LMFDB - Embedded newform 819.2.s.a.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,0,-2,3,0,4,6,0,-3,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.a.802.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{16} +2.00000 q^{17} +(0.500000 + 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{25} +(1.00000 - 3.46410i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(3.50000 + 6.06218i) q^{29} +(-1.50000 - 2.59808i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(7.50000 - 2.59808i) q^{35} +2.00000 q^{37} +(-0.500000 - 0.866025i) q^{38} +(4.50000 - 7.79423i) q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(1.00000 - 3.46410i) q^{52} +(1.50000 + 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{55} +(6.00000 + 5.19615i) q^{56} +(-3.50000 - 6.06218i) q^{58} +4.00000 q^{59} +(6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(1.50000 - 2.59808i) q^{67} -2.00000 q^{68} +(-7.50000 + 2.59808i) q^{70} +(6.50000 - 11.2583i) q^{71} +(6.50000 + 11.2583i) q^{73} -2.00000 q^{74} +(-0.500000 - 0.866025i) q^{76} +(-7.50000 + 2.59808i) q^{77} +(1.50000 - 2.59808i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-1.50000 - 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} +(-3.50000 + 6.06218i) q^{86} +(-4.50000 + 7.79423i) q^{88} -6.00000 q^{89} +(-8.00000 + 5.19615i) q^{91} +(-0.500000 + 0.866025i) q^{94} +3.00000 q^{95} +(2.50000 - 4.33013i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} - 2 q^{16} + 4 q^{17} + q^{19} - 3 q^{20} + 3 q^{22} - 4 q^{25} + 2 q^{26} - 4 q^{28} + 7 q^{29} - 3 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 2 * q^13 - 4 * q^14 - 2 * q^16 + 4 * q^17 + q^19 - 3 * q^20 + 3 * q^22 - 4 * q^25 + 2 * q^26 - 4 * q^28 + 7 * q^29 - 3 * q^31 - 10 * q^32 - 4 * q^34 + 15 * q^35 + 4 * q^37 - q^38 + 9 * q^40 + 3 * q^41 + 7 * q^43 + 3 * q^44 + q^47 + 2 * q^49 + 4 * q^50 + 2 * q^52 + 3 * q^53 + 9 * q^55 + 12 * q^56 - 7 * q^58 + 8 * q^59 + 13 * q^61 + 3 * q^62 + 14 * q^64 + 15 * q^65 + 3 * q^67 - 4 * q^68 - 15 * q^70 + 13 * q^71 + 13 * q^73 - 4 * q^74 - q^76 - 15 * q^77 + 3 * q^79 - 3 * q^80 - 3 * q^82 + 6 * q^85 - 7 * q^86 - 9 * q^88 - 12 * q^89 - 16 * q^91 - q^94 + 6 * q^95 + 5 * q^97 - 2 * q^98

Character values

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

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

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 $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	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
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	3.00000			1.06066
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		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
$16$	−1.00000			−0.250000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	3.50000	+	6.06218i	0.649934	+	1.12572i	0.983138	+	0.182864i	$0.0585367\pi$
$29$	3.50000	+	6.06218i	0.649934	+	1.12572i	−0.333205	+	0.942855i	$0.608130\pi$
$30$		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	$0.920161\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	−2.00000			−0.342997
$35$	7.50000	−	2.59808i	1.26773	−	0.439155i
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−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	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	−0.465478	−	0.885059i	$-0.654118\pi$
$43$	3.50000	−	6.06218i	0.533745	−	0.924473i	0.999223	−	0.0394140i	$-0.0125491\pi$
$44$	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
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	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
$56$	6.00000	+	5.19615i	0.801784	+	0.694365i
$57$		0			0
$58$	−3.50000	−	6.06218i	−0.459573	−	0.796003i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$		0			0
$64$	7.00000			0.875000
$65$	7.50000	+	7.79423i	0.930261	+	0.966755i
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	−2.00000			−0.242536
$69$		0			0
$70$	−7.50000	+	2.59808i	−0.896421	+	0.310530i
$71$	6.50000	−	11.2583i	0.771408	−	1.33612i	−0.165383	−	0.986229i	$-0.552886\pi$
$71$	6.50000	−	11.2583i	0.771408	−	1.33612i	0.936791	−	0.349889i	$-0.113781\pi$
$72$		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	$0.558156\pi$
$74$	−2.00000			−0.232495
$75$		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	$0.112689\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$		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
$88$	−4.50000	+	7.79423i	−0.479702	+	0.830868i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	−8.00000	+	5.19615i	−0.838628	+	0.544705i
$92$		0			0
$93$		0			0
$94$	−0.500000	+	0.866025i	−0.0515711	+	0.0893237i
$95$	3.00000			0.307794
$96$		0			0
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−2.50000	+	4.33013i	−0.248759	+	0.430864i	−0.963182	−	0.268851i	$-0.913356\pi$
$101$	−2.50000	+	4.33013i	−0.248759	+	0.430864i	0.714423	+	0.699715i	$0.246689\pi$
$102$		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
$107$	−8.00000			−0.773389			−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000			−0.773389			−0.386695	+	0.922208i	$0.626383\pi$
