LMFDB - Embedded newform 185.2.f.b.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(43,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	185.43
Dual form			185.2.f.b.142.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(2.00000 - 2.00000i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} +3.00000i q^{8} -5.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +4.00000i q^{11} +(2.00000 - 2.00000i) q^{12} -4.00000i q^{13} +(-6.00000 + 2.00000i) q^{15} -1.00000 q^{16} -2.00000 q^{17} +5.00000 q^{18} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{22} +4.00000i q^{23} +(6.00000 + 6.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +(-4.00000 - 4.00000i) q^{27} +(1.00000 + 1.00000i) q^{29} +(-2.00000 - 6.00000i) q^{30} +(-6.00000 + 6.00000i) q^{31} +5.00000i q^{32} +(8.00000 + 8.00000i) q^{33} -2.00000i q^{34} -5.00000i q^{36} +(-6.00000 + 1.00000i) q^{37} +(-8.00000 - 8.00000i) q^{39} +(3.00000 - 6.00000i) q^{40} -12.0000i q^{43} +4.00000i q^{44} +(-5.00000 + 10.0000i) q^{45} -4.00000 q^{46} +(8.00000 - 8.00000i) q^{47} +(-2.00000 + 2.00000i) q^{48} +7.00000i q^{49} +(-4.00000 + 3.00000i) q^{50} +(-4.00000 + 4.00000i) q^{51} -4.00000i q^{52} +(-9.00000 - 9.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +(4.00000 - 8.00000i) q^{55} +(-1.00000 + 1.00000i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(-6.00000 + 2.00000i) q^{60} +(1.00000 - 1.00000i) q^{61} +(-6.00000 - 6.00000i) q^{62} -7.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +(-8.00000 + 8.00000i) q^{66} +(6.00000 + 6.00000i) q^{67} -2.00000 q^{68} +(8.00000 + 8.00000i) q^{69} -4.00000 q^{71} +15.0000 q^{72} +(11.0000 - 11.0000i) q^{73} +(-1.00000 - 6.00000i) q^{74} +(14.0000 + 2.00000i) q^{75} +(8.00000 - 8.00000i) q^{78} +(6.00000 - 6.00000i) q^{79} +(2.00000 + 1.00000i) q^{80} -1.00000 q^{81} +(-2.00000 - 2.00000i) q^{83} +(4.00000 + 2.00000i) q^{85} +12.0000 q^{86} +4.00000 q^{87} -12.0000 q^{88} +(1.00000 + 1.00000i) q^{89} +(-10.0000 - 5.00000i) q^{90} +4.00000i q^{92} +24.0000i q^{93} +(8.00000 + 8.00000i) q^{94} +(10.0000 + 10.0000i) q^{96} +4.00000 q^{97} -7.00000 q^{98} +20.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} + 2 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} + 4 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 10 q^{18} - 4 q^{20} - 8 q^{22} + 12 q^{24} + 6 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{29} - 4 q^{30} - 12 q^{31}+ \cdots + 40 q^{99}+O(q^{100}) $ 2 * q + 4 * q^3 + 2 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 + 4 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 10 * q^18 - 4 * q^20 - 8 * q^22 + 12 * q^24 + 6 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^29 - 4 * q^30 - 12 * q^31 + 16 * q^33 - 12 * q^37 - 16 * q^39 + 6 * q^40 - 10 * q^45 - 8 * q^46 + 16 * q^47 - 4 * q^48 - 8 * q^50 - 8 * q^51 - 18 * q^53 + 8 * q^54 + 8 * q^55 - 2 * q^58 - 8 * q^59 - 12 * q^60 + 2 * q^61 - 12 * q^62 - 14 * q^64 - 8 * q^65 - 16 * q^66 + 12 * q^67 - 4 * q^68 + 16 * q^69 - 8 * q^71 + 30 * q^72 + 22 * q^73 - 2 * q^74 + 28 * q^75 + 16 * q^78 + 12 * q^79 + 4 * q^80 - 2 * q^81 - 4 * q^83 + 8 * q^85 + 24 * q^86 + 8 * q^87 - 24 * q^88 + 2 * q^89 - 20 * q^90 + 16 * q^94 + 20 * q^96 + 8 * q^97 - 14 * q^98 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	2.00000	−	2.00000i	1.15470	−	1.15470i	0.985599	−	0.169102i	$-0.0540867\pi$
$4$	1.00000			0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	2.00000	+	2.00000i	0.816497	+	0.816497i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$			3.00000i			1.06066i
$9$		−	5.00000i		−	1.66667i
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$	2.00000	−	2.00000i	0.577350	−	0.577350i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$		0			0
$15$	−6.00000	+	2.00000i	−1.54919	+	0.516398i
$16$	−1.00000			−0.250000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	5.00000			1.17851
$19$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$19$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$		0			0
$22$	−4.00000			−0.852803
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	6.00000	+	6.00000i	1.22474	+	1.22474i
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$	−4.00000	−	4.00000i	−0.769800	−	0.769800i
$28$		0			0
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	0.793832	−	0.608137i	$-0.208083\pi$
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	−0.608137	+	0.793832i	$0.708083\pi$
$30$	−2.00000	−	6.00000i	−0.365148	−	1.09545i
$31$	−6.00000	+	6.00000i	−1.07763	+	1.07763i	−0.0809104	+	0.996721i	$0.525783\pi$
$31$	−6.00000	+	6.00000i	−1.07763	+	1.07763i	−0.996721	+	0.0809104i	$0.974217\pi$
$32$			5.00000i			0.883883i
$33$	8.00000	+	8.00000i	1.39262	+	1.39262i
$34$		−	2.00000i		−	0.342997i
$35$		0			0
$36$		−	5.00000i		−	0.833333i
$37$	−6.00000	+	1.00000i	−0.986394	+	0.164399i
$37$	−6.00000	+	1.00000i	−0.986394	+	0.164399i
$38$		0			0
$39$	−8.00000	−	8.00000i	−1.28103	−	1.28103i
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$			4.00000i			0.603023i
$45$	−5.00000	+	10.0000i	−0.745356	+	1.49071i
$46$	−4.00000			−0.589768
$47$	8.00000	−	8.00000i	1.16692	−	1.16692i	0.183992	−	0.982928i	$-0.441098\pi$
$47$	8.00000	−	8.00000i	1.16692	−	1.16692i	0.982928	−	0.183992i	$-0.0589021\pi$
$48$	−2.00000	+	2.00000i	−0.288675	+	0.288675i
$49$			7.00000i			1.00000i
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	−4.00000	+	4.00000i	−0.560112	+	0.560112i
$52$		−	4.00000i		−	0.554700i
$53$	−9.00000	−	9.00000i	−1.23625	−	1.23625i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−9.00000	−	9.00000i	−1.23625	−	1.23625i	−0.274721	−	0.961524i	$-0.588586\pi$
$54$	4.00000	−	4.00000i	0.544331	−	0.544331i
$55$	4.00000	−	8.00000i	0.539360	−	1.07872i
$56$		0			0
$57$		0			0
$58$	−1.00000	+	1.00000i	−0.131306	+	0.131306i
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	−0.917800	−	0.397044i	$-0.870036\pi$
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	0.397044	+	0.917800i	$0.370036\pi$
$60$	−6.00000	+	2.00000i	−0.774597	+	0.258199i
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	1.00000	−	1.00000i	0.128037	−	0.128037i	0.768221	+	0.640184i	$0.221142\pi$
$62$	−6.00000	−	6.00000i	−0.762001	−	0.762001i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−4.00000	+	8.00000i	−0.496139	+	0.992278i
$66$	−8.00000	+	8.00000i	−0.984732	+	0.984732i
$67$	6.00000	+	6.00000i	0.733017	+	0.733017i	0.971216	−	0.238200i	$-0.0765572\pi$
$67$	6.00000	+	6.00000i	0.733017	+	0.733017i	−0.238200	+	0.971216i	$0.576557\pi$
$68$	−2.00000			−0.242536
$69$	8.00000	+	8.00000i	0.963087	+	0.963087i
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$	15.0000			1.76777
$73$	11.0000	−	11.0000i	1.28745	−	1.28745i	0.351123	−	0.936329i	$-0.385800\pi$
$73$	11.0000	−	11.0000i	1.28745	−	1.28745i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	−1.00000	−	6.00000i	−0.116248	−	0.697486i
$75$	14.0000	+	2.00000i	1.61658	+	0.230940i
$76$		0			0
$77$		0			0
$78$	8.00000	−	8.00000i	0.905822	−	0.905822i
