			0
$985$	40.4382	+	16.4829i	1.28847	+	0.525188i
$986$		0			0
$987$	27.6526	−	4.37973i	0.880190	−	0.139408i
$988$		0			0
$989$	28.8277			0.916666
$990$		0			0
$991$	6.50787			0.206729			0.103365	−	0.994644i	$-0.467039\pi$
$991$	6.50787			0.206729			0.103365	+	0.994644i	$0.467039\pi$
$992$		0			0
$993$	29.0768	−	4.60531i	0.922724	−	0.146145i
$994$		0			0
$995$	−46.0647	+	19.3864i	−1.46035	+	0.614591i
$996$		0			0
$997$	−4.13075	+	26.0805i	−0.130822	+	0.825978i	0.831789	+	0.555092i	$0.187317\pi$
$997$	−4.13075	+	26.0805i	−0.130822	+	0.825978i	−0.962611	+	0.270886i	$0.912683\pi$
$998$		0			0
$999$	12.1175	−	3.93723i	0.383382	−	0.124568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cm.a.17.1		32
4.3	odd	2		55.2.l.a.17.1	yes	32
5.3	odd	4	inner	880.2.cm.a.193.1		32
11.2	odd	10	inner	880.2.cm.a.497.1		32
12.11	even	2		495.2.bj.a.127.4		32
20.3	even	4		55.2.l.a.28.1	yes	32
20.7	even	4		275.2.bm.b.193.4		32
20.19	odd	2		275.2.bm.b.182.4		32
44.3	odd	10		605.2.e.b.362.1		32
44.7	even	10		605.2.m.c.602.1		32
44.15	odd	10		605.2.m.d.602.4		32
44.19	even	10		605.2.e.b.362.16		32
44.27	odd	10		605.2.m.c.282.4		32
44.31	odd	10		605.2.m.e.112.4		32
44.35	even	10		55.2.l.a.2.1	✓	32
44.39	even	10		605.2.m.d.282.1		32
44.43	even	2		605.2.m.e.457.4		32
55.13	even	20	inner	880.2.cm.a.673.1		32
60.23	odd	4		495.2.bj.a.28.4		32
132.35	odd	10		495.2.bj.a.442.4		32
220.3	even	20		605.2.e.b.483.16		32
220.43	odd	4		605.2.m.e.578.4		32
220.63	odd	20		605.2.e.b.483.1		32
220.79	even	10		275.2.bm.b.57.4		32
220.83	odd	20		605.2.m.d.403.4		32
220.103	even	20		605.2.m.d.118.1		32
220.123	odd	20		55.2.l.a.13.1	yes	32
220.163	even	20		605.2.m.e.233.4		32
220.167	odd	20		275.2.bm.b.68.4		32
220.183	odd	20		605.2.m.c.118.4		32
220.203	even	20		605.2.m.c.403.1		32
660.563	even	20		495.2.bj.a.343.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	44.35	even	10
55.2.l.a.13.1	yes	32	220.123	odd	20
55.2.l.a.17.1	yes	32	4.3	odd	2
55.2.l.a.28.1	yes	32	20.3	even	4
275.2.bm.b.57.4		32	220.79	even	10
275.2.bm.b.68.4		32	220.167	odd	20
275.2.bm.b.182.4		32	20.19	odd	2
275.2.bm.b.193.4		32	20.7	even	4
495.2.bj.a.28.4		32	60.23	odd	4
495.2.bj.a.127.4		32	12.11	even	2
495.2.bj.a.343.4		32	660.563	even	20
495.2.bj.a.442.4		32	132.35	odd	10
605.2.e.b.362.1		32	44.3	odd	10
605.2.e.b.362.16		32	44.19	even	10
605.2.e.b.483.1		32	220.63	odd	20
605.2.e.b.483.16		32	220.3	even	20
605.2.m.c.118.4		32	220.183	odd	20
605.2.m.c.282.4		32	44.27	odd	10
605.2.m.c.403.1		32	220.203	even	20
