LMFDB - Embedded newform 1350.2.j.g.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(199,1350)]

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([2, 3]))

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

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

chi := DirichletCharacter("1350.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.199
Dual form			1350.2.j.g.1099.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.85337 + 2.22474i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.85337 + 2.22474i) q^{7} +1.00000i q^{8} +(2.44949 + 4.24264i) q^{11} +(-3.85337 - 2.22474i) q^{13} +(2.22474 - 3.85337i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.89898i q^{17} -2.55051 q^{19} +(-4.24264 - 2.44949i) q^{22} +(2.12132 + 1.22474i) q^{23} +4.44949 q^{26} +4.44949i q^{28} +(-1.22474 - 2.12132i) q^{29} +(0.224745 - 0.389270i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.44949 + 4.24264i) q^{34} -3.34847i q^{37} +(2.20881 - 1.27526i) q^{38} +(4.50000 - 7.79423i) q^{41} +(6.45145 - 3.72474i) q^{43} +4.89898 q^{44} -2.44949 q^{46} +(-0.953512 + 0.550510i) q^{47} +(6.39898 - 11.0834i) q^{49} +(-3.85337 + 2.22474i) q^{52} +8.44949i q^{53} +(-2.22474 - 3.85337i) q^{56} +(2.12132 + 1.22474i) q^{58} +(0.275255 - 0.476756i) q^{59} +(-4.00000 - 6.92820i) q^{61} +0.449490i q^{62} -1.00000 q^{64} +(-12.4261 - 7.17423i) q^{67} +(-4.24264 - 2.44949i) q^{68} +1.34847 q^{71} -1.00000i q^{73} +(1.67423 + 2.89986i) q^{74} +(-1.27526 + 2.20881i) q^{76} +(-18.8776 - 10.8990i) q^{77} +(-6.34847 - 10.9959i) q^{79} +9.00000i q^{82} +(0.476756 - 0.275255i) q^{83} +(-3.72474 + 6.45145i) q^{86} +(-4.24264 + 2.44949i) q^{88} -9.00000 q^{89} +19.7980 q^{91} +(2.12132 - 1.22474i) q^{92} +(0.550510 - 0.953512i) q^{94} +(9.35131 - 5.39898i) q^{97} +12.7980i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 8 q^{14} - 4 q^{16} - 40 q^{19} + 16 q^{26} - 8 q^{31} + 36 q^{41} + 12 q^{49} - 8 q^{56} + 12 q^{59} - 32 q^{61} - 8 q^{64} - 48 q^{71} - 16 q^{74} - 20 q^{76} + 8 q^{79} - 20 q^{86} - 72 q^{89} + 80 q^{91} + 24 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 8 * q^14 - 4 * q^16 - 40 * q^19 + 16 * q^26 - 8 * q^31 + 36 * q^41 + 12 * q^49 - 8 * q^56 + 12 * q^59 - 32 * q^61 - 8 * q^64 - 48 * q^71 - 16 * q^74 - 20 * q^76 + 8 * q^79 - 20 * q^86 - 72 * q^89 + 80 * q^91 + 24 * q^94

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.85337	+	2.22474i	−1.45644	+	0.840875i	−0.998834	−	0.0482818i	$-0.984625\pi$
$7$	−3.85337	+	2.22474i	−1.45644	+	0.840875i	−0.457604	+	0.889156i	$0.651292\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	0.953149	+	0.302502i	$0.0978220\pi$
$11$	2.44949	+	4.24264i	0.738549	+	1.27920i	−0.214600	+	0.976702i	$0.568845\pi$
$12$		0			0
$13$	−3.85337	−	2.22474i	−1.06873	−	0.617033i	−0.140898	−	0.990024i	$-0.544999\pi$
$13$	−3.85337	−	2.22474i	−1.06873	−	0.617033i	−0.927835	+	0.372991i	$0.878332\pi$
$14$	2.22474	−	3.85337i	0.594588	−	1.02986i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$		0			0
$19$	−2.55051			−0.585127			−0.292564	−	0.956246i	$-0.594508\pi$
$19$	−2.55051			−0.585127			−0.292564	+	0.956246i	$0.594508\pi$
$20$		0			0
$21$		0			0
$22$	−4.24264	−	2.44949i	−0.904534	−	0.522233i
$23$	2.12132	+	1.22474i	0.442326	+	0.255377i	0.704584	−	0.709621i	$-0.251134\pi$
$23$	2.12132	+	1.22474i	0.442326	+	0.255377i	−0.262258	+	0.964998i	$0.584467\pi$
$24$		0			0
$25$		0			0
$26$	4.44949			0.872617
$27$		0			0
$28$			4.44949i			0.840875i
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	0.729616	−	0.683857i	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$		0			0
$31$	0.224745	−	0.389270i	0.0403654	−	0.0699149i	−0.845137	−	0.534550i	$-0.820481\pi$
$31$	0.224745	−	0.389270i	0.0403654	−	0.0699149i	0.885502	+	0.464635i	$0.153814\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	2.44949	+	4.24264i	0.420084	+	0.727607i
$35$		0			0
$36$		0			0
$37$		−	3.34847i		−	0.550485i	−0.961375	−	0.275242i	$-0.911242\pi$
$37$		−	3.34847i		−	0.550485i	0.961375	−	0.275242i	$-0.0887581\pi$
$38$	2.20881	−	1.27526i	0.358316	−	0.206874i
$39$		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
$43$	6.45145	−	3.72474i	0.983836	−	0.568018i	0.0804103	−	0.996762i	$-0.474377\pi$
$43$	6.45145	−	3.72474i	0.983836	−	0.568018i	0.903426	+	0.428744i	$0.141044\pi$
$44$	4.89898			0.738549
$45$		0			0
$46$	−2.44949			−0.361158
$47$	−0.953512	+	0.550510i	−0.139084	+	0.0803002i	−0.567927	−	0.823079i	$-0.692255\pi$
$47$	−0.953512	+	0.550510i	−0.139084	+	0.0803002i	0.428843	+	0.903379i	$0.358921\pi$
$48$		0			0
$49$	6.39898	−	11.0834i	0.914140	−	1.58334i
$50$		0			0
$51$		0			0
$52$	−3.85337	+	2.22474i	−0.534366	+	0.308517i
$53$			8.44949i			1.16063i	0.814393	+	0.580313i	$0.197070\pi$
$53$			8.44949i			1.16063i	−0.814393	+	0.580313i	$0.802930\pi$
$54$		0			0
$55$		0			0
$56$	−2.22474	−	3.85337i	−0.297294	−	0.514928i
$57$		0			0
$58$	2.12132	+	1.22474i	0.278543	+	0.160817i
$59$	0.275255	−	0.476756i	0.0358352	−	0.0620683i	−0.847552	−	0.530713i	$-0.821924\pi$
$59$	0.275255	−	0.476756i	0.0358352	−	0.0620683i	0.883387	+	0.468645i	$0.155258\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$			0.449490i			0.0570853i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−12.4261	−	7.17423i	−1.51809	−	0.876472i	−0.999773	−	0.0212861i	$-0.993224\pi$
$67$	−12.4261	−	7.17423i	−1.51809	−	0.876472i	−0.518321	−	0.855186i	$-0.673443\pi$
$68$	−4.24264	−	2.44949i	−0.514496	−	0.297044i
$69$		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
$73$		−	1.00000i		−	0.117041i	−0.998286	−	0.0585206i	$-0.981362\pi$
$73$		−	1.00000i		−	0.117041i	0.998286	−	0.0585206i	$-0.0186383\pi$
$74$	1.67423	+	2.89986i	0.194626	+	0.337102i
$75$		0			0
$76$	−1.27526	+	2.20881i	−0.146282	+	0.253368i
$77$	−18.8776	−	10.8990i	−2.15130	−	1.24205i
$78$		0			0
$79$	−6.34847	−	10.9959i	−0.714259	−	1.23713i	−0.963245	−	0.268625i	$-0.913431\pi$
$79$	−6.34847	−	10.9959i	−0.714259	−	1.23713i	0.248986	−	0.968507i	$-0.419903\pi$
$80$		0			0
$81$		0			0
$82$			9.00000i			0.993884i
$83$	0.476756	−	0.275255i	0.0523308	−	0.0302132i	−0.473606	−	0.880737i	$-0.657048\pi$
