LMFDB - Embedded newform 756.2.bo.b.169.4

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			169.4
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.b.85.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.377044 - 1.69051i) q^{3} +(0.491885 + 2.78962i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.71568 + 1.27480i) q^{9} +O(q^{10})$	\(q+(-0.377044 - 1.69051i) q^{3} +(0.491885 + 2.78962i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.71568 + 1.27480i) q^{9} +(0.658350 - 3.73369i) q^{11} +(-0.581608 - 0.211688i) q^{13} +(4.53043 - 1.88335i) q^{15} +(-3.28448 - 5.68889i) q^{17} +(0.623998 - 1.08080i) q^{19} +(-0.797809 + 1.53737i) q^{21} +(6.17422 - 5.18079i) q^{23} +(-2.84155 + 1.03424i) q^{25} +(3.17899 + 4.11023i) q^{27} +(7.04249 - 2.56326i) q^{29} +(3.34513 - 2.80690i) q^{31} +(-6.56008 + 0.294816i) q^{33} +(1.41633 - 2.45315i) q^{35} +(-5.09143 - 8.81861i) q^{37} +(-0.138569 + 1.06303i) q^{39} +(3.25345 + 1.18416i) q^{41} +(-1.17879 + 6.68524i) q^{43} +(-4.89200 - 6.94864i) q^{45} +(-2.09562 - 1.75843i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-8.37875 + 7.69742i) q^{51} -12.0845 q^{53} +10.7394 q^{55} +(-2.06237 - 0.647369i) q^{57} +(-1.37705 - 7.80964i) q^{59} +(5.60602 + 4.70401i) q^{61} +(2.89975 + 0.769051i) q^{63} +(0.304444 - 1.72659i) q^{65} +(4.58242 + 1.66787i) q^{67} +(-11.0862 - 8.48423i) q^{69} +(-5.88875 - 10.1996i) q^{71} +(-6.36336 + 11.0217i) q^{73} +(2.81979 + 4.41373i) q^{75} +(-2.90429 + 2.43699i) q^{77} +(-8.33017 + 3.03193i) q^{79} +(5.74978 - 6.92387i) q^{81} +(-7.09112 + 2.58096i) q^{83} +(14.2542 - 11.9607i) q^{85} +(-6.98855 - 10.9390i) q^{87} +(0.430724 - 0.746036i) q^{89} +(0.309467 + 0.536012i) q^{91} +(-6.00637 - 4.59667i) q^{93} +(3.32194 + 1.20909i) q^{95} +(-0.650292 + 3.68799i) q^{97} +(2.97183 + 10.9787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * 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
$3$	−0.377044	−	1.69051i	−0.217687	−	0.976019i
$3$	−0.377044	−	1.69051i	−0.217687	−	0.976019i
$4$		0			0
$5$	0.491885	+	2.78962i	0.219978	+	1.24755i	0.872057	+	0.489404i	$0.162786\pi$
$5$	0.491885	+	2.78962i	0.219978	+	1.24755i	−0.652079	+	0.758151i	$0.726103\pi$
$6$		0			0
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$8$		0			0
$9$	−2.71568	+	1.27480i	−0.905225	+	0.424932i
$10$		0			0
$11$	0.658350	−	3.73369i	0.198500	−	1.12575i	−0.708846	−	0.705363i	$-0.750784\pi$
$11$	0.658350	−	3.73369i	0.198500	−	1.12575i	0.907346	−	0.420385i	$-0.138105\pi$
$12$		0			0
$13$	−0.581608	−	0.211688i	−0.161309	−	0.0587116i	0.260104	−	0.965581i	$-0.416243\pi$
$13$	−0.581608	−	0.211688i	−0.161309	−	0.0587116i	−0.421412	+	0.906869i	$0.638466\pi$
$14$		0			0
$15$	4.53043	−	1.88335i	1.16975	−	0.486278i
$16$		0			0
$17$	−3.28448	−	5.68889i	−0.796603	−	1.37976i	−0.921816	−	0.387628i	$-0.873295\pi$
$17$	−3.28448	−	5.68889i	−0.796603	−	1.37976i	0.125213	−	0.992130i	$-0.460039\pi$
$18$		0			0
$19$	0.623998	−	1.08080i	0.143155	−	0.247952i	−0.785528	−	0.618826i	$-0.787609\pi$
$19$	0.623998	−	1.08080i	0.143155	−	0.247952i	0.928683	+	0.370874i	$0.120942\pi$
$20$		0			0
$21$	−0.797809	+	1.53737i	−0.174096	+	0.335481i
$22$		0			0
$23$	6.17422	−	5.18079i	1.28741	−	1.08027i	0.295238	−	0.955424i	$-0.404601\pi$
$23$	6.17422	−	5.18079i	1.28741	−	1.08027i	0.992176	−	0.124846i	$-0.0398435\pi$
$24$		0			0
$25$	−2.84155	+	1.03424i	−0.568310	+	0.206848i
$26$		0			0
$27$	3.17899	+	4.11023i	0.611797	+	0.791015i
$28$		0			0
$29$	7.04249	−	2.56326i	1.30776	−	0.475985i	0.408242	−	0.912874i	$-0.366142\pi$
$29$	7.04249	−	2.56326i	1.30776	−	0.475985i	0.899515	+	0.436889i	$0.143920\pi$
$30$		0			0
$31$	3.34513	−	2.80690i	0.600803	−	0.504134i	−0.290900	−	0.956753i	$-0.593955\pi$
$31$	3.34513	−	2.80690i	0.600803	−	0.504134i	0.891704	+	0.452619i	$0.149510\pi$
$32$		0			0
$33$	−6.56008	+	0.294816i	−1.14196	+	0.0513208i
$34$		0			0
$35$	1.41633	−	2.45315i	0.239403	−	0.414658i
$36$		0			0
$37$	−5.09143	−	8.81861i	−0.837026	−	1.44977i	−0.892371	−	0.451303i	$-0.850959\pi$
$37$	−5.09143	−	8.81861i	−0.837026	−	1.44977i	0.0553450	−	0.998467i	$-0.482374\pi$
$38$		0			0
$39$	−0.138569	+	1.06303i	−0.0221889	+	0.170221i
$40$		0			0
$41$	3.25345	+	1.18416i	0.508104	+	0.184935i	0.583335	−	0.812231i	$-0.301747\pi$
$41$	3.25345	+	1.18416i	0.508104	+	0.184935i	−0.0752313	+	0.997166i	$0.523970\pi$
$42$		0			0
$43$	−1.17879	+	6.68524i	−0.179763	+	1.01949i	0.752737	+	0.658321i	$0.228733\pi$
$43$	−1.17879	+	6.68524i	−0.179763	+	1.01949i	−0.932501	+	0.361168i	$0.882378\pi$
$44$		0			0
$45$	−4.89200	−	6.94864i	−0.729256	−	1.03584i
$46$		0			0
$47$	−2.09562	−	1.75843i	−0.305677	−	0.256493i	0.477026	−	0.878889i	$-0.341715\pi$
$47$	−2.09562	−	1.75843i	−0.305677	−	0.256493i	−0.782703	+	0.622396i	$0.786159\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	−8.37875	+	7.69742i	−1.17326	+	1.07785i
$52$		0			0
$53$	−12.0845			−1.65993			−0.829967	−	0.557812i	$-0.811641\pi$
$53$	−12.0845			−1.65993			−0.829967	+	0.557812i	$0.811641\pi$
$54$		0			0
$55$	10.7394			1.44810
$56$		0			0
$57$	−2.06237	−	0.647369i	−0.273168	−	0.0857461i
$58$		0			0
$59$	−1.37705	−	7.80964i	−0.179277	−	1.01673i	−0.933091	−	0.359641i	$-0.882899\pi$
$59$	−1.37705	−	7.80964i	−0.179277	−	1.01673i	0.753814	−	0.657088i	$-0.228212\pi$
$60$		0			0
$61$	5.60602	+	4.70401i	0.717777	+	0.602286i	0.926769	−	0.375631i	$-0.122574\pi$
$61$	5.60602	+	4.70401i	0.717777	+	0.602286i	−0.208992	+	0.977917i	$0.567018\pi$
$62$		0			0
$63$	2.89975	+	0.769051i	0.365334	+	0.0968913i
$64$		0			0
$65$	0.304444	−	1.72659i	0.0377617	−	0.214157i
$66$		0			0
$67$	4.58242	+	1.66787i	0.559832	+	0.203762i	0.606410	−	0.795152i	$-0.292609\pi$
$67$	4.58242	+	1.66787i	0.559832	+	0.203762i	−0.0465774	+	0.998915i	$0.514831\pi$
$68$		0			0
$69$	−11.0862	−	8.48423i	−1.33462	−	1.02138i
$70$		0			0
$71$	−5.88875	−	10.1996i	−0.698866	−	1.21047i	−0.968860	−	0.247609i	$-0.920355\pi$
$71$	−5.88875	−	10.1996i	−0.698866	−	1.21047i	0.269994	−	0.962862i	$-0.412978\pi$
$72$		0			0
$73$	−6.36336	+	11.0217i	−0.744775	+	1.28999i	0.205524	+	0.978652i	$0.434110\pi$
$73$	−6.36336	+	11.0217i	−0.744775	+	1.28999i	−0.950300	+	0.311337i	$0.899223\pi$
$74$		0			0
$75$	2.81979	+	4.41373i	0.325601	+	0.509654i
$76$		0			0
$77$	−2.90429	+	2.43699i	−0.330975	+	0.277721i
$78$		0			0
$79$	−8.33017	+	3.03193i	−0.937217	+	0.341119i	−0.765066	−	0.643951i	$-0.777294\pi$
$79$	−8.33017	+	3.03193i	−0.937217	+	0.341119i	−0.172151	+	0.985071i	$0.555072\pi$
$80$		0			0
$81$	5.74978	−	6.92387i	0.638865	−	0.769319i
$82$		0			0
$83$	−7.09112	+	2.58096i	−0.778351	+	0.283297i	−0.700485	−	0.713667i	$-0.747033\pi$
