LMFDB - Embedded newform 756.2.ba.a.71.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(71,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("756.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ba (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.11
Character	$\chi$	$=$	756.71
Dual form			756.2.ba.a.575.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.802493 + 1.16448i) q^{2} +(-0.712009 - 1.86897i) q^{4} +(2.73233 + 1.57751i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.74775 + 0.670717i) q^{8} +O(q^{10})$	\(q+(-0.802493 + 1.16448i) q^{2} +(-0.712009 - 1.86897i) q^{4} +(2.73233 + 1.57751i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.74775 + 0.670717i) q^{8} +(-4.02965 + 1.91579i) q^{10} +(2.55685 + 4.42859i) q^{11} +(2.38370 - 4.12868i) q^{13} +(-0.112741 + 1.40971i) q^{14} +(-2.98609 + 2.66145i) q^{16} -7.22631i q^{17} +0.531576i q^{19} +(1.00287 - 6.22984i) q^{20} +(-7.20884 - 0.576526i) q^{22} +(-1.59577 + 2.76396i) q^{23} +(2.47708 + 4.29042i) q^{25} +(2.89485 + 6.08899i) q^{26} +(-1.55110 - 1.26257i) q^{28} +(1.50966 - 0.871600i) q^{29} +(-1.47432 - 0.851200i) q^{31} +(-0.702876 - 5.61302i) q^{32} +(8.41487 + 5.79907i) q^{34} +3.15502 q^{35} +3.11392 q^{37} +(-0.619007 - 0.426586i) q^{38} +(6.44969 + 6.16722i) q^{40} +(2.32723 + 1.34363i) q^{41} +(4.39025 - 2.53471i) q^{43} +(6.45640 - 7.93187i) q^{44} +(-1.93797 - 4.07630i) q^{46} +(-1.47750 - 2.55911i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-6.98393 - 0.558538i) q^{50} +(-9.41359 - 1.51539i) q^{52} +13.6811i q^{53} +16.1338i q^{55} +(2.71498 - 0.793018i) q^{56} +(-0.196531 + 2.45741i) q^{58} +(-3.71140 + 6.42833i) q^{59} +(3.23838 + 5.60903i) q^{61} +(2.17433 - 1.03373i) q^{62} +(7.10028 + 3.68593i) q^{64} +(13.0261 - 7.52061i) q^{65} +(-1.72700 - 0.997087i) q^{67} +(-13.5057 + 5.14520i) q^{68} +(-2.53188 + 3.67395i) q^{70} -13.0667 q^{71} -6.59684 q^{73} +(-2.49890 + 3.62609i) q^{74} +(0.993498 - 0.378487i) q^{76} +(4.42859 + 2.55685i) q^{77} +(1.73014 - 0.998899i) q^{79} +(-12.3574 + 2.56136i) q^{80} +(-3.43221 + 1.63175i) q^{82} +(3.28016 + 5.68140i) q^{83} +(11.3996 - 19.7446i) q^{85} +(-0.571535 + 7.14643i) q^{86} +(4.05525 + 13.8836i) q^{88} +9.77920i q^{89} -4.76739i q^{91} +(6.30196 + 1.01448i) q^{92} +(4.16571 + 0.333152i) q^{94} +(-0.838566 + 1.45244i) q^{95} +(-6.15806 - 10.6661i) q^{97} +(0.607219 + 1.27722i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) $ 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.802493	+	1.16448i	−0.567448	+	0.823409i
$2$	−0.802493	+	1.16448i	−0.567448	+	0.823409i
$3$		0			0
$3$		0			0
$4$	−0.712009	−	1.86897i	−0.356005	−	0.934484i
$5$	2.73233	+	1.57751i	1.22193	+	0.705484i	0.965330	−	0.261033i	$-0.0840630\pi$
$5$	2.73233	+	1.57751i	1.22193	+	0.705484i	0.256604	+	0.966517i	$0.417396\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$	2.74775	+	0.670717i	0.971477	+	0.237134i
$9$		0			0
$10$	−4.02965	+	1.91579i	−1.27429	+	0.605826i
$11$	2.55685	+	4.42859i	0.770919	+	1.33527i	0.937060	+	0.349169i	$0.113536\pi$
$11$	2.55685	+	4.42859i	0.770919	+	1.33527i	−0.166141	+	0.986102i	$0.553131\pi$
$12$		0			0
$13$	2.38370	−	4.12868i	0.661118	−	1.14509i	−0.319204	−	0.947686i	$-0.603416\pi$
$13$	2.38370	−	4.12868i	0.661118	−	1.14509i	0.980322	−	0.197404i	$-0.0632511\pi$
$14$	−0.112741	+	1.40971i	−0.0301314	+	0.376762i
$15$		0			0
$16$	−2.98609	+	2.66145i	−0.746521	+	0.665361i
$17$		−	7.22631i		−	1.75264i	−0.481731	−	0.876319i	$-0.659992\pi$
$17$		−	7.22631i		−	1.75264i	0.481731	−	0.876319i	$-0.340008\pi$
$18$		0			0
$19$			0.531576i			0.121952i	0.998139	+	0.0609759i	$0.0194213\pi$
$19$			0.531576i			0.121952i	−0.998139	+	0.0609759i	$0.980579\pi$
$20$	1.00287	−	6.22984i	0.224249	−	1.39303i
$21$		0			0
$22$	−7.20884	−	0.576526i	−1.53693	−	0.122916i
$23$	−1.59577	+	2.76396i	−0.332742	+	0.576325i	−0.983048	−	0.183346i	$-0.941307\pi$
$23$	−1.59577	+	2.76396i	−0.332742	+	0.576325i	0.650307	+	0.759672i	$0.274640\pi$
$24$		0			0
$25$	2.47708	+	4.29042i	0.495415	+	0.858084i
$26$	2.89485	+	6.08899i	0.567727	+	1.19415i
$27$		0			0
$28$	−1.55110	−	1.26257i	−0.293131	−	0.238603i
$29$	1.50966	−	0.871600i	0.280336	−	0.161852i	−0.353240	−	0.935533i	$-0.614920\pi$
$29$	1.50966	−	0.871600i	0.280336	−	0.161852i	0.633575	+	0.773681i	$0.281587\pi$
$30$		0			0
$31$	−1.47432	−	0.851200i	−0.264796	−	0.152880i	0.361724	−	0.932285i	$-0.382188\pi$
$31$	−1.47432	−	0.851200i	−0.264796	−	0.152880i	−0.626520	+	0.779405i	$0.715521\pi$
$32$	−0.702876	−	5.61302i	−0.124252	−	0.992251i
$33$		0			0
$34$	8.41487	+	5.79907i	1.44314	+	0.994532i
$35$	3.15502			0.533296
$36$		0			0
$37$	3.11392			0.511926			0.255963	−	0.966687i	$-0.417608\pi$
$37$	3.11392			0.511926			0.255963	+	0.966687i	$0.417608\pi$
$38$	−0.619007	−	0.426586i	−0.100416	−	0.0692014i
$39$		0			0
$40$	6.44969	+	6.16722i	1.01979	+	0.975124i
$41$	2.32723	+	1.34363i	0.363452	+	0.209839i	0.670594	−	0.741825i	$-0.266039\pi$
$41$	2.32723	+	1.34363i	0.363452	+	0.209839i	−0.307142	+	0.951664i	$0.599373\pi$
$42$		0			0
$43$	4.39025	−	2.53471i	0.669507	−	0.386540i	−0.126383	−	0.991982i	$-0.540337\pi$
$43$	4.39025	−	2.53471i	0.669507	−	0.386540i	0.795890	+	0.605441i	$0.207003\pi$
$44$	6.45640	−	7.93187i	0.973339	−	1.19577i
$45$		0			0
$46$	−1.93797	−	4.07630i	−0.285738	−	0.601017i
$47$	−1.47750	−	2.55911i	−0.215516	−	0.373285i	0.737916	−	0.674892i	$-0.235810\pi$
$47$	−1.47750	−	2.55911i	−0.215516	−	0.373285i	−0.953432	+	0.301608i	$0.902477\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−6.98393	−	0.558538i	−0.987677	−	0.0789893i
$51$		0			0
$52$	−9.41359	−	1.51539i	−1.30543	−	0.210147i
$53$			13.6811i			1.87925i	0.342209	+	0.939624i	$0.388825\pi$
$53$			13.6811i			1.87925i	−0.342209	+	0.939624i	$0.611175\pi$
$54$		0			0
$55$			16.1338i			2.17548i
$56$	2.71498	−	0.793018i	0.362805	−	0.105971i
$57$		0			0
$58$	−0.196531	+	2.45741i	−0.0258058	+	0.322674i
$59$	−3.71140	+	6.42833i	−0.483183	+	0.836898i	−0.999814	−	0.0193107i	$-0.993853\pi$
$59$	−3.71140	+	6.42833i	−0.483183	+	0.836898i	0.516630	+	0.856209i	$0.327186\pi$
$60$		0			0
$61$	3.23838	+	5.60903i	0.414632	+	0.718163i	0.995390	−	0.0959130i	$-0.0305771\pi$
$61$	3.23838	+	5.60903i	0.414632	+	0.718163i	−0.580758	+	0.814076i	$0.697244\pi$
$62$	2.17433	−	1.03373i	0.276141	−	0.131284i
$63$		0			0
$64$	7.10028	+	3.68593i	0.887535	+	0.460741i
$65$	13.0261	−	7.52061i	1.61569	−	0.932816i
$66$		0			0
$67$	−1.72700	−	0.997087i	−0.210987	−	0.121814i	0.390783	−	0.920483i	$-0.372204\pi$
$67$	−1.72700	−	0.997087i	−0.210987	−	0.121814i	−0.601770	+	0.798669i	$0.705538\pi$
$68$	−13.5057	+	5.14520i	−1.63781	+	0.623947i
$69$		0			0
$70$	−2.53188	+	3.67395i	−0.302618	+	0.439120i
$71$	−13.0667			−1.55074			−0.775368	−	0.631509i	$-0.782436\pi$
$71$	−13.0667			−1.55074			−0.775368	+	0.631509i	$0.782436\pi$
$72$		0			0
$73$	−6.59684			−0.772101			−0.386051	−	0.922478i	$-0.626161\pi$
$73$	−6.59684			−0.772101			−0.386051	+	0.922478i	$0.626161\pi$
$74$	−2.49890	+	3.62609i	−0.290491	+	0.421524i
$75$		0			0
$76$	0.993498	−	0.378487i	0.113962	−	0.0434154i
$77$	4.42859	+	2.55685i	0.504685	+	0.291380i
$78$		0			0
$79$	1.73014	−	0.998899i	0.194656	−	0.112385i	−0.399504	−	0.916731i	$-0.630818\pi$
$79$	1.73014	−	0.998899i	0.194656	−	0.112385i	0.594161	+	0.804346i	$0.297484\pi$
$80$	−12.3574	+	2.56136i	−1.38160	+	0.286369i
$81$		0			0