$108$		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	$0.942150\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$		0			0
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$		0			0
$115$		0			0
$116$	−3.50000	−	6.06218i	−0.324967	−	0.562859i
$117$		0			0
$118$	−4.00000			−0.368230
$119$	4.00000	+	3.46410i	0.366679	+	0.317554i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−6.50000	−	11.2583i	−0.588482	−	1.01928i
$123$		0			0
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$	3.00000			0.268328
$126$		0			0
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	0.511859	−	0.859069i	$-0.328957\pi$
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	−0.999905	+	0.0137486i	$0.995624\pi$
$128$	3.00000			0.265165
$129$		0			0
$130$	−7.50000	−	7.79423i	−0.657794	−	0.683599i
$131$	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
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	−1.50000	+	2.59808i	−0.129580	+	0.224440i
$135$		0			0
$136$	6.00000			0.514496
$137$	−10.0000			−0.854358			−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000			−0.854358			−0.427179	+	0.904167i	$0.640493\pi$
$138$		0			0
$139$	7.50000	−	12.9904i	0.636142	−	1.10183i	−0.350130	−	0.936701i	$-0.613863\pi$
$139$	7.50000	−	12.9904i	0.636142	−	1.10183i	0.986272	−	0.165129i	$-0.0528040\pi$
$140$	−7.50000	+	2.59808i	−0.633866	+	0.219578i
$141$		0			0
$142$	−6.50000	+	11.2583i	−0.545468	+	0.944778i
$143$	−7.50000	−	7.79423i	−0.627182	−	0.651786i
$144$		0			0
$145$	21.0000			1.74396
$146$	−6.50000	−	11.2583i	−0.537944	−	0.931746i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		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	$0.507211\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$		0			0
$154$	7.50000	−	2.59808i	0.604367	−	0.209359i
$155$	−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	$-0.440579\pi$
$158$	−1.50000	+	2.59808i	−0.119334	+	0.206692i
$159$		0			0
$160$	−7.50000	+	12.9904i	−0.592927	+	1.02698i
$161$		0			0
$162$		0			0
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$		0			0
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	−0.999994	−	0.00345033i	$-0.998902\pi$
$167$	−6.50000	−	11.2583i	−0.502985	−	0.871196i	0.497009	−	0.867745i	$-0.334432\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$		0			0
$172$	−3.50000	+	6.06218i	−0.266872	+	0.462237i
$173$	9.50000	+	16.4545i	0.722272	+	1.25101i	0.960087	+	0.279701i	$0.0902353\pi$
$173$	9.50000	+	16.4545i	0.722272	+	1.25101i	−0.237816	+	0.971310i	$0.576431\pi$
$174$		0			0
$175$	2.00000	−	10.3923i	0.151186	−	0.785584i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	6.00000			0.449719
$179$	8.50000	−	14.7224i	0.635320	−	1.10041i	−0.351127	−	0.936328i	$-0.614202\pi$
$179$	8.50000	−	14.7224i	0.635320	−	1.10041i	0.986447	−	0.164079i	$-0.0524651\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	8.00000	−	5.19615i	0.592999	−	0.385164i
$183$		0			0
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$		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
$191$	−8.50000	−	14.7224i	−0.615038	−	1.06528i	−0.990378	−	0.138390i	$-0.955807\pi$
$191$	−8.50000	−	14.7224i	−0.615038	−	1.06528i	0.375339	−	0.926887i	$-0.377526\pi$
$192$		0			0
$193$	−3.50000	+	6.06218i	−0.251936	+	0.436365i	−0.964059	−	0.265689i	$-0.914400\pi$
$193$	−3.50000	+	6.06218i	−0.251936	+	0.436365i	0.712123	+	0.702055i	$0.247734\pi$
$194$	−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	0.847664	−	0.530534i	$-0.178008\pi$
$197$	−0.500000	−	0.866025i	−0.0356235	−	0.0617018i	−0.883287	+	0.468832i	$0.844675\pi$
$198$		0			0
$199$	−20.0000			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$	−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
$205$	9.00000			0.628587
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$		0			0
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	0.720035	−	0.693938i	$-0.244126\pi$
$211$	−3.50000	−	6.06218i	−0.240950	−	0.417338i	−0.960985	+	0.276600i	$0.910792\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$		0			0
$214$	8.00000			0.546869
$215$	−10.5000	−	18.1865i	−0.716094	−	1.24031i
$216$		0			0
$217$	1.50000	−	7.79423i	0.101827	−	0.529107i
$218$	3.50000	+	6.06218i	0.237050	+	0.410582i
$219$		0			0
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	−2.00000	+	6.92820i	−0.134535	+	0.466041i
$222$		0			0
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	0.976440	−	0.215788i	$-0.0692320\pi$
$223$	4.50000	+	7.79423i	0.301342	+	0.521940i	−0.675098	+	0.737728i	$0.735899\pi$
$224$	−10.0000	−	8.66025i	−0.668153	−	0.578638i
$225$		0			0
$226$	−7.50000	+	12.9904i	−0.498893	+	0.864107i
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$		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
$236$	−4.00000			−0.260378
$237$		0			0
$238$	−4.00000	−	3.46410i	−0.259281	−	0.224544i
$239$	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
$241$	−26.0000			−1.67481			−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000			−1.67481			−0.837404	+	0.546585i	$0.815928\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$	19.5000	+	7.79423i	1.24581	+	0.497955i
