LMFDB - Embedded newform 756.2.e.a.323.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (of order $2$, degree $1$, 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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.6
Character	$\chi$	$=$	756.323
Dual form			756.2.e.a.323.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.904694 + 1.08698i) q^{2} +(-0.363059 - 1.96677i) q^{4} -2.20652i q^{5} -1.00000i q^{7} +(2.46630 + 1.38469i) q^{8} +O(q^{10})$	\(q+(-0.904694 + 1.08698i) q^{2} +(-0.363059 - 1.96677i) q^{4} -2.20652i q^{5} -1.00000i q^{7} +(2.46630 + 1.38469i) q^{8} +(2.39844 + 1.99622i) q^{10} -2.61856 q^{11} +4.38677 q^{13} +(1.08698 + 0.904694i) q^{14} +(-3.73638 + 1.42811i) q^{16} +5.03227i q^{17} -6.26632i q^{19} +(-4.33971 + 0.801094i) q^{20} +(2.36899 - 2.84632i) q^{22} -5.55840 q^{23} +0.131290 q^{25} +(-3.96868 + 4.76834i) q^{26} +(-1.96677 + 0.363059i) q^{28} -7.73803i q^{29} -7.01459i q^{31} +(1.82795 - 5.35337i) q^{32} +(-5.46999 - 4.55266i) q^{34} -2.20652 q^{35} -8.26904 q^{37} +(6.81138 + 5.66910i) q^{38} +(3.05533 - 5.44193i) q^{40} -0.297458i q^{41} -1.46845i q^{43} +(0.950689 + 5.15010i) q^{44} +(5.02865 - 6.04188i) q^{46} -5.24497 q^{47} -1.00000 q^{49} +(-0.118778 + 0.142710i) q^{50} +(-1.59265 - 8.62777i) q^{52} -11.3489i q^{53} +5.77789i q^{55} +(1.38469 - 2.46630i) q^{56} +(8.41110 + 7.00055i) q^{58} -5.17152 q^{59} -6.40298 q^{61} +(7.62473 + 6.34605i) q^{62} +(4.16528 + 6.83011i) q^{64} -9.67948i q^{65} +5.83901i q^{67} +(9.89733 - 1.82701i) q^{68} +(1.99622 - 2.39844i) q^{70} +7.44057 q^{71} +10.5489 q^{73} +(7.48095 - 8.98830i) q^{74} +(-12.3244 + 2.27504i) q^{76} +2.61856i q^{77} -1.43602i q^{79} +(3.15114 + 8.24437i) q^{80} +(0.323331 + 0.269108i) q^{82} +6.64214 q^{83} +11.1038 q^{85} +(1.59617 + 1.32849i) q^{86} +(-6.45815 - 3.62588i) q^{88} -6.50422i q^{89} -4.38677i q^{91} +(2.01803 + 10.9321i) q^{92} +(4.74510 - 5.70119i) q^{94} -13.8267 q^{95} -16.5544 q^{97} +(0.904694 - 1.08698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.904694	+	1.08698i	−0.639715	+	0.768612i
$2$	−0.904694	+	1.08698i	−0.639715	+	0.768612i
$3$		0			0
$3$		0			0
$4$	−0.363059	−	1.96677i	−0.181529	−	0.983386i
$5$		−	2.20652i		−	0.986784i	−0.869807	−	0.493392i	$-0.835757\pi$
$5$		−	2.20652i		−	0.986784i	0.869807	−	0.493392i	$-0.164243\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.46630	+	1.38469i	0.871969	+	0.489561i
$9$		0			0
$10$	2.39844	+	1.99622i	0.758454	+	0.631260i
$11$	−2.61856			−0.789525			−0.394762	−	0.918783i	$-0.629173\pi$
$11$	−2.61856			−0.789525			−0.394762	+	0.918783i	$0.629173\pi$
$12$		0			0
$13$	4.38677			1.21667			0.608336	−	0.793680i	$-0.291837\pi$
$13$	4.38677			1.21667			0.608336	+	0.793680i	$0.291837\pi$
$14$	1.08698	+	0.904694i	0.290508	+	0.241790i
$15$		0			0
$16$	−3.73638	+	1.42811i	−0.934094	+	0.357026i
$17$			5.03227i			1.22051i	0.792207	+	0.610253i	$0.208932\pi$
$17$			5.03227i			1.22051i	−0.792207	+	0.610253i	$0.791068\pi$
$18$		0			0
$19$		−	6.26632i		−	1.43759i	−0.695220	−	0.718797i	$-0.744693\pi$
$19$		−	6.26632i		−	1.43759i	0.695220	−	0.718797i	$-0.255307\pi$
$20$	−4.33971	+	0.801094i	−0.970389	+	0.179130i
$21$		0			0
$22$	2.36899	−	2.84632i	0.505071	−	0.606838i
$23$	−5.55840			−1.15901			−0.579503	−	0.814970i	$-0.696753\pi$
$23$	−5.55840			−1.15901			−0.579503	+	0.814970i	$0.696753\pi$
$24$		0			0
$25$	0.131290			0.0262581
$26$	−3.96868	+	4.76834i	−0.778323	+	0.935148i
$27$		0			0
$28$	−1.96677	+	0.363059i	−0.371685	+	0.0686116i
$29$		−	7.73803i		−	1.43692i	−0.695570	−	0.718458i	$-0.744848\pi$
$29$		−	7.73803i		−	1.43692i	0.695570	−	0.718458i	$-0.255152\pi$
$30$		0			0
$31$		−	7.01459i		−	1.25986i	−0.776653	−	0.629928i	$-0.783084\pi$
$31$		−	7.01459i		−	1.25986i	0.776653	−	0.629928i	$-0.216916\pi$
$32$	1.82795	−	5.35337i	0.323139	−	0.946351i
$33$		0			0
$34$	−5.46999	−	4.55266i	−0.938095	−	0.780776i
$35$	−2.20652			−0.372969
$36$		0			0
$37$	−8.26904			−1.35942			−0.679711	−	0.733480i	$-0.737895\pi$
$37$	−8.26904			−1.35942			−0.679711	+	0.733480i	$0.737895\pi$
$38$	6.81138	+	5.66910i	1.10495	+	0.919650i
$39$		0			0
$40$	3.05533	−	5.44193i	0.483091	−	0.860445i
$41$		−	0.297458i		−	0.0464551i	−0.999730	−	0.0232276i	$-0.992606\pi$
$41$		−	0.297458i		−	0.0464551i	0.999730	−	0.0232276i	$-0.00739423\pi$
$42$		0			0
$43$		−	1.46845i		−	0.223936i	−0.993712	−	0.111968i	$-0.964285\pi$
$43$		−	1.46845i		−	0.223936i	0.993712	−	0.111968i	$-0.0357154\pi$
$44$	0.950689	+	5.15010i	0.143322	+	0.776407i
$45$		0			0
$46$	5.02865	−	6.04188i	0.741434	−	0.890827i
$47$	−5.24497			−0.765058			−0.382529	−	0.923943i	$-0.624947\pi$
$47$	−5.24497			−0.765058			−0.382529	+	0.923943i	$0.624947\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.118778	+	0.142710i	−0.0167977	+	0.0201823i
$51$		0			0
$52$	−1.59265	−	8.62777i	−0.220861	−	1.19646i
$53$		−	11.3489i		−	1.55890i	−0.626466	−	0.779449i	$-0.715499\pi$
$53$		−	11.3489i		−	1.55890i	0.626466	−	0.779449i	$-0.284501\pi$
$54$		0			0
$55$			5.77789i			0.779090i
$56$	1.38469	−	2.46630i	0.185037	−	0.329573i
$57$		0			0
$58$	8.41110	+	7.00055i	1.10443	+	0.919217i
$59$	−5.17152			−0.673274			−0.336637	−	0.941635i	$-0.609290\pi$
$59$	−5.17152			−0.673274			−0.336637	+	0.941635i	$0.609290\pi$
$60$		0			0
$61$	−6.40298			−0.819818			−0.409909	−	0.912126i	$-0.634440\pi$
$61$	−6.40298			−0.819818			−0.409909	+	0.912126i	$0.634440\pi$
$62$	7.62473	+	6.34605i	0.968341	+	0.805949i
$63$		0			0
$64$	4.16528	+	6.83011i	0.520660	+	0.853764i
$65$		−	9.67948i		−	1.20059i
$66$		0			0
$67$			5.83901i			0.713348i	0.934229	+	0.356674i	$0.116089\pi$
$67$			5.83901i			0.713348i	−0.934229	+	0.356674i	$0.883911\pi$
$68$	9.89733	−	1.82701i	1.20023	−	0.221557i
$69$		0			0
$70$	1.99622	−	2.39844i	0.238594	−	0.286669i
$71$	7.44057			0.883033			0.441517	−	0.897253i	$-0.354441\pi$
$71$	7.44057			0.883033			0.441517	+	0.897253i	$0.354441\pi$
$72$		0			0
$73$	10.5489			1.23465			0.617325	−	0.786708i	$-0.288216\pi$
$73$	10.5489			1.23465			0.617325	+	0.786708i	$0.288216\pi$
$74$	7.48095	−	8.98830i	0.869643	−	1.04487i
$75$		0			0
$76$	−12.3244	+	2.27504i	−1.41371	+	0.260965i
$77$			2.61856i			0.298412i
$78$		0			0
$79$		−	1.43602i		−	0.161565i	−0.996732	−	0.0807826i	$-0.974258\pi$
$79$		−	1.43602i		−	0.161565i	0.996732	−	0.0807826i	$-0.0257419\pi$
$80$	3.15114	+	8.24437i	0.352308	+	0.921749i
$81$		0			0
$82$	0.323331	+	0.269108i	0.0357060	+	0.0297181i
