LMFDB - Embedded newform 300.2.x.a.53.7

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			53.7
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.7

$q$-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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

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	−0.0763784	+	0.997079i	$0.524336\pi$
$7$	−2.84010	+	2.84010i	−1.07346	+	1.07346i	−0.997079	+	0.0763784i	$0.975664\pi$
$8$		0			0
$9$	−1.52689	+	2.58236i	−0.508965	+	0.860787i
$10$		0			0
$11$	−4.71560	−	1.53219i	−1.42181	−	0.461973i	−0.505630	−	0.862750i	$-0.668740\pi$
$11$	−4.71560	−	1.53219i	−1.42181	−	0.461973i	−0.916175	+	0.400778i	$0.868740\pi$
$12$		0			0
$13$	−0.188444	+	0.369843i	−0.0522651	+	0.102576i	−0.915662	−	0.401950i	$-0.868333\pi$
$13$	−0.188444	+	0.369843i	−0.0522651	+	0.102576i	0.863397	+	0.504526i	$0.168333\pi$
$14$		0			0
$15$	−1.63527	−	3.51083i	−0.422224	−	0.906492i
$16$		0			0
$17$	7.50930	+	1.18936i	1.82127	+	0.288461i	0.971211	−	0.238222i	$-0.0765645\pi$
$17$	7.50930	+	1.18936i	1.82127	+	0.288461i	0.850062	+	0.526683i	$0.176564\pi$
$18$		0			0
$19$	2.68725	+	3.69868i	0.616497	+	0.848536i	0.997092	−	0.0762063i	$-0.0242808\pi$
$19$	2.68725	+	3.69868i	0.616497	+	0.848536i	−0.380595	+	0.924742i	$0.624281\pi$
$20$		0			0
$21$	−6.71031	−	1.83541i	−1.46431	−	0.400520i
$22$		0			0
$23$	−0.153636	−	0.301528i	−0.0320354	−	0.0628730i	0.874434	−	0.485144i	$-0.161233\pi$
$23$	−0.153636	−	0.301528i	−0.0320354	−	0.0628730i	−0.906469	+	0.422271i	$0.861233\pi$
$24$		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	0.507409	−	0.861705i	$-0.330603\pi$
$29$	−0.836442	−	0.607711i	−0.155323	−	0.112849i	−0.662732	+	0.748856i	$0.730603\pi$
$30$		0			0
$31$	−2.24457	+	1.63078i	−0.403138	+	0.292897i	−0.770818	−	0.637056i	$-0.780152\pi$
$31$	−2.24457	+	1.63078i	−0.403138	+	0.292897i	0.367680	+	0.929952i	$0.380152\pi$
$32$		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	0.771372	−	0.636384i	$-0.219571\pi$
$37$	4.31832	+	2.20029i	0.709928	+	0.361726i	−0.0614445	+	0.998111i	$0.519571\pi$
$38$		0			0
$39$	−0.718148	+	0.0338990i	−0.114996	+	0.00542818i
$40$		0			0
$41$	−5.67438	+	1.84372i	−0.886189	+	0.287940i	−0.716525	−	0.697562i	$-0.754268\pi$
$41$	−5.67438	+	1.84372i	−0.886189	+	0.287940i	−0.169664	+	0.985502i	$0.554268\pi$
$42$		0			0
$43$	2.46472	+	2.46472i	0.375866	+	0.375866i	0.869608	−	0.493742i	$-0.164371\pi$
$43$	2.46472	+	2.46472i	0.375866	+	0.375866i	−0.493742	+	0.869608i	$0.664371\pi$
$44$		0			0
$45$	3.87853	−	5.47330i	0.578177	−	0.815912i
$46$		0			0
$47$	1.21046	+	7.64252i	0.176563	+	1.11478i	0.903663	+	0.428245i	$0.140868\pi$
$47$	1.21046	+	7.64252i	0.176563	+	1.11478i	−0.727100	+	0.686532i	$0.759132\pi$
$48$		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	−0.692826	−	0.721105i	$-0.743635\pi$
$53$	−8.21858	+	1.30170i	−1.12891	+	0.178802i	−0.436083	+	0.899906i	$0.643635\pi$
$54$		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	0.922115	+	0.386917i	$0.126460\pi$
$59$	3.09959	+	9.53955i	0.403532	+	1.24194i	−0.518583	+	0.855028i	$0.673540\pi$
$60$		0			0
$61$	3.00345	−	9.24368i	0.384553	−	1.18353i	−0.552251	−	0.833678i	$-0.686231\pi$
$61$	3.00345	−	9.24368i	0.384553	−	1.18353i	0.936804	−	0.349855i	$-0.113769\pi$
$62$		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	−0.810935	−	0.585136i	$-0.801041\pi$
$67$	1.15518	−	7.29349i	0.141127	−	0.891041i	0.952062	−	0.305905i	$-0.0989590\pi$
$68$		0			0
$69$	0.321787	−	0.489922i	0.0387387	−	0.0589797i
$70$		0			0
$71$	1.25910	−	1.73301i	0.149428	−	0.205670i	−0.727741	−	0.685852i	$-0.759430\pi$
$71$	1.25910	−	1.73301i	0.149428	−	0.205670i	0.877169	+	0.480182i	$0.159430\pi$
$72$		0			0
$73$	12.7520	−	6.49745i	1.49250	−	0.760469i	0.498201	−	0.867061i	$-0.333994\pi$
$73$	12.7520	−	6.49745i	1.49250	−	0.760469i	0.994303	+	0.106592i	$0.0339940\pi$
$74$		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	−0.982573	−	0.185877i	$-0.940487\pi$
