LMFDB - Embedded newform 532.2.k.b.277.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(121,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("532.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.k (of order $3$, degree $2$, 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:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.12
Character	$\chi$	$=$	532.277
Dual form			532.2.k.b.121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58842 + 2.75122i) q^{3} +2.85036 q^{5} +(1.33785 + 2.28258i) q^{7} +(-3.54616 + 6.14212i) q^{9} +(0.978605 - 1.69499i) q^{11} +(-2.81153 - 4.86971i) q^{13} +(4.52757 + 7.84197i) q^{15} +(0.0951900 + 0.164874i) q^{17} +(-1.31004 - 4.15738i) q^{19} +(-4.15482 + 7.30641i) q^{21} +(2.03261 - 3.52059i) q^{23} +3.12454 q^{25} -13.0006 q^{27} +(-3.37321 - 5.84257i) q^{29} +(2.76493 - 4.78900i) q^{31} +6.21774 q^{33} +(3.81335 + 6.50616i) q^{35} +(-1.08132 - 1.87290i) q^{37} +(8.93177 - 15.4703i) q^{39} +(-5.78624 + 10.0221i) q^{41} +(-1.76396 + 3.05527i) q^{43} +(-10.1078 + 17.5072i) q^{45} +(-0.322245 + 0.558144i) q^{47} +(-3.42032 + 6.10749i) q^{49} +(-0.302403 + 0.523778i) q^{51} -0.986923 q^{53} +(2.78937 - 4.83134i) q^{55} +(9.35699 - 10.2079i) q^{57} +(0.517408 + 0.896178i) q^{59} +(-6.63206 + 11.4871i) q^{61} +(-18.7641 + 0.122851i) q^{63} +(-8.01386 - 13.8804i) q^{65} +2.98339 q^{67} +12.9146 q^{69} +(-7.31183 + 12.6645i) q^{71} +(-1.60909 - 2.78703i) q^{73} +(4.96308 + 8.59630i) q^{75} +(5.17818 - 0.0339023i) q^{77} +17.3324 q^{79} +(-10.0120 - 17.3413i) q^{81} +1.00867 q^{83} +(0.271326 + 0.469950i) q^{85} +(10.7161 - 18.5609i) q^{87} +(3.33188 - 5.77099i) q^{89} +(7.35409 - 12.9325i) q^{91} +17.5675 q^{93} +(-3.73407 - 11.8500i) q^{95} +(-0.455589 + 0.789103i) q^{97} +(6.94057 + 12.0214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 12 q^{5} - 6 q^{7} - 15 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} + 3 q^{17} - 19 q^{19} + 12 q^{21} + 8 q^{23} + 16 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} - 14 q^{33} + 18 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) $ 24 * q - q^3 + 12 * q^5 - 6 * q^7 - 15 * q^9 + q^11 - 7 * q^13 - 2 * q^15 + 3 * q^17 - 19 * q^19 + 12 * q^21 + 8 * q^23 + 16 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 - 14 * q^33 + 18 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 + 11 * q^47 - 32 * q^49 + 8 * q^51 + 14 * q^53 - 11 * q^55 + 11 * q^57 - 8 * q^59 - 6 * q^61 - 37 * q^63 + 3 * q^65 + 54 * q^67 + 108 * q^69 - 13 * q^71 - 10 * q^73 + 25 * q^75 + 2 * q^77 + 28 * q^79 - 40 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 - 37 * q^89 - 39 * q^91 - 10 * q^93 + 2 * q^95 - 21 * q^97 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.58842	+	2.75122i	0.917075	+	1.58842i	0.803835	+	0.594852i	$0.202790\pi$
$3$	1.58842	+	2.75122i	0.917075	+	1.58842i	0.113240	+	0.993568i	$0.463877\pi$
$4$		0			0
$5$	2.85036			1.27472			0.637359	−	0.770567i	$-0.280027\pi$
$5$	2.85036			1.27472			0.637359	+	0.770567i	$0.280027\pi$
$6$		0			0
$7$	1.33785	+	2.28258i	0.505659	+	0.862733i
$7$	1.33785	+	2.28258i	0.505659	+	0.862733i
$8$		0			0
$9$	−3.54616	+	6.14212i	−1.18205	+	2.04737i
$10$		0			0
$11$	0.978605	−	1.69499i	0.295060	−	0.511060i	−0.679939	−	0.733269i	$-0.737994\pi$
$11$	0.978605	−	1.69499i	0.295060	−	0.511060i	0.974999	+	0.222209i	$0.0713269\pi$
$12$		0			0
$13$	−2.81153	−	4.86971i	−0.779777	−	1.35061i	−0.932070	−	0.362279i	$-0.881999\pi$
$13$	−2.81153	−	4.86971i	−0.779777	−	1.35061i	0.152292	−	0.988335i	$-0.451334\pi$
$14$		0			0
$15$	4.52757	+	7.84197i	1.16901	+	2.02479i
$16$		0			0
$17$	0.0951900	+	0.164874i	0.0230870	+	0.0399878i	0.877338	−	0.479873i	$-0.159317\pi$
$17$	0.0951900	+	0.164874i	0.0230870	+	0.0399878i	−0.854251	+	0.519861i	$0.825984\pi$
$18$		0			0
$19$	−1.31004	−	4.15738i	−0.300543	−	0.953768i
$19$	−1.31004	−	4.15738i	−0.300543	−	0.953768i
$20$		0			0
$21$	−4.15482	+	7.30641i	−0.906656	+	1.59439i
$22$		0			0
$23$	2.03261	−	3.52059i	0.423829	−	0.734093i	−0.572481	−	0.819918i	$-0.694019\pi$
$23$	2.03261	−	3.52059i	0.423829	−	0.734093i	0.996310	+	0.0858246i	$0.0273525\pi$
$24$		0			0
$25$	3.12454			0.624908
$26$		0			0
$27$	−13.0006			−2.50197
$28$		0			0
$29$	−3.37321	−	5.84257i	−0.626389	−	1.08494i	−0.988270	−	0.152714i	$-0.951199\pi$
$29$	−3.37321	−	5.84257i	−0.626389	−	1.08494i	0.361881	−	0.932224i	$-0.382135\pi$
$30$		0			0
$31$	2.76493	−	4.78900i	0.496596	−	0.860129i	−0.503396	−	0.864056i	$-0.667916\pi$
$31$	2.76493	−	4.78900i	0.496596	−	0.860129i	0.999992	+	0.00392619i	$0.00124975\pi$
$32$		0			0
$33$	6.21774			1.08237
$34$		0			0
$35$	3.81335	+	6.50616i	0.644573	+	1.09974i
$36$		0			0
$37$	−1.08132	−	1.87290i	−0.177768	−	0.307903i	0.763348	−	0.645988i	$-0.223554\pi$
$37$	−1.08132	−	1.87290i	−0.177768	−	0.307903i	−0.941116	+	0.338085i	$0.890221\pi$
$38$		0			0
$39$	8.93177	−	15.4703i	1.43023	−	2.47723i
$40$		0			0
$41$	−5.78624	+	10.0221i	−0.903659	+	1.56518i	−0.0809512	+	0.996718i	$0.525796\pi$
$41$	−5.78624	+	10.0221i	−0.903659	+	1.56518i	−0.822708	+	0.568465i	$0.807538\pi$
$42$		0			0
$43$	−1.76396	+	3.05527i	−0.269001	+	0.465924i	−0.968604	−	0.248608i	$-0.920027\pi$
$43$	−1.76396	+	3.05527i	−0.269001	+	0.465924i	0.699603	+	0.714532i	$0.253360\pi$
$44$		0			0
$45$	−10.1078	+	17.5072i	−1.50678	+	2.60983i
$46$		0			0
$47$	−0.322245	+	0.558144i	−0.0470042	+	0.0814136i	−0.888570	−	0.458741i	$-0.848301\pi$
$47$	−0.322245	+	0.558144i	−0.0470042	+	0.0814136i	0.841566	+	0.540154i	$0.181634\pi$
$48$		0			0
$49$	−3.42032	+	6.10749i	−0.488618	+	0.872498i
$50$		0			0
$51$	−0.302403	+	0.523778i	−0.0423450	+	0.0733436i
$52$		0			0
$53$	−0.986923			−0.135564			−0.0677821	−	0.997700i	$-0.521592\pi$
$53$	−0.986923			−0.135564			−0.0677821	+	0.997700i	$0.521592\pi$
$54$		0			0
$55$	2.78937	−	4.83134i	0.376119	−	0.651457i
$56$		0			0
$57$	9.35699	−	10.2079i	1.23936	−	1.35207i
$58$		0			0
$59$	0.517408	+	0.896178i	0.0673608	+	0.116672i	0.897739	−	0.440528i	$-0.145209\pi$
$59$	0.517408	+	0.896178i	0.0673608	+	0.116672i	−0.830378	+	0.557201i	$0.811875\pi$
$60$		0			0
$61$	−6.63206	+	11.4871i	−0.849148	+	1.47077i	0.0328220	+	0.999461i	$0.489551\pi$
$61$	−6.63206	+	11.4871i	−0.849148	+	1.47077i	−0.881970	+	0.471306i	$0.843783\pi$
$62$		0			0
$63$	−18.7641	+	0.122851i	−2.36405	+	0.0154778i
$64$		0			0
$65$	−8.01386	−	13.8804i	−0.993997	−	1.72165i
$66$		0			0
$67$	2.98339			0.364479			0.182240	−	0.983254i	$-0.441665\pi$
$67$	2.98339			0.364479			0.182240	+	0.983254i	$0.441665\pi$
$68$		0			0
