LMFDB - Embedded newform 2394.2.o.i.1261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(505,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2394.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.o (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.1161862439$
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 266)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2394.1261
Dual form			2394.2.o.i.505.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(2.50000 - 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 4.33013i) q^{19} -1.00000 q^{20} +(1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{35} -4.00000 q^{37} +(3.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +1.00000 q^{46} +1.00000 q^{49} +4.00000 q^{50} +(2.50000 + 4.33013i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(1.00000 + 1.73205i) q^{55} -1.00000 q^{56} +6.00000 q^{58} +(-3.50000 - 6.06218i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +5.00000 q^{65} +(-6.00000 + 10.3923i) q^{67} +(-0.500000 + 0.866025i) q^{70} +(-7.50000 - 12.9904i) q^{71} +(7.00000 + 12.1244i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(4.00000 + 1.73205i) q^{76} +2.00000 q^{77} +(2.00000 + 3.46410i) q^{79} +(0.500000 - 0.866025i) q^{80} +(1.00000 - 1.73205i) q^{82} +7.00000 q^{83} +(-4.00000 + 6.92820i) q^{86} -2.00000 q^{88} +(2.50000 - 4.33013i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.50000 - 2.59808i) q^{95} +(-6.00000 - 10.3923i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - q^{10} + 4 q^{11} + 5 q^{13} + q^{14} - q^{16} - q^{19} - 2 q^{20} + 2 q^{22} + q^{23} + 4 q^{25} + 10 q^{26} - q^{28} + 6 q^{29} + 8 q^{31} + q^{32} + q^{35} - 8 q^{37} + 7 q^{38} - q^{40} - 2 q^{41} + 8 q^{43} - 2 q^{44} + 2 q^{46} + 2 q^{49} + 8 q^{50} + 5 q^{52} - 2 q^{53} + 2 q^{55} - 2 q^{56} + 12 q^{58} - 7 q^{59} + 7 q^{61} + 4 q^{62} + 2 q^{64} + 10 q^{65} - 12 q^{67} - q^{70} - 15 q^{71} + 14 q^{73} - 4 q^{74} + 8 q^{76} + 4 q^{77} + 4 q^{79} + q^{80} + 2 q^{82} + 14 q^{83} - 8 q^{86} - 4 q^{88} + 5 q^{91} + q^{92} + 7 q^{95} - 12 q^{97} + q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + q^5 + 2 * q^7 - 2 * q^8 - q^10 + 4 * q^11 + 5 * q^13 + q^14 - q^16 - q^19 - 2 * q^20 + 2 * q^22 + q^23 + 4 * q^25 + 10 * q^26 - q^28 + 6 * q^29 + 8 * q^31 + q^32 + q^35 - 8 * q^37 + 7 * q^38 - q^40 - 2 * q^41 + 8 * q^43 - 2 * q^44 + 2 * q^46 + 2 * q^49 + 8 * q^50 + 5 * q^52 - 2 * q^53 + 2 * q^55 - 2 * q^56 + 12 * q^58 - 7 * q^59 + 7 * q^61 + 4 * q^62 + 2 * q^64 + 10 * q^65 - 12 * q^67 - q^70 - 15 * q^71 + 14 * q^73 - 4 * q^74 + 8 * q^76 + 4 * q^77 + 4 * q^79 + q^80 + 2 * q^82 + 14 * q^83 - 8 * q^86 - 4 * q^88 + 5 * q^91 + q^92 + 7 * q^95 - 12 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$2$	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	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	5.00000			0.980581
$27$		0			0
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	3.50000	−	2.59808i	0.567775	−	0.421464i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	1.00000			0.147442
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	4.00000			0.565685
$51$		0			0
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$		0			0
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−1.00000			−0.133631
$57$		0			0
$58$	6.00000			0.787839
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	0.543065	−	0.839691i	$-0.317264\pi$
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	−0.998726	+	0.0504625i	$0.983930\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$	5.00000			0.620174
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$		0			0
$69$		0			0
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	−7.50000	−	12.9904i	−0.890086	−	1.54167i	−0.839771	−	0.542941i	$-0.817311\pi$
$71$	−7.50000	−	12.9904i	−0.890086	−	1.54167i	−0.0503155	−	0.998733i	$-0.516023\pi$
$72$		0			0
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	4.00000	+	1.73205i	0.458831	+	0.198680i
$77$	2.00000			0.227921
$78$		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	$0.761089\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$		0			0
$88$	−2.00000			−0.213201
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	2.50000	−	4.33013i	0.262071	−	0.453921i
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$		0			0
$95$	3.50000	−	2.59808i	0.359092	−	0.266557i
$96$		0			0
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	−0.991371	−	0.131084i	$-0.958154\pi$
$97$	−6.00000	−	10.3923i	−0.609208	−	1.05518i	0.382164	−	0.924095i	$-0.375179\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	−2.50000	+	4.33013i	−0.245145	+	0.424604i
$105$		0			0
$106$	−2.00000			−0.194257
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	5.00000			0.470360			0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000			0.470360			0.235180	+	0.971952i	$0.424432\pi$
$114$		0			0
$115$	1.00000			0.0932505
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$	3.50000	−	6.06218i	0.322201	−	0.558069i
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	7.00000			0.633750
$123$		0			0
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	9.00000			0.804984
