LMFDB - Embedded newform 1638.2.r.c.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.c.1387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(2.50000 + 2.59808i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{23} +4.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +(-0.500000 - 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} -10.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +(1.50000 - 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} -4.00000 q^{38} -3.00000 q^{40} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 2.59808i) q^{46} -6.00000 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-3.50000 + 0.866025i) q^{52} -12.0000 q^{53} +(-0.500000 + 0.866025i) q^{56} +(3.00000 - 5.19615i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(-7.50000 - 7.79423i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(3.00000 + 5.19615i) q^{68} -3.00000 q^{70} +(-1.50000 + 2.59808i) q^{71} +2.00000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} -4.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-9.00000 + 15.5885i) q^{85} +8.00000 q^{86} +(-3.00000 - 5.19615i) q^{89} +(-3.50000 + 0.866025i) q^{91} -3.00000 q^{92} +(3.00000 + 5.19615i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 6 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 6 * q^5 - q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 6 q^{5} - q^{7} + 2 q^{8} + 3 q^{10} + 5 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 3 q^{20} + 3 q^{23} + 8 q^{25} + 2 q^{26} - q^{28} + 6 q^{29} - 20 q^{31} - q^{32} - 12 q^{34} + 3 q^{35} - 8 q^{37} - 8 q^{38} - 6 q^{40} - 8 q^{43} + 3 q^{46} - 12 q^{47} - q^{49} - 4 q^{50} - 7 q^{52} - 24 q^{53} - q^{56} + 6 q^{58} + 3 q^{59} - 11 q^{61} + 10 q^{62} + 2 q^{64} - 15 q^{65} - 2 q^{67} + 6 q^{68} - 6 q^{70} - 3 q^{71} + 4 q^{73} - 8 q^{74} + 4 q^{76} - 8 q^{79} + 3 q^{80} - 18 q^{85} + 16 q^{86} - 6 q^{89} - 7 q^{91} - 6 q^{92} + 6 q^{94} - 12 q^{95} - 2 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 6 * q^5 - q^7 + 2 * q^8 + 3 * q^10 + 5 * q^13 + 2 * q^14 - q^16 + 6 * q^17 + 4 * q^19 + 3 * q^20 + 3 * q^23 + 8 * q^25 + 2 * q^26 - q^28 + 6 * q^29 - 20 * q^31 - q^32 - 12 * q^34 + 3 * q^35 - 8 * q^37 - 8 * q^38 - 6 * q^40 - 8 * q^43 + 3 * q^46 - 12 * q^47 - q^49 - 4 * q^50 - 7 * q^52 - 24 * q^53 - q^56 + 6 * q^58 + 3 * q^59 - 11 * q^61 + 10 * q^62 + 2 * q^64 - 15 * q^65 - 2 * q^67 + 6 * q^68 - 6 * q^70 - 3 * q^71 + 4 * q^73 - 8 * q^74 + 4 * q^76 - 8 * q^79 + 3 * q^80 - 18 * q^85 + 16 * q^86 - 6 * q^89 - 7 * q^91 - 6 * q^92 + 6 * q^94 - 12 * q^95 - 2 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		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	$0.0149348\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$		0			0
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	−3.00000			−0.474342
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$		0			0
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	0.262776	+	0.964857i	$0.415362\pi$
$61$	−5.50000	+	9.52628i	−0.704203	+	1.21972i	−0.966978	+	0.254858i	$0.917971\pi$
$62$	5.00000	+	8.66025i	0.635001	+	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.50000	−	7.79423i	−0.930261	−	0.966755i
$66$		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	$0.872318\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$		0			0
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$	8.00000			0.862662
$87$		0			0
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	−3.50000	+	0.866025i	−0.366900	+	0.0907841i
$92$	−3.00000			−0.312772
$93$		0			0
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$		0			0
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$		0			0
$111$		0			0
$112$	1.00000			0.0944911
$113$	−9.00000	+	15.5885i	−0.846649	+	1.46644i	0.0375328	+	0.999295i	$0.488050\pi$
$113$	−9.00000	+	15.5885i	−0.846649	+	1.46644i	−0.884182	+	0.467143i	$0.845283\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−3.00000			−0.276172
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	11.0000			0.995893
$123$		0			0
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	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	$0.995624\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.00000	+	10.3923i	−0.263117	+	0.911465i
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$	2.00000	+	3.46410i	0.173422	+	0.300376i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	1.50000	+	2.59808i	0.126773	+	0.219578i
$141$		0			0
$142$	3.00000			0.251754
$143$		0			0
$144$		0			0
$145$	−9.00000	−	15.5885i	−0.747409	−	1.29455i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$	8.00000			0.657596