$83$	−7.09112	+	2.58096i	−0.778351	+	0.283297i	−0.0778664	+	0.996964i	$0.524811\pi$
$84$		0			0
$85$	14.2542	−	11.9607i	1.54609	−	1.29732i
$86$		0			0
$87$	−6.98855	−	10.9390i	−0.749251	−	1.17278i
$88$		0			0
$89$	0.430724	−	0.746036i	0.0456567	−	0.0790797i	−0.842294	−	0.539018i	$-0.818795\pi$
$89$	0.430724	−	0.746036i	0.0456567	−	0.0790797i	0.887951	+	0.459939i	$0.152129\pi$
$90$		0			0
$91$	0.309467	+	0.536012i	0.0324410	+	0.0561894i
$92$		0			0
$93$	−6.00637	−	4.59667i	−0.622831	−	0.476652i
$94$		0			0
$95$	3.32194	+	1.20909i	0.340824	+	0.124050i
$96$		0			0
$97$	−0.650292	+	3.68799i	−0.0660272	+	0.374459i	0.933833	+	0.357710i	$0.116442\pi$
$97$	−0.650292	+	3.68799i	−0.0660272	+	0.374459i	−0.999860	+	0.0167483i	$0.994669\pi$
$98$		0			0
$99$	2.97183	+	10.9787i	0.298680	+	1.10340i
$100$		0			0
$101$	−2.11434	−	1.77414i	−0.210385	−	0.176534i	0.531506	−	0.847054i	$-0.321626\pi$
$101$	−2.11434	−	1.77414i	−0.210385	−	0.176534i	−0.741891	+	0.670521i	$0.766071\pi$
$102$		0			0
$103$	2.36109	+	13.3904i	0.232645	+	1.31939i	0.847517	+	0.530768i	$0.178096\pi$
$103$	2.36109	+	13.3904i	0.232645	+	1.31939i	−0.614872	+	0.788627i	$0.710792\pi$
$104$		0			0
$105$	−4.68110	−	1.46937i	−0.456829	−	0.143396i
$106$		0			0
$107$	9.77292			0.944784			0.472392	−	0.881389i	$-0.343391\pi$
$107$	9.77292			0.944784			0.472392	+	0.881389i	$0.343391\pi$
$108$		0			0
$109$	17.4940			1.67562			0.837809	−	0.545964i	$-0.183836\pi$
$109$	17.4940			1.67562			0.837809	+	0.545964i	$0.183836\pi$
$110$		0			0
$111$	−12.9883	+	11.9321i	−1.23279	+	1.13255i
$112$		0			0
$113$	1.24979	+	7.08789i	0.117570	+	0.666772i	0.985446	+	0.169991i	$0.0543738\pi$
$113$	1.24979	+	7.08789i	0.117570	+	0.666772i	−0.867876	+	0.496781i	$0.834515\pi$
$114$		0			0
$115$	17.4894	+	14.6754i	1.63090	+	1.36849i
$116$		0			0
$117$	1.84932	−	0.166556i	0.170969	−	0.0153981i
$118$		0			0
$119$	−1.14069	+	6.46916i	−0.104567	+	0.593027i
$120$		0			0
$121$	−3.17037	−	1.15392i	−0.288215	−	0.104902i
$122$		0			0
$123$	0.775144	−	5.94649i	0.0698923	−	0.536177i
$124$		0			0
$125$	2.79878	+	4.84763i	0.250330	+	0.433585i
$126$		0			0
$127$	5.15801	−	8.93393i	0.457699	−	0.792758i	−0.541140	−	0.840933i	$-0.682007\pi$
$127$	5.15801	−	8.93393i	0.457699	−	0.792758i	0.998839	+	0.0481743i	$0.0153403\pi$
$128$		0			0
$129$	11.7459	−	0.527874i	1.03417	−	0.0464767i
$130$		0			0
$131$	10.5448	−	8.84812i	0.921302	−	0.773064i	−0.0529336	−	0.998598i	$-0.516857\pi$
$131$	10.5448	−	8.84812i	0.921302	−	0.773064i	0.974235	+	0.225534i	$0.0724127\pi$
$132$		0			0
$133$	−1.17273	+	0.426840i	−0.101689	+	0.0370117i
$134$		0			0
$135$	−9.90228	+	10.8899i	−0.852252	+	0.937256i
$136$		0			0
$137$	0.457675	−	0.166580i	0.0391018	−	0.0142319i	−0.322395	−	0.946605i	$-0.604488\pi$
$137$	0.457675	−	0.166580i	0.0391018	−	0.0142319i	0.361497	+	0.932373i	$0.382266\pi$
$138$		0			0
$139$	−8.97624	+	7.53196i	−0.761355	+	0.638852i	−0.938479	−	0.345336i	$-0.887765\pi$
$139$	−8.97624	+	7.53196i	−0.761355	+	0.638852i	0.177125	+	0.984188i	$0.443320\pi$
$140$		0			0
$141$	−2.18251	+	4.20567i	−0.183801	+	0.354182i
$142$		0			0
$143$	−1.17328	+	2.03218i	−0.0981144	+	0.169939i
$144$		0			0
$145$	10.6146	+	18.3850i	0.881494	+	1.52679i
$146$		0			0
$147$	1.59936	−	0.664871i	0.131913	−	0.0548376i
$148$		0			0
$149$	0.628791	+	0.228861i	0.0515126	+	0.0187490i	0.367648	−	0.929965i	$-0.380163\pi$
$149$	0.628791	+	0.228861i	0.0515126	+	0.0187490i	−0.316135	+	0.948714i	$0.602385\pi$
$150$		0			0
$151$	1.66174	−	9.42421i	0.135231	−	0.766931i	−0.839468	−	0.543409i	$-0.817133\pi$
$151$	1.66174	−	9.42421i	0.135231	−	0.766931i	0.974699	−	0.223522i	$-0.0717556\pi$
$152$		0			0
$153$	16.1718	+	11.2621i	1.30741	+	0.910489i
$154$		0			0
$155$	9.47559	+	7.95097i	0.761098	+	0.638637i
$156$		0			0
$157$	−1.95408	−	11.0822i	−0.155953	−	0.884453i	−0.957909	−	0.287070i	$-0.907319\pi$
$157$	−1.95408	−	11.0822i	−0.155953	−	0.884453i	0.801957	−	0.597382i	$-0.203792\pi$
$158$		0			0
$159$	4.55639	+	20.4290i	0.361345	+	1.62013i
$160$		0			0
$161$	−8.05988			−0.635207
$162$		0			0
$163$	18.2878			1.43241			0.716207	−	0.697888i	$-0.245877\pi$
$163$	18.2878			1.43241			0.716207	+	0.697888i	$0.245877\pi$
$164$		0			0
$165$	−4.04922	−	18.1551i	−0.315232	−	1.41337i
$166$		0			0
$167$	−0.486884	−	2.76126i	−0.0376762	−	0.213673i	0.960157	−	0.279460i	$-0.0901553\pi$
$167$	−0.486884	−	2.76126i	−0.0376762	−	0.213673i	−0.997834	+	0.0657871i	$0.979044\pi$
$168$		0			0
$169$	−9.66512	−	8.11000i	−0.743471	−	0.623846i
$170$		0			0
$171$	−0.316780	+	3.73056i	−0.0242247	+	0.285283i
$172$		0			0
$173$	−3.20550	+	18.1793i	−0.243710	+	1.38215i	0.579761	+	0.814786i	$0.303146\pi$
$173$	−3.20550	+	18.1793i	−0.243710	+	1.38215i	−0.823471	+	0.567359i	$0.807965\pi$
$174$		0			0
$175$	2.84155	+	1.03424i	0.214801	+	0.0781812i
$176$		0			0
$177$	−12.6831	+	5.27250i	−0.953320	+	0.396305i
$178$		0			0
$179$	−2.24251	−	3.88414i	−0.167613	−	0.290314i	0.769967	−	0.638084i	$-0.220273\pi$
$179$	−2.24251	−	3.88414i	−0.167613	−	0.290314i	−0.937580	+	0.347769i	$0.886939\pi$
$180$		0			0
$181$	−7.49700	+	12.9852i	−0.557247	+	0.965181i	0.440477	+	0.897764i	$0.354809\pi$
$181$	−7.49700	+	12.9852i	−0.557247	+	0.965181i	−0.997725	+	0.0674172i	$0.978524\pi$
$182$		0			0
$183$	5.83847	−	11.2507i	0.431592	−	0.831673i
$184$		0			0
$185$	22.0962	−	18.5409i	1.62454	−	1.36315i
$186$		0			0
$187$	−23.4029	+	8.51794i	−1.71139	+	0.622894i
$188$		0			0
$189$	0.206757	−	5.19204i	0.0150393	−	0.377665i
$190$		0			0
$191$	1.95856	−	0.712858i	0.141716	−	0.0515806i	−0.270188	−	0.962808i	$-0.587086\pi$
$191$	1.95856	−	0.712858i	0.141716	−	0.0515806i	0.411905	+	0.911227i	$0.364864\pi$
$192$		0			0
$193$	−13.5675	+	11.3845i	−0.976611	+	0.819474i	−0.983575	−	0.180502i	$-0.942228\pi$
$193$	−13.5675	+	11.3845i	−0.976611	+	0.819474i	0.00696374	+	0.999976i	$0.497783\pi$
$194$		0			0
$195$	−3.03361	+	0.136333i	−0.217241	+	0.00976303i
$196$		0			0
$197$	12.3264	−	21.3499i	0.878218	−	1.52112i	0.0249242	−	0.999689i	$-0.492066\pi$
$197$	12.3264	−	21.3499i	0.878218	−	1.52112i	0.853294	−	0.521430i	$-0.174601\pi$
$198$		0			0
$199$	12.2759	+	21.2624i	0.870214	+	1.50725i	0.861775	+	0.507290i	$0.169353\pi$
$199$	12.2759	+	21.2624i	0.870214	+	1.50725i	0.00843836	+	0.999964i	$0.497314\pi$
$200$		0			0
$201$	1.09177	−	8.37551i	0.0770078	−	0.590763i
$202$		0			0
$203$	−7.04249	−	2.56326i	−0.494286	−	0.179905i
$204$		0			0
$205$	−1.70303	+	9.65836i	−0.118945	+	0.674569i
$206$		0			0
$207$	−10.1627	+	21.9402i	−0.706359	+	1.52495i
$208$		0			0
$209$	−3.62454	−	3.04135i	−0.250715	−	0.210375i
$210$		0			0
$211$	−1.74184	−	9.87849i	−0.119913	−	0.680063i	−0.984200	−	0.177063i	$-0.943340\pi$
