LMFDB - Embedded newform 810.2.e.e.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(271,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("810.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.e (of order $3$, degree $2$, not 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	810.271
Dual form			810.2.e.e.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +(3.00000 + 5.19615i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.00000 q^{17} -4.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(3.00000 - 5.19615i) q^{22} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{26} +2.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} -2.00000 q^{35} +8.00000 q^{37} +(2.00000 + 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-4.00000 - 6.92820i) q^{43} -6.00000 q^{44} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.00000 + 3.46410i) q^{52} +6.00000 q^{53} +6.00000 q^{55} +(-1.00000 - 1.73205i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(1.00000 + 1.73205i) q^{70} +12.0000 q^{71} -10.0000 q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(6.00000 - 10.3923i) q^{77} +(2.00000 + 3.46410i) q^{79} -1.00000 q^{80} +(6.00000 + 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{88} -12.0000 q^{89} -8.00000 q^{91} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + q^5 - 2 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 2 q^{8} - 2 q^{10} + 6 q^{11} + 4 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{19} + q^{20} + 6 q^{22} - q^{25} - 8 q^{26} + 4 q^{28} - 6 q^{29} + 4 q^{31} - q^{32} - 6 q^{34} - 4 q^{35} + 16 q^{37} + 4 q^{38} + q^{40} - 8 q^{43} - 12 q^{44} + 3 q^{49} - q^{50} + 4 q^{52} + 12 q^{53} + 12 q^{55} - 2 q^{56} - 6 q^{58} + 6 q^{59} - 2 q^{61} - 8 q^{62} + 2 q^{64} - 4 q^{65} + 4 q^{67} - 6 q^{68} + 2 q^{70} + 24 q^{71} - 20 q^{73} - 8 q^{74} + 4 q^{76} + 12 q^{77} + 4 q^{79} - 2 q^{80} + 12 q^{83} + 6 q^{85} - 8 q^{86} + 6 q^{88} - 24 q^{89} - 16 q^{91} - 4 q^{95} - 2 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + q^5 - 2 * q^7 + 2 * q^8 - 2 * q^10 + 6 * q^11 + 4 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 8 * q^19 + q^20 + 6 * q^22 - q^25 - 8 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 - 6 * q^34 - 4 * q^35 + 16 * q^37 + 4 * q^38 + q^40 - 8 * q^43 - 12 * q^44 + 3 * q^49 - q^50 + 4 * q^52 + 12 * q^53 + 12 * q^55 - 2 * q^56 - 6 * q^58 + 6 * q^59 - 2 * q^61 - 8 * q^62 + 2 * q^64 - 4 * q^65 + 4 * q^67 - 6 * q^68 + 2 * q^70 + 24 * q^71 - 20 * q^73 - 8 * q^74 + 4 * q^76 + 12 * q^77 + 4 * q^79 - 2 * q^80 + 12 * q^83 + 6 * q^85 - 8 * q^86 + 6 * q^88 - 24 * q^89 - 16 * q^91 - 4 * q^95 - 2 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−4.00000			−0.784465
$27$		0			0
$28$	2.00000			0.377964
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	−2.00000			−0.338062
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−6.00000			−0.904534
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$		0			0
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$	1.00000	+	1.73205i	0.119523	+	0.207020i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	6.00000	−	10.3923i	0.683763	−	1.18431i
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$		0			0
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$		0			0
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−12.0000			−1.27200			−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000			−1.27200			−0.635999	+	0.771690i	$0.719412\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	1.00000			0.100000
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	−0.911078	−	0.412235i	$-0.864748\pi$
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	0.812545	+	0.582899i	$0.198082\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$		0			0
$112$	−1.00000	+	1.73205i	−0.0944911	+	0.163663i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	−6.00000			−0.552345
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	6.00000			0.514496
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$	24.0000			2.00698
$144$		0			0
$145$	−6.00000			−0.498273
