LMFDB - Embedded newform 1350.2.e.k.451.1

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:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1350.451
Dual form			1350.2.e.k.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +(2.44949 - 4.24264i) q^{11} +(-2.22474 - 3.85337i) q^{13} +(-2.22474 - 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.89898 q^{17} +2.55051 q^{19} +(2.44949 + 4.24264i) q^{22} +(1.22474 + 2.12132i) q^{23} +4.44949 q^{26} +4.44949 q^{28} +(1.22474 - 2.12132i) q^{29} +(0.224745 + 0.389270i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.44949 + 4.24264i) q^{34} +3.34847 q^{37} +(-1.27526 + 2.20881i) q^{38} +(4.50000 + 7.79423i) q^{41} +(-3.72474 + 6.45145i) q^{43} -4.89898 q^{44} -2.44949 q^{46} +(-0.550510 + 0.953512i) q^{47} +(-6.39898 - 11.0834i) q^{49} +(-2.22474 + 3.85337i) q^{52} +8.44949 q^{53} +(-2.22474 + 3.85337i) q^{56} +(1.22474 + 2.12132i) q^{58} +(-0.275255 - 0.476756i) q^{59} +(-4.00000 + 6.92820i) q^{61} -0.449490 q^{62} +1.00000 q^{64} +(7.17423 + 12.4261i) q^{67} +(-2.44949 - 4.24264i) q^{68} +1.34847 q^{71} -1.00000 q^{73} +(-1.67423 + 2.89986i) q^{74} +(-1.27526 - 2.20881i) q^{76} +(10.8990 + 18.8776i) q^{77} +(6.34847 - 10.9959i) q^{79} -9.00000 q^{82} +(-0.275255 + 0.476756i) q^{83} +(-3.72474 - 6.45145i) q^{86} +(2.44949 - 4.24264i) q^{88} +9.00000 q^{89} +19.7980 q^{91} +(1.22474 - 2.12132i) q^{92} +(-0.550510 - 0.953512i) q^{94} +(5.39898 - 9.35131i) q^{97} +12.7980 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} - 4 q^{13} - 4 q^{14} - 2 q^{16} + 20 q^{19} + 8 q^{26} + 8 q^{28} - 4 q^{31} - 2 q^{32} - 16 q^{37} - 10 q^{38} + 18 q^{41} - 10 q^{43} - 12 q^{47} - 6 q^{49} - 4 q^{52} + 24 q^{53} - 4 q^{56} - 6 q^{59} - 16 q^{61} + 8 q^{62} + 4 q^{64} + 14 q^{67} - 24 q^{71} - 4 q^{73} + 8 q^{74} - 10 q^{76} + 24 q^{77} - 4 q^{79} - 36 q^{82} - 6 q^{83} - 10 q^{86} + 36 q^{89} + 40 q^{91} - 12 q^{94} + 2 q^{97} + 12 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 - 4 * q^13 - 4 * q^14 - 2 * q^16 + 20 * q^19 + 8 * q^26 + 8 * q^28 - 4 * q^31 - 2 * q^32 - 16 * q^37 - 10 * q^38 + 18 * q^41 - 10 * q^43 - 12 * q^47 - 6 * q^49 - 4 * q^52 + 24 * q^53 - 4 * q^56 - 6 * q^59 - 16 * q^61 + 8 * q^62 + 4 * q^64 + 14 * q^67 - 24 * q^71 - 4 * q^73 + 8 * q^74 - 10 * q^76 + 24 * q^77 - 4 * q^79 - 36 * q^82 - 6 * q^83 - 10 * q^86 + 36 * q^89 + 40 * q^91 - 12 * q^94 + 2 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$7$	−2.22474	+	3.85337i	−0.840875	+	1.45644i	0.0482818	+	0.998834i	$0.484625\pi$
$7$	−2.22474	+	3.85337i	−0.840875	+	1.45644i	−0.889156	+	0.457604i	$0.848708\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	2.44949	−	4.24264i	0.738549	−	1.27920i	−0.214600	−	0.976702i	$-0.568845\pi$
$11$	2.44949	−	4.24264i	0.738549	−	1.27920i	0.953149	−	0.302502i	$-0.0978220\pi$
$12$		0			0
$13$	−2.22474	−	3.85337i	−0.617033	−	1.06873i	−0.990024	−	0.140898i	$-0.955001\pi$
$13$	−2.22474	−	3.85337i	−0.617033	−	1.06873i	0.372991	−	0.927835i	$-0.378332\pi$
$14$	−2.22474	−	3.85337i	−0.594588	−	1.02986i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.89898			1.18818			0.594089	−	0.804400i	$-0.297513\pi$
$17$	4.89898			1.18818			0.594089	+	0.804400i	$0.297513\pi$
$18$		0			0
$19$	2.55051			0.585127			0.292564	−	0.956246i	$-0.405492\pi$
$19$	2.55051			0.585127			0.292564	+	0.956246i	$0.405492\pi$
$20$		0			0
$21$		0			0
$22$	2.44949	+	4.24264i	0.522233	+	0.904534i
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	0.964998	−	0.262258i	$-0.0844671\pi$
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	−0.709621	+	0.704584i	$0.751134\pi$
$24$		0			0
$25$		0			0
$26$	4.44949			0.872617
$27$		0			0
$28$	4.44949			0.840875
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	−0.729616	−	0.683857i	$-0.760301\pi$
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	0.957046	+	0.289938i	$0.0936346\pi$
$30$		0			0
$31$	0.224745	+	0.389270i	0.0403654	+	0.0699149i	0.885502	−	0.464635i	$-0.153814\pi$
$31$	0.224745	+	0.389270i	0.0403654	+	0.0699149i	−0.845137	+	0.534550i	$0.820481\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−2.44949	+	4.24264i	−0.420084	+	0.727607i
$35$		0			0
$36$		0			0
$37$	3.34847			0.550485			0.275242	−	0.961375i	$-0.411242\pi$
$37$	3.34847			0.550485			0.275242	+	0.961375i	$0.411242\pi$
$38$	−1.27526	+	2.20881i	−0.206874	+	0.358316i
$39$		0			0
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	−3.72474	+	6.45145i	−0.568018	+	0.983836i	0.428744	+	0.903426i	$0.358956\pi$
$43$	−3.72474	+	6.45145i	−0.568018	+	0.983836i	−0.996762	+	0.0804103i	$0.974377\pi$
$44$	−4.89898			−0.738549
$45$		0			0
$46$	−2.44949			−0.361158
$47$	−0.550510	+	0.953512i	−0.0803002	+	0.139084i	−0.903379	−	0.428843i	$-0.858921\pi$
$47$	−0.550510	+	0.953512i	−0.0803002	+	0.139084i	0.823079	+	0.567927i	$0.192255\pi$
$48$		0			0
$49$	−6.39898	−	11.0834i	−0.914140	−	1.58334i
$50$		0			0
$51$		0			0
$52$	−2.22474	+	3.85337i	−0.308517	+	0.534366i
$53$	8.44949			1.16063			0.580313	−	0.814393i	$-0.302930\pi$
$53$	8.44949			1.16063			0.580313	+	0.814393i	$0.302930\pi$
$54$		0			0
$55$		0			0
$56$	−2.22474	+	3.85337i	−0.297294	+	0.514928i
$57$		0			0
$58$	1.22474	+	2.12132i	0.160817	+	0.278543i
$59$	−0.275255	−	0.476756i	−0.0358352	−	0.0620683i	0.847552	−	0.530713i	$-0.178076\pi$
$59$	−0.275255	−	0.476756i	−0.0358352	−	0.0620683i	−0.883387	+	0.468645i	$0.844742\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−0.449490			−0.0570853
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	7.17423	+	12.4261i	0.876472	+	1.51809i	0.855186	+	0.518321i	$0.173443\pi$
$67$	7.17423	+	12.4261i	0.876472	+	1.51809i	0.0212861	+	0.999773i	$0.493224\pi$
$68$	−2.44949	−	4.24264i	−0.297044	−	0.514496i
$69$		0			0
$70$		0			0
$71$	1.34847			0.160034			0.0800169	−	0.996794i	$-0.474503\pi$
$71$	1.34847			0.160034			0.0800169	+	0.996794i	$0.474503\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	−1.67423	+	2.89986i	−0.194626	+	0.337102i
$75$		0			0
$76$	−1.27526	−	2.20881i	−0.146282	−	0.253368i
$77$	10.8990	+	18.8776i	1.24205	+	2.15130i
$78$		0			0
$79$	6.34847	−	10.9959i	0.714259	−	1.23713i	−0.248986	−	0.968507i	$-0.580097\pi$
$79$	6.34847	−	10.9959i	0.714259	−	1.23713i	0.963245	−	0.268625i	$-0.0865693\pi$
$80$		0			0
$81$		0			0
$82$	−9.00000			−0.993884
$83$	−0.275255	+	0.476756i	−0.0302132	+	0.0523308i	−0.880737	−	0.473606i	$-0.842952\pi$
