LMFDB - Embedded newform 585.2.n.a.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(307,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("585.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
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			343.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	585.343
Dual form			585.2.n.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +4.00000 q^{7} +3.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +4.00000 q^{7} +3.00000i q^{8} +(-2.00000 - 1.00000i) q^{10} +(-2.00000 - 2.00000i) q^{11} +(-2.00000 + 3.00000i) q^{13} +4.00000i q^{14} -1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +(2.00000 + 2.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(2.00000 - 2.00000i) q^{22} +(6.00000 - 6.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +4.00000 q^{28} +(-4.00000 + 4.00000i) q^{31} +5.00000i q^{32} +(-1.00000 + 1.00000i) q^{34} +(-4.00000 + 8.00000i) q^{35} -6.00000 q^{37} +(-2.00000 + 2.00000i) q^{38} +(-6.00000 - 3.00000i) q^{40} +(-5.00000 + 5.00000i) q^{41} +(4.00000 - 4.00000i) q^{43} +(-2.00000 - 2.00000i) q^{44} +(6.00000 + 6.00000i) q^{46} +9.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +(-2.00000 + 3.00000i) q^{52} +(7.00000 + 7.00000i) q^{53} +(6.00000 - 2.00000i) q^{55} +12.0000i q^{56} +(2.00000 - 2.00000i) q^{59} -8.00000 q^{61} +(-4.00000 - 4.00000i) q^{62} -7.00000 q^{64} +(-4.00000 - 7.00000i) q^{65} -8.00000i q^{67} +(1.00000 + 1.00000i) q^{68} +(-8.00000 - 4.00000i) q^{70} +(8.00000 - 8.00000i) q^{71} -4.00000i q^{73} -6.00000i q^{74} +(2.00000 + 2.00000i) q^{76} +(-8.00000 - 8.00000i) q^{77} +8.00000i q^{79} +(1.00000 - 2.00000i) q^{80} +(-5.00000 - 5.00000i) q^{82} +(-3.00000 + 1.00000i) q^{85} +(4.00000 + 4.00000i) q^{86} +(6.00000 - 6.00000i) q^{88} +(5.00000 - 5.00000i) q^{89} +(-8.00000 + 12.0000i) q^{91} +(6.00000 - 6.00000i) q^{92} +(-6.00000 + 2.00000i) q^{95} -2.00000i q^{97} +9.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 2 q^{5} + 8 q^{7}+O(q^{10}) $ 2 * q + 2 * q^4 - 2 * q^5 + 8 * q^7	$ 2 q + 2 q^{4} - 2 q^{5} + 8 q^{7} - 4 q^{10} - 4 q^{11} - 4 q^{13} - 2 q^{16} + 2 q^{17} + 4 q^{19} - 2 q^{20} + 4 q^{22} + 12 q^{23} - 6 q^{25} - 6 q^{26} + 8 q^{28} - 8 q^{31} - 2 q^{34} - 8 q^{35} - 12 q^{37} - 4 q^{38} - 12 q^{40} - 10 q^{41} + 8 q^{43} - 4 q^{44} + 12 q^{46} + 18 q^{49} + 8 q^{50} - 4 q^{52} + 14 q^{53} + 12 q^{55} + 4 q^{59} - 16 q^{61} - 8 q^{62} - 14 q^{64} - 8 q^{65} + 2 q^{68} - 16 q^{70} + 16 q^{71} + 4 q^{76} - 16 q^{77} + 2 q^{80} - 10 q^{82} - 6 q^{85} + 8 q^{86} + 12 q^{88} + 10 q^{89} - 16 q^{91} + 12 q^{92} - 12 q^{95}+O(q^{100}) $ 2 * q + 2 * q^4 - 2 * q^5 + 8 * q^7 - 4 * q^10 - 4 * q^11 - 4 * q^13 - 2 * q^16 + 2 * q^17 + 4 * q^19 - 2 * q^20 + 4 * q^22 + 12 * q^23 - 6 * q^25 - 6 * q^26 + 8 * q^28 - 8 * q^31 - 2 * q^34 - 8 * q^35 - 12 * q^37 - 4 * q^38 - 12 * q^40 - 10 * q^41 + 8 * q^43 - 4 * q^44 + 12 * q^46 + 18 * q^49 + 8 * q^50 - 4 * q^52 + 14 * q^53 + 12 * q^55 + 4 * q^59 - 16 * q^61 - 8 * q^62 - 14 * q^64 - 8 * q^65 + 2 * q^68 - 16 * q^70 + 16 * q^71 + 4 * q^76 - 16 * q^77 + 2 * q^80 - 10 * q^82 - 6 * q^85 + 8 * q^86 + 12 * q^88 + 10 * q^89 - 16 * q^91 + 12 * q^92 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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	$0.884973\pi$
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$			3.00000i			1.06066i
$9$		0			0
$10$	−2.00000	−	1.00000i	−0.632456	−	0.316228i
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	0.338091	−	0.941113i	$-0.390219\pi$
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$			4.00000i			1.06904i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$		0			0
$19$	2.00000	+	2.00000i	0.458831	+	0.458831i	0.898272	−	0.439440i	$-0.144823\pi$
$19$	2.00000	+	2.00000i	0.458831	+	0.458831i	−0.439440	+	0.898272i	$0.644823\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$		0			0
$22$	2.00000	−	2.00000i	0.426401	−	0.426401i
$23$	6.00000	−	6.00000i	1.25109	−	1.25109i	0.295853	−	0.955233i	$-0.404396\pi$
$23$	6.00000	−	6.00000i	1.25109	−	1.25109i	0.955233	−	0.295853i	$-0.0956039\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	−3.00000	−	2.00000i	−0.588348	−	0.392232i
$27$		0			0
$28$	4.00000			0.755929
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−4.00000	+	4.00000i	−0.718421	+	0.718421i	−0.968282	−	0.249861i	$-0.919615\pi$
$31$	−4.00000	+	4.00000i	−0.718421	+	0.718421i	0.249861	+	0.968282i	$0.419615\pi$
$32$			5.00000i			0.883883i
$33$		0			0
$34$	−1.00000	+	1.00000i	−0.171499	+	0.171499i
$35$	−4.00000	+	8.00000i	−0.676123	+	1.35225i
$36$		0			0
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	−2.00000	+	2.00000i	−0.324443	+	0.324443i
$39$		0			0
$40$	−6.00000	−	3.00000i	−0.948683	−	0.474342i
$41$	−5.00000	+	5.00000i	−0.780869	+	0.780869i	−0.979977	−	0.199109i	$-0.936195\pi$
$41$	−5.00000	+	5.00000i	−0.780869	+	0.780869i	0.199109	+	0.979977i	$0.436195\pi$
$42$		0			0
$43$	4.00000	−	4.00000i	0.609994	−	0.609994i	−0.332950	−	0.942944i	$-0.608044\pi$
$43$	4.00000	−	4.00000i	0.609994	−	0.609994i	0.942944	+	0.332950i	$0.108044\pi$
$44$	−2.00000	−	2.00000i	−0.301511	−	0.301511i
$45$		0			0
$46$	6.00000	+	6.00000i	0.884652	+	0.884652i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$		0			0
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	7.00000	+	7.00000i	0.961524	+	0.961524i	0.999287	−	0.0377628i	$-0.0120231\pi$
$53$	7.00000	+	7.00000i	0.961524	+	0.961524i	−0.0377628	+	0.999287i	$0.512023\pi$
$54$		0			0
$55$	6.00000	−	2.00000i	0.809040	−	0.269680i
$56$			12.0000i			1.60357i
$57$		0			0
$58$		0			0
$59$	2.00000	−	2.00000i	0.260378	−	0.260378i	−0.564830	−	0.825208i	$-0.691058\pi$
$59$	2.00000	−	2.00000i	0.260378	−	0.260378i	0.825208	+	0.564830i	$0.191058\pi$
$60$		0			0
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$	−4.00000	−	4.00000i	−0.508001	−	0.508001i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−4.00000	−	7.00000i	−0.496139	−	0.868243i
$66$		0			0
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$	1.00000	+	1.00000i	0.121268	+	0.121268i
$69$		0			0
$70$	−8.00000	−	4.00000i	−0.956183	−	0.478091i
$71$	8.00000	−	8.00000i	0.949425	−	0.949425i	−0.0493559	−	0.998781i	$-0.515717\pi$
$71$	8.00000	−	8.00000i	0.949425	−	0.949425i	0.998781	+	0.0493559i	$0.0157169\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		−	6.00000i		−	0.697486i
