LMFDB - Embedded newform 756.2.bp.a.193.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.18
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12192 - 1.31958i) q^{3} +(-3.46735 + 1.26201i) q^{5} +(2.63004 - 0.287949i) q^{7} +(-0.482607 - 2.96093i) q^{9} +O(q^{10})$	\(q+(1.12192 - 1.31958i) q^{3} +(-3.46735 + 1.26201i) q^{5} +(2.63004 - 0.287949i) q^{7} +(-0.482607 - 2.96093i) q^{9} +(3.20611 + 1.16693i) q^{11} +(4.78306 - 1.74089i) q^{13} +(-2.22474 + 5.99133i) q^{15} +(-1.70869 - 2.95953i) q^{17} +(-3.04435 + 5.27296i) q^{19} +(2.57071 - 3.79361i) q^{21} +(1.20960 - 6.86000i) q^{23} +(6.59961 - 5.53773i) q^{25} +(-4.44864 - 2.68507i) q^{27} +(-3.91654 - 1.42550i) q^{29} +(5.38357 - 1.95946i) q^{31} +(5.13685 - 2.92154i) q^{33} +(-8.75585 + 4.31755i) q^{35} +10.4524 q^{37} +(3.06894 - 8.26479i) q^{39} +(2.06082 - 0.750076i) q^{41} +(-1.17583 - 6.66848i) q^{43} +(5.41009 + 9.65751i) q^{45} +(3.98002 + 1.44861i) q^{47} +(6.83417 - 1.51463i) q^{49} +(-5.82235 - 1.06559i) q^{51} +(3.81085 - 6.60059i) q^{53} -12.5894 q^{55} +(3.54262 + 9.93309i) q^{57} +(5.75369 + 4.82792i) q^{59} +(-13.5080 - 4.91652i) q^{61} +(-2.12187 - 7.64838i) q^{63} +(-14.3875 + 12.0726i) q^{65} +(-1.01486 + 5.75556i) q^{67} +(-7.69528 - 9.29252i) q^{69} +(-2.57834 + 4.46582i) q^{71} -11.0808 q^{73} +(0.0967071 - 14.9216i) q^{75} +(8.76820 + 2.14587i) q^{77} +(1.26225 + 7.15856i) q^{79} +(-8.53418 + 2.85793i) q^{81} +(-2.56076 - 0.932040i) q^{83} +(9.65957 + 8.10534i) q^{85} +(-6.27510 + 3.56891i) q^{87} +(-7.82880 + 13.5599i) q^{89} +(12.0783 - 5.95588i) q^{91} +(3.45424 - 9.30242i) q^{93} +(3.90127 - 22.1252i) q^{95} +(1.49652 + 8.48716i) q^{97} +(1.90790 - 10.0562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.12192	−	1.31958i	0.647739	−	0.761863i
$3$	1.12192	−	1.31958i	0.647739	−	0.761863i
$4$		0			0
$5$	−3.46735	+	1.26201i	−1.55065	+	0.564389i	−0.968569	−	0.248745i	$-0.919982\pi$
$5$	−3.46735	+	1.26201i	−1.55065	+	0.564389i	−0.582076	+	0.813134i	$0.697760\pi$
$6$		0			0
$7$	2.63004	−	0.287949i	0.994060	−	0.108834i
$7$	2.63004	−	0.287949i	0.994060	−	0.108834i
$8$		0			0
$9$	−0.482607	−	2.96093i	−0.160869	−	0.986976i
$10$		0			0
$11$	3.20611	+	1.16693i	0.966679	+	0.351842i	0.776647	−	0.629936i	$-0.216919\pi$
$11$	3.20611	+	1.16693i	0.966679	+	0.351842i	0.190032	+	0.981778i	$0.439141\pi$
$12$		0			0
$13$	4.78306	−	1.74089i	1.32658	−	0.482836i	0.421020	−	0.907051i	$-0.361672\pi$
$13$	4.78306	−	1.74089i	1.32658	−	0.482836i	0.905562	+	0.424215i	$0.139450\pi$
$14$		0			0
$15$	−2.22474	+	5.99133i	−0.574426	+	1.54696i
$16$		0			0
$17$	−1.70869	−	2.95953i	−0.414417	−	0.717791i	0.580950	−	0.813939i	$-0.302681\pi$
$17$	−1.70869	−	2.95953i	−0.414417	−	0.717791i	−0.995367	+	0.0961479i	$0.969348\pi$
$18$		0			0
$19$	−3.04435	+	5.27296i	−0.698421	+	1.20970i	0.270593	+	0.962694i	$0.412780\pi$
$19$	−3.04435	+	5.27296i	−0.698421	+	1.20970i	−0.969014	+	0.247006i	$0.920553\pi$
$20$		0			0
$21$	2.57071	−	3.79361i	0.560974	−	0.827833i
$22$		0			0
$23$	1.20960	−	6.86000i	0.252220	−	1.43041i	−0.550890	−	0.834578i	$-0.685712\pi$
$23$	1.20960	−	6.86000i	0.252220	−	1.43041i	0.803110	−	0.595831i	$-0.203177\pi$
$24$		0			0
$25$	6.59961	−	5.53773i	1.31992	−	1.10755i
$26$		0			0
$27$	−4.44864	−	2.68507i	−0.856141	−	0.516742i
$28$		0			0
$29$	−3.91654	−	1.42550i	−0.727282	−	0.264709i	−0.0482683	−	0.998834i	$-0.515370\pi$
$29$	−3.91654	−	1.42550i	−0.727282	−	0.264709i	−0.679014	+	0.734125i	$0.737592\pi$
$30$		0			0
$31$	5.38357	−	1.95946i	0.966917	−	0.351929i	0.190177	−	0.981750i	$-0.439094\pi$
$31$	5.38357	−	1.95946i	0.966917	−	0.351929i	0.776741	+	0.629821i	$0.216872\pi$
$32$		0			0
$33$	5.13685	−	2.92154i	0.894211	−	0.508575i
$34$		0			0
$35$	−8.75585	+	4.31755i	−1.48001	+	0.729800i
$36$		0			0
$37$	10.4524			1.71837			0.859185	−	0.511665i	$-0.170971\pi$
$37$	10.4524			1.71837			0.859185	+	0.511665i	$0.170971\pi$
$38$		0			0
$39$	3.06894	−	8.26479i	0.491424	−	1.32342i
$40$		0			0
$41$	2.06082	−	0.750076i	0.321846	−	0.117142i	−0.176045	−	0.984382i	$-0.556330\pi$
$41$	2.06082	−	0.750076i	0.321846	−	0.117142i	0.497890	+	0.867240i	$0.334108\pi$
$42$		0			0
$43$	−1.17583	−	6.66848i	−0.179313	−	1.01693i	−0.933047	−	0.359755i	$-0.882860\pi$
$43$	−1.17583	−	6.66848i	−0.179313	−	1.01693i	0.753734	−	0.657180i	$-0.228251\pi$
$44$		0			0
$45$	5.41009	+	9.65751i	0.806489	+	1.43966i
$46$		0			0
$47$	3.98002	+	1.44861i	0.580545	+	0.211301i	0.615566	−	0.788085i	$-0.288928\pi$
$47$	3.98002	+	1.44861i	0.580545	+	0.211301i	−0.0350208	+	0.999387i	$0.511150\pi$
$48$		0			0
$49$	6.83417	−	1.51463i	0.976310	−	0.216376i
$50$		0			0
$51$	−5.82235	−	1.06559i	−0.815292	−	0.149212i
$52$		0			0
$53$	3.81085	−	6.60059i	0.523461	−	0.906661i	−0.476166	−	0.879355i	$-0.657974\pi$
$53$	3.81085	−	6.60059i	0.523461	−	0.906661i	0.999627	−	0.0273056i	$-0.00869271\pi$
$54$		0			0
$55$	−12.5894			−1.69755
$56$		0			0
$57$	3.54262	+	9.93309i	0.469231	+	1.31567i
$58$		0			0
$59$	5.75369	+	4.82792i	0.749067	+	0.628542i	0.935256	−	0.353972i	$-0.115169\pi$
$59$	5.75369	+	4.82792i	0.749067	+	0.628542i	−0.186189	+	0.982514i	$0.559614\pi$
$60$		0			0
$61$	−13.5080	−	4.91652i	−1.72953	−	0.629496i	−0.730929	−	0.682454i	$-0.760913\pi$
$61$	−13.5080	−	4.91652i	−1.72953	−	0.629496i	−0.998597	+	0.0529578i	$0.983135\pi$
$62$		0			0
$63$	−2.12187	−	7.64838i	−0.267330	−	0.963605i
$64$		0			0
$65$	−14.3875	+	12.0726i	−1.78455	+	1.49742i
$66$		0			0
$67$	−1.01486	+	5.75556i	−0.123985	+	0.703154i	0.857920	+	0.513782i	$0.171756\pi$
$67$	−1.01486	+	5.75556i	−0.123985	+	0.703154i	−0.981906	+	0.189372i	$0.939355\pi$
$68$		0			0
$69$	−7.69528	−	9.29252i	−0.926403	−	1.11869i
$70$		0			0
$71$	−2.57834	+	4.46582i	−0.305993	+	0.529996i	−0.977482	−	0.211019i	$-0.932322\pi$
$71$	−2.57834	+	4.46582i	−0.305993	+	0.529996i	0.671489	+	0.741015i	$0.265655\pi$
$72$		0			0
$73$	−11.0808			−1.29691			−0.648455	−	0.761253i	$-0.724585\pi$
$73$	−11.0808			−1.29691			−0.648455	+	0.761253i	$0.724585\pi$
$74$		0			0
$75$	0.0967071	−	14.9216i	0.0111668	−	1.72300i
$76$		0			0
$77$	8.76820	+	2.14587i	0.999229	+	0.244545i
$78$		0			0
$79$	1.26225	+	7.15856i	0.142014	+	0.805401i	0.969716	+	0.244234i	$0.0785363\pi$
$79$	1.26225	+	7.15856i	0.142014	+	0.805401i	−0.827703	+	0.561167i	$0.810353\pi$
$80$		0			0
$81$	−8.53418	+	2.85793i	−0.948242	+	0.317548i
$82$		0			0
$83$	−2.56076	−	0.932040i	−0.281080	−	0.102305i	0.197633	−	0.980276i	$-0.436674\pi$
$83$	−2.56076	−	0.932040i	−0.281080	−	0.102305i	−0.478713	+	0.877971i	$0.658897\pi$
$84$		0			0
$85$	9.65957	+	8.10534i	1.04773	+	0.879148i
$86$		0			0
$87$	−6.27510	+	3.56891i	−0.672761	+	0.382627i
$88$		0			0