$83$	6.64214			0.729069			0.364535	−	0.931190i	$-0.381228\pi$
$83$	6.64214			0.729069			0.364535	+	0.931190i	$0.381228\pi$
$84$		0			0
$85$	11.1038			1.20437
$86$	1.59617	+	1.32849i	0.172120	+	0.143255i
$87$		0			0
$88$	−6.45815	−	3.62588i	−0.688441	−	0.386520i
$89$		−	6.50422i		−	0.689446i	−0.938704	−	0.344723i	$-0.887973\pi$
$89$		−	6.50422i		−	0.689446i	0.938704	−	0.344723i	$-0.112027\pi$
$90$		0			0
$91$		−	4.38677i		−	0.459859i
$92$	2.01803	+	10.9321i	0.210394	+	1.13975i
$93$		0			0
$94$	4.74510	−	5.70119i	0.489419	−	0.588033i
$95$	−13.8267			−1.41859
$96$		0			0
$97$	−16.5544			−1.68084			−0.840422	−	0.541933i	$-0.817693\pi$
$97$	−16.5544			−1.68084			−0.840422	+	0.541933i	$0.817693\pi$
$98$	0.904694	−	1.08698i	0.0913879	−	0.109802i
$99$		0			0
$100$	−0.0476661	−	0.258218i	−0.00476661	−	0.0258218i
$101$			1.43497i			0.142785i	0.997448	+	0.0713924i	$0.0227443\pi$
$101$			1.43497i			0.142785i	−0.997448	+	0.0713924i	$0.977256\pi$
$102$		0			0
$103$			6.22593i			0.613459i	0.951797	+	0.306729i	$0.0992346\pi$
$103$			6.22593i			0.613459i	−0.951797	+	0.306729i	$0.900765\pi$
$104$	10.8191	+	6.07431i	1.06090	+	0.595635i
$105$		0			0
$106$	12.3361	+	10.2673i	1.19819	+	0.997250i
$107$	19.7923			1.91339			0.956697	−	0.291086i	$-0.0940167\pi$
$107$	19.7923			1.91339			0.956697	+	0.291086i	$0.0940167\pi$
$108$		0			0
$109$	13.6019			1.30282			0.651411	−	0.758725i	$-0.274178\pi$
$109$	13.6019			1.30282			0.651411	+	0.758725i	$0.274178\pi$
$110$	−6.28046	−	5.22722i	−0.598818	−	0.498396i
$111$		0			0
$112$	1.42811	+	3.73638i	0.134943	+	0.353054i
$113$			10.5332i			0.990882i	0.868642	+	0.495441i	$0.164993\pi$
$113$			10.5332i			0.990882i	−0.868642	+	0.495441i	$0.835007\pi$
$114$		0			0
$115$			12.2647i			1.14369i
$116$	−15.2189	+	2.80936i	−1.41304	+	0.260842i
$117$		0			0
$118$	4.67864	−	5.62134i	0.430703	−	0.517487i
$119$	5.03227			0.461308
$120$		0			0
$121$	−4.14316			−0.376651
$122$	5.79274	−	6.95993i	0.524450	−	0.630122i
$123$		0			0
$124$	−13.7961	+	2.54671i	−1.23893	+	0.228701i
$125$		−	11.3223i		−	1.01269i
$126$		0			0
$127$		−	4.27441i		−	0.379293i	−0.981852	−	0.189646i	$-0.939266\pi$
$127$		−	4.27441i		−	0.379293i	0.981852	−	0.189646i	$-0.0607341\pi$
$128$	−11.1925	−	1.65158i	−0.989288	−	0.145980i
$129$		0			0
$130$	10.5214	+	8.75696i	0.922789	+	0.768036i
$131$	−11.8058			−1.03148			−0.515738	−	0.856746i	$-0.672482\pi$
$131$	−11.8058			−1.03148			−0.515738	+	0.856746i	$0.672482\pi$
$132$		0			0
$133$	−6.26632			−0.543359
$134$	−6.34689	−	5.28251i	−0.548288	−	0.456339i
$135$		0			0
$136$	−6.96812	+	12.4111i	−0.597512	+	1.06424i
$137$		−	12.7470i		−	1.08905i	−0.838746	−	0.544523i	$-0.816711\pi$
$137$		−	12.7470i		−	1.08905i	0.838746	−	0.544523i	$-0.183289\pi$
$138$		0			0
$139$			8.94876i			0.759024i	0.925187	+	0.379512i	$0.123908\pi$
$139$			8.94876i			0.759024i	−0.925187	+	0.379512i	$0.876092\pi$
$140$	0.801094	+	4.33971i	0.0677048	+	0.366772i
$141$		0			0
$142$	−6.73144	+	8.08777i	−0.564890	+	0.678710i
$143$	−11.4870			−0.960592
$144$		0			0
$145$	−17.0741			−1.41793
$146$	−9.54349	+	11.4664i	−0.789825	+	0.948967i
$147$		0			0
$148$	3.00215	+	16.2633i	0.246775	+	1.33684i
$149$		−	11.4101i		−	0.934751i	−0.884059	−	0.467375i	$-0.845200\pi$
$149$		−	11.4101i		−	0.934751i	0.884059	−	0.467375i	$-0.154800\pi$
$150$		0			0
$151$		−	9.84010i		−	0.800776i	−0.916346	−	0.400388i	$-0.868875\pi$
$151$		−	9.84010i		−	0.800776i	0.916346	−	0.400388i	$-0.131125\pi$
$152$	8.67690	−	15.4546i	0.703790	−	1.25354i
$153$		0			0
$154$	−2.84632	−	2.36899i	−0.229363	−	0.190899i
$155$	−15.4778			−1.24321
$156$		0			0
$157$	14.5144			1.15838			0.579189	−	0.815193i	$-0.303369\pi$
$157$	14.5144			1.15838			0.579189	+	0.815193i	$0.303369\pi$
$158$	1.56093	+	1.29916i	0.124181	+	0.103356i
$159$		0			0
$160$	−11.8123	−	4.03340i	−0.933844	−	0.318869i
$161$			5.55840i			0.438063i
$162$		0			0
$163$			8.15575i			0.638808i	0.947619	+	0.319404i	$0.103483\pi$
$163$			8.15575i			0.638808i	−0.947619	+	0.319404i	$0.896517\pi$
$164$	−0.585032	+	0.107995i	−0.0456833	+	0.00843297i
$165$		0			0
$166$	−6.00910	+	7.21988i	−0.466397	+	0.560372i
$167$	−0.0393039			−0.00304143			−0.00152071	−	0.999999i	$-0.500484\pi$
$167$	−0.0393039			−0.00304143			−0.00152071	+	0.999999i	$0.500484\pi$
$168$		0			0
$169$	6.24376			0.480289
$170$	−10.0455	+	12.0696i	−0.770457	+	0.925697i
$171$		0			0
$172$	−2.88810	+	0.533132i	−0.220215	+	0.0406509i
$173$			14.4982i			1.10228i	0.834414	+	0.551138i	$0.185806\pi$
$173$			14.4982i			1.10228i	−0.834414	+	0.551138i	$0.814194\pi$
$174$		0			0
$175$		−	0.131290i		−	0.00992463i
$176$	9.78392	−	3.73958i	0.737491	−	0.281881i
$177$		0			0
$178$	7.06997	+	5.88433i	0.529917	+	0.441049i
$179$	−12.9597			−0.968651			−0.484326	−	0.874888i	$-0.660935\pi$
$179$	−12.9597			−0.968651			−0.484326	+	0.874888i	$0.660935\pi$
$180$		0			0
$181$	16.7683			1.24638			0.623189	−	0.782071i	$-0.285837\pi$
$181$	16.7683			1.24638			0.623189	+	0.782071i	$0.285837\pi$
$182$	4.76834	+	3.96868i	0.353453	+	0.294178i
$183$		0			0
$184$	−13.7087	−	7.69665i	−1.01062	−	0.567405i
$185$			18.2458i			1.34146i
$186$		0			0
$187$		−	13.1773i		−	0.963619i
$188$	1.90423	+	10.3157i	0.138880	+	0.752347i
$189$		0			0
$190$	12.5090	−	15.0294i	0.907496	−	1.09035i
$191$	16.4137			1.18766			0.593828	−	0.804592i	$-0.297616\pi$
$191$	16.4137			1.18766			0.593828	+	0.804592i	$0.297616\pi$
$192$		0			0
$193$	−10.1071			−0.727526			−0.363763	−	0.931491i	$-0.618508\pi$
$193$	−10.1071			−0.727526			−0.363763	+	0.931491i	$0.618508\pi$
$194$	14.9767	−	17.9943i	1.07526	−	1.29192i
$195$		0			0
$196$	0.363059	+	1.96677i	0.0259328	+	0.140484i
$197$			3.22221i			0.229573i	0.993390	+	0.114786i	$0.0366184\pi$
$197$			3.22221i			0.229573i	−0.993390	+	0.114786i	$0.963382\pi$
$198$		0			0
$199$			19.2657i			1.36571i	0.730554	+	0.682855i	$0.239262\pi$
$199$			19.2657i			1.36571i	−0.730554	+	0.682855i	$0.760738\pi$
$200$	0.323802	+	0.181796i	0.0228962	+	0.0128549i
$201$		0			0
$202$	−1.55979	−	1.29821i	−0.109746	−	0.0913416i
$203$	−7.73803			−0.543103
$204$		0			0
$205$	−0.656346			−0.0458412
$206$	−6.76747	−	5.63256i	−0.471512	−	0.392439i
$207$		0			0
$208$	−16.3906	+	6.26477i	−1.13649	+	0.434384i
$209$			16.4087i			1.13502i
$210$		0			0
$211$			16.3943i			1.12863i	0.825560	+	0.564315i	$0.190860\pi$
$211$			16.3943i			1.12863i	−0.825560	+	0.564315i	$0.809140\pi$
$212$	−22.3208	+	4.12033i	−1.53300	+	0.282985i