$83$	−0.275255	+	0.476756i	−0.0302132	+	0.0523308i	0.850523	+	0.525937i	$0.176285\pi$
$84$		0			0
$85$		0			0
$86$	−3.72474	−	6.45145i	−0.401650	−	0.695677i
$87$		0			0
$88$	2.44949	−	4.24264i	0.261116	−	0.452267i
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$		0			0
$91$	19.7980			2.07539
$92$	1.22474	−	2.12132i	0.127688	−	0.221163i
$93$		0			0
$94$	−0.550510	−	0.953512i	−0.0567808	−	0.0983472i
$95$		0			0
$96$		0			0
$97$	5.39898	−	9.35131i	0.548183	−	0.949481i	−0.450216	−	0.892920i	$-0.648653\pi$
$97$	5.39898	−	9.35131i	0.548183	−	0.949481i	0.998399	−	0.0565616i	$-0.0180137\pi$
$98$	12.7980			1.29279
$99$		0			0
$100$		0			0
$101$	1.77526	−	3.07483i	0.176644	−	0.305957i	−0.764085	−	0.645116i	$-0.776809\pi$
$101$	1.77526	−	3.07483i	0.176644	−	0.305957i	0.940729	+	0.339159i	$0.110142\pi$
$102$		0			0
$103$	6.34847	+	10.9959i	0.625533	+	1.08346i	0.988437	+	0.151629i	$0.0484519\pi$
$103$	6.34847	+	10.9959i	0.625533	+	1.08346i	−0.362904	+	0.931826i	$0.618215\pi$
$104$	−2.22474	−	3.85337i	−0.218154	−	0.377854i
$105$		0			0
$106$	−4.22474	+	7.31747i	−0.410343	+	0.710736i
$107$	15.2474			1.47403			0.737013	−	0.675878i	$-0.236236\pi$
$107$	15.2474			1.47403			0.737013	+	0.675878i	$0.236236\pi$
$108$		0			0
$109$	10.4495			1.00088			0.500440	−	0.865771i	$-0.333172\pi$
$109$	10.4495			1.00088			0.500440	+	0.865771i	$0.333172\pi$
$110$		0			0
$111$		0			0
$112$	−2.22474	−	3.85337i	−0.210219	−	0.364109i
$113$	−6.94949	−	12.0369i	−0.653753	−	1.13233i	−0.982205	−	0.187813i	$-0.939860\pi$
$113$	−6.94949	−	12.0369i	−0.653753	−	1.13233i	0.328452	−	0.944521i	$-0.393473\pi$
$114$		0			0
$115$		0			0
$116$	−2.44949			−0.227429
$117$		0			0
$118$	0.550510			0.0506786
$119$	−10.8990	+	18.8776i	−0.999108	+	1.73051i
$120$		0			0
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$		0			0
$124$	0.224745	−	0.389270i	0.0201827	−	0.0349574i
$125$		0			0
$126$		0			0
$127$	−11.3485			−1.00701			−0.503507	−	0.863991i	$-0.667957\pi$
$127$	−11.3485			−1.00701			−0.503507	+	0.863991i	$0.667957\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	7.89898	+	13.6814i	0.690137	+	1.19535i	0.971793	+	0.235837i	$0.0757831\pi$
$131$	7.89898	+	13.6814i	0.690137	+	1.19535i	−0.281656	+	0.959516i	$0.590884\pi$
$132$		0			0
$133$	−5.67423	+	9.82806i	−0.492019	+	0.852201i
$134$	−14.3485			−1.23952
$135$		0			0
$136$	4.89898			0.420084
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$		0			0
$142$	−0.674235	+	1.16781i	−0.0565805	+	0.0980003i
$143$	−21.7980			−1.82284
$144$		0			0
$145$		0			0
$146$	0.500000	−	0.866025i	0.0413803	−	0.0716728i
$147$		0			0
$148$	−1.67423	−	2.89986i	−0.137621	−	0.238367i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$	2.55051			0.206874
$153$		0			0
$154$	−21.7980			−1.75653
$155$		0			0
$156$		0			0
$157$	0.101021	+	0.174973i	0.00806231	+	0.0139643i	0.870028	−	0.493002i	$-0.164100\pi$
$157$	0.101021	+	0.174973i	0.00806231	+	0.0139643i	−0.861966	+	0.506966i	$0.830767\pi$
$158$	6.34847	+	10.9959i	0.505057	+	0.874785i
$159$		0			0
$160$		0			0
$161$	−10.8990			−0.858960
$162$		0			0
$163$	2.55051			0.199771			0.0998857	−	0.994999i	$-0.468152\pi$
$163$	2.55051			0.199771			0.0998857	+	0.994999i	$0.468152\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	−0.275255	−	0.476756i	−0.0213639	−	0.0370034i
$167$	−9.79796	−	16.9706i	−0.758189	−	1.31322i	−0.943773	−	0.330593i	$-0.892751\pi$
$167$	−9.79796	−	16.9706i	−0.758189	−	1.31322i	0.185584	−	0.982628i	$-0.440582\pi$
$168$		0			0
$169$	−3.39898	+	5.88721i	−0.261460	+	0.452862i
$170$		0			0
$171$		0			0
$172$	7.44949			0.568018
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	−0.989944	−	0.141462i	$-0.954820\pi$
$173$	−4.89898	+	8.48528i	−0.372463	+	0.645124i	0.617481	+	0.786586i	$0.288153\pi$
$174$		0			0
$175$		0			0
$176$	2.44949	+	4.24264i	0.184637	+	0.319801i
$177$		0			0
$178$	−4.50000	+	7.79423i	−0.337289	+	0.584202i
$179$	15.2474			1.13965			0.569824	−	0.821767i	$-0.307011\pi$
$179$	15.2474			1.13965			0.569824	+	0.821767i	$0.307011\pi$
$180$		0			0
$181$	−1.79796			−0.133641			−0.0668206	−	0.997765i	$-0.521286\pi$
$181$	−1.79796			−0.133641			−0.0668206	+	0.997765i	$0.521286\pi$
$182$	−9.89898	+	17.1455i	−0.733761	+	1.27091i
$183$		0			0
$184$	1.22474	+	2.12132i	0.0902894	+	0.156386i
$185$		0			0
$186$		0			0
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	1.10102			0.0803002
$189$		0			0
$190$		0			0
$191$	−5.44949	+	9.43879i	−0.394311	+	0.682967i	−0.993013	−	0.118005i	$-0.962350\pi$
$191$	−5.44949	+	9.43879i	−0.394311	+	0.682967i	0.598702	+	0.800972i	$0.295683\pi$
$192$		0			0
$193$	−10.0000	−	17.3205i	−0.719816	−	1.24676i	−0.961073	−	0.276296i	$-0.910893\pi$
$193$	−10.0000	−	17.3205i	−0.719816	−	1.24676i	0.241257	−	0.970461i	$-0.422440\pi$
$194$	5.39898	+	9.35131i	0.387624	+	0.671385i
$195$		0			0
$196$	−6.39898	+	11.0834i	−0.457070	+	0.791668i
$197$	−24.2474			−1.72756			−0.863780	−	0.503870i	$-0.831909\pi$
$197$	−24.2474			−1.72756			−0.863780	+	0.503870i	$0.831909\pi$
$198$		0			0
$199$	5.79796			0.411006			0.205503	−	0.978656i	$-0.434117\pi$
$199$	5.79796			0.411006			0.205503	+	0.978656i	$0.434117\pi$
$200$		0			0
$201$		0			0
$202$	1.77526	+	3.07483i	0.124907	+	0.216344i
$203$	5.44949	+	9.43879i	0.382479	+	0.662473i
$204$		0			0
$205$		0			0
$206$	−12.6969			−0.884638
$207$		0			0
$208$	4.44949			0.308517
$209$	6.24745	−	10.8209i	0.432145	−	0.748497i
$210$		0			0
$211$	−0.724745	−	1.25529i	−0.0498935	−	0.0864181i	0.840000	−	0.542586i	$-0.182555\pi$
$211$	−0.724745	−	1.25529i	−0.0498935	−	0.0864181i	−0.889894	+	0.456168i	$0.849222\pi$
$212$	−4.22474	−	7.31747i	−0.290157	−	0.502566i
$213$		0			0
$214$	−7.62372	+	13.2047i	−0.521147	+	0.902653i
$215$		0			0
$216$		0			0
$217$	−2.00000			−0.135769
$218$	−5.22474	+	9.04952i	−0.353864	+	0.612911i
$219$		0			0
$220$		0			0
$221$	−10.8990	−	18.8776i	−0.733145	−	1.26984i
$222$		0			0
$223$	0.898979	−	1.55708i	0.0602001	−	0.104270i	−0.834355	−	0.551228i	$-0.814159\pi$
$223$	0.898979	−	1.55708i	0.0602001	−	0.104270i	0.894555	+	0.446958i	$0.147493\pi$
$224$	4.44949			0.297294
$225$		0			0
$226$	13.8990			0.924546
$227$	14.1742	−	24.5505i	0.940777	−	1.62947i	0.176783	−	0.984250i	$-0.443431\pi$
$227$	14.1742	−	24.5505i	0.940777	−	1.62947i	0.763994	−	0.645224i	$-0.223236\pi$
$228$		0			0
$229$	10.5732	+	18.3133i	0.698698	+	1.21018i	0.968918	+	0.247381i	$0.0795701\pi$
