LMFDB - Embedded newform 855.2.n.a.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	855.647
Dual form			855.2.n.a.818.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(1.00000 - 2.00000i) q^{10} +4.24264i q^{11} +(2.00000 - 2.00000i) q^{13} +4.24264 q^{14} +1.00000 q^{16} -1.00000i q^{19} +(-0.707107 - 2.12132i) q^{20} +(-3.00000 - 3.00000i) q^{22} +(4.00000 - 3.00000i) q^{25} +2.82843i q^{26} +(3.00000 - 3.00000i) q^{28} +2.82843 q^{29} +8.00000 q^{31} +(3.53553 - 3.53553i) q^{32} +(8.48528 + 4.24264i) q^{35} +(0.707107 + 0.707107i) q^{38} +(6.00000 + 3.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} -4.24264 q^{44} +(-5.65685 + 5.65685i) q^{47} +11.0000i q^{49} +(-0.707107 + 4.94975i) q^{50} +(2.00000 + 2.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-3.00000 - 9.00000i) q^{55} +12.7279i q^{56} +(-2.00000 + 2.00000i) q^{58} +8.48528 q^{59} -14.0000 q^{61} +(-5.65685 + 5.65685i) q^{62} +7.00000i q^{64} +(-2.82843 + 5.65685i) q^{65} +(6.00000 + 6.00000i) q^{67} +(-9.00000 + 3.00000i) q^{70} -11.3137i q^{71} +(1.00000 - 1.00000i) q^{73} +1.00000 q^{76} +(12.7279 - 12.7279i) q^{77} -4.00000i q^{79} +(-2.12132 + 0.707107i) q^{80} +(4.00000 + 4.00000i) q^{82} +(7.07107 + 7.07107i) q^{83} +9.89949i q^{86} +(9.00000 - 9.00000i) q^{88} +5.65685 q^{89} -12.0000 q^{91} -8.00000i q^{94} +(0.707107 + 2.12132i) q^{95} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{7}+O(q^{10}) $ 4 * q - 12 * q^7	$ 4 q - 12 q^{7} + 4 q^{10} + 8 q^{13} + 4 q^{16} - 12 q^{22} + 16 q^{25} + 12 q^{28} + 32 q^{31} + 24 q^{40} + 28 q^{43} + 8 q^{52} - 12 q^{55} - 8 q^{58} - 56 q^{61} + 24 q^{67} - 36 q^{70} + 4 q^{73} + 4 q^{76} + 16 q^{82} + 36 q^{88} - 48 q^{91}+O(q^{100}) $ 4 * q - 12 * q^7 + 4 * q^10 + 8 * q^13 + 4 * q^16 - 12 * q^22 + 16 * q^25 + 12 * q^28 + 32 * q^31 + 24 * q^40 + 28 * q^43 + 8 * q^52 - 12 * q^55 - 8 * q^58 - 56 * q^61 + 24 * q^67 - 36 * q^70 + 4 * q^73 + 4 * q^76 + 16 * q^82 + 36 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	−0.911438	−	0.411438i	$-0.865027\pi$
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i	0.411438	+	0.911438i	$0.365027\pi$
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$		0			0
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$	−2.12132	−	2.12132i	−0.750000	−	0.750000i
$9$		0			0
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$			4.24264i			1.27920i	0.768706	+	0.639602i	$0.220901\pi$
$11$			4.24264i			1.27920i	−0.768706	+	0.639602i	$0.779099\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	4.24264			1.13389
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.707107	−	2.12132i	−0.158114	−	0.474342i
$21$		0			0
$22$	−3.00000	−	3.00000i	−0.639602	−	0.639602i
$23$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$23$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$24$		0			0
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$			2.82843i			0.554700i
$27$		0			0
$28$	3.00000	−	3.00000i	0.566947	−	0.566947i
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	3.53553	−	3.53553i	0.625000	−	0.625000i
$33$		0			0
$34$		0			0
$35$	8.48528	+	4.24264i	1.43427	+	0.717137i
$36$		0			0
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	6.00000	+	3.00000i	0.948683	+	0.474342i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	7.00000	−	7.00000i	1.06749	−	1.06749i	0.0699387	−	0.997551i	$-0.477720\pi$
$43$	7.00000	−	7.00000i	1.06749	−	1.06749i	0.997551	−	0.0699387i	$-0.0222804\pi$
$44$	−4.24264			−0.639602
$45$		0			0
$46$		0			0
$47$	−5.65685	+	5.65685i	−0.825137	+	0.825137i	−0.986840	−	0.161703i	$-0.948301\pi$
$47$	−5.65685	+	5.65685i	−0.825137	+	0.825137i	0.161703	+	0.986840i	$0.448301\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$	−0.707107	+	4.94975i	−0.100000	+	0.700000i
$51$		0			0
$52$	2.00000	+	2.00000i	0.277350	+	0.277350i
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$	−3.00000	−	9.00000i	−0.404520	−	1.21356i
$56$			12.7279i			1.70084i
$57$		0			0
$58$	−2.00000	+	2.00000i	−0.262613	+	0.262613i
$59$	8.48528			1.10469			0.552345	−	0.833616i	$-0.313733\pi$
$59$	8.48528			1.10469			0.552345	+	0.833616i	$0.313733\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	−5.65685	+	5.65685i	−0.718421	+	0.718421i
$63$		0			0
$64$			7.00000i			0.875000i
$65$	−2.82843	+	5.65685i	−0.350823	+	0.701646i
$66$		0			0
$67$	6.00000	+	6.00000i	0.733017	+	0.733017i	0.971216	−	0.238200i	$-0.0765572\pi$
$67$	6.00000	+	6.00000i	0.733017	+	0.733017i	−0.238200	+	0.971216i	$0.576557\pi$
$68$		0			0
$69$		0			0
$70$	−9.00000	+	3.00000i	−1.07571	+	0.358569i
$71$		−	11.3137i		−	1.34269i	−0.741145	−	0.671345i	$-0.765717\pi$
$71$		−	11.3137i		−	1.34269i	0.741145	−	0.671345i	$-0.234283\pi$
$72$		0			0
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	−0.646160	−	0.763202i	$-0.723626\pi$
$73$	1.00000	−	1.00000i	0.117041	−	0.117041i	0.763202	+	0.646160i	$0.223626\pi$
$74$		0			0
$75$		0			0
$76$	1.00000			0.114708
$77$	12.7279	−	12.7279i	1.45048	−	1.45048i
$78$		0			0
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	−2.12132	+	0.707107i	−0.237171	+	0.0790569i
$81$		0			0
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$	7.07107	+	7.07107i	0.776151	+	0.776151i	0.979174	−	0.203023i	$-0.0650767\pi$
