LMFDB - Embedded newform 819.2.n.c.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (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:	$6.53974792554$
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 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	819.100
Dual form			819.2.n.c.172.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +3.00000 q^{10} +3.00000 q^{11} +(-1.00000 - 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{25} +(2.50000 - 2.59808i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(2.50000 - 4.33013i) q^{32} -2.00000 q^{34} +(-1.50000 + 7.79423i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(4.50000 - 7.79423i) q^{40} +(1.50000 - 2.59808i) q^{41} +(3.50000 + 6.06218i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{47} +(5.50000 - 4.33013i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-3.50000 - 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(4.50000 - 7.79423i) q^{55} +(-7.50000 + 2.59808i) q^{56} +7.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} -13.0000 q^{61} +(1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-10.5000 - 2.59808i) q^{65} -3.00000 q^{67} +(1.00000 + 1.73205i) q^{68} +(-7.50000 + 2.59808i) q^{70} +(6.50000 + 11.2583i) q^{71} +(6.50000 + 11.2583i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{76} +(-7.50000 + 2.59808i) q^{77} +(1.50000 - 2.59808i) q^{79} +3.00000 q^{80} +3.00000 q^{82} +(3.00000 + 5.19615i) q^{85} +(-3.50000 + 6.06218i) q^{86} +9.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(5.50000 + 7.79423i) q^{91} +1.00000 q^{94} +(-1.50000 + 2.59808i) q^{95} +(2.50000 + 4.33013i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 3 q^{5} - 5 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 + 3 * q^5 - 5 * q^7 + 6 * q^8	$ 2 q + q^{2} + q^{4} + 3 q^{5} - 5 q^{7} + 6 q^{8} + 6 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{14} + q^{16} - 2 q^{17} - 2 q^{19} - 3 q^{20} + 3 q^{22} - 4 q^{25} + 5 q^{26} - q^{28} + 7 q^{29} - 3 q^{31} + 5 q^{32} - 4 q^{34} - 3 q^{35} - 2 q^{37} - q^{38} + 9 q^{40} + 3 q^{41} + 7 q^{43} + 3 q^{44} + q^{47} + 11 q^{49} + 4 q^{50} - 7 q^{52} + 3 q^{53} + 9 q^{55} - 15 q^{56} + 14 q^{58} - 4 q^{59} - 26 q^{61} + 3 q^{62} + 14 q^{64} - 21 q^{65} - 6 q^{67} + 2 q^{68} - 15 q^{70} + 13 q^{71} + 13 q^{73} + 2 q^{74} - q^{76} - 15 q^{77} + 3 q^{79} + 6 q^{80} + 6 q^{82} + 6 q^{85} - 7 q^{86} + 18 q^{88} + 6 q^{89} + 11 q^{91} + 2 q^{94} - 3 q^{95} + 5 q^{97} + 13 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 3 * q^5 - 5 * q^7 + 6 * q^8 + 6 * q^10 + 6 * q^11 - 2 * q^13 - 4 * q^14 + q^16 - 2 * q^17 - 2 * q^19 - 3 * q^20 + 3 * q^22 - 4 * q^25 + 5 * q^26 - q^28 + 7 * q^29 - 3 * q^31 + 5 * q^32 - 4 * q^34 - 3 * q^35 - 2 * q^37 - q^38 + 9 * q^40 + 3 * q^41 + 7 * q^43 + 3 * q^44 + q^47 + 11 * q^49 + 4 * q^50 - 7 * q^52 + 3 * q^53 + 9 * q^55 - 15 * q^56 + 14 * q^58 - 4 * q^59 - 26 * q^61 + 3 * q^62 + 14 * q^64 - 21 * q^65 - 6 * q^67 + 2 * q^68 - 15 * q^70 + 13 * q^71 + 13 * q^73 + 2 * q^74 - q^76 - 15 * q^77 + 3 * q^79 + 6 * q^80 + 6 * q^82 + 6 * q^85 - 7 * q^86 + 18 * q^88 + 6 * q^89 + 11 * q^91 + 2 * q^94 - 3 * q^95 + 5 * q^97 + 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	3.00000			1.06066
$9$		0			0
$10$	3.00000			0.948683
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−1.00000			−0.229416			−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000			−0.229416			−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	2.50000	−	2.59808i	0.490290	−	0.509525i
$27$		0			0
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$		0			0
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−1.50000	+	7.79423i	−0.253546	+	1.31747i
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$		0			0
$40$	4.50000	−	7.79423i	0.711512	−	1.23238i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	0.999223	+	0.0394140i	$0.0125491\pi$
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	−0.465478	+	0.885059i	$0.654118\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$		0			0
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	−0.827253	−	0.561830i	$-0.810098\pi$
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	0.900185	+	0.435507i	$0.143431\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	4.50000	−	7.79423i	0.606780	−	1.05097i
$56$	−7.50000	+	2.59808i	−1.00223	+	0.347183i
$57$		0			0
$58$	7.00000			0.919145
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	1.50000	−	2.59808i	0.190500	−	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$	−10.5000	−	2.59808i	−1.30236	−	0.322252i
$66$		0			0
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$		0			0
$70$	−7.50000	+	2.59808i	−0.896421	+	0.310530i
$71$	6.50000	+	11.2583i	0.771408	+	1.33612i	0.936791	+	0.349889i	$0.113781\pi$
$71$	6.50000	+	11.2583i	0.771408	+	1.33612i	−0.165383	+	0.986229i	$0.552886\pi$
$72$		0			0
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	0.942455	+	0.334332i	$0.108511\pi$
$73$	6.50000	+	11.2583i	0.760767	+	1.31769i	−0.181688	+	0.983356i	$0.558156\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$	−7.50000	+	2.59808i	−0.854704	+	0.296078i
$78$		0			0
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	1.50000	−	2.59808i	0.168763	−	0.292306i	0.937985	+	0.346675i	$0.112689\pi$
$80$	3.00000			0.335410
$81$		0			0
$82$	3.00000			0.331295
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$	−3.50000	+	6.06218i	−0.377415	+	0.653701i
$87$		0			0
$88$	9.00000			0.959403
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	5.50000	+	7.79423i	0.576557	+	0.817057i
$92$		0			0
$93$		0			0
$94$	1.00000			0.103142
$95$	−1.50000	+	2.59808i	−0.153897	+	0.266557i
$96$		0			0
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	0.964579	−	0.263795i	$-0.0849741\pi$
$97$	2.50000	+	4.33013i	0.253837	+	0.439658i	−0.710742	+	0.703452i	$0.751641\pi$
$98$	6.50000	+	2.59808i	0.656599	+	0.262445i
$99$		0			0
$100$	−4.00000			−0.400000
