LMFDB - Embedded newform 552.2.q.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	552.49
Dual form			552.2.q.c.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{3} +(1.04288 - 1.20354i) q^{5} +(-1.78166 + 1.14501i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{3} +(1.04288 - 1.20354i) q^{5} +(-1.78166 + 1.14501i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.0868331 - 0.603937i) q^{11} +(5.90388 + 3.79419i) q^{13} +(0.661555 + 1.44860i) q^{15} +(3.22865 + 0.948018i) q^{17} +(0.314355 - 0.0923029i) q^{19} +(-0.301404 - 2.09631i) q^{21} +(1.94811 + 4.38234i) q^{23} +(0.350648 + 2.43881i) q^{25} +(0.959493 - 0.281733i) q^{27} +(1.40447 + 0.412389i) q^{29} +(-0.416852 - 0.912778i) q^{31} +(0.513289 + 0.329871i) q^{33} +(-0.479991 + 3.33841i) q^{35} +(-4.42152 - 5.10271i) q^{37} +(-5.90388 + 3.79419i) q^{39} +(3.44416 - 3.97478i) q^{41} +(-2.57129 + 5.63035i) q^{43} -1.59252 q^{45} +7.88224 q^{47} +(-1.04462 + 2.28739i) q^{49} +(-2.20358 + 2.54306i) q^{51} +(0.377926 - 0.242878i) q^{53} +(-0.636309 - 0.734340i) q^{55} +(-0.0466260 + 0.324291i) q^{57} +(8.15894 + 5.24344i) q^{59} +(0.274569 + 0.601223i) q^{61} +(2.03208 + 0.596672i) q^{63} +(10.7235 - 3.14870i) q^{65} +(0.991012 + 6.89264i) q^{67} +(-4.79559 - 0.0484290i) q^{69} +(-1.70692 - 11.8719i) q^{71} +(-8.91307 + 2.61711i) q^{73} +(-2.36408 - 0.694158i) q^{75} +(0.536804 + 1.17544i) q^{77} +(-12.6328 - 8.11860i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.572429 + 0.660618i) q^{83} +(4.50807 - 2.89716i) q^{85} +(-0.958560 + 1.10624i) q^{87} +(1.91740 - 4.19851i) q^{89} -14.8631 q^{91} +1.00346 q^{93} +(0.216743 - 0.474600i) q^{95} +(4.31611 - 4.98106i) q^{97} +(-0.513289 + 0.329871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$		0			0
$5$	1.04288	−	1.20354i	0.466389	−	0.538241i	−0.473015	−	0.881054i	$-0.656834\pi$
$5$	1.04288	−	1.20354i	0.466389	−	0.538241i	0.939404	+	0.342813i	$0.111380\pi$
$6$		0			0
$7$	−1.78166	+	1.14501i	−0.673405	+	0.432771i	−0.832152	−	0.554548i	$-0.812891\pi$
$7$	−1.78166	+	1.14501i	−0.673405	+	0.432771i	0.158746	+	0.987319i	$0.449255\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	0.0868331	−	0.603937i	0.0261812	−	0.182094i	−0.972535	−	0.232758i	$-0.925225\pi$
$11$	0.0868331	−	0.603937i	0.0261812	−	0.182094i	0.998716	+	0.0506645i	$0.0161339\pi$
$12$		0			0
$13$	5.90388	+	3.79419i	1.63744	+	1.05232i	0.943012	+	0.332759i	$0.107980\pi$
$13$	5.90388	+	3.79419i	1.63744	+	1.05232i	0.694429	+	0.719561i	$0.255657\pi$
$14$		0			0
$15$	0.661555	+	1.44860i	0.170813	+	0.374028i
$16$		0			0
$17$	3.22865	+	0.948018i	0.783063	+	0.229928i	0.648741	−	0.761010i	$-0.275296\pi$
$17$	3.22865	+	0.948018i	0.783063	+	0.229928i	0.134323	+	0.990938i	$0.457114\pi$
$18$		0			0
$19$	0.314355	−	0.0923029i	0.0721179	−	0.0211757i	−0.245475	−	0.969403i	$-0.578944\pi$
$19$	0.314355	−	0.0923029i	0.0721179	−	0.0211757i	0.317592	+	0.948227i	$0.397126\pi$
$20$		0			0
$21$	−0.301404	−	2.09631i	−0.0657717	−	0.457452i
$22$		0			0
$23$	1.94811	+	4.38234i	0.406208	+	0.913781i
$23$	1.94811	+	4.38234i	0.406208	+	0.913781i
$24$		0			0
$25$	0.350648	+	2.43881i	0.0701296	+	0.487762i
$26$		0			0
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$		0			0
$29$	1.40447	+	0.412389i	0.260803	+	0.0765788i	0.409520	−	0.912301i	$-0.365696\pi$
$29$	1.40447	+	0.412389i	0.260803	+	0.0765788i	−0.148717	+	0.988880i	$0.547514\pi$
$30$		0			0
$31$	−0.416852	−	0.912778i	−0.0748688	−	0.163940i	0.868497	−	0.495695i	$-0.165087\pi$
$31$	−0.416852	−	0.912778i	−0.0748688	−	0.163940i	−0.943366	+	0.331755i	$0.892359\pi$
$32$		0			0
$33$	0.513289	+	0.329871i	0.0893522	+	0.0574231i
$34$		0			0
$35$	−0.479991	+	3.33841i	−0.0811333	+	0.564294i
$36$		0			0
$37$	−4.42152	−	5.10271i	−0.726894	−	0.838880i	0.265225	−	0.964187i	$-0.414554\pi$
$37$	−4.42152	−	5.10271i	−0.726894	−	0.838880i	−0.992118	+	0.125307i	$0.960008\pi$
$38$		0			0
$39$	−5.90388	+	3.79419i	−0.945377	+	0.607557i
$40$		0			0
$41$	3.44416	−	3.97478i	0.537888	−	0.620756i	−0.420130	−	0.907464i	$-0.638016\pi$
$41$	3.44416	−	3.97478i	0.537888	−	0.620756i	0.958018	+	0.286708i	$0.0925610\pi$
$42$		0			0
$43$	−2.57129	+	5.63035i	−0.392119	+	0.858620i	0.605890	+	0.795548i	$0.292817\pi$
$43$	−2.57129	+	5.63035i	−0.392119	+	0.858620i	−0.998009	+	0.0630719i	$0.979910\pi$
$44$		0			0
$45$	−1.59252			−0.237398
$46$		0			0
$47$	7.88224			1.14974			0.574871	−	0.818244i	$-0.305052\pi$
$47$	7.88224			1.14974			0.574871	+	0.818244i	$0.305052\pi$
$48$		0			0
$49$	−1.04462	+	2.28739i	−0.149231	+	0.326771i
$50$		0			0
$51$	−2.20358	+	2.54306i	−0.308563	+	0.356100i
$52$		0			0
$53$	0.377926	−	0.242878i	0.0519121	−	0.0333619i	−0.514427	−	0.857534i	$-0.671995\pi$
$53$	0.377926	−	0.242878i	0.0519121	−	0.0333619i	0.566339	+	0.824172i	$0.308359\pi$
$54$		0			0
$55$	−0.636309	−	0.734340i	−0.0857999	−	0.0990184i
$56$		0			0
$57$	−0.0466260	+	0.324291i	−0.00617577	+	0.0429534i
$58$		0			0
$59$	8.15894	+	5.24344i	1.06220	+	0.682637i	0.950380	−	0.311091i	$-0.100694\pi$
$59$	8.15894	+	5.24344i	1.06220	+	0.682637i	0.111824	+	0.993728i	$0.464331\pi$
$60$		0			0
$61$	0.274569	+	0.601223i	0.0351550	+	0.0769787i	0.926395	−	0.376554i	$-0.122891\pi$
$61$	0.274569	+	0.601223i	0.0351550	+	0.0769787i	−0.891240	+	0.453532i	$0.850164\pi$
$62$		0			0
$63$	2.03208	+	0.596672i	0.256018	+	0.0751736i
$64$		0			0
$65$	10.7235	−	3.14870i	1.33009	−	0.390549i
$66$		0			0
$67$	0.991012	+	6.89264i	0.121071	+	0.842070i	0.956346	+	0.292237i	$0.0943995\pi$
$67$	0.991012	+	6.89264i	0.121071	+	0.842070i	−0.835275	+	0.549833i	$0.814691\pi$
$68$		0			0
$69$	−4.79559	−	0.0484290i	−0.577321	−	0.00583016i
$70$		0			0
$71$	−1.70692	−	11.8719i	−0.202574	−	1.40894i	−0.796608	−	0.604496i	$-0.793375\pi$
$71$	−1.70692	−	11.8719i	−0.202574	−	1.40894i	0.594034	−	0.804440i	$-0.297535\pi$
$72$		0			0
$73$	−8.91307	+	2.61711i	−1.04320	+	0.306310i	−0.758065	−	0.652179i	$-0.773855\pi$
$73$	−8.91307	+	2.61711i	−1.04320	+	0.306310i	−0.285131	+	0.958489i	$0.592037\pi$
$74$		0			0
$75$	−2.36408	−	0.694158i	−0.272981	−	0.0801544i
$76$		0			0
$77$	0.536804	+	1.17544i	0.0611745	+	0.133954i
$78$		0			0
$79$	−12.6328	−	8.11860i	−1.42130	−	0.913414i	−0.999979	−	0.00650218i	$-0.997930\pi$
$79$	−12.6328	−	8.11860i	−1.42130	−	0.913414i	−0.421321	−	0.906912i	$-0.638433\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	0.572429	+	0.660618i	0.0628322	+	0.0725122i	0.786296	−	0.617851i	$-0.211996\pi$
$83$	0.572429	+	0.660618i	0.0628322	+	0.0725122i	−0.723463	+	0.690363i	$0.757451\pi$
$84$		0			0
$85$	4.50807	−	2.89716i	0.488969	−	0.314241i
$86$		0			0
$87$	−0.958560	+	1.10624i	−0.102768	+	0.118601i
