LMFDB - Embedded newform 552.2.q.b.73.3

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			73.3
Character	$\chi$	$=$	552.73
Dual form			552.2.q.b.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{3} +(2.00868 + 1.29090i) q^{5} +(0.340497 + 2.36821i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{3} +(2.00868 + 1.29090i) q^{5} +(0.340497 + 2.36821i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-0.459205 + 1.00552i) q^{11} +(0.117503 - 0.817251i) q^{13} +(-2.29100 - 0.672698i) q^{15} +(-0.0178616 - 0.0206133i) q^{17} +(-2.16398 + 2.49736i) q^{19} +(-0.993906 - 2.17635i) q^{21} +(-2.91084 + 3.81143i) q^{23} +(0.291291 + 0.637838i) q^{25} +(-0.654861 + 0.755750i) q^{27} +(5.03137 + 5.80651i) q^{29} +(2.85303 + 0.837726i) q^{31} +(0.157317 - 1.09416i) q^{33} +(-2.37317 + 5.19651i) q^{35} +(-0.444524 + 0.285679i) q^{37} +(0.117503 + 0.817251i) q^{39} +(0.728630 + 0.468262i) q^{41} +(-0.841847 + 0.247188i) q^{43} +2.38772 q^{45} +4.46690 q^{47} +(1.22398 - 0.359393i) q^{49} +(0.0229455 + 0.0147462i) q^{51} +(1.44990 + 10.0843i) q^{53} +(-2.22042 + 1.42698i) q^{55} +(1.37273 - 3.00586i) q^{57} +(-0.787424 + 5.47665i) q^{59} +(-3.25915 - 0.956973i) q^{61} +(1.56679 + 1.80818i) q^{63} +(1.29101 - 1.48991i) q^{65} +(-4.92867 - 10.7923i) q^{67} +(1.71912 - 4.47712i) q^{69} +(0.565792 + 1.23891i) q^{71} +(-0.761068 + 0.878319i) q^{73} +(-0.459192 - 0.529935i) q^{75} +(-2.53764 - 0.745117i) q^{77} +(2.04718 - 14.2384i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-3.18579 + 2.04738i) q^{83} +(-0.00926838 - 0.0644630i) q^{85} +(-6.46344 - 4.15380i) q^{87} +(7.92794 - 2.32785i) q^{89} +1.97543 q^{91} -2.97348 q^{93} +(-7.57057 + 2.22292i) q^{95} +(-9.52360 - 6.12045i) q^{97} +(0.157317 + 1.09416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$		0			0
$5$	2.00868	+	1.29090i	0.898308	+	0.577307i	0.906288	−	0.422661i	$-0.138904\pi$
$5$	2.00868	+	1.29090i	0.898308	+	0.577307i	−0.00798008	+	0.999968i	$0.502540\pi$
$6$		0			0
$7$	0.340497	+	2.36821i	0.128696	+	0.895098i	0.947210	+	0.320613i	$0.103889\pi$
$7$	0.340497	+	2.36821i	0.128696	+	0.895098i	−0.818515	+	0.574486i	$0.805202\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	−0.459205	+	1.00552i	−0.138456	+	0.303175i	−0.966140	−	0.258018i	$-0.916930\pi$
$11$	−0.459205	+	1.00552i	−0.138456	+	0.303175i	0.827684	+	0.561194i	$0.189658\pi$
$12$		0			0
$13$	0.117503	−	0.817251i	0.0325895	−	0.226665i	−0.967017	−	0.254711i	$-0.918020\pi$
$13$	0.117503	−	0.817251i	0.0325895	−	0.226665i	0.999607	+	0.0280466i	$0.00892867\pi$
$14$		0			0
$15$	−2.29100	−	0.672698i	−0.591534	−	0.173690i
$16$		0			0
$17$	−0.0178616	−	0.0206133i	−0.00433206	−	0.00499947i	0.753579	−	0.657357i	$-0.228326\pi$
$17$	−0.0178616	−	0.0206133i	−0.00433206	−	0.00499947i	−0.757911	+	0.652357i	$0.773780\pi$
$18$		0			0
$19$	−2.16398	+	2.49736i	−0.496450	+	0.572934i	−0.947578	−	0.319525i	$-0.896477\pi$
$19$	−2.16398	+	2.49736i	−0.496450	+	0.572934i	0.451127	+	0.892460i	$0.351022\pi$
$20$		0			0
$21$	−0.993906	−	2.17635i	−0.216888	−	0.474918i
$22$		0			0
$23$	−2.91084	+	3.81143i	−0.606951	+	0.794739i
$23$	−2.91084	+	3.81143i	−0.606951	+	0.794739i
$24$		0			0
$25$	0.291291	+	0.637838i	0.0582582	+	0.127568i
$26$		0			0
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$		0			0
$29$	5.03137	+	5.80651i	0.934301	+	1.07824i	0.996779	+	0.0801947i	$0.0255542\pi$
$29$	5.03137	+	5.80651i	0.934301	+	1.07824i	−0.0624780	+	0.998046i	$0.519900\pi$
$30$		0			0
$31$	2.85303	+	0.837726i	0.512420	+	0.150460i	0.527713	−	0.849423i	$-0.323050\pi$
$31$	2.85303	+	0.837726i	0.512420	+	0.150460i	−0.0152926	+	0.999883i	$0.504868\pi$
$32$		0			0
$33$	0.157317	−	1.09416i	0.0273853	−	0.190469i
$34$		0			0
$35$	−2.37317	+	5.19651i	−0.401139	+	0.878371i
$36$		0			0
$37$	−0.444524	+	0.285679i	−0.0730794	+	0.0469653i	−0.576670	−	0.816977i	$-0.695648\pi$
$37$	−0.444524	+	0.285679i	−0.0730794	+	0.0469653i	0.503591	+	0.863942i	$0.332012\pi$
$38$		0			0
$39$	0.117503	+	0.817251i	0.0188155	+	0.130865i
$40$		0			0
$41$	0.728630	+	0.468262i	0.113793	+	0.0731303i	0.596299	−	0.802762i	$-0.296637\pi$
$41$	0.728630	+	0.468262i	0.113793	+	0.0731303i	−0.482506	+	0.875892i	$0.660274\pi$
$42$		0			0
$43$	−0.841847	+	0.247188i	−0.128380	+	0.0376959i	−0.345292	−	0.938495i	$-0.612220\pi$
$43$	−0.841847	+	0.247188i	−0.128380	+	0.0376959i	0.216911	+	0.976191i	$0.430402\pi$
$44$		0			0
$45$	2.38772			0.355940
$46$		0			0
$47$	4.46690			0.651564			0.325782	−	0.945445i	$-0.394372\pi$
$47$	4.46690			0.651564			0.325782	+	0.945445i	$0.394372\pi$
$48$		0			0
$49$	1.22398	−	0.359393i	0.174854	−	0.0513418i
$50$		0			0
$51$	0.0229455	+	0.0147462i	0.00321301	+	0.00206488i
$52$		0			0
$53$	1.44990	+	10.0843i	0.199159	+	1.38518i	0.806732	+	0.590918i	$0.201234\pi$
$53$	1.44990	+	10.0843i	0.199159	+	1.38518i	−0.607573	+	0.794264i	$0.707857\pi$
$54$		0			0
$55$	−2.22042	+	1.42698i	−0.299401	+	0.192413i
$56$		0			0
$57$	1.37273	−	3.00586i	0.181823	−	0.398137i
$58$		0			0
$59$	−0.787424	+	5.47665i	−0.102514	+	0.712999i	0.872136	+	0.489263i	$0.162734\pi$
$59$	−0.787424	+	5.47665i	−0.102514	+	0.712999i	−0.974650	+	0.223736i	$0.928175\pi$
$60$		0			0
$61$	−3.25915	−	0.956973i	−0.417292	−	0.122528i	0.0663450	−	0.997797i	$-0.478866\pi$
$61$	−3.25915	−	0.956973i	−0.417292	−	0.122528i	−0.483637	+	0.875269i	$0.660684\pi$
$62$		0			0
$63$	1.56679	+	1.80818i	0.197398	+	0.227809i
$64$		0			0
$65$	1.29101	−	1.48991i	0.160131	−	0.184801i
$66$		0			0
$67$	−4.92867	−	10.7923i	−0.602133	−	1.31849i	−0.927826	−	0.373013i	$-0.878325\pi$
$67$	−4.92867	−	10.7923i	−0.602133	−	1.31849i	0.325693	−	0.945476i	$-0.394402\pi$
$68$		0			0
$69$	1.71912	−	4.47712i	0.206958	−	0.538982i
$70$		0			0
$71$	0.565792	+	1.23891i	0.0671471	+	0.147032i	0.940230	−	0.340540i	$-0.110610\pi$
$71$	0.565792	+	1.23891i	0.0671471	+	0.147032i	−0.873083	+	0.487572i	$0.837883\pi$
$72$		0			0
$73$	−0.761068	+	0.878319i	−0.0890762	+	0.102799i	−0.798538	−	0.601945i	$-0.794393\pi$
$73$	−0.761068	+	0.878319i	−0.0890762	+	0.102799i	0.709462	+	0.704744i	$0.248938\pi$
$74$		0			0
$75$	−0.459192	−	0.529935i	−0.0530229	−	0.0611917i
$76$		0			0
$77$	−2.53764	−	0.745117i	−0.289190	−	0.0849140i
$78$		0			0
$79$	2.04718	−	14.2384i	0.230326	−	1.60195i	−0.466374	−	0.884588i	$-0.654440\pi$
$79$	2.04718	−	14.2384i	0.230326	−	1.60195i	0.696700	−	0.717363i	$-0.254651\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	−3.18579	+	2.04738i	−0.349686	+	0.224729i	−0.703678	−	0.710519i	$-0.748460\pi$
$83$	−3.18579	+	2.04738i	−0.349686	+	0.224729i	0.353992	+	0.935248i	$0.384824\pi$
$84$		0			0
$85$	−0.00926838	−	0.0644630i	−0.00100530	−	0.00699199i
$86$		0			0