$75$		0			0
$76$	2.00000	+	2.00000i	0.229416	+	0.229416i
$77$	−8.00000	−	8.00000i	−0.911685	−	0.911685i
$78$		0			0
$79$			8.00000i			0.900070i	0.893011	+	0.450035i	$0.148589\pi$
$79$			8.00000i			0.900070i	−0.893011	+	0.450035i	$0.851411\pi$
$80$	1.00000	−	2.00000i	0.111803	−	0.223607i
$81$		0			0
$82$	−5.00000	−	5.00000i	−0.552158	−	0.552158i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−3.00000	+	1.00000i	−0.325396	+	0.108465i
$86$	4.00000	+	4.00000i	0.431331	+	0.431331i
$87$		0			0
$88$	6.00000	−	6.00000i	0.639602	−	0.639602i
$89$	5.00000	−	5.00000i	0.529999	−	0.529999i	−0.390573	−	0.920572i	$-0.627723\pi$
$89$	5.00000	−	5.00000i	0.529999	−	0.529999i	0.920572	+	0.390573i	$0.127723\pi$
$90$		0			0
$91$	−8.00000	+	12.0000i	−0.838628	+	1.25794i
$92$	6.00000	−	6.00000i	0.625543	−	0.625543i
$93$		0			0
$94$		0			0
$95$	−6.00000	+	2.00000i	−0.615587	+	0.205196i
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$			9.00000i			0.909137i
$99$		0			0
$100$	−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	$-0.0964900\pi$
$102$		0			0
$103$	14.0000	−	14.0000i	1.37946	−	1.37946i	0.533936	−	0.845525i	$-0.320712\pi$
$103$	14.0000	−	14.0000i	1.37946	−	1.37946i	0.845525	−	0.533936i	$-0.179288\pi$
$104$	−9.00000	−	6.00000i	−0.882523	−	0.588348i
$105$		0			0
$106$	−7.00000	+	7.00000i	−0.679900	+	0.679900i
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	−0.205308	−	0.978697i	$-0.565820\pi$
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	0.978697	+	0.205308i	$0.0658197\pi$
$108$		0			0
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	0.991575	−	0.129532i	$-0.0413474\pi$
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	−0.129532	+	0.991575i	$0.541347\pi$
$110$	2.00000	+	6.00000i	0.190693	+	0.572078i
$111$		0			0
$112$	−4.00000			−0.377964
$113$	−11.0000	−	11.0000i	−1.03479	−	1.03479i	−0.999372	−	0.0354205i	$-0.988723\pi$
$113$	−11.0000	−	11.0000i	−1.03479	−	1.03479i	−0.0354205	−	0.999372i	$-0.511277\pi$
$114$		0			0
$115$	6.00000	+	18.0000i	0.559503	+	1.67851i
$116$		0			0
$117$		0			0
$118$	2.00000	+	2.00000i	0.184115	+	0.184115i
$119$	4.00000	+	4.00000i	0.366679	+	0.366679i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		−	8.00000i		−	0.724286i
$123$		0			0
$124$	−4.00000	+	4.00000i	−0.359211	+	0.359211i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−6.00000	−	6.00000i	−0.532414	−	0.532414i	0.388876	−	0.921290i	$-0.372863\pi$
$127$	−6.00000	−	6.00000i	−0.532414	−	0.532414i	−0.921290	+	0.388876i	$0.872863\pi$
$128$			3.00000i			0.265165i
$129$		0			0
$130$	7.00000	−	4.00000i	0.613941	−	0.350823i
$131$	−16.0000			−1.39793			−0.698963	−	0.715158i	$-0.746355\pi$
$131$	−16.0000			−1.39793			−0.698963	+	0.715158i	$0.746355\pi$
$132$		0			0
$133$	8.00000	+	8.00000i	0.693688	+	0.693688i
$134$	8.00000			0.691095
$135$		0			0
$136$	−3.00000	+	3.00000i	−0.257248	+	0.257248i
$137$	22.0000			1.87959			0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000			1.87959			0.939793	+	0.341743i	$0.111017\pi$
$138$		0			0
$139$		−	16.0000i		−	1.35710i	−0.734553	−	0.678551i	$-0.762608\pi$
$139$		−	16.0000i		−	1.35710i	0.734553	−	0.678551i	$-0.237392\pi$
$140$	−4.00000	+	8.00000i	−0.338062	+	0.676123i
$141$		0			0
$142$	8.00000	+	8.00000i	0.671345	+	0.671345i
$143$	10.0000	−	2.00000i	0.836242	−	0.167248i
$144$		0			0
$145$		0			0
$146$	4.00000			0.331042
$147$		0			0
$148$	−6.00000			−0.493197
$149$	−15.0000	−	15.0000i	−1.22885	−	1.22885i	−0.964400	−	0.264448i	$-0.914810\pi$
$149$	−15.0000	−	15.0000i	−1.22885	−	1.22885i	−0.264448	−	0.964400i	$-0.585190\pi$
$150$		0			0
$151$	4.00000	+	4.00000i	0.325515	+	0.325515i	0.850878	−	0.525363i	$-0.176070\pi$
$151$	4.00000	+	4.00000i	0.325515	+	0.325515i	−0.525363	+	0.850878i	$0.676070\pi$
$152$	−6.00000	+	6.00000i	−0.486664	+	0.486664i
$153$		0			0
$154$	8.00000	−	8.00000i	0.644658	−	0.644658i
$155$	−4.00000	−	12.0000i	−0.321288	−	0.963863i
$156$		0			0
$157$	7.00000	−	7.00000i	0.558661	−	0.558661i	−0.370265	−	0.928926i	$-0.620733\pi$
$157$	7.00000	−	7.00000i	0.558661	−	0.558661i	0.928926	+	0.370265i	$0.120733\pi$
$158$	−8.00000			−0.636446
$159$		0			0
$160$	−10.0000	−	5.00000i	−0.790569	−	0.395285i
$161$	24.0000	−	24.0000i	1.89146	−	1.89146i
$162$		0			0
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	−5.00000	+	5.00000i	−0.390434	+	0.390434i
$165$		0			0
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−1.00000	−	3.00000i	−0.0766965	−	0.230089i
$171$		0			0
$172$	4.00000	−	4.00000i	0.304997	−	0.304997i
$173$	7.00000	−	7.00000i	0.532200	−	0.532200i	−0.389026	−	0.921227i	$-0.627189\pi$
$173$	7.00000	−	7.00000i	0.532200	−	0.532200i	0.921227	+	0.389026i	$0.127189\pi$
$174$		0			0
$175$	−12.0000	−	16.0000i	−0.907115	−	1.20949i
$176$	2.00000	+	2.00000i	0.150756	+	0.150756i
$177$		0			0
$178$	5.00000	+	5.00000i	0.374766	+	0.374766i
$179$	−8.00000			−0.597948			−0.298974	−	0.954261i	$-0.596644\pi$
$179$	−8.00000			−0.597948			−0.298974	+	0.954261i	$0.596644\pi$
$180$		0			0
$181$			22.0000i			1.63525i	0.575753	+	0.817624i	$0.304709\pi$
$181$			22.0000i			1.63525i	−0.575753	+	0.817624i	$0.695291\pi$
$182$	−12.0000	−	8.00000i	−0.889499	−	0.592999i
$183$		0			0
$184$	18.0000	+	18.0000i	1.32698	+	1.32698i
$185$	6.00000	−	12.0000i	0.441129	−	0.882258i
$186$		0			0
$187$		−	4.00000i		−	0.292509i
$188$		0			0
$189$		0			0
$190$	−2.00000	−	6.00000i	−0.145095	−	0.435286i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$		0			0
$193$			18.0000i			1.29567i	0.761781	+	0.647834i	$0.224325\pi$
$193$			18.0000i			1.29567i	−0.761781	+	0.647834i	$0.775675\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	9.00000			0.642857
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		0			0
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	12.0000	−	9.00000i	0.848528	−	0.636396i
$201$		0			0
$202$	6.00000			0.422159
$203$		0			0
$204$		0			0
$205$	−5.00000	−	15.0000i	−0.349215	−	1.04765i
$206$	14.0000	+	14.0000i	0.975426	+	0.975426i
$207$		0			0
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$		−	8.00000i		−	0.553372i
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	7.00000	+	7.00000i	0.480762	+	0.480762i
$213$		0			0
$214$	8.00000	+	8.00000i	0.546869	+	0.546869i
$215$	4.00000	+	12.0000i	0.272798	+	0.818393i
$216$		0			0
$217$	−16.0000	+	16.0000i	−1.08615	+	1.08615i