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	−1.00000			−0.0813788			−0.0406894	−	0.999172i	$-0.512955\pi$
$151$	−1.00000			−0.0813788			−0.0406894	+	0.999172i	$0.512955\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$		0			0
$154$		0			0
$155$	30.0000			2.40966
$156$		0			0
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$		0			0
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	−3.00000			−0.236433
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	18.0000			1.38054
$171$		0			0
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$		0			0
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	2.50000	+	2.59808i	0.185312	+	0.192582i
$183$		0			0
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$	12.0000	+	20.7846i	0.882258	+	1.52811i
$186$		0			0
$187$		0			0
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$		0			0
$190$	12.0000			0.870572
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.00000	+	10.3923i	0.427482	+	0.740421i	0.996649	−	0.0818013i	$-0.0260673\pi$
$197$	6.00000	+	10.3923i	0.427482	+	0.740421i	−0.569166	+	0.822222i	$0.692734\pi$
$198$		0			0
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	4.00000			0.282843
$201$		0			0
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$	−6.00000			−0.421117
$204$		0			0
$205$		0			0
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$		0			0
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$		0			0
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		0			0
$214$	−9.00000	+	15.5885i	−0.615227	+	1.06561i
$215$	12.0000	−	20.7846i	0.818393	−	1.41750i
$216$		0			0
$217$	5.00000	−	8.66025i	0.339422	−	0.587896i
$218$	8.00000	+	13.8564i	0.541828	+	0.938474i
$219$		0			0
$220$		0			0
$221$	21.0000	−	5.19615i	1.41261	−	0.349531i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	18.0000			1.19734
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$	−4.50000	+	7.79423i	−0.296721	+	0.513936i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$		0			0
$235$	18.0000			1.17419
$236$	1.50000	+	2.59808i	0.0976417	+	0.169120i
$237$		0			0
$238$	3.00000	−	5.19615i	0.194461	−	0.336817i
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$		0			0
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.825131	−	0.564942i	$-0.191101\pi$
$242$	−11.0000			−0.707107
$243$		0			0
$244$	−5.50000	−	9.52628i	−0.352101	−	0.609858i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$		0			0
$247$	14.0000	−	3.46410i	0.890799	−	0.220416i
$248$	−10.0000			−0.635001
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$		0			0
$253$		0			0
$254$	−5.50000	+	9.52628i	−0.345101	+	0.597732i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	8.00000			0.497096
$260$	10.5000	−	2.59808i	0.651182	−	0.161126i
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	−0.896093	−	0.443866i	$-0.853607\pi$
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	0.0636476	−	0.997972i	$-0.479727\pi$
$264$		0			0
$265$	36.0000			2.21146
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$		0			0
$268$	2.00000			0.122169
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−3.00000			−0.181237
$275$		0			0
$276$		0			0
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−16.0000			−0.959616
$279$		0			0
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$	−1.50000	−	2.59808i	−0.0890086	−	0.154167i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−9.00000	+	15.5885i	−0.528498	+	0.915386i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		0			0
$295$	−4.50000	+	7.79423i	−0.262000	+	0.453798i
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$		0			0
$299$	−3.00000	+	10.3923i	−0.173494	+	0.601003i
$300$		0			0
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$	0.500000	+	0.866025i	0.0287718	+	0.0498342i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	16.5000	−	28.5788i	0.944787	−	1.63642i
$306$		0			0
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$		0			0
$309$		0			0
$310$	−15.0000	−	25.9808i	−0.851943	−	1.47561i
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$		0			0
$313$	8.00000			0.452187			0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000			0.452187			0.226093	+	0.974106i	$0.427405\pi$
$314$	−1.00000	−	1.73205i	−0.0564333	−	0.0977453i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	12.0000			0.673987			0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000			0.673987			0.336994	+	0.941507i	$0.390590\pi$
$318$		0			0
$319$		0			0
$320$	−3.00000			−0.167705
$321$		0			0
$322$	1.50000	+	2.59808i	0.0835917	+	0.144785i
$323$	−12.0000	−	20.7846i	−0.667698	−	1.15649i
$324$		0			0
