LMFDB - Embedded newform 448.2.p.d.383.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(255,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("448.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.p (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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			383.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	448.383
Dual form			448.2.p.d.255.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 1.50000i) q^{3} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +O(q^{10})$	\(q+(-0.866025 - 1.50000i) q^{3} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-0.866025 + 0.500000i) q^{11} -3.46410i q^{13} -3.00000i q^{15} +(-1.50000 + 0.866025i) q^{17} +(2.59808 - 4.50000i) q^{19} +(-1.50000 + 4.33013i) q^{21} +(0.866025 + 0.500000i) q^{23} +(-1.00000 - 1.73205i) q^{25} -5.19615 q^{27} -4.00000 q^{29} +(-0.866025 - 1.50000i) q^{31} +(1.50000 + 0.866025i) q^{33} +(-0.866025 - 4.50000i) q^{35} +(1.50000 - 2.59808i) q^{37} +(-5.19615 + 3.00000i) q^{39} -3.46410i q^{41} +2.00000i q^{43} +(4.33013 - 7.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(2.59808 + 1.50000i) q^{51} +(-0.500000 - 0.866025i) q^{53} -1.73205 q^{55} -9.00000 q^{57} +(2.59808 + 4.50000i) q^{59} +(4.50000 + 2.59808i) q^{61} +(3.00000 - 5.19615i) q^{65} +(-2.59808 + 1.50000i) q^{67} -1.73205i q^{69} +14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-1.73205 + 3.00000i) q^{75} +(2.50000 + 0.866025i) q^{77} +(7.79423 + 4.50000i) q^{79} +(4.50000 + 7.79423i) q^{81} +13.8564 q^{83} -3.00000 q^{85} +(3.46410 + 6.00000i) q^{87} +(13.5000 + 7.79423i) q^{89} +(-6.92820 + 6.00000i) q^{91} +(-1.50000 + 2.59808i) q^{93} +(7.79423 - 4.50000i) q^{95} -17.3205i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5}+O(q^{10}) $ 4 * q + 6 * q^5	$ 4 q + 6 q^{5} - 6 q^{17} - 6 q^{21} - 4 q^{25} - 16 q^{29} + 6 q^{33} + 6 q^{37} - 4 q^{49} - 2 q^{53} - 36 q^{57} + 18 q^{61} + 12 q^{65} + 30 q^{73} + 10 q^{77} + 18 q^{81} - 12 q^{85} + 54 q^{89} - 6 q^{93}+O(q^{100}) $ 4 * q + 6 * q^5 - 6 * q^17 - 6 * q^21 - 4 * q^25 - 16 * q^29 + 6 * q^33 + 6 * q^37 - 4 * q^49 - 2 * q^53 - 36 * q^57 + 18 * q^61 + 12 * q^65 + 30 * q^73 + 10 * q^77 + 18 * q^81 - 12 * q^85 + 54 * q^89 - 6 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$7$	−1.73205	−	2.00000i	−0.654654	−	0.755929i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i	−0.624844	−	0.780750i	$-0.714837\pi$
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i	0.363727	+	0.931505i	$0.381504\pi$
$12$		0			0
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$		−	3.00000i		−	0.774597i
$16$		0			0
$17$	−1.50000	+	0.866025i	−0.363803	+	0.210042i	−0.670748	−	0.741685i	$-0.734027\pi$
$17$	−1.50000	+	0.866025i	−0.363803	+	0.210042i	0.306944	+	0.951727i	$0.400693\pi$
$18$		0			0
$19$	2.59808	−	4.50000i	0.596040	−	1.03237i	−0.397360	−	0.917663i	$-0.630073\pi$
$19$	2.59808	−	4.50000i	0.596040	−	1.03237i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$		0			0
$21$	−1.50000	+	4.33013i	−0.327327	+	0.944911i
$22$		0			0
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	0.587565	−	0.809177i	$-0.300087\pi$
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	−0.406986	+	0.913434i	$0.633420\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	−0.866025	−	1.50000i	−0.155543	−	0.269408i	0.777714	−	0.628619i	$-0.216379\pi$
$31$	−0.866025	−	1.50000i	−0.155543	−	0.269408i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$	1.50000	+	0.866025i	0.261116	+	0.150756i
$34$		0			0
$35$	−0.866025	−	4.50000i	−0.146385	−	0.760639i
$36$		0			0
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$		0			0
$39$	−5.19615	+	3.00000i	−0.832050	+	0.480384i
$40$		0			0
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.33013	−	7.50000i	0.631614	−	1.09399i	−0.355608	−	0.934635i	$-0.615726\pi$
$47$	4.33013	−	7.50000i	0.631614	−	1.09399i	0.987222	−	0.159352i	$-0.0509405\pi$
$48$		0			0
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$	2.59808	+	1.50000i	0.363803	+	0.210042i
$52$		0			0
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	0.829640	−	0.558298i	$-0.188546\pi$
$53$	−0.500000	−	0.866025i	−0.0686803	−	0.118958i	−0.898321	+	0.439340i	$0.855212\pi$
$54$		0			0
$55$	−1.73205			−0.233550
$56$		0			0
$57$	−9.00000			−1.19208
$58$		0			0
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	0.984102	−	0.177605i	$-0.0568349\pi$
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	−0.645861	+	0.763455i	$0.723502\pi$
$60$		0			0
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	0.759608	−	0.650381i	$-0.225391\pi$
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	−0.183442	+	0.983030i	$0.558724\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$		0			0
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	−0.650236	−	0.759733i	$-0.725330\pi$
$67$	−2.59808	+	1.50000i	−0.317406	+	0.183254i	0.332830	+	0.942987i	$0.391996\pi$
$68$		0			0
$69$		−	1.73205i		−	0.208514i
$70$		0			0
$71$			14.0000i			1.66149i	0.556650	+	0.830747i	$0.312086\pi$
$71$			14.0000i			1.66149i	−0.556650	+	0.830747i	$0.687914\pi$
$72$		0			0
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.00787336	−	0.999969i	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$		0			0
$75$	−1.73205	+	3.00000i	−0.200000	+	0.346410i
$76$		0			0
$77$	2.50000	+	0.866025i	0.284901	+	0.0986928i
$78$		0			0
$79$	7.79423	+	4.50000i	0.876919	+	0.506290i	0.869641	−	0.493684i	$-0.164350\pi$
$79$	7.79423	+	4.50000i	0.876919	+	0.506290i	0.00727784	+	0.999974i	$0.497683\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$	13.8564			1.52094			0.760469	−	0.649374i	$-0.224969\pi$
$83$	13.8564			1.52094			0.760469	+	0.649374i	$0.224969\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$		0			0
$87$	3.46410	+	6.00000i	0.371391	+	0.643268i
$88$		0			0
$89$	13.5000	+	7.79423i	1.43100	+	0.826187i	0.997197	−	0.0748225i	$-0.0238390\pi$
$89$	13.5000	+	7.79423i	1.43100	+	0.826187i	0.433800	+	0.901009i	$0.357172\pi$
$90$		0			0
$91$	−6.92820	+	6.00000i	−0.726273	+	0.628971i
$92$		0			0
