LMFDB - Embedded newform 595.2.x.a.16.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [595,2,Mod(16,595)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("595.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(595, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 595 = 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	595.x (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.75109892027$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	595.16
Dual form			595.2.x.a.186.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(1.73205 - 1.00000i) q^{11} +(-5.19615 - 3.00000i) q^{12} -2.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-1.13397 - 3.96410i) q^{17} +(2.00000 - 3.46410i) q^{19} -2.00000i q^{20} +(6.00000 + 5.19615i) q^{21} +(0.866025 + 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{25} +9.00000i q^{27} +(3.46410 - 4.00000i) q^{28} +(5.19615 - 3.00000i) q^{31} +(-3.00000 + 5.19615i) q^{33} +(-0.500000 + 2.59808i) q^{35} +12.0000 q^{36} +(4.33013 + 2.50000i) q^{37} +(5.19615 - 3.00000i) q^{39} +6.00000i q^{41} +12.0000 q^{43} +(3.46410 + 2.00000i) q^{44} +(-5.19615 + 3.00000i) q^{45} +(4.00000 - 6.92820i) q^{47} -12.0000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(8.89230 + 8.59808i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-4.00000 - 6.92820i) q^{53} -2.00000 q^{55} +12.0000i q^{57} +(-4.50000 - 7.79423i) q^{59} +(3.00000 + 5.19615i) q^{60} +(1.73205 + 1.00000i) q^{61} +(-15.5885 - 3.00000i) q^{63} -8.00000 q^{64} +(1.73205 + 1.00000i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(5.73205 - 5.92820i) q^{68} -3.00000 q^{69} -16.0000i q^{71} +(-11.2583 + 6.50000i) q^{73} +(-2.59808 - 1.50000i) q^{75} +8.00000 q^{76} +(-4.00000 - 3.46410i) q^{77} +(-6.92820 - 4.00000i) q^{79} +(3.46410 - 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +6.00000 q^{83} +(-3.00000 + 15.5885i) q^{84} +(-1.00000 + 4.00000i) q^{85} +(6.50000 - 11.2583i) q^{89} +(1.73205 + 5.00000i) q^{91} +2.00000i q^{92} +(-9.00000 + 15.5885i) q^{93} +(-3.46410 + 2.00000i) q^{95} -5.00000i q^{97} -12.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 12 q^{9} - 8 q^{13} + 12 q^{15} - 8 q^{16} - 8 q^{17} + 8 q^{19} + 24 q^{21} + 2 q^{25} - 12 q^{33} - 2 q^{35} + 48 q^{36} + 48 q^{43} + 16 q^{47} - 22 q^{49} - 6 q^{51} - 8 q^{52} - 16 q^{53}+ \cdots - 36 q^{93}+O(q^{100}) $ 4 * q + 4 * q^4 + 12 * q^9 - 8 * q^13 + 12 * q^15 - 8 * q^16 - 8 * q^17 + 8 * q^19 + 24 * q^21 + 2 * q^25 - 12 * q^33 - 2 * q^35 + 48 * q^36 + 48 * q^43 + 16 * q^47 - 22 * q^49 - 6 * q^51 - 8 * q^52 - 16 * q^53 - 8 * q^55 - 18 * q^59 + 12 * q^60 - 32 * q^64 - 4 * q^67 + 16 * q^68 - 12 * q^69 + 32 * q^76 - 16 * q^77 - 18 * q^81 + 24 * q^83 - 12 * q^84 - 4 * q^85 + 26 * q^89 - 36 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/595\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−1.00000			$\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$		0			0
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$		0			0
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$		0			0
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	−0.215615	−	0.976478i	$-0.569176\pi$
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	0.737848	+	0.674967i	$0.235842\pi$
$12$	−5.19615	−	3.00000i	−1.50000	−	0.866025i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−1.13397	−	3.96410i	−0.275029	−	0.961436i
$17$	−1.13397	−	3.96410i	−0.275029	−	0.961436i
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$		−	2.00000i		−	0.447214i
$21$	6.00000	+	5.19615i	1.30931	+	1.13389i
$22$		0			0
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	0.587565	−	0.809177i	$-0.300087\pi$
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	−0.406986	+	0.913434i	$0.633420\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$			9.00000i			1.73205i
$28$	3.46410	−	4.00000i	0.654654	−	0.755929i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	5.19615	−	3.00000i	0.933257	−	0.538816i	0.0454165	−	0.998968i	$-0.485539\pi$
$31$	5.19615	−	3.00000i	0.933257	−	0.538816i	0.887840	+	0.460152i	$0.152205\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$	−0.500000	+	2.59808i	−0.0845154	+	0.439155i
$36$	12.0000			2.00000
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	0.811752	−	0.584002i	$-0.198514\pi$
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	−0.0998840	+	0.994999i	$0.531847\pi$
$38$		0			0
$39$	5.19615	−	3.00000i	0.832050	−	0.480384i
$40$		0			0
$41$			6.00000i			0.937043i	0.883452	+	0.468521i	$0.155213\pi$
$41$			6.00000i			0.937043i	−0.883452	+	0.468521i	$0.844787\pi$
$42$		0			0
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$	3.46410	+	2.00000i	0.522233	+	0.301511i
$45$	−5.19615	+	3.00000i	−0.774597	+	0.447214i
$46$		0			0
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$		−	12.0000i		−	1.73205i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	8.89230	+	8.59808i	1.24517	+	1.20397i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	−0.998313	−	0.0580651i	$-0.981507\pi$
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	0.448871	−	0.893597i	$-0.351826\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$			12.0000i			1.58944i
$58$		0			0
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$	3.00000	+	5.19615i	0.387298	+	0.670820i
$61$	1.73205	+	1.00000i	0.221766	+	0.128037i	0.606768	−	0.794879i	$-0.292466\pi$
$61$	1.73205	+	1.00000i	0.221766	+	0.128037i	−0.385002	+	0.922916i	$0.625799\pi$
$62$		0			0
$63$	−15.5885	−	3.00000i	−1.96396	−	0.377964i
$64$	−8.00000			−1.00000
$65$	1.73205	+	1.00000i	0.214834	+	0.124035i
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	5.73205	−	5.92820i	0.695113	−	0.718900i
$69$	−3.00000			−0.361158
$70$		0			0
$71$		−	16.0000i		−	1.89885i	−0.313993	−	0.949425i	$-0.601667\pi$
$71$		−	16.0000i		−	1.89885i	0.313993	−	0.949425i	$-0.398333\pi$
$72$		0			0
$73$	−11.2583	+	6.50000i	−1.31769	+	0.760767i	−0.983356	−	0.181688i	$-0.941844\pi$
$73$	−11.2583	+	6.50000i	−1.31769	+	0.760767i	−0.334332	+	0.942455i	$0.608511\pi$
$74$		0			0
$75$	−2.59808	−	1.50000i	−0.300000	−	0.173205i
$76$	8.00000			0.917663
$77$	−4.00000	−	3.46410i	−0.455842	−	0.394771i
$78$		0			0
$79$	−6.92820	−	4.00000i	−0.779484	−	0.450035i	0.0567635	−	0.998388i	$-0.481922\pi$
$79$	−6.92820	−	4.00000i	−0.779484	−	0.450035i	−0.836247	+	0.548352i	$0.815255\pi$
