LMFDB - Embedded newform 592.2.be.e.399.2

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			399.2
Root			$1.55981i$ of defining polynomial
Character	$\chi$	$=$	592.399
Dual form			592.2.be.e.319.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.779906 + 1.35084i) q^{3} +(0.765103 + 2.85540i) q^{5} +(1.56078 + 0.901118i) q^{7} +(0.283492 + 0.491022i) q^{9} +O(q^{10})$	\(q+(-0.779906 + 1.35084i) q^{3} +(0.765103 + 2.85540i) q^{5} +(1.56078 + 0.901118i) q^{7} +(0.283492 + 0.491022i) q^{9} -1.54245 q^{11} +(-0.0484102 - 0.180669i) q^{13} +(-4.45389 - 1.19342i) q^{15} +(6.14536 + 1.64665i) q^{17} +(-1.97736 + 0.529832i) q^{19} +(-2.43453 + 1.40558i) q^{21} +(-2.76570 - 2.76570i) q^{23} +(-3.23781 + 1.86935i) q^{25} -5.56383 q^{27} +(-2.00959 - 2.00959i) q^{29} +(2.52803 - 2.52803i) q^{31} +(1.20297 - 2.08361i) q^{33} +(-1.37890 + 5.14611i) q^{35} +(-4.82388 + 3.70542i) q^{37} +(0.281810 + 0.0755109i) q^{39} +(-0.407173 - 0.235082i) q^{41} +(-1.11902 - 1.11902i) q^{43} +(-1.18517 + 1.18517i) q^{45} +12.7439i q^{47} +(-1.87597 - 3.24928i) q^{49} +(-7.01716 + 7.01716i) q^{51} +(4.29003 + 7.43055i) q^{53} +(-1.18014 - 4.40433i) q^{55} +(0.826439 - 3.08431i) q^{57} +(0.461229 - 1.72133i) q^{59} +(1.13593 - 0.304373i) q^{61} +1.02184i q^{63} +(0.478845 - 0.276461i) q^{65} +(1.09686 - 1.89982i) q^{67} +(5.89299 - 1.57902i) q^{69} +(10.3129 + 5.95417i) q^{71} -13.4642i q^{73} -5.83168i q^{75} +(-2.40744 - 1.38993i) q^{77} +(-5.27411 + 1.41319i) q^{79} +(3.48879 - 6.04276i) q^{81} +(14.4843 - 8.36253i) q^{83} +18.8073i q^{85} +(4.28191 - 1.14733i) q^{87} +(1.52247 - 5.68195i) q^{89} +(0.0872466 - 0.325609i) q^{91} +(1.44333 + 5.38658i) q^{93} +(-3.02577 - 5.24078i) q^{95} +(-5.97490 + 5.97490i) q^{97} +(-0.437273 - 0.757380i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.779906	+	1.35084i	−0.450279	+	0.779906i	−0.998403	−	0.0564907i	$-0.982009\pi$
$3$	−0.779906	+	1.35084i	−0.450279	+	0.779906i	0.548124	+	0.836397i	$0.315342\pi$
$4$		0			0
$5$	0.765103	+	2.85540i	0.342164	+	1.27697i	0.895890	+	0.444276i	$0.146539\pi$
$5$	0.765103	+	2.85540i	0.342164	+	1.27697i	−0.553726	+	0.832699i	$0.686794\pi$
$6$		0			0
$7$	1.56078	+	0.901118i	0.589920	+	0.340591i	0.765066	−	0.643952i	$-0.222706\pi$
$7$	1.56078	+	0.901118i	0.589920	+	0.340591i	−0.175146	+	0.984543i	$0.556040\pi$
$8$		0			0
$9$	0.283492	+	0.491022i	0.0944973	+	0.163674i
$10$		0			0
$11$	−1.54245			−0.465068			−0.232534	−	0.972588i	$-0.574702\pi$
$11$	−1.54245			−0.465068			−0.232534	+	0.972588i	$0.574702\pi$
$12$		0			0
$13$	−0.0484102	−	0.180669i	−0.0134266	−	0.0501087i	0.958888	−	0.283786i	$-0.0915906\pi$
$13$	−0.0484102	−	0.180669i	−0.0134266	−	0.0501087i	−0.972314	+	0.233678i	$0.924924\pi$
$14$		0			0
$15$	−4.45389	−	1.19342i	−1.14999	−	0.308139i
$16$		0			0
$17$	6.14536	+	1.64665i	1.49047	+	0.399370i	0.909896	−	0.414837i	$-0.136162\pi$
$17$	6.14536	+	1.64665i	1.49047	+	0.399370i	0.580574	+	0.814208i	$0.302828\pi$
$18$		0			0
$19$	−1.97736	+	0.529832i	−0.453638	+	0.121552i	−0.478401	−	0.878142i	$-0.658783\pi$
$19$	−1.97736	+	0.529832i	−0.453638	+	0.121552i	0.0247634	+	0.999693i	$0.492117\pi$
$20$		0			0
$21$	−2.43453	+	1.40558i	−0.531258	+	0.306722i
$22$		0			0
$23$	−2.76570	−	2.76570i	−0.576688	−	0.576688i	0.357301	−	0.933989i	$-0.383697\pi$
$23$	−2.76570	−	2.76570i	−0.576688	−	0.576688i	−0.933989	+	0.357301i	$0.883697\pi$
$24$		0			0
$25$	−3.23781	+	1.86935i	−0.647563	+	0.373871i
$26$		0			0
$27$	−5.56383			−1.07076
$28$		0			0
$29$	−2.00959	−	2.00959i	−0.373171	−	0.373171i	0.495460	−	0.868631i	$-0.334999\pi$
$29$	−2.00959	−	2.00959i	−0.373171	−	0.373171i	−0.868631	+	0.495460i	$0.834999\pi$
$30$		0			0
$31$	2.52803	−	2.52803i	0.454047	−	0.454047i	−0.442648	−	0.896695i	$-0.645961\pi$
$31$	2.52803	−	2.52803i	0.454047	−	0.454047i	0.896695	+	0.442648i	$0.145961\pi$
$32$		0			0
$33$	1.20297	−	2.08361i	0.209410	−	0.362709i
$34$		0			0
$35$	−1.37890	+	5.14611i	−0.233076	+	0.869851i
$36$		0			0
$37$	−4.82388	+	3.70542i	−0.793042	+	0.609167i
$37$	−4.82388	+	3.70542i	−0.793042	+	0.609167i
$38$		0			0
$39$	0.281810	+	0.0755109i	0.0451258	+	0.0120914i
$40$		0			0
$41$	−0.407173	−	0.235082i	−0.0635898	−	0.0367136i	0.467868	−	0.883798i	$-0.345022\pi$
$41$	−0.407173	−	0.235082i	−0.0635898	−	0.0367136i	−0.531458	+	0.847085i	$0.678356\pi$
$42$		0			0
$43$	−1.11902	−	1.11902i	−0.170649	−	0.170649i	0.616615	−	0.787264i	$-0.288503\pi$
$43$	−1.11902	−	1.11902i	−0.170649	−	0.170649i	−0.787264	+	0.616615i	$0.788503\pi$
$44$		0			0
$45$	−1.18517	+	1.18517i	−0.176674	+	0.176674i
$46$		0			0
$47$			12.7439i			1.85889i	0.368960	+	0.929445i	$0.379714\pi$
$47$			12.7439i			1.85889i	−0.368960	+	0.929445i	$0.620286\pi$
$48$		0			0
$49$	−1.87597	−	3.24928i	−0.267996	−	0.464183i
$50$		0			0
$51$	−7.01716	+	7.01716i	−0.982599	+	0.982599i
$52$		0			0
$53$	4.29003	+	7.43055i	0.589281	+	1.02066i	0.994327	+	0.106368i	$0.0339221\pi$
$53$	4.29003	+	7.43055i	0.589281	+	1.02066i	−0.405046	+	0.914296i	$0.632745\pi$
$54$		0			0
$55$	−1.18014	−	4.40433i	−0.159130	−	0.593880i
$56$		0			0
$57$	0.826439	−	3.08431i	0.109464	−	0.408527i
$58$		0			0
$59$	0.461229	−	1.72133i	0.0600470	−	0.224098i	−0.929381	−	0.369121i	$-0.879659\pi$
$59$	0.461229	−	1.72133i	0.0600470	−	0.224098i	0.989428	+	0.145023i	$0.0463255\pi$
$60$		0			0
$61$	1.13593	−	0.304373i	0.145442	−	0.0389710i	−0.185364	−	0.982670i	$-0.559346\pi$
$61$	1.13593	−	0.304373i	0.145442	−	0.0389710i	0.330805	+	0.943699i	$0.392680\pi$
$62$		0			0
$63$			1.02184i			0.128740i
$64$		0			0
$65$	0.478845	−	0.276461i	0.0593934	−	0.0342908i
$66$		0			0
$67$	1.09686	−	1.89982i	0.134003	−	0.232100i	−0.791213	−	0.611541i	$-0.790550\pi$
$67$	1.09686	−	1.89982i	0.134003	−	0.232100i	0.925216	+	0.379440i	$0.123883\pi$
$68$		0			0
$69$	5.89299	−	1.57902i	0.709433	−	0.190092i
$70$		0			0
$71$	10.3129	+	5.95417i	1.22392	+	0.706630i	0.965751	−	0.259469i	$-0.0835477\pi$
$71$	10.3129	+	5.95417i	1.22392	+	0.706630i	0.258169	+	0.966100i	$0.416881\pi$
$72$		0			0
$73$		−	13.4642i		−	1.57586i	−0.615764	−	0.787931i	$-0.711152\pi$
$73$		−	13.4642i		−	1.57586i	0.615764	−	0.787931i	$-0.288848\pi$
$74$		0			0
$75$		−	5.83168i		−	0.673385i
$76$		0			0
$77$	−2.40744	−	1.38993i	−0.274353	−	0.158398i
$78$		0			0
$79$	−5.27411	+	1.41319i	−0.593383	+	0.158997i	−0.542999	−	0.839733i	$-0.682711\pi$
$79$	−5.27411	+	1.41319i	−0.593383	+	0.158997i	−0.0503843	+	0.998730i	$0.516045\pi$
$80$		0			0
$81$	3.48879	−	6.04276i	0.387643	−	0.671418i
$82$		0			0
$83$	14.4843	−	8.36253i	1.58986	−	0.917907i	0.596534	−	0.802588i	$-0.296544\pi$