$325$	10.0000	+	10.3923i	0.554700	+	0.576461i
$326$	20.0000			1.10770
$327$		0			0
$328$		0			0
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$		0			0
$333$		0			0
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	3.00000	+	5.19615i	0.163908	+	0.283896i
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	11.5000	−	6.06218i	0.625518	−	0.329739i
$339$		0			0
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$		0			0
$342$		0			0
$343$	1.00000			0.0539949
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	−9.00000			−0.483843
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	0.340293	+	0.940319i	$0.389474\pi$
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	−0.984487	+	0.175457i	$0.943860\pi$
$348$		0			0
$349$	−14.5000	−	25.1147i	−0.776167	−	1.34436i	−0.934136	−	0.356917i	$-0.883828\pi$
$349$	−14.5000	−	25.1147i	−0.776167	−	1.34436i	0.157969	−	0.987444i	$-0.449505\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$	4.50000	−	7.79423i	0.238835	−	0.413675i
$356$	6.00000			0.317999
$357$		0			0
$358$	3.00000	−	5.19615i	0.158555	−	0.274625i
$359$	9.00000			0.475002			0.237501	−	0.971387i	$-0.423672\pi$
$359$	9.00000			0.475002			0.237501	+	0.971387i	$0.423672\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−2.50000	−	4.33013i	−0.131397	−	0.227586i
$363$		0			0
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$	−6.00000			−0.314054
$366$		0			0
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	0.966507	−	0.256639i	$-0.0826151\pi$
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	−0.705509	+	0.708700i	$0.749282\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$		0			0
$370$	12.0000	−	20.7846i	0.623850	−	1.08054i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	0.0708063	+	0.997490i	$0.477443\pi$
$373$	−16.0000	+	27.7128i	−0.828449	+	1.43492i	−0.899255	+	0.437425i	$0.855891\pi$
$374$		0			0
$375$		0			0
$376$	−6.00000			−0.309426
$377$	−6.00000	+	20.7846i	−0.309016	+	1.07046i
$378$		0			0
$379$	14.0000	+	24.2487i	0.719132	+	1.24557i	0.961344	+	0.275349i	$0.0887935\pi$
$379$	14.0000	+	24.2487i	0.719132	+	1.24557i	−0.242213	+	0.970223i	$0.577873\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$		0			0
$382$	24.0000			1.22795
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$		0			0
$385$		0			0
$386$	−2.50000	+	4.33013i	−0.127247	+	0.220398i
$387$		0			0
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$		0			0
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$	12.0000			0.603786
$396$		0			0
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	14.0000			0.701757
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$		0			0
$403$	−25.0000	−	25.9808i	−1.24534	−	1.29419i
$404$	6.00000			0.298511
$405$		0			0
$406$	3.00000	+	5.19615i	0.148888	+	0.257881i
$407$		0			0
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$		0			0
$411$		0			0
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$	1.50000	+	2.59808i	0.0738102	+	0.127843i
$414$		0			0
$415$		0			0
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$		0			0
$424$	−12.0000			−0.582772
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$		0			0
$427$	−5.50000	−	9.52628i	−0.266164	−	0.461009i
$428$	18.0000			0.870063
$429$		0			0
$430$	−24.0000			−1.15738
$431$	−16.5000	−	28.5788i	−0.794777	−	1.37659i	−0.922981	−	0.384846i	$-0.874254\pi$
$431$	−16.5000	−	28.5788i	−0.794777	−	1.37659i	0.128204	−	0.991748i	$-0.459079\pi$
$432$		0			0
$433$	2.00000	−	3.46410i	0.0961139	−	0.166474i	−0.813959	−	0.580922i	$-0.802692\pi$
$433$	2.00000	−	3.46410i	0.0961139	−	0.166474i	0.910073	+	0.414448i	$0.136025\pi$
$434$	−10.0000			−0.480015
$435$		0			0
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	12.0000			0.574038
$438$		0			0
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$		0			0
$441$		0			0
$442$	−15.0000	−	15.5885i	−0.713477	−	0.741467i
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	−0.740087	−	0.672511i	$-0.765216\pi$
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	0.952455	+	0.304679i	$0.0985491\pi$
$450$		0			0
$451$		0			0
$452$	−9.00000	−	15.5885i	−0.423324	−	0.733219i
$453$		0			0
$454$	15.0000			0.703985
$455$	10.5000	−	2.59808i	0.492248	−	0.121800i
$456$		0			0
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	−0.975498	−	0.220008i	$-0.929392\pi$
$457$	−14.5000	−	25.1147i	−0.678281	−	1.17482i	0.297217	−	0.954810i	$-0.403942\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$		0			0
$460$	9.00000			0.419627
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	−0.510887	−	0.859648i	$-0.670683\pi$
$461$	10.5000	−	18.1865i	0.489034	−	0.847031i	0.999920	+	0.0126168i	$0.00401615\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$		0			0