$80$	3.46410	−	2.00000i	0.387298	−	0.223607i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−3.00000	+	15.5885i	−0.327327	+	1.70084i
$85$	−1.00000	+	4.00000i	−0.108465	+	0.433861i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	−0.283164	−	0.959072i	$-0.591384\pi$
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	0.972162	−	0.234309i	$-0.0752827\pi$
$90$		0			0
$91$	1.73205	+	5.00000i	0.181568	+	0.524142i
$92$			2.00000i			0.208514i
$93$	−9.00000	+	15.5885i	−0.933257	+	1.61645i
$94$		0			0
$95$	−3.46410	+	2.00000i	−0.355409	+	0.205196i
$96$		0			0
$97$		−	5.00000i		−	0.507673i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$		−	5.00000i		−	0.507673i	0.967247	−	0.253837i	$-0.0816925\pi$
$98$		0			0
$99$		−	12.0000i		−	1.20605i
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$		0			0
$105$	−2.59808	−	7.50000i	−0.253546	−	0.731925i
$106$		0			0
$107$	−2.59808	−	1.50000i	−0.251166	−	0.145010i	0.369132	−	0.929377i	$-0.379655\pi$
$107$	−2.59808	−	1.50000i	−0.251166	−	0.145010i	−0.620298	+	0.784366i	$0.712988\pi$
$108$	−15.5885	+	9.00000i	−1.50000	+	0.866025i
$109$	12.1244	−	7.00000i	1.16130	−	0.670478i	0.209687	−	0.977769i	$-0.432756\pi$
$109$	12.1244	−	7.00000i	1.16130	−	0.670478i	0.951616	+	0.307290i	$0.0994222\pi$
$110$		0			0
$111$	−15.0000			−1.42374
$112$	10.3923	+	2.00000i	0.981981	+	0.188982i
$113$		−	18.0000i		−	1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$		−	18.0000i		−	1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$		0			0
$115$	−0.500000	−	0.866025i	−0.0466252	−	0.0807573i
$116$		0			0
$117$	−6.00000	+	10.3923i	−0.554700	+	0.960769i
$118$		0			0
$119$	−8.92820	+	6.26795i	−0.818447	+	0.574582i
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		0			0
$123$	−9.00000	−	15.5885i	−0.811503	−	1.40556i
$124$	10.3923	+	6.00000i	0.933257	+	0.538816i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$		0			0
$129$	−31.1769	+	18.0000i	−2.74497	+	1.58481i
$130$		0			0
$131$	10.3923	+	6.00000i	0.907980	+	0.524222i	0.879781	−	0.475380i	$-0.157689\pi$
$131$	10.3923	+	6.00000i	0.907980	+	0.524222i	0.0281993	+	0.999602i	$0.491023\pi$
$132$	−12.0000			−1.04447
$133$	−10.3923	−	2.00000i	−0.901127	−	0.173422i
$134$		0			0
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$		−	2.00000i		−	0.169638i	−0.996396	−	0.0848189i	$-0.972969\pi$
$139$		−	2.00000i		−	0.169638i	0.996396	−	0.0848189i	$-0.0270312\pi$
$140$	−5.00000	+	1.73205i	−0.422577	+	0.146385i
$141$			24.0000i			2.02116i
$142$		0			0
$143$	−3.46410	+	2.00000i	−0.289683	+	0.167248i
$144$	12.0000	+	20.7846i	1.00000	+	1.73205i
$145$		0			0
$146$		0			0
$147$	7.79423	−	19.5000i	0.642857	−	1.60833i
$148$			10.0000i			0.821995i
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$		0			0
$153$	−24.0000	−	6.00000i	−1.94029	−	0.485071i
$154$		0			0
$155$	−6.00000			−0.481932
$156$	10.3923	+	6.00000i	0.832050	+	0.480384i
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.853646	+	0.520854i	$0.174386\pi$
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.0242497	+	0.999706i	$0.492280\pi$
$158$		0			0
$159$	20.7846	+	12.0000i	1.64833	+	0.951662i
$160$		0			0
$161$	0.500000	−	2.59808i	0.0394055	−	0.204757i
$162$		0			0
$163$	11.2583	+	6.50000i	0.881820	+	0.509119i	0.871258	−	0.490825i	$-0.163305\pi$
$163$	11.2583	+	6.50000i	0.881820	+	0.509119i	0.0105623	+	0.999944i	$0.496638\pi$
$164$	−10.3923	+	6.00000i	−0.811503	+	0.468521i
$165$	5.19615	−	3.00000i	0.404520	−	0.233550i
$166$		0			0
$167$		−	11.0000i		−	0.851206i	−0.904910	−	0.425603i	$-0.860062\pi$
$167$		−	11.0000i		−	0.851206i	0.904910	−	0.425603i	$-0.139938\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−12.0000	−	20.7846i	−0.917663	−	1.58944i
$172$	12.0000	+	20.7846i	0.914991	+	1.58481i
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$		0			0
$175$	1.73205	−	2.00000i	0.130931	−	0.151186i
$176$			8.00000i			0.603023i
$177$	23.3827	+	13.5000i	1.75755	+	1.01472i
$178$		0			0
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$	−10.3923	−	6.00000i	−0.774597	−	0.447214i
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$		0			0
$183$	−6.00000			−0.443533
$184$		0			0
$185$	−2.50000	−	4.33013i	−0.183804	−	0.318357i
$186$		0			0
$187$	−5.92820	−	5.73205i	−0.433513	−	0.419169i
$188$	16.0000			1.16692
$189$	22.5000	−	7.79423i	1.63663	−	0.566947i
$190$		0			0
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	20.7846	−	12.0000i	1.50000	−	0.866025i
$193$	5.19615	−	3.00000i	0.374027	−	0.215945i	−0.301189	−	0.953564i	$-0.597384\pi$
$193$	5.19615	−	3.00000i	0.374027	−	0.215945i	0.675216	+	0.737620i	$0.264050\pi$
$194$		0			0
$195$	−6.00000			−0.429669
$196$	−13.0000	−	5.19615i	−0.928571	−	0.371154i
$197$			7.00000i			0.498729i	0.968410	+	0.249365i	$0.0802218\pi$
$197$			7.00000i			0.498729i	−0.968410	+	0.249365i	$0.919778\pi$
$198$		0			0
$199$	13.8564	−	8.00000i	0.982255	−	0.567105i	0.0793045	−	0.996850i	$-0.474730\pi$
$199$	13.8564	−	8.00000i	0.982255	−	0.567105i	0.902950	+	0.429745i	$0.141397\pi$
$200$		0			0
$201$	5.19615	+	3.00000i	0.366508	+	0.211604i
$202$		0			0
$203$		0			0
$204$	−6.00000	+	24.0000i	−0.420084	+	1.68034i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$		0			0
$207$	5.19615	−	3.00000i	0.361158	−	0.208514i
$208$	4.00000	−	6.92820i	0.277350	−	0.480384i
$209$		−	8.00000i		−	0.553372i
$210$		0			0
$211$			2.00000i			0.137686i	0.997628	+	0.0688428i	$0.0219307\pi$
$211$			2.00000i			0.137686i	−0.997628	+	0.0688428i	$0.978069\pi$
$212$	8.00000	−	13.8564i	0.549442	−	0.951662i
$213$	24.0000	+	41.5692i	1.64445	+	2.84828i
$214$		0			0
$215$	−10.3923	−	6.00000i	−0.708749	−	0.409197i
$216$		0			0
$217$	−12.0000	−	10.3923i	−0.814613	−	0.705476i
$218$		0			0
$219$	19.5000	−	33.7750i	1.31769	−	2.28230i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	2.26795	+	7.92820i	0.152559	+	0.533309i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$		0			0
$227$	9.52628	−	5.50000i	0.632281	−	0.365048i	−0.149354	−	0.988784i	$-0.547719\pi$
$227$	9.52628	−	5.50000i	0.632281	−	0.365048i	0.781635	+	0.623736i	$0.214386\pi$
$228$	−20.7846	+	12.0000i	−1.37649	+	0.794719i
$229$	−9.50000	+	16.4545i	−0.627778	+	1.08734i	0.360219	+	0.932868i	$0.382702\pi$
$229$	−9.50000	+	16.4545i	−0.627778	+	1.08734i	−0.987997	+	0.154475i	$0.950631\pi$
