LMFDB - Embedded newform 320.3.i.a.273.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(177,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("320.177");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.i (of order $4$, degree $2$, 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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.11
Character	$\chi$	$=$	320.273
Dual form			320.3.i.a.177.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.119786i q^{3} +(-3.85807 + 3.18046i) q^{5} +(-4.73972 - 4.73972i) q^{7} +8.98565 q^{9} +O(q^{10})$	\(q+0.119786i q^{3} +(-3.85807 + 3.18046i) q^{5} +(-4.73972 - 4.73972i) q^{7} +8.98565 q^{9} +(-2.49487 + 2.49487i) q^{11} -18.4567i q^{13} +(-0.380972 - 0.462141i) q^{15} +(10.7165 - 10.7165i) q^{17} +(-0.469722 + 0.469722i) q^{19} +(0.567750 - 0.567750i) q^{21} +(27.9445 - 27.9445i) q^{23} +(4.76941 - 24.5408i) q^{25} +2.15442i q^{27} +(15.6079 - 15.6079i) q^{29} -49.2667 q^{31} +(-0.298849 - 0.298849i) q^{33} +(33.3606 + 3.21171i) q^{35} +29.1310i q^{37} +2.21084 q^{39} -16.4684i q^{41} +4.48974 q^{43} +(-34.6673 + 28.5785i) q^{45} +(40.6666 - 40.6666i) q^{47} -4.07009i q^{49} +(1.28369 + 1.28369i) q^{51} -78.7038 q^{53} +(1.69056 - 17.5602i) q^{55} +(-0.0562658 - 0.0562658i) q^{57} +(-3.26583 - 3.26583i) q^{59} +(-23.0393 - 23.0393i) q^{61} +(-42.5895 - 42.5895i) q^{63} +(58.7006 + 71.2071i) q^{65} +58.9247 q^{67} +(3.34734 + 3.34734i) q^{69} -76.8059i q^{71} +(18.7472 - 18.7472i) q^{73} +(2.93964 + 0.571306i) q^{75} +23.6499 q^{77} +141.697i q^{79} +80.6128 q^{81} +120.053i q^{83} +(-7.26169 + 75.4286i) q^{85} +(1.86960 + 1.86960i) q^{87} -87.7260 q^{89} +(-87.4794 + 87.4794i) q^{91} -5.90143i q^{93} +(0.318290 - 3.30615i) q^{95} +(34.6438 - 34.6438i) q^{97} +(-22.4180 + 22.4180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^5 - 108 * q^9	$ 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 380 * q^95 - 4 * q^97 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.119786i			0.0399285i	0.999801	+	0.0199643i	$0.00635524\pi$
$3$			0.119786i			0.0399285i	−0.999801	+	0.0199643i	$0.993645\pi$
$4$		0			0
$5$	−3.85807	+	3.18046i	−0.771614	+	0.636091i
$5$	−3.85807	+	3.18046i	−0.771614	+	0.636091i
$6$		0			0
$7$	−4.73972	−	4.73972i	−0.677103	−	0.677103i	0.282241	−	0.959344i	$-0.408922\pi$
$7$	−4.73972	−	4.73972i	−0.677103	−	0.677103i	−0.959344	+	0.282241i	$0.908922\pi$
$8$		0			0
$9$	8.98565			0.998406
$10$		0			0
$11$	−2.49487	+	2.49487i	−0.226806	+	0.226806i	−0.811357	−	0.584551i	$-0.801271\pi$
$11$	−2.49487	+	2.49487i	−0.226806	+	0.226806i	0.584551	+	0.811357i	$0.301271\pi$
$12$		0			0
$13$		−	18.4567i		−	1.41974i	−0.704331	−	0.709871i	$-0.748753\pi$
$13$		−	18.4567i		−	1.41974i	0.704331	−	0.709871i	$-0.251247\pi$
$14$		0			0
$15$	−0.380972	−	0.462141i	−0.0253982	−	0.0308094i
$16$		0			0
$17$	10.7165	−	10.7165i	0.630385	−	0.630385i	−0.317780	−	0.948165i	$-0.602937\pi$
$17$	10.7165	−	10.7165i	0.630385	−	0.630385i	0.948165	+	0.317780i	$0.102937\pi$
$18$		0			0
$19$	−0.469722	+	0.469722i	−0.0247222	+	0.0247222i	−0.719360	−	0.694638i	$-0.755565\pi$
$19$	−0.469722	+	0.469722i	−0.0247222	+	0.0247222i	0.694638	+	0.719360i	$0.255565\pi$
$20$		0			0
$21$	0.567750	−	0.567750i	0.0270357	−	0.0270357i
$22$		0			0
$23$	27.9445	−	27.9445i	1.21498	−	1.21498i	0.245608	−	0.969369i	$-0.421012\pi$
$23$	27.9445	−	27.9445i	1.21498	−	1.21498i	0.969369	−	0.245608i	$-0.0789876\pi$
$24$		0			0
$25$	4.76941	−	24.5408i	0.190776	−	0.981634i
$26$		0			0
$27$			2.15442i			0.0797934i
$28$		0			0
$29$	15.6079	−	15.6079i	0.538203	−	0.538203i	−0.384798	−	0.923001i	$-0.625729\pi$
$29$	15.6079	−	15.6079i	0.538203	−	0.538203i	0.923001	+	0.384798i	$0.125729\pi$
$30$		0			0
$31$	−49.2667			−1.58925			−0.794624	−	0.607102i	$-0.792332\pi$
$31$	−49.2667			−1.58925			−0.794624	+	0.607102i	$0.792332\pi$
$32$		0			0
$33$	−0.298849	−	0.298849i	−0.00905602	−	0.00905602i
$34$		0			0
$35$	33.3606	+	3.21171i	0.953161	+	0.0917630i
$36$		0			0
$37$			29.1310i			0.787325i	0.919255	+	0.393662i	$0.128792\pi$
$37$			29.1310i			0.787325i	−0.919255	+	0.393662i	$0.871208\pi$
$38$		0			0
$39$	2.21084			0.0566882
$40$		0			0
$41$		−	16.4684i		−	0.401669i	−0.979625	−	0.200834i	$-0.935635\pi$
$41$		−	16.4684i		−	0.401669i	0.979625	−	0.200834i	$-0.0643653\pi$
$42$		0			0
$43$	4.48974			0.104413			0.0522063	−	0.998636i	$-0.483375\pi$
$43$	4.48974			0.104413			0.0522063	+	0.998636i	$0.483375\pi$
$44$		0			0
$45$	−34.6673	+	28.5785i	−0.770384	+	0.635077i
$46$		0			0
$47$	40.6666	−	40.6666i	0.865246	−	0.865246i	−0.126695	−	0.991942i	$-0.540437\pi$
$47$	40.6666	−	40.6666i	0.865246	−	0.865246i	0.991942	+	0.126695i	$0.0404370\pi$
$48$		0			0
$49$		−	4.07009i		−	0.0830632i
$50$		0			0
$51$	1.28369	+	1.28369i	0.0251703	+	0.0251703i
$52$		0			0
$53$	−78.7038			−1.48498			−0.742488	−	0.669859i	$-0.766354\pi$
$53$	−78.7038			−1.48498			−0.742488	+	0.669859i	$0.766354\pi$
$54$		0			0
$55$	1.69056	−	17.5602i	0.0307374	−	0.319276i
$56$		0			0
$57$	−0.0562658	−	0.0562658i	−0.000987120	−	0.000987120i
$58$		0			0
$59$	−3.26583	−	3.26583i	−0.0553530	−	0.0553530i	0.678888	−	0.734241i	$-0.262462\pi$
$59$	−3.26583	−	3.26583i	−0.0553530	−	0.0553530i	−0.734241	+	0.678888i	$0.762462\pi$
$60$		0			0
$61$	−23.0393	−	23.0393i	−0.377694	−	0.377694i	0.492576	−	0.870269i	$-0.336055\pi$
$61$	−23.0393	−	23.0393i	−0.377694	−	0.377694i	−0.870269	+	0.492576i	$0.836055\pi$
$62$		0			0
$63$	−42.5895	−	42.5895i	−0.676023	−	0.676023i
$64$		0			0
$65$	58.7006	+	71.2071i	0.903086	+	1.09549i
$66$		0			0
$67$	58.9247			0.879474			0.439737	−	0.898127i	$-0.355072\pi$
$67$	58.9247			0.879474			0.439737	+	0.898127i	$0.355072\pi$
$68$		0			0
$69$	3.34734	+	3.34734i	0.0485122	+	0.0485122i
$70$		0			0
$71$		−	76.8059i		−	1.08177i	−0.841096	−	0.540886i	$-0.818089\pi$
$71$		−	76.8059i		−	1.08177i	0.841096	−	0.540886i	$-0.181911\pi$
$72$		0			0
$73$	18.7472	−	18.7472i	0.256811	−	0.256811i	−0.566945	−	0.823756i	$-0.691875\pi$
$73$	18.7472	−	18.7472i	0.256811	−	0.256811i	0.823756	+	0.566945i	$0.191875\pi$
$74$		0			0
$75$	2.93964	+	0.571306i	0.0391952	+	0.00761742i
$76$		0			0
$77$	23.6499			0.307142
$78$		0			0
$79$			141.697i			1.79363i	0.442407	+	0.896815i	$0.354125\pi$
$79$			141.697i			1.79363i	−0.442407	+	0.896815i	$0.645875\pi$
$80$		0			0
