LMFDB - Embedded newform 756.2.bo.a.169.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.5
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.a.85.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550546 + 1.64222i) q^{3} +(-0.678318 - 3.84693i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.39380 - 1.80824i) q^{9} +O(q^{10})$	\(q+(-0.550546 + 1.64222i) q^{3} +(-0.678318 - 3.84693i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.39380 - 1.80824i) q^{9} +(-0.451184 + 2.55879i) q^{11} +(-5.45221 - 1.98444i) q^{13} +(6.69097 + 1.00396i) q^{15} +(1.37898 + 2.38847i) q^{17} +(-3.22450 + 5.58499i) q^{19} +(-1.47734 + 0.904132i) q^{21} +(-3.42672 + 2.87536i) q^{23} +(-9.64031 + 3.50878i) q^{25} +(4.28743 - 2.93563i) q^{27} +(4.03650 - 1.46917i) q^{29} +(-7.31463 + 6.13770i) q^{31} +(-3.95371 - 2.14968i) q^{33} +(1.95314 - 3.38294i) q^{35} +(1.27882 + 2.21498i) q^{37} +(6.26059 - 7.86122i) q^{39} +(-6.76212 - 2.46121i) q^{41} +(0.345401 - 1.95887i) q^{43} +(-5.33242 + 10.4353i) q^{45} +(2.43116 + 2.03998i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-4.68160 + 0.949638i) q^{51} +5.86437 q^{53} +10.1495 q^{55} +(-7.39657 - 8.37014i) q^{57} +(-1.65224 - 9.37030i) q^{59} +(-9.86168 - 8.27493i) q^{61} +(-0.671442 - 2.92390i) q^{63} +(-3.93568 + 22.3203i) q^{65} +(-13.6880 - 4.98203i) q^{67} +(-2.83541 - 7.21045i) q^{69} +(-0.294622 - 0.510301i) q^{71} +(-2.27808 + 3.94575i) q^{73} +(-0.454777 - 17.7633i) q^{75} +(-1.99039 + 1.67013i) q^{77} +(5.29605 - 1.92761i) q^{79} +(2.46054 + 8.65712i) q^{81} +(1.61574 - 0.588081i) q^{83} +(8.25290 - 6.92500i) q^{85} +(0.190420 + 7.43768i) q^{87} +(1.22942 - 2.12941i) q^{89} +(-2.90106 - 5.02478i) q^{91} +(-6.05244 - 15.3913i) q^{93} +(23.6723 + 8.61602i) q^{95} +(1.12954 - 6.40592i) q^{97} +(5.70695 - 5.30938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	$ 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) $ 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.550546	+	1.64222i	−0.317858	+	0.948138i
$3$	−0.550546	+	1.64222i	−0.317858	+	0.948138i
$4$		0			0
$5$	−0.678318	−	3.84693i	−0.303353	−	1.72040i	−0.631158	−	0.775655i	$-0.717420\pi$
$5$	−0.678318	−	3.84693i	−0.303353	−	1.72040i	0.327805	−	0.944746i	$-0.393691\pi$
$6$		0			0
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$		0			0
$9$	−2.39380	−	1.80824i	−0.797933	−	0.602747i
$10$		0			0
$11$	−0.451184	+	2.55879i	−0.136037	+	0.771504i	0.838095	+	0.545524i	$0.183669\pi$
$11$	−0.451184	+	2.55879i	−0.136037	+	0.771504i	−0.974132	+	0.225980i	$0.927442\pi$
$12$		0			0
$13$	−5.45221	−	1.98444i	−1.51217	−	0.550385i	−0.552992	−	0.833187i	$-0.686514\pi$
$13$	−5.45221	−	1.98444i	−1.51217	−	0.550385i	−0.959178	+	0.282802i	$0.908736\pi$
$14$		0			0
$15$	6.69097	+	1.00396i	1.72760	+	0.259222i
$16$		0			0
$17$	1.37898	+	2.38847i	0.334453	+	0.579289i	0.983380	−	0.181561i	$-0.0581151\pi$
$17$	1.37898	+	2.38847i	0.334453	+	0.579289i	−0.648927	+	0.760851i	$0.724782\pi$
$18$		0			0
$19$	−3.22450	+	5.58499i	−0.739750	+	1.28129i	0.212857	+	0.977083i	$0.431723\pi$
$19$	−3.22450	+	5.58499i	−0.739750	+	1.28129i	−0.952608	+	0.304202i	$0.901610\pi$
$20$		0			0
$21$	−1.47734	+	0.904132i	−0.322383	+	0.197298i
$22$		0			0
$23$	−3.42672	+	2.87536i	−0.714520	+	0.599553i	−0.925863	−	0.377859i	$-0.876661\pi$
$23$	−3.42672	+	2.87536i	−0.714520	+	0.599553i	0.211344	+	0.977412i	$0.432216\pi$
$24$		0			0
$25$	−9.64031	+	3.50878i	−1.92806	+	0.701757i
$26$		0			0
$27$	4.28743	−	2.93563i	0.825116	−	0.564963i
$28$		0			0
$29$	4.03650	−	1.46917i	0.749559	−	0.272817i	0.0611390	−	0.998129i	$-0.480527\pi$
$29$	4.03650	−	1.46917i	0.749559	−	0.272817i	0.688420	+	0.725312i	$0.258304\pi$
$30$		0			0
$31$	−7.31463	+	6.13770i	−1.31375	+	1.10236i	−0.326155	+	0.945316i	$0.605753\pi$
$31$	−7.31463	+	6.13770i	−1.31375	+	1.10236i	−0.987591	+	0.157047i	$0.949802\pi$
$32$		0			0
$33$	−3.95371	−	2.14968i	−0.688252	−	0.374211i
$34$		0			0
$35$	1.95314	−	3.38294i	0.330141	−	0.571820i
$36$		0			0
$37$	1.27882	+	2.21498i	0.210237	+	0.364141i	0.951789	−	0.306755i	$-0.0992432\pi$
$37$	1.27882	+	2.21498i	0.210237	+	0.364141i	−0.741552	+	0.670896i	$0.765910\pi$
$38$		0			0
$39$	6.26059	−	7.86122i	1.00250	−	1.25880i
$40$		0			0
$41$	−6.76212	−	2.46121i	−1.05607	−	0.384377i	−0.245117	−	0.969494i	$-0.578826\pi$
$41$	−6.76212	−	2.46121i	−1.05607	−	0.384377i	−0.810949	+	0.585117i	$0.801049\pi$
$42$		0			0
$43$	0.345401	−	1.95887i	0.0526732	−	0.298724i	−0.947079	−	0.321002i	$-0.895981\pi$
$43$	0.345401	−	1.95887i	0.0526732	−	0.298724i	0.999752	+	0.0222772i	$0.00709165\pi$
$44$		0			0
$45$	−5.33242	+	10.4353i	−0.794910	+	1.55561i
$46$		0			0
$47$	2.43116	+	2.03998i	0.354620	+	0.297562i	0.802642	−	0.596461i	$-0.203427\pi$
$47$	2.43116	+	2.03998i	0.354620	+	0.297562i	−0.448022	+	0.894023i	$0.647871\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	−4.68160	+	0.949638i	−0.655555	+	0.132976i
$52$		0			0
$53$	5.86437			0.805533			0.402766	−	0.915303i	$-0.368049\pi$
$53$	5.86437			0.805533			0.402766	+	0.915303i	$0.368049\pi$
$54$		0			0
$55$	10.1495			1.36856
$56$		0			0
$57$	−7.39657	−	8.37014i	−0.979700	−	1.10865i
$58$		0			0
$59$	−1.65224	−	9.37030i	−0.215103	−	1.21991i	−0.880728	−	0.473623i	$-0.842946\pi$
$59$	−1.65224	−	9.37030i	−0.215103	−	1.21991i	0.665625	−	0.746287i	$-0.268165\pi$
$60$		0			0
$61$	−9.86168	−	8.27493i	−1.26266	−	1.05950i	−0.995394	−	0.0958734i	$-0.969436\pi$
$61$	−9.86168	−	8.27493i	−1.26266	−	1.05950i	−0.267265	−	0.963623i	$-0.586120\pi$
$62$		0			0
$63$	−0.671442	−	2.92390i	−0.0845937	−	0.368376i
$64$		0			0
$65$	−3.93568	+	22.3203i	−0.488161	+	2.76850i
$66$		0			0
$67$	−13.6880	−	4.98203i	−1.67226	−	0.608651i	−0.680040	−	0.733175i	$-0.738037\pi$
$67$	−13.6880	−	4.98203i	−1.67226	−	0.608651i	−0.992217	+	0.124524i	$0.960260\pi$
$68$		0			0
$69$	−2.83541	−	7.21045i	−0.341344	−	0.868036i
$70$		0			0
$71$	−0.294622	−	0.510301i	−0.0349652	−	0.0605615i	0.848013	−	0.529975i	$-0.177799\pi$
$71$	−0.294622	−	0.510301i	−0.0349652	−	0.0605615i	−0.882978	+	0.469413i	$0.844465\pi$
$72$		0			0
$73$	−2.27808	+	3.94575i	−0.266629	+	0.461815i	−0.967989	−	0.250992i	$-0.919243\pi$
$73$	−2.27808	+	3.94575i	−0.266629	+	0.461815i	0.701360	+	0.712807i	$0.252577\pi$
$74$		0			0
$75$	−0.454777	−	17.7633i	−0.0525131	−	2.05113i
$76$		0			0
$77$	−1.99039	+	1.67013i	−0.226825	+	0.190329i
$78$		0			0
$79$	5.29605	−	1.92761i	0.595852	−	0.216873i	−0.0264492	−	0.999650i	$-0.508420\pi$
$79$	5.29605	−	1.92761i	0.595852	−	0.216873i	0.622301	+	0.782778i	$0.286198\pi$
$80$		0			0
$81$	2.46054	+	8.65712i	0.273393	+	0.961902i
$82$		0			0
$83$	1.61574	−	0.588081i	0.177351	−	0.0645503i	−0.251819	−	0.967774i	$-0.581029\pi$
$83$	1.61574	−	0.588081i	0.177351	−	0.0645503i	0.429169	+	0.903224i	$0.358806\pi$
$84$		0			0