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$		0			0
$95$	7.79423	−	4.50000i	0.799671	−	0.461690i
$96$		0			0
$97$		−	17.3205i		−	1.75863i	−0.476240	−	0.879316i	$-0.658000\pi$
$97$		−	17.3205i		−	1.75863i	0.476240	−	0.879316i	$-0.342000\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.50000	−	4.33013i	0.746278	−	0.430864i	−0.0780696	−	0.996948i	$-0.524876\pi$
$101$	7.50000	−	4.33013i	0.746278	−	0.430864i	0.824347	+	0.566084i	$0.191542\pi$
$102$		0			0
$103$	−4.33013	+	7.50000i	−0.426660	+	0.738997i	−0.996574	−	0.0827075i	$-0.973643\pi$
$103$	−4.33013	+	7.50000i	−0.426660	+	0.738997i	0.569914	+	0.821705i	$0.306977\pi$
$104$		0			0
$105$	−6.00000	+	5.19615i	−0.585540	+	0.507093i
$106$		0			0
$107$	11.2583	+	6.50000i	1.08838	+	0.628379i	0.933146	−	0.359498i	$-0.117052\pi$
$107$	11.2583	+	6.50000i	1.08838	+	0.628379i	0.155238	+	0.987877i	$0.450386\pi$
$108$		0			0
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	0.996962	−	0.0778949i	$-0.0248199\pi$
$109$	4.50000	+	7.79423i	0.431022	+	0.746552i	−0.565940	+	0.824447i	$0.691487\pi$
$110$		0			0
$111$	−5.19615			−0.493197
$112$		0			0
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	0.866025	+	1.50000i	0.0807573	+	0.139876i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.33013	+	1.50000i	0.396942	+	0.137505i
$120$		0			0
$121$	−5.00000	+	8.66025i	−0.454545	+	0.787296i
$122$		0			0
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$		0			0
$129$	3.00000	−	1.73205i	0.264135	−	0.152499i
$130$		0			0
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	−0.956916	−	0.290365i	$-0.906223\pi$
$131$	−2.59808	+	4.50000i	−0.226995	+	0.393167i	0.729921	+	0.683531i	$0.239557\pi$
$132$		0			0
$133$	−13.5000	+	2.59808i	−1.17060	+	0.225282i
$134$		0			0
$135$	−7.79423	−	4.50000i	−0.670820	−	0.387298i
$136$		0			0
$137$	−0.500000	−	0.866025i	−0.0427179	−	0.0739895i	0.843876	−	0.536538i	$-0.180268\pi$
$137$	−0.500000	−	0.866025i	−0.0427179	−	0.0739895i	−0.886594	+	0.462549i	$0.846935\pi$
$138$		0			0
$139$	−6.92820			−0.587643			−0.293821	−	0.955860i	$-0.594927\pi$
$139$	−6.92820			−0.587643			−0.293821	+	0.955860i	$0.594927\pi$
$140$		0			0
$141$	−15.0000			−1.26323
$142$		0			0
$143$	1.73205	+	3.00000i	0.144841	+	0.250873i
$144$		0			0
$145$	−6.00000	−	3.46410i	−0.498273	−	0.287678i
$146$		0			0
$147$	11.2583	−	4.50000i	0.928571	−	0.371154i
$148$		0			0
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	−0.725956	−	0.687741i	$-0.758602\pi$
$151$	−6.06218	+	3.50000i	−0.493333	+	0.284826i	0.232623	+	0.972567i	$0.425269\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	3.00000i		−	0.240966i
$156$		0			0
$157$	−1.50000	+	0.866025i	−0.119713	+	0.0691164i	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−1.50000	+	0.866025i	−0.119713	+	0.0691164i	0.438948	+	0.898513i	$0.355351\pi$
$158$		0			0
$159$	−0.866025	+	1.50000i	−0.0686803	+	0.118958i
$160$		0			0
$161$	−0.500000	−	2.59808i	−0.0394055	−	0.204757i
$162$		0			0
$163$	−18.1865	−	10.5000i	−1.42448	−	0.822423i	−0.427802	−	0.903873i	$-0.640712\pi$
$163$	−18.1865	−	10.5000i	−1.42448	−	0.822423i	−0.996678	+	0.0814491i	$0.974045\pi$
$164$		0			0
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$		0			0
$167$	17.3205			1.34030			0.670151	−	0.742225i	$-0.266230\pi$
$167$	17.3205			1.34030			0.670151	+	0.742225i	$0.266230\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.5000	+	6.06218i	0.798300	+	0.460899i	0.842876	−	0.538107i	$-0.180860\pi$
$173$	10.5000	+	6.06218i	0.798300	+	0.460899i	−0.0445762	+	0.999006i	$0.514194\pi$
$174$		0			0
$175$	−1.73205	+	5.00000i	−0.130931	+	0.377964i
$176$		0			0
$177$	4.50000	−	7.79423i	0.338241	−	0.585850i
$178$		0			0
$179$	16.4545	−	9.50000i	1.22987	−	0.710063i	0.262864	−	0.964833i	$-0.415333\pi$
$179$	16.4545	−	9.50000i	1.22987	−	0.710063i	0.967002	+	0.254770i	$0.0819996\pi$
$180$		0			0
$181$		−	6.92820i		−	0.514969i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$		−	6.92820i		−	0.514969i	0.966282	−	0.257485i	$-0.0828937\pi$
$182$		0			0
$183$		−	9.00000i		−	0.665299i
$184$		0			0
$185$	4.50000	−	2.59808i	0.330847	−	0.191014i
$186$		0			0
$187$	0.866025	−	1.50000i	0.0633300	−	0.109691i
$188$		0			0
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$		0			0
$191$	−0.866025	−	0.500000i	−0.0626634	−	0.0361787i	0.468341	−	0.883548i	$-0.344852\pi$
$191$	−0.866025	−	0.500000i	−0.0626634	−	0.0361787i	−0.531004	+	0.847369i	$0.678185\pi$
$192$		0			0
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	0.998911	+	0.0466572i	$0.0148568\pi$
$193$	7.50000	+	12.9904i	0.539862	+	0.935068i	−0.459049	+	0.888411i	$0.651810\pi$
$194$		0			0
$195$	−10.3923			−0.744208
$196$		0			0
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	−11.2583	−	19.5000i	−0.798082	−	1.38232i	−0.920864	−	0.389885i	$-0.872515\pi$
$199$	−11.2583	−	19.5000i	−0.798082	−	1.38232i	0.122782	−	0.992434i	$-0.460818\pi$
$200$		0			0
$201$	4.50000	+	2.59808i	0.317406	+	0.183254i
$202$		0			0
$203$	6.92820	+	8.00000i	0.486265	+	0.561490i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			5.19615i			0.359425i
$210$		0			0
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$		0			0
$213$	21.0000	−	12.1244i	1.43890	−	0.830747i
$214$		0			0
$215$	−1.73205	+	3.00000i	−0.118125	+	0.204598i
$216$		0			0
$217$	−1.50000	+	4.33013i	−0.101827	+	0.293948i
$218$		0			0
$219$	−12.9904	−	7.50000i	−0.877809	−	0.506803i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$		0			0
$223$	−6.92820			−0.463947			−0.231973	−	0.972722i	$-0.574518\pi$
$223$	−6.92820			−0.463947			−0.231973	+	0.972722i	$0.574518\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.52628	−	16.5000i	−0.632281	−	1.09514i	−0.987084	−	0.160202i	$-0.948785\pi$
$227$	−9.52628	−	16.5000i	−0.632281	−	1.09514i	0.354803	−	0.934941i	$-0.384548\pi$
$228$		0			0
$229$	13.5000	+	7.79423i	0.892105	+	0.515057i	0.874630	−	0.484790i	$-0.161104\pi$
$229$	13.5000	+	7.79423i	0.892105	+	0.515057i	0.0174746	+	0.999847i	$0.494437\pi$
$230$		0			0
$231$	−0.866025	−	4.50000i	−0.0569803	−	0.296078i
$232$		0			0