$88$		0			0
$89$	1.91740	−	4.19851i	0.203244	−	0.445042i	−0.780373	−	0.625314i	$-0.784971\pi$
$89$	1.91740	−	4.19851i	0.203244	−	0.445042i	0.983617	+	0.180273i	$0.0576980\pi$
$90$		0			0
$91$	−14.8631			−1.55808
$92$		0			0
$93$	1.00346			0.104054
$94$		0			0
$95$	0.216743	−	0.474600i	0.0222373	−	0.0486930i
$96$		0			0
$97$	4.31611	−	4.98106i	0.438235	−	0.505750i	−0.493071	−	0.869989i	$-0.664126\pi$
$97$	4.31611	−	4.98106i	0.438235	−	0.505750i	0.931305	+	0.364239i	$0.118671\pi$
$98$		0			0
$99$	−0.513289	+	0.329871i	−0.0515875	+	0.0331533i
$100$		0			0
$101$	−10.6828	−	12.3287i	−1.06298	−	1.22675i	−0.973000	−	0.230805i	$-0.925864\pi$
$101$	−10.6828	−	12.3287i	−1.06298	−	1.22675i	−0.0899830	−	0.995943i	$-0.528681\pi$
$102$		0			0
$103$	1.95729	−	13.6132i	0.192857	−	1.34135i	−0.631541	−	0.775342i	$-0.717577\pi$
$103$	1.95729	−	13.6132i	0.192857	−	1.34135i	0.824399	−	0.566010i	$-0.191514\pi$
$104$		0			0
$105$	−2.83733	−	1.82344i	−0.276895	−	0.177950i
$106$		0			0
$107$	0.386999	+	0.847410i	0.0374126	+	0.0819223i	0.927416	−	0.374032i	$-0.122025\pi$
$107$	0.386999	+	0.847410i	0.0374126	+	0.0819223i	−0.890003	+	0.455955i	$0.849298\pi$
$108$		0			0
$109$	−6.28227	−	1.84464i	−0.601733	−	0.176685i	−0.0333427	−	0.999444i	$-0.510615\pi$
$109$	−6.28227	−	1.84464i	−0.601733	−	0.176685i	−0.568390	+	0.822759i	$0.692433\pi$
$110$		0			0
$111$	6.47835	−	1.90222i	0.614898	−	0.180550i
$112$		0			0
$113$	−2.44946	−	17.0364i	−0.230426	−	1.60265i	−0.696269	−	0.717781i	$-0.745158\pi$
$113$	−2.44946	−	17.0364i	−0.230426	−	1.60265i	0.465843	−	0.884868i	$-0.345751\pi$
$114$		0			0
$115$	7.30597	+	2.22561i	0.681285	+	0.207539i
$116$		0			0
$117$	−0.998759	−	6.94652i	−0.0923353	−	0.642206i
$118$		0			0
$119$	−6.83786	+	2.00778i	−0.626825	+	0.184053i
$120$		0			0
$121$	10.1972	+	2.99417i	0.927020	+	0.272198i
$122$		0			0
$123$	2.18483	+	4.78410i	0.196999	+	0.431368i
$124$		0			0
$125$	9.99945	+	6.42626i	0.894378	+	0.574782i
$126$		0			0
$127$	2.13035	−	14.8169i	0.189038	−	1.31479i	−0.645468	−	0.763787i	$-0.723338\pi$
$127$	2.13035	−	14.8169i	0.189038	−	1.31479i	0.834506	−	0.550999i	$-0.185753\pi$
$128$		0			0
$129$	−4.05339	−	4.67786i	−0.356881	−	0.411863i
$130$		0			0
$131$	−7.87374	+	5.06015i	−0.687932	+	0.442107i	−0.837350	−	0.546667i	$-0.815896\pi$
$131$	−7.87374	+	5.06015i	−0.687932	+	0.442107i	0.149418	+	0.988774i	$0.452260\pi$
$132$		0			0
$133$	−0.454387	+	0.524390i	−0.0394003	+	0.0454704i
$134$		0			0
$135$	0.661555	−	1.44860i	0.0569376	−	0.124676i
$136$		0			0
$137$	−8.60086			−0.734821			−0.367411	−	0.930059i	$-0.619756\pi$
$137$	−8.60086			−0.734821			−0.367411	+	0.930059i	$0.619756\pi$
$138$		0			0
$139$	−14.4890			−1.22894			−0.614472	−	0.788939i	$-0.710631\pi$
$139$	−14.4890			−1.22894			−0.614472	+	0.788939i	$0.710631\pi$
$140$		0			0
$141$	−3.27440	+	7.16993i	−0.275754	+	0.603817i
$142$		0			0
$143$	2.80411	−	3.23611i	0.234491	−	0.270617i
$144$		0			0
$145$	1.96102	−	1.26027i	0.162854	−	0.104660i
$146$		0			0
$147$	−1.64674	−	1.90044i	−0.135821	−	0.156745i
$148$		0			0
$149$	−2.64844	+	18.4203i	−0.216969	+	1.50905i	0.532171	+	0.846637i	$0.321376\pi$
$149$	−2.64844	+	18.4203i	−0.216969	+	1.50905i	−0.749139	+	0.662412i	$0.769533\pi$
$150$		0			0
$151$	7.79373	+	5.00873i	0.634245	+	0.407605i	0.817879	−	0.575390i	$-0.195150\pi$
$151$	7.79373	+	5.00873i	0.634245	+	0.407605i	−0.183634	+	0.982995i	$0.558786\pi$
$152$		0			0
$153$	−1.39785	−	3.06087i	−0.113010	−	0.247457i
$154$		0			0
$155$	−1.53329	−	0.450216i	−0.123157	−	0.0361622i
$156$		0			0
$157$	−17.5112	+	5.14175i	−1.39755	+	0.410357i	−0.891841	−	0.452350i	$-0.850586\pi$
$157$	−17.5112	+	5.14175i	−1.39755	+	0.410357i	−0.505705	+	0.862706i	$0.668768\pi$
$158$		0			0
$159$	0.0639337	+	0.444668i	0.00507027	+	0.0352645i
$160$		0			0
$161$	−8.48867	−	5.57726i	−0.669001	−	0.439550i
$162$		0			0
$163$	−1.27018	−	8.83431i	−0.0994883	−	0.691956i	−0.977131	−	0.212640i	$-0.931794\pi$
$163$	−1.27018	−	8.83431i	−0.0994883	−	0.691956i	0.877642	−	0.479316i	$-0.159115\pi$
$164$		0			0
$165$	0.932311	−	0.273751i	0.0725803	−	0.0213115i
$166$		0			0
$167$	7.88205	+	2.31438i	0.609932	+	0.179092i	0.572089	−	0.820192i	$-0.306133\pi$
$167$	7.88205	+	2.31438i	0.609932	+	0.179092i	0.0378427	+	0.999284i	$0.487951\pi$
$168$		0			0
$169$	15.0595	+	32.9757i	1.15842	+	2.53659i
$170$		0			0
$171$	−0.275616	−	0.177128i	−0.0210769	−	0.0135453i
$172$		0			0
$173$	2.24361	−	15.6046i	0.170578	−	1.18640i	−0.707088	−	0.707126i	$-0.749991\pi$
$173$	2.24361	−	15.6046i	0.170578	−	1.18640i	0.877666	−	0.479273i	$-0.159099\pi$
$174$		0			0
$175$	−3.41719	−	3.94365i	−0.258315	−	0.298112i
$176$		0			0
$177$	−8.15894	+	5.24344i	−0.613264	+	0.394121i
$178$		0			0
$179$	−2.31516	+	2.67184i	−0.173043	+	0.199702i	−0.835646	−	0.549269i	$-0.814906\pi$
$179$	−2.31516	+	2.67184i	−0.173043	+	0.199702i	0.662603	+	0.748971i	$0.269452\pi$
$180$		0			0
$181$	−3.36170	+	7.36109i	−0.249873	+	0.547145i	−0.992455	−	0.122610i	$-0.960874\pi$
$181$	−3.36170	+	7.36109i	−0.249873	+	0.547145i	0.742582	+	0.669755i	$0.233601\pi$
$182$		0			0
$183$	−0.660952			−0.0488590
$184$		0			0
$185$	−10.7524			−0.790535
$186$		0			0
$187$	0.852897	−	1.86758i	0.0623700	−	0.136571i
$188$		0			0
$189$	−1.38691	+	1.60058i	−0.100883	+	0.116425i
$190$		0			0
$191$	16.0403	−	10.3085i	1.16064	−	0.745895i	0.188907	−	0.981995i	$-0.439506\pi$
$191$	16.0403	−	10.3085i	1.16064	−	0.745895i	0.971729	+	0.236100i	$0.0758693\pi$
$192$		0			0
$193$	11.2150	+	12.9428i	0.807275	+	0.931645i	0.998757	−	0.0498516i	$-0.0158748\pi$
$193$	11.2150	+	12.9428i	0.807275	+	0.931645i	−0.191482	+	0.981496i	$0.561329\pi$
$194$		0			0
$195$	−1.59054	+	11.0625i	−0.113901	+	0.792199i
$196$		0			0
$197$	1.22528	+	0.787436i	0.0872972	+	0.0561025i	0.583561	−	0.812069i	$-0.301659\pi$
$197$	1.22528	+	0.787436i	0.0872972	+	0.0561025i	−0.496264	+	0.868172i	$0.665295\pi$
$198$		0			0
$199$	−0.582156	−	1.27474i	−0.0412679	−	0.0903642i	0.887875	−	0.460084i	$-0.152181\pi$
$199$	−0.582156	−	1.27474i	−0.0412679	−	0.0903642i	−0.929143	+	0.369720i	$0.879454\pi$
$200$		0			0
$201$	−6.68144	−	1.96185i	−0.471273	−	0.138378i
$202$		0			0
$203$	−2.97448	+	0.873386i	−0.208768	+	0.0612997i
$204$		0			0
$205$	−1.19198	−	8.29040i	−0.0832515	−	0.579027i
$206$		0			0
$207$	2.03621	−	4.34210i	0.141526	−	0.301797i
$208$		0			0
$209$	−0.0284488	−	0.197865i	−0.00196784	−	0.0136866i
$210$		0			0
$211$	−8.49415	+	2.49411i	−0.584761	+	0.171701i	−0.560714	−	0.828009i	$-0.689473\pi$
$211$	−8.49415	+	2.49411i	−0.584761	+	0.171701i	−0.0240471	+	0.999711i	$0.507655\pi$
$212$		0			0
$213$	11.5081	+	3.37910i	0.788525	+	0.231532i
$214$		0			0