$82$	−3.43221	+	1.63175i	−0.379024	+	0.180197i
$83$	3.28016	+	5.68140i	0.360044	+	0.623615i	0.987968	−	0.154660i	$-0.0494282\pi$
$83$	3.28016	+	5.68140i	0.360044	+	0.623615i	−0.627923	+	0.778275i	$0.716095\pi$
$84$		0			0
$85$	11.3996	−	19.7446i	1.23646	−	2.14161i
$86$	−0.571535	+	7.14643i	−0.0616302	+	0.770620i
$87$		0			0
$88$	4.05525	+	13.8836i	0.432292	+	1.48000i
$89$			9.77920i			1.03659i	0.855201	+	0.518297i	$0.173434\pi$
$89$			9.77920i			1.03659i	−0.855201	+	0.518297i	$0.826566\pi$
$90$		0			0
$91$		−	4.76739i		−	0.499758i
$92$	6.30196	+	1.01448i	0.657025	+	0.105767i
$93$		0			0
$94$	4.16571	+	0.333152i	0.429660	+	0.0343620i
$95$	−0.838566	+	1.45244i	−0.0860350	+	0.149017i
$96$		0			0
$97$	−6.15806	−	10.6661i	−0.625257	−	1.08298i	−0.988491	−	0.151279i	$-0.951661\pi$
$97$	−6.15806	−	10.6661i	−0.625257	−	1.08298i	0.363234	−	0.931698i	$-0.381672\pi$
$98$	0.607219	+	1.27722i	0.0613384	+	0.129018i
$99$		0			0
$100$	6.25496	−	7.68439i	0.625496	−	0.768439i
$101$	3.16824	−	1.82918i	0.315251	−	0.182010i	−0.334023	−	0.942565i	$-0.608406\pi$
$101$	3.16824	−	1.82918i	0.315251	−	0.182010i	0.649274	+	0.760555i	$0.275073\pi$
$102$		0			0
$103$	2.62116	+	1.51333i	0.258270	+	0.149112i	0.623545	−	0.781787i	$-0.285692\pi$
$103$	2.62116	+	1.51333i	0.258270	+	0.149112i	−0.365275	+	0.930900i	$0.619025\pi$
$104$	9.31898	−	9.74581i	0.913801	−	0.955655i
$105$		0			0
$106$	−15.9314	−	10.9790i	−1.54739	−	1.06638i
$107$	4.00810			0.387478			0.193739	−	0.981053i	$-0.437939\pi$
$107$	4.00810			0.387478			0.193739	+	0.981053i	$0.437939\pi$
$108$		0			0
$109$	−1.58898			−0.152197			−0.0760984	−	0.997100i	$-0.524246\pi$
$109$	−1.58898			−0.152197			−0.0760984	+	0.997100i	$0.524246\pi$
$110$	−18.7874	−	12.9473i	−1.79131	−	1.23447i
$111$		0			0
$112$	−1.25530	+	3.79792i	−0.118615	+	0.358870i
$113$	−5.56042	−	3.21031i	−0.523080	−	0.302001i	0.215114	−	0.976589i	$-0.430988\pi$
$113$	−5.56042	−	3.21031i	−0.523080	−	0.302001i	−0.738194	+	0.674588i	$0.764321\pi$
$114$		0			0
$115$	−8.72035	+	5.03470i	−0.813177	+	0.469488i
$116$	−2.70388	−	2.20091i	−0.251049	−	0.204349i
$117$		0			0
$118$	−4.50727	−	9.48053i	−0.414928	−	0.872754i
$119$	−3.61316	−	6.25817i	−0.331217	−	0.573685i
$120$		0			0
$121$	−7.57496	+	13.1202i	−0.688632	+	1.19275i
$122$	−9.13036	−	0.730199i	−0.826624	−	0.0661091i
$123$		0			0
$124$	−0.541135	+	3.36152i	−0.0485954	+	0.301874i
$125$		−	0.144654i		−	0.0129383i
$126$		0			0
$127$			5.15607i			0.457527i	0.973482	+	0.228764i	$0.0734683\pi$
$127$			5.15607i			0.457527i	−0.973482	+	0.228764i	$0.926532\pi$
$128$	−9.99010	+	5.31017i	−0.883008	+	0.469357i
$129$		0			0
$130$	−1.69577	+	21.2038i	−0.148729	+	1.85969i
$131$	7.48154	−	12.9584i	0.653666	−	1.13218i	−0.328561	−	0.944483i	$-0.606564\pi$
$131$	7.48154	−	12.9584i	0.653666	−	1.13218i	0.982227	−	0.187699i	$-0.0601030\pi$
$132$		0			0
$133$	0.265788	+	0.460358i	0.0230467	+	0.0399181i
$134$	2.54699	−	1.21090i	0.220027	−	0.104606i
$135$		0			0
$136$	4.84681	−	19.8561i	0.415610	−	1.70265i
$137$	−0.472178	+	0.272612i	−0.0403409	+	0.0232908i	−0.520035	−	0.854145i	$-0.674081\pi$
$137$	−0.472178	+	0.272612i	−0.0403409	+	0.0232908i	0.479694	+	0.877436i	$0.340748\pi$
$138$		0			0
$139$	−8.99978	−	5.19603i	−0.763351	−	0.440721i	0.0671463	−	0.997743i	$-0.478611\pi$
$139$	−8.99978	−	5.19603i	−0.763351	−	0.440721i	−0.830498	+	0.557022i	$0.811944\pi$
$140$	−2.24640	−	5.89663i	−0.189856	−	0.498356i
$141$		0			0
$142$	10.4860	−	15.2159i	0.879963	−	1.27689i
$143$	24.3790			2.03867
$144$		0			0
$145$	5.49983			0.456736
$146$	5.29392	−	7.68186i	0.438128	−	0.635755i
$147$		0			0
$148$	−2.21714	−	5.81982i	−0.182248	−	0.478387i
$149$	−11.1828	−	6.45637i	−0.916127	−	0.528926i	−0.0337298	−	0.999431i	$-0.510739\pi$
$149$	−11.1828	−	6.45637i	−0.916127	−	0.528926i	−0.882398	+	0.470505i	$0.844072\pi$
$150$		0			0
$151$	2.78931	−	1.61041i	0.226991	−	0.131053i	−0.382192	−	0.924083i	$-0.624831\pi$
$151$	2.78931	−	1.61041i	0.226991	−	0.131053i	0.609183	+	0.793030i	$0.291497\pi$
$152$	−0.356537	+	1.46064i	−0.0289189	+	0.118473i
$153$		0			0
$154$	−6.53131	+	3.10514i	−0.526308	+	0.250219i
$155$	−2.68555	−	4.65151i	−0.215709	−	0.373618i
$156$		0			0
$157$	3.13601	−	5.43172i	0.250281	−	0.433499i	−0.713322	−	0.700836i	$-0.752810\pi$
$157$	3.13601	−	5.43172i	0.250281	−	0.433499i	0.963603	+	0.267337i	$0.0861438\pi$
$158$	−0.225235	+	2.81632i	−0.0179187	+	0.224054i
$159$		0			0
$160$	6.93410	−	16.4454i	0.548189	−	1.30012i
$161$			3.19155i			0.251529i
$162$		0			0
$163$			17.5965i			1.37826i	0.724636	+	0.689132i	$0.242008\pi$
$163$			17.5965i			1.37826i	−0.724636	+	0.689132i	$0.757992\pi$
$164$	0.854187	−	5.30619i	0.0667008	−	0.414344i
$165$		0			0
$166$	−9.24816	−	0.739620i	−0.717797	−	0.0574057i
$167$	−1.40973	+	2.44173i	−0.109088	+	0.188946i	−0.915401	−	0.402543i	$-0.868126\pi$
$167$	−1.40973	+	2.44173i	−0.109088	+	0.188946i	0.806313	+	0.591489i	$0.201460\pi$
$168$		0			0
$169$	−4.86401	−	8.42471i	−0.374154	−	0.648054i
$170$	13.8441	+	29.1195i	1.06179	+	2.23336i
$171$		0			0
$172$	−7.86320	−	6.40050i	−0.599563	−	0.488034i
$173$	−3.41022	+	1.96889i	−0.259274	+	0.149692i	−0.624003	−	0.781422i	$-0.714495\pi$
$173$	−3.41022	+	1.96889i	−0.259274	+	0.149692i	0.364729	+	0.931114i	$0.381162\pi$
$174$		0			0
$175$	4.29042	+	2.47708i	0.324325	+	0.187249i
$176$	−19.4214	−	6.41924i	−1.46395	−	0.483869i
$177$		0			0
$178$	−11.3876	−	7.84774i	−0.853540	−	0.588213i
$179$	−1.19273			−0.0891491			−0.0445746	−	0.999006i	$-0.514193\pi$
$179$	−1.19273			−0.0891491			−0.0445746	+	0.999006i	$0.514193\pi$
$180$		0			0
$181$	−0.516134			−0.0383639			−0.0191820	−	0.999816i	$-0.506106\pi$
$181$	−0.516134			−0.0383639			−0.0191820	+	0.999816i	$0.506106\pi$
$182$	5.55151	+	3.82580i	0.411505	+	0.283587i
$183$		0			0
$184$	−6.23862	+	6.52436i	−0.459917	+	0.480982i
$185$	8.50826	+	4.91224i	0.625540	+	0.361155i
$186$		0			0
$187$	32.0024	−	18.4766i	2.34025	−	1.35114i
$188$	−3.73090	+	4.58352i	−0.272104	+	0.334287i
$189$		0			0
$190$	−1.01839	−	2.14206i	−0.0738815	−	0.155402i
$191$	−13.1346	−	22.7498i	−0.950385	−	1.64611i	−0.744593	−	0.667518i	$-0.767357\pi$
$191$	−13.1346	−	22.7498i	−0.950385	−	1.64611i	−0.205791	−	0.978596i	$-0.565977\pi$
$192$		0			0
$193$	8.21149	−	14.2227i	0.591076	−	1.02377i	−0.403012	−	0.915195i	$-0.632037\pi$
$193$	8.21149	−	14.2227i	0.591076	−	1.02377i	0.994088	−	0.108579i	$-0.0346300\pi$
$194$	17.3622	+	1.38854i	1.24653	+	0.0996913i
$195$		0			0
$196$	−1.97458	−	0.317866i	−0.141041	−	0.0227047i
$197$		−	5.79981i		−	0.413219i	−0.978423	−	0.206610i	$-0.933757\pi$
$197$		−	5.79981i		−	0.413219i	0.978423	−	0.206610i	$-0.0662430\pi$
$198$		0			0
$199$		−	25.1918i		−	1.78580i	−0.450253	−	0.892901i	$-0.648666\pi$
$199$		−	25.1918i		−	1.78580i	0.450253	−	0.892901i	$-0.351334\pi$
$200$	3.92873	+	13.4504i	0.277803	+	0.951089i
$201$		0			0
$202$	−0.412450	+	5.15724i	−0.0290198	+	0.362862i
$203$	0.871600	−	1.50966i	0.0611743	−	0.105957i
$204$		0			0
$205$	4.23917	+	7.34245i	0.296076	+	0.512819i
$206$	−3.86569	+	1.83784i	−0.269335	+	0.128048i
$207$		0			0
$208$	3.87034	+	18.6727i	0.268360	+	1.29472i
$209$	−2.35413	+	1.35916i	−0.162839	+	0.0940150i
$210$		0			0
$211$	−12.6040	−	7.27691i	−0.867694	−	0.500963i	−0.00111255	−	0.999999i	$-0.500354\pi$
$211$	−12.6040	−	7.27691i	−0.867694	−	0.500963i	−0.866581	+	0.499036i	$0.833687\pi$
$212$	25.5696	−	9.74109i	1.75613	−	0.669021i
