LMFDB - Embedded newform 1350.2.e.d.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(451,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1350.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.e (of order $3$, degree $2$, not 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:	$10.7798042729$
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 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			901.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1350.901
Dual form			1350.2.e.d.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{17} -7.00000 q^{19} +4.00000 q^{26} -2.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} -2.00000 q^{37} +(3.50000 + 6.06218i) q^{38} +(4.50000 - 7.79423i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{52} -12.0000 q^{53} +(1.00000 + 1.73205i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{71} +1.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(3.50000 - 6.06218i) q^{76} +(-1.00000 - 1.73205i) q^{79} -9.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-0.500000 + 0.866025i) q^{86} -15.0000 q^{89} -8.00000 q^{91} +(-3.00000 + 5.19615i) q^{94} +(8.50000 + 14.7224i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 2 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8} - 4 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 14 q^{19} + 8 q^{26} - 4 q^{28} - 6 q^{29} + 10 q^{31} - q^{32} + 6 q^{34} - 4 q^{37} + 7 q^{38} + 9 q^{41} - q^{43} - 6 q^{47} + 3 q^{49} - 4 q^{52} - 24 q^{53} + 2 q^{56} - 6 q^{58} - 9 q^{59} + 4 q^{61} - 20 q^{62} + 2 q^{64} - 13 q^{67} + 6 q^{68} - 12 q^{71} + 2 q^{73} + 2 q^{74} + 7 q^{76} - 2 q^{79} - 18 q^{82} - 9 q^{83} - q^{86} - 30 q^{89} - 16 q^{91} - 6 q^{94} + 17 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^7 + 2 * q^8 - 4 * q^13 + 2 * q^14 - q^16 - 12 * q^17 - 14 * q^19 + 8 * q^26 - 4 * q^28 - 6 * q^29 + 10 * q^31 - q^32 + 6 * q^34 - 4 * q^37 + 7 * q^38 + 9 * q^41 - q^43 - 6 * q^47 + 3 * q^49 - 4 * q^52 - 24 * q^53 + 2 * q^56 - 6 * q^58 - 9 * q^59 + 4 * q^61 - 20 * q^62 + 2 * q^64 - 13 * q^67 + 6 * q^68 - 12 * q^71 + 2 * q^73 + 2 * q^74 + 7 * q^76 - 2 * q^79 - 18 * q^82 - 9 * q^83 - q^86 - 30 * q^89 - 16 * q^91 - 6 * q^94 + 17 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	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			0
$5$		0			0
$6$		0			0
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$		0			0
$26$	4.00000			0.784465
$27$		0			0
$28$	−2.00000			−0.377964
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$		0			0
$36$		0			0
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$		0			0
$40$		0			0
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$		0			0
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	−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
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$		0			0
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		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	$0.750904\pi$
$62$	−10.0000			−1.27000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−6.50000	+	11.2583i	−0.794101	+	1.37542i	0.129307	+	0.991605i	$0.458725\pi$
$67$	−6.50000	+	11.2583i	−0.794101	+	1.37542i	−0.923408	+	0.383819i	$0.874609\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$		0			0
$76$	3.50000	−	6.06218i	0.401478	−	0.695379i
$77$		0			0
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$		0			0
$81$		0			0
$82$	−9.00000			−0.993884
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$		0			0
$85$		0			0
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		0			0
$88$		0			0
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$		0			0
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$		0			0
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	0.868976	+	0.494854i	$0.164778\pi$
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	−0.00593185	+	0.999982i	$0.501888\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	−0.812545	−	0.582899i	$-0.801918\pi$
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	0.911078	+	0.412235i	$0.135252\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	9.00000			0.870063			0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000			0.870063			0.435031	+	0.900415i	$0.356737\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$		0			0