$215$	4.09483	+	8.96643i	0.279265	+	0.611505i
$216$		0			0
$217$	1.78783	+	1.14897i	0.121365	+	0.0779969i
$218$		0			0
$219$	1.32201	−	9.19480i	0.0893334	−	0.621327i
$220$		0			0
$221$	15.4646	+	17.8471i	1.04026	+	1.20053i
$222$		0			0
$223$	19.6777	−	12.6461i	1.31772	−	0.846845i	0.322695	−	0.946503i	$-0.395411\pi$
$223$	19.6777	−	12.6461i	1.31772	−	0.846845i	0.995022	+	0.0996581i	$0.0317749\pi$
$224$		0			0
$225$	1.61350	−	1.86208i	0.107567	−	0.124139i
$226$		0			0
$227$	0.760198	−	1.66460i	0.0504561	−	0.110483i	−0.882725	−	0.469890i	$-0.844294\pi$
$227$	0.760198	−	1.66460i	0.0504561	−	0.110483i	0.933181	+	0.359407i	$0.117021\pi$
$228$		0			0
$229$	−17.4465			−1.15290			−0.576450	−	0.817132i	$-0.695562\pi$
$229$	−17.4465			−1.15290			−0.576450	+	0.817132i	$0.695562\pi$
$230$		0			0
$231$	−1.29221			−0.0850213
$232$		0			0
$233$	2.41471	−	5.28747i	0.158193	−	0.346394i	−0.813895	−	0.581012i	$-0.802657\pi$
$233$	2.41471	−	5.28747i	0.158193	−	0.346394i	0.972088	+	0.234618i	$0.0753841\pi$
$234$		0			0
$235$	8.22020	−	9.48662i	0.536227	−	0.618839i
$236$		0			0
$237$	12.6328	−	8.11860i	0.820588	−	0.527360i
$238$		0			0
$239$	−0.343600	−	0.396536i	−0.0222256	−	0.0256498i	0.744528	−	0.667591i	$-0.232675\pi$
$239$	−0.343600	−	0.396536i	−0.0222256	−	0.0256498i	−0.766754	+	0.641942i	$0.778129\pi$
$240$		0			0
$241$	0.221336	−	1.53943i	0.0142575	−	0.0991633i	−0.981450	−	0.191718i	$-0.938594\pi$
$241$	0.221336	−	1.53943i	0.0142575	−	0.0991633i	0.995708	+	0.0925546i	$0.0295033\pi$
$242$		0			0
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$		0			0
$245$	1.66357	+	3.64272i	0.106282	+	0.232725i
$246$		0			0
$247$	2.20613	+	0.647777i	0.140372	+	0.0412171i
$248$		0			0
$249$	−0.838715	+	0.246269i	−0.0531514	+	0.0156067i
$250$		0			0
$251$	0.201785	+	1.40345i	0.0127366	+	0.0885848i	0.995198	−	0.0978799i	$-0.0312061\pi$
$251$	0.201785	+	1.40345i	0.0127366	+	0.0885848i	−0.982462	+	0.186465i	$0.940297\pi$
$252$		0			0
$253$	2.81582	−	0.796002i	0.177029	−	0.0500442i
$254$		0			0
$255$	0.762630	+	5.30421i	0.0477577	+	0.332162i
$256$		0			0
$257$	−13.3025	+	3.90597i	−0.829788	+	0.243648i	−0.668926	−	0.743329i	$-0.733246\pi$
$257$	−13.3025	+	3.90597i	−0.829788	+	0.243648i	−0.160862	+	0.986977i	$0.551427\pi$
$258$		0			0
$259$	13.7203	+	4.02864i	0.852537	+	0.250328i
$260$		0			0
$261$	−0.608069	−	1.33148i	−0.0376385	−	0.0824168i
$262$		0			0
$263$	−11.7942	−	7.57970i	−0.727264	−	0.467384i	0.123893	−	0.992296i	$-0.460462\pi$
$263$	−11.7942	−	7.57970i	−0.727264	−	0.467384i	−0.851157	+	0.524911i	$0.824098\pi$
$264$		0			0
$265$	0.101815	−	0.708142i	0.00625447	−	0.0435008i
$266$		0			0
$267$	3.02259	+	3.48825i	0.184979	+	0.213477i
$268$		0			0
$269$	−5.54642	+	3.56447i	−0.338171	+	0.217329i	−0.698693	−	0.715421i	$-0.746235\pi$
$269$	−5.54642	+	3.56447i	−0.338171	+	0.217329i	0.360522	+	0.932751i	$0.382598\pi$
$270$		0			0
$271$	0.767457	−	0.885692i	0.0466197	−	0.0538020i	−0.731961	−	0.681347i	$-0.761395\pi$
$271$	0.767457	−	0.885692i	0.0466197	−	0.0538020i	0.778580	+	0.627545i	$0.215940\pi$
$272$		0			0
$273$	6.17435	−	13.5199i	0.373689	−	0.818265i
$274$		0			0
$275$	1.50334			0.0906546
$276$		0			0
$277$	13.3575			0.802573			0.401286	−	0.915953i	$-0.368563\pi$
$277$	13.3575			0.802573			0.401286	+	0.915953i	$0.368563\pi$
$278$		0			0
$279$	−0.416852	+	0.912778i	−0.0249563	+	0.0546466i
$280$		0			0
$281$	−16.9550	+	19.5671i	−1.01145	+	1.16728i	−0.0255961	+	0.999672i	$0.508148\pi$
$281$	−16.9550	+	19.5671i	−1.01145	+	1.16728i	−0.985854	+	0.167604i	$0.946397\pi$
$282$		0			0
$283$	−0.0611930	+	0.0393263i	−0.00363754	+	0.00233771i	−0.542458	−	0.840083i	$-0.682506\pi$
$283$	−0.0611930	+	0.0393263i	−0.00363754	+	0.00233771i	0.538821	+	0.842420i	$0.318870\pi$
$284$		0			0
$285$	0.341673	+	0.394312i	0.0202390	+	0.0233570i
$286$		0			0
$287$	−1.58520	+	11.0253i	−0.0935713	+	0.650803i
$288$		0			0
$289$	−4.77585	−	3.06925i	−0.280932	−	0.180544i
$290$		0			0
$291$	2.73795	+	5.99528i	0.160502	+	0.351450i
$292$		0			0
$293$	15.1079	+	4.43607i	0.882611	+	0.259158i	0.691471	−	0.722405i	$-0.256963\pi$
$293$	15.1079	+	4.43607i	0.882611	+	0.259158i	0.191141	+	0.981563i	$0.438781\pi$
$294$		0			0
$295$	14.8195	−	4.35139i	0.862824	−	0.253348i
$296$		0			0
$297$	−0.0868331	−	0.603937i	−0.00503857	−	0.0350440i
$298$		0			0
$299$	−5.12605	+	33.2643i	−0.296447	+	1.92372i
$300$		0			0
$301$	−1.86560	−	12.9755i	−0.107531	−	0.747897i
$302$		0			0
$303$	15.6524	−	4.59595i	0.899205	−	0.264030i
$304$		0			0
$305$	1.00994	+	0.296545i	0.0578290	+	0.0169801i
$306$		0			0
$307$	3.44847	+	7.55110i	0.196815	+	0.430964i	0.982148	−	0.188109i	$-0.0602358\pi$
$307$	3.44847	+	7.55110i	0.196815	+	0.430964i	−0.785334	+	0.619073i	$0.787509\pi$
$308$		0			0
$309$	11.5699	+	7.43555i	0.658191	+	0.422994i
$310$		0			0
$311$	4.14795	−	28.8497i	0.235209	−	1.63591i	−0.439794	−	0.898099i	$-0.644948\pi$
$311$	4.14795	−	28.8497i	0.235209	−	1.63591i	0.675003	−	0.737815i	$-0.264142\pi$
$312$		0			0
$313$	21.3191	+	24.6036i	1.20503	+	1.39068i	0.898593	+	0.438784i	$0.144591\pi$
$313$	21.3191	+	24.6036i	1.20503	+	1.39068i	0.306434	+	0.951892i	$0.400864\pi$
$314$		0			0
$315$	2.83733	−	1.82344i	0.159865	−	0.102739i
$316$		0			0
$317$	−10.7911	+	12.4536i	−0.606087	+	0.699461i	−0.973003	−	0.230793i	$-0.925868\pi$
$317$	−10.7911	+	12.4536i	−0.606087	+	0.699461i	0.366916	+	0.930254i	$0.380414\pi$
$318$		0			0
$319$	0.371012	−	0.812402i	0.0207727	−	0.0454858i
$320$		0			0
$321$	−0.931597			−0.0519967
$322$		0			0
$323$	1.10245			0.0613418
$324$		0			0
$325$	−7.18313	+	15.7289i	−0.398449	+	0.872481i
$326$		0			0
$327$	4.28770	−	4.94826i	0.237110	−	0.273640i
$328$		0			0
$329$	−14.0435	+	9.02520i	−0.774243	+	0.497576i
$330$		0			0
$331$	14.3489	+	16.5596i	0.788689	+	0.910195i	0.997705	−	0.0677169i	$-0.0215715\pi$
$331$	14.3489	+	16.5596i	0.788689	+	0.910195i	−0.209016	+	0.977912i	$0.567026\pi$
$332$		0			0
$333$	−0.960888	+	6.68312i	−0.0526564	+	0.366233i
$334$		0			0
$335$	9.32910	+	5.99545i	0.509703	+	0.327566i
$336$		0			0
$337$	−1.39072	−	3.04525i	−0.0757573	−	0.165885i	0.867964	−	0.496627i	$-0.165428\pi$
$337$	−1.39072	−	3.04525i	−0.0757573	−	0.165885i	−0.943721	+	0.330742i	$0.892701\pi$
$338$		0			0
$339$	16.5144	+	4.84906i	0.896939	+	0.263365i
$340$		0			0
$341$	−0.587457	+	0.172493i	−0.0318126	+	0.00934102i
$342$		0			0
$343$	−2.86775	−	19.9456i	−0.154844	−	1.07696i
$344$		0			0
$345$	−5.05949	+	5.72119i	−0.272394	+	0.308019i
$346$		0			0
$347$	1.12055	+	7.79358i	0.0601541	+	0.418381i	0.997541	+	0.0700903i	$0.0223288\pi$
$347$	1.12055	+	7.79358i	0.0601541	+	0.418381i	−0.937387	+	0.348291i	$0.886762\pi$