$87$	−6.46344	−	4.15380i	−0.692954	−	0.445334i
$88$		0			0
$89$	7.92794	−	2.32785i	0.840360	−	0.246752i	0.166898	−	0.985974i	$-0.446625\pi$
$89$	7.92794	−	2.32785i	0.840360	−	0.246752i	0.673461	+	0.739222i	$0.264807\pi$
$90$		0			0
$91$	1.97543			0.207081
$92$		0			0
$93$	−2.97348			−0.308336
$94$		0			0
$95$	−7.57057	+	2.22292i	−0.776725	+	0.228067i
$96$		0			0
$97$	−9.52360	−	6.12045i	−0.966975	−	0.621437i	−0.0410551	−	0.999157i	$-0.513072\pi$
$97$	−9.52360	−	6.12045i	−0.966975	−	0.621437i	−0.925920	+	0.377720i	$0.876708\pi$
$98$		0			0
$99$	0.157317	+	1.09416i	0.0158109	+	0.109967i
$100$		0			0
$101$	9.28473	−	5.96693i	0.923865	−	0.593732i	0.0100882	−	0.999949i	$-0.496789\pi$
$101$	9.28473	−	5.96693i	0.923865	−	0.593732i	0.913776	+	0.406217i	$0.133152\pi$
$102$		0			0
$103$	6.09862	−	13.3541i	0.600915	−	1.31582i	−0.327703	−	0.944781i	$-0.606274\pi$
$103$	6.09862	−	13.3541i	0.600915	−	1.31582i	0.928617	−	0.371039i	$-0.120998\pi$
$104$		0			0
$105$	0.813011	−	5.65462i	0.0793418	−	0.551834i
$106$		0			0
$107$	10.7397	+	3.15345i	1.03824	+	0.304855i	0.756058	−	0.654505i	$-0.227123\pi$
$107$	10.7397	+	3.15345i	1.03824	+	0.304855i	0.282184	+	0.959360i	$0.408941\pi$
$108$		0			0
$109$	−7.59672	−	8.76708i	−0.727634	−	0.839734i	0.264569	−	0.964367i	$-0.414770\pi$
$109$	−7.59672	−	8.76708i	−0.727634	−	0.839734i	−0.992203	+	0.124633i	$0.960225\pi$
$110$		0			0
$111$	0.346033	−	0.399344i	0.0328440	−	0.0379040i
$112$		0			0
$113$	−7.54876	−	16.5295i	−0.710128	−	1.55496i	−0.827243	−	0.561845i	$-0.810092\pi$
$113$	−7.54876	−	16.5295i	−0.710128	−	1.55496i	0.117115	−	0.993118i	$-0.462635\pi$
$114$		0			0
$115$	−10.7671	+	3.89835i	−1.00404	+	0.363523i
$116$		0			0
$117$	−0.342990	−	0.751042i	−0.0317094	−	0.0694339i
$118$		0			0
$119$	0.0427349	−	0.0493187i	0.00391750	−	0.00452103i
$120$		0			0
$121$	6.40327	+	7.38977i	0.582115	+	0.671797i
$122$		0			0
$123$	−0.831040	−	0.244015i	−0.0749324	−	0.0220021i
$124$		0			0
$125$	1.46076	−	10.1598i	0.130655	−	0.908724i
$126$		0			0
$127$	4.36298	−	9.55359i	0.387152	−	0.847744i	−0.611262	−	0.791429i	$-0.709338\pi$
$127$	4.36298	−	9.55359i	0.387152	−	0.847744i	0.998413	−	0.0563149i	$-0.0179351\pi$
$128$		0			0
$129$	0.738105	−	0.474351i	0.0649865	−	0.0417643i
$130$		0			0
$131$	0.813825	+	5.66028i	0.0711042	+	0.494541i	0.993990	+	0.109468i	$0.0349147\pi$
$131$	0.813825	+	5.66028i	0.0711042	+	0.494541i	−0.922886	+	0.385073i	$0.874176\pi$
$132$		0			0
$133$	−6.65110	−	4.27440i	−0.576724	−	0.370638i
$134$		0			0
$135$	−2.29100	+	0.672698i	−0.197178	+	0.0578967i
$136$		0			0
$137$	12.6447			1.08031			0.540155	−	0.841566i	$-0.318366\pi$
$137$	12.6447			1.08031			0.540155	+	0.841566i	$0.318366\pi$
$138$		0			0
$139$	4.49641			0.381381			0.190690	−	0.981650i	$-0.438927\pi$
$139$	4.49641			0.381381			0.190690	+	0.981650i	$0.438927\pi$
$140$		0			0
$141$	−4.28596	+	1.25847i	−0.360943	+	0.105982i
$142$		0			0
$143$	0.767803	+	0.493437i	0.0642069	+	0.0412633i
$144$		0			0
$145$	2.61078	+	18.1584i	0.216814	+	1.50797i
$146$		0			0
$147$	−1.07315	+	0.689670i	−0.0885117	+	0.0568830i
$148$		0			0
$149$	−0.329968	+	0.722529i	−0.0270320	+	0.0591919i	−0.922666	−	0.385599i	$-0.873995\pi$
$149$	−0.329968	+	0.722529i	−0.0270320	+	0.0591919i	0.895634	+	0.444791i	$0.146722\pi$
$150$		0			0
$151$	1.72754	−	12.0153i	0.140585	−	0.977789i	−0.790363	−	0.612638i	$-0.790108\pi$
$151$	1.72754	−	12.0153i	0.140585	−	0.977789i	0.930948	−	0.365151i	$-0.118983\pi$
$152$		0			0
$153$	−0.0261705	−	0.00768435i	−0.00211576	−	0.000621243i
$154$		0			0
$155$	4.64941	+	5.36570i	0.373449	+	0.430983i
$156$		0			0
$157$	−0.399130	+	0.460620i	−0.0318540	+	0.0367615i	−0.771453	−	0.636286i	$-0.780470\pi$
$157$	−0.399130	+	0.460620i	−0.0318540	+	0.0367615i	0.739599	+	0.673048i	$0.235015\pi$
$158$		0			0
$159$	−4.23224	−	9.26731i	−0.335638	−	0.734945i
$160$		0			0
$161$	−10.0174	−	5.59568i	−0.789482	−	0.441002i
$162$		0			0
$163$	8.25927	+	18.0853i	0.646916	+	1.41655i	0.894228	+	0.447612i	$0.147725\pi$
$163$	8.25927	+	18.0853i	0.646916	+	1.41655i	−0.247312	+	0.968936i	$0.579547\pi$
$164$		0			0
$165$	1.72845	−	1.99474i	0.134560	−	0.155290i
$166$		0			0
$167$	−8.49682	−	9.80586i	−0.657504	−	0.758800i	0.324863	−	0.945761i	$-0.394682\pi$
$167$	−8.49682	−	9.80586i	−0.657504	−	0.758800i	−0.982367	+	0.186961i	$0.940136\pi$
$168$		0			0
$169$	11.8193	+	3.47046i	0.909178	+	0.266959i
$170$		0			0
$171$	−0.470277	+	3.27085i	−0.0359630	+	0.250128i
$172$		0			0
$173$	−9.72634	+	21.2977i	−0.739480	+	1.61923i	0.0449291	+	0.998990i	$0.485694\pi$
$173$	−9.72634	+	21.2977i	−0.739480	+	1.61923i	−0.784409	+	0.620244i	$0.787033\pi$
$174$		0			0
$175$	−1.41135	+	0.907020i	−0.106688	+	0.0685643i
$176$		0			0
$177$	−0.787424	−	5.47665i	−0.0591864	−	0.411650i
$178$		0			0
$179$	0.952018	+	0.611825i	0.0711572	+	0.0457299i	0.575736	−	0.817636i	$-0.304716\pi$
$179$	0.952018	+	0.611825i	0.0711572	+	0.0457299i	−0.504579	+	0.863366i	$0.668352\pi$
$180$		0			0
$181$	−7.68826	+	2.25748i	−0.571464	+	0.167797i	−0.554682	−	0.832062i	$-0.687160\pi$
$181$	−7.68826	+	2.25748i	−0.571464	+	0.167797i	−0.0167817	+	0.999859i	$0.505342\pi$
$182$		0			0
$183$	3.39674			0.251095
$184$		0			0
$185$	−1.26169			−0.0927612
$186$		0			0
$187$	0.0289292	−	0.00849438i	0.00211551	−	0.000621171i
$188$		0			0
$189$	−2.01275	−	1.29352i	−0.146406	−	0.0940894i
$190$		0			0
$191$	−1.16914	−	8.13156i	−0.0845962	−	0.588379i	−0.987390	−	0.158306i	$-0.949397\pi$
$191$	−1.16914	−	8.13156i	−0.0845962	−	0.588379i	0.902794	−	0.430073i	$-0.141512\pi$
$192$		0			0
$193$	−14.9112	+	9.58287i	−1.07333	+	0.689790i	−0.953008	−	0.302944i	$-0.902030\pi$
$193$	−14.9112	+	9.58287i	−1.07333	+	0.689790i	−0.120326	+	0.992734i	$0.538394\pi$
$194$		0			0
$195$	−0.818963	+	1.79328i	−0.0586471	+	0.128419i
$196$		0			0
$197$	0.370305	−	2.57553i	0.0263831	−	0.183499i	−0.972368	−	0.233451i	$-0.924998\pi$
$197$	0.370305	−	2.57553i	0.0263831	−	0.183499i	0.998752	+	0.0499528i	$0.0159071\pi$
$198$		0			0
$199$	19.3223	+	5.67355i	1.36972	+	0.402187i	0.882181	−	0.470911i	$-0.156075\pi$
$199$	19.3223	+	5.67355i	1.36972	+	0.402187i	0.487544	+	0.873099i	$0.337893\pi$
$200$		0			0
$201$	7.76957	+	8.96656i	0.548023	+	0.632452i
$202$		0			0
$203$	−12.0378	+	13.8924i	−0.844891	+	0.975057i
$204$		0			0
$205$	0.859104	+	1.88118i	0.0600024	+	0.131387i
$206$		0			0
$207$	−0.388134	+	4.78010i	−0.0269772	+	0.332240i
$208$		0			0
$209$	−1.51744	−	3.32272i	−0.104963	−	0.229837i
$210$		0			0
$211$	9.86378	−	11.3834i	0.679051	−	0.783666i	−0.306713	−	0.951802i	$-0.599229\pi$
$211$	9.86378	−	11.3834i	0.679051	−	0.783666i	0.985764	+	0.168136i	$0.0537747\pi$
$212$		0			0
$213$	−0.891915	−	1.02932i	−0.0611130	−	0.0705282i
