LMFDB - Embedded newform 504.2.j.a.323.9

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			323.9
Character	$\chi$	$=$	504.323
Dual form			504.2.j.a.323.10

$q$-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	$-0.254228\pi$
$5$	3.11999			1.39530			0.697652	+	0.716437i	$0.254228\pi$
$6$		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	$0.0738540\pi$
$13$			1.65814i			0.459886i	−0.973204	+	0.229943i	$0.926146\pi$
$14$	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	$-0.512888\pi$
$23$	−0.388249			−0.0809554			−0.0404777	+	0.999180i	$0.512888\pi$
$24$		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	$-0.282007\pi$
$29$	6.81281			1.26511			0.632554	+	0.774516i	$0.282007\pi$
$30$		0			0
$31$			1.59877i			0.287147i	0.989640	+	0.143573i	$0.0458593\pi$
$31$			1.59877i			0.287147i	−0.989640	+	0.143573i	$0.954141\pi$
$32$	−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	$-0.658087\pi$
$37$		−	10.6958i		−	1.75837i	0.476479	−	0.879186i	$-0.341913\pi$
$38$	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	$-0.182398\pi$
$47$	11.5212			1.68053			0.840267	+	0.542172i	$0.182398\pi$
$48$		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	$-0.328956\pi$
$53$	7.45281			1.02372			0.511861	+	0.859068i	$0.328956\pi$
$54$		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	$-0.857669\pi$
$61$		−	6.75419i		−	0.864786i	0.901685	−	0.432393i	$-0.142331\pi$
$62$	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	$-0.858802\pi$
$71$	−15.2213			−1.80644			−0.903218	+	0.429182i	$0.858802\pi$
$72$		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	$0.0361921\pi$
$79$			2.01684i			0.226912i	−0.993543	+	0.113456i	$0.963808\pi$
$80$	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	$-0.265509\pi$
$101$	13.5036			1.34366			0.671830	+	0.740705i	$0.265509\pi$
$102$		0			0
$103$			10.2021i			1.00524i	0.864508	+	0.502620i	$0.167630\pi$
$103$			10.2021i			1.00524i	−0.864508	+	0.502620i	$0.832370\pi$
$104$	−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	$-0.898598\pi$
$109$		−	6.53986i		−	0.626405i	0.949686	−	0.313203i	$-0.101402\pi$
$110$	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	$0.0495096\pi$
$127$			3.49155i			0.309825i	−0.987928	+	0.154912i	$0.950490\pi$
$128$	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	$-0.538512\pi$
$149$	−2.94652			−0.241388			−0.120694	+	0.992690i	$0.538512\pi$
$150$		0			0
$151$			3.58975i			0.292129i	0.989275	+	0.146065i	$0.0466608\pi$
$151$			3.58975i			0.292129i	−0.989275	+	0.146065i	$0.953339\pi$
$152$	−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	$-0.766893\pi$
$157$		−	16.7551i		−	1.33721i	0.743620	−	0.668603i	$-0.233107\pi$
$158$	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	$-0.268537\pi$
$167$	17.1810			1.32950			0.664751	+	0.747065i	$0.268537\pi$
$168$		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	$-0.754416\pi$
$173$	−18.8574			−1.43370			−0.716849	+	0.697228i	$0.754416\pi$
$174$		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	$0.00548736\pi$
$181$			0.463832i			0.0344764i	−0.999851	+	0.0172382i	$0.994513\pi$
$182$	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	$-0.539767\pi$
$191$	−3.44417			−0.249211			−0.124606	+	0.992206i	$0.539767\pi$
$192$		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	$-0.458833\pi$
$197$	3.62039			0.257942			0.128971	+	0.991648i	$0.458833\pi$
$198$		0			0
$199$		−	23.2359i		−	1.64715i	−0.567209	−	0.823574i	$-0.691977\pi$
$199$		−	23.2359i		−	1.64715i	0.567209	−	0.823574i	$-0.308023\pi$
$200$	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	$-0.895738\pi$
$223$		−	9.60873i		−	0.643448i	0.946833	−	0.321724i	$-0.104262\pi$
$224$	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	$-0.984456\pi$
$229$		−	1.47738i		−	0.0976283i	0.998808	−	0.0488141i	$-0.0155442\pi$
$230$	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	$-0.797125\pi$
$239$	−24.8490			−1.60735			−0.803675	+	0.595068i	$0.797125\pi$
$240$		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	$-0.475230\pi$
$263$	2.52143			0.155478			0.0777390	+	0.996974i	$0.475230\pi$
$264$		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	$-0.371836\pi$
$269$	12.8535			0.783695			0.391847	+	0.920030i	$0.371836\pi$