$79$	6.00000	−	6.00000i	0.675053	−	0.675053i	−0.283824	−	0.958876i	$-0.591603\pi$
$79$	6.00000	−	6.00000i	0.675053	−	0.675053i	0.958876	+	0.283824i	$0.0916031\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.00000	−	2.00000i	−0.219529	−	0.219529i	0.588771	−	0.808300i	$-0.299612\pi$
$83$	−2.00000	−	2.00000i	−0.219529	−	0.219529i	−0.808300	+	0.588771i	$0.799612\pi$
$84$		0			0
$85$	4.00000	+	2.00000i	0.433861	+	0.216930i
$86$	12.0000			1.29399
$87$	4.00000			0.428845
$88$	−12.0000			−1.27920
$89$	1.00000	+	1.00000i	0.106000	+	0.106000i	0.758118	−	0.652118i	$-0.226119\pi$
$89$	1.00000	+	1.00000i	0.106000	+	0.106000i	−0.652118	+	0.758118i	$0.726119\pi$
$90$	−10.0000	−	5.00000i	−1.05409	−	0.527046i
$91$		0			0
$92$			4.00000i			0.417029i
$93$			24.0000i			2.48868i
$94$	8.00000	+	8.00000i	0.825137	+	0.825137i
$95$		0			0
$96$	10.0000	+	10.0000i	1.02062	+	1.02062i
$97$	4.00000			0.406138			0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000			0.406138			0.203069	+	0.979164i	$0.434908\pi$
$98$	−7.00000			−0.707107
$99$	20.0000			2.01008
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	6.00000i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$101$		−	6.00000i		−	0.597022i	0.954406	−	0.298511i	$-0.0964900\pi$
$102$	−4.00000	−	4.00000i	−0.396059	−	0.396059i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	12.0000			1.17670
$105$		0			0
$106$	9.00000	−	9.00000i	0.874157	−	0.874157i
$107$	−6.00000	+	6.00000i	−0.580042	+	0.580042i	−0.934915	−	0.354873i	$-0.884524\pi$
$107$	−6.00000	+	6.00000i	−0.580042	+	0.580042i	0.354873	+	0.934915i	$0.384524\pi$
$108$	−4.00000	−	4.00000i	−0.384900	−	0.384900i
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	−0.836031	−	0.548683i	$-0.815129\pi$
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	0.548683	+	0.836031i	$0.315129\pi$
$110$	8.00000	+	4.00000i	0.762770	+	0.381385i
$111$	−10.0000	+	14.0000i	−0.949158	+	1.32882i
$112$		0			0
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$	4.00000	−	8.00000i	0.373002	−	0.746004i
$116$	1.00000	+	1.00000i	0.0928477	+	0.0928477i
$117$	−20.0000			−1.84900
$118$	−4.00000	−	4.00000i	−0.368230	−	0.368230i
$119$		0			0
$120$	−6.00000	−	18.0000i	−0.547723	−	1.64317i
$121$	−5.00000			−0.454545
$122$	1.00000	+	1.00000i	0.0905357	+	0.0905357i
$123$		0			0
$124$	−6.00000	+	6.00000i	−0.538816	+	0.538816i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	12.0000	−	12.0000i	1.06483	−	1.06483i	0.0670802	−	0.997748i	$-0.478632\pi$
$127$	12.0000	−	12.0000i	1.06483	−	1.06483i	0.997748	−	0.0670802i	$-0.0213683\pi$
$128$			3.00000i			0.265165i
$129$	−24.0000	−	24.0000i	−2.11308	−	2.11308i
$130$	−8.00000	−	4.00000i	−0.701646	−	0.350823i
$131$	16.0000	−	16.0000i	1.39793	−	1.39793i	0.591957	−	0.805970i	$-0.298356\pi$
$131$	16.0000	−	16.0000i	1.39793	−	1.39793i	0.805970	−	0.591957i	$-0.201644\pi$
$132$	8.00000	+	8.00000i	0.696311	+	0.696311i
$133$		0			0
$134$	−6.00000	+	6.00000i	−0.518321	+	0.518321i
$135$	4.00000	+	12.0000i	0.344265	+	1.03280i
$136$		−	6.00000i		−	0.514496i
$137$	−7.00000	+	7.00000i	−0.598050	+	0.598050i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−7.00000	+	7.00000i	−0.598050	+	0.598050i	0.341743	+	0.939793i	$0.388983\pi$
$138$	−8.00000	+	8.00000i	−0.681005	+	0.681005i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$		−	32.0000i		−	2.69489i
$142$		−	4.00000i		−	0.335673i
$143$	16.0000			1.33799
$144$			5.00000i			0.416667i
$145$	−1.00000	−	3.00000i	−0.0830455	−	0.249136i
$146$	11.0000	+	11.0000i	0.910366	+	0.910366i
$147$	14.0000	+	14.0000i	1.15470	+	1.15470i
$148$	−6.00000	+	1.00000i	−0.493197	+	0.0821995i
$149$		−	10.0000i		−	0.819232i	−0.912258	−	0.409616i	$-0.865663\pi$
$149$		−	10.0000i		−	0.819232i	0.912258	−	0.409616i	$-0.134337\pi$
$150$	−2.00000	+	14.0000i	−0.163299	+	1.14310i
$151$			8.00000i			0.651031i	0.945537	+	0.325515i	$0.105538\pi$
$151$			8.00000i			0.651031i	−0.945537	+	0.325515i	$0.894462\pi$
$152$		0			0
$153$			10.0000i			0.808452i
$154$		0			0
$155$	18.0000	−	6.00000i	1.44579	−	0.481932i
$156$	−8.00000	−	8.00000i	−0.640513	−	0.640513i
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.222108	+	0.975022i	$0.571294\pi$
$157$	−15.0000	+	15.0000i	−1.19713	+	1.19713i	−0.975022	+	0.222108i	$0.928706\pi$
$158$	6.00000	+	6.00000i	0.477334	+	0.477334i
$159$	−36.0000			−2.85499
$160$	5.00000	−	10.0000i	0.395285	−	0.790569i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	−8.00000	−	24.0000i	−0.622799	−	1.86840i
$166$	2.00000	−	2.00000i	0.155230	−	0.155230i
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	−2.00000	+	4.00000i	−0.153393	+	0.306786i
$171$		0			0
$172$		−	12.0000i		−	0.914991i
$173$	5.00000	−	5.00000i	0.380143	−	0.380143i	−0.491011	−	0.871154i	$-0.663372\pi$
$173$	5.00000	−	5.00000i	0.380143	−	0.380143i	0.871154	+	0.491011i	$0.163372\pi$
$174$			4.00000i			0.303239i
$175$		0			0
$176$		−	4.00000i		−	0.301511i
$177$			16.0000i			1.20263i
$178$	−1.00000	+	1.00000i	−0.0749532	+	0.0749532i
$179$	16.0000	+	16.0000i	1.19590	+	1.19590i	0.975384	+	0.220512i	$0.0707728\pi$
$179$	16.0000	+	16.0000i	1.19590	+	1.19590i	0.220512	+	0.975384i	$0.429227\pi$
$180$	−5.00000	+	10.0000i	−0.372678	+	0.745356i
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$		−	4.00000i		−	0.295689i
$184$	−12.0000			−0.884652
$185$	13.0000	+	4.00000i	0.955779	+	0.294086i
$186$	−24.0000			−1.75977
$187$		−	8.00000i		−	0.585018i
$188$	8.00000	−	8.00000i	0.583460	−	0.583460i
$189$		0			0
$190$		0			0
$191$	−14.0000	−	14.0000i	−1.01300	−	1.01300i	−0.999914	−	0.0130901i	$-0.995833\pi$
$191$	−14.0000	−	14.0000i	−1.01300	−	1.01300i	−0.0130901	−	0.999914i	$-0.504167\pi$
$192$	−14.0000	+	14.0000i	−1.01036	+	1.01036i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$			4.00000i			0.287183i
$195$	8.00000	+	24.0000i	0.572892	+	1.71868i
$196$			7.00000i			0.500000i
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$			20.0000i			1.42134i
$199$	18.0000	+	18.0000i	1.27599	+	1.27599i	0.942894	+	0.333092i	$0.108092\pi$
$199$	18.0000	+	18.0000i	1.27599	+	1.27599i	0.333092	+	0.942894i	$0.391908\pi$
$200$	−12.0000	+	9.00000i	−0.848528	+	0.636396i
$201$	24.0000			1.69283
$202$	6.00000			0.422159
$203$		0			0
$204$	−4.00000	+	4.00000i	−0.280056	+	0.280056i
$205$		0			0
$206$		−	4.00000i		−	0.278693i
$207$	20.0000			1.39010
$208$			4.00000i			0.277350i
$209$		0			0
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	−9.00000	−	9.00000i	−0.618123	−	0.618123i
$213$	−8.00000	+	8.00000i	−0.548151	+	0.548151i
$214$	−6.00000	−	6.00000i	−0.410152	−	0.410152i
$215$	−12.0000	+	24.0000i	−0.818393	+	1.63679i
$216$	12.0000	−	12.0000i	0.816497	−	0.816497i
$217$		0			0
$218$	−3.00000	−	3.00000i	−0.203186	−	0.203186i
$219$		−	44.0000i		−	2.97324i
$220$	4.00000	−	8.00000i	0.269680	−	0.539360i
$221$			8.00000i			0.538138i
$222$	−14.0000	−	10.0000i	−0.939618	−	0.671156i
$223$	−4.00000	−	4.00000i	−0.267860	−	0.267860i	0.560378	−	0.828237i	$-0.310656\pi$
$223$	−4.00000	−	4.00000i	−0.267860	−	0.267860i	−0.828237	+	0.560378i	$0.810656\pi$
$224$		0			0
$225$	20.0000	−	15.0000i	1.33333	−	1.00000i