$83$	7.07107	+	7.07107i	0.776151	+	0.776151i	−0.203023	+	0.979174i	$0.565077\pi$
$84$		0			0
$85$		0			0
$86$			9.89949i			1.06749i
$87$		0			0
$88$	9.00000	−	9.00000i	0.959403	−	0.959403i
$89$	5.65685			0.599625			0.299813	−	0.953998i	$-0.403076\pi$
$89$	5.65685			0.599625			0.299813	+	0.953998i	$0.403076\pi$
$90$		0			0
$91$	−12.0000			−1.25794
$92$		0			0
$93$		0			0
$94$		−	8.00000i		−	0.825137i
$95$	0.707107	+	2.12132i	0.0725476	+	0.217643i
$96$		0			0
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	−7.77817	−	7.77817i	−0.785714	−	0.785714i
$99$		0			0
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	12.7279i		−	1.26648i	−0.773957	−	0.633238i	$-0.781726\pi$
$101$		−	12.7279i		−	1.26648i	0.773957	−	0.633238i	$-0.218274\pi$
$102$		0			0
$103$	10.0000	−	10.0000i	0.985329	−	0.985329i	−0.0145647	−	0.999894i	$-0.504636\pi$
$103$	10.0000	−	10.0000i	0.985329	−	0.985329i	0.999894	+	0.0145647i	$0.00463624\pi$
$104$	−8.48528			−0.832050
$105$		0			0
$106$	6.00000			0.582772
$107$	5.65685	−	5.65685i	0.546869	−	0.546869i	−0.378665	−	0.925534i	$-0.623617\pi$
$107$	5.65685	−	5.65685i	0.546869	−	0.546869i	0.925534	+	0.378665i	$0.123617\pi$
$108$		0			0
$109$			10.0000i			0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$			10.0000i			0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$	8.48528	+	4.24264i	0.809040	+	0.404520i
$111$		0			0
$112$	−3.00000	−	3.00000i	−0.283473	−	0.283473i
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	0.478806	−	0.877920i	$-0.341070\pi$
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	−0.877920	+	0.478806i	$0.841070\pi$
$114$		0			0
$115$		0			0
$116$			2.82843i			0.262613i
$117$		0			0
$118$	−6.00000	+	6.00000i	−0.552345	+	0.552345i
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	9.89949	−	9.89949i	0.896258	−	0.896258i
$123$		0			0
$124$			8.00000i			0.718421i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$		0			0
$127$	−12.0000	−	12.0000i	−1.06483	−	1.06483i	−0.997748	−	0.0670802i	$-0.978632\pi$
$127$	−12.0000	−	12.0000i	−1.06483	−	1.06483i	−0.0670802	−	0.997748i	$-0.521368\pi$
$128$	2.12132	+	2.12132i	0.187500	+	0.187500i
$129$		0			0
$130$	−2.00000	−	6.00000i	−0.175412	−	0.526235i
$131$		−	18.3848i		−	1.60629i	−0.595787	−	0.803143i	$-0.703160\pi$
$131$		−	18.3848i		−	1.60629i	0.595787	−	0.803143i	$-0.296840\pi$
$132$		0			0
$133$	−3.00000	+	3.00000i	−0.260133	+	0.260133i
$134$	−8.48528			−0.733017
$135$		0			0
$136$		0			0
$137$	2.82843	−	2.82843i	0.241649	−	0.241649i	−0.575883	−	0.817532i	$-0.695342\pi$
$137$	2.82843	−	2.82843i	0.241649	−	0.241649i	0.817532	+	0.575883i	$0.195342\pi$
$138$		0			0
$139$		−	10.0000i		−	0.848189i	−0.905618	−	0.424094i	$-0.860592\pi$
$139$		−	10.0000i		−	0.848189i	0.905618	−	0.424094i	$-0.139408\pi$
$140$	−4.24264	+	8.48528i	−0.358569	+	0.717137i
$141$		0			0
$142$	8.00000	+	8.00000i	0.671345	+	0.671345i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$		0			0
$145$	−6.00000	+	2.00000i	−0.498273	+	0.166091i
$146$			1.41421i			0.117041i
$147$		0			0
$148$		0			0
$149$	7.07107			0.579284			0.289642	−	0.957135i	$-0.406464\pi$
$149$	7.07107			0.579284			0.289642	+	0.957135i	$0.406464\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−2.12132	+	2.12132i	−0.172062	+	0.172062i
$153$		0			0
$154$			18.0000i			1.45048i
$155$	−16.9706	+	5.65685i	−1.36311	+	0.454369i
$156$		0			0
$157$	11.0000	+	11.0000i	0.877896	+	0.877896i	0.993317	−	0.115421i	$-0.0368217\pi$
$157$	11.0000	+	11.0000i	0.877896	+	0.877896i	−0.115421	+	0.993317i	$0.536822\pi$
$158$	2.82843	+	2.82843i	0.225018	+	0.225018i
$159$		0			0
$160$	−5.00000	+	10.0000i	−0.395285	+	0.790569i
$161$		0			0
$162$		0			0
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	−0.745184	−	0.666858i	$-0.767639\pi$
$163$	−1.00000	+	1.00000i	−0.0783260	+	0.0783260i	0.666858	+	0.745184i	$0.267639\pi$
$164$	5.65685			0.441726
$165$		0			0
$166$	−10.0000			−0.776151
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	−0.297966	−	0.954577i	$-0.596308\pi$
$167$	8.48528	−	8.48528i	0.656611	−	0.656611i	0.954577	+	0.297966i	$0.0963081\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$		0			0
$172$	7.00000	+	7.00000i	0.533745	+	0.533745i
$173$	−18.3848	−	18.3848i	−1.39777	−	1.39777i	−0.806405	−	0.591364i	$-0.798590\pi$
$173$	−18.3848	−	18.3848i	−1.39777	−	1.39777i	−0.591364	−	0.806405i	$-0.701410\pi$
$174$		0			0
$175$	−21.0000	−	3.00000i	−1.58745	−	0.226779i
$176$			4.24264i			0.319801i
$177$		0			0
$178$	−4.00000	+	4.00000i	−0.299813	+	0.299813i
$179$	−14.1421			−1.05703			−0.528516	−	0.848923i	$-0.677252\pi$
$179$	−14.1421			−1.05703			−0.528516	+	0.848923i	$0.677252\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	8.48528	−	8.48528i	0.628971	−	0.628971i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−5.65685	−	5.65685i	−0.412568	−	0.412568i
$189$		0			0
$190$	−2.00000	−	1.00000i	−0.145095	−	0.0725476i
$191$		−	7.07107i		−	0.511645i	−0.966724	−	0.255822i	$-0.917654\pi$
$191$		−	7.07107i		−	0.511645i	0.966724	−	0.255822i	$-0.0823462\pi$
$192$		0			0
$193$	−14.0000	+	14.0000i	−1.00774	+	1.00774i	−0.00777226	+	0.999970i	$0.502474\pi$
$193$	−14.0000	+	14.0000i	−1.00774	+	1.00774i	−0.999970	+	0.00777226i	$0.997526\pi$
$194$		0			0
$195$		0			0
$196$	−11.0000			−0.785714
