LMFDB - Embedded newform 513.2.h.c.334.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(235,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("513.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.h (of order $3$, degree $2$, not 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:	$4.09632562369$
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			334.2
Character	$\chi$	$=$	513.334
Dual form			513.2.h.c.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09768 q^{2} +2.40028 q^{4} +(-1.44796 - 2.50795i) q^{5} +(0.116480 + 0.201749i) q^{7} -0.839660 q^{8} +O(q^{10})$	\(q-2.09768 q^{2} +2.40028 q^{4} +(-1.44796 - 2.50795i) q^{5} +(0.116480 + 0.201749i) q^{7} -0.839660 q^{8} +(3.03737 + 5.26088i) q^{10} +(1.99611 + 3.45736i) q^{11} +3.83588 q^{13} +(-0.244338 - 0.423206i) q^{14} -3.03922 q^{16} +(-0.0780996 + 0.135272i) q^{17} +(-1.94973 - 3.89853i) q^{19} +(-3.47552 - 6.01977i) q^{20} +(-4.18721 - 7.25245i) q^{22} +0.942219 q^{23} +(-1.69320 + 2.93270i) q^{25} -8.04647 q^{26} +(0.279585 + 0.484255i) q^{28} +(1.62851 - 2.82066i) q^{29} +(2.40142 - 4.15938i) q^{31} +8.05464 q^{32} +(0.163828 - 0.283759i) q^{34} +(0.337318 - 0.584251i) q^{35} -11.1188 q^{37} +(4.08992 + 8.17789i) q^{38} +(1.21580 + 2.10582i) q^{40} +(0.0537438 + 0.0930869i) q^{41} +10.9595 q^{43} +(4.79122 + 8.29864i) q^{44} -1.97648 q^{46} +(3.39588 - 5.88185i) q^{47} +(3.47286 - 6.01518i) q^{49} +(3.55179 - 6.15189i) q^{50} +9.20719 q^{52} +(-4.03453 - 6.98802i) q^{53} +(5.78059 - 10.0123i) q^{55} +(-0.0978037 - 0.169401i) q^{56} +(-3.41610 + 5.91685i) q^{58} +(-5.74337 - 9.94781i) q^{59} +(-2.49285 + 4.31775i) q^{61} +(-5.03742 + 8.72506i) q^{62} -10.8177 q^{64} +(-5.55422 - 9.62019i) q^{65} +7.13847 q^{67} +(-0.187461 + 0.324692i) q^{68} +(-0.707586 + 1.22557i) q^{70} +(3.33230 - 5.77171i) q^{71} +(5.38628 - 9.32931i) q^{73} +23.3236 q^{74} +(-4.67990 - 9.35757i) q^{76} +(-0.465014 + 0.805427i) q^{77} -16.2165 q^{79} +(4.40068 + 7.62219i) q^{80} +(-0.112737 - 0.195267i) q^{82} +(5.46298 + 9.46217i) q^{83} +0.452341 q^{85} -22.9895 q^{86} +(-1.67605 - 2.90301i) q^{88} +(-1.25911 - 2.18084i) q^{89} +(0.446804 + 0.773887i) q^{91} +2.26159 q^{92} +(-7.12349 + 12.3383i) q^{94} +(-6.95417 + 10.5348i) q^{95} +2.08738 q^{97} +(-7.28497 + 12.6179i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.09768			−1.48329			−0.741643	−	0.670794i	$-0.765953\pi$
$2$	−2.09768			−1.48329			−0.741643	+	0.670794i	$0.765953\pi$
$3$		0			0
$3$		0			0
$4$	2.40028			1.20014
$5$	−1.44796	−	2.50795i	−0.647549	−	1.12159i	−0.983706	−	0.179782i	$-0.942461\pi$
$5$	−1.44796	−	2.50795i	−0.647549	−	1.12159i	0.336157	−	0.941806i	$-0.390873\pi$
$6$		0			0
$7$	0.116480	+	0.201749i	0.0440253	+	0.0762541i	0.887198	−	0.461388i	$-0.152648\pi$
$7$	0.116480	+	0.201749i	0.0440253	+	0.0762541i	−0.843173	+	0.537642i	$0.819315\pi$
$8$	−0.839660			−0.296865
$9$		0			0
$10$	3.03737	+	5.26088i	0.960501	+	1.66364i
$11$	1.99611	+	3.45736i	0.601849	+	1.04243i	0.992541	+	0.121912i	$0.0389026\pi$
$11$	1.99611	+	3.45736i	0.601849	+	1.04243i	−0.390691	+	0.920522i	$0.627764\pi$
$12$		0			0
$13$	3.83588			1.06388			0.531941	−	0.846781i	$-0.321463\pi$
$13$	3.83588			1.06388			0.531941	+	0.846781i	$0.321463\pi$
$14$	−0.244338	−	0.423206i	−0.0653022	−	0.113107i
$15$		0			0
$16$	−3.03922			−0.759804
$17$	−0.0780996	+	0.135272i	−0.0189419	+	0.0328084i	−0.875341	−	0.483506i	$-0.839363\pi$
$17$	−0.0780996	+	0.135272i	−0.0189419	+	0.0328084i	0.856399	+	0.516314i	$0.172696\pi$
$18$		0			0
$19$	−1.94973	−	3.89853i	−0.447299	−	0.894384i
$19$	−1.94973	−	3.89853i	−0.447299	−	0.894384i
$20$	−3.47552	−	6.01977i	−0.777149	−	1.34606i
$21$		0			0
$22$	−4.18721	−	7.25245i	−0.892715	−	1.54623i
$23$	0.942219			0.196466			0.0982331	−	0.995163i	$-0.468681\pi$
$23$	0.942219			0.196466			0.0982331	+	0.995163i	$0.468681\pi$
$24$		0			0
$25$	−1.69320	+	2.93270i	−0.338640	+	0.586541i
$26$	−8.04647			−1.57804
$27$		0			0
$28$	0.279585	+	0.484255i	0.0528365	+	0.0915156i
$29$	1.62851	−	2.82066i	0.302406	−	0.523783i	−0.674274	−	0.738481i	$-0.735543\pi$
$29$	1.62851	−	2.82066i	0.302406	−	0.523783i	0.976681	+	0.214698i	$0.0688767\pi$
$30$		0			0
$31$	2.40142	−	4.15938i	0.431307	−	0.747046i	−0.565679	−	0.824626i	$-0.691386\pi$
$31$	2.40142	−	4.15938i	0.431307	−	0.747046i	0.996986	+	0.0775795i	$0.0247191\pi$
$32$	8.05464			1.42387
$33$		0			0
$34$	0.163828	−	0.283759i	0.0280963	−	0.0486642i
$35$	0.337318	−	0.584251i	0.0570171	−	0.0987565i
$36$		0			0
$37$	−11.1188			−1.82791			−0.913956	−	0.405814i	$-0.866988\pi$
$37$	−11.1188			−1.82791			−0.913956	+	0.405814i	$0.866988\pi$
$38$	4.08992	+	8.17789i	0.663473	+	1.32663i
$39$		0			0
$40$	1.21580	+	2.10582i	0.192234	+	0.332960i
$41$	0.0537438	+	0.0930869i	0.00839337	+	0.0145377i	0.870192	−	0.492714i	$-0.163995\pi$
$41$	0.0537438	+	0.0930869i	0.00839337	+	0.0145377i	−0.861798	+	0.507251i	$0.830662\pi$
$42$		0			0
$43$	10.9595			1.67131			0.835653	−	0.549258i	$-0.185090\pi$
$43$	10.9595			1.67131			0.835653	+	0.549258i	$0.185090\pi$
$44$	4.79122	+	8.29864i	0.722304	+	1.25107i
$45$		0			0
$46$	−1.97648			−0.291416
$47$	3.39588	−	5.88185i	0.495341	−	0.857955i	−0.504645	−	0.863327i	$-0.668377\pi$
$47$	3.39588	−	5.88185i	0.495341	−	0.857955i	0.999986	+	0.00537174i	$0.00170989\pi$
$48$		0			0
$49$	3.47286	−	6.01518i	0.496124	−	0.859311i
$50$	3.55179	−	6.15189i	0.502300	−	0.870008i
$51$		0			0
$52$	9.20719			1.27681
$53$	−4.03453	−	6.98802i	−0.554186	−	0.959878i	−0.997966	−	0.0637424i	$-0.979696\pi$
$53$	−4.03453	−	6.98802i	−0.554186	−	0.959878i	0.443781	−	0.896135i	$-0.353637\pi$
$54$		0			0
$55$	5.78059	−	10.0123i	0.779454	−	1.35005i
$56$	−0.0978037	−	0.169401i	−0.0130696	−	0.0226371i
$57$		0			0
$58$	−3.41610	+	5.91685i	−0.448555	+	0.776921i
$59$	−5.74337	−	9.94781i	−0.747723	−	1.29509i	−0.948912	−	0.315542i	$-0.897814\pi$
$59$	−5.74337	−	9.94781i	−0.747723	−	1.29509i	0.201189	−	0.979553i	$-0.435520\pi$
$60$		0			0
$61$	−2.49285	+	4.31775i	−0.319177	+	0.552831i	−0.980317	−	0.197432i	$-0.936740\pi$
$61$	−2.49285	+	4.31775i	−0.319177	+	0.552831i	0.661139	+	0.750263i	$0.270073\pi$
$62$	−5.03742	+	8.72506i	−0.639752	+	1.10808i
$63$		0			0
$64$	−10.8177			−1.35221
$65$	−5.55422	−	9.62019i	−0.688916	−	1.19324i
$66$		0			0
$67$	7.13847			0.872102			0.436051	−	0.899922i	$-0.356377\pi$
$67$	7.13847			0.872102			0.436051	+	0.899922i	$0.356377\pi$
$68$	−0.187461	+	0.324692i	−0.0227330	+	0.0393747i
$69$		0			0
$70$	−0.707586	+	1.22557i	−0.0845727	+	0.146484i
$71$	3.33230	−	5.77171i	0.395471	−	0.684976i	−0.597690	−	0.801727i	$-0.703915\pi$
$71$	3.33230	−	5.77171i	0.395471	−	0.684976i	0.993161	+	0.116751i	$0.0372480\pi$
$72$		0			0
$73$	5.38628	−	9.32931i	0.630416	−	1.09191i	−0.357051	−	0.934085i	$-0.616218\pi$
$73$	5.38628	−	9.32931i	0.630416	−	1.09191i	0.987467	−	0.157828i	$-0.0504490\pi$
$74$	23.3236			2.71132
$75$		0			0
$76$	−4.67990	−	9.35757i	−0.536821	−	1.07339i
$77$	−0.465014	+	0.805427i	−0.0529932	+	0.0917869i
$78$		0			0