$85$	8.25290	−	6.92500i	0.895152	−	0.751122i
$86$		0			0
$87$	0.190420	+	7.43768i	0.0204152	+	0.797403i
$88$		0			0
$89$	1.22942	−	2.12941i	0.130318	−	0.225717i	−0.793481	−	0.608595i	$-0.791734\pi$
$89$	1.22942	−	2.12941i	0.130318	−	0.225717i	0.923799	+	0.382878i	$0.125067\pi$
$90$		0			0
$91$	−2.90106	−	5.02478i	−0.304114	−	0.526740i
$92$		0			0
$93$	−6.05244	−	15.3913i	−0.627609	−	1.59601i
$94$		0			0
$95$	23.6723	+	8.61602i	2.42873	+	0.883985i
$96$		0			0
$97$	1.12954	−	6.40592i	0.114687	−	0.650423i	−0.872218	−	0.489118i	$-0.837319\pi$
$97$	1.12954	−	6.40592i	0.114687	−	0.650423i	0.986905	−	0.161305i	$-0.0515702\pi$
$98$		0			0
$99$	5.70695	−	5.30938i	0.573570	−	0.533613i
$100$		0			0
$101$	5.02351	+	4.21522i	0.499858	+	0.419430i	0.857543	−	0.514412i	$-0.171990\pi$
$101$	5.02351	+	4.21522i	0.499858	+	0.419430i	−0.357686	+	0.933842i	$0.616434\pi$
$102$		0			0
$103$	−0.807940	−	4.58206i	−0.0796087	−	0.451483i	−0.998390	−	0.0567172i	$-0.981937\pi$
$103$	−0.807940	−	4.58206i	−0.0796087	−	0.451483i	0.918782	−	0.394766i	$-0.129174\pi$
$104$		0			0
$105$	4.48024	+	5.06995i	0.437227	+	0.494777i
$106$		0			0
$107$	−15.8391			−1.53122			−0.765609	−	0.643306i	$-0.777562\pi$
$107$	−15.8391			−1.53122			−0.765609	+	0.643306i	$0.777562\pi$
$108$		0			0
$109$	15.6942			1.50323			0.751613	−	0.659604i	$-0.229276\pi$
$109$	15.6942			1.50323			0.751613	+	0.659604i	$0.229276\pi$
$110$		0			0
$111$	−4.34155	+	0.880660i	−0.412081	+	0.0835885i
$112$		0			0
$113$	2.43808	+	13.8270i	0.229355	+	1.30074i	0.854181	+	0.519975i	$0.174059\pi$
$113$	2.43808	+	13.8270i	0.229355	+	1.30074i	−0.624826	+	0.780764i	$0.714830\pi$
$114$		0			0
$115$	13.3857	+	11.2319i	1.24822	+	1.04738i
$116$		0			0
$117$	9.46314	+	14.6092i	0.874867	+	1.35063i
$118$		0			0
$119$	−0.478916	+	2.71607i	−0.0439022	+	0.248982i
$120$		0			0
$121$	3.99278	+	1.45325i	0.362980	+	0.132114i
$122$		0			0
$123$	7.76472	−	9.74991i	0.700121	−	0.879119i
$124$		0			0
$125$	10.2716	+	17.7909i	0.918716	+	1.59126i
$126$		0			0
$127$	−5.96400	+	10.3300i	−0.529219	+	0.916635i	0.470200	+	0.882560i	$0.344182\pi$
$127$	−5.96400	+	10.3300i	−0.529219	+	0.916635i	−0.999419	+	0.0340750i	$0.989151\pi$
$128$		0			0
$129$	3.02674	+	1.64567i	0.266489	+	0.144893i
$130$		0			0
$131$	8.75667	−	7.34772i	0.765074	−	0.641973i	−0.174368	−	0.984680i	$-0.555788\pi$
$131$	8.75667	−	7.34772i	0.765074	−	0.641973i	0.939442	+	0.342707i	$0.111344\pi$
$132$		0			0
$133$	−6.06007	+	2.20569i	−0.525475	+	0.191257i
$134$		0			0
$135$	−14.2014	−	14.5022i	−1.22226	−	1.24815i
$136$		0			0
$137$	−11.5130	+	4.19039i	−0.983623	+	0.358010i	−0.783248	−	0.621710i	$-0.786438\pi$
$137$	−11.5130	+	4.19039i	−0.983623	+	0.358010i	−0.200375	+	0.979719i	$0.564216\pi$
$138$		0			0
$139$	−14.1464	+	11.8702i	−1.19988	+	1.00682i	−0.200246	+	0.979746i	$0.564174\pi$
$139$	−14.1464	+	11.8702i	−1.19988	+	1.00682i	−0.999633	+	0.0270728i	$0.991381\pi$
$140$		0			0
$141$	−4.68857	+	2.86940i	−0.394849	+	0.241647i
$142$		0			0
$143$	7.53771	−	13.0557i	0.630335	−	1.09177i
$144$		0			0
$145$	−8.38981	−	14.5316i	−0.696736	−	1.20678i
$146$		0			0
$147$	−1.71288	−	0.257013i	−0.141276	−	0.0211981i
$148$		0			0
$149$	15.4906	+	5.63811i	1.26904	+	0.461892i	0.886792	−	0.462169i	$-0.152929\pi$
$149$	15.4906	+	5.63811i	1.26904	+	0.461892i	0.382246	+	0.924061i	$0.375151\pi$
$150$		0			0
$151$	−2.32576	+	13.1900i	−0.189267	+	1.07339i	0.731082	+	0.682290i	$0.239016\pi$
$151$	−2.32576	+	13.1900i	−0.189267	+	1.07339i	−0.920349	+	0.391098i	$0.872095\pi$
$152$		0			0
$153$	1.01792	−	8.21105i	0.0822938	−	0.663824i
$154$		0			0
$155$	28.5730	+	23.9756i	2.29504	+	1.92576i
$156$		0			0
$157$	−1.68816	−	9.57402i	−0.134730	−	0.764090i	−0.975048	−	0.221996i	$-0.928743\pi$
$157$	−1.68816	−	9.57402i	−0.134730	−	0.764090i	0.840318	−	0.542094i	$-0.182368\pi$
$158$		0			0
$159$	−3.22860	+	9.63060i	−0.256045	+	0.763756i
$160$		0			0
$161$	−4.47326			−0.352542
$162$		0			0
$163$	9.25287			0.724741			0.362370	−	0.932034i	$-0.381968\pi$
$163$	9.25287			0.724741			0.362370	+	0.932034i	$0.381968\pi$
$164$		0			0
$165$	−5.58779	+	16.6678i	−0.435009	+	1.29759i
$166$		0			0
$167$	−1.48911	−	8.44518i	−0.115231	−	0.653508i	−0.986636	−	0.162942i	$-0.947901\pi$
$167$	−1.48911	−	8.44518i	−0.115231	−	0.653508i	0.871405	−	0.490565i	$-0.163210\pi$
$168$		0			0
$169$	15.8300	+	13.2829i	1.21769	+	1.02176i
$170$		0			0
$171$	17.8178	−	7.53868i	1.36256	−	0.576497i
$172$		0			0
$173$	1.73931	−	9.86413i	0.132237	−	0.749956i	−0.844506	−	0.535546i	$-0.820106\pi$
$173$	1.73931	−	9.86413i	0.132237	−	0.749956i	0.976744	−	0.214410i	$-0.0687829\pi$
$174$		0			0
$175$	−9.64031	−	3.50878i	−0.728739	−	0.265239i
$176$		0			0
$177$	16.2978	+	2.44544i	1.22502	+	0.183811i
$178$		0			0
$179$	−4.13167	−	7.15627i	−0.308816	−	0.534885i	0.669288	−	0.743003i	$-0.266599\pi$
$179$	−4.13167	−	7.15627i	−0.308816	−	0.534885i	−0.978104	+	0.208119i	$0.933266\pi$
$180$		0			0
$181$	−0.843184	+	1.46044i	−0.0626734	+	0.108553i	−0.895660	−	0.444740i	$-0.853296\pi$
$181$	−0.843184	+	1.46044i	−0.0626734	+	0.108553i	0.832986	+	0.553294i	$0.186629\pi$
$182$		0			0
$183$	19.0186	−	11.6394i	1.40590	−	0.860406i
$184$		0			0
$185$	7.65344	−	6.42200i	0.562692	−	0.472155i
$186$		0			0
$187$	−6.73377	+	2.45089i	−0.492422	+	0.179227i
$188$		0			0
$189$	5.17135	+	0.507082i	0.376160	+	0.0368848i
$190$		0			0
$191$	13.2725	−	4.83079i	0.960363	−	0.349544i	0.186187	−	0.982514i	$-0.440387\pi$
$191$	13.2725	−	4.83079i	0.960363	−	0.349544i	0.774176	+	0.632971i	$0.218165\pi$
$192$		0			0
$193$	−11.3873	+	9.55508i	−0.819676	+	0.687790i	−0.952896	−	0.303297i	$-0.901913\pi$
$193$	−11.3873	+	9.55508i	−0.819676	+	0.687790i	0.133220	+	0.991086i	$0.457468\pi$
$194$		0			0
$195$	−34.4882	−	18.7516i	−2.46975	−	1.34283i
$196$		0			0
$197$	−4.30988	+	7.46493i	−0.307066	+	0.531854i	−0.977719	−	0.209917i	$-0.932681\pi$
$197$	−4.30988	+	7.46493i	−0.307066	+	0.531854i	0.670653	+	0.741771i	$0.266014\pi$
$198$		0			0
$199$	−1.16750	−	2.02217i	−0.0827619	−	0.143348i	0.821673	−	0.569959i	$-0.193041\pi$
$199$	−1.16750	−	2.02217i	−0.0827619	−	0.143348i	−0.904435	+	0.426611i	$0.859707\pi$
$200$		0			0
$201$	15.7175	−	19.7359i	1.10863	−	1.39207i
$202$		0			0
$203$	4.03650	+	1.46917i	0.283307	+	0.103115i
$204$		0			0
$205$	−4.88124	+	27.6829i	−0.340921	+	1.93346i
$206$		0			0
$207$	13.4022	−	0.686698i	0.931517	−	0.0477288i
$208$		0			0
$209$	−12.8360	−	10.7707i	−0.887884	−	0.745023i
$210$		0			0
$211$	−0.0920359	−	0.521961i	−0.00633601	−	0.0359333i	0.981476	−	0.191586i	$-0.0613631\pi$
$211$	−0.0920359	−	0.521961i	−0.00633601	−	0.0359333i	−0.987812	+	0.155653i	$0.950252\pi$
$212$		0			0
$213$	1.00023	−	0.202892i	0.0685347	−	0.0139019i
$214$		0			0
$215$	−7.76992			−0.529904
$216$		0			0
$217$	−9.54857			−0.648199
$218$		0			0