$83$	0.476756	−	0.275255i	0.0523308	−	0.0302132i	0.525937	+	0.850523i	$0.323715\pi$
$84$		0			0
$85$		0			0
$86$	−3.72474	+	6.45145i	−0.401650	+	0.695677i
$87$		0			0
$88$	−4.24264	+	2.44949i	−0.452267	+	0.261116i
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$		0			0
$91$	19.7980			2.07539
$92$	2.12132	−	1.22474i	0.221163	−	0.127688i
$93$		0			0
$94$	0.550510	−	0.953512i	0.0567808	−	0.0983472i
$95$		0			0
$96$		0			0
$97$	9.35131	−	5.39898i	0.949481	−	0.548183i	0.0565616	−	0.998399i	$-0.481986\pi$
$97$	9.35131	−	5.39898i	0.949481	−	0.548183i	0.892920	+	0.450216i	$0.148653\pi$
$98$			12.7980i			1.29279i
$99$		0			0
$100$		0			0
$101$	1.77526	+	3.07483i	0.176644	+	0.305957i	0.940729	−	0.339159i	$-0.110142\pi$
$101$	1.77526	+	3.07483i	0.176644	+	0.305957i	−0.764085	+	0.645116i	$0.776809\pi$
$102$		0			0
$103$	10.9959	+	6.34847i	1.08346	+	0.625533i	0.931826	−	0.362904i	$-0.118215\pi$
$103$	10.9959	+	6.34847i	1.08346	+	0.625533i	0.151629	+	0.988437i	$0.451548\pi$
$104$	2.22474	−	3.85337i	0.218154	−	0.377854i
$105$		0			0
$106$	−4.22474	−	7.31747i	−0.410343	−	0.710736i
$107$		−	15.2474i		−	1.47403i	−0.675878	−	0.737013i	$-0.736236\pi$
$107$		−	15.2474i		−	1.47403i	0.675878	−	0.737013i	$-0.263764\pi$
$108$		0			0
$109$	−10.4495			−1.00088			−0.500440	−	0.865771i	$-0.666828\pi$
$109$	−10.4495			−1.00088			−0.500440	+	0.865771i	$0.666828\pi$
$110$		0			0
$111$		0			0
$112$	3.85337	+	2.22474i	0.364109	+	0.210219i
$113$	−12.0369	−	6.94949i	−1.13233	−	0.653753i	−0.187813	−	0.982205i	$-0.560140\pi$
$113$	−12.0369	−	6.94949i	−1.13233	−	0.653753i	−0.944521	+	0.328452i	$0.893473\pi$
$114$		0			0
$115$		0			0
$116$	−2.44949			−0.227429
$117$		0			0
$118$			0.550510i			0.0506786i
$119$	10.8990	+	18.8776i	0.999108	+	1.73051i
$120$		0			0
$121$	−6.50000	+	11.2583i	−0.590909	+	1.02348i
$122$	6.92820	+	4.00000i	0.627250	+	0.362143i
$123$		0			0
$124$	−0.224745	−	0.389270i	−0.0201827	−	0.0349574i
$125$		0			0
$126$		0			0
$127$			11.3485i			1.00701i	0.863991	+	0.503507i	$0.167957\pi$
$127$			11.3485i			1.00701i	−0.863991	+	0.503507i	$0.832043\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	7.89898	−	13.6814i	0.690137	−	1.19535i	−0.281656	−	0.959516i	$-0.590884\pi$
$131$	7.89898	−	13.6814i	0.690137	−	1.19535i	0.971793	−	0.235837i	$-0.0757831\pi$
$132$		0			0
$133$	9.82806	−	5.67423i	0.852201	−	0.492019i
$134$	14.3485			1.23952
$135$		0			0
$136$	4.89898			0.420084
$137$	2.59808	−	1.50000i	0.221969	−	0.128154i	−0.384893	−	0.922961i	$-0.625762\pi$
$137$	2.59808	−	1.50000i	0.221969	−	0.128154i	0.606861	+	0.794808i	$0.292428\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$		0			0
$142$	−1.16781	+	0.674235i	−0.0980003	+	0.0565805i
$143$		−	21.7980i		−	1.82284i
$144$		0			0
$145$		0			0
$146$	0.500000	+	0.866025i	0.0413803	+	0.0716728i
$147$		0			0
$148$	−2.89986	−	1.67423i	−0.238367	−	0.137621i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	−0.910195	−	0.414181i	$-0.864068\pi$
$151$	−10.0000	−	17.3205i	−0.813788	−	1.40952i	0.0964061	−	0.995342i	$-0.469265\pi$
$152$		−	2.55051i		−	0.206874i
$153$		0			0
$154$	21.7980			1.75653
$155$		0			0
$156$		0			0
$157$	−0.174973	−	0.101021i	−0.0139643	−	0.00806231i	0.493002	−	0.870028i	$-0.335900\pi$
$157$	−0.174973	−	0.101021i	−0.0139643	−	0.00806231i	−0.506966	+	0.861966i	$0.669233\pi$
$158$	10.9959	+	6.34847i	0.874785	+	0.505057i
$159$		0			0
$160$		0			0
$161$	−10.8990			−0.858960
$162$		0			0
$163$			2.55051i			0.199771i	0.994999	+	0.0998857i	$0.0318477\pi$
$163$			2.55051i			0.199771i	−0.994999	+	0.0998857i	$0.968152\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−0.275255	+	0.476756i	−0.0213639	+	0.0370034i
$167$	16.9706	+	9.79796i	1.31322	+	0.758189i	0.982628	−	0.185584i	$-0.0594178\pi$
$167$	16.9706	+	9.79796i	1.31322	+	0.758189i	0.330593	+	0.943773i	$0.392751\pi$
$168$		0			0
$169$	3.39898	+	5.88721i	0.261460	+	0.452862i
$170$		0			0
$171$		0			0
$172$		−	7.44949i		−	0.568018i
$173$	8.48528	−	4.89898i	0.645124	−	0.372463i	−0.141462	−	0.989944i	$-0.545180\pi$
$173$	8.48528	−	4.89898i	0.645124	−	0.372463i	0.786586	+	0.617481i	$0.211847\pi$
$174$		0			0
$175$		0			0
$176$	2.44949	−	4.24264i	0.184637	−	0.319801i
$177$		0			0
$178$	7.79423	−	4.50000i	0.584202	−	0.337289i
$179$	−15.2474			−1.13965			−0.569824	−	0.821767i	$-0.692989\pi$
$179$	−15.2474			−1.13965			−0.569824	+	0.821767i	$0.692989\pi$
$180$		0			0
$181$	−1.79796			−0.133641			−0.0668206	−	0.997765i	$-0.521286\pi$
$181$	−1.79796			−0.133641			−0.0668206	+	0.997765i	$0.521286\pi$
$182$	−17.1455	+	9.89898i	−1.27091	+	0.733761i
$183$		0			0
$184$	−1.22474	+	2.12132i	−0.0902894	+	0.156386i
$185$		0			0
$186$		0			0
$187$	20.7846	−	12.0000i	1.51992	−	0.877527i
$188$			1.10102i			0.0803002i
$189$		0			0
$190$		0			0
$191$	−5.44949	−	9.43879i	−0.394311	−	0.682967i	0.598702	−	0.800972i	$-0.295683\pi$
$191$	−5.44949	−	9.43879i	−0.394311	−	0.682967i	−0.993013	+	0.118005i	$0.962350\pi$
$192$		0			0
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.276296	−	0.961073i	$-0.589107\pi$
$193$	−17.3205	−	10.0000i	−1.24676	−	0.719816i	−0.970461	+	0.241257i	$0.922440\pi$
$194$	−5.39898	+	9.35131i	−0.387624	+	0.671385i
$195$		0			0
$196$	−6.39898	−	11.0834i	−0.457070	−	0.791668i
$197$			24.2474i			1.72756i	0.503870	+	0.863780i	$0.331909\pi$
$197$			24.2474i			1.72756i	−0.503870	+	0.863780i	$0.668091\pi$
$198$		0			0
$199$	−5.79796			−0.411006			−0.205503	−	0.978656i	$-0.565883\pi$
$199$	−5.79796			−0.411006			−0.205503	+	0.978656i	$0.565883\pi$
$200$		0			0
$201$		0			0
$202$	−3.07483	−	1.77526i	−0.216344	−	0.124907i
$203$	9.43879	+	5.44949i	0.662473	+	0.382479i
$204$		0			0
$205$		0			0
$206$	−12.6969			−0.884638
$207$		0			0
$208$			4.44949i			0.308517i
$209$	−6.24745	−	10.8209i	−0.432145	−	0.748497i
$210$		0			0
$211$	−0.724745	+	1.25529i	−0.0498935	+	0.0864181i	−0.889894	−	0.456168i	$-0.849222\pi$
$211$	−0.724745	+	1.25529i	−0.0498935	+	0.0864181i	0.840000	+	0.542586i	$0.182555\pi$
$212$	7.31747	+	4.22474i	0.502566	+	0.290157i
$213$		0			0
$214$	7.62372	+	13.2047i	0.521147	+	0.902653i
$215$		0			0
$216$		0			0
$217$			2.00000i			0.135769i
$218$	9.04952	−	5.22474i	0.612911	−	0.353864i
