LMFDB - Embedded newform 504.2.j.a.323.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(323,504)]

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([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("504.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.j (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			323.15
Character	$\chi$	$=$	504.323
Dual form			504.2.j.a.323.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.386593 - 1.36035i) q^{2} +(-1.70109 - 1.05180i) q^{4} -3.11999 q^{5} -1.00000i q^{7} +(-2.08845 + 1.90746i) q^{8} +O(q^{10})$	\(q+(0.386593 - 1.36035i) q^{2} +(-1.70109 - 1.05180i) q^{4} -3.11999 q^{5} -1.00000i q^{7} +(-2.08845 + 1.90746i) q^{8} +(-1.20617 + 4.24428i) q^{10} +5.48338i q^{11} -1.65814i q^{13} +(-1.36035 - 0.386593i) q^{14} +(1.78742 + 3.57842i) q^{16} +4.14743i q^{17} -2.94109 q^{19} +(5.30739 + 3.28162i) q^{20} +(7.45930 + 2.11984i) q^{22} +0.388249 q^{23} +4.73436 q^{25} +(-2.25565 - 0.641027i) q^{26} +(-1.05180 + 1.70109i) q^{28} -6.81281 q^{29} -1.59877i q^{31} +(5.55891 - 1.04812i) q^{32} +(5.64195 + 1.60337i) q^{34} +3.11999i q^{35} +10.6958i q^{37} +(-1.13701 + 4.00091i) q^{38} +(6.51594 - 5.95125i) q^{40} -4.43752i q^{41} -4.18690 q^{43} +(5.76743 - 9.32772i) q^{44} +(0.150094 - 0.528153i) q^{46} -11.5212 q^{47} -1.00000 q^{49} +(1.83027 - 6.44037i) q^{50} +(-1.74404 + 2.82065i) q^{52} -7.45281 q^{53} -17.1081i q^{55} +(1.90746 + 2.08845i) q^{56} +(-2.63379 + 9.26779i) q^{58} -11.5212i q^{59} +6.75419i q^{61} +(-2.17488 - 0.618072i) q^{62} +(0.723225 - 7.96724i) q^{64} +5.17340i q^{65} +5.03553 q^{67} +(4.36228 - 7.05516i) q^{68} +(4.24428 + 1.20617i) q^{70} +15.2213 q^{71} -16.4687 q^{73} +(14.5500 + 4.13491i) q^{74} +(5.00307 + 3.09345i) q^{76} +5.48338 q^{77} -2.01684i q^{79} +(-5.57675 - 11.1647i) q^{80} +(-6.03658 - 1.71552i) q^{82} -6.21127i q^{83} -12.9400i q^{85} +(-1.61863 + 5.69564i) q^{86} +(-10.4593 - 11.4517i) q^{88} +5.93308i q^{89} -1.65814 q^{91} +(-0.660446 - 0.408361i) q^{92} +(-4.45400 + 15.6728i) q^{94} +9.17620 q^{95} +14.1578 q^{97} +(-0.386593 + 1.36035i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

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 $

$2$	0.386593	−	1.36035i	0.273363	−	0.961911i
$2$	0.386593	−	1.36035i	0.273363	−	0.961911i
$3$		0			0
$3$		0			0
$4$	−1.70109	−	1.05180i	−0.850546	−	0.525901i
$5$	−3.11999			−1.39530			−0.697652	−	0.716437i	$-0.745772\pi$
$5$	−3.11999			−1.39530			−0.697652	+	0.716437i	$0.745772\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.08845	+	1.90746i	−0.738378	+	0.674387i
$9$		0			0
$10$	−1.20617	+	4.24428i	−0.381424	+	1.34216i
$11$			5.48338i			1.65330i	0.562716	+	0.826650i	$0.309756\pi$
$11$			5.48338i			1.65330i	−0.562716	+	0.826650i	$0.690244\pi$
$12$		0			0
$13$		−	1.65814i		−	0.459886i	−0.973204	−	0.229943i	$-0.926146\pi$
$13$		−	1.65814i		−	0.459886i	0.973204	−	0.229943i	$-0.0738540\pi$
$14$	−1.36035	−	0.386593i	−0.363568	−	0.103321i
$15$		0			0
$16$	1.78742	+	3.57842i	0.446856	+	0.894606i
$17$			4.14743i			1.00590i	0.864316	+	0.502950i	$0.167752\pi$
$17$			4.14743i			1.00590i	−0.864316	+	0.502950i	$0.832248\pi$
$18$		0			0
$19$	−2.94109			−0.674733			−0.337367	−	0.941373i	$-0.609536\pi$
$19$	−2.94109			−0.674733			−0.337367	+	0.941373i	$0.609536\pi$
$20$	5.30739	+	3.28162i	1.18677	+	0.733792i
$21$		0			0
$22$	7.45930	+	2.11984i	1.59033	+	0.451951i
$23$	0.388249			0.0809554			0.0404777	−	0.999180i	$-0.487112\pi$
$23$	0.388249			0.0809554			0.0404777	+	0.999180i	$0.487112\pi$
$24$		0			0
$25$	4.73436			0.946871
$26$	−2.25565	−	0.641027i	−0.442370	−	0.125716i
$27$		0			0
$28$	−1.05180	+	1.70109i	−0.198772	+	0.321476i
$29$	−6.81281			−1.26511			−0.632554	−	0.774516i	$-0.717993\pi$
$29$	−6.81281			−1.26511			−0.632554	+	0.774516i	$0.717993\pi$
$30$		0			0
$31$		−	1.59877i		−	0.287147i	−0.989640	−	0.143573i	$-0.954141\pi$
$31$		−	1.59877i		−	0.287147i	0.989640	−	0.143573i	$-0.0458593\pi$
$32$	5.55891	−	1.04812i	0.982685	−	0.185284i
$33$		0			0
$34$	5.64195	+	1.60337i	0.967586	+	0.274975i
$35$			3.11999i			0.527375i
$36$		0			0
$37$			10.6958i			1.75837i	0.476479	+	0.879186i	$0.341913\pi$
$37$			10.6958i			1.75837i	−0.476479	+	0.879186i	$0.658087\pi$
$38$	−1.13701	+	4.00091i	−0.184447	+	0.649034i
$39$		0			0
$40$	6.51594	−	5.95125i	1.03026	−	0.940975i
$41$		−	4.43752i		−	0.693025i	−0.938045	−	0.346512i	$-0.887366\pi$
$41$		−	4.43752i		−	0.693025i	0.938045	−	0.346512i	$-0.112634\pi$
$42$		0			0
$43$	−4.18690			−0.638497			−0.319248	−	0.947671i	$-0.603430\pi$
$43$	−4.18690			−0.638497			−0.319248	+	0.947671i	$0.603430\pi$
$44$	5.76743	−	9.32772i	0.869473	−	1.40621i
$45$		0			0
$46$	0.150094	−	0.528153i	0.0221302	−	0.0778719i
$47$	−11.5212			−1.68053			−0.840267	−	0.542172i	$-0.817602\pi$
$47$	−11.5212			−1.68053			−0.840267	+	0.542172i	$0.817602\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	1.83027	−	6.44037i	0.258839	−	0.910806i
$51$		0			0
$52$	−1.74404	+	2.82065i	−0.241855	+	0.391154i
$53$	−7.45281			−1.02372			−0.511861	−	0.859068i	$-0.671044\pi$
$53$	−7.45281			−1.02372			−0.511861	+	0.859068i	$0.671044\pi$
$54$		0			0
$55$		−	17.1081i		−	2.30686i
$56$	1.90746	+	2.08845i	0.254895	+	0.279081i
$57$		0			0
$58$	−2.63379	+	9.26779i	−0.345833	+	1.21692i
$59$		−	11.5212i		−	1.49993i	−0.661479	−	0.749964i	$-0.730071\pi$
$59$		−	11.5212i		−	1.49993i	0.661479	−	0.749964i	$-0.269929\pi$
$60$		0			0
$61$			6.75419i			0.864786i	0.901685	+	0.432393i	$0.142331\pi$
$61$			6.75419i			0.864786i	−0.901685	+	0.432393i	$0.857669\pi$
$62$	−2.17488	−	0.618072i	−0.276210	−	0.0784953i
$63$		0			0
$64$	0.723225	−	7.96724i	0.0904031	−	0.995905i
$65$			5.17340i			0.641681i
$66$		0			0
$67$	5.03553			0.615188			0.307594	−	0.951518i	$-0.400476\pi$
$67$	5.03553			0.615188			0.307594	+	0.951518i	$0.400476\pi$
$68$	4.36228	−	7.05516i	0.529004	−	0.855564i
$69$		0			0
$70$	4.24428	+	1.20617i	0.507288	+	0.144165i
$71$	15.2213			1.80644			0.903218	−	0.429182i	$-0.141198\pi$
$71$	15.2213			1.80644			0.903218	+	0.429182i	$0.141198\pi$
$72$		0			0
$73$	−16.4687			−1.92751			−0.963755	−	0.266789i	$-0.914037\pi$
$73$	−16.4687			−1.92751			−0.963755	+	0.266789i	$0.914037\pi$
$74$	14.5500	+	4.13491i	1.69140	+	0.480673i
$75$		0			0
$76$	5.00307	+	3.09345i	0.573892	+	0.354843i
$77$	5.48338			0.624889
$78$		0			0
$79$		−	2.01684i		−	0.226912i	−0.993543	−	0.113456i	$-0.963808\pi$
$79$		−	2.01684i		−	0.226912i	0.993543	−	0.113456i	$-0.0361921\pi$