$218$	−9.00000	+	9.00000i	−0.609557	+	0.609557i
$219$		0			0
$220$	6.00000	−	2.00000i	0.404520	−	0.134840i
$221$	−5.00000	+	1.00000i	−0.336336	+	0.0672673i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$			20.0000i			1.33631i
$225$		0			0
$226$	11.0000	−	11.0000i	0.731709	−	0.731709i
$227$			24.0000i			1.59294i	0.604681	+	0.796468i	$0.293301\pi$
$227$			24.0000i			1.59294i	−0.604681	+	0.796468i	$0.706699\pi$
$228$		0			0
$229$	9.00000	−	9.00000i	0.594737	−	0.594737i	−0.344170	−	0.938907i	$-0.611840\pi$
$229$	9.00000	−	9.00000i	0.594737	−	0.594737i	0.938907	+	0.344170i	$0.111840\pi$
$230$	−18.0000	+	6.00000i	−1.18688	+	0.395628i
$231$		0			0
$232$		0			0
$233$	7.00000	−	7.00000i	0.458585	−	0.458585i	−0.439606	−	0.898191i	$-0.644882\pi$
$233$	7.00000	−	7.00000i	0.458585	−	0.458585i	0.898191	+	0.439606i	$0.144882\pi$
$234$		0			0
$235$		0			0
$236$	2.00000	−	2.00000i	0.130189	−	0.130189i
$237$		0			0
$238$	−4.00000	+	4.00000i	−0.259281	+	0.259281i
$239$	12.0000	+	12.0000i	0.776215	+	0.776215i	0.979185	−	0.202970i	$-0.0650593\pi$
$239$	12.0000	+	12.0000i	0.776215	+	0.776215i	−0.202970	+	0.979185i	$0.565059\pi$
$240$		0			0
$241$	−13.0000	−	13.0000i	−0.837404	−	0.837404i	0.151113	−	0.988517i	$-0.451714\pi$
$241$	−13.0000	−	13.0000i	−0.837404	−	0.837404i	−0.988517	+	0.151113i	$0.951714\pi$
$242$	3.00000			0.192847
$243$		0			0
$244$	−8.00000			−0.512148
$245$	−9.00000	+	18.0000i	−0.574989	+	1.14998i
$246$		0			0
$247$	−10.0000	+	2.00000i	−0.636285	+	0.127257i
$248$	−12.0000	−	12.0000i	−0.762001	−	0.762001i
$249$		0			0
$250$	2.00000	+	11.0000i	0.126491	+	0.695701i
$251$			28.0000i			1.76734i	0.468106	+	0.883672i	$0.344936\pi$
$251$			28.0000i			1.76734i	−0.468106	+	0.883672i	$0.655064\pi$
$252$		0			0
$253$	−24.0000			−1.50887
$254$	6.00000	−	6.00000i	0.376473	−	0.376473i
$255$		0			0
$256$	−17.0000			−1.06250
$257$	−5.00000	−	5.00000i	−0.311891	−	0.311891i	0.533751	−	0.845642i	$-0.320782\pi$
$257$	−5.00000	−	5.00000i	−0.311891	−	0.311891i	−0.845642	+	0.533751i	$0.820782\pi$
$258$		0			0
$259$	−24.0000			−1.49129
$260$	−4.00000	−	7.00000i	−0.248069	−	0.434122i
$261$		0			0
$262$		−	16.0000i		−	0.988483i
$263$	−10.0000	−	10.0000i	−0.616626	−	0.616626i	0.328038	−	0.944664i	$-0.393613\pi$
$263$	−10.0000	−	10.0000i	−0.616626	−	0.616626i	−0.944664	+	0.328038i	$0.893613\pi$
$264$		0			0
$265$	−21.0000	+	7.00000i	−1.29002	+	0.430007i
$266$	−8.00000	+	8.00000i	−0.490511	+	0.490511i
$267$		0			0
$268$		−	8.00000i		−	0.488678i
$269$			18.0000i			1.09748i	0.835993	+	0.548740i	$0.184892\pi$
$269$			18.0000i			1.09748i	−0.835993	+	0.548740i	$0.815108\pi$
$270$		0			0
$271$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$271$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$272$	−1.00000	−	1.00000i	−0.0606339	−	0.0606339i
$273$		0			0
$274$			22.0000i			1.32907i
$275$	−2.00000	+	14.0000i	−0.120605	+	0.844232i
$276$		0			0
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	0.791466	−	0.611213i	$-0.209318\pi$
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	−0.611213	+	0.791466i	$0.709318\pi$
$278$	16.0000			0.959616
$279$		0			0
$280$	−24.0000	−	12.0000i	−1.43427	−	0.717137i
$281$	−13.0000	−	13.0000i	−0.775515	−	0.775515i	0.203550	−	0.979065i	$-0.434752\pi$
$281$	−13.0000	−	13.0000i	−0.775515	−	0.775515i	−0.979065	+	0.203550i	$0.934752\pi$
$282$		0			0
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$	8.00000	−	8.00000i	0.474713	−	0.474713i
$285$		0			0
$286$	2.00000	+	10.0000i	0.118262	+	0.591312i
$287$	−20.0000	+	20.0000i	−1.18056	+	1.18056i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$		0			0
$292$		−	4.00000i		−	0.234082i
$293$			18.0000i			1.05157i	0.850617	+	0.525786i	$0.176229\pi$
$293$			18.0000i			1.05157i	−0.850617	+	0.525786i	$0.823771\pi$
$294$		0			0
$295$	2.00000	+	6.00000i	0.116445	+	0.349334i
$296$		−	18.0000i		−	1.04623i
$297$		0			0
$298$	15.0000	−	15.0000i	0.868927	−	0.868927i
$299$	6.00000	+	30.0000i	0.346989	+	1.73494i
$300$		0			0
$301$	16.0000	−	16.0000i	0.922225	−	0.922225i
$302$	−4.00000	+	4.00000i	−0.230174	+	0.230174i
$303$		0			0
$304$	−2.00000	−	2.00000i	−0.114708	−	0.114708i
$305$	8.00000	−	16.0000i	0.458079	−	0.916157i
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	−8.00000	−	8.00000i	−0.455842	−	0.455842i
$309$		0			0
$310$	12.0000	−	4.00000i	0.681554	−	0.227185i
$311$		−	12.0000i		−	0.680458i	−0.940343	−	0.340229i	$-0.889495\pi$
$311$		−	12.0000i		−	0.680458i	0.940343	−	0.340229i	$-0.110505\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$	7.00000	+	7.00000i	0.395033	+	0.395033i
$315$		0			0
$316$			8.00000i			0.450035i
$317$		−	26.0000i		−	1.46031i	−0.683284	−	0.730153i	$-0.739449\pi$
$317$		−	26.0000i		−	1.46031i	0.683284	−	0.730153i	$-0.260551\pi$
$318$		0			0
$319$		0			0
$320$	7.00000	−	14.0000i	0.391312	−	0.782624i
$321$		0			0
$322$	24.0000	+	24.0000i	1.33747	+	1.33747i
$323$			4.00000i			0.222566i
$324$		0			0
$325$	18.0000	−	1.00000i	0.998460	−	0.0554700i
$326$	−4.00000			−0.221540
$327$		0			0
$328$	−15.0000	−	15.0000i	−0.828236	−	0.828236i
$329$		0			0
$330$		0			0
$331$	−6.00000	+	6.00000i	−0.329790	+	0.329790i	−0.852506	−	0.522717i	$-0.824919\pi$
$331$	−6.00000	+	6.00000i	−0.329790	+	0.329790i	0.522717	+	0.852506i	$0.324919\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	16.0000	+	8.00000i	0.874173	+	0.437087i
$336$		0			0
$337$	−1.00000	−	1.00000i	−0.0544735	−	0.0544735i	0.679345	−	0.733819i	$-0.262264\pi$
$337$	−1.00000	−	1.00000i	−0.0544735	−	0.0544735i	−0.733819	+	0.679345i	$0.762264\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$		0			0
$340$	−3.00000	+	1.00000i	−0.162698	+	0.0542326i
$341$	16.0000			0.866449
$342$		0			0
$343$	8.00000			0.431959
$344$	12.0000	+	12.0000i	0.646997	+	0.646997i
$345$		0			0
$346$	7.00000	+	7.00000i	0.376322	+	0.376322i
$347$	−24.0000	+	24.0000i	−1.28839	+	1.28839i	−0.352621	+	0.935766i	$0.614710\pi$
$347$	−24.0000	+	24.0000i	−1.28839	+	1.28839i	−0.935766	+	0.352621i	$0.885290\pi$
$348$		0			0
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	−0.782826	−	0.622240i	$-0.786223\pi$
$349$	−3.00000	+	3.00000i	−0.160586	+	0.160586i	0.622240	+	0.782826i	$0.286223\pi$
$350$	16.0000	−	12.0000i	0.855236	−	0.641427i
$351$		0			0
$352$	10.0000	−	10.0000i	0.533002	−	0.533002i
