LMFDB - Embedded newform 592.2.be.e.399.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 885 x^{16} + 9292 x^{14} + 58264 x^{12} + 224256 x^{10} + 523884 x^{8} + 706272 x^{6} + \cdots + 144 $ x^20 + 46x^18 + 885x^16 + 9292x^14 + 58264x^12 + 224256x^10 + 523884x^8 + 706272x^6 + 490896x^4 + 133632*x^2 + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			399.5
Root			$-1.78239i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.e.319.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891195 - 1.54359i) q^{3} +(0.343889 + 1.28341i) q^{5} +(-3.85429 - 2.22528i) q^{7} +(-0.0884563 - 0.153211i) q^{9} +O(q^{10})$	\(q+(0.891195 - 1.54359i) q^{3} +(0.343889 + 1.28341i) q^{5} +(-3.85429 - 2.22528i) q^{7} +(-0.0884563 - 0.153211i) q^{9} -5.75028 q^{11} +(-1.47388 - 5.50060i) q^{13} +(2.28754 + 0.612945i) q^{15} +(-2.89105 - 0.774655i) q^{17} +(2.87151 - 0.769419i) q^{19} +(-6.86985 + 3.96631i) q^{21} +(-5.07450 - 5.07450i) q^{23} +(2.80124 - 1.61730i) q^{25} +5.03184 q^{27} +(0.304192 + 0.304192i) q^{29} +(3.58445 - 3.58445i) q^{31} +(-5.12462 + 8.87609i) q^{33} +(1.53050 - 5.71189i) q^{35} +(2.86110 + 5.36788i) q^{37} +(-9.80421 - 2.62703i) q^{39} +(2.70605 + 1.56234i) q^{41} +(4.11786 + 4.11786i) q^{43} +(0.166213 - 0.166213i) q^{45} +3.97717i q^{47} +(6.40371 + 11.0916i) q^{49} +(-3.77225 + 3.77225i) q^{51} +(-7.17253 - 12.4232i) q^{53} +(-1.97746 - 7.37997i) q^{55} +(1.37140 - 5.11815i) q^{57} +(-1.58812 + 5.92696i) q^{59} +(-14.9646 + 4.00976i) q^{61} +0.787359i q^{63} +(6.55269 - 3.78319i) q^{65} +(2.83868 - 4.91673i) q^{67} +(-12.3553 + 3.31060i) q^{69} +(7.69199 + 4.44097i) q^{71} -4.42802i q^{73} -5.76530i q^{75} +(22.1632 + 12.7960i) q^{77} +(5.98922 - 1.60481i) q^{79} +(4.74972 - 8.22676i) q^{81} +(-9.97206 + 5.75737i) q^{83} -3.97681i q^{85} +(0.740642 - 0.198455i) q^{87} +(-0.876996 + 3.27299i) q^{89} +(-6.55959 + 24.4807i) q^{91} +(-2.33850 - 8.72739i) q^{93} +(1.97496 + 3.42074i) q^{95} +(7.07937 - 7.07937i) q^{97} +(0.508648 + 0.881004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	$ 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.891195	−	1.54359i	0.514532	−	0.891195i	−0.485326	−	0.874333i	$-0.661299\pi$
$3$	0.891195	−	1.54359i	0.514532	−	0.891195i	0.999858	−	0.0168617i	$-0.00536749\pi$
$4$		0			0
$5$	0.343889	+	1.28341i	0.153792	+	0.573959i	0.999206	+	0.0398476i	$0.0126872\pi$
$5$	0.343889	+	1.28341i	0.153792	+	0.573959i	−0.845414	+	0.534112i	$0.820646\pi$
$6$		0			0
$7$	−3.85429	−	2.22528i	−1.45679	−	0.841075i	−0.457934	−	0.888986i	$-0.651410\pi$
$7$	−3.85429	−	2.22528i	−1.45679	−	0.841075i	−0.998852	+	0.0479108i	$0.984744\pi$
$8$		0			0
$9$	−0.0884563	−	0.153211i	−0.0294854	−	0.0510703i
$10$		0			0
$11$	−5.75028			−1.73377			−0.866887	−	0.498505i	$-0.833882\pi$
$11$	−5.75028			−1.73377			−0.866887	+	0.498505i	$0.833882\pi$
$12$		0			0
$13$	−1.47388	−	5.50060i	−0.408781	−	1.52559i	−0.796974	−	0.604014i	$-0.793567\pi$
$13$	−1.47388	−	5.50060i	−0.408781	−	1.52559i	0.388193	−	0.921578i	$-0.373099\pi$
$14$		0			0
$15$	2.28754	+	0.612945i	0.590640	+	0.158262i
$16$		0			0
$17$	−2.89105	−	0.774655i	−0.701183	−	0.187882i	−0.109423	−	0.993995i	$-0.534900\pi$
$17$	−2.89105	−	0.774655i	−0.701183	−	0.187882i	−0.591761	+	0.806114i	$0.701567\pi$
$18$		0			0
$19$	2.87151	−	0.769419i	0.658770	−	0.176517i	0.0860790	−	0.996288i	$-0.472566\pi$
$19$	2.87151	−	0.769419i	0.658770	−	0.176517i	0.572691	+	0.819771i	$0.305900\pi$
$20$		0			0
$21$	−6.86985	+	3.96631i	−1.49912	+	0.865520i
$22$		0			0
$23$	−5.07450	−	5.07450i	−1.05811	−	1.05811i	−0.998204	−	0.0599019i	$-0.980921\pi$
$23$	−5.07450	−	5.07450i	−1.05811	−	1.05811i	−0.0599019	−	0.998204i	$-0.519079\pi$
$24$		0			0
$25$	2.80124	−	1.61730i	0.560248	−	0.323459i
$26$		0			0
$27$	5.03184			0.968378
$28$		0			0
$29$	0.304192	+	0.304192i	0.0564870	+	0.0564870i	0.734786	−	0.678299i	$-0.237283\pi$
$29$	0.304192	+	0.304192i	0.0564870	+	0.0564870i	−0.678299	+	0.734786i	$0.737283\pi$
$30$		0			0
$31$	3.58445	−	3.58445i	0.643787	−	0.643787i	−0.307698	−	0.951484i	$-0.599559\pi$
$31$	3.58445	−	3.58445i	0.643787	−	0.643787i	0.951484	+	0.307698i	$0.0995585\pi$
$32$		0			0
$33$	−5.12462	+	8.87609i	−0.892081	+	1.54513i
$34$		0			0
$35$	1.53050	−	5.71189i	0.258701	−	0.965486i
$36$		0			0
$37$	2.86110	+	5.36788i	0.470362	+	0.882474i
$37$	2.86110	+	5.36788i	0.470362	+	0.882474i
$38$		0			0
$39$	−9.80421	−	2.62703i	−1.56993	−	0.420662i
$40$		0			0
$41$	2.70605	+	1.56234i	0.422614	+	0.243996i	0.696195	−	0.717853i	$-0.254875\pi$
$41$	2.70605	+	1.56234i	0.422614	+	0.243996i	−0.273581	+	0.961849i	$0.588208\pi$
$42$		0			0
$43$	4.11786	+	4.11786i	0.627967	+	0.627967i	0.947556	−	0.319589i	$-0.103545\pi$
$43$	4.11786	+	4.11786i	0.627967	+	0.627967i	−0.319589	+	0.947556i	$0.603545\pi$
$44$		0			0
$45$	0.166213	−	0.166213i	0.0247776	−	0.0247776i
$46$		0			0
$47$			3.97717i			0.580131i	0.957007	+	0.290065i	$0.0936770\pi$
$47$			3.97717i			0.580131i	−0.957007	+	0.290065i	$0.906323\pi$
$48$		0			0
$49$	6.40371	+	11.0916i	0.914816	+	1.58451i
$50$		0			0
$51$	−3.77225	+	3.77225i	−0.528220	+	0.528220i
$52$		0			0
$53$	−7.17253	−	12.4232i	−0.985222	−	1.70646i	−0.640944	−	0.767588i	$-0.721457\pi$
$53$	−7.17253	−	12.4232i	−0.985222	−	1.70646i	−0.344279	−	0.938867i	$-0.611877\pi$
$54$		0			0
$55$	−1.97746	−	7.37997i	−0.266640	−	0.995115i
$56$		0			0
$57$	1.37140	−	5.11815i	0.181647	−	0.677916i
$58$		0			0
$59$	−1.58812	+	5.92696i	−0.206756	+	0.771624i	0.782151	+	0.623089i	$0.214122\pi$
$59$	−1.58812	+	5.92696i	−0.206756	+	0.771624i	−0.988907	+	0.148535i	$0.952544\pi$
$60$		0			0
$61$	−14.9646	+	4.00976i	−1.91602	+	0.513397i	−0.924946	+	0.380098i	$0.875890\pi$
$61$	−14.9646	+	4.00976i	−1.91602	+	0.513397i	−0.991076	+	0.133298i	$0.957443\pi$
$62$		0			0
$63$			0.787359i			0.0991979i
$64$		0			0
$65$	6.55269	−	3.78319i	0.812761	−	0.469248i
$66$		0			0
$67$	2.83868	−	4.91673i	0.346800	−	0.600674i	−0.638879	−	0.769307i	$-0.720602\pi$
$67$	2.83868	−	4.91673i	0.346800	−	0.600674i	0.985679	+	0.168632i	$0.0539351\pi$
$68$		0			0
$69$	−12.3553	+	3.31060i	−1.48741	+	0.398550i
$70$		0			0
$71$	7.69199	+	4.44097i	0.912871	+	0.527046i	0.881354	−	0.472457i	$-0.156633\pi$
$71$	7.69199	+	4.44097i	0.912871	+	0.527046i	0.0315174	+	0.999503i	$0.489966\pi$
$72$		0			0
$73$		−	4.42802i		−	0.518260i	−0.965842	−	0.259130i	$-0.916564\pi$
$73$		−	4.42802i		−	0.518260i	0.965842	−	0.259130i	$-0.0834358\pi$
$74$		0			0
$75$		−	5.76530i		−	0.665720i
$76$		0			0
$77$	22.1632	+	12.7960i	2.52574	+	1.45823i
$78$		0			0
$79$	5.98922	−	1.60481i	0.673840	−	0.180555i	0.0943559	−	0.995539i	$-0.469921\pi$
$79$	5.98922	−	1.60481i	0.673840	−	0.180555i	0.579484	+	0.814984i	$0.303254\pi$
$80$		0			0
$81$	4.74972	−	8.22676i	0.527747	−	0.914084i