$469$	2.00000			0.0923514
$470$	−9.00000	−	15.5885i	−0.415139	−	0.719042i
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$		0			0
$474$		0			0
$475$	8.00000	−	13.8564i	0.367065	−	0.635776i
$476$	−6.00000			−0.275010
$477$		0			0
$478$	10.5000	+	18.1865i	0.480259	+	0.831833i
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	0.973321	+	0.229447i	$0.0736918\pi$
$479$	15.0000	+	25.9808i	0.685367	+	1.18709i	−0.287954	+	0.957644i	$0.592975\pi$
$480$		0			0
$481$	8.00000	−	27.7128i	0.364769	−	1.26360i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$		0			0
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$	−5.50000	+	9.52628i	−0.248973	+	0.431234i
$489$		0			0
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$	36.0000			1.62136
$494$	−10.0000	−	10.3923i	−0.449921	−	0.467572i
$495$		0			0
$496$	5.00000	+	8.66025i	0.224507	+	0.388857i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$		0			0
$499$	−22.0000			−0.984855			−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000			−0.984855			−0.492428	+	0.870353i	$0.663890\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	−3.00000			−0.133897
$503$	21.0000	−	36.3731i	0.936344	−	1.62179i	0.164124	−	0.986440i	$-0.447520\pi$
$503$	21.0000	−	36.3731i	0.936344	−	1.62179i	0.772220	−	0.635355i	$-0.219146\pi$
$504$		0			0
$505$	9.00000	+	15.5885i	0.400495	+	0.693677i
$506$		0			0
$507$		0			0
$508$	11.0000			0.488046
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$	−42.0000			−1.85074
$516$		0			0
$517$		0			0
$518$	−4.00000	−	6.92820i	−0.175750	−	0.304408i
$519$		0			0
$520$	−7.50000	−	7.79423i	−0.328897	−	0.341800i
$521$	36.0000			1.57719			0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000			1.57719			0.788594	+	0.614914i	$0.210809\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$		0			0
$526$	−13.5000	+	23.3827i	−0.588628	+	1.01953i
$527$	−30.0000	+	51.9615i	−1.30682	+	2.26348i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−18.0000	−	31.1769i	−0.781870	−	1.35424i
$531$		0			0
$532$	−4.00000			−0.173422
$533$		0			0
$534$		0			0
$535$	27.0000	+	46.7654i	1.16731	+	2.02184i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	−9.00000			−0.388018
$539$		0			0
$540$		0			0
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	−1.00000	+	1.73205i	−0.0429537	+	0.0743980i
$543$		0			0
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	48.0000			2.05609
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$		0			0
$550$		0			0
$551$	24.0000			1.02243
$552$		0			0
$553$	2.00000	−	3.46410i	0.0850487	−	0.147309i
$554$	26.0000			1.10463
$555$		0			0
$556$	8.00000	+	13.8564i	0.339276	+	0.587643i
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	0.999952	+	0.00979220i	$0.00311700\pi$
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	−0.491496	+	0.870880i	$0.663550\pi$
$558$		0			0
$559$	−28.0000	+	6.92820i	−1.18427	+	0.293032i
$560$	−3.00000			−0.126773
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	27.0000	−	46.7654i	1.13590	−	1.96743i
$566$	15.5000	−	26.8468i	0.651514	−	1.12845i
$567$		0			0
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.759220	−	0.650835i	$-0.774419\pi$
$569$	−22.5000	−	38.9711i	−0.943249	−	1.63376i	−0.184030	−	0.982921i	$-0.558914\pi$
$570$		0			0
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.00000	+	10.3923i	0.250217	+	0.433389i
$576$		0			0
$577$	−28.0000			−1.16566			−0.582828	−	0.812596i	$-0.698054\pi$
$577$	−28.0000			−1.16566			−0.582828	+	0.812596i	$0.698054\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$		0			0
$580$	18.0000			0.747409
$581$		0			0
$582$		0			0
$583$		0			0
$584$	2.00000			0.0827606
$585$		0			0
$586$	6.00000			0.247858
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$		0			0
$589$	−20.0000	+	34.6410i	−0.824086	+	1.42736i
$590$	9.00000			0.370524
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	−9.00000	−	15.5885i	−0.368964	−	0.639064i
$596$		0			0
$597$		0			0
$598$	10.5000	−	2.59808i	0.429377	−	0.106243i
$599$	−3.00000			−0.122577			−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000			−0.122577			−0.0612883	+	0.998120i	$0.519521\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	−4.00000	+	6.92820i	−0.163028	+	0.282372i
$603$		0			0
$604$	0.500000	−	0.866025i	0.0203447	−	0.0352381i
$605$	−16.5000	+	28.5788i	−0.670820	+	1.16190i
$606$		0			0
$607$	5.00000	−	8.66025i	0.202944	−	0.351509i	−0.746532	−	0.665350i	$-0.768282\pi$
$607$	5.00000	−	8.66025i	0.202944	−	0.351509i	0.949476	+	0.313841i	$0.101616\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$		0			0
