LMFDB - Embedded newform 300.2.x.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	300.17
Dual form			300.2.x.a.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.858227 - 1.50448i) q^{3} +(-2.22846 + 0.184289i) q^{5} +(-2.84010 - 2.84010i) q^{7} +(-1.52689 - 2.58236i) q^{9} +O(q^{10})$	\(q+(0.858227 - 1.50448i) q^{3} +(-2.22846 + 0.184289i) q^{5} +(-2.84010 - 2.84010i) q^{7} +(-1.52689 - 2.58236i) q^{9} +(-4.71560 + 1.53219i) q^{11} +(-0.188444 - 0.369843i) q^{13} +(-1.63527 + 3.51083i) q^{15} +(7.50930 - 1.18936i) q^{17} +(2.68725 - 3.69868i) q^{19} +(-6.71031 + 1.83541i) q^{21} +(-0.153636 + 0.301528i) q^{23} +(4.93208 - 0.821362i) q^{25} +(-5.19552 + 0.0809244i) q^{27} +(-0.836442 + 0.607711i) q^{29} +(-2.24457 - 1.63078i) q^{31} +(-1.74191 + 8.40946i) q^{33} +(6.85245 + 5.80565i) q^{35} +(4.31832 - 2.20029i) q^{37} +(-0.718148 - 0.0338990i) q^{39} +(-5.67438 - 1.84372i) q^{41} +(2.46472 - 2.46472i) q^{43} +(3.87853 + 5.47330i) q^{45} +(1.21046 - 7.64252i) q^{47} +9.13235i q^{49} +(4.65532 - 12.3183i) q^{51} +(-8.21858 - 1.30170i) q^{53} +(10.2262 - 4.28346i) q^{55} +(-3.25831 - 7.21721i) q^{57} +(3.09959 - 9.53955i) q^{59} +(3.00345 + 9.24368i) q^{61} +(-2.99763 + 11.6707i) q^{63} +(0.488099 + 0.789452i) q^{65} +(1.15518 + 7.29349i) q^{67} +(0.321787 + 0.489922i) q^{69} +(1.25910 + 1.73301i) q^{71} +(12.7520 + 6.49745i) q^{73} +(2.99712 - 8.12510i) q^{75} +(17.7443 + 9.04119i) q^{77} +(-4.46331 - 6.14322i) q^{79} +(-4.33719 + 7.88599i) q^{81} +(1.02557 + 6.47518i) q^{83} +(-16.5150 + 4.03432i) q^{85} +(0.196429 + 1.77996i) q^{87} +(-4.13129 - 12.7148i) q^{89} +(-0.515190 + 1.58559i) q^{91} +(-4.37982 + 1.97733i) q^{93} +(-5.30680 + 8.73760i) q^{95} +(2.19961 + 0.348384i) q^{97} +(11.1569 + 9.83788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{20}\right)$

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
$3$	0.858227	−	1.50448i	0.495497	−	0.868609i
$3$	0.858227	−	1.50448i	0.495497	−	0.868609i
$4$		0			0
$5$	−2.22846	+	0.184289i	−0.996598	+	0.0824166i
$5$	−2.22846	+	0.184289i	−0.996598	+	0.0824166i
$6$		0			0
$7$	−2.84010	−	2.84010i	−1.07346	−	1.07346i	−0.997079	−	0.0763784i	$-0.975664\pi$
$7$	−2.84010	−	2.84010i	−1.07346	−	1.07346i	−0.0763784	−	0.997079i	$-0.524336\pi$
$8$		0			0
$9$	−1.52689	−	2.58236i	−0.508965	−	0.860787i
$10$		0			0
$11$	−4.71560	+	1.53219i	−1.42181	+	0.461973i	−0.916175	−	0.400778i	$-0.868740\pi$
$11$	−4.71560	+	1.53219i	−1.42181	+	0.461973i	−0.505630	+	0.862750i	$0.668740\pi$
$12$		0			0
$13$	−0.188444	−	0.369843i	−0.0522651	−	0.102576i	0.863397	−	0.504526i	$-0.168333\pi$
$13$	−0.188444	−	0.369843i	−0.0522651	−	0.102576i	−0.915662	+	0.401950i	$0.868333\pi$
$14$		0			0
$15$	−1.63527	+	3.51083i	−0.422224	+	0.906492i
$16$		0			0
$17$	7.50930	−	1.18936i	1.82127	−	0.288461i	0.850062	−	0.526683i	$-0.176564\pi$
$17$	7.50930	−	1.18936i	1.82127	−	0.288461i	0.971211	+	0.238222i	$0.0765645\pi$
$18$		0			0
$19$	2.68725	−	3.69868i	0.616497	−	0.848536i	−0.380595	−	0.924742i	$-0.624281\pi$
$19$	2.68725	−	3.69868i	0.616497	−	0.848536i	0.997092	+	0.0762063i	$0.0242808\pi$
$20$		0			0
$21$	−6.71031	+	1.83541i	−1.46431	+	0.400520i
$22$		0			0
$23$	−0.153636	+	0.301528i	−0.0320354	+	0.0628730i	−0.906469	−	0.422271i	$-0.861233\pi$
$23$	−0.153636	+	0.301528i	−0.0320354	+	0.0628730i	0.874434	+	0.485144i	$0.161233\pi$
$24$		0			0
$25$	4.93208	−	0.821362i	0.986415	−	0.164272i
$26$		0			0
$27$	−5.19552	+	0.0809244i	−0.999879	+	0.0155739i
$28$		0			0
$29$	−0.836442	+	0.607711i	−0.155323	+	0.112849i	−0.662732	−	0.748856i	$-0.730603\pi$
$29$	−0.836442	+	0.607711i	−0.155323	+	0.112849i	0.507409	+	0.861705i	$0.330603\pi$
$30$		0			0
$31$	−2.24457	−	1.63078i	−0.403138	−	0.292897i	0.367680	−	0.929952i	$-0.380152\pi$
$31$	−2.24457	−	1.63078i	−0.403138	−	0.292897i	−0.770818	+	0.637056i	$0.780152\pi$
$32$		0			0
$33$	−1.74191	+	8.40946i	−0.303227	+	1.46390i
$34$		0			0
$35$	6.85245	+	5.80565i	1.15828	+	0.981335i
$36$		0			0
$37$	4.31832	−	2.20029i	0.709928	−	0.361726i	−0.0614445	−	0.998111i	$-0.519571\pi$
$37$	4.31832	−	2.20029i	0.709928	−	0.361726i	0.771372	+	0.636384i	$0.219571\pi$
$38$		0			0
$39$	−0.718148	−	0.0338990i	−0.114996	−	0.00542818i
$40$		0			0
$41$	−5.67438	−	1.84372i	−0.886189	−	0.287940i	−0.169664	−	0.985502i	$-0.554268\pi$
$41$	−5.67438	−	1.84372i	−0.886189	−	0.287940i	−0.716525	+	0.697562i	$0.754268\pi$
$42$		0			0
$43$	2.46472	−	2.46472i	0.375866	−	0.375866i	−0.493742	−	0.869608i	$-0.664371\pi$
$43$	2.46472	−	2.46472i	0.375866	−	0.375866i	0.869608	+	0.493742i	$0.164371\pi$
$44$		0			0
$45$	3.87853	+	5.47330i	0.578177	+	0.815912i
$46$		0			0
$47$	1.21046	−	7.64252i	0.176563	−	1.11478i	−0.727100	−	0.686532i	$-0.759132\pi$
$47$	1.21046	−	7.64252i	0.176563	−	1.11478i	0.903663	−	0.428245i	$-0.140868\pi$
$48$		0			0
$49$			9.13235i			1.30462i
$50$		0			0
$51$	4.65532	−	12.3183i	0.651875	−	1.72491i
$52$		0			0
$53$	−8.21858	−	1.30170i	−1.12891	−	0.178802i	−0.436083	−	0.899906i	$-0.643635\pi$
$53$	−8.21858	−	1.30170i	−1.12891	−	0.178802i	−0.692826	+	0.721105i	$0.743635\pi$
$54$		0			0
$55$	10.2262	−	4.28346i	1.37889	−	0.577581i
$56$		0			0
$57$	−3.25831	−	7.21721i	−0.431573	−	0.955942i
$58$		0			0
$59$	3.09959	−	9.53955i	0.403532	−	1.24194i	−0.518583	−	0.855028i	$-0.673540\pi$
$59$	3.09959	−	9.53955i	0.403532	−	1.24194i	0.922115	−	0.386917i	$-0.126460\pi$
$60$		0			0
$61$	3.00345	+	9.24368i	0.384553	+	1.18353i	0.936804	+	0.349855i	$0.113769\pi$
$61$	3.00345	+	9.24368i	0.384553	+	1.18353i	−0.552251	+	0.833678i	$0.686231\pi$
$62$		0			0
$63$	−2.99763	+	11.6707i	−0.377666	+	1.47037i
$64$		0			0
$65$	0.488099	+	0.789452i	0.0605412	+	0.0979195i
$66$		0			0
$67$	1.15518	+	7.29349i	0.141127	+	0.891041i	0.952062	+	0.305905i	$0.0989590\pi$
$67$	1.15518	+	7.29349i	0.141127	+	0.891041i	−0.810935	+	0.585136i	$0.801041\pi$
$68$		0			0
$69$	0.321787	+	0.489922i	0.0387387	+	0.0589797i
$70$		0			0
$71$	1.25910	+	1.73301i	0.149428	+	0.205670i	0.877169	−	0.480182i	$-0.159430\pi$
$71$	1.25910	+	1.73301i	0.149428	+	0.205670i	−0.727741	+	0.685852i	$0.759430\pi$
$72$		0			0
$73$	12.7520	+	6.49745i	1.49250	+	0.760469i	0.994303	−	0.106592i	$-0.0339940\pi$
$73$	12.7520	+	6.49745i	1.49250	+	0.760469i	0.498201	+	0.867061i	$0.333994\pi$
$74$		0			0
$75$	2.99712	−	8.12510i	0.346077	−	0.938206i
$76$		0			0
$77$	17.7443	+	9.04119i	2.02216	+	1.03034i
$78$		0			0
$79$	−4.46331	−	6.14322i	−0.502162	−	0.691166i	0.480411	−	0.877043i	$-0.340487\pi$
$79$	−4.46331	−	6.14322i	−0.502162	−	0.691166i	−0.982573	+	0.185877i	$0.940487\pi$
$80$		0			0
$81$	−4.33719	+	7.88599i	−0.481910	+	0.876221i
$82$		0			0
$83$	1.02557	+	6.47518i	0.112571	+	0.710743i	0.977827	+	0.209414i	$0.0671555\pi$