$79$	−16.2165			−1.82450			−0.912252	−	0.409630i	$-0.865658\pi$
$79$	−16.2165			−1.82450			−0.912252	+	0.409630i	$0.865658\pi$
$80$	4.40068	+	7.62219i	0.492011	+	0.852187i
$81$		0			0
$82$	−0.112737	−	0.195267i	−0.0124498	−	0.0215636i
$83$	5.46298	+	9.46217i	0.599640	+	1.03861i	0.992874	+	0.119169i	$0.0380230\pi$
$83$	5.46298	+	9.46217i	0.599640	+	1.03861i	−0.393234	+	0.919439i	$0.628644\pi$
$84$		0			0
$85$	0.452341			0.0490633
$86$	−22.9895			−2.47903
$87$		0			0
$88$	−1.67605	−	2.90301i	−0.178668	−	0.309462i
$89$	−1.25911	−	2.18084i	−0.133465	−	0.231169i	0.791545	−	0.611111i	$-0.209277\pi$
$89$	−1.25911	−	2.18084i	−0.133465	−	0.231169i	−0.925010	+	0.379942i	$0.875944\pi$
$90$		0			0
$91$	0.446804	+	0.773887i	0.0468378	+	0.0811254i
$92$	2.26159			0.235787
$93$		0			0
$94$	−7.12349	+	12.3383i	−0.734732	+	1.27259i
$95$	−6.95417	+	10.5348i	−0.713483	+	1.08084i
$96$		0			0
$97$	2.08738			0.211942			0.105971	−	0.994369i	$-0.466205\pi$
$97$	2.08738			0.211942			0.105971	+	0.994369i	$0.466205\pi$
$98$	−7.28497	+	12.6179i	−0.735894	+	1.27460i
$99$		0			0
$100$	−4.06415	+	7.03931i	−0.406415	+	0.703931i
$101$	7.17324	−	12.4244i	0.713764	−	1.23627i	−0.249671	−	0.968331i	$-0.580322\pi$
$101$	7.17324	−	12.4244i	0.713764	−	1.23627i	0.963434	−	0.267944i	$-0.0863442\pi$
$102$		0			0
$103$	−4.99968	+	8.65971i	−0.492633	+	0.853266i	−0.999964	−	0.00848542i	$-0.997299\pi$
$103$	−4.99968	+	8.65971i	−0.492633	+	0.853266i	0.507331	+	0.861752i	$0.330632\pi$
$104$	−3.22084			−0.315829
$105$		0			0
$106$	8.46318	+	14.6587i	0.822016	+	1.42377i
$107$	14.9853			1.44869			0.724343	−	0.689440i	$-0.242143\pi$
$107$	14.9853			1.44869			0.724343	+	0.689440i	$0.242143\pi$
$108$		0			0
$109$	−4.14328	+	7.17637i	−0.396854	+	0.687371i	−0.993336	−	0.115255i	$-0.963231\pi$
$109$	−4.14328	+	7.17637i	−0.396854	+	0.687371i	0.596482	+	0.802627i	$0.296565\pi$
$110$	−12.1258	+	21.0026i	−1.15615	+	2.00252i
$111$		0			0
$112$	−0.354008	−	0.613160i	−0.0334506	−	0.0579382i
$113$	−2.80310	+	4.85511i	−0.263693	+	0.456730i	−0.967220	−	0.253938i	$-0.918274\pi$
$113$	−2.80310	+	4.85511i	−0.263693	+	0.456730i	0.703527	+	0.710668i	$0.251607\pi$
$114$		0			0
$115$	−1.36430	−	2.36303i	−0.127221	−	0.220354i
$116$	3.90888	−	6.77037i	0.362930	−	0.628613i
$117$		0			0
$118$	12.0478	+	20.8674i	1.10909	+	1.92100i
$119$	−0.0363882			−0.00333570
$120$		0			0
$121$	−2.46890	+	4.27626i	−0.224446	+	0.388751i
$122$	5.22922	−	9.05727i	0.473431	−	0.820007i
$123$		0			0
$124$	5.76407	−	9.98367i	0.517629	−	0.896560i
$125$	−4.67288			−0.417955
$126$		0			0
$127$	0.496673	+	0.860264i	0.0440726	+	0.0763361i	0.887220	−	0.461346i	$-0.152633\pi$
$127$	0.496673	+	0.860264i	0.0440726	+	0.0763361i	−0.843148	+	0.537682i	$0.819300\pi$
$128$	6.58275			0.581838
$129$		0			0
$130$	11.6510	+	20.1801i	1.02186	+	1.76991i
$131$	−2.25839	−	3.91164i	−0.197316	−	0.341761i	0.750341	−	0.661051i	$-0.229889\pi$
$131$	−2.25839	−	3.91164i	−0.197316	−	0.341761i	−0.947657	+	0.319289i	$0.896556\pi$
$132$		0			0
$133$	0.559421	−	0.847458i	0.0485080	−	0.0734839i
$134$	−14.9742			−1.29358
$135$		0			0
$136$	0.0655771	−	0.113583i	0.00562319	−	0.00973965i
$137$	−9.48849	+	16.4345i	−0.810656	+	1.40410i	0.101749	+	0.994810i	$0.467556\pi$
$137$	−9.48849	+	16.4345i	−0.810656	+	1.40410i	−0.912405	+	0.409288i	$0.865777\pi$
$138$		0			0
$139$	2.31700			0.196525			0.0982626	−	0.995161i	$-0.468671\pi$
$139$	2.31700			0.196525			0.0982626	+	0.995161i	$0.468671\pi$
$140$	0.809657	−	1.40237i	0.0684285	−	0.118522i
$141$		0			0
$142$	−6.99011	+	12.1072i	−0.586597	+	1.01602i
$143$	7.65684	+	13.2620i	0.640297	+	1.10903i
$144$		0			0
$145$	−9.43208			−0.783292
$146$	−11.2987	+	19.5699i	−0.935088	+	1.61962i
$147$		0			0
$148$	−26.6881			−2.19375
$149$	3.18224	+	5.51181i	0.260699	+	0.451545i	0.966428	−	0.256938i	$-0.0827135\pi$
$149$	3.18224	+	5.51181i	0.260699	+	0.451545i	−0.705729	+	0.708482i	$0.749380\pi$
$150$		0			0
$151$	−8.60251	−	14.9000i	−0.700062	−	1.21254i	−0.968444	−	0.249231i	$-0.919822\pi$
$151$	−8.60251	−	14.9000i	−0.700062	−	1.21254i	0.268382	−	0.963313i	$-0.413511\pi$
$152$	1.63711	+	3.27344i	0.132787	+	0.265511i
$153$		0			0
$154$	0.975452	−	1.68953i	0.0786041	−	0.136146i
$155$	−13.9087			−1.11717
$156$		0			0
$157$	6.74714	+	11.6864i	0.538480	+	0.932675i	0.998986	+	0.0450187i	$0.0143347\pi$
$157$	6.74714	+	11.6864i	0.538480	+	0.932675i	−0.460506	+	0.887657i	$0.652332\pi$
$158$	34.0172			2.70626
$159$		0			0
$160$	−11.6628	−	20.2006i	−0.922027	−	1.59700i
$161$	0.109750	+	0.190092i	0.00864949	+	0.0149813i
$162$		0			0
$163$	17.6579			1.38308			0.691538	−	0.722340i	$-0.256934\pi$
$163$	17.6579			1.38308			0.691538	+	0.722340i	$0.256934\pi$
$164$	0.129000	+	0.223435i	0.0100732	+	0.0174473i
$165$		0			0
$166$	−11.4596	−	19.8486i	−0.889439	−	1.54055i
$167$	−9.33365			−0.722260			−0.361130	−	0.932516i	$-0.617609\pi$
$167$	−9.33365			−0.722260			−0.361130	+	0.932516i	$0.617609\pi$
$168$		0			0
$169$	1.71400			0.131846
$170$	−0.948870			−0.0727750
$171$		0			0
$172$	26.3058			2.00580
$173$	10.0127			0.761253			0.380627	−	0.924729i	$-0.375708\pi$
$173$	10.0127			0.761253			0.380627	+	0.924729i	$0.375708\pi$
$174$		0			0
$175$	−0.788895			−0.0596348
$176$	−6.06661	−	10.5077i	−0.457288	−	0.792046i
$177$		0			0
$178$	2.64121	+	4.57472i	0.197967	+	0.342890i
$179$	1.07944			0.0806809			0.0403404	−	0.999186i	$-0.487156\pi$
$179$	1.07944			0.0806809			0.0403404	+	0.999186i	$0.487156\pi$
$180$		0			0
$181$	2.63111	+	4.55721i	0.195569	+	0.338735i	0.947087	−	0.320978i	$-0.104011\pi$
$181$	2.63111	+	4.55721i	0.195569	+	0.338735i	−0.751518	+	0.659712i	$0.770678\pi$
$182$	−0.937253	−	1.62337i	−0.0694738	−	0.120332i
$183$		0			0
$184$	−0.791144			−0.0583239
$185$	16.0996	+	27.8852i	1.18366	+	2.05016i
$186$		0			0
$187$	−0.623581			−0.0456008
$188$	8.15107	−	14.1181i	0.594478	−	1.02967i
$189$		0			0
$190$	14.5877	−	22.0986i	1.05830	−	1.60320i
$191$	1.40254	+	2.42927i	0.101484	+	0.175776i	0.912296	−	0.409531i	$-0.134308\pi$
$191$	1.40254	+	2.42927i	0.101484	+	0.175776i	−0.810812	+	0.585306i	$0.800974\pi$
$192$		0			0
$193$	1.87807	+	3.25291i	0.135186	+	0.234150i	0.925669	−	0.378335i	$-0.123503\pi$
$193$	1.87807	+	3.25291i	0.135186	+	0.234150i	−0.790482	+	0.612485i	$0.790170\pi$
$194$	−4.37867			−0.314370
$195$		0			0
$196$	8.33585	−	14.4381i	0.595418	−	1.03129i
$197$	−1.68702			−0.120195			−0.0600975	−	0.998193i	$-0.519141\pi$
$197$	−1.68702			−0.120195			−0.0600975	+	0.998193i	$0.519141\pi$
$198$		0			0
$199$	−5.27449	−	9.13569i	−0.373899	−	0.647612i	0.616263	−	0.787541i	$-0.288646\pi$
$199$	−5.27449	−	9.13569i	−0.373899	−	0.647612i	−0.990162	+	0.139929i	$0.955313\pi$
$200$	1.42171	−	2.46248i	0.100530	−	0.174123i
$201$		0			0
$202$	−15.0472	+	26.0625i	−1.05872	+	1.83375i
$203$	0.758755			0.0532541
$204$		0			0
$205$	0.155638	−	0.269573i	0.0108702	−	0.0188278i
$206$	10.4878	−	18.1653i	0.730717	−	1.26564i
$207$		0			0
$208$	−11.6581			−0.808342
$209$	9.58676	−	14.5228i	0.663130	−	1.00456i
$210$		0			0