$229$	10.5732	+	18.3133i	0.698698	+	1.21018i	−0.270221	+	0.962798i	$0.587097\pi$
$230$		0			0
$231$		0			0
$232$	1.22474	−	2.12132i	0.0804084	−	0.139272i
$233$	−5.69694			−0.373219			−0.186609	−	0.982434i	$-0.559750\pi$
$233$	−5.69694			−0.373219			−0.186609	+	0.982434i	$0.559750\pi$
$234$		0			0
$235$		0			0
$236$	−0.275255	+	0.476756i	−0.0179176	+	0.0310342i
$237$		0			0
$238$	−10.8990	−	18.8776i	−0.706476	−	1.22365i
$239$	4.77526	+	8.27098i	0.308886	+	0.535006i	0.978119	−	0.208047i	$-0.0667107\pi$
$239$	4.77526	+	8.27098i	0.308886	+	0.535006i	−0.669233	+	0.743052i	$0.733377\pi$
$240$		0			0
$241$	11.3990	−	19.7436i	0.734273	−	1.27180i	−0.220769	−	0.975326i	$-0.570857\pi$
$241$	11.3990	−	19.7436i	0.734273	−	1.27180i	0.955042	−	0.296472i	$-0.0958100\pi$
$242$	13.0000			0.835672
$243$		0			0
$244$	8.00000			0.512148
$245$		0			0
$246$		0			0
$247$	−5.67423	−	9.82806i	−0.361043	−	0.625345i
$248$	0.224745	+	0.389270i	0.0142713	+	0.0247186i
$249$		0			0
$250$		0			0
$251$	5.44949			0.343969			0.171984	−	0.985100i	$-0.444982\pi$
$251$	5.44949			0.343969			0.171984	+	0.985100i	$0.444982\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$	5.67423	−	9.82806i	0.356033	−	0.616667i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.39898	+	5.88721i	0.212023	+	0.367234i	0.952347	−	0.305016i	$-0.0986616\pi$
$257$	3.39898	+	5.88721i	0.212023	+	0.367234i	−0.740325	+	0.672249i	$0.765328\pi$
$258$		0			0
$259$	−7.44949	+	12.9029i	−0.462889	+	0.801747i
$260$		0			0
$261$		0			0
$262$	−15.7980			−0.976001
$263$	7.77526	−	13.4671i	0.479443	−	0.830419i	−0.520279	−	0.853996i	$-0.674172\pi$
$263$	7.77526	−	13.4671i	0.479443	−	0.830419i	0.999722	+	0.0235770i	$0.00750547\pi$
$264$		0			0
$265$		0			0
$266$	−5.67423	−	9.82806i	−0.347910	−	0.602597i
$267$		0			0
$268$	7.17423	−	12.4261i	0.438236	−	0.759047i
$269$	−9.55051			−0.582305			−0.291152	−	0.956677i	$-0.594039\pi$
$269$	−9.55051			−0.582305			−0.291152	+	0.956677i	$0.594039\pi$
$270$		0			0
$271$	0.651531			0.0395777			0.0197888	−	0.999804i	$-0.493701\pi$
$271$	0.651531			0.0395777			0.0197888	+	0.999804i	$0.493701\pi$
$272$	−2.44949	+	4.24264i	−0.148522	+	0.257248i
$273$		0			0
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$		0			0
$276$		0			0
$277$	3.22474	−	5.58542i	0.193756	−	0.335595i	−0.752736	−	0.658323i	$-0.771266\pi$
$277$	3.22474	−	5.58542i	0.193756	−	0.335595i	0.946492	+	0.322727i	$0.104600\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$		0			0
$281$	14.4495	−	25.0273i	0.861984	−	1.49300i	−0.00802643	−	0.999968i	$-0.502555\pi$
$281$	14.4495	−	25.0273i	0.861984	−	1.49300i	0.870011	−	0.493033i	$-0.164112\pi$
$282$		0			0
$283$	−5.62372	−	9.74058i	−0.334296	−	0.579017i	0.649054	−	0.760743i	$-0.275165\pi$
$283$	−5.62372	−	9.74058i	−0.334296	−	0.579017i	−0.983349	+	0.181726i	$0.941832\pi$
$284$	−0.674235	−	1.16781i	−0.0400085	−	0.0692967i
$285$		0			0
$286$	10.8990	−	18.8776i	0.644470	−	1.11626i
$287$	−40.0454			−2.36381
$288$		0			0
$289$	7.00000			0.411765
$290$		0			0
$291$		0			0
$292$	0.500000	+	0.866025i	0.0292603	+	0.0506803i
$293$	−14.0227	−	24.2880i	−0.819215	−	1.41892i	−0.906261	−	0.422718i	$-0.861076\pi$
$293$	−14.0227	−	24.2880i	−0.819215	−	1.41892i	0.0870462	−	0.996204i	$-0.472257\pi$
$294$		0			0
$295$		0			0
$296$	3.34847			0.194626
$297$		0			0
$298$	6.00000			0.347571
$299$	5.44949	−	9.43879i	0.315152	−	0.545859i
$300$		0			0
$301$	−16.5732	−	28.7056i	−0.955264	−	1.65457i
$302$	−10.0000	−	17.3205i	−0.575435	−	0.996683i
$303$		0			0
$304$	−1.27526	+	2.20881i	−0.0731409	+	0.126684i
$305$		0			0
$306$		0			0
$307$	−6.69694			−0.382214			−0.191107	−	0.981569i	$-0.561208\pi$
$307$	−6.69694			−0.382214			−0.191107	+	0.981569i	$0.561208\pi$
$308$	10.8990	−	18.8776i	0.621027	−	1.07565i
$309$		0			0
$310$		0			0
$311$	−5.44949	−	9.43879i	−0.309012	−	0.535225i	0.669134	−	0.743141i	$-0.266665\pi$
$311$	−5.44949	−	9.43879i	−0.309012	−	0.535225i	−0.978147	+	0.207917i	$0.933332\pi$
$312$		0			0
$313$	−1.94949	+	3.37662i	−0.110192	+	0.190858i	−0.915847	−	0.401526i	$-0.868480\pi$
$313$	−1.94949	+	3.37662i	−0.110192	+	0.190858i	0.805656	+	0.592384i	$0.201813\pi$
$314$	−0.202041			−0.0114018
$315$		0			0
$316$	−12.6969			−0.714259
$317$	−8.57321	+	14.8492i	−0.481520	+	0.834017i	−0.999775	−	0.0212094i	$-0.993248\pi$
$317$	−8.57321	+	14.8492i	−0.481520	+	0.834017i	0.518255	+	0.855226i	$0.326582\pi$
$318$		0			0
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$		0			0
$321$		0			0
$322$	5.44949	−	9.43879i	0.303688	−	0.526003i
$323$	12.4949			0.695235
$324$		0			0
$325$		0			0
$326$	−1.27526	+	2.20881i	−0.0706298	+	0.122334i
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−2.44949	−	4.24264i	−0.135045	−	0.233904i
$330$		0			0
$331$	4.17423	−	7.22999i	0.229437	−	0.397396i	−0.728205	−	0.685360i	$-0.759645\pi$
$331$	4.17423	−	7.22999i	0.229437	−	0.397396i	0.957641	+	0.287964i	$0.0929783\pi$
$332$	0.550510			0.0302132
$333$		0			0
$334$	19.5959			1.07224
$335$		0			0
$336$		0			0
$337$	5.55051	+	9.61377i	0.302356	+	0.523695i	0.976669	−	0.214750i	$-0.0688937\pi$
$337$	5.55051	+	9.61377i	0.302356	+	0.523695i	−0.674313	+	0.738445i	$0.735560\pi$
$338$	−3.39898	−	5.88721i	−0.184880	−	0.320222i
$339$		0			0
$340$		0			0
$341$	2.20204			0.119247
$342$		0			0
$343$	25.7980			1.39296
$344$	−3.72474	+	6.45145i	−0.200825	+	0.347839i
$345$		0			0
$346$	−4.89898	−	8.48528i	−0.263371	−	0.456172i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$		0			0
$352$	−4.89898			−0.261116
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	−0.960574	−	0.278024i	$-0.910320\pi$
$353$	−4.50000	+	7.79423i	−0.239511	+	0.414845i	0.721063	+	0.692869i	$0.243654\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	−	7.79423i	−0.238500	−	0.413093i
$357$		0			0
$358$	−7.62372	+	13.2047i	−0.402926	+	0.697889i
$359$	33.7980			1.78379			0.891894	−	0.452244i	$-0.149377\pi$
$359$	33.7980			1.78379			0.891894	+	0.452244i	$0.149377\pi$
$360$		0			0
$361$	−12.4949			−0.657626
$362$	0.898979	−	1.55708i	0.0472493	−	0.0818382i
$363$		0			0
$364$	−9.89898	−	17.1455i	−0.518848	−	0.898670i
$365$		0			0
$366$		0			0
$367$	−8.34847	+	14.4600i	−0.435787	+	0.754804i	−0.997359	−	0.0726228i	$-0.976863\pi$
$367$	−8.34847	+	14.4600i	−0.435787	+	0.754804i	0.561573	+	0.827427i	$0.310196\pi$
$368$	−2.44949			−0.127688
$369$		0			0
$370$		0			0
$371$	−18.7980	+	32.5590i	−0.975941	+	1.69038i