$353$	−36.0000			−1.91609			−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000			−1.91609			−0.958043	+	0.286623i	$0.907467\pi$
$354$		0			0
$355$	8.00000	+	24.0000i	0.424596	+	1.27379i
$356$	5.00000	−	5.00000i	0.264999	−	0.264999i
$357$		0			0
$358$		−	8.00000i		−	0.422813i
$359$	4.00000	−	4.00000i	0.211112	−	0.211112i	−0.593628	−	0.804740i	$-0.702305\pi$
$359$	4.00000	−	4.00000i	0.211112	−	0.211112i	0.804740	+	0.593628i	$0.202305\pi$
$360$		0			0
$361$		−	11.0000i		−	0.578947i
$362$	−22.0000			−1.15629
$363$		0			0
$364$	−8.00000	+	12.0000i	−0.419314	+	0.628971i
$365$	8.00000	+	4.00000i	0.418739	+	0.209370i
$366$		0			0
$367$	−10.0000	+	10.0000i	−0.521996	+	0.521996i	−0.918174	−	0.396178i	$-0.870336\pi$
$367$	−10.0000	+	10.0000i	−0.521996	+	0.521996i	0.396178	+	0.918174i	$0.370336\pi$
$368$	−6.00000	+	6.00000i	−0.312772	+	0.312772i
$369$		0			0
$370$	12.0000	+	6.00000i	0.623850	+	0.311925i
$371$	28.0000	+	28.0000i	1.45369	+	1.45369i
$372$		0			0
$373$	3.00000	+	3.00000i	0.155334	+	0.155334i	0.780496	−	0.625161i	$-0.214967\pi$
$373$	3.00000	+	3.00000i	0.155334	+	0.155334i	−0.625161	+	0.780496i	$0.714967\pi$
$374$	4.00000			0.206835
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−14.0000	−	14.0000i	−0.719132	−	0.719132i	0.249296	−	0.968427i	$-0.419801\pi$
$379$	−14.0000	−	14.0000i	−0.719132	−	0.719132i	−0.968427	+	0.249296i	$0.919801\pi$
$380$	−6.00000	+	2.00000i	−0.307794	+	0.102598i
$381$		0			0
$382$		−	20.0000i		−	1.02329i
$383$	−12.0000			−0.613171			−0.306586	−	0.951843i	$-0.599187\pi$
$383$	−12.0000			−0.613171			−0.306586	+	0.951843i	$0.599187\pi$
$384$		0			0
$385$	24.0000	−	8.00000i	1.22315	−	0.407718i
$386$	−18.0000			−0.916176
$387$		0			0
$388$		−	2.00000i		−	0.101535i
$389$	−24.0000			−1.21685			−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000			−1.21685			−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$			27.0000i			1.36371i
$393$		0			0
$394$	−12.0000			−0.604551
$395$	−16.0000	−	8.00000i	−0.805047	−	0.402524i
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$			20.0000i			1.00251i
$399$		0			0
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	5.00000	+	5.00000i	0.249688	+	0.249688i	0.820843	−	0.571154i	$-0.193504\pi$
$401$	5.00000	+	5.00000i	0.249688	+	0.249688i	−0.571154	+	0.820843i	$0.693504\pi$
$402$		0			0
$403$	−4.00000	−	20.0000i	−0.199254	−	0.996271i
$404$		−	6.00000i		−	0.298511i
$405$		0			0
$406$		0			0
$407$	12.0000	+	12.0000i	0.594818	+	0.594818i
$408$		0			0
$409$	13.0000	+	13.0000i	0.642809	+	0.642809i	0.951245	−	0.308436i	$-0.0998057\pi$
$409$	13.0000	+	13.0000i	0.642809	+	0.642809i	−0.308436	+	0.951245i	$0.599806\pi$
$410$	15.0000	−	5.00000i	0.740797	−	0.246932i
$411$		0			0
$412$	14.0000	−	14.0000i	0.689730	−	0.689730i
$413$	8.00000	−	8.00000i	0.393654	−	0.393654i
$414$		0			0
$415$		0			0
$416$	−15.0000	−	10.0000i	−0.735436	−	0.490290i
$417$		0			0
$418$	8.00000			0.391293
$419$			16.0000i			0.781651i	0.920465	+	0.390826i	$0.127810\pi$
$419$			16.0000i			0.781651i	−0.920465	+	0.390826i	$0.872190\pi$
$420$		0			0
$421$	7.00000	−	7.00000i	0.341159	−	0.341159i	−0.515644	−	0.856803i	$-0.672447\pi$
$421$	7.00000	−	7.00000i	0.341159	−	0.341159i	0.856803	+	0.515644i	$0.172447\pi$
$422$		−	20.0000i		−	0.973585i
$423$		0			0
$424$	−21.0000	+	21.0000i	−1.01985	+	1.01985i
$425$	1.00000	−	7.00000i	0.0485071	−	0.339550i
$426$		0			0
$427$	−32.0000			−1.54859
$428$	8.00000	−	8.00000i	0.386695	−	0.386695i
$429$		0			0
$430$	−12.0000	+	4.00000i	−0.578691	+	0.192897i
$431$	−4.00000	+	4.00000i	−0.192673	+	0.192673i	−0.796850	−	0.604177i	$-0.793502\pi$
$431$	−4.00000	+	4.00000i	−0.192673	+	0.192673i	0.604177	+	0.796850i	$0.293502\pi$
$432$		0			0
$433$	−5.00000	+	5.00000i	−0.240285	+	0.240285i	−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−5.00000	+	5.00000i	−0.240285	+	0.240285i	0.576683	+	0.816968i	$0.304347\pi$
$434$	−16.0000	−	16.0000i	−0.768025	−	0.768025i
$435$		0			0
$436$	9.00000	+	9.00000i	0.431022	+	0.431022i
$437$	24.0000			1.14808
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	6.00000	+	18.0000i	0.286039	+	0.858116i
$441$		0			0
$442$	−1.00000	−	5.00000i	−0.0475651	−	0.237826i
$443$	8.00000	+	8.00000i	0.380091	+	0.380091i	0.871135	−	0.491044i	$-0.163384\pi$
$443$	8.00000	+	8.00000i	0.380091	+	0.380091i	−0.491044	+	0.871135i	$0.663384\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$			8.00000i			0.378811i
$447$		0			0
$448$	−28.0000			−1.32288
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	−0.632765	−	0.774344i	$-0.718080\pi$
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	0.774344	+	0.632765i	$0.218080\pi$
$450$		0			0
$451$	20.0000			0.941763
$452$	−11.0000	−	11.0000i	−0.517396	−	0.517396i
$453$		0			0
$454$	−24.0000			−1.12638
$455$	−16.0000	−	28.0000i	−0.750092	−	1.31266i
$456$		0			0
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	9.00000	+	9.00000i	0.420542	+	0.420542i
$459$		0			0
$460$	6.00000	+	18.0000i	0.279751	+	0.839254i
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	−0.915237	−	0.402916i	$-0.867997\pi$
$461$	−11.0000	+	11.0000i	−0.512321	+	0.512321i	0.402916	+	0.915237i	$0.367997\pi$
$462$		0			0
$463$			12.0000i			0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$			12.0000i			0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$		0			0
$465$		0			0
$466$	7.00000	+	7.00000i	0.324269	+	0.324269i
$467$	12.0000	+	12.0000i	0.555294	+	0.555294i	0.927964	−	0.372670i	$-0.121558\pi$
$467$	12.0000	+	12.0000i	0.555294	+	0.555294i	−0.372670	+	0.927964i	$0.621558\pi$
$468$		0			0
$469$		−	32.0000i		−	1.47762i
$470$		0			0
$471$		0			0
$472$	6.00000	+	6.00000i	0.276172	+	0.276172i
$473$	−16.0000			−0.735681
$474$		0			0
$475$	2.00000	−	14.0000i	0.0917663	−	0.642364i
$476$	4.00000	+	4.00000i	0.183340	+	0.183340i
$477$		0			0
$478$	−12.0000	+	12.0000i	−0.548867	+	0.548867i
$479$	8.00000	−	8.00000i	0.365529	−	0.365529i	−0.500314	−	0.865844i	$-0.666782\pi$
$479$	8.00000	−	8.00000i	0.365529	−	0.365529i	0.865844	+	0.500314i	$0.166782\pi$
$480$		0			0
$481$	12.0000	−	18.0000i	0.547153	−	0.820729i
$482$	13.0000	−	13.0000i	0.592134	−	0.592134i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	4.00000	+	2.00000i	0.181631	+	0.0908153i
$486$		0			0
$487$			32.0000i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$487$			32.0000i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$488$		−	24.0000i		−	1.08643i