$211$	0.969377	+	1.67901i	0.0667347	+	0.115588i	0.897462	−	0.441091i	$-0.145409\pi$
$211$	0.969377	+	1.67901i	0.0667347	+	0.115588i	−0.830727	+	0.556679i	$0.812075\pi$
$212$	−9.68401	−	16.7732i	−0.665100	−	1.15199i
$213$		0			0
$214$	−31.4345			−2.14882
$215$	−15.8689	−	27.4858i	−1.08225	−	1.87452i
$216$		0			0
$217$	1.11887			0.0759538
$218$	8.69129	−	15.0538i	0.588648	−	1.01957i
$219$		0			0
$220$	13.8750	−	24.0322i	0.935454	−	1.62025i
$221$	−0.299581	+	0.518889i	−0.0201520	+	0.0349043i
$222$		0			0
$223$	26.8854			1.80038			0.900188	−	0.435501i	$-0.143429\pi$
$223$	26.8854			1.80038			0.900188	+	0.435501i	$0.143429\pi$
$224$	0.938204	+	1.62502i	0.0626864	+	0.108576i
$225$		0			0
$226$	5.88002	−	10.1845i	0.391133	−	0.677462i
$227$	−14.0953	−	24.4137i	−0.935536	−	1.62040i	−0.773675	−	0.633583i	$-0.781584\pi$
$227$	−14.0953	−	24.4137i	−0.935536	−	1.62040i	−0.161861	−	0.986814i	$-0.551750\pi$
$228$		0			0
$229$	5.73812	−	9.93871i	0.379185	−	0.656768i	−0.611758	−	0.791045i	$-0.709538\pi$
$229$	5.73812	−	9.93871i	0.379185	−	0.656768i	0.990944	+	0.134276i	$0.0428709\pi$
$230$	2.86187	+	4.95690i	0.188706	+	0.326848i
$231$		0			0
$232$	−1.36739	+	2.36840i	−0.0897738	+	0.155493i
$233$	−8.82310	+	15.2821i	−0.578021	+	1.00116i	0.417686	+	0.908592i	$0.362841\pi$
$233$	−8.82310	+	15.2821i	−0.578021	+	1.00116i	−0.995706	+	0.0925695i	$0.970492\pi$
$234$		0			0
$235$	−19.6685			−1.28303
$236$	−13.7857	−	23.8775i	−0.897372	−	1.55429i
$237$		0			0
$238$	0.0763309			0.00494780
$239$	5.38677	−	9.33017i	0.348441	−	0.603518i	−0.637531	−	0.770424i	$-0.720044\pi$
$239$	5.38677	−	9.33017i	0.348441	−	0.603518i	0.985973	+	0.166906i	$0.0533777\pi$
$240$		0			0
$241$	3.84999	−	6.66838i	0.248000	−	0.429548i	−0.714971	−	0.699154i	$-0.753560\pi$
$241$	3.84999	−	6.66838i	0.248000	−	0.429548i	0.962971	+	0.269606i	$0.0868934\pi$
$242$	5.17898	−	8.97025i	0.332917	−	0.576629i
$243$		0			0
$244$	−5.98354	+	10.3638i	−0.383057	+	0.663474i
$245$	−20.1143			−1.28506
$246$		0			0
$247$	−7.47894	−	14.9543i	−0.475874	−	0.951520i
$248$	−2.01637	+	3.49246i	−0.128040	+	0.221772i
$249$		0			0
$250$	9.80223			0.619948
$251$	6.55110	+	11.3468i	0.413502	+	0.716206i	0.995270	−	0.0971489i	$-0.0309723\pi$
$251$	6.55110	+	11.3468i	0.413502	+	0.716206i	−0.581768	+	0.813355i	$0.697639\pi$
$252$		0			0
$253$	1.88077	+	3.25759i	0.118243	+	0.204803i
$254$	−1.04186	−	1.80456i	−0.0653724	−	0.113228i
$255$		0			0
$256$	7.82678			0.489174
$257$	15.3304			0.956282			0.478141	−	0.878283i	$-0.341311\pi$
$257$	15.3304			0.956282			0.478141	+	0.878283i	$0.341311\pi$
$258$		0			0
$259$	−1.29511	−	2.24320i	−0.0804744	−	0.139386i
$260$	−13.3317	−	23.0911i	−0.826796	−	1.43205i
$261$		0			0
$262$	4.73738	+	8.20538i	0.292676	+	0.506930i
$263$	15.5237			0.957235			0.478618	−	0.878023i	$-0.341138\pi$
$263$	15.5237			0.957235			0.478618	+	0.878023i	$0.341138\pi$
$264$		0			0
$265$	−11.6837	+	20.2368i	−0.717725	+	1.24314i
$266$	−1.17349	+	1.77770i	−0.0719513	+	0.108998i
$267$		0			0
$268$	17.1343			1.04664
$269$	−8.94841	+	15.4991i	−0.545594	+	0.944996i	0.452975	+	0.891523i	$0.350363\pi$
$269$	−8.94841	+	15.4991i	−0.545594	+	0.944996i	−0.998569	+	0.0534733i	$0.982971\pi$
$270$		0			0
$271$	7.63638	−	13.2266i	0.463877	−	0.803458i	−0.535273	−	0.844679i	$-0.679791\pi$
$271$	7.63638	−	13.2266i	0.463877	−	0.803458i	0.999150	+	0.0412207i	$0.0131247\pi$
$272$	0.237362	−	0.411122i	0.0143922	−	0.0249280i
$273$		0			0
$274$	19.9039	−	34.4745i	1.20244	−	2.08268i
$275$	−13.5192			−0.815240
$276$		0			0
$277$	−1.57024	−	2.71974i	−0.0943468	−	0.163413i	0.814989	−	0.579476i	$-0.196743\pi$
$277$	−1.57024	−	2.71974i	−0.0943468	−	0.163413i	−0.909336	+	0.416063i	$0.863410\pi$
$278$	−4.86033			−0.291503
$279$		0			0
$280$	−0.283232	+	0.490573i	−0.0169264	+	0.0293173i
$281$	−6.43313	+	11.1425i	−0.383768	+	0.664706i	−0.991597	−	0.129362i	$-0.958707\pi$
$281$	−6.43313	+	11.1425i	−0.383768	+	0.664706i	0.607829	+	0.794068i	$0.292041\pi$
$282$		0			0
$283$	12.5986	+	21.8214i	0.748909	+	1.29715i	0.948346	+	0.317238i	$0.102755\pi$
$283$	12.5986	+	21.8214i	0.748909	+	1.29715i	−0.199437	+	0.979911i	$0.563911\pi$
$284$	7.99845	−	13.8537i	0.474621	−	0.822067i
$285$		0			0
$286$	−16.0616	−	27.8196i	−0.949744	−	1.64501i
$287$	−0.0125202	+	0.0216855i	−0.000739041	+	0.00128006i
$288$		0			0
$289$	8.48780	+	14.7013i	0.499282	+	0.864782i
$290$	19.7855			1.16185
$291$		0			0
$292$	12.9286	−	22.3929i	0.756587	−	1.31045i
$293$	−6.70012	+	11.6049i	−0.391425	+	0.677968i	−0.992638	−	0.121121i	$-0.961351\pi$
$293$	−6.70012	+	11.6049i	−0.391425	+	0.677968i	0.601213	+	0.799089i	$0.294684\pi$
$294$		0			0
$295$	−16.6324	+	28.8081i	−0.968375	+	1.67727i
$296$	9.33598			0.542643
$297$		0			0
$298$	−6.67534	−	11.5620i	−0.386692	−	0.669770i
$299$	3.61424			0.209017
$300$		0			0
$301$	1.27656	+	2.21107i	0.0735797	+	0.127444i
$302$	18.0453	+	31.2555i	1.03839	+	1.79855i
$303$		0			0
$304$	5.92566	+	11.8485i	0.339860	+	0.679557i
$305$	14.4382			0.826731
$306$		0			0
$307$	−0.844211	+	1.46222i	−0.0481817	+	0.0834531i	−0.889110	−	0.457693i	$-0.848676\pi$
$307$	−0.844211	+	1.46222i	−0.0481817	+	0.0834531i	0.840929	+	0.541146i	$0.182009\pi$
$308$	−1.11616	+	1.93325i	−0.0635993	+	0.110157i
$309$		0			0
$310$	29.1760			1.65708
$311$	8.88963	−	15.3973i	0.504085	−	0.873100i	−0.495904	−	0.868377i	$-0.665163\pi$
$311$	8.88963	−	15.3973i	0.504085	−	0.873100i	0.999989	−	0.00472299i	$-0.00150338\pi$
$312$		0			0
$313$	−3.66578	+	6.34932i	−0.207202	+	0.358885i	−0.950832	−	0.309707i	$-0.899769\pi$
$313$	−3.66578	+	6.34932i	−0.207202	+	0.358885i	0.743630	+	0.668591i	$0.233102\pi$
$314$	−14.1534	−	24.5144i	−0.798721	−	1.38343i
$315$		0			0
$316$	−38.9242			−2.18966
$317$	−1.58306	+	2.74193i	−0.0889133	+	0.154002i	−0.907052	−	0.421019i	$-0.861673\pi$
$317$	−1.58306	+	2.74193i	−0.0889133	+	0.154002i	0.818139	+	0.575021i	$0.195006\pi$
$318$		0			0
$319$	13.0027			0.728012
$320$	15.6636	+	27.1301i	0.875620	+	1.51662i
$321$		0			0
$322$	−0.230220	−	0.398753i	−0.0128297	−	0.0222216i
$323$	0.679637	+	0.0407288i	0.0378160	+	0.00226621i
$324$		0			0
$325$	−6.49491	+	11.2495i	−0.360273	+	0.624011i
$326$	−37.0408			−2.05150
$327$		0			0
$328$	−0.0451265	−	0.0781614i	−0.00249169	−	0.00431574i
$329$	1.58221			0.0872301
$330$		0			0
$331$	5.29356	+	9.16871i	0.290960	+	0.503958i	0.974037	−	0.226389i	$-0.0726919\pi$
$331$	5.29356	+	9.16871i	0.290960	+	0.503958i	−0.683077	+	0.730347i	$0.739359\pi$
$332$	13.1127	+	22.7118i	0.719652	+	1.24647i
$333$		0			0
$334$	19.5791			1.07132
$335$	−10.3362	−	17.9029i	−0.564729	−	0.978140i
$336$		0			0
$337$	−12.0290	−	20.8349i	−0.655264	−	1.13495i	−0.981828	−	0.189775i	$-0.939224\pi$
$337$	−12.0290	−	20.8349i	−0.655264	−	1.13495i	0.326564	−	0.945175i	$-0.394109\pi$
$338$	−3.59543			−0.195565
$339$		0			0
$340$	1.08575			0.0588828
$341$	19.1740			1.03833
$342$		0			0
$343$	3.24880			0.175419
$344$	−9.20224			−0.496152
$345$		0			0
$346$	−21.0035			−1.12916
$347$	5.09837	+	8.83063i	0.273695	+	0.474053i	0.969805	−	0.243882i	$-0.0784209\pi$