$610$	−33.0000			−1.33613
$611$	−15.0000	−	15.5885i	−0.606835	−	0.630641i
$612$		0			0
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	0.998002	−	0.0631797i	$-0.0201241\pi$
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	−0.553716	+	0.832705i	$0.686791\pi$
$614$	6.50000	+	11.2583i	0.262319	+	0.454349i
$615$		0			0
$616$		0			0
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$		0			0
$619$	−37.0000			−1.48716			−0.743578	−	0.668649i	$-0.766873\pi$
$619$	−37.0000			−1.48716			−0.743578	+	0.668649i	$0.766873\pi$
$620$	−15.0000	+	25.9808i	−0.602414	+	1.04341i
$621$		0			0
$622$	−3.00000	−	5.19615i	−0.120289	−	0.208347i
$623$	6.00000			0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−48.0000			−1.91389
$630$		0			0
$631$	−2.50000	+	4.33013i	−0.0995234	+	0.172380i	−0.911487	−	0.411328i	$-0.865065\pi$
$631$	−2.50000	+	4.33013i	−0.0995234	+	0.172380i	0.811964	+	0.583707i	$0.198398\pi$
$632$	−4.00000			−0.159111
$633$		0			0
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$	16.5000	+	28.5788i	0.654783	+	1.13412i
$636$		0			0
$637$	1.00000	−	3.46410i	0.0396214	−	0.137253i
$638$		0			0
$639$		0			0
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	−20.5000	+	35.5070i	−0.808441	+	1.40026i	0.105502	+	0.994419i	$0.466355\pi$
$643$	−20.5000	+	35.5070i	−0.808441	+	1.40026i	−0.913943	+	0.405842i	$0.866978\pi$
$644$	1.50000	−	2.59808i	0.0591083	−	0.102379i
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	−18.0000	−	31.1769i	−0.707653	−	1.22569i	−0.965726	−	0.259565i	$-0.916421\pi$
$647$	−18.0000	−	31.1769i	−0.707653	−	1.22569i	0.258073	−	0.966126i	$-0.416913\pi$
$648$		0			0
$649$		0			0
$650$	4.00000	−	13.8564i	0.156893	−	0.543493i
$651$		0			0
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$		0			0
$655$	45.0000			1.75830
$656$		0			0
$657$		0			0
$658$	−6.00000			−0.233904
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	−0.801660	−	0.597781i	$-0.796049\pi$
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	0.918523	+	0.395367i	$0.129383\pi$
$660$		0			0
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$662$	−10.0000			−0.388661
$663$		0			0
$664$		0			0
$665$	−6.00000	−	10.3923i	−0.232670	−	0.402996i
$666$		0			0
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	12.0000			0.464294
$669$		0			0
$670$	3.00000	−	5.19615i	0.115900	−	0.200745i
$671$		0			0
$672$		0			0
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	51.0000			1.96009			0.980045	−	0.198778i	$-0.0636972\pi$
$677$	51.0000			1.96009			0.980045	+	0.198778i	$0.0636972\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$		0			0
$682$		0			0
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	−0.998917	−	0.0465244i	$-0.985185\pi$
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	0.539750	+	0.841825i	$0.318519\pi$
$684$		0			0
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	8.00000			0.304997
$689$	−30.0000	−	31.1769i	−1.14291	−	1.18775i
$690$		0			0
$691$	0.500000	+	0.866025i	0.0190209	+	0.0329452i	0.875379	−	0.483437i	$-0.160612\pi$
$691$	0.500000	+	0.866025i	0.0190209	+	0.0329452i	−0.856358	+	0.516382i	$0.827278\pi$
$692$	4.50000	+	7.79423i	0.171064	+	0.296292i
$693$		0			0
$694$	24.0000			0.911028
$695$	−24.0000	+	41.5692i	−0.910372	+	1.57681i
$696$		0			0
$697$		0			0
$698$	−14.5000	+	25.1147i	−0.548833	+	0.950607i
$699$		0			0
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	−32.0000			−1.20690
$704$		0			0
$705$		0			0
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$	6.00000			0.225653
$708$		0			0
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	−9.00000			−0.337764
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−15.0000	−	25.9808i	−0.561754	−	0.972987i
$714$		0			0
$715$		0			0
$716$	−6.00000			−0.224231
$717$		0			0
$718$	−4.50000	−	7.79423i	−0.167939	−	0.290878i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		0			0
$721$	−7.00000	+	12.1244i	−0.260694	+	0.451535i
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$		0			0
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$		0			0
$727$	−52.0000			−1.92857			−0.964287	−	0.264861i	$-0.914674\pi$
$727$	−52.0000			−1.92857			−0.964287	+	0.264861i	$0.914674\pi$
$728$	−3.50000	+	0.866025i	−0.129719	+	0.0320970i
$729$		0			0
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$		0			0
$733$	35.0000			1.29275			0.646377	−	0.763018i	$-0.276283\pi$
$733$	35.0000			1.29275			0.646377	+	0.763018i	$0.276283\pi$
$734$	5.00000	−	8.66025i	0.184553	−	0.319656i
$735$		0			0
$736$	−3.00000			−0.110581
$737$		0			0
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	−24.0000			−0.882258
$741$		0			0
$742$	−12.0000			−0.440534