$197$	−4.24264	+	4.24264i	−0.302276	+	0.302276i	−0.841904	−	0.539628i	$-0.818565\pi$
$197$	−4.24264	+	4.24264i	−0.302276	+	0.302276i	0.539628	+	0.841904i	$0.318565\pi$
$198$		0			0
$199$			14.0000i			0.992434i	0.868199	+	0.496217i	$0.165278\pi$
$199$			14.0000i			0.992434i	−0.868199	+	0.496217i	$0.834722\pi$
$200$	−14.8492	−	2.12132i	−1.05000	−	0.150000i
$201$		0			0
$202$	9.00000	+	9.00000i	0.633238	+	0.633238i
$203$	−8.48528	−	8.48528i	−0.595550	−	0.595550i
$204$		0			0
$205$	4.00000	+	12.0000i	0.279372	+	0.838116i
$206$			14.1421i			0.985329i
$207$		0			0
$208$	2.00000	−	2.00000i	0.138675	−	0.138675i
$209$	4.24264			0.293470
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$			8.00000i			0.546869i
$215$	−9.89949	+	19.7990i	−0.675140	+	1.35028i
$216$		0			0
$217$	−24.0000	−	24.0000i	−1.62923	−	1.62923i
$218$	−7.07107	−	7.07107i	−0.478913	−	0.478913i
$219$		0			0
$220$	9.00000	−	3.00000i	0.606780	−	0.202260i
$221$		0			0
$222$		0			0
$223$	2.00000	−	2.00000i	0.133930	−	0.133930i	−0.636964	−	0.770894i	$-0.719810\pi$
$223$	2.00000	−	2.00000i	0.133930	−	0.133930i	0.770894	+	0.636964i	$0.219810\pi$
$224$	−21.2132			−1.41737
$225$		0			0
$226$	6.00000			0.399114
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	−0.367024	−	0.930212i	$-0.619623\pi$
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	0.930212	+	0.367024i	$0.119623\pi$
$228$		0			0
$229$		−	20.0000i		−	1.32164i	−0.750546	−	0.660819i	$-0.770209\pi$
$229$		−	20.0000i		−	1.32164i	0.750546	−	0.660819i	$-0.229791\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000	−	6.00000i	−0.393919	−	0.393919i
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	0.154205	−	0.988039i	$-0.450718\pi$
$233$	−12.7279	−	12.7279i	−0.833834	−	0.833834i	−0.988039	+	0.154205i	$0.950718\pi$
$234$		0			0
$235$	8.00000	−	16.0000i	0.521862	−	1.04372i
$236$			8.48528i			0.552345i
$237$		0			0
$238$		0			0
$239$	−1.41421			−0.0914779			−0.0457389	−	0.998953i	$-0.514564\pi$
$239$	−1.41421			−0.0914779			−0.0457389	+	0.998953i	$0.514564\pi$
$240$		0			0
$241$	−6.00000			−0.386494			−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000			−0.386494			−0.193247	+	0.981150i	$0.561902\pi$
$242$	4.94975	−	4.94975i	0.318182	−	0.318182i
$243$		0			0
$244$		−	14.0000i		−	0.896258i
$245$	−7.77817	−	23.3345i	−0.496929	−	1.49079i
$246$		0			0
$247$	−2.00000	−	2.00000i	−0.127257	−	0.127257i
$248$	−16.9706	−	16.9706i	−1.07763	−	1.07763i
$249$		0			0
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$			7.07107i			0.446322i	0.974782	+	0.223161i	$0.0716375\pi$
$251$			7.07107i			0.446322i	−0.974782	+	0.223161i	$0.928362\pi$
$252$		0			0
$253$		0			0
$254$	16.9706			1.06483
$255$		0			0
$256$	−17.0000			−1.06250
$257$	−18.3848	+	18.3848i	−1.14681	+	1.14681i	−0.159635	+	0.987176i	$0.551032\pi$
$257$	−18.3848	+	18.3848i	−1.14681	+	1.14681i	−0.987176	+	0.159635i	$0.948968\pi$
$258$		0			0
$259$		0			0
$260$	−5.65685	−	2.82843i	−0.350823	−	0.175412i
$261$		0			0
$262$	13.0000	+	13.0000i	0.803143	+	0.803143i
$263$	−15.5563	−	15.5563i	−0.959246	−	0.959246i	0.0399559	−	0.999201i	$-0.487278\pi$
$263$	−15.5563	−	15.5563i	−0.959246	−	0.959246i	−0.999201	+	0.0399559i	$0.987278\pi$
$264$		0			0
$265$	12.0000	+	6.00000i	0.737154	+	0.368577i
$266$		−	4.24264i		−	0.260133i
$267$		0			0
$268$	−6.00000	+	6.00000i	−0.366508	+	0.366508i
$269$	25.4558			1.55207			0.776035	−	0.630690i	$-0.217228\pi$
$269$	25.4558			1.55207			0.776035	+	0.630690i	$0.217228\pi$
$270$		0			0
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$		0			0
$273$		0			0
$274$			4.00000i			0.241649i
$275$	12.7279	+	16.9706i	0.767523	+	1.02336i
$276$		0			0
$277$	−15.0000	−	15.0000i	−0.901263	−	0.901263i	0.0942828	−	0.995545i	$-0.469944\pi$
$277$	−15.0000	−	15.0000i	−0.901263	−	0.901263i	−0.995545	+	0.0942828i	$0.969944\pi$
$278$	7.07107	+	7.07107i	0.424094	+	0.424094i
$279$		0			0
$280$	−9.00000	−	27.0000i	−0.537853	−	1.61356i
$281$			25.4558i			1.51857i	0.650759	+	0.759284i	$0.274451\pi$
$281$			25.4558i			1.51857i	−0.650759	+	0.759284i	$0.725549\pi$
$282$		0			0
$283$	21.0000	−	21.0000i	1.24832	−	1.24832i	0.291859	−	0.956461i	$-0.405726\pi$
$283$	21.0000	−	21.0000i	1.24832	−	1.24832i	0.956461	−	0.291859i	$-0.0942738\pi$
$284$	11.3137			0.671345
$285$		0			0
$286$	−12.0000			−0.709575
$287$	−16.9706	+	16.9706i	−1.00174	+	1.00174i
$288$		0			0
$289$			17.0000i			1.00000i
$290$	2.82843	−	5.65685i	0.166091	−	0.332182i
$291$		0			0
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	12.7279	+	12.7279i	0.743573	+	0.743573i	0.973264	−	0.229691i	$-0.0737714\pi$
$293$	12.7279	+	12.7279i	0.743573	+	0.743573i	−0.229691	+	0.973264i	$0.573771\pi$
$294$		0			0
$295$	−18.0000	+	6.00000i	−1.04800	+	0.349334i
$296$		0			0
$297$		0			0
$298$	−5.00000	+	5.00000i	−0.289642	+	0.289642i
$299$		0			0
$300$		0			0
$301$	−42.0000			−2.42084
$302$	11.3137	−	11.3137i	0.651031	−	0.651031i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$	29.6985	−	9.89949i	1.70053	−	0.566843i
$306$		0			0
$307$	22.0000	+	22.0000i	1.25561	+	1.25561i	0.953169	+	0.302437i	$0.0978002\pi$
$307$	22.0000	+	22.0000i	1.25561	+	1.25561i	0.302437	+	0.953169i	$0.402200\pi$
$308$	12.7279	+	12.7279i	0.725241	+	0.725241i
$309$		0			0
$310$	8.00000	−	16.0000i	0.454369	−	0.908739i
