LMFDB - Embedded newform 731.2.f.a.302.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (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:	$5.83706438776$
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			302.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	731.302
Dual form			731.2.f.a.259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} -3.00000i q^{8} -3.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} -3.00000i q^{8} -3.00000i q^{9} +(-1.00000 + 1.00000i) q^{10} +(2.00000 - 2.00000i) q^{11} +(2.00000 + 2.00000i) q^{14} -1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -3.00000 q^{18} -8.00000i q^{19} +(-1.00000 - 1.00000i) q^{20} +(-2.00000 - 2.00000i) q^{22} +(-4.00000 + 4.00000i) q^{23} -3.00000i q^{25} +(-2.00000 + 2.00000i) q^{28} +(1.00000 + 1.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} -5.00000i q^{32} +(4.00000 + 1.00000i) q^{34} +4.00000 q^{35} -3.00000i q^{36} +(-5.00000 - 5.00000i) q^{37} -8.00000 q^{38} +(-3.00000 + 3.00000i) q^{40} +(1.00000 - 1.00000i) q^{41} -1.00000i q^{43} +(2.00000 - 2.00000i) q^{44} +(-3.00000 + 3.00000i) q^{45} +(4.00000 + 4.00000i) q^{46} +12.0000 q^{47} -1.00000i q^{49} -3.00000 q^{50} -4.00000 q^{55} +(6.00000 + 6.00000i) q^{56} +(1.00000 - 1.00000i) q^{58} +(7.00000 - 7.00000i) q^{61} +(-4.00000 + 4.00000i) q^{62} +(6.00000 + 6.00000i) q^{63} -7.00000 q^{64} -4.00000 q^{67} +(-1.00000 + 4.00000i) q^{68} -4.00000i q^{70} +(10.0000 + 10.0000i) q^{71} -9.00000 q^{72} +(-9.00000 - 9.00000i) q^{73} +(-5.00000 + 5.00000i) q^{74} -8.00000i q^{76} +8.00000i q^{77} +(-12.0000 + 12.0000i) q^{79} +(1.00000 + 1.00000i) q^{80} -9.00000 q^{81} +(-1.00000 - 1.00000i) q^{82} +4.00000i q^{83} +(5.00000 - 3.00000i) q^{85} -1.00000 q^{86} +(-6.00000 - 6.00000i) q^{88} +12.0000 q^{89} +(3.00000 + 3.00000i) q^{90} +(-4.00000 + 4.00000i) q^{92} -12.0000i q^{94} +(-8.00000 + 8.00000i) q^{95} +(7.00000 + 7.00000i) q^{97} -1.00000 q^{98} +(-6.00000 - 6.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 2 * q + 2 * q^4 - 2 * q^5 - 4 * q^7	$ 2 q + 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{10} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 2 q^{17} - 6 q^{18} - 2 q^{20} - 4 q^{22} - 8 q^{23} - 4 q^{28} + 2 q^{29} - 8 q^{31} + 8 q^{34} + 8 q^{35} - 10 q^{37} - 16 q^{38} - 6 q^{40} + 2 q^{41} + 4 q^{44} - 6 q^{45} + 8 q^{46} + 24 q^{47} - 6 q^{50} - 8 q^{55} + 12 q^{56} + 2 q^{58} + 14 q^{61} - 8 q^{62} + 12 q^{63} - 14 q^{64} - 8 q^{67} - 2 q^{68} + 20 q^{71} - 18 q^{72} - 18 q^{73} - 10 q^{74} - 24 q^{79} + 2 q^{80} - 18 q^{81} - 2 q^{82} + 10 q^{85} - 2 q^{86} - 12 q^{88} + 24 q^{89} + 6 q^{90} - 8 q^{92} - 16 q^{95} + 14 q^{97} - 2 q^{98} - 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^10 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 2 * q^17 - 6 * q^18 - 2 * q^20 - 4 * q^22 - 8 * q^23 - 4 * q^28 + 2 * q^29 - 8 * q^31 + 8 * q^34 + 8 * q^35 - 10 * q^37 - 16 * q^38 - 6 * q^40 + 2 * q^41 + 4 * q^44 - 6 * q^45 + 8 * q^46 + 24 * q^47 - 6 * q^50 - 8 * q^55 + 12 * q^56 + 2 * q^58 + 14 * q^61 - 8 * q^62 + 12 * q^63 - 14 * q^64 - 8 * q^67 - 2 * q^68 + 20 * q^71 - 18 * q^72 - 18 * q^73 - 10 * q^74 - 24 * q^79 + 2 * q^80 - 18 * q^81 - 2 * q^82 + 10 * q^85 - 2 * q^86 - 12 * q^88 + 24 * q^89 + 6 * q^90 - 8 * q^92 - 16 * q^95 + 14 * q^97 - 2 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$3$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$4$	1.00000			0.500000
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	0.447214	−	0.894427i	$-0.352416\pi$
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$		−	3.00000i		−	1.06066i
$9$		−	3.00000i		−	1.00000i
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	−0.338091	−	0.941113i	$-0.609781\pi$
$11$	2.00000	−	2.00000i	0.603023	−	0.603023i	0.941113	+	0.338091i	$0.109781\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.00000	+	2.00000i	0.534522	+	0.534522i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$18$	−3.00000			−0.707107
$19$		−	8.00000i		−	1.83533i	−0.397360	−	0.917663i	$-0.630073\pi$
$19$		−	8.00000i		−	1.83533i	0.397360	−	0.917663i	$-0.369927\pi$
$20$	−1.00000	−	1.00000i	−0.223607	−	0.223607i
$21$		0			0
$22$	−2.00000	−	2.00000i	−0.426401	−	0.426401i
$23$	−4.00000	+	4.00000i	−0.834058	+	0.834058i	−0.988069	−	0.154011i	$-0.950781\pi$
$23$	−4.00000	+	4.00000i	−0.834058	+	0.834058i	0.154011	+	0.988069i	$0.450781\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$		0			0
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	0.793832	−	0.608137i	$-0.208083\pi$
$29$	1.00000	+	1.00000i	0.185695	+	0.185695i	−0.608137	+	0.793832i	$0.708083\pi$
$30$		0			0
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	0.249861	−	0.968282i	$-0.419615\pi$
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	−0.968282	+	0.249861i	$0.919615\pi$
$32$		−	5.00000i		−	0.883883i
$33$		0			0
$34$	4.00000	+	1.00000i	0.685994	+	0.171499i
$35$	4.00000			0.676123
$36$		−	3.00000i		−	0.500000i
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−8.00000			−1.29777
$39$		0			0
$40$	−3.00000	+	3.00000i	−0.474342	+	0.474342i
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	2.00000	−	2.00000i	0.301511	−	0.301511i
$45$	−3.00000	+	3.00000i	−0.447214	+	0.447214i
$46$	4.00000	+	4.00000i	0.589768	+	0.589768i
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−3.00000			−0.424264
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$	6.00000	+	6.00000i	0.801784	+	0.801784i
$57$		0			0
$58$	1.00000	−	1.00000i	0.131306	−	0.131306i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	7.00000	−	7.00000i	0.896258	−	0.896258i	−0.0988447	−	0.995103i	$-0.531515\pi$
$61$	7.00000	−	7.00000i	0.896258	−	0.896258i	0.995103	+	0.0988447i	$0.0315147\pi$
$62$	−4.00000	+	4.00000i	−0.508001	+	0.508001i
$63$	6.00000	+	6.00000i	0.755929	+	0.755929i
$64$	−7.00000			−0.875000
$65$		0			0
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.00000	+	4.00000i	−0.121268	+	0.485071i
$69$		0			0
$70$		−	4.00000i		−	0.478091i
$71$	10.0000	+	10.0000i	1.18678	+	1.18678i	0.977952	+	0.208830i	$0.0669654\pi$
$71$	10.0000	+	10.0000i	1.18678	+	1.18678i	0.208830	+	0.977952i	$0.433035\pi$
$72$	−9.00000			−1.06066
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.998493	−	0.0548772i	$-0.982523\pi$
$73$	−9.00000	−	9.00000i	−1.05337	−	1.05337i	−0.0548772	−	0.998493i	$-0.517477\pi$