$126$		0			0
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	2.50000	+	4.33013i	0.219265	+	0.379777i
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$		0			0
$133$	−0.500000	−	4.33013i	−0.0433555	−	0.375470i
$134$	−12.0000			−1.03664
$135$		0			0
$136$		0			0
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$		0			0
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$	−1.00000			−0.0845154
$141$		0			0
$142$	7.50000	−	12.9904i	0.629386	−	1.09013i
$143$	5.00000	−	8.66025i	0.418121	−	0.724207i
$144$		0			0
$145$	6.00000			0.498273
$146$	−7.00000	+	12.1244i	−0.579324	+	1.00342i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	19.0000			1.54620			0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000			1.54620			0.773099	+	0.634285i	$0.218706\pi$
$152$	0.500000	+	4.33013i	0.0405554	+	0.351220i
$153$		0			0
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$		0			0
$160$	1.00000			0.0790569
$161$	0.500000	−	0.866025i	0.0394055	−	0.0682524i
$162$		0			0
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	−0.824737	−	0.565516i	$-0.808677\pi$
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	0.902120	+	0.431486i	$0.142010\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$	−8.00000			−0.609994
$173$	−6.50000	−	11.2583i	−0.494186	−	0.855955i	0.505792	−	0.862656i	$-0.331200\pi$
$173$	−6.50000	−	11.2583i	−0.494186	−	0.855955i	−0.999978	+	0.00670064i	$0.997867\pi$
$174$		0			0
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−11.5000	+	19.9186i	−0.854788	+	1.48054i	0.0220530	+	0.999757i	$0.492980\pi$
$181$	−11.5000	+	19.9186i	−0.854788	+	1.48054i	−0.876841	+	0.480780i	$0.840354\pi$
$182$	5.00000			0.370625
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	4.00000	+	1.73205i	0.290191	+	0.125656i
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$		0			0
$193$	1.50000	+	2.59808i	0.107972	+	0.187014i	0.914949	−	0.403570i	$-0.132231\pi$
$193$	1.50000	+	2.59808i	0.107972	+	0.187014i	−0.806976	+	0.590584i	$0.798898\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−18.0000			−1.26648
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	3.00000	+	5.19615i	0.209020	+	0.362033i
$207$		0			0
$208$	−5.00000			−0.346688
$209$	−1.00000	−	8.66025i	−0.0691714	−	0.599042i
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	−1.00000	−	1.73205i	−0.0686803	−	0.118958i
$213$		0			0
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$		0			0
$217$	4.00000			0.271538
$218$	−5.00000	+	8.66025i	−0.338643	+	0.586546i
$219$		0			0
$220$	−2.00000			−0.134840
$221$		0			0
$222$		0			0
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	2.50000	+	4.33013i	0.166298	+	0.288036i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	27.0000			1.78421			0.892105	−	0.451828i	$-0.149228\pi$
$229$	27.0000			1.78421			0.892105	+	0.451828i	$0.149228\pi$
$230$	0.500000	+	0.866025i	0.0329690	+	0.0571040i
$231$		0			0
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−5.50000	−	9.52628i	−0.360317	−	0.624087i	0.627696	−	0.778459i	$-0.283998\pi$
$233$	−5.50000	−	9.52628i	−0.360317	−	0.624087i	−0.988013	+	0.154371i	$0.950665\pi$
$234$		0			0
$235$		0			0
$236$	7.00000			0.455661
$237$		0			0
$238$		0			0
$239$	5.00000			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$240$		0			0
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$		0			0
$247$	−20.0000	−	8.66025i	−1.27257	−	0.551039i
$248$	−4.00000			−0.254000
$249$		0			0
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	−0.688338	−	0.725390i	$-0.741659\pi$
$251$	4.50000	−	7.79423i	0.284037	−	0.491967i	0.972375	+	0.233423i	$0.0749927\pi$
$252$		0			0
$253$	1.00000	−	1.73205i	0.0628695	−	0.108893i
$254$	−13.0000			−0.815693
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	−0.560781	−	0.827964i	$-0.689499\pi$
$257$	7.00000	−	12.1244i	0.436648	−	0.756297i	0.997429	+	0.0716680i	$0.0228322\pi$
$258$		0			0
$259$	−4.00000			−0.248548
$260$	−2.50000	+	4.33013i	−0.155043	+	0.268543i
$261$		0			0
$262$	−7.50000	+	12.9904i	−0.463352	+	0.802548i
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$	3.50000	−	2.59808i	0.214599	−	0.159298i
$267$		0			0
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$		0			0
$273$		0			0
$274$	−9.00000			−0.543710
$275$	4.00000	−	6.92820i	0.241209	−	0.417786i
$276$		0			0
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	12.0000			0.719712
$279$		0			0
$280$	−0.500000	−	0.866025i	−0.0298807	−	0.0517549i
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	0.951101	−	0.308879i	$-0.0999539\pi$
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	−0.743048	+	0.669238i	$0.766621\pi$
$284$	15.0000			0.890086
$285$		0			0
$286$	10.0000			0.591312
$287$	−1.00000	−	1.73205i	−0.0590281	−	0.102240i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$		0			0
$292$	−14.0000			−0.819288
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$		0			0
$295$	3.50000	−	6.06218i	0.203778	−	0.352954i
$296$	4.00000			0.232495
$297$		0			0
$298$	2.00000	−	3.46410i	0.115857	−	0.200670i
$299$	−2.50000	−	4.33013i	−0.144579	−	0.250418i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	9.50000	+	16.4545i	0.546664	+	0.946849i