$219$	−5.22562	−	5.91344i	−0.353115	−	0.399593i
$220$		0			0
$221$	−2.77873	−	15.7590i	−0.186918	−	1.06006i
$222$		0			0
$223$	−8.20151	−	6.88188i	−0.549214	−	0.460845i	0.325461	−	0.945555i	$-0.394480\pi$
$223$	−8.20151	−	6.88188i	−0.549214	−	0.460845i	−0.874675	+	0.484711i	$0.838925\pi$
$224$		0			0
$225$	29.4217	+	9.03266i	1.96144	+	0.602178i
$226$		0			0
$227$	3.81524	−	21.6373i	0.253227	−	1.43612i	−0.547357	−	0.836899i	$-0.684366\pi$
$227$	3.81524	−	21.6373i	0.253227	−	1.43612i	0.800584	−	0.599221i	$-0.204523\pi$
$228$		0			0
$229$	8.43819	+	3.07125i	0.557612	+	0.202954i	0.605425	−	0.795902i	$-0.293003\pi$
$229$	8.43819	+	3.07125i	0.557612	+	0.202954i	−0.0478136	+	0.998856i	$0.515225\pi$
$230$		0			0
$231$	−1.64693	−	4.18814i	−0.108360	−	0.275560i
$232$		0			0
$233$	−14.6625	−	25.3962i	−0.960571	−	1.66376i	−0.721070	−	0.692862i	$-0.756349\pi$
$233$	−14.6625	−	25.3962i	−0.960571	−	1.66376i	−0.239501	−	0.970896i	$-0.576984\pi$
$234$		0			0
$235$	6.19857	−	10.7362i	0.404350	−	0.700355i
$236$		0			0
$237$	0.249839	+	9.75854i	0.0162288	+	0.633885i
$238$		0			0
$239$	−3.47252	+	2.91379i	−0.224618	+	0.188477i	−0.748151	−	0.663528i	$-0.769058\pi$
$239$	−3.47252	+	2.91379i	−0.224618	+	0.188477i	0.523533	+	0.852006i	$0.324614\pi$
$240$		0			0
$241$	7.50260	−	2.73072i	0.483285	−	0.175901i	−0.0888761	−	0.996043i	$-0.528328\pi$
$241$	7.50260	−	2.73072i	0.483285	−	0.175901i	0.572161	+	0.820141i	$0.306105\pi$
$242$		0			0
$243$	−15.5716	−	0.725390i	−0.998917	−	0.0465338i
$244$		0			0
$245$	3.67070	−	1.33603i	0.234512	−	0.0853555i
$246$		0			0
$247$	28.6637	−	24.0517i	1.82383	−	1.53037i
$248$		0			0
$249$	0.0762217	+	2.97717i	0.00483036	+	0.188671i
$250$		0			0
$251$	−13.3070	+	23.0484i	−0.839930	+	1.45480i	0.0500232	+	0.998748i	$0.484070\pi$
$251$	−13.3070	+	23.0484i	−0.839930	+	1.45480i	−0.889953	+	0.456053i	$0.849263\pi$
$252$		0			0
$253$	−5.81135	−	10.0656i	−0.365357	−	0.632816i
$254$		0			0
$255$	6.82880	+	17.3656i	0.427636	+	1.08748i
$256$		0			0
$257$	−28.8962	−	10.5174i	−1.80250	−	0.656055i	−0.998076	−	0.0619956i	$-0.980254\pi$
$257$	−28.8962	−	10.5174i	−1.80250	−	0.656055i	−0.804421	−	0.594060i	$-0.797524\pi$
$258$		0			0
$259$	−0.444130	+	2.51878i	−0.0275969	+	0.156510i
$260$		0			0
$261$	−12.3192	−	3.78207i	−0.762538	−	0.234104i
$262$		0			0
$263$	−0.106866	−	0.0896714i	−0.00658965	−	0.00552938i	0.639487	−	0.768802i	$-0.279147\pi$
$263$	−0.106866	−	0.0896714i	−0.00658965	−	0.00552938i	−0.646076	+	0.763273i	$0.723591\pi$
$264$		0			0
$265$	−3.97790	−	22.5598i	−0.244361	−	1.38584i
$266$		0			0
$267$	2.82012	+	3.19132i	0.172589	+	0.195305i
$268$		0			0
$269$	3.65554			0.222882			0.111441	−	0.993771i	$-0.464453\pi$
$269$	3.65554			0.222882			0.111441	+	0.993771i	$0.464453\pi$
$270$		0			0
$271$	−0.183721			−0.0111602			−0.00558012	−	0.999984i	$-0.501776\pi$
$271$	−0.183721			−0.0111602			−0.00558012	+	0.999984i	$0.501776\pi$
$272$		0			0
$273$	9.84898	−	1.99781i	0.596087	−	0.120913i
$274$		0			0
$275$	−4.62869	−	26.2506i	−0.279121	−	1.58297i
$276$		0			0
$277$	−16.0714	−	13.4855i	−0.965637	−	0.810266i	0.0162239	−	0.999868i	$-0.494836\pi$
$277$	−16.0714	−	13.4855i	−0.965637	−	0.810266i	−0.981861	+	0.189603i	$0.939280\pi$
$278$		0			0
$279$	28.6082	−	1.46582i	1.71273	−	0.0877562i
$280$		0			0
$281$	−1.03341	+	5.86077i	−0.0616482	+	0.349624i	0.938344	+	0.345703i	$0.112359\pi$
$281$	−1.03341	+	5.86077i	−0.0616482	+	0.349624i	−0.999992	+	0.00392157i	$0.998752\pi$
$282$		0			0
$283$	−12.5899	−	4.58236i	−0.748393	−	0.272393i	−0.0604637	−	0.998170i	$-0.519258\pi$
$283$	−12.5899	−	4.58236i	−0.748393	−	0.272393i	−0.687929	+	0.725778i	$0.741480\pi$
$284$		0			0
$285$	−27.1821	+	34.1317i	−1.61013	+	2.02179i
$286$		0			0
$287$	−3.59805	−	6.23200i	−0.212386	−	0.367864i
$288$		0			0
$289$	4.69680	−	8.13510i	0.276282	−	0.478535i
$290$		0			0
$291$	9.89810	+	5.38171i	0.580237	+	0.315481i
$292$		0			0
$293$	18.4245	−	15.4600i	1.07637	−	0.903182i	0.0807563	−	0.996734i	$-0.474266\pi$
$293$	18.4245	−	15.4600i	1.07637	−	0.903182i	0.995614	+	0.0935516i	$0.0298220\pi$
$294$		0			0
$295$	−34.9262	+	12.7121i	−2.03348	+	0.740126i
$296$		0			0
$297$	5.57725	+	12.2951i	0.323625	+	0.713437i
$298$		0			0
$299$	24.3891	−	8.87692i	1.41046	−	0.513365i
$300$		0			0
$301$	1.52373	−	1.27856i	0.0878262	−	0.0736949i
$302$		0			0
$303$	−9.68801	+	5.92905i	−0.556562	+	0.340615i
$304$		0			0
$305$	−25.1437	+	43.5502i	−1.43973	+	2.49368i
$306$		0			0
$307$	10.1751	+	17.6238i	0.580723	+	1.00584i	0.995394	+	0.0958699i	$0.0305633\pi$
$307$	10.1751	+	17.6238i	0.580723	+	1.00584i	−0.414671	+	0.909971i	$0.636103\pi$
$308$		0			0
$309$	7.96957	+	1.19581i	0.453373	+	0.0680275i
$310$		0			0
$311$	26.1932	+	9.53354i	1.48528	+	0.540597i	0.952202	−	0.305469i	$-0.0988134\pi$
$311$	26.1932	+	9.53354i	1.48528	+	0.540597i	0.533077	+	0.846067i	$0.321036\pi$
$312$		0			0
$313$	−4.82469	+	27.3622i	−0.272708	+	1.54660i	0.473443	+	0.880824i	$0.343011\pi$
$313$	−4.82469	+	27.3622i	−0.272708	+	1.54660i	−0.746151	+	0.665777i	$0.768100\pi$
$314$		0			0
$315$	−10.7926	+	4.56632i	−0.608093	+	0.257283i
$316$		0			0
$317$	−5.87372	−	4.92864i	−0.329901	−	0.276820i	0.462758	−	0.886484i	$-0.346860\pi$
$317$	−5.87372	−	4.92864i	−0.329901	−	0.276820i	−0.792660	+	0.609665i	$0.791304\pi$
$318$		0			0
$319$	1.93808	+	10.9914i	0.108512	+	0.615401i
$320$		0			0
$321$	8.72013	−	26.0113i	0.486710	−	1.45181i
$322$		0			0
$323$	−17.7861			−0.989647
$324$		0			0
$325$	59.5239			3.30179
$326$		0			0
$327$	−8.64035	+	25.7733i	−0.477813	+	1.42527i
$328$		0			0
$329$	0.551098	+	3.12543i	0.0303830	+	0.172311i
$330$		0			0
$331$	1.15992	+	0.973286i	0.0637548	+	0.0534966i	0.674108	−	0.738633i	$-0.264528\pi$
$331$	1.15992	+	0.973286i	0.0637548	+	0.0534966i	−0.610353	+	0.792129i	$0.708973\pi$
$332$		0			0
$333$	0.943981	−	7.61463i	0.0517298	−	0.417279i
$334$		0			0
$335$	−9.88070	+	56.0362i	−0.539840	+	3.06159i
$336$		0			0
$337$	21.6950	+	7.89634i	1.18180	+	0.430141i	0.856838	−	0.515585i	$-0.172426\pi$
$337$	21.6950	+	7.89634i	1.18180	+	0.430141i	0.324964	+	0.945726i	$0.394648\pi$
$338$		0			0
$339$	−24.0494	−	3.60855i	−1.30618	−	0.195990i
$340$		0			0
$341$	−12.4049	−	21.4858i	−0.671760	−	1.16352i
$342$		0			0
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$		0			0
$345$	−25.8148	+	15.7986i	−1.38982	+	0.850569i
$346$		0			0
$347$	3.71889	−	3.12052i	0.199641	−	0.167518i	−0.537487	−	0.843272i	$-0.680626\pi$
$347$	3.71889	−	3.12052i	0.199641	−	0.167518i	0.737127	+	0.675754i	$0.236182\pi$
$348$		0			0
$349$	−24.4835	+	8.91126i	−1.31057	+	0.477009i	−0.900425	−	0.435011i	$-0.856745\pi$
$349$	−24.4835	+	8.91126i	−1.31057	+	0.477009i	−0.410146	+	0.912020i	$0.634522\pi$
$350$		0			0
$351$	−29.2015	+	7.49752i	−1.55866	+	0.400188i
$352$		0			0