$82$		0			0
$83$	−9.97206	+	5.75737i	−1.09458	+	0.631953i	−0.934791	−	0.355199i	$-0.884413\pi$
$83$	−9.97206	+	5.75737i	−1.09458	+	0.631953i	−0.159784	+	0.987152i	$0.551080\pi$
$84$		0			0
$85$		−	3.97681i		−	0.431346i
$86$		0			0
$87$	0.740642	−	0.198455i	0.0794052	−	0.0212766i
$88$		0			0
$89$	−0.876996	+	3.27299i	−0.0929614	+	0.346937i	−0.996702	−	0.0811429i	$-0.974143\pi$
$89$	−0.876996	+	3.27299i	−0.0929614	+	0.346937i	0.903741	+	0.428079i	$0.140810\pi$
$90$		0			0
$91$	−6.55959	+	24.4807i	−0.687632	+	2.56628i
$92$		0			0
$93$	−2.33850	−	8.72739i	−0.242491	−	0.904988i
$94$		0			0
$95$	1.97496	+	3.42074i	0.202627	+	0.350960i
$96$		0			0
$97$	7.07937	−	7.07937i	0.718801	−	0.718801i	−0.249559	−	0.968360i	$-0.580286\pi$
$97$	7.07937	−	7.07937i	0.718801	−	0.718801i	0.968360	+	0.249559i	$0.0802856\pi$
$98$		0			0
$99$	0.508648	+	0.881004i	0.0511211	+	0.0885443i
$100$		0			0
$101$		−	2.17180i		−	0.216102i	−0.994145	−	0.108051i	$-0.965539\pi$
$101$		−	2.17180i		−	0.216102i	0.994145	−	0.108051i	$-0.0344610\pi$
$102$		0			0
$103$	4.29476	−	4.29476i	0.423175	−	0.423175i	−0.463120	−	0.886295i	$-0.653270\pi$
$103$	4.29476	−	4.29476i	0.423175	−	0.423175i	0.886295	+	0.463120i	$0.153270\pi$
$104$		0			0
$105$	−7.45288	−	7.45288i	−0.727326	−	0.727326i
$106$		0			0
$107$	−11.7842	−	6.80360i	−1.13922	−	0.657729i	−0.192982	−	0.981202i	$-0.561816\pi$
$107$	−11.7842	−	6.80360i	−1.13922	−	0.657729i	−0.946237	+	0.323474i	$0.895149\pi$
$108$		0			0
$109$	−2.29946	−	0.616138i	−0.220248	−	0.0590153i	0.147007	−	0.989135i	$-0.453036\pi$
$109$	−2.29946	−	0.616138i	−0.220248	−	0.0590153i	−0.367256	+	0.930120i	$0.619703\pi$
$110$		0			0
$111$	10.8356	+	0.367447i	1.02847	+	0.0348766i
$112$		0			0
$113$	3.30311	−	12.3274i	0.310730	−	1.15966i	−0.617169	−	0.786831i	$-0.711720\pi$
$113$	3.30311	−	12.3274i	0.310730	−	1.15966i	0.927899	−	0.372831i	$-0.121613\pi$
$114$		0			0
$115$	4.76761	−	8.25774i	0.444582	−	0.770038i
$116$		0			0
$117$	−0.712377	+	0.712377i	−0.0658593	+	0.0658593i
$118$		0			0
$119$	9.41914	+	9.41914i	0.863451	+	0.863451i
$120$		0			0
$121$	22.0657			2.00597
$122$		0			0
$123$	4.82323	−	2.78469i	0.434896	−	0.251087i
$124$		0			0
$125$	7.73659	+	7.73659i	0.691982	+	0.691982i
$126$		0			0
$127$	−5.92133	+	3.41868i	−0.525433	+	0.303359i	−0.739155	−	0.673536i	$-0.764775\pi$
$127$	−5.92133	+	3.41868i	−0.525433	+	0.303359i	0.213722	+	0.976895i	$0.431441\pi$
$128$		0			0
$129$	10.0261	−	2.68649i	0.882750	−	0.236532i
$130$		0			0
$131$	0.205986	+	0.0551937i	0.0179971	+	0.00482230i	0.267806	−	0.963473i	$-0.413701\pi$
$131$	0.205986	+	0.0551937i	0.0179971	+	0.00482230i	−0.249809	+	0.968295i	$0.580368\pi$
$132$		0			0
$133$	−12.7798	−	3.42434i	−1.10815	−	0.296928i
$134$		0			0
$135$	1.73040	+	6.45793i	0.148929	+	0.555810i
$136$		0			0
$137$	7.36907			0.629582			0.314791	−	0.949161i	$-0.398066\pi$
$137$	7.36907			0.629582			0.314791	+	0.949161i	$0.398066\pi$
$138$		0			0
$139$	−5.23736	−	9.07137i	−0.444227	−	0.769424i	0.553771	−	0.832669i	$-0.313188\pi$
$139$	−5.23736	−	9.07137i	−0.444227	−	0.769424i	−0.997998	+	0.0632453i	$0.979855\pi$
$140$		0			0
$141$	6.13915	+	3.54444i	0.517009	+	0.298495i
$142$		0			0
$143$	8.47522	+	31.6300i	0.708734	+	2.64503i
$144$		0			0
$145$	−0.285795	+	0.495011i	−0.0237340	+	0.0411085i
$146$		0			0
$147$	22.8278			1.88281
$148$		0			0
$149$	3.25770			0.266881			0.133441	−	0.991057i	$-0.457397\pi$
$149$	3.25770			0.266881			0.133441	+	0.991057i	$0.457397\pi$
$150$		0			0
$151$	7.29197	−	12.6301i	0.593412	−	1.02782i	−0.400357	−	0.916359i	$-0.631114\pi$
$151$	7.29197	−	12.6301i	0.593412	−	1.02782i	0.993769	−	0.111461i	$-0.0355529\pi$
$152$		0			0
$153$	0.137046	+	0.511464i	0.0110795	+	0.0413494i
$154$		0			0
$155$	5.83298	+	3.36768i	0.468517	+	0.270498i
$156$		0			0
$157$	−5.66746	−	9.81633i	−0.452313	−	0.783428i	0.546217	−	0.837644i	$-0.316067\pi$
$157$	−5.66746	−	9.81633i	−0.452313	−	0.783428i	−0.998529	+	0.0542156i	$0.982734\pi$
$158$		0			0
$159$	−25.5685			−2.02771
$160$		0			0
$161$	8.26644	+	30.8508i	0.651487	+	2.43138i
$162$		0			0
$163$	7.68231	+	2.05847i	0.601725	+	0.161232i	0.546806	−	0.837259i	$-0.315843\pi$
$163$	7.68231	+	2.05847i	0.601725	+	0.161232i	0.0549186	+	0.998491i	$0.482510\pi$
$164$		0			0
$165$	−13.1540	−	3.52460i	−1.02404	−	0.274390i
$166$		0			0
$167$	−2.01661	+	0.540349i	−0.156050	+	0.0418135i	−0.335998	−	0.941863i	$-0.609074\pi$
$167$	−2.01661	+	0.540349i	−0.156050	+	0.0418135i	0.179948	+	0.983676i	$0.442407\pi$
$168$		0			0
$169$	−16.8259	+	9.71446i	−1.29430	+	0.747266i
$170$		0			0
$171$	−0.371887	−	0.371887i	−0.0284389	−	0.0284389i
$172$		0			0
$173$	−2.49984	+	1.44329i	−0.190060	+	0.109731i	−0.592011	−	0.805930i	$-0.701666\pi$
$173$	−2.49984	+	1.44329i	−0.190060	+	0.109731i	0.401951	+	0.915661i	$0.368332\pi$
$174$		0			0
$175$	−14.3957			−1.08821
$176$		0			0
$177$	7.73349	+	7.73349i	0.581285	+	0.581285i
$178$		0			0
$179$	−4.37603	+	4.37603i	−0.327080	+	0.327080i	−0.851475	−	0.524395i	$-0.824291\pi$
$179$	−4.37603	+	4.37603i	−0.327080	+	0.327080i	0.524395	+	0.851475i	$0.324291\pi$
$180$		0			0
$181$	2.49638	−	4.32386i	0.185555	−	0.321390i	−0.758209	−	0.652012i	$-0.773925\pi$
$181$	2.49638	−	4.32386i	0.185555	−	0.321390i	0.943763	+	0.330622i	$0.107258\pi$
$182$		0			0
$183$	−7.14695	+	26.6728i	−0.528317	+	1.97171i
$184$		0			0
$185$	−5.90530	+	5.51793i	−0.434166	+	0.405686i
$186$		0			0
$187$	16.6244	+	4.45448i	1.21569	+	0.325744i
$188$		0			0
$189$	−19.3942	−	11.1972i	−1.41072	−	0.814479i
$190$		0			0
$191$	0.0361140	+	0.0361140i	0.00261312	+	0.00261312i	0.708412	−	0.705799i	$-0.249412\pi$
$191$	0.0361140	+	0.0361140i	0.00261312	+	0.00261312i	−0.705799	+	0.708412i	$0.749412\pi$
$192$		0			0
$193$	11.5037	−	11.5037i	0.828056	−	0.828056i	−0.159192	−	0.987248i	$-0.550889\pi$
$193$	11.5037	−	11.5037i	0.828056	−	0.828056i	0.987248	+	0.159192i	$0.0508888\pi$
$194$		0			0
$195$		−	13.4863i		−	0.965771i
$196$		0			0
$197$	5.77184	+	9.99711i	0.411226	+	0.712265i	0.995024	−	0.0996342i	$-0.0317673\pi$
$197$	5.77184	+	9.99711i	0.411226	+	0.712265i	−0.583798	+	0.811899i	$0.698434\pi$
$198$		0			0
$199$	−1.87340	+	1.87340i	−0.132802	+	0.132802i	−0.770383	−	0.637581i	$-0.779935\pi$
$199$	−1.87340	+	1.87340i	−0.132802	+	0.132802i	0.637581	+	0.770383i	$0.279935\pi$
$200$		0			0
$201$	−5.05963	−	8.76353i	−0.356879	−	0.618132i
$202$		0			0
$203$	−0.495533	−	1.84935i	−0.0347796	−	0.129799i
$204$		0			0
$205$	−1.07454	+	4.01025i	−0.0750493	+	0.280088i
$206$		0			0
$207$	−0.328597	+	1.22634i	−0.0228391	+	0.0852365i
$208$		0			0
$209$	−16.5120	+	4.42437i	−1.14216	+	0.306040i
$210$		0			0
$211$			1.86327i			0.128273i	0.997941	+	0.0641364i	$0.0204293\pi$