$226$		−	2.00000i		−	0.133038i
$227$	16.0000			1.06196			0.530979	−	0.847385i	$-0.321824\pi$
$227$	16.0000			1.06196			0.530979	+	0.847385i	$0.321824\pi$
$228$		0			0
$229$		−	16.0000i		−	1.05731i	−0.848837	−	0.528655i	$-0.822697\pi$
$229$		−	16.0000i		−	1.05731i	0.848837	−	0.528655i	$-0.177303\pi$
$230$	8.00000	+	4.00000i	0.527504	+	0.263752i
$231$		0			0
$232$	−3.00000	+	3.00000i	−0.196960	+	0.196960i
$233$	−13.0000	+	13.0000i	−0.851658	+	0.851658i	−0.990337	−	0.138679i	$-0.955714\pi$
$233$	−13.0000	+	13.0000i	−0.851658	+	0.851658i	0.138679	+	0.990337i	$0.455714\pi$
$234$		−	20.0000i		−	1.30744i
$235$	−24.0000	+	8.00000i	−1.56559	+	0.521862i
$236$	−4.00000	+	4.00000i	−0.260378	+	0.260378i
$237$		−	24.0000i		−	1.55897i
$238$		0			0
$239$	14.0000	−	14.0000i	0.905585	−	0.905585i	−0.0903274	−	0.995912i	$-0.528791\pi$
$239$	14.0000	−	14.0000i	0.905585	−	0.905585i	0.995912	+	0.0903274i	$0.0287913\pi$
$240$	6.00000	−	2.00000i	0.387298	−	0.129099i
$241$	13.0000	+	13.0000i	0.837404	+	0.837404i	0.988517	−	0.151113i	$-0.0482857\pi$
$241$	13.0000	+	13.0000i	0.837404	+	0.837404i	−0.151113	+	0.988517i	$0.548286\pi$
$242$		−	5.00000i		−	0.321412i
$243$	10.0000	−	10.0000i	0.641500	−	0.641500i
$244$	1.00000	−	1.00000i	0.0640184	−	0.0640184i
$245$	7.00000	−	14.0000i	0.447214	−	0.894427i
$246$		0			0
$247$		0			0
$248$	−18.0000	−	18.0000i	−1.14300	−	1.14300i
$249$	−8.00000			−0.506979
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	4.00000	−	4.00000i	0.252478	−	0.252478i	−0.569508	−	0.821986i	$-0.692866\pi$
$251$	4.00000	−	4.00000i	0.252478	−	0.252478i	0.821986	+	0.569508i	$0.192866\pi$
$252$		0			0
$253$	−16.0000			−1.00591
$254$	12.0000	+	12.0000i	0.752947	+	0.752947i
$255$	12.0000	−	4.00000i	0.751469	−	0.250490i
$256$	−17.0000			−1.06250
$257$	−14.0000			−0.873296			−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000			−0.873296			−0.436648	+	0.899632i	$0.643834\pi$
$258$	24.0000	−	24.0000i	1.49417	−	1.49417i
$259$		0			0
$260$	−4.00000	+	8.00000i	−0.248069	+	0.496139i
$261$	5.00000	−	5.00000i	0.309492	−	0.309492i
$262$	16.0000	+	16.0000i	0.988483	+	0.988483i
$263$	−8.00000	+	8.00000i	−0.493301	+	0.493301i	−0.909345	−	0.416044i	$-0.863416\pi$
$263$	−8.00000	+	8.00000i	−0.493301	+	0.493301i	0.416044	+	0.909345i	$0.363416\pi$
$264$	−24.0000	+	24.0000i	−1.47710	+	1.47710i
$265$	9.00000	+	27.0000i	0.552866	+	1.65860i
$266$		0			0
$267$	4.00000			0.244796
$268$	6.00000	+	6.00000i	0.366508	+	0.366508i
$269$		−	14.0000i		−	0.853595i	−0.904347	−	0.426798i	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$	−12.0000	+	4.00000i	−0.730297	+	0.243432i
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	−7.00000	−	7.00000i	−0.422885	−	0.422885i
$275$	−16.0000	+	12.0000i	−0.964836	+	0.723627i
$276$	8.00000	+	8.00000i	0.481543	+	0.481543i
$277$			4.00000i			0.240337i	0.992754	+	0.120168i	$0.0383434\pi$
$277$			4.00000i			0.240337i	−0.992754	+	0.120168i	$0.961657\pi$
$278$		−	4.00000i		−	0.239904i
$279$	30.0000	+	30.0000i	1.79605	+	1.79605i
$280$		0			0
$281$	−15.0000	−	15.0000i	−0.894825	−	0.894825i	0.100148	−	0.994973i	$-0.468068\pi$
$281$	−15.0000	−	15.0000i	−0.894825	−	0.894825i	−0.994973	+	0.100148i	$0.968068\pi$
$282$	32.0000			1.90557
$283$	−4.00000			−0.237775			−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$	−4.00000			−0.237356
$285$		0			0
$286$			16.0000i			0.946100i
$287$		0			0
$288$	25.0000			1.47314
$289$	−13.0000			−0.764706
$290$	3.00000	−	1.00000i	0.176166	−	0.0587220i
$291$	8.00000	−	8.00000i	0.468968	−	0.468968i
$292$	11.0000	−	11.0000i	0.643726	−	0.643726i
$293$	1.00000	+	1.00000i	0.0584206	+	0.0584206i	0.735714	−	0.677293i	$-0.236847\pi$
$293$	1.00000	+	1.00000i	0.0584206	+	0.0584206i	−0.677293	+	0.735714i	$0.736847\pi$
$294$	−14.0000	+	14.0000i	−0.816497	+	0.816497i
$295$	12.0000	−	4.00000i	0.698667	−	0.232889i
$296$	−3.00000	−	18.0000i	−0.174371	−	1.04623i
$297$	16.0000	−	16.0000i	0.928414	−	0.928414i
$298$	10.0000			0.579284
$299$	16.0000			0.925304
$300$	14.0000	+	2.00000i	0.808290	+	0.115470i
$301$		0			0
$302$	−8.00000			−0.460348
$303$	−12.0000	−	12.0000i	−0.689382	−	0.689382i
$304$		0			0
$305$	−3.00000	+	1.00000i	−0.171780	+	0.0572598i
$306$	−10.0000			−0.571662
$307$	−6.00000	−	6.00000i	−0.342438	−	0.342438i	0.514845	−	0.857283i	$-0.327849\pi$
$307$	−6.00000	−	6.00000i	−0.342438	−	0.342438i	−0.857283	+	0.514845i	$0.827849\pi$
$308$		0			0
$309$	−8.00000	+	8.00000i	−0.455104	+	0.455104i
$310$	6.00000	+	18.0000i	0.340777	+	1.02233i
$311$	−6.00000	+	6.00000i	−0.340229	+	0.340229i	−0.856453	−	0.516225i	$-0.827337\pi$
$311$	−6.00000	+	6.00000i	−0.340229	+	0.340229i	0.516225	+	0.856453i	$0.327337\pi$
$312$	24.0000	−	24.0000i	1.35873	−	1.35873i
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	−15.0000	−	15.0000i	−0.846499	−	0.846499i
$315$		0			0
$316$	6.00000	−	6.00000i	0.337526	−	0.337526i
$317$	19.0000	+	19.0000i	1.06715	+	1.06715i	0.997577	+	0.0695692i	$0.0221625\pi$
$317$	19.0000	+	19.0000i	1.06715	+	1.06715i	0.0695692	+	0.997577i	$0.477838\pi$
$318$		−	36.0000i		−	2.01878i
$319$	−4.00000	+	4.00000i	−0.223957	+	0.223957i
$320$	14.0000	+	7.00000i	0.782624	+	0.391312i
$321$			24.0000i			1.33955i
$322$		0			0
$323$		0			0
$324$	−1.00000			−0.0555556
$325$	16.0000	−	12.0000i	0.887520	−	0.665640i
$326$			4.00000i			0.221540i
$327$			12.0000i			0.663602i
$328$		0			0
$329$		0			0
$330$	24.0000	−	8.00000i	1.32116	−	0.440386i
$331$	−4.00000	−	4.00000i	−0.219860	−	0.219860i	0.588579	−	0.808439i	$-0.299687\pi$
$331$	−4.00000	−	4.00000i	−0.219860	−	0.219860i	−0.808439	+	0.588579i	$0.799687\pi$
$332$	−2.00000	−	2.00000i	−0.109764	−	0.109764i
$333$	5.00000	+	30.0000i	0.273998	+	1.64399i
$334$		−	12.0000i		−	0.656611i
$335$	−6.00000	−	18.0000i	−0.327815	−	0.983445i
$336$		0			0
$337$	15.0000	+	15.0000i	0.817102	+	0.817102i	0.985687	−	0.168585i	$-0.0539198\pi$
$337$	15.0000	+	15.0000i	0.817102	+	0.817102i	−0.168585	+	0.985687i	$0.553920\pi$
$338$		−	3.00000i		−	0.163178i
$339$	−4.00000	+	4.00000i	−0.217250	+	0.217250i
$340$	4.00000	+	2.00000i	0.216930	+	0.108465i
$341$	−24.0000	−	24.0000i	−1.29967	−	1.29967i
$342$		0			0
$343$		0			0
$344$	36.0000			1.94099
$345$	−8.00000	−	24.0000i	−0.430706	−	1.29212i
$346$	5.00000	+	5.00000i	0.268802	+	0.268802i
$347$		−	28.0000i		−	1.50312i	−0.659665	−	0.751559i	$-0.729302\pi$
$347$		−	28.0000i		−	1.50312i	0.659665	−	0.751559i	$-0.270698\pi$
$348$	4.00000			0.214423
$349$			34.0000i			1.81998i	0.414632	+	0.909989i	$0.363910\pi$
$349$			34.0000i			1.81998i	−0.414632	+	0.909989i	$0.636090\pi$
$350$		0			0
$351$	−16.0000	+	16.0000i	−0.854017	+	0.854017i
$352$	−20.0000			−1.06600
$353$	−4.00000			−0.212899			−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$354$	−16.0000			−0.850390
$355$	8.00000	+	4.00000i	0.424596	+	0.212298i
$356$	1.00000	+	1.00000i	0.0529999	+	0.0529999i
$357$		0			0
$358$	−16.0000	+	16.0000i	−0.845626	+	0.845626i
$359$			20.0000i			1.05556i	0.849381	+	0.527780i	$0.176975\pi$
$359$			20.0000i			1.05556i	−0.849381	+	0.527780i	$0.823025\pi$