$74$	−5.00000	+	5.00000i	−0.581238	+	0.581238i
$75$		0			0
$76$		−	8.00000i		−	0.917663i
$77$			8.00000i			0.911685i
$78$		0			0
$79$	−12.0000	+	12.0000i	−1.35011	+	1.35011i	−0.464568	+	0.885537i	$0.653790\pi$
$79$	−12.0000	+	12.0000i	−1.35011	+	1.35011i	−0.885537	+	0.464568i	$0.846210\pi$
$80$	1.00000	+	1.00000i	0.111803	+	0.111803i
$81$	−9.00000			−1.00000
$82$	−1.00000	−	1.00000i	−0.110432	−	0.110432i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$	5.00000	−	3.00000i	0.542326	−	0.325396i
$86$	−1.00000			−0.107833
$87$		0			0
$88$	−6.00000	−	6.00000i	−0.639602	−	0.639602i
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$	3.00000	+	3.00000i	0.316228	+	0.316228i
$91$		0			0
$92$	−4.00000	+	4.00000i	−0.417029	+	0.417029i
$93$		0			0
$94$		−	12.0000i		−	1.23771i
$95$	−8.00000	+	8.00000i	−0.820783	+	0.820783i
$96$		0			0
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	0.966691	−	0.255948i	$-0.0823876\pi$
$97$	7.00000	+	7.00000i	0.710742	+	0.710742i	−0.255948	+	0.966691i	$0.582388\pi$
$98$	−1.00000			−0.101015
$99$	−6.00000	−	6.00000i	−0.603023	−	0.603023i
$100$		−	3.00000i		−	0.300000i
$101$	16.0000			1.59206			0.796030	−	0.605257i	$-0.206930\pi$
$101$	16.0000			1.59206			0.796030	+	0.605257i	$0.206930\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000	−	6.00000i	−0.580042	−	0.580042i	0.354873	−	0.934915i	$-0.384524\pi$
$107$	−6.00000	−	6.00000i	−0.580042	−	0.580042i	−0.934915	+	0.354873i	$0.884524\pi$
$108$		0			0
$109$	9.00000	−	9.00000i	0.862044	−	0.862044i	−0.129532	−	0.991575i	$-0.541347\pi$
$109$	9.00000	−	9.00000i	0.862044	−	0.862044i	0.991575	+	0.129532i	$0.0413474\pi$
$110$			4.00000i			0.381385i
$111$		0			0
$112$	2.00000	−	2.00000i	0.188982	−	0.188982i
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	−0.431671	−	0.902031i	$-0.642076\pi$
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	0.902031	+	0.431671i	$0.142076\pi$
$114$		0			0
$115$	8.00000			0.746004
$116$	1.00000	+	1.00000i	0.0928477	+	0.0928477i
$117$		0			0
$118$		0			0
$119$	−6.00000	−	10.0000i	−0.550019	−	0.916698i
$120$		0			0
$121$			3.00000i			0.272727i
$122$	−7.00000	−	7.00000i	−0.633750	−	0.633750i
$123$		0			0
$124$	−4.00000	−	4.00000i	−0.359211	−	0.359211i
$125$	−8.00000	+	8.00000i	−0.715542	+	0.715542i
$126$	6.00000	−	6.00000i	0.534522	−	0.534522i
$127$			20.0000i			1.77471i	0.461084	+	0.887357i	$0.347461\pi$
$127$			20.0000i			1.77471i	−0.461084	+	0.887357i	$0.652539\pi$
$128$		−	3.00000i		−	0.265165i
$129$		0			0
$130$		0			0
$131$	8.00000	+	8.00000i	0.698963	+	0.698963i	0.964187	−	0.265224i	$-0.0854458\pi$
$131$	8.00000	+	8.00000i	0.698963	+	0.698963i	−0.265224	+	0.964187i	$0.585446\pi$
$132$		0			0
$133$	16.0000	+	16.0000i	1.38738	+	1.38738i
$134$			4.00000i			0.345547i
$135$		0			0
$136$	12.0000	+	3.00000i	1.02899	+	0.257248i
$137$	−4.00000			−0.341743			−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000			−0.341743			−0.170872	+	0.985293i	$0.554658\pi$
$138$		0			0
$139$	10.0000	+	10.0000i	0.848189	+	0.848189i	0.989907	−	0.141718i	$-0.0452627\pi$
$139$	10.0000	+	10.0000i	0.848189	+	0.848189i	−0.141718	+	0.989907i	$0.545263\pi$
$140$	4.00000			0.338062
$141$		0			0
$142$	10.0000	−	10.0000i	0.839181	−	0.839181i
$143$		0			0
$144$			3.00000i			0.250000i
$145$		−	2.00000i		−	0.166091i
$146$	−9.00000	+	9.00000i	−0.744845	+	0.744845i
$147$		0			0
$148$	−5.00000	−	5.00000i	−0.410997	−	0.410997i
$149$	−18.0000			−1.47462			−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000			−1.47462			−0.737309	+	0.675556i	$0.763904\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−24.0000			−1.94666
$153$	12.0000	+	3.00000i	0.970143	+	0.242536i
$154$	8.00000			0.644658
$155$			8.00000i			0.642575i
$156$		0			0
$157$	6.00000			0.478852			0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000			0.478852			0.239426	+	0.970915i	$0.423041\pi$
$158$	12.0000	+	12.0000i	0.954669	+	0.954669i
$159$		0			0
$160$	−5.00000	+	5.00000i	−0.395285	+	0.395285i
$161$		−	16.0000i		−	1.26098i
$162$			9.00000i			0.707107i
$163$	16.0000	−	16.0000i	1.25322	−	1.25322i	0.298947	−	0.954270i	$-0.403365\pi$
$163$	16.0000	−	16.0000i	1.25322	−	1.25322i	0.954270	−	0.298947i	$-0.0966354\pi$
$164$	1.00000	−	1.00000i	0.0780869	−	0.0780869i
$165$		0			0
$166$	4.00000			0.310460
$167$	16.0000	+	16.0000i	1.23812	+	1.23812i	0.960770	+	0.277347i	$0.0894553\pi$
$167$	16.0000	+	16.0000i	1.23812	+	1.23812i	0.277347	+	0.960770i	$0.410545\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−3.00000	−	5.00000i	−0.230089	−	0.383482i
$171$	−24.0000			−1.83533
$172$		−	1.00000i		−	0.0762493i
$173$	3.00000	+	3.00000i	0.228086	+	0.228086i	0.811893	−	0.583807i	$-0.198437\pi$
$173$	3.00000	+	3.00000i	0.228086	+	0.228086i	−0.583807	+	0.811893i	$0.698437\pi$
$174$		0			0
$175$	6.00000	+	6.00000i	0.453557	+	0.453557i
$176$	−2.00000	+	2.00000i	−0.150756	+	0.150756i
$177$		0			0
$178$		−	12.0000i		−	0.899438i
$179$		−	20.0000i		−	1.49487i	−0.664335	−	0.747435i	$-0.731285\pi$
$179$		−	20.0000i		−	1.49487i	0.664335	−	0.747435i	$-0.268715\pi$
$180$	−3.00000	+	3.00000i	−0.223607	+	0.223607i
$181$	9.00000	−	9.00000i	0.668965	−	0.668965i	−0.288512	−	0.957476i	$-0.593160\pi$
$181$	9.00000	−	9.00000i	0.668965	−	0.668965i	0.957476	+	0.288512i	$0.0931604\pi$
$182$		0			0
$183$		0			0
$184$	12.0000	+	12.0000i	0.884652	+	0.884652i
$185$			10.0000i			0.735215i
$186$		0			0
$187$	6.00000	+	10.0000i	0.438763	+	0.731272i
$188$	12.0000			0.875190
$189$		0			0
$190$	8.00000	+	8.00000i	0.580381	+	0.580381i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	9.00000	−	9.00000i	0.647834	−	0.647834i	−0.304635	−	0.952469i	$-0.598534\pi$
$193$	9.00000	−	9.00000i	0.647834	−	0.647834i	0.952469	+	0.304635i	$0.0985345\pi$
$194$	7.00000	−	7.00000i	0.502571	−	0.502571i
$195$		0			0
$196$		−	1.00000i		−	0.0714286i
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$	−6.00000	+	6.00000i	−0.426401	+	0.426401i
$199$	18.0000	+	18.0000i	1.27599	+	1.27599i	0.942894	+	0.333092i	$0.108092\pi$
$199$	18.0000	+	18.0000i	1.27599	+	1.27599i	0.333092	+	0.942894i	$0.391908\pi$
$200$	−9.00000			−0.636396
$201$		0			0
$202$		−	16.0000i		−	1.12576i
$203$	−4.00000			−0.280745
$204$		0			0
$205$	−2.00000			−0.139686
$206$		−	8.00000i		−	0.557386i
$207$	12.0000	+	12.0000i	0.834058	+	0.834058i
$208$		0			0