$89$	−7.82880	+	13.5599i	−0.829851	+	1.43734i	0.0683041	+	0.997665i	$0.478241\pi$
$89$	−7.82880	+	13.5599i	−0.829851	+	1.43734i	−0.898155	+	0.439679i	$0.855092\pi$
$90$		0			0
$91$	12.0783	−	5.95588i	1.26615	−	0.624346i
$92$		0			0
$93$	3.45424	−	9.30242i	0.358188	−	0.964616i
$94$		0			0
$95$	3.90127	−	22.1252i	0.400262	−	2.27000i
$96$		0			0
$97$	1.49652	+	8.48716i	0.151948	+	0.861741i	0.961523	+	0.274724i	$0.0885865\pi$
$97$	1.49652	+	8.48716i	0.151948	+	0.861741i	−0.809575	+	0.587017i	$0.800302\pi$
$98$		0			0
$99$	1.90790	−	10.0562i	0.191751	−	1.01069i
$100$		0			0
$101$	2.10979	+	11.9652i	0.209932	+	1.19058i	0.889488	+	0.456959i	$0.151061\pi$
$101$	2.10979	+	11.9652i	0.209932	+	1.19058i	−0.679556	+	0.733624i	$0.737828\pi$
$102$		0			0
$103$	5.74846	−	2.09227i	0.566412	−	0.206157i	−0.0429112	−	0.999079i	$-0.513663\pi$
$103$	5.74846	−	2.09227i	0.566412	−	0.206157i	0.609324	+	0.792922i	$0.291441\pi$
$104$		0			0
$105$	−4.12596	+	16.3980i	−0.402653	+	1.60028i
$106$		0			0
$107$	3.78482	+	6.55549i	0.365892	+	0.633744i	0.988919	−	0.148457i	$-0.0474306\pi$
$107$	3.78482	+	6.55549i	0.365892	+	0.633744i	−0.623027	+	0.782200i	$0.714097\pi$
$108$		0			0
$109$	−3.12912	+	5.41980i	−0.299716	+	0.519122i	−0.976071	−	0.217453i	$-0.930225\pi$
$109$	−3.12912	+	5.41980i	−0.299716	+	0.519122i	0.676355	+	0.736576i	$0.263558\pi$
$110$		0			0
$111$	11.7268	−	13.7929i	1.11305	−	1.30916i
$112$		0			0
$113$	0.0140405	−	0.0796277i	0.00132082	−	0.00749074i	−0.984140	−	0.177392i	$-0.943234\pi$
$113$	0.0140405	−	0.0796277i	0.00132082	−	0.00749074i	0.985461	+	0.169902i	$0.0543450\pi$
$114$		0			0
$115$	4.46328	+	25.3125i	0.416203	+	2.36041i
$116$		0			0
$117$	−7.46299	−	13.3221i	−0.689954	−	1.23163i
$118$		0			0
$119$	−5.34609	−	7.29165i	−0.490076	−	0.668425i
$120$		0			0
$121$	0.490937	+	0.411945i	0.0446307	+	0.0374496i
$122$		0			0
$123$	1.32228	−	3.56094i	0.119226	−	0.321080i
$124$		0			0
$125$	−6.66978	+	11.5524i	−0.596563	+	1.03328i
$126$		0			0
$127$	−5.35654	−	9.27780i	−0.475316	−	0.823272i	0.524284	−	0.851543i	$-0.324333\pi$
$127$	−5.35654	−	9.27780i	−0.475316	−	0.823272i	−0.999600	+	0.0282717i	$0.991000\pi$
$128$		0			0
$129$	−10.1188	−	5.92987i	−0.890912	−	0.522096i
$130$		0			0
$131$	−3.71021	+	21.0416i	−0.324162	+	1.83842i	0.191336	+	0.981525i	$0.438718\pi$
$131$	−3.71021	+	21.0416i	−0.324162	+	1.83842i	−0.515498	+	0.856891i	$0.672393\pi$
$132$		0			0
$133$	−6.48839	+	14.7447i	−0.562615	+	1.27853i
$134$		0			0
$135$	18.8136	+	3.69585i	1.61921	+	0.318088i
$136$		0			0
$137$	0.238472	−	0.200102i	0.0203740	−	0.0170958i	−0.632544	−	0.774525i	$-0.717989\pi$
$137$	0.238472	−	0.200102i	0.0203740	−	0.0170958i	0.652918	+	0.757429i	$0.273545\pi$
$138$		0			0
$139$	0.556460	+	0.466925i	0.0471983	+	0.0396041i	0.666082	−	0.745879i	$-0.267970\pi$
$139$	0.556460	+	0.466925i	0.0471983	+	0.0396041i	−0.618883	+	0.785483i	$0.712415\pi$
$140$		0			0
$141$	6.37680	−	3.62675i	0.537024	−	0.305428i
$142$		0			0
$143$	17.3665			1.45226
$144$		0			0
$145$	15.3790			1.27716
$146$		0			0
$147$	5.66869	−	10.7176i	0.467545	−	0.883969i
$148$		0			0
$149$	13.3383	+	11.1922i	1.09272	+	0.916899i	0.996914	−	0.0785018i	$-0.0250136\pi$
$149$	13.3383	+	11.1922i	1.09272	+	0.916899i	0.0958031	+	0.995400i	$0.469458\pi$
$150$		0			0
$151$	−0.913446	−	0.332467i	−0.0743352	−	0.0270558i	0.304585	−	0.952485i	$-0.401482\pi$
$151$	−0.913446	−	0.332467i	−0.0743352	−	0.0270558i	−0.378920	+	0.925429i	$0.623704\pi$
$152$		0			0
$153$	−7.93833	+	6.48758i	−0.641776	+	0.524490i
$154$		0			0
$155$	−16.1938	+	13.5883i	−1.30072	+	1.09143i
$156$		0			0
$157$	−4.30987	−	3.61641i	−0.343965	−	0.288621i	0.454396	−	0.890800i	$-0.349855\pi$
$157$	−4.30987	−	3.61641i	−0.343965	−	0.288621i	−0.798361	+	0.602179i	$0.794299\pi$
$158$		0			0
$159$	−4.43458	−	12.4341i	−0.351685	−	0.986085i
$160$		0			0
$161$	1.20597	−	18.3903i	0.0950439	−	1.44936i
$162$		0			0
$163$	−3.36959	−	5.83631i	−0.263927	−	0.457135i	0.703355	−	0.710839i	$-0.251684\pi$
$163$	−3.36959	−	5.83631i	−0.263927	−	0.457135i	−0.967282	+	0.253704i	$0.918351\pi$
$164$		0			0
$165$	−14.1242	+	16.6128i	−1.09957	+	1.29330i
$166$		0			0
$167$	3.05052	−	17.3004i	0.236057	−	1.33874i	−0.604321	−	0.796741i	$-0.706555\pi$
$167$	3.05052	−	17.3004i	0.236057	−	1.33874i	0.840377	−	0.542002i	$-0.182333\pi$
$168$		0			0
$169$	9.88838	−	8.29733i	0.760644	−	0.638256i
$170$		0			0
$171$	17.0821	+	6.46932i	1.30630	+	0.494721i
$172$		0			0
$173$	3.34058	−	2.80308i	0.253980	−	0.213114i	−0.506904	−	0.862002i	$-0.669210\pi$
$173$	3.34058	−	2.80308i	0.253980	−	0.213114i	0.760884	+	0.648888i	$0.224766\pi$
$174$		0			0
$175$	15.7626	−	16.4648i	1.19154	−	1.24462i
$176$		0			0
$177$	12.8260	−	2.17596i	0.964062	−	0.163555i
$178$		0			0
$179$	1.10815	+	1.91937i	0.0828269	+	0.143460i	0.904463	−	0.426552i	$-0.140272\pi$
$179$	1.10815	+	1.91937i	0.0828269	+	0.143460i	−0.821636	+	0.570012i	$0.806938\pi$
$180$		0			0
$181$	5.60822	+	9.71372i	0.416856	+	0.722015i	0.995621	−	0.0934788i	$-0.0297987\pi$
$181$	5.60822	+	9.71372i	0.416856	+	0.722015i	−0.578766	+	0.815494i	$0.696465\pi$
$182$		0			0
$183$	−21.6426	+	12.3091i	−1.59987	+	0.909912i
$184$		0			0
$185$	−36.2422	+	13.1911i	−2.66458	+	0.969829i
$186$		0			0
$187$	−2.02467	−	11.4825i	−0.148059	−	0.839683i
$188$		0			0
$189$	−12.4732	−	5.78086i	−0.907295	−	0.420495i
$190$		0			0
$191$	−1.33359	−	7.56314i	−0.0964948	−	0.547249i	−0.994279	−	0.106814i	$-0.965935\pi$
$191$	−1.33359	−	7.56314i	−0.0964948	−	0.547249i	0.897784	−	0.440436i	$-0.145176\pi$
$192$		0			0
$193$	0.0662158	−	0.0241006i	0.00476632	−	0.00173480i	−0.339636	−	0.940557i	$-0.610304\pi$
$193$	0.0662158	−	0.0241006i	0.00476632	−	0.00173480i	0.344402	+	0.938822i	$0.388082\pi$
$194$		0			0
$195$	−0.210827	+	32.5299i	−0.0150976	+	2.32952i
$196$		0			0
$197$	0.522192	+	0.904463i	0.0372046	+	0.0644403i	0.884028	−	0.467434i	$-0.154821\pi$
$197$	0.522192	+	0.904463i	0.0372046	+	0.0644403i	−0.846824	+	0.531874i	$0.821488\pi$
$198$		0			0
$199$	−5.84389	−	10.1219i	−0.414263	−	0.717524i	0.581088	−	0.813841i	$-0.302627\pi$
$199$	−5.84389	−	10.1219i	−0.414263	−	0.717524i	−0.995351	+	0.0963168i	$0.969294\pi$
$200$		0			0
$201$	6.45636	+	7.79646i	0.455397	+	0.549920i
$202$		0			0
$203$	−10.7111	−	2.62136i	−0.751772	−	0.183983i
$204$		0			0
$205$	−6.19897	+	5.20155i	−0.432955	+	0.363292i
$206$		0			0
$207$	−20.8957	−	0.270862i	−1.45235	−	0.0188262i
$208$		0			0
$209$	−15.9137	+	13.3532i	−1.10077	+	0.923658i
$210$		0			0
$211$	−0.211994	+	1.20228i	−0.0145943	+	0.0827684i	−0.991235	−	0.132111i	$-0.957825\pi$
$211$	−0.211994	+	1.20228i	−0.0145943	+	0.0827684i	0.976641	+	0.214879i	$0.0689357\pi$
$212$		0			0
$213$	3.00034	+	8.41262i	0.205580	+	0.576423i