$69$	12.9146			1.55473
$70$		0			0
$71$	−7.31183	+	12.6645i	−0.867754	+	1.50299i	−0.00346797	+	0.999994i	$0.501104\pi$
$71$	−7.31183	+	12.6645i	−0.867754	+	1.50299i	−0.864286	+	0.503000i	$0.832229\pi$
$72$		0			0
$73$	−1.60909	−	2.78703i	−0.188330	−	0.326197i	0.756364	−	0.654152i	$-0.226974\pi$
$73$	−1.60909	−	2.78703i	−0.188330	−	0.326197i	−0.944694	+	0.327954i	$0.893641\pi$
$74$		0			0
$75$	4.96308	+	8.59630i	0.573087	+	0.992616i
$76$		0			0
$77$	5.17818	−	0.0339023i	0.590108	−	0.00386352i
$78$		0			0
$79$	17.3324			1.95005			0.975024	−	0.222102i	$-0.0712916\pi$
$79$	17.3324			1.95005			0.975024	+	0.222102i	$0.0712916\pi$
$80$		0			0
$81$	−10.0120	−	17.3413i	−1.11244	−	1.92681i
$82$		0			0
$83$	1.00867			0.110716			0.0553579	−	0.998467i	$-0.482370\pi$
$83$	1.00867			0.110716			0.0553579	+	0.998467i	$0.482370\pi$
$84$		0			0
$85$	0.271326	+	0.469950i	0.0294294	+	0.0509732i
$86$		0			0
$87$	10.7161	−	18.5609i	1.14889	−	1.98994i
$88$		0			0
$89$	3.33188	−	5.77099i	0.353179	−	0.611724i	−0.633625	−	0.773640i	$-0.718434\pi$
$89$	3.33188	−	5.77099i	0.353179	−	0.611724i	0.986805	+	0.161916i	$0.0517673\pi$
$90$		0			0
$91$	7.35409	−	12.9325i	0.770918	−	1.35569i
$92$		0			0
$93$	17.5675			1.82166
$94$		0			0
$95$	−3.73407	−	11.8500i	−0.383108	−	1.21579i
$96$		0			0
$97$	−0.455589	+	0.789103i	−0.0462580	+	0.0801212i	−0.888227	−	0.459404i	$-0.848063\pi$
$97$	−0.455589	+	0.789103i	−0.0462580	+	0.0801212i	0.841969	+	0.539525i	$0.181396\pi$
$98$		0			0
$99$	6.94057	+	12.0214i	0.697554	+	1.20820i
$100$		0			0
$101$	9.24643			0.920054			0.460027	−	0.887905i	$-0.347840\pi$
$101$	9.24643			0.920054			0.460027	+	0.887905i	$0.347840\pi$
$102$		0			0
$103$	7.49973	+	12.9899i	0.738971	+	1.27993i	0.952959	+	0.303099i	$0.0980212\pi$
$103$	7.49973	+	12.9899i	0.738971	+	1.27993i	−0.213988	+	0.976836i	$0.568646\pi$
$104$		0			0
$105$	−11.8427	+	20.8259i	−1.15573	+	2.03240i
$106$		0			0
$107$	−9.23202	−	15.9903i	−0.892493	−	1.54584i	−0.836877	−	0.547391i	$-0.815621\pi$
$107$	−9.23202	−	15.9903i	−0.892493	−	1.54584i	−0.0556158	−	0.998452i	$-0.517712\pi$
$108$		0			0
$109$	−4.32098	−	7.48416i	−0.413875	−	0.716853i	0.581435	−	0.813593i	$-0.302492\pi$
$109$	−4.32098	−	7.48416i	−0.413875	−	0.716853i	−0.995310	+	0.0967406i	$0.969158\pi$
$110$		0			0
$111$	3.43518	−	5.94990i	0.326053	−	0.564740i
$112$		0			0
$113$	−1.31120			−0.123347			−0.0616736	−	0.998096i	$-0.519644\pi$
$113$	−1.31120			−0.123347			−0.0616736	+	0.998096i	$0.519644\pi$
$114$		0			0
$115$	5.79367	−	10.0349i	0.540262	−	0.935762i
$116$		0			0
$117$	39.8805			3.68695
$118$		0			0
$119$	−0.248988	+	0.437855i	−0.0228247	+	0.0401381i
$120$		0			0
$121$	3.58467	+	6.20882i	0.325879	+	0.564438i
$122$		0			0
$123$	−36.7639			−3.31489
$124$		0			0
$125$	−5.34574			−0.478137
$126$		0			0
$127$	0.666587	+	1.15456i	0.0591500	+	0.102451i	0.894084	−	0.447899i	$-0.147828\pi$
$127$	0.666587	+	1.15456i	0.0591500	+	0.102451i	−0.834934	+	0.550350i	$0.814494\pi$
$128$		0			0
$129$	−11.2076			−0.986777
$130$		0			0
$131$	−1.00818			−0.0880848			−0.0440424	−	0.999030i	$-0.514024\pi$
$131$	−1.00818			−0.0880848			−0.0440424	+	0.999030i	$0.514024\pi$
$132$		0			0
$133$	7.73691	−	8.55220i	0.670875	−	0.741570i
$134$		0			0
$135$	−37.0564			−3.18931
$136$		0			0
$137$	−7.98734			−0.682404			−0.341202	−	0.939990i	$-0.610834\pi$
$137$	−7.98734			−0.682404			−0.341202	+	0.939990i	$0.610834\pi$
$138$		0			0
$139$	−6.74538	−	11.6833i	−0.572136	−	0.990968i	−0.996346	−	0.0854044i	$-0.972782\pi$
$139$	−6.74538	−	11.6833i	−0.572136	−	0.990968i	0.424211	−	0.905563i	$-0.360552\pi$
$140$		0			0
$141$	−2.04744			−0.172425
$142$		0			0
$143$	−11.0055			−0.920326
$144$		0			0
$145$	−9.61485	−	16.6534i	−0.798470	−	1.38299i
$146$		0			0
$147$	−22.2360	+	0.291177i	−1.83399	+	0.0240158i
$148$		0			0
$149$	20.5504			1.68355			0.841776	−	0.539827i	$-0.181510\pi$
$149$	20.5504			1.68355			0.841776	+	0.539827i	$0.181510\pi$
$150$		0			0
$151$	−6.60649	+	11.4428i	−0.537629	+	0.931200i	0.461403	+	0.887191i	$0.347346\pi$
$151$	−6.60649	+	11.4428i	−0.537629	+	0.931200i	−0.999031	+	0.0440091i	$0.985987\pi$
$152$		0			0
$153$	−1.35023			−0.109160
$154$		0			0
$155$	7.88104	−	13.6504i	0.633020	−	1.09642i
$156$		0			0
$157$	9.42953	+	16.3324i	0.752559	+	1.30347i	0.946579	+	0.322472i	$0.104514\pi$
$157$	9.42953	+	16.3324i	0.752559	+	1.30347i	−0.194020	+	0.980998i	$0.562153\pi$
$158$		0			0
$159$	−1.56765	−	2.71525i	−0.124323	−	0.215333i
$160$		0			0
$161$	10.7553	−	0.0704167i	0.847639	−	0.00554961i
$162$		0			0
$163$	5.26051	+	9.11148i	0.412035	+	0.713666i	0.995112	−	0.0987511i	$-0.0314848\pi$
$163$	5.26051	+	9.11148i	0.412035	+	0.713666i	−0.583077	+	0.812417i	$0.698151\pi$
$164$		0			0
$165$	17.7228			1.37972
$166$		0			0
$167$	−9.32105	−	16.1445i	−0.721284	−	1.24930i	−0.960485	−	0.278331i	$-0.910219\pi$
$167$	−9.32105	−	16.1445i	−0.721284	−	1.24930i	0.239201	−	0.970970i	$-0.423115\pi$
$168$		0			0
$169$	−9.30937	+	16.1243i	−0.716106	+	1.24033i
$170$		0			0
$171$	30.1807	+	6.69631i	2.30798	+	0.512080i
$172$		0			0
$173$	−3.94940			−0.300267			−0.150134	−	0.988666i	$-0.547970\pi$
$173$	−3.94940			−0.300267			−0.150134	+	0.988666i	$0.547970\pi$
$174$		0			0
$175$	4.18016	+	7.13200i	0.315990	+	0.539129i
$176$		0			0
$177$	−1.64372	+	2.84701i	−0.123550	+	0.213995i
$178$		0			0
$179$	6.49357	−	11.2472i	0.485352	−	0.840654i	−0.514506	−	0.857487i	$-0.672025\pi$
$179$	6.49357	−	11.2472i	0.485352	−	0.840654i	0.999858	+	0.0168324i	$0.00535818\pi$
$180$		0			0
$181$	7.82120	+	13.5467i	0.581345	+	1.00692i	0.995320	+	0.0966310i	$0.0308067\pi$
$181$	7.82120	+	13.5467i	0.581345	+	1.00692i	−0.413975	+	0.910288i	$0.635860\pi$
$182$		0			0
$183$	−42.1380			−3.11493
$184$		0			0
$185$	−3.08215	−	5.33843i	−0.226604	−	0.392489i
$186$		0			0
$187$	0.372614			0.0272482
$188$		0			0
$189$	−17.3929	−	29.6749i	−1.26514	−	2.15853i
$190$		0			0
$191$	3.30842	+	5.73035i	0.239389	+	0.414633i	0.960539	−	0.278145i	$-0.0897197\pi$
$191$	3.30842	+	5.73035i	0.239389	+	0.414633i	−0.721150	+	0.692779i	$0.756386\pi$
$192$		0			0
$193$	−4.68500	−	8.11467i	−0.337234	−	0.584106i	0.646677	−	0.762764i	$-0.276158\pi$
$193$	−4.68500	−	8.11467i	−0.337234	−	0.584106i	−0.983911	+	0.178657i	$0.942825\pi$
$194$		0			0
$195$	25.4587	−	44.0958i	1.82314	−	3.15777i
$196$		0			0
$197$	−15.3895			−1.09646			−0.548228	−	0.836329i	$-0.684697\pi$
$197$	−15.3895			−1.09646			−0.548228	+	0.836329i	$0.684697\pi$
$198$		0			0
$199$	13.5102			0.957711			0.478856	−	0.877894i	$-0.341052\pi$
