LMFDB - Embedded newform 2394.2.o.b.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 798)
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.b.505.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-0.500000 - 4.33013i) q^{19} +3.00000 q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(-1.50000 - 2.59808i) q^{35} +8.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(-3.00000 + 5.19615i) q^{44} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{49} +4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-9.00000 - 15.5885i) q^{55} +1.00000 q^{56} -6.00000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(6.50000 - 11.2583i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +15.0000 q^{65} +(-7.00000 + 12.1244i) q^{67} +6.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-1.50000 - 2.59808i) q^{71} +(2.00000 + 3.46410i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(4.00000 + 1.73205i) q^{76} +6.00000 q^{77} +(-4.00000 - 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.00000 - 5.19615i) q^{82} -15.0000 q^{83} +(-9.00000 + 15.5885i) q^{85} +(2.00000 - 3.46410i) q^{86} +6.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} -6.00000 q^{94} +(-10.5000 + 7.79423i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8} - 3 q^{10} + 12 q^{11} - 5 q^{13} - q^{14} - q^{16} - 6 q^{17} - q^{19} + 6 q^{20} - 6 q^{22} - 3 q^{23} - 4 q^{25} + 10 q^{26} - q^{28} + 6 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 3 q^{35} + 16 q^{37} - 7 q^{38} - 3 q^{40} + 6 q^{41} + 4 q^{43} - 6 q^{44} + 6 q^{46} + 6 q^{47} + 2 q^{49} + 8 q^{50} - 5 q^{52} + 12 q^{53} - 18 q^{55} + 2 q^{56} - 12 q^{58} - 9 q^{59} + 13 q^{61} + 4 q^{62} + 2 q^{64} + 30 q^{65} - 14 q^{67} + 12 q^{68} - 3 q^{70} - 3 q^{71} + 4 q^{73} - 8 q^{74} + 8 q^{76} + 12 q^{77} - 8 q^{79} - 3 q^{80} + 6 q^{82} - 30 q^{83} - 18 q^{85} + 4 q^{86} + 12 q^{88} - 6 q^{89} - 5 q^{91} - 3 q^{92} - 12 q^{94} - 21 q^{95} - 8 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^7 + 2 * q^8 - 3 * q^10 + 12 * q^11 - 5 * q^13 - q^14 - q^16 - 6 * q^17 - q^19 + 6 * q^20 - 6 * q^22 - 3 * q^23 - 4 * q^25 + 10 * q^26 - q^28 + 6 * q^29 - 8 * q^31 - q^32 - 6 * q^34 - 3 * q^35 + 16 * q^37 - 7 * q^38 - 3 * q^40 + 6 * q^41 + 4 * q^43 - 6 * q^44 + 6 * q^46 + 6 * q^47 + 2 * q^49 + 8 * q^50 - 5 * q^52 + 12 * q^53 - 18 * q^55 + 2 * q^56 - 12 * q^58 - 9 * q^59 + 13 * q^61 + 4 * q^62 + 2 * q^64 + 30 * q^65 - 14 * q^67 + 12 * q^68 - 3 * q^70 - 3 * q^71 + 4 * q^73 - 8 * q^74 + 8 * q^76 + 12 * q^77 - 8 * q^79 - 3 * q^80 + 6 * q^82 - 30 * q^83 - 18 * q^85 + 4 * q^86 + 12 * q^88 - 6 * q^89 - 5 * q^91 - 3 * q^92 - 12 * q^94 - 21 * q^95 - 8 * 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
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$		0			0
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$19$	−0.500000	−	4.33013i	−0.114708	−	0.993399i
$20$	3.00000			0.670820
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		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	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−3.50000	+	2.59808i	−0.567775	+	0.421464i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$		0			0
$46$	3.00000			0.442326
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	4.00000			0.565685
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	−9.00000	−	15.5885i	−1.21356	−	2.10195i
$56$	1.00000			0.133631
$57$		0			0
$58$	−6.00000			−0.787839
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$	15.0000			1.86052
$66$		0			0
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	0.0212861	+	0.999773i	$0.493224\pi$
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	−0.876472	+	0.481452i	$0.840109\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$		0			0
$76$	4.00000	+	1.73205i	0.458831	+	0.198680i
$77$	6.00000			0.683763
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−15.0000			−1.64646			−0.823232	−	0.567705i	$-0.807831\pi$
$83$	−15.0000			−1.64646			−0.823232	+	0.567705i	$0.807831\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$		0			0
$88$	6.00000			0.639602
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−2.50000	+	4.33013i	−0.262071	+	0.453921i
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$		0			0
$94$	−6.00000			−0.618853
$95$	−10.5000	+	7.79423i	−1.07728	+	0.799671i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−2.50000	+	4.33013i	−0.245145	+	0.424604i
$105$		0			0
$106$	−12.0000			−1.16554
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$	−9.00000	+	15.5885i	−0.858116	+	1.48630i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−21.0000			−1.97551			−0.987757	−	0.156001i	$-0.950140\pi$
$113$	−21.0000			−1.97551			−0.987757	+	0.156001i	$0.950140\pi$
$114$		0			0
$115$	9.00000			0.839254
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$	−4.50000	+	7.79423i	−0.414259	+	0.717517i
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$		0			0
$121$	25.0000			2.27273
$122$	−13.0000			−1.17696
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	−0.419064	−	0.907957i	$-0.637642\pi$