$348$		0			0
$349$	12.1901	−	3.57934i	0.652522	−	0.191598i	0.0613161	−	0.998118i	$-0.480470\pi$
$349$	12.1901	−	3.57934i	0.652522	−	0.191598i	0.591206	+	0.806521i	$0.298652\pi$
$350$		0			0
$351$	6.73368	+	1.97719i	0.359417	+	0.105534i
$352$		0			0
$353$	0.967555	+	2.11865i	0.0514978	+	0.112764i	0.933632	−	0.358234i	$-0.116621\pi$
$353$	0.967555	+	2.11865i	0.0514978	+	0.112764i	−0.882134	+	0.470998i	$0.843894\pi$
$354$		0			0
$355$	−16.0685	−	10.3266i	−0.852826	−	0.548078i
$356$		0			0
$357$	1.01421	−	7.05399i	0.0536778	−	0.373337i
$358$		0			0
$359$	−13.1122	−	15.1323i	−0.692036	−	0.798652i	0.295618	−	0.955306i	$-0.404475\pi$
$359$	−13.1122	−	15.1323i	−0.692036	−	0.798652i	−0.987653	+	0.156655i	$0.949929\pi$
$360$		0			0
$361$	−15.8935	+	10.2141i	−0.836501	+	0.537587i
$362$		0			0
$363$	−6.95968	+	8.03189i	−0.365288	+	0.421565i
$364$		0			0
$365$	−6.14542	+	13.4566i	−0.321666	+	0.704351i
$366$		0			0
$367$	−16.9852			−0.886620			−0.443310	−	0.896368i	$-0.646196\pi$
$367$	−16.9852			−0.886620			−0.443310	+	0.896368i	$0.646196\pi$
$368$		0			0
$369$	−5.25938			−0.273793
$370$		0			0
$371$	−0.395240	+	0.865454i	−0.0205198	+	0.0449321i
$372$		0			0
$373$	16.4461	−	18.9798i	0.851548	−	0.982739i	−0.148433	−	0.988923i	$-0.547423\pi$
$373$	16.4461	−	18.9798i	0.851548	−	0.982739i	0.999981	+	0.00618337i	$0.00196824\pi$
$374$		0			0
$375$	−9.99945	+	6.42626i	−0.516369	+	0.331851i
$376$		0			0
$377$	6.72713	+	7.76352i	0.346465	+	0.399842i
$378$		0			0
$379$	−0.835333	+	5.80987i	−0.0429082	+	0.298433i	0.957055	+	0.289905i	$0.0936237\pi$
$379$	−0.835333	+	5.80987i	−0.0429082	+	0.298433i	−0.999964	+	0.00852802i	$0.997285\pi$
$380$		0			0
$381$	12.5929	+	8.09299i	0.645155	+	0.414616i
$382$		0			0
$383$	−4.82257	−	10.5600i	−0.246422	−	0.539589i	0.745490	−	0.666517i	$-0.232216\pi$
$383$	−4.82257	−	10.5600i	−0.246422	−	0.539589i	−0.991912	+	0.126928i	$0.959488\pi$
$384$		0			0
$385$	1.97451	+	0.579769i	0.100630	+	0.0295478i
$386$		0			0
$387$	5.93897	−	1.74384i	0.301895	−	0.0886444i
$388$		0			0
$389$	−4.89639	−	34.0551i	−0.248257	−	1.72666i	−0.608282	−	0.793721i	$-0.708141\pi$
$389$	−4.89639	−	34.0551i	−0.248257	−	1.72666i	0.360025	−	0.932943i	$-0.382768\pi$
$390$		0			0
$391$	2.13522	+	15.9959i	0.107983	+	0.808947i
$392$		0			0
$393$	−1.33200	−	9.26427i	−0.0671905	−	0.467320i
$394$		0			0
$395$	−22.9455	+	6.73742i	−1.15452	+	0.338996i
$396$		0			0
$397$	−12.5841	−	3.69504i	−0.631580	−	0.185449i	−0.0497532	−	0.998762i	$-0.515843\pi$
$397$	−12.5841	−	3.69504i	−0.631580	−	0.185449i	−0.581826	+	0.813313i	$0.697662\pi$
$398$		0			0
$399$	−0.288243	−	0.631165i	−0.0144302	−	0.0315978i
$400$		0			0
$401$	−21.3758	−	13.7374i	−1.06746	−	0.686013i	−0.115830	−	0.993269i	$-0.536953\pi$
$401$	−21.3758	−	13.7374i	−1.06746	−	0.686013i	−0.951627	+	0.307257i	$0.900589\pi$
$402$		0			0
$403$	1.00221	−	6.97055i	0.0499238	−	0.347228i
$404$		0			0
$405$	1.04288	+	1.20354i	0.0518210	+	0.0598046i
$406$		0			0
$407$	−3.46565	+	2.22724i	−0.171786	+	0.110400i
$408$		0			0
$409$	−7.75834	+	8.95360i	−0.383625	+	0.442727i	−0.914416	−	0.404776i	$-0.867350\pi$
$409$	−7.75834	+	8.95360i	−0.383625	+	0.442727i	0.530791	+	0.847503i	$0.321895\pi$
$410$		0			0
$411$	3.57293	−	7.82362i	0.176240	−	0.385911i
$412$		0			0
$413$	−20.5403			−1.01072
$414$		0			0
$415$	1.39206			0.0683333
$416$		0			0
$417$	6.01896	−	13.1797i	0.294750	−	0.645412i
$418$		0			0
$419$	21.7713	−	25.1255i	1.06360	−	1.22746i	0.0907855	−	0.995870i	$-0.471062\pi$
$419$	21.7713	−	25.1255i	1.06360	−	1.22746i	0.972814	−	0.231589i	$-0.0743923\pi$
$420$		0			0
$421$	16.3585	−	10.5130i	0.797267	−	0.512372i	−0.0774560	−	0.996996i	$-0.524680\pi$
$421$	16.3585	−	10.5130i	0.797267	−	0.512372i	0.874723	+	0.484623i	$0.161043\pi$
$422$		0			0
$423$	−5.16177	−	5.95700i	−0.250974	−	0.289639i
$424$		0			0
$425$	−1.17992	+	8.20649i	−0.0572343	+	0.398073i
$426$		0			0
$427$	−1.17759	−	0.756793i	−0.0569877	−	0.0366238i
$428$		0			0
$429$	1.77880	+	3.89503i	0.0858814	+	0.188054i
$430$		0			0
$431$	20.6752	+	6.07078i	0.995889	+	0.292419i	0.738768	−	0.673960i	$-0.235408\pi$
$431$	20.6752	+	6.07078i	0.995889	+	0.292419i	0.257121	+	0.966379i	$0.417226\pi$
$432$		0			0
$433$	27.1054	−	7.95887i	1.30260	−	0.382479i	0.444418	−	0.895820i	$-0.353411\pi$
$433$	27.1054	−	7.95887i	1.30260	−	0.382479i	0.858185	+	0.513341i	$0.171592\pi$
$434$		0			0
$435$	0.331745	+	2.30734i	0.0159060	+	0.110628i
$436$		0			0
$437$	1.01690	+	1.19779i	0.0486449	+	0.0572982i
$438$		0			0
$439$	5.15614	+	35.8618i	0.246089	+	1.71159i	0.620400	+	0.784285i	$0.286970\pi$
$439$	5.15614	+	35.8618i	0.246089	+	1.71159i	−0.374311	+	0.927303i	$0.622121\pi$
$440$		0			0
$441$	2.41278	−	0.708455i	0.114894	−	0.0337360i
$442$		0			0
$443$	15.7016	+	4.61042i	0.746008	+	0.219048i	0.632576	−	0.774498i	$-0.281998\pi$
$443$	15.7016	+	4.61042i	0.746008	+	0.219048i	0.113432	+	0.993546i	$0.463816\pi$
$444$		0			0
$445$	−3.05349	−	6.68620i	−0.144749	−	0.316956i
$446$		0			0
$447$	−15.6555	−	10.0612i	−0.740479	−	0.475877i
$448$		0			0
$449$	2.28480	−	15.8911i	0.107826	−	0.749947i	−0.862133	−	0.506681i	$-0.830872\pi$
$449$	2.28480	−	15.8911i	0.107826	−	0.749947i	0.969960	−	0.243266i	$-0.0782188\pi$
$450$		0			0
$451$	−2.10145	−	2.42520i	−0.0989534	−	0.114198i
$452$		0			0
$453$	−7.79373	+	5.00873i	−0.366182	+	0.235331i
$454$		0			0
$455$	−15.5004	+	17.8884i	−0.726669	+	0.838621i
$456$		0			0
$457$	8.43285	−	18.4654i	0.394472	−	0.863773i	−0.603329	−	0.797492i	$-0.706159\pi$
$457$	8.43285	−	18.4654i	0.394472	−	0.863773i	0.997801	−	0.0662807i	$-0.0211133\pi$
$458$		0			0
$459$	3.36496			0.157063
$460$		0			0
$461$	−4.27022			−0.198884			−0.0994420	−	0.995043i	$-0.531706\pi$
$461$	−4.27022			−0.198884			−0.0994420	+	0.995043i	$0.531706\pi$
$462$		0			0
$463$	−10.4784	+	22.9444i	−0.486971	+	1.06632i	0.493517	+	0.869736i	$0.335711\pi$
$463$	−10.4784	+	22.9444i	−0.486971	+	1.06632i	−0.980488	+	0.196581i	$0.937016\pi$
$464$		0			0
$465$	1.04648	−	1.20771i	0.0485295	−	0.0560060i
$466$		0			0
$467$	−35.0699	+	22.5381i	−1.62284	+	1.04294i	−0.668723	+	0.743512i	$0.733159\pi$
$467$	−35.0699	+	22.5381i	−1.62284	+	1.04294i	−0.954120	+	0.299425i	$0.903205\pi$
$468$		0			0
$469$	−9.65776	−	11.1456i	−0.445954	−	0.514658i
$470$		0			0
$471$	2.59731	−	18.0647i	0.119678	−	0.832378i
$472$		0			0
$473$	3.17711	+	2.04180i	0.146083	+	0.0938821i
$474$		0			0
$475$	0.335337	+	0.734286i	0.0153863	+	0.0336913i
$476$		0			0
$477$	−0.431044	−	0.126566i	−0.0197361	−	0.00579505i
$478$		0			0
$479$	−41.6984	+	12.2438i	−1.90525	+	0.559432i	−0.918976	+	0.394314i	$0.870982\pi$
