LMFDB - Embedded newform 880.2.cd.c.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(49,880)]

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, 5, 4]))

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

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

chi := DirichletCharacter("880.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cd (of order $10$, 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 $\Q(\zeta_{10})$
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} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.4
Root			$0.972539 - 1.33858i$ of defining polynomial
Character	$\chi$	$=$	880.49
Dual form			880.2.cd.c.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16075 - 1.59764i) q^{3} +(0.264988 - 2.22031i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-0.278050 - 0.855749i) q^{9} +O(q^{10})$	\(q+(1.16075 - 1.59764i) q^{3} +(0.264988 - 2.22031i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-0.278050 - 0.855749i) q^{9} +(3.27115 - 0.547326i) q^{11} +(3.51868 - 1.14329i) q^{13} +(-3.23967 - 3.00058i) q^{15} +(2.11573 + 0.687441i) q^{17} +(-4.27714 - 3.10753i) q^{19} +4.42960 q^{21} +3.85415i q^{23} +(-4.85956 - 1.17671i) q^{25} +(3.94448 + 1.28164i) q^{27} +(0.152450 - 0.110762i) q^{29} +(-0.212253 - 0.653249i) q^{31} +(2.92256 - 5.86142i) q^{33} +(4.37854 - 2.44649i) q^{35} +(1.52422 + 2.09791i) q^{37} +(2.25775 - 6.94864i) q^{39} +(-6.40421 - 4.65293i) q^{41} -8.41368i q^{43} +(-1.97371 + 0.390594i) q^{45} +(-7.06117 + 9.71886i) q^{47} +(0.608337 - 1.87227i) q^{49} +(3.55411 - 2.58222i) q^{51} +(-12.0371 + 3.91110i) q^{53} +(-0.348420 - 7.40801i) q^{55} +(-9.92940 + 3.22626i) q^{57} +(0.278050 - 0.202015i) q^{59} +(0.535643 - 1.64854i) q^{61} +(1.18632 - 1.63283i) q^{63} +(-1.60605 - 8.11552i) q^{65} +0.650461i q^{67} +(6.15754 + 4.47371i) q^{69} +(-1.43619 + 4.42013i) q^{71} +(5.20684 + 7.16660i) q^{73} +(-7.52070 + 6.39795i) q^{75} +(5.30606 + 5.21449i) q^{77} +(-2.23551 - 6.88019i) q^{79} +(8.80999 - 6.40083i) q^{81} +(-3.02593 - 0.983185i) q^{83} +(2.08698 - 4.51541i) q^{85} -0.372127i q^{87} -9.92195 q^{89} +(6.71389 + 4.87793i) q^{91} +(-1.29003 - 0.419156i) q^{93} +(-8.03307 + 8.67314i) q^{95} +(2.15710 - 0.700884i) q^{97} +(-1.37792 - 2.64710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{5} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^5 + 2 * q^9	$ 16 q - 2 q^{5} + 2 q^{9} + 6 q^{11} + 16 q^{15} - 6 q^{19} + 8 q^{21} - 16 q^{25} + 2 q^{29} - 8 q^{31} - 22 q^{35} - 30 q^{39} - 52 q^{41} + 12 q^{45} - 10 q^{49} + 42 q^{51} + 8 q^{55} - 2 q^{59} - 40 q^{61} - 40 q^{65} + 26 q^{69} - 36 q^{71} + 20 q^{75} - 38 q^{79} + 68 q^{81} + 58 q^{85} + 24 q^{89} + 20 q^{91} - 48 q^{95} + 72 q^{99}+O(q^{100}) $ 16 * q - 2 * q^5 + 2 * q^9 + 6 * q^11 + 16 * q^15 - 6 * q^19 + 8 * q^21 - 16 * q^25 + 2 * q^29 - 8 * q^31 - 22 * q^35 - 30 * q^39 - 52 * q^41 + 12 * q^45 - 10 * q^49 + 42 * q^51 + 8 * q^55 - 2 * q^59 - 40 * q^61 - 40 * q^65 + 26 * q^69 - 36 * q^71 + 20 * q^75 - 38 * q^79 + 68 * q^81 + 58 * q^85 + 24 * q^89 + 20 * q^91 - 48 * q^95 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	1.16075	−	1.59764i	0.670160	−	0.922396i	−0.329604	−	0.944119i	$-0.606915\pi$
$3$	1.16075	−	1.59764i	0.670160	−	0.922396i	0.999764	+	0.0217231i	$0.00691523\pi$
$4$		0			0
$5$	0.264988	−	2.22031i	0.118506	−	0.992953i
$5$	0.264988	−	2.22031i	0.118506	−	0.992953i
$6$		0			0
$7$	1.31845	+	1.81468i	0.498326	+	0.685886i	0.981896	−	0.189419i	$-0.0606604\pi$
$7$	1.31845	+	1.81468i	0.498326	+	0.685886i	−0.483571	+	0.875305i	$0.660660\pi$
$8$		0			0
$9$	−0.278050	−	0.855749i	−0.0926832	−	0.285250i
$10$		0			0
$11$	3.27115	−	0.547326i	0.986289	−	0.165025i
$11$	3.27115	−	0.547326i	0.986289	−	0.165025i
$12$		0			0
$13$	3.51868	−	1.14329i	0.975906	−	0.317091i	0.222708	−	0.974885i	$-0.428510\pi$
$13$	3.51868	−	1.14329i	0.975906	−	0.317091i	0.753198	+	0.657794i	$0.228510\pi$
$14$		0			0
$15$	−3.23967	−	3.00058i	−0.836478	−	0.774747i
$16$		0			0
$17$	2.11573	+	0.687441i	0.513139	+	0.166729i	0.554129	−	0.832431i	$-0.313051\pi$
$17$	2.11573	+	0.687441i	0.513139	+	0.166729i	−0.0409903	+	0.999160i	$0.513051\pi$
$18$		0			0
$19$	−4.27714	−	3.10753i	−0.981244	−	0.712916i	−0.0232580	−	0.999729i	$-0.507404\pi$
$19$	−4.27714	−	3.10753i	−0.981244	−	0.712916i	−0.957986	+	0.286814i	$0.907404\pi$
$20$		0			0
$21$	4.42960			0.966617
$22$		0			0
$23$			3.85415i			0.803647i	0.915717	+	0.401823i	$0.131623\pi$
$23$			3.85415i			0.803647i	−0.915717	+	0.401823i	$0.868377\pi$
$24$		0			0
$25$	−4.85956	−	1.17671i	−0.971913	−	0.235342i
$26$		0			0
$27$	3.94448	+	1.28164i	0.759116	+	0.246652i
$28$		0			0
$29$	0.152450	−	0.110762i	0.0283093	−	0.0205679i	−0.573541	−	0.819177i	$-0.694431\pi$
$29$	0.152450	−	0.110762i	0.0283093	−	0.0205679i	0.601850	+	0.798609i	$0.294431\pi$
$30$		0			0
$31$	−0.212253	−	0.653249i	−0.0381218	−	0.117327i	0.930185	−	0.367092i	$-0.119647\pi$
$31$	−0.212253	−	0.653249i	−0.0381218	−	0.117327i	−0.968306	+	0.249765i	$0.919647\pi$
$32$		0			0
$33$	2.92256	−	5.86142i	0.508753	−	1.02034i
$34$		0			0
$35$	4.37854	−	2.44649i	0.740108	−	0.413532i
$36$		0			0
$37$	1.52422	+	2.09791i	0.250580	+	0.344894i	0.915714	−	0.401830i	$-0.131626\pi$
$37$	1.52422	+	2.09791i	0.250580	+	0.344894i	−0.665134	+	0.746724i	$0.731626\pi$
$38$		0			0
$39$	2.25775	−	6.94864i	0.361529	−	1.11267i
$40$		0			0
$41$	−6.40421	−	4.65293i	−1.00017	−	0.726666i	−0.0380448	−	0.999276i	$-0.512113\pi$
$41$	−6.40421	−	4.65293i	−1.00017	−	0.726666i	−0.962124	+	0.272611i	$0.912113\pi$
$42$		0			0
$43$		−	8.41368i		−	1.28307i	−0.767092	−	0.641537i	$-0.778297\pi$
$43$		−	8.41368i		−	1.28307i	0.767092	−	0.641537i	$-0.221703\pi$
$44$		0			0
$45$	−1.97371	+	0.390594i	−0.294223	+	0.0582263i
$46$		0			0
$47$	−7.06117	+	9.71886i	−1.02998	+	1.41764i	−0.125012	+	0.992155i	$0.539897\pi$
$47$	−7.06117	+	9.71886i	−1.02998	+	1.41764i	−0.904965	+	0.425486i	$0.860103\pi$
$48$		0			0
$49$	0.608337	−	1.87227i	0.0869053	−	0.267467i
$50$		0			0
$51$	3.55411	−	2.58222i	0.497676	−	0.361582i
$52$		0			0
$53$	−12.0371	+	3.91110i	−1.65343	+	0.537231i	−0.979479	−	0.201549i	$-0.935403\pi$
$53$	−12.0371	+	3.91110i	−1.65343	+	0.537231i	−0.673947	+	0.738779i	$0.735403\pi$
$54$		0			0
$55$	−0.348420	−	7.40801i	−0.0469809	−	0.998896i
$56$		0			0
$57$	−9.92940	+	3.22626i	−1.31518	+	0.427328i
$58$		0			0
$59$	0.278050	−	0.202015i	0.0361990	−	0.0263001i	−0.569539	−	0.821965i	$-0.692878\pi$
$59$	0.278050	−	0.202015i	0.0361990	−	0.0263001i	0.605738	+	0.795664i	$0.292878\pi$
$60$		0			0
$61$	0.535643	−	1.64854i	0.0685821	−	0.211074i	−0.910892	−	0.412645i	$-0.864605\pi$
$61$	0.535643	−	1.64854i	0.0685821	−	0.211074i	0.979474	+	0.201572i	$0.0646049\pi$
$62$		0			0
$63$	1.18632	−	1.63283i	0.149462	−	0.205717i
$64$		0			0
$65$	−1.60605	−	8.11552i	−0.199206	−	1.00661i
$66$		0			0
$67$			0.650461i			0.0794664i	0.999210	+	0.0397332i	$0.0126508\pi$
$67$			0.650461i			0.0794664i	−0.999210	+	0.0397332i	$0.987349\pi$
$68$		0			0
$69$	6.15754	+	4.47371i	0.741281	+	0.538572i
$70$		0			0
$71$	−1.43619	+	4.42013i	−0.170444	+	0.524573i	−0.999396	−	0.0347464i	$-0.988938\pi$