$214$		0			0
$215$	−2.01009	−	0.590217i	−0.137087	−	0.0402525i
$216$		0			0
$217$	−1.01246	+	7.04182i	−0.0687303	+	0.478030i
$218$		0			0
$219$	0.482788	−	1.05716i	0.0326238	−	0.0714361i
$220$		0			0
$221$	−0.0189451	+	0.0121752i	−0.00127438	+	0.000818996i
$222$		0			0
$223$	−3.45586	−	24.0361i	−0.231422	−	1.60957i	−0.691962	−	0.721934i	$-0.743253\pi$
$223$	−3.45586	−	24.0361i	−0.231422	−	1.60957i	0.460540	−	0.887639i	$-0.347656\pi$
$224$		0			0
$225$	0.589891	+	0.379100i	0.0393261	+	0.0252733i
$226$		0			0
$227$	−5.62906	+	1.65284i	−0.373614	+	0.109703i	−0.463148	−	0.886281i	$-0.653280\pi$
$227$	−5.62906	+	1.65284i	−0.373614	+	0.109703i	0.0895345	+	0.995984i	$0.471462\pi$
$228$		0			0
$229$	7.50194			0.495742			0.247871	−	0.968793i	$-0.420269\pi$
$229$	7.50194			0.495742			0.247871	+	0.968793i	$0.420269\pi$
$230$		0			0
$231$	2.64477			0.174013
$232$		0			0
$233$	−11.8044	+	3.46607i	−0.773329	+	0.227070i	−0.644508	−	0.764598i	$-0.722938\pi$
$233$	−11.8044	+	3.46607i	−0.773329	+	0.227070i	−0.128822	+	0.991668i	$0.541119\pi$
$234$		0			0
$235$	8.97256	+	5.76631i	0.585305	+	0.376153i
$236$		0			0
$237$	2.04718	+	14.2384i	0.132979	+	0.924887i
$238$		0			0
$239$	19.9678	−	12.8325i	1.29161	−	0.830067i	0.299337	−	0.954147i	$-0.403234\pi$
$239$	19.9678	−	12.8325i	1.29161	−	0.830067i	0.992272	+	0.124080i	$0.0395980\pi$
$240$		0			0
$241$	−3.85869	+	8.44935i	−0.248560	+	0.544270i	−0.992250	−	0.124254i	$-0.960346\pi$
$241$	−3.85869	+	8.44935i	−0.248560	+	0.544270i	0.743691	+	0.668524i	$0.233074\pi$
$242$		0			0
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$		0			0
$245$	2.92252	+	0.858129i	0.186713	+	0.0548239i
$246$		0			0
$247$	1.78670	+	2.06196i	0.113685	+	0.131199i
$248$		0			0
$249$	2.47993	−	2.86199i	0.157159	−	0.181371i
$250$		0			0
$251$	−2.20777	−	4.83434i	−0.139353	−	0.305141i	0.827069	−	0.562100i	$-0.190007\pi$
$251$	−2.20777	−	4.83434i	−0.139353	−	0.305141i	−0.966422	+	0.256960i	$0.917279\pi$
$252$		0			0
$253$	−2.49580	−	4.67713i	−0.156909	−	0.294049i
$254$		0			0
$255$	0.0270543	+	0.0592406i	0.00169420	+	0.00370979i
$256$		0			0
$257$	−2.11444	+	2.44020i	−0.131895	+	0.152215i	−0.817855	−	0.575424i	$-0.804837\pi$
$257$	−2.11444	+	2.44020i	−0.131895	+	0.152215i	0.685960	+	0.727639i	$0.259383\pi$
$258$		0			0
$259$	−0.827905	−	0.955454i	−0.0514435	−	0.0593690i
$260$		0			0
$261$	7.37189	+	2.16458i	0.456308	+	0.133984i
$262$		0			0
$263$	2.83933	−	19.7480i	0.175081	−	1.21771i	−0.692870	−	0.721062i	$-0.743654\pi$
$263$	2.83933	−	19.7480i	0.175081	−	1.21771i	0.867951	−	0.496650i	$-0.165437\pi$
$264$		0			0
$265$	−10.1054	+	22.1277i	−0.620770	+	1.35930i
$266$		0			0
$267$	−6.95097	+	4.46712i	−0.425392	+	0.273383i
$268$		0			0
$269$	0.974073	+	6.77483i	0.0593903	+	0.413069i	0.997729	+	0.0673520i	$0.0214550\pi$
$269$	0.974073	+	6.77483i	0.0593903	+	0.413069i	−0.938339	+	0.345717i	$0.887636\pi$
$270$		0			0
$271$	5.53042	+	3.55418i	0.335949	+	0.215901i	0.697728	−	0.716362i	$-0.254194\pi$
$271$	5.53042	+	3.55418i	0.335949	+	0.215901i	−0.361779	+	0.932264i	$0.617831\pi$
$272$		0			0
$273$	−1.89541	+	0.556543i	−0.114716	+	0.0336835i
$274$		0			0
$275$	−0.775121			−0.0467415
$276$		0			0
$277$	−12.4643			−0.748908			−0.374454	−	0.927246i	$-0.622170\pi$
$277$	−12.4643			−0.748908			−0.374454	+	0.927246i	$0.622170\pi$
$278$		0			0
$279$	2.85303	−	0.837726i	0.170807	−	0.0501534i
$280$		0			0
$281$	−4.36122	−	2.80279i	−0.260169	−	0.167200i	0.404054	−	0.914735i	$-0.367601\pi$
$281$	−4.36122	−	2.80279i	−0.260169	−	0.167200i	−0.664222	+	0.747535i	$0.731237\pi$
$282$		0			0
$283$	3.07705	+	21.4013i	0.182912	+	1.27218i	0.849834	+	0.527050i	$0.176702\pi$
$283$	3.07705	+	21.4013i	0.182912	+	1.27218i	−0.666923	+	0.745127i	$0.732389\pi$
$284$		0			0
$285$	6.63764	−	4.26575i	0.393180	−	0.252682i
$286$		0			0
$287$	−0.860846	+	1.88499i	−0.0508141	+	0.111267i
$288$		0			0
$289$	2.41925	−	16.8262i	0.142309	−	0.989778i
$290$		0			0
$291$	10.8622	+	3.18942i	0.636751	+	0.186967i
$292$		0			0
$293$	−7.14025	−	8.24029i	−0.417138	−	0.481403i	0.507825	−	0.861460i	$-0.330450\pi$
$293$	−7.14025	−	8.24029i	−0.417138	−	0.481403i	−0.924963	+	0.380058i	$0.875904\pi$
$294$		0			0
$295$	−8.65148	+	9.98434i	−0.503709	+	0.581311i
$296$		0			0
$297$	−0.459205	−	1.00552i	−0.0266458	−	0.0583461i
$298$		0			0
$299$	2.77287	+	2.82674i	0.160359	+	0.163475i
$300$		0			0
$301$	−0.872040	−	1.90950i	−0.0502635	−	0.110062i
$302$		0			0
$303$	−7.22755	+	8.34104i	−0.415212	+	0.479180i
$304$		0			0
$305$	−5.31123	−	6.12949i	−0.304120	−	0.350973i
$306$		0			0
$307$	14.7772	+	4.33898i	0.843380	+	0.247639i	0.674755	−	0.738041i	$-0.264249\pi$
$307$	14.7772	+	4.33898i	0.843380	+	0.247639i	0.168625	+	0.985680i	$0.446067\pi$
$308$		0			0
$309$	−2.08929	+	14.5314i	−0.118856	+	0.826660i
$310$		0			0
$311$	−3.24147	+	7.09782i	−0.183807	+	0.402481i	−0.978996	−	0.203881i	$-0.934644\pi$
$311$	−3.24147	+	7.09782i	−0.183807	+	0.402481i	0.795189	+	0.606362i	$0.207372\pi$
$312$		0			0
$313$	−27.5359	+	17.6963i	−1.55642	+	1.00025i	−0.572865	+	0.819650i	$0.694168\pi$
$313$	−27.5359	+	17.6963i	−1.55642	+	1.00025i	−0.983556	+	0.180602i	$0.942195\pi$
$314$		0			0
$315$	0.813011	+	5.65462i	0.0458080	+	0.318602i
$316$		0			0
$317$	28.3403	+	18.2132i	1.59175	+	1.02296i	0.971040	+	0.238917i	$0.0767925\pi$
$317$	28.3403	+	18.2132i	1.59175	+	1.02296i	0.620711	+	0.784039i	$0.286844\pi$
$318$		0			0
$319$	−8.14898	+	2.39276i	−0.456255	+	0.133969i
$320$		0			0
$321$	−11.1931			−0.624736
$322$		0			0
$323$	0.0901310			0.00501502
$324$		0			0
$325$	0.555502	−	0.163110i	0.0308137	−	0.00904772i
$326$		0			0
$327$	9.75897	+	6.27171i	0.539672	+	0.346826i
$328$		0			0
$329$	1.52097	+	10.5785i	0.0838535	+	0.583214i
$330$		0			0
$331$	−5.84664	+	3.75741i	−0.321361	+	0.206526i	−0.691368	−	0.722503i	$-0.742992\pi$
$331$	−5.84664	+	3.75741i	−0.321361	+	0.206526i	0.370007	+	0.929029i	$0.379355\pi$
$332$		0			0
$333$	−0.219508	+	0.480656i	−0.0120290	+	0.0263398i
$334$		0			0
$335$	4.03164	−	28.0407i	0.220272	−	1.53202i
$336$		0			0
$337$	13.8461	+	4.06557i	0.754242	+	0.221466i	0.636180	−	0.771541i	$-0.280514\pi$
$337$	13.8461	+	4.06557i	0.754242	+	0.221466i	0.118062	+	0.993006i	$0.462332\pi$
$338$		0			0
$339$	11.8999	+	13.7332i	0.646313	+	0.745885i
$340$		0			0
$341$	−2.15248	+	2.48409i	−0.116563	+	0.134521i
$342$		0			0
$343$	8.22522	+	18.0107i	0.444120	+	0.972487i
$344$		0			0
$345$	9.23267	−	6.77388i	0.497070	−	0.364694i
$346$		0			0
$347$	6.34345	+	13.8902i	0.340534	+	0.745666i	0.999981	−	0.00608503i	$-0.00193694\pi$
$347$	6.34345	+	13.8902i	0.340534	+	0.745666i	−0.659447	+	0.751751i	$0.729210\pi$
$348$		0			0