$353$	−29.4202	+	10.7081i	−1.56588	+	0.569933i	−0.972074	−	0.234676i	$-0.924597\pi$
$353$	−29.4202	+	10.7081i	−1.56588	+	0.569933i	−0.593805	+	0.804609i	$0.702375\pi$
$354$		0			0
$355$	−1.76324	+	1.47954i	−0.0935833	+	0.0785257i
$356$		0			0
$357$	−4.19673	−	2.28181i	−0.222114	−	0.120766i
$358$		0			0
$359$	−1.25782	+	2.17861i	−0.0663854	+	0.114983i	−0.897308	−	0.441406i	$-0.854480\pi$
$359$	−1.25782	+	2.17861i	−0.0663854	+	0.114983i	0.830922	+	0.556388i	$0.187813\pi$
$360$		0			0
$361$	−11.2948	−	19.5631i	−0.594461	−	1.02964i
$362$		0			0
$363$	−4.58477	+	5.75695i	−0.240638	+	0.302162i
$364$		0			0
$365$	16.7243	+	6.08715i	0.875390	+	0.318616i
$366$		0			0
$367$	−3.69631	+	20.9628i	−0.192946	+	1.09425i	0.722368	+	0.691509i	$0.243054\pi$
$367$	−3.69631	+	20.9628i	−0.192946	+	1.09425i	−0.915314	+	0.402741i	$0.868057\pi$
$368$		0			0
$369$	11.7367	+	18.1192i	0.610988	+	0.943247i
$370$		0			0
$371$	4.49236	+	3.76954i	0.233232	+	0.195705i
$372$		0			0
$373$	−2.37890	−	13.4914i	−0.123175	−	0.698558i	−0.982375	−	0.186919i	$-0.940150\pi$
$373$	−2.37890	−	13.4914i	−0.123175	−	0.698558i	0.859201	−	0.511639i	$-0.170961\pi$
$374$		0			0
$375$	−34.8715	+	7.07351i	−1.80076	+	0.365274i
$376$		0			0
$377$	−24.9233			−1.28362
$378$		0			0
$379$	−8.40098			−0.431529			−0.215765	−	0.976445i	$-0.569224\pi$
$379$	−8.40098			−0.431529			−0.215765	+	0.976445i	$0.569224\pi$
$380$		0			0
$381$	−13.6806	−	15.4813i	−0.700880	−	0.793133i
$382$		0			0
$383$	2.90293	+	16.4633i	0.148333	+	0.841237i	0.964631	+	0.263605i	$0.0849117\pi$
$383$	2.90293	+	16.4633i	0.148333	+	0.841237i	−0.816298	+	0.577631i	$0.803977\pi$
$384$		0			0
$385$	7.77500	+	6.52400i	0.396251	+	0.332494i
$386$		0			0
$387$	−4.36892	+	4.06456i	−0.222085	+	0.206613i
$388$		0			0
$389$	2.86193	−	16.2308i	0.145106	−	0.822935i	−0.822177	−	0.569233i	$-0.807240\pi$
$389$	2.86193	−	16.2308i	0.145106	−	0.822935i	0.967282	−	0.253703i	$-0.0816485\pi$
$390$		0			0
$391$	−11.5931	−	4.21954i	−0.586288	−	0.213391i
$392$		0			0
$393$	7.24565	+	18.4257i	0.365495	+	0.929452i
$394$		0			0
$395$	−11.0078	−	19.0660i	−0.553861	−	0.959316i
$396$		0			0
$397$	−1.01951	+	1.76585i	−0.0511678	+	0.0886253i	−0.890475	−	0.455032i	$-0.849628\pi$
$397$	−1.01951	+	1.76585i	−0.0511678	+	0.0886253i	0.839307	+	0.543658i	$0.182961\pi$
$398$		0			0
$399$	−0.285881	−	11.1663i	−0.0143119	−	0.559016i
$400$		0			0
$401$	−12.1592	+	10.2028i	−0.607203	+	0.509504i	−0.893752	−	0.448562i	$-0.851936\pi$
$401$	−12.1592	+	10.2028i	−0.607203	+	0.509504i	0.286549	+	0.958066i	$0.407492\pi$
$402$		0			0
$403$	52.0608	−	18.9486i	2.59333	−	0.943895i
$404$		0			0
$405$	31.6343	−	15.3378i	1.57192	−	0.762142i
$406$		0			0
$407$	−6.24466	+	2.27287i	−0.309536	+	0.112662i
$408$		0			0
$409$	18.0344	−	15.1326i	0.891742	−	0.748260i	−0.0768170	−	0.997045i	$-0.524476\pi$
$409$	18.0344	−	15.1326i	0.891742	−	0.748260i	0.968559	+	0.248785i	$0.0800313\pi$
$410$		0			0
$411$	−0.543121	−	21.2140i	−0.0267902	−	1.04641i
$412$		0			0
$413$	4.75743	−	8.24011i	0.234098	−	0.405469i
$414$		0			0
$415$	−3.35829	−	5.81674i	−0.164852	−	0.285532i
$416$		0			0
$417$	−11.7053	−	29.7666i	−0.573212	−	1.45768i
$418$		0			0
$419$	36.0263	+	13.1125i	1.76000	+	0.640587i	0.999957	−	0.00928854i	$-0.00295668\pi$
$419$	36.0263	+	13.1125i	1.76000	+	0.640587i	0.760041	+	0.649875i	$0.225179\pi$
$420$		0			0
$421$	−1.60634	+	9.11000i	−0.0782882	+	0.443994i	0.920316	+	0.391176i	$0.127932\pi$
$421$	−1.60634	+	9.11000i	−0.0782882	+	0.443994i	−0.998604	+	0.0528184i	$0.983180\pi$
$422$		0			0
$423$	−2.13092	−	9.27941i	−0.103609	−	0.451181i
$424$		0			0
$425$	−21.6745	−	18.1870i	−1.05137	−	0.882201i
$426$		0			0
$427$	−2.23546	−	12.6779i	−0.108182	−	0.613528i
$428$		0			0
$429$	17.2905	+	19.5664i	0.834795	+	0.944674i
$430$		0			0
$431$	30.6140			1.47462			0.737312	−	0.675552i	$-0.236095\pi$
$431$	30.6140			1.47462			0.737312	+	0.675552i	$0.236095\pi$
$432$		0			0
$433$	14.9376			0.717854			0.358927	−	0.933366i	$-0.383143\pi$
$433$	14.9376			0.717854			0.358927	+	0.933366i	$0.383143\pi$
$434$		0			0
$435$	28.4831	−	5.77764i	1.36566	−	0.277017i
$436$		0			0
$437$	−5.00941	−	28.4098i	−0.239632	−	1.35902i
$438$		0			0
$439$	21.0415	+	17.6559i	1.00425	+	0.842669i	0.987568	−	0.157192i	$-0.0502441\pi$
$439$	21.0415	+	17.6559i	1.00425	+	0.842669i	0.0166858	+	0.999861i	$0.494689\pi$
$440$		0			0
$441$	1.36509	−	2.67143i	0.0650043	−	0.127211i
$442$		0			0
$443$	2.54351	−	14.4250i	0.120846	−	0.685350i	−0.862843	−	0.505472i	$-0.831318\pi$
$443$	2.54351	−	14.4250i	0.120846	−	0.685350i	0.983689	−	0.179878i	$-0.0575704\pi$
$444$		0			0
$445$	−9.02564	−	3.28506i	−0.427856	−	0.155727i
$446$		0			0
$447$	−17.7873	+	22.3350i	−0.841311	+	1.05641i
$448$		0			0
$449$	8.00684	+	13.8683i	0.377866	+	0.654484i	0.990752	−	0.135688i	$-0.0433246\pi$
$449$	8.00684	+	13.8683i	0.377866	+	0.654484i	−0.612885	+	0.790172i	$0.709991\pi$
$450$		0			0
$451$	9.34868	−	16.1924i	0.440212	−	0.762470i
$452$		0			0
$453$	−20.3805	−	11.0811i	−0.957560	−	0.520636i
$454$		0			0
$455$	−17.3621	+	14.5686i	−0.813950	+	0.682985i
$456$		0			0
$457$	−15.2803	+	5.56157i	−0.714781	+	0.260159i	−0.673709	−	0.738997i	$-0.735300\pi$
$457$	−15.2803	+	5.56157i	−0.714781	+	0.260159i	−0.0410726	+	0.999156i	$0.513077\pi$
$458$		0			0
$459$	12.9240	+	6.19221i	0.603240	+	0.289028i
$460$		0			0
$461$	−15.8758	+	5.77833i	−0.739411	+	0.269124i	−0.684143	−	0.729348i	$-0.739824\pi$
$461$	−15.8758	+	5.77833i	−0.739411	+	0.269124i	−0.0552683	+	0.998472i	$0.517601\pi$
$462$		0			0
$463$	−2.24634	+	1.88490i	−0.104396	+	0.0875988i	−0.693492	−	0.720465i	$-0.743929\pi$
$463$	−2.24634	+	1.88490i	−0.104396	+	0.0875988i	0.589096	+	0.808063i	$0.299484\pi$
$464$		0			0
$465$	−55.1040	+	33.7235i	−2.55539	+	1.56389i
$466$		0			0
$467$	−9.63515	+	16.6886i	−0.445861	+	0.772255i	−0.998112	−	0.0614237i	$-0.980436\pi$
$467$	−9.63515	+	16.6886i	−0.445861	+	0.772255i	0.552250	+	0.833678i	$0.313769\pi$
$468$		0			0
$469$	−7.28324	−	12.6149i	−0.336309	−	0.582504i
$470$		0			0
$471$	16.6521	+	2.49861i	0.767288	+	0.115130i
$472$		0			0
$473$	4.85649	+	1.76762i	0.223302	+	0.0812751i
$474$		0			0
$475$	11.4886	−	65.1551i	0.527133	−	2.98952i
$476$		0			0
$477$	−14.0381	−	10.6042i	−0.642761	−	0.485532i
$478$		0			0
$479$	−17.3618	−	14.5683i	−0.793280	−	0.665641i	0.153275	−	0.988184i	$-0.451018\pi$
$479$	−17.3618	−	14.5683i	−0.793280	−	0.665641i	−0.946555	+	0.322543i	$0.895462\pi$
$480$		0			0
$481$	−2.57689	−	14.6143i	−0.117496	−	0.666354i
$482$		0			0
$483$	2.46274	−	7.34609i	0.112058	−	0.334259i
$484$		0			0
$485$	−25.4093			−1.15378
$486$		0			0
$487$	5.47149			0.247937			0.123968	−	0.992286i	$-0.460438\pi$
$487$	5.47149			0.247937			0.123968	+	0.992286i	$0.460438\pi$
$488$		0			0
$489$	−5.09413	+	15.1953i	−0.230365	+	0.687154i