$219$		0			0
$220$		0			0
$221$	−10.8990	+	18.8776i	−0.733145	+	1.26984i
$222$		0			0
$223$	−1.55708	+	0.898979i	−0.104270	+	0.0602001i	−0.551228	−	0.834355i	$-0.685841\pi$
$223$	−1.55708	+	0.898979i	−0.104270	+	0.0602001i	0.446958	+	0.894555i	$0.352507\pi$
$224$	−4.44949			−0.297294
$225$		0			0
$226$	13.8990			0.924546
$227$	24.5505	−	14.1742i	1.62947	−	0.940777i	0.645224	−	0.763994i	$-0.276764\pi$
$227$	24.5505	−	14.1742i	1.62947	−	0.940777i	0.984250	−	0.176783i	$-0.0565692\pi$
$228$		0			0
$229$	−10.5732	+	18.3133i	−0.698698	+	1.21018i	0.270221	+	0.962798i	$0.412903\pi$
$229$	−10.5732	+	18.3133i	−0.698698	+	1.21018i	−0.968918	+	0.247381i	$0.920430\pi$
$230$		0			0
$231$		0			0
$232$	2.12132	−	1.22474i	0.139272	−	0.0804084i
$233$		−	5.69694i		−	0.373219i	−0.982434	−	0.186609i	$-0.940250\pi$
$233$		−	5.69694i		−	0.373219i	0.982434	−	0.186609i	$-0.0597499\pi$
$234$		0			0
$235$		0			0
$236$	−0.275255	−	0.476756i	−0.0179176	−	0.0310342i
$237$		0			0
$238$	−18.8776	−	10.8990i	−1.22365	−	0.706476i
$239$	−4.77526	+	8.27098i	−0.308886	+	0.535006i	−0.978119	−	0.208047i	$-0.933289\pi$
$239$	−4.77526	+	8.27098i	−0.308886	+	0.535006i	0.669233	+	0.743052i	$0.266623\pi$
$240$		0			0
$241$	11.3990	+	19.7436i	0.734273	+	1.27180i	0.955042	+	0.296472i	$0.0958100\pi$
$241$	11.3990	+	19.7436i	0.734273	+	1.27180i	−0.220769	+	0.975326i	$0.570857\pi$
$242$		−	13.0000i		−	0.835672i
$243$		0			0
$244$	−8.00000			−0.512148
$245$		0			0
$246$		0			0
$247$	9.82806	+	5.67423i	0.625345	+	0.361043i
$248$	0.389270	+	0.224745i	0.0247186	+	0.0142713i
$249$		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
$253$			12.0000i			0.754434i
$254$	−5.67423	−	9.82806i	−0.356033	−	0.616667i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.88721	−	3.39898i	−0.367234	−	0.212023i	0.305016	−	0.952347i	$-0.401338\pi$
$257$	−5.88721	−	3.39898i	−0.367234	−	0.212023i	−0.672249	+	0.740325i	$0.734672\pi$
$258$		0			0
$259$	7.44949	+	12.9029i	0.462889	+	0.801747i
$260$		0			0
$261$		0			0
$262$			15.7980i			0.976001i
$263$	−13.4671	+	7.77526i	−0.830419	+	0.479443i	−0.853996	−	0.520279i	$-0.825828\pi$
$263$	−13.4671	+	7.77526i	−0.830419	+	0.479443i	0.0235770	+	0.999722i	$0.492495\pi$
$264$		0			0
$265$		0			0
$266$	−5.67423	+	9.82806i	−0.347910	+	0.602597i
$267$		0			0
$268$	−12.4261	+	7.17423i	−0.759047	+	0.438236i
$269$	9.55051			0.582305			0.291152	−	0.956677i	$-0.405961\pi$
$269$	9.55051			0.582305			0.291152	+	0.956677i	$0.405961\pi$
$270$		0			0
$271$	0.651531			0.0395777			0.0197888	−	0.999804i	$-0.493701\pi$
$271$	0.651531			0.0395777			0.0197888	+	0.999804i	$0.493701\pi$
$272$	−4.24264	+	2.44949i	−0.257248	+	0.148522i
$273$		0			0
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$		0			0
$276$		0			0
$277$	5.58542	−	3.22474i	0.335595	−	0.193756i	−0.322727	−	0.946492i	$-0.604600\pi$
$277$	5.58542	−	3.22474i	0.335595	−	0.193756i	0.658323	+	0.752736i	$0.271266\pi$
$278$		−	4.00000i		−	0.239904i
$279$		0			0
$280$		0			0
$281$	14.4495	+	25.0273i	0.861984	+	1.49300i	0.870011	+	0.493033i	$0.164112\pi$
$281$	14.4495	+	25.0273i	0.861984	+	1.49300i	−0.00802643	+	0.999968i	$0.502555\pi$
$282$		0			0
$283$	−9.74058	−	5.62372i	−0.579017	−	0.334296i	0.181726	−	0.983349i	$-0.441832\pi$
$283$	−9.74058	−	5.62372i	−0.579017	−	0.334296i	−0.760743	+	0.649054i	$0.775165\pi$
$284$	0.674235	−	1.16781i	0.0400085	−	0.0692967i
$285$		0			0
$286$	10.8990	+	18.8776i	0.644470	+	1.11626i
$287$			40.0454i			2.36381i
$288$		0			0
$289$	−7.00000			−0.411765
$290$		0			0
$291$		0			0
$292$	−0.866025	−	0.500000i	−0.0506803	−	0.0292603i
$293$	−24.2880	−	14.0227i	−1.41892	−	0.819215i	−0.422718	−	0.906261i	$-0.638924\pi$
$293$	−24.2880	−	14.0227i	−1.41892	−	0.819215i	−0.996204	+	0.0870462i	$0.972257\pi$
$294$		0			0
$295$		0			0
$296$	3.34847			0.194626
$297$		0			0
$298$			6.00000i			0.347571i
$299$	−5.44949	−	9.43879i	−0.315152	−	0.545859i
$300$		0			0
$301$	−16.5732	+	28.7056i	−0.955264	+	1.65457i
$302$	17.3205	+	10.0000i	0.996683	+	0.575435i
$303$		0			0
$304$	1.27526	+	2.20881i	0.0731409	+	0.126684i
$305$		0			0
$306$		0			0
$307$			6.69694i			0.382214i	0.981569	+	0.191107i	$0.0612078\pi$
$307$			6.69694i			0.382214i	−0.981569	+	0.191107i	$0.938792\pi$
$308$	−18.8776	+	10.8990i	−1.07565	+	0.621027i
$309$		0			0
$310$		0			0
$311$	−5.44949	+	9.43879i	−0.309012	+	0.535225i	−0.978147	−	0.207917i	$-0.933332\pi$
$311$	−5.44949	+	9.43879i	−0.309012	+	0.535225i	0.669134	+	0.743141i	$0.266665\pi$
$312$		0			0
$313$	3.37662	−	1.94949i	0.190858	−	0.110192i	−0.401526	−	0.915847i	$-0.631520\pi$
$313$	3.37662	−	1.94949i	0.190858	−	0.110192i	0.592384	+	0.805656i	$0.298187\pi$
$314$	0.202041			0.0114018
$315$		0			0
$316$	−12.6969			−0.714259
$317$	−14.8492	+	8.57321i	−0.834017	+	0.481520i	−0.855226	−	0.518255i	$-0.826582\pi$
$317$	−14.8492	+	8.57321i	−0.834017	+	0.481520i	0.0212094	+	0.999775i	$0.493248\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$		0			0
$322$	9.43879	−	5.44949i	0.526003	−	0.303688i
$323$			12.4949i			0.695235i
$324$		0			0
$325$		0			0
$326$	−1.27526	−	2.20881i	−0.0706298	−	0.122334i
$327$		0			0
$328$	7.79423	+	4.50000i	0.430364	+	0.248471i
$329$	2.44949	−	4.24264i	0.135045	−	0.233904i
$330$		0			0
$331$	4.17423	+	7.22999i	0.229437	+	0.397396i	0.957641	−	0.287964i	$-0.0929783\pi$
$331$	4.17423	+	7.22999i	0.229437	+	0.397396i	−0.728205	+	0.685360i	$0.759645\pi$
$332$		−	0.550510i		−	0.0302132i
$333$		0			0
$334$	−19.5959			−1.07224
$335$		0			0
$336$		0			0
$337$	−9.61377	−	5.55051i	−0.523695	−	0.302356i	0.214750	−	0.976669i	$-0.431106\pi$
$337$	−9.61377	−	5.55051i	−0.523695	−	0.302356i	−0.738445	+	0.674313i	$0.764440\pi$
$338$	−5.88721	−	3.39898i	−0.320222	−	0.184880i
$339$		0			0
$340$		0			0
$341$	2.20204			0.119247
$342$		0			0
$343$			25.7980i			1.39296i
$344$	3.72474	+	6.45145i	0.200825	+	0.347839i
$345$		0			0
$346$	−4.89898	+	8.48528i	−0.263371	+	0.456172i
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$		0			0
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	0.990282	−	0.139072i	$-0.0444119\pi$
$349$	7.00000	+	12.1244i	0.374701	+	0.649002i	−0.615581	+	0.788074i	$0.711079\pi$