$213$		0			0
$214$	−3.21647	+	4.66734i	−0.219874	+	0.319053i
$215$	15.9941			1.09079
$216$		0			0
$217$	−1.70240			−0.115566
$218$	1.27515	−	1.85033i	0.0863638	−	0.125320i
$219$		0			0
$220$	30.1536	−	11.4874i	2.03296	−	0.774482i
$221$	−29.8351	−	17.2253i	−2.00693	−	1.15870i
$222$		0			0
$223$	13.1948	−	7.61804i	0.883591	−	0.510141i	0.0117502	−	0.999931i	$-0.496260\pi$
$223$	13.1948	−	7.61804i	0.883591	−	0.510141i	0.871841	+	0.489789i	$0.162926\pi$
$224$	−3.41522	−	4.50958i	−0.228189	−	0.301309i
$225$		0			0
$226$	8.20053	−	3.89872i	0.545491	−	0.259339i
$227$	−2.90472	−	5.03112i	−0.192793	−	0.333927i	0.753382	−	0.657583i	$-0.228421\pi$
$227$	−2.90472	−	5.03112i	−0.192793	−	0.333927i	−0.946175	+	0.323656i	$0.895088\pi$
$228$		0			0
$229$	−7.47034	+	12.9390i	−0.493654	+	0.855034i	−0.999973	−	0.00731207i	$-0.997672\pi$
$229$	−7.47034	+	12.9390i	−0.493654	+	0.855034i	0.506319	+	0.862346i	$0.331006\pi$
$230$	1.13524	−	14.1949i	0.0748554	−	0.935987i
$231$		0			0
$232$	4.73275	−	1.38239i	0.310721	−	0.0907583i
$233$		−	0.536725i		−	0.0351620i	−0.999845	−	0.0175810i	$-0.994404\pi$
$233$		−	0.536725i		−	0.0351620i	0.999845	−	0.0175810i	$-0.00559649\pi$
$234$		0			0
$235$		−	9.32310i		−	0.608172i
$236$	14.6569	+	2.35946i	0.954083	+	0.153588i
$237$		0			0
$238$	10.1870	+	0.814705i	0.660327	+	0.0528095i
$239$	−10.0017	+	17.3234i	−0.646956	+	1.12056i	0.336890	+	0.941544i	$0.390625\pi$
$239$	−10.0017	+	17.3234i	−0.646956	+	1.12056i	−0.983846	+	0.179017i	$0.942708\pi$
$240$		0			0
$241$	8.07407	+	13.9847i	0.520096	+	0.900833i	0.999727	+	0.0233628i	$0.00743728\pi$
$241$	8.07407	+	13.9847i	0.520096	+	0.900833i	−0.479631	+	0.877470i	$0.659229\pi$
$242$	−9.19932	−	19.3497i	−0.591355	−	1.24385i
$243$		0			0
$244$	8.17735	−	10.0461i	0.523501	−	0.643136i
$245$	2.73233	−	1.57751i	0.174562	−	0.100783i
$246$		0			0
$247$	2.19471	+	1.26711i	0.139646	+	0.0806246i
$248$	−3.48015	−	3.32774i	−0.220990	−	0.211312i
$249$		0			0
$250$	0.168446	+	0.116084i	0.0106535	+	0.00734180i
$251$	−25.4053			−1.60357			−0.801785	−	0.597613i	$-0.796116\pi$
$251$	−25.4053			−1.60357			−0.801785	+	0.597613i	$0.796116\pi$
$252$		0			0
$253$	−16.3206			−1.02607
$254$	−6.00412	−	4.13771i	−0.376732	−	0.259623i
$255$		0			0
$256$	1.83342	−	15.8946i	0.114589	−	0.993413i
$257$	5.65981	+	3.26769i	0.353049	+	0.203833i	0.666027	−	0.745927i	$-0.267993\pi$
$257$	5.65981	+	3.26769i	0.353049	+	0.203833i	−0.312978	+	0.949760i	$0.601327\pi$
$258$		0			0
$259$	2.69674	−	1.55696i	0.167567	−	0.0967449i
$260$	−23.3305	−	18.9906i	−1.44689	−	1.17775i
$261$		0			0
$262$	9.08588	+	19.1111i	0.561327	+	1.18069i
$263$	2.54968	+	4.41617i	0.157220	+	0.272313i	0.933865	−	0.357625i	$-0.116414\pi$
$263$	2.54968	+	4.41617i	0.157220	+	0.272313i	−0.776645	+	0.629938i	$0.783080\pi$
$264$		0			0
$265$	−21.5821	+	37.3813i	−1.32578	+	2.29632i
$266$	−0.749369	−	0.0599306i	−0.0459468	−	0.00367458i
$267$		0			0
$268$	−0.633880	+	3.93765i	−0.0387204	+	0.240530i
$269$		−	23.1813i		−	1.41339i	−0.707519	−	0.706694i	$-0.750186\pi$
$269$		−	23.1813i		−	1.41339i	0.707519	−	0.706694i	$-0.249814\pi$
$270$		0			0
$271$			3.33548i			0.202616i	0.994855	+	0.101308i	$0.0323027\pi$
$271$			3.33548i			0.202616i	−0.994855	+	0.101308i	$0.967697\pi$
$272$	19.2324	+	21.5784i	1.16614	+	1.30838i
$273$		0			0
$274$	0.0614694	−	0.768609i	0.00371350	−	0.0464334i
$275$	−12.6670	+	21.9399i	−0.763850	+	1.32303i
$276$		0			0
$277$	−6.01165	−	10.4125i	−0.361205	−	0.625625i	0.626954	−	0.779056i	$-0.284301\pi$
$277$	−6.01165	−	10.4125i	−0.361205	−	0.625625i	−0.988159	+	0.153430i	$0.950968\pi$
$278$	13.2729	−	6.31025i	0.796056	−	0.378464i
$279$		0			0
$280$	8.66921	+	2.11613i	0.518084	+	0.126463i
$281$	−16.0334	+	9.25689i	−0.956472	+	0.552220i	−0.895086	−	0.445894i	$-0.852886\pi$
$281$	−16.0334	+	9.25689i	−0.956472	+	0.552220i	−0.0613869	+	0.998114i	$0.519552\pi$
$282$		0			0
$283$	−18.7908	−	10.8489i	−1.11700	−	0.644899i	−0.176365	−	0.984325i	$-0.556434\pi$
$283$	−18.7908	−	10.8489i	−1.11700	−	0.644899i	−0.940633	+	0.339426i	$0.889767\pi$
$284$	9.30364	+	24.4213i	0.552069	+	1.44914i
$285$		0			0
$286$	−19.5640	+	28.3888i	−1.15684	+	1.67866i
$287$	2.68725			0.158624
$288$		0			0
$289$	−35.2196			−2.07174
$290$	−4.41358	+	6.40442i	−0.259174	+	0.376081i
$291$		0			0
$292$	4.69701	+	12.3293i	0.274872	+	0.721517i
$293$	11.5943	+	6.69399i	0.677348	+	0.391067i	0.798855	−	0.601524i	$-0.205439\pi$
$293$	11.5943	+	6.69399i	0.677348	+	0.391067i	−0.121507	+	0.992591i	$0.538773\pi$
$294$		0			0
$295$	−20.2815	+	11.7095i	−1.18084	+	0.681756i
$296$	8.55629	+	2.08856i	0.497324	+	0.121395i
$297$		0			0
$298$	16.4924	−	7.84086i	0.955378	−	0.454209i
$299$	7.60767	+	13.1769i	0.439963	+	0.762038i
$300$		0			0
$301$	2.53471	−	4.39025i	0.146098	−	0.253050i
$302$	−0.363120	+	4.54043i	−0.0208952	+	0.261272i
$303$		0			0
$304$	−1.41476	−	1.58733i	−0.0811420	−	0.0910396i
$305$			20.4343i			1.17006i
$306$		0			0
$307$			14.9315i			0.852187i	0.904679	+	0.426093i	$0.140111\pi$
$307$			14.9315i			0.852187i	−0.904679	+	0.426093i	$0.859889\pi$
$308$	1.62547	−	10.0974i	0.0926198	−	0.575353i
$309$		0			0
$310$	7.57171	+	0.605546i	0.430044	+	0.0343927i
$311$	3.83776	−	6.64720i	0.217619	−	0.376928i	−0.736460	−	0.676481i	$-0.763504\pi$
$311$	3.83776	−	6.64720i	0.217619	−	0.376928i	0.954080	+	0.299553i	$0.0968375\pi$
$312$		0			0
$313$	11.6398	+	20.1608i	0.657923	+	1.13956i	0.981152	+	0.193236i	$0.0618982\pi$
$313$	11.6398	+	20.1608i	0.657923	+	1.13956i	−0.323229	+	0.946321i	$0.604768\pi$
$314$	3.80849	+	8.01072i	0.214925	+	0.452071i
$315$		0			0
$316$	−3.09879	−	2.52236i	−0.174320	−	0.141894i
$317$	−23.4749	+	13.5533i	−1.31848	+	0.761226i	−0.983485	−	0.180992i	$-0.942069\pi$
$317$	−23.4749	+	13.5533i	−1.31848	+	0.761226i	−0.334998	+	0.942219i	$0.608736\pi$
$318$		0			0
$319$	7.71992	+	4.45710i	0.432233	+	0.249550i
$320$	13.5857	+	21.2719i	0.759464	+	1.18914i
$321$		0			0
$322$	−3.71648	−	2.56119i	−0.207111	−	0.142730i
$323$	3.84133			0.213737
$324$		0			0
$325$	23.6184			1.31011
$326$	−20.4907	−	14.1211i	−1.13488	−	0.782094i
$327$		0			0
$328$	5.49345	+	5.25286i	0.303325	+	0.290041i
$329$	−2.55911	−	1.47750i	−0.141088	−	0.0814574i
$330$		0			0
$331$	−15.5271	+	8.96456i	−0.853445	+	0.492737i	−0.861812	−	0.507228i	$-0.830670\pi$
$331$	−15.5271	+	8.96456i	−0.853445	+	0.492737i	0.00836643	+	0.999965i	$0.497337\pi$
$332$	8.28286	−	10.1757i	0.454581	−	0.558466i
$333$		0			0
$334$	−1.71203	−	3.60107i	−0.0936782	−	0.197042i
$335$	−3.14583	−	5.44873i	−0.171875	−	0.297696i
$336$		0			0
$337$	−3.33464	+	5.77577i	−0.181650	+	0.314626i	−0.942442	−	0.334368i	$-0.891477\pi$
$337$	−3.33464	+	5.77577i	−0.181650	+	0.314626i	0.760793	+	0.648995i	$0.224810\pi$
$338$	13.7137	+	1.09675i	0.745927	+	0.0596554i
$339$		0			0
$340$	−45.0187	−	7.24708i	−2.44148	−	0.393028i
$341$		−	8.70556i		−	0.471432i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	13.7634	−	4.02015i	0.742073	−	0.216752i
$345$		0			0
$346$	0.443951	−	5.55114i	0.0238670	−	0.298431i
$347$	15.7139	−	27.2173i	0.843568	−	1.46110i	−0.0432902	−	0.999063i	$-0.513784\pi$
$347$	15.7139	−	27.2173i	0.843568	−	1.46110i	0.886859	−	0.462041i	$-0.152883\pi$
$348$		0			0
$349$	−3.17117	−	5.49263i	−0.169749	−	0.294014i	0.768583	−	0.639751i	$-0.220962\pi$
$349$	−3.17117	−	5.49263i	−0.169749	−	0.294014i	−0.938332	+	0.345737i	$0.887629\pi$