$372$		0			0
$373$	−7.79796	−	13.5065i	−0.403763	−	0.699338i	0.590414	−	0.807101i	$-0.298965\pi$
$373$	−7.79796	−	13.5065i	−0.403763	−	0.699338i	−0.994177	+	0.107763i	$0.965631\pi$
$374$	12.0000	+	20.7846i	0.620505	+	1.07475i
$375$		0			0
$376$	−0.550510	+	0.953512i	−0.0283904	+	0.0491736i
$377$	−10.8990			−0.561326
$378$		0			0
$379$	0.898979			0.0461775			0.0230887	−	0.999733i	$-0.492650\pi$
$379$	0.898979			0.0461775			0.0230887	+	0.999733i	$0.492650\pi$
$380$		0			0
$381$		0			0
$382$	−5.44949	−	9.43879i	−0.278820	−	0.482931i
$383$	13.2247	+	22.9059i	0.675753	+	1.17044i	0.976248	+	0.216655i	$0.0695147\pi$
$383$	13.2247	+	22.9059i	0.675753	+	1.17044i	−0.300495	+	0.953783i	$0.597152\pi$
$384$		0			0
$385$		0			0
$386$	20.0000			1.01797
$387$		0			0
$388$	−10.7980			−0.548183
$389$	−6.79796	+	11.7744i	−0.344670	+	0.596986i	−0.985294	−	0.170869i	$-0.945343\pi$
$389$	−6.79796	+	11.7744i	−0.344670	+	0.596986i	0.640624	+	0.767855i	$0.278676\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$	−6.39898	−	11.0834i	−0.323197	−	0.559794i
$393$		0			0
$394$	12.1237	−	20.9989i	0.610784	−	1.05791i
$395$		0			0
$396$		0			0
$397$	21.5959			1.08387			0.541934	−	0.840421i	$-0.317692\pi$
$397$	21.5959			1.08387			0.541934	+	0.840421i	$0.317692\pi$
$398$	−2.89898	+	5.02118i	−0.145313	+	0.251689i
$399$		0			0
$400$		0			0
$401$	4.65153	+	8.05669i	0.232286	+	0.402332i	0.958481	−	0.285158i	$-0.0920460\pi$
$401$	4.65153	+	8.05669i	0.232286	+	0.402332i	−0.726194	+	0.687490i	$0.758713\pi$
$402$		0			0
$403$	1.00000	−	1.73205i	0.0498135	−	0.0862796i
$404$	−3.55051			−0.176644
$405$		0			0
$406$	−10.8990			−0.540907
$407$	8.20204	−	14.2064i	0.406560	−	0.704183i
$408$		0			0
$409$	−4.94949	−	8.57277i	−0.244737	−	0.423896i	0.717321	−	0.696743i	$-0.245368\pi$
$409$	−4.94949	−	8.57277i	−0.244737	−	0.423896i	−0.962058	+	0.272847i	$0.912035\pi$
$410$		0			0
$411$		0			0
$412$	6.34847	−	10.9959i	0.312767	−	0.541728i
$413$	2.44949			0.120532
$414$		0			0
$415$		0			0
$416$	−2.22474	+	3.85337i	−0.109077	+	0.188927i
$417$		0			0
$418$	6.24745	+	10.8209i	0.305573	+	0.529267i
$419$	4.07321	+	7.05501i	0.198990	+	0.344660i	0.948201	−	0.317671i	$-0.102901\pi$
$419$	4.07321	+	7.05501i	0.198990	+	0.344660i	−0.749212	+	0.662331i	$0.769567\pi$
$420$		0			0
$421$	−9.02270	+	15.6278i	−0.439740	+	0.761651i	−0.997669	−	0.0682369i	$-0.978263\pi$
$421$	−9.02270	+	15.6278i	−0.439740	+	0.761651i	0.557929	+	0.829888i	$0.311596\pi$
$422$	1.44949			0.0705601
$423$		0			0
$424$	8.44949			0.410343
$425$		0			0
$426$		0			0
$427$	−17.7980	−	30.8270i	−0.861304	−	1.49182i
$428$	−7.62372	−	13.2047i	−0.368507	−	0.638272i
$429$		0			0
$430$		0			0
$431$	−10.6515			−0.513066			−0.256533	−	0.966535i	$-0.582580\pi$
$431$	−10.6515			−0.513066			−0.256533	+	0.966535i	$0.582580\pi$
$432$		0			0
$433$	−29.5959			−1.42229			−0.711145	−	0.703046i	$-0.751823\pi$
$433$	−29.5959			−1.42229			−0.711145	+	0.703046i	$0.751823\pi$
$434$	1.00000	−	1.73205i	0.0480015	−	0.0831411i
$435$		0			0
$436$	−5.22474	−	9.04952i	−0.250220	−	0.433394i
$437$	3.12372	+	5.41045i	0.149428	+	0.258817i
$438$		0			0
$439$	5.67423	−	9.82806i	0.270816	−	0.469068i	−0.698255	−	0.715849i	$-0.746040\pi$
$439$	5.67423	−	9.82806i	0.270816	−	0.469068i	0.969071	+	0.246782i	$0.0793730\pi$
$440$		0			0
$441$		0			0
$442$	21.7980			1.03682
$443$	13.8990	−	24.0737i	0.660360	−	1.14378i	−0.320161	−	0.947363i	$-0.603737\pi$
$443$	13.8990	−	24.0737i	0.660360	−	1.14378i	0.980521	−	0.196415i	$-0.0629298\pi$
$444$		0			0
$445$		0			0
$446$	0.898979	+	1.55708i	0.0425679	+	0.0737298i
$447$		0			0
$448$	−2.22474	+	3.85337i	−0.105109	+	0.182055i
$449$	−10.5959			−0.500052			−0.250026	−	0.968239i	$-0.580439\pi$
$449$	−10.5959			−0.500052			−0.250026	+	0.968239i	$0.580439\pi$
$450$		0			0
$451$	44.0908			2.07616
$452$	−6.94949	+	12.0369i	−0.326877	+	0.566167i
$453$		0			0
$454$	14.1742	+	24.5505i	0.665230	+	1.15221i
$455$		0			0
$456$		0			0
$457$	7.84847	−	13.5939i	0.367136	−	0.635898i	−0.621981	−	0.783033i	$-0.713672\pi$
$457$	7.84847	−	13.5939i	0.367136	−	0.635898i	0.989116	+	0.147135i	$0.0470051\pi$
$458$	−21.1464			−0.988108
$459$		0			0
$460$		0			0
$461$	9.67423	−	16.7563i	0.450574	−	0.780417i	−0.547848	−	0.836578i	$-0.684553\pi$
$461$	9.67423	−	16.7563i	0.450574	−	0.780417i	0.998422	+	0.0561610i	$0.0178860\pi$
$462$		0			0
$463$	−4.67423	−	8.09601i	−0.217230	−	0.376254i	0.736730	−	0.676187i	$-0.236369\pi$
$463$	−4.67423	−	8.09601i	−0.217230	−	0.376254i	−0.953960	+	0.299933i	$0.903036\pi$
$464$	1.22474	+	2.12132i	0.0568574	+	0.0984798i
$465$		0			0
$466$	2.84847	−	4.93369i	0.131953	−	0.228549i
$467$	−4.34847			−0.201223			−0.100612	−	0.994926i	$-0.532080\pi$
$467$	−4.34847			−0.201223			−0.100612	+	0.994926i	$0.532080\pi$
$468$		0			0
$469$	−63.8434			−2.94801
$470$		0			0
$471$		0			0
$472$	−0.275255	−	0.476756i	−0.0126696	−	0.0219445i
$473$	18.2474	+	31.6055i	0.839019	+	1.45322i
$474$		0			0
$475$		0			0
$476$	21.7980			0.999108
$477$		0			0
$478$	−9.55051			−0.436830
$479$	−12.1237	+	20.9989i	−0.553947	+	0.959465i	0.444038	+	0.896008i	$0.353546\pi$
$479$	−12.1237	+	20.9989i	−0.553947	+	0.959465i	−0.997985	+	0.0634563i	$0.979788\pi$
$480$		0			0
$481$	−7.44949	−	12.9029i	−0.339667	−	0.588321i
$482$	11.3990	+	19.7436i	0.519209	+	0.899297i
$483$		0			0
$484$	−6.50000	+	11.2583i	−0.295455	+	0.511742i
$485$		0			0
$486$		0			0
$487$	−19.5505			−0.885918			−0.442959	−	0.896542i	$-0.646071\pi$
$487$	−19.5505			−0.885918			−0.442959	+	0.896542i	$0.646071\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$		0			0
$490$		0			0
$491$	−1.37628	−	2.38378i	−0.0621105	−	0.107578i	0.833298	−	0.552824i	$-0.186450\pi$
$491$	−1.37628	−	2.38378i	−0.0621105	−	0.107578i	−0.895409	+	0.445245i	$0.853116\pi$
$492$		0			0
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$	11.3485			0.510592
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	−3.17423	−	5.49794i	−0.142098	−	0.246121i	0.786188	−	0.617987i	$-0.212052\pi$
$499$	−3.17423	−	5.49794i	−0.142098	−	0.246121i	−0.928287	+	0.371866i	$0.878718\pi$
$500$		0			0
$501$		0			0
$502$	−2.72474	+	4.71940i	−0.121611	+	0.210637i
$503$	−26.4495			−1.17932			−0.589662	−	0.807650i	$-0.700739\pi$
$503$	−26.4495			−1.17932			−0.589662	+	0.807650i	$0.700739\pi$
$504$		0			0
$505$		0			0
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$		0			0