$101$	5.00000			0.497519			0.248759	−	0.968565i	$-0.419977\pi$
$101$	5.00000			0.497519			0.248759	+	0.968565i	$0.419977\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	−3.00000	−	10.3923i	−0.294174	−	1.01905i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$		0			0
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	0.648292	−	0.761392i	$-0.275484\pi$
$109$	−3.50000	−	6.06218i	−0.335239	−	0.580651i	−0.983531	+	0.180741i	$0.942150\pi$
$110$	9.00000			0.858116
$111$		0			0
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$		0			0
$116$	−3.50000	−	6.06218i	−0.324967	−	0.562859i
$117$		0			0
$118$	−4.00000			−0.368230
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−6.50000	−	11.2583i	−0.588482	−	1.01928i
$123$		0			0
$124$	−3.00000			−0.269408
$125$	3.00000			0.268328
$126$		0			0
$127$	−5.50000	+	9.52628i	−0.488046	+	0.845321i	−0.999905	−	0.0137486i	$-0.995624\pi$
$127$	−5.50000	+	9.52628i	−0.488046	+	0.845321i	0.511859	+	0.859069i	$0.328957\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		0			0
$130$	−3.00000	−	10.3923i	−0.263117	−	0.911465i
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	−0.735901	−	0.677089i	$-0.763241\pi$
$131$	2.50000	−	4.33013i	0.218426	−	0.378325i	0.954327	+	0.298764i	$0.0965744\pi$
$132$		0			0
$133$	2.50000	−	0.866025i	0.216777	−	0.0750939i
$134$	−1.50000	−	2.59808i	−0.129580	−	0.224440i
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	−0.569442	−	0.822031i	$-0.692841\pi$
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	0.996621	+	0.0821359i	$0.0261741\pi$
$138$		0			0
$139$	7.50000	+	12.9904i	0.636142	+	1.10183i	0.986272	+	0.165129i	$0.0528040\pi$
$139$	7.50000	+	12.9904i	0.636142	+	1.10183i	−0.350130	+	0.936701i	$0.613863\pi$
$140$	6.00000	+	5.19615i	0.507093	+	0.439155i
$141$		0			0
$142$	−6.50000	+	11.2583i	−0.545468	+	0.944778i
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$		0			0
$145$	−10.5000	−	18.1865i	−0.871978	−	1.51031i
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$		0			0
$151$	10.5000	+	18.1865i	0.854478	+	1.48000i	0.877129	+	0.480256i	$0.159456\pi$
$151$	10.5000	+	18.1865i	0.854478	+	1.48000i	−0.0226507	+	0.999743i	$0.507211\pi$
$152$	−3.00000			−0.243332
$153$		0			0
$154$	−6.00000	−	5.19615i	−0.483494	−	0.418718i
$155$	−9.00000			−0.722897
$156$		0			0
$157$	−9.50000	−	16.4545i	−0.758183	−	1.31321i	−0.943777	−	0.330584i	$-0.892754\pi$
$157$	−9.50000	−	16.4545i	−0.758183	−	1.31321i	0.185594	−	0.982627i	$-0.440579\pi$
$158$	3.00000			0.238667
$159$		0			0
$160$	−7.50000	−	12.9904i	−0.592927	−	1.02698i
$161$		0			0
$162$		0			0
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$		0			0
$167$	−6.50000	+	11.2583i	−0.502985	+	0.871196i	0.497009	+	0.867745i	$0.334432\pi$
$167$	−6.50000	+	11.2583i	−0.502985	+	0.871196i	−0.999994	+	0.00345033i	$0.998902\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$		0			0
$172$	7.00000			0.533745
$173$	−19.0000			−1.44454			−0.722272	−	0.691609i	$-0.756902\pi$
$173$	−19.0000			−1.44454			−0.722272	+	0.691609i	$0.756902\pi$
$174$		0			0
$175$	8.00000	+	6.92820i	0.604743	+	0.523723i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−17.0000			−1.27064			−0.635320	−	0.772249i	$-0.719132\pi$
$179$	−17.0000			−1.27064			−0.635320	+	0.772249i	$0.719132\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−4.00000	+	8.66025i	−0.296500	+	0.641941i
$183$		0			0
$184$		0			0
$185$	−6.00000			−0.441129
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$	−0.500000	−	0.866025i	−0.0364662	−	0.0631614i
$189$		0			0
$190$	−3.00000			−0.217643
$191$	17.0000			1.23008			0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000			1.23008			0.615038	+	0.788497i	$0.289140\pi$
$192$		0			0
$193$	7.00000			0.503871			0.251936	−	0.967744i	$-0.418933\pi$
$193$	7.00000			0.503871			0.251936	+	0.967744i	$0.418933\pi$
$194$	−2.50000	+	4.33013i	−0.179490	+	0.310885i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	−0.500000	+	0.866025i	−0.0356235	+	0.0617018i	−0.883287	−	0.468832i	$-0.844675\pi$
$197$	−0.500000	+	0.866025i	−0.0356235	+	0.0617018i	0.847664	+	0.530534i	$0.178008\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	−6.00000	−	10.3923i	−0.424264	−	0.734847i
$201$		0			0
$202$	2.50000	+	4.33013i	0.175899	+	0.304667i
$203$	−3.50000	+	18.1865i	−0.245652	+	1.27644i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−5.00000			−0.348367
$207$		0			0
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−3.50000	+	6.06218i	−0.240950	+	0.417338i	−0.960985	−	0.276600i	$-0.910792\pi$
$211$	−3.50000	+	6.06218i	−0.240950	+	0.417338i	0.720035	+	0.693938i	$0.244126\pi$
$212$	3.00000			0.206041
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	21.0000			1.43219
$216$		0			0
$217$	6.00000	+	5.19615i	0.407307	+	0.352738i
$218$	3.50000	−	6.06218i	0.237050	−	0.410582i
$219$		0			0
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	7.00000	+	1.73205i	0.470871	+	0.116510i
$222$		0			0
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	−0.675098	−	0.737728i	$-0.735899\pi$
$223$	4.50000	−	7.79423i	0.301342	−	0.521940i	0.976440	+	0.215788i	$0.0692320\pi$
$224$	−2.50000	+	12.9904i	−0.167038	+	0.867956i
$225$		0			0
$226$	−7.50000	+	12.9904i	−0.498893	+	0.864107i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$		0			0
$232$	10.5000	−	18.1865i	0.689359	−	1.19400i
$233$	−10.5000	+	18.1865i	−0.687878	+	1.19144i	0.284645	+	0.958633i	$0.408124\pi$
$233$	−10.5000	+	18.1865i	−0.687878	+	1.19144i	−0.972523	+	0.232806i	$0.925209\pi$
$234$		0			0
$235$	−1.50000	−	2.59808i	−0.0978492	−	0.169480i
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$	5.00000	−	1.73205i	0.324102	−	0.112272i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−6.50000	+	11.2583i	−0.416120	+	0.720741i
$245$	−3.00000	−	20.7846i	−0.191663	−	1.32788i
$246$		0			0
$247$	1.00000	+	3.46410i	0.0636285	+	0.220416i
$248$	−4.50000	−	7.79423i	−0.285750	−	0.494934i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	−0.958613	−	0.284711i	$-0.908102\pi$