$199$	13.5102			0.957711			0.478856	+	0.877894i	$0.341052\pi$
$200$		0			0
$201$	4.73888	+	8.20798i	0.334255	+	0.578946i
$202$		0			0
$203$	8.82328	−	15.5161i	0.619273	−	1.08902i
$204$		0			0
$205$	−16.4929	+	28.5665i	−1.15191	+	1.99517i
$206$		0			0
$207$	14.4159	+	24.9691i	1.00198	+	1.73547i
$208$		0			0
$209$	−8.32874	−	1.84793i	−0.576111	−	0.127824i
$210$		0			0
$211$	5.34366	−	9.25549i	0.367873	−	0.637174i	−0.621360	−	0.783525i	$-0.713420\pi$
$211$	5.34366	−	9.25549i	0.367873	−	0.637174i	0.989233	+	0.146351i	$0.0467528\pi$
$212$		0			0
$213$	−46.4570			−3.18318
$214$		0			0
$215$	−5.02791	+	8.70860i	−0.342901	+	0.593921i
$216$		0			0
$217$	14.6303	−	0.0957867i	0.993171	−	0.00650243i
$218$		0			0
$219$	5.11183	−	8.85395i	0.345426	−	0.598295i
$220$		0			0
$221$	0.535259	−	0.927095i	0.0360054	−	0.0623632i
$222$		0			0
$223$	6.95138	−	12.0401i	0.465499	−	0.806267i	−0.533725	−	0.845658i	$-0.679208\pi$
$223$	6.95138	−	12.0401i	0.465499	−	0.806267i	0.999224	+	0.0393907i	$0.0125417\pi$
$224$		0			0
$225$	−11.0801	+	19.1913i	−0.738673	+	1.27942i
$226$		0			0
$227$	−12.8500	+	22.2568i	−0.852884	+	1.47724i	0.0257110	+	0.999669i	$0.491815\pi$
$227$	−12.8500	+	22.2568i	−0.852884	+	1.47724i	−0.878595	+	0.477568i	$0.841518\pi$
$228$		0			0
$229$	0.385216	+	0.667214i	0.0254558	+	0.0440907i	0.878473	−	0.477793i	$-0.158563\pi$
$229$	0.385216	+	0.667214i	0.0254558	+	0.0440907i	−0.853017	+	0.521883i	$0.825230\pi$
$230$		0			0
$231$	8.31840	+	14.1925i	0.547310	+	0.933797i
$232$		0			0
$233$	−19.6982			−1.29047			−0.645236	−	0.763984i	$-0.723241\pi$
$233$	−19.6982			−1.29047			−0.645236	+	0.763984i	$0.723241\pi$
$234$		0			0
$235$	−0.918512	+	1.59091i	−0.0599171	+	0.103779i
$236$		0			0
$237$	27.5311	+	47.6853i	1.78834	+	3.09749i
$238$		0			0
$239$	4.16702			0.269542			0.134771	−	0.990877i	$-0.456970\pi$
$239$	4.16702			0.269542			0.134771	+	0.990877i	$0.456970\pi$
$240$		0			0
$241$	25.5185			1.64379			0.821896	−	0.569638i	$-0.192917\pi$
$241$	25.5185			1.64379			0.821896	+	0.569638i	$0.192917\pi$
$242$		0			0
$243$	12.3055	−	21.3138i	0.789401	−	1.36728i
$244$		0			0
$245$	−9.74914	+	17.4085i	−0.622850	+	1.11219i
$246$		0			0
$247$	−16.5620	+	18.0681i	−1.05382	+	1.14964i
$248$		0			0
$249$	1.60219	+	2.77508i	0.101535	+	0.175863i
$250$		0			0
$251$	7.07385	+	12.2523i	0.446497	+	0.773356i	0.998155	−	0.0607146i	$-0.0193380\pi$
$251$	7.07385	+	12.2523i	0.446497	+	0.773356i	−0.551658	+	0.834070i	$0.686005\pi$
$252$		0			0
$253$	−3.97825	−	6.89053i	−0.250110	−	0.433204i
$254$		0			0
$255$	−0.861958	+	1.49296i	−0.0539779	+	0.0934925i
$256$		0			0
$257$	−2.61985	+	4.53771i	−0.163422	+	0.283055i	−0.936094	−	0.351751i	$-0.885586\pi$
$257$	−2.61985	+	4.53771i	−0.163422	+	0.283055i	0.772672	+	0.634806i	$0.218920\pi$
$258$		0			0
$259$	2.82840	−	4.97385i	0.175748	−	0.309060i
$260$		0			0
$261$	47.8477			2.96170
$262$		0			0
$263$	5.82127	+	10.0827i	0.358955	+	0.621729i	0.987787	−	0.155813i	$-0.0497998\pi$
$263$	5.82127	+	10.0827i	0.358955	+	0.621729i	−0.628831	+	0.777542i	$0.716466\pi$
$264$		0			0
$265$	−2.81308			−0.172806
$266$		0			0
$267$	21.1697			1.29557
$268$		0			0
$269$	−11.8538	−	20.5314i	−0.722740	−	1.25182i	−0.959898	−	0.280351i	$-0.909549\pi$
$269$	−11.8538	−	20.5314i	−0.722740	−	1.25182i	0.237158	−	0.971471i	$-0.423784\pi$
$270$		0			0
$271$	12.2584			0.744642			0.372321	−	0.928104i	$-0.378562\pi$
$271$	12.2584			0.744642			0.372321	+	0.928104i	$0.378562\pi$
$272$		0			0
$273$	47.2615	−	0.309428i	2.86040	−	0.0187274i
$274$		0			0
$275$	3.05769	−	5.29607i	0.184385	−	0.319365i
$276$		0			0
$277$	3.73156	−	6.46325i	0.224208	−	0.388339i	−0.731874	−	0.681440i	$-0.761354\pi$
$277$	3.73156	−	6.46325i	0.224208	−	0.388339i	0.956081	+	0.293101i	$0.0946873\pi$
$278$		0			0
$279$	19.6097	+	33.9651i	1.17400	+	2.03344i
$280$		0			0
$281$	−9.43708	−	16.3455i	−0.562969	−	0.975091i	−0.997235	−	0.0743066i	$-0.976326\pi$
$281$	−9.43708	−	16.3455i	−0.562969	−	0.975091i	0.434266	−	0.900785i	$-0.357008\pi$
$282$		0			0
$283$	8.07820	+	13.9919i	0.480199	+	0.831730i	0.999742	−	0.0227149i	$-0.00723101\pi$
$283$	8.07820	+	13.9919i	0.480199	+	0.831730i	−0.519543	+	0.854444i	$0.673898\pi$
$284$		0			0
$285$	26.6708	−	29.0961i	1.57984	−	1.72350i
$286$		0			0
$287$	−30.6172	+	0.200455i	−1.80728	+	0.0118325i
$288$		0			0
$289$	8.48188	−	14.6910i	0.498934	−	0.864179i
$290$		0			0
$291$	−2.89466			−0.169688
$292$		0			0
$293$	−10.8581			−0.634334			−0.317167	−	0.948370i	$-0.602732\pi$
$293$	−10.8581			−0.634334			−0.317167	+	0.948370i	$0.602732\pi$
$294$		0			0
$295$	1.47480	+	2.55443i	0.0858661	+	0.148724i
$296$		0			0
$297$	−12.7225	+	22.0360i	−0.738233	+	1.27866i
$298$		0			0
$299$	−22.8590			−1.32197
$300$		0			0
$301$	−9.33379	+	0.0611096i	−0.537991	+	0.00352230i
$302$		0			0
$303$	14.6872	+	25.4390i	0.843759	+	1.46143i
$304$		0			0
$305$	−18.9037	+	32.7422i	−1.08242	+	1.87481i
$306$		0			0
$307$	2.12730	−	3.68459i	0.121411	−	0.210291i	−0.798913	−	0.601446i	$-0.794591\pi$
$307$	2.12730	−	3.68459i	0.121411	−	0.210291i	0.920324	+	0.391156i	$0.127925\pi$
$308$		0			0
$309$	−23.8255	+	41.2669i	−1.35538	+	2.34759i
$310$		0			0
$311$	−11.2164	+	19.4275i	−0.636026	+	1.10163i	0.350270	+	0.936649i	$0.386090\pi$
$311$	−11.2164	+	19.4275i	−0.636026	+	1.10163i	−0.986297	+	0.164981i	$0.947244\pi$
$312$		0			0
$313$	−11.0380	+	19.1184i	−0.623907	+	1.08064i	0.364844	+	0.931069i	$0.381122\pi$
$313$	−11.0380	+	19.1184i	−0.623907	+	1.08064i	−0.988751	+	0.149570i	$0.952211\pi$
$314$		0			0
$315$	−53.4844	+	0.350170i	−3.01350	+	0.0197298i
$316$		0			0
$317$	5.32538	−	9.22383i	0.299103	−	0.518062i	−0.676828	−	0.736141i	$-0.736646\pi$
$317$	5.32538	−	9.22383i	0.299103	−	0.518062i	0.975931	+	0.218079i	$0.0699792\pi$
$318$		0			0
$319$	−13.2042			−0.739291
$320$		0			0
$321$	29.3286	−	50.7987i	1.63697	−	2.83531i
$322$		0			0
$323$	0.560741	−	0.611732i	0.0312005	−	0.0340377i
$324$		0			0
$325$	−8.78472	−	15.2156i	−0.487289	−	0.844009i
$326$		0			0
$327$	13.7271	−	23.7760i	0.759109	−	1.31481i
$328$		0			0
$329$	−1.70512	+	0.0111637i	−0.0940064	+	0.000615473i
$330$		0			0
$331$	0.328728	+	0.569374i	0.0180685	+	0.0312956i	0.874918	−	0.484271i	$-0.160915\pi$
$331$	0.328728	+	0.569374i	0.0180685	+	0.0312956i	−0.856850	+	0.515566i	$0.827582\pi$
$332$		0			0
$333$	15.3381			0.840523
$334$		0			0
$335$	8.50373			0.464608
$336$		0			0
$337$	9.12455	−	15.8042i	0.497046	−	0.860909i	−0.502948	−	0.864316i	$-0.667751\pi$
$337$	9.12455	−	15.8042i	0.497046	−	0.860909i	0.999994	+	0.00340783i	$0.00108475\pi$