$71$	−1.43619	+	4.42013i	−0.170444	+	0.524573i	0.828952	+	0.559320i	$0.188938\pi$
$72$		0			0
$73$	5.20684	+	7.16660i	0.609415	+	0.838787i	0.996529	−	0.0832444i	$-0.0265282\pi$
$73$	5.20684	+	7.16660i	0.609415	+	0.838787i	−0.387115	+	0.922032i	$0.626528\pi$
$74$		0			0
$75$	−7.52070	+	6.39795i	−0.868416	+	0.738772i
$76$		0			0
$77$	5.30606	+	5.21449i	0.604682	+	0.594246i
$78$		0			0
$79$	−2.23551	−	6.88019i	−0.251514	−	0.774082i	−0.994496	−	0.104770i	$-0.966589\pi$
$79$	−2.23551	−	6.88019i	−0.251514	−	0.774082i	0.742982	−	0.669311i	$-0.233411\pi$
$80$		0			0
$81$	8.80999	−	6.40083i	0.978888	−	0.711203i
$82$		0			0
$83$	−3.02593	−	0.983185i	−0.332139	−	0.107919i	0.138200	−	0.990404i	$-0.455868\pi$
$83$	−3.02593	−	0.983185i	−0.332139	−	0.107919i	−0.470339	+	0.882486i	$0.655868\pi$
$84$		0			0
$85$	2.08698	−	4.51541i	0.226364	−	0.489765i
$86$		0			0
$87$		−	0.372127i		−	0.0398962i
$88$		0			0
$89$	−9.92195			−1.05172			−0.525862	−	0.850570i	$-0.676257\pi$
$89$	−9.92195			−1.05172			−0.525862	+	0.850570i	$0.676257\pi$
$90$		0			0
$91$	6.71389	+	4.87793i	0.703807	+	0.511346i
$92$		0			0
$93$	−1.29003	−	0.419156i	−0.133770	−	0.0434644i
$94$		0			0
$95$	−8.03307	+	8.67314i	−0.824175	+	0.889845i
$96$		0			0
$97$	2.15710	−	0.700884i	0.219020	−	0.0711640i	−0.197451	−	0.980313i	$-0.563266\pi$
$97$	2.15710	−	0.700884i	0.219020	−	0.0711640i	0.416472	+	0.909149i	$0.363266\pi$
$98$		0			0
$99$	−1.37792	−	2.64710i	−0.138486	−	0.266044i
$100$		0			0
$101$	3.05830	+	9.41247i	0.304312	+	0.936576i	0.979933	+	0.199327i	$0.0638756\pi$
$101$	3.05830	+	9.41247i	0.304312	+	0.936576i	−0.675621	+	0.737249i	$0.736124\pi$
$102$		0			0
$103$	6.01958	+	8.28525i	0.593127	+	0.816370i	0.995057	−	0.0993007i	$-0.0316606\pi$
$103$	6.01958	+	8.28525i	0.593127	+	0.816370i	−0.401930	+	0.915670i	$0.631661\pi$
$104$		0			0
$105$	1.17379	−	9.83508i	0.114550	−	0.959805i
$106$		0			0
$107$	5.90536	−	8.12803i	0.570893	−	0.785767i	−0.421767	−	0.906704i	$-0.638590\pi$
$107$	5.90536	−	8.12803i	0.570893	−	0.785767i	0.992660	+	0.120937i	$0.0385900\pi$
$108$		0			0
$109$	8.80173			0.843053			0.421527	−	0.906816i	$-0.361494\pi$
$109$	8.80173			0.843053			0.421527	+	0.906816i	$0.361494\pi$
$110$		0			0
$111$	5.12094			0.486058
$112$		0			0
$113$	0.135985	−	0.187168i	0.0127924	−	0.0176073i	−0.802573	−	0.596554i	$-0.796536\pi$
$113$	0.135985	−	0.187168i	0.0127924	−	0.0176073i	0.815365	+	0.578947i	$0.196536\pi$
$114$		0			0
$115$	8.55742	+	1.02130i	0.797984	+	0.0952370i
$116$		0			0
$117$	−1.95673	−	2.69321i	−0.180900	−	0.248988i
$118$		0			0
$119$	1.54198	+	4.74573i	0.141353	+	0.435040i
$120$		0			0
$121$	10.4009	−	3.58078i	0.945533	−	0.325525i
$122$		0			0
$123$	−14.8674	+	4.83071i	−1.34055	+	0.435570i
$124$		0			0
$125$	−3.90039	+	10.4779i	−0.348861	+	0.937174i
$126$		0			0
$127$	−2.31140	−	0.751018i	−0.205103	−	0.0666421i	0.204664	−	0.978832i	$-0.434390\pi$
$127$	−2.31140	−	0.751018i	−0.205103	−	0.0666421i	−0.409767	+	0.912190i	$0.634390\pi$
$128$		0			0
$129$	−13.4420	−	9.76619i	−1.18350	−	0.859865i
$130$		0			0
$131$	−1.58846			−0.138785			−0.0693924	−	0.997589i	$-0.522106\pi$
$131$	−1.58846			−0.138785			−0.0693924	+	0.997589i	$0.522106\pi$
$132$		0			0
$133$		−	11.8588i		−	1.02829i
$134$		0			0
$135$	3.89088	−	8.41836i	0.334874	−	0.724537i
$136$		0			0
$137$	17.7866	+	5.77920i	1.51961	+	0.493750i	0.945664	−	0.325145i	$-0.105413\pi$
$137$	17.7866	+	5.77920i	1.51961	+	0.493750i	0.573943	+	0.818895i	$0.305413\pi$
$138$		0			0
$139$	−9.40675	+	6.83441i	−0.797870	+	0.579687i	−0.910289	−	0.413974i	$-0.864140\pi$
$139$	−9.40675	+	6.83441i	−0.797870	+	0.579687i	0.112418	+	0.993661i	$0.464140\pi$
$140$		0			0
$141$	7.33095	+	22.5624i	0.617378	+	1.90009i
$142$		0			0
$143$	10.8844	−	5.66573i	0.910197	−	0.473792i
$144$		0			0
$145$	−0.205528	−	0.367838i	−0.0170682	−	0.0305472i
$146$		0			0
$147$	−2.28508	−	3.14514i	−0.188470	−	0.259407i
$148$		0			0
$149$	−1.82800	+	5.62600i	−0.149755	+	0.460900i	−0.997592	−	0.0693580i	$-0.977905\pi$
$149$	−1.82800	+	5.62600i	−0.149755	+	0.460900i	0.847836	+	0.530258i	$0.177905\pi$
$150$		0			0
$151$	10.3375	+	7.51064i	0.841254	+	0.611207i	0.922721	−	0.385469i	$-0.125960\pi$
$151$	10.3375	+	7.51064i	0.841254	+	0.611207i	−0.0814664	+	0.996676i	$0.525960\pi$
$152$		0			0
$153$		−	2.00167i		−	0.161826i
$154$		0			0
$155$	−1.50666	+	0.298166i	−0.121018	+	0.0239492i
$156$		0			0
$157$	−8.43394	+	11.6083i	−0.673102	+	0.926445i	−0.999826	−	0.0186749i	$-0.994055\pi$
$157$	−8.43394	+	11.6083i	−0.673102	+	0.926445i	0.326724	+	0.945120i	$0.394055\pi$
$158$		0			0
$159$	−7.72359	+	23.7708i	−0.612520	+	1.88514i
$160$		0			0
$161$	−6.99407	+	5.08149i	−0.551210	+	0.400478i
$162$		0			0
$163$	−3.44963	+	1.12085i	−0.270196	+	0.0877921i	−0.440982	−	0.897516i	$-0.645370\pi$
$163$	−3.44963	+	1.12085i	−0.270196	+	0.0877921i	0.170785	+	0.985308i	$0.445370\pi$
$164$		0			0
$165$	−12.2397	−	8.04221i	−0.952862	−	0.626085i
$166$		0			0
$167$	3.63370	−	1.18066i	0.281184	−	0.0913623i	−0.165030	−	0.986289i	$-0.552772\pi$
$167$	3.63370	−	1.18066i	0.281184	−	0.0913623i	0.446214	+	0.894926i	$0.352772\pi$
$168$		0			0
$169$	0.556767	−	0.404515i	0.0428282	−	0.0311165i
$170$		0			0
$171$	−1.47000	+	4.52421i	−0.112414	+	0.345975i
$172$		0			0
$173$	1.23855	−	1.70472i	0.0941651	−	0.129607i	−0.759335	−	0.650700i	$-0.774476\pi$
$173$	1.23855	−	1.70472i	0.0941651	−	0.129607i	0.853500	+	0.521093i	$0.174476\pi$
$174$		0			0
$175$	−4.27171	−	10.3700i	−0.322911	−	0.783899i
$176$		0			0
$177$		−	0.678711i		−	0.0510151i
$178$		0			0
$179$	−4.06448	−	2.95302i	−0.303793	−	0.220719i	0.425435	−	0.904989i	$-0.360121\pi$
$179$	−4.06448	−	2.95302i	−0.303793	−	0.220719i	−0.729229	+	0.684270i	$0.760121\pi$
$180$		0			0
$181$	−4.83538	+	14.8818i	−0.359411	+	1.10615i	0.593997	+	0.804467i	$0.297549\pi$
$181$	−4.83538	+	14.8818i	−0.359411	+	1.10615i	−0.953408	+	0.301685i	$0.902451\pi$
$182$		0			0
$183$	−2.01202	−	2.76931i	−0.148733	−	0.204713i
$184$		0			0
$185$	5.06191	−	2.82832i	0.372159	−	0.207943i
$186$		0			0
$187$	7.29712	+	1.09073i	0.533618	+	0.0797622i
$188$		0			0
$189$	2.87481	+	8.84777i	0.209112	+	0.643580i
$190$		0			0
$191$	2.52078	−	1.83145i	0.182397	−	0.132519i	−0.492840	−	0.870120i	$-0.664041\pi$
$191$	2.52078	−	1.83145i	0.182397	−	0.132519i	0.675237	+	0.737601i	$0.264041\pi$
$192$		0			0
$193$	−9.16474	−	2.97780i	−0.659692	−	0.214347i	−0.0400095	−	0.999199i	$-0.512739\pi$
$193$	−9.16474	−	2.97780i	−0.659692	−	0.214347i	−0.619683	+	0.784852i	$0.712739\pi$
$194$		0			0
$195$	−14.8299	−	6.85421i	−1.06199	−	0.490841i
$196$		0			0
$197$		−	14.3974i		−	1.02577i	−0.858457	−	0.512885i	$-0.828577\pi$
$197$		−	14.3974i		−	1.02577i	0.858457	−	0.512885i	$-0.171423\pi$
$198$		0			0
$199$	14.7978			1.04899			0.524493	−	0.851415i	$-0.324255\pi$
$199$	14.7978			1.04899			0.524493	+	0.851415i	$0.324255\pi$
$200$		0			0
$201$	1.03920	+	0.755023i	0.0732995	+	0.0532552i
$202$		0			0
$203$	0.401995	+	0.130616i	0.0282145	+	0.00916745i
$204$		0			0
$205$	−12.0280	+	12.9864i	−0.840071	+	0.907007i
$206$		0			0