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	0.995846	−	0.0910585i	$-0.0290250\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−7.50000	−	12.9904i	−0.657794	−	1.13933i
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$	−0.500000	−	4.33013i	−0.0433555	−	0.375470i
$134$	14.0000			1.20942
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	3.00000			0.253546
$141$		0			0
$142$	−1.50000	+	2.59808i	−0.125877	+	0.218026i
$143$	−15.0000	+	25.9808i	−1.25436	+	2.17262i
$144$		0			0
$145$	−18.0000			−1.49482
$146$	2.00000	−	3.46410i	0.165521	−	0.286691i
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	−12.0000	−	20.7846i	−0.983078	−	1.70274i	−0.650183	−	0.759778i	$-0.725308\pi$
$149$	−12.0000	−	20.7846i	−0.983078	−	1.70274i	−0.332896	−	0.942964i	$-0.608026\pi$
$150$		0			0
$151$	−19.0000			−1.54620			−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−19.0000			−1.54620			−0.773099	+	0.634285i	$0.781294\pi$
$152$	−0.500000	−	4.33013i	−0.0405554	−	0.351220i
$153$		0			0
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	6.00000	+	10.3923i	0.481932	+	0.834730i
$156$		0			0
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	−0.975470	−	0.220131i	$-0.929352\pi$
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	0.297097	−	0.954847i	$-0.403982\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	3.00000			0.237171
$161$	−1.50000	+	2.59808i	−0.118217	+	0.204757i
$162$		0			0
$163$	14.0000			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	7.50000	+	12.9904i	0.582113	+	1.00825i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	18.0000			1.38054
$171$		0			0
$172$	−4.00000			−0.304997
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$		0			0
$178$	6.00000			0.449719
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$		0			0
$181$	−2.50000	+	4.33013i	−0.185824	+	0.321856i	−0.943854	−	0.330364i	$-0.892829\pi$
$181$	−2.50000	+	4.33013i	−0.185824	+	0.321856i	0.758030	+	0.652219i	$0.226162\pi$
$182$	5.00000			0.370625
$183$		0			0
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	−12.0000	−	20.7846i	−0.882258	−	1.52811i
$186$		0			0
$187$	−18.0000	−	31.1769i	−1.31629	−	2.27988i
$188$	3.00000	+	5.19615i	0.218797	+	0.378968i
$189$		0			0
$190$	12.0000	+	5.19615i	0.870572	+	0.376969i
$191$	15.0000			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	−4.00000	+	6.92820i	−0.287183	+	0.497416i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	11.0000	−	19.0526i	0.779769	−	1.35060i	−0.152305	−	0.988334i	$-0.548670\pi$
$199$	11.0000	−	19.0526i	0.779769	−	1.35060i	0.932075	−	0.362267i	$-0.117997\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	6.00000			0.422159
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$		0			0
$208$	5.00000			0.346688
$209$	−3.00000	−	25.9808i	−0.207514	−	1.79713i
$210$		0			0
$211$	5.00000	+	8.66025i	0.344214	+	0.596196i	0.985211	−	0.171347i	$-0.0548120\pi$
$211$	5.00000	+	8.66025i	0.344214	+	0.596196i	−0.640996	+	0.767544i	$0.721479\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$		0			0
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$		0			0
$217$	−4.00000			−0.271538
$218$	2.00000	−	3.46410i	0.135457	−	0.234619i
$219$		0			0
$220$	18.0000			1.21356
$221$	30.0000			2.01802
$222$		0			0
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	10.5000	+	18.1865i	0.698450	+	1.20975i
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$		0			0
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$	−4.50000	−	7.79423i	−0.296721	−	0.513936i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	−0.972523	−	0.232806i	$-0.925209\pi$
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	0.284645	−	0.958633i	$-0.408124\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$	9.00000			0.585850
$237$		0			0
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	9.00000			0.582162			0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000			0.582162			0.291081	+	0.956698i	$0.405985\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	−12.5000	−	21.6506i	−0.803530	−	1.39176i
$243$		0			0
$244$	6.50000	+	11.2583i	0.416120	+	0.720741i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$		0			0
$247$	20.0000	+	8.66025i	1.27257	+	0.551039i
$248$	−4.00000			−0.254000
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$		0			0
$253$	−9.00000	+	15.5885i	−0.565825	+	0.980038i
$254$	−13.0000			−0.815693
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	8.00000			0.497096
$260$	−7.50000	+	12.9904i	−0.465130	+	0.805629i
$261$		0			0
$262$	−7.50000	+	12.9904i	−0.463352	+	0.802548i
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	0.536614	−	0.843828i	$-0.319703\pi$
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	−0.999083	+	0.0428069i	$0.986370\pi$
$264$		0			0
$265$	−36.0000			−2.21146
$266$	−3.50000	+	2.59808i	−0.214599	+	0.159298i
$267$		0			0
$268$	−7.00000	−	12.1244i	−0.427593	−	0.740613i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$		0			0
$274$	3.00000			0.181237
$275$	−12.0000	+	20.7846i	−0.723627	+	1.25336i
$276$		0			0