$230$		0			0
$231$	15.5885	+	3.00000i	1.02565	+	0.197386i
$232$		0			0
$233$	−18.1865	−	10.5000i	−1.19144	−	0.687878i	−0.232806	−	0.972523i	$-0.574791\pi$
$233$	−18.1865	−	10.5000i	−1.19144	−	0.687878i	−0.958633	+	0.284645i	$0.908124\pi$
$234$		0			0
$235$	−6.92820	+	4.00000i	−0.451946	+	0.260931i
$236$	9.00000	−	15.5885i	0.585850	−	1.01472i
$237$	24.0000			1.55897
$238$		0			0
$239$	−11.0000			−0.711531			−0.355765	−	0.934575i	$-0.615780\pi$
$239$	−11.0000			−0.711531			−0.355765	+	0.934575i	$0.615780\pi$
$240$	−6.00000	+	10.3923i	−0.387298	+	0.670820i
$241$	−13.8564	+	8.00000i	−0.892570	+	0.515325i	−0.874782	−	0.484516i	$-0.838996\pi$
$241$	−13.8564	+	8.00000i	−0.892570	+	0.515325i	−0.0177875	+	0.999842i	$0.505662\pi$
$242$		0			0
$243$		0			0
$244$			4.00000i			0.256074i
$245$	6.92820	−	1.00000i	0.442627	−	0.0638877i
$246$		0			0
$247$	−4.00000	+	6.92820i	−0.254514	+	0.440831i
$248$		0			0
$249$	−15.5885	+	9.00000i	−0.987878	+	0.570352i
$250$		0			0
$251$	−17.0000			−1.07303			−0.536515	−	0.843891i	$-0.680260\pi$
$251$	−17.0000			−1.07303			−0.536515	+	0.843891i	$0.680260\pi$
$252$	−10.3923	−	30.0000i	−0.654654	−	1.88982i
$253$	2.00000			0.125739
$254$		0			0
$255$	−3.40192	−	11.8923i	−0.213037	−	0.744725i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$		0			0
$259$	2.50000	−	12.9904i	0.155342	−	0.807183i
$260$			4.00000i			0.248069i
$261$		0			0
$262$		0			0
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$		0			0
$265$			8.00000i			0.491436i
$266$		0			0
$267$			39.0000i			2.38676i
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−5.19615	+	3.00000i	−0.316815	+	0.182913i	−0.649972	−	0.759958i	$-0.725219\pi$
$269$	−5.19615	+	3.00000i	−0.316815	+	0.182913i	0.333157	+	0.942871i	$0.391886\pi$
$270$		0			0
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$	16.0000	+	4.00000i	0.970143	+	0.242536i
$273$	−12.0000	−	10.3923i	−0.726273	−	0.628971i
$274$		0			0
$275$	1.73205	+	1.00000i	0.104447	+	0.0603023i
$276$	−3.00000	−	5.19615i	−0.180579	−	0.312772i
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.947604	−	0.319447i	$-0.896503\pi$
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.197153	+	0.980373i	$0.563170\pi$
$278$		0			0
$279$		−	36.0000i		−	2.15526i
$280$		0			0
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$		0			0
$283$	16.4545	−	9.50000i	0.978117	−	0.564716i	0.0764162	−	0.997076i	$-0.475652\pi$
$283$	16.4545	−	9.50000i	0.978117	−	0.564716i	0.901701	+	0.432360i	$0.142319\pi$
$284$	27.7128	−	16.0000i	1.64445	−	0.949425i
$285$	6.00000	−	10.3923i	0.355409	−	0.615587i
$286$		0			0
$287$	15.0000	−	5.19615i	0.885422	−	0.306719i
$288$		0			0
$289$	−14.4282	+	8.99038i	−0.848718	+	0.528846i
$290$		0			0
$291$	7.50000	+	12.9904i	0.439658	+	0.761510i
$292$	−22.5167	−	13.0000i	−1.31769	−	0.760767i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$		0			0
$295$			9.00000i			0.524000i
$296$		0			0
$297$	9.00000	+	15.5885i	0.522233	+	0.904534i
$298$		0			0
$299$	−1.73205	−	1.00000i	−0.100167	−	0.0578315i
$300$		−	6.00000i		−	0.346410i
$301$	−10.3923	−	30.0000i	−0.599002	−	1.72917i
$302$		0			0
$303$	−15.5885	−	9.00000i	−0.895533	−	0.517036i
$304$	8.00000	+	13.8564i	0.458831	+	0.794719i
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$	2.00000	−	10.3923i	0.113961	−	0.592157i
$309$		−	42.0000i		−	2.38930i
$310$		0			0
$311$	−27.7128	+	16.0000i	−1.57145	+	0.907277i	−0.575458	+	0.817832i	$0.695176\pi$
$311$	−27.7128	+	16.0000i	−1.57145	+	0.907277i	−0.995992	+	0.0894452i	$0.971491\pi$
$312$		0			0
$313$	5.19615	+	3.00000i	0.293704	+	0.169570i	0.639611	−	0.768699i	$-0.279095\pi$
$313$	5.19615	+	3.00000i	0.293704	+	0.169570i	−0.345907	+	0.938269i	$0.612429\pi$
$314$		0			0
$315$	12.0000	+	10.3923i	0.676123	+	0.585540i
$316$		−	16.0000i		−	0.900070i
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$		0			0
$319$		0			0
$320$	6.92820	+	4.00000i	0.387298	+	0.223607i
$321$	9.00000			0.502331
$322$		0			0
$323$	−16.0000	−	4.00000i	−0.890264	−	0.222566i
$324$	9.00000	−	15.5885i	0.500000	−	0.866025i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$		0			0
$327$	−21.0000	+	36.3731i	−1.16130	+	2.01144i
$328$		0			0
$329$	−20.7846	−	4.00000i	−1.14589	−	0.220527i
$330$		0			0
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	25.9808	−	15.0000i	1.42374	−	0.821995i
$334$		0			0
$335$			2.00000i			0.109272i
$336$	−30.0000	+	10.3923i	−1.63663	+	0.566947i
$337$			27.0000i			1.47078i	0.677642	+	0.735392i	$0.263002\pi$
$337$			27.0000i			1.47078i	−0.677642	+	0.735392i	$0.736998\pi$
$338$		0			0
$339$	27.0000	+	46.7654i	1.46644	+	2.53995i
$340$	−7.92820	+	2.26795i	−0.429967	+	0.122997i
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$	2.59808	+	1.50000i	0.139876	+	0.0807573i
$346$		0			0
$347$	−19.9186	+	11.5000i	−1.06929	+	0.617352i	−0.927986	−	0.372615i	$-0.878461\pi$
$347$	−19.9186	+	11.5000i	−1.06929	+	0.617352i	−0.141299	+	0.989967i	$0.545128\pi$
$348$		0			0
$349$	−15.0000			−0.802932			−0.401466	−	0.915874i	$-0.631499\pi$
$349$	−15.0000			−0.802932			−0.401466	+	0.915874i	$0.631499\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$		0			0
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	−8.00000	+	13.8564i	−0.424596	+	0.735422i
$356$	26.0000			1.37800
$357$	13.7942	−	29.6769i	0.730068	−	1.57067i
$358$		0			0
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	−0.902891	−	0.429870i	$-0.858559\pi$
$359$	−1.50000	+	2.59808i	−0.0791670	+	0.137121i	0.823724	+	0.566991i	$0.191893\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$		−	21.0000i		−	1.10221i
$364$	−6.92820	+	8.00000i	−0.363137	+	0.419314i
$365$	13.0000			0.680451
$366$		0			0
$367$	−20.7846	+	12.0000i	−1.08495	+	0.626395i	−0.932227	−	0.361874i	$-0.882137\pi$
$367$	−20.7846	+	12.0000i	−1.08495	+	0.626395i	−0.152721	+	0.988269i	$0.548804\pi$
$368$	−3.46410	+	2.00000i	−0.180579	+	0.104257i
$369$	31.1769	+	18.0000i	1.62301	+	0.937043i
$370$		0			0
$371$	−13.8564	+	16.0000i	−0.719389	+	0.830679i
$372$	−36.0000			−1.86651
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	−0.838975	−	0.544170i	$-0.816844\pi$
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	0.890753	+	0.454488i	$0.150178\pi$
$374$		0			0
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	10.0000i		−	0.513665i	−0.966456	−	0.256833i	$-0.917321\pi$