$211$	−1.74184	−	9.87849i	−0.119913	−	0.680063i	0.864286	−	0.503001i	$-0.167771\pi$
$212$		0			0
$213$	−15.0223	+	13.8007i	−1.02931	+	0.945609i
$214$		0			0
$215$	−19.2291			−1.31141
$216$		0			0
$217$	−4.36676			−0.296435
$218$		0			0
$219$	21.0316	+	6.60170i	1.42118	+	0.446101i
$220$		0			0
$221$	0.706010	+	4.00398i	0.0474914	+	0.269337i
$222$		0			0
$223$	−11.3648	−	9.53621i	−0.761044	−	0.638592i	0.177354	−	0.984147i	$-0.443246\pi$
$223$	−11.3648	−	9.53621i	−0.761044	−	0.638592i	−0.938398	+	0.345555i	$0.887691\pi$
$224$		0			0
$225$	6.39829	−	6.43106i	0.426552	−	0.428738i
$226$		0			0
$227$	−1.06478	+	6.03865i	−0.0706717	+	0.400799i	0.928867	+	0.370415i	$0.120784\pi$
$227$	−1.06478	+	6.03865i	−0.0706717	+	0.400799i	−0.999538	+	0.0303847i	$0.990327\pi$
$228$		0			0
$229$	−5.05603	−	1.84025i	−0.334112	−	0.121607i	0.169516	−	0.985527i	$-0.445780\pi$
$229$	−5.05603	−	1.84025i	−0.334112	−	0.121607i	−0.503628	+	0.863921i	$0.668002\pi$
$230$		0			0
$231$	5.21481	+	3.99089i	0.343110	+	0.262581i
$232$		0			0
$233$	−0.667800	−	1.15666i	−0.0437490	−	0.0757756i	0.843322	−	0.537409i	$-0.180597\pi$
$233$	−0.667800	−	1.15666i	−0.0437490	−	0.0757756i	−0.887071	+	0.461633i	$0.847264\pi$
$234$		0			0
$235$	3.87455	−	6.71091i	0.252748	−	0.437772i
$236$		0			0
$237$	8.26637	+	12.9391i	0.536958	+	0.840484i
$238$		0			0
$239$	4.45672	−	3.73963i	0.288281	−	0.241896i	−0.487166	−	0.873310i	$-0.661969\pi$
$239$	4.45672	−	3.73963i	0.288281	−	0.241896i	0.775447	+	0.631413i	$0.217525\pi$
$240$		0			0
$241$	−4.01473	+	1.46124i	−0.258611	+	0.0941268i	−0.468072	−	0.883690i	$-0.655051\pi$
$241$	−4.01473	+	1.46124i	−0.258611	+	0.0941268i	0.209461	+	0.977817i	$0.432829\pi$
$242$		0			0
$243$	−13.8728	−	7.10948i	−0.889942	−	0.456074i
$244$		0			0
$245$	−2.66182	+	0.968824i	−0.170058	+	0.0618959i
$246$		0			0
$247$	−0.591713	+	0.496506i	−0.0376498	+	0.0315919i
$248$		0			0
$249$	7.03681	+	11.0145i	0.445940	+	0.698016i
$250$		0			0
$251$	−6.87016	+	11.8995i	−0.433641	+	0.751087i	−0.997184	−	0.0749992i	$-0.976105\pi$
$251$	−6.87016	+	11.8995i	−0.433641	+	0.751087i	0.563543	+	0.826087i	$0.309438\pi$
$252$		0			0
$253$	−15.2786	−	26.4634i	−0.960560	−	1.66374i
$254$		0			0
$255$	−25.5942	−	19.5873i	−1.60277	−	1.22660i
$256$		0			0
$257$	−13.4442	−	4.89329i	−0.838626	−	0.305235i	−0.113232	−	0.993569i	$-0.536120\pi$
$257$	−13.4442	−	4.89329i	−0.838626	−	0.305235i	−0.725394	+	0.688334i	$0.758343\pi$
$258$		0			0
$259$	−1.76823	+	10.0282i	−0.109873	+	0.623119i
$260$		0			0
$261$	−15.8575	+	15.9387i	−0.981553	+	0.986582i
$262$		0			0
$263$	−11.3534	−	9.52661i	−0.700079	−	0.587436i	0.221717	−	0.975111i	$-0.428834\pi$
$263$	−11.3534	−	9.52661i	−0.700079	−	0.587436i	−0.921796	+	0.387675i	$0.873278\pi$
$264$		0			0
$265$	−5.94418	−	33.7111i	−0.365148	−	2.07086i
$266$		0			0
$267$	−1.42359	−	0.446857i	−0.0871221	−	0.0273472i
$268$		0			0
$269$	26.2959			1.60329			0.801646	−	0.597800i	$-0.203958\pi$
$269$	26.2959			1.60329			0.801646	+	0.597800i	$0.203958\pi$
$270$		0			0
$271$	−0.277729			−0.0168709			−0.00843543	−	0.999964i	$-0.502685\pi$
$271$	−0.277729			−0.0168709			−0.00843543	+	0.999964i	$0.502685\pi$
$272$		0			0
$273$	0.789454	−	0.725259i	0.0477799	−	0.0438947i
$274$		0			0
$275$	1.99079	+	11.2904i	0.120049	+	0.680834i
$276$		0			0
$277$	−18.1572	−	15.2357i	−1.09096	−	0.915425i	−0.0941762	−	0.995556i	$-0.530022\pi$
$277$	−18.1572	−	15.2357i	−1.09096	−	0.915425i	−0.996784	+	0.0801310i	$0.974466\pi$
$278$		0			0
$279$	−5.50606	+	11.8870i	−0.329639	+	0.711656i
$280$		0			0
$281$	−0.826871	+	4.68942i	−0.0493270	+	0.279747i	−0.999487	−	0.0320141i	$-0.989808\pi$
$281$	−0.826871	+	4.68942i	−0.0493270	+	0.279747i	0.950160	+	0.311761i	$0.100919\pi$
$282$		0			0
$283$	14.0955	+	5.13036i	0.837893	+	0.304968i	0.725094	−	0.688650i	$-0.241796\pi$
$283$	14.0955	+	5.13036i	0.837893	+	0.304968i	0.112799	+	0.993618i	$0.464018\pi$
$284$		0			0
$285$	0.791461	−	6.07167i	0.0468821	−	0.359655i
$286$		0			0
$287$	−1.73113	−	2.99840i	−0.102185	−	0.176990i
$288$		0			0
$289$	−13.0756	+	22.6476i	−0.769154	+	1.33221i
$290$		0			0
$291$	6.47979	−	0.291208i	0.379852	−	0.0170709i
$292$		0			0
$293$	10.1070	−	8.48077i	0.590456	−	0.495452i	−0.297906	−	0.954595i	$-0.596288\pi$
$293$	10.1070	−	8.48077i	0.590456	−	0.495452i	0.888362	+	0.459144i	$0.151844\pi$
$294$		0			0
$295$	21.1086	−	7.68289i	1.22899	−	0.447315i
$296$		0			0
$297$	17.4392	−	9.16339i	1.01193	−	0.531714i
$298$		0			0
$299$	−4.68769	+	1.70618i	−0.271096	+	0.0986708i
$300$		0			0
$301$	5.20019	−	4.36348i	0.299734	−	0.251507i
$302$		0			0
$303$	−2.20201	+	4.24325i	−0.126502	+	0.243768i
$304$		0			0
$305$	−10.3649	+	17.9525i	−0.593490	+	1.02796i
$306$		0			0
$307$	2.20414	+	3.81768i	0.125797	+	0.217886i	0.922044	−	0.387085i	$-0.126518\pi$
$307$	2.20414	+	3.81768i	0.125797	+	0.217886i	−0.796247	+	0.604971i	$0.793185\pi$
$308$		0			0
$309$	21.7464	−	9.04022i	1.23711	−	0.514280i
$310$		0			0
$311$	12.1789	+	4.43276i	0.690602	+	0.251359i	0.663393	−	0.748271i	$-0.269116\pi$
$311$	12.1789	+	4.43276i	0.690602	+	0.251359i	0.0272093	+	0.999630i	$0.491338\pi$
$312$		0			0
$313$	−1.65545	+	9.38852i	−0.0935716	+	0.530671i	0.901604	+	0.432562i	$0.142390\pi$
$313$	−1.65545	+	9.38852i	−0.0935716	+	0.530671i	−0.995176	+	0.0981086i	$0.968721\pi$
$314$		0			0
$315$	−0.719014	+	8.46748i	−0.0405119	+	0.477089i
$316$		0			0
$317$	17.6555	+	14.8147i	0.991629	+	0.832075i	0.985803	−	0.167908i	$-0.0537010\pi$
$317$	17.6555	+	14.8147i	0.991629	+	0.832075i	0.00582619	+	0.999983i	$0.498145\pi$
$318$		0			0
$319$	−4.93397	−	27.9820i	−0.276249	−	1.56669i
$320$		0			0
$321$	−3.68482	−	16.5213i	−0.205667	−	0.922127i
$322$		0			0
$323$	−8.19803			−0.456151
$324$		0			0
$325$	1.87160			0.103818
$326$		0			0
$327$	−6.59600	−	29.5738i	−0.364760	−	1.63543i
$328$		0			0
$329$	0.475037	+	2.69407i	0.0261897	+	0.148529i
$330$		0			0
$331$	24.4673	+	20.5305i	1.34485	+	1.12846i	0.980352	+	0.197254i	$0.0632023\pi$
$331$	24.4673	+	20.5305i	1.34485	+	1.12846i	0.364493	+	0.931206i	$0.381242\pi$
$332$		0			0
$333$	25.0686	+	17.4579i	1.37375	+	0.956690i
$334$		0			0
$335$	−2.39868	+	13.6036i	−0.131054	+	0.743244i
$336$		0			0
$337$	−17.9642	−	6.53844i	−0.978573	−	0.356171i	−0.197287	−	0.980346i	$-0.563213\pi$
$337$	−17.9642	−	6.53844i	−0.978573	−	0.356171i	−0.781285	+	0.624174i	$0.785435\pi$
$338$		0			0
$339$	11.5109	−	4.78523i	0.625189	−	0.259898i
$340$		0			0
$341$	−8.27781	−	14.3376i	−0.448269	−	0.776424i
$342$		0			0
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$		0			0
$345$	18.2146	−	35.0994i	0.980643	−	1.88969i
$346$		0			0
