LMFDB - Embedded newform 513.2.g.c.505.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(64,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-1,0,-17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.12
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.803309 + 1.39137i) q^{2} +(-0.290611 + 0.503353i) q^{4} -3.75880 q^{5} +(2.27973 - 3.94861i) q^{7} +2.27943 q^{8} +(-3.01948 - 5.22989i) q^{10} +(1.29616 - 2.24501i) q^{11} +(0.268857 - 0.465674i) q^{13} +7.32531 q^{14} +(2.41231 + 4.17825i) q^{16} +(1.73001 - 2.99646i) q^{17} +(-4.01417 - 1.69894i) q^{19} +(1.09235 - 1.89200i) q^{20} +4.16486 q^{22} +(-0.104462 + 0.180933i) q^{23} +9.12855 q^{25} +0.863901 q^{26} +(1.32503 + 2.29502i) q^{28} +0.853801 q^{29} +(3.83524 + 6.64283i) q^{31} +(-1.59623 + 2.76475i) q^{32} +5.55892 q^{34} +(-8.56903 + 14.8420i) q^{35} +4.41513 q^{37} +(-0.860764 - 6.94999i) q^{38} -8.56793 q^{40} -0.939316 q^{41} +(-1.99417 - 3.45401i) q^{43} +(0.753355 + 1.30485i) q^{44} -0.335660 q^{46} +3.14090 q^{47} +(-6.89432 - 11.9413i) q^{49} +(7.33305 + 12.7012i) q^{50} +(0.156266 + 0.270660i) q^{52} +(-5.68786 - 9.85167i) q^{53} +(-4.87199 + 8.43853i) q^{55} +(5.19649 - 9.00059i) q^{56} +(0.685866 + 1.18796i) q^{58} -2.40432 q^{59} -7.18979 q^{61} +(-6.16176 + 10.6725i) q^{62} +4.52018 q^{64} +(-1.01058 + 1.75037i) q^{65} +(-0.140263 + 0.242942i) q^{67} +(1.00552 + 1.74161i) q^{68} -27.5343 q^{70} +(-3.43003 + 5.94099i) q^{71} +(-0.416690 + 0.721728i) q^{73} +(3.54671 + 6.14309i) q^{74} +(2.02173 - 1.52682i) q^{76} +(-5.90977 - 10.2360i) q^{77} +(5.91744 + 10.2493i) q^{79} +(-9.06739 - 15.7052i) q^{80} +(-0.754561 - 1.30694i) q^{82} +(-3.63125 + 6.28951i) q^{83} +(-6.50274 + 11.2631i) q^{85} +(3.20387 - 5.54927i) q^{86} +(2.95450 - 5.11735i) q^{88} +(3.20392 + 5.54936i) q^{89} +(-1.22584 - 2.12322i) q^{91} +(-0.0607154 - 0.105162i) q^{92} +(2.52311 + 4.37015i) q^{94} +(15.0885 + 6.38597i) q^{95} +(3.18119 + 5.50998i) q^{97} +(11.0765 - 19.1851i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.803309	+	1.39137i	0.568025	+	0.983849i	0.996761	+	0.0804188i	$0.0256258\pi$
$2$	0.803309	+	1.39137i	0.568025	+	0.983849i	−0.428736	+	0.903430i	$0.641041\pi$
$3$		0			0
$3$		0			0
$4$	−0.290611	+	0.503353i	−0.145306	+	0.251677i
$5$	−3.75880			−1.68098			−0.840492	−	0.541823i	$-0.817734\pi$
$5$	−3.75880			−1.68098			−0.840492	+	0.541823i	$0.817734\pi$
$6$		0			0
$7$	2.27973	−	3.94861i	0.861656	−	1.49243i	−0.00867312	−	0.999962i	$-0.502761\pi$
$7$	2.27973	−	3.94861i	0.861656	−	1.49243i	0.870329	−	0.492470i	$-0.163906\pi$
$8$	2.27943			0.805902
$9$		0			0
$10$	−3.01948	−	5.22989i	−0.954842	−	1.65383i
$11$	1.29616	−	2.24501i	0.390806	−	0.676896i	−0.601750	−	0.798684i	$-0.705530\pi$
$11$	1.29616	−	2.24501i	0.390806	−	0.676896i	0.992556	+	0.121789i	$0.0388630\pi$
$12$		0			0
$13$	0.268857	−	0.465674i	0.0745675	−	0.129155i	−0.826331	−	0.563185i	$-0.809576\pi$
$13$	0.268857	−	0.465674i	0.0745675	−	0.129155i	0.900898	+	0.434031i	$0.142909\pi$
$14$	7.32531			1.95777
$15$		0			0
$16$	2.41231	+	4.17825i	0.603078	+	1.04456i
$17$	1.73001	−	2.99646i	0.419588	−	0.726748i	−0.576310	−	0.817231i	$-0.695508\pi$
$17$	1.73001	−	2.99646i	0.419588	−	0.726748i	0.995898	+	0.0904832i	$0.0288411\pi$
$18$		0			0
$19$	−4.01417	−	1.69894i	−0.920915	−	0.389764i
$19$	−4.01417	−	1.69894i	−0.920915	−	0.389764i
$20$	1.09235	−	1.89200i	0.244256	−	0.423065i
$21$		0			0
$22$	4.16486			0.887951
$23$	−0.104462	+	0.180933i	−0.0217818	+	0.0377271i	−0.876711	−	0.481018i	$-0.840267\pi$
$23$	−0.104462	+	0.180933i	−0.0217818	+	0.0377271i	0.854929	+	0.518745i	$0.173601\pi$
$24$		0			0
$25$	9.12855			1.82571
$26$	0.863901			0.169425
$27$		0			0
$28$	1.32503	+	2.29502i	0.250407	+	0.433717i
$29$	0.853801			0.158547			0.0792735	−	0.996853i	$-0.474740\pi$
$29$	0.853801			0.158547			0.0792735	+	0.996853i	$0.474740\pi$
$30$		0			0
$31$	3.83524	+	6.64283i	0.688829	+	1.19309i	0.972217	+	0.234082i	$0.0752084\pi$
$31$	3.83524	+	6.64283i	0.688829	+	1.19309i	−0.283388	+	0.959005i	$0.591458\pi$
$32$	−1.59623	+	2.76475i	−0.282176	+	0.488744i
$33$		0			0
$34$	5.55892			0.953347
$35$	−8.56903	+	14.8420i	−1.44843	+	2.50876i
$36$		0			0
$37$	4.41513			0.725843			0.362921	−	0.931820i	$-0.381779\pi$
$37$	4.41513			0.725843			0.362921	+	0.931820i	$0.381779\pi$
$38$	−0.860764	−	6.94999i	−0.139634	−	1.12744i
$39$		0			0
$40$	−8.56793			−1.35471
$41$	−0.939316			−0.146697			−0.0733483	−	0.997306i	$-0.523368\pi$
$41$	−0.939316			−0.146697			−0.0733483	+	0.997306i	$0.523368\pi$
$42$		0			0
$43$	−1.99417	−	3.45401i	−0.304108	−	0.526731i	0.672954	−	0.739684i	$-0.265025\pi$
$43$	−1.99417	−	3.45401i	−0.304108	−	0.526731i	−0.977062	+	0.212953i	$0.931692\pi$
$44$	0.753355	+	1.30485i	0.113573	+	0.196713i
$45$		0			0
$46$	−0.335660			−0.0494904
$47$	3.14090			0.458147			0.229073	−	0.973409i	$-0.426430\pi$
$47$	3.14090			0.458147			0.229073	+	0.973409i	$0.426430\pi$
$48$		0			0
$49$	−6.89432	−	11.9413i	−0.984903	−	1.70590i
$50$	7.33305	+	12.7012i	1.03705	+	1.79622i
$51$		0			0
$52$	0.156266	+	0.270660i	0.0216701	+	0.0375338i
$53$	−5.68786	−	9.85167i	−0.781288	−	1.35323i	−0.931192	−	0.364530i	$-0.881230\pi$
$53$	−5.68786	−	9.85167i	−0.781288	−	1.35323i	0.149903	−	0.988701i	$-0.452104\pi$
$54$		0			0
$55$	−4.87199	+	8.43853i	−0.656939	+	1.13785i
$56$	5.19649	−	9.00059i	0.694410	−	1.20275i
$57$		0			0
$58$	0.685866	+	1.18796i	0.0900587	+	0.155986i
$59$	−2.40432			−0.313016			−0.156508	−	0.987677i	$-0.550024\pi$
$59$	−2.40432			−0.313016			−0.156508	+	0.987677i	$0.550024\pi$
$60$		0			0
$61$	−7.18979			−0.920558			−0.460279	−	0.887774i	$-0.652251\pi$
$61$	−7.18979			−0.920558			−0.460279	+	0.887774i	$0.652251\pi$
$62$	−6.16176	+	10.6725i	−0.782545	+	1.35541i
$63$		0			0
$64$	4.52018			0.565023
$65$	−1.01058	+	1.75037i	−0.125347	+	0.217107i
$66$		0			0
$67$	−0.140263	+	0.242942i	−0.0171358	+	0.0296801i	−0.874466	−	0.485087i	$-0.838788\pi$
$67$	−0.140263	+	0.242942i	−0.0171358	+	0.0296801i	0.857330	+	0.514767i	$0.172121\pi$
$68$	1.00552	+	1.74161i	0.121937	+	0.211201i
$69$		0			0
$70$	−27.5343			−3.29098
$71$	−3.43003	+	5.94099i	−0.407070	+	0.705066i	−0.994560	−	0.104165i	$-0.966783\pi$
$71$	−3.43003	+	5.94099i	−0.407070	+	0.705066i	0.587490	+	0.809231i	$0.300116\pi$
$72$		0			0
$73$	−0.416690	+	0.721728i	−0.0487698	+	0.0844718i	−0.889380	−	0.457169i	$-0.848863\pi$
$73$	−0.416690	+	0.721728i	−0.0487698	+	0.0844718i	0.840610	+	0.541641i	$0.182197\pi$
$74$	3.54671	+	6.14309i	0.412297	+	0.714120i
$75$		0			0
$76$	2.02173	−	1.52682i	0.231908	−	0.175138i
$77$	−5.90977	−	10.2360i	−0.673481	−	1.16650i
$78$		0			0
$79$	5.91744	+	10.2493i	0.665764	+	1.15314i	0.979077	+	0.203488i	$0.0652278\pi$
$79$	5.91744	+	10.2493i	0.665764	+	1.15314i	−0.313313	+	0.949650i	$0.601439\pi$
$80$	−9.06739	−	15.7052i	−1.01377	−	1.75589i
$81$		0			0
$82$	−0.754561	−	1.30694i	−0.0833273	−	0.144327i
$83$	−3.63125	+	6.28951i	−0.398582	+	0.690364i	−0.993551	−	0.113385i	$-0.963831\pi$