$81$	80.6128			0.995220
$82$		0			0
$83$			120.053i			1.44642i	0.690628	+	0.723210i	$0.257334\pi$
$83$			120.053i			1.44642i	−0.690628	+	0.723210i	$0.742666\pi$
$84$		0			0
$85$	−7.26169	+	75.4286i	−0.0854316	+	0.887396i
$86$		0			0
$87$	1.86960	+	1.86960i	0.0214897	+	0.0214897i
$88$		0			0
$89$	−87.7260			−0.985686			−0.492843	−	0.870118i	$-0.664042\pi$
$89$	−87.7260			−0.985686			−0.492843	+	0.870118i	$0.664042\pi$
$90$		0			0
$91$	−87.4794	+	87.4794i	−0.961312	+	0.961312i
$92$		0			0
$93$		−	5.90143i		−	0.0634563i
$94$		0			0
$95$	0.318290	−	3.30615i	0.00335043	−	0.0348015i
$96$		0			0
$97$	34.6438	−	34.6438i	0.357153	−	0.357153i	−0.505609	−	0.862762i	$-0.668732\pi$
$97$	34.6438	−	34.6438i	0.357153	−	0.357153i	0.862762	+	0.505609i	$0.168732\pi$
$98$		0			0
$99$	−22.4180	+	22.4180i	−0.226444	+	0.226444i
$100$		0			0
$101$	−29.5707	+	29.5707i	−0.292780	+	0.292780i	−0.838177	−	0.545398i	$-0.816379\pi$
$101$	−29.5707	+	29.5707i	−0.292780	+	0.292780i	0.545398	+	0.838177i	$0.316379\pi$
$102$		0			0
$103$	−48.5504	+	48.5504i	−0.471363	+	0.471363i	−0.902356	−	0.430992i	$-0.858164\pi$
$103$	−48.5504	+	48.5504i	−0.471363	+	0.471363i	0.430992	+	0.902356i	$0.358164\pi$
$104$		0			0
$105$	−0.384716	+	3.99612i	−0.00366396	+	0.0380583i
$106$		0			0
$107$		−	62.1016i		−	0.580389i	−0.956968	−	0.290194i	$-0.906280\pi$
$107$		−	62.1016i		−	0.580389i	0.956968	−	0.290194i	$-0.0937200\pi$
$108$		0			0
$109$	−31.6457	+	31.6457i	−0.290327	+	0.290327i	−0.837209	−	0.546882i	$-0.815814\pi$
$109$	−31.6457	+	31.6457i	−0.290327	+	0.290327i	0.546882	+	0.837209i	$0.315814\pi$
$110$		0			0
$111$	−3.48947			−0.0314367
$112$		0			0
$113$	−56.1211	−	56.1211i	−0.496647	−	0.496647i	0.413745	−	0.910393i	$-0.364220\pi$
$113$	−56.1211	−	56.1211i	−0.496647	−	0.496647i	−0.910393	+	0.413745i	$0.864220\pi$
$114$		0			0
$115$	−18.9356	+	196.688i	−0.164657	+	1.71033i
$116$		0			0
$117$		−	165.845i		−	1.41748i
$118$		0			0
$119$	−101.587			−0.853671
$120$		0			0
$121$			108.551i			0.897118i
$122$		0			0
$123$	1.97268			0.0160380
$124$		0			0
$125$	59.6503	+	109.849i	0.477202	+	0.878793i
$126$		0			0
$127$	60.1440	−	60.1440i	0.473575	−	0.473575i	−0.429495	−	0.903069i	$-0.641308\pi$
$127$	60.1440	−	60.1440i	0.473575	−	0.473575i	0.903069	+	0.429495i	$0.141308\pi$
$128$		0			0
$129$			0.537806i			0.00416904i
$130$		0			0
$131$	−129.876	−	129.876i	−0.991422	−	0.991422i	0.00854147	−	0.999964i	$-0.497281\pi$
$131$	−129.876	−	129.876i	−0.991422	−	0.991422i	−0.999964	+	0.00854147i	$0.997281\pi$
$132$		0			0
$133$	4.45270			0.0334789
$134$		0			0
$135$	−6.85204	−	8.31191i	−0.0507558	−	0.0615697i
$136$		0			0
$137$	69.8267	+	69.8267i	0.509684	+	0.509684i	0.914429	−	0.404745i	$-0.132640\pi$
$137$	69.8267	+	69.8267i	0.509684	+	0.509684i	−0.404745	+	0.914429i	$0.632640\pi$
$138$		0			0
$139$	16.8371	+	16.8371i	0.121130	+	0.121130i	0.765073	−	0.643943i	$-0.222703\pi$
$139$	16.8371	+	16.8371i	0.121130	+	0.121130i	−0.643943	+	0.765073i	$0.722703\pi$
$140$		0			0
$141$	4.87127	+	4.87127i	0.0345480	+	0.0345480i
$142$		0			0
$143$	46.0469	+	46.0469i	0.322006	+	0.322006i
$144$		0			0
$145$	−10.5761	+	109.857i	−0.0729389	+	0.757631i
$146$		0			0
$147$	0.487538			0.00331659
$148$		0			0
$149$	126.048	+	126.048i	0.845963	+	0.845963i	0.989627	−	0.143664i	$-0.0458883\pi$
$149$	126.048	+	126.048i	0.845963	+	0.845963i	−0.143664	+	0.989627i	$0.545888\pi$
$150$		0			0
$151$			170.000i			1.12583i	0.826516	+	0.562914i	$0.190320\pi$
$151$			170.000i			1.12583i	−0.826516	+	0.562914i	$0.809680\pi$
$152$		0			0
$153$	96.2951	−	96.2951i	0.629380	−	0.629380i
$154$		0			0
$155$	190.074	−	156.690i	1.22629	−	1.01091i
$156$		0			0
$157$	12.1854			0.0776137			0.0388069	−	0.999247i	$-0.487644\pi$
$157$	12.1854			0.0776137			0.0388069	+	0.999247i	$0.487644\pi$
$158$		0			0
$159$		−	9.42757i		−	0.0592929i
$160$		0			0
$161$	−264.898			−1.64533
$162$		0			0
$163$		−	285.780i		−	1.75325i	−0.481170	−	0.876627i	$-0.659788\pi$
$163$		−	285.780i		−	1.75325i	0.481170	−	0.876627i	$-0.340212\pi$
$164$		0			0
$165$	2.10345	+	0.202504i	0.0127482	+	0.00122730i
$166$		0			0
$167$	102.579	+	102.579i	0.614248	+	0.614248i	0.944050	−	0.329802i	$-0.106982\pi$
$167$	102.579	+	102.579i	0.614248	+	0.614248i	−0.329802	+	0.944050i	$0.606982\pi$
$168$		0			0
$169$	−171.648			−1.01567
$170$		0			0
$171$	−4.22075	+	4.22075i	−0.0246828	+	0.0246828i
$172$		0			0
$173$		−	68.3056i		−	0.394830i	−0.980320	−	0.197415i	$-0.936745\pi$
$173$		−	68.3056i		−	0.394830i	0.980320	−	0.197415i	$-0.0632546\pi$
$174$		0			0
$175$	−138.922	+	93.7110i	−0.793842	+	0.535492i
$176$		0			0
$177$	0.391199	−	0.391199i	0.00221016	−	0.00221016i
$178$		0			0
$179$	165.892	−	165.892i	0.926773	−	0.926773i	−0.0707227	−	0.997496i	$-0.522531\pi$
$179$	165.892	−	165.892i	0.926773	−	0.926773i	0.997496	+	0.0707227i	$0.0225305\pi$
$180$		0			0
$181$	101.633	−	101.633i	0.561506	−	0.561506i	−0.368229	−	0.929735i	$-0.620036\pi$
$181$	101.633	−	101.633i	0.561506	−	0.561506i	0.929735	+	0.368229i	$0.120036\pi$
$182$		0			0
$183$	2.75978	−	2.75978i	0.0150807	−	0.0150807i
$184$		0			0
$185$	−92.6499	−	112.389i	−0.500810	−	0.607511i
$186$		0			0
$187$			53.4726i			0.285950i
$188$		0			0
$189$	10.2114	−	10.2114i	0.0540283	−	0.0540283i
$190$		0			0
$191$	144.454			0.756301			0.378151	−	0.925744i	$-0.376560\pi$
$191$	144.454			0.756301			0.378151	+	0.925744i	$0.376560\pi$
$192$		0			0
$193$	−32.7772	−	32.7772i	−0.169830	−	0.169830i	0.617075	−	0.786905i	$-0.288318\pi$
$193$	−32.7772	−	32.7772i	−0.169830	−	0.169830i	−0.786905	+	0.617075i	$0.788318\pi$
$194$		0			0
$195$	−8.52958	+	7.03148i	−0.0437414	+	0.0360589i
$196$		0			0
$197$		−	335.205i		−	1.70155i	−0.525530	−	0.850775i	$-0.676133\pi$
$197$		−	335.205i		−	1.70155i	0.525530	−	0.850775i	$-0.323867\pi$
$198$		0			0
$199$	184.734			0.928313			0.464156	−	0.885753i	$-0.346358\pi$
$199$	184.734			0.928313			0.464156	+	0.885753i	$0.346358\pi$
$200$		0			0
$201$			7.05833i			0.0351161i
$202$		0			0
$203$	−147.954			−0.728838
$204$		0			0
$205$	52.3771	+	63.5363i	0.255498	+	0.309933i
$206$		0			0
$207$	251.099	−	251.099i	1.21304	−	1.21304i
$208$		0			0
$209$		−	2.34378i		−	0.0112143i
$210$		0			0
$211$	−187.999	−	187.999i	−0.890989	−	0.890989i	0.103627	−	0.994616i	$-0.466955\pi$