$508$	5.67423	+	9.82806i	0.251753	+	0.436050i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	2.22474	−	3.85337i	0.0984169	−	0.170463i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.79796			−0.299845
$515$		0			0
$516$		0			0
$517$	2.69694	+	4.67123i	0.118611	+	0.205441i
$518$	−7.44949	−	12.9029i	−0.327312	−	0.566921i
$519$		0			0
$520$		0			0
$521$	−29.3939			−1.28777			−0.643885	−	0.765123i	$-0.722678\pi$
$521$	−29.3939			−1.28777			−0.643885	+	0.765123i	$0.722678\pi$
$522$		0			0
$523$	−5.65153			−0.247124			−0.123562	−	0.992337i	$-0.539432\pi$
$523$	−5.65153			−0.247124			−0.123562	+	0.992337i	$0.539432\pi$
$524$	7.89898	−	13.6814i	0.345069	−	0.597676i
$525$		0			0
$526$	7.77526	+	13.4671i	0.339017	+	0.587195i
$527$	1.10102	+	1.90702i	0.0479612	+	0.0830712i
$528$		0			0
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$		0			0
$531$		0			0
$532$	11.3485			0.492019
$533$	20.0227	−	34.6803i	0.867280	−	1.50217i
$534$		0			0
$535$		0			0
$536$	7.17423	+	12.4261i	0.309880	+	0.536727i
$537$		0			0
$538$	4.77526	−	8.27098i	0.205876	−	0.356587i
$539$	−62.6969			−2.70055
$540$		0			0
$541$	−18.2020			−0.782567			−0.391283	−	0.920270i	$-0.627969\pi$
$541$	−18.2020			−0.782567			−0.391283	+	0.920270i	$0.627969\pi$
$542$	−0.325765	+	0.564242i	−0.0139928	+	0.0242363i
$543$		0			0
$544$	−2.44949	−	4.24264i	−0.105021	−	0.181902i
$545$		0			0
$546$		0			0
$547$	−15.1742	+	26.2825i	−0.648803	+	1.12376i	0.334606	+	0.942358i	$0.391397\pi$
$547$	−15.1742	+	26.2825i	−0.648803	+	1.12376i	−0.983409	+	0.181402i	$0.941936\pi$
$548$	−3.00000			−0.128154
$549$		0			0
$550$		0			0
$551$	3.12372	−	5.41045i	0.133075	−	0.230493i
$552$		0			0
$553$	28.2474	+	48.9260i	1.20120	+	2.08055i
$554$	3.22474	+	5.58542i	0.137006	+	0.237302i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	17.3939			0.737002			0.368501	−	0.929627i	$-0.379871\pi$
$557$	17.3939			0.737002			0.368501	+	0.929627i	$0.379871\pi$
$558$		0			0
$559$	33.1464			1.40194
$560$		0			0
$561$		0			0
$562$	14.4495	+	25.0273i	0.609515	+	1.05571i
$563$	14.9722	+	25.9326i	0.631003	+	1.09293i	0.987347	+	0.158574i	$0.0506897\pi$
$563$	14.9722	+	25.9326i	0.631003	+	1.09293i	−0.356344	+	0.934355i	$0.615977\pi$
$564$		0			0
$565$		0			0
$566$	11.2474			0.472766
$567$		0			0
$568$	1.34847			0.0565805
$569$	7.10102	−	12.2993i	0.297690	−	0.515615i	−0.677917	−	0.735139i	$-0.737117\pi$
$569$	7.10102	−	12.2993i	0.297690	−	0.515615i	0.975607	+	0.219524i	$0.0704504\pi$
$570$		0			0
$571$	13.9722	+	24.2005i	0.584718	+	1.01276i	0.994911	+	0.100762i	$0.0321282\pi$
$571$	13.9722	+	24.2005i	0.584718	+	1.01276i	−0.410192	+	0.911999i	$0.634538\pi$
$572$	10.8990	+	18.8776i	0.455709	+	0.789312i
$573$		0			0
$574$	20.0227	−	34.6803i	0.835732	−	1.44753i
$575$		0			0
$576$		0			0
$577$	−18.3939			−0.765747			−0.382874	−	0.923801i	$-0.625066\pi$
$577$	−18.3939			−0.765747			−0.382874	+	0.923801i	$0.625066\pi$
$578$	−3.50000	+	6.06218i	−0.145581	+	0.252153i
$579$		0			0
$580$		0			0
$581$	−1.22474	−	2.12132i	−0.0508110	−	0.0880072i
$582$		0			0
$583$	20.6969	−	35.8481i	0.857180	−	1.48468i
$584$	−1.00000			−0.0413803
$585$		0			0
$586$	28.0454			1.15855
$587$	1.34847	−	2.33562i	0.0556573	−	0.0964012i	−0.836854	−	0.547426i	$-0.815608\pi$
$587$	1.34847	−	2.33562i	0.0556573	−	0.0964012i	0.892512	+	0.451024i	$0.148941\pi$
$588$		0			0
$589$	0.573214	+	0.992836i	0.0236189	+	0.0409091i
$590$		0			0
$591$		0			0
$592$	−1.67423	+	2.89986i	−0.0688106	+	0.119183i
$593$	−1.89898			−0.0779817			−0.0389909	−	0.999240i	$-0.512414\pi$
$593$	−1.89898			−0.0779817			−0.0389909	+	0.999240i	$0.512414\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	5.44949	+	9.43879i	0.222846	+	0.385981i
$599$	−18.6742	−	32.3447i	−0.763009	−	1.32157i	−0.941293	−	0.337591i	$-0.890388\pi$
$599$	−18.6742	−	32.3447i	−0.763009	−	1.32157i	0.178285	−	0.983979i	$-0.442945\pi$
$600$		0			0
$601$	−16.2474	+	28.1414i	−0.662747	+	1.14791i	0.317144	+	0.948378i	$0.397276\pi$
$601$	−16.2474	+	28.1414i	−0.662747	+	1.14791i	−0.979891	+	0.199534i	$0.936057\pi$
$602$	33.1464			1.35095
$603$		0			0
$604$	20.0000			0.813788
$605$		0			0
$606$		0			0
$607$	5.67423	+	9.82806i	0.230310	+	0.398909i	0.957899	−	0.287104i	$-0.0926926\pi$
$607$	5.67423	+	9.82806i	0.230310	+	0.398909i	−0.727589	+	0.686013i	$0.759359\pi$
$608$	−1.27526	−	2.20881i	−0.0517184	−	0.0895789i
$609$		0			0
$610$		0			0
$611$	4.89898			0.198191
$612$		0			0
$613$	−32.0454			−1.29430			−0.647151	−	0.762362i	$-0.724040\pi$
$613$	−32.0454			−1.29430			−0.647151	+	0.762362i	$0.724040\pi$
$614$	3.34847	−	5.79972i	0.135133	−	0.234058i
$615$		0			0
$616$	10.8990	+	18.8776i	0.439132	+	0.760600i
$617$	−7.19694	−	12.4655i	−0.289738	−	0.501841i	0.684009	−	0.729473i	$-0.260235\pi$
$617$	−7.19694	−	12.4655i	−0.289738	−	0.501841i	−0.973747	+	0.227633i	$0.926901\pi$
$618$		0			0
$619$	−20.8712	+	36.1499i	−0.838883	+	1.45299i	0.0519458	+	0.998650i	$0.483458\pi$
$619$	−20.8712	+	36.1499i	−0.838883	+	1.45299i	−0.890829	+	0.454339i	$0.849876\pi$
$620$		0			0
$621$		0			0
$622$	10.8990			0.437009
$623$	−20.0227	+	34.6803i	−0.802193	+	1.38944i
$624$		0			0
$625$		0			0
$626$	−1.94949	−	3.37662i	−0.0779173	−	0.134957i
$627$		0			0
$628$	0.101021	−	0.174973i	0.00403116	−	0.00698217i
$629$	16.4041			0.654074
$630$		0			0
$631$	−25.7980			−1.02700			−0.513500	−	0.858089i	$-0.671651\pi$
$631$	−25.7980			−1.02700			−0.513500	+	0.858089i	$0.671651\pi$
$632$	6.34847	−	10.9959i	0.252529	−	0.437392i
$633$		0			0
$634$	−8.57321	−	14.8492i	−0.340486	−	0.589739i
$635$		0			0
$636$		0			0
$637$	−28.4722	+	49.3153i	−1.12811	+	1.95394i
$638$	12.0000			0.475085
$639$		0			0
$640$		0			0
$641$	22.1969	−	38.4462i	0.876726	−	1.51853i	0.0218141	−	0.999762i	$-0.493056\pi$
$641$	22.1969	−	38.4462i	0.876726	−	1.51853i	0.854912	−	0.518773i	$-0.173611\pi$
$642$		0			0
$643$	16.1742	+	28.0146i	0.637850	+	1.10479i	0.985904	+	0.167313i	$0.0535092\pi$
$643$	16.1742	+	28.0146i	0.637850	+	1.10479i	−0.348054	+	0.937474i	$0.613157\pi$
$644$	5.44949	+	9.43879i	0.214740	+	0.371941i
$645$		0			0
$646$	−6.24745	+	10.8209i	−0.245803	+	0.425743i
$647$	0.247449			0.00972821			0.00486411	−	0.999988i	$-0.498452\pi$
$647$	0.247449			0.00972821			0.00486411	+	0.999988i	$0.498452\pi$
$648$		0			0
$649$	−2.69694			−0.105864
$650$		0			0
$651$		0			0
$652$	−1.27526	−	2.20881i	−0.0499428	−	0.0865035i
$653$	−3.12372	−	5.41045i	−0.122241	−	0.211727i	0.798410	−	0.602114i	$-0.205675\pi$