$360$	−30.0000	−	15.0000i	−1.58114	−	0.790569i
$361$			19.0000i			1.00000i
$362$		−	8.00000i		−	0.420471i
$363$	−10.0000	+	10.0000i	−0.524864	+	0.524864i
$364$		0			0
$365$	−33.0000	+	11.0000i	−1.72730	+	0.575766i
$366$	4.00000			0.209083
$367$	−16.0000	+	16.0000i	−0.835193	+	0.835193i	−0.988222	−	0.153029i	$-0.951097\pi$
$367$	−16.0000	+	16.0000i	−0.835193	+	0.835193i	0.153029	+	0.988222i	$0.451097\pi$
$368$		−	4.00000i		−	0.208514i
$369$		0			0
$370$	−4.00000	+	13.0000i	−0.207950	+	0.675838i
$371$		0			0
$372$			24.0000i			1.24434i
$373$	−9.00000	+	9.00000i	−0.466002	+	0.466002i	−0.900617	−	0.434614i	$-0.856885\pi$
$373$	−9.00000	+	9.00000i	−0.466002	+	0.466002i	0.434614	+	0.900617i	$0.356885\pi$
$374$	8.00000			0.413670
$375$	−26.0000	−	18.0000i	−1.34263	−	0.929516i
$376$	24.0000	+	24.0000i	1.23771	+	1.23771i
$377$	4.00000	−	4.00000i	0.206010	−	0.206010i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$		−	48.0000i		−	2.45911i
$382$	14.0000	−	14.0000i	0.716302	−	0.716302i
$383$			20.0000i			1.02195i	0.859595	+	0.510976i	$0.170716\pi$
$383$			20.0000i			1.02195i	−0.859595	+	0.510976i	$0.829284\pi$
$384$	6.00000	+	6.00000i	0.306186	+	0.306186i
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−60.0000			−3.04997
$388$	4.00000			0.203069
$389$	1.00000	−	1.00000i	0.0507020	−	0.0507020i	−0.681301	−	0.732003i	$-0.738586\pi$
$389$	1.00000	−	1.00000i	0.0507020	−	0.0507020i	0.732003	+	0.681301i	$0.238586\pi$
$390$	−24.0000	+	8.00000i	−1.21529	+	0.405096i
$391$		−	8.00000i		−	0.404577i
$392$	−21.0000			−1.06066
$393$		−	64.0000i		−	3.22837i
$394$	−5.00000	−	5.00000i	−0.251896	−	0.251896i
$395$	−18.0000	+	6.00000i	−0.905678	+	0.301893i
$396$	20.0000			1.00504
$397$	1.00000	+	1.00000i	0.0501886	+	0.0501886i	0.731756	−	0.681567i	$-0.238701\pi$
$397$	1.00000	+	1.00000i	0.0501886	+	0.0501886i	−0.681567	+	0.731756i	$0.738701\pi$
$398$	−18.0000	+	18.0000i	−0.902258	+	0.902258i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	−0.681697	−	0.731635i	$-0.738758\pi$
$401$	1.00000	−	1.00000i	0.0499376	−	0.0499376i	0.731635	+	0.681697i	$0.238758\pi$
$402$			24.0000i			1.19701i
$403$	24.0000	+	24.0000i	1.19553	+	1.19553i
$404$		−	6.00000i		−	0.298511i
$405$	2.00000	+	1.00000i	0.0993808	+	0.0496904i
$406$		0			0
$407$	−4.00000	−	24.0000i	−0.198273	−	1.18964i
$408$	−12.0000	−	12.0000i	−0.594089	−	0.594089i
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	0.629036	−	0.777376i	$-0.283450\pi$
$409$	−3.00000	−	3.00000i	−0.148340	−	0.148340i	−0.777376	+	0.629036i	$0.783450\pi$
$410$		0			0
$411$			28.0000i			1.38114i
$412$	−4.00000			−0.197066
$413$		0			0
$414$			20.0000i			0.982946i
$415$	2.00000	+	6.00000i	0.0981761	+	0.294528i
$416$	20.0000			0.980581
$417$	−8.00000	+	8.00000i	−0.391762	+	0.391762i
$418$		0			0
$419$		−	16.0000i		−	0.781651i	−0.920465	−	0.390826i	$-0.872190\pi$
$419$		−	16.0000i		−	0.781651i	0.920465	−	0.390826i	$-0.127810\pi$
$420$		0			0
$421$	3.00000	−	3.00000i	0.146211	−	0.146211i	−0.630212	−	0.776423i	$-0.717032\pi$
$421$	3.00000	−	3.00000i	0.146211	−	0.146211i	0.776423	+	0.630212i	$0.217032\pi$
$422$			8.00000i			0.389434i
$423$	−40.0000	−	40.0000i	−1.94487	−	1.94487i
$424$	27.0000	−	27.0000i	1.31124	−	1.31124i
$425$	−6.00000	−	8.00000i	−0.291043	−	0.388057i
$426$	−8.00000	−	8.00000i	−0.387601	−	0.387601i
$427$		0			0
$428$	−6.00000	+	6.00000i	−0.290021	+	0.290021i
$429$	32.0000	−	32.0000i	1.54497	−	1.54497i
$430$	−24.0000	−	12.0000i	−1.15738	−	0.578691i
$431$	2.00000	−	2.00000i	0.0963366	−	0.0963366i	−0.657296	−	0.753633i	$-0.728300\pi$
$431$	2.00000	−	2.00000i	0.0963366	−	0.0963366i	0.753633	+	0.657296i	$0.228300\pi$
$432$	4.00000	+	4.00000i	0.192450	+	0.192450i
$433$	11.0000	+	11.0000i	0.528626	+	0.528626i	0.920163	−	0.391536i	$-0.128056\pi$
$433$	11.0000	+	11.0000i	0.528626	+	0.528626i	−0.391536	+	0.920163i	$0.628056\pi$
$434$		0			0
$435$	−8.00000	−	4.00000i	−0.383571	−	0.191785i
$436$	−3.00000	+	3.00000i	−0.143674	+	0.143674i
$437$		0			0
$438$	44.0000			2.10240
$439$	10.0000	+	10.0000i	0.477274	+	0.477274i	0.904259	−	0.426985i	$-0.140424\pi$
$439$	10.0000	+	10.0000i	0.477274	+	0.477274i	−0.426985	+	0.904259i	$0.640424\pi$
$440$	24.0000	+	12.0000i	1.14416	+	0.572078i
$441$	35.0000			1.66667
$442$	−8.00000			−0.380521
$443$	2.00000	−	2.00000i	0.0950229	−	0.0950229i	−0.657997	−	0.753020i	$-0.728596\pi$
$443$	2.00000	−	2.00000i	0.0950229	−	0.0950229i	0.753020	+	0.657997i	$0.228596\pi$
$444$	−10.0000	+	14.0000i	−0.474579	+	0.664411i
$445$	−1.00000	−	3.00000i	−0.0474045	−	0.142214i
$446$	4.00000	−	4.00000i	0.189405	−	0.189405i
$447$	−20.0000	−	20.0000i	−0.945968	−	0.945968i
$448$		0			0
$449$	−23.0000	+	23.0000i	−1.08544	+	1.08544i	−0.0894454	+	0.995992i	$0.528509\pi$
$449$	−23.0000	+	23.0000i	−1.08544	+	1.08544i	−0.995992	+	0.0894454i	$0.971491\pi$
$450$	15.0000	+	20.0000i	0.707107	+	0.942809i
$451$		0			0
$452$	−2.00000			−0.0940721
$453$	16.0000	+	16.0000i	0.751746	+	0.751746i
$454$			16.0000i			0.750917i
$455$		0			0
$456$		0			0
$457$	−20.0000			−0.935561			−0.467780	−	0.883845i	$-0.654946\pi$
$457$	−20.0000			−0.935561			−0.467780	+	0.883845i	$0.654946\pi$
$458$	16.0000			0.747631
$459$	8.00000	+	8.00000i	0.373408	+	0.373408i
$460$	4.00000	−	8.00000i	0.186501	−	0.373002i
$461$	21.0000	+	21.0000i	0.978068	+	0.978068i	0.999765	−	0.0216971i	$-0.00690694\pi$
$461$	21.0000	+	21.0000i	0.978068	+	0.978068i	−0.0216971	+	0.999765i	$0.506907\pi$
$462$		0			0
$463$		−	20.0000i		−	0.929479i	−0.885448	−	0.464739i	$-0.846148\pi$
$463$		−	20.0000i		−	0.929479i	0.885448	−	0.464739i	$-0.153852\pi$
$464$	−1.00000	−	1.00000i	−0.0464238	−	0.0464238i
$465$	24.0000	−	48.0000i	1.11297	−	2.22595i
$466$	−13.0000	−	13.0000i	−0.602213	−	0.602213i
$467$	−4.00000			−0.185098			−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000			−0.185098			−0.0925490	+	0.995708i	$0.529501\pi$
$468$	−20.0000			−0.924500
$469$		0			0
$470$	−8.00000	−	24.0000i	−0.369012	−	1.10704i
$471$			60.0000i			2.76465i
$472$	−12.0000	−	12.0000i	−0.552345	−	0.552345i
$473$	48.0000			2.20704
$474$	24.0000			1.10236
$475$		0			0
$476$		0			0
$477$	−45.0000	+	45.0000i	−2.06041	+	2.06041i
$478$	14.0000	+	14.0000i	0.640345	+	0.640345i
$479$	10.0000	−	10.0000i	0.456912	−	0.456912i	−0.440729	−	0.897640i	$-0.645280\pi$
$479$	10.0000	−	10.0000i	0.456912	−	0.456912i	0.897640	+	0.440729i	$0.145280\pi$
$480$	−10.0000	−	30.0000i	−0.456435	−	1.36931i
$481$	4.00000	+	24.0000i	0.182384	+	1.09431i
$482$	−13.0000	+	13.0000i	−0.592134	+	0.592134i
$483$		0			0
$484$	−5.00000			−0.227273
$485$	−8.00000	−	4.00000i	−0.363261	−	0.181631i
$486$	10.0000	+	10.0000i	0.453609	+	0.453609i
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$	3.00000	+	3.00000i	0.135804	+	0.135804i
$489$	8.00000	−	8.00000i	0.361773	−	0.361773i
$490$	14.0000	+	7.00000i	0.632456	+	0.316228i
$491$	8.00000			0.361035			0.180517	−	0.983572i	$-0.442223\pi$
$491$	8.00000			0.361035			0.180517	+	0.983572i	$0.442223\pi$
$492$		0			0
$493$	−2.00000	−	2.00000i	−0.0900755	−	0.0900755i
$494$		0			0