$490$		0			0
$491$	−3.70200	−	20.9951i	−0.167069	−	0.947496i	−0.946905	−	0.321512i	$-0.895809\pi$
$491$	−3.70200	−	20.9951i	−0.167069	−	0.947496i	0.779836	−	0.625984i	$-0.215302\pi$
$492$		0			0
$493$	9.07533	+	7.61511i	0.408732	+	0.342967i
$494$		0			0
$495$	−24.2959	−	18.3528i	−1.09202	−	0.824897i
$496$		0			0
$497$	0.102321	−	0.580292i	0.00458973	−	0.0260297i
$498$		0			0
$499$	2.29020	+	0.833563i	0.102523	+	0.0373154i	0.392772	−	0.919636i	$-0.371516\pi$
$499$	2.29020	+	0.833563i	0.102523	+	0.0373154i	−0.290249	+	0.956951i	$0.593738\pi$
$500$		0			0
$501$	14.6887	+	2.20400i	0.656243	+	0.0984676i
$502$		0			0
$503$	−10.0718	−	17.4449i	−0.449081	−	0.777831i	0.549245	−	0.835661i	$-0.314915\pi$
$503$	−10.0718	−	17.4449i	−0.449081	−	0.777831i	−0.998326	+	0.0578298i	$0.981582\pi$
$504$		0			0
$505$	12.8081	−	22.1844i	0.569955	−	0.987191i
$506$		0			0
$507$	−30.5287	+	18.6835i	−1.35583	+	0.829763i
$508$		0			0
$509$	−28.5580	+	23.9630i	−1.26581	+	1.06214i	−0.270772	+	0.962643i	$0.587279\pi$
$509$	−28.5580	+	23.9630i	−1.26581	+	1.06214i	−0.995038	+	0.0994972i	$0.968277\pi$
$510$		0			0
$511$	−4.28139	+	1.55830i	−0.189398	+	0.0689351i
$512$		0			0
$513$	2.57068	+	33.4112i	0.113498	+	1.47514i
$514$		0			0
$515$	−17.0788	+	6.21618i	−0.752583	+	0.273918i
$516$		0			0
$517$	−6.31678	+	5.30041i	−0.277812	+	0.233112i
$518$		0			0
$519$	15.2415	+	8.28700i	0.669029	+	0.363759i
$520$		0			0
$521$	12.3378	−	21.3697i	0.540530	−	0.936226i	−0.458343	−	0.888775i	$-0.651557\pi$
$521$	12.3378	−	21.3697i	0.540530	−	0.936226i	0.998874	−	0.0474505i	$-0.0151097\pi$
$522$		0			0
$523$	−2.22320	−	3.85069i	−0.0972136	−	0.168379i	0.813317	−	0.581821i	$-0.197660\pi$
$523$	−2.22320	−	3.85069i	−0.0972136	−	0.168379i	−0.910530	+	0.413442i	$0.864326\pi$
$524$		0			0
$525$	11.0696	−	13.8998i	0.483119	−	0.606637i
$526$		0			0
$527$	−24.7465	−	9.00698i	−1.07797	−	0.392350i
$528$		0			0
$529$	−0.519199	+	2.94452i	−0.0225739	+	0.128023i
$530$		0			0
$531$	−12.9886	+	25.4183i	−0.563659	+	1.10306i
$532$		0			0
$533$	31.9843	+	26.8381i	1.38540	+	1.16249i
$534$		0			0
$535$	10.7439	+	60.9318i	0.464500	+	2.63431i
$536$		0			0
$537$	14.0269	−	2.84528i	0.605304	−	0.122783i
$538$		0			0
$539$	−2.59826			−0.111915
$540$		0			0
$541$	−30.1369			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$541$	−30.1369			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$542$		0			0
$543$	−1.93415	−	2.18873i	−0.0830025	−	0.0939276i
$544$		0			0
$545$	−10.6456	−	60.3743i	−0.456008	−	2.58615i
$546$		0			0
$547$	−1.57433	−	1.32102i	−0.0673133	−	0.0564826i	0.608510	−	0.793546i	$-0.291767\pi$
$547$	−1.57433	−	1.32102i	−0.0673133	−	0.0564826i	−0.675824	+	0.737063i	$0.736212\pi$
$548$		0			0
$549$	8.64381	+	37.6408i	0.368909	+	1.60647i
$550$		0			0
$551$	−4.81040	+	27.2811i	−0.204930	+	1.16222i
$552$		0			0
$553$	5.29605	+	1.92761i	0.225211	+	0.0819701i
$554$		0			0
$555$	6.33279	+	16.1043i	0.268812	+	0.683588i
$556$		0			0
$557$	9.53788	+	16.5201i	0.404133	+	0.699979i	0.994220	−	0.107361i	$-0.0342399\pi$
$557$	9.53788	+	16.5201i	0.404133	+	0.699979i	−0.590087	+	0.807340i	$0.700907\pi$
$558$		0			0
$559$	−5.77045	+	9.99471i	−0.244064	+	0.422731i
$560$		0			0
$561$	−0.317662	−	12.4077i	−0.0134117	−	0.523853i
$562$		0			0
$563$	−25.5294	+	21.4217i	−1.07594	+	0.902817i	−0.995577	−	0.0939490i	$-0.970051\pi$
$563$	−25.5294	+	21.4217i	−1.07594	+	0.902817i	−0.0803584	+	0.996766i	$0.525606\pi$
$564$		0			0
$565$	51.5379	−	18.7583i	2.16822	−	0.789166i
$566$		0			0
$567$	−3.67981	+	8.21334i	−0.154537	+	0.344928i
$568$		0			0
$569$	42.9764	−	15.6421i	1.80167	−	0.655753i	0.803494	−	0.595313i	$-0.202972\pi$
$569$	42.9764	−	15.6421i	1.80167	−	0.655753i	0.998172	−	0.0604396i	$-0.0192503\pi$
$570$		0			0
$571$	−15.1779	+	12.7358i	−0.635177	+	0.532977i	−0.902533	−	0.430621i	$-0.858294\pi$
$571$	−15.1779	+	12.7358i	−0.635177	+	0.532977i	0.267356	+	0.963598i	$0.413850\pi$
$572$		0			0
$573$	0.626123	+	24.4560i	0.0261567	+	1.02166i
$574$		0			0
$575$	22.9456	−	39.7429i	0.956897	−	1.65739i
$576$		0			0
$577$	21.3573	+	36.9919i	0.889114	+	1.53999i	0.840924	+	0.541153i	$0.182012\pi$
$577$	21.3573	+	36.9919i	0.889114	+	1.53999i	0.0481898	+	0.998838i	$0.484655\pi$
$578$		0			0
$579$	−9.42235	−	23.9610i	−0.391579	−	0.995786i
$580$		0			0
$581$	1.61574	+	0.588081i	0.0670322	+	0.0243977i
$582$		0			0
$583$	−2.64591	+	15.0057i	−0.109582	+	0.621472i
$584$		0			0
$585$	49.7818	−	46.3137i	2.05822	−	1.91484i
$586$		0			0
$587$	−17.3037	−	14.5195i	−0.714199	−	0.599285i	0.211575	−	0.977362i	$-0.432141\pi$
$587$	−17.3037	−	14.5195i	−0.714199	−	0.599285i	−0.925774	+	0.378077i	$0.876585\pi$
$588$		0			0
$589$	−10.6930	−	60.6431i	−0.440598	−	2.49876i
$590$		0			0
$591$	−9.88630	−	11.1876i	−0.406668	−	0.460195i
$592$		0			0
$593$	11.7212			0.481332			0.240666	−	0.970608i	$-0.422634\pi$
$593$	11.7212			0.481332			0.240666	+	0.970608i	$0.422634\pi$
$594$		0			0
$595$	10.7734			0.441666
$596$		0			0
$597$	3.96362	−	0.803999i	0.162220	−	0.0329055i
$598$		0			0
$599$	−1.83954	−	10.4326i	−0.0751617	−	0.426263i	−0.999049	−	0.0435989i	$-0.986118\pi$
$599$	−1.83954	−	10.4326i	−0.0751617	−	0.426263i	0.923887	−	0.382665i	$-0.124993\pi$
$600$		0			0
$601$	−5.10147	−	4.28064i	−0.208093	−	0.174611i	0.532784	−	0.846251i	$-0.321146\pi$
$601$	−5.10147	−	4.28064i	−0.208093	−	0.174611i	−0.740878	+	0.671640i	$0.765590\pi$
$602$		0			0
$603$	23.7576	+	36.6772i	0.967485	+	1.49361i
$604$		0			0
$605$	2.88219	−	16.3457i	0.117178	−	0.664548i
$606$		0			0
$607$	−9.06017	−	3.29763i	−0.367741	−	0.133847i	0.151538	−	0.988451i	$-0.451577\pi$
$607$	−9.06017	−	3.29763i	−0.367741	−	0.133847i	−0.519279	+	0.854605i	$0.673800\pi$
$608$		0			0
$609$	−4.63498	+	5.81999i	−0.187819	+	0.235838i
$610$		0			0
$611$	−9.20694	−	15.9469i	−0.372473	−	0.645142i
$612$		0			0
$613$	−6.04047	+	10.4624i	−0.243972	+	0.422573i	−0.961842	−	0.273605i	$-0.911784\pi$
$613$	−6.04047	+	10.4624i	−0.243972	+	0.422573i	0.717870	+	0.696177i	$0.245117\pi$
$614$		0			0
$615$	−42.7742	−	23.2568i	−1.72482	−	0.937805i
$616$		0			0
$617$	−20.6884	+	17.3596i	−0.832883	+	0.698872i	−0.955951	−	0.293526i	$-0.905171\pi$
$617$	−20.6884	+	17.3596i	−0.832883	+	0.698872i	0.123068	+	0.992398i	$0.460727\pi$
$618$		0			0
$619$	24.4523	−	8.89991i	0.982820	−	0.357717i	0.199884	−	0.979819i	$-0.435943\pi$
$619$	24.4523	−	8.89991i	0.982820	−	0.357717i	0.782936	+	0.622102i	$0.213721\pi$
$620$		0			0
$621$	−6.25082	+	22.3875i	−0.250837	+	0.898378i
$622$		0			0
$623$	2.31055	−	0.840970i	0.0925701	−	0.0336928i
$624$		0			0
$625$	22.1786	−	18.6100i	0.887143	−	0.744401i
$626$		0			0
$627$	24.7547	−	15.1498i	0.988606	−	0.605025i
$628$		0			0
$629$	−3.52695	+	6.10885i	−0.140629	+	0.243576i
$630$		0			0
