LMFDB - Embedded newform 1710.2.l.c.1531.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, 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("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1531.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1710.1531
Dual form			1710.2.l.c.1261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} -1.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(2.50000 - 4.33013i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(0.500000 - 0.866025i) q^{22} +(3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +6.00000 q^{26} +(2.50000 + 4.33013i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} +(-2.50000 + 4.33013i) q^{35} +7.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(0.500000 + 0.866025i) q^{44} -7.00000 q^{46} +(-4.00000 - 6.92820i) q^{47} +18.0000 q^{49} +1.00000 q^{50} +(-3.00000 + 5.19615i) q^{52} +(5.50000 + 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{55} -5.00000 q^{56} -6.00000 q^{58} +(-4.00000 + 6.92820i) q^{59} +(2.00000 + 3.46410i) q^{61} +1.00000 q^{64} -6.00000 q^{65} +(-6.00000 - 10.3923i) q^{67} -4.00000 q^{68} +(-2.50000 - 4.33013i) q^{70} +(1.00000 - 1.73205i) q^{71} +(1.00000 - 1.73205i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(4.00000 - 1.73205i) q^{76} +5.00000 q^{77} +(-5.00000 + 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.50000 - 4.33013i) q^{82} +10.0000 q^{83} +(-2.00000 - 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} -1.00000 q^{88} +(6.50000 + 11.2583i) q^{89} +(15.0000 + 25.9808i) q^{91} +(3.50000 - 6.06218i) q^{92} +8.00000 q^{94} +(3.50000 + 2.59808i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(-9.00000 + 15.5885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + q^{5} - 10 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + q^5 - 10 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + q^{5} - 10 q^{7} + 2 q^{8} + q^{10} - 2 q^{11} - 6 q^{13} + 5 q^{14} - q^{16} + 4 q^{17} - q^{19} - 2 q^{20} + q^{22} + 7 q^{23} - q^{25} + 12 q^{26} + 5 q^{28} + 6 q^{29} - q^{32} + 4 q^{34} - 5 q^{35} + 14 q^{37} - 7 q^{38} + q^{40} - 5 q^{41} - 6 q^{43} + q^{44} - 14 q^{46} - 8 q^{47} + 36 q^{49} + 2 q^{50} - 6 q^{52} + 11 q^{53} - q^{55} - 10 q^{56} - 12 q^{58} - 8 q^{59} + 4 q^{61} + 2 q^{64} - 12 q^{65} - 12 q^{67} - 8 q^{68} - 5 q^{70} + 2 q^{71} + 2 q^{73} - 7 q^{74} + 8 q^{76} + 10 q^{77} - 10 q^{79} + q^{80} - 5 q^{82} + 20 q^{83} - 4 q^{85} - 6 q^{86} - 2 q^{88} + 13 q^{89} + 30 q^{91} + 7 q^{92} + 16 q^{94} + 7 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + q^5 - 10 * q^7 + 2 * q^8 + q^10 - 2 * q^11 - 6 * q^13 + 5 * q^14 - q^16 + 4 * q^17 - q^19 - 2 * q^20 + q^22 + 7 * q^23 - q^25 + 12 * q^26 + 5 * q^28 + 6 * q^29 - q^32 + 4 * q^34 - 5 * q^35 + 14 * q^37 - 7 * q^38 + q^40 - 5 * q^41 - 6 * q^43 + q^44 - 14 * q^46 - 8 * q^47 + 36 * q^49 + 2 * q^50 - 6 * q^52 + 11 * q^53 - q^55 - 10 * q^56 - 12 * q^58 - 8 * q^59 + 4 * q^61 + 2 * q^64 - 12 * q^65 - 12 * q^67 - 8 * q^68 - 5 * q^70 + 2 * q^71 + 2 * q^73 - 7 * q^74 + 8 * q^76 + 10 * q^77 - 10 * q^79 + q^80 - 5 * q^82 + 20 * q^83 - 4 * q^85 - 6 * q^86 - 2 * q^88 + 13 * q^89 + 30 * q^91 + 7 * q^92 + 16 * q^94 + 7 * q^95 - 2 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−5.00000			−1.88982			−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−5.00000			−1.88982			−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	2.50000	−	4.33013i	0.668153	−	1.15728i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	6.00000			1.17670
$27$		0			0
$28$	2.50000	+	4.33013i	0.472456	+	0.818317i
$29$	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
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	−2.50000	+	4.33013i	−0.422577	+	0.731925i
$36$		0			0
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	−3.50000	−	2.59808i	−0.567775	−	0.421464i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$		0			0
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	−7.00000			−1.03209
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$	18.0000			2.57143
$50$	1.00000			0.141421
$51$		0			0
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	5.50000	+	9.52628i	0.755483	+	1.30854i	0.945134	+	0.326683i	$0.105931\pi$
$53$	5.50000	+	9.52628i	0.755483	+	1.30854i	−0.189651	+	0.981852i	$0.560736\pi$
$54$		0			0
$55$	−0.500000	+	0.866025i	−0.0674200	+	0.116775i
$56$	−5.00000			−0.668153
$57$		0			0
$58$	−6.00000			−0.787839
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000			−0.744208
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	−2.50000	−	4.33013i	−0.298807	−	0.517549i
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	−0.800566	−	0.599245i	$-0.795468\pi$
$71$	1.00000	−	1.73205i	0.118678	−	0.205557i	0.919244	+	0.393688i	$0.128801\pi$
$72$		0			0
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$		0			0
$76$	4.00000	−	1.73205i	0.458831	−	0.198680i
$77$	5.00000			0.569803
$78$		0			0
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	0.434730	+	0.900561i	$0.356844\pi$
$79$	−5.00000	+	8.66025i	−0.562544	+	0.974355i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	10.0000			1.09764			0.548821	−	0.835940i	$-0.315077\pi$
$83$	10.0000			1.09764			0.548821	+	0.835940i	$0.315077\pi$
$84$		0			0
$85$	−2.00000	−	3.46410i	−0.216930	−	0.375735i
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$		0			0
$88$	−1.00000			−0.106600
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	0.972162	+	0.234309i	$0.0752827\pi$
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	−0.283164	+	0.959072i	$0.591384\pi$
$90$		0			0
$91$	15.0000	+	25.9808i	1.57243	+	2.72352i
$92$	3.50000	−	6.06218i	0.364900	−	0.632026i
$93$		0			0
$94$	8.00000			0.825137
$95$	3.50000	+	2.59808i	0.359092	+	0.266557i
$96$		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	$0.199042\pi$