$653$	−3.12372	−	5.41045i	−0.122241	−	0.211727i	−0.920651	+	0.390387i	$0.872341\pi$
$654$		0			0
$655$		0			0
$656$	−9.00000			−0.351391
$657$		0			0
$658$	4.89898			0.190982
$659$	22.0732	−	38.2319i	0.859850	−	1.48930i	−0.0122208	−	0.999925i	$-0.503890\pi$
$659$	22.0732	−	38.2319i	0.859850	−	1.48930i	0.872071	−	0.489379i	$-0.162777\pi$
$660$		0			0
$661$	25.6969	+	44.5084i	0.999495	+	1.73118i	0.527265	+	0.849701i	$0.323218\pi$
$661$	25.6969	+	44.5084i	0.999495	+	1.73118i	0.472230	+	0.881475i	$0.343449\pi$
$662$	4.17423	+	7.22999i	0.162236	+	0.281001i
$663$		0			0
$664$	−0.275255	+	0.476756i	−0.0106820	+	0.0185017i
$665$		0			0
$666$		0			0
$667$	6.00000			0.232321
$668$	−9.79796	+	16.9706i	−0.379094	+	0.656611i
$669$		0			0
$670$		0			0
$671$	19.5959	+	33.9411i	0.756492	+	1.31028i
$672$		0			0
$673$	3.34847	−	5.79972i	0.129074	−	0.223563i	−0.794244	−	0.607599i	$-0.792133\pi$
$673$	3.34847	−	5.79972i	0.129074	−	0.223563i	0.923318	+	0.384036i	$0.125466\pi$
$674$	−11.1010			−0.427595
$675$		0			0
$676$	6.79796			0.261460
$677$	18.9217	−	32.7733i	0.727219	−	1.25958i	−0.230835	−	0.972993i	$-0.574146\pi$
$677$	18.9217	−	32.7733i	0.727219	−	1.25958i	0.958054	−	0.286588i	$-0.0925210\pi$
$678$		0			0
$679$	24.0227	+	41.6085i	0.921907	+	1.59679i
$680$		0			0
$681$		0			0
$682$	−1.10102	+	1.90702i	−0.0421603	+	0.0730237i
$683$	11.9444			0.457039			0.228520	−	0.973539i	$-0.426611\pi$
$683$	11.9444			0.457039			0.228520	+	0.973539i	$0.426611\pi$
$684$		0			0
$685$		0			0
$686$	−12.8990	+	22.3417i	−0.492485	+	0.853010i
$687$		0			0
$688$	−3.72474	−	6.45145i	−0.142005	−	0.245959i
$689$	−18.7980	−	32.5590i	−0.716145	−	1.24040i
$690$		0			0
$691$	2.52270	−	4.36945i	0.0959682	−	0.166222i	−0.814044	−	0.580803i	$-0.802739\pi$
$691$	2.52270	−	4.36945i	0.0959682	−	0.166222i	0.910012	+	0.414581i	$0.136072\pi$
$692$	9.79796			0.372463
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$	22.0454	+	38.1838i	0.835029	+	1.44631i
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$		0			0
$701$	−14.2020			−0.536404			−0.268202	−	0.963363i	$-0.586429\pi$
$701$	−14.2020			−0.536404			−0.268202	+	0.963363i	$0.586429\pi$
$702$		0			0
$703$	8.54031			0.322104
$704$	2.44949	−	4.24264i	0.0923186	−	0.159901i
$705$		0			0
$706$	−4.50000	−	7.79423i	−0.169360	−	0.293340i
$707$	7.89898	+	13.6814i	0.297072	+	0.514543i
$708$		0			0
$709$	0.224745	−	0.389270i	0.00844047	−	0.0146193i	−0.861774	−	0.507292i	$-0.830647\pi$
$709$	0.224745	−	0.389270i	0.00844047	−	0.0146193i	0.870215	+	0.492673i	$0.163980\pi$
$710$		0			0
$711$		0			0
$712$	9.00000			0.337289
$713$	−0.550510	+	0.953512i	−0.0206168	+	0.0357093i
$714$		0			0
$715$		0			0
$716$	−7.62372	−	13.2047i	−0.284912	−	0.493482i
$717$		0			0
$718$	−16.8990	+	29.2699i	−0.630664	+	1.09234i
$719$	−52.0454			−1.94097			−0.970483	−	0.241169i	$-0.922469\pi$
$719$	−52.0454			−1.94097			−0.970483	+	0.241169i	$0.922469\pi$
$720$		0			0
$721$	−56.4949			−2.10398
$722$	6.24745	−	10.8209i	0.232506	−	0.402712i
$723$		0			0
$724$	0.898979	+	1.55708i	0.0334103	+	0.0578684i
$725$		0			0
$726$		0			0
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	−0.678676	−	0.734438i	$-0.737446\pi$
$727$	8.00000	−	13.8564i	0.296704	−	0.513906i	0.975380	+	0.220532i	$0.0707793\pi$
$728$	19.7980			0.733761
$729$		0			0
$730$		0			0
$731$	−18.2474	+	31.6055i	−0.674906	+	1.16897i
$732$		0			0
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	0.519575	−	0.854425i	$-0.326090\pi$
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	−0.999741	+	0.0227529i	$0.992757\pi$
$734$	−8.34847	−	14.4600i	−0.308148	−	0.533727i
$735$		0			0
$736$	1.22474	−	2.12132i	0.0451447	−	0.0781929i
$737$	70.2929			2.58927
$738$		0			0
$739$	−41.0454			−1.50988			−0.754940	−	0.655794i	$-0.772334\pi$
$739$	−41.0454			−1.50988			−0.754940	+	0.655794i	$0.772334\pi$
$740$		0			0
$741$		0			0
$742$	−18.7980	−	32.5590i	−0.690095	−	1.19528i
$743$	17.3258	+	30.0091i	0.635621	+	1.10093i	0.986383	+	0.164463i	$0.0525891\pi$
$743$	17.3258	+	30.0091i	0.635621	+	1.10093i	−0.350763	+	0.936464i	$0.614078\pi$
$744$		0			0
$745$		0			0
$746$	15.5959			0.571007
$747$		0			0
$748$	−24.0000			−0.877527
$749$	−33.9217	+	58.7541i	−1.23947	+	2.14683i
$750$		0			0
$751$	25.0227	+	43.3406i	0.913091	+	1.58152i	0.809672	+	0.586883i	$0.199645\pi$
$751$	25.0227	+	43.3406i	0.913091	+	1.58152i	0.103420	+	0.994638i	$0.467022\pi$
$752$	−0.550510	−	0.953512i	−0.0200750	−	0.0347710i
$753$		0			0
$754$	5.44949	−	9.43879i	0.198459	−	0.343741i
$755$		0			0
$756$		0			0
$757$	6.04541			0.219724			0.109862	−	0.993947i	$-0.464959\pi$
$757$	6.04541			0.219724			0.109862	+	0.993947i	$0.464959\pi$
$758$	−0.449490	+	0.778539i	−0.0163262	+	0.0282778i
$759$		0			0
$760$		0			0
$761$	2.05051	+	3.55159i	0.0743309	+	0.128745i	0.900795	−	0.434244i	$-0.142985\pi$
$761$	2.05051	+	3.55159i	0.0743309	+	0.128745i	−0.826464	+	0.562989i	$0.809651\pi$
$762$		0			0
$763$	−23.2474	+	40.2658i	−0.841614	+	1.45772i
$764$	10.8990			0.394311
$765$		0			0
$766$	−26.4495			−0.955659
$767$	−1.22474	+	2.12132i	−0.0442230	+	0.0765964i
$768$		0			0
$769$	−25.0959	−	43.4674i	−0.904982	−	1.56747i	−0.820941	−	0.571012i	$-0.806551\pi$
$769$	−25.0959	−	43.4674i	−0.904982	−	1.56747i	−0.0840405	−	0.996462i	$-0.526783\pi$
$770$		0			0
$771$		0			0
$772$	−10.0000	+	17.3205i	−0.359908	+	0.623379i
$773$	49.5959			1.78384			0.891921	−	0.452192i	$-0.149358\pi$
$773$	49.5959			1.78384			0.891921	+	0.452192i	$0.149358\pi$
$774$		0			0
$775$		0			0
$776$	5.39898	−	9.35131i	0.193812	−	0.335692i
$777$		0			0
$778$	−6.79796	−	11.7744i	−0.243719	−	0.422133i
$779$	11.4773	+	19.8793i	0.411217	+	0.712248i
$780$		0			0
$781$	3.30306	−	5.72107i	0.118193	−	0.204716i
$782$	−12.0000			−0.429119
$783$		0			0
$784$	12.7980			0.457070
$785$		0			0
$786$		0			0
$787$	−2.65153	−	4.59259i	−0.0945169	−	0.163708i	0.814890	−	0.579616i	$-0.196797\pi$
$787$	−2.65153	−	4.59259i	−0.0945169	−	0.163708i	−0.909407	+	0.415908i	$0.863464\pi$
$788$	12.1237	+	20.9989i	0.431890	+	0.748055i
$789$		0			0
$790$		0			0
$791$	61.8434			2.19890
$792$		0			0
$793$	35.5959			1.26405
$794$	−10.7980	+	18.7026i	−0.383205	+	0.663731i
$795$		0			0
$796$	−2.89898	−	5.02118i	−0.102752	−	0.177971i
$797$	−2.87628	−	4.98186i	−0.101883	−	0.176466i	0.810577	−	0.585631i	$-0.199153\pi$
$797$	−2.87628	−	4.98186i	−0.101883	−	0.176466i	−0.912460	+	0.409165i	$0.865820\pi$