$83$	1.02557	+	6.47518i	0.112571	+	0.710743i	−0.865256	+	0.501329i	$0.832844\pi$
$84$		0			0
$85$	−16.5150	+	4.03432i	−1.79130	+	0.437583i
$86$		0			0
$87$	0.196429	+	1.77996i	0.0210594	+	0.190832i
$88$		0			0
$89$	−4.13129	−	12.7148i	−0.437916	−	1.34777i	−0.890069	−	0.455826i	$-0.849344\pi$
$89$	−4.13129	−	12.7148i	−0.437916	−	1.34777i	0.452153	−	0.891941i	$-0.350656\pi$
$90$		0			0
$91$	−0.515190	+	1.58559i	−0.0540066	+	0.166215i
$92$		0			0
$93$	−4.37982	+	1.97733i	−0.454166	+	0.205040i
$94$		0			0
$95$	−5.30680	+	8.73760i	−0.544466	+	0.896458i
$96$		0			0
$97$	2.19961	+	0.348384i	0.223337	+	0.0353730i	0.267100	−	0.963669i	$-0.413935\pi$
$97$	2.19961	+	0.348384i	0.223337	+	0.0353730i	−0.0437632	+	0.999042i	$0.513935\pi$
$98$		0			0
$99$	11.1569	+	9.83788i	1.12131	+	0.988744i
$100$		0			0
$101$			12.5854i			1.25230i	0.779704	+	0.626149i	$0.215370\pi$
$101$			12.5854i			1.25230i	−0.779704	+	0.626149i	$0.784630\pi$
$102$		0			0
$103$	0.211229	−	1.33365i	0.0208130	−	0.131408i	−0.975094	−	0.221792i	$-0.928809\pi$
$103$	0.211229	−	1.33365i	0.0208130	−	0.131408i	0.995907	+	0.0903839i	$0.0288094\pi$
$104$		0			0
$105$	14.6154	−	5.32678i	1.42632	−	0.519841i
$106$		0			0
$107$	−2.51075	+	2.51075i	−0.242723	+	0.242723i	−0.817976	−	0.575253i	$-0.804904\pi$
$107$	−2.51075	+	2.51075i	−0.242723	+	0.242723i	0.575253	+	0.817976i	$0.304904\pi$
$108$		0			0
$109$	−10.8158	−	3.51428i	−1.03597	−	0.336607i	−0.258822	−	0.965925i	$-0.583334\pi$
$109$	−10.8158	−	3.51428i	−1.03597	−	0.336607i	−0.777148	+	0.629318i	$0.783334\pi$
$110$		0			0
$111$	0.395808	−	8.38516i	0.0375684	−	0.795884i
$112$		0			0
$113$	6.91215	−	3.52192i	0.650240	−	0.331314i	−0.0975678	−	0.995229i	$-0.531106\pi$
$113$	6.91215	−	3.52192i	0.650240	−	0.331314i	0.747808	+	0.663915i	$0.231106\pi$
$114$		0			0
$115$	0.286804	−	0.700258i	0.0267446	−	0.0652994i
$116$		0			0
$117$	−0.667333	+	1.05134i	−0.0616950	+	0.0971967i
$118$		0			0
$119$	−24.7051	−	17.9493i	−2.26471	−	1.64541i
$120$		0			0
$121$	10.9900	−	7.98474i	0.999095	−	0.725885i
$122$		0			0
$123$	−7.64373	+	6.95464i	−0.689212	+	0.627079i
$124$		0			0
$125$	−10.8396	+	2.73930i	−0.969520	+	0.245011i
$126$		0			0
$127$	8.79185	−	17.2550i	0.780151	−	1.53113i	−0.0657772	−	0.997834i	$-0.520953\pi$
$127$	8.79185	−	17.2550i	0.780151	−	1.53113i	0.845928	−	0.533297i	$-0.179047\pi$
$128$		0			0
$129$	−1.59282	−	5.82340i	−0.140240	−	0.512722i
$130$		0			0
$131$	1.96392	−	2.70310i	0.171588	−	0.236171i	−0.714558	−	0.699576i	$-0.753372\pi$
$131$	1.96392	−	2.70310i	0.171588	−	0.236171i	0.886147	+	0.463405i	$0.153372\pi$
$132$		0			0
$133$	−18.1367	+	2.87257i	−1.57265	+	0.249083i
$134$		0			0
$135$	11.5631	−	1.13782i	0.995194	−	0.0979275i
$136$		0			0
$137$	1.08309	+	2.12568i	0.0925343	+	0.181609i	0.932635	−	0.360822i	$-0.117504\pi$
$137$	1.08309	+	2.12568i	0.0925343	+	0.181609i	−0.840100	+	0.542431i	$0.817504\pi$
$138$		0			0
$139$	−1.62858	+	0.529159i	−0.138135	+	0.0448827i	−0.377268	−	0.926104i	$-0.623137\pi$
$139$	−1.62858	+	0.529159i	−0.138135	+	0.0448827i	0.239134	+	0.970987i	$0.423137\pi$
$140$		0			0
$141$	−10.4591	−	8.38012i	−0.880819	−	0.705733i
$142$		0			0
$143$	1.45530	+	1.45530i	0.121698	+	0.121698i
$144$		0			0
$145$	1.75198	−	1.50841i	0.145494	−	0.125266i
$146$		0			0
$147$	13.7394	+	7.83762i	1.13321	+	0.646436i
$148$		0			0
$149$	7.67808			0.629012			0.314506	−	0.949255i	$-0.398161\pi$
$149$	7.67808			0.629012			0.314506	+	0.949255i	$0.398161\pi$
$150$		0			0
$151$	−18.9987			−1.54609			−0.773045	−	0.634352i	$-0.781267\pi$
$151$	−18.9987			−1.54609			−0.773045	+	0.634352i	$0.781267\pi$
$152$		0			0
$153$	−14.5373	−	17.5757i	−1.17527	−	1.42091i
$154$		0			0
$155$	5.30248	+	3.22048i	0.425906	+	0.258675i
$156$		0			0
$157$	−3.65415	−	3.65415i	−0.291633	−	0.291633i	0.546092	−	0.837725i	$-0.316115\pi$
$157$	−3.65415	−	3.65415i	−0.291633	−	0.291633i	−0.837725	+	0.546092i	$0.816115\pi$
$158$		0			0
$159$	−9.01178	+	11.2475i	−0.714680	+	0.891985i
$160$		0			0
$161$	1.29271	−	0.420028i	0.101880	−	0.0331029i
$162$		0			0
$163$	1.70981	+	3.35569i	0.133923	+	0.262838i	0.948223	−	0.317606i	$-0.102879\pi$
$163$	1.70981	+	3.35569i	0.133923	+	0.262838i	−0.814300	+	0.580444i	$0.802879\pi$
$164$		0			0
$165$	2.33200	−	19.0612i	0.181546	−	1.48391i
$166$		0			0
$167$	3.33491	−	0.528199i	0.258063	−	0.0408732i	−0.0260621	−	0.999660i	$-0.508297\pi$
$167$	3.33491	−	0.528199i	0.258063	−	0.0408732i	0.284126	+	0.958787i	$0.408297\pi$
$168$		0			0
$169$	7.53994	−	10.3778i	0.579995	−	0.798295i
$170$		0			0
$171$	−13.6545	−	1.29195i	−1.04418	−	0.0987982i
$172$		0			0
$173$	5.42968	−	10.6563i	0.412811	−	0.810187i	−0.587189	−	0.809450i	$-0.699765\pi$
$173$	5.42968	−	10.6563i	0.412811	−	0.810187i	1.00000		0.000736755i	$-0.000234516\pi$
$174$		0			0
$175$	−16.3403	−	11.6748i	−1.23521	−	0.882535i
$176$		0			0
$177$	−11.6919	−	12.8504i	−0.878815	−	0.965892i
$178$		0			0
$179$	1.75204	−	1.27293i	0.130954	−	0.0951434i	−0.520380	−	0.853935i	$-0.674210\pi$
$179$	1.75204	−	1.27293i	0.130954	−	0.0951434i	0.651334	+	0.758791i	$0.274210\pi$
$180$		0			0
$181$	−0.486921	−	0.353769i	−0.0361925	−	0.0262954i	0.569542	−	0.821962i	$-0.307121\pi$
$181$	−0.486921	−	0.353769i	−0.0361925	−	0.0262954i	−0.605734	+	0.795667i	$0.707121\pi$
$182$		0			0
$183$	16.4845	+	3.41455i	1.21857	+	0.252411i
$184$		0			0
$185$	−9.21772	+	5.69909i	−0.677700	+	0.419005i
$186$		0			0
$187$	−33.5885	+	17.1142i	−2.45623	+	1.25151i
$188$		0			0
$189$	14.9856	+	14.5260i	1.09005	+	1.05661i
$190$		0			0
$191$	20.1158	+	6.53603i	1.45553	+	0.472931i	0.926702	−	0.375798i	$-0.122631\pi$
$191$	20.1158	+	6.53603i	1.45553	+	0.472931i	0.528829	+	0.848728i	$0.322631\pi$
$192$		0			0
$193$	0.525247	−	0.525247i	0.0378081	−	0.0378081i	−0.687950	−	0.725758i	$-0.741489\pi$
$193$	0.525247	−	0.525247i	0.0378081	−	0.0378081i	0.725758	+	0.687950i	$0.241489\pi$
$194$		0			0
$195$	1.60661	−	0.0568042i	0.115052	−	0.00406784i
$196$		0			0
$197$	−0.380297	+	2.40110i	−0.0270950	+	0.171071i	−0.997525	−	0.0703111i	$-0.977601\pi$
$197$	−0.380297	+	2.40110i	−0.0270950	+	0.171071i	0.970430	+	0.241382i	$0.0776008\pi$
$198$		0			0
$199$			26.6540i			1.88945i	0.327865	+	0.944725i	$0.393671\pi$
$199$			26.6540i			1.88945i	−0.327865	+	0.944725i	$0.606329\pi$
$200$		0			0
$201$	11.9643	+	4.52153i	0.843895	+	0.318924i
$202$		0			0
$203$	4.10154	+	0.649620i	0.287872	+	0.0455944i
$204$		0			0
$205$	12.9849	+	3.06293i	0.906905	+	0.213924i
$206$		0			0
$207$	1.01324	−	0.0636573i	0.0704252	−	0.00442449i
$208$		0			0
$209$	−7.00490	+	21.5589i	−0.484539	+	1.49126i
$210$		0			0
$211$	−2.55687	−	7.86925i	−0.176022	−	0.541741i	0.823656	−	0.567089i	$-0.191931\pi$
$211$	−2.55687	−	7.86925i	−0.176022	−	0.541741i	−0.999679	+	0.0253480i	$0.991931\pi$