$347$	5.09837	+	8.83063i	0.273695	+	0.474053i	−0.696110	+	0.717935i	$0.745088\pi$
$348$		0			0
$349$	15.5177	+	26.8775i	0.830644	+	1.43872i	0.897528	+	0.440957i	$0.145361\pi$
$349$	15.5177	+	26.8775i	0.830644	+	1.43872i	−0.0668845	+	0.997761i	$0.521306\pi$
$350$	1.65485			0.0884556
$351$		0			0
$352$	16.0779	+	27.8478i	0.856957	+	1.48429i
$353$	5.38668	+	9.33000i	0.286704	+	0.496586i	0.973021	−	0.230717i	$-0.0741070\pi$
$353$	5.38668	+	9.33000i	0.286704	+	0.496586i	−0.686317	+	0.727303i	$0.740774\pi$
$354$		0			0
$355$	−19.3002			−1.02435
$356$	−3.02222	−	5.23463i	−0.160177	−	0.277435i
$357$		0			0
$358$	−2.26432			−0.119673
$359$	−3.13116	+	5.42333i	−0.165256	+	0.286232i	−0.936746	−	0.350009i	$-0.886178\pi$
$359$	−3.13116	+	5.42333i	−0.165256	+	0.286232i	0.771490	+	0.636241i	$0.219512\pi$
$360$		0			0
$361$	−11.3971	+	15.2022i	−0.599847	+	0.800115i
$362$	−5.51923	−	9.55959i	−0.290084	−	0.502441i
$363$		0			0
$364$	1.07245	+	1.85754i	0.0562119	+	0.0973618i
$365$	−31.1965			−1.63290
$366$		0			0
$367$	2.54229	−	4.40338i	0.132707	−	0.229855i	−0.792012	−	0.610505i	$-0.790967\pi$
$367$	2.54229	−	4.40338i	0.132707	−	0.229855i	0.924719	+	0.380650i	$0.124300\pi$
$368$	−2.86361			−0.149276
$369$		0			0
$370$	−33.7718	−	58.4944i	−1.75571	−	3.04098i
$371$	0.939885	−	1.62793i	0.0487964	−	0.0845178i
$372$		0			0
$373$	16.7194	−	28.9589i	0.865698	−	1.49943i	−0.000654553	−	1.00000i	$-0.500208\pi$
$373$	16.7194	−	28.9589i	0.865698	−	1.49943i	0.866352	−	0.499433i	$-0.166458\pi$
$374$	1.30808			0.0676390
$375$		0			0
$376$	−2.85139	+	4.93875i	−0.147049	+	0.254697i
$377$	6.24677	−	10.8197i	0.321725	−	0.557244i
$378$		0			0
$379$	−0.685446			−0.0352090			−0.0176045	−	0.999845i	$-0.505604\pi$
$379$	−0.685446			−0.0352090			−0.0176045	+	0.999845i	$0.505604\pi$
$380$	−16.6920	+	25.2864i	−0.856279	+	1.29716i
$381$		0			0
$382$	−2.94209	−	5.09584i	−0.150530	−	0.260726i
$383$	−15.2686	−	26.4461i	−0.780191	−	1.35133i	−0.931830	−	0.362895i	$-0.881788\pi$
$383$	−15.2686	−	26.4461i	−0.780191	−	1.35133i	0.151639	−	0.988436i	$-0.451545\pi$
$384$		0			0
$385$	2.69329			0.137263
$386$	−3.93960	−	6.82359i	−0.200520	−	0.347311i
$387$		0			0
$388$	5.01031			0.254360
$389$	−14.6852	+	25.4355i	−0.744568	+	1.28963i	0.205828	+	0.978588i	$0.434011\pi$
$389$	−14.6852	+	25.4355i	−0.744568	+	1.28963i	−0.950396	+	0.311042i	$0.899322\pi$
$390$		0			0
$391$	−0.0735869	+	0.127456i	−0.00372145	+	0.00644574i
$392$	−2.91603	+	5.05071i	−0.147282	+	0.255099i
$393$		0			0
$394$	3.53883			0.178284
$395$	23.4810	+	40.6702i	1.18146	+	2.04634i
$396$		0			0
$397$	−7.59749	+	13.1592i	−0.381307	+	0.660443i	−0.991249	−	0.132002i	$-0.957859\pi$
$397$	−7.59749	+	13.1592i	−0.381307	+	0.660443i	0.609942	+	0.792446i	$0.291193\pi$
$398$	11.0642	+	19.1638i	0.554599	+	0.960594i
$399$		0			0
$400$	5.14600	−	8.91313i	0.257300	−	0.445656i
$401$	−6.63762	−	11.4967i	−0.331467	−	0.574117i	0.651333	−	0.758792i	$-0.274210\pi$
$401$	−6.63762	−	11.4967i	−0.331467	−	0.574117i	−0.982800	+	0.184675i	$0.940877\pi$
$402$		0			0
$403$	9.21156	−	15.9549i	0.458860	−	0.794769i
$404$	17.2178	−	29.8221i	0.856616	−	1.48370i
$405$		0			0
$406$	−1.59163			−0.0789912
$407$	−22.1942	−	38.4416i	−1.10013	−	1.90548i
$408$		0			0
$409$	−1.28290			−0.0634351			−0.0317175	−	0.999497i	$-0.510098\pi$
$409$	−1.28290			−0.0634351			−0.0317175	+	0.999497i	$0.510098\pi$
$410$	−0.326480	+	0.565479i	−0.0161237	+	0.0279270i
$411$		0			0
$412$	−12.0006	+	20.7857i	−0.591229	+	1.02404i
$413$	1.33798	−	2.31744i	0.0658375	−	0.114034i
$414$		0			0
$415$	15.8204	−	27.4017i	0.776593	−	1.34510i
$416$	30.8966			1.51483
$417$		0			0
$418$	−20.1100	+	30.4643i	−0.983612	+	1.49006i
$419$	−10.5202	+	18.2215i	−0.513945	+	0.890178i	0.485924	+	0.874001i	$0.338483\pi$
$419$	−10.5202	+	18.2215i	−0.513945	+	0.890178i	−0.999869	+	0.0161776i	$0.994850\pi$
$420$		0			0
$421$	−28.1722			−1.37303			−0.686514	−	0.727117i	$-0.740860\pi$
$421$	−28.1722			−1.37303			−0.686514	+	0.727117i	$0.740860\pi$
$422$	−2.03345	−	3.52203i	−0.0989867	−	0.171450i
$423$		0			0
$424$	3.38764	+	5.86756i	0.164518	+	0.284954i
$425$	−0.264476	−	0.458086i	−0.0128290	−	0.0222204i
$426$		0			0
$427$	−1.16147			−0.0562075
$428$	35.9689			1.73862
$429$		0			0
$430$	33.2880	+	57.6565i	1.60529	+	2.78044i
$431$	−2.96192	−	5.13019i	−0.142671	−	0.247113i	0.785831	−	0.618441i	$-0.212236\pi$
$431$	−2.96192	−	5.13019i	−0.142671	−	0.247113i	−0.928501	+	0.371329i	$0.878902\pi$
$432$		0			0
$433$	11.4140	+	19.7696i	0.548522	+	0.950067i	0.998376	+	0.0569656i	$0.0181425\pi$
$433$	11.4140	+	19.7696i	0.548522	+	0.950067i	−0.449854	+	0.893102i	$0.648524\pi$
$434$	−2.34703			−0.112661
$435$		0			0
$436$	−9.94503	+	17.2253i	−0.476280	+	0.824942i
$437$	−1.83707	−	3.67327i	−0.0878791	−	0.175716i
$438$		0			0
$439$	−17.9956			−0.858883			−0.429442	−	0.903095i	$-0.641290\pi$
$439$	−17.9956			−0.858883			−0.429442	+	0.903095i	$0.641290\pi$
$440$	−4.85373	+	8.40690i	−0.231392	+	0.400783i
$441$		0			0
$442$	0.628426	−	1.08847i	0.0298912	−	0.0517730i
$443$	−12.0466	+	20.8654i	−0.572353	+	0.991345i	0.423970	+	0.905676i	$0.360636\pi$
$443$	−12.0466	+	20.8654i	−0.572353	+	0.991345i	−0.996324	+	0.0856688i	$0.972697\pi$
$444$		0			0
$445$	−3.64629	+	6.31556i	−0.172851	+	0.299386i
$446$	−56.3970			−2.67048
$447$		0			0
$448$	−1.26004	−	2.18245i	−0.0595313	−	0.103111i
$449$	−4.61776			−0.217926			−0.108963	−	0.994046i	$-0.534753\pi$
$449$	−4.61776			−0.217926			−0.108963	+	0.994046i	$0.534753\pi$
$450$		0			0
$451$	−0.214557	+	0.371623i	−0.0101031	+	0.0174991i
$452$	−6.72822	+	11.6536i	−0.316469	+	0.548140i
$453$		0			0
$454$	29.5674	+	51.2123i	1.38767	+	2.40351i
$455$	1.29391	−	2.24112i	0.0606595	−	0.105065i
$456$		0			0
$457$	−6.98057	−	12.0907i	−0.326537	−	0.565579i	0.655285	−	0.755382i	$-0.272549\pi$
$457$	−6.98057	−	12.0907i	−0.326537	−	0.565579i	−0.981822	+	0.189803i	$0.939215\pi$
$458$	−12.0368	+	20.8483i	−0.562441	+	0.974176i
$459$		0			0
$460$	−3.27470	−	5.67194i	−0.152684	−	0.264456i
$461$	21.0682			0.981242			0.490621	−	0.871373i	$-0.336770\pi$
$461$	21.0682			0.981242			0.490621	+	0.871373i	$0.336770\pi$
$462$		0			0
$463$	3.01504	−	5.22221i	0.140121	−	0.242696i	−0.787421	−	0.616415i	$-0.788584\pi$
$463$	3.01504	−	5.22221i	0.140121	−	0.242696i	0.927542	+	0.373719i	$0.121918\pi$
$464$	−4.94939	+	8.57259i	−0.229770	+	0.397973i
$465$		0			0
$466$	18.5081	−	32.0569i	0.857370	−	1.48501i
$467$	7.89487			0.365331			0.182666	−	0.983175i	$-0.441527\pi$
$467$	7.89487			0.365331			0.182666	+	0.983175i	$0.441527\pi$
$468$		0			0
$469$	0.831489	+	1.44018i	0.0383946	+	0.0665014i
$470$	41.2582			1.90310
$471$		0			0
$472$	4.82248	+	8.35278i	0.221973	+	0.384468i
$473$	21.8763	+	37.8909i	1.00587	+	1.74223i
$474$		0			0
$475$	14.7345	+	0.882999i	0.676066	+	0.0405148i
$476$	−0.0873418			−0.00400330
$477$		0			0
$478$	−11.2998	+	19.5717i	−0.516839	+	0.895191i
$479$	1.58178	−	2.73972i	0.0722732	−	0.125181i	−0.827624	−	0.561283i	$-0.810308\pi$