$211$	−187.999	−	187.999i	−0.890989	−	0.890989i	−0.994616	+	0.103627i	$0.966955\pi$
$212$		0			0
$213$	9.20023			0.0431936
$214$		0			0
$215$	−17.3217	+	14.2794i	−0.0805662	+	0.0664159i
$216$		0			0
$217$	233.510	+	233.510i	1.07608	+	1.07608i
$218$		0			0
$219$	2.24564	+	2.24564i	0.0102541	+	0.0102541i
$220$		0			0
$221$	−197.791	−	197.791i	−0.894984	−	0.894984i
$222$		0			0
$223$	−282.322	−	282.322i	−1.26602	−	1.26602i	−0.948128	−	0.317889i	$-0.897026\pi$
$223$	−282.322	−	282.322i	−1.26602	−	1.26602i	−0.317889	−	0.948128i	$-0.602974\pi$
$224$		0			0
$225$	42.8563	−	220.515i	0.190472	−	0.980069i
$226$		0			0
$227$	−146.872			−0.647015			−0.323507	−	0.946226i	$-0.604862\pi$
$227$	−146.872			−0.647015			−0.323507	+	0.946226i	$0.604862\pi$
$228$		0			0
$229$	194.697	+	194.697i	0.850205	+	0.850205i	0.990158	−	0.139953i	$-0.0446953\pi$
$229$	194.697	+	194.697i	0.850205	+	0.850205i	−0.139953	+	0.990158i	$0.544695\pi$
$230$		0			0
$231$			2.83292i			0.0122637i
$232$		0			0
$233$	−87.0218	+	87.0218i	−0.373484	+	0.373484i	−0.868745	−	0.495260i	$-0.835073\pi$
$233$	−87.0218	+	87.0218i	−0.373484	+	0.373484i	0.495260	+	0.868745i	$0.335073\pi$
$234$		0			0
$235$	−27.5563	+	286.233i	−0.117261	+	1.21801i
$236$		0			0
$237$	−16.9732			−0.0716169
$238$		0			0
$239$			334.837i			1.40099i	0.713657	+	0.700495i	$0.247037\pi$
$239$			334.837i			1.40099i	−0.713657	+	0.700495i	$0.752963\pi$
$240$		0			0
$241$	−378.876			−1.57210			−0.786049	−	0.618164i	$-0.787877\pi$
$241$	−378.876			−1.57210			−0.786049	+	0.618164i	$0.787877\pi$
$242$		0			0
$243$			29.0460i			0.119531i
$244$		0			0
$245$	12.9448	+	15.7027i	0.0528357	+	0.0640927i
$246$		0			0
$247$	8.66949	+	8.66949i	0.0350991	+	0.0350991i
$248$		0			0
$249$	−14.3806			−0.0577534
$250$		0			0
$251$	181.937	−	181.937i	0.724849	−	0.724849i	−0.244740	−	0.969589i	$-0.578703\pi$
$251$	181.937	−	181.937i	0.724849	−	0.724849i	0.969589	+	0.244740i	$0.0787026\pi$
$252$		0			0
$253$			139.435i			0.551128i
$254$		0			0
$255$	−9.03526	−	0.869845i	−0.0354324	−	0.00341116i
$256$		0			0
$257$	38.2528	−	38.2528i	0.148843	−	0.148843i	−0.628758	−	0.777601i	$-0.716436\pi$
$257$	38.2528	−	38.2528i	0.148843	−	0.148843i	0.777601	+	0.628758i	$0.216436\pi$
$258$		0			0
$259$	138.073	−	138.073i	0.533100	−	0.533100i
$260$		0			0
$261$	140.247	−	140.247i	0.537345	−	0.537345i
$262$		0			0
$263$	165.962	−	165.962i	0.631034	−	0.631034i	−0.317294	−	0.948327i	$-0.602774\pi$
$263$	165.962	−	165.962i	0.631034	−	0.631034i	0.948327	+	0.317294i	$0.102774\pi$
$264$		0			0
$265$	303.645	−	250.314i	1.14583	−	0.944580i
$266$		0			0
$267$		−	10.5083i		−	0.0393570i
$268$		0			0
$269$	310.294	−	310.294i	1.15351	−	1.15351i	0.167665	−	0.985844i	$-0.446377\pi$
$269$	310.294	−	310.294i	1.15351	−	1.15351i	0.985844	−	0.167665i	$-0.0536228\pi$
$270$		0			0
$271$	272.486			1.00548			0.502741	−	0.864437i	$-0.332325\pi$
$271$	272.486			1.00548			0.502741	+	0.864437i	$0.332325\pi$
$272$		0			0
$273$	−10.4788	−	10.4788i	−0.0383838	−	0.0383838i
$274$		0			0
$275$	49.3270	+	73.1251i	0.179371	+	0.265910i
$276$		0			0
$277$			143.172i			0.516868i	0.966029	+	0.258434i	$0.0832064\pi$
$277$			143.172i			0.516868i	−0.966029	+	0.258434i	$0.916794\pi$
$278$		0			0
$279$	−442.693			−1.58671
$280$		0			0
$281$			139.408i			0.496115i	0.968745	+	0.248057i	$0.0797921\pi$
$281$			139.408i			0.496115i	−0.968745	+	0.248057i	$0.920208\pi$
$282$		0			0
$283$	336.283			1.18828			0.594140	−	0.804362i	$-0.297493\pi$
$283$	336.283			1.18828			0.594140	+	0.804362i	$0.297493\pi$
$284$		0			0
$285$	0.396029	+	0.0381266i	0.00138957	+	0.000133777i
$286$		0			0
$287$	−78.0557	+	78.0557i	−0.271971	+	0.271971i
$288$		0			0
$289$			59.3116i			0.205230i
$290$		0			0
$291$	4.14983	+	4.14983i	0.0142606	+	0.0142606i
$292$		0			0
$293$	−33.1195			−0.113036			−0.0565179	−	0.998402i	$-0.518000\pi$
$293$	−33.1195			−0.113036			−0.0565179	+	0.998402i	$0.518000\pi$
$294$		0			0
$295$	22.9866	+	2.21297i	0.0779207	+	0.00750161i
$296$		0			0
$297$	−5.37499	−	5.37499i	−0.0180976	−	0.0180976i
$298$		0			0
$299$	−515.762	−	515.762i	−1.72496	−	1.72496i
$300$		0			0
$301$	−21.2801	−	21.2801i	−0.0706981	−	0.0706981i
$302$		0			0
$303$	−3.54215	−	3.54215i	−0.0116903	−	0.0116903i
$304$		0			0
$305$	162.163	+	15.6118i	0.531681	+	0.0511862i
$306$		0			0
$307$	−479.642			−1.56235			−0.781176	−	0.624310i	$-0.785380\pi$
$307$	−479.642			−1.56235			−0.781176	+	0.624310i	$0.785380\pi$
$308$		0			0
$309$	−5.81564	−	5.81564i	−0.0188208	−	0.0188208i
$310$		0			0
$311$			328.043i			1.05480i	0.849617	+	0.527401i	$0.176833\pi$
$311$			328.043i			1.05480i	−0.849617	+	0.527401i	$0.823167\pi$
$312$		0			0
$313$	90.2171	−	90.2171i	0.288233	−	0.288233i	−0.548148	−	0.836381i	$-0.684667\pi$
$313$	90.2171	−	90.2171i	0.288233	−	0.288233i	0.836381	+	0.548148i	$0.184667\pi$
$314$		0			0
$315$	299.767	+	28.8593i	0.951642	+	0.0916167i
$316$		0			0
$317$	324.328			1.02312			0.511558	−	0.859249i	$-0.329068\pi$
$317$	324.328			1.02312			0.511558	+	0.859249i	$0.329068\pi$
$318$		0			0
$319$			77.8792i			0.244135i
$320$		0			0
$321$	7.43887			0.0231741
$322$		0			0
$323$			10.0676i			0.0311690i
$324$		0			0
$325$	−452.942	−	88.0274i	−1.39367	−	0.270853i
$326$		0			0
$327$	−3.79069	−	3.79069i	−0.0115923	−	0.0115923i
$328$		0			0
$329$	−385.496			−1.17172
$330$		0			0
$331$	−248.635	+	248.635i	−0.751162	+	0.751162i	−0.974696	−	0.223534i	$-0.928241\pi$
$331$	−248.635	+	248.635i	−0.751162	+	0.751162i	0.223534	+	0.974696i	$0.428241\pi$
$332$		0			0
$333$			261.761i			0.786069i
$334$		0			0
$335$	−227.336	+	187.407i	−0.678614	+	0.559425i
$336$		0			0
$337$	−82.9415	+	82.9415i	−0.246117	+	0.246117i	−0.819375	−	0.573258i	$-0.805679\pi$
$337$	−82.9415	+	82.9415i	−0.246117	+	0.246117i	0.573258	+	0.819375i	$0.305679\pi$
$338$		0			0
$339$	6.72250	−	6.72250i	0.0198304	−	0.0198304i
$340$		0			0
$341$	122.914	−	122.914i	0.360451	−	0.360451i
$342$		0			0
$343$	−251.537	+	251.537i	−0.733345	+	0.733345i
$344$		0			0
$345$	−23.5604	−	2.26821i	−0.0682909	−	0.00657452i
$346$		0			0
$347$			288.892i			0.832540i	0.909241	+	0.416270i	$0.136663\pi$
$347$			288.892i			0.832540i	−0.909241	+	0.416270i	$0.863337\pi$
$348$		0			0
$349$	−345.135	+	345.135i	−0.988927	+	0.988927i	−0.999939	−	0.0110128i	$-0.996494\pi$
$349$	−345.135	+	345.135i	−0.988927	+	0.988927i	0.0110128	+	0.999939i	$0.496494\pi$