$347$	28.2347	−	23.6917i	1.51572	−	1.27184i	0.664147	−	0.747602i	$-0.268795\pi$
$347$	28.2347	−	23.6917i	1.51572	−	1.27184i	0.851572	−	0.524237i	$-0.175649\pi$
$348$		0			0
$349$	27.5710	−	10.0350i	1.47584	−	0.537163i	0.526162	−	0.850384i	$-0.323631\pi$
$349$	27.5710	−	10.0350i	1.47584	−	0.537163i	0.949680	+	0.313222i	$0.101408\pi$
$350$		0			0
$351$	−0.978840	−	3.06350i	−0.0522466	−	0.163517i
$352$		0			0
$353$	6.24993	−	2.27479i	0.332650	−	0.121075i	−0.170295	−	0.985393i	$-0.554472\pi$
$353$	6.24993	−	2.27479i	0.332650	−	0.121075i	0.502945	+	0.864318i	$0.332250\pi$
$354$		0			0
$355$	25.5564	−	21.4444i	1.35639	−	1.13815i
$356$		0			0
$357$	11.3663	−	0.510812i	0.601568	−	0.0270350i
$358$		0			0
$359$	14.5242	−	25.1567i	0.766560	−	1.32772i	−0.172857	−	0.984947i	$-0.555300\pi$
$359$	14.5242	−	25.1567i	0.766560	−	1.32772i	0.939418	−	0.342774i	$-0.111367\pi$
$360$		0			0
$361$	8.72125	+	15.1057i	0.459013	+	0.795034i
$362$		0			0
$363$	−0.755348	+	5.79463i	−0.0396455	+	0.304139i
$364$		0			0
$365$	−33.8763	−	12.3300i	−1.77317	−	0.645380i
$366$		0			0
$367$	−1.38025	+	7.82780i	−0.0720486	+	0.408608i	0.927358	+	0.374174i	$0.122074\pi$
$367$	−1.38025	+	7.82780i	−0.0720486	+	0.408608i	−0.999407	+	0.0344335i	$0.989037\pi$
$368$		0			0
$369$	−10.3449	+	0.931699i	−0.538533	+	0.0485023i
$370$		0			0
$371$	9.25727	+	7.76777i	0.480613	+	0.403282i
$372$		0			0
$373$	−1.92757	−	10.9318i	−0.0998059	−	0.566027i	−0.993168	−	0.116691i	$-0.962771\pi$
$373$	−1.92757	−	10.9318i	−0.0998059	−	0.566027i	0.893362	−	0.449337i	$-0.148340\pi$
$374$		0			0
$375$	7.13972	−	6.55914i	0.368693	−	0.338713i
$376$		0			0
$377$	−4.63857			−0.238899
$378$		0			0
$379$	28.5563			1.46684			0.733418	−	0.679777i	$-0.237924\pi$
$379$	28.5563			1.46684			0.733418	+	0.679777i	$0.237924\pi$
$380$		0			0
$381$	−17.0477	−	5.35120i	−0.873382	−	0.274150i
$382$		0			0
$383$	2.98314	+	16.9182i	0.152431	+	0.864480i	0.961097	+	0.276212i	$0.0890791\pi$
$383$	2.98314	+	16.9182i	0.152431	+	0.864480i	−0.808666	+	0.588268i	$0.799810\pi$
$384$		0			0
$385$	−8.22685	−	6.90315i	−0.419279	−	0.351817i
$386$		0			0
$387$	−5.32112	−	19.6577i	−0.270488	−	0.999255i
$388$		0			0
$389$	−4.82378	+	27.3570i	−0.244575	+	1.38706i	0.576902	+	0.816814i	$0.304262\pi$
$389$	−4.82378	+	27.3570i	−0.244575	+	1.38706i	−0.821477	+	0.570242i	$0.806850\pi$
$390$		0			0
$391$	−49.7520	−	18.1083i	−2.51607	−	0.915774i
$392$		0			0
$393$	−18.9337	−	14.4900i	−0.955080	−	0.730922i
$394$		0			0
$395$	−12.5554	−	21.7466i	−0.631732	−	1.09419i
$396$		0			0
$397$	−2.88573	+	4.99823i	−0.144831	+	0.250854i	−0.929310	−	0.369301i	$-0.879597\pi$
$397$	−2.88573	+	4.99823i	−0.144831	+	0.250854i	0.784479	+	0.620155i	$0.212930\pi$
$398$		0			0
$399$	1.16375	+	1.82158i	0.0582604	+	0.0911932i
$400$		0			0
$401$	−23.0845	+	19.3702i	−1.15278	+	0.967301i	−0.999781	−	0.0209252i	$-0.993339\pi$
$401$	−23.0845	+	19.3702i	−1.15278	+	0.967301i	−0.153003	+	0.988226i	$0.548894\pi$
$402$		0			0
$403$	−2.53974	+	0.924390i	−0.126513	+	0.0460471i
$404$		0			0
$405$	22.1432	+	12.6340i	1.10030	+	0.627786i
$406$		0			0
$407$	−36.2779	+	13.2041i	−1.79823	+	0.654501i
$408$		0			0
$409$	−15.6219	+	13.1083i	−0.772453	+	0.648165i	−0.941336	−	0.337471i	$-0.890429\pi$
$409$	−15.6219	+	13.1083i	−0.772453	+	0.648165i	0.168883	+	0.985636i	$0.445984\pi$
$410$		0			0
$411$	−0.454170	−	0.710898i	−0.0224025	−	0.0350660i
$412$		0			0
$413$	−3.96506	+	6.86768i	−0.195108	+	0.337936i
$414$		0			0
$415$	−10.6879	−	18.5120i	−0.524648	−	0.908717i
$416$		0			0
$417$	16.1173	+	12.3346i	0.789268	+	0.604027i
$418$		0			0
$419$	−3.87119	−	1.40900i	−0.189120	−	0.0688340i	0.245724	−	0.969340i	$-0.420974\pi$
$419$	−3.87119	−	1.40900i	−0.189120	−	0.0688340i	−0.434844	+	0.900506i	$0.643197\pi$
$420$		0			0
$421$	−1.64345	+	9.32049i	−0.0800971	+	0.454253i	0.918210	+	0.396093i	$0.129634\pi$
$421$	−1.64345	+	9.32049i	−0.0800971	+	0.454253i	−0.998307	+	0.0581596i	$0.981477\pi$
$422$		0			0
$423$	7.93265	+	2.10384i	0.385699	+	0.102292i
$424$		0			0
$425$	15.2167	+	12.7683i	0.738118	+	0.619355i
$426$		0			0
$427$	−1.27078	−	7.20696i	−0.0614974	−	0.348769i
$428$		0			0
$429$	3.87780	+	1.21722i	0.187222	+	0.0587680i
$430$		0			0
$431$	−17.5768			−0.846646			−0.423323	−	0.905979i	$-0.639136\pi$
$431$	−17.5768			−0.846646			−0.423323	+	0.905979i	$0.639136\pi$
$432$		0			0
$433$	10.2769			0.493878			0.246939	−	0.969031i	$-0.420575\pi$
$433$	10.2769			0.493878			0.246939	+	0.969031i	$0.420575\pi$
$434$		0			0
$435$	27.0780	−	24.8761i	1.29829	−	1.19272i
$436$		0			0
$437$	−1.74667	−	9.90587i	−0.0835547	−	0.473862i
$438$		0			0
$439$	−7.94284	−	6.66483i	−0.379091	−	0.318095i	0.433255	−	0.901272i	$-0.357365\pi$
$439$	−7.94284	−	6.66483i	−0.379091	−	0.318095i	−0.812345	+	0.583177i	$0.801810\pi$
$440$		0			0
$441$	−1.72700	−	2.45305i	−0.0822382	−	0.116812i
$442$		0			0
$443$	1.09215	−	6.19390i	0.0518897	−	0.294281i	−0.947809	−	0.318840i	$-0.896707\pi$
$443$	1.09215	−	6.19390i	0.0518897	−	0.294281i	0.999698	+	0.0245584i	$0.00781796\pi$
$444$		0			0
$445$	2.29302	+	0.834592i	0.108700	+	0.0395635i
$446$		0			0
$447$	0.149811	−	1.14927i	0.00708582	−	0.0543586i
$448$		0			0
$449$	9.67993	+	16.7661i	0.456824	+	0.791243i	0.998791	−	0.0491572i	$-0.0156535\pi$
$449$	9.67993	+	16.7661i	0.456824	+	0.791243i	−0.541967	+	0.840400i	$0.682320\pi$
$450$		0			0
$451$	6.56319	−	11.3678i	0.309049	−	0.535288i
$452$		0			0
$453$	−16.5583	+	0.744146i	−0.777977	+	0.0349630i
$454$		0			0
$455$	−1.34305	+	1.12695i	−0.0629630	+	0.0528323i
$456$		0			0
$457$	−32.7074	+	11.9045i	−1.52999	+	0.556870i	−0.963619	−	0.267281i	$-0.913875\pi$
$457$	−32.7074	+	11.9045i	−1.52999	+	0.556870i	−0.566370	+	0.824151i	$0.691653\pi$
$458$		0			0
$459$	12.9413	−	31.5849i	0.604048	−	1.47426i
$460$		0			0
$461$	−12.1205	+	4.41150i	−0.564508	+	0.205464i	−0.608481	−	0.793569i	$-0.708221\pi$
$461$	−12.1205	+	4.41150i	−0.564508	+	0.205464i	0.0439727	+	0.999033i	$0.485999\pi$
$462$		0			0
$463$	7.93530	−	6.65851i	0.368785	−	0.309447i	−0.439496	−	0.898245i	$-0.644843\pi$
$463$	7.93530	−	6.65851i	0.368785	−	0.309447i	0.808281	+	0.588797i	$0.200398\pi$
$464$		0			0
$465$	9.86850	−	19.0165i	0.457641	−	0.881869i
$466$		0			0
$467$	1.34705	−	2.33317i	0.0623343	−	0.107966i	−0.833174	−	0.553011i	$-0.813479\pi$
$467$	1.34705	−	2.33317i	0.0623343	−	0.107966i	0.895508	+	0.445045i	$0.146812\pi$
$468$		0			0
$469$	−2.43826	−	4.22318i	−0.112588	−	0.195009i
$470$		0			0
$471$	−17.9978	+	7.48187i	−0.829294	+	0.344746i
$472$		0			0
$473$	24.1845	+	8.80245i	1.11201	+	0.404737i
$474$		0			0
$475$	−0.655319	+	3.71650i	−0.0300681	+	0.170525i
$476$		0			0
$477$	32.8176	−	15.4053i	1.50261	−	0.705360i