$83$	−3.63125	+	6.28951i	−0.398582	+	0.690364i	0.594970	+	0.803748i	$0.297164\pi$
$84$		0			0
$85$	−6.50274	+	11.2631i	−0.705322	+	1.22165i
$86$	3.20387	−	5.54927i	0.345483	−	0.598393i
$87$		0			0
$88$	2.95450	−	5.11735i	0.314951	−	0.545512i
$89$	3.20392	+	5.54936i	0.339615	+	0.588231i	0.984360	−	0.176167i	$-0.0563698\pi$
$89$	3.20392	+	5.54936i	0.339615	+	0.588231i	−0.644745	+	0.764398i	$0.723037\pi$
$90$		0			0
$91$	−1.22584	−	2.12322i	−0.128503	−	0.222574i
$92$	−0.0607154	−	0.105162i	−0.00633002	−	0.0109639i
$93$		0			0
$94$	2.52311	+	4.37015i	0.260239	+	0.450747i
$95$	15.0885	+	6.38597i	1.54804	+	0.655187i
$96$		0			0
$97$	3.18119	+	5.50998i	0.323001	+	0.559453i	0.981106	−	0.193473i	$-0.0619751\pi$
$97$	3.18119	+	5.50998i	0.323001	+	0.559453i	−0.658105	+	0.752926i	$0.728642\pi$
$98$	11.0765	−	19.1851i	1.11890	−	1.93799i
$99$		0			0
$100$	−2.65286	+	4.59489i	−0.265286	+	0.459489i
$101$	2.31014			0.229868			0.114934	−	0.993373i	$-0.463334\pi$
$101$	2.31014			0.229868			0.114934	+	0.993373i	$0.463334\pi$
$102$		0			0
$103$	−3.73572	−	6.47046i	−0.368092	−	0.637554i	0.621175	−	0.783672i	$-0.286655\pi$
$103$	−3.73572	−	6.47046i	−0.368092	−	0.637554i	−0.989267	+	0.146118i	$0.953322\pi$
$104$	0.612842	−	1.06147i	0.0600941	−	0.104086i
$105$		0			0
$106$	9.13823	−	15.8279i	0.887583	−	1.53734i
$107$	8.56202			0.827722			0.413861	−	0.910340i	$-0.364180\pi$
$107$	8.56202			0.827722			0.413861	+	0.910340i	$0.364180\pi$
$108$		0			0
$109$	5.16271	−	8.94207i	0.494498	−	0.856495i	−0.505482	−	0.862837i	$-0.668685\pi$
$109$	5.16271	−	8.94207i	0.494498	−	0.856495i	0.999980	+	0.00634184i	$0.00201868\pi$
$110$	−15.6549			−1.49263
$111$		0			0
$112$	21.9977			2.07858
$113$	7.77287	+	13.4630i	0.731210	+	1.26649i	0.956366	+	0.292170i	$0.0943774\pi$
$113$	7.77287	+	13.4630i	0.731210	+	1.26649i	−0.225156	+	0.974323i	$0.572289\pi$
$114$		0			0
$115$	0.392650	−	0.680090i	0.0366148	−	0.0634187i
$116$	−0.248124	+	0.429764i	−0.0230377	+	0.0399026i
$117$		0			0
$118$	−1.93141	−	3.34531i	−0.177801	−	0.307960i
$119$	−7.88789	−	13.6622i	−0.723082	−	1.25241i
$120$		0			0
$121$	2.13996	+	3.70651i	0.194541	+	0.336956i
$122$	−5.77562	−	10.0037i	−0.522900	−	0.905690i
$123$		0			0
$124$	−4.45825			−0.400363
$125$	−15.5184			−1.38801
$126$		0			0
$127$	6.30706	+	10.9241i	0.559661	+	0.969361i	0.997525	+	0.0703197i	$0.0224020\pi$
$127$	6.30706	+	10.9241i	0.559661	+	0.969361i	−0.437864	+	0.899041i	$0.644265\pi$
$128$	6.82357	+	11.8188i	0.603124	+	1.04464i
$129$		0			0
$130$	−3.24723			−0.284801
$131$	−19.7774			−1.72796			−0.863980	−	0.503526i	$-0.832036\pi$
$131$	−19.7774			−1.72796			−0.863980	+	0.503526i	$0.832036\pi$
$132$		0			0
$133$	−15.8597	+	11.9773i	−1.37521	+	1.03856i
$134$	−0.450697			−0.0389343
$135$		0			0
$136$	3.94344	−	6.83023i	0.338147	−	0.585688i
$137$	−11.7148			−1.00086			−0.500430	−	0.865777i	$-0.666825\pi$
$137$	−11.7148			−1.00086			−0.500430	+	0.865777i	$0.666825\pi$
$138$		0			0
$139$	−8.92017	+	15.4502i	−0.756599	+	1.31047i	0.187976	+	0.982174i	$0.439807\pi$
$139$	−8.92017	+	15.4502i	−0.756599	+	1.31047i	−0.944575	+	0.328294i	$0.893526\pi$
$140$	−4.98051	−	8.62650i	−0.420930	−	0.729072i
$141$		0			0
$142$	−11.0215			−0.924904
$143$	−0.696961	−	1.20717i	−0.0582828	−	0.100949i
$144$		0			0
$145$	−3.20927			−0.266515
$146$	−1.33892			−0.110810
$147$		0			0
$148$	−1.28309	+	2.22237i	−0.105469	+	0.182678i
$149$	16.1092			1.31972			0.659859	−	0.751389i	$-0.270616\pi$
$149$	16.1092			1.31972			0.659859	+	0.751389i	$0.270616\pi$
$150$		0			0
$151$	−0.821225	+	1.42240i	−0.0668303	+	0.115754i	−0.897504	−	0.441005i	$-0.854622\pi$
$151$	−0.821225	+	1.42240i	−0.0668303	+	0.115754i	0.830674	+	0.556759i	$0.187955\pi$
$152$	−9.15005	−	3.87262i	−0.742167	−	0.314111i
$153$		0			0
$154$	9.49474	−	16.4454i	0.765108	−	1.32521i
$155$	−14.4159	−	24.9690i	−1.15791	−	2.00556i
$156$		0			0
$157$	10.6210			0.847648			0.423824	−	0.905745i	$-0.360688\pi$
$157$	10.6210			0.847648			0.423824	+	0.905745i	$0.360688\pi$
$158$	−9.50707	+	16.4667i	−0.756342	+	1.31002i
$159$		0			0
$160$	5.99991	−	10.3921i	0.474334	−	0.821571i
$161$	0.476288	+	0.824956i	0.0375368	+	0.0650156i
$162$		0			0
$163$	−22.0892			−1.73016			−0.865080	−	0.501634i	$-0.832732\pi$
$163$	−22.0892			−1.73016			−0.865080	+	0.501634i	$0.832732\pi$
$164$	0.272976	−	0.472808i	0.0213158	−	0.0369201i
$165$		0			0
$166$	−11.6681			−0.905618
$167$	6.54741	−	11.3404i	0.506654	−	0.877550i	−0.493316	−	0.869850i	$-0.664216\pi$
$167$	6.54741	−	11.3404i	0.506654	−	0.877550i	0.999970	−	0.00770038i	$-0.00245113\pi$
$168$		0			0
$169$	6.35543	+	11.0079i	0.488879	+	0.846764i
$170$	−20.8949			−1.60256
$171$		0			0
$172$	2.31811			0.176755
$173$	6.28949	+	10.8937i	0.478181	+	0.828234i	0.999687	−	0.0250137i	$-0.00796295\pi$
$173$	6.28949	+	10.8937i	0.478181	+	0.828234i	−0.521506	+	0.853248i	$0.674630\pi$
$174$		0			0
$175$	20.8106	−	36.0450i	1.57313	−	2.72475i
$176$	12.5069			0.942746
$177$		0			0
$178$	−5.14748	+	8.91570i	−0.385820	+	0.668260i
$179$	23.1728			1.73202			0.866008	−	0.500031i	$-0.166678\pi$
$179$	23.1728			1.73202			0.866008	+	0.500031i	$0.166678\pi$
$180$		0			0
$181$	1.87031	+	3.23948i	0.139019	+	0.240789i	0.927126	−	0.374751i	$-0.122272\pi$
$181$	1.87031	+	3.23948i	0.139019	+	0.240789i	−0.788106	+	0.615539i	$0.788938\pi$
$182$	1.96946	−	3.41120i	0.145986	−	0.252855i
$183$		0			0
$184$	−0.238113	+	0.412425i	−0.0175540	+	0.0304044i
$185$	−16.5956			−1.22013
$186$		0			0
$187$	−4.48472	−	7.76776i	−0.327955	−	0.568035i
$188$	−0.912779	+	1.58098i	−0.0665712	+	0.115305i
$189$		0			0
$190$	3.23544	+	26.1236i	0.234723	+	1.89520i
$191$	7.37837	−	12.7797i	0.533880	−	0.924707i	−0.465337	−	0.885134i	$-0.654067\pi$
$191$	7.37837	−	12.7797i	0.533880	−	0.924707i	0.999217	−	0.0395734i	$-0.0125999\pi$
$192$		0			0
$193$	−5.67586			−0.408558			−0.204279	−	0.978913i	$-0.565485\pi$
$193$	−5.67586			−0.408558			−0.204279	+	0.978913i	$0.565485\pi$
$194$	−5.11095	+	8.85243i	−0.366945	+	0.635568i
$195$		0			0
$196$	8.01426			0.572447
$197$	12.2959			0.876046			0.438023	−	0.898964i	$-0.355679\pi$
$197$	12.2959			0.876046			0.438023	+	0.898964i	$0.355679\pi$
$198$		0			0
$199$	0.0159042	+	0.0275469i	0.00112742	+	0.00195275i	0.866589	−	0.499023i	$-0.166308\pi$
$199$	0.0159042	+	0.0275469i	0.00112742	+	0.00195275i	−0.865461	+	0.500976i	$0.832974\pi$
$200$	20.8079			1.47134
$201$		0			0
$202$	1.85576	+	3.21427i	0.130571	+	0.226155i
$203$	1.94644	−	3.37132i	0.136613	−	0.236621i
$204$		0			0
$205$	3.53070			0.246595
$206$	6.00188	−	10.3956i	0.418171	−	0.724293i
$207$		0			0
$208$	2.59427			0.179880
$209$	−9.01714	+	6.80977i	−0.623729	+	0.471041i
$210$		0			0
$211$	−22.3398			−1.53794			−0.768969	−	0.639286i	$-0.779230\pi$
$211$	−22.3398			−1.53794			−0.768969	+	0.639286i	$0.779230\pi$
$212$	6.61183			0.454102
$213$		0			0
$214$	6.87795	+	11.9130i	0.470167	+	0.814353i
$215$	7.49569	+	12.9829i	0.511202	+	0.885427i