$379$		−	10.0000i		−	0.513665i	0.966456	−	0.256833i	$-0.0826790\pi$
$380$	−6.92820	−	4.00000i	−0.355409	−	0.205196i
$381$	−10.3923	+	6.00000i	−0.532414	+	0.307389i
$382$		0			0
$383$	17.0000	−	29.4449i	0.868659	−	1.50456i	0.00529229	−	0.999986i	$-0.498315\pi$
$383$	17.0000	−	29.4449i	0.868659	−	1.50456i	0.863367	−	0.504576i	$-0.168351\pi$
$384$		0			0
$385$	1.73205	+	5.00000i	0.0882735	+	0.254824i
$386$		0			0
$387$	36.0000	−	62.3538i	1.82998	−	3.16962i
$388$	8.66025	−	5.00000i	0.439658	−	0.253837i
$389$	−18.5000	−	32.0429i	−0.937987	−	1.62464i	−0.769218	−	0.638986i	$-0.779354\pi$
$389$	−18.5000	−	32.0429i	−0.937987	−	1.62464i	−0.168769	−	0.985656i	$-0.553979\pi$
$390$		0			0
$391$	1.00000	−	4.00000i	0.0505722	−	0.202289i
$392$		0			0
$393$	−36.0000			−1.81596
$394$		0			0
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	20.7846	−	12.0000i	1.04447	−	0.603023i
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	0.542834	−	0.839840i	$-0.317351\pi$
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	−0.455905	+	0.890028i	$0.650684\pi$
$398$		0			0
$399$	30.0000	−	10.3923i	1.50188	−	0.520266i
$400$	−4.00000			−0.200000
$401$	24.2487	+	14.0000i	1.21092	+	0.699127i	0.962960	−	0.269643i	$-0.0869057\pi$
$401$	24.2487	+	14.0000i	1.21092	+	0.699127i	0.247962	+	0.968770i	$0.420239\pi$
$402$		0			0
$403$	−10.3923	+	6.00000i	−0.517678	+	0.298881i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$			9.00000i			0.447214i
$406$		0			0
$407$	10.0000			0.495682
$408$		0			0
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$		0			0
$411$	31.1769	+	18.0000i	1.53784	+	0.887875i
$412$	−28.0000			−1.37946
$413$	−15.5885	+	18.0000i	−0.767058	+	0.885722i
$414$		0			0
$415$	−5.19615	−	3.00000i	−0.255069	−	0.147264i
$416$		0			0
$417$	3.00000	+	5.19615i	0.146911	+	0.254457i
$418$		0			0
$419$			30.0000i			1.46560i	0.680446	+	0.732798i	$0.261786\pi$
$419$			30.0000i			1.46560i	−0.680446	+	0.732798i	$0.738214\pi$
$420$	10.3923	−	12.0000i	0.507093	−	0.585540i
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$		0			0
$423$	−24.0000	−	41.5692i	−1.16692	−	2.02116i
$424$		0			0
$425$	2.86603	−	2.96410i	0.139023	−	0.143780i
$426$		0			0
$427$	1.00000	−	5.19615i	0.0483934	−	0.251459i
$428$		−	6.00000i		−	0.290021i
$429$	6.00000	−	10.3923i	0.289683	−	0.501745i
$430$		0			0
$431$	24.2487	−	14.0000i	1.16802	−	0.674356i	0.214807	−	0.976657i	$-0.431088\pi$
$431$	24.2487	−	14.0000i	1.16802	−	0.674356i	0.953213	+	0.302300i	$0.0977546\pi$
$432$	−31.1769	−	18.0000i	−1.50000	−	0.866025i
$433$	36.0000			1.73005			0.865025	−	0.501729i	$-0.167303\pi$
$433$	36.0000			1.73005			0.865025	+	0.501729i	$0.167303\pi$
$434$		0			0
$435$		0			0
$436$	24.2487	+	14.0000i	1.16130	+	0.670478i
$437$	3.46410	−	2.00000i	0.165710	−	0.0956730i
$438$		0			0
$439$	19.0526	+	11.0000i	0.909329	+	0.525001i	0.880215	−	0.474575i	$-0.157398\pi$
$439$	19.0526	+	11.0000i	0.909329	+	0.525001i	0.0291138	+	0.999576i	$0.490731\pi$
$440$		0			0
$441$	6.00000	+	41.5692i	0.285714	+	1.97949i
$442$		0			0
$443$	−7.00000	+	12.1244i	−0.332580	+	0.576046i	−0.983017	−	0.183515i	$-0.941252\pi$
$443$	−7.00000	+	12.1244i	−0.332580	+	0.576046i	0.650437	+	0.759560i	$0.274586\pi$
$444$	−15.0000	−	25.9808i	−0.711868	−	1.23299i
$445$	−11.2583	+	6.50000i	−0.533696	+	0.308130i
$446$		0			0
$447$		−	9.00000i		−	0.425685i
$448$	6.92820	+	20.0000i	0.327327	+	0.944911i
$449$		−	6.00000i		−	0.283158i	−0.989927	−	0.141579i	$-0.954782\pi$
$449$		−	6.00000i		−	0.283158i	0.989927	−	0.141579i	$-0.0452178\pi$
$450$		0			0
$451$	6.00000	+	10.3923i	0.282529	+	0.489355i
$452$	31.1769	−	18.0000i	1.46644	−	0.846649i
$453$	41.5692	+	24.0000i	1.95309	+	1.12762i
$454$		0			0
$455$	1.00000	−	5.19615i	0.0468807	−	0.243599i
$456$		0			0
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.0474665	+	0.998873i	$0.515115\pi$
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.841316	+	0.540544i	$0.818219\pi$
$458$		0			0
$459$	35.6769	−	10.2058i	1.66526	−	0.476365i
$460$	1.00000	−	1.73205i	0.0466252	−	0.0807573i
$461$	15.0000			0.698620			0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000			0.698620			0.349310	+	0.937007i	$0.386416\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$	15.5885	−	9.00000i	0.722897	−	0.417365i
$466$		0			0
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	−0.579111	−	0.815249i	$-0.696600\pi$
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	0.995582	+	0.0939008i	$0.0299336\pi$
$468$	−24.0000			−1.10940
$469$	−3.46410	+	4.00000i	−0.159957	+	0.184703i
$470$		0			0
$471$	−57.1577	−	33.0000i	−2.63369	−	1.52056i
$472$		0			0
$473$	20.7846	−	12.0000i	0.955677	−	0.551761i
$474$		0			0
$475$	4.00000			0.183533
$476$	−19.7846	−	9.19615i	−0.906826	−	0.421505i
$477$	−48.0000			−2.19777
$478$		0			0
$479$	−27.7128	+	16.0000i	−1.26623	+	0.731059i	−0.974273	−	0.225372i	$-0.927640\pi$
$479$	−27.7128	+	16.0000i	−1.26623	+	0.731059i	−0.291958	+	0.956431i	$0.594307\pi$
$480$		0			0
$481$	−8.66025	−	5.00000i	−0.394874	−	0.227980i
$482$		0			0
$483$	2.59808	+	7.50000i	0.118217	+	0.341262i
$484$	−14.0000			−0.636364
$485$	−2.50000	+	4.33013i	−0.113519	+	0.196621i
$486$		0			0
$487$	−23.3827	+	13.5000i	−1.05957	+	0.611743i	−0.925313	−	0.379203i	$-0.876198\pi$
$487$	−23.3827	+	13.5000i	−1.05957	+	0.611743i	−0.134257	+	0.990947i	$0.542865\pi$
$488$		0			0
$489$	−39.0000			−1.76364
$490$		0			0
$491$	−5.00000			−0.225647			−0.112823	−	0.993615i	$-0.535989\pi$
$491$	−5.00000			−0.225647			−0.112823	+	0.993615i	$0.535989\pi$
$492$	18.0000	−	31.1769i	0.811503	−	1.40556i
$493$		0			0
$494$		0			0
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$			24.0000i			1.07763i
$497$	−40.0000	+	13.8564i	−1.79425	+	0.621545i
$498$		0			0
$499$	13.8564	+	8.00000i	0.620298	+	0.358129i	0.776985	−	0.629519i	$-0.216748\pi$
$499$	13.8564	+	8.00000i	0.620298	+	0.358129i	−0.156687	+	0.987648i	$0.550081\pi$
$500$	1.73205	−	1.00000i	0.0774597	−	0.0447214i
$501$	16.5000	+	28.5788i	0.737166	+	1.27681i
$502$		0			0
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$		−	6.00000i		−	0.266996i
$506$		0			0
$507$	23.3827	−	13.5000i	1.03846	−	0.599556i
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	−12.5000	+	21.6506i	−0.554053	+	0.959648i	0.443924	+	0.896065i	$0.353586\pi$