$798$		0			0
$799$	−2.69694	+	4.67123i	−0.0954108	+	0.165256i
$800$		0			0
$801$		0			0
$802$	−9.30306			−0.328503
$803$	−2.44949	+	4.24264i	−0.0864406	+	0.149720i
$804$		0			0
$805$		0			0
$806$	1.00000	+	1.73205i	0.0352235	+	0.0610089i
$807$		0			0
$808$	1.77526	−	3.07483i	0.0624533	−	0.108172i
$809$	35.6969			1.25504			0.627519	−	0.778601i	$-0.284071\pi$
$809$	35.6969			1.25504			0.627519	+	0.778601i	$0.284071\pi$
$810$		0			0
$811$	−33.4495			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$811$	−33.4495			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$812$	5.44949	−	9.43879i	0.191240	−	0.331237i
$813$		0			0
$814$	8.20204	+	14.2064i	0.287481	+	0.497932i
$815$		0			0
$816$		0			0
$817$	−9.50000	+	16.4545i	−0.332363	+	0.575669i
$818$	9.89898			0.346110
$819$		0			0
$820$		0			0
$821$	−25.5959	+	44.3334i	−0.893304	+	1.54725i	−0.0574136	+	0.998350i	$0.518285\pi$
$821$	−25.5959	+	44.3334i	−0.893304	+	1.54725i	−0.835890	+	0.548897i	$0.815048\pi$
$822$		0			0
$823$	13.4495	+	23.2952i	0.468820	+	0.812020i	0.999365	−	0.0356371i	$-0.0113461\pi$
$823$	13.4495	+	23.2952i	0.468820	+	0.812020i	−0.530545	+	0.847657i	$0.678013\pi$
$824$	6.34847	+	10.9959i	0.221159	+	0.383059i
$825$		0			0
$826$	−1.22474	+	2.12132i	−0.0426143	+	0.0738102i
$827$	−17.9444			−0.623987			−0.311994	−	0.950084i	$-0.600997\pi$
$827$	−17.9444			−0.623987			−0.311994	+	0.950084i	$0.600997\pi$
$828$		0			0
$829$	26.7423			0.928800			0.464400	−	0.885626i	$-0.346270\pi$
$829$	26.7423			0.928800			0.464400	+	0.885626i	$0.346270\pi$
$830$		0			0
$831$		0			0
$832$	−2.22474	−	3.85337i	−0.0771292	−	0.133592i
$833$	−31.3485	−	54.2971i	−1.08616	−	1.88128i
$834$		0			0
$835$		0			0
$836$	−12.4949			−0.432145
$837$		0			0
$838$	−8.14643			−0.281414
$839$	11.3258	−	19.6168i	0.391009	−	0.677247i	−0.601574	−	0.798817i	$-0.705460\pi$
$839$	11.3258	−	19.6168i	0.391009	−	0.677247i	0.992583	+	0.121570i	$0.0387928\pi$
$840$		0			0
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−9.02270	−	15.6278i	−0.310943	−	0.538569i
$843$		0			0
$844$	−0.724745	+	1.25529i	−0.0249467	+	0.0432090i
$845$		0			0
$846$		0			0
$847$	57.8434			1.98752
$848$	−4.22474	+	7.31747i	−0.145078	+	0.251283i
$849$		0			0
$850$		0			0
$851$	4.10102	+	7.10318i	0.140581	+	0.243494i
$852$		0			0
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	−0.139986	−	0.990153i	$-0.544706\pi$
$853$	23.0000	−	39.8372i	0.787505	−	1.36400i	0.927491	−	0.373845i	$-0.121961\pi$
$854$	35.5959			1.21807
$855$		0			0
$856$	15.2474			0.521147
$857$	−20.0505	+	34.7285i	−0.684912	+	1.18630i	0.288552	+	0.957464i	$0.406826\pi$
$857$	−20.0505	+	34.7285i	−0.684912	+	1.18630i	−0.973464	+	0.228839i	$0.926507\pi$
$858$		0			0
$859$	2.82577	+	4.89437i	0.0964139	+	0.166994i	0.910198	−	0.414174i	$-0.135929\pi$
$859$	2.82577	+	4.89437i	0.0964139	+	0.166994i	−0.813784	+	0.581168i	$0.802596\pi$
$860$		0			0
$861$		0			0
$862$	5.32577	−	9.22450i	0.181396	−	0.314188i
$863$	−19.8434			−0.675476			−0.337738	−	0.941240i	$-0.609662\pi$
$863$	−19.8434			−0.675476			−0.337738	+	0.941240i	$0.609662\pi$
$864$		0			0
$865$		0			0
$866$	14.7980	−	25.6308i	0.502855	−	0.870971i
$867$		0			0
$868$	1.00000	+	1.73205i	0.0339422	+	0.0587896i
$869$	−31.1010	−	53.8685i	−1.05503	−	1.82737i
$870$		0			0
$871$	31.9217	−	55.2900i	1.08162	−	1.87343i
$872$	10.4495			0.353864
$873$		0			0
$874$	−6.24745			−0.211323
$875$		0			0
$876$		0			0
$877$	6.10102	+	10.5673i	0.206017	+	0.356832i	0.950456	−	0.310858i	$-0.100617\pi$
$877$	6.10102	+	10.5673i	0.206017	+	0.356832i	−0.744439	+	0.667690i	$0.767283\pi$
$878$	5.67423	+	9.82806i	0.191496	+	0.331681i
$879$		0			0
$880$		0			0
$881$	−9.30306			−0.313428			−0.156714	−	0.987644i	$-0.550090\pi$
$881$	−9.30306			−0.313428			−0.156714	+	0.987644i	$0.550090\pi$
$882$		0			0
$883$	28.2020			0.949074			0.474537	−	0.880235i	$-0.342615\pi$
$883$	28.2020			0.949074			0.474537	+	0.880235i	$0.342615\pi$
$884$	−10.8990	+	18.8776i	−0.366572	+	0.634922i
$885$		0			0
$886$	13.8990	+	24.0737i	0.466945	+	0.808773i
$887$	27.2474	+	47.1940i	0.914880	+	1.58462i	0.807077	+	0.590446i	$0.201048\pi$
$887$	27.2474	+	47.1940i	0.914880	+	1.58462i	0.107803	+	0.994172i	$0.465619\pi$
$888$		0			0
$889$	25.2474	−	43.7299i	0.846772	−	1.46665i
$890$		0			0
$891$		0			0
$892$	−1.79796			−0.0602001
$893$	−1.40408	+	2.43194i	−0.0469858	+	0.0813818i
$894$		0			0
$895$		0			0
$896$	−2.22474	−	3.85337i	−0.0743235	−	0.128732i
$897$		0			0
$898$	5.29796	−	9.17633i	0.176795	−	0.306218i
$899$	1.10102			0.0367211
$900$		0			0
$901$	41.3939			1.37903
$902$	−22.0454	+	38.1838i	−0.734032	+	1.27138i
$903$		0			0
$904$	−6.94949	−	12.0369i	−0.231137	−	0.400340i
$905$		0			0
$906$		0			0
$907$	−10.8258	+	18.7508i	−0.359464	+	0.622609i	−0.987871	−	0.155275i	$-0.950374\pi$
$907$	−10.8258	+	18.7508i	−0.359464	+	0.622609i	0.628408	+	0.777884i	$0.283707\pi$
$908$	−28.3485			−0.940777
$909$		0			0
$910$		0			0
$911$	3.67423	−	6.36396i	0.121733	−	0.210847i	−0.798718	−	0.601705i	$-0.794488\pi$
$911$	3.67423	−	6.36396i	0.121733	−	0.210847i	0.920451	+	0.390858i	$0.127822\pi$
$912$		0			0
$913$	1.34847	+	2.33562i	0.0446278	+	0.0772976i
$914$	7.84847	+	13.5939i	0.259604	+	0.449648i
$915$		0			0
$916$	10.5732	−	18.3133i	0.349349	−	0.605090i
$917$	−70.2929			−2.32127
$918$		0			0
$919$	−11.3485			−0.374351			−0.187176	−	0.982326i	$-0.559933\pi$
$919$	−11.3485			−0.374351			−0.187176	+	0.982326i	$0.559933\pi$
$920$		0			0
$921$		0			0
$922$	9.67423	+	16.7563i	0.318604	+	0.551838i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$		0			0
$925$		0			0
$926$	9.34847			0.307210
$927$		0			0
$928$	−2.44949			−0.0804084
$929$	13.5959	−	23.5488i	0.446068	−	0.772612i	−0.552058	−	0.833806i	$-0.686157\pi$
$929$	13.5959	−	23.5488i	0.446068	−	0.772612i	0.998126	+	0.0611938i	$0.0194908\pi$
$930$		0			0
$931$	−16.3207	−	28.2682i	−0.534888	−	0.926453i
$932$	2.84847	+	4.93369i	0.0933047	+	0.161609i
$933$		0			0
$934$	2.17423	−	3.76588i	0.0711431	−	0.123224i
$935$		0			0
$936$		0			0
$937$	26.7980			0.875451			0.437726	−	0.899109i	$-0.355784\pi$
$937$	26.7980			0.875451			0.437726	+	0.899109i	$0.355784\pi$
$938$	31.9217	−	55.2900i	1.04228	−	1.80528i
$939$		0			0
$940$		0			0
$941$	−14.8207	−	25.6701i	−0.483140	−	0.836823i	0.516673	−	0.856183i	$-0.327170\pi$
$941$	−14.8207	−	25.6701i	−0.483140	−	0.836823i	−0.999813	+	0.0193603i	$0.993837\pi$
