LMFDB - Embedded newform 363.2.d.b.362.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(362,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("363.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			362.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	363.362
Dual form			363.2.d.b.362.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} -1.00000 q^{4} -2.82843i q^{5} +(1.00000 - 1.41421i) q^{6} +1.41421i q^{7} -3.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} -4.24264i q^{13} +1.41421i q^{14} +(-4.00000 - 2.82843i) q^{15} -1.00000 q^{16} +6.00000 q^{17} +(-1.00000 - 2.82843i) q^{18} +4.24264i q^{19} +2.82843i q^{20} +(2.00000 + 1.41421i) q^{21} +(-3.00000 + 4.24264i) q^{24} -3.00000 q^{25} -4.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} -1.41421i q^{28} -2.00000 q^{29} +(-4.00000 - 2.82843i) q^{30} -2.00000 q^{31} +5.00000 q^{32} +6.00000 q^{34} +4.00000 q^{35} +(1.00000 + 2.82843i) q^{36} +8.00000 q^{37} +4.24264i q^{38} +(-6.00000 - 4.24264i) q^{39} +8.48528i q^{40} +6.00000 q^{41} +(2.00000 + 1.41421i) q^{42} +4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} -2.82843i q^{47} +(-1.00000 + 1.41421i) q^{48} +5.00000 q^{49} -3.00000 q^{50} +(6.00000 - 8.48528i) q^{51} +4.24264i q^{52} -5.65685i q^{53} +(-5.00000 - 1.41421i) q^{54} -4.24264i q^{56} +(6.00000 + 4.24264i) q^{57} -2.00000 q^{58} +11.3137i q^{59} +(4.00000 + 2.82843i) q^{60} +9.89949i q^{61} -2.00000 q^{62} +(4.00000 - 1.41421i) q^{63} +7.00000 q^{64} -12.0000 q^{65} +2.00000 q^{67} -6.00000 q^{68} +4.00000 q^{70} -2.82843i q^{71} +(3.00000 + 8.48528i) q^{72} +1.41421i q^{73} +8.00000 q^{74} +(-3.00000 + 4.24264i) q^{75} -4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} -4.24264i q^{79} +2.82843i q^{80} +(-7.00000 + 5.65685i) q^{81} +6.00000 q^{82} -16.0000 q^{83} +(-2.00000 - 1.41421i) q^{84} -16.9706i q^{85} +4.24264i q^{86} +(-2.00000 + 2.82843i) q^{87} +(-8.00000 + 2.82843i) q^{90} +6.00000 q^{91} +(-2.00000 + 2.82843i) q^{93} -2.82843i q^{94} +12.0000 q^{95} +(5.00000 - 7.07107i) q^{96} -2.00000 q^{97} +5.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9} - 2 q^{12} - 8 q^{15} - 2 q^{16} + 12 q^{17} - 2 q^{18} + 4 q^{21} - 6 q^{24} - 6 q^{25} - 10 q^{27} - 4 q^{29} - 8 q^{30} - 4 q^{31} + 10 q^{32}+ \cdots + 10 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9 - 2 * q^12 - 8 * q^15 - 2 * q^16 + 12 * q^17 - 2 * q^18 + 4 * q^21 - 6 * q^24 - 6 * q^25 - 10 * q^27 - 4 * q^29 - 8 * q^30 - 4 * q^31 + 10 * q^32 + 12 * q^34 + 8 * q^35 + 2 * q^36 + 16 * q^37 - 12 * q^39 + 12 * q^41 + 4 * q^42 - 16 * q^45 - 2 * q^48 + 10 * q^49 - 6 * q^50 + 12 * q^51 - 10 * q^54 + 12 * q^57 - 4 * q^58 + 8 * q^60 - 4 * q^62 + 8 * q^63 + 14 * q^64 - 24 * q^65 + 4 * q^67 - 12 * q^68 + 8 * q^70 + 6 * q^72 + 16 * q^74 - 6 * q^75 - 12 * q^78 - 14 * q^81 + 12 * q^82 - 32 * q^83 - 4 * q^84 - 4 * q^87 - 16 * q^90 + 12 * q^91 - 4 * q^93 + 24 * q^95 + 10 * q^96 - 4 * q^97 + 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$	−1.00000			−0.500000
$5$		−	2.82843i		−	1.26491i	−0.774597	−	0.632456i	$-0.782047\pi$
$5$		−	2.82843i		−	1.26491i	0.774597	−	0.632456i	$-0.217953\pi$
$6$	1.00000	−	1.41421i	0.408248	−	0.577350i
$7$			1.41421i			0.534522i	0.963624	+	0.267261i	$0.0861187\pi$
$7$			1.41421i			0.534522i	−0.963624	+	0.267261i	$0.913881\pi$
$8$	−3.00000			−1.06066
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$		−	2.82843i		−	0.894427i
$11$		0			0
$11$		0			0
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$		−	4.24264i		−	1.17670i	−0.808608	−	0.588348i	$-0.799778\pi$
$13$		−	4.24264i		−	1.17670i	0.808608	−	0.588348i	$-0.200222\pi$
$14$			1.41421i			0.377964i
$15$	−4.00000	−	2.82843i	−1.03280	−	0.730297i
$16$	−1.00000			−0.250000
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.00000	−	2.82843i	−0.235702	−	0.666667i
$19$			4.24264i			0.973329i	0.873589	+	0.486664i	$0.161786\pi$
$19$			4.24264i			0.973329i	−0.873589	+	0.486664i	$0.838214\pi$
$20$			2.82843i			0.632456i
$21$	2.00000	+	1.41421i	0.436436	+	0.308607i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−3.00000	+	4.24264i	−0.612372	+	0.866025i
$25$	−3.00000			−0.600000
$26$		−	4.24264i		−	0.832050i
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$		−	1.41421i		−	0.267261i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−4.00000	−	2.82843i	−0.730297	−	0.516398i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	6.00000			1.02899
$35$	4.00000			0.676123
$36$	1.00000	+	2.82843i	0.166667	+	0.471405i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$			4.24264i			0.688247i
$39$	−6.00000	−	4.24264i	−0.960769	−	0.679366i
$40$			8.48528i			1.34164i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	2.00000	+	1.41421i	0.308607	+	0.218218i
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$	−8.00000	+	2.82843i	−1.19257	+	0.421637i
$46$		0			0
$47$		−	2.82843i		−	0.412568i	−0.978492	−	0.206284i	$-0.933863\pi$
$47$		−	2.82843i		−	0.412568i	0.978492	−	0.206284i	$-0.0661372\pi$
$48$	−1.00000	+	1.41421i	−0.144338	+	0.204124i
$49$	5.00000			0.714286
$50$	−3.00000			−0.424264
$51$	6.00000	−	8.48528i	0.840168	−	1.18818i
$52$			4.24264i			0.588348i
$53$		−	5.65685i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$53$		−	5.65685i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$		0			0
$56$		−	4.24264i		−	0.566947i
$57$	6.00000	+	4.24264i	0.794719	+	0.561951i
$58$	−2.00000			−0.262613
$59$			11.3137i			1.47292i	0.676481	+	0.736460i	$0.263504\pi$
$59$			11.3137i			1.47292i	−0.676481	+	0.736460i	$0.736496\pi$
$60$	4.00000	+	2.82843i	0.516398	+	0.365148i
$61$			9.89949i			1.26750i	0.773538	+	0.633750i	$0.218485\pi$
$61$			9.89949i			1.26750i	−0.773538	+	0.633750i	$0.781515\pi$
$62$	−2.00000			−0.254000
$63$	4.00000	−	1.41421i	0.503953	−	0.178174i
$64$	7.00000			0.875000
$65$	−12.0000			−1.48842
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−6.00000			−0.727607
$69$		0			0
$70$	4.00000			0.478091
$71$		−	2.82843i		−	0.335673i	−0.985815	−	0.167836i	$-0.946322\pi$
$71$		−	2.82843i		−	0.335673i	0.985815	−	0.167836i	$-0.0536780\pi$
$72$	3.00000	+	8.48528i	0.353553	+	1.00000i
$73$			1.41421i			0.165521i	0.996569	+	0.0827606i	$0.0263737\pi$
$73$			1.41421i			0.165521i	−0.996569	+	0.0827606i	$0.973626\pi$
$74$	8.00000			0.929981
$75$	−3.00000	+	4.24264i	−0.346410	+	0.489898i
$76$		−	4.24264i		−	0.486664i