$207$	3.29819	−	1.07165i	0.229240	−	0.0744845i
$208$		0			0
$209$	−15.6920	−	7.82420i	−1.08544	−	0.541211i
$210$		0			0
$211$	2.09250	+	6.44005i	0.144054	+	0.443352i	0.996888	−	0.0788298i	$-0.0251184\pi$
$211$	2.09250	+	6.44005i	0.144054	+	0.443352i	−0.852834	+	0.522181i	$0.825118\pi$
$212$		0			0
$213$	5.39471	+	7.42518i	0.369640	+	0.508765i
$214$		0			0
$215$	−18.6810	−	2.22952i	−1.27403	−	0.152052i
$216$		0			0
$217$	0.905596	−	1.24645i	0.0614759	−	0.0846143i
$218$		0			0
$219$	17.4935			1.18210
$220$		0			0
$221$	8.23051			0.553644
$222$		0			0
$223$	−5.12388	+	7.05242i	−0.343121	+	0.472265i	−0.945350	−	0.326058i	$-0.894279\pi$
$223$	−5.12388	+	7.05242i	−0.343121	+	0.472265i	0.602229	+	0.798323i	$0.294279\pi$
$224$		0			0
$225$	0.344231	+	4.48575i	0.0229487	+	0.299050i
$226$		0			0
$227$	2.23795	+	3.08028i	0.148538	+	0.204445i	0.876802	−	0.480852i	$-0.159672\pi$
$227$	2.23795	+	3.08028i	0.148538	+	0.204445i	−0.728264	+	0.685297i	$0.759672\pi$
$228$		0			0
$229$	0.838570	+	2.58085i	0.0554142	+	0.170547i	0.974933	−	0.222499i	$-0.0714213\pi$
$229$	0.838570	+	2.58085i	0.0554142	+	0.170547i	−0.919519	+	0.393046i	$0.871421\pi$
$230$		0			0
$231$	14.4899	−	2.42443i	0.953364	−	0.159516i
$232$		0			0
$233$	−9.99634	+	3.24801i	−0.654882	+	0.212784i	−0.617566	−	0.786519i	$-0.711881\pi$
$233$	−9.99634	+	3.24801i	−0.654882	+	0.212784i	−0.0373166	+	0.999303i	$0.511881\pi$
$234$		0			0
$235$	19.7078	+	18.2534i	1.28559	+	1.19072i
$236$		0			0
$237$	−13.5869	−	4.41466i	−0.882565	−	0.286763i
$238$		0			0
$239$	−16.2124	−	11.7790i	−1.04869	−	0.761919i	−0.0767288	−	0.997052i	$-0.524448\pi$
$239$	−16.2124	−	11.7790i	−1.04869	−	0.761919i	−0.971963	+	0.235133i	$0.924448\pi$
$240$		0			0
$241$	28.4450			1.83230			0.916152	−	0.400832i	$-0.131279\pi$
$241$	28.4450			1.83230			0.916152	+	0.400832i	$0.131279\pi$
$242$		0			0
$243$		−	9.06251i		−	0.581361i
$244$		0			0
$245$	−3.99582	−	1.84683i	−0.255283	−	0.117989i
$246$		0			0
$247$	−18.6027	−	6.04438i	−1.18366	−	0.384595i
$248$		0			0
$249$	−5.08313	+	3.69311i	−0.322130	+	0.234041i
$250$		0			0
$251$	7.36604	+	22.6703i	0.464940	+	1.43094i	0.859058	+	0.511879i	$0.171050\pi$
$251$	7.36604	+	22.6703i	0.464940	+	1.43094i	−0.394117	+	0.919060i	$0.628950\pi$
$252$		0			0
$253$	2.10948	+	12.6075i	0.132622	+	0.792628i
$254$		0			0
$255$	−4.79152	−	8.57550i	−0.300057	−	0.537018i
$256$		0			0
$257$	−14.5044	−	19.9636i	−0.904758	−	1.24529i	−0.968925	−	0.247354i	$-0.920439\pi$
$257$	−14.5044	−	19.9636i	−0.904758	−	1.24529i	0.0641671	−	0.997939i	$-0.479561\pi$
$258$		0			0
$259$	−1.79744	+	5.53196i	−0.111688	+	0.343739i
$260$		0			0
$261$	−0.137173	−	0.0996619i	−0.00849079	−	0.00616892i
$262$		0			0
$263$			5.44098i			0.335505i	0.985829	+	0.167753i	$0.0536510\pi$
$263$			5.44098i			0.335505i	−0.985829	+	0.167753i	$0.946349\pi$
$264$		0			0
$265$	5.49416	+	27.7625i	0.337504	+	1.70544i
$266$		0			0
$267$	−11.5169	+	15.8517i	−0.704824	+	0.970107i
$268$		0			0
$269$	2.07213	−	6.37738i	0.126340	−	0.388835i	−0.867803	−	0.496909i	$-0.834468\pi$
$269$	2.07213	−	6.37738i	0.126340	−	0.388835i	0.994143	+	0.108074i	$0.0344682\pi$
$270$		0			0
$271$	−4.09349	+	2.97409i	−0.248662	+	0.180663i	−0.705134	−	0.709075i	$-0.749113\pi$
$271$	−4.09349	+	2.97409i	−0.248662	+	0.180663i	0.456472	+	0.889738i	$0.349113\pi$
$272$		0			0
$273$	15.5863	−	5.06430i	0.943327	−	0.306505i
$274$		0			0
$275$	−16.5404	−	1.18943i	−0.997424	−	0.0717254i
$276$		0			0
$277$	10.1703	−	3.30453i	0.611074	−	0.198550i	0.0129009	−	0.999917i	$-0.495893\pi$
$277$	10.1703	−	3.30453i	0.611074	−	0.198550i	0.598173	+	0.801367i	$0.295893\pi$
$278$		0			0
$279$	−0.500000	+	0.363271i	−0.0299342	+	0.0217485i
$280$		0			0
$281$	−4.23963	+	13.0482i	−0.252915	+	0.778392i	0.741319	+	0.671153i	$0.234201\pi$
$281$	−4.23963	+	13.0482i	−0.252915	+	0.778392i	−0.994233	+	0.107238i	$0.965799\pi$
$282$		0			0
$283$	−12.9132	+	17.7735i	−0.767611	+	1.05653i	0.228932	+	0.973442i	$0.426477\pi$
$283$	−12.9132	+	17.7735i	−0.767611	+	1.05653i	−0.996543	+	0.0830832i	$0.973523\pi$
$284$		0			0
$285$	4.53213	+	22.9013i	0.268460	+	1.35655i
$286$		0			0
$287$		−	17.7563i		−	1.04812i
$288$		0			0
$289$	−9.74956	−	7.08347i	−0.573504	−	0.416675i
$290$		0			0
$291$	1.38410	−	4.25981i	0.0811372	−	0.249715i
$292$		0			0
$293$	8.25135	+	11.3570i	0.482049	+	0.663483i	0.978897	−	0.204354i	$-0.0655094\pi$
$293$	8.25135	+	11.3570i	0.482049	+	0.663483i	−0.496848	+	0.867837i	$0.665509\pi$
$294$		0			0
$295$	−0.374856	−	0.670888i	−0.0218250	−	0.0390606i
$296$		0			0
$297$	13.6045	+	2.03352i	0.789412	+	0.117997i
$298$		0			0
$299$	4.40641	+	13.5615i	0.254829	+	0.784283i
$300$		0			0
$301$	15.2682	−	11.0930i	0.880043	−	0.639389i
$302$		0			0
$303$	18.5876	+	6.03949i	1.06783	+	0.346960i
$304$		0			0
$305$	−3.51833	−	1.62614i	−0.201459	−	0.0931123i
$306$		0			0
$307$			6.86951i			0.392064i	0.980598	+	0.196032i	$0.0628056\pi$
$307$			6.86951i			0.392064i	−0.980598	+	0.196032i	$0.937194\pi$
$308$		0			0
$309$	20.2241			1.15051
$310$		0			0
$311$	−4.45087	−	3.23374i	−0.252385	−	0.183369i	0.454398	−	0.890799i	$-0.349854\pi$
$311$	−4.45087	−	3.23374i	−0.252385	−	0.183369i	−0.706783	+	0.707430i	$0.749854\pi$
$312$		0			0
$313$	−13.5354	−	4.39793i	−0.765068	−	0.248586i	−0.0996156	−	0.995026i	$-0.531761\pi$
$313$	−13.5354	−	4.39793i	−0.765068	−	0.248586i	−0.665452	+	0.746440i	$0.731761\pi$
$314$		0			0
$315$	−3.31103	−	3.06668i	−0.186555	−	0.172788i
$316$		0			0
$317$	−17.7718	+	5.77442i	−0.998166	+	0.324324i	−0.762132	−	0.647421i	$-0.775847\pi$
$317$	−17.7718	+	5.77442i	−0.998166	+	0.324324i	−0.236033	+	0.971745i	$0.575847\pi$
$318$		0			0
$319$	0.438065	−	0.445758i	0.0245269	−	0.0249577i
$320$		0			0
$321$	−6.13099	−	18.8693i	−0.342199	−	1.05318i
$322$		0			0
$323$	−6.91303	−	9.51497i	−0.384651	−	0.529427i
$324$		0			0
$325$	−18.4446	+	1.41541i	−1.02312	+	0.0785130i
$326$		0			0
$327$	10.2166	−	14.0620i	0.564981	−	0.777629i
$328$		0			0
$329$	−26.9464			−1.48560
$330$		0			0
$331$	−0.468249			−0.0257373			−0.0128686	−	0.999917i	$-0.504096\pi$
$331$	−0.468249			−0.0257373			−0.0128686	+	0.999917i	$0.504096\pi$
$332$		0			0
$333$	1.37148	−	1.88767i	0.0751564	−	0.103444i
$334$		0			0
$335$	1.44423	+	0.172364i	0.0789065	+	0.00941726i
$336$		0			0
$337$	−20.0360	−	27.5771i	−1.09143	−	1.50222i	−0.846282	−	0.532735i	$-0.821164\pi$
$337$	−20.0360	−	27.5771i	−1.09143	−	1.50222i	−0.245146	−	0.969486i	$-0.578836\pi$
$338$		0			0
$339$	−0.141181	−	0.434511i	−0.00766790	−	0.0235994i
$340$		0			0
$341$	−1.05185	−	2.02070i	−0.0569611	−	0.109427i
$342$		0			0
$343$	19.1327	−	6.21658i	1.03307	−	0.335664i
$344$		0			0
$345$	11.5647	−	12.4862i	0.622623	−	0.672233i
$346$		0			0
$347$	−3.41707	−	1.11027i	−0.183438	−	0.0596026i	0.215858	−	0.976425i	$-0.430745\pi$
$347$	−3.41707	−	1.11027i	−0.183438	−	0.0596026i	−0.399296	+	0.916822i	$0.630745\pi$
$348$		0			0
$349$	−5.15433	−	3.74484i	−0.275905	−	0.200457i	0.441224	−	0.897397i	$-0.354544\pi$
$349$	−5.15433	−	3.74484i	−0.275905	−	0.200457i	−0.717129	+	0.696940i	$0.754544\pi$
$350$		0			0
$351$	15.3446			0.819037
$352$		0			0