$211$			1.86327i			0.128273i	−0.997941	+	0.0641364i	$0.979571\pi$
$212$		0			0
$213$	13.7101	−	7.91554i	0.939402	−	0.542364i
$214$		0			0
$215$	−3.86882	+	6.70099i	−0.263851	+	0.457004i
$216$		0			0
$217$	−21.7919	+	5.83913i	−1.47933	+	0.396386i
$218$		0			0
$219$	−6.83506	−	3.94623i	−0.461871	−	0.266661i
$220$		0			0
$221$			17.0443i			1.14652i
$222$		0			0
$223$			1.91596i			0.128302i	0.997940	+	0.0641510i	$0.0204339\pi$
$223$			1.91596i			0.128302i	−0.997940	+	0.0641510i	$0.979566\pi$
$224$		0			0
$225$	−0.495575	−	0.286120i	−0.0330383	−	0.0190747i
$226$		0			0
$227$	−14.7173	+	3.94348i	−0.976819	+	0.261738i	−0.711704	−	0.702479i	$-0.752076\pi$
$227$	−14.7173	+	3.94348i	−0.976819	+	0.261738i	−0.265115	+	0.964217i	$0.585410\pi$
$228$		0			0
$229$	6.08674	−	10.5425i	0.402223	−	0.696671i	−0.591771	−	0.806106i	$-0.701571\pi$
$229$	6.08674	−	10.5425i	0.402223	−	0.696671i	0.993994	+	0.109435i	$0.0349043\pi$
$230$		0			0
$231$	39.5035	−	22.8074i	2.59914	−	1.50061i
$232$		0			0
$233$		−	25.1053i		−	1.64470i	−0.568981	−	0.822351i	$-0.692662\pi$
$233$		−	25.1053i		−	1.64470i	0.568981	−	0.822351i	$-0.307338\pi$
$234$		0			0
$235$	−5.10435	+	1.36771i	−0.332971	+	0.0892194i
$236$		0			0
$237$	2.86039	−	10.6751i	0.185802	−	0.693424i
$238$		0			0
$239$	4.94747	−	18.4642i	0.320025	−	1.19435i	−0.599194	−	0.800604i	$-0.704512\pi$
$239$	4.94747	−	18.4642i	0.320025	−	1.19435i	0.919219	−	0.393746i	$-0.128821\pi$
$240$		0			0
$241$	−3.59167	−	13.4043i	−0.231360	−	0.863445i	−0.979756	−	0.200194i	$-0.935843\pi$
$241$	−3.59167	−	13.4043i	−0.231360	−	0.863445i	0.748397	−	0.663251i	$-0.230824\pi$
$242$		0			0
$243$	−0.918089	−	1.59018i	−0.0588954	−	0.102010i
$244$		0			0
$245$	−12.0329	+	12.0329i	−0.768752	+	0.768752i
$246$		0			0
$247$	−8.46453	−	14.6610i	−0.538585	−	0.932857i
$248$		0			0
$249$			20.5238i			1.30064i
$250$		0			0
$251$	11.4447	−	11.4447i	0.722383	−	0.722383i	−0.246707	−	0.969090i	$-0.579348\pi$
$251$	11.4447	−	11.4447i	0.722383	−	0.722383i	0.969090	+	0.246707i	$0.0793485\pi$
$252$		0			0
$253$	29.1798	+	29.1798i	1.83452	+	1.83452i
$254$		0			0
$255$	−6.13858	−	3.54411i	−0.384413	−	0.221941i
$256$		0			0
$257$	12.1126	+	3.24557i	0.755564	+	0.202453i	0.615985	−	0.787758i	$-0.288758\pi$
$257$	12.1126	+	3.24557i	0.755564	+	0.202453i	0.139580	+	0.990211i	$0.455425\pi$
$258$		0			0
$259$	0.917501	−	27.0561i	0.0570107	−	1.68118i
$260$		0			0
$261$	0.0196978	−	0.0735131i	0.00121926	−	0.00455035i
$262$		0			0
$263$	−2.12917	+	3.68784i	−0.131290	+	0.227402i	−0.924174	−	0.381971i	$-0.875245\pi$
$263$	−2.12917	+	3.68784i	−0.131290	+	0.227402i	0.792884	+	0.609373i	$0.208579\pi$
$264$		0			0
$265$	13.4775	−	13.4775i	0.827917	−	0.827917i
$266$		0			0
$267$	4.27060	+	4.27060i	0.261356	+	0.261356i
$268$		0			0
$269$	−3.33345			−0.203244			−0.101622	−	0.994823i	$-0.532403\pi$
$269$	−3.33345			−0.203244			−0.101622	+	0.994823i	$0.532403\pi$
$270$		0			0
$271$	3.28446	−	1.89628i	0.199517	−	0.115191i	−0.396913	−	0.917856i	$-0.629919\pi$
$271$	3.28446	−	1.89628i	0.199517	−	0.115191i	0.596430	+	0.802665i	$0.296585\pi$
$272$		0			0
$273$	31.9424	+	31.9424i	1.93324	+	1.93324i
$274$		0			0
$275$	−16.1079	+	9.29990i	−0.971343	+	0.560805i
$276$		0			0
$277$	−29.9324	+	8.02035i	−1.79846	+	0.481896i	−0.993736	−	0.111751i	$-0.964354\pi$
$277$	−29.9324	+	8.02035i	−1.79846	+	0.481896i	−0.804725	+	0.593647i	$0.797688\pi$
$278$		0			0
$279$	−0.866244	−	0.232109i	−0.0518607	−	0.0138960i
$280$		0			0
$281$	3.74665	+	1.00391i	0.223506	+	0.0598883i	0.368834	−	0.929495i	$-0.379757\pi$
$281$	3.74665	+	1.00391i	0.223506	+	0.0598883i	−0.145328	+	0.989384i	$0.546424\pi$
$282$		0			0
$283$	−5.07167	−	18.9277i	−0.301480	−	1.12514i	−0.935933	−	0.352177i	$-0.885442\pi$
$283$	−5.07167	−	18.9277i	−0.301480	−	1.12514i	0.634454	−	0.772961i	$-0.281225\pi$
$284$		0			0
$285$	7.04031			0.417032
$286$		0			0
$287$	−6.95327	−	12.0434i	−0.410438	−	0.710900i
$288$		0			0
$289$	−6.96433	−	4.02086i	−0.409667	−	0.236521i
$290$		0			0
$291$	−4.61858	−	17.2368i	−0.270746	−	1.01044i
$292$		0			0
$293$	12.1600	−	21.0617i	0.710395	−	1.23044i	−0.254315	−	0.967122i	$-0.581850\pi$
$293$	12.1600	−	21.0617i	0.710395	−	1.23044i	0.964709	−	0.263318i	$-0.0848168\pi$
$294$		0			0
$295$	−8.15287			−0.474678
$296$		0			0
$297$	−28.9345			−1.67895
$298$		0			0
$299$	−20.4336	+	35.3920i	−1.18170	+	2.04677i
$300$		0			0
$301$	−6.70805	−	25.0348i	−0.386646	−	1.44298i
$302$		0			0
$303$	−3.35238	−	1.93549i	−0.192589	−	0.111191i
$304$		0			0
$305$	−10.2923	−	17.8269i	−0.589338	−	1.02076i
$306$		0			0
$307$	−11.5722			−0.660458			−0.330229	−	0.943901i	$-0.607126\pi$
$307$	−11.5722			−0.660458			−0.330229	+	0.943901i	$0.607126\pi$
$308$		0			0
$309$	−2.80190	−	10.4568i	−0.159394	−	0.594868i
$310$		0			0
$311$	−1.97355	−	0.528811i	−0.111910	−	0.0299861i	0.202430	−	0.979297i	$-0.435116\pi$
$311$	−1.97355	−	0.528811i	−0.111910	−	0.0299861i	−0.314339	+	0.949311i	$0.601783\pi$
$312$		0			0
$313$	−12.3992	−	3.32237i	−0.700846	−	0.187791i	−0.109237	−	0.994016i	$-0.534841\pi$
$313$	−12.3992	−	3.32237i	−0.700846	−	0.187791i	−0.591610	+	0.806225i	$0.701507\pi$
$314$		0			0
$315$	−1.01051	+	0.270764i	−0.0569356	+	0.0152558i
$316$		0			0
$317$	−5.40141	+	3.11850i	−0.303373	+	0.175153i	−0.643957	−	0.765061i	$-0.722709\pi$
$317$	−5.40141	+	3.11850i	−0.303373	+	0.175153i	0.340584	+	0.940214i	$0.389375\pi$
$318$		0			0
$319$	−1.74919	−	1.74919i	−0.0979356	−	0.0979356i
$320$		0			0
$321$	−21.0040	+	12.1267i	−1.17233	+	0.676844i
$322$		0			0
$323$	−8.89773			−0.495083
$324$		0			0
$325$	−13.0248	−	13.0248i	−0.722486	−	0.722486i
$326$		0			0
$327$	−3.00033	+	3.00033i	−0.165919	+	0.165919i
$328$		0			0
$329$	8.85031	−	15.3292i	0.487934	−	0.845126i
$330$		0			0
$331$	−1.44803	+	5.40414i	−0.0795912	+	0.297038i	−0.994235	−	0.107222i	$-0.965804\pi$
$331$	−1.44803	+	5.40414i	−0.0795912	+	0.297038i	0.914644	+	0.404260i	$0.132471\pi$
$332$		0			0
$333$	0.569335	−	0.913174i	0.0311993	−	0.0500416i
$334$		0			0
$335$	7.28639	+	1.95238i	0.398098	+	0.106670i
$336$		0			0
$337$	1.19071	+	0.687458i	0.0648622	+	0.0374482i	0.532080	−	0.846694i	$-0.321410\pi$
$337$	1.19071	+	0.687458i	0.0648622	+	0.0374482i	−0.467218	+	0.884142i	$0.654744\pi$
$338$		0			0
$339$	−16.0848	−	16.0848i	−0.873604	−	0.873604i
$340$		0			0
$341$	−20.6116	+	20.6116i	−1.11618	+	1.11618i
$342$		0			0
$343$		−	25.8462i		−	1.39557i
$344$		0			0
$345$	−8.49774	−	14.7185i	−0.457503	−	0.792418i
$346$		0			0
$347$	−1.28407	+	1.28407i	−0.0689327	+	0.0689327i	−0.740733	−	0.671800i	$-0.765521\pi$
$347$	−1.28407	+	1.28407i	−0.0689327	+	0.0689327i	0.671800	+	0.740733i	$0.265521\pi$
$348$		0			0
$349$	7.55773	+	13.0904i	0.404556	+	0.700711i	0.994270	−	0.106901i	$-0.0340928\pi$