$209$	−16.0000	−	16.0000i	−1.10674	−	1.10674i
$210$		0			0
$211$	4.00000	−	4.00000i	0.275371	−	0.275371i	−0.555887	−	0.831258i	$-0.687621\pi$
$211$	4.00000	−	4.00000i	0.275371	−	0.275371i	0.831258	+	0.555887i	$0.187621\pi$
$212$		0			0
$213$		0			0
$214$	−6.00000	+	6.00000i	−0.410152	+	0.410152i
$215$	−1.00000	+	1.00000i	−0.0681994	+	0.0681994i
$216$		0			0
$217$	16.0000			1.08615
$218$	−9.00000	−	9.00000i	−0.609557	−	0.609557i
$219$		0			0
$220$	−4.00000			−0.269680
$221$		0			0
$222$		0			0
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	10.0000	+	10.0000i	0.668153	+	0.668153i
$225$	−9.00000			−0.600000
$226$	−5.00000	−	5.00000i	−0.332595	−	0.332595i
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$		0			0
$229$		−	22.0000i		−	1.45380i	−0.686743	−	0.726900i	$-0.740960\pi$
$229$		−	22.0000i		−	1.45380i	0.686743	−	0.726900i	$-0.259040\pi$
$230$		−	8.00000i		−	0.527504i
$231$		0			0
$232$	3.00000	−	3.00000i	0.196960	−	0.196960i
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	0.937526	−	0.347916i	$-0.113111\pi$
$233$	9.00000	+	9.00000i	0.589610	+	0.589610i	−0.347916	+	0.937526i	$0.613111\pi$
$234$		0			0
$235$	−12.0000	−	12.0000i	−0.782794	−	0.782794i
$236$		0			0
$237$		0			0
$238$	−10.0000	+	6.00000i	−0.648204	+	0.388922i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	0.355091	−	0.934832i	$-0.384450\pi$
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	−0.934832	+	0.355091i	$0.884450\pi$
$242$	3.00000			0.192847
$243$		0			0
$244$	7.00000	−	7.00000i	0.448129	−	0.448129i
$245$	−1.00000	+	1.00000i	−0.0638877	+	0.0638877i
$246$		0			0
$247$		0			0
$248$	−12.0000	+	12.0000i	−0.762001	+	0.762001i
$249$		0			0
$250$	8.00000	+	8.00000i	0.505964	+	0.505964i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	6.00000	+	6.00000i	0.377964	+	0.377964i
$253$			16.0000i			1.00591i
$254$	20.0000			1.25491
$255$		0			0
$256$	−17.0000			−1.06250
$257$			18.0000i			1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$			18.0000i			1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$		0			0
$259$	20.0000			1.24274
$260$		0			0
$261$	3.00000	−	3.00000i	0.185695	−	0.185695i
$262$	8.00000	−	8.00000i	0.494242	−	0.494242i
$263$		−	24.0000i		−	1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$		−	24.0000i		−	1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$		0			0
$265$		0			0
$266$	16.0000	−	16.0000i	0.981023	−	0.981023i
$267$		0			0
$268$	−4.00000			−0.244339
$269$	−15.0000	−	15.0000i	−0.914566	−	0.914566i	0.0820612	−	0.996627i	$-0.473850\pi$
$269$	−15.0000	−	15.0000i	−0.914566	−	0.914566i	−0.996627	+	0.0820612i	$0.973850\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	1.00000	−	4.00000i	0.0606339	−	0.242536i
$273$		0			0
$274$			4.00000i			0.241649i
$275$	−6.00000	−	6.00000i	−0.361814	−	0.361814i
$276$		0			0
$277$	−11.0000	−	11.0000i	−0.660926	−	0.660926i	0.294672	−	0.955598i	$-0.404789\pi$
$277$	−11.0000	−	11.0000i	−0.660926	−	0.660926i	−0.955598	+	0.294672i	$0.904789\pi$
$278$	10.0000	−	10.0000i	0.599760	−	0.599760i
$279$	−12.0000	+	12.0000i	−0.718421	+	0.718421i
$280$		−	12.0000i		−	0.717137i
$281$		−	8.00000i		−	0.477240i	−0.971113	−	0.238620i	$-0.923305\pi$
$281$		−	8.00000i		−	0.477240i	0.971113	−	0.238620i	$-0.0766950\pi$
$282$		0			0
$283$	2.00000	−	2.00000i	0.118888	−	0.118888i	−0.645160	−	0.764048i	$-0.723209\pi$
$283$	2.00000	−	2.00000i	0.118888	−	0.118888i	0.764048	+	0.645160i	$0.223209\pi$
$284$	10.0000	+	10.0000i	0.593391	+	0.593391i
$285$		0			0
$286$		0			0
$287$			4.00000i			0.236113i
$288$	−15.0000			−0.883883
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$	−2.00000			−0.117444
$291$		0			0
$292$	−9.00000	−	9.00000i	−0.526685	−	0.526685i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$		0			0
$296$	−15.0000	+	15.0000i	−0.871857	+	0.871857i
$297$		0			0
$298$			18.0000i			1.04271i
$299$		0			0
$300$		0			0
$301$	2.00000	+	2.00000i	0.115278	+	0.115278i
$302$		0			0
$303$		0			0
$304$			8.00000i			0.458831i
$305$	−14.0000			−0.801638
$306$	3.00000	−	12.0000i	0.171499	−	0.685994i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$			8.00000i			0.455842i
$309$		0			0
$310$	8.00000			0.454369
$311$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$311$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$312$		0			0
$313$	−13.0000	+	13.0000i	−0.734803	+	0.734803i	−0.971567	−	0.236764i	$-0.923913\pi$
$313$	−13.0000	+	13.0000i	−0.734803	+	0.734803i	0.236764	+	0.971567i	$0.423913\pi$
$314$		−	6.00000i		−	0.338600i
$315$		−	12.0000i		−	0.676123i
$316$	−12.0000	+	12.0000i	−0.675053	+	0.675053i
$317$	−5.00000	+	5.00000i	−0.280828	+	0.280828i	−0.833439	−	0.552611i	$-0.813631\pi$
$317$	−5.00000	+	5.00000i	−0.280828	+	0.280828i	0.552611	+	0.833439i	$0.313631\pi$
$318$		0			0
$319$	4.00000			0.223957
$320$	7.00000	+	7.00000i	0.391312	+	0.391312i
$321$		0			0
$322$	−16.0000			−0.891645
$323$	32.0000	+	8.00000i	1.78053	+	0.445132i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	−16.0000	−	16.0000i	−0.886158	−	0.886158i
$327$		0			0
$328$	−3.00000	−	3.00000i	−0.165647	−	0.165647i
$329$	−24.0000	+	24.0000i	−1.32316	+	1.32316i
$330$		0			0
$331$			8.00000i			0.439720i	0.975531	+	0.219860i	$0.0705600\pi$
$331$			8.00000i			0.439720i	−0.975531	+	0.219860i	$0.929440\pi$
$332$			4.00000i			0.219529i
$333$	−15.0000	+	15.0000i	−0.821995	+	0.821995i
$334$	16.0000	−	16.0000i	0.875481	−	0.875481i
$335$	4.00000	+	4.00000i	0.218543	+	0.218543i
$336$		0			0
$337$	−3.00000	−	3.00000i	−0.163420	−	0.163420i	0.620660	−	0.784080i	$-0.286865\pi$
$337$	−3.00000	−	3.00000i	−0.163420	−	0.163420i	−0.784080	+	0.620660i	$0.786865\pi$
$338$			13.0000i			0.707107i
$339$		0			0
$340$	5.00000	−	3.00000i	0.271163	−	0.162698i
$341$	−16.0000			−0.866449
$342$			24.0000i			1.29777i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−3.00000			−0.161749
$345$		0			0
$346$	3.00000	−	3.00000i	0.161281	−	0.161281i
$347$	−8.00000	+	8.00000i	−0.429463	+	0.429463i	−0.888445	−	0.458983i	$-0.848214\pi$
$347$	−8.00000	+	8.00000i	−0.429463	+	0.429463i	0.458983	+	0.888445i	$0.348214\pi$
$348$		0			0
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$	6.00000	−	6.00000i	0.320713	−	0.320713i
$351$		0			0
$352$	−10.0000	−	10.0000i	−0.533002	−	0.533002i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$		−	20.0000i		−	1.06149i
$356$	12.0000			0.635999