$479$	−41.6984	+	12.2438i	−1.90525	+	0.559432i	−0.986274	+	0.165118i	$0.947199\pi$
$480$		0			0
$481$	−6.74347	−	46.9019i	−0.307476	−	2.13854i
$482$		0			0
$483$	8.59957	−	5.40469i	0.391294	−	0.245922i
$484$		0			0
$485$	−1.49375	−	10.3893i	−0.0678277	−	0.471752i
$486$		0			0
$487$	5.74678	−	1.68741i	0.260411	−	0.0764637i	−0.148921	−	0.988849i	$-0.547580\pi$
$487$	5.74678	−	1.68741i	0.260411	−	0.0764637i	0.409332	+	0.912385i	$0.365762\pi$
$488$		0			0
$489$	8.56362	+	2.51451i	0.387260	+	0.113710i
$490$		0			0
$491$	−12.1109	−	26.5192i	−0.546558	−	1.19680i	−0.958371	−	0.285527i	$-0.907831\pi$
$491$	−12.1109	−	26.5192i	−0.546558	−	1.19680i	0.411813	−	0.911268i	$-0.364896\pi$
$492$		0			0
$493$	4.14359	+	2.66292i	0.186618	+	0.119932i
$494$		0			0
$495$	−0.138283	+	0.961781i	−0.00621537	+	0.0432288i
$496$		0			0
$497$	16.6346	+	19.1973i	0.746162	+	0.861117i
$498$		0			0
$499$	22.4469	−	14.4257i	1.00486	−	0.645785i	0.0688024	−	0.997630i	$-0.478082\pi$
$499$	22.4469	−	14.4257i	1.00486	−	0.645785i	0.936058	+	0.351846i	$0.114446\pi$
$500$		0			0
$501$	−5.37956	+	6.20834i	−0.240341	+	0.277368i
$502$		0			0
$503$	−1.53539	+	3.36204i	−0.0684598	+	0.149906i	−0.940769	−	0.339049i	$-0.889895\pi$
$503$	−1.53539	+	3.36204i	−0.0684598	+	0.149906i	0.872309	+	0.488955i	$0.162622\pi$
$504$		0			0
$505$	−25.9790			−1.15605
$506$		0			0
$507$	−36.2517			−1.60999
$508$		0			0
$509$	−12.2594	+	26.8444i	−0.543390	+	1.18986i	0.416411	+	0.909176i	$0.363288\pi$
$509$	−12.2594	+	26.8444i	−0.543390	+	1.18986i	−0.959801	+	0.280681i	$0.909440\pi$
$510$		0			0
$511$	12.8835	−	14.8683i	0.569932	−	0.657736i
$512$		0			0
$513$	0.275616	−	0.177128i	0.0121688	−	0.00782039i
$514$		0			0
$515$	−14.3429	−	16.5526i	−0.632025	−	0.729395i
$516$		0			0
$517$	0.684439	−	4.76038i	0.0301016	−	0.209361i
$518$		0			0
$519$	13.2624	+	8.52326i	0.582157	+	0.374129i
$520$		0			0
$521$	−9.72902	−	21.3036i	−0.426236	−	0.933327i	−0.993922	−	0.110082i	$-0.964889\pi$
$521$	−9.72902	−	21.3036i	−0.426236	−	0.933327i	0.567686	−	0.823245i	$-0.307839\pi$
$522$		0			0
$523$	−14.9454	−	4.38836i	−0.653516	−	0.191889i	−0.0618656	−	0.998084i	$-0.519705\pi$
$523$	−14.9454	−	4.38836i	−0.653516	−	0.191889i	−0.591650	+	0.806195i	$0.701523\pi$
$524$		0			0
$525$	5.00682	−	1.47013i	0.218515	−	0.0641619i
$526$		0			0
$527$	−0.480539	−	3.34223i	−0.0209326	−	0.145590i
$528$		0			0
$529$	−15.4098	+	17.0745i	−0.669990	+	0.742370i
$530$		0			0
$531$	−1.38025	−	9.59984i	−0.0598977	−	0.416598i
$532$		0			0
$533$	35.4150	−	10.3988i	1.53399	−	0.450421i
$534$		0			0
$535$	1.42349	+	0.417974i	0.0615428	+	0.0180706i
$536$		0			0
$537$	−1.46864	−	3.21586i	−0.0633763	−	0.138775i
$538$		0			0
$539$	1.29074	+	0.829506i	0.0555959	+	0.0357293i
$540$		0			0
$541$	0.724714	−	5.04050i	0.0311579	−	0.216708i	−0.968294	−	0.249814i	$-0.919631\pi$
$541$	0.724714	−	5.04050i	0.0311579	−	0.216708i	0.999452	+	0.0331056i	$0.0105398\pi$
$542$		0			0
$543$	−5.29938	−	6.11581i	−0.227418	−	0.262455i
$544$		0			0
$545$	−8.77174	+	5.63726i	−0.375740	+	0.241474i
$546$		0			0
$547$	−8.14245	+	9.39688i	−0.348146	+	0.401782i	−0.902633	−	0.430410i	$-0.858369\pi$
$547$	−8.14245	+	9.39688i	−0.348146	+	0.401782i	0.554487	+	0.832192i	$0.312914\pi$
$548$		0			0
$549$	0.274569	−	0.601223i	0.0117183	−	0.0256596i
$550$		0			0
$551$	0.479566			0.0204302
$552$		0			0
$553$	31.8032			1.35241
$554$		0			0
$555$	4.46672	−	9.78076i	0.189602	−	0.415170i
$556$		0			0
$557$	14.8153	−	17.0978i	0.627746	−	0.724458i	−0.349412	−	0.936969i	$-0.613619\pi$
$557$	14.8153	−	17.0978i	0.627746	−	0.724458i	0.977159	+	0.212511i	$0.0681642\pi$
$558$		0			0
$559$	−36.5432	+	23.4849i	−1.54561	+	0.993306i
$560$		0			0
$561$	1.34451	+	1.55165i	0.0567652	+	0.0655105i
$562$		0			0
$563$	4.39440	−	30.5637i	0.185202	−	1.28811i	−0.659025	−	0.752121i	$-0.729031\pi$
$563$	4.39440	−	30.5637i	0.185202	−	1.28811i	0.844227	−	0.535986i	$-0.180060\pi$
$564$		0			0
$565$	−23.0585	−	14.8188i	−0.970080	−	0.623433i
$566$		0			0
$567$	−0.879794	−	1.92648i	−0.0369479	−	0.0809046i
$568$		0			0
$569$	19.3143	+	5.67119i	0.809698	+	0.237749i	0.660274	−	0.751024i	$-0.270440\pi$
$569$	19.3143	+	5.67119i	0.809698	+	0.237749i	0.149424	+	0.988773i	$0.452258\pi$
$570$		0			0
$571$	36.5101	−	10.7203i	1.52790	−	0.448631i	0.593492	−	0.804840i	$-0.297749\pi$
$571$	36.5101	−	10.7203i	1.52790	−	0.448631i	0.934406	+	0.356209i	$0.115931\pi$
$572$		0			0
$573$	2.71354	+	18.8731i	0.113360	+	0.788434i
$574$		0			0
$575$	−10.0046	+	6.28772i	−0.417220	+	0.262216i
$576$		0			0
$577$	−3.91524	−	27.2311i	−0.162993	−	1.13364i	−0.892952	−	0.450152i	$-0.851370\pi$
$577$	−3.91524	−	27.2311i	−0.162993	−	1.13364i	0.729958	−	0.683492i	$-0.239539\pi$
$578$		0			0
$579$	−16.4321	+	4.82490i	−0.682894	+	0.200516i
$580$		0			0
$581$	−1.77629	−	0.521565i	−0.0736928	−	0.0216382i
$582$		0			0
$583$	−0.113867	−	0.249333i	−0.00471588	−	0.0103263i
$584$		0			0
$585$	−9.40203	−	6.04232i	−0.388726	−	0.249819i
$586$		0			0
$587$	0.265332	−	1.84543i	0.0109514	−	0.0761688i	−0.983613	−	0.180294i	$-0.942295\pi$
$587$	0.265332	−	1.84543i	0.0109514	−	0.0761688i	0.994564	+	0.104125i	$0.0332042\pi$
$588$		0			0
$589$	−0.215291	−	0.248459i	−0.00887092	−	0.0102376i
$590$		0			0
$591$	−1.22528	+	0.787436i	−0.0504011	+	0.0323908i
$592$		0			0
$593$	−1.73276	+	1.99971i	−0.0711559	+	0.0821183i	−0.790211	−	0.612834i	$-0.790029\pi$
$593$	−1.73276	+	1.99971i	−0.0711559	+	0.0821183i	0.719055	+	0.694953i	$0.244575\pi$
$594$		0			0
$595$	−4.71460	+	10.3235i	−0.193280	+	0.423223i
$596$		0			0
$597$	1.40138			0.0573548
$598$		0			0
$599$	−41.9363			−1.71347			−0.856735	−	0.515757i	$-0.827511\pi$
$599$	−41.9363			−1.71347			−0.856735	+	0.515757i	$0.827511\pi$
$600$		0			0
$601$	−7.43166	+	16.2731i	−0.303144	+	0.663793i	−0.998493	−	0.0548796i	$-0.982523\pi$
$601$	−7.43166	+	16.2731i	−0.303144	+	0.663793i	0.695349	+	0.718672i	$0.255250\pi$
$602$		0			0
$603$	4.56013	−	5.26267i	0.185703	−	0.214313i
$604$		0			0
$605$	14.2381	−	9.15025i	0.578860	−	0.372011i
$606$		0			0
$607$	10.2561	+	11.8361i	0.416281	+	0.480414i	0.924700	−	0.380696i	$-0.124315\pi$
$607$	10.2561	+	11.8361i	0.416281	+	0.480414i	−0.508419	+	0.861110i	$0.669770\pi$
$608$		0			0
$609$	0.441184	−	3.06850i	0.0178777	−	0.124342i
$610$		0			0
$611$	46.5358	+	29.9067i	1.88264	+	1.20990i
$612$		0			0
$613$	−15.1839	−	33.2480i	−0.613271	−	1.34288i	−0.920314	−	0.391180i	$-0.872067\pi$
$613$	−15.1839	−	33.2480i	−0.613271	−	1.34288i	0.307043	−	0.951696i	$-0.400660\pi$
$614$		0			0
$615$	8.03638	+	2.35970i	0.324058	+	0.0951521i
$616$		0			0
$617$	29.4764	−	8.65505i	1.18667	−	0.348439i	0.371931	−	0.928260i	$-0.378696\pi$