$353$			12.1971i			0.649186i	0.945854	+	0.324593i	$0.105227\pi$
$353$			12.1971i			0.649186i	−0.945854	+	0.324593i	$0.894773\pi$
$354$		0			0
$355$	9.43350	+	4.36007i	0.500678	+	0.231408i
$356$		0			0
$357$	9.37181	+	3.04509i	0.496009	+	0.161163i
$358$		0			0
$359$	−19.5093	+	14.1744i	−1.02966	+	0.748094i	−0.968241	−	0.250018i	$-0.919564\pi$
$359$	−19.5093	+	14.1744i	−1.02966	+	0.748094i	−0.0614222	+	0.998112i	$0.519564\pi$
$360$		0			0
$361$	2.76592	+	8.51262i	0.145575	+	0.448032i
$362$		0			0
$363$	6.35204	−	20.7732i	0.333396	−	1.09031i
$364$		0			0
$365$	17.2918	−	9.66174i	0.905096	−	0.505719i
$366$		0			0
$367$	−11.9849	−	16.4958i	−0.625606	−	0.861073i	0.372140	−	0.928177i	$-0.378624\pi$
$367$	−11.9849	−	16.4958i	−0.625606	−	0.861073i	−0.997746	+	0.0671034i	$0.978624\pi$
$368$		0			0
$369$	−2.20105	+	6.77414i	−0.114582	+	0.352648i
$370$		0			0
$371$	−22.9677	−	16.6870i	−1.19242	−	0.866347i
$372$		0			0
$373$		−	7.51997i		−	0.389369i	−0.980866	−	0.194685i	$-0.937632\pi$
$373$		−	7.51997i		−	0.389369i	0.980866	−	0.194685i	$-0.0623684\pi$
$374$		0			0
$375$	12.2125	+	18.3937i	0.630653	+	0.949845i
$376$		0			0
$377$	0.409791	−	0.564029i	0.0211053	−	0.0290490i
$378$		0			0
$379$	7.16649	−	22.0562i	0.368118	−	1.13295i	−0.579888	−	0.814696i	$-0.696904\pi$
$379$	7.16649	−	22.0562i	0.368118	−	1.13295i	0.948006	−	0.318254i	$-0.103096\pi$
$380$		0			0
$381$	−3.88281	+	2.82103i	−0.198922	+	0.144526i
$382$		0			0
$383$	−2.32095	+	0.754123i	−0.118595	+	0.0385339i	−0.367713	−	0.929939i	$-0.619859\pi$
$383$	−2.32095	+	0.754123i	−0.118595	+	0.0385339i	0.249118	+	0.968473i	$0.419859\pi$
$384$		0			0
$385$	12.9838	−	10.3993i	0.661717	−	0.529999i
$386$		0			0
$387$	−7.20000	+	2.33942i	−0.365997	+	0.118919i
$388$		0			0
$389$	27.4849	−	19.9689i	1.39354	−	1.01246i	0.398071	−	0.917355i	$-0.369680\pi$
$389$	27.4849	−	19.9689i	1.39354	−	1.01246i	0.995467	−	0.0951096i	$-0.0303201\pi$
$390$		0			0
$391$	−2.64950	+	8.15434i	−0.133991	+	0.412383i
$392$		0			0
$393$	−1.84381	+	2.53779i	−0.0930080	+	0.128015i
$394$		0			0
$395$	−15.8685	+	3.14036i	−0.798433	+	0.158009i
$396$		0			0
$397$		−	27.4961i		−	1.37999i	−0.723814	−	0.689995i	$-0.757613\pi$
$397$		−	27.4961i		−	1.37999i	0.723814	−	0.689995i	$-0.242387\pi$
$398$		0			0
$399$	−18.9460	−	13.7651i	−0.948487	−	0.689116i
$400$		0			0
$401$	−0.583247	+	1.79505i	−0.0291259	+	0.0896404i	−0.964563	−	0.263853i	$-0.915006\pi$
$401$	−0.583247	+	1.79505i	−0.0291259	+	0.0896404i	0.935437	+	0.353494i	$0.115006\pi$
$402$		0			0
$403$	−1.49370	−	2.05591i	−0.0744067	−	0.102412i
$404$		0			0
$405$	−11.8773	−	21.2571i	−0.590188	−	1.05627i
$406$		0			0
$407$	6.13420	+	6.02834i	0.304061	+	0.298814i
$408$		0			0
$409$	−4.18949	−	12.8939i	−0.207157	−	0.637563i	−0.999618	−	0.0276408i	$-0.991201\pi$
$409$	−4.18949	−	12.8939i	−0.207157	−	0.637563i	0.792461	−	0.609923i	$-0.208799\pi$
$410$		0			0
$411$	29.8788	−	21.7082i	1.47381	−	1.07079i
$412$		0			0
$413$	0.733187	+	0.238227i	0.0360778	+	0.0117224i
$414$		0			0
$415$	−2.98481	+	6.45798i	−0.146519	+	0.317010i
$416$		0			0
$417$			22.9616i			1.12444i
$418$		0			0
$419$	−22.1368			−1.08145			−0.540727	−	0.841198i	$-0.681851\pi$
$419$	−22.1368			−1.08145			−0.540727	+	0.841198i	$0.681851\pi$
$420$		0			0
$421$	−14.4835	−	10.5229i	−0.705881	−	0.512853i	0.175961	−	0.984397i	$-0.443697\pi$
$421$	−14.4835	−	10.5229i	−0.705881	−	0.512853i	−0.881842	+	0.471544i	$0.843697\pi$
$422$		0			0
$423$	10.2803	+	3.34026i	0.499843	+	0.162409i
$424$		0			0
$425$	−9.47259	−	5.83026i	−0.459488	−	0.282809i
$426$		0			0
$427$	3.69780	−	1.20149i	0.178949	−	0.0581440i
$428$		0			0
$429$	3.58227	−	23.9658i	0.172954	−	1.15708i
$430$		0			0
$431$	−10.3353	−	31.8087i	−0.497833	−	1.53217i	−0.812495	−	0.582968i	$-0.801891\pi$
$431$	−10.3353	−	31.8087i	−0.497833	−	1.53217i	0.314662	−	0.949204i	$-0.398109\pi$
$432$		0			0
$433$	18.5102	+	25.4771i	0.889543	+	1.22435i	0.973685	+	0.227897i	$0.0731848\pi$
$433$	18.5102	+	25.4771i	0.889543	+	1.22435i	−0.0841428	+	0.996454i	$0.526815\pi$
$434$		0			0
$435$	−0.826238	−	0.0986091i	−0.0396151	−	0.00472794i
$436$		0			0
$437$	11.9769	−	16.4848i	0.572932	−	0.788574i
$438$		0			0
$439$	35.6208			1.70009			0.850045	−	0.526710i	$-0.176575\pi$
$439$	35.6208			1.70009			0.850045	+	0.526710i	$0.176575\pi$
$440$		0			0
$441$	−1.77134			−0.0843495
$442$		0			0
$443$	13.8056	−	19.0018i	0.655926	−	0.902805i	−0.343412	−	0.939185i	$-0.611583\pi$
$443$	13.8056	−	19.0018i	0.655926	−	0.902805i	0.999338	+	0.0363802i	$0.0115827\pi$
$444$		0			0
$445$	−2.62920	+	22.0298i	−0.124636	+	1.04431i
$446$		0			0
$447$	6.86646	+	9.45086i	0.324772	+	0.447011i
$448$		0			0
$449$	9.70066	+	29.8555i	0.457802	+	1.40897i	0.867814	+	0.496890i	$0.165525\pi$
$449$	9.70066	+	29.8555i	0.457802	+	1.40897i	−0.410011	+	0.912080i	$0.634475\pi$
$450$		0			0
$451$	−23.4958	−	11.7152i	−1.10637	−	0.551649i
$452$		0			0
$453$	23.9985	−	7.79760i	1.12755	−	0.366363i
$454$		0			0
$455$	12.6096	−	13.6143i	0.591148	−	0.638250i
$456$		0			0
$457$	37.1964	+	12.0859i	1.73998	+	0.565352i	0.994830	−	0.101550i	$-0.0323803\pi$
$457$	37.1964	+	12.0859i	1.73998	+	0.565352i	0.745145	+	0.666903i	$0.232380\pi$
$458$		0			0
$459$	7.46440	+	5.42320i	0.348408	+	0.253133i
$460$		0			0
$461$	−8.88399			−0.413769			−0.206884	−	0.978365i	$-0.566332\pi$
$461$	−8.88399			−0.413769			−0.206884	+	0.978365i	$0.566332\pi$
$462$		0			0
$463$			4.21081i			0.195693i	0.995202	+	0.0978464i	$0.0311954\pi$
$463$			4.21081i			0.195693i	−0.995202	+	0.0978464i	$0.968805\pi$
$464$		0			0
$465$	−1.27250	+	2.75319i	−0.0590107	+	0.127676i
$466$		0			0
$467$	6.39912	+	2.07920i	0.296116	+	0.0962139i	0.453307	−	0.891354i	$-0.350244\pi$
$467$	6.39912	+	2.07920i	0.296116	+	0.0962139i	−0.157191	+	0.987568i	$0.550244\pi$
$468$		0			0
$469$	−1.18038	+	0.857597i	−0.0545049	+	0.0396002i
$470$		0			0
$471$	8.75618	+	26.9487i	0.403463	+	1.24173i
$472$		0			0
$473$	−4.60503	−	27.5224i	−0.211740	−	1.26548i
$474$		0			0
$475$	17.1284	+	20.1342i	0.785905	+	0.923820i
$476$		0			0
$477$	6.69383	+	9.21327i	0.306490	+	0.421847i
$478$		0			0
$479$	6.43046	−	19.7909i	0.293815	−	0.904270i	−0.689802	−	0.723998i	$-0.742302\pi$
$479$	6.43046	−	19.7909i	0.293815	−	0.904270i	0.983617	−	0.180272i	$-0.0576977\pi$
$480$		0			0
$481$	7.76176	+	5.63925i	0.353906	+	0.257128i
$482$		0			0
$483$			17.0723i			0.776818i
$484$		0			0
$485$	−0.984576	−	4.97516i	−0.0447073	−	0.225910i
$486$		0			0
$487$	9.27489	−	12.7658i	0.420285	−	0.578473i	−0.545404	−	0.838173i	$-0.683624\pi$
$487$	9.27489	−	12.7658i	0.420285	−	0.578473i	0.965689	+	0.259700i	$0.0836237\pi$
$488$		0			0
$489$	−2.21345	+	6.81230i	−0.100096	+	0.308063i
$490$		0			0
$491$	15.6386	−	11.3621i	0.705759	−	0.512764i	−0.176044	−	0.984382i	$-0.556330\pi$
$491$	15.6386	−	11.3621i	0.705759	−	0.512764i	0.881803	+	0.471618i	$0.156330\pi$
$492$		0			0
$493$	0.398685	−	0.129541i	0.0179559	−	0.00583422i
$494$		0			0
$495$	−6.24252	+	2.35795i	−0.280580	+	0.105982i
$496$		0			0
$497$	−9.91469	+	3.22148i	−0.444734	+	0.144503i
$498$		0			0
$499$	33.5416	−	24.3694i	1.50153	−	1.09092i	0.531758	−	0.846896i	$-0.321532\pi$