$112$	1.00000	−	1.73205i	0.0944911	−	0.163663i
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	9.00000			0.828517
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	2.00000	−	3.46410i	0.181071	−	0.313625i
$123$		0			0
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$		0			0
$126$		0			0
$127$	−20.0000			−1.77471			−0.887357	−	0.461084i	$-0.847461\pi$
$127$	−20.0000			−1.77471			−0.887357	+	0.461084i	$0.847461\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$	−7.00000	−	12.1244i	−0.606977	−	1.05131i
$134$	13.0000			1.12303
$135$		0			0
$136$	−6.00000			−0.514496
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$		0			0
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−0.500000	−	0.866025i	−0.0413803	−	0.0716728i
$147$		0			0
$148$	1.00000	−	1.73205i	0.0821995	−	0.142374i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	0.935857	−	0.352381i	$-0.114628\pi$
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	−0.773099	+	0.634285i	$0.781294\pi$
$152$	−7.00000			−0.567775
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	−1.00000	+	1.73205i	−0.0795557	+	0.137795i
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.00000			0.548282			0.274141	−	0.961689i	$-0.411606\pi$
$163$	7.00000			0.548282			0.274141	+	0.961689i	$0.411606\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$	1.00000			0.0762493
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	7.50000	+	12.9904i	0.562149	+	0.973670i
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	4.00000	+	6.92820i	0.296500	+	0.513553i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	1.00000	−	1.73205i	0.0719816	−	0.124676i	0.899770	+	0.436365i	$0.143734\pi$
$194$	8.50000	−	14.7224i	0.610264	−	1.05701i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$		0			0
$201$		0			0
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$	6.00000	−	10.3923i	0.421117	−	0.729397i
$204$		0			0
$205$		0			0
$206$	−2.00000			−0.139347
$207$		0			0
$208$	4.00000			0.277350
$209$		0			0
$210$		0			0
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		0			0
$214$	−4.50000	−	7.79423i	−0.307614	−	0.532803i
$215$		0			0
$216$		0			0
$217$	20.0000			1.35769
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$		0			0
$220$		0			0
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$		0			0
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	−0.999128	−	0.0417488i	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	3.00000			0.199557
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$		0			0
$231$		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
$235$		0			0
$236$	−4.50000	−	7.79423i	−0.292925	−	0.507361i
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	−11.0000			−0.707107
$243$		0			0
$244$	−4.00000			−0.256074
$245$		0			0
$246$		0			0
$247$	14.0000	−	24.2487i	0.890799	−	1.54291i
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$		0			0
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$		0			0
$253$		0			0
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	−2.00000	−	3.46410i	−0.124274	−	0.215249i
$260$		0			0
$261$		0			0
$262$	12.0000			0.741362
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$		0			0
$265$		0			0
$266$	−7.00000	+	12.1244i	−0.429198	+	0.743392i
$267$		0			0
$268$	−6.50000	−	11.2583i	−0.397051	−	0.687712i
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$		0			0
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$		0			0
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$		0			0
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	0.432360	+	0.901701i	$0.357681\pi$
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	−0.997076	+	0.0764162i	$0.975652\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$		0			0
$287$	18.0000			1.06251
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$	−0.500000	+	0.866025i	−0.0292603	+	0.0506803i
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	−0.986341	−	0.164714i	$-0.947330\pi$
$293$	−6.00000	+	10.3923i	−0.350524	+	0.607125i	0.635818	+	0.771839i	$0.280663\pi$
$294$		0			0
$295$		0			0
$296$	−2.00000			−0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$		0			0