$214$		0			0
$215$	12.4927	+	21.6380i	0.851997	+	1.47570i
$216$		0			0
$217$	13.5948	−	6.70364i	0.922872	−	0.455072i
$218$		0			0
$219$	−12.4317	+	14.6221i	−0.840059	+	0.988068i
$220$		0			0
$221$	−13.3250	−	11.1810i	−0.896334	−	0.752114i
$222$		0			0
$223$	−12.9792	+	10.8908i	−0.869151	+	0.729304i	−0.963919	−	0.266195i	$-0.914234\pi$
$223$	−12.9792	+	10.8908i	−0.869151	+	0.729304i	0.0947680	+	0.995499i	$0.469789\pi$
$224$		0			0
$225$	−19.5818	−	16.8684i	−1.30546	−	1.12456i
$226$		0			0
$227$	−10.7218	−	3.90243i	−0.711633	−	0.259013i	−0.0392636	−	0.999229i	$-0.512501\pi$
$227$	−10.7218	−	3.90243i	−0.711633	−	0.259013i	−0.672370	+	0.740216i	$0.734723\pi$
$228$		0			0
$229$	14.7080	+	12.3415i	0.971931	+	0.815547i	0.982852	−	0.184394i	$-0.0590321\pi$
$229$	14.7080	+	12.3415i	0.971931	+	0.815547i	−0.0109218	+	0.999940i	$0.503477\pi$
$230$		0			0
$231$	12.6688	−	9.16290i	0.833549	−	0.602874i
$232$		0			0
$233$	−1.62397			−0.106390			−0.0531948	−	0.998584i	$-0.516940\pi$
$233$	−1.62397			−0.106390			−0.0531948	+	0.998584i	$0.516940\pi$
$234$		0			0
$235$	−15.6283			−1.01948
$236$		0			0
$237$	10.8625	+	6.36566i	0.705592	+	0.413494i
$238$		0			0
$239$	−15.9586	−	13.3909i	−1.03228	−	0.866183i	−0.0411562	−	0.999153i	$-0.513104\pi$
$239$	−15.9586	−	13.3909i	−1.03228	−	0.866183i	−0.991120	+	0.132970i	$0.957549\pi$
$240$		0			0
$241$	−7.51887	+	6.30908i	−0.484333	+	0.406403i	−0.851990	−	0.523558i	$-0.824604\pi$
$241$	−7.51887	+	6.30908i	−0.484333	+	0.406403i	0.367657	+	0.929961i	$0.380160\pi$
$242$		0			0
$243$	−5.80336	+	14.4679i	−0.372286	+	0.928118i
$244$		0			0
$245$	−21.7850	+	13.8766i	−1.39179	+	0.886540i
$246$		0			0
$247$	−5.38163	+	30.5208i	−0.342425	+	1.94199i
$248$		0			0
$249$	−4.10286	+	2.33347i	−0.260008	+	0.147877i
$250$		0			0
$251$	4.66650	+	8.08262i	0.294547	+	0.510170i	0.974879	−	0.222733i	$-0.0714979\pi$
$251$	4.66650	+	8.08262i	0.294547	+	0.510170i	−0.680332	+	0.732904i	$0.738165\pi$
$252$		0			0
$253$	11.8833	−	20.5824i	0.747094	−	1.29400i
$254$		0			0
$255$	21.5329	−	3.65310i	1.34844	−	0.228766i
$256$		0			0
$257$	−13.8447	−	11.6171i	−0.863608	−	0.724653i	0.0991340	−	0.995074i	$-0.468393\pi$
$257$	−13.8447	−	11.6171i	−0.863608	−	0.724653i	−0.962742	+	0.270421i	$0.912837\pi$
$258$		0			0
$259$	27.4903	−	3.00976i	1.70816	−	0.187018i
$260$		0			0
$261$	−2.33066	+	12.2845i	−0.144264	+	0.760394i
$262$		0			0
$263$	−3.46943	−	19.6761i	−0.213935	−	1.21328i	−0.882746	−	0.469851i	$-0.844308\pi$
$263$	−3.46943	−	19.6761i	−0.213935	−	1.21328i	0.668811	−	0.743432i	$-0.266803\pi$
$264$		0			0
$265$	−4.88353	+	27.6959i	−0.299993	+	1.70134i
$266$		0			0
$267$	9.11014	+	25.5438i	0.557532	+	1.56326i
$268$		0			0
$269$	−2.10306	+	3.64261i	−0.128226	+	0.222094i	−0.922989	−	0.384826i	$-0.874262\pi$
$269$	−2.10306	+	3.64261i	−0.128226	+	0.222094i	0.794763	+	0.606919i	$0.207595\pi$
$270$		0			0
$271$	−9.01676	−	15.6175i	−0.547729	−	0.948695i	−0.998430	−	0.0560198i	$-0.982159\pi$
$271$	−9.01676	−	15.6175i	−0.547729	−	0.948695i	0.450700	−	0.892675i	$-0.351174\pi$
$272$		0			0
$273$	5.69159	−	22.6204i	0.344470	−	1.36905i
$274$		0			0
$275$	27.6212	−	10.0533i	1.66562	−	0.606237i
$276$		0			0
$277$	2.07288	+	11.7559i	0.124547	+	0.706343i	0.981576	+	0.191074i	$0.0611969\pi$
$277$	2.07288	+	11.7559i	0.124547	+	0.706343i	−0.857028	+	0.515269i	$0.827692\pi$
$278$		0			0
$279$	−8.39996	−	14.9947i	−0.502893	−	0.897710i
$280$		0			0
$281$	3.32461	+	18.8548i	0.198329	+	1.12478i	0.907597	+	0.419842i	$0.137915\pi$
$281$	3.32461	+	18.8548i	0.198329	+	1.12478i	−0.709268	+	0.704939i	$0.750974\pi$
$282$		0			0
$283$	−0.0447573	+	0.253831i	−0.00266054	+	0.0150887i	−0.986109	−	0.166099i	$-0.946883\pi$
$283$	−0.0447573	+	0.253831i	−0.00266054	+	0.0150887i	0.983449	+	0.181187i	$0.0579941\pi$
$284$		0			0
$285$	−24.8192	−	29.9707i	−1.47016	−	1.77531i
$286$		0			0
$287$	5.20404	−	2.56614i	0.307185	−	0.151474i
$288$		0			0
$289$	2.66079	−	4.60862i	0.156517	−	0.271095i
$290$		0			0
$291$	12.8785	+	7.54711i	0.754951	+	0.442419i
$292$		0			0
$293$	−9.50362	−	7.97448i	−0.555207	−	0.465874i	0.321492	−	0.946912i	$-0.395816\pi$
$293$	−9.50362	−	7.97448i	−0.555207	−	0.465874i	−0.876700	+	0.481038i	$0.840260\pi$
$294$		0			0
$295$	−26.0429	−	9.47886i	−1.51628	−	0.551880i
$296$		0			0
$297$	−11.1295	−	13.7999i	−0.645802	−	0.800751i
$298$		0			0
$299$	−6.15691	−	34.9176i	−0.356063	−	2.01934i
$300$		0			0
$301$	−5.01266	−	17.1998i	−0.288925	−	0.991378i
$302$		0			0
$303$	18.1561	+	10.6399i	1.04304	+	0.611247i
$304$		0			0
$305$	53.0417			3.03716
$306$		0			0
$307$	−4.47644	+	7.75342i	−0.255484	+	0.442511i	−0.965027	−	0.262151i	$-0.915568\pi$
$307$	−4.47644	+	7.75342i	−0.255484	+	0.442511i	0.709543	+	0.704662i	$0.248901\pi$
$308$		0			0
$309$	3.68837	−	9.93293i	0.209824	−	0.565064i
$310$		0			0
$311$	2.25971	−	12.8154i	0.128136	−	0.726696i	−0.851259	−	0.524745i	$-0.824161\pi$
$311$	2.25971	−	12.8154i	0.128136	−	0.726696i	0.979396	−	0.201951i	$-0.0647283\pi$
$312$		0			0
$313$	−5.39440	+	4.52644i	−0.304909	+	0.255849i	−0.782384	−	0.622796i	$-0.785997\pi$
$313$	−5.39440	+	4.52644i	−0.304909	+	0.255849i	0.477475	+	0.878645i	$0.341552\pi$
$314$		0			0
$315$	17.0096	+	23.8418i	0.958382	+	1.34333i
$316$		0			0
$317$	24.9690	+	9.08799i	1.40240	+	0.510432i	0.928890	−	0.370356i	$-0.120764\pi$
$317$	24.9690	+	9.08799i	1.40240	+	0.510432i	0.473511	+	0.880788i	$0.342986\pi$
$318$		0			0
$319$	−10.8934	−	9.14064i	−0.609913	−	0.511777i
$320$		0			0
$321$	12.8968	+	2.36033i	0.719828	+	0.131741i
$322$		0			0
$323$	20.8073			1.15775
$324$		0			0
$325$	21.9257	−	37.9765i	1.21622	−	2.10656i
$326$		0			0
$327$	3.64127	+	10.2097i	0.201363	+	0.564598i
$328$		0			0
$329$	10.8847	+	2.66385i	0.600093	+	0.146863i
$330$		0			0
$331$	1.18338	+	0.430715i	0.0650445	+	0.0236742i	0.374337	−	0.927293i	$-0.377870\pi$
$331$	1.18338	+	0.430715i	0.0650445	+	0.0236742i	−0.309293	+	0.950967i	$0.600092\pi$
$332$		0			0
$333$	−5.04442	−	30.9489i	−0.276432	−	1.69599i
$334$		0			0
$335$	−3.74471	−	21.2373i	−0.204595	−	1.16032i
$336$		0			0
$337$	15.1141	−	5.50108i	0.823317	−	0.299663i	0.104204	−	0.994556i	$-0.466771\pi$
$337$	15.1141	−	5.50108i	0.823317	−	0.299663i	0.719113	+	0.694893i	$0.244548\pi$
$338$		0			0
$339$	−0.0893232	−	0.107863i	−0.00485137	−	0.00585833i
$340$		0			0
$341$	19.5469			1.05852
$342$		0			0
$343$	17.5380	−	5.95142i	0.946962	−	0.321346i
$344$		0			0
$345$	38.4095	+	22.5089i	2.06790	+	1.21184i
$346$		0			0
$347$	3.71286	−	1.35137i	0.199317	−	0.0725454i	−0.240433	−	0.970666i	$-0.577289\pi$
$347$	3.71286	−	1.35137i	0.199317	−	0.0725454i	0.439750	+	0.898120i	$0.355067\pi$
$348$		0			0