$77$		0			0
$78$	−6.00000	−	4.24264i	−0.679366	−	0.480384i
$79$		−	4.24264i		−	0.477334i	−0.971101	−	0.238667i	$-0.923290\pi$
$79$		−	4.24264i		−	0.477334i	0.971101	−	0.238667i	$-0.0767105\pi$
$80$			2.82843i			0.316228i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	6.00000			0.662589
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$	−2.00000	−	1.41421i	−0.218218	−	0.154303i
$85$		−	16.9706i		−	1.84072i
$86$			4.24264i			0.457496i
$87$	−2.00000	+	2.82843i	−0.214423	+	0.303239i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−8.00000	+	2.82843i	−0.843274	+	0.298142i
$91$	6.00000			0.628971
$92$		0			0
$93$	−2.00000	+	2.82843i	−0.207390	+	0.293294i
$94$		−	2.82843i		−	0.291730i
$95$	12.0000			1.23117
$96$	5.00000	−	7.07107i	0.510310	−	0.721688i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	5.00000			0.505076
$99$		0			0
$100$	3.00000			0.300000
$101$	−10.0000			−0.995037			−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000			−0.995037			−0.497519	+	0.867453i	$0.665755\pi$
$102$	6.00000	−	8.48528i	0.594089	−	0.840168i
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$			12.7279i			1.24808i
$105$	4.00000	−	5.65685i	0.390360	−	0.552052i
$106$		−	5.65685i		−	0.549442i
$107$	−16.0000			−1.54678			−0.773389	−	0.633932i	$-0.781440\pi$
$107$	−16.0000			−1.54678			−0.773389	+	0.633932i	$0.781440\pi$
$108$	5.00000	+	1.41421i	0.481125	+	0.136083i
$109$			4.24264i			0.406371i	0.979140	+	0.203186i	$0.0651295\pi$
$109$			4.24264i			0.406371i	−0.979140	+	0.203186i	$0.934871\pi$
$110$		0			0
$111$	8.00000	−	11.3137i	0.759326	−	1.07385i
$112$		−	1.41421i		−	0.133631i
$113$		−	2.82843i		−	0.266076i	−0.991111	−	0.133038i	$-0.957527\pi$
$113$		−	2.82843i		−	0.266076i	0.991111	−	0.133038i	$-0.0424732\pi$
$114$	6.00000	+	4.24264i	0.561951	+	0.397360i
$115$		0			0
$116$	2.00000			0.185695
$117$	−12.0000	+	4.24264i	−1.10940	+	0.392232i
$118$			11.3137i			1.04151i
$119$			8.48528i			0.777844i
$120$	12.0000	+	8.48528i	1.09545	+	0.774597i
$121$		0			0
$122$			9.89949i			0.896258i
$123$	6.00000	−	8.48528i	0.541002	−	0.765092i
$124$	2.00000			0.179605
$125$		−	5.65685i		−	0.505964i
$126$	4.00000	−	1.41421i	0.356348	−	0.125988i
$127$			9.89949i			0.878438i	0.898380	+	0.439219i	$0.144745\pi$
$127$			9.89949i			0.878438i	−0.898380	+	0.439219i	$0.855255\pi$
$128$	−3.00000			−0.265165
$129$	6.00000	+	4.24264i	0.528271	+	0.373544i
$130$	−12.0000			−1.05247
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−6.00000			−0.520266
$134$	2.00000			0.172774
$135$	−4.00000	+	14.1421i	−0.344265	+	1.21716i
$136$	−18.0000			−1.54349
$137$		−	2.82843i		−	0.241649i	−0.992674	−	0.120824i	$-0.961446\pi$
$137$		−	2.82843i		−	0.241649i	0.992674	−	0.120824i	$-0.0385538\pi$
$138$		0			0
$139$			1.41421i			0.119952i	0.998200	+	0.0599760i	$0.0191024\pi$
$139$			1.41421i			0.119952i	−0.998200	+	0.0599760i	$0.980898\pi$
$140$	−4.00000			−0.338062
$141$	−4.00000	−	2.82843i	−0.336861	−	0.238197i
$142$		−	2.82843i		−	0.237356i
$143$		0			0
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$			5.65685i			0.469776i
$146$			1.41421i			0.117041i
$147$	5.00000	−	7.07107i	0.412393	−	0.583212i
$148$	−8.00000			−0.657596
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	−3.00000	+	4.24264i	−0.244949	+	0.346410i
$151$			4.24264i			0.345261i	0.984987	+	0.172631i	$0.0552267\pi$
$151$			4.24264i			0.345261i	−0.984987	+	0.172631i	$0.944773\pi$
$152$		−	12.7279i		−	1.03237i
$153$	−6.00000	−	16.9706i	−0.485071	−	1.37199i
$154$		0			0
$155$			5.65685i			0.454369i
$156$	6.00000	+	4.24264i	0.480384	+	0.339683i
$157$	−20.0000			−1.59617			−0.798087	−	0.602542i	$-0.794154\pi$
$157$	−20.0000			−1.59617			−0.798087	+	0.602542i	$0.794154\pi$
$158$		−	4.24264i		−	0.337526i
$159$	−8.00000	−	5.65685i	−0.634441	−	0.448618i
$160$		−	14.1421i		−	1.11803i
$161$		0			0
$162$	−7.00000	+	5.65685i	−0.549972	+	0.444444i
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−16.0000			−1.24184
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	−6.00000	−	4.24264i	−0.462910	−	0.327327i
$169$	−5.00000			−0.384615
$170$		−	16.9706i		−	1.30158i
$171$	12.0000	−	4.24264i	0.917663	−	0.324443i
$172$		−	4.24264i		−	0.323498i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	−2.00000	+	2.82843i	−0.151620	+	0.214423i
$175$		−	4.24264i		−	0.320713i
$176$		0			0
$177$	16.0000	+	11.3137i	1.20263	+	0.850390i
$178$		0			0
$179$		−	2.82843i		−	0.211407i	−0.994398	−	0.105703i	$-0.966291\pi$
$179$		−	2.82843i		−	0.211407i	0.994398	−	0.105703i	$-0.0337094\pi$
$180$	8.00000	−	2.82843i	0.596285	−	0.210819i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	6.00000			0.444750
$183$	14.0000	+	9.89949i	1.03491	+	0.731792i
$184$		0			0
$185$		−	22.6274i		−	1.66360i
$186$	−2.00000	+	2.82843i	−0.146647	+	0.207390i
$187$		0			0
$188$			2.82843i			0.206284i
$189$	2.00000	−	7.07107i	0.145479	−	0.514344i
$190$	12.0000			0.870572
$191$		−	19.7990i		−	1.43260i	−0.697790	−	0.716302i	$-0.745833\pi$
$191$		−	19.7990i		−	1.43260i	0.697790	−	0.716302i	$-0.254167\pi$
$192$	7.00000	−	9.89949i	0.505181	−	0.714435i
$193$		−	21.2132i		−	1.52696i	−0.645832	−	0.763480i	$-0.723489\pi$
$193$		−	21.2132i		−	1.52696i	0.645832	−	0.763480i	$-0.276511\pi$
$194$	−2.00000			−0.143592
$195$	−12.0000	+	16.9706i	−0.859338	+	1.21529i
$196$	−5.00000			−0.357143
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	9.00000			0.636396
$201$	2.00000	−	2.82843i	0.141069	−	0.199502i
$202$	−10.0000			−0.703598
$203$		−	2.82843i		−	0.198517i
$204$	−6.00000	+	8.48528i	−0.420084	+	0.594089i
$205$		−	16.9706i		−	1.18528i
$206$	8.00000			0.557386
$207$		0			0
$208$			4.24264i			0.294174i
$209$		0			0
$210$	4.00000	−	5.65685i	0.276026	−	0.390360i
$211$			26.8701i			1.84981i	0.380197	+	0.924906i	$0.375856\pi$
$211$			26.8701i			1.84981i	−0.380197	+	0.924906i	$0.624144\pi$
$212$			5.65685i			0.388514i
$213$	−4.00000	−	2.82843i	−0.274075	−	0.193801i
$214$	−16.0000			−1.09374
$215$	12.0000			0.818393
$216$	15.0000	+	4.24264i	1.02062	+	0.288675i
$217$		−	2.82843i		−	0.192006i
$218$			4.24264i			0.287348i
$219$	2.00000	+	1.41421i	0.135147	+	0.0955637i
$220$		0			0
$221$		−	25.4558i		−	1.71235i
$222$	8.00000	−	11.3137i	0.536925	−	0.759326i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$			7.07107i			0.472456i
$225$	3.00000	+	8.48528i	0.200000	+	0.565685i
$226$		−	2.82843i		−	0.188144i