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	0.232740	−	0.972539i	$-0.425231\pi$
$252$		0			0
$253$		0			0
$254$	−11.0000			−0.690201
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	0.833150	−	0.553047i	$-0.186535\pi$
$257$	−1.00000	−	1.73205i	−0.0623783	−	0.108042i	−0.895528	+	0.445005i	$0.853202\pi$
$258$		0			0
$259$	4.00000	+	3.46410i	0.248548	+	0.215249i
$260$	−7.50000	+	7.79423i	−0.465130	+	0.483378i
$261$		0			0
$262$	5.00000			0.308901
$263$	27.0000			1.66489			0.832446	−	0.554107i	$-0.186940\pi$
$263$	27.0000			1.66489			0.832446	+	0.554107i	$0.186940\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	2.00000	+	1.73205i	0.122628	+	0.106199i
$267$		0			0
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	−6.00000	−	10.3923i	−0.361814	−	0.626680i
$276$		0			0
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	−7.50000	+	12.9904i	−0.449820	+	0.779111i
$279$		0			0
$280$	−4.50000	+	23.3827i	−0.268926	+	1.39738i
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	1.00000			0.0594438			0.0297219	−	0.999558i	$-0.490538\pi$
$283$	1.00000			0.0594438			0.0297219	+	0.999558i	$0.490538\pi$
$284$	13.0000			0.771408
$285$		0			0
$286$	7.50000	−	7.79423i	0.443484	−	0.460882i
$287$	−1.50000	+	7.79423i	−0.0885422	+	0.460079i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	10.5000	−	18.1865i	0.616581	−	1.06795i
$291$		0			0
$292$	13.0000			0.760767
$293$	5.50000	+	9.52628i	0.321313	+	0.556531i	0.980759	−	0.195221i	$-0.0625424\pi$
$293$	5.50000	+	9.52628i	0.321313	+	0.556531i	−0.659446	+	0.751752i	$0.729209\pi$
$294$		0			0
$295$	6.00000	+	10.3923i	0.349334	+	0.605063i
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$		0			0
$298$	−7.50000	−	12.9904i	−0.434463	−	0.752513i
$299$		0			0
$300$		0			0
$301$	−14.0000	−	12.1244i	−0.806947	−	0.698836i
$302$	−10.5000	+	18.1865i	−0.604207	+	1.04652i
$303$		0			0
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−19.5000	+	33.7750i	−1.11657	+	1.93395i
$306$		0			0
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	−1.50000	+	7.79423i	−0.0854704	+	0.444117i
$309$		0			0
$310$	−4.50000	−	7.79423i	−0.255583	−	0.442682i
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	0.709771	−	0.704433i	$-0.248799\pi$
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	−0.964942	+	0.262463i	$0.915465\pi$
$312$		0			0
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$	9.50000	−	16.4545i	0.536116	−	0.928580i
$315$		0			0
$316$	−1.50000	−	2.59808i	−0.0843816	−	0.146153i
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	−0.964281	−	0.264883i	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$		0			0
$319$	10.5000	−	18.1865i	0.587887	−	1.01825i
$320$	10.5000	−	18.1865i	0.586968	−	1.01666i
$321$		0			0
$322$		0			0
$323$	1.00000	−	1.73205i	0.0556415	−	0.0963739i
$324$		0			0
$325$	−10.0000	+	10.3923i	−0.554700	+	0.576461i
$326$	−0.500000	−	0.866025i	−0.0276924	−	0.0479647i
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	−0.500000	+	2.59808i	−0.0275659	+	0.143237i
$330$		0			0
$331$	−29.0000			−1.59398			−0.796992	−	0.603990i	$-0.793577\pi$
$331$	−29.0000			−1.59398			−0.796992	+	0.603990i	$0.793577\pi$
$332$		0			0
$333$		0			0
$334$	−13.0000			−0.711328
$335$	−4.50000	+	7.79423i	−0.245861	+	0.425844i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	−11.5000	−	6.06218i	−0.625518	−	0.329739i
$339$		0			0
$340$	6.00000			0.325396
$341$	−4.50000	−	7.79423i	−0.243689	−	0.422081i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	10.5000	+	18.1865i	0.566122	+	0.980552i
$345$		0			0
$346$	−9.50000	−	16.4545i	−0.510723	−	0.884598i
$347$	−4.00000	+	6.92820i	−0.214731	+	0.371925i	−0.953189	−	0.302374i	$-0.902221\pi$
$347$	−4.00000	+	6.92820i	−0.214731	+	0.371925i	0.738458	+	0.674299i	$0.235554\pi$
$348$		0			0
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	0.374701	+	0.927146i	$0.377745\pi$
$349$	−11.5000	+	19.9186i	−0.615581	+	1.06622i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	−2.00000	+	10.3923i	−0.106904	+	0.555492i
$351$		0			0
$352$	7.50000	−	12.9904i	0.399751	−	0.692390i
$353$	25.0000			1.33062			0.665308	−	0.746569i	$-0.268300\pi$
$353$	25.0000			1.33062			0.665308	+	0.746569i	$0.268300\pi$
$354$		0			0
$355$	39.0000			2.06991
$356$	6.00000			0.317999
$357$		0			0
$358$	−8.50000	−	14.7224i	−0.449239	−	0.778105i
$359$	8.50000	−	14.7224i	0.448613	−	0.777020i	−0.549683	−	0.835373i	$-0.685252\pi$
$359$	8.50000	−	14.7224i	0.448613	−	0.777020i	0.998296	+	0.0583530i	$0.0185849\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	−11.0000	−	19.0526i	−0.578147	−	1.00138i
$363$		0			0
$364$	9.50000	−	0.866025i	0.497935	−	0.0453921i
$365$	39.0000			2.04135
$366$		0			0
$367$	−31.0000			−1.61819			−0.809093	−	0.587680i	$-0.800041\pi$
$367$	−31.0000			−1.61819			−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$		0			0
$370$	−3.00000	−	5.19615i	−0.155963	−	0.270135i
$371$	−6.00000	−	5.19615i	−0.311504	−	0.269771i
$372$		0			0
$373$	−9.00000			−0.466002			−0.233001	−	0.972476i	$-0.574855\pi$
$373$	−9.00000			−0.466002			−0.233001	+	0.972476i	$0.574855\pi$
$374$	−6.00000			−0.310253
$375$		0			0
$376$	1.50000	−	2.59808i	0.0773566	−	0.133986i
$377$	−24.5000	−	6.06218i	−1.26181	−	0.312218i
$378$		0			0
$379$	16.5000	−	28.5788i	0.847548	−	1.46800i	−0.0358418	−	0.999357i	$-0.511411\pi$
$379$	16.5000	−	28.5788i	0.847548	−	1.46800i	0.883390	−	0.468639i	$-0.155255\pi$
$380$	1.50000	+	2.59808i	0.0769484	+	0.133278i
$381$		0			0
$382$	8.50000	+	14.7224i	0.434898	+	0.753265i
$383$	21.0000			1.07305			0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000			1.07305			0.536525	+	0.843884i	$0.319737\pi$
$384$		0			0
$385$	−4.50000	+	23.3827i	−0.229341	+	1.19169i
$386$	3.50000	+	6.06218i	0.178145	+	0.308557i
$387$		0			0
$388$	5.00000			0.253837
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	−0.892735	−	0.450582i	$-0.851216\pi$
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	0.0561516	−	0.998422i	$-0.482117\pi$