$489$		0			0
$490$	−18.0000	−	9.00000i	−0.813157	−	0.406579i
$491$		−	32.0000i		−	1.44414i	−0.691820	−	0.722070i	$-0.743191\pi$
$491$		−	32.0000i		−	1.44414i	0.691820	−	0.722070i	$-0.256809\pi$
$492$		0			0
$493$		0			0
$494$	−2.00000	−	10.0000i	−0.0899843	−	0.449921i
$495$		0			0
$496$	4.00000	−	4.00000i	0.179605	−	0.179605i
$497$	32.0000	−	32.0000i	1.43540	−	1.43540i
$498$		0			0
$499$	18.0000	+	18.0000i	0.805791	+	0.805791i	0.983994	−	0.178203i	$-0.0570284\pi$
$499$	18.0000	+	18.0000i	0.805791	+	0.805791i	−0.178203	+	0.983994i	$0.557028\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$		0			0
$502$	−28.0000			−1.24970
$503$	6.00000	+	6.00000i	0.267527	+	0.267527i	0.828103	−	0.560576i	$-0.189420\pi$
$503$	6.00000	+	6.00000i	0.267527	+	0.267527i	−0.560576	+	0.828103i	$0.689420\pi$
$504$		0			0
$505$	12.0000	+	6.00000i	0.533993	+	0.266996i
$506$		−	24.0000i		−	1.06693i
$507$		0			0
$508$	−6.00000	−	6.00000i	−0.266207	−	0.266207i
$509$	−23.0000	−	23.0000i	−1.01946	−	1.01946i	−0.999807	−	0.0196502i	$-0.993745\pi$
$509$	−23.0000	−	23.0000i	−1.01946	−	1.01946i	−0.0196502	−	0.999807i	$-0.506255\pi$
$510$		0			0
$511$		−	16.0000i		−	0.707798i
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$	5.00000	−	5.00000i	0.220541	−	0.220541i
$515$	14.0000	+	42.0000i	0.616914	+	1.85074i
$516$		0			0
$517$		0			0
$518$		−	24.0000i		−	1.05450i
$519$		0			0
$520$	21.0000	−	12.0000i	0.920911	−	0.526235i
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$	12.0000	+	12.0000i	0.524723	+	0.524723i	0.918994	−	0.394271i	$-0.129003\pi$
$523$	12.0000	+	12.0000i	0.524723	+	0.524723i	−0.394271	+	0.918994i	$0.629003\pi$
$524$	−16.0000			−0.698963
$525$		0			0
$526$	10.0000	−	10.0000i	0.436021	−	0.436021i
$527$	−8.00000			−0.348485
$528$		0			0
$529$		−	49.0000i		−	2.13043i
$530$	−7.00000	−	21.0000i	−0.304061	−	0.912182i
$531$		0			0
$532$	8.00000	+	8.00000i	0.346844	+	0.346844i
$533$	−5.00000	−	25.0000i	−0.216574	−	1.08287i
$534$		0			0
$535$	8.00000	+	24.0000i	0.345870	+	1.03761i
$536$	24.0000			1.03664
$537$		0			0
$538$	−18.0000			−0.776035
$539$	−18.0000	−	18.0000i	−0.775315	−	0.775315i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$		0			0
$543$		0			0
$544$	−5.00000	+	5.00000i	−0.214373	+	0.214373i
$545$	−27.0000	+	9.00000i	−1.15655	+	0.385518i
$546$		0			0
$547$	12.0000	−	12.0000i	0.513083	−	0.513083i	−0.402387	−	0.915470i	$-0.631819\pi$
$547$	12.0000	−	12.0000i	0.513083	−	0.513083i	0.915470	+	0.402387i	$0.131819\pi$
$548$	22.0000			0.939793
$549$		0			0
$550$	−14.0000	−	2.00000i	−0.596962	−	0.0852803i
$551$		0			0
$552$		0			0
$553$			32.0000i			1.36078i
$554$	−3.00000	+	3.00000i	−0.127458	+	0.127458i
$555$		0			0
$556$		−	16.0000i		−	0.678551i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	4.00000	+	20.0000i	0.169182	+	0.845910i
$560$	4.00000	−	8.00000i	0.169031	−	0.338062i
$561$		0			0
$562$	13.0000	−	13.0000i	0.548372	−	0.548372i
$563$	−24.0000	+	24.0000i	−1.01148	+	1.01148i	−0.0115461	+	0.999933i	$0.503675\pi$
$563$	−24.0000	+	24.0000i	−1.01148	+	1.01148i	−0.999933	+	0.0115461i	$0.996325\pi$
$564$		0			0
$565$	33.0000	−	11.0000i	1.38832	−	0.462773i
$566$		0			0
$567$		0			0
$568$	24.0000	+	24.0000i	1.00702	+	1.00702i
$569$	42.0000			1.76073			0.880366	−	0.474295i	$-0.157297\pi$
$569$	42.0000			1.76073			0.880366	+	0.474295i	$0.157297\pi$
$570$		0			0
$571$		−	12.0000i		−	0.502184i	−0.967963	−	0.251092i	$-0.919210\pi$
$571$		−	12.0000i		−	0.502184i	0.967963	−	0.251092i	$-0.0807897\pi$
$572$	10.0000	−	2.00000i	0.418121	−	0.0836242i
$573$		0			0
$574$	−20.0000	−	20.0000i	−0.834784	−	0.834784i
$575$	−42.0000	−	6.00000i	−1.75152	−	0.250217i
$576$		0			0
$577$			44.0000i			1.83174i	0.401470	+	0.915872i	$0.368499\pi$
$577$			44.0000i			1.83174i	−0.401470	+	0.915872i	$0.631501\pi$
$578$	15.0000			0.623918
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		−	28.0000i		−	1.15964i
$584$	12.0000			0.496564
$585$		0			0
$586$	−18.0000			−0.743573
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$	−6.00000	+	2.00000i	−0.247016	+	0.0823387i
$591$		0			0
$592$	6.00000			0.246598
$593$		−	4.00000i		−	0.164260i	−0.996622	−	0.0821302i	$-0.973828\pi$
$593$		−	4.00000i		−	0.164260i	0.996622	−	0.0821302i	$-0.0261723\pi$
$594$		0			0
$595$	−12.0000	+	4.00000i	−0.491952	+	0.163984i
$596$	−15.0000	−	15.0000i	−0.614424	−	0.614424i
$597$		0			0
$598$	−30.0000	+	6.00000i	−1.22679	+	0.245358i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$	16.0000	+	16.0000i	0.652111	+	0.652111i
$603$		0			0
$604$	4.00000	+	4.00000i	0.162758	+	0.162758i
$605$	6.00000	+	3.00000i	0.243935	+	0.121967i
$606$		0			0
$607$	14.0000	−	14.0000i	0.568242	−	0.568242i	−0.363393	−	0.931636i	$-0.618382\pi$
$607$	14.0000	−	14.0000i	0.568242	−	0.568242i	0.931636	+	0.363393i	$0.118382\pi$
$608$	−10.0000	+	10.0000i	−0.405554	+	0.405554i
$609$		0			0
$610$	16.0000	+	8.00000i	0.647821	+	0.323911i
$611$		0			0
$612$		0			0
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$		−	12.0000i		−	0.484281i
$615$		0			0
$616$	24.0000	−	24.0000i	0.966988	−	0.966988i
$617$		−	4.00000i		−	0.161034i	−0.996753	−	0.0805170i	$-0.974343\pi$
$617$		−	4.00000i		−	0.161034i	0.996753	−	0.0805170i	$-0.0256571\pi$
$618$		0			0
$619$	14.0000	−	14.0000i	0.562708	−	0.562708i	−0.367368	−	0.930076i	$-0.619741\pi$
$619$	14.0000	−	14.0000i	0.562708	−	0.562708i	0.930076	+	0.367368i	$0.119741\pi$
$620$	−4.00000	−	12.0000i	−0.160644	−	0.481932i
$621$		0			0
$622$	12.0000			0.481156
$623$	20.0000	−	20.0000i	0.801283	−	0.801283i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−9.00000	+	9.00000i	−0.359712	+	0.359712i
$627$		0			0
$628$	7.00000	−	7.00000i	0.279330	−	0.279330i
$629$	−6.00000	−	6.00000i	−0.239236	−	0.239236i
$630$		0			0
$631$	−16.0000	−	16.0000i	−0.636950	−	0.636950i	0.312852	−	0.949802i	$-0.398716\pi$
$631$	−16.0000	−	16.0000i	−0.636950	−	0.636950i	−0.949802	+	0.312852i	$0.898716\pi$
$632$	−24.0000			−0.954669
$633$		0			0
$634$	26.0000			1.03259
$635$	18.0000	−	6.00000i	0.714308	−	0.238103i
$636$		0			0
$637$	−18.0000	+	27.0000i	−0.713186	+	1.06978i
$638$		0			0
$639$		0			0
$640$	−6.00000	−	3.00000i	−0.237171	−	0.118585i
$641$			18.0000i			0.710957i	0.934684	+	0.355479i	$0.115682\pi$
$641$			18.0000i			0.710957i	−0.934684	+	0.355479i	$0.884318\pi$
$642$		0			0
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$	24.0000	−	24.0000i	0.945732	−	0.945732i
