LMFDB - Embedded newform 504.2.i.b.125.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(125,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.i (of order $2$, degree $1$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.6
Character	$\chi$	$=$	504.125
Dual form			504.2.i.b.125.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 - 1.08335i) q^{2} +(-0.347296 + 1.96962i) q^{4} +3.85006i q^{5} +(1.87939 + 1.86223i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.909039 - 1.08335i) q^{2} +(-0.347296 + 1.96962i) q^{4} +3.85006i q^{5} +(1.87939 + 1.86223i) q^{7} +(2.44949 - 1.41421i) q^{8} +(4.17096 - 3.49985i) q^{10} -4.26757 q^{11} -1.89096 q^{13} +(0.309016 - 3.72888i) q^{14} +(-3.75877 - 1.36808i) q^{16} -6.66850 q^{17} +2.89712 q^{19} +(-7.58313 - 1.33711i) q^{20} +(3.87939 + 4.62327i) q^{22} -1.73479i q^{23} -9.82295 q^{25} +(1.71896 + 2.04857i) q^{26} +(-4.32059 + 3.05492i) q^{28} -3.12142 q^{29} +1.29349i q^{31} +(1.93476 + 5.31570i) q^{32} +(6.06192 + 7.22432i) q^{34} +(-7.16970 + 7.23574i) q^{35} -2.26103i q^{37} +(-2.63359 - 3.13860i) q^{38} +(5.44480 + 9.43068i) q^{40} +8.49777 q^{41} -2.09602i q^{43} +(1.48211 - 8.40547i) q^{44} +(-1.87939 + 1.57699i) q^{46} +9.89908 q^{47} +(0.0641778 + 6.99971i) q^{49} +(8.92944 + 10.6417i) q^{50} +(0.656724 - 3.72447i) q^{52} +5.05618 q^{53} -16.4304i q^{55} +(7.23713 + 1.90367i) q^{56} +(2.83750 + 3.38160i) q^{58} +2.67422i q^{59} -13.1300 q^{61} +(1.40131 - 1.17584i) q^{62} +(4.00000 - 6.92820i) q^{64} -7.28031i q^{65} +10.8674i q^{67} +(2.31594 - 13.1344i) q^{68} +(14.3564 + 1.18973i) q^{70} +15.5358i q^{71} +9.43068i q^{73} +(-2.44949 + 2.05537i) q^{74} +(-1.00616 + 5.70621i) q^{76} +(-8.02040 - 7.94720i) q^{77} +4.08378 q^{79} +(5.26719 - 14.4715i) q^{80} +(-7.72481 - 9.20607i) q^{82} +11.7973i q^{83} -25.6741i q^{85} +(-2.27073 + 1.90536i) q^{86} +(-10.4534 + 6.03525i) q^{88} -11.3004 q^{89} +(-3.55384 - 3.52141i) q^{91} +(3.41687 + 0.602486i) q^{92} +(-8.99865 - 10.7242i) q^{94} +11.1541i q^{95} +1.98175i q^{97} +(7.52479 - 6.43253i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{22} - 72 q^{25} - 24 q^{28} - 72 q^{49} + 48 q^{58} + 96 q^{64} - 24 q^{70} + 48 q^{79} - 144 q^{88}+O(q^{100}) $ 24 * q + 48 * q^22 - 72 * q^25 - 24 * q^28 - 72 * q^49 + 48 * q^58 + 96 * q^64 - 24 * q^70 + 48 * q^79 - 144 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.909039	−	1.08335i	−0.642788	−	0.766044i
$2$	−0.909039	−	1.08335i	−0.642788	−	0.766044i
$3$		0			0
$3$		0			0
$4$	−0.347296	+	1.96962i	−0.173648	+	0.984808i
$5$			3.85006i			1.72180i	0.508776	+	0.860899i	$0.330098\pi$
$5$			3.85006i			1.72180i	−0.508776	+	0.860899i	$0.669902\pi$
$6$		0			0
$7$	1.87939	+	1.86223i	0.710341	+	0.703858i
$7$	1.87939	+	1.86223i	0.710341	+	0.703858i
$8$	2.44949	−	1.41421i	0.866025	−	0.500000i
$9$		0			0
$10$	4.17096	−	3.49985i	1.31897	−	1.10675i
$11$	−4.26757			−1.28672			−0.643360	−	0.765564i	$-0.722460\pi$
$11$	−4.26757			−1.28672			−0.643360	+	0.765564i	$0.722460\pi$
$12$		0			0
$13$	−1.89096			−0.524458			−0.262229	−	0.965006i	$-0.584458\pi$
$13$	−1.89096			−0.524458			−0.262229	+	0.965006i	$0.584458\pi$
$14$	0.309016	−	3.72888i	0.0825881	−	0.996584i
$15$		0			0
$16$	−3.75877	−	1.36808i	−0.939693	−	0.342020i
$17$	−6.66850			−1.61735			−0.808674	−	0.588257i	$-0.799814\pi$
$17$	−6.66850			−1.61735			−0.808674	+	0.588257i	$0.799814\pi$
$18$		0			0
$19$	2.89712			0.664645			0.332322	−	0.943166i	$-0.392168\pi$
$19$	2.89712			0.664645			0.332322	+	0.943166i	$0.392168\pi$
$20$	−7.58313	−	1.33711i	−1.69564	−	0.298987i
$21$		0			0
$22$	3.87939	+	4.62327i	0.827088	+	0.985685i
$23$		−	1.73479i		−	0.361729i	−0.983508	−	0.180864i	$-0.942111\pi$
$23$		−	1.73479i		−	0.361729i	0.983508	−	0.180864i	$-0.0578895\pi$
$24$		0			0
$25$	−9.82295			−1.96459
$26$	1.71896	+	2.04857i	0.337115	+	0.401758i
$27$		0			0
$28$	−4.32059	+	3.05492i	−0.816514	+	0.577326i
$29$	−3.12142			−0.579634			−0.289817	−	0.957082i	$-0.593594\pi$
$29$	−3.12142			−0.579634			−0.289817	+	0.957082i	$0.593594\pi$
$30$		0			0
$31$			1.29349i			0.232318i	0.993231	+	0.116159i	$0.0370583\pi$
$31$			1.29349i			0.232318i	−0.993231	+	0.116159i	$0.962942\pi$
$32$	1.93476	+	5.31570i	0.342020	+	0.939693i
$33$		0			0
$34$	6.06192	+	7.22432i	1.03961	+	1.23896i
$35$	−7.16970	+	7.23574i	−1.21190	+	1.22306i
$36$		0			0
$37$		−	2.26103i		−	0.371711i	−0.982577	−	0.185856i	$-0.940494\pi$
$37$		−	2.26103i		−	0.371711i	0.982577	−	0.185856i	$-0.0595057\pi$
$38$	−2.63359	−	3.13860i	−0.427226	−	0.509148i
$39$		0			0
$40$	5.44480	+	9.43068i	0.860899	+	1.49112i
$41$	8.49777			1.32713			0.663565	−	0.748119i	$-0.269043\pi$
$41$	8.49777			1.32713			0.663565	+	0.748119i	$0.269043\pi$
$42$		0			0
$43$		−	2.09602i		−	0.319640i	−0.987146	−	0.159820i	$-0.948909\pi$
$43$		−	2.09602i		−	0.319640i	0.987146	−	0.159820i	$-0.0510914\pi$
$44$	1.48211	−	8.40547i	0.223437	−	1.26717i
$45$		0			0
$46$	−1.87939	+	1.57699i	−0.277100	+	0.232515i
$47$	9.89908			1.44393			0.721965	−	0.691930i	$-0.243239\pi$
$47$	9.89908			1.44393			0.721965	+	0.691930i	$0.243239\pi$
$48$		0			0
$49$	0.0641778	+	6.99971i	0.00916825	+	0.999958i
$50$	8.92944	+	10.6417i	1.26281	+	1.50496i
$51$		0			0
$52$	0.656724	−	3.72447i	0.0910712	−	0.516490i
$53$	5.05618			0.694520			0.347260	−	0.937769i	$-0.387112\pi$
$53$	5.05618			0.694520			0.347260	+	0.937769i	$0.387112\pi$
$54$		0			0
$55$		−	16.4304i		−	2.21547i
$56$	7.23713	+	1.90367i	0.967102	+	0.254388i
$57$		0			0
$58$	2.83750	+	3.38160i	0.372582	+	0.444025i
$59$			2.67422i			0.348154i	0.984732	+	0.174077i	$0.0556942\pi$
$59$			2.67422i			0.348154i	−0.984732	+	0.174077i	$0.944306\pi$
$60$		0			0
$61$	−13.1300			−1.68112			−0.840562	−	0.541715i	$-0.817775\pi$
$61$	−13.1300			−1.68112			−0.840562	+	0.541715i	$0.817775\pi$
$62$	1.40131	−	1.17584i	0.177966	−	0.149331i
$63$		0			0
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$		−	7.28031i		−	0.903011i
$66$		0			0
$67$			10.8674i			1.32767i	0.747880	+	0.663834i	$0.231072\pi$
$67$			10.8674i			1.32767i	−0.747880	+	0.663834i	$0.768928\pi$
$68$	2.31594	−	13.1344i	0.280850	−	1.59278i
$69$		0			0
$70$	14.3564	+	1.18973i	1.71592	+	0.142200i
$71$			15.5358i			1.84376i	0.387479	+	0.921879i	$0.373346\pi$
$71$			15.5358i			1.84376i	−0.387479	+	0.921879i	$0.626654\pi$
$72$		0			0
$73$			9.43068i			1.10378i	0.833918	+	0.551889i	$0.186093\pi$
$73$			9.43068i			1.10378i	−0.833918	+	0.551889i	$0.813907\pi$
$74$	−2.44949	+	2.05537i	−0.284747	+	0.238931i
$75$		0			0
$76$	−1.00616	+	5.70621i	−0.115414	+	0.654547i
$77$	−8.02040	−	7.94720i	−0.914010	−	0.905668i
$78$		0			0
$79$	4.08378			0.459461			0.229730	−	0.973254i	$-0.426216\pi$