$349$	−4.79142	−	1.74393i	−0.256479	−	0.0933506i	0.210581	−	0.977576i	$-0.432464\pi$
$349$	−4.79142	−	1.74393i	−0.256479	−	0.0933506i	−0.467060	+	0.884226i	$0.654687\pi$
$350$		0			0
$351$	−25.9525	−	5.09826i	−1.38524	−	0.272125i
$352$		0			0
$353$	4.21009	−	3.53269i	0.224081	−	0.188026i	−0.523835	−	0.851820i	$-0.675499\pi$
$353$	4.21009	−	3.53269i	0.224081	−	0.188026i	0.747916	+	0.663794i	$0.231055\pi$
$354$		0			0
$355$	3.30410	−	18.7385i	0.175363	−	0.994534i
$356$		0			0
$357$	−15.6198	−	1.12600i	−0.826689	−	0.0595944i
$358$		0			0
$359$	−0.771216	+	1.33578i	−0.0407032	+	0.0705000i	−0.885659	−	0.464336i	$-0.846293\pi$
$359$	−0.771216	+	1.33578i	−0.0407032	+	0.0705000i	0.844956	+	0.534836i	$0.179626\pi$
$360$		0			0
$361$	−9.03608	−	15.6509i	−0.475583	−	0.823734i
$362$		0			0
$363$	1.09439	−	0.185665i	0.0574404	−	0.00974489i
$364$		0			0
$365$	38.4210	−	13.9841i	2.01105	−	0.731962i
$366$		0			0
$367$	−4.49468	−	1.63593i	−0.234620	−	0.0853948i	0.222034	−	0.975039i	$-0.428730\pi$
$367$	−4.49468	−	1.63593i	−0.234620	−	0.0853948i	−0.456655	+	0.889644i	$0.650953\pi$
$368$		0			0
$369$	−3.21549	−	5.73994i	−0.167391	−	0.298809i
$370$		0			0
$371$	8.12205	−	18.4571i	0.421676	−	0.958246i
$372$		0			0
$373$	−2.43188	+	0.885133i	−0.125918	+	0.0458304i	−0.404211	−	0.914666i	$-0.632454\pi$
$373$	−2.43188	+	0.885133i	−0.125918	+	0.0458304i	0.278293	+	0.960496i	$0.410232\pi$
$374$		0			0
$375$	7.76143	+	21.7622i	0.400799	+	1.12379i
$376$		0			0
$377$	−21.2147			−1.09261
$378$		0			0
$379$	−32.5536			−1.67217			−0.836083	−	0.548603i	$-0.815160\pi$
$379$	−32.5536			−1.67217			−0.836083	+	0.548603i	$0.815160\pi$
$380$		0			0
$381$	−18.2524	−	3.34051i	−0.935101	−	0.171139i
$382$		0			0
$383$	−1.10771	+	0.403175i	−0.0566015	+	0.0206013i	−0.370166	−	0.928966i	$-0.620699\pi$
$383$	−1.10771	+	0.403175i	−0.0566015	+	0.0206013i	0.313564	+	0.949567i	$0.398477\pi$
$384$		0			0
$385$	−33.1105	+	3.62509i	−1.68747	+	0.184752i
$386$		0			0
$387$	−19.1774	+	6.69982i	−0.974844	+	0.340571i
$388$		0			0
$389$	22.6427	+	8.24126i	1.14803	+	0.417849i	0.844807	−	0.535071i	$-0.179715\pi$
$389$	22.6427	+	8.24126i	1.14803	+	0.417849i	0.303223	+	0.952920i	$0.401937\pi$
$390$		0			0
$391$	−22.3692	+	8.14173i	−1.13126	+	0.411745i
$392$		0			0
$393$	23.6037	+	28.5029i	1.19065	+	1.43778i
$394$		0			0
$395$	−13.4108	−	23.2282i	−0.674772	−	1.16874i
$396$		0			0
$397$	−13.9994	+	24.2477i	−0.702612	+	1.21696i	0.264935	+	0.964266i	$0.414650\pi$
$397$	−13.9994	+	24.2477i	−0.702612	+	1.21696i	−0.967547	+	0.252693i	$0.918684\pi$
$398$		0			0
$399$	12.1774	+	25.1043i	0.609634	+	1.25679i
$400$		0			0
$401$	0.485030	−	2.75074i	0.0242212	−	0.137365i	−0.970299	−	0.241908i	$-0.922227\pi$
$401$	0.485030	−	2.75074i	0.0242212	−	0.137365i	0.994520	+	0.104543i	$0.0333379\pi$
$402$		0			0
$403$	22.3387	−	18.7444i	1.11277	−	0.933726i
$404$		0			0
$405$	25.9842	−	20.6797i	1.29117	−	1.02758i
$406$		0			0
$407$	33.5117	+	12.1973i	1.66111	+	0.604595i
$408$		0			0
$409$	−1.67676	+	0.610291i	−0.0829104	+	0.0301769i	−0.383142	−	0.923689i	$-0.625158\pi$
$409$	−1.67676	+	0.610291i	−0.0829104	+	0.0301769i	0.300232	+	0.953866i	$0.402936\pi$
$410$		0			0
$411$	0.00349444	−	0.539181i	0.000172368	−	0.0265958i
$412$		0			0
$413$	16.5226	+	11.0408i	0.813024	+	0.543284i
$414$		0			0
$415$	10.0553			0.493595
$416$		0			0
$417$	1.24045	−	0.210445i	0.0607450	−	0.0103055i
$418$		0			0
$419$	9.69387	−	3.52828i	0.473577	−	0.172368i	−0.0941952	−	0.995554i	$-0.530028\pi$
$419$	9.69387	−	3.52828i	0.473577	−	0.172368i	0.567772	+	0.823186i	$0.307806\pi$
$420$		0			0
$421$	6.08483	+	34.5088i	0.296556	+	1.68185i	0.660809	+	0.750554i	$0.270213\pi$
$421$	6.08483	+	34.5088i	0.296556	+	1.68185i	−0.364253	+	0.931300i	$0.618675\pi$
$422$		0			0
$423$	2.36844	−	12.4836i	0.115157	−	0.606976i
$424$		0			0
$425$	−27.6657	−	10.0695i	−1.34199	−	0.488443i
$426$		0			0
$427$	−36.9423	−	9.04100i	−1.78776	−	0.437525i
$428$		0			0
$429$	19.4838	−	22.9166i	0.940686	−	1.10642i
$430$		0			0
$431$	−7.18243	+	12.4403i	−0.345965	+	0.599230i	−0.985529	−	0.169509i	$-0.945782\pi$
$431$	−7.18243	+	12.4403i	−0.345965	+	0.599230i	0.639563	+	0.768739i	$0.279115\pi$
$432$		0			0
$433$	−27.2469			−1.30940			−0.654700	−	0.755889i	$-0.727205\pi$
$433$	−27.2469			−1.30940			−0.654700	+	0.755889i	$0.727205\pi$
$434$		0			0
$435$	17.2539	−	20.2939i	0.827263	−	0.973017i
$436$		0			0
$437$	32.4901	+	27.2624i	1.55421	+	1.30414i
$438$		0			0
$439$	1.02834	+	0.374287i	0.0490802	+	0.0178637i	0.366444	−	0.930440i	$-0.380575\pi$
$439$	1.02834	+	0.374287i	0.0490802	+	0.0178637i	−0.317363	+	0.948304i	$0.602797\pi$
$440$		0			0
$441$	−7.78293	−	19.5045i	−0.370616	−	0.928786i
$442$		0			0
$443$	18.7669	−	15.7473i	0.891643	−	0.748177i	−0.0768960	−	0.997039i	$-0.524501\pi$
$443$	18.7669	−	15.7473i	0.891643	−	0.748177i	0.968539	+	0.248862i	$0.0800565\pi$
$444$		0			0
$445$	10.0324	−	56.8968i	0.475584	−	2.69717i
$446$		0			0
$447$	29.7335	−	5.04435i	1.40635	−	0.238590i
$448$		0			0
$449$	−13.7473	+	23.8110i	−0.648776	+	1.12371i	0.334640	+	0.942346i	$0.391385\pi$
$449$	−13.7473	+	23.8110i	−0.648776	+	1.12371i	−0.983416	+	0.181367i	$0.941948\pi$
$450$		0			0
$451$	7.48249			0.352337
$452$		0			0
$453$	−1.46353	+	0.832369i	−0.0687625	+	0.0391081i
$454$		0			0
$455$	−34.3634	+	35.8941i	−1.61098	+	1.68274i
$456$		0			0
$457$	−0.0730491	−	0.414282i	−0.00341709	−	0.0193793i	0.983052	−	0.183329i	$-0.0586875\pi$
$457$	−0.0730491	−	0.414282i	−0.00341709	−	0.0193793i	−0.986469	+	0.163950i	$0.947576\pi$
$458$		0			0
$459$	−0.345227	+	17.7538i	−0.0161138	+	0.828677i
$460$		0			0
$461$	−36.4028	−	13.2495i	−1.69545	−	0.617093i	−0.700154	−	0.713992i	$-0.746885\pi$
$461$	−36.4028	−	13.2495i	−1.69545	−	0.617093i	−0.995294	+	0.0968992i	$0.969108\pi$
$462$		0			0
$463$	31.2064	+	26.1853i	1.45029	+	1.21693i	0.932371	+	0.361502i	$0.117736\pi$
$463$	31.2064	+	26.1853i	1.45029	+	1.21693i	0.517914	+	0.855432i	$0.326709\pi$
$464$		0			0
$465$	−0.237296	+	36.6140i	−0.0110043	+	1.69794i
$466$		0			0
$467$	−10.9485	+	18.9634i	−0.506638	+	0.877523i	0.493332	+	0.869841i	$0.335779\pi$
$467$	−10.9485	+	18.9634i	−0.506638	+	0.877523i	−0.999970	+	0.00768200i	$0.997555\pi$
$468$		0			0
$469$	−1.01181	+	15.4296i	−0.0467213	+	0.712471i
$470$		0			0
$471$	−9.60746	+	1.62993i	−0.442689	+	0.0751030i
$472$		0			0
$473$	4.01179	−	22.7520i	0.184463	−	1.04614i
$474$		0			0
$475$	9.10874	+	51.6582i	0.417938	+	2.37024i
$476$		0			0
$477$	−21.3830	−	8.09817i	−0.979061	−	0.370790i
$478$		0			0
$479$	−1.03309	−	5.85893i	−0.0472030	−	0.267701i	0.952068	−	0.305888i	$-0.0989532\pi$
$479$	−1.03309	−	5.85893i	−0.0472030	−	0.267701i	−0.999271	+	0.0381861i	$0.987842\pi$