$390$		0			0
$391$		0			0
$392$	16.5000	−	12.9904i	0.833376	−	0.656113i
$393$		0			0
$394$	−1.00000			−0.0503793
$395$	−4.50000	−	7.79423i	−0.226420	−	0.392170i
$396$		0			0
$397$	−1.00000			−0.0501886			−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000			−0.0501886			−0.0250943	+	0.999685i	$0.507989\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	0.839976	−	0.542623i	$-0.182569\pi$
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	−0.889914	+	0.456129i	$0.849236\pi$
$402$		0			0
$403$	−7.50000	+	7.79423i	−0.373602	+	0.388258i
$404$	2.50000	−	4.33013i	0.124380	−	0.215432i
$405$		0			0
$406$	−17.5000	+	6.06218i	−0.868510	+	0.300861i
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		0			0
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$		0			0
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$	2.00000	−	10.3923i	0.0984136	−	0.511372i
$414$		0			0
$415$		0			0
$416$	−17.5000	−	4.33013i	−0.858008	−	0.212302i
$417$		0			0
$418$	−1.50000	−	2.59808i	−0.0733674	−	0.127076i
$419$	−12.5000	+	21.6506i	−0.610665	+	1.05770i	0.380464	+	0.924796i	$0.375764\pi$
$419$	−12.5000	+	21.6506i	−0.610665	+	1.05770i	−0.991129	+	0.132907i	$0.957569\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	−7.00000			−0.340755
$423$		0			0
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	8.00000			0.388057
$426$		0			0
$427$	32.5000	−	11.2583i	1.57279	−	0.544829i
$428$	8.00000			0.386695
$429$		0			0
$430$	10.5000	+	18.1865i	0.506355	+	0.877033i
$431$	−9.00000			−0.433515			−0.216757	−	0.976226i	$-0.569548\pi$
$431$	−9.00000			−0.433515			−0.216757	+	0.976226i	$0.569548\pi$
$432$		0			0
$433$	−13.5000	−	23.3827i	−0.648769	−	1.12370i	−0.983417	−	0.181357i	$-0.941951\pi$
$433$	−13.5000	−	23.3827i	−0.648769	−	1.12370i	0.334649	−	0.942343i	$-0.391382\pi$
$434$	−1.50000	+	7.79423i	−0.0720023	+	0.374135i
$435$		0			0
$436$	−7.00000			−0.335239
$437$		0			0
$438$		0			0
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	13.5000	−	23.3827i	0.643587	−	1.11473i
$441$		0			0
$442$	2.00000	+	6.92820i	0.0951303	+	0.329541i
$443$	−5.50000	+	9.52628i	−0.261313	+	0.452607i	−0.966591	−	0.256323i	$-0.917489\pi$
$443$	−5.50000	+	9.52628i	−0.261313	+	0.452607i	0.705278	+	0.708931i	$0.250822\pi$
$444$		0			0
$445$	18.0000			0.853282
$446$	9.00000			0.426162
$447$		0			0
$448$	−17.5000	+	6.06218i	−0.826797	+	0.286411i
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	0.986937	−	0.161106i	$-0.0515060\pi$
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	−0.632990	+	0.774160i	$0.718173\pi$
$450$		0			0
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	15.0000			0.705541
$453$		0			0
$454$	−4.00000			−0.187729
$455$	28.5000	−	2.59808i	1.33610	−	0.121800i
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	13.0000			0.607450
$459$		0			0
$460$		0			0
$461$	17.5000	+	30.3109i	0.815056	+	1.41172i	0.909288	+	0.416169i	$0.136627\pi$
$461$	17.5000	+	30.3109i	0.815056	+	1.41172i	−0.0942312	+	0.995550i	$0.530039\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	7.00000			0.324967
$465$		0			0
$466$	−21.0000			−0.972806
$467$	−3.50000	+	6.06218i	−0.161961	+	0.280524i	−0.935572	−	0.353137i	$-0.885115\pi$
$467$	−3.50000	+	6.06218i	−0.161961	+	0.280524i	0.773611	+	0.633661i	$0.218448\pi$
$468$		0			0
$469$	7.50000	−	2.59808i	0.346318	−	0.119968i
$470$	1.50000	−	2.59808i	0.0691898	−	0.119840i
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	10.5000	+	18.1865i	0.482791	+	0.836218i
$474$		0			0
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$	−4.00000	−	3.46410i	−0.183340	−	0.158777i
$477$		0			0
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	35.0000			1.59919			0.799595	−	0.600539i	$-0.205047\pi$
$479$	35.0000			1.59919			0.799595	+	0.600539i	$0.205047\pi$
$480$		0			0
$481$	−5.00000	+	5.19615i	−0.227980	+	0.236924i
$482$	26.0000			1.18427
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$	15.0000			0.681115
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$	−39.0000			−1.76545
$489$		0			0
$490$	16.5000	−	12.9904i	0.745394	−	0.586846i
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		0			0
$493$	7.00000	+	12.1244i	0.315264	+	0.546054i
$494$	−2.50000	+	2.59808i	−0.112480	+	0.116893i
$495$		0			0
$496$	1.50000	−	2.59808i	0.0673520	−	0.116657i
$497$	−26.0000	−	22.5167i	−1.16626	−	1.01001i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	11.5000	−	19.9186i	0.513270	−	0.889010i
$503$	−15.5000	−	26.8468i	−0.691111	−	1.19704i	−0.971474	−	0.237145i	$-0.923788\pi$
$503$	−15.5000	−	26.8468i	−0.691111	−	1.19704i	0.280363	−	0.959894i	$-0.409545\pi$
$504$		0			0
$505$	7.50000	−	12.9904i	0.333746	−	0.578064i
$506$		0			0
$507$		0			0
$508$	5.50000	+	9.52628i	0.244023	+	0.422660i
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	−0.946111	−	0.323843i	$-0.895025\pi$
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	0.192599	−	0.981278i	$-0.438308\pi$
$510$		0			0
$511$	−26.0000	−	22.5167i	−1.15017	−	0.996078i
$512$	11.0000			0.486136
$513$		0			0
$514$	1.00000	−	1.73205i	0.0441081	−	0.0763975i
$515$	7.50000	+	12.9904i	0.330489	+	0.572425i
$516$		0			0
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$	−1.00000	+	5.19615i	−0.0439375	+	0.228306i
$519$		0			0
$520$	−31.5000	−	7.79423i	−1.38137	−	0.341800i
$521$	−8.50000	−	14.7224i	−0.372392	−	0.645001i	0.617541	−	0.786539i	$-0.288129\pi$
$521$	−8.50000	−	14.7224i	−0.372392	−	0.645001i	−0.989933	+	0.141537i	$0.954796\pi$
$522$		0			0
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	−2.50000	−	4.33013i	−0.109213	−	0.189162i
$525$		0			0
$526$	13.5000	+	23.3827i	0.588628	+	1.01953i
$527$	6.00000			0.261364
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	0.500000	−	2.59808i	0.0216777	−	0.112641i
$533$	−10.5000	−	2.59808i	−0.454805	−	0.112535i
$534$		0			0
$535$	24.0000			1.03761
$536$	−9.00000			−0.388741
$537$		0			0
$538$	18.0000			0.776035
$539$	16.5000	−	12.9904i	0.710705	−	0.559535i
