LMFDB - Embedded newform 833.2.e.b.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(18,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("833.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.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:	$6.65153848837$
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 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	833.18
Dual form			833.2.e.b.324.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} -2.00000 q^{13} +(0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(2.00000 + 3.46410i) q^{19} +2.00000 q^{20} +(-2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} -1.00000 q^{34} +3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{40} -6.00000 q^{41} +4.00000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(2.00000 - 3.46410i) q^{46} +1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(3.00000 + 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(5.00000 + 8.66025i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(0.500000 + 0.866025i) q^{68} -4.00000 q^{71} +(4.50000 + 7.79423i) q^{72} +(3.00000 - 5.19615i) q^{73} +(-1.00000 + 1.73205i) q^{74} +4.00000 q^{76} +(-6.00000 - 10.3923i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 - 5.19615i) q^{82} -4.00000 q^{83} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-5.00000 - 8.66025i) q^{89} -6.00000 q^{90} -4.00000 q^{92} +(-4.00000 + 6.92820i) q^{95} +2.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 2 q^{5} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + q^4 + 2 * q^5 + 6 * q^8 + 3 * q^9	$ 2 q + q^{2} + q^{4} + 2 q^{5} + 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{13} + q^{16} - q^{17} - 3 q^{18} + 4 q^{19} + 4 q^{20} - 4 q^{23} + q^{25} - 2 q^{26} + 12 q^{29} - 4 q^{31} + 5 q^{32} - 2 q^{34} + 6 q^{36} + 2 q^{37} - 4 q^{38} + 6 q^{40} - 12 q^{41} + 8 q^{43} - 6 q^{45} + 4 q^{46} + 2 q^{50} - 2 q^{52} - 6 q^{53} + 6 q^{58} + 12 q^{59} + 10 q^{61} - 8 q^{62} + 14 q^{64} - 4 q^{65} - 4 q^{67} + q^{68} - 8 q^{71} + 9 q^{72} + 6 q^{73} - 2 q^{74} + 8 q^{76} - 12 q^{79} - 2 q^{80} - 9 q^{81} - 6 q^{82} - 8 q^{83} - 4 q^{85} + 4 q^{86} - 10 q^{89} - 12 q^{90} - 8 q^{92} - 8 q^{95} + 4 q^{97}+O(q^{100}) $ 2 * q + q^2 + q^4 + 2 * q^5 + 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^13 + q^16 - q^17 - 3 * q^18 + 4 * q^19 + 4 * q^20 - 4 * q^23 + q^25 - 2 * q^26 + 12 * q^29 - 4 * q^31 + 5 * q^32 - 2 * q^34 + 6 * q^36 + 2 * q^37 - 4 * q^38 + 6 * q^40 - 12 * q^41 + 8 * q^43 - 6 * q^45 + 4 * q^46 + 2 * q^50 - 2 * q^52 - 6 * q^53 + 6 * q^58 + 12 * q^59 + 10 * q^61 - 8 * q^62 + 14 * q^64 - 4 * q^65 - 4 * q^67 + q^68 - 8 * q^71 + 9 * q^72 + 6 * q^73 - 2 * q^74 + 8 * q^76 - 12 * q^79 - 2 * q^80 - 9 * q^81 - 6 * q^82 - 8 * q^83 - 4 * q^85 + 4 * q^86 - 10 * q^89 - 12 * q^90 - 8 * q^92 - 8 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	−1.00000			−0.171499
$35$		0			0
$36$	3.00000			0.500000
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	3.00000	+	5.19615i	0.474342	+	0.821584i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$		0			0
$50$	1.00000			0.141421
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	7.00000			0.875000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	0.500000	+	0.866025i	0.0606339	+	0.105021i
$69$		0			0
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$	4.50000	+	7.79423i	0.530330	+	0.918559i
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	−0.635323	−	0.772246i	$-0.719133\pi$
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	0.986447	+	0.164083i	$0.0524664\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$		0			0
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	−0.976453	−	0.215728i	$-0.930788\pi$
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	0.301401	−	0.953498i	$-0.402546\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$		0			0
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$	−4.00000			−0.417029
$93$		0			0
$94$		0			0
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$		0			0
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	−0.973176	−	0.230063i	$-0.926107\pi$
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	0.685828	+	0.727764i	$0.259440\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	12.0000			1.07331
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	−8.00000	−	13.8564i	−0.698963	−	1.21064i	−0.968826	−	0.247741i	$-0.920312\pi$
$131$	−8.00000	−	13.8564i	−0.698963	−	1.21064i	0.269863	−	0.962899i	$-0.413022\pi$
$132$		0			0
$133$		0			0
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$		0			0
$142$	−2.00000	−	3.46410i	−0.167836	−	0.290701i
$143$		0			0