$478$		0			0
$479$	16.7015	+	14.0142i	0.763111	+	0.640326i	0.938935	−	0.344095i	$-0.111814\pi$
$479$	16.7015	+	14.0142i	0.763111	+	0.640326i	−0.175824	+	0.984422i	$0.556259\pi$
$480$		0			0
$481$	1.09442	+	6.20676i	0.0499013	+	0.283004i
$482$		0			0
$483$	3.03893	+	13.6253i	0.138276	+	0.619974i
$484$		0			0
$485$	−10.6080			−0.481682
$486$		0			0
$487$	−21.2996			−0.965177			−0.482589	−	0.875847i	$-0.660303\pi$
$487$	−21.2996			−0.965177			−0.482589	+	0.875847i	$0.660303\pi$
$488$		0			0
$489$	−6.89532	−	30.9158i	−0.311817	−	1.39806i
$490$		0			0
$491$	0.698981	+	3.96412i	0.0315446	+	0.178898i	0.996509	−	0.0834813i	$-0.0266039\pi$
$491$	0.698981	+	3.96412i	0.0315446	+	0.178898i	−0.964965	+	0.262379i	$0.915493\pi$
$492$		0			0
$493$	−37.7130	−	31.6449i	−1.69851	−	1.42522i
$494$		0			0
$495$	−29.1647	+	13.6905i	−1.31086	+	0.615344i
$496$		0			0
$497$	−2.04514	+	11.5986i	−0.0917371	+	0.520267i
$498$		0			0
$499$	1.14891	+	0.418168i	0.0514321	+	0.0187198i	0.367608	−	0.929981i	$-0.380177\pi$
$499$	1.14891	+	0.418168i	0.0514321	+	0.0187198i	−0.316176	+	0.948701i	$0.602399\pi$
$500$		0			0
$501$	−4.48437	+	1.86420i	−0.200347	+	0.0832864i
$502$		0			0
$503$	0.273145	+	0.473102i	0.0121790	+	0.0210946i	0.872051	−	0.489416i	$-0.162790\pi$
$503$	0.273145	+	0.473102i	0.0121790	+	0.0210946i	−0.859872	+	0.510510i	$0.829457\pi$
$504$		0			0
$505$	3.90917	−	6.77087i	0.173956	−	0.301300i
$506$		0			0
$507$	−10.0659	+	19.3969i	−0.447042	+	0.861445i
$508$		0			0
$509$	9.17079	−	7.69521i	0.406488	−	0.341084i	−0.416507	−	0.909133i	$-0.636746\pi$
$509$	9.17079	−	7.69521i	0.406488	−	0.341084i	0.822995	+	0.568048i	$0.192301\pi$
$510$		0			0
$511$	11.9592	−	4.35280i	0.529044	−	0.192556i
$512$		0			0
$513$	6.42600	−	0.871066i	0.283715	−	0.0384585i
$514$		0			0
$515$	−36.1927	+	13.1731i	−1.59484	+	0.580474i
$516$		0			0
$517$	−7.94507	+	6.66671i	−0.349424	+	0.293202i
$518$		0			0
$519$	31.9409	−	1.43546i	1.40205	−	0.0630095i
$520$		0			0
$521$	10.4506	−	18.1010i	0.457850	−	0.793020i	−0.540997	−	0.841025i	$-0.681953\pi$
$521$	10.4506	−	18.1010i	0.457850	−	0.793020i	0.998847	+	0.0480046i	$0.0152862\pi$
$522$		0			0
$523$	−19.9086	−	34.4828i	−0.870544	−	1.50783i	−0.861435	−	0.507868i	$-0.830434\pi$
$523$	−19.9086	−	34.4828i	−0.870544	−	1.50783i	−0.00910952	−	0.999959i	$-0.502900\pi$
$524$		0			0
$525$	0.677007	−	5.19364i	0.0295470	−	0.226669i
$526$		0			0
$527$	−26.9551	−	9.81087i	−1.17418	−	0.427368i
$528$		0			0
$529$	7.28656	−	41.3241i	0.316807	−	1.79670i
$530$		0			0
$531$	13.6953	+	19.4530i	0.594327	+	0.844187i
$532$		0			0
$533$	−1.64156	−	1.37743i	−0.0711039	−	0.0596633i
$534$		0			0
$535$	4.80715	+	27.2627i	0.207831	+	1.17867i
$536$		0			0
$537$	−5.72067	+	5.25548i	−0.246865	+	0.226791i
$538$		0			0
$539$	3.79128			0.163302
$540$		0			0
$541$	31.6548			1.36094			0.680472	−	0.732774i	$-0.261775\pi$
$541$	31.6548			1.36094			0.680472	+	0.732774i	$0.261775\pi$
$542$		0			0
$543$	24.7783	+	7.77779i	1.06334	+	0.333777i
$544$		0			0
$545$	8.60501	+	48.8015i	0.368598	+	2.09043i
$546$		0			0
$547$	−17.8018	−	14.9375i	−0.761149	−	0.638680i	0.177276	−	0.984161i	$-0.443271\pi$
$547$	−17.8018	−	14.9375i	−0.761149	−	0.638680i	−0.938426	+	0.345481i	$0.887716\pi$
$548$		0			0
$549$	−21.2208	−	5.62802i	−0.905681	−	0.240198i
$550$		0			0
$551$	1.62414	−	9.21095i	0.0691907	−	0.392400i
$552$		0			0
$553$	8.33017	+	3.03193i	0.354235	+	0.128931i
$554$		0			0
$555$	−39.6748	−	30.3631i	−1.68410	−	1.28884i
$556$		0			0
$557$	11.7450	+	20.3430i	0.497654	+	0.861961i	0.999996	−	0.00270729i	$-0.000861757\pi$
$557$	11.7450	+	20.3430i	0.497654	+	0.861961i	−0.502343	+	0.864669i	$0.667528\pi$
$558$		0			0
$559$	2.10078	−	3.63865i	0.0888534	−	0.153899i
$560$		0			0
$561$	23.2236	+	36.3512i	0.980502	+	1.53475i
$562$		0			0
$563$	32.2406	−	27.0531i	1.35878	−	1.14015i	0.382422	−	0.923988i	$-0.375090\pi$
$563$	32.2406	−	27.0531i	1.35878	−	1.14015i	0.976357	−	0.216164i	$-0.0693545\pi$
$564$		0			0
$565$	−19.1577	+	6.97285i	−0.805972	+	0.293350i
$566$		0			0
$567$	−8.85517	+	1.60810i	−0.371882	+	0.0675340i
$568$		0			0
$569$	18.6415	−	6.78493i	0.781490	−	0.284439i	0.0796964	−	0.996819i	$-0.474605\pi$
$569$	18.6415	−	6.78493i	0.781490	−	0.284439i	0.701794	+	0.712380i	$0.252383\pi$
$570$		0			0
$571$	20.3290	−	17.0581i	0.850743	−	0.713858i	−0.109210	−	0.994019i	$-0.534832\pi$
$571$	20.3290	−	17.0581i	0.850743	−	0.713858i	0.959953	+	0.280160i	$0.0903877\pi$
$572$		0			0
$573$	−1.94356	−	3.04220i	−0.0811934	−	0.127090i
$574$		0			0
$575$	−12.1862	+	21.1071i	−0.508200	+	0.880227i
$576$		0			0
$577$	19.8913	+	34.4528i	0.828086	+	1.43429i	0.899538	+	0.436843i	$0.143904\pi$
$577$	19.8913	+	34.4528i	0.828086	+	1.43429i	−0.0714514	+	0.997444i	$0.522763\pi$
$578$		0			0
$579$	24.3612	+	18.6436i	1.01242	+	0.774802i
$580$		0			0
$581$	7.09112	+	2.58096i	0.294189	+	0.107076i
$582$		0			0
$583$	−7.95583	+	45.1197i	−0.329497	+	1.86867i
$584$		0			0
$585$	1.37428	+	5.07696i	0.0568195	+	0.209906i
$586$		0			0
$587$	−26.5289	−	22.2604i	−1.09496	−	0.918784i	−0.0978883	−	0.995197i	$-0.531209\pi$
$587$	−26.5289	−	22.2604i	−1.09496	−	0.918784i	−0.997076	+	0.0764130i	$0.975653\pi$
$588$		0			0
$589$	−0.946330	−	5.36690i	−0.0389928	−	0.221139i
$590$		0			0
$591$	−40.7399	−	12.7881i	−1.67582	−	0.526030i
$592$		0			0
$593$	9.39174			0.385672			0.192836	−	0.981231i	$-0.438231\pi$
$593$	9.39174			0.385672			0.192836	+	0.981231i	$0.438231\pi$
$594$		0			0
$595$	−18.6076			−0.762836
$596$		0			0
$597$	31.3159	−	28.7694i	1.28167	−	1.17745i
$598$		0			0
$599$	1.30016	+	7.37357i	0.0531230	+	0.301276i	0.999780	−	0.0209669i	$-0.00667445\pi$
$599$	1.30016	+	7.37357i	0.0531230	+	0.301276i	−0.946657	+	0.322243i	$0.895563\pi$
$600$		0			0
$601$	−2.39764	−	2.01186i	−0.0978020	−	0.0820656i	0.592576	−	0.805515i	$-0.298111\pi$
$601$	−2.39764	−	2.01186i	−0.0978020	−	0.0820656i	−0.690378	+	0.723449i	$0.742556\pi$
$602$		0			0
$603$	−14.5706	+	1.31228i	−0.593359	+	0.0534402i
$604$		0			0
$605$	1.65954	−	9.41171i	0.0674698	−	0.382640i
$606$		0			0
$607$	−21.3829	−	7.78275i	−0.867906	−	0.315892i	−0.130587	−	0.991437i	$-0.541686\pi$
$607$	−21.3829	−	7.78275i	−0.867906	−	0.315892i	−0.737319	+	0.675545i	$0.763908\pi$
$608$		0			0
$609$	−1.67789	+	12.8719i	−0.0679915	+	0.521595i
$610$		0			0
$611$	0.846588	+	1.46633i	0.0342493	+	0.0593215i
$612$		0			0
$613$	3.55596	−	6.15911i	0.143624	−	0.248764i	−0.785235	−	0.619198i	$-0.787458\pi$
$613$	3.55596	−	6.15911i	0.143624	−	0.248764i	0.928859	+	0.370434i	$0.120791\pi$
$614$		0			0
$615$	16.9697	−	0.762635i	0.684285	−	0.0307524i
$616$		0			0