$227$	−24.0000			−1.59294			−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000			−1.59294			−0.796468	+	0.604681i	$0.793301\pi$
$228$	−6.00000	−	4.24264i	−0.397360	−	0.280976i
$229$	−24.0000			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$	−12.0000	+	4.24264i	−0.784465	+	0.277350i
$235$	−8.00000			−0.521862
$236$		−	11.3137i		−	0.736460i
$237$	−6.00000	−	4.24264i	−0.389742	−	0.275589i
$238$			8.48528i			0.550019i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	4.00000	+	2.82843i	0.258199	+	0.182574i
$241$			4.24264i			0.273293i	0.990620	+	0.136646i	$0.0436324\pi$
$241$			4.24264i			0.273293i	−0.990620	+	0.136646i	$0.956368\pi$
$242$		0			0
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$		−	9.89949i		−	0.633750i
$245$		−	14.1421i		−	0.903508i
$246$	6.00000	−	8.48528i	0.382546	−	0.541002i
$247$	18.0000			1.14531
$248$	6.00000			0.381000
$249$	−16.0000	+	22.6274i	−1.01396	+	1.43395i
$250$		−	5.65685i		−	0.357771i
$251$			25.4558i			1.60676i	0.595468	+	0.803379i	$0.296967\pi$
$251$			25.4558i			1.60676i	−0.595468	+	0.803379i	$0.703033\pi$
$252$	−4.00000	+	1.41421i	−0.251976	+	0.0890871i
$253$		0			0
$254$			9.89949i			0.621150i
$255$	−24.0000	−	16.9706i	−1.50294	−	1.06274i
$256$	−17.0000			−1.06250
$257$			11.3137i			0.705730i	0.935674	+	0.352865i	$0.114792\pi$
$257$			11.3137i			0.705730i	−0.935674	+	0.352865i	$0.885208\pi$
$258$	6.00000	+	4.24264i	0.373544	+	0.264135i
$259$			11.3137i			0.703000i
$260$	12.0000			0.744208
$261$	2.00000	+	5.65685i	0.123797	+	0.350150i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−16.0000			−0.982872
$266$	−6.00000			−0.367884
$267$		0			0
$268$	−2.00000			−0.122169
$269$			28.2843i			1.72452i	0.506464	+	0.862261i	$0.330952\pi$
$269$			28.2843i			1.72452i	−0.506464	+	0.862261i	$0.669048\pi$
$270$	−4.00000	+	14.1421i	−0.243432	+	0.860663i
$271$		−	29.6985i		−	1.80405i	−0.431679	−	0.902027i	$-0.642079\pi$
$271$		−	29.6985i		−	1.80405i	0.431679	−	0.902027i	$-0.357921\pi$
$272$	−6.00000			−0.363803
$273$	6.00000	−	8.48528i	0.363137	−	0.513553i
$274$		−	2.82843i		−	0.170872i
$275$		0			0
$276$		0			0
$277$		−	4.24264i		−	0.254916i	−0.991844	−	0.127458i	$-0.959318\pi$
$277$		−	4.24264i		−	0.254916i	0.991844	−	0.127458i	$-0.0406817\pi$
$278$			1.41421i			0.0848189i
$279$	2.00000	+	5.65685i	0.119737	+	0.338667i
$280$	−12.0000			−0.717137
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	−4.00000	−	2.82843i	−0.238197	−	0.168430i
$283$		−	26.8701i		−	1.59726i	−0.601823	−	0.798630i	$-0.705559\pi$
$283$		−	26.8701i		−	1.59726i	0.601823	−	0.798630i	$-0.294441\pi$
$284$			2.82843i			0.167836i
$285$	12.0000	−	16.9706i	0.710819	−	1.00525i
$286$		0			0
$287$			8.48528i			0.500870i
$288$	−5.00000	−	14.1421i	−0.294628	−	0.833333i
$289$	19.0000			1.11765
$290$			5.65685i			0.332182i
$291$	−2.00000	+	2.82843i	−0.117242	+	0.165805i
$292$		−	1.41421i		−	0.0827606i
$293$	−2.00000			−0.116841			−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000			−0.116841			−0.0584206	+	0.998292i	$0.518606\pi$
$294$	5.00000	−	7.07107i	0.291606	−	0.412393i
$295$	32.0000			1.86311
$296$	−24.0000			−1.39497
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$	3.00000	−	4.24264i	0.173205	−	0.244949i
$301$	−6.00000			−0.345834
$302$			4.24264i			0.244137i
$303$	−10.0000	+	14.1421i	−0.574485	+	0.812444i
$304$		−	4.24264i		−	0.243332i
$305$	28.0000			1.60328
$306$	−6.00000	−	16.9706i	−0.342997	−	0.970143i
$307$			4.24264i			0.242140i	0.992644	+	0.121070i	$0.0386326\pi$
$307$			4.24264i			0.242140i	−0.992644	+	0.121070i	$0.961367\pi$
$308$		0			0
$309$	8.00000	−	11.3137i	0.455104	−	0.643614i
$310$			5.65685i			0.321288i
$311$			28.2843i			1.60385i	0.597422	+	0.801927i	$0.296192\pi$
$311$			28.2843i			1.60385i	−0.597422	+	0.801927i	$0.703808\pi$
$312$	18.0000	+	12.7279i	1.01905	+	0.720577i
$313$	12.0000			0.678280			0.339140	−	0.940736i	$-0.389864\pi$
$313$	12.0000			0.678280			0.339140	+	0.940736i	$0.389864\pi$
$314$	−20.0000			−1.12867
$315$	−4.00000	−	11.3137i	−0.225374	−	0.637455i
$316$			4.24264i			0.238667i
$317$			25.4558i			1.42974i	0.699256	+	0.714871i	$0.253515\pi$
$317$			25.4558i			1.42974i	−0.699256	+	0.714871i	$0.746485\pi$
$318$	−8.00000	−	5.65685i	−0.448618	−	0.317221i
$319$		0			0
$320$		−	19.7990i		−	1.10680i
$321$	−16.0000	+	22.6274i	−0.893033	+	1.26294i
$322$		0			0
$323$			25.4558i			1.41640i
$324$	7.00000	−	5.65685i	0.388889	−	0.314270i
$325$			12.7279i			0.706018i
$326$	20.0000			1.10770
$327$	6.00000	+	4.24264i	0.331801	+	0.234619i
$328$	−18.0000			−0.993884
$329$	4.00000			0.220527
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	16.0000			0.878114
$333$	−8.00000	−	22.6274i	−0.438397	−	1.23997i
$334$	12.0000			0.656611
$335$		−	5.65685i		−	0.309067i
$336$	−2.00000	−	1.41421i	−0.109109	−	0.0771517i
$337$			32.5269i			1.77185i	0.463825	+	0.885927i	$0.346477\pi$
$337$			32.5269i			1.77185i	−0.463825	+	0.885927i	$0.653523\pi$
$338$	−5.00000			−0.271964
$339$	−4.00000	−	2.82843i	−0.217250	−	0.153619i
$340$			16.9706i			0.920358i
$341$		0			0
$342$	12.0000	−	4.24264i	0.648886	−	0.229416i
$343$			16.9706i			0.916324i
$344$		−	12.7279i		−	0.686244i
$345$		0			0
$346$	6.00000			0.322562
$347$	−16.0000			−0.858925			−0.429463	−	0.903085i	$-0.641297\pi$
$347$	−16.0000			−0.858925			−0.429463	+	0.903085i	$0.641297\pi$
$348$	2.00000	−	2.82843i	0.107211	−	0.151620i
$349$			4.24264i			0.227103i	0.993532	+	0.113552i	$0.0362227\pi$
$349$			4.24264i			0.227103i	−0.993532	+	0.113552i	$0.963777\pi$
$350$		−	4.24264i		−	0.226779i
$351$	−6.00000	+	21.2132i	−0.320256	+	1.13228i
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$	16.0000	+	11.3137i	0.850390	+	0.601317i
$355$	−8.00000			−0.424596
$356$		0			0
$357$	12.0000	+	8.48528i	0.635107	+	0.449089i
$358$		−	2.82843i		−	0.149487i
$359$	20.0000			1.05556			0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000			1.05556			0.527780	+	0.849381i	$0.323025\pi$
$360$	24.0000	−	8.48528i	1.26491	−	0.447214i
$361$	1.00000			0.0526316
$362$	−10.0000			−0.525588
$363$		0			0
$364$	−6.00000			−0.314485
$365$	4.00000			0.209370
$366$	14.0000	+	9.89949i	0.731792	+	0.517455i
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$		0			0
$369$	−6.00000	−	16.9706i	−0.312348	−	0.883452i
$370$		−	22.6274i		−	1.17634i
$371$	8.00000			0.415339
$372$	2.00000	−	2.82843i	0.103695	−	0.146647i