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	6.00000	+	10.3923i	0.498273	+	0.863034i
$146$	6.00000			0.496564
$147$		0			0
$148$	2.00000			0.164399
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	6.00000	+	10.3923i	0.486664	+	0.842927i
$153$	−3.00000			−0.242536
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	−0.823359	−	0.567521i	$-0.807902\pi$
$157$	1.00000	−	1.73205i	0.0798087	−	0.138233i	0.903167	+	0.429289i	$0.141236\pi$
$158$	6.00000	−	10.3923i	0.477334	−	0.826767i
$159$		0			0
$160$	10.0000			0.790569
$161$		0			0
$162$	−9.00000			−0.707107
$163$	−12.0000	−	20.7846i	−0.939913	−	1.62798i	−0.765631	−	0.643280i	$-0.777573\pi$
$163$	−12.0000	−	20.7846i	−0.939913	−	1.62798i	−0.174282	−	0.984696i	$-0.555760\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	−4.00000			−0.309529			−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000			−0.309529			−0.154765	+	0.987951i	$0.549462\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	−6.00000	+	10.3923i	−0.458831	+	0.794719i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	−0.892956	−	0.450145i	$-0.851372\pi$
$173$	−11.0000	−	19.0526i	−0.836315	−	1.44854i	0.0566411	−	0.998395i	$-0.481961\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	5.00000	−	8.66025i	0.374766	−	0.649113i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	3.00000	+	5.19615i	0.223607	+	0.387298i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		0			0
$184$	−6.00000	−	10.3923i	−0.442326	−	0.766131i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−8.00000			−0.580381
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$		0			0
$202$	10.0000			0.703598
$203$		0			0
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	4.00000	−	6.92820i	0.273434	−	0.473602i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$		0			0
$217$		0			0
$218$	−6.00000			−0.406371
$219$		0			0
$220$		0			0
$221$	1.00000	−	1.73205i	0.0672673	−	0.116510i
$222$		0			0
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	−7.00000	−	12.1244i	−0.465633	−	0.806500i
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	−0.125435	−	0.992102i	$-0.540033\pi$
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	0.921903	−	0.387421i	$-0.126634\pi$
$228$		0			0
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	0.749714	−	0.661762i	$-0.230191\pi$
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	−0.947960	+	0.318390i	$0.896858\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	18.0000			1.18176
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$		0			0
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	−5.50000	+	9.52628i	−0.353553	+	0.612372i
$243$		0			0
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$	−4.00000	−	6.92820i	−0.254514	−	0.440831i
$248$	−6.00000	+	10.3923i	−0.381000	+	0.659912i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		0			0
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$		0			0
$259$		0			0
$260$	−4.00000			−0.248069
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	8.00000	−	13.8564i	0.494242	−	0.856052i
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	0.307029	+	0.951700i	$0.400665\pi$
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	−0.977711	+	0.209955i	$0.932668\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	−1.00000			−0.0606339
$273$		0			0
$274$	6.00000			0.362473
$275$		0			0
$276$		0			0
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	−4.00000	−	6.92820i	−0.239904	−	0.415526i
$279$	−12.0000			−0.718421
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	−0.524057	−	0.851683i	$-0.675582\pi$
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	0.999608	+	0.0280052i	$0.00891551\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	15.0000			0.883883
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−6.00000	+	10.3923i	−0.352332	+	0.610257i
$291$		0			0
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$		0			0
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$	4.00000	+	6.92820i	0.231326	+	0.400668i
$300$		0			0
$301$		0			0
$302$	16.0000			0.920697
$303$		0			0
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$	−4.00000	−	6.92820i	−0.227185	−	0.393496i
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	0.129689	+	0.991555i	$0.458602\pi$
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	−0.923556	+	0.383464i	$0.874731\pi$
$312$		0			0
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	0.989158	+	0.146852i	$0.0469141\pi$
$313$	11.0000	+	19.0526i	0.621757	+	1.07691i	−0.367402	+	0.930062i	$0.619753\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−12.0000			−0.675053