$233$	3.50000	−	6.06218i	0.229293	−	0.397146i	−0.728306	−	0.685252i	$-0.759692\pi$
$233$	3.50000	−	6.06218i	0.229293	−	0.397146i	0.957599	+	0.288106i	$0.0930254\pi$
$234$		0			0
$235$	12.9904	−	7.50000i	0.847399	−	0.489246i
$236$		0			0
$237$		−	15.5885i		−	1.01258i
$238$		0			0
$239$		−	20.0000i		−	1.29369i	−0.762620	−	0.646846i	$-0.776088\pi$
$239$		−	20.0000i		−	1.29369i	0.762620	−	0.646846i	$-0.223912\pi$
$240$		0			0
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	−0.637883	−	0.770133i	$-0.720190\pi$
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	0.348013	+	0.937490i	$0.386857\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.50000	+	9.52628i	−0.479157	+	0.608612i
$246$		0			0
$247$	−15.5885	−	9.00000i	−0.991870	−	0.572656i
$248$		0			0
$249$	−12.0000	−	20.7846i	−0.760469	−	1.31717i
$250$		0			0
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$		0			0
$253$	−1.00000			−0.0628695
$254$		0			0
$255$	2.59808	+	4.50000i	0.162698	+	0.281801i
$256$		0			0
$257$	4.50000	+	2.59808i	0.280702	+	0.162064i	0.633741	−	0.773545i	$-0.281518\pi$
$257$	4.50000	+	2.59808i	0.280702	+	0.162064i	−0.353039	+	0.935609i	$0.614852\pi$
$258$		0			0
$259$	−7.79423	+	1.50000i	−0.484310	+	0.0932055i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	19.9186	−	11.5000i	1.22823	−	0.709120i	0.261573	−	0.965184i	$-0.415759\pi$
$263$	19.9186	−	11.5000i	1.22823	−	0.709120i	0.966660	+	0.256063i	$0.0824256\pi$
$264$		0			0
$265$		−	1.73205i		−	0.106399i
$266$		0			0
$267$		−	27.0000i		−	1.65237i
$268$		0			0
$269$	−19.5000	+	11.2583i	−1.18894	+	0.686433i	−0.958065	−	0.286552i	$-0.907491\pi$
$269$	−19.5000	+	11.2583i	−1.18894	+	0.686433i	−0.230871	+	0.972984i	$0.574158\pi$
$270$		0			0
$271$	−7.79423	+	13.5000i	−0.473466	+	0.820067i	−0.999539	−	0.0303728i	$-0.990331\pi$
$271$	−7.79423	+	13.5000i	−0.473466	+	0.820067i	0.526073	+	0.850439i	$0.323664\pi$
$272$		0			0
$273$	15.0000	+	5.19615i	0.907841	+	0.314485i
$274$		0			0
$275$	1.73205	+	1.00000i	0.104447	+	0.0603023i
$276$		0			0
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	0.601975	−	0.798515i	$-0.294381\pi$
$277$	−6.50000	−	11.2583i	−0.390547	−	0.676448i	−0.992522	+	0.122068i	$0.961047\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$		0			0
$283$	−6.06218	−	10.5000i	−0.360359	−	0.624160i	0.627661	−	0.778487i	$-0.284012\pi$
$283$	−6.06218	−	10.5000i	−0.360359	−	0.624160i	−0.988020	+	0.154327i	$0.950679\pi$
$284$		0			0
$285$	−13.5000	−	7.79423i	−0.799671	−	0.461690i
$286$		0			0
$287$	−6.92820	+	6.00000i	−0.408959	+	0.354169i
$288$		0			0
$289$	−7.00000	+	12.1244i	−0.411765	+	0.713197i
$290$		0			0
$291$	−25.9808	+	15.0000i	−1.52302	+	0.879316i
$292$		0			0
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$		0			0
$295$			9.00000i			0.524000i
$296$		0			0
$297$	4.50000	−	2.59808i	0.261116	−	0.150756i
$298$		0			0
$299$	1.73205	−	3.00000i	0.100167	−	0.173494i
$300$		0			0
$301$	4.00000	−	3.46410i	0.230556	−	0.199667i
$302$		0			0
$303$	−12.9904	−	7.50000i	−0.746278	−	0.430864i
$304$		0			0
$305$	4.50000	+	7.79423i	0.257669	+	0.446296i
$306$		0			0
$307$	20.7846			1.18624			0.593120	−	0.805114i	$-0.297896\pi$
$307$	20.7846			1.18624			0.593120	+	0.805114i	$0.297896\pi$
$308$		0			0
$309$	15.0000			0.853320
$310$		0			0
$311$	4.33013	+	7.50000i	0.245539	+	0.425286i	0.962283	−	0.272050i	$-0.0877017\pi$
$311$	4.33013	+	7.50000i	0.245539	+	0.425286i	−0.716744	+	0.697336i	$0.754368\pi$
$312$		0			0
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	0.541793	−	0.840512i	$-0.317746\pi$
$313$	1.50000	+	0.866025i	0.0847850	+	0.0489506i	−0.457008	+	0.889463i	$0.651079\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.50000	−	9.52628i	0.308911	−	0.535049i	−0.669214	−	0.743070i	$-0.733369\pi$
$317$	5.50000	−	9.52628i	0.308911	−	0.535049i	0.978124	+	0.208021i	$0.0667022\pi$
$318$		0			0
$319$	3.46410	−	2.00000i	0.193952	−	0.111979i
$320$		0			0
$321$		−	22.5167i		−	1.25676i
$322$		0			0
$323$			9.00000i			0.500773i
$324$		0			0
$325$	−6.00000	+	3.46410i	−0.332820	+	0.192154i
$326$		0			0
$327$	7.79423	−	13.5000i	0.431022	−	0.746552i
$328$		0			0
$329$	−22.5000	+	4.33013i	−1.24047	+	0.238728i
$330$		0			0
$331$	6.06218	+	3.50000i	0.333207	+	0.192377i	0.657264	−	0.753660i	$-0.271714\pi$
$331$	6.06218	+	3.50000i	0.333207	+	0.192377i	−0.324057	+	0.946038i	$0.605047\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.19615			−0.283896
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$		0			0
$339$	13.8564	+	24.0000i	0.752577	+	1.30350i
$340$		0			0
$341$	1.50000	+	0.866025i	0.0812296	+	0.0468979i
$342$		0			0
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$		0			0
$345$	1.50000	−	2.59808i	0.0807573	−	0.139876i
$346$		0			0
$347$	11.2583	−	6.50000i	0.604379	−	0.348938i	−0.166383	−	0.986061i	$-0.553209\pi$
$347$	11.2583	−	6.50000i	0.604379	−	0.348938i	0.770762	+	0.637123i	$0.219876\pi$
$348$		0			0
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$		0			0
$351$			18.0000i			0.960769i
$352$		0			0
$353$	−25.5000	+	14.7224i	−1.35723	+	0.783596i	−0.989249	−	0.146238i	$-0.953283\pi$
$353$	−25.5000	+	14.7224i	−1.35723	+	0.783596i	−0.367979	+	0.929834i	$0.619950\pi$
$354$		0			0
$355$	−12.1244	+	21.0000i	−0.643494	+	1.11456i
$356$		0			0
$357$	−1.50000	−	7.79423i	−0.0793884	−	0.412514i
$358$		0			0
$359$	19.9186	+	11.5000i	1.05126	+	0.606947i	0.923003	−	0.384794i	$-0.125727\pi$
$359$	19.9186	+	11.5000i	1.05126	+	0.606947i	0.128260	+	0.991741i	$0.459061\pi$
$360$		0			0
$361$	−4.00000	−	6.92820i	−0.210526	−	0.364642i
$362$		0			0
$363$	17.3205			0.909091
$364$		0			0
$365$	15.0000			0.785136
$366$		0			0
$367$	0.866025	+	1.50000i	0.0452062	+	0.0782994i	0.887743	−	0.460339i	$-0.152272\pi$
$367$	0.866025	+	1.50000i	0.0452062	+	0.0782994i	−0.842537	+	0.538639i	$0.818939\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.866025	+	2.50000i	−0.0449618	+	0.129794i
$372$		0			0
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	0.196663	+	0.980471i	$0.436990\pi$
$373$	−14.5000	+	25.1147i	−0.750782	+	1.30039i	−0.947444	+	0.319921i	$0.896344\pi$
$374$		0			0
