LMFDB - Embedded newform 320.3.t.a.113.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(17,320)]

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, 3, 1]))

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

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

chi := DirichletCharacter("320.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.t (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			113.11
Character	$\chi$	$=$	320.113
Dual form			320.3.t.a.17.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.119786 q^{3} +(-3.18046 - 3.85807i) q^{5} +(4.73972 + 4.73972i) q^{7} -8.98565 q^{9} +O(q^{10})$	\(q+0.119786 q^{3} +(-3.18046 - 3.85807i) q^{5} +(4.73972 + 4.73972i) q^{7} -8.98565 q^{9} +(-2.49487 - 2.49487i) q^{11} -18.4567 q^{13} +(-0.380972 - 0.462141i) q^{15} +(10.7165 - 10.7165i) q^{17} +(0.469722 + 0.469722i) q^{19} +(0.567750 + 0.567750i) q^{21} +(-27.9445 + 27.9445i) q^{23} +(-4.76941 + 24.5408i) q^{25} -2.15442 q^{27} +(-15.6079 - 15.6079i) q^{29} -49.2667 q^{31} +(-0.298849 - 0.298849i) q^{33} +(3.21171 - 33.3606i) q^{35} -29.1310 q^{37} -2.21084 q^{39} +16.4684i q^{41} +4.48974i q^{43} +(28.5785 + 34.6673i) q^{45} +(40.6666 - 40.6666i) q^{47} -4.07009i q^{49} +(1.28369 - 1.28369i) q^{51} -78.7038i q^{53} +(-1.69056 + 17.5602i) q^{55} +(0.0562658 + 0.0562658i) q^{57} +(3.26583 - 3.26583i) q^{59} +(-23.0393 + 23.0393i) q^{61} +(-42.5895 - 42.5895i) q^{63} +(58.7006 + 71.2071i) q^{65} -58.9247i q^{67} +(-3.34734 + 3.34734i) q^{69} +76.8059i q^{71} +(-18.7472 + 18.7472i) q^{73} +(-0.571306 + 2.93964i) q^{75} -23.6499i q^{77} +141.697i q^{79} +80.6128 q^{81} +120.053 q^{83} +(-75.4286 - 7.26169i) q^{85} +(-1.86960 - 1.86960i) q^{87} +87.7260 q^{89} +(-87.4794 - 87.4794i) q^{91} -5.90143 q^{93} +(0.318290 - 3.30615i) q^{95} +(34.6438 - 34.6438i) q^{97} +(22.4180 + 22.4180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

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
$3$	0.119786			0.0399285			0.0199643	−	0.999801i	$-0.493645\pi$
$3$	0.119786			0.0399285			0.0199643	+	0.999801i	$0.493645\pi$
$4$		0			0
$5$	−3.18046	−	3.85807i	−0.636091	−	0.771614i
$5$	−3.18046	−	3.85807i	−0.636091	−	0.771614i
$6$		0			0
$7$	4.73972	+	4.73972i	0.677103	+	0.677103i	0.959344	−	0.282241i	$-0.0910777\pi$
$7$	4.73972	+	4.73972i	0.677103	+	0.677103i	−0.282241	+	0.959344i	$0.591078\pi$
$8$		0			0
$9$	−8.98565			−0.998406
$10$		0			0
$11$	−2.49487	−	2.49487i	−0.226806	−	0.226806i	0.584551	−	0.811357i	$-0.301271\pi$
$11$	−2.49487	−	2.49487i	−0.226806	−	0.226806i	−0.811357	+	0.584551i	$0.801271\pi$
$12$		0			0
$13$	−18.4567			−1.41974			−0.709871	−	0.704331i	$-0.751247\pi$
$13$	−18.4567			−1.41974			−0.709871	+	0.704331i	$0.751247\pi$
$14$		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	$-0.244435\pi$
$19$	0.469722	+	0.469722i	0.0247222	+	0.0247222i	−0.694638	+	0.719360i	$0.744435\pi$
$20$		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	$0.578988\pi$
$23$	−27.9445	+	27.9445i	−1.21498	+	1.21498i	−0.969369	+	0.245608i	$0.921012\pi$
$24$		0			0
$25$	−4.76941	+	24.5408i	−0.190776	+	0.981634i
$26$		0			0
$27$	−2.15442			−0.0797934
$28$		0			0
$29$	−15.6079	−	15.6079i	−0.538203	−	0.538203i	0.384798	−	0.923001i	$-0.374271\pi$
$29$	−15.6079	−	15.6079i	−0.538203	−	0.538203i	−0.923001	+	0.384798i	$0.874271\pi$
$30$		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
$35$	3.21171	−	33.3606i	0.0917630	−	0.953161i
$36$		0			0
$37$	−29.1310			−0.787325			−0.393662	−	0.919255i	$-0.628792\pi$
$37$	−29.1310			−0.787325			−0.393662	+	0.919255i	$0.628792\pi$
$38$		0			0
$39$	−2.21084			−0.0566882
$40$		0			0
$41$			16.4684i			0.401669i	0.979625	+	0.200834i	$0.0643653\pi$
$41$			16.4684i			0.401669i	−0.979625	+	0.200834i	$0.935635\pi$
$42$		0			0
$43$			4.48974i			0.104413i	0.998636	+	0.0522063i	$0.0166253\pi$
$43$			4.48974i			0.104413i	−0.998636	+	0.0522063i	$0.983375\pi$
$44$		0			0
$45$	28.5785	+	34.6673i	0.635077	+	0.770384i
$46$		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
$53$		−	78.7038i		−	1.48498i	−0.669859	−	0.742488i	$-0.733646\pi$
$53$		−	78.7038i		−	1.48498i	0.669859	−	0.742488i	$-0.266354\pi$
$54$		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	$-0.737538\pi$
$59$	3.26583	−	3.26583i	0.0553530	−	0.0553530i	0.734241	+	0.678888i	$0.237538\pi$
$60$		0			0
$61$	−23.0393	+	23.0393i	−0.377694	+	0.377694i	−0.870269	−	0.492576i	$-0.836055\pi$
$61$	−23.0393	+	23.0393i	−0.377694	+	0.377694i	0.492576	+	0.870269i	$0.336055\pi$
$62$		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
$67$		−	58.9247i		−	0.879474i	−0.898127	−	0.439737i	$-0.855072\pi$