$83$	14.4843	−	8.36253i	1.58986	−	0.917907i	0.993328	−	0.115319i	$-0.0367891\pi$
$84$		0			0
$85$			18.8073i			2.03994i
$86$		0			0
$87$	4.28191	−	1.14733i	0.459069	−	0.123007i
$88$		0			0
$89$	1.52247	−	5.68195i	0.161382	−	0.602285i	−0.837092	−	0.547062i	$-0.815746\pi$
$89$	1.52247	−	5.68195i	0.161382	−	0.602285i	0.998474	−	0.0552234i	$-0.0175871\pi$
$90$		0			0
$91$	0.0872466	−	0.325609i	0.00914593	−	0.0341331i
$92$		0			0
$93$	1.44333	+	5.38658i	0.149666	+	0.558562i
$94$		0			0
$95$	−3.02577	−	5.24078i	−0.310437	−	0.537693i
$96$		0			0
$97$	−5.97490	+	5.97490i	−0.606659	+	0.606659i	−0.942071	−	0.335412i	$-0.891124\pi$
$97$	−5.97490	+	5.97490i	−0.606659	+	0.606659i	0.335412	+	0.942071i	$0.391124\pi$
$98$		0			0
$99$	−0.437273	−	0.757380i	−0.0439476	−	0.0761195i
$100$		0			0
$101$		−	5.02954i		−	0.500458i	−0.968187	−	0.250229i	$-0.919494\pi$
$101$		−	5.02954i		−	0.500458i	0.968187	−	0.250229i	$-0.0805058\pi$
$102$		0			0
$103$	5.59657	−	5.59657i	0.551447	−	0.551447i	−0.375412	−	0.926858i	$-0.622499\pi$
$103$	5.59657	−	5.59657i	0.551447	−	0.551447i	0.926858	+	0.375412i	$0.122499\pi$
$104$		0			0
$105$	−5.87615	−	5.87615i	−0.573453	−	0.573453i
$106$		0			0
$107$	−0.0767275	−	0.0442986i	−0.00741753	−	0.00428251i	0.496287	−	0.868159i	$-0.334697\pi$
$107$	−0.0767275	−	0.0442986i	−0.00741753	−	0.00428251i	−0.503704	+	0.863876i	$0.668030\pi$
$108$		0			0
$109$	8.85767	+	2.37341i	0.848411	+	0.227331i	0.656730	−	0.754126i	$-0.271939\pi$
$109$	8.85767	+	2.37341i	0.848411	+	0.227331i	0.191681	+	0.981457i	$0.438606\pi$
$110$		0			0
$111$	−1.24324	−	9.40617i	−0.118003	−	0.892794i
$112$		0			0
$113$	1.12803	−	4.20988i	0.106116	−	0.396032i	−0.892353	−	0.451338i	$-0.850947\pi$
$113$	1.12803	−	4.20988i	0.106116	−	0.396032i	0.998469	+	0.0553062i	$0.0176135\pi$
$114$		0			0
$115$	5.78114	−	10.0132i	0.539094	−	0.933738i
$116$		0			0
$117$	0.0749888	−	0.0749888i	0.00693272	−	0.00693272i
$118$		0			0
$119$	8.10775	+	8.10775i	0.743236	+	0.743236i
$120$		0			0
$121$	−8.62083			−0.783712
$122$		0			0
$123$	0.635114	−	0.366683i	0.0572663	−	0.0330627i
$124$		0			0
$125$	2.63648	+	2.63648i	0.235814	+	0.235814i
$126$		0			0
$127$	13.3135	−	7.68653i	1.18138	−	0.682069i	0.225046	−	0.974348i	$-0.427747\pi$
$127$	13.3135	−	7.68653i	1.18138	−	0.682069i	0.956333	+	0.292279i	$0.0944136\pi$
$128$		0			0
$129$	2.38435	−	0.638883i	0.209930	−	0.0562506i
$130$		0			0
$131$	13.3524	+	3.57776i	1.16660	+	0.312591i	0.789601	−	0.613621i	$-0.210288\pi$
$131$	13.3524	+	3.57776i	1.16660	+	0.312591i	0.377004	+	0.926212i	$0.376954\pi$
$132$		0			0
$133$	−3.56367	−	0.954882i	−0.309009	−	0.0827988i
$134$		0			0
$135$	−4.25690	−	15.8870i	−0.366376	−	1.36733i
$136$		0			0
$137$	−9.79691			−0.837007			−0.418503	−	0.908215i	$-0.637445\pi$
$137$	−9.79691			−0.837007			−0.418503	+	0.908215i	$0.637445\pi$
$138$		0			0
$139$	0.961667	+	1.66566i	0.0815675	+	0.141279i	0.903923	−	0.427694i	$-0.140674\pi$
$139$	0.961667	+	1.66566i	0.0815675	+	0.141279i	−0.822356	+	0.568973i	$0.807341\pi$
$140$		0			0
$141$	−17.2150	−	9.93906i	−1.44976	−	0.837020i
$142$		0			0
$143$	0.0746706	+	0.278674i	0.00624427	+	0.0233039i
$144$		0			0
$145$	4.20064	−	7.27571i	0.348844	−	0.604215i
$146$		0			0
$147$	5.85233			0.482692
$148$		0			0
$149$	2.24830			0.184188			0.0920939	−	0.995750i	$-0.470644\pi$
$149$	2.24830			0.184188			0.0920939	+	0.995750i	$0.470644\pi$
$150$		0			0
$151$	−8.84886	+	15.3267i	−0.720110	+	1.24727i	0.240845	+	0.970564i	$0.422575\pi$
$151$	−8.84886	+	15.3267i	−0.720110	+	1.24727i	−0.960955	+	0.276704i	$0.910758\pi$
$152$		0			0
$153$	0.933621	+	3.48432i	0.0754788	+	0.281691i
$154$		0			0
$155$	9.15273	+	5.28433i	0.735165	+	0.424448i
$156$		0			0
$157$	1.48117	+	2.56546i	0.118210	+	0.204746i	0.919058	−	0.394121i	$-0.128951\pi$
$157$	1.48117	+	2.56546i	0.118210	+	0.204746i	−0.800848	+	0.598867i	$0.795618\pi$
$158$		0			0
$159$	−13.3833			−1.06136
$160$		0			0
$161$	−1.82443	−	6.80887i	−0.143785	−	0.536614i
$162$		0			0
$163$	15.9614	+	4.27683i	1.25019	+	0.334988i	0.822410	−	0.568895i	$-0.192629\pi$
$163$	15.9614	+	4.27683i	1.25019	+	0.334988i	0.427780	+	0.903883i	$0.359296\pi$
$164$		0			0
$165$	6.86993	+	1.84079i	0.534823	+	0.143305i
$166$		0			0
$167$	5.88550	−	1.57702i	0.455434	−	0.122033i	−0.0238070	−	0.999717i	$-0.507579\pi$
$167$	5.88550	−	1.57702i	0.455434	−	0.122033i	0.479241	+	0.877683i	$0.340912\pi$
$168$		0			0
$169$	11.2280	−	6.48251i	0.863695	−	0.498654i
$170$		0			0
$171$	−0.820725	−	0.820725i	−0.0627624	−	0.0627624i
$172$		0			0
$173$	14.9418	−	8.62667i	1.13601	−	0.655873i	0.190568	−	0.981674i	$-0.438967\pi$
$173$	14.9418	−	8.62667i	1.13601	−	0.655873i	0.945438	+	0.325801i	$0.105634\pi$
$174$		0			0
$175$	−6.73803			−0.509347
$176$		0			0
$177$	1.96552	+	1.96552i	0.147738	+	0.147738i
$178$		0			0
$179$	−14.1327	+	14.1327i	−1.05633	+	1.05633i	−0.0580108	+	0.998316i	$0.518476\pi$
$179$	−14.1327	+	14.1327i	−1.05633	+	1.05633i	−0.998316	+	0.0580108i	$0.981524\pi$
$180$		0			0
$181$	−10.8778	+	18.8409i	−0.808541	+	1.40043i	0.105334	+	0.994437i	$0.466409\pi$
$181$	−10.8778	+	18.8409i	−0.808541	+	1.40043i	−0.913875	+	0.405997i	$0.866924\pi$
$182$		0			0
$183$	−0.474765	+	1.77185i	−0.0350956	+	0.130979i
$184$		0			0
$185$	−14.2712	−	10.9391i	−1.04924	−	0.804259i
$186$		0			0
$187$	−9.47894	−	2.53988i	−0.693169	−	0.185734i
$188$		0			0
$189$	−8.68392	−	5.01367i	−0.631662	−	0.364690i
$190$		0			0
$191$	12.2059	+	12.2059i	0.883189	+	0.883189i	0.993857	−	0.110668i	$-0.0352991\pi$
$191$	12.2059	+	12.2059i	0.883189	+	0.883189i	−0.110668	+	0.993857i	$0.535299\pi$
$192$		0			0
$193$	18.0908	−	18.0908i	1.30220	−	1.30220i	0.375298	−	0.926904i	$-0.377540\pi$
$193$	18.0908	−	18.0908i	1.30220	−	1.30220i	0.926904	−	0.375298i	$-0.122460\pi$
$194$		0			0
$195$			0.862456i			0.0617617i
$196$		0			0
$197$	−7.04657	−	12.2050i	−0.502048	−	0.869572i	−0.999997	−	0.00236593i	$-0.999247\pi$
$197$	−7.04657	−	12.2050i	−0.502048	−	0.869572i	0.497950	−	0.867206i	$-0.334086\pi$
$198$		0			0
$199$	−17.0897	+	17.0897i	−1.21146	+	1.21146i	−0.240909	+	0.970548i	$0.577445\pi$
$199$	−17.0897	+	17.0897i	−1.21146	+	1.21146i	−0.970548	+	0.240909i	$0.922555\pi$
$200$		0			0
$201$	1.71090	+	2.96337i	0.120678	+	0.209020i
$202$		0			0
$203$	−1.32565	−	4.94740i	−0.0930425	−	0.347239i
$204$		0			0
$205$	0.359723	−	1.34251i	0.0251242	−	0.0937647i
$206$		0			0
$207$	0.573967	−	2.14207i	0.0398934	−	0.148884i
$208$		0			0
$209$	3.04999	−	0.817242i	0.210972	−	0.0565298i
$210$		0			0
$211$		−	20.3907i		−	1.40376i	−0.712297	−	0.701878i	$-0.752345\pi$