$349$	7.55773	+	13.0904i	0.404556	+	0.700711i	−0.589714	+	0.807612i	$0.700759\pi$
$350$		0			0
$351$	−7.41634	−	27.6781i	−0.395855	−	1.47735i
$352$		0			0
$353$	0.734975	−	2.74297i	0.0391188	−	0.145993i	−0.943604	−	0.331076i	$-0.892588\pi$
$353$	0.734975	−	2.74297i	0.0391188	−	0.145993i	0.982723	+	0.185082i	$0.0592552\pi$
$354$		0			0
$355$	−3.05441	+	11.3992i	−0.162111	+	0.605007i
$356$		0			0
$357$	22.9336	−	6.14505i	1.21378	−	0.325230i
$358$		0			0
$359$		−	21.6598i		−	1.14316i	−0.820546	−	0.571581i	$-0.806330\pi$
$359$		−	21.6598i		−	1.14316i	0.820546	−	0.571581i	$-0.193670\pi$
$360$		0			0
$361$	−8.80091	+	5.08121i	−0.463206	+	0.267432i
$362$		0			0
$363$	19.6648	−	34.0604i	1.03213	−	1.78771i
$364$		0			0
$365$	5.68297	−	1.52275i	0.297460	−	0.0797042i
$366$		0			0
$367$	28.2628	+	16.3175i	1.47530	+	0.851767i	0.999612	−	0.0278447i	$-0.00886439\pi$
$367$	28.2628	+	16.3175i	1.47530	+	0.851767i	0.475692	+	0.879612i	$0.342198\pi$
$368$		0			0
$369$		−	0.552794i		−	0.0287773i
$370$		0			0
$371$			63.8434i			3.31459i
$372$		0			0
$373$	8.70367	+	5.02507i	0.450659	+	0.260188i	0.708109	−	0.706104i	$-0.249549\pi$
$373$	8.70367	+	5.02507i	0.450659	+	0.260188i	−0.257449	+	0.966292i	$0.582882\pi$
$374$		0			0
$375$	18.8370	−	5.04735i	0.972737	−	0.260644i
$376$		0			0
$377$	1.22489	−	2.12158i	0.0630852	−	0.109267i
$378$		0			0
$379$	−16.5421	+	9.55058i	−0.849710	+	0.490580i	−0.860553	−	0.509361i	$-0.829882\pi$
$379$	−16.5421	+	9.55058i	−0.849710	+	0.490580i	0.0108430	+	0.999941i	$0.496549\pi$
$380$		0			0
$381$			12.1868i			0.624351i
$382$		0			0
$383$	−19.5202	+	5.23042i	−0.997435	+	0.267262i	−0.720371	−	0.693589i	$-0.756028\pi$
$383$	−19.5202	+	5.23042i	−0.997435	+	0.267262i	−0.277064	+	0.960851i	$0.589362\pi$
$384$		0			0
$385$	−8.80078	+	32.8450i	−0.448529	+	1.67393i
$386$		0			0
$387$	0.266650	−	0.995150i	0.0135546	−	0.0505863i
$388$		0			0
$389$	4.23572	+	15.8079i	0.214760	+	0.801494i	0.986251	+	0.165254i	$0.0528444\pi$
$389$	4.23572	+	15.8079i	0.214760	+	0.801494i	−0.771491	+	0.636240i	$0.780489\pi$
$390$		0			0
$391$	10.7397	+	18.6016i	0.543128	+	0.940725i
$392$		0			0
$393$	0.268770	−	0.268770i	0.0135577	−	0.0135577i
$394$		0			0
$395$	4.11926	+	7.13476i	0.207262	+	0.358989i
$396$		0			0
$397$			11.9845i			0.601484i	0.953706	+	0.300742i	$0.0972343\pi$
$397$			11.9845i			0.601484i	−0.953706	+	0.300742i	$0.902766\pi$
$398$		0			0
$399$	−16.6751	+	16.6751i	−0.834799	+	0.834799i
$400$		0			0
$401$	16.3593	+	16.3593i	0.816946	+	0.816946i	0.985664	−	0.168718i	$-0.0539629\pi$
$401$	16.3593	+	16.3593i	0.816946	+	0.816946i	−0.168718	+	0.985664i	$0.553963\pi$
$402$		0			0
$403$	−24.9997	−	14.4336i	−1.24532	−	0.718988i
$404$		0			0
$405$	12.1917	+	3.26676i	0.605810	+	0.162326i
$406$		0			0
$407$	−16.4521	−	30.8668i	−0.815501	−	1.53001i
$408$		0			0
$409$	−9.44117	+	35.2349i	−0.466836	+	1.74226i	0.183894	+	0.982946i	$0.441130\pi$
$409$	−9.44117	+	35.2349i	−0.466836	+	1.74226i	−0.650730	+	0.759309i	$0.725537\pi$
$410$		0			0
$411$	6.56728	−	11.3749i	0.323940	−	0.561081i
$412$		0			0
$413$	19.3102	−	19.3102i	0.950193	−	0.950193i
$414$		0			0
$415$	−10.8184	−	10.8184i	−0.531053	−	0.531053i
$416$		0			0
$417$	−18.6700			−0.914275
$418$		0			0
$419$	27.1744	−	15.6891i	1.32756	−	0.766464i	0.342634	−	0.939469i	$-0.388681\pi$
$419$	27.1744	−	15.6891i	1.32756	−	0.766464i	0.984921	+	0.173005i	$0.0553475\pi$
$420$		0			0
$421$	−5.06371	−	5.06371i	−0.246790	−	0.246790i	0.572862	−	0.819652i	$-0.305833\pi$
$421$	−5.06371	−	5.06371i	−0.246790	−	0.246790i	−0.819652	+	0.572862i	$0.805833\pi$
$422$		0			0
$423$	0.609346	−	0.351806i	0.0296274	−	0.0171054i
$424$		0			0
$425$	−9.35138	+	2.50570i	−0.453609	+	0.121544i
$426$		0			0
$427$	66.6008	+	17.8456i	3.22304	+	0.863611i
$428$		0			0
$429$	56.3769	+	15.1061i	2.72190	+	0.729332i
$430$		0			0
$431$	2.15112	+	8.02810i	0.103616	+	0.386700i	0.998184	−	0.0602309i	$-0.0191837\pi$
$431$	2.15112	+	8.02810i	0.103616	+	0.386700i	−0.894569	+	0.446931i	$0.852517\pi$
$432$		0			0
$433$	−27.1920			−1.30676			−0.653382	−	0.757028i	$-0.726651\pi$
$433$	−27.1920			−1.30676			−0.653382	+	0.757028i	$0.726651\pi$
$434$		0			0
$435$	0.509398	+	0.882303i	0.0244238	+	0.0423032i
$436$		0			0
$437$	−18.4759	−	10.6671i	−0.883822	−	0.510275i
$438$		0			0
$439$	2.49791	+	9.32231i	0.119219	+	0.444930i	0.999568	−	0.0293963i	$-0.00935848\pi$
$439$	2.49791	+	9.32231i	0.119219	+	0.444930i	−0.880349	+	0.474326i	$0.842692\pi$
$440$		0			0
$441$	1.13290	−	1.96224i	0.0539475	−	0.0934398i
$442$		0			0
$443$	30.3459			1.44178			0.720890	−	0.693050i	$-0.243733\pi$
$443$	30.3459			1.44178			0.720890	+	0.693050i	$0.243733\pi$
$444$		0			0
$445$	−4.50219			−0.213424
$446$		0			0
$447$	2.90325	−	5.02857i	0.137319	−	0.237843i
$448$		0			0
$449$	−4.98928	−	18.6202i	−0.235458	−	0.878743i	−0.977942	−	0.208878i	$-0.933019\pi$
$449$	−4.98928	−	18.6202i	−0.235458	−	0.878743i	0.742483	−	0.669865i	$-0.233648\pi$
$450$		0			0
$451$	−15.5605	−	8.98387i	−0.732716	−	0.423034i
$452$		0			0
$453$	−12.9971	−	22.5117i	−0.610659	−	1.05769i
$454$		0			0
$455$	−33.6746			−1.57869
$456$		0			0
$457$	4.05912	+	15.1488i	0.189878	+	0.708633i	0.993534	+	0.113539i	$0.0362187\pi$
$457$	4.05912	+	15.1488i	0.189878	+	0.708633i	−0.803656	+	0.595094i	$0.797115\pi$
$458$		0			0
$459$	−14.5473	−	3.89794i	−0.679011	−	0.181940i
$460$		0			0
$461$	29.7533	+	7.97236i	1.38575	+	0.371310i	0.873205	−	0.487352i	$-0.162037\pi$
$461$	29.7533	+	7.97236i	1.38575	+	0.371310i	0.512542	+	0.858662i	$0.328704\pi$
$462$		0			0
$463$	30.0819	−	8.06042i	1.39802	−	0.374600i	0.520390	−	0.853929i	$-0.325787\pi$
$463$	30.0819	−	8.06042i	1.39802	−	0.374600i	0.877635	+	0.479329i	$0.159120\pi$
$464$		0			0
$465$	10.3967	−	6.00251i	0.482133	−	0.278360i
$466$		0			0
$467$	13.4906	+	13.4906i	0.624272	+	0.624272i	0.946621	−	0.322349i	$-0.104473\pi$
$467$	13.4906	+	13.4906i	0.624272	+	0.624272i	−0.322349	+	0.946621i	$0.604473\pi$
$468$		0			0
$469$	−21.8822	+	12.6337i	−1.01043	+	0.583369i
$470$		0			0
$471$	−20.2032			−0.930916
$472$		0			0
$473$	−23.6788	−	23.6788i	−1.08875	−	1.08875i
$474$		0			0
$475$	6.79941	−	6.79941i	0.311978	−	0.311978i
$476$		0			0
$477$	−1.26891	+	2.19782i	−0.0580994	+	0.100631i
$478$		0			0
$479$	−2.58158	+	9.63460i	−0.117956	+	0.440216i	−0.999491	−	0.0319016i	$-0.989844\pi$
$479$	−2.58158	+	9.63460i	−0.117956	+	0.440216i	0.881535	+	0.472118i	$0.156510\pi$
$480$		0			0
$481$	25.3096	−	23.6494i	1.15402	−	1.07832i
$482$		0			0
$483$	54.9881	+	14.7340i	2.50204	+	0.670421i
$484$		0			0
$485$	11.5203	+	6.65123i	0.523108	+	0.302017i
$486$		0			0
$487$	20.1867	+	20.1867i	0.914748	+	0.914748i	0.996641	−	0.0818934i	$-0.0260967\pi$
$487$	20.1867	+	20.1867i	0.914748	+	0.914748i	−0.0818934	+	0.996641i	$0.526097\pi$