$146$	5.00000	+	8.66025i	0.413803	+	0.716728i
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$	−12.0000			−0.966988
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$		0			0
$162$		0			0
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$		0			0
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−12.0000	+	20.7846i	−0.928588	+	1.60836i	−0.142901	+	0.989737i	$0.545643\pi$
$167$	−12.0000	+	20.7846i	−0.928588	+	1.60836i	−0.785687	+	0.618624i	$0.787690\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−6.00000			−0.460179
$171$		0			0
$172$	8.00000			0.609994
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$	3.00000	−	5.19615i	0.226134	−	0.391675i
$177$		0			0
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	4.00000	+	6.92820i	0.296500	+	0.513553i
$183$		0			0
$184$		0			0
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$		0			0
$187$	18.0000	+	31.1769i	1.31629	+	2.27988i
$188$		0			0
$189$		0			0
$190$	4.00000			0.290191
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$		0			0
$206$	2.00000			0.139347
$207$		0			0
$208$	−4.00000			−0.277350
$209$	−12.0000	−	20.7846i	−0.830057	−	1.43770i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−8.00000			−0.545595
$216$		0			0
$217$	−8.00000			−0.543075
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$		0			0
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$		0			0
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.861435	−	0.507869i	$-0.830434\pi$
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.00910984	−	0.999959i	$-0.502900\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	−6.00000			−0.399114
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	25.0000			1.60706
$243$		0			0
$244$	2.00000			0.128037
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$		0			0
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$		0			0
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$		0			0
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−8.00000	−	13.8564i	−0.497096	−	0.860995i
$260$	4.00000			0.248069
$261$		0			0
$262$	6.00000			0.370681
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	4.00000	−	6.92820i	0.245256	−	0.424795i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	−3.00000	−	5.19615i	−0.181902	−	0.315063i
$273$		0			0
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$		0			0
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$	20.0000			1.19952
$279$		0			0
$280$	−2.00000			−0.119523
$281$	6.00000	+	10.3923i	0.357930	+	0.619953i	0.987615	−	0.156898i	$-0.0501493\pi$
$281$	6.00000	+	10.3923i	0.357930	+	0.619953i	−0.629685	+	0.776851i	$0.716816\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$	−12.0000	−	20.7846i	−0.709575	−	1.22902i
$287$		0			0
$288$		0			0
$289$	19.0000			1.11765
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$		0			0
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$		0			0
$295$	−3.00000	−	5.19615i	−0.174667	−	0.302532i
$296$	8.00000			0.464991
$297$		0			0
$298$	−6.00000			−0.347571
$299$		0			0
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	8.00000	−	13.8564i	0.460348	−	0.797347i
$303$		0			0
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	−2.00000			−0.114520
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	6.00000	+	10.3923i	0.341882	+	0.592157i
$309$		0			0
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		0			0
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$		0			0
$323$	−24.0000			−1.33540
$324$		0			0
$325$	−4.00000			−0.221880
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	24.0000			1.31322
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$		0			0
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	−0.991250	−	0.131995i	$-0.957862\pi$
$337$	−7.00000	+	12.1244i	−0.381314	+	0.660456i	0.609936	+	0.792451i	$0.291195\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$		0			0
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	24.0000			1.29967
$342$		0			0
$343$	−20.0000			−1.07990
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	0.994388	+	0.105797i	$0.0337393\pi$