$631$	9.44090	+	16.3521i	0.375836	+	0.650967i	0.990452	−	0.137859i	$-0.0440222\pi$
$631$	9.44090	+	16.3521i	0.375836	+	0.650967i	−0.614616	+	0.788827i	$0.710689\pi$
$632$		0			0
$633$	0.907847	+	0.136220i	0.0360837	+	0.00541427i
$634$		0			0
$635$	43.7841	+	15.9361i	1.73752	+	0.632405i
$636$		0			0
$637$	1.00753	−	5.71397i	0.0399197	−	0.226396i
$638$		0			0
$639$	−0.217480	+	1.75430i	−0.00860337	+	0.0693992i
$640$		0			0
$641$	17.4067	+	14.6059i	0.687521	+	0.576899i	0.918193	−	0.396133i	$-0.129648\pi$
$641$	17.4067	+	14.6059i	0.687521	+	0.576899i	−0.230672	+	0.973032i	$0.574092\pi$
$642$		0			0
$643$	3.47855	+	19.7278i	0.137181	+	0.777989i	0.973316	+	0.229467i	$0.0736983\pi$
$643$	3.47855	+	19.7278i	0.137181	+	0.777989i	−0.836136	+	0.548522i	$0.815191\pi$
$644$		0			0
$645$	4.27770	−	12.7599i	0.168434	−	0.502422i
$646$		0			0
$647$	−32.8500			−1.29147			−0.645734	−	0.763562i	$-0.723448\pi$
$647$	−32.8500			−1.29147			−0.645734	+	0.763562i	$0.723448\pi$
$648$		0			0
$649$	24.7221			0.970427
$650$		0			0
$651$	5.25693	−	15.6809i	0.206035	−	0.614582i
$652$		0			0
$653$	−7.88152	−	44.6983i	−0.308428	−	1.74918i	−0.606915	−	0.794767i	$-0.707593\pi$
$653$	−7.88152	−	44.6983i	−0.308428	−	1.74918i	0.298487	−	0.954414i	$-0.403518\pi$
$654$		0			0
$655$	−34.2060	−	28.7022i	−1.33654	−	1.12149i
$656$		0			0
$657$	12.5881	−	5.32602i	0.491110	−	0.207788i
$658$		0			0
$659$	1.89352	−	10.7387i	0.0737612	−	0.418321i	−0.925459	−	0.378847i	$-0.876321\pi$
$659$	1.89352	−	10.7387i	0.0737612	−	0.418321i	0.999221	−	0.0394738i	$-0.0125682\pi$
$660$		0			0
$661$	27.7385	+	10.0960i	1.07890	+	0.392688i	0.819499	−	0.573081i	$-0.194252\pi$
$661$	27.7385	+	10.0960i	1.07890	+	0.392688i	0.259403	+	0.965769i	$0.416474\pi$
$662$		0			0
$663$	27.4095	+	4.11274i	1.06450	+	0.159725i
$664$		0			0
$665$	12.5958	+	21.8165i	0.488443	+	0.846009i
$666$		0			0
$667$	−9.60756	+	16.6408i	−0.372006	+	0.644334i
$668$		0			0
$669$	15.8169	−	9.67992i	0.611517	−	0.374247i
$670$		0			0
$671$	25.6232	−	21.5005i	0.989174	−	0.830016i
$672$		0			0
$673$	6.06237	−	2.20652i	0.233687	−	0.0850552i	−0.222522	−	0.974928i	$-0.571429\pi$
$673$	6.06237	−	2.20652i	0.233687	−	0.0850552i	0.456209	+	0.889872i	$0.349207\pi$
$674$		0			0
$675$	−31.0316	+	43.3441i	−1.19441	+	1.66831i
$676$		0			0
$677$	−12.9318	+	4.70679i	−0.497009	+	0.180897i	−0.578348	−	0.815790i	$-0.696303\pi$
$677$	−12.9318	+	4.70679i	−0.497009	+	0.180897i	0.0813390	+	0.996686i	$0.474080\pi$
$678$		0			0
$679$	4.98292	−	4.18117i	0.191227	−	0.160459i
$680$		0			0
$681$	33.4329	+	18.1778i	1.28115	+	0.696576i
$682$		0			0
$683$	10.8606	−	18.8112i	0.415571	−	0.719790i	−0.579917	−	0.814675i	$-0.696915\pi$
$683$	10.8606	−	18.8112i	0.415571	−	0.719790i	0.995488	+	0.0948853i	$0.0302484\pi$
$684$		0			0
$685$	23.9296	+	41.4474i	0.914305	+	1.58362i
$686$		0			0
$687$	−9.68930	+	12.1665i	−0.369670	+	0.464182i
$688$		0			0
$689$	−31.9737	−	11.6375i	−1.21810	−	0.443353i
$690$		0			0
$691$	−8.21796	+	46.6064i	−0.312626	+	1.77299i	0.272608	+	0.962125i	$0.412114\pi$
$691$	−8.21796	+	46.6064i	−0.312626	+	1.77299i	−0.585234	+	0.810864i	$0.698997\pi$
$692$		0			0
$693$	7.78458	−	0.398864i	0.295712	−	0.0151516i
$694$		0			0
$695$	55.2596	+	46.3683i	2.09612	+	1.75885i
$696$		0			0
$697$	−3.44633	−	19.5451i	−0.130539	−	0.740324i
$698$		0			0
$699$	49.7786	−	10.0973i	1.88280	−	0.381916i
$700$		0			0
$701$	−19.4295			−0.733842			−0.366921	−	0.930252i	$-0.619588\pi$
$701$	−19.4295			−0.733842			−0.366921	+	0.930252i	$0.619588\pi$
$702$		0			0
$703$	−16.4942			−0.622091
$704$		0			0
$705$	14.2187	+	16.0902i	0.535508	+	0.605994i
$706$		0			0
$707$	1.13874	+	6.45810i	0.0428266	+	0.242882i
$708$		0			0
$709$	−20.9655	−	17.5921i	−0.787375	−	0.660686i	0.157719	−	0.987484i	$-0.449586\pi$
$709$	−20.9655	−	17.5921i	−0.787375	−	0.660686i	−0.945094	+	0.326798i	$0.894030\pi$
$710$		0			0
$711$	−16.1632	−	4.96223i	−0.606169	−	0.186098i
$712$		0			0
$713$	7.41707	−	42.0643i	0.277772	−	1.57532i
$714$		0			0
$715$	−55.3374	−	20.1412i	−2.06950	−	0.753237i
$716$		0			0
$717$	−2.87331	−	7.30682i	−0.107306	−	0.272878i
$718$		0			0
$719$	−5.42617	−	9.39841i	−0.202362	−	0.350501i	0.746927	−	0.664906i	$-0.231528\pi$
$719$	−5.42617	−	9.39841i	−0.202362	−	0.350501i	−0.949289	+	0.314405i	$0.898195\pi$
$720$		0			0
$721$	2.32637	−	4.02939i	0.0866386	−	0.150062i
$722$		0			0
$723$	0.353931	+	13.8243i	0.0131628	+	0.514132i
$724$		0			0
$725$	−33.7581	+	28.3264i	−1.25374	+	1.05202i
$726$		0			0
$727$	−23.2309	+	8.45537i	−0.861588	+	0.313592i	−0.734756	−	0.678332i	$-0.762703\pi$
$727$	−23.2309	+	8.45537i	−0.861588	+	0.313592i	−0.126832	+	0.991924i	$0.540481\pi$
$728$		0			0
$729$	9.76412	−	25.1726i	0.361634	−	0.932320i
$730$		0			0
$731$	5.15500	−	1.87627i	0.190665	−	0.0693962i
$732$		0			0
$733$	−22.6354	+	18.9933i	−0.836056	+	0.701534i	−0.956673	−	0.291165i	$-0.905957\pi$
$733$	−22.6354	+	18.9933i	−0.836056	+	0.701534i	0.120617	+	0.992699i	$0.461513\pi$
$734$		0			0
$735$	0.173163	+	6.76365i	0.00638723	+	0.249481i
$736$		0			0
$737$	18.9238	−	32.7769i	0.697066	−	1.20735i
$738$		0			0
$739$	18.7668	+	32.5050i	0.690348	+	1.19572i	0.971724	+	0.236120i	$0.0758758\pi$
$739$	18.7668	+	32.5050i	0.690348	+	1.19572i	−0.281376	+	0.959598i	$0.590791\pi$
$740$		0			0
$741$	23.7176	+	60.3138i	0.871288	+	2.21568i
$742$		0			0
$743$	−7.96754	−	2.89995i	−0.292301	−	0.106389i	0.191708	−	0.981452i	$-0.438597\pi$
$743$	−7.96754	−	2.89995i	−0.292301	−	0.106389i	−0.484009	+	0.875063i	$0.660820\pi$
$744$		0			0
$745$	11.1819	−	63.4156i	0.409673	−	2.32337i
$746$		0			0
$747$	−4.93115	−	1.51390i	−0.180421	−	0.0553906i
$748$		0			0
$749$	−12.1334	−	10.1811i	−0.443345	−	0.372011i
$750$		0			0
$751$	3.32907	+	18.8801i	0.121479	+	0.688944i	0.983337	+	0.181793i	$0.0581901\pi$
$751$	3.32907	+	18.8801i	0.121479	+	0.688944i	−0.861857	+	0.507151i	$0.830699\pi$
$752$		0			0
$753$	−30.5245	−	34.5422i	−1.11237	−	1.25879i
$754$		0			0
$755$	52.3187			1.90407
$756$		0			0
$757$	−12.9535			−0.470804			−0.235402	−	0.971898i	$-0.575641\pi$
$757$	−12.9535			−0.470804			−0.235402	+	0.971898i	$0.575641\pi$
$758$		0			0
$759$	19.7293	−	4.00199i	0.716129	−	0.145263i
$760$		0			0
$761$	−0.00844815	−	0.0479118i	−0.000306245	−	0.00173680i	0.984654	−	0.174517i	$-0.0558362\pi$
$761$	−0.00844815	−	0.0479118i	−0.000306245	−	0.00173680i	−0.984960	+	0.172780i	$0.944725\pi$
$762$		0			0
$763$	12.0224	+	10.0880i	0.435241	+	0.365210i
$764$		0			0
$765$	−32.2778	+	1.65384i	−1.16701	+	0.0597948i
$766$		0			0
$767$	−9.58647	+	54.3676i	−0.346147	+	1.96310i
$768$		0			0
$769$	−10.6836	−	3.88850i	−0.385259	−	0.140223i	0.142127	−	0.989848i	$-0.454606\pi$
$769$	−10.6836	−	3.88850i	−0.385259	−	0.140223i	−0.527386	+	0.849626i	$0.676828\pi$
$770$		0			0
$771$	33.1806	−	41.6638i	1.19497	−	1.50048i
$772$		0			0