$480$		0			0
$481$	49.9946	−	18.1966i	2.27956	−	0.829691i
$482$		0			0
$483$	−22.9146	−	22.2238i	−1.04265	−	1.01122i
$484$		0			0
$485$	−15.8998	−	27.5393i	−0.721974	−	1.25050i
$486$		0			0
$487$	−14.4934	+	25.1033i	−0.656759	+	1.13754i	0.324691	+	0.945820i	$0.394740\pi$
$487$	−14.4934	+	25.1033i	−0.656759	+	1.13754i	−0.981450	+	0.191720i	$0.938594\pi$
$488$		0			0
$489$	−11.4819	−	2.10139i	−0.519230	−	0.0950279i
$490$		0			0
$491$	1.79104	−	10.1575i	0.0808285	−	0.458401i	−0.917351	−	0.398080i	$-0.869676\pi$
$491$	1.79104	−	10.1575i	0.0808285	−	0.458401i	0.998179	−	0.0603209i	$-0.0192124\pi$
$492$		0			0
$493$	2.47331	+	14.0268i	0.111392	+	0.631737i
$494$		0			0
$495$	6.07573	+	37.2762i	0.273084	+	1.67544i
$496$		0			0
$497$	−5.49521	+	12.4877i	−0.246494	+	0.560150i
$498$		0			0
$499$	−20.5847	−	17.2726i	−0.921499	−	0.773229i	0.0527726	−	0.998607i	$-0.483194\pi$
$499$	−20.5847	−	17.2726i	−0.921499	−	0.773229i	−0.974272	+	0.225377i	$0.927639\pi$
$500$		0			0
$501$	−19.4069	−	23.4350i	−0.867035	−	1.04700i
$502$		0			0
$503$	−2.93883	+	5.09021i	−0.131036	+	0.226961i	−0.924076	−	0.382208i	$-0.875164\pi$
$503$	−2.93883	+	5.09021i	−0.131036	+	0.226961i	0.793040	+	0.609169i	$0.208497\pi$
$504$		0			0
$505$	−22.4156	−	38.8250i	−0.997481	−	1.72769i
$506$		0			0
$507$	0.144899	−	22.3575i	0.00643519	−	0.992930i
$508$		0			0
$509$	2.30613	−	13.0787i	0.102217	−	0.579703i	−0.890078	−	0.455808i	$-0.849350\pi$
$509$	2.30613	−	13.0787i	0.102217	−	0.579703i	0.992295	−	0.123895i	$-0.0395385\pi$
$510$		0			0
$511$	−29.1429	+	3.19070i	−1.28921	+	0.141148i
$512$		0			0
$513$	27.7015	−	15.2832i	1.22305	−	0.674770i
$514$		0			0
$515$	−17.2914	+	14.5092i	−0.761952	+	0.639354i
$516$		0			0
$517$	11.0700	+	9.28879i	0.486856	+	0.408521i
$518$		0			0
$519$	0.0489511	−	7.55300i	0.00214871	−	0.331540i
$520$		0			0
$521$	21.1633			0.927183			0.463591	−	0.886049i	$-0.346561\pi$
$521$	21.1633			0.927183			0.463591	+	0.886049i	$0.346561\pi$
$522$		0			0
$523$	−16.1311			−0.705365			−0.352683	−	0.935743i	$-0.614730\pi$
$523$	−16.1311			−0.705365			−0.352683	+	0.935743i	$0.614730\pi$
$524$		0			0
$525$	−4.04231	−	39.2722i	−0.176421	−	1.71398i
$526$		0			0
$527$	−14.9979	−	12.5847i	−0.653319	−	0.548200i
$528$		0			0
$529$	−23.9835	−	8.72929i	−1.04276	−	0.379535i
$530$		0			0
$531$	11.5183	−	19.3663i	0.499854	−	0.840424i
$532$		0			0
$533$	8.55121	−	7.17532i	0.370394	−	0.310797i
$534$		0			0
$535$	−21.3964	−	17.9537i	−0.925047	−	0.776206i
$536$		0			0
$537$	3.77602	+	0.691076i	0.162947	+	0.0298221i
$538$		0			0
$539$	23.6786	+	3.11892i	1.01991	+	0.134341i
$540$		0			0
$541$	−7.06437	−	12.2358i	−0.303721	−	0.526060i	0.673255	−	0.739410i	$-0.264896\pi$
$541$	−7.06437	−	12.2358i	−0.303721	−	0.526060i	−0.976976	+	0.213351i	$0.931562\pi$
$542$		0			0
$543$	19.1100	+	3.49746i	0.820090	+	0.150090i
$544$		0			0
$545$	4.00991	−	22.7413i	0.171766	−	0.974131i
$546$		0			0
$547$	−0.227841	+	0.191182i	−0.00974180	+	0.00817434i	−0.647646	−	0.761942i	$-0.724246\pi$
$547$	−0.227841	+	0.191182i	−0.00974180	+	0.00817434i	0.637904	+	0.770116i	$0.279802\pi$
$548$		0			0
$549$	−8.03839	+	42.3690i	−0.343070	+	1.80827i
$550$		0			0
$551$	19.4399	−	16.3120i	0.828168	−	0.694915i
$552$		0			0
$553$	5.38105	+	18.4638i	0.228825	+	0.785160i
$554$		0			0
$555$	−23.2540	+	62.6240i	−0.987077	+	2.65824i
$556$		0			0
$557$	14.0463	+	24.3289i	0.595160	+	1.03085i	0.993524	+	0.113620i	$0.0362445\pi$
$557$	14.0463	+	24.3289i	0.595160	+	1.03085i	−0.398365	+	0.917227i	$0.630422\pi$
$558$		0			0
$559$	−17.2332	−	29.8488i	−0.728886	−	1.26247i
$560$		0			0
$561$	−17.4236	−	10.2107i	−0.735627	−	0.431095i
$562$		0			0
$563$	41.3824	−	15.0620i	1.74406	−	0.634786i	0.744596	−	0.667515i	$-0.232642\pi$
$563$	41.3824	−	15.0620i	1.74406	−	0.634786i	0.999464	+	0.0327289i	$0.0104198\pi$
$564$		0			0
$565$	0.0518077	+	0.293816i	0.00217957	+	0.0123609i
$566$		0			0
$567$	−21.6223	+	9.97386i	−0.908050	+	0.418863i
$568$		0			0
$569$	−3.94015	−	22.3457i	−0.165180	−	0.936781i	−0.948879	−	0.315641i	$-0.897781\pi$
$569$	−3.94015	−	22.3457i	−0.165180	−	0.936781i	0.783699	−	0.621141i	$-0.213330\pi$
$570$		0			0
$571$	−2.18833	+	0.796487i	−0.0915787	+	0.0333319i	−0.387403	−	0.921910i	$-0.626628\pi$
$571$	−2.18833	+	0.796487i	−0.0915787	+	0.0333319i	0.295824	+	0.955242i	$0.404406\pi$
$572$		0			0
$573$	−11.4764	−	6.72543i	−0.479432	−	0.280959i
$574$		0			0
$575$	−30.0059	−	51.9718i	−1.25133	−	2.16737i
$576$		0			0
$577$	−0.0876658	−	0.151842i	−0.00364957	−	0.00632125i	0.864195	−	0.503157i	$-0.167828\pi$
$577$	−0.0876658	−	0.151842i	−0.00364957	−	0.00632125i	−0.867844	+	0.496836i	$0.834495\pi$
$578$		0			0
$579$	0.0424859	−	0.114416i	0.00176565	−	0.00475498i
$580$		0			0
$581$	−7.00327	−	1.71393i	−0.290544	−	0.0711059i
$582$		0			0
$583$	19.9204	−	16.7152i	0.825020	−	0.692274i
$584$		0			0
$585$	42.6895	+	36.7741i	1.76499	+	1.52042i
$586$		0			0
$587$	−22.3459	+	18.7505i	−0.922316	+	0.773915i	−0.974422	−	0.224727i	$-0.927851\pi$
$587$	−22.3459	+	18.7505i	−0.922316	+	0.773915i	0.0521061	+	0.998642i	$0.483407\pi$
$588$		0			0
$589$	−6.05729	+	34.3526i	−0.249586	+	1.41547i
$590$		0			0
$591$	1.77937	+	0.325655i	0.0731935	+	0.0133957i
$592$		0			0
$593$	12.7609	+	22.1026i	0.524028	+	0.907644i	0.999609	+	0.0279716i	$0.00890479\pi$
$593$	12.7609	+	22.1026i	0.524028	+	0.907644i	−0.475580	+	0.879672i	$0.657762\pi$
$594$		0			0
$595$	27.7389	+	18.5359i	1.13719	+	0.759897i
$596$		0			0
$597$	−19.9131	−	3.64444i	−0.814988	−	0.149157i
$598$		0			0
$599$	26.5865	+	22.3087i	1.08629	+	0.911509i	0.996428	−	0.0844449i	$-0.0269117\pi$
$599$	26.5865	+	22.3087i	1.08629	+	0.911509i	0.0898660	+	0.995954i	$0.471356\pi$
$600$		0			0
$601$	−2.58855	+	2.17205i	−0.105589	+	0.0885999i	−0.694054	−	0.719923i	$-0.744177\pi$
$601$	−2.58855	+	2.17205i	−0.105589	+	0.0885999i	0.588465	+	0.808523i	$0.299733\pi$
$602$		0			0
$603$	17.5316	+	0.227254i	0.713941	+	0.00925451i
$604$		0			0
$605$	−2.22213	−	0.808789i	−0.0903425	−	0.0328820i
$606$		0			0
$607$	8.51421	+	7.14427i	0.345581	+	0.289977i	0.799013	−	0.601314i	$-0.205356\pi$
$607$	8.51421	+	7.14427i	0.345581	+	0.289977i	−0.453432	+	0.891291i	$0.649800\pi$
$608$		0			0
$609$	−15.4761	+	11.1933i	−0.627122	+	0.453573i
$610$		0			0
$611$	21.5585			0.872164
$612$		0			0
$613$	−8.18490			−0.330585			−0.165293	−	0.986245i	$-0.552857\pi$
$613$	−8.18490			−0.330585			−0.165293	+	0.986245i	$0.552857\pi$
$614$		0			0
$615$	−0.0908363	+	14.0158i	−0.00366287	+	0.565170i
$616$		0			0
$617$	2.76516	+	2.32024i	0.111321	+	0.0934095i	0.696749	−	0.717315i	$-0.254629\pi$
$617$	2.76516	+	2.32024i	0.111321	+	0.0934095i	−0.585428	+	0.810724i	$0.699074\pi$