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	2.00000	−	3.46410i	0.115087	−	0.199337i
$303$		0			0
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$		0			0
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.0000	+	25.9808i	−0.850572	+	1.47323i	0.0301210	+	0.999546i	$0.490411\pi$
$311$	−15.0000	+	25.9808i	−0.850572	+	1.47323i	−0.880693	+	0.473688i	$0.842923\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	2.00000			0.112509
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	−0.887788	−	0.460252i	$-0.847759\pi$
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	0.0453045	−	0.998973i	$-0.485574\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	42.0000			2.33694
$324$		0			0
$325$		0			0
$326$	−3.50000	−	6.06218i	−0.193847	−	0.335753i
$327$		0			0
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$	9.00000			0.493939
$333$		0			0
$334$	12.0000			0.656611
$335$		0			0
$336$		0			0
$337$	7.00000	−	12.1244i	0.381314	−	0.660456i	−0.609936	−	0.792451i	$-0.708805\pi$
$337$	7.00000	−	12.1244i	0.381314	−	0.660456i	0.991250	+	0.131995i	$0.0421382\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	20.0000			1.07990
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$		0			0
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	−	12.9904i	0.397499	−	0.688489i
$357$		0			0
$358$	−4.50000	−	7.79423i	−0.237832	−	0.411938i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	8.00000	+	13.8564i	0.420471	+	0.728277i
$363$		0			0
$364$	4.00000	−	6.92820i	0.209657	−	0.363137i
$365$		0			0
$366$		0			0
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	24.0000			1.23606
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$		0			0
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$		0			0
$385$		0			0
$386$	−2.00000			−0.101797
$387$		0			0
$388$	−17.0000			−0.863044
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$		0			0
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$		0			0
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	8.00000	+	13.8564i	0.401004	+	0.694559i
$399$		0			0
$400$		0			0
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$		0			0
$403$	20.0000	+	34.6410i	0.996271	+	1.72559i
$404$	−12.0000			−0.597022
$405$		0			0
$406$	−12.0000			−0.595550
$407$		0			0
$408$		0			0
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$		0			0
$411$		0			0
$412$	1.00000	+	1.73205i	0.0492665	+	0.0853320i
$413$	−18.0000			−0.885722
$414$		0			0
$415$		0			0
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$		0			0
$418$		0			0
$419$	1.50000	−	2.59808i	0.0732798	−	0.126924i	−0.827057	−	0.562118i	$-0.809987\pi$
$419$	1.50000	−	2.59808i	0.0732798	−	0.126924i	0.900337	+	0.435194i	$0.143320\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	5.00000			0.243396
$423$		0			0
$424$	−12.0000			−0.582772
$425$		0			0
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	−4.50000	+	7.79423i	−0.217516	+	0.376748i
$429$		0			0
$430$		0			0
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−10.0000	−	17.3205i	−0.480015	−	0.831411i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$		0			0
$438$		0			0
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	0.909798	−	0.415051i	$-0.136236\pi$
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	−0.814344	+	0.580383i	$0.802903\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$		0			0
$445$		0			0
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$		0			0
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	15.0000			0.707894			0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000			0.707894			0.353947	+	0.935266i	$0.384839\pi$
$450$		0			0
$451$		0			0
$452$	−1.50000	−	2.59808i	−0.0705541	−	0.122203i
$453$		0			0
$454$	7.50000	−	12.9904i	0.351992	−	0.609669i
$455$		0			0
$456$		0			0
$457$	−9.50000	−	16.4545i	−0.444391	−	0.769708i	0.553618	−	0.832771i	$-0.313247\pi$
$457$	−9.50000	−	16.4545i	−0.444391	−	0.769708i	−0.998010	+	0.0630623i	$0.979913\pi$
$458$	−10.0000			−0.467269
$459$		0			0
$460$		0			0
$461$	3.00000	+	5.19615i	0.139724	+	0.242009i	0.927392	−	0.374091i	$-0.122045\pi$
$461$	3.00000	+	5.19615i	0.139724	+	0.242009i	−0.787668	+	0.616100i	$0.788712\pi$
$462$		0			0
$463$	13.0000	−	22.5167i	0.604161	−	1.04644i	−0.388022	−	0.921650i	$-0.626842\pi$