$216$		0			0
$217$	34.9732			2.37414
$218$	16.5890			1.12355
$219$		0			0
$220$	−2.83171	−	4.90466i	−0.190914	−	0.330672i
$221$	−0.930249	−	1.61124i	−0.0625753	−	0.108384i
$222$		0			0
$223$	3.43392	+	5.94773i	0.229952	+	0.398289i	0.957794	−	0.287456i	$-0.0928096\pi$
$223$	3.43392	+	5.94773i	0.229952	+	0.398289i	−0.727841	+	0.685746i	$0.759476\pi$
$224$	7.27795	+	12.6058i	0.486278	+	0.842258i
$225$		0			0
$226$	−12.4880	+	21.6299i	−0.830692	+	1.43880i
$227$	−4.44987	+	7.70739i	−0.295348	+	0.511558i	−0.975066	−	0.221916i	$-0.928769\pi$
$227$	−4.44987	+	7.70739i	−0.295348	+	0.511558i	0.679718	+	0.733474i	$0.262102\pi$
$228$		0			0
$229$	−4.13454	−	7.16123i	−0.273218	−	0.473228i	0.696466	−	0.717590i	$-0.254755\pi$
$229$	−4.13454	−	7.16123i	−0.273218	−	0.473228i	−0.969684	+	0.244362i	$0.921421\pi$
$230$	1.26168			0.0831926
$231$		0			0
$232$	1.94618			0.127773
$233$	−0.668571	+	1.15800i	−0.0437995	+	0.0758630i	−0.887094	−	0.461589i	$-0.847280\pi$
$233$	−0.668571	+	1.15800i	−0.0437995	+	0.0758630i	0.843295	+	0.537452i	$0.180613\pi$
$234$		0			0
$235$	−11.8060			−0.770138
$236$	0.698722	−	1.21022i	0.0454829	−	0.0787788i
$237$		0			0
$238$	12.6728	−	21.9500i	0.821457	−	1.42281i
$239$	−3.40198	−	5.89240i	−0.220056	−	0.381147i	0.734769	−	0.678317i	$-0.237291\pi$
$239$	−3.40198	−	5.89240i	−0.220056	−	0.381147i	−0.954825	+	0.297170i	$0.903957\pi$
$240$		0			0
$241$	7.42157			0.478065			0.239033	−	0.971012i	$-0.423170\pi$
$241$	7.42157			0.478065			0.239033	+	0.971012i	$0.423170\pi$
$242$	−3.43809	+	5.95495i	−0.221009	+	0.382799i
$243$		0			0
$244$	2.08943	−	3.61900i	0.133762	−	0.231683i
$245$	25.9144	+	44.8850i	1.65561	+	2.86760i
$246$		0			0
$247$	−1.87039	+	1.41252i	−0.119010	+	0.0898768i
$248$	8.74218	+	15.1419i	0.555129	+	0.961511i
$249$		0			0
$250$	−12.4661	−	21.5919i	−0.788423	−	1.36559i
$251$	7.83717	+	13.5744i	0.494678	+	0.856807i	0.999981	−	0.00613456i	$-0.00195270\pi$
$251$	7.83717	+	13.5744i	0.494678	+	0.856807i	−0.505303	+	0.862942i	$0.668619\pi$
$252$		0			0
$253$	0.270797	+	0.469035i	0.0170249	+	0.0294880i
$254$	−10.1330	+	17.5509i	−0.635803	+	1.10124i
$255$		0			0
$256$	−6.44268	+	11.1591i	−0.402668	+	0.697441i
$257$	−3.69675	+	6.40296i	−0.230597	+	0.399406i	−0.957984	−	0.286822i	$-0.907401\pi$
$257$	−3.69675	+	6.40296i	−0.230597	+	0.399406i	0.727387	+	0.686228i	$0.240735\pi$
$258$		0			0
$259$	10.0653	−	17.4336i	0.625427	−	1.08327i
$260$	−0.587371	−	1.01736i	−0.0364272	−	0.0630937i
$261$		0			0
$262$	−15.8874	−	27.5177i	−0.981525	−	1.70005i
$263$	1.41631	+	2.45312i	0.0873335	+	0.151266i	0.906383	−	0.422457i	$-0.138832\pi$
$263$	1.41631	+	2.45312i	0.0873335	+	0.151266i	−0.819050	+	0.573723i	$0.805499\pi$
$264$		0			0
$265$	21.3795	+	37.0304i	1.31333	+	2.27476i
$266$	−29.4051	−	12.4453i	−1.80294	−	0.763068i
$267$		0			0
$268$	−0.0815237	−	0.141203i	−0.00497985	−	0.00862536i
$269$	5.71883	−	9.90530i	0.348683	−	0.603937i	−0.637333	−	0.770589i	$-0.719962\pi$
$269$	5.71883	−	9.90530i	0.348683	−	0.603937i	0.986016	+	0.166652i	$0.0532956\pi$
$270$		0			0
$271$	13.8181	−	23.9337i	0.839390	−	1.45387i	−0.0510155	−	0.998698i	$-0.516246\pi$
$271$	13.8181	−	23.9337i	0.839390	−	1.45387i	0.890405	−	0.455168i	$-0.150421\pi$
$272$	16.6933			1.01218
$273$		0			0
$274$	−9.41058	−	16.2996i	−0.568514	−	0.984695i
$275$	11.8320	−	20.4937i	0.713499	−	1.23582i
$276$		0			0
$277$	−5.19514	+	8.99825i	−0.312146	+	0.540653i	−0.978827	−	0.204691i	$-0.934381\pi$
$277$	−5.19514	+	8.99825i	−0.312146	+	0.540653i	0.666681	+	0.745343i	$0.267714\pi$
$278$	−28.6626			−1.71907
$279$		0			0
$280$	−19.5326	+	33.8314i	−1.16729	+	2.02181i
$281$	−8.50448			−0.507335			−0.253667	−	0.967292i	$-0.581637\pi$
$281$	−8.50448			−0.507335			−0.253667	+	0.967292i	$0.581637\pi$
$282$		0			0
$283$	−1.36691			−0.0812541			−0.0406270	−	0.999174i	$-0.512936\pi$
$283$	−1.36691			−0.0812541			−0.0406270	+	0.999174i	$0.512936\pi$
$284$	−1.99361	−	3.45304i	−0.118299	−	0.204900i
$285$		0			0
$286$	1.11975	−	1.93947i	0.0662123	−	0.114683i
$287$	−2.14139	+	3.70899i	−0.126402	+	0.218935i
$288$		0			0
$289$	2.51415	+	4.35464i	0.147891	+	0.256155i
$290$	−2.57803	−	4.46528i	−0.151387	−	0.262210i
$291$		0			0
$292$	−0.242189	−	0.419484i	−0.0141731	−	0.0245485i
$293$	0.373905	+	0.647623i	0.0218438	+	0.0378345i	0.876741	−	0.480963i	$-0.159713\pi$
$293$	0.373905	+	0.647623i	0.0218438	+	0.0378345i	−0.854897	+	0.518798i	$0.826380\pi$
$294$		0			0
$295$	9.03735			0.526175
$296$	10.0640			0.584958
$297$		0			0
$298$	12.9407	+	22.4139i	0.749633	+	1.29840i
$299$	0.0561705	+	0.0972901i	0.00324842	+	0.00562643i
$300$		0			0
$301$	−18.1847			−1.04815
$302$	−2.63879			−0.151845
$303$		0			0
$304$	−2.58485	−	20.8706i	−0.148251	−	1.19701i
$305$	27.0250			1.54744
$306$		0			0
$307$	5.56496	−	9.63880i	0.317609	−	0.550115i	−0.662379	−	0.749169i	$-0.730453\pi$
$307$	5.56496	−	9.63880i	0.317609	−	0.550115i	0.979989	+	0.199053i	$0.0637866\pi$
$308$	6.86978			0.391442
$309$		0			0
$310$	23.1608	−	40.1157i	1.31545	−	2.27842i
$311$	−6.07360	−	10.5198i	−0.344402	−	0.596522i	0.640843	−	0.767672i	$-0.278585\pi$
$311$	−6.07360	−	10.5198i	−0.344402	−	0.596522i	−0.985245	+	0.171150i	$0.945252\pi$
$312$		0			0
$313$	−26.3132			−1.48731			−0.743656	−	0.668563i	$-0.766910\pi$
$313$	−26.3132			−1.48731			−0.743656	+	0.668563i	$0.766910\pi$
$314$	8.53194	+	14.7778i	0.481485	+	0.833957i
$315$		0			0
$316$	−6.87870			−0.386957
$317$	13.4516			0.755520			0.377760	−	0.925904i	$-0.376694\pi$
$317$	13.4516			0.755520			0.377760	+	0.925904i	$0.376694\pi$
$318$		0			0
$319$	1.10666	−	1.91679i	0.0619611	−	0.107320i
$320$	−16.9904			−0.949795
$321$		0			0
$322$	−0.765214	+	1.32539i	−0.0426437	+	0.0738610i
$323$	−12.0354	+	9.08913i	−0.669665	+	0.505733i
$324$		0			0
$325$	2.45427	−	4.25093i	0.136139	−	0.235799i
$326$	−17.7445	−	30.7343i	−0.982775	−	1.70222i
$327$		0			0
$328$	−2.14111			−0.118223
$329$	7.16039	−	12.4022i	0.394765	−	0.683753i
$330$		0			0
$331$	2.15691	−	3.73589i	0.118555	−	0.205343i	−0.800640	−	0.599145i	$-0.795507\pi$
$331$	2.15691	−	3.73589i	0.118555	−	0.205343i	0.919195	+	0.393802i	$0.128841\pi$
$332$	−2.11056	−	3.65560i	−0.115832	−	0.200627i
$333$		0			0
$334$	21.0384			1.15117
$335$	0.527219	−	0.913169i	0.0288050	−	0.0498918i
$336$		0			0
$337$	−2.91534			−0.158809			−0.0794044	−	0.996842i	$-0.525302\pi$
$337$	−2.91534			−0.158809			−0.0794044	+	0.996842i	$0.525302\pi$
$338$	−10.2108	+	17.6855i	−0.555392	+	0.961967i
$339$		0			0
$340$	−3.77954	−	6.54635i	−0.204974	−	0.355026i
$341$	19.8843			1.07679
$342$		0			0
$343$	−30.9525			−1.67128
$344$	−4.54558	−	7.87318i	−0.245082	−	0.424494i
$345$		0			0
$346$	−10.1048	+	17.5020i	−0.543238	+	0.940916i
$347$	14.7943			0.794199			0.397099	−	0.917776i	$-0.370017\pi$
$347$	14.7943			0.794199			0.397099	+	0.917776i	$0.370017\pi$
$348$		0			0
$349$	0.668641	−	1.15812i	0.0357915	−	0.0619927i	−0.847575	−	0.530676i	$-0.821938\pi$