$79$	−4.46331	+	6.14322i	−0.502162	+	0.691166i	0.480411	+	0.877043i	$0.340487\pi$
$80$		0			0
$81$	−4.33719	−	7.88599i	−0.481910	−	0.876221i
$82$		0			0
$83$	1.02557	−	6.47518i	0.112571	−	0.710743i	−0.865256	−	0.501329i	$-0.832844\pi$
$83$	1.02557	−	6.47518i	0.112571	−	0.710743i	0.977827	−	0.209414i	$-0.0671555\pi$
$84$		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	0.452153	+	0.891941i	$0.350656\pi$
$89$	−4.13129	+	12.7148i	−0.437916	+	1.34777i	−0.890069	+	0.455826i	$0.849344\pi$
$90$		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	−0.0437632	−	0.999042i	$-0.513935\pi$
$97$	2.19961	−	0.348384i	0.223337	−	0.0353730i	0.267100	+	0.963669i	$0.413935\pi$
$98$		0			0
$99$	11.1569	−	9.83788i	1.12131	−	0.988744i
$100$		0			0
$101$		−	12.5854i		−	1.25230i	−0.779704	−	0.626149i	$-0.784630\pi$
$101$		−	12.5854i		−	1.25230i	0.779704	−	0.626149i	$-0.215370\pi$
$102$		0			0
$103$	0.211229	+	1.33365i	0.0208130	+	0.131408i	0.995907	−	0.0903839i	$-0.0288094\pi$
$103$	0.211229	+	1.33365i	0.0208130	+	0.131408i	−0.975094	+	0.221792i	$0.928809\pi$
$104$		0			0
$105$	14.6154	+	5.32678i	1.42632	+	0.519841i
$106$		0			0
$107$	−2.51075	−	2.51075i	−0.242723	−	0.242723i	0.575253	−	0.817976i	$-0.304904\pi$
$107$	−2.51075	−	2.51075i	−0.242723	−	0.242723i	−0.817976	+	0.575253i	$0.804904\pi$
$108$		0			0
$109$	−10.8158	+	3.51428i	−1.03597	+	0.336607i	−0.777148	−	0.629318i	$-0.783334\pi$
$109$	−10.8158	+	3.51428i	−1.03597	+	0.336607i	−0.258822	+	0.965925i	$0.583334\pi$
$110$		0			0
$111$	0.395808	+	8.38516i	0.0375684	+	0.795884i
$112$		0			0
$113$	6.91215	+	3.52192i	0.650240	+	0.331314i	0.747808	−	0.663915i	$-0.231106\pi$
$113$	6.91215	+	3.52192i	0.650240	+	0.331314i	−0.0975678	+	0.995229i	$0.531106\pi$
$114$		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	0.845928	+	0.533297i	$0.179047\pi$
$127$	8.79185	+	17.2550i	0.780151	+	1.53113i	−0.0657772	+	0.997834i	$0.520953\pi$
$128$		0			0
$129$	−1.59282	+	5.82340i	−0.140240	+	0.512722i
$130$		0			0
$131$	1.96392	+	2.70310i	0.171588	+	0.236171i	0.886147	−	0.463405i	$-0.153372\pi$
$131$	1.96392	+	2.70310i	0.171588	+	0.236171i	−0.714558	+	0.699576i	$0.753372\pi$
$132$		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	−0.840100	−	0.542431i	$-0.817504\pi$
$137$	1.08309	−	2.12568i	0.0925343	−	0.181609i	0.932635	+	0.360822i	$0.117504\pi$
$138$		0			0
$139$	−1.62858	−	0.529159i	−0.138135	−	0.0448827i	0.239134	−	0.970987i	$-0.423137\pi$
$139$	−1.62858	−	0.529159i	−0.138135	−	0.0448827i	−0.377268	+	0.926104i	$0.623137\pi$
$140$		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	−0.837725	−	0.546092i	$-0.816115\pi$
$157$	−3.65415	+	3.65415i	−0.291633	+	0.291633i	0.546092	+	0.837725i	$0.316115\pi$
$158$		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	−0.814300	−	0.580444i	$-0.802879\pi$
$163$	1.70981	−	3.35569i	0.133923	−	0.262838i	0.948223	+	0.317606i	$0.102879\pi$
$164$		0			0
$165$	2.33200	+	19.0612i	0.181546	+	1.48391i
$166$		0			0
$167$	3.33491	+	0.528199i	0.258063	+	0.0408732i	0.284126	−	0.958787i	$-0.408297\pi$
$167$	3.33491	+	0.528199i	0.258063	+	0.0408732i	−0.0260621	+	0.999660i	$0.508297\pi$
$168$		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	1.00000		0.000736755i	$0.000234516\pi$
$173$	5.42968	+	10.6563i	0.412811	+	0.810187i	−0.587189	+	0.809450i	$0.699765\pi$
$174$		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	0.651334	−	0.758791i	$-0.274210\pi$
$179$	1.75204	+	1.27293i	0.130954	+	0.0951434i	−0.520380	+	0.853935i	$0.674210\pi$
$180$		0			0
$181$	−0.486921	+	0.353769i	−0.0361925	+	0.0262954i	−0.605734	−	0.795667i	$-0.707121\pi$
$181$	−0.486921	+	0.353769i	−0.0361925	+	0.0262954i	0.569542	+	0.821962i	$0.307121\pi$
$182$		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	0.528829	−	0.848728i	$-0.322631\pi$
$191$	20.1158	−	6.53603i	1.45553	−	0.472931i	0.926702	+	0.375798i	$0.122631\pi$
$192$		0			0
$193$	0.525247	+	0.525247i	0.0378081	+	0.0378081i	0.725758	−	0.687950i	$-0.241489\pi$
$193$	0.525247	+	0.525247i	0.0378081	+	0.0378081i	−0.687950	+	0.725758i	$0.741489\pi$