$80$	−5.57675	−	11.1647i	−0.623499	−	1.24825i
$81$		0			0
$82$	−6.03658	−	1.71552i	−0.666628	−	0.189447i
$83$		−	6.21127i		−	0.681775i	−0.940104	−	0.340888i	$-0.889272\pi$
$83$		−	6.21127i		−	0.681775i	0.940104	−	0.340888i	$-0.110728\pi$
$84$		0			0
$85$		−	12.9400i		−	1.40354i
$86$	−1.61863	+	5.69564i	−0.174541	+	0.614177i
$87$		0			0
$88$	−10.4593	−	11.4517i	−1.11496	−	1.22076i
$89$			5.93308i			0.628905i	0.949273	+	0.314453i	$0.101821\pi$
$89$			5.93308i			0.628905i	−0.949273	+	0.314453i	$0.898179\pi$
$90$		0			0
$91$	−1.65814			−0.173821
$92$	−0.660446	−	0.408361i	−0.0688563	−	0.0425746i
$93$		0			0
$94$	−4.45400	+	15.6728i	−0.459396	+	1.61652i
$95$	9.17620			0.941458
$96$		0			0
$97$	14.1578			1.43751			0.718753	−	0.695265i	$-0.244713\pi$
$97$	14.1578			1.43751			0.718753	+	0.695265i	$0.244713\pi$
$98$	−0.386593	+	1.36035i	−0.0390518	+	0.137416i
$99$		0			0
$100$	−8.05357	−	4.97961i	−0.805357	−	0.497961i
$101$	−13.5036			−1.34366			−0.671830	−	0.740705i	$-0.734491\pi$
$101$	−13.5036			−1.34366			−0.671830	+	0.740705i	$0.734491\pi$
$102$		0			0
$103$		−	10.2021i		−	1.00524i	−0.864508	−	0.502620i	$-0.832370\pi$
$103$		−	10.2021i		−	1.00524i	0.864508	−	0.502620i	$-0.167630\pi$
$104$	3.16284	+	3.46295i	0.310142	+	0.339570i
$105$		0			0
$106$	−2.88121	+	10.1384i	−0.279847	+	0.984729i
$107$			6.99660i			0.676386i	0.941077	+	0.338193i	$0.109816\pi$
$107$			6.99660i			0.676386i	−0.941077	+	0.338193i	$0.890184\pi$
$108$		0			0
$109$			6.53986i			0.626405i	0.949686	+	0.313203i	$0.101402\pi$
$109$			6.53986i			0.626405i	−0.949686	+	0.313203i	$0.898598\pi$
$110$	−23.2730	−	6.61387i	−2.21899	−	0.630608i
$111$		0			0
$112$	3.57842	−	1.78742i	0.338129	−	0.168896i
$113$			13.4345i			1.26382i	0.775044	+	0.631908i	$0.217728\pi$
$113$			13.4345i			1.26382i	−0.775044	+	0.631908i	$0.782272\pi$
$114$		0			0
$115$	−1.21133			−0.112957
$116$	11.5892	+	7.16573i	1.07603	+	0.665322i
$117$		0			0
$118$	−15.6728	−	4.45400i	−1.44280	−	0.410024i
$119$	4.14743			0.380194
$120$		0			0
$121$	−19.0674			−1.73340
$122$	9.18805	+	2.61113i	0.831847	+	0.236400i
$123$		0			0
$124$	−1.68159	+	2.71965i	−0.151011	+	0.244232i
$125$	0.828803			0.0741304
$126$		0			0
$127$		−	3.49155i		−	0.309825i	−0.987928	−	0.154912i	$-0.950490\pi$
$127$		−	3.49155i		−	0.309825i	0.987928	−	0.154912i	$-0.0495096\pi$
$128$	−10.5586	−	4.06392i	−0.933259	−	0.359203i
$129$		0			0
$130$	7.03762	+	2.00000i	0.617240	+	0.175412i
$131$		−	9.26178i		−	0.809205i	−0.914493	−	0.404603i	$-0.867410\pi$
$131$		−	9.26178i		−	0.809205i	0.914493	−	0.404603i	$-0.132590\pi$
$132$		0			0
$133$			2.94109i			0.255025i
$134$	1.94670	−	6.85008i	0.168170	−	0.591757i
$135$		0			0
$136$	−7.91104	−	8.66169i	−0.678366	−	0.742734i
$137$		−	3.67521i		−	0.313994i	−0.987599	−	0.156997i	$-0.949819\pi$
$137$		−	3.67521i		−	0.313994i	0.987599	−	0.156997i	$-0.0501814\pi$
$138$		0			0
$139$	0.410254			0.0347973			0.0173986	−	0.999849i	$-0.494462\pi$
$139$	0.410254			0.0347973			0.0173986	+	0.999849i	$0.494462\pi$
$140$	3.28162	−	5.30739i	0.277347	−	0.448557i
$141$		0			0
$142$	5.88445	−	20.7063i	0.493812	−	1.73763i
$143$	9.09222			0.760330
$144$		0			0
$145$	21.2559			1.76521
$146$	−6.36667	+	22.4031i	−0.526909	+	1.85409i
$147$		0			0
$148$	11.2498	−	18.1945i	0.924730	−	1.49558i
$149$	2.94652			0.241388			0.120694	−	0.992690i	$-0.461488\pi$
$149$	2.94652			0.241388			0.120694	+	0.992690i	$0.461488\pi$
$150$		0			0
$151$		−	3.58975i		−	0.292129i	−0.989275	−	0.146065i	$-0.953339\pi$
$151$		−	3.58975i		−	0.292129i	0.989275	−	0.146065i	$-0.0466608\pi$
$152$	6.14232	−	5.61001i	0.498208	−	0.455032i
$153$		0			0
$154$	2.11984	−	7.45930i	0.170821	−	0.601087i
$155$			4.98814i			0.400657i
$156$		0			0
$157$			16.7551i			1.33721i	0.743620	+	0.668603i	$0.233107\pi$
$157$			16.7551i			1.33721i	−0.743620	+	0.668603i	$0.766893\pi$
$158$	−2.74360	−	0.779696i	−0.218269	−	0.0620292i
$159$		0			0
$160$	−17.3437	+	3.27013i	−1.37114	+	0.258527i
$161$		−	0.388249i		−	0.0305983i
$162$		0			0
$163$	−11.6681			−0.913917			−0.456958	−	0.889488i	$-0.651061\pi$
$163$	−11.6681			−0.913917			−0.456958	+	0.889488i	$0.651061\pi$
$164$	−4.66740	+	7.54863i	−0.364463	+	0.589449i
$165$		0			0
$166$	−8.44948	−	2.40123i	−0.655807	−	0.186372i
$167$	−17.1810			−1.32950			−0.664751	−	0.747065i	$-0.731463\pi$
$167$	−17.1810			−1.32950			−0.664751	+	0.747065i	$0.731463\pi$
$168$		0			0
$169$	10.2506			0.788505
$170$	−17.6028	−	5.00250i	−1.35008	−	0.383674i
$171$		0			0
$172$	7.12230	+	4.40379i	0.543070	+	0.335786i
$173$	18.8574			1.43370			0.716849	−	0.697228i	$-0.245584\pi$
$173$	18.8574			1.43370			0.716849	+	0.697228i	$0.245584\pi$
$174$		0			0
$175$		−	4.73436i		−	0.357884i
$176$	−19.6218	+	9.80111i	−1.47905	+	0.738787i
$177$		0			0
$178$	8.07105	+	2.29369i	0.604951	+	0.171919i
$179$		−	10.4376i		−	0.780145i	−0.920784	−	0.390073i	$-0.872450\pi$
$179$		−	10.4376i		−	0.780145i	0.920784	−	0.390073i	$-0.127550\pi$
$180$		0			0
$181$		−	0.463832i		−	0.0344764i	−0.999851	−	0.0172382i	$-0.994513\pi$
$181$		−	0.463832i		−	0.0344764i	0.999851	−	0.0172382i	$-0.00548736\pi$
$182$	−0.641027	+	2.25565i	−0.0475161	+	0.167200i
$183$		0			0
$184$	−0.810837	+	0.740567i	−0.0597757	+	0.0545953i
$185$		−	33.3707i		−	2.45346i
$186$		0			0
$187$	−22.7419			−1.66305
$188$	19.5986	+	12.1180i	1.42937	+	0.883795i
$189$		0			0
$190$	3.54746	−	12.4828i	0.257359	−	0.905599i
$191$	3.44417			0.249211			0.124606	−	0.992206i	$-0.460233\pi$
$191$	3.44417			0.249211			0.124606	+	0.992206i	$0.460233\pi$
$192$		0			0
$193$	−10.8325			−0.779740			−0.389870	−	0.920870i	$-0.627480\pi$
$193$	−10.8325			−0.779740			−0.389870	+	0.920870i	$0.627480\pi$
$194$	5.47331	−	19.2595i	0.392961	−	1.38275i
$195$		0			0
$196$	1.70109	+	1.05180i	0.121507	+	0.0751287i
$197$	−3.62039			−0.257942			−0.128971	−	0.991648i	$-0.541167\pi$
$197$	−3.62039			−0.257942			−0.128971	+	0.991648i	$0.541167\pi$
$198$		0			0
$199$			23.2359i			1.64715i	0.567209	+	0.823574i	$0.308023\pi$
$199$			23.2359i			1.64715i	−0.567209	+	0.823574i	$0.691977\pi$
$200$	−9.88746	+	9.03058i	−0.699149	+	0.638558i
$201$		0			0
$202$	−5.22041	+	18.3696i	−0.367306	+	1.29248i
$203$			6.81281i			0.478166i
$204$		0			0
$205$			13.8450i			0.966980i
$206$	−13.8784	−	3.94405i	−0.966951	−	0.274795i
$207$		0			0
$208$	5.93354	−	2.96380i	0.411417	−	0.205503i
$209$		−	16.1271i		−	1.11554i
$210$		0			0