605.2.m.c.602.1		32	44.7	even	10
605.2.m.d.118.1		32	220.103	even	20
605.2.m.d.282.1		32	44.39	even	10
605.2.m.d.403.4		32	220.83	odd	20
605.2.m.d.602.4		32	44.15	odd	10
605.2.m.e.112.4		32	44.31	odd	10
605.2.m.e.233.4		32	220.163	even	20
605.2.m.e.457.4		32	44.43	even	2
605.2.m.e.578.4		32	220.43	odd	4
880.2.cm.a.17.1		32	1.1	even	1	trivial
880.2.cm.a.193.1		32	5.3	odd	4	inner
880.2.cm.a.497.1		32	11.2	odd	10	inner
880.2.cm.a.673.1		32	55.13	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.98021 + 0.313634i) q^{3} +(-0.867371 - 2.06099i) q^{5} +(-0.282837 + 1.78576i) q^{7} +(0.969677 - 0.315067i) q^{9} +O(q^{10})\)	\(q+(-1.98021 + 0.313634i) q^{3} +(-0.867371 - 2.06099i) q^{5} +(-0.282837 + 1.78576i) q^{7} +(0.969677 - 0.315067i) q^{9} +(-1.72268 - 2.83415i) q^{11} +(-1.02411 + 2.00993i) q^{13} +(2.36397 + 3.80914i) q^{15} +(1.52724 + 2.99738i) q^{17} +(-1.05647 - 0.767569i) q^{19} -3.62488i q^{21} +(3.16488 - 3.16488i) q^{23} +(-3.49534 + 3.57528i) q^{25} +(3.53776 - 1.80258i) q^{27} +(2.37569 - 1.72604i) q^{29} +(1.23925 + 3.81401i) q^{31} +(4.30014 + 5.07190i) q^{33} +(3.92576 - 0.965994i) q^{35} +(3.16942 + 0.501987i) q^{37} +(1.39757 - 4.30127i) q^{39} +(0.766287 - 1.05470i) q^{41} +(4.55431 + 4.55431i) q^{43} +(-1.49042 - 1.72521i) q^{45} +(1.20824 + 7.62854i) q^{47} +(3.54845 + 1.15296i) q^{49} +(-3.96433 - 5.45644i) q^{51} +(5.67482 + 2.89146i) q^{53} +(-4.34694 + 6.00867i) q^{55} +(2.33276 + 1.18860i) q^{57} +(7.28135 + 10.0219i) q^{59} +(-8.85435 - 2.87695i) q^{61} +(0.288374 + 1.82072i) q^{63} +(5.03072 + 0.367324i) q^{65} +(2.46236 + 2.46236i) q^{67} +(-5.27449 + 7.25972i) q^{69} +(2.09243 - 6.43984i) q^{71} +(9.32763 + 1.47735i) q^{73} +(5.80015 - 8.17604i) q^{75} +(5.54835 - 2.27469i) q^{77} +(0.353860 + 1.08907i) q^{79} +(-8.91472 + 6.47692i) q^{81} +(9.32422 - 4.75092i) q^{83} +(4.85288 - 5.74747i) q^{85} +(-4.16301 + 4.16301i) q^{87} +3.85743i q^{89} +(-3.29960 - 2.39730i) q^{91} +(-3.65016 - 7.16385i) q^{93} +(-0.665600 + 2.84313i) q^{95} +(0.353228 - 0.693249i) q^{97} +(-2.56339 - 2.20545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 2 q^{5}+O(q^{10}) \) 32 * q + 4 * q^3 - 2 * q^5	\( 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53} + 64 q^{55} + 30 q^{57} - 60 q^{61} + 30 q^{63} + 8 q^{67} - 24 q^{71} + 50 q^{73} - 34 q^{75} + 70 q^{77} - 12 q^{81} - 90 q^{83} + 30 q^{85} - 20 q^{91} - 8 q^{93} + 40 q^{95} - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

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