$499$	33.5416	−	24.3694i	1.50153	−	1.09092i	0.969769	−	0.244026i	$-0.0784684\pi$
$500$		0			0
$501$	2.33156	−	7.17579i	0.104166	−	0.320591i
$502$		0			0
$503$	−19.1978	+	26.4236i	−0.855990	+	1.17817i	0.126521	+	0.991964i	$0.459619\pi$
$503$	−19.1978	+	26.4236i	−0.855990	+	1.17817i	−0.982511	+	0.186205i	$0.940381\pi$
$504$		0			0
$505$	21.7090	−	4.29618i	0.966039	−	0.191178i
$506$		0			0
$507$		−	1.35905i		−	0.0603576i
$508$		0			0
$509$	13.4662	+	9.78379i	0.596881	+	0.433659i	0.844770	−	0.535129i	$-0.179737\pi$
$509$	13.4662	+	9.78379i	0.596881	+	0.433659i	−0.247890	+	0.968788i	$0.579737\pi$
$510$		0			0
$511$	−6.14019	+	18.8975i	−0.271626	+	0.835978i
$512$		0			0
$513$	−12.8884	−	17.7393i	−0.569036	−	0.783211i
$514$		0			0
$515$	19.9909	−	11.1699i	0.880906	−	0.492203i
$516$		0			0
$517$	−17.7788	+	35.6566i	−0.781909	+	1.56818i
$518$		0			0
$519$	−1.28587	−	3.95750i	−0.0564434	−	0.173715i
$520$		0			0
$521$	−11.3717	+	8.26206i	−0.498205	+	0.361967i	−0.808331	−	0.588728i	$-0.799629\pi$
$521$	−11.3717	+	8.26206i	−0.498205	+	0.361967i	0.310126	+	0.950696i	$0.399629\pi$
$522$		0			0
$523$	−14.9009	−	4.84159i	−0.651570	−	0.211708i	−0.0354635	−	0.999371i	$-0.511291\pi$
$523$	−14.9009	−	4.84159i	−0.651570	−	0.211708i	−0.616106	+	0.787663i	$0.711291\pi$
$524$		0			0
$525$	−21.5259	−	5.21235i	−0.939467	−	0.227486i
$526$		0			0
$527$		−	1.52801i		−	0.0665611i
$528$		0			0
$529$	8.14550			0.354152
$530$		0			0
$531$	−0.250186	−	0.181770i	−0.0108571	−	0.00788817i
$532$		0			0
$533$	−27.8540	−	9.05031i	−1.20649	−	0.392012i
$534$		0			0
$535$	−16.4819	−	15.2656i	−0.712575	−	0.659988i
$536$		0			0
$537$	−9.43570	+	3.06584i	−0.407180	+	0.132301i
$538$		0			0
$539$	0.965221	−	6.45743i	0.0415750	−	0.278141i
$540$		0			0
$541$	−12.2489	−	37.6983i	−0.526623	−	1.62078i	−0.761084	−	0.648653i	$-0.775333\pi$
$541$	−12.2489	−	37.6983i	−0.526623	−	1.62078i	0.234461	−	0.972125i	$-0.424667\pi$
$542$		0			0
$543$	18.1630	+	24.9992i	0.779448	+	1.07282i
$544$		0			0
$545$	2.33235	−	19.5426i	0.0999070	−	0.837113i
$546$		0			0
$547$	24.1970	−	33.3043i	1.03459	−	1.42399i	0.133145	−	0.991097i	$-0.457492\pi$
$547$	24.1970	−	33.3043i	1.03459	−	1.42399i	0.901445	−	0.432895i	$-0.142508\pi$
$548$		0			0
$549$	−1.55967			−0.0665651
$550$		0			0
$551$	−0.996247			−0.0424415
$552$		0			0
$553$	9.53798	−	13.1279i	0.405596	−	0.558255i
$554$		0			0
$555$	1.35699	−	11.3701i	0.0576009	−	0.482633i
$556$		0			0
$557$	17.5606	+	24.1702i	0.744069	+	1.02412i	0.998374	+	0.0569987i	$0.0181531\pi$
$557$	17.5606	+	24.1702i	0.744069	+	1.02412i	−0.254306	+	0.967124i	$0.581847\pi$
$558$		0			0
$559$	−9.61926	−	29.6050i	−0.406851	−	1.25216i
$560$		0			0
$561$	10.2127	−	10.3921i	0.431182	−	0.438754i
$562$		0			0
$563$	2.05218	−	0.666795i	0.0864892	−	0.0281021i	−0.265453	−	0.964124i	$-0.585521\pi$
$563$	2.05218	−	0.666795i	0.0864892	−	0.0281021i	0.351942	+	0.936022i	$0.385521\pi$
$564$		0			0
$565$	−0.379536	−	0.351527i	−0.0159672	−	0.0147889i
$566$		0			0
$567$	23.2310	+	7.54820i	0.975610	+	0.316995i
$568$		0			0
$569$	0.580298	+	0.421611i	0.0243274	+	0.0176749i	0.599882	−	0.800088i	$-0.295214\pi$
$569$	0.580298	+	0.421611i	0.0243274	+	0.0176749i	−0.575555	+	0.817763i	$0.695214\pi$
$570$		0			0
$571$	21.6311			0.905235			0.452617	−	0.891705i	$-0.350490\pi$
$571$	21.6311			0.905235			0.452617	+	0.891705i	$0.350490\pi$
$572$		0			0
$573$		−	6.15315i		−	0.257051i
$574$		0			0
$575$	4.53522	−	18.7295i	0.189132	−	0.781074i
$576$		0			0
$577$	−22.2810	−	7.23952i	−0.927568	−	0.301385i	−0.194000	−	0.981001i	$-0.562146\pi$
$577$	−22.2810	−	7.23952i	−0.927568	−	0.301385i	−0.733568	+	0.679616i	$0.762146\pi$
$578$		0			0
$579$	−15.3954	+	11.1854i	−0.639812	+	0.464851i
$580$		0			0
$581$	−2.20536	−	6.78739i	−0.0914936	−	0.281588i
$582$		0			0
$583$	−37.2346	+	19.3820i	−1.54210	+	0.802722i
$584$		0			0
$585$	−6.49828	+	3.63089i	−0.268671	+	0.150119i
$586$		0			0
$587$	1.32095	+	1.81814i	0.0545216	+	0.0750425i	0.835407	−	0.549632i	$-0.185232\pi$
$587$	1.32095	+	1.81814i	0.0545216	+	0.0750425i	−0.780886	+	0.624674i	$0.785232\pi$
$588$		0			0
$589$	−1.12215	+	3.45362i	−0.0462374	+	0.142304i
$590$		0			0
$591$	−23.0018	−	16.7118i	−0.946167	−	0.687431i
$592$		0			0
$593$			25.4034i			1.04319i	0.853193	+	0.521596i	$0.174663\pi$
$593$			25.4034i			1.04319i	−0.853193	+	0.521596i	$0.825337\pi$
$594$		0			0
$595$	10.9456	−	2.16612i	0.448726	−	0.0888022i
$596$		0			0
$597$	17.1765	−	23.6415i	0.702988	−	0.967580i
$598$		0			0
$599$	−5.63194	+	17.3333i	−0.230115	+	0.708220i	0.767617	+	0.640909i	$0.221442\pi$
$599$	−5.63194	+	17.3333i	−0.230115	+	0.708220i	−0.997732	+	0.0673118i	$0.978558\pi$
$600$		0			0
$601$	28.0242	−	20.3608i	1.14313	−	0.830533i	0.155579	−	0.987824i	$-0.450276\pi$
$601$	28.0242	−	20.3608i	1.14313	−	0.830533i	0.987552	+	0.157290i	$0.0502758\pi$
$602$		0			0
$603$	0.556631	−	0.180860i	0.0226678	−	0.00736520i
$604$		0			0
$605$	−5.19433	−	24.0420i	−0.211180	−	0.977447i
$606$		0			0
$607$	−24.2027	+	7.86394i	−0.982358	+	0.319187i	−0.755794	−	0.654809i	$-0.772749\pi$
$607$	−24.2027	+	7.86394i	−0.982358	+	0.319187i	−0.226564	+	0.973996i	$0.572749\pi$
$608$		0			0
$609$	0.675293	−	0.490629i	0.0273643	−	0.0198813i
$610$		0			0
$611$	−13.7345	+	42.2705i	−0.555639	+	1.71008i
$612$		0			0
$613$	−21.7843	+	29.9835i	−0.879859	+	1.21102i	0.0966016	+	0.995323i	$0.469203\pi$
$613$	−21.7843	+	29.9835i	−0.879859	+	1.21102i	−0.976460	+	0.215698i	$0.930797\pi$
$614$		0			0
$615$	6.78600	+	34.2903i	0.273638	+	1.38272i
$616$		0			0
$617$			27.5937i			1.11088i	0.831557	+	0.555439i	$0.187450\pi$
$617$			27.5937i			1.11088i	−0.831557	+	0.555439i	$0.812550\pi$
$618$		0			0
$619$	−16.5391	−	12.0164i	−0.664764	−	0.482979i	0.203504	−	0.979074i	$-0.434767\pi$
$619$	−16.5391	−	12.0164i	−0.664764	−	0.482979i	−0.868268	+	0.496095i	$0.834767\pi$
$620$		0			0
$621$	−4.93964	+	15.2026i	−0.198221	+	0.610061i
$622$		0			0
$623$	−13.0816	−	18.0052i	−0.524101	−	0.721364i
$624$		0			0
$625$	22.2307	+	11.4366i	0.889228	+	0.457464i
$626$		0			0
$627$	−30.7148	+	15.9882i	−1.22663	+	0.638507i
$628$		0			0
$629$	1.78265	+	5.48642i	0.0710787	+	0.218758i
$630$		0			0
$631$	0.614155	−	0.446210i	0.0244491	−	0.0177633i	−0.575494	−	0.817806i	$-0.695190\pi$
$631$	0.614155	−	0.446210i	0.0244491	−	0.0177633i	0.599943	+	0.800043i	$0.295190\pi$
$632$		0			0
$633$	12.7177	+	4.13224i	0.505485	+	0.164242i
$634$		0			0
$635$	−2.27998	+	4.93301i	−0.0904784	+	0.195760i
$636$		0			0
$637$		−	7.28342i		−	0.288579i
$638$		0			0
$639$	4.18186			0.165432
$640$		0			0
$641$	12.0584	+	8.76094i	0.476278	+	0.346037i	0.799883	−	0.600156i	$-0.204895\pi$
$641$	12.0584	+	8.76094i	0.476278	+	0.346037i	−0.323605	+	0.946192i	$0.604895\pi$
$642$		0			0
$643$	−26.2820	−	8.53955i	−1.03646	−	0.336767i	−0.259120	−	0.965845i	$-0.583432\pi$
$643$	−26.2820	−	8.53955i	−1.03646	−	0.336767i	−0.777342	+	0.629078i	$0.783432\pi$
$644$		0			0
$645$	−25.2460	+	27.2575i	−0.994059	+	1.07326i
$646$		0			0
$647$	−23.7560	+	7.71879i	−0.933945	+	0.303457i	−0.736175	−	0.676791i	$-0.763370\pi$