$211$	5.81404			0.400255			0.200128	−	0.979770i	$-0.435864\pi$
$211$	5.81404			0.400255			0.200128	+	0.979770i	$0.435864\pi$
$212$	12.6779	+	7.83888i	0.870722	+	0.538377i
$213$		0			0
$214$	9.51780	+	2.70484i	0.650624	+	0.184899i
$215$	13.0631			0.890896
$216$		0			0
$217$	−1.59877			−0.108531
$218$	8.89648	+	2.52827i	0.602546	+	0.171236i
$219$		0			0
$220$	−17.9943	+	29.1024i	−1.21318	+	1.96209i
$221$	6.87704			0.462599
$222$		0			0
$223$			9.60873i			0.643448i	0.946833	+	0.321724i	$0.104262\pi$
$223$			9.60873i			0.643448i	−0.946833	+	0.321724i	$0.895738\pi$
$224$	−1.04812	−	5.55891i	−0.0700306	−	0.371420i
$225$		0			0
$226$	18.2756	+	5.19370i	1.21568	+	0.345480i
$227$			12.9929i			0.862370i	0.902264	+	0.431185i	$0.141904\pi$
$227$			12.9929i			0.862370i	−0.902264	+	0.431185i	$0.858096\pi$
$228$		0			0
$229$			1.47738i			0.0976283i	0.998808	+	0.0488141i	$0.0155442\pi$
$229$			1.47738i			0.0976283i	−0.998808	+	0.0488141i	$0.984456\pi$
$230$	−0.468293	+	1.64783i	−0.0308783	+	0.108655i
$231$		0			0
$232$	14.2282	−	12.9951i	0.934127	−	0.853173i
$233$		−	12.8931i		−	0.844658i	−0.906443	−	0.422329i	$-0.861213\pi$
$233$		−	12.8931i		−	0.844658i	0.906443	−	0.422329i	$-0.138787\pi$
$234$		0			0
$235$	35.9460			2.34486
$236$	−12.1180	+	19.5986i	−0.788814	+	1.27576i
$237$		0			0
$238$	1.60337	−	5.64195i	0.103931	−	0.365713i
$239$	24.8490			1.60735			0.803675	−	0.595068i	$-0.202875\pi$
$239$	24.8490			1.60735			0.803675	+	0.595068i	$0.202875\pi$
$240$		0			0
$241$	20.8088			1.34041			0.670206	−	0.742175i	$-0.266206\pi$
$241$	20.8088			1.34041			0.670206	+	0.742175i	$0.266206\pi$
$242$	−7.37133	+	25.9383i	−0.473847	+	1.66738i
$243$		0			0
$244$	7.10408	−	11.4895i	0.454792	−	0.735540i
$245$	3.11999			0.199329
$246$		0			0
$247$			4.87676i			0.310301i
$248$	3.04958	+	3.33894i	0.193648	+	0.212023i
$249$		0			0
$250$	0.320410	−	1.12746i	0.0202645	−	0.0713069i
$251$		−	20.1787i		−	1.27367i	−0.771001	−	0.636834i	$-0.780244\pi$
$251$		−	20.1787i		−	1.27367i	0.771001	−	0.636834i	$-0.219756\pi$
$252$		0			0
$253$			2.12891i			0.133844i
$254$	−4.74972	−	1.34981i	−0.298024	−	0.0846946i
$255$		0			0
$256$	−9.61024	+	12.7923i	−0.600640	+	0.799520i
$257$			17.8844i			1.11560i	0.829976	+	0.557800i	$0.188354\pi$
$257$			17.8844i			1.11560i	−0.829976	+	0.557800i	$0.811646\pi$
$258$		0			0
$259$	10.6958			0.664602
$260$	5.44139	−	8.80042i	0.337461	−	0.545779i
$261$		0			0
$262$	−12.5992	−	3.58054i	−0.778384	−	0.221207i
$263$	−2.52143			−0.155478			−0.0777390	−	0.996974i	$-0.524770\pi$
$263$	−2.52143			−0.155478			−0.0777390	+	0.996974i	$0.524770\pi$
$264$		0			0
$265$	23.2527			1.42840
$266$	4.00091	+	1.13701i	0.245312	+	0.0697144i
$267$		0			0
$268$	−8.56590	−	5.29639i	−0.523246	−	0.323528i
$269$	−12.8535			−0.783695			−0.391847	−	0.920030i	$-0.628164\pi$
$269$	−12.8535			−0.783695			−0.391847	+	0.920030i	$0.628164\pi$
$270$		0			0
$271$			27.7743i			1.68717i	0.536995	+	0.843586i	$0.319560\pi$
$271$			27.7743i			1.68717i	−0.536995	+	0.843586i	$0.680440\pi$
$272$	−14.8413	+	7.41321i	−0.899884	+	0.449492i
$273$		0			0
$274$	−4.99956	−	1.42081i	−0.302035	−	0.0858344i
$275$			25.9603i			1.56546i
$276$		0			0
$277$		−	23.3940i		−	1.40561i	−0.711382	−	0.702806i	$-0.751930\pi$
$277$		−	23.3940i		−	1.40561i	0.711382	−	0.702806i	$-0.248070\pi$
$278$	0.158601	−	0.558088i	0.00951228	−	0.0334719i
$279$		0			0
$280$	−5.95125	−	6.51594i	−0.355655	−	0.389402i
$281$			29.1013i			1.73604i	0.496531	+	0.868019i	$0.334607\pi$
$281$			29.1013i			1.73604i	−0.496531	+	0.868019i	$0.665393\pi$
$282$		0			0
$283$	−0.415808			−0.0247172			−0.0123586	−	0.999924i	$-0.503934\pi$
$283$	−0.415808			−0.0247172			−0.0123586	+	0.999924i	$0.503934\pi$
$284$	−25.8928	−	16.0098i	−1.53646	−	0.950007i
$285$		0			0
$286$	3.51499	−	12.3686i	0.207846	−	0.731370i
$287$	−4.43752			−0.261939
$288$		0			0
$289$	−0.201184			−0.0118343
$290$	8.21740	−	28.9155i	0.482542	−	1.69797i
$291$		0			0
$292$	28.0147	+	17.3218i	1.63944	+	1.01368i
$293$	−14.1198			−0.824887			−0.412444	−	0.910983i	$-0.635325\pi$
$293$	−14.1198			−0.824887			−0.412444	+	0.910983i	$0.635325\pi$
$294$		0			0
$295$			35.9460i			2.09285i
$296$	−20.4017	−	22.3375i	−1.18582	−	1.29834i
$297$		0			0
$298$	1.13910	−	4.00829i	0.0659865	−	0.232194i
$299$		−	0.643772i		−	0.0372303i
$300$		0			0
$301$			4.18690i			0.241329i
$302$	−4.88330	−	1.38777i	−0.281002	−	0.0798573i
$303$		0			0
$304$	−5.25698	−	10.5245i	−0.301509	−	0.603621i
$305$		−	21.0730i		−	1.20664i
$306$		0			0
$307$	33.8671			1.93289			0.966447	−	0.256864i	$-0.0826893\pi$
$307$	33.8671			1.93289			0.966447	+	0.256864i	$0.0826893\pi$
$308$	−9.32772	−	5.76743i	−0.531496	−	0.328630i
$309$		0			0
$310$	6.78560	+	1.92838i	0.385396	+	0.109525i
$311$	−18.2024			−1.03216			−0.516081	−	0.856540i	$-0.672610\pi$
$311$	−18.2024			−1.03216			−0.516081	+	0.856540i	$0.672610\pi$
$312$		0			0
$313$	−6.21910			−0.351524			−0.175762	−	0.984433i	$-0.556239\pi$
$313$	−6.21910			−0.351524			−0.175762	+	0.984433i	$0.556239\pi$
$314$	22.7928	+	6.47742i	1.28627	+	0.365542i
$315$		0			0
$316$	−2.12131	+	3.43082i	−0.119333	+	0.192999i
$317$	22.4002			1.25812			0.629059	−	0.777357i	$-0.283440\pi$
$317$	22.4002			1.25812			0.629059	+	0.777357i	$0.283440\pi$
$318$		0			0
$319$		−	37.3572i		−	2.09160i
$320$	−2.25646	+	24.8577i	−0.126140	+	1.38959i
$321$		0			0
$322$	−0.528153	−	0.150094i	−0.0294328	−	0.00836443i
$323$		−	12.1980i		−	0.678714i
$324$		0			0
$325$		−	7.85024i		−	0.435453i
$326$	−4.51081	+	15.8727i	−0.249831	+	0.879107i
$327$		0			0
$328$	8.46438	+	9.26754i	0.467367	+	0.511714i
$329$			11.5212i			0.635182i
$330$		0			0
$331$	22.1097			1.21526			0.607630	−	0.794220i	$-0.292120\pi$
$331$	22.1097			1.21526			0.607630	+	0.794220i	$0.292120\pi$
$332$	−6.53303	+	10.5659i	−0.358546	+	0.579881i
$333$		0			0
$334$	−6.64205	+	23.3721i	−0.363437	+	1.27886i
$335$	−15.7108			−0.858374
$336$		0			0
$337$	−19.1994			−1.04586			−0.522930	−	0.852376i	$-0.675161\pi$
$337$	−19.1994			−1.04586			−0.522930	+	0.852376i	$0.675161\pi$
$338$	3.96280	−	13.9443i	0.215548	−	0.758471i
$339$		0			0
$340$	−13.6103	+	22.0120i	−0.738121	+	1.19377i
$341$	8.76664			0.474740
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	8.74412	−	7.98633i	0.471452	−	0.430594i
$345$		0			0
$346$	7.29013	−	25.6526i	0.391920	−	1.37909i
$347$		−	3.40174i		−	0.182615i	−0.995823	−	0.0913076i	$-0.970895\pi$
$347$		−	3.40174i		−	0.182615i	0.995823	−	0.0913076i	$-0.0291046\pi$