$277$	−4.00000			−0.240337			−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000			−0.240337			−0.120168	+	0.992754i	$0.538343\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	−0.762561	−	0.646916i	$-0.776058\pi$
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	0.941526	+	0.336939i	$0.109392\pi$
$282$		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	$0.766621\pi$
$284$	3.00000			0.178017
$285$		0			0
$286$	30.0000			1.77394
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	9.00000	+	15.5885i	0.528498	+	0.915386i
$291$		0			0
$292$	−4.00000			−0.234082
$293$	27.0000			1.57736			0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000			1.57736			0.788678	+	0.614806i	$0.210766\pi$
$294$		0			0
$295$	−13.5000	+	23.3827i	−0.786000	+	1.36139i
$296$	8.00000			0.464991
$297$		0			0
$298$	−12.0000	+	20.7846i	−0.695141	+	1.20402i
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$		0			0
$301$	2.00000	+	3.46410i	0.115278	+	0.199667i
$302$	9.50000	+	16.4545i	0.546664	+	0.946849i
$303$		0			0
$304$	−3.50000	+	2.59808i	−0.200739	+	0.149010i
$305$	−39.0000			−2.23313
$306$		0			0
$307$	12.5000	+	21.6506i	0.713413	+	1.23567i	0.963569	+	0.267461i	$0.0861848\pi$
$307$	12.5000	+	21.6506i	0.713413	+	1.23567i	−0.250156	+	0.968206i	$0.580482\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$		0			0
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	−0.546335	−	0.837567i	$-0.683977\pi$
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	0.998522	+	0.0543564i	$0.0173107\pi$
$314$	−8.50000	+	14.7224i	−0.479683	+	0.830835i
$315$		0			0
$316$	8.00000			0.450035
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$		0			0
$322$	3.00000			0.167183
$323$	−21.0000	+	15.5885i	−1.16847	+	0.867365i
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	−7.00000	−	12.1244i	−0.387694	−	0.671506i
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	7.50000	−	12.9904i	0.411616	−	0.712940i
$333$		0			0
$334$	12.0000			0.656611
$335$	42.0000			2.29471
$336$		0			0
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	0.789865	−	0.613280i	$-0.210150\pi$
$337$	−2.50000	−	4.33013i	−0.136184	−	0.235877i	−0.926049	+	0.377403i	$0.876817\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$		0			0
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$	−24.0000			−1.29967
$342$		0			0
$343$	1.00000			0.0539949
$344$	2.00000	+	3.46410i	0.107833	+	0.186772i
$345$		0			0
$346$	7.50000	−	12.9904i	0.403202	−	0.698367i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−3.00000	+	5.19615i	−0.159901	+	0.276956i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$		0			0
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	0.979791	−	0.200026i	$-0.0641026\pi$
$359$	6.00000	+	10.3923i	0.316668	+	0.548485i	−0.663123	+	0.748511i	$0.730769\pi$
$360$		0			0
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$	5.00000			0.262794
$363$		0			0
$364$	−2.50000	−	4.33013i	−0.131036	−	0.226960i
$365$	6.00000	−	10.3923i	0.314054	−	0.543958i
$366$		0			0
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	0.296810	+	0.954937i	$0.404077\pi$
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	−0.975404	+	0.220423i	$0.929256\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$	−12.0000	+	20.7846i	−0.623850	+	1.08054i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	−16.0000			−0.828449			−0.414224	−	0.910175i	$-0.635947\pi$
$373$	−16.0000			−0.828449			−0.414224	+	0.910175i	$0.635947\pi$
$374$	−18.0000	+	31.1769i	−0.930758	+	1.61212i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$	15.0000	+	25.9808i	0.772539	+	1.33808i
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−1.50000	−	12.9904i	−0.0769484	−	0.666392i
$381$		0			0
$382$	−7.50000	−	12.9904i	−0.383733	−	0.664646i
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$	−9.00000	−	15.5885i	−0.458682	−	0.794461i
$386$	−2.50000	+	4.33013i	−0.127247	+	0.220398i
$387$		0			0
$388$	8.00000			0.406138
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	1.00000			0.0505076
$393$		0			0
$394$		0			0
$395$	−12.0000	+	20.7846i	−0.603786	+	1.04579i
$396$		0			0
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−22.0000			−1.10276
$399$		0			0
$400$	4.00000			0.200000
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$		0			0
$406$	−6.00000			−0.297775
$407$	48.0000			2.37927
$408$		0			0
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	−0.0487958	−	0.998809i	$-0.515538\pi$
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	0.889392	−	0.457146i	$-0.151128\pi$
$410$	−18.0000			−0.888957
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	−4.50000	−	7.79423i	−0.221431	−	0.383529i
$414$		0			0
$415$	22.5000	+	38.9711i	1.10448	+	1.91302i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$		0			0
$418$	−21.0000	+	15.5885i	−1.02714	+	0.762456i
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	0.512524	−	0.858673i	$-0.328710\pi$
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	−0.999895	+	0.0145228i	$0.995377\pi$
$422$	5.00000	−	8.66025i	0.243396	−	0.421575i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	24.0000			1.16417
$426$		0			0