$617$	2.93269	−	2.46082i	0.118066	−	0.0990690i	−0.581843	−	0.813301i	$-0.697668\pi$
$617$	2.93269	−	2.46082i	0.118066	−	0.0990690i	0.699909	+	0.714232i	$0.253224\pi$
$618$		0			0
$619$	−21.9122	+	7.97540i	−0.880726	+	0.320558i	−0.742503	−	0.669843i	$-0.766361\pi$
$619$	−21.9122	+	7.97540i	−0.880726	+	0.320558i	−0.138224	+	0.990401i	$0.544139\pi$
$620$		0			0
$621$	40.9221	+	8.90780i	1.64215	+	0.357458i
$622$		0			0
$623$	−0.809497	+	0.294633i	−0.0324318	+	0.0118042i
$624$		0			0
$625$	−23.7286	+	19.9107i	−0.949145	+	0.796427i
$626$		0			0
$627$	−3.77484	+	7.27407i	−0.150752	+	0.290498i
$628$		0			0
$629$	−33.4454	+	57.9291i	−1.33355	+	2.30978i
$630$		0			0
$631$	0.871491	+	1.50947i	0.0346935	+	0.0600910i	0.882851	−	0.469654i	$-0.155621\pi$
$631$	0.871491	+	1.50947i	0.0346935	+	0.0600910i	−0.848157	+	0.529744i	$0.822288\pi$
$632$		0			0
$633$	−16.0430	+	6.66924i	−0.637651	+	0.265078i
$634$		0			0
$635$	27.4594	+	9.99441i	1.08969	+	0.396616i
$636$		0			0
$637$	0.107477	−	0.609531i	0.00425838	−	0.0241505i
$638$		0			0
$639$	28.9944	+	20.1919i	1.14700	+	0.798778i
$640$		0			0
$641$	11.2313	+	9.42417i	0.443609	+	0.372232i	0.837058	−	0.547114i	$-0.184274\pi$
$641$	11.2313	+	9.42417i	0.443609	+	0.372232i	−0.393449	+	0.919347i	$0.628718\pi$
$642$		0			0
$643$	5.20722	+	29.5316i	0.205353	+	1.16461i	0.896884	+	0.442267i	$0.145825\pi$
$643$	5.20722	+	29.5316i	0.205353	+	1.16461i	−0.691531	+	0.722347i	$0.743063\pi$
$644$		0			0
$645$	7.25022	+	32.5070i	0.285477	+	1.27996i
$646$		0			0
$647$	−47.2238			−1.85656			−0.928280	−	0.371883i	$-0.878712\pi$
$647$	−47.2238			−1.85656			−0.928280	+	0.371883i	$0.878712\pi$
$648$		0			0
$649$	−30.0653			−1.18017
$650$		0			0
$651$	1.64646	+	7.38207i	0.0645299	+	0.289326i
$652$		0			0
$653$	5.96750	+	33.8434i	0.233526	+	1.32439i	0.845695	+	0.533666i	$0.179186\pi$
$653$	5.96750	+	33.8434i	0.233526	+	1.32439i	−0.612169	+	0.790727i	$0.709703\pi$
$654$		0			0
$655$	29.8697	+	25.0636i	1.16711	+	0.979318i
$656$		0			0
$657$	3.23043	−	38.0433i	0.126031	−	1.48421i
$658$		0			0
$659$	−4.77609	+	27.0865i	−0.186050	+	1.05514i	0.738549	+	0.674200i	$0.235511\pi$
$659$	−4.77609	+	27.0865i	−0.186050	+	1.05514i	−0.924599	+	0.380942i	$0.875600\pi$
$660$		0			0
$661$	16.3524	+	5.95179i	0.636035	+	0.231498i	0.639856	−	0.768495i	$-0.278994\pi$
$661$	16.3524	+	5.95179i	0.636035	+	0.231498i	−0.00382110	+	0.999993i	$0.501216\pi$
$662$		0			0
$663$	6.50259	−	2.70320i	0.252540	−	0.104984i
$664$		0			0
$665$	−1.76757	−	3.06152i	−0.0685434	−	0.118721i
$666$		0			0
$667$	30.2022	−	52.3118i	1.16943	−	2.02552i
$668$		0			0
$669$	−11.8361	+	22.8079i	−0.457608	+	0.881806i
$670$		0			0
$671$	21.2540	−	17.8342i	0.820502	−	0.688483i
$672$		0			0
$673$	−30.7026	+	11.1748i	−1.18350	+	0.430759i	−0.857437	−	0.514590i	$-0.827944\pi$
$673$	−30.7026	+	11.1748i	−1.18350	+	0.430759i	−0.326063	+	0.945348i	$0.605722\pi$
$674$		0			0
$675$	−13.2842	−	8.39160i	−0.511311	−	0.322993i
$676$		0			0
$677$	18.7034	−	6.80748i	0.718830	−	0.261633i	0.0434011	−	0.999058i	$-0.486181\pi$
$677$	18.7034	−	6.80748i	0.718830	−	0.261633i	0.675429	+	0.737425i	$0.263958\pi$
$678$		0			0
$679$	2.86875	−	2.40716i	0.110092	−	0.0923785i
$680$		0			0
$681$	10.6099	−	0.476818i	0.406572	−	0.0182717i
$682$		0			0
$683$	−4.29478	+	7.43878i	−0.164335	+	0.284637i	−0.936419	−	0.350884i	$-0.885881\pi$
$683$	−4.29478	+	7.43878i	−0.164335	+	0.284637i	0.772084	+	0.635521i	$0.219215\pi$
$684$		0			0
$685$	0.689818	+	1.19480i	0.0263566	+	0.0456510i
$686$		0			0
$687$	−1.20461	+	9.24115i	−0.0459588	+	0.352572i
$688$		0			0
$689$	7.02844	+	2.55814i	0.267762	+	0.0974575i
$690$		0			0
$691$	4.01752	−	22.7845i	0.152834	−	0.866763i	−0.807906	−	0.589311i	$-0.799399\pi$
$691$	4.01752	−	22.7845i	0.152834	−	0.866763i	0.960740	−	0.277451i	$-0.0894898\pi$
$692$		0			0
$693$	4.78045	−	10.3205i	0.181594	−	0.392042i
$694$		0			0
$695$	−25.4266	−	21.3354i	−0.964484	−	0.809298i
$696$		0			0
$697$	−3.94935	−	22.3979i	−0.149592	−	0.848380i
$698$		0			0
$699$	−1.70357	+	1.56504i	−0.0644348	+	0.0591952i
$700$		0			0
$701$	−17.0749			−0.644911			−0.322455	−	0.946585i	$-0.604508\pi$
$701$	−17.0749			−0.644911			−0.322455	+	0.946585i	$0.604508\pi$
$702$		0			0
$703$	−12.7082			−0.479297
$704$		0			0
$705$	−12.8058	−	4.01966i	−0.482293	−	0.151389i
$706$		0			0
$707$	0.479282	+	2.71814i	0.0180253	+	0.102226i
$708$		0			0
$709$	31.3757	+	26.3273i	1.17834	+	0.988744i	0.999989	+	0.00477712i	$0.00152061\pi$
$709$	31.3757	+	26.3273i	1.17834	+	0.988744i	0.178351	+	0.983967i	$0.442924\pi$
$710$		0			0
$711$	18.7569	−	18.8530i	0.703440	−	0.707044i
$712$		0			0
$713$	6.11164	−	34.6608i	0.228883	−	1.29806i
$714$		0			0
$715$	−6.24611	−	2.27340i	−0.233591	−	0.0850203i
$716$		0			0
$717$	−8.00227	−	6.12413i	−0.298850	−	0.228710i
$718$		0			0
$719$	−12.1060	−	20.9681i	−0.451476	−	0.781980i	0.547002	−	0.837132i	$-0.315769\pi$
$719$	−12.1060	−	20.9681i	−0.451476	−	0.781980i	−0.998478	+	0.0551516i	$0.982436\pi$
$720$		0			0
$721$	6.79848	−	11.7753i	0.253189	−	0.438536i
$722$		0			0
$723$	3.98398	+	6.23600i	0.148166	+	0.231919i
$724$		0			0
$725$	−17.3606	+	14.5672i	−0.644755	+	0.541014i
$726$		0			0
$727$	26.8145	−	9.75966i	0.994493	−	0.361966i	0.207035	−	0.978334i	$-0.433619\pi$
$727$	26.8145	−	9.75966i	0.994493	−	0.361966i	0.787458	+	0.616368i	$0.211396\pi$
$728$		0			0
$729$	−6.78801	+	26.1328i	−0.251408	+	0.967881i
$730$		0			0
$731$	41.9033	−	15.2515i	1.54985	−	0.564099i
$732$		0			0
$733$	21.1074	−	17.7112i	0.779621	−	0.654180i	−0.163532	−	0.986538i	$-0.552289\pi$
$733$	21.1074	−	17.7112i	0.779621	−	0.654180i	0.943153	+	0.332358i	$0.107844\pi$
$734$		0			0
$735$	2.64144	+	4.13456i	0.0974308	+	0.152505i
$736$		0			0
$737$	9.24412	−	16.0113i	0.340512	−	0.589784i
$738$		0			0
$739$	7.53163	+	13.0452i	0.277055	+	0.479874i	0.970652	−	0.240490i	$-0.0773081\pi$
$739$	7.53163	+	13.0452i	0.277055	+	0.479874i	−0.693596	+	0.720364i	$0.743975\pi$
$740$		0			0
$741$	1.06245	+	0.813094i	0.0390302	+	0.0298698i
$742$		0			0
$743$	3.17289	+	1.15484i	0.116402	+	0.0423669i	0.399564	−	0.916705i	$-0.369161\pi$
$743$	3.17289	+	1.15484i	0.116402	+	0.0423669i	−0.283163	+	0.959072i	$0.591384\pi$
$744$		0			0
$745$	−0.329142	+	1.86666i	−0.0120588	+	0.0683891i
$746$		0			0
$747$	15.9670	−	16.0488i	0.584201	−	0.587194i
$748$		0			0
$749$	−7.48649	−	6.28191i	−0.273550	−	0.229536i
$750$		0			0
$751$	5.38881	+	30.5615i	0.196641	+	1.11520i	0.910063	+	0.414470i	$0.136033\pi$
$751$	5.38881	+	30.5615i	0.196641	+	1.11520i	−0.713422	+	0.700734i	$0.752856\pi$
$752$		0			0
$753$	22.7066	+	7.12747i	0.827473	+	0.259740i
$754$		0			0
$755$	27.1073			0.986537
$756$		0			0