$212$		0			0
$213$	3.68786	−	0.406978i	0.252688	−	0.0278856i
$214$		0			0
$215$	−5.03831	+	5.94676i	−0.343610	+	0.405565i
$216$		0			0
$217$	1.74324	+	11.0064i	0.118339	+	0.747163i
$218$		0			0
$219$	20.7193	−	13.6087i	1.40008	−	0.919593i
$220$		0			0
$221$	−1.85496	−	2.55313i	−0.124778	−	0.171742i
$222$		0			0
$223$	−11.3838	−	5.80036i	−0.762319	−	0.388421i	0.0291937	−	0.999574i	$-0.490706\pi$
$223$	−11.3838	−	5.80036i	−0.762319	−	0.388421i	−0.791513	+	0.611153i	$0.790706\pi$
$224$		0			0
$225$	−9.65181	−	11.4823i	−0.643454	−	0.765485i
$226$		0			0
$227$	−21.6298	−	11.0209i	−1.43562	−	0.731484i	−0.448848	−	0.893608i	$-0.648165\pi$
$227$	−21.6298	−	11.0209i	−1.43562	−	0.731484i	−0.986770	+	0.162124i	$0.948165\pi$
$228$		0			0
$229$	4.36425	+	6.00687i	0.288398	+	0.396945i	0.928493	−	0.371350i	$-0.121105\pi$
$229$	4.36425	+	6.00687i	0.288398	+	0.396945i	−0.640095	+	0.768296i	$0.721105\pi$
$230$		0			0
$231$	28.8309	−	18.9365i	1.89694	−	1.24593i
$232$		0			0
$233$	−2.77715	−	17.5342i	−0.181937	−	1.14871i	−0.894490	−	0.447087i	$-0.852461\pi$
$233$	−2.77715	−	17.5342i	−0.181937	−	1.14871i	0.712553	−	0.701618i	$-0.247539\pi$
$234$		0			0
$235$	−1.28902	+	17.2541i	−0.0840865	+	1.12554i
$236$		0			0
$237$	−13.0729	+	1.44267i	−0.849173	+	0.0937114i
$238$		0			0
$239$	0.224620	+	0.691308i	0.0145294	+	0.0447170i	0.958058	−	0.286573i	$-0.0925161\pi$
$239$	0.224620	+	0.691308i	0.0145294	+	0.0447170i	−0.943529	+	0.331290i	$0.892516\pi$
$240$		0			0
$241$	−4.44165	+	13.6700i	−0.286112	+	0.880561i	0.699951	+	0.714190i	$0.253205\pi$
$241$	−4.44165	+	13.6700i	−0.286112	+	0.880561i	−0.986063	+	0.166371i	$0.946795\pi$
$242$		0			0
$243$	8.14199	+	13.2932i	0.522309	+	0.852756i
$244$		0			0
$245$	−1.68299	−	20.3511i	−0.107522	−	1.30018i
$246$		0			0
$247$	−1.87433	−	0.296864i	−0.119261	−	0.0188890i
$248$		0			0
$249$	10.6219	+	4.01423i	0.673137	+	0.254391i
$250$		0			0
$251$			10.6776i			0.673961i	0.941512	+	0.336981i	$0.109406\pi$
$251$			10.6776i			0.673961i	−0.941512	+	0.336981i	$0.890594\pi$
$252$		0			0
$253$	0.262488	−	1.65729i	0.0165025	−	0.104193i
$254$		0			0
$255$	−8.10407	+	28.3088i	−0.507497	+	1.77276i
$256$		0			0
$257$	9.29989	−	9.29989i	0.580111	−	0.580111i	−0.354822	−	0.934934i	$-0.615459\pi$
$257$	9.29989	−	9.29989i	0.580111	−	0.580111i	0.934934	+	0.354822i	$0.115459\pi$
$258$		0			0
$259$	−18.5135	−	6.01541i	−1.15037	−	0.373779i
$260$		0			0
$261$	2.84649	+	1.23209i	0.176193	+	0.0762642i
$262$		0			0
$263$	23.1320	−	11.7863i	1.42638	−	0.726776i	0.441055	−	0.897480i	$-0.354604\pi$
$263$	23.1320	−	11.7863i	1.42638	−	0.726776i	0.985322	+	0.170704i	$0.0546042\pi$
$264$		0			0
$265$	18.5547	+	1.38618i	1.13980	+	0.0851525i
$266$		0			0
$267$	−22.6747	−	4.69676i	−1.38767	−	0.287437i
$268$		0			0
$269$	13.6649	+	9.92811i	0.833162	+	0.605328i	0.920452	−	0.390855i	$-0.127821\pi$
$269$	13.6649	+	9.92811i	0.833162	+	0.605328i	−0.0872901	+	0.996183i	$0.527821\pi$
$270$		0			0
$271$	12.7884	−	9.29128i	0.776837	−	0.564405i	−0.127191	−	0.991878i	$-0.540596\pi$
$271$	12.7884	−	9.29128i	0.776837	−	0.564405i	0.904028	+	0.427473i	$0.140596\pi$
$272$		0			0
$273$	1.94334	+	2.13589i	0.117616	+	0.129270i
$274$		0			0
$275$	−21.9992	+	11.4301i	−1.32660	+	0.689260i
$276$		0			0
$277$	7.77059	−	15.2506i	0.466890	−	0.916323i	−0.530742	−	0.847534i	$-0.678087\pi$
$277$	7.77059	−	15.2506i	0.466890	−	0.916323i	0.997631	−	0.0687889i	$-0.0219135\pi$
$278$		0			0
$279$	−0.784033	+	8.28633i	−0.0469388	+	0.496090i
$280$		0			0
$281$	−16.0338	+	22.0687i	−0.956499	+	1.31651i	−0.00791912	+	0.999969i	$0.502521\pi$
$281$	−16.0338	+	22.0687i	−0.956499	+	1.31651i	−0.948580	+	0.316539i	$0.897479\pi$
$282$		0			0
$283$	−3.01460	+	0.477465i	−0.179199	+	0.0283824i	−0.245389	−	0.969425i	$-0.578916\pi$
$283$	−3.01460	+	0.477465i	−0.179199	+	0.0283824i	0.0661898	+	0.997807i	$0.478916\pi$
$284$		0			0
$285$	8.59106	+	15.4828i	0.508891	+	0.917121i
$286$		0			0
$287$	10.8795	+	21.3522i	0.642195	+	1.26038i
$288$		0			0
$289$	38.8070	−	12.6092i	2.28277	−	0.741716i
$290$		0			0
$291$	2.41190	−	3.01027i	0.141388	−	0.176465i
$292$		0			0
$293$	−10.5577	−	10.5577i	−0.616788	−	0.616788i	0.327918	−	0.944706i	$-0.393653\pi$
$293$	−10.5577	−	10.5577i	−0.616788	−	0.616788i	−0.944706	+	0.327918i	$0.893653\pi$
$294$		0			0
$295$	−5.14928	+	21.8297i	−0.299802	+	1.27098i
$296$		0			0
$297$	24.3760	−	8.34213i	1.41444	−	0.484060i
$298$		0			0
$299$	0.140470			0.00812359
$300$		0			0
$301$	−14.0001			−0.806953
$302$		0			0
$303$	18.9345	+	10.8012i	1.08776	+	0.620510i
$304$		0			0
$305$	−8.39659	−	20.0457i	−0.480787	−	1.14781i
$306$		0			0
$307$	17.3293	+	17.3293i	0.989033	+	0.989033i	0.999941	−	0.0109073i	$-0.00347197\pi$
$307$	17.3293	+	17.3293i	0.989033	+	0.989033i	−0.0109073	+	0.999941i	$0.503472\pi$
$308$		0			0
$309$	−1.82516	−	1.46236i	−0.103830	−	0.0831907i
$310$		0			0
$311$	4.35394	−	1.41468i	0.246889	−	0.0802191i	−0.182958	−	0.983121i	$-0.558567\pi$
$311$	4.35394	−	1.41468i	0.246889	−	0.0802191i	0.429847	+	0.902902i	$0.358567\pi$
$312$		0			0
$313$	−4.00451	−	7.85929i	−0.226348	−	0.444233i	0.749703	−	0.661774i	$-0.230196\pi$
$313$	−4.00451	−	7.85929i	−0.226348	−	0.444233i	−0.976051	+	0.217541i	$0.930196\pi$
$314$		0			0
$315$	4.52933	−	26.5601i	0.255199	−	1.49649i
$316$		0			0
$317$	17.3151	−	2.74245i	0.972515	−	0.154031i	0.350095	−	0.936714i	$-0.386149\pi$
$317$	17.3151	−	2.74245i	0.972515	−	0.154031i	0.622420	+	0.782683i	$0.286149\pi$
$318$		0			0
$319$	3.01319	−	4.14731i	0.168707	−	0.232205i
$320$		0			0
$321$	1.62257	+	5.93215i	0.0905630	+	0.331100i
$322$		0			0
$323$	15.7803	−	30.9706i	0.878040	−	1.72325i
$324$		0			0
$325$	−1.23320	−	1.66931i	−0.0684054	−	0.0925967i
$326$		0			0
$327$	−14.5696	+	13.2561i	−0.805700	+	0.733065i
$328$		0			0
$329$	−25.1434	+	18.2677i	−1.38620	+	1.00713i
$330$		0			0
$331$	12.7358	+	9.25307i	0.700020	+	0.508595i	0.879939	−	0.475087i	$-0.157583\pi$
$331$	12.7358	+	9.25307i	0.700020	+	0.508595i	−0.179918	+	0.983682i	$0.557583\pi$
$332$		0			0
$333$	−12.2756	−	7.79185i	−0.672698	−	0.426991i
$334$		0			0
$335$	−3.91837	−	16.0404i	−0.214084	−	0.876379i
$336$		0			0
$337$	3.48017	−	1.77323i	0.189577	−	0.0965942i	−0.356626	−	0.934247i	$-0.616073\pi$
$337$	3.48017	−	1.77323i	0.189577	−	0.0965942i	0.546203	+	0.837653i	$0.316073\pi$
$338$		0			0
$339$	0.633553	−	13.4218i	0.0344098	−	0.728970i
$340$		0			0
$341$	13.0832	+	4.25098i	0.708493	+	0.230203i
$342$		0			0
$343$	6.05609	−	6.05609i	0.326998	−	0.326998i
$344$		0			0
$345$	−0.807378	−	1.03247i	−0.0434678	−	0.0555863i
$346$		0			0
$347$	−0.587119	+	3.70692i	−0.0315182	+	0.198998i	−0.998423	−	0.0561397i	$-0.982121\pi$
$347$	−0.587119	+	3.70692i	−0.0315182	+	0.198998i	0.966905	+	0.255138i	$0.0821208\pi$