$618$		0			0
$619$	23.6190	−	19.8187i	0.949328	−	0.796581i	−0.0298563	−	0.999554i	$-0.509505\pi$
$619$	23.6190	−	19.8187i	0.949328	−	0.796581i	0.979184	+	0.202974i	$0.0650605\pi$
$620$		0			0
$621$	−23.8007	+	27.2698i	−0.955089	+	1.09430i
$622$		0			0
$623$	−16.6855	+	37.9172i	−0.668489	+	1.51912i
$624$		0			0
$625$	1.06714	−	6.05206i	0.0426856	−	0.242082i
$626$		0			0
$627$	−0.233190	+	35.9806i	−0.00931273	+	1.43693i
$628$		0			0
$629$	−17.8599	−	30.9343i	−0.712122	−	1.23343i
$630$		0			0
$631$	−6.77841	+	11.7405i	−0.269844	+	0.467384i	−0.968821	−	0.247760i	$-0.920305\pi$
$631$	−6.77841	+	11.7405i	−0.269844	+	0.467384i	0.698977	+	0.715144i	$0.253639\pi$
$632$		0			0
$633$	1.34867	+	1.62860i	0.0536048	+	0.0647311i
$634$		0			0
$635$	30.2817	+	25.4094i	1.20169	+	1.00834i
$636$		0			0
$637$	30.0514	−	19.1421i	1.19068	−	0.758438i
$638$		0			0
$639$	14.4673	+	5.47905i	0.572318	+	0.216748i
$640$		0			0
$641$	5.73491	+	32.5243i	0.226515	+	1.28463i	0.859767	+	0.510686i	$0.170609\pi$
$641$	5.73491	+	32.5243i	0.226515	+	1.28463i	−0.633252	+	0.773946i	$0.718280\pi$
$642$		0			0
$643$	1.27040	−	7.20477i	0.0500995	−	0.284128i	−0.949457	−	0.313896i	$-0.898366\pi$
$643$	1.27040	−	7.20477i	0.0500995	−	0.284128i	0.999557	+	0.0297677i	$0.00947675\pi$
$644$		0			0
$645$	42.5690	+	7.79086i	1.67615	+	0.306765i
$646$		0			0
$647$	6.56835	−	11.3767i	0.258228	−	0.447265i	−0.707539	−	0.706674i	$-0.750195\pi$
$647$	6.56835	−	11.3767i	0.258228	−	0.447265i	0.965767	+	0.259410i	$0.0835280\pi$
$648$		0			0
$649$	12.8131	+	22.1930i	0.502960	+	0.871151i
$650$		0			0
$651$	6.40616	−	25.4603i	0.251077	−	0.997870i
$652$		0			0
$653$	4.03848	−	1.46988i	0.158038	−	0.0575210i	−0.261790	−	0.965125i	$-0.584313\pi$
$653$	4.03848	−	1.46988i	0.158038	−	0.0575210i	0.419828	+	0.907604i	$0.362091\pi$
$654$		0			0
$655$	−13.6902	−	77.6410i	−0.534920	−	3.03368i
$656$		0			0
$657$	5.34768	+	32.8095i	0.208633	+	1.28002i
$658$		0			0
$659$	−1.63768	−	9.28774i	−0.0637950	−	0.361799i	−0.999948	−	0.0102062i	$-0.996751\pi$
$659$	−1.63768	−	9.28774i	−0.0637950	−	0.361799i	0.936153	−	0.351593i	$-0.114360\pi$
$660$		0			0
$661$	−3.05866	+	17.3465i	−0.118968	+	0.674702i	0.865741	+	0.500493i	$0.166848\pi$
$661$	−3.05866	+	17.3465i	−0.118968	+	0.674702i	−0.984709	+	0.174209i	$0.944263\pi$
$662$		0			0
$663$	−29.7037	+	5.03930i	−1.15360	+	0.195710i
$664$		0			0
$665$	3.88956	−	59.3134i	0.150831	−	2.30007i
$666$		0			0
$667$	−14.5164	+	25.1431i	−0.562077	+	0.973546i
$668$		0			0
$669$	−0.190190	+	29.3458i	−0.00735318	+	1.13457i
$670$		0			0
$671$	−37.5710	−	31.5258i	−1.45041	−	1.21704i
$672$		0			0
$673$	−4.18614	−	1.52363i	−0.161364	−	0.0587316i	0.260075	−	0.965588i	$-0.416253\pi$
$673$	−4.18614	−	1.52363i	−0.161364	−	0.0587316i	−0.421439	+	0.906857i	$0.638475\pi$
$674$		0			0
$675$	−44.2285	+	6.91493i	−1.70236	+	0.266156i
$676$		0			0
$677$	3.78535	+	21.4678i	0.145483	+	0.825074i	0.966978	+	0.254859i	$0.0820290\pi$
$677$	3.78535	+	21.4678i	0.145483	+	0.825074i	−0.821495	+	0.570215i	$0.806860\pi$
$678$		0			0
$679$	6.37975	+	21.8906i	0.244832	+	0.840085i
$680$		0			0
$681$	−17.1786	+	9.77017i	−0.658285	+	0.374394i
$682$		0			0
$683$	−40.8134			−1.56168			−0.780841	−	0.624729i	$-0.785209\pi$
$683$	−40.8134			−1.56168			−0.780841	+	0.624729i	$0.785209\pi$
$684$		0			0
$685$	−0.574334	+	0.994776i	−0.0219442	+	0.0380084i
$686$		0			0
$687$	32.7867	−	5.56234i	1.25089	−	0.212216i
$688$		0			0
$689$	6.73662	−	38.2053i	0.256645	−	1.45551i
$690$		0			0
$691$	−23.7027	+	19.8889i	−0.901693	+	0.756610i	−0.970521	−	0.241018i	$-0.922519\pi$
$691$	−23.7027	+	19.8889i	−0.901693	+	0.756610i	0.0688274	+	0.997629i	$0.478074\pi$
$692$		0			0
$693$	2.12217	−	26.9976i	0.0806145	−	1.02555i
$694$		0			0
$695$	−2.51870	−	0.916734i	−0.0955399	−	0.0347737i
$696$		0			0
$697$	−5.74116	−	4.81740i	−0.217462	−	0.182472i
$698$		0			0
$699$	−1.82195	+	2.14296i	−0.0689127	+	0.0810542i
$700$		0			0
$701$	−14.2267			−0.537335			−0.268667	−	0.963233i	$-0.586583\pi$
$701$	−14.2267			−0.537335			−0.268667	+	0.963233i	$0.586583\pi$
$702$		0			0
$703$	−31.8208	+	55.1153i	−1.20015	+	2.07871i
$704$		0			0
$705$	−17.5336	+	20.6228i	−0.660354	+	0.776700i
$706$		0			0
$707$	8.99418	+	30.8614i	0.338261	+	1.16066i
$708$		0			0
$709$	−32.6796	−	11.8944i	−1.22731	−	0.446703i	−0.354632	−	0.935006i	$-0.615394\pi$
$709$	−32.6796	−	11.8944i	−1.22731	−	0.446703i	−0.872674	+	0.488303i	$0.837616\pi$
$710$		0			0
$711$	20.5868	−	7.19219i	0.772065	−	0.269728i
$712$		0			0
$713$	−6.92991	−	39.3015i	−0.259527	−	1.47185i
$714$		0			0
$715$	−60.2158	+	21.9167i	−2.25194	+	0.819640i
$716$		0			0
$717$	−35.5746	+	6.03530i	−1.32856	+	0.225393i
$718$		0			0
$719$	−30.1836			−1.12566			−0.562829	−	0.826573i	$-0.690287\pi$
$719$	−30.1836			−1.12566			−0.562829	+	0.826573i	$0.690287\pi$
$720$		0			0
$721$	14.5162	−	7.15800i	0.540611	−	0.266578i
$722$		0			0
$723$	−0.110177	+	17.0000i	−0.00409754	+	0.632238i
$724$		0			0
$725$	−33.7417	+	12.2810i	−1.25313	+	0.456103i
$726$		0			0
$727$	21.8641	+	7.95788i	0.810894	+	0.295141i	0.713993	−	0.700153i	$-0.246885\pi$
$727$	21.8641	+	7.95788i	0.810894	+	0.295141i	0.0969012	+	0.995294i	$0.469107\pi$
$728$		0			0
$729$	12.5808	+	23.8898i	0.465955	+	0.884809i
$730$		0			0
$731$	−17.7264	+	14.8743i	−0.655636	+	0.550144i
$732$		0			0
$733$	8.15366	−	46.2417i	0.301162	−	1.70798i	−0.339878	−	0.940470i	$-0.610386\pi$
$733$	8.15366	−	46.2417i	0.301162	−	1.70798i	0.641040	−	0.767507i	$-0.278503\pi$
$734$		0			0
$735$	−6.12963	+	44.3154i	−0.226095	+	1.63460i
$736$		0			0
$737$	−9.97009	+	17.2687i	−0.367253	+	0.636101i
$738$		0			0
$739$	−5.82569	−	10.0904i	−0.214301	−	0.371181i	0.738755	−	0.673974i	$-0.235414\pi$
$739$	−5.82569	−	10.0904i	−0.214301	−	0.371181i	−0.953056	+	0.302793i	$0.902081\pi$
$740$		0			0
$741$	34.2370	+	41.3433i	1.25773	+	1.51878i
$742$		0			0
$743$	−3.23983	+	1.17920i	−0.118858	+	0.0432607i	−0.400764	−	0.916181i	$-0.631255\pi$
$743$	−3.23983	+	1.17920i	−0.118858	+	0.0432607i	0.281907	+	0.959442i	$0.409033\pi$
$744$		0			0
$745$	−60.3732	−	21.9741i	−2.21190	−	0.805067i
$746$		0			0
$747$	−1.52386	+	8.03203i	−0.0557552	+	0.293877i
$748$		0			0
$749$	11.8418	+	16.1514i	0.432692	+	0.590158i
$750$		0			0
$751$	23.1093	−	8.41110i	0.843271	−	0.306926i	0.115977	−	0.993252i	$-0.463000\pi$
$751$	23.1093	−	8.41110i	0.843271	−	0.306926i	0.727294	+	0.686326i	$0.240778\pi$
$752$		0			0
$753$	15.9011	+	2.91018i	0.579469	+	0.106053i
$754$		0			0
$755$	3.58681			0.130537
$756$		0			0
$757$	49.9552			1.81565			0.907826	−	0.419347i	$-0.137741\pi$
$757$	49.9552			1.81565			0.907826	+	0.419347i	$0.137741\pi$
$758$		0			0