$350$		0			0
$351$	39.7634			0.113286
$352$		0			0
$353$	242.242	+	242.242i	0.686239	+	0.686239i	0.961399	−	0.275159i	$-0.0887306\pi$
$353$	242.242	+	242.242i	0.686239	+	0.686239i	−0.275159	+	0.961399i	$0.588731\pi$
$354$		0			0
$355$	244.278	+	296.322i	0.688106	+	0.834711i
$356$		0			0
$357$		−	12.1686i		−	0.0340858i
$358$		0			0
$359$	221.083			0.615831			0.307916	−	0.951414i	$-0.400369\pi$
$359$	221.083			0.615831			0.307916	+	0.951414i	$0.400369\pi$
$360$		0			0
$361$			360.559i			0.998778i
$362$		0			0
$363$	−13.0029			−0.0358206
$364$		0			0
$365$	−12.7034	+	131.953i	−0.0348038	+	0.361514i
$366$		0			0
$367$	71.5971	−	71.5971i	0.195087	−	0.195087i	−0.602803	−	0.797890i	$-0.705949\pi$
$367$	71.5971	−	71.5971i	0.195087	−	0.195087i	0.797890	+	0.602803i	$0.205949\pi$
$368$		0			0
$369$		−	147.980i		−	0.401028i
$370$		0			0
$371$	373.034	+	373.034i	1.00548	+	1.00548i
$372$		0			0
$373$	−174.847			−0.468758			−0.234379	−	0.972145i	$-0.575306\pi$
$373$	−174.847			−0.468758			−0.234379	+	0.972145i	$0.575306\pi$
$374$		0			0
$375$	−13.1583	+	7.14524i	−0.0350889	+	0.0190540i
$376$		0			0
$377$	−288.070	−	288.070i	−0.764110	−	0.764110i
$378$		0			0
$379$	329.561	+	329.561i	0.869553	+	0.869553i	0.992423	−	0.122870i	$-0.0392098\pi$
$379$	329.561	+	329.561i	0.869553	+	0.869553i	−0.122870	+	0.992423i	$0.539210\pi$
$380$		0			0
$381$	7.20438	+	7.20438i	0.0189091	+	0.0189091i
$382$		0			0
$383$	1.40406	+	1.40406i	0.00366594	+	0.00366594i	0.708937	−	0.705271i	$-0.249175\pi$
$383$	1.40406	+	1.40406i	0.00366594	+	0.00366594i	−0.705271	+	0.708937i	$0.749175\pi$
$384$		0			0
$385$	−91.2431	+	75.2175i	−0.236995	+	0.195370i
$386$		0			0
$387$	40.3433			0.104246
$388$		0			0
$389$	276.184	+	276.184i	0.709984	+	0.709984i	0.966532	−	0.256548i	$-0.0825851\pi$
$389$	276.184	+	276.184i	0.709984	+	0.709984i	−0.256548	+	0.966532i	$0.582585\pi$
$390$		0			0
$391$		−	598.936i		−	1.53181i
$392$		0			0
$393$	15.5573	−	15.5573i	0.0395860	−	0.0395860i
$394$		0			0
$395$	−450.660	−	546.676i	−1.14091	−	1.38399i
$396$		0			0
$397$	−692.870			−1.74526			−0.872632	−	0.488378i	$-0.837589\pi$
$397$	−692.870			−1.74526			−0.872632	+	0.488378i	$0.837589\pi$
$398$		0			0
$399$			0.533369i			0.00133676i
$400$		0			0
$401$	755.828			1.88486			0.942429	−	0.334407i	$-0.108536\pi$
$401$	755.828			1.88486			0.942429	+	0.334407i	$0.108536\pi$
$402$		0			0
$403$			909.298i			2.25632i
$404$		0			0
$405$	−311.010	+	256.385i	−0.767925	+	0.633050i
$406$		0			0
$407$	−72.6780	−	72.6780i	−0.178570	−	0.178570i
$408$		0			0
$409$	−43.3293			−0.105940			−0.0529698	−	0.998596i	$-0.516869\pi$
$409$	−43.3293			−0.105940			−0.0529698	+	0.998596i	$0.516869\pi$
$410$		0			0
$411$	−8.36423	+	8.36423i	−0.0203509	+	0.0203509i
$412$		0			0
$413$			30.9582i			0.0749594i
$414$		0			0
$415$	−381.823	−	463.172i	−0.920055	−	1.11608i
$416$		0			0
$417$	−2.01684	+	2.01684i	−0.00483655	+	0.00483655i
$418$		0			0
$419$	345.453	−	345.453i	0.824471	−	0.824471i	−0.162274	−	0.986746i	$-0.551883\pi$
$419$	345.453	−	345.453i	0.824471	−	0.824471i	0.986746	+	0.162274i	$0.0518830\pi$
$420$		0			0
$421$	−371.173	+	371.173i	−0.881645	+	0.881645i	−0.993702	−	0.112056i	$-0.964256\pi$
$421$	−371.173	+	371.173i	−0.881645	+	0.881645i	0.112056	+	0.993702i	$0.464256\pi$
$422$		0			0
$423$	365.416	−	365.416i	0.863867	−	0.863867i
$424$		0			0
$425$	−211.881	−	314.104i	−0.498544	−	0.739069i
$426$		0			0
$427$			218.400i			0.511475i
$428$		0			0
$429$	−5.51575	+	5.51575i	−0.0128572	+	0.0128572i
$430$		0			0
$431$	150.726			0.349712			0.174856	−	0.984594i	$-0.444054\pi$
$431$	150.726			0.349712			0.174856	+	0.984594i	$0.444054\pi$
$432$		0			0
$433$	249.306	+	249.306i	0.575765	+	0.575765i	0.933734	−	0.357969i	$-0.116531\pi$
$433$	249.306	+	249.306i	0.575765	+	0.575765i	−0.357969	+	0.933734i	$0.616531\pi$
$434$		0			0
$435$	−13.1592	−	1.26687i	−0.0302511	−	0.00291234i
$436$		0			0
$437$			26.2522i			0.0600738i
$438$		0			0
$439$	−106.380			−0.242324			−0.121162	−	0.992633i	$-0.538662\pi$
$439$	−106.380			−0.242324			−0.121162	+	0.992633i	$0.538662\pi$
$440$		0			0
$441$		−	36.5725i		−	0.0829307i
$442$		0			0
$443$	−235.281			−0.531108			−0.265554	−	0.964096i	$-0.585555\pi$
$443$	−235.281			−0.531108			−0.265554	+	0.964096i	$0.585555\pi$
$444$		0			0
$445$	338.453	−	279.009i	0.760569	−	0.626986i
$446$		0			0
$447$	−15.0988	+	15.0988i	−0.0337780	+	0.0337780i
$448$		0			0
$449$			78.1899i			0.174142i	0.996202	+	0.0870712i	$0.0277508\pi$
$449$			78.1899i			0.174142i	−0.996202	+	0.0870712i	$0.972249\pi$
$450$		0			0
$451$	41.0865	+	41.0865i	0.0911009	+	0.0911009i
$452$		0			0
$453$	−20.3635			−0.0449526
$454$		0			0
$455$	59.2774	−	615.726i	0.130280	−	1.35324i
$456$		0			0
$457$	401.924	+	401.924i	0.879483	+	0.879483i	0.993481	−	0.113998i	$-0.0363659\pi$
$457$	401.924	+	401.924i	0.879483	+	0.879483i	−0.113998	+	0.993481i	$0.536366\pi$
$458$		0			0
$459$	23.0879	+	23.0879i	0.0503005	+	0.0503005i
$460$		0			0
$461$	158.945	+	158.945i	0.344783	+	0.344783i	0.858162	−	0.513379i	$-0.171606\pi$
$461$	158.945	+	158.945i	0.344783	+	0.344783i	−0.513379	+	0.858162i	$0.671606\pi$
$462$		0			0
$463$	200.675	+	200.675i	0.433422	+	0.433422i	0.889791	−	0.456369i	$-0.150850\pi$
$463$	200.675	+	200.675i	0.433422	+	0.433422i	−0.456369	+	0.889791i	$0.650850\pi$
$464$		0			0
$465$	18.7692	+	22.7681i	0.0403640	+	0.0489638i
$466$		0			0
$467$	188.298			0.403208			0.201604	−	0.979467i	$-0.435385\pi$
$467$	188.298			0.403208			0.201604	+	0.979467i	$0.435385\pi$
$468$		0			0
$469$	−279.287	−	279.287i	−0.595494	−	0.595494i
$470$		0			0
$471$			1.45963i			0.00309900i
$472$		0			0
$473$	−11.2013	+	11.2013i	−0.0236814	+	0.0236814i
$474$		0			0
$475$	9.28707	+	13.7677i	0.0195517	+	0.0289845i
$476$		0			0
$477$	−707.204			−1.48261
$478$		0			0
$479$			175.422i			0.366225i	0.983092	+	0.183112i	$0.0586172\pi$
$479$			175.422i			0.366225i	−0.983092	+	0.183112i	$0.941383\pi$
$480$		0			0
$481$	537.661			1.11780
$482$		0			0
$483$		−	31.7309i		−	0.0656955i
$484$		0			0
$485$	−23.4752	+	243.842i	−0.0484025	+	0.502766i
$486$		0			0
$487$	53.3922	+	53.3922i	0.109635	+	0.109635i	0.759796	−	0.650161i	$-0.225299\pi$
$487$	53.3922	+	53.3922i	0.109635	+	0.109635i	−0.650161	+	0.759796i	$0.725299\pi$