$617$	29.4764	−	8.65505i	1.18667	−	0.348439i	0.814744	+	0.579821i	$0.196878\pi$
$618$		0			0
$619$	0.793907	+	5.52174i	0.0319098	+	0.221938i	0.999536	−	0.0304489i	$-0.00969368\pi$
$619$	0.793907	+	5.52174i	0.0319098	+	0.221938i	−0.967627	+	0.252386i	$0.918785\pi$
$620$		0			0
$621$	3.10384	+	3.65598i	0.124553	+	0.146709i
$622$		0			0
$623$	1.39117	+	9.67577i	0.0557359	+	0.387651i
$624$		0			0
$625$	6.34206	−	1.86220i	0.253682	−	0.0744879i
$626$		0			0
$627$	0.191803	+	0.0563184i	0.00765987	+	0.00224914i
$628$		0			0
$629$	−9.43810	−	20.6665i	−0.376322	−	0.824029i
$630$		0			0
$631$	5.69741	+	3.66150i	0.226810	+	0.145762i	0.649111	−	0.760694i	$-0.275141\pi$
$631$	5.69741	+	3.66150i	0.226810	+	0.145762i	−0.422301	+	0.906456i	$0.638777\pi$
$632$		0			0
$633$	1.25988	−	8.76264i	0.0500756	−	0.348284i
$634$		0			0
$635$	−15.6111	−	18.0161i	−0.619507	−	0.714949i
$636$		0			0
$637$	−14.8461	+	9.54102i	−0.588224	+	0.378029i
$638$		0			0
$639$	−7.85439	+	9.06445i	−0.310715	+	0.358584i
$640$		0			0
$641$	17.0747	−	37.3883i	0.674409	−	1.47675i	−0.194052	−	0.980991i	$-0.562163\pi$
$641$	17.0747	−	37.3883i	0.674409	−	1.47675i	0.868461	−	0.495758i	$-0.165110\pi$
$642$		0			0
$643$	−44.7063			−1.76305			−0.881523	−	0.472141i	$-0.843481\pi$
$643$	−44.7063			−1.76305			−0.881523	+	0.472141i	$0.843481\pi$
$644$		0			0
$645$	−9.85720			−0.388127
$646$		0			0
$647$	13.6261	−	29.8369i	0.535695	−	1.17301i	−0.427453	−	0.904038i	$-0.640589\pi$
$647$	13.6261	−	29.8369i	0.535695	−	1.17301i	0.963148	−	0.268972i	$-0.0866838\pi$
$648$		0			0
$649$	3.87517	−	4.47219i	0.152114	−	0.175549i
$650$		0			0
$651$	−1.78783	+	1.14897i	−0.0700704	+	0.0450315i
$652$		0			0
$653$	15.0102	+	17.3227i	0.587395	+	0.677890i	0.969178	−	0.246362i	$-0.0792353\pi$
$653$	15.0102	+	17.3227i	0.587395	+	0.677890i	−0.381783	+	0.924252i	$0.624690\pi$
$654$		0			0
$655$	−2.12123	+	14.7535i	−0.0828835	+	0.576467i
$656$		0			0
$657$	7.81470	+	5.02221i	0.304881	+	0.195935i
$658$		0			0
$659$	−2.02158	−	4.42664i	−0.0787495	−	0.172437i	0.866162	−	0.499763i	$-0.166580\pi$
$659$	−2.02158	−	4.42664i	−0.0787495	−	0.172437i	−0.944911	+	0.327326i	$0.893852\pi$
$660$		0			0
$661$	−15.7020	−	4.61054i	−0.610739	−	0.179329i	−0.0382860	−	0.999267i	$-0.512190\pi$
$661$	−15.7020	−	4.61054i	−0.610739	−	0.179329i	−0.572453	+	0.819938i	$0.694008\pi$
$662$		0			0
$663$	−22.6585	+	6.65315i	−0.879985	+	0.258387i
$664$		0			0
$665$	0.157257	+	1.09375i	0.00609818	+	0.0424138i
$666$		0			0
$667$	0.928826	+	6.95824i	0.0359643	+	0.269424i
$668$		0			0
$669$	3.32888	+	23.1528i	0.128702	+	0.895141i
$670$		0			0
$671$	0.386943	−	0.113617i	0.0149378	−	0.00438612i
$672$		0			0
$673$	−9.74305	−	2.86082i	−0.375567	−	0.110276i	0.0885008	−	0.996076i	$-0.471792\pi$
$673$	−9.74305	−	2.86082i	−0.375567	−	0.110276i	−0.464068	+	0.885800i	$0.653611\pi$
$674$		0			0
$675$	1.02354	+	2.24123i	0.0393959	+	0.0862651i
$676$		0			0
$677$	−15.4266	−	9.91408i	−0.592893	−	0.381029i	0.209515	−	0.977805i	$-0.432812\pi$
$677$	−15.4266	−	9.91408i	−0.592893	−	0.381029i	−0.802408	+	0.596776i	$0.796448\pi$
$678$		0			0
$679$	−1.98652	+	13.8165i	−0.0762356	+	0.530230i
$680$		0			0
$681$	1.19838	+	1.38300i	0.0459219	+	0.0529967i
$682$		0			0
$683$	−15.5026	+	9.96291i	−0.593190	+	0.381220i	−0.802520	−	0.596625i	$-0.796508\pi$
$683$	−15.5026	+	9.96291i	−0.593190	+	0.381220i	0.209330	+	0.977845i	$0.432872\pi$
$684$		0			0
$685$	−8.96964	+	10.3515i	−0.342712	+	0.395511i
$686$		0			0
$687$	7.24756	−	15.8699i	0.276512	−	0.605476i
$688$		0			0
$689$	3.15275			0.120110
$690$		0			0
$691$	0.496461			0.0188863			0.00944314	−	0.999955i	$-0.496994\pi$
$691$	0.496461			0.0188863			0.00944314	+	0.999955i	$0.496994\pi$
$692$		0			0
$693$	0.536804	−	1.17544i	0.0203915	−	0.0446512i
$694$		0			0
$695$	−15.1103	+	17.4382i	−0.573166	+	0.661469i
$696$		0			0
$697$	14.8882	−	9.56804i	0.563929	−	0.362415i
$698$		0			0
$699$	3.80655	+	4.39299i	0.143977	+	0.166158i
$700$		0			0
$701$	−4.70166	+	32.7008i	−0.177579	+	1.23509i	0.684763	+	0.728765i	$0.259906\pi$
$701$	−4.70166	+	32.7008i	−0.177579	+	1.23509i	−0.862343	+	0.506325i	$0.831004\pi$
$702$		0			0
$703$	−1.86092	−	1.19594i	−0.0701859	−	0.0451058i
$704$		0			0
$705$	5.21454	+	11.4182i	0.196391	+	0.430036i
$706$		0			0
$707$	33.1496	+	9.73361i	1.24672	+	0.366070i
$708$		0			0
$709$	34.4504	−	10.1155i	1.29381	−	0.379897i	0.438836	−	0.898567i	$-0.355391\pi$
$709$	34.4504	−	10.1155i	1.29381	−	0.379897i	0.854975	+	0.518670i	$0.173573\pi$
$710$		0			0
$711$	2.13709	+	14.8638i	0.0801471	+	0.557435i
$712$		0			0
$713$	3.18803	−	3.60497i	0.119393	−	0.135007i
$714$		0			0
$715$	−0.970465	−	6.74973i	−0.0362933	−	0.252426i
$716$		0			0
$717$	0.503438	−	0.147823i	0.0188012	−	0.00552054i
$718$		0			0
$719$	10.8983	+	3.20003i	0.406438	+	0.119341i	0.478560	−	0.878055i	$-0.341159\pi$
$719$	10.8983	+	3.20003i	0.406438	+	0.119341i	−0.0721219	+	0.997396i	$0.522977\pi$
$720$		0			0
$721$	12.1000	+	26.4953i	0.450628	+	0.986737i
$722$		0			0
$723$	1.30837	+	0.840836i	0.0486587	+	0.0312710i
$724$		0			0
$725$	−0.513265	+	3.56984i	−0.0190622	+	0.132580i
$726$		0			0
$727$	12.0869	+	13.9490i	0.448277	+	0.517339i	0.934242	−	0.356639i	$-0.116077\pi$
$727$	12.0869	+	13.9490i	0.448277	+	0.517339i	−0.485965	+	0.873978i	$0.661532\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	−13.6395	+	15.7408i	−0.504475	+	0.582195i
$732$		0			0
$733$	−15.4536	+	33.8387i	−0.570792	+	1.24986i	0.375582	+	0.926789i	$0.377443\pi$
$733$	−15.4536	+	33.8387i	−0.570792	+	1.24986i	−0.946375	+	0.323072i	$0.895285\pi$
$734$		0			0
$735$	−4.00460			−0.147712
$736$		0			0
$737$	4.24877			0.156506
$738$		0			0
$739$	−12.6027	+	27.5960i	−0.463596	+	1.01513i	0.523057	+	0.852298i	$0.324791\pi$
$739$	−12.6027	+	27.5960i	−0.463596	+	1.01513i	−0.986653	+	0.162836i	$0.947936\pi$
$740$		0			0
$741$	−1.50570	+	1.73767i	−0.0553132	+	0.0638348i
$742$		0			0
$743$	42.5202	−	27.3261i	1.55991	−	1.00250i	0.577366	−	0.816486i	$-0.304081\pi$
$743$	42.5202	−	27.3261i	1.55991	−	1.00250i	0.982548	−	0.186010i	$-0.0595557\pi$
$744$		0			0
$745$	19.4076	+	22.3976i	0.711041	+	0.820585i
$746$		0			0
$747$	0.124401	−	0.865225i	0.00455158	−	0.0316569i
$748$		0			0
$749$	−1.65979	−	1.06668i	−0.0606475	−	0.0389758i
$750$		0			0
$751$	−21.9890	−	48.1492i	−0.802391	−	1.75699i	−0.637154	−	0.770737i	$-0.719888\pi$
$751$	−21.9890	−	48.1492i	−0.802391	−	1.75699i	−0.165237	−	0.986254i	$-0.552839\pi$
$752$		0			0
$753$	−1.36045	−	0.399463i	−0.0495774	−	0.0145572i
$754$		0			0
$755$	14.1561	−	4.15661i	0.515194	−	0.151275i
$756$		0			0
$757$	−6.92682	−	48.1771i	−0.251759	−	1.75102i	−0.587642	−	0.809121i	$-0.699944\pi$