$463$	13.0000	−	22.5167i	0.604161	−	1.04644i	0.992183	−	0.124788i	$-0.0398251\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$		0			0
$469$	−26.0000			−1.20057
$470$		0			0
$471$		0			0
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	12.0000			0.550019
$477$		0			0
$478$		0			0
$479$	18.0000	+	31.1769i	0.822441	+	1.42451i	0.903859	+	0.427830i	$0.140722\pi$
$479$	18.0000	+	31.1769i	0.822441	+	1.42451i	−0.0814184	+	0.996680i	$0.525945\pi$
$480$		0			0
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$	9.50000	−	16.4545i	0.432713	−	0.749481i
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$		0			0
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	2.00000	+	3.46410i	0.0905357	+	0.156813i
$489$		0			0
$490$		0			0
$491$	−1.50000	+	2.59808i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$491$	−1.50000	+	2.59808i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$	−28.0000			−1.25978
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$		0			0
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$		0			0
$502$	7.50000	+	12.9904i	0.334741	+	0.579789i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	10.0000	−	17.3205i	0.443678	−	0.768473i
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000			0.132324
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−2.00000	+	3.46410i	−0.0878750	+	0.152204i
$519$		0			0
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	1.00000			0.0437269			0.0218635	−	0.999761i	$-0.493040\pi$
$523$	1.00000			0.0437269			0.0218635	+	0.999761i	$0.493040\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	3.00000	−	5.19615i	0.130806	−	0.226563i
$527$	−30.0000	+	51.9615i	−1.30682	+	2.26348i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$	14.0000			0.606977
$533$	18.0000	+	31.1769i	0.779667	+	1.35042i
$534$		0			0
$535$		0			0
$536$	−6.50000	+	11.2583i	−0.280757	+	0.486286i
$537$		0			0
$538$	−15.0000	−	25.9808i	−0.646696	−	1.12011i
$539$		0			0
$540$		0			0
$541$	32.0000			1.37579			0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000			1.37579			0.687894	+	0.725811i	$0.258536\pi$
$542$	14.0000	+	24.2487i	0.601351	+	1.04157i
$543$		0			0
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$		0			0
$546$		0			0
$547$	2.50000	+	4.33013i	0.106892	+	0.185143i	0.914510	−	0.404564i	$-0.132577\pi$
$547$	2.50000	+	4.33013i	0.106892	+	0.185143i	−0.807617	+	0.589707i	$0.799243\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$		0			0
$551$	21.0000	+	36.3731i	0.894630	+	1.54954i
$552$		0			0
$553$	2.00000	−	3.46410i	0.0850487	−	0.147309i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	−9.00000	+	15.5885i	−0.379642	+	0.657559i
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	−0.945134	−	0.326682i	$-0.894069\pi$
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	0.755482	+	0.655169i	$0.227403\pi$
$564$		0			0
$565$		0			0
$566$	19.0000			0.798630
$567$		0			0
$568$	−6.00000			−0.251754
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.0294311	−	0.999567i	$-0.509370\pi$
$570$		0			0
$571$	−17.5000	+	30.3109i	−0.732352	+	1.26847i	0.223523	+	0.974699i	$0.428244\pi$
$571$	−17.5000	+	30.3109i	−0.732352	+	1.26847i	−0.955875	+	0.293773i	$0.905089\pi$
$572$		0			0
$573$		0			0
$574$	−9.00000	−	15.5885i	−0.375653	−	0.650650i
$575$		0			0
$576$		0			0
$577$	−35.0000			−1.45707			−0.728535	−	0.685009i	$-0.759798\pi$
$577$	−35.0000			−1.45707			−0.728535	+	0.685009i	$0.759798\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$		0			0
$581$	9.00000	−	15.5885i	0.373383	−	0.646718i
$582$		0			0
$583$		0			0
$584$	1.00000			0.0413803
$585$		0			0
$586$	12.0000			0.495715
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	−0.951151	−	0.308725i	$-0.900098\pi$
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	0.208212	−	0.978084i	$-0.433236\pi$
$588$		0			0
$589$	−35.0000	+	60.6218i	−1.44215	+	2.49788i
$590$		0			0
$591$		0			0
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−9.00000			−0.369586			−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000			−0.369586			−0.184793	+	0.982777i	$0.559161\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$		0			0
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$		0			0
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	0.949799	−	0.312861i	$-0.101287\pi$