$211$		−	20.3907i		−	1.40376i	0.712297	−	0.701878i	$-0.247655\pi$
$212$		0			0
$213$	−16.0862	+	9.28740i	−1.10221	+	0.636362i
$214$		0			0
$215$	2.33909	−	4.05142i	0.159524	−	0.276304i
$216$		0			0
$217$	6.22375	−	1.66765i	0.422495	−	0.113207i
$218$		0			0
$219$	18.1879	+	10.5008i	1.22902	+	0.709578i
$220$		0			0
$221$		−	1.18999i		−	0.0800476i
$222$		0			0
$223$		−	13.1972i		−	0.883748i	−0.897077	−	0.441874i	$-0.854314\pi$
$223$		−	13.1972i		−	0.883748i	0.897077	−	0.441874i	$-0.145686\pi$
$224$		0			0
$225$	−1.83579	−	1.05989i	−0.122386	−	0.0706595i
$226$		0			0
$227$	15.1366	−	4.05585i	1.00465	−	0.269196i	0.281260	−	0.959632i	$-0.409248\pi$
$227$	15.1366	−	4.05585i	1.00465	−	0.269196i	0.723394	+	0.690435i	$0.242581\pi$
$228$		0			0
$229$	−12.3968	+	21.4719i	−0.819206	+	1.41891i	0.0870628	+	0.996203i	$0.472252\pi$
$229$	−12.3968	+	21.4719i	−0.819206	+	1.41891i	−0.906268	+	0.422703i	$0.861081\pi$
$230$		0			0
$231$	3.75515	−	2.16804i	0.247071	−	0.142646i
$232$		0			0
$233$			26.1029i			1.71006i	0.518578	+	0.855031i	$0.326462\pi$
$233$			26.1029i			1.71006i	−0.518578	+	0.855031i	$0.673538\pi$
$234$		0			0
$235$	−36.3890	+	9.75040i	−2.37376	+	0.636046i
$236$		0			0
$237$	2.20432	−	8.22662i	0.143186	−	0.534376i
$238$		0			0
$239$	−3.50212	+	13.0701i	−0.226533	+	0.845434i	0.755251	+	0.655435i	$0.227515\pi$
$239$	−3.50212	+	13.0701i	−0.226533	+	0.845434i	−0.981784	+	0.189998i	$0.939152\pi$
$240$		0			0
$241$	−2.23148	−	8.32801i	−0.143743	−	0.536454i	−0.999808	−	0.0195872i	$-0.993765\pi$
$241$	−2.23148	−	8.32801i	−0.143743	−	0.536454i	0.856066	−	0.516867i	$-0.172902\pi$
$242$		0			0
$243$	−2.90388	−	5.02967i	−0.186284	−	0.322654i
$244$		0			0
$245$	7.84269	−	7.84269i	0.501051	−	0.501051i
$246$		0			0
$247$	0.191449	+	0.331599i	0.0121816	+	0.0210991i
$248$		0			0
$249$			26.0880i			1.65326i
$250$		0			0
$251$	5.16698	−	5.16698i	0.326137	−	0.326137i	−0.524978	−	0.851115i	$-0.675927\pi$
$251$	5.16698	−	5.16698i	0.326137	−	0.326137i	0.851115	+	0.524978i	$0.175927\pi$
$252$		0			0
$253$	4.26596	+	4.26596i	0.268199	+	0.268199i
$254$		0			0
$255$	−25.4057	−	14.6680i	−1.59096	−	0.918544i
$256$		0			0
$257$	−0.0415252	−	0.0111266i	−0.00259027	−	0.000694060i	0.257524	−	0.966272i	$-0.417093\pi$
$257$	−0.0415252	−	0.0111266i	−0.00259027	−	0.000694060i	−0.260114	+	0.965578i	$0.583760\pi$
$258$		0			0
$259$	−10.8681	+	1.43646i	−0.675308	+	0.0892575i
$260$		0			0
$261$	0.417050	−	1.55645i	0.0258148	−	0.0963420i
$262$		0			0
$263$	3.77009	−	6.52998i	0.232473	−	0.402656i	−0.726062	−	0.687629i	$-0.758651\pi$
$263$	3.77009	−	6.52998i	0.232473	−	0.402656i	0.958535	+	0.284973i	$0.0919848\pi$
$264$		0			0
$265$	−17.9349	+	17.9349i	−1.10173	+	1.10173i
$266$		0			0
$267$	6.48800	+	6.48800i	0.397059	+	0.397059i
$268$		0			0
$269$	3.36592			0.205224			0.102612	−	0.994721i	$-0.467280\pi$
$269$	3.36592			0.205224			0.102612	+	0.994721i	$0.467280\pi$
$270$		0			0
$271$	−19.8553	+	11.4635i	−1.20612	+	0.696356i	−0.961910	−	0.273365i	$-0.911863\pi$
$271$	−19.8553	+	11.4635i	−1.20612	+	0.696356i	−0.244214	+	0.969721i	$0.578530\pi$
$272$		0			0
$273$	0.371800	+	0.371800i	0.0225024	+	0.0225024i
$274$		0			0
$275$	4.99418	−	2.88339i	0.301160	−	0.173875i
$276$		0			0
$277$	−14.8209	+	3.97124i	−0.890500	+	0.238609i	−0.674932	−	0.737880i	$-0.735827\pi$
$277$	−14.8209	+	3.97124i	−0.890500	+	0.238609i	−0.215568	+	0.976489i	$0.569160\pi$
$278$		0			0
$279$	1.95799	+	0.524642i	0.117222	+	0.0314095i
$280$		0			0
$281$	14.8966	+	3.99154i	0.888659	+	0.238115i	0.674139	−	0.738604i	$-0.264515\pi$
$281$	14.8966	+	3.99154i	0.888659	+	0.238115i	0.214520	+	0.976720i	$0.431181\pi$
$282$		0			0
$283$	−3.78333	−	14.1196i	−0.224895	−	0.839321i	−0.982446	−	0.186545i	$-0.940271\pi$
$283$	−3.78333	−	14.1196i	−0.224895	−	0.839321i	0.757551	−	0.652776i	$-0.226396\pi$
$284$		0			0
$285$	9.43926			0.559134
$286$		0			0
$287$	−0.423673	−	0.733823i	−0.0250086	−	0.0433162i
$288$		0			0
$289$	20.3316	+	11.7385i	1.19598	+	0.690498i
$290$		0			0
$291$	−3.41126	−	12.7310i	−0.199971	−	0.746303i
$292$		0			0
$293$	9.41971	−	16.3154i	0.550305	−	0.953157i	−0.447947	−	0.894060i	$-0.647845\pi$
$293$	9.41971	−	16.3154i	0.550305	−	0.953157i	0.998252	−	0.0590968i	$-0.0188221\pi$
$294$		0			0
$295$	5.26798			0.306714
$296$		0			0
$297$	8.58195			0.497975
$298$		0			0
$299$	−0.365789	+	0.633565i	−0.0211541	+	0.0366400i
$300$		0			0
$301$	−0.738178	−	2.75492i	−0.0425478	−	0.158791i
$302$		0			0
$303$	6.79409	+	3.92257i	0.390310	+	0.225346i
$304$		0			0
$305$	1.73821	+	3.01067i	0.0995298	+	0.172391i
$306$		0			0
$307$	−25.5513			−1.45829			−0.729144	−	0.684360i	$-0.760082\pi$
$307$	−25.5513			−1.45829			−0.729144	+	0.684360i	$0.760082\pi$
$308$		0			0
$309$	3.19526	+	11.9249i	0.181772	+	0.678382i
$310$		0			0
$311$	14.0863	+	3.77442i	0.798762	+	0.214028i	0.635040	−	0.772479i	$-0.280983\pi$
$311$	14.0863	+	3.77442i	0.798762	+	0.214028i	0.163722	+	0.986507i	$0.447650\pi$
$312$		0			0
$313$	11.7954	+	3.16056i	0.666714	+	0.178646i	0.576274	−	0.817256i	$-0.304506\pi$
$313$	11.7954	+	3.16056i	0.666714	+	0.178646i	0.0904400	+	0.995902i	$0.471173\pi$
$314$		0			0
$315$	−2.91776	+	0.781812i	−0.164397	+	0.0440501i
$316$		0			0
$317$	11.3383	−	6.54618i	0.636823	−	0.367670i	−0.146566	−	0.989201i	$-0.546822\pi$
$317$	11.3383	−	6.54618i	0.636823	−	0.367670i	0.783390	+	0.621531i	$0.213489\pi$
$318$		0			0
$319$	3.09969	+	3.09969i	0.173550	+	0.173550i
$320$		0			0
$321$	0.119681	−	0.0690976i	0.00667992	−	0.00385665i
$322$		0			0
$323$	−13.0240			−0.724677
$324$		0			0
$325$	0.494478	+	0.494478i	0.0274287	+	0.0274287i
$326$		0			0
$327$	−10.1142	+	10.1142i	−0.559319	+	0.559319i
$328$		0			0
$329$	−11.4838	+	19.8905i	−0.633121	+	1.09660i
$330$		0			0
$331$	−4.05724	+	15.1418i	−0.223006	+	0.832270i	0.760187	+	0.649704i	$0.225107\pi$
$331$	−4.05724	+	15.1418i	−0.223006	+	0.832270i	−0.983194	+	0.182566i	$0.941560\pi$
$332$		0			0
$333$	−3.18698	−	1.31818i	−0.174645	−	0.0722358i
$334$		0			0
$335$	6.26397	+	1.67843i	0.342237	+	0.0917022i
$336$		0			0
$337$	2.26339	+	1.30677i	0.123295	+	0.0711841i	0.560379	−	0.828236i	$-0.310656\pi$
$337$	2.26339	+	1.30677i	0.123295	+	0.0711841i	−0.437084	+	0.899421i	$0.643989\pi$
$338$		0			0
$339$	4.80710	+	4.80710i	0.261086	+	0.261086i
$340$		0			0
$341$	−3.89937	+	3.89937i	−0.211162	+	0.211162i
$342$		0			0
$343$		−	19.3775i		−	1.04629i
$344$		0			0
$345$	9.01749	+	15.6188i	0.485485	+	0.840885i
$346$		0			0
$347$	−22.8956	+	22.8956i	−1.22910	+	1.22910i	−0.264795	+	0.964305i	$0.585304\pi$
$347$	−22.8956	+	22.8956i	−1.22910	+	1.22910i	−0.964305	+	0.264795i	$0.914696\pi$