$357$		0			0
$358$	−20.0000			−1.05703
$359$			20.0000i			1.05556i	0.849381	+	0.527780i	$0.176975\pi$
$359$			20.0000i			1.05556i	−0.849381	+	0.527780i	$0.823025\pi$
$360$	9.00000	+	9.00000i	0.474342	+	0.474342i
$361$	−45.0000			−2.36842
$362$	−9.00000	−	9.00000i	−0.473029	−	0.473029i
$363$		0			0
$364$		0			0
$365$			18.0000i			0.942163i
$366$		0			0
$367$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$367$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$368$	4.00000	−	4.00000i	0.208514	−	0.208514i
$369$	−3.00000	−	3.00000i	−0.156174	−	0.156174i
$370$	10.0000			0.519875
$371$		0			0
$372$		0			0
$373$	−20.0000			−1.03556			−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000			−1.03556			−0.517780	+	0.855514i	$0.673242\pi$
$374$	10.0000	−	6.00000i	0.517088	−	0.310253i
$375$		0			0
$376$		−	36.0000i		−	1.85656i
$377$		0			0
$378$		0			0
$379$	−2.00000	−	2.00000i	−0.102733	−	0.102733i	0.653872	−	0.756605i	$-0.273143\pi$
$379$	−2.00000	−	2.00000i	−0.102733	−	0.102733i	−0.756605	+	0.653872i	$0.773143\pi$
$380$	−8.00000	+	8.00000i	−0.410391	+	0.410391i
$381$		0			0
$382$		−	8.00000i		−	0.409316i
$383$		−	24.0000i		−	1.22634i	−0.789950	−	0.613171i	$-0.789894\pi$
$383$		−	24.0000i		−	1.22634i	0.789950	−	0.613171i	$-0.210106\pi$
$384$		0			0
$385$	8.00000	−	8.00000i	0.407718	−	0.407718i
$386$	−9.00000	−	9.00000i	−0.458088	−	0.458088i
$387$	−3.00000			−0.152499
$388$	7.00000	+	7.00000i	0.355371	+	0.355371i
$389$		−	30.0000i		−	1.52106i	−0.649303	−	0.760530i	$-0.724939\pi$
$389$		−	30.0000i		−	1.52106i	0.649303	−	0.760530i	$-0.275061\pi$
$390$		0			0
$391$	−12.0000	−	20.0000i	−0.606866	−	1.01144i
$392$	−3.00000			−0.151523
$393$		0			0
$394$	5.00000	+	5.00000i	0.251896	+	0.251896i
$395$	24.0000			1.20757
$396$	−6.00000	−	6.00000i	−0.301511	−	0.301511i
$397$	−15.0000	+	15.0000i	−0.752828	+	0.752828i	−0.975006	−	0.222178i	$-0.928683\pi$
$397$	−15.0000	+	15.0000i	−0.752828	+	0.752828i	0.222178	+	0.975006i	$0.428683\pi$
$398$	18.0000	−	18.0000i	0.902258	−	0.902258i
$399$		0			0
$400$			3.00000i			0.150000i
$401$	5.00000	−	5.00000i	0.249688	−	0.249688i	−0.571154	−	0.820843i	$-0.693504\pi$
$401$	5.00000	−	5.00000i	0.249688	−	0.249688i	0.820843	+	0.571154i	$0.193504\pi$
$402$		0			0
$403$		0			0
$404$	16.0000			0.796030
$405$	9.00000	+	9.00000i	0.447214	+	0.447214i
$406$			4.00000i			0.198517i
$407$	−20.0000			−0.991363
$408$		0			0
$409$	22.0000			1.08783			0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000			1.08783			0.543915	+	0.839140i	$0.316941\pi$
$410$			2.00000i			0.0987730i
$411$		0			0
$412$	8.00000			0.394132
$413$		0			0
$414$	12.0000	−	12.0000i	0.589768	−	0.589768i
$415$	4.00000	−	4.00000i	0.196352	−	0.196352i
$416$		0			0
$417$		0			0
$418$	−16.0000	+	16.0000i	−0.782586	+	0.782586i
$419$	4.00000	−	4.00000i	0.195413	−	0.195413i	−0.602617	−	0.798030i	$-0.705875\pi$
$419$	4.00000	−	4.00000i	0.195413	−	0.195413i	0.798030	+	0.602617i	$0.205875\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−4.00000	−	4.00000i	−0.194717	−	0.194717i
$423$		−	36.0000i		−	1.75038i
$424$		0			0
$425$	12.0000	+	3.00000i	0.582086	+	0.145521i
$426$		0			0
$427$			28.0000i			1.35501i
$428$	−6.00000	−	6.00000i	−0.290021	−	0.290021i
$429$		0			0
$430$	1.00000	+	1.00000i	0.0482243	+	0.0482243i
$431$	−20.0000	+	20.0000i	−0.963366	+	0.963366i	−0.999352	−	0.0359862i	$-0.988543\pi$
$431$	−20.0000	+	20.0000i	−0.963366	+	0.963366i	0.0359862	+	0.999352i	$0.488543\pi$
$432$		0			0
$433$		−	30.0000i		−	1.44171i	−0.693087	−	0.720854i	$-0.743750\pi$
$433$		−	30.0000i		−	1.44171i	0.693087	−	0.720854i	$-0.256250\pi$
$434$		−	16.0000i		−	0.768025i
$435$		0			0
$436$	9.00000	−	9.00000i	0.431022	−	0.431022i
$437$	32.0000	+	32.0000i	1.53077	+	1.53077i
$438$		0			0
$439$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$439$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$440$			12.0000i			0.572078i
$441$	−3.00000			−0.142857
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−12.0000	−	12.0000i	−0.568855	−	0.568855i
$446$	4.00000			0.189405
$447$		0			0
$448$	14.0000	−	14.0000i	0.661438	−	0.661438i
$449$	−7.00000	+	7.00000i	−0.330350	+	0.330350i	−0.852720	−	0.522369i	$-0.825048\pi$
$449$	−7.00000	+	7.00000i	−0.330350	+	0.330350i	0.522369	+	0.852720i	$0.325048\pi$
$450$			9.00000i			0.424264i
$451$		−	4.00000i		−	0.188353i
$452$	5.00000	−	5.00000i	0.235180	−	0.235180i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$			26.0000i			1.21623i	0.793849	+	0.608114i	$0.208074\pi$
$457$			26.0000i			1.21623i	−0.793849	+	0.608114i	$0.791926\pi$
$458$	−22.0000			−1.02799
$459$		0			0
$460$	8.00000			0.373002
$461$			24.0000i			1.11779i	0.829238	+	0.558896i	$0.188775\pi$
$461$			24.0000i			1.11779i	−0.829238	+	0.558896i	$0.811225\pi$
$462$		0			0
$463$	28.0000			1.30127			0.650635	−	0.759390i	$-0.274503\pi$
$463$	28.0000			1.30127			0.650635	+	0.759390i	$0.274503\pi$
$464$	−1.00000	−	1.00000i	−0.0464238	−	0.0464238i
$465$		0			0
$466$	9.00000	−	9.00000i	0.416917	−	0.416917i
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$		0			0
$469$	8.00000	−	8.00000i	0.369406	−	0.369406i
$470$	−12.0000	+	12.0000i	−0.553519	+	0.553519i
$471$		0			0
$472$		0			0
$473$	−2.00000	−	2.00000i	−0.0919601	−	0.0919601i
$474$		0			0
$475$	−24.0000			−1.10120
$476$	−6.00000	−	10.0000i	−0.275010	−	0.458349i
$477$		0			0
$478$		−	8.00000i		−	0.365911i
$479$	−16.0000	−	16.0000i	−0.731059	−	0.731059i	0.239771	−	0.970830i	$-0.422928\pi$
$479$	−16.0000	−	16.0000i	−0.731059	−	0.731059i	−0.970830	+	0.239771i	$0.922928\pi$
$480$		0			0
$481$		0			0
$482$	−9.00000	+	9.00000i	−0.409939	+	0.409939i
$483$		0			0
$484$			3.00000i			0.136364i
$485$		−	14.0000i		−	0.635707i
$486$		0			0
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	−0.380861	−	0.924632i	$-0.624372\pi$
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	0.924632	+	0.380861i	$0.124372\pi$
$488$	−21.0000	−	21.0000i	−0.950625	−	0.950625i
$489$		0			0
$490$	1.00000	+	1.00000i	0.0451754	+	0.0451754i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$	−5.00000	+	3.00000i	−0.225189	+	0.135113i
$494$		0			0
$495$			12.0000i			0.539360i
$496$	4.00000	+	4.00000i	0.179605	+	0.179605i
$497$	−40.0000			−1.79425
$498$		0			0
$499$	−12.0000	+	12.0000i	−0.537194	+	0.537194i	−0.922704	−	0.385510i	$-0.874026\pi$