$540$		0			0
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	−0.127222	−	0.991874i	$-0.540606\pi$
$541$	18.5000	−	32.0429i	0.795377	−	1.37763i	0.922599	−	0.385759i	$-0.126061\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$		0			0
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$	−21.0000			−0.899541
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$		0			0
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	−3.50000	+	6.06218i	−0.149105	+	0.258257i
$552$		0			0
$553$	−1.50000	+	7.79423i	−0.0637865	+	0.331444i
$554$	−22.0000			−0.934690
$555$		0			0
$556$	15.0000			0.636142
$557$	−3.00000			−0.127114			−0.0635570	−	0.997978i	$-0.520244\pi$
$557$	−3.00000			−0.127114			−0.0635570	+	0.997978i	$0.520244\pi$
$558$		0			0
$559$	17.5000	−	18.1865i	0.740171	−	0.769208i
$560$	−7.50000	+	2.59808i	−0.316933	+	0.109789i
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	−0.820798	−	0.571218i	$-0.806471\pi$
$563$	2.00000	−	3.46410i	0.0842900	−	0.145994i	0.905088	+	0.425223i	$0.139804\pi$
$564$		0			0
$565$	45.0000			1.89316
$566$	0.500000	+	0.866025i	0.0210166	+	0.0364018i
$567$		0			0
$568$	19.5000	+	33.7750i	0.818202	+	1.41717i
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	−21.5000	−	37.2391i	−0.899747	−	1.55841i	−0.827817	−	0.560998i	$-0.810418\pi$
$571$	−21.5000	−	37.2391i	−0.899747	−	1.55841i	−0.0719297	−	0.997410i	$-0.522916\pi$
$572$	−10.5000	−	2.59808i	−0.439027	−	0.108631i
$573$		0			0
$574$	−7.50000	+	2.59808i	−0.313044	+	0.108442i
$575$		0			0
$576$		0			0
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	0.876245	−	0.481865i	$-0.160040\pi$
$577$	0.500000	+	0.866025i	0.0208153	+	0.0360531i	−0.855430	+	0.517918i	$0.826707\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$		0			0
$580$	−21.0000			−0.871978
$581$		0			0
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	19.5000	+	33.7750i	0.806916	+	1.39762i
$585$		0			0
$586$	−5.50000	+	9.52628i	−0.227203	+	0.393527i
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	0.293640	+	0.955916i	$0.405133\pi$
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	−0.974668	+	0.223659i	$0.928200\pi$
$588$		0			0
$589$	1.50000	+	2.59808i	0.0618064	+	0.107052i
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$		0			0
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	13.5000	−	23.3827i	0.554379	−	0.960212i	−0.443573	−	0.896238i	$-0.646289\pi$
$593$	13.5000	−	23.3827i	0.554379	−	0.960212i	0.997952	−	0.0639736i	$-0.0203773\pi$
$594$		0			0
$595$	−12.0000	−	10.3923i	−0.491952	−	0.426043i
$596$	−7.50000	+	12.9904i	−0.307212	+	0.532107i
$597$		0			0
$598$		0			0
$599$	−12.5000	−	21.6506i	−0.510736	−	0.884621i	−0.999923	−	0.0124417i	$-0.996040\pi$
$599$	−12.5000	−	21.6506i	−0.510736	−	0.884621i	0.489186	−	0.872179i	$-0.337294\pi$
$600$		0			0
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	0.249565	+	0.968358i	$0.419712\pi$
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	−0.963405	+	0.268049i	$0.913621\pi$
$602$	3.50000	−	18.1865i	0.142649	−	0.741228i
$603$		0			0
$604$	21.0000			0.854478
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$		0			0
$607$	11.0000			0.446476			0.223238	−	0.974764i	$-0.428337\pi$
$607$	11.0000			0.446476			0.223238	+	0.974764i	$0.428337\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	−39.0000			−1.57906
$611$	−3.50000	−	0.866025i	−0.141595	−	0.0350356i
$612$		0			0
$613$	−25.0000			−1.00974			−0.504870	−	0.863195i	$-0.668460\pi$
$613$	−25.0000			−1.00974			−0.504870	+	0.863195i	$0.668460\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$		0			0
$616$	−22.5000	+	7.79423i	−0.906551	+	0.314038i
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	−0.979484	−	0.201522i	$-0.935411\pi$
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	0.315219	−	0.949019i	$-0.397922\pi$
$618$		0			0
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	0.734068	−	0.679076i	$-0.237620\pi$
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	−0.955131	+	0.296183i	$0.904286\pi$
$620$	−4.50000	+	7.79423i	−0.180724	+	0.313024i
$621$		0			0
$622$	4.50000	−	7.79423i	0.180434	−	0.312520i
$623$	−12.0000	−	10.3923i	−0.480770	−	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−19.0000			−0.759393
$627$		0			0
$628$	−19.0000			−0.758183
$629$	4.00000			0.159490
$630$		0			0
$631$	−12.5000	−	21.6506i	−0.497617	−	0.861898i	0.502379	−	0.864647i	$-0.332458\pi$
$631$	−12.5000	−	21.6506i	−0.497617	−	0.861898i	−0.999996	+	0.00274930i	$0.999125\pi$
$632$	4.50000	−	7.79423i	0.179000	−	0.310038i
$633$		0			0
$634$	−9.00000			−0.357436
$635$	16.5000	+	28.5788i	0.654783	+	1.13412i
$636$		0			0
$637$	−20.5000	−	14.7224i	−0.812240	−	0.583324i
$638$	21.0000			0.831398
$639$		0			0
$640$	−9.00000			−0.355756
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		0			0
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$		0			0
$645$		0			0
$646$	2.00000			0.0786889
$647$	−9.00000			−0.353827			−0.176913	−	0.984226i	$-0.556611\pi$
$647$	−9.00000			−0.353827			−0.176913	+	0.984226i	$0.556611\pi$
$648$		0			0
$649$	−6.00000	+	10.3923i	−0.235521	+	0.407934i
$650$	−14.0000	−	3.46410i	−0.549125	−	0.135873i
$651$		0			0
$652$	−0.500000	+	0.866025i	−0.0195815	+	0.0339162i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	−7.50000	−	12.9904i	−0.293049	−	0.507576i
$656$	3.00000			0.117130
$657$		0			0
$658$	−2.50000	+	0.866025i	−0.0974601	+	0.0337612i
$659$	14.5000	+	25.1147i	0.564840	+	0.978331i	0.997065	+	0.0765653i	$0.0243954\pi$
$659$	14.5000	+	25.1147i	0.564840	+	0.978331i	−0.432225	+	0.901766i	$0.642271\pi$
$660$		0			0
$661$	−9.00000			−0.350059			−0.175030	−	0.984563i	$-0.556002\pi$
$661$	−9.00000			−0.350059			−0.175030	+	0.984563i	$0.556002\pi$
$662$	−14.5000	−	25.1147i	−0.563559	−	0.976112i
$663$		0			0
$664$		0			0
$665$	1.50000	−	7.79423i	0.0581675	−	0.302247i
$666$		0			0
$667$		0			0
$668$	6.50000	+	11.2583i	0.251493	+	0.435598i
$669$		0			0
$670$	−9.00000			−0.347700