$348$		0			0
$349$	−3.78425	−	6.55452i	−0.202566	−	0.350855i	0.746788	−	0.665062i	$-0.231595\pi$
$349$	−3.78425	−	6.55452i	−0.202566	−	0.350855i	−0.949355	+	0.314207i	$0.898262\pi$
$350$		0			0
$351$	0.269346	+	1.00521i	0.0143766	+	0.0536543i
$352$		0			0
$353$	5.78171	−	21.5776i	0.307729	−	1.14846i	−0.622841	−	0.782349i	$-0.714022\pi$
$353$	5.78171	−	21.5776i	0.307729	−	1.14846i	0.930570	−	0.366113i	$-0.119312\pi$
$354$		0			0
$355$	−9.11111	+	34.0031i	−0.483568	+	1.80470i
$356$		0			0
$357$	−17.2755	+	4.62897i	−0.914319	+	0.244991i
$358$		0			0
$359$			23.0306i			1.21551i	0.794124	+	0.607755i	$0.207930\pi$
$359$			23.0306i			1.21551i	−0.794124	+	0.607755i	$0.792070\pi$
$360$		0			0
$361$	−12.8253	+	7.40466i	−0.675013	+	0.389719i
$362$		0			0
$363$	6.72344	−	11.6453i	0.352889	−	0.611222i
$364$		0			0
$365$	38.4456	−	10.3015i	2.01234	−	0.539204i
$366$		0			0
$367$	−6.15399	−	3.55301i	−0.321235	−	0.185465i	0.330708	−	0.943733i	$-0.392713\pi$
$367$	−6.15399	−	3.55301i	−0.321235	−	0.185465i	−0.651943	+	0.758268i	$0.726046\pi$
$368$		0			0
$369$		−	0.266575i		−	0.0138773i
$370$		0			0
$371$			15.4633i			0.802814i
$372$		0			0
$373$	4.61823	+	2.66634i	0.239123	+	0.138058i	0.614774	−	0.788704i	$-0.289247\pi$
$373$	4.61823	+	2.66634i	0.239123	+	0.138058i	−0.375651	+	0.926761i	$0.622581\pi$
$374$		0			0
$375$	−5.61767	+	1.50525i	−0.290095	+	0.0777308i
$376$		0			0
$377$	−0.265786	+	0.460355i	−0.0136887	+	0.0237095i
$378$		0			0
$379$	4.22932	−	2.44180i	0.217246	−	0.125427i	−0.387429	−	0.921900i	$-0.626637\pi$
$379$	4.22932	−	2.44180i	0.217246	−	0.125427i	0.604674	+	0.796473i	$0.293303\pi$
$380$		0			0
$381$			23.9791i			1.22849i
$382$		0			0
$383$	−4.16786	+	1.11677i	−0.212968	+	0.0570645i	−0.363725	−	0.931506i	$-0.618495\pi$
$383$	−4.16786	+	1.11677i	−0.212968	+	0.0570645i	0.150758	+	0.988571i	$0.451829\pi$
$384$		0			0
$385$	2.12688	−	7.93764i	0.108396	−	0.404540i
$386$		0			0
$387$	0.232231	−	0.866697i	0.0118050	−	0.0440567i
$388$		0			0
$389$	−2.15590	−	8.04594i	−0.109309	−	0.407945i	0.889490	−	0.456955i	$-0.151060\pi$
$389$	−2.15590	−	8.04594i	−0.109309	−	0.407945i	−0.998798	+	0.0490100i	$0.984393\pi$
$390$		0			0
$391$	−12.4421	−	21.5503i	−0.629224	−	1.08985i
$392$		0			0
$393$	−15.2466	+	15.2466i	−0.769089	+	0.769089i
$394$		0			0
$395$	−8.07047	−	13.9785i	−0.406069	−	0.703333i
$396$		0			0
$397$		−	10.4552i		−	0.524733i	−0.964968	−	0.262367i	$-0.915497\pi$
$397$		−	10.4552i		−	0.524733i	0.964968	−	0.262367i	$-0.0845030\pi$
$398$		0			0
$399$	4.06922	−	4.06922i	0.203716	−	0.203716i
$400$		0			0
$401$	−17.9909	−	17.9909i	−0.898420	−	0.898420i	0.0968762	−	0.995296i	$-0.469115\pi$
$401$	−17.9909	−	17.9909i	−0.898420	−	0.898420i	−0.995296	+	0.0968762i	$0.969115\pi$
$402$		0			0
$403$	−0.579119	−	0.334355i	−0.0288480	−	0.0166554i
$404$		0			0
$405$	19.9238	+	5.33856i	0.990021	+	0.265275i
$406$		0			0
$407$	7.44062	−	5.71544i	0.368818	−	0.283304i
$408$		0			0
$409$	4.36699	−	16.2978i	0.215934	−	0.805876i	−0.769902	−	0.638162i	$-0.779695\pi$
$409$	4.36699	−	16.2978i	0.215934	−	0.805876i	0.985836	−	0.167714i	$-0.0536384\pi$
$410$		0			0
$411$	7.64067	−	13.2340i	0.376887	−	0.652787i
$412$		0			0
$413$	2.27100	−	2.27100i	0.111749	−	0.111749i
$414$		0			0
$415$	34.9604	+	34.9604i	1.71614	+	1.71614i
$416$		0			0
$417$	−3.00004			−0.146913
$418$		0			0
$419$	−3.24985	+	1.87630i	−0.158765	+	0.0916633i	−0.577278	−	0.816548i	$-0.695885\pi$
$419$	−3.24985	+	1.87630i	−0.158765	+	0.0916633i	0.418512	+	0.908211i	$0.362552\pi$
$420$		0			0
$421$	−19.5023	−	19.5023i	−0.950486	−	0.950486i	0.0483448	−	0.998831i	$-0.484605\pi$
$421$	−19.5023	−	19.5023i	−0.950486	−	0.950486i	−0.998831	+	0.0483448i	$0.984605\pi$
$422$		0			0
$423$	−6.25755	+	3.61280i	−0.304252	+	0.175660i
$424$		0			0
$425$	−22.9757	+	6.15632i	−1.11449	+	0.298625i
$426$		0			0
$427$	2.04722	+	0.548552i	0.0990721	+	0.0265463i
$428$		0			0
$429$	−0.434680	−	0.116472i	−0.0209865	−	0.00562333i
$430$		0			0
$431$	−7.18028	−	26.7972i	−0.345862	−	1.29077i	−0.891602	−	0.452820i	$-0.850418\pi$
$431$	−7.18028	−	26.7972i	−0.345862	−	1.29077i	0.545740	−	0.837955i	$-0.316249\pi$
$432$		0			0
$433$	−40.1109			−1.92761			−0.963803	−	0.266614i	$-0.914095\pi$
$433$	−40.1109			−1.92761			−0.963803	+	0.266614i	$0.914095\pi$
$434$		0			0
$435$	6.55221	+	11.3488i	0.314154	+	0.544131i
$436$		0			0
$437$	6.93414	+	4.00343i	0.331705	+	0.191510i
$438$		0			0
$439$	−5.43088	−	20.2683i	−0.259202	−	0.967354i	−0.965704	−	0.259644i	$-0.916395\pi$
$439$	−5.43088	−	20.2683i	−0.259202	−	0.967354i	0.706503	−	0.707710i	$-0.250272\pi$
$440$		0			0
$441$	1.06365	−	1.84229i	0.0506498	−	0.0877281i
$442$		0			0
$443$	21.3749			1.01555			0.507777	−	0.861489i	$-0.330467\pi$
$443$	21.3749			1.01555			0.507777	+	0.861489i	$0.330467\pi$
$444$		0			0
$445$	17.3891			0.824322
$446$		0			0
$447$	−1.75346	+	3.03709i	−0.0829359	+	0.143649i
$448$		0			0
$449$	−1.91140	−	7.13345i	−0.0902046	−	0.336648i	0.906044	−	0.423183i	$-0.139087\pi$
$449$	−1.91140	−	7.13345i	−0.0902046	−	0.336648i	−0.996249	+	0.0865349i	$0.972421\pi$
$450$		0			0
$451$	0.628047	+	0.362603i	0.0295736	+	0.0170743i
$452$		0			0
$453$	−13.8026	−	23.9068i	−0.648501	−	1.12324i
$454$		0			0
$455$	0.996497			0.0467165
$456$		0			0
$457$	3.60236	+	13.4442i	0.168511	+	0.628892i	0.997566	+	0.0697252i	$0.0222122\pi$
$457$	3.60236	+	13.4442i	0.168511	+	0.628892i	−0.829055	+	0.559167i	$0.811121\pi$
$458$		0			0
$459$	−34.1917	−	9.16165i	−1.59593	−	0.427629i
$460$		0			0
$461$	−7.57783	−	2.03047i	−0.352935	−	0.0945686i	0.0779958	−	0.996954i	$-0.475148\pi$
$461$	−7.57783	−	2.03047i	−0.352935	−	0.0945686i	−0.430931	+	0.902385i	$0.641815\pi$
$462$		0			0
$463$	36.9117	−	9.89046i	1.71543	−	0.459649i	0.738687	−	0.674049i	$-0.235446\pi$
$463$	36.9117	−	9.89046i	1.71543	−	0.459649i	0.976746	+	0.214400i	$0.0687797\pi$
$464$		0			0
$465$	−14.2765	+	8.24257i	−0.662059	+	0.382240i
$466$		0			0
$467$	−18.4825	−	18.4825i	−0.855267	−	0.855267i	0.135509	−	0.990776i	$-0.456733\pi$
$467$	−18.4825	−	18.4825i	−0.855267	−	0.855267i	−0.990776	+	0.135509i	$0.956733\pi$
$468$		0			0
$469$	3.42393	−	1.97681i	0.158102	−	0.0912804i
$470$		0			0
$471$	−4.62069			−0.212910
$472$		0			0
$473$	1.72604	+	1.72604i	0.0793633	+	0.0793633i
$474$		0			0
$475$	5.41188	−	5.41188i	0.248314	−	0.248314i
$476$		0			0
$477$	−2.43238	+	4.21300i	−0.111371	+	0.192900i
$478$		0			0
$479$	−3.30587	+	12.3377i	−0.151049	+	0.563722i	0.848362	+	0.529416i	$0.177589\pi$
$479$	−3.30587	+	12.3377i	−0.151049	+	0.563722i	−0.999411	+	0.0343063i	$0.989078\pi$
$480$		0			0