$349$	19.5916	−	22.6099i	1.04872	−	1.21028i	0.0716304	−	0.997431i	$-0.477180\pi$
$349$	19.5916	−	22.6099i	1.04872	−	1.21028i	0.977085	−	0.212851i	$-0.0682748\pi$
$350$		0			0
$351$	0.540689	+	0.623988i	0.0288598	+	0.0333060i
$352$		0			0
$353$	−8.99544	−	2.64130i	−0.478779	−	0.140582i	0.0334336	−	0.999441i	$-0.489356\pi$
$353$	−8.99544	−	2.64130i	−0.478779	−	0.140582i	−0.512212	+	0.858859i	$0.671174\pi$
$354$		0			0
$355$	−0.462816	+	3.21895i	−0.0245637	+	0.170844i
$356$		0			0
$357$	−0.0271091	+	0.0593607i	−0.00143477	+	0.00314170i
$358$		0			0
$359$	2.38113	−	1.53026i	0.125671	−	0.0807639i	−0.476295	−	0.879286i	$-0.658021\pi$
$359$	2.38113	−	1.53026i	0.125671	−	0.0807639i	0.601966	+	0.798522i	$0.294384\pi$
$360$		0			0
$361$	1.14996	+	7.99814i	0.0605241	+	0.420954i
$362$		0			0
$363$	−8.22583	−	5.28642i	−0.431744	−	0.277465i
$364$		0			0
$365$	−2.66256	+	0.781798i	−0.139365	+	0.0409212i
$366$		0			0
$367$	−12.6848			−0.662139			−0.331070	−	0.943606i	$-0.607409\pi$
$367$	−12.6848			−0.662139			−0.331070	+	0.943606i	$0.607409\pi$
$368$		0			0
$369$	0.866124			0.0450886
$370$		0			0
$371$	−23.3880	+	6.86733i	−1.21424	+	0.356534i
$372$		0			0
$373$	−23.9304	−	15.3792i	−1.23907	−	0.796303i	−0.253792	−	0.967259i	$-0.581678\pi$
$373$	−23.9304	−	15.3792i	−1.23907	−	0.796303i	−0.985279	+	0.170956i	$0.945314\pi$
$374$		0			0
$375$	1.46076	+	10.1598i	0.0754336	+	0.524652i
$376$		0			0
$377$	5.33657	−	3.42961i	0.274848	−	0.176634i
$378$		0			0
$379$	0.666819	−	1.46013i	0.0342522	−	0.0750019i	−0.891733	−	0.452563i	$-0.850510\pi$
$379$	0.666819	−	1.46013i	0.0342522	−	0.0750019i	0.925985	+	0.377561i	$0.123237\pi$
$380$		0			0
$381$	−1.49469	+	10.3958i	−0.0765752	+	0.532592i
$382$		0			0
$383$	25.0684	+	7.36075i	1.28094	+	0.376117i	0.850247	−	0.526384i	$-0.176452\pi$
$383$	25.0684	+	7.36075i	1.28094	+	0.376117i	0.430689	+	0.902501i	$0.358271\pi$
$384$		0			0
$385$	−4.13542	−	4.77253i	−0.210761	−	0.243231i
$386$		0			0
$387$	−0.574566	+	0.663085i	−0.0292068	+	0.0337065i
$388$		0			0
$389$	−9.41038	−	20.6059i	−0.477125	−	1.04476i	−0.983244	−	0.182295i	$-0.941647\pi$
$389$	−9.41038	−	20.6059i	−0.477125	−	1.04476i	0.506119	−	0.862464i	$-0.331080\pi$
$390$		0			0
$391$	0.130558	−	0.00807611i	0.00660262	−	0.000408427i
$392$		0			0
$393$	−2.37554	−	5.20172i	−0.119830	−	0.262392i
$394$		0			0
$395$	22.4925	−	25.9577i	1.13172	−	1.30608i
$396$		0			0
$397$	15.5109	+	17.9005i	0.778468	+	0.898399i	0.996998	−	0.0774307i	$-0.0246717\pi$
$397$	15.5109	+	17.9005i	0.778468	+	0.898399i	−0.218530	+	0.975830i	$0.570126\pi$
$398$		0			0
$399$	7.58592	+	2.22743i	0.379771	+	0.111511i
$400$		0			0
$401$	1.83173	−	12.7400i	0.0914723	−	0.636204i	−0.891578	−	0.452867i	$-0.850401\pi$
$401$	1.83173	−	12.7400i	0.0914723	−	0.636204i	0.983050	−	0.183337i	$-0.0586898\pi$
$402$		0			0
$403$	1.01987	−	2.23321i	0.0508035	−	0.111244i
$404$		0			0
$405$	2.00868	−	1.29090i	0.0998120	−	0.0641453i
$406$		0			0
$407$	−0.0831272	−	0.578163i	−0.00412046	−	0.0286585i
$408$		0			0
$409$	29.3246	+	18.8457i	1.45001	+	0.931862i	0.999230	+	0.0392248i	$0.0124888\pi$
$409$	29.3246	+	18.8457i	1.45001	+	0.931862i	0.450775	+	0.892637i	$0.351148\pi$
$410$		0			0
$411$	−12.1325	+	3.56242i	−0.598452	+	0.175721i
$412$		0			0
$413$	−13.2380			−0.651398
$414$		0			0
$415$	−9.04218			−0.443863
$416$		0			0
$417$	−4.31428	+	1.26679i	−0.211271	+	0.0620348i
$418$		0			0
$419$	−22.8127	−	14.6609i	−1.11447	−	0.716230i	−0.152211	−	0.988348i	$-0.548639\pi$
$419$	−22.8127	−	14.6609i	−1.11447	−	0.716230i	−0.962264	+	0.272118i	$0.912276\pi$
$420$		0			0
$421$	0.177538	+	1.23480i	0.00865266	+	0.0601806i	0.993690	−	0.112159i	$-0.0357765\pi$
$421$	0.177538	+	1.23480i	0.00865266	+	0.0601806i	−0.985038	+	0.172339i	$0.944867\pi$
$422$		0			0
$423$	3.75779	−	2.41499i	0.182710	−	0.117421i
$424$		0			0
$425$	0.00794507	−	0.0173973i	0.000385392	−	0.000843891i
$426$		0			0
$427$	1.15658	−	8.04420i	0.0559709	−	0.389286i
$428$		0			0
$429$	−0.875719	−	0.257134i	−0.0422801	−	0.0124146i
$430$		0			0
$431$	0.596594	+	0.688506i	0.0287369	+	0.0331642i	0.769936	−	0.638121i	$-0.220288\pi$
$431$	0.596594	+	0.688506i	0.0287369	+	0.0331642i	−0.741199	+	0.671285i	$0.765743\pi$
$432$		0			0
$433$	8.45174	−	9.75382i	0.406165	−	0.468739i	−0.515408	−	0.856945i	$-0.672360\pi$
$433$	8.45174	−	9.75382i	0.406165	−	0.468739i	0.921573	+	0.388206i	$0.126905\pi$
$434$		0			0
$435$	−7.62083	−	16.6873i	−0.365391	−	0.800095i
$436$		0			0
$437$	−3.21955	−	15.5173i	−0.154012	−	0.742292i
$438$		0			0
$439$	1.31223	+	2.87338i	0.0626293	+	0.137139i	0.938359	−	0.345664i	$-0.112346\pi$
$439$	1.31223	+	2.87338i	0.0626293	+	0.137139i	−0.875729	+	0.482803i	$0.839619\pi$
$440$		0			0
$441$	0.835375	−	0.964074i	0.0397798	−	0.0459083i
$442$		0			0
$443$	−14.6124	−	16.8636i	−0.694256	−	0.801215i	0.293708	−	0.955895i	$-0.405111\pi$
$443$	−14.6124	−	16.8636i	−0.694256	−	0.801215i	−0.987965	+	0.154681i	$0.950565\pi$
$444$		0			0
$445$	18.9297	+	5.55826i	0.897353	+	0.263487i
$446$		0			0
$447$	0.113042	−	0.786224i	0.00534670	−	0.0371871i
$448$		0			0
$449$	−2.67298	+	5.85301i	−0.126146	+	0.276221i	−0.962159	−	0.272488i	$-0.912153\pi$
$449$	−2.67298	+	5.85301i	−0.126146	+	0.276221i	0.836013	+	0.548709i	$0.184881\pi$
$450$		0			0
$451$	−0.805437	+	0.517623i	−0.0379265	+	0.0243739i
$452$		0			0
$453$	1.72754	+	12.0153i	0.0811667	+	0.564527i
$454$		0			0
$455$	3.96800	+	2.55008i	0.186023	+	0.119550i
$456$		0			0
$457$	−30.7011	+	9.01465i	−1.43614	+	0.421688i	−0.904932	−	0.425556i	$-0.860079\pi$
$457$	−30.7011	+	9.01465i	−1.43614	+	0.421688i	−0.531204	+	0.847244i	$0.678260\pi$
$458$		0			0
$459$	0.0272754			0.00127310
$460$		0			0
$461$	−30.9531			−1.44163			−0.720816	−	0.693127i	$-0.756233\pi$
$461$	−30.9531			−1.44163			−0.720816	+	0.693127i	$0.756233\pi$
$462$		0			0
$463$	−37.2399	+	10.9346i	−1.73068	+	0.508175i	−0.987050	−	0.160412i	$-0.948718\pi$
$463$	−37.2399	+	10.9346i	−1.73068	+	0.508175i	−0.743634	+	0.668587i	$0.766899\pi$
$464$		0			0
$465$	−5.97276	−	3.83846i	−0.276980	−	0.178004i
$466$		0			0
$467$	−3.54064	−	24.6257i	−0.163841	−	1.13954i	−0.891308	−	0.453399i	$-0.850211\pi$
$467$	−3.54064	−	24.6257i	−0.163841	−	1.13954i	0.727466	−	0.686143i	$-0.240698\pi$
$468$		0			0
$469$	23.8802	−	15.3469i	1.10268	−	0.708653i
$470$		0			0
$471$	0.253191	−	0.554410i	0.0116664	−	0.0255459i
$472$		0			0
$473$	0.138028	−	0.960003i	0.00634651	−	0.0441410i
$474$		0			0
$475$	−2.22326	−	0.652808i	−0.102010	−	0.0299529i
$476$		0			0
$477$	6.67170	+	7.69956i	0.305476	+	0.352538i
$478$		0			0
$479$	−7.24750	+	8.36406i	−0.331147	+	0.382164i	−0.896768	−	0.442502i	$-0.854091\pi$