$67$		−	58.9247i		−	0.879474i	0.898127	−	0.439737i	$-0.144928\pi$
$68$		0			0
$69$	−3.34734	+	3.34734i	−0.0485122	+	0.0485122i
$70$		0			0
$71$			76.8059i			1.08177i	0.841096	+	0.540886i	$0.181911\pi$
$71$			76.8059i			1.08177i	−0.841096	+	0.540886i	$0.818089\pi$
$72$		0			0
$73$	−18.7472	+	18.7472i	−0.256811	+	0.256811i	−0.823756	−	0.566945i	$-0.808125\pi$
$73$	−18.7472	+	18.7472i	−0.256811	+	0.256811i	0.566945	+	0.823756i	$0.308125\pi$
$74$		0			0
$75$	−0.571306	+	2.93964i	−0.00761742	+	0.0391952i
$76$		0			0
$77$		−	23.6499i		−	0.307142i
$78$		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
$83$	120.053			1.44642			0.723210	−	0.690628i	$-0.242666\pi$
$83$	120.053			1.44642			0.723210	+	0.690628i	$0.242666\pi$
$84$		0			0
$85$	−75.4286	−	7.26169i	−0.887396	−	0.0854316i
$86$		0			0
$87$	−1.86960	−	1.86960i	−0.0214897	−	0.0214897i
$88$		0			0
$89$	87.7260			0.985686			0.492843	−	0.870118i	$-0.335958\pi$
$89$	87.7260			0.985686			0.492843	+	0.870118i	$0.335958\pi$
$90$		0			0
$91$	−87.4794	−	87.4794i	−0.961312	−	0.961312i
$92$		0			0
$93$	−5.90143			−0.0634563
$94$		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	0.545398	−	0.838177i	$-0.316379\pi$
$101$	−29.5707	−	29.5707i	−0.292780	−	0.292780i	−0.838177	+	0.545398i	$0.816379\pi$
$102$		0			0
$103$	48.5504	−	48.5504i	0.471363	−	0.471363i	−0.430992	−	0.902356i	$-0.641836\pi$
$103$	48.5504	−	48.5504i	0.471363	−	0.471363i	0.902356	+	0.430992i	$0.141836\pi$
$104$		0			0
$105$	0.384716	−	3.99612i	0.00366396	−	0.0380583i
$106$		0			0
$107$	62.1016			0.580389			0.290194	−	0.956968i	$-0.406280\pi$
$107$	62.1016			0.580389			0.290194	+	0.956968i	$0.406280\pi$
$108$		0			0
$109$	31.6457	+	31.6457i	0.290327	+	0.290327i	0.837209	−	0.546882i	$-0.184186\pi$
$109$	31.6457	+	31.6457i	0.290327	+	0.290327i	−0.546882	+	0.837209i	$0.684186\pi$
$110$		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
$115$	196.688	+	18.9356i	1.71033	+	0.164657i
$116$		0			0
$117$	165.845			1.41748
$118$		0			0
$119$	101.587			0.853671
$120$		0			0
$121$		−	108.551i		−	0.897118i
$122$		0			0
$123$			1.97268i			0.0160380i
$124$		0			0
$125$	109.849	−	59.6503i	0.878793	−	0.477202i
$126$		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	−0.999964	−	0.00854147i	$-0.997281\pi$
$131$	−129.876	+	129.876i	−0.991422	+	0.991422i	0.00854147	+	0.999964i	$0.497281\pi$
$132$		0			0
$133$			4.45270i			0.0334789i
$134$		0			0
$135$	6.85204	+	8.31191i	0.0507558	+	0.0615697i
$136$		0			0
$137$	−69.8267	−	69.8267i	−0.509684	−	0.509684i	0.404745	−	0.914429i	$-0.367360\pi$
$137$	−69.8267	−	69.8267i	−0.509684	−	0.509684i	−0.914429	+	0.404745i	$0.867360\pi$
$138$		0			0
$139$	−16.8371	+	16.8371i	−0.121130	+	0.121130i	−0.765073	−	0.643943i	$-0.777297\pi$
$139$	−16.8371	+	16.8371i	−0.121130	+	0.121130i	0.643943	+	0.765073i	$0.277297\pi$
$140$		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
$147$		−	0.487538i		−	0.00331659i
$148$		0			0
$149$	−126.048	+	126.048i	−0.845963	+	0.845963i	−0.989627	−	0.143664i	$-0.954112\pi$
$149$	−126.048	+	126.048i	−0.845963	+	0.845963i	0.143664	+	0.989627i	$0.454112\pi$
$150$		0			0
$151$		−	170.000i		−	1.12583i	−0.826516	−	0.562914i	$-0.809680\pi$
$151$		−	170.000i		−	1.12583i	0.826516	−	0.562914i	$-0.190320\pi$
$152$		0			0
$153$	−96.2951	+	96.2951i	−0.629380	+	0.629380i
$154$		0			0
$155$	156.690	+	190.074i	1.01091	+	1.22629i
$156$		0			0
$157$		−	12.1854i		−	0.0776137i	−0.999247	−	0.0388069i	$-0.987644\pi$
$157$		−	12.1854i		−	0.0776137i	0.999247	−	0.0388069i	$-0.0123557\pi$
$158$		0			0
$159$		−	9.42757i		−	0.0592929i
$160$		0			0
$161$	−264.898			−1.64533
$162$		0			0
$163$	−285.780			−1.75325			−0.876627	−	0.481170i	$-0.840212\pi$
$163$	−285.780			−1.75325			−0.876627	+	0.481170i	$0.840212\pi$
$164$		0			0
$165$	−0.202504	+	2.10345i	−0.00122730	+	0.0127482i
$166$		0			0
$167$	−102.579	−	102.579i	−0.614248	−	0.614248i	0.329802	−	0.944050i	$-0.393018\pi$
$167$	−102.579	−	102.579i	−0.614248	−	0.614248i	−0.944050	+	0.329802i	$0.893018\pi$
$168$		0			0
$169$	171.648			1.01567
$170$		0			0
$171$	−4.22075	−	4.22075i	−0.0246828	−	0.0246828i
$172$		0			0
$173$	−68.3056			−0.394830			−0.197415	−	0.980320i	$-0.563255\pi$
$173$	−68.3056			−0.394830			−0.197415	+	0.980320i	$0.563255\pi$
$174$		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	$-0.477469\pi$
$179$	−165.892	−	165.892i	−0.926773	−	0.926773i	−0.997496	+	0.0707227i	$0.977469\pi$
$180$		0			0
$181$	101.633	+	101.633i	0.561506	+	0.561506i	0.929735	−	0.368229i	$-0.120036\pi$
$181$	101.633	+	101.633i	0.561506	+	0.561506i	−0.368229	+	0.929735i	$0.620036\pi$