$373$			4.24264i			0.219676i	0.993950	+	0.109838i	$0.0350331\pi$
$373$			4.24264i			0.219676i	−0.993950	+	0.109838i	$0.964967\pi$
$374$		0			0
$375$	−8.00000	−	5.65685i	−0.413118	−	0.292119i
$376$			8.48528i			0.437595i
$377$			8.48528i			0.437014i
$378$	2.00000	−	7.07107i	0.102869	−	0.363696i
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$	−12.0000			−0.615587
$381$	14.0000	+	9.89949i	0.717242	+	0.507166i
$382$		−	19.7990i		−	1.01300i
$383$		−	5.65685i		−	0.289052i	−0.989501	−	0.144526i	$-0.953834\pi$
$383$		−	5.65685i		−	0.289052i	0.989501	−	0.144526i	$-0.0461657\pi$
$384$	−3.00000	+	4.24264i	−0.153093	+	0.216506i
$385$		0			0
$386$		−	21.2132i		−	1.07972i
$387$	12.0000	−	4.24264i	0.609994	−	0.215666i
$388$	2.00000			0.101535
$389$		−	19.7990i		−	1.00385i	−0.864912	−	0.501924i	$-0.832626\pi$
$389$		−	19.7990i		−	1.00385i	0.864912	−	0.501924i	$-0.167374\pi$
$390$	−12.0000	+	16.9706i	−0.607644	+	0.859338i
$391$		0			0
$392$	−15.0000			−0.757614
$393$		0			0
$394$	22.0000			1.10834
$395$	−12.0000			−0.603786
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	2.00000			0.100251
$399$	−6.00000	+	8.48528i	−0.300376	+	0.424795i
$400$	3.00000			0.150000
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$	2.00000	−	2.82843i	0.0997509	−	0.141069i
$403$			8.48528i			0.422682i
$404$	10.0000			0.497519
$405$	16.0000	+	19.7990i	0.795046	+	0.983820i
$406$		−	2.82843i		−	0.140372i
$407$		0			0
$408$	−18.0000	+	25.4558i	−0.891133	+	1.26025i
$409$		−	4.24264i		−	0.209785i	−0.994484	−	0.104893i	$-0.966550\pi$
$409$		−	4.24264i		−	0.209785i	0.994484	−	0.104893i	$-0.0334499\pi$
$410$		−	16.9706i		−	0.838116i
$411$	−4.00000	−	2.82843i	−0.197305	−	0.139516i
$412$	−8.00000			−0.394132
$413$	−16.0000			−0.787309
$414$		0			0
$415$			45.2548i			2.22147i
$416$		−	21.2132i		−	1.04006i
$417$	2.00000	+	1.41421i	0.0979404	+	0.0692543i
$418$		0			0
$419$			31.1127i			1.51995i	0.649950	+	0.759977i	$0.274790\pi$
$419$			31.1127i			1.51995i	−0.649950	+	0.759977i	$0.725210\pi$
$420$	−4.00000	+	5.65685i	−0.195180	+	0.276026i
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$			26.8701i			1.30801i
$423$	−8.00000	+	2.82843i	−0.388973	+	0.137523i
$424$			16.9706i			0.824163i
$425$	−18.0000			−0.873128
$426$	−4.00000	−	2.82843i	−0.193801	−	0.137038i
$427$	−14.0000			−0.677507
$428$	16.0000			0.773389
$429$		0			0
$430$	12.0000			0.578691
$431$	−32.0000			−1.54139			−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000			−1.54139			−0.770693	+	0.637207i	$0.780090\pi$
$432$	5.00000	+	1.41421i	0.240563	+	0.0680414i
$433$	30.0000			1.44171			0.720854	−	0.693087i	$-0.243750\pi$
$433$	30.0000			1.44171			0.720854	+	0.693087i	$0.243750\pi$
$434$		−	2.82843i		−	0.135769i
$435$	8.00000	+	5.65685i	0.383571	+	0.271225i
$436$		−	4.24264i		−	0.203186i
$437$		0			0
$438$	2.00000	+	1.41421i	0.0955637	+	0.0675737i
$439$		−	26.8701i		−	1.28244i	−0.767358	−	0.641219i	$-0.778429\pi$
$439$		−	26.8701i		−	1.28244i	0.767358	−	0.641219i	$-0.221571\pi$
$440$		0			0
$441$	−5.00000	−	14.1421i	−0.238095	−	0.673435i
$442$		−	25.4558i		−	1.21081i
$443$			28.2843i			1.34383i	0.740630	+	0.671913i	$0.234527\pi$
$443$			28.2843i			1.34383i	−0.740630	+	0.671913i	$0.765473\pi$
$444$	−8.00000	+	11.3137i	−0.379663	+	0.536925i
$445$		0			0
$446$	24.0000			1.13643
$447$	6.00000	−	8.48528i	0.283790	−	0.401340i
$448$			9.89949i			0.467707i
$449$		−	5.65685i		−	0.266963i	−0.991051	−	0.133482i	$-0.957384\pi$
$449$		−	5.65685i		−	0.266963i	0.991051	−	0.133482i	$-0.0426157\pi$
$450$	3.00000	+	8.48528i	0.141421	+	0.400000i
$451$		0			0
$452$			2.82843i			0.133038i
$453$	6.00000	+	4.24264i	0.281905	+	0.199337i
$454$	−24.0000			−1.12638
$455$		−	16.9706i		−	0.795592i
$456$	−18.0000	−	12.7279i	−0.842927	−	0.596040i
$457$			9.89949i			0.463079i	0.972826	+	0.231539i	$0.0743762\pi$
$457$			9.89949i			0.463079i	−0.972826	+	0.231539i	$0.925624\pi$
$458$	−24.0000			−1.12145
$459$	−30.0000	−	8.48528i	−1.40028	−	0.396059i
$460$		0			0
$461$	22.0000			1.02464			0.512321	−	0.858794i	$-0.328786\pi$
$461$	22.0000			1.02464			0.512321	+	0.858794i	$0.328786\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	2.00000			0.0928477
$465$	8.00000	+	5.65685i	0.370991	+	0.262330i
$466$	−10.0000			−0.463241
$467$			28.2843i			1.30884i	0.756131	+	0.654420i	$0.227087\pi$
$467$			28.2843i			1.30884i	−0.756131	+	0.654420i	$0.772913\pi$
$468$	12.0000	−	4.24264i	0.554700	−	0.196116i
$469$			2.82843i			0.130605i
$470$	−8.00000			−0.369012
$471$	−20.0000	+	28.2843i	−0.921551	+	1.30327i
$472$		−	33.9411i		−	1.56227i
$473$		0			0
$474$	−6.00000	−	4.24264i	−0.275589	−	0.194871i
$475$		−	12.7279i		−	0.583997i
$476$		−	8.48528i		−	0.388922i
$477$	−16.0000	+	5.65685i	−0.732590	+	0.259010i
$478$	−16.0000			−0.731823
$479$	28.0000			1.27935			0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000			1.27935			0.639676	+	0.768644i	$0.279068\pi$
$480$	−20.0000	−	14.1421i	−0.912871	−	0.645497i
$481$		−	33.9411i		−	1.54758i
$482$			4.24264i			0.193247i
$483$		0			0
$484$		0			0
$485$			5.65685i			0.256865i
$486$	1.00000	+	15.5563i	0.0453609	+	0.705650i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$		−	29.6985i		−	1.34439i
$489$	20.0000	−	28.2843i	0.904431	−	1.27906i
$490$		−	14.1421i		−	0.638877i
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	−6.00000	+	8.48528i	−0.270501	+	0.382546i
$493$	−12.0000			−0.540453
$494$	18.0000			0.809858
$495$		0			0
$496$	2.00000			0.0898027
$497$	4.00000			0.179425
$498$	−16.0000	+	22.6274i	−0.716977	+	1.01396i
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$			5.65685i			0.252982i
$501$	12.0000	−	16.9706i	0.536120	−	0.758189i
$502$			25.4558i			1.13615i
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$	−12.0000	+	4.24264i	−0.534522	+	0.188982i
$505$			28.2843i			1.25863i
$506$		0			0
$507$	−5.00000	+	7.07107i	−0.222058	+	0.314037i
$508$		−	9.89949i		−	0.439219i
$509$		−	33.9411i		−	1.50441i	−0.658927	−	0.752207i	$-0.728989\pi$
$509$		−	33.9411i		−	1.50441i	0.658927	−	0.752207i	$-0.271011\pi$
$510$	−24.0000	−	16.9706i	−1.06274	−	0.751469i
$511$	−2.00000			−0.0884748
$512$	−11.0000			−0.486136
$513$	6.00000	−	21.2132i	0.264906	−	0.936586i
$514$			11.3137i			0.499026i
$515$		−	22.6274i		−	0.997083i
$516$	−6.00000	−	4.24264i	−0.264135	−	0.186772i
$517$		0			0
$518$			11.3137i			0.497096i
$519$	6.00000	−	8.48528i	0.263371	−	0.372463i