$479$	1.58178	−	2.73972i	0.0722732	−	0.125181i	0.899897	+	0.436102i	$0.143641\pi$
$480$		0			0
$481$	−42.6502			−1.94468
$482$	−8.07607	+	13.9882i	−0.367855	+	0.637143i
$483$		0			0
$484$	−5.92605	+	10.2642i	−0.269366	+	0.466556i
$485$	−3.02246	−	5.23505i	−0.137243	−	0.237711i
$486$		0			0
$487$	−0.354706			−0.0160733			−0.00803664	−	0.999968i	$-0.502558\pi$
$487$	−0.354706			−0.0160733			−0.00803664	+	0.999968i	$0.502558\pi$
$488$	2.09315	−	3.62544i	0.0947524	−	0.164116i
$489$		0			0
$490$	42.1935			1.90611
$491$	−11.1322	−	19.2816i	−0.502391	−	0.870166i	−0.999996	−	0.00276254i	$-0.999121\pi$
$491$	−11.1322	−	19.2816i	−0.502391	−	0.870166i	0.497606	−	0.867403i	$-0.334213\pi$
$492$		0			0
$493$	0.254372	+	0.440585i	0.0114563	+	0.0198429i
$494$	15.6885	+	31.3694i	0.705857	+	1.41138i
$495$		0			0
$496$	−7.29843	+	12.6412i	−0.327709	+	0.567609i
$497$	1.55259			0.0696430
$498$		0			0
$499$	−1.04133	−	1.80363i	−0.0466163	−	0.0807417i	0.841776	−	0.539827i	$-0.181510\pi$
$499$	−1.04133	−	1.80363i	−0.0466163	−	0.0807417i	−0.888392	+	0.459086i	$0.848177\pi$
$500$	−11.2162			−0.501605
$501$		0			0
$502$	−13.7421	−	23.8021i	−0.613341	−	1.06234i
$503$	−5.29375	−	9.16905i	−0.236037	−	0.408828i	0.723537	−	0.690286i	$-0.242515\pi$
$503$	−5.29375	−	9.16905i	−0.236037	−	0.408828i	−0.959574	+	0.281458i	$0.909182\pi$
$504$		0			0
$505$	−41.5463			−1.84879
$506$	−3.94526	−	6.83340i	−0.175388	−	0.303782i
$507$		0			0
$508$	1.19216	+	2.06487i	0.0528933	+	0.0916139i
$509$	32.1442			1.42477			0.712383	−	0.701791i	$-0.247616\pi$
$509$	32.1442			1.42477			0.712383	+	0.701791i	$0.247616\pi$
$510$		0			0
$511$	2.50957			0.111017
$512$	−29.5836			−1.30742
$513$		0			0
$514$	−32.1583			−1.41844
$515$	28.9574			1.27602
$516$		0			0
$517$	27.1142			1.19248
$518$	2.71674	+	4.70553i	0.119367	+	0.206749i
$519$		0			0
$520$	4.66366	+	8.07769i	0.204515	+	0.354230i
$521$	28.1078			1.23143			0.615713	−	0.787971i	$-0.288868\pi$
$521$	28.1078			1.23143			0.615713	+	0.787971i	$0.288868\pi$
$522$		0			0
$523$	−2.78655	−	4.82644i	−0.121847	−	0.211045i	0.798649	−	0.601797i	$-0.205548\pi$
$523$	−2.78655	−	4.82644i	−0.121847	−	0.211045i	−0.920496	+	0.390752i	$0.872215\pi$
$524$	−5.42076	−	9.38903i	−0.236807	−	0.410161i
$525$		0			0
$526$	−32.5639			−1.41985
$527$	0.375099	+	0.649691i	0.0163396	+	0.0283010i
$528$		0			0
$529$	−22.1122			−0.961401
$530$	24.5087	−	42.4504i	1.06459	−	1.84393i
$531$		0			0
$532$	1.34277	−	2.03414i	0.0582164	−	0.0881910i
$533$	0.206155	+	0.357071i	0.00892956	+	0.0154664i
$534$		0			0
$535$	−21.6982	−	37.5824i	−0.938095	−	1.62483i
$536$	−5.99389			−0.258896
$537$		0			0
$538$	18.7709	−	32.5122i	0.809272	−	1.40170i
$539$	27.7289			1.19437
$540$		0			0
$541$	−8.42025	−	14.5843i	−0.362015	−	0.627028i	0.626277	−	0.779600i	$-0.284578\pi$
$541$	−8.42025	−	14.5843i	−0.362015	−	0.627028i	−0.988292	+	0.152572i	$0.951244\pi$
$542$	−16.0187	+	27.7452i	−0.688062	+	1.19176i
$543$		0			0
$544$	−0.629064	+	1.08957i	−0.0269709	+	0.0467150i
$545$	23.9973			1.02793
$546$		0			0
$547$	−17.9657	+	31.1175i	−0.768158	+	1.33049i	0.170402	+	0.985375i	$0.445493\pi$
$547$	−17.9657	+	31.1175i	−0.768158	+	1.33049i	−0.938561	+	0.345115i	$0.887840\pi$
$548$	−22.7750	+	39.4475i	−0.972901	+	1.68511i
$549$		0			0
$550$	28.3591			1.20923
$551$	−14.1716	−	0.849264i	−0.603730	−	0.0361799i
$552$		0			0
$553$	−1.88890	−	3.27168i	−0.0803243	−	0.139126i
$554$	3.29387	+	5.70516i	0.139943	+	0.242389i
$555$		0			0
$556$	5.56144			0.235858
$557$	−17.6614	−	30.5904i	−0.748338	−	1.29616i	−0.948619	−	0.316421i	$-0.897519\pi$
$557$	−17.6614	−	30.5904i	−0.748338	−	1.29616i	0.200281	−	0.979738i	$-0.435814\pi$
$558$		0			0
$559$	42.0393			1.77807
$560$	−1.02518	+	1.77567i	−0.0433218	+	0.0750356i
$561$		0			0
$562$	13.4947	−	23.3735i	0.569239	−	0.985950i
$563$	−16.3299	+	28.2843i	−0.688225	+	1.19204i	0.284186	+	0.958769i	$0.408277\pi$
$563$	−16.3299	+	28.2843i	−0.688225	+	1.19204i	−0.972412	+	0.233272i	$0.925057\pi$
$564$		0			0
$565$	16.2351			0.683017
$566$	−26.4279	−	45.7744i	−1.11085	−	1.92404i
$567$		0			0
$568$	−2.79800	+	4.84628i	−0.117401	+	0.203345i
$569$	18.7889	+	32.5434i	0.787674	+	1.36429i	0.927389	+	0.374099i	$0.122048\pi$
$569$	18.7889	+	32.5434i	0.787674	+	1.36429i	−0.139715	+	0.990192i	$0.544619\pi$
$570$		0			0
$571$	−11.1825	+	19.3686i	−0.467973	+	0.810552i	−0.999330	−	0.0365954i	$-0.988349\pi$
$571$	−11.1825	+	19.3686i	−0.467973	+	0.810552i	0.531358	+	0.847148i	$0.321682\pi$
$572$	18.3786	+	31.8326i	0.768446	+	1.33099i
$573$		0			0
$574$	0.0262633	−	0.0454894i	0.00109621	−	0.00189869i
$575$	−1.59536	+	2.76325i	−0.0665312	+	0.115235i
$576$		0			0
$577$	9.05688			0.377043			0.188521	−	0.982069i	$-0.439631\pi$
$577$	9.05688			0.377043			0.188521	+	0.982069i	$0.439631\pi$
$578$	−17.8047	−	30.8387i	−0.740579	−	1.28272i
$579$		0			0
$580$	−22.6396			−0.940060
$581$	−1.27266	+	2.20431i	−0.0527987	+	0.0914500i
$582$		0			0
$583$	16.1067	−	27.8977i	0.667073	−	1.15540i
$584$	−4.52264	+	7.83345i	−0.187148	+	0.324150i
$585$		0			0
$586$	14.0547	−	24.3435i	0.580596	−	1.00562i
$587$	5.31798			0.219496			0.109748	−	0.993959i	$-0.464996\pi$
$587$	5.31798			0.219496			0.109748	+	0.993959i	$0.464996\pi$
$588$		0			0
$589$	−20.8976	−	1.25233i	−0.861070	−	0.0516015i
$590$	34.8895	−	60.4304i	1.43638	−	2.48788i
$591$		0			0
$592$	33.7923			1.38886
$593$	−11.4291	−	19.7957i	−0.469336	−	0.812914i	0.530050	−	0.847967i	$-0.322173\pi$
$593$	−11.4291	−	19.7957i	−0.469336	−	0.812914i	−0.999385	+	0.0350531i	$0.988840\pi$
$594$		0			0
$595$	0.0526887	+	0.0912596i	0.00216003	+	0.00374128i
$596$	7.63827	+	13.2299i	0.312876	+	0.541917i
$597$		0			0
$598$	−7.58154			−0.310032
$599$	17.0936			0.698427			0.349213	−	0.937043i	$-0.386449\pi$
$599$	17.0936			0.698427			0.349213	+	0.937043i	$0.386449\pi$
$600$		0			0
$601$	−8.89147	−	15.4005i	−0.362691	−	0.628199i	0.625712	−	0.780054i	$-0.284808\pi$
$601$	−8.89147	−	15.4005i	−0.362691	−	0.628199i	−0.988403	+	0.151856i	$0.951475\pi$
$602$	−2.67782	−	4.63812i	−0.109140	−	0.189036i
$603$		0			0
$604$	−20.6484	−	35.7641i	−0.840173	−	1.45522i
$605$	14.2995			0.581358
$606$		0			0
$607$	−15.1824	+	26.2967i	−0.616235	+	1.06735i	0.373931	+	0.927456i	$0.378010\pi$
$607$	−15.1824	+	26.2967i	−0.616235	+	1.06735i	−0.990166	+	0.139894i	$0.955324\pi$
$608$	−15.7044	−	31.4013i	−0.636897	−	1.27349i
$609$		0			0
$610$	−30.2869			−1.22628
$611$	13.0262	−	22.5621i	0.526984	−	0.912764i
$612$		0			0
$613$	−5.65795	+	9.79986i	−0.228522	+	0.395812i	−0.957370	−	0.288863i	$-0.906723\pi$
$613$	−5.65795	+	9.79986i	−0.228522	+	0.395812i	0.728848	+	0.684676i	$0.240056\pi$
$614$	1.77089	−	3.06727i	0.0714672	−	0.123785i
$615$		0			0
$616$	0.390453	−	0.676285i	0.0157318	−	0.0272483i
$617$	40.8408			1.64419			0.822094	−	0.569351i	$-0.192805\pi$
$617$	40.8408			1.64419			0.822094	+	0.569351i	$0.192805\pi$
$618$		0			0
$619$	15.9954	+	27.7048i	0.642908	+	1.11355i	0.984781	+	0.173802i	$0.0556054\pi$