$488$		0			0
$489$	34.2324			0.0700048
$490$		0			0
$491$	−96.7903	+	96.7903i	−0.197129	+	0.197129i	−0.798768	−	0.601639i	$-0.794515\pi$
$491$	−96.7903	+	96.7903i	−0.197129	+	0.197129i	0.601639	+	0.798768i	$0.294515\pi$
$492$		0			0
$493$		−	334.525i		−	0.678550i
$494$		0			0
$495$	15.1908	−	157.790i	0.0306884	−	0.318767i
$496$		0			0
$497$	−364.038	+	364.038i	−0.732472	+	0.732472i
$498$		0			0
$499$	−139.686	+	139.686i	−0.279931	+	0.279931i	−0.833081	−	0.553150i	$-0.813426\pi$
$499$	−139.686	+	139.686i	−0.279931	+	0.279931i	0.553150	+	0.833081i	$0.313426\pi$
$500$		0			0
$501$	−12.2875	+	12.2875i	−0.0245260	+	0.0245260i
$502$		0			0
$503$	−319.688	+	319.688i	−0.635562	+	0.635562i	−0.949458	−	0.313895i	$-0.898366\pi$
$503$	−319.688	+	319.688i	−0.635562	+	0.635562i	0.313895	+	0.949458i	$0.398366\pi$
$504$		0			0
$505$	20.0376	−	208.134i	0.0396784	−	0.412147i
$506$		0			0
$507$		−	20.5610i		−	0.0405542i
$508$		0			0
$509$	702.440	−	702.440i	1.38004	−	1.38004i	0.535510	−	0.844529i	$-0.320119\pi$
$509$	702.440	−	702.440i	1.38004	−	1.38004i	0.844529	−	0.535510i	$-0.179881\pi$
$510$		0			0
$511$	−177.713			−0.347775
$512$		0			0
$513$	−1.01198	−	1.01198i	−0.00197267	−	0.00197267i
$514$		0			0
$515$	32.8985	−	341.723i	0.0638806	−	0.663541i
$516$		0			0
$517$			202.915i			0.392486i
$518$		0			0
$519$	8.18202			0.0157650
$520$		0			0
$521$		−	614.419i		−	1.17931i	−0.807656	−	0.589654i	$-0.799264\pi$
$521$		−	614.419i		−	1.17931i	0.807656	−	0.589654i	$-0.200736\pi$
$522$		0			0
$523$	178.970			0.342199			0.171100	−	0.985254i	$-0.445268\pi$
$523$	178.970			0.342199			0.171100	+	0.985254i	$0.445268\pi$
$524$		0			0
$525$	−11.2252	−	16.6409i	−0.0213814	−	0.0316969i
$526$		0			0
$527$	−527.968	+	527.968i	−1.00184	+	1.00184i
$528$		0			0
$529$		−	1032.79i		−	1.95234i
$530$		0			0
$531$	−29.3456	−	29.3456i	−0.0552648	−	0.0552648i
$532$		0			0
$533$	−303.952			−0.570266
$534$		0			0
$535$	197.511	+	239.592i	0.369180	+	0.447836i
$536$		0			0
$537$	19.8715	+	19.8715i	0.0370047	+	0.0370047i
$538$		0			0
$539$	10.1543	+	10.1543i	0.0188392	+	0.0188392i
$540$		0			0
$541$	216.557	+	216.557i	0.400291	+	0.400291i	0.878336	−	0.478045i	$-0.158654\pi$
$541$	216.557	+	216.557i	0.400291	+	0.400291i	−0.478045	+	0.878336i	$0.658654\pi$
$542$		0			0
$543$	12.1741	+	12.1741i	0.0224201	+	0.0224201i
$544$		0			0
$545$	21.4436	−	222.739i	0.0393460	−	0.408695i
$546$		0			0
$547$	−204.888			−0.374567			−0.187284	−	0.982306i	$-0.559968\pi$
$547$	−204.888			−0.374567			−0.187284	+	0.982306i	$0.559968\pi$
$548$		0			0
$549$	−207.023	−	207.023i	−0.377091	−	0.377091i
$550$		0			0
$551$			14.6627i			0.0266111i
$552$		0			0
$553$	671.603	−	671.603i	1.21447	−	1.21447i
$554$		0			0
$555$	13.4626	−	11.0981i	0.0242570	−	0.0199966i
$556$		0			0
$557$	345.777			0.620784			0.310392	−	0.950609i	$-0.399540\pi$
$557$	345.777			0.620784			0.310392	+	0.950609i	$0.399540\pi$
$558$		0			0
$559$		−	82.8656i		−	0.148239i
$560$		0			0
$561$	−6.40525			−0.0114176
$562$		0			0
$563$			319.750i			0.567940i	0.958833	+	0.283970i	$0.0916516\pi$
$563$			319.750i			0.567940i	−0.958833	+	0.283970i	$0.908348\pi$
$564$		0			0
$565$	395.010	+	38.0285i	0.699133	+	0.0673071i
$566$		0			0
$567$	−382.082	−	382.082i	−0.673866	−	0.673866i
$568$		0			0
$569$	−146.472			−0.257420			−0.128710	−	0.991682i	$-0.541084\pi$
$569$	−146.472			−0.257420			−0.128710	+	0.991682i	$0.541084\pi$
$570$		0			0
$571$	221.670	−	221.670i	0.388214	−	0.388214i	−0.485836	−	0.874050i	$-0.661485\pi$
$571$	221.670	−	221.670i	0.388214	−	0.388214i	0.874050	+	0.485836i	$0.161485\pi$
$572$		0			0
$573$			17.3034i			0.0301980i
$574$		0			0
$575$	−552.502	−	819.060i	−0.960873	−	1.42445i
$576$		0			0
$577$	−293.131	+	293.131i	−0.508026	+	0.508026i	−0.913920	−	0.405894i	$-0.866960\pi$
$577$	−293.131	+	293.131i	−0.508026	+	0.508026i	0.405894	+	0.913920i	$0.366960\pi$
$578$		0			0
$579$	3.92624	−	3.92624i	0.00678107	−	0.00678107i
$580$		0			0
$581$	569.017	−	569.017i	0.979375	−	0.979375i
$582$		0			0
$583$	196.355	−	196.355i	0.336801	−	0.336801i
$584$		0			0
$585$	527.463	+	639.842i	0.901646	+	1.09375i
$586$		0			0
$587$			176.460i			0.300614i	0.988639	+	0.150307i	$0.0480262\pi$
$587$			176.460i			0.300614i	−0.988639	+	0.150307i	$0.951974\pi$
$588$		0			0
$589$	23.1416	−	23.1416i	0.0392897	−	0.0392897i
$590$		0			0
$591$	40.1528			0.0679404
$592$		0			0
$593$	−311.192	−	311.192i	−0.524776	−	0.524776i	0.394234	−	0.919010i	$-0.371010\pi$
$593$	−311.192	−	311.192i	−0.524776	−	0.524776i	−0.919010	+	0.394234i	$0.871010\pi$
$594$		0			0
$595$	391.929	−	323.092i	0.658704	−	0.543012i
$596$		0			0
$597$			22.1285i			0.0370661i
$598$		0			0
$599$	550.344			0.918771			0.459386	−	0.888237i	$-0.348070\pi$
$599$	550.344			0.918771			0.459386	+	0.888237i	$0.348070\pi$
$600$		0			0
$601$			440.349i			0.732693i	0.930478	+	0.366347i	$0.119392\pi$
$601$			440.349i			0.732693i	−0.930478	+	0.366347i	$0.880608\pi$
$602$		0			0
$603$	529.477			0.878071
$604$		0			0
$605$	−345.243	−	418.799i	−0.570649	−	0.692229i
$606$		0			0
$607$	12.8864	−	12.8864i	0.0212296	−	0.0212296i	−0.696412	−	0.717642i	$-0.745221\pi$
$607$	12.8864	−	12.8864i	0.0212296	−	0.0212296i	0.717642	+	0.696412i	$0.245221\pi$
$608$		0			0
$609$		−	17.7228i		−	0.0291014i
$610$		0			0
$611$	−750.569	−	750.569i	−1.22843	−	1.22843i
$612$		0			0
$613$	228.861			0.373346			0.186673	−	0.982422i	$-0.440229\pi$
$613$	228.861			0.373346			0.186673	+	0.982422i	$0.440229\pi$
$614$		0			0
$615$	−7.61073	+	6.27402i	−0.0123752	+	0.0102017i
$616$		0			0
$617$	−236.901	−	236.901i	−0.383957	−	0.383957i	0.488569	−	0.872525i	$-0.337519\pi$
$617$	−236.901	−	236.901i	−0.383957	−	0.383957i	−0.872525	+	0.488569i	$0.837519\pi$
$618$		0			0
$619$	−204.389	−	204.389i	−0.330192	−	0.330192i	0.522468	−	0.852659i	$-0.325012\pi$
$619$	−204.389	−	204.389i	−0.330192	−	0.330192i	−0.852659	+	0.522468i	$0.825012\pi$
$620$		0			0
$621$	60.2042	+	60.2042i	0.0969471	+	0.0969471i
$622$		0			0
$623$	415.797	+	415.797i	0.667411	+	0.667411i
$624$		0			0
$625$	−579.505	−	234.091i	−0.927209	−	0.374545i
$626$		0			0
$627$	0.280751			0.000447769
$628$		0			0
$629$	312.184	+	312.184i	0.496317	+	0.496317i
$630$		0			0
$631$		−	219.606i		−	0.348029i	−0.984743	−	0.174014i	$-0.944326\pi$