$481$	0.902981	+	0.692148i	0.0411724	+	0.0315592i
$482$		0			0
$483$	10.6206	+	2.84577i	0.483252	+	0.129487i
$484$		0			0
$485$	−21.6322	−	12.4893i	−0.982266	−	0.567111i
$486$		0			0
$487$	7.26027	+	7.26027i	0.328994	+	0.328994i	0.852204	−	0.523210i	$-0.175266\pi$
$487$	7.26027	+	7.26027i	0.328994	+	0.328994i	−0.523210	+	0.852204i	$0.675266\pi$
$488$		0			0
$489$	−18.2257	+	18.2257i	−0.824194	+	0.824194i
$490$		0			0
$491$			3.53901i			0.159713i	0.996806	+	0.0798567i	$0.0254463\pi$
$491$			3.53901i			0.159713i	−0.996806	+	0.0798567i	$0.974554\pi$
$492$		0			0
$493$	−9.04056	−	15.6587i	−0.407166	−	0.705233i
$494$		0			0
$495$	1.82807	−	1.82807i	0.0821654	−	0.0821654i
$496$		0			0
$497$	10.7308	+	18.5863i	0.481343	+	0.833711i
$498$		0			0
$499$	−10.1628	−	37.9280i	−0.454948	−	1.69789i	−0.688239	−	0.725484i	$-0.741616\pi$
$499$	−10.1628	−	37.9280i	−0.454948	−	1.69789i	0.233291	−	0.972407i	$-0.425051\pi$
$500$		0			0
$501$	−2.45985	+	9.18028i	−0.109898	+	0.410145i
$502$		0			0
$503$	−3.53671	+	13.1992i	−0.157694	+	0.588522i	0.841166	+	0.540778i	$0.181870\pi$
$503$	−3.53671	+	13.1992i	−0.157694	+	0.588522i	−0.998860	+	0.0477442i	$0.984797\pi$
$504$		0			0
$505$	14.3613	−	3.84811i	0.639072	−	0.171239i
$506$		0			0
$507$			20.2230i			0.898135i
$508$		0			0
$509$	32.6841	−	18.8702i	1.44870	−	0.836405i	0.450292	−	0.892882i	$-0.351320\pi$
$509$	32.6841	−	18.8702i	1.44870	−	0.836405i	0.998404	+	0.0564767i	$0.0179867\pi$
$510$		0			0
$511$	12.1328	−	21.0146i	0.536724	−	0.929633i
$512$		0			0
$513$	11.0017	−	2.94789i	0.485736	−	0.130153i
$514$		0			0
$515$	20.2624	+	11.6985i	0.892869	+	0.515498i
$516$		0			0
$517$		−	19.6569i		−	0.864510i
$518$		0			0
$519$			26.9120i			1.18130i
$520$		0			0
$521$	−11.0597	−	6.38534i	−0.484536	−	0.279747i	0.237769	−	0.971322i	$-0.423584\pi$
$521$	−11.0597	−	6.38534i	−0.484536	−	0.279747i	−0.722305	+	0.691575i	$0.756917\pi$
$522$		0			0
$523$	40.9627	−	10.9759i	1.79117	−	0.479944i	0.798630	−	0.601823i	$-0.205559\pi$
$523$	40.9627	−	10.9759i	1.79117	−	0.479944i	0.992545	+	0.121879i	$0.0388920\pi$
$524$		0			0
$525$	5.25503	−	9.10198i	0.229348	−	0.397243i
$526$		0			0
$527$	19.6984	−	11.3729i	0.858076	−	0.495410i
$528$		0			0
$529$		−	7.70183i		−	0.334862i
$530$		0			0
$531$	0.975967	−	0.261510i	0.0423534	−	0.0113486i
$532$		0			0
$533$	−0.0227607	+	0.0849441i	−0.000985876	+	0.00367934i
$534$		0			0
$535$	0.0677860	−	0.252981i	0.00293065	−	0.0109373i
$536$		0			0
$537$	−8.06879	−	30.1131i	−0.348194	−	1.29948i
$538$		0			0
$539$	2.89360	+	5.01187i	0.124636	+	0.215876i
$540$		0			0
$541$	23.1784	−	23.1784i	0.996516	−	0.996516i	−0.00347753	−	0.999994i	$-0.501107\pi$
$541$	23.1784	−	23.1784i	0.996516	−	0.996516i	0.999994	+	0.00347753i	$0.00110694\pi$
$542$		0			0
$543$	−16.9673	−	29.3883i	−0.728138	−	1.26117i
$544$		0			0
$545$			27.1081i			1.16118i
$546$		0			0
$547$	17.1290	−	17.1290i	0.732382	−	0.732382i	−0.238709	−	0.971091i	$-0.576724\pi$
$547$	17.1290	−	17.1290i	0.732382	−	0.732382i	0.971091	+	0.238709i	$0.0767242\pi$
$548$		0			0
$549$	0.471482	+	0.471482i	0.0201224	+	0.0201224i
$550$		0			0
$551$	5.03842	+	2.90893i	0.214644	+	0.123925i
$552$		0			0
$553$	−9.50519	−	2.54691i	−0.404202	−	0.108305i
$554$		0			0
$555$	25.9072	−	10.7466i	1.09970	−	0.456169i
$556$		0			0
$557$	−0.768717	+	2.86889i	−0.0325716	+	0.121559i	−0.980297	−	0.197527i	$-0.936709\pi$
$557$	−0.768717	+	2.86889i	−0.0325716	+	0.121559i	0.947726	+	0.319086i	$0.103376\pi$
$558$		0			0
$559$	−0.148001	+	0.256345i	−0.00625976	+	0.0108422i
$560$		0			0
$561$	10.8236	−	10.8236i	0.456975	−	0.456975i
$562$		0			0
$563$	−28.5309	−	28.5309i	−1.20243	−	1.20243i	−0.973424	−	0.229010i	$-0.926451\pi$
$563$	−28.5309	−	28.5309i	−1.20243	−	1.20243i	−0.229010	−	0.973424i	$-0.573549\pi$
$564$		0			0
$565$	12.8840			0.542032
$566$		0			0
$567$	10.8905	−	6.28762i	0.457357	−	0.264055i
$568$		0			0
$569$	33.0193	+	33.0193i	1.38424	+	1.38424i	0.836930	+	0.547309i	$0.184348\pi$
$569$	33.0193	+	33.0193i	1.38424	+	1.38424i	0.547309	+	0.836930i	$0.315652\pi$
$570$		0			0
$571$	9.96795	−	5.75500i	0.417146	−	0.240839i	−0.276710	−	0.960954i	$-0.589244\pi$
$571$	9.96795	−	5.75500i	0.417146	−	0.240839i	0.693855	+	0.720114i	$0.255911\pi$
$572$		0			0
$573$	−26.0077	+	6.96874i	−1.08649	+	0.291123i
$574$		0			0
$575$	14.1249	+	3.78475i	0.589048	+	0.157835i
$576$		0			0
$577$	23.8843	+	6.39978i	0.994317	+	0.266426i	0.719063	−	0.694945i	$-0.244571\pi$
$577$	23.8843	+	6.39978i	0.994317	+	0.266426i	0.275254	+	0.961371i	$0.411238\pi$
$578$		0			0
$579$	10.3286	+	38.5468i	0.429241	+	1.60195i
$580$		0			0
$581$	30.1425			1.25052
$582$		0			0
$583$	−6.61717	−	11.4613i	−0.274055	−	0.474678i
$584$		0			0
$585$	0.271497	+	0.156749i	0.0112250	+	0.00648078i
$586$		0			0
$587$	6.27006	+	23.4002i	0.258793	+	0.965828i	0.965941	+	0.258763i	$0.0833148\pi$
$587$	6.27006	+	23.4002i	0.258793	+	0.965828i	−0.707148	+	0.707065i	$0.750019\pi$
$588$		0			0
$589$	−3.65939	+	6.33825i	−0.150782	+	0.261163i
$590$		0			0
$591$	21.9827			0.904246
$592$		0			0
$593$	14.3019			0.587309			0.293654	−	0.955912i	$-0.405129\pi$
$593$	14.3019			0.587309			0.293654	+	0.955912i	$0.405129\pi$
$594$		0			0
$595$	−16.9476	+	29.3542i	−0.694785	+	1.20340i
$596$		0			0
$597$	−9.75704	−	36.4138i	−0.399329	−	1.49032i
$598$		0			0
$599$	−13.5021	−	7.79542i	−0.551679	−	0.318512i	0.198120	−	0.980178i	$-0.436517\pi$
$599$	−13.5021	−	7.79542i	−0.551679	−	0.318512i	−0.749799	+	0.661666i	$0.769850\pi$
$600$		0			0
$601$	−0.0850404	−	0.147294i	−0.00346887	−	0.00600826i	0.864286	−	0.503001i	$-0.167771\pi$
$601$	−0.0850404	−	0.147294i	−0.00346887	−	0.00600826i	−0.867755	+	0.496993i	$0.834438\pi$
$602$		0			0
$603$	1.24381			0.0506518
$604$		0			0
$605$	−6.59582	−	24.6159i	−0.268158	−	1.00078i
$606$		0			0
$607$	−0.959286	−	0.257040i	−0.0389362	−	0.0104329i	0.239298	−	0.970946i	$-0.423083\pi$
$607$	−0.959286	−	0.257040i	−0.0389362	−	0.0104329i	−0.278235	+	0.960513i	$0.589749\pi$
$608$		0			0
$609$	7.71702	+	2.06777i	0.312709	+	0.0837902i
$610$		0			0
$611$	2.30243	−	0.616935i	0.0931465	−	0.0249585i
$612$		0			0
$613$	−11.3579	+	6.55749i	−0.458742	+	0.264855i	−0.711515	−	0.702671i	$-0.751991\pi$
$613$	−11.3579	+	6.55749i	−0.458742	+	0.264855i	0.252773	+	0.967526i	$0.418657\pi$
$614$		0			0
$615$	1.53296	+	1.53296i	0.0618148	+	0.0618148i
$616$		0			0
$617$	−29.1140	+	16.8090i	−1.17208	+	0.676703i	−0.954170	−	0.299265i	$-0.903259\pi$
$617$	−29.1140	+	16.8090i	−1.17208	+	0.676703i	−0.217914	+	0.975968i	$0.569925\pi$
$618$		0			0
$619$	6.96530			0.279959			0.139980	−	0.990154i	$-0.455296\pi$