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	0.971589	−	0.236675i	$-0.0760576\pi$
$317$	5.00000	+	8.66025i	0.280828	+	0.486408i	−0.690761	+	0.723083i	$0.742724\pi$
$318$		0			0
$319$		0			0
$320$	7.00000	+	12.1244i	0.391312	+	0.677772i
$321$		0			0
$322$		0			0
$323$	−4.00000			−0.222566
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	12.0000	−	20.7846i	0.664619	−	1.15115i
$327$		0			0
$328$	−18.0000			−0.993884
$329$		0			0
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	−2.00000	+	3.46410i	−0.109764	+	0.190117i
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	−2.00000	−	3.46410i	−0.109435	−	0.189547i
$335$	−8.00000			−0.437087
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$	−1.00000	+	1.73205i	−0.0542326	+	0.0939336i
$341$		0			0
$342$	−12.0000			−0.648886
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$	11.0000	−	19.0526i	0.591364	−	1.02427i
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	0.0140303	+	0.999902i	$0.495534\pi$
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	−0.872955	+	0.487800i	$0.837799\pi$
$348$		0			0
$349$	−18.0000			−0.963518			−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000			−0.963518			−0.481759	+	0.876304i	$0.660002\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$		0			0
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	−10.0000			−0.529999
$357$		0			0
$358$	−12.0000			−0.634220
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	−9.00000	+	15.5885i	−0.474342	+	0.821584i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$		0			0
$364$		0			0
$365$	12.0000			0.628109
$366$		0			0
$367$	−14.0000	+	24.2487i	−0.730794	+	1.26577i	0.225750	+	0.974185i	$0.427517\pi$
$367$	−14.0000	+	24.2487i	−0.730794	+	1.26577i	−0.956544	+	0.291587i	$0.905817\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	−4.00000			−0.207950
$371$		0			0
$372$		0			0
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	0.777847	−	0.628454i	$-0.216312\pi$
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$		0			0
$382$	−8.00000	+	13.8564i	−0.409316	+	0.708955i
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	0.990702	+	0.136047i	$0.0434398\pi$
$383$	12.0000	+	20.7846i	0.613171	+	1.06204i	−0.377531	+	0.925997i	$0.623227\pi$
$384$		0			0
$385$		0			0
$386$	−2.00000			−0.101797
$387$	6.00000	+	10.3923i	0.304997	+	0.528271i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		0			0
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	12.0000	−	20.7846i	0.603786	−	1.04579i
$396$		0			0
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	0.780870	−	0.624694i	$-0.214776\pi$
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	−0.931436	+	0.363906i	$0.881443\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.00000	+	12.1244i	0.349563	+	0.605461i	0.986172	−	0.165726i	$-0.0529966\pi$
$401$	7.00000	+	12.1244i	0.349563	+	0.605461i	−0.636609	+	0.771187i	$0.719663\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$	−18.0000			−0.894427
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$	6.00000	−	10.3923i	0.296319	−	0.513239i
$411$		0			0
$412$	−8.00000			−0.394132
$413$		0			0
$414$	12.0000			0.589768
$415$	−4.00000	−	6.92820i	−0.196352	−	0.340092i
$416$	−5.00000	+	8.66025i	−0.245145	+	0.424604i
$417$		0			0
$418$		0			0
$419$	8.00000			0.390826			0.195413	−	0.980721i	$-0.437395\pi$
$419$	8.00000			0.390826			0.195413	+	0.980721i	$0.437395\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$		0			0
$424$	−9.00000	+	15.5885i	−0.437079	+	0.757042i
$425$	0.500000	+	0.866025i	0.0242536	+	0.0420084i
$426$		0			0
$427$		0			0
$428$	−8.00000			−0.386695
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$	8.00000	−	13.8564i	0.382692	−	0.662842i
$438$		0			0
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$		0			0
$441$		0			0
$442$	2.00000			0.0951303
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	−0.979242	−	0.202695i	$-0.935030\pi$
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	0.314082	−	0.949396i	$-0.398303\pi$
$444$		0			0
$445$	10.0000	−	17.3205i	0.474045	−	0.821071i
$446$	12.0000	+	20.7846i	0.568216	+	0.984180i
$447$		0			0
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$	1.50000	+	2.59808i	0.0707107	+	0.122474i
$451$		0			0
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	24.0000			1.12638
$455$		0			0
$456$		0			0
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	0.927622	−	0.373519i	$-0.121849\pi$
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	−0.787288	+	0.616585i	$0.788516\pi$
$458$	3.00000	−	5.19615i	0.140181	−	0.242800i
$459$		0			0
$460$	−4.00000	−	6.92820i	−0.186501	−	0.323029i