$194$		0			0
$195$	1.60661	+	0.0568042i	0.115052	+	0.00406784i
$196$		0			0
$197$	−0.380297	−	2.40110i	−0.0270950	−	0.171071i	0.970430	−	0.241382i	$-0.0776008\pi$
$197$	−0.380297	−	2.40110i	−0.0270950	−	0.171071i	−0.997525	+	0.0703111i	$0.977601\pi$
$198$		0			0
$199$		−	26.6540i		−	1.88945i	−0.327865	−	0.944725i	$-0.606329\pi$
$199$		−	26.6540i		−	1.88945i	0.327865	−	0.944725i	$-0.393671\pi$
$200$		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	−0.999679	−	0.0253480i	$-0.991931\pi$
$211$	−2.55687	+	7.86925i	−0.176022	+	0.541741i	0.823656	+	0.567089i	$0.191931\pi$
$212$		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	−0.791513	−	0.611153i	$-0.790706\pi$
$223$	−11.3838	+	5.80036i	−0.762319	+	0.388421i	0.0291937	+	0.999574i	$0.490706\pi$
$224$		0			0
$225$	−9.65181	+	11.4823i	−0.643454	+	0.765485i
$226$		0			0
$227$	−21.6298	+	11.0209i	−1.43562	+	0.731484i	−0.986770	−	0.162124i	$-0.948165\pi$
$227$	−21.6298	+	11.0209i	−1.43562	+	0.731484i	−0.448848	+	0.893608i	$0.648165\pi$
$228$		0			0
$229$	4.36425	−	6.00687i	0.288398	−	0.396945i	−0.640095	−	0.768296i	$-0.721105\pi$
$229$	4.36425	−	6.00687i	0.288398	−	0.396945i	0.928493	+	0.371350i	$0.121105\pi$
$230$		0			0
$231$	28.8309	+	18.9365i	1.89694	+	1.24593i
$232$		0			0
$233$	−2.77715	+	17.5342i	−0.181937	+	1.14871i	0.712553	+	0.701618i	$0.247539\pi$
$233$	−2.77715	+	17.5342i	−0.181937	+	1.14871i	−0.894490	+	0.447087i	$0.852461\pi$
$234$		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	−0.943529	−	0.331290i	$-0.892516\pi$
$239$	0.224620	−	0.691308i	0.0145294	−	0.0447170i	0.958058	+	0.286573i	$0.0925161\pi$
$240$		0			0
$241$	−4.44165	−	13.6700i	−0.286112	−	0.880561i	−0.986063	−	0.166371i	$-0.946795\pi$
$241$	−4.44165	−	13.6700i	−0.286112	−	0.880561i	0.699951	−	0.714190i	$-0.253205\pi$
$242$		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	$-0.890594\pi$
$251$		−	10.6776i		−	0.673961i	0.941512	−	0.336981i	$-0.109406\pi$
$252$		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	0.934934	−	0.354822i	$-0.115459\pi$
$257$	9.29989	+	9.29989i	0.580111	+	0.580111i	−0.354822	+	0.934934i	$0.615459\pi$
$258$		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	0.985322	−	0.170704i	$-0.0546042\pi$
$263$	23.1320	+	11.7863i	1.42638	+	0.726776i	0.441055	+	0.897480i	$0.354604\pi$
$264$		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	−0.0872901	−	0.996183i	$-0.527821\pi$
$269$	13.6649	−	9.92811i	0.833162	−	0.605328i	0.920452	+	0.390855i	$0.127821\pi$
$270$		0			0
$271$	12.7884	+	9.29128i	0.776837	+	0.564405i	0.904028	−	0.427473i	$-0.140596\pi$
$271$	12.7884	+	9.29128i	0.776837	+	0.564405i	−0.127191	+	0.991878i	$0.540596\pi$
$272$		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	0.997631	+	0.0687889i	$0.0219135\pi$
$277$	7.77059	+	15.2506i	0.466890	+	0.916323i	−0.530742	+	0.847534i	$0.678087\pi$
$278$		0			0
$279$	−0.784033	−	8.28633i	−0.0469388	−	0.496090i
$280$		0			0
$281$	−16.0338	−	22.0687i	−0.956499	−	1.31651i	−0.948580	−	0.316539i	$-0.897479\pi$
$281$	−16.0338	−	22.0687i	−0.956499	−	1.31651i	−0.00791912	−	0.999969i	$-0.502521\pi$
$282$		0			0
$283$	−3.01460	−	0.477465i	−0.179199	−	0.0283824i	0.0661898	−	0.997807i	$-0.478916\pi$
$283$	−3.01460	−	0.477465i	−0.179199	−	0.0283824i	−0.245389	+	0.969425i	$0.578916\pi$
$284$		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	−0.944706	−	0.327918i	$-0.893653\pi$
$293$	−10.5577	+	10.5577i	−0.616788	+	0.616788i	0.327918	+	0.944706i	$0.393653\pi$
$294$		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	−0.0109073	−	0.999941i	$-0.503472\pi$
$307$	17.3293	−	17.3293i	0.989033	−	0.989033i	0.999941	+	0.0109073i	$0.00347197\pi$
$308$		0			0
$309$	−1.82516	+	1.46236i	−0.103830	+	0.0831907i
$310$		0			0
$311$	4.35394	+	1.41468i	0.246889	+	0.0802191i	0.429847	−	0.902902i	$-0.358567\pi$
$311$	4.35394	+	1.41468i	0.246889	+	0.0802191i	−0.182958	+	0.983121i	$0.558567\pi$
$312$		0			0