$479$	−7.24750	+	8.36406i	−0.331147	+	0.382164i	0.565621	+	0.824665i	$0.308637\pi$
$480$		0			0
$481$	0.181238	+	0.396856i	0.00826375	+	0.0180951i
$482$		0			0
$483$	11.1881	+	2.54679i	0.509077	+	0.115883i
$484$		0			0
$485$	−11.2290	−	24.5880i	−0.509881	−	1.11648i
$486$		0			0
$487$	14.9332	−	17.2338i	0.676686	−	0.780937i	−0.308721	−	0.951153i	$-0.599901\pi$
$487$	14.9332	−	17.2338i	0.676686	−	0.780937i	0.985407	+	0.170215i	$0.0544464\pi$
$488$		0			0
$489$	−13.0199	−	15.0258i	−0.588781	−	0.679489i
$490$		0			0
$491$	−11.8043	−	3.46604i	−0.532719	−	0.156420i	0.00429985	−	0.999991i	$-0.498631\pi$
$491$	−11.8043	−	3.46604i	−0.532719	−	0.156420i	−0.537019	+	0.843570i	$0.680449\pi$
$492$		0			0
$493$	0.0298234	−	0.207426i	0.00134318	−	0.00934202i
$494$		0			0
$495$	−1.09645	+	2.40090i	−0.0492819	+	0.107912i
$496$		0			0
$497$	−2.74135	+	1.76176i	−0.122966	+	0.0790256i
$498$		0			0
$499$	−4.63535	−	32.2396i	−0.207507	−	1.44324i	−0.781256	−	0.624210i	$-0.785421\pi$
$499$	−4.63535	−	32.2396i	−0.207507	−	1.44324i	0.573750	−	0.819031i	$-0.305488\pi$
$500$		0			0
$501$	10.9153	+	7.01482i	0.487658	+	0.313399i
$502$		0			0
$503$	−29.1427	+	8.55706i	−1.29941	+	0.381540i	−0.857020	−	0.515284i	$-0.827687\pi$
$503$	−29.1427	+	8.55706i	−1.29941	+	0.381540i	−0.442387	+	0.896824i	$0.645868\pi$
$504$		0			0
$505$	26.3527			1.17268
$506$		0			0
$507$	−12.3183			−0.547075
$508$		0			0
$509$	24.1996	−	7.10564i	1.07263	−	0.314952i	0.302702	−	0.953085i	$-0.402111\pi$
$509$	24.1996	−	7.10564i	1.07263	−	0.314952i	0.769926	+	0.638133i	$0.220293\pi$
$510$		0			0
$511$	−2.33918	−	1.50330i	−0.103479	−	0.0665022i
$512$		0			0
$513$	−0.470277	−	3.27085i	−0.0207632	−	0.144412i
$514$		0			0
$515$	29.4890	−	18.9514i	1.29944	−	0.835099i
$516$		0			0
$517$	−2.05122	+	4.49155i	−0.0902127	+	0.197538i
$518$		0			0
$519$	3.33209	−	23.1752i	0.146263	−	1.01728i
$520$		0			0
$521$	30.7962	+	9.04259i	1.34921	+	0.396163i	0.874946	−	0.484221i	$-0.160897\pi$
$521$	30.7962	+	9.04259i	1.34921	+	0.396163i	0.474262	+	0.880384i	$0.342715\pi$
$522$		0			0
$523$	11.1304	+	12.8452i	0.486701	+	0.561682i	0.944981	−	0.327125i	$-0.106080\pi$
$523$	11.1304	+	12.8452i	0.486701	+	0.561682i	−0.458280	+	0.888808i	$0.651534\pi$
$524$		0			0
$525$	1.09864	−	1.26790i	0.0479487	−	0.0553358i
$526$		0			0
$527$	−0.0336913	−	0.0737736i	−0.00146762	−	0.00321363i
$528$		0			0
$529$	−6.05407	−	22.1889i	−0.263220	−	0.964736i
$530$		0			0
$531$	2.29848	+	5.03297i	0.0997455	+	0.218412i
$532$		0			0
$533$	0.468304	−	0.540452i	0.0202845	−	0.0234096i
$534$		0			0
$535$	17.5017	+	20.1981i	0.756666	+	0.873239i
$536$		0			0
$537$	−1.08583	−	0.318827i	−0.0468568	−	0.0137584i
$538$		0			0
$539$	−0.200681	+	1.39577i	−0.00864396	+	0.0601200i
$540$		0			0
$541$	15.1432	−	33.1590i	0.651057	−	1.42562i	−0.239569	−	0.970879i	$-0.577006\pi$
$541$	15.1432	−	33.1590i	0.651057	−	1.42562i	0.890626	−	0.454736i	$-0.150266\pi$
$542$		0			0
$543$	6.74083	−	4.33207i	0.289277	−	0.185907i
$544$		0			0
$545$	−3.94195	−	27.4168i	−0.168854	−	1.17441i
$546$		0			0
$547$	−12.9554	−	8.32591i	−0.553932	−	0.355990i	0.233534	−	0.972349i	$-0.424971\pi$
$547$	−12.9554	−	8.32591i	−0.553932	−	0.355990i	−0.787466	+	0.616358i	$0.788607\pi$
$548$		0			0
$549$	−3.25915	+	0.956973i	−0.139097	+	0.0408426i
$550$		0			0
$551$	−25.3887			−1.08160
$552$		0			0
$553$	34.4167			1.46355
$554$		0			0
$555$	1.21058	−	0.355459i	0.0513863	−	0.0150884i
$556$		0			0
$557$	1.30716	+	0.840061i	0.0553862	+	0.0355945i	0.568041	−	0.823000i	$-0.307702\pi$
$557$	1.30716	+	0.840061i	0.0553862	+	0.0355945i	−0.512655	+	0.858595i	$0.671338\pi$
$558$		0			0
$559$	0.103096	+	0.717046i	0.00436048	+	0.0303278i
$560$		0			0
$561$	−0.0253642	+	0.0163006i	−0.00107088	+	0.000688212i
$562$		0			0
$563$	−14.3080	+	31.3301i	−0.603008	+	1.32040i	0.324246	+	0.945973i	$0.394889\pi$
$563$	−14.3080	+	31.3301i	−0.603008	+	1.32040i	−0.927255	+	0.374431i	$0.877838\pi$
$564$		0			0
$565$	6.17486	−	42.9471i	0.259778	−	1.80680i
$566$		0			0
$567$	2.29565	+	0.674062i	0.0964080	+	0.0283080i
$568$		0			0
$569$	−4.73506	−	5.46455i	−0.198504	−	0.229086i	0.647767	−	0.761839i	$-0.275703\pi$
$569$	−4.73506	−	5.46455i	−0.198504	−	0.229086i	−0.846271	+	0.532753i	$0.821158\pi$
$570$		0			0
$571$	−20.9839	+	24.2168i	−0.878150	+	1.01344i	0.121632	+	0.992575i	$0.461187\pi$
$571$	−20.9839	+	24.2168i	−0.878150	+	1.01344i	−0.999782	+	0.0208643i	$0.993358\pi$
$572$		0			0
$573$	3.41271	+	7.47279i	0.142568	+	0.312180i
$574$		0			0
$575$	−3.27898	−	0.746406i	−0.136743	−	0.0311273i
$576$		0			0
$577$	12.4049	+	27.1630i	0.516425	+	1.13081i	0.970776	+	0.239989i	$0.0771439\pi$
$577$	12.4049	+	27.1630i	0.516425	+	1.13081i	−0.454351	+	0.890823i	$0.650129\pi$
$578$		0			0
$579$	11.6074	−	13.3957i	0.482388	−	0.556706i
$580$		0			0
$581$	−5.93338	−	6.84748i	−0.246158	−	0.284081i
$582$		0			0
$583$	−10.8057	−	3.17285i	−0.447527	−	0.131406i
$584$		0			0
$585$	0.280564	−	1.95137i	0.0115999	−	0.0806791i
$586$		0			0
$587$	2.32723	−	5.09592i	0.0960550	−	0.210331i	−0.855505	−	0.517795i	$-0.826753\pi$
$587$	2.32723	−	5.09592i	0.0960550	−	0.210331i	0.951560	+	0.307464i	$0.0994803\pi$
$588$		0			0
$589$	−8.26601	+	5.31224i	−0.340595	+	0.218887i
$590$		0			0
$591$	0.370305	+	2.57553i	0.0152323	+	0.105943i
$592$		0			0
$593$	20.9460	+	13.4612i	0.860149	+	0.552784i	0.894725	−	0.446618i	$-0.147372\pi$
$593$	20.9460	+	13.4612i	0.860149	+	0.552784i	−0.0345761	+	0.999402i	$0.511008\pi$
$594$		0			0
$595$	0.149506	−	0.0438989i	0.00612915	−	0.00179968i
$596$		0			0
$597$	−20.1381			−0.824197
$598$		0			0
$599$	4.56153			0.186379			0.0931896	−	0.995648i	$-0.470294\pi$
$599$	4.56153			0.186379			0.0931896	+	0.995648i	$0.470294\pi$
$600$		0			0
$601$	0.912222	−	0.267853i	0.0372103	−	0.0109259i	−0.263074	−	0.964776i	$-0.584736\pi$
$601$	0.912222	−	0.267853i	0.0372103	−	0.0109259i	0.300285	+	0.953850i	$0.402918\pi$
$602$		0			0
$603$	−9.98102	−	6.41441i	−0.406459	−	0.261215i
$604$		0			0
$605$	3.32266	+	23.1096i	0.135085	+	0.939540i
$606$		0			0
$607$	−15.1166	+	9.71488i	−0.613566	+	0.394315i	−0.810193	−	0.586164i	$-0.800638\pi$
$607$	−15.1166	+	9.71488i	−0.613566	+	0.394315i	0.196627	+	0.980478i	$0.437001\pi$
$608$		0			0
$609$	7.63628	−	16.7211i	0.309438	−	0.677574i
$610$		0			0
$611$	0.524874	−	3.65058i	0.0212341	−	0.147687i
$612$		0			0
$613$	−11.7361	−	3.44604i	−0.474018	−	0.139184i	0.0359929	−	0.999352i	$-0.488541\pi$
$613$	−11.7361	−	3.44604i	−0.474018	−	0.139184i	−0.510011	+	0.860168i	$0.670359\pi$
$614$		0			0
$615$	−1.35429	−	1.56294i	−0.0546103	−	0.0630237i
$616$		0			0
$617$	29.3271	−	33.8453i	1.18067	−	1.36256i	0.263202	−	0.964741i	$-0.415222\pi$
$617$	29.3271	−	33.8453i	1.18067	−	1.36256i	0.917464	−	0.397820i	$-0.130233\pi$