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$		0			0
$471$		0			0
$472$	18.0000	−	31.1769i	0.828517	−	1.43503i
$473$		0			0
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	−18.0000			−0.824163
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	0.0814184	+	0.996680i	$0.474055\pi$
$479$	−18.0000	+	31.1769i	−0.822441	+	1.42451i	−0.903859	+	0.427830i	$0.859278\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	−18.0000			−0.819878
$483$		0			0
$484$	11.0000			0.500000
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$		0			0
$487$	−10.0000	+	17.3205i	−0.453143	+	0.784867i	−0.998579	−	0.0532853i	$-0.983031\pi$
$487$	−10.0000	+	17.3205i	−0.453143	+	0.784867i	0.545436	+	0.838152i	$0.316364\pi$
$488$	15.0000	+	25.9808i	0.679018	+	1.17609i
$489$		0			0
$490$		0			0
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$		0			0
$493$	−3.00000	+	5.19615i	−0.135113	+	0.234023i
$494$	4.00000	−	6.92820i	0.179969	−	0.311715i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.833404	+	0.552664i	$0.186389\pi$
$499$	20.0000	+	34.6410i	0.895323	+	1.55074i	0.0619186	+	0.998081i	$0.480278\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	20.0000			0.889988
$506$		0			0
$507$		0			0
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$		0			0
$512$	11.0000			0.486136
$513$		0			0
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	−13.0000	+	22.5167i	−0.569540	+	0.986473i	0.427071	+	0.904218i	$0.359545\pi$
$521$	−13.0000	+	22.5167i	−0.569540	+	0.986473i	−0.996611	+	0.0822547i	$0.973788\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	18.0000	+	31.1769i	0.787085	+	1.36327i	0.927746	+	0.373213i	$0.121744\pi$
$523$	18.0000	+	31.1769i	0.787085	+	1.36327i	−0.140660	+	0.990058i	$0.544923\pi$
$524$	−16.0000			−0.698963
$525$		0			0
$526$	16.0000			0.697633
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$	36.0000			1.56227
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$	8.00000	−	13.8564i	0.345870	−	0.599065i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	−22.0000			−0.948487
$539$		0			0
$540$		0			0
$541$	−3.00000	−	5.19615i	−0.128980	−	0.223400i	0.794302	−	0.607524i	$-0.207837\pi$
$541$	−3.00000	−	5.19615i	−0.128980	−	0.223400i	−0.923282	+	0.384124i	$0.874504\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$		0			0
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	−15.0000	+	25.9808i	−0.640184	+	1.10883i
$550$		0			0
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		0			0
$553$		0			0
$554$	−14.0000			−0.594803
$555$		0			0
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$	−6.00000	−	10.3923i	−0.254000	−	0.439941i
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	−14.0000	−	24.2487i	−0.588984	−	1.02015i
$566$	16.0000			0.672530
$567$		0			0
$568$	−12.0000			−0.503509
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	0.921869	+	0.387503i	$0.126662\pi$
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	−0.125347	+	0.992113i	$0.540004\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.00000			−0.166812
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	−0.682730	−	0.730670i	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$		0			0
$580$	12.0000			0.498273
$581$		0			0
$582$		0			0
$583$		0			0
$584$	9.00000	−	15.5885i	0.372423	−	0.645055i
$585$	6.00000	−	10.3923i	0.248069	−	0.429669i
$586$	3.00000	+	5.19615i	0.123929	+	0.214651i
$587$	4.00000			0.165098			0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000			0.165098			0.0825488	+	0.996587i	$0.473694\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$	12.0000	+	20.7846i	0.494032	+	0.855689i
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−9.00000	−	15.5885i	−0.369586	−	0.640141i	0.619915	−	0.784669i	$-0.287167\pi$
$593$	−9.00000	−	15.5885i	−0.369586	−	0.640141i	−0.989501	+	0.144528i	$0.953834\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	−4.00000	+	6.92820i	−0.163572	+	0.283315i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	−8.00000	−	13.8564i	−0.325515	−	0.563809i
$605$	−11.0000	+	19.0526i	−0.447214	+	0.774597i
$606$		0			0
$607$	−10.0000	−	17.3205i	−0.405887	−	0.703018i	0.588537	−	0.808470i	$-0.299704\pi$
$607$	−10.0000	−	17.3205i	−0.405887	−	0.703018i	−0.994424	+	0.105453i	$0.966371\pi$
$608$	20.0000			0.811107
$609$		0			0
$610$	−20.0000			−0.809776
$611$		0			0
$612$	−1.50000	+	2.59808i	−0.0606339	+	0.105021i
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	−0.474509	−	0.880251i	$-0.657374\pi$
$613$	13.0000	−	22.5167i	0.525065	−	0.909439i	0.999574	−	0.0291886i	$-0.00929235\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$		0			0