$499$	−12.0000	+	12.0000i	−0.537194	+	0.537194i	0.385510	+	0.922704i	$0.374026\pi$
$500$	−8.00000	+	8.00000i	−0.357771	+	0.357771i
$501$		0			0
$502$		0			0
$503$	2.00000	−	2.00000i	0.0891756	−	0.0891756i	−0.661112	−	0.750287i	$-0.729915\pi$
$503$	2.00000	−	2.00000i	0.0891756	−	0.0891756i	0.750287	+	0.661112i	$0.229915\pi$
$504$	18.0000	−	18.0000i	0.801784	−	0.801784i
$505$	−16.0000	−	16.0000i	−0.711991	−	0.711991i
$506$	16.0000			0.711287
$507$		0			0
$508$			20.0000i			0.887357i
$509$	34.0000			1.50702			0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000			1.50702			0.753512	+	0.657434i	$0.228358\pi$
$510$		0			0
$511$	36.0000			1.59255
$512$			11.0000i			0.486136i
$513$		0			0
$514$	18.0000			0.793946
$515$	−8.00000	−	8.00000i	−0.352522	−	0.352522i
$516$		0			0
$517$	24.0000	−	24.0000i	1.05552	−	1.05552i
$518$		−	20.0000i		−	0.878750i
$519$		0			0
$520$		0			0
$521$	−5.00000	+	5.00000i	−0.219054	+	0.219054i	−0.808100	−	0.589046i	$-0.799504\pi$
$521$	−5.00000	+	5.00000i	−0.219054	+	0.219054i	0.589046	+	0.808100i	$0.299504\pi$
$522$	−3.00000	−	3.00000i	−0.131306	−	0.131306i
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	8.00000	+	8.00000i	0.349482	+	0.349482i
$525$		0			0
$526$	−24.0000			−1.04645
$527$	20.0000	−	12.0000i	0.871214	−	0.522728i
$528$		0			0
$529$		−	9.00000i		−	0.391304i
$530$		0			0
$531$		0			0
$532$	16.0000	+	16.0000i	0.693688	+	0.693688i
$533$		0			0
$534$		0			0
$535$			12.0000i			0.518805i
$536$			12.0000i			0.518321i
$537$		0			0
$538$	−15.0000	+	15.0000i	−0.646696	+	0.646696i
$539$	−2.00000	−	2.00000i	−0.0861461	−	0.0861461i
$540$		0			0
$541$	13.0000	+	13.0000i	0.558914	+	0.558914i	0.928998	−	0.370084i	$-0.120671\pi$
$541$	13.0000	+	13.0000i	0.558914	+	0.558914i	−0.370084	+	0.928998i	$0.620671\pi$
$542$			28.0000i			1.20270i
$543$		0			0
$544$	20.0000	+	5.00000i	0.857493	+	0.214373i
$545$	−18.0000			−0.771035
$546$		0			0
$547$	−2.00000	−	2.00000i	−0.0855138	−	0.0855138i	0.663056	−	0.748570i	$-0.269259\pi$
$547$	−2.00000	−	2.00000i	−0.0855138	−	0.0855138i	−0.748570	+	0.663056i	$0.769259\pi$
$548$	−4.00000			−0.170872
$549$	−21.0000	−	21.0000i	−0.896258	−	0.896258i
$550$	−6.00000	+	6.00000i	−0.255841	+	0.255841i
$551$	8.00000	−	8.00000i	0.340811	−	0.340811i
$552$		0			0
$553$		−	48.0000i		−	2.04117i
$554$	−11.0000	+	11.0000i	−0.467345	+	0.467345i
$555$		0			0
$556$	10.0000	+	10.0000i	0.424094	+	0.424094i
$557$	8.00000			0.338971			0.169485	−	0.985533i	$-0.445789\pi$
$557$	8.00000			0.338971			0.169485	+	0.985533i	$0.445789\pi$
$558$	12.0000	+	12.0000i	0.508001	+	0.508001i
$559$		0			0
$560$	−4.00000			−0.169031
$561$		0			0
$562$	−8.00000			−0.337460
$563$			40.0000i			1.68580i	0.538071	+	0.842900i	$0.319153\pi$
$563$			40.0000i			1.68580i	−0.538071	+	0.842900i	$0.680847\pi$
$564$		0			0
$565$	−10.0000			−0.420703
$566$	−2.00000	−	2.00000i	−0.0840663	−	0.0840663i
$567$	18.0000	−	18.0000i	0.755929	−	0.755929i
$568$	30.0000	−	30.0000i	1.25877	−	1.25877i
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$		0			0
$571$	−32.0000	+	32.0000i	−1.33916	+	1.33916i	−0.442283	+	0.896876i	$0.645831\pi$
$571$	−32.0000	+	32.0000i	−1.33916	+	1.33916i	−0.896876	+	0.442283i	$0.854169\pi$
$572$		0			0
$573$		0			0
$574$	4.00000			0.166957
$575$	12.0000	+	12.0000i	0.500435	+	0.500435i
$576$			21.0000i			0.875000i
$577$	12.0000			0.499567			0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000			0.499567			0.249783	+	0.968302i	$0.419641\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$		0			0
$580$		−	2.00000i		−	0.0830455i
$581$	−8.00000	−	8.00000i	−0.331896	−	0.331896i
$582$		0			0
$583$		0			0
$584$	−27.0000	+	27.0000i	−1.11727	+	1.11727i
$585$		0			0
$586$			6.00000i			0.247858i
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$		0			0
$589$	−32.0000	+	32.0000i	−1.31854	+	1.31854i
$590$		0			0
$591$		0			0
$592$	5.00000	+	5.00000i	0.205499	+	0.205499i
$593$		−	36.0000i		−	1.47834i	−0.673517	−	0.739171i	$-0.735217\pi$
$593$		−	36.0000i		−	1.47834i	0.673517	−	0.739171i	$-0.264783\pi$
$594$		0			0
$595$	−4.00000	+	16.0000i	−0.163984	+	0.655936i
$596$	−18.0000			−0.737309
$597$		0			0
$598$		0			0
$599$	44.0000			1.79779			0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000			1.79779			0.898896	+	0.438163i	$0.144371\pi$
$600$		0			0
$601$	−1.00000	+	1.00000i	−0.0407909	+	0.0407909i	−0.727208	−	0.686417i	$-0.759182\pi$
$601$	−1.00000	+	1.00000i	−0.0407909	+	0.0407909i	0.686417	+	0.727208i	$0.259182\pi$
$602$	2.00000	−	2.00000i	0.0815139	−	0.0815139i
$603$			12.0000i			0.488678i
$604$		0			0
$605$	3.00000	−	3.00000i	0.121967	−	0.121967i
$606$		0			0
$607$	−14.0000	−	14.0000i	−0.568242	−	0.568242i	0.363393	−	0.931636i	$-0.381618\pi$
$607$	−14.0000	−	14.0000i	−0.568242	−	0.568242i	−0.931636	+	0.363393i	$0.881618\pi$
$608$	−40.0000			−1.62221
$609$		0			0
$610$			14.0000i			0.566843i
$611$		0			0
$612$	12.0000	+	3.00000i	0.485071	+	0.121268i
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$		−	16.0000i		−	0.645707i
$615$		0			0
$616$	24.0000			0.966988
$617$	−29.0000	−	29.0000i	−1.16750	−	1.16750i	−0.982795	−	0.184701i	$-0.940868\pi$
$617$	−29.0000	−	29.0000i	−1.16750	−	1.16750i	−0.184701	−	0.982795i	$-0.559132\pi$
$618$		0			0
$619$	30.0000	−	30.0000i	1.20580	−	1.20580i	0.233428	−	0.972374i	$-0.425006\pi$
$619$	30.0000	−	30.0000i	1.20580	−	1.20580i	0.972374	−	0.233428i	$-0.0749942\pi$
$620$			8.00000i			0.321288i
$621$		0			0
$622$		0			0
$623$	−24.0000	+	24.0000i	−0.961540	+	0.961540i
$624$		0			0
$625$	1.00000			0.0400000
$626$	13.0000	+	13.0000i	0.519584	+	0.519584i
$627$		0			0
$628$	6.00000			0.239426
$629$	25.0000	−	15.0000i	0.996815	−	0.598089i
$630$	−12.0000			−0.478091
$631$			8.00000i			0.318475i	0.987240	+	0.159237i	$0.0509036\pi$
$631$			8.00000i			0.318475i	−0.987240	+	0.159237i	$0.949096\pi$
$632$	36.0000	+	36.0000i	1.43200	+	1.43200i
$633$		0			0
$634$	5.00000	+	5.00000i	0.198575	+	0.198575i
$635$	20.0000	−	20.0000i	0.793676	−	0.793676i
$636$		0			0
$637$		0			0
$638$		−	4.00000i		−	0.158362i
$639$	30.0000	−	30.0000i	1.18678	−	1.18678i
$640$	−3.00000	+	3.00000i	−0.118585	+	0.118585i
$641$	−31.0000	−	31.0000i	−1.22443	−	1.22443i	−0.966042	−	0.258384i	$-0.916810\pi$
$641$	−31.0000	−	31.0000i	−1.22443	−	1.22443i	−0.258384	−	0.966042i	$-0.583190\pi$
$642$		0			0
$643$	6.00000	+	6.00000i	0.236617	+	0.236617i	0.815448	−	0.578831i	$-0.196491\pi$