$488$		0			0
$489$	10.0239	−	10.0239i	0.453295	−	0.453295i
$490$		0			0
$491$			26.6696i			1.20358i	0.798653	+	0.601792i	$0.205546\pi$
$491$			26.6696i			1.20358i	−0.798653	+	0.601792i	$0.794454\pi$
$492$		0			0
$493$	−0.643790	−	1.11508i	−0.0289949	−	0.0502206i
$494$		0			0
$495$	−0.955773	+	0.955773i	−0.0429588	+	0.0429588i
$496$		0			0
$497$	−19.7648	−	34.2336i	−0.886572	−	1.53559i
$498$		0			0
$499$	−0.692496	−	2.58443i	−0.0310004	−	0.115695i	0.948692	−	0.316202i	$-0.102408\pi$
$499$	−0.692496	−	2.58443i	−0.0310004	−	0.115695i	−0.979692	+	0.200507i	$0.935741\pi$
$500$		0			0
$501$	−0.963112	+	3.59438i	−0.0430287	+	0.160585i
$502$		0			0
$503$	−9.54362	+	35.6173i	−0.425529	+	1.58810i	0.337236	+	0.941420i	$0.390508\pi$
$503$	−9.54362	+	35.6173i	−0.425529	+	1.58810i	−0.762765	+	0.646676i	$0.776159\pi$
$504$		0			0
$505$	2.78731	−	0.746858i	0.124034	−	0.0332347i
$506$		0			0
$507$			34.6299i			1.53797i
$508$		0			0
$509$	−2.08720	+	1.20505i	−0.0925136	+	0.0534128i	−0.545543	−	0.838083i	$-0.683677\pi$
$509$	−2.08720	+	1.20505i	−0.0925136	+	0.0534128i	0.453029	+	0.891496i	$0.350343\pi$
$510$		0			0
$511$	−9.85356	+	17.0669i	−0.435896	+	0.754994i
$512$		0			0
$513$	14.4490	−	3.87159i	0.637938	−	0.170935i
$514$		0			0
$515$	6.98886	+	4.03502i	0.307966	+	0.177804i
$516$		0			0
$517$		−	22.8698i		−	1.00581i
$518$		0			0
$519$			5.14500i			0.225840i
$520$		0			0
$521$	−29.6740	−	17.1323i	−1.30004	−	0.750578i	−0.319629	−	0.947543i	$-0.603558\pi$
$521$	−29.6740	−	17.1323i	−1.30004	−	0.750578i	−0.980411	+	0.196964i	$0.936892\pi$
$522$		0			0
$523$	−9.41249	+	2.52207i	−0.411579	+	0.110282i	−0.458667	−	0.888608i	$-0.651673\pi$
$523$	−9.41249	+	2.52207i	−0.411579	+	0.110282i	0.0470872	+	0.998891i	$0.485006\pi$
$524$		0			0
$525$	−12.8294	+	22.2212i	−0.559921	+	0.969811i
$526$		0			0
$527$	−13.1396	+	7.58613i	−0.572368	+	0.330457i
$528$		0			0
$529$			28.5011i			1.23918i
$530$		0			0
$531$	1.04855	−	0.280959i	0.0455033	−	0.0121926i
$532$		0			0
$533$	4.60540	−	17.1876i	0.199482	−	0.744477i
$534$		0			0
$535$	4.67937	−	17.4636i	0.202307	−	0.755019i
$536$		0			0
$537$	2.85492	+	10.6547i	0.123199	+	0.459784i
$538$		0			0
$539$	−36.8231	−	63.7795i	−1.58608	−	2.74718i
$540$		0			0
$541$	20.8409	−	20.8409i	0.896020	−	0.896020i	−0.0990613	−	0.995081i	$-0.531584\pi$
$541$	20.8409	−	20.8409i	0.896020	−	0.896020i	0.995081	+	0.0990613i	$0.0315840\pi$
$542$		0			0
$543$	−4.44953	−	7.70681i	−0.190948	−	0.330731i
$544$		0			0
$545$		−	3.16304i		−	0.135490i
$546$		0			0
$547$	−25.9711	+	25.9711i	−1.11044	+	1.11044i	−0.117352	+	0.993090i	$0.537441\pi$
$547$	−25.9711	+	25.9711i	−1.11044	+	1.11044i	−0.993090	+	0.117352i	$0.962559\pi$
$548$		0			0
$549$	1.93805	+	1.93805i	0.0827141	+	0.0827141i
$550$		0			0
$551$	1.10754	+	0.639439i	0.0471828	+	0.0272410i
$552$		0			0
$553$	−26.6553	−	7.14228i	−1.13350	−	0.303721i
$554$		0			0
$555$	3.25467	+	14.0329i	0.138153	+	0.595665i
$556$		0			0
$557$	−8.71248	+	32.5154i	−0.369160	+	1.37772i	0.492533	+	0.870294i	$0.336071\pi$
$557$	−8.71248	+	32.5154i	−0.369160	+	1.37772i	−0.861693	+	0.507430i	$0.830596\pi$
$558$		0			0
$559$	16.5814	−	28.7199i	0.701320	−	1.21472i
$560$		0			0
$561$	21.6915	−	21.6915i	0.915814	−	0.915814i
$562$		0			0
$563$	23.9510	+	23.9510i	1.00941	+	1.00941i	0.999955	+	0.00945898i	$0.00301093\pi$
$563$	23.9510	+	23.9510i	1.00941	+	1.00941i	0.00945898	+	0.999955i	$0.496989\pi$
$564$		0			0
$565$	16.9570			0.713387
$566$		0			0
$567$	−36.6136	+	21.1389i	−1.53763	+	0.887750i
$568$		0			0
$569$	7.13224	+	7.13224i	0.298999	+	0.298999i	0.840622	−	0.541623i	$-0.182190\pi$
$569$	7.13224	+	7.13224i	0.298999	+	0.298999i	−0.541623	+	0.840622i	$0.682190\pi$
$570$		0			0
$571$	15.8957	−	9.17738i	0.665214	−	0.384061i	−0.129047	−	0.991639i	$-0.541192\pi$
$571$	15.8957	−	9.17738i	0.665214	−	0.384061i	0.794261	+	0.607577i	$0.207858\pi$
$572$		0			0
$573$	0.0879301	−	0.0235608i	0.00367333	−	0.000984266i
$574$		0			0
$575$	−22.4219	−	6.00792i	−0.935056	−	0.250548i
$576$		0			0
$577$	37.0866	+	9.93733i	1.54394	+	0.413696i	0.927535	−	0.373736i	$-0.121924\pi$
$577$	37.0866	+	9.93733i	1.54394	+	0.413696i	0.616401	+	0.787433i	$0.288590\pi$
$578$		0			0
$579$	−7.50503	−	28.0091i	−0.311898	−	1.16402i
$580$		0			0
$581$	51.2470			2.12608
$582$		0			0
$583$	41.2440	+	71.4367i	1.70815	+	2.95861i
$584$		0			0
$585$	−1.15925	−	0.669295i	−0.0479292	−	0.0276719i
$586$		0			0
$587$	−9.00700	−	33.6146i	−0.371759	−	1.38742i	−0.858023	−	0.513611i	$-0.828307\pi$
$587$	−9.00700	−	33.6146i	−0.371759	−	1.38742i	0.486264	−	0.873812i	$-0.338359\pi$
$588$		0			0
$589$	7.53485	−	13.0507i	0.310468	−	0.537746i
$590$		0			0
$591$	20.5753			0.846356
$592$		0			0
$593$	43.8019			1.79873			0.899364	−	0.437201i	$-0.144030\pi$
$593$	43.8019			1.79873			0.899364	+	0.437201i	$0.144030\pi$
$594$		0			0
$595$	−8.84950	+	15.3278i	−0.362794	+	0.628378i
$596$		0			0
$597$	1.22220	+	4.56133i	0.0500215	+	0.186683i
$598$		0			0
$599$	5.16523	+	2.98215i	0.211046	+	0.121847i	0.601797	−	0.798649i	$-0.294452\pi$
$599$	5.16523	+	2.98215i	0.211046	+	0.121847i	−0.390752	+	0.920496i	$0.627785\pi$
$600$		0			0
$601$	−13.3306	−	23.0893i	−0.543768	−	0.941833i	−0.998683	−	0.0512988i	$-0.983664\pi$
$601$	−13.3306	−	23.0893i	−0.543768	−	0.941833i	0.454916	−	0.890535i	$-0.349669\pi$
$602$		0			0
$603$	−1.00440			−0.0409021
$604$		0			0
$605$	7.58815	+	28.3193i	0.308502	+	1.15135i
$606$		0			0
$607$	14.5486	+	3.89828i	0.590509	+	0.158226i	0.541686	−	0.840581i	$-0.317786\pi$
$607$	14.5486	+	3.89828i	0.590509	+	0.158226i	0.0488229	+	0.998807i	$0.484453\pi$
$608$		0			0
$609$	−3.29627	−	0.883232i	−0.133572	−	0.0357904i
$610$		0			0
$611$	21.8768	−	5.86188i	0.885042	−	0.237146i
$612$		0			0
$613$	8.22272	−	4.74739i	0.332113	−	0.191745i	−0.324666	−	0.945829i	$-0.605252\pi$
$613$	8.22272	−	4.74739i	0.332113	−	0.191745i	0.656779	+	0.754083i	$0.271919\pi$
$614$		0			0
$615$	5.23257	+	5.23257i	0.210998	+	0.210998i
$616$		0			0
$617$	−34.3650	+	19.8406i	−1.38348	+	0.798754i	−0.992570	−	0.121674i	$-0.961174\pi$
$617$	−34.3650	+	19.8406i	−1.38348	+	0.798754i	−0.390912	+	0.920428i	$0.627840\pi$
$618$		0			0
$619$	−16.6754			−0.670242			−0.335121	−	0.942175i	$-0.608777\pi$
$619$	−16.6754			−0.670242			−0.335121	+	0.942175i	$0.608777\pi$
$620$		0			0
$621$	−25.5341	−	25.5341i	−1.02465	−	1.02465i
$622$		0			0
$623$	10.6635	−	10.6635i	0.427225	−	0.427225i
$624$		0			0
$625$	0.817778	−	1.41643i	0.0327111	−	0.0566573i
$626$		0			0
$627$	−7.88595	+	29.4308i	−0.314935	+	1.17535i
$628$		0			0
$629$	−4.11333	−	17.7352i	−0.164009	−	0.707148i
$630$		0			0
$631$	−20.5598	−	5.50899i	−0.818474	−	0.219310i	−0.174795	−	0.984605i	$-0.555926\pi$