$495$	−40.0000	−	20.0000i	−1.79787	−	0.898933i
$496$	6.00000	−	6.00000i	0.269408	−	0.269408i
$497$		0			0
$498$		−	8.00000i		−	0.358489i
$499$	−12.0000	−	12.0000i	−0.537194	−	0.537194i	0.385510	−	0.922704i	$-0.374026\pi$
$499$	−12.0000	−	12.0000i	−0.537194	−	0.537194i	−0.922704	+	0.385510i	$0.874026\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	−24.0000	+	24.0000i	−1.07224	+	1.07224i
$502$	4.00000	+	4.00000i	0.178529	+	0.178529i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	−6.00000	+	12.0000i	−0.266996	+	0.533993i
$506$		−	16.0000i		−	0.711287i
$507$	−6.00000	+	6.00000i	−0.266469	+	0.266469i
$508$	12.0000	−	12.0000i	0.532414	−	0.532414i
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$	4.00000	+	12.0000i	0.177123	+	0.531369i
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$		−	14.0000i		−	0.617514i
$515$	8.00000	+	4.00000i	0.352522	+	0.176261i
$516$	−24.0000	−	24.0000i	−1.05654	−	1.05654i
$517$	32.0000	+	32.0000i	1.40736	+	1.40736i
$518$		0			0
$519$		−	20.0000i		−	0.877903i
$520$	−24.0000	−	12.0000i	−1.05247	−	0.526235i
$521$		−	2.00000i		−	0.0876216i	−0.999040	−	0.0438108i	$-0.986050\pi$
$521$		−	2.00000i		−	0.0876216i	0.999040	−	0.0438108i	$-0.0139499\pi$
$522$	5.00000	+	5.00000i	0.218844	+	0.218844i
$523$		−	40.0000i		−	1.74908i	−0.484955	−	0.874539i	$-0.661164\pi$
$523$		−	40.0000i		−	1.74908i	0.484955	−	0.874539i	$-0.338836\pi$
$524$	16.0000	−	16.0000i	0.698963	−	0.698963i
$525$		0			0
$526$	−8.00000	−	8.00000i	−0.348817	−	0.348817i
$527$	12.0000	−	12.0000i	0.522728	−	0.522728i
$528$	−8.00000	−	8.00000i	−0.348155	−	0.348155i
$529$	7.00000			0.304348
$530$	−27.0000	+	9.00000i	−1.17281	+	0.390935i
$531$	20.0000	+	20.0000i	0.867926	+	0.867926i
$532$		0			0
$533$		0			0
$534$			4.00000i			0.173097i
$535$	18.0000	−	6.00000i	0.778208	−	0.259403i
$536$	−18.0000	+	18.0000i	−0.777482	+	0.777482i
$537$	64.0000			2.76180
$538$	14.0000			0.603583
$539$	−28.0000			−1.20605
$540$	4.00000	+	12.0000i	0.172133	+	0.516398i
$541$	19.0000	+	19.0000i	0.816874	+	0.816874i	0.985654	−	0.168780i	$-0.0539827\pi$
$541$	19.0000	+	19.0000i	0.816874	+	0.816874i	−0.168780	+	0.985654i	$0.553983\pi$
$542$		−	20.0000i		−	0.859074i
$543$	−16.0000	+	16.0000i	−0.686626	+	0.686626i
$544$		−	10.0000i		−	0.428746i
$545$	9.00000	−	3.00000i	0.385518	−	0.128506i
$546$		0			0
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	−7.00000	+	7.00000i	−0.299025	+	0.299025i
$549$	−5.00000	−	5.00000i	−0.213395	−	0.213395i
$550$	−12.0000	−	16.0000i	−0.511682	−	0.682242i
$551$		0			0
$552$	−24.0000	+	24.0000i	−1.02151	+	1.02151i
$553$		0			0
$554$	−4.00000			−0.169944
$555$	34.0000	−	18.0000i	1.44322	−	0.764057i
$556$	−4.00000			−0.169638
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$	−30.0000	+	30.0000i	−1.27000	+	1.27000i
$559$	−48.0000			−2.03018
$560$		0			0
$561$	−16.0000	−	16.0000i	−0.675521	−	0.675521i
$562$	15.0000	−	15.0000i	0.632737	−	0.632737i
$563$			24.0000i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$563$			24.0000i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$564$		−	32.0000i		−	1.34744i
$565$	4.00000	+	2.00000i	0.168281	+	0.0841406i
$566$		−	4.00000i		−	0.168133i
$567$		0			0
$568$		−	12.0000i		−	0.503509i
$569$	11.0000	+	11.0000i	0.461144	+	0.461144i	0.899030	−	0.437886i	$-0.144273\pi$
$569$	11.0000	+	11.0000i	0.461144	+	0.461144i	−0.437886	+	0.899030i	$0.644273\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	16.0000			0.668994
$573$	−56.0000			−2.33943
$574$		0			0
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$			35.0000i			1.45833i
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$		−	13.0000i		−	0.540729i
$579$	28.0000	+	28.0000i	1.16364	+	1.16364i
$580$	−1.00000	−	3.00000i	−0.0415227	−	0.124568i
$581$		0			0
$582$	8.00000	+	8.00000i	0.331611	+	0.331611i
$583$	36.0000	−	36.0000i	1.49097	−	1.49097i
$584$	33.0000	+	33.0000i	1.36555	+	1.36555i
$585$	40.0000	+	20.0000i	1.65380	+	0.826898i
$586$	−1.00000	+	1.00000i	−0.0413096	+	0.0413096i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	14.0000	+	14.0000i	0.577350	+	0.577350i
$589$		0			0
$590$	4.00000	+	12.0000i	0.164677	+	0.494032i
$591$			20.0000i			0.822690i
$592$	6.00000	−	1.00000i	0.246598	−	0.0410997i
$593$	−9.00000	−	9.00000i	−0.369586	−	0.369586i	0.497740	−	0.867326i	$-0.334163\pi$
$593$	−9.00000	−	9.00000i	−0.369586	−	0.369586i	−0.867326	+	0.497740i	$0.834163\pi$
$594$	16.0000	+	16.0000i	0.656488	+	0.656488i
$595$		0			0
$596$		−	10.0000i		−	0.409616i
$597$	72.0000			2.94676
$598$			16.0000i			0.654289i
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$	−6.00000	+	42.0000i	−0.244949	+	1.71464i
$601$	−40.0000			−1.63163			−0.815817	−	0.578310i	$-0.803712\pi$
$601$	−40.0000			−1.63163			−0.815817	+	0.578310i	$0.803712\pi$
$602$		0			0
$603$	30.0000	−	30.0000i	1.22169	−	1.22169i
$604$			8.00000i			0.325515i
$605$	10.0000	+	5.00000i	0.406558	+	0.203279i
$606$	12.0000	−	12.0000i	0.487467	−	0.487467i
$607$		−	4.00000i		−	0.162355i	−0.996700	−	0.0811775i	$-0.974132\pi$
$607$		−	4.00000i		−	0.162355i	0.996700	−	0.0811775i	$-0.0258681\pi$
$608$		0			0
$609$		0			0
$610$	−1.00000	−	3.00000i	−0.0404888	−	0.121466i
$611$	−32.0000	−	32.0000i	−1.29458	−	1.29458i
$612$			10.0000i			0.404226i
$613$	3.00000	−	3.00000i	0.121169	−	0.121169i	−0.643922	−	0.765091i	$-0.722694\pi$
$613$	3.00000	−	3.00000i	0.121169	−	0.121169i	0.765091	+	0.643922i	$0.222694\pi$
$614$	6.00000	−	6.00000i	0.242140	−	0.242140i
$615$		0			0
$616$		0			0
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	0.276593	−	0.960987i	$-0.410795\pi$
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	−0.960987	+	0.276593i	$0.910795\pi$
$618$	−8.00000	−	8.00000i	−0.321807	−	0.321807i
$619$	−16.0000			−0.643094			−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000			−0.643094			−0.321547	+	0.946894i	$0.604203\pi$
$620$	18.0000	−	6.00000i	0.722897	−	0.240966i
$621$	16.0000	−	16.0000i	0.642058	−	0.642058i
$622$	−6.00000	−	6.00000i	−0.240578	−	0.240578i
$623$		0			0
$624$	8.00000	+	8.00000i	0.320256	+	0.320256i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−6.00000			−0.239808
$627$		0			0
$628$	−15.0000	+	15.0000i	−0.598565	+	0.598565i
$629$	12.0000	−	2.00000i	0.478471	−	0.0797452i
$630$		0			0
$631$	26.0000	−	26.0000i	1.03504	−	1.03504i	0.0356804	−	0.999363i	$-0.488640\pi$
$631$	26.0000	−	26.0000i	1.03504	−	1.03504i	0.999363	−	0.0356804i	$-0.0113598\pi$
$632$	18.0000	+	18.0000i	0.716002	+	0.716002i
$633$	16.0000	−	16.0000i	0.635943	−	0.635943i
$634$	−19.0000	+	19.0000i	−0.754586	+	0.754586i
$635$	−36.0000	+	12.0000i	−1.42862	+	0.476205i
$636$	−36.0000			−1.42749
$637$	28.0000			1.10940
$638$	−4.00000	−	4.00000i	−0.158362	−	0.158362i
$639$			20.0000i			0.791188i
$640$	3.00000	−	6.00000i	0.118585	−	0.237171i
$641$	−24.0000			−0.947943			−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000			−0.947943			−0.473972	+	0.880540i	$0.657180\pi$
$642$	−24.0000			−0.947204
$643$	−8.00000			−0.315489			−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000			−0.315489			−0.157745	+	0.987480i	$0.550422\pi$