$647$	−23.7560	+	7.71879i	−0.933945	+	0.303457i	−0.197770	+	0.980248i	$0.563370\pi$
$648$		0			0
$649$	0.798974	−	0.813005i	0.0313625	−	0.0319132i
$650$		0			0
$651$	−0.940197	−	2.89363i	−0.0368492	−	0.113410i
$652$		0			0
$653$	−16.3187	−	22.4607i	−0.638599	−	0.878956i	0.359941	−	0.932975i	$-0.382797\pi$
$653$	−16.3187	−	22.4607i	−0.638599	−	0.878956i	−0.998540	+	0.0540191i	$0.982797\pi$
$654$		0			0
$655$	−0.420923	+	3.52688i	−0.0164468	+	0.137807i
$656$		0			0
$657$	4.68505	−	6.44842i	0.182781	−	0.251577i
$658$		0			0
$659$	−21.5863			−0.840883			−0.420442	−	0.907320i	$-0.638125\pi$
$659$	−21.5863			−0.840883			−0.420442	+	0.907320i	$0.638125\pi$
$660$		0			0
$661$	−16.0174			−0.623003			−0.311502	−	0.950246i	$-0.600832\pi$
$661$	−16.0174			−0.623003			−0.311502	+	0.950246i	$0.600832\pi$
$662$		0			0
$663$	9.55357	−	13.1494i	0.371030	−	0.510679i
$664$		0			0
$665$	−26.3302	−	3.14243i	−1.02104	−	0.121858i
$666$		0			0
$667$	0.426892	+	0.587567i	0.0165293	+	0.0227507i
$668$		0			0
$669$	5.31966	+	16.3722i	0.205670	+	0.632986i
$670$		0			0
$671$	0.849880	−	5.68579i	0.0328093	−	0.219498i
$672$		0			0
$673$	−29.8127	+	9.68673i	−1.14920	+	0.373396i	−0.820840	−	0.571158i	$-0.806494\pi$
$673$	−29.8127	+	9.68673i	−1.14920	+	0.373396i	−0.328355	+	0.944554i	$0.606494\pi$
$674$		0			0
$675$	−17.6603	−	10.8697i	−0.679747	−	0.418376i
$676$		0			0
$677$	29.1654	+	9.47642i	1.12092	+	0.364209i	0.810118	−	0.586267i	$-0.199403\pi$
$677$	29.1654	+	9.47642i	1.12092	+	0.364209i	0.310801	+	0.950475i	$0.399403\pi$
$678$		0			0
$679$	4.11590	+	2.99038i	0.157954	+	0.114760i
$680$		0			0
$681$	7.51888			0.288124
$682$		0			0
$683$			3.27236i			0.125213i	0.998038	+	0.0626066i	$0.0199414\pi$
$683$			3.27236i			0.125213i	−0.998038	+	0.0626066i	$0.980059\pi$
$684$		0			0
$685$	17.5448	−	37.9603i	0.670354	−	1.45039i
$686$		0			0
$687$	5.09664	+	1.65600i	0.194449	+	0.0631802i
$688$		0			0
$689$	−37.8832	+	27.5238i	−1.44324	+	1.04857i
$690$		0			0
$691$	11.2774	+	34.7084i	0.429014	+	1.32037i	0.899098	+	0.437748i	$0.144224\pi$
$691$	11.2774	+	34.7084i	0.429014	+	1.32037i	−0.470083	+	0.882622i	$0.655776\pi$
$692$		0			0
$693$	2.98694	−	5.99054i	0.113465	−	0.227562i
$694$		0			0
$695$	12.6818	+	22.6970i	0.481049	+	0.860944i
$696$		0			0
$697$	−10.3509	−	14.2468i	−0.392070	−	0.539638i
$698$		0			0
$699$	−6.41413	+	19.7407i	−0.242605	+	0.746660i
$700$		0			0
$701$	−37.6684	−	27.3677i	−1.42272	−	1.03366i	−0.991316	−	0.131502i	$-0.958020\pi$
$701$	−37.6684	−	27.3677i	−1.42272	−	1.03366i	−0.431399	−	0.902161i	$-0.641980\pi$
$702$		0			0
$703$		−	13.7096i		−	0.517068i
$704$		0			0
$705$	52.0381	−	10.2983i	1.95987	−	0.387855i
$706$		0			0
$707$	−13.0485	+	17.9597i	−0.490738	+	0.675443i
$708$		0			0
$709$	11.0000	−	33.8544i	0.413112	−	1.27143i	−0.500817	−	0.865553i	$-0.666967\pi$
$709$	11.0000	−	33.8544i	0.413112	−	1.27143i	0.913929	−	0.405874i	$-0.133033\pi$
$710$		0			0
$711$	−5.26613	+	3.82607i	−0.197495	+	0.143489i
$712$		0			0
$713$	2.51772	−	0.818057i	0.0942894	−	0.0306365i
$714$		0			0
$715$	−9.69546	−	25.6681i	−0.362590	−	0.959931i
$716$		0			0
$717$	−37.6371	+	12.2290i	−1.40558	+	0.456702i
$718$		0			0
$719$	−17.8722	+	12.9849i	−0.666522	+	0.484256i	−0.868859	−	0.495060i	$-0.835146\pi$
$719$	−17.8722	+	12.9849i	−0.666522	+	0.484256i	0.202337	+	0.979316i	$0.435146\pi$
$720$		0			0
$721$	−7.09862	+	21.8473i	−0.264366	+	0.813636i
$722$		0			0
$723$	33.0176	−	45.4448i	1.22794	−	1.69011i
$724$		0			0
$725$	−0.871176	+	0.358863i	−0.0323547	+	0.0133278i
$726$		0			0
$727$			45.5415i			1.68904i	0.535522	+	0.844521i	$0.320115\pi$
$727$			45.5415i			1.68904i	−0.535522	+	0.844521i	$0.679885\pi$
$728$		0			0
$729$	11.9514	+	8.68317i	0.442643	+	0.321599i
$730$		0			0
$731$	5.78391	−	17.8011i	0.213926	−	0.658396i
$732$		0			0
$733$	−6.68835	−	9.20572i	−0.247040	−	0.340021i	0.667432	−	0.744671i	$-0.267393\pi$
$733$	−6.68835	−	9.20572i	−0.247040	−	0.340021i	−0.914472	+	0.404650i	$0.867393\pi$
$734$		0			0
$735$	−7.58871	+	4.24016i	−0.279914	+	0.156401i
$736$		0			0
$737$	0.356014	+	2.12776i	0.0131140	+	0.0783769i
$738$		0			0
$739$	−1.34045	−	4.12547i	−0.0493091	−	0.151758i	0.923370	−	0.383911i	$-0.125423\pi$
$739$	−1.34045	−	4.12547i	−0.0493091	−	0.151758i	−0.972679	+	0.232153i	$0.925423\pi$
$740$		0			0
$741$	−31.2498	+	22.7043i	−1.14799	+	0.834064i
$742$		0			0
$743$	−16.4480	−	5.34429i	−0.603420	−	0.196063i	−0.00865478	−	0.999963i	$-0.502755\pi$
$743$	−16.4480	−	5.34429i	−0.603420	−	0.196063i	−0.594765	+	0.803900i	$0.702755\pi$
$744$		0			0
$745$	12.0071	+	5.54955i	0.439905	+	0.203320i
$746$		0			0
$747$			2.86281i			0.104745i
$748$		0			0
$749$	22.5357			0.823437
$750$		0			0
$751$	−25.4946	−	18.5229i	−0.930310	−	0.675910i	0.0157586	−	0.999876i	$-0.494984\pi$
$751$	−25.4946	−	18.5229i	−0.930310	−	0.675910i	−0.946069	+	0.323966i	$0.894984\pi$
$752$		0			0
$753$	44.7691	+	14.5464i	1.63148	+	0.530099i
$754$		0			0
$755$	19.4153	−	20.9623i	0.706594	−	0.762895i
$756$		0			0
$757$	8.82332	−	2.86687i	0.320689	−	0.104198i	−0.144249	−	0.989541i	$-0.546077\pi$
$757$	8.82332	−	2.86687i	0.320689	−	0.104198i	0.464938	+	0.885343i	$0.346077\pi$
$758$		0			0
$759$	22.5908	+	11.2640i	0.819995	+	0.408858i
$760$		0			0
$761$	−1.28492	−	3.95459i	−0.0465784	−	0.143354i	0.925062	−	0.379815i	$-0.124012\pi$
$761$	−1.28492	−	3.95459i	−0.0465784	−	0.143354i	−0.971641	+	0.236461i	$0.924012\pi$
$762$		0			0
$763$	11.6046	+	15.9724i	0.420115	+	0.578239i
$764$		0			0
$765$	−4.44434	−	0.530419i	−0.160685	−	0.0191773i
$766$		0			0
$767$	0.747406	−	1.02872i	0.0269873	−	0.0371448i
$768$		0			0
$769$	−16.8800			−0.608709			−0.304355	−	0.952559i	$-0.598441\pi$
$769$	−16.8800			−0.608709			−0.304355	+	0.952559i	$0.598441\pi$
$770$		0			0
$771$	−48.7305			−1.75499
$772$		0			0
$773$	−4.98301	+	6.85852i	−0.179226	+	0.246684i	−0.889173	−	0.457572i	$-0.848719\pi$
$773$	−4.98301	+	6.85852i	−0.179226	+	0.246684i	0.709946	+	0.704256i	$0.248719\pi$
$774$		0			0
$775$	0.262774	+	3.42427i	0.00943912	+	0.123003i
$776$		0			0
$777$	6.75168	+	9.29289i	0.242215	+	0.333381i
$778$		0			0
$779$	12.9326	+	39.8025i	0.463359	+	1.42607i
$780$		0			0
$781$	−2.27873	+	15.2450i	−0.0815395	+	0.545509i
$782$		0			0
$783$	0.743294	−	0.241511i	0.0265632	−	0.00863089i
$784$		0			0
$785$	23.5392	+	21.8020i	0.840150	+	0.778148i
$786$		0			0
$787$	50.9924	+	16.5684i	1.81768	+	0.590601i	0.999886	+	0.0150924i	$0.00480424\pi$
$787$	50.9924	+	16.5684i	1.81768	+	0.590601i	0.817796	+	0.575508i	$0.195196\pi$
$788$		0			0
$789$	8.69272	+	6.31563i	0.309469	+	0.224842i
$790$		0			0
$791$	0.518940			0.0184514
$792$		0			0
$793$		−	6.41307i		−	0.227735i
$794$		0			0
$795$	50.7318	+	23.4477i	1.79927	+	0.831605i
$796$		0			0
$797$	−27.1477	−	8.82082i	−0.961621	−	0.312450i	−0.214192	−	0.976792i	$-0.568712\pi$
$797$	−27.1477	−	8.82082i	−0.961621	−	0.312450i	−0.747429	+	0.664342i	$0.768712\pi$
$798$		0			0
$799$	−21.6206	+	15.7083i	−0.764883	+	0.555720i
$800$		0			0
$801$	2.75879	+	8.49070i	0.0974772	+	0.300004i
$802$		0			0
$803$	20.9548	+	20.5932i	0.739480	+	0.726718i
$804$		0			0
$805$	9.42915	+	16.8756i	0.332334	+	0.594785i
$806$		0			0