$757$	−40.3330			−1.46593			−0.732963	−	0.680268i	$-0.761863\pi$
$757$	−40.3330			−1.46593			−0.732963	+	0.680268i	$0.761863\pi$
$758$		0			0
$759$	−38.9760	+	35.8066i	−1.41474	+	1.29970i
$760$		0			0
$761$	−1.14299	−	6.48224i	−0.0414335	−	0.234981i	0.957057	−	0.289899i	$-0.0936216\pi$
$761$	−1.14299	−	6.48224i	−0.0414335	−	0.234981i	−0.998491	+	0.0549174i	$0.982510\pi$
$762$		0			0
$763$	−13.4012	−	11.2449i	−0.485154	−	0.407093i
$764$		0			0
$765$	−23.4624	+	50.6527i	−0.848284	+	1.83135i
$766$		0			0
$767$	−0.852303	+	4.83365i	−0.0307749	+	0.174533i
$768$		0			0
$769$	20.0707	+	7.30512i	0.723767	+	0.263430i	0.677524	−	0.735501i	$-0.263053\pi$
$769$	20.0707	+	7.30512i	0.723767	+	0.263430i	0.0462427	+	0.998930i	$0.485275\pi$
$770$		0			0
$771$	−3.20311	+	24.5726i	−0.115357	+	0.884960i
$772$		0			0
$773$	15.2608	+	26.4324i	0.548892	+	0.950708i	0.998351	+	0.0574074i	$0.0182834\pi$
$773$	15.2608	+	26.4324i	0.548892	+	0.950708i	−0.449459	+	0.893301i	$0.648383\pi$
$774$		0			0
$775$	−6.60236	+	11.4356i	−0.237164	+	0.410780i
$776$		0			0
$777$	17.6194	−	0.791834i	0.632094	−	0.0284069i
$778$		0			0
$779$	3.30998	−	2.77741i	0.118592	−	0.0995109i
$780$		0			0
$781$	−41.9590	+	15.2718i	−1.50141	+	0.546469i
$782$		0			0
$783$	32.9236	+	20.7977i	1.17659	+	0.743249i
$784$		0			0
$785$	29.9538	−	10.9023i	1.06910	−	0.389120i
$786$		0			0
$787$	−3.73528	+	3.13427i	−0.133148	+	0.111725i	−0.706930	−	0.707284i	$-0.749920\pi$
$787$	−3.73528	+	3.13427i	−0.133148	+	0.111725i	0.573781	+	0.819008i	$0.305476\pi$
$788$		0			0
$789$	−11.8241	+	22.7850i	−0.420951	+	0.811167i
$790$		0			0
$791$	3.59861	−	6.23298i	0.127952	−	0.221619i
$792$		0			0
$793$	−2.26472	−	3.92261i	−0.0804226	−	0.139296i
$794$		0			0
$795$	−54.7479	+	22.7593i	−1.94171	+	0.807190i
$796$		0			0
$797$	−32.6052	−	11.8673i	−1.15494	−	0.420363i	−0.307651	−	0.951499i	$-0.599543\pi$
$797$	−32.6052	−	11.8673i	−1.15494	−	0.420363i	−0.847286	+	0.531137i	$0.821765\pi$
$798$		0			0
$799$	−3.12050	+	17.6972i	−0.110395	+	0.626084i
$800$		0			0
$801$	−0.218662	+	2.57508i	−0.00772605	+	0.0909859i
$802$		0			0
$803$	36.9621	+	31.0149i	1.30437	+	1.09449i
$804$		0			0
$805$	−3.96453	−	22.4840i	−0.139731	−	0.792456i
$806$		0			0
$807$	−9.91473	−	44.4536i	−0.349015	−	1.56484i
$808$		0			0
$809$	26.9270			0.946704			0.473352	−	0.880873i	$-0.343044\pi$
$809$	26.9270			0.946704			0.473352	+	0.880873i	$0.343044\pi$
$810$		0			0
$811$	14.1589			0.497188			0.248594	−	0.968608i	$-0.420032\pi$
$811$	14.1589			0.497188			0.248594	+	0.968608i	$0.420032\pi$
$812$		0			0
$813$	0.104716	+	0.469505i	0.00367256	+	0.0164663i
$814$		0			0
$815$	8.99551	+	51.0161i	0.315099	+	1.78701i
$816$		0			0
$817$	6.48982	+	5.44560i	0.227050	+	0.190518i
$818$		0			0
$819$	−1.52372	−	1.06113i	−0.0532430	−	0.0370788i
$820$		0			0
$821$	4.24554	−	24.0777i	0.148170	−	0.840316i	−0.816596	−	0.577209i	$-0.804142\pi$
$821$	4.24554	−	24.0777i	0.148170	−	0.840316i	0.964767	−	0.263107i	$-0.0847472\pi$
$822$		0			0
$823$	−31.9212	−	11.6184i	−1.11270	−	0.404991i	−0.280720	−	0.959790i	$-0.590573\pi$
$823$	−31.9212	−	11.6184i	−1.11270	−	0.404991i	−0.831985	+	0.554798i	$0.812795\pi$
$824$		0			0
$825$	18.3359	−	7.62243i	0.638374	−	0.265379i
$826$		0			0
$827$	6.18618	+	10.7148i	0.215115	+	0.372590i	0.953308	−	0.302000i	$-0.0976541\pi$
$827$	6.18618	+	10.7148i	0.215115	+	0.372590i	−0.738193	+	0.674589i	$0.764321\pi$
$828$		0			0
$829$	−10.0487	+	17.4048i	−0.349004	+	0.604493i	−0.986073	−	0.166314i	$-0.946813\pi$
$829$	−10.0487	+	17.4048i	−0.349004	+	0.604493i	0.637069	+	0.770807i	$0.280147\pi$
$830$		0			0
$831$	−18.9101	+	36.4395i	−0.655984	+	1.26407i
$832$		0			0
$833$	5.03212	−	4.22245i	0.174352	−	0.146299i
$834$		0			0
$835$	7.46336	−	2.71644i	0.258280	−	0.0940063i
$836$		0			0
$837$	22.1712	+	4.82616i	0.766347	+	0.166816i
$838$		0			0
$839$	−37.7783	+	13.7502i	−1.30425	+	0.474709i	−0.898379	−	0.439221i	$-0.855255\pi$
$839$	−37.7783	+	13.7502i	−1.30425	+	0.474709i	−0.405873	+	0.913930i	$0.633032\pi$
$840$		0			0
$841$	20.8111	−	17.4625i	0.717622	−	0.602157i
$842$		0			0
$843$	8.23930	−	0.370282i	0.283776	−	0.0127532i
$844$		0			0
$845$	17.8697	−	30.9512i	0.614735	−	1.06475i
$846$		0			0
$847$	1.68692	+	2.92183i	0.0579632	+	0.100395i
$848$		0			0
$849$	3.35830	−	25.7631i	0.115256	−	0.884187i
$850$		0			0
$851$	−77.1230	−	28.0705i	−2.64374	−	0.962243i
$852$		0			0
$853$	−2.79903	+	15.8741i	−0.0958370	+	0.543518i	0.898651	+	0.438665i	$0.144548\pi$
$853$	−2.79903	+	15.8741i	−0.0958370	+	0.543518i	−0.994488	+	0.104854i	$0.966563\pi$
$854$		0			0
$855$	−10.5627	+	0.951312i	−0.361235	+	0.0325342i
$856$		0			0
$857$	25.7401	+	21.5985i	0.879264	+	0.737790i	0.966028	−	0.258439i	$-0.0832081\pi$
$857$	25.7401	+	21.5985i	0.879264	+	0.737790i	−0.0867638	+	0.996229i	$0.527653\pi$
$858$		0			0
$859$	5.15581	+	29.2400i	0.175914	+	0.997657i	0.937084	+	0.349105i	$0.113514\pi$
$859$	5.15581	+	29.2400i	0.175914	+	0.997657i	−0.761170	+	0.648553i	$0.775375\pi$
$860$		0			0
$861$	−4.41613	+	4.05702i	−0.150501	+	0.138263i
$862$		0			0
$863$	24.2627			0.825913			0.412956	−	0.910751i	$-0.364496\pi$
$863$	24.2627			0.825913			0.412956	+	0.910751i	$0.364496\pi$
$864$		0			0
$865$	−52.2900			−1.77791
$866$		0			0
$867$	43.2162	+	13.5654i	1.46770	+	0.460704i
$868$		0			0
$869$	5.83612	+	33.0983i	0.197977	+	1.12278i
$870$		0			0
$871$	−2.31211	−	1.94009i	−0.0783427	−	0.0657373i
$872$		0			0
$873$	−2.93546	−	10.8444i	−0.0993502	−	0.367026i
$874$		0			0
$875$	0.972005	−	5.51252i	0.0328598	−	0.186357i
$876$		0			0
$877$	27.6659	+	10.0696i	0.934212	+	0.340025i	0.763878	−	0.645361i	$-0.223293\pi$
$877$	27.6659	+	10.0696i	0.934212	+	0.340025i	0.170334	+	0.985386i	$0.445515\pi$
$878$		0			0
$879$	−18.1476	−	13.8884i	−0.612105	−	0.468443i
$880$		0			0
$881$	−9.77794	−	16.9359i	−0.329427	−	0.570584i	0.652971	−	0.757383i	$-0.273522\pi$
$881$	−9.77794	−	16.9359i	−0.329427	−	0.570584i	−0.982398	+	0.186798i	$0.940189\pi$
$882$		0			0
$883$	8.47934	−	14.6866i	0.285353	−	0.494245i	−0.687342	−	0.726334i	$-0.741223\pi$
$883$	8.47934	−	14.6866i	0.285353	−	0.494245i	0.972695	+	0.232089i	$0.0745560\pi$
$884$		0			0
$885$	−20.9469	−	32.7875i	−0.704122	−	1.10214i
$886$		0			0
$887$	14.4502	−	12.1251i	0.485189	−	0.407122i	−0.367109	−	0.930178i	$-0.619652\pi$
$887$	14.4502	−	12.1251i	0.485189	−	0.407122i	0.852299	+	0.523056i	$0.175208\pi$
$888$		0			0
$889$	−9.69389	+	3.52829i	−0.325122	+	0.118335i
$890$		0			0
$891$	−22.0662	−	26.0262i	−0.739245	−	0.871911i
$892$		0			0
$893$	−3.20816	+	1.16768i	−0.107357	+	0.0390748i
$894$		0			0
$895$	9.73220	−	8.16629i	0.325312	−	0.272969i
$896$		0			0
$897$	4.65178	+	7.28129i	0.155319	+	0.243115i