$303$		0			0
$304$	−3.50000	+	2.59808i	−0.200739	+	0.149010i
$305$	7.00000			0.400819
$306$		0			0
$307$	−9.50000	−	16.4545i	−0.542194	−	0.939107i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$	−9.50000	−	16.4545i	−0.542194	−	0.939107i	0.456584	−	0.889680i	$-0.349073\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$		0			0
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	−14.0000	+	24.2487i	−0.791327	+	1.37062i	0.133819	+	0.991006i	$0.457276\pi$
$313$	−14.0000	+	24.2487i	−0.791327	+	1.37062i	−0.925146	+	0.379612i	$0.876057\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	−0.372061	−	0.928208i	$-0.621349\pi$
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	0.989882	−	0.141890i	$-0.0453179\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	1.00000			0.0557278
$323$		0			0
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$		0			0
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$		0			0
$330$		0			0
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$	−3.50000	+	6.06218i	−0.192087	+	0.332705i
$333$		0			0
$334$	2.00000			0.109435
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$		0			0
$341$	8.00000			0.433224
$342$		0			0
$343$	1.00000			0.0539949
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	6.50000	−	11.2583i	0.349442	−	0.605252i
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−18.0000			−0.958043			−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000			−0.958043			−0.479022	+	0.877803i	$0.659008\pi$
$354$		0			0
$355$	7.50000	−	12.9904i	0.398059	−	0.689458i
$356$		0			0
$357$		0			0
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	0.808409	−	0.588621i	$-0.200329\pi$
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	−0.913965	+	0.405793i	$0.866996\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$	−23.0000			−1.20885
$363$		0			0
$364$	2.50000	+	4.33013i	0.131036	+	0.226960i
$365$	−7.00000	+	12.1244i	−0.366397	+	0.634618i
$366$		0			0
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	−0.529607	−	0.848243i	$-0.677661\pi$
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	0.999404	+	0.0345320i	$0.0109941\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	2.00000	−	3.46410i	0.103975	−	0.180090i
$371$	−1.00000	+	1.73205i	−0.0519174	+	0.0899236i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.0000	−	25.9808i	−0.772539	−	1.33808i
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	0.500000	+	4.33013i	0.0256495	+	0.222131i
$381$		0			0
$382$	−8.50000	−	14.7224i	−0.434898	−	0.753265i
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$		0			0
$385$	1.00000	+	1.73205i	0.0509647	+	0.0882735i
$386$	−1.50000	+	2.59808i	−0.0763480	+	0.132239i
$387$		0			0
$388$	12.0000			0.609208
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000			−0.0505076
$393$		0			0
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−2.00000	+	3.46410i	−0.100631	+	0.174298i
$396$		0			0
$397$	3.00000	+	5.19615i	0.150566	+	0.260787i	0.931436	−	0.363906i	$-0.118557\pi$
$397$	3.00000	+	5.19615i	0.150566	+	0.260787i	−0.780870	+	0.624694i	$0.785224\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	−0.988691	−	0.149966i	$-0.952083\pi$
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	0.364471	−	0.931215i	$-0.381250\pi$
$402$		0			0
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$		0			0
$406$	6.00000			0.297775
$407$	−8.00000			−0.396545
$408$		0			0
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$	2.00000			0.0987730
$411$		0			0
$412$	−3.00000	+	5.19615i	−0.147799	+	0.255996i
$413$	−3.50000	−	6.06218i	−0.172224	−	0.298300i
$414$		0			0
$415$	3.50000	+	6.06218i	0.171808	+	0.297581i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$		0			0
$418$	7.00000	−	5.19615i	0.342381	−	0.254152i
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	−0.899192	−	0.437555i	$-0.855845\pi$
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	0.0706626	−	0.997500i	$-0.477489\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$		0			0
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$		0			0
$426$		0			0
$427$	3.50000	−	6.06218i	0.169377	−	0.293369i
$428$	−9.00000	+	15.5885i	−0.435031	+	0.753497i
$429$		0			0
$430$	−8.00000			−0.385794
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−1.00000	+	1.73205i	−0.0480569	+	0.0832370i	−0.889053	−	0.457804i	$-0.848636\pi$
$433$	−1.00000	+	1.73205i	−0.0480569	+	0.0832370i	0.840996	+	0.541041i	$0.181970\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$		0			0
$436$	−10.0000			−0.478913
$437$	−4.00000	−	1.73205i	−0.191346	−	0.0828552i
$438$		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	$0.674958\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$		0			0
$442$		0			0
$443$	−17.0000	+	29.4449i	−0.807694	+	1.39897i	0.106763	+	0.994285i	$0.465952\pi$
$443$	−17.0000	+	29.4449i	−0.807694	+	1.39897i	−0.914457	+	0.404683i	$0.867382\pi$
$444$		0			0
$445$		0			0
$446$	−1.00000	+	1.73205i	−0.0473514	+	0.0820150i
$447$		0			0
$448$	1.00000			0.0472456
$449$	−37.0000			−1.74614			−0.873069	−	0.487597i	$-0.837874\pi$
$449$	−37.0000			−1.74614			−0.873069	+	0.487597i	$0.837874\pi$