$757$	−6.92682	−	48.1771i	−0.251759	−	1.75102i	0.335883	−	0.941904i	$-0.390965\pi$
$758$		0			0
$759$	−0.445664	+	2.89203i	−0.0161766	+	0.104974i
$760$		0			0
$761$	−1.25326	−	8.71659i	−0.0454305	−	0.315976i	−0.999847	−	0.0174978i	$-0.994430\pi$
$761$	−1.25326	−	8.71659i	−0.0454305	−	0.315976i	0.954416	−	0.298478i	$-0.0964791\pi$
$762$		0			0
$763$	13.3050	−	3.90671i	0.481674	−	0.141432i
$764$		0			0
$765$	−5.14168	−	1.50973i	−0.185898	−	0.0545846i
$766$		0			0
$767$	28.2748	+	61.9132i	1.02094	+	2.23556i
$768$		0			0
$769$	37.2868	+	23.9628i	1.34460	+	0.864121i	0.997286	−	0.0736288i	$-0.0234580\pi$
$769$	37.2868	+	23.9628i	1.34460	+	0.864121i	0.347312	+	0.937750i	$0.387094\pi$
$770$		0			0
$771$	1.97307	−	13.7230i	0.0710583	−	0.494221i
$772$		0			0
$773$	15.3271	+	17.6884i	0.551278	+	0.636208i	0.961180	−	0.275921i	$-0.0889828\pi$
$773$	15.3271	+	17.6884i	0.551278	+	0.636208i	−0.409903	+	0.912129i	$0.634437\pi$
$774$		0			0
$775$	2.07992	−	1.33669i	0.0747131	−	0.0480152i
$776$		0			0
$777$	−9.36419	+	10.8069i	−0.335939	+	0.387694i
$778$		0			0
$779$	0.715806	−	1.56740i	0.0256464	−	0.0561578i
$780$		0			0
$781$	−7.31811			−0.261862
$782$		0			0
$783$	1.46376			0.0523106
$784$		0			0
$785$	−12.0737	+	26.4377i	−0.430929	+	0.943603i
$786$		0			0
$787$	12.1920	−	14.0703i	0.434597	−	0.501551i	−0.495631	−	0.868533i	$-0.665063\pi$
$787$	12.1920	−	14.0703i	0.434597	−	0.501551i	0.930228	+	0.366981i	$0.119609\pi$
$788$		0			0
$789$	11.7942	−	7.57970i	0.419886	−	0.269844i
$790$		0			0
$791$	23.8709	+	27.5485i	0.848751	+	0.979511i
$792$		0			0
$793$	−0.660132	+	4.59132i	−0.0234420	+	0.163042i
$794$		0			0
$795$	0.601853	+	0.386787i	0.0213455	+	0.0137179i
$796$		0			0
$797$	2.04652	+	4.48124i	0.0724913	+	0.158734i	0.942409	−	0.334464i	$-0.108555\pi$
$797$	2.04652	+	4.48124i	0.0724913	+	0.158734i	−0.869917	+	0.493198i	$0.835828\pi$
$798$		0			0
$799$	25.4490	+	7.47250i	0.900321	+	0.264358i
$800$		0			0
$801$	−4.42865	+	1.30037i	−0.156479	+	0.0459463i
$802$		0			0
$803$	0.806624	+	5.61019i	0.0284651	+	0.197979i
$804$		0			0
$805$	−15.5651	+	4.40010i	−0.548598	+	0.155083i
$806$		0			0
$807$	−0.938287	−	6.52593i	−0.0330293	−	0.229724i
$808$		0			0
$809$	−43.9531	+	12.9058i	−1.54531	+	0.453744i	−0.939695	−	0.342015i	$-0.888891\pi$
$809$	−43.9531	+	12.9058i	−1.54531	+	0.453744i	−0.605614	+	0.795758i	$0.707073\pi$
$810$		0			0
$811$	5.22633	+	1.53459i	0.183521	+	0.0538868i	0.372202	−	0.928152i	$-0.378603\pi$
$811$	5.22633	+	1.53459i	0.183521	+	0.0538868i	−0.188681	+	0.982039i	$0.560421\pi$
$812$		0			0
$813$	0.486841	+	1.06603i	0.0170743	+	0.0373874i
$814$		0			0
$815$	−11.9571	−	7.68437i	−0.418840	−	0.269172i
$816$		0			0
$817$	−0.288601	+	2.00726i	−0.0100969	+	0.0702253i
$818$		0			0
$819$	9.73326	+	11.2328i	0.340108	+	0.392505i
$820$		0			0
$821$	32.8373	−	21.1033i	1.14603	−	0.736509i	0.177185	−	0.984178i	$-0.443301\pi$
$821$	32.8373	−	21.1033i	1.14603	−	0.736509i	0.968845	+	0.247669i	$0.0796646\pi$
$822$		0			0
$823$	−4.98834	+	5.75685i	−0.173883	+	0.200671i	−0.836001	−	0.548728i	$-0.815112\pi$
$823$	−4.98834	+	5.75685i	−0.173883	+	0.200671i	0.662118	+	0.749399i	$0.269658\pi$
$824$		0			0
$825$	−0.624509	+	1.36748i	−0.0217426	+	0.0476097i
$826$		0			0
$827$	−11.6181			−0.404001			−0.202001	−	0.979385i	$-0.564744\pi$
$827$	−11.6181			−0.404001			−0.202001	+	0.979385i	$0.564744\pi$
$828$		0			0
$829$	−43.2708			−1.50286			−0.751429	−	0.659814i	$-0.770635\pi$
$829$	−43.2708			−1.50286			−0.751429	+	0.659814i	$0.770635\pi$
$830$		0			0
$831$	−5.54890	+	12.1504i	−0.192489	+	0.421492i
$832$		0			0
$833$	−5.54120	+	6.39489i	−0.191991	+	0.221570i
$834$		0			0
$835$	11.0055	−	7.07279i	0.380860	−	0.244764i
$836$		0			0
$837$	−0.657126	−	0.758363i	−0.0227136	−	0.0262129i
$838$		0			0
$839$	4.28017	−	29.7692i	0.147768	−	1.02775i	−0.772095	−	0.635507i	$-0.780791\pi$
$839$	4.28017	−	29.7692i	0.147768	−	1.02775i	0.919863	−	0.392241i	$-0.128300\pi$
$840$		0			0
$841$	−22.5939	−	14.5202i	−0.779099	−	0.500697i
$842$		0			0
$843$	−10.7555	−	23.5513i	−0.370439	−	0.811149i
$844$		0			0
$845$	55.3929	+	16.2648i	1.90557	+	0.559527i
$846$		0			0
$847$	−21.5964	+	6.34126i	−0.742060	+	0.217888i
$848$		0			0
$849$	−0.0103520	−	0.0719998i	−0.000355280	−	0.00247103i
$850$		0			0
$851$	13.7482	−	29.3172i	0.471282	−	1.00498i
$852$		0			0
$853$	−3.90446	−	27.1561i	−0.133686	−	0.929808i	−0.940691	−	0.339263i	$-0.889822\pi$
$853$	−3.90446	−	27.1561i	−0.133686	−	0.929808i	0.807005	−	0.590544i	$-0.201087\pi$
$854$		0			0
$855$	−0.500615	+	0.146994i	−0.0171207	+	0.00502708i
$856$		0			0
$857$	23.2702	+	6.83274i	0.794894	+	0.233402i	0.653872	−	0.756605i	$-0.273143\pi$
$857$	23.2702	+	6.83274i	0.794894	+	0.233402i	0.141021	+	0.990007i	$0.454961\pi$
$858$		0			0
$859$	21.2615	+	46.5562i	0.725434	+	1.58848i	0.806129	+	0.591739i	$0.201559\pi$
$859$	21.2615	+	46.5562i	0.725434	+	1.58848i	−0.0806957	+	0.996739i	$0.525714\pi$
$860$		0			0
$861$	−9.37045	−	6.02202i	−0.319344	−	0.205230i
$862$		0			0
$863$	6.55876	−	45.6172i	0.223263	−	1.55283i	−0.502314	−	0.864685i	$-0.667518\pi$
$863$	6.55876	−	45.6172i	0.223263	−	1.55283i	0.725577	−	0.688141i	$-0.241573\pi$
$864$		0			0
$865$	−16.4411	−	18.9740i	−0.559013	−	0.645135i
$866$		0			0
$867$	4.77585	−	3.06925i	0.162196	−	0.104237i
$868$		0			0
$869$	−6.00007	+	6.92445i	−0.203538	+	0.234896i
$870$		0			0
$871$	−20.3012	+	44.4534i	−0.687879	+	1.50625i
$872$		0			0
$873$	−6.59089			−0.223068
$874$		0			0
$875$	−25.1738			−0.851028
$876$		0			0
$877$	−19.9842	+	43.7592i	−0.674817	+	1.47764i	0.193226	+	0.981154i	$0.438105\pi$
$877$	−19.9842	+	43.7592i	−0.674817	+	1.47764i	−0.868043	+	0.496489i	$0.834622\pi$
$878$		0			0
$879$	−10.3112	+	11.8998i	−0.347789	+	0.401370i
$880$		0			0
$881$	29.6598	−	19.0612i	0.999265	−	0.642189i	0.0646718	−	0.997907i	$-0.479400\pi$
$881$	29.6598	−	19.0612i	0.999265	−	0.642189i	0.934593	+	0.355718i	$0.115764\pi$
$882$		0			0
$883$	−9.64522	−	11.1312i	−0.324587	−	0.374594i	0.569879	−	0.821728i	$-0.306990\pi$
$883$	−9.64522	−	11.1312i	−0.324587	−	0.374594i	−0.894467	+	0.447135i	$0.852445\pi$
$884$		0			0
$885$	−2.19807	+	15.2879i	−0.0738873	+	0.513897i
$886$		0			0
$887$	31.0797	+	19.9737i	1.04356	+	0.670653i	0.945864	−	0.324564i	$-0.105218\pi$
$887$	31.0797	+	19.9737i	1.04356	+	0.670653i	0.0976921	+	0.995217i	$0.468854\pi$
$888$		0			0
$889$	13.1699	+	28.8380i	0.441703	+	0.967194i
$890$		0			0
$891$	0.585433	+	0.171899i	0.0196127	+	0.00575882i
$892$		0			0
$893$	2.47782	−	0.727553i	0.0829170	−	0.0243466i
$894$		0			0
$895$	0.801247	+	5.57279i	0.0267827	+	0.186278i
$896$		0			0
$897$	−28.1288	−	18.4813i	−0.939194	−	0.617073i