$619$	6.96530			0.279959			0.139980	+	0.990154i	$0.455296\pi$
$620$		0			0
$621$	15.3879	+	15.3879i	0.617494	+	0.617494i
$622$		0			0
$623$	7.49636	−	7.49636i	0.300335	−	0.300335i
$624$		0			0
$625$	−14.8578	+	25.7345i	−0.594312	+	1.02938i
$626$		0			0
$627$	−1.27474	+	4.75741i	−0.0509084	+	0.189993i
$628$		0			0
$629$	−35.7460	+	14.8279i	−1.42529	+	0.591228i
$630$		0			0
$631$	23.3425	+	6.25460i	0.929250	+	0.248992i	0.691535	−	0.722343i	$-0.256935\pi$
$631$	23.3425	+	6.25460i	0.929250	+	0.248992i	0.237715	+	0.971335i	$0.423602\pi$
$632$		0			0
$633$	27.5446	+	15.9029i	1.09480	+	0.632082i
$634$		0			0
$635$	32.1343	+	32.1343i	1.27521	+	1.27521i
$636$		0			0
$637$	−0.496229	+	0.496229i	−0.0196613	+	0.0196613i
$638$		0			0
$639$			6.75184i			0.267099i
$640$		0			0
$641$	−17.7264	−	30.7030i	−0.700149	−	1.21269i	−0.968414	−	0.249349i	$-0.919783\pi$
$641$	−17.7264	−	30.7030i	−0.700149	−	1.21269i	0.268264	−	0.963345i	$-0.413550\pi$
$642$		0			0
$643$	15.7257	−	15.7257i	0.620159	−	0.620159i	−0.325413	−	0.945572i	$-0.605503\pi$
$643$	15.7257	−	15.7257i	0.620159	−	0.620159i	0.945572	+	0.325413i	$0.105503\pi$
$644$		0			0
$645$	3.64854	+	6.31945i	0.143661	+	0.248828i
$646$		0			0
$647$	−10.3416	−	38.5954i	−0.406571	−	1.51734i	−0.801140	−	0.598477i	$-0.795773\pi$
$647$	−10.3416	−	38.5954i	−0.406571	−	1.51734i	0.394569	−	0.918866i	$-0.370894\pi$
$648$		0			0
$649$	−0.711426	+	2.65508i	−0.0279259	+	0.104221i
$650$		0			0
$651$	−2.60122	+	9.70788i	−0.101950	+	0.380482i
$652$		0			0
$653$	1.23833	−	0.331809i	0.0484595	−	0.0129847i	−0.234508	−	0.972114i	$-0.575348\pi$
$653$	1.23833	−	0.331809i	0.0484595	−	0.0129847i	0.282967	+	0.959130i	$0.408681\pi$
$654$		0			0
$655$			40.8638i			1.59668i
$656$		0			0
$657$	6.61121	−	3.81698i	0.257928	−	0.148915i
$658$		0			0
$659$	−2.31203	+	4.00455i	−0.0900637	+	0.155995i	−0.907538	−	0.419971i	$-0.862040\pi$
$659$	−2.31203	+	4.00455i	−0.0900637	+	0.155995i	0.817474	+	0.575965i	$0.195374\pi$
$660$		0			0
$661$	−20.7179	+	5.55134i	−0.805832	+	0.215922i	−0.638143	−	0.769918i	$-0.720297\pi$
$661$	−20.7179	+	5.55134i	−0.805832	+	0.215922i	−0.167689	+	0.985840i	$0.553631\pi$
$662$		0			0
$663$	1.60749	+	0.928083i	0.0624296	+	0.0360438i
$664$		0			0
$665$		−	10.9063i		−	0.422928i
$666$		0			0
$667$			11.1158i			0.430406i
$668$		0			0
$669$	17.8272	+	10.2926i	0.689241	+	0.397933i
$670$		0			0
$671$	−1.75213	+	0.469481i	−0.0676402	+	0.0181241i
$672$		0			0
$673$	−9.43426	+	16.3406i	−0.363664	+	0.629884i	−0.988561	−	0.150823i	$-0.951808\pi$
$673$	−9.43426	+	16.3406i	−0.363664	+	0.629884i	0.624897	+	0.780707i	$0.285141\pi$
$674$		0			0
$675$	18.0146	−	10.4008i	0.693384	−	0.400325i
$676$		0			0
$677$		−	14.1728i		−	0.544706i	−0.962197	−	0.272353i	$-0.912198\pi$
$677$		−	14.1728i		−	0.544706i	0.962197	−	0.272353i	$-0.0878019\pi$
$678$		0			0
$679$	−14.7096	+	3.94143i	−0.564503	+	0.151258i
$680$		0			0
$681$	−6.32637	+	23.6103i	−0.242427	+	0.904750i
$682$		0			0
$683$	11.8352	−	44.1695i	0.452860	−	1.69010i	−0.241442	−	0.970415i	$-0.577621\pi$
$683$	11.8352	−	44.1695i	0.452860	−	1.69010i	0.694303	−	0.719683i	$-0.255713\pi$
$684$		0			0
$685$	−7.49564	−	27.9741i	−0.286394	−	1.06884i
$686$		0			0
$687$	−19.3367	−	33.4922i	−0.737742	−	1.27781i
$688$		0			0
$689$	1.13479	−	1.13479i	0.0432321	−	0.0432321i
$690$		0			0
$691$	−16.6867	−	28.9021i	−0.634790	−	1.09949i	−0.986559	−	0.163402i	$-0.947753\pi$
$691$	−16.6867	−	28.9021i	−0.634790	−	1.09949i	0.351769	−	0.936087i	$-0.385580\pi$
$692$		0			0
$693$		−	1.57614i		−	0.0598726i
$694$		0			0
$695$	−4.02034	+	4.02034i	−0.152500	+	0.152500i
$696$		0			0
$697$	−2.11513	−	2.11513i	−0.0801164	−	0.0801164i
$698$		0			0
$699$	−35.2608	−	20.3579i	−1.33369	−	0.770005i
$700$		0			0
$701$	8.36231	+	2.24067i	0.315840	+	0.0846291i	0.413257	−	0.910615i	$-0.364391\pi$
$701$	8.36231	+	2.24067i	0.315840	+	0.0846291i	−0.0974166	+	0.995244i	$0.531058\pi$
$702$		0			0
$703$	7.57531	−	9.88280i	0.285708	−	0.372737i
$704$		0			0
$705$	15.2088	−	56.7600i	0.572797	−	2.13771i
$706$		0			0
$707$	4.53221	−	7.85001i	0.170451	−	0.295230i
$708$		0			0
$709$	−1.04984	+	1.04984i	−0.0394274	+	0.0394274i	−0.726546	−	0.687118i	$-0.758875\pi$
$709$	−1.04984	+	1.04984i	−0.0394274	+	0.0394274i	0.687118	+	0.726546i	$0.258875\pi$
$710$		0			0
$711$	−2.18908	−	2.18908i	−0.0820968	−	0.0820968i
$712$		0			0
$713$	−13.9835			−0.523687
$714$		0			0
$715$	−0.738597	+	0.426429i	−0.0276220	+	0.0159475i
$716$		0			0
$717$	−14.9242	−	14.9242i	−0.557356	−	0.557356i
$718$		0			0
$719$	−37.8524	+	21.8541i	−1.41166	+	0.815021i	−0.995545	−	0.0942921i	$-0.969941\pi$
$719$	−37.8524	+	21.8541i	−1.41166	+	0.815021i	−0.416113	+	0.909313i	$0.636608\pi$
$720$		0			0
$721$	13.7782	−	3.69186i	0.513127	−	0.137492i
$722$		0			0
$723$	12.9901	+	3.48070i	0.483108	+	0.129449i
$724$		0			0
$725$	10.2633	+	2.75004i	0.381169	+	0.102134i
$726$		0			0
$727$	−4.98946	−	18.6209i	−0.185049	−	0.690612i	−0.994620	−	0.103590i	$-0.966967\pi$
$727$	−4.98946	−	18.6209i	−0.185049	−	0.690612i	0.809571	−	0.587022i	$-0.199700\pi$
$728$		0			0
$729$	29.9918			1.11081
$730$		0			0
$731$	−5.03416	−	8.71941i	−0.186195	−	0.322499i
$732$		0			0
$733$	−44.6696	−	25.7900i	−1.64991	−	0.952576i	−0.977105	−	0.212757i	$-0.931756\pi$
$733$	−44.6696	−	25.7900i	−1.64991	−	0.952576i	−0.672805	−	0.739820i	$-0.734911\pi$
$734$		0			0
$735$	4.47764	+	16.7108i	0.165160	+	0.616386i
$736$		0			0
$737$	−1.69186	+	2.93039i	−0.0623205	+	0.107942i
$738$		0			0
$739$	8.11653			0.298572			0.149286	−	0.988794i	$-0.452303\pi$
$739$	8.11653			0.298572			0.149286	+	0.988794i	$0.452303\pi$
$740$		0			0
$741$	−0.597249			−0.0219405
$742$		0			0
$743$	−17.1488	+	29.7026i	−0.629130	+	1.08968i	0.358597	+	0.933492i	$0.383255\pi$
$743$	−17.1488	+	29.7026i	−0.629130	+	1.08968i	−0.987727	+	0.156192i	$0.950078\pi$
$744$		0			0
$745$	1.72018	+	6.41980i	0.0630225	+	0.235203i
$746$		0			0
$747$	8.21238	+	4.74142i	0.300475	+	0.173480i
$748$		0			0
$749$	−0.0798366	−	0.138281i	−0.00291717	−	0.00505268i
$750$		0			0
$751$	−3.62139			−0.132146			−0.0660732	−	0.997815i	$-0.521047\pi$
$751$	−3.62139			−0.132146			−0.0660732	+	0.997815i	$0.521047\pi$
$752$		0			0
$753$	2.94999	+	11.0095i	0.107504	+	0.401209i
$754$		0			0
$755$	−50.5341	−	13.5406i	−1.83913	−	0.492792i
$756$		0			0
$757$	9.02937	+	2.41941i	0.328178	+	0.0879351i	0.419146	−	0.907919i	$-0.362329\pi$
$757$	9.02937	+	2.41941i	0.328178	+	0.0879351i	−0.0909681	+	0.995854i	$0.528996\pi$
$758$		0			0
$759$	−9.08968	+	2.43557i	−0.329934	+	0.0884056i
$760$		0			0