$427$	6.50000	−	11.2583i	0.314557	−	0.544829i
$428$		0			0
$429$		0			0
$430$	−12.0000			−0.578691
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$		0			0
$433$	−4.00000	+	6.92820i	−0.192228	+	0.332948i	−0.945988	−	0.324201i	$-0.894905\pi$
$433$	−4.00000	+	6.92820i	−0.192228	+	0.332948i	0.753760	+	0.657149i	$0.228238\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$		0			0
$436$	−4.00000			−0.191565
$437$	12.0000	+	5.19615i	0.574038	+	0.248566i
$438$		0			0
$439$	11.0000	+	19.0526i	0.525001	+	0.909329i	0.999576	+	0.0291138i	$0.00926853\pi$
$439$	11.0000	+	19.0526i	0.525001	+	0.909329i	−0.474575	+	0.880215i	$0.657398\pi$
$440$	−9.00000	−	15.5885i	−0.429058	−	0.743151i
$441$		0			0
$442$	−15.0000	−	25.9808i	−0.713477	−	1.23578i
$443$	−9.00000	+	15.5885i	−0.427603	+	0.740630i	−0.996660	−	0.0816684i	$-0.973975\pi$
$443$	−9.00000	+	15.5885i	−0.427603	+	0.740630i	0.569057	+	0.822298i	$0.307309\pi$
$444$		0			0
$445$	18.0000			0.853282
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$		0			0
$448$	1.00000			0.0472456
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$		0			0
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$	10.5000	−	18.1865i	0.493878	−	0.855423i
$453$		0			0
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$	15.0000			0.703211
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	−2.50000	−	4.33013i	−0.116817	−	0.202334i
$459$		0			0
$460$	−4.50000	+	7.79423i	−0.209814	+	0.363408i
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	0.741998	−	0.670402i	$-0.233878\pi$
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	−0.951584	+	0.307388i	$0.900545\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−10.5000	+	18.1865i	−0.486403	+	0.842475i
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$	−7.00000	+	12.1244i	−0.323230	+	0.559851i
$470$	9.00000	+	15.5885i	0.415139	+	0.719042i
$471$		0			0
$472$	−4.50000	−	7.79423i	−0.207129	−	0.358758i
$473$	12.0000	+	20.7846i	0.551761	+	0.955677i
$474$		0			0
$475$	16.0000	+	6.92820i	0.734130	+	0.317888i
$476$	6.00000			0.275010
$477$		0			0
$478$	−4.50000	−	7.79423i	−0.205825	−	0.356500i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	−20.0000	+	34.6410i	−0.911922	+	1.57949i
$482$	8.00000			0.364390
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−12.0000	+	20.7846i	−0.544892	+	0.943781i
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$	6.50000	−	11.2583i	0.294241	−	0.509641i
$489$		0			0
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$		0			0
$493$	−36.0000			−1.62136
$494$	−2.50000	−	21.6506i	−0.112480	−	0.974108i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	−3.00000			−0.133897
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	−0.464107	−	0.885779i	$-0.653625\pi$
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	0.999161	−	0.0409609i	$-0.0130419\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	18.0000			0.800198
$507$		0			0
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.00000			0.264649
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$		0			0
$517$	18.0000	−	31.1769i	0.791639	−	1.37116i
$518$	−4.00000	−	6.92820i	−0.175750	−	0.304408i
$519$		0			0
$520$	15.0000			0.657794
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$		0			0
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	15.0000			0.655278
$525$		0			0
$526$	−7.50000	+	12.9904i	−0.327016	+	0.566408i
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	18.0000	+	31.1769i	0.781870	+	1.35424i
$531$		0			0
$532$	4.00000	+	1.73205i	0.173422	+	0.0750939i
$533$	−30.0000			−1.29944
$534$		0			0
$535$		0			0
$536$	−7.00000	+	12.1244i	−0.302354	+	0.523692i
$537$		0			0
$538$	9.00000	−	15.5885i	0.388018	−	0.672066i
$539$	6.00000			0.258438
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	−1.00000	+	1.73205i	−0.0429537	+	0.0743980i
$543$		0			0
$544$	6.00000			0.257248
$545$	6.00000	−	10.3923i	0.257012	−	0.445157i
$546$		0			0
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	−0.529098	−	0.848561i	$-0.677470\pi$
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	0.999424	+	0.0339321i	$0.0108030\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$		0			0
$550$	24.0000			1.02336
$551$	−24.0000	−	10.3923i	−1.02243	−	0.442727i
$552$		0			0
$553$	−4.00000	−	6.92820i	−0.170097	−	0.294617i
$554$	2.00000	+	3.46410i	0.0849719	+	0.147176i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−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	$0.947432\pi$
$558$		0			0
$559$	−20.0000			−0.845910
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$		0			0
$562$	−6.00000			−0.253095
$563$	−15.0000			−0.632175			−0.316087	−	0.948730i	$-0.602369\pi$
$563$	−15.0000			−0.632175			−0.316087	+	0.948730i	$0.602369\pi$
$564$		0			0
$565$	31.5000	+	54.5596i	1.32521	+	2.29534i
$566$	3.50000	−	6.06218i	0.147116	−	0.254812i
$567$		0			0
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	39.0000			1.63497			0.817483	−	0.575953i	$-0.195369\pi$
$569$	39.0000			1.63497			0.817483	+	0.575953i	$0.195369\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	−15.0000	−	25.9808i	−0.627182	−	1.08631i