$942$		0			0
$943$	−11.0227	+	19.0919i	−0.358949	+	0.621717i
$944$	0.550510			0.0179176
$945$		0			0
$946$	−36.4949			−1.18655
$947$	−4.07321	+	7.05501i	−0.132362	+	0.229257i	−0.924587	−	0.380972i	$-0.875589\pi$
$947$	−4.07321	+	7.05501i	−0.132362	+	0.229257i	0.792225	+	0.610229i	$0.208923\pi$
$948$		0			0
$949$	2.22474	+	3.85337i	0.0722183	+	0.125086i
$950$		0			0
$951$		0			0
$952$	−10.8990	+	18.8776i	−0.353238	+	0.611826i
$953$	−21.7980			−0.706105			−0.353053	−	0.935603i	$-0.614856\pi$
$953$	−21.7980			−0.706105			−0.353053	+	0.935603i	$0.614856\pi$
$954$		0			0
$955$		0			0
$956$	4.77526	−	8.27098i	0.154443	−	0.267503i
$957$		0			0
$958$	−12.1237	−	20.9989i	−0.391700	−	0.678444i
$959$	6.67423	+	11.5601i	0.215522	+	0.373296i
$960$		0			0
$961$	15.3990	−	26.6718i	0.496741	−	0.860381i
$962$	14.8990			0.480362
$963$		0			0
$964$	−22.7980			−0.734273
$965$		0			0
$966$		0			0
$967$	−16.0000	−	27.7128i	−0.514525	−	0.891184i	−0.999858	−	0.0168544i	$-0.994635\pi$
$967$	−16.0000	−	27.7128i	−0.514525	−	0.891184i	0.485333	−	0.874330i	$-0.338699\pi$
$968$	−6.50000	−	11.2583i	−0.208918	−	0.361856i
$969$		0			0
$970$		0			0
$971$	−22.8434			−0.733079			−0.366539	−	0.930403i	$-0.619457\pi$
$971$	−22.8434			−0.733079			−0.366539	+	0.930403i	$0.619457\pi$
$972$		0			0
$973$	−17.7980			−0.570576
$974$	9.77526	−	16.9312i	0.313219	−	0.542512i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	0.785020	−	0.619471i	$-0.212653\pi$
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	−0.928987	+	0.370111i	$0.879319\pi$
$978$		0			0
$979$	22.0454	−	38.1838i	0.704574	−	1.22036i
$980$		0			0
$981$		0			0
$982$	2.75255			0.0878374
$983$	−11.4495	+	19.8311i	−0.365182	+	0.632514i	−0.988805	−	0.149211i	$-0.952327\pi$
$983$	−11.4495	+	19.8311i	−0.365182	+	0.632514i	0.623623	+	0.781725i	$0.285660\pi$
$984$		0			0
$985$		0			0
$986$	6.00000	+	10.3923i	0.191079	+	0.330958i
$987$		0			0
$988$	−5.67423	+	9.82806i	−0.180521	+	0.312672i
$989$	−18.2474			−0.580235
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	0.224745	−	0.389270i	0.00713566	−	0.0123593i
$993$		0			0
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$		0			0
$997$	−18.0227	+	31.2162i	−0.570785	+	0.988628i	0.425701	+	0.904864i	$0.360028\pi$
$997$	−18.0227	+	31.2162i	−0.570785	+	0.988628i	−0.996486	+	0.0837642i	$0.973306\pi$
$998$	6.34847			0.200957
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.e.k.451.1		4
3.2	odd	2		450.2.e.m.151.1	yes	4
5.2	odd	4		1350.2.j.g.1099.1		8
5.3	odd	4		1350.2.j.g.1099.4		8
5.4	even	2		1350.2.e.n.451.2		4
9.2	odd	6		4050.2.a.br.1.2		2
9.4	even	3	inner	1350.2.e.k.901.1		4
9.5	odd	6		450.2.e.m.301.2	yes	4
9.7	even	3		4050.2.a.by.1.2		2
15.2	even	4		450.2.j.f.349.3		8
15.8	even	4		450.2.j.f.349.2		8
15.14	odd	2		450.2.e.l.151.2	✓	4
45.2	even	12		4050.2.c.y.649.2		4
45.4	even	6		1350.2.e.n.901.2		4
45.7	odd	12		4050.2.c.w.649.4		4
45.13	odd	12		1350.2.j.g.199.1		8
45.14	odd	6		450.2.e.l.301.1	yes	4
45.22	odd	12		1350.2.j.g.199.4		8
45.23	even	12		450.2.j.f.49.3		8
45.29	odd	6		4050.2.a.bu.1.1		2
45.32	even	12		450.2.j.f.49.2		8
45.34	even	6		4050.2.a.bl.1.1		2
45.38	even	12		4050.2.c.y.649.3		4
45.43	odd	12		4050.2.c.w.649.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.e.l.151.2	✓	4	15.14	odd	2
450.2.e.l.301.1	yes	4	45.14	odd	6
450.2.e.m.151.1	yes	4	3.2	odd	2
450.2.e.m.301.2	yes	4	9.5	odd	6
450.2.j.f.49.2		8	45.32	even	12
450.2.j.f.49.3		8	45.23	even	12
450.2.j.f.349.2		8	15.8	even	4
450.2.j.f.349.3		8	15.2	even	4
1350.2.e.k.451.1		4	1.1	even	1	trivial
1350.2.e.k.901.1		4	9.4	even	3	inner
1350.2.e.n.451.2		4	5.4	even	2
1350.2.e.n.901.2		4	45.4	even	6
1350.2.j.g.199.1		8	45.13	odd	12
1350.2.j.g.199.4		8	45.22	odd	12
1350.2.j.g.1099.1		8	5.2	odd	4
1350.2.j.g.1099.4		8	5.3	odd	4
4050.2.a.bl.1.1		2	45.34	even	6
4050.2.a.br.1.2		2	9.2	odd	6
4050.2.a.bu.1.1		2	45.29	odd	6
4050.2.a.by.1.2		2	9.7	even	3
4050.2.c.w.649.1		4	45.43	odd	12
4050.2.c.w.649.4		4	45.7	odd	12
4050.2.c.y.649.2		4	45.2	even	12
4050.2.c.y.649.3		4	45.38	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.22474 + 3.85337i) q^{7} +1.00000 q^{8} +(2.44949 - 4.24264i) q^{11} +(-2.22474 - 3.85337i) q^{13} +(-2.22474 - 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.89898 q^{17} +2.55051 q^{19} +(2.44949 + 4.24264i) q^{22} +(1.22474 + 2.12132i) q^{23} +4.44949 q^{26} +4.44949 q^{28} +(1.22474 - 2.12132i) q^{29} +(0.224745 + 0.389270i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.44949 + 4.24264i) q^{34} +3.34847 q^{37} +(-1.27526 + 2.20881i) q^{38} +(4.50000 + 7.79423i) q^{41} +(-3.72474 + 6.45145i) q^{43} -4.89898 q^{44} -2.44949 q^{46} +(-0.550510 + 0.953512i) q^{47} +(-6.39898 - 11.0834i) q^{49} +(-2.22474 + 3.85337i) q^{52} +8.44949 q^{53} +(-2.22474 + 3.85337i) q^{56} +(1.22474 + 2.12132i) q^{58} +(-0.275255 - 0.476756i) q^{59} +(-4.00000 + 6.92820i) q^{61} -0.449490 q^{62} +1.00000 q^{64} +(7.17423 + 12.4261i) q^{67} +(-2.44949 - 4.24264i) q^{68} +1.34847 q^{71} -1.00000 q^{73} +(-1.67423 + 2.89986i) q^{74} +(-1.27526 - 2.20881i) q^{76} +(10.8990 + 18.8776i) q^{77} +(6.34847 - 10.9959i) q^{79} -9.00000 q^{82} +(-0.275255 + 0.476756i) q^{83} +(-3.72474 - 6.45145i) q^{86} +(2.44949 - 4.24264i) q^{88} +9.00000 q^{89} +19.7980 q^{91} +(1.22474 - 2.12132i) q^{92} +(-0.550510 - 0.953512i) q^{94} +(5.39898 - 9.35131i) q^{97} +12.7980 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} - 4 q^{13} - 4 q^{14} - 2 q^{16} + 20 q^{19} + 8 q^{26} + 8 q^{28} - 4 q^{31} - 2 q^{32} - 16 q^{37} - 10 q^{38} + 18 q^{41} - 10 q^{43} - 12 q^{47} - 6 q^{49} - 4 q^{52} + 24 q^{53} - 4 q^{56} - 6 q^{59} - 16 q^{61} + 8 q^{62} + 4 q^{64} + 14 q^{67} - 24 q^{71} - 4 q^{73} + 8 q^{74} - 10 q^{76} + 24 q^{77} - 4 q^{79} - 36 q^{82} - 6 q^{83} - 10 q^{86} + 36 q^{89} + 40 q^{91} - 12 q^{94} + 2 q^{97} + 12 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 - 4 * q^13 - 4 * q^14 - 2 * q^16 + 20 * q^19 + 8 * q^26 + 8 * q^28 - 4 * q^31 - 2 * q^32 - 16 * q^37 - 10 * q^38 + 18 * q^41 - 10 * q^43 - 12 * q^47 - 6 * q^49 - 4 * q^52 + 24 * q^53 - 4 * q^56 - 6 * q^59 - 16 * q^61 + 8 * q^62 + 4 * q^64 + 14 * q^67 - 24 * q^71 - 4 * q^73 + 8 * q^74 - 10 * q^76 + 24 * q^77 - 4 * q^79 - 36 * q^82 - 6 * q^83 - 10 * q^86 + 36 * q^89 + 40 * q^91 - 12 * q^94 + 2 * q^97 + 12 * q^98

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