$313$	−4.00451	+	7.85929i	−0.226348	+	0.444233i	−0.976051	−	0.217541i	$-0.930196\pi$
$313$	−4.00451	+	7.85929i	−0.226348	+	0.444233i	0.749703	+	0.661774i	$0.230196\pi$
$314$		0			0
$315$	4.52933	+	26.5601i	0.255199	+	1.49649i
$316$		0			0
$317$	17.3151	+	2.74245i	0.972515	+	0.154031i	0.622420	−	0.782683i	$-0.286149\pi$
$317$	17.3151	+	2.74245i	0.972515	+	0.154031i	0.350095	+	0.936714i	$0.386149\pi$
$318$		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	−0.179918	−	0.983682i	$-0.557583\pi$
$331$	12.7358	−	9.25307i	0.700020	−	0.508595i	0.879939	+	0.475087i	$0.157583\pi$
$332$		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	0.546203	−	0.837653i	$-0.316073\pi$
$337$	3.48017	+	1.77323i	0.189577	+	0.0965942i	−0.356626	+	0.934247i	$0.616073\pi$
$338$		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	0.966905	−	0.255138i	$-0.0821208\pi$
$347$	−0.587119	−	3.70692i	−0.0315182	−	0.198998i	−0.998423	+	0.0561397i	$0.982121\pi$
$348$		0			0
$349$		−	12.9374i		−	0.692525i	−0.938138	−	0.346262i	$-0.887451\pi$
$349$		−	12.9374i		−	0.692525i	0.938138	−	0.346262i	$-0.112549\pi$
$350$		0			0
$351$	1.00900	−	1.90628i	0.0538562	−	0.101750i
$352$		0			0
$353$	26.1583	−	4.14307i	1.39227	−	0.220513i	0.585159	−	0.810919i	$-0.301032\pi$
$353$	26.1583	−	4.14307i	1.39227	−	0.220513i	0.807107	+	0.590405i	$0.201032\pi$
$354$		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	0.982543	−	0.186033i	$-0.0595631\pi$
$359$	1.48360	+	4.56607i	0.0783016	+	0.240988i	−0.904242	+	0.427021i	$0.859563\pi$
$360$		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	−0.595782	−	0.803146i	$-0.703158\pi$
$367$	4.19594	−	26.4921i	0.219026	−	1.38288i	0.814808	−	0.579731i	$-0.196842\pi$
$368$		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	−0.375170	−	0.926956i	$-0.622416\pi$
$373$	2.97876	−	1.51776i	0.154234	−	0.0785864i	0.529404	+	0.848370i	$0.322416\pi$
$374$		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	−0.845260	−	0.534355i	$-0.820555\pi$
$379$	−1.47681	+	2.03266i	−0.0758588	+	0.104411i	0.769401	+	0.638766i	$0.220555\pi$
$380$		0			0
$381$	−18.4143	+	28.0358i	−0.943393	+	1.43632i
$382$		0			0
$383$	−1.45004	+	9.15521i	−0.0740938	+	0.467810i	0.922545	+	0.385889i	$0.126105\pi$
$383$	−1.45004	+	9.15521i	−0.0740938	+	0.467810i	−0.996639	+	0.0819203i	$0.973895\pi$
$384$		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	−0.820798	−	0.571218i	$-0.806471\pi$
$389$	3.53033	−	10.8652i	0.178995	−	0.550890i	0.999793	+	0.0203282i	$0.00647113\pi$
$390$		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	−0.394468	−	0.918910i	$-0.629071\pi$
$397$	−9.67691	+	1.53267i	−0.485670	+	0.0769226i	−0.0912023	+	0.995832i	$0.529071\pi$
$398$		0			0
$399$	−11.2437	−	29.7515i	−0.562888	−	1.48944i
$400$		0			0
$401$			27.1537i			1.35599i	0.735066	+	0.677996i	$0.237151\pi$
$401$			27.1537i			1.35599i	−0.735066	+	0.677996i	$0.762849\pi$
$402$		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	−0.936250	−	0.351335i	$-0.885728\pi$
$409$	−30.0764	+	9.77241i	−1.48718	+	0.483215i	−0.550932	+	0.834550i	$0.685728\pi$
$410$		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	−0.213310	−	0.976985i	$-0.568424\pi$
$419$	13.3040	−	9.66590i	0.649941	−	0.472210i	0.863251	+	0.504775i	$0.168424\pi$
$420$		0			0
$421$	11.1129	+	8.07400i	0.541610	+	0.393503i	0.824683	−	0.565596i	$-0.191354\pi$
$421$	11.1129	+	8.07400i	0.541610	+	0.393503i	−0.283073	+	0.959098i	$0.591354\pi$
$422$		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	0.739638	−	0.673005i	$-0.234997\pi$
$431$	−2.67787	−	3.68577i	−0.128989	−	0.177537i	−0.868626	+	0.495468i	$0.834997\pi$
$432$		0			0
$433$	21.2003	+	3.35781i	1.01882	+	0.161366i	0.643434	−	0.765501i	$-0.277509\pi$
$433$	21.2003	+	3.35781i	1.01882	+	0.161366i	0.375389	+	0.926867i	$0.377509\pi$
$434$		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	0.549071	−	0.835776i	$-0.314982\pi$
$439$	10.5185	+	3.41768i	0.502022	+	0.163117i	−0.0470490	+	0.998893i	$0.514982\pi$
$440$		0			0
$441$	23.5830	+	13.9441i	1.12300	+	0.664006i