$573$		0			0
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$	−6.00000	−	10.3923i	−0.250217	−	0.433389i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	19.0000			0.790296
$579$		0			0
$580$	9.00000	−	15.5885i	0.373705	−	0.647275i
$581$	−15.0000			−0.622305
$582$		0			0
$583$	36.0000	−	62.3538i	1.49097	−	2.58243i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	−13.5000	−	23.3827i	−0.557680	−	0.965930i
$587$	18.0000	+	31.1769i	0.742940	+	1.28681i	0.951151	+	0.308725i	$0.0999023\pi$
$587$	18.0000	+	31.1769i	0.742940	+	1.28681i	−0.208212	+	0.978084i	$0.566764\pi$
$588$		0			0
$589$	2.00000	+	17.3205i	0.0824086	+	0.713679i
$590$	27.0000			1.11157
$591$		0			0
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	−0.619915	−	0.784669i	$-0.712833\pi$
$593$	9.00000	−	15.5885i	0.369586	−	0.640141i	0.989501	+	0.144528i	$0.0461663\pi$
$594$		0			0
$595$	−9.00000	+	15.5885i	−0.368964	+	0.639064i
$596$	24.0000			0.983078
$597$		0			0
$598$	−7.50000	+	12.9904i	−0.306698	+	0.531216i
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	2.00000	−	3.46410i	0.0815139	−	0.141186i
$603$		0			0
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$	−37.5000	−	64.9519i	−1.52459	−	2.64067i
$606$		0			0
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$	4.00000	+	1.73205i	0.162221	+	0.0702439i
$609$		0			0
$610$	19.5000	+	33.7750i	0.789532	+	1.36751i
$611$	15.0000	+	25.9808i	0.606835	+	1.05107i
$612$		0			0
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	0.972924	+	0.231127i	$0.0742412\pi$
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	−0.286300	+	0.958140i	$0.592425\pi$
$614$	12.5000	−	21.6506i	0.504459	−	0.873749i
$615$		0			0
$616$	6.00000			0.241747
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	−0.455211	−	0.890384i	$-0.650436\pi$
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	0.998700	−	0.0509678i	$-0.0162306\pi$
$618$		0			0
$619$	−25.0000			−1.00483			−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000			−1.00483			−0.502417	+	0.864625i	$0.667556\pi$
$620$	−12.0000			−0.481932
$621$		0			0
$622$		0			0
$623$	−3.00000	+	5.19615i	−0.120192	+	0.208179i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−16.0000			−0.639489
$627$		0			0
$628$	17.0000			0.678374
$629$	−24.0000	−	41.5692i	−0.956943	−	1.65747i
$630$		0			0
$631$	20.0000	−	34.6410i	0.796187	−	1.37904i	−0.125895	−	0.992044i	$-0.540180\pi$
$631$	20.0000	−	34.6410i	0.796187	−	1.37904i	0.922082	−	0.386994i	$-0.126486\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$		0			0
$634$	−18.0000			−0.714871
$635$	−39.0000			−1.54767
$636$		0			0
$637$	−2.50000	+	4.33013i	−0.0990536	+	0.171566i
$638$	−36.0000			−1.42525
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$	−1.50000	−	2.59808i	−0.0591083	−	0.102379i
$645$		0			0
$646$	24.0000	+	10.3923i	0.944267	+	0.408880i
$647$	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
$649$	−27.0000	−	46.7654i	−1.05984	−	1.83570i
$650$	−10.0000	+	17.3205i	−0.392232	+	0.679366i
$651$		0			0
$652$	−7.00000	+	12.1244i	−0.274141	+	0.474826i
$653$	−30.0000			−1.17399			−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000			−1.17399			−0.586995	+	0.809590i	$0.699689\pi$
$654$		0			0
$655$	−22.5000	+	38.9711i	−0.879148	+	1.52273i
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$		0			0
$658$	−6.00000			−0.233904
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	−0.801660	−	0.597781i	$-0.796049\pi$
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	0.918523	+	0.395367i	$0.129383\pi$
$660$		0			0
$661$	24.5000	−	42.4352i	0.952940	−	1.65054i	0.213925	−	0.976850i	$-0.431375\pi$
$661$	24.5000	−	42.4352i	0.952940	−	1.65054i	0.739014	−	0.673690i	$-0.235292\pi$
$662$	−4.00000	−	6.92820i	−0.155464	−	0.269272i
$663$		0			0
$664$	−15.0000			−0.582113
$665$	−10.5000	+	7.79423i	−0.407173	+	0.302247i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$		0			0
$670$	−21.0000	−	36.3731i	−0.811301	−	1.40521i
$671$	39.0000	−	67.5500i	1.50558	−	2.60774i
$672$		0			0
$673$	−13.0000			−0.501113			−0.250557	−	0.968102i	$-0.580614\pi$
$673$	−13.0000			−0.501113			−0.250557	+	0.968102i	$0.580614\pi$
$674$	−2.50000	+	4.33013i	−0.0962964	+	0.166790i
$675$		0			0
$676$	12.0000			0.461538
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$		0			0
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	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
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	30.0000	+	51.9615i	1.14291	+	1.97958i
$690$		0			0
$691$	−13.0000			−0.494543			−0.247272	−	0.968946i	$-0.579534\pi$
$691$	−13.0000			−0.494543			−0.247272	+	0.968946i	$0.579534\pi$
$692$	−15.0000			−0.570214
$693$		0			0
$694$	6.00000	−	10.3923i	0.227757	−	0.394486i
$695$	−12.0000			−0.455186
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$	−1.00000	−	1.73205i	−0.0378506	−	0.0655591i
$699$		0			0
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	−6.00000	−	10.3923i	−0.226617	−	0.392512i	0.730186	−	0.683248i	$-0.239433\pi$
$701$	−6.00000	−	10.3923i	−0.226617	−	0.392512i	−0.956803	+	0.290736i	$0.906100\pi$