$350$	−6.32753	+	3.00826i	−0.338221	+	0.160798i
$351$		0			0
$352$	23.0606	−	17.4644i	1.22914	−	0.930855i
$353$	−22.5568	+	13.0232i	−1.20058	+	0.693155i	−0.960684	−	0.277644i	$-0.910447\pi$
$353$	−22.5568	+	13.0232i	−1.20058	+	0.693155i	−0.239896	+	0.970799i	$0.577113\pi$
$354$		0			0
$355$	−35.7026	−	20.6129i	−1.89490	−	1.09402i
$356$	18.2770	−	6.96288i	0.968680	−	0.369032i
$357$		0			0
$358$	0.957161	−	1.38891i	0.0505875	−	0.0734062i
$359$	−31.2925			−1.65156			−0.825778	−	0.563996i	$-0.809263\pi$
$359$	−31.2925			−1.65156			−0.825778	+	0.563996i	$0.809263\pi$
$360$		0			0
$361$	18.7174			0.985128
$362$	0.414194	−	0.601025i	0.0217695	−	0.0315892i
$363$		0			0
$364$	−8.91010	+	3.39443i	−0.467016	+	0.177916i
$365$	−18.0247	−	10.4066i	−0.943457	−	0.544705i
$366$		0			0
$367$	19.3046	−	11.1455i	1.00769	−	0.581792i	0.0971776	−	0.995267i	$-0.469019\pi$
$367$	19.3046	−	11.1455i	1.00769	−	0.581792i	0.910515	+	0.413475i	$0.135685\pi$
$368$	−2.59101	−	12.5005i	−0.135066	−	0.651633i
$369$		0			0
$370$	−12.5480	+	5.96562i	−0.652340	+	0.310138i
$371$	6.84057	+	11.8482i	0.355144	+	0.615128i
$372$		0			0
$373$	9.29840	−	16.1053i	0.481453	−	0.833901i	−0.518321	−	0.855186i	$-0.673443\pi$
$373$	9.29840	−	16.1053i	0.481453	−	0.833901i	0.999773	+	0.0212856i	$0.00677594\pi$
$374$	−4.16616	+	52.0934i	−0.215427	+	2.69368i
$375$		0			0
$376$	−2.34337	−	8.02279i	−0.120850	−	0.413744i
$377$		−	8.31051i		−	0.428013i
$378$		0			0
$379$			21.2022i			1.08908i	0.838733	+	0.544542i	$0.183297\pi$
$379$			21.2022i			1.08908i	−0.838733	+	0.544542i	$0.816703\pi$
$380$	3.31163	+	0.533103i	0.169883	+	0.0273476i
$381$		0			0
$382$	37.0320	+	2.96162i	1.89472	+	0.151530i
$383$	5.85031	−	10.1330i	0.298937	−	0.517774i	−0.676956	−	0.736023i	$-0.736701\pi$
$383$	5.85031	−	10.1330i	0.298937	−	0.517774i	0.975893	+	0.218250i	$0.0700347\pi$
$384$		0			0
$385$	8.06691	+	13.9723i	0.411128	+	0.712094i
$386$	9.97235	+	20.9757i	0.507579	+	1.06764i
$387$		0			0
$388$	−15.5500	+	19.1036i	−0.789430	+	0.969837i
$389$	20.6139	−	11.9014i	1.04517	−	0.603427i	0.123874	−	0.992298i	$-0.460468\pi$
$389$	20.6139	−	11.9014i	1.04517	−	0.603427i	0.921292	+	0.388871i	$0.127135\pi$
$390$		0			0
$391$	19.9732	+	11.5316i	1.01009	+	0.583176i
$392$	1.95473	−	2.04426i	0.0987290	−	0.103251i
$393$		0			0
$394$	6.75374	+	4.65431i	0.340249	+	0.234481i
$395$	6.30309			0.317143
$396$		0			0
$397$	−9.08225			−0.455825			−0.227912	−	0.973682i	$-0.573190\pi$
$397$	−9.08225			−0.455825			−0.227912	+	0.973682i	$0.573190\pi$
$398$	29.3353	+	20.2163i	1.47045	+	1.01335i
$399$		0			0
$400$	−18.8155	−	6.21896i	−0.940774	−	0.310948i
$401$	22.6865	+	13.0981i	1.13291	+	0.654087i	0.944666	−	0.328035i	$-0.106386\pi$
$401$	22.6865	+	13.0981i	1.13291	+	0.654087i	0.188246	+	0.982122i	$0.439720\pi$
$402$		0			0
$403$	−7.02866	+	4.05800i	−0.350123	+	0.202143i
$404$	−5.67450	−	4.61894i	−0.282317	−	0.229801i
$405$		0			0
$406$	1.05850	+	2.22645i	0.0525327	+	0.110497i
$407$	7.96183	+	13.7903i	0.394653	+	0.683560i
$408$		0			0
$409$	−4.62676	+	8.01379i	−0.228779	+	0.396256i	−0.957446	−	0.288611i	$-0.906807\pi$
$409$	−4.62676	+	8.01379i	−0.228779	+	0.396256i	0.728668	+	0.684867i	$0.240140\pi$
$410$	−11.9520	−	0.955860i	−0.590268	−	0.0472066i
$411$		0			0
$412$	0.962070	−	5.97636i	0.0473978	−	0.294434i
$413$			7.42280i			0.365252i
$414$		0			0
$415$			20.6979i			1.01602i
$416$	−24.8498	−	10.4778i	−1.21836	−	0.513715i
$417$		0			0
$418$	0.306467	−	3.83205i	0.0149898	−	0.187432i
$419$	14.3147	−	24.7937i	0.699317	−	1.21125i	−0.269387	−	0.963032i	$-0.586821\pi$
$419$	14.3147	−	24.7937i	0.699317	−	1.21125i	0.968704	−	0.248220i	$-0.0798457\pi$
$420$		0			0
$421$	−6.82164	−	11.8154i	−0.332466	−	0.575849i	0.650528	−	0.759482i	$-0.274547\pi$
$421$	−6.82164	−	11.8154i	−0.332466	−	0.575849i	−0.982995	+	0.183633i	$0.941214\pi$
$422$	18.5884	−	8.83736i	0.904869	−	0.430196i
$423$		0			0
$424$	−9.17617	+	37.5924i	−0.445634	+	1.82565i
$425$	31.0039	−	17.9001i	1.50391	−	0.868283i
$426$		0			0
$427$	5.60903	+	3.23838i	0.271440	+	0.156716i
$428$	−2.85380	−	7.49101i	−0.137944	−	0.362092i
$429$		0			0
$430$	−12.8352	+	18.6248i	−0.618968	+	0.898167i
$431$	−11.9995			−0.577994			−0.288997	−	0.957330i	$-0.593322\pi$
$431$	−11.9995			−0.577994			−0.288997	+	0.957330i	$0.593322\pi$
$432$		0			0
$433$	18.6726			0.897349			0.448674	−	0.893695i	$-0.351896\pi$
$433$	18.6726			0.897349			0.448674	+	0.893695i	$0.351896\pi$
$434$	1.36616	−	1.98240i	0.0655780	−	0.0951584i
$435$		0			0
$436$	1.13137	+	2.96975i	0.0541827	+	0.142225i
$437$	−1.46925	−	0.848274i	−0.0702839	−	0.0405784i
$438$		0			0
$439$	−22.6620	+	13.0839i	−1.08160	+	0.624461i	−0.931327	−	0.364184i	$-0.881348\pi$
$439$	−22.6620	+	13.0839i	−1.08160	+	0.624461i	−0.150271	+	0.988645i	$0.548015\pi$
$440$	−10.8212	+	44.3317i	−0.515882	+	2.11343i
$441$		0			0
$442$	44.0010	−	20.9191i	2.09291	−	0.995020i
$443$	17.3363	+	30.0273i	0.823671	+	1.42664i	0.902931	+	0.429786i	$0.141411\pi$
$443$	17.3363	+	30.0273i	0.823671	+	1.42664i	−0.0792601	+	0.996854i	$0.525256\pi$
$444$		0			0
$445$	−15.4268	+	26.7200i	−0.731300	+	1.26665i
$446$	−1.71774	+	21.4785i	−0.0813372	+	1.01704i
$447$		0			0
$448$	7.99198	−	0.358033i	0.377586	−	0.0169155i
$449$		−	14.5939i		−	0.688731i	−0.938836	−	0.344365i	$-0.888094\pi$
$449$		−	14.5939i		−	0.688731i	0.938836	−	0.344365i	$-0.111906\pi$
$450$		0			0
$451$			13.7418i			0.647076i
$452$	−2.04090	+	12.6780i	−0.0959958	+	0.596324i
$453$		0			0
$454$	8.18963	+	0.654964i	0.384358	+	0.0307390i
$455$	7.52061	−	13.0261i	0.352571	−	0.610672i
$456$		0			0
$457$	0.0109808	+	0.0190193i	0.000513661	+	0.000889687i	0.866282	−	0.499555i	$-0.166503\pi$
$457$	0.0109808	+	0.0190193i	0.000513661	+	0.000889687i	−0.865768	+	0.500445i	$0.833170\pi$
$458$	−9.07227	−	19.0825i	−0.423919	−	0.891667i
$459$		0			0
$460$	15.6187	+	12.7133i	0.728224	+	0.592761i
$461$	−7.01426	+	4.04969i	−0.326687	+	0.188613i	−0.654369	−	0.756175i	$-0.727066\pi$
$461$	−7.01426	+	4.04969i	−0.326687	+	0.188613i	0.327682	+	0.944788i	$0.393732\pi$
$462$		0			0
$463$	−27.8853	−	16.0996i	−1.29594	−	0.748211i	−0.316239	−	0.948680i	$-0.602420\pi$
$463$	−27.8853	−	16.0996i	−1.29594	−	0.748211i	−0.979700	+	0.200469i	$0.935753\pi$
$464$	−2.18824	+	6.62054i	−0.101587	+	0.307351i
$465$		0			0
$466$	0.625003	+	0.430718i	0.0289527	+	0.0199526i
$467$	11.6187			0.537648			0.268824	−	0.963189i	$-0.413365\pi$
$467$	11.6187			0.537648			0.268824	+	0.963189i	$0.413365\pi$
$468$		0			0
$469$	−1.99417			−0.0920824
$470$	10.8565	+	7.48173i	0.500774	+	0.345106i
$471$		0			0
$472$	−14.5096	+	15.1742i	−0.667858	+	0.698448i
$473$	22.4504	+	12.9618i	1.03227	+	0.595982i
$474$		0			0
$475$	−2.28068	+	1.31675i	−0.104645	+	0.0604168i
$476$	−9.12372	+	11.2087i	−0.418185	+	0.513752i
$477$		0			0
$478$	−12.1464	−	25.5487i	−0.555566	−	1.16857i
$479$	−3.05275	−	5.28752i	−0.139484	−	0.241593i	0.787818	−	0.615909i	$-0.211211\pi$
$479$	−3.05275	−	5.28752i	−0.139484	−	0.241593i	−0.927301	+	0.374316i	$0.877878\pi$
$480$		0			0
$481$	7.42264	−	12.8564i	0.338443	−	0.586201i
$482$	−22.7642	−	1.82056i	−1.03688	−	0.0829244i
$483$		0			0
$484$	29.9147	+	4.81564i	1.35976	+	0.218893i
$485$		−	38.8576i		−	1.76443i
$486$		0			0
$487$		−	18.6740i		−	0.846201i	−0.906083	−	0.423100i	$-0.860942\pi$
$487$		−	18.6740i		−	0.846201i	0.906083	−	0.423100i	$-0.139058\pi$
$488$	5.13618	+	17.5843i	0.232504	+	0.796002i