$350$		0			0
$351$		0			0
$352$			4.89898i			0.261116i
$353$	7.79423	−	4.50000i	0.414845	−	0.239511i	−0.278024	−	0.960574i	$-0.589680\pi$
$353$	7.79423	−	4.50000i	0.414845	−	0.239511i	0.692869	+	0.721063i	$0.256346\pi$
$354$		0			0
$355$		0			0
$356$	−4.50000	+	7.79423i	−0.238500	+	0.413093i
$357$		0			0
$358$	13.2047	−	7.62372i	0.697889	−	0.402926i
$359$	−33.7980			−1.78379			−0.891894	−	0.452244i	$-0.850623\pi$
$359$	−33.7980			−1.78379			−0.891894	+	0.452244i	$0.850623\pi$
$360$		0			0
$361$	−12.4949			−0.657626
$362$	1.55708	−	0.898979i	0.0818382	−	0.0472493i
$363$		0			0
$364$	9.89898	−	17.1455i	0.518848	−	0.898670i
$365$		0			0
$366$		0			0
$367$	−14.4600	+	8.34847i	−0.754804	+	0.435787i	−0.827427	−	0.561573i	$-0.810196\pi$
$367$	−14.4600	+	8.34847i	−0.754804	+	0.435787i	0.0726228	+	0.997359i	$0.476863\pi$
$368$		−	2.44949i		−	0.127688i
$369$		0			0
$370$		0			0
$371$	−18.7980	−	32.5590i	−0.975941	−	1.69038i
$372$		0			0
$373$	−13.5065	−	7.79796i	−0.699338	−	0.403763i	0.107763	−	0.994177i	$-0.465631\pi$
$373$	−13.5065	−	7.79796i	−0.699338	−	0.403763i	−0.807101	+	0.590414i	$0.798965\pi$
$374$	−12.0000	+	20.7846i	−0.620505	+	1.07475i
$375$		0			0
$376$	−0.550510	−	0.953512i	−0.0283904	−	0.0491736i
$377$			10.8990i			0.561326i
$378$		0			0
$379$	−0.898979			−0.0461775			−0.0230887	−	0.999733i	$-0.507350\pi$
$379$	−0.898979			−0.0461775			−0.0230887	+	0.999733i	$0.507350\pi$
$380$		0			0
$381$		0			0
$382$	9.43879	+	5.44949i	0.482931	+	0.278820i
$383$	22.9059	+	13.2247i	1.17044	+	0.675753i	0.953783	−	0.300495i	$-0.0971520\pi$
$383$	22.9059	+	13.2247i	1.17044	+	0.675753i	0.216655	+	0.976248i	$0.430485\pi$
$384$		0			0
$385$		0			0
$386$	20.0000			1.01797
$387$		0			0
$388$		−	10.7980i		−	0.548183i
$389$	6.79796	+	11.7744i	0.344670	+	0.596986i	0.985294	−	0.170869i	$-0.0546574\pi$
$389$	6.79796	+	11.7744i	0.344670	+	0.596986i	−0.640624	+	0.767855i	$0.721324\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	11.0834	+	6.39898i	0.559794	+	0.323197i
$393$		0			0
$394$	−12.1237	−	20.9989i	−0.610784	−	1.05791i
$395$		0			0
$396$		0			0
$397$		−	21.5959i		−	1.08387i	−0.840421	−	0.541934i	$-0.817692\pi$
$397$		−	21.5959i		−	1.08387i	0.840421	−	0.541934i	$-0.182308\pi$
$398$	5.02118	−	2.89898i	0.251689	−	0.145313i
$399$		0			0
$400$		0			0
$401$	4.65153	−	8.05669i	0.232286	−	0.402332i	−0.726194	−	0.687490i	$-0.758713\pi$
$401$	4.65153	−	8.05669i	0.232286	−	0.402332i	0.958481	+	0.285158i	$0.0920460\pi$
$402$		0			0
$403$	−1.73205	+	1.00000i	−0.0862796	+	0.0498135i
$404$	3.55051			0.176644
$405$		0			0
$406$	−10.8990			−0.540907
$407$	14.2064	−	8.20204i	0.704183	−	0.406560i
$408$		0			0
$409$	4.94949	−	8.57277i	0.244737	−	0.423896i	−0.717321	−	0.696743i	$-0.754632\pi$
$409$	4.94949	−	8.57277i	0.244737	−	0.423896i	0.962058	+	0.272847i	$0.0879652\pi$
$410$		0			0
$411$		0			0
$412$	10.9959	−	6.34847i	0.541728	−	0.312767i
$413$			2.44949i			0.120532i
$414$		0			0
$415$		0			0
$416$	−2.22474	−	3.85337i	−0.109077	−	0.188927i
$417$		0			0
$418$	10.8209	+	6.24745i	0.529267	+	0.305573i
$419$	−4.07321	+	7.05501i	−0.198990	+	0.344660i	−0.948201	−	0.317671i	$-0.897099\pi$
$419$	−4.07321	+	7.05501i	−0.198990	+	0.344660i	0.749212	+	0.662331i	$0.230433\pi$
$420$		0			0
$421$	−9.02270	−	15.6278i	−0.439740	−	0.761651i	0.557929	−	0.829888i	$-0.311596\pi$
$421$	−9.02270	−	15.6278i	−0.439740	−	0.761651i	−0.997669	+	0.0682369i	$0.978263\pi$
$422$		−	1.44949i		−	0.0705601i
$423$		0			0
$424$	−8.44949			−0.410343
$425$		0			0
$426$		0			0
$427$	30.8270	+	17.7980i	1.49182	+	0.861304i
$428$	−13.2047	−	7.62372i	−0.638272	−	0.368507i
$429$		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
$433$		−	29.5959i		−	1.42229i	−0.703046	−	0.711145i	$-0.748177\pi$
$433$		−	29.5959i		−	1.42229i	0.703046	−	0.711145i	$-0.251823\pi$
$434$	−1.00000	−	1.73205i	−0.0480015	−	0.0831411i
$435$		0			0
$436$	−5.22474	+	9.04952i	−0.250220	+	0.433394i
$437$	−5.41045	−	3.12372i	−0.258817	−	0.149428i
$438$		0			0
$439$	−5.67423	−	9.82806i	−0.270816	−	0.469068i	0.698255	−	0.715849i	$-0.253960\pi$
$439$	−5.67423	−	9.82806i	−0.270816	−	0.469068i	−0.969071	+	0.246782i	$0.920627\pi$
$440$		0			0
$441$		0			0
$442$		−	21.7980i		−	1.03682i
$443$	−24.0737	+	13.8990i	−1.14378	+	0.660360i	−0.947363	−	0.320161i	$-0.896263\pi$
$443$	−24.0737	+	13.8990i	−1.14378	+	0.660360i	−0.196415	+	0.980521i	$0.562930\pi$
$444$		0			0
$445$		0			0
$446$	0.898979	−	1.55708i	0.0425679	−	0.0737298i
$447$		0			0
$448$	3.85337	−	2.22474i	0.182055	−	0.105109i
$449$	10.5959			0.500052			0.250026	−	0.968239i	$-0.419561\pi$
$449$	10.5959			0.500052			0.250026	+	0.968239i	$0.419561\pi$
$450$		0			0
$451$	44.0908			2.07616
$452$	−12.0369	+	6.94949i	−0.566167	+	0.326877i
$453$		0			0
$454$	−14.1742	+	24.5505i	−0.665230	+	1.15221i
$455$		0			0
$456$		0			0
$457$	13.5939	−	7.84847i	0.635898	−	0.367136i	−0.147135	−	0.989116i	$-0.547005\pi$
$457$	13.5939	−	7.84847i	0.635898	−	0.367136i	0.783033	+	0.621981i	$0.213672\pi$
$458$		−	21.1464i		−	0.988108i
$459$		0			0
$460$		0			0
$461$	9.67423	+	16.7563i	0.450574	+	0.780417i	0.998422	−	0.0561610i	$-0.0178860\pi$
$461$	9.67423	+	16.7563i	0.450574	+	0.780417i	−0.547848	+	0.836578i	$0.684553\pi$
$462$		0			0
$463$	−8.09601	−	4.67423i	−0.376254	−	0.217230i	0.299933	−	0.953960i	$-0.403036\pi$
$463$	−8.09601	−	4.67423i	−0.376254	−	0.217230i	−0.676187	+	0.736730i	$0.736369\pi$
$464$	−1.22474	+	2.12132i	−0.0568574	+	0.0984798i
$465$		0			0
$466$	2.84847	+	4.93369i	0.131953	+	0.228549i
$467$			4.34847i			0.201223i	0.994926	+	0.100612i	$0.0320799\pi$
$467$			4.34847i			0.201223i	−0.994926	+	0.100612i	$0.967920\pi$
$468$		0			0
$469$	63.8434			2.94801
$470$		0			0
$471$		0			0
$472$	0.476756	+	0.275255i	0.0219445	+	0.0126696i
$473$	31.6055	+	18.2474i	1.45322	+	0.839019i
$474$		0			0
$475$		0			0
$476$	21.7980			0.999108
$477$		0			0
$478$		−	9.55051i		−	0.436830i
$479$	12.1237	+	20.9989i	0.553947	+	0.959465i	0.997985	+	0.0634563i	$0.0202124\pi$
$479$	12.1237	+	20.9989i	0.553947	+	0.959465i	−0.444038	+	0.896008i	$0.646454\pi$
$480$		0			0
$481$	−7.44949	+	12.9029i	−0.339667	+	0.588321i