$79$	4.08378			0.459461			0.229730	+	0.973254i	$0.426216\pi$
$80$	5.26719	−	14.4715i	0.588890	−	1.61796i
$81$		0			0
$82$	−7.72481	−	9.20607i	−0.853062	−	1.01664i
$83$			11.7973i			1.29492i	0.762100	+	0.647459i	$0.224168\pi$
$83$			11.7973i			1.29492i	−0.762100	+	0.647459i	$0.775832\pi$
$84$		0			0
$85$		−	25.6741i		−	2.78475i
$86$	−2.27073	+	1.90536i	−0.244859	+	0.205461i
$87$		0			0
$88$	−10.4534	+	6.03525i	−1.11433	+	0.643360i
$89$	−11.3004			−1.19784			−0.598919	−	0.800809i	$-0.704403\pi$
$89$	−11.3004			−1.19784			−0.598919	+	0.800809i	$0.704403\pi$
$90$		0			0
$91$	−3.55384	−	3.52141i	−0.372544	−	0.369144i
$92$	3.41687	+	0.602486i	0.356233	+	0.0628135i
$93$		0			0
$94$	−8.99865	−	10.7242i	−0.928140	−	1.10611i
$95$			11.1541i			1.14438i
$96$		0			0
$97$			1.98175i			0.201216i	0.994926	+	0.100608i	$0.0320788\pi$
$97$			1.98175i			0.201216i	−0.994926	+	0.100608i	$0.967921\pi$
$98$	7.52479	−	6.43253i	0.760119	−	0.649784i
$99$		0			0
$100$	3.41147	−	19.3474i	0.341147	−	1.93474i
$101$			3.85006i			0.383095i	0.981483	+	0.191548i	$0.0613506\pi$
$101$			3.85006i			0.383095i	−0.981483	+	0.191548i	$0.938649\pi$
$102$		0			0
$103$			1.29349i			0.127452i	0.997967	+	0.0637258i	$0.0202983\pi$
$103$			1.29349i			0.127452i	−0.997967	+	0.0637258i	$0.979702\pi$
$104$	−4.63189	+	2.67422i	−0.454194	+	0.262229i
$105$		0			0
$106$	−4.59627	−	5.47762i	−0.446429	−	0.532033i
$107$	12.2118			1.18056			0.590280	−	0.807198i	$-0.299017\pi$
$107$	12.2118			1.18056			0.590280	+	0.807198i	$0.299017\pi$
$108$		0			0
$109$			1.05796i			0.101334i	0.998716	+	0.0506672i	$0.0161348\pi$
$109$			1.05796i			0.101334i	−0.998716	+	0.0506672i	$0.983865\pi$
$110$	−17.7999	+	14.9359i	−1.69715	+	1.42408i
$111$		0			0
$112$	−4.51649	−	9.57086i	−0.426768	−	0.904361i
$113$		−	1.93689i		−	0.182207i	−0.995841	−	0.0911034i	$-0.970961\pi$
$113$		−	1.93689i		−	0.182207i	0.995841	−	0.0911034i	$-0.0290394\pi$
$114$		0			0
$115$	6.67904			0.622824
$116$	1.08406	−	6.14801i	0.100652	−	0.570828i
$117$		0			0
$118$	2.89712	−	2.43097i	0.266702	−	0.223789i
$119$	−12.5327	−	12.4183i	−1.14887	−	1.13838i
$120$		0			0
$121$	7.21213			0.655649
$122$	11.9357	+	14.2244i	1.08061	+	1.28782i
$123$		0			0
$124$	−2.54768	−	0.449226i	−0.228789	−	0.0403416i
$125$		−	18.5686i		−	1.66083i
$126$		0			0
$127$	15.4338			1.36952			0.684762	−	0.728766i	$-0.259906\pi$
$127$	15.4338			1.36952			0.684762	+	0.728766i	$0.259906\pi$
$128$	−11.1418	+	1.96460i	−0.984808	+	0.173648i
$129$		0			0
$130$	−7.88713	+	6.61808i	−0.691747	+	0.580444i
$131$		−	16.8232i		−	1.46985i	−0.678151	−	0.734923i	$-0.737218\pi$
$131$		−	16.8232i		−	1.46985i	0.678151	−	0.734923i	$-0.262782\pi$
$132$		0			0
$133$	5.44480	+	5.39511i	0.472124	+	0.467816i
$134$	11.7732	−	9.87892i	1.01705	−	0.853409i
$135$		0			0
$136$	−16.3344	+	9.43068i	−1.40066	+	0.808674i
$137$		−	3.26034i		−	0.278549i	−0.990254	−	0.139275i	$-0.955523\pi$
$137$		−	3.26034i		−	0.278549i	0.990254	−	0.139275i	$-0.0444771\pi$
$138$		0			0
$139$	−10.8896			−0.923645			−0.461822	−	0.886972i	$-0.652804\pi$
$139$	−10.8896			−0.923645			−0.461822	+	0.886972i	$0.652804\pi$
$140$	−11.7616	−	16.6345i	−0.994038	−	1.40587i
$141$		0			0
$142$	16.8307	−	14.1226i	1.41240	−	1.18514i
$143$	8.06980			0.674831
$144$		0			0
$145$		−	12.0177i		−	0.998013i
$146$	10.2167	−	8.57285i	0.845543	−	0.709494i
$147$		0			0
$148$	4.45336	+	0.785248i	0.366064	+	0.0645470i
$149$	20.4251			1.67329			0.836643	−	0.547749i	$-0.184515\pi$
$149$	20.4251			1.67329			0.836643	+	0.547749i	$0.184515\pi$
$150$		0			0
$151$	12.0155			0.977806			0.488903	−	0.872338i	$-0.337397\pi$
$151$	12.0155			0.977806			0.488903	+	0.872338i	$0.337397\pi$
$152$	7.09647	−	4.09715i	0.575599	−	0.332322i
$153$		0			0
$154$	−1.31875	+	15.9132i	−0.106268	+	1.28232i
$155$	−4.98002			−0.400005
$156$		0			0
$157$	−13.1300			−1.04789			−0.523944	−	0.851753i	$-0.675540\pi$
$157$	−13.1300			−1.04789			−0.523944	+	0.851753i	$0.675540\pi$
$158$	−3.71231	−	4.42416i	−0.295336	−	0.351967i
$159$		0			0
$160$	−20.4658	+	7.44893i	−1.61796	+	0.588890i
$161$	3.23058	−	3.26034i	0.254606	−	0.256951i
$162$		0			0
$163$			9.41155i			0.737170i	0.929594	+	0.368585i	$0.120158\pi$
$163$			9.41155i			0.737170i	−0.929594	+	0.368585i	$0.879842\pi$
$164$	−2.95125	+	16.7373i	−0.230454	+	1.30697i
$165$		0			0
$166$	12.7806	−	10.7242i	0.991965	−	0.832357i
$167$	3.43791			0.266034			0.133017	−	0.991114i	$-0.457534\pi$
$167$	3.43791			0.266034			0.133017	+	0.991114i	$0.457534\pi$
$168$		0			0
$169$	−9.42427			−0.724944
$170$	−27.8140	+	23.3388i	−2.13324	+	1.79000i
$171$		0			0
$172$	4.12836	+	0.727940i	0.314784	+	0.0555049i
$173$			9.37013i			0.712398i	0.934410	+	0.356199i	$0.115927\pi$
$173$			9.37013i			0.712398i	−0.934410	+	0.356199i	$0.884073\pi$
$174$		0			0
$175$	−18.4611	−	18.2926i	−1.39553	−	1.38279i
$176$	16.0408	+	5.83838i	1.20912	+	0.440084i
$177$		0			0
$178$	10.2725	+	12.2423i	0.769956	+	0.917597i
$179$	−5.29703			−0.395919			−0.197959	−	0.980210i	$-0.563431\pi$
$179$	−5.29703			−0.395919			−0.197959	+	0.980210i	$0.563431\pi$
$180$		0			0
$181$	12.7806			0.949972			0.474986	−	0.879993i	$-0.342453\pi$
$181$	12.7806			0.949972			0.474986	+	0.879993i	$0.342453\pi$
$182$	−0.584338	+	7.05116i	−0.0433140	+	0.522666i
$183$		0			0
$184$	−2.45336	−	4.24935i	−0.180864	−	0.313266i
$185$	8.70510			0.640012
$186$		0			0
$187$	28.4583			2.08107
$188$	−3.43791	+	19.4974i	−0.250736	+	1.42199i
$189$		0			0
$190$	12.0838	−	10.1395i	0.876649	−	0.735596i
$191$		−	8.03280i		−	0.581233i	−0.956840	−	0.290616i	$-0.906140\pi$
$191$		−	8.03280i		−	0.581233i	0.956840	−	0.290616i	$-0.0938603\pi$
$192$		0			0
$193$	−15.5621			−1.12019			−0.560093	−	0.828430i	$-0.689235\pi$
$193$	−15.5621			−1.12019			−0.560093	+	0.828430i	$0.689235\pi$
$194$	2.14693	−	1.80149i	0.154140	−	0.129339i
$195$		0			0
$196$	−13.8090	−	2.30457i	−0.986358	−	0.164612i
$197$	17.1464			1.22163			0.610816	−	0.791772i	$-0.290841\pi$
$197$	17.1464			1.22163			0.610816	+	0.791772i	$0.290841\pi$
$198$		0			0
$199$			1.13748i			0.0806337i	0.999187	+	0.0403169i	$0.0128367\pi$
$199$			1.13748i			0.0806337i	−0.999187	+	0.0403169i	$0.987163\pi$
$200$	−24.0612	+	13.8917i	−1.70138	+	0.982295i
$201$		0			0
$202$	4.17096	−	3.49985i	0.293468	−	0.246249i
$203$	−5.86636	−	5.81282i	−0.411738	−	0.407980i
$204$		0			0
$205$			32.7169i			2.28505i
$206$	1.40131	−	1.17584i	0.0976337	−	0.0819244i
$207$		0			0
$208$	7.10769	+	2.58699i	0.492829	+	0.179375i
$209$	−12.3637			−0.855212
$210$		0			0
$211$		−	22.3750i		−	1.54036i	−0.637827	−	0.770180i	$-0.720167\pi$
$211$		−	22.3750i		−	1.54036i	0.637827	−	0.770180i	$-0.279833\pi$
$212$	−1.75599	+	9.95874i	−0.120602	+	0.683969i