$671$	−39.0000			−1.50558
$672$		0			0
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	−0.135615	−	0.990762i	$-0.543301\pi$
$673$	20.5000	−	35.5070i	0.790217	−	1.36870i	0.925832	−	0.377934i	$-0.123365\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$		0			0
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	3.50000	−	6.06218i	0.134516	−	0.232988i	−0.790897	−	0.611950i	$-0.790385\pi$
$677$	3.50000	−	6.06218i	0.134516	−	0.232988i	0.925412	+	0.378962i	$0.123719\pi$
$678$		0			0
$679$	−10.0000	−	8.66025i	−0.383765	−	0.332350i
$680$	9.00000	+	15.5885i	0.345134	+	0.597790i
$681$		0			0
$682$	4.50000	−	7.79423i	0.172314	−	0.298456i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$	−15.0000	−	25.9808i	−0.573121	−	0.992674i
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$		0			0
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	7.50000	−	7.79423i	0.285727	−	0.296936i
$690$		0			0
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$	−9.50000	+	16.4545i	−0.361136	+	0.625506i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	45.0000			1.70695
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	−23.0000			−0.870563
$699$		0			0
$700$	10.0000	−	3.46410i	0.377964	−	0.130931i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	1.00000	+	1.73205i	0.0377157	+	0.0653255i
$704$	21.0000			0.791467
$705$		0			0
$706$	12.5000	+	21.6506i	0.470444	+	0.814832i
$707$	−12.5000	+	4.33013i	−0.470111	+	0.162851i
$708$		0			0
$709$	11.0000			0.413114			0.206557	−	0.978435i	$-0.433774\pi$
$709$	11.0000			0.413114			0.206557	+	0.978435i	$0.433774\pi$
$710$	19.5000	+	33.7750i	0.731822	+	1.26755i
$711$		0			0
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$		0			0
$714$		0			0
$715$	−31.5000	−	7.79423i	−1.17803	−	0.291488i
$716$	−8.50000	+	14.7224i	−0.317660	+	0.550203i
$717$		0			0
$718$	17.0000			0.634434
$719$	9.00000			0.335643			0.167822	−	0.985817i	$-0.446327\pi$
$719$	9.00000			0.335643			0.167822	+	0.985817i	$0.446327\pi$
$720$		0			0
$721$	2.50000	−	12.9904i	0.0931049	−	0.483787i
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$		0			0
$724$	−11.0000	+	19.0526i	−0.408812	+	0.708083i
$725$	−28.0000			−1.03989
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	16.5000	+	23.3827i	0.611531	+	0.866620i
$729$		0			0
$730$	19.5000	+	33.7750i	0.721727	+	1.25007i
$731$	−14.0000			−0.517809
$732$		0			0
$733$	4.50000	−	7.79423i	0.166211	−	0.287886i	−0.770873	−	0.636988i	$-0.780180\pi$
$733$	4.50000	−	7.79423i	0.166211	−	0.287886i	0.937085	+	0.349102i	$0.113513\pi$
$734$	−15.5000	−	26.8468i	−0.572115	−	0.990933i
$735$		0			0
$736$		0			0
$737$	−9.00000			−0.331519
$738$		0			0
$739$	1.00000			0.0367856			0.0183928	−	0.999831i	$-0.494145\pi$
$739$	1.00000			0.0367856			0.0183928	+	0.999831i	$0.494145\pi$
$740$	−3.00000	+	5.19615i	−0.110282	+	0.191014i
$741$		0			0
$742$	1.50000	−	7.79423i	0.0550667	−	0.286135i
$743$	25.5000	−	44.1673i	0.935504	−	1.62034i	0.161772	−	0.986828i	$-0.448279\pi$
$743$	25.5000	−	44.1673i	0.935504	−	1.62034i	0.773732	−	0.633513i	$-0.218388\pi$
$744$		0			0
$745$	−22.5000	+	38.9711i	−0.824336	+	1.42779i
$746$	−4.50000	−	7.79423i	−0.164757	−	0.285367i
$747$		0			0
$748$	3.00000	+	5.19615i	0.109691	+	0.189990i
$749$	−16.0000	−	13.8564i	−0.584627	−	0.506302i
$750$		0			0
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	−0.999921	−	0.0125942i	$-0.995991\pi$
$751$	−14.0000	−	24.2487i	−0.510867	−	0.884848i	0.489053	−	0.872254i	$-0.337342\pi$
$752$	1.00000			0.0364662
$753$		0			0
$754$	−7.00000	−	24.2487i	−0.254925	−	0.883086i
$755$	63.0000			2.29280
$756$		0			0
$757$	−1.50000	+	2.59808i	−0.0545184	+	0.0944287i	−0.891997	−	0.452042i	$-0.850696\pi$
$757$	−1.50000	+	2.59808i	−0.0545184	+	0.0944287i	0.837478	+	0.546471i	$0.184029\pi$
$758$	33.0000			1.19861
$759$		0			0
$760$	−4.50000	+	7.79423i	−0.163232	+	0.282726i
$761$	9.00000			0.326250			0.163125	−	0.986605i	$-0.447843\pi$
$761$	9.00000			0.326250			0.163125	+	0.986605i	$0.447843\pi$
$762$		0			0
$763$	14.0000	+	12.1244i	0.506834	+	0.438931i
$764$	8.50000	−	14.7224i	0.307519	−	0.532639i
$765$		0			0
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$	14.0000	+	3.46410i	0.505511	+	0.125081i
$768$		0			0
$769$	−9.50000	+	16.4545i	−0.342579	+	0.593364i	−0.984911	−	0.173063i	$-0.944634\pi$
$769$	−9.50000	+	16.4545i	−0.342579	+	0.593364i	0.642332	+	0.766426i	$0.277967\pi$
$770$	−22.5000	+	7.79423i	−0.810844	+	0.280885i
$771$		0			0
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	−6.00000	+	10.3923i	−0.215526	+	0.373303i
$776$	7.50000	+	12.9904i	0.269234	+	0.466328i
$777$		0			0
$778$	16.5000	−	28.5788i	0.591554	−	1.02460i
$779$	−1.50000	+	2.59808i	−0.0537431	+	0.0930857i
$780$		0			0
$781$	19.5000	+	33.7750i	0.697765	+	1.20856i
$782$		0			0
$783$		0			0
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$	−57.0000			−2.03442
$786$		0			0
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$	0.500000	+	0.866025i	0.0178118	+	0.0308509i
$789$		0			0
$790$	4.50000	−	7.79423i	0.160103	−	0.277306i
$791$	−30.0000	−	25.9808i	−1.06668	−	0.923770i
$792$		0			0
$793$	13.0000	+	45.0333i	0.461644	+	1.59918i
$794$	−0.500000	−	0.866025i	−0.0177443	−	0.0307341i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	0.891368	−	0.453279i	$-0.149746\pi$
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	−0.838236	+	0.545308i	$0.816413\pi$
$798$		0			0
$799$	1.00000	+	1.73205i	0.0353775	+	0.0612756i
$800$	−20.0000			−0.707107
$801$		0			0
$802$	1.00000	−	1.73205i	0.0353112	−	0.0611608i
$803$	19.5000	+	33.7750i	0.688140	+	1.19189i
$804$		0			0
$805$		0			0
$806$	−10.5000	−	2.59808i	−0.369847	−	0.0915133i
$807$		0			0
$808$	15.0000			0.527698
$809$	−11.0000			−0.386739			−0.193370	−	0.981126i	$-0.561942\pi$
$809$	−11.0000			−0.386739			−0.193370	+	0.981126i	$0.561942\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	14.0000	+	12.1244i	0.491304	+	0.425481i
$813$		0			0