$213$		0			0
$214$	−17.9060	+	21.5139i	−1.22403	+	1.47066i
$215$	−3.24015			−0.220976
$216$		0			0
$217$	−7.01459			−0.476181
$218$	−12.3055	+	14.7850i	−0.833434	+	1.00136i
$219$		0			0
$220$	11.3638	−	2.09771i	0.766146	−	0.141428i
$221$			22.0754i			1.48495i
$222$		0			0
$223$			1.67978i			0.112487i	0.998417	+	0.0562434i	$0.0179123\pi$
$223$			1.67978i			0.112487i	−0.998417	+	0.0562434i	$0.982088\pi$
$224$	−5.35337	−	1.82795i	−0.357687	−	0.122135i
$225$		0			0
$226$	−11.4494	−	9.52933i	−0.761604	−	0.633882i
$227$	17.0700			1.13297			0.566486	−	0.824071i	$-0.308302\pi$
$227$	17.0700			1.13297			0.566486	+	0.824071i	$0.308302\pi$
$228$		0			0
$229$	−2.96057			−0.195640			−0.0978199	−	0.995204i	$-0.531187\pi$
$229$	−2.96057			−0.195640			−0.0978199	+	0.995204i	$0.531187\pi$
$230$	−13.3315	−	11.0958i	−0.879053	−	0.731635i
$231$		0			0
$232$	10.7148	−	19.0843i	0.703458	−	1.25295i
$233$		−	17.4367i		−	1.14232i	−0.820840	−	0.571158i	$-0.806494\pi$
$233$		−	17.4367i		−	1.14232i	0.820840	−	0.571158i	$-0.193506\pi$
$234$		0			0
$235$			11.5731i			0.754947i
$236$	1.87756	+	10.1712i	0.122219	+	0.662088i
$237$		0			0
$238$	−4.55266	+	5.46999i	−0.295105	+	0.354567i
$239$	9.08289			0.587523			0.293762	−	0.955879i	$-0.405093\pi$
$239$	9.08289			0.587523			0.293762	+	0.955879i	$0.405093\pi$
$240$		0			0
$241$	−18.7521			−1.20793			−0.603964	−	0.797011i	$-0.706413\pi$
$241$	−18.7521			−1.20793			−0.603964	+	0.797011i	$0.706413\pi$
$242$	3.74829	−	4.50354i	0.240949	−	0.289498i
$243$		0			0
$244$	2.32466	+	12.5932i	0.148821	+	0.806197i
$245$			2.20652i			0.140969i
$246$		0			0
$247$		−	27.4889i		−	1.74908i
$248$	9.71301	−	17.3001i	0.616777	−	1.09856i
$249$		0			0
$250$	12.3071	+	10.2432i	0.778369	+	0.647836i
$251$	19.3470			1.22117			0.610585	−	0.791951i	$-0.290935\pi$
$251$	19.3470			1.22117			0.610585	+	0.791951i	$0.290935\pi$
$252$		0			0
$253$	14.5550			0.915065
$254$	4.64621	+	3.86703i	0.291529	+	0.242639i
$255$		0			0
$256$	11.9210	−	10.6719i	0.745064	−	0.666993i
$257$			7.34328i			0.458061i	0.973419	+	0.229031i	$0.0735556\pi$
$257$			7.34328i			0.458061i	−0.973419	+	0.229031i	$0.926444\pi$
$258$		0			0
$259$			8.26904i			0.513813i
$260$	−19.0373	+	3.51422i	−1.18064	+	0.217942i
$261$		0			0
$262$	10.6806	−	12.8327i	0.659851	−	0.792806i
$263$	25.8764			1.59560			0.797802	−	0.602919i	$-0.205996\pi$
$263$	25.8764			1.59560			0.797802	+	0.602919i	$0.205996\pi$
$264$		0			0
$265$	−25.0416			−1.53829
$266$	5.66910	−	6.81138i	0.347595	−	0.417632i
$267$		0			0
$268$	11.4840	−	2.11990i	0.701496	−	0.129494i
$269$		−	11.4390i		−	0.697448i	−0.937225	−	0.348724i	$-0.886615\pi$
$269$		−	11.4390i		−	0.697448i	0.937225	−	0.348724i	$-0.113385\pi$
$270$		0			0
$271$			16.9336i			1.02865i	0.857597	+	0.514323i	$0.171957\pi$
$271$			16.9336i			1.02865i	−0.857597	+	0.514323i	$0.828043\pi$
$272$	−7.18662	−	18.8025i	−0.435753	−	1.14007i
$273$		0			0
$274$	13.8557	+	11.5321i	0.837055	+	0.696680i
$275$	−0.343792			−0.0207314
$276$		0			0
$277$	28.1049			1.68866			0.844330	−	0.535824i	$-0.179999\pi$
$277$	28.1049			1.68866			0.844330	+	0.535824i	$0.179999\pi$
$278$	−9.72714	−	8.09589i	−0.583395	−	0.485559i
$279$		0			0
$280$	−5.44193	−	3.05533i	−0.325218	−	0.182591i
$281$			8.99396i			0.536534i	0.963345	+	0.268267i	$0.0864510\pi$
$281$			8.99396i			0.536534i	−0.963345	+	0.268267i	$0.913549\pi$
$282$		0			0
$283$		−	20.9206i		−	1.24360i	−0.783177	−	0.621799i	$-0.786402\pi$
$283$		−	20.9206i		−	1.24360i	0.783177	−	0.621799i	$-0.213598\pi$
$284$	−2.70136	−	14.6339i	−0.160296	−	0.868362i
$285$		0			0
$286$	10.3922	−	12.4862i	0.614505	−	0.738323i
$287$	−0.297458			−0.0175584
$288$		0			0
$289$	−8.32376			−0.489633
$290$	15.4468	−	18.5592i	0.907068	−	1.08983i
$291$		0			0
$292$	−3.82985	−	20.7472i	−0.224125	−	1.21414i
$293$			19.8728i			1.16098i	0.814268	+	0.580489i	$0.197139\pi$
$293$			19.8728i			1.16098i	−0.814268	+	0.580489i	$0.802861\pi$
$294$		0			0
$295$			11.4110i			0.664376i
$296$	−20.3939	−	11.4500i	−1.18537	−	0.665520i
$297$		0			0
$298$	12.4026	+	10.3226i	0.718461	+	0.597974i
$299$	−24.3834			−1.41013
$300$		0			0
$301$	−1.46845			−0.0846398
$302$	10.6960	+	8.90228i	0.615486	+	0.512268i
$303$		0			0
$304$	8.94897	+	23.4133i	0.513259	+	1.34285i
$305$			14.1283i			0.808983i
$306$		0			0
$307$		−	27.7034i		−	1.58112i	−0.612385	−	0.790559i	$-0.709790\pi$
$307$		−	27.7034i		−	1.58112i	0.612385	−	0.790559i	$-0.290210\pi$
$308$	5.15010	−	0.950689i	0.293454	−	0.0541706i
$309$		0			0
$310$	14.0027	−	16.8241i	0.795298	−	0.955543i
$311$	−17.5337			−0.994247			−0.497124	−	0.867680i	$-0.665610\pi$
$311$	−17.5337			−0.994247			−0.497124	+	0.867680i	$0.665610\pi$
$312$		0			0
$313$	7.69621			0.435016			0.217508	−	0.976059i	$-0.430207\pi$
$313$	7.69621			0.435016			0.217508	+	0.976059i	$0.430207\pi$
$314$	−13.1311	+	15.7769i	−0.741032	+	0.890344i
$315$		0			0
$316$	−2.82433	+	0.521360i	−0.158881	+	0.0293288i
$317$		−	24.6839i		−	1.38639i	−0.720752	−	0.693193i	$-0.756203\pi$
$317$		−	24.6839i		−	1.38639i	0.720752	−	0.693193i	$-0.243797\pi$
$318$		0			0
$319$			20.2625i			1.13448i
$320$	15.0707	−	9.19076i	0.842480	−	0.513779i
$321$		0			0
$322$	−6.04188	−	5.02865i	−0.336701	−	0.280236i
$323$	31.5338			1.75459
$324$		0			0
$325$	0.575941			0.0319475
$326$	−8.86516	−	7.37846i	−0.490996	−	0.408655i
$327$		0			0
$328$	0.411886	−	0.733621i	0.0227426	−	0.0405074i
$329$			5.24497i			0.289165i
$330$		0			0
$331$		−	1.39054i		−	0.0764308i	−0.999270	−	0.0382154i	$-0.987833\pi$
$331$		−	1.39054i		−	0.0764308i	0.999270	−	0.0382154i	$-0.0121673\pi$
$332$	−2.41148	−	13.0636i	−0.132347	−	0.716956i
$333$		0			0
$334$	0.0355580	−	0.0427226i	0.00194565	−	0.00233768i
$335$	12.8839			0.703920
$336$		0			0
$337$	26.2175			1.42816			0.714079	−	0.700065i	$-0.246846\pi$
$337$	26.2175			1.42816			0.714079	+	0.700065i	$0.246846\pi$
$338$	−5.64869	+	6.78686i	−0.307248	+	0.369156i
$339$		0			0
$340$	−4.03132	−	21.8386i	−0.218629	−	1.18436i
$341$			18.3681i			0.994688i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	2.03334	−	3.62163i	0.109630	−	0.195265i
$345$		0			0
$346$	−15.7592	−	13.1164i	−0.847222	−	0.705142i
$347$	−4.69907			−0.252260			−0.126130	−	0.992014i	$-0.540256\pi$
$347$	−4.69907			−0.252260			−0.126130	+	0.992014i	$0.540256\pi$
$348$		0			0
$349$	−17.6012			−0.942170			−0.471085	−	0.882088i	$-0.656138\pi$
$349$	−17.6012			−0.942170			−0.471085	+	0.882088i	$0.656138\pi$