$338$		0			0
$339$	−2.08274	−	3.60740i	−0.113119	−	0.195927i
$340$		0			0
$341$	−5.41155	−	9.37307i	−0.293052	−	0.507580i
$342$		0			0
$343$	−18.5167	+	0.363736i	−0.999807	+	0.0196399i
$344$		0			0
$345$	36.8111			1.98184
$346$		0			0
$347$	0.591098	+	1.02381i	0.0317318	+	0.0549611i	0.881455	−	0.472268i	$-0.156564\pi$
$347$	0.591098	+	1.02381i	0.0317318	+	0.0549611i	−0.849723	+	0.527229i	$0.823231\pi$
$348$		0			0
$349$	13.0348			0.697735			0.348868	−	0.937172i	$-0.386566\pi$
$349$	13.0348			0.697735			0.348868	+	0.937172i	$0.386566\pi$
$350$		0			0
$351$	36.5516	+	63.3093i	1.95098	+	3.37920i
$352$		0			0
$353$	−1.99549	+	3.45629i	−0.106209	+	0.183960i	−0.914232	−	0.405192i	$-0.867205\pi$
$353$	−1.99549	+	3.45629i	−0.106209	+	0.183960i	0.808022	+	0.589152i	$0.200538\pi$
$354$		0			0
$355$	−20.8413	+	36.0982i	−1.10614	+	1.91589i
$356$		0			0
$357$	−1.60013	+	0.0104763i	−0.0846881	+	0.000554465i
$358$		0			0
$359$	−17.3988			−0.918274			−0.459137	−	0.888365i	$-0.651841\pi$
$359$	−17.3988			−0.918274			−0.459137	+	0.888365i	$0.651841\pi$
$360$		0			0
$361$	−15.5676	+	10.8926i	−0.819348	+	0.573297i
$362$		0			0
$363$	−11.3879	+	19.7244i	−0.597710	+	1.03526i
$364$		0			0
$365$	−4.58649	−	7.94403i	−0.240068	−	0.415810i
$366$		0			0
$367$	31.9647			1.66854			0.834271	−	0.551355i	$-0.185889\pi$
$367$	31.9647			1.66854			0.834271	+	0.551355i	$0.185889\pi$
$368$		0			0
$369$	−41.0378	−	71.0796i	−2.13634	−	3.70026i
$370$		0			0
$371$	−1.32035	−	2.25273i	−0.0685493	−	0.116956i
$372$		0			0
$373$	2.07791	+	3.59905i	0.107590	+	0.186352i	0.914794	−	0.403922i	$-0.132353\pi$
$373$	2.07791	+	3.59905i	0.107590	+	0.186352i	−0.807203	+	0.590274i	$0.799020\pi$
$374$		0			0
$375$	−8.49128	−	14.7073i	−0.438488	−	0.759483i
$376$		0			0
$377$	−18.9677	+	32.8531i	−0.976889	+	1.69202i
$378$		0			0
$379$	−20.2143			−1.03834			−0.519169	−	0.854671i	$-0.673759\pi$
$379$	−20.2143			−1.03834			−0.519169	+	0.854671i	$0.673759\pi$
$380$		0			0
$381$	−2.11764	+	3.66786i	−0.108490	+	0.187910i
$382$		0			0
$383$	11.8318			0.604577			0.302288	−	0.953217i	$-0.402249\pi$
$383$	11.8318			0.604577			0.302288	+	0.953217i	$0.402249\pi$
$384$		0			0
$385$	14.7597	−	0.0966336i	0.752222	−	0.00492490i
$386$		0			0
$387$	−12.5105	−	21.6689i	−0.635947	−	1.10149i
$388$		0			0
$389$	−37.1025			−1.88117			−0.940585	−	0.339557i	$-0.889723\pi$
$389$	−37.1025			−1.88117			−0.940585	+	0.339557i	$0.889723\pi$
$390$		0			0
$391$	0.773937			0.0391397
$392$		0			0
$393$	−1.60141	−	2.77372i	−0.0807803	−	0.139916i
$394$		0			0
$395$	49.4035			2.48576
$396$		0			0
$397$	−5.71410			−0.286782			−0.143391	−	0.989666i	$-0.545801\pi$
$397$	−5.71410			−0.286782			−0.143391	+	0.989666i	$0.545801\pi$
$398$		0			0
$399$	35.8185	+	7.70148i	1.79317	+	0.385556i
$400$		0			0
$401$	−13.2768			−0.663011			−0.331505	−	0.943453i	$-0.607557\pi$
$401$	−13.2768			−0.663011			−0.331505	+	0.943453i	$0.607557\pi$
$402$		0			0
$403$	−31.0947			−1.54894
$404$		0			0
$405$	−28.5377	−	49.4288i	−1.41805	−	2.45614i
$406$		0			0
$407$	−4.23274			−0.209809
$408$		0			0
$409$	−14.9809			−0.740757			−0.370378	−	0.928881i	$-0.620772\pi$
$409$	−14.9809			−0.740757			−0.370378	+	0.928881i	$0.620772\pi$
$410$		0			0
$411$	−12.6872	−	21.9750i	−0.625816	−	1.08394i
$412$		0			0
$413$	−1.35338	+	2.37997i	−0.0665955	+	0.117111i
$414$		0			0
$415$	2.87507			0.141132
$416$		0			0
$417$	21.4290	−	37.1161i	1.04938	−	1.81758i
$418$		0			0
$419$	11.6652			0.569881			0.284940	−	0.958545i	$-0.408026\pi$
$419$	11.6652			0.569881			0.284940	+	0.958545i	$0.408026\pi$
$420$		0			0
$421$	0.0530323	−	0.0918546i	0.00258464	−	0.00447672i	−0.864730	−	0.502237i	$-0.832511\pi$
$421$	0.0530323	−	0.0918546i	0.00258464	−	0.00447672i	0.867315	+	0.497760i	$0.165844\pi$
$422$		0			0
$423$	−2.28546	−	3.95853i	−0.111123	−	0.192470i
$424$		0			0
$425$	0.297425	+	0.515155i	0.0144272	+	0.0249887i
$426$		0			0
$427$	−35.0928	+	0.229757i	−1.69826	+	0.0111187i
$428$		0			0
$429$	−17.4814	−	30.2786i	−0.844008	−	1.46186i
$430$		0			0
$431$	−5.10523			−0.245911			−0.122955	−	0.992412i	$-0.539237\pi$
$431$	−5.10523			−0.245911			−0.122955	+	0.992412i	$0.539237\pi$
$432$		0			0
$433$	−7.34596	−	12.7236i	−0.353024	−	0.611456i	0.633753	−	0.773535i	$-0.281513\pi$
$433$	−7.34596	−	12.7236i	−0.353024	−	0.611456i	−0.986778	+	0.162079i	$0.948180\pi$
$434$		0			0
$435$	30.5449	−	52.9052i	1.46451	−	2.53661i
$436$		0			0
$437$	−17.2992	−	3.83824i	−0.827533	−	0.183608i
$438$		0			0
$439$	29.2018			1.39373			0.696864	−	0.717203i	$-0.254578\pi$
$439$	29.2018			1.39373			0.696864	+	0.717203i	$0.254578\pi$
$440$		0			0
$441$	−25.3839	−	42.6662i	−1.20876	−	2.03172i
$442$		0			0
$443$	17.8779	−	30.9654i	0.849405	−	1.47121i	−0.0323360	−	0.999477i	$-0.510295\pi$
$443$	17.8779	−	30.9654i	0.849405	−	1.47121i	0.881741	−	0.471735i	$-0.156372\pi$
$444$		0			0
$445$	9.49706	−	16.4494i	0.450204	−	0.779776i
$446$		0			0
$447$	32.6426	+	56.5387i	1.54394	+	2.67419i
$448$		0			0
$449$	5.62378			0.265403			0.132701	−	0.991156i	$-0.457635\pi$
$449$	5.62378			0.265403			0.132701	+	0.991156i	$0.457635\pi$
$450$		0			0
$451$	11.3249	+	19.6153i	0.533268	+	0.923647i
$452$		0			0
$453$	−41.9755			−1.97218
$454$		0			0
$455$	20.9618	−	36.8621i	0.982704	−	1.72812i
$456$		0			0
$457$	−10.7762	−	18.6649i	−0.504090	−	0.873109i	−0.999989	−	0.00472862i	$-0.998495\pi$
$457$	−10.7762	−	18.6649i	−0.504090	−	0.873109i	0.495899	−	0.868380i	$-0.334839\pi$
$458$		0			0
$459$	−1.23753	−	2.14346i	−0.0577629	−	0.100048i
$460$		0			0
$461$	11.4084	−	19.7599i	0.531340	−	0.920309i	−0.467990	−	0.883734i	$-0.655022\pi$
$461$	11.4084	−	19.7599i	0.531340	−	0.920309i	0.999331	−	0.0365752i	$-0.0116448\pi$
$462$		0			0
$463$	3.25507			0.151276			0.0756380	−	0.997135i	$-0.475901\pi$
$463$	3.25507			0.151276			0.0756380	+	0.997135i	$0.475901\pi$
$464$		0			0
$465$	50.0736			2.32211
$466$		0			0
$467$	16.4571	+	28.5046i	0.761546	+	1.31904i	0.942054	+	0.335463i	$0.108893\pi$
$467$	16.4571	+	28.5046i	0.761546	+	1.31904i	−0.180508	+	0.983574i	$0.557774\pi$
$468$		0			0
$469$	3.99132	+	6.80982i	0.184302	+	0.314448i
$470$		0			0
$471$	−29.9561	+	51.8855i	−1.38031	+	2.39076i
$472$		0			0
$473$	3.45244	+	5.97979i	0.158743	+	0.274951i
$474$		0			0
$475$	−4.09326	−	12.9899i	−0.187812	−	0.596017i
$476$		0			0
$477$	3.49978	−	6.06180i	0.160244	−	0.277551i
$478$		0			0
$479$	16.0470			0.733207			0.366604	−	0.930377i	$-0.380520\pi$
$479$	16.0470			0.733207			0.366604	+	0.930377i	$0.380520\pi$