$619$	15.9954	+	27.7048i	0.642908	+	1.11355i	−0.341873	+	0.939746i	$0.611061\pi$
$620$	−33.3847			−1.34076
$621$		0			0
$622$	−18.6476	+	32.2987i	−0.747702	+	1.29506i
$623$	0.293322	−	0.508049i	0.0117517	−	0.0203546i
$624$		0			0
$625$	15.2322	+	26.3829i	0.609286	+	1.05531i
$626$	7.68965	−	13.3189i	0.307340	−	0.532329i
$627$		0			0
$628$	16.1950	+	28.0506i	0.646252	+	1.11934i
$629$	0.868370	−	1.50406i	0.0346242	−	0.0599708i
$630$		0			0
$631$	−11.2738	−	19.5268i	−0.448802	−	0.777348i	0.549506	−	0.835490i	$-0.314816\pi$
$631$	−11.2738	−	19.5268i	−0.448802	−	0.777348i	−0.998308	+	0.0581416i	$0.981483\pi$
$632$	13.6164			0.541631
$633$		0			0
$634$	3.32075	−	5.75171i	0.131884	−	0.228430i
$635$	1.43833	−	2.49126i	0.0570784	−	0.0988627i
$636$		0			0
$637$	13.3215	−	23.0735i	0.527817	−	0.914206i
$638$	−27.2756			−1.07985
$639$		0			0
$640$	−9.53158	−	16.5092i	−0.376769	−	0.652583i
$641$	−40.0084			−1.58024			−0.790118	−	0.612954i	$-0.789981\pi$
$641$	−40.0084			−1.58024			−0.790118	+	0.612954i	$0.789981\pi$
$642$		0			0
$643$	−16.5535	−	28.6714i	−0.652805	−	1.13069i	−0.982439	−	0.186582i	$-0.940259\pi$
$643$	−16.5535	−	28.6714i	−0.652805	−	1.13069i	0.329635	−	0.944109i	$-0.393074\pi$
$644$	0.263430	+	0.456274i	0.0103806	+	0.0179797i
$645$		0			0
$646$	−1.42566	−	0.0854361i	−0.0560920	−	0.00336144i
$647$	25.5295			1.00367			0.501834	−	0.864964i	$-0.332659\pi$
$647$	25.5295			1.00367			0.501834	+	0.864964i	$0.332659\pi$
$648$		0			0
$649$	22.9288	−	39.7138i	0.900033	−	1.55890i
$650$	13.6243	−	23.5979i	0.534388	−	0.925587i
$651$		0			0
$652$	42.3840			1.65988
$653$	−6.52259	+	11.2975i	−0.255249	+	0.442104i	−0.964963	−	0.262386i	$-0.915491\pi$
$653$	−6.52259	+	11.2975i	−0.255249	+	0.442104i	0.709714	+	0.704490i	$0.248824\pi$
$654$		0			0
$655$	−6.54012	+	11.3278i	−0.255544	+	0.442615i
$656$	−0.163339	−	0.282911i	−0.00637732	−	0.0110458i
$657$		0			0
$658$	−3.31898			−0.129387
$659$	−2.93764	+	5.08815i	−0.114434	+	0.198206i	−0.917553	−	0.397612i	$-0.869839\pi$
$659$	−2.93764	+	5.08815i	−0.114434	+	0.198206i	0.803119	+	0.595818i	$0.203172\pi$
$660$		0			0
$661$	−9.09106			−0.353601			−0.176801	−	0.984247i	$-0.556575\pi$
$661$	−9.09106			−0.353601			−0.176801	+	0.984247i	$0.556575\pi$
$662$	−11.1042	−	19.2331i	−0.431578	−	0.747514i
$663$		0			0
$664$	−4.58705	−	7.94501i	−0.178012	−	0.308326i
$665$	−2.93540	−	0.175910i	−0.113830	−	0.00682152i
$666$		0			0
$667$	1.53441	−	2.65768i	0.0594126	−	0.102906i
$668$	−22.4034			−0.866812
$669$		0			0
$670$	21.6822	+	37.5546i	0.837655	+	1.45086i
$671$	−19.9040			−0.768386
$672$		0			0
$673$	−14.8147	−	25.6597i	−0.571063	−	0.989110i	−0.996457	−	0.0841018i	$-0.973198\pi$
$673$	−14.8147	−	25.6597i	−0.571063	−	0.989110i	0.425394	−	0.905008i	$-0.360135\pi$
$674$	25.2331	+	43.7051i	0.971944	+	1.68346i
$675$		0			0
$676$	4.11407			0.158234
$677$	12.3841	+	21.4499i	0.475961	+	0.824388i	0.999621	−	0.0275394i	$-0.00876717\pi$
$677$	12.3841	+	21.4499i	0.475961	+	0.824388i	−0.523660	+	0.851927i	$0.675434\pi$
$678$		0			0
$679$	0.243139	+	0.421128i	0.00933080	+	0.0161614i
$680$	−0.379813			−0.0145652
$681$		0			0
$682$	−40.2209			−1.54014
$683$	−34.2166			−1.30926			−0.654631	−	0.755949i	$-0.727176\pi$
$683$	−34.2166			−1.30926			−0.654631	+	0.755949i	$0.727176\pi$
$684$		0			0
$685$	54.9559			2.09976
$686$	−6.81495			−0.260196
$687$		0			0
$688$	−33.3082			−1.26987
$689$	−15.4760	−	26.8052i	−0.589588	−	1.02120i
$690$		0			0
$691$	−9.86385	−	17.0847i	−0.375239	−	0.649932i	0.615124	−	0.788430i	$-0.289106\pi$
$691$	−9.86385	−	17.0847i	−0.375239	−	0.649932i	−0.990363	+	0.138498i	$0.955773\pi$
$692$	24.0333			0.913611
$693$		0			0
$694$	−10.6948	−	18.5239i	−0.405968	−	0.703157i
$695$	−3.35493	−	5.81091i	−0.127260	−	0.220420i
$696$		0			0
$697$	−0.0167895			−0.000635946
$698$	−32.5513	−	56.3804i	−1.23208	−	2.13403i
$699$		0			0
$700$	−1.89357			−0.0715702
$701$	−17.7815	+	30.7985i	−0.671598	+	1.16324i	0.305852	+	0.952079i	$0.401059\pi$
$701$	−17.7815	+	30.7985i	−0.671598	+	1.16324i	−0.977451	+	0.211163i	$0.932275\pi$
$702$		0			0
$703$	21.6786	+	43.3468i	0.817623	+	1.63486i
$704$	−21.5932	−	37.4005i	−0.813825	−	1.40959i
$705$		0			0
$706$	−11.2996	−	19.5714i	−0.425264	−	0.736579i
$707$	3.34215			0.125695
$708$		0			0
$709$	−14.7000	+	25.4612i	−0.552071	+	0.956215i	0.446054	+	0.895006i	$0.352829\pi$
$709$	−14.7000	+	25.4612i	−0.552071	+	0.956215i	−0.998125	+	0.0612093i	$0.980504\pi$
$710$	40.4857			1.51940
$711$		0			0
$712$	1.05722	+	1.83117i	0.0396212	+	0.0686259i
$713$	2.26266	−	3.91904i	0.0847373	−	0.146769i
$714$		0			0
$715$	22.1737	−	38.4059i	0.829248	−	1.43630i
$716$	2.59095			0.0968283
$717$		0			0
$718$	6.56819	−	11.3764i	0.245122	−	0.424565i
$719$	−2.60428	+	4.51075i	−0.0971234	+	0.168223i	−0.910493	−	0.413525i	$-0.864297\pi$
$719$	−2.60428	+	4.51075i	−0.0971234	+	0.168223i	0.813369	+	0.581747i	$0.197631\pi$
$720$		0			0
$721$	−2.32945			−0.0867534
$722$	23.9075	−	31.8894i	0.889745	−	1.18680i
$723$		0			0
$724$	6.31539	+	10.9386i	0.234710	+	0.406529i
$725$	5.51477	+	9.55187i	0.204814	+	0.354747i
$726$		0			0
$727$	−11.5553			−0.428563			−0.214282	−	0.976772i	$-0.568741\pi$
$727$	−11.5553			−0.428563			−0.214282	+	0.976772i	$0.568741\pi$
$728$	−0.375163	−	0.649802i	−0.0139045	−	0.0240833i
$729$		0			0
$730$	65.4405			2.42206
$731$	−0.855931	+	1.48252i	−0.0316578	+	0.0548328i
$732$		0			0
$733$	−0.617068	+	1.06879i	−0.0227919	+	0.0394768i	−0.877196	−	0.480132i	$-0.840589\pi$
$733$	−0.617068	+	1.06879i	−0.0227919	+	0.0394768i	0.854404	+	0.519609i	$0.173922\pi$
$734$	−5.33293	+	9.23690i	−0.196842	+	0.340940i
$735$		0			0
$736$	7.58923			0.279743
$737$	14.2492	+	24.6803i	0.524874	+	0.909109i
$738$		0			0
$739$	−7.03784	+	12.1899i	−0.258891	+	0.448413i	−0.965945	−	0.258747i	$-0.916690\pi$
$739$	−7.03784	+	12.1899i	−0.258891	+	0.448413i	0.707054	+	0.707160i	$0.250024\pi$
$740$	38.6434	+	66.9324i	1.42056	+	2.46048i
$741$		0			0
$742$	−1.97158	+	3.41488i	−0.0723790	+	0.125364i
$743$	−4.40509	−	7.62984i	−0.161607	−	0.279912i	0.773838	−	0.633383i	$-0.218334\pi$
$743$	−4.40509	−	7.62984i	−0.161607	−	0.279912i	−0.935445	+	0.353472i	$0.885001\pi$
$744$		0			0
$745$	9.21554	−	15.9618i	0.337631	−	0.584795i
$746$	−35.0720	+	60.7465i	−1.28408	+	2.22409i
$747$		0			0
$748$	−1.49677			−0.0547273
$749$	1.74549	+	3.02328i	0.0637788	+	0.110468i
$750$		0			0
$751$	41.4480			1.51246			0.756229	−	0.654307i	$-0.227039\pi$
$751$	41.4480			1.51246			0.756229	+	0.654307i	$0.227039\pi$
$752$	−10.3208	+	17.8762i	−0.376362	+	0.651878i
$753$		0			0
$754$	−13.1037	+	22.6964i	−0.477210	+	0.826552i
$755$	−24.9122	+	43.1493i	−0.906649	+	1.57036i
$756$		0			0
$757$	−24.6418	+	42.6808i	−0.895621	+	1.55126i	−0.0625859	+	0.998040i	$0.519935\pi$
$757$	−24.6418	+	42.6808i	−0.895621	+	1.55126i	−0.833035	+	0.553221i	$0.813399\pi$
$758$	1.43785			0.0522250
$759$		0			0
$760$	5.83914	−	8.84561i	0.211808	−	0.320864i
$761$	−11.0780	+	19.1877i	−0.401578	+	0.695553i	−0.993917	−	0.110136i	$-0.964871\pi$