$520$	36.0000			1.57870
$521$		−	19.7990i		−	0.867409i	−0.901055	−	0.433705i	$-0.857206\pi$
$521$		−	19.7990i		−	0.867409i	0.901055	−	0.433705i	$-0.142794\pi$
$522$	2.00000	+	5.65685i	0.0875376	+	0.247594i
$523$		−	21.2132i		−	0.927589i	−0.885943	−	0.463794i	$-0.846488\pi$
$523$		−	21.2132i		−	0.927589i	0.885943	−	0.463794i	$-0.153512\pi$
$524$		0			0
$525$	−6.00000	−	4.24264i	−0.261861	−	0.185164i
$526$		0			0
$527$	−12.0000			−0.522728
$528$		0			0
$529$	23.0000			1.00000
$530$	−16.0000			−0.694996
$531$	32.0000	−	11.3137i	1.38868	−	0.490973i
$532$	6.00000			0.260133
$533$		−	25.4558i		−	1.10262i
$534$		0			0
$535$			45.2548i			1.95654i
$536$	−6.00000			−0.259161
$537$	−4.00000	−	2.82843i	−0.172613	−	0.122056i
$538$			28.2843i			1.21942i
$539$		0			0
$540$	4.00000	−	14.1421i	0.172133	−	0.608581i
$541$		−	35.3553i		−	1.52004i	−0.649897	−	0.760022i	$-0.725188\pi$
$541$		−	35.3553i		−	1.52004i	0.649897	−	0.760022i	$-0.274812\pi$
$542$		−	29.6985i		−	1.27566i
$543$	−10.0000	+	14.1421i	−0.429141	+	0.606897i
$544$	30.0000			1.28624
$545$	12.0000			0.514024
$546$	6.00000	−	8.48528i	0.256776	−	0.363137i
$547$			35.3553i			1.51169i	0.654753	+	0.755843i	$0.272772\pi$
$547$			35.3553i			1.51169i	−0.654753	+	0.755843i	$0.727228\pi$
$548$			2.82843i			0.120824i
$549$	28.0000	−	9.89949i	1.19501	−	0.422500i
$550$		0			0
$551$		−	8.48528i		−	0.361485i
$552$		0			0
$553$	6.00000			0.255146
$554$		−	4.24264i		−	0.180253i
$555$	−32.0000	−	22.6274i	−1.35832	−	0.960480i
$556$		−	1.41421i		−	0.0599760i
$557$	−2.00000			−0.0847427			−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000			−0.0847427			−0.0423714	+	0.999102i	$0.513491\pi$
$558$	2.00000	+	5.65685i	0.0846668	+	0.239474i
$559$	18.0000			0.761319
$560$	−4.00000			−0.169031
$561$		0			0
$562$	6.00000			0.253095
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$	4.00000	+	2.82843i	0.168430	+	0.119098i
$565$	−8.00000			−0.336563
$566$		−	26.8701i		−	1.12943i
$567$	−8.00000	−	9.89949i	−0.335968	−	0.415740i
$568$			8.48528i			0.356034i
$569$	−38.0000			−1.59304			−0.796521	−	0.604610i	$-0.793329\pi$
$569$	−38.0000			−1.59304			−0.796521	+	0.604610i	$0.793329\pi$
$570$	12.0000	−	16.9706i	0.502625	−	0.710819i
$571$		−	26.8701i		−	1.12448i	−0.826975	−	0.562238i	$-0.809940\pi$
$571$		−	26.8701i		−	1.12448i	0.826975	−	0.562238i	$-0.190060\pi$
$572$		0			0
$573$	−28.0000	−	19.7990i	−1.16972	−	0.827115i
$574$			8.48528i			0.354169i
$575$		0			0
$576$	−7.00000	−	19.7990i	−0.291667	−	0.824958i
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	19.0000			0.790296
$579$	−30.0000	−	21.2132i	−1.24676	−	0.881591i
$580$		−	5.65685i		−	0.234888i
$581$		−	22.6274i		−	0.938743i
$582$	−2.00000	+	2.82843i	−0.0829027	+	0.117242i
$583$		0			0
$584$		−	4.24264i		−	0.175562i
$585$	12.0000	+	33.9411i	0.496139	+	1.40329i
$586$	−2.00000			−0.0826192
$587$			11.3137i			0.466967i	0.972361	+	0.233483i	$0.0750124\pi$
$587$			11.3137i			0.466967i	−0.972361	+	0.233483i	$0.924988\pi$
$588$	−5.00000	+	7.07107i	−0.206197	+	0.291606i
$589$		−	8.48528i		−	0.349630i
$590$	32.0000			1.31742
$591$	22.0000	−	31.1127i	0.904959	−	1.27981i
$592$	−8.00000			−0.328798
$593$	−22.0000			−0.903432			−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000			−0.903432			−0.451716	+	0.892162i	$0.649188\pi$
$594$		0			0
$595$	24.0000			0.983904
$596$	−6.00000			−0.245770
$597$	2.00000	−	2.82843i	0.0818546	−	0.115760i
$598$		0			0
$599$		−	33.9411i		−	1.38680i	−0.720554	−	0.693398i	$-0.756113\pi$
$599$		−	33.9411i		−	1.38680i	0.720554	−	0.693398i	$-0.243887\pi$
$600$	9.00000	−	12.7279i	0.367423	−	0.519615i
$601$		−	29.6985i		−	1.21143i	−0.795683	−	0.605713i	$-0.792888\pi$
$601$		−	29.6985i		−	1.21143i	0.795683	−	0.605713i	$-0.207112\pi$
$602$	−6.00000			−0.244542
$603$	−2.00000	−	5.65685i	−0.0814463	−	0.230365i
$604$		−	4.24264i		−	0.172631i
$605$		0			0
$606$	−10.0000	+	14.1421i	−0.406222	+	0.574485i
$607$		−	4.24264i		−	0.172203i	−0.996286	−	0.0861017i	$-0.972559\pi$
$607$		−	4.24264i		−	0.172203i	0.996286	−	0.0861017i	$-0.0274410\pi$
$608$			21.2132i			0.860309i
$609$	−4.00000	−	2.82843i	−0.162088	−	0.114614i
$610$	28.0000			1.13369
$611$	−12.0000			−0.485468
$612$	6.00000	+	16.9706i	0.242536	+	0.685994i
$613$			4.24264i			0.171359i	0.996323	+	0.0856793i	$0.0273061\pi$
$613$			4.24264i			0.171359i	−0.996323	+	0.0856793i	$0.972694\pi$
$614$			4.24264i			0.171219i
$615$	−24.0000	−	16.9706i	−0.967773	−	0.684319i
$616$		0			0
$617$			31.1127i			1.25255i	0.779602	+	0.626275i	$0.215421\pi$
$617$			31.1127i			1.25255i	−0.779602	+	0.626275i	$0.784579\pi$
$618$	8.00000	−	11.3137i	0.321807	−	0.455104i
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		−	5.65685i		−	0.227185i
$621$		0			0
$622$			28.2843i			1.13410i
$623$		0			0
$624$	6.00000	+	4.24264i	0.240192	+	0.169842i
$625$	−31.0000			−1.24000
$626$	12.0000			0.479616
$627$		0			0
$628$	20.0000			0.798087
$629$	48.0000			1.91389
$630$	−4.00000	−	11.3137i	−0.159364	−	0.450749i
$631$	−14.0000			−0.557331			−0.278666	−	0.960388i	$-0.589892\pi$
$631$	−14.0000			−0.557331			−0.278666	+	0.960388i	$0.589892\pi$
$632$			12.7279i			0.506290i
$633$	38.0000	+	26.8701i	1.51036	+	1.06799i
$634$			25.4558i			1.01098i
$635$	28.0000			1.11115
$636$	8.00000	+	5.65685i	0.317221	+	0.224309i
$637$		−	21.2132i		−	0.840498i
$638$		0			0
$639$	−8.00000	+	2.82843i	−0.316475	+	0.111891i
$640$			8.48528i			0.335410i
$641$			28.2843i			1.11716i	0.829450	+	0.558581i	$0.188654\pi$
$641$			28.2843i			1.11716i	−0.829450	+	0.558581i	$0.811346\pi$
$642$	−16.0000	+	22.6274i	−0.631470	+	0.893033i
$643$	12.0000			0.473234			0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$644$		0			0
$645$	12.0000	−	16.9706i	0.472500	−	0.668215i
$646$			25.4558i			1.00155i
$647$		−	5.65685i		−	0.222394i	−0.993798	−	0.111197i	$-0.964532\pi$
$647$		−	5.65685i		−	0.222394i	0.993798	−	0.111197i	$-0.0354684\pi$
$648$	21.0000	−	16.9706i	0.824958	−	0.666667i
$649$		0			0
$650$			12.7279i			0.499230i
$651$	−4.00000	−	2.82843i	−0.156772	−	0.110855i
$652$	−20.0000			−0.783260
$653$			11.3137i			0.442740i	0.975190	+	0.221370i	$0.0710528\pi$
$653$			11.3137i			0.442740i	−0.975190	+	0.221370i	$0.928947\pi$
$654$	6.00000	+	4.24264i	0.234619	+	0.165900i
$655$		0			0
$656$	−6.00000			−0.234261
$657$	4.00000	−	1.41421i	0.156055	−	0.0551737i
$658$	4.00000			0.155936