$348$		0			0
$349$			0.872003i			0.0466773i	0.999728	+	0.0233386i	$0.00742959\pi$
$349$			0.872003i			0.0466773i	−0.999728	+	0.0233386i	$0.992570\pi$
$350$	−6.44037	−	1.83027i	−0.344252	−	0.0978321i
$351$		0			0
$352$	5.74725	+	30.4816i	0.306329	+	1.62467i
$353$			6.37269i			0.339184i	0.985514	+	0.169592i	$0.0542450\pi$
$353$			6.37269i			0.339184i	−0.985514	+	0.169592i	$0.945755\pi$
$354$		0			0
$355$	−47.4903			−2.52053
$356$	6.24043	−	10.0927i	0.330742	−	0.534912i
$357$		0			0
$358$	−14.1988	−	4.03512i	−0.750430	−	0.213263i
$359$	6.15450			0.324822			0.162411	−	0.986723i	$-0.448073\pi$
$359$	6.15450			0.324822			0.162411	+	0.986723i	$0.448073\pi$
$360$		0			0
$361$	−10.3500			−0.544735
$362$	−0.630973	−	0.179314i	−0.0331632	−	0.00942456i
$363$		0			0
$364$	2.82065	+	1.74404i	0.147842	+	0.0914125i
$365$	51.3821			2.68946
$366$		0			0
$367$		−	14.1419i		−	0.738201i	−0.929389	−	0.369101i	$-0.879666\pi$
$367$		−	14.1419i		−	0.738201i	0.929389	−	0.369101i	$-0.120334\pi$
$368$	0.693965	+	1.38932i	0.0361754	+	0.0724232i
$369$		0			0
$370$	−45.3958	−	12.9009i	−2.36001	−	0.670685i
$371$			7.45281i			0.386930i
$372$		0			0
$373$		−	30.8957i		−	1.59972i	−0.600186	−	0.799860i	$-0.704907\pi$
$373$		−	30.8957i		−	1.59972i	0.600186	−	0.799860i	$-0.295093\pi$
$374$	−8.79187	+	30.9369i	−0.454617	+	1.59971i
$375$		0			0
$376$	24.0613	−	21.9761i	1.24087	−	1.13333i
$377$			11.2966i			0.581806i
$378$		0			0
$379$	−27.3446			−1.40460			−0.702300	−	0.711881i	$-0.747843\pi$
$379$	−27.3446			−1.40460			−0.702300	+	0.711881i	$0.747843\pi$
$380$	−15.6095	−	9.65155i	−0.800753	−	0.495114i
$381$		0			0
$382$	1.33149	−	4.68526i	0.0681250	−	0.239719i
$383$	−8.62880			−0.440911			−0.220456	−	0.975397i	$-0.570754\pi$
$383$	−8.62880			−0.440911			−0.220456	+	0.975397i	$0.570754\pi$
$384$		0			0
$385$	−17.1081			−0.871909
$386$	−4.18777	+	14.7360i	−0.213152	+	0.750040i
$387$		0			0
$388$	−24.0837	−	14.8912i	−1.22266	−	0.755986i
$389$	−7.11018			−0.360501			−0.180250	−	0.983621i	$-0.557691\pi$
$389$	−7.11018			−0.360501			−0.180250	+	0.983621i	$0.557691\pi$
$390$		0			0
$391$			1.61023i			0.0814330i
$392$	2.08845	−	1.90746i	0.105483	−	0.0963411i
$393$		0			0
$394$	−1.39962	+	4.92499i	−0.0705118	+	0.248118i
$395$			6.29252i			0.316611i
$396$		0			0
$397$		−	14.0677i		−	0.706038i	−0.935616	−	0.353019i	$-0.885155\pi$
$397$		−	14.0677i		−	0.706038i	0.935616	−	0.353019i	$-0.114845\pi$
$398$	31.6089	+	8.98283i	1.58441	+	0.450269i
$399$		0			0
$400$	8.46230	+	16.9415i	0.423115	+	0.847077i
$401$		−	5.92345i		−	0.295803i	−0.989002	−	0.147902i	$-0.952748\pi$
$401$		−	5.92345i		−	0.295803i	0.989002	−	0.147902i	$-0.0472519\pi$
$402$		0			0
$403$	−2.65098			−0.132055
$404$	22.9709	+	14.2031i	1.14284	+	0.706632i
$405$		0			0
$406$	9.26779	+	2.63379i	0.459953	+	0.130713i
$407$	−58.6489			−2.90712
$408$		0			0
$409$	−23.6481			−1.16933			−0.584663	−	0.811276i	$-0.698773\pi$
$409$	−23.6481			−1.16933			−0.584663	+	0.811276i	$0.698773\pi$
$410$	18.8341	+	5.35240i	0.930149	+	0.264336i
$411$		0			0
$412$	−10.7306	+	17.3546i	−0.528657	+	0.855002i
$413$	−11.5212			−0.566919
$414$		0			0
$415$			19.3791i			0.951283i
$416$	−1.73794	−	9.21746i	−0.0852094	−	0.451923i
$417$		0			0
$418$	−21.9385	−	6.23464i	−1.07305	−	0.304946i
$419$		−	24.0507i		−	1.17495i	−0.809241	−	0.587477i	$-0.800121\pi$
$419$		−	24.0507i		−	1.17495i	0.809241	−	0.587477i	$-0.199879\pi$
$420$		0			0
$421$			17.2740i			0.841881i	0.907088	+	0.420941i	$0.138300\pi$
$421$			17.2740i			0.841881i	−0.907088	+	0.420941i	$0.861700\pi$
$422$	2.24767	−	7.90912i	0.109415	−	0.385010i
$423$		0			0
$424$	15.5648	−	14.2159i	0.755893	−	0.690385i
$425$			19.6354i			0.952458i
$426$		0			0
$427$	6.75419			0.326858
$428$	7.35904	−	11.9018i	0.355712	−	0.575298i
$429$		0			0
$430$	5.05011	−	17.7704i	0.243538	−	0.856963i
$431$	−10.2315			−0.492836			−0.246418	−	0.969164i	$-0.579254\pi$
$431$	−10.2315			−0.492836			−0.246418	+	0.969164i	$0.579254\pi$
$432$		0			0
$433$	−10.5332			−0.506192			−0.253096	−	0.967441i	$-0.581449\pi$
$433$	−10.5332			−0.506192			−0.253096	+	0.967441i	$0.581449\pi$
$434$	−0.618072	+	2.17488i	−0.0296684	+	0.104397i
$435$		0			0
$436$	6.87864	−	11.1249i	0.329427	−	0.532786i
$437$	−1.14188			−0.0546233
$438$		0			0
$439$			17.3145i			0.826374i	0.910646	+	0.413187i	$0.135584\pi$
$439$			17.3145i			0.826374i	−0.910646	+	0.413187i	$0.864416\pi$
$440$	32.6329	+	35.7294i	1.55571	+	1.70333i
$441$		0			0
$442$	2.65862	−	9.35516i	0.126457	−	0.444980i
$443$			3.09962i			0.147267i	0.997285	+	0.0736336i	$0.0234595\pi$
$443$			3.09962i			0.147267i	−0.997285	+	0.0736336i	$0.976540\pi$
$444$		0			0
$445$		−	18.5112i		−	0.877513i
$446$	13.0712	+	3.71467i	0.618940	+	0.175895i
$447$		0			0
$448$	−7.96724	−	0.723225i	−0.376417	−	0.0341692i
$449$			5.06298i			0.238937i	0.992838	+	0.119468i	$0.0381190\pi$
$449$			5.06298i			0.238937i	−0.992838	+	0.119468i	$0.961881\pi$
$450$		0			0
$451$	24.3326			1.14578
$452$	14.1305	−	22.8534i	0.664642	−	1.07493i
$453$		0			0
$454$	17.6749	+	5.02297i	0.829523	+	0.235740i
$455$	5.17340			0.242533
$456$		0			0
$457$	−35.6475			−1.66752			−0.833760	−	0.552127i	$-0.813816\pi$
$457$	−35.6475			−1.66752			−0.833760	+	0.552127i	$0.813816\pi$
$458$	2.00976	+	0.571147i	0.0939097	+	0.0266879i
$459$		0			0
$460$	2.06059	+	1.27408i	0.0960754	+	0.0594044i
$461$	15.3638			0.715563			0.357782	−	0.933805i	$-0.383533\pi$
$461$	15.3638			0.715563			0.357782	+	0.933805i	$0.383533\pi$
$462$		0			0
$463$		−	19.0189i		−	0.883884i	−0.897044	−	0.441942i	$-0.854290\pi$
$463$		−	19.0189i		−	0.883884i	0.897044	−	0.441942i	$-0.145710\pi$
$464$	−12.1774	−	24.3791i	−0.565321	−	1.13177i
$465$		0			0
$466$	−17.5392	−	4.98440i	−0.812486	−	0.230898i
$467$		−	16.4557i		−	0.761477i	−0.924683	−	0.380739i	$-0.875670\pi$
$467$		−	16.4557i		−	0.761477i	0.924683	−	0.380739i	$-0.124330\pi$
$468$		0			0
$469$		−	5.03553i		−	0.232519i
$470$	13.8965	−	48.8990i	0.640996	−	2.25554i
$471$		0			0
$472$	21.9761	+	24.0613i	1.01153	+	1.10751i
$473$		−	22.9584i		−	1.05563i
$474$		0			0
$475$	−13.9242			−0.638886
$476$	−7.05516	−	4.36228i	−0.323373	−	0.199945i
$477$		0			0
$478$	9.60647	−	33.8033i	0.439390	−	1.54613i
$479$	−27.7577			−1.26828			−0.634141	−	0.773218i	$-0.718646\pi$
$479$	−27.7577			−1.26828			−0.634141	+	0.773218i	$0.718646\pi$
$480$		0			0
$481$	17.7351			0.808651
$482$	8.04453	−	28.3072i	0.366418	−	1.28936i
$483$		0			0