$311$		−	7.07107i		−	0.400963i	−0.979697	−	0.200482i	$-0.935749\pi$
$311$		−	7.07107i		−	0.400963i	0.979697	−	0.200482i	$-0.0642507\pi$
$312$		0			0
$313$	5.00000	−	5.00000i	0.282617	−	0.282617i	−0.551535	−	0.834152i	$-0.685958\pi$
$313$	5.00000	−	5.00000i	0.282617	−	0.282617i	0.834152	+	0.551535i	$0.185958\pi$
$314$	−15.5563			−0.877896
$315$		0			0
$316$	4.00000			0.225018
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	−0.877227	−	0.480076i	$-0.840609\pi$
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	0.480076	+	0.877227i	$0.340609\pi$
$318$		0			0
$319$			12.0000i			0.671871i
$320$	−4.94975	−	14.8492i	−0.276699	−	0.830098i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	2.00000	−	14.0000i	0.110940	−	0.776580i
$326$		−	1.41421i		−	0.0783260i
$327$		0			0
$328$	−12.0000	+	12.0000i	−0.662589	+	0.662589i
$329$	33.9411			1.87123
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	−7.07107	+	7.07107i	−0.388075	+	0.388075i
$333$		0			0
$334$			12.0000i			0.656611i
$335$	−16.9706	−	8.48528i	−0.927201	−	0.463600i
$336$		0			0
$337$	4.00000	+	4.00000i	0.217894	+	0.217894i	0.807610	−	0.589716i	$-0.200761\pi$
$337$	4.00000	+	4.00000i	0.217894	+	0.217894i	−0.589716	+	0.807610i	$0.700761\pi$
$338$	−3.53553	−	3.53553i	−0.192308	−	0.192308i
$339$		0			0
$340$		0			0
$341$			33.9411i			1.83801i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−29.6985			−1.60123
$345$		0			0
$346$	26.0000			1.39777
$347$	12.7279	−	12.7279i	0.683271	−	0.683271i	−0.277465	−	0.960736i	$-0.589494\pi$
$347$	12.7279	−	12.7279i	0.683271	−	0.683271i	0.960736	+	0.277465i	$0.0894943\pi$
$348$		0			0
$349$			8.00000i			0.428230i	0.976808	+	0.214115i	$0.0686868\pi$
$349$			8.00000i			0.428230i	−0.976808	+	0.214115i	$0.931313\pi$
$350$	16.9706	−	12.7279i	0.907115	−	0.680336i
$351$		0			0
$352$	15.0000	+	15.0000i	0.799503	+	0.799503i
$353$	−1.41421	−	1.41421i	−0.0752710	−	0.0752710i	0.668469	−	0.743740i	$-0.266950\pi$
$353$	−1.41421	−	1.41421i	−0.0752710	−	0.0752710i	−0.743740	+	0.668469i	$0.766950\pi$
$354$		0			0
$355$	8.00000	+	24.0000i	0.424596	+	1.27379i
$356$			5.65685i			0.299813i
$357$		0			0
$358$	10.0000	−	10.0000i	0.528516	−	0.528516i
$359$	35.3553			1.86598			0.932992	−	0.359898i	$-0.117188\pi$
$359$	35.3553			1.86598			0.932992	+	0.359898i	$0.117188\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−9.89949	+	9.89949i	−0.520306	+	0.520306i
$363$		0			0
$364$		−	12.0000i		−	0.628971i
$365$	−1.41421	+	2.82843i	−0.0740233	+	0.148047i
$366$		0			0
$367$	−21.0000	−	21.0000i	−1.09619	−	1.09619i	−0.994852	−	0.101339i	$-0.967687\pi$
$367$	−21.0000	−	21.0000i	−1.09619	−	1.09619i	−0.101339	−	0.994852i	$-0.532313\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$			25.4558i			1.32160i
$372$		0			0
$373$	−6.00000	+	6.00000i	−0.310668	+	0.310668i	−0.845168	−	0.534500i	$-0.820500\pi$
$373$	−6.00000	+	6.00000i	−0.310668	+	0.310668i	0.534500	+	0.845168i	$0.320500\pi$
$374$		0			0
$375$		0			0
$376$	24.0000			1.23771
$377$	5.65685	−	5.65685i	0.291343	−	0.291343i
$378$		0			0
$379$		−	20.0000i		−	1.02733i	−0.857991	−	0.513665i	$-0.828287\pi$
$379$		−	20.0000i		−	1.02733i	0.857991	−	0.513665i	$-0.171713\pi$
$380$	−2.12132	+	0.707107i	−0.108821	+	0.0362738i
$381$		0			0
$382$	5.00000	+	5.00000i	0.255822	+	0.255822i
$383$	8.48528	+	8.48528i	0.433578	+	0.433578i	0.889843	−	0.456266i	$-0.150813\pi$
$383$	8.48528	+	8.48528i	0.433578	+	0.433578i	−0.456266	+	0.889843i	$0.650813\pi$
$384$		0			0
$385$	−18.0000	+	36.0000i	−0.917365	+	1.83473i
$386$		−	19.7990i		−	1.00774i
$387$		0			0
$388$		0			0
$389$	1.41421			0.0717035			0.0358517	−	0.999357i	$-0.488586\pi$
$389$	1.41421			0.0717035			0.0358517	+	0.999357i	$0.488586\pi$
$390$		0			0
$391$		0			0
$392$	23.3345	−	23.3345i	1.17857	−	1.17857i
$393$		0			0
$394$		−	6.00000i		−	0.302276i
$395$	2.82843	+	8.48528i	0.142314	+	0.426941i
$396$		0			0
$397$	7.00000	+	7.00000i	0.351320	+	0.351320i	0.860601	−	0.509281i	$-0.170088\pi$
$397$	7.00000	+	7.00000i	0.351320	+	0.351320i	−0.509281	+	0.860601i	$0.670088\pi$
$398$	−9.89949	−	9.89949i	−0.496217	−	0.496217i
$399$		0			0
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$			2.82843i			0.141245i	0.997503	+	0.0706225i	$0.0224986\pi$
$401$			2.82843i			0.141245i	−0.997503	+	0.0706225i	$0.977501\pi$
$402$		0			0
$403$	16.0000	−	16.0000i	0.797017	−	0.797017i
$404$	12.7279			0.633238
$405$		0			0
$406$	12.0000			0.595550
$407$		0			0
$408$		0			0
$409$		−	10.0000i		−	0.494468i	−0.968956	−	0.247234i	$-0.920478\pi$
$409$		−	10.0000i		−	0.494468i	0.968956	−	0.247234i	$-0.0795217\pi$
$410$	−11.3137	−	5.65685i	−0.558744	−	0.279372i
$411$		0			0
$412$	10.0000	+	10.0000i	0.492665	+	0.492665i
$413$	−25.4558	−	25.4558i	−1.25260	−	1.25260i
$414$		0			0
$415$	−20.0000	−	10.0000i	−0.981761	−	0.490881i
$416$		−	14.1421i		−	0.693375i
$417$		0			0
$418$	−3.00000	+	3.00000i	−0.146735	+	0.146735i
$419$	26.8701			1.31269			0.656344	−	0.754462i	$-0.272102\pi$
$419$	26.8701			1.31269			0.656344	+	0.754462i	$0.272102\pi$
$420$		0			0
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	−14.1421	+	14.1421i	−0.688428	+	0.688428i
$423$		0			0
$424$			18.0000i			0.874157i
$425$		0			0
$426$		0			0
$427$	42.0000	+	42.0000i	2.03252	+	2.03252i
$428$	5.65685	+	5.65685i	0.273434	+	0.273434i
$429$		0			0