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−20.0000			−0.777910			−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000			−0.777910			−0.388955	+	0.921257i	$0.627164\pi$
$662$	−20.0000			−0.777322
$663$	−36.0000	−	25.4558i	−1.39812	−	0.988623i
$664$	48.0000			1.86276
$665$			16.9706i			0.658090i
$666$	−8.00000	−	22.6274i	−0.309994	−	0.876795i
$667$		0			0
$668$	−12.0000			−0.464294
$669$	24.0000	−	33.9411i	0.927894	−	1.31224i
$670$		−	5.65685i		−	0.218543i
$671$		0			0
$672$	10.0000	+	7.07107i	0.385758	+	0.272772i
$673$		−	4.24264i		−	0.163542i	−0.996651	−	0.0817709i	$-0.973942\pi$
$673$		−	4.24264i		−	0.163542i	0.996651	−	0.0817709i	$-0.0260576\pi$
$674$			32.5269i			1.25289i
$675$	15.0000	+	4.24264i	0.577350	+	0.163299i
$676$	5.00000			0.192308
$677$	−38.0000			−1.46046			−0.730229	−	0.683202i	$-0.760587\pi$
$677$	−38.0000			−1.46046			−0.730229	+	0.683202i	$0.760587\pi$
$678$	−4.00000	−	2.82843i	−0.153619	−	0.108625i
$679$		−	2.82843i		−	0.108545i
$680$			50.9117i			1.95237i
$681$	−24.0000	+	33.9411i	−0.919682	+	1.30063i
$682$		0			0
$683$		−	31.1127i		−	1.19049i	−0.803543	−	0.595247i	$-0.797054\pi$
$683$		−	31.1127i		−	1.19049i	0.803543	−	0.595247i	$-0.202946\pi$
$684$	−12.0000	+	4.24264i	−0.458831	+	0.162221i
$685$	−8.00000			−0.305664
$686$			16.9706i			0.647939i
$687$	−24.0000	+	33.9411i	−0.915657	+	1.29493i
$688$		−	4.24264i		−	0.161749i
$689$	−24.0000			−0.914327
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−16.0000			−0.607352
$695$	4.00000			0.151729
$696$	6.00000	−	8.48528i	0.227429	−	0.321634i
$697$	36.0000			1.36360
$698$			4.24264i			0.160586i
$699$	−10.0000	+	14.1421i	−0.378235	+	0.534905i
$700$			4.24264i			0.160357i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	−6.00000	+	21.2132i	−0.226455	+	0.800641i
$703$			33.9411i			1.28011i
$704$		0			0
$705$	−8.00000	+	11.3137i	−0.301297	+	0.426099i
$706$		0			0
$707$		−	14.1421i		−	0.531870i
$708$	−16.0000	−	11.3137i	−0.601317	−	0.425195i
$709$	−32.0000			−1.20179			−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000			−1.20179			−0.600893	+	0.799330i	$0.705188\pi$
$710$	−8.00000			−0.300235
$711$	−12.0000	+	4.24264i	−0.450035	+	0.159111i
$712$		0			0
$713$		0			0
$714$	12.0000	+	8.48528i	0.449089	+	0.317554i
$715$		0			0
$716$			2.82843i			0.105703i
$717$	−16.0000	+	22.6274i	−0.597531	+	0.845036i
$718$	20.0000			0.746393
$719$		−	19.7990i		−	0.738378i	−0.929354	−	0.369189i	$-0.879636\pi$
$719$		−	19.7990i		−	0.738378i	0.929354	−	0.369189i	$-0.120364\pi$
$720$	8.00000	−	2.82843i	0.298142	−	0.105409i
$721$			11.3137i			0.421345i
$722$	1.00000			0.0372161
$723$	6.00000	+	4.24264i	0.223142	+	0.157786i
$724$	10.0000			0.371647
$725$	6.00000			0.222834
$726$		0			0
$727$	2.00000			0.0741759			0.0370879	−	0.999312i	$-0.488192\pi$
$727$	2.00000			0.0741759			0.0370879	+	0.999312i	$0.488192\pi$
$728$	−18.0000			−0.667124
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	4.00000			0.148047
$731$			25.4558i			0.941518i
$732$	−14.0000	−	9.89949i	−0.517455	−	0.365896i
$733$			1.41421i			0.0522352i	0.999659	+	0.0261176i	$0.00831443\pi$
$733$			1.41421i			0.0522352i	−0.999659	+	0.0261176i	$0.991686\pi$
$734$	8.00000			0.295285
$735$	−20.0000	−	14.1421i	−0.737711	−	0.521641i
$736$		0			0
$737$		0			0
$738$	−6.00000	−	16.9706i	−0.220863	−	0.624695i
$739$		−	4.24264i		−	0.156068i	−0.996951	−	0.0780340i	$-0.975136\pi$
$739$		−	4.24264i		−	0.156068i	0.996951	−	0.0780340i	$-0.0248643\pi$
$740$			22.6274i			0.831800i
$741$	18.0000	−	25.4558i	0.661247	−	0.935144i
$742$	8.00000			0.293689
$743$	−16.0000			−0.586983			−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000			−0.586983			−0.293492	+	0.955962i	$0.594817\pi$
$744$	6.00000	−	8.48528i	0.219971	−	0.311086i
$745$		−	16.9706i		−	0.621753i
$746$			4.24264i			0.155334i
$747$	16.0000	+	45.2548i	0.585409	+	1.65579i
$748$		0			0
$749$		−	22.6274i		−	0.826788i
$750$	−8.00000	−	5.65685i	−0.292119	−	0.206559i
$751$	2.00000			0.0729810			0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000			0.0729810			0.0364905	+	0.999334i	$0.488382\pi$
$752$			2.82843i			0.103142i
$753$	36.0000	+	25.4558i	1.31191	+	0.927663i
$754$			8.48528i			0.309016i
$755$	12.0000			0.436725
$756$	−2.00000	+	7.07107i	−0.0727393	+	0.257172i
$757$	20.0000			0.726912			0.363456	−	0.931611i	$-0.381597\pi$
$757$	20.0000			0.726912			0.363456	+	0.931611i	$0.381597\pi$
$758$	12.0000			0.435860
$759$		0			0
$760$	−36.0000			−1.30586
$761$	−10.0000			−0.362500			−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000			−0.362500			−0.181250	+	0.983437i	$0.558014\pi$
$762$	14.0000	+	9.89949i	0.507166	+	0.358621i
$763$	−6.00000			−0.217215
$764$			19.7990i			0.716302i
$765$	−48.0000	+	16.9706i	−1.73544	+	0.613572i
$766$		−	5.65685i		−	0.204390i
$767$	48.0000			1.73318
$768$	−17.0000	+	24.0416i	−0.613435	+	0.867528i
$769$			35.3553i			1.27495i	0.770473	+	0.637473i	$0.220020\pi$
$769$			35.3553i			1.27495i	−0.770473	+	0.637473i	$0.779980\pi$
$770$		0			0
$771$	16.0000	+	11.3137i	0.576226	+	0.407453i
$772$			21.2132i			0.763480i
$773$		−	33.9411i		−	1.22078i	−0.792102	−	0.610389i	$-0.791013\pi$
$773$		−	33.9411i		−	1.22078i	0.792102	−	0.610389i	$-0.208987\pi$
$774$	12.0000	−	4.24264i	0.431331	−	0.152499i
$775$	6.00000			0.215526
$776$	6.00000			0.215387
$777$	16.0000	+	11.3137i	0.573997	+	0.405877i
$778$		−	19.7990i		−	0.709828i
$779$			25.4558i			0.912050i
$780$	12.0000	−	16.9706i	0.429669	−	0.607644i
$781$		0			0
$782$		0			0
$783$	10.0000	+	2.82843i	0.357371	+	0.101080i
$784$	−5.00000			−0.178571
$785$			56.5685i			2.01902i
$786$		0			0
$787$		−	21.2132i		−	0.756169i	−0.925771	−	0.378085i	$-0.876583\pi$
$787$		−	21.2132i		−	0.756169i	0.925771	−	0.378085i	$-0.123417\pi$
$788$	−22.0000			−0.783718
$789$		0			0
$790$	−12.0000			−0.426941
$791$	4.00000			0.142224
$792$		0			0
$793$	42.0000			1.49146
$794$	2.00000			0.0709773
$795$	−16.0000	+	22.6274i	−0.567462	+	0.802512i
$796$	−2.00000			−0.0708881
$797$		−	2.82843i		−	0.100188i	−0.998745	−	0.0500940i	$-0.984048\pi$
$797$		−	2.82843i		−	0.100188i	0.998745	−	0.0500940i	$-0.0159521\pi$
$798$	−6.00000	+	8.48528i	−0.212398	+	0.300376i
$799$		−	16.9706i		−	0.600375i
$800$	−15.0000			−0.530330
$801$		0			0
$802$		−	2.82843i		−	0.0998752i
$803$		0			0
$804$	−2.00000	+	2.82843i	−0.0705346	+	0.0997509i
$805$		0			0
$806$			8.48528i			0.298881i