$484$	32.4354	+	20.0552i	1.47434	+	0.911598i
$485$	−44.1722			−2.00576
$486$		0			0
$487$			17.5490i			0.795221i	0.917554	+	0.397611i	$0.130161\pi$
$487$			17.5490i			0.795221i	−0.917554	+	0.397611i	$0.869839\pi$
$488$	−12.8833	−	14.1058i	−0.583201	−	0.638539i
$489$		0			0
$490$	1.20617	−	4.24428i	0.0544891	−	0.191737i
$491$			11.6865i			0.527406i	0.964604	+	0.263703i	$0.0849439\pi$
$491$			11.6865i			0.527406i	−0.964604	+	0.263703i	$0.915056\pi$
$492$		0			0
$493$		−	28.2557i		−	1.27257i
$494$	6.63408	+	1.88532i	0.298482	+	0.0848246i
$495$		0			0
$496$	5.72106	−	2.85767i	0.256883	−	0.128313i
$497$		−	15.2213i		−	0.682769i
$498$		0			0
$499$	12.8124			0.573562			0.286781	−	0.957996i	$-0.407415\pi$
$499$	12.8124			0.573562			0.286781	+	0.957996i	$0.407415\pi$
$500$	−1.40987	−	0.871738i	−0.0630513	−	0.0389853i
$501$		0			0
$502$	−27.4500	−	7.80094i	−1.22515	−	0.348173i
$503$	24.4646			1.09082			0.545410	−	0.838169i	$-0.316374\pi$
$503$	24.4646			1.09082			0.545410	+	0.838169i	$0.316374\pi$
$504$		0			0
$505$	42.1312			1.87481
$506$	2.89606	+	0.823023i	0.128746	+	0.0365879i
$507$		0			0
$508$	−3.67242	+	5.93944i	−0.162937	+	0.263520i
$509$	13.8535			0.614046			0.307023	−	0.951702i	$-0.400667\pi$
$509$	13.8535			0.614046			0.307023	+	0.951702i	$0.400667\pi$
$510$		0			0
$511$			16.4687i			0.728530i
$512$	13.6867	+	18.0187i	0.604874	+	0.796321i
$513$		0			0
$514$	24.3290	+	6.91399i	1.07311	+	0.304963i
$515$			31.8304i			1.40261i
$516$		0			0
$517$		−	63.1749i		−	2.77843i
$518$	4.13491	−	14.5500i	0.181677	−	0.639288i
$519$		0			0
$520$	−9.86802	−	10.8044i	−0.432741	−	0.473803i
$521$		−	11.9375i		−	0.522990i	−0.965205	−	0.261495i	$-0.915785\pi$
$521$		−	11.9375i		−	0.522990i	0.965205	−	0.261495i	$-0.0842155\pi$
$522$		0			0
$523$	−14.4656			−0.632535			−0.316267	−	0.948670i	$-0.602430\pi$
$523$	−14.4656			−0.632535			−0.316267	+	0.948670i	$0.602430\pi$
$524$	−9.74156	+	15.7551i	−0.425562	+	0.688266i
$525$		0			0
$526$	−0.974768	+	3.43002i	−0.0425019	+	0.149556i
$527$	6.63077			0.288841
$528$		0			0
$529$	−22.8493			−0.993446
$530$	8.98934	−	31.6318i	0.390472	−	1.37400i
$531$		0			0
$532$	3.09345	−	5.00307i	0.134118	−	0.216911i
$533$	−7.35805			−0.318713
$534$		0			0
$535$		−	21.8293i		−	0.943764i
$536$	−10.5164	+	9.60506i	−0.454241	+	0.414875i
$537$		0			0
$538$	−4.96909	+	17.4853i	−0.214233	+	0.753844i
$539$		−	5.48338i		−	0.236186i
$540$		0			0
$541$			22.4119i			0.963563i	0.876292	+	0.481781i	$0.160010\pi$
$541$			22.4119i			0.963563i	−0.876292	+	0.481781i	$0.839990\pi$
$542$	37.7828	+	10.7374i	1.62291	+	0.461210i
$543$		0			0
$544$	4.34702	+	23.0552i	0.186377	+	0.988483i
$545$		−	20.4043i		−	0.874025i
$546$		0			0
$547$	−35.7026			−1.52653			−0.763266	−	0.646084i	$-0.776406\pi$
$547$	−35.7026			−1.52653			−0.763266	+	0.646084i	$0.776406\pi$
$548$	−3.86560	+	6.25187i	−0.165130	+	0.267067i
$549$		0			0
$550$	35.3150	+	10.0361i	1.50584	+	0.427939i
$551$	20.0371			0.853610
$552$		0			0
$553$	−2.01684			−0.0857646
$554$	−31.8240	−	9.04398i	−1.35207	−	0.384242i
$555$		0			0
$556$	−0.697879	−	0.431506i	−0.0295967	−	0.0182999i
$557$	−6.50159			−0.275481			−0.137741	−	0.990468i	$-0.543984\pi$
$557$	−6.50159			−0.275481			−0.137741	+	0.990468i	$0.543984\pi$
$558$		0			0
$559$			6.94248i			0.293636i
$560$	−11.1647	+	5.57675i	−0.471793	+	0.235661i
$561$		0			0
$562$	39.5879	+	11.2504i	1.66991	+	0.474568i
$563$			10.2444i			0.431750i	0.976421	+	0.215875i	$0.0692603\pi$
$563$			10.2444i			0.431750i	−0.976421	+	0.215875i	$0.930740\pi$
$564$		0			0
$565$		−	41.9157i		−	1.76341i
$566$	−0.160749	+	0.565643i	−0.00675676	+	0.0237758i
$567$		0			0
$568$	−31.7889	+	29.0340i	−1.33383	+	1.21824i
$569$			8.12955i			0.340808i	0.985374	+	0.170404i	$0.0545073\pi$
$569$			8.12955i			0.340808i	−0.985374	+	0.170404i	$0.945493\pi$
$570$		0			0
$571$	12.4322			0.520273			0.260136	−	0.965572i	$-0.416232\pi$
$571$	12.4322			0.520273			0.260136	+	0.965572i	$0.416232\pi$
$572$	−15.4667	−	9.56322i	−0.646695	−	0.399858i
$573$		0			0
$574$	−1.71552	+	6.03658i	−0.0716043	+	0.251962i
$575$	1.83811			0.0766544
$576$		0			0
$577$	−8.73519			−0.363651			−0.181825	−	0.983331i	$-0.558201\pi$
$577$	−8.73519			−0.363651			−0.181825	+	0.983331i	$0.558201\pi$
$578$	−0.0777762	+	0.273680i	−0.00323506	+	0.0113836i
$579$		0			0
$580$	−36.1583	−	22.3570i	−1.50139	−	0.928325i
$581$	−6.21127			−0.257687
$582$		0			0
$583$		−	40.8665i		−	1.69252i
$584$	34.3939	−	31.4132i	1.42323	−	1.29989i
$585$		0			0
$586$	−5.45862	+	19.2078i	−0.225493	+	0.793468i
$587$		−	1.73075i		−	0.0714356i	−0.999362	−	0.0357178i	$-0.988628\pi$
$587$		−	1.73075i		−	0.0714356i	0.999362	−	0.0357178i	$-0.0113718\pi$
$588$		0			0
$589$			4.70212i			0.193748i
$590$	48.8990	+	13.8965i	2.01314	+	0.572108i
$591$		0			0
$592$	−38.2740	+	19.1179i	−1.57305	+	0.785739i
$593$			44.7702i			1.83849i	0.393683	+	0.919246i	$0.371201\pi$
$593$			44.7702i			1.83849i	−0.393683	+	0.919246i	$0.628799\pi$
$594$		0			0
$595$	−12.9400			−0.530486
$596$	−5.01229	−	3.09915i	−0.205311	−	0.126946i
$597$		0			0
$598$	−0.875753	−	0.248878i	−0.0358122	−	0.0101774i
$599$	−30.6963			−1.25422			−0.627109	−	0.778932i	$-0.715762\pi$
$599$	−30.6963			−1.25422			−0.627109	+	0.778932i	$0.715762\pi$
$600$		0			0
$601$	23.2391			0.947942			0.473971	−	0.880540i	$-0.342820\pi$
$601$	23.2391			0.947942			0.473971	+	0.880540i	$0.342820\pi$
$602$	5.69564	+	1.61863i	0.232137	+	0.0659704i
$603$		0			0
$604$	−3.77570	+	6.10649i	−0.153631	+	0.248469i
$605$	59.4902			2.41862
$606$		0			0
$607$			26.7110i			1.08417i	0.840325	+	0.542084i	$0.182364\pi$
$607$			26.7110i			1.08417i	−0.840325	+	0.542084i	$0.817636\pi$
$608$	−16.3493	+	3.08263i	−0.663051	+	0.125017i
$609$		0			0
$610$	−28.6667	−	8.14669i	−1.16068	−	0.329850i
$611$			19.1037i			0.772855i
$612$		0			0
$613$			24.9292i			1.00688i	0.864030	+	0.503440i	$0.167933\pi$
$613$			24.9292i			1.00688i	−0.864030	+	0.503440i	$0.832067\pi$
$614$	13.0928	−	46.0710i	0.528381	−	1.85927i
$615$		0			0
$616$	−11.4517	+	10.4593i	−0.461404	+	0.421417i
$617$		−	4.95198i		−	0.199359i	−0.995020	−	0.0996796i	$-0.968218\pi$
$617$		−	4.95198i		−	0.199359i	0.995020	−	0.0996796i	$-0.0317818\pi$
$618$		0			0
$619$	47.0773			1.89220			0.946099	−	0.323879i	$-0.104987\pi$
$619$	47.0773			1.89220			0.946099	+	0.323879i	$0.104987\pi$
$620$	5.24654	−	8.48528i	0.210706	−	0.340777i
$621$		0			0
$622$	−7.03692	+	24.7616i	−0.282155	+	0.992848i
$623$	5.93308			0.237704