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	24.0000	−	41.5692i	0.964641	−	1.67081i	0.254066	−	0.967187i	$-0.418232\pi$
$619$	24.0000	−	41.5692i	0.964641	−	1.67081i	0.710575	−	0.703621i	$-0.248435\pi$
$620$	−4.00000	+	6.92820i	−0.160644	+	0.278243i
$621$		0			0
$622$	−28.0000			−1.12270
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$		0			0
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	−2.00000			−0.0797452
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	−18.0000	−	31.1769i	−0.716002	−	1.24015i
$633$		0			0
$634$	−5.00000	+	8.66025i	−0.198575	+	0.343943i
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$	3.00000	−	5.19615i	0.118585	−	0.205396i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	32.0000			1.26196			0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000			1.26196			0.630978	+	0.775800i	$0.282654\pi$
$644$		0			0
$645$		0			0
$646$	−2.00000	−	3.46410i	−0.0786889	−	0.136293i
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	−0.933878	−	0.357591i	$-0.883598\pi$
$647$	−4.00000	+	6.92820i	−0.157256	+	0.272376i	0.776622	+	0.629967i	$0.216932\pi$
$648$	−13.5000	+	23.3827i	−0.530330	+	0.918559i
$649$		0			0
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	−24.0000			−0.939913
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	0.801337	−	0.598213i	$-0.204122\pi$
$653$	−3.00000	−	5.19615i	−0.117399	−	0.203341i	−0.918736	+	0.394872i	$0.870789\pi$
$654$		0			0
$655$	16.0000	−	27.7128i	0.625172	−	1.08283i
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	18.0000			0.702247
$658$		0			0
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$		0			0
$661$	−19.0000	+	32.9090i	−0.739014	+	1.28001i	0.213925	+	0.976850i	$0.431375\pi$
$661$	−19.0000	+	32.9090i	−0.739014	+	1.28001i	−0.952940	+	0.303160i	$0.901958\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−6.00000			−0.232495
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	−2.00000	+	3.46410i	−0.0773823	+	0.134030i
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$		0			0
$672$		0			0
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$		0			0
$676$	−4.50000	+	7.79423i	−0.173077	+	0.299778i
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	−0.995877	−	0.0907112i	$-0.971086\pi$
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	0.419380	−	0.907811i	$-0.362247\pi$
$678$		0			0
$679$		0			0
$680$	−6.00000			−0.230089
$681$		0			0
$682$		0			0
$683$	20.0000	−	34.6410i	0.765279	−	1.32550i	−0.174820	−	0.984600i	$-0.555934\pi$
$683$	20.0000	−	34.6410i	0.765279	−	1.32550i	0.940099	−	0.340901i	$-0.110732\pi$
$684$	6.00000	+	10.3923i	0.229416	+	0.397360i
$685$	12.0000			0.458496
$686$		0			0
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	−32.0000			−1.21470
$695$	−8.00000	−	13.8564i	−0.303457	−	0.525603i
$696$		0			0
$697$	3.00000	−	5.19615i	0.113633	−	0.196818i
$698$	−9.00000	−	15.5885i	−0.340655	−	0.590032i
$699$		0			0
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$		0			0
$705$		0			0
$706$	30.0000			1.12906
$707$		0			0
$708$		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	$0.612910\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$	18.0000	−	31.1769i	0.675053	−	1.16923i
$712$	−15.0000	−	25.9808i	−0.562149	−	0.973670i
$713$	16.0000			0.599205
$714$		0			0
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$		0			0
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	0.826319	−	0.563202i	$-0.190431\pi$
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	−0.900907	+	0.434013i	$0.857097\pi$
$720$	−6.00000			−0.223607
$721$		0			0
$722$	3.00000			0.111648
$723$		0			0
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	6.00000	+	10.3923i	0.222070	+	0.384636i
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$		0			0
$733$	25.0000	+	43.3013i	0.923396	+	1.59937i	0.794121	+	0.607760i	$0.207932\pi$
$733$	25.0000	+	43.3013i	0.923396	+	1.59937i	0.129275	+	0.991609i	$0.458735\pi$
$734$	−28.0000			−1.03350
$735$		0			0
$736$	−20.0000			−0.737210
$737$		0			0
$738$	9.00000	−	15.5885i	0.331295	−	0.573819i
$739$	−14.0000	+	24.2487i	−0.514998	+	0.892003i	0.484850	+	0.874597i	$0.338874\pi$
$739$	−14.0000	+	24.2487i	−0.514998	+	0.892003i	−0.999849	+	0.0174060i	$0.994459\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$		0			0
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$		0			0
$745$	−10.0000	+	17.3205i	−0.366372	+	0.634574i
$746$	3.00000	−	5.19615i	0.109838	−	0.190245i
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	0.623856	−	0.781540i	$-0.285565\pi$
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	−0.988761	+	0.149505i	$0.952232\pi$
$752$		0			0
$753$		0			0
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	32.0000			1.16460