$489$		0			0
$490$	−0.355702	+	4.44767i	−0.0160690	+	0.200925i
$491$	−1.67975	+	2.90941i	−0.0758060	+	0.131300i	−0.901437	−	0.432911i	$-0.857486\pi$
$491$	−1.67975	+	2.90941i	−0.0758060	+	0.131300i	0.825630	+	0.564211i	$0.190820\pi$
$492$		0			0
$493$	−6.29845	−	10.9092i	−0.283668	−	0.491327i
$494$	−3.23676	+	1.53883i	−0.145629	+	0.0692353i
$495$		0			0
$496$	6.66787	−	1.38207i	0.299396	−	0.0620568i
$497$	−11.3161	+	6.53337i	−0.507598	+	0.293062i
$498$		0			0
$499$	37.5927	+	21.7041i	1.68288	+	0.971610i	0.959733	+	0.280915i	$0.0906378\pi$
$499$	37.5927	+	21.7041i	1.68288	+	0.971610i	0.723146	+	0.690696i	$0.242696\pi$
$500$	−0.270354	+	0.102995i	−0.0120906	+	0.00460608i
$501$		0			0
$502$	20.3876	−	29.5839i	0.909943	−	1.32039i
$503$	7.34385			0.327446			0.163723	−	0.986506i	$-0.447650\pi$
$503$	7.34385			0.327446			0.163723	+	0.986506i	$0.447650\pi$
$504$		0			0
$505$	11.5422			0.513622
$506$	13.0972	−	19.0050i	0.582240	−	0.844873i
$507$		0			0
$508$	9.63653	−	3.67117i	0.427552	−	0.162882i
$509$	−7.79196	−	4.49869i	−0.345372	−	0.199401i	0.317273	−	0.948334i	$-0.397233\pi$
$509$	−7.79196	−	4.49869i	−0.345372	−	0.199401i	−0.662645	+	0.748933i	$0.730566\pi$
$510$		0			0
$511$	−5.71303	+	3.29842i	−0.252730	+	0.145913i
$512$	17.0376	+	14.8903i	0.752962	+	0.658064i
$513$		0			0
$514$	−8.34710	+	3.96841i	−0.368175	+	0.175039i
$515$	4.77457	+	8.26980i	0.210393	+	0.364411i
$516$		0			0
$517$	7.55551	−	13.0865i	0.332291	−	0.575544i
$518$	−0.351068	+	4.38974i	−0.0154251	+	0.192874i
$519$		0			0
$520$	40.8366	−	11.9280i	1.79080	−	0.523075i
$521$			9.29655i			0.407289i	0.979045	+	0.203645i	$0.0652787\pi$
$521$			9.29655i			0.407289i	−0.979045	+	0.203645i	$0.934721\pi$
$522$		0			0
$523$		−	9.26367i		−	0.405072i	−0.979275	−	0.202536i	$-0.935082\pi$
$523$		−	9.26367i		−	0.405072i	0.979275	−	0.202536i	$-0.0649183\pi$
$524$	−29.5458	−	4.75626i	−1.29071	−	0.207778i
$525$		0			0
$526$	−7.18863	−	0.574909i	−0.313439	−	0.0250672i
$527$	−6.15103	+	10.6539i	−0.267943	+	0.464091i
$528$		0			0
$529$	6.40702	+	11.0973i	0.278566	+	0.482490i
$530$	−26.2102	−	55.1301i	−1.13850	−	2.39470i
$531$		0			0
$532$	0.671151	−	0.824528i	0.0290981	−	0.0357478i
$533$	11.0948	−	6.40559i	0.480570	−	0.277457i
$534$		0			0
$535$	10.9514	+	6.32282i	0.473472	+	0.273359i
$536$	−4.07662	−	3.89808i	−0.176083	−	0.168371i
$537$		0			0
$538$	26.9940	+	18.6028i	1.16380	+	0.802025i
$539$	5.11370			0.220263
$540$		0			0
$541$	−39.0275			−1.67792			−0.838962	−	0.544189i	$-0.816837\pi$
$541$	−39.0275			−1.67792			−0.838962	+	0.544189i	$0.816837\pi$
$542$	−3.88409	−	2.67670i	−0.166836	−	0.114974i
$543$		0			0
$544$	−40.5614	+	5.07920i	−1.73906	+	0.217769i
$545$	−4.34162	−	2.50663i	−0.185974	−	0.107372i
$546$		0			0
$547$	15.6709	−	9.04762i	0.670041	−	0.386848i	−0.126051	−	0.992024i	$-0.540230\pi$
$547$	15.6709	−	9.04762i	0.670041	−	0.386848i	0.796092	+	0.605175i	$0.206897\pi$
$548$	0.845698	+	0.688383i	0.0361264	+	0.0294063i
$549$		0			0
$550$	−15.3833	−	32.3571i	−0.655947	−	1.37971i
$551$	0.463321	+	0.802496i	0.0197381	+	0.0341875i
$552$		0			0
$553$	0.998899	−	1.73014i	0.0424775	−	0.0735732i
$554$	16.9494	+	1.35552i	0.720111	+	0.0575907i
$555$		0			0
$556$	−3.30328	+	20.5199i	−0.140090	+	0.870239i
$557$		−	11.4867i		−	0.486705i	−0.969938	−	0.243353i	$-0.921753\pi$
$557$		−	11.4867i		−	0.486705i	0.969938	−	0.243353i	$-0.0782472\pi$
$558$		0			0
$559$		−	24.1679i		−	1.02219i
$560$	−9.42116	+	8.39691i	−0.398117	+	0.354834i
$561$		0			0
$562$	2.08727	−	26.0991i	0.0880462	−	1.10092i
$563$	1.41954	−	2.45871i	0.0598263	−	0.103622i	−0.834561	−	0.550915i	$-0.814279\pi$
$563$	1.41954	−	2.45871i	0.0598263	−	0.103622i	0.894387	+	0.447293i	$0.147612\pi$
$564$		0			0
$565$	−10.1286	−	17.5432i	−0.426113	−	0.738050i
$566$	27.7128	−	13.1753i	1.16485	−	0.553799i
$567$		0			0
$568$	−35.9041	−	8.76408i	−1.50650	−	0.367733i
$569$	−5.82245	+	3.36159i	−0.244090	+	0.140925i	−0.617055	−	0.786920i	$-0.711674\pi$
$569$	−5.82245	+	3.36159i	−0.244090	+	0.140925i	0.372965	+	0.927845i	$0.378341\pi$
$570$		0			0
$571$	−14.0370	−	8.10429i	−0.587432	−	0.339154i	0.176650	−	0.984274i	$-0.443474\pi$
$571$	−14.0370	−	8.10429i	−0.587432	−	0.339154i	−0.764081	+	0.645120i	$0.776807\pi$
$572$	−17.3581	−	45.5636i	−0.725777	−	1.90511i
$573$		0			0
$574$	−2.15650	+	3.12924i	−0.0900107	+	0.130612i
$575$	−15.8114			−0.659381
$576$		0			0
$577$	−5.47679			−0.228002			−0.114001	−	0.993481i	$-0.536367\pi$
$577$	−5.47679			−0.228002			−0.114001	+	0.993481i	$0.536367\pi$
$578$	28.2635	−	41.0124i	1.17561	−	1.70589i
$579$		0			0
$580$	−3.91593	−	10.2790i	−0.162600	−	0.426813i
$581$	5.68140	+	3.28016i	0.235704	+	0.136084i
$582$		0			0
$583$	−60.5882	+	34.9806i	−2.50931	+	1.44875i
$584$	−18.1265	−	4.42461i	−0.750079	−	0.183092i
$585$		0			0
$586$	−17.0994	+	8.12944i	−0.706368	+	0.335824i
$587$	−18.7598	−	32.4930i	−0.774301	−	1.34113i	−0.935187	−	0.354155i	$-0.884769\pi$
$587$	−18.7598	−	32.4930i	−0.774301	−	1.34113i	0.160886	−	0.986973i	$-0.448565\pi$
$588$		0			0
$589$	0.452477	−	0.783713i	0.0186440	−	0.0322923i
$590$	2.64030	−	33.0142i	0.108700	−	1.35917i
$591$		0			0
$592$	−9.29844	+	8.28754i	−0.382164	+	0.340616i
$593$			47.4039i			1.94665i	0.229438	+	0.973323i	$0.426311\pi$
$593$			47.4039i			1.94665i	−0.229438	+	0.973323i	$0.573689\pi$
$594$		0			0
$595$		−	22.7992i		−	0.934674i
$596$	−4.10452	+	25.4972i	−0.168128	+	1.04441i
$597$		0			0
$598$	−21.4493	−	1.71540i	−0.877126	−	0.0701479i
$599$	15.9337	−	27.5979i	0.651032	−	1.12762i	−0.331841	−	0.943335i	$-0.607670\pi$
$599$	15.9337	−	27.5979i	0.651032	−	1.12762i	0.982873	−	0.184285i	$-0.0589970\pi$
$600$		0			0
$601$	12.7566	+	22.0950i	0.520351	+	0.901274i	0.999720	+	0.0236606i	$0.00753212\pi$
$601$	12.7566	+	22.0950i	0.520351	+	0.901274i	−0.479369	+	0.877613i	$0.659135\pi$
$602$	3.07825	+	6.47476i	0.125460	+	0.263892i
$603$		0			0
$604$	−4.99582	−	4.06650i	−0.203277	−	0.165464i
$605$	−41.3945	+	23.8991i	−1.68293	+	0.971638i
$606$		0			0
$607$	13.9168	+	8.03488i	0.564866	+	0.326126i	0.755096	−	0.655614i	$-0.227590\pi$
$607$	13.9168	+	8.03488i	0.564866	+	0.326126i	−0.190230	+	0.981740i	$0.560923\pi$
$608$	2.98374	−	0.373632i	0.121007	−	0.0151528i
$609$		0			0
$610$	−23.7952	−	16.3984i	−0.963441	−	0.663951i
$611$	−14.0877			−0.569926
$612$		0			0
$613$	10.1572			0.410246			0.205123	−	0.978736i	$-0.434240\pi$
$613$	10.1572			0.410246			0.205123	+	0.978736i	$0.434240\pi$
$614$	−17.3874	−	11.9824i	−0.701698	−	0.483572i
$615$		0			0
$616$	10.4538	+	9.99592i	0.421194	+	0.402747i
$617$	3.85193	+	2.22391i	0.155073	+	0.0895312i	0.575528	−	0.817782i	$-0.304796\pi$
$617$	3.85193	+	2.22391i	0.155073	+	0.0895312i	−0.420456	+	0.907313i	$0.638130\pi$
$618$		0			0
$619$	32.5736	−	18.8064i	1.30924	−	0.755892i	0.327273	−	0.944930i	$-0.393870\pi$
$619$	32.5736	−	18.8064i	1.30924	−	0.755892i	0.981970	+	0.189038i	$0.0605369\pi$
$620$	−6.78139	+	8.33113i	−0.272347	+	0.334586i
$621$		0			0
$622$	4.66072	+	9.80331i	0.186878	+	0.393077i
$623$	4.88960	+	8.46904i	0.195898	+	0.339305i
$624$		0			0
$625$	12.6136	−	21.8473i	0.504543	−	0.873894i
$626$	−32.8177	−	2.62459i	−1.31166	−	0.104900i
$627$		0			0
$628$	−12.3846	−	1.99366i	−0.494199	−	0.0795557i
$629$		−	22.5022i		−	0.897221i
$630$		0			0
$631$		−	21.9573i		−	0.874106i	−0.899436	−	0.437053i	$-0.856022\pi$
$631$		−	21.9573i		−	0.874106i	0.899436	−	0.437053i	$-0.143978\pi$