$480$		0			0
$481$	−6.08032	+	10.5314i	−0.277239	+	0.480191i
$482$		0			0
$483$	17.2777	+	29.4785i	0.786164	+	1.34132i
$484$		0			0
$485$	−1.29859	+	2.24922i	−0.0589660	+	0.102132i
$486$		0			0
$487$	1.02790	−	1.78038i	0.0465787	−	0.0806767i	−0.841796	−	0.539796i	$-0.818502\pi$
$487$	1.02790	−	1.78038i	0.0465787	−	0.0806767i	0.888375	+	0.459119i	$0.151835\pi$
$488$		0			0
$489$	−16.7118	+	28.9457i	−0.755734	+	1.30897i
$490$		0			0
$491$	13.7152	−	23.7554i	0.618958	−	1.07207i	−0.370718	−	0.928745i	$-0.620889\pi$
$491$	13.7152	−	23.7554i	0.618958	−	1.07207i	0.989676	−	0.143321i	$-0.0457782\pi$
$492$		0			0
$493$	0.642192	−	1.11231i	0.0289229	−	0.0500959i
$494$		0			0
$495$	19.7831	+	34.2654i	0.889185	+	1.54011i
$496$		0			0
$497$	−38.6897	+	0.253307i	−1.73547	+	0.0113624i
$498$		0			0
$499$	6.27346			0.280838			0.140419	−	0.990092i	$-0.455155\pi$
$499$	6.27346			0.280838			0.140419	+	0.990092i	$0.455155\pi$
$500$		0			0
$501$	29.6115	−	51.2886i	1.32294	−	2.29141i
$502$		0			0
$503$	−9.35263	−	16.1992i	−0.417013	−	0.722288i	0.578624	−	0.815594i	$-0.303590\pi$
$503$	−9.35263	−	16.1992i	−0.417013	−	0.722288i	−0.995637	+	0.0933063i	$0.970256\pi$
$504$		0			0
$505$	26.3556			1.17281
$506$		0			0
$507$	−59.1488			−2.62689
$508$		0			0
$509$	−15.9094	+	27.5558i	−0.705170	+	1.22139i	0.261460	+	0.965214i	$0.415796\pi$
$509$	−15.9094	+	27.5558i	−0.705170	+	1.22139i	−0.966630	+	0.256176i	$0.917537\pi$
$510$		0			0
$511$	4.20889	−	7.40151i	0.186190	−	0.327423i
$512$		0			0
$513$	17.0313	+	54.0485i	0.751950	+	2.38630i
$514$		0			0
$515$	21.3769	+	37.0259i	0.941980	+	1.63156i
$516$		0			0
$517$	0.630700	+	1.09240i	0.0277382	+	0.0480439i
$518$		0			0
$519$	−6.27330	−	10.8657i	−0.275367	−	0.476950i
$520$		0			0
$521$	−6.49298	+	11.2462i	−0.284463	+	0.492704i	−0.972479	−	0.232992i	$-0.925149\pi$
$521$	−6.49298	+	11.2462i	−0.284463	+	0.492704i	0.688016	+	0.725696i	$0.258482\pi$
$522$		0			0
$523$	−6.34661	+	10.9927i	−0.277518	+	0.480675i	−0.970767	−	0.240023i	$-0.922845\pi$
$523$	−6.34661	+	10.9927i	−0.277518	+	0.480675i	0.693249	+	0.720698i	$0.256178\pi$
$524$		0			0
$525$	−12.9819	+	22.8292i	−0.566576	+	0.996346i
$526$		0			0
$527$	1.05277			0.0458596
$528$		0			0
$529$	3.23698	+	5.60661i	0.140738	+	0.243766i
$530$		0			0
$531$	−7.33924			−0.318496
$532$		0			0
$533$	65.0727			2.81861
$534$		0			0
$535$	−26.3146	−	45.5781i	−1.13768	−	1.97051i
$536$		0			0
$537$	41.2580			1.78042
$538$		0			0
$539$	7.00500	+	11.7742i	0.301727	+	0.507152i
$540$		0			0
$541$	−0.575266	+	0.996390i	−0.0247326	+	0.0428381i	−0.878127	−	0.478428i	$-0.841207\pi$
$541$	−0.575266	+	0.996390i	−0.0247326	+	0.0428381i	0.853394	+	0.521266i	$0.174540\pi$
$542$		0			0
$543$	−24.8467	+	43.0357i	−1.06627	+	1.84684i
$544$		0			0
$545$	−12.3163	−	21.3325i	−0.527574	−	0.913785i
$546$		0			0
$547$	−15.5089	−	26.8621i	−0.663111	−	1.14854i	−0.979794	−	0.200011i	$-0.935902\pi$
$547$	−15.5089	−	26.8621i	−0.663111	−	1.14854i	0.316682	−	0.948532i	$-0.397431\pi$
$548$		0			0
$549$	−47.0366	−	81.4698i	−2.00747	−	3.47705i
$550$		0			0
$551$	−19.8708	+	21.6777i	−0.846523	+	0.923501i
$552$		0			0
$553$	23.1881	+	39.5625i	0.986059	+	1.68237i
$554$		0			0
$555$	9.79149	−	16.9594i	0.415625	−	0.719884i
$556$		0			0
$557$	6.28770			0.266418			0.133209	−	0.991088i	$-0.457472\pi$
$557$	6.28770			0.266418			0.133209	+	0.991088i	$0.457472\pi$
$558$		0			0
$559$	19.8377			0.839044
$560$		0			0
$561$	0.591867	+	1.02514i	0.0249886	+	0.0432816i
$562$		0			0
$563$	−8.24585	+	14.2822i	−0.347521	+	0.601924i	−0.985808	−	0.167874i	$-0.946310\pi$
$563$	−8.24585	+	14.2822i	−0.347521	+	0.601924i	0.638287	+	0.769798i	$0.279643\pi$
$564$		0			0
$565$	−3.73739			−0.157233
$566$		0			0
$567$	26.1883	−	46.0531i	1.09980	−	1.93405i
$568$		0			0
$569$	4.81526	+	8.34028i	0.201866	+	0.349643i	0.949130	−	0.314885i	$-0.101966\pi$
$569$	4.81526	+	8.34028i	0.201866	+	0.349643i	−0.747263	+	0.664528i	$0.768633\pi$
$570$		0			0
$571$	4.54817	−	7.87767i	0.190335	−	0.329670i	−0.755026	−	0.655695i	$-0.772376\pi$
$571$	4.54817	−	7.87767i	0.190335	−	0.329670i	0.945361	+	0.326025i	$0.105709\pi$
$572$		0			0
$573$	−10.5103	+	18.2044i	−0.439075	+	0.760500i
$574$		0			0
$575$	6.35097	−	11.0002i	0.264854	−	0.458740i
$576$		0			0
$577$	−14.3237	+	24.8094i	−0.596304	+	1.03283i	0.397057	+	0.917794i	$0.370032\pi$
$577$	−14.3237	+	24.8094i	−0.596304	+	1.03283i	−0.993361	+	0.115036i	$0.963302\pi$
$578$		0			0
$579$	14.8835	−	25.7790i	0.618538	−	1.07134i
$580$		0			0
$581$	1.34945	+	2.30237i	0.0559845	+	0.0955183i
$582$		0			0
$583$	−0.965807	+	1.67283i	−0.0399996	+	0.0692814i
$584$		0			0
$585$	113.674			4.69982
$586$		0			0
$587$	5.36250	−	9.28811i	0.221334	−	0.383361i	−0.733879	−	0.679280i	$-0.762292\pi$
$587$	5.36250	−	9.28811i	0.221334	−	0.383361i	0.955213	+	0.295918i	$0.0956256\pi$
$588$		0			0
$589$	−23.5318	−	5.22110i	−0.969613	−	0.215131i
$590$		0			0
$591$	−24.4450	−	42.3400i	−1.00553	−	1.74163i
$592$		0			0
$593$	11.5939	−	20.0813i	0.476106	−	0.824640i	−0.523519	−	0.852014i	$-0.675381\pi$
$593$	11.5939	−	20.0813i	0.476106	−	0.824640i	0.999625	+	0.0273738i	$0.00871443\pi$
$594$		0			0
$595$	−0.709704	+	1.24804i	−0.0290950	+	0.0511648i
$596$		0			0
$597$	21.4598	+	37.1695i	0.878293	+	1.52125i
$598$		0			0
$599$	44.5700			1.82108			0.910541	−	0.413419i	$-0.135666\pi$
$599$	44.5700			1.82108			0.910541	+	0.413419i	$0.135666\pi$
$600$		0			0
$601$	−39.5150			−1.61185			−0.805926	−	0.592017i	$-0.798332\pi$
$601$	−39.5150			−1.61185			−0.805926	+	0.592017i	$0.798332\pi$
$602$		0			0
$603$	−10.5796	+	18.3244i	−0.430833	+	0.746225i
$604$		0			0
$605$	10.2176	+	17.6974i	0.415404	+	0.719500i
$606$		0			0
$607$	2.29021	+	3.96676i	0.0929567	+	0.161006i	0.908754	−	0.417332i	$-0.137035\pi$
$607$	2.29021	+	3.96676i	0.0929567	+	0.161006i	−0.815797	+	0.578338i	$0.803702\pi$
$608$		0			0
$609$	56.7033	−	0.371245i	2.29773	−	0.0150436i
$610$		0			0
$611$	3.62400			0.146611
$612$		0			0
$613$	−5.84990	−	10.1323i	−0.236275	−	0.409241i	0.723367	−	0.690463i	$-0.242593\pi$
$613$	−5.84990	−	10.1323i	−0.236275	−	0.409241i	−0.959642	+	0.281223i	$0.909260\pi$
$614$		0			0
$615$	−104.790			−4.22555
$616$		0			0
$617$	−11.0865	−	19.2024i	−0.446327	−	0.773061i	0.551816	−	0.833966i	$-0.313935\pi$
$617$	−11.0865	−	19.2024i	−0.446327	−	0.773061i	−0.998144	+	0.0609042i	$0.980602\pi$
$618$		0			0
$619$	12.0994	−	20.9568i	0.486318	−	0.842327i	−0.513559	−	0.858054i	$-0.671673\pi$
$619$	12.0994	−	20.9568i	0.486318	−	0.842327i	0.999876	+	0.0157277i	$0.00500648\pi$