$773$	8.95878	+	15.5171i	0.322225	+	0.558110i	0.980947	−	0.194277i	$-0.0622360\pi$
$773$	8.95878	+	15.5171i	0.322225	+	0.558110i	−0.658722	+	0.752386i	$0.728903\pi$
$774$		0			0
$775$	48.9794	−	84.8348i	1.75939	−	3.04736i
$776$		0			0
$777$	−3.89189	−	2.11607i	−0.139621	−	0.0759135i
$778$		0			0
$779$	35.5503	−	29.8302i	1.27372	−	1.06878i
$780$		0			0
$781$	1.43868	−	0.523637i	0.0514801	−	0.0187372i
$782$		0			0
$783$	12.9933	−	18.1486i	0.464342	−	0.648579i
$784$		0			0
$785$	−35.6855	+	12.9885i	−1.27367	+	0.463578i
$786$		0			0
$787$	9.26210	−	7.77182i	0.330158	−	0.277035i	−0.462606	−	0.886564i	$-0.653086\pi$
$787$	9.26210	−	7.77182i	0.330158	−	0.277035i	0.792764	+	0.609528i	$0.208641\pi$
$788$		0			0
$789$	0.206095	−	0.126130i	0.00733719	−	0.00449035i
$790$		0			0
$791$	−7.02018	+	12.1593i	−0.249609	+	0.432335i
$792$		0			0
$793$	37.3468	+	64.6865i	1.32622	+	2.29709i
$794$		0			0
$795$	39.2383	+	5.88761i	1.39164	+	0.208812i
$796$		0			0
$797$	36.2672	+	13.2002i	1.28465	+	0.467575i	0.891968	−	0.452099i	$-0.149325\pi$
$797$	36.2672	+	13.2002i	1.28465	+	0.467575i	0.392683	+	0.919674i	$0.371547\pi$
$798$		0			0
$799$	−1.51991	+	8.61985i	−0.0537706	+	0.304948i
$800$		0			0
$801$	−6.79346	+	2.87430i	−0.240035	+	0.101558i
$802$		0			0
$803$	−9.06852	−	7.60939i	−0.320021	−	0.268530i
$804$		0			0
$805$	3.03429	+	17.2083i	0.106945	+	0.606514i
$806$		0			0
$807$	−2.01254	+	6.00322i	−0.0708449	+	0.211323i
$808$		0			0
$809$	7.41250			0.260610			0.130305	−	0.991474i	$-0.458404\pi$
$809$	7.41250			0.260610			0.130305	+	0.991474i	$0.458404\pi$
$810$		0			0
$811$	−20.6463			−0.724990			−0.362495	−	0.931986i	$-0.618075\pi$
$811$	−20.6463			−0.724990			−0.362495	+	0.931986i	$0.618075\pi$
$812$		0			0
$813$	0.101147	−	0.301710i	0.00354737	−	0.0105814i
$814$		0			0
$815$	−6.27639	−	35.5952i	−0.219852	−	1.24684i
$816$		0			0
$817$	9.82651	+	8.24542i	0.343786	+	0.288471i
$818$		0			0
$819$	−2.14146	+	17.2741i	−0.0748287	+	0.603607i
$820$		0			0
$821$	3.54676	−	20.1147i	0.123783	−	0.702006i	−0.858241	−	0.513247i	$-0.828442\pi$
$821$	3.54676	−	20.1147i	0.123783	−	0.702006i	0.982023	−	0.188759i	$-0.0604465\pi$
$822$		0			0
$823$	−23.8887	−	8.69478i	−0.832709	−	0.303081i	−0.109739	−	0.993960i	$-0.535001\pi$
$823$	−23.8887	−	8.69478i	−0.832709	−	0.303081i	−0.722970	+	0.690879i	$0.757224\pi$
$824$		0			0
$825$	45.6577	+	6.85083i	1.58960	+	0.238515i
$826$		0			0
$827$	5.19319	+	8.99486i	0.180585	+	0.312782i	0.942080	−	0.335389i	$-0.108868\pi$
$827$	5.19319	+	8.99486i	0.180585	+	0.312782i	−0.761495	+	0.648171i	$0.775534\pi$
$828$		0			0
$829$	19.0543	−	33.0031i	0.661784	−	1.14624i	−0.318363	−	0.947969i	$-0.603133\pi$
$829$	19.0543	−	33.0031i	0.661784	−	1.14624i	0.980147	−	0.198275i	$-0.0635338\pi$
$830$		0			0
$831$	30.9943	−	18.9684i	1.07518	−	0.658008i
$832$		0			0
$833$	−2.11273	+	1.77279i	−0.0732017	+	0.0614235i
$834$		0			0
$835$	−31.4779	+	11.4570i	−1.08934	+	0.396487i
$836$		0			0
$837$	−13.3429	+	47.7880i	−0.461199	+	1.65180i
$838$		0			0
$839$	−17.7231	+	6.45067i	−0.611868	+	0.222702i	−0.629321	−	0.777146i	$-0.716667\pi$
$839$	−17.7231	+	6.45067i	−0.611868	+	0.222702i	0.0174521	+	0.999848i	$0.494445\pi$
$840$		0			0
$841$	−8.08040	+	6.78026i	−0.278635	+	0.233802i
$842$		0			0
$843$	−9.05575	−	4.92372i	−0.311897	−	0.169582i
$844$		0			0
$845$	40.3607	−	69.9068i	1.38845	−	2.40487i
$846$		0			0
$847$	2.12451	+	3.67976i	0.0729991	+	0.126438i
$848$		0			0
$849$	14.4566	−	18.1527i	0.496149	−	0.622998i
$850$		0			0
$851$	−10.7510	−	3.91305i	−0.368540	−	0.134138i
$852$		0			0
$853$	5.79942	−	32.8901i	0.198568	−	1.12614i	−0.708677	−	0.705533i	$-0.750707\pi$
$853$	5.79942	−	32.8901i	0.198568	−	1.12614i	0.907245	−	0.420603i	$-0.138181\pi$
$854$		0			0
$855$	−41.0869	−	63.4302i	−1.40514	−	2.16927i
$856$		0			0
$857$	−2.90682	−	2.43911i	−0.0992950	−	0.0833184i	0.591789	−	0.806093i	$-0.298422\pi$
$857$	−2.90682	−	2.43911i	−0.0992950	−	0.0833184i	−0.691084	+	0.722775i	$0.742866\pi$
$858$		0			0
$859$	−2.42819	−	13.7709i	−0.0828487	−	0.469858i	−0.997800	−	0.0662942i	$-0.978882\pi$
$859$	−2.42819	−	13.7709i	−0.0828487	−	0.469858i	0.914951	−	0.403564i	$-0.132229\pi$
$860$		0			0
$861$	12.2152	−	2.47780i	0.416294	−	0.0844431i
$862$		0			0
$863$	−30.2672			−1.03031			−0.515153	−	0.857098i	$-0.672265\pi$
$863$	−30.2672			−1.03031			−0.515153	+	0.857098i	$0.672265\pi$
$864$		0			0
$865$	−39.1264			−1.33034
$866$		0			0
$867$	10.7738	+	12.1919i	0.365899	+	0.414060i
$868$		0			0
$869$	2.54284	+	14.4212i	0.0862601	+	0.489205i
$870$		0			0
$871$	64.7433	+	54.3261i	2.19374	+	1.84077i
$872$		0			0
$873$	−14.2873	+	13.2920i	−0.483553	+	0.449866i
$874$		0			0
$875$	−3.56727	+	20.2310i	−0.120596	+	0.683933i
$876$		0			0
$877$	23.1159	+	8.41350i	0.780569	+	0.284104i	0.701410	−	0.712758i	$-0.252554\pi$
$877$	23.1159	+	8.41350i	0.780569	+	0.284104i	0.0791591	+	0.996862i	$0.474776\pi$
$878$		0			0
$879$	15.2452	+	38.7686i	0.514209	+	1.30763i
$880$		0			0
$881$	13.3319	+	23.0916i	0.449164	+	0.777974i	0.998332	−	0.0577375i	$-0.0183887\pi$
$881$	13.3319	+	23.0916i	0.449164	+	0.777974i	−0.549168	+	0.835712i	$0.685055\pi$
$882$		0			0
$883$	−0.422504	+	0.731798i	−0.0142184	+	0.0246270i	−0.873047	−	0.487636i	$-0.837859\pi$
$883$	−0.422504	+	0.731798i	−0.0142184	+	0.0246270i	0.858829	+	0.512263i	$0.171193\pi$
$884$		0			0
$885$	−1.64763	−	64.3552i	−0.0553843	−	2.16328i
$886$		0			0
$887$	−22.8939	+	19.2103i	−0.768703	+	0.645018i	−0.940376	−	0.340136i	$-0.889527\pi$
$887$	−22.8939	+	19.2103i	−0.768703	+	0.645018i	0.171674	+	0.985154i	$0.445082\pi$
$888$		0			0
$889$	−11.2087	+	4.07962i	−0.375926	+	0.136826i
$890$		0			0
$891$	−23.2619	+	2.39005i	−0.779303	+	0.0800696i
$892$		0			0
$893$	−19.2325	+	7.00007i	−0.643592	+	0.234248i
$894$		0			0
$895$	−24.7271	+	20.7485i	−0.826535	+	0.693545i
$896$		0			0
$897$	1.15055	+	44.9396i	0.0384156	+	1.50049i
$898$		0			0
$899$	−20.5082	+	35.5212i	−0.683987	+	1.18470i
$900$		0			0
$901$	8.08687	+	14.0069i	0.269413	+	0.466637i
$902$		0			0
$903$	1.26080	+	3.20621i	0.0419567	+	0.106696i
$904$		0			0
$905$	6.19015	+	2.25303i	0.205768	+	0.0748933i
$906$		0			0
$907$	−5.61171	+	31.8256i	−0.186334	+	1.05675i	0.737896	+	0.674915i	$0.235820\pi$
$907$	−5.61171	+	31.8256i	−0.186334	+	1.05675i	−0.924230	+	0.381837i	$0.875292\pi$
$908$		0			0
$909$	−4.40313	−	19.1741i	−0.146043	−	0.635965i
$910$		0			0
$911$	−4.15436	−	3.48592i	−0.137640	−	0.115494i	0.571368	−	0.820694i	$-0.306413\pi$
$911$	−4.15436	−	3.48592i	−0.137640	−	0.115494i	−0.709008	+	0.705200i	$0.750857\pi$
$912$		0			0
$913$	0.775781	+	4.39967i	0.0256746	+	0.145608i
$914$		0			0
$915$	−57.6765	−	65.2681i	−1.90672	−	2.15770i
$916$		0			0
$917$	11.4310			0.377486
$918$		0			0
$919$	−2.83209			−0.0934219			−0.0467110	−	0.998908i	$-0.514874\pi$