$632$	5.42398	−	1.58429i	0.215754	−	0.0630196i
$633$		0			0
$634$	3.05603	−	38.2124i	0.121370	−	1.51761i
$635$	−8.13375	+	14.0881i	−0.322778	+	0.559068i
$636$		0			0
$637$	−2.38370	−	4.12868i	−0.0944454	−	0.163584i
$638$	−11.3854	+	5.41287i	−0.450751	+	0.214298i
$639$		0			0
$640$	−35.6731	−	1.25035i	−1.41010	−	0.0494244i
$641$	23.3369	−	13.4735i	0.921750	−	0.532173i	0.0375573	−	0.999294i	$-0.488042\pi$
$641$	23.3369	−	13.4735i	0.921750	−	0.532173i	0.884193	+	0.467122i	$0.154709\pi$
$642$		0			0
$643$	−22.9917	−	13.2743i	−0.906704	−	0.523486i	−0.0273346	−	0.999626i	$-0.508702\pi$
$643$	−22.9917	−	13.2743i	−0.906704	−	0.523486i	−0.879369	+	0.476141i	$0.842035\pi$
$644$	5.96490	−	2.27241i	0.235050	−	0.0895455i
$645$		0			0
$646$	−3.08264	+	4.47314i	−0.121285	+	0.175993i
$647$	23.8568			0.937906			0.468953	−	0.883223i	$-0.344631\pi$
$647$	23.8568			0.937906			0.468953	+	0.883223i	$0.344631\pi$
$648$		0			0
$649$	−37.9580			−1.48998
$650$	−18.9536	+	27.5030i	−0.743421	+	1.07876i
$651$		0			0
$652$	32.8873	−	12.5289i	1.28797	−	0.490668i
$653$	−23.4749	−	13.5532i	−0.918642	−	0.530378i	−0.0354406	−	0.999372i	$-0.511283\pi$
$653$	−23.4749	−	13.5532i	−0.918642	−	0.530378i	−0.883202	+	0.468993i	$0.844617\pi$
$654$		0			0
$655$	40.8841	−	23.6044i	1.59747	−	0.922301i
$656$	−10.5253	+	2.18161i	−0.410944	+	0.0851775i
$657$		0			0
$658$	3.77419	−	1.79434i	0.147133	−	0.0699505i
$659$	14.6668	+	25.4036i	0.571338	+	0.989586i	0.996429	+	0.0844352i	$0.0269086\pi$
$659$	14.6668	+	25.4036i	0.571338	+	0.989586i	−0.425091	+	0.905150i	$0.639758\pi$
$660$		0			0
$661$	9.65945	−	16.7307i	0.375709	−	0.650747i	−0.614724	−	0.788742i	$-0.710733\pi$
$661$	9.65945	−	16.7307i	0.375709	−	0.650747i	0.990433	+	0.137995i	$0.0440659\pi$
$662$	2.02136	−	25.2749i	0.0785622	−	0.982337i
$663$		0			0
$664$	5.20245	+	17.8111i	0.201894	+	0.691206i
$665$			1.67713i			0.0650364i
$666$		0			0
$667$			5.56350i			0.215420i
$668$	5.56725	+	0.896212i	0.215403	+	0.0346755i
$669$		0			0
$670$	8.86943	+	0.709331i	0.342656	+	0.0274038i
$671$	−16.5601	+	28.6829i	−0.639295	+	1.10729i
$672$		0			0
$673$	24.8176	+	42.9853i	0.956648	+	1.65696i	0.730552	+	0.682857i	$0.239263\pi$
$673$	24.8176	+	42.9853i	0.956648	+	1.65696i	0.226096	+	0.974105i	$0.427404\pi$
$674$	−4.04972	−	8.51813i	−0.155989	−	0.328106i
$675$		0			0
$676$	−12.2823	+	15.0891i	−0.472396	+	0.580352i
$677$	−27.9037	+	16.1102i	−1.07243	+	0.619166i	−0.928844	−	0.370472i	$-0.879196\pi$
$677$	−27.9037	+	16.1102i	−1.07243	+	0.619166i	−0.143584	+	0.989638i	$0.545863\pi$
$678$		0			0
$679$	−10.6661	−	6.15806i	−0.409327	−	0.236325i
$680$	44.5663	−	46.6075i	1.70904	−	1.78732i
$681$		0			0
$682$	10.1374	+	6.98615i	0.388182	+	0.267513i
$683$	−48.7831			−1.86663			−0.933316	−	0.359055i	$-0.883099\pi$
$683$	−48.7831			−1.86663			−0.933316	+	0.359055i	$0.883099\pi$
$684$		0			0
$685$	−1.72019			−0.0657252
$686$	1.16448	+	0.802493i	0.0444599	+	0.0306393i
$687$		0			0
$688$	−6.36367	+	19.2533i	−0.242613	+	0.734025i
$689$	56.4850	+	32.6116i	2.15191	+	1.24240i
$690$		0			0
$691$	33.1524	−	19.1405i	1.26118	−	0.728140i	0.287874	−	0.957668i	$-0.407052\pi$
$691$	33.1524	−	19.1405i	1.26118	−	0.728140i	0.973302	+	0.229528i	$0.0737182\pi$
$692$	6.10790	+	4.97172i	0.232188	+	0.188997i
$693$		0			0
$694$	19.0836	+	40.1402i	0.724404	+	1.52370i
$695$	−16.3936	−	28.3945i	−0.621843	−	1.07706i
$696$		0			0
$697$	9.70946	−	16.8173i	0.367772	−	0.637000i
$698$	8.94088	+	0.715045i	0.338417	+	0.0270649i
$699$		0			0
$700$	1.57476	−	9.78236i	0.0595202	−	0.369739i
$701$			16.4250i			0.620365i	0.950677	+	0.310183i	$0.100390\pi$
$701$			16.4250i			0.620365i	−0.950677	+	0.310183i	$0.899610\pi$
$702$		0			0
$703$			1.65529i			0.0624303i
$704$	1.83087	+	40.8686i	0.0690036	+	1.54029i
$705$		0			0
$706$	2.93651	−	36.7179i	0.110517	−	1.38190i
$707$	1.82918	−	3.16824i	0.0687935	−	0.119154i
$708$		0			0
$709$	2.30143	+	3.98619i	0.0864320	+	0.149705i	0.906001	−	0.423277i	$-0.139120\pi$
$709$	2.30143	+	3.98619i	0.0864320	+	0.149705i	−0.819569	+	0.572981i	$0.805787\pi$
$710$	52.6543	−	25.0331i	1.97608	−	0.939476i
$711$		0			0
$712$	−6.55907	+	26.8708i	−0.245812	+	1.00703i
$713$	4.70536	−	2.71664i	0.176217	−	0.101739i
$714$		0			0
$715$	66.6114	+	38.4581i	2.49113	+	1.43825i
$716$	0.849237	+	2.22918i	0.0317375	+	0.0833084i
$717$		0			0
$718$	25.1120	−	36.4394i	0.937173	−	1.35991i
$719$	27.4630			1.02420			0.512099	−	0.858927i	$-0.328868\pi$
$719$	27.4630			1.02420			0.512099	+	0.858927i	$0.328868\pi$
$720$		0			0
$721$	3.02665			0.112718
$722$	−15.0206	+	21.7960i	−0.559009	+	0.811163i
$723$		0			0
$724$	0.367492	+	0.964637i	0.0136577	+	0.0358505i
$725$	7.47906	+	4.31804i	0.277765	+	0.160368i
$726$		0			0
$727$	12.1777	−	7.03079i	0.451645	−	0.260758i	−0.256879	−	0.966443i	$-0.582694\pi$
$727$	12.1777	−	7.03079i	0.451645	−	0.260758i	0.708525	+	0.705686i	$0.249361\pi$
$728$	3.19757	−	13.0996i	0.118510	−	0.485504i
$729$		0			0
$730$	26.5829	−	12.6381i	0.983878	−	0.467759i
$731$	−18.3166	−	31.7253i	−0.677465	−	1.17340i
$732$		0			0
$733$	18.2356	−	31.5851i	0.673549	−	1.16662i	−0.303342	−	0.952882i	$-0.598102\pi$
$733$	18.2356	−	31.5851i	0.673549	−	1.16662i	0.976891	−	0.213739i	$-0.0685642\pi$
$734$	−2.51313	+	31.4240i	−0.0927612	+	1.15988i
$735$		0			0
$736$	16.6358	+	7.01438i	0.613203	+	0.258554i
$737$		−	10.1976i		−	0.375633i
$738$		0			0
$739$			0.413262i			0.0152021i	0.999971	+	0.00760104i	$0.00241951\pi$
$739$			0.413262i			0.0152021i	−0.999971	+	0.00760104i	$0.997580\pi$
$740$	3.12287	−	19.3992i	0.114799	−	0.713130i
$741$		0			0
$742$	−19.2865	−	1.54243i	−0.708028	−	0.0566244i
$743$	8.68868	−	15.0492i	0.318757	−	0.552103i	−0.661472	−	0.749970i	$-0.730068\pi$
$743$	8.68868	−	15.0492i	0.318757	−	0.552103i	0.980229	+	0.197867i	$0.0634013\pi$
$744$		0			0
$745$	−20.3700	−	35.2818i	−0.746298	−	1.29263i
$746$	11.2923	+	23.7522i	0.413442	+	0.869628i
$747$		0			0
$748$	−57.3182	−	46.6560i	−2.09576	−	1.70591i
$749$	3.47112	−	2.00405i	0.126832	−	0.0732264i
$750$		0			0
$751$	3.19940	+	1.84717i	0.116748	+	0.0674044i	0.557237	−	0.830354i	$-0.311862\pi$
$751$	3.19940	+	1.84717i	0.116748	+	0.0674044i	−0.440489	+	0.897758i	$0.645195\pi$
$752$	11.2229	+	3.70943i	0.409256	+	0.135269i
$753$		0			0
$754$	9.67739	+	6.66913i	0.352430	+	0.242875i
$755$	10.1617			0.369824
$756$		0			0
$757$	−2.01887			−0.0733772			−0.0366886	−	0.999327i	$-0.511681\pi$
$757$	−2.01887			−0.0733772			−0.0366886	+	0.999327i	$0.511681\pi$
$758$	−24.6895	−	17.0146i	−0.896762	−	0.617999i
$759$		0			0
$760$	−3.27835	+	3.42850i	−0.118918	+	0.124365i
$761$	16.4382	+	9.49062i	0.595886	+	0.344035i	0.767421	−	0.641143i	$-0.221540\pi$
$761$	16.4382	+	9.49062i	0.595886	+	0.344035i	−0.171536	+	0.985178i	$0.554873\pi$
$762$		0			0
$763$	−1.37610	+	0.794490i	−0.0498181	+	0.0287625i
$764$	−33.1666	+	40.7461i	−1.19993	+	1.47414i
$765$		0			0
$766$	7.10484	+	14.9442i	0.256708	+	0.539957i
$767$	17.6937	+	30.6464i	0.638882	+	1.10658i
$768$		0			0
$769$	−11.1454	+	19.3043i	−0.401912	+	0.696131i	−0.993957	−	0.109774i	$-0.964987\pi$
$769$	−11.1454	+	19.3043i	−0.401912	+	0.696131i	0.592045	+	0.805905i	$0.298321\pi$
$770$	−22.7440	−	1.81895i	−0.819639	−	0.0655504i
$771$		0			0
$772$	−32.4285	−	5.22031i	−1.16713	−	0.187883i
$773$			38.1241i			1.37123i	0.727965	+	0.685614i	$0.240466\pi$
$773$			38.1241i			1.37123i	−0.727965	+	0.685614i	$0.759534\pi$