$644$		0			0
$645$	24.0000	+	72.0000i	0.944999	+	2.83500i
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		−	3.00000i		−	0.117851i
$649$	−16.0000	−	16.0000i	−0.628055	−	0.628055i
$650$	12.0000	+	16.0000i	0.470679	+	0.627572i
$651$		0			0
$652$	4.00000			0.156652
$653$	36.0000			1.40879			0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000			1.40879			0.704394	+	0.709809i	$0.251219\pi$
$654$	−12.0000			−0.469237
$655$	−48.0000	+	16.0000i	−1.87552	+	0.625172i
$656$		0			0
$657$	−55.0000	−	55.0000i	−2.14575	−	2.14575i
$658$		0			0
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$	−8.00000	−	24.0000i	−0.311400	−	0.934199i
$661$	21.0000	−	21.0000i	0.816805	−	0.816805i	−0.168838	−	0.985644i	$-0.554002\pi$
$661$	21.0000	−	21.0000i	0.816805	−	0.816805i	0.985644	+	0.168838i	$0.0540016\pi$
$662$	4.00000	−	4.00000i	0.155464	−	0.155464i
$663$	16.0000	+	16.0000i	0.621389	+	0.621389i
$664$	6.00000	−	6.00000i	0.232845	−	0.232845i
$665$		0			0
$666$	−30.0000	+	5.00000i	−1.16248	+	0.193746i
$667$	−4.00000	+	4.00000i	−0.154881	+	0.154881i
$668$	−12.0000			−0.464294
$669$	−16.0000			−0.618596
$670$	18.0000	−	6.00000i	0.695401	−	0.231800i
$671$	4.00000	+	4.00000i	0.154418	+	0.154418i
$672$		0			0
$673$	9.00000	+	9.00000i	0.346925	+	0.346925i	0.858963	−	0.512038i	$-0.171109\pi$
$673$	9.00000	+	9.00000i	0.346925	+	0.346925i	−0.512038	+	0.858963i	$0.671109\pi$
$674$	−15.0000	+	15.0000i	−0.577778	+	0.577778i
$675$	4.00000	−	28.0000i	0.153960	−	1.07772i
$676$	−3.00000			−0.115385
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	0.993935	−	0.109973i	$-0.0350764\pi$
$677$	23.0000	+	23.0000i	0.883962	+	0.883962i	−0.109973	+	0.993935i	$0.535076\pi$
$678$	−4.00000	−	4.00000i	−0.153619	−	0.153619i
$679$		0			0
$680$	−6.00000	+	12.0000i	−0.230089	+	0.460179i
$681$	32.0000	−	32.0000i	1.22624	−	1.22624i
$682$	24.0000	−	24.0000i	0.919007	−	0.919007i
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	21.0000	−	7.00000i	0.802369	−	0.267456i
$686$		0			0
$687$	−32.0000	−	32.0000i	−1.22088	−	1.22088i
$688$			12.0000i			0.457496i
$689$	−36.0000	+	36.0000i	−1.37149	+	1.37149i
$690$	24.0000	−	8.00000i	0.913664	−	0.304555i
$691$			16.0000i			0.608669i	0.952565	+	0.304334i	$0.0984340\pi$
$691$			16.0000i			0.608669i	−0.952565	+	0.304334i	$0.901566\pi$
$692$	5.00000	−	5.00000i	0.190071	−	0.190071i
$693$		0			0
$694$	28.0000			1.06287
$695$	8.00000	+	4.00000i	0.303457	+	0.151729i
$696$			12.0000i			0.454859i
$697$		0			0
$698$	−34.0000			−1.28692
$699$			52.0000i			1.96682i
$700$		0			0
$701$	15.0000	+	15.0000i	0.566542	+	0.566542i	0.931158	−	0.364616i	$-0.118800\pi$
$701$	15.0000	+	15.0000i	0.566542	+	0.566542i	−0.364616	+	0.931158i	$0.618800\pi$
$702$	−16.0000	−	16.0000i	−0.603881	−	0.603881i
$703$		0			0
$704$		−	28.0000i		−	1.05529i
$705$	−32.0000	+	64.0000i	−1.20519	+	2.41038i
$706$		−	4.00000i		−	0.150542i
$707$		0			0
$708$			16.0000i			0.601317i
$709$	3.00000	−	3.00000i	0.112667	−	0.112667i	−0.648526	−	0.761193i	$-0.724614\pi$
$709$	3.00000	−	3.00000i	0.112667	−	0.112667i	0.761193	+	0.648526i	$0.224614\pi$
$710$	−4.00000	+	8.00000i	−0.150117	+	0.300235i
$711$	−30.0000	−	30.0000i	−1.12509	−	1.12509i
$712$	−3.00000	+	3.00000i	−0.112430	+	0.112430i
$713$	−24.0000	−	24.0000i	−0.898807	−	0.898807i
$714$		0			0
$715$	−32.0000	−	16.0000i	−1.19673	−	0.598366i
$716$	16.0000	+	16.0000i	0.597948	+	0.597948i
$717$		−	56.0000i		−	2.09136i
$718$	−20.0000			−0.746393
$719$		−	8.00000i		−	0.298350i	−0.988811	−	0.149175i	$-0.952338\pi$
$719$		−	8.00000i		−	0.298350i	0.988811	−	0.149175i	$-0.0476617\pi$
$720$	5.00000	−	10.0000i	0.186339	−	0.372678i
$721$		0			0
$722$	−19.0000			−0.707107
$723$	52.0000			1.93390
$724$	−8.00000			−0.297318
$725$	−1.00000	+	7.00000i	−0.0371391	+	0.259973i
$726$	−10.0000	−	10.0000i	−0.371135	−	0.371135i
$727$			12.0000i			0.445055i	0.974926	+	0.222528i	$0.0714308\pi$
$727$			12.0000i			0.445055i	−0.974926	+	0.222528i	$0.928569\pi$
$728$		0			0
$729$		−	43.0000i		−	1.59259i
$730$	−11.0000	−	33.0000i	−0.407128	−	1.22138i
$731$			24.0000i			0.887672i
$732$		−	4.00000i		−	0.147844i
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	−0.853506	−	0.521083i	$-0.825528\pi$
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	0.521083	+	0.853506i	$0.325528\pi$
$734$	−16.0000	−	16.0000i	−0.590571	−	0.590571i
$735$	−14.0000	−	42.0000i	−0.516398	−	1.54919i
$736$	−20.0000			−0.737210
$737$	−24.0000	+	24.0000i	−0.884051	+	0.884051i
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	13.0000	+	4.00000i	0.477890	+	0.147043i
$741$		0			0
$742$		0			0
$743$	16.0000	−	16.0000i	0.586983	−	0.586983i	−0.349830	−	0.936813i	$-0.613761\pi$
$743$	16.0000	−	16.0000i	0.586983	−	0.586983i	0.936813	+	0.349830i	$0.113761\pi$
$744$	−72.0000			−2.63965
$745$	−10.0000	+	20.0000i	−0.366372	+	0.732743i
$746$	−9.00000	−	9.00000i	−0.329513	−	0.329513i
$747$	−10.0000	+	10.0000i	−0.365881	+	0.365881i
$748$		−	8.00000i		−	0.292509i
$749$		0			0
$750$	18.0000	−	26.0000i	0.657267	−	0.949386i
$751$		−	4.00000i		−	0.145962i	−0.997333	−	0.0729810i	$-0.976749\pi$
$751$		−	4.00000i		−	0.145962i	0.997333	−	0.0729810i	$-0.0232513\pi$
$752$	−8.00000	+	8.00000i	−0.291730	+	0.291730i
$753$		−	16.0000i		−	0.583072i
$754$	4.00000	+	4.00000i	0.145671	+	0.145671i
$755$	8.00000	−	16.0000i	0.291150	−	0.582300i
$756$		0			0
$757$	12.0000			0.436147			0.218074	−	0.975932i	$-0.430023\pi$
$757$	12.0000			0.436147			0.218074	+	0.975932i	$0.430023\pi$
$758$	8.00000			0.290573
$759$	−32.0000	+	32.0000i	−1.16153	+	1.16153i
$760$		0			0
$761$		−	16.0000i		−	0.580000i	−0.957027	−	0.290000i	$-0.906345\pi$
$761$		−	16.0000i		−	0.580000i	0.957027	−	0.290000i	$-0.0936552\pi$
$762$	48.0000			1.73886
$763$		0			0
$764$	−14.0000	−	14.0000i	−0.506502	−	0.506502i
$765$	10.0000	−	20.0000i	0.361551	−	0.723102i
$766$	−20.0000			−0.722629
$767$	16.0000	+	16.0000i	0.577727	+	0.577727i
$768$	−34.0000	+	34.0000i	−1.22687	+	1.22687i
$769$	3.00000	+	3.00000i	0.108183	+	0.108183i	0.759126	−	0.650943i	$-0.225627\pi$
$769$	3.00000	+	3.00000i	0.108183	+	0.108183i	−0.650943	+	0.759126i	$0.725627\pi$
$770$		0			0
$771$	−28.0000	+	28.0000i	−1.00840	+	1.00840i
$772$			14.0000i			0.503871i
$773$	−29.0000	−	29.0000i	−1.04306	−	1.04306i	−0.999030	−	0.0440272i	$-0.985981\pi$
$773$	−29.0000	−	29.0000i	−1.04306	−	1.04306i	−0.0440272	−	0.999030i	$-0.514019\pi$
$774$		−	60.0000i		−	2.15666i
$775$	−42.0000	−	6.00000i	−1.50868	−	0.215526i
$776$			12.0000i			0.430775i
$777$		0			0
$778$	1.00000	+	1.00000i	0.0358517	+	0.0358517i
$779$		0			0
$780$	8.00000	+	24.0000i	0.286446	+	0.859338i
$781$		−	16.0000i		−	0.572525i
$782$	8.00000			0.286079
$783$		−	8.00000i		−	0.285897i
$784$		−	7.00000i		−	0.250000i
$785$	45.0000	−	15.0000i	1.60612	−	0.535373i
$786$	64.0000			2.28280
$787$	−18.0000	+	18.0000i	−0.641631	+	0.641631i	−0.950956	−	0.309326i	$-0.899897\pi$
$787$	−18.0000	+	18.0000i	−0.641631	+	0.641631i	0.309326	+	0.950956i	$0.399897\pi$
$788$	−5.00000	+	5.00000i	−0.178118	+	0.178118i