$761$	−11.0780	+	19.1877i	−0.401578	+	0.695553i	0.592339	+	0.805689i	$0.298205\pi$
$762$		0			0
$763$	−1.93044			−0.0698865
$764$	3.36649	+	5.83093i	0.121795	+	0.210956i
$765$		0			0
$766$	32.0288	+	55.4755i	1.15725	+	2.00441i
$767$	−22.0309	−	38.1586i	−0.795489	−	1.37783i
$768$		0			0
$769$	−14.8372			−0.535045			−0.267522	−	0.963552i	$-0.586205\pi$
$769$	−14.8372			−0.535045			−0.267522	+	0.963552i	$0.586205\pi$
$770$	−5.64968			−0.203600
$771$		0			0
$772$	4.50789	+	7.80790i	0.162243	+	0.281013i
$773$	6.80948	+	11.7944i	0.244920	+	0.424214i	0.962109	−	0.272665i	$-0.0879050\pi$
$773$	6.80948	+	11.7944i	0.244920	+	0.424214i	−0.717189	+	0.696879i	$0.754572\pi$
$774$		0			0
$775$	8.13215	+	14.0853i	0.292115	+	0.505959i
$776$	−1.75269			−0.0629180
$777$		0			0
$778$	30.8049	−	53.3556i	1.10441	−	1.91289i
$779$	0.258116	−	0.391016i	0.00924798	−	0.0140096i
$780$		0			0
$781$	26.6065			0.952056
$782$	0.154362	−	0.267363i	0.00551998	−	0.00956088i
$783$		0			0
$784$	−10.5548	+	18.2814i	−0.376957	+	0.652908i
$785$	19.5392	−	33.8429i	0.697385	−	1.20791i
$786$		0			0
$787$	−5.32744	+	9.22739i	−0.189903	+	0.328921i	−0.945218	−	0.326441i	$-0.894151\pi$
$787$	−5.32744	+	9.22739i	−0.189903	+	0.328921i	0.755315	+	0.655362i	$0.227484\pi$
$788$	−4.04931			−0.144251
$789$		0			0
$790$	−49.2557	−	85.3133i	−1.75244	−	3.03531i
$791$	−1.30602			−0.0464367
$792$		0			0
$793$	−9.56229	+	16.5624i	−0.339567	+	0.588147i
$794$	15.9371	−	27.6039i	0.565588	−	0.979627i
$795$		0			0
$796$	−12.6603	−	21.9282i	−0.448731	−	0.777225i
$797$	−8.09555	+	14.0219i	−0.286759	+	0.496681i	−0.973034	−	0.230661i	$-0.925911\pi$
$797$	−8.09555	+	14.0219i	−0.286759	+	0.496681i	0.686275	+	0.727342i	$0.259245\pi$
$798$		0			0
$799$	0.530434	+	0.918739i	0.0187654	+	0.0325027i
$800$	−13.6381	+	23.6219i	−0.482179	+	0.835159i
$801$		0			0
$802$	13.9236	+	24.1164i	0.491660	+	0.851581i
$803$	43.0064			1.51766
$804$		0			0
$805$	0.317827	−	0.550493i	0.0112019	−	0.0194023i
$806$	−19.3229	+	33.4683i	−0.680621	+	1.17887i
$807$		0			0
$808$	−6.02308	+	10.4323i	−0.211891	+	0.367006i
$809$	−17.3230			−0.609044			−0.304522	−	0.952505i	$-0.598497\pi$
$809$	−17.3230			−0.609044			−0.304522	+	0.952505i	$0.598497\pi$
$810$		0			0
$811$	6.38818	+	11.0646i	0.224319	+	0.388532i	0.956115	−	0.292992i	$-0.0946508\pi$
$811$	6.38818	+	11.0646i	0.224319	+	0.388532i	−0.731796	+	0.681524i	$0.761318\pi$
$812$	1.82122			0.0639124
$813$		0			0
$814$	46.5565	+	80.6382i	1.63180	+	2.82637i
$815$	−25.5680	−	44.2851i	−0.895609	−	1.55124i
$816$		0			0
$817$	−21.3680	−	42.7259i	−0.747573	−	1.49479i
$818$	2.69111			0.0940924
$819$		0			0
$820$	0.373575	−	0.647051i	0.0130458	−	0.0225960i
$821$	−0.301311	+	0.521886i	−0.0105158	+	0.0182139i	−0.871235	−	0.490865i	$-0.836681\pi$
$821$	−0.301311	+	0.521886i	−0.0105158	+	0.0182139i	0.860720	+	0.509079i	$0.170014\pi$
$822$		0			0
$823$	14.2808			0.497796			0.248898	−	0.968530i	$-0.419932\pi$
$823$	14.2808			0.497796			0.248898	+	0.968530i	$0.419932\pi$
$824$	4.19804	−	7.27121i	0.146245	−	0.253305i
$825$		0			0
$826$	−2.80665	+	4.86126i	−0.0976559	+	0.169145i
$827$	−8.44965	−	14.6352i	−0.293823	−	0.508917i	0.680887	−	0.732388i	$-0.261594\pi$
$827$	−8.44965	−	14.6352i	−0.293823	−	0.508917i	−0.974710	+	0.223472i	$0.928261\pi$
$828$		0			0
$829$	−17.2370			−0.598665			−0.299333	−	0.954149i	$-0.596764\pi$
$829$	−17.2370			−0.598665			−0.299333	+	0.954149i	$0.596764\pi$
$830$	−33.1862	+	57.4802i	−1.15191	+	1.99517i
$831$		0			0
$832$	−41.4953			−1.43859
$833$	0.542459	+	0.939566i	0.0187951	+	0.0325540i
$834$		0			0
$835$	13.5148	+	23.4083i	0.467698	+	0.810078i
$836$	23.0109	−	34.8588i	0.795849	−	1.20562i
$837$		0			0
$838$	22.0680	−	38.2230i	0.762328	−	1.32039i
$839$	35.2360			1.21648			0.608241	−	0.793753i	$-0.291876\pi$
$839$	35.2360			1.21648			0.608241	+	0.793753i	$0.291876\pi$
$840$		0			0
$841$	9.19592	+	15.9278i	0.317101	+	0.549235i
$842$	59.0963			2.03659
$843$		0			0
$844$	2.32678	+	4.03009i	0.0800909	+	0.138722i
$845$	−2.48181	−	4.29861i	−0.0853767	−	0.147877i
$846$		0			0
$847$	−1.15031			−0.0395251
$848$	12.2618	+	21.2381i	0.421073	+	0.729319i
$849$		0			0
$850$	0.554787	+	0.960920i	0.0190290	+	0.0329593i
$851$	−10.4763			−0.359123
$852$		0			0
$853$	−10.6623			−0.365070			−0.182535	−	0.983199i	$-0.558430\pi$
$853$	−10.6623			−0.365070			−0.182535	+	0.983199i	$0.558430\pi$
$854$	2.43640			0.0833718
$855$		0			0
$856$	−12.5826			−0.430064
$857$	−10.8816			−0.371708			−0.185854	−	0.982577i	$-0.559505\pi$
$857$	−10.8816			−0.371708			−0.185854	+	0.982577i	$0.559505\pi$
$858$		0			0
$859$	−20.4985			−0.699398			−0.349699	−	0.936862i	$-0.613716\pi$
$859$	−20.4985			−0.699398			−0.349699	+	0.936862i	$0.613716\pi$
$860$	−38.0899	−	65.9736i	−1.29885	−	2.24968i
$861$		0			0
$862$	6.21317	+	10.7615i	0.211621	+	0.366539i
$863$	−3.92789			−0.133707			−0.0668535	−	0.997763i	$-0.521296\pi$
$863$	−3.92789			−0.133707			−0.0668535	+	0.997763i	$0.521296\pi$
$864$		0			0
$865$	−14.4981	−	25.1114i	−0.492949	−	0.853813i
$866$	−23.9430	−	41.4704i	−0.813615	−	1.40922i
$867$		0			0
$868$	2.68560			0.0911551
$869$	−32.3700	−	56.0665i	−1.09808	−	1.90192i
$870$		0			0
$871$	27.3823			0.927815
$872$	3.47895	−	6.02571i	0.117812	−	0.204056i
$873$		0			0
$874$	3.85360	+	7.70536i	0.130350	+	0.260638i
$875$	−0.544297	−	0.942751i	−0.0184006	−	0.0318708i
$876$		0			0
$877$	16.8575	+	29.1980i	0.569236	+	0.985946i	0.996642	+	0.0818860i	$0.0260943\pi$
$877$	16.8575	+	29.1980i	0.569236	+	0.985946i	−0.427406	+	0.904060i	$0.640572\pi$
$878$	37.7491			1.27397
$879$		0			0
$880$	−17.5685	+	30.4295i	−0.592233	+	1.02578i
$881$	−51.0567			−1.72014			−0.860072	−	0.510173i	$-0.829581\pi$
$881$	−51.0567			−1.72014			−0.860072	+	0.510173i	$0.829581\pi$
$882$		0			0
$883$	8.14977	+	14.1158i	0.274262	+	0.475035i	0.969949	−	0.243310i	$-0.0782332\pi$
$883$	8.14977	+	14.1158i	0.274262	+	0.475035i	−0.695687	+	0.718345i	$0.744900\pi$
$884$	−0.719078	+	1.24548i	−0.0241852	+	0.0418900i
$885$		0			0
$886$	25.2701	−	43.7690i	0.848964	−	1.47045i
$887$	−16.8984			−0.567393			−0.283697	−	0.958914i	$-0.591561\pi$
$887$	−16.8984			−0.567393			−0.283697	+	0.958914i	$0.591561\pi$
$888$		0			0
$889$	−0.115705	+	0.200407i	−0.00388062	+	0.00672144i
$890$	7.64877	−	13.2481i	0.256387	−	0.444076i
$891$		0			0
$892$	64.5324			2.16070
$893$	−29.5516	−	1.77095i	−0.988907	−	0.0592625i
$894$		0			0
$895$	−1.56298	−	2.70717i	−0.0522448	−	0.0904907i
$896$	0.766759	+	1.32807i	0.0256156	+	0.0443675i
$897$		0			0
$898$	9.68661			0.323246
$899$	−7.82146	−	13.5472i	−0.260860	−	0.451823i
$900$		0			0
$901$	1.26038			0.0419894
$902$	0.450073	−	0.779548i	0.0149858	−	0.0259561i
$903$		0			0
$904$	2.35365	−	4.07664i	0.0782813	−	0.135587i
$905$	7.61949	−	13.1973i	0.253280	−	0.438695i
$906$		0			0
$907$	28.0593			0.931695			0.465848	−	0.884865i	$-0.345750\pi$
$907$	28.0593			0.931695			0.465848	+	0.884865i	$0.345750\pi$
$908$	−33.8326	−	58.5998i	−1.12277	−	1.94470i
$909$		0			0
$910$	−2.71422	+	4.70116i	−0.0899754	+	0.155842i