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.850814	+	0.525467i	$0.176109\pi$
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.0296605	+	0.999560i	$0.490557\pi$
$744$		0			0
$745$		0			0
$746$	32.0000			1.17160
$747$		0			0
$748$		0			0
$749$	18.0000			0.657706
$750$		0			0
$751$	−8.50000	−	14.7224i	−0.310169	−	0.537229i	0.668229	−	0.743955i	$-0.267052\pi$
$751$	−8.50000	−	14.7224i	−0.310169	−	0.537229i	−0.978399	+	0.206726i	$0.933719\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$	21.0000	−	5.19615i	0.764775	−	0.189233i
$755$	3.00000			0.109181
$756$		0			0
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.755779	+	0.654827i	$0.227258\pi$
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.189207	+	0.981937i	$0.439408\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	8.00000	−	13.8564i	0.289619	−	0.501636i
$764$	−12.0000	−	20.7846i	−0.434145	−	0.751961i
$765$		0			0
$766$	6.00000			0.216789
$767$	10.5000	−	2.59808i	0.379133	−	0.0938111i
$768$		0			0
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	0.941984	−	0.335657i	$-0.108958\pi$
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	−0.761680	+	0.647954i	$0.775625\pi$
$770$		0			0
$771$		0			0
$772$	5.00000			0.179954
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	0.459418	+	0.888220i	$0.348058\pi$
$773$	−15.0000	+	25.9808i	−0.539513	+	0.934463i	−0.998930	+	0.0462427i	$0.985275\pi$
$774$		0			0
$775$	−40.0000			−1.43684
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−6.00000			−0.214149
$786$		0			0
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.188119	+	0.982146i	$0.560239\pi$
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.756504	+	0.653989i	$0.773094\pi$
$788$	−12.0000			−0.427482
$789$		0			0
$790$	−6.00000	−	10.3923i	−0.213470	−	0.369742i
$791$	−9.00000	−	15.5885i	−0.320003	−	0.554262i
$792$		0			0
$793$	−38.5000	+	9.52628i	−1.36718	+	0.338288i
$794$	−7.00000			−0.248421
$795$		0			0
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	−0.967737	−	0.251961i	$-0.918924\pi$
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	0.702074	+	0.712104i	$0.252258\pi$
$798$		0			0
$799$	−18.0000	+	31.1769i	−0.636794	+	1.10296i
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$		0			0
$804$		0			0
$805$	9.00000			0.317208
$806$	−10.0000	+	34.6410i	−0.352235	+	1.22018i
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$		0			0
$811$	−19.0000			−0.667180			−0.333590	−	0.942718i	$-0.608260\pi$
$811$	−19.0000			−0.667180			−0.333590	+	0.942718i	$0.608260\pi$
$812$	3.00000	−	5.19615i	0.105279	−	0.182349i
$813$		0			0
$814$		0			0
$815$	30.0000	−	51.9615i	1.05085	−	1.82013i
$816$		0			0
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	−22.0000			−0.769212
$819$		0			0
$820$		0			0
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	0.951526	−	0.307568i	$-0.0995151\pi$
$821$	6.00000	+	10.3923i	0.209401	+	0.362694i	−0.742125	+	0.670262i	$0.766182\pi$
$822$		0			0
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	−0.730215	−	0.683217i	$-0.760580\pi$
$823$	6.50000	−	11.2583i	0.226576	−	0.392441i	0.956791	+	0.290776i	$0.0939136\pi$
$824$	14.0000			0.487713
$825$		0			0
$826$	1.50000	−	2.59808i	0.0521917	−	0.0903986i
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$		0			0
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$	−6.00000			−0.207888
$834$		0			0
$835$	18.0000	+	31.1769i	0.622916	+	1.07892i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.152493	+	0.988304i	$0.548730\pi$
$839$	−27.0000	+	46.7654i	−0.932144	+	1.61452i	−0.779650	+	0.626215i	$0.784603\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−13.0000	−	22.5167i	−0.448010	−	0.775975i
$843$		0			0
$844$	−4.00000			−0.137686
$845$	1.50000	−	38.9711i	0.0516016	−	1.34065i
$846$		0			0
$847$	5.50000	+	9.52628i	0.188982	+	0.327327i
$848$	6.00000	+	10.3923i	0.206041	+	0.356873i
$849$		0			0
$850$	−24.0000			−0.823193
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$		0			0
$853$	17.0000			0.582069			0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000			0.582069			0.291034	+	0.956713i	$0.406001\pi$
$854$	−5.50000	+	9.52628i	−0.188206	+	0.325983i
$855$		0			0
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	12.0000	+	20.7846i	0.409197	+	0.708749i
$861$		0			0
$862$	−16.5000	+	28.5788i	−0.561992	+	0.973399i
$863$	57.0000			1.94030			0.970151	−	0.242500i	$-0.0779676\pi$
$863$	57.0000			1.94030			0.970151	+	0.242500i	$0.0779676\pi$
$864$		0			0
$865$	−13.5000	+	23.3827i	−0.459014	+	0.795035i
$866$	−4.00000			−0.135926
$867$		0			0
$868$	5.00000	+	8.66025i	0.169711	+	0.293948i
$869$		0			0