$919$	−2.83209			−0.0934219			−0.0467110	+	0.998908i	$0.514874\pi$
$920$		0			0
$921$	−34.5440	+	7.00707i	−1.13826	+	0.230891i
$922$		0			0
$923$	0.593680	+	3.36692i	0.0195412	+	0.110824i
$924$		0			0
$925$	−20.1001	−	16.8660i	−0.660888	−	0.554551i
$926$		0			0
$927$	−6.35141	+	12.4295i	−0.208608	+	0.408237i
$928$		0			0
$929$	−4.27831	+	24.2635i	−0.140367	+	0.796059i	0.830605	+	0.556863i	$0.187995\pi$
$929$	−4.27831	+	24.2635i	−0.140367	+	0.796059i	−0.970971	+	0.239196i	$0.923116\pi$
$930$		0			0
$931$	−6.06007	−	2.20569i	−0.198611	−	0.0722884i
$932$		0			0
$933$	−30.0768	+	37.7664i	−0.984669	+	1.23642i
$934$		0			0
$935$	13.9961	+	24.2419i	0.457720	+	0.792794i
$936$		0			0
$937$	8.66673	−	15.0112i	0.283130	−	0.490395i	−0.689024	−	0.724738i	$-0.741961\pi$
$937$	8.66673	−	15.0112i	0.283130	−	0.490395i	0.972154	+	0.234343i	$0.0752940\pi$
$938$		0			0
$939$	−42.2786	−	22.9874i	−1.37971	−	0.750164i
$940$		0			0
$941$	−3.06642	+	2.57303i	−0.0999624	+	0.0838785i	−0.691399	−	0.722473i	$-0.743005\pi$
$941$	−3.06642	+	2.57303i	−0.0999624	+	0.0838785i	0.591437	+	0.806351i	$0.298561\pi$
$942$		0			0
$943$	30.2487	−	11.0096i	0.985034	−	0.358523i
$944$		0			0
$945$	−1.55711	−	20.2378i	−0.0506528	−	0.658336i
$946$		0			0
$947$	18.9555	−	6.89923i	0.615970	−	0.224195i	−0.0151434	−	0.999885i	$-0.504820\pi$
$947$	18.9555	−	6.89923i	0.615970	−	0.224195i	0.631113	+	0.775691i	$0.282598\pi$
$948$		0			0
$949$	20.2507	−	16.9923i	0.657365	−	0.551595i
$950$		0			0
$951$	11.3277	−	6.93252i	0.367325	−	0.224802i
$952$		0			0
$953$	−13.9075	+	24.0886i	−0.450509	+	0.780305i	−0.998418	−	0.0562335i	$-0.982091\pi$
$953$	−13.9075	+	24.0886i	−0.450509	+	0.780305i	0.547908	+	0.836538i	$0.315424\pi$
$954$		0			0
$955$	−27.5867	−	47.7815i	−0.892684	−	1.54617i
$956$		0			0
$957$	−19.1174	−	2.86852i	−0.617977	−	0.0927260i
$958$		0			0
$959$	−11.5130	−	4.19039i	−0.371775	−	0.135315i
$960$		0			0
$961$	10.4493	−	59.2610i	0.337074	−	1.91164i
$962$		0			0
$963$	37.9155	+	28.6408i	1.22181	+	0.922937i
$964$		0			0
$965$	44.4820	+	37.3248i	1.43193	+	1.20153i
$966$		0			0
$967$	6.55380	+	37.1684i	0.210756	+	1.19526i	0.888121	+	0.459609i	$0.152010\pi$
$967$	6.55380	+	37.1684i	0.210756	+	1.19526i	−0.677365	+	0.735647i	$0.736878\pi$
$968$		0			0
$969$	9.79208	−	29.2088i	0.314567	−	0.938322i
$970$		0			0
$971$	16.8305			0.540117			0.270059	−	0.962844i	$-0.412957\pi$
$971$	16.8305			0.540117			0.270059	+	0.962844i	$0.412957\pi$
$972$		0			0
$973$	−18.4668			−0.592018
$974$		0			0
$975$	−32.7707	+	97.7516i	−1.04950	+	3.13056i
$976$		0			0
$977$	9.28149	+	52.6379i	0.296941	+	1.68404i	0.659207	+	0.751962i	$0.270892\pi$
$977$	9.28149	+	52.6379i	0.296941	+	1.68404i	−0.362266	+	0.932075i	$0.617997\pi$
$978$		0			0
$979$	4.89402	+	4.10657i	0.156414	+	0.131247i
$980$		0			0
$981$	−37.5686	−	28.3788i	−1.19947	−	0.906065i
$982$		0			0
$983$	7.89778	−	44.7905i	0.251900	−	1.42860i	−0.552007	−	0.833840i	$-0.686138\pi$
$983$	7.89778	−	44.7905i	0.251900	−	1.42860i	0.803906	−	0.594756i	$-0.202751\pi$
$984$		0			0
$985$	31.6405	+	11.5162i	1.00815	+	0.366937i
$986$		0			0
$987$	−5.43606	−	0.815668i	−0.173032	−	0.0259630i
$988$		0			0
$989$	4.44885	+	7.70563i	0.141465	+	0.245025i
$990$		0			0
$991$	−6.33099	+	10.9656i	−0.201110	+	0.348333i	−0.948886	−	0.315618i	$-0.897788\pi$
$991$	−6.33099	+	10.9656i	−0.201110	+	0.348333i	0.747776	+	0.663951i	$0.231122\pi$
$992$		0			0
$993$	−2.23694	+	1.36900i	−0.0709872	+	0.0434440i
$994$		0			0
$995$	−6.98722	+	5.86297i	−0.221510	+	0.185869i
$996$		0			0
$997$	−19.7630	+	7.19315i	−0.625901	+	0.227809i	−0.635446	−	0.772145i	$-0.719184\pi$
$997$	−19.7630	+	7.19315i	−0.625901	+	0.227809i	0.00954538	+	0.999954i	$0.496962\pi$
$998$		0			0
$999$	11.9852	+	5.74243i	0.379196	+	0.181683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.a.169.5	yes	54
27.4	even	9	inner	756.2.bo.a.85.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.a.85.5	✓	54	27.4	even	9	inner
756.2.bo.a.169.5	yes	54	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.550546 + 1.64222i) q^{3} +(-0.678318 - 3.84693i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.39380 - 1.80824i) q^{9} +O(q^{10})\)	\(q+(-0.550546 + 1.64222i) q^{3} +(-0.678318 - 3.84693i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-2.39380 - 1.80824i) q^{9} +(-0.451184 + 2.55879i) q^{11} +(-5.45221 - 1.98444i) q^{13} +(6.69097 + 1.00396i) q^{15} +(1.37898 + 2.38847i) q^{17} +(-3.22450 + 5.58499i) q^{19} +(-1.47734 + 0.904132i) q^{21} +(-3.42672 + 2.87536i) q^{23} +(-9.64031 + 3.50878i) q^{25} +(4.28743 - 2.93563i) q^{27} +(4.03650 - 1.46917i) q^{29} +(-7.31463 + 6.13770i) q^{31} +(-3.95371 - 2.14968i) q^{33} +(1.95314 - 3.38294i) q^{35} +(1.27882 + 2.21498i) q^{37} +(6.26059 - 7.86122i) q^{39} +(-6.76212 - 2.46121i) q^{41} +(0.345401 - 1.95887i) q^{43} +(-5.33242 + 10.4353i) q^{45} +(2.43116 + 2.03998i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-4.68160 + 0.949638i) q^{51} +5.86437 q^{53} +10.1495 q^{55} +(-7.39657 - 8.37014i) q^{57} +(-1.65224 - 9.37030i) q^{59} +(-9.86168 - 8.27493i) q^{61} +(-0.671442 - 2.92390i) q^{63} +(-3.93568 + 22.3203i) q^{65} +(-13.6880 - 4.98203i) q^{67} +(-2.83541 - 7.21045i) q^{69} +(-0.294622 - 0.510301i) q^{71} +(-2.27808 + 3.94575i) q^{73} +(-0.454777 - 17.7633i) q^{75} +(-1.99039 + 1.67013i) q^{77} +(5.29605 - 1.92761i) q^{79} +(2.46054 + 8.65712i) q^{81} +(1.61574 - 0.588081i) q^{83} +(8.25290 - 6.92500i) q^{85} +(0.190420 + 7.43768i) q^{87} +(1.22942 - 2.12941i) q^{89} +(-2.90106 - 5.02478i) q^{91} +(-6.05244 - 15.3913i) q^{93} +(23.6723 + 8.61602i) q^{95} +(1.12954 - 6.40592i) q^{97} +(5.70695 - 5.30938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9}+O(q^{10}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9	\( 54 q - 3 q^{3} - 3 q^{5} + 3 q^{9} - 9 q^{13} + 3 q^{15} - 3 q^{21} - 45 q^{25} + 15 q^{27} + 6 q^{29} - 9 q^{31} + 6 q^{33} + 6 q^{35} + 30 q^{39} + 9 q^{41} + 9 q^{43} - 21 q^{45} - 27 q^{47} - 108 q^{51} - 84 q^{53} - 57 q^{57} - 66 q^{59} + 3 q^{63} + 30 q^{65} + 63 q^{67} + 42 q^{69} + 42 q^{71} + 3 q^{75} - 9 q^{77} + 36 q^{79} + 3 q^{81} + 12 q^{83} + 18 q^{85} + 39 q^{87} + 12 q^{89} + 21 q^{93} + 120 q^{95} + 18 q^{97} + 39 q^{99}+O(q^{100}) \) 54 * q - 3 * q^3 - 3 * q^5 + 3 * q^9 - 9 * q^13 + 3 * q^15 - 3 * q^21 - 45 * q^25 + 15 * q^27 + 6 * q^29 - 9 * q^31 + 6 * q^33 + 6 * q^35 + 30 * q^39 + 9 * q^41 + 9 * q^43 - 21 * q^45 - 27 * q^47 - 108 * q^51 - 84 * q^53 - 57 * q^57 - 66 * q^59 + 3 * q^63 + 30 * q^65 + 63 * q^67 + 42 * q^69 + 42 * q^71 + 3 * q^75 - 9 * q^77 + 36 * q^79 + 3 * q^81 + 12 * q^83 + 18 * q^85 + 39 * q^87 + 12 * q^89 + 21 * q^93 + 120 * q^95 + 18 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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