$645$		0			0
$646$	−4.00000			−0.157378
$647$	−14.0000	−	14.0000i	−0.550397	−	0.550397i	0.376159	−	0.926555i	$-0.377245\pi$
$647$	−14.0000	−	14.0000i	−0.550397	−	0.550397i	−0.926555	+	0.376159i	$0.877245\pi$
$648$		0			0
$649$	−8.00000			−0.314027
$650$	1.00000	+	18.0000i	0.0392232	+	0.706018i
$651$		0			0
$652$			4.00000i			0.156652i
$653$	17.0000	+	17.0000i	0.665261	+	0.665261i	0.956615	−	0.291354i	$-0.0941057\pi$
$653$	17.0000	+	17.0000i	0.665261	+	0.665261i	−0.291354	+	0.956615i	$0.594106\pi$
$654$		0			0
$655$	16.0000	−	32.0000i	0.625172	−	1.25034i
$656$	5.00000	−	5.00000i	0.195217	−	0.195217i
$657$		0			0
$658$		0			0
$659$			8.00000i			0.311636i	0.987786	+	0.155818i	$0.0498013\pi$
$659$			8.00000i			0.311636i	−0.987786	+	0.155818i	$0.950199\pi$
$660$		0			0
$661$	−31.0000	−	31.0000i	−1.20576	−	1.20576i	−0.972387	−	0.233373i	$-0.925024\pi$
$661$	−31.0000	−	31.0000i	−1.20576	−	1.20576i	−0.233373	−	0.972387i	$-0.574976\pi$
$662$	−6.00000	−	6.00000i	−0.233197	−	0.233197i
$663$		0			0
$664$		0			0
$665$	−24.0000	+	8.00000i	−0.930680	+	0.310227i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−8.00000	+	16.0000i	−0.309067	+	0.618134i
$671$	16.0000	+	16.0000i	0.617673	+	0.617673i
$672$		0			0
$673$	−33.0000	+	33.0000i	−1.27206	+	1.27206i	−0.327049	+	0.945007i	$0.606054\pi$
$673$	−33.0000	+	33.0000i	−1.27206	+	1.27206i	−0.945007	+	0.327049i	$0.893946\pi$
$674$	1.00000	−	1.00000i	0.0385186	−	0.0385186i
$675$		0			0
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	−1.00000	+	1.00000i	−0.0384331	+	0.0384331i	−0.726062	−	0.687629i	$-0.758652\pi$
$677$	−1.00000	+	1.00000i	−0.0384331	+	0.0384331i	0.687629	+	0.726062i	$0.258652\pi$
$678$		0			0
$679$		−	8.00000i		−	0.307012i
$680$	−3.00000	−	9.00000i	−0.115045	−	0.345134i
$681$		0			0
$682$			16.0000i			0.612672i
$683$			24.0000i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$			24.0000i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$		0			0
$685$	−22.0000	+	44.0000i	−0.840577	+	1.68115i
$686$			8.00000i			0.305441i
$687$		0			0
$688$	−4.00000	+	4.00000i	−0.152499	+	0.152499i
$689$	−35.0000	+	7.00000i	−1.33339	+	0.266679i
$690$		0			0
$691$	−30.0000	+	30.0000i	−1.14125	+	1.14125i	−0.153033	+	0.988221i	$0.548904\pi$
$691$	−30.0000	+	30.0000i	−1.14125	+	1.14125i	−0.988221	+	0.153033i	$0.951096\pi$
$692$	7.00000	−	7.00000i	0.266100	−	0.266100i
$693$		0			0
$694$	−24.0000	−	24.0000i	−0.911028	−	0.911028i
$695$	32.0000	+	16.0000i	1.21383	+	0.606915i
$696$		0			0
$697$	−10.0000			−0.378777
$698$	−3.00000	−	3.00000i	−0.113552	−	0.113552i
$699$		0			0
$700$	−12.0000	−	16.0000i	−0.453557	−	0.604743i
$701$			18.0000i			0.679851i	0.940452	+	0.339925i	$0.110402\pi$
$701$			18.0000i			0.679851i	−0.940452	+	0.339925i	$0.889598\pi$
$702$		0			0
$703$	−12.0000	−	12.0000i	−0.452589	−	0.452589i
$704$	14.0000	+	14.0000i	0.527645	+	0.527645i
$705$		0			0
$706$		−	36.0000i		−	1.35488i
$707$		−	24.0000i		−	0.902613i
$708$		0			0
$709$	1.00000	−	1.00000i	0.0375558	−	0.0375558i	−0.688080	−	0.725635i	$-0.741546\pi$
$709$	1.00000	−	1.00000i	0.0375558	−	0.0375558i	0.725635	+	0.688080i	$0.241546\pi$
$710$	−24.0000	+	8.00000i	−0.900704	+	0.300235i
$711$		0			0
$712$	15.0000	+	15.0000i	0.562149	+	0.562149i
$713$			48.0000i			1.79761i
$714$		0			0
$715$	−6.00000	+	22.0000i	−0.224387	+	0.822753i
$716$	−8.00000			−0.298974
$717$		0			0
$718$	4.00000	+	4.00000i	0.149279	+	0.149279i
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$	56.0000	−	56.0000i	2.08555	−	2.08555i
$722$	11.0000			0.409378
$723$		0			0
$724$			22.0000i			0.817624i
$725$		0			0
$726$		0			0
$727$	−22.0000	−	22.0000i	−0.815935	−	0.815935i	0.169581	−	0.985516i	$-0.445758\pi$
$727$	−22.0000	−	22.0000i	−0.815935	−	0.815935i	−0.985516	+	0.169581i	$0.945758\pi$
$728$	−36.0000	−	24.0000i	−1.33425	−	0.889499i
$729$		0			0
$730$	−4.00000	+	8.00000i	−0.148047	+	0.296093i
$731$	8.00000			0.295891
$732$		0			0
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$	−10.0000	−	10.0000i	−0.369107	−	0.369107i
$735$		0			0
$736$	30.0000	+	30.0000i	1.10581	+	1.10581i
$737$	−16.0000	+	16.0000i	−0.589368	+	0.589368i
$738$		0			0
$739$	6.00000	−	6.00000i	0.220714	−	0.220714i	−0.588085	−	0.808799i	$-0.700118\pi$
$739$	6.00000	−	6.00000i	0.220714	−	0.220714i	0.808799	+	0.588085i	$0.200118\pi$
$740$	6.00000	−	12.0000i	0.220564	−	0.441129i
$741$		0			0
$742$	−28.0000	+	28.0000i	−1.02791	+	1.02791i
$743$	44.0000			1.61420			0.807102	−	0.590412i	$-0.201035\pi$
$743$	44.0000			1.61420			0.807102	+	0.590412i	$0.201035\pi$
$744$		0			0
$745$	45.0000	−	15.0000i	1.64867	−	0.549557i
$746$	−3.00000	+	3.00000i	−0.109838	+	0.109838i
$747$		0			0
$748$		−	4.00000i		−	0.146254i
$749$	32.0000	−	32.0000i	1.16925	−	1.16925i
$750$		0			0
$751$			4.00000i			0.145962i	0.997333	+	0.0729810i	$0.0232513\pi$
$751$			4.00000i			0.145962i	−0.997333	+	0.0729810i	$0.976749\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.0000	+	4.00000i	−0.436725	+	0.145575i
$756$		0			0
$757$	25.0000	−	25.0000i	0.908640	−	0.908640i	−0.0875221	−	0.996163i	$-0.527895\pi$
$757$	25.0000	−	25.0000i	0.908640	−	0.908640i	0.996163	+	0.0875221i	$0.0278948\pi$
$758$	14.0000	−	14.0000i	0.508503	−	0.508503i
$759$		0			0
$760$	−6.00000	−	18.0000i	−0.217643	−	0.652929i
$761$	−23.0000	−	23.0000i	−0.833749	−	0.833749i	0.154278	−	0.988027i	$-0.450695\pi$
$761$	−23.0000	−	23.0000i	−0.833749	−	0.833749i	−0.988027	+	0.154278i	$0.950695\pi$
$762$		0			0
$763$	36.0000	+	36.0000i	1.30329	+	1.30329i
$764$	−20.0000			−0.723575
$765$		0			0
$766$		−	12.0000i		−	0.433578i
$767$	2.00000	+	10.0000i	0.0722158	+	0.361079i
$768$		0			0
$769$	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	$0.725627\pi$
$770$	8.00000	+	24.0000i	0.288300	+	0.864900i
$771$		0			0
$772$			18.0000i			0.647834i
$773$	20.0000			0.719350			0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000			0.719350			0.359675	+	0.933078i	$0.382888\pi$
$774$		0			0
$775$	28.0000	+	4.00000i	1.00579	+	0.143684i
$776$	6.00000			0.215387
$777$		0			0
$778$		−	24.0000i		−	0.860442i
$779$	−20.0000			−0.716574
$780$		0			0
$781$	−32.0000			−1.14505
$782$			12.0000i			0.429119i
$783$		0			0
$784$	−9.00000			−0.321429
$785$	7.00000	+	21.0000i	0.249841	+	0.749522i
$786$		0			0
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$			12.0000i			0.427482i