$348$		0			0
$349$			12.9374i			0.692525i	0.938138	+	0.346262i	$0.112549\pi$
$349$			12.9374i			0.692525i	−0.938138	+	0.346262i	$0.887451\pi$
$350$		0			0
$351$	1.00900	+	1.90628i	0.0538562	+	0.101750i
$352$		0			0
$353$	26.1583	+	4.14307i	1.39227	+	0.220513i	0.807107	−	0.590405i	$-0.201032\pi$
$353$	26.1583	+	4.14307i	1.39227	+	0.220513i	0.585159	+	0.810919i	$0.301032\pi$
$354$		0			0
$355$	−3.12523	−	3.62990i	−0.165870	−	0.192655i
$356$		0			0
$357$	−48.2068	+	21.7636i	−2.55137	+	1.15185i
$358$		0			0
$359$	1.48360	−	4.56607i	0.0783016	−	0.240988i	−0.904242	−	0.427021i	$-0.859563\pi$
$359$	1.48360	−	4.56607i	0.0783016	−	0.240988i	0.982543	+	0.186033i	$0.0595631\pi$
$360$		0			0
$361$	−0.587610	−	1.80848i	−0.0309269	−	0.0951831i
$362$		0			0
$363$	−2.58089	−	23.3870i	−0.135462	−	1.22750i
$364$		0			0
$365$	−29.6147	−	12.1293i	−1.55010	−	0.634875i
$366$		0			0
$367$	4.19594	+	26.4921i	0.219026	+	1.38288i	0.814808	+	0.579731i	$0.196842\pi$
$367$	4.19594	+	26.4921i	0.219026	+	1.38288i	−0.595782	+	0.803146i	$0.703158\pi$
$368$		0			0
$369$	3.90303	+	17.4685i	0.203184	+	0.909372i
$370$		0			0
$371$	19.6447	+	27.0386i	1.01990	+	1.40377i
$372$		0			0
$373$	2.97876	+	1.51776i	0.154234	+	0.0785864i	0.529404	−	0.848370i	$-0.322416\pi$
$373$	2.97876	+	1.51776i	0.154234	+	0.0785864i	−0.375170	+	0.926956i	$0.622416\pi$
$374$		0			0
$375$	−5.18159	+	18.6588i	−0.267576	+	0.963537i
$376$		0			0
$377$	0.382380	+	0.194832i	0.0196936	+	0.0100344i
$378$		0			0
$379$	−1.47681	−	2.03266i	−0.0758588	−	0.104411i	0.769401	−	0.638766i	$-0.220555\pi$
$379$	−1.47681	−	2.03266i	−0.0758588	−	0.104411i	−0.845260	+	0.534355i	$0.820555\pi$
$380$		0			0
$381$	−18.4143	−	28.0358i	−0.943393	−	1.43632i
$382$		0			0
$383$	−1.45004	−	9.15521i	−0.0740938	−	0.467810i	−0.996639	−	0.0819203i	$-0.973895\pi$
$383$	−1.45004	−	9.15521i	−0.0740938	−	0.467810i	0.922545	−	0.385889i	$-0.126105\pi$
$384$		0			0
$385$	−41.2088	−	16.8779i	−2.10019	−	0.860175i
$386$		0			0
$387$	−10.1282	−	2.60143i	−0.514844	−	0.132238i
$388$		0			0
$389$	3.53033	+	10.8652i	0.178995	+	0.550890i	0.999793	−	0.0203282i	$-0.00647113\pi$
$389$	3.53033	+	10.8652i	0.178995	+	0.550890i	−0.820798	+	0.571218i	$0.806471\pi$
$390$		0			0
$391$	−0.795077	+	2.44700i	−0.0402088	+	0.123750i
$392$		0			0
$393$	−2.38127	−	5.27454i	−0.120119	−	0.266066i
$394$		0			0
$395$	11.0784	+	12.8674i	0.557417	+	0.647429i
$396$		0			0
$397$	−9.67691	−	1.53267i	−0.485670	−	0.0769226i	−0.0912023	−	0.995832i	$-0.529071\pi$
$397$	−9.67691	−	1.53267i	−0.485670	−	0.0769226i	−0.394468	+	0.918910i	$0.629071\pi$
$398$		0			0
$399$	−11.2437	+	29.7515i	−0.562888	+	1.48944i
$400$		0			0
$401$		−	27.1537i		−	1.35599i	−0.735066	−	0.677996i	$-0.762849\pi$
$401$		−	27.1537i		−	1.35599i	0.735066	−	0.677996i	$-0.237151\pi$
$402$		0			0
$403$	−0.180155	+	1.13745i	−0.00897414	+	0.0566605i
$404$		0			0
$405$	8.21195	−	18.3729i	0.408055	−	0.912957i
$406$		0			0
$407$	−16.9922	+	16.9922i	−0.842271	+	0.842271i
$408$		0			0
$409$	−30.0764	−	9.77241i	−1.48718	−	0.483215i	−0.550932	−	0.834550i	$-0.685728\pi$
$409$	−30.0764	−	9.77241i	−1.48718	−	0.483215i	−0.936250	+	0.351335i	$0.885728\pi$
$410$		0			0
$411$	4.12756	+	0.194835i	0.203598	+	0.00961050i
$412$		0			0
$413$	−35.8964	+	18.2902i	−1.76635	+	0.900000i
$414$		0			0
$415$	−3.47874	−	14.2407i	−0.170765	−	0.699047i
$416$		0			0
$417$	−0.601587	+	2.90430i	−0.0294598	+	0.142224i
$418$		0			0
$419$	13.3040	+	9.66590i	0.649941	+	0.472210i	0.863251	−	0.504775i	$-0.168424\pi$
$419$	13.3040	+	9.66590i	0.649941	+	0.472210i	−0.213310	+	0.976985i	$0.568424\pi$
$420$		0			0
$421$	11.1129	−	8.07400i	0.541610	−	0.393503i	−0.283073	−	0.959098i	$-0.591354\pi$
$421$	11.1129	−	8.07400i	0.541610	−	0.393503i	0.824683	+	0.565596i	$0.191354\pi$
$422$		0			0
$423$	−21.5840	+	8.54349i	−1.04945	+	0.415399i
$424$		0			0
$425$	36.0595	−	12.0338i	1.74914	−	0.583727i
$426$		0			0
$427$	17.7229	−	34.7831i	0.857670	−	1.68327i
$428$		0			0
$429$	3.43843	−	0.940484i	0.166009	−	0.0454070i
$430$		0			0
$431$	−2.67787	+	3.68577i	−0.128989	+	0.177537i	−0.868626	−	0.495468i	$-0.834997\pi$
$431$	−2.67787	+	3.68577i	−0.128989	+	0.177537i	0.739638	+	0.673005i	$0.234997\pi$
$432$		0			0
$433$	21.2003	−	3.35781i	1.01882	−	0.161366i	0.375389	−	0.926867i	$-0.377509\pi$
$433$	21.2003	−	3.35781i	1.01882	−	0.161366i	0.643434	+	0.765501i	$0.277509\pi$
$434$		0			0
$435$	−0.765763	−	3.93037i	−0.0367155	−	0.188447i
$436$		0			0
$437$	0.702398	+	1.37853i	0.0336003	+	0.0659442i
$438$		0			0
$439$	10.5185	−	3.41768i	0.502022	−	0.163117i	−0.0470490	−	0.998893i	$-0.514982\pi$
$439$	10.5185	−	3.41768i	0.502022	−	0.163117i	0.549071	+	0.835776i	$0.314982\pi$
$440$		0			0
$441$	23.5830	−	13.9441i	1.12300	−	0.664006i
$442$		0			0
$443$	−11.3624	−	11.3624i	−0.539846	−	0.539846i	0.383638	−	0.923484i	$-0.374671\pi$
$443$	−11.3624	−	11.3624i	−0.539846	−	0.539846i	−0.923484	+	0.383638i	$0.874671\pi$
$444$		0			0
$445$	11.5496	+	27.5731i	0.547505	+	1.30709i
$446$		0			0
$447$	6.58953	−	11.5515i	0.311674	−	0.546366i
$448$		0			0
$449$	−16.5317			−0.780178			−0.390089	−	0.920777i	$-0.627556\pi$
$449$	−16.5317			−0.780178			−0.390089	+	0.920777i	$0.627556\pi$
$450$		0			0
$451$	29.5830			1.39301
$452$		0			0
$453$	−16.3052	+	28.5830i	−0.766083	+	1.34295i
$454$		0			0
$455$	0.855873	−	3.62837i	0.0401240	−	0.170101i
$456$		0			0
$457$	−16.5635	−	16.5635i	−0.774807	−	0.774807i	0.204136	−	0.978943i	$-0.434562\pi$
$457$	−16.5635	−	16.5635i	−0.774807	−	0.774807i	−0.978943	+	0.204136i	$0.934562\pi$
$458$		0			0
$459$	−38.9185	+	6.78701i	−1.81656	+	0.316791i
$460$		0			0
$461$	14.5158	−	4.71648i	0.676070	−	0.219669i	0.0491963	−	0.998789i	$-0.484334\pi$
$461$	14.5158	−	4.71648i	0.676070	−	0.219669i	0.626874	+	0.779121i	$0.284334\pi$
$462$		0			0
$463$	−1.93184	−	3.79146i	−0.0897804	−	0.176204i	0.841750	−	0.539868i	$-0.181526\pi$
$463$	−1.93184	−	3.79146i	−0.0897804	−	0.176204i	−0.931530	+	0.363664i	$0.881526\pi$
$464$		0			0
$465$	9.39586	−	5.21356i	0.435723	−	0.241773i
$466$		0			0
$467$	−30.6114	+	4.84837i	−1.41653	+	0.224356i	−0.817295	−	0.576219i	$-0.804528\pi$
$467$	−30.6114	+	4.84837i	−1.41653	+	0.224356i	−0.599233	+	0.800575i	$0.704528\pi$
$468$		0			0
$469$	17.4334	−	23.9951i	0.805001	−	1.10799i
$470$		0			0
$471$	−8.63368	+	2.36149i	−0.397819	+	0.108812i
$472$		0			0
$473$	−7.84621	+	15.3990i	−0.360769	+	0.708049i
$474$		0			0
$475$	10.2158	−	20.4494i	0.468731	−	0.938282i
$476$		0			0
$477$	9.18746	+	23.2109i	0.420665	+	1.06275i
$478$		0			0
$479$	23.7090	−	17.2256i	1.08329	−	0.787059i	0.105039	−	0.994468i	$-0.466503\pi$
$479$	23.7090	−	17.2256i	1.08329	−	0.787059i	0.978254	+	0.207409i	$0.0665032\pi$
$480$		0			0