$450$		0			0
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$	−2.50000	+	4.33013i	−0.117590	+	0.203672i
$453$		0			0
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$	5.00000			0.234404
$456$		0			0
$457$	−39.0000			−1.82434			−0.912172	−	0.409809i	$-0.865595\pi$
$457$	−39.0000			−1.82434			−0.912172	+	0.409809i	$0.865595\pi$
$458$	13.5000	+	23.3827i	0.630814	+	1.09260i
$459$		0			0
$460$	−0.500000	+	0.866025i	−0.0233126	+	0.0403786i
$461$	−18.5000	−	32.0429i	−0.861631	−	1.49239i	−0.870354	−	0.492427i	$-0.836110\pi$
$461$	−18.5000	−	32.0429i	−0.861631	−	1.49239i	0.00872311	−	0.999962i	$-0.497223\pi$
$462$		0			0
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	5.50000	−	9.52628i	0.254783	−	0.441296i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−6.00000	+	10.3923i	−0.277054	+	0.479872i
$470$		0			0
$471$		0			0
$472$	3.50000	+	6.06218i	0.161101	+	0.279034i
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$		0			0
$475$	−16.0000	−	6.92820i	−0.734130	−	0.317888i
$476$		0			0
$477$		0			0
$478$	2.50000	+	4.33013i	0.114347	+	0.198055i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	−10.0000	+	17.3205i	−0.455961	+	0.789747i
$482$	4.00000			0.182195
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	6.00000	−	10.3923i	0.272446	−	0.471890i
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$		0			0
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	0.998467	−	0.0553560i	$-0.0176294\pi$
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	−0.547173	+	0.837020i	$0.684296\pi$
$492$		0			0
$493$		0			0
$494$	−2.50000	−	21.6506i	−0.112480	−	0.974108i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−7.50000	−	12.9904i	−0.336421	−	0.582698i
$498$		0			0
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	−0.999054	−	0.0434940i	$-0.986151\pi$
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	0.461860	−	0.886953i	$-0.347182\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$		0			0
$502$	9.00000			0.401690
$503$	8.00000	−	13.8564i	0.356702	−	0.617827i	−0.630705	−	0.776022i	$-0.717234\pi$
$503$	8.00000	−	13.8564i	0.356702	−	0.617827i	0.987408	+	0.158196i	$0.0505677\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$	2.00000			0.0889108
$507$		0			0
$508$	−6.50000	−	11.2583i	−0.288391	−	0.499508i
$509$	17.5000	−	30.3109i	0.775674	−	1.34351i	−0.158741	−	0.987320i	$-0.550744\pi$
$509$	17.5000	−	30.3109i	0.775674	−	1.34351i	0.934415	−	0.356186i	$-0.115923\pi$
$510$		0			0
$511$	7.00000	+	12.1244i	0.309662	+	0.536350i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	14.0000			0.617514
$515$	3.00000	+	5.19615i	0.132196	+	0.228970i
$516$		0			0
$517$		0			0
$518$	−2.00000	−	3.46410i	−0.0878750	−	0.152204i
$519$		0			0
$520$	−5.00000			−0.219265
$521$	38.0000			1.66481			0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000			1.66481			0.832405	+	0.554168i	$0.186963\pi$
$522$		0			0
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	−0.378695	−	0.925521i	$-0.623627\pi$
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	0.990873	−	0.134801i	$-0.0430394\pi$
$524$	−15.0000			−0.655278
$525$		0			0
$526$	1.50000	−	2.59808i	0.0654031	−	0.113282i
$527$		0			0
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−1.00000	−	1.73205i	−0.0434372	−	0.0752355i
$531$		0			0
$532$	4.00000	+	1.73205i	0.173422	+	0.0750939i
$533$	−10.0000			−0.433148
$534$		0			0
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$	−7.00000	+	12.1244i	−0.301791	+	0.522718i
$539$	2.00000			0.0861461
$540$		0			0
$541$	−18.0000	+	31.1769i	−0.773880	+	1.34040i	0.161541	+	0.986866i	$0.448354\pi$
$541$	−18.0000	+	31.1769i	−0.773880	+	1.34040i	−0.935422	+	0.353534i	$0.884980\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$		0			0
$544$		0			0
$545$	−5.00000	+	8.66025i	−0.214176	+	0.370965i
$546$		0			0
$547$	−10.0000	+	17.3205i	−0.427569	+	0.740571i	−0.996657	−	0.0817056i	$-0.973963\pi$
$547$	−10.0000	+	17.3205i	−0.427569	+	0.740571i	0.569087	+	0.822277i	$0.307297\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$		0			0
$550$	8.00000			0.341121
$551$	−24.0000	−	10.3923i	−1.02243	−	0.442727i
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	−0.886433	−	0.462856i	$-0.846825\pi$
$557$	−1.00000	+	1.73205i	−0.0423714	+	0.0733893i	0.844062	+	0.536246i	$0.180158\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$		0			0
$562$	−22.0000			−0.928014
$563$	3.00000			0.126435			0.0632175	−	0.998000i	$-0.479864\pi$
$563$	3.00000			0.126435			0.0632175	+	0.998000i	$0.479864\pi$
$564$		0			0
$565$	2.50000	+	4.33013i	0.105176	+	0.182170i
$566$	−3.50000	+	6.06218i	−0.147116	+	0.254812i
$567$		0			0
$568$	7.50000	+	12.9904i	0.314693	+	0.545064i
$569$	−31.0000			−1.29959			−0.649794	−	0.760111i	$-0.725145\pi$
$569$	−31.0000			−1.29959			−0.649794	+	0.760111i	$0.725145\pi$
$570$		0			0
$571$	−30.0000			−1.25546			−0.627730	−	0.778431i	$-0.716016\pi$
$571$	−30.0000			−1.25546			−0.627730	+	0.778431i	$0.716016\pi$
$572$	5.00000	+	8.66025i	0.209061	+	0.362103i
$573$		0			0
$574$	1.00000	−	1.73205i	0.0417392	−	0.0722944i
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$		0			0