$349$	0.668641	−	1.15812i	0.0357915	−	0.0619927i	0.883366	+	0.468683i	$0.155271\pi$
$350$	66.8694			3.57432
$351$		0			0
$352$	4.13793	+	7.16711i	0.220552	+	0.382008i
$353$	−10.3662	+	17.9549i	−0.551739	+	0.955641i	0.446410	+	0.894829i	$0.352702\pi$
$353$	−10.3662	+	17.9549i	−0.551739	+	0.955641i	−0.998149	+	0.0608121i	$0.980631\pi$
$354$		0			0
$355$	12.8928	−	22.3310i	0.684279	−	1.18521i
$356$	−3.72438			−0.197392
$357$		0			0
$358$	18.6149	+	32.2420i	0.983829	+	1.70404i
$359$	2.38736	−	4.13504i	0.126000	−	0.218239i	−0.796123	−	0.605135i	$-0.793119\pi$
$359$	2.38736	−	4.13504i	0.126000	−	0.218239i	0.922123	+	0.386896i	$0.126453\pi$
$360$		0			0
$361$	13.2272	+	13.6397i	0.696168	+	0.717879i
$362$	−3.00488	+	5.20460i	−0.157933	+	0.273548i
$363$		0			0
$364$	1.42497			0.0746888
$365$	1.56625	−	2.71283i	0.0819814	−	0.141996i
$366$		0			0
$367$	21.7614			1.13594			0.567969	−	0.823050i	$-0.307729\pi$
$367$	21.7614			1.13594			0.567969	+	0.823050i	$0.307729\pi$
$368$	−1.00798			−0.0525444
$369$		0			0
$370$	−13.3314	−	23.0906i	−0.693065	−	1.20042i
$371$	−51.8671			−2.69281
$372$		0			0
$373$	11.3702	+	19.6938i	0.588727	+	1.01971i	0.994399	+	0.105687i	$0.0337041\pi$
$373$	11.3702	+	19.6938i	0.588727	+	1.01971i	−0.405672	+	0.914019i	$0.632963\pi$
$374$	7.20523	−	12.4798i	0.372574	−	0.645317i
$375$		0			0
$376$	7.15946			0.369221
$377$	0.229550	−	0.397593i	0.0118224	−	0.0204771i
$378$		0			0
$379$	−21.1367			−1.08572			−0.542859	−	0.839824i	$-0.682658\pi$
$379$	−21.1367			−1.08572			−0.542859	+	0.839824i	$0.682658\pi$
$380$	−7.59928	+	5.73899i	−0.389835	+	0.294404i
$381$		0			0
$382$	23.7084			1.21303
$383$	9.57967			0.489498			0.244749	−	0.969586i	$-0.421294\pi$
$383$	9.57967			0.489498			0.244749	+	0.969586i	$0.421294\pi$
$384$		0			0
$385$	22.2136	+	38.4751i	1.13211	+	1.96087i
$386$	−4.55947	−	7.89724i	−0.232071	−	0.401959i
$387$		0			0
$388$	−3.69795			−0.187735
$389$	−34.4668			−1.74754			−0.873768	−	0.486343i	$-0.838330\pi$
$389$	−34.4668			−1.74754			−0.873768	+	0.486343i	$0.838330\pi$
$390$		0			0
$391$	0.361439	+	0.626030i	0.0182787	+	0.0316597i
$392$	−15.7152	−	27.2194i	−0.793735	−	1.37479i
$393$		0			0
$394$	9.87741	+	17.1082i	0.497617	+	0.861897i
$395$	−22.2425	−	38.5251i	−1.11914	−	1.93841i
$396$		0			0
$397$	17.8313	−	30.8848i	0.894928	−	1.55006i	0.0610353	−	0.998136i	$-0.480560\pi$
$397$	17.8313	−	30.8848i	0.894928	−	1.55006i	0.833893	−	0.551926i	$-0.186107\pi$
$398$	−0.0255520	+	0.0442574i	−0.00128081	+	0.00221842i
$399$		0			0
$400$	22.0209	+	38.1414i	1.10105	+	1.90707i
$401$	−1.13355			−0.0566066			−0.0283033	−	0.999599i	$-0.509010\pi$
$401$	−1.13355			−0.0566066			−0.0283033	+	0.999599i	$0.509010\pi$
$402$		0			0
$403$	4.12452			0.205457
$404$	−0.671354	+	1.16282i	−0.0334011	+	0.0578524i
$405$		0			0
$406$	6.25436			0.310399
$407$	5.72270	−	9.91201i	0.283664	−	0.491320i
$408$		0			0
$409$	−6.71319	+	11.6276i	−0.331946	+	0.574947i	−0.982893	−	0.184176i	$-0.941038\pi$
$409$	−6.71319	+	11.6276i	−0.331946	+	0.574947i	0.650947	+	0.759123i	$0.274372\pi$
$410$	2.83624	+	4.91251i	0.140072	+	0.242612i
$411$		0			0
$412$	4.34257			0.213943
$413$	−5.48120	+	9.49371i	−0.269712	+	0.467155i
$414$		0			0
$415$	13.6491	−	23.6410i	0.670010	−	1.16049i
$416$	0.858315	+	1.48665i	0.0420824	+	0.0728888i
$417$		0			0
$418$	−16.7185	−	7.07585i	−0.817727	−	0.346091i
$419$	−1.95049	−	3.37834i	−0.0952875	−	0.165043i	0.814441	−	0.580246i	$-0.197044\pi$
$419$	−1.95049	−	3.37834i	−0.0952875	−	0.165043i	−0.909729	+	0.415203i	$0.863710\pi$
$420$		0			0
$421$	−13.6227	−	23.5953i	−0.663932	−	1.14996i	−0.979574	−	0.201085i	$-0.935553\pi$
$421$	−13.6227	−	23.5953i	−0.663932	−	1.14996i	0.315642	−	0.948878i	$-0.397780\pi$
$422$	−17.9458	−	31.0830i	−0.873588	−	1.51310i
$423$		0			0
$424$	−12.9651	−	22.4562i	−0.629642	−	1.09057i
$425$	15.7925	−	27.3533i	0.766047	−	1.32683i
$426$		0			0
$427$	−16.3908	+	28.3896i	−0.793205	+	1.37387i
$428$	−2.48822	+	4.30972i	−0.120273	+	0.208318i
$429$		0			0
$430$	−12.0427	+	20.8586i	−0.580751	+	1.00589i
$431$	−20.2776	−	35.1217i	−0.976735	−	1.69176i	−0.674086	−	0.738653i	$-0.735462\pi$
$431$	−20.2776	−	35.1217i	−0.976735	−	1.69176i	−0.302650	−	0.953102i	$-0.597871\pi$
$432$		0			0
$433$	−9.37164	−	16.2322i	−0.450372	−	0.780068i	0.548037	−	0.836454i	$-0.315375\pi$
$433$	−9.37164	−	16.2322i	−0.450372	−	0.780068i	−0.998409	+	0.0563866i	$0.982042\pi$
$434$	28.0943	+	48.6608i	1.34857	+	2.33579i
$435$		0			0
$436$	3.00068	+	5.19733i	0.143707	+	0.248907i
$437$	0.726722	−	0.548822i	0.0347638	−	0.0262537i
$438$		0			0
$439$	−8.15172	−	14.1192i	−0.389060	−	0.673872i	0.603263	−	0.797542i	$-0.293867\pi$
$439$	−8.15172	−	14.1192i	−0.389060	−	0.673872i	−0.992323	+	0.123670i	$0.960534\pi$
$440$	−11.1054	+	19.2351i	−0.529428	+	0.916997i
$441$		0			0
$442$	1.49455	−	2.58864i	0.0710887	−	0.123129i
$443$	26.4906			1.25861			0.629303	−	0.777160i	$-0.283341\pi$
$443$	26.4906			1.25861			0.629303	+	0.777160i	$0.283341\pi$
$444$		0			0
$445$	−12.0429	−	20.8589i	−0.570888	−	0.988807i
$446$	−5.51700	+	9.55573i	−0.261238	+	0.452477i
$447$		0			0
$448$	10.3048	−	17.8484i	0.486855	−	0.843258i
$449$	−19.2529			−0.908602			−0.454301	−	0.890848i	$-0.650111\pi$
$449$	−19.2529			−0.908602			−0.454301	+	0.890848i	$0.650111\pi$
$450$		0			0
$451$	−1.21750	+	2.10877i	−0.0573299	+	0.0992982i
$452$	−9.03553			−0.424995
$453$		0			0
$454$	−14.2985			−0.671061
$455$	4.60769	+	7.98075i	0.216012	+	0.374143i
$456$		0			0
$457$	18.2664	−	31.6384i	0.854467	−	1.47998i	−0.0226720	−	0.999743i	$-0.507217\pi$
$457$	18.2664	−	31.6384i	0.854467	−	1.47998i	0.877139	−	0.480237i	$-0.159449\pi$
$458$	6.64263	−	11.5054i	0.310390	−	0.537610i
$459$		0			0
$460$	0.228217	+	0.395283i	0.0106407	+	0.0184302i
$461$	−2.91815	−	5.05439i	−0.135912	−	0.235406i	0.790034	−	0.613064i	$-0.210063\pi$
$461$	−2.91815	−	5.05439i	−0.135912	−	0.235406i	−0.925945	+	0.377657i	$0.876730\pi$
$462$		0			0
$463$	6.34039	+	10.9819i	0.294663	+	0.510371i	0.974906	−	0.222615i	$-0.0714593\pi$
$463$	6.34039	+	10.9819i	0.294663	+	0.510371i	−0.680243	+	0.732986i	$0.738126\pi$
$464$	2.05964	+	3.56739i	0.0956162	+	0.165612i
$465$		0			0
$466$	−2.14828			−0.0995170
$467$	24.0640			1.11355			0.556774	−	0.830664i	$-0.312039\pi$
$467$	24.0640			1.11355			0.556774	+	0.830664i	$0.312039\pi$
$468$		0			0
$469$	0.639521	+	1.10768i	0.0295303	+	0.0511481i
$470$	−9.48386	−	16.4265i	−0.437458	−	0.757699i
$471$		0			0
$472$	−5.48049			−0.252260
$473$	−10.3390			−0.475390
$474$		0			0
$475$	−36.6436	−	15.5089i	−1.68132	−	0.711596i
$476$	9.16923			0.420271
$477$		0			0
$478$	5.46568	−	9.46683i	0.249994	−	0.433003i
$479$	−5.01131			−0.228973			−0.114486	−	0.993425i	$-0.536522\pi$
$479$	−5.01131			−0.228973			−0.114486	+	0.993425i	$0.536522\pi$
$480$		0			0
$481$	1.18704	−	2.05601i	0.0541243	−	0.0937460i
$482$	5.96182	+	10.3262i	0.271553	+	0.470344i
$483$		0			0
$484$	−2.48758			−0.113072
$485$	−11.9574	−	20.7109i	−0.542959	−	0.940433i