$375$	−18.1865	+	10.5000i	−0.939149	+	0.542218i
$376$		0			0
$377$			13.8564i			0.713641i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$	−9.00000	+	5.19615i	−0.461084	+	0.266207i
$382$		0			0
$383$	−2.59808	+	4.50000i	−0.132755	+	0.229939i	−0.924738	−	0.380605i	$-0.875716\pi$
$383$	−2.59808	+	4.50000i	−0.132755	+	0.229939i	0.791982	+	0.610544i	$0.209049\pi$
$384$		0			0
$385$	3.00000	+	3.46410i	0.152894	+	0.176547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$		0			0
$391$	−1.73205			−0.0875936
$392$		0			0
$393$	9.00000			0.453990
$394$		0			0
$395$	7.79423	+	13.5000i	0.392170	+	0.679259i
$396$		0			0
$397$	−16.5000	−	9.52628i	−0.828111	−	0.478110i	0.0250943	−	0.999685i	$-0.492011\pi$
$397$	−16.5000	−	9.52628i	−0.828111	−	0.478110i	−0.853206	+	0.521575i	$0.825345\pi$
$398$		0			0
$399$	15.5885	+	18.0000i	0.780399	+	0.901127i
$400$		0			0
$401$	11.5000	−	19.9186i	0.574283	−	0.994687i	−0.421837	−	0.906672i	$-0.638614\pi$
$401$	11.5000	−	19.9186i	0.574283	−	0.994687i	0.996119	−	0.0880147i	$-0.0280523\pi$
$402$		0			0
$403$	−5.19615	+	3.00000i	−0.258839	+	0.149441i
$404$		0			0
$405$			15.5885i			0.774597i
$406$		0			0
$407$			3.00000i			0.148704i
$408$		0			0
$409$	22.5000	−	12.9904i	1.11255	−	0.642333i	0.173064	−	0.984911i	$-0.444633\pi$
$409$	22.5000	−	12.9904i	1.11255	−	0.642333i	0.939490	+	0.342578i	$0.111300\pi$
$410$		0			0
$411$	−0.866025	+	1.50000i	−0.0427179	+	0.0739895i
$412$		0			0
$413$	4.50000	−	12.9904i	0.221431	−	0.639215i
$414$		0			0
$415$	20.7846	+	12.0000i	1.02028	+	0.589057i
$416$		0			0
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$		0			0
$419$	−20.7846			−1.01539			−0.507697	−	0.861536i	$-0.669503\pi$
$419$	−20.7846			−1.01539			−0.507697	+	0.861536i	$0.669503\pi$
$420$		0			0
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.00000	+	1.73205i	0.145521	+	0.0840168i
$426$		0			0
$427$	−2.59808	−	13.5000i	−0.125730	−	0.653311i
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$		0			0
$431$	−19.9186	+	11.5000i	−0.959444	+	0.553936i	−0.896002	−	0.444050i	$-0.853541\pi$
$431$	−19.9186	+	11.5000i	−0.959444	+	0.553936i	−0.0634424	+	0.997985i	$0.520208\pi$
$432$		0			0
$433$		−	10.3923i		−	0.499422i	−0.968320	−	0.249711i	$-0.919664\pi$
$433$		−	10.3923i		−	0.499422i	0.968320	−	0.249711i	$-0.0803357\pi$
$434$		0			0
$435$			12.0000i			0.575356i
$436$		0			0
$437$	4.50000	−	2.59808i	0.215264	−	0.124283i
$438$		0			0
$439$	11.2583	−	19.5000i	0.537331	−	0.930684i	−0.461716	−	0.887028i	$-0.652766\pi$
$439$	11.2583	−	19.5000i	0.537331	−	0.930684i	0.999047	−	0.0436563i	$-0.0139007\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.7224	+	8.50000i	0.699484	+	0.403847i	0.807155	−	0.590339i	$-0.201006\pi$
$443$	14.7224	+	8.50000i	0.699484	+	0.403847i	−0.107671	+	0.994187i	$0.534339\pi$
$444$		0			0
$445$	13.5000	+	23.3827i	0.639961	+	1.10845i
$446$		0			0
$447$	−1.73205			−0.0819232
$448$		0			0
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$	1.73205	+	3.00000i	0.0815591	+	0.141264i
$452$		0			0
$453$	10.5000	+	6.06218i	0.493333	+	0.284826i
$454$		0			0
$455$	−15.5885	+	3.00000i	−0.730798	+	0.140642i
$456$		0			0
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	−0.986396	−	0.164386i	$-0.947436\pi$
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	0.635561	+	0.772051i	$0.280769\pi$
$458$		0			0
$459$	7.79423	−	4.50000i	0.363803	−	0.210042i
$460$		0			0
$461$			17.3205i			0.806696i	0.915047	+	0.403348i	$0.132154\pi$
$461$			17.3205i			0.806696i	−0.915047	+	0.403348i	$0.867846\pi$
$462$		0			0
$463$			30.0000i			1.39422i	0.716965	+	0.697109i	$0.245531\pi$
$463$			30.0000i			1.39422i	−0.716965	+	0.697109i	$0.754469\pi$
$464$		0			0
$465$	−4.50000	+	2.59808i	−0.208683	+	0.120483i
$466$		0			0
$467$	4.33013	−	7.50000i	0.200374	−	0.347059i	−0.748275	−	0.663389i	$-0.769117\pi$
$467$	4.33013	−	7.50000i	0.200374	−	0.347059i	0.948649	+	0.316330i	$0.102451\pi$
$468$		0			0
$469$	7.50000	+	2.59808i	0.346318	+	0.119968i
$470$		0			0
$471$	2.59808	+	1.50000i	0.119713	+	0.0691164i
$472$		0			0
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$		0			0
$475$	−10.3923			−0.476832
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.06218	−	10.5000i	−0.276988	−	0.479757i	0.693647	−	0.720315i	$-0.256003\pi$
$479$	−6.06218	−	10.5000i	−0.276988	−	0.479757i	−0.970635	+	0.240558i	$0.922670\pi$
$480$		0			0
$481$	−9.00000	−	5.19615i	−0.410365	−	0.236924i
$482$		0			0
$483$	−3.46410	+	3.00000i	−0.157622	+	0.136505i
$484$		0			0
$485$	15.0000	−	25.9808i	0.681115	−	1.17973i
$486$		0			0
$487$	26.8468	−	15.5000i	1.21654	−	0.702372i	0.252367	−	0.967632i	$-0.418791\pi$
$487$	26.8468	−	15.5000i	1.21654	−	0.702372i	0.964177	+	0.265260i	$0.0854576\pi$
$488$		0			0
$489$			36.3731i			1.64485i
$490$		0			0
$491$			32.0000i			1.44414i	0.691820	+	0.722070i	$0.256809\pi$
$491$			32.0000i			1.44414i	−0.691820	+	0.722070i	$0.743191\pi$
$492$		0			0
$493$	6.00000	−	3.46410i	0.270226	−	0.156015i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	28.0000	−	24.2487i	1.25597	−	1.08770i
$498$		0			0
$499$	30.3109	+	17.5000i	1.35690	+	0.783408i	0.989205	−	0.146538i	$-0.0468131\pi$
$499$	30.3109	+	17.5000i	1.35690	+	0.783408i	0.367697	+	0.929946i	$0.380146\pi$
$500$		0			0
$501$	−15.0000	−	25.9808i	−0.670151	−	1.16073i
$502$		0			0
$503$	6.92820			0.308913			0.154457	−	0.988000i	$-0.450637\pi$
$503$	6.92820			0.308913			0.154457	+	0.988000i	$0.450637\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$		0			0
$507$	−0.866025	−	1.50000i	−0.0384615	−	0.0666173i
$508$		0			0
$509$	−10.5000	−	6.06218i	−0.465404	−	0.268701i	0.248910	−	0.968527i	$-0.419928\pi$
$509$	−10.5000	−	6.06218i	−0.465404	−	0.268701i	−0.714314	+	0.699825i	$0.753261\pi$
$510$		0			0
$511$	−21.6506	−	7.50000i	−0.957768	−	0.331780i
$512$		0			0
$513$	−13.5000	+	23.3827i	−0.596040	+	1.03237i
$514$		0			0
$515$	−12.9904	+	7.50000i	−0.572425	+	0.330489i
$516$		0			0
$517$			8.66025i			0.380878i
$518$		0			0
$519$		−	21.0000i		−	0.921798i
$520$		0			0
$521$	1.50000	−	0.866025i	0.0657162	−	0.0379413i	−0.466782	−	0.884372i	$-0.654587\pi$