$509$	−12.5000	+	21.6506i	−0.554053	+	0.959648i	−0.997977	+	0.0635830i	$0.979747\pi$
$510$		0			0
$511$	26.0000	+	22.5167i	1.15017	+	0.996078i
$512$		0			0
$513$	31.1769	+	18.0000i	1.37649	+	0.794719i
$514$		0			0
$515$	12.1244	−	7.00000i	0.534263	−	0.308457i
$516$	−62.3538	−	36.0000i	−2.74497	−	1.58481i
$517$		−	16.0000i		−	0.703679i
$518$		0			0
$519$	18.0000			0.790112
$520$		0			0
$521$	1.73205	−	1.00000i	0.0758825	−	0.0438108i	−0.461579	−	0.887099i	$-0.652717\pi$
$521$	1.73205	−	1.00000i	0.0758825	−	0.0438108i	0.537461	+	0.843288i	$0.319383\pi$
$522$		0			0
$523$	19.0000	−	32.9090i	0.830812	−	1.43901i	−0.0665832	−	0.997781i	$-0.521210\pi$
$523$	19.0000	−	32.9090i	0.830812	−	1.43901i	0.897395	−	0.441228i	$-0.145457\pi$
$524$			24.0000i			1.04844i
$525$	−1.50000	+	7.79423i	−0.0654654	+	0.340168i
$526$		0			0
$527$	−17.7846	−	17.1962i	−0.774710	−	0.749076i
$528$	−12.0000	−	20.7846i	−0.522233	−	0.904534i
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	−54.0000			−2.34340
$532$	−6.92820	−	20.0000i	−0.300376	−	0.867110i
$533$		−	12.0000i		−	0.519778i
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$		0			0
$537$	−23.3827	−	13.5000i	−1.00904	−	0.582568i
$538$		0			0
$539$	−5.19615	+	13.0000i	−0.223814	+	0.559950i
$540$	18.0000			0.774597
$541$	−6.92820	−	4.00000i	−0.297867	−	0.171973i	0.343617	−	0.939110i	$-0.388348\pi$
$541$	−6.92820	−	4.00000i	−0.297867	−	0.171973i	−0.641484	+	0.767136i	$0.721681\pi$
$542$		0			0
$543$	30.0000	+	51.9615i	1.28742	+	2.22988i
$544$		0			0
$545$	−14.0000			−0.599694
$546$		0			0
$547$			15.0000i			0.641354i	0.947189	+	0.320677i	$0.103910\pi$
$547$			15.0000i			0.641354i	−0.947189	+	0.320677i	$0.896090\pi$
$548$	12.0000	−	20.7846i	0.512615	−	0.887875i
$549$	10.3923	−	6.00000i	0.443533	−	0.256074i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−4.00000	+	20.7846i	−0.170097	+	0.883852i
$554$		0			0
$555$	12.9904	+	7.50000i	0.551411	+	0.318357i
$556$	3.46410	−	2.00000i	0.146911	−	0.0848189i
$557$	−18.0000	−	31.1769i	−0.762684	−	1.32101i	−0.941462	−	0.337119i	$-0.890548\pi$
$557$	−18.0000	−	31.1769i	−0.762684	−	1.32101i	0.178778	−	0.983890i	$-0.442786\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$	−8.00000	−	6.92820i	−0.338062	−	0.292770i
$561$	24.0000	+	6.00000i	1.01328	+	0.253320i
$562$		0			0
$563$	−5.00000	−	8.66025i	−0.210725	−	0.364986i	0.741217	−	0.671266i	$-0.234249\pi$
$563$	−5.00000	−	8.66025i	−0.210725	−	0.364986i	−0.951942	+	0.306280i	$0.900916\pi$
$564$	−41.5692	+	24.0000i	−1.75038	+	1.01058i
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$		0			0
$567$	−15.5885	+	18.0000i	−0.654654	+	0.755929i
$568$		0			0
$569$	−23.0000	+	39.8372i	−0.964210	+	1.67006i	−0.252488	+	0.967600i	$0.581249\pi$
$569$	−23.0000	+	39.8372i	−0.964210	+	1.67006i	−0.711722	+	0.702461i	$0.752085\pi$
$570$		0			0
$571$	−13.8564	+	8.00000i	−0.579873	+	0.334790i	−0.761083	−	0.648655i	$-0.775332\pi$
$571$	−13.8564	+	8.00000i	−0.579873	+	0.334790i	0.181210	+	0.983444i	$0.441999\pi$
$572$	−6.92820	−	4.00000i	−0.289683	−	0.167248i
$573$			24.0000i			1.00261i
$574$		0			0
$575$			1.00000i			0.0417029i
$576$	−24.0000	+	41.5692i	−1.00000	+	1.73205i
$577$	−6.00000	−	10.3923i	−0.249783	−	0.432637i	0.713682	−	0.700470i	$-0.247026\pi$
$577$	−6.00000	−	10.3923i	−0.249783	−	0.432637i	−0.963466	+	0.267832i	$0.913693\pi$
$578$		0			0
$579$	−9.00000	+	15.5885i	−0.374027	+	0.647834i
$580$		0			0
$581$	−5.19615	−	15.0000i	−0.215573	−	0.622305i
$582$		0			0
$583$	−13.8564	−	8.00000i	−0.573874	−	0.331326i
$584$		0			0
$585$	10.3923	−	6.00000i	0.429669	−	0.248069i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	41.5692	−	6.00000i	1.71429	−	0.247436i
$589$		−	24.0000i		−	0.988903i
$590$		0			0
$591$	−10.5000	−	18.1865i	−0.431912	−	0.748094i
$592$	−17.3205	+	10.0000i	−0.711868	+	0.410997i
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	0.374236	+	0.927333i	$0.377905\pi$
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	−0.990212	+	0.139569i	$0.955428\pi$
$594$		0			0
$595$	10.8660	−	0.964102i	0.445464	−	0.0395243i
$596$	−6.00000			−0.245770
$597$	−24.0000	+	41.5692i	−0.982255	+	1.70131i
$598$		0			0
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	−0.921723	−	0.387849i	$-0.873218\pi$
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	0.124975	−	0.992160i	$-0.460115\pi$
$600$		0			0
$601$		−	44.0000i		−	1.79480i	−0.441221	−	0.897399i	$-0.645454\pi$
$601$		−	44.0000i		−	1.79480i	0.441221	−	0.897399i	$-0.354546\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	16.0000	−	27.7128i	0.651031	−	1.12762i
$605$	6.06218	−	3.50000i	0.246463	−	0.142295i
$606$		0			0
$607$	4.33013	+	2.50000i	0.175754	+	0.101472i	0.585296	−	0.810819i	$-0.300978\pi$
$607$	4.33013	+	2.50000i	0.175754	+	0.101472i	−0.409542	+	0.912291i	$0.634311\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.00000	+	13.8564i	−0.323645	+	0.560570i
$612$	−13.6077	−	47.5692i	−0.550058	−	1.92287i
$613$	−12.0000	−	20.7846i	−0.484675	−	0.839482i	0.515170	−	0.857088i	$-0.327729\pi$
$613$	−12.0000	−	20.7846i	−0.484675	−	0.839482i	−0.999845	+	0.0176058i	$0.994396\pi$
$614$		0			0
$615$			18.0000i			0.725830i
$616$		0			0
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$		0			0
$619$	6.92820	−	4.00000i	0.278468	−	0.160774i	−0.354262	−	0.935146i	$-0.615268\pi$
$619$	6.92820	−	4.00000i	0.278468	−	0.160774i	0.632730	+	0.774373i	$0.281934\pi$
$620$	−6.00000	−	10.3923i	−0.240966	−	0.417365i
$621$	−4.50000	+	7.79423i	−0.180579	+	0.312772i
$622$		0			0
$623$	−33.7750	−	6.50000i	−1.35317	−	0.260417i
$624$			24.0000i			0.960769i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	12.0000	+	20.7846i	0.479234	+	0.830057i
$628$	−22.0000	+	38.1051i	−0.877896	+	1.52056i
$629$	5.00000	−	20.0000i	0.199363	−	0.797452i
$630$		0			0
$631$	23.0000			0.915616			0.457808	−	0.889051i	$-0.348635\pi$
$631$	23.0000			0.915616			0.457808	+	0.889051i	$0.348635\pi$
$632$		0			0
$633$	−3.00000	−	5.19615i	−0.119239	−	0.206529i
$634$		0			0
$635$	−3.46410	−	2.00000i	−0.137469	−	0.0793676i
$636$			48.0000i			1.90332i
$637$	11.0000	−	8.66025i	0.435836	−	0.343132i
$638$		0			0
$639$	−83.1384	−	48.0000i	−3.28891	−	1.89885i
$640$		0			0
$641$	−13.8564	+	8.00000i	−0.547295	+	0.315981i	−0.748030	−	0.663665i	$-0.769000\pi$
$641$	−13.8564	+	8.00000i	−0.547295	+	0.315981i	0.200735	+	0.979646i	$0.435667\pi$
$642$		0			0