$481$	−1.62753	−	1.18247i	−0.0742088	−	0.0539159i
$482$		0			0
$483$	0.477519	−	2.30534i	0.0217279	−	0.104896i
$484$		0			0
$485$	−4.96595	−	0.370996i	−0.225492	−	0.0168460i
$486$		0			0
$487$	18.5821	−	9.46803i	0.842033	−	0.429037i	0.0209053	−	0.999781i	$-0.493345\pi$
$487$	18.5821	−	9.46803i	0.842033	−	0.429037i	0.821128	+	0.570744i	$0.193345\pi$
$488$		0			0
$489$	6.51596	+	0.307575i	0.294662	+	0.0139090i
$490$		0			0
$491$	−8.67143	−	2.81752i	−0.391336	−	0.127153i	0.106738	−	0.994287i	$-0.465959\pi$
$491$	−8.67143	−	2.81752i	−0.391336	−	0.127153i	−0.498074	+	0.867134i	$0.665959\pi$
$492$		0			0
$493$	−5.55831	+	5.55831i	−0.250334	+	0.250334i
$494$		0			0
$495$	−26.6757	−	19.8672i	−1.19898	−	0.892966i
$496$		0			0
$497$	1.34593	−	8.49789i	0.0603734	−	0.381183i
$498$		0			0
$499$		−	9.70109i		−	0.434280i	−0.976140	−	0.217140i	$-0.930327\pi$
$499$		−	9.70109i		−	0.434280i	0.976140	−	0.217140i	$-0.0696729\pi$
$500$		0			0
$501$	2.06745	−	5.47061i	0.0923669	−	0.244409i
$502$		0			0
$503$	−8.01914	−	1.27011i	−0.357556	−	0.0566313i	−0.0249274	−	0.999689i	$-0.507935\pi$
$503$	−8.01914	−	1.27011i	−0.357556	−	0.0566313i	−0.332628	+	0.943058i	$0.607935\pi$
$504$		0			0
$505$	−2.31936	−	28.0461i	−0.103210	−	1.24804i
$506$		0			0
$507$	−9.14222	−	20.2502i	−0.406020	−	0.899342i
$508$		0			0
$509$	−11.1835	+	34.4193i	−0.495700	+	1.52561i	0.320163	+	0.947362i	$0.396262\pi$
$509$	−11.1835	+	34.4193i	−0.495700	+	1.52561i	−0.815863	+	0.578245i	$0.803738\pi$
$510$		0			0
$511$	−17.7634	−	54.6703i	−0.785809	−	2.41847i
$512$		0			0
$513$	−13.6623	+	19.4340i	−0.603207	+	0.858034i
$514$		0			0
$515$	−0.224939	+	3.01091i	−0.00991198	+	0.132676i
$516$		0			0
$517$	6.00177	+	37.8937i	0.263958	+	1.66656i
$518$		0			0
$519$	−11.3723	−	17.3144i	−0.499189	−	0.760017i
$520$		0			0
$521$	9.60734	+	13.2234i	0.420905	+	0.579326i	0.965836	−	0.259155i	$-0.0834440\pi$
$521$	9.60734	+	13.2234i	0.420905	+	0.579326i	−0.544930	+	0.838481i	$0.683444\pi$
$522$		0			0
$523$	−9.11004	−	4.64180i	−0.398354	−	0.202972i	0.243325	−	0.969945i	$-0.421762\pi$
$523$	−9.11004	−	4.64180i	−0.398354	−	0.202972i	−0.641679	+	0.766973i	$0.721762\pi$
$524$		0			0
$525$	−31.5882	+	14.5640i	−1.37862	+	0.635625i
$526$		0			0
$527$	−18.7948	−	9.57641i	−0.818713	−	0.417155i
$528$		0			0
$529$	13.4517	+	18.5147i	0.584859	+	0.804989i
$530$		0			0
$531$	−29.3673	+	6.56163i	−1.27443	+	0.284751i
$532$		0			0
$533$	0.387419	+	2.44607i	0.0167810	+	0.105951i
$534$		0			0
$535$	5.13240	−	6.05781i	0.221893	−	0.261902i
$536$		0			0
$537$	−0.411448	−	3.72837i	−0.0177553	−	0.160891i
$538$		0			0
$539$	−13.9925	−	43.0645i	−0.602699	−	1.85492i
$540$		0			0
$541$	5.41906	−	16.6781i	0.232983	−	0.717049i	−0.764399	−	0.644743i	$-0.776964\pi$
$541$	5.41906	−	16.6781i	0.232983	−	0.717049i	0.997383	−	0.0723059i	$-0.0230358\pi$
$542$		0			0
$543$	−0.950125	+	0.428947i	−0.0407738	+	0.0184079i
$544$		0			0
$545$	24.7503	+	5.83819i	1.06019	+	0.250081i
$546$		0			0
$547$	16.0041	+	2.53481i	0.684288	+	0.108381i	0.488893	−	0.872344i	$-0.337401\pi$
$547$	16.0041	+	2.53481i	0.684288	+	0.108381i	0.195395	+	0.980725i	$0.437401\pi$
$548$		0			0
$549$	19.2846	−	21.8701i	0.823046	−	0.933395i
$550$		0			0
$551$			4.72680i			0.201369i
$552$		0			0
$553$	−4.77111	+	30.1236i	−0.202888	+	1.28099i
$554$		0			0
$555$	0.663252	+	18.7589i	0.0281535	+	0.796273i
$556$		0			0
$557$	0.351406	−	0.351406i	0.0148895	−	0.0148895i	−0.699623	−	0.714512i	$-0.746649\pi$
$557$	0.351406	−	0.351406i	0.0148895	−	0.0148895i	0.714512	+	0.699623i	$0.246649\pi$
$558$		0			0
$559$	−1.37602	−	0.447097i	−0.0581995	−	0.0189102i
$560$		0			0
$561$	−3.07865	+	65.2209i	−0.129981	+	2.75363i
$562$		0			0
$563$	9.57089	−	4.87661i	0.403365	−	0.205525i	−0.240525	−	0.970643i	$-0.577320\pi$
$563$	9.57089	−	4.87661i	0.403365	−	0.205525i	0.643890	+	0.765118i	$0.277320\pi$
$564$		0			0
$565$	−14.7544	+	9.12229i	−0.620722	+	0.383777i
$566$		0			0
$567$	34.7151	−	10.0790i	1.45790	−	0.423276i
$568$		0			0
$569$	−34.5553	−	25.1059i	−1.44863	−	1.05249i	−0.986148	−	0.165865i	$-0.946958\pi$
$569$	−34.5553	−	25.1059i	−1.44863	−	1.05249i	−0.462484	−	0.886628i	$-0.653042\pi$
$570$		0			0
$571$	−37.4429	+	27.2039i	−1.56694	+	1.13845i	−0.636920	+	0.770930i	$0.719792\pi$
$571$	−37.4429	+	27.2039i	−1.56694	+	1.13845i	−0.930017	+	0.367517i	$0.880208\pi$
$572$		0			0
$573$	27.0972	−	24.6544i	1.13200	−	1.02995i
$574$		0			0
$575$	−0.510082	+	1.61335i	−0.0212719	+	0.0672814i
$576$		0			0
$577$	−3.73707	+	7.33441i	−0.155576	+	0.305335i	−0.955618	−	0.294609i	$-0.904811\pi$
$577$	−3.73707	+	7.33441i	−0.155576	+	0.305335i	0.800042	+	0.599944i	$0.204811\pi$
$578$		0			0
$579$	−0.339441	−	1.24100i	−0.0141067	−	0.0515743i
$580$		0			0
$581$	15.4774	−	21.3029i	0.642113	−	0.883792i
$582$		0			0
$583$	40.7500	−	6.45416i	1.68769	−	0.267304i
$584$		0			0
$585$	1.29338	−	2.46586i	0.0534745	−	0.101951i
$586$		0			0
$587$	0.885671	+	1.73823i	0.0365556	+	0.0717444i	0.908562	−	0.417750i	$-0.137181\pi$
$587$	0.885671	+	1.73823i	0.0365556	+	0.0717444i	−0.872006	+	0.489495i	$0.837181\pi$
$588$		0			0
$589$	−12.0635	+	3.91966i	−0.497066	+	0.161507i
$590$		0			0
$591$	3.28602	+	2.63284i	0.135169	+	0.108300i
$592$		0			0
$593$	26.3630	+	26.3630i	1.08260	+	1.08260i	0.996266	+	0.0863319i	$0.0275146\pi$
$593$	26.3630	+	26.3630i	1.08260	+	1.08260i	0.0863319	+	0.996266i	$0.472485\pi$
$594$		0			0
$595$	58.3621	+	35.4464i	2.39261	+	1.45316i
$596$		0			0
$597$	40.1002	+	22.8751i	1.64119	+	0.936217i
$598$		0			0
$599$	27.2293			1.11256			0.556280	−	0.830995i	$-0.312228\pi$
$599$	27.2293			1.11256			0.556280	+	0.830995i	$0.312228\pi$
$600$		0			0
$601$	−0.707518			−0.0288602			−0.0144301	−	0.999896i	$-0.504593\pi$
$601$	−0.707518			−0.0288602			−0.0144301	+	0.999896i	$0.504593\pi$
$602$		0			0
$603$	17.0706	−	14.1195i	0.695168	−	0.574989i
$604$		0			0
$605$	−23.0194	+	19.8190i	−0.935871	+	0.805758i
$606$		0			0
$607$	−15.7536	−	15.7536i	−0.639418	−	0.639418i	0.310994	−	0.950412i	$-0.399338\pi$
$607$	−15.7536	−	15.7536i	−0.639418	−	0.639418i	−0.950412	+	0.310994i	$0.899338\pi$
$608$		0			0
$609$	4.49739	−	5.61315i	0.182243	−	0.227456i
$610$		0			0
$611$	−3.05464	+	0.992512i	−0.123577	+	0.0401527i
$612$		0			0
$613$	−7.04615	−	13.8288i	−0.284591	−	0.558542i	0.703813	−	0.710385i	$-0.251479\pi$
$613$	−7.04615	−	13.8288i	−0.284591	−	0.558542i	−0.988405	+	0.151843i	$0.951479\pi$
$614$		0			0
$615$	15.7521	−	16.9068i	0.635186	−	0.681748i
$616$		0			0
$617$	30.2739	−	4.79492i	1.21878	−	0.193036i	0.486282	−	0.873802i	$-0.338353\pi$
$617$	30.2739	−	4.79492i	1.21878	−	0.193036i	0.732501	+	0.680766i	$0.238353\pi$
$618$		0			0
$619$	−24.7268	+	34.0335i	−0.993852	+	1.36792i	−0.0648299	+	0.997896i	$0.520650\pi$