$430$	−7.00000	−	21.0000i	−0.337570	−	1.01271i
$431$			19.7990i			0.953684i	0.878989	+	0.476842i	$0.158219\pi$
$431$			19.7990i			0.953684i	−0.878989	+	0.476842i	$0.841781\pi$
$432$		0			0
$433$	18.0000	−	18.0000i	0.865025	−	0.865025i	−0.126892	−	0.991917i	$-0.540500\pi$
$433$	18.0000	−	18.0000i	0.865025	−	0.865025i	0.991917	+	0.126892i	$0.0405001\pi$
$434$	33.9411			1.62923
$435$		0			0
$436$	−10.0000			−0.478913
$437$		0			0
$438$		0			0
$439$			12.0000i			0.572729i	0.958121	+	0.286364i	$0.0924468\pi$
$439$			12.0000i			0.572729i	−0.958121	+	0.286364i	$0.907553\pi$
$440$	−12.7279	+	25.4558i	−0.606780	+	1.21356i
$441$		0			0
$442$		0			0
$443$	25.4558	+	25.4558i	1.20944	+	1.20944i	0.971207	+	0.238236i	$0.0765693\pi$
$443$	25.4558	+	25.4558i	1.20944	+	1.20944i	0.238236	+	0.971207i	$0.423431\pi$
$444$		0			0
$445$	−12.0000	+	4.00000i	−0.568855	+	0.189618i
$446$			2.82843i			0.133930i
$447$		0			0
$448$	21.0000	−	21.0000i	0.992157	−	0.992157i
$449$	−28.2843			−1.33482			−0.667409	−	0.744692i	$-0.732597\pi$
$449$	−28.2843			−1.33482			−0.667409	+	0.744692i	$0.732597\pi$
$450$		0			0
$451$	24.0000			1.13012
$452$	4.24264	−	4.24264i	0.199557	−	0.199557i
$453$		0			0
$454$			12.0000i			0.563188i
$455$	25.4558	−	8.48528i	1.19339	−	0.397796i
$456$		0			0
$457$	−17.0000	−	17.0000i	−0.795226	−	0.795226i	0.187112	−	0.982339i	$-0.440087\pi$
$457$	−17.0000	−	17.0000i	−0.795226	−	0.795226i	−0.982339	+	0.187112i	$0.940087\pi$
$458$	14.1421	+	14.1421i	0.660819	+	0.660819i
$459$		0			0
$460$		0			0
$461$		−	35.3553i		−	1.64666i	−0.567561	−	0.823331i	$-0.692113\pi$
$461$		−	35.3553i		−	1.64666i	0.567561	−	0.823331i	$-0.307887\pi$
$462$		0			0
$463$	−9.00000	+	9.00000i	−0.418265	+	0.418265i	−0.884606	−	0.466340i	$-0.845572\pi$
$463$	−9.00000	+	9.00000i	−0.418265	+	0.418265i	0.466340	+	0.884606i	$0.345572\pi$
$464$	2.82843			0.131306
$465$		0			0
$466$	18.0000			0.833834
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	−0.875632	−	0.482980i	$-0.839555\pi$
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	0.482980	+	0.875632i	$0.339555\pi$
$468$		0			0
$469$		−	36.0000i		−	1.66233i
$470$	5.65685	+	16.9706i	0.260931	+	0.782794i
$471$		0			0
$472$	−18.0000	−	18.0000i	−0.828517	−	0.828517i
$473$	29.6985	+	29.6985i	1.36554	+	1.36554i
$474$		0			0
$475$	−3.00000	−	4.00000i	−0.137649	−	0.183533i
$476$		0			0
$477$		0			0
$478$	1.00000	−	1.00000i	0.0457389	−	0.0457389i
$479$	15.5563			0.710788			0.355394	−	0.934717i	$-0.384347\pi$
$479$	15.5563			0.710788			0.355394	+	0.934717i	$0.384347\pi$
$480$		0			0
$481$		0			0
$482$	4.24264	−	4.24264i	0.193247	−	0.193247i
$483$		0			0
$484$		−	7.00000i		−	0.318182i
$485$		0			0
$486$		0			0
$487$	−14.0000	−	14.0000i	−0.634401	−	0.634401i	0.314768	−	0.949169i	$-0.398073\pi$
$487$	−14.0000	−	14.0000i	−0.634401	−	0.634401i	−0.949169	+	0.314768i	$0.898073\pi$
$488$	29.6985	+	29.6985i	1.34439	+	1.34439i
$489$		0			0
$490$	22.0000	+	11.0000i	0.993859	+	0.496929i
$491$		−	12.7279i		−	0.574403i	−0.957870	−	0.287202i	$-0.907275\pi$
$491$		−	12.7279i		−	0.574403i	0.957870	−	0.287202i	$-0.0927249\pi$
$492$		0			0
$493$		0			0
$494$	2.82843			0.127257
$495$		0			0
$496$	8.00000			0.359211
$497$	−33.9411	+	33.9411i	−1.52247	+	1.52247i
$498$		0			0
$499$		−	26.0000i		−	1.16392i	−0.813217	−	0.581960i	$-0.802286\pi$
$499$		−	26.0000i		−	1.16392i	0.813217	−	0.581960i	$-0.197714\pi$
$500$	−9.19239	−	6.36396i	−0.411096	−	0.284605i
$501$		0			0
$502$	−5.00000	−	5.00000i	−0.223161	−	0.223161i
$503$	−1.41421	−	1.41421i	−0.0630567	−	0.0630567i	0.674875	−	0.737932i	$-0.264197\pi$
$503$	−1.41421	−	1.41421i	−0.0630567	−	0.0630567i	−0.737932	+	0.674875i	$0.764197\pi$
$504$		0			0
$505$	9.00000	+	27.0000i	0.400495	+	1.20148i
$506$		0			0
$507$		0			0
$508$	12.0000	−	12.0000i	0.532414	−	0.532414i
$509$	−39.5980			−1.75515			−0.877575	−	0.479440i	$-0.840840\pi$
$509$	−39.5980			−1.75515			−0.877575	+	0.479440i	$0.840840\pi$
$510$		0			0
$511$	−6.00000			−0.265424
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$		0			0
$514$		−	26.0000i		−	1.14681i
$515$	−14.1421	+	28.2843i	−0.623177	+	1.24635i
$516$		0			0
$517$	−24.0000	−	24.0000i	−1.05552	−	1.05552i
$518$		0			0
$519$		0			0
$520$	18.0000	−	6.00000i	0.789352	−	0.263117i
$521$			19.7990i			0.867409i	0.901055	+	0.433705i	$0.142794\pi$
$521$			19.7990i			0.867409i	−0.901055	+	0.433705i	$0.857206\pi$
$522$		0			0
$523$	−16.0000	+	16.0000i	−0.699631	+	0.699631i	−0.964331	−	0.264700i	$-0.914727\pi$
$523$	−16.0000	+	16.0000i	−0.699631	+	0.699631i	0.264700	+	0.964331i	$0.414727\pi$
$524$	18.3848			0.803143
$525$		0			0
$526$	22.0000			0.959246
$527$		0			0
$528$		0			0
$529$		−	23.0000i		−	1.00000i
$530$	−12.7279	+	4.24264i	−0.552866	+	0.184289i
$531$		0			0
$532$	−3.00000	−	3.00000i	−0.130066	−	0.130066i
$533$	−11.3137	−	11.3137i	−0.490051	−	0.490051i
$534$		0			0
$535$	−8.00000	+	16.0000i	−0.345870	+	0.691740i
$536$		−	25.4558i		−	1.09952i
$537$		0			0
$538$	−18.0000	+	18.0000i	−0.776035	+	0.776035i
$539$	−46.6690			−2.01018
$540$		0			0
$541$	−36.0000			−1.54776			−0.773880	−	0.633332i	$-0.781687\pi$
$541$	−36.0000			−1.54776			−0.773880	+	0.633332i	$0.781687\pi$
$542$	−15.5563	+	15.5563i	−0.668202	+	0.668202i
$543$		0			0
$544$		0			0