$759$	−13.8282	−	38.7727i	−0.501932	−	1.40736i
$760$		0			0
$761$	20.4241	−	7.43376i	0.740373	−	0.269474i	0.0558241	−	0.998441i	$-0.482221\pi$
$761$	20.4241	−	7.43376i	0.740373	−	0.269474i	0.684549	+	0.728967i	$0.259999\pi$
$762$		0			0
$763$	−6.66908	+	15.1553i	−0.241437	+	0.548658i
$764$		0			0
$765$	19.3375	−	32.5130i	0.699150	−	1.17551i
$766$		0			0
$767$	35.9251	+	13.0757i	1.29718	+	0.472135i
$768$		0			0
$769$	39.2362	−	14.2808i	1.41489	−	0.514980i	0.482332	−	0.875988i	$-0.339790\pi$
$769$	39.2362	−	14.2808i	1.41489	−	0.514980i	0.932562	+	0.361009i	$0.117568\pi$
$770$		0			0
$771$	−30.8623	+	5.23585i	−1.11148	+	0.188565i
$772$		0			0
$773$	9.12755	+	15.8094i	0.328295	+	0.568624i	0.982174	−	0.187976i	$-0.0601926\pi$
$773$	9.12755	+	15.8094i	0.328295	+	0.568624i	−0.653879	+	0.756600i	$0.726859\pi$
$774$		0			0
$775$	24.6785	−	42.7444i	0.886478	−	1.53542i
$776$		0			0
$777$	26.8702	−	39.6524i	0.963961	−	1.42252i
$778$		0			0
$779$	−2.31872	+	13.1501i	−0.0830766	+	0.471151i
$780$		0			0
$781$	−13.4778	+	11.3092i	−0.482272	+	0.404674i
$782$		0			0
$783$	13.5957	+	16.8577i	0.485870	+	0.602446i
$784$		0			0
$785$	19.5078	+	7.10024i	0.696262	+	0.253419i
$786$		0			0
$787$	15.2277	−	5.54244i	0.542810	−	0.197567i	−0.0560389	−	0.998429i	$-0.517847\pi$
$787$	15.2277	−	5.54244i	0.542810	−	0.197567i	0.598849	+	0.800862i	$0.295625\pi$
$788$		0			0
$789$	−29.8568	−	17.4968i	−1.06293	−	0.622902i
$790$		0			0
$791$	0.0139984	−	0.213467i	0.000497724	−	0.00759000i
$792$		0			0
$793$	−73.1688			−2.59830
$794$		0			0
$795$	31.0682	+	37.5167i	1.10187	+	1.33058i
$796$		0			0
$797$	−12.0493	+	4.38558i	−0.426807	+	0.155345i	−0.546487	−	0.837467i	$-0.684035\pi$
$797$	−12.0493	+	4.38558i	−0.426807	+	0.155345i	0.119680	+	0.992812i	$0.461813\pi$
$798$		0			0
$799$	−2.51340	−	14.2542i	−0.0889176	−	0.504277i
$800$		0			0
$801$	43.9280	+	16.6364i	1.55212	+	0.587819i
$802$		0			0
$803$	−35.5263	−	12.9305i	−1.25370	−	0.456308i
$804$		0			0
$805$	19.0273	+	65.2877i	0.670624	+	2.30109i
$806$		0			0
$807$	2.44727	+	6.86188i	0.0861481	+	0.241549i
$808$		0			0
$809$	19.8646	−	34.4065i	0.698401	−	1.20967i	−0.270619	−	0.962687i	$-0.587228\pi$
$809$	19.8646	−	34.4065i	0.698401	−	1.20967i	0.969021	−	0.246980i	$-0.0794383\pi$
$810$		0			0
$811$	41.3088			1.45055			0.725274	−	0.688461i	$-0.241713\pi$
$811$	41.3088			1.45055			0.725274	+	0.688461i	$0.241713\pi$
$812$		0			0
$813$	−30.7247	−	5.62314i	−1.07756	−	0.197212i
$814$		0			0
$815$	19.0490	+	15.9840i	0.667259	+	0.559897i
$816$		0			0
$817$	38.7423	+	14.1010i	1.35542	+	0.493333i
$818$		0			0
$819$	−23.4640	−	32.8887i	−0.819899	−	1.14922i
$820$		0			0
$821$	−12.6864	+	10.6452i	−0.442759	+	0.371519i	−0.836741	−	0.547599i	$-0.815542\pi$
$821$	−12.6864	+	10.6452i	−0.442759	+	0.371519i	0.393981	+	0.919118i	$0.371097\pi$
$822$		0			0
$823$	0.406700	−	2.30651i	0.0141767	−	0.0803998i	−0.976899	−	0.213703i	$-0.931447\pi$
$823$	0.406700	−	2.30651i	0.0141767	−	0.0803998i	0.991075	+	0.133304i	$0.0425585\pi$
$824$		0			0
$825$	17.7225	−	47.7275i	0.617019	−	1.66166i
$826$		0			0
$827$	−12.5082	+	21.6649i	−0.434954	+	0.753362i	−0.997292	−	0.0735453i	$-0.976569\pi$
$827$	−12.5082	+	21.6649i	−0.434954	+	0.753362i	0.562338	+	0.826907i	$0.309902\pi$
$828$		0			0
$829$	42.7994			1.48649			0.743243	−	0.669022i	$-0.233287\pi$
$829$	42.7994			1.48649			0.743243	+	0.669022i	$0.233287\pi$
$830$		0			0
$831$	17.8385	+	10.4538i	0.618810	+	0.362638i
$832$		0			0
$833$	−16.1600	−	17.6379i	−0.559912	−	0.611117i
$834$		0			0
$835$	11.2560	+	63.8362i	0.389532	+	2.20914i
$836$		0			0
$837$	−29.2108	−	5.73835i	−1.00967	−	0.198346i
$838$		0			0
$839$	38.4252	+	13.9856i	1.32658	+	0.482837i	0.905563	−	0.424213i	$-0.139449\pi$
$839$	38.4252	+	13.9856i	1.32658	+	0.482837i	0.421022	+	0.907050i	$0.361671\pi$
$840$		0			0
$841$	−8.90810	−	7.47478i	−0.307176	−	0.257751i
$842$		0			0
$843$	28.6104	+	16.7664i	0.985395	+	0.577465i
$844$		0			0
$845$	−23.8151	+	41.2490i	−0.819265	+	1.41901i
$846$		0			0
$847$	1.40980	+	0.942066i	0.0484414	+	0.0323698i
$848$		0			0
$849$	0.284738	+	0.343838i	0.00977217	+	0.0118005i
$850$		0			0
$851$	12.6433	−	71.7037i	0.433407	−	2.45797i
$852$		0			0
$853$	−8.33235	−	47.2551i	−0.285294	−	1.61798i	−0.704233	−	0.709969i	$-0.748709\pi$
$853$	−8.33235	−	47.2551i	−0.285294	−	1.61798i	0.418938	−	0.908015i	$-0.362402\pi$
$854$		0			0
$855$	−67.3939	−	0.873597i	−2.30482	−	0.0298764i
$856$		0			0
$857$	3.93458	+	22.3141i	0.134403	+	0.762236i	0.975274	+	0.221000i	$0.0709322\pi$
$857$	3.93458	+	22.3141i	0.134403	+	0.762236i	−0.840871	+	0.541236i	$0.817957\pi$
$858$		0			0
$859$	37.5667	−	13.6731i	1.28176	−	0.466522i	0.390745	−	0.920499i	$-0.372218\pi$
$859$	37.5667	−	13.6731i	1.28176	−	0.466522i	0.891013	+	0.453977i	$0.149995\pi$
$860$		0			0
$861$	2.45226	−	9.74616i	0.0835729	−	0.332148i
$862$		0			0
$863$	−12.6690	−	21.9433i	−0.431257	−	0.746959i	0.565725	−	0.824594i	$-0.308597\pi$
$863$	−12.6690	−	21.9433i	−0.431257	−	0.746959i	−0.996982	+	0.0776348i	$0.975263\pi$
$864$		0			0
$865$	−8.04544	+	13.9351i	−0.273553	+	0.473808i
$866$		0			0
$867$	−3.09628	−	8.68163i	−0.105155	−	0.294843i
$868$		0			0
$869$	−4.30662	+	24.4241i	−0.146092	+	0.828530i
$870$		0			0
$871$	5.16567	+	29.2960i	0.175032	+	0.992656i
$872$		0			0
$873$	24.4076	−	8.52704i	0.826073	−	0.288597i
$874$		0			0
$875$	−14.2153	+	32.3038i	−0.480564	+	1.09207i
$876$		0			0
$877$	10.9071	+	9.15215i	0.368307	+	0.309046i	0.808091	−	0.589057i	$-0.200501\pi$
$877$	10.9071	+	9.15215i	0.368307	+	0.309046i	−0.439785	+	0.898103i	$0.644945\pi$
$878$		0			0
$879$	−21.1853	+	3.59413i	−0.714562	+	0.121227i
$880$		0			0
$881$	22.2828	−	38.5949i	0.750726	−	1.30030i	−0.196745	−	0.980455i	$-0.563037\pi$
$881$	22.2828	−	38.5949i	0.750726	−	1.30030i	0.947471	−	0.319841i	$-0.103630\pi$
$882$		0			0
$883$	2.21229	+	3.83180i	0.0744495	+	0.128950i	0.900847	−	0.434137i	$-0.142947\pi$
$883$	2.21229	+	3.83180i	0.0744495	+	0.128950i	−0.826397	+	0.563088i	$0.809613\pi$
$884$		0			0
$885$	−41.7262	+	23.7314i	−1.40261	+	0.797722i
$886$		0			0
$887$	−6.24949	+	35.4426i	−0.209837	+	1.19005i	0.679807	+	0.733392i	$0.262064\pi$
$887$	−6.24949	+	35.4426i	−0.209837	+	1.19005i	−0.889644	+	0.456655i	$0.849047\pi$
$888$		0			0
$889$	−16.7594	−	22.8585i	−0.562093	−	0.766651i
$890$		0			0
$891$	−30.6965	−	0.795945i	−1.02837	−	0.0266652i
$892$		0			0
$893$	−19.7550	+	16.5764i	−0.661076	+	0.554708i
$894$		0			0
$895$	−6.26460	−	5.25663i	−0.209403	−	0.175710i
$896$		0			0
$897$	−52.9842	−	31.0500i	−1.76909	−	1.03673i
$898$		0			0
$899$	−23.8781			−0.796381
$900$		0			0
$901$	−26.0462			−0.867724
$902$		0			0
$903$	−28.3203	−	12.6821i	−0.942442	−	0.422033i