$98$	−9.00000	+	15.5885i	−0.909137	+	1.57467i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	15.0000			1.47799			0.738997	−	0.673709i	$-0.235300\pi$
$103$	15.0000			1.47799			0.738997	+	0.673709i	$0.235300\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	−11.0000			−1.06841
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$		0			0
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$		0			0
$112$	2.50000	−	4.33013i	0.236228	−	0.409159i
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$	7.00000			0.652753
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$		0			0
$118$	−4.00000	−	6.92820i	−0.368230	−	0.637793i
$119$	−10.0000	+	17.3205i	−0.916698	+	1.58777i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	−4.00000			−0.362143
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	0.955366	−	0.295423i	$-0.0954607\pi$
$127$	2.50000	+	4.33013i	0.221839	+	0.384237i	−0.733527	+	0.679660i	$0.762127\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$	2.50000	−	21.6506i	0.216777	−	1.87735i
$134$	12.0000			1.03664
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−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
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	0.975417	+	0.220366i	$0.0707252\pi$
$139$	8.00000	+	13.8564i	0.678551	+	1.17529i	−0.296866	+	0.954919i	$0.595942\pi$
$140$	5.00000			0.422577
$141$		0			0
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	3.00000	+	5.19615i	0.250873	+	0.434524i
$144$		0			0
$145$	6.00000			0.498273
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$		0			0
$148$	−3.50000	−	6.06218i	−0.287698	−	0.498308i
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	−0.936245	−	0.351348i	$-0.885723\pi$
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	0.772399	+	0.635138i	$0.219057\pi$
$150$		0			0
$151$	−20.0000			−1.62758			−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000			−1.62758			−0.813788	+	0.581161i	$0.802599\pi$
$152$	−0.500000	+	4.33013i	−0.0405554	+	0.351220i
$153$		0			0
$154$	−2.50000	+	4.33013i	−0.201456	+	0.348932i
$155$		0			0
$156$		0			0
$157$	−4.50000	+	7.79423i	−0.359139	+	0.622047i	−0.987817	−	0.155618i	$-0.950263\pi$
$157$	−4.50000	+	7.79423i	−0.359139	+	0.622047i	0.628678	+	0.777666i	$0.283596\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−17.5000	−	30.3109i	−1.37919	−	2.38883i
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	−5.00000	+	8.66025i	−0.388075	+	0.672166i
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	0.911099	+	0.412188i	$0.135235\pi$
$167$	10.5000	+	18.1865i	0.812514	+	1.40732i	−0.0985846	+	0.995129i	$0.531432\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	4.00000			0.306786
$171$		0			0
$172$	6.00000			0.457496
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$		0			0
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$		0			0
$178$	−13.0000			−0.974391
$179$	−7.00000			−0.523205			−0.261602	−	0.965176i	$-0.584251\pi$
$179$	−7.00000			−0.523205			−0.261602	+	0.965176i	$0.584251\pi$
$180$		0			0
$181$	−9.00000	−	15.5885i	−0.668965	−	1.15868i	−0.978194	−	0.207693i	$-0.933404\pi$
$181$	−9.00000	−	15.5885i	−0.668965	−	1.15868i	0.309229	−	0.950988i	$-0.399929\pi$
$182$	−30.0000			−2.22375
$183$		0			0
$184$	3.50000	+	6.06218i	0.258023	+	0.446910i
$185$	3.50000	−	6.06218i	0.257325	−	0.445700i
$186$		0			0
$187$	−2.00000	+	3.46410i	−0.146254	+	0.253320i
$188$	−4.00000	+	6.92820i	−0.291730	+	0.505291i
$189$		0			0
$190$	−4.00000	+	1.73205i	−0.290191	+	0.125656i
$191$	14.0000			1.01300			0.506502	−	0.862239i	$-0.330938\pi$
$191$	14.0000			1.01300			0.506502	+	0.862239i	$0.330938\pi$
$192$		0			0
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$	−9.00000	−	15.5885i	−0.642857	−	1.11346i
$197$	−1.00000			−0.0712470			−0.0356235	−	0.999365i	$-0.511342\pi$
$197$	−1.00000			−0.0712470			−0.0356235	+	0.999365i	$0.511342\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	−2.00000			−0.140720
$203$	−15.0000	−	25.9808i	−1.05279	−	1.82349i
$204$		0			0
$205$	2.50000	+	4.33013i	0.174608	+	0.302429i
$206$	−7.50000	+	12.9904i	−0.522550	+	0.905083i
$207$		0			0
$208$	6.00000			0.416025
$209$	0.500000	−	4.33013i	0.0345857	−	0.299521i
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	5.50000	−	9.52628i	0.377742	−	0.654268i
$213$		0			0
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$		0			0
$217$		0			0
$218$	8.00000	+	13.8564i	0.541828	+	0.938474i
$219$		0			0
$220$	1.00000			0.0674200
$221$	−24.0000			−1.61441
$222$		0			0
$223$	10.5000	−	18.1865i	0.703132	−	1.21786i	−0.264229	−	0.964460i	$-0.585118\pi$
$223$	10.5000	−	18.1865i	0.703132	−	1.21786i	0.967361	−	0.253401i	$-0.0815490\pi$
$224$	2.50000	+	4.33013i	0.167038	+	0.289319i
$225$		0			0
$226$	2.00000	−	3.46410i	0.133038	−	0.230429i
$227$	−2.00000			−0.132745			−0.0663723	−	0.997795i	$-0.521143\pi$
$227$	−2.00000			−0.132745			−0.0663723	+	0.997795i	$0.521143\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−3.50000	+	6.06218i	−0.230783	+	0.399728i
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	0.404674	+	0.914461i	$0.367385\pi$
$233$	−9.00000	+	15.5885i	−0.589610	+	1.02123i	−0.994283	+	0.106773i	$0.965948\pi$
$234$		0			0
$235$	−8.00000			−0.521862
$236$	8.00000			0.520756
$237$		0			0
$238$	−10.0000	−	17.3205i	−0.648204	−	1.12272i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$		0			0
$244$	2.00000	−	3.46410i	0.128037	−	0.221766i
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$		0			0
$247$	24.0000	−	10.3923i	1.52708	−	0.661247i
$248$		0			0
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$		0			0
$253$	−3.50000	−	6.06218i	−0.220043	−	0.381126i
$254$	−5.00000			−0.313728
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	−35.0000			−2.17479
$260$	3.00000	+	5.19615i	0.186052	+	0.322252i