$620$		0			0
$621$	−26.4252	+	45.7698i	−1.06041	+	1.83668i
$622$		0			0
$623$	17.6303	−	0.115428i	0.706343	−	0.00462453i
$624$		0			0
$625$	−30.8600			−1.23440
$626$		0			0
$627$	−8.14547	−	25.8495i	−0.325299	−	1.03233i
$628$		0			0
$629$	0.205862	−	0.356563i	0.00820824	−	0.0142171i
$630$		0			0
$631$	−5.06477	−	8.77243i	−0.201625	−	0.349225i	0.747427	−	0.664344i	$-0.231289\pi$
$631$	−5.06477	−	8.77243i	−0.201625	−	0.349225i	−0.949052	+	0.315119i	$0.897956\pi$
$632$		0			0
$633$	33.9519			1.34947
$634$		0			0
$635$	1.90001	+	3.29092i	0.0753996	+	0.130596i
$636$		0			0
$637$	39.3580	−	0.515387i	1.55942	−	0.0204204i
$638$		0			0
$639$	−51.8578	−	89.8203i	−2.05146	−	3.55324i
$640$		0			0
$641$	−7.84954	−	13.5958i	−0.310038	−	0.537002i	0.668332	−	0.743863i	$-0.267008\pi$
$641$	−7.84954	−	13.5958i	−0.310038	−	0.537002i	−0.978370	+	0.206861i	$0.933675\pi$
$642$		0			0
$643$	−5.22469	+	9.04943i	−0.206042	+	0.356875i	−0.950464	−	0.310834i	$-0.899392\pi$
$643$	−5.22469	+	9.04943i	−0.206042	+	0.356875i	0.744422	+	0.667709i	$0.232725\pi$
$644$		0			0
$645$	−31.9457			−1.25786
$646$		0			0
$647$	−6.88048	+	11.9173i	−0.270499	+	0.468519i	−0.968990	−	0.247101i	$-0.920522\pi$
$647$	−6.88048	+	11.9173i	−0.270499	+	0.468519i	0.698490	+	0.715619i	$0.253856\pi$
$648$		0			0
$649$	2.02535			0.0795021
$650$		0			0
$651$	23.5026	+	40.0991i	0.921140	+	1.57161i
$652$		0			0
$653$	−15.3234	−	26.5409i	−0.599652	−	1.03863i	−0.992872	−	0.119183i	$-0.961972\pi$
$653$	−15.3234	−	26.5409i	−0.599652	−	1.03863i	0.393220	−	0.919444i	$-0.371361\pi$
$654$		0			0
$655$	−2.87366			−0.112283
$656$		0			0
$657$	22.8244			0.890464
$658$		0			0
$659$	4.36257	+	7.55619i	0.169941	+	0.294347i	0.938399	−	0.345553i	$-0.112309\pi$
$659$	4.36257	+	7.55619i	0.169941	+	0.294347i	−0.768458	+	0.639901i	$0.778975\pi$
$660$		0			0
$661$	20.3588			0.791864			0.395932	−	0.918280i	$-0.370422\pi$
$661$	20.3588			0.791864			0.395932	+	0.918280i	$0.370422\pi$
$662$		0			0
$663$	3.40086			0.132079
$664$		0			0
$665$	22.0530	−	24.3768i	0.855177	−	0.945293i
$666$		0			0
$667$	−27.4257			−1.06193
$668$		0			0
$669$	44.1668			1.70759
$670$		0			0
$671$	12.9803	+	22.4826i	0.501100	+	0.867930i
$672$		0			0
$673$	−10.4493			−0.402790			−0.201395	−	0.979510i	$-0.564547\pi$
$673$	−10.4493			−0.402790			−0.201395	+	0.979510i	$0.564547\pi$
$674$		0			0
$675$	−40.6209			−1.56350
$676$		0			0
$677$	15.3568	+	26.5988i	0.590210	+	1.02227i	0.994204	+	0.107512i	$0.0342884\pi$
$677$	15.3568	+	26.5988i	0.590210	+	1.02227i	−0.403994	+	0.914762i	$0.632378\pi$
$678$		0			0
$679$	−2.41070	+	0.0157832i	−0.0925141	+	0.000605703i
$680$		0			0
$681$	−81.6447			−3.12863
$682$		0			0
$683$	13.3390	−	23.1038i	0.510403	−	0.884044i	−0.489524	−	0.871990i	$-0.662830\pi$
$683$	13.3390	−	23.1038i	0.510403	−	0.884044i	0.999927	−	0.0120541i	$-0.00383704\pi$
$684$		0			0
$685$	−22.7668			−0.869874
$686$		0			0
$687$	−1.22377	+	2.11963i	−0.0466897	+	0.0808690i
$688$		0			0
$689$	2.77476	+	4.80603i	0.105710	+	0.183095i
$690$		0			0
$691$	−18.7601	−	32.4935i	−0.713669	−	1.23611i	−0.963471	−	0.267814i	$-0.913699\pi$
$691$	−18.7601	−	32.4935i	−0.713669	−	1.23611i	0.249802	−	0.968297i	$-0.419635\pi$
$692$		0			0
$693$	−18.1544	+	31.9252i	−0.689629	+	1.21274i
$694$		0			0
$695$	−19.2267	−	33.3017i	−0.729312	−	1.26321i
$696$		0			0
$697$	−2.20317			−0.0834510
$698$		0			0
$699$	−31.2890	−	54.1941i	−1.18346	−	2.04981i
$700$		0			0
$701$	1.01872	−	1.76447i	0.0384765	−	0.0666432i	−0.846146	−	0.532951i	$-0.821083\pi$
$701$	1.01872	−	1.76447i	0.0384765	−	0.0666432i	0.884622	+	0.466308i	$0.154416\pi$
$702$		0			0
$703$	−6.36979	+	6.94902i	−0.240241	+	0.262087i
$704$		0			0
$705$	−5.83593			−0.219794
$706$		0			0
$707$	12.3703	+	21.1057i	0.465234	+	0.793761i
$708$		0			0
$709$	8.49192	−	14.7084i	0.318921	−	0.552387i	−0.661342	−	0.750084i	$-0.730013\pi$
$709$	8.49192	−	14.7084i	0.318921	−	0.552387i	0.980263	+	0.197697i	$0.0633463\pi$
$710$		0			0
$711$	−61.4634	+	106.458i	−2.30506	+	3.99248i
$712$		0			0
$713$	−11.2401	−	19.4683i	−0.420943	−	0.729095i
$714$		0			0
$715$	−31.3696			−1.17316
$716$		0			0
$717$	6.61898	+	11.4644i	0.247190	+	0.428146i
$718$		0			0
$719$	−3.68685			−0.137496			−0.0687481	−	0.997634i	$-0.521900\pi$
$719$	−3.68685			−0.137496			−0.0687481	+	0.997634i	$0.521900\pi$
$720$		0			0
$721$	−19.6170	+	34.4973i	−0.730575	+	1.28475i
$722$		0			0
$723$	40.5341	+	70.2071i	1.50748	+	2.61103i
$724$		0			0
$725$	−10.5397	−	18.2553i	−0.391435	−	0.677986i
$726$		0			0
$727$	−5.31640	+	9.20827i	−0.197174	+	0.341516i	−0.947611	−	0.319426i	$-0.896510\pi$
$727$	−5.31640	+	9.20827i	−0.197174	+	0.341516i	0.750437	+	0.660942i	$0.229843\pi$
$728$		0			0
$729$	18.1135			0.670872
$730$		0			0
$731$	−0.671645			−0.0248417
$732$		0			0
$733$	−14.9730	−	25.9339i	−0.553039	−	0.957892i	−0.998053	−	0.0623685i	$-0.980135\pi$
$733$	−14.9730	−	25.9339i	−0.553039	−	0.957892i	0.445014	−	0.895524i	$-0.353199\pi$
$734$		0			0
$735$	−63.3805	+	0.829957i	−2.33782	+	0.0306134i
$736$		0			0
$737$	2.91956	−	5.05683i	0.107543	−	0.186271i
$738$		0			0
$739$	2.82989	+	4.90151i	0.104099	+	0.180305i	0.913370	−	0.407131i	$-0.133471\pi$
$739$	2.82989	+	4.90151i	0.104099	+	0.180305i	−0.809271	+	0.587436i	$0.800137\pi$
$740$		0			0
$741$	−76.0168	−	16.8661i	−2.79255	−	0.619593i
$742$		0			0
$743$	−7.19297	+	12.4586i	−0.263884	+	0.457061i	−0.967271	−	0.253747i	$-0.918337\pi$
$743$	−7.19297	+	12.4586i	−0.263884	+	0.457061i	0.703386	+	0.710808i	$0.251670\pi$
$744$		0			0
$745$	58.5759			2.14606
$746$		0			0
$747$	−3.57690	+	6.19537i	−0.130872	+	0.226677i
$748$		0			0
$749$	24.1481	−	42.4654i	0.882353	−	1.55165i
$750$		0			0
$751$	−8.45163	+	14.6386i	−0.308404	+	0.534172i	−0.978013	−	0.208542i	$-0.933128\pi$
$751$	−8.45163	+	14.6386i	−0.308404	+	0.534172i	0.669609	+	0.742714i	$0.266462\pi$
$752$		0			0
$753$	−22.4725	+	38.9235i	−0.818943	+	1.41845i
$754$		0			0
$755$	−18.8309	+	32.6160i	−0.685325	+	1.18702i
$756$		0			0
$757$	16.3902	−	28.3886i	0.595711	−	1.03180i	−0.397735	−	0.917500i	$-0.630204\pi$
$757$	16.3902	−	28.3886i	0.595711	−	1.03180i	0.993446	−	0.114302i	$-0.0364631\pi$
$758$		0			0
$759$	12.6383	−	21.8901i	0.458740	−	0.794560i
$760$		0			0
$761$	14.0769	+	24.3820i	0.510288	+	0.883845i	0.999929	+	0.0119211i	$0.00379468\pi$
$761$	14.0769	+	24.3820i	0.510288	+	0.883845i	−0.489641	+	0.871924i	$0.662872\pi$
$762$		0			0
$763$	11.3024	−	19.8757i	0.409173	−	0.719547i
$764$		0			0
$765$	−3.84865			−0.139148