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	−0.405571	+	0.914063i	$0.632927\pi$
$350$	2.00000			0.106904
$351$		0			0
$352$	−6.00000			−0.319801
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	−0.920677	−	0.390324i	$-0.872363\pi$
$353$	−15.0000	−	25.9808i	−0.798369	−	1.38282i	0.122308	−	0.992492i	$-0.460970\pi$
$354$		0			0
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	6.00000	−	10.3923i	0.317999	−	0.550791i
$357$		0			0
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$		0			0
$364$	4.00000	−	6.92820i	0.209657	−	0.363137i
$365$	−5.00000	+	8.66025i	−0.261712	+	0.453298i
$366$		0			0
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$		0			0
$369$		0			0
$370$	−8.00000			−0.415900
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$		0			0
$373$	14.0000	−	24.2487i	0.724893	−	1.25555i	−0.234126	−	0.972206i	$-0.575223\pi$
$373$	14.0000	−	24.2487i	0.724893	−	1.25555i	0.959018	−	0.283344i	$-0.0914439\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$		0			0
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$		0			0
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$	−6.00000	−	10.3923i	−0.305788	−	0.529641i
$386$	−10.0000			−0.508987
$387$		0			0
$388$	2.00000			0.101535
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$		0			0
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	4.00000			0.201262
$396$		0			0
$397$	−16.0000			−0.803017			−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000			−0.803017			−0.401508	+	0.915855i	$0.631514\pi$
$398$	8.00000	+	13.8564i	0.401004	+	0.694559i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.0699455	+	0.997551i	$0.522283\pi$
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.828932	+	0.559350i	$0.811051\pi$
$402$		0			0
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	6.00000			0.298511
$405$		0			0
$406$	12.0000			0.595550
$407$	24.0000	+	41.5692i	1.18964	+	2.06051i
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$		0			0
$411$		0			0
$412$	−1.00000	−	1.73205i	−0.0492665	−	0.0853320i
$413$	−12.0000			−0.590481
$414$		0			0
$415$	12.0000			0.589057
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$		0			0
$418$	−12.0000	+	20.7846i	−0.586939	+	1.01661i
$419$	−3.00000	+	5.19615i	−0.146560	+	0.253849i	−0.929954	−	0.367677i	$-0.880153\pi$
$419$	−3.00000	+	5.19615i	−0.146560	+	0.253849i	0.783394	+	0.621525i	$0.213487\pi$
$420$		0			0
$421$	−7.00000	−	12.1244i	−0.341159	−	0.590905i	0.643489	−	0.765455i	$-0.277486\pi$
$421$	−7.00000	−	12.1244i	−0.341159	−	0.590905i	−0.984648	+	0.174550i	$0.944153\pi$
$422$	−4.00000			−0.194717
$423$		0			0
$424$	6.00000			0.291386
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$	−2.00000	+	3.46410i	−0.0967868	+	0.167640i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$		0			0
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	38.0000			1.82616			0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000			1.82616			0.913082	+	0.407777i	$0.133696\pi$
$434$	4.00000	+	6.92820i	0.192006	+	0.332564i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$		0			0
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	−13.0000	+	22.5167i	−0.615568	+	1.06619i
$447$		0			0
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$		0			0
$454$		0			0
$455$	−4.00000	+	6.92820i	−0.187523	+	0.324799i
$456$		0			0
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	0.383437	−	0.923567i	$-0.374740\pi$
$458$	14.0000			0.654177
$459$		0			0
$460$		0			0
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	0.576685	−	0.816967i	$-0.304346\pi$
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	−0.995856	+	0.0909401i	$0.971013\pi$
$462$		0			0
$463$	17.0000	−	29.4449i	0.790057	−	1.36842i	−0.135874	−	0.990726i	$-0.543384\pi$
$463$	17.0000	−	29.4449i	0.790057	−	1.36842i	0.925931	−	0.377693i	$-0.123282\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−8.00000			−0.369406
$470$		0			0
$471$		0			0
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	24.0000	−	41.5692i	1.10352	−	1.91135i
$474$		0			0