$213$		0			0
$214$	−11.1010	−	13.2297i	−0.758850	−	0.904362i
$215$	8.06980			0.550356
$216$		0			0
$217$	−2.40879	+	2.43097i	−0.163519	+	0.165025i
$218$	1.14614	−	0.961729i	0.0776266	−	0.0651365i
$219$		0			0
$220$	32.3615	+	5.70621i	2.18181	+	0.384713i
$221$	12.6099			0.848231
$222$		0			0
$223$			22.5858i			1.51246i	0.654307	+	0.756229i	$0.272961\pi$
$223$			22.5858i			1.51246i	−0.654307	+	0.756229i	$0.727039\pi$
$224$	−6.26292	+	13.5932i	−0.418459	+	0.908236i
$225$		0			0
$226$	−2.09833	+	1.76070i	−0.139579	+	0.117120i
$227$		−	15.7228i		−	1.04356i	−0.853081	−	0.521779i	$-0.825269\pi$
$227$		−	15.7228i		−	1.04356i	0.853081	−	0.521779i	$-0.174731\pi$
$228$		0			0
$229$	7.68520			0.507852			0.253926	−	0.967224i	$-0.418278\pi$
$229$	7.68520			0.507852			0.253926	+	0.967224i	$0.418278\pi$
$230$	−6.07151	−	7.23574i	−0.400343	−	0.477111i
$231$		0			0
$232$	−7.64590	+	4.41436i	−0.501978	+	0.289817i
$233$			20.2528i			1.32680i	0.748263	+	0.663402i	$0.230888\pi$
$233$			20.2528i			1.32680i	−0.748263	+	0.663402i	$0.769112\pi$
$234$		0			0
$235$			38.1120i			2.48615i
$236$	−5.26719	−	0.928748i	−0.342865	−	0.0604563i
$237$		0			0
$238$	−2.06067	+	24.8660i	−0.133574	+	1.61182i
$239$		−	16.9223i		−	1.09461i	−0.836933	−	0.547305i	$-0.815654\pi$
$239$		−	16.9223i		−	1.09461i	0.836933	−	0.547305i	$-0.184346\pi$
$240$		0			0
$241$		−	16.8796i		−	1.08731i	−0.839308	−	0.543656i	$-0.817040\pi$
$241$		−	16.8796i		−	1.08731i	0.839308	−	0.543656i	$-0.182960\pi$
$242$	−6.55611	−	7.81327i	−0.421443	−	0.502256i
$243$		0			0
$244$	4.56000	−	25.8611i	0.291924	−	1.65558i
$245$	−26.9493	+	0.247088i	−1.72173	+	0.0157859i
$246$		0			0
$247$	−5.47834			−0.348578
$248$	1.82928	+	3.16840i	0.116159	+	0.201194i
$249$		0			0
$250$	−20.1163	+	16.8796i	−1.27227	+	1.06756i
$251$		−	0.928748i		−	0.0586220i	−0.999570	−	0.0293110i	$-0.990669\pi$
$251$		−	0.928748i		−	0.0586220i	0.999570	−	0.0293110i	$-0.00933132\pi$
$252$		0			0
$253$			7.40333i			0.465444i
$254$	−14.0299	−	16.7202i	−0.880314	−	1.04912i
$255$		0			0
$256$	12.2567	+	10.2846i	0.766044	+	0.642788i
$257$	−19.0322			−1.18719			−0.593597	−	0.804763i	$-0.702292\pi$
$257$	−19.0322			−1.18719			−0.593597	+	0.804763i	$0.702292\pi$
$258$		0			0
$259$	4.21057	−	4.24935i	0.261632	−	0.264042i
$260$	14.3394	+	2.52842i	0.889292	+	0.156806i
$261$		0			0
$262$	−18.2254	+	15.2929i	−1.12597	+	0.944799i
$263$			1.61631i			0.0996659i	0.998758	+	0.0498330i	$0.0158689\pi$
$263$			1.61631i			0.0996659i	−0.998758	+	0.0498330i	$0.984131\pi$
$264$		0			0
$265$			19.4666i			1.19582i
$266$	0.895257	−	10.8030i	0.0548918	−	0.662374i
$267$		0			0
$268$	−21.4047	−	3.77422i	−1.30750	−	0.230547i
$269$		−	6.52428i		−	0.397792i	−0.980021	−	0.198896i	$-0.936264\pi$
$269$		−	6.52428i		−	0.397792i	0.980021	−	0.198896i	$-0.0637357\pi$
$270$		0			0
$271$			12.7059i			0.771830i	0.922534	+	0.385915i	$0.126114\pi$
$271$			12.7059i			0.771830i	−0.922534	+	0.385915i	$0.873886\pi$
$272$	25.0653	+	9.12304i	1.51981	+	0.553166i
$273$		0			0
$274$	−3.53209	+	2.96377i	−0.213381	+	0.179048i
$275$	41.9201			2.52788
$276$		0			0
$277$		−	3.10359i		−	0.186476i	−0.995644	−	0.0932382i	$-0.970278\pi$
$277$		−	3.10359i		−	0.186476i	0.995644	−	0.0932382i	$-0.0297218\pi$
$278$	9.89908	+	11.7973i	0.593707	+	0.707553i
$279$		0			0
$280$	−7.32923	+	27.8634i	−0.438005	+	1.66515i
$281$			19.1444i			1.14206i	0.820929	+	0.571030i	$0.193456\pi$
$281$			19.1444i			1.14206i	−0.820929	+	0.571030i	$0.806544\pi$
$282$		0			0
$283$	6.22289			0.369912			0.184956	−	0.982747i	$-0.440786\pi$
$283$	6.22289			0.369912			0.184956	+	0.982747i	$0.440786\pi$
$284$	−30.5995	−	5.39552i	−1.81575	−	0.320165i
$285$		0			0
$286$	−7.33577	−	8.74242i	−0.433773	−	0.516950i
$287$	15.9706	+	15.8248i	0.942714	+	0.934110i
$288$		0			0
$289$	27.4688			1.61581
$290$	−13.0193	+	10.9245i	−0.764522	+	0.641510i
$291$		0			0
$292$	−18.5748	−	3.27524i	−1.08701	−	0.191669i
$293$			7.01846i			0.410023i	0.978760	+	0.205011i	$0.0657231\pi$
$293$			7.01846i			0.410023i	−0.978760	+	0.205011i	$0.934277\pi$
$294$		0			0
$295$	−10.2959			−0.599451
$296$	−3.19758	−	5.53837i	−0.185856	−	0.321911i
$297$		0			0
$298$	−18.5672	−	22.1275i	−1.07557	−	1.28181i
$299$			3.28042i			0.189712i
$300$		0			0
$301$	3.90328	−	3.93923i	0.224981	−	0.227054i
$302$	−10.9225	−	13.0170i	−0.628522	−	0.749043i
$303$		0			0
$304$	−10.8896	−	3.96349i	−0.624562	−	0.227322i
$305$		−	50.5513i		−	2.89456i
$306$		0			0
$307$	22.6640			1.29350			0.646752	−	0.762700i	$-0.276127\pi$
$307$	22.6640			1.29350			0.646752	+	0.762700i	$0.276127\pi$
$308$	18.4384	−	13.0371i	1.05063	−	0.742856i
$309$		0			0
$310$	4.52704	+	5.39511i	0.257118	+	0.306422i
$311$	−11.5077			−0.652543			−0.326271	−	0.945276i	$-0.605792\pi$
$311$	−11.5077			−0.652543			−0.326271	+	0.945276i	$0.605792\pi$
$312$		0			0
$313$			14.8979i			0.842077i	0.907043	+	0.421038i	$0.138334\pi$
$313$			14.8979i			0.842077i	−0.907043	+	0.421038i	$0.861666\pi$
$314$	11.9357	+	14.2244i	0.673570	+	0.802729i
$315$		0			0
$316$	−1.41828	+	8.04347i	−0.0797846	+	0.452481i
$317$	9.59763			0.539057			0.269528	−	0.962992i	$-0.413132\pi$
$317$	9.59763			0.539057			0.269528	+	0.962992i	$0.413132\pi$
$318$		0			0
$319$	13.3209			0.745827
$320$	26.6740	+	15.4002i	1.49112	+	0.860899i
$321$		0			0
$322$	−6.46881	−	0.536078i	−0.360493	−	0.0298745i
$323$	−19.3194			−1.07496
$324$		0			0
$325$	18.5748			1.03035
$326$	10.1960	−	8.55547i	0.564705	−	0.473844i
$327$		0			0
$328$	20.8152	−	12.0177i	1.14933	−	0.663565i
$329$	18.6042	+	18.4344i	1.02568	+	1.01632i
$330$		0			0
$331$		−	4.50216i		−	0.247461i	−0.992316	−	0.123731i	$-0.960514\pi$
$331$		−	4.50216i		−	0.247461i	0.992316	−	0.123731i	$-0.0394859\pi$
$332$	−23.2361	−	4.09715i	−1.27525	−	0.224860i
$333$		0			0
$334$	−3.12520	−	3.72447i	−0.171003	−	0.203794i
$335$	−41.8403			−2.28598
$336$		0			0
$337$	15.0351			0.819013			0.409507	−	0.912307i	$-0.365701\pi$
$337$	15.0351			0.819013			0.409507	+	0.912307i	$0.365701\pi$
$338$	8.56703	+	10.2098i	0.465985	+	0.555339i
$339$		0			0
$340$	50.5681	+	8.91652i	2.74244	+	0.483566i
$341$		−	5.52007i		−	0.298929i
$342$		0			0
$343$	−12.9145	+	13.2747i	−0.697316	+	0.716764i
$344$	−2.96422	−	5.13418i	−0.159820	−	0.276817i
$345$		0			0
$346$	10.1511	−	8.51781i	0.545728	−	0.457920i
$347$	−1.74192			−0.0935112			−0.0467556	−	0.998906i	$-0.514888\pi$
$347$	−1.74192			−0.0935112			−0.0467556	+	0.998906i	$0.514888\pi$
$348$		0			0
$349$	6.02232			0.322367			0.161184	−	0.986924i	$-0.448469\pi$
$349$	6.02232			0.322367			0.161184	+	0.986924i	$0.448469\pi$
$350$	−3.03545	+	36.6285i	−0.162252	+	1.95788i
$351$		0			0
$352$	−8.25671	−	22.6851i	−0.440084	−	1.20912i