$774$		0			0
$775$		−	8.43394i		−	0.302956i
$776$	−9.76691	−	33.4381i	−0.350612	−	1.20036i
$777$		0			0
$778$	−2.68357	+	33.5552i	−0.0962107	+	1.20301i
$779$	−0.714239	+	1.23710i	−0.0255903	+	0.0443236i
$780$		0			0
$781$	−33.4097	−	57.8673i	−1.19549	−	2.07065i
$782$	−29.4566	+	14.0044i	−1.05337	+	0.500795i
$783$		0			0
$784$	0.811836	+	3.91675i	0.0289942	+	0.139884i
$785$	17.1372	−	9.89416i	0.611653	−	0.353138i
$786$		0			0
$787$	14.7144	+	8.49538i	0.524513	+	0.302828i	0.738779	−	0.673948i	$-0.235403\pi$
$787$	14.7144	+	8.49538i	0.524513	+	0.302828i	−0.214266	+	0.976775i	$0.568736\pi$
$788$	−10.8397	+	4.12952i	−0.386147	+	0.147108i
$789$		0			0
$790$	−5.05819	+	7.33980i	−0.179962	+	0.261138i
$791$	−6.42062			−0.228291
$792$		0			0
$793$	30.8772			1.09648
$794$	7.28844	−	10.5761i	0.258657	−	0.375330i
$795$		0			0
$796$	−47.0828	+	17.9368i	−1.66880	+	0.635754i
$797$	−17.5585	−	10.1374i	−0.621955	−	0.359086i	0.155675	−	0.987808i	$-0.450245\pi$
$797$	−17.5585	−	10.1374i	−0.621955	−	0.359086i	−0.777630	+	0.628723i	$0.783578\pi$
$798$		0			0
$799$	−18.4929	+	10.6769i	−0.654233	+	0.377721i
$800$	22.3411	−	16.9195i	0.789878	−	0.598195i
$801$		0			0
$802$	−33.4582	+	15.9068i	−1.18145	+	0.561689i
$803$	−16.8671	−	29.2147i	−0.595228	−	1.03096i
$804$		0			0
$805$	−5.03470	+	8.72035i	−0.177450	+	0.307352i
$806$	0.915010	−	11.4412i	0.0322299	−	0.403000i
$807$		0			0
$808$	9.93239	−	2.90115i	0.349420	−	0.102062i
$809$		−	22.1960i		−	0.780368i	−0.920737	−	0.390184i	$-0.872411\pi$
$809$		−	22.1960i		−	0.780368i	0.920737	−	0.390184i	$-0.127589\pi$
$810$		0			0
$811$			55.5158i			1.94942i	0.223463	+	0.974712i	$0.428264\pi$
$811$			55.5158i			1.94942i	−0.223463	+	0.974712i	$0.571736\pi$
$812$	−3.44208	−	0.554104i	−0.120794	−	0.0194452i
$813$		0			0
$814$	−22.4478	−	1.79526i	−0.786795	−	0.0629237i
$815$	−27.7587	+	48.0794i	−0.972343	+	1.68415i
$816$		0			0
$817$	1.34739	+	2.33375i	0.0471393	+	0.0816476i
$818$	−5.61892	−	11.8188i	−0.196461	−	0.413233i
$819$		0			0
$820$	10.7045	−	13.1508i	0.373817	−	0.459245i
$821$	26.1556	−	15.1010i	0.912838	−	0.527027i	0.0314945	−	0.999504i	$-0.489973\pi$
$821$	26.1556	−	15.1010i	0.912838	−	0.527027i	0.881343	+	0.472477i	$0.156640\pi$
$822$		0			0
$823$	−20.0335	−	11.5664i	−0.698324	−	0.403178i	0.108399	−	0.994108i	$-0.465428\pi$
$823$	−20.0335	−	11.5664i	−0.698324	−	0.403178i	−0.806723	+	0.590930i	$0.798761\pi$
$824$	6.18727	+	5.91630i	0.215544	+	0.206104i
$825$		0			0
$826$	−8.64367	−	5.95675i	−0.300752	−	0.207262i
$827$	−26.5467			−0.923119			−0.461559	−	0.887109i	$-0.652710\pi$
$827$	−26.5467			−0.923119			−0.461559	+	0.887109i	$0.652710\pi$
$828$		0			0
$829$	44.5548			1.54745			0.773727	−	0.633520i	$-0.218390\pi$
$829$	44.5548			1.54745			0.773727	+	0.633520i	$0.218390\pi$
$830$	−24.1023	−	16.6100i	−0.836601	−	0.576540i
$831$		0			0
$832$	32.1429	−	20.5287i	1.11436	−	0.711703i
$833$	−6.25817	−	3.61316i	−0.216833	−	0.125188i
$834$		0			0
$835$	−7.70370	+	4.44773i	−0.266597	+	0.153920i
$836$	4.21639	+	3.43206i	0.145827	+	0.118700i
$837$		0			0
$838$	17.3843	+	36.5659i	0.600530	+	1.26315i
$839$	24.4985	+	42.4327i	0.845782	+	1.46494i	0.884940	+	0.465705i	$0.154199\pi$
$839$	24.4985	+	42.4327i	0.845782	+	1.46494i	−0.0391577	+	0.999233i	$0.512467\pi$
$840$		0			0
$841$	−12.9806	+	22.4831i	−0.447608	+	0.775280i
$842$	19.2331	+	1.53816i	0.662816	+	0.0530086i
$843$		0			0
$844$	−4.62617	+	28.7377i	−0.159239	+	0.989191i
$845$		−	30.6921i		−	1.05584i
$846$		0			0
$847$			15.1499i			0.520557i
$848$	−36.4116	−	40.8530i	−1.25038	−	1.40290i
$849$		0			0
$850$	−4.03617	+	50.4680i	−0.138440	+	1.73104i
$851$	−4.96911	+	8.60676i	−0.170339	+	0.295036i
$852$		0			0
$853$	−17.4025	−	30.1421i	−0.595852	−	1.03205i	−0.993426	−	0.114476i	$-0.963481\pi$
$853$	−17.4025	−	30.1421i	−0.595852	−	1.03205i	0.397574	−	0.917570i	$-0.369852\pi$
$854$	−8.27223	+	3.93281i	−0.283070	+	0.134578i
$855$		0			0
$856$	11.0133	+	2.68830i	0.376426	+	0.0918842i
$857$	16.9081	−	9.76190i	0.577570	−	0.333460i	−0.182597	−	0.983188i	$-0.558450\pi$
$857$	16.9081	−	9.76190i	0.577570	−	0.333460i	0.760167	+	0.649728i	$0.225117\pi$
$858$		0			0
$859$	17.6783	+	10.2066i	0.603176	+	0.348244i	0.770290	−	0.637694i	$-0.220112\pi$
$859$	17.6783	+	10.2066i	0.603176	+	0.348244i	−0.167114	+	0.985938i	$0.553445\pi$
$860$	−11.3880	−	29.8925i	−0.388327	−	1.01933i
$861$		0			0
$862$	9.62950	−	13.9731i	0.327982	−	0.475926i
$863$	−38.2894			−1.30339			−0.651694	−	0.758482i	$-0.725941\pi$
$863$	−38.2894			−1.30339			−0.651694	+	0.758482i	$0.725941\pi$
$864$		0			0
$865$	−12.4238			−0.422421
$866$	−14.9846	+	21.7438i	−0.509199	+	0.738885i
$867$		0			0
$868$	1.21212	+	3.18173i	0.0411422	+	0.107995i
$869$	8.84743	+	5.10807i	0.300129	+	0.173279i
$870$		0			0
$871$	−8.23331	+	4.75350i	−0.278975	+	0.161066i
$872$	−4.36612	−	1.06576i	−0.147856	−	0.0360911i
$873$		0			0
$874$	2.16686	−	1.03018i	0.0732952	−	0.0348462i
$875$	−0.0723271	−	0.125274i	−0.00244510	−	0.00423504i
$876$		0			0
$877$	28.5255	−	49.4076i	0.963238	−	1.66838i	0.248960	−	0.968514i	$-0.419911\pi$
$877$	28.5255	−	49.4076i	0.963238	−	1.66838i	0.714277	−	0.699863i	$-0.246756\pi$
$878$	2.95020	−	36.8891i	0.0995644	−	1.24495i
$879$		0			0
$880$	−42.9393	−	48.1770i	−1.44748	−	1.62405i
$881$			42.6383i			1.43652i	0.695774	+	0.718261i	$0.255062\pi$
$881$			42.6383i			1.43652i	−0.695774	+	0.718261i	$0.744938\pi$
$882$		0			0
$883$		−	0.262142i		−	0.00882176i	−0.999990	−	0.00441088i	$-0.998596\pi$
$883$		−	0.262142i		−	0.00882176i	0.999990	−	0.00441088i	$-0.00140403\pi$
$884$	−10.9507	+	68.0255i	−0.368312	+	2.28795i
$885$		0			0
$886$	−48.8783	−	3.90903i	−1.64210	−	0.131327i
$887$	−8.58006	+	14.8611i	−0.288090	+	0.498987i	−0.973354	−	0.229308i	$-0.926354\pi$
$887$	−8.58006	+	14.8611i	−0.288090	+	0.498987i	0.685264	+	0.728295i	$0.259687\pi$
$888$		0			0
$889$	2.57804	+	4.46529i	0.0864645	+	0.149761i
$890$	−18.7349	−	39.4067i	−0.627995	−	1.32092i
$891$		0			0
$892$	−23.6327	−	19.2366i	−0.791282	−	0.644089i
$893$	1.36036	−	0.785405i	0.0455227	−	0.0262826i
$894$		0			0
$895$	−3.25894	−	1.88155i	−0.108934	−	0.0628933i
$896$	−5.99659	+	9.59379i	−0.200332	+	0.320506i
$897$		0			0
$898$	16.9943	+	11.7115i	0.567107	+	0.390819i
$899$	−2.96762			−0.0989757
$900$		0			0
$901$	98.8641			3.29364
$902$	−16.0020	−	11.0277i	−0.532808	−	0.367182i
$903$		0			0
$904$	−13.1254	−	12.5506i	−0.436546	−	0.417427i
$905$	−1.41025	−	0.814206i	−0.0468782	−	0.0270651i
$906$		0			0
$907$	−44.7570	+	25.8405i	−1.48613	+	0.858019i	−0.999875	−	0.0157966i	$-0.994972\pi$
$907$	−44.7570	+	25.8405i	−1.48613	+	0.858019i	−0.486257	+	0.873816i	$0.661638\pi$
$908$	−7.33481	+	9.01102i	−0.243414	+	0.299041i
$909$		0			0
$910$	9.13331	+	19.2109i	0.302766	+	0.636835i
$911$	−15.9334	−	27.5975i	−0.527898	−	0.914347i	−0.999471	−	0.0325198i	$-0.989647\pi$
$911$	−15.9334	−	27.5975i	−0.527898	−	0.914347i	0.471573	−	0.881827i	$-0.343687\pi$
$912$		0			0
$913$	−16.7737	+	29.0530i	−0.555130	+	0.961513i
$914$	−0.0309596	−	0.00247599i	−0.00102405	−	8.18984e-5i
$915$		0			0
$916$	29.5016	+	4.74914i	0.974759	+	0.156916i
$917$		−	14.9631i		−	0.494125i
$918$		0			0
$919$		−	49.4568i		−	1.63143i	−0.578455	−	0.815714i	$-0.696344\pi$
$919$		−	49.4568i		−	1.63143i	0.578455	−	0.815714i	$-0.303656\pi$
$920$	−27.3382	+	7.98521i	−0.901314	+	0.263265i
$921$		0			0