$246$		0			0
$247$	−3.50000	+	0.866025i	−0.222700	+	0.0551039i
$248$	−4.50000	−	7.79423i	−0.285750	−	0.494934i
$249$		0			0
$250$	−3.00000			−0.189737
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	0.232740	+	0.972539i	$0.425231\pi$
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	−0.958613	+	0.284711i	$0.908102\pi$
$252$		0			0
$253$		0			0
$254$	5.50000	+	9.52628i	0.345101	+	0.597732i
$255$		0			0
$256$	−17.0000			−1.06250
$257$	2.00000			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$258$		0			0
$259$	4.00000	+	3.46410i	0.248548	+	0.215249i
$260$	−7.50000	−	7.79423i	−0.465130	−	0.483378i
$261$		0			0
$262$	−2.50000	+	4.33013i	−0.154451	+	0.267516i
$263$	−13.5000	+	23.3827i	−0.832446	+	1.44184i	0.0636476	+	0.997972i	$0.479727\pi$
$263$	−13.5000	+	23.3827i	−0.832446	+	1.44184i	−0.896093	+	0.443866i	$0.853607\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	0.500000	−	2.59808i	0.0306570	−	0.159298i
$267$		0			0
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	12.0000			0.723627
$276$		0			0
$277$	22.0000			1.32185			0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000			1.32185			0.660926	+	0.750451i	$0.270164\pi$
$278$	−7.50000	+	12.9904i	−0.449820	+	0.779111i
$279$		0			0
$280$	22.5000	−	7.79423i	1.34463	−	0.465794i
$281$	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
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	−0.880504	−	0.474039i	$-0.842796\pi$
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	0.850782	+	0.525519i	$0.176129\pi$
$284$	−6.50000	+	11.2583i	−0.385704	+	0.668059i
$285$		0			0
$286$	7.50000	+	7.79423i	0.443484	+	0.460882i
$287$	−1.50000	+	7.79423i	−0.0885422	+	0.460079i
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−21.0000			−1.23316
$291$		0			0
$292$	−6.50000	−	11.2583i	−0.380384	−	0.658844i
$293$	5.50000	−	9.52628i	0.321313	−	0.556531i	−0.659446	−	0.751752i	$-0.729209\pi$
$293$	5.50000	−	9.52628i	0.321313	−	0.556531i	0.980759	+	0.195221i	$0.0625424\pi$
$294$		0			0
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	6.00000			0.348743
$297$		0			0
$298$	−7.50000	−	12.9904i	−0.434463	−	0.752513i
$299$		0			0
$300$		0			0
$301$	17.5000	−	6.06218i	1.00868	−	0.349418i
$302$	−10.5000	−	18.1865i	−0.604207	−	1.04652i
$303$		0			0
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	39.0000			2.23313
$306$		0			0
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	7.50000	−	2.59808i	0.427352	−	0.148039i
$309$		0			0
$310$	9.00000			0.511166
$311$	−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
$319$	−21.0000			−1.17577
$320$	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
$325$	14.0000	−	3.46410i	0.776580	−	0.192154i
$326$	−0.500000	−	0.866025i	−0.0276924	−	0.0479647i
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	2.50000	−	0.866025i	0.137829	−	0.0477455i
$330$		0			0
$331$	14.5000	+	25.1147i	0.796992	+	1.38043i	0.921567	+	0.388221i	$0.126910\pi$
$331$	14.5000	+	25.1147i	0.796992	+	1.38043i	−0.124574	+	0.992210i	$0.539757\pi$
$332$		0			0
$333$		0			0
$334$	6.50000	+	11.2583i	0.355664	+	0.616028i
$335$	−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	$0.375472\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$		0			0
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	9.00000			0.487377
$342$		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
$347$	8.00000			0.429463			0.214731	−	0.976673i	$-0.431112\pi$
$347$	8.00000			0.429463			0.214731	+	0.976673i	$0.431112\pi$
$348$		0			0
$349$	−11.5000	−	19.9186i	−0.615581	−	1.06622i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−11.5000	−	19.9186i	−0.615581	−	1.06622i	0.374701	−	0.927146i	$-0.377745\pi$
$350$	−2.00000	+	10.3923i	−0.106904	+	0.555492i
$351$		0			0
$352$	7.50000	−	12.9904i	0.399751	−	0.692390i
$353$	−12.5000	+	21.6506i	−0.665308	+	1.15235i	0.313894	+	0.949458i	$0.398366\pi$
$353$	−12.5000	+	21.6506i	−0.665308	+	1.15235i	−0.979202	+	0.202889i	$0.934967\pi$
$354$		0			0
$355$	−19.5000	−	33.7750i	−1.03495	−	1.79259i
$356$	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
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	22.0000			1.15629
$363$		0			0
$364$	8.00000	−	5.19615i	0.419314	−	0.272352i
$365$	39.0000			2.04135
$366$		0			0
$367$	15.5000	−	26.8468i	0.809093	−	1.40139i	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	15.5000	−	26.8468i	0.809093	−	1.40139i	0.913493	−	0.406855i	$-0.133375\pi$
$368$		0			0
$369$		0			0
$370$	−3.00000	+	5.19615i	−0.155963	+	0.270135i
$371$	−1.50000	+	7.79423i	−0.0778761	+	0.404656i
$372$		0			0
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	0.958690	−	0.284453i	$-0.0918121\pi$
$373$	4.50000	+	7.79423i	0.233001	+	0.403570i	−0.725689	+	0.688023i	$0.758479\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$		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	0.883390	+	0.468639i	$0.155255\pi$
$379$	16.5000	+	28.5788i	0.847548	+	1.46800i	−0.0358418	+	0.999357i	$0.511411\pi$