$624$		0			0
$625$	−26.2576			−1.05031
$626$	−2.40426	+	8.46014i	−0.0960936	+	0.338135i
$627$		0			0
$628$	17.6231	−	28.5020i	0.703238	−	1.13735i
$629$	−44.3599			−1.76875
$630$		0			0
$631$			9.73191i			0.387421i	0.981059	+	0.193711i	$0.0620523\pi$
$631$			9.73191i			0.387421i	−0.981059	+	0.193711i	$0.937948\pi$
$632$	3.84703	+	4.21206i	0.153027	+	0.167547i
$633$		0			0
$634$	8.65975	−	30.4720i	0.343923	−	1.21020i
$635$			10.8936i			0.432300i
$636$		0			0
$637$			1.65814i			0.0656980i
$638$	−50.8188	−	14.4420i	−2.01194	−	0.571766i
$639$		0			0
$640$	32.9428	+	12.6794i	1.30218	+	0.501197i
$641$		−	43.9546i		−	1.73610i	−0.496474	−	0.868051i	$-0.665372\pi$
$641$		−	43.9546i		−	1.73610i	0.496474	−	0.868051i	$-0.334628\pi$
$642$		0			0
$643$	−30.6029			−1.20686			−0.603429	−	0.797416i	$-0.706199\pi$
$643$	−30.6029			−1.20686			−0.603429	+	0.797416i	$0.706199\pi$
$644$	−0.408361	+	0.660446i	−0.0160917	+	0.0260252i
$645$		0			0
$646$	−16.5935	−	4.71566i	−0.652863	−	0.185535i
$647$	19.5958			0.770391			0.385195	−	0.922835i	$-0.374134\pi$
$647$	19.5958			0.770391			0.385195	+	0.922835i	$0.374134\pi$
$648$		0			0
$649$	63.1749			2.47983
$650$	−10.6791	−	3.03485i	−0.418867	−	0.119037i
$651$		0			0
$652$	19.8485	+	12.2725i	0.777328	+	0.480630i
$653$	7.43907			0.291113			0.145557	−	0.989350i	$-0.453503\pi$
$653$	7.43907			0.291113			0.145557	+	0.989350i	$0.453503\pi$
$654$		0			0
$655$			28.8967i			1.12909i
$656$	15.8793	−	7.93173i	0.619984	−	0.309682i
$657$		0			0
$658$	15.6728	+	4.45400i	0.610989	+	0.173635i
$659$			28.4918i			1.10988i	0.831889	+	0.554942i	$0.187260\pi$
$659$			28.4918i			1.10988i	−0.831889	+	0.554942i	$0.812740\pi$
$660$		0			0
$661$			7.08125i			0.275429i	0.990472	+	0.137714i	$0.0439756\pi$
$661$			7.08125i			0.275429i	−0.990472	+	0.137714i	$0.956024\pi$
$662$	8.54746	−	30.0769i	0.332207	−	1.16897i
$663$		0			0
$664$	11.8477	+	12.9719i	0.459781	+	0.503407i
$665$		−	9.17620i		−	0.355838i
$666$		0			0
$667$	−2.64506			−0.102417
$668$	29.2264	+	18.0710i	1.13080	+	0.699187i
$669$		0			0
$670$	−6.07370	+	21.3722i	−0.234648	+	0.825680i
$671$	−37.0358			−1.42975
$672$		0			0
$673$	−19.7718			−0.762145			−0.381073	−	0.924545i	$-0.624445\pi$
$673$	−19.7718			−0.762145			−0.381073	+	0.924545i	$0.624445\pi$
$674$	−7.42237	+	26.1179i	−0.285899	+	1.00602i
$675$		0			0
$676$	−17.4371	−	10.7816i	−0.670659	−	0.414676i
$677$	−19.0768			−0.733183			−0.366591	−	0.930382i	$-0.619475\pi$
$677$	−19.0768			−0.733183			−0.366591	+	0.930382i	$0.619475\pi$
$678$		0			0
$679$		−	14.1578i		−	0.543326i
$680$	24.6824	+	27.0244i	0.946527	+	1.03634i
$681$		0			0
$682$	3.38912	−	11.9257i	0.129776	−	0.456658i
$683$			10.5466i			0.403555i	0.979431	+	0.201778i	$0.0646718\pi$
$683$			10.5466i			0.403555i	−0.979431	+	0.201778i	$0.935328\pi$
$684$		0			0
$685$			11.4666i			0.438117i
$686$	1.36035	+	0.386593i	0.0519383	+	0.0147602i
$687$		0			0
$688$	−7.48377	−	14.9825i	−0.285316	−	0.571203i
$689$			12.3578i			0.470796i
$690$		0			0
$691$	29.2552			1.11292			0.556461	−	0.830874i	$-0.312159\pi$
$691$	29.2552			1.11292			0.556461	+	0.830874i	$0.312159\pi$
$692$	−32.0781	−	19.8342i	−1.21943	−	0.753984i
$693$		0			0
$694$	−4.62755	−	1.31509i	−0.175660	−	0.0499202i
$695$	−1.27999			−0.0485527
$696$		0			0
$697$	18.4043			0.697114
$698$	1.18623	+	0.337111i	0.0448994	+	0.0127598i
$699$		0			0
$700$	−4.97961	+	8.05357i	−0.188212	+	0.304396i
$701$	13.5828			0.513016			0.256508	−	0.966542i	$-0.417428\pi$
$701$	13.5828			0.513016			0.256508	+	0.966542i	$0.417428\pi$
$702$		0			0
$703$		−	31.4572i		−	1.18643i
$704$	43.6874	+	3.96571i	1.64653	+	0.149463i
$705$		0			0
$706$	8.66908	+	2.46364i	0.326265	+	0.0927203i
$707$			13.5036i			0.507856i
$708$		0			0
$709$		−	6.52460i		−	0.245036i	−0.992466	−	0.122518i	$-0.960903\pi$
$709$		−	6.52460i		−	0.245036i	0.992466	−	0.122518i	$-0.0390970\pi$
$710$	−18.3594	+	64.6034i	−0.689018	+	2.42452i
$711$		0			0
$712$	−11.3171	−	12.3909i	−0.424126	−	0.464369i
$713$		−	0.620719i		−	0.0232461i
$714$		0			0
$715$	−28.3677			−1.06089
$716$	−10.9783	+	17.7554i	−0.410279	+	0.663549i
$717$		0			0
$718$	2.37929	−	8.37225i	0.0887942	−	0.312450i
$719$	−1.06415			−0.0396860			−0.0198430	−	0.999803i	$-0.506317\pi$
$719$	−1.06415			−0.0396860			−0.0198430	+	0.999803i	$0.506317\pi$
$720$		0			0
$721$	−10.2021			−0.379945
$722$	−4.00122	+	14.0795i	−0.148910	+	0.523986i
$723$		0			0
$724$	−0.487860	+	0.789021i	−0.0181312	+	0.0293237i
$725$	−32.2543			−1.19789
$726$		0			0
$727$		−	1.07254i		−	0.0397781i	−0.999802	−	0.0198891i	$-0.993669\pi$
$727$		−	1.07254i		−	0.0397781i	0.999802	−	0.0198891i	$-0.00633130\pi$
$728$	3.46295	−	3.16284i	0.128345	−	0.117222i
$729$		0			0
$730$	19.8640	−	69.8975i	0.735198	−	2.58702i
$731$		−	17.3649i		−	0.642264i
$732$		0			0
$733$			12.5340i			0.462952i	0.972841	+	0.231476i	$0.0743555\pi$
$733$			12.5340i			0.462952i	−0.972841	+	0.231476i	$0.925644\pi$
$734$	−19.2379	−	5.46716i	−0.710084	−	0.201797i
$735$		0			0
$736$	2.15824	−	0.406932i	0.0795537	−	0.0149997i
$737$			27.6117i			1.01709i
$738$		0			0
$739$	11.3506			0.417537			0.208768	−	0.977965i	$-0.433055\pi$
$739$	11.3506			0.417537			0.208768	+	0.977965i	$0.433055\pi$
$740$	−35.0994	+	56.7666i	−1.29028	+	2.08678i
$741$		0			0
$742$	10.1384	+	2.88121i	0.372193	+	0.105772i
$743$	−34.5495			−1.26750			−0.633750	−	0.773538i	$-0.718485\pi$
$743$	−34.5495			−1.26750			−0.633750	+	0.773538i	$0.718485\pi$
$744$		0			0
$745$	−9.19311			−0.336809
$746$	−42.0289	−	11.9441i	−1.53879	−	0.437304i
$747$		0			0
$748$	38.6861	+	23.9200i	1.41450	+	0.874602i
$749$	6.99660			0.255650
$750$		0			0
$751$			44.8163i			1.63537i	0.575667	+	0.817684i	$0.304743\pi$
$751$			44.8163i			1.63537i	−0.575667	+	0.817684i	$0.695257\pi$
$752$	−20.5932	−	41.2276i	−0.750957	−	1.50342i
$753$		0			0
$754$	15.3673	+	4.36720i	0.559645	+	0.159044i
$755$			11.2000i			0.407609i
$756$		0			0
$757$		−	11.9597i		−	0.434683i	−0.976096	−	0.217342i	$-0.930261\pi$
$757$		−	11.9597i		−	0.434683i	0.976096	−	0.217342i	$-0.0697386\pi$
$758$	−10.5713	+	37.1982i	−0.383965	+	1.35110i
$759$		0			0
$760$	−19.1640	+	17.5032i	−0.695151	+	0.634907i
$761$			35.3858i			1.28273i	0.767234	+	0.641367i	$0.221632\pi$
$761$			35.3858i			1.28273i	−0.767234	+	0.641367i	$0.778368\pi$
$762$		0			0
$763$	6.53986			0.236759
$764$	−5.85884	−	3.62258i	−0.211965	−	0.131060i
$765$		0			0
$766$	−3.33584	+	11.7382i	−0.120529	+	0.424117i