$261$		0			0
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$		0			0
$265$	11.0000			0.675725
$266$	17.5000	+	12.9904i	1.07299	+	0.796491i
$267$		0			0
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	16.0000	−	27.7128i	0.975537	−	1.68968i	0.297386	−	0.954757i	$-0.403885\pi$
$269$	16.0000	−	27.7128i	0.975537	−	1.68968i	0.678151	−	0.734923i	$-0.262782\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$		0			0
$274$	12.0000			0.724947
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	−14.0000			−0.841178			−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000			−0.841178			−0.420589	+	0.907251i	$0.638177\pi$
$278$	−16.0000			−0.959616
$279$		0			0
$280$	−2.50000	+	4.33013i	−0.149404	+	0.258775i
$281$	−5.50000	−	9.52628i	−0.328102	−	0.568290i	0.654033	−	0.756466i	$-0.273076\pi$
$281$	−5.50000	−	9.52628i	−0.328102	−	0.568290i	−0.982135	+	0.188176i	$0.939742\pi$
$282$		0			0
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	0.328291	+	0.944577i	$0.393527\pi$
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	−0.982173	+	0.187980i	$0.939806\pi$
$284$	−2.00000			−0.118678
$285$		0			0
$286$	−6.00000			−0.354787
$287$	12.5000	−	21.6506i	0.737852	−	1.27800i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$		0			0
$292$	−2.00000			−0.117041
$293$	−5.00000			−0.292103			−0.146052	−	0.989277i	$-0.546657\pi$
$293$	−5.00000			−0.292103			−0.146052	+	0.989277i	$0.546657\pi$
$294$		0			0
$295$	4.00000	+	6.92820i	0.232889	+	0.403376i
$296$	7.00000			0.406867
$297$		0			0
$298$	−2.00000	−	3.46410i	−0.115857	−	0.200670i
$299$	21.0000	−	36.3731i	1.21446	−	2.10351i
$300$		0			0
$301$	15.0000	−	25.9808i	0.864586	−	1.49751i
$302$	10.0000	−	17.3205i	0.575435	−	0.996683i
$303$		0			0
$304$	−3.50000	−	2.59808i	−0.200739	−	0.149010i
$305$	4.00000			0.229039
$306$		0			0
$307$	−9.00000	+	15.5885i	−0.513657	+	0.889680i	0.486217	+	0.873838i	$0.338376\pi$
$307$	−9.00000	+	15.5885i	−0.513657	+	0.889680i	−0.999875	+	0.0158424i	$0.994957\pi$
$308$	−2.50000	−	4.33013i	−0.142451	−	0.246732i
$309$		0			0
$310$		0			0
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$		0			0
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−4.50000	−	7.79423i	−0.253950	−	0.439854i
$315$		0			0
$316$	10.0000			0.562544
$317$	1.50000	+	2.59808i	0.0842484	+	0.145922i	0.905071	−	0.425261i	$-0.139818\pi$
$317$	1.50000	+	2.59808i	0.0842484	+	0.145922i	−0.820822	+	0.571184i	$0.806484\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	35.0000			1.95047
$323$	14.0000	+	10.3923i	0.778981	+	0.578243i
$324$		0			0
$325$	−3.00000	+	5.19615i	−0.166410	+	0.288231i
$326$	5.00000	−	8.66025i	0.276924	−	0.479647i
$327$		0			0
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	20.0000	+	34.6410i	1.10264	+	1.90982i
$330$		0			0
$331$	15.0000			0.824475			0.412237	−	0.911077i	$-0.364747\pi$
$331$	15.0000			0.824475			0.412237	+	0.911077i	$0.364747\pi$
$332$	−5.00000	−	8.66025i	−0.274411	−	0.475293i
$333$		0			0
$334$	−21.0000			−1.14907
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	−0.891976	−	0.452082i	$-0.850681\pi$
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	0.837503	+	0.546433i	$0.184015\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$		0			0
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$		0			0
$342$		0			0
$343$	−55.0000			−2.96972
$344$	−3.00000	+	5.19615i	−0.161749	+	0.280158i
$345$		0			0
$346$	−4.50000	−	7.79423i	−0.241921	−	0.419020i
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	−0.891618	−	0.452788i	$-0.850429\pi$
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	0.837935	+	0.545770i	$0.183763\pi$
$348$		0			0
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$	−5.00000			−0.267261
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−36.0000			−1.91609			−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000			−1.91609			−0.958043	+	0.286623i	$0.907467\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	6.50000	−	11.2583i	0.344499	−	0.596690i
$357$		0			0
$358$	3.50000	−	6.06218i	0.184981	−	0.320396i
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	−0.999590	−	0.0286287i	$-0.990886\pi$
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	0.524588	+	0.851356i	$0.324219\pi$
$360$		0			0
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	18.0000			0.946059
$363$		0			0
$364$	15.0000	−	25.9808i	0.786214	−	1.36176i
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	−7.00000			−0.364900
$369$		0			0
$370$	3.50000	+	6.06218i	0.181956	+	0.315158i
$371$	−27.5000	−	47.6314i	−1.42773	−	2.47290i
$372$		0			0
$373$	5.00000			0.258890			0.129445	−	0.991587i	$-0.458680\pi$
$373$	5.00000			0.258890			0.129445	+	0.991587i	$0.458680\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	−4.00000	−	6.92820i	−0.206284	−	0.357295i
$377$	18.0000	−	31.1769i	0.927047	−	1.60569i
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	0.500000	−	4.33013i	0.0256495	−	0.222131i
$381$		0			0
$382$	−7.00000	+	12.1244i	−0.358151	+	0.620336i
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$		0			0
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	2.00000	+	3.46410i	0.101797	+	0.176318i
$387$		0			0
$388$	2.00000			0.101535
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$		0			0
$391$	28.0000			1.41602
$392$	18.0000			0.909137
$393$		0			0
$394$	0.500000	−	0.866025i	0.0251896	−	0.0436297i
$395$	5.00000	+	8.66025i	0.251577	+	0.435745i
$396$		0			0
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	−0.0714068	−	0.997447i	$-0.522749\pi$
$397$	16.5000	−	28.5788i	0.828111	−	1.43433i	0.899518	−	0.436884i	$-0.143918\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$		0			0
$404$	1.00000	−	1.73205i	0.0497519	−	0.0861727i
$405$		0			0
$406$	30.0000			1.48888
$407$	−7.00000			−0.346977