$911$	−0.311791	−	0.540037i	−0.0103301	−	0.0178922i	0.860814	−	0.508919i	$-0.169955\pi$
$911$	−0.311791	−	0.540037i	−0.0103301	−	0.0178922i	−0.871144	+	0.491027i	$0.836622\pi$
$912$		0			0
$913$	−21.8094	+	37.7750i	−0.721787	+	1.25017i
$914$	14.6430	+	25.3625i	0.484349	+	0.838916i
$915$		0			0
$916$	13.7731	−	23.8557i	0.455076	−	0.788214i
$917$	0.526114	−	0.911255i	0.0173738	−	0.0300923i
$918$		0			0
$919$	5.40184			0.178190			0.0890951	−	0.996023i	$-0.471603\pi$
$919$	5.40184			0.178190			0.0890951	+	0.996023i	$0.471603\pi$
$920$	1.14555	+	1.98415i	0.0377676	+	0.0654154i
$921$		0			0
$922$	−44.1943			−1.45546
$923$	12.7823	−	22.1396i	0.420735	−	0.728734i
$924$		0			0
$925$	18.8262	−	32.6080i	0.619003	−	1.07214i
$926$	−6.32461	+	10.9545i	−0.207839	+	0.359988i
$927$		0			0
$928$	13.1170	−	22.7194i	0.430588	−	0.745800i
$929$	−31.5693			−1.03576			−0.517878	−	0.855455i	$-0.673278\pi$
$929$	−31.5693			−1.03576			−0.517878	+	0.855455i	$0.673278\pi$
$930$		0			0
$931$	−30.2215	−	1.81109i	−0.990470	−	0.0593561i
$932$	−21.1779	+	36.6812i	−0.693706	+	1.20153i
$933$		0			0
$934$	−16.5609			−0.541891
$935$	0.902923	+	1.56391i	0.0295287	+	0.0511453i
$936$		0			0
$937$	−16.0412	−	27.7842i	−0.524043	−	0.907669i	−0.999608	−	0.0279884i	$-0.991090\pi$
$937$	−16.0412	−	27.7842i	−0.524043	−	0.907669i	0.475565	−	0.879680i	$-0.342243\pi$
$938$	−1.74420	−	3.02104i	−0.0569502	−	0.0986406i
$939$		0			0
$940$	−47.2098			−1.53981
$941$	12.1419			0.395814			0.197907	−	0.980221i	$-0.436586\pi$
$941$	12.1419			0.395814			0.197907	+	0.980221i	$0.436586\pi$
$942$		0			0
$943$	0.0506384	+	0.0877083i	0.00164901	+	0.00285617i
$944$	17.4553	+	30.2335i	0.568123	+	0.984018i
$945$		0			0
$946$	−45.8896	−	79.4831i	−1.49200	−	2.58422i
$947$	11.2264			0.364808			0.182404	−	0.983224i	$-0.441612\pi$
$947$	11.2264			0.364808			0.182404	+	0.983224i	$0.441612\pi$
$948$		0			0
$949$	20.6611	−	35.7861i	0.670689	−	1.16167i
$950$	−30.9084	−	1.85225i	−1.00280	−	0.0600950i
$951$		0			0
$952$	0.0305537			0.000990251
$953$	16.9828	−	29.4151i	0.550127	−	0.952849i	−0.448137	−	0.893965i	$-0.647912\pi$
$953$	16.9828	−	29.4151i	0.550127	−	0.952849i	0.998265	−	0.0588840i	$-0.0187542\pi$
$954$		0			0
$955$	4.06165	−	7.03499i	0.131432	−	0.227647i
$956$	12.9298	−	22.3950i	0.418178	−	0.724306i
$957$		0			0
$958$	−3.31807	+	5.74706i	−0.107202	+	0.185679i
$959$	−4.42088			−0.142758
$960$		0			0
$961$	3.96639	+	6.86999i	0.127948	+	0.221612i
$962$	89.4667			2.88452
$963$		0			0
$964$	9.24106	−	16.0060i	0.297634	−	0.515518i
$965$	5.43876	−	9.42020i	0.175080	−	0.303247i
$966$		0			0
$967$	−1.05905	−	1.83434i	−0.0340569	−	0.0589883i	0.848495	−	0.529204i	$-0.177509\pi$
$967$	−1.05905	−	1.83434i	−0.0340569	−	0.0589883i	−0.882551	+	0.470216i	$0.844176\pi$
$968$	2.07304	−	3.59061i	0.0666300	−	0.115406i
$969$		0			0
$970$	6.34016	+	10.9815i	0.203570	+	0.352594i
$971$	−2.65960	+	4.60656i	−0.0853506	+	0.147832i	−0.905541	−	0.424260i	$-0.860534\pi$
$971$	−2.65960	+	4.60656i	−0.0853506	+	0.147832i	0.820190	+	0.572091i	$0.193868\pi$
$972$		0			0
$973$	0.269884	+	0.467453i	0.00865208	+	0.0149858i
$974$	0.744062			0.0238413
$975$		0			0
$976$	7.57632	−	13.1226i	0.242512	−	0.420043i
$977$	15.4794	−	26.8112i	0.495231	−	0.857766i	−0.504753	−	0.863264i	$-0.668417\pi$
$977$	15.4794	−	26.8112i	0.495231	−	0.857766i	0.999985	+	0.00549755i	$0.00174993\pi$
$978$		0			0
$979$	5.02664	−	8.70640i	0.160652	−	0.278258i
$980$	−48.2800			−1.54225
$981$		0			0
$982$	23.3519	+	40.4467i	0.745189	+	1.29071i
$983$	−0.802834			−0.0256064			−0.0128032	−	0.999918i	$-0.504076\pi$
$983$	−0.802834			−0.0256064			−0.0128032	+	0.999918i	$0.504076\pi$
$984$		0			0
$985$	2.44274	+	4.23095i	0.0778322	+	0.134809i
$986$	−0.533591	−	0.924207i	−0.0169930	−	0.0294328i
$987$		0			0
$988$	−17.9515	−	35.8945i	−0.571115	−	1.14196i
$989$	10.3262			0.328355
$990$		0			0
$991$	3.89118	−	6.73973i	0.123608	−	0.214094i	−0.797580	−	0.603213i	$-0.793887\pi$
$991$	3.89118	−	6.73973i	0.123608	−	0.214094i	0.921188	+	0.389118i	$0.127220\pi$
$992$	19.3425	−	33.5023i	0.614127	−	1.06370i
$993$		0			0
$994$	−3.25683			−0.103300
$995$	−15.2745	+	26.4563i	−0.484236	+	0.838721i
$996$		0			0
$997$	−17.7148	+	30.6829i	−0.561032	+	0.971736i	0.436375	+	0.899765i	$0.356262\pi$
$997$	−17.7148	+	30.6829i	−0.561032	+	0.971736i	−0.997407	+	0.0719707i	$0.977071\pi$
$998$	2.18438	+	3.78345i	0.0691453	+	0.119763i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.h.c.334.2		32
3.2	odd	2		171.2.h.c.49.15	yes	32
9.2	odd	6		171.2.g.c.106.2	✓	32
9.7	even	3		513.2.g.c.505.15		32
19.7	even	3		513.2.g.c.64.15		32
57.26	odd	6		171.2.g.c.121.2	yes	32
171.7	even	3	inner	513.2.h.c.235.2		32
171.83	odd	6		171.2.h.c.7.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.2	✓	32	9.2	odd	6
171.2.g.c.121.2	yes	32	57.26	odd	6
171.2.h.c.7.15	yes	32	171.83	odd	6
171.2.h.c.49.15	yes	32	3.2	odd	2
513.2.g.c.64.15		32	19.7	even	3
513.2.g.c.505.15		32	9.7	even	3
513.2.h.c.235.2		32	171.7	even	3	inner
513.2.h.c.334.2		32	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q-2.09768 q^{2} +2.40028 q^{4} +(-1.44796 - 2.50795i) q^{5} +(0.116480 + 0.201749i) q^{7} -0.839660 q^{8} +O(q^{10})\)	\(q-2.09768 q^{2} +2.40028 q^{4} +(-1.44796 - 2.50795i) q^{5} +(0.116480 + 0.201749i) q^{7} -0.839660 q^{8} +(3.03737 + 5.26088i) q^{10} +(1.99611 + 3.45736i) q^{11} +3.83588 q^{13} +(-0.244338 - 0.423206i) q^{14} -3.03922 q^{16} +(-0.0780996 + 0.135272i) q^{17} +(-1.94973 - 3.89853i) q^{19} +(-3.47552 - 6.01977i) q^{20} +(-4.18721 - 7.25245i) q^{22} +0.942219 q^{23} +(-1.69320 + 2.93270i) q^{25} -8.04647 q^{26} +(0.279585 + 0.484255i) q^{28} +(1.62851 - 2.82066i) q^{29} +(2.40142 - 4.15938i) q^{31} +8.05464 q^{32} +(0.163828 - 0.283759i) q^{34} +(0.337318 - 0.584251i) q^{35} -11.1188 q^{37} +(4.08992 + 8.17789i) q^{38} +(1.21580 + 2.10582i) q^{40} +(0.0537438 + 0.0930869i) q^{41} +10.9595 q^{43} +(4.79122 + 8.29864i) q^{44} -1.97648 q^{46} +(3.39588 - 5.88185i) q^{47} +(3.47286 - 6.01518i) q^{49} +(3.55179 - 6.15189i) q^{50} +9.20719 q^{52} +(-4.03453 - 6.98802i) q^{53} +(5.78059 - 10.0123i) q^{55} +(-0.0978037 - 0.169401i) q^{56} +(-3.41610 + 5.91685i) q^{58} +(-5.74337 - 9.94781i) q^{59} +(-2.49285 + 4.31775i) q^{61} +(-5.03742 + 8.72506i) q^{62} -10.8177 q^{64} +(-5.55422 - 9.62019i) q^{65} +7.13847 q^{67} +(-0.187461 + 0.324692i) q^{68} +(-0.707586 + 1.22557i) q^{70} +(3.33230 - 5.77171i) q^{71} +(5.38628 - 9.32931i) q^{73} +23.3236 q^{74} +(-4.67990 - 9.35757i) q^{76} +(-0.465014 + 0.805427i) q^{77} -16.2165 q^{79} +(4.40068 + 7.62219i) q^{80} +(-0.112737 - 0.195267i) q^{82} +(5.46298 + 9.46217i) q^{83} +0.452341 q^{85} -22.9895 q^{86} +(-1.67605 - 2.90301i) q^{88} +(-1.25911 - 2.18084i) q^{89} +(0.446804 + 0.773887i) q^{91} +2.26159 q^{92} +(-7.12349 + 12.3383i) q^{94} +(-6.95417 + 10.5348i) q^{95} +2.08738 q^{97} +(-7.28497 + 12.6179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

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