$702$		0			0
$703$	−4.00000	−	34.6410i	−0.150863	−	1.30651i
$704$	6.00000			0.226134
$705$		0			0
$706$	−6.00000	−	10.3923i	−0.225813	−	0.391120i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	9.00000			0.337764
$711$		0			0
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	90.0000			3.36581
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$		0			0
$721$	−4.00000			−0.148968
$722$	13.0000	+	13.8564i	0.483810	+	0.515682i
$723$		0			0
$724$	−2.50000	−	4.33013i	−0.0929118	−	0.160928i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$		0			0
$727$	−10.0000	−	17.3205i	−0.370879	−	0.642382i	0.618822	−	0.785532i	$-0.287610\pi$
$727$	−10.0000	−	17.3205i	−0.370879	−	0.642382i	−0.989701	+	0.143149i	$0.954277\pi$
$728$	−2.50000	+	4.33013i	−0.0926562	+	0.160485i
$729$		0			0
$730$	−12.0000			−0.444140
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$	26.0000			0.959678
$735$		0			0
$736$	−1.50000	−	2.59808i	−0.0552907	−	0.0957664i
$737$	−42.0000	+	72.7461i	−1.54709	+	2.67964i
$738$		0			0
$739$	17.0000	+	29.4449i	0.625355	+	1.08315i	0.988472	+	0.151403i	$0.0483792\pi$
$739$	17.0000	+	29.4449i	0.625355	+	1.08315i	−0.363117	+	0.931744i	$0.618287\pi$
$740$	24.0000			0.882258
$741$		0			0
$742$	−12.0000			−0.440534
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	0.991798	−	0.127815i	$-0.0407965\pi$
$743$	10.5000	+	18.1865i	0.385208	+	0.667199i	−0.606590	+	0.795015i	$0.707463\pi$
$744$		0			0
$745$	−36.0000	+	62.3538i	−1.31894	+	2.28447i
$746$	8.00000	+	13.8564i	0.292901	+	0.507319i
$747$		0			0
$748$	36.0000			1.31629
$749$		0			0
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	−6.00000			−0.218797
$753$		0			0
$754$	15.0000	−	25.9808i	0.546268	−	0.946164i
$755$	28.5000	+	49.3634i	1.03722	+	1.79652i
$756$		0			0
$757$	14.0000	+	24.2487i	0.508839	+	0.881334i	0.999948	+	0.0102362i	$0.00325836\pi$
$757$	14.0000	+	24.2487i	0.508839	+	0.881334i	−0.491109	+	0.871098i	$0.663408\pi$
$758$	8.00000	+	13.8564i	0.290573	+	0.503287i
$759$		0			0
$760$	−10.5000	+	7.79423i	−0.380875	+	0.282726i
$761$	−24.0000			−0.869999			−0.435000	−	0.900431i	$-0.643252\pi$
$761$	−24.0000			−0.869999			−0.435000	+	0.900431i	$0.643252\pi$
$762$		0			0
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−7.50000	+	12.9904i	−0.271340	+	0.469975i
$765$		0			0
$766$	3.00000	−	5.19615i	0.108394	−	0.187745i
$767$	45.0000			1.62486
$768$		0			0
$769$	20.0000	−	34.6410i	0.721218	−	1.24919i	−0.239293	−	0.970947i	$-0.576916\pi$
$769$	20.0000	−	34.6410i	0.721218	−	1.24919i	0.960512	−	0.278240i	$-0.0897509\pi$
$770$	−9.00000	+	15.5885i	−0.324337	+	0.561769i
$771$		0			0
$772$	5.00000			0.179954
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	−0.104102	−	0.994567i	$-0.533197\pi$
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	0.913371	−	0.407128i	$-0.133470\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	−4.00000	−	6.92820i	−0.143592	−	0.248708i
$777$		0			0
$778$		0			0
$779$	21.0000	−	15.5885i	0.752403	−	0.558514i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−25.5000	+	44.1673i	−0.910134	+	1.57640i
$786$		0			0
$787$	29.0000			1.03374			0.516869	−	0.856064i	$-0.327097\pi$
$787$	29.0000			1.03374			0.516869	+	0.856064i	$0.327097\pi$
$788$		0			0
$789$		0			0
$790$	24.0000			0.853882
$791$	−21.0000			−0.746674
$792$		0			0
$793$	32.5000	+	56.2917i	1.15411	+	1.99898i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	11.0000	+	19.0526i	0.389885	+	0.675300i
$797$	9.00000			0.318796			0.159398	−	0.987214i	$-0.449045\pi$
$797$	9.00000			0.318796			0.159398	+	0.987214i	$0.449045\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$	12.0000	+	20.7846i	0.423471	+	0.733473i
$804$		0			0
$805$	9.00000			0.317208
$806$	−20.0000			−0.704470
$807$		0			0
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	21.0000			0.738321			0.369160	−	0.929366i	$-0.379645\pi$
$809$	21.0000			0.738321			0.369160	+	0.929366i	$0.379645\pi$
$810$		0			0
$811$	−10.0000	+	17.3205i	−0.351147	+	0.608205i	−0.986451	−	0.164057i	$-0.947542\pi$
$811$	−10.0000	+	17.3205i	−0.351147	+	0.608205i	0.635303	+	0.772263i	$0.280875\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$		0			0
$814$	−24.0000	−	41.5692i	−0.841200	−	1.45700i
$815$	−21.0000	−	36.3731i	−0.735598	−	1.27409i
$816$		0			0
$817$	14.0000	−	10.3923i	0.489798	−	0.363581i
$818$	−34.0000			−1.18878
$819$		0			0
$820$	9.00000	+	15.5885i	0.314294	+	0.544373i
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$		0			0
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	−0.730215	−	0.683217i	$-0.760580\pi$
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	0.956791	+	0.290776i	$0.0939136\pi$
$824$	−4.00000			−0.139347
$825$		0			0
$826$	−4.50000	+	7.79423i	−0.156575	+	0.271196i
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	0.362441	+	0.932007i	$0.381944\pi$
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	−0.988362	+	0.152121i	$0.951390\pi$
$828$		0			0
$829$	−1.00000			−0.0347314			−0.0173657	−	0.999849i	$-0.505528\pi$
$829$	−1.00000			−0.0347314			−0.0173657	+	0.999849i	$0.505528\pi$