$380$	−3.00000			−0.153897
$381$		0			0
$382$	8.50000	+	14.7224i	0.434898	+	0.753265i
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$		0			0
$385$	−4.50000	+	23.3827i	−0.229341	+	1.19169i
$386$	3.50000	−	6.06218i	0.178145	−	0.308557i
$387$		0			0
$388$	−2.50000	+	4.33013i	−0.126918	+	0.219829i
$389$	−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
$392$	3.00000	+	20.7846i	0.151523	+	1.04978i
$393$		0			0
$394$	0.500000	+	0.866025i	0.0251896	+	0.0436297i
$395$	−4.50000	−	7.79423i	−0.226420	−	0.392170i
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$		0			0
$403$	10.5000	−	2.59808i	0.523042	−	0.129419i
$404$	2.50000	−	4.33013i	0.124380	−	0.215432i
$405$		0			0
$406$	3.50000	−	18.1865i	0.173702	−	0.902583i
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	−9.00000			−0.444478
$411$		0			0
$412$	2.50000	−	4.33013i	0.123166	−	0.213330i
$413$	8.00000	+	6.92820i	0.393654	+	0.340915i
$414$		0			0
$415$		0			0
$416$	5.00000	−	17.3205i	0.245145	−	0.849208i
$417$		0			0
$418$	3.00000			0.146735
$419$	−12.5000	−	21.6506i	−0.610665	−	1.05770i	−0.991129	−	0.132907i	$-0.957569\pi$
$419$	−12.5000	−	21.6506i	−0.610665	−	1.05770i	0.380464	−	0.924796i	$-0.375764\pi$
$420$		0			0
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$	3.50000	+	6.06218i	0.170377	+	0.295102i
$423$		0			0
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−4.00000	−	6.92820i	−0.194029	−	0.336067i
$426$		0			0
$427$	−6.50000	+	33.7750i	−0.314557	+	1.63449i
$428$	8.00000			0.386695
$429$		0			0
$430$	10.5000	+	18.1865i	0.506355	+	0.877033i
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$		0			0
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	0.334649	+	0.942343i	$0.391382\pi$
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	−0.983417	+	0.181357i	$0.941951\pi$
$434$	−1.50000	+	7.79423i	−0.0720023	+	0.374135i
$435$		0			0
$436$	3.50000	+	6.06218i	0.167620	+	0.290326i
$437$		0			0
$438$		0			0
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$	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
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−4.50000	−	7.79423i	−0.213081	−	0.369067i
$447$		0			0
$448$	14.0000	+	12.1244i	0.661438	+	0.572822i
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	−0.632990	−	0.774160i	$-0.718173\pi$
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	0.986937	+	0.161106i	$0.0515060\pi$
$450$		0			0
$451$	−9.00000			−0.423793
$452$	−7.50000	+	12.9904i	−0.352770	+	0.611016i
$453$		0			0
$454$	−4.00000			−0.187729
$455$	1.50000	+	28.5788i	0.0703211	+	1.33980i
$456$		0			0
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	−6.50000	+	11.2583i	−0.303725	+	0.526067i
$459$		0			0
$460$		0			0
$461$	17.5000	−	30.3109i	0.815056	−	1.41172i	−0.0942312	−	0.995550i	$-0.530039\pi$
$461$	17.5000	−	30.3109i	0.815056	−	1.41172i	0.909288	−	0.416169i	$-0.136627\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−3.50000	−	6.06218i	−0.162483	−	0.281430i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	−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
$472$	12.0000			0.552345
$473$	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
$478$	−4.00000			−0.182956
$479$	−17.5000	+	30.3109i	−0.799595	+	1.38494i	0.120284	+	0.992739i	$0.461619\pi$
$479$	−17.5000	+	30.3109i	−0.799595	+	1.38494i	−0.919880	+	0.392200i	$0.871714\pi$
$480$		0			0
$481$	−2.00000	+	6.92820i	−0.0911922	+	0.315899i
$482$	26.0000			1.18427
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	−7.50000	−	12.9904i	−0.340557	−	0.589863i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	19.5000	+	33.7750i	0.882724	+	1.52892i
$489$		0			0
$490$	−19.5000	−	7.79423i	−0.880920	−	0.352107i
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	0.984145	−	0.177365i	$-0.0567572\pi$
$491$	7.50000	+	12.9904i	0.338470	+	0.586248i	−0.645675	+	0.763612i	$0.723424\pi$
$492$		0			0
$493$	7.00000	+	12.1244i	0.315264	+	0.546054i
$494$	3.50000	−	0.866025i	0.157472	−	0.0389643i
$495$		0			0
$496$	1.50000	+	2.59808i	0.0673520	+	0.116657i
$497$	32.5000	−	11.2583i	1.45782	−	0.505005i
$498$		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	$-0.0774314\pi$
$500$	−3.00000			−0.134164
$501$		0			0
$502$	11.5000	−	19.9186i	0.513270	−	0.889010i
$503$	−15.5000	+	26.8468i	−0.691111	+	1.19704i	0.280363	+	0.959894i	$0.409545\pi$
$503$	−15.5000	+	26.8468i	−0.691111	+	1.19704i	−0.971474	+	0.237145i	$0.923788\pi$
$504$		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
$509$	34.0000			1.50702			0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000			1.50702			0.753512	+	0.657434i	$0.228358\pi$
$510$		0			0
$511$	−6.50000	+	33.7750i	−0.287543	+	1.49412i
$512$	11.0000			0.486136
$513$		0			0
$514$	−2.00000			−0.0882162
$515$	7.50000	+	12.9904i	0.330489	+	0.572425i
$516$		0			0
$517$	1.50000	+	2.59808i	0.0659699	+	0.114263i
$518$	−4.00000	−	3.46410i	−0.175750	−	0.152204i
$519$		0			0
$520$	22.5000	+	23.3827i	0.986690	+	1.02540i
$521$	−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