$521$	1.50000	−	0.866025i	0.0657162	−	0.0379413i	0.532498	+	0.846431i	$0.321253\pi$
$522$		0			0
$523$	12.9904	−	22.5000i	0.568030	−	0.983856i	−0.428731	−	0.903432i	$-0.641039\pi$
$523$	12.9904	−	22.5000i	0.568030	−	0.983856i	0.996761	−	0.0804241i	$-0.0256275\pi$
$524$		0			0
$525$	9.00000	−	1.73205i	0.392792	−	0.0755929i
$526$		0			0
$527$	2.59808	+	1.50000i	0.113174	+	0.0653410i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$	11.2583	+	19.5000i	0.486740	+	0.843059i
$536$		0			0
$537$	−28.5000	−	16.4545i	−1.22987	−	0.710063i
$538$		0			0
$539$	−2.59808	−	6.50000i	−0.111907	−	0.279975i
$540$		0			0
$541$	−9.50000	+	16.4545i	−0.408437	+	0.707433i	−0.994715	−	0.102677i	$-0.967259\pi$
$541$	−9.50000	+	16.4545i	−0.408437	+	0.707433i	0.586278	+	0.810110i	$0.300593\pi$
$542$		0			0
$543$	−10.3923	+	6.00000i	−0.445976	+	0.257485i
$544$		0			0
$545$			15.5885i			0.667736i
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.3923	+	18.0000i	−0.442727	+	0.766826i
$552$		0			0
$553$	−4.50000	−	23.3827i	−0.191359	−	0.994333i
$554$		0			0
$555$	−7.79423	−	4.50000i	−0.330847	−	0.191014i
$556$		0			0
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	0.929672	+	0.368389i	$0.120091\pi$
$557$	18.5000	+	32.0429i	0.783870	+	1.35770i	−0.145802	+	0.989314i	$0.546576\pi$
$558$		0			0
$559$	6.92820			0.293032
$560$		0			0
$561$	−3.00000			−0.126660
$562$		0			0
$563$	−11.2583	−	19.5000i	−0.474482	−	0.821827i	0.525091	−	0.851046i	$-0.324031\pi$
$563$	−11.2583	−	19.5000i	−0.474482	−	0.821827i	−0.999573	+	0.0292191i	$0.990698\pi$
$564$		0			0
$565$	−24.0000	−	13.8564i	−1.00969	−	0.582943i
$566$		0			0
$567$	7.79423	−	22.5000i	0.327327	−	0.944911i
$568$		0			0
$569$	6.50000	−	11.2583i	0.272494	−	0.471974i	−0.697006	−	0.717066i	$-0.745485\pi$
$569$	6.50000	−	11.2583i	0.272494	−	0.471974i	0.969500	+	0.245092i	$0.0788181\pi$
$570$		0			0
$571$	−18.1865	+	10.5000i	−0.761083	+	0.439411i	−0.829684	−	0.558233i	$-0.811480\pi$
$571$	−18.1865	+	10.5000i	−0.761083	+	0.439411i	0.0686016	+	0.997644i	$0.478146\pi$
$572$		0			0
$573$			1.73205i			0.0723575i
$574$		0			0
$575$		−	2.00000i		−	0.0834058i
$576$		0			0
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−28.5000	+	16.4545i	−1.18647	+	0.685009i	−0.228968	+	0.973434i	$0.573535\pi$
$578$		0			0
$579$	12.9904	−	22.5000i	0.539862	−	0.935068i
$580$		0			0
$581$	−24.0000	−	27.7128i	−0.995688	−	1.14972i
$582$		0			0
$583$	0.866025	+	0.500000i	0.0358671	+	0.0207079i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.92820			0.285958			0.142979	−	0.989726i	$-0.454332\pi$
$587$	6.92820			0.285958			0.142979	+	0.989726i	$0.454332\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$		0			0
$591$	13.8564	+	24.0000i	0.569976	+	0.987228i
$592$		0			0
$593$	−13.5000	−	7.79423i	−0.554379	−	0.320071i	0.196508	−	0.980502i	$-0.437040\pi$
$593$	−13.5000	−	7.79423i	−0.554379	−	0.320071i	−0.750886	+	0.660432i	$0.770373\pi$
$594$		0			0
$595$	5.19615	+	6.00000i	0.213021	+	0.245976i
$596$		0			0
$597$	−19.5000	+	33.7750i	−0.798082	+	1.38232i
$598$		0			0
$599$	−14.7224	+	8.50000i	−0.601542	+	0.347301i	−0.769648	−	0.638468i	$-0.779568\pi$
$599$	−14.7224	+	8.50000i	−0.601542	+	0.347301i	0.168106	+	0.985769i	$0.446235\pi$
$600$		0			0
$601$			38.1051i			1.55434i	0.629291	+	0.777170i	$0.283346\pi$
$601$			38.1051i			1.55434i	−0.629291	+	0.777170i	$0.716654\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−15.0000	+	8.66025i	−0.609837	+	0.352089i
$606$		0			0
$607$	7.79423	−	13.5000i	0.316358	−	0.547948i	−0.663367	−	0.748294i	$-0.730873\pi$
$607$	7.79423	−	13.5000i	0.316358	−	0.547948i	0.979725	+	0.200346i	$0.0642066\pi$
$608$		0			0
$609$	6.00000	−	17.3205i	0.243132	−	0.701862i
$610$		0			0
$611$	−25.9808	−	15.0000i	−1.05107	−	0.606835i
$612$		0			0
$613$	−15.5000	−	26.8468i	−0.626039	−	1.08433i	−0.988339	−	0.152270i	$-0.951342\pi$
$613$	−15.5000	−	26.8468i	−0.626039	−	1.08433i	0.362300	−	0.932062i	$-0.381992\pi$
$614$		0			0
$615$	−10.3923			−0.419058
$616$		0			0
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$		0			0
$619$	−7.79423	−	13.5000i	−0.313276	−	0.542611i	0.665793	−	0.746136i	$-0.268093\pi$
$619$	−7.79423	−	13.5000i	−0.313276	−	0.542611i	−0.979070	+	0.203526i	$0.934760\pi$
$620$		0			0
$621$	−4.50000	−	2.59808i	−0.180579	−	0.104257i
$622$		0			0
$623$	−7.79423	−	40.5000i	−0.312269	−	1.62260i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$		0			0
$627$	7.79423	−	4.50000i	0.311272	−	0.179713i
$628$		0			0
$629$			5.19615i			0.207184i
$630$		0			0
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$		0			0
$633$	15.0000	−	8.66025i	0.596196	−	0.344214i
$634$		0			0
$635$	5.19615	−	9.00000i	0.206203	−	0.357154i
$636$		0			0
$637$	24.0000	+	3.46410i	0.950915	+	0.137253i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.50000	+	11.2583i	0.256735	+	0.444677i	0.965365	−	0.260902i	$-0.0840201\pi$
$641$	6.50000	+	11.2583i	0.256735	+	0.444677i	−0.708631	+	0.705580i	$0.750687\pi$
$642$		0			0
$643$	−13.8564			−0.546443			−0.273222	−	0.961951i	$-0.588089\pi$
$643$	−13.8564			−0.546443			−0.273222	+	0.961951i	$0.588089\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	−16.4545	−	28.5000i	−0.646892	−	1.12045i	−0.983861	−	0.178935i	$-0.942735\pi$
$647$	−16.4545	−	28.5000i	−0.646892	−	1.12045i	0.336968	−	0.941516i	$-0.390598\pi$
$648$		0			0
$649$	−4.50000	−	2.59808i	−0.176640	−	0.101983i
$650$		0			0
$651$	7.79423	−	1.50000i	0.305480	−	0.0587896i
$652$		0			0
$653$	15.5000	−	26.8468i	0.606562	−	1.05060i	−0.385241	−	0.922816i	$-0.625882\pi$
$653$	15.5000	−	26.8468i	0.606562	−	1.05060i	0.991803	−	0.127780i	$-0.0407851\pi$
$654$		0			0
$655$	−7.79423	+	4.50000i	−0.304546	+	0.175830i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	38.0000i		−	1.48027i	−0.672458	−	0.740135i	$-0.734762\pi$
$659$		−	38.0000i		−	1.48027i	0.672458	−	0.740135i	$-0.265238\pi$
$660$		0			0
$661$	34.5000	−	19.9186i	1.34189	−	0.774743i	0.354809	−	0.934939i	$-0.384546\pi$
$661$	34.5000	−	19.9186i	1.34189	−	0.774743i	0.987085	+	0.160196i	$0.0512125\pi$
$662$		0			0
$663$	5.19615	−	9.00000i	0.201802	−	0.349531i