$408$		0			0
$409$	1.50000	+	2.59808i	0.0741702	+	0.128467i	0.900725	−	0.434389i	$-0.143036\pi$
$409$	1.50000	+	2.59808i	0.0741702	+	0.128467i	−0.826555	+	0.562856i	$0.809703\pi$
$410$	−5.00000			−0.246932
$411$		0			0
$412$	−7.50000	−	12.9904i	−0.369498	−	0.639990i
$413$	20.0000	−	34.6410i	0.984136	−	1.70457i
$414$		0			0
$415$	5.00000	−	8.66025i	0.245440	−	0.425115i
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$		0			0
$418$	3.50000	+	2.59808i	0.171191	+	0.127076i
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	−6.50000	−	11.2583i	−0.316415	−	0.548047i
$423$		0			0
$424$	5.50000	+	9.52628i	0.267104	+	0.462637i
$425$	−4.00000			−0.194029
$426$		0			0
$427$	−10.0000	−	17.3205i	−0.483934	−	0.838198i
$428$	−2.00000	−	3.46410i	−0.0966736	−	0.167444i
$429$		0			0
$430$	−6.00000			−0.289346
$431$	−2.00000	−	3.46410i	−0.0963366	−	0.166860i	0.813829	−	0.581104i	$-0.197379\pi$
$431$	−2.00000	−	3.46410i	−0.0963366	−	0.166860i	−0.910166	+	0.414244i	$0.864046\pi$
$432$		0			0
$433$	−3.00000	−	5.19615i	−0.144171	−	0.249711i	0.784892	−	0.619632i	$-0.212718\pi$
$433$	−3.00000	−	5.19615i	−0.144171	−	0.249711i	−0.929063	+	0.369921i	$0.879385\pi$
$434$		0			0
$435$		0			0
$436$	−16.0000			−0.766261
$437$	−28.0000	+	12.1244i	−1.33942	+	0.579987i
$438$		0			0
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$	−0.500000	+	0.866025i	−0.0238366	+	0.0412861i
$441$		0			0
$442$	12.0000	−	20.7846i	0.570782	−	0.988623i
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	0.996551	+	0.0829786i	$0.0264433\pi$
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	−0.426414	+	0.904528i	$0.640223\pi$
$444$		0			0
$445$	13.0000			0.616259
$446$	10.5000	+	18.1865i	0.497189	+	0.861157i
$447$		0			0
$448$	−5.00000			−0.236228
$449$	39.0000			1.84052			0.920262	−	0.391303i	$-0.127976\pi$
$449$	39.0000			1.84052			0.920262	+	0.391303i	$0.127976\pi$
$450$		0			0
$451$	2.50000	−	4.33013i	0.117720	−	0.203898i
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$		0			0
$454$	1.00000	−	1.73205i	0.0469323	−	0.0812892i
$455$	30.0000			1.40642
$456$		0			0
$457$	8.00000			0.374224			0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000			0.374224			0.187112	+	0.982339i	$0.440087\pi$
$458$	−5.00000	+	8.66025i	−0.233635	+	0.404667i
$459$		0			0
$460$	−3.50000	−	6.06218i	−0.163188	−	0.282650i
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$		0			0
$463$	−9.00000			−0.418265			−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000			−0.418265			−0.209133	+	0.977887i	$0.567064\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	−38.0000			−1.75843			−0.879215	−	0.476425i	$-0.841932\pi$
$467$	−38.0000			−1.75843			−0.879215	+	0.476425i	$0.841932\pi$
$468$		0			0
$469$	30.0000	+	51.9615i	1.38527	+	2.39936i
$470$	4.00000	−	6.92820i	0.184506	−	0.319574i
$471$		0			0
$472$	−4.00000	+	6.92820i	−0.184115	+	0.318896i
$473$	3.00000	−	5.19615i	0.137940	−	0.238919i
$474$		0			0
$475$	4.00000	−	1.73205i	0.183533	−	0.0794719i
$476$	20.0000			0.916698
$477$		0			0
$478$		0			0
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.723681	+	0.690134i	$0.242449\pi$
$479$	21.0000	+	36.3731i	0.959514	+	1.66193i	0.235833	+	0.971794i	$0.424218\pi$
$480$		0			0
$481$	−21.0000	−	36.3731i	−0.957518	−	1.65847i
$482$	−26.0000			−1.18427
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−13.0000			−0.589086			−0.294543	−	0.955638i	$-0.595167\pi$
$487$	−13.0000			−0.589086			−0.294543	+	0.955638i	$0.595167\pi$
$488$	2.00000	+	3.46410i	0.0905357	+	0.156813i
$489$		0			0
$490$	9.00000	+	15.5885i	0.406579	+	0.704215i
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	0.205731	+	0.978609i	$0.434043\pi$
$491$	−16.5000	+	28.5788i	−0.744635	+	1.28974i	−0.950365	+	0.311136i	$0.899290\pi$
$492$		0			0
$493$	24.0000			1.08091
$494$	−3.00000	+	25.9808i	−0.134976	+	1.16893i
$495$		0			0
$496$		0			0
$497$	−5.00000	+	8.66025i	−0.224281	+	0.388465i
$498$		0			0
$499$	3.50000	−	6.06218i	0.156682	−	0.271380i	−0.776989	−	0.629515i	$-0.783254\pi$
$499$	3.50000	−	6.06218i	0.156682	−	0.271380i	0.933670	+	0.358134i	$0.116587\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	0.500000	+	0.866025i	0.0222939	+	0.0386142i	0.876957	−	0.480569i	$-0.159570\pi$
$503$	0.500000	+	0.866025i	0.0222939	+	0.0386142i	−0.854663	+	0.519183i	$0.826236\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$	7.00000			0.311188
$507$		0			0
$508$	2.50000	−	4.33013i	0.110920	−	0.192118i
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	0.887336	−	0.461123i	$-0.152553\pi$
$509$	1.00000	+	1.73205i	0.0443242	+	0.0767718i	−0.843012	+	0.537895i	$0.819220\pi$
$510$		0			0
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.0000			−0.793946
$515$	7.50000	−	12.9904i	0.330489	−	0.572425i
$516$		0			0
$517$	4.00000	+	6.92820i	0.175920	+	0.304702i
$518$	17.5000	−	30.3109i	0.768906	−	1.33178i
$519$		0			0
$520$	−6.00000			−0.263117
$521$	14.0000			0.613351			0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000			0.613351			0.306676	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$	10.5000	+	18.1865i	0.457822	+	0.792971i
$527$		0			0
$528$		0			0
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$	−5.50000	+	9.52628i	−0.238905	+	0.413795i
$531$		0			0
$532$	−20.0000	+	8.66025i	−0.867110	+	0.375470i
$533$	30.0000			1.29944
$534$		0			0
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$		0			0
$538$	16.0000	+	27.7128i	0.689809	+	1.19478i
$539$	−18.0000			−0.775315
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$		0			0
$544$	−4.00000			−0.171499
$545$	−8.00000	−	13.8564i	−0.342682	−	0.593543i
$546$		0			0
$547$	−7.00000	−	12.1244i	−0.299298	−	0.518400i	0.676677	−	0.736280i	$-0.263419\pi$
$547$	−7.00000	−	12.1244i	−0.299298	−	0.518400i	−0.975976	+	0.217880i	$0.930086\pi$