$482$	−19.7436	−	11.3990i	−0.899297	−	0.519209i
$483$		0			0
$484$	6.50000	+	11.2583i	0.295455	+	0.511742i
$485$		0			0
$486$		0			0
$487$			19.5505i			0.885918i	0.896542	+	0.442959i	$0.146071\pi$
$487$			19.5505i			0.885918i	−0.896542	+	0.442959i	$0.853929\pi$
$488$	6.92820	−	4.00000i	0.313625	−	0.181071i
$489$		0			0
$490$		0			0
$491$	−1.37628	+	2.38378i	−0.0621105	+	0.107578i	−0.895409	−	0.445245i	$-0.853116\pi$
$491$	−1.37628	+	2.38378i	−0.0621105	+	0.107578i	0.833298	+	0.552824i	$0.186450\pi$
$492$		0			0
$493$	−10.3923	+	6.00000i	−0.468046	+	0.270226i
$494$	−11.3485			−0.510592
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	−5.19615	+	3.00000i	−0.233079	+	0.134568i
$498$		0			0
$499$	3.17423	−	5.49794i	0.142098	−	0.246121i	−0.786188	−	0.617987i	$-0.787948\pi$
$499$	3.17423	−	5.49794i	0.142098	−	0.246121i	0.928287	+	0.371866i	$0.121282\pi$
$500$		0			0
$501$		0			0
$502$	−4.71940	+	2.72474i	−0.210637	+	0.121611i
$503$		−	26.4495i		−	1.17932i	−0.807650	−	0.589662i	$-0.799261\pi$
$503$		−	26.4495i		−	1.17932i	0.807650	−	0.589662i	$-0.200739\pi$
$504$		0			0
$505$		0			0
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$		0			0
$508$	9.82806	+	5.67423i	0.436050	+	0.251753i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	2.22474	+	3.85337i	0.0984169	+	0.170463i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	6.79796			0.299845
$515$		0			0
$516$		0			0
$517$	−4.67123	−	2.69694i	−0.205441	−	0.118611i
$518$	−12.9029	−	7.44949i	−0.566921	−	0.327312i
$519$		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
$523$		−	5.65153i		−	0.247124i	−0.992337	−	0.123562i	$-0.960568\pi$
$523$		−	5.65153i		−	0.247124i	0.992337	−	0.123562i	$-0.0394318\pi$
$524$	−7.89898	−	13.6814i	−0.345069	−	0.597676i
$525$		0			0
$526$	7.77526	−	13.4671i	0.339017	−	0.587195i
$527$	−1.90702	−	1.10102i	−0.0830712	−	0.0479612i
$528$		0			0
$529$	−8.50000	−	14.7224i	−0.369565	−	0.640106i
$530$		0			0
$531$		0			0
$532$		−	11.3485i		−	0.492019i
$533$	−34.6803	+	20.0227i	−1.50217	+	0.867280i
$534$		0			0
$535$		0			0
$536$	7.17423	−	12.4261i	0.309880	−	0.536727i
$537$		0			0
$538$	−8.27098	+	4.77526i	−0.356587	+	0.205876i
$539$	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	$0.627969\pi$
$542$	−0.564242	+	0.325765i	−0.0242363	+	0.0139928i
$543$		0			0
$544$	2.44949	−	4.24264i	0.105021	−	0.181902i
$545$		0			0
$546$		0			0
$547$	−26.2825	+	15.1742i	−1.12376	+	0.648803i	−0.942358	−	0.334606i	$-0.891397\pi$
$547$	−26.2825	+	15.1742i	−1.12376	+	0.648803i	−0.181402	+	0.983409i	$0.558064\pi$
$548$		−	3.00000i		−	0.128154i
$549$		0			0
$550$		0			0
$551$	3.12372	+	5.41045i	0.133075	+	0.230493i
$552$		0			0
$553$	48.9260	+	28.2474i	2.08055	+	1.20120i
$554$	−3.22474	+	5.58542i	−0.137006	+	0.237302i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$		−	17.3939i		−	0.737002i	−0.929627	−	0.368501i	$-0.879871\pi$
$557$		−	17.3939i		−	0.737002i	0.929627	−	0.368501i	$-0.120129\pi$
$558$		0			0
$559$	−33.1464			−1.40194
$560$		0			0
$561$		0			0
$562$	−25.0273	−	14.4495i	−1.05571	−	0.609515i
$563$	25.9326	+	14.9722i	1.09293	+	0.631003i	0.934355	−	0.356344i	$-0.115977\pi$
$563$	25.9326	+	14.9722i	1.09293	+	0.631003i	0.158574	+	0.987347i	$0.449310\pi$
$564$		0			0
$565$		0			0
$566$	11.2474			0.472766
$567$		0			0
$568$			1.34847i			0.0565805i
$569$	−7.10102	−	12.2993i	−0.297690	−	0.515615i	0.677917	−	0.735139i	$-0.262883\pi$
$569$	−7.10102	−	12.2993i	−0.297690	−	0.515615i	−0.975607	+	0.219524i	$0.929550\pi$
$570$		0			0
$571$	13.9722	−	24.2005i	0.584718	−	1.01276i	−0.410192	−	0.911999i	$-0.634538\pi$
$571$	13.9722	−	24.2005i	0.584718	−	1.01276i	0.994911	−	0.100762i	$-0.0321282\pi$
$572$	−18.8776	−	10.8990i	−0.789312	−	0.455709i
$573$		0			0
$574$	−20.0227	−	34.6803i	−0.835732	−	1.44753i
$575$		0			0
$576$		0			0
$577$			18.3939i			0.765747i	0.923801	+	0.382874i	$0.125066\pi$
$577$			18.3939i			0.765747i	−0.923801	+	0.382874i	$0.874934\pi$
$578$	6.06218	−	3.50000i	0.252153	−	0.145581i
$579$		0			0
$580$		0			0
$581$	−1.22474	+	2.12132i	−0.0508110	+	0.0880072i
$582$		0			0
$583$	−35.8481	+	20.6969i	−1.48468	+	0.857180i
$584$	1.00000			0.0413803
$585$		0			0
$586$	28.0454			1.15855
$587$	2.33562	−	1.34847i	0.0964012	−	0.0556573i	−0.451024	−	0.892512i	$-0.648941\pi$
$587$	2.33562	−	1.34847i	0.0964012	−	0.0556573i	0.547426	+	0.836854i	$0.315608\pi$
$588$		0			0
$589$	−0.573214	+	0.992836i	−0.0236189	+	0.0409091i
$590$		0			0
$591$		0			0
$592$	−2.89986	+	1.67423i	−0.119183	+	0.0688106i
$593$		−	1.89898i		−	0.0779817i	−0.999240	−	0.0389909i	$-0.987586\pi$
$593$		−	1.89898i		−	0.0779817i	0.999240	−	0.0389909i	$-0.0124143\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	9.43879	+	5.44949i	0.385981	+	0.222846i
$599$	18.6742	−	32.3447i	0.763009	−	1.32157i	−0.178285	−	0.983979i	$-0.557055\pi$
$599$	18.6742	−	32.3447i	0.763009	−	1.32157i	0.941293	−	0.337591i	$-0.109612\pi$
$600$		0			0
$601$	−16.2474	−	28.1414i	−0.662747	−	1.14791i	−0.979891	−	0.199534i	$-0.936057\pi$
$601$	−16.2474	−	28.1414i	−0.662747	−	1.14791i	0.317144	−	0.948378i	$-0.397276\pi$
$602$		−	33.1464i		−	1.35095i
$603$		0			0
$604$	−20.0000			−0.813788
$605$		0			0
$606$		0			0
$607$	−9.82806	−	5.67423i	−0.398909	−	0.230310i	0.287104	−	0.957899i	$-0.407307\pi$
$607$	−9.82806	−	5.67423i	−0.398909	−	0.230310i	−0.686013	+	0.727589i	$0.740641\pi$
$608$	−2.20881	−	1.27526i	−0.0895789	−	0.0517184i
$609$		0			0
$610$		0			0
$611$	4.89898			0.198191
$612$		0			0
$613$		−	32.0454i		−	1.29430i	−0.762362	−	0.647151i	$-0.775960\pi$
$613$		−	32.0454i		−	1.29430i	0.762362	−	0.647151i	$-0.224040\pi$
$614$	−3.34847	−	5.79972i	−0.135133	−	0.234058i
$615$		0			0
$616$	10.8990	−	18.8776i	0.439132	−	0.760600i
$617$	12.4655	+	7.19694i	0.501841	+	0.289738i	0.729473	−	0.684009i	$-0.239765\pi$
$617$	12.4655	+	7.19694i	0.501841	+	0.289738i	−0.227633	+	0.973747i	$0.573099\pi$
$618$		0			0
$619$	20.8712	+	36.1499i	0.838883	+	1.45299i	0.890829	+	0.454339i	$0.150124\pi$
$619$	20.8712	+	36.1499i	0.838883	+	1.45299i	−0.0519458	+	0.998650i	$0.516542\pi$
$620$		0			0
$621$		0			0
$622$		−	10.8990i		−	0.437009i
$623$	34.6803	−	20.0227i	1.38944	−	0.802193i
$624$		0			0