$631$	−20.5598	−	5.50899i	−0.818474	−	0.219310i	−0.643679	+	0.765295i	$0.722593\pi$
$632$		0			0
$633$	2.87613	+	1.66054i	0.114316	+	0.0660004i
$634$		0			0
$635$	−6.42386	−	6.42386i	−0.254923	−	0.254923i
$636$		0			0
$637$	51.5719	−	51.5719i	2.04335	−	2.04335i
$638$		0			0
$639$		−	1.57133i		−	0.0621608i
$640$		0			0
$641$	10.6978	+	18.5291i	0.422538	+	0.731857i	0.996187	−	0.0872443i	$-0.0278061\pi$
$641$	10.6978	+	18.5291i	0.422538	+	0.731857i	−0.573649	+	0.819101i	$0.694473\pi$
$642$		0			0
$643$	11.7909	−	11.7909i	0.464988	−	0.464988i	−0.435299	−	0.900286i	$-0.643357\pi$
$643$	11.7909	−	11.7909i	0.464988	−	0.464988i	0.900286	+	0.435299i	$0.143357\pi$
$644$		0			0
$645$	6.89574	+	11.9438i	0.271520	+	0.470286i
$646$		0			0
$647$	−7.69313	−	28.7111i	−0.302448	−	1.12875i	−0.935120	−	0.354331i	$-0.884709\pi$
$647$	−7.69313	−	28.7111i	−0.302448	−	1.12875i	0.632672	−	0.774420i	$-0.281958\pi$
$648$		0			0
$649$	9.13214	−	34.0816i	0.358468	−	1.33782i
$650$		0			0
$651$	−10.4076	+	38.8417i	−0.407906	+	1.52233i
$652$		0			0
$653$	−26.0991	+	6.99323i	−1.02134	+	0.273666i	−0.730359	−	0.683064i	$-0.760647\pi$
$653$	−26.0991	+	6.99323i	−1.02134	+	0.273666i	−0.290977	+	0.956730i	$0.593980\pi$
$654$		0			0
$655$			0.283345i			0.0110712i
$656$		0			0
$657$	−0.678420	+	0.391686i	−0.0264677	+	0.0152811i
$658$		0			0
$659$	−4.70995	+	8.15787i	−0.183474	+	0.317786i	−0.943061	−	0.332619i	$-0.892068\pi$
$659$	−4.70995	+	8.15787i	−0.183474	+	0.317786i	0.759587	+	0.650405i	$0.225401\pi$
$660$		0			0
$661$	3.71420	−	0.995216i	0.144465	−	0.0387094i	−0.185862	−	0.982576i	$-0.559508\pi$
$661$	3.71420	−	0.995216i	0.144465	−	0.0387094i	0.330327	+	0.943867i	$0.392841\pi$
$662$		0			0
$663$	26.3095	+	15.1898i	1.02177	+	0.589922i
$664$		0			0
$665$		−	17.5794i		−	0.681698i
$666$		0			0
$667$		−	3.08724i		−	0.119538i
$668$		0			0
$669$	2.95746	+	1.70749i	0.114342	+	0.0660154i
$670$		0			0
$671$	86.0506	−	23.0572i	3.32195	−	0.890113i
$672$		0			0
$673$	−0.262570	+	0.454784i	−0.0101213	+	0.0175306i	−0.871042	−	0.491209i	$-0.836555\pi$
$673$	−0.262570	+	0.454784i	−0.0101213	+	0.0175306i	0.860920	+	0.508740i	$0.169888\pi$
$674$		0			0
$675$	14.0954	−	8.13798i	0.542532	−	0.313231i
$676$		0			0
$677$		−	19.2335i		−	0.739204i	−0.929190	−	0.369602i	$-0.879494\pi$
$677$		−	19.2335i		−	0.739204i	0.929190	−	0.369602i	$-0.120506\pi$
$678$		0			0
$679$	−43.0395	+	11.5324i	−1.65170	+	0.442573i
$680$		0			0
$681$	−7.02882	+	26.2319i	−0.269345	+	1.00521i
$682$		0			0
$683$	0.271850	−	1.01456i	0.0104021	−	0.0388210i	−0.960530	−	0.278177i	$-0.910270\pi$
$683$	0.271850	−	1.01456i	0.0104021	−	0.0388210i	0.970932	+	0.239356i	$0.0769364\pi$
$684$		0			0
$685$	2.53415	+	9.45756i	0.0968247	+	0.361355i
$686$		0			0
$687$	−10.8489	−	18.7909i	−0.413913	−	0.716918i
$688$		0			0
$689$	−57.7635	+	57.7635i	−2.20061	+	2.20061i
$690$		0			0
$691$	−5.01874	−	8.69271i	−0.190922	−	0.330686i	0.754634	−	0.656146i	$-0.227814\pi$
$691$	−5.01874	−	8.69271i	−0.190922	−	0.330686i	−0.945556	+	0.325460i	$0.894481\pi$
$692$		0			0
$693$		−	4.52753i		−	0.171987i
$694$		0			0
$695$	9.84124	−	9.84124i	0.373299	−	0.373299i
$696$		0			0
$697$	−6.61306	−	6.61306i	−0.250487	−	0.250487i
$698$		0			0
$699$	−38.7524	−	22.3737i	−1.46575	−	0.846251i
$700$		0			0
$701$	41.8432	+	11.2118i	1.58039	+	0.423465i	0.939048	−	0.343786i	$-0.111710\pi$
$701$	41.8432	+	11.2118i	1.58039	+	0.423465i	0.641346	+	0.767251i	$0.278376\pi$
$702$		0			0
$703$	12.3458	+	13.2125i	0.465632	+	0.498320i
$704$		0			0
$705$	−2.43779	+	9.09795i	−0.0918124	+	0.342649i
$706$		0			0
$707$	−4.83285	+	8.37074i	−0.181758	+	0.314814i
$708$		0			0
$709$	11.5153	−	11.5153i	0.432465	−	0.432465i	−0.457001	−	0.889466i	$-0.651076\pi$
$709$	11.5153	−	11.5153i	0.432465	−	0.432465i	0.889466	+	0.457001i	$0.151076\pi$
$710$		0			0
$711$	−0.775658	−	0.775658i	−0.0290894	−	0.0290894i
$712$		0			0
$713$	−36.3786			−1.36239
$714$		0			0
$715$	−37.6797	+	21.7544i	−1.40914	+	0.813569i
$716$		0			0
$717$	−24.0921	−	24.0921i	−0.899736	−	0.899736i
$718$		0			0
$719$	−11.8692	+	6.85266i	−0.442645	+	0.255561i	−0.704719	−	0.709487i	$-0.748927\pi$
$719$	−11.8692	+	6.85266i	−0.442645	+	0.255561i	0.262074	+	0.965048i	$0.415594\pi$
$720$		0			0
$721$	−26.1103	+	6.99622i	−0.972397	+	0.260553i
$722$		0			0
$723$	−23.8916	−	6.40175i	−0.888540	−	0.238084i
$724$		0			0
$725$	1.34408	+	0.360146i	0.0499179	+	0.0133755i
$726$		0			0
$727$	2.89947	+	10.8210i	0.107535	+	0.401327i	0.998620	−	0.0525091i	$-0.0167219\pi$
$727$	2.89947	+	10.8210i	0.107535	+	0.401327i	−0.891085	+	0.453836i	$0.850055\pi$
$728$		0			0
$729$	25.2255			0.934279
$730$		0			0
$731$	−8.71502	−	15.0949i	−0.322337	−	0.558304i
$732$		0			0
$733$	−6.71841	−	3.87888i	−0.248150	−	0.143270i	0.370767	−	0.928726i	$-0.379095\pi$
$733$	−6.71841	−	3.87888i	−0.248150	−	0.143270i	−0.618917	+	0.785456i	$0.712428\pi$
$734$		0			0
$735$	7.85024	+	29.2975i	0.289561	+	1.08065i
$736$		0			0
$737$	−16.3232	+	28.2726i	−0.601272	+	1.04143i
$738$		0			0
$739$	5.78521			0.212812			0.106406	−	0.994323i	$-0.466066\pi$
$739$	5.78521			0.212812			0.106406	+	0.994323i	$0.466066\pi$
$740$		0			0
$741$	−30.1742			−1.10848
$742$		0			0
$743$	−0.402795	+	0.697662i	−0.0147771	+	0.0255947i	−0.873319	−	0.487148i	$-0.838037\pi$
$743$	−0.402795	+	0.697662i	−0.0147771	+	0.0255947i	0.858542	+	0.512743i	$0.171371\pi$
$744$		0			0
$745$	1.12029	+	4.18097i	0.0410442	+	0.153179i
$746$		0			0
$747$	1.76418	+	1.01855i	0.0645481	+	0.0372668i
$748$		0			0
$749$	30.2798	+	52.4461i	1.10640	+	1.91634i
$750$		0			0
$751$	−19.7670			−0.721307			−0.360654	−	0.932700i	$-0.617446\pi$
$751$	−19.7670			−0.721307			−0.360654	+	0.932700i	$0.617446\pi$
$752$		0			0
$753$	−7.46652	−	27.8654i	−0.272095	−	1.01547i
$754$		0			0
$755$	18.7172	+	5.01526i	0.681189	+	0.182524i
$756$		0			0
$757$	−8.34674	−	2.23650i	−0.303367	−	0.0812871i	0.103924	−	0.994585i	$-0.466860\pi$
$757$	−8.34674	−	2.23650i	−0.303367	−	0.0812871i	−0.407292	+	0.913298i	$0.633527\pi$
$758$		0			0
$759$	71.0466	−	19.0369i	2.57883	−	0.690995i
$760$		0			0
$761$	3.57456	−	2.06377i	0.129578	−	0.0748117i	−0.433810	−	0.901004i	$-0.642831\pi$
$761$	3.57456	−	2.06377i	0.129578	−	0.0748117i	0.563388	+	0.826193i	$0.309498\pi$
$762$		0			0
$763$	7.49171	+	7.49171i	0.271218	+	0.271218i
$764$		0			0
$765$	−0.609290	+	0.351774i	−0.0220289	+	0.0127184i
$766$		0			0
$767$	34.9425			1.26170
$768$		0			0
$769$	2.69051	+	2.69051i	0.0970223	+	0.0970223i	0.753952	−	0.656930i	$-0.228145\pi$
$769$	2.69051	+	2.69051i	0.0970223	+	0.0970223i	−0.656930	+	0.753952i	$0.728145\pi$
$770$		0			0
$771$	15.8045	−	15.8045i	0.569187	−	0.569187i
$772$		0			0
$773$	−15.8795	+	27.5040i	−0.571145	+	0.989252i	0.425304	+	0.905050i	$0.360167\pi$