$830$	22.5000	−	38.9711i	0.780986	−	1.35271i
$831$		0			0
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	36.0000			1.24583
$836$	24.0000	+	10.3923i	0.830057	+	0.359425i
$837$		0			0
$838$	−12.0000	−	20.7846i	−0.414533	−	0.717992i
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$		0			0
$844$	−10.0000			−0.344214
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$	25.0000			0.859010
$848$	−12.0000			−0.412082
$849$		0			0
$850$	−12.0000	−	20.7846i	−0.411597	−	0.712906i
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$	17.0000	+	29.4449i	0.582069	+	1.00817i	0.995234	+	0.0975167i	$0.0310899\pi$
$853$	17.0000	+	29.4449i	0.582069	+	1.00817i	−0.413165	+	0.910656i	$0.635577\pi$
$854$	−13.0000			−0.444851
$855$		0			0
$856$		0			0
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	−0.999897	−	0.0143666i	$-0.995427\pi$
$857$	−15.0000	−	25.9808i	−0.512390	−	0.887486i	0.487507	−	0.873119i	$-0.337907\pi$
$858$		0			0
$859$	−22.0000	+	38.1051i	−0.750630	+	1.30013i	0.196887	+	0.980426i	$0.436917\pi$
$859$	−22.0000	+	38.1051i	−0.750630	+	1.30013i	−0.947518	+	0.319704i	$0.896417\pi$
$860$	6.00000	+	10.3923i	0.204598	+	0.354375i
$861$		0			0
$862$	−24.0000			−0.817443
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		0			0
$865$	22.5000	−	38.9711i	0.765023	−	1.32506i
$866$	8.00000			0.271851
$867$		0			0
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	−24.0000	−	41.5692i	−0.814144	−	1.41014i
$870$		0			0
$871$	−35.0000	−	60.6218i	−1.18593	−	2.05409i
$872$	2.00000	+	3.46410i	0.0677285	+	0.117309i
$873$		0			0
$874$	−1.50000	−	12.9904i	−0.0507383	−	0.439406i
$875$	−3.00000			−0.101419
$876$		0			0
$877$	14.0000	+	24.2487i	0.472746	+	0.818821i	0.999514	−	0.0311889i	$-0.00992933\pi$
$877$	14.0000	+	24.2487i	0.472746	+	0.818821i	−0.526767	+	0.850010i	$0.676596\pi$
$878$	11.0000	−	19.0526i	0.371232	−	0.642993i
$879$		0			0
$880$	−9.00000	+	15.5885i	−0.303390	+	0.525487i
$881$	−24.0000			−0.808581			−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000			−0.808581			−0.404290	+	0.914631i	$0.632481\pi$
$882$		0			0
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	−0.882361	−	0.470573i	$-0.844047\pi$
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	0.848709	+	0.528861i	$0.177381\pi$
$884$	−15.0000	+	25.9808i	−0.504505	+	0.873828i
$885$		0			0
$886$	18.0000			0.604722
$887$	−27.0000	+	46.7654i	−0.906571	+	1.57023i	−0.0877772	+	0.996140i	$0.527976\pi$
$887$	−27.0000	+	46.7654i	−0.906571	+	1.57023i	−0.818794	+	0.574087i	$0.805357\pi$
$888$		0			0
$889$	6.50000	−	11.2583i	0.218003	−	0.377592i
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$		0			0
$892$	−16.0000			−0.535720
$893$	−24.0000	−	10.3923i	−0.803129	−	0.347765i
$894$		0			0
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	7.50000	+	12.9904i	0.250278	+	0.433495i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$	−72.0000			−2.39867
$902$	18.0000	−	31.1769i	0.599334	−	1.03808i
$903$		0			0
$904$	−21.0000			−0.698450
$905$	15.0000			0.498617
$906$		0			0
$907$	17.0000	+	29.4449i	0.564476	+	0.977701i	0.997098	+	0.0761255i	$0.0242550\pi$
$907$	17.0000	+	29.4449i	0.564476	+	0.977701i	−0.432623	+	0.901575i	$0.642412\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$		0			0
$910$	−7.50000	−	12.9904i	−0.248623	−	0.430627i
$911$	15.0000			0.496972			0.248486	−	0.968635i	$-0.420067\pi$
$911$	15.0000			0.496972			0.248486	+	0.968635i	$0.420067\pi$
$912$		0			0
$913$	−90.0000			−2.97857
$914$	−8.50000	−	14.7224i	−0.281155	−	0.486975i
$915$		0			0
$916$	−2.50000	+	4.33013i	−0.0826023	+	0.143071i
$917$	−7.50000	−	12.9904i	−0.247672	−	0.428980i
$918$		0			0
$919$	29.0000			0.956622			0.478311	−	0.878191i	$-0.341249\pi$
$919$	29.0000			0.956622			0.478311	+	0.878191i	$0.341249\pi$
$920$	9.00000			0.296721
$921$		0			0
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$	15.0000			0.493731
$924$		0			0
$925$	−16.0000	+	27.7128i	−0.526077	+	0.911192i
$926$	−2.50000	−	4.33013i	−0.0821551	−	0.142297i
$927$		0			0
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	0.599228	−	0.800578i	$-0.295474\pi$
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	−0.992935	+	0.118657i	$0.962141\pi$
$930$		0			0
$931$	−0.500000	−	4.33013i	−0.0163868	−	0.141914i
$932$	21.0000			0.687878
$933$		0			0
$934$		0			0
$935$	−54.0000	+	93.5307i	−1.76599	+	3.05878i
$936$		0			0
$937$	14.0000	−	24.2487i	0.457360	−	0.792171i	−0.541460	−	0.840726i	$-0.682128\pi$
$937$	14.0000	−	24.2487i	0.457360	−	0.792171i	0.998820	+	0.0485554i	$0.0154617\pi$
$938$	14.0000			0.457116
$939$		0			0
$940$	9.00000	−	15.5885i	0.293548	−	0.508439i
$941$	−1.50000	+	2.59808i	−0.0488986	+	0.0846949i	−0.889439	−	0.457054i	$-0.848904\pi$
$941$	−1.50000	+	2.59808i	−0.0488986	+	0.0846949i	0.840540	+	0.541749i	$0.182238\pi$
$942$		0			0
$943$	−18.0000			−0.586161
$944$	−4.50000	+	7.79423i	−0.146463	+	0.253681i
$945$		0			0
$946$	12.0000	−	20.7846i	0.390154	−	0.675766i
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	0.910644	−	0.413192i	$-0.135586\pi$