$789$		0			0
$790$	8.00000	−	16.0000i	0.284627	−	0.569254i
$791$	−44.0000	−	44.0000i	−1.56446	−	1.56446i
$792$		0			0
$793$	16.0000	−	24.0000i	0.568177	−	0.852265i
$794$			22.0000i			0.780751i
$795$		0			0
$796$	20.0000			0.708881
$797$	5.00000	+	5.00000i	0.177109	+	0.177109i	0.790094	−	0.612985i	$-0.210032\pi$
$797$	5.00000	+	5.00000i	0.177109	+	0.177109i	−0.612985	+	0.790094i	$0.710032\pi$
$798$		0			0
$799$		0			0
$800$	20.0000	−	15.0000i	0.707107	−	0.530330i
$801$		0			0
$802$	−5.00000	+	5.00000i	−0.176556	+	0.176556i
$803$	−8.00000	+	8.00000i	−0.282314	+	0.282314i
$804$		0			0
$805$	24.0000	+	72.0000i	0.845889	+	2.53767i
$806$	20.0000	−	4.00000i	0.704470	−	0.140894i
$807$		0			0
$808$	18.0000			0.633238
$809$			16.0000i			0.562530i	0.959630	+	0.281265i	$0.0907540\pi$
$809$			16.0000i			0.562530i	−0.959630	+	0.281265i	$0.909246\pi$
$810$		0			0
$811$	−18.0000	+	18.0000i	−0.632065	+	0.632065i	−0.948586	−	0.316520i	$-0.897485\pi$
$811$	−18.0000	+	18.0000i	−0.632065	+	0.632065i	0.316520	+	0.948586i	$0.397485\pi$
$812$		0			0
$813$		0			0
$814$	−12.0000	+	12.0000i	−0.420600	+	0.420600i
$815$	−8.00000	−	4.00000i	−0.280228	−	0.140114i
$816$		0			0
$817$	16.0000			0.559769
$818$	−13.0000	+	13.0000i	−0.454534	+	0.454534i
$819$		0			0
$820$	−5.00000	−	15.0000i	−0.174608	−	0.523823i
$821$	−27.0000	+	27.0000i	−0.942306	+	0.942306i	−0.998424	−	0.0561177i	$-0.982128\pi$
$821$	−27.0000	+	27.0000i	−0.942306	+	0.942306i	0.0561177	+	0.998424i	$0.482128\pi$
$822$		0			0
$823$	−18.0000	+	18.0000i	−0.627441	+	0.627441i	−0.947423	−	0.319983i	$-0.896323\pi$
$823$	−18.0000	+	18.0000i	−0.627441	+	0.627441i	0.319983	+	0.947423i	$0.396323\pi$
$824$	42.0000	+	42.0000i	1.46314	+	1.46314i
$825$		0			0
$826$	8.00000	+	8.00000i	0.278356	+	0.278356i
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$		0			0
$829$	−16.0000			−0.555703			−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000			−0.555703			−0.277851	+	0.960624i	$0.589622\pi$
$830$		0			0
$831$		0			0
$832$	14.0000	−	21.0000i	0.485363	−	0.728044i
$833$	9.00000	+	9.00000i	0.311832	+	0.311832i
$834$		0			0
$835$		0			0
$836$		−	8.00000i		−	0.276686i
$837$		0			0
$838$	−16.0000			−0.552711
$839$	−32.0000	+	32.0000i	−1.10476	+	1.10476i	−0.110935	+	0.993828i	$0.535385\pi$
$839$	−32.0000	+	32.0000i	−1.10476	+	1.10476i	−0.993828	+	0.110935i	$0.964615\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$	7.00000	+	7.00000i	0.241236	+	0.241236i
$843$		0			0
$844$	−20.0000			−0.688428
$845$	29.0000	+	2.00000i	0.997630	+	0.0688021i
$846$		0			0
$847$		−	12.0000i		−	0.412325i
$848$	−7.00000	−	7.00000i	−0.240381	−	0.240381i
$849$		0			0
$850$	7.00000	+	1.00000i	0.240098	+	0.0342997i
$851$	−36.0000	+	36.0000i	−1.23406	+	1.23406i
$852$		0			0
$853$		−	28.0000i		−	0.958702i	−0.877623	−	0.479351i	$-0.840872\pi$
$853$		−	28.0000i		−	0.958702i	0.877623	−	0.479351i	$-0.159128\pi$
$854$		−	32.0000i		−	1.09502i
$855$		0			0
$856$	24.0000	+	24.0000i	0.820303	+	0.820303i
$857$	9.00000	+	9.00000i	0.307434	+	0.307434i	0.843913	−	0.536479i	$-0.180246\pi$
$857$	9.00000	+	9.00000i	0.307434	+	0.307434i	−0.536479	+	0.843913i	$0.680246\pi$
$858$		0			0
$859$		−	36.0000i		−	1.22830i	−0.789188	−	0.614152i	$-0.789498\pi$
$859$		−	36.0000i		−	1.22830i	0.789188	−	0.614152i	$-0.210502\pi$
$860$	4.00000	+	12.0000i	0.136399	+	0.409197i
$861$		0			0
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	7.00000	+	21.0000i	0.238007	+	0.714021i
$866$	−5.00000	−	5.00000i	−0.169907	−	0.169907i
$867$		0			0
$868$	−16.0000	+	16.0000i	−0.543075	+	0.543075i
$869$	16.0000	−	16.0000i	0.542763	−	0.542763i
$870$		0			0
$871$	24.0000	+	16.0000i	0.813209	+	0.542139i
$872$	−27.0000	+	27.0000i	−0.914335	+	0.914335i
$873$		0			0
$874$			24.0000i			0.811812i
$875$	44.0000	−	8.00000i	1.48747	−	0.270449i
$876$		0			0
$877$		−	14.0000i		−	0.472746i	−0.971662	−	0.236373i	$-0.924041\pi$
$877$		−	14.0000i		−	0.472746i	0.971662	−	0.236373i	$-0.0759588\pi$
$878$		0			0
$879$		0			0
$880$	−6.00000	+	2.00000i	−0.202260	+	0.0674200i
$881$			40.0000i			1.34763i	0.738898	+	0.673817i	$0.235346\pi$
$881$			40.0000i			1.34763i	−0.738898	+	0.673817i	$0.764654\pi$
$882$		0			0
$883$	24.0000	−	24.0000i	0.807664	−	0.807664i	−0.176616	−	0.984280i	$-0.556515\pi$
$883$	24.0000	−	24.0000i	0.807664	−	0.807664i	0.984280	+	0.176616i	$0.0565149\pi$
$884$	−5.00000	+	1.00000i	−0.168168	+	0.0336336i
$885$		0			0
$886$	−8.00000	+	8.00000i	−0.268765	+	0.268765i
$887$	−14.0000	+	14.0000i	−0.470074	+	0.470074i	−0.901938	−	0.431865i	$-0.857856\pi$
$887$	−14.0000	+	14.0000i	−0.470074	+	0.470074i	0.431865	+	0.901938i	$0.357856\pi$
$888$		0			0
$889$	−24.0000	−	24.0000i	−0.804934	−	0.804934i
$890$	−15.0000	+	5.00000i	−0.502801	+	0.167600i
$891$		0			0
$892$	8.00000			0.267860
$893$		0			0
$894$		0			0
$895$	8.00000	−	16.0000i	0.267411	−	0.534821i
$896$			12.0000i			0.400892i
$897$		0			0
$898$	3.00000	+	3.00000i	0.100111	+	0.100111i
$899$		0			0
$900$		0			0
$901$			14.0000i			0.466408i
$902$			20.0000i			0.665927i
$903$		0			0
$904$	33.0000	−	33.0000i	1.09756	−	1.09756i
$905$	−44.0000	−	22.0000i	−1.46261	−	0.731305i
$906$		0			0
$907$	−12.0000	−	12.0000i	−0.398453	−	0.398453i	0.479234	−	0.877687i	$-0.340915\pi$
$907$	−12.0000	−	12.0000i	−0.398453	−	0.398453i	−0.877687	+	0.479234i	$0.840915\pi$
$908$			24.0000i			0.796468i
$909$		0			0
$910$	28.0000	−	16.0000i	0.928191	−	0.530395i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		0			0
$914$	−10.0000			−0.330771
$915$		0			0
$916$	9.00000	−	9.00000i	0.297368	−	0.297368i
$917$	−64.0000			−2.11347
$918$		0			0
$919$			4.00000i			0.131948i	0.997821	+	0.0659739i	$0.0210154\pi$
$919$			4.00000i			0.131948i	−0.997821	+	0.0659739i	$0.978985\pi$
$920$	−54.0000	+	18.0000i	−1.78033	+	0.593442i
$921$		0			0
$922$	−11.0000	−	11.0000i	−0.362266	−	0.362266i
$923$	8.00000	+	40.0000i	0.263323	+	1.31662i
$924$		0			0
$925$	18.0000	+	24.0000i	0.591836	+	0.789115i
$926$	−12.0000			−0.394344
$927$		0			0
$928$		0			0
$929$	5.00000	+	5.00000i	0.164045	+	0.164045i	0.784356	−	0.620311i	$-0.212994\pi$
$929$	5.00000	+	5.00000i	0.164045	+	0.164045i	−0.620311	+	0.784356i	$0.712994\pi$
$930$		0			0
$931$	18.0000	+	18.0000i	0.589926	+	0.589926i
$932$	7.00000	−	7.00000i	0.229293	−	0.229293i
$933$		0			0
$934$	−12.0000	+	12.0000i	−0.392652	+	0.392652i
$935$	8.00000	+	4.00000i	0.261628	+	0.130814i