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	−3.00000	+	5.19615i	−0.124568	+	0.215758i
$581$	7.00000			0.290409
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$		0			0
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$		0			0
$589$	−2.00000	−	17.3205i	−0.0824086	−	0.713679i
$590$	7.00000			0.288185
$591$		0			0
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	21.0000	−	36.3731i	0.862367	−	1.49366i	−0.00727173	−	0.999974i	$-0.502315\pi$
$593$	21.0000	−	36.3731i	0.862367	−	1.49366i	0.869638	−	0.493689i	$-0.164352\pi$
$594$		0			0
$595$		0			0
$596$	4.00000			0.163846
$597$		0			0
$598$	2.50000	−	4.33013i	0.102233	−	0.177072i
$599$	2.50000	−	4.33013i	0.102147	−	0.176924i	−0.810422	−	0.585847i	$-0.800762\pi$
$599$	2.50000	−	4.33013i	0.102147	−	0.176924i	0.912569	+	0.408923i	$0.134095\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$	−4.00000	+	6.92820i	−0.163028	+	0.282372i
$603$		0			0
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$		0			0
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$	−4.00000	−	1.73205i	−0.162221	−	0.0702439i
$609$		0			0
$610$	3.50000	+	6.06218i	0.141711	+	0.245450i
$611$		0			0
$612$		0			0
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	0.999845	−	0.0176058i	$-0.00560439\pi$
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	−0.515170	+	0.857088i	$0.672271\pi$
$614$	9.50000	−	16.4545i	0.383389	−	0.664049i
$615$		0			0
$616$	−2.00000			−0.0805823
$617$	6.50000	−	11.2583i	0.261680	−	0.453243i	−0.705008	−	0.709199i	$-0.749057\pi$
$617$	6.50000	−	11.2583i	0.261680	−	0.453243i	0.966689	+	0.255956i	$0.0823901\pi$
$618$		0			0
$619$	−17.0000			−0.683288			−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000			−0.683288			−0.341644	+	0.939829i	$0.610984\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$		0			0
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−28.0000			−1.11911
$627$		0			0
$628$	7.00000			0.279330
$629$		0			0
$630$		0			0
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	−0.775356	−	0.631524i	$-0.782430\pi$
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	0.934594	+	0.355716i	$0.115763\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$		0			0
$634$	22.0000			0.873732
$635$	−13.0000			−0.515889
$636$		0			0
$637$	2.50000	−	4.33013i	0.0990536	−	0.171566i
$638$	12.0000			0.475085
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	4.50000	+	7.79423i	0.177463	+	0.307374i	0.941011	−	0.338377i	$-0.109878\pi$
$643$	4.50000	+	7.79423i	0.177463	+	0.307374i	−0.763548	+	0.645751i	$0.776544\pi$
$644$	0.500000	+	0.866025i	0.0197028	+	0.0341262i
$645$		0			0
$646$		0			0
$647$	24.0000			0.943537			0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$		0			0
$649$	−7.00000	−	12.1244i	−0.274774	−	0.475923i
$650$	10.0000	−	17.3205i	0.392232	−	0.679366i
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$		0			0
$658$		0			0
$659$	−11.0000	+	19.0526i	−0.428499	+	0.742182i	−0.996740	−	0.0806799i	$-0.974291\pi$
$659$	−11.0000	+	19.0526i	−0.428499	+	0.742182i	0.568241	+	0.822862i	$0.307624\pi$
$660$		0			0
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	−0.982632	−	0.185565i	$-0.940588\pi$
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	0.652020	+	0.758202i	$0.273922\pi$
$662$	−9.00000	−	15.5885i	−0.349795	−	0.605863i
$663$		0			0
$664$	−7.00000			−0.271653
$665$	3.50000	−	2.59808i	0.135724	−	0.100749i
$666$		0			0
$667$	−3.00000	−	5.19615i	−0.116160	−	0.201196i
$668$	1.00000	+	1.73205i	0.0386912	+	0.0670151i
$669$		0			0
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	7.00000	−	12.1244i	0.270232	−	0.468056i
$672$		0			0
$673$	23.0000			0.886585			0.443292	−	0.896377i	$-0.353810\pi$
$673$	23.0000			0.886585			0.443292	+	0.896377i	$0.353810\pi$
$674$	6.50000	−	11.2583i	0.250371	−	0.433655i
$675$		0			0
$676$	12.0000			0.461538
$677$	−34.0000			−1.30673			−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000			−1.30673			−0.653363	+	0.757045i	$0.726642\pi$
$678$		0			0
$679$	−6.00000	−	10.3923i	−0.230259	−	0.398820i
$680$		0			0
$681$		0			0
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	30.0000			1.14792			0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000			1.14792			0.573959	+	0.818884i	$0.305407\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	5.00000	+	8.66025i	0.190485	+	0.329929i
$690$		0			0
$691$	−29.0000			−1.10321			−0.551606	−	0.834105i	$-0.685985\pi$
$691$	−29.0000			−1.10321			−0.551606	+	0.834105i	$0.685985\pi$
$692$	13.0000			0.494186
$693$		0			0
$694$	−9.00000	+	15.5885i	−0.341635	+	0.591730i
$695$	12.0000			0.455186
$696$		0			0
$697$		0			0
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	3.00000	+	5.19615i	0.113308	+	0.196256i	0.917102	−	0.398652i	$-0.130522\pi$
$701$	3.00000	+	5.19615i	0.113308	+	0.196256i	−0.803794	+	0.594908i	$0.797189\pi$
$702$		0			0
$703$	2.00000	+	17.3205i	0.0754314	+	0.653255i
$704$	2.00000			0.0753778
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	−9.00000	+	15.5885i	−0.338480	+	0.586264i
$708$		0			0
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	−0.347325	−	0.937745i	$-0.612910\pi$
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	0.985773	−	0.168080i	$-0.0537568\pi$