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	−1.50000	+	2.59808i	−0.0525427	+	0.0910066i
$816$		0			0
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$	−14.0000			−0.489499
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.761056	−	0.648686i	$-0.775319\pi$
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.181250	−	0.983437i	$-0.558014\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	−7.50000	+	12.9904i	−0.261275	+	0.452541i
$825$		0			0
$826$	10.0000	−	3.46410i	0.347945	−	0.120532i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$		0			0
$829$	11.0000			0.382046			0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000			0.382046			0.191023	+	0.981586i	$0.438820\pi$
$830$		0			0
$831$		0			0
$832$	−7.00000	−	24.2487i	−0.242681	−	0.840673i
$833$	2.00000	+	13.8564i	0.0692959	+	0.480096i
$834$		0			0
$835$	19.5000	+	33.7750i	0.674825	+	1.16883i
$836$	−1.50000	+	2.59808i	−0.0518786	+	0.0898563i
$837$		0			0
$838$	−25.0000			−0.863611
$839$	18.5000	+	32.0429i	0.638691	+	1.10625i	0.985720	+	0.168391i	$0.0538571\pi$
$839$	18.5000	+	32.0429i	0.638691	+	1.10625i	−0.347029	+	0.937854i	$0.612810\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	9.00000	+	15.5885i	0.310160	+	0.537214i
$843$		0			0
$844$	3.50000	+	6.06218i	0.120475	+	0.208669i
$845$	1.50000	+	38.9711i	0.0516016	+	1.34065i
$846$		0			0
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$		0			0
$850$	4.00000	+	6.92820i	0.137199	+	0.237635i
$851$		0			0
$852$		0			0
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$	26.0000	+	22.5167i	0.889702	+	0.770504i
$855$		0			0
$856$	12.0000	+	20.7846i	0.410152	+	0.710403i
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	−0.996559	−	0.0828900i	$-0.973585\pi$
$859$	−12.5000	+	21.6506i	−0.426494	+	0.738710i	0.570064	+	0.821600i	$0.306918\pi$
$860$	10.5000	−	18.1865i	0.358047	−	0.620156i
$861$		0			0
$862$	−4.50000	−	7.79423i	−0.153271	−	0.265472i
$863$	18.5000	−	32.0429i	0.629747	−	1.09075i	−0.357855	−	0.933777i	$-0.616492\pi$
$863$	18.5000	−	32.0429i	0.629747	−	1.09075i	0.987602	−	0.156977i	$-0.0501749\pi$
$864$		0			0
$865$	−28.5000	+	49.3634i	−0.969029	+	1.67841i
$866$	13.5000	−	23.3827i	0.458749	−	0.794576i
$867$		0			0
$868$	7.50000	−	2.59808i	0.254567	−	0.0881845i
$869$	4.50000	−	7.79423i	0.152652	−	0.264401i
$870$		0			0
$871$	3.00000	+	10.3923i	0.101651	+	0.352130i
$872$	−10.5000	−	18.1865i	−0.355575	−	0.615874i
$873$		0			0
$874$		0			0
$875$	−7.50000	+	2.59808i	−0.253546	+	0.0878310i
$876$		0			0
$877$	−45.0000			−1.51954			−0.759771	−	0.650191i	$-0.774689\pi$
$877$	−45.0000			−1.51954			−0.759771	+	0.650191i	$0.774689\pi$
$878$	−8.00000	+	13.8564i	−0.269987	+	0.467631i
$879$		0			0
$880$	9.00000			0.303390
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	−0.711582	−	0.702603i	$-0.752021\pi$
$881$	7.50000	−	12.9904i	0.252681	−	0.437657i	0.964263	+	0.264946i	$0.0853542\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	5.00000	−	5.19615i	0.168168	−	0.174766i
$885$		0			0
$886$	−11.0000			−0.369552
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$	5.50000	−	28.5788i	0.184464	−	0.958503i
$890$	9.00000	+	15.5885i	0.301681	+	0.522526i
$891$		0			0
$892$	−4.50000	−	7.79423i	−0.150671	−	0.260970i
$893$	−0.500000	+	0.866025i	−0.0167319	+	0.0289804i
$894$		0			0
$895$	−25.5000	+	44.1673i	−0.852371	+	1.47635i
$896$	6.00000	+	5.19615i	0.200446	+	0.173591i
$897$		0			0
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	−21.0000			−0.700389
$900$		0			0
$901$	−6.00000			−0.199889
$902$	9.00000			0.299667
$903$		0			0
$904$	22.5000	+	38.9711i	0.748339	+	1.29616i
$905$	−33.0000	+	57.1577i	−1.09696	+	1.89999i
$906$		0			0
$907$	−47.0000			−1.56061			−0.780305	−	0.625400i	$-0.784936\pi$
$907$	−47.0000			−1.56061			−0.780305	+	0.625400i	$0.784936\pi$
$908$	2.00000	+	3.46410i	0.0663723	+	0.114960i
$909$		0			0
$910$	16.5000	+	23.3827i	0.546970	+	0.775128i
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$		0			0
$914$	−9.00000	+	15.5885i	−0.297694	+	0.515620i
$915$		0			0
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$	−2.50000	+	12.9904i	−0.0825573	+	0.428980i
$918$		0			0
$919$	−25.0000			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$920$		0			0
$921$		0			0
$922$	−17.5000	+	30.3109i	−0.576332	+	0.998236i
$923$	32.5000	−	33.7750i	1.06975	−	1.11172i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$		0			0
$928$	−17.5000	−	30.3109i	−0.574466	−	0.995004i
$929$	13.0000			0.426516			0.213258	−	0.976996i	$-0.431592\pi$
$929$	13.0000			0.426516			0.213258	+	0.976996i	$0.431592\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$	10.5000	+	18.1865i	0.343939	+	0.595720i
$933$		0			0
$934$	−7.00000			−0.229047
$935$	9.00000	+	15.5885i	0.294331	+	0.509797i
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	6.00000	+	5.19615i	0.195907	+	0.169660i
$939$		0			0
$940$	−3.00000			−0.0978492
$941$	−8.50000	−	14.7224i	−0.277092	−	0.479938i	0.693569	−	0.720390i	$-0.256037\pi$
$941$	−8.50000	−	14.7224i	−0.277092	−	0.479938i	−0.970661	+	0.240453i	$0.922704\pi$
$942$		0			0
$943$		0			0
$944$	−4.00000			−0.130189
$945$		0			0
$946$	−10.5000	+	18.1865i	−0.341384	+	0.591295i
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	32.5000	−	33.7750i	1.05499	−	1.09638i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		0			0
$952$	3.00000	−	15.5885i	0.0972306	−	0.505225i
$953$	−16.5000	−	28.5788i	−0.534487	−	0.925759i	−0.999188	−	0.0402915i	$-0.987171\pi$
$953$	−16.5000	−	28.5788i	−0.534487	−	0.925759i	0.464701	−	0.885468i	$-0.346162\pi$
$954$		0			0
$955$	25.5000	−	44.1673i	0.825161	−	1.42922i
$956$	2.00000	−	3.46410i	0.0646846	−	0.112037i
$957$		0			0
$958$	17.5000	+	30.3109i	0.565399	+	0.979300i
$959$	−5.00000	+	25.9808i	−0.161458	+	0.838963i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	−7.00000	−	1.73205i	−0.225689	−	0.0558436i
$963$		0			0
$964$	−13.0000	−	22.5167i	−0.418702	−	0.725213i
$965$	10.5000	−	18.1865i	0.338007	−	0.585445i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−6.00000			−0.192847