$353$	0.766006			0.0407704			0.0203852	−	0.999792i	$-0.493511\pi$
$353$	0.766006			0.0407704			0.0203852	+	0.999792i	$0.493511\pi$
$354$		0			0
$355$	−59.8136			−3.17458
$356$	3.92458	−	22.2574i	0.208002	−	1.17964i
$357$		0			0
$358$	4.81521	+	5.73854i	0.254492	+	0.303291i
$359$		−	14.0308i		−	0.740517i	−0.928929	−	0.370259i	$-0.879269\pi$
$359$		−	14.0308i		−	0.740517i	0.928929	−	0.370259i	$-0.120731\pi$
$360$		0			0
$361$	−10.6067			−0.558247
$362$	−11.6180	−	13.8458i	−0.610630	−	0.727721i
$363$		0			0
$364$	8.17006	−	5.77673i	0.428227	−	0.302783i
$365$	−36.3087			−1.90048
$366$		0			0
$367$		−	25.1728i		−	1.31401i	−0.753886	−	0.657005i	$-0.771823\pi$
$367$		−	25.1728i		−	1.31401i	0.753886	−	0.657005i	$-0.228177\pi$
$368$	−2.37333	+	6.52068i	−0.123718	+	0.339914i
$369$		0			0
$370$	−7.91328	−	9.43068i	−0.411392	−	0.490278i
$371$	9.50251	+	9.41579i	0.493346	+	0.488843i
$372$		0			0
$373$			28.7777i			1.49005i	0.667035	+	0.745026i	$0.267563\pi$
$373$			28.7777i			1.49005i	−0.667035	+	0.745026i	$0.732437\pi$
$374$	−25.8697	−	30.8303i	−1.33769	−	1.59420i
$375$		0			0
$376$	24.2477	−	13.9994i	1.25048	−	0.721965i
$377$	5.90249			0.303994
$378$		0			0
$379$		−	18.1830i		−	0.933996i	−0.884258	−	0.466998i	$-0.845335\pi$
$379$		−	18.1830i		−	0.933996i	0.884258	−	0.466998i	$-0.154665\pi$
$380$	−21.9693	−	3.87377i	−1.12700	−	0.198720i
$381$		0			0
$382$	−8.70233	+	7.30212i	−0.445250	+	0.373609i
$383$	−27.8680			−1.42399			−0.711993	−	0.702186i	$-0.752207\pi$
$383$	−27.8680			−1.42399			−0.711993	+	0.702186i	$0.752207\pi$
$384$		0			0
$385$	30.5972	−	30.8790i	1.55938	−	1.57374i
$386$	14.1466	+	16.8592i	0.720042	+	0.858112i
$387$		0			0
$388$	−3.90328	−	0.688253i	−0.198159	−	0.0349408i
$389$	−12.7142			−0.644634			−0.322317	−	0.946632i	$-0.604462\pi$
$389$	−12.7142			−0.644634			−0.322317	+	0.946632i	$0.604462\pi$
$390$		0			0
$391$			11.5684i			0.585041i
$392$	10.0563	+	17.0549i	0.507919	+	0.861405i
$393$		0			0
$394$	−15.5868	−	18.5756i	−0.785250	−	0.935825i
$395$			15.7228i			0.791099i
$396$		0			0
$397$	11.1177			0.557981			0.278990	−	0.960294i	$-0.410000\pi$
$397$	11.1177			0.557981			0.278990	+	0.960294i	$0.410000\pi$
$398$	1.23229	−	1.03401i	0.0617690	−	0.0518304i
$399$		0			0
$400$	36.9222	+	13.4386i	1.84611	+	0.671929i
$401$			13.6548i			0.681887i	0.940084	+	0.340944i	$0.110747\pi$
$401$			13.6548i			0.681887i	−0.940084	+	0.340944i	$0.889253\pi$
$402$		0			0
$403$		−	2.44595i		−	0.121841i
$404$	−7.58313	−	1.33711i	−0.377275	−	0.0665238i
$405$		0			0
$406$	−0.964571	+	11.6394i	−0.0478709	+	0.577654i
$407$			9.64911i			0.478288i
$408$		0			0
$409$		−	27.3936i		−	1.35453i	−0.735741	−	0.677263i	$-0.763166\pi$
$409$		−	27.3936i		−	1.35453i	0.735741	−	0.677263i	$-0.236834\pi$
$410$	35.4439	−	29.7410i	1.75045	−	1.46880i
$411$		0			0
$412$	−2.54768	−	0.449226i	−0.125515	−	0.0221318i
$413$	−4.98002	+	5.02589i	−0.245051	+	0.247308i
$414$		0			0
$415$	−45.4201			−2.22959
$416$	−3.65855	−	10.0518i	−0.179375	−	0.492829i
$417$		0			0
$418$	11.2390	+	13.3942i	0.549720	+	0.655130i
$419$		−	14.0369i		−	0.685748i	−0.939381	−	0.342874i	$-0.888600\pi$
$419$		−	14.0369i		−	0.685748i	0.939381	−	0.342874i	$-0.111400\pi$
$420$		0			0
$421$		−	21.7723i		−	1.06112i	−0.847649	−	0.530558i	$-0.821982\pi$
$421$		−	21.7723i		−	1.06112i	0.847649	−	0.530558i	$-0.178018\pi$
$422$	−24.2400	+	20.3398i	−1.17998	+	0.990124i
$423$		0			0
$424$	12.3851	−	7.15052i	0.601472	−	0.347260i
$425$	65.5043			3.17743
$426$		0			0
$427$	−24.6763	−	24.4511i	−1.19417	−	1.18327i
$428$	−4.24112	+	24.0526i	−0.205002	+	1.16263i
$429$		0			0
$430$	−7.33577	−	8.74242i	−0.353762	−	0.421597i
$431$		−	9.81588i		−	0.472814i	−0.971654	−	0.236407i	$-0.924030\pi$
$431$		−	9.81588i		−	0.472814i	0.971654	−	0.236407i	$-0.0759699\pi$
$432$		0			0
$433$		−	18.8614i		−	0.906419i	−0.891404	−	0.453209i	$-0.850279\pi$
$433$		−	18.8614i		−	0.906419i	0.891404	−	0.453209i	$-0.149721\pi$
$434$	4.82328	+	0.399711i	0.231525	+	0.0191867i
$435$		0			0
$436$	−2.08378	−	0.367426i	−0.0997949	−	0.0175965i
$437$		−	5.02589i		−	0.240421i
$438$		0			0
$439$		−	6.31145i		−	0.301229i	−0.988593	−	0.150615i	$-0.951875\pi$
$439$		−	6.31145i		−	0.301229i	0.988593	−	0.150615i	$-0.0481252\pi$
$440$	−23.2361	−	40.2461i	−1.10774	−	1.91866i
$441$		0			0
$442$	−11.4629	−	13.6609i	−0.545233	−	0.649783i
$443$	27.4565			1.30450			0.652249	−	0.758005i	$-0.273826\pi$
$443$	27.4565			1.30450			0.652249	+	0.758005i	$0.273826\pi$
$444$		0			0
$445$		−	43.5071i		−	2.06244i
$446$	24.4684	−	20.5314i	1.15861	−	0.972190i
$447$		0			0
$448$	20.4195	−	5.57183i	0.964729	−	0.263244i
$449$		−	15.3967i		−	0.726616i	−0.931669	−	0.363308i	$-0.881647\pi$
$449$		−	15.3967i		−	0.726616i	0.931669	−	0.363308i	$-0.118353\pi$
$450$		0			0
$451$	−36.2648			−1.70764
$452$	3.81492	+	0.672673i	0.179439	+	0.0316399i
$453$		0			0
$454$	−17.0333	+	14.2926i	−0.799412	+	0.670786i
$455$	13.5576	−	13.6825i	0.635592	−	0.641446i
$456$		0			0
$457$	−4.00000			−0.187112			−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000			−0.187112			−0.0935561	+	0.995614i	$0.529823\pi$
$458$	−6.98615	−	8.32577i	−0.326441	−	0.389037i
$459$		0			0
$460$	−2.31961	+	13.1551i	−0.108152	+	0.613362i
$461$			38.1415i			1.77643i	0.459432	+	0.888213i	$0.348053\pi$
$461$			38.1415i			1.77643i	−0.459432	+	0.888213i	$0.651947\pi$
$462$		0			0
$463$	10.4688			0.486528			0.243264	−	0.969960i	$-0.421782\pi$
$463$	10.4688			0.486528			0.243264	+	0.969960i	$0.421782\pi$
$464$	11.7327	+	4.27036i	0.544678	+	0.198246i
$465$		0			0
$466$	21.9409	−	18.4106i	1.01639	−	0.852854i
$467$			12.6140i			0.583706i	0.956463	+	0.291853i	$0.0942718\pi$
$467$			12.6140i			0.583706i	−0.956463	+	0.291853i	$0.905728\pi$
$468$		0			0
$469$	−20.2377	+	20.4241i	−0.934490	+	0.943097i
$470$	41.2887	−	34.6453i	1.90450	−	1.59807i
$471$		0			0
$472$	3.78192	+	6.55048i	0.174077	+	0.301510i
$473$			8.94491i			0.411287i
$474$		0			0
$475$	−28.4583			−1.30575
$476$	28.8118	−	20.3717i	1.32059	−	0.933736i
$477$		0			0
$478$	−18.3327	+	15.3830i	−0.838520	+	0.703602i
$479$	7.73177			0.353273			0.176637	−	0.984276i	$-0.443478\pi$
$479$	7.73177			0.353273			0.176637	+	0.984276i	$0.443478\pi$
$480$		0			0
$481$			4.27552i			0.194947i
$482$	−18.2865	+	15.3442i	−0.832929	+	0.698910i
$483$		0			0
$484$	−2.50475	+	14.2051i	−0.113852	+	0.645688i
$485$	−7.62984			−0.346453
$486$		0			0
$487$	15.5330			0.703868			0.351934	−	0.936025i	$-0.385524\pi$
$487$	15.5330			0.703868			0.351934	+	0.936025i	$0.385524\pi$
$488$	−32.1618	+	18.5686i	−1.45590	+	0.840562i
$489$		0			0
$490$	24.7656	+	28.9709i	1.11880	+	1.30877i
$491$	−24.5354			−1.10727			−0.553634	−	0.832760i	$-0.686759\pi$