$710$	15.0000			0.562940
$711$		0			0
$712$		0			0
$713$	2.00000	−	3.46410i	0.0749006	−	0.129732i
$714$		0			0
$715$	10.0000			0.373979
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	25.0000	+	43.3013i	0.932343	+	1.61486i	0.779305	+	0.626644i	$0.215572\pi$
$719$	25.0000	+	43.3013i	0.932343	+	1.61486i	0.153037	+	0.988220i	$0.451094\pi$
$720$		0			0
$721$	6.00000			0.223452
$722$	−13.0000	−	13.8564i	−0.483810	−	0.515682i
$723$		0			0
$724$	−11.5000	−	19.9186i	−0.427394	−	0.740268i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	−0.951694	−	0.307049i	$-0.900659\pi$
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	0.209935	−	0.977715i	$-0.432675\pi$
$728$	−2.50000	+	4.33013i	−0.0926562	+	0.160485i
$729$		0			0
$730$	−14.0000			−0.518163
$731$		0			0
$732$		0			0
$733$	13.0000			0.480166			0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000			0.480166			0.240083	+	0.970752i	$0.422825\pi$
$734$	18.0000			0.664392
$735$		0			0
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$		0			0
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	0.968839	+	0.247691i	$0.0796718\pi$
$739$	19.0000	+	32.9090i	0.698926	+	1.21058i	−0.269913	+	0.962885i	$0.586995\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	−2.00000			−0.0734223
$743$	−21.5000	−	37.2391i	−0.788759	−	1.36617i	−0.926728	−	0.375733i	$-0.877391\pi$
$743$	−21.5000	−	37.2391i	−0.788759	−	1.36617i	0.137969	−	0.990437i	$-0.455942\pi$
$744$		0			0
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$		0			0
$748$		0			0
$749$	18.0000			0.657706
$750$		0			0
$751$	24.0000	−	41.5692i	0.875772	−	1.51688i	0.0198348	−	0.999803i	$-0.493686\pi$
$751$	24.0000	−	41.5692i	0.875772	−	1.51688i	0.855938	−	0.517079i	$-0.172981\pi$
$752$		0			0
$753$		0			0
$754$	15.0000	−	25.9808i	0.546268	−	0.946164i
$755$	9.50000	+	16.4545i	0.345740	+	0.598840i
$756$		0			0
$757$	−17.0000	−	29.4449i	−0.617876	−	1.07019i	−0.989873	−	0.141958i	$-0.954660\pi$
$757$	−17.0000	−	29.4449i	−0.617876	−	1.07019i	0.371997	−	0.928234i	$-0.378673\pi$
$758$	−6.00000	−	10.3923i	−0.217930	−	0.377466i
$759$		0			0
$760$	−3.50000	+	2.59808i	−0.126958	+	0.0942421i
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	5.00000	+	8.66025i	0.181012	+	0.313522i
$764$	8.50000	−	14.7224i	0.307519	−	0.532639i
$765$		0			0
$766$	−18.0000	+	31.1769i	−0.650366	+	1.12647i
$767$	−35.0000			−1.26378
$768$		0			0
$769$	6.00000	−	10.3923i	0.216366	−	0.374756i	−0.737329	−	0.675534i	$-0.763913\pi$
$769$	6.00000	−	10.3923i	0.216366	−	0.374756i	0.953694	+	0.300778i	$0.0972464\pi$
$770$	−1.00000	+	1.73205i	−0.0360375	+	0.0624188i
$771$		0			0
$772$	−3.00000			−0.107972
$773$	8.50000	−	14.7224i	0.305724	−	0.529529i	−0.671698	−	0.740825i	$-0.734435\pi$
$773$	8.50000	−	14.7224i	0.305724	−	0.529529i	0.977422	+	0.211296i	$0.0677683\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	6.00000	+	10.3923i	0.215387	+	0.373062i
$777$		0			0
$778$	−30.0000			−1.07555
$779$	−7.00000	+	5.19615i	−0.250801	+	0.186171i
$780$		0			0
$781$	−15.0000	−	25.9808i	−0.536742	−	0.929665i
$782$		0			0
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	3.50000	−	6.06218i	0.124920	−	0.216368i
$786$		0			0
$787$	25.0000			0.891154			0.445577	−	0.895244i	$-0.352999\pi$
$787$	25.0000			0.891154			0.445577	+	0.895244i	$0.352999\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$		0			0
$790$	−4.00000			−0.142314
$791$	5.00000			0.177780
$792$		0			0
$793$	−17.5000	−	30.3109i	−0.621443	−	1.07637i
$794$	−3.00000	+	5.19615i	−0.106466	+	0.184405i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−7.00000			−0.247953			−0.123976	−	0.992285i	$-0.539565\pi$
$797$	−7.00000			−0.247953			−0.123976	+	0.992285i	$0.539565\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	12.5000	−	21.6506i	0.441390	−	0.764511i
$803$	14.0000	+	24.2487i	0.494049	+	0.855718i
$804$		0			0
$805$	1.00000			0.0352454
$806$	20.0000			0.704470
$807$		0			0
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$	−33.0000			−1.16022			−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000			−1.16022			−0.580109	+	0.814539i	$0.696990\pi$
$810$		0			0
$811$	6.00000	−	10.3923i	0.210688	−	0.364923i	−0.741242	−	0.671238i	$-0.765763\pi$
$811$	6.00000	−	10.3923i	0.210688	−	0.364923i	0.951930	+	0.306315i	$0.0990961\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$		0			0
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$	28.0000	−	20.7846i	0.979596	−	0.727161i
$818$	4.00000			0.139857
$819$		0			0
$820$	1.00000	+	1.73205i	0.0349215	+	0.0604858i
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	0.0542853	+	0.998525i	$0.482712\pi$
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	−0.891891	+	0.452250i	$0.850621\pi$
$822$		0			0
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	0.819159	+	0.573567i	$0.194441\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	3.50000	−	6.06218i	0.121781	−	0.210930i
$827$	3.00000	−	5.19615i	0.104320	−	0.180688i	−0.809140	−	0.587616i	$-0.800067\pi$
$827$	3.00000	−	5.19615i	0.104320	−	0.180688i	0.913460	+	0.406928i	$0.133400\pi$
$828$		0			0