$601$	5.00000	+	8.66025i	0.203954	+	0.353259i	−0.745845	+	0.666120i	$0.767954\pi$
$602$	−2.00000			−0.0815139
$603$		0			0
$604$	−4.00000			−0.162758
$605$		0			0
$606$		0			0
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$	3.50000	−	6.06218i	0.141944	−	0.245854i
$609$		0			0
$610$		0			0
$611$	24.0000			0.970936
$612$		0			0
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$		0			0
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	−0.761114	−	0.648618i	$-0.775347\pi$
$617$	4.50000	−	7.79423i	0.181163	−	0.313784i	0.942277	+	0.334835i	$0.108680\pi$
$618$		0			0
$619$	−11.5000	−	19.9186i	−0.462224	−	0.800595i	0.536847	−	0.843679i	$-0.319615\pi$
$619$	−11.5000	−	19.9186i	−0.462224	−	0.800595i	−0.999071	+	0.0430838i	$0.986282\pi$
$620$		0			0
$621$		0			0
$622$	30.0000			1.20289
$623$	−15.0000	−	25.9808i	−0.600962	−	1.04090i
$624$		0			0
$625$		0			0
$626$	−9.50000	+	16.4545i	−0.379696	+	0.657653i
$627$		0			0
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$	12.0000			0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	−1.00000	−	1.73205i	−0.0397779	−	0.0688973i
$633$		0			0
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$		0			0
$636$		0			0
$637$	6.00000	+	10.3923i	0.237729	+	0.411758i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	−6.50000	+	11.2583i	−0.256335	+	0.443985i	−0.965257	−	0.261301i	$-0.915848\pi$
$643$	−6.50000	+	11.2583i	−0.256335	+	0.443985i	0.708922	+	0.705287i	$0.249182\pi$
$644$		0			0
$645$		0			0
$646$	−21.0000	−	36.3731i	−0.826234	−	1.43108i
$647$	−48.0000			−1.88707			−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000			−1.88707			−0.943537	+	0.331266i	$0.892524\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−3.50000	+	6.06218i	−0.137071	+	0.237413i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$		0			0
$655$		0			0
$656$	−9.00000			−0.351391
$657$		0			0
$658$	−12.0000			−0.467809
$659$	16.5000	+	28.5788i	0.642749	+	1.11327i	0.984817	+	0.173598i	$0.0555394\pi$
$659$	16.5000	+	28.5788i	0.642749	+	1.11327i	−0.342068	+	0.939675i	$0.611127\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	−5.50000	+	9.52628i	−0.213764	+	0.370249i
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	0.884655	−	0.466246i	$-0.154394\pi$
$673$	1.00000	+	1.73205i	0.0385472	+	0.0667657i	−0.846108	+	0.533011i	$0.821060\pi$
$674$	−14.0000			−0.539260
$675$		0			0
$676$	3.00000			0.115385
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	0.957984	−	0.286820i	$-0.0925982\pi$
$677$	6.00000	+	10.3923i	0.230599	+	0.399409i	−0.727386	+	0.686229i	$0.759265\pi$
$678$		0			0
$679$	−17.0000	+	29.4449i	−0.652400	+	1.12999i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.00000			−0.114792			−0.0573959	−	0.998351i	$-0.518280\pi$
$683$	−3.00000			−0.114792			−0.0573959	+	0.998351i	$0.518280\pi$
$684$		0			0
$685$		0			0
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	−0.979086	−	0.203445i	$-0.934786\pi$
$691$	−17.5000	−	30.3109i	−0.665731	−	1.15308i	0.313355	−	0.949636i	$-0.398547\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$	−27.0000	+	46.7654i	−1.02270	+	1.77136i
$698$	5.00000	−	8.66025i	0.189253	−	0.327795i
$699$		0			0
$700$		0			0
$701$	48.0000			1.81293			0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000			1.81293			0.906467	+	0.422276i	$0.138769\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$		0			0
$706$	−7.50000	+	12.9904i	−0.282266	+	0.488899i
$707$	−12.0000	+	20.7846i	−0.451306	+	0.781686i
$708$		0			0
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$		0			0
$711$		0			0
$712$	−15.0000			−0.562149
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$		0			0
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	−18.0000			−0.671287			−0.335643	−	0.941989i	$-0.608954\pi$
$719$	−18.0000			−0.671287			−0.335643	+	0.941989i	$0.608954\pi$
$720$		0			0
$721$	4.00000			0.148968
$722$	−15.0000	−	25.9808i	−0.558242	−	0.966904i
$723$		0			0
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$		0			0
$726$		0			0
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	−0.951694	−	0.307049i	$-0.900659\pi$
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	0.209935	−	0.977715i	$-0.432675\pi$
$728$	−8.00000			−0.296500
$729$		0			0