$545$	−7.07107	−	21.2132i	−0.302891	−	0.908674i
$546$		0			0
$547$	30.0000	+	30.0000i	1.28271	+	1.28271i	0.939121	+	0.343586i	$0.111642\pi$
$547$	30.0000	+	30.0000i	1.28271	+	1.28271i	0.343586	+	0.939121i	$0.388358\pi$
$548$	2.82843	+	2.82843i	0.120824	+	0.120824i
$549$		0			0
$550$	−21.0000	−	3.00000i	−0.895443	−	0.127920i
$551$		−	2.82843i		−	0.120495i
$552$		0			0
$553$	−12.0000	+	12.0000i	−0.510292	+	0.510292i
$554$	21.2132			0.901263
$555$		0			0
$556$	10.0000			0.424094
$557$	12.7279	−	12.7279i	0.539299	−	0.539299i	−0.384024	−	0.923323i	$-0.625462\pi$
$557$	12.7279	−	12.7279i	0.539299	−	0.539299i	0.923323	+	0.384024i	$0.125462\pi$
$558$		0			0
$559$		−	28.0000i		−	1.18427i
$560$	8.48528	+	4.24264i	0.358569	+	0.179284i
$561$		0			0
$562$	−18.0000	−	18.0000i	−0.759284	−	0.759284i
$563$	−14.1421	−	14.1421i	−0.596020	−	0.596020i	0.343231	−	0.939251i	$-0.388479\pi$
$563$	−14.1421	−	14.1421i	−0.596020	−	0.596020i	−0.939251	+	0.343231i	$0.888479\pi$
$564$		0			0
$565$	12.0000	+	6.00000i	0.504844	+	0.252422i
$566$			29.6985i			1.24832i
$567$		0			0
$568$	−24.0000	+	24.0000i	−1.00702	+	1.00702i
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$		0			0
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$	−8.48528	+	8.48528i	−0.354787	+	0.354787i
$573$		0			0
$574$		−	24.0000i		−	1.00174i
$575$		0			0
$576$		0			0
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	0.869177	−	0.494502i	$-0.164649\pi$
$577$	9.00000	+	9.00000i	0.374675	+	0.374675i	−0.494502	+	0.869177i	$0.664649\pi$
$578$	−12.0208	−	12.0208i	−0.500000	−	0.500000i
$579$		0			0
$580$	−2.00000	−	6.00000i	−0.0830455	−	0.249136i
$581$		−	42.4264i		−	1.76014i
$582$		0			0
$583$	18.0000	−	18.0000i	0.745484	−	0.745484i
$584$	−4.24264			−0.175562
$585$		0			0
$586$	−18.0000			−0.743573
$587$	−19.7990	+	19.7990i	−0.817192	+	0.817192i	−0.985700	−	0.168508i	$-0.946105\pi$
$587$	−19.7990	+	19.7990i	−0.817192	+	0.817192i	0.168508	+	0.985700i	$0.446105\pi$
$588$		0			0
$589$		−	8.00000i		−	0.329634i
$590$	8.48528	−	16.9706i	0.349334	−	0.698667i
$591$		0			0
$592$		0			0
$593$	−5.65685	−	5.65685i	−0.232299	−	0.232299i	0.581353	−	0.813652i	$-0.302524\pi$
$593$	−5.65685	−	5.65685i	−0.232299	−	0.232299i	−0.813652	+	0.581353i	$0.802524\pi$
$594$		0			0
$595$		0			0
$596$			7.07107i			0.289642i
$597$		0			0
$598$		0			0
$599$	−14.1421			−0.577832			−0.288916	−	0.957354i	$-0.593295\pi$
$599$	−14.1421			−0.577832			−0.288916	+	0.957354i	$0.593295\pi$
$600$		0			0
$601$	34.0000			1.38689			0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000			1.38689			0.693444	+	0.720510i	$0.256092\pi$
$602$	29.6985	−	29.6985i	1.21042	−	1.21042i
$603$		0			0
$604$		−	16.0000i		−	0.651031i
$605$	14.8492	−	4.94975i	0.603708	−	0.201236i
$606$		0			0
$607$	14.0000	+	14.0000i	0.568242	+	0.568242i	0.931636	−	0.363393i	$-0.118382\pi$
$607$	14.0000	+	14.0000i	0.568242	+	0.568242i	−0.363393	+	0.931636i	$0.618382\pi$
$608$	−3.53553	−	3.53553i	−0.143385	−	0.143385i
$609$		0			0
$610$	−14.0000	+	28.0000i	−0.566843	+	1.13369i
$611$			22.6274i			0.915407i
$612$		0			0
$613$	11.0000	−	11.0000i	0.444286	−	0.444286i	−0.449164	−	0.893449i	$-0.648278\pi$
$613$	11.0000	−	11.0000i	0.444286	−	0.444286i	0.893449	+	0.449164i	$0.148278\pi$
$614$	−31.1127			−1.25561
$615$		0			0
$616$	−54.0000			−2.17572
$617$	−22.6274	+	22.6274i	−0.910946	+	0.910946i	−0.996347	−	0.0854011i	$-0.972783\pi$
$617$	−22.6274	+	22.6274i	−0.910946	+	0.910946i	0.0854011	+	0.996347i	$0.472783\pi$
$618$		0			0
$619$			30.0000i			1.20580i	0.797816	+	0.602901i	$0.205989\pi$
$619$			30.0000i			1.20580i	−0.797816	+	0.602901i	$0.794011\pi$
$620$	−5.65685	−	16.9706i	−0.227185	−	0.681554i
$621$		0			0
$622$	5.00000	+	5.00000i	0.200482	+	0.200482i
$623$	−16.9706	−	16.9706i	−0.679911	−	0.679911i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			7.07107i			0.282617i
$627$		0			0
$628$	−11.0000	+	11.0000i	−0.438948	+	0.438948i
$629$		0			0
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$	−8.48528	+	8.48528i	−0.337526	+	0.337526i
$633$		0			0
$634$		−	10.0000i		−	0.397151i
$635$	33.9411	+	16.9706i	1.34691	+	0.673456i
$636$		0			0
$637$	22.0000	+	22.0000i	0.871672	+	0.871672i
$638$	−8.48528	−	8.48528i	−0.335936	−	0.335936i
$639$		0			0
$640$	−6.00000	−	3.00000i	−0.237171	−	0.118585i
$641$		−	33.9411i		−	1.34059i	−0.742093	−	0.670297i	$-0.766167\pi$
$641$		−	33.9411i		−	1.34059i	0.742093	−	0.670297i	$-0.233833\pi$
$642$		0			0
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	−0.987262	−	0.159103i	$-0.949140\pi$
$643$	−21.0000	+	21.0000i	−0.828159	+	0.828159i	0.159103	+	0.987262i	$0.449140\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.7279	−	12.7279i	0.500386	−	0.500386i	−0.411172	−	0.911558i	$-0.634880\pi$
$647$	12.7279	−	12.7279i	0.500386	−	0.500386i	0.911558	+	0.411172i	$0.134880\pi$
$648$		0			0
$649$			36.0000i			1.41312i
$650$	8.48528	+	11.3137i	0.332820	+	0.443760i
$651$		0			0
$652$	−1.00000	−	1.00000i	−0.0391630	−	0.0391630i
$653$	8.48528	+	8.48528i	0.332055	+	0.332055i	0.853366	−	0.521312i	$-0.174557\pi$
$653$	8.48528	+	8.48528i	0.332055	+	0.332055i	−0.521312	+	0.853366i	$0.674557\pi$
$654$		0			0
$655$	13.0000	+	39.0000i	0.507952	+	1.52386i
$656$		−	5.65685i		−	0.220863i
$657$		0			0
$658$	−24.0000	+	24.0000i	−0.935617	+	0.935617i