$350$	0.142710	+	0.118778i	0.00762819	+	0.00634893i
$351$		0			0
$352$	−4.78660	+	14.0181i	−0.255126	+	0.747168i
$353$			9.58823i			0.510330i	0.966898	+	0.255165i	$0.0821298\pi$
$353$			9.58823i			0.510330i	−0.966898	+	0.255165i	$0.917870\pi$
$354$		0			0
$355$		−	16.4177i		−	0.871363i
$356$	−12.7923	+	2.36141i	−0.677991	+	0.125155i
$357$		0			0
$358$	11.7245	−	14.0869i	0.619661	−	0.744517i
$359$	33.7013			1.77869			0.889344	−	0.457239i	$-0.151162\pi$
$359$	33.7013			1.77869			0.889344	+	0.457239i	$0.151162\pi$
$360$		0			0
$361$	−20.2668			−1.06667
$362$	−15.1702	+	18.2268i	−0.797327	+	0.957981i
$363$		0			0
$364$	−8.62777	+	1.59265i	−0.452218	+	0.0834778i
$365$		−	23.2762i		−	1.21833i
$366$		0			0
$367$			4.15289i			0.216779i	0.994109	+	0.108389i	$0.0345693\pi$
$367$			4.15289i			0.216779i	−0.994109	+	0.108389i	$0.965431\pi$
$368$	20.7683	−	7.93799i	1.08262	−	0.413796i
$369$		0			0
$370$	−19.8328	−	16.5068i	−1.03106	−	0.858149i
$371$	−11.3489			−0.589208
$372$		0			0
$373$	6.21570			0.321837			0.160918	−	0.986968i	$-0.448554\pi$
$373$	6.21570			0.321837			0.160918	+	0.986968i	$0.448554\pi$
$374$	14.3235	+	11.9214i	0.740649	+	0.616442i
$375$		0			0
$376$	−12.9357	−	7.26265i	−0.667107	−	0.374543i
$377$		−	33.9450i		−	1.74825i
$378$		0			0
$379$		−	29.4944i		−	1.51502i	−0.652821	−	0.757512i	$-0.726415\pi$
$379$		−	29.4944i		−	1.51502i	0.652821	−	0.757512i	$-0.273585\pi$
$380$	5.01992	+	27.1940i	0.257516	+	1.39502i
$381$		0			0
$382$	−14.8494	+	17.8414i	−0.759762	+	0.912847i
$383$	23.6674			1.20935			0.604674	−	0.796473i	$-0.293303\pi$
$383$	23.6674			1.20935			0.604674	+	0.796473i	$0.293303\pi$
$384$		0			0
$385$	5.77789			0.294468
$386$	9.14385	−	10.9863i	0.465410	−	0.559186i
$387$		0			0
$388$	6.01021	+	32.5587i	0.305122	+	1.65292i
$389$			31.9344i			1.61914i	0.587025	+	0.809569i	$0.300299\pi$
$389$			31.9344i			1.61914i	−0.587025	+	0.809569i	$0.699701\pi$
$390$		0			0
$391$		−	27.9714i		−	1.41457i
$392$	−2.46630	−	1.38469i	−0.124567	−	0.0699373i
$393$		0			0
$394$	−3.50248	−	2.91511i	−0.176452	−	0.146861i
$395$	−3.16861			−0.159430
$396$		0			0
$397$	−7.50196			−0.376513			−0.188256	−	0.982120i	$-0.560284\pi$
$397$	−7.50196			−0.376513			−0.188256	+	0.982120i	$0.560284\pi$
$398$	−20.9415	−	17.4296i	−1.04970	−	0.873666i
$399$		0			0
$400$	−0.490551	+	0.187497i	−0.0245275	+	0.00937483i
$401$			11.3393i			0.566257i	0.959082	+	0.283129i	$0.0913724\pi$
$401$			11.3393i			0.566257i	−0.959082	+	0.283129i	$0.908628\pi$
$402$		0			0
$403$		−	30.7714i		−	1.53283i
$404$	2.82226	−	0.520978i	0.140413	−	0.0259196i
$405$		0			0
$406$	7.00055	−	8.41110i	0.347431	−	0.417436i
$407$	21.6530			1.07330
$408$		0			0
$409$	6.73161			0.332856			0.166428	−	0.986054i	$-0.446777\pi$
$409$	6.73161			0.332856			0.166428	+	0.986054i	$0.446777\pi$
$410$	0.593792	−	0.713436i	0.0293253	−	0.0352341i
$411$		0			0
$412$	12.2450	−	2.26038i	0.603266	−	0.111361i
$413$			5.17152i			0.254474i
$414$		0			0
$415$		−	14.6560i		−	0.719434i
$416$	8.01881	−	23.4840i	0.393154	−	1.15140i
$417$		0			0
$418$	−17.8360	−	14.8449i	−0.872387	−	0.726086i
$419$	24.8185			1.21246			0.606230	−	0.795289i	$-0.292681\pi$
$419$	24.8185			1.21246			0.606230	+	0.795289i	$0.292681\pi$
$420$		0			0
$421$	35.1518			1.71319			0.856596	−	0.515988i	$-0.172575\pi$
$421$	35.1518			1.71319			0.856596	+	0.515988i	$0.172575\pi$
$422$	−17.8203	−	14.8318i	−0.867479	−	0.722002i
$423$		0			0
$424$	15.7147	−	27.9899i	0.763175	−	1.35931i
$425$			0.660689i			0.0320481i
$426$		0			0
$427$			6.40298i			0.309862i
$428$	−7.18576	−	38.9269i	−0.347337	−	1.88160i
$429$		0			0
$430$	2.93134	−	3.52198i	0.141362	−	0.169845i
$431$	−25.3565			−1.22138			−0.610690	−	0.791869i	$-0.709108\pi$
$431$	−25.3565			−1.22138			−0.610690	+	0.791869i	$0.709108\pi$
$432$		0			0
$433$	−17.8476			−0.857702			−0.428851	−	0.903375i	$-0.641081\pi$
$433$	−17.8476			−0.857702			−0.428851	+	0.903375i	$0.641081\pi$
$434$	6.34605	−	7.62473i	0.304620	−	0.365999i
$435$		0			0
$436$	−4.93827	−	26.7517i	−0.236500	−	1.28118i
$437$			34.8307i			1.66618i
$438$		0			0
$439$			19.5918i			0.935064i	0.883976	+	0.467532i	$0.154857\pi$
$439$			19.5918i			0.935064i	−0.883976	+	0.467532i	$0.845143\pi$
$440$	−8.00057	+	14.2500i	−0.381412	+	0.679342i
$441$		0			0
$442$	−23.9956	−	19.9715i	−1.14135	−	0.949947i
$443$	26.1483			1.24234			0.621171	−	0.783675i	$-0.286657\pi$
$443$	26.1483			1.24234			0.621171	+	0.783675i	$0.286657\pi$
$444$		0			0
$445$	−14.3517			−0.680334
$446$	−1.82590	−	1.51969i	−0.0864587	−	0.0719594i
$447$		0			0
$448$	6.83011	−	4.16528i	0.322692	−	0.196791i
$449$		−	8.96462i		−	0.423067i	−0.977371	−	0.211533i	$-0.932154\pi$
$449$		−	8.96462i		−	0.423067i	0.977371	−	0.211533i	$-0.0678457\pi$
$450$		0			0
$451$			0.778911i			0.0366775i
$452$	20.7164	−	3.82417i	0.974419	−	0.179874i
$453$		0			0
$454$	−15.4431	+	18.5547i	−0.724780	+	0.870816i
$455$	−9.67948			−0.453781
$456$		0			0
$457$	5.36068			0.250762			0.125381	−	0.992109i	$-0.459985\pi$
$457$	5.36068			0.250762			0.125381	+	0.992109i	$0.459985\pi$
$458$	2.67841	−	3.21808i	0.125154	−	0.150371i
$459$		0			0
$460$	24.1219	−	4.45280i	1.12469	−	0.207613i
$461$		−	25.2744i		−	1.17714i	−0.808445	−	0.588572i	$-0.799690\pi$
$461$		−	25.2744i		−	1.17714i	0.808445	−	0.588572i	$-0.200310\pi$
$462$		0			0
$463$			18.5077i			0.860126i	0.902799	+	0.430063i	$0.141509\pi$
$463$			18.5077i			0.860126i	−0.902799	+	0.430063i	$0.858491\pi$
$464$	11.0507	+	28.9122i	0.513017	+	1.34221i
$465$		0			0
$466$	18.9534	+	15.7749i	0.877998	+	0.730757i
$467$	25.2539			1.16861			0.584306	−	0.811533i	$-0.301367\pi$
$467$	25.2539			1.16861			0.584306	+	0.811533i	$0.301367\pi$
$468$		0			0
$469$	5.83901			0.269620
$470$	−12.5798	−	10.4701i	−0.580261	−	0.482951i
$471$		0			0
$472$	−12.7545	−	7.16093i	−0.587074	−	0.329609i
$473$			3.84521i			0.176803i
$474$		0			0
$475$		−	0.822709i		−	0.0377485i
$476$	−1.82701	−	9.89733i	−0.0837408	−	0.453643i
$477$		0			0
$478$	−8.21723	+	9.87293i	−0.375848	+	0.451578i
$479$	−37.2953			−1.70406			−0.852032	−	0.523489i	$-0.824630\pi$
$479$	−37.2953			−1.70406			−0.852032	+	0.523489i	$0.824630\pi$
$480$		0			0
$481$	−36.2744			−1.65397
$482$	16.9649	−	20.3832i	0.772730	−	0.928428i
$483$		0			0
$484$	1.50421	+	8.14864i	0.0683731	+	0.370393i
$485$			36.5275i			1.65863i
$486$		0			0
$487$		−	35.4694i		−	1.60727i	−0.595122	−	0.803635i	$-0.702896\pi$
$487$		−	35.4694i		−	1.60727i	0.595122	−	0.803635i	$-0.297104\pi$