$442$		0			0
$443$	−11.3624	+	11.3624i	−0.539846	+	0.539846i	−0.923484	−	0.383638i	$-0.874671\pi$
$443$	−11.3624	+	11.3624i	−0.539846	+	0.539846i	0.383638	+	0.923484i	$0.374671\pi$
$444$		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	−0.978943	−	0.204136i	$-0.934562\pi$
$457$	−16.5635	+	16.5635i	−0.774807	+	0.774807i	0.204136	+	0.978943i	$0.434562\pi$
$458$		0			0
$459$	−38.9185	−	6.78701i	−1.81656	−	0.316791i
$460$		0			0
$461$	14.5158	+	4.71648i	0.676070	+	0.219669i	0.626874	−	0.779121i	$-0.284334\pi$
$461$	14.5158	+	4.71648i	0.676070	+	0.219669i	0.0491963	+	0.998789i	$0.484334\pi$
$462$		0			0
$463$	−1.93184	+	3.79146i	−0.0897804	+	0.176204i	−0.931530	−	0.363664i	$-0.881526\pi$
$463$	−1.93184	+	3.79146i	−0.0897804	+	0.176204i	0.841750	+	0.539868i	$0.181526\pi$
$464$		0			0
$465$	9.39586	+	5.21356i	0.435723	+	0.241773i
$466$		0			0
$467$	−30.6114	−	4.84837i	−1.41653	−	0.224356i	−0.599233	−	0.800575i	$-0.704528\pi$
$467$	−30.6114	−	4.84837i	−1.41653	−	0.224356i	−0.817295	+	0.576219i	$0.804528\pi$
$468$		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	0.978254	−	0.207409i	$-0.0665032\pi$
$479$	23.7090	+	17.2256i	1.08329	+	0.787059i	0.105039	+	0.994468i	$0.466503\pi$
$480$		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	0.821128	−	0.570744i	$-0.193345\pi$
$487$	18.5821	+	9.46803i	0.842033	+	0.429037i	0.0209053	+	0.999781i	$0.493345\pi$
$488$		0			0
$489$	6.51596	−	0.307575i	0.294662	−	0.0139090i
$490$		0			0
$491$	−8.67143	+	2.81752i	−0.391336	+	0.127153i	−0.498074	−	0.867134i	$-0.665959\pi$
$491$	−8.67143	+	2.81752i	−0.391336	+	0.127153i	0.106738	+	0.994287i	$0.465959\pi$
$492$		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	$0.0696729\pi$
$499$			9.70109i			0.434280i	−0.976140	+	0.217140i	$0.930327\pi$
$500$		0			0
$501$	2.06745	+	5.47061i	0.0923669	+	0.244409i
$502$		0			0
$503$	−8.01914	+	1.27011i	−0.357556	+	0.0566313i	−0.332628	−	0.943058i	$-0.607935\pi$
$503$	−8.01914	+	1.27011i	−0.357556	+	0.0566313i	−0.0249274	+	0.999689i	$0.507935\pi$
$504$		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	−0.815863	−	0.578245i	$-0.803738\pi$
$509$	−11.1835	−	34.4193i	−0.495700	−	1.52561i	0.320163	−	0.947362i	$-0.396262\pi$
$510$		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	−0.544930	−	0.838481i	$-0.683444\pi$
$521$	9.60734	−	13.2234i	0.420905	−	0.579326i	0.965836	+	0.259155i	$0.0834440\pi$
$522$		0			0
$523$	−9.11004	+	4.64180i	−0.398354	+	0.202972i	−0.641679	−	0.766973i	$-0.721762\pi$
$523$	−9.11004	+	4.64180i	−0.398354	+	0.202972i	0.243325	+	0.969945i	$0.421762\pi$
$524$		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	0.997383	+	0.0723059i	$0.0230358\pi$
$541$	5.41906	+	16.6781i	0.232983	+	0.717049i	−0.764399	+	0.644743i	$0.776964\pi$
$542$		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	0.195395	−	0.980725i	$-0.437401\pi$
$547$	16.0041	−	2.53481i	0.684288	−	0.108381i	0.488893	+	0.872344i	$0.337401\pi$
$548$		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	0.714512	−	0.699623i	$-0.246649\pi$
$557$	0.351406	+	0.351406i	0.0148895	+	0.0148895i	−0.699623	+	0.714512i	$0.746649\pi$
$558$		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	0.643890	−	0.765118i	$-0.277320\pi$
$563$	9.57089	+	4.87661i	0.403365	+	0.205525i	−0.240525	+	0.970643i	$0.577320\pi$
$564$		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	−0.462484	+	0.886628i	$0.653042\pi$
$569$	−34.5553	+	25.1059i	−1.44863	+	1.05249i	−0.986148	+	0.165865i	$0.946958\pi$
$570$		0			0
$571$	−37.4429	−	27.2039i	−1.56694	−	1.13845i	−0.930017	−	0.367517i	$-0.880208\pi$
$571$	−37.4429	−	27.2039i	−1.56694	−	1.13845i	−0.636920	−	0.770930i	$-0.719792\pi$
$572$		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	0.800042	−	0.599944i	$-0.204811\pi$
$577$	−3.73707	−	7.33441i	−0.155576	−	0.305335i	−0.955618	+	0.294609i	$0.904811\pi$
$578$		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	−0.872006	−	0.489495i	$-0.837181\pi$