$643$			31.0000i			1.22252i	0.791430	+	0.611260i	$0.209337\pi$
$643$			31.0000i			1.22252i	−0.791430	+	0.611260i	$0.790663\pi$
$644$	5.00000	−	1.73205i	0.197028	−	0.0682524i
$645$	36.0000			1.41750
$646$		0			0
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$		0			0
$649$	−15.5885	−	9.00000i	−0.611900	−	0.353281i
$650$		0			0
$651$	46.7654	+	9.00000i	1.83288	+	0.352738i
$652$			26.0000i			1.01824i
$653$	29.4449	+	17.0000i	1.15227	+	0.665261i	0.949439	−	0.313953i	$-0.101653\pi$
$653$	29.4449	+	17.0000i	1.15227	+	0.665261i	0.202828	+	0.979214i	$0.434987\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$	−20.7846	−	12.0000i	−0.811503	−	0.468521i
$657$			78.0000i			3.04307i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$	10.3923	+	6.00000i	0.404520	+	0.233550i
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	0.926030	−	0.377450i	$-0.123199\pi$
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	−0.789896	+	0.613241i	$0.789865\pi$
$662$		0			0
$663$	−17.7846	−	17.1962i	−0.690697	−	0.667843i
$664$		0			0
$665$	8.00000	+	6.92820i	0.310227	+	0.268664i
$666$		0			0
$667$		0			0
$668$	19.0526	−	11.0000i	0.737166	−	0.425603i
$669$	−10.3923	+	6.00000i	−0.401790	+	0.231973i
$670$		0			0
$671$	4.00000			0.154418
$672$		0			0
$673$		−	29.0000i		−	1.11787i	−0.829212	−	0.558934i	$-0.811211\pi$
$673$		−	29.0000i		−	1.11787i	0.829212	−	0.558934i	$-0.188789\pi$
$674$		0			0
$675$	−7.79423	+	4.50000i	−0.300000	+	0.173205i
$676$	−9.00000	−	15.5885i	−0.346154	−	0.599556i
$677$	12.9904	+	7.50000i	0.499261	+	0.288248i	0.728408	−	0.685143i	$-0.240260\pi$
$677$	12.9904	+	7.50000i	0.499261	+	0.288248i	−0.229147	+	0.973392i	$0.573594\pi$
$678$		0			0
$679$	−12.5000	+	4.33013i	−0.479706	+	0.166175i
$680$		0			0
$681$	−16.5000	+	28.5788i	−0.632281	+	1.09514i
$682$		0			0
$683$	−2.59808	+	1.50000i	−0.0994126	+	0.0573959i	−0.548882	−	0.835900i	$-0.684946\pi$
$683$	−2.59808	+	1.50000i	−0.0994126	+	0.0573959i	0.449469	+	0.893296i	$0.351613\pi$
$684$	24.0000	−	41.5692i	0.917663	−	1.58944i
$685$			12.0000i			0.458496i
$686$		0			0
$687$		−	57.0000i		−	2.17469i
$688$	−24.0000	+	41.5692i	−0.914991	+	1.58481i
$689$	8.00000	+	13.8564i	0.304776	+	0.527887i
$690$		0			0
$691$	−17.3205	−	10.0000i	−0.658903	−	0.380418i	0.132956	−	0.991122i	$-0.457553\pi$
$691$	−17.3205	−	10.0000i	−0.658903	−	0.380418i	−0.791859	+	0.610704i	$0.790887\pi$
$692$		−	12.0000i		−	0.456172i
$693$	−30.0000	+	10.3923i	−1.13961	+	0.394771i
$694$		0			0
$695$	−1.00000	+	1.73205i	−0.0379322	+	0.0657004i
$696$		0			0
$697$	23.7846	−	6.80385i	0.900906	−	0.257714i
$698$		0			0
$699$	63.0000			2.38288
$700$	5.19615	+	1.00000i	0.196396	+	0.0377964i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	17.3205	−	10.0000i	0.653255	−	0.377157i
$704$	−13.8564	+	8.00000i	−0.522233	+	0.301511i
$705$	12.0000	−	20.7846i	0.451946	−	0.782794i
$706$		0			0
$707$	10.3923	−	12.0000i	0.390843	−	0.451306i
$708$			54.0000i			2.02944i
$709$	32.9090	+	19.0000i	1.23592	+	0.713560i	0.968258	−	0.249952i	$-0.0804150\pi$
$709$	32.9090	+	19.0000i	1.23592	+	0.713560i	0.267664	+	0.963512i	$0.413748\pi$
$710$		0			0
$711$	−41.5692	+	24.0000i	−1.55897	+	0.900070i
$712$		0			0
$713$	6.00000			0.224702
$714$		0			0
$715$	4.00000			0.149592
$716$	−9.00000	+	15.5885i	−0.336346	+	0.582568i
$717$	28.5788	−	16.5000i	1.06730	−	0.616204i
$718$		0			0
$719$	−17.3205	−	10.0000i	−0.645946	−	0.372937i	0.140955	−	0.990016i	$-0.454983\pi$
$719$	−17.3205	−	10.0000i	−0.645946	−	0.372937i	−0.786901	+	0.617079i	$0.788316\pi$
$720$		−	24.0000i		−	0.894427i
$721$	36.3731	+	7.00000i	1.35460	+	0.260694i
$722$		0			0
$723$	24.0000	−	41.5692i	0.892570	−	1.54598i
$724$	34.6410	−	20.0000i	1.28742	−	0.743294i
$725$		0			0
$726$		0			0
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−13.6077	−	47.5692i	−0.503299	−	1.75941i
$732$	−6.00000	−	10.3923i	−0.221766	−	0.384111i
$733$	26.0000	−	45.0333i	0.960332	−	1.66334i	0.238667	−	0.971102i	$-0.423290\pi$
$733$	26.0000	−	45.0333i	0.960332	−	1.66334i	0.721665	−	0.692242i	$-0.243377\pi$
$734$		0			0
$735$	−16.5000	+	12.9904i	−0.608612	+	0.479157i
$736$		0			0
$737$	−3.46410	−	2.00000i	−0.127602	−	0.0736709i
$738$		0			0
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	0.996235	−	0.0866983i	$-0.0276316\pi$
$739$	11.5000	+	19.9186i	0.423034	+	0.732717i	−0.573200	+	0.819415i	$0.694298\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$		−	24.0000i		−	0.881662i
$742$		0			0
$743$		−	9.00000i		−	0.330178i	−0.986279	−	0.165089i	$-0.947209\pi$
$743$		−	9.00000i		−	0.330178i	0.986279	−	0.165089i	$-0.0527911\pi$
$744$		0			0
$745$	2.59808	−	1.50000i	0.0951861	−	0.0549557i
$746$		0			0
$747$	18.0000	−	31.1769i	0.658586	−	1.14070i
$748$	4.00000	−	16.0000i	0.146254	−	0.585018i
$749$	−1.50000	+	7.79423i	−0.0548088	+	0.284795i
$750$		0			0
$751$	−1.73205	−	1.00000i	−0.0632034	−	0.0364905i	0.468065	−	0.883694i	$-0.344951\pi$
$751$	−1.73205	−	1.00000i	−0.0632034	−	0.0364905i	−0.531269	+	0.847203i	$0.678285\pi$
$752$	16.0000	+	27.7128i	0.583460	+	1.01058i
$753$	44.1673	−	25.5000i	1.60955	−	0.929272i
$754$		0			0
$755$			16.0000i			0.582300i
$756$	36.0000	+	31.1769i	1.30931	+	1.13389i
$757$	−8.00000			−0.290765			−0.145382	−	0.989376i	$-0.546441\pi$
$757$	−8.00000			−0.290765			−0.145382	+	0.989376i	$0.546441\pi$
$758$		0			0
$759$	−5.19615	+	3.00000i	−0.188608	+	0.108893i
$760$		0			0
$761$	9.50000	−	16.4545i	0.344375	−	0.596475i	−0.640865	−	0.767653i	$-0.721424\pi$
$761$	9.50000	−	16.4545i	0.344375	−	0.596475i	0.985240	+	0.171179i	$0.0547576\pi$
$762$		0			0
$763$	−28.0000	−	24.2487i	−1.01367	−	0.877862i
$764$	16.0000			0.578860
$765$	17.7846	+	17.1962i	0.643004	+	0.621728i
$766$		0			0
$767$	9.00000	+	15.5885i	0.324971	+	0.562867i
$768$	41.5692	+	24.0000i	1.50000	+	0.866025i
$769$	15.0000			0.540914			0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000			0.540914			0.270457	+	0.962732i	$0.412825\pi$
$770$		0			0
$771$		−	54.0000i		−	1.94476i
$772$	10.3923	+	6.00000i	0.374027	+	0.215945i
$773$	−10.0000	−	17.3205i	−0.359675	−	0.622975i	0.628231	−	0.778027i	$-0.283779\pi$
$773$	−10.0000	−	17.3205i	−0.359675	−	0.622975i	−0.987906	+	0.155051i	$0.950446\pi$
$774$		0			0
$775$	5.19615	+	3.00000i	0.186651	+	0.107763i
$776$		0			0
$777$	12.9904	+	37.5000i	0.466027	+	1.34531i
$778$		0			0