$488$	−15.7917	−	8.86613i	−0.714856	−	0.401351i
$489$		0			0
$490$	−2.39844	−	1.99622i	−0.108351	−	0.0901801i
$491$	−25.6126			−1.15588			−0.577940	−	0.816079i	$-0.696143\pi$
$491$	−25.6126			−1.15588			−0.577940	+	0.816079i	$0.696143\pi$
$492$		0			0
$493$	38.9399			1.75376
$494$	29.8800	+	24.8691i	1.34436	+	1.11891i
$495$		0			0
$496$	10.0176	+	26.2091i	0.449802	+	1.17683i
$497$		−	7.44057i		−	0.333755i
$498$		0			0
$499$			36.8181i			1.64820i	0.566442	+	0.824102i	$0.308319\pi$
$499$			36.8181i			1.64820i	−0.566442	+	0.824102i	$0.691681\pi$
$500$	−22.2683	+	4.11065i	−0.995869	+	0.183834i
$501$		0			0
$502$	−17.5031	+	21.0298i	−0.781200	+	0.938605i
$503$	−42.9451			−1.91483			−0.957414	−	0.288718i	$-0.906771\pi$
$503$	−42.9451			−1.91483			−0.957414	+	0.288718i	$0.906771\pi$
$504$		0			0
$505$	3.16628			0.140898
$506$	−13.1678	+	15.8210i	−0.585381	+	0.703330i
$507$		0			0
$508$	−8.40679	+	1.55186i	−0.372991	+	0.0688527i
$509$			6.27075i			0.277946i	0.990296	+	0.138973i	$0.0443802\pi$
$509$			6.27075i			0.277946i	−0.990296	+	0.138973i	$0.955620\pi$
$510$		0			0
$511$		−	10.5489i		−	0.466654i
$512$	0.815265	+	22.6127i	0.0360300	+	0.999351i
$513$		0			0
$514$	−7.98201	−	6.64342i	−0.352072	−	0.293029i
$515$	13.7376			0.605351
$516$		0			0
$517$	13.7343			0.604032
$518$	−8.98830	−	7.48095i	−0.394923	−	0.328694i
$519$		0			0
$520$	13.4031	−	23.8725i	0.587763	−	1.04688i
$521$			13.8276i			0.605798i	0.953023	+	0.302899i	$0.0979545\pi$
$521$			13.8276i			0.605798i	−0.953023	+	0.302899i	$0.902046\pi$
$522$		0			0
$523$			8.15433i			0.356564i	0.983979	+	0.178282i	$0.0570539\pi$
$523$			8.15433i			0.356564i	−0.983979	+	0.178282i	$0.942946\pi$
$524$	4.28619	+	23.2193i	0.187243	+	1.01434i
$525$		0			0
$526$	−23.4102	+	28.1271i	−1.02073	+	1.22640i
$527$	35.2993			1.53766
$528$		0			0
$529$	7.89583			0.343297
$530$	22.6550	−	27.2198i	0.984070	−	1.18235i
$531$		0			0
$532$	2.27504	+	12.3244i	0.0986356	+	0.534332i
$533$		−	1.30488i		−	0.0565206i
$534$		0			0
$535$		−	43.6720i		−	1.88811i
$536$	−8.08520	+	14.4007i	−0.349227	+	0.622017i
$537$		0			0
$538$	12.4340	+	10.3488i	0.536067	+	0.446168i
$539$	2.61856			0.112789
$540$		0			0
$541$	24.7919			1.06589			0.532943	−	0.846151i	$-0.321086\pi$
$541$	24.7919			1.06589			0.532943	+	0.846151i	$0.321086\pi$
$542$	−18.4066	−	15.3198i	−0.790629	−	0.658040i
$543$		0			0
$544$	26.9396	+	9.19875i	1.15503	+	0.394393i
$545$		−	30.0127i		−	1.28560i
$546$		0			0
$547$		−	5.90150i		−	0.252330i	−0.992009	−	0.126165i	$-0.959733\pi$
$547$		−	5.90150i		−	0.252330i	0.992009	−	0.126165i	$-0.0402668\pi$
$548$	−25.0704	+	4.62789i	−1.07095	+	0.197694i
$549$		0			0
$550$	0.311026	−	0.373695i	0.0132622	−	0.0159344i
$551$	−48.4890			−2.06570
$552$		0			0
$553$	−1.43602			−0.0610659
$554$	−25.4263	+	30.5495i	−1.08026	+	1.29792i
$555$		0			0
$556$	17.6002	−	3.24892i	0.746413	−	0.137785i
$557$			13.0313i			0.552153i	0.961136	+	0.276076i	$0.0890342\pi$
$557$			13.0313i			0.552153i	−0.961136	+	0.276076i	$0.910966\pi$
$558$		0			0
$559$		−	6.44173i		−	0.272456i
$560$	8.24437	−	3.15114i	0.348388	−	0.133160i
$561$		0			0
$562$	−9.77627	−	8.13678i	−0.412387	−	0.343229i
$563$	−26.3725			−1.11147			−0.555735	−	0.831359i	$-0.687563\pi$
$563$	−26.3725			−1.11147			−0.555735	+	0.831359i	$0.687563\pi$
$564$		0			0
$565$	23.2417			0.977786
$566$	22.7403	+	18.9267i	0.955845	+	0.795549i
$567$		0			0
$568$	18.3507	+	10.3029i	0.769978	+	0.432299i
$569$		−	37.5392i		−	1.57372i	−0.617129	−	0.786862i	$-0.711704\pi$
$569$		−	37.5392i		−	1.57372i	0.617129	−	0.786862i	$-0.288296\pi$
$570$		0			0
$571$			26.8818i			1.12497i	0.826808	+	0.562485i	$0.190154\pi$
$571$			26.8818i			1.12497i	−0.826808	+	0.562485i	$0.809846\pi$
$572$	4.17046	+	22.5923i	0.174376	+	0.944632i
$573$		0			0
$574$	0.269108	−	0.323331i	0.0112324	−	0.0134956i
$575$	−0.729765			−0.0304333
$576$		0			0
$577$	−25.4265			−1.05852			−0.529259	−	0.848460i	$-0.677530\pi$
$577$	−25.4265			−1.05852			−0.529259	+	0.848460i	$0.677530\pi$
$578$	7.53045	−	9.04777i	0.313226	−	0.376338i
$579$		0			0
$580$	6.19889	+	33.5808i	0.257395	+	1.39437i
$581$		−	6.64214i		−	0.275562i
$582$		0			0
$583$			29.7179i			1.23079i
$584$	26.0167	+	14.6069i	1.07658	+	0.604437i
$585$		0			0
$586$	−21.6013	−	17.9788i	−0.892342	−	0.742696i
$587$	13.2956			0.548768			0.274384	−	0.961620i	$-0.411526\pi$
$587$	13.2956			0.548768			0.274384	+	0.961620i	$0.411526\pi$
$588$		0			0
$589$	−43.9557			−1.81116
$590$	−12.4036	−	10.3235i	−0.510647	−	0.425011i
$591$		0			0
$592$	30.8963	−	11.8091i	1.26983	−	0.485350i
$593$			38.1748i			1.56765i	0.620982	+	0.783825i	$0.286734\pi$
$593$			38.1748i			1.56765i	−0.620982	+	0.783825i	$0.713266\pi$
$594$		0			0
$595$		−	11.1038i		−	0.455211i
$596$	−22.4410	+	4.14253i	−0.919220	+	0.169685i
$597$		0			0
$598$	22.0595	−	26.5044i	0.902082	−	1.08384i
$599$	−16.5977			−0.678164			−0.339082	−	0.940757i	$-0.610116\pi$
$599$	−16.5977			−0.678164			−0.339082	+	0.940757i	$0.610116\pi$
$600$		0			0
$601$	20.0204			0.816651			0.408326	−	0.912836i	$-0.366113\pi$
$601$	20.0204			0.816651			0.408326	+	0.912836i	$0.366113\pi$
$602$	1.32849	−	1.59617i	0.0541453	−	0.0650552i
$603$		0			0
$604$	−19.3532	+	3.57253i	−0.787471	+	0.145364i
$605$			9.14194i			0.371673i
$606$		0			0
$607$		−	12.3393i		−	0.500837i	−0.968138	−	0.250418i	$-0.919432\pi$
$607$		−	12.3393i		−	0.500837i	0.968138	−	0.250418i	$-0.0805681\pi$
$608$	−33.5460	−	11.4545i	−1.36047	−	0.464543i
$609$		0			0
$610$	−15.3572	−	12.7818i	−0.621794	−	0.517519i
$611$	−23.0085			−0.930824
$612$		0			0
$613$	−15.8890			−0.641749			−0.320875	−	0.947122i	$-0.603977\pi$
$613$	−15.8890			−0.641749			−0.320875	+	0.947122i	$0.603977\pi$
$614$	30.1131	+	25.0631i	1.21527	+	1.01147i
$615$		0			0
$616$	−3.62588	+	6.45815i	−0.146091	+	0.260206i
$617$		−	43.4512i		−	1.74928i	−0.484773	−	0.874640i	$-0.661098\pi$
$617$		−	43.4512i		−	1.74928i	0.484773	−	0.874640i	$-0.338902\pi$
$618$		0			0
$619$			14.3026i			0.574868i	0.957800	+	0.287434i	$0.0928023\pi$
$619$			14.3026i			0.574868i	−0.957800	+	0.287434i	$0.907198\pi$
$620$	5.61934	+	30.4413i	0.225678	+	1.22255i
$621$		0			0
$622$	15.8627	−	19.0589i	0.636035	−	0.764190i
$623$	−6.50422			−0.260586
$624$		0			0
$625$	−24.3263			−0.973052
$626$	−6.96271	+	8.36564i	−0.278286	+	0.334358i
$627$		0			0
$628$	−5.26959	−	28.5466i	−0.210280	−	1.13913i
$629$		−	41.6121i		−	1.65918i
$630$		0			0