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−4.00000	−	6.92820i	−0.145287	−	0.251644i
$759$		0			0
$760$	−12.0000	+	20.7846i	−0.435286	+	0.753937i
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	0.993572	−	0.113203i	$-0.0361109\pi$
$761$	11.0000	+	19.0526i	0.398750	+	0.690655i	−0.594822	+	0.803857i	$0.702778\pi$
$762$		0			0
$763$		0			0
$764$	16.0000			0.578860
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$	−12.0000	+	20.7846i	−0.433578	+	0.750978i
$767$	−12.0000	+	20.7846i	−0.433295	+	0.750489i
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$		0			0
$772$	1.00000	+	1.73205i	0.0359908	+	0.0623379i
$773$	13.0000	−	22.5167i	0.467578	−	0.809868i	−0.531736	−	0.846910i	$-0.678460\pi$
$773$	13.0000	−	22.5167i	0.467578	−	0.809868i	0.999314	+	0.0370420i	$0.0117935\pi$
$774$	−6.00000	+	10.3923i	−0.215666	+	0.373544i
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	6.00000			0.215387
$777$		0			0
$778$	−6.00000			−0.215110
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$	2.00000	+	3.46410i	0.0715199	+	0.123876i
$783$		0			0
$784$		0			0
$785$	4.00000			0.142766
$786$		0			0
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	−0.426193	−	0.904632i	$-0.640145\pi$
$787$	16.0000	−	27.7128i	0.570338	−	0.987855i	0.996531	−	0.0832226i	$-0.0265213\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$	24.0000			0.853882
$791$		0			0
$792$		0			0
$793$	−10.0000	−	17.3205i	−0.355110	−	0.615069i
$794$	3.00000	−	5.19615i	0.106466	−	0.184405i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	−50.0000			−1.77109			−0.885545	−	0.464553i	$-0.846215\pi$
$797$	−50.0000			−1.77109			−0.885545	+	0.464553i	$0.846215\pi$
$798$		0			0
$799$		0			0
$800$	−2.50000	−	4.33013i	−0.0883883	−	0.153093i
$801$	15.0000	−	25.9808i	0.529999	−	0.917985i
$802$	−7.00000	+	12.1244i	−0.247179	+	0.428126i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	15.0000	−	25.9808i	0.527698	−	0.914000i
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	−0.998804	−	0.0488972i	$-0.984429\pi$
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	0.541748	+	0.840541i	$0.317763\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	40.0000			1.40459			0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	24.0000	−	41.5692i	0.840683	−	1.45611i
$816$		0			0
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	−26.0000			−0.909069
$819$		0			0
$820$	−12.0000			−0.419058
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	−0.985997	−	0.166762i	$-0.946669\pi$
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	0.637419	+	0.770517i	$0.280002\pi$
$824$	−12.0000	−	20.7846i	−0.418040	−	0.724066i
$825$		0			0
$826$		0			0
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$		0			0
$832$	−14.0000			−0.485363
$833$		0			0
$834$		0			0
$835$	−4.00000	−	6.92820i	−0.138426	−	0.239760i
$836$		0			0
$837$		0			0
$838$	4.00000	+	6.92820i	0.138178	+	0.239331i
$839$	20.0000			0.690477			0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000			0.690477			0.345238	+	0.938515i	$0.387798\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$		0			0
$844$	4.00000	−	6.92820i	0.137686	−	0.238479i
$845$	−9.00000	−	15.5885i	−0.309609	−	0.536259i
$846$		0			0
$847$		0			0
$848$	−6.00000			−0.206041
$849$		0			0
$850$	−0.500000	+	0.866025i	−0.0171499	+	0.0297044i
$851$	4.00000	−	6.92820i	0.137118	−	0.237496i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	−24.0000			−0.820783
$856$	−12.0000	−	20.7846i	−0.410152	−	0.710403i
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	−0.938699	−	0.344739i	$-0.887967\pi$
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	0.767902	+	0.640567i	$0.221301\pi$
$858$		0			0
$859$	−26.0000	−	45.0333i	−0.887109	−	1.53652i	−0.843278	−	0.537478i	$-0.819377\pi$
$859$	−26.0000	−	45.0333i	−0.887109	−	1.53652i	−0.0438309	−	0.999039i	$-0.513956\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$	−12.0000			−0.408722
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	0.697133	−	0.716942i	$-0.254459\pi$
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	−0.969456	+	0.245264i	$0.921125\pi$
$864$		0			0
$865$	22.0000	−	38.1051i	0.748022	−	1.29561i
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	−9.00000	+	15.5885i	−0.304778	+	0.527892i
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$	16.0000			0.541208
$875$		0			0
$876$		0			0
$877$	−3.00000	−	5.19615i	−0.101303	−	0.175462i	0.810919	−	0.585159i	$-0.198968\pi$
$877$	−3.00000	−	5.19615i	−0.101303	−	0.175462i	−0.912222	+	0.409697i	$0.865634\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$		0			0
$880$		0			0