$779$	20.7846	+	12.0000i	0.744686	+	0.429945i
$780$	−6.00000	−	10.3923i	−0.214834	−	0.372104i
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$		0			0
$783$		0			0
$784$	−4.00000	−	27.7128i	−0.142857	−	0.989743i
$785$		−	22.0000i		−	0.785214i
$786$		0			0
$787$	−17.3205	+	10.0000i	−0.617409	+	0.356462i	−0.775860	−	0.630905i	$-0.782684\pi$
$787$	−17.3205	+	10.0000i	−0.617409	+	0.356462i	0.158450	+	0.987367i	$0.449350\pi$
$788$	−12.1244	+	7.00000i	−0.431912	+	0.249365i
$789$	−20.7846	−	12.0000i	−0.739952	−	0.427211i
$790$		0			0
$791$	−45.0000	+	15.5885i	−1.60002	+	0.554262i
$792$		0			0
$793$	−3.46410	−	2.00000i	−0.123014	−	0.0710221i
$794$		0			0
$795$	−12.0000	−	20.7846i	−0.425596	−	0.737154i
$796$	27.7128	+	16.0000i	0.982255	+	0.567105i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$		0			0
$799$	−32.0000	−	8.00000i	−1.13208	−	0.283020i
$800$		0			0
$801$	−39.0000	−	67.5500i	−1.37800	−	2.38676i
$802$		0			0
$803$	−13.0000	+	22.5167i	−0.458760	+	0.794596i
$804$			12.0000i			0.423207i
$805$	−1.73205	+	2.00000i	−0.0610468	+	0.0704907i
$806$		0			0
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$		0			0
$809$	25.9808	−	15.0000i	0.913435	−	0.527372i	0.0319002	−	0.999491i	$-0.489844\pi$
$809$	25.9808	−	15.0000i	0.913435	−	0.527372i	0.881535	+	0.472119i	$0.156511\pi$
$810$		0			0
$811$			14.0000i			0.491606i	0.969320	+	0.245803i	$0.0790517\pi$
$811$			14.0000i			0.491606i	−0.969320	+	0.245803i	$0.920948\pi$
$812$		0			0
$813$			21.0000i			0.736502i
$814$		0			0
$815$	−6.50000	−	11.2583i	−0.227685	−	0.394362i
$816$	−47.5692	+	13.6077i	−1.66526	+	0.476365i
$817$	24.0000	−	41.5692i	0.839654	−	1.45432i
$818$		0			0
$819$	31.1769	+	6.00000i	1.08941	+	0.209657i
$820$	12.0000			0.419058
$821$	−36.3731	−	21.0000i	−1.26943	−	0.732905i	−0.294549	−	0.955636i	$-0.595169\pi$
$821$	−36.3731	−	21.0000i	−1.26943	−	0.732905i	−0.974880	+	0.222731i	$0.928503\pi$
$822$		0			0
$823$	26.8468	−	15.5000i	0.935820	−	0.540296i	0.0471726	−	0.998887i	$-0.484979\pi$
$823$	26.8468	−	15.5000i	0.935820	−	0.540296i	0.888648	+	0.458591i	$0.151646\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		0			0
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	10.3923	+	6.00000i	0.361158	+	0.208514i
$829$	20.5000	+	35.5070i	0.711994	+	1.23321i	0.964107	+	0.265513i	$0.0855412\pi$
$829$	20.5000	+	35.5070i	0.711994	+	1.23321i	−0.252113	+	0.967698i	$0.581125\pi$
$830$		0			0
$831$	33.0000	−	57.1577i	1.14476	−	1.98278i
$832$	16.0000			0.554700
$833$	23.4019	+	16.8923i	0.810829	+	0.585284i
$834$		0			0
$835$	−5.50000	+	9.52628i	−0.190335	+	0.329670i
$836$	13.8564	−	8.00000i	0.479234	−	0.276686i
$837$	27.0000	+	46.7654i	0.933257	+	1.61645i
$838$		0			0
$839$		−	4.00000i		−	0.138095i	−0.997613	−	0.0690477i	$-0.978004\pi$
$839$		−	4.00000i		−	0.138095i	0.997613	−	0.0690477i	$-0.0219961\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−44.1673	+	25.5000i	−1.52120	+	0.878267i
$844$	−3.46410	+	2.00000i	−0.119239	+	0.0688428i
$845$	7.79423	+	4.50000i	0.268130	+	0.154805i
$846$		0			0
$847$	18.1865	+	3.50000i	0.624897	+	0.120261i
$848$	32.0000			1.09888
$849$	−28.5000	+	49.3634i	−0.978117	+	1.69415i
$850$		0			0
$851$	2.50000	+	4.33013i	0.0856989	+	0.148435i
$852$	−48.0000	+	83.1384i	−1.64445	+	2.84828i
$853$		−	15.0000i		−	0.513590i	−0.966466	−	0.256795i	$-0.917333\pi$
$853$		−	15.0000i		−	0.513590i	0.966466	−	0.256795i	$-0.0826666\pi$
$854$		0			0
$855$			24.0000i			0.820783i
$856$		0			0
$857$	21.6506	−	12.5000i	0.739572	−	0.426992i	−0.0823419	−	0.996604i	$-0.526240\pi$
$857$	21.6506	−	12.5000i	0.739572	−	0.426992i	0.821914	+	0.569612i	$0.192907\pi$
$858$		0			0
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	−0.965139	−	0.261739i	$-0.915704\pi$
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	0.709242	+	0.704965i	$0.249037\pi$
$860$		−	24.0000i		−	0.818393i
$861$	−31.1769	+	36.0000i	−1.06251	+	1.22688i
$862$		0			0
$863$	−8.00000	+	13.8564i	−0.272323	+	0.471678i	−0.969456	−	0.245264i	$-0.921125\pi$
$863$	−8.00000	+	13.8564i	−0.272323	+	0.471678i	0.697133	+	0.716942i	$0.254459\pi$
$864$		0			0
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$		0			0
$867$	24.0000	−	45.0000i	0.815083	−	1.52828i
$868$	6.00000	−	31.1769i	0.203653	−	1.05821i
$869$	−16.0000			−0.542763
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$		0			0
$873$	−25.9808	−	15.0000i	−0.879316	−	0.507673i
$874$		0			0
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$	78.0000			2.63538
$877$	−45.8993	−	26.5000i	−1.54991	−	0.894841i	−0.998147	−	0.0608407i	$-0.980622\pi$
$877$	−45.8993	−	26.5000i	−1.54991	−	0.894841i	−0.551763	−	0.834001i	$-0.686045\pi$
$878$		0			0
$879$	−41.5692	+	24.0000i	−1.40209	+	0.809500i
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$			20.0000i			0.673817i	0.941537	+	0.336909i	$0.109381\pi$
$881$			20.0000i			0.673817i	−0.941537	+	0.336909i	$0.890619\pi$
$882$		0			0
$883$	50.0000			1.68263			0.841317	−	0.540542i	$-0.181781\pi$
$883$	50.0000			1.68263			0.841317	+	0.540542i	$0.181781\pi$
$884$	−11.4641	+	11.8564i	−0.385579	+	0.398774i
$885$	−13.5000	−	23.3827i	−0.453798	−	0.786000i
$886$		0			0
$887$	16.4545	+	9.50000i	0.552487	+	0.318979i	0.750125	−	0.661296i	$-0.229993\pi$
$887$	16.4545	+	9.50000i	0.552487	+	0.318979i	−0.197637	+	0.980275i	$0.563327\pi$
$888$		0			0
$889$	−3.46410	−	10.0000i	−0.116182	−	0.335389i
$890$		0			0
$891$	−15.5885	−	9.00000i	−0.522233	−	0.301511i
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$	−16.0000	−	27.7128i	−0.535420	−	0.927374i
$894$		0			0
$895$		−	9.00000i		−	0.300837i
$896$		0			0
$897$	6.00000			0.200334
$898$		0			0
$899$		0			0
$900$	6.00000	+	10.3923i	0.200000	+	0.346410i
$901$	−22.9282	+	23.7128i	−0.763849	+	0.789988i
$902$		0			0
$903$	72.0000	+	62.3538i	2.39601	+	2.07501i
$904$		0			0
$905$	−10.0000	+	17.3205i	−0.332411	+	0.575753i
$906$		0			0
$907$	−14.7224	+	8.50000i	−0.488850	+	0.282238i	−0.724097	−	0.689698i	$-0.757743\pi$
$907$	−14.7224	+	8.50000i	−0.488850	+	0.282238i	0.235247	+	0.971936i	$0.424410\pi$
$908$	19.0526	+	11.0000i	0.632281	+	0.365048i
$909$	36.0000			1.19404
$910$		0			0
$911$		−	8.00000i		−	0.265052i	−0.991180	−	0.132526i	$-0.957691\pi$
$911$		−	8.00000i		−	0.265052i	0.991180	−	0.132526i	$-0.0423088\pi$
$912$	−41.5692	−	24.0000i	−1.37649	−	0.794719i