$761$	−42.7692	+	24.6928i	−1.55038	+	0.895114i	−0.552272	+	0.833664i	$0.686239\pi$
$761$	−42.7692	+	24.6928i	−1.55038	+	0.895114i	−0.998110	+	0.0614495i	$0.980428\pi$
$762$		0			0
$763$	11.6862	+	11.6862i	0.423068	+	0.423068i
$764$		0			0
$765$	−9.23483	+	5.33173i	−0.333886	+	0.192769i
$766$		0			0
$767$	−0.333320			−0.0120355
$768$		0			0
$769$	15.9586	+	15.9586i	0.575480	+	0.575480i	0.933655	−	0.358175i	$-0.116601\pi$
$769$	15.9586	+	15.9586i	0.575480	+	0.575480i	−0.358175	+	0.933655i	$0.616601\pi$
$770$		0			0
$771$	0.0474160	−	0.0474160i	0.00170765	−	0.00170765i
$772$		0			0
$773$	−6.71902	+	11.6377i	−0.241666	+	0.418579i	−0.961189	−	0.275890i	$-0.911027\pi$
$773$	−6.71902	+	11.6377i	−0.241666	+	0.418579i	0.719523	+	0.694469i	$0.244361\pi$
$774$		0			0
$775$	−3.45950	+	12.9110i	−0.124269	+	0.463779i
$776$		0			0
$777$	6.53564	−	15.8013i	0.234465	−	0.566868i
$778$		0			0
$779$	0.929682	+	0.249108i	0.0333093	+	0.00892521i
$780$		0			0
$781$	−15.9072	−	9.18404i	−0.569205	−	0.328631i
$782$		0			0
$783$	11.1810	+	11.1810i	0.399576	+	0.399576i
$784$		0			0
$785$	−6.19217	+	6.19217i	−0.221008	+	0.221008i
$786$		0			0
$787$		−	25.8978i		−	0.923158i	−0.887099	−	0.461579i	$-0.847283\pi$
$787$		−	25.8978i		−	0.923158i	0.887099	−	0.461579i	$-0.152717\pi$
$788$		0			0
$789$	5.88063	+	10.1855i	0.209356	+	0.362615i
$790$		0			0
$791$	5.55421	−	5.55421i	0.197485	−	0.197485i
$792$		0			0
$793$	−0.109982	−	0.190494i	−0.00390556	−	0.00676464i
$794$		0			0
$795$	−10.2396	−	38.2147i	−0.363161	−	1.35533i
$796$		0			0
$797$	−10.4734	+	39.0871i	−0.370985	+	1.38454i	0.488138	+	0.872766i	$0.337676\pi$
$797$	−10.4734	+	39.0871i	−0.370985	+	1.38454i	−0.859123	+	0.511769i	$0.828990\pi$
$798$		0			0
$799$	−20.9847	+	78.3160i	−0.742385	+	2.77062i
$800$		0			0
$801$	3.22157	−	0.863218i	0.113829	−	0.0305003i
$802$		0			0
$803$			20.7679i			0.732882i
$804$		0			0
$805$	18.0462	−	10.4190i	0.636045	−	0.367221i
$806$		0			0
$807$	−2.62510	+	4.54681i	−0.0924080	+	0.160055i
$808$		0			0
$809$	−29.9066	+	8.01345i	−1.05146	+	0.281738i	−0.742855	−	0.669452i	$-0.766529\pi$
$809$	−29.9066	+	8.01345i	−1.05146	+	0.281738i	−0.308605	+	0.951190i	$0.599862\pi$
$810$		0			0
$811$	−33.3471	−	19.2529i	−1.17097	−	0.676062i	−0.217064	−	0.976157i	$-0.569648\pi$
$811$	−33.3471	−	19.2529i	−1.17097	−	0.676062i	−0.953909	+	0.300095i	$0.902982\pi$
$812$		0			0
$813$		−	35.7617i		−	1.25422i
$814$		0			0
$815$			48.8483i			1.71108i
$816$		0			0
$817$	2.80560	+	1.61981i	0.0981555	+	0.0566701i
$818$		0			0
$819$	0.184615	−	0.0494674i	0.00645097	−	0.00172853i
$820$		0			0
$821$	−3.10162	+	5.37216i	−0.108247	+	0.187490i	−0.915060	−	0.403317i	$-0.867857\pi$
$821$	−3.10162	+	5.37216i	−0.108247	+	0.187490i	0.806813	+	0.590807i	$0.201190\pi$
$822$		0			0
$823$	−22.1164	+	12.7689i	−0.770929	+	0.445096i	−0.833206	−	0.552963i	$-0.813497\pi$
$823$	−22.1164	+	12.7689i	−0.770929	+	0.445096i	0.0622771	+	0.998059i	$0.480164\pi$
$824$		0			0
$825$			8.99510i			0.313169i
$826$		0			0
$827$	−19.6291	+	5.25961i	−0.682571	+	0.182894i	−0.583411	−	0.812177i	$-0.698282\pi$
$827$	−19.6291	+	5.25961i	−0.682571	+	0.182894i	−0.0991604	+	0.995071i	$0.531616\pi$
$828$		0			0
$829$	5.24130	−	19.5608i	0.182038	−	0.679375i	−0.813207	−	0.581974i	$-0.802280\pi$
$829$	5.24130	−	19.5608i	0.182038	−	0.679375i	0.995245	−	0.0974009i	$-0.0310529\pi$
$830$		0			0
$831$	6.19439	−	23.1178i	0.214881	−	0.801947i
$832$		0			0
$833$	−6.17812	−	23.0571i	−0.214059	−	0.798880i
$834$		0			0
$835$	9.00603	+	15.5989i	0.311666	+	0.539822i
$836$		0			0
$837$	−14.0655	+	14.0655i	−0.486175	+	0.486175i
$838$		0			0
$839$	−22.3343	−	38.6841i	−0.771065	−	1.33552i	−0.936980	−	0.349384i	$-0.886391\pi$
$839$	−22.3343	−	38.6841i	−0.771065	−	1.33552i	0.165915	−	0.986140i	$-0.446942\pi$
$840$		0			0
$841$		−	20.9231i		−	0.721487i
$842$		0			0
$843$	−17.0099	+	17.0099i	−0.585852	+	0.585852i
$844$		0			0
$845$	27.1008	+	27.1008i	0.932295	+	0.932295i
$846$		0			0
$847$	−13.4552	−	7.76839i	−0.462328	−	0.266925i
$848$		0			0
$849$	22.0239	+	5.90128i	0.755857	+	0.202531i
$850$		0			0
$851$	23.5895	+	3.09334i	0.808637	+	0.106038i
$852$		0			0
$853$	−8.42853	+	31.4557i	−0.288587	+	1.07702i	0.657591	+	0.753375i	$0.271576\pi$
$853$	−8.42853	+	31.4557i	−0.288587	+	1.07702i	−0.946178	+	0.323647i	$0.895091\pi$
$854$		0			0
$855$	1.71556	−	2.97144i	0.0586710	−	0.101621i
$856$		0			0
$857$	9.11103	−	9.11103i	0.311227	−	0.311227i	−0.534158	−	0.845385i	$-0.679371\pi$
$857$	9.11103	−	9.11103i	0.311227	−	0.311227i	0.845385	+	0.534158i	$0.179371\pi$
$858$		0			0
$859$	23.9326	+	23.9326i	0.816569	+	0.816569i	0.985609	−	0.169040i	$-0.0540667\pi$
$859$	23.9326	+	23.9326i	0.816569	+	0.816569i	−0.169040	+	0.985609i	$0.554067\pi$
$860$		0			0
$861$	1.32170			0.0450434
$862$		0			0
$863$	11.6273	−	6.71300i	0.395797	−	0.228513i	−0.288872	−	0.957368i	$-0.593280\pi$
$863$	11.6273	−	6.71300i	0.395797	−	0.228513i	0.684669	+	0.728854i	$0.259947\pi$
$864$		0			0
$865$	36.0646	+	36.0646i	1.22623	+	1.22623i
$866$		0			0
$867$	−31.7135	+	18.3098i	−1.07705	+	0.621834i
$868$		0			0
$869$	8.13507	−	2.17979i	0.275963	−	0.0739442i
$870$		0			0
$871$	−0.396339	−	0.106199i	−0.0134294	−	0.00359841i
$872$		0			0
$873$	−4.62765	−	1.23997i	−0.156622	−	0.0419668i
$874$		0			0
$875$	1.73919	+	6.49076i	0.0587955	+	0.219428i
$876$		0			0
$877$	13.6723			0.461682			0.230841	−	0.972992i	$-0.425852\pi$
$877$	13.6723			0.461682			0.230841	+	0.972992i	$0.425852\pi$
$878$		0			0
$879$	14.6930	+	25.4490i	0.495582	+	0.858373i
$880$		0			0
$881$	23.5497	+	13.5964i	0.793410	+	0.458075i	0.841162	−	0.540784i	$-0.181872\pi$
$881$	23.5497	+	13.5964i	0.793410	+	0.458075i	−0.0477517	+	0.998859i	$0.515206\pi$
$882$		0			0
$883$	10.9758	+	40.9624i	0.369366	+	1.37849i	0.861405	+	0.507919i	$0.169585\pi$
$883$	10.9758	+	40.9624i	0.369366	+	1.37849i	−0.492039	+	0.870573i	$0.663748\pi$
$884$		0			0
$885$	−4.10853	+	7.11619i	−0.138107	+	0.239208i
$886$		0			0
$887$	−0.342701			−0.0115068			−0.00575338	−	0.999983i	$-0.501831\pi$
$887$	−0.342701			−0.0115068			−0.00575338	+	0.999983i	$0.501831\pi$
$888$		0			0
$889$	27.7059			0.929226
$890$		0			0
$891$	−5.38130	+	9.32068i	−0.180280	+	0.312255i
$892$		0			0
$893$	−6.75213	−	25.1993i	−0.225951	−	0.843262i
$894$		0			0
$895$	−51.1675	−	29.5416i	−1.71034	−	0.987465i
$896$		0			0
$897$	−0.570562	−	0.988243i	−0.0190505	−	0.0329965i
$898$		0			0
$899$	−10.1606			−0.338874
$900$		0			0
$901$	14.1283	+	52.7276i	0.470682	+	1.75661i
$902$		0			0
$903$	4.29715	+	1.15142i	0.143000	+	0.0383168i
$904$		0			0
$905$	−62.1210	−	16.6453i	−2.06497	−	0.553308i