$643$	6.00000	+	6.00000i	0.236617	+	0.236617i	−0.578831	+	0.815448i	$0.696491\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$	8.00000	−	32.0000i	0.314756	−	1.25902i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$			27.0000i			1.06066i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	16.0000	−	16.0000i	0.626608	−	0.626608i
$653$	33.0000	−	33.0000i	1.29139	−	1.29139i	0.357462	−	0.933928i	$-0.383642\pi$
$653$	33.0000	−	33.0000i	1.29139	−	1.29139i	0.933928	−	0.357462i	$-0.116358\pi$
$654$		0			0
$655$		−	16.0000i		−	0.625172i
$656$	−1.00000	+	1.00000i	−0.0390434	+	0.0390434i
$657$	−27.0000	+	27.0000i	−1.05337	+	1.05337i
$658$	24.0000	+	24.0000i	0.935617	+	0.935617i
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$		0			0
$661$		−	32.0000i		−	1.24466i	−0.782757	−	0.622328i	$-0.786187\pi$
$661$		−	32.0000i		−	1.24466i	0.782757	−	0.622328i	$-0.213813\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$	12.0000			0.465690
$665$		−	32.0000i		−	1.24091i
$666$	15.0000	+	15.0000i	0.581238	+	0.581238i
$667$	−8.00000			−0.309761
$668$	16.0000	+	16.0000i	0.619059	+	0.619059i
$669$		0			0
$670$	4.00000	−	4.00000i	0.154533	−	0.154533i
$671$		−	28.0000i		−	1.08093i
$672$		0			0
$673$	5.00000	−	5.00000i	0.192736	−	0.192736i	−0.604141	−	0.796877i	$-0.706484\pi$
$673$	5.00000	−	5.00000i	0.192736	−	0.192736i	0.796877	+	0.604141i	$0.206484\pi$
$674$	−3.00000	+	3.00000i	−0.115556	+	0.115556i
$675$		0			0
$676$	−13.0000			−0.500000
$677$	5.00000	+	5.00000i	0.192166	+	0.192166i	0.796631	−	0.604466i	$-0.206613\pi$
$677$	5.00000	+	5.00000i	0.192166	+	0.192166i	−0.604466	+	0.796631i	$0.706613\pi$
$678$		0			0
$679$	−28.0000			−1.07454
$680$	−9.00000	−	15.0000i	−0.345134	−	0.575224i
$681$		0			0
$682$			16.0000i			0.612672i
$683$	6.00000	+	6.00000i	0.229584	+	0.229584i	0.812519	−	0.582935i	$-0.198096\pi$
$683$	6.00000	+	6.00000i	0.229584	+	0.229584i	−0.582935	+	0.812519i	$0.698096\pi$
$684$	−24.0000			−0.917663
$685$	4.00000	+	4.00000i	0.152832	+	0.152832i
$686$	−12.0000	+	12.0000i	−0.458162	+	0.458162i
$687$		0			0
$688$			1.00000i			0.0381246i
$689$		0			0
$690$		0			0
$691$	−4.00000	+	4.00000i	−0.152167	+	0.152167i	−0.779085	−	0.626918i	$-0.784316\pi$
$691$	−4.00000	+	4.00000i	−0.152167	+	0.152167i	0.626918	+	0.779085i	$0.284316\pi$
$692$	3.00000	+	3.00000i	0.114043	+	0.114043i
$693$	24.0000			0.911685
$694$	8.00000	+	8.00000i	0.303676	+	0.303676i
$695$		−	20.0000i		−	0.758643i
$696$		0			0
$697$	3.00000	+	5.00000i	0.113633	+	0.189389i
$698$	28.0000			1.05982
$699$		0			0
$700$	6.00000	+	6.00000i	0.226779	+	0.226779i
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$		0			0
$703$	−40.0000	+	40.0000i	−1.50863	+	1.50863i
$704$	−14.0000	+	14.0000i	−0.527645	+	0.527645i
$705$		0			0
$706$		−	6.00000i		−	0.225813i
$707$	−32.0000	+	32.0000i	−1.20348	+	1.20348i
$708$		0			0
$709$	−13.0000	−	13.0000i	−0.488225	−	0.488225i	0.419521	−	0.907746i	$-0.362198\pi$
$709$	−13.0000	−	13.0000i	−0.488225	−	0.488225i	−0.907746	+	0.419521i	$0.862198\pi$
$710$	−20.0000			−0.750587
$711$	36.0000	+	36.0000i	1.35011	+	1.35011i
$712$		−	36.0000i		−	1.34916i
$713$	32.0000			1.19841
$714$		0			0
$715$		0			0
$716$		−	20.0000i		−	0.747435i
$717$		0			0
$718$	20.0000			0.746393
$719$	−4.00000	−	4.00000i	−0.149175	−	0.149175i	0.628575	−	0.777749i	$-0.283639\pi$
$719$	−4.00000	−	4.00000i	−0.149175	−	0.149175i	−0.777749	+	0.628575i	$0.783639\pi$
$720$	3.00000	−	3.00000i	0.111803	−	0.111803i
$721$	−16.0000	+	16.0000i	−0.595871	+	0.595871i
$722$			45.0000i			1.67473i
$723$		0			0
$724$	9.00000	−	9.00000i	0.334482	−	0.334482i
$725$	3.00000	−	3.00000i	0.111417	−	0.111417i
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	18.0000			0.666210
$731$	4.00000	+	1.00000i	0.147945	+	0.0369863i
$732$		0			0
$733$		−	4.00000i		−	0.147743i	−0.997268	−	0.0738717i	$-0.976464\pi$
$733$		−	4.00000i		−	0.147743i	0.997268	−	0.0738717i	$-0.0235355\pi$
$734$		0			0
$735$		0			0
$736$	20.0000	+	20.0000i	0.737210	+	0.737210i
$737$	−8.00000	+	8.00000i	−0.294684	+	0.294684i
$738$	−3.00000	+	3.00000i	−0.110432	+	0.110432i
$739$			20.0000i			0.735712i	0.929883	+	0.367856i	$0.119908\pi$
$739$			20.0000i			0.735712i	−0.929883	+	0.367856i	$0.880092\pi$
$740$			10.0000i			0.367607i
$741$		0			0
$742$		0			0
$743$	30.0000	+	30.0000i	1.10059	+	1.10059i	0.994339	+	0.106254i	$0.0338857\pi$
$743$	30.0000	+	30.0000i	1.10059	+	1.10059i	0.106254	+	0.994339i	$0.466114\pi$
$744$		0			0
$745$	18.0000	+	18.0000i	0.659469	+	0.659469i
$746$			20.0000i			0.732252i
$747$	12.0000			0.439057
$748$	6.00000	+	10.0000i	0.219382	+	0.365636i
$749$	24.0000			0.876941
$750$		0			0
$751$	14.0000	+	14.0000i	0.510867	+	0.510867i	0.914792	−	0.403925i	$-0.132354\pi$
$751$	14.0000	+	14.0000i	0.510867	+	0.510867i	−0.403925	+	0.914792i	$0.632354\pi$
$752$	−12.0000			−0.437595
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	−2.00000	+	2.00000i	−0.0726433	+	0.0726433i
$759$		0			0
$760$	24.0000	+	24.0000i	0.870572	+	0.870572i
$761$	−12.0000			−0.435000			−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000			−0.435000			−0.217500	+	0.976060i	$0.569790\pi$
$762$		0			0
$763$			36.0000i			1.30329i
$764$	8.00000			0.289430
$765$	−9.00000	−	15.0000i	−0.325396	−	0.542326i
$766$	−24.0000			−0.867155
$767$		0			0
$768$		0			0
$769$	32.0000			1.15395			0.576975	−	0.816762i	$-0.304233\pi$
$769$	32.0000			1.15395			0.576975	+	0.816762i	$0.304233\pi$
$770$	−8.00000	−	8.00000i	−0.288300	−	0.288300i
$771$		0			0
$772$	9.00000	−	9.00000i	0.323917	−	0.323917i
$773$			14.0000i			0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$			14.0000i			0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$			3.00000i			0.107833i
$775$	−12.0000	+	12.0000i	−0.431053	+	0.431053i
$776$	21.0000	−	21.0000i	0.753856	−	0.753856i
$777$		0			0
$778$	−30.0000			−1.07555
$779$	−8.00000	−	8.00000i	−0.286630	−	0.286630i
$780$		0			0
$781$	40.0000			1.43131
$782$	−20.0000	+	12.0000i	−0.715199	+	0.429119i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−6.00000	−	6.00000i	−0.214149	−	0.214149i
$786$		0			0
$787$	6.00000	+	6.00000i	0.213877	+	0.213877i	0.805912	−	0.592035i	$-0.201675\pi$
$787$	6.00000	+	6.00000i	0.213877	+	0.213877i	−0.592035	+	0.805912i	$0.701675\pi$
$788$	−5.00000	+	5.00000i	−0.178118	+	0.178118i
$789$		0			0
$790$		−	24.0000i		−	0.853882i