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$	−2.50000	+	4.33013i	−0.109213	+	0.189162i
$525$		0			0
$526$	13.5000	−	23.3827i	0.588628	−	1.01953i
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$		0			0
$529$	−23.0000			−1.00000
$530$	−9.00000			−0.390935
$531$		0			0
$532$	0.500000	−	2.59808i	0.0216777	−	0.112641i
$533$	−10.5000	+	2.59808i	−0.454805	+	0.112535i
$534$		0			0
$535$	−12.0000	+	20.7846i	−0.518805	+	0.898597i
$536$	4.50000	−	7.79423i	0.194370	−	0.336659i
$537$		0			0
$538$	18.0000			0.776035
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		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	$-0.126061\pi$
$542$	16.0000			0.687259
$543$		0			0
$544$	−10.0000			−0.428746
$545$	−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	$0.704275\pi$
$548$	10.0000			0.427179
$549$		0			0
$550$	−12.0000			−0.511682
$551$	−3.50000	+	6.06218i	−0.149105	+	0.258257i
$552$		0			0
$553$	7.50000	−	2.59808i	0.318932	−	0.110481i
$554$	−22.0000			−0.934690
$555$		0			0
$556$	−7.50000	+	12.9904i	−0.318071	+	0.550915i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$		0			0
$559$	17.5000	+	18.1865i	0.740171	+	0.769208i
$560$	−7.50000	+	2.59808i	−0.316933	+	0.109789i
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$		0			0
$565$	−22.5000	−	38.9711i	−0.946582	−	1.63953i
$566$	0.500000	−	0.866025i	0.0210166	−	0.0364018i
$567$		0			0
$568$	19.5000	−	33.7750i	0.818202	−	1.41717i
$569$	−10.0000			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$		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	$-0.522916\pi$
$572$	7.50000	+	7.79423i	0.313591	+	0.325893i
$573$		0			0
$574$	1.50000	−	7.79423i	0.0626088	−	0.325325i
$575$		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	$0.826707\pi$
$578$	13.0000			0.540729
$579$		0			0
$580$	−21.0000			−0.871978
$581$		0			0
$582$		0			0
$583$	−9.00000			−0.372742
$584$	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	−0.974668	−	0.223659i	$-0.928200\pi$
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	0.293640	−	0.955916i	$-0.405133\pi$
$588$		0			0
$589$	1.50000	−	2.59808i	0.0618064	−	0.107052i
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$		0			0
$592$	−2.00000			−0.0821995
$593$	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
$595$	15.0000	−	5.19615i	0.614940	−	0.213021i
$596$	−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	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$	−17.5000	+	6.06218i	−0.713247	+	0.247076i
$603$		0			0
$604$	−10.5000	−	18.1865i	−0.427239	−	0.740000i
$605$	6.00000			0.243935
$606$		0			0
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	0.732551	−	0.680712i	$-0.238329\pi$
$607$	−5.50000	−	9.52628i	−0.223238	−	0.386660i	−0.955789	+	0.294052i	$0.904996\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$		0			0
$610$	−39.0000			−1.57906
$611$	2.50000	+	2.59808i	0.101139	+	0.105107i
$612$		0			0
$613$	12.5000	−	21.6506i	0.504870	−	0.874461i	−0.495114	−	0.868828i	$-0.664874\pi$
$613$	12.5000	−	21.6506i	0.504870	−	0.874461i	0.999984	−	0.00563283i	$-0.00179300\pi$
$614$	−12.0000			−0.484281
$615$		0			0
$616$	−22.5000	+	7.79423i	−0.906551	+	0.314038i
$617$	−16.5000	+	28.5788i	−0.664265	+	1.15054i	0.315219	+	0.949019i	$0.397922\pi$
$617$	−16.5000	+	28.5788i	−0.664265	+	1.15054i	−0.979484	+	0.201522i	$0.935411\pi$
$618$		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	$0.904286\pi$
$620$	9.00000			0.361449
$621$		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
$626$	9.50000	−	16.4545i	0.379696	−	0.657653i
$627$		0			0
$628$	9.50000	+	16.4545i	0.379091	+	0.656605i
$629$	4.00000			0.159490
$630$		0			0
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	−0.999996	−	0.00274930i	$-0.999125\pi$
$631$	−12.5000	+	21.6506i	−0.497617	+	0.861898i	0.502379	+	0.864647i	$0.332458\pi$
$632$	4.50000	−	7.79423i	0.179000	−	0.310038i
$633$		0			0
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	−33.0000			−1.30957
$636$		0			0
$637$	−25.0000	−	3.46410i	−0.990536	−	0.137253i
$638$	21.0000			0.831398
$639$		0			0
$640$	4.50000	−	7.79423i	0.177878	−	0.308094i
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$		0			0
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$		0			0
$645$		0			0
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$	4.50000	−	7.79423i	0.176913	−	0.306423i	−0.763908	−	0.645325i	$-0.776722\pi$
$647$	4.50000	−	7.79423i	0.176913	−	0.306423i	0.940822	+	0.338902i	$0.110055\pi$
$648$		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
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$		0			0
$655$	−7.50000	−	12.9904i	−0.293049	−	0.507576i
$656$	−1.50000	−	2.59808i	−0.0585652	−	0.101438i
$657$		0			0
$658$	−2.50000	+	0.866025i	−0.0974601	+	0.0337612i
$659$	14.5000	−	25.1147i	0.564840	−	0.978331i	−0.432225	−	0.901766i	$-0.642271\pi$
$659$	14.5000	−	25.1147i	0.564840	−	0.978331i	0.997065	−	0.0765653i	$-0.0243954\pi$
$660$		0			0
$661$	4.50000	−	7.79423i	0.175030	−	0.303160i	−0.765142	−	0.643862i	$-0.777331\pi$