$548$	−6.00000	+	10.3923i	−0.256307	+	0.443937i
$549$		0			0
$550$	−1.00000			−0.0426401
$551$	−24.0000	+	10.3923i	−1.02243	+	0.442727i
$552$		0			0
$553$	25.0000	−	43.3013i	1.06311	−	1.84136i
$554$	7.00000	−	12.1244i	0.297402	−	0.515115i
$555$		0			0
$556$	8.00000	−	13.8564i	0.339276	−	0.587643i
$557$	0.500000	+	0.866025i	0.0211857	+	0.0366947i	0.876424	−	0.481540i	$-0.159923\pi$
$557$	0.500000	+	0.866025i	0.0211857	+	0.0366947i	−0.855238	+	0.518235i	$0.826589\pi$
$558$		0			0
$559$	36.0000			1.52264
$560$	−2.50000	−	4.33013i	−0.105644	−	0.182981i
$561$		0			0
$562$	11.0000			0.464007
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$		0			0
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$	−11.0000	−	19.0526i	−0.462364	−	0.800839i
$567$		0			0
$568$	1.00000	−	1.73205i	0.0419591	−	0.0726752i
$569$	−33.0000			−1.38343			−0.691716	−	0.722170i	$-0.743145\pi$
$569$	−33.0000			−1.38343			−0.691716	+	0.722170i	$0.743145\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$		0			0
$574$	12.5000	+	21.6506i	0.521740	+	0.903680i
$575$	3.50000	−	6.06218i	0.145960	−	0.252810i
$576$		0			0
$577$	−32.0000			−1.33218			−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000			−1.33218			−0.666089	+	0.745873i	$0.732033\pi$
$578$	−1.00000			−0.0415945
$579$		0			0
$580$	−3.00000	−	5.19615i	−0.124568	−	0.215758i
$581$	−50.0000			−2.07435
$582$		0			0
$583$	−5.50000	−	9.52628i	−0.227787	−	0.394538i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$		0			0
$586$	2.50000	−	4.33013i	0.103274	−	0.178876i
$587$	−10.0000	+	17.3205i	−0.412744	+	0.714894i	−0.995189	−	0.0979766i	$-0.968763\pi$
$587$	−10.0000	+	17.3205i	−0.412744	+	0.714894i	0.582445	+	0.812870i	$0.302096\pi$
$588$		0			0
$589$		0			0
$590$	−8.00000			−0.329355
$591$		0			0
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	11.0000	+	19.0526i	0.451716	+	0.782395i	0.998493	−	0.0548835i	$-0.0174787\pi$
$593$	11.0000	+	19.0526i	0.451716	+	0.782395i	−0.546777	+	0.837278i	$0.684145\pi$
$594$		0			0
$595$	10.0000	+	17.3205i	0.409960	+	0.710072i
$596$	4.00000			0.163846
$597$		0			0
$598$	21.0000	+	36.3731i	0.858754	+	1.48741i
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	0.936099	−	0.351738i	$-0.114409\pi$
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	−0.772663	+	0.634816i	$0.781076\pi$
$600$		0			0
$601$	−3.00000			−0.122373			−0.0611863	−	0.998126i	$-0.519488\pi$
$601$	−3.00000			−0.122373			−0.0611863	+	0.998126i	$0.519488\pi$
$602$	15.0000	+	25.9808i	0.611354	+	1.05890i
$603$		0			0
$604$	10.0000	+	17.3205i	0.406894	+	0.704761i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	−1.00000			−0.0405887			−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000			−0.0405887			−0.0202944	+	0.999794i	$0.506460\pi$
$608$	4.00000	−	1.73205i	0.162221	−	0.0702439i
$609$		0			0
$610$	−2.00000	+	3.46410i	−0.0809776	+	0.140257i
$611$	−24.0000	+	41.5692i	−0.970936	+	1.68171i
$612$		0			0
$613$	−17.5000	+	30.3109i	−0.706818	+	1.22425i	0.259213	+	0.965820i	$0.416537\pi$
$613$	−17.5000	+	30.3109i	−0.706818	+	1.22425i	−0.966031	+	0.258425i	$0.916796\pi$
$614$	−9.00000	−	15.5885i	−0.363210	−	0.629099i
$615$		0			0
$616$	5.00000			0.201456
$617$	24.0000	+	41.5692i	0.966204	+	1.67351i	0.706346	+	0.707867i	$0.250342\pi$
$617$	24.0000	+	41.5692i	0.966204	+	1.67351i	0.259858	+	0.965647i	$0.416324\pi$
$618$		0			0
$619$	43.0000			1.72832			0.864158	−	0.503221i	$-0.167852\pi$
$619$	43.0000			1.72832			0.864158	+	0.503221i	$0.167852\pi$
$620$		0			0
$621$		0			0
$622$	−10.0000	+	17.3205i	−0.400963	+	0.694489i
$623$	−32.5000	−	56.2917i	−1.30209	−	2.25528i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$	9.00000			0.359139
$629$	14.0000	−	24.2487i	0.558217	−	0.966859i
$630$		0			0
$631$	−19.0000	−	32.9090i	−0.756378	−	1.31009i	−0.944686	−	0.327975i	$-0.893634\pi$
$631$	−19.0000	−	32.9090i	−0.756378	−	1.31009i	0.188308	−	0.982110i	$-0.439700\pi$
$632$	−5.00000	+	8.66025i	−0.198889	+	0.344486i
$633$		0			0
$634$	−3.00000			−0.119145
$635$	5.00000			0.198419
$636$		0			0
$637$	−54.0000	−	93.5307i	−2.13956	−	3.70582i
$638$	6.00000			0.237542
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	0.486409	+	0.873731i	$0.338307\pi$
$641$	−13.0000	+	22.5167i	−0.513469	+	0.889355i	−0.999878	+	0.0156233i	$0.995027\pi$
$642$		0			0
$643$	22.0000	−	38.1051i	0.867595	−	1.50272i	0.00314839	−	0.999995i	$-0.498998\pi$
$643$	22.0000	−	38.1051i	0.867595	−	1.50272i	0.864447	−	0.502724i	$-0.167669\pi$
$644$	−17.5000	+	30.3109i	−0.689597	+	1.19442i
$645$		0			0
$646$	−16.0000	+	6.92820i	−0.629512	+	0.272587i
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$		0			0
$649$	4.00000	−	6.92820i	0.157014	−	0.271956i
$650$	−3.00000	−	5.19615i	−0.117670	−	0.203810i
$651$		0			0
$652$	5.00000	+	8.66025i	0.195815	+	0.339162i
$653$	−9.00000			−0.352197			−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000			−0.352197			−0.176099	+	0.984373i	$0.556348\pi$
$654$		0			0
$655$	1.50000	+	2.59808i	0.0586098	+	0.101515i
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$		0			0
$658$	−40.0000			−1.55936
$659$	−5.50000	−	9.52628i	−0.214250	−	0.371091i	0.738791	−	0.673935i	$-0.235397\pi$
$659$	−5.50000	−	9.52628i	−0.214250	−	0.371091i	−0.953040	+	0.302844i	$0.902064\pi$
$660$		0			0
$661$	10.0000	+	17.3205i	0.388955	+	0.673690i	0.992309	−	0.123784i	$-0.0395028\pi$
$661$	10.0000	+	17.3205i	0.388955	+	0.673690i	−0.603354	+	0.797473i	$0.706170\pi$
$662$	−7.50000	+	12.9904i	−0.291496	+	0.504885i
$663$		0			0
$664$	10.0000			0.388075
$665$	−17.5000	−	12.9904i	−0.678621	−	0.503745i
$666$		0			0
$667$	−21.0000	+	36.3731i	−0.813123	+	1.40837i
$668$	10.5000	−	18.1865i	0.406257	−	0.703658i
$669$		0			0
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	−2.00000	−	3.46410i	−0.0772091	−	0.133730i
$672$		0			0