$906$		0			0
$907$	47.8067	−	12.8098i	1.58739	−	0.425341i	0.646189	−	0.763177i	$-0.276362\pi$
$907$	47.8067	−	12.8098i	1.58739	−	0.425341i	0.941205	+	0.337836i	$0.109695\pi$
$908$		0			0
$909$	2.46961	−	1.42583i	0.0819120	−	0.0472919i
$910$		0			0
$911$	−7.87108	−	7.87108i	−0.260780	−	0.260780i	0.564591	−	0.825371i	$-0.309034\pi$
$911$	−7.87108	−	7.87108i	−0.260780	−	0.260780i	−0.825371	+	0.564591i	$0.809034\pi$
$912$		0			0
$913$	−22.3414	+	12.8988i	−0.739393	+	0.426889i
$914$		0			0
$915$	−5.42258			−0.179265
$916$		0			0
$917$	17.6162	+	17.6162i	0.581738	+	0.581738i
$918$		0			0
$919$	−29.0886	+	29.0886i	−0.959546	+	0.959546i	−0.999213	−	0.0396673i	$-0.987370\pi$
$919$	−29.0886	+	29.0886i	−0.959546	+	0.959546i	0.0396673	+	0.999213i	$0.487370\pi$
$920$		0			0
$921$	19.9276	−	34.5156i	0.656637	−	1.13733i
$922$		0			0
$923$	0.576486	−	2.15147i	0.0189753	−	0.0708166i
$924$		0			0
$925$	8.69211	−	21.0150i	0.285795	−	0.690969i
$926$		0			0
$927$	4.33463	+	1.16146i	0.142368	+	0.0381473i
$928$		0			0
$929$	−3.02874	−	1.74865i	−0.0993699	−	0.0573712i	0.449492	−	0.893285i	$-0.351605\pi$
$929$	−3.02874	−	1.74865i	−0.0993699	−	0.0573712i	−0.548861	+	0.835913i	$0.684939\pi$
$930$		0			0
$931$	5.43105	+	5.43105i	0.177995	+	0.177995i
$932$		0			0
$933$	−16.0846	+	16.0846i	−0.526588	+	0.526588i
$934$		0			0
$935$		−	29.0095i		−	0.948711i
$936$		0			0
$937$	27.0972	+	46.9337i	0.885227	+	1.53326i	0.845454	+	0.534049i	$0.179330\pi$
$937$	27.0972	+	46.9337i	0.885227	+	1.53326i	0.0397727	+	0.999209i	$0.487337\pi$
$938$		0			0
$939$	−13.4687	+	13.4687i	−0.439534	+	0.439534i
$940$		0			0
$941$	18.2467	+	31.6042i	0.594825	+	1.03027i	0.993572	+	0.113206i	$0.0361121\pi$
$941$	18.2467	+	31.6042i	0.594825	+	1.03027i	−0.398746	+	0.917061i	$0.630555\pi$
$942$		0			0
$943$	0.475954	+	1.77628i	0.0154992	+	0.0578438i
$944$		0			0
$945$	7.67194	−	28.6321i	0.249568	−	0.931401i
$946$		0			0
$947$	−6.15413	+	22.9675i	−0.199983	+	0.746345i	0.790938	+	0.611896i	$0.209593\pi$
$947$	−6.15413	+	22.9675i	−0.199983	+	0.746345i	−0.990921	+	0.134449i	$0.957074\pi$
$948$		0			0
$949$	−2.43256	+	0.651803i	−0.0789643	+	0.0211584i
$950$		0			0
$951$			20.4216i			0.662217i
$952$		0			0
$953$	−24.7361	+	14.2814i	−0.801280	+	0.462619i	−0.843918	−	0.536471i	$-0.819757\pi$
$953$	−24.7361	+	14.2814i	−0.801280	+	0.462619i	0.0426386	+	0.999091i	$0.486424\pi$
$954$		0			0
$955$	−25.5140	+	44.1916i	−0.825614	+	1.43001i
$956$		0			0
$957$	−6.60466	+	1.76971i	−0.213498	+	0.0572067i
$958$		0			0
$959$	−15.2908	−	8.82817i	−0.493767	−	0.285077i
$960$		0			0
$961$			18.2182i			0.587683i
$962$		0			0
$963$		−	0.0502332i		−	0.00161874i
$964$		0			0
$965$	65.4977	+	37.8151i	2.10845	+	1.21731i
$966$		0			0
$967$	51.2489	−	13.7321i	1.64805	−	0.441594i	0.688986	−	0.724774i	$-0.258056\pi$
$967$	51.2489	−	13.7321i	1.64805	−	0.441594i	0.959067	+	0.283180i	$0.0913894\pi$
$968$		0			0
$969$	10.1575	−	17.5934i	0.326307	−	0.565180i
$970$		0			0
$971$	21.4391	−	12.3778i	0.688012	−	0.397224i	−0.114855	−	0.993382i	$-0.536640\pi$
$971$	21.4391	−	12.3778i	0.688012	−	0.397224i	0.802867	+	0.596158i	$0.203307\pi$
$972$		0			0
$973$			3.46630i			0.111125i
$974$		0			0
$975$	−1.05361	+	0.282313i	−0.0337424	+	0.00904125i
$976$		0			0
$977$	−7.65276	+	28.5605i	−0.244833	+	0.913731i	0.728634	+	0.684904i	$0.240156\pi$
$977$	−7.65276	+	28.5605i	−0.244833	+	0.913731i	−0.973467	+	0.228827i	$0.926511\pi$
$978$		0			0
$979$	−2.34835	+	8.76415i	−0.0750535	+	0.280103i
$980$		0			0
$981$	1.34568	+	5.02216i	0.0429643	+	0.160345i
$982$		0			0
$983$	−18.0335	−	31.2350i	−0.575180	−	0.996241i	−0.996022	−	0.0891073i	$-0.971599\pi$
$983$	−18.0335	−	31.2350i	−0.575180	−	0.996241i	0.420842	−	0.907134i	$-0.361735\pi$
$984$		0			0
$985$	29.4589	−	29.4589i	0.938639	−	0.938639i
$986$		0			0
$987$	−17.9125	−	31.0254i	−0.570162	−	0.987550i
$988$		0			0
$989$			6.18974i			0.196822i
$990$		0			0
$991$	−12.2236	+	12.2236i	−0.388297	+	0.388297i	−0.874080	−	0.485783i	$-0.838535\pi$
$991$	−12.2236	+	12.2236i	−0.388297	+	0.388297i	0.485783	+	0.874080i	$0.338535\pi$
$992$		0			0
$993$	−17.2899	−	17.2899i	−0.548678	−	0.548678i
$994$		0			0
$995$	−61.8733	−	35.7226i	−1.96152	−	1.13248i
$996$		0			0
$997$	9.99795	+	2.67894i	0.316638	+	0.0848430i	0.413638	−	0.910441i	$-0.364258\pi$
$997$	9.99795	+	2.67894i	0.316638	+	0.0848430i	−0.0969997	+	0.995284i	$0.530925\pi$
$998$		0			0
$999$	26.8393	−	20.6163i	0.849157	−	0.652271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.e.399.2	yes	20
4.3	odd	2		592.2.be.f.399.4	yes	20
37.23	odd	12		592.2.be.f.319.4	yes	20
148.23	even	12	inner	592.2.be.e.319.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.e.319.2	✓	20	148.23	even	12	inner
592.2.be.e.399.2	yes	20	1.1	even	1	trivial
592.2.be.f.319.4	yes	20	37.23	odd	12
592.2.be.f.399.4	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)

\(f(q)\)	\(=\)	\(q+(-0.779906 + 1.35084i) q^{3} +(0.765103 + 2.85540i) q^{5} +(1.56078 + 0.901118i) q^{7} +(0.283492 + 0.491022i) q^{9} +O(q^{10})\)	\(q+(-0.779906 + 1.35084i) q^{3} +(0.765103 + 2.85540i) q^{5} +(1.56078 + 0.901118i) q^{7} +(0.283492 + 0.491022i) q^{9} -1.54245 q^{11} +(-0.0484102 - 0.180669i) q^{13} +(-4.45389 - 1.19342i) q^{15} +(6.14536 + 1.64665i) q^{17} +(-1.97736 + 0.529832i) q^{19} +(-2.43453 + 1.40558i) q^{21} +(-2.76570 - 2.76570i) q^{23} +(-3.23781 + 1.86935i) q^{25} -5.56383 q^{27} +(-2.00959 - 2.00959i) q^{29} +(2.52803 - 2.52803i) q^{31} +(1.20297 - 2.08361i) q^{33} +(-1.37890 + 5.14611i) q^{35} +(-4.82388 + 3.70542i) q^{37} +(0.281810 + 0.0755109i) q^{39} +(-0.407173 - 0.235082i) q^{41} +(-1.11902 - 1.11902i) q^{43} +(-1.18517 + 1.18517i) q^{45} +12.7439i q^{47} +(-1.87597 - 3.24928i) q^{49} +(-7.01716 + 7.01716i) q^{51} +(4.29003 + 7.43055i) q^{53} +(-1.18014 - 4.40433i) q^{55} +(0.826439 - 3.08431i) q^{57} +(0.461229 - 1.72133i) q^{59} +(1.13593 - 0.304373i) q^{61} +1.02184i q^{63} +(0.478845 - 0.276461i) q^{65} +(1.09686 - 1.89982i) q^{67} +(5.89299 - 1.57902i) q^{69} +(10.3129 + 5.95417i) q^{71} -13.4642i q^{73} -5.83168i q^{75} +(-2.40744 - 1.38993i) q^{77} +(-5.27411 + 1.41319i) q^{79} +(3.48879 - 6.04276i) q^{81} +(14.4843 - 8.36253i) q^{83} +18.8073i q^{85} +(4.28191 - 1.14733i) q^{87} +(1.52247 - 5.68195i) q^{89} +(0.0872466 - 0.325609i) q^{91} +(1.44333 + 5.38658i) q^{93} +(-3.02577 - 5.24078i) q^{95} +(-5.97490 + 5.97490i) q^{97} +(-0.437273 - 0.757380i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 4 q^{5} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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