$631$			20.8394i			0.829604i	0.909912	+	0.414802i	$0.136149\pi$
$631$			20.8394i			0.829604i	−0.909912	+	0.414802i	$0.863851\pi$
$632$	1.98844	−	3.54166i	0.0790960	−	0.140880i
$633$		0			0
$634$	26.8309	+	22.3314i	1.06559	+	0.886892i
$635$	−9.43155			−0.374280
$636$		0			0
$637$	−4.38677			−0.173810
$638$	−22.0249	−	18.3313i	−0.871976	−	0.725744i
$639$		0			0
$640$	−3.64423	+	24.6964i	−0.144051	+	0.976213i
$641$			1.38336i			0.0546395i	0.999627	+	0.0273198i	$0.00869723\pi$
$641$			1.38336i			0.0546395i	−0.999627	+	0.0273198i	$0.991303\pi$
$642$		0			0
$643$			34.8129i			1.37289i	0.727183	+	0.686443i	$0.240829\pi$
$643$			34.8129i			1.37289i	−0.727183	+	0.686443i	$0.759171\pi$
$644$	10.9321	−	2.01803i	0.430785	−	0.0795213i
$645$		0			0
$646$	−28.5285	+	34.2767i	−1.12244	+	1.34860i
$647$	−17.8682			−0.702473			−0.351236	−	0.936287i	$-0.614239\pi$
$647$	−17.8682			−0.702473			−0.351236	+	0.936287i	$0.614239\pi$
$648$		0			0
$649$	13.5419			0.531566
$650$	−0.521050	+	0.626038i	−0.0204373	+	0.0245552i
$651$		0			0
$652$	16.0405	−	2.96102i	0.628195	−	0.115962i
$653$		−	31.7513i		−	1.24252i	−0.783603	−	0.621261i	$-0.786621\pi$
$653$		−	31.7513i		−	1.24252i	0.783603	−	0.621261i	$-0.213379\pi$
$654$		0			0
$655$			26.0497i			1.01784i
$656$	0.424802	+	1.11142i	0.0165857	+	0.0433935i
$657$		0			0
$658$	−5.70119	−	4.74510i	−0.222256	−	0.184983i
$659$	−26.8898			−1.04748			−0.523739	−	0.851879i	$-0.675463\pi$
$659$	−26.8898			−1.04748			−0.523739	+	0.851879i	$0.675463\pi$
$660$		0			0
$661$	9.17059			0.356695			0.178347	−	0.983968i	$-0.442925\pi$
$661$	9.17059			0.356695			0.178347	+	0.983968i	$0.442925\pi$
$662$	1.51149	+	1.25801i	0.0587456	+	0.0488939i
$663$		0			0
$664$	16.3815	+	9.19729i	0.635726	+	0.356924i
$665$			13.8267i			0.536178i
$666$		0			0
$667$			43.0111i			1.66540i
$668$	0.0142696	+	0.0773017i	0.000552108	+	0.00299089i
$669$		0			0
$670$	−11.6559	+	14.0045i	−0.450308	+	0.541042i
$671$	16.7666			0.647267
$672$		0			0
$673$	−49.1712			−1.89541			−0.947706	−	0.319146i	$-0.896604\pi$
$673$	−49.1712			−1.89541			−0.947706	+	0.319146i	$0.896604\pi$
$674$	−23.7188	+	28.4980i	−0.913615	+	1.09770i
$675$		0			0
$676$	−2.26685	−	12.2801i	−0.0871866	−	0.472310i
$677$			15.6856i			0.602847i	0.953490	+	0.301423i	$0.0974617\pi$
$677$			15.6856i			0.602847i	−0.953490	+	0.301423i	$0.902538\pi$
$678$		0			0
$679$			16.5544i			0.635299i
$680$	27.3853	+	15.3753i	1.05018	+	0.589615i
$681$		0			0
$682$	−19.9658	−	16.6175i	−0.764529	−	0.636317i
$683$	22.7178			0.869273			0.434637	−	0.900606i	$-0.356877\pi$
$683$	22.7178			0.869273			0.434637	+	0.900606i	$0.356877\pi$
$684$		0			0
$685$	−28.1264			−1.07465
$686$	−1.08698	−	0.904694i	−0.0415012	−	0.0345414i
$687$		0			0
$688$	2.09710	+	5.48667i	0.0799510	+	0.209177i
$689$		−	49.7852i		−	1.89667i
$690$		0			0
$691$		−	0.252762i		−	0.00961553i	−0.999988	−	0.00480776i	$-0.998470\pi$
$691$		−	0.252762i		−	0.00961553i	0.999988	−	0.00480776i	$-0.00153036\pi$
$692$	28.5146	−	5.26368i	1.08396	−	0.200095i
$693$		0			0
$694$	4.25122	−	5.10781i	0.161374	−	0.193890i
$695$	19.7456			0.748992
$696$		0			0
$697$	1.49689			0.0566987
$698$	15.9237	−	19.1322i	0.602721	−	0.724164i
$699$		0			0
$700$	−0.258218	+	0.0476661i	−0.00975973	+	0.00180161i
$701$			30.8464i			1.16505i	0.812813	+	0.582525i	$0.197935\pi$
$701$			30.8464i			1.16505i	−0.812813	+	0.582525i	$0.802065\pi$
$702$		0			0
$703$			51.8165i			1.95430i
$704$	−10.9070	−	17.8850i	−0.411074	−	0.674068i
$705$		0			0
$706$	−10.4222	−	8.67441i	−0.392246	−	0.326466i
$707$	1.43497			0.0539676
$708$		0			0
$709$	5.48850			0.206125			0.103062	−	0.994675i	$-0.467136\pi$
$709$	5.48850			0.206125			0.103062	+	0.994675i	$0.467136\pi$
$710$	17.8458	+	14.8530i	0.669740	+	0.557424i
$711$		0			0
$712$	9.00631	−	16.0414i	0.337526	−	0.601176i
$713$			38.9899i			1.46018i
$714$		0			0
$715$			25.3463i			0.947897i
$716$	4.70512	+	25.4887i	0.175839	+	0.952558i
$717$		0			0
$718$	−30.4894	+	36.6327i	−1.13785	+	1.36712i
$719$	5.25761			0.196076			0.0980380	−	0.995183i	$-0.468743\pi$
$719$	5.25761			0.196076			0.0980380	+	0.995183i	$0.468743\pi$
$720$		0			0
$721$	6.22593			0.231866
$722$	18.3353	−	22.0297i	0.682368	−	0.819859i
$723$		0			0
$724$	−6.08787	−	32.9794i	−0.226254	−	1.22567i
$725$		−	1.01593i		−	0.0377307i
$726$		0			0
$727$		−	10.2672i		−	0.380790i	−0.981708	−	0.190395i	$-0.939023\pi$
$727$		−	10.2672i		−	0.380790i	0.981708	−	0.190395i	$-0.0609769\pi$
$728$	6.07431	−	10.8191i	0.225129	−	0.400982i
$729$		0			0
$730$	25.3008	+	21.0578i	0.936426	+	0.779386i
$731$	7.38962			0.273315
$732$		0			0
$733$	37.9665			1.40232			0.701162	−	0.713002i	$-0.252665\pi$
$733$	37.9665			1.40232			0.701162	+	0.713002i	$0.252665\pi$
$734$	−4.51411	−	3.75709i	−0.166619	−	0.138677i
$735$		0			0
$736$	−10.1605	+	29.7562i	−0.374521	+	1.09683i
$737$		−	15.2898i		−	0.563206i
$738$		0			0
$739$		−	19.8184i		−	0.729032i	−0.931197	−	0.364516i	$-0.881234\pi$
$739$		−	19.8184i		−	0.729032i	0.931197	−	0.364516i	$-0.118766\pi$
$740$	35.8853	−	6.62428i	1.31917	−	0.243513i
$741$		0			0
$742$	10.2673	−	12.3361i	0.376925	−	0.452872i
$743$	17.9899			0.659987			0.329993	−	0.943983i	$-0.392953\pi$
$743$	17.9899			0.659987			0.329993	+	0.943983i	$0.392953\pi$
$744$		0			0
$745$	−25.1765			−0.922397
$746$	−5.62330	+	6.75635i	−0.205884	+	0.247368i
$747$		0			0
$748$	−25.9167	+	4.78413i	−0.947609	+	0.174925i
$749$		−	19.7923i		−	0.723195i
$750$		0			0
$751$		−	41.6685i		−	1.52050i	−0.649628	−	0.760252i	$-0.725075\pi$
$751$		−	41.6685i		−	1.52050i	0.649628	−	0.760252i	$-0.274925\pi$
$752$	19.5972	−	7.49038i	0.714636	−	0.273146i
$753$		0			0
$754$	36.8976	+	30.7098i	1.34373	+	1.11838i
$755$	−21.7123			−0.790193
$756$		0			0
$757$	24.1980			0.879491			0.439745	−	0.898122i	$-0.355069\pi$
$757$	24.1980			0.879491			0.439745	+	0.898122i	$0.355069\pi$
$758$	32.0598	+	26.6834i	1.16447	+	0.969184i
$759$		0			0
$760$	−34.1009	−	19.1457i	−1.23697	−	0.694488i
$761$		−	1.86001i		−	0.0674254i	−0.999432	−	0.0337127i	$-0.989267\pi$
$761$		−	1.86001i		−	0.0674254i	0.999432	−	0.0337127i	$-0.0107331\pi$
$762$		0			0
$763$		−	13.6019i		−	0.492420i
$764$	−5.95915	−	32.2821i	−0.215594	−	1.16792i
$765$		0			0
$766$	−21.4117	+	25.7260i	−0.773638	+	0.929519i
$767$	−22.6863			−0.819153
$768$		0			0
$769$	2.43531			0.0878195			0.0439098	−	0.999036i	$-0.486019\pi$
$769$	2.43531			0.0878195			0.0439098	+	0.999036i	$0.486019\pi$