$766$		0			0
$767$	2.90942	−	5.03926i	0.105053	−	0.181957i
$768$		0			0
$769$	4.63448	+	8.02715i	0.167123	+	0.289466i	0.937407	−	0.348235i	$-0.113219\pi$
$769$	4.63448	+	8.02715i	0.167123	+	0.289466i	−0.770284	+	0.637701i	$0.779885\pi$
$770$		0			0
$771$	−16.6457			−0.599480
$772$		0			0
$773$	−0.250331			−0.00900380			−0.00450190	−	0.999990i	$-0.501433\pi$
$773$	−0.250331			−0.00900380			−0.00450190	+	0.999990i	$0.501433\pi$
$774$		0			0
$775$	8.63913	−	14.9634i	0.310327	−	0.537501i
$776$		0			0
$777$	18.1769	−	0.119006i	0.652091	−	0.00426933i
$778$		0			0
$779$	49.2457	+	10.9263i	1.76441	+	0.391476i
$780$		0			0
$781$	14.3108	+	24.7870i	0.512080	+	0.886948i
$782$		0			0
$783$	43.8538	+	75.9571i	1.56721	+	2.71448i
$784$		0			0
$785$	26.8775	+	46.5533i	0.959300	+	1.66156i
$786$		0			0
$787$	12.9458	−	22.4227i	0.461466	−	0.799283i	−0.537568	−	0.843220i	$-0.680657\pi$
$787$	12.9458	−	22.4227i	0.461466	−	0.799283i	0.999034	+	0.0439372i	$0.0139901\pi$
$788$		0			0
$789$	−18.4933	+	32.0313i	−0.658377	+	1.14034i
$790$		0			0
$791$	−1.75419	−	2.99292i	−0.0623717	−	0.106416i
$792$		0			0
$793$	74.5848			2.64858
$794$		0			0
$795$	−4.46836	−	7.73942i	−0.158476	−	0.274489i
$796$		0			0
$797$	−40.5377			−1.43592			−0.717959	−	0.696086i	$-0.754923\pi$
$797$	−40.5377			−1.43592			−0.717959	+	0.696086i	$0.754923\pi$
$798$		0			0
$799$	−0.122698			−0.00434074
$800$		0			0
$801$	23.6308	+	40.9297i	0.834952	+	1.44618i
$802$		0			0
$803$	−6.29866			−0.222275
$804$		0			0
$805$	30.6566	−	0.200713i	1.08050	−	0.00707420i
$806$		0			0
$807$	37.6577	−	65.2250i	1.32561	−	2.29603i
$808$		0			0
$809$	3.90668	−	6.76656i	0.137351	−	0.237900i	−0.789142	−	0.614211i	$-0.789474\pi$
$809$	3.90668	−	6.76656i	0.137351	−	0.237900i	0.926493	+	0.376311i	$0.122808\pi$
$810$		0			0
$811$	14.0324	+	24.3049i	0.492745	+	0.853460i	0.999965	−	0.00835697i	$-0.00266014\pi$
$811$	14.0324	+	24.3049i	0.492745	+	0.853460i	−0.507220	+	0.861817i	$0.669327\pi$
$812$		0			0
$813$	19.4714	+	33.7255i	0.682892	+	1.18280i
$814$		0			0
$815$	14.9943	+	25.9710i	0.525229	+	0.909723i
$816$		0			0
$817$	15.0127	+	3.33093i	0.525230	+	0.116535i
$818$		0			0
$819$	53.3540	+	91.0303i	1.86434	+	3.18086i
$820$		0			0
$821$	7.96065	−	13.7883i	0.277829	−	0.481213i	−0.693016	−	0.720922i	$-0.743719\pi$
$821$	7.96065	−	13.7883i	0.277829	−	0.481213i	0.970845	+	0.239709i	$0.0770519\pi$
$822$		0			0
$823$	28.9114			1.00779			0.503894	−	0.863766i	$-0.331900\pi$
$823$	28.9114			1.00779			0.503894	+	0.863766i	$0.331900\pi$
$824$		0			0
$825$	19.4276			0.676381
$826$		0			0
$827$	−1.72201	−	2.98261i	−0.0598803	−	0.103716i	0.834531	−	0.550961i	$-0.185739\pi$
$827$	−1.72201	−	2.98261i	−0.0598803	−	0.103716i	−0.894412	+	0.447245i	$0.852405\pi$
$828$		0			0
$829$	14.6904	−	25.4446i	0.510220	−	0.883727i	−0.489710	−	0.871885i	$-0.662897\pi$
$829$	14.6904	−	25.4446i	0.510220	−	0.883727i	0.999930	−	0.0118413i	$-0.00376930\pi$
$830$		0			0
$831$	23.7091			0.822460
$832$		0			0
$833$	−1.33255	+	0.0174495i	−0.0461700	+	0.000604589i
$834$		0			0
$835$	−26.5683	−	46.0177i	−0.919435	−	1.59251i
$836$		0			0
$837$	−35.9458	+	62.2600i	−1.24247	+	2.15202i
$838$		0			0
$839$	12.5315	−	21.7052i	0.432635	−	0.749345i	−0.564465	−	0.825457i	$-0.690917\pi$
$839$	12.5315	−	21.7052i	0.432635	−	0.749345i	0.997099	+	0.0761121i	$0.0242507\pi$
$840$		0			0
$841$	−8.25709	+	14.3017i	−0.284727	+	0.493162i
$842$		0			0
$843$	29.9801	−	51.9271i	1.03257	−	1.78846i
$844$		0			0
$845$	−26.5350	+	45.9600i	−0.912833	+	1.58107i
$846$		0			0
$847$	−9.37638	+	16.4887i	−0.322176	+	0.566560i
$848$		0			0
$849$	−25.6632	+	44.4499i	−0.880757	+	1.52552i
$850$		0			0
$851$	−8.79161			−0.301372
$852$		0			0
$853$	−23.2723	+	40.3088i	−0.796829	+	1.38015i	0.124843	+	0.992177i	$0.460157\pi$
$853$	−23.2723	+	40.3088i	−0.796829	+	1.38015i	−0.921671	+	0.387971i	$0.873176\pi$
$854$		0			0
$855$	86.0259	+	19.0869i	2.94202	+	0.652757i
$856$		0			0
$857$	0.765982	+	1.32672i	0.0261655	+	0.0453199i	0.878812	−	0.477169i	$-0.158337\pi$
$857$	0.765982	+	1.32672i	0.0261655	+	0.0453199i	−0.852646	+	0.522489i	$0.825004\pi$
$858$		0			0
$859$	−9.23183	+	15.9900i	−0.314986	+	0.545572i	−0.979435	−	0.201762i	$-0.935333\pi$
$859$	−9.23183	+	15.9900i	−0.314986	+	0.545572i	0.664449	+	0.747334i	$0.268666\pi$
$860$		0			0
$861$	−49.1845	−	83.9165i	−1.67620	−	2.85987i
$862$		0			0
$863$	5.23845	+	9.07326i	0.178319	+	0.308857i	0.941305	−	0.337558i	$-0.109601\pi$
$863$	5.23845	+	9.07326i	0.178319	+	0.308857i	−0.762986	+	0.646415i	$0.776267\pi$
$864$		0			0
$865$	−11.2572			−0.382756
$866$		0			0
$867$	53.8911			1.83024
$868$		0			0
$869$	16.9616	−	29.3783i	0.575382	−	0.996590i
$870$		0			0
$871$	−8.38788	−	14.5282i	−0.284213	−	0.492271i
$872$		0			0
$873$	−3.23118	−	5.59656i	−0.109359	−	0.189415i
$874$		0			0
$875$	−7.15179	−	12.2021i	−0.241774	−	0.412505i
$876$		0			0
$877$	27.2642			0.920648			0.460324	−	0.887751i	$-0.347733\pi$
$877$	27.2642			0.920648			0.460324	+	0.887751i	$0.347733\pi$
$878$		0			0
$879$	−17.2471	−	29.8729i	−0.581732	−	1.00759i
$880$		0			0
$881$	−23.2319			−0.782703			−0.391351	−	0.920241i	$-0.627992\pi$
$881$	−23.2319			−0.782703			−0.391351	+	0.920241i	$0.627992\pi$
$882$		0			0
$883$	0.118706	+	0.205604i	0.00399476	+	0.00691912i	0.868016	−	0.496536i	$-0.165395\pi$
$883$	0.118706	+	0.205604i	0.00399476	+	0.00691912i	−0.864021	+	0.503456i	$0.832062\pi$
$884$		0			0
$885$	−4.68520	+	8.11500i	−0.157491	+	0.272783i
$886$		0			0
$887$	−1.22614	+	2.12374i	−0.0411699	+	0.0713083i	−0.885876	−	0.463922i	$-0.846442\pi$
$887$	−1.22614	+	2.12374i	−0.0411699	+	0.0713083i	0.844706	+	0.535230i	$0.179775\pi$
$888$		0			0
$889$	−1.74359	+	3.06617i	−0.0584780	+	0.102836i
$890$		0			0
$891$	−39.1911			−1.31295
$892$		0			0
$893$	2.74257	+	0.608504i	0.0917765	+	0.0203628i
$894$		0			0
$895$	18.5090	−	32.0585i	0.618687	−	1.07160i
$896$		0			0
$897$	−36.3097	−	62.8902i	−1.21234	−	2.09984i
$898$		0			0
$899$	−37.3067			−1.24425
$900$		0			0
$901$	−0.0939452	−	0.162718i	−0.00312977	−	0.00542092i
$902$		0			0
$903$	−14.9941	−	25.5823i	−0.498973	−	0.851325i
$904$		0			0
$905$	22.2932	+	38.6130i	0.741051	+	1.28354i
$906$		0			0
$907$	15.9116	+	27.5597i	0.528337	+	0.915106i	0.999454	+	0.0330355i	$0.0105174\pi$
$907$	15.9116	+	27.5597i	0.528337	+	0.915106i	−0.471118	+	0.882070i	$0.656149\pi$
$908$		0			0
$909$	−32.7893	+	56.7927i	−1.08755	+	1.88370i
$910$		0			0
$911$	6.75206			0.223706			0.111853	−	0.993725i	$-0.464321\pi$