$922$	0.913135	−	11.4178i	0.0300725	−	0.376025i
$923$	−31.1471	+	53.9484i	−1.02522	+	1.77573i
$924$		0			0
$925$	7.71342	+	13.3600i	0.253616	+	0.439275i
$926$	41.1253	−	19.5519i	1.35146	−	0.642517i
$927$		0			0
$928$	−5.95341	−	7.86109i	−0.195430	−	0.258053i
$929$	−20.6955	+	11.9486i	−0.678998	+	0.392020i	−0.799477	−	0.600696i	$-0.794890\pi$
$929$	−20.6955	+	11.9486i	−0.678998	+	0.392020i	0.120479	+	0.992716i	$0.461557\pi$
$930$		0			0
$931$	0.460358	+	0.265788i	0.0150876	+	0.00871084i
$932$	−1.00312	+	0.382153i	−0.0328583	+	0.0125178i
$933$		0			0
$934$	−9.32390	+	13.5297i	−0.305087	+	0.442704i
$935$	116.588			3.81284
$936$		0			0
$937$	35.2010			1.14997			0.574983	−	0.818165i	$-0.305009\pi$
$937$	35.2010			1.14997			0.574983	+	0.818165i	$0.305009\pi$
$938$	1.60031	−	2.32217i	0.0522520	−	0.0758214i
$939$		0			0
$940$	−17.4246	+	6.63814i	−0.568327	+	0.216512i
$941$	−13.0422	−	7.52990i	−0.425163	−	0.245468i	0.272121	−	0.962263i	$-0.412275\pi$
$941$	−13.0422	−	7.52990i	−0.425163	−	0.245468i	−0.697284	+	0.716795i	$0.745608\pi$
$942$		0			0
$943$	−7.42746	+	4.28824i	−0.241871	+	0.139644i
$944$	−6.02610	−	29.0732i	−0.196133	−	0.946254i
$945$		0			0
$946$	−33.1100	+	15.7413i	−1.07650	+	0.511793i
$947$	1.64196	+	2.84396i	0.0533565	+	0.0924162i	0.891470	−	0.453080i	$-0.149675\pi$
$947$	1.64196	+	2.84396i	0.0533565	+	0.0924162i	−0.838114	+	0.545496i	$0.816341\pi$
$948$		0			0
$949$	−15.7249	+	27.2362i	−0.510450	+	0.884126i
$950$	0.296905	−	3.71249i	0.00963288	−	0.120449i
$951$		0			0
$952$	−5.73059	−	19.6193i	−0.185730	−	0.635865i
$953$			15.4731i			0.501222i	0.968088	+	0.250611i	$0.0806316\pi$
$953$			15.4731i			0.501222i	−0.968088	+	0.250611i	$0.919368\pi$
$954$		0			0
$955$		−	82.8797i		−	2.68192i
$956$	39.4983	+	6.35840i	1.27747	+	0.205645i
$957$		0			0
$958$	8.60701	+	0.688344i	0.278080	+	0.0222394i
$959$	−0.272612	+	0.472178i	−0.00880310	+	0.0152474i
$960$		0			0
$961$	−14.0509	−	24.3369i	−0.453255	−	0.785061i
$962$	9.01434	+	18.9607i	0.290634	+	0.611316i
$963$		0			0
$964$	20.3881	−	25.0474i	0.656658	−	0.806723i
$965$	44.8730	−	25.9074i	1.44451	−	0.833989i
$966$		0			0
$967$	30.8548	+	17.8141i	0.992225	+	0.572861i	0.905939	−	0.423409i	$-0.139167\pi$
$967$	30.8548	+	17.8141i	0.992225	+	0.572861i	0.0862862	+	0.996270i	$0.472500\pi$
$968$	−29.6140	+	30.9704i	−0.951831	+	0.995427i
$969$		0			0
$970$	45.2488	+	31.1830i	1.45285	+	1.00123i
$971$	−10.9461			−0.351278			−0.175639	−	0.984455i	$-0.556199\pi$
$971$	−10.9461			−0.351278			−0.175639	+	0.984455i	$0.556199\pi$
$972$		0			0
$973$	−10.3921			−0.333154
$974$	21.7455	+	14.9858i	0.696769	+	0.480175i
$975$		0			0
$976$	−24.5982	−	8.13029i	−0.787370	−	0.260244i
$977$	−30.9200	−	17.8516i	−0.989217	−	0.571125i	−0.0841770	−	0.996451i	$-0.526826\pi$
$977$	−30.9200	−	17.8516i	−0.989217	−	0.571125i	−0.905040	+	0.425326i	$0.860159\pi$
$978$		0			0
$979$	−43.3081	+	25.0039i	−1.38413	+	0.799129i
$980$	−4.89376	−	3.98343i	−0.156325	−	0.127246i
$981$		0			0
$982$	−2.03995	−	4.29081i	−0.0650975	−	0.136925i
$983$	7.62459	+	13.2062i	0.243187	+	0.421212i	0.961620	−	0.274384i	$-0.0884739\pi$
$983$	7.62459	+	13.2062i	0.243187	+	0.421212i	−0.718433	+	0.695596i	$0.755141\pi$
$984$		0			0
$985$	9.14926	−	15.8470i	0.291520	−	0.504927i
$986$	17.7580	+	1.42019i	0.565530	+	0.0452282i
$987$		0			0
$988$	0.805546	−	5.00403i	0.0256278	−	0.159200i
$989$			16.1793i			0.514472i
$990$		0			0
$991$			35.4971i			1.12760i	0.825911	+	0.563801i	$0.190661\pi$
$991$			35.4971i			1.12760i	−0.825911	+	0.563801i	$0.809339\pi$
$992$	−3.74153	+	8.87368i	−0.118794	+	0.281740i
$993$		0			0
$994$	1.47316	−	18.4203i	0.0467259	−	0.584258i
$995$	39.7404	−	68.8324i	1.25985	−	2.18213i
$996$		0			0
$997$	23.0368	+	39.9010i	0.729584	+	1.26368i	0.957059	+	0.289893i	$0.0936196\pi$
$997$	23.0368	+	39.9010i	0.729584	+	1.26368i	−0.227475	+	0.973784i	$0.573047\pi$
$998$	−55.4418	+	26.3583i	−1.75498	+	0.834358i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ba.a.71.11		72
3.2	odd	2		252.2.ba.a.239.26	yes	72
4.3	odd	2	inner	756.2.ba.a.71.2		72
9.2	odd	6	inner	756.2.ba.a.575.2		72
9.7	even	3		252.2.ba.a.155.35	yes	72
12.11	even	2		252.2.ba.a.239.35	yes	72
36.7	odd	6		252.2.ba.a.155.26	✓	72
36.11	even	6	inner	756.2.ba.a.575.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.26	✓	72	36.7	odd	6
252.2.ba.a.155.35	yes	72	9.7	even	3
252.2.ba.a.239.26	yes	72	3.2	odd	2
252.2.ba.a.239.35	yes	72	12.11	even	2
756.2.ba.a.71.2		72	4.3	odd	2	inner
756.2.ba.a.71.11		72	1.1	even	1	trivial
756.2.ba.a.575.2		72	9.2	odd	6	inner
756.2.ba.a.575.11		72	36.11	even	6	inner

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.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.802493 + 1.16448i) q^{2} +(-0.712009 - 1.86897i) q^{4} +(2.73233 + 1.57751i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.74775 + 0.670717i) q^{8} +O(q^{10})\)	\(q+(-0.802493 + 1.16448i) q^{2} +(-0.712009 - 1.86897i) q^{4} +(2.73233 + 1.57751i) q^{5} +(0.866025 - 0.500000i) q^{7} +(2.74775 + 0.670717i) q^{8} +(-4.02965 + 1.91579i) q^{10} +(2.55685 + 4.42859i) q^{11} +(2.38370 - 4.12868i) q^{13} +(-0.112741 + 1.40971i) q^{14} +(-2.98609 + 2.66145i) q^{16} -7.22631i q^{17} +0.531576i q^{19} +(1.00287 - 6.22984i) q^{20} +(-7.20884 - 0.576526i) q^{22} +(-1.59577 + 2.76396i) q^{23} +(2.47708 + 4.29042i) q^{25} +(2.89485 + 6.08899i) q^{26} +(-1.55110 - 1.26257i) q^{28} +(1.50966 - 0.871600i) q^{29} +(-1.47432 - 0.851200i) q^{31} +(-0.702876 - 5.61302i) q^{32} +(8.41487 + 5.79907i) q^{34} +3.15502 q^{35} +3.11392 q^{37} +(-0.619007 - 0.426586i) q^{38} +(6.44969 + 6.16722i) q^{40} +(2.32723 + 1.34363i) q^{41} +(4.39025 - 2.53471i) q^{43} +(6.45640 - 7.93187i) q^{44} +(-1.93797 - 4.07630i) q^{46} +(-1.47750 - 2.55911i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-6.98393 - 0.558538i) q^{50} +(-9.41359 - 1.51539i) q^{52} +13.6811i q^{53} +16.1338i q^{55} +(2.71498 - 0.793018i) q^{56} +(-0.196531 + 2.45741i) q^{58} +(-3.71140 + 6.42833i) q^{59} +(3.23838 + 5.60903i) q^{61} +(2.17433 - 1.03373i) q^{62} +(7.10028 + 3.68593i) q^{64} +(13.0261 - 7.52061i) q^{65} +(-1.72700 - 0.997087i) q^{67} +(-13.5057 + 5.14520i) q^{68} +(-2.53188 + 3.67395i) q^{70} -13.0667 q^{71} -6.59684 q^{73} +(-2.49890 + 3.62609i) q^{74} +(0.993498 - 0.378487i) q^{76} +(4.42859 + 2.55685i) q^{77} +(1.73014 - 0.998899i) q^{79} +(-12.3574 + 2.56136i) q^{80} +(-3.43221 + 1.63175i) q^{82} +(3.28016 + 5.68140i) q^{83} +(11.3996 - 19.7446i) q^{85} +(-0.571535 + 7.14643i) q^{86} +(4.05525 + 13.8836i) q^{88} +9.77920i q^{89} -4.76739i q^{91} +(6.30196 + 1.01448i) q^{92} +(4.16571 + 0.333152i) q^{94} +(-0.838566 + 1.45244i) q^{95} +(-6.15806 - 10.6661i) q^{97} +(0.607219 + 1.27722i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 42 q^{20} + 36 q^{25} - 30 q^{32} - 12 q^{34} - 12 q^{40} + 60 q^{41} - 24 q^{46} + 36 q^{49} + 78 q^{50} - 18 q^{52} - 18 q^{58} - 60 q^{64} - 24 q^{65} - 78 q^{68} - 24 q^{73} + 12 q^{76} - 36 q^{82} - 30 q^{86} + 24 q^{88} + 114 q^{92} + 42 q^{94} - 12 q^{97}+O(q^{100}) \) 72 * q + 42 * q^20 + 36 * q^25 - 30 * q^32 - 12 * q^34 - 12 * q^40 + 60 * q^41 - 24 * q^46 + 36 * q^49 + 78 * q^50 - 18 * q^52 - 18 * q^58 - 60 * q^64 - 24 * q^65 - 78 * q^68 - 24 * q^73 + 12 * q^76 - 36 * q^82 - 30 * q^86 + 24 * q^88 + 114 * q^92 + 42 * q^94 - 12 * q^97

Introduction

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