$631$		−	219.606i		−	0.348029i	0.984743	−	0.174014i	$-0.0556739\pi$
$632$		0			0
$633$	22.5195	−	22.5195i	0.0355759	−	0.0355759i
$634$		0			0
$635$	−40.7545	+	423.325i	−0.0641803	+	0.666654i
$636$		0			0
$637$	−75.1203			−0.117928
$638$		0			0
$639$		−	690.151i		−	1.08005i
$640$		0			0
$641$	−399.195			−0.622770			−0.311385	−	0.950284i	$-0.600793\pi$
$641$	−399.195			−0.622770			−0.311385	+	0.950284i	$0.600793\pi$
$642$		0			0
$643$		−	864.637i		−	1.34469i	−0.740237	−	0.672346i	$-0.765287\pi$
$643$		−	864.637i		−	1.34469i	0.740237	−	0.672346i	$-0.234713\pi$
$644$		0			0
$645$	−1.71047	−	2.07489i	−0.00265189	−	0.00321689i
$646$		0			0
$647$	569.775	+	569.775i	0.880641	+	0.880641i	0.993600	−	0.112959i	$-0.0360329\pi$
$647$	569.775	+	569.775i	0.880641	+	0.880641i	−0.112959	+	0.993600i	$0.536033\pi$
$648$		0			0
$649$	16.2956			0.0251088
$650$		0			0
$651$	−27.9711	+	27.9711i	−0.0429664	+	0.0429664i
$652$		0			0
$653$			139.259i			0.213261i	0.994299	+	0.106630i	$0.0340062\pi$
$653$			139.259i			0.213261i	−0.994299	+	0.106630i	$0.965994\pi$
$654$		0			0
$655$	914.138	+	88.0061i	1.39563	+	0.134361i
$656$		0			0
$657$	168.456	−	168.456i	0.256402	−	0.256402i
$658$		0			0
$659$	−348.410	+	348.410i	−0.528695	+	0.528695i	−0.920183	−	0.391488i	$-0.871960\pi$
$659$	−348.410	+	348.410i	−0.528695	+	0.528695i	0.391488	+	0.920183i	$0.371960\pi$
$660$		0			0
$661$	270.659	−	270.659i	0.409469	−	0.409469i	−0.472084	−	0.881553i	$-0.656498\pi$
$661$	270.659	−	270.659i	0.409469	−	0.409469i	0.881553	+	0.472084i	$0.156498\pi$
$662$		0			0
$663$	23.6926	−	23.6926i	0.0357354	−	0.0357354i
$664$		0			0
$665$	−17.1788	+	14.1616i	−0.0258328	+	0.0212956i
$666$		0			0
$667$		−	872.309i		−	1.30781i
$668$		0			0
$669$	33.8181	−	33.8181i	0.0505502	−	0.0505502i
$670$		0			0
$671$	114.960			0.171326
$672$		0			0
$673$	−29.4792	−	29.4792i	−0.0438027	−	0.0438027i	0.684866	−	0.728669i	$-0.259861\pi$
$673$	−29.4792	−	29.4792i	−0.0438027	−	0.0438027i	−0.728669	+	0.684866i	$0.759861\pi$
$674$		0			0
$675$	52.8713	+	10.2753i	0.0783278	+	0.0152227i
$676$		0			0
$677$			519.409i			0.767221i	0.923495	+	0.383611i	$0.125319\pi$
$677$			519.409i			0.767221i	−0.923495	+	0.383611i	$0.874681\pi$
$678$		0			0
$679$	−328.404			−0.483659
$680$		0			0
$681$		−	17.5932i		−	0.0258343i
$682$		0			0
$683$	−254.873			−0.373167			−0.186583	−	0.982439i	$-0.559741\pi$
$683$	−254.873			−0.373167			−0.186583	+	0.982439i	$0.559741\pi$
$684$		0			0
$685$	−491.477	−	47.3157i	−0.717485	−	0.0690739i
$686$		0			0
$687$	−23.3219	+	23.3219i	−0.0339474	+	0.0339474i
$688$		0			0
$689$			1452.61i			2.10828i
$690$		0			0
$691$	422.293	+	422.293i	0.611133	+	0.611133i	0.943241	−	0.332108i	$-0.107760\pi$
$691$	422.293	+	422.293i	0.611133	+	0.611133i	−0.332108	+	0.943241i	$0.607760\pi$
$692$		0			0
$693$	212.510			0.306652
$694$		0			0
$695$	−118.508	−	11.4091i	−0.170516	−	0.0164160i
$696$		0			0
$697$	−176.484	−	176.484i	−0.253206	−	0.253206i
$698$		0			0
$699$	−10.4240	−	10.4240i	−0.0149127	−	0.0149127i
$700$		0			0
$701$	203.994	+	203.994i	0.291004	+	0.291004i	0.837477	−	0.546473i	$-0.184030\pi$
$701$	203.994	+	203.994i	0.291004	+	0.291004i	−0.546473	+	0.837477i	$0.684030\pi$
$702$		0			0
$703$	−13.6835	−	13.6835i	−0.0194644	−	0.0194644i
$704$		0			0
$705$	−34.2865	−	3.30084i	−0.0486334	−	0.00468205i
$706$		0			0
$707$	280.314			0.396484
$708$		0			0
$709$	−407.106	−	407.106i	−0.574197	−	0.574197i	0.359101	−	0.933299i	$-0.383083\pi$
$709$	−407.106	−	407.106i	−0.574197	−	0.574197i	−0.933299	+	0.359101i	$0.883083\pi$
$710$		0			0
$711$			1273.24i			1.79077i
$712$		0			0
$713$	−1376.73	+	1376.73i	−1.93090	+	1.93090i
$714$		0			0
$715$	−324.102	−	31.2021i	−0.453290	−	0.0436392i
$716$		0			0
$717$	−40.1086			−0.0559394
$718$		0			0
$719$			725.464i			1.00899i	0.863415	+	0.504495i	$0.168321\pi$
$719$			725.464i			1.00899i	−0.863415	+	0.504495i	$0.831679\pi$
$720$		0			0
$721$	460.231			0.638323
$722$		0			0
$723$		−	45.3838i		−	0.0627716i
$724$		0			0
$725$	−308.590	−	457.471i	−0.425642	−	0.630995i
$726$		0			0
$727$	−442.782	−	442.782i	−0.609054	−	0.609054i	0.333645	−	0.942699i	$-0.391721\pi$
$727$	−442.782	−	442.782i	−0.609054	−	0.609054i	−0.942699	+	0.333645i	$0.891721\pi$
$728$		0			0
$729$	722.036			0.990447
$730$		0			0
$731$	48.1145	−	48.1145i	0.0658201	−	0.0658201i
$732$		0			0
$733$			358.600i			0.489222i	0.969621	+	0.244611i	$0.0786603\pi$
$733$			358.600i			0.489222i	−0.969621	+	0.244611i	$0.921340\pi$
$734$		0			0
$735$	−1.88096	+	1.55059i	−0.00255913	+	0.00210965i
$736$		0			0
$737$	−147.009	+	147.009i	−0.199470	+	0.199470i
$738$		0			0
$739$	575.294	−	575.294i	0.778477	−	0.778477i	−0.201095	−	0.979572i	$-0.564450\pi$
$739$	575.294	−	575.294i	0.778477	−	0.778477i	0.979572	+	0.201095i	$0.0644499\pi$
$740$		0			0
$741$	−1.03848	+	1.03848i	−0.00140146	+	0.00140146i
$742$		0			0
$743$	55.8927	−	55.8927i	0.0752258	−	0.0752258i	−0.668493	−	0.743719i	$-0.733060\pi$
$743$	55.8927	−	55.8927i	0.0752258	−	0.0752258i	0.743719	+	0.668493i	$0.233060\pi$
$744$		0			0
$745$	−887.195	−	85.4124i	−1.19087	−	0.114647i
$746$		0			0
$747$			1078.75i			1.44411i
$748$		0			0
$749$	−294.344	+	294.344i	−0.392983	+	0.392983i
$750$		0			0
$751$	63.5053			0.0845610			0.0422805	−	0.999106i	$-0.486538\pi$
$751$	63.5053			0.0845610			0.0422805	+	0.999106i	$0.486538\pi$
$752$		0			0
$753$	21.7934	+	21.7934i	0.0289421	+	0.0289421i
$754$		0			0
$755$	−540.677	−	655.872i	−0.716129	−	0.868704i
$756$		0			0
$757$		−	495.675i		−	0.654789i	−0.944888	−	0.327395i	$-0.893829\pi$
$757$		−	495.675i		−	0.654789i	0.944888	−	0.327395i	$-0.106171\pi$
$758$		0			0
$759$	−16.7023			−0.0220057
$760$		0			0
$761$		−	228.669i		−	0.300485i	−0.988649	−	0.150243i	$-0.951995\pi$
$761$		−	228.669i		−	0.300485i	0.988649	−	0.150243i	$-0.0480055\pi$
$762$		0			0
$763$	299.983			0.393163
$764$		0			0
$765$	−65.2510	+	677.775i	−0.0852954	+	0.885981i
$766$		0			0
$767$	−60.2763	+	60.2763i	−0.0785871	+	0.0785871i
$768$		0			0
$769$		−	804.229i		−	1.04581i	−0.852391	−	0.522906i	$-0.824848\pi$
$769$		−	804.229i		−	1.04581i	0.852391	−	0.522906i	$-0.175152\pi$
$770$		0			0
$771$	4.58213	+	4.58213i	0.00594310	+	0.00594310i
$772$		0			0
$773$	186.546			0.241328			0.120664	−	0.992693i	$-0.461498\pi$
$773$	186.546			0.241328			0.120664	+	0.992693i	$0.461498\pi$