$773$	−15.8795	+	27.5040i	−0.571145	+	0.989252i	−0.996449	+	0.0842010i	$0.973166\pi$
$774$		0			0
$775$	4.24379	−	15.8380i	0.152441	−	0.568919i
$776$		0			0
$777$	−40.9460	−	25.5285i	−1.46893	−	0.915830i
$778$		0			0
$779$	8.97254	+	2.40418i	0.321475	+	0.0861388i
$780$		0			0
$781$	−44.2311	−	25.5368i	−1.58271	−	0.913779i
$782$		0			0
$783$	1.53064	+	1.53064i	0.0547007	+	0.0547007i
$784$		0			0
$785$	10.6494	−	10.6494i	0.380094	−	0.380094i
$786$		0			0
$787$		−	28.8707i		−	1.02913i	−0.857452	−	0.514565i	$-0.827954\pi$
$787$		−	28.8707i		−	1.02913i	0.857452	−	0.514565i	$-0.172046\pi$
$788$		0			0
$789$	3.79502	+	6.57316i	0.135106	+	0.234011i
$790$		0			0
$791$	−40.1630	+	40.1630i	−1.42803	+	1.42803i
$792$		0			0
$793$	44.1121	+	76.4044i	1.56647	+	2.71320i
$794$		0			0
$795$	−8.79273	−	32.8149i	−0.311846	−	1.16382i
$796$		0			0
$797$	−2.95939	+	11.0446i	−0.104827	+	0.391219i	−0.998325	−	0.0578468i	$-0.981577\pi$
$797$	−2.95939	+	11.0446i	−0.104827	+	0.391219i	0.893499	+	0.449066i	$0.148243\pi$
$798$		0			0
$799$	3.08094	−	11.4982i	0.108996	−	0.406778i
$800$		0			0
$801$	0.579034	−	0.155152i	0.0204591	−	0.00548201i
$802$		0			0
$803$			25.4623i			0.898546i
$804$		0			0
$805$	−36.7515	+	21.2185i	−1.29532	+	0.747854i
$806$		0			0
$807$	−2.97076	+	5.14550i	−0.104576	+	0.181130i
$808$		0			0
$809$	17.9285	−	4.80394i	0.630334	−	0.168897i	0.0705126	−	0.997511i	$-0.477536\pi$
$809$	17.9285	−	4.80394i	0.630334	−	0.168897i	0.559821	+	0.828613i	$0.310870\pi$
$810$		0			0
$811$	−42.0521	−	24.2788i	−1.47665	−	0.852544i	−0.476997	−	0.878905i	$-0.658275\pi$
$811$	−42.0521	−	24.2788i	−1.47665	−	0.852544i	−0.999652	+	0.0263610i	$0.991608\pi$
$812$		0			0
$813$		−	6.75983i		−	0.237078i
$814$		0			0
$815$			10.5675i			0.370162i
$816$		0			0
$817$	14.9928	+	8.65611i	0.524532	+	0.302839i
$818$		0			0
$819$	4.33095	−	1.16047i	0.151336	−	0.0405502i
$820$		0			0
$821$	3.56782	−	6.17965i	0.124518	−	0.215671i	−0.797027	−	0.603944i	$-0.793595\pi$
$821$	3.56782	−	6.17965i	0.124518	−	0.215671i	0.921544	+	0.388273i	$0.126928\pi$
$822$		0			0
$823$	20.8962	−	12.0644i	0.728395	−	0.420539i	−0.0894399	−	0.995992i	$-0.528508\pi$
$823$	20.8962	−	12.0644i	0.728395	−	0.420539i	0.817835	+	0.575453i	$0.195174\pi$
$824$		0			0
$825$			33.1521i			1.15421i
$826$		0			0
$827$	22.5876	−	6.05233i	0.785449	−	0.210460i	0.156263	−	0.987715i	$-0.450055\pi$
$827$	22.5876	−	6.05233i	0.785449	−	0.210460i	0.629186	+	0.777255i	$0.283389\pi$
$828$		0			0
$829$	−7.56351	+	28.2274i	−0.262692	+	0.980379i	0.700957	+	0.713204i	$0.252757\pi$
$829$	−7.56351	+	28.2274i	−0.262692	+	0.980379i	−0.963648	+	0.267175i	$0.913910\pi$
$830$		0			0
$831$	−14.2954	+	53.3511i	−0.495902	+	1.85073i
$832$		0			0
$833$	−9.92134	−	37.0269i	−0.343754	−	1.28291i
$834$		0			0
$835$	−1.38698	−	2.40232i	−0.0479985	−	0.0831358i
$836$		0			0
$837$	18.0364	−	18.0364i	0.623429	−	0.623429i
$838$		0			0
$839$	−15.3254	−	26.5444i	−0.529091	−	0.916413i	−0.999424	−	0.0339241i	$-0.989200\pi$
$839$	−15.3254	−	26.5444i	−0.529091	−	0.916413i	0.470333	−	0.882489i	$-0.344134\pi$
$840$		0			0
$841$		−	28.8149i		−	0.993618i
$842$		0			0
$843$	4.88863	−	4.88863i	0.168373	−	0.168373i
$844$		0			0
$845$	−18.2539	−	18.2539i	−0.627954	−	0.627954i
$846$		0			0
$847$	−85.0475	−	49.1022i	−2.92227	−	1.68717i
$848$		0			0
$849$	−33.7366	−	9.03970i	−1.15784	−	0.310242i
$850$		0			0
$851$	12.7206	−	41.7579i	0.436058	−	1.43144i
$852$		0			0
$853$	6.46543	−	24.1293i	0.221372	−	0.826172i	−0.762453	−	0.647043i	$-0.776005\pi$
$853$	6.46543	−	24.1293i	0.221372	−	0.826172i	0.983826	−	0.179129i	$-0.0573280\pi$
$854$		0			0
$855$	0.349396	−	0.605172i	0.0119491	−	0.0206964i
$856$		0			0
$857$	9.84740	−	9.84740i	0.336381	−	0.336381i	−0.518622	−	0.855003i	$-0.673555\pi$
$857$	9.84740	−	9.84740i	0.336381	−	0.336381i	0.855003	+	0.518622i	$0.173555\pi$
$858$		0			0
$859$	−15.0312	−	15.0312i	−0.512859	−	0.512859i	0.402543	−	0.915401i	$-0.368127\pi$
$859$	−15.0312	−	15.0312i	−0.512859	−	0.512859i	−0.915401	+	0.402543i	$0.868127\pi$
$860$		0			0
$861$	−24.7869			−0.844734
$862$		0			0
$863$	49.0690	−	28.3300i	1.67033	−	0.964365i	0.702877	−	0.711312i	$-0.251899\pi$
$863$	49.0690	−	28.3300i	1.67033	−	0.964365i	0.967452	−	0.253053i	$-0.0814347\pi$
$864$		0			0
$865$	−2.71200	−	2.71200i	−0.0922108	−	0.0922108i
$866$		0			0
$867$	−12.4132	+	7.16674i	−0.421573	+	0.243395i
$868$		0			0
$869$	−34.4397	+	9.22808i	−1.16829	+	0.313041i
$870$		0			0
$871$	−31.2288	−	8.36774i	−1.05815	−	0.283530i
$872$		0			0
$873$	−1.71085	−	0.458421i	−0.0579035	−	0.0155152i
$874$		0			0
$875$	−12.6030	−	47.0351i	−0.426060	−	1.59008i
$876$		0			0
$877$	14.3759			0.485438			0.242719	−	0.970097i	$-0.421961\pi$
$877$	14.3759			0.485438			0.242719	+	0.970097i	$0.421961\pi$
$878$		0			0
$879$	−21.6739	−	37.5402i	−0.731041	−	1.26620i
$880$		0			0
$881$	−8.35489	−	4.82370i	−0.281483	−	0.162515i	0.352611	−	0.935770i	$-0.385294\pi$
$881$	−8.35489	−	4.82370i	−0.281483	−	0.162515i	−0.634095	+	0.773255i	$0.718627\pi$
$882$		0			0
$883$	10.6624	+	39.7924i	0.358817	+	1.33912i	0.875613	+	0.483014i	$0.160458\pi$
$883$	10.6624	+	39.7924i	0.358817	+	1.33912i	−0.516796	+	0.856109i	$0.672875\pi$
$884$		0			0
$885$	−7.26579	+	12.5847i	−0.244237	+	0.423031i
$886$		0			0
$887$	8.00890			0.268913			0.134456	−	0.990920i	$-0.457071\pi$
$887$	8.00890			0.268913			0.134456	+	0.990920i	$0.457071\pi$
$888$		0			0
$889$	30.4300			1.02059
$890$		0			0
$891$	−27.3122	+	47.3061i	−0.914993	+	1.58481i
$892$		0			0
$893$	3.06011	+	11.4205i	0.102403	+	0.382172i
$894$		0			0
$895$	−7.12112	−	4.11138i	−0.238033	−	0.137428i
$896$		0			0
$897$	36.4206	+	63.0823i	1.21605	+	2.10626i
$898$		0			0
$899$	2.18072			0.0727311
$900$		0			0
$901$	11.1125	+	41.4723i	0.370210	+	1.38164i
$902$		0			0
$903$	−44.6217	−	11.9564i	−1.48492	−	0.397883i
$904$		0			0
$905$	6.40778	+	1.71696i	0.213002	+	0.0570737i
$906$		0			0
$907$	48.6626	−	13.0391i	1.61581	−	0.432956i	0.666046	−	0.745911i	$-0.267985\pi$
$907$	48.6626	−	13.0391i	1.61581	−	0.432956i	0.949768	+	0.312955i	$0.101319\pi$
$908$		0			0
$909$	−0.332743	+	0.192109i	−0.0110364	+	0.00637186i
$910$		0			0
$911$	−7.11353	−	7.11353i	−0.235682	−	0.235682i	0.579378	−	0.815059i	$-0.303296\pi$
$911$	−7.11353	−	7.11353i	−0.235682	−	0.235682i	−0.815059	+	0.579378i	$0.803296\pi$
$912$		0			0
$913$	57.3421	−	33.1065i	1.89775	−	1.09566i
$914$		0			0
$915$	−36.6899			−1.21293
$916$		0			0
$917$	−0.671108	−	0.671108i	−0.0221619	−	0.0221619i
$918$		0			0
$919$	−23.7769	+	23.7769i	−0.784327	+	0.784327i	−0.980558	−	0.196231i	$-0.937130\pi$
$919$	−23.7769	+	23.7769i	−0.784327	+	0.784327i	0.196231	+	0.980558i	$0.437130\pi$
$920$		0			0
$921$	−10.3131	+	17.8627i	−0.339827	+	0.588597i
$922$		0			0