$618$		0			0
$619$	0.891449	+	1.95200i	0.0358303	+	0.0784575i	0.926701	−	0.375800i	$-0.122632\pi$
$619$	0.891449	+	1.95200i	0.0358303	+	0.0784575i	−0.890871	+	0.454257i	$0.849905\pi$
$620$		0			0
$621$	−0.974298	−	4.69582i	−0.0390972	−	0.188437i
$622$		0			0
$623$	8.21228	+	17.9824i	0.329018	+	0.720449i
$624$		0			0
$625$	18.3455	−	21.1718i	0.733820	−	0.846873i
$626$		0			0
$627$	2.39209	+	2.76062i	0.0955308	+	0.110248i
$628$		0			0
$629$	0.0138287	+	0.00406047i	0.000551386	+	0.000161901i
$630$		0			0
$631$	−3.03444	+	21.1050i	−0.120799	+	0.840176i	0.835855	+	0.548950i	$0.184972\pi$
$631$	−3.03444	+	21.1050i	−0.120799	+	0.840176i	−0.956654	+	0.291226i	$0.905937\pi$
$632$		0			0
$633$	−6.25715	+	13.7013i	−0.248699	+	0.544576i
$634$		0			0
$635$	21.0965	−	13.5579i	0.837190	−	0.538029i
$636$		0			0
$637$	−0.149893	−	1.04253i	−0.00593898	−	0.0413065i
$638$		0			0
$639$	1.14578	+	0.736348i	0.0453264	+	0.0291295i
$640$		0			0
$641$	−11.2876	+	3.31435i	−0.445835	+	0.130909i	−0.496941	−	0.867784i	$-0.665544\pi$
$641$	−11.2876	+	3.31435i	−0.445835	+	0.130909i	0.0511060	+	0.998693i	$0.483725\pi$
$642$		0			0
$643$	5.88411			0.232047			0.116023	−	0.993246i	$-0.462985\pi$
$643$	5.88411			0.232047			0.116023	+	0.993246i	$0.462985\pi$
$644$		0			0
$645$	2.09495			0.0824887
$646$		0			0
$647$	−35.3367	+	10.3758i	−1.38923	+	0.407915i	−0.888972	−	0.457962i	$-0.848580\pi$
$647$	−35.3367	+	10.3758i	−1.38923	+	0.407915i	−0.500258	+	0.865876i	$0.666762\pi$
$648$		0			0
$649$	−5.14529	−	3.30667i	−0.201970	−	0.129798i
$650$		0			0
$651$	−1.01246	−	7.04182i	−0.0396815	−	0.275991i
$652$		0			0
$653$	21.0982	−	13.5590i	0.825635	−	0.530603i	−0.0582534	−	0.998302i	$-0.518553\pi$
$653$	21.0982	−	13.5590i	0.825635	−	0.530603i	0.883888	+	0.467699i	$0.154917\pi$
$654$		0			0
$655$	−5.67213	+	12.4202i	−0.221629	+	0.485299i
$656$		0			0
$657$	−0.165396	+	1.15035i	−0.00645271	+	0.0448796i
$658$		0			0
$659$	0.491664	+	0.144366i	0.0191525	+	0.00562369i	0.291295	−	0.956633i	$-0.405914\pi$
$659$	0.491664	+	0.144366i	0.0191525	+	0.00562369i	−0.272142	+	0.962257i	$0.587732\pi$
$660$		0			0
$661$	−27.0324	−	31.1970i	−1.05144	−	1.21342i	−0.976339	−	0.216246i	$-0.930619\pi$
$661$	−27.0324	−	31.1970i	−1.05144	−	1.21342i	−0.0750978	−	0.997176i	$-0.523927\pi$
$662$		0			0
$663$	0.0147475	−	0.0170195i	0.000572745	−	0.000660983i
$664$		0			0
$665$	−7.84210	−	17.1718i	−0.304103	−	0.665894i
$666$		0			0
$667$	−36.7766	+	2.27494i	−1.42400	+	0.0880859i
$668$		0			0
$669$	10.0876	+	22.0888i	0.390010	+	0.854002i
$670$		0			0
$671$	2.45887	−	2.83769i	0.0949237	−	0.109548i
$672$		0			0
$673$	−31.0307	−	35.8113i	−1.19615	−	1.38043i	−0.905910	−	0.423471i	$-0.860812\pi$
$673$	−31.0307	−	35.8113i	−1.19615	−	1.38043i	−0.290236	−	0.956955i	$-0.593734\pi$
$674$		0			0
$675$	−0.672801	−	0.197552i	−0.0258961	−	0.00760379i
$676$		0			0
$677$	−2.75160	+	19.1378i	−0.105753	+	0.735526i	0.866089	+	0.499890i	$0.166626\pi$
$677$	−2.75160	+	19.1378i	−0.105753	+	0.735526i	−0.971841	+	0.235636i	$0.924283\pi$
$678$		0			0
$679$	11.2517	−	24.6379i	0.431802	−	0.945514i
$680$		0			0
$681$	4.93538	−	3.17178i	0.189124	−	0.121543i
$682$		0			0
$683$	5.00117	+	34.7839i	0.191364	+	1.33097i	0.828401	+	0.560135i	$0.189251\pi$
$683$	5.00117	+	34.7839i	0.191364	+	1.33097i	−0.637037	+	0.770833i	$0.719840\pi$
$684$		0			0
$685$	25.3991	+	16.3230i	0.970450	+	0.623671i
$686$		0			0
$687$	−7.19806	+	2.11354i	−0.274623	+	0.0806366i
$688$		0			0
$689$	8.41175			0.320462
$690$		0			0
$691$	−44.4339			−1.69035			−0.845173	−	0.534493i	$-0.820503\pi$
$691$	−44.4339			−1.69035			−0.845173	+	0.534493i	$0.820503\pi$
$692$		0			0
$693$	−2.53764	+	0.745117i	−0.0963968	+	0.0283047i
$694$		0			0
$695$	9.03184	+	5.80441i	0.342597	+	0.220174i
$696$		0			0
$697$	−0.00336202	−	0.0233834i	−0.000127346	−	0.000885709i
$698$		0			0
$699$	10.3497	−	6.65135i	0.391461	−	0.251577i
$700$		0			0
$701$	−7.63108	+	16.7097i	−0.288222	+	0.631118i	−0.997254	−	0.0740583i	$-0.976405\pi$
$701$	−7.63108	+	16.7097i	−0.288222	+	0.631118i	0.709032	+	0.705176i	$0.249132\pi$
$702$		0			0
$703$	0.248498	−	1.72834i	0.00937227	−	0.0651856i
$704$		0			0
$705$	−10.2337	−	3.00488i	−0.385422	−	0.113170i
$706$		0			0
$707$	17.2924	+	19.9564i	0.650346	+	0.750539i
$708$		0			0
$709$	−3.26562	+	3.76873i	−0.122643	+	0.141538i	−0.813750	−	0.581215i	$-0.802578\pi$
$709$	−3.26562	+	3.76873i	−0.122643	+	0.141538i	0.691107	+	0.722752i	$0.257123\pi$
$710$		0			0
$711$	−5.97569	−	13.0849i	−0.224106	−	0.490723i
$712$		0			0
$713$	−11.4977	+	8.43567i	−0.430590	+	0.315918i
$714$		0			0
$715$	0.905292	+	1.98231i	0.0338560	+	0.0741343i
$716$		0			0
$717$	−15.5436	+	17.9383i	−0.580487	+	0.669918i
$718$		0			0
$719$	17.2488	+	19.9062i	0.643272	+	0.742376i	0.979950	−	0.199244i	$-0.0638488\pi$
$719$	17.2488	+	19.9062i	0.643272	+	0.742376i	−0.336678	+	0.941620i	$0.609303\pi$
$720$		0			0
$721$	33.7019	+	9.89576i	1.25512	+	0.368537i
$722$		0			0
$723$	1.32193	−	9.19421i	0.0491630	−	0.341936i
$724$		0			0
$725$	−2.23802	+	4.90058i	−0.0831180	+	0.182003i
$726$		0			0
$727$	−22.6963	+	14.5860i	−0.841759	+	0.540966i	−0.888994	−	0.457918i	$-0.848595\pi$
$727$	−22.6963	+	14.5860i	−0.841759	+	0.540966i	0.0472352	+	0.998884i	$0.484959\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	0.0201321	+	0.0129381i	0.000744612	+	0.000478533i
$732$		0			0
$733$	−27.5814	+	8.09864i	−1.01874	+	0.299130i	−0.748126	−	0.663557i	$-0.769046\pi$
$733$	−27.5814	+	8.09864i	−1.01874	+	0.299130i	−0.270618	+	0.962687i	$0.587228\pi$
$734$		0			0
$735$	−3.04590			−0.112350
$736$		0			0
$737$	13.1151			0.483102
$738$		0			0
$739$	−15.0643	+	4.42329i	−0.554151	+	0.162713i	−0.546805	−	0.837260i	$-0.684156\pi$
$739$	−15.0643	+	4.42329i	−0.554151	+	0.162713i	−0.00734514	+	0.999973i	$0.502338\pi$
$740$		0			0
$741$	−2.29525	−	1.47507i	−0.0843180	−	0.0541879i
$742$		0			0
$743$	5.62065	+	39.0924i	0.206201	+	1.43416i	0.785406	+	0.618981i	$0.212454\pi$
$743$	5.62065	+	39.0924i	0.206201	+	1.43416i	−0.579205	+	0.815182i	$0.696637\pi$
$744$		0			0
$745$	−1.59551	+	1.02537i	−0.0584550	+	0.0375667i
$746$		0			0
$747$	−1.57316	+	3.44473i	−0.0575588	+	0.126036i
$748$		0			0
$749$	−3.81120	+	26.5075i	−0.139258	+	0.968563i
$750$		0			0
$751$	−3.41924	−	1.00398i	−0.124770	−	0.0366357i	0.218752	−	0.975781i	$-0.429802\pi$
$751$	−3.41924	−	1.00398i	−0.124770	−	0.0366357i	−0.343521	+	0.939145i	$0.611620\pi$
$752$		0			0
$753$	3.48033	+	4.01651i	0.126830	+	0.146370i
$754$		0			0
$755$	18.9806	−	21.9047i	0.690773	−	0.797195i
$756$		0			0
$757$	−3.22676	−	7.06563i	−0.117279	−	0.256805i	0.841884	−	0.539658i	$-0.181446\pi$