$619$	−24.7268	+	34.0335i	−0.993852	+	1.36792i	−0.929022	+	0.370024i	$0.879350\pi$
$620$		0			0
$621$	0.773820	−	1.57903i	0.0310523	−	0.0633643i
$622$		0			0
$623$	−24.3781	+	47.8446i	−0.976686	+	1.91685i
$624$		0			0
$625$	23.6507	−	8.10204i	0.946029	−	0.324082i
$626$		0			0
$627$	26.4230	+	29.0411i	1.05523	+	1.15979i
$628$		0			0
$629$	29.8106	−	21.6587i	1.18863	−	0.863589i
$630$		0			0
$631$	35.3783	+	25.7038i	1.40839	+	1.02325i	0.993554	+	0.113357i	$0.0361603\pi$
$631$	35.3783	+	25.7038i	1.40839	+	1.02325i	0.414834	+	0.909897i	$0.363840\pi$
$632$		0			0
$633$	−14.0335	−	2.90684i	−0.557780	−	0.115537i
$634$		0			0
$635$	−16.4124	+	40.0723i	−0.651306	+	1.59022i
$636$		0			0
$637$	3.37753	−	1.72094i	0.133823	−	0.0681861i
$638$		0			0
$639$	2.55273	−	5.89758i	0.100985	−	0.233305i
$640$		0			0
$641$	−41.9572	−	13.6327i	−1.65721	−	0.538460i	−0.676924	−	0.736053i	$-0.736687\pi$
$641$	−41.9572	−	13.6327i	−1.65721	−	0.538460i	−0.980284	+	0.197593i	$0.936687\pi$
$642$		0			0
$643$	−21.6567	+	21.6567i	−0.854057	+	0.854057i	−0.990630	−	0.136573i	$-0.956391\pi$
$643$	−21.6567	+	21.6567i	−0.854057	+	0.854057i	0.136573	+	0.990630i	$0.456391\pi$
$644$		0			0
$645$	4.62274	+	12.6837i	0.182020	+	0.499420i
$646$		0			0
$647$	−4.83284	+	30.5133i	−0.189998	+	1.19960i	0.689709	+	0.724087i	$0.257739\pi$
$647$	−4.83284	+	30.5133i	−0.189998	+	1.19960i	−0.879707	+	0.475516i	$0.842261\pi$
$648$		0			0
$649$			49.7338i			1.95222i
$650$		0			0
$651$	18.0550	+	6.82332i	0.707629	+	0.267427i
$652$		0			0
$653$	29.5562	+	4.68124i	1.15662	+	0.183191i	0.705127	−	0.709081i	$-0.250890\pi$
$653$	29.5562	+	4.68124i	1.15662	+	0.183191i	0.451497	+	0.892272i	$0.350890\pi$
$654$		0			0
$655$	−3.87836	+	6.38569i	−0.151540	+	0.249510i
$656$		0			0
$657$	−2.69214	−	42.8511i	−0.105030	−	1.67178i
$658$		0			0
$659$	3.30930	−	10.1850i	0.128912	−	0.396750i	−0.865682	−	0.500595i	$-0.833115\pi$
$659$	3.30930	−	10.1850i	0.128912	−	0.396750i	0.994594	+	0.103845i	$0.0331145\pi$
$660$		0			0
$661$	8.67556	+	26.7006i	0.337440	+	1.03853i	0.965507	+	0.260375i	$0.0838463\pi$
$661$	8.67556	+	26.7006i	0.337440	+	1.03853i	−0.628067	+	0.778159i	$0.716154\pi$
$662$		0			0
$663$	−5.43310	+	0.599576i	−0.211004	+	0.0232856i
$664$		0			0
$665$	39.8875	−	9.74380i	1.54677	−	0.377848i
$666$		0			0
$667$	−0.0547341	−	0.345578i	−0.00211931	−	0.0133808i
$668$		0			0
$669$	−18.4964	+	12.1487i	−0.715113	+	0.469696i
$670$		0			0
$671$	−28.3262	−	38.9876i	−1.09352	−	1.50510i
$672$		0			0
$673$	−22.9797	−	11.7087i	−0.885803	−	0.451339i	−0.0489715	−	0.998800i	$-0.515594\pi$
$673$	−22.9797	−	11.7087i	−0.885803	−	0.451339i	−0.836831	+	0.547461i	$0.815594\pi$
$674$		0			0
$675$	−25.5582	+	4.66653i	−0.983737	+	0.179615i
$676$		0			0
$677$	−3.98966	−	2.03283i	−0.153335	−	0.0781281i	0.375639	−	0.926766i	$-0.377423\pi$
$677$	−3.98966	−	2.03283i	−0.153335	−	0.0781281i	−0.528974	+	0.848638i	$0.677423\pi$
$678$		0			0
$679$	−5.25767	−	7.23656i	−0.201771	−	0.277714i
$680$		0			0
$681$	−35.1439	+	23.0830i	−1.34672	+	0.884543i
$682$		0			0
$683$	−4.57286	−	28.8719i	−0.174976	−	1.10475i	−0.906273	−	0.422693i	$-0.861085\pi$
$683$	−4.57286	−	28.8719i	−0.174976	−	1.10475i	0.731297	−	0.682059i	$-0.238915\pi$
$684$		0			0
$685$	−2.80535	−	4.53739i	−0.107187	−	0.173365i
$686$		0			0
$687$	12.7827	−	1.41065i	0.487691	−	0.0538196i
$688$		0			0
$689$	1.06732	+	3.28488i	0.0406618	+	0.125144i
$690$		0			0
$691$	−7.71677	+	23.7498i	−0.293560	+	0.903484i	0.690141	+	0.723674i	$0.257548\pi$
$691$	−7.71677	+	23.7498i	−0.293560	+	0.903484i	−0.983701	+	0.179810i	$0.942452\pi$
$692$		0			0
$693$	−3.74610	−	59.6273i	−0.142303	−	2.26505i
$694$		0			0
$695$	3.53172	−	1.47934i	0.133966	−	0.0561146i
$696$		0			0
$697$	−44.8035	−	7.09617i	−1.69705	−	0.268787i
$698$		0			0
$699$	−28.7632	−	10.8702i	−1.08793	−	0.411148i
$700$		0			0
$701$		−	6.88847i		−	0.260174i	−0.991503	−	0.130087i	$-0.958474\pi$
$701$		−	6.88847i		−	0.260174i	0.991503	−	0.130087i	$-0.0415257\pi$
$702$		0			0
$703$	3.46622	−	21.8848i	0.130731	−	0.825402i
$704$		0			0
$705$	24.8522	+	16.7473i	0.935987	+	0.630738i
$706$		0			0
$707$	35.7439	−	35.7439i	1.34429	−	1.34429i
$708$		0			0
$709$	−3.31523	−	1.07719i	−0.124506	−	0.0404545i	0.246101	−	0.969244i	$-0.420850\pi$
$709$	−3.31523	−	1.07719i	−0.124506	−	0.0404545i	−0.370607	+	0.928790i	$0.620850\pi$
$710$		0			0
$711$	−9.04901	+	20.9059i	−0.339365	+	0.784034i
$712$		0			0
$713$	0.836575	−	0.426256i	0.0313300	−	0.0159634i
$714$		0			0
$715$	−3.51127	−	2.97488i	−0.131314	−	0.111254i
$716$		0			0
$717$	1.23283	+	0.255364i	0.0460409	+	0.00953675i
$718$		0			0
$719$	13.0340	+	9.46973i	0.486085	+	0.353161i	0.803677	−	0.595066i	$-0.202874\pi$
$719$	13.0340	+	9.46973i	0.486085	+	0.353161i	−0.317592	+	0.948228i	$0.602874\pi$
$720$		0			0
$721$	−4.38760	+	3.18778i	−0.163403	+	0.118719i
$722$		0			0
$723$	16.7542	+	18.4143i	0.623096	+	0.684835i
$724$		0			0
$725$	−3.62624	+	3.68430i	−0.134675	+	0.136831i
$726$		0			0
$727$	12.5508	−	24.6324i	0.465484	−	0.913564i	−0.532270	−	0.846575i	$-0.678661\pi$
$727$	12.5508	−	24.6324i	0.465484	−	0.913564i	0.997754	−	0.0669890i	$-0.0213392\pi$
$728$		0			0
$729$	26.9869	−	0.840889i	0.999515	−	0.0311440i
$730$		0			0
$731$	15.5769	−	21.4398i	0.576132	−	0.792978i
$732$		0			0
$733$	19.6261	−	3.10847i	0.724907	−	0.114814i	0.216933	−	0.976186i	$-0.430395\pi$
$733$	19.6261	−	3.10847i	0.724907	−	0.114814i	0.507974	+	0.861372i	$0.330395\pi$
$734$		0			0
$735$	−32.0621	−	14.9338i	−1.18263	−	0.550842i
$736$		0			0
$737$	−16.6223	−	32.6232i	−0.612292	−	1.20169i
$738$		0			0
$739$	40.3184	−	13.1002i	1.48313	−	0.481900i	0.548087	−	0.836421i	$-0.315356\pi$
$739$	40.3184	−	13.1002i	1.48313	−	0.481900i	0.935048	+	0.354522i	$0.115356\pi$
$740$		0			0
$741$	−2.05522	+	2.56510i	−0.0755005	+	0.0942314i
$742$		0			0
$743$	27.1592	+	27.1592i	0.996375	+	0.996375i	0.999993	−	0.00361798i	$-0.00115164\pi$
$743$	27.1592	+	27.1592i	0.996375	+	0.996375i	−0.00361798	+	0.999993i	$0.501152\pi$
$744$		0			0
$745$	−17.1103	+	1.41499i	−0.626873	+	0.0518411i
$746$		0			0
$747$	15.1553	−	12.5353i	0.554504	−	0.458643i
$748$		0			0
$749$	14.2616			0.521106
$750$		0			0
$751$	−7.33413			−0.267626			−0.133813	−	0.991007i	$-0.542722\pi$
$751$	−7.33413			−0.267626			−0.133813	+	0.991007i	$0.542722\pi$
$752$		0			0
$753$	16.0641	+	9.16376i	0.585409	+	0.333946i
$754$		0			0
$755$	42.3378	−	3.50125i	1.54083	−	0.127423i
$756$		0			0
$757$	15.2951	+	15.2951i	0.555911	+	0.555911i	0.928141	−	0.372230i	$-0.121407\pi$
$757$	15.2951	+	15.2951i	0.555911	+	0.555911i	−0.372230	+	0.928141i	$0.621407\pi$
$758$		0			0
$759$	−2.26807	−	1.81723i	−0.0823258	−	0.0659614i
$760$		0			0