$807$	−7.78350	−	10.7131i	−0.273992	−	0.377118i
$808$		0			0
$809$	−11.4170	+	35.1378i	−0.401399	+	1.23538i	0.522466	+	0.852660i	$0.325012\pi$
$809$	−11.4170	+	35.1378i	−0.401399	+	1.23538i	−0.923865	+	0.382718i	$0.874988\pi$
$810$		0			0
$811$	−31.0475	−	22.5573i	−1.09022	−	0.792094i	−0.110787	−	0.993844i	$-0.535337\pi$
$811$	−31.0475	−	22.5573i	−1.09022	−	0.792094i	−0.979437	+	0.201750i	$0.935337\pi$
$812$		0			0
$813$			9.99209i			0.350438i
$814$		0			0
$815$	1.57453	+	7.95628i	0.0551535	+	0.278696i
$816$		0			0
$817$	−26.1458	+	35.9865i	−0.914724	+	1.25901i
$818$		0			0
$819$	2.30749	−	7.10171i	0.0806301	−	0.248154i
$820$		0			0
$821$	8.29214	−	6.02459i	0.289398	−	0.210260i	−0.433608	−	0.901101i	$-0.642760\pi$
$821$	8.29214	−	6.02459i	0.289398	−	0.210260i	0.723006	+	0.690842i	$0.242760\pi$
$822$		0			0
$823$	23.9948	−	7.79637i	0.836405	−	0.271764i	0.140664	−	0.990057i	$-0.455076\pi$
$823$	23.9948	−	7.79637i	0.836405	−	0.271764i	0.695741	+	0.718293i	$0.255076\pi$
$824$		0			0
$825$	−21.0996	+	25.0449i	−0.734593	+	0.871953i
$826$		0			0
$827$	17.4505	−	5.67001i	0.606813	−	0.197165i	0.0105362	−	0.999944i	$-0.496646\pi$
$827$	17.4505	−	5.67001i	0.606813	−	0.197165i	0.596277	+	0.802779i	$0.296646\pi$
$828$		0			0
$829$	19.7259	−	14.3317i	0.685110	−	0.497761i	−0.189939	−	0.981796i	$-0.560829\pi$
$829$	19.7259	−	14.3317i	0.685110	−	0.497761i	0.875049	+	0.484035i	$0.160829\pi$
$830$		0			0
$831$	6.52575	−	20.0842i	0.226376	−	0.696713i
$832$		0			0
$833$	2.57415	−	3.54301i	0.0891890	−	0.122758i
$834$		0			0
$835$	−1.65855	−	8.38081i	−0.0573964	−	0.290030i
$836$		0			0
$837$		−	2.84876i		−	0.0984676i
$838$		0			0
$839$	34.2059	+	24.8520i	1.18092	+	0.857988i	0.992275	−	0.124058i	$-0.0395908\pi$
$839$	34.2059	+	24.8520i	1.18092	+	0.857988i	0.188644	+	0.982046i	$0.439591\pi$
$840$		0			0
$841$	−8.95052	+	27.5469i	−0.308639	+	0.949892i
$842$		0			0
$843$	15.9252	+	21.9191i	0.548492	+	0.754935i
$844$		0			0
$845$	−0.750612	−	1.34339i	−0.0258218	−	0.0462139i
$846$		0			0
$847$	20.2110	+	14.1532i	0.694457	+	0.486311i
$848$		0			0
$849$	13.4066	+	41.2613i	0.460113	+	1.41608i
$850$		0			0
$851$	−8.08567	+	5.87458i	−0.277173	+	0.201378i
$852$		0			0
$853$	14.6353	+	4.75529i	0.501103	+	0.162818i	0.548652	−	0.836051i	$-0.315141\pi$
$853$	14.6353	+	4.75529i	0.501103	+	0.162818i	−0.0475493	+	0.998869i	$0.515141\pi$
$854$		0			0
$855$	9.65562	+	4.46273i	0.330215	+	0.152622i
$856$		0			0
$857$		−	36.1038i		−	1.23328i	−0.787245	−	0.616641i	$-0.788493\pi$
$857$		−	36.1038i		−	1.23328i	0.787245	−	0.616641i	$-0.211507\pi$
$858$		0			0
$859$	48.3509			1.64971			0.824855	−	0.565344i	$-0.191257\pi$
$859$	48.3509			1.64971			0.824855	+	0.565344i	$0.191257\pi$
$860$		0			0
$861$	−28.3680	−	20.6106i	−0.966781	−	0.702407i
$862$		0			0
$863$	−35.3685	−	11.4919i	−1.20396	−	0.391190i	−0.362743	−	0.931889i	$-0.618160\pi$
$863$	−35.3685	−	11.4919i	−1.20396	−	0.391190i	−0.841216	+	0.540699i	$0.818160\pi$
$864$		0			0
$865$	−3.45680	−	3.20169i	−0.117535	−	0.108861i
$866$		0			0
$867$	−22.6336	+	7.35411i	−0.768679	+	0.249759i
$868$		0			0
$869$	−11.0784	−	21.2826i	−0.375809	−	0.721962i
$870$		0			0
$871$	0.743664	+	2.28876i	0.0251981	+	0.0775517i
$872$		0			0
$873$	−1.19956	−	1.65105i	−0.0405990	−	0.0558797i
$874$		0			0
$875$	−24.1566	+	6.73660i	−0.816642	+	0.227739i
$876$		0			0
$877$	15.1609	−	20.8672i	0.511947	−	0.704634i	−0.472299	−	0.881438i	$-0.656576\pi$
$877$	15.1609	−	20.8672i	0.511947	−	0.704634i	0.984246	+	0.176804i	$0.0565758\pi$
$878$		0			0
$879$	27.7221			0.935044
$880$		0			0
$881$	−45.6820			−1.53906			−0.769532	−	0.638608i	$-0.779511\pi$
$881$	−45.6820			−1.53906			−0.769532	+	0.638608i	$0.779511\pi$
$882$		0			0
$883$	2.91912	−	4.01783i	0.0982364	−	0.135211i	−0.757069	−	0.653335i	$-0.773369\pi$
$883$	2.91912	−	4.01783i	0.0982364	−	0.135211i	0.855306	+	0.518124i	$0.173369\pi$
$884$		0			0
$885$	−1.50695	−	0.179850i	−0.0506556	−	0.00604560i
$886$		0			0
$887$	−17.0006	−	23.3994i	−0.570826	−	0.785674i	0.421827	−	0.906677i	$-0.361389\pi$
$887$	−17.0006	−	23.3994i	−0.570826	−	0.785674i	−0.992652	+	0.121002i	$0.961389\pi$
$888$		0			0
$889$	−1.68459	−	5.18463i	−0.0564993	−	0.173887i
$890$		0			0
$891$	25.3155	−	25.7600i	0.848100	−	0.862994i
$892$		0			0
$893$	60.4033	−	19.6262i	2.02132	−	0.656766i
$894$		0			0
$895$	−7.63365	+	8.24189i	−0.255165	+	0.275496i
$896$		0			0
$897$	26.7811	+	8.70172i	0.894196	+	0.290542i
$898$		0			0
$899$	−0.104713	−	0.0760785i	−0.00349237	−	0.00253736i
$900$		0			0
$901$	−28.1559			−0.938010
$902$		0			0
$903$		−	37.2692i		−	1.24024i
$904$		0			0
$905$	31.7608	+	14.6795i	1.05577	+	0.487964i
$906$		0			0
$907$	−12.6041	−	4.09531i	−0.418511	−	0.135983i	0.0921887	−	0.995742i	$-0.470614\pi$
$907$	−12.6041	−	4.09531i	−0.418511	−	0.135983i	−0.510700	+	0.859759i	$0.670614\pi$
$908$		0			0
$909$	7.20435	−	5.23427i	0.238953	−	0.173610i
$910$		0			0
$911$	−4.24361	−	13.0605i	−0.140597	−	0.432713i	0.855822	−	0.517271i	$-0.173052\pi$
$911$	−4.24361	−	13.0605i	−0.140597	−	0.432713i	−0.996419	+	0.0845580i	$0.973052\pi$
$912$		0			0
$913$	−10.4364	−	1.55997i	−0.345395	−	0.0516276i
$914$		0			0
$915$	−6.68188	+	3.73348i	−0.220896	+	0.123425i
$916$		0			0
$917$	−2.09430	−	2.88256i	−0.0691600	−	0.0951906i
$918$		0			0
$919$	18.3494	−	56.4737i	0.605292	−	1.86290i	0.110517	−	0.993874i	$-0.464749\pi$
$919$	18.3494	−	56.4737i	0.605292	−	1.86290i	0.494774	−	0.869022i	$-0.335251\pi$
$920$		0			0
$921$	10.9750	+	7.97379i	0.361638	+	0.262745i
$922$		0			0
$923$			17.1950i			0.565981i
$924$		0			0
$925$	−4.93842	−	11.9885i	−0.162374	−	0.394179i
$926$		0			0
$927$	5.41635	−	7.45496i	0.177896	−	0.244853i
$928$		0			0
$929$	−6.05305	+	18.6294i	−0.198594	+	0.611210i	0.801322	+	0.598234i	$0.204131\pi$
$929$	−6.05305	+	18.6294i	−0.198594	+	0.611210i	−0.999916	+	0.0129763i	$0.995869\pi$
$930$		0			0
$931$	−8.42007	+	6.11754i	−0.275957	+	0.200494i
$932$		0			0
$933$	−10.3327	+	3.35730i	−0.338277	+	0.109913i
$934$		0			0
$935$	4.35541	−	15.9128i	0.142437	−	0.520406i
$936$		0			0
$937$	38.5608	−	12.5292i	1.25973	−	0.409310i	0.398329	−	0.917242i	$-0.369590\pi$
$937$	38.5608	−	12.5292i	1.25973	−	0.409310i	0.861397	+	0.507933i	$0.169590\pi$
$938$		0			0
$939$	−22.7376	+	16.5198i	−0.742012	+	0.539104i
$940$		0			0
$941$	−0.126602	+	0.389640i	−0.00412709	+	0.0127019i	−0.953099	−	0.302659i	$-0.902126\pi$
$941$	−0.126602	+	0.389640i	−0.00412709	+	0.0127019i	0.948972	+	0.315361i	$0.102126\pi$
$942$		0			0
$943$	17.9331	−	24.6828i	0.583982	−	0.803783i
$944$		0			0
$945$	20.4066	−	4.03843i	0.663826	−	0.131370i
$946$		0			0
$947$			2.45729i			0.0798511i	0.999203	+	0.0399256i	$0.0127121\pi$
$947$			2.45729i			0.0798511i	−0.999203	+	0.0399256i	$0.987288\pi$
$948$		0			0
$949$	26.5147	+	19.2640i	0.860703	+	0.625337i
$950$		0			0
$951$	−11.4033	+	35.0956i	−0.369776	+	1.13805i
$952$		0			0
$953$	−35.8704	−	49.3714i	−1.16196	−	1.59930i	−0.703742	−	0.710456i	$-0.748489\pi$
$953$	−35.8704	−	49.3714i	−1.16196	−	1.59930i	−0.458215	−	0.888841i	$-0.651511\pi$
$954$		0			0
$955$	−3.39842	−	6.08222i	−0.109970	−	0.196816i