$486$		0			0
$487$	−31.5079			−1.42776			−0.713880	−	0.700268i	$-0.753064\pi$
$487$	−31.5079			−1.42776			−0.713880	+	0.700268i	$0.753064\pi$
$488$	−16.3887			−0.741879
$489$		0			0
$490$	−41.6345	+	72.1130i	−1.88085	+	3.25773i
$491$	−30.6070			−1.38127			−0.690636	−	0.723202i	$-0.742669\pi$
$491$	−30.6070			−1.38127			−0.690636	+	0.723202i	$0.742669\pi$
$492$		0			0
$493$	1.47708	−	2.55838i	0.0665244	−	0.115224i
$494$	−3.46785	−	1.46772i	−0.156026	−	0.0660357i
$495$		0			0
$496$	−18.5036	+	32.0492i	−0.830836	+	1.43905i
$497$	15.6391	+	27.0877i	0.701509	+	1.21505i
$498$		0			0
$499$	−10.9239			−0.489021			−0.244511	−	0.969647i	$-0.578627\pi$
$499$	−10.9239			−0.489021			−0.244511	+	0.969647i	$0.578627\pi$
$500$	4.50982	−	7.81123i	0.201685	−	0.349329i
$501$		0			0
$502$	−12.5913	+	21.8088i	−0.561979	+	0.973376i
$503$	15.0754	+	26.1113i	0.672178	+	1.16425i	0.977285	+	0.211928i	$0.0679742\pi$
$503$	15.0754	+	26.1113i	0.672178	+	1.16425i	−0.305108	+	0.952318i	$0.598693\pi$
$504$		0			0
$505$	−8.68336			−0.386405
$506$	−0.435068	+	0.753560i	−0.0193411	+	0.0334998i
$507$		0			0
$508$	−7.33160			−0.325287
$509$	1.38957	−	2.40680i	0.0615916	−	0.106680i	−0.833585	−	0.552391i	$-0.813716\pi$
$509$	1.38957	−	2.40680i	0.0615916	−	0.106680i	0.895177	+	0.445711i	$0.147049\pi$
$510$		0			0
$511$	1.89988	+	3.29069i	0.0840457	+	0.145571i
$512$	6.59240			0.291346
$513$		0			0
$514$	−11.8785			−0.523940
$515$	14.0418	+	24.3212i	0.618757	+	1.07172i
$516$		0			0
$517$	4.07109	−	7.05134i	0.179046	−	0.310118i
$518$	32.3422			1.42103
$519$		0			0
$520$	−2.30355	+	3.98986i	−0.101017	+	0.174967i
$521$	−13.4298			−0.588371			−0.294186	−	0.955748i	$-0.595048\pi$
$521$	−13.4298			−0.588371			−0.294186	+	0.955748i	$0.595048\pi$
$522$		0			0
$523$	5.62130	+	9.73637i	0.245802	+	0.425742i	0.962357	−	0.271789i	$-0.0876153\pi$
$523$	5.62130	+	9.73637i	0.245802	+	0.425742i	−0.716555	+	0.697531i	$0.754282\pi$
$524$	5.74753	−	9.95502i	0.251082	−	0.434887i
$525$		0			0
$526$	−2.27547	+	3.94123i	−0.0992153	+	0.171846i
$527$	26.5400			1.15610
$528$		0			0
$529$	11.4782	+	19.8808i	0.499051	+	0.864382i
$530$	−34.3487	+	59.4938i	−1.49201	+	2.58424i
$531$		0			0
$532$	−1.41980	−	11.4637i	−0.0615560	−	0.497016i
$533$	−0.252542	+	0.437415i	−0.0109388	+	0.0189465i
$534$		0			0
$535$	−32.1829			−1.39139
$536$	−0.319719	+	0.553770i	−0.0138098	+	0.0239192i
$537$		0			0
$538$	18.3760			0.792244
$539$	−35.7445			−1.53962
$540$		0			0
$541$	9.55755	+	16.5542i	0.410911	+	0.711719i	0.994990	−	0.0999781i	$-0.0318773\pi$
$541$	9.55755	+	16.5542i	0.410911	+	0.711719i	−0.584078	+	0.811697i	$0.698544\pi$
$542$	44.4008			1.90718
$543$		0			0
$544$	5.52298	+	9.56608i	0.236796	+	0.410142i
$545$	−19.4056	+	33.6114i	−0.831243	+	1.43976i
$546$		0			0
$547$	−41.0410			−1.75479			−0.877393	−	0.479772i	$-0.840719\pi$
$547$	−41.0410			−1.75479			−0.877393	+	0.479772i	$0.840719\pi$
$548$	3.40444	−	5.89667i	0.145431	−	0.251893i
$549$		0			0
$550$	38.0191			1.62114
$551$	−3.42731	−	1.45056i	−0.146008	−	0.0617959i
$552$		0			0
$553$	53.9607			2.29464
$554$	−16.6932			−0.709227
$555$		0			0
$556$	−5.18460	−	8.97999i	−0.219876	−	0.380836i
$557$	19.9467	+	34.5487i	0.845169	+	1.46388i	0.885475	+	0.464688i	$0.153833\pi$
$557$	19.9467	+	34.5487i	0.845169	+	1.46388i	−0.0403059	+	0.999187i	$0.512833\pi$
$558$		0			0
$559$	−2.14459			−0.0907064
$560$	−82.6848			−3.49407
$561$		0			0
$562$	−6.83172	−	11.8329i	−0.288179	−	0.499140i
$563$	−4.46506	−	7.73371i	−0.188180	−	0.325937i	0.756464	−	0.654036i	$-0.226925\pi$
$563$	−4.46506	−	7.73371i	−0.188180	−	0.325937i	−0.944643	+	0.328099i	$0.893592\pi$
$564$		0			0
$565$	−29.2166	−	50.6047i	−1.22915	−	2.12896i
$566$	−1.09805	−	1.90187i	−0.0461544	−	0.0799417i
$567$		0			0
$568$	−7.81854	+	13.5421i	−0.328058	+	0.568214i
$569$	2.87302	−	4.97622i	0.120443	−	0.208614i	−0.799499	−	0.600667i	$-0.794902\pi$
$569$	2.87302	−	4.97622i	0.120443	−	0.208614i	0.919943	+	0.392053i	$0.128235\pi$
$570$		0			0
$571$	−6.75539	−	11.7007i	−0.282704	−	0.489658i	0.689346	−	0.724433i	$-0.257898\pi$
$571$	−6.75539	−	11.7007i	−0.282704	−	0.489658i	−0.972050	+	0.234774i	$0.924565\pi$
$572$	0.810179			0.0338753
$573$		0			0
$574$	−6.88078			−0.287198
$575$	−0.953584	+	1.65166i	−0.0397672	+	0.0688788i
$576$		0			0
$577$	−10.9961			−0.457774			−0.228887	−	0.973453i	$-0.573509\pi$
$577$	−10.9961			−0.457774			−0.228887	+	0.973453i	$0.573509\pi$
$578$	−4.03928	+	6.99625i	−0.168012	+	0.291005i
$579$		0			0
$580$	0.932648	−	1.61539i	0.0387261	−	0.0670756i
$581$	16.5565	+	28.6768i	0.686881	+	1.18971i
$582$		0			0
$583$	−29.4895			−1.22133
$584$	−0.949817	+	1.64513i	−0.0393037	+	0.0680760i
$585$		0			0
$586$	−0.600723	+	1.04048i	−0.0248156	+	0.0429820i
$587$	−14.2331	−	24.6525i	−0.587464	−	1.01752i	−0.994563	−	0.104133i	$-0.966793\pi$
$587$	−14.2331	−	24.6525i	−0.587464	−	1.01752i	0.407100	−	0.913384i	$-0.366540\pi$
$588$		0			0
$589$	−4.10954	−	33.1813i	−0.169331	−	1.36721i
$590$	7.25979	+	12.5743i	0.298881	+	0.517677i
$591$		0			0
$592$	10.6507	+	18.4475i	0.437740	+	0.758188i
$593$	2.56192	+	4.43738i	0.105206	+	0.182222i	0.913822	−	0.406114i	$-0.133117\pi$
$593$	2.56192	+	4.43738i	0.105206	+	0.182222i	−0.808617	+	0.588336i	$0.799783\pi$
$594$		0			0
$595$	29.6490	+	51.3535i	1.21549	+	2.10529i
$596$	−4.68152	+	8.10862i	−0.191762	+	0.332142i
$597$		0			0
$598$	−0.0902445	+	0.156308i	−0.00369037	+	0.00639191i
$599$	13.5015	−	23.3853i	0.551656	−	0.955497i	−0.446499	−	0.894784i	$-0.647329\pi$
$599$	13.5015	−	23.3853i	0.551656	−	0.955497i	0.998155	−	0.0607125i	$-0.0193373\pi$
$600$		0			0
$601$	20.4168	−	35.3630i	0.832819	−	1.44249i	−0.0629745	−	0.998015i	$-0.520059\pi$
$601$	20.4168	−	35.3630i	0.832819	−	1.44249i	0.895794	−	0.444470i	$-0.146608\pi$
$602$	−14.6079	−	25.3017i	−0.595374	−	1.03122i
$603$		0			0
$604$	−0.477314	−	0.826732i	−0.0194216	−	0.0336393i
$605$	−8.04366	−	13.9320i	−0.327021	−	0.566417i
$606$		0			0
$607$	−0.992746	−	1.71949i	−0.0402943	−	0.0697918i	0.845175	−	0.534490i	$-0.179496\pi$
$607$	−0.992746	−	1.71949i	−0.0402943	−	0.0697918i	−0.885469	+	0.464698i	$0.846163\pi$
$608$	11.1047	−	8.38630i	0.450355	−	0.340109i
$609$		0			0
$610$	21.7094	+	37.6018i	0.878988	+	1.52245i
$611$	0.844451	−	1.46263i	0.0341628	−	0.0591718i
$612$		0			0
$613$	−14.2449	+	24.6729i	−0.575346	+	0.996528i	0.420658	+	0.907219i	$0.361799\pi$
$613$	−14.2449	+	24.6729i	−0.575346	+	0.996528i	−0.996004	+	0.0893089i	$0.971534\pi$
$614$	17.8815			0.721640
$615$		0			0
$616$	−13.4709	−	23.3323i	−0.542759	−	0.940087i
$617$	14.7097	−	25.4779i	0.592189	−	1.02570i	−0.401748	−	0.915750i	$-0.631597\pi$
$617$	14.7097	−	25.4779i	0.592189	−	1.02570i	0.993937	−	0.109951i	$-0.0350695\pi$
$618$		0			0
$619$	−14.3363	+	24.8312i	−0.576224	+	0.998049i	0.419684	+	0.907670i	$0.362141\pi$
$619$	−14.3363	+	24.8312i	−0.576224	+	0.998049i	−0.995907	+	0.0903786i	$0.971192\pi$
$620$	16.7577			0.673004