$587$	0.885671	−	1.73823i	0.0365556	−	0.0717444i	0.908562	+	0.417750i	$0.137181\pi$
$588$		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	0.0863319	−	0.996266i	$-0.472485\pi$
$593$	26.3630	−	26.3630i	1.08260	−	1.08260i	0.996266	−	0.0863319i	$-0.0275146\pi$
$594$		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	−0.950412	−	0.310994i	$-0.899338\pi$
$607$	−15.7536	+	15.7536i	−0.639418	+	0.639418i	0.310994	+	0.950412i	$0.399338\pi$
$608$		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	−0.988405	−	0.151843i	$-0.951479\pi$
$613$	−7.04615	+	13.8288i	−0.284591	+	0.558542i	0.703813	+	0.710385i	$0.251479\pi$
$614$		0			0
$615$	15.7521	+	16.9068i	0.635186	+	0.681748i
$616$		0			0
$617$	30.2739	+	4.79492i	1.21878	+	0.193036i	0.732501	−	0.680766i	$-0.238353\pi$
$617$	30.2739	+	4.79492i	1.21878	+	0.193036i	0.486282	+	0.873802i	$0.338353\pi$
$618$		0			0
$619$	−24.7268	−	34.0335i	−0.993852	−	1.36792i	−0.929022	−	0.370024i	$-0.879350\pi$
$619$	−24.7268	−	34.0335i	−0.993852	−	1.36792i	−0.0648299	−	0.997896i	$-0.520650\pi$
$620$		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	0.414834	−	0.909897i	$-0.363840\pi$
$631$	35.3783	−	25.7038i	1.40839	−	1.02325i	0.993554	−	0.113357i	$-0.0361603\pi$
$632$		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	−0.980284	−	0.197593i	$-0.936687\pi$
$641$	−41.9572	+	13.6327i	−1.65721	+	0.538460i	−0.676924	+	0.736053i	$0.736687\pi$
$642$		0			0
$643$	−21.6567	−	21.6567i	−0.854057	−	0.854057i	0.136573	−	0.990630i	$-0.456391\pi$
$643$	−21.6567	−	21.6567i	−0.854057	−	0.854057i	−0.990630	+	0.136573i	$0.956391\pi$
$644$		0			0
$645$	4.62274	−	12.6837i	0.182020	−	0.499420i
$646$		0			0
$647$	−4.83284	−	30.5133i	−0.189998	−	1.19960i	−0.879707	−	0.475516i	$-0.842261\pi$
$647$	−4.83284	−	30.5133i	−0.189998	−	1.19960i	0.689709	−	0.724087i	$-0.257739\pi$
$648$		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	0.451497	−	0.892272i	$-0.350890\pi$
$653$	29.5562	−	4.68124i	1.15662	−	0.183191i	0.705127	+	0.709081i	$0.250890\pi$
$654$		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	0.994594	−	0.103845i	$-0.0331145\pi$
$659$	3.30930	+	10.1850i	0.128912	+	0.396750i	−0.865682	+	0.500595i	$0.833115\pi$
$660$		0			0
$661$	8.67556	−	26.7006i	0.337440	−	1.03853i	−0.628067	−	0.778159i	$-0.716154\pi$
$661$	8.67556	−	26.7006i	0.337440	−	1.03853i	0.965507	−	0.260375i	$-0.0838463\pi$
$662$		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	−0.836831	−	0.547461i	$-0.815594\pi$
$673$	−22.9797	+	11.7087i	−0.885803	+	0.451339i	−0.0489715	+	0.998800i	$0.515594\pi$
$674$		0			0
$675$	−25.5582	−	4.66653i	−0.983737	−	0.179615i
$676$		0			0
$677$	−3.98966	+	2.03283i	−0.153335	+	0.0781281i	−0.528974	−	0.848638i	$-0.677423\pi$
$677$	−3.98966	+	2.03283i	−0.153335	+	0.0781281i	0.375639	+	0.926766i	$0.377423\pi$
$678$		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	0.731297	+	0.682059i	$0.238915\pi$
$683$	−4.57286	+	28.8719i	−0.174976	+	1.10475i	−0.906273	+	0.422693i	$0.861085\pi$
$684$		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	−0.983701	−	0.179810i	$-0.942452\pi$
$691$	−7.71677	−	23.7498i	−0.293560	−	0.903484i	0.690141	−	0.723674i	$-0.257548\pi$
$692$		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	$0.0415257\pi$
$701$			6.88847i			0.260174i	−0.991503	+	0.130087i	$0.958474\pi$
$702$		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	−0.370607	−	0.928790i	$-0.620850\pi$
$709$	−3.31523	+	1.07719i	−0.124506	+	0.0404545i	0.246101	+	0.969244i	$0.420850\pi$
$710$		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	−0.317592	−	0.948228i	$-0.602874\pi$
$719$	13.0340	−	9.46973i	0.486085	−	0.353161i	0.803677	+	0.595066i	$0.202874\pi$
$720$		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	0.997754	+	0.0669890i	$0.0213392\pi$
$727$	12.5508	+	24.6324i	0.465484	+	0.913564i	−0.532270	+	0.846575i	$0.678661\pi$
$728$		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	0.507974	−	0.861372i	$-0.330395\pi$