$491$	−24.5354			−1.10727			−0.553634	+	0.832760i	$0.686759\pi$
$492$		0			0
$493$	20.8152			0.937470
$494$	4.98002	+	5.93496i	0.224062	+	0.267027i
$495$		0			0
$496$	1.76960	−	4.86194i	0.0794575	−	0.218308i
$497$	−28.9312	+	29.1977i	−1.29774	+	1.30970i
$498$		0			0
$499$		−	24.7811i		−	1.10936i	−0.832065	−	0.554678i	$-0.812841\pi$
$499$		−	24.7811i		−	1.10936i	0.832065	−	0.554678i	$-0.187159\pi$
$500$	36.5731	+	6.44882i	1.63560	+	0.288400i
$501$		0			0
$502$	−1.00616	+	0.844268i	−0.0449071	+	0.0376815i
$503$	29.6972			1.32413			0.662067	−	0.749445i	$-0.269679\pi$
$503$	29.6972			1.32413			0.662067	+	0.749445i	$0.269679\pi$
$504$		0			0
$505$	−14.8229			−0.659613
$506$	8.02040	−	6.72992i	0.356550	−	0.299181i
$507$		0			0
$508$	−5.36009	+	30.3986i	−0.237816	+	1.34872i
$509$		−	0.853285i		−	0.0378212i	−0.999821	−	0.0189106i	$-0.993980\pi$
$509$		−	0.853285i		−	0.0378212i	0.999821	−	0.0189106i	$-0.00601979\pi$
$510$		0			0
$511$	−17.5621	+	17.7239i	−0.776902	+	0.784058i
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$	17.3010	+	20.6185i	0.763113	+	0.909443i
$515$	−4.98002			−0.219446
$516$		0			0
$517$	−42.2450			−1.85793
$518$	−8.43110	−	0.698696i	−0.370441	−	0.0306989i
$519$		0			0
$520$	−10.2959	−	17.8330i	−0.451506	−	0.782031i
$521$	7.52443			0.329651			0.164826	−	0.986323i	$-0.447294\pi$
$521$	7.52443			0.329651			0.164826	+	0.986323i	$0.447294\pi$
$522$		0			0
$523$	26.8746			1.17514			0.587572	−	0.809172i	$-0.300084\pi$
$523$	26.8746			1.17514			0.587572	+	0.809172i	$0.300084\pi$
$524$	33.1352	+	5.84262i	1.44752	+	0.255236i
$525$		0			0
$526$	1.75103	−	1.46929i	0.0763485	−	0.0640640i
$527$		−	8.62566i		−	0.375739i
$528$		0			0
$529$	19.9905			0.869152
$530$	21.0891	−	17.6959i	0.916054	−	0.768661i
$531$		0			0
$532$	−12.5173	+	8.85047i	−0.542692	+	0.383716i
$533$	−16.0690			−0.696024
$534$		0			0
$535$			47.0162i			2.03269i
$536$	15.3689	+	26.6197i	0.663834	+	1.14979i
$537$		0			0
$538$	−7.06808	+	5.93083i	−0.304727	+	0.255696i
$539$	−0.273883	−	29.8717i	−0.0117970	−	1.28667i
$540$		0			0
$541$			6.85099i			0.294547i	0.989096	+	0.147274i	$0.0470498\pi$
$541$			6.85099i			0.294547i	−0.989096	+	0.147274i	$0.952950\pi$
$542$	13.7650	−	11.5502i	0.591256	−	0.496122i
$543$		0			0
$544$	−12.9019	−	35.4478i	−0.553166	−	1.51981i
$545$	−4.07321			−0.174477
$546$		0			0
$547$			31.1464i			1.33172i	0.746075	+	0.665862i	$0.231936\pi$
$547$			31.1464i			1.33172i	−0.746075	+	0.665862i	$0.768064\pi$
$548$	6.42161	+	1.13230i	0.274318	+	0.0483696i
$549$		0			0
$550$	−38.1070	−	45.4142i	−1.62489	−	1.93647i
$551$	−9.04314			−0.385251
$552$		0			0
$553$	7.67499	+	7.60495i	0.326374	+	0.323395i
$554$	−3.36227	+	2.82128i	−0.142849	+	0.119865i
$555$		0			0
$556$	3.78192	−	21.4483i	0.160389	−	0.909612i
$557$	39.8687			1.68929			0.844645	−	0.535327i	$-0.179812\pi$
$557$	39.8687			1.68929			0.844645	+	0.535327i	$0.179812\pi$
$558$		0			0
$559$			3.96349i			0.167638i
$560$	36.8484	−	17.3888i	1.55713	−	0.734809i
$561$		0			0
$562$	20.7401	−	17.4030i	0.874868	−	0.734102i
$563$		−	1.74547i		−	0.0735630i	−0.999323	−	0.0367815i	$-0.988289\pi$
$563$		−	1.74547i		−	0.0735630i	0.999323	−	0.0367815i	$-0.0117106\pi$
$564$		0			0
$565$	7.45712			0.313724
$566$	−5.65685	−	6.74157i	−0.237775	−	0.283369i
$567$		0			0
$568$	21.9709	+	38.0547i	0.921879	+	1.59674i
$569$			19.3890i			0.812828i	0.913689	+	0.406414i	$0.133221\pi$
$569$			19.3890i			0.812828i	−0.913689	+	0.406414i	$0.866779\pi$
$570$		0			0
$571$		−	31.9821i		−	1.33841i	−0.743079	−	0.669204i	$-0.766635\pi$
$571$		−	31.9821i		−	1.33841i	0.743079	−	0.669204i	$-0.233365\pi$
$572$	−2.80261	+	15.8944i	−0.117183	+	0.664579i
$573$		0			0
$574$	2.62595	−	31.6871i	0.109605	−	1.32260i
$575$			17.0407i			0.710648i
$576$		0			0
$577$			25.4118i			1.05791i	0.848650	+	0.528954i	$0.177416\pi$
$577$			25.4118i			1.05791i	−0.848650	+	0.528954i	$0.822584\pi$
$578$	−24.9702	−	29.7584i	−1.03863	−	1.23779i
$579$		0			0
$580$	23.6702	+	4.17369i	0.982851	+	0.173303i
$581$	−21.9693	+	22.1716i	−0.911438	+	0.919833i
$582$		0			0
$583$	−21.5776			−0.893653
$584$	13.3370	+	23.1003i	0.551889	+	0.955899i
$585$		0			0
$586$	7.60345	−	6.38005i	0.314096	−	0.263557i
$587$		−	43.0919i		−	1.77859i	−0.457331	−	0.889297i	$-0.651194\pi$
$587$		−	43.0919i		−	1.77859i	0.457331	−	0.889297i	$-0.348806\pi$
$588$		0			0
$589$			3.74741i			0.154409i
$590$	9.35938	+	11.1541i	0.385320	+	0.459206i
$591$		0			0
$592$	−3.09327	+	8.49870i	−0.127133	+	0.349294i
$593$	−10.7417			−0.441109			−0.220555	−	0.975375i	$-0.570787\pi$
$593$	−10.7417			−0.441109			−0.220555	+	0.975375i	$0.570787\pi$
$594$		0			0
$595$	47.8112	−	48.2515i	1.96007	−	1.97812i
$596$	−7.09355	+	40.2295i	−0.290563	+	1.64786i
$597$		0			0
$598$	3.55384	−	2.98203i	0.145327	−	0.121944i
$599$			38.7489i			1.58324i	0.611015	+	0.791619i	$0.290761\pi$
$599$			38.7489i			1.58324i	−0.611015	+	0.791619i	$0.709239\pi$
$600$		0			0
$601$		−	20.5499i		−	0.838248i	−0.907929	−	0.419124i	$-0.862337\pi$
$601$		−	20.5499i		−	0.838248i	0.907929	−	0.419124i	$-0.137663\pi$
$602$	−7.81580	−	0.647705i	−0.318548	−	0.0263985i
$603$		0			0
$604$	−4.17293	+	23.6659i	−0.169794	+	0.962951i
$605$			27.7671i			1.12889i
$606$		0			0
$607$		−	16.8254i		−	0.682923i	−0.939896	−	0.341461i	$-0.889078\pi$
$607$		−	16.8254i		−	0.682923i	0.939896	−	0.341461i	$-0.110922\pi$
$608$	5.60523	+	15.4002i	0.227322	+	0.624562i
$609$		0			0
$610$	−54.7648	+	45.9531i	−2.21736	+	1.86059i
$611$	−18.7188			−0.757280
$612$		0			0
$613$			18.8231i			0.760258i	0.924933	+	0.380129i	$0.124120\pi$
$613$			18.8231i			0.760258i	−0.924933	+	0.380129i	$0.875880\pi$
$614$	−20.6025	−	24.5531i	−0.831448	−	0.990881i
$615$		0			0
$616$	−30.8849	−	8.12403i	−1.24439	−	0.327327i
$617$		−	0.932689i		−	0.0375486i	−0.999824	−	0.0187743i	$-0.994024\pi$
$617$		−	0.932689i		−	0.0375486i	0.999824	−	0.0187743i	$-0.00597640\pi$
$618$		0			0
$619$	−15.3704			−0.617789			−0.308894	−	0.951096i	$-0.599959\pi$
$619$	−15.3704			−0.617789			−0.308894	+	0.951096i	$0.599959\pi$
$620$	1.72954	−	9.80873i	0.0694602	−	0.393928i
$621$		0			0
$622$	10.4610	+	12.4669i	0.419446	+	0.499877i
$623$	−21.2378	−	21.0439i	−0.850874	−	0.843108i
$624$		0			0
$625$	22.3756			0.895023
$626$	16.1396	−	13.5427i	0.645068	−	0.541277i
$627$		0			0
$628$	4.56000	−	25.8611i	0.181964	−	1.03197i
$629$			15.0777i			0.601187i
$630$		0			0
$631$	0.340489			0.0135547			0.00677733	−	0.999977i	$-0.497843\pi$
$631$	0.340489			0.0135547			0.00677733	+	0.999977i	$0.497843\pi$
$632$	10.0032	−	5.77533i	0.397905	−	0.229730i
$633$		0			0
$634$	−8.72462	−	10.3976i	−0.346499	−	0.412941i
$635$			59.4209i			2.35805i
$636$		0			0