$770$	−5.22722	+	6.28046i	−0.188376	+	0.226332i
$771$		0			0
$772$	3.66948	+	19.8784i	0.132067	+	0.715439i
$773$		−	12.7681i		−	0.459236i	−0.973281	−	0.229618i	$-0.926252\pi$
$773$		−	12.7681i		−	0.459236i	0.973281	−	0.229618i	$-0.0737476\pi$
$774$		0			0
$775$		−	0.920948i		−	0.0330814i
$776$	−40.8281	−	22.9227i	−1.46564	−	0.822876i
$777$		0			0
$778$	−34.7121	−	28.8908i	−1.24449	−	1.03579i
$779$	−1.86397			−0.0667836
$780$		0			0
$781$	−19.4836			−0.697177
$782$	30.4044	+	25.3055i	1.08726	+	0.904924i
$783$		0			0
$784$	3.73638	−	1.42811i	0.133442	−	0.0510038i
$785$		−	32.0263i		−	1.14307i
$786$		0			0
$787$		−	35.2630i		−	1.25699i	−0.777813	−	0.628496i	$-0.783671\pi$
$787$		−	35.2630i		−	1.25699i	0.777813	−	0.628496i	$-0.216329\pi$
$788$	6.33734	−	1.16985i	0.225759	−	0.0416742i
$789$		0			0
$790$	2.86662	−	3.44422i	0.101990	−	0.122540i
$791$	10.5332			0.374518
$792$		0			0
$793$	−28.0884			−0.997449
$794$	6.78698	−	8.15450i	0.240861	−	0.289392i
$795$		0			0
$796$	37.8913	−	6.99458i	1.34302	−	0.247916i
$797$		−	12.0226i		−	0.425862i	−0.977067	−	0.212931i	$-0.931699\pi$
$797$		−	12.0226i		−	0.425862i	0.977067	−	0.212931i	$-0.0683009\pi$
$798$		0			0
$799$		−	26.3941i		−	0.933757i
$800$	0.239993	−	0.702847i	0.00848502	−	0.0248494i
$801$		0			0
$802$	−12.3256	−	10.2586i	−0.435232	−	0.362243i
$803$	−27.6228			−0.974787
$804$		0			0
$805$	12.2647			0.432274
$806$	33.4479	+	27.8387i	1.17815	+	0.980576i
$807$		0			0
$808$	−1.98698	+	3.53907i	−0.0699019	+	0.124504i
$809$		−	25.2491i		−	0.887712i	−0.896098	−	0.443856i	$-0.853610\pi$
$809$		−	25.2491i		−	0.887712i	0.896098	−	0.443856i	$-0.146390\pi$
$810$		0			0
$811$			15.6600i			0.549896i	0.961459	+	0.274948i	$0.0886607\pi$
$811$			15.6600i			0.549896i	−0.961459	+	0.274948i	$0.911339\pi$
$812$	2.80936	+	15.2189i	0.0985891	+	0.534080i
$813$		0			0
$814$	−19.5893	+	23.5364i	−0.686605	+	0.824949i
$815$	17.9958			0.630365
$816$		0			0
$817$	−9.20176			−0.321929
$818$	−6.09004	+	7.31713i	−0.212933	+	0.255838i
$819$		0			0
$820$	0.238292	+	1.29088i	0.00832151	+	0.0450795i
$821$		−	33.5606i		−	1.17127i	−0.810574	−	0.585636i	$-0.800845\pi$
$821$		−	33.5606i		−	1.17127i	0.810574	−	0.585636i	$-0.199155\pi$
$822$		0			0
$823$			9.44460i			0.329218i	0.986359	+	0.164609i	$0.0526363\pi$
$823$			9.44460i			0.329218i	−0.986359	+	0.164609i	$0.947364\pi$
$824$	−8.62096	+	15.3550i	−0.300325	+	0.534917i
$825$		0			0
$826$	−5.62134	−	4.67864i	−0.195592	−	0.162791i
$827$	−29.0336			−1.00960			−0.504798	−	0.863238i	$-0.668433\pi$
$827$	−29.0336			−1.00960			−0.504798	+	0.863238i	$0.668433\pi$
$828$		0			0
$829$	−17.9731			−0.624232			−0.312116	−	0.950044i	$-0.601038\pi$
$829$	−17.9731			−0.624232			−0.312116	+	0.950044i	$0.601038\pi$
$830$	15.9308	+	13.2592i	0.552965	+	0.460233i
$831$		0			0
$832$	18.2721	+	29.9621i	0.633472	+	1.03875i
$833$		−	5.03227i		−	0.174358i
$834$		0			0
$835$			0.0867246i			0.00300123i
$836$	32.2722	−	5.95733i	1.11616	−	0.206039i
$837$		0			0
$838$	−22.4531	+	26.9772i	−0.775629	+	0.931912i
$839$	5.95414			0.205560			0.102780	−	0.994704i	$-0.467226\pi$
$839$	5.95414			0.205560			0.102780	+	0.994704i	$0.467226\pi$
$840$		0			0
$841$	−30.8771			−1.06473
$842$	−31.8016	+	38.2093i	−1.09595	+	1.31678i
$843$		0			0
$844$	32.2438	−	5.95209i	1.10988	−	0.204879i
$845$		−	13.7770i		−	0.473942i
$846$		0			0
$847$			4.14316i			0.142361i
$848$	16.2075	+	42.4039i	0.556568	+	1.45616i
$849$		0			0
$850$	−0.718157	−	0.597721i	−0.0246326	−	0.0205017i
$851$	45.9627			1.57558
$852$		0			0
$853$	30.1711			1.03304			0.516520	−	0.856275i	$-0.327227\pi$
$853$	30.1711			1.03304			0.516520	+	0.856275i	$0.327227\pi$
$854$	−6.95993	−	5.79274i	−0.238164	−	0.198223i
$855$		0			0
$856$	48.8138	+	27.4061i	1.66842	+	0.936723i
$857$			12.8259i			0.438124i	0.975711	+	0.219062i	$0.0702998\pi$
$857$			12.8259i			0.438124i	−0.975711	+	0.219062i	$0.929700\pi$
$858$		0			0
$859$		−	11.9691i		−	0.408381i	−0.978931	−	0.204191i	$-0.934544\pi$
$859$		−	11.9691i		−	0.408381i	0.978931	−	0.204191i	$-0.0654562\pi$
$860$	1.17636	+	6.37263i	0.0401136	+	0.217305i
$861$		0			0
$862$	22.9399	−	27.5621i	0.781336	−	0.938768i
$863$	38.7579			1.31933			0.659667	−	0.751558i	$-0.270697\pi$
$863$	38.7579			1.31933			0.659667	+	0.751558i	$0.270697\pi$
$864$		0			0
$865$	31.9904			1.08771
$866$	16.1466	−	19.4000i	0.548685	−	0.659240i
$867$		0			0
$868$	2.54671	+	13.7961i	0.0864408	+	0.468270i
$869$			3.76031i			0.127560i
$870$		0			0
$871$			25.6144i			0.867910i
$872$	33.5463	+	18.8343i	1.13602	+	0.637810i
$873$		0			0
$874$	−37.8604	−	31.5112i	−1.28065	−	1.06588i
$875$	−11.3223			−0.382763
$876$		0			0
$877$	27.9599			0.944140			0.472070	−	0.881561i	$-0.343507\pi$
$877$	27.9599			0.944140			0.472070	+	0.881561i	$0.343507\pi$
$878$	−21.2959	−	17.7246i	−0.718702	−	0.598175i
$879$		0			0
$880$	−8.25143	−	21.5884i	−0.278156	−	0.727744i
$881$		−	22.8190i		−	0.768793i	−0.923168	−	0.384396i	$-0.874410\pi$
$881$		−	22.8190i		−	0.768793i	0.923168	−	0.384396i	$-0.125590\pi$
$882$		0			0
$883$			9.24714i			0.311191i	0.987821	+	0.155596i	$0.0497296\pi$
$883$			9.24714i			0.311191i	−0.987821	+	0.155596i	$0.950270\pi$
$884$	43.4173	−	8.01467i	1.46028	−	0.269563i
$885$		0			0
$886$	−23.6562	+	28.4227i	−0.794744	+	0.954879i
$887$	−21.2573			−0.713750			−0.356875	−	0.934152i	$-0.616158\pi$
$887$	−21.2573			−0.713750			−0.356875	+	0.934152i	$0.616158\pi$
$888$		0			0
$889$	−4.27441			−0.143359
$890$	12.9839	−	15.6000i	0.435220	−	0.522913i
$891$		0			0
$892$	3.30375	−	0.609860i	0.110618	−	0.0204196i
$893$			32.8667i			1.09984i
$894$		0			0
$895$			28.5957i			0.955849i
$896$	−1.65158	+	11.1925i	−0.0551753	+	0.373916i
$897$		0			0
$898$	9.74438	+	8.11024i	0.325174	+	0.270642i
$899$	−54.2791			−1.81031
$900$		0			0
$901$	57.1110			1.90264
$902$	−0.846662	−	0.704676i	−0.0281908	−	0.0234631i
$903$		0			0
$904$	−14.5852	+	25.9781i	−0.485097	+	0.864018i
$905$		−	36.9995i		−	1.22991i
$906$		0			0
$907$		−	25.3238i		−	0.840862i	−0.907325	−	0.420431i	$-0.861879\pi$
$907$		−	25.3238i		−	0.840862i	0.907325	−	0.420431i	$-0.138121\pi$
$908$	−6.19739	−	33.5727i	−0.205668	−	1.11415i
$909$		0			0
$910$	8.75696	−	10.5214i	0.290290	−	0.348782i
$911$	−23.0658			−0.764204			−0.382102	−	0.924120i	$-0.624800\pi$
$911$	−23.0658			−0.764204			−0.382102	+	0.924120i	$0.624800\pi$
$912$		0			0
$913$	−17.3928			−0.575618
$914$	−4.84978	+	5.82696i	−0.160416	+	0.192739i
$915$		0			0