$774$		0			0
$775$	−234.973	+	1209.05i	−0.303191	+	1.56006i
$776$		0			0
$777$	16.5391	+	16.5391i	0.0212859	+	0.0212859i
$778$		0			0
$779$	7.73557	+	7.73557i	0.00993013	+	0.00993013i
$780$		0			0
$781$	191.620	+	191.620i	0.245353	+	0.245353i
$782$		0			0
$783$	33.6260	+	33.6260i	0.0429450	+	0.0429450i
$784$		0			0
$785$	−47.0120	+	38.7550i	−0.0598878	+	0.0493694i
$786$		0			0
$787$	−1134.28			−1.44127			−0.720635	−	0.693315i	$-0.756150\pi$
$787$	−1134.28			−1.44127			−0.720635	+	0.693315i	$0.756150\pi$
$788$		0			0
$789$	19.8798	+	19.8798i	0.0251962	+	0.0251962i
$790$		0			0
$791$			531.997i			0.672563i
$792$		0			0
$793$	−425.229	+	425.229i	−0.536228	+	0.536228i
$794$		0			0
$795$	29.9840	+	36.3722i	0.0377157	+	0.0457512i
$796$		0			0
$797$	250.905			0.314812			0.157406	−	0.987534i	$-0.449687\pi$
$797$	250.905			0.314812			0.157406	+	0.987534i	$0.449687\pi$
$798$		0			0
$799$		−	871.610i		−	1.09088i
$800$		0			0
$801$	−788.276			−0.984114
$802$		0			0
$803$			93.5435i			0.116493i
$804$		0			0
$805$	1022.00	−	842.496i	1.26956	−	1.04658i
$806$		0			0
$807$	37.1687	+	37.1687i	0.0460579	+	0.0460579i
$808$		0			0
$809$	1099.77			1.35942			0.679712	−	0.733479i	$-0.262105\pi$
$809$	1099.77			1.35942			0.679712	+	0.733479i	$0.262105\pi$
$810$		0			0
$811$	376.722	−	376.722i	0.464515	−	0.464515i	−0.435617	−	0.900132i	$-0.643470\pi$
$811$	376.722	−	376.722i	0.464515	−	0.464515i	0.900132	+	0.435617i	$0.143470\pi$
$812$		0			0
$813$			32.6399i			0.0401474i
$814$		0			0
$815$	908.912	+	1102.56i	1.11523	+	1.35284i
$816$		0			0
$817$	−2.10893	+	2.10893i	−0.00258131	+	0.00258131i
$818$		0			0
$819$	−786.059	+	786.059i	−0.959779	+	0.959779i
$820$		0			0
$821$	−164.380	+	164.380i	−0.200220	+	0.200220i	−0.800094	−	0.599874i	$-0.795217\pi$
$821$	−164.380	+	164.380i	−0.200220	+	0.200220i	0.599874	+	0.800094i	$0.295217\pi$
$822$		0			0
$823$	−794.892	+	794.892i	−0.965847	+	0.965847i	−0.999436	−	0.0335887i	$-0.989306\pi$
$823$	−794.892	+	794.892i	−0.965847	+	0.965847i	0.0335887	+	0.999436i	$0.489306\pi$
$824$		0			0
$825$	−8.75933	+	5.90867i	−0.0106174	+	0.00716202i
$826$		0			0
$827$		−	696.994i		−	0.842798i	−0.906875	−	0.421399i	$-0.861539\pi$
$827$		−	696.994i		−	0.842798i	0.906875	−	0.421399i	$-0.138461\pi$
$828$		0			0
$829$	−857.248	+	857.248i	−1.03407	+	1.03407i	−0.0346759	+	0.999399i	$0.511040\pi$
$829$	−857.248	+	857.248i	−1.03407	+	1.03407i	−0.999399	+	0.0346759i	$0.988960\pi$
$830$		0			0
$831$	−17.1500			−0.0206378
$832$		0			0
$833$	−43.6173	−	43.6173i	−0.0523617	−	0.0523617i
$834$		0			0
$835$	−722.008	−	69.5094i	−0.864681	−	0.0832448i
$836$		0			0
$837$		−	106.141i		−	0.126811i
$838$		0			0
$839$	−428.122			−0.510277			−0.255139	−	0.966905i	$-0.582121\pi$
$839$	−428.122			−0.510277			−0.255139	+	0.966905i	$0.582121\pi$
$840$		0			0
$841$			353.787i			0.420675i
$842$		0			0
$843$	−16.6991			−0.0198091
$844$		0			0
$845$	662.231	−	545.919i	0.783705	−	0.646058i
$846$		0			0
$847$	514.503	−	514.503i	0.607441	−	0.607441i
$848$		0			0
$849$			40.2818i			0.0474462i
$850$		0			0
$851$	814.051	+	814.051i	0.956582	+	0.956582i
$852$		0			0
$853$	1569.13			1.83955			0.919773	−	0.392451i	$-0.128373\pi$
$853$	1569.13			1.83955			0.919773	+	0.392451i	$0.128373\pi$
$854$		0			0
$855$	2.86005	−	29.7079i	0.00334508	−	0.0347461i
$856$		0			0
$857$	454.985	+	454.985i	0.530904	+	0.530904i	0.920841	−	0.389937i	$-0.127503\pi$
$857$	454.985	+	454.985i	0.530904	+	0.530904i	−0.389937	+	0.920841i	$0.627503\pi$
$858$		0			0
$859$	620.538	+	620.538i	0.722396	+	0.722396i	0.969093	−	0.246697i	$-0.0793452\pi$
$859$	620.538	+	620.538i	0.722396	+	0.722396i	−0.246697	+	0.969093i	$0.579345\pi$
$860$		0			0
$861$	−9.34995	−	9.34995i	−0.0108594	−	0.0108594i
$862$		0			0
$863$	234.305	+	234.305i	0.271500	+	0.271500i	0.829704	−	0.558204i	$-0.188509\pi$
$863$	234.305	+	234.305i	0.271500	+	0.271500i	−0.558204	+	0.829704i	$0.688509\pi$
$864$		0			0
$865$	217.243	+	263.528i	0.251148	+	0.304656i
$866$		0			0
$867$	−7.10467			−0.00819454
$868$		0			0
$869$	−353.514	−	353.514i	−0.406806	−	0.406806i
$870$		0			0
$871$		−	1087.55i		−	1.24863i
$872$		0			0
$873$	311.297	−	311.297i	0.356584	−	0.356584i
$874$		0			0
$875$	237.929	−	803.380i	0.271918	−	0.918149i
$876$		0			0
$877$	1505.10			1.71620			0.858098	−	0.513485i	$-0.171646\pi$
$877$	1505.10			1.71620			0.858098	+	0.513485i	$0.171646\pi$
$878$		0			0
$879$		−	3.96723i		−	0.00451335i
$880$		0			0
$881$	−1589.76			−1.80450			−0.902250	−	0.431213i	$-0.858086\pi$
$881$	−1589.76			−1.80450			−0.902250	+	0.431213i	$0.858086\pi$
$882$		0			0
$883$		−	512.240i		−	0.580114i	−0.957009	−	0.290057i	$-0.906326\pi$
$883$		−	512.240i		−	0.580114i	0.957009	−	0.290057i	$-0.0936742\pi$
$884$		0			0
$885$	−0.265082	+	2.75346i	−0.000299528	+	0.00311126i
$886$		0			0
$887$	495.921	+	495.921i	0.559099	+	0.559099i	0.929051	−	0.369952i	$-0.120626\pi$
$887$	495.921	+	495.921i	0.559099	+	0.559099i	−0.369952	+	0.929051i	$0.620626\pi$
$888$		0			0
$889$	−570.132			−0.641318
$890$		0			0
$891$	−201.118	+	201.118i	−0.225722	+	0.225722i
$892$		0			0
$893$			38.2039i			0.0427816i
$894$		0			0
$895$	−112.411	+	1167.64i	−0.125599	+	1.30462i
$896$		0			0
$897$	61.7808	−	61.7808i	0.0688749	−	0.0688749i
$898$		0			0
$899$	−768.949	+	768.949i	−0.855338	+	0.855338i
$900$		0			0
$901$	−843.432	+	843.432i	−0.936106	+	0.936106i
$902$		0			0
$903$	2.54905	−	2.54905i	0.00282287	−	0.00282287i
$904$		0			0
$905$	−68.8678	+	715.344i	−0.0760970	+	0.790435i
$906$		0			0
$907$		−	530.597i		−	0.585002i	−0.956265	−	0.292501i	$-0.905512\pi$
$907$		−	530.597i		−	0.585002i	0.956265	−	0.292501i	$-0.0944875\pi$
$908$		0			0
$909$	−265.712	+	265.712i	−0.292313	+	0.292313i
$910$		0			0
$911$	−964.958			−1.05923			−0.529615	−	0.848238i	$-0.677663\pi$
$911$	−964.958			−1.05923			−0.529615	+	0.848238i	$0.677663\pi$
$912$		0			0
$913$	−299.516	−	299.516i	−0.328057	−	0.328057i
$914$		0			0
$915$	−1.87007	+	19.4248i	−0.00204379	+	0.0212292i
$916$		0			0
$917$			1231.15i			1.34259i
$918$		0			0
$919$	−0.377866			−0.000411171			−0.000205586	−	1.00000i	$-0.500065\pi$
$919$	−0.377866			−0.000411171			−0.000205586		1.00000i	$0.500065\pi$
$920$		0			0
$921$		−	57.4542i		−	0.0623824i
$922$		0			0
$923$	−1417.58			−1.53584
$924$		0			0
$925$	714.899	+	138.938i	0.772864	+	0.150203i