$673$	−40.0000			−1.54189			−0.770943	−	0.636904i	$-0.780215\pi$
$673$	−40.0000			−1.54189			−0.770943	+	0.636904i	$0.780215\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$		0			0
$676$	23.0000			0.884615
$677$	−21.0000			−0.807096			−0.403548	−	0.914959i	$-0.632223\pi$
$677$	−21.0000			−0.807096			−0.403548	+	0.914959i	$0.632223\pi$
$678$		0			0
$679$	5.00000	−	8.66025i	0.191882	−	0.332350i
$680$	−2.00000	−	3.46410i	−0.0766965	−	0.132842i
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	27.5000	−	47.6314i	1.04995	−	1.81858i
$687$		0			0
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	33.0000	−	57.1577i	1.25720	−	2.17753i
$690$		0			0
$691$	1.00000			0.0380418			0.0190209	−	0.999819i	$-0.493945\pi$
$691$	1.00000			0.0380418			0.0190209	+	0.999819i	$0.493945\pi$
$692$	9.00000			0.342129
$693$		0			0
$694$	−1.00000	−	1.73205i	−0.0379595	−	0.0657477i
$695$	16.0000			0.606915
$696$		0			0
$697$	10.0000	+	17.3205i	0.378777	+	0.656061i
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$		0			0
$700$	2.50000	−	4.33013i	0.0944911	−	0.163663i
$701$	17.0000	−	29.4449i	0.642081	−	1.11212i	−0.342886	−	0.939377i	$-0.611405\pi$
$701$	17.0000	−	29.4449i	0.642081	−	1.11212i	0.984967	−	0.172740i	$-0.0552621\pi$
$702$		0			0
$703$	−3.50000	+	30.3109i	−0.132005	+	1.14320i
$704$	−1.00000			−0.0376889
$705$		0			0
$706$	18.0000	−	31.1769i	0.677439	−	1.17336i
$707$	−5.00000	−	8.66025i	−0.188044	−	0.325702i
$708$		0			0
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	0.901135	−	0.433539i	$-0.142735\pi$
$709$	2.00000	+	3.46410i	0.0751116	+	0.130097i	−0.826023	+	0.563636i	$0.809402\pi$
$710$	2.00000			0.0750587
$711$		0			0
$712$	6.50000	+	11.2583i	0.243598	+	0.421924i
$713$		0			0
$714$		0			0
$715$	6.00000			0.224387
$716$	3.50000	+	6.06218i	0.130801	+	0.226554i
$717$		0			0
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	−22.0000	+	38.1051i	−0.820462	+	1.42108i	0.0848774	+	0.996391i	$0.472950\pi$
$719$	−22.0000	+	38.1051i	−0.820462	+	1.42108i	−0.905339	+	0.424690i	$0.860383\pi$
$720$		0			0
$721$	−75.0000			−2.79315
$722$	13.0000	−	13.8564i	0.483810	−	0.515682i
$723$		0			0
$724$	−9.00000	+	15.5885i	−0.334482	+	0.579340i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$		0			0
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	0.400362	+	0.916357i	$0.368884\pi$
$727$	−16.0000	+	27.7128i	−0.593407	+	1.02781i	−0.993770	+	0.111454i	$0.964449\pi$
$728$	15.0000	+	25.9808i	0.555937	+	0.962911i
$729$		0			0
$730$	2.00000			0.0740233
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	19.0000			0.701781			0.350891	−	0.936416i	$-0.385879\pi$
$733$	19.0000			0.701781			0.350891	+	0.936416i	$0.385879\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	3.50000	−	6.06218i	0.129012	−	0.223455i
$737$	6.00000	+	10.3923i	0.221013	+	0.382805i
$738$		0			0
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	−0.00311943	−	0.999995i	$-0.500993\pi$
$739$	23.5000	−	40.7032i	0.864461	−	1.49729i	0.867581	−	0.497296i	$-0.165674\pi$
$740$	−7.00000			−0.257325
$741$		0			0
$742$	55.0000			2.01911
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	−0.695024	−	0.718986i	$-0.744606\pi$
$743$	7.50000	−	12.9904i	0.275148	−	0.476571i	0.970173	+	0.242415i	$0.0779397\pi$
$744$		0			0
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$	−2.50000	+	4.33013i	−0.0915315	+	0.158537i
$747$		0			0
$748$	4.00000			0.146254
$749$	−20.0000			−0.730784
$750$		0			0
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	8.00000			0.291730
$753$		0			0
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$	−10.0000	+	17.3205i	−0.363937	+	0.630358i
$756$		0			0
$757$	6.50000	−	11.2583i	0.236247	−	0.409191i	−0.723388	−	0.690442i	$-0.757416\pi$
$757$	6.50000	−	11.2583i	0.236247	−	0.409191i	0.959634	+	0.281251i	$0.0907494\pi$
$758$	2.00000	−	3.46410i	0.0726433	−	0.125822i
$759$		0			0
$760$	3.50000	+	2.59808i	0.126958	+	0.0942421i
$761$	31.0000			1.12375			0.561875	−	0.827222i	$-0.310080\pi$
$761$	31.0000			1.12375			0.561875	+	0.827222i	$0.310080\pi$
$762$		0			0
$763$	−40.0000	+	69.2820i	−1.44810	+	2.50818i
$764$	−7.00000	−	12.1244i	−0.253251	−	0.438644i
$765$		0			0
$766$	16.0000	+	27.7128i	0.578103	+	1.00130i
$767$	48.0000			1.73318
$768$		0			0
$769$	−3.00000	−	5.19615i	−0.108183	−	0.187378i	0.806851	−	0.590755i	$-0.201170\pi$
$769$	−3.00000	−	5.19615i	−0.108183	−	0.187378i	−0.915034	+	0.403376i	$0.867837\pi$
$770$	2.50000	+	4.33013i	0.0900937	+	0.156047i
$771$		0			0
$772$	−4.00000			−0.143963
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$		0			0
$775$		0			0
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	10.0000			0.358517
$779$	−17.5000	−	12.9904i	−0.627003	−	0.465429i
$780$		0			0
$781$	−1.00000	+	1.73205i	−0.0357828	+	0.0619777i
$782$	−14.0000	+	24.2487i	−0.500639	+	0.867132i
$783$		0			0
$784$	−9.00000	+	15.5885i	−0.321429	+	0.556731i
$785$	4.50000	+	7.79423i	0.160612	+	0.278188i
$786$		0			0
$787$	−26.0000			−0.926800			−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000			−0.926800			−0.463400	+	0.886149i	$0.653371\pi$
$788$	0.500000	+	0.866025i	0.0178118	+	0.0308509i
$789$		0			0
$790$	−10.0000			−0.355784
$791$	20.0000			0.711118
$792$		0			0
$793$	12.0000	−	20.7846i	0.426132	−	0.738083i
$794$	16.5000	+	28.5788i	0.585563	+	1.01423i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−47.0000			−1.66483			−0.832413	−	0.554156i	$-0.813041\pi$
$797$	−47.0000			−1.66483			−0.832413	+	0.554156i	$0.813041\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$	−35.0000			−1.23359
$806$		0			0
$807$		0			0
$808$	1.00000	+	1.73205i	0.0351799	+	0.0609333i
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$		0			0
$811$	−21.5000	−	37.2391i	−0.754967	−	1.30764i	−0.945391	−	0.325939i	$-0.894319\pi$
$811$	−21.5000	−	37.2391i	−0.754967	−	1.30764i	0.190424	−	0.981702i	$-0.439014\pi$