$661$	4.50000	−	7.79423i	0.175030	−	0.303160i	0.940172	+	0.340701i	$0.110665\pi$
$662$	−14.5000	−	25.1147i	−0.563559	−	0.976112i
$663$		0			0
$664$		0			0
$665$	6.00000	+	5.19615i	0.232670	+	0.201498i
$666$		0			0
$667$		0			0
$668$	6.50000	+	11.2583i	0.251493	+	0.435598i
$669$		0			0
$670$	4.50000	+	7.79423i	0.173850	+	0.301117i
$671$	−39.0000			−1.50558
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$	−14.0000			−0.539260
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	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
$679$	12.5000	−	4.33013i	0.479706	−	0.166175i
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$		0			0
$682$	−9.00000			−0.344628
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	−15.0000	+	25.9808i	−0.573121	+	0.992674i
$686$	10.0000	−	15.5885i	0.381802	−	0.595170i
$687$		0			0
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	−10.5000	+	2.59808i	−0.400018	+	0.0989788i
$690$		0			0
$691$	−4.00000			−0.152167			−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$	−9.50000	−	16.4545i	−0.361136	−	0.625506i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	−22.5000	−	38.9711i	−0.853474	−	1.47826i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	11.5000	+	19.9186i	0.435281	+	0.753930i
$699$		0			0
$700$	−2.00000	+	10.3923i	−0.0755929	+	0.392792i
$701$	−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
$704$	−10.5000	+	18.1865i	−0.395734	+	0.685431i
$705$		0			0
$706$	12.5000	−	21.6506i	0.470444	−	0.814832i
$707$	−12.5000	+	4.33013i	−0.470111	+	0.162851i
$708$		0			0
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	0.744071	−	0.668101i	$-0.232892\pi$
$709$	−5.50000	−	9.52628i	−0.206557	−	0.357767i	−0.950628	+	0.310334i	$0.899559\pi$
$710$	19.5000	+	33.7750i	0.731822	+	1.26755i
$711$		0			0
$712$	−18.0000			−0.674579
$713$		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
$718$	−8.50000	+	14.7224i	−0.317217	+	0.549436i
$719$	−4.50000	−	7.79423i	−0.167822	−	0.290676i	0.769832	−	0.638247i	$-0.220340\pi$
$719$	−4.50000	−	7.79423i	−0.167822	−	0.290676i	−0.937654	+	0.347571i	$0.887007\pi$
$720$		0			0
$721$	−12.5000	+	4.33013i	−0.465524	+	0.161262i
$722$	−9.00000	+	15.5885i	−0.334945	+	0.580142i
$723$		0			0
$724$	22.0000			0.817624
$725$	14.0000	−	24.2487i	0.519947	−	0.900575i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−24.0000	+	15.5885i	−0.889499	+	0.577747i
$729$		0			0
$730$	−39.0000			−1.44345
$731$	7.00000	−	12.1244i	0.258904	−	0.448435i
$732$		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
$737$	4.50000	+	7.79423i	0.165760	+	0.287104i
$738$		0			0
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	−0.875075	−	0.483987i	$-0.839188\pi$
$739$	−0.500000	+	0.866025i	−0.0183928	+	0.0318573i	0.856683	+	0.515844i	$0.172522\pi$
$740$	−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	0.773732	+	0.633513i	$0.218388\pi$
$743$	25.5000	+	44.1673i	0.935504	+	1.62034i	0.161772	+	0.986828i	$0.448279\pi$
$744$		0			0
$745$	45.0000			1.64867
$746$	−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
$751$	28.0000			1.02173			0.510867	−	0.859660i	$-0.329324\pi$
$751$	28.0000			1.02173			0.510867	+	0.859660i	$0.329324\pi$
$752$	−0.500000	+	0.866025i	−0.0182331	+	0.0315807i
$753$		0			0
$754$	24.5000	−	6.06218i	0.892237	−	0.220771i
$755$	63.0000			2.29280
$756$		0			0
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	0.837478	−	0.546471i	$-0.184029\pi$
$757$	−1.50000	−	2.59808i	−0.0545184	−	0.0944287i	−0.891997	+	0.452042i	$0.850696\pi$
$758$	−16.5000	−	28.5788i	−0.599307	−	1.03803i
$759$		0			0
$760$	9.00000			0.326464
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	0.772863	−	0.634573i	$-0.218824\pi$
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	−0.935988	+	0.352032i	$0.885491\pi$
$762$		0			0
$763$	3.50000	−	18.1865i	0.126709	−	0.658397i
$764$	8.50000	+	14.7224i	0.307519	+	0.532639i
$765$		0			0
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$	−4.00000	+	13.8564i	−0.144432	+	0.500326i
$768$		0			0
$769$	−9.50000	−	16.4545i	−0.342579	−	0.593364i	0.642332	−	0.766426i	$-0.277967\pi$
$769$	−9.50000	−	16.4545i	−0.342579	−	0.593364i	−0.984911	+	0.173063i	$0.944634\pi$
$770$	4.50000	−	23.3827i	0.162169	−	0.842654i
$771$		0			0
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$		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
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$	−57.0000			−2.03442
$786$		0			0
$787$	−20.0000			−0.712923			−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000			−0.712923			−0.356462	+	0.934310i	$0.616017\pi$
$788$	0.500000	+	0.866025i	0.0178118	+	0.0308509i
$789$		0			0
$790$	4.50000	+	7.79423i	0.160103	+	0.277306i
$791$	37.5000	−	12.9904i	1.33335	−	0.461885i
$792$		0			0
$793$	−45.5000	+	11.2583i	−1.61575	+	0.399795i
$794$	−0.500000	−	0.866025i	−0.0177443	−	0.0307341i
$795$		0			0
$796$	20.0000			0.708881
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	−0.838236	−	0.545308i	$-0.816413\pi$
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	0.891368	+	0.453279i	$0.149746\pi$