$182$		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
$187$	−53.4726			−0.285950
$188$		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
$195$	7.03148	+	8.52958i	0.0360589	+	0.0437414i
$196$		0			0
$197$	335.205			1.70155			0.850775	−	0.525530i	$-0.176133\pi$
$197$	335.205			1.70155			0.850775	+	0.525530i	$0.176133\pi$
$198$		0			0
$199$	−184.734			−0.928313			−0.464156	−	0.885753i	$-0.653642\pi$
$199$	−184.734			−0.928313			−0.464156	+	0.885753i	$0.653642\pi$
$200$		0			0
$201$		−	7.05833i		−	0.0351161i
$202$		0			0
$203$		−	147.954i		−	0.728838i
$204$		0			0
$205$	63.5363	−	52.3771i	0.309933	−	0.255498i
$206$		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	−0.994616	−	0.103627i	$-0.966955\pi$
$211$	−187.999	+	187.999i	−0.890989	+	0.890989i	0.103627	+	0.994616i	$0.466955\pi$
$212$		0			0
$213$			9.20023i			0.0431936i
$214$		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
$227$			146.872i			0.647015i	0.946226	+	0.323507i	$0.104862\pi$
$227$			146.872i			0.647015i	−0.946226	+	0.323507i	$0.895138\pi$
$228$		0			0
$229$	−194.697	+	194.697i	−0.850205	+	0.850205i	−0.990158	−	0.139953i	$-0.955305\pi$
$229$	−194.697	+	194.697i	−0.850205	+	0.850205i	0.139953	+	0.990158i	$0.455305\pi$
$230$		0			0
$231$		−	2.83292i		−	0.0122637i
$232$		0			0
$233$	87.0218	−	87.0218i	0.373484	−	0.373484i	−0.495260	−	0.868745i	$-0.664927\pi$
$233$	87.0218	−	87.0218i	0.373484	−	0.373484i	0.868745	+	0.495260i	$0.164927\pi$
$234$		0			0
$235$	−286.233	−	27.5563i	−1.21801	−	0.117261i
$236$		0			0
$237$			16.9732i			0.0716169i
$238$		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
$243$	29.0460			0.119531
$244$		0			0
$245$	−15.7027	+	12.9448i	−0.0640927	+	0.0528357i
$246$		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	0.969589	−	0.244740i	$-0.0787026\pi$
$251$	181.937	+	181.937i	0.724849	+	0.724849i	−0.244740	+	0.969589i	$0.578703\pi$
$252$		0			0
$253$	139.435			0.551128
$254$		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	−0.948327	−	0.317294i	$-0.897226\pi$
$263$	−165.962	+	165.962i	−0.631034	+	0.631034i	0.317294	+	0.948327i	$0.397226\pi$
$264$		0			0
$265$	−303.645	+	250.314i	−1.14583	+	0.944580i
$266$		0			0
$267$	10.5083			0.0393570
$268$		0			0
$269$	−310.294	−	310.294i	−1.15351	−	1.15351i	−0.985844	−	0.167665i	$-0.946377\pi$
$269$	−310.294	−	310.294i	−1.15351	−	1.15351i	−0.167665	−	0.985844i	$-0.553623\pi$
$270$		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
$275$	73.1251	−	49.3270i	0.265910	−	0.179371i
$276$		0			0
$277$	−143.172			−0.516868			−0.258434	−	0.966029i	$-0.583206\pi$
$277$	−143.172			−0.516868			−0.258434	+	0.966029i	$0.583206\pi$
$278$		0			0
$279$	442.693			1.58671
$280$		0			0
$281$		−	139.408i		−	0.496115i	−0.968745	−	0.248057i	$-0.920208\pi$
$281$		−	139.408i		−	0.496115i	0.968745	−	0.248057i	$-0.0797921\pi$
$282$		0			0
$283$			336.283i			1.18828i	0.804362	+	0.594140i	$0.202507\pi$
$283$			336.283i			1.18828i	−0.804362	+	0.594140i	$0.797493\pi$
$284$		0			0
$285$	0.0381266	−	0.396029i	0.000133777	−	0.00138957i
$286$		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
$293$		−	33.1195i		−	0.113036i	−0.998402	−	0.0565179i	$-0.982000\pi$
$293$		−	33.1195i		−	0.113036i	0.998402	−	0.0565179i	$-0.0179998\pi$
$294$		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
$307$			479.642i			1.56235i	0.624310	+	0.781176i	$0.285380\pi$
$307$			479.642i			1.56235i	−0.624310	+	0.781176i	$0.714620\pi$
$308$		0			0
$309$	5.81564	−	5.81564i	0.0188208	−	0.0188208i
$310$		0			0
$311$		−	328.043i		−	1.05480i	−0.849617	−	0.527401i	$-0.823167\pi$
$311$		−	328.043i		−	1.05480i	0.849617	−	0.527401i	$-0.176833\pi$
$312$		0			0
$313$	−90.2171	+	90.2171i	−0.288233	+	0.288233i	−0.836381	−	0.548148i	$-0.815333\pi$
$313$	−90.2171	+	90.2171i	−0.288233	+	0.288233i	0.548148	+	0.836381i	$0.315333\pi$
$314$		0			0
$315$	−28.8593	+	299.767i	−0.0916167	+	0.951642i
$316$		0			0
$317$		−	324.328i		−	1.02312i	−0.859249	−	0.511558i	$-0.829068\pi$
$317$		−	324.328i		−	1.02312i	0.859249	−	0.511558i	$-0.170932\pi$
$318$		0			0
$319$			77.8792i			0.244135i
$320$		0			0
$321$	7.43887			0.0231741
$322$		0			0
$323$	10.0676			0.0311690
$324$		0			0
$325$	88.0274	−	452.942i	0.270853	−	1.39367i
$326$		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	0.223534	−	0.974696i	$-0.428241\pi$
$331$	−248.635	−	248.635i	−0.751162	−	0.751162i	−0.974696	+	0.223534i	$0.928241\pi$
$332$		0			0
$333$	261.761			0.786069
$334$		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
$347$	−288.892			−0.832540			−0.416270	−	0.909241i	$-0.636663\pi$