$791$			20.0000i			0.711118i
$792$	−18.0000	+	18.0000i	−0.639602	+	0.639602i
$793$		0			0
$794$	15.0000	+	15.0000i	0.532330	+	0.532330i
$795$		0			0
$796$	18.0000	+	18.0000i	0.637993	+	0.637993i
$797$			40.0000i			1.41687i	0.705775	+	0.708436i	$0.250599\pi$
$797$			40.0000i			1.41687i	−0.705775	+	0.708436i	$0.749401\pi$
$798$		0			0
$799$	−12.0000	+	48.0000i	−0.424529	+	1.69812i
$800$	−15.0000			−0.530330
$801$		−	36.0000i		−	1.27200i
$802$	−5.00000	−	5.00000i	−0.176556	−	0.176556i
$803$	−36.0000			−1.27041
$804$		0			0
$805$	−16.0000	+	16.0000i	−0.563926	+	0.563926i
$806$		0			0
$807$		0			0
$808$		−	48.0000i		−	1.68863i
$809$	−17.0000	+	17.0000i	−0.597688	+	0.597688i	−0.939697	−	0.342009i	$-0.888893\pi$
$809$	−17.0000	+	17.0000i	−0.597688	+	0.597688i	0.342009	+	0.939697i	$0.388893\pi$
$810$	9.00000	−	9.00000i	0.316228	−	0.316228i
$811$	−36.0000	−	36.0000i	−1.26413	−	1.26413i	−0.949072	−	0.315059i	$-0.897976\pi$
$811$	−36.0000	−	36.0000i	−1.26413	−	1.26413i	−0.315059	−	0.949072i	$-0.602024\pi$
$812$	−4.00000			−0.140372
$813$		0			0
$814$			20.0000i			0.701000i
$815$	−32.0000			−1.12091
$816$		0			0
$817$	−8.00000			−0.279885
$818$		−	22.0000i		−	0.769212i
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	23.0000	+	23.0000i	0.802706	+	0.802706i	0.983518	−	0.180812i	$-0.0578726\pi$
$821$	23.0000	+	23.0000i	0.802706	+	0.802706i	−0.180812	+	0.983518i	$0.557873\pi$
$822$		0			0
$823$	24.0000	−	24.0000i	0.836587	−	0.836587i	−0.151821	−	0.988408i	$-0.548514\pi$
$823$	24.0000	−	24.0000i	0.836587	−	0.836587i	0.988408	+	0.151821i	$0.0485136\pi$
$824$		−	24.0000i		−	0.836080i
$825$		0			0
$826$		0			0
$827$	−14.0000	+	14.0000i	−0.486828	+	0.486828i	−0.907304	−	0.420476i	$-0.861863\pi$
$827$	−14.0000	+	14.0000i	−0.486828	+	0.486828i	0.420476	+	0.907304i	$0.361863\pi$
$828$	12.0000	+	12.0000i	0.417029	+	0.417029i
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	−4.00000	−	4.00000i	−0.138842	−	0.138842i
$831$		0			0
$832$		0			0
$833$	4.00000	+	1.00000i	0.138592	+	0.0346479i
$834$		0			0
$835$		−	32.0000i		−	1.10741i
$836$	−16.0000	−	16.0000i	−0.553372	−	0.553372i
$837$		0			0
$838$	−4.00000	−	4.00000i	−0.138178	−	0.138178i
$839$	22.0000	−	22.0000i	0.759524	−	0.759524i	−0.216711	−	0.976236i	$-0.569533\pi$
$839$	22.0000	−	22.0000i	0.759524	−	0.759524i	0.976236	+	0.216711i	$0.0695331\pi$
$840$		0			0
$841$		−	27.0000i		−	0.931034i
$842$			4.00000i			0.137849i
$843$		0			0
$844$	4.00000	−	4.00000i	0.137686	−	0.137686i
$845$	13.0000	+	13.0000i	0.447214	+	0.447214i
$846$	−36.0000			−1.23771
$847$	−6.00000	−	6.00000i	−0.206162	−	0.206162i
$848$		0			0
$849$		0			0
$850$	3.00000	−	12.0000i	0.102899	−	0.411597i
$851$	40.0000			1.37118
$852$		0			0
$853$	21.0000	+	21.0000i	0.719026	+	0.719026i	0.968406	−	0.249380i	$-0.0802267\pi$
$853$	21.0000	+	21.0000i	0.719026	+	0.719026i	−0.249380	+	0.968406i	$0.580227\pi$
$854$	28.0000			0.958140
$855$	24.0000	+	24.0000i	0.820783	+	0.820783i
$856$	−18.0000	+	18.0000i	−0.615227	+	0.615227i
$857$	−27.0000	+	27.0000i	−0.922302	+	0.922302i	−0.997192	−	0.0748894i	$-0.976140\pi$
$857$	−27.0000	+	27.0000i	−0.922302	+	0.922302i	0.0748894	+	0.997192i	$0.476140\pi$
$858$		0			0
$859$			52.0000i			1.77422i	0.461561	+	0.887109i	$0.347290\pi$
$859$			52.0000i			1.77422i	−0.461561	+	0.887109i	$0.652710\pi$
$860$	−1.00000	+	1.00000i	−0.0340997	+	0.0340997i
$861$		0			0
$862$	20.0000	+	20.0000i	0.681203	+	0.681203i
$863$	4.00000			0.136162			0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000			0.136162			0.0680808	+	0.997680i	$0.478312\pi$
$864$		0			0
$865$		−	6.00000i		−	0.204006i
$866$	−30.0000			−1.01944
$867$		0			0
$868$	16.0000			0.543075
$869$			48.0000i			1.62829i
$870$		0			0
$871$		0			0
$872$	−27.0000	−	27.0000i	−0.914335	−	0.914335i
$873$	21.0000	−	21.0000i	0.710742	−	0.710742i
$874$	32.0000	−	32.0000i	1.08242	−	1.08242i
$875$		−	32.0000i		−	1.08180i
$876$		0			0
$877$	21.0000	−	21.0000i	0.709120	−	0.709120i	−0.257230	−	0.966350i	$-0.582810\pi$
$877$	21.0000	−	21.0000i	0.709120	−	0.709120i	0.966350	+	0.257230i	$0.0828100\pi$
$878$		0			0
$879$		0			0
$880$	4.00000			0.134840
$881$	−19.0000	−	19.0000i	−0.640126	−	0.640126i	0.310460	−	0.950586i	$-0.399517\pi$
$881$	−19.0000	−	19.0000i	−0.640126	−	0.640126i	−0.950586	+	0.310460i	$0.899517\pi$
$882$			3.00000i			0.101015i
$883$	40.0000			1.34611			0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000			1.34611			0.673054	+	0.739594i	$0.264982\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.00000	−	2.00000i	−0.0671534	−	0.0671534i	0.672732	−	0.739886i	$-0.265121\pi$
$887$	−2.00000	−	2.00000i	−0.0671534	−	0.0671534i	−0.739886	+	0.672732i	$0.765121\pi$
$888$		0			0
$889$	−40.0000	−	40.0000i	−1.34156	−	1.34156i
$890$	−12.0000	+	12.0000i	−0.402241	+	0.402241i
$891$	−18.0000	+	18.0000i	−0.603023	+	0.603023i
$892$			4.00000i			0.133930i
$893$		−	96.0000i		−	3.21252i
$894$		0			0
$895$	−20.0000	+	20.0000i	−0.668526	+	0.668526i
$896$	6.00000	+	6.00000i	0.200446	+	0.200446i
$897$		0			0
$898$	7.00000	+	7.00000i	0.233593	+	0.233593i
$899$		−	8.00000i		−	0.266815i
$900$	−9.00000			−0.300000
$901$		0			0
$902$	−4.00000			−0.133185
$903$		0			0
$904$	−15.0000	−	15.0000i	−0.498893	−	0.498893i
$905$	−18.0000			−0.598340
$906$		0			0
$907$	−18.0000	+	18.0000i	−0.597680	+	0.597680i	−0.939695	−	0.342014i	$-0.888891\pi$
$907$	−18.0000	+	18.0000i	−0.597680	+	0.597680i	0.342014	+	0.939695i	$0.388891\pi$
$908$		0			0
$909$		−	48.0000i		−	1.59206i
$910$		0			0
$911$	30.0000	−	30.0000i	0.993944	−	0.993944i	−0.00603743	−	0.999982i	$-0.501922\pi$
$911$	30.0000	−	30.0000i	0.993944	−	0.993944i	0.999982	+	0.00603743i	$0.00192179\pi$
$912$		0			0
$913$	8.00000	+	8.00000i	0.264761	+	0.264761i
$914$	26.0000			0.860004
$915$		0			0
$916$		−	22.0000i		−	0.726900i
$917$	−32.0000			−1.05673
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		−	24.0000i		−	0.791257i
$921$		0			0
$922$	24.0000			0.790398
$923$		0			0
$924$		0			0
$925$	−15.0000	+	15.0000i	−0.493197	+	0.493197i
$926$		−	28.0000i		−	0.920137i
$927$		−	24.0000i		−	0.788263i
$928$	5.00000	−	5.00000i	0.164133	−	0.164133i
$929$	−9.00000	+	9.00000i	−0.295280	+	0.295280i	−0.839162	−	0.543882i	$-0.816954\pi$
$929$	−9.00000	+	9.00000i	−0.295280	+	0.295280i	0.543882	+	0.839162i	$0.316954\pi$
$930$		0			0
$931$	−8.00000			−0.262189