$621$		0			0
$622$	9.75796	−	16.9013i	0.391258	−	0.677679i
$623$	29.2163			1.17053
$624$		0			0
$625$	12.6877			0.507508
$626$	−21.1377	−	36.6115i	−0.844831	−	1.46329i
$627$		0			0
$628$	−3.08658	+	5.34611i	−0.123168	+	0.213333i
$629$	7.63820	−	13.2298i	0.304555	−	0.527505i
$630$		0			0
$631$	9.49043	+	16.4379i	0.377808	+	0.654383i	0.990743	−	0.135750i	$-0.0433446\pi$
$631$	9.49043	+	16.4379i	0.377808	+	0.654383i	−0.612935	+	0.790133i	$0.710011\pi$
$632$	13.4884	+	23.3626i	0.536541	+	0.929316i
$633$		0			0
$634$	10.8058	+	18.7162i	0.429154	+	0.743317i
$635$	−23.7070	−	41.0616i	−0.940782	−	1.62948i
$636$		0			0
$637$	−7.41434			−0.293767
$638$	3.55596			0.140782
$639$		0			0
$640$	−25.6484	−	44.4243i	−1.01384	−	1.75603i
$641$	−2.73944	−	4.74484i	−0.108201	−	0.187410i	0.806840	−	0.590770i	$-0.201176\pi$
$641$	−2.73944	−	4.74484i	−0.108201	−	0.187410i	−0.915042	+	0.403359i	$0.867842\pi$
$642$		0			0
$643$	22.3400			0.881004			0.440502	−	0.897752i	$-0.354801\pi$
$643$	22.3400			0.881004			0.440502	+	0.897752i	$0.354801\pi$
$644$	−0.553659			−0.0218172
$645$		0			0
$646$	−22.3145	−	9.44428i	−0.877951	−	0.371580i
$647$	−4.90902			−0.192994			−0.0964968	−	0.995333i	$-0.530764\pi$
$647$	−4.90902			−0.192994			−0.0964968	+	0.995333i	$0.530764\pi$
$648$		0			0
$649$	−3.11638	+	5.39772i	−0.122328	+	0.211879i
$650$	7.88616			0.309321
$651$		0			0
$652$	6.41937	−	11.1187i	0.251402	−	0.435441i
$653$	19.2926	+	33.4157i	0.754977	+	1.30766i	0.945386	+	0.325953i	$0.105685\pi$
$653$	19.2926	+	33.4157i	0.754977	+	1.30766i	−0.190409	+	0.981705i	$0.560981\pi$
$654$		0			0
$655$	74.3392			2.90467
$656$	−2.26592	−	3.92470i	−0.0884695	−	0.153234i
$657$		0			0
$658$	23.0080			0.896946
$659$	20.4933			0.798304			0.399152	−	0.916885i	$-0.369304\pi$
$659$	20.4933			0.798304			0.399152	+	0.916885i	$0.369304\pi$
$660$		0			0
$661$	23.2088	−	40.1988i	0.902718	−	1.56355i	0.0787667	−	0.996893i	$-0.474902\pi$
$661$	23.2088	−	40.1988i	0.902718	−	1.56355i	0.823951	−	0.566660i	$-0.191765\pi$
$662$	6.93068			0.269368
$663$		0			0
$664$	−8.27720	+	14.3365i	−0.321218	+	0.556365i
$665$	59.6133	−	45.0201i	2.31170	−	1.74581i
$666$		0			0
$667$	−0.0891895	+	0.154481i	−0.00345343	+	0.00598152i
$668$	3.80550	+	6.59132i	0.147239	+	0.255026i
$669$		0			0
$670$	1.69408			0.0654479
$671$	−9.31909	+	16.1411i	−0.359760	+	0.623122i
$672$		0			0
$673$	12.7950	−	22.1615i	0.493209	−	0.854263i	−0.506760	−	0.862087i	$-0.669157\pi$
$673$	12.7950	−	22.1615i	0.493209	−	0.854263i	0.999969	+	0.00782366i	$0.00249037\pi$
$674$	−2.34192	−	4.05632i	−0.0902074	−	0.156244i
$675$		0			0
$676$	−7.38784			−0.284148
$677$	−15.8898	+	27.5220i	−0.610695	+	1.05775i	0.380428	+	0.924810i	$0.375777\pi$
$677$	−15.8898	+	27.5220i	−0.610695	+	1.05775i	−0.991123	+	0.132944i	$0.957557\pi$
$678$		0			0
$679$	29.0090			1.11326
$680$	−14.8226	+	25.6735i	−0.568420	+	0.984532i
$681$		0			0
$682$	15.9732	+	27.6664i	0.611646	+	1.05940i
$683$	−46.5132			−1.77978			−0.889890	−	0.456176i	$-0.849219\pi$
$683$	−46.5132			−1.77978			−0.889890	+	0.456176i	$0.849219\pi$
$684$		0			0
$685$	44.0334			1.68243
$686$	−24.8644	−	43.0665i	−0.949329	−	1.64429i
$687$		0			0
$688$	9.62113	−	16.6643i	0.366802	−	0.635320i
$689$	−6.11689			−0.233035
$690$		0			0
$691$	−8.31573	+	14.4033i	−0.316345	+	0.547926i	−0.979723	−	0.200359i	$-0.935789\pi$
$691$	−8.31573	+	14.4033i	−0.316345	+	0.547926i	0.663377	+	0.748285i	$0.269122\pi$
$692$	−7.31118			−0.277929
$693$		0			0
$694$	11.8844	+	20.5844i	0.451125	+	0.781371i
$695$	33.5291	−	58.0741i	1.27183	−	2.20288i
$696$		0			0
$697$	−1.62502	+	2.81462i	−0.0615521	+	0.106611i
$698$	2.14850			0.0813220
$699$		0			0
$700$	12.0956	+	20.9502i	0.457170	+	0.791842i
$701$	−18.3672	+	31.8130i	−0.693721	+	1.20156i	0.276889	+	0.960902i	$0.410697\pi$
$701$	−18.3672	+	31.8130i	−0.693721	+	1.20156i	−0.970610	+	0.240658i	$0.922637\pi$
$702$		0			0
$703$	−17.7231	−	7.50105i	−0.668439	−	0.282907i
$704$	5.85887	−	10.1479i	0.220814	−	0.382462i
$705$		0			0
$706$	−33.3092			−1.25361
$707$	5.26650	−	9.12185i	0.198067	−	0.343062i
$708$		0			0
$709$	−39.7998			−1.49471			−0.747356	−	0.664424i	$-0.768677\pi$
$709$	−39.7998			−1.49471			−0.747356	+	0.664424i	$0.768677\pi$
$710$	41.4276			1.55475
$711$		0			0
$712$	7.30313	+	12.6494i	0.273696	+	0.474056i
$713$	−1.60254			−0.0600157
$714$		0			0
$715$	2.61974	+	4.53752i	0.0979726	+	0.169693i
$716$	−6.73427	+	11.6641i	−0.251671	+	0.435908i
$717$		0			0
$718$	7.67116			0.286285
$719$	−11.0069	+	19.0645i	−0.410487	+	0.710985i	−0.994943	−	0.100441i	$-0.967975\pi$
$719$	−11.0069	+	19.0645i	−0.410487	+	0.710985i	0.584456	+	0.811425i	$0.301308\pi$
$720$		0			0
$721$	−34.0657			−1.26867
$722$	−8.35236	+	29.3608i	−0.310843	+	1.09270i
$723$		0			0
$724$	−2.17414			−0.0808011
$725$	7.79397			0.289461
$726$		0			0
$727$	8.41740	+	14.5794i	0.312184	+	0.540719i	0.978835	−	0.204652i	$-0.0656061\pi$
$727$	8.41740	+	14.5794i	0.312184	+	0.540719i	−0.666651	+	0.745370i	$0.732273\pi$
$728$	−2.79423	−	4.83974i	−0.103561	−	0.179373i
$729$		0			0
$730$	5.03274			0.186270
$731$	−13.7997			−0.510401
$732$		0			0
$733$	11.6819	+	20.2337i	0.431481	+	0.747347i	0.997001	−	0.0773873i	$-0.0246578\pi$
$733$	11.6819	+	20.2337i	0.431481	+	0.747347i	−0.565520	+	0.824735i	$0.691324\pi$
$734$	17.4812	+	30.2783i	0.645242	+	1.11759i
$735$		0			0
$736$	−0.333490	−	0.577621i	−0.0122926	−	0.0212914i
$737$	0.363605	+	0.629782i	0.0133935	+	0.0231983i
$738$		0			0
$739$	26.2097	−	45.3966i	0.964141	−	1.66994i	0.252235	−	0.967666i	$-0.418834\pi$
$739$	26.2097	−	45.3966i	0.964141	−	1.66994i	0.711906	−	0.702275i	$-0.247832\pi$
$740$	4.82286	−	8.35343i	0.177292	−	0.307078i
$741$		0			0
$742$	−41.6653	−	72.1665i	−1.52958	−	2.64932i
$743$	−13.1393			−0.482033			−0.241016	−	0.970521i	$-0.577481\pi$
$743$	−13.1393			−0.482033			−0.241016	+	0.970521i	$0.577481\pi$
$744$		0			0
$745$	−60.5513			−2.21843
$746$	−18.2676	+	31.6404i	−0.668824	+	1.15844i
$747$		0			0
$748$	5.21324			0.190615
$749$	19.5191	−	33.8080i	0.713212	−	1.23532i
$750$		0			0
$751$	24.1989	−	41.9138i	0.883032	−	1.52946i	0.0350783	−	0.999385i	$-0.488832\pi$
$751$	24.1989	−	41.9138i	0.883032	−	1.52946i	0.847953	−	0.530071i	$-0.177835\pi$
$752$	7.57682	+	13.1234i	0.276298	+	0.478563i
$753$		0			0
$754$	0.737600			0.0268618
$755$	3.08682	−	5.34652i	0.112341	−	0.194580i
$756$		0			0
$757$	−8.62645	+	14.9414i	−0.313533	+	0.543056i	−0.979125	−	0.203261i	$-0.934846\pi$
$757$	−8.62645	+	14.9414i	−0.313533	+	0.543056i	0.665591	+	0.746317i	$0.268179\pi$
$758$	−16.9793	−	29.4090i	−0.616715	−	1.06818i
$759$		0			0
$760$	34.3932	+	14.5564i	1.24757	+	0.528016i
$761$	−14.8377	−	25.6997i	−0.537867	−	0.931612i	−0.999019	−	0.0442911i	$-0.985897\pi$
$761$	−14.8377	−	25.6997i	−0.537867	−	0.931612i	0.461152	−	0.887321i	$-0.347436\pi$
$762$		0			0
$763$	−23.5391	−	40.7710i	−0.852174	−	1.47601i
$764$	4.28847	+	7.42785i	0.155151	+	0.268730i
$765$		0			0