$936$		0			0
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	−0.945711	−	0.325008i	$-0.894633\pi$
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	0.325008	+	0.945711i	$0.394633\pi$
$938$	32.0000			1.04484
$939$		0			0
$940$		0			0
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	−0.276448	−	0.961029i	$-0.589157\pi$
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	0.961029	+	0.276448i	$0.0891575\pi$
$942$		0			0
$943$			60.0000i			1.95387i
$944$	−2.00000	+	2.00000i	−0.0650945	+	0.0650945i
$945$		0			0
$946$		−	16.0000i		−	0.520205i
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	12.0000	+	8.00000i	0.389536	+	0.259691i
$950$	14.0000	+	2.00000i	0.454220	+	0.0648886i
$951$		0			0
$952$	−12.0000	+	12.0000i	−0.388922	+	0.388922i
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.00419731	−	0.999991i	$-0.498664\pi$
$953$	31.0000	−	31.0000i	1.00419	−	1.00419i	0.999991	−	0.00419731i	$-0.00133605\pi$
$954$		0			0
$955$	20.0000	−	40.0000i	0.647185	−	1.29437i
$956$	12.0000	+	12.0000i	0.388108	+	0.388108i
$957$		0			0
$958$	8.00000	+	8.00000i	0.258468	+	0.258468i
$959$	88.0000			2.84167
$960$		0			0
$961$		−	1.00000i		−	0.0322581i
$962$	18.0000	+	12.0000i	0.580343	+	0.386896i
$963$		0			0
$964$	−13.0000	−	13.0000i	−0.418702	−	0.418702i
$965$	−36.0000	−	18.0000i	−1.15888	−	0.579441i
$966$		0			0
$967$			12.0000i			0.385894i	0.981209	+	0.192947i	$0.0618045\pi$
$967$			12.0000i			0.385894i	−0.981209	+	0.192947i	$0.938195\pi$
$968$	9.00000			0.289271
$969$		0			0
$970$	−2.00000	+	4.00000i	−0.0642161	+	0.128432i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$		0			0
$973$		−	64.0000i		−	2.05175i
$974$	−32.0000			−1.02535
$975$		0			0
$976$	8.00000			0.256074
$977$		−	34.0000i		−	1.08776i	−0.839164	−	0.543878i	$-0.816955\pi$
$977$		−	34.0000i		−	1.08776i	0.839164	−	0.543878i	$-0.183045\pi$
$978$		0			0
$979$	−20.0000			−0.639203
$980$	−9.00000	+	18.0000i	−0.287494	+	0.574989i
$981$		0			0
$982$	32.0000			1.02116
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$		0			0
$985$	−24.0000	−	12.0000i	−0.764704	−	0.382352i
$986$		0			0
$987$		0			0
$988$	−10.0000	+	2.00000i	−0.318142	+	0.0636285i
$989$		−	48.0000i		−	1.52631i
$990$		0			0
$991$	−12.0000			−0.381193			−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000			−0.381193			−0.190596	+	0.981669i	$0.561042\pi$
$992$	−20.0000	−	20.0000i	−0.635001	−	0.635001i
$993$		0			0
$994$	32.0000	+	32.0000i	1.01498	+	1.01498i
$995$	−20.0000	+	40.0000i	−0.634043	+	1.26809i
$996$		0			0
$997$	9.00000	−	9.00000i	0.285033	−	0.285033i	−0.550079	−	0.835112i	$-0.685403\pi$
$997$	9.00000	−	9.00000i	0.285033	−	0.285033i	0.835112	+	0.550079i	$0.185403\pi$
$998$	−18.0000	+	18.0000i	−0.569780	+	0.569780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.n.a.343.1	yes	2
3.2	odd	2		585.2.n.b.343.1	yes	2
5.2	odd	4		585.2.w.a.577.1	yes	2
13.8	odd	4		585.2.w.a.73.1	yes	2
15.2	even	4		585.2.w.c.577.1	yes	2
39.8	even	4		585.2.w.c.73.1	yes	2
65.47	even	4	inner	585.2.n.a.307.1	✓	2
195.47	odd	4		585.2.n.b.307.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.n.a.307.1	✓	2	65.47	even	4	inner
585.2.n.a.343.1	yes	2	1.1	even	1	trivial
585.2.n.b.307.1	yes	2	195.47	odd	4
585.2.n.b.343.1	yes	2	3.2	odd	2
585.2.w.a.73.1	yes	2	13.8	odd	4
585.2.w.a.577.1	yes	2	5.2	odd	4
585.2.w.c.73.1	yes	2	39.8	even	4
585.2.w.c.577.1	yes	2	15.2	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +4.00000 q^{7} +3.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +4.00000 q^{7} +3.00000i q^{8} +(-2.00000 - 1.00000i) q^{10} +(-2.00000 - 2.00000i) q^{11} +(-2.00000 + 3.00000i) q^{13} +4.00000i q^{14} -1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +(2.00000 + 2.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(2.00000 - 2.00000i) q^{22} +(6.00000 - 6.00000i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(-3.00000 - 2.00000i) q^{26} +4.00000 q^{28} +(-4.00000 + 4.00000i) q^{31} +5.00000i q^{32} +(-1.00000 + 1.00000i) q^{34} +(-4.00000 + 8.00000i) q^{35} -6.00000 q^{37} +(-2.00000 + 2.00000i) q^{38} +(-6.00000 - 3.00000i) q^{40} +(-5.00000 + 5.00000i) q^{41} +(4.00000 - 4.00000i) q^{43} +(-2.00000 - 2.00000i) q^{44} +(6.00000 + 6.00000i) q^{46} +9.00000 q^{49} +(4.00000 - 3.00000i) q^{50} +(-2.00000 + 3.00000i) q^{52} +(7.00000 + 7.00000i) q^{53} +(6.00000 - 2.00000i) q^{55} +12.0000i q^{56} +(2.00000 - 2.00000i) q^{59} -8.00000 q^{61} +(-4.00000 - 4.00000i) q^{62} -7.00000 q^{64} +(-4.00000 - 7.00000i) q^{65} -8.00000i q^{67} +(1.00000 + 1.00000i) q^{68} +(-8.00000 - 4.00000i) q^{70} +(8.00000 - 8.00000i) q^{71} -4.00000i q^{73} -6.00000i q^{74} +(2.00000 + 2.00000i) q^{76} +(-8.00000 - 8.00000i) q^{77} +8.00000i q^{79} +(1.00000 - 2.00000i) q^{80} +(-5.00000 - 5.00000i) q^{82} +(-3.00000 + 1.00000i) q^{85} +(4.00000 + 4.00000i) q^{86} +(6.00000 - 6.00000i) q^{88} +(5.00000 - 5.00000i) q^{89} +(-8.00000 + 12.0000i) q^{91} +(6.00000 - 6.00000i) q^{92} +(-6.00000 + 2.00000i) q^{95} -2.00000i q^{97} +9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 2 q^{5} + 8 q^{7}+O(q^{10}) \) 2 * q + 2 * q^4 - 2 * q^5 + 8 * q^7	\( 2 q + 2 q^{4} - 2 q^{5} + 8 q^{7} - 4 q^{10} - 4 q^{11} - 4 q^{13} - 2 q^{16} + 2 q^{17} + 4 q^{19} - 2 q^{20} + 4 q^{22} + 12 q^{23} - 6 q^{25} - 6 q^{26} + 8 q^{28} - 8 q^{31} - 2 q^{34} - 8 q^{35} - 12 q^{37} - 4 q^{38} - 12 q^{40} - 10 q^{41} + 8 q^{43} - 4 q^{44} + 12 q^{46} + 18 q^{49} + 8 q^{50} - 4 q^{52} + 14 q^{53} + 12 q^{55} + 4 q^{59} - 16 q^{61} - 8 q^{62} - 14 q^{64} - 8 q^{65} + 2 q^{68} - 16 q^{70} + 16 q^{71} + 4 q^{76} - 16 q^{77} + 2 q^{80} - 10 q^{82} - 6 q^{85} + 8 q^{86} + 12 q^{88} + 10 q^{89} - 16 q^{91} + 12 q^{92} - 12 q^{95}+O(q^{100}) \) 2 * q + 2 * q^4 - 2 * q^5 + 8 * q^7 - 4 * q^10 - 4 * q^11 - 4 * q^13 - 2 * q^16 + 2 * q^17 + 4 * q^19 - 2 * q^20 + 4 * q^22 + 12 * q^23 - 6 * q^25 - 6 * q^26 + 8 * q^28 - 8 * q^31 - 2 * q^34 - 8 * q^35 - 12 * q^37 - 4 * q^38 - 12 * q^40 - 10 * q^41 + 8 * q^43 - 4 * q^44 + 12 * q^46 + 18 * q^49 + 8 * q^50 - 4 * q^52 + 14 * q^53 + 12 * q^55 + 4 * q^59 - 16 * q^61 - 8 * q^62 - 14 * q^64 - 8 * q^65 + 2 * q^68 - 16 * q^70 + 16 * q^71 + 4 * q^76 - 16 * q^77 + 2 * q^80 - 10 * q^82 - 6 * q^85 + 8 * q^86 + 12 * q^88 + 10 * q^89 - 16 * q^91 + 12 * q^92 - 12 * q^95

Introduction

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