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$	12.0000			0.550019
$477$		0			0
$478$	12.0000			0.548867
$479$	18.0000	+	31.1769i	0.822441	+	1.42451i	0.903859	+	0.427830i	$0.140722\pi$
$479$	18.0000	+	31.1769i	0.822441	+	1.42451i	−0.0814184	+	0.996680i	$0.525945\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$	5.00000	−	8.66025i	0.227744	−	0.394464i
$483$		0			0
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$		0			0
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	−0.925746	−	0.378147i	$-0.876561\pi$
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	0.790358	+	0.612646i	$0.209895\pi$
$492$		0			0
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$	16.0000			0.719874
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	9.00000	+	15.5885i	0.401690	+	0.695747i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$		0			0
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	−0.594675	−	0.803966i	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		0			0
$511$	10.0000	+	17.3205i	0.442374	+	0.766214i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.00000			−0.264649
$515$	1.00000	+	1.73205i	0.0440653	+	0.0763233i
$516$		0			0
$517$		0			0
$518$	−8.00000	+	13.8564i	−0.351500	+	0.608816i
$519$		0			0
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−3.00000	−	5.19615i	−0.131056	−	0.226995i
$525$		0			0
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−6.00000			−0.260623
$531$		0			0
$532$	−8.00000			−0.346844
$533$		0			0
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$		0			0
$538$	9.00000	+	15.5885i	0.388018	+	0.672066i
$539$	18.0000			0.775315
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$	−4.00000	−	6.92820i	−0.171815	−	0.297592i
$543$		0			0
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$	1.00000	−	1.73205i	0.0428353	−	0.0741929i
$546$		0			0
$547$	20.0000	+	34.6410i	0.855138	+	1.48114i	0.876517	+	0.481371i	$0.159861\pi$
$547$	20.0000	+	34.6410i	0.855138	+	1.48114i	−0.0213785	+	0.999771i	$0.506805\pi$
$548$	−6.00000			−0.256307
$549$		0			0
$550$	−6.00000			−0.255841
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$	4.00000	−	6.92820i	0.170097	−	0.294617i
$554$	−4.00000	+	6.92820i	−0.169944	+	0.294351i
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−42.0000			−1.77960			−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000			−1.77960			−0.889799	+	0.456354i	$0.849155\pi$
$558$		0			0
$559$	−32.0000			−1.35346
$560$	1.00000	+	1.73205i	0.0422577	+	0.0731925i
$561$		0			0
$562$	6.00000	−	10.3923i	0.253095	−	0.438373i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	12.0000			0.503509
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	0.945573	+	0.325409i	$0.105502\pi$
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	−0.190974	+	0.981595i	$0.561165\pi$
$570$		0			0
$571$	−22.0000	+	38.1051i	−0.920671	+	1.59465i	−0.122292	+	0.992494i	$0.539025\pi$
$571$	−22.0000	+	38.1051i	−0.920671	+	1.59465i	−0.798379	+	0.602155i	$0.794309\pi$
$572$	−12.0000	+	20.7846i	−0.501745	+	0.869048i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	12.0000	−	20.7846i	0.497844	−	0.862291i
$582$		0			0
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	18.0000			0.743573
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	−0.951151	−	0.308725i	$-0.900098\pi$
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	0.208212	−	0.978084i	$-0.433236\pi$
$588$		0			0
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$	−3.00000	+	5.19615i	−0.123508	+	0.213922i
$591$		0			0
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$		0			0
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$	16.0000			0.652111
$603$		0			0
$604$	−16.0000			−0.651031
$605$	12.5000	+	21.6506i	0.508197	+	0.880223i
$606$		0			0
$607$	−19.0000	+	32.9090i	−0.771186	+	1.33573i	0.165727	+	0.986172i	$0.447003\pi$
$607$	−19.0000	+	32.9090i	−0.771186	+	1.33573i	−0.936913	+	0.349562i	$0.886330\pi$
$608$	2.00000	−	3.46410i	0.0811107	−	0.140488i
$609$		0			0
$610$	1.00000	+	1.73205i	0.0404888	+	0.0701287i
$611$		0			0
$612$		0			0