$798$		0			0
$799$	1.00000	−	1.73205i	0.0353775	−	0.0612756i
$800$	10.0000	+	17.3205i	0.353553	+	0.612372i
$801$		0			0
$802$	−2.00000			−0.0706225
$803$	−39.0000			−1.37628
$804$		0			0
$805$		0			0
$806$	−10.5000	+	2.59808i	−0.369847	+	0.0915133i
$807$		0			0
$808$	−7.50000	+	12.9904i	−0.263849	+	0.457000i
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	−0.752995	−	0.658026i	$-0.771392\pi$
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	0.946365	+	0.323100i	$0.104725\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	3.50000	−	18.1865i	0.122826	−	0.638222i
$813$		0			0
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	3.00000			0.105085
$816$		0			0
$817$	7.00000			0.244899
$818$	−14.0000			−0.489499
$819$		0			0
$820$	−9.00000			−0.314294
$821$	54.0000			1.88461			0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000			1.88461			0.942306	+	0.334751i	$0.108652\pi$
$822$		0			0
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$	−7.50000	+	12.9904i	−0.261275	+	0.452541i
$825$		0			0
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$	−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
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		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
$835$	−39.0000			−1.34965
$836$	3.00000			0.103757
$837$		0			0
$838$	12.5000	+	21.6506i	0.431805	+	0.747909i
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	−0.347029	−	0.937854i	$-0.612810\pi$
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	0.985720	−	0.168391i	$-0.0538571\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	−18.0000			−0.620321
$843$		0			0
$844$	3.50000	+	6.06218i	0.120475	+	0.208669i
$845$	−34.5000	+	18.1865i	−1.18684	+	0.625636i
$846$		0			0
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$	−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	$0.532754\pi$
$854$	6.50000	−	33.7750i	0.222425	−	1.15576i
$855$		0			0
$856$	−24.0000			−0.820303
$857$	−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
$865$	57.0000			1.93806
$866$	13.5000	−	23.3827i	0.458749	−	0.794576i
$867$		0			0
$868$	−1.50000	+	7.79423i	−0.0509133	+	0.264553i
$869$	4.50000	+	7.79423i	0.152652	+	0.264401i
$870$		0			0
$871$	7.50000	+	7.79423i	0.254128	+	0.264097i
$872$	−10.5000	−	18.1865i	−0.355575	−	0.615874i
$873$		0			0
$874$		0			0
$875$	6.00000	+	5.19615i	0.202837	+	0.175662i
$876$		0			0
$877$	22.5000	+	38.9711i	0.759771	+	1.31596i	0.942967	+	0.332886i	$0.108022\pi$
$877$	22.5000	+	38.9711i	0.759771	+	1.31596i	−0.183196	+	0.983076i	$0.558644\pi$
$878$	16.0000			0.539974
$879$		0			0
$880$	−4.50000	−	7.79423i	−0.151695	−	0.262743i
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	0.964263	−	0.264946i	$-0.0853542\pi$
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	−0.711582	+	0.702603i	$0.752021\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	2.00000	−	6.92820i	0.0672673	−	0.233021i
$885$		0			0
$886$	5.50000	−	9.52628i	0.184776	−	0.320042i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		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
$893$	1.00000			0.0334637
$894$		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
$899$	10.5000	−	18.1865i	0.350195	−	0.606555i
$900$		0			0
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$	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
$907$	23.5000	−	40.7032i	0.780305	−	1.35153i	−0.151460	−	0.988463i	$-0.548397\pi$
$907$	23.5000	−	40.7032i	0.780305	−	1.35153i	0.931764	−	0.363064i	$-0.118269\pi$
$908$	−4.00000			−0.132745
$909$		0			0
$910$	−1.50000	−	28.5788i	−0.0497245	−	0.947379i
$911$	−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
$914$	18.0000			0.595387
$915$		0			0
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$	12.5000	−	4.33013i	0.412786	−	0.142993i
$918$		0			0
$919$	12.5000	+	21.6506i	0.412337	+	0.714189i	0.995145	−	0.0984214i	$-0.0313793\pi$
$919$	12.5000	+	21.6506i	0.412337	+	0.714189i	−0.582808	+	0.812610i	$0.698046\pi$
$920$		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
$926$	8.00000			0.262896
$927$		0			0
$928$	−17.5000	−	30.3109i	−0.574466	−	0.995004i
$929$	−6.50000	−	11.2583i	−0.213258	−	0.369374i	0.739474	−	0.673185i	$-0.235074\pi$
$929$	−6.50000	−	11.2583i	−0.213258	−	0.369374i	−0.952732	+	0.303811i	$0.901741\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$	10.5000	−	18.1865i	0.343939	−	0.595720i
$933$		0			0
$934$	3.50000	−	6.06218i	0.114523	−	0.198361i
$935$	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	$0.382997\pi$
$938$	−7.50000	+	2.59808i	−0.244884	+	0.0848302i
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$	−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
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	−45.5000	+	11.2583i	−1.47699	+	0.365461i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		0			0
$952$	12.0000	+	10.3923i	0.388922	+	0.336817i
$953$	−16.5000	+	28.5788i	−0.534487	+	0.925759i	0.464701	+	0.885468i	$0.346162\pi$