$637$	−0.121358	−	13.2362i	−0.00480837	−	0.524436i
$638$	−12.1092	−	14.4312i	−0.479408	−	0.571336i
$639$		0			0
$640$	−7.56384	−	42.8967i	−0.298987	−	1.69564i
$641$			18.3848i			0.726155i	0.931759	+	0.363078i	$0.118274\pi$
$641$			18.3848i			0.726155i	−0.931759	+	0.363078i	$0.881726\pi$
$642$		0			0
$643$	33.7963			1.33280			0.666399	−	0.745595i	$-0.267835\pi$
$643$	33.7963			1.33280			0.666399	+	0.745595i	$0.267835\pi$
$644$	5.29964	+	7.49531i	0.208835	+	0.295357i
$645$		0			0
$646$	17.5621	+	20.9297i	0.690972	+	0.823469i
$647$	−5.48783			−0.215749			−0.107874	−	0.994165i	$-0.534404\pi$
$647$	−5.48783			−0.215749			−0.107874	+	0.994165i	$0.534404\pi$
$648$		0			0
$649$		−	11.4124i		−	0.447977i
$650$	−16.8852	−	20.1230i	−0.662293	−	0.789290i
$651$		0			0
$652$	−18.5371	−	3.26860i	−0.725970	−	0.128008i
$653$	−9.80285			−0.383615			−0.191808	−	0.981433i	$-0.561435\pi$
$653$	−9.80285			−0.383615			−0.191808	+	0.981433i	$0.561435\pi$
$654$		0			0
$655$	64.7701			2.53078
$656$	−31.9412	−	11.6256i	−1.24709	−	0.453905i
$657$		0			0
$658$	3.05898	−	36.9124i	0.119251	−	1.43900i
$659$	−1.86609			−0.0726925			−0.0363462	−	0.999339i	$-0.511572\pi$
$659$	−1.86609			−0.0726925			−0.0363462	+	0.999339i	$0.511572\pi$
$660$		0			0
$661$	−45.7988			−1.78137			−0.890684	−	0.454623i	$-0.849774\pi$
$661$	−45.7988			−1.78137			−0.890684	+	0.454623i	$0.849774\pi$
$662$	−4.87742	+	4.09264i	−0.189566	+	0.159065i
$663$		0			0
$664$	16.6838	+	28.8973i	0.647459	+	1.12143i
$665$	−20.7715	+	20.9628i	−0.805484	+	0.812903i
$666$		0			0
$667$			5.41501i			0.209670i
$668$	−1.19398	+	6.77137i	−0.0461963	+	0.261992i
$669$		0			0
$670$	38.0344	+	45.3277i	1.46940	+	1.75116i
$671$	56.0332			2.16314
$672$		0			0
$673$	−10.8229			−0.417194			−0.208597	−	0.978002i	$-0.566890\pi$
$673$	−10.8229			−0.417194			−0.208597	+	0.978002i	$0.566890\pi$
$674$	−13.6675	−	16.2883i	−0.526451	−	0.627400i
$675$		0			0
$676$	3.27301	−	18.5622i	0.125885	−	0.713930i
$677$		−	43.1674i		−	1.65906i	−0.558465	−	0.829528i	$-0.688609\pi$
$677$		−	43.1674i		−	1.65906i	0.558465	−	0.829528i	$-0.311391\pi$
$678$		0			0
$679$	−3.69047	+	3.72447i	−0.141627	+	0.142932i
$680$	−36.3087	−	62.8884i	−1.39237	−	2.41166i
$681$		0			0
$682$	−5.98017	+	5.01796i	−0.228993	+	0.192148i
$683$	−32.9182			−1.25958			−0.629791	−	0.776765i	$-0.716859\pi$
$683$	−32.9182			−1.25958			−0.629791	+	0.776765i	$0.716859\pi$
$684$		0			0
$685$	12.5525			0.479606
$686$	26.1209	+	1.92371i	0.997299	+	0.0734477i
$687$		0			0
$688$	−2.86753	+	7.87846i	−0.109323	+	0.300364i
$689$	−9.56104			−0.364247
$690$		0			0
$691$	−43.5584			−1.65704			−0.828521	−	0.559959i	$-0.810817\pi$
$691$	−43.5584			−1.65704			−0.828521	+	0.559959i	$0.810817\pi$
$692$	−18.4556	−	3.25421i	−0.701575	−	0.123707i
$693$		0			0
$694$	1.58347	+	1.88711i	0.0601078	+	0.0716337i
$695$		−	41.9256i		−	1.59033i
$696$		0			0
$697$	−56.6674			−2.14643
$698$	−5.47452	−	6.52428i	−0.207214	−	0.246948i
$699$		0			0
$700$	42.4409	−	30.0083i	1.60412	−	1.13421i
$701$	−15.0594			−0.568784			−0.284392	−	0.958708i	$-0.591792\pi$
$701$	−15.0594			−0.568784			−0.284392	+	0.958708i	$0.591792\pi$
$702$		0			0
$703$		−	6.55048i		−	0.247056i
$704$	−17.0703	+	29.5666i	−0.643360	+	1.11433i
$705$		0			0
$706$	−0.696329	−	0.829853i	−0.0262067	−	0.0312319i
$707$	−7.16970	+	7.23574i	−0.269645	+	0.272128i
$708$		0			0
$709$			34.9779i			1.31362i	0.754054	+	0.656812i	$0.228096\pi$
$709$			34.9779i			1.31362i	−0.754054	+	0.656812i	$0.771904\pi$
$710$	54.3729	+	64.7991i	2.04058	+	2.43187i
$711$		0			0
$712$	−27.6802	+	15.9812i	−1.03736	+	0.598919i
$713$	2.24394			0.0840362
$714$		0			0
$715$			31.0692i			1.16192i
$716$	1.83964	−	10.4331i	0.0687506	−	0.389904i
$717$		0			0
$718$	−15.2003	+	12.7545i	−0.567269	+	0.475995i
$719$	−27.5299			−1.02669			−0.513346	−	0.858181i	$-0.671594\pi$
$719$	−27.5299			−1.02669			−0.513346	+	0.858181i	$0.671594\pi$
$720$		0			0
$721$	−2.40879	+	2.43097i	−0.0897079	+	0.0905341i
$722$	9.64190	+	11.4908i	0.358834	+	0.427642i
$723$		0			0
$724$	−4.43865	+	25.1728i	−0.164961	+	0.935540i
$725$	30.6616			1.13874
$726$		0			0
$727$		−	20.1548i		−	0.747502i	−0.927529	−	0.373751i	$-0.878071\pi$
$727$		−	20.1548i		−	0.747502i	0.927529	−	0.373751i	$-0.121929\pi$
$728$	−13.6851	−	3.59976i	−0.507205	−	0.133416i
$729$		0			0
$730$	33.0060	+	39.3350i	1.22161	+	1.45585i
$731$			13.9773i			0.516969i
$732$		0			0
$733$	33.4891			1.23695			0.618473	−	0.785806i	$-0.287752\pi$
$733$	33.4891			1.23695			0.618473	+	0.785806i	$0.287752\pi$
$734$	−27.2710	+	22.8831i	−1.00659	+	0.844629i
$735$		0			0
$736$	9.22163	−	3.35640i	0.339914	−	0.123718i
$737$		−	46.3775i		−	1.70834i
$738$		0			0
$739$			45.2321i			1.66389i	0.554859	+	0.831944i	$0.312772\pi$
$739$			45.2321i			1.66389i	−0.554859	+	0.831944i	$0.687228\pi$
$740$	−3.02325	+	17.1457i	−0.111137	+	0.630289i
$741$		0			0
$742$	1.56244	−	18.8539i	0.0573591	−	0.692147i
$743$		−	24.5437i		−	0.900422i	−0.892922	−	0.450211i	$-0.851349\pi$
$743$		−	24.5437i		−	0.900422i	0.892922	−	0.450211i	$-0.148651\pi$
$744$		0			0
$745$			78.6377i			2.88106i
$746$	31.1763	−	26.1600i	1.14145	−	0.957787i
$747$		0			0
$748$	−9.88345	+	56.0518i	−0.361375	+	2.04946i
$749$	22.9507	+	22.7412i	0.838600	+	0.830947i
$750$		0			0
$751$	−0.556132			−0.0202936			−0.0101468	−	0.999949i	$-0.503230\pi$
$751$	−0.556132			−0.0202936			−0.0101468	+	0.999949i	$0.503230\pi$
$752$	−37.2084	−	13.5427i	−1.35685	−	0.493853i
$753$		0			0
$754$	−5.36559	−	6.39447i	−0.195403	−	0.232873i
$755$			46.2603i			1.68358i
$756$		0			0
$757$			21.0069i			0.763510i	0.924264	+	0.381755i	$0.124680\pi$
$757$			21.0069i			0.763510i	−0.924264	+	0.381755i	$0.875320\pi$
$758$	−19.6985	+	16.5290i	−0.715483	+	0.600361i
$759$		0			0
$760$	15.7743	+	27.3218i	0.572192	+	0.991066i
$761$	3.86588			0.140138			0.0700691	−	0.997542i	$-0.477678\pi$
$761$	3.86588			0.140138			0.0700691	+	0.997542i	$0.477678\pi$
$762$		0			0
$763$	−1.97017	+	1.98832i	−0.0713250	+	0.0719819i
$764$	15.8215	+	2.78976i	0.572403	+	0.100930i
$765$		0			0
$766$	25.3331	+	30.1908i	0.915321	+	1.09084i
$767$		−	5.05685i		−	0.182592i
$768$		0			0
$769$		−	50.3456i		−	1.81551i	−0.419501	−	0.907755i	$-0.637795\pi$
$769$		−	50.3456i		−	1.81551i	0.419501	−	0.907755i	$-0.362205\pi$
$770$	−61.2668	−	5.07726i	−2.20790	−	0.182972i
$771$		0			0
$772$	5.40467	−	30.6514i	0.194518	−	1.10317i
$773$		−	9.69268i		−	0.348621i	−0.984691	−	0.174311i	$-0.944230\pi$
$773$		−	9.69268i		−	0.348621i	0.984691	−	0.174311i	$-0.0557697\pi$
$774$		0			0
$775$		−	12.7059i		−	0.456410i
$776$	2.80261	+	4.85427i	0.100608	+	0.174258i
$777$		0			0
$778$	11.5577	+	13.7739i	0.414363	+	0.493818i