$613$	8.00000			0.323117			0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000			0.323117			0.161558	+	0.986863i	$0.448348\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$		0			0
$616$	6.00000	−	10.3923i	0.241747	−	0.418718i
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$		0			0
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	0.592025	−	0.805919i	$-0.298329\pi$
$619$	−10.0000	−	17.3205i	−0.401934	−	0.696170i	−0.993959	+	0.109749i	$0.964995\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$	12.0000			0.481156
$623$	12.0000	+	20.7846i	0.480770	+	0.832718i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	48.0000			1.91389
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$		0			0
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	1.00000	−	1.73205i	0.0396838	−	0.0687343i
$636$		0			0
$637$	−6.00000	−	10.3923i	−0.237729	−	0.411758i
$638$	−36.0000			−1.42525
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$		0			0
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	−0.823891	−	0.566748i	$-0.808201\pi$
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	0.902764	+	0.430137i	$0.141535\pi$
$644$		0			0
$645$		0			0
$646$	12.0000	+	20.7846i	0.472134	+	0.817760i
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$		0			0
$649$	36.0000			1.41312
$650$	2.00000	+	3.46410i	0.0784465	+	0.135873i
$651$		0			0
$652$	−10.0000	+	17.3205i	−0.391630	+	0.678323i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.0000	−	25.9808i	−0.584317	−	1.01207i	−0.994960	−	0.100271i	$-0.968029\pi$
$659$	−15.0000	−	25.9808i	−0.584317	−	1.01207i	0.410643	−	0.911796i	$-0.365304\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	8.00000			0.310227
$666$		0			0
$667$		0			0
$668$	−12.0000	−	20.7846i	−0.464294	−	0.804181i
$669$		0			0
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	6.00000	−	10.3923i	0.231627	−	0.401190i
$672$		0			0
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	0.698988	−	0.715134i	$-0.253634\pi$
$673$	−7.00000	−	12.1244i	−0.269830	−	0.467360i	−0.968818	+	0.247774i	$0.920301\pi$
$674$	14.0000			0.539260
$675$		0			0
$676$	3.00000			0.115385
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$	3.00000	−	5.19615i	0.115045	−	0.199263i
$681$		0			0
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$		0			0
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$		0			0
$695$	10.0000	+	17.3205i	0.379322	+	0.657004i
$696$		0			0
$697$		0			0
$698$	11.0000	−	19.0526i	0.416356	−	0.721150i
$699$		0			0
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−32.0000			−1.20690
$704$	3.00000	+	5.19615i	0.113067	+	0.195837i
$705$		0			0
$706$	−15.0000	+	25.9808i	−0.564532	+	0.977799i
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$		0			0
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$	−12.0000			−0.450352
$711$		0			0
$712$	−12.0000			−0.449719
$713$		0			0
$714$		0			0
$715$	12.0000	−	20.7846i	0.448775	−	0.777300i
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$		0			0
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	4.00000			0.148968
$722$	1.50000	+	2.59808i	0.0558242	+	0.0966904i
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	5.00000	+	8.66025i	0.185440	+	0.321191i	0.943725	−	0.330732i	$-0.107296\pi$
$727$	5.00000	+	8.66025i	0.185440	+	0.321191i	−0.758285	+	0.651923i	$0.773962\pi$
$728$	−8.00000			−0.296500
$729$		0			0
$730$	10.0000			0.370117
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	−13.0000	+	22.5167i	−0.479839	+	0.831105i
$735$		0			0
$736$		0			0
$737$	24.0000			0.884051
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	4.00000	+	6.92820i	0.147043	+	0.254686i
$741$		0			0
$742$	−6.00000	+	10.3923i	−0.220267	+	0.381514i
$743$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$743$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	−28.0000			−1.02515
$747$		0			0
$748$	−36.0000			−1.31629
$749$	12.0000	+	20.7846i	0.438470	+	0.759453i
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$		0			0
$753$		0			0
$754$	12.0000	+	20.7846i	0.437014	+	0.756931i
$755$	16.0000			0.582300
$756$		0			0