$870$		0			0
$871$	2.00000	−	6.92820i	0.0677674	−	0.234753i
$872$	−16.0000			−0.541828
$873$		0			0
$874$	−6.00000	−	10.3923i	−0.202953	−	0.351525i
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−7.00000	+	12.1244i	−0.236239	+	0.409177i
$879$		0			0
$880$		0			0
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$881$	−3.00000	−	5.19615i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−6.00000	+	20.7846i	−0.201802	+	0.699062i
$885$		0			0
$886$	9.00000	+	15.5885i	0.302361	+	0.523704i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$		0			0
$889$	11.0000			0.368928
$890$	9.00000	−	15.5885i	0.301681	−	0.522526i
$891$		0			0
$892$	8.00000			0.267860
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$	−9.00000	−	15.5885i	−0.300837	−	0.521065i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−9.00000			−0.300334
$899$	−30.0000	−	51.9615i	−1.00056	−	1.73301i
$900$		0			0
$901$	−36.0000	+	62.3538i	−1.19933	+	2.07731i
$902$		0			0
$903$		0			0
$904$	−9.00000	+	15.5885i	−0.299336	+	0.518464i
$905$	−15.0000			−0.498617
$906$		0			0
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	0.726092	−	0.687598i	$-0.241335\pi$
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	−0.958523	+	0.285015i	$0.908001\pi$
$908$	−7.50000	−	12.9904i	−0.248896	−	0.431101i
$909$		0			0
$910$	−7.50000	−	7.79423i	−0.248623	−	0.258376i
$911$	−21.0000			−0.695761			−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000			−0.695761			−0.347881	+	0.937539i	$0.613099\pi$
$912$		0			0
$913$		0			0
$914$	−14.5000	+	25.1147i	−0.479617	+	0.830722i
$915$		0			0
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$	7.50000	−	12.9904i	0.247672	−	0.428980i
$918$		0			0
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	−0.802507	−	0.596643i	$-0.796501\pi$
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	0.917961	+	0.396670i	$0.129834\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		0			0
$922$	−21.0000			−0.691598
$923$	−10.5000	+	2.59808i	−0.345612	+	0.0855167i
$924$		0			0
$925$	−16.0000	−	27.7128i	−0.526077	−	0.911192i
$926$	15.5000	+	26.8468i	0.509362	+	0.882240i
$927$		0			0
$928$	−6.00000			−0.196960
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$	−4.00000			−0.131095
$932$	−1.50000	+	2.59808i	−0.0491341	+	0.0851028i
$933$		0			0
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$		0			0
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	−1.00000	−	1.73205i	−0.0326512	−	0.0565535i
$939$		0			0
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$	−15.0000			−0.488986			−0.244493	−	0.969651i	$-0.578622\pi$
$941$	−15.0000			−0.488986			−0.244493	+	0.969651i	$0.578622\pi$
$942$		0			0
$943$		0			0
$944$	−3.00000			−0.0976417
$945$		0			0
$946$		0			0
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927599\pi$
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	0.291835	−	0.956469i	$-0.405734\pi$
$948$		0			0
$949$	5.00000	+	5.19615i	0.162307	+	0.168674i
$950$	−16.0000			−0.519109
$951$		0			0
$952$	3.00000	+	5.19615i	0.0972306	+	0.168408i
$953$	−7.50000	+	12.9904i	−0.242949	+	0.420800i	−0.961553	−	0.274620i	$-0.911448\pi$
$953$	−7.50000	+	12.9904i	−0.242949	+	0.420800i	0.718604	+	0.695419i	$0.244781\pi$
$954$		0			0
$955$	36.0000	−	62.3538i	1.16493	−	2.01772i
$956$	10.5000	−	18.1865i	0.339594	−	0.588195i
$957$		0			0
$958$	15.0000	−	25.9808i	0.484628	−	0.839400i
$959$	1.50000	+	2.59808i	0.0484375	+	0.0838963i
$960$		0			0
$961$	69.0000			2.22581
$962$	−28.0000	+	6.92820i	−0.902756	+	0.223374i
$963$		0			0
$964$	14.0000	+	24.2487i	0.450910	+	0.780998i
$965$	7.50000	+	12.9904i	0.241434	+	0.418175i
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	5.50000	−	9.52628i	0.176777	−	0.306186i
$969$		0			0
$970$	−6.00000			−0.192648
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	−0.840953	−	0.541108i	$-0.818005\pi$
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	0.889090	+	0.457732i	$0.151338\pi$
$972$		0			0
$973$	8.00000	+	13.8564i	0.256468	+	0.444216i
$974$	−13.0000			−0.416547
$975$		0			0
$976$	11.0000			0.352101
$977$	19.5000	+	33.7750i	0.623860	+	1.08056i	0.988760	+	0.149511i	$0.0477699\pi$
$977$	19.5000	+	33.7750i	0.623860	+	1.08056i	−0.364900	+	0.931047i	$0.618897\pi$
$978$		0			0
$979$		0			0
$980$	−3.00000			−0.0958315
$981$		0			0
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	30.0000			0.956851			0.478426	−	0.878128i	$-0.341208\pi$
$983$	30.0000			0.956851			0.478426	+	0.878128i	$0.341208\pi$
$984$		0			0
$985$	−18.0000	−	31.1769i	−0.573528	−	0.993379i
$986$	−18.0000	−	31.1769i	−0.573237	−	0.992875i
$987$		0			0