$767$	−19.1037			−0.689796
$768$		0			0
$769$	−8.89574			−0.320789			−0.160394	−	0.987053i	$-0.551277\pi$
$769$	−8.89574			−0.320789			−0.160394	+	0.987053i	$0.551277\pi$
$770$	−6.61387	+	23.2730i	−0.238348	+	0.838699i
$771$		0			0
$772$	18.4271	+	11.3936i	0.663204	+	0.410066i
$773$	1.97112			0.0708962			0.0354481	−	0.999372i	$-0.488714\pi$
$773$	1.97112			0.0708962			0.0354481	+	0.999372i	$0.488714\pi$
$774$		0			0
$775$		−	7.56913i		−	0.271891i
$776$	−29.5678	+	27.0054i	−1.06142	+	0.969436i
$777$		0			0
$778$	−2.74875	+	9.67232i	−0.0985474	+	0.346770i
$779$			13.0512i			0.467607i
$780$		0			0
$781$			83.4641i			2.98658i
$782$	2.19048	+	0.622506i	0.0783313	+	0.0222608i
$783$		0			0
$784$	−1.78742	−	3.57842i	−0.0638365	−	0.127801i
$785$		−	52.2759i		−	1.86581i
$786$		0			0
$787$	−1.69609			−0.0604590			−0.0302295	−	0.999543i	$-0.509624\pi$
$787$	−1.69609			−0.0604590			−0.0302295	+	0.999543i	$0.509624\pi$
$788$	6.15862	+	3.80794i	0.219392	+	0.135652i
$789$		0			0
$790$	8.56001	+	2.43264i	0.304552	+	0.0865496i
$791$	13.4345			0.477677
$792$		0			0
$793$	11.1994			0.397703
$794$	−19.1370	−	5.43848i	−0.679146	−	0.193004i
$795$		0			0
$796$	24.4395	−	39.5263i	0.866237	−	1.40097i
$797$	−22.4897			−0.796628			−0.398314	−	0.917249i	$-0.630404\pi$
$797$	−22.4897			−0.796628			−0.398314	+	0.917249i	$0.630404\pi$
$798$		0			0
$799$		−	47.7832i		−	1.69045i
$800$	26.3178	−	4.96219i	0.930476	−	0.175440i
$801$		0			0
$802$	−8.05795	−	2.28997i	−0.284536	−	0.0808615i
$803$		−	90.3038i		−	3.18675i
$804$		0			0
$805$			1.21133i			0.0426939i
$806$	−1.02485	+	3.60626i	−0.0360989	+	0.127025i
$807$		0			0
$808$	28.2016	−	25.7575i	0.992128	−	0.906147i
$809$			36.3829i			1.27915i	0.768727	+	0.639577i	$0.220890\pi$
$809$			36.3829i			1.27915i	−0.768727	+	0.639577i	$0.779110\pi$
$810$		0			0
$811$	−6.67771			−0.234486			−0.117243	−	0.993103i	$-0.537406\pi$
$811$	−6.67771			−0.234486			−0.117243	+	0.993103i	$0.537406\pi$
$812$	7.16573	−	11.5892i	0.251468	−	0.406702i
$813$		0			0
$814$	−22.6733	+	79.7829i	−0.794697	+	2.79639i
$815$	36.4044			1.27519
$816$		0			0
$817$	12.3141			0.430815
$818$	−9.14221	+	32.1697i	−0.319650	+	1.12479i
$819$		0			0
$820$	14.5623	−	23.5517i	0.508536	−	0.822461i
$821$	20.3477			0.710139			0.355070	−	0.934840i	$-0.384457\pi$
$821$	20.3477			0.710139			0.355070	+	0.934840i	$0.384457\pi$
$822$		0			0
$823$		−	0.441780i		−	0.0153995i	−0.999970	−	0.00769974i	$-0.997549\pi$
$823$		−	0.441780i		−	0.0153995i	0.999970	−	0.00769974i	$-0.00245093\pi$
$824$	19.4600	+	21.3065i	0.677921	+	0.742246i
$825$		0			0
$826$	−4.45400	+	15.6728i	−0.154975	+	0.545326i
$827$		−	32.9989i		−	1.14749i	−0.819035	−	0.573743i	$-0.805491\pi$
$827$		−	32.9989i		−	1.14749i	0.819035	−	0.573743i	$-0.194509\pi$
$828$		0			0
$829$			34.2694i			1.19023i	0.803642	+	0.595113i	$0.202893\pi$
$829$			34.2694i			1.19023i	−0.803642	+	0.595113i	$0.797107\pi$
$830$	26.3623	+	7.49183i	0.915050	+	0.260045i
$831$		0			0
$832$	−13.2108	−	1.19921i	−0.458003	−	0.0415751i
$833$		−	4.14743i		−	0.143700i
$834$		0			0
$835$	53.6045			1.85506
$836$	−16.9626	+	27.4337i	−0.586662	+	0.948815i
$837$		0			0
$838$	−32.7173	−	9.29785i	−1.13020	−	0.321189i
$839$	54.5494			1.88325			0.941626	−	0.336660i	$-0.109297\pi$
$839$	54.5494			1.88325			0.941626	+	0.336660i	$0.109297\pi$
$840$		0			0
$841$	17.4144			0.600497
$842$	23.4986	+	6.67800i	0.809815	+	0.230139i
$843$		0			0
$844$	−9.89022	−	6.11522i	−0.340435	−	0.210495i
$845$	−31.9817			−1.10020
$846$		0			0
$847$			19.0674i			0.655164i
$848$	−13.3213	−	26.6693i	−0.457456	−	0.915828i
$849$		0			0
$850$	26.7110	+	7.59092i	0.916180	+	0.260366i
$851$			4.15261i			0.142350i
$852$		0			0
$853$			37.3044i			1.27728i	0.769506	+	0.638639i	$0.220502\pi$
$853$			37.3044i			1.27728i	−0.769506	+	0.638639i	$0.779498\pi$
$854$	2.61113	−	9.18805i	0.0893509	−	0.314409i
$855$		0			0
$856$	−13.3457	−	14.6120i	−0.456147	−	0.499429i
$857$			27.8499i			0.951333i	0.879626	+	0.475667i	$0.157793\pi$
$857$			27.8499i			0.951333i	−0.879626	+	0.475667i	$0.842207\pi$
$858$		0			0
$859$	−46.7277			−1.59433			−0.797164	−	0.603763i	$-0.793667\pi$
$859$	−46.7277			−1.59433			−0.797164	+	0.603763i	$0.793667\pi$
$860$	−22.2215	−	13.7398i	−0.757748	−	0.468523i
$861$		0			0
$862$	−3.95545	+	13.9185i	−0.134723	+	0.474065i
$863$	21.6286			0.736247			0.368123	−	0.929777i	$-0.380000\pi$
$863$	21.6286			0.736247			0.368123	+	0.929777i	$0.380000\pi$
$864$		0			0
$865$	−58.8348			−2.00044
$866$	−4.07205	+	14.3288i	−0.138374	+	0.486912i
$867$		0			0
$868$	2.71965	+	1.68159i	0.0923108	+	0.0570768i
$869$	11.0591			0.375153
$870$		0			0
$871$		−	8.34964i		−	0.282917i
$872$	−12.4745	−	13.6582i	−0.422440	−	0.462524i
$873$		0			0
$874$	−0.441442	+	1.55335i	−0.0149320	+	0.0525428i
$875$		−	0.828803i		−	0.0280187i
$876$		0			0
$877$		−	22.7567i		−	0.768438i	−0.923242	−	0.384219i	$-0.874471\pi$
$877$		−	22.7567i		−	0.768438i	0.923242	−	0.384219i	$-0.125529\pi$
$878$	23.5537	+	6.69365i	0.794898	+	0.225900i
$879$		0			0
$880$	61.2200	−	30.5794i	2.06373	−	1.03083i
$881$			18.6695i			0.628992i	0.949259	+	0.314496i	$0.101835\pi$
$881$			18.6695i			0.628992i	−0.949259	+	0.314496i	$0.898165\pi$
$882$		0			0
$883$	6.60315			0.222214			0.111107	−	0.993808i	$-0.464560\pi$
$883$	6.60315			0.222214			0.111107	+	0.993808i	$0.464560\pi$
$884$	−11.6985	−	7.23328i	−0.393462	−	0.243282i
$885$		0			0
$886$	4.21655	+	1.19829i	0.141658	+	0.0402574i
$887$	−24.9136			−0.836515			−0.418258	−	0.908328i	$-0.637359\pi$
$887$	−24.9136			−0.836515			−0.418258	+	0.908328i	$0.637359\pi$
$888$		0			0
$889$	−3.49155			−0.117103
$890$	−25.1816	−	7.15629i	−0.844090	−	0.239879i
$891$		0			0
$892$	10.1065	−	16.3453i	0.338390	−	0.547282i
$893$	33.8848			1.13391
$894$		0			0
$895$			32.5653i			1.08854i
$896$	−4.06392	+	10.5586i	−0.135766	+	0.352739i
$897$		0			0
$898$	6.88742	+	1.95731i	0.229836	+	0.0653164i
$899$			10.8921i			0.363272i
$900$		0			0
$901$		−	30.9100i		−	1.02976i
$902$	9.40683	−	33.1008i	0.313213	−	1.10214i
$903$		0			0
$904$	−25.6258	−	28.0573i	−0.852301	−	0.933173i
$905$			1.44715i			0.0481050i
$906$		0			0
$907$	34.0223			1.12969			0.564847	−	0.825196i	$-0.308935\pi$
$907$	34.0223			1.12969			0.564847	+	0.825196i	$0.308935\pi$
$908$	13.6660	−	22.1021i	0.453521	−	0.733485i
$909$		0			0
$910$	2.00000	−	7.03762i	0.0662994	−	0.233295i
$911$	20.9906			0.695449			0.347725	−	0.937597i	$-0.386954\pi$