$766$	7.69544	+	13.3289i	0.278048	+	0.481592i
$767$	−0.646418	+	1.11963i	−0.0233408	+	0.0404275i
$768$		0			0
$769$	4.88919	−	8.46833i	0.176309	−	0.305376i	−0.764305	−	0.644855i	$-0.776918\pi$
$769$	4.88919	−	8.46833i	0.176309	−	0.305376i	0.940613	+	0.339479i	$0.110251\pi$
$770$	−35.6888	+	61.8148i	−1.28614	+	2.22765i
$771$		0			0
$772$	1.64947	−	2.85696i	0.0593657	−	0.102824i
$773$	−10.7481	−	18.6163i	−0.386583	−	0.669581i	0.605405	−	0.795918i	$-0.293011\pi$
$773$	−10.7481	−	18.6163i	−0.386583	−	0.669581i	−0.991987	+	0.126337i	$0.959678\pi$
$774$		0			0
$775$	35.0102	+	60.6394i	1.25760	+	2.17823i
$776$	7.25131	+	12.5596i	0.260307	+	0.450865i
$777$		0			0
$778$	−27.6875	−	47.9561i	−0.992645	−	1.71931i
$779$	3.77058	+	1.59584i	0.135095	+	0.0571770i
$780$		0			0
$781$	8.89172	+	15.4009i	0.318171	+	0.551088i
$782$	−0.580694	+	1.00579i	−0.0207656	+	0.0359670i
$783$		0			0
$784$	33.2625	−	57.6124i	1.18795	−	2.05758i
$785$	−39.9222			−1.42488
$786$		0			0
$787$	10.9841	+	19.0250i	0.391541	+	0.678169i	0.992653	−	0.120996i	$-0.0386088\pi$
$787$	10.9841	+	19.0250i	0.391541	+	0.678169i	−0.601112	+	0.799165i	$0.705275\pi$
$788$	−3.57332	+	6.18918i	−0.127294	+	0.220480i
$789$		0			0
$790$	35.7352	−	61.8951i	1.27140	−	2.20213i
$791$	70.8801			2.52021
$792$		0			0
$793$	−1.93302	+	3.34810i	−0.0686437	+	0.118894i
$794$	57.2963			2.03337
$795$		0			0
$796$	−0.0184878			−0.000655282
$797$	16.8742	+	29.2269i	0.597713	+	1.03527i	0.993158	+	0.116780i	$0.0372573\pi$
$797$	16.8742	+	29.2269i	0.597713	+	1.03527i	−0.395444	+	0.918490i	$0.629409\pi$
$798$		0			0
$799$	5.43377	−	9.41157i	0.192233	−	0.332957i
$800$	−14.5713	+	25.2382i	−0.515172	+	0.892305i
$801$		0			0
$802$	−0.910589	−	1.57719i	−0.0321540	−	0.0556924i
$803$	1.08019	+	1.87094i	0.0381191	+	0.0660242i
$804$		0			0
$805$	−1.79027	−	3.10084i	−0.0630988	−	0.109290i
$806$	3.31327	+	5.73875i	0.116705	+	0.202139i
$807$		0			0
$808$	5.26582			0.185251
$809$	11.4422			0.402288			0.201144	−	0.979562i	$-0.435534\pi$
$809$	11.4422			0.402288			0.201144	+	0.979562i	$0.435534\pi$
$810$		0			0
$811$	18.0483	+	31.2606i	0.633762	+	1.09771i	0.986776	+	0.162090i	$0.0518235\pi$
$811$	18.0483	+	31.2606i	0.633762	+	1.09771i	−0.353014	+	0.935618i	$0.614843\pi$
$812$	1.13131	+	1.95949i	0.0397012	+	0.0687646i
$813$		0			0
$814$	18.3884			0.644513
$815$	83.0288			2.90837
$816$		0			0
$817$	2.13680	+	17.2530i	0.0747572	+	0.603605i
$818$	−21.5711			−0.754215
$819$		0			0
$820$	−1.02606	+	1.77719i	−0.0358316	+	0.0620621i
$821$	29.8000			1.04003			0.520014	−	0.854158i	$-0.325927\pi$
$821$	29.8000			1.04003			0.520014	+	0.854158i	$0.325927\pi$
$822$		0			0
$823$	1.97734	−	3.42485i	0.0689256	−	0.119383i	−0.829503	−	0.558502i	$-0.811376\pi$
$823$	1.97734	−	3.42485i	0.0689256	−	0.119383i	0.898429	+	0.439120i	$0.144710\pi$
$824$	−8.51534	−	14.7490i	−0.296646	−	0.513806i
$825$		0			0
$826$	−17.6124			−0.612813
$827$	22.5669	+	39.0870i	0.784728	+	1.35919i	0.929161	+	0.369675i	$0.120531\pi$
$827$	22.5669	+	39.0870i	0.784728	+	1.35919i	−0.144433	+	0.989515i	$0.546136\pi$
$828$		0			0
$829$	−37.7440			−1.31090			−0.655452	−	0.755237i	$-0.727522\pi$
$829$	−37.7440			−1.31090			−0.655452	+	0.755237i	$0.727522\pi$
$830$	43.8579			1.52233
$831$		0			0
$832$	1.21528	−	2.10493i	0.0421323	−	0.0729754i
$833$	−47.7089			−1.65302
$834$		0			0
$835$	−24.6104	+	42.6264i	−0.851678	+	1.47515i
$836$	−0.807237	−	6.51780i	−0.0279189	−	0.225423i
$837$		0			0
$838$	3.13369	−	5.42771i	0.108251	−	0.187497i
$839$	−10.4100	−	18.0306i	−0.359392	−	0.622486i	0.628467	−	0.777836i	$-0.283683\pi$
$839$	−10.4100	−	18.0306i	−0.359392	−	0.622486i	−0.987859	+	0.155350i	$0.950349\pi$
$840$		0			0
$841$	−28.2710			−0.974863
$842$	21.8865	−	37.9086i	0.754260	−	1.30642i
$843$		0			0
$844$	6.49221	−	11.2448i	0.223471	−	0.387063i
$845$	−23.8888	−	41.3766i	−0.821799	−	1.42340i
$846$		0			0
$847$	19.5141			0.670511
$848$	27.4418	−	47.5306i	0.942356	−	1.63221i
$849$		0			0
$850$	50.7449			1.74054
$851$	−0.461212	+	0.798842i	−0.0158101	+	0.0273840i
$852$		0			0
$853$	14.2391	+	24.6629i	0.487539	+	0.844442i	0.999897	−	0.0143294i	$-0.00456135\pi$
$853$	14.2391	+	24.6629i	0.487539	+	0.844442i	−0.512358	+	0.858772i	$0.671228\pi$
$854$	−52.6674			−1.80224
$855$		0			0
$856$	19.5166			0.667062
$857$	2.78592	+	4.82535i	0.0951651	+	0.164831i	0.909677	−	0.415315i	$-0.136329\pi$
$857$	2.78592	+	4.82535i	0.0951651	+	0.164831i	−0.814512	+	0.580146i	$0.802995\pi$
$858$		0			0
$859$	3.07779	−	5.33088i	0.105013	−	0.181887i	−0.808731	−	0.588179i	$-0.799845\pi$
$859$	3.07779	−	5.33088i	0.105013	−	0.181887i	0.913743	+	0.406292i	$0.133178\pi$
$860$	−8.71332			−0.297122
$861$		0			0
$862$	32.5783	−	56.4272i	1.10962	−	1.92192i
$863$	−26.1393			−0.889794			−0.444897	−	0.895582i	$-0.646760\pi$
$863$	−26.1393			−0.889794			−0.444897	+	0.895582i	$0.646760\pi$
$864$		0			0
$865$	−23.6409	−	40.9473i	−0.803815	−	1.39225i
$866$	15.0566	−	26.0789i	0.511646	−	0.886196i
$867$		0			0
$868$	−10.1636	+	17.6039i	−0.344975	+	0.597514i
$869$	30.6797			1.04074
$870$		0			0
$871$	0.0754211	+	0.130633i	0.00255555	+	0.00442634i
$872$	11.7681	−	20.3829i	0.398517	−	0.690251i
$873$		0			0
$874$	1.34740	+	0.570267i	0.0455764	+	0.0192896i
$875$	−35.3777	+	61.2760i	−1.19598	+	2.07151i
$876$		0			0
$877$	0.794874			0.0268410			0.0134205	−	0.999910i	$-0.495728\pi$
$877$	0.794874			0.0268410			0.0134205	+	0.999910i	$0.495728\pi$
$878$	13.0967	−	22.6842i	0.441992	−	0.765553i
$879$		0			0
$880$	−47.0110			−1.58474
$881$	−36.2565			−1.22151			−0.610756	−	0.791819i	$-0.709134\pi$
$881$	−36.2565			−1.22151			−0.610756	+	0.791819i	$0.709134\pi$
$882$		0			0
$883$	−27.3417	−	47.3571i	−0.920120	−	1.59369i	−0.799227	−	0.601029i	$-0.794758\pi$
$883$	−27.3417	−	47.3571i	−0.920120	−	1.59369i	−0.120893	−	0.992666i	$-0.538576\pi$
$884$	1.08136			0.0363701
$885$		0			0
$886$	21.2801	+	36.8583i	0.714920	+	1.23828i
$887$	−25.1527	+	43.5658i	−0.844545	+	1.46280i	0.0414702	+	0.999140i	$0.486796\pi$
$887$	−25.1527	+	43.5658i	−0.844545	+	1.46280i	−0.886015	+	0.463656i	$0.846537\pi$
$888$		0			0
$889$	57.5135			1.92894
$890$	19.3483	−	33.5123i	0.648558	−	1.12333i
$891$		0			0
$892$	−3.99174			−0.133653
$893$	−12.6081	−	5.33620i	−0.421914	−	0.178569i
$894$		0			0
$895$	−87.1018			−2.91149
$896$	62.2235			2.07874
$897$		0			0
$898$	−15.4661	−	26.7880i	−0.516109	−	0.893927i
$899$	3.27453	+	5.67166i	0.109212	+	0.189160i
$900$		0			0
$901$	−39.3602			−1.31128
$902$	−3.91212			−0.130259
$903$		0			0
$904$	17.7177	+	30.6880i	0.589284	+	1.02067i
$905$	−7.03013	−	12.1765i	−0.233689	−	0.404762i
$906$		0			0
$907$	6.06193	+	10.4996i	0.201283	+	0.348633i	0.948942	−	0.315450i	$-0.102156\pi$
$907$	6.06193	+	10.4996i	0.201283	+	0.348633i	−0.747659	+	0.664083i	$0.768822\pi$
$908$	−2.58636	−	4.47971i	−0.0858314	−	0.148664i
$909$		0			0
$910$	−7.40280	+	12.8220i	−0.245400	+	0.425046i
$911$	−10.4969	+	18.1811i	−0.347777	+	0.602367i	−0.985854	−	0.167605i	$-0.946397\pi$