$812$	−15.0000	+	25.9808i	−0.526397	+	0.911746i
$813$		0			0
$814$	3.50000	−	6.06218i	0.122675	−	0.212479i
$815$	−5.00000	+	8.66025i	−0.175142	+	0.303355i
$816$		0			0
$817$	−21.0000	−	15.5885i	−0.734697	−	0.545371i
$818$	−3.00000			−0.104893
$819$		0			0
$820$	2.50000	−	4.33013i	0.0873038	−	0.151215i
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	0.955636	+	0.294549i	$0.0951694\pi$
$821$	21.0000	+	36.3731i	0.732905	+	1.26943i	−0.222731	+	0.974880i	$0.571497\pi$
$822$		0			0
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	0.993831	−	0.110910i	$-0.0353764\pi$
$823$	11.5000	+	19.9186i	0.400865	+	0.694318i	−0.592966	+	0.805228i	$0.702043\pi$
$824$	15.0000			0.522550
$825$		0			0
$826$	20.0000	+	34.6410i	0.695889	+	1.20532i
$827$	−15.0000	−	25.9808i	−0.521601	−	0.903440i	−0.999684	−	0.0251251i	$-0.992002\pi$
$827$	−15.0000	−	25.9808i	−0.521601	−	0.903440i	0.478083	−	0.878315i	$-0.341332\pi$
$828$		0			0
$829$	−28.0000			−0.972480			−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000			−0.972480			−0.486240	+	0.873825i	$0.661632\pi$
$830$	5.00000	+	8.66025i	0.173553	+	0.300602i
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	36.0000	−	62.3538i	1.24733	−	2.16043i
$834$		0			0
$835$	21.0000			0.726735
$836$	−4.00000	+	1.73205i	−0.138343	+	0.0599042i
$837$		0			0
$838$	−1.50000	+	2.59808i	−0.0518166	+	0.0897491i
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$		0			0
$844$	13.0000			0.447478
$845$	11.5000	+	19.9186i	0.395612	+	0.685220i
$846$		0			0
$847$	50.0000			1.71802
$848$	−11.0000			−0.377742
$849$		0			0
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	24.5000	+	42.4352i	0.839849	+	1.45466i
$852$		0			0
$853$	−9.00000	+	15.5885i	−0.308154	+	0.533739i	−0.977959	−	0.208799i	$-0.933045\pi$
$853$	−9.00000	+	15.5885i	−0.308154	+	0.533739i	0.669804	+	0.742538i	$0.266378\pi$
$854$	20.0000			0.684386
$855$		0			0
$856$	4.00000			0.136717
$857$	−18.0000	+	31.1769i	−0.614868	+	1.06498i	0.375539	+	0.926806i	$0.377458\pi$
$857$	−18.0000	+	31.1769i	−0.614868	+	1.06498i	−0.990408	+	0.138177i	$0.955876\pi$
$858$		0			0
$859$	8.50000	+	14.7224i	0.290016	+	0.502323i	0.973813	−	0.227349i	$-0.0730059\pi$
$859$	8.50000	+	14.7224i	0.290016	+	0.502323i	−0.683797	+	0.729672i	$0.739673\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$		0			0
$862$	4.00000			0.136241
$863$	1.00000			0.0340404			0.0170202	−	0.999855i	$-0.494582\pi$
$863$	1.00000			0.0340404			0.0170202	+	0.999855i	$0.494582\pi$
$864$		0			0
$865$	4.50000	+	7.79423i	0.153005	+	0.265012i
$866$	6.00000			0.203888
$867$		0			0
$868$		0			0
$869$	5.00000	−	8.66025i	0.169613	−	0.293779i
$870$		0			0
$871$	−36.0000	+	62.3538i	−1.21981	+	2.11278i
$872$	8.00000	−	13.8564i	0.270914	−	0.469237i
$873$		0			0
$874$	3.50000	−	30.3109i	0.118389	−	1.02528i
$875$	5.00000			0.169031
$876$		0			0
$877$	3.50000	−	6.06218i	0.118187	−	0.204705i	−0.800862	−	0.598848i	$-0.795625\pi$
$877$	3.50000	−	6.06218i	0.118187	−	0.204705i	0.919049	+	0.394143i	$0.128959\pi$
$878$	16.0000	+	27.7128i	0.539974	+	0.935262i
$879$		0			0
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	18.0000	+	31.1769i	0.605748	+	1.04919i	0.991933	+	0.126765i	$0.0404595\pi$
$883$	18.0000	+	31.1769i	0.605748	+	1.04919i	−0.386185	+	0.922422i	$0.626207\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−24.0000			−0.806296
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$	−12.5000	−	21.6506i	−0.419237	−	0.726139i
$890$	−6.50000	+	11.2583i	−0.217880	+	0.377380i
$891$		0			0
$892$	−21.0000			−0.703132
$893$	32.0000	−	13.8564i	1.07084	−	0.463687i
$894$		0			0
$895$	−3.50000	+	6.06218i	−0.116992	+	0.202636i
$896$	2.50000	−	4.33013i	0.0835191	−	0.144659i
$897$		0			0
$898$	−19.5000	+	33.7750i	−0.650723	+	1.12709i
$899$		0			0
$900$		0			0
$901$	44.0000			1.46585
$902$	2.50000	+	4.33013i	0.0832409	+	0.144177i
$903$		0			0
$904$	−4.00000			−0.133038
$905$	−18.0000			−0.598340
$906$		0			0
$907$	−11.0000	+	19.0526i	−0.365249	+	0.632630i	−0.988816	−	0.149140i	$-0.952349\pi$
$907$	−11.0000	+	19.0526i	−0.365249	+	0.632630i	0.623567	+	0.781770i	$0.285683\pi$
$908$	1.00000	+	1.73205i	0.0331862	+	0.0574801i
$909$		0			0
$910$	−15.0000	+	25.9808i	−0.497245	+	0.861254i
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$		0			0
$913$	−10.0000			−0.330952
$914$	−4.00000	+	6.92820i	−0.132308	+	0.229165i
$915$		0			0
$916$	−5.00000	−	8.66025i	−0.165205	−	0.286143i
$917$	7.50000	−	12.9904i	0.247672	−	0.428980i
$918$		0			0
$919$	−26.0000			−0.857661			−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000			−0.857661			−0.428830	+	0.903385i	$0.641074\pi$
$920$	7.00000			0.230783
$921$		0			0
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−3.50000	−	6.06218i	−0.115079	−	0.199323i
$926$	4.50000	−	7.79423i	0.147879	−	0.256134i
$927$		0			0
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	−0.962431	−	0.271526i	$-0.912472\pi$
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	0.716364	+	0.697727i	$0.245805\pi$
$930$		0			0
$931$	−9.00000	+	77.9423i	−0.294963	+	2.55446i
$932$	18.0000			0.589610
$933$		0			0
$934$	19.0000	−	32.9090i	0.621699	−	1.07681i
$935$	2.00000	+	3.46410i	0.0654070	+	0.113288i
$936$		0			0
$937$	11.0000	+	19.0526i	0.359354	+	0.622420i	0.987853	−	0.155391i	$-0.0496636\pi$
$937$	11.0000	+	19.0526i	0.359354	+	0.622420i	−0.628499	+	0.777811i	$0.716330\pi$
$938$	−60.0000			−1.95907
$939$		0			0
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	23.0000	+	39.8372i	0.749779	+	1.29865i	0.947929	+	0.318483i	$0.103173\pi$
$941$	23.0000	+	39.8372i	0.749779	+	1.29865i	−0.198150	+	0.980172i	$0.563493\pi$
$942$		0			0
$943$	−35.0000			−1.13976
$944$	−4.00000	−	6.92820i	−0.130189	−	0.225494i
$945$		0			0
$946$	3.00000	+	5.19615i	0.0975384	+	0.168941i