$270$		0			0
$271$		−	27.7743i		−	1.68717i	−0.536995	−	0.843586i	$-0.680440\pi$
$271$		−	27.7743i		−	1.68717i	0.536995	−	0.843586i	$-0.319560\pi$
$272$	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	$0.248070\pi$
$277$			23.3940i			1.40561i	−0.711382	+	0.702806i	$0.751930\pi$
$278$	−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	$-0.364675\pi$
$293$	14.1198			0.824887			0.412444	+	0.910983i	$0.364675\pi$
$294$		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	$-0.327390\pi$
$311$	18.2024			1.03216			0.516081	+	0.856540i	$0.327390\pi$
$312$		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	$-0.716560\pi$
$317$	−22.4002			−1.25812			−0.629059	+	0.777357i	$0.716560\pi$
$318$		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	$-0.992570\pi$
$349$		−	0.872003i		−	0.0466773i	0.999728	−	0.0233386i	$-0.00742959\pi$
$350$	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	$-0.551927\pi$
$359$	−6.15450			−0.324822			−0.162411	+	0.986723i	$0.551927\pi$
$360$		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	$0.120334\pi$
$367$			14.1419i			0.738201i	−0.929389	+	0.369101i	$0.879666\pi$
$368$	−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	$0.295093\pi$
$373$			30.8957i			1.59972i	−0.600186	+	0.799860i	$0.704907\pi$
$374$	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	$-0.429246\pi$
$383$	8.62880			0.440911			0.220456	+	0.975397i	$0.429246\pi$
$384$		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	$-0.442309\pi$
$389$	7.11018			0.360501			0.180250	+	0.983621i	$0.442309\pi$
$390$		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	$0.114845\pi$
$397$			14.0677i			0.706038i	−0.935616	+	0.353019i	$0.885155\pi$
$398$	−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	$-0.861700\pi$
$421$		−	17.2740i		−	0.841881i	0.907088	−	0.420941i	$-0.138300\pi$
$422$	−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	$-0.420746\pi$
$431$	10.2315			0.492836			0.246418	+	0.969164i	$0.420746\pi$
$432$		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	$-0.864416\pi$
$439$		−	17.3145i		−	0.826374i	0.910646	−	0.413187i	$-0.135584\pi$
$440$	−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	$-0.616467\pi$
$461$	−15.3638			−0.715563			−0.357782	+	0.933805i	$0.616467\pi$
$462$		0			0
$463$			19.0189i			0.883884i	0.897044	+	0.441942i	$0.145710\pi$
$463$			19.0189i			0.883884i	−0.897044	+	0.441942i	$0.854290\pi$
$464$	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	$-0.281354\pi$
$479$	27.7577			1.26828			0.634141	+	0.773218i	$0.281354\pi$
$480$		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	$-0.869839\pi$
$487$		−	17.5490i		−	0.795221i	0.917554	−	0.397611i	$-0.130161\pi$
$488$	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	$-0.683626\pi$
$503$	−24.4646			−1.09082			−0.545410	+	0.838169i	$0.683626\pi$
$504$		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	$-0.599333\pi$
$509$	−13.8535			−0.614046			−0.307023	+	0.951702i	$0.599333\pi$
$510$		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	$-0.839990\pi$
$541$		−	22.4119i		−	0.963563i	0.876292	−	0.481781i	$-0.160010\pi$
$542$	−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	$-0.456016\pi$
$557$	6.50159			0.275481			0.137741	+	0.990468i	$0.456016\pi$
$558$		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	$-0.284238\pi$
$599$	30.6963			1.25422			0.627109	+	0.778932i	$0.284238\pi$
$600$		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	$-0.817636\pi$
$607$		−	26.7110i		−	1.08417i	0.840325	−	0.542084i	$-0.182364\pi$
$608$	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	$-0.832067\pi$
$613$		−	24.9292i		−	1.00688i	0.864030	−	0.503440i	$-0.167933\pi$
$614$	−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	$-0.937948\pi$
$631$		−	9.73191i		−	0.387421i	0.981059	−	0.193711i	$-0.0620523\pi$
$632$	−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	$-0.625866\pi$
$647$	−19.5958			−0.770391			−0.385195	+	0.922835i	$0.625866\pi$
$648$		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	$-0.546497\pi$
$653$	−7.43907			−0.291113			−0.145557	+	0.989350i	$0.546497\pi$
$654$		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	$-0.956024\pi$