$904$		0			0
$905$	−31.7045	−	26.6032i	−1.05389	−	0.884321i
$906$		0			0
$907$	−12.6617	−	4.60848i	−0.420424	−	0.153022i	0.123140	−	0.992389i	$-0.460704\pi$
$907$	−12.6617	−	4.60848i	−0.420424	−	0.153022i	−0.543565	+	0.839367i	$0.682926\pi$
$908$		0			0
$909$	34.4099	−	12.0214i	1.14130	−	0.398726i
$910$		0			0
$911$	34.6782	−	29.0984i	1.14894	−	0.964074i	0.149244	−	0.988800i	$-0.452316\pi$
$911$	34.6782	−	29.0984i	1.14894	−	0.964074i	0.999694	+	0.0247266i	$0.00787151\pi$
$912$		0			0
$913$	−7.12245	−	5.97645i	−0.235719	−	0.197792i
$914$		0			0
$915$	59.5084	−	69.9931i	1.96729	−	2.31390i
$916$		0			0
$917$	−3.69907	+	56.4086i	−0.122154	+	1.86277i
$918$		0			0
$919$	8.46587	+	14.6633i	0.279263	+	0.483698i	0.971202	−	0.238258i	$-0.0765764\pi$
$919$	8.46587	+	14.6633i	0.279263	+	0.483698i	−0.691939	+	0.721956i	$0.743243\pi$
$920$		0			0
$921$	5.20910	+	14.6057i	0.171646	+	0.481275i
$922$		0			0
$923$	−4.55786	+	25.8489i	−0.150024	+	0.850827i
$924$		0			0
$925$	68.9820	−	57.8828i	2.26811	−	1.90317i
$926$		0			0
$927$	−8.96930	−	16.0110i	−0.294590	−	0.525871i
$928$		0			0
$929$	32.3875	−	27.1763i	1.06260	−	0.891626i	0.0682365	−	0.997669i	$-0.478263\pi$
$929$	32.3875	−	27.1763i	1.06260	−	0.891626i	0.994361	+	0.106044i	$0.0338183\pi$
$930$		0			0
$931$	−12.8190	+	40.6474i	−0.420126	+	1.33216i
$932$		0			0
$933$	−14.3758	−	17.3597i	−0.470644	−	0.568332i
$934$		0			0
$935$	21.5113	+	37.2587i	0.703495	+	1.21849i
$936$		0			0
$937$	11.4756	+	19.8764i	0.374893	+	0.649333i	0.990311	−	0.138868i	$-0.0443462\pi$
$937$	11.4756	+	19.8764i	0.374893	+	0.649333i	−0.615418	+	0.788201i	$0.711013\pi$
$938$		0			0
$939$	−0.0790466	+	12.1967i	−0.00257959	+	0.398023i
$940$		0			0
$941$	−31.7125	+	11.5424i	−1.03380	+	0.376271i	−0.802526	−	0.596618i	$-0.796511\pi$
$941$	−31.7125	+	11.5424i	−1.03380	+	0.376271i	−0.231272	+	0.972889i	$0.574289\pi$
$942$		0			0
$943$	−2.65275	−	15.0445i	−0.0863855	−	0.489916i
$944$		0			0
$945$	50.5446	+	4.30287i	1.64422	+	0.139972i
$946$		0			0
$947$	−2.73089	−	15.4877i	−0.0887420	−	0.503281i	−0.996486	−	0.0837569i	$-0.973308\pi$
$947$	−2.73089	−	15.4877i	−0.0887420	−	0.503281i	0.907744	−	0.419524i	$-0.137803\pi$
$948$		0			0
$949$	−53.0002	+	19.2905i	−1.72046	+	0.626196i
$950$		0			0
$951$	40.0056	−	22.7528i	1.29727	−	0.737810i
$952$		0			0
$953$	14.5947	+	25.2788i	0.472770	+	0.818862i	0.999514	−	0.0311619i	$-0.00992073\pi$
$953$	14.5947	+	25.2788i	0.472770	+	0.818862i	−0.526744	+	0.850024i	$0.676587\pi$
$954$		0			0
$955$	14.1688	+	24.5410i	0.458491	+	0.794129i
$956$		0			0
$957$	−24.2833	+	4.11972i	−0.784968	+	0.133171i
$958$		0			0
$959$	0.569570	−	0.594942i	0.0183924	−	0.0192117i
$960$		0			0
$961$	1.39595	−	1.17134i	0.0450307	−	0.0377853i
$962$		0			0
$963$	17.5838	−	14.3703i	0.566629	−	0.463076i
$964$		0			0
$965$	−0.199178	+	0.167130i	−0.00641177	+	0.00538012i
$966$		0			0
$967$	0.571499	−	3.24113i	0.0183782	−	0.104228i	−0.974239	−	0.225519i	$-0.927592\pi$
$967$	0.571499	−	3.24113i	0.0183782	−	0.104228i	0.992617	+	0.121291i	$0.0387034\pi$
$968$		0			0
$969$	23.3441	−	27.4570i	0.749919	−	0.882046i
$970$		0			0
$971$	−18.8463	−	32.6428i	−0.604808	−	1.04756i	−0.992082	−	0.125594i	$-0.959916\pi$
$971$	−18.8463	−	32.6428i	−0.604808	−	1.04756i	0.387274	−	0.921965i	$-0.373417\pi$
$972$		0			0
$973$	1.59796	+	1.06780i	0.0512282	+	0.0342320i
$974$		0			0
$975$	−25.5144	−	71.5393i	−0.817113	−	2.29109i
$976$		0			0
$977$	−20.5596	−	17.2516i	−0.657760	−	0.551926i	0.251654	−	0.967817i	$-0.419025\pi$
$977$	−20.5596	−	17.2516i	−0.657760	−	0.551926i	−0.909415	+	0.415891i	$0.863470\pi$
$978$		0			0
$979$	−40.9234	+	34.3388i	−1.30792	+	1.09747i
$980$		0			0
$981$	17.5578	+	6.64947i	0.560576	+	0.212301i
$982$		0			0
$983$	−13.2426	−	4.81991i	−0.422373	−	0.153731i	0.122084	−	0.992520i	$-0.461042\pi$
$983$	−13.2426	−	4.81991i	−0.422373	−	0.153731i	−0.544458	+	0.838788i	$0.683264\pi$
$984$		0			0
$985$	−2.95206	−	2.47708i	−0.0940606	−	0.0789262i
$986$		0			0
$987$	15.7269	−	11.3747i	0.500593	−	0.362060i
$988$		0			0
$989$	−47.1681			−1.49986
$990$		0			0
$991$	−27.5599			−0.875469			−0.437734	−	0.899104i	$-0.644219\pi$
$991$	−27.5599			−0.875469			−0.437734	+	0.899104i	$0.644219\pi$
$992$		0			0
$993$	1.89602	−	1.07834i	0.0601683	−	0.0342202i
$994$		0			0
$995$	33.0368	+	27.7212i	1.04734	+	0.878820i
$996$		0			0
$997$	23.9155	−	20.0675i	0.757412	−	0.635544i	−0.180040	−	0.983659i	$-0.557623\pi$
$997$	23.9155	−	20.0675i	0.757412	−	0.635544i	0.937452	+	0.348115i	$0.113178\pi$
$998$		0			0
$999$	−46.4991	−	28.0655i	−1.47117	−	0.887954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.18	✓	144
7.2	even	3		756.2.bq.a.625.15	yes	144
27.7	even	9		756.2.bq.a.277.15	yes	144
189.142	even	9	inner	756.2.bp.a.709.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.18	✓	144	1.1	even	1	trivial
756.2.bp.a.709.18	yes	144	189.142	even	9	inner
756.2.bq.a.277.15	yes	144	27.7	even	9
756.2.bq.a.625.15	yes	144	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12192 - 1.31958i) q^{3} +(-3.46735 + 1.26201i) q^{5} +(2.63004 - 0.287949i) q^{7} +(-0.482607 - 2.96093i) q^{9} +O(q^{10})\)	\(q+(1.12192 - 1.31958i) q^{3} +(-3.46735 + 1.26201i) q^{5} +(2.63004 - 0.287949i) q^{7} +(-0.482607 - 2.96093i) q^{9} +(3.20611 + 1.16693i) q^{11} +(4.78306 - 1.74089i) q^{13} +(-2.22474 + 5.99133i) q^{15} +(-1.70869 - 2.95953i) q^{17} +(-3.04435 + 5.27296i) q^{19} +(2.57071 - 3.79361i) q^{21} +(1.20960 - 6.86000i) q^{23} +(6.59961 - 5.53773i) q^{25} +(-4.44864 - 2.68507i) q^{27} +(-3.91654 - 1.42550i) q^{29} +(5.38357 - 1.95946i) q^{31} +(5.13685 - 2.92154i) q^{33} +(-8.75585 + 4.31755i) q^{35} +10.4524 q^{37} +(3.06894 - 8.26479i) q^{39} +(2.06082 - 0.750076i) q^{41} +(-1.17583 - 6.66848i) q^{43} +(5.41009 + 9.65751i) q^{45} +(3.98002 + 1.44861i) q^{47} +(6.83417 - 1.51463i) q^{49} +(-5.82235 - 1.06559i) q^{51} +(3.81085 - 6.60059i) q^{53} -12.5894 q^{55} +(3.54262 + 9.93309i) q^{57} +(5.75369 + 4.82792i) q^{59} +(-13.5080 - 4.91652i) q^{61} +(-2.12187 - 7.64838i) q^{63} +(-14.3875 + 12.0726i) q^{65} +(-1.01486 + 5.75556i) q^{67} +(-7.69528 - 9.29252i) q^{69} +(-2.57834 + 4.46582i) q^{71} -11.0808 q^{73} +(0.0967071 - 14.9216i) q^{75} +(8.76820 + 2.14587i) q^{77} +(1.26225 + 7.15856i) q^{79} +(-8.53418 + 2.85793i) q^{81} +(-2.56076 - 0.932040i) q^{83} +(9.65957 + 8.10534i) q^{85} +(-6.27510 + 3.56891i) q^{87} +(-7.82880 + 13.5599i) q^{89} +(12.0783 - 5.95588i) q^{91} +(3.45424 - 9.30242i) q^{93} +(3.90127 - 22.1252i) q^{95} +(1.49652 + 8.48716i) q^{97} +(1.90790 - 10.0562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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