$807$	40.0000	+	28.2843i	1.40807	+	0.995654i
$808$	30.0000			1.05540
$809$	50.0000			1.75791			0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000			1.75791			0.878953	+	0.476908i	$0.158243\pi$
$810$	16.0000	+	19.7990i	0.562183	+	0.695666i
$811$		−	26.8701i		−	0.943535i	−0.881723	−	0.471768i	$-0.843616\pi$
$811$		−	26.8701i		−	0.943535i	0.881723	−	0.471768i	$-0.156384\pi$
$812$			2.82843i			0.0992583i
$813$	−42.0000	−	29.6985i	−1.47300	−	1.04157i
$814$		0			0
$815$		−	56.5685i		−	1.98151i
$816$	−6.00000	+	8.48528i	−0.210042	+	0.297044i
$817$	−18.0000			−0.629740
$818$		−	4.24264i		−	0.148340i
$819$	−6.00000	−	16.9706i	−0.209657	−	0.592999i
$820$			16.9706i			0.592638i
$821$	42.0000			1.46581			0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000			1.46581			0.732905	+	0.680331i	$0.238164\pi$
$822$	−4.00000	−	2.82843i	−0.139516	−	0.0986527i
$823$	−24.0000			−0.836587			−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000			−0.836587			−0.418294	+	0.908312i	$0.637372\pi$
$824$	−24.0000			−0.836080
$825$		0			0
$826$	−16.0000			−0.556711
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$			45.2548i			1.57082i
$831$	−6.00000	−	4.24264i	−0.208138	−	0.147176i
$832$		−	29.6985i		−	1.02961i
$833$	30.0000			1.03944
$834$	2.00000	+	1.41421i	0.0692543	+	0.0489702i
$835$		−	33.9411i		−	1.17458i
$836$		0			0
$837$	10.0000	+	2.82843i	0.345651	+	0.0977647i
$838$			31.1127i			1.07477i
$839$		−	33.9411i		−	1.17178i	−0.810391	−	0.585889i	$-0.800745\pi$
$839$		−	33.9411i		−	1.17178i	0.810391	−	0.585889i	$-0.199255\pi$
$840$	−12.0000	+	16.9706i	−0.414039	+	0.585540i
$841$	−25.0000			−0.862069
$842$	−20.0000			−0.689246
$843$	6.00000	−	8.48528i	0.206651	−	0.292249i
$844$		−	26.8701i		−	0.924906i
$845$			14.1421i			0.486504i
$846$	−8.00000	+	2.82843i	−0.275046	+	0.0972433i
$847$		0			0
$848$			5.65685i			0.194257i
$849$	−38.0000	−	26.8701i	−1.30416	−	0.922178i
$850$	−18.0000			−0.617395
$851$		0			0
$852$	4.00000	+	2.82843i	0.137038	+	0.0969003i
$853$			41.0122i			1.40423i	0.712063	+	0.702115i	$0.247761\pi$
$853$			41.0122i			1.40423i	−0.712063	+	0.702115i	$0.752239\pi$
$854$	−14.0000			−0.479070
$855$	−12.0000	−	33.9411i	−0.410391	−	1.16076i
$856$	48.0000			1.64061
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−12.0000			−0.409197
$861$	12.0000	+	8.48528i	0.408959	+	0.289178i
$862$	−32.0000			−1.08992
$863$		−	33.9411i		−	1.15537i	−0.816260	−	0.577685i	$-0.803956\pi$
$863$		−	33.9411i		−	1.15537i	0.816260	−	0.577685i	$-0.196044\pi$
$864$	−25.0000	−	7.07107i	−0.850517	−	0.240563i
$865$		−	16.9706i		−	0.577016i
$866$	30.0000			1.01944
$867$	19.0000	−	26.8701i	0.645274	−	0.912555i
$868$			2.82843i			0.0960031i
$869$		0			0
$870$	8.00000	+	5.65685i	0.271225	+	0.191785i
$871$		−	8.48528i		−	0.287513i
$872$		−	12.7279i		−	0.431022i
$873$	2.00000	+	5.65685i	0.0676897	+	0.191456i
$874$		0			0
$875$	8.00000			0.270449
$876$	−2.00000	−	1.41421i	−0.0675737	−	0.0477818i
$877$			35.3553i			1.19386i	0.802291	+	0.596932i	$0.203614\pi$
$877$			35.3553i			1.19386i	−0.802291	+	0.596932i	$0.796386\pi$
$878$		−	26.8701i		−	0.906821i
$879$	−2.00000	+	2.82843i	−0.0674583	+	0.0954005i
$880$		0			0
$881$			31.1127i			1.04821i	0.851653	+	0.524107i	$0.175601\pi$
$881$			31.1127i			1.04821i	−0.851653	+	0.524107i	$0.824399\pi$
$882$	−5.00000	−	14.1421i	−0.168359	−	0.476190i
$883$	46.0000			1.54802			0.774012	−	0.633171i	$-0.218247\pi$
$883$	46.0000			1.54802			0.774012	+	0.633171i	$0.218247\pi$
$884$			25.4558i			0.856173i
$885$	32.0000	−	45.2548i	1.07567	−	1.52122i
$886$			28.2843i			0.950229i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$	−24.0000	+	33.9411i	−0.805387	+	1.13899i
$889$	−14.0000			−0.469545
$890$		0			0
$891$		0			0
$892$	−24.0000			−0.803579
$893$	12.0000			0.401565
$894$	6.00000	−	8.48528i	0.200670	−	0.283790i
$895$	−8.00000			−0.267411
$896$		−	4.24264i		−	0.141737i
$897$		0			0
$898$		−	5.65685i		−	0.188772i
$899$	4.00000			0.133407
$900$	−3.00000	−	8.48528i	−0.100000	−	0.282843i
$901$		−	33.9411i		−	1.13074i
$902$		0			0
$903$	−6.00000	+	8.48528i	−0.199667	+	0.282372i
$904$			8.48528i			0.282216i
$905$			28.2843i			0.940201i
$906$	6.00000	+	4.24264i	0.199337	+	0.140952i
$907$	12.0000			0.398453			0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000			0.398453			0.199227	+	0.979953i	$0.436157\pi$
$908$	24.0000			0.796468
$909$	10.0000	+	28.2843i	0.331679	+	0.938130i
$910$		−	16.9706i		−	0.562569i
$911$		−	36.7696i		−	1.21823i	−0.793082	−	0.609115i	$-0.791525\pi$
$911$		−	36.7696i		−	1.21823i	0.793082	−	0.609115i	$-0.208475\pi$
$912$	−6.00000	−	4.24264i	−0.198680	−	0.140488i
$913$		0			0
$914$			9.89949i			0.327446i
$915$	28.0000	−	39.5980i	0.925651	−	1.30907i
$916$	24.0000			0.792982
$917$		0			0
$918$	−30.0000	−	8.48528i	−0.990148	−	0.280056i
$919$		−	21.2132i		−	0.699759i	−0.936795	−	0.349880i	$-0.886223\pi$
$919$		−	21.2132i		−	0.699759i	0.936795	−	0.349880i	$-0.113777\pi$
$920$		0			0
$921$	6.00000	+	4.24264i	0.197707	+	0.139800i
$922$	22.0000			0.724531
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−24.0000			−0.789115
$926$	24.0000			0.788689
$927$	−8.00000	−	22.6274i	−0.262754	−	0.743182i
$928$	−10.0000			−0.328266
$929$		−	2.82843i		−	0.0927977i	−0.998923	−	0.0463988i	$-0.985225\pi$
$929$		−	2.82843i		−	0.0927977i	0.998923	−	0.0463988i	$-0.0147745\pi$
$930$	8.00000	+	5.65685i	0.262330	+	0.185496i
$931$			21.2132i			0.695235i
$932$	10.0000			0.327561
$933$	40.0000	+	28.2843i	1.30954	+	0.925985i
$934$			28.2843i			0.925490i
$935$		0			0
$936$	36.0000	−	12.7279i	1.17670	−	0.416025i
$937$		−	35.3553i		−	1.15501i	−0.816388	−	0.577504i	$-0.804027\pi$
$937$		−	35.3553i		−	1.15501i	0.816388	−	0.577504i	$-0.195973\pi$
$938$			2.82843i			0.0923514i
$939$	12.0000	−	16.9706i	0.391605	−	0.553813i
$940$	8.00000			0.260931
$941$	−38.0000			−1.23876			−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000			−1.23876			−0.619382	+	0.785090i	$0.712617\pi$
$942$	−20.0000	+	28.2843i	−0.651635	+	0.921551i
$943$		0			0
$944$		−	11.3137i		−	0.368230i
$945$	−20.0000	−	5.65685i	−0.650600	−	0.184017i
$946$		0			0
$947$		−	31.1127i		−	1.01103i	−0.862819	−	0.505513i	$-0.831303\pi$
$947$		−	31.1127i		−	1.01103i	0.862819	−	0.505513i	$-0.168697\pi$
$948$	6.00000	+	4.24264i	0.194871	+	0.137795i
$949$	6.00000			0.194768
$950$		−	12.7279i		−	0.412948i
$951$	36.0000	+	25.4558i	1.16738	+	0.825462i