$347$	−288.892			−0.832540			−0.416270	+	0.909241i	$0.636663\pi$
$348$		0			0
$349$	345.135	+	345.135i	0.988927	+	0.988927i	0.999939	−	0.0110128i	$-0.00350555\pi$
$349$	345.135	+	345.135i	0.988927	+	0.988927i	−0.0110128	+	0.999939i	$0.503506\pi$
$350$		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
$355$	296.322	−	244.278i	0.834711	−	0.688106i
$356$		0			0
$357$	12.1686			0.0340858
$358$		0			0
$359$	−221.083			−0.615831			−0.307916	−	0.951414i	$-0.599631\pi$
$359$	−221.083			−0.615831			−0.307916	+	0.951414i	$0.599631\pi$
$360$		0			0
$361$		−	360.559i		−	0.998778i
$362$		0			0
$363$		−	13.0029i		−	0.0358206i
$364$		0			0
$365$	131.953	+	12.7034i	0.361514	+	0.0348038i
$366$		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
$373$		−	174.847i		−	0.468758i	−0.972145	−	0.234379i	$-0.924694\pi$
$373$		−	174.847i		−	0.468758i	0.972145	−	0.234379i	$-0.0753056\pi$
$374$		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	$-0.960790\pi$
$379$	−329.561	+	329.561i	−0.869553	+	0.869553i	0.122870	+	0.992423i	$0.460790\pi$
$380$		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
$387$		−	40.3433i		−	0.104246i
$388$		0			0
$389$	−276.184	+	276.184i	−0.709984	+	0.709984i	−0.966532	−	0.256548i	$-0.917415\pi$
$389$	−276.184	+	276.184i	−0.709984	+	0.709984i	0.256548	+	0.966532i	$0.417415\pi$
$390$		0			0
$391$			598.936i			1.53181i
$392$		0			0
$393$	−15.5573	+	15.5573i	−0.0395860	+	0.0395860i
$394$		0			0
$395$	546.676	−	450.660i	1.38399	−	1.14091i
$396$		0			0
$397$			692.870i			1.74526i	0.488378	+	0.872632i	$0.337589\pi$
$397$			692.870i			1.74526i	−0.488378	+	0.872632i	$0.662411\pi$
$398$		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
$403$	909.298			2.25632
$404$		0			0
$405$	−256.385	−	311.010i	−0.633050	−	0.767925i
$406$		0			0
$407$	72.6780	+	72.6780i	0.178570	+	0.178570i
$408$		0			0
$409$	43.3293			0.105940			0.0529698	−	0.998596i	$-0.483131\pi$
$409$	43.3293			0.105940			0.0529698	+	0.998596i	$0.483131\pi$
$410$		0			0
$411$	−8.36423	−	8.36423i	−0.0203509	−	0.0203509i
$412$		0			0
$413$	30.9582			0.0749594
$414$		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	$-0.448117\pi$
$419$	−345.453	−	345.453i	−0.824471	−	0.824471i	−0.986746	+	0.162274i	$0.948117\pi$
$420$		0			0
$421$	−371.173	−	371.173i	−0.881645	−	0.881645i	0.112056	−	0.993702i	$-0.464256\pi$
$421$	−371.173	−	371.173i	−0.881645	−	0.881645i	−0.993702	+	0.112056i	$0.964256\pi$
$422$		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
$427$	−218.400			−0.511475
$428$		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
$435$	−1.26687	+	13.1592i	−0.00291234	+	0.0302511i
$436$		0			0
$437$	−26.2522			−0.0600738
$438$		0			0
$439$	106.380			0.242324			0.121162	−	0.992633i	$-0.461338\pi$
$439$	106.380			0.242324			0.121162	+	0.992633i	$0.461338\pi$
$440$		0			0
$441$			36.5725i			0.0829307i
$442$		0			0
$443$		−	235.281i		−	0.531108i	−0.964096	−	0.265554i	$-0.914445\pi$
$443$		−	235.281i		−	0.531108i	0.964096	−	0.265554i	$-0.0855548\pi$
$444$		0			0
$445$	−279.009	−	338.453i	−0.626986	−	0.760569i
$446$		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
$453$		−	20.3635i		−	0.0449526i
$454$		0			0
$455$	−59.2774	+	615.726i	−0.130280	+	1.35324i
$456$		0			0
$457$	−401.924	−	401.924i	−0.879483	−	0.879483i	0.113998	−	0.993481i	$-0.463634\pi$
$457$	−401.924	−	401.924i	−0.879483	−	0.879483i	−0.993481	+	0.113998i	$0.963634\pi$
$458$		0			0
$459$	−23.0879	+	23.0879i	−0.0503005	+	0.0503005i
$460$		0			0
$461$	158.945	−	158.945i	0.344783	−	0.344783i	−0.513379	−	0.858162i	$-0.671606\pi$
$461$	158.945	−	158.945i	0.344783	−	0.344783i	0.858162	+	0.513379i	$0.171606\pi$
$462$		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
$467$		−	188.298i		−	0.403208i	−0.979467	−	0.201604i	$-0.935385\pi$
$467$		−	188.298i		−	0.403208i	0.979467	−	0.201604i	$-0.0646154\pi$
$468$		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
$475$	−13.7677	+	9.28707i	−0.0289845	+	0.0195517i
$476$		0			0
$477$			707.204i			1.48261i
$478$		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
$483$	−31.7309			−0.0656955
$484$		0			0
$485$	−243.842	−	23.4752i	−0.502766	−	0.0484025i
$486$		0			0
$487$	−53.3922	−	53.3922i	−0.109635	−	0.109635i	0.650161	−	0.759796i	$-0.274701\pi$
$487$	−53.3922	−	53.3922i	−0.109635	−	0.109635i	−0.759796	+	0.650161i	$0.774701\pi$
$488$		0			0
$489$	−34.2324			−0.0700048
$490$		0			0
$491$	−96.7903	−	96.7903i	−0.197129	−	0.197129i	0.601639	−	0.798768i	$-0.294515\pi$
$491$	−96.7903	−	96.7903i	−0.197129	−	0.197129i	−0.798768	+	0.601639i	$0.794515\pi$
$492$		0			0
$493$	−334.525			−0.678550