$664$		0			0
$665$	−22.5000	−	7.79423i	−0.872513	−	0.302247i
$666$		0			0
$667$	−3.46410	−	2.00000i	−0.134131	−	0.0774403i
$668$		0			0
$669$	6.00000	+	10.3923i	0.231973	+	0.401790i
$670$		0			0
$671$	−5.19615			−0.200595
$672$		0			0
$673$	24.0000			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$674$		0			0
$675$	5.19615	+	9.00000i	0.200000	+	0.346410i
$676$		0			0
$677$	37.5000	+	21.6506i	1.44124	+	0.832102i	0.997933	−	0.0642672i	$-0.0204710\pi$
$677$	37.5000	+	21.6506i	1.44124	+	0.832102i	0.443309	+	0.896369i	$0.353804\pi$
$678$		0			0
$679$	−34.6410	+	30.0000i	−1.32940	+	1.15129i
$680$		0			0
$681$	−16.5000	+	28.5788i	−0.632281	+	1.09514i
$682$		0			0
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	−0.853318	−	0.521391i	$-0.825413\pi$
$683$	−21.6506	+	12.5000i	−0.828439	+	0.478299i	0.0248792	+	0.999690i	$0.492080\pi$
$684$		0			0
$685$		−	1.73205i		−	0.0661783i
$686$		0			0
$687$		−	27.0000i		−	1.03011i
$688$		0			0
$689$	−3.00000	+	1.73205i	−0.114291	+	0.0659859i
$690$		0			0
$691$	−6.06218	+	10.5000i	−0.230616	+	0.399439i	−0.957990	−	0.286803i	$-0.907407\pi$
$691$	−6.06218	+	10.5000i	−0.230616	+	0.399439i	0.727373	+	0.686242i	$0.240741\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.3923	−	6.00000i	−0.394203	−	0.227593i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$		0			0
$699$	−12.1244			−0.458585
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$	−7.79423	−	13.5000i	−0.293965	−	0.509162i
$704$		0			0
$705$	−22.5000	−	12.9904i	−0.847399	−	0.489246i
$706$		0			0
$707$	−21.6506	−	7.50000i	−0.814256	−	0.282067i
$708$		0			0
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	−0.938069	−	0.346449i	$-0.887387\pi$
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	0.769068	+	0.639167i	$0.220721\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	1.73205i		−	0.0648658i
$714$		0			0
$715$			6.00000i			0.224387i
$716$		0			0
$717$	−30.0000	+	17.3205i	−1.12037	+	0.646846i
$718$		0			0
$719$	12.9904	−	22.5000i	0.484459	−	0.839108i	−0.515381	−	0.856961i	$-0.672350\pi$
$719$	12.9904	−	22.5000i	0.484459	−	0.839108i	0.999841	+	0.0178527i	$0.00568298\pi$
$720$		0			0
$721$	22.5000	−	4.33013i	0.837944	−	0.161262i
$722$		0			0
$723$	7.79423	+	4.50000i	0.289870	+	0.167357i
$724$		0			0
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−1.73205	−	3.00000i	−0.0640622	−	0.110959i
$732$		0			0
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.392337	−	0.919822i	$-0.628333\pi$
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.992757	+	0.120137i	$0.961667\pi$
$734$		0			0
$735$	20.7846	+	3.00000i	0.766652	+	0.110657i
$736$		0			0
$737$	1.50000	−	2.59808i	0.0552532	−	0.0957014i
$738$		0			0
$739$	44.1673	−	25.5000i	1.62472	−	0.938033i	0.639087	−	0.769135i	$-0.279313\pi$
$739$	44.1673	−	25.5000i	1.62472	−	0.938033i	0.985634	−	0.168898i	$-0.0540208\pi$
$740$		0			0
$741$			31.1769i			1.14531i
$742$		0			0
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$		0			0
$745$	1.50000	−	0.866025i	0.0549557	−	0.0317287i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.50000	−	33.7750i	−0.237505	−	1.23411i
$750$		0			0
$751$	−21.6506	−	12.5000i	−0.790043	−	0.456131i	0.0499348	−	0.998752i	$-0.484099\pi$
$751$	−21.6506	−	12.5000i	−0.790043	−	0.456131i	−0.839978	+	0.542621i	$0.817432\pi$
$752$		0			0
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$		0			0
$755$	−12.1244			−0.441250
$756$		0			0
$757$	48.0000			1.74459			0.872295	−	0.488980i	$-0.162631\pi$
$757$	48.0000			1.74459			0.872295	+	0.488980i	$0.162631\pi$
$758$		0			0
$759$	0.866025	+	1.50000i	0.0314347	+	0.0544466i
$760$		0			0
$761$	16.5000	+	9.52628i	0.598125	+	0.345327i	0.768303	−	0.640086i	$-0.221101\pi$
$761$	16.5000	+	9.52628i	0.598125	+	0.345327i	−0.170179	+	0.985413i	$0.554435\pi$
$762$		0			0
$763$	7.79423	−	22.5000i	0.282170	−	0.814555i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.5885	−	9.00000i	0.562867	−	0.324971i
$768$		0			0
$769$		−	3.46410i		−	0.124919i	−0.998048	−	0.0624593i	$-0.980106\pi$
$769$		−	3.46410i		−	0.124919i	0.998048	−	0.0624593i	$-0.0198944\pi$
$770$		0			0
$771$		−	9.00000i		−	0.324127i
$772$		0			0
$773$	−22.5000	+	12.9904i	−0.809269	+	0.467232i	−0.846702	−	0.532068i	$-0.821415\pi$
$773$	−22.5000	+	12.9904i	−0.809269	+	0.467232i	0.0374331	+	0.999299i	$0.488082\pi$
$774$		0			0
$775$	−1.73205	+	3.00000i	−0.0622171	+	0.107763i
$776$		0			0
$777$	9.00000	+	10.3923i	0.322873	+	0.372822i
$778$		0			0
$779$	−15.5885	−	9.00000i	−0.558514	−	0.322458i
$780$		0			0
$781$	−7.00000	−	12.1244i	−0.250480	−	0.433844i
$782$		0			0
$783$	20.7846			0.742781
$784$		0			0
$785$	−3.00000			−0.107075
$786$		0			0
$787$	2.59808	+	4.50000i	0.0926114	+	0.160408i	0.908609	−	0.417647i	$-0.137145\pi$
$787$	2.59808	+	4.50000i	0.0926114	+	0.160408i	−0.815998	+	0.578055i	$0.803812\pi$
$788$		0			0
$789$	−34.5000	−	19.9186i	−1.22823	−	0.709120i
$790$		0			0
$791$	27.7128	+	32.0000i	0.985354	+	1.13779i
$792$		0			0
$793$	9.00000	−	15.5885i	0.319599	−	0.553562i
$794$		0			0
$795$	−2.59808	+	1.50000i	−0.0921443	+	0.0531995i
$796$		0			0
$797$			10.3923i			0.368114i	0.982916	+	0.184057i	$0.0589232\pi$
$797$			10.3923i			0.368114i	−0.982916	+	0.184057i	$0.941077\pi$
$798$		0			0
$799$			15.0000i			0.530662i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.33013	+	7.50000i	−0.152807	+	0.264669i
$804$		0			0
$805$	1.50000	−	4.33013i	0.0528681	−	0.152617i
$806$		0			0
$807$	33.7750	+	19.5000i	1.18894	+	0.686433i
$808$		0			0
$809$	−21.5000	−	37.2391i	−0.755900	−	1.30926i	−0.944926	−	0.327285i	$-0.893866\pi$
$809$	−21.5000	−	37.2391i	−0.755900	−	1.30926i	0.189026	−	0.981972i	$-0.439467\pi$
$810$		0			0
$811$	13.8564			0.486564			0.243282	−	0.969956i	$-0.421776\pi$
$811$	13.8564			0.486564			0.243282	+	0.969956i	$0.421776\pi$
$812$		0			0
$813$	27.0000			0.946931
$814$		0			0
$815$	−18.1865	−	31.5000i	−0.637046	−	1.10340i
$816$		0			0
$817$	9.00000	+	5.19615i	0.314870	+	0.181790i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.50000	+	9.52628i	−0.191951	+	0.332469i	−0.945897	−	0.324468i	$-0.894815\pi$