$789$			32.0000i			1.13923i
$790$	−6.00000	−	18.0000i	−0.213470	−	0.640411i
$791$		0			0
$792$			60.0000i			2.13201i
$793$	−4.00000	−	4.00000i	−0.142044	−	0.142044i
$794$	−1.00000	+	1.00000i	−0.0354887	+	0.0354887i
$795$	72.0000	+	36.0000i	2.55358	+	1.27679i
$796$	18.0000	+	18.0000i	0.637993	+	0.637993i
$797$		−	20.0000i		−	0.708436i	−0.935163	−	0.354218i	$-0.884747\pi$
$797$		−	20.0000i		−	0.708436i	0.935163	−	0.354218i	$-0.115253\pi$
$798$		0			0
$799$	−16.0000	+	16.0000i	−0.566039	+	0.566039i
$800$	−20.0000	+	15.0000i	−0.707107	+	0.530330i
$801$	5.00000	−	5.00000i	0.176666	−	0.176666i
$802$	1.00000	+	1.00000i	0.0353112	+	0.0353112i
$803$	44.0000	+	44.0000i	1.55273	+	1.55273i
$804$	24.0000			0.846415
$805$		0			0
$806$	−24.0000	+	24.0000i	−0.845364	+	0.845364i
$807$	−28.0000	−	28.0000i	−0.985647	−	0.985647i
$808$	18.0000			0.633238
$809$	−1.00000	−	1.00000i	−0.0351581	−	0.0351581i	0.689309	−	0.724467i	$-0.257914\pi$
$809$	−1.00000	−	1.00000i	−0.0351581	−	0.0351581i	−0.724467	+	0.689309i	$0.757914\pi$
$810$	−1.00000	+	2.00000i	−0.0351364	+	0.0702728i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$	−40.0000	+	40.0000i	−1.40286	+	1.40286i
$814$	24.0000	−	4.00000i	0.841200	−	0.140200i
$815$	−8.00000	−	4.00000i	−0.280228	−	0.140114i
$816$	4.00000	−	4.00000i	0.140028	−	0.140028i
$817$		0			0
$818$	3.00000	−	3.00000i	0.104893	−	0.104893i
$819$		0			0
$820$		0			0
$821$	42.0000			1.46581			0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000			1.46581			0.732905	+	0.680331i	$0.238164\pi$
$822$	−28.0000			−0.976612
$823$	−4.00000	−	4.00000i	−0.139431	−	0.139431i	0.633946	−	0.773377i	$-0.281434\pi$
$823$	−4.00000	−	4.00000i	−0.139431	−	0.139431i	−0.773377	+	0.633946i	$0.781434\pi$
$824$		−	12.0000i		−	0.418040i
$825$	−8.00000	+	56.0000i	−0.278524	+	1.94967i
$826$		0			0
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$	20.0000			0.695048
$829$	27.0000	+	27.0000i	0.937749	+	0.937749i	0.998173	−	0.0604240i	$-0.0192453\pi$
$829$	27.0000	+	27.0000i	0.937749	+	0.937749i	−0.0604240	+	0.998173i	$0.519245\pi$
$830$	−6.00000	+	2.00000i	−0.208263	+	0.0694210i
$831$	8.00000	+	8.00000i	0.277517	+	0.277517i
$832$			28.0000i			0.970725i
$833$		−	14.0000i		−	0.485071i
$834$	−8.00000	−	8.00000i	−0.277017	−	0.277017i
$835$	24.0000	+	12.0000i	0.830554	+	0.415277i
$836$		0			0
$837$	48.0000			1.65912
$838$	16.0000			0.552711
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$		−	27.0000i		−	0.931034i
$842$	3.00000	+	3.00000i	0.103387	+	0.103387i
$843$	−60.0000			−2.06651
$844$	8.00000			0.275371
$845$	6.00000	+	3.00000i	0.206406	+	0.103203i
$846$	40.0000	−	40.0000i	1.37523	−	1.37523i
$847$		0			0
$848$	9.00000	+	9.00000i	0.309061	+	0.309061i
$849$	−8.00000	+	8.00000i	−0.274559	+	0.274559i
$850$	8.00000	−	6.00000i	0.274398	−	0.205798i
$851$	−4.00000	−	24.0000i	−0.137118	−	0.822709i
$852$	−8.00000	+	8.00000i	−0.274075	+	0.274075i
$853$	−28.0000			−0.958702			−0.479351	−	0.877623i	$-0.659128\pi$
$853$	−28.0000			−0.958702			−0.479351	+	0.877623i	$0.659128\pi$
$854$		0			0
$855$		0			0
$856$	−18.0000	−	18.0000i	−0.615227	−	0.615227i
$857$	52.0000			1.77629			0.888143	−	0.459567i	$-0.151995\pi$
$857$	52.0000			1.77629			0.888143	+	0.459567i	$0.151995\pi$
$858$	32.0000	+	32.0000i	1.09246	+	1.09246i
$859$	32.0000	−	32.0000i	1.09183	−	1.09183i	0.0964922	−	0.995334i	$-0.469238\pi$
$859$	32.0000	−	32.0000i	1.09183	−	1.09183i	0.995334	−	0.0964922i	$-0.0307623\pi$
$860$	−12.0000	+	24.0000i	−0.409197	+	0.818393i
$861$		0			0
$862$	2.00000	+	2.00000i	0.0681203	+	0.0681203i
$863$	24.0000	+	24.0000i	0.816970	+	0.816970i	0.985668	−	0.168698i	$-0.0539563\pi$
$863$	24.0000	+	24.0000i	0.816970	+	0.816970i	−0.168698	+	0.985668i	$0.553956\pi$
$864$	20.0000	−	20.0000i	0.680414	−	0.680414i
$865$	−15.0000	+	5.00000i	−0.510015	+	0.170005i
$866$	−11.0000	+	11.0000i	−0.373795	+	0.373795i
$867$	−26.0000	+	26.0000i	−0.883006	+	0.883006i
$868$		0			0
$869$	24.0000	+	24.0000i	0.814144	+	0.814144i
$870$	4.00000	−	8.00000i	0.135613	−	0.271225i
$871$	24.0000	−	24.0000i	0.813209	−	0.813209i
$872$	−9.00000	−	9.00000i	−0.304778	−	0.304778i
$873$		−	20.0000i		−	0.676897i
$874$		0			0
$875$		0			0
$876$		−	44.0000i		−	1.48662i
$877$	1.00000	−	1.00000i	0.0337676	−	0.0337676i	−0.690021	−	0.723789i	$-0.742399\pi$
$877$	1.00000	−	1.00000i	0.0337676	−	0.0337676i	0.723789	+	0.690021i	$0.242399\pi$
$878$	−10.0000	+	10.0000i	−0.337484	+	0.337484i
$879$	4.00000			0.134917
$880$	−4.00000	+	8.00000i	−0.134840	+	0.269680i
$881$		−	42.0000i		−	1.41502i	−0.706705	−	0.707508i	$-0.749819\pi$
$881$		−	42.0000i		−	1.41502i	0.706705	−	0.707508i	$-0.250181\pi$
$882$			35.0000i			1.17851i
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$			8.00000i			0.269069i
$885$	16.0000	−	32.0000i	0.537834	−	1.07567i
$886$	2.00000	+	2.00000i	0.0671913	+	0.0671913i
$887$	32.0000	+	32.0000i	1.07445	+	1.07445i	0.996996	+	0.0774593i	$0.0246808\pi$
$887$	32.0000	+	32.0000i	1.07445	+	1.07445i	0.0774593	+	0.996996i	$0.475319\pi$
$888$	−42.0000	−	30.0000i	−1.40943	−	1.00673i
$889$		0			0
$890$	3.00000	−	1.00000i	0.100560	−	0.0335201i
$891$		−	4.00000i		−	0.134005i
$892$	−4.00000	−	4.00000i	−0.133930	−	0.133930i
$893$		0			0
$894$	20.0000	−	20.0000i	0.668900	−	0.668900i
$895$	−16.0000	−	48.0000i	−0.534821	−	1.60446i
$896$		0			0
$897$	32.0000	−	32.0000i	1.06845	−	1.06845i
$898$	−23.0000	−	23.0000i	−0.767520	−	0.767520i
$899$	−12.0000			−0.400222
$900$	20.0000	−	15.0000i	0.666667	−	0.500000i
$901$	18.0000	+	18.0000i	0.599667	+	0.599667i
$902$		0			0
$903$		0			0
$904$		−	6.00000i		−	0.199557i
$905$	16.0000	+	8.00000i	0.531858	+	0.265929i
$906$	−16.0000	+	16.0000i	−0.531564	+	0.531564i
$907$	32.0000			1.06254			0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000			1.06254			0.531271	+	0.847202i	$0.321714\pi$
$908$	16.0000			0.530979
$909$	−30.0000			−0.995037
$910$		0			0
$911$	34.0000	+	34.0000i	1.12647	+	1.12647i	0.990747	+	0.135724i	$0.0433359\pi$
$911$	34.0000	+	34.0000i	1.12647	+	1.12647i	0.135724	+	0.990747i	$0.456664\pi$
$912$		0			0
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$		−	20.0000i		−	0.661541i
$915$	−4.00000	+	8.00000i	−0.132236	+	0.264472i
$916$		−	16.0000i		−	0.528655i
$917$		0			0
$918$	−8.00000	+	8.00000i	−0.264039	+	0.264039i
$919$	−6.00000	−	6.00000i	−0.197922	−	0.197922i	0.601187	−	0.799109i	$-0.294695\pi$
$919$	−6.00000	−	6.00000i	−0.197922	−	0.197922i	−0.799109	+	0.601187i	$0.794695\pi$
$920$	24.0000	+	12.0000i	0.791257	+	0.395628i
$921$	−24.0000			−0.790827
$922$	−21.0000	+	21.0000i	−0.691598	+	0.691598i
$923$			16.0000i			0.526646i
$924$		0			0
$925$	−22.0000	−	21.0000i	−0.723356	−	0.690476i
$926$	20.0000			0.657241
$927$			20.0000i			0.656886i
$928$	−5.00000	+	5.00000i	−0.164133	+	0.164133i
$929$	−22.0000			−0.721797			−0.360898	−	0.932605i	$-0.617530\pi$
$929$	−22.0000			−0.721797			−0.360898	+	0.932605i	$0.617530\pi$
$930$	48.0000	+	24.0000i	1.57398	+	0.786991i
$931$		0			0
$932$	−13.0000	+	13.0000i	−0.425829	+	0.425829i
$933$			24.0000i			0.785725i