$779$	24.6191			0.882070
$780$		0			0
$781$		−	66.3000i		−	2.37240i
$782$	12.5327	−	10.5162i	0.448167	−	0.376057i
$783$		0			0
$784$	9.33493	−	26.3981i	0.333390	−	0.942789i
$785$		−	50.5513i		−	1.80425i
$786$		0			0
$787$	45.4123			1.61877			0.809387	−	0.587275i	$-0.199799\pi$
$787$	45.4123			1.61877			0.809387	+	0.587275i	$0.199799\pi$
$788$	−5.95489	+	33.7719i	−0.212134	+	1.20307i
$789$		0			0
$790$	17.0333	−	14.2926i	0.606017	−	0.508509i
$791$	3.60693	−	3.64015i	0.128248	−	0.129429i
$792$		0			0
$793$	24.8283			0.881680
$794$	−10.1064	−	12.0444i	−0.358663	−	0.427438i
$795$		0			0
$796$	−2.24040	−	0.395042i	−0.0794087	−	0.0140019i
$797$		−	9.02688i		−	0.319748i	−0.987137	−	0.159874i	$-0.948891\pi$
$797$		−	9.02688i		−	0.319748i	0.987137	−	0.159874i	$-0.0511089\pi$
$798$		0			0
$799$	−66.0120			−2.33534
$800$	−19.0050	−	52.2159i	−0.671929	−	1.84611i
$801$		0			0
$802$	14.7929	−	12.4127i	0.522356	−	0.438309i
$803$		−	40.2461i		−	1.42025i
$804$		0			0
$805$	12.5525	+	12.4379i	0.442417	+	0.438379i
$806$	−2.64982	+	2.22346i	−0.0933358	+	0.0783180i
$807$		0			0
$808$	5.44480	+	9.43068i	0.191548	+	0.331770i
$809$		−	7.47526i		−	0.262816i	−0.991328	−	0.131408i	$-0.958050\pi$
$809$		−	7.47526i		−	0.262816i	0.991328	−	0.131408i	$-0.0419498\pi$
$810$		0			0
$811$	−30.6565			−1.07650			−0.538248	−	0.842787i	$-0.680914\pi$
$811$	−30.6565			−1.07650			−0.538248	+	0.842787i	$0.680914\pi$
$812$	13.4864	−	9.53570i	0.473279	−	0.334637i
$813$		0			0
$814$	10.4534	−	8.77141i	0.366390	−	0.307438i
$815$	−36.2350			−1.26926
$816$		0			0
$817$		−	6.07242i		−	0.212447i
$818$	−29.6769	+	24.9018i	−1.03763	+	0.870672i
$819$		0			0
$820$	−64.4397	−	11.3625i	−2.25033	−	0.396795i
$821$	−43.5330			−1.51931			−0.759655	−	0.650326i	$-0.774632\pi$
$821$	−43.5330			−1.51931			−0.759655	+	0.650326i	$0.774632\pi$
$822$		0			0
$823$	−10.8621			−0.378631			−0.189315	−	0.981916i	$-0.560627\pi$
$823$	−10.8621			−0.378631			−0.189315	+	0.981916i	$0.560627\pi$
$824$	1.82928	+	3.16840i	0.0637258	+	0.110376i
$825$		0			0
$826$	9.97184	+	0.826378i	0.346965	+	0.0287534i
$827$	19.1266			0.665097			0.332548	−	0.943086i	$-0.392091\pi$
$827$	19.1266			0.665097			0.332548	+	0.943086i	$0.392091\pi$
$828$		0			0
$829$	40.3540			1.40155			0.700777	−	0.713381i	$-0.252837\pi$
$829$	40.3540			1.40155			0.700777	+	0.713381i	$0.252837\pi$
$830$	41.2887	+	49.2059i	1.43315	+	1.70796i
$831$		0			0
$832$	−7.56384	+	13.1010i	−0.262229	+	0.454194i
$833$	−0.427969	−	46.6775i	−0.0148283	−	1.61728i
$834$		0			0
$835$			13.2362i			0.458057i
$836$	4.29385	−	24.3516i	0.148506	−	0.842219i
$837$		0			0
$838$	−15.2069	+	12.7601i	−0.525314	+	0.440790i
$839$	5.26719			0.181844			0.0909218	−	0.995858i	$-0.471019\pi$
$839$	5.26719			0.181844			0.0909218	+	0.995858i	$0.471019\pi$
$840$		0			0
$841$	−19.2567			−0.664025
$842$	−23.5870	+	19.7918i	−0.812862	+	0.682072i
$843$		0			0
$844$	44.0702	+	7.77076i	1.51696	+	0.267481i
$845$		−	36.2840i		−	1.24821i
$846$		0			0
$847$	13.5544	+	13.4307i	0.465734	+	0.461483i
$848$	−19.0050	−	6.91726i	−0.652635	−	0.237540i
$849$		0			0
$850$	−59.5460	−	70.9641i	−2.04241	−	2.43405i
$851$	−3.92241			−0.134459
$852$		0			0
$853$	19.5388			0.668997			0.334498	−	0.942396i	$-0.391433\pi$
$853$	19.5388			0.668997			0.334498	+	0.942396i	$0.391433\pi$
$854$	−4.05739	+	48.9601i	−0.138841	+	1.67538i
$855$		0			0
$856$	29.9127	−	17.2701i	1.02240	−	0.590280i
$857$	41.0742			1.40307			0.701535	−	0.712635i	$-0.252498\pi$
$857$	41.0742			1.40307			0.701535	+	0.712635i	$0.252498\pi$
$858$		0			0
$859$	27.7594			0.947138			0.473569	−	0.880757i	$-0.342965\pi$
$859$	27.7594			0.947138			0.473569	+	0.880757i	$0.342965\pi$
$860$	−2.80261	+	15.8944i	−0.0955683	+	0.541995i
$861$		0			0
$862$	−10.6340	+	8.92302i	−0.362197	+	0.303919i
$863$			39.5640i			1.34677i	0.739290	+	0.673387i	$0.235161\pi$
$863$			39.5640i			1.34677i	−0.739290	+	0.673387i	$0.764839\pi$
$864$		0			0
$865$	−36.0755			−1.22661
$866$	−20.4335	+	17.1457i	−0.694357	+	0.582635i
$867$		0			0
$868$	−3.95152	−	5.58865i	−0.134123	−	0.189691i
$869$	−17.4278			−0.591198
$870$		0			0
$871$		−	20.5499i		−	0.696307i
$872$	1.49618	+	2.59147i	0.0506672	+	0.0877581i
$873$		0			0
$874$	−5.44480	+	4.56873i	−0.184173	+	0.154540i
$875$	34.5791	−	34.8976i	1.16899	−	1.17975i
$876$		0			0
$877$		−	3.90183i		−	0.131755i	−0.997828	−	0.0658777i	$-0.979015\pi$
$877$		−	3.90183i		−	0.131755i	0.997828	−	0.0658777i	$-0.0209847\pi$
$878$	−6.83751	+	5.73736i	−0.230755	+	0.193626i
$879$		0			0
$880$	−22.4781	+	61.7580i	−0.757736	+	2.08186i
$881$	−33.3425			−1.12334			−0.561668	−	0.827362i	$-0.689840\pi$
$881$	−33.3425			−1.12334			−0.561668	+	0.827362i	$0.689840\pi$
$882$		0			0
$883$			33.1652i			1.11610i	0.829808	+	0.558049i	$0.188450\pi$
$883$			33.1652i			1.11610i	−0.829808	+	0.558049i	$0.811550\pi$
$884$	−4.37936	+	24.8366i	−0.147294	+	0.835345i
$885$		0			0
$886$	−24.9590	−	29.7450i	−0.838516	−	0.999304i
$887$	−10.7550			−0.361118			−0.180559	−	0.983564i	$-0.557791\pi$
$887$	−10.7550			−0.361118			−0.180559	+	0.983564i	$0.557791\pi$
$888$		0			0
$889$	29.0060	+	28.7413i	0.972830	+	0.963951i
$890$	−47.1335	+	39.5497i	−1.57992	+	1.32571i
$891$		0			0
$892$	−44.4854	−	7.84397i	−1.48948	−	0.262636i
$893$	28.6788			0.959700
$894$		0			0
$895$		−	20.3939i		−	0.681692i
$896$	−24.5983	−	17.0564i	−0.821773	−	0.569815i
$897$		0			0
$898$	−16.6800	+	13.9962i	−0.556620	+	0.467060i
$899$		−	4.03754i		−	0.134660i
$900$		0			0
$901$	−33.7171			−1.12328
$902$	32.9661	+	39.2875i	1.09765	+	1.30813i
$903$		0			0
$904$	−2.73917	−	4.74438i	−0.0911034	−	0.157796i
$905$			49.2059i			1.63566i
$906$		0			0
$907$			24.3365i			0.808081i	0.914741	+	0.404040i	$0.132394\pi$
$907$			24.3365i			0.808081i	−0.914741	+	0.404040i	$0.867606\pi$
$908$	30.9678	+	5.46047i	1.02770	+	0.181212i
$909$		0			0
$910$	−27.1474	−	2.24973i	−0.899926	−	0.0745780i
$911$			25.4294i			0.842515i	0.906941	+	0.421258i	$0.138411\pi$
$911$			25.4294i			0.842515i	−0.906941	+	0.421258i	$0.861589\pi$
$912$		0			0
$913$		−	50.3456i		−	1.66620i
$914$	3.63616	+	4.33340i	0.120273	+	0.143336i
$915$		0			0
$916$	−2.66904	+	15.1369i	−0.0881876	+	0.500137i
$917$	31.3286	−	31.6172i	1.03456	−	1.04409i
$918$		0			0
$919$	35.3655			1.16660			0.583300	−	0.812257i	$-0.301761\pi$
$919$	35.3655			1.16660			0.583300	+	0.812257i	$0.301761\pi$
$920$	16.3602	−	9.44559i	0.539381	−	0.311412i
$921$		0			0
$922$	41.3206	−	34.6721i	1.36082	−	1.14186i
$923$		−	29.3775i		−	0.966974i
$924$		0			0
$925$			22.2100i			0.730260i
$926$	−9.51659	−	11.3414i	−0.312734	−	0.372702i
$927$		0			0
$928$	−6.03920	−	16.5926i	−0.198246	−	0.544678i