$733$	19.6261	+	3.10847i	0.724907	+	0.114814i	0.216933	+	0.976186i	$0.430395\pi$
$734$		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	0.935048	−	0.354522i	$-0.115356\pi$
$739$	40.3184	+	13.1002i	1.48313	+	0.481900i	0.548087	+	0.836421i	$0.315356\pi$
$740$		0			0
$741$	−2.05522	−	2.56510i	−0.0755005	−	0.0942314i
$742$		0			0
$743$	27.1592	−	27.1592i	0.996375	−	0.996375i	−0.00361798	−	0.999993i	$-0.501152\pi$
$743$	27.1592	−	27.1592i	0.996375	−	0.996375i	0.999993	+	0.00361798i	$0.00115164\pi$
$744$		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	−0.372230	−	0.928141i	$-0.621407\pi$
$757$	15.2951	−	15.2951i	0.555911	−	0.555911i	0.928141	+	0.372230i	$0.121407\pi$
$758$		0			0
$759$	−2.26807	+	1.81723i	−0.0823258	+	0.0659614i
$760$		0			0
$761$	−10.8598	−	3.52857i	−0.393669	−	0.127911i	0.105492	−	0.994420i	$-0.466358\pi$
$761$	−10.8598	−	3.52857i	−0.393669	−	0.127911i	−0.499161	+	0.866509i	$0.666358\pi$
$762$		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	0.980661	−	0.195714i	$-0.0627025\pi$
$769$	13.6293	+	18.7591i	0.491485	+	0.676471i	−0.489176	+	0.872185i	$0.662702\pi$
$770$		0			0
$771$	−6.01005	+	21.9729i	−0.216447	+	0.791334i
$772$		0			0
$773$	−15.7994	−	31.0081i	−0.568265	−	1.11528i	−0.979063	−	0.203556i	$-0.934750\pi$
$773$	−15.7994	−	31.0081i	−0.568265	−	1.11528i	0.410799	−	0.911726i	$-0.365250\pi$
$774$		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	−0.392718	−	0.919659i	$-0.628465\pi$
$787$	−38.3652	−	19.5480i	−1.36757	−	0.696812i	−0.974854	+	0.222847i	$0.928465\pi$
$788$		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	0.875976	+	0.482354i	$0.160218\pi$
$797$	5.41838	+	34.2103i	0.191929	+	1.21179i	−0.684047	+	0.729438i	$0.739782\pi$
$798$		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	0.986817	−	0.161838i	$-0.0517422\pi$
$809$	2.65484	+	8.17077i	0.0933393	+	0.287269i	−0.893478	+	0.449107i	$0.851742\pi$
$810$		0			0
$811$	−6.69438	+	20.6032i	−0.235072	+	0.723476i	0.762040	+	0.647530i	$0.224198\pi$
$811$	−6.69438	+	20.6032i	−0.235072	+	0.723476i	−0.997112	+	0.0759463i	$0.975802\pi$
$812$		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	0.0333736	+	0.999443i	$0.489375\pi$
$821$	−26.5748	+	36.5770i	−0.927466	+	1.27655i	−0.960840	+	0.277105i	$0.910625\pi$
$822$		0			0
$823$	−2.87584	+	1.46531i	−0.100245	+	0.0510776i	−0.503394	−	0.864057i	$-0.667916\pi$
$823$	−2.87584	+	1.46531i	−0.100245	+	0.0510776i	0.403149	+	0.915134i	$0.367916\pi$
$824$		0			0
$825$	−1.68400	−	42.9068i	−0.0586292	−	1.49382i
$826$		0			0
$827$	18.7516	−	9.55443i	0.652058	−	0.332240i	−0.0964773	−	0.995335i	$-0.530758\pi$
$827$	18.7516	−	9.55443i	0.652058	−	0.332240i	0.748535	+	0.663095i	$0.230758\pi$
$828$		0			0
$829$	−32.8299	+	45.1864i	−1.14023	+	1.56939i	−0.373232	+	0.927738i	$0.621750\pi$
$829$	−32.8299	+	45.1864i	−1.14023	+	1.56939i	−0.766997	+	0.641651i	$0.778250\pi$
$830$		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	−0.697391	−	0.716691i	$-0.745656\pi$
$839$	8.34410	−	25.6805i	0.288070	−	0.886590i	0.985461	−	0.169899i	$-0.0543441\pi$
$840$		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	−0.967904	−	0.251320i	$-0.919135\pi$
$853$	−3.65179	−	23.0565i	−0.125035	−	0.789439i	0.842869	−	0.538119i	$-0.180865\pi$
$854$		0			0
$855$	30.6666	−	0.362696i	1.04877	−	0.0124039i
$856$		0			0
$857$	−23.9274	−	23.9274i	−0.817343	−	0.817343i	0.168379	−	0.985722i	$-0.446147\pi$
$857$	−23.9274	−	23.9274i	−0.817343	−	0.817343i	−0.985722	+	0.168379i	$0.946147\pi$
$858$		0			0
$859$	12.3998	−	4.02894i	0.423076	−	0.137466i	−0.0897381	−	0.995965i	$-0.528603\pi$
$859$	12.3998	−	4.02894i	0.423076	−	0.137466i	0.512814	+	0.858500i	$0.328603\pi$
$860$		0			0
$861$	41.4609	−	1.95709i	1.41298	−	0.0666975i
$862$		0			0
$863$	−48.0446	−	24.4799i	−1.63546	−	0.833307i	−0.998026	−	0.0627991i	$-0.979997\pi$
$863$	−48.0446	−	24.4799i	−1.63546	−	0.833307i	−0.637431	−	0.770508i	$-0.720003\pi$
$864$		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	0.874225	+	0.485521i	$0.161370\pi$