$659$	16.9706			0.661079			0.330540	−	0.943792i	$-0.392769\pi$
$659$	16.9706			0.661079			0.330540	+	0.943792i	$0.392769\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	14.1421	−	14.1421i	0.549650	−	0.549650i
$663$		0			0
$664$		−	30.0000i		−	1.16423i
$665$	4.24264	−	8.48528i	0.164523	−	0.329045i
$666$		0			0
$667$		0			0
$668$	8.48528	+	8.48528i	0.328305	+	0.328305i
$669$		0			0
$670$	18.0000	−	6.00000i	0.695401	−	0.231800i
$671$		−	59.3970i		−	2.29299i
$672$		0			0
$673$	12.0000	−	12.0000i	0.462566	−	0.462566i	−0.436930	−	0.899496i	$-0.643934\pi$
$673$	12.0000	−	12.0000i	0.462566	−	0.462566i	0.899496	+	0.436930i	$0.143934\pi$
$674$	−5.65685			−0.217894
$675$		0			0
$676$	−5.00000			−0.192308
$677$	12.7279	−	12.7279i	0.489174	−	0.489174i	−0.418872	−	0.908045i	$-0.637574\pi$
$677$	12.7279	−	12.7279i	0.489174	−	0.489174i	0.908045	+	0.418872i	$0.137574\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−24.0000	−	24.0000i	−0.919007	−	0.919007i
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$		0			0
$685$	−4.00000	+	8.00000i	−0.152832	+	0.305664i
$686$			16.9706i			0.647939i
$687$		0			0
$688$	7.00000	−	7.00000i	0.266872	−	0.266872i
$689$	−16.9706			−0.646527
$690$		0			0
$691$	2.00000			0.0760836			0.0380418	−	0.999276i	$-0.487888\pi$
$691$	2.00000			0.0760836			0.0380418	+	0.999276i	$0.487888\pi$
$692$	18.3848	−	18.3848i	0.698884	−	0.698884i
$693$		0			0
$694$			18.0000i			0.683271i
$695$	7.07107	+	21.2132i	0.268221	+	0.804663i
$696$		0			0
$697$		0			0
$698$	−5.65685	−	5.65685i	−0.214115	−	0.214115i
$699$		0			0
$700$	3.00000	−	21.0000i	0.113389	−	0.793725i
$701$		−	1.41421i		−	0.0534141i	−0.999643	−	0.0267071i	$-0.991498\pi$
$701$		−	1.41421i		−	0.0534141i	0.999643	−	0.0267071i	$-0.00850213\pi$
$702$		0			0
$703$		0			0
$704$	−29.6985			−1.11930
$705$		0			0
$706$	2.00000			0.0752710
$707$	−38.1838	+	38.1838i	−1.43605	+	1.43605i
$708$		0			0
$709$			4.00000i			0.150223i	0.997175	+	0.0751116i	$0.0239313\pi$
$709$			4.00000i			0.150223i	−0.997175	+	0.0751116i	$0.976069\pi$
$710$	−22.6274	−	11.3137i	−0.849192	−	0.424596i
$711$		0			0
$712$	−12.0000	−	12.0000i	−0.449719	−	0.449719i
$713$		0			0
$714$		0			0
$715$	−24.0000	−	12.0000i	−0.897549	−	0.448775i
$716$		−	14.1421i		−	0.528516i
$717$		0			0
$718$	−25.0000	+	25.0000i	−0.932992	+	0.932992i
$719$	1.41421			0.0527413			0.0263706	−	0.999652i	$-0.491605\pi$
$719$	1.41421			0.0527413			0.0263706	+	0.999652i	$0.491605\pi$
$720$		0			0
$721$	−60.0000			−2.23452
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$		0			0
$724$			14.0000i			0.520306i
$725$	11.3137	−	8.48528i	0.420181	−	0.315135i
$726$		0			0
$727$	21.0000	+	21.0000i	0.778847	+	0.778847i	0.979635	−	0.200788i	$-0.0643502\pi$
$727$	21.0000	+	21.0000i	0.778847	+	0.778847i	−0.200788	+	0.979635i	$0.564350\pi$
$728$	25.4558	+	25.4558i	0.943456	+	0.943456i
$729$		0			0
$730$	−1.00000	−	3.00000i	−0.0370117	−	0.111035i
$731$		0			0
$732$		0			0
$733$	−15.0000	+	15.0000i	−0.554038	+	0.554038i	−0.927604	−	0.373566i	$-0.878135\pi$
$733$	−15.0000	+	15.0000i	−0.554038	+	0.554038i	0.373566	+	0.927604i	$0.378135\pi$
$734$	29.6985			1.09619
$735$		0			0
$736$		0			0
$737$	−25.4558	+	25.4558i	−0.937678	+	0.937678i
$738$		0			0
$739$		−	52.0000i		−	1.91285i	−0.291977	−	0.956425i	$-0.594313\pi$
$739$		−	52.0000i		−	1.91285i	0.291977	−	0.956425i	$-0.405687\pi$
$740$		0			0
$741$		0			0
$742$	−18.0000	−	18.0000i	−0.660801	−	0.660801i
$743$	28.2843	+	28.2843i	1.03765	+	1.03765i	0.999263	+	0.0383863i	$0.0122217\pi$
$743$	28.2843	+	28.2843i	1.03765	+	1.03765i	0.0383863	+	0.999263i	$0.487778\pi$
$744$		0			0
$745$	−15.0000	+	5.00000i	−0.549557	+	0.183186i
$746$		−	8.48528i		−	0.310668i
$747$		0			0
$748$		0			0
$749$	−33.9411			−1.24018
$750$		0			0
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$	−5.65685	+	5.65685i	−0.206284	+	0.206284i
$753$		0			0
$754$			8.00000i			0.291343i
$755$	33.9411	−	11.3137i	1.23524	−	0.411748i
$756$		0			0
$757$	−7.00000	−	7.00000i	−0.254419	−	0.254419i	0.568360	−	0.822780i	$-0.307578\pi$
$757$	−7.00000	−	7.00000i	−0.254419	−	0.254419i	−0.822780	+	0.568360i	$0.807578\pi$
$758$	14.1421	+	14.1421i	0.513665	+	0.513665i
$759$		0			0
$760$	3.00000	−	6.00000i	0.108821	−	0.217643i
$761$			24.0416i			0.871508i	0.900066	+	0.435754i	$0.143518\pi$
$761$			24.0416i			0.871508i	−0.900066	+	0.435754i	$0.856482\pi$
$762$		0			0
$763$	30.0000	−	30.0000i	1.08607	−	1.08607i
$764$	7.07107			0.255822
$765$		0			0
$766$	−12.0000			−0.433578
$767$	16.9706	−	16.9706i	0.612772	−	0.612772i
$768$		0			0
$769$			16.0000i			0.576975i	0.957484	+	0.288487i	$0.0931523\pi$
$769$			16.0000i			0.576975i	−0.957484	+	0.288487i	$0.906848\pi$
$770$	−12.7279	−	38.1838i	−0.458682	−	1.37605i
$771$		0			0
$772$	−14.0000	−	14.0000i	−0.503871	−	0.503871i
$773$	−32.5269	−	32.5269i	−1.16991	−	1.16991i	−0.982230	−	0.187682i	$-0.939903\pi$
$773$	−32.5269	−	32.5269i	−1.16991	−	1.16991i	−0.187682	−	0.982230i	$-0.560097\pi$
$774$		0			0
$775$	32.0000	−	24.0000i	1.14947	−	0.862105i
$776$		0			0
$777$		0			0
$778$	−1.00000	+	1.00000i	−0.0358517	+	0.0358517i
$779$	−5.65685			−0.202678
$780$		0			0
$781$	48.0000			1.71758
$782$		0			0
$783$		0			0
$784$			11.0000i			0.392857i
$785$	−31.1127	−	15.5563i	−1.11046	−	0.555230i