$661$		−	7.08125i		−	0.275429i	0.990472	−	0.137714i	$-0.0439756\pi$
$662$	−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	$-0.380525\pi$
$677$	19.0768			0.733183			0.366591	+	0.930382i	$0.380525\pi$
$678$		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	$-0.582572\pi$
$701$	−13.5828			−0.513016			−0.256508	+	0.966542i	$0.582572\pi$
$702$		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	$0.0390970\pi$
$709$			6.52460i			0.245036i	−0.992466	+	0.122518i	$0.960903\pi$
$710$	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	$-0.493683\pi$
$719$	1.06415			0.0396860			0.0198430	+	0.999803i	$0.493683\pi$
$720$		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	$0.00633130\pi$
$727$			1.07254i			0.0397781i	−0.999802	+	0.0198891i	$0.993669\pi$
$728$	−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	$-0.925644\pi$
$733$		−	12.5340i		−	0.462952i	0.972841	−	0.231476i	$-0.0743555\pi$
$734$	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	$-0.281515\pi$
$743$	34.5495			1.26750			0.633750	+	0.773538i	$0.281515\pi$
$744$		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	$-0.695257\pi$
$751$		−	44.8163i		−	1.63537i	0.575667	−	0.817684i	$-0.304743\pi$
$752$	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	$0.0697386\pi$
$757$			11.9597i			0.434683i	−0.976096	+	0.217342i	$0.930261\pi$
$758$	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	$-0.511286\pi$
$773$	−1.97112			−0.0708962			−0.0354481	+	0.999372i	$0.511286\pi$
$774$		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	$-0.369596\pi$
$797$	22.4897			0.796628			0.398314	+	0.917249i	$0.369596\pi$
$798$		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	$-0.615543\pi$
$821$	−20.3477			−0.710139			−0.355070	+	0.934840i	$0.615543\pi$
$822$		0			0
$823$			0.441780i			0.0153995i	0.999970	+	0.00769974i	$0.00245093\pi$
$823$			0.441780i			0.0153995i	−0.999970	+	0.00769974i	$0.997549\pi$
$824$	−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	$-0.797107\pi$
$829$		−	34.2694i		−	1.19023i	0.803642	−	0.595113i	$-0.202893\pi$
$830$	−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	$-0.890703\pi$
$839$	−54.5494			−1.88325			−0.941626	+	0.336660i	$0.890703\pi$
$840$		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	$-0.779498\pi$
$853$		−	37.3044i		−	1.27728i	0.769506	−	0.638639i	$-0.220502\pi$
$854$	−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	$-0.620000\pi$
$863$	−21.6286			−0.736247			−0.368123	+	0.929777i	$0.620000\pi$
$864$		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	$0.125529\pi$
$877$			22.7567i			0.768438i	−0.923242	+	0.384219i	$0.874471\pi$
$878$	−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	$-0.362641\pi$
$887$	24.9136			0.836515			0.418258	+	0.908328i	$0.362641\pi$
$888$		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	$-0.613046\pi$
$911$	−20.9906			−0.695449			−0.347725	+	0.937597i	$0.613046\pi$
$912$		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	$0.376094\pi$
$919$			56.0942i			1.85038i	−0.379507	+	0.925189i	$0.623906\pi$
$920$	−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	$-0.593500\pi$
$941$	−17.7633			−0.579065			−0.289533	+	0.957168i	$0.593500\pi$
$942$		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	$-0.701712\pi$
$967$		−	50.1180i		−	1.61169i	0.592129	−	0.805843i	$-0.298288\pi$
$968$	−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	$-0.498482\pi$
$983$	0.298981			0.00953601			0.00476801	+	0.999989i	$0.498482\pi$
$984$		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	$-0.982625\pi$
$991$		−	3.43504i		−	0.109118i	0.998511	−	0.0545588i	$-0.0173752\pi$
$992$	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	$0.266946\pi$
$997$			46.9672i			1.48747i	−0.668477	+	0.743733i	$0.733054\pi$
$998$	−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.323.9	✓	24
3.2	odd	2	inner	504.2.j.a.323.16	yes	24
4.3	odd	2		2016.2.j.a.1583.22		24
8.3	odd	2	inner	504.2.j.a.323.15	yes	24
8.5	even	2		2016.2.j.a.1583.4		24
12.11	even	2		2016.2.j.a.1583.3		24
24.5	odd	2		2016.2.j.a.1583.21		24
24.11	even	2	inner	504.2.j.a.323.10	yes	24

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

Groups

Database

Properties

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