$923$	13.0909	−	48.8560i	0.430893	−	1.60812i
$924$		0			0
$925$	16.6961	+	10.4095i	0.548964	+	0.342261i
$926$		0			0
$927$	−1.03790	−	0.278105i	−0.0340892	−	0.00913416i
$928$		0			0
$929$	8.44051	+	4.87313i	0.276924	+	0.159882i	0.632030	−	0.774944i	$-0.282222\pi$
$929$	8.44051	+	4.87313i	0.276924	+	0.159882i	−0.355106	+	0.934826i	$0.615555\pi$
$930$		0			0
$931$	26.9224	+	26.9224i	0.882345	+	0.882345i
$932$		0			0
$933$	−2.57509	+	2.57509i	−0.0843046	+	0.0843046i
$934$		0			0
$935$			22.8677i			0.747855i
$936$		0			0
$937$	−0.223837	−	0.387697i	−0.00731244	−	0.0126655i	0.862346	−	0.506319i	$-0.168994\pi$
$937$	−0.223837	−	0.387697i	−0.00731244	−	0.0126655i	−0.869658	+	0.493654i	$0.835661\pi$
$938$		0			0
$939$	−16.1785	+	16.1785i	−0.527966	+	0.527966i
$940$		0			0
$941$	−12.1978	−	21.1273i	−0.397638	−	0.688729i	0.595796	−	0.803136i	$-0.296837\pi$
$941$	−12.1978	−	21.1273i	−0.397638	−	0.688729i	−0.993434	+	0.114407i	$0.963503\pi$
$942$		0			0
$943$	−5.80376	−	21.6599i	−0.188996	−	0.705344i
$944$		0			0
$945$	7.70122	−	28.7413i	0.250521	−	0.934956i
$946$		0			0
$947$	−6.88877	+	25.7092i	−0.223855	+	0.835438i	0.759005	+	0.651085i	$0.225686\pi$
$947$	−6.88877	+	25.7092i	−0.223855	+	0.835438i	−0.982860	+	0.184353i	$0.940981\pi$
$948$		0			0
$949$	−24.3567	+	6.52637i	−0.790653	+	0.211855i
$950$		0			0
$951$			11.1168i			0.360486i
$952$		0			0
$953$	−48.9515	+	28.2622i	−1.58569	+	0.915501i	−0.591689	+	0.806166i	$0.701539\pi$
$953$	−48.9515	+	28.2622i	−1.58569	+	0.915501i	−0.994005	+	0.109335i	$0.965128\pi$
$954$		0			0
$955$	−0.0339300	+	0.0587684i	−0.00109795	+	0.00190170i
$956$		0			0
$957$	−4.25890	+	1.14117i	−0.137671	+	0.0368887i
$958$		0			0
$959$	−28.4026	−	16.3982i	−0.917166	−	0.529526i
$960$		0			0
$961$			5.30340i			0.171078i
$962$		0			0
$963$			2.40728i			0.0775737i
$964$		0			0
$965$	18.7200	+	10.8080i	0.602619	+	0.347922i
$966$		0			0
$967$	47.8315	−	12.8164i	1.53816	−	0.412148i	0.612488	−	0.790480i	$-0.290169\pi$
$967$	47.8315	−	12.8164i	1.53816	−	0.412148i	0.925670	+	0.378332i	$0.123502\pi$
$968$		0			0
$969$	−7.92961	+	13.7345i	−0.254736	+	0.441215i
$970$		0			0
$971$	49.3625	−	28.4995i	1.58412	−	0.914591i	0.589869	−	0.807499i	$-0.299179\pi$
$971$	49.3625	−	28.4995i	1.58412	−	0.914591i	0.994249	−	0.107092i	$-0.0341539\pi$
$972$		0			0
$973$			46.6183i			1.49451i
$974$		0			0
$975$	−31.7126	+	8.49737i	−1.01562	+	0.272134i
$976$		0			0
$977$	15.4118	−	57.5177i	0.493068	−	1.84015i	−0.0475265	−	0.998870i	$-0.515134\pi$
$977$	15.4118	−	57.5177i	0.493068	−	1.84015i	0.540594	−	0.841284i	$-0.318199\pi$
$978$		0			0
$979$	5.04297	−	18.8206i	0.161174	−	0.601509i
$980$		0			0
$981$	0.109003	+	0.406803i	0.00348019	+	0.0129882i
$982$		0			0
$983$	−13.9938	−	24.2379i	−0.446332	−	0.773069i	0.551812	−	0.833968i	$-0.313937\pi$
$983$	−13.9938	−	24.2379i	−0.446332	−	0.773069i	−0.998144	+	0.0608991i	$0.980603\pi$
$984$		0			0
$985$	−10.8455	+	10.8455i	−0.345568	+	0.345568i
$986$		0			0
$987$	−15.7747	−	27.3226i	−0.502114	−	0.869688i
$988$		0			0
$989$		−	41.7921i		−	1.32891i
$990$		0			0
$991$	22.4023	−	22.4023i	0.711633	−	0.711633i	−0.255244	−	0.966877i	$-0.582156\pi$
$991$	22.4023	−	22.4023i	0.711633	−	0.711633i	0.966877	+	0.255244i	$0.0821557\pi$
$992$		0			0
$993$	7.05132	+	7.05132i	0.223767	+	0.223767i
$994$		0			0
$995$	−3.04858	−	1.76010i	−0.0966466	−	0.0557989i
$996$		0			0
$997$	9.63104	+	2.58063i	0.305018	+	0.0817294i	0.408082	−	0.912945i	$-0.366198\pi$
$997$	9.63104	+	2.58063i	0.305018	+	0.0817294i	−0.103064	+	0.994675i	$0.532865\pi$
$998$		0			0
$999$	14.3966	+	27.0103i	0.455488	+	0.854568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.e.399.5	yes	20
4.3	odd	2		592.2.be.f.399.1	yes	20
37.23	odd	12		592.2.be.f.319.1	yes	20
148.23	even	12	inner	592.2.be.e.319.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.319.5	✓	20	148.23	even	12	inner
592.2.be.e.399.5	yes	20	1.1	even	1	trivial
592.2.be.f.319.1	yes	20	37.23	odd	12
592.2.be.f.399.1	yes	20	4.3	odd	2

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.891195 - 1.54359i) q^{3} +(0.343889 + 1.28341i) q^{5} +(-3.85429 - 2.22528i) q^{7} +(-0.0884563 - 0.153211i) q^{9} +O(q^{10})\)	\(q+(0.891195 - 1.54359i) q^{3} +(0.343889 + 1.28341i) q^{5} +(-3.85429 - 2.22528i) q^{7} +(-0.0884563 - 0.153211i) q^{9} -5.75028 q^{11} +(-1.47388 - 5.50060i) q^{13} +(2.28754 + 0.612945i) q^{15} +(-2.89105 - 0.774655i) q^{17} +(2.87151 - 0.769419i) q^{19} +(-6.86985 + 3.96631i) q^{21} +(-5.07450 - 5.07450i) q^{23} +(2.80124 - 1.61730i) q^{25} +5.03184 q^{27} +(0.304192 + 0.304192i) q^{29} +(3.58445 - 3.58445i) q^{31} +(-5.12462 + 8.87609i) q^{33} +(1.53050 - 5.71189i) q^{35} +(2.86110 + 5.36788i) q^{37} +(-9.80421 - 2.62703i) q^{39} +(2.70605 + 1.56234i) q^{41} +(4.11786 + 4.11786i) q^{43} +(0.166213 - 0.166213i) q^{45} +3.97717i q^{47} +(6.40371 + 11.0916i) q^{49} +(-3.77225 + 3.77225i) q^{51} +(-7.17253 - 12.4232i) q^{53} +(-1.97746 - 7.37997i) q^{55} +(1.37140 - 5.11815i) q^{57} +(-1.58812 + 5.92696i) q^{59} +(-14.9646 + 4.00976i) q^{61} +0.787359i q^{63} +(6.55269 - 3.78319i) q^{65} +(2.83868 - 4.91673i) q^{67} +(-12.3553 + 3.31060i) q^{69} +(7.69199 + 4.44097i) q^{71} -4.42802i q^{73} -5.76530i q^{75} +(22.1632 + 12.7960i) q^{77} +(5.98922 - 1.60481i) q^{79} +(4.74972 - 8.22676i) q^{81} +(-9.97206 + 5.75737i) q^{83} -3.97681i q^{85} +(0.740642 - 0.198455i) q^{87} +(-0.876996 + 3.27299i) q^{89} +(-6.55959 + 24.4807i) q^{91} +(-2.33850 - 8.72739i) q^{93} +(1.97496 + 3.42074i) q^{95} +(7.07937 - 7.07937i) q^{97} +(0.508648 + 0.881004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9} + 4 q^{11} + 4 q^{13} + 8 q^{15} - 4 q^{17} + 10 q^{19} - 18 q^{21} + 8 q^{23} + 42 q^{25} + 68 q^{27} - 8 q^{29} + 28 q^{31} - 20 q^{33} - 10 q^{35} - 24 q^{37} - 14 q^{39} - 6 q^{41} + 32 q^{43} + 8 q^{45} - 12 q^{49} - 58 q^{51} + 6 q^{53} + 26 q^{55} - 2 q^{57} - 56 q^{59} - 8 q^{61} + 6 q^{65} + 20 q^{67} + 26 q^{69} - 30 q^{71} + 60 q^{77} + 50 q^{79} - 22 q^{81} + 36 q^{83} - 32 q^{87} - 20 q^{89} - 50 q^{91} - 50 q^{93} - 72 q^{95} + 32 q^{97} - 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 4 * q^5 - 6 * q^7 - 16 * q^9 + 4 * q^11 + 4 * q^13 + 8 * q^15 - 4 * q^17 + 10 * q^19 - 18 * q^21 + 8 * q^23 + 42 * q^25 + 68 * q^27 - 8 * q^29 + 28 * q^31 - 20 * q^33 - 10 * q^35 - 24 * q^37 - 14 * q^39 - 6 * q^41 + 32 * q^43 + 8 * q^45 - 12 * q^49 - 58 * q^51 + 6 * q^53 + 26 * q^55 - 2 * q^57 - 56 * q^59 - 8 * q^61 + 6 * q^65 + 20 * q^67 + 26 * q^69 - 30 * q^71 + 60 * q^77 + 50 * q^79 - 22 * q^81 + 36 * q^83 - 32 * q^87 - 20 * q^89 - 50 * q^91 - 50 * q^93 - 72 * q^95 + 32 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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