$988$	−4.00000	+	13.8564i	−0.127257	+	0.440831i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	0.698853	−	0.715265i	$-0.253694\pi$
$991$	−8.50000	−	14.7224i	−0.270011	−	0.467673i	−0.968864	+	0.247592i	$0.920361\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$		0			0
$994$	−1.50000	+	2.59808i	−0.0475771	+	0.0824060i
$995$	21.0000	−	36.3731i	0.665745	−	1.15310i
$996$		0			0
$997$	−17.5000	+	30.3109i	−0.554231	+	0.959955i	0.443732	+	0.896159i	$0.353654\pi$
$997$	−17.5000	+	30.3109i	−0.554231	+	0.959955i	−0.997963	+	0.0637961i	$0.979679\pi$
$998$	11.0000	+	19.0526i	0.348199	+	0.603098i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.c.757.1		2
3.2	odd	2		182.2.g.b.29.1	✓	2
12.11	even	2		1456.2.s.e.1121.1		2
13.9	even	3	inner	1638.2.r.c.1387.1		2
21.2	odd	6		1274.2.h.j.263.1		2
21.5	even	6		1274.2.h.i.263.1		2
21.11	odd	6		1274.2.e.d.471.1		2
21.17	even	6		1274.2.e.i.471.1		2
21.20	even	2		1274.2.g.g.393.1		2
39.2	even	12		2366.2.d.f.337.2		2
39.11	even	12		2366.2.d.f.337.1		2
39.23	odd	6		2366.2.a.n.1.1		1
39.29	odd	6		2366.2.a.f.1.1		1
39.35	odd	6		182.2.g.b.113.1	yes	2
156.35	even	6		1456.2.s.e.113.1		2
273.74	odd	6		1274.2.h.j.373.1		2
273.152	even	6		1274.2.e.i.165.1		2
273.191	odd	6		1274.2.e.d.165.1		2
273.230	even	6		1274.2.g.g.295.1		2
273.269	even	6		1274.2.h.i.373.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.b.29.1	✓	2	3.2	odd	2
182.2.g.b.113.1	yes	2	39.35	odd	6
1274.2.e.d.165.1		2	273.191	odd	6
1274.2.e.d.471.1		2	21.11	odd	6
1274.2.e.i.165.1		2	273.152	even	6
1274.2.e.i.471.1		2	21.17	even	6
1274.2.g.g.295.1		2	273.230	even	6
1274.2.g.g.393.1		2	21.20	even	2
1274.2.h.i.263.1		2	21.5	even	6
1274.2.h.i.373.1		2	273.269	even	6
1274.2.h.j.263.1		2	21.2	odd	6
1274.2.h.j.373.1		2	273.74	odd	6
1456.2.s.e.113.1		2	156.35	even	6
1456.2.s.e.1121.1		2	12.11	even	2
1638.2.r.c.757.1		2	1.1	even	1	trivial
1638.2.r.c.1387.1		2	13.9	even	3	inner
2366.2.a.f.1.1		1	39.29	odd	6
2366.2.a.n.1.1		1	39.23	odd	6
2366.2.d.f.337.1		2	39.11	even	12
2366.2.d.f.337.2		2	39.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(2.50000 + 2.59808i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(1.50000 - 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{23} +4.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +(-0.500000 - 0.866025i) q^{28} +(3.00000 + 5.19615i) q^{29} -10.0000 q^{31} +(-0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +(1.50000 - 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} -4.00000 q^{38} -3.00000 q^{40} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 2.59808i) q^{46} -6.00000 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-3.50000 + 0.866025i) q^{52} -12.0000 q^{53} +(-0.500000 + 0.866025i) q^{56} +(3.00000 - 5.19615i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(-7.50000 - 7.79423i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(3.00000 + 5.19615i) q^{68} -3.00000 q^{70} +(-1.50000 + 2.59808i) q^{71} +2.00000 q^{73} +(-4.00000 + 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{76} -4.00000 q^{79} +(1.50000 + 2.59808i) q^{80} +(-9.00000 + 15.5885i) q^{85} +8.00000 q^{86} +(-3.00000 - 5.19615i) q^{89} +(-3.50000 + 0.866025i) q^{91} -3.00000 q^{92} +(3.00000 + 5.19615i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 6 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 6 * q^5 - q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 6 q^{5} - q^{7} + 2 q^{8} + 3 q^{10} + 5 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 3 q^{20} + 3 q^{23} + 8 q^{25} + 2 q^{26} - q^{28} + 6 q^{29} - 20 q^{31} - q^{32} - 12 q^{34} + 3 q^{35} - 8 q^{37} - 8 q^{38} - 6 q^{40} - 8 q^{43} + 3 q^{46} - 12 q^{47} - q^{49} - 4 q^{50} - 7 q^{52} - 24 q^{53} - q^{56} + 6 q^{58} + 3 q^{59} - 11 q^{61} + 10 q^{62} + 2 q^{64} - 15 q^{65} - 2 q^{67} + 6 q^{68} - 6 q^{70} - 3 q^{71} + 4 q^{73} - 8 q^{74} + 4 q^{76} - 8 q^{79} + 3 q^{80} - 18 q^{85} + 16 q^{86} - 6 q^{89} - 7 q^{91} - 6 q^{92} + 6 q^{94} - 12 q^{95} - 2 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 6 * q^5 - q^7 + 2 * q^8 + 3 * q^10 + 5 * q^13 + 2 * q^14 - q^16 + 6 * q^17 + 4 * q^19 + 3 * q^20 + 3 * q^23 + 8 * q^25 + 2 * q^26 - q^28 + 6 * q^29 - 20 * q^31 - q^32 - 12 * q^34 + 3 * q^35 - 8 * q^37 - 8 * q^38 - 6 * q^40 - 8 * q^43 + 3 * q^46 - 12 * q^47 - q^49 - 4 * q^50 - 7 * q^52 - 24 * q^53 - q^56 + 6 * q^58 + 3 * q^59 - 11 * q^61 + 10 * q^62 + 2 * q^64 - 15 * q^65 - 2 * q^67 + 6 * q^68 - 6 * q^70 - 3 * q^71 + 4 * q^73 - 8 * q^74 + 4 * q^76 - 8 * q^79 + 3 * q^80 - 18 * q^85 + 16 * q^86 - 6 * q^89 - 7 * q^91 - 6 * q^92 + 6 * q^94 - 12 * q^95 - 2 * q^97 - q^98

Introduction

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