$821$	−5.50000	+	9.52628i	−0.191951	+	0.332469i	0.753946	+	0.656937i	$0.228148\pi$
$822$		0			0
$823$	−7.79423	+	4.50000i	−0.271690	+	0.156860i	−0.629655	−	0.776875i	$-0.716804\pi$
$823$	−7.79423	+	4.50000i	−0.271690	+	0.156860i	0.357966	+	0.933735i	$0.383471\pi$
$824$		0			0
$825$		−	3.46410i		−	0.120605i
$826$		0			0
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$		0			0
$829$	7.50000	−	4.33013i	0.260486	−	0.150392i	−0.364070	−	0.931371i	$-0.618613\pi$
$829$	7.50000	−	4.33013i	0.260486	−	0.150392i	0.624556	+	0.780980i	$0.285280\pi$
$830$		0			0
$831$	−11.2583	+	19.5000i	−0.390547	+	0.676448i
$832$		0			0
$833$	−4.50000	−	11.2583i	−0.155916	−	0.390078i
$834$		0			0
$835$	25.9808	+	15.0000i	0.899101	+	0.519096i
$836$		0			0
$837$	4.50000	+	7.79423i	0.155543	+	0.269408i
$838$		0			0
$839$	−48.4974			−1.67432			−0.837158	−	0.546960i	$-0.815785\pi$
$839$	−48.4974			−1.67432			−0.837158	+	0.546960i	$0.815785\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	3.46410	+	6.00000i	0.119310	+	0.206651i
$844$		0			0
$845$	1.50000	+	0.866025i	0.0516016	+	0.0297922i
$846$		0			0
$847$	25.9808	−	5.00000i	0.892710	−	0.171802i
$848$		0			0
$849$	−10.5000	+	18.1865i	−0.360359	+	0.624160i
$850$		0			0
$851$	2.59808	−	1.50000i	0.0890609	−	0.0514193i
$852$		0			0
$853$			24.2487i			0.830260i	0.909762	+	0.415130i	$0.136264\pi$
$853$			24.2487i			0.830260i	−0.909762	+	0.415130i	$0.863736\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.5000	+	12.9904i	−0.768585	+	0.443743i	−0.832370	−	0.554221i	$-0.813016\pi$
$857$	−22.5000	+	12.9904i	−0.768585	+	0.443743i	0.0637844	+	0.997964i	$0.479683\pi$
$858$		0			0
$859$	−25.1147	+	43.5000i	−0.856904	+	1.48420i	0.0179638	+	0.999839i	$0.494282\pi$
$859$	−25.1147	+	43.5000i	−0.856904	+	1.48420i	−0.874868	+	0.484362i	$0.839052\pi$
$860$		0			0
$861$	15.0000	+	5.19615i	0.511199	+	0.177084i
$862$		0			0
$863$	−30.3109	−	17.5000i	−1.03179	−	0.595707i	−0.114296	−	0.993447i	$-0.536461\pi$
$863$	−30.3109	−	17.5000i	−1.03179	−	0.595707i	−0.917498	+	0.397740i	$0.869795\pi$
$864$		0			0
$865$	10.5000	+	18.1865i	0.357011	+	0.618361i
$866$		0			0
$867$	24.2487			0.823529
$868$		0			0
$869$	−9.00000			−0.305304
$870$		0			0
$871$	5.19615	+	9.00000i	0.176065	+	0.304953i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−24.2487	+	21.0000i	−0.819756	+	0.709930i
$876$		0			0
$877$	0.500000	−	0.866025i	0.0168838	−	0.0292436i	−0.857460	−	0.514551i	$-0.827959\pi$
$877$	0.500000	−	0.866025i	0.0168838	−	0.0292436i	0.874344	+	0.485307i	$0.161292\pi$
$878$		0			0
$879$	31.1769	−	18.0000i	1.05157	−	0.607125i
$880$		0			0
$881$			13.8564i			0.466834i	0.972377	+	0.233417i	$0.0749907\pi$
$881$			13.8564i			0.466834i	−0.972377	+	0.233417i	$0.925009\pi$
$882$		0			0
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$		0			0
$885$	13.5000	−	7.79423i	0.453798	−	0.262000i
$886$		0			0
$887$	−12.9904	+	22.5000i	−0.436174	+	0.755476i	−0.997391	−	0.0721931i	$-0.977000\pi$
$887$	−12.9904	+	22.5000i	−0.436174	+	0.755476i	0.561216	+	0.827669i	$0.310334\pi$
$888$		0			0
$889$	−12.0000	+	10.3923i	−0.402467	+	0.348547i
$890$		0			0
$891$	−7.79423	−	4.50000i	−0.261116	−	0.150756i
$892$		0			0
$893$	−22.5000	−	38.9711i	−0.752934	−	1.30412i
$894$		0			0
$895$	32.9090			1.10003
$896$		0			0
$897$	−6.00000			−0.200334
$898$		0			0
$899$	3.46410	+	6.00000i	0.115534	+	0.200111i
$900$		0			0
$901$	1.50000	+	0.866025i	0.0499722	+	0.0288515i
$902$		0			0
$903$	−8.66025	−	3.00000i	−0.288195	−	0.0998337i
$904$		0			0
$905$	6.00000	−	10.3923i	0.199447	−	0.345452i
$906$		0			0
$907$	−6.06218	+	3.50000i	−0.201291	+	0.116216i	−0.597258	−	0.802049i	$-0.703743\pi$
$907$	−6.06218	+	3.50000i	−0.201291	+	0.116216i	0.395966	+	0.918265i	$0.370410\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			26.0000i			0.861418i	0.902491	+	0.430709i	$0.141737\pi$
$911$			26.0000i			0.861418i	−0.902491	+	0.430709i	$0.858263\pi$
$912$		0			0
$913$	−12.0000	+	6.92820i	−0.397142	+	0.229290i
$914$		0			0
$915$	7.79423	−	13.5000i	0.257669	−	0.446296i
$916$		0			0
$917$	13.5000	−	2.59808i	0.445809	−	0.0857960i
$918$		0			0
$919$	−0.866025	−	0.500000i	−0.0285675	−	0.0164935i	0.485648	−	0.874154i	$-0.338584\pi$
$919$	−0.866025	−	0.500000i	−0.0285675	−	0.0164935i	−0.514216	+	0.857661i	$0.671917\pi$
$920$		0			0
$921$	−18.0000	−	31.1769i	−0.593120	−	1.02731i
$922$		0			0
$923$	48.4974			1.59631
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.50000	+	4.33013i	0.246067	+	0.142067i	0.617962	−	0.786208i	$-0.287959\pi$
$929$	7.50000	+	4.33013i	0.246067	+	0.142067i	−0.371895	+	0.928275i	$0.621292\pi$
$930$		0			0
$931$	28.5788	+	22.5000i	0.936634	+	0.737408i
$932$		0			0
$933$	7.50000	−	12.9904i	0.245539	−	0.425286i
$934$		0			0
$935$	2.59808	−	1.50000i	0.0849662	−	0.0490552i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		−	3.00000i		−	0.0979013i
$940$		0			0
$941$	−49.5000	+	28.5788i	−1.61365	+	0.931644i	−0.625140	+	0.780513i	$0.714958\pi$
$941$	−49.5000	+	28.5788i	−1.61365	+	0.931644i	−0.988514	+	0.151131i	$0.951708\pi$
$942$		0			0
$943$	1.73205	−	3.00000i	0.0564033	−	0.0976934i
$944$		0			0
$945$	4.50000	+	23.3827i	0.146385	+	0.760639i
$946$		0			0
$947$	−25.1147	−	14.5000i	−0.816119	−	0.471187i	0.0329571	−	0.999457i	$-0.489508\pi$
$947$	−25.1147	−	14.5000i	−0.816119	−	0.471187i	−0.849076	+	0.528270i	$0.822841\pi$
$948$		0			0
$949$	−15.0000	−	25.9808i	−0.486921	−	0.843371i
$950$		0			0
$951$	−19.0526			−0.617822
$952$		0			0
$953$	−8.00000			−0.259145			−0.129573	−	0.991570i	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		0			0
$955$	−0.866025	−	1.50000i	−0.0280239	−	0.0485389i
$956$		0			0
$957$	−6.00000	−	3.46410i	−0.193952	−	0.111979i
$958$		0			0
$959$	−0.866025	+	2.50000i	−0.0279654	+	0.0807292i
$960$		0			0
$961$	14.0000	−	24.2487i	0.451613	−	0.782216i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			25.9808i			0.836350i
$966$		0			0
$967$			6.00000i			0.192947i	0.995336	+	0.0964735i	$0.0307563\pi$
$967$			6.00000i			0.192947i	−0.995336	+	0.0964735i	$0.969244\pi$
$968$		0			0
$969$	13.5000	−	7.79423i	0.433682	−	0.250387i