$494$		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	$-0.186574\pi$
$499$	139.686	+	139.686i	0.279931	+	0.279931i	−0.553150	+	0.833081i	$0.686574\pi$
$500$		0			0
$501$	−12.2875	−	12.2875i	−0.0245260	−	0.0245260i
$502$		0			0
$503$	319.688	−	319.688i	0.635562	−	0.635562i	−0.313895	−	0.949458i	$-0.601634\pi$
$503$	319.688	−	319.688i	0.635562	−	0.635562i	0.949458	+	0.313895i	$0.101634\pi$
$504$		0			0
$505$	−20.0376	+	208.134i	−0.0396784	+	0.412147i
$506$		0			0
$507$	20.5610			0.0405542
$508$		0			0
$509$	−702.440	−	702.440i	−1.38004	−	1.38004i	−0.844529	−	0.535510i	$-0.820119\pi$
$509$	−702.440	−	702.440i	−1.38004	−	1.38004i	−0.535510	−	0.844529i	$-0.679881\pi$
$510$		0			0
$511$	−177.713			−0.347775
$512$		0			0
$513$	−1.01198	−	1.01198i	−0.00197267	−	0.00197267i
$514$		0			0
$515$	−341.723	−	32.8985i	−0.663541	−	0.0638806i
$516$		0			0
$517$	−202.915			−0.392486
$518$		0			0
$519$	−8.18202			−0.0157650
$520$		0			0
$521$			614.419i			1.17931i	0.807656	+	0.589654i	$0.200736\pi$
$521$			614.419i			1.17931i	−0.807656	+	0.589654i	$0.799264\pi$
$522$		0			0
$523$			178.970i			0.342199i	0.985254	+	0.171100i	$0.0547320\pi$
$523$			178.970i			0.342199i	−0.985254	+	0.171100i	$0.945268\pi$
$524$		0			0
$525$	−16.6409	+	11.2252i	−0.0316969	+	0.0213814i
$526$		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
$533$		−	303.952i		−	0.570266i
$534$		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	−0.478045	−	0.878336i	$-0.658654\pi$
$541$	216.557	−	216.557i	0.400291	−	0.400291i	0.878336	+	0.478045i	$0.158654\pi$
$542$		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
$547$			204.888i			0.374567i	0.982306	+	0.187284i	$0.0599683\pi$
$547$			204.888i			0.374567i	−0.982306	+	0.187284i	$0.940032\pi$
$548$		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
$555$	11.0981	+	13.4626i	0.0199966	+	0.0242570i
$556$		0			0
$557$		−	345.777i		−	0.620784i	−0.950609	−	0.310392i	$-0.899540\pi$
$557$		−	345.777i		−	0.620784i	0.950609	−	0.310392i	$-0.100460\pi$
$558$		0			0
$559$		−	82.8656i		−	0.148239i
$560$		0			0
$561$	−6.40525			−0.0114176
$562$		0			0
$563$	319.750			0.567940			0.283970	−	0.958833i	$-0.408348\pi$
$563$	319.750			0.567940			0.283970	+	0.958833i	$0.408348\pi$
$564$		0			0
$565$	−38.0285	+	395.010i	−0.0673071	+	0.699133i
$566$		0			0
$567$	382.082	+	382.082i	0.673866	+	0.673866i
$568$		0			0
$569$	146.472			0.257420			0.128710	−	0.991682i	$-0.458916\pi$
$569$	146.472			0.257420			0.128710	+	0.991682i	$0.458916\pi$
$570$		0			0
$571$	221.670	+	221.670i	0.388214	+	0.388214i	0.874050	−	0.485836i	$-0.161485\pi$
$571$	221.670	+	221.670i	0.388214	+	0.388214i	−0.485836	+	0.874050i	$0.661485\pi$
$572$		0			0
$573$	17.3034			0.0301980
$574$		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
$587$	−176.460			−0.300614			−0.150307	−	0.988639i	$-0.548026\pi$
$587$	−176.460			−0.300614			−0.150307	+	0.988639i	$0.548026\pi$
$588$		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
$595$	−323.092	−	391.929i	−0.543012	−	0.658704i
$596$		0			0
$597$	−22.1285			−0.0370661
$598$		0			0
$599$	−550.344			−0.918771			−0.459386	−	0.888237i	$-0.651930\pi$
$599$	−550.344			−0.918771			−0.459386	+	0.888237i	$0.651930\pi$
$600$		0			0
$601$		−	440.349i		−	0.732693i	−0.930478	−	0.366347i	$-0.880608\pi$
$601$		−	440.349i		−	0.732693i	0.930478	−	0.366347i	$-0.119392\pi$
$602$		0			0
$603$			529.477i			0.878071i
$604$		0			0
$605$	−418.799	+	345.243i	−0.692229	+	0.570649i
$606$		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
$613$			228.861i			0.373346i	0.982422	+	0.186673i	$0.0597706\pi$
$613$			228.861i			0.373346i	−0.982422	+	0.186673i	$0.940229\pi$
$614$		0			0
$615$	7.61073	−	6.27402i	0.0123752	−	0.0102017i
$616$		0			0
$617$	236.901	+	236.901i	0.383957	+	0.383957i	0.872525	−	0.488569i	$-0.162481\pi$
$617$	236.901	+	236.901i	0.383957	+	0.383957i	−0.488569	+	0.872525i	$0.662481\pi$
$618$		0			0
$619$	204.389	−	204.389i	0.330192	−	0.330192i	−0.522468	−	0.852659i	$-0.674988\pi$
$619$	204.389	−	204.389i	0.330192	−	0.330192i	0.852659	+	0.522468i	$0.174988\pi$
$620$		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
$627$		−	0.280751i		−	0.000447769i
$628$		0			0
$629$	−312.184	+	312.184i	−0.496317	+	0.496317i
$630$		0			0
$631$			219.606i			0.348029i	0.984743	+	0.174014i	$0.0556739\pi$
$631$			219.606i			0.348029i	−0.984743	+	0.174014i	$0.944326\pi$
$632$		0			0
$633$	−22.5195	+	22.5195i	−0.0355759	+	0.0355759i
$634$		0			0
$635$	−423.325	−	40.7545i	−0.666654	−	0.0641803i
$636$		0			0
$637$			75.1203i			0.117928i
$638$		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