$913$	10.3923	−	6.00000i	0.343935	−	0.198571i
$914$		0			0
$915$	5.19615	+	3.00000i	0.171780	+	0.0991769i
$916$	−38.0000			−1.25556
$917$	6.00000	−	31.1769i	0.198137	−	1.02955i
$918$		0			0
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$		0			0
$921$	−46.7654	+	27.0000i	−1.54097	+	0.889680i
$922$		0			0
$923$			32.0000i			1.05329i
$924$	10.3923	+	30.0000i	0.341882	+	0.986928i
$925$			5.00000i			0.164399i
$926$		0			0
$927$	42.0000	+	72.7461i	1.37946	+	2.38930i
$928$		0			0
$929$	25.9808	+	15.0000i	0.852401	+	0.492134i	0.861460	−	0.507825i	$-0.169550\pi$
$929$	25.9808	+	15.0000i	0.852401	+	0.492134i	−0.00905914	+	0.999959i	$0.502884\pi$
$930$		0			0
$931$	4.00000	+	27.7128i	0.131095	+	0.908251i
$932$		−	42.0000i		−	1.37576i
$933$	48.0000	−	83.1384i	1.57145	−	2.72183i
$934$		0			0
$935$	2.26795	+	7.92820i	0.0741699	+	0.259280i
$936$		0			0
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$	−18.0000			−0.587408
$940$	−13.8564	−	8.00000i	−0.451946	−	0.260931i
$941$	8.66025	−	5.00000i	0.282316	−	0.162995i	−0.352155	−	0.935942i	$-0.614551\pi$
$941$	8.66025	−	5.00000i	0.282316	−	0.162995i	0.634472	+	0.772946i	$0.281218\pi$
$942$		0			0
$943$	−3.00000	+	5.19615i	−0.0976934	+	0.169210i
$944$	36.0000			1.17170
$945$	−23.3827	−	4.50000i	−0.760639	−	0.146385i
$946$		0			0
$947$	28.5788	+	16.5000i	0.928687	+	0.536178i	0.886396	−	0.462927i	$-0.153201\pi$
$947$	28.5788	+	16.5000i	0.928687	+	0.536178i	0.0422912	+	0.999105i	$0.486534\pi$
$948$	24.0000	+	41.5692i	0.779484	+	1.35011i
$949$	22.5167	−	13.0000i	0.730922	−	0.421998i
$950$		0			0
$951$	−54.0000			−1.75107
$952$		0			0
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		0			0
$955$	−6.92820	+	4.00000i	−0.224191	+	0.129437i
$956$	−11.0000	−	19.0526i	−0.355765	−	0.616204i
$957$		0			0
$958$		0			0
$959$	−20.7846	+	24.0000i	−0.671170	+	0.775000i
$960$	−24.0000			−0.774597
$961$	2.50000	−	4.33013i	0.0806452	−	0.139682i
$962$		0			0
$963$	−15.5885	+	9.00000i	−0.502331	+	0.290021i
$964$	−27.7128	−	16.0000i	−0.892570	−	0.515325i
$965$	−6.00000			−0.193147
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$		0			0
$969$	47.5692	−	13.6077i	1.52814	−	0.437142i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$	−5.00000	+	1.73205i	−0.160293	+	0.0555270i
$974$		0			0
$975$	5.19615	+	3.00000i	0.166410	+	0.0960769i
$976$	−6.92820	+	4.00000i	−0.221766	+	0.128037i
$977$	13.0000	+	22.5167i	0.415907	+	0.720372i	0.995523	−	0.0945177i	$-0.0301309\pi$
$977$	13.0000	+	22.5167i	0.415907	+	0.720372i	−0.579616	+	0.814890i	$0.696798\pi$
$978$		0			0
$979$		−	26.0000i		−	0.830964i
$980$	8.66025	+	11.0000i	0.276642	+	0.351382i
$981$		−	84.0000i		−	2.68191i
$982$		0			0
$983$	11.2583	−	6.50000i	0.359085	−	0.207318i	−0.309594	−	0.950869i	$-0.600193\pi$
$983$	11.2583	−	6.50000i	0.359085	−	0.207318i	0.668679	+	0.743551i	$0.266860\pi$
$984$		0			0
$985$	3.50000	−	6.06218i	0.111519	−	0.193157i
$986$		0			0
$987$	60.0000	−	20.7846i	1.90982	−	0.661581i
$988$	−16.0000			−0.509028
$989$	10.3923	+	6.00000i	0.330456	+	0.190789i
$990$		0			0
$991$	29.4449	−	17.0000i	0.935347	−	0.540023i	0.0468483	−	0.998902i	$-0.485082\pi$
$991$	29.4449	−	17.0000i	0.935347	−	0.540023i	0.888499	+	0.458879i	$0.151749\pi$
$992$		0			0
$993$		−	39.0000i		−	1.23763i
$994$		0			0
$995$	−16.0000			−0.507234
$996$	−31.1769	−	18.0000i	−0.987878	−	0.570352i
$997$	1.73205	−	1.00000i	0.0548546	−	0.0316703i	−0.472322	−	0.881426i	$-0.656584\pi$
$997$	1.73205	−	1.00000i	0.0548546	−	0.0316703i	0.527176	+	0.849756i	$0.323251\pi$
$998$		0			0
$999$	−22.5000	+	38.9711i	−0.711868	+	1.23299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	595.2.x.a.16.1	✓	4
7.4	even	3	inner	595.2.x.a.186.2	yes	4
17.16	even	2	inner	595.2.x.a.16.2	yes	4
119.67	even	6	inner	595.2.x.a.186.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.x.a.16.1	✓	4	1.1	even	1	trivial
595.2.x.a.16.2	yes	4	17.16	even	2	inner
595.2.x.a.186.1	yes	4	119.67	even	6	inner
595.2.x.a.186.2	yes	4	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(1.73205 - 1.00000i) q^{11} +(-5.19615 - 3.00000i) q^{12} -2.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-1.13397 - 3.96410i) q^{17} +(2.00000 - 3.46410i) q^{19} -2.00000i q^{20} +(6.00000 + 5.19615i) q^{21} +(0.866025 + 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{25} +9.00000i q^{27} +(3.46410 - 4.00000i) q^{28} +(5.19615 - 3.00000i) q^{31} +(-3.00000 + 5.19615i) q^{33} +(-0.500000 + 2.59808i) q^{35} +12.0000 q^{36} +(4.33013 + 2.50000i) q^{37} +(5.19615 - 3.00000i) q^{39} +6.00000i q^{41} +12.0000 q^{43} +(3.46410 + 2.00000i) q^{44} +(-5.19615 + 3.00000i) q^{45} +(4.00000 - 6.92820i) q^{47} -12.0000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(8.89230 + 8.59808i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-4.00000 - 6.92820i) q^{53} -2.00000 q^{55} +12.0000i q^{57} +(-4.50000 - 7.79423i) q^{59} +(3.00000 + 5.19615i) q^{60} +(1.73205 + 1.00000i) q^{61} +(-15.5885 - 3.00000i) q^{63} -8.00000 q^{64} +(1.73205 + 1.00000i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(5.73205 - 5.92820i) q^{68} -3.00000 q^{69} -16.0000i q^{71} +(-11.2583 + 6.50000i) q^{73} +(-2.59808 - 1.50000i) q^{75} +8.00000 q^{76} +(-4.00000 - 3.46410i) q^{77} +(-6.92820 - 4.00000i) q^{79} +(3.46410 - 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +6.00000 q^{83} +(-3.00000 + 15.5885i) q^{84} +(-1.00000 + 4.00000i) q^{85} +(6.50000 - 11.2583i) q^{89} +(1.73205 + 5.00000i) q^{91} +2.00000i q^{92} +(-9.00000 + 15.5885i) q^{93} +(-3.46410 + 2.00000i) q^{95} -5.00000i q^{97} -12.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 12 q^{9} - 8 q^{13} + 12 q^{15} - 8 q^{16} - 8 q^{17} + 8 q^{19} + 24 q^{21} + 2 q^{25} - 12 q^{33} - 2 q^{35} + 48 q^{36} + 48 q^{43} + 16 q^{47} - 22 q^{49} - 6 q^{51} - 8 q^{52} - 16 q^{53}+ \cdots - 36 q^{93}+O(q^{100}) \) 4 * q + 4 * q^4 + 12 * q^9 - 8 * q^13 + 12 * q^15 - 8 * q^16 - 8 * q^17 + 8 * q^19 + 24 * q^21 + 2 * q^25 - 12 * q^33 - 2 * q^35 + 48 * q^36 + 48 * q^43 + 16 * q^47 - 22 * q^49 - 6 * q^51 - 8 * q^52 - 16 * q^53 - 8 * q^55 - 18 * q^59 + 12 * q^60 - 32 * q^64 - 4 * q^67 + 16 * q^68 - 12 * q^69 + 32 * q^76 - 16 * q^77 - 18 * q^81 + 24 * q^83 - 12 * q^84 - 4 * q^85 + 26 * q^89 - 36 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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