$761$	−10.8598	+	3.52857i	−0.393669	+	0.127911i	−0.499161	−	0.866509i	$-0.666358\pi$
$761$	−10.8598	+	3.52857i	−0.393669	+	0.127911i	0.105492	+	0.994420i	$0.466358\pi$
$762$		0			0
$763$	20.7372	+	40.6990i	0.750736	+	1.47340i
$764$		0			0
$765$	35.6347	+	36.4877i	1.28838	+	1.31922i
$766$		0			0
$767$	−4.11224	+	0.651314i	−0.148484	+	0.0235176i
$768$		0			0
$769$	13.6293	−	18.7591i	0.491485	−	0.676471i	−0.489176	−	0.872185i	$-0.662702\pi$
$769$	13.6293	−	18.7591i	0.491485	−	0.676471i	0.980661	+	0.195714i	$0.0627025\pi$
$770$		0			0
$771$	−6.01005	−	21.9729i	−0.216447	−	0.791334i
$772$		0			0
$773$	−15.7994	+	31.0081i	−0.568265	+	1.11528i	0.410799	+	0.911726i	$0.365250\pi$
$773$	−15.7994	+	31.0081i	−0.568265	+	1.11528i	−0.979063	+	0.203556i	$0.934750\pi$
$774$		0			0
$775$	−12.4099	−	6.19952i	−0.445776	−	0.222693i
$776$		0			0
$777$	−24.9388	+	22.6906i	−0.894676	+	0.814020i
$778$		0			0
$779$	−22.0678	+	16.0332i	−0.790661	+	0.574449i
$780$		0			0
$781$	−8.59271	−	6.24297i	−0.307471	−	0.223391i
$782$		0			0
$783$	4.29658	−	3.22506i	0.153547	−	0.115254i
$784$		0			0
$785$	8.81656	+	7.46972i	0.314677	+	0.266606i
$786$		0			0
$787$	−38.3652	+	19.5480i	−1.36757	+	0.696812i	−0.974854	−	0.222847i	$-0.928465\pi$
$787$	−38.3652	+	19.5480i	−1.36757	+	0.696812i	−0.392718	+	0.919659i	$0.628465\pi$
$788$		0			0
$789$	2.12023	−	44.9168i	0.0754820	−	1.59908i
$790$		0			0
$791$	−29.6338	−	9.62861i	−1.05366	−	0.342354i
$792$		0			0
$793$	2.85273	−	2.85273i	0.101303	−	0.101303i
$794$		0			0
$795$	18.0096	−	26.7254i	0.638734	−	0.947852i
$796$		0			0
$797$	5.41838	−	34.2103i	0.191929	−	1.21179i	−0.684047	−	0.729438i	$-0.739782\pi$
$797$	5.41838	−	34.2103i	0.191929	−	1.21179i	0.875976	−	0.482354i	$-0.160218\pi$
$798$		0			0
$799$		−	58.8297i		−	2.08124i
$800$		0			0
$801$	−26.5262	+	30.0827i	−0.937257	+	1.06292i
$802$		0			0
$803$	−70.0884	−	11.1009i	−2.47337	−	0.391743i
$804$		0			0
$805$	−2.80336	+	1.17425i	−0.0988053	+	0.0413869i
$806$		0			0
$807$	26.6642	−	12.0379i	0.938623	−	0.423754i
$808$		0			0
$809$	2.65484	−	8.17077i	0.0933393	−	0.287269i	−0.893478	−	0.449107i	$-0.851742\pi$
$809$	2.65484	−	8.17077i	0.0933393	−	0.287269i	0.986817	+	0.161838i	$0.0517422\pi$
$810$		0			0
$811$	−6.69438	−	20.6032i	−0.235072	−	0.723476i	−0.997112	−	0.0759463i	$-0.975802\pi$
$811$	−6.69438	−	20.6032i	−0.235072	−	0.723476i	0.762040	−	0.647530i	$-0.224198\pi$
$812$		0			0
$813$	−3.00321	−	27.2138i	−0.105327	−	0.954430i
$814$		0			0
$815$	−4.42866	−	7.16292i	−0.155129	−	0.250906i
$816$		0			0
$817$	−2.49290	−	15.7395i	−0.0872155	−	0.550657i
$818$		0			0
$819$	4.88121	−	1.09062i	0.170563	−	0.0381095i
$820$		0			0
$821$	−26.5748	−	36.5770i	−0.927466	−	1.27655i	−0.960840	−	0.277105i	$-0.910625\pi$
$821$	−26.5748	−	36.5770i	−0.927466	−	1.27655i	0.0333736	−	0.999443i	$-0.489375\pi$
$822$		0			0
$823$	−2.87584	−	1.46531i	−0.100245	−	0.0510776i	0.403149	−	0.915134i	$-0.367916\pi$
$823$	−2.87584	−	1.46531i	−0.100245	−	0.0510776i	−0.503394	+	0.864057i	$0.667916\pi$
$824$		0			0
$825$	−1.68400	+	42.9068i	−0.0586292	+	1.49382i
$826$		0			0
$827$	18.7516	+	9.55443i	0.652058	+	0.332240i	0.748535	−	0.663095i	$-0.230758\pi$
$827$	18.7516	+	9.55443i	0.652058	+	0.332240i	−0.0964773	+	0.995335i	$0.530758\pi$
$828$		0			0
$829$	−32.8299	−	45.1864i	−1.14023	−	1.56939i	−0.766997	−	0.641651i	$-0.778250\pi$
$829$	−32.8299	−	45.1864i	−1.14023	−	1.56939i	−0.373232	−	0.927738i	$-0.621750\pi$
$830$		0			0
$831$	−16.2753	−	24.7792i	−0.564584	−	0.859580i
$832$		0			0
$833$	10.8616	+	68.5775i	0.376333	+	2.37607i
$834$		0			0
$835$	−7.33438	+	1.79166i	−0.253817	+	0.0620029i
$836$		0			0
$837$	11.7937	+	8.29111i	0.407650	+	0.286583i
$838$		0			0
$839$	8.34410	+	25.6805i	0.288070	+	0.886590i	0.985461	+	0.169899i	$0.0543441\pi$
$839$	8.34410	+	25.6805i	0.288070	+	0.886590i	−0.697391	+	0.716691i	$0.745656\pi$
$840$		0			0
$841$	−8.63117	+	26.5640i	−0.297627	+	0.916000i
$842$		0			0
$843$	19.4411	+	43.0625i	0.669588	+	1.48315i
$844$		0			0
$845$	−14.8899	+	24.5161i	−0.512229	+	0.843380i
$846$		0			0
$847$	−53.8903	−	8.53538i	−1.85169	−	0.293279i
$848$		0			0
$849$	−1.86887	+	4.94516i	−0.0641395	+	0.169718i
$850$		0			0
$851$			1.64014i			0.0562234i
$852$		0			0
$853$	−3.65179	+	23.0565i	−0.125035	+	0.789439i	0.842869	+	0.538119i	$0.180865\pi$
$853$	−3.65179	+	23.0565i	−0.125035	+	0.789439i	−0.967904	+	0.251320i	$0.919135\pi$
$854$		0			0
$855$	30.6666	+	0.362696i	1.04877	+	0.0124039i
$856$		0			0
$857$	−23.9274	+	23.9274i	−0.817343	+	0.817343i	−0.985722	−	0.168379i	$-0.946147\pi$
$857$	−23.9274	+	23.9274i	−0.817343	+	0.817343i	0.168379	+	0.985722i	$0.446147\pi$
$858$		0			0
$859$	12.3998	+	4.02894i	0.423076	+	0.137466i	0.512814	−	0.858500i	$-0.328603\pi$
$859$	12.3998	+	4.02894i	0.423076	+	0.137466i	−0.0897381	+	0.995965i	$0.528603\pi$
$860$		0			0
$861$	41.4609	+	1.95709i	1.41298	+	0.0666975i
$862$		0			0
$863$	−48.0446	+	24.4799i	−1.63546	+	0.833307i	−0.637431	+	0.770508i	$0.720003\pi$
$863$	−48.0446	+	24.4799i	−1.63546	+	0.833307i	−0.998026	+	0.0627991i	$0.979997\pi$
$864$		0			0
$865$	−10.1360	+	24.7479i	−0.344633	+	0.841453i
$866$		0			0
$867$	14.3350	−	69.2058i	0.486843	−	2.35035i
$868$		0			0
$869$	30.4598	+	22.1303i	1.03328	+	0.750719i
$870$		0			0
$871$	2.47976	−	1.80165i	0.0840234	−	0.0610466i
$872$		0			0
$873$	−2.45892	−	6.21213i	−0.0832218	−	0.210249i
$874$		0			0
$875$	38.5654	+	23.0056i	1.30375	+	0.777730i
$876$		0			0
$877$	22.3043	−	43.7747i	0.753163	−	1.47817i	−0.121062	−	0.992645i	$-0.538630\pi$
$877$	22.3043	−	43.7747i	0.753163	−	1.47817i	0.874225	−	0.485521i	$-0.161370\pi$
$878$		0			0
$879$	−24.9447	+	6.82292i	−0.841365	+	0.230131i
$880$		0			0
$881$	−6.95200	+	9.56861i	−0.234219	+	0.322375i	−0.909907	−	0.414813i	$-0.863847\pi$
$881$	−6.95200	+	9.56861i	−0.234219	+	0.322375i	0.675688	+	0.737188i	$0.263847\pi$
$882$		0			0
$883$	−20.9091	+	3.31167i	−0.703647	+	0.111447i	−0.497997	−	0.867179i	$-0.665931\pi$
$883$	−20.9091	+	3.31167i	−0.703647	+	0.111447i	−0.205650	+	0.978626i	$0.565931\pi$
$884$		0			0
$885$	28.4231	+	26.4818i	0.955431	+	0.890177i
$886$		0			0
$887$	−12.0304	−	23.6111i	−0.403943	−	0.792782i	0.596005	−	0.802981i	$-0.296754\pi$
$887$	−12.0304	−	23.6111i	−0.403943	−	0.792782i	−0.999948	+	0.0101983i	$0.996754\pi$
$888$		0			0
$889$	−73.9756	+	24.0361i	−2.48106	+	0.806146i
$890$		0			0
$891$	8.36958	−	43.8325i	0.280392	−	1.46844i
$892$		0			0
$893$	−25.0145	−	25.0145i	−0.837077	−	0.837077i
$894$		0			0
$895$	−3.66977	+	3.15956i	−0.122667	+	0.105613i
$896$		0			0
$897$	0.120555	−	0.211334i	0.00402522	−	0.00705623i
$898$		0			0
$899$	2.86850			0.0956698
$900$		0			0
$901$	−63.2640			−2.10763
$902$		0			0
$903$	−12.0153	+	21.0628i	−0.399843	+	0.700927i
$904$		0			0