$911$	20.9906			0.695449			0.347725	+	0.937597i	$0.386954\pi$
$912$		0			0
$913$	34.0587			1.12718
$914$	−13.7811	+	48.4930i	−0.455838	+	1.60401i
$915$		0			0
$916$	1.55392	−	2.51316i	0.0513428	−	0.0830373i
$917$	−9.26178			−0.305851
$918$		0			0
$919$		−	56.0942i		−	1.85038i	−0.379507	−	0.925189i	$-0.623906\pi$
$919$		−	56.0942i		−	1.85038i	0.379507	−	0.925189i	$-0.376094\pi$
$920$	2.52980	−	2.31056i	0.0834052	−	0.0761770i
$921$		0			0
$922$	5.93954	−	20.9001i	0.195608	−	0.688308i
$923$		−	25.2391i		−	0.830755i
$924$		0			0
$925$			50.6376i			1.66495i
$926$	−25.8723	−	7.35259i	−0.850218	−	0.241621i
$927$		0			0
$928$	−37.8718	+	7.14066i	−1.24320	+	0.234404i
$929$		−	21.7754i		−	0.714427i	−0.934023	−	0.357213i	$-0.883727\pi$
$929$		−	21.7754i		−	0.714427i	0.934023	−	0.357213i	$-0.116273\pi$
$930$		0			0
$931$	2.94109			0.0963905
$932$	−13.5610	+	21.9324i	−0.444207	+	0.718420i
$933$		0			0
$934$	−22.3854	−	6.36165i	−0.732473	−	0.208159i
$935$	70.9547			2.32047
$936$		0			0
$937$	−7.58652			−0.247841			−0.123920	−	0.992292i	$-0.539547\pi$
$937$	−7.58652			−0.247841			−0.123920	+	0.992292i	$0.539547\pi$
$938$	−6.85008	−	1.94670i	−0.223663	−	0.0635621i
$939$		0			0
$940$	−61.1474	−	37.8080i	−1.99441	−	1.23316i
$941$	17.7633			0.579065			0.289533	−	0.957168i	$-0.406500\pi$
$941$	17.7633			0.579065			0.289533	+	0.957168i	$0.406500\pi$
$942$		0			0
$943$		−	1.72286i		−	0.0561041i
$944$	41.2276	−	20.5932i	1.34184	−	0.670252i
$945$		0			0
$946$	−31.2313	−	8.87555i	−1.01542	−	0.288569i
$947$		−	12.7864i		−	0.415501i	−0.978182	−	0.207751i	$-0.933386\pi$
$947$		−	12.7864i		−	0.415501i	0.978182	−	0.207751i	$-0.0666143\pi$
$948$		0			0
$949$			27.3074i			0.886435i
$950$	−5.38300	+	18.9417i	−0.174648	+	0.614551i
$951$		0			0
$952$	−8.66169	+	7.91104i	−0.280727	+	0.256398i
$953$			13.9943i			0.453319i	0.973974	+	0.226659i	$0.0727804\pi$
$953$			13.9943i			0.453319i	−0.973974	+	0.226659i	$0.927220\pi$
$954$		0			0
$955$	−10.7458			−0.347725
$956$	−42.2705	−	26.1363i	−1.36712	−	0.845308i
$957$		0			0
$958$	−10.7309	+	37.7601i	−0.346701	+	1.21997i
$959$	−3.67521			−0.118679
$960$		0			0
$961$	28.4439			0.917547
$962$	6.85627	−	24.1259i	0.221055	−	0.777850i
$963$		0			0
$964$	−35.3976	−	21.8867i	−1.14008	−	0.704924i
$965$	33.7973			1.08797
$966$		0			0
$967$			50.1180i			1.61169i	0.592129	+	0.805843i	$0.298288\pi$
$967$			50.1180i			1.61169i	−0.592129	+	0.805843i	$0.701712\pi$
$968$	39.8213	−	36.3703i	1.27990	−	1.16898i
$969$		0			0
$970$	−17.0767	+	60.0896i	−0.548299	+	1.92936i
$971$		−	12.0972i		−	0.388217i	−0.980980	−	0.194108i	$-0.937819\pi$
$971$		−	12.0972i		−	0.388217i	0.980980	−	0.194108i	$-0.0621813\pi$
$972$		0			0
$973$		−	0.410254i		−	0.0131521i
$974$	23.8727	+	6.78433i	0.764932	+	0.217384i
$975$		0			0
$976$	−24.1694	+	12.0726i	−0.773643	+	0.386435i
$977$			6.37204i			0.203860i	0.994792	+	0.101930i	$0.0325017\pi$
$977$			6.37204i			0.203860i	−0.994792	+	0.101930i	$0.967498\pi$
$978$		0			0
$979$	−32.5333			−1.03977
$980$	−5.30739	−	3.28162i	−0.169538	−	0.104827i
$981$		0			0
$982$	15.8977	+	4.51794i	0.507318	+	0.144173i
$983$	−0.298981			−0.00953601			−0.00476801	−	0.999989i	$-0.501518\pi$
$983$	−0.298981			−0.00953601			−0.00476801	+	0.999989i	$0.501518\pi$
$984$		0			0
$985$	11.2956			0.359908
$986$	−38.4375	−	10.9235i	−1.22410	−	0.347874i
$987$		0			0
$988$	5.12939	−	8.29581i	0.163187	−	0.263925i
$989$	−1.62556			−0.0516898
$990$		0			0
$991$			3.43504i			0.109118i	0.998511	+	0.0545588i	$0.0173752\pi$
$991$			3.43504i			0.109118i	−0.998511	+	0.0545588i	$0.982625\pi$
$992$	−1.67570	−	8.88739i	−0.0532036	−	0.282175i
$993$		0			0
$994$	−20.7063	−	5.88445i	−0.656763	−	0.186643i
$995$		−	72.4958i		−	2.29827i
$996$		0			0
$997$		−	46.9672i		−	1.48747i	−0.668477	−	0.743733i	$-0.733054\pi$
$997$		−	46.9672i		−	1.48747i	0.668477	−	0.743733i	$-0.266946\pi$
$998$	4.95319	−	17.4293i	0.156790	−	0.551716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.j.a.323.15	yes	24
3.2	odd	2	inner	504.2.j.a.323.10	yes	24
4.3	odd	2		2016.2.j.a.1583.4		24
8.3	odd	2	inner	504.2.j.a.323.9	✓	24
8.5	even	2		2016.2.j.a.1583.22		24
12.11	even	2		2016.2.j.a.1583.21		24
24.5	odd	2		2016.2.j.a.1583.3		24
24.11	even	2	inner	504.2.j.a.323.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.j.a.323.9	✓	24	8.3	odd	2	inner
504.2.j.a.323.10	yes	24	3.2	odd	2	inner
504.2.j.a.323.15	yes	24	1.1	even	1	trivial
504.2.j.a.323.16	yes	24	24.11	even	2	inner
2016.2.j.a.1583.3		24	24.5	odd	2
2016.2.j.a.1583.4		24	4.3	odd	2
2016.2.j.a.1583.21		24	12.11	even	2
2016.2.j.a.1583.22		24	8.5	even	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.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.386593 - 1.36035i) q^{2} +(-1.70109 - 1.05180i) q^{4} -3.11999 q^{5} -1.00000i q^{7} +(-2.08845 + 1.90746i) q^{8} +O(q^{10})\)	\(q+(0.386593 - 1.36035i) q^{2} +(-1.70109 - 1.05180i) q^{4} -3.11999 q^{5} -1.00000i q^{7} +(-2.08845 + 1.90746i) q^{8} +(-1.20617 + 4.24428i) q^{10} +5.48338i q^{11} -1.65814i q^{13} +(-1.36035 - 0.386593i) q^{14} +(1.78742 + 3.57842i) q^{16} +4.14743i q^{17} -2.94109 q^{19} +(5.30739 + 3.28162i) q^{20} +(7.45930 + 2.11984i) q^{22} +0.388249 q^{23} +4.73436 q^{25} +(-2.25565 - 0.641027i) q^{26} +(-1.05180 + 1.70109i) q^{28} -6.81281 q^{29} -1.59877i q^{31} +(5.55891 - 1.04812i) q^{32} +(5.64195 + 1.60337i) q^{34} +3.11999i q^{35} +10.6958i q^{37} +(-1.13701 + 4.00091i) q^{38} +(6.51594 - 5.95125i) q^{40} -4.43752i q^{41} -4.18690 q^{43} +(5.76743 - 9.32772i) q^{44} +(0.150094 - 0.528153i) q^{46} -11.5212 q^{47} -1.00000 q^{49} +(1.83027 - 6.44037i) q^{50} +(-1.74404 + 2.82065i) q^{52} -7.45281 q^{53} -17.1081i q^{55} +(1.90746 + 2.08845i) q^{56} +(-2.63379 + 9.26779i) q^{58} -11.5212i q^{59} +6.75419i q^{61} +(-2.17488 - 0.618072i) q^{62} +(0.723225 - 7.96724i) q^{64} +5.17340i q^{65} +5.03553 q^{67} +(4.36228 - 7.05516i) q^{68} +(4.24428 + 1.20617i) q^{70} +15.2213 q^{71} -16.4687 q^{73} +(14.5500 + 4.13491i) q^{74} +(5.00307 + 3.09345i) q^{76} +5.48338 q^{77} -2.01684i q^{79} +(-5.57675 - 11.1647i) q^{80} +(-6.03658 - 1.71552i) q^{82} -6.21127i q^{83} -12.9400i q^{85} +(-1.61863 + 5.69564i) q^{86} +(-10.4593 - 11.4517i) q^{88} +5.93308i q^{89} -1.65814 q^{91} +(-0.660446 - 0.408361i) q^{92} +(-4.45400 + 15.6728i) q^{94} +9.17620 q^{95} +14.1578 q^{97} +(-0.386593 + 1.36035i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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