$757$	−3.22676	−	7.06563i	−0.117279	−	0.256805i	−0.959163	+	0.282853i	$0.908719\pi$
$758$		0			0
$759$	3.71240	+	3.78453i	0.134752	+	0.137370i
$760$		0			0
$761$	21.9092	+	47.9745i	0.794209	+	1.73907i	0.664190	+	0.747563i	$0.268776\pi$
$761$	21.9092	+	47.9745i	0.794209	+	1.73907i	0.130018	+	0.991512i	$0.458496\pi$
$762$		0			0
$763$	18.1756	−	20.9758i	0.658001	−	0.759374i
$764$		0			0
$765$	−0.0426484	−	0.0492189i	−0.00154196	−	0.00177951i
$766$		0			0
$767$	4.38327	+	1.28705i	0.158271	+	0.0464725i
$768$		0			0
$769$	0.111491	−	0.775438i	0.00402047	−	0.0279630i	−0.987712	−	0.156282i	$-0.950049\pi$
$769$	0.111491	−	0.775438i	0.00402047	−	0.0279630i	0.991733	+	0.128319i	$0.0409582\pi$
$770$		0			0
$771$	1.34131	−	2.93706i	0.0483061	−	0.105776i
$772$		0			0
$773$	−24.5895	+	15.8027i	−0.884424	+	0.568385i	−0.902133	−	0.431459i	$-0.857999\pi$
$773$	−24.5895	+	15.8027i	−0.884424	+	0.568385i	0.0177091	+	0.999843i	$0.494363\pi$
$774$		0			0
$775$	0.296729	+	2.06380i	0.0106588	+	0.0741338i
$776$		0			0
$777$	1.06355	+	0.683503i	0.0381547	+	0.0245205i
$778$		0			0
$779$	−2.74616	+	0.806345i	−0.0983914	+	0.0288903i
$780$		0			0
$781$	−1.50556			−0.0538733
$782$		0			0
$783$	−7.68311			−0.274572
$784$		0			0
$785$	−1.39634	+	0.410002i	−0.0498374	+	0.0146336i
$786$		0			0
$787$	30.3763	+	19.5217i	1.08280	+	0.695872i	0.955202	−	0.295954i	$-0.0956375\pi$
$787$	30.3763	+	19.5217i	1.08280	+	0.695872i	0.127596	+	0.991826i	$0.459274\pi$
$788$		0			0
$789$	2.83933	+	19.7480i	0.101083	+	0.703046i
$790$		0			0
$791$	36.5749	−	23.5053i	1.30045	−	0.835751i
$792$		0			0
$793$	−1.16505	+	2.55110i	−0.0413720	+	0.0905922i
$794$		0			0
$795$	3.46195	−	24.0784i	0.122783	−	0.853974i
$796$		0			0
$797$	28.2627	+	8.29868i	1.00112	+	0.293954i	0.740914	−	0.671600i	$-0.234392\pi$
$797$	28.2627	+	8.29868i	1.00112	+	0.293954i	0.260203	+	0.965554i	$0.416211\pi$
$798$		0			0
$799$	−0.0797858	−	0.0920777i	−0.00282262	−	0.00325747i
$800$		0			0
$801$	5.41087	−	6.24448i	0.191184	−	0.220638i
$802$		0			0
$803$	−0.533680	−	1.16860i	−0.0188332	−	0.0412389i
$804$		0			0
$805$	−12.8983	−	24.1714i	−0.454604	−	0.851929i
$806$		0			0
$807$	−2.84331	−	6.22597i	−0.100089	−	0.219165i
$808$		0			0
$809$	−28.4894	+	32.8785i	−1.00163	+	1.15595i	−0.0138847	+	0.999904i	$0.504420\pi$
$809$	−28.4894	+	32.8785i	−1.00163	+	1.15595i	−0.987750	+	0.156044i	$0.950126\pi$
$810$		0			0
$811$	31.3883	+	36.2240i	1.10219	+	1.27200i	0.959340	+	0.282252i	$0.0910813\pi$
$811$	31.3883	+	36.2240i	1.10219	+	1.27200i	0.142850	+	0.989744i	$0.454373\pi$
$812$		0			0
$813$	−6.30773	−	1.85212i	−0.221222	−	0.0649565i
$814$		0			0
$815$	−6.75605	+	46.9893i	−0.236654	+	1.64597i
$816$		0			0
$817$	1.20442	−	2.63731i	0.0421372	−	0.0922677i
$818$		0			0
$819$	1.66184	−	1.06800i	0.0580693	−	0.0373189i
$820$		0			0
$821$	4.86864	+	33.8622i	0.169917	+	1.18180i	0.879052	+	0.476725i	$0.158176\pi$
$821$	4.86864	+	33.8622i	0.169917	+	1.18180i	−0.709136	+	0.705072i	$0.750915\pi$
$822$		0			0
$823$	27.7539	+	17.8364i	0.967440	+	0.621736i	0.926048	−	0.377407i	$-0.123184\pi$
$823$	27.7539	+	17.8364i	0.967440	+	0.621736i	0.0413929	+	0.999143i	$0.486820\pi$
$824$		0			0
$825$	0.743723	−	0.218377i	0.0258931	−	0.00760290i
$826$		0			0
$827$	−28.4393			−0.988932			−0.494466	−	0.869197i	$-0.664636\pi$
$827$	−28.4393			−0.988932			−0.494466	+	0.869197i	$0.664636\pi$
$828$		0			0
$829$	47.4233			1.64708			0.823539	−	0.567260i	$-0.191996\pi$
$829$	47.4233			1.64708			0.823539	+	0.567260i	$0.191996\pi$
$830$		0			0
$831$	11.9594	−	3.51160i	0.414868	−	0.121816i
$832$		0			0
$833$	−0.0292705	−	0.0188110i	−0.00101416	−	0.000651762i
$834$		0			0
$835$	−4.40901	−	30.6653i	−0.152580	−	1.06122i
$836$		0			0
$837$	−2.50145	+	1.60759i	−0.0864628	+	0.0555663i
$838$		0			0
$839$	14.8169	−	32.4444i	0.511535	−	1.12011i	−0.461011	−	0.887395i	$-0.652513\pi$
$839$	14.8169	−	32.4444i	0.511535	−	1.12011i	0.972546	−	0.232711i	$-0.0747597\pi$
$840$		0			0
$841$	−4.27374	+	29.7245i	−0.147370	+	1.02498i
$842$		0			0
$843$	4.97420	+	1.46056i	0.171320	+	0.0503042i
$844$		0			0
$845$	19.2612	+	22.2286i	0.662605	+	0.764687i
$846$		0			0
$847$	−15.3202	+	17.6805i	−0.526409	+	0.607508i
$848$		0			0
$849$	−8.98186	−	19.6675i	−0.308257	−	0.674988i
$850$		0			0
$851$	0.205093	−	2.52584i	0.00703049	−	0.0865846i
$852$		0			0
$853$	−5.47700	−	11.9930i	−0.187529	−	0.410631i	0.792393	−	0.610010i	$-0.208835\pi$
$853$	−5.47700	−	11.9930i	−0.187529	−	0.410631i	−0.979922	+	0.199379i	$0.936107\pi$
$854$		0			0
$855$	−5.16697	+	5.96300i	−0.176707	+	0.203930i
$856$		0			0
$857$	−7.25626	−	8.37417i	−0.247869	−	0.286056i	0.618157	−	0.786054i	$-0.287879\pi$
$857$	−7.25626	−	8.37417i	−0.247869	−	0.286056i	−0.866026	+	0.499998i	$0.833334\pi$
$858$		0			0
$859$	−7.20065	−	2.11430i	−0.245683	−	0.0721391i	0.156572	−	0.987666i	$-0.449956\pi$
$859$	−7.20065	−	2.11430i	−0.245683	−	0.0721391i	−0.402256	+	0.915527i	$0.631774\pi$
$860$		0			0
$861$	0.294913	−	2.05116i	0.0100506	−	0.0699034i
$862$		0			0
$863$	−6.25455	+	13.6955i	−0.212907	+	0.466202i	−0.985711	−	0.168443i	$-0.946126\pi$
$863$	−6.25455	+	13.6955i	−0.212907	+	0.466202i	0.772804	+	0.634645i	$0.218853\pi$
$864$		0			0
$865$	−47.0303	+	30.2245i	−1.59908	+	1.02766i
$866$		0			0
$867$	2.41925	+	16.8262i	0.0821619	+	0.571449i
$868$		0			0
$869$	13.3770	+	8.59684i	0.453782	+	0.291628i
$870$		0			0
$871$	−9.39915	+	2.75984i	−0.318478	+	0.0935136i
$872$		0			0
$873$	−11.3207			−0.383148
$874$		0			0
$875$	24.5580			0.830212
$876$		0			0
$877$	−4.41890	+	1.29751i	−0.149216	+	0.0438136i	−0.355487	−	0.934681i	$-0.615685\pi$
$877$	−4.41890	+	1.29751i	−0.149216	+	0.0438136i	0.206272	+	0.978495i	$0.433867\pi$
$878$		0			0
$879$	9.17258	+	5.89486i	0.309383	+	0.198829i
$880$		0			0
$881$	5.97897	+	41.5846i	0.201437	+	1.40102i	0.800026	+	0.599966i	$0.204819\pi$
$881$	5.97897	+	41.5846i	0.201437	+	1.40102i	−0.598589	+	0.801056i	$0.704272\pi$
$882$		0			0
$883$	5.73477	−	3.68552i	0.192991	−	0.124027i	−0.440577	−	0.897715i	$-0.645226\pi$
$883$	5.73477	−	3.68552i	0.192991	−	0.124027i	0.633568	+	0.773687i	$0.281590\pi$
$884$		0			0
$885$	5.48812	−	12.0173i	0.184481	−	0.403957i
$886$		0			0
$887$	7.76730	−	54.0227i	0.260800	−	1.81391i	−0.266063	−	0.963956i	$-0.585723\pi$
$887$	7.76730	−	54.0227i	0.260800	−	1.81391i	0.526863	−	0.849950i	$-0.323368\pi$
$888$		0			0
$889$	24.1105	+	7.07947i	0.808639	+	0.237438i
$890$		0			0
$891$	0.723891	+	0.835415i	0.0242513	+	0.0279875i
$892$		0			0
$893$	−9.66627	+	11.1555i	−0.323469	+	0.373303i
$894$		0			0
$895$	1.12249	+	2.45792i	0.0375208	+	0.0821591i
$896$		0			0
$897$	−3.45693	−	1.93103i	−0.115424	−	0.0644752i
$898$		0			0
$899$	9.49039	+	20.7811i	0.316522	+	0.693087i