$898$		0			0
$899$	16.3632	−	28.3420i	0.545745	−	0.945258i
$900$		0			0
$901$	39.6913	+	68.7474i	1.32231	+	2.29031i
$902$		0			0
$903$	−9.33723	−	7.14577i	−0.310723	−	0.237796i
$904$		0			0
$905$	−39.9113	−	14.5265i	−1.32670	−	0.482879i
$906$		0			0
$907$	8.75875	−	49.6733i	0.290829	−	1.64938i	−0.392857	−	0.919600i	$-0.628513\pi$
$907$	8.75875	−	49.6733i	0.290829	−	1.64938i	0.683686	−	0.729776i	$-0.260376\pi$
$908$		0			0
$909$	8.00353	+	2.12264i	0.265460	+	0.0704035i
$910$		0			0
$911$	−7.27530	−	6.10470i	−0.241041	−	0.202258i	0.514262	−	0.857633i	$-0.328066\pi$
$911$	−7.27530	−	6.10470i	−0.241041	−	0.202258i	−0.755303	+	0.655375i	$0.772510\pi$
$912$		0			0
$913$	4.96805	+	28.1752i	0.164418	+	0.932463i
$914$		0			0
$915$	34.2569	+	10.7531i	1.13250	+	0.355486i
$916$		0			0
$917$	−13.7652			−0.454568
$918$		0			0
$919$	−35.2549			−1.16295			−0.581476	−	0.813564i	$-0.697525\pi$
$919$	−35.2549			−1.16295			−0.581476	+	0.813564i	$0.697525\pi$
$920$		0			0
$921$	5.62278	−	5.16556i	0.185277	−	0.170211i
$922$		0			0
$923$	1.26581	+	7.17875i	0.0416645	+	0.236291i
$924$		0			0
$925$	23.5881	+	19.7928i	0.775573	+	0.650783i
$926$		0			0
$927$	−23.4820	−	33.3540i	−0.771250	−	1.09549i
$928$		0			0
$929$	−5.93945	+	33.6843i	−0.194867	+	1.10515i	0.717741	+	0.696310i	$0.245176\pi$
$929$	−5.93945	+	33.6843i	−0.194867	+	1.10515i	−0.912608	+	0.408836i	$0.865935\pi$
$930$		0			0
$931$	1.17273	+	0.426840i	0.0384347	+	0.0139891i
$932$		0			0
$933$	2.90165	−	22.2600i	0.0949959	−	0.728758i
$934$		0			0
$935$	−35.2733	−	61.0952i	−1.15356	−	1.99803i
$936$		0			0
$937$	21.6372	−	37.4768i	0.706858	−	1.22431i	−0.259159	−	0.965835i	$-0.583446\pi$
$937$	21.6372	−	37.4768i	0.706858	−	1.22431i	0.966017	−	0.258479i	$-0.0832212\pi$
$938$		0			0
$939$	16.4956	−	0.741328i	0.538314	−	0.0241923i
$940$		0			0
$941$	36.8639	−	30.9325i	1.20173	−	1.00837i	0.202150	−	0.979355i	$-0.435207\pi$
$941$	36.8639	−	30.9325i	1.20173	−	1.00837i	0.999579	−	0.0290153i	$-0.00923716\pi$
$942$		0			0
$943$	26.2224	−	9.54419i	0.853920	−	0.310802i
$944$		0			0
$945$	14.5855	−	1.97711i	0.474466	−	0.0643155i
$946$		0			0
$947$	7.44280	−	2.70896i	0.241859	−	0.0880294i	−0.218247	−	0.975894i	$-0.570034\pi$
$947$	7.44280	−	2.70896i	0.241859	−	0.0880294i	0.460106	+	0.887864i	$0.347812\pi$
$948$		0			0
$949$	6.03413	−	5.06324i	0.195876	−	0.164360i
$950$		0			0
$951$	18.3875	−	35.4326i	0.596257	−	1.14898i
$952$		0			0
$953$	−14.3666	+	24.8838i	−0.465381	+	0.806064i	−0.999219	−	0.0395232i	$-0.987416\pi$
$953$	−14.3666	+	24.8838i	−0.465381	+	0.806064i	0.533837	+	0.845587i	$0.320749\pi$
$954$		0			0
$955$	2.95199	+	5.11299i	0.0955240	+	0.165453i
$956$		0			0
$957$	−45.4436	+	18.8914i	−1.46898	+	0.610672i
$958$		0			0
$959$	−0.457675	−	0.166580i	−0.0147791	−	0.00537915i
$960$		0			0
$961$	−2.07187	+	11.7501i	−0.0668344	+	0.379037i
$962$		0			0
$963$	−26.5401	+	12.4585i	−0.855242	+	0.401469i
$964$		0			0
$965$	−38.4320	−	32.2483i	−1.23717	−	1.03811i
$966$		0			0
$967$	−2.15761	−	12.2364i	−0.0693840	−	0.393496i	−0.999646	−	0.0266008i	$-0.991532\pi$
$967$	−2.15761	−	12.2364i	−0.0693840	−	0.393496i	0.930262	−	0.366896i	$-0.119579\pi$
$968$		0			0
$969$	3.09102	+	13.8589i	0.0992979	+	0.445212i
$970$		0			0
$971$	−13.0379			−0.418408			−0.209204	−	0.977872i	$-0.567087\pi$
$971$	−13.0379			−0.418408			−0.209204	+	0.977872i	$0.567087\pi$
$972$		0			0
$973$	11.7176			0.375650
$974$		0			0
$975$	−0.705678	−	3.16397i	−0.0225998	−	0.101328i
$976$		0			0
$977$	3.34500	+	18.9704i	0.107016	+	0.606918i	0.990396	+	0.138260i	$0.0441511\pi$
$977$	3.34500	+	18.9704i	0.107016	+	0.606918i	−0.883380	+	0.468658i	$0.844738\pi$
$978$		0			0
$979$	−2.50190	−	2.09934i	−0.0799610	−	0.0670953i
$980$		0			0
$981$	−47.5079	+	22.3013i	−1.51681	+	0.712024i
$982$		0			0
$983$	4.80176	−	27.2321i	0.153152	−	0.868569i	−0.807303	−	0.590136i	$-0.799074\pi$
$983$	4.80176	−	27.2321i	0.153152	−	0.868569i	0.960456	−	0.278433i	$-0.0898150\pi$
$984$		0			0
$985$	65.6213	+	23.8842i	2.09087	+	0.761014i
$986$		0			0
$987$	4.37526	−	1.81884i	0.139266	−	0.0578944i
$988$		0			0
$989$	27.3567	+	47.3832i	0.869893	+	1.50670i
$990$		0			0
$991$	−6.34138	+	10.9836i	−0.201441	+	0.348905i	−0.948993	−	0.315298i	$-0.897896\pi$
$991$	−6.34138	+	10.9836i	−0.201441	+	0.348905i	0.747552	+	0.664203i	$0.231229\pi$
$992$		0			0
$993$	25.4819	−	49.1033i	0.808643	−	1.55825i
$994$		0			0
$995$	−53.2758	+	44.7037i	−1.68896	+	1.41720i
$996$		0			0
$997$	56.2768	−	20.4831i	1.78231	−	0.648706i	0.782650	−	0.622462i	$-0.213867\pi$
$997$	56.2768	−	20.4831i	1.78231	−	0.648706i	0.999656	−	0.0262442i	$-0.00835473\pi$
$998$		0			0
$999$	20.0609	−	48.9612i	0.634700	−	1.54907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.169.4	yes	54
27.4	even	9	inner	756.2.bo.b.85.4	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.85.4	✓	54	27.4	even	9	inner
756.2.bo.b.169.4	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)

\(f(q)\)	\(=\)	\(q+(-0.377044 - 1.69051i) q^{3} +(0.491885 + 2.78962i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.71568 + 1.27480i) q^{9} +O(q^{10})\)	\(q+(-0.377044 - 1.69051i) q^{3} +(0.491885 + 2.78962i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-2.71568 + 1.27480i) q^{9} +(0.658350 - 3.73369i) q^{11} +(-0.581608 - 0.211688i) q^{13} +(4.53043 - 1.88335i) q^{15} +(-3.28448 - 5.68889i) q^{17} +(0.623998 - 1.08080i) q^{19} +(-0.797809 + 1.53737i) q^{21} +(6.17422 - 5.18079i) q^{23} +(-2.84155 + 1.03424i) q^{25} +(3.17899 + 4.11023i) q^{27} +(7.04249 - 2.56326i) q^{29} +(3.34513 - 2.80690i) q^{31} +(-6.56008 + 0.294816i) q^{33} +(1.41633 - 2.45315i) q^{35} +(-5.09143 - 8.81861i) q^{37} +(-0.138569 + 1.06303i) q^{39} +(3.25345 + 1.18416i) q^{41} +(-1.17879 + 6.68524i) q^{43} +(-4.89200 - 6.94864i) q^{45} +(-2.09562 - 1.75843i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-8.37875 + 7.69742i) q^{51} -12.0845 q^{53} +10.7394 q^{55} +(-2.06237 - 0.647369i) q^{57} +(-1.37705 - 7.80964i) q^{59} +(5.60602 + 4.70401i) q^{61} +(2.89975 + 0.769051i) q^{63} +(0.304444 - 1.72659i) q^{65} +(4.58242 + 1.66787i) q^{67} +(-11.0862 - 8.48423i) q^{69} +(-5.88875 - 10.1996i) q^{71} +(-6.36336 + 11.0217i) q^{73} +(2.81979 + 4.41373i) q^{75} +(-2.90429 + 2.43699i) q^{77} +(-8.33017 + 3.03193i) q^{79} +(5.74978 - 6.92387i) q^{81} +(-7.09112 + 2.58096i) q^{83} +(14.2542 - 11.9607i) q^{85} +(-6.98855 - 10.9390i) q^{87} +(0.430724 - 0.746036i) q^{89} +(0.309467 + 0.536012i) q^{91} +(-6.00637 - 4.59667i) q^{93} +(3.32194 + 1.20909i) q^{95} +(-0.650292 + 3.68799i) q^{97} +(2.97183 + 10.9787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more