$932$	9.00000	+	9.00000i	0.294805	+	0.294805i
$933$		0			0
$934$	−8.00000			−0.261768
$935$	4.00000	−	16.0000i	0.130814	−	0.523256i
$936$		0			0
$937$		−	12.0000i		−	0.392023i	−0.980602	−	0.196011i	$-0.937201\pi$
$937$		−	12.0000i		−	0.392023i	0.980602	−	0.196011i	$-0.0627990\pi$
$938$	−8.00000	−	8.00000i	−0.261209	−	0.261209i
$939$		0			0
$940$	−12.0000	−	12.0000i	−0.391397	−	0.391397i
$941$	−13.0000	+	13.0000i	−0.423788	+	0.423788i	−0.886506	−	0.462718i	$-0.846874\pi$
$941$	−13.0000	+	13.0000i	−0.423788	+	0.423788i	0.462718	+	0.886506i	$0.346874\pi$
$942$		0			0
$943$			8.00000i			0.260516i
$944$		0			0
$945$		0			0
$946$	−2.00000	+	2.00000i	−0.0650256	+	0.0650256i
$947$	−22.0000	−	22.0000i	−0.714904	−	0.714904i	0.252653	−	0.967557i	$-0.418697\pi$
$947$	−22.0000	−	22.0000i	−0.714904	−	0.714904i	−0.967557	+	0.252653i	$0.918697\pi$
$948$		0			0
$949$		0			0
$950$			24.0000i			0.778663i
$951$		0			0
$952$	−30.0000	+	18.0000i	−0.972306	+	0.583383i
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	−8.00000	−	8.00000i	−0.258874	−	0.258874i
$956$	8.00000			0.258738
$957$		0			0
$958$	−16.0000	+	16.0000i	−0.516937	+	0.516937i
$959$	8.00000	−	8.00000i	0.258333	−	0.258333i
$960$		0			0
$961$			1.00000i			0.0322581i
$962$		0			0
$963$	−18.0000	+	18.0000i	−0.580042	+	0.580042i
$964$	−9.00000	−	9.00000i	−0.289870	−	0.289870i
$965$	−18.0000			−0.579441
$966$		0			0
$967$			20.0000i			0.643157i	0.946883	+	0.321578i	$0.104213\pi$
$967$			20.0000i			0.643157i	−0.946883	+	0.321578i	$0.895787\pi$
$968$	9.00000			0.289271
$969$		0			0
$970$	−14.0000			−0.449513
$971$			4.00000i			0.128366i	0.997938	+	0.0641831i	$0.0204442\pi$
$971$			4.00000i			0.128366i	−0.997938	+	0.0641831i	$0.979556\pi$
$972$		0			0
$973$	−40.0000			−1.28234
$974$	−12.0000	−	12.0000i	−0.384505	−	0.384505i
$975$		0			0
$976$	−7.00000	+	7.00000i	−0.224065	+	0.224065i
$977$			24.0000i			0.767828i	0.923369	+	0.383914i	$0.125424\pi$
$977$			24.0000i			0.767828i	−0.923369	+	0.383914i	$0.874576\pi$
$978$		0			0
$979$	24.0000	−	24.0000i	0.767043	−	0.767043i
$980$	−1.00000	+	1.00000i	−0.0319438	+	0.0319438i
$981$	−27.0000	−	27.0000i	−0.862044	−	0.862044i
$982$		0			0
$983$	6.00000	+	6.00000i	0.191370	+	0.191370i	0.796288	−	0.604918i	$-0.206794\pi$
$983$	6.00000	+	6.00000i	0.191370	+	0.191370i	−0.604918	+	0.796288i	$0.706794\pi$
$984$		0			0
$985$	10.0000			0.318626
$986$	3.00000	+	5.00000i	0.0955395	+	0.159232i
$987$		0			0
$988$		0			0
$989$	4.00000	+	4.00000i	0.127193	+	0.127193i
$990$	12.0000			0.381385
$991$	−6.00000	−	6.00000i	−0.190596	−	0.190596i	0.605357	−	0.795954i	$-0.293030\pi$
$991$	−6.00000	−	6.00000i	−0.190596	−	0.190596i	−0.795954	+	0.605357i	$0.793030\pi$
$992$	−20.0000	+	20.0000i	−0.635001	+	0.635001i
$993$		0			0
$994$			40.0000i			1.26872i
$995$		−	36.0000i		−	1.14128i
$996$		0			0
$997$	25.0000	−	25.0000i	0.791758	−	0.791758i	−0.190022	−	0.981780i	$-0.560856\pi$
$997$	25.0000	−	25.0000i	0.791758	−	0.791758i	0.981780	+	0.190022i	$0.0608559\pi$
$998$	12.0000	+	12.0000i	0.379853	+	0.379853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.a.302.1	yes	2
17.4	even	4	inner	731.2.f.a.259.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.a.259.1	✓	2	17.4	even	4	inner
731.2.f.a.302.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} -3.00000i q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} -3.00000i q^{8} -3.00000i q^{9} +(-1.00000 + 1.00000i) q^{10} +(2.00000 - 2.00000i) q^{11} +(2.00000 + 2.00000i) q^{14} -1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -3.00000 q^{18} -8.00000i q^{19} +(-1.00000 - 1.00000i) q^{20} +(-2.00000 - 2.00000i) q^{22} +(-4.00000 + 4.00000i) q^{23} -3.00000i q^{25} +(-2.00000 + 2.00000i) q^{28} +(1.00000 + 1.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} -5.00000i q^{32} +(4.00000 + 1.00000i) q^{34} +4.00000 q^{35} -3.00000i q^{36} +(-5.00000 - 5.00000i) q^{37} -8.00000 q^{38} +(-3.00000 + 3.00000i) q^{40} +(1.00000 - 1.00000i) q^{41} -1.00000i q^{43} +(2.00000 - 2.00000i) q^{44} +(-3.00000 + 3.00000i) q^{45} +(4.00000 + 4.00000i) q^{46} +12.0000 q^{47} -1.00000i q^{49} -3.00000 q^{50} -4.00000 q^{55} +(6.00000 + 6.00000i) q^{56} +(1.00000 - 1.00000i) q^{58} +(7.00000 - 7.00000i) q^{61} +(-4.00000 + 4.00000i) q^{62} +(6.00000 + 6.00000i) q^{63} -7.00000 q^{64} -4.00000 q^{67} +(-1.00000 + 4.00000i) q^{68} -4.00000i q^{70} +(10.0000 + 10.0000i) q^{71} -9.00000 q^{72} +(-9.00000 - 9.00000i) q^{73} +(-5.00000 + 5.00000i) q^{74} -8.00000i q^{76} +8.00000i q^{77} +(-12.0000 + 12.0000i) q^{79} +(1.00000 + 1.00000i) q^{80} -9.00000 q^{81} +(-1.00000 - 1.00000i) q^{82} +4.00000i q^{83} +(5.00000 - 3.00000i) q^{85} -1.00000 q^{86} +(-6.00000 - 6.00000i) q^{88} +12.0000 q^{89} +(3.00000 + 3.00000i) q^{90} +(-4.00000 + 4.00000i) q^{92} -12.0000i q^{94} +(-8.00000 + 8.00000i) q^{95} +(7.00000 + 7.00000i) q^{97} -1.00000 q^{98} +(-6.00000 - 6.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 2 * q + 2 * q^4 - 2 * q^5 - 4 * q^7	\( 2 q + 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{10} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 2 q^{17} - 6 q^{18} - 2 q^{20} - 4 q^{22} - 8 q^{23} - 4 q^{28} + 2 q^{29} - 8 q^{31} + 8 q^{34} + 8 q^{35} - 10 q^{37} - 16 q^{38} - 6 q^{40} + 2 q^{41} + 4 q^{44} - 6 q^{45} + 8 q^{46} + 24 q^{47} - 6 q^{50} - 8 q^{55} + 12 q^{56} + 2 q^{58} + 14 q^{61} - 8 q^{62} + 12 q^{63} - 14 q^{64} - 8 q^{67} - 2 q^{68} + 20 q^{71} - 18 q^{72} - 18 q^{73} - 10 q^{74} - 24 q^{79} + 2 q^{80} - 18 q^{81} - 2 q^{82} + 10 q^{85} - 2 q^{86} - 12 q^{88} + 24 q^{89} + 6 q^{90} - 8 q^{92} - 16 q^{95} + 14 q^{97} - 2 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^10 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 2 * q^17 - 6 * q^18 - 2 * q^20 - 4 * q^22 - 8 * q^23 - 4 * q^28 + 2 * q^29 - 8 * q^31 + 8 * q^34 + 8 * q^35 - 10 * q^37 - 16 * q^38 - 6 * q^40 + 2 * q^41 + 4 * q^44 - 6 * q^45 + 8 * q^46 + 24 * q^47 - 6 * q^50 - 8 * q^55 + 12 * q^56 + 2 * q^58 + 14 * q^61 - 8 * q^62 + 12 * q^63 - 14 * q^64 - 8 * q^67 - 2 * q^68 + 20 * q^71 - 18 * q^72 - 18 * q^73 - 10 * q^74 - 24 * q^79 + 2 * q^80 - 18 * q^81 - 2 * q^82 + 10 * q^85 - 2 * q^86 - 12 * q^88 + 24 * q^89 + 6 * q^90 - 8 * q^92 - 16 * q^95 + 14 * q^97 - 2 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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