$900$		0			0
$901$	0.181973	−	0.210008i	0.00606240	−	0.00699638i
$902$		0			0
$903$	1.37468	+	1.58647i	0.0457466	+	0.0527944i
$904$		0			0
$905$	−18.3574	−	5.39022i	−0.610221	−	0.179177i
$906$		0			0
$907$	4.24229	−	29.5058i	0.140863	−	0.979724i	−0.789674	−	0.613527i	$-0.789750\pi$
$907$	4.24229	−	29.5058i	0.140863	−	0.979724i	0.930537	−	0.366198i	$-0.119341\pi$
$908$		0			0
$909$	4.58484	−	10.0394i	0.152070	−	0.332986i
$910$		0			0
$911$	−1.86204	+	1.19666i	−0.0616921	+	0.0396471i	−0.571123	−	0.820864i	$-0.693492\pi$
$911$	−1.86204	+	1.19666i	−0.0616921	+	0.0396471i	0.509431	+	0.860511i	$0.329856\pi$
$912$		0			0
$913$	−0.595751	−	4.14354i	−0.0197165	−	0.137131i
$914$		0			0
$915$	6.82296	+	4.38485i	0.225560	+	0.144959i
$916$		0			0
$917$	−13.1276	+	3.85462i	−0.433512	+	0.127291i
$918$		0			0
$919$	12.4132			0.409473			0.204736	−	0.978817i	$-0.434366\pi$
$919$	12.4132			0.409473			0.204736	+	0.978817i	$0.434366\pi$
$920$		0			0
$921$	−15.4011			−0.507482
$922$		0			0
$923$	1.07898	−	0.316818i	0.0355152	−	0.0104282i
$924$		0			0
$925$	−0.311703	−	0.200319i	−0.0102487	−	0.00658645i
$926$		0			0
$927$	−2.08929	−	14.5314i	−0.0686214	−	0.477272i
$928$		0			0
$929$	−37.9663	+	24.3994i	−1.24563	+	0.800519i	−0.986251	−	0.165255i	$-0.947155\pi$
$929$	−37.9663	+	24.3994i	−1.24563	+	0.800519i	−0.259382	+	0.965775i	$0.583519\pi$
$930$		0			0
$931$	−1.75113	+	3.83444i	−0.0573910	+	0.125669i
$932$		0			0
$933$	1.11048	−	7.72354i	0.0363554	−	0.252857i
$934$		0			0
$935$	0.0690748	+	0.0202822i	0.00225899	+	0.000663299i
$936$		0			0
$937$	−15.1787	−	17.5171i	−0.495865	−	0.572259i	0.451558	−	0.892242i	$-0.350868\pi$
$937$	−15.1787	−	17.5171i	−0.495865	−	0.572259i	−0.947423	+	0.319983i	$0.896323\pi$
$938$		0			0
$939$	21.4349	−	24.7372i	0.699501	−	0.807268i
$940$		0			0
$941$	−4.52251	−	9.90291i	−0.147429	−	0.322826i	0.821481	−	0.570235i	$-0.193148\pi$
$941$	−4.52251	−	9.90291i	−0.147429	−	0.322826i	−0.968911	+	0.247410i	$0.920421\pi$
$942$		0			0
$943$	−3.90567	+	1.41409i	−0.127186	+	0.0460492i
$944$		0			0
$945$	−2.37317	−	5.19651i	−0.0771992	−	0.169043i
$946$		0			0
$947$	19.5393	−	22.5495i	0.634941	−	0.732761i	−0.343531	−	0.939141i	$-0.611623\pi$
$947$	19.5393	−	22.5495i	0.634941	−	0.732761i	0.978472	+	0.206380i	$0.0661684\pi$
$948$		0			0
$949$	0.628379	+	0.725189i	0.0203981	+	0.0235406i
$950$		0			0
$951$	−32.3236	−	9.49107i	−1.04816	−	0.307769i
$952$		0			0
$953$	4.40315	−	30.6246i	0.142632	−	0.992027i	−0.785257	−	0.619170i	$-0.787469\pi$
$953$	4.40315	−	30.6246i	0.142632	−	0.992027i	0.927889	−	0.372857i	$-0.121622\pi$
$954$		0			0
$955$	8.14859	−	17.8429i	0.263682	−	0.577384i
$956$		0			0
$957$	7.14477	−	4.59166i	0.230958	−	0.148427i
$958$		0			0
$959$	4.30548	+	29.9453i	0.139031	+	0.966983i
$960$		0			0
$961$	−18.6408	−	11.9797i	−0.601318	−	0.386443i
$962$		0			0
$963$	10.7397	−	3.15345i	0.346081	−	0.101618i
$964$		0			0
$965$	−42.3224			−1.36241
$966$		0			0
$967$	8.80421			0.283124			0.141562	−	0.989929i	$-0.454788\pi$
$967$	8.80421			0.283124			0.141562	+	0.989929i	$0.454788\pi$
$968$		0			0
$969$	−0.0864800	+	0.0253928i	−0.00277814	+	0.000815735i
$970$		0			0
$971$	−9.37086	−	6.02229i	−0.300725	−	0.193264i	0.381572	−	0.924339i	$-0.375383\pi$
$971$	−9.37086	−	6.02229i	−0.300725	−	0.193264i	−0.682298	+	0.731075i	$0.739019\pi$
$972$		0			0
$973$	1.53101	+	10.6484i	0.0490821	+	0.341373i
$974$		0			0
$975$	−0.487047	+	0.313006i	−0.0155980	+	0.0100242i
$976$		0			0
$977$	10.1102	−	22.1382i	0.323454	−	0.708264i	−0.676140	−	0.736773i	$-0.736349\pi$
$977$	10.1102	−	22.1382i	0.323454	−	0.708264i	0.999594	+	0.0285087i	$0.00907584\pi$
$978$		0			0
$979$	−1.29985	+	9.04065i	−0.0415434	+	0.288940i
$980$		0			0
$981$	−11.1306	−	3.26824i	−0.355373	−	0.104347i
$982$		0			0
$983$	3.08247	+	3.55736i	0.0983154	+	0.113462i	0.802775	−	0.596282i	$-0.203356\pi$
$983$	3.08247	+	3.55736i	0.0983154	+	0.113462i	−0.704460	+	0.709744i	$0.748811\pi$
$984$		0			0
$985$	4.06857	−	4.69537i	0.129635	−	0.149607i
$986$		0			0
$987$	−4.43968	−	9.72154i	−0.141316	−	0.309440i
$988$		0			0
$989$	1.50833	−	3.92817i	0.0479623	−	0.124909i
$990$		0			0
$991$	−2.39108	−	5.23573i	−0.0759550	−	0.166318i	0.867845	−	0.496835i	$-0.165504\pi$
$991$	−2.39108	−	5.23573i	−0.0759550	−	0.166318i	−0.943800	+	0.330516i	$0.892777\pi$
$992$		0			0
$993$	4.55123	−	5.25240i	0.144429	−	0.166680i
$994$		0			0
$995$	31.4884	+	36.3395i	0.998249	+	1.15204i
$996$		0			0
$997$	25.6642	+	7.53568i	0.812792	+	0.238657i	0.661609	−	0.749849i	$-0.269874\pi$
$997$	25.6642	+	7.53568i	0.812792	+	0.238657i	0.151183	+	0.988506i	$0.451692\pi$
$998$		0			0
$999$	0.0752002	−	0.523029i	0.00237923	−	0.0165479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.73.3	✓	30
23.6	even	11	inner	552.2.q.b.121.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.73.3	✓	30	1.1	even	1	trivial
552.2.q.b.121.3	yes	30	23.6	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)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{3} +(2.00868 + 1.29090i) q^{5} +(0.340497 + 2.36821i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{3} +(2.00868 + 1.29090i) q^{5} +(0.340497 + 2.36821i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-0.459205 + 1.00552i) q^{11} +(0.117503 - 0.817251i) q^{13} +(-2.29100 - 0.672698i) q^{15} +(-0.0178616 - 0.0206133i) q^{17} +(-2.16398 + 2.49736i) q^{19} +(-0.993906 - 2.17635i) q^{21} +(-2.91084 + 3.81143i) q^{23} +(0.291291 + 0.637838i) q^{25} +(-0.654861 + 0.755750i) q^{27} +(5.03137 + 5.80651i) q^{29} +(2.85303 + 0.837726i) q^{31} +(0.157317 - 1.09416i) q^{33} +(-2.37317 + 5.19651i) q^{35} +(-0.444524 + 0.285679i) q^{37} +(0.117503 + 0.817251i) q^{39} +(0.728630 + 0.468262i) q^{41} +(-0.841847 + 0.247188i) q^{43} +2.38772 q^{45} +4.46690 q^{47} +(1.22398 - 0.359393i) q^{49} +(0.0229455 + 0.0147462i) q^{51} +(1.44990 + 10.0843i) q^{53} +(-2.22042 + 1.42698i) q^{55} +(1.37273 - 3.00586i) q^{57} +(-0.787424 + 5.47665i) q^{59} +(-3.25915 - 0.956973i) q^{61} +(1.56679 + 1.80818i) q^{63} +(1.29101 - 1.48991i) q^{65} +(-4.92867 - 10.7923i) q^{67} +(1.71912 - 4.47712i) q^{69} +(0.565792 + 1.23891i) q^{71} +(-0.761068 + 0.878319i) q^{73} +(-0.459192 - 0.529935i) q^{75} +(-2.53764 - 0.745117i) q^{77} +(2.04718 - 14.2384i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-3.18579 + 2.04738i) q^{83} +(-0.00926838 - 0.0644630i) q^{85} +(-6.46344 - 4.15380i) q^{87} +(7.92794 - 2.32785i) q^{89} +1.97543 q^{91} -2.97348 q^{93} +(-7.57057 + 2.22292i) q^{95} +(-9.52360 - 6.12045i) q^{97} +(0.157317 + 1.09416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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