$911$	−10.4969	+	18.1811i	−0.347777	+	0.602367i	0.638077	+	0.769972i	$0.279730\pi$
$912$		0			0
$913$	9.41334	+	16.3044i	0.311536	+	0.539596i
$914$	58.6943			1.94144
$915$		0			0
$916$	4.80617			0.158800
$917$	−45.0871	+	78.0932i	−1.48891	+	2.57886i
$918$		0			0
$919$	−5.58553			−0.184250			−0.0921248	−	0.995747i	$-0.529366\pi$
$919$	−5.58553			−0.184250			−0.0921248	+	0.995747i	$0.529366\pi$
$920$	0.895020	−	1.55022i	0.0295079	−	0.0511093i
$921$		0			0
$922$	4.68836	−	8.12048i	0.154403	−	0.267434i
$923$	1.84438	+	3.19455i	0.0607084	+	0.105150i
$924$		0			0
$925$	40.3037			1.32518
$926$	−10.1866	+	17.6437i	−0.334752	+	0.579808i
$927$		0			0
$928$	−1.36286	+	2.36055i	−0.0447382	+	0.0774889i
$929$	10.8938	+	18.8685i	0.357413	+	0.619057i	0.987528	−	0.157445i	$-0.0503257\pi$
$929$	10.8938	+	18.8685i	0.357413	+	0.619057i	−0.630115	+	0.776502i	$0.716992\pi$
$930$		0			0
$931$	7.38742	+	59.6476i	0.242113	+	1.95487i
$932$	−0.388588	−	0.673054i	−0.0127286	−	0.0220466i
$933$		0			0
$934$	19.3308	+	33.4819i	0.632523	+	1.09556i
$935$	16.8571	+	29.1974i	0.551288	+	0.954858i
$936$		0			0
$937$	−23.1526	−	40.1014i	−0.756362	−	1.31006i	−0.944694	−	0.327952i	$-0.893642\pi$
$937$	−23.1526	−	40.1014i	−0.756362	−	1.31006i	0.188333	−	0.982105i	$-0.439692\pi$
$938$	−1.02747	+	1.77962i	−0.0335480	+	0.0581068i
$939$		0			0
$940$	3.43095	−	5.94258i	0.111905	−	0.193826i
$941$	13.1076	−	22.7030i	0.427295	−	0.740097i	−0.569336	−	0.822105i	$-0.692800\pi$
$941$	13.1076	−	22.7030i	0.427295	−	0.740097i	0.996632	+	0.0820075i	$0.0261331\pi$
$942$		0			0
$943$	0.0981225	−	0.169953i	0.00319531	−	0.00553444i
$944$	−5.79997	−	10.0458i	−0.188773	−	0.326965i
$945$		0			0
$946$	−8.30544	−	14.3855i	−0.270033	−	0.467711i
$947$	−17.9942	−	31.1669i	−0.584733	−	1.01279i	−0.994909	−	0.100781i	$-0.967866\pi$
$947$	−17.9942	−	31.1669i	−0.584733	−	1.01279i	0.410175	−	0.912007i	$-0.365468\pi$
$948$		0			0
$949$	0.224060	+	0.388083i	0.00727329	+	0.0125977i
$950$	−7.85753	−	63.4433i	−0.254932	−	2.05837i
$951$		0			0
$952$	−17.9799	−	31.1421i	−0.582733	−	1.00932i
$953$	6.73210	−	11.6603i	0.218074	−	0.377716i	−0.736145	−	0.676824i	$-0.763356\pi$
$953$	6.73210	−	11.6603i	0.218074	−	0.377716i	0.954219	+	0.299108i	$0.0966892\pi$
$954$		0			0
$955$	−27.7338	+	48.0363i	−0.897444	+	1.55442i
$956$	3.95461			0.127901
$957$		0			0
$958$	−4.02563	−	6.97260i	−0.130062	−	0.225274i
$959$	−26.7065	+	46.2570i	−0.862397	+	1.49372i
$960$		0			0
$961$	−13.9181	+	24.1069i	−0.448971	+	0.777641i
$962$	3.81423			0.122976
$963$		0			0
$964$	−2.15679	+	3.73567i	−0.0694655	+	0.120318i
$965$	21.3344			0.686779
$966$		0			0
$967$	12.6766			0.407653			0.203826	−	0.979007i	$-0.434662\pi$
$967$	12.6766			0.407653			0.203826	+	0.979007i	$0.434662\pi$
$968$	4.87789	+	8.44875i	0.156781	+	0.271553i
$969$		0			0
$970$	19.2110	−	33.2745i	0.616829	−	1.06838i
$971$	−5.76415	+	9.98379i	−0.184980	+	0.320395i	−0.943570	−	0.331174i	$-0.892555\pi$
$971$	−5.76415	+	9.98379i	−0.184980	+	0.320395i	0.758590	+	0.651569i	$0.225889\pi$
$972$		0			0
$973$	40.6711	+	70.4445i	1.30386	+	2.25835i
$974$	−25.3106	−	43.8392i	−0.811004	−	1.40470i
$975$		0			0
$976$	−17.3440	−	30.0407i	−0.555168	−	0.961580i
$977$	19.0964	+	33.0759i	0.610947	+	1.05819i	0.991081	+	0.133260i	$0.0425446\pi$
$977$	19.0964	+	33.0759i	0.610947	+	1.05819i	−0.380134	+	0.924932i	$0.624122\pi$
$978$		0			0
$979$	16.6111			0.530895
$980$	−30.1240			−0.962276
$981$		0			0
$982$	−24.5868	−	42.5857i	−0.784598	−	1.35896i
$983$	−7.91585	−	13.7107i	−0.252476	−	0.437302i	0.711731	−	0.702453i	$-0.247912\pi$
$983$	−7.91585	−	13.7107i	−0.252476	−	0.437302i	−0.964207	+	0.265150i	$0.914578\pi$
$984$		0			0
$985$	−46.2178			−1.47262
$986$	4.74621			0.151150
$987$		0			0
$988$	−0.167442	−	1.35196i	−0.00532704	−	0.0430117i
$989$	0.833258			0.0264961
$990$		0			0
$991$	−10.1647	+	17.6058i	−0.322893	+	0.559267i	−0.981084	−	0.193584i	$-0.937989\pi$
$991$	−10.1647	+	17.6058i	−0.322893	+	0.559267i	0.658191	+	0.752851i	$0.271322\pi$
$992$	−24.4877			−0.777485
$993$		0			0
$994$	−25.1260	+	43.5196i	−0.796950	+	1.38036i
$995$	−0.0597808	−	0.103543i	−0.00189518	−	0.00328255i
$996$		0			0
$997$	36.2674			1.14860			0.574300	−	0.818645i	$-0.305274\pi$
$997$	36.2674			1.14860			0.574300	+	0.818645i	$0.305274\pi$
$998$	−8.77527	−	15.1992i	−0.277776	−	0.481123i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.c.505.12		32
3.2	odd	2		171.2.g.c.106.5	✓	32
9.4	even	3		513.2.h.c.334.5		32
9.5	odd	6		171.2.h.c.49.12	yes	32
19.7	even	3		513.2.h.c.235.5		32
57.26	odd	6		171.2.h.c.7.12	yes	32
171.121	even	3	inner	513.2.g.c.64.12		32
171.140	odd	6		171.2.g.c.121.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.5	✓	32	3.2	odd	2
171.2.g.c.121.5	yes	32	171.140	odd	6
171.2.h.c.7.12	yes	32	57.26	odd	6
171.2.h.c.49.12	yes	32	9.5	odd	6
513.2.g.c.64.12		32	171.121	even	3	inner
513.2.g.c.505.12		32	1.1	even	1	trivial
513.2.h.c.235.5		32	19.7	even	3
513.2.h.c.334.5		32	9.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.803309 + 1.39137i) q^{2} +(-0.290611 + 0.503353i) q^{4} -3.75880 q^{5} +(2.27973 - 3.94861i) q^{7} +2.27943 q^{8} +(-3.01948 - 5.22989i) q^{10} +(1.29616 - 2.24501i) q^{11} +(0.268857 - 0.465674i) q^{13} +7.32531 q^{14} +(2.41231 + 4.17825i) q^{16} +(1.73001 - 2.99646i) q^{17} +(-4.01417 - 1.69894i) q^{19} +(1.09235 - 1.89200i) q^{20} +4.16486 q^{22} +(-0.104462 + 0.180933i) q^{23} +9.12855 q^{25} +0.863901 q^{26} +(1.32503 + 2.29502i) q^{28} +0.853801 q^{29} +(3.83524 + 6.64283i) q^{31} +(-1.59623 + 2.76475i) q^{32} +5.55892 q^{34} +(-8.56903 + 14.8420i) q^{35} +4.41513 q^{37} +(-0.860764 - 6.94999i) q^{38} -8.56793 q^{40} -0.939316 q^{41} +(-1.99417 - 3.45401i) q^{43} +(0.753355 + 1.30485i) q^{44} -0.335660 q^{46} +3.14090 q^{47} +(-6.89432 - 11.9413i) q^{49} +(7.33305 + 12.7012i) q^{50} +(0.156266 + 0.270660i) q^{52} +(-5.68786 - 9.85167i) q^{53} +(-4.87199 + 8.43853i) q^{55} +(5.19649 - 9.00059i) q^{56} +(0.685866 + 1.18796i) q^{58} -2.40432 q^{59} -7.18979 q^{61} +(-6.16176 + 10.6725i) q^{62} +4.52018 q^{64} +(-1.01058 + 1.75037i) q^{65} +(-0.140263 + 0.242942i) q^{67} +(1.00552 + 1.74161i) q^{68} -27.5343 q^{70} +(-3.43003 + 5.94099i) q^{71} +(-0.416690 + 0.721728i) q^{73} +(3.54671 + 6.14309i) q^{74} +(2.02173 - 1.52682i) q^{76} +(-5.90977 - 10.2360i) q^{77} +(5.91744 + 10.2493i) q^{79} +(-9.06739 - 15.7052i) q^{80} +(-0.754561 - 1.30694i) q^{82} +(-3.63125 + 6.28951i) q^{83} +(-6.50274 + 11.2631i) q^{85} +(3.20387 - 5.54927i) q^{86} +(2.95450 - 5.11735i) q^{88} +(3.20392 + 5.54936i) q^{89} +(-1.22584 - 2.12322i) q^{91} +(-0.0607154 - 0.105162i) q^{92} +(2.52311 + 4.37015i) q^{94} +(15.0885 + 6.38597i) q^{95} +(3.18119 + 5.50998i) q^{97} +(11.0765 - 19.1851i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Introduction

L-functions

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Database

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