$625$		0			0
$626$	−1.94949	+	3.37662i	−0.0779173	+	0.134957i
$627$		0			0
$628$	−0.174973	+	0.101021i	−0.00698217	+	0.00403116i
$629$	−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	$0.671651\pi$
$632$	10.9959	−	6.34847i	0.437392	−	0.252529i
$633$		0			0
$634$	8.57321	−	14.8492i	0.340486	−	0.589739i
$635$		0			0
$636$		0			0
$637$	−49.3153	+	28.4722i	−1.95394	+	1.12811i
$638$			12.0000i			0.475085i
$639$		0			0
$640$		0			0
$641$	22.1969	+	38.4462i	0.876726	+	1.51853i	0.854912	+	0.518773i	$0.173611\pi$
$641$	22.1969	+	38.4462i	0.876726	+	1.51853i	0.0218141	+	0.999762i	$0.493056\pi$
$642$		0			0
$643$	28.0146	+	16.1742i	1.10479	+	0.637850i	0.937474	−	0.348054i	$-0.113157\pi$
$643$	28.0146	+	16.1742i	1.10479	+	0.637850i	0.167313	+	0.985904i	$0.446491\pi$
$644$	−5.44949	+	9.43879i	−0.214740	+	0.371941i
$645$		0			0
$646$	−6.24745	−	10.8209i	−0.245803	−	0.425743i
$647$		−	0.247449i		−	0.00972821i	−0.999988	−	0.00486411i	$-0.998452\pi$
$647$		−	0.247449i		−	0.00972821i	0.999988	−	0.00486411i	$-0.00154830\pi$
$648$		0			0
$649$	2.69694			0.105864
$650$		0			0
$651$		0			0
$652$	2.20881	+	1.27526i	0.0865035	+	0.0499428i
$653$	−5.41045	−	3.12372i	−0.211727	−	0.122241i	0.390387	−	0.920651i	$-0.372341\pi$
$653$	−5.41045	−	3.12372i	−0.211727	−	0.122241i	−0.602114	+	0.798410i	$0.705675\pi$
$654$		0			0
$655$		0			0
$656$	−9.00000			−0.351391
$657$		0			0
$658$			4.89898i			0.190982i
$659$	−22.0732	−	38.2319i	−0.859850	−	1.48930i	−0.872071	−	0.489379i	$-0.837223\pi$
$659$	−22.0732	−	38.2319i	−0.859850	−	1.48930i	0.0122208	−	0.999925i	$-0.496110\pi$
$660$		0			0
$661$	25.6969	−	44.5084i	0.999495	−	1.73118i	0.472230	−	0.881475i	$-0.343449\pi$
$661$	25.6969	−	44.5084i	0.999495	−	1.73118i	0.527265	−	0.849701i	$-0.323218\pi$
$662$	−7.22999	−	4.17423i	−0.281001	−	0.162236i
$663$		0			0
$664$	0.275255	+	0.476756i	0.0106820	+	0.0185017i
$665$		0			0
$666$		0			0
$667$		−	6.00000i		−	0.232321i
$668$	16.9706	−	9.79796i	0.656611	−	0.379094i
$669$		0			0
$670$		0			0
$671$	19.5959	−	33.9411i	0.756492	−	1.31028i
$672$		0			0
$673$	−5.79972	+	3.34847i	−0.223563	+	0.129074i	−0.607599	−	0.794244i	$-0.707867\pi$
$673$	−5.79972	+	3.34847i	−0.223563	+	0.129074i	0.384036	+	0.923318i	$0.374534\pi$
$674$	11.1010			0.427595
$675$		0			0
$676$	6.79796			0.261460
$677$	32.7733	−	18.9217i	1.25958	−	0.727219i	0.286588	−	0.958054i	$-0.407479\pi$
$677$	32.7733	−	18.9217i	1.25958	−	0.727219i	0.972993	+	0.230835i	$0.0741456\pi$
$678$		0			0
$679$	−24.0227	+	41.6085i	−0.921907	+	1.59679i
$680$		0			0
$681$		0			0
$682$	−1.90702	+	1.10102i	−0.0730237	+	0.0421603i
$683$			11.9444i			0.457039i	0.973539	+	0.228520i	$0.0733885\pi$
$683$			11.9444i			0.457039i	−0.973539	+	0.228520i	$0.926611\pi$
$684$		0			0
$685$		0			0
$686$	−12.8990	−	22.3417i	−0.492485	−	0.853010i
$687$		0			0
$688$	−6.45145	−	3.72474i	−0.245959	−	0.142005i
$689$	18.7980	−	32.5590i	0.716145	−	1.24040i
$690$		0			0
$691$	2.52270	+	4.36945i	0.0959682	+	0.166222i	0.910012	−	0.414581i	$-0.136072\pi$
$691$	2.52270	+	4.36945i	0.0959682	+	0.166222i	−0.814044	+	0.580803i	$0.802739\pi$
$692$		−	9.79796i		−	0.372463i
$693$		0			0
$694$	12.0000			0.455514
$695$		0			0
$696$		0			0
$697$	−38.1838	−	22.0454i	−1.44631	−	0.835029i
$698$	−12.1244	−	7.00000i	−0.458914	−	0.264954i
$699$		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
$703$			8.54031i			0.322104i
$704$	−2.44949	−	4.24264i	−0.0923186	−	0.159901i
$705$		0			0
$706$	−4.50000	+	7.79423i	−0.169360	+	0.293340i
$707$	−13.6814	−	7.89898i	−0.514543	−	0.297072i
$708$		0			0
$709$	−0.224745	−	0.389270i	−0.00844047	−	0.0146193i	0.861774	−	0.507292i	$-0.169353\pi$
$709$	−0.224745	−	0.389270i	−0.00844047	−	0.0146193i	−0.870215	+	0.492673i	$0.836020\pi$
$710$		0			0
$711$		0			0
$712$		−	9.00000i		−	0.337289i
$713$	0.953512	−	0.550510i	0.0357093	−	0.0206168i
$714$		0			0
$715$		0			0
$716$	−7.62372	+	13.2047i	−0.284912	+	0.493482i
$717$		0			0
$718$	29.2699	−	16.8990i	1.09234	−	0.630664i
$719$	52.0454			1.94097			0.970483	−	0.241169i	$-0.0775309\pi$
$719$	52.0454			1.94097			0.970483	+	0.241169i	$0.0775309\pi$
$720$		0			0
$721$	−56.4949			−2.10398
$722$	10.8209	−	6.24745i	0.402712	−	0.232506i
$723$		0			0
$724$	−0.898979	+	1.55708i	−0.0334103	+	0.0578684i
$725$		0			0
$726$		0			0
$727$	13.8564	−	8.00000i	0.513906	−	0.296704i	−0.220532	−	0.975380i	$-0.570779\pi$
$727$	13.8564	−	8.00000i	0.513906	−	0.296704i	0.734438	+	0.678676i	$0.237446\pi$
$728$			19.7980i			0.733761i
$729$		0			0
$730$		0			0
$731$	−18.2474	−	31.6055i	−0.674906	−	1.16897i
$732$		0			0
$733$	−22.5167	−	13.0000i	−0.831672	−	0.480166i	0.0227529	−	0.999741i	$-0.492757\pi$
$733$	−22.5167	−	13.0000i	−0.831672	−	0.480166i	−0.854425	+	0.519575i	$0.826090\pi$
$734$	8.34847	−	14.4600i	0.308148	−	0.533727i
$735$		0			0
$736$	1.22474	+	2.12132i	0.0451447	+	0.0781929i
$737$		−	70.2929i		−	2.58927i
$738$		0			0
$739$	41.0454			1.50988			0.754940	−	0.655794i	$-0.227666\pi$
$739$	41.0454			1.50988			0.754940	+	0.655794i	$0.227666\pi$
$740$		0			0
$741$		0			0
$742$	32.5590	+	18.7980i	1.19528	+	0.690095i
$743$	30.0091	+	17.3258i	1.10093	+	0.635621i	0.936464	−	0.350763i	$-0.114078\pi$
$743$	30.0091	+	17.3258i	1.10093	+	0.635621i	0.164463	+	0.986383i	$0.447411\pi$
$744$		0			0
$745$		0			0
$746$	15.5959			0.571007
$747$		0			0
$748$		−	24.0000i		−	0.877527i
$749$	33.9217	+	58.7541i	1.23947	+	2.14683i
$750$		0			0
$751$	25.0227	−	43.3406i	0.913091	−	1.58152i	0.103420	−	0.994638i	$-0.467022\pi$
$751$	25.0227	−	43.3406i	0.913091	−	1.58152i	0.809672	−	0.586883i	$-0.199645\pi$
$752$	0.953512	+	0.550510i	0.0347710	+	0.0200750i
$753$		0			0
$754$	−5.44949	−	9.43879i	−0.198459	−	0.343741i
$755$		0			0
$756$		0			0
$757$		−	6.04541i		−	0.219724i	−0.993947	−	0.109862i	$-0.964959\pi$
$757$		−	6.04541i		−	0.219724i	0.993947	−	0.109862i	$-0.0350409\pi$
$758$	0.778539	−	0.449490i	0.0282778	−	0.0163262i
$759$		0			0
$760$		0			0
$761$	2.05051	−	3.55159i	0.0743309	−	0.128745i	−0.826464	−	0.562989i	$-0.809651\pi$
$761$	2.05051	−	3.55159i	0.0743309	−	0.128745i	0.900795	+	0.434244i	$0.142985\pi$
$762$		0			0
$763$	40.2658	−	23.2474i	1.45772	−	0.841614i