$947$	3.00000	+	5.19615i	0.0974869	+	0.168852i	−0.813157	+	0.582045i	$0.802253\pi$
$948$		0			0
$949$	−20.0000			−0.649227
$950$	−2.00000	−	17.3205i	−0.0648886	−	0.561951i
$951$		0			0
$952$	−3.00000	−	5.19615i	−0.0972306	−	0.168408i
$953$	27.0000	+	46.7654i	0.874616	+	1.51488i	0.857171	+	0.515031i	$0.172220\pi$
$953$	27.0000	+	46.7654i	0.874616	+	1.51488i	0.0174443	+	0.999848i	$0.494447\pi$
$954$		0			0
$955$	−22.5000	−	38.9711i	−0.728083	−	1.26108i
$956$	−4.50000	+	7.79423i	−0.145540	+	0.252083i
$957$		0			0
$958$	18.0000			0.581554
$959$	−1.50000	+	2.59808i	−0.0484375	+	0.0838963i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	40.0000			1.28965
$963$		0			0
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$	−7.50000	+	12.9904i	−0.241434	+	0.418175i
$966$		0			0
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	25.0000			0.803530
$969$		0			0
$970$	24.0000			0.770594
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	0.999408	+	0.0344175i	$0.0109576\pi$
$971$	16.5000	+	28.5788i	0.529510	+	0.917139i	−0.469897	+	0.882721i	$0.655709\pi$
$972$		0			0
$973$	2.00000	−	3.46410i	0.0641171	−	0.111054i
$974$	−4.00000	−	6.92820i	−0.128168	−	0.221994i
$975$		0			0
$976$	−13.0000			−0.416120
$977$	3.00000			0.0959785			0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000			0.0959785			0.0479893	+	0.998848i	$0.484719\pi$
$978$		0			0
$979$	−18.0000	+	31.1769i	−0.575282	+	0.996419i
$980$	3.00000			0.0958315
$981$		0			0
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$		0			0
$985$		0			0
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$	−17.5000	+	12.9904i	−0.556749	+	0.413279i
$989$	−12.0000			−0.381578
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$	−1.50000	+	2.59808i	−0.0475771	+	0.0824060i
$995$	−66.0000			−2.09234
$996$		0			0
$997$	30.5000	−	52.8275i	0.965945	−	1.67307i	0.258889	−	0.965907i	$-0.416643\pi$
$997$	30.5000	−	52.8275i	0.965945	−	1.67307i	0.707055	−	0.707158i	$-0.250023\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.o.b.1261.1		2
3.2	odd	2		798.2.k.h.463.1	✓	2
19.11	even	3	inner	2394.2.o.b.505.1		2
57.11	odd	6		798.2.k.h.505.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.k.h.463.1	✓	2	3.2	odd	2
798.2.k.h.505.1	yes	2	57.11	odd	6
2394.2.o.b.505.1		2	19.11	even	3	inner
2394.2.o.b.1261.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +1.00000 q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-0.500000 - 4.33013i) q^{19} +3.00000 q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +5.00000 q^{26} +(-0.500000 + 0.866025i) q^{28} +(3.00000 - 5.19615i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +(-1.50000 - 2.59808i) q^{35} +8.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(-3.00000 + 5.19615i) q^{44} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +1.00000 q^{49} +4.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-9.00000 - 15.5885i) q^{55} +1.00000 q^{56} -6.00000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(6.50000 - 11.2583i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +15.0000 q^{65} +(-7.00000 + 12.1244i) q^{67} +6.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-1.50000 - 2.59808i) q^{71} +(2.00000 + 3.46410i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(4.00000 + 1.73205i) q^{76} +6.00000 q^{77} +(-4.00000 - 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.00000 - 5.19615i) q^{82} -15.0000 q^{83} +(-9.00000 + 15.5885i) q^{85} +(2.00000 - 3.46410i) q^{86} +6.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} -6.00000 q^{94} +(-10.5000 + 7.79423i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 3 q^{5} + 2 q^{7} + 2 q^{8} - 3 q^{10} + 12 q^{11} - 5 q^{13} - q^{14} - q^{16} - 6 q^{17} - q^{19} + 6 q^{20} - 6 q^{22} - 3 q^{23} - 4 q^{25} + 10 q^{26} - q^{28} + 6 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 3 q^{35} + 16 q^{37} - 7 q^{38} - 3 q^{40} + 6 q^{41} + 4 q^{43} - 6 q^{44} + 6 q^{46} + 6 q^{47} + 2 q^{49} + 8 q^{50} - 5 q^{52} + 12 q^{53} - 18 q^{55} + 2 q^{56} - 12 q^{58} - 9 q^{59} + 13 q^{61} + 4 q^{62} + 2 q^{64} + 30 q^{65} - 14 q^{67} + 12 q^{68} - 3 q^{70} - 3 q^{71} + 4 q^{73} - 8 q^{74} + 8 q^{76} + 12 q^{77} - 8 q^{79} - 3 q^{80} + 6 q^{82} - 30 q^{83} - 18 q^{85} + 4 q^{86} + 12 q^{88} - 6 q^{89} - 5 q^{91} - 3 q^{92} - 12 q^{94} - 21 q^{95} - 8 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^5 + 2 * q^7 + 2 * q^8 - 3 * q^10 + 12 * q^11 - 5 * q^13 - q^14 - q^16 - 6 * q^17 - q^19 + 6 * q^20 - 6 * q^22 - 3 * q^23 - 4 * q^25 + 10 * q^26 - q^28 + 6 * q^29 - 8 * q^31 - q^32 - 6 * q^34 - 3 * q^35 + 16 * q^37 - 7 * q^38 - 3 * q^40 + 6 * q^41 + 4 * q^43 - 6 * q^44 + 6 * q^46 + 6 * q^47 + 2 * q^49 + 8 * q^50 - 5 * q^52 + 12 * q^53 - 18 * q^55 + 2 * q^56 - 12 * q^58 - 9 * q^59 + 13 * q^61 + 4 * q^62 + 2 * q^64 + 30 * q^65 - 14 * q^67 + 12 * q^68 - 3 * q^70 - 3 * q^71 + 4 * q^73 - 8 * q^74 + 8 * q^76 + 12 * q^77 - 8 * q^79 - 3 * q^80 + 6 * q^82 - 30 * q^83 - 18 * q^85 + 4 * q^86 + 12 * q^88 - 6 * q^89 - 5 * q^91 - 3 * q^92 - 12 * q^94 - 21 * q^95 - 8 * q^97 - q^98

Introduction

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