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	0.479801	+	0.877377i	$0.340709\pi$
$947$	−16.0000	+	27.7128i	−0.519930	+	0.900545i	−0.999732	+	0.0231683i	$0.992625\pi$
$948$		0			0
$949$	−12.0000			−0.389536
$950$	−0.500000	+	4.33013i	−0.0162221	+	0.140488i
$951$		0			0
$952$	−10.0000	+	17.3205i	−0.324102	+	0.561361i
$953$	−18.0000	+	31.1769i	−0.583077	+	1.00992i	0.412035	+	0.911168i	$0.364818\pi$
$953$	−18.0000	+	31.1769i	−0.583077	+	1.00992i	−0.995112	+	0.0987513i	$0.968515\pi$
$954$		0			0
$955$	7.00000	−	12.1244i	0.226515	−	0.392335i
$956$		0			0
$957$		0			0
$958$	−42.0000			−1.35696
$959$	30.0000	+	51.9615i	0.968751	+	1.67793i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	42.0000			1.35413
$963$		0			0
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$		0			0
$967$	−12.0000	+	20.7846i	−0.385894	+	0.668388i	−0.991893	−	0.127078i	$-0.959440\pi$
$967$	−12.0000	+	20.7846i	−0.385894	+	0.668388i	0.605999	+	0.795466i	$0.292774\pi$
$968$	−10.0000			−0.321412
$969$		0			0
$970$	−2.00000			−0.0642161
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$		0			0
$973$	−40.0000	−	69.2820i	−1.28234	−	2.22108i
$974$	6.50000	−	11.2583i	0.208273	−	0.360740i
$975$		0			0
$976$	−4.00000			−0.128037
$977$	6.00000			0.191957			0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000			0.191957			0.0959785	+	0.995383i	$0.469402\pi$
$978$		0			0
$979$	−6.50000	−	11.2583i	−0.207741	−	0.359818i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	−16.5000	−	28.5788i	−0.526536	−	0.911987i
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	−0.841112	−	0.540860i	$-0.818099\pi$
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	0.888955	+	0.457995i	$0.151432\pi$
$984$		0			0
$985$	−0.500000	+	0.866025i	−0.0159313	+	0.0275939i
$986$	−12.0000	+	20.7846i	−0.382158	+	0.661917i
$987$		0			0
$988$	−21.0000	−	15.5885i	−0.668099	−	0.495935i
$989$	−42.0000			−1.33552
$990$		0			0
$991$	−5.00000	+	8.66025i	−0.158830	+	0.275102i	−0.934447	−	0.356102i	$-0.884106\pi$
$991$	−5.00000	+	8.66025i	−0.158830	+	0.275102i	0.775617	+	0.631204i	$0.217439\pi$
$992$		0			0
$993$		0			0
$994$	−5.00000	−	8.66025i	−0.158590	−	0.274687i
$995$	4.00000			0.126809
$996$		0			0
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$	3.50000	+	6.06218i	0.110791	+	0.191895i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.c.1531.1		2
3.2	odd	2		570.2.i.e.391.1	yes	2
19.7	even	3	inner	1710.2.l.c.1261.1		2
57.26	odd	6		570.2.i.e.121.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.e.121.1	✓	2	57.26	odd	6
570.2.i.e.391.1	yes	2	3.2	odd	2
1710.2.l.c.1261.1		2	19.7	even	3	inner
1710.2.l.c.1531.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} -1.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(2.50000 - 4.33013i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.500000 + 4.33013i) q^{19} -1.00000 q^{20} +(0.500000 - 0.866025i) q^{22} +(3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +6.00000 q^{26} +(2.50000 + 4.33013i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.500000 - 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{34} +(-2.50000 + 4.33013i) q^{35} +7.00000 q^{37} +(-3.50000 - 2.59808i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(0.500000 + 0.866025i) q^{44} -7.00000 q^{46} +(-4.00000 - 6.92820i) q^{47} +18.0000 q^{49} +1.00000 q^{50} +(-3.00000 + 5.19615i) q^{52} +(5.50000 + 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{55} -5.00000 q^{56} -6.00000 q^{58} +(-4.00000 + 6.92820i) q^{59} +(2.00000 + 3.46410i) q^{61} +1.00000 q^{64} -6.00000 q^{65} +(-6.00000 - 10.3923i) q^{67} -4.00000 q^{68} +(-2.50000 - 4.33013i) q^{70} +(1.00000 - 1.73205i) q^{71} +(1.00000 - 1.73205i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(4.00000 - 1.73205i) q^{76} +5.00000 q^{77} +(-5.00000 + 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.50000 - 4.33013i) q^{82} +10.0000 q^{83} +(-2.00000 - 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} -1.00000 q^{88} +(6.50000 + 11.2583i) q^{89} +(15.0000 + 25.9808i) q^{91} +(3.50000 - 6.06218i) q^{92} +8.00000 q^{94} +(3.50000 + 2.59808i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(-9.00000 + 15.5885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + q^{5} - 10 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + q^5 - 10 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + q^{5} - 10 q^{7} + 2 q^{8} + q^{10} - 2 q^{11} - 6 q^{13} + 5 q^{14} - q^{16} + 4 q^{17} - q^{19} - 2 q^{20} + q^{22} + 7 q^{23} - q^{25} + 12 q^{26} + 5 q^{28} + 6 q^{29} - q^{32} + 4 q^{34} - 5 q^{35} + 14 q^{37} - 7 q^{38} + q^{40} - 5 q^{41} - 6 q^{43} + q^{44} - 14 q^{46} - 8 q^{47} + 36 q^{49} + 2 q^{50} - 6 q^{52} + 11 q^{53} - q^{55} - 10 q^{56} - 12 q^{58} - 8 q^{59} + 4 q^{61} + 2 q^{64} - 12 q^{65} - 12 q^{67} - 8 q^{68} - 5 q^{70} + 2 q^{71} + 2 q^{73} - 7 q^{74} + 8 q^{76} + 10 q^{77} - 10 q^{79} + q^{80} - 5 q^{82} + 20 q^{83} - 4 q^{85} - 6 q^{86} - 2 q^{88} + 13 q^{89} + 30 q^{91} + 7 q^{92} + 16 q^{94} + 7 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + q^5 - 10 * q^7 + 2 * q^8 + q^10 - 2 * q^11 - 6 * q^13 + 5 * q^14 - q^16 + 4 * q^17 - q^19 - 2 * q^20 + q^22 + 7 * q^23 - q^25 + 12 * q^26 + 5 * q^28 + 6 * q^29 - q^32 + 4 * q^34 - 5 * q^35 + 14 * q^37 - 7 * q^38 + q^40 - 5 * q^41 - 6 * q^43 + q^44 - 14 * q^46 - 8 * q^47 + 36 * q^49 + 2 * q^50 - 6 * q^52 + 11 * q^53 - q^55 - 10 * q^56 - 12 * q^58 - 8 * q^59 + 4 * q^61 + 2 * q^64 - 12 * q^65 - 12 * q^67 - 8 * q^68 - 5 * q^70 + 2 * q^71 + 2 * q^73 - 7 * q^74 + 8 * q^76 + 10 * q^77 - 10 * q^79 + q^80 - 5 * q^82 + 20 * q^83 - 4 * q^85 - 6 * q^86 - 2 * q^88 + 13 * q^89 + 30 * q^91 + 7 * q^92 + 16 * q^94 + 7 * q^95 - 2 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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