$730$		0			0
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$		0			0
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	−0.994471	−	0.105010i	$-0.966513\pi$
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	0.588177	+	0.808732i	$0.299846\pi$
$734$	−5.00000	+	8.66025i	−0.184553	+	0.319656i
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−25.0000			−0.919640			−0.459820	−	0.888012i	$-0.652086\pi$
$739$	−25.0000			−0.919640			−0.459820	+	0.888012i	$0.652086\pi$
$740$		0			0
$741$		0			0
$742$	−12.0000	+	20.7846i	−0.440534	+	0.763027i
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$		0			0
$745$		0			0
$746$	4.00000			0.146450
$747$		0			0
$748$		0			0
$749$	9.00000	+	15.5885i	0.328853	+	0.569590i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$		0			0
$756$		0			0
$757$	10.0000			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$		0			0
$760$		0			0
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	−0.610527	−	0.791995i	$-0.709042\pi$
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	0.991152	+	0.132734i	$0.0423756\pi$
$762$		0			0
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	−6.00000			−0.217072
$765$		0			0
$766$	24.0000			0.867155
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$		0			0
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$		0			0
$772$	1.00000	+	1.73205i	0.0359908	+	0.0623379i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$		0			0
$775$		0			0
$776$	8.50000	+	14.7224i	0.305132	+	0.528505i
$777$		0			0
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$	−31.5000	+	54.5596i	−1.12860	+	1.95480i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−3.00000			−0.107143
$785$		0			0
$786$		0			0
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$		0			0
$790$		0			0
$791$	−6.00000			−0.213335
$792$		0			0
$793$	−16.0000			−0.568177
$794$	−11.0000	−	19.0526i	−0.390375	−	0.676150i
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	18.0000	−	31.1769i	0.637593	−	1.10434i	−0.348367	−	0.937358i	$-0.613264\pi$
$797$	18.0000	−	31.1769i	0.637593	−	1.10434i	0.985959	−	0.166985i	$-0.0534030\pi$
$798$		0			0
$799$	18.0000	+	31.1769i	0.636794	+	1.10296i
$800$		0			0
$801$		0			0
$802$	−18.0000			−0.635602
$803$		0			0
$804$		0			0
$805$		0			0
$806$	20.0000	−	34.6410i	0.704470	−	1.22018i
$807$		0			0
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	39.0000			1.37117			0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000			1.37117			0.685583	+	0.727994i	$0.259547\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$	6.00000	+	10.3923i	0.210559	+	0.364698i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.50000	+	6.06218i	0.122449	+	0.212089i
$818$	−31.0000			−1.08389
$819$		0			0
$820$		0			0
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	0.577016	−	0.816733i	$-0.304217\pi$
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	−0.995819	+	0.0913446i	$0.970884\pi$
$822$		0			0
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$	1.00000	−	1.73205i	0.0348367	−	0.0603388i
$825$		0			0
$826$	9.00000	+	15.5885i	0.313150	+	0.542392i
$827$	−27.0000			−0.938882			−0.469441	−	0.882964i	$-0.655545\pi$
$827$	−27.0000			−0.938882			−0.469441	+	0.882964i	$0.655545\pi$
$828$		0			0
$829$	32.0000			1.11141			0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000			1.11141			0.555703	+	0.831381i	$0.312449\pi$
$830$		0			0
$831$		0			0
$832$	−2.00000	+	3.46410i	−0.0693375	+	0.120096i
$833$	−9.00000	+	15.5885i	−0.311832	+	0.540108i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−3.00000			−0.103633
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$		0			0
$846$		0			0
$847$	22.0000			0.755929
$848$	6.00000	+	10.3923i	0.206041	+	0.356873i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−5.00000	−	8.66025i	−0.171197	−	0.296521i	0.767642	−	0.640879i	$-0.221430\pi$
$853$	−5.00000	−	8.66025i	−0.171197	−	0.296521i	−0.938839	+	0.344358i	$0.888097\pi$
$854$	8.00000			0.273754
$855$		0			0
$856$	9.00000			0.307614
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	0.978984	+	0.203938i	$0.0653741\pi$
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	−0.312877	+	0.949794i	$0.601293\pi$
$858$		0			0
$859$	15.5000	−	26.8468i	0.528853	−	0.916001i	−0.470581	−	0.882357i	$-0.655956\pi$