$643$	−864.637			−1.34469			−0.672346	−	0.740237i	$-0.734713\pi$
$643$	−864.637			−1.34469			−0.672346	+	0.740237i	$0.734713\pi$
$644$		0			0
$645$	2.07489	−	1.71047i	0.00321689	−	0.00265189i
$646$		0			0
$647$	−569.775	−	569.775i	−0.880641	−	0.880641i	0.112959	−	0.993600i	$-0.463967\pi$
$647$	−569.775	−	569.775i	−0.880641	−	0.880641i	−0.993600	+	0.112959i	$0.963967\pi$
$648$		0			0
$649$	−16.2956			−0.0251088
$650$		0			0
$651$	−27.9711	−	27.9711i	−0.0429664	−	0.0429664i
$652$		0			0
$653$	139.259			0.213261			0.106630	−	0.994299i	$-0.465994\pi$
$653$	139.259			0.213261			0.106630	+	0.994299i	$0.465994\pi$
$654$		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	$-0.128040\pi$
$659$	348.410	+	348.410i	0.528695	+	0.528695i	−0.391488	+	0.920183i	$0.628040\pi$
$660$		0			0
$661$	270.659	+	270.659i	0.409469	+	0.409469i	0.881553	−	0.472084i	$-0.156498\pi$
$661$	270.659	+	270.659i	0.409469	+	0.409469i	−0.472084	+	0.881553i	$0.656498\pi$
$662$		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
$667$	872.309			1.30781
$668$		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
$675$	10.2753	−	52.8713i	0.0152227	−	0.0783278i
$676$		0			0
$677$	−519.409			−0.767221			−0.383611	−	0.923495i	$-0.625319\pi$
$677$	−519.409			−0.767221			−0.383611	+	0.923495i	$0.625319\pi$
$678$		0			0
$679$	328.404			0.483659
$680$		0			0
$681$			17.5932i			0.0258343i
$682$		0			0
$683$		−	254.873i		−	0.373167i	−0.982439	−	0.186583i	$-0.940259\pi$
$683$		−	254.873i		−	0.373167i	0.982439	−	0.186583i	$-0.0597415\pi$
$684$		0			0
$685$	−47.3157	+	491.477i	−0.0690739	+	0.717485i
$686$		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	−0.332108	−	0.943241i	$-0.607760\pi$
$691$	422.293	−	422.293i	0.611133	−	0.611133i	0.943241	+	0.332108i	$0.107760\pi$
$692$		0			0
$693$			212.510i			0.306652i
$694$		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	−0.546473	−	0.837477i	$-0.684030\pi$
$701$	203.994	−	203.994i	0.291004	−	0.291004i	0.837477	+	0.546473i	$0.184030\pi$
$702$		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
$707$		−	280.314i		−	0.396484i
$708$		0			0
$709$	407.106	−	407.106i	0.574197	−	0.574197i	−0.359101	−	0.933299i	$-0.616917\pi$
$709$	407.106	−	407.106i	0.574197	−	0.574197i	0.933299	+	0.359101i	$0.116917\pi$
$710$		0			0
$711$		−	1273.24i		−	1.79077i
$712$		0			0
$713$	1376.73	−	1376.73i	1.93090	−	1.93090i
$714$		0			0
$715$	31.2021	−	324.102i	0.0436392	−	0.453290i
$716$		0			0
$717$			40.1086i			0.0559394i
$718$		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
$723$	−45.3838			−0.0627716
$724$		0			0
$725$	457.471	−	308.590i	0.630995	−	0.425642i
$726$		0			0
$727$	442.782	+	442.782i	0.609054	+	0.609054i	0.942699	−	0.333645i	$-0.108279\pi$
$727$	442.782	+	442.782i	0.609054	+	0.609054i	−0.333645	+	0.942699i	$0.608279\pi$
$728$		0			0
$729$	−722.036			−0.990447
$730$		0			0
$731$	48.1145	+	48.1145i	0.0658201	+	0.0658201i
$732$		0			0
$733$	358.600			0.489222			0.244611	−	0.969621i	$-0.421340\pi$
$733$	358.600			0.489222			0.244611	+	0.969621i	$0.421340\pi$
$734$		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	$-0.435550\pi$
$739$	−575.294	−	575.294i	−0.778477	−	0.778477i	−0.979572	+	0.201095i	$0.935550\pi$
$740$		0			0
$741$	−1.03848	−	1.03848i	−0.00140146	−	0.00140146i
$742$		0			0
$743$	−55.8927	+	55.8927i	−0.0752258	+	0.0752258i	−0.743719	−	0.668493i	$-0.766940\pi$
$743$	−55.8927	+	55.8927i	−0.0752258	+	0.0752258i	0.668493	+	0.743719i	$0.266940\pi$
$744$		0			0
$745$	887.195	+	85.4124i	1.19087	+	0.114647i
$746$		0			0
$747$	−1078.75			−1.44411
$748$		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
$755$	−655.872	+	540.677i	−0.868704	+	0.716129i
$756$		0			0
$757$	495.675			0.654789			0.327395	−	0.944888i	$-0.393829\pi$
$757$	495.675			0.654789			0.327395	+	0.944888i	$0.393829\pi$
$758$		0			0
$759$	16.7023			0.0220057
$760$		0			0
$761$			228.669i			0.300485i	0.988649	+	0.150243i	$0.0480055\pi$
$761$			228.669i			0.300485i	−0.988649	+	0.150243i	$0.951995\pi$
$762$		0			0
$763$			299.983i			0.393163i
$764$		0			0
$765$	677.775	+	65.2510i	0.885981	+	0.0852954i
$766$		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
$773$			186.546i			0.241328i	0.992693	+	0.120664i	$0.0385023\pi$
$773$			186.546i			0.241328i	−0.992693	+	0.120664i	$0.961498\pi$
$774$		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
$787$			1134.28i			1.44127i	0.693315	+	0.720635i	$0.256150\pi$
$787$			1134.28i			1.44127i	−0.693315	+	0.720635i	$0.743850\pi$
$788$		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
$795$	−36.3722	+	29.9840i	−0.0457512	+	0.0377157i
$796$		0			0