$956$		0			0
$957$	−0.203675	−	1.21728i	−0.00658387	−	0.0393492i
$958$		0			0
$959$	12.9632	+	39.8965i	0.418603	+	1.28833i
$960$		0			0
$961$	24.6978	−	17.9440i	0.796705	−	0.578840i
$962$		0			0
$963$	−8.59754	−	2.79351i	−0.277052	−	0.0900196i
$964$		0			0
$965$	−9.04020	+	19.5595i	−0.291014	+	0.629642i
$966$		0			0
$967$			17.1997i			0.553106i	0.960999	+	0.276553i	$0.0891921\pi$
$967$			17.1997i			0.553106i	−0.960999	+	0.276553i	$0.910808\pi$
$968$		0			0
$969$	−23.2258			−0.746119
$970$		0			0
$971$	22.0125	+	15.9930i	0.706415	+	0.513241i	0.882015	−	0.471221i	$-0.156187\pi$
$971$	22.0125	+	15.9930i	0.706415	+	0.513241i	−0.175600	+	0.984462i	$0.556187\pi$
$972$		0			0
$973$	−24.8046	−	8.05950i	−0.795198	−	0.258376i
$974$		0			0
$975$	−19.1482	+	31.1106i	−0.613234	+	0.996338i
$976$		0			0
$977$	−18.2339	+	5.92454i	−0.583353	+	0.189543i	−0.585802	−	0.810454i	$-0.699220\pi$
$977$	−18.2339	+	5.92454i	−0.583353	+	0.189543i	0.00244904	+	0.999997i	$0.499220\pi$
$978$		0			0
$979$	−32.4562	+	5.43055i	−1.03730	+	0.173561i
$980$		0			0
$981$	−2.44732	−	7.53207i	−0.0781369	−	0.240481i
$982$		0			0
$983$	−14.1835	−	19.5219i	−0.452384	−	0.622653i	0.520524	−	0.853847i	$-0.325737\pi$
$983$	−14.1835	−	19.5219i	−0.452384	−	0.622653i	−0.972908	+	0.231194i	$0.925737\pi$
$984$		0			0
$985$	−31.9667	−	3.81513i	−1.01854	−	0.121560i
$986$		0			0
$987$	−31.2781	+	43.0506i	−0.995593	+	1.37032i
$988$		0			0
$989$	32.4276			1.03114
$990$		0			0
$991$	−27.7081			−0.880177			−0.440089	−	0.897954i	$-0.645053\pi$
$991$	−27.7081			−0.880177			−0.440089	+	0.897954i	$0.645053\pi$
$992$		0			0
$993$	−0.543521	+	0.748092i	−0.0172481	+	0.0237400i
$994$		0			0
$995$	3.92123	−	32.8556i	0.124311	−	1.04159i
$996$		0			0
$997$	19.6856	+	27.0950i	0.623451	+	0.858106i	0.997598	−	0.0692628i	$-0.0220647\pi$
$997$	19.6856	+	27.0950i	0.623451	+	0.858106i	−0.374148	+	0.927369i	$0.622065\pi$
$998$		0			0
$999$	3.32350	+	10.2287i	0.105151	+	0.323621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cd.c.49.4		16
4.3	odd	2		55.2.j.a.49.4	yes	16
5.4	even	2	inner	880.2.cd.c.49.1		16
11.9	even	5	inner	880.2.cd.c.449.1		16
12.11	even	2		495.2.ba.a.379.1		16
20.3	even	4		275.2.h.d.126.1		16
20.7	even	4		275.2.h.d.126.4		16
20.19	odd	2		55.2.j.a.49.1	yes	16
44.3	odd	10		605.2.b.g.364.2		8
44.7	even	10		605.2.j.g.124.1		16
44.15	odd	10		605.2.j.h.124.4		16
44.19	even	10		605.2.b.f.364.7		8
44.27	odd	10		605.2.j.h.444.1		16
44.31	odd	10		55.2.j.a.9.1	✓	16
44.35	even	10		605.2.j.d.9.4		16
44.39	even	10		605.2.j.g.444.4		16
44.43	even	2		605.2.j.d.269.1		16
55.9	even	10	inner	880.2.cd.c.449.4		16
60.59	even	2		495.2.ba.a.379.4		16
132.119	even	10		495.2.ba.a.64.4		16
220.3	even	20		3025.2.a.bl.1.2		8
220.19	even	10		605.2.b.f.364.2		8
220.39	even	10		605.2.j.g.444.1		16
220.47	even	20		3025.2.a.bl.1.7		8
220.59	odd	10		605.2.j.h.124.1		16
220.63	odd	20		3025.2.a.bk.1.7		8
220.79	even	10		605.2.j.d.9.1		16
220.107	odd	20		3025.2.a.bk.1.2		8
220.119	odd	10		55.2.j.a.9.4	yes	16
220.139	even	10		605.2.j.g.124.4		16
220.159	odd	10		605.2.j.h.444.4		16
220.163	even	20		275.2.h.d.251.1		16
220.179	odd	10		605.2.b.g.364.7		8
220.207	even	20		275.2.h.d.251.4		16
220.219	even	2		605.2.j.d.269.4		16
660.119	even	10		495.2.ba.a.64.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	44.31	odd	10
55.2.j.a.9.4	yes	16	220.119	odd	10
55.2.j.a.49.1	yes	16	20.19	odd	2
55.2.j.a.49.4	yes	16	4.3	odd	2
275.2.h.d.126.1		16	20.3	even	4
275.2.h.d.126.4		16	20.7	even	4
275.2.h.d.251.1		16	220.163	even	20
275.2.h.d.251.4		16	220.207	even	20
495.2.ba.a.64.1		16	660.119	even	10
495.2.ba.a.64.4		16	132.119	even	10
495.2.ba.a.379.1		16	12.11	even	2
495.2.ba.a.379.4		16	60.59	even	2
605.2.b.f.364.2		8	220.19	even	10
605.2.b.f.364.7		8	44.19	even	10
605.2.b.g.364.2		8	44.3	odd	10
605.2.b.g.364.7		8	220.179	odd	10
605.2.j.d.9.1		16	220.79	even	10
605.2.j.d.9.4		16	44.35	even	10
605.2.j.d.269.1		16	44.43	even	2
605.2.j.d.269.4		16	220.219	even	2
605.2.j.g.124.1		16	44.7	even	10
605.2.j.g.124.4		16	220.139	even	10
605.2.j.g.444.1		16	220.39	even	10
605.2.j.g.444.4		16	44.39	even	10
605.2.j.h.124.1		16	220.59	odd	10
605.2.j.h.124.4		16	44.15	odd	10
605.2.j.h.444.1		16	44.27	odd	10
605.2.j.h.444.4		16	220.159	odd	10
880.2.cd.c.49.1		16	5.4	even	2	inner
880.2.cd.c.49.4		16	1.1	even	1	trivial
880.2.cd.c.449.1		16	11.9	even	5	inner
880.2.cd.c.449.4		16	55.9	even	10	inner
3025.2.a.bk.1.2		8	220.107	odd	20
3025.2.a.bk.1.7		8	220.63	odd	20
3025.2.a.bl.1.2		8	220.3	even	20
3025.2.a.bl.1.7		8	220.47	even	20

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.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16075 - 1.59764i) q^{3} +(0.264988 - 2.22031i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-0.278050 - 0.855749i) q^{9} +O(q^{10})\)	\(q+(1.16075 - 1.59764i) q^{3} +(0.264988 - 2.22031i) q^{5} +(1.31845 + 1.81468i) q^{7} +(-0.278050 - 0.855749i) q^{9} +(3.27115 - 0.547326i) q^{11} +(3.51868 - 1.14329i) q^{13} +(-3.23967 - 3.00058i) q^{15} +(2.11573 + 0.687441i) q^{17} +(-4.27714 - 3.10753i) q^{19} +4.42960 q^{21} +3.85415i q^{23} +(-4.85956 - 1.17671i) q^{25} +(3.94448 + 1.28164i) q^{27} +(0.152450 - 0.110762i) q^{29} +(-0.212253 - 0.653249i) q^{31} +(2.92256 - 5.86142i) q^{33} +(4.37854 - 2.44649i) q^{35} +(1.52422 + 2.09791i) q^{37} +(2.25775 - 6.94864i) q^{39} +(-6.40421 - 4.65293i) q^{41} -8.41368i q^{43} +(-1.97371 + 0.390594i) q^{45} +(-7.06117 + 9.71886i) q^{47} +(0.608337 - 1.87227i) q^{49} +(3.55411 - 2.58222i) q^{51} +(-12.0371 + 3.91110i) q^{53} +(-0.348420 - 7.40801i) q^{55} +(-9.92940 + 3.22626i) q^{57} +(0.278050 - 0.202015i) q^{59} +(0.535643 - 1.64854i) q^{61} +(1.18632 - 1.63283i) q^{63} +(-1.60605 - 8.11552i) q^{65} +0.650461i q^{67} +(6.15754 + 4.47371i) q^{69} +(-1.43619 + 4.42013i) q^{71} +(5.20684 + 7.16660i) q^{73} +(-7.52070 + 6.39795i) q^{75} +(5.30606 + 5.21449i) q^{77} +(-2.23551 - 6.88019i) q^{79} +(8.80999 - 6.40083i) q^{81} +(-3.02593 - 0.983185i) q^{83} +(2.08698 - 4.51541i) q^{85} -0.372127i q^{87} -9.92195 q^{89} +(6.71389 + 4.87793i) q^{91} +(-1.29003 - 0.419156i) q^{93} +(-8.03307 + 8.67314i) q^{95} +(2.15710 - 0.700884i) q^{97} +(-1.37792 - 2.64710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{5} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^5 + 2 * q^9	\( 16 q - 2 q^{5} + 2 q^{9} + 6 q^{11} + 16 q^{15} - 6 q^{19} + 8 q^{21} - 16 q^{25} + 2 q^{29} - 8 q^{31} - 22 q^{35} - 30 q^{39} - 52 q^{41} + 12 q^{45} - 10 q^{49} + 42 q^{51} + 8 q^{55} - 2 q^{59} - 40 q^{61} - 40 q^{65} + 26 q^{69} - 36 q^{71} + 20 q^{75} - 38 q^{79} + 68 q^{81} + 58 q^{85} + 24 q^{89} + 20 q^{91} - 48 q^{95} + 72 q^{99}+O(q^{100}) \) 16 * q - 2 * q^5 + 2 * q^9 + 6 * q^11 + 16 * q^15 - 6 * q^19 + 8 * q^21 - 16 * q^25 + 2 * q^29 - 8 * q^31 - 22 * q^35 - 30 * q^39 - 52 * q^41 + 12 * q^45 - 10 * q^49 + 42 * q^51 + 8 * q^55 - 2 * q^59 - 40 * q^61 - 40 * q^65 + 26 * q^69 - 36 * q^71 + 20 * q^75 - 38 * q^79 + 68 * q^81 + 58 * q^85 + 24 * q^89 + 20 * q^91 - 48 * q^95 + 72 * q^99

Introduction

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