$757$	−40.0000			−1.45382			−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000			−1.45382			−0.726912	+	0.686730i	$0.759045\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$		0			0
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	18.0000	−	31.1769i	0.652499	−	1.13016i	−0.330015	−	0.943976i	$-0.607054\pi$
$761$	18.0000	−	31.1769i	0.652499	−	1.13016i	0.982514	−	0.186187i	$-0.0596129\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	−12.0000			−0.434145
$765$		0			0
$766$		0			0
$767$	−12.0000	−	20.7846i	−0.433295	−	0.750489i
$768$		0			0
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	−0.964193	−	0.265200i	$-0.914562\pi$
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$770$	−6.00000	+	10.3923i	−0.216225	+	0.374513i
$771$		0			0
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$		0			0
$778$	−9.00000	+	15.5885i	−0.322666	+	0.558873i
$779$		0			0
$780$		0			0
$781$	36.0000	+	62.3538i	1.28818	+	2.23120i
$782$		0			0
$783$		0			0
$784$	−3.00000			−0.107143
$785$	−2.00000	−	3.46410i	−0.0713831	−	0.123639i
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$	−2.00000	−	3.46410i	−0.0711568	−	0.123247i
$791$	−12.0000			−0.426671
$792$		0			0
$793$	−8.00000			−0.284088
$794$	8.00000	+	13.8564i	0.283909	+	0.491745i
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	−0.661441	−	0.749997i	$-0.730055\pi$
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	0.980237	+	0.197826i	$0.0633881\pi$
$798$		0			0
$799$		0			0
$800$	1.00000			0.0353553
$801$		0			0
$802$	36.0000			1.27120
$803$	−30.0000	−	51.9615i	−1.05868	−	1.83368i
$804$		0			0
$805$		0			0
$806$	−8.00000	+	13.8564i	−0.281788	+	0.488071i
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	24.0000			0.843795			0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000			0.843795			0.421898	+	0.906644i	$0.361364\pi$
$810$		0			0
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$	−6.00000	−	10.3923i	−0.210559	−	0.364698i
$813$		0			0
$814$	24.0000	−	41.5692i	0.841200	−	1.45700i
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$		0			0
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	−22.0000			−0.769212
$819$		0			0
$820$		0			0
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	−0.999626	−	0.0273557i	$-0.991291\pi$
$821$	−15.0000	−	25.9808i	−0.523504	−	0.906735i	0.476122	−	0.879379i	$-0.342042\pi$
$822$		0			0
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−1.00000	+	1.73205i	−0.0348367	+	0.0603388i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$		0			0
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	9.00000	−	15.5885i	0.311832	−	0.540108i
$834$		0			0
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$	24.0000			0.830057
$837$		0			0
$838$	6.00000			0.207267
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−7.00000	+	12.1244i	−0.241236	+	0.417833i
$843$		0			0
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−3.00000			−0.103203
$846$		0			0
$847$	50.0000			1.71802
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$	−3.00000	+	5.19615i	−0.102899	+	0.178227i
$851$		0			0
$852$		0			0
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$854$	4.00000			0.136877
$855$		0			0
$856$	−12.0000			−0.410152
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$	4.00000	−	6.92820i	0.136399	−	0.236250i
$861$		0			0
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	18.0000			0.612018
$866$	−19.0000	−	32.9090i	−0.645646	−	1.11829i
$867$		0			0
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	2.00000			0.0677285
$873$		0			0
$874$		0			0
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$		0			0
$877$	14.0000	−	24.2487i	0.472746	−	0.818821i	−0.526767	−	0.850010i	$-0.676596\pi$
$877$	14.0000	−	24.2487i	0.472746	−	0.818821i	0.999514	+	0.0311889i	$0.00992933\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$		0			0
$880$	−3.00000	−	5.19615i	−0.101130	−	0.175162i
$881$	36.0000			1.21287			0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000			1.21287			0.606435	+	0.795133i	$0.292599\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	−0.109881	−	0.993945i	$-0.535047\pi$