$797$		−	250.905i		−	0.314812i	−0.987534	−	0.157406i	$-0.949687\pi$
$797$		−	250.905i		−	0.314812i	0.987534	−	0.157406i	$-0.0503132\pi$
$798$		0			0
$799$		−	871.610i		−	1.09088i
$800$		0			0
$801$	−788.276			−0.984114
$802$		0			0
$803$	93.5435			0.116493
$804$		0			0
$805$	842.496	+	1022.00i	1.04658	+	1.26956i
$806$		0			0
$807$	−37.1687	−	37.1687i	−0.0460579	−	0.0460579i
$808$		0			0
$809$	−1099.77			−1.35942			−0.679712	−	0.733479i	$-0.737895\pi$
$809$	−1099.77			−1.35942			−0.679712	+	0.733479i	$0.737895\pi$
$810$		0			0
$811$	376.722	+	376.722i	0.464515	+	0.464515i	0.900132	−	0.435617i	$-0.143470\pi$
$811$	376.722	+	376.722i	0.464515	+	0.464515i	−0.435617	+	0.900132i	$0.643470\pi$
$812$		0			0
$813$	32.6399			0.0401474
$814$		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	0.599874	−	0.800094i	$-0.295217\pi$
$821$	−164.380	−	164.380i	−0.200220	−	0.200220i	−0.800094	+	0.599874i	$0.795217\pi$
$822$		0			0
$823$	794.892	−	794.892i	0.965847	−	0.965847i	−0.0335887	−	0.999436i	$-0.510694\pi$
$823$	794.892	−	794.892i	0.965847	−	0.965847i	0.999436	+	0.0335887i	$0.0106936\pi$
$824$		0			0
$825$	8.75933	−	5.90867i	0.0106174	−	0.00716202i
$826$		0			0
$827$	696.994			0.842798			0.421399	−	0.906875i	$-0.361539\pi$
$827$	696.994			0.842798			0.421399	+	0.906875i	$0.361539\pi$
$828$		0			0
$829$	857.248	+	857.248i	1.03407	+	1.03407i	0.999399	+	0.0346759i	$0.0110399\pi$
$829$	857.248	+	857.248i	1.03407	+	1.03407i	0.0346759	+	0.999399i	$0.488960\pi$
$830$		0			0
$831$	−17.1500			−0.0206378
$832$		0			0
$833$	−43.6173	−	43.6173i	−0.0523617	−	0.0523617i
$834$		0			0
$835$	−69.5094	+	722.008i	−0.0832448	+	0.864681i
$836$		0			0
$837$	106.141			0.126811
$838$		0			0
$839$	428.122			0.510277			0.255139	−	0.966905i	$-0.417879\pi$
$839$	428.122			0.510277			0.255139	+	0.966905i	$0.417879\pi$
$840$		0			0
$841$		−	353.787i		−	0.420675i
$842$		0			0
$843$		−	16.6991i		−	0.0198091i
$844$		0			0
$845$	−545.919	−	662.231i	−0.646058	−	0.783705i
$846$		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
$853$			1569.13i			1.83955i	0.392451	+	0.919773i	$0.371627\pi$
$853$			1569.13i			1.83955i	−0.392451	+	0.919773i	$0.628373\pi$
$854$		0			0
$855$	−2.86005	+	29.7079i	−0.00334508	+	0.0347461i
$856$		0			0
$857$	−454.985	−	454.985i	−0.530904	−	0.530904i	0.389937	−	0.920841i	$-0.372497\pi$
$857$	−454.985	−	454.985i	−0.530904	−	0.530904i	−0.920841	+	0.389937i	$0.872497\pi$
$858$		0			0
$859$	−620.538	+	620.538i	−0.722396	+	0.722396i	−0.969093	−	0.246697i	$-0.920655\pi$
$859$	−620.538	+	620.538i	−0.722396	+	0.722396i	0.246697	+	0.969093i	$0.420655\pi$
$860$		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
$867$			7.10467i			0.00819454i
$868$		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
$875$	803.380	+	237.929i	0.918149	+	0.271918i
$876$		0			0
$877$		−	1505.10i		−	1.71620i	−0.513485	−	0.858098i	$-0.671646\pi$
$877$		−	1505.10i		−	1.71620i	0.513485	−	0.858098i	$-0.328354\pi$
$878$		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
$883$	−512.240			−0.580114			−0.290057	−	0.957009i	$-0.593674\pi$
$883$	−512.240			−0.580114			−0.290057	+	0.957009i	$0.593674\pi$
$884$		0			0
$885$	−2.75346	−	0.265082i	−0.00311126	−	0.000299528i
$886$		0			0
$887$	−495.921	−	495.921i	−0.559099	−	0.559099i	0.369952	−	0.929051i	$-0.379374\pi$
$887$	−495.921	−	495.921i	−0.559099	−	0.559099i	−0.929051	+	0.369952i	$0.879374\pi$
$888$		0			0
$889$	570.132			0.641318
$890$		0			0
$891$	−201.118	−	201.118i	−0.225722	−	0.225722i
$892$		0			0
$893$	38.2039			0.0427816
$894$		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
$907$	530.597			0.585002			0.292501	−	0.956265i	$-0.405512\pi$
$907$	530.597			0.585002			0.292501	+	0.956265i	$0.405512\pi$
$908$		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
$915$	19.4248	+	1.87007i	0.0212292	+	0.00204379i
$916$		0			0
$917$	−1231.15			−1.34259
$918$		0			0
$919$	0.377866			0.000411171			0.000205586	−	1.00000i	$-0.499935\pi$
$919$	0.377866			0.000411171			0.000205586		1.00000i	$0.499935\pi$
$920$		0			0
$921$			57.4542i			0.0623824i
$922$		0			0
$923$		−	1417.58i		−	1.53584i
$924$		0			0
$925$	138.938	−	714.899i	0.150203	−	0.772864i
$926$		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
$933$		−	39.2948i		−	0.0421166i
$934$		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	$0.164686\pi$
$937$	1277.81	+	1277.81i	1.36372	+	1.36372i	0.494603	+	0.869119i	$0.335314\pi$
$938$		0			0
$939$	−10.8067	+	10.8067i	−0.0115087	+	0.0115087i
$940$		0			0
$941$	−557.710	+	557.710i	−0.592678	+	0.592678i	−0.938354	−	0.345676i	$-0.887650\pi$