$905$	1.15028	+	0.698625i	0.0382366	+	0.0232231i
$906$		0			0
$907$	24.4142	+	24.4142i	0.810659	+	0.810659i	0.984733	−	0.174073i	$-0.0556929\pi$
$907$	24.4142	+	24.4142i	0.810659	+	0.810659i	−0.174073	+	0.984733i	$0.555693\pi$
$908$		0			0
$909$	32.5001	−	19.2166i	1.07796	−	0.637375i
$910$		0			0
$911$	−29.3166	+	9.52554i	−0.971303	+	0.315595i	−0.751342	−	0.659913i	$-0.770593\pi$
$911$	−29.3166	+	9.52554i	−0.971303	+	0.315595i	−0.219961	+	0.975509i	$0.570593\pi$
$912$		0			0
$913$	−14.7574	−	28.9630i	−0.488397	−	0.958534i
$914$		0			0
$915$	−37.3644	−	4.57127i	−1.23523	−	0.151121i
$916$		0			0
$917$	−13.2548	+	2.09936i	−0.437713	+	0.0693269i
$918$		0			0
$919$	−15.8783	+	21.8546i	−0.523777	+	0.720918i	−0.986166	−	0.165760i	$-0.946992\pi$
$919$	−15.8783	+	21.8546i	−0.523777	+	0.720918i	0.462389	+	0.886677i	$0.346992\pi$
$920$		0			0
$921$	40.9439	−	11.1990i	1.34915	−	0.369020i
$922$		0			0
$923$	0.403669	−	0.792245i	0.0132869	−	0.0260771i
$924$		0			0
$925$	19.4910	−	14.3989i	0.640862	−	0.473434i
$926$		0			0
$927$	−3.76648	+	1.49087i	−0.123707	+	0.0489665i
$928$		0			0
$929$	8.85751	−	6.43535i	0.290605	−	0.211137i	−0.432925	−	0.901430i	$-0.642518\pi$
$929$	8.85751	−	6.43535i	0.290605	−	0.211137i	0.723530	+	0.690293i	$0.242518\pi$
$930$		0			0
$931$	33.7776	+	24.5409i	1.10702	+	0.804295i
$932$		0			0
$933$	1.60831	−	7.76451i	0.0526538	−	0.254198i
$934$		0			0
$935$	71.6967	−	44.3283i	2.34473	−	1.44969i
$936$		0			0
$937$	8.29377	−	4.22589i	0.270946	−	0.138054i	−0.313239	−	0.949674i	$-0.601414\pi$
$937$	8.29377	−	4.22589i	0.270946	−	0.138054i	0.584185	+	0.811620i	$0.301414\pi$
$938$		0			0
$939$	−15.2609	−	0.720365i	−0.498020	−	0.0235082i
$940$		0			0
$941$	−16.5696	−	5.38379i	−0.540153	−	0.175506i	0.0262187	−	0.999656i	$-0.491653\pi$
$941$	−16.5696	−	5.38379i	−0.540153	−	0.175506i	−0.566372	+	0.824150i	$0.691653\pi$
$942$		0			0
$943$	1.42772	−	1.42772i	0.0464931	−	0.0464931i
$944$		0			0
$945$	−36.0719	−	29.6089i	−1.17342	−	0.963177i
$946$		0			0
$947$	4.45223	−	28.1103i	0.144678	−	0.913462i	−0.803403	−	0.595435i	$-0.796980\pi$
$947$	4.45223	−	28.1103i	0.144678	−	0.913462i	0.948082	−	0.318027i	$-0.103020\pi$
$948$		0			0
$949$		−	5.94063i		−	0.192841i
$950$		0			0
$951$	10.7344	−	28.4038i	0.348086	−	0.921058i
$952$		0			0
$953$	−10.3056	−	1.63224i	−0.333830	−	0.0528735i	−0.0127306	−	0.999919i	$-0.504052\pi$
$953$	−10.3056	−	1.63224i	−0.333830	−	0.0528735i	−0.321099	+	0.947045i	$0.604052\pi$
$954$		0			0
$955$	−46.0319	−	10.8582i	−1.48956	−	0.351362i
$956$		0			0
$957$	−3.65352	−	8.09261i	−0.118101	−	0.261597i
$958$		0			0
$959$	2.96106	−	9.11321i	0.0956177	−	0.294281i
$960$		0			0
$961$	−7.20085	−	22.1619i	−0.232286	−	0.714901i
$962$		0			0
$963$	10.3173	+	2.65001i	0.332471	+	0.0853955i
$964$		0			0
$965$	−1.07370	+	1.26729i	−0.0345635	+	0.0407955i
$966$		0			0
$967$	3.51292	+	22.1797i	0.112968	+	0.713251i	0.977541	+	0.210744i	$0.0675887\pi$
$967$	3.51292	+	22.1797i	0.112968	+	0.713251i	−0.864573	+	0.502507i	$0.832411\pi$
$968$		0			0
$969$	−33.0514	−	50.3209i	−1.06177	−	1.61654i
$970$		0			0
$971$	11.1728	+	15.3781i	0.358554	+	0.493507i	0.949745	−	0.313025i	$-0.101342\pi$
$971$	11.1728	+	15.3781i	0.358554	+	0.493507i	−0.591191	+	0.806531i	$0.701342\pi$
$972$		0			0
$973$	6.12821	+	3.12248i	0.196461	+	0.100102i
$974$		0			0
$975$	−3.56980	+	0.422667i	−0.114325	+	0.0135362i
$976$		0			0
$977$	19.9407	+	10.1603i	0.637958	+	0.325056i	0.742880	−	0.669425i	$-0.233459\pi$
$977$	19.9407	+	10.1603i	0.637958	+	0.325056i	−0.104922	+	0.994480i	$0.533459\pi$
$978$		0			0
$979$	38.9630	+	53.6280i	1.24526	+	1.71396i
$980$		0			0
$981$	7.43951	+	33.2964i	0.237525	+	1.06307i
$982$		0			0
$983$	−0.682136	−	4.30684i	−0.0217568	−	0.137367i	0.974419	−	0.224739i	$-0.0721530\pi$
$983$	−0.682136	−	4.30684i	−0.0217568	−	0.137367i	−0.996176	+	0.0873723i	$0.972153\pi$
$984$		0			0
$985$	0.404980	−	5.42084i	0.0129037	−	0.172722i
$986$		0			0
$987$	5.90464	+	53.5054i	0.187947	+	1.70310i
$988$		0			0
$989$	0.364513	+	1.12185i	0.0115908	+	0.0356729i
$990$		0			0
$991$	−16.7179	+	51.4526i	−0.531063	+	1.63444i	0.220942	+	0.975287i	$0.429087\pi$
$991$	−16.7179	+	51.4526i	−0.531063	+	1.63444i	−0.752005	+	0.659157i	$0.770913\pi$
$992$		0			0
$993$	24.8512	−	11.2194i	0.788628	−	0.356037i
$994$		0			0
$995$	−4.91204	−	59.3973i	−0.155722	−	1.88302i
$996$		0			0
$997$	−5.05321	−	0.800350i	−0.160037	−	0.0253473i	0.0759018	−	0.997115i	$-0.475816\pi$
$997$	−5.05321	−	0.800350i	−0.160037	−	0.0253473i	−0.235939	+	0.971768i	$0.575816\pi$
$998$		0			0
$999$	−22.2579	+	11.7811i	−0.704208	+	0.372739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.17.7	yes	80
3.2	odd	2	inner	300.2.x.a.17.5	✓	80
25.3	odd	20	inner	300.2.x.a.53.5	yes	80
75.53	even	20	inner	300.2.x.a.53.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.5	✓	80	3.2	odd	2	inner
300.2.x.a.17.7	yes	80	1.1	even	1	trivial
300.2.x.a.53.5	yes	80	25.3	odd	20	inner
300.2.x.a.53.7	yes	80	75.53	even	20	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.858227 - 1.50448i) q^{3} +(-2.22846 + 0.184289i) q^{5} +(-2.84010 - 2.84010i) q^{7} +(-1.52689 - 2.58236i) q^{9} +O(q^{10})\)	\(q+(0.858227 - 1.50448i) q^{3} +(-2.22846 + 0.184289i) q^{5} +(-2.84010 - 2.84010i) q^{7} +(-1.52689 - 2.58236i) q^{9} +(-4.71560 + 1.53219i) q^{11} +(-0.188444 - 0.369843i) q^{13} +(-1.63527 + 3.51083i) q^{15} +(7.50930 - 1.18936i) q^{17} +(2.68725 - 3.69868i) q^{19} +(-6.71031 + 1.83541i) q^{21} +(-0.153636 + 0.301528i) q^{23} +(4.93208 - 0.821362i) q^{25} +(-5.19552 + 0.0809244i) q^{27} +(-0.836442 + 0.607711i) q^{29} +(-2.24457 - 1.63078i) q^{31} +(-1.74191 + 8.40946i) q^{33} +(6.85245 + 5.80565i) q^{35} +(4.31832 - 2.20029i) q^{37} +(-0.718148 - 0.0338990i) q^{39} +(-5.67438 - 1.84372i) q^{41} +(2.46472 - 2.46472i) q^{43} +(3.87853 + 5.47330i) q^{45} +(1.21046 - 7.64252i) q^{47} +9.13235i q^{49} +(4.65532 - 12.3183i) q^{51} +(-8.21858 - 1.30170i) q^{53} +(10.2262 - 4.28346i) q^{55} +(-3.25831 - 7.21721i) q^{57} +(3.09959 - 9.53955i) q^{59} +(3.00345 + 9.24368i) q^{61} +(-2.99763 + 11.6707i) q^{63} +(0.488099 + 0.789452i) q^{65} +(1.15518 + 7.29349i) q^{67} +(0.321787 + 0.489922i) q^{69} +(1.25910 + 1.73301i) q^{71} +(12.7520 + 6.49745i) q^{73} +(2.99712 - 8.12510i) q^{75} +(17.7443 + 9.04119i) q^{77} +(-4.46331 - 6.14322i) q^{79} +(-4.33719 + 7.88599i) q^{81} +(1.02557 + 6.47518i) q^{83} +(-16.5150 + 4.03432i) q^{85} +(0.196429 + 1.77996i) q^{87} +(-4.13129 - 12.7148i) q^{89} +(-0.515190 + 1.58559i) q^{91} +(-4.37982 + 1.97733i) q^{93} +(-5.30680 + 8.73760i) q^{95} +(2.19961 + 0.348384i) q^{97} +(11.1569 + 9.83788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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