$829$	−31.0000			−1.07667			−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000			−1.07667			−0.538337	+	0.842729i	$0.680947\pi$
$830$	−3.50000	+	6.06218i	−0.121487	+	0.210421i
$831$		0			0
$832$	2.50000	−	4.33013i	0.0866719	−	0.150120i
$833$		0			0
$834$		0			0
$835$	2.00000			0.0692129
$836$	8.00000	+	3.46410i	0.276686	+	0.119808i
$837$		0			0
$838$	14.0000	+	24.2487i	0.483622	+	0.837658i
$839$	27.0000	+	46.7654i	0.932144	+	1.61452i	0.779650	+	0.626215i	$0.215397\pi$
$839$	27.0000	+	46.7654i	0.932144	+	1.61452i	0.152493	+	0.988304i	$0.451270\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	17.0000	−	29.4449i	0.585859	−	1.01474i
$843$		0			0
$844$	−8.00000			−0.275371
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$		0			0
$847$	−7.00000			−0.240523
$848$	2.00000			0.0686803
$849$		0			0
$850$		0			0
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$		0			0
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	0.552948	−	0.833215i	$-0.313503\pi$
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	−0.998060	+	0.0622597i	$0.980169\pi$
$854$	7.00000			0.239535
$855$		0			0
$856$	−18.0000			−0.615227
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	0.960461	−	0.278416i	$-0.0898092\pi$
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	−0.721345	+	0.692576i	$0.756476\pi$
$858$		0			0
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	−0.999672	−	0.0255910i	$-0.991853\pi$
$859$	−14.0000	+	24.2487i	−0.477674	+	0.827355i	0.521999	+	0.852946i	$0.325187\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$		0			0
$862$	12.0000			0.408722
$863$	32.0000			1.08929			0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000			1.08929			0.544646	+	0.838666i	$0.316664\pi$
$864$		0			0
$865$	6.50000	−	11.2583i	0.221007	−	0.382795i
$866$	−2.00000			−0.0679628
$867$		0			0
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	4.00000	+	6.92820i	0.135691	+	0.235023i
$870$		0			0
$871$	30.0000	+	51.9615i	1.01651	+	1.76065i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$		0			0
$874$	−0.500000	−	4.33013i	−0.0169128	−	0.146469i
$875$	9.00000			0.304256
$876$		0			0
$877$	23.0000	+	39.8372i	0.776655	+	1.34521i	0.933860	+	0.357640i	$0.116418\pi$
$877$	23.0000	+	39.8372i	0.776655	+	1.34521i	−0.157205	+	0.987566i	$0.550248\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$		0			0
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−17.0000	+	29.4449i	−0.572096	+	0.990899i	0.424255	+	0.905543i	$0.360536\pi$
$883$	−17.0000	+	29.4449i	−0.572096	+	0.990899i	−0.996351	+	0.0853558i	$0.972797\pi$
$884$		0			0
$885$		0			0
$886$	−34.0000			−1.14225
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	0.261540	+	0.965193i	$0.415770\pi$
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	−0.966651	+	0.256096i	$0.917564\pi$
$888$		0			0
$889$	−6.50000	+	11.2583i	−0.218003	+	0.377592i
$890$		0			0
$891$		0			0
$892$	−2.00000			−0.0669650
$893$		0			0
$894$		0			0
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$		0			0
$898$	−18.5000	−	32.0429i	−0.617353	−	1.06929i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$		0			0
$902$	2.00000	−	3.46410i	0.0665927	−	0.115342i
$903$		0			0
$904$	−5.00000			−0.166298
$905$	−23.0000			−0.764546
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−1.50000	+	2.59808i	−0.0497792	+	0.0862202i
$909$		0			0
$910$	2.50000	+	4.33013i	0.0828742	+	0.143542i
$911$	−9.00000			−0.298183			−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000			−0.298183			−0.149092	+	0.988823i	$0.547635\pi$
$912$		0			0
$913$	14.0000			0.463332
$914$	−19.5000	−	33.7750i	−0.645003	−	1.11718i
$915$		0			0
$916$	−13.5000	+	23.3827i	−0.446053	+	0.772586i
$917$	7.50000	+	12.9904i	0.247672	+	0.428980i
$918$		0			0
$919$	3.00000			0.0989609			0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000			0.0989609			0.0494804	+	0.998775i	$0.484243\pi$
$920$	−1.00000			−0.0329690
$921$		0			0
$922$	18.5000	−	32.0429i	0.609265	−	1.05528i
$923$	−75.0000			−2.46866
$924$		0			0
$925$	−8.00000	+	13.8564i	−0.263038	+	0.455596i
$926$	−2.50000	−	4.33013i	−0.0821551	−	0.142297i
$927$		0			0
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	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
$931$	−0.500000	−	4.33013i	−0.0163868	−	0.141914i
$932$	11.0000			0.360317
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$		0			0
$936$		0			0
$937$	−29.0000	+	50.2295i	−0.947389	+	1.64093i	−0.196492	+	0.980505i	$0.562955\pi$
$937$	−29.0000	+	50.2295i	−0.947389	+	1.64093i	−0.750896	+	0.660420i	$0.770378\pi$
$938$	−12.0000			−0.391814
$939$		0			0
$940$		0			0
$941$	8.50000	−	14.7224i	0.277092	−	0.479938i	−0.693569	−	0.720390i	$-0.743963\pi$
$941$	8.50000	−	14.7224i	0.277092	−	0.479938i	0.970661	+	0.240453i	$0.0772960\pi$
$942$		0			0
$943$	−2.00000			−0.0651290
$944$	−3.50000	+	6.06218i	−0.113915	+	0.197307i
$945$		0			0
$946$	−8.00000	+	13.8564i	−0.260102	+	0.450511i
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$		0			0
$949$	70.0000			2.27230
$950$	−2.00000	−	17.3205i	−0.0648886	−	0.561951i
$951$		0			0
$952$		0			0
$953$	−11.0000	−	19.0526i	−0.356325	−	0.617173i	0.631019	−	0.775768i	$-0.282637\pi$