$970$		0			0
$971$	−30.3109	+	52.5000i	−0.972723	+	1.68481i	−0.285469	+	0.958388i	$0.592149\pi$
$971$	−30.3109	+	52.5000i	−0.972723	+	1.68481i	−0.687254	+	0.726417i	$0.741184\pi$
$972$		0			0
$973$	12.0000	+	13.8564i	0.384702	+	0.444216i
$974$		0			0
$975$	10.3923	+	6.00000i	0.332820	+	0.192154i
$976$		0			0
$977$	15.5000	+	26.8468i	0.495889	+	0.858905i	0.999989	−	0.00474056i	$-0.00150897\pi$
$977$	15.5000	+	26.8468i	0.495889	+	0.858905i	−0.504100	+	0.863645i	$0.668176\pi$
$978$		0			0
$979$	−15.5885			−0.498209
$980$		0			0
$981$		0			0
$982$		0			0
$983$	30.3109	+	52.5000i	0.966767	+	1.67449i	0.704790	+	0.709416i	$0.251041\pi$
$983$	30.3109	+	52.5000i	0.966767	+	1.67449i	0.261977	+	0.965074i	$0.415626\pi$
$984$		0			0
$985$	−24.0000	−	13.8564i	−0.764704	−	0.441502i
$986$		0			0
$987$	25.9808	+	30.0000i	0.826977	+	0.954911i
$988$		0			0
$989$	−1.00000	+	1.73205i	−0.0317982	+	0.0550760i
$990$		0			0
$991$	19.9186	−	11.5000i	0.632735	−	0.365310i	−0.149076	−	0.988826i	$-0.547630\pi$
$991$	19.9186	−	11.5000i	0.632735	−	0.365310i	0.781810	+	0.623516i	$0.214296\pi$
$992$		0			0
$993$		−	12.1244i		−	0.384755i
$994$		0			0
$995$		−	39.0000i		−	1.23638i
$996$		0			0
$997$	−19.5000	+	11.2583i	−0.617571	+	0.356555i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−19.5000	+	11.2583i	−0.617571	+	0.356555i	0.158352	+	0.987383i	$0.449382\pi$
$998$		0			0
$999$	−7.79423	+	13.5000i	−0.246598	+	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.p.d.383.1		4
4.3	odd	2	inner	448.2.p.d.383.2		4
7.2	even	3		3136.2.f.e.3135.3		4
7.3	odd	6	inner	448.2.p.d.255.2		4
7.5	odd	6		3136.2.f.e.3135.2		4
8.3	odd	2		28.2.f.a.19.2	yes	4
8.5	even	2		28.2.f.a.19.1	yes	4
24.5	odd	2		252.2.bf.e.19.2		4
24.11	even	2		252.2.bf.e.19.1		4
28.3	even	6	inner	448.2.p.d.255.1		4
28.19	even	6		3136.2.f.e.3135.4		4
28.23	odd	6		3136.2.f.e.3135.1		4
40.3	even	4		700.2.t.b.299.2		4
40.13	odd	4		700.2.t.a.299.2		4
40.19	odd	2		700.2.p.a.551.1		4
40.27	even	4		700.2.t.a.299.1		4
40.29	even	2		700.2.p.a.551.2		4
40.37	odd	4		700.2.t.b.299.1		4
56.3	even	6		28.2.f.a.3.1	✓	4
56.5	odd	6		196.2.d.b.195.4		4
56.11	odd	6		196.2.f.a.31.1		4
56.13	odd	2		196.2.f.a.19.1		4
56.19	even	6		196.2.d.b.195.1		4
56.27	even	2		196.2.f.a.19.2		4
56.37	even	6		196.2.d.b.195.3		4
56.45	odd	6		28.2.f.a.3.2	yes	4
56.51	odd	6		196.2.d.b.195.2		4
56.53	even	6		196.2.f.a.31.2		4
168.5	even	6		1764.2.b.a.1567.2		4
168.59	odd	6		252.2.bf.e.199.2		4
168.101	even	6		252.2.bf.e.199.1		4
168.107	even	6		1764.2.b.a.1567.3		4
168.131	odd	6		1764.2.b.a.1567.4		4
168.149	odd	6		1764.2.b.a.1567.1		4
280.3	odd	12		700.2.t.b.199.1		4
280.59	even	6		700.2.p.a.451.2		4
280.157	even	12		700.2.t.b.199.2		4
280.213	even	12		700.2.t.a.199.1		4
280.227	odd	12		700.2.t.a.199.2		4
280.269	odd	6		700.2.p.a.451.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.f.a.3.1	✓	4	56.3	even	6
28.2.f.a.3.2	yes	4	56.45	odd	6
28.2.f.a.19.1	yes	4	8.5	even	2
28.2.f.a.19.2	yes	4	8.3	odd	2
196.2.d.b.195.1		4	56.19	even	6
196.2.d.b.195.2		4	56.51	odd	6
196.2.d.b.195.3		4	56.37	even	6
196.2.d.b.195.4		4	56.5	odd	6
196.2.f.a.19.1		4	56.13	odd	2
196.2.f.a.19.2		4	56.27	even	2
196.2.f.a.31.1		4	56.11	odd	6
196.2.f.a.31.2		4	56.53	even	6
252.2.bf.e.19.1		4	24.11	even	2
252.2.bf.e.19.2		4	24.5	odd	2
252.2.bf.e.199.1		4	168.101	even	6
252.2.bf.e.199.2		4	168.59	odd	6
448.2.p.d.255.1		4	28.3	even	6	inner
448.2.p.d.255.2		4	7.3	odd	6	inner
448.2.p.d.383.1		4	1.1	even	1	trivial
448.2.p.d.383.2		4	4.3	odd	2	inner
700.2.p.a.451.1		4	280.269	odd	6
700.2.p.a.451.2		4	280.59	even	6
700.2.p.a.551.1		4	40.19	odd	2
700.2.p.a.551.2		4	40.29	even	2
700.2.t.a.199.1		4	280.213	even	12
700.2.t.a.199.2		4	280.227	odd	12
700.2.t.a.299.1		4	40.27	even	4
700.2.t.a.299.2		4	40.13	odd	4
700.2.t.b.199.1		4	280.3	odd	12
700.2.t.b.199.2		4	280.157	even	12
700.2.t.b.299.1		4	40.37	odd	4
700.2.t.b.299.2		4	40.3	even	4
1764.2.b.a.1567.1		4	168.149	odd	6
1764.2.b.a.1567.2		4	168.5	even	6
1764.2.b.a.1567.3		4	168.107	even	6
1764.2.b.a.1567.4		4	168.131	odd	6
3136.2.f.e.3135.1		4	28.23	odd	6
3136.2.f.e.3135.2		4	7.5	odd	6
3136.2.f.e.3135.3		4	7.2	even	3
3136.2.f.e.3135.4		4	28.19	even	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{3} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +O(q^{10})\)	\(q+(-0.866025 - 1.50000i) q^{3} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(-0.866025 + 0.500000i) q^{11} -3.46410i q^{13} -3.00000i q^{15} +(-1.50000 + 0.866025i) q^{17} +(2.59808 - 4.50000i) q^{19} +(-1.50000 + 4.33013i) q^{21} +(0.866025 + 0.500000i) q^{23} +(-1.00000 - 1.73205i) q^{25} -5.19615 q^{27} -4.00000 q^{29} +(-0.866025 - 1.50000i) q^{31} +(1.50000 + 0.866025i) q^{33} +(-0.866025 - 4.50000i) q^{35} +(1.50000 - 2.59808i) q^{37} +(-5.19615 + 3.00000i) q^{39} -3.46410i q^{41} +2.00000i q^{43} +(4.33013 - 7.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(2.59808 + 1.50000i) q^{51} +(-0.500000 - 0.866025i) q^{53} -1.73205 q^{55} -9.00000 q^{57} +(2.59808 + 4.50000i) q^{59} +(4.50000 + 2.59808i) q^{61} +(3.00000 - 5.19615i) q^{65} +(-2.59808 + 1.50000i) q^{67} -1.73205i q^{69} +14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-1.73205 + 3.00000i) q^{75} +(2.50000 + 0.866025i) q^{77} +(7.79423 + 4.50000i) q^{79} +(4.50000 + 7.79423i) q^{81} +13.8564 q^{83} -3.00000 q^{85} +(3.46410 + 6.00000i) q^{87} +(13.5000 + 7.79423i) q^{89} +(-6.92820 + 6.00000i) q^{91} +(-1.50000 + 2.59808i) q^{93} +(7.79423 - 4.50000i) q^{95} -17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5}+O(q^{10}) \) 4 * q + 6 * q^5	\( 4 q + 6 q^{5} - 6 q^{17} - 6 q^{21} - 4 q^{25} - 16 q^{29} + 6 q^{33} + 6 q^{37} - 4 q^{49} - 2 q^{53} - 36 q^{57} + 18 q^{61} + 12 q^{65} + 30 q^{73} + 10 q^{77} + 18 q^{81} - 12 q^{85} + 54 q^{89} - 6 q^{93}+O(q^{100}) \) 4 * q + 6 * q^5 - 6 * q^17 - 6 * q^21 - 4 * q^25 - 16 * q^29 + 6 * q^33 + 6 * q^37 - 4 * q^49 - 2 * q^53 - 36 * q^57 + 18 * q^61 + 12 * q^65 + 30 * q^73 + 10 * q^77 + 18 * q^81 - 12 * q^85 + 54 * q^89 - 6 * q^93

Introduction

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