$859$	15.5000	−	26.8468i	0.528853	−	0.916001i	0.999434	−	0.0336436i	$-0.0107111\pi$
$860$		0			0
$861$		0			0
$862$	3.00000	+	5.19615i	0.102180	+	0.176982i
$863$	12.0000			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$864$		0			0
$865$		0			0
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$		0			0
$868$	−10.0000	+	17.3205i	−0.339422	+	0.587896i
$869$		0			0
$870$		0			0
$871$	−26.0000	−	45.0333i	−0.880976	−	1.52590i
$872$	2.00000			0.0677285
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.00000	+	8.66025i	−0.168838	+	0.292436i	−0.938012	−	0.346604i	$-0.887335\pi$
$877$	−5.00000	+	8.66025i	−0.168838	+	0.292436i	0.769174	+	0.639040i	$0.220668\pi$
$878$	2.00000	−	3.46410i	0.0674967	−	0.116908i
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	−0.911986	−	0.410222i	$-0.865451\pi$
$887$	−3.00000	+	5.19615i	−0.100730	+	0.174470i	0.811256	+	0.584692i	$0.198785\pi$
$888$		0			0
$889$	−20.0000	−	34.6410i	−0.670778	−	1.16182i
$890$		0			0
$891$		0			0
$892$	16.0000			0.535720
$893$	21.0000	+	36.3731i	0.702738	+	1.21718i
$894$		0			0
$895$		0			0
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$		0			0
$898$	−7.50000	−	12.9904i	−0.250278	−	0.433495i
$899$	−60.0000			−2.00111
$900$		0			0
$901$	72.0000			2.39867
$902$		0			0
$903$		0			0
$904$	−1.50000	+	2.59808i	−0.0498893	+	0.0864107i
$905$		0			0
$906$		0			0
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	0.802049	−	0.597258i	$-0.203743\pi$
$907$	−3.50000	−	6.06218i	−0.116216	−	0.201291i	−0.918265	+	0.395966i	$0.870410\pi$
$908$	−15.0000			−0.497792
$909$		0			0
$910$		0			0
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	0.948136	−	0.317865i	$-0.102966\pi$
$911$	6.00000	+	10.3923i	0.198789	+	0.344312i	−0.749347	+	0.662177i	$0.769633\pi$
$912$		0			0
$913$		0			0
$914$	−9.50000	+	16.4545i	−0.314232	+	0.544266i
$915$		0			0
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$	−24.0000			−0.792550
$918$		0			0
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$		0			0
$921$		0			0
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$		0			0
$926$	−26.0000			−0.854413
$927$		0			0
$928$	6.00000			0.196960
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.844746	−	0.535167i	$-0.820249\pi$
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.0410949	−	0.999155i	$-0.513085\pi$
$930$		0			0
$931$	−10.5000	+	18.1865i	−0.344124	+	0.596040i
$932$	−1.50000	+	2.59808i	−0.0491341	+	0.0851028i
$933$		0			0
$934$	7.50000	+	12.9904i	0.245407	+	0.425058i
$935$		0			0
$936$		0			0
$937$	−23.0000			−0.751377			−0.375689	−	0.926746i	$-0.622594\pi$
$937$	−23.0000			−0.751377			−0.375689	+	0.926746i	$0.622594\pi$
$938$	13.0000	+	22.5167i	0.424465	+	0.735195i
$939$		0			0
$940$		0			0
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.0290288	+	0.999579i	$0.509241\pi$
$941$	−27.0000	+	46.7654i	−0.880175	+	1.52451i	−0.851146	+	0.524929i	$0.824092\pi$
$942$		0			0
$943$		0			0
$944$	9.00000			0.292925
$945$		0			0
$946$		0			0
$947$	10.5000	+	18.1865i	0.341204	+	0.590983i	0.984657	−	0.174503i	$-0.0558319\pi$
$947$	10.5000	+	18.1865i	0.341204	+	0.590983i	−0.643452	+	0.765486i	$0.722499\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	18.0000	−	31.1769i	0.581554	−	1.00728i
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	−8.00000			−0.257930
$963$		0			0
$964$	−19.0000			−0.611949
$965$		0			0
$966$		0			0
$967$	10.0000	−	17.3205i	0.321578	−	0.556990i	−0.659236	−	0.751936i	$-0.729120\pi$
$967$	10.0000	−	17.3205i	0.321578	−	0.556990i	0.980814	+	0.194946i	$0.0624533\pi$
$968$	5.50000	−	9.52628i	0.176777	−	0.306186i
$969$		0			0
$970$		0			0
$971$	21.0000			0.673922			0.336961	−	0.941519i	$-0.390601\pi$
$971$	21.0000			0.673922			0.336961	+	0.941519i	$0.390601\pi$
$972$		0			0
$973$	8.00000			0.256468
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	7.50000	−	12.9904i	0.239946	−	0.415599i	−0.720752	−	0.693193i	$-0.756204\pi$
$977$	7.50000	−	12.9904i	0.239946	−	0.415599i	0.960699	+	0.277594i	$0.0895368\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	3.00000			0.0957338
$983$	15.0000	+	25.9808i	0.478426	+	0.828658i	0.999694	−	0.0247352i	$-0.00787426\pi$
$983$	15.0000	+	25.9808i	0.478426	+	0.828658i	−0.521268	+	0.853393i	$0.674541\pi$