$881$	−46.0000			−1.54978			−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000			−1.54978			−0.774890	+	0.632096i	$0.782195\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$	−1.00000	−	1.73205i	−0.0336336	−	0.0582552i
$885$		0			0
$886$	14.0000	−	24.2487i	0.470339	−	0.814651i
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$		0			0
$889$		0			0
$890$	20.0000			0.670402
$891$		0			0
$892$	12.0000	−	20.7846i	0.401790	−	0.695920i
$893$		0			0
$894$		0			0
$895$	−24.0000			−0.802232
$896$		0			0
$897$		0			0
$898$	17.0000	+	29.4449i	0.567297	+	0.982588i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$	−3.00000	−	5.19615i	−0.0999445	−	0.173109i
$902$		0			0
$903$		0			0
$904$	−42.0000			−1.39690
$905$	−2.00000	−	3.46410i	−0.0664822	−	0.115151i
$906$		0			0
$907$	−16.0000	+	27.7128i	−0.531271	+	0.920189i	0.468063	+	0.883695i	$0.344952\pi$
$907$	−16.0000	+	27.7128i	−0.531271	+	0.920189i	−0.999334	+	0.0364935i	$0.988381\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	30.0000			0.995037
$910$		0			0
$911$	−4.00000			−0.132526			−0.0662630	−	0.997802i	$-0.521108\pi$
$911$	−4.00000			−0.132526			−0.0662630	+	0.997802i	$0.521108\pi$
$912$		0			0
$913$		0			0
$914$	−3.00000	+	5.19615i	−0.0992312	+	0.171873i
$915$		0			0
$916$	−6.00000			−0.198246
$917$		0			0
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	12.0000	−	20.7846i	0.395628	−	0.685248i
$921$		0			0
$922$	−1.00000	−	1.73205i	−0.0329332	−	0.0570421i
$923$	8.00000			0.263323
$924$		0			0
$925$	2.00000			0.0657596
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$	12.0000	−	20.7846i	0.394132	−	0.682656i
$928$	15.0000	−	25.9808i	0.492399	−	0.852860i
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$		0			0
$932$	6.00000			0.196537
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$	−9.00000	−	15.5885i	−0.294174	−	0.509525i
$937$	10.0000			0.326686			0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000			0.326686			0.163343	+	0.986569i	$0.447772\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$		0			0
$943$	12.0000	+	20.7846i	0.390774	+	0.676840i
$944$	12.0000			0.390567
$945$		0			0
$946$		0			0
$947$	−16.0000	−	27.7128i	−0.519930	−	0.900545i	−0.999732	−	0.0231683i	$-0.992625\pi$
$947$	−16.0000	−	27.7128i	−0.519930	−	0.900545i	0.479801	−	0.877377i	$-0.340709\pi$
$948$		0			0
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$		0			0
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	−9.00000	−	15.5885i	−0.291386	−	0.504695i
$955$	−16.0000	+	27.7128i	−0.517748	+	0.896766i
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$	−36.0000			−1.16311
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	12.0000	−	20.7846i	0.386695	−	0.669775i
$964$	9.00000	+	15.5885i	0.289870	+	0.502070i
$965$	−4.00000			−0.128765
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	16.5000	+	28.5788i	0.530330	+	0.918559i
$969$		0			0
$970$	−2.00000	+	3.46410i	−0.0642161	+	0.111226i
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$		0			0
$973$		0			0
$974$	−20.0000			−0.640841
$975$		0			0
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−18.0000			−0.574696
$982$	10.0000	+	17.3205i	0.319113	+	0.552720i
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	−0.945705	−	0.325027i	$-0.894626\pi$
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	0.754334	+	0.656490i	$0.227960\pi$
$984$		0			0
$985$	−18.0000	−	31.1769i	−0.573528	−	0.993379i
$986$	−6.00000			−0.191079
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−8.00000	−	13.8564i	−0.254385	−	0.440608i
$990$		0			0
$991$	6.00000	−	10.3923i	0.190596	−	0.330122i	−0.754852	−	0.655895i	$-0.772291\pi$
$991$	6.00000	−	10.3923i	0.190596	−	0.330122i	0.945448	+	0.325773i	$0.105625\pi$
$992$	10.0000	+	17.3205i	0.317500	+	0.549927i
$993$		0			0
$994$		0			0
$995$	40.0000			1.26809
$996$		0			0
$997$	−23.0000	+	39.8372i	−0.728417	+	1.26166i	0.229135	+	0.973395i	$0.426410\pi$
$997$	−23.0000	+	39.8372i	−0.728417	+	1.26166i	−0.957552	+	0.288261i	$0.906923\pi$
$998$	−20.0000	+	34.6410i	−0.633089	+	1.09654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.e.b.18.1		2
7.2	even	3	inner	833.2.e.b.324.1		2
7.3	odd	6		833.2.a.a.1.1		1
7.4	even	3		17.2.a.a.1.1	✓	1
7.5	odd	6		833.2.e.a.324.1		2
7.6	odd	2		833.2.e.a.18.1		2
21.11	odd	6		153.2.a.c.1.1		1
21.17	even	6		7497.2.a.l.1.1		1
28.11	odd	6		272.2.a.b.1.1		1
35.4	even	6		425.2.a.d.1.1		1
35.18	odd	12		425.2.b.b.324.2		2
35.32	odd	12		425.2.b.b.324.1		2
56.11	odd	6		1088.2.a.h.1.1		1
56.53	even	6		1088.2.a.i.1.1		1
77.32	odd	6		2057.2.a.e.1.1		1
84.11	even	6		2448.2.a.o.1.1		1
91.25	even	6		2873.2.a.c.1.1		1
105.74	odd	6		3825.2.a.d.1.1		1
119.4	even	12		289.2.b.a.288.2		2