$929$	14.1030			0.462704			0.231352	−	0.972870i	$-0.425685\pi$
$929$	14.1030			0.462704			0.231352	+	0.972870i	$0.425685\pi$
$930$		0			0
$931$	0.185931	+	20.2790i	0.00609363	+	0.664617i
$932$	−39.8902	−	7.03372i	−1.30665	−	0.230397i
$933$		0			0
$934$	13.6654	−	11.4666i	0.447145	−	0.375199i
$935$			109.566i			3.58319i
$936$		0			0
$937$			27.6868i			0.904488i	0.891894	+	0.452244i	$0.149376\pi$
$937$			27.6868i			0.904488i	−0.891894	+	0.452244i	$0.850624\pi$
$938$	40.5233	+	3.35821i	1.32313	+	0.109650i
$939$		0			0
$940$	−75.0660	−	13.2362i	−2.44838	−	0.431716i
$941$		−	22.4187i		−	0.730828i	−0.930845	−	0.365414i	$-0.880927\pi$
$941$		−	22.4187i		−	0.730828i	0.930845	−	0.365414i	$-0.119073\pi$
$942$		0			0
$943$		−	14.7418i		−	0.480061i
$944$	3.65855	−	10.0518i	0.119076	−	0.327158i
$945$		0			0
$946$	9.69047	−	8.13127i	0.315064	−	0.264370i
$947$	−8.37044			−0.272003			−0.136001	−	0.990709i	$-0.543425\pi$
$947$	−8.37044			−0.272003			−0.136001	+	0.990709i	$0.543425\pi$
$948$		0			0
$949$		−	17.8330i		−	0.578885i
$950$	25.8697	+	30.8303i	0.839323	+	1.00027i
$951$		0			0
$952$	−48.2608	−	12.6946i	−1.56414	−	0.411434i
$953$			11.0633i			0.358376i	0.983815	+	0.179188i	$0.0573470\pi$
$953$			11.0633i			0.358376i	−0.983815	+	0.179188i	$0.942653\pi$
$954$		0			0
$955$	30.9267			1.00077
$956$	33.3304	+	5.87704i	1.07798	+	0.190077i
$957$		0			0
$958$	−7.02848	−	8.37621i	−0.227080	−	0.270623i
$959$	6.07151	−	6.12743i	0.196059	−	0.197865i
$960$		0			0
$961$	29.3269			0.946028
$962$	4.63189	−	3.88662i	0.149338	−	0.125310i
$963$		0			0
$964$	33.2463	+	5.86223i	1.07079	+	0.188810i
$965$		−	59.9151i		−	1.92873i
$966$		0			0
$967$	31.3756			1.00897			0.504485	−	0.863420i	$-0.331682\pi$
$967$	31.3756			1.00897			0.504485	+	0.863420i	$0.331682\pi$
$968$	17.6660	−	10.1995i	0.567808	−	0.327824i
$969$		0			0
$970$	6.93582	+	8.26579i	0.222696	+	0.265399i
$971$			39.3173i			1.26175i	0.775883	+	0.630876i	$0.217304\pi$
$971$			39.3173i			1.26175i	−0.775883	+	0.630876i	$0.782696\pi$
$972$		0			0
$973$	−20.4658	−	20.2790i	−0.656102	−	0.650114i
$974$	−14.1201	−	16.8277i	−0.452438	−	0.539195i
$975$		0			0
$976$	49.3527	+	17.9629i	1.57974	+	0.574979i
$977$		−	50.7462i		−	1.62352i	−0.583994	−	0.811758i	$-0.698511\pi$
$977$		−	50.7462i		−	1.62352i	0.583994	−	0.811758i	$-0.301489\pi$
$978$		0			0
$979$	48.2252			1.54128
$980$	8.87272	−	53.1655i	0.283429	−	1.69831i
$981$		0			0
$982$	22.3037	+	26.5805i	0.711738	+	0.848217i
$983$	−3.43791			−0.109652			−0.0548262	−	0.998496i	$-0.517460\pi$
$983$	−3.43791			−0.109652			−0.0548262	+	0.998496i	$0.517460\pi$
$984$		0			0
$985$			66.0147i			2.10340i
$986$	−18.9218	−	22.5502i	−0.602594	−	0.718143i
$987$		0			0
$988$	1.90261	−	10.7902i	0.0605300	−	0.343283i
$989$	−3.63616			−0.115623
$990$		0			0
$991$	38.5371			1.22417			0.612086	−	0.790791i	$-0.290330\pi$
$991$	38.5371			1.22417			0.612086	+	0.790791i	$0.290330\pi$
$992$	−6.87583	+	2.50260i	−0.218308	+	0.0794575i
$993$		0			0
$994$	57.9310	+	4.80081i	1.83746	+	0.152272i
$995$	−4.37936			−0.138835
$996$		0			0
$997$	15.0580			0.476893			0.238446	−	0.971156i	$-0.423362\pi$
$997$	15.0580			0.476893			0.238446	+	0.971156i	$0.423362\pi$
$998$	−26.8467	+	22.5270i	−0.849816	+	0.713081i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.i.b.125.6	yes	24
3.2	odd	2	inner	504.2.i.b.125.19	yes	24
4.3	odd	2		2016.2.i.b.881.6		24
7.6	odd	2	inner	504.2.i.b.125.5	✓	24
8.3	odd	2		2016.2.i.b.881.19		24
8.5	even	2	inner	504.2.i.b.125.17	yes	24
12.11	even	2		2016.2.i.b.881.9		24
21.20	even	2	inner	504.2.i.b.125.20	yes	24
24.5	odd	2	inner	504.2.i.b.125.8	yes	24
24.11	even	2		2016.2.i.b.881.16		24
28.27	even	2		2016.2.i.b.881.15		24
56.13	odd	2	inner	504.2.i.b.125.18	yes	24
56.27	even	2		2016.2.i.b.881.10		24
84.83	odd	2		2016.2.i.b.881.20		24
168.83	odd	2		2016.2.i.b.881.5		24
168.125	even	2	inner	504.2.i.b.125.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.i.b.125.5	✓	24	7.6	odd	2	inner
504.2.i.b.125.6	yes	24	1.1	even	1	trivial
504.2.i.b.125.7	yes	24	168.125	even	2	inner
504.2.i.b.125.8	yes	24	24.5	odd	2	inner
504.2.i.b.125.17	yes	24	8.5	even	2	inner
504.2.i.b.125.18	yes	24	56.13	odd	2	inner
504.2.i.b.125.19	yes	24	3.2	odd	2	inner
504.2.i.b.125.20	yes	24	21.20	even	2	inner
2016.2.i.b.881.5		24	168.83	odd	2
2016.2.i.b.881.6		24	4.3	odd	2
2016.2.i.b.881.9		24	12.11	even	2
2016.2.i.b.881.10		24	56.27	even	2
2016.2.i.b.881.15		24	28.27	even	2
2016.2.i.b.881.16		24	24.11	even	2
2016.2.i.b.881.19		24	8.3	odd	2
2016.2.i.b.881.20		24	84.83	odd	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909039 - 1.08335i) q^{2} +(-0.347296 + 1.96962i) q^{4} +3.85006i q^{5} +(1.87939 + 1.86223i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.909039 - 1.08335i) q^{2} +(-0.347296 + 1.96962i) q^{4} +3.85006i q^{5} +(1.87939 + 1.86223i) q^{7} +(2.44949 - 1.41421i) q^{8} +(4.17096 - 3.49985i) q^{10} -4.26757 q^{11} -1.89096 q^{13} +(0.309016 - 3.72888i) q^{14} +(-3.75877 - 1.36808i) q^{16} -6.66850 q^{17} +2.89712 q^{19} +(-7.58313 - 1.33711i) q^{20} +(3.87939 + 4.62327i) q^{22} -1.73479i q^{23} -9.82295 q^{25} +(1.71896 + 2.04857i) q^{26} +(-4.32059 + 3.05492i) q^{28} -3.12142 q^{29} +1.29349i q^{31} +(1.93476 + 5.31570i) q^{32} +(6.06192 + 7.22432i) q^{34} +(-7.16970 + 7.23574i) q^{35} -2.26103i q^{37} +(-2.63359 - 3.13860i) q^{38} +(5.44480 + 9.43068i) q^{40} +8.49777 q^{41} -2.09602i q^{43} +(1.48211 - 8.40547i) q^{44} +(-1.87939 + 1.57699i) q^{46} +9.89908 q^{47} +(0.0641778 + 6.99971i) q^{49} +(8.92944 + 10.6417i) q^{50} +(0.656724 - 3.72447i) q^{52} +5.05618 q^{53} -16.4304i q^{55} +(7.23713 + 1.90367i) q^{56} +(2.83750 + 3.38160i) q^{58} +2.67422i q^{59} -13.1300 q^{61} +(1.40131 - 1.17584i) q^{62} +(4.00000 - 6.92820i) q^{64} -7.28031i q^{65} +10.8674i q^{67} +(2.31594 - 13.1344i) q^{68} +(14.3564 + 1.18973i) q^{70} +15.5358i q^{71} +9.43068i q^{73} +(-2.44949 + 2.05537i) q^{74} +(-1.00616 + 5.70621i) q^{76} +(-8.02040 - 7.94720i) q^{77} +4.08378 q^{79} +(5.26719 - 14.4715i) q^{80} +(-7.72481 - 9.20607i) q^{82} +11.7973i q^{83} -25.6741i q^{85} +(-2.27073 + 1.90536i) q^{86} +(-10.4534 + 6.03525i) q^{88} -11.3004 q^{89} +(-3.55384 - 3.52141i) q^{91} +(3.41687 + 0.602486i) q^{92} +(-8.99865 - 10.7242i) q^{94} +11.1541i q^{95} +1.98175i q^{97} +(7.52479 - 6.43253i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{22} - 72 q^{25} - 24 q^{28} - 72 q^{49} + 48 q^{58} + 96 q^{64} - 24 q^{70} + 48 q^{79} - 144 q^{88}+O(q^{100}) \) 24 * q + 48 * q^22 - 72 * q^25 - 24 * q^28 - 72 * q^49 + 48 * q^58 + 96 * q^64 - 24 * q^70 + 48 * q^79 - 144 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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