$898$		0			0
$899$	−0.209035	−	1.45387i	−0.00697172	−	0.0484894i
$900$		0			0
$901$	1.45044	−	0.425889i	0.0483213	−	0.0141884i
$902$		0			0
$903$	12.5780	+	3.69322i	0.418568	+	0.122903i
$904$		0			0
$905$	5.35356	+	11.7227i	0.177958	+	0.389674i
$906$		0			0
$907$	44.9540	+	28.8902i	1.49267	+	0.959284i	0.995809	+	0.0914558i	$0.0291520\pi$
$907$	44.9540	+	28.8902i	1.49267	+	0.959284i	0.496865	+	0.867828i	$0.334484\pi$
$908$		0			0
$909$	−2.32160	+	16.1471i	−0.0770028	+	0.535566i
$910$		0			0
$911$	32.7360	+	37.7793i	1.08459	+	1.25168i	0.965945	+	0.258748i	$0.0833100\pi$
$911$	32.7360	+	37.7793i	1.08459	+	1.25168i	0.118646	+	0.992937i	$0.462145\pi$
$912$		0			0
$913$	0.448678	−	0.288348i	0.0148491	−	0.00954291i
$914$		0			0
$915$	−0.689291	+	0.795485i	−0.0227873	+	0.0262979i
$916$		0			0
$917$	8.23446	−	18.0310i	0.271926	−	0.595435i
$918$		0			0
$919$	9.90491			0.326733			0.163366	−	0.986565i	$-0.447765\pi$
$919$	9.90491			0.326733			0.163366	+	0.986565i	$0.447765\pi$
$920$		0			0
$921$	−8.30127			−0.273536
$922$		0			0
$923$	34.9668	−	76.5667i	1.15095	−	2.52022i
$924$		0			0
$925$	10.8941	−	12.5725i	0.358197	−	0.413381i
$926$		0			0
$927$	−11.5699	+	7.43555i	−0.380007	+	0.244216i
$928$		0			0
$929$	−32.6587	−	37.6902i	−1.07150	−	1.23658i	−0.970350	−	0.241704i	$-0.922294\pi$
$929$	−32.6587	−	37.6902i	−1.07150	−	1.23658i	−0.101148	−	0.994871i	$-0.532252\pi$
$930$		0			0
$931$	−0.117248	+	0.815474i	−0.00384263	+	0.0267261i
$932$		0			0
$933$	24.5195	+	15.7577i	0.802731	+	0.515884i
$934$		0			0
$935$	−1.35825	−	2.97416i	−0.0444196	−	0.0972654i
$936$		0			0
$937$	−8.32195	−	2.44355i	−0.271866	−	0.0798272i	0.142958	−	0.989729i	$-0.454339\pi$
$937$	−8.32195	−	2.44355i	−0.271866	−	0.0798272i	−0.414824	+	0.909902i	$0.636157\pi$
$938$		0			0
$939$	−31.2365	+	9.17185i	−1.01936	+	0.299312i
$940$		0			0
$941$	4.75065	+	33.0415i	0.154867	+	1.07712i	0.907914	+	0.419156i	$0.137674\pi$
$941$	4.75065	+	33.0415i	0.154867	+	1.07712i	−0.753048	+	0.657966i	$0.771417\pi$
$942$		0			0
$943$	24.1284	+	7.35020i	0.785729	+	0.239355i
$944$		0			0
$945$	0.479991	+	3.33841i	0.0156141	+	0.108598i
$946$		0			0
$947$	27.2123	−	7.99026i	0.884282	−	0.259649i	0.192103	−	0.981375i	$-0.438469\pi$
$947$	27.2123	−	7.99026i	0.884282	−	0.259649i	0.692179	+	0.721726i	$0.256651\pi$
$948$		0			0
$949$	−62.5515	−	18.3668i	−2.03051	−	0.596211i
$950$		0			0
$951$	−6.84538	−	14.9893i	−0.221977	−	0.486061i
$952$		0			0
$953$	43.3828	+	27.8804i	1.40531	+	0.903136i	0.999939	−	0.0110177i	$-0.00350712\pi$
$953$	43.3828	+	27.8804i	1.40531	+	0.903136i	0.405368	+	0.914154i	$0.367143\pi$
$954$		0			0
$955$	4.32135	−	30.0557i	0.139836	−	0.972579i
$956$		0			0
$957$	0.584863	+	0.674968i	0.0189059	+	0.0218186i
$958$		0			0
$959$	15.3238	−	9.84804i	0.494833	−	0.318010i
$960$		0			0
$961$	19.6413	−	22.6673i	0.633590	−	0.731202i
$962$		0			0
$963$	0.386999	−	0.847410i	0.0124709	−	0.0273074i
$964$		0			0
$965$	27.2731			0.877953
$966$		0			0
$967$	23.6167			0.759463			0.379731	−	0.925097i	$-0.376016\pi$
$967$	23.6167			0.759463			0.379731	+	0.925097i	$0.376016\pi$
$968$		0			0
$969$	−0.457973	+	1.00282i	−0.0147122	+	0.0322152i
$970$		0			0
$971$	30.3140	−	34.9843i	0.972824	−	1.12270i	−0.0195963	−	0.999808i	$-0.506238\pi$
$971$	30.3140	−	34.9843i	0.972824	−	1.12270i	0.992420	−	0.122891i	$-0.0392164\pi$
$972$		0			0
$973$	25.8146	−	16.5900i	0.827578	−	0.531852i
$974$		0			0
$975$	−11.3235	−	13.0680i	−0.362642	−	0.418511i
$976$		0			0
$977$	−5.53433	+	38.4921i	−0.177059	+	1.23147i	0.686465	+	0.727163i	$0.259162\pi$
$977$	−5.53433	+	38.4921i	−0.177059	+	1.23147i	−0.863523	+	0.504309i	$0.831747\pi$
$978$		0			0
$979$	−2.36915	−	1.52256i	−0.0757182	−	0.0486612i
$980$		0			0
$981$	2.71993	+	5.95581i	0.0868406	+	0.190154i
$982$		0			0
$983$	−47.6821	−	14.0007i	−1.52082	−	0.446554i	−0.588595	−	0.808428i	$-0.700319\pi$
$983$	−47.6821	−	14.0007i	−1.52082	−	0.446554i	−0.932227	+	0.361874i	$0.882137\pi$
$984$		0			0
$985$	2.22553	−	0.653473i	0.0709111	−	0.0208214i
$986$		0			0
$987$	−2.37574	−	16.5236i	−0.0756205	−	0.525952i
$988$		0			0
$989$	−29.6832	−	0.299761i	−0.943872	−	0.00953184i
$990$		0			0
$991$	1.26145	+	8.77356i	0.0400712	+	0.278701i	0.999999	−	0.00154673i	$-0.000492339\pi$
$991$	1.26145	+	8.77356i	0.0400712	+	0.278701i	−0.959928	+	0.280248i	$0.909583\pi$
$992$		0			0
$993$	−21.0239	+	6.17316i	−0.667172	+	0.195899i
$994$		0			0
$995$	−2.14133	−	0.628750i	−0.0678846	−	0.0199327i
$996$		0			0
$997$	12.7782	+	27.9803i	0.404689	+	0.886145i	0.996773	+	0.0802691i	$0.0255780\pi$
$997$	12.7782	+	27.9803i	0.404689	+	0.886145i	−0.592084	+	0.805876i	$0.701695\pi$
$998$		0			0
$999$	−5.68002	−	3.65033i	−0.179708	−	0.115491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.49.2	✓	30
23.8	even	11	inner	552.2.q.c.169.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.49.2	✓	30	1.1	even	1	trivial
552.2.q.c.169.2	yes	30	23.8	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{3} +(1.04288 - 1.20354i) q^{5} +(-1.78166 + 1.14501i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{3} +(1.04288 - 1.20354i) q^{5} +(-1.78166 + 1.14501i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.0868331 - 0.603937i) q^{11} +(5.90388 + 3.79419i) q^{13} +(0.661555 + 1.44860i) q^{15} +(3.22865 + 0.948018i) q^{17} +(0.314355 - 0.0923029i) q^{19} +(-0.301404 - 2.09631i) q^{21} +(1.94811 + 4.38234i) q^{23} +(0.350648 + 2.43881i) q^{25} +(0.959493 - 0.281733i) q^{27} +(1.40447 + 0.412389i) q^{29} +(-0.416852 - 0.912778i) q^{31} +(0.513289 + 0.329871i) q^{33} +(-0.479991 + 3.33841i) q^{35} +(-4.42152 - 5.10271i) q^{37} +(-5.90388 + 3.79419i) q^{39} +(3.44416 - 3.97478i) q^{41} +(-2.57129 + 5.63035i) q^{43} -1.59252 q^{45} +7.88224 q^{47} +(-1.04462 + 2.28739i) q^{49} +(-2.20358 + 2.54306i) q^{51} +(0.377926 - 0.242878i) q^{53} +(-0.636309 - 0.734340i) q^{55} +(-0.0466260 + 0.324291i) q^{57} +(8.15894 + 5.24344i) q^{59} +(0.274569 + 0.601223i) q^{61} +(2.03208 + 0.596672i) q^{63} +(10.7235 - 3.14870i) q^{65} +(0.991012 + 6.89264i) q^{67} +(-4.79559 - 0.0484290i) q^{69} +(-1.70692 - 11.8719i) q^{71} +(-8.91307 + 2.61711i) q^{73} +(-2.36408 - 0.694158i) q^{75} +(0.536804 + 1.17544i) q^{77} +(-12.6328 - 8.11860i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.572429 + 0.660618i) q^{83} +(4.50807 - 2.89716i) q^{85} +(-0.958560 + 1.10624i) q^{87} +(1.91740 - 4.19851i) q^{89} -14.8631 q^{91} +1.00346 q^{93} +(0.216743 - 0.474600i) q^{95} +(4.31611 - 4.98106i) q^{97} +(-0.513289 + 0.329871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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