$941$	−557.710	+	557.710i	−0.592678	+	0.592678i	0.345676	+	0.938354i	$0.387650\pi$
$942$		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
$947$		−	978.575i		−	1.03334i	−0.856184	−	0.516671i	$-0.827171\pi$
$947$		−	978.575i		−	1.03334i	0.856184	−	0.516671i	$-0.172829\pi$
$948$		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	−0.748836	−	0.662755i	$-0.769387\pi$
$953$	−82.0352	+	82.0352i	−0.0860810	+	0.0860810i	0.662755	+	0.748836i	$0.269387\pi$
$954$		0			0
$955$	−459.428	−	557.312i	−0.481077	−	0.583573i
$956$		0			0
$957$			9.32880i			0.00974796i
$958$		0			0
$959$		−	661.919i		−	0.690217i
$960$		0			0
$961$	1466.20			1.52571
$962$		0			0
$963$	−558.024			−0.579464
$964$		0			0
$965$	−22.2103	+	230.703i	−0.0230159	+	0.239071i
$966$		0			0
$967$	241.731	+	241.731i	0.249980	+	0.249980i	0.820962	−	0.570982i	$-0.193438\pi$
$967$	241.731	+	241.731i	0.249980	+	0.249980i	−0.570982	+	0.820962i	$0.693438\pi$
$968$		0			0
$969$	1.20595			0.00124453
$970$		0			0
$971$	970.962	+	970.962i	0.999961	+	0.999961i	1.00000		3.91262e-5i	$-1.24543e-5\pi$
$971$	970.962	+	970.962i	0.999961	+	0.999961i	−3.91262e−5		1.00000i	$0.500012\pi$
$972$		0			0
$973$	−159.606			−0.164035
$974$		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	−0.556569	−	0.830801i	$-0.687883\pi$
$983$	269.570	−	269.570i	0.274232	−	0.274232i	0.830801	+	0.556569i	$0.187883\pi$
$984$		0			0
$985$	−1066.11	−	1293.25i	−1.08234	−	1.31294i
$986$		0			0
$987$	46.1769			0.0467851
$988$		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
$995$	587.539	+	712.718i	0.590491	+	0.716299i
$996$		0			0
$997$	1154.22			1.15769			0.578845	−	0.815437i	$-0.303504\pi$
$997$	1154.22			1.15769			0.578845	+	0.815437i	$0.303504\pi$
$998$		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.t.a.113.11		44
4.3	odd	2		80.3.t.a.53.5	yes	44
5.2	odd	4		320.3.i.a.177.12		44
8.3	odd	2		640.3.t.b.353.11		44
8.5	even	2		640.3.t.a.353.12		44
16.3	odd	4		80.3.i.a.13.16	✓	44
16.5	even	4		640.3.i.a.33.12		44
16.11	odd	4		640.3.i.b.33.11		44
16.13	even	4		320.3.i.a.273.11		44
20.3	even	4		400.3.i.b.357.7		44
20.7	even	4		80.3.i.a.37.16	yes	44
20.19	odd	2		400.3.t.b.293.18		44
40.27	even	4		640.3.i.b.97.12		44
40.37	odd	4		640.3.i.a.97.11		44
80.3	even	4		400.3.t.b.157.18		44
80.19	odd	4		400.3.i.b.93.7		44
80.27	even	4		640.3.t.b.417.11		44
80.37	odd	4		640.3.t.a.417.12		44
80.67	even	4		80.3.t.a.77.5	yes	44
80.77	odd	4	inner	320.3.t.a.17.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.16	✓	44	16.3	odd	4
80.3.i.a.37.16	yes	44	20.7	even	4
80.3.t.a.53.5	yes	44	4.3	odd	2
80.3.t.a.77.5	yes	44	80.67	even	4
320.3.i.a.177.12		44	5.2	odd	4
320.3.i.a.273.11		44	16.13	even	4
320.3.t.a.17.11		44	80.77	odd	4	inner
320.3.t.a.113.11		44	1.1	even	1	trivial
400.3.i.b.93.7		44	80.19	odd	4
400.3.i.b.357.7		44	20.3	even	4
400.3.t.b.157.18		44	80.3	even	4
400.3.t.b.293.18		44	20.19	odd	2
640.3.i.a.33.12		44	16.5	even	4
640.3.i.a.97.11		44	40.37	odd	4
640.3.i.b.33.11		44	16.11	odd	4
640.3.i.b.97.12		44	40.27	even	4
640.3.t.a.353.12		44	8.5	even	2
640.3.t.a.417.12		44	80.37	odd	4
640.3.t.b.353.11		44	8.3	odd	2
640.3.t.b.417.11		44	80.27	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.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.119786 q^{3} +(-3.18046 - 3.85807i) q^{5} +(4.73972 + 4.73972i) q^{7} -8.98565 q^{9} +O(q^{10})\)	\(q+0.119786 q^{3} +(-3.18046 - 3.85807i) q^{5} +(4.73972 + 4.73972i) q^{7} -8.98565 q^{9} +(-2.49487 - 2.49487i) q^{11} -18.4567 q^{13} +(-0.380972 - 0.462141i) q^{15} +(10.7165 - 10.7165i) q^{17} +(0.469722 + 0.469722i) q^{19} +(0.567750 + 0.567750i) q^{21} +(-27.9445 + 27.9445i) q^{23} +(-4.76941 + 24.5408i) q^{25} -2.15442 q^{27} +(-15.6079 - 15.6079i) q^{29} -49.2667 q^{31} +(-0.298849 - 0.298849i) q^{33} +(3.21171 - 33.3606i) q^{35} -29.1310 q^{37} -2.21084 q^{39} +16.4684i q^{41} +4.48974i q^{43} +(28.5785 + 34.6673i) q^{45} +(40.6666 - 40.6666i) q^{47} -4.07009i q^{49} +(1.28369 - 1.28369i) q^{51} -78.7038i q^{53} +(-1.69056 + 17.5602i) q^{55} +(0.0562658 + 0.0562658i) q^{57} +(3.26583 - 3.26583i) q^{59} +(-23.0393 + 23.0393i) q^{61} +(-42.5895 - 42.5895i) q^{63} +(58.7006 + 71.2071i) q^{65} -58.9247i q^{67} +(-3.34734 + 3.34734i) q^{69} +76.8059i q^{71} +(-18.7472 + 18.7472i) q^{73} +(-0.571306 + 2.93964i) q^{75} -23.6499i q^{77} +141.697i q^{79} +80.6128 q^{81} +120.053 q^{83} +(-75.4286 - 7.26169i) q^{85} +(-1.86960 - 1.86960i) q^{87} +87.7260 q^{89} +(-87.4794 - 87.4794i) q^{91} -5.90143 q^{93} +(0.318290 - 3.30615i) q^{95} +(34.6438 - 34.6438i) q^{97} +(22.4180 + 22.4180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more