$952$		−	25.4558i		−	0.825029i
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$	−16.0000	+	5.65685i	−0.518019	+	0.183147i
$955$	−56.0000			−1.81212
$956$	16.0000			0.517477
$957$		0			0
$958$	28.0000			0.904639
$959$	4.00000			0.129167
$960$	−28.0000	−	19.7990i	−0.903696	−	0.639010i
$961$	−27.0000			−0.870968
$962$		−	33.9411i		−	1.09431i
$963$	16.0000	+	45.2548i	0.515593	+	1.45832i
$964$		−	4.24264i		−	0.136646i
$965$	−60.0000			−1.93147
$966$		0			0
$967$			4.24264i			0.136434i	0.997671	+	0.0682171i	$0.0217310\pi$
$967$			4.24264i			0.136434i	−0.997671	+	0.0682171i	$0.978269\pi$
$968$		0			0
$969$	36.0000	+	25.4558i	1.15649	+	0.817760i
$970$			5.65685i			0.181631i
$971$		−	33.9411i		−	1.08922i	−0.838689	−	0.544611i	$-0.816677\pi$
$971$		−	33.9411i		−	1.08922i	0.838689	−	0.544611i	$-0.183323\pi$
$972$	−1.00000	−	15.5563i	−0.0320750	−	0.498970i
$973$	−2.00000			−0.0641171
$974$	2.00000			0.0640841
$975$	18.0000	+	12.7279i	0.576461	+	0.407620i
$976$		−	9.89949i		−	0.316875i
$977$			25.4558i			0.814405i	0.913338	+	0.407202i	$0.133496\pi$
$977$			25.4558i			0.814405i	−0.913338	+	0.407202i	$0.866504\pi$
$978$	20.0000	−	28.2843i	0.639529	−	0.904431i
$979$		0			0
$980$			14.1421i			0.451754i
$981$	12.0000	−	4.24264i	0.383131	−	0.135457i
$982$	20.0000			0.638226
$983$			11.3137i			0.360851i	0.983589	+	0.180426i	$0.0577475\pi$
$983$			11.3137i			0.360851i	−0.983589	+	0.180426i	$0.942252\pi$
$984$	−18.0000	+	25.4558i	−0.573819	+	0.811503i
$985$		−	62.2254i		−	1.98267i
$986$	−12.0000			−0.382158
$987$	4.00000	−	5.65685i	0.127321	−	0.180060i
$988$	−18.0000			−0.572656
$989$		0			0
$990$		0			0
$991$	−42.0000			−1.33417			−0.667087	−	0.744980i	$-0.732459\pi$
$991$	−42.0000			−1.33417			−0.667087	+	0.744980i	$0.732459\pi$
$992$	−10.0000			−0.317500
$993$	−20.0000	+	28.2843i	−0.634681	+	0.897574i
$994$	4.00000			0.126872
$995$		−	5.65685i		−	0.179334i
$996$	16.0000	−	22.6274i	0.506979	−	0.716977i
$997$		−	29.6985i		−	0.940560i	−0.882517	−	0.470280i	$-0.844153\pi$
$997$		−	29.6985i		−	0.940560i	0.882517	−	0.470280i	$-0.155847\pi$
$998$	−14.0000			−0.443162
$999$	−40.0000	−	11.3137i	−1.26554	−	0.357950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.d.b.362.1	yes	2
3.2	odd	2		363.2.d.a.362.2	yes	2
11.2	odd	10		363.2.f.f.161.1		8
11.3	even	5		363.2.f.a.233.2		8
11.4	even	5		363.2.f.a.215.1		8
11.5	even	5		363.2.f.a.239.2		8
11.6	odd	10		363.2.f.f.239.2		8
11.7	odd	10		363.2.f.f.215.1		8
11.8	odd	10		363.2.f.f.233.2		8
11.9	even	5		363.2.f.a.161.1		8
11.10	odd	2		363.2.d.a.362.1	✓	2
33.2	even	10		363.2.f.a.161.2		8
33.5	odd	10		363.2.f.f.239.1		8
33.8	even	10		363.2.f.a.233.1		8
33.14	odd	10		363.2.f.f.233.1		8
33.17	even	10		363.2.f.a.239.1		8
33.20	odd	10		363.2.f.f.161.2		8
33.26	odd	10		363.2.f.f.215.2		8
33.29	even	10		363.2.f.a.215.2		8
33.32	even	2	inner	363.2.d.b.362.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.a.362.1	✓	2	11.10	odd	2
363.2.d.a.362.2	yes	2	3.2	odd	2
363.2.d.b.362.1	yes	2	1.1	even	1	trivial
363.2.d.b.362.2	yes	2	33.32	even	2	inner
363.2.f.a.161.1		8	11.9	even	5
363.2.f.a.161.2		8	33.2	even	10
363.2.f.a.215.1		8	11.4	even	5
363.2.f.a.215.2		8	33.29	even	10
363.2.f.a.233.1		8	33.8	even	10
363.2.f.a.233.2		8	11.3	even	5
363.2.f.a.239.1		8	33.17	even	10
363.2.f.a.239.2		8	11.5	even	5
363.2.f.f.161.1		8	11.2	odd	10
363.2.f.f.161.2		8	33.20	odd	10
363.2.f.f.215.1		8	11.7	odd	10
363.2.f.f.215.2		8	33.26	odd	10
363.2.f.f.233.1		8	33.14	odd	10
363.2.f.f.233.2		8	11.8	odd	10
363.2.f.f.239.1		8	33.5	odd	10
363.2.f.f.239.2		8	11.6	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.00000 - 1.41421i) q^{3} -1.00000 q^{4} -2.82843i q^{5} +(1.00000 - 1.41421i) q^{6} +1.41421i q^{7} -3.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} -2.82843i q^{10} +(-1.00000 + 1.41421i) q^{12} -4.24264i q^{13} +1.41421i q^{14} +(-4.00000 - 2.82843i) q^{15} -1.00000 q^{16} +6.00000 q^{17} +(-1.00000 - 2.82843i) q^{18} +4.24264i q^{19} +2.82843i q^{20} +(2.00000 + 1.41421i) q^{21} +(-3.00000 + 4.24264i) q^{24} -3.00000 q^{25} -4.24264i q^{26} +(-5.00000 - 1.41421i) q^{27} -1.41421i q^{28} -2.00000 q^{29} +(-4.00000 - 2.82843i) q^{30} -2.00000 q^{31} +5.00000 q^{32} +6.00000 q^{34} +4.00000 q^{35} +(1.00000 + 2.82843i) q^{36} +8.00000 q^{37} +4.24264i q^{38} +(-6.00000 - 4.24264i) q^{39} +8.48528i q^{40} +6.00000 q^{41} +(2.00000 + 1.41421i) q^{42} +4.24264i q^{43} +(-8.00000 + 2.82843i) q^{45} -2.82843i q^{47} +(-1.00000 + 1.41421i) q^{48} +5.00000 q^{49} -3.00000 q^{50} +(6.00000 - 8.48528i) q^{51} +4.24264i q^{52} -5.65685i q^{53} +(-5.00000 - 1.41421i) q^{54} -4.24264i q^{56} +(6.00000 + 4.24264i) q^{57} -2.00000 q^{58} +11.3137i q^{59} +(4.00000 + 2.82843i) q^{60} +9.89949i q^{61} -2.00000 q^{62} +(4.00000 - 1.41421i) q^{63} +7.00000 q^{64} -12.0000 q^{65} +2.00000 q^{67} -6.00000 q^{68} +4.00000 q^{70} -2.82843i q^{71} +(3.00000 + 8.48528i) q^{72} +1.41421i q^{73} +8.00000 q^{74} +(-3.00000 + 4.24264i) q^{75} -4.24264i q^{76} +(-6.00000 - 4.24264i) q^{78} -4.24264i q^{79} +2.82843i q^{80} +(-7.00000 + 5.65685i) q^{81} +6.00000 q^{82} -16.0000 q^{83} +(-2.00000 - 1.41421i) q^{84} -16.9706i q^{85} +4.24264i q^{86} +(-2.00000 + 2.82843i) q^{87} +(-8.00000 + 2.82843i) q^{90} +6.00000 q^{91} +(-2.00000 + 2.82843i) q^{93} -2.82843i q^{94} +12.0000 q^{95} +(5.00000 - 7.07107i) q^{96} -2.00000 q^{97} +5.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{6} - 6 q^{8} - 2 q^{9} - 2 q^{12} - 8 q^{15} - 2 q^{16} + 12 q^{17} - 2 q^{18} + 4 q^{21} - 6 q^{24} - 6 q^{25} - 10 q^{27} - 4 q^{29} - 8 q^{30} - 4 q^{31} + 10 q^{32}+ \cdots + 10 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^6 - 6 * q^8 - 2 * q^9 - 2 * q^12 - 8 * q^15 - 2 * q^16 + 12 * q^17 - 2 * q^18 + 4 * q^21 - 6 * q^24 - 6 * q^25 - 10 * q^27 - 4 * q^29 - 8 * q^30 - 4 * q^31 + 10 * q^32 + 12 * q^34 + 8 * q^35 + 2 * q^36 + 16 * q^37 - 12 * q^39 + 12 * q^41 + 4 * q^42 - 16 * q^45 - 2 * q^48 + 10 * q^49 - 6 * q^50 + 12 * q^51 - 10 * q^54 + 12 * q^57 - 4 * q^58 + 8 * q^60 - 4 * q^62 + 8 * q^63 + 14 * q^64 - 24 * q^65 + 4 * q^67 - 12 * q^68 + 8 * q^70 + 6 * q^72 + 16 * q^74 - 6 * q^75 - 12 * q^78 - 14 * q^81 + 12 * q^82 - 32 * q^83 - 4 * q^84 - 4 * q^87 - 16 * q^90 + 12 * q^91 - 4 * q^93 + 24 * q^95 + 10 * q^96 - 4 * q^97 + 10 * q^98

Introduction

L-functions

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