$887$	24.0000	−	41.5692i	0.805841	−	1.39576i	0.915722	−	0.401813i	$-0.131620\pi$
$888$		0			0
$889$	−2.00000	−	3.46410i	−0.0670778	−	0.116182i
$890$	12.0000			0.402241
$891$		0			0
$892$	26.0000			0.870544
$893$		0			0
$894$		0			0
$895$	−3.00000	+	5.19615i	−0.100279	+	0.173688i
$896$	−1.00000	+	1.73205i	−0.0334077	+	0.0578638i
$897$		0			0
$898$	−6.00000	−	10.3923i	−0.200223	−	0.346796i
$899$	−24.0000			−0.800445
$900$		0			0
$901$	36.0000			1.19933
$902$		0			0
$903$		0			0
$904$	3.00000	−	5.19615i	0.0997785	−	0.172821i
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$		0			0
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	0.979531	+	0.201291i	$0.0645138\pi$
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	−0.315442	+	0.948945i	$0.602153\pi$
$908$		0			0
$909$		0			0
$910$	8.00000			0.265197
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$	−36.0000	+	62.3538i	−1.19143	+	2.06361i
$914$	−13.0000	+	22.5167i	−0.430002	+	0.744785i
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	12.0000			0.396275
$918$		0			0
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$		0			0
$921$		0			0
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$	24.0000	−	41.5692i	0.789970	−	1.36827i
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	−34.0000			−1.11731
$927$		0			0
$928$	6.00000			0.196960
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	0.994157	+	0.107944i	$0.0344268\pi$
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	−0.403596	+	0.914937i	$0.632240\pi$
$930$		0			0
$931$	−6.00000	+	10.3923i	−0.196642	+	0.340594i
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	36.0000			1.17733
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	4.00000	+	6.92820i	0.130605	+	0.226214i
$939$		0			0
$940$		0			0
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	0.288988	+	0.957333i	$0.406681\pi$
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	−0.973568	+	0.228395i	$0.926652\pi$
$942$		0			0
$943$		0			0
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−48.0000			−1.56061
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$		0			0
$949$	−20.0000	+	34.6410i	−0.649227	+	1.12449i
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$		0			0
$955$	12.0000			0.388311
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		0			0
$958$	18.0000	−	31.1769i	0.581554	−	1.00728i
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−32.0000			−1.03172
$963$		0			0
$964$	−10.0000			−0.322078
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$		0			0
$967$	−1.00000	+	1.73205i	−0.0321578	+	0.0556990i	−0.881656	−	0.471892i	$-0.843571\pi$
$967$	−1.00000	+	1.73205i	−0.0321578	+	0.0556990i	0.849499	+	0.527591i	$0.176905\pi$
$968$	−12.5000	+	21.6506i	−0.401765	+	0.695878i
$969$		0			0
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	6.00000			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$972$		0			0
$973$	40.0000			1.28234
$974$	−19.0000	−	32.9090i	−0.608799	−	1.05447i
$975$		0			0
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$978$		0			0
$979$	−36.0000	−	62.3538i	−1.15056	−	1.99284i
$980$	3.00000			0.0958315
$981$		0			0
$982$	6.00000			0.191468
$983$	−24.0000	−	41.5692i	−0.765481	−	1.32585i	−0.939992	−	0.341197i	$-0.889168\pi$
$983$	−24.0000	−	41.5692i	−0.765481	−	1.32585i	0.174511	−	0.984655i	$-0.444166\pi$
$984$		0			0
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$	−18.0000	+	31.1769i	−0.573237	+	0.992875i
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$		0			0
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		0			0
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$	−8.00000	+	13.8564i	−0.253617	+	0.439278i
$996$		0			0
$997$	−22.0000	−	38.1051i	−0.696747	−	1.20680i	−0.969588	−	0.244742i	$-0.921297\pi$
$997$	−22.0000	−	38.1051i	−0.696747	−	1.20680i	0.272841	−	0.962059i	$-0.412037\pi$
$998$	−4.00000			−0.126618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.e.e.271.1		2
3.2	odd	2		810.2.e.h.271.1		2
9.2	odd	6		810.2.e.h.541.1		2
9.4	even	3		90.2.a.b.1.1	yes	1