$953$	−11.0000	−	19.0526i	−0.356325	−	0.617173i	−0.987344	+	0.158595i	$0.949304\pi$
$954$		0			0
$955$	−8.50000	−	14.7224i	−0.275054	−	0.476407i
$956$	−2.50000	+	4.33013i	−0.0808558	+	0.140046i
$957$		0			0
$958$	24.0000			0.775405
$959$	−4.50000	+	7.79423i	−0.145313	+	0.251689i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−20.0000			−0.644826
$963$		0			0
$964$	2.00000	+	3.46410i	0.0644157	+	0.111571i
$965$	−1.50000	+	2.59808i	−0.0482867	+	0.0836350i
$966$		0			0
$967$	28.5000	+	49.3634i	0.916498	+	1.58742i	0.804693	+	0.593691i	$0.202330\pi$
$967$	28.5000	+	49.3634i	0.916498	+	1.58742i	0.111805	+	0.993730i	$0.464337\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	12.0000			0.385297
$971$	−20.5000	−	35.5070i	−0.657876	−	1.13948i	−0.981164	−	0.193175i	$-0.938122\pi$
$971$	−20.5000	−	35.5070i	−0.657876	−	1.13948i	0.323288	−	0.946301i	$-0.395212\pi$
$972$		0			0
$973$	6.00000	−	10.3923i	0.192351	−	0.333162i
$974$	−8.00000	−	13.8564i	−0.256337	−	0.443988i
$975$		0			0
$976$	−7.00000			−0.224065
$977$	37.0000			1.18373			0.591867	−	0.806035i	$-0.298391\pi$
$977$	37.0000			1.18373			0.591867	+	0.806035i	$0.298391\pi$
$978$		0			0
$979$		0			0
$980$	−1.00000			−0.0319438
$981$		0			0
$982$	−10.0000	+	17.3205i	−0.319113	+	0.552720i
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	0.977961	+	0.208788i	$0.0669518\pi$
$983$	21.0000	+	36.3731i	0.669796	+	1.16012i	−0.308165	+	0.951333i	$0.599715\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$		0			0
$987$		0			0
$988$	17.5000	−	12.9904i	0.556749	−	0.413279i
$989$	8.00000			0.254385
$990$		0			0
$991$	15.5000	+	26.8468i	0.492374	+	0.852816i	0.999961	−	0.00878379i	$-0.00279600\pi$
$991$	15.5000	+	26.8468i	0.492374	+	0.852816i	−0.507588	+	0.861600i	$0.669463\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$	7.50000	−	12.9904i	0.237886	−	0.412030i
$995$	4.00000			0.126809
$996$		0			0
$997$	−8.50000	+	14.7224i	−0.269198	+	0.466264i	−0.968655	−	0.248410i	$-0.920092\pi$
$997$	−8.50000	+	14.7224i	−0.269198	+	0.466264i	0.699457	+	0.714675i	$0.253425\pi$
$998$	12.0000	−	20.7846i	0.379853	−	0.657925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.o.i.1261.1		2
3.2	odd	2		266.2.f.a.197.1	✓	2
19.11	even	3	inner	2394.2.o.i.505.1		2
57.11	odd	6		266.2.f.a.239.1	yes	2
57.26	odd	6		5054.2.a.b.1.1		1
57.50	even	6		5054.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.a.197.1	✓	2	3.2	odd	2
266.2.f.a.239.1	yes	2	57.11	odd	6
2394.2.o.i.505.1		2	19.11	even	3	inner
2394.2.o.i.1261.1		2	1.1	even	1	trivial
5054.2.a.a.1.1		1	57.50	even	6
5054.2.a.b.1.1		1	57.26	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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +2.00000 q^{11} +(2.50000 - 4.33013i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 4.33013i) q^{19} -1.00000 q^{20} +(1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{35} -4.00000 q^{37} +(3.50000 - 2.59808i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-1.00000 + 1.73205i) q^{44} +1.00000 q^{46} +1.00000 q^{49} +4.00000 q^{50} +(2.50000 + 4.33013i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(1.00000 + 1.73205i) q^{55} -1.00000 q^{56} +6.00000 q^{58} +(-3.50000 - 6.06218i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +5.00000 q^{65} +(-6.00000 + 10.3923i) q^{67} +(-0.500000 + 0.866025i) q^{70} +(-7.50000 - 12.9904i) q^{71} +(7.00000 + 12.1244i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(4.00000 + 1.73205i) q^{76} +2.00000 q^{77} +(2.00000 + 3.46410i) q^{79} +(0.500000 - 0.866025i) q^{80} +(1.00000 - 1.73205i) q^{82} +7.00000 q^{83} +(-4.00000 + 6.92820i) q^{86} -2.00000 q^{88} +(2.50000 - 4.33013i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.50000 - 2.59808i) q^{95} +(-6.00000 - 10.3923i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + q^5 + 2 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + q^{5} + 2 q^{7} - 2 q^{8} - q^{10} + 4 q^{11} + 5 q^{13} + q^{14} - q^{16} - q^{19} - 2 q^{20} + 2 q^{22} + q^{23} + 4 q^{25} + 10 q^{26} - q^{28} + 6 q^{29} + 8 q^{31} + q^{32} + q^{35} - 8 q^{37} + 7 q^{38} - q^{40} - 2 q^{41} + 8 q^{43} - 2 q^{44} + 2 q^{46} + 2 q^{49} + 8 q^{50} + 5 q^{52} - 2 q^{53} + 2 q^{55} - 2 q^{56} + 12 q^{58} - 7 q^{59} + 7 q^{61} + 4 q^{62} + 2 q^{64} + 10 q^{65} - 12 q^{67} - q^{70} - 15 q^{71} + 14 q^{73} - 4 q^{74} + 8 q^{76} + 4 q^{77} + 4 q^{79} + q^{80} + 2 q^{82} + 14 q^{83} - 8 q^{86} - 4 q^{88} + 5 q^{91} + q^{92} + 7 q^{95} - 12 q^{97} + q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + q^5 + 2 * q^7 - 2 * q^8 - q^10 + 4 * q^11 + 5 * q^13 + q^14 - q^16 - q^19 - 2 * q^20 + 2 * q^22 + q^23 + 4 * q^25 + 10 * q^26 - q^28 + 6 * q^29 + 8 * q^31 + q^32 + q^35 - 8 * q^37 + 7 * q^38 - q^40 - 2 * q^41 + 8 * q^43 - 2 * q^44 + 2 * q^46 + 2 * q^49 + 8 * q^50 + 5 * q^52 - 2 * q^53 + 2 * q^55 - 2 * q^56 + 12 * q^58 - 7 * q^59 + 7 * q^61 + 4 * q^62 + 2 * q^64 + 10 * q^65 - 12 * q^67 - q^70 - 15 * q^71 + 14 * q^73 - 4 * q^74 + 8 * q^76 + 4 * q^77 + 4 * q^79 + q^80 + 2 * q^82 + 14 * q^83 - 8 * q^86 - 4 * q^88 + 5 * q^91 + q^92 + 7 * q^95 - 12 * q^97 + q^98

Introduction

L-functions

Modular forms

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