$969$		0			0
$970$	7.50000	+	12.9904i	0.240810	+	0.417096i
$971$	1.00000			0.0320915			0.0160458	−	0.999871i	$-0.494892\pi$
$971$	1.00000			0.0320915			0.0160458	+	0.999871i	$0.494892\pi$
$972$		0			0
$973$	−30.0000	−	25.9808i	−0.961756	−	0.832905i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	5.00000			0.159964			0.0799821	−	0.996796i	$-0.474514\pi$
$977$	5.00000			0.159964			0.0799821	+	0.996796i	$0.474514\pi$
$978$		0			0
$979$	9.00000	+	15.5885i	0.287641	+	0.498209i
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$		0			0
$982$	15.0000			0.478669
$983$	23.5000	+	40.7032i	0.749534	+	1.29823i	0.948046	+	0.318132i	$0.103056\pi$
$983$	23.5000	+	40.7032i	0.749534	+	1.29823i	−0.198513	+	0.980098i	$0.563611\pi$
$984$		0			0
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$	−7.00000	+	12.1244i	−0.222925	+	0.386118i
$987$		0			0
$988$	3.50000	+	0.866025i	0.111350	+	0.0275519i
$989$		0			0
$990$		0			0
$991$	13.0000			0.412959			0.206479	−	0.978451i	$-0.433799\pi$
$991$	13.0000			0.412959			0.206479	+	0.978451i	$0.433799\pi$
$992$	−15.0000			−0.476250
$993$		0			0
$994$	6.50000	−	33.7750i	0.206167	−	1.07128i
$995$	−30.0000	−	51.9615i	−0.951064	−	1.64729i
$996$		0			0
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	31.0000			0.981288
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.c.100.1		2
3.2	odd	2		91.2.g.a.9.1	✓	2
7.4	even	3		819.2.s.a.802.1		2
13.3	even	3		819.2.s.a.289.1		2
21.2	odd	6		637.2.f.b.295.1		2
21.5	even	6		637.2.f.a.295.1		2
21.11	odd	6		91.2.h.a.74.1	yes	2
21.17	even	6		637.2.h.a.165.1		2
21.20	even	2		637.2.g.a.373.1		2
39.17	odd	6		1183.2.e.c.170.1		2
39.29	odd	6		91.2.h.a.16.1	yes	2
39.35	odd	6		1183.2.e.a.170.1		2
91.81	even	3	inner	819.2.n.c.172.1		2
273.68	even	6		637.2.f.a.393.1		2
273.74	odd	6		1183.2.e.a.508.1		2
273.95	odd	6		1183.2.e.c.508.1		2
273.107	odd	6		637.2.f.b.393.1		2
273.146	even	6		637.2.h.a.471.1		2
273.152	even	6		8281.2.a.j.1.1		1
273.173	even	6		8281.2.a.g.1.1		1
273.185	even	6		637.2.g.a.263.1		2
273.191	odd	6		8281.2.a.i.1.1		1
273.212	odd	6		8281.2.a.c.1.1		1
273.263	odd	6		91.2.g.a.81.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.a.9.1	✓	2	3.2	odd	2
91.2.g.a.81.1	yes	2	273.263	odd	6
91.2.h.a.16.1	yes	2	39.29	odd	6
91.2.h.a.74.1	yes	2	21.11	odd	6
637.2.f.a.295.1		2	21.5	even	6
637.2.f.a.393.1		2	273.68	even	6
637.2.f.b.295.1		2	21.2	odd	6
637.2.f.b.393.1		2	273.107	odd	6
637.2.g.a.263.1		2	273.185	even	6
637.2.g.a.373.1		2	21.20	even	2
637.2.h.a.165.1		2	21.17	even	6
637.2.h.a.471.1		2	273.146	even	6
819.2.n.c.100.1		2	1.1	even	1	trivial
819.2.n.c.172.1		2	91.81	even	3	inner
819.2.s.a.289.1		2	13.3	even	3
819.2.s.a.802.1		2	7.4	even	3
1183.2.e.a.170.1		2	39.35	odd	6
1183.2.e.a.508.1		2	273.74	odd	6
1183.2.e.c.170.1		2	39.17	odd	6
1183.2.e.c.508.1		2	273.95	odd	6
8281.2.a.c.1.1		1	273.212	odd	6
8281.2.a.g.1.1		1	273.173	even	6
8281.2.a.i.1.1		1	273.191	odd	6
8281.2.a.j.1.1		1	273.152	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +3.00000 q^{8} +3.00000 q^{10} +3.00000 q^{11} +(-1.00000 - 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{25} +(2.50000 - 2.59808i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(2.50000 - 4.33013i) q^{32} -2.00000 q^{34} +(-1.50000 + 7.79423i) q^{35} +(-1.00000 - 1.73205i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(4.50000 - 7.79423i) q^{40} +(1.50000 - 2.59808i) q^{41} +(3.50000 + 6.06218i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{47} +(5.50000 - 4.33013i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-3.50000 - 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(4.50000 - 7.79423i) q^{55} +(-7.50000 + 2.59808i) q^{56} +7.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} -13.0000 q^{61} +(1.50000 - 2.59808i) q^{62} +7.00000 q^{64} +(-10.5000 - 2.59808i) q^{65} -3.00000 q^{67} +(1.00000 + 1.73205i) q^{68} +(-7.50000 + 2.59808i) q^{70} +(6.50000 + 11.2583i) q^{71} +(6.50000 + 11.2583i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{76} +(-7.50000 + 2.59808i) q^{77} +(1.50000 - 2.59808i) q^{79} +3.00000 q^{80} +3.00000 q^{82} +(3.00000 + 5.19615i) q^{85} +(-3.50000 + 6.06218i) q^{86} +9.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(5.50000 + 7.79423i) q^{91} +1.00000 q^{94} +(-1.50000 + 2.59808i) q^{95} +(2.50000 + 4.33013i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 3 q^{5} - 5 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 + 3 * q^5 - 5 * q^7 + 6 * q^8	\( 2 q + q^{2} + q^{4} + 3 q^{5} - 5 q^{7} + 6 q^{8} + 6 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{14} + q^{16} - 2 q^{17} - 2 q^{19} - 3 q^{20} + 3 q^{22} - 4 q^{25} + 5 q^{26} - q^{28} + 7 q^{29} - 3 q^{31} + 5 q^{32} - 4 q^{34} - 3 q^{35} - 2 q^{37} - q^{38} + 9 q^{40} + 3 q^{41} + 7 q^{43} + 3 q^{44} + q^{47} + 11 q^{49} + 4 q^{50} - 7 q^{52} + 3 q^{53} + 9 q^{55} - 15 q^{56} + 14 q^{58} - 4 q^{59} - 26 q^{61} + 3 q^{62} + 14 q^{64} - 21 q^{65} - 6 q^{67} + 2 q^{68} - 15 q^{70} + 13 q^{71} + 13 q^{73} + 2 q^{74} - q^{76} - 15 q^{77} + 3 q^{79} + 6 q^{80} + 6 q^{82} + 6 q^{85} - 7 q^{86} + 18 q^{88} + 6 q^{89} + 11 q^{91} + 2 q^{94} - 3 q^{95} + 5 q^{97} + 13 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 3 * q^5 - 5 * q^7 + 6 * q^8 + 6 * q^10 + 6 * q^11 - 2 * q^13 - 4 * q^14 + q^16 - 2 * q^17 - 2 * q^19 - 3 * q^20 + 3 * q^22 - 4 * q^25 + 5 * q^26 - q^28 + 7 * q^29 - 3 * q^31 + 5 * q^32 - 4 * q^34 - 3 * q^35 - 2 * q^37 - q^38 + 9 * q^40 + 3 * q^41 + 7 * q^43 + 3 * q^44 + q^47 + 11 * q^49 + 4 * q^50 - 7 * q^52 + 3 * q^53 + 9 * q^55 - 15 * q^56 + 14 * q^58 - 4 * q^59 - 26 * q^61 + 3 * q^62 + 14 * q^64 - 21 * q^65 - 6 * q^67 + 2 * q^68 - 15 * q^70 + 13 * q^71 + 13 * q^73 + 2 * q^74 - q^76 - 15 * q^77 + 3 * q^79 + 6 * q^80 + 6 * q^82 + 6 * q^85 - 7 * q^86 + 18 * q^88 + 6 * q^89 + 11 * q^91 + 2 * q^94 - 3 * q^95 + 5 * q^97 + 13 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more