9.5	odd	6		90.2.a.a.1.1	✓	1
9.7	even	3	inner	810.2.e.e.541.1		2
36.23	even	6		720.2.a.g.1.1		1
36.31	odd	6		720.2.a.b.1.1		1
45.4	even	6		450.2.a.a.1.1		1
45.13	odd	12		450.2.c.a.199.1		2
45.14	odd	6		450.2.a.e.1.1		1
45.22	odd	12		450.2.c.a.199.2		2
45.23	even	12		450.2.c.d.199.2		2
45.32	even	12		450.2.c.d.199.1		2
63.13	odd	6		4410.2.a.bf.1.1		1
63.41	even	6		4410.2.a.k.1.1		1
72.5	odd	6		2880.2.a.k.1.1		1
72.13	even	6		2880.2.a.bf.1.1		1
72.59	even	6		2880.2.a.h.1.1		1
72.67	odd	6		2880.2.a.u.1.1		1
180.23	odd	12		3600.2.f.a.2449.2		2
180.59	even	6		3600.2.a.ba.1.1		1
180.67	even	12		3600.2.f.u.2449.1		2
180.103	even	12		3600.2.f.u.2449.2		2
180.139	odd	6		3600.2.a.bj.1.1		1
180.167	odd	12		3600.2.f.a.2449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.a.a.1.1	✓	1	9.5	odd	6
90.2.a.b.1.1	yes	1	9.4	even	3
450.2.a.a.1.1		1	45.4	even	6
450.2.a.e.1.1		1	45.14	odd	6
450.2.c.a.199.1		2	45.13	odd	12
450.2.c.a.199.2		2	45.22	odd	12
450.2.c.d.199.1		2	45.32	even	12
450.2.c.d.199.2		2	45.23	even	12
720.2.a.b.1.1		1	36.31	odd	6
720.2.a.g.1.1		1	36.23	even	6
810.2.e.e.271.1		2	1.1	even	1	trivial
810.2.e.e.541.1		2	9.7	even	3	inner
810.2.e.h.271.1		2	3.2	odd	2
810.2.e.h.541.1		2	9.2	odd	6
2880.2.a.h.1.1		1	72.59	even	6
2880.2.a.k.1.1		1	72.5	odd	6
2880.2.a.u.1.1		1	72.67	odd	6
2880.2.a.bf.1.1		1	72.13	even	6
3600.2.a.ba.1.1		1	180.59	even	6
3600.2.a.bj.1.1		1	180.139	odd	6
3600.2.f.a.2449.1		2	180.167	odd	12
3600.2.f.a.2449.2		2	180.23	odd	12
3600.2.f.u.2449.1		2	180.67	even	12
3600.2.f.u.2449.2		2	180.103	even	12
4410.2.a.k.1.1		1	63.41	even	6
4410.2.a.bf.1.1		1	63.13	odd	6

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +1.00000 q^{8} -1.00000 q^{10} +(3.00000 + 5.19615i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.00000 q^{17} -4.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(3.00000 - 5.19615i) q^{22} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{26} +2.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} -2.00000 q^{35} +8.00000 q^{37} +(2.00000 + 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-4.00000 - 6.92820i) q^{43} -6.00000 q^{44} +(1.50000 - 2.59808i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.00000 + 3.46410i) q^{52} +6.00000 q^{53} +6.00000 q^{55} +(-1.00000 - 1.73205i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(1.00000 + 1.73205i) q^{70} +12.0000 q^{71} -10.0000 q^{73} +(-4.00000 - 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(6.00000 - 10.3923i) q^{77} +(2.00000 + 3.46410i) q^{79} -1.00000 q^{80} +(6.00000 + 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{88} -12.0000 q^{89} -8.00000 q^{91} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + q^5 - 2 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + q^{5} - 2 q^{7} + 2 q^{8} - 2 q^{10} + 6 q^{11} + 4 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{19} + q^{20} + 6 q^{22} - q^{25} - 8 q^{26} + 4 q^{28} - 6 q^{29} + 4 q^{31} - q^{32} - 6 q^{34} - 4 q^{35} + 16 q^{37} + 4 q^{38} + q^{40} - 8 q^{43} - 12 q^{44} + 3 q^{49} - q^{50} + 4 q^{52} + 12 q^{53} + 12 q^{55} - 2 q^{56} - 6 q^{58} + 6 q^{59} - 2 q^{61} - 8 q^{62} + 2 q^{64} - 4 q^{65} + 4 q^{67} - 6 q^{68} + 2 q^{70} + 24 q^{71} - 20 q^{73} - 8 q^{74} + 4 q^{76} + 12 q^{77} + 4 q^{79} - 2 q^{80} + 12 q^{83} + 6 q^{85} - 8 q^{86} + 6 q^{88} - 24 q^{89} - 16 q^{91} - 4 q^{95} - 2 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + q^5 - 2 * q^7 + 2 * q^8 - 2 * q^10 + 6 * q^11 + 4 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 8 * q^19 + q^20 + 6 * q^22 - q^25 - 8 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 - 6 * q^34 - 4 * q^35 + 16 * q^37 + 4 * q^38 + q^40 - 8 * q^43 - 12 * q^44 + 3 * q^49 - q^50 + 4 * q^52 + 12 * q^53 + 12 * q^55 - 2 * q^56 - 6 * q^58 + 6 * q^59 - 2 * q^61 - 8 * q^62 + 2 * q^64 - 4 * q^65 + 4 * q^67 - 6 * q^68 + 2 * q^70 + 24 * q^71 - 20 * q^73 - 8 * q^74 + 4 * q^76 + 12 * q^77 + 4 * q^79 - 2 * q^80 + 12 * q^83 + 6 * q^85 - 8 * q^86 + 6 * q^88 - 24 * q^89 - 16 * q^91 - 4 * q^95 - 2 * q^97 - 6 * q^98

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