$764$	−10.8990			−0.394311
$765$		0			0
$766$	−26.4495			−0.955659
$767$	−2.12132	+	1.22474i	−0.0765964	+	0.0442230i
$768$		0			0
$769$	25.0959	−	43.4674i	0.904982	−	1.56747i	0.0840405	−	0.996462i	$-0.473217\pi$
$769$	25.0959	−	43.4674i	0.904982	−	1.56747i	0.820941	−	0.571012i	$-0.193449\pi$
$770$		0			0
$771$		0			0
$772$	−17.3205	+	10.0000i	−0.623379	+	0.359908i
$773$			49.5959i			1.78384i	0.452192	+	0.891921i	$0.350642\pi$
$773$			49.5959i			1.78384i	−0.452192	+	0.891921i	$0.649358\pi$
$774$		0			0
$775$		0			0
$776$	5.39898	+	9.35131i	0.193812	+	0.335692i
$777$		0			0
$778$	−11.7744	−	6.79796i	−0.422133	−	0.243719i
$779$	−11.4773	+	19.8793i	−0.411217	+	0.712248i
$780$		0			0
$781$	3.30306	+	5.72107i	0.118193	+	0.204716i
$782$			12.0000i			0.429119i
$783$		0			0
$784$	−12.7980			−0.457070
$785$		0			0
$786$		0			0
$787$	4.59259	+	2.65153i	0.163708	+	0.0945169i	0.579616	−	0.814890i	$-0.303203\pi$
$787$	4.59259	+	2.65153i	0.163708	+	0.0945169i	−0.415908	+	0.909407i	$0.636536\pi$
$788$	20.9989	+	12.1237i	0.748055	+	0.431890i
$789$		0			0
$790$		0			0
$791$	61.8434			2.19890
$792$		0			0
$793$			35.5959i			1.26405i
$794$	10.7980	+	18.7026i	0.383205	+	0.663731i
$795$		0			0
$796$	−2.89898	+	5.02118i	−0.102752	+	0.177971i
$797$	4.98186	+	2.87628i	0.176466	+	0.101883i	0.585631	−	0.810577i	$-0.300847\pi$
$797$	4.98186	+	2.87628i	0.176466	+	0.101883i	−0.409165	+	0.912460i	$0.634180\pi$
$798$		0			0
$799$	2.69694	+	4.67123i	0.0954108	+	0.165256i
$800$		0			0
$801$		0			0
$802$			9.30306i			0.328503i
$803$	4.24264	−	2.44949i	0.149720	−	0.0864406i
$804$		0			0
$805$		0			0
$806$	1.00000	−	1.73205i	0.0352235	−	0.0610089i
$807$		0			0
$808$	−3.07483	+	1.77526i	−0.108172	+	0.0624533i
$809$	−35.6969			−1.25504			−0.627519	−	0.778601i	$-0.715929\pi$
$809$	−35.6969			−1.25504			−0.627519	+	0.778601i	$0.715929\pi$
$810$		0			0
$811$	−33.4495			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$811$	−33.4495			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$812$	9.43879	−	5.44949i	0.331237	−	0.191240i
$813$		0			0
$814$	−8.20204	+	14.2064i	−0.287481	+	0.497932i
$815$		0			0
$816$		0			0
$817$	−16.4545	+	9.50000i	−0.575669	+	0.332363i
$818$			9.89898i			0.346110i
$819$		0			0
$820$		0			0
$821$	−25.5959	−	44.3334i	−0.893304	−	1.54725i	−0.835890	−	0.548897i	$-0.815048\pi$
$821$	−25.5959	−	44.3334i	−0.893304	−	1.54725i	−0.0574136	−	0.998350i	$-0.518285\pi$
$822$		0			0
$823$	23.2952	+	13.4495i	0.812020	+	0.468820i	0.847657	−	0.530545i	$-0.178013\pi$
$823$	23.2952	+	13.4495i	0.812020	+	0.468820i	−0.0356371	+	0.999365i	$0.511346\pi$
$824$	−6.34847	+	10.9959i	−0.221159	+	0.383059i
$825$		0			0
$826$	−1.22474	−	2.12132i	−0.0426143	−	0.0738102i
$827$			17.9444i			0.623987i	0.950084	+	0.311994i	$0.100997\pi$
$827$			17.9444i			0.623987i	−0.950084	+	0.311994i	$0.899003\pi$
$828$		0			0
$829$	−26.7423			−0.928800			−0.464400	−	0.885626i	$-0.653730\pi$
$829$	−26.7423			−0.928800			−0.464400	+	0.885626i	$0.653730\pi$
$830$		0			0
$831$		0			0
$832$	3.85337	+	2.22474i	0.133592	+	0.0771292i
$833$	−54.2971	−	31.3485i	−1.88128	−	1.08616i
$834$		0			0
$835$		0			0
$836$	−12.4949			−0.432145
$837$		0			0
$838$		−	8.14643i		−	0.281414i
$839$	−11.3258	−	19.6168i	−0.391009	−	0.677247i	0.601574	−	0.798817i	$-0.294540\pi$
$839$	−11.3258	−	19.6168i	−0.391009	−	0.677247i	−0.992583	+	0.121570i	$0.961207\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$	15.6278	+	9.02270i	0.538569	+	0.310943i
$843$		0			0
$844$	0.724745	+	1.25529i	0.0249467	+	0.0432090i
$845$		0			0
$846$		0			0
$847$		−	57.8434i		−	1.98752i
$848$	7.31747	−	4.22474i	0.251283	−	0.145078i
$849$		0			0
$850$		0			0
$851$	4.10102	−	7.10318i	0.140581	−	0.243494i
$852$		0			0
$853$	−39.8372	+	23.0000i	−1.36400	+	0.787505i	−0.990153	−	0.139986i	$-0.955294\pi$
$853$	−39.8372	+	23.0000i	−1.36400	+	0.787505i	−0.373845	+	0.927491i	$0.621961\pi$
$854$	−35.5959			−1.21807
$855$		0			0
$856$	15.2474			0.521147
$857$	−34.7285	+	20.0505i	−1.18630	+	0.684912i	−0.957464	−	0.288552i	$-0.906826\pi$
$857$	−34.7285	+	20.0505i	−1.18630	+	0.684912i	−0.228839	+	0.973464i	$0.573493\pi$
$858$		0			0
$859$	−2.82577	+	4.89437i	−0.0964139	+	0.166994i	−0.910198	−	0.414174i	$-0.864071\pi$
$859$	−2.82577	+	4.89437i	−0.0964139	+	0.166994i	0.813784	+	0.581168i	$0.197404\pi$
$860$		0			0
$861$		0			0
$862$	9.22450	−	5.32577i	0.314188	−	0.181396i
$863$		−	19.8434i		−	0.675476i	−0.941240	−	0.337738i	$-0.890338\pi$
$863$		−	19.8434i		−	0.675476i	0.941240	−	0.337738i	$-0.109662\pi$
$864$		0			0
$865$		0			0
$866$	14.7980	+	25.6308i	0.502855	+	0.870971i
$867$		0			0
$868$	1.73205	+	1.00000i	0.0587896	+	0.0339422i
$869$	31.1010	−	53.8685i	1.05503	−	1.82737i
$870$		0			0
$871$	31.9217	+	55.2900i	1.08162	+	1.87343i
$872$		−	10.4495i		−	0.353864i
$873$		0			0
$874$	6.24745			0.211323
$875$		0			0
$876$		0			0
$877$	−10.5673	−	6.10102i	−0.356832	−	0.206017i	0.310858	−	0.950456i	$-0.399383\pi$
$877$	−10.5673	−	6.10102i	−0.356832	−	0.206017i	−0.667690	+	0.744439i	$0.732717\pi$
$878$	9.82806	+	5.67423i	0.331681	+	0.191496i
$879$		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
$883$			28.2020i			0.949074i	0.880235	+	0.474537i	$0.157385\pi$
$883$			28.2020i			0.949074i	−0.880235	+	0.474537i	$0.842615\pi$
$884$	10.8990	+	18.8776i	0.366572	+	0.634922i
$885$		0			0
$886$	13.8990	−	24.0737i	0.466945	−	0.808773i
$887$	−47.1940	−	27.2474i	−1.58462	−	0.914880i	−0.994172	−	0.107803i	$-0.965619\pi$
$887$	−47.1940	−	27.2474i	−1.58462	−	0.914880i	−0.590446	−	0.807077i	$-0.701048\pi$
$888$		0			0
$889$	−25.2474	−	43.7299i	−0.846772	−	1.46665i
$890$		0			0
$891$		0			0
$892$			1.79796i			0.0602001i
$893$	2.43194	−	1.40408i	0.0813818	−	0.0469858i
$894$		0			0
$895$		0			0
$896$	−2.22474	+	3.85337i	−0.0743235	+	0.128732i
$897$		0			0
$898$	−9.17633	+	5.29796i	−0.306218	+	0.176795i
$899$	−1.10102			−0.0367211
$900$		0			0
$901$	41.3939			1.37903
$902$	−38.1838	+	22.0454i	−1.27138	+	0.734032i
$903$		0			0
$904$	6.94949	−	12.0369i	0.231137	−	0.400340i
$905$		0			0
$906$		0			0
$907$	−18.7508	+	10.8258i	−0.622609	+	0.359464i	−0.777884	−	0.628408i	$-0.783707\pi$