$934$		−	4.00000i		−	0.130884i
$935$	−8.00000	+	16.0000i	−0.261628	+	0.523256i
$936$		−	60.0000i		−	1.96116i
$937$	−17.0000	+	17.0000i	−0.555366	+	0.555366i	−0.927985	−	0.372619i	$-0.878460\pi$
$937$	−17.0000	+	17.0000i	−0.555366	+	0.555366i	0.372619	+	0.927985i	$0.378460\pi$
$938$		0			0
$939$	12.0000	+	12.0000i	0.391605	+	0.391605i
$940$	−24.0000	+	8.00000i	−0.782794	+	0.260931i
$941$	−24.0000			−0.782378			−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000			−0.782378			−0.391189	+	0.920310i	$0.627936\pi$
$942$	−60.0000			−1.95491
$943$		0			0
$944$	4.00000	−	4.00000i	0.130189	−	0.130189i
$945$		0			0
$946$			48.0000i			1.56061i
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		−	24.0000i		−	0.779484i
$949$	−44.0000	−	44.0000i	−1.42830	−	1.42830i
$950$		0			0
$951$	76.0000			2.46447
$952$		0			0
$953$	−41.0000	+	41.0000i	−1.32812	+	1.32812i	−0.421111	+	0.907009i	$0.638360\pi$
$953$	−41.0000	+	41.0000i	−1.32812	+	1.32812i	−0.907009	+	0.421111i	$0.861640\pi$
$954$	−45.0000	−	45.0000i	−1.45693	−	1.45693i
$955$	14.0000	+	42.0000i	0.453029	+	1.35909i
$956$	14.0000	−	14.0000i	0.452792	−	0.452792i
$957$			16.0000i			0.517207i
$958$	10.0000	+	10.0000i	0.323085	+	0.323085i
$959$		0			0
$960$	42.0000	−	14.0000i	1.35554	−	0.451848i
$961$		−	41.0000i		−	1.32258i
$962$	−24.0000	+	4.00000i	−0.773791	+	0.128965i
$963$	30.0000	+	30.0000i	0.966736	+	0.966736i
$964$	13.0000	+	13.0000i	0.418702	+	0.418702i
$965$	14.0000	−	28.0000i	0.450676	−	0.901352i
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		−	15.0000i		−	0.482118i
$969$		0			0
$970$	4.00000	−	8.00000i	0.128432	−	0.256865i
$971$	−48.0000			−1.54039			−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000			−1.54039			−0.770197	+	0.637806i	$0.779842\pi$
$972$	10.0000	−	10.0000i	0.320750	−	0.320750i
$973$		0			0
$974$			20.0000i			0.640841i
$975$	8.00000	−	56.0000i	0.256205	−	1.79344i
$976$	−1.00000	+	1.00000i	−0.0320092	+	0.0320092i
$977$		−	18.0000i		−	0.575871i	−0.957650	−	0.287936i	$-0.907031\pi$
$977$		−	18.0000i		−	0.575871i	0.957650	−	0.287936i	$-0.0929689\pi$
$978$	8.00000	+	8.00000i	0.255812	+	0.255812i
$979$	−4.00000	+	4.00000i	−0.127841	+	0.127841i
$980$	7.00000	−	14.0000i	0.223607	−	0.447214i
$981$	15.0000	+	15.0000i	0.478913	+	0.478913i
$982$			8.00000i			0.255290i
$983$	−12.0000	+	12.0000i	−0.382741	+	0.382741i	−0.872089	−	0.489348i	$-0.837235\pi$
$983$	−12.0000	+	12.0000i	−0.382741	+	0.382741i	0.489348	+	0.872089i	$0.337235\pi$
$984$		0			0
$985$	15.0000	−	5.00000i	0.477940	−	0.159313i
$986$	2.00000	−	2.00000i	0.0636930	−	0.0636930i
$987$		0			0
$988$		0			0
$989$	48.0000			1.52631
$990$	20.0000	−	40.0000i	0.635642	−	1.27128i
$991$	−18.0000	+	18.0000i	−0.571789	+	0.571789i	−0.932628	−	0.360839i	$-0.882490\pi$
$991$	−18.0000	+	18.0000i	−0.571789	+	0.571789i	0.360839	+	0.932628i	$0.382490\pi$
$992$	−30.0000	−	30.0000i	−0.952501	−	0.952501i
$993$	−16.0000			−0.507745
$994$		0			0
$995$	−18.0000	−	54.0000i	−0.570638	−	1.71192i
$996$	−8.00000			−0.253490
$997$	28.0000			0.886769			0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000			0.886769			0.443384	+	0.896332i	$0.353778\pi$
$998$	12.0000	−	12.0000i	0.379853	−	0.379853i
$999$	28.0000	+	20.0000i	0.885881	+	0.632772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.f.b.43.1	✓	2
5.2	odd	4		185.2.k.a.117.1	yes	2
5.3	odd	4		925.2.k.b.857.1		2
5.4	even	2		925.2.f.a.43.1		2
37.31	odd	4		185.2.k.a.68.1	yes	2
185.68	even	4		925.2.f.a.882.1		2
185.142	even	4	inner	185.2.f.b.142.1	yes	2
185.179	odd	4		925.2.k.b.68.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.f.b.43.1	✓	2	1.1	even	1	trivial
185.2.f.b.142.1	yes	2	185.142	even	4	inner
185.2.k.a.68.1	yes	2	37.31	odd	4
185.2.k.a.117.1	yes	2	5.2	odd	4
925.2.f.a.43.1		2	5.4	even	2
925.2.f.a.882.1		2	185.68	even	4
925.2.k.b.68.1		2	185.179	odd	4
925.2.k.b.857.1		2	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(2.00000 - 2.00000i) q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +(2.00000 + 2.00000i) q^{6} +3.00000i q^{8} -5.00000i q^{9} +(1.00000 - 2.00000i) q^{10} +4.00000i q^{11} +(2.00000 - 2.00000i) q^{12} -4.00000i q^{13} +(-6.00000 + 2.00000i) q^{15} -1.00000 q^{16} -2.00000 q^{17} +5.00000 q^{18} +(-2.00000 - 1.00000i) q^{20} -4.00000 q^{22} +4.00000i q^{23} +(6.00000 + 6.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +(-4.00000 - 4.00000i) q^{27} +(1.00000 + 1.00000i) q^{29} +(-2.00000 - 6.00000i) q^{30} +(-6.00000 + 6.00000i) q^{31} +5.00000i q^{32} +(8.00000 + 8.00000i) q^{33} -2.00000i q^{34} -5.00000i q^{36} +(-6.00000 + 1.00000i) q^{37} +(-8.00000 - 8.00000i) q^{39} +(3.00000 - 6.00000i) q^{40} -12.0000i q^{43} +4.00000i q^{44} +(-5.00000 + 10.0000i) q^{45} -4.00000 q^{46} +(8.00000 - 8.00000i) q^{47} +(-2.00000 + 2.00000i) q^{48} +7.00000i q^{49} +(-4.00000 + 3.00000i) q^{50} +(-4.00000 + 4.00000i) q^{51} -4.00000i q^{52} +(-9.00000 - 9.00000i) q^{53} +(4.00000 - 4.00000i) q^{54} +(4.00000 - 8.00000i) q^{55} +(-1.00000 + 1.00000i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(-6.00000 + 2.00000i) q^{60} +(1.00000 - 1.00000i) q^{61} +(-6.00000 - 6.00000i) q^{62} -7.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +(-8.00000 + 8.00000i) q^{66} +(6.00000 + 6.00000i) q^{67} -2.00000 q^{68} +(8.00000 + 8.00000i) q^{69} -4.00000 q^{71} +15.0000 q^{72} +(11.0000 - 11.0000i) q^{73} +(-1.00000 - 6.00000i) q^{74} +(14.0000 + 2.00000i) q^{75} +(8.00000 - 8.00000i) q^{78} +(6.00000 - 6.00000i) q^{79} +(2.00000 + 1.00000i) q^{80} -1.00000 q^{81} +(-2.00000 - 2.00000i) q^{83} +(4.00000 + 2.00000i) q^{85} +12.0000 q^{86} +4.00000 q^{87} -12.0000 q^{88} +(1.00000 + 1.00000i) q^{89} +(-10.0000 - 5.00000i) q^{90} +4.00000i q^{92} +24.0000i q^{93} +(8.00000 + 8.00000i) q^{94} +(10.0000 + 10.0000i) q^{96} +4.00000 q^{97} -7.00000 q^{98} +20.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} + 2 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} + 4 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 10 q^{18} - 4 q^{20} - 8 q^{22} + 12 q^{24} + 6 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{29} - 4 q^{30} - 12 q^{31}+ \cdots + 40 q^{99}+O(q^{100}) \) 2 * q + 4 * q^3 + 2 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 + 4 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 10 * q^18 - 4 * q^20 - 8 * q^22 + 12 * q^24 + 6 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^29 - 4 * q^30 - 12 * q^31 + 16 * q^33 - 12 * q^37 - 16 * q^39 + 6 * q^40 - 10 * q^45 - 8 * q^46 + 16 * q^47 - 4 * q^48 - 8 * q^50 - 8 * q^51 - 18 * q^53 + 8 * q^54 + 8 * q^55 - 2 * q^58 - 8 * q^59 - 12 * q^60 + 2 * q^61 - 12 * q^62 - 14 * q^64 - 8 * q^65 - 16 * q^66 + 12 * q^67 - 4 * q^68 + 16 * q^69 - 8 * q^71 + 30 * q^72 + 22 * q^73 - 2 * q^74 + 28 * q^75 + 16 * q^78 + 12 * q^79 + 4 * q^80 - 2 * q^81 - 4 * q^83 + 8 * q^85 + 24 * q^86 + 8 * q^87 - 24 * q^88 + 2 * q^89 - 20 * q^90 + 16 * q^94 + 20 * q^96 + 8 * q^97 - 14 * q^98 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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