$877$	22.3043	+	43.7747i	0.753163	+	1.47817i	−0.121062	+	0.992645i	$0.538630\pi$
$878$		0			0
$879$	−24.9447	−	6.82292i	−0.841365	−	0.230131i
$880$		0			0
$881$	−6.95200	−	9.56861i	−0.234219	−	0.322375i	0.675688	−	0.737188i	$-0.263847\pi$
$881$	−6.95200	−	9.56861i	−0.234219	−	0.322375i	−0.909907	+	0.414813i	$0.863847\pi$
$882$		0			0
$883$	−20.9091	−	3.31167i	−0.703647	−	0.111447i	−0.205650	−	0.978626i	$-0.565931\pi$
$883$	−20.9091	−	3.31167i	−0.703647	−	0.111447i	−0.497997	+	0.867179i	$0.665931\pi$
$884$		0			0
$885$	28.4231	−	26.4818i	0.955431	−	0.890177i
$886$		0			0
$887$	−12.0304	+	23.6111i	−0.403943	+	0.792782i	−0.999948	−	0.0101983i	$-0.996754\pi$
$887$	−12.0304	+	23.6111i	−0.403943	+	0.792782i	0.596005	+	0.802981i	$0.296754\pi$
$888$		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	−0.174073	−	0.984733i	$-0.555693\pi$
$907$	24.4142	−	24.4142i	0.810659	−	0.810659i	0.984733	+	0.174073i	$0.0556929\pi$
$908$		0			0
$909$	32.5001	+	19.2166i	1.07796	+	0.637375i
$910$		0			0
$911$	−29.3166	−	9.52554i	−0.971303	−	0.315595i	−0.219961	−	0.975509i	$-0.570593\pi$
$911$	−29.3166	−	9.52554i	−0.971303	−	0.315595i	−0.751342	+	0.659913i	$0.770593\pi$
$912$		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	0.462389	−	0.886677i	$-0.346992\pi$
$919$	−15.8783	−	21.8546i	−0.523777	−	0.720918i	−0.986166	+	0.165760i	$0.946992\pi$
$920$		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	0.723530	−	0.690293i	$-0.242518\pi$
$929$	8.85751	+	6.43535i	0.290605	+	0.211137i	−0.432925	+	0.901430i	$0.642518\pi$
$930$		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	0.584185	−	0.811620i	$-0.301414\pi$
$937$	8.29377	+	4.22589i	0.270946	+	0.138054i	−0.313239	+	0.949674i	$0.601414\pi$
$938$		0			0
$939$	−15.2609	+	0.720365i	−0.498020	+	0.0235082i
$940$		0			0
$941$	−16.5696	+	5.38379i	−0.540153	+	0.175506i	−0.566372	−	0.824150i	$-0.691653\pi$
$941$	−16.5696	+	5.38379i	−0.540153	+	0.175506i	0.0262187	+	0.999656i	$0.491653\pi$
$942$		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	0.948082	+	0.318027i	$0.103020\pi$
$947$	4.45223	+	28.1103i	0.144678	+	0.913462i	−0.803403	+	0.595435i	$0.796980\pi$
$948$		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	−0.321099	−	0.947045i	$-0.604052\pi$
$953$	−10.3056	+	1.63224i	−0.333830	+	0.0528735i	−0.0127306	+	0.999919i	$0.504052\pi$
$954$		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	−0.864573	−	0.502507i	$-0.832411\pi$
$967$	3.51292	−	22.1797i	0.112968	−	0.713251i	0.977541	−	0.210744i	$-0.0675887\pi$
$968$		0			0
$969$	−33.0514	+	50.3209i	−1.06177	+	1.61654i
$970$		0			0
$971$	11.1728	−	15.3781i	0.358554	−	0.493507i	−0.591191	−	0.806531i	$-0.701342\pi$
$971$	11.1728	−	15.3781i	0.358554	−	0.493507i	0.949745	+	0.313025i	$0.101342\pi$
$972$		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	−0.104922	−	0.994480i	$-0.533459\pi$
$977$	19.9407	−	10.1603i	0.637958	−	0.325056i	0.742880	+	0.669425i	$0.233459\pi$
$978$		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	−0.996176	−	0.0873723i	$-0.972153\pi$
$983$	−0.682136	+	4.30684i	−0.0217568	+	0.137367i	0.974419	+	0.224739i	$0.0721530\pi$
$984$		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	−0.752005	−	0.659157i	$-0.770913\pi$
$991$	−16.7179	−	51.4526i	−0.531063	−	1.63444i	0.220942	−	0.975287i	$-0.429087\pi$
$992$		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	−0.235939	−	0.971768i	$-0.575816\pi$
$997$	−5.05321	+	0.800350i	−0.160037	+	0.0253473i	0.0759018	+	0.997115i	$0.475816\pi$
$998$		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.53.7	yes	80
3.2	odd	2	inner	300.2.x.a.53.5	yes	80
25.17	odd	20	inner	300.2.x.a.17.5	✓	80
75.17	even	20	inner	300.2.x.a.17.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.5	✓	80	25.17	odd	20	inner
300.2.x.a.17.7	yes	80	75.17	even	20	inner
300.2.x.a.53.5	yes	80	3.2	odd	2	inner
300.2.x.a.53.7	yes	80	1.1	even	1	trivial

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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