$907$	−18.7508	+	10.8258i	−0.622609	+	0.359464i	0.155275	+	0.987871i	$0.450374\pi$
$908$		−	28.3485i		−	0.940777i
$909$		0			0
$910$		0			0
$911$	3.67423	+	6.36396i	0.121733	+	0.210847i	0.920451	−	0.390858i	$-0.127822\pi$
$911$	3.67423	+	6.36396i	0.121733	+	0.210847i	−0.798718	+	0.601705i	$0.794488\pi$
$912$		0			0
$913$	2.33562	+	1.34847i	0.0772976	+	0.0446278i
$914$	−7.84847	+	13.5939i	−0.259604	+	0.449648i
$915$		0			0
$916$	10.5732	+	18.3133i	0.349349	+	0.605090i
$917$			70.2929i			2.32127i
$918$		0			0
$919$	11.3485			0.374351			0.187176	−	0.982326i	$-0.440067\pi$
$919$	11.3485			0.374351			0.187176	+	0.982326i	$0.440067\pi$
$920$		0			0
$921$		0			0
$922$	−16.7563	−	9.67423i	−0.551838	−	0.318604i
$923$	−5.19615	−	3.00000i	−0.171033	−	0.0987462i
$924$		0			0
$925$		0			0
$926$	9.34847			0.307210
$927$		0			0
$928$		−	2.44949i		−	0.0804084i
$929$	−13.5959	−	23.5488i	−0.446068	−	0.772612i	0.552058	−	0.833806i	$-0.313843\pi$
$929$	−13.5959	−	23.5488i	−0.446068	−	0.772612i	−0.998126	+	0.0611938i	$0.980509\pi$
$930$		0			0
$931$	−16.3207	+	28.2682i	−0.534888	+	0.926453i
$932$	−4.93369	−	2.84847i	−0.161609	−	0.0933047i
$933$		0			0
$934$	−2.17423	−	3.76588i	−0.0711431	−	0.123224i
$935$		0			0
$936$		0			0
$937$		−	26.7980i		−	0.875451i	−0.899109	−	0.437726i	$-0.855784\pi$
$937$		−	26.7980i		−	0.875451i	0.899109	−	0.437726i	$-0.144216\pi$
$938$	−55.2900	+	31.9217i	−1.80528	+	1.04228i
$939$		0			0
$940$		0			0
$941$	−14.8207	+	25.6701i	−0.483140	+	0.836823i	−0.999813	−	0.0193603i	$-0.993837\pi$
$941$	−14.8207	+	25.6701i	−0.483140	+	0.836823i	0.516673	+	0.856183i	$0.327170\pi$
$942$		0			0
$943$	19.0919	−	11.0227i	0.621717	−	0.358949i
$944$	−0.550510			−0.0179176
$945$		0			0
$946$	−36.4949			−1.18655
$947$	−7.05501	+	4.07321i	−0.229257	+	0.132362i	−0.610229	−	0.792225i	$-0.708923\pi$
$947$	−7.05501	+	4.07321i	−0.229257	+	0.132362i	0.380972	+	0.924587i	$0.375589\pi$
$948$		0			0
$949$	−2.22474	+	3.85337i	−0.0722183	+	0.125086i
$950$		0			0
$951$		0			0
$952$	−18.8776	+	10.8990i	−0.611826	+	0.353238i
$953$		−	21.7980i		−	0.706105i	−0.935603	−	0.353053i	$-0.885144\pi$
$953$		−	21.7980i		−	0.706105i	0.935603	−	0.353053i	$-0.114856\pi$
$954$		0			0
$955$		0			0
$956$	4.77526	+	8.27098i	0.154443	+	0.267503i
$957$		0			0
$958$	−20.9989	−	12.1237i	−0.678444	−	0.391700i
$959$	−6.67423	+	11.5601i	−0.215522	+	0.373296i
$960$		0			0
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$		−	14.8990i		−	0.480362i
$963$		0			0
$964$	22.7980			0.734273
$965$		0			0
$966$		0			0
$967$	27.7128	+	16.0000i	0.891184	+	0.514525i	0.874330	−	0.485333i	$-0.161301\pi$
$967$	27.7128	+	16.0000i	0.891184	+	0.514525i	0.0168544	+	0.999858i	$0.494635\pi$
$968$	−11.2583	−	6.50000i	−0.361856	−	0.208918i
$969$		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
$973$		−	17.7980i		−	0.570576i
$974$	−9.77526	−	16.9312i	−0.313219	−	0.542512i
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	7.79423	+	4.50000i	0.249359	+	0.143968i	0.619471	−	0.785020i	$-0.287347\pi$
$977$	7.79423	+	4.50000i	0.249359	+	0.143968i	−0.370111	+	0.928987i	$0.620681\pi$
$978$		0			0
$979$	−22.0454	−	38.1838i	−0.704574	−	1.22036i
$980$		0			0
$981$		0			0
$982$		−	2.75255i		−	0.0878374i
$983$	19.8311	−	11.4495i	0.632514	−	0.365182i	−0.149211	−	0.988805i	$-0.547673\pi$
$983$	19.8311	−	11.4495i	0.632514	−	0.365182i	0.781725	+	0.623623i	$0.214340\pi$
$984$		0			0
$985$		0			0
$986$	6.00000	−	10.3923i	0.191079	−	0.330958i
$987$		0			0
$988$	9.82806	−	5.67423i	0.312672	−	0.180521i
$989$	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	$0.581789\pi$
$992$	0.389270	−	0.224745i	0.0123593	−	0.00713566i
$993$		0			0
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$		0			0
$997$	−31.2162	+	18.0227i	−0.988628	+	0.570785i	−0.904864	−	0.425701i	$-0.860028\pi$
$997$	−31.2162	+	18.0227i	−0.988628	+	0.570785i	−0.0837642	+	0.996486i	$0.526694\pi$
$998$			6.34847i			0.200957i
$999$		0			0

Twists

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

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

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.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.85337 + 2.22474i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-3.85337 + 2.22474i) q^{7} +1.00000i q^{8} +(2.44949 + 4.24264i) q^{11} +(-3.85337 - 2.22474i) q^{13} +(2.22474 - 3.85337i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.89898i q^{17} -2.55051 q^{19} +(-4.24264 - 2.44949i) q^{22} +(2.12132 + 1.22474i) q^{23} +4.44949 q^{26} +4.44949i q^{28} +(-1.22474 - 2.12132i) q^{29} +(0.224745 - 0.389270i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.44949 + 4.24264i) q^{34} -3.34847i q^{37} +(2.20881 - 1.27526i) q^{38} +(4.50000 - 7.79423i) q^{41} +(6.45145 - 3.72474i) q^{43} +4.89898 q^{44} -2.44949 q^{46} +(-0.953512 + 0.550510i) q^{47} +(6.39898 - 11.0834i) q^{49} +(-3.85337 + 2.22474i) q^{52} +8.44949i q^{53} +(-2.22474 - 3.85337i) q^{56} +(2.12132 + 1.22474i) q^{58} +(0.275255 - 0.476756i) q^{59} +(-4.00000 - 6.92820i) q^{61} +0.449490i q^{62} -1.00000 q^{64} +(-12.4261 - 7.17423i) q^{67} +(-4.24264 - 2.44949i) q^{68} +1.34847 q^{71} -1.00000i q^{73} +(1.67423 + 2.89986i) q^{74} +(-1.27526 + 2.20881i) q^{76} +(-18.8776 - 10.8990i) q^{77} +(-6.34847 - 10.9959i) q^{79} +9.00000i q^{82} +(0.476756 - 0.275255i) q^{83} +(-3.72474 + 6.45145i) q^{86} +(-4.24264 + 2.44949i) q^{88} -9.00000 q^{89} +19.7980 q^{91} +(2.12132 - 1.22474i) q^{92} +(0.550510 - 0.953512i) q^{94} +(9.35131 - 5.39898i) q^{97} +12.7980i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 8 q^{14} - 4 q^{16} - 40 q^{19} + 16 q^{26} - 8 q^{31} + 36 q^{41} + 12 q^{49} - 8 q^{56} + 12 q^{59} - 32 q^{61} - 8 q^{64} - 48 q^{71} - 16 q^{74} - 20 q^{76} + 8 q^{79} - 20 q^{86} - 72 q^{89} + 80 q^{91} + 24 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 8 * q^14 - 4 * q^16 - 40 * q^19 + 16 * q^26 - 8 * q^31 + 36 * q^41 + 12 * q^49 - 8 * q^56 + 12 * q^59 - 32 * q^61 - 8 * q^64 - 48 * q^71 - 16 * q^74 - 20 * q^76 + 8 * q^79 - 20 * q^86 - 72 * q^89 + 80 * q^91 + 24 * q^94

Introduction

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