$926$		0			0
$927$	−436.257	+	436.257i	−0.470612	+	0.470612i
$928$		0			0
$929$			170.314i			0.183330i	0.995790	+	0.0916650i	$0.0292189\pi$
$929$			170.314i			0.183330i	−0.995790	+	0.0916650i	$0.970781\pi$
$930$		0			0
$931$	1.91181	+	1.91181i	0.00205350	+	0.00205350i
$932$		0			0
$933$	−39.2948			−0.0421166
$934$		0			0
$935$	−170.067	−	206.301i	−0.181890	−	0.220643i
$936$		0			0
$937$	−1277.81	−	1277.81i	−1.36372	−	1.36372i	−0.869119	−	0.494603i	$-0.835314\pi$
$937$	−1277.81	−	1277.81i	−1.36372	−	1.36372i	−0.494603	−	0.869119i	$-0.664686\pi$
$938$		0			0
$939$	10.8067	+	10.8067i	0.0115087	+	0.0115087i
$940$		0			0
$941$	−557.710	−	557.710i	−0.592678	−	0.592678i	0.345676	−	0.938354i	$-0.387650\pi$
$941$	−557.710	−	557.710i	−0.592678	−	0.592678i	−0.938354	+	0.345676i	$0.887650\pi$
$942$		0			0
$943$	−460.201	−	460.201i	−0.488018	−	0.488018i
$944$		0			0
$945$	−6.91937	+	71.8729i	−0.00732208	+	0.0760559i
$946$		0			0
$947$	978.575			1.03334			0.516671	−	0.856184i	$-0.327171\pi$
$947$	978.575			1.03334			0.516671	+	0.856184i	$0.327171\pi$
$948$		0			0
$949$	−346.011	−	346.011i	−0.364606	−	0.364606i
$950$		0			0
$951$			38.8498i			0.0408515i
$952$		0			0
$953$	82.0352	−	82.0352i	0.0860810	−	0.0860810i	−0.662755	−	0.748836i	$-0.730613\pi$
$953$	82.0352	−	82.0352i	0.0860810	−	0.0860810i	0.748836	+	0.662755i	$0.230613\pi$
$954$		0			0
$955$	−557.312	+	459.428i	−0.583573	+	0.481077i
$956$		0			0
$957$	−9.32880			−0.00974796
$958$		0			0
$959$		−	661.919i		−	0.690217i
$960$		0			0
$961$	1466.20			1.52571
$962$		0			0
$963$		−	558.024i		−	0.579464i
$964$		0			0
$965$	230.703	+	22.2103i	0.239071	+	0.0230159i
$966$		0			0
$967$	−241.731	−	241.731i	−0.249980	−	0.249980i	0.570982	−	0.820962i	$-0.306562\pi$
$967$	−241.731	−	241.731i	−0.249980	−	0.249980i	−0.820962	+	0.570982i	$0.806562\pi$
$968$		0			0
$969$	−1.20595			−0.00124453
$970$		0			0
$971$	970.962	−	970.962i	0.999961	−	0.999961i	−3.91262e−5	−	1.00000i	$-0.500012\pi$
$971$	970.962	−	970.962i	0.999961	−	0.999961i	1.00000		3.91262e-5i	$1.24543e-5\pi$
$972$		0			0
$973$		−	159.606i		−	0.164035i
$974$		0			0
$975$	10.5444	−	54.2559i	0.0108148	−	0.0556470i
$976$		0			0
$977$	1199.24	−	1199.24i	1.22747	−	1.22747i	0.262558	−	0.964916i	$-0.415434\pi$
$977$	1199.24	−	1199.24i	1.22747	−	1.22747i	0.964916	−	0.262558i	$-0.0845662\pi$
$978$		0			0
$979$	218.865	−	218.865i	0.223559	−	0.223559i
$980$		0			0
$981$	−284.357	+	284.357i	−0.289864	+	0.289864i
$982$		0			0
$983$	−269.570	+	269.570i	−0.274232	+	0.274232i	−0.830801	−	0.556569i	$-0.812117\pi$
$983$	−269.570	+	269.570i	−0.274232	+	0.274232i	0.556569	+	0.830801i	$0.312117\pi$
$984$		0			0
$985$	1066.11	+	1293.25i	1.08234	+	1.31294i
$986$		0			0
$987$		−	46.1769i		−	0.0467851i
$988$		0			0
$989$	125.463	−	125.463i	0.126859	−	0.126859i
$990$		0			0
$991$	514.885			0.519561			0.259781	−	0.965668i	$-0.416350\pi$
$991$	514.885			0.519561			0.259781	+	0.965668i	$0.416350\pi$
$992$		0			0
$993$	−29.7828	−	29.7828i	−0.0299928	−	0.0299928i
$994$		0			0
$995$	−712.718	+	587.539i	−0.716299	+	0.590491i
$996$		0			0
$997$		−	1154.22i		−	1.15769i	−0.815437	−	0.578845i	$-0.803504\pi$
$997$		−	1154.22i		−	1.15769i	0.815437	−	0.578845i	$-0.196496\pi$
$998$		0			0
$999$	−62.7605			−0.0628233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.i.a.273.11		44
4.3	odd	2		80.3.i.a.13.16	✓	44
5.2	odd	4		320.3.t.a.17.11		44
8.3	odd	2		640.3.i.b.33.11		44
8.5	even	2		640.3.i.a.33.12		44
16.3	odd	4		640.3.t.b.353.11		44
16.5	even	4		320.3.t.a.113.11		44
16.11	odd	4		80.3.t.a.53.5	yes	44
16.13	even	4		640.3.t.a.353.12		44
20.3	even	4		400.3.t.b.157.18		44
20.7	even	4		80.3.t.a.77.5	yes	44
20.19	odd	2		400.3.i.b.93.7		44
40.27	even	4		640.3.t.b.417.11		44
40.37	odd	4		640.3.t.a.417.12		44
80.27	even	4		80.3.i.a.37.16	yes	44
80.37	odd	4	inner	320.3.i.a.177.12		44
80.43	even	4		400.3.i.b.357.7		44
80.59	odd	4		400.3.t.b.293.18		44
80.67	even	4		640.3.i.b.97.12		44
80.77	odd	4		640.3.i.a.97.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.16	✓	44	4.3	odd	2
80.3.i.a.37.16	yes	44	80.27	even	4
80.3.t.a.53.5	yes	44	16.11	odd	4
80.3.t.a.77.5	yes	44	20.7	even	4
320.3.i.a.177.12		44	80.37	odd	4	inner
320.3.i.a.273.11		44	1.1	even	1	trivial
320.3.t.a.17.11		44	5.2	odd	4
320.3.t.a.113.11		44	16.5	even	4
400.3.i.b.93.7		44	20.19	odd	2
400.3.i.b.357.7		44	80.43	even	4
400.3.t.b.157.18		44	20.3	even	4
400.3.t.b.293.18		44	80.59	odd	4
640.3.i.a.33.12		44	8.5	even	2
640.3.i.a.97.11		44	80.77	odd	4
640.3.i.b.33.11		44	8.3	odd	2
640.3.i.b.97.12		44	80.67	even	4
640.3.t.a.353.12		44	16.13	even	4
640.3.t.a.417.12		44	40.37	odd	4
640.3.t.b.353.11		44	16.3	odd	4
640.3.t.b.417.11		44	40.27	even	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.119786i q^{3} +(-3.85807 + 3.18046i) q^{5} +(-4.73972 - 4.73972i) q^{7} +8.98565 q^{9} +O(q^{10})\)	\(q+0.119786i q^{3} +(-3.85807 + 3.18046i) q^{5} +(-4.73972 - 4.73972i) q^{7} +8.98565 q^{9} +(-2.49487 + 2.49487i) q^{11} -18.4567i q^{13} +(-0.380972 - 0.462141i) q^{15} +(10.7165 - 10.7165i) q^{17} +(-0.469722 + 0.469722i) q^{19} +(0.567750 - 0.567750i) q^{21} +(27.9445 - 27.9445i) q^{23} +(4.76941 - 24.5408i) q^{25} +2.15442i q^{27} +(15.6079 - 15.6079i) q^{29} -49.2667 q^{31} +(-0.298849 - 0.298849i) q^{33} +(33.3606 + 3.21171i) q^{35} +29.1310i q^{37} +2.21084 q^{39} -16.4684i q^{41} +4.48974 q^{43} +(-34.6673 + 28.5785i) q^{45} +(40.6666 - 40.6666i) q^{47} -4.07009i q^{49} +(1.28369 + 1.28369i) q^{51} -78.7038 q^{53} +(1.69056 - 17.5602i) q^{55} +(-0.0562658 - 0.0562658i) q^{57} +(-3.26583 - 3.26583i) q^{59} +(-23.0393 - 23.0393i) q^{61} +(-42.5895 - 42.5895i) q^{63} +(58.7006 + 71.2071i) q^{65} +58.9247 q^{67} +(3.34734 + 3.34734i) q^{69} -76.8059i q^{71} +(18.7472 - 18.7472i) q^{73} +(2.93964 + 0.571306i) q^{75} +23.6499 q^{77} +141.697i q^{79} +80.6128 q^{81} +120.053i q^{83} +(-7.26169 + 75.4286i) q^{85} +(1.86960 + 1.86960i) q^{87} -87.7260 q^{89} +(-87.4794 + 87.4794i) q^{91} -5.90143i q^{93} +(0.318290 - 3.30615i) q^{95} +(34.6438 - 34.6438i) q^{97} +(-22.4180 + 22.4180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^5 - 108 * q^9	\( 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 380 * q^95 - 4 * q^97 + 92 * q^99

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