$953$	−16.5000	+	28.5788i	−0.534487	+	0.925759i	−0.999188	+	0.0402915i	$0.987171\pi$
$954$		0			0
$955$	−51.0000			−1.65032
$956$	−4.00000			−0.129369
$957$		0			0
$958$	17.5000	−	30.3109i	0.565399	−	0.979300i
$959$	−20.0000	−	17.3205i	−0.645834	−	0.559308i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	2.00000	−	6.92820i	0.0644826	−	0.223374i
$963$		0			0
$964$	26.0000			0.837404
$965$	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	$0.541058\pi$
$968$	3.00000	+	5.19615i	0.0964237	+	0.167011i
$969$		0			0
$970$	7.50000	+	12.9904i	0.240810	+	0.417096i
$971$	−0.500000	−	0.866025i	−0.0160458	−	0.0277921i	0.857891	−	0.513832i	$-0.171774\pi$
$971$	−0.500000	−	0.866025i	−0.0160458	−	0.0277921i	−0.873937	+	0.486040i	$0.838441\pi$
$972$		0			0
$973$	37.5000	−	12.9904i	1.20219	−	0.416452i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	−2.50000	+	4.33013i	−0.0799821	+	0.138533i	−0.903242	−	0.429132i	$-0.858820\pi$
$977$	−2.50000	+	4.33013i	−0.0799821	+	0.138533i	0.823260	+	0.567665i	$0.192153\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$	−19.5000	−	7.79423i	−0.622905	−	0.248978i
$981$		0			0
$982$	−7.50000	−	12.9904i	−0.239335	−	0.414540i
$983$	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
$985$	−3.00000			−0.0955879
$986$	−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
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	−0.950603	−	0.310409i	$-0.899534\pi$
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	0.744124	+	0.668042i	$0.232867\pi$
$992$	7.50000	+	12.9904i	0.238125	+	0.412445i
$993$		0			0
$994$	−32.5000	+	11.2583i	−1.03084	+	0.357093i
$995$	−30.0000	+	51.9615i	−0.951064	+	1.64729i
$996$		0			0
$997$	2.00000			0.0633406			0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000			0.0633406			0.0316703	+	0.999498i	$0.489917\pi$
$998$	−15.5000	+	26.8468i	−0.490644	+	0.849820i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.a.9.1	✓	2	39.35	odd	6
91.2.g.a.81.1	yes	2	21.11	odd	6
91.2.h.a.16.1	yes	2	3.2	odd	2
91.2.h.a.74.1	yes	2	273.74	odd	6
637.2.f.a.295.1		2	273.152	even	6
637.2.f.a.393.1		2	21.5	even	6
637.2.f.b.295.1		2	273.191	odd	6
637.2.f.b.393.1		2	21.2	odd	6
637.2.g.a.263.1		2	21.17	even	6
637.2.g.a.373.1		2	273.230	even	6
637.2.h.a.165.1		2	273.269	even	6
637.2.h.a.471.1		2	21.20	even	2
819.2.n.c.100.1		2	13.9	even	3
819.2.n.c.172.1		2	7.4	even	3
819.2.s.a.289.1		2	1.1	even	1	trivial
819.2.s.a.802.1		2	91.74	even	3	inner
1183.2.e.a.170.1		2	39.29	odd	6
1183.2.e.a.508.1		2	273.263	odd	6
1183.2.e.c.170.1		2	39.23	odd	6
1183.2.e.c.508.1		2	273.179	odd	6
8281.2.a.c.1.1		1	273.23	odd	6
8281.2.a.g.1.1		1	273.257	even	6
8281.2.a.i.1.1		1	273.107	odd	6
8281.2.a.j.1.1		1	273.68	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{16} +2.00000 q^{17} +(0.500000 + 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 - 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{25} +(1.00000 - 3.46410i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(3.50000 + 6.06218i) q^{29} +(-1.50000 - 2.59808i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(7.50000 - 2.59808i) q^{35} +2.00000 q^{37} +(-0.500000 - 0.866025i) q^{38} +(4.50000 - 7.79423i) q^{40} +(1.50000 + 2.59808i) q^{41} +(3.50000 - 6.06218i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{47} +(1.00000 + 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(1.00000 - 3.46410i) q^{52} +(1.50000 + 2.59808i) q^{53} +(4.50000 + 7.79423i) q^{55} +(6.00000 + 5.19615i) q^{56} +(-3.50000 - 6.06218i) q^{58} +4.00000 q^{59} +(6.50000 + 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +7.00000 q^{64} +(7.50000 + 7.79423i) q^{65} +(1.50000 - 2.59808i) q^{67} -2.00000 q^{68} +(-7.50000 + 2.59808i) q^{70} +(6.50000 - 11.2583i) q^{71} +(6.50000 + 11.2583i) q^{73} -2.00000 q^{74} +(-0.500000 - 0.866025i) q^{76} +(-7.50000 + 2.59808i) q^{77} +(1.50000 - 2.59808i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-1.50000 - 2.59808i) q^{82} +(3.00000 - 5.19615i) q^{85} +(-3.50000 + 6.06218i) q^{86} +(-4.50000 + 7.79423i) q^{88} -6.00000 q^{89} +(-8.00000 + 5.19615i) q^{91} +(-0.500000 + 0.866025i) q^{94} +3.00000 q^{95} +(2.50000 - 4.33013i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 2 q^{13} - 4 q^{14} - 2 q^{16} + 4 q^{17} + q^{19} - 3 q^{20} + 3 q^{22} - 4 q^{25} + 2 q^{26} - 4 q^{28} + 7 q^{29} - 3 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 2 * q^13 - 4 * q^14 - 2 * q^16 + 4 * q^17 + q^19 - 3 * q^20 + 3 * q^22 - 4 * q^25 + 2 * q^26 - 4 * q^28 + 7 * q^29 - 3 * q^31 - 10 * q^32 - 4 * q^34 + 15 * q^35 + 4 * q^37 - q^38 + 9 * q^40 + 3 * q^41 + 7 * q^43 + 3 * q^44 + q^47 + 2 * q^49 + 4 * q^50 + 2 * q^52 + 3 * q^53 + 9 * q^55 + 12 * q^56 - 7 * q^58 + 8 * q^59 + 13 * q^61 + 3 * q^62 + 14 * q^64 + 15 * q^65 + 3 * q^67 - 4 * q^68 - 15 * q^70 + 13 * q^71 + 13 * q^73 - 4 * q^74 - q^76 - 15 * q^77 + 3 * q^79 - 3 * q^80 - 3 * q^82 + 6 * q^85 - 7 * q^86 - 9 * q^88 - 12 * q^89 - 16 * q^91 - q^94 + 6 * q^95 + 5 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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