$984$		0			0
$985$		0			0
$986$	18.0000	−	31.1769i	0.573237	−	0.992875i
$987$		0			0
$988$	14.0000	+	24.2487i	0.445399	+	0.771454i
$989$		0			0
$990$		0			0
$991$	44.0000			1.39771			0.698853	−	0.715265i	$-0.253694\pi$
$991$	44.0000			1.39771			0.698853	+	0.715265i	$0.253694\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$		0			0
$994$	−6.00000	+	10.3923i	−0.190308	+	0.329624i
$995$		0			0
$996$		0			0
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	0.554554	−	0.832148i	$-0.312889\pi$
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	−0.997938	+	0.0641836i	$0.979556\pi$
$998$	11.0000			0.348199
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.e.d.901.1		2
3.2	odd	2		450.2.e.f.301.1	yes	2
5.2	odd	4		1350.2.j.b.199.2		4
5.3	odd	4		1350.2.j.b.199.1		4
5.4	even	2		1350.2.e.h.901.1		2
9.2	odd	6		450.2.e.f.151.1	yes	2
9.4	even	3		4050.2.a.u.1.1		1
9.5	odd	6		4050.2.a.d.1.1		1
9.7	even	3	inner	1350.2.e.d.451.1		2
15.2	even	4		450.2.j.b.49.1		4
15.8	even	4		450.2.j.b.49.2		4
15.14	odd	2		450.2.e.c.301.1	yes	2
45.2	even	12		450.2.j.b.349.2		4
45.4	even	6		4050.2.a.o.1.1		1
45.7	odd	12		1350.2.j.b.1099.1		4
45.13	odd	12		4050.2.c.m.649.1		2
45.14	odd	6		4050.2.a.bg.1.1		1
45.22	odd	12		4050.2.c.m.649.2		2
45.23	even	12		4050.2.c.h.649.2		2
45.29	odd	6		450.2.e.c.151.1	✓	2
45.32	even	12		4050.2.c.h.649.1		2
45.34	even	6		1350.2.e.h.451.1		2
45.38	even	12		450.2.j.b.349.1		4
45.43	odd	12		1350.2.j.b.1099.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.c.151.1	✓	2	45.29	odd	6
450.2.e.c.301.1	yes	2	15.14	odd	2
450.2.e.f.151.1	yes	2	9.2	odd	6
450.2.e.f.301.1	yes	2	3.2	odd	2
450.2.j.b.49.1		4	15.2	even	4
450.2.j.b.49.2		4	15.8	even	4
450.2.j.b.349.1		4	45.38	even	12
450.2.j.b.349.2		4	45.2	even	12
1350.2.e.d.451.1		2	9.7	even	3	inner
1350.2.e.d.901.1		2	1.1	even	1	trivial
1350.2.e.h.451.1		2	45.34	even	6
1350.2.e.h.901.1		2	5.4	even	2
1350.2.j.b.199.1		4	5.3	odd	4
1350.2.j.b.199.2		4	5.2	odd	4
1350.2.j.b.1099.1		4	45.7	odd	12
1350.2.j.b.1099.2		4	45.43	odd	12
4050.2.a.d.1.1		1	9.5	odd	6
4050.2.a.o.1.1		1	45.4	even	6
4050.2.a.u.1.1		1	9.4	even	3
4050.2.a.bg.1.1		1	45.14	odd	6
4050.2.c.h.649.1		2	45.32	even	12
4050.2.c.h.649.2		2	45.23	even	12
4050.2.c.m.649.1		2	45.13	odd	12
4050.2.c.m.649.2		2	45.22	odd	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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-2.00000 + 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{17} -7.00000 q^{19} +4.00000 q^{26} -2.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} -2.00000 q^{37} +(3.50000 + 6.06218i) q^{38} +(4.50000 - 7.79423i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{52} -12.0000 q^{53} +(1.00000 + 1.73205i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-6.50000 + 11.2583i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{71} +1.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(3.50000 - 6.06218i) q^{76} +(-1.00000 - 1.73205i) q^{79} -9.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(-0.500000 + 0.866025i) q^{86} -15.0000 q^{89} -8.00000 q^{91} +(-3.00000 + 5.19615i) q^{94} +(8.50000 + 14.7224i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 2 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 2 q^{7} + 2 q^{8} - 4 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 14 q^{19} + 8 q^{26} - 4 q^{28} - 6 q^{29} + 10 q^{31} - q^{32} + 6 q^{34} - 4 q^{37} + 7 q^{38} + 9 q^{41} - q^{43} - 6 q^{47} + 3 q^{49} - 4 q^{52} - 24 q^{53} + 2 q^{56} - 6 q^{58} - 9 q^{59} + 4 q^{61} - 20 q^{62} + 2 q^{64} - 13 q^{67} + 6 q^{68} - 12 q^{71} + 2 q^{73} + 2 q^{74} + 7 q^{76} - 2 q^{79} - 18 q^{82} - 9 q^{83} - q^{86} - 30 q^{89} - 16 q^{91} - 6 q^{94} + 17 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^7 + 2 * q^8 - 4 * q^13 + 2 * q^14 - q^16 - 12 * q^17 - 14 * q^19 + 8 * q^26 - 4 * q^28 - 6 * q^29 + 10 * q^31 - q^32 + 6 * q^34 - 4 * q^37 + 7 * q^38 + 9 * q^41 - q^43 - 6 * q^47 + 3 * q^49 - 4 * q^52 - 24 * q^53 + 2 * q^56 - 6 * q^58 - 9 * q^59 + 4 * q^61 - 20 * q^62 + 2 * q^64 - 13 * q^67 + 6 * q^68 - 12 * q^71 + 2 * q^73 + 2 * q^74 + 7 * q^76 - 2 * q^79 - 18 * q^82 - 9 * q^83 - q^86 - 30 * q^89 - 16 * q^91 - 6 * q^94 + 17 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more