$911$	6.75206			0.223706			0.111853	+	0.993725i	$0.464321\pi$
$912$		0			0
$913$	0.987089	−	1.70969i	0.0326679	−	0.0565824i
$914$		0			0
$915$	−120.108			−3.97066
$916$		0			0
$917$	−1.34879	−	2.30124i	−0.0445409	−	0.0759937i
$918$		0			0
$919$	11.6395	+	20.1602i	0.383951	+	0.665022i	0.991623	−	0.129166i	$-0.0412299\pi$
$919$	11.6395	+	20.1602i	0.383951	+	0.665022i	−0.607672	+	0.794188i	$0.707897\pi$
$920$		0			0
$921$	13.5162			0.445373
$922$		0			0
$923$	82.2296			2.70662
$924$		0			0
$925$	−3.37862	−	5.85195i	−0.111088	−	0.192411i
$926$		0			0
$927$	−106.381			−3.49401
$928$		0			0
$929$	20.6470			0.677406			0.338703	−	0.940893i	$-0.390012\pi$
$929$	20.6470			0.677406			0.338703	+	0.940893i	$0.390012\pi$
$930$		0			0
$931$	29.8719	+	6.21855i	0.979012	+	0.203805i
$932$		0			0
$933$	−71.2657			−2.33313
$934$		0			0
$935$	1.06208			0.0347338
$936$		0			0
$937$	29.9229	+	51.8280i	0.977538	+	1.69315i	0.671291	+	0.741193i	$0.265740\pi$
$937$	29.9229	+	51.8280i	0.977538	+	1.69315i	0.306247	+	0.951952i	$0.400927\pi$
$938$		0			0
$939$	−70.1322			−2.28868
$940$		0			0
$941$	40.1284			1.30815			0.654074	−	0.756431i	$-0.273059\pi$
$941$	40.1284			1.30815			0.654074	+	0.756431i	$0.273059\pi$
$942$		0			0
$943$	23.5224	+	40.7419i	0.765993	+	1.32674i
$944$		0			0
$945$	−49.5759	−	84.5842i	−1.61270	−	2.75152i
$946$		0			0
$947$	5.12447			0.166523			0.0832614	−	0.996528i	$-0.473466\pi$
$947$	5.12447			0.166523			0.0832614	+	0.996528i	$0.473466\pi$
$948$		0			0
$949$	−9.04802	+	15.6716i	−0.293711	+	0.508723i
$950$		0			0
$951$	33.8358			1.09720
$952$		0			0
$953$	9.36697	−	16.2241i	0.303426	−	0.525549i	−0.673484	−	0.739202i	$-0.735203\pi$
$953$	9.36697	−	16.2241i	0.303426	−	0.525549i	0.976910	+	0.213653i	$0.0685361\pi$
$954$		0			0
$955$	9.43017	+	16.3335i	0.305153	+	0.528541i
$956$		0			0
$957$	−20.9737	−	36.3276i	−0.677985	−	1.17430i
$958$		0			0
$959$	−10.6858	−	18.2317i	−0.345064	−	0.588733i
$960$		0			0
$961$	0.210332	+	0.364305i	0.00678490	+	0.0117518i
$962$		0			0
$963$	130.953			4.21989
$964$		0			0
$965$	−13.3539	−	23.1297i	−0.429878	−	0.744571i
$966$		0			0
$967$	−26.0944	+	45.1968i	−0.839139	+	1.45343i	0.0514757	+	0.998674i	$0.483608\pi$
$967$	−26.0944	+	45.1968i	−0.839139	+	1.45343i	−0.890615	+	0.454758i	$0.849726\pi$
$968$		0			0
$969$	2.57370	+	0.571037i	0.0826793	+	0.0183444i
$970$		0			0
$971$	3.37028			0.108157			0.0540787	−	0.998537i	$-0.482778\pi$
$971$	3.37028			0.108157			0.0540787	+	0.998537i	$0.482778\pi$
$972$		0			0
$973$	17.6438	−	31.0274i	0.565635	−	0.994692i
$974$		0			0
$975$	27.9077	−	48.3375i	0.893761	−	1.54804i
$976$		0			0
$977$	−24.6157	+	42.6356i	−0.787525	+	1.36403i	0.139954	+	0.990158i	$0.455305\pi$
$977$	−24.6157	+	42.6356i	−0.787525	+	1.36403i	−0.927479	+	0.373876i	$0.878029\pi$
$978$		0			0
$979$	−6.52120	−	11.2950i	−0.208418	−	0.360991i
$980$		0			0
$981$	61.2915			1.95689
$982$		0			0
$983$	6.01639	+	10.4207i	0.191893	+	0.332369i	0.945878	−	0.324524i	$-0.105204\pi$
$983$	6.01639	+	10.4207i	0.191893	+	0.332369i	−0.753984	+	0.656892i	$0.771871\pi$
$984$		0			0
$985$	−43.8656			−1.39767
$986$		0			0
$987$	−2.73916	−	4.67344i	−0.0871885	−	0.148757i
$988$		0			0
$989$	7.17088	+	12.4203i	0.228021	+	0.394944i
$990$		0			0
$991$	−6.59156	−	11.4169i	−0.209388	−	0.362670i	0.742134	−	0.670252i	$-0.233814\pi$
$991$	−6.59156	−	11.4169i	−0.209388	−	0.362670i	−0.951522	+	0.307581i	$0.900480\pi$
$992$		0			0
$993$	−1.04432	+	1.80881i	−0.0331404	+	0.0574008i
$994$		0			0
$995$	38.5088			1.22081
$996$		0			0
$997$	27.5313			0.871924			0.435962	−	0.899965i	$-0.356408\pi$
$997$	27.5313			0.871924			0.435962	+	0.899965i	$0.356408\pi$
$998$		0			0
$999$	14.0578	+	24.3489i	0.444770	+	0.770364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.k.b.277.12	yes	24
7.2	even	3		532.2.l.b.429.1	yes	24
19.7	even	3		532.2.l.b.501.1	yes	24
133.121	even	3	inner	532.2.k.b.121.12	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.k.b.121.12	✓	24	133.121	even	3	inner
532.2.k.b.277.12	yes	24	1.1	even	1	trivial
532.2.l.b.429.1	yes	24	7.2	even	3
532.2.l.b.501.1	yes	24	19.7	even	3

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:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58842 + 2.75122i) q^{3} +2.85036 q^{5} +(1.33785 + 2.28258i) q^{7} +(-3.54616 + 6.14212i) q^{9} +(0.978605 - 1.69499i) q^{11} +(-2.81153 - 4.86971i) q^{13} +(4.52757 + 7.84197i) q^{15} +(0.0951900 + 0.164874i) q^{17} +(-1.31004 - 4.15738i) q^{19} +(-4.15482 + 7.30641i) q^{21} +(2.03261 - 3.52059i) q^{23} +3.12454 q^{25} -13.0006 q^{27} +(-3.37321 - 5.84257i) q^{29} +(2.76493 - 4.78900i) q^{31} +6.21774 q^{33} +(3.81335 + 6.50616i) q^{35} +(-1.08132 - 1.87290i) q^{37} +(8.93177 - 15.4703i) q^{39} +(-5.78624 + 10.0221i) q^{41} +(-1.76396 + 3.05527i) q^{43} +(-10.1078 + 17.5072i) q^{45} +(-0.322245 + 0.558144i) q^{47} +(-3.42032 + 6.10749i) q^{49} +(-0.302403 + 0.523778i) q^{51} -0.986923 q^{53} +(2.78937 - 4.83134i) q^{55} +(9.35699 - 10.2079i) q^{57} +(0.517408 + 0.896178i) q^{59} +(-6.63206 + 11.4871i) q^{61} +(-18.7641 + 0.122851i) q^{63} +(-8.01386 - 13.8804i) q^{65} +2.98339 q^{67} +12.9146 q^{69} +(-7.31183 + 12.6645i) q^{71} +(-1.60909 - 2.78703i) q^{73} +(4.96308 + 8.59630i) q^{75} +(5.17818 - 0.0339023i) q^{77} +17.3324 q^{79} +(-10.0120 - 17.3413i) q^{81} +1.00867 q^{83} +(0.271326 + 0.469950i) q^{85} +(10.7161 - 18.5609i) q^{87} +(3.33188 - 5.77099i) q^{89} +(7.35409 - 12.9325i) q^{91} +17.5675 q^{93} +(-3.73407 - 11.8500i) q^{95} +(-0.455589 + 0.789103i) q^{97} +(6.94057 + 12.0214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 12 q^{5} - 6 q^{7} - 15 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} + 3 q^{17} - 19 q^{19} + 12 q^{21} + 8 q^{23} + 16 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} - 14 q^{33} + 18 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) \) 24 * q - q^3 + 12 * q^5 - 6 * q^7 - 15 * q^9 + q^11 - 7 * q^13 - 2 * q^15 + 3 * q^17 - 19 * q^19 + 12 * q^21 + 8 * q^23 + 16 * q^25 + 20 * q^27 - 22 * q^29 - 7 * q^31 - 14 * q^33 + 18 * q^35 + 9 * q^37 + 12 * q^39 - 11 * q^41 - 9 * q^43 - 28 * q^45 + 11 * q^47 - 32 * q^49 + 8 * q^51 + 14 * q^53 - 11 * q^55 + 11 * q^57 - 8 * q^59 - 6 * q^61 - 37 * q^63 + 3 * q^65 + 54 * q^67 + 108 * q^69 - 13 * q^71 - 10 * q^73 + 25 * q^75 + 2 * q^77 + 28 * q^79 - 40 * q^81 - 12 * q^83 - 19 * q^85 + 19 * q^87 - 37 * q^89 - 39 * q^91 - 10 * q^93 + 2 * q^95 - 21 * q^97 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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