$916$	1.07486	+	5.82276i	0.0355143	+	0.192389i
$917$			11.8058i			0.389862i
$918$		0			0
$919$			15.0198i			0.495458i	0.968829	+	0.247729i	$0.0796843\pi$
$919$			15.0198i			0.495458i	−0.968829	+	0.247729i	$0.920316\pi$
$920$	−16.9828	+	30.2484i	−0.559906	+	0.997261i
$921$		0			0
$922$	27.4728	+	22.8656i	0.904767	+	0.753037i
$923$	32.6401			1.07436
$924$		0			0
$925$	−1.08565			−0.0356958
$926$	−20.1175	−	16.7438i	−0.661104	−	0.550236i
$927$		0			0
$928$	−41.4246	−	14.1447i	−1.35983	−	0.464324i
$929$		−	37.6911i		−	1.23660i	−0.785940	−	0.618302i	$-0.787821\pi$
$929$		−	37.6911i		−	1.23660i	0.785940	−	0.618302i	$-0.212179\pi$
$930$		0			0
$931$			6.26632i			0.205370i
$932$	−34.2940	+	6.33054i	−1.12334	+	0.207364i
$933$		0			0
$934$	−22.8471	+	27.4506i	−0.747579	+	0.898210i
$935$	−29.0759			−0.950883
$936$		0			0
$937$	26.3144			0.859654			0.429827	−	0.902911i	$-0.358575\pi$
$937$	26.3144			0.859654			0.429827	+	0.902911i	$0.358575\pi$
$938$	−5.28251	+	6.34689i	−0.172480	+	0.207233i
$939$		0			0
$940$	22.7617	−	4.20172i	0.742404	−	0.137045i
$941$		−	8.57667i		−	0.279592i	−0.990180	−	0.139796i	$-0.955355\pi$
$941$		−	8.57667i		−	0.279592i	0.990180	−	0.139796i	$-0.0446446\pi$
$942$		0			0
$943$			1.65339i			0.0538418i
$944$	19.3227	−	7.38547i	0.628901	−	0.240377i
$945$		0			0
$946$	−4.17967	−	3.47874i	−0.135893	−	0.113103i
$947$	−42.8623			−1.39284			−0.696418	−	0.717636i	$-0.745224\pi$
$947$	−42.8623			−1.39284			−0.696418	+	0.717636i	$0.745224\pi$
$948$		0			0
$949$	46.2754			1.50216
$950$	0.894269	+	0.744299i	0.0290139	+	0.0241483i
$951$		0			0
$952$	12.4111	+	6.96812i	0.402246	+	0.225838i
$953$			13.5224i			0.438034i	0.975721	+	0.219017i	$0.0702851\pi$
$953$			13.5224i			0.438034i	−0.975721	+	0.219017i	$0.929715\pi$
$954$		0			0
$955$		−	36.2172i		−	1.17196i
$956$	−3.29762	−	17.8640i	−0.106653	−	0.577762i
$957$		0			0
$958$	33.7408	−	40.5393i	1.09012	−	1.30976i
$959$	−12.7470			−0.411621
$960$		0			0
$961$	−18.2044			−0.587239
$962$	32.8172	−	39.4296i	1.05807	−	1.27126i
$963$		0			0
$964$	6.80811	+	36.8811i	0.219274	+	1.18786i
$965$			22.3015i			0.717911i
$966$		0			0
$967$		−	51.8334i		−	1.66685i	−0.552633	−	0.833425i	$-0.686377\pi$
$967$		−	51.8334i		−	1.66685i	0.552633	−	0.833425i	$-0.313623\pi$
$968$	−10.2183	−	5.73698i	−0.328428	−	0.184393i
$969$		0			0
$970$	−39.7047	−	33.0462i	−1.27484	−	1.06105i
$971$	−17.5922			−0.564561			−0.282281	−	0.959332i	$-0.591091\pi$
$971$	−17.5922			−0.564561			−0.282281	+	0.959332i	$0.591091\pi$
$972$		0			0
$973$	8.94876			0.286884
$974$	38.5546	+	32.0889i	1.23537	+	1.02820i
$975$		0			0
$976$	23.9240	−	9.14414i	0.765787	−	0.292697i
$977$			35.0009i			1.11978i	0.828568	+	0.559889i	$0.189156\pi$
$977$			35.0009i			1.11978i	−0.828568	+	0.559889i	$0.810844\pi$
$978$		0			0
$979$			17.0317i			0.544335i
$980$	4.33971	−	0.801094i	0.138627	−	0.0255900i
$981$		0			0
$982$	23.1715	−	27.8404i	0.739434	−	0.888423i
$983$	25.0441			0.798784			0.399392	−	0.916780i	$-0.369221\pi$
$983$	25.0441			0.798784			0.399392	+	0.916780i	$0.369221\pi$
$984$		0			0
$985$	7.10985			0.226539
$986$	−35.2287	+	42.3269i	−1.12191	+	1.34796i
$987$		0			0
$988$	−54.0644	+	9.98009i	−1.72002	+	0.317509i
$989$			8.16221i			0.259543i
$990$		0			0
$991$			6.50583i			0.206664i	0.994647	+	0.103332i	$0.0329505\pi$
$991$			6.50583i			0.206664i	−0.994647	+	0.103332i	$0.967050\pi$
$992$	−37.5517	−	12.8223i	−1.19227	−	0.407109i
$993$		0			0
$994$	8.08777	+	6.73144i	0.256528	+	0.213508i
$995$	42.5101			1.34766
$996$		0			0
$997$	−20.3134			−0.643331			−0.321665	−	0.946853i	$-0.604243\pi$
$997$	−20.3134			−0.643331			−0.321665	+	0.946853i	$0.604243\pi$
$998$	−40.0206	−	33.3091i	−1.26683	−	1.05438i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.a.323.6	yes	24
3.2	odd	2	inner	756.2.e.a.323.19	yes	24
4.3	odd	2	inner	756.2.e.a.323.20	yes	24
12.11	even	2	inner	756.2.e.a.323.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.a.323.5	✓	24	12.11	even	2	inner
756.2.e.a.323.6	yes	24	1.1	even	1	trivial
756.2.e.a.323.19	yes	24	3.2	odd	2	inner
756.2.e.a.323.20	yes	24	4.3	odd	2	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.904694 + 1.08698i) q^{2} +(-0.363059 - 1.96677i) q^{4} -2.20652i q^{5} -1.00000i q^{7} +(2.46630 + 1.38469i) q^{8} +O(q^{10})\)	\(q+(-0.904694 + 1.08698i) q^{2} +(-0.363059 - 1.96677i) q^{4} -2.20652i q^{5} -1.00000i q^{7} +(2.46630 + 1.38469i) q^{8} +(2.39844 + 1.99622i) q^{10} -2.61856 q^{11} +4.38677 q^{13} +(1.08698 + 0.904694i) q^{14} +(-3.73638 + 1.42811i) q^{16} +5.03227i q^{17} -6.26632i q^{19} +(-4.33971 + 0.801094i) q^{20} +(2.36899 - 2.84632i) q^{22} -5.55840 q^{23} +0.131290 q^{25} +(-3.96868 + 4.76834i) q^{26} +(-1.96677 + 0.363059i) q^{28} -7.73803i q^{29} -7.01459i q^{31} +(1.82795 - 5.35337i) q^{32} +(-5.46999 - 4.55266i) q^{34} -2.20652 q^{35} -8.26904 q^{37} +(6.81138 + 5.66910i) q^{38} +(3.05533 - 5.44193i) q^{40} -0.297458i q^{41} -1.46845i q^{43} +(0.950689 + 5.15010i) q^{44} +(5.02865 - 6.04188i) q^{46} -5.24497 q^{47} -1.00000 q^{49} +(-0.118778 + 0.142710i) q^{50} +(-1.59265 - 8.62777i) q^{52} -11.3489i q^{53} +5.77789i q^{55} +(1.38469 - 2.46630i) q^{56} +(8.41110 + 7.00055i) q^{58} -5.17152 q^{59} -6.40298 q^{61} +(7.62473 + 6.34605i) q^{62} +(4.16528 + 6.83011i) q^{64} -9.67948i q^{65} +5.83901i q^{67} +(9.89733 - 1.82701i) q^{68} +(1.99622 - 2.39844i) q^{70} +7.44057 q^{71} +10.5489 q^{73} +(7.48095 - 8.98830i) q^{74} +(-12.3244 + 2.27504i) q^{76} +2.61856i q^{77} -1.43602i q^{79} +(3.15114 + 8.24437i) q^{80} +(0.323331 + 0.269108i) q^{82} +6.64214 q^{83} +11.1038 q^{85} +(1.59617 + 1.32849i) q^{86} +(-6.45815 - 3.62588i) q^{88} -6.50422i q^{89} -4.38677i q^{91} +(2.01803 + 10.9321i) q^{92} +(4.74510 - 5.70119i) q^{94} -13.8267 q^{95} -16.5544 q^{97} +(0.904694 - 1.08698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} - 16 q^{10} + 8 q^{16} + 16 q^{22} - 24 q^{25} - 8 q^{28} - 8 q^{34} + 16 q^{37} - 8 q^{40} - 24 q^{49} - 8 q^{52} + 32 q^{58} - 80 q^{61} + 40 q^{64} - 24 q^{70} - 32 q^{82} + 56 q^{85} + 56 q^{88} + 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 - 16 * q^10 + 8 * q^16 + 16 * q^22 - 24 * q^25 - 8 * q^28 - 8 * q^34 + 16 * q^37 - 8 * q^40 - 24 * q^49 - 8 * q^52 + 32 * q^58 - 80 * q^61 + 40 * q^64 - 24 * q^70 - 32 * q^82 + 56 * q^85 + 56 * q^88 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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