119.11	odd	48		289.2.d.d.155.1		8
119.25	even	24		289.2.c.a.251.1		4
119.32	even	24		289.2.c.a.38.1		4
119.39	odd	48		289.2.d.d.110.2		8
119.46	odd	48		289.2.d.d.110.1		8
119.53	even	24		289.2.c.a.38.2		4
119.60	even	24		289.2.c.a.251.2		4
119.67	even	6		289.2.a.a.1.1		1
119.74	odd	48		289.2.d.d.155.2		8
119.81	even	12		289.2.b.a.288.1		2
119.88	odd	48		289.2.d.d.179.2		8
119.95	odd	48		289.2.d.d.134.1		8
119.109	odd	48		289.2.d.d.134.2		8
119.116	odd	48		289.2.d.d.179.1		8
133.18	odd	6		6137.2.a.b.1.1		1
140.39	odd	6		6800.2.a.n.1.1		1
161.137	odd	6		8993.2.a.a.1.1		1
168.11	even	6		9792.2.a.i.1.1		1
168.53	odd	6		9792.2.a.n.1.1		1
357.305	odd	6		2601.2.a.g.1.1		1
476.67	odd	6		4624.2.a.d.1.1		1
595.424	even	6		7225.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.a.a.1.1	✓	1	7.4	even	3
153.2.a.c.1.1		1	21.11	odd	6
272.2.a.b.1.1		1	28.11	odd	6
289.2.a.a.1.1		1	119.67	even	6
289.2.b.a.288.1		2	119.81	even	12
289.2.b.a.288.2		2	119.4	even	12
289.2.c.a.38.1		4	119.32	even	24
289.2.c.a.38.2		4	119.53	even	24
289.2.c.a.251.1		4	119.25	even	24
289.2.c.a.251.2		4	119.60	even	24
289.2.d.d.110.1		8	119.46	odd	48
289.2.d.d.110.2		8	119.39	odd	48
289.2.d.d.134.1		8	119.95	odd	48
289.2.d.d.134.2		8	119.109	odd	48
289.2.d.d.155.1		8	119.11	odd	48
289.2.d.d.155.2		8	119.74	odd	48
289.2.d.d.179.1		8	119.116	odd	48
289.2.d.d.179.2		8	119.88	odd	48
425.2.a.d.1.1		1	35.4	even	6
425.2.b.b.324.1		2	35.32	odd	12
425.2.b.b.324.2		2	35.18	odd	12
833.2.a.a.1.1		1	7.3	odd	6
833.2.e.a.18.1		2	7.6	odd	2
833.2.e.a.324.1		2	7.5	odd	6
833.2.e.b.18.1		2	1.1	even	1	trivial
833.2.e.b.324.1		2	7.2	even	3	inner
1088.2.a.h.1.1		1	56.11	odd	6
1088.2.a.i.1.1		1	56.53	even	6
2057.2.a.e.1.1		1	77.32	odd	6
2448.2.a.o.1.1		1	84.11	even	6
2601.2.a.g.1.1		1	357.305	odd	6
2873.2.a.c.1.1		1	91.25	even	6
3825.2.a.d.1.1		1	105.74	odd	6
4624.2.a.d.1.1		1	476.67	odd	6
6137.2.a.b.1.1		1	133.18	odd	6
6800.2.a.n.1.1		1	140.39	odd	6
7225.2.a.g.1.1		1	595.424	even	6
7497.2.a.l.1.1		1	21.17	even	6
8993.2.a.a.1.1		1	161.137	odd	6
9792.2.a.i.1.1		1	168.11	even	6
9792.2.a.n.1.1		1	168.53	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{10} -2.00000 q^{13} +(0.500000 + 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(2.00000 + 3.46410i) q^{19} +2.00000 q^{20} +(-2.00000 - 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.50000 - 4.33013i) q^{32} -1.00000 q^{34} +3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 + 5.19615i) q^{40} -6.00000 q^{41} +4.00000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(2.00000 - 3.46410i) q^{46} +1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(3.00000 + 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(5.00000 + 8.66025i) q^{61} -4.00000 q^{62} +7.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(0.500000 + 0.866025i) q^{68} -4.00000 q^{71} +(4.50000 + 7.79423i) q^{72} +(3.00000 - 5.19615i) q^{73} +(-1.00000 + 1.73205i) q^{74} +4.00000 q^{76} +(-6.00000 - 10.3923i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 - 5.19615i) q^{82} -4.00000 q^{83} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-5.00000 - 8.66025i) q^{89} -6.00000 q^{90} -4.00000 q^{92} +(-4.00000 + 6.92820i) q^{95} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 2 q^{5} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + q^4 + 2 * q^5 + 6 * q^8 + 3 * q^9	\( 2 q + q^{2} + q^{4} + 2 q^{5} + 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{13} + q^{16} - q^{17} - 3 q^{18} + 4 q^{19} + 4 q^{20} - 4 q^{23} + q^{25} - 2 q^{26} + 12 q^{29} - 4 q^{31} + 5 q^{32} - 2 q^{34} + 6 q^{36} + 2 q^{37} - 4 q^{38} + 6 q^{40} - 12 q^{41} + 8 q^{43} - 6 q^{45} + 4 q^{46} + 2 q^{50} - 2 q^{52} - 6 q^{53} + 6 q^{58} + 12 q^{59} + 10 q^{61} - 8 q^{62} + 14 q^{64} - 4 q^{65} - 4 q^{67} + q^{68} - 8 q^{71} + 9 q^{72} + 6 q^{73} - 2 q^{74} + 8 q^{76} - 12 q^{79} - 2 q^{80} - 9 q^{81} - 6 q^{82} - 8 q^{83} - 4 q^{85} + 4 q^{86} - 10 q^{89} - 12 q^{90} - 8 q^{92} - 8 q^{95} + 4 q^{97}+O(q^{100}) \) 2 * q + q^2 + q^4 + 2 * q^5 + 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^13 + q^16 - q^17 - 3 * q^18 + 4 * q^19 + 4 * q^20 - 4 * q^23 + q^25 - 2 * q^26 + 12 * q^29 - 4 * q^31 + 5 * q^32 - 2 * q^34 + 6 * q^36 + 2 * q^37 - 4 * q^38 + 6 * q^40 - 12 * q^41 + 8 * q^43 - 6 * q^45 + 4 * q^46 + 2 * q^50 - 2 * q^52 - 6 * q^53 + 6 * q^58 + 12 * q^59 + 10 * q^61 - 8 * q^62 + 14 * q^64 - 4 * q^65 - 4 * q^67 + q^68 - 8 * q^71 + 9 * q^72 + 6 * q^73 - 2 * q^74 + 8 * q^76 - 12 * q^79 - 2 * q^80 - 9 * q^81 - 6 * q^82 - 8 * q^83 - 4 * q^85 + 4 * q^86 - 10 * q^89 - 12 * q^90 - 8 * q^92 - 8 * q^95 + 4 * q^97

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