$786$		0			0
$787$	−24.0000	−	24.0000i	−0.855508	−	0.855508i	0.135297	−	0.990805i	$-0.456801\pi$
$787$	−24.0000	−	24.0000i	−0.855508	−	0.855508i	−0.990805	+	0.135297i	$0.956801\pi$
$788$	−4.24264	−	4.24264i	−0.151138	−	0.151138i
$789$		0			0
$790$	−8.00000	−	4.00000i	−0.284627	−	0.142314i
$791$			25.4558i			0.905106i
$792$		0			0
$793$	−28.0000	+	28.0000i	−0.994309	+	0.994309i
$794$	−9.89949			−0.351320
$795$		0			0
$796$	−14.0000			−0.496217
$797$	−4.24264	+	4.24264i	−0.150282	+	0.150282i	−0.778244	−	0.627962i	$-0.783889\pi$
$797$	−4.24264	+	4.24264i	−0.150282	+	0.150282i	0.627962	+	0.778244i	$0.283889\pi$
$798$		0			0
$799$		0			0
$800$	3.53553	−	24.7487i	0.125000	−	0.875000i
$801$		0			0
$802$	−2.00000	−	2.00000i	−0.0706225	−	0.0706225i
$803$	4.24264	+	4.24264i	0.149720	+	0.149720i
$804$		0			0
$805$		0			0
$806$			22.6274i			0.797017i
$807$		0			0
$808$	−27.0000	+	27.0000i	−0.949857	+	0.949857i
$809$	−18.3848			−0.646374			−0.323187	−	0.946335i	$-0.604754\pi$
$809$	−18.3848			−0.646374			−0.323187	+	0.946335i	$0.604754\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	8.48528	−	8.48528i	0.297775	−	0.297775i
$813$		0			0
$814$		0			0
$815$	1.41421	−	2.82843i	0.0495377	−	0.0990755i
$816$		0			0
$817$	−7.00000	−	7.00000i	−0.244899	−	0.244899i
$818$	7.07107	+	7.07107i	0.247234	+	0.247234i
$819$		0			0
$820$	−12.0000	+	4.00000i	−0.419058	+	0.139686i
$821$		−	35.3553i		−	1.23391i	−0.786998	−	0.616955i	$-0.788366\pi$
$821$		−	35.3553i		−	1.23391i	0.786998	−	0.616955i	$-0.211634\pi$
$822$		0			0
$823$	−9.00000	+	9.00000i	−0.313720	+	0.313720i	−0.846349	−	0.532629i	$-0.821204\pi$
$823$	−9.00000	+	9.00000i	−0.313720	+	0.313720i	0.532629	+	0.846349i	$0.321204\pi$
$824$	−42.4264			−1.47799
$825$		0			0
$826$	36.0000			1.25260
$827$	16.9706	−	16.9706i	0.590124	−	0.590124i	−0.347541	−	0.937665i	$-0.612983\pi$
$827$	16.9706	−	16.9706i	0.590124	−	0.590124i	0.937665	+	0.347541i	$0.112983\pi$
$828$		0			0
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$	21.2132	−	7.07107i	0.736321	−	0.245440i
$831$		0			0
$832$	14.0000	+	14.0000i	0.485363	+	0.485363i
$833$		0			0
$834$		0			0
$835$	−12.0000	+	24.0000i	−0.415277	+	0.830554i
$836$			4.24264i			0.146735i
$837$		0			0
$838$	−19.0000	+	19.0000i	−0.656344	+	0.656344i
$839$	−11.3137			−0.390593			−0.195296	−	0.980744i	$-0.562567\pi$
$839$	−11.3137			−0.390593			−0.195296	+	0.980744i	$0.562567\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	−18.3848	+	18.3848i	−0.633581	+	0.633581i
$843$		0			0
$844$			20.0000i			0.688428i
$845$	−3.53553	−	10.6066i	−0.121626	−	0.364878i
$846$		0			0
$847$	21.0000	+	21.0000i	0.721569	+	0.721569i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−21.0000	+	21.0000i	−0.719026	+	0.719026i	−0.968406	−	0.249380i	$-0.919773\pi$
$853$	−21.0000	+	21.0000i	−0.719026	+	0.719026i	0.249380	+	0.968406i	$0.419773\pi$
$854$	−59.3970			−2.03252
$855$		0			0
$856$	−24.0000			−0.820303
$857$	−24.0416	+	24.0416i	−0.821246	+	0.821246i	−0.986287	−	0.165040i	$-0.947225\pi$
$857$	−24.0416	+	24.0416i	−0.821246	+	0.821246i	0.165040	+	0.986287i	$0.447225\pi$
$858$		0			0
$859$			44.0000i			1.50126i	0.660722	+	0.750630i	$0.270250\pi$
$859$			44.0000i			1.50126i	−0.660722	+	0.750630i	$0.729750\pi$
$860$	−19.7990	−	9.89949i	−0.675140	−	0.337570i
$861$		0			0
$862$	−14.0000	−	14.0000i	−0.476842	−	0.476842i
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	0.934265	−	0.356580i	$-0.116057\pi$
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	−0.356580	+	0.934265i	$0.616057\pi$
$864$		0			0
$865$	52.0000	+	26.0000i	1.76805	+	0.884027i
$866$			25.4558i			0.865025i
$867$		0			0
$868$	24.0000	−	24.0000i	0.814613	−	0.814613i
$869$	16.9706			0.575687
$870$		0			0
$871$	24.0000			0.813209
$872$	21.2132	−	21.2132i	0.718370	−	0.718370i
$873$		0			0
$874$		0			0
$875$	46.6690	−	8.48528i	1.57770	−	0.286855i
$876$		0			0
$877$	−22.0000	−	22.0000i	−0.742887	−	0.742887i	0.230245	−	0.973133i	$-0.426047\pi$
$877$	−22.0000	−	22.0000i	−0.742887	−	0.742887i	−0.973133	+	0.230245i	$0.926047\pi$
$878$	−8.48528	−	8.48528i	−0.286364	−	0.286364i
$879$		0			0
$880$	−3.00000	−	9.00000i	−0.101130	−	0.303390i
$881$		−	24.0416i		−	0.809983i	−0.914320	−	0.404992i	$-0.867274\pi$
$881$		−	24.0416i		−	0.809983i	0.914320	−	0.404992i	$-0.132726\pi$
$882$		0			0
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	−0.259135	−	0.965841i	$-0.583437\pi$
$883$	21.0000	−	21.0000i	0.706706	−	0.706706i	0.965841	+	0.259135i	$0.0834374\pi$
$884$		0			0
$885$		0			0
$886$	−36.0000			−1.20944
$887$	−22.6274	+	22.6274i	−0.759754	+	0.759754i	−0.976277	−	0.216523i	$-0.930528\pi$
$887$	−22.6274	+	22.6274i	−0.759754	+	0.759754i	0.216523	+	0.976277i	$0.430528\pi$
$888$		0			0
$889$			72.0000i			2.41480i
$890$	5.65685	−	11.3137i	0.189618	−	0.379236i
$891$		0			0
$892$	2.00000	+	2.00000i	0.0669650	+	0.0669650i
$893$	5.65685	+	5.65685i	0.189299	+	0.189299i
$894$		0			0
$895$	30.0000	−	10.0000i	1.00279	−	0.334263i
$896$		−	12.7279i		−	0.425210i
$897$		0			0
$898$	20.0000	−	20.0000i	0.667409	−	0.667409i
$899$	22.6274			0.754667
$900$		0			0
$901$		0			0
$902$	−16.9706	+	16.9706i	−0.565058	+	0.565058i
$903$		0			0
$904$			18.0000i			0.598671i
$905$	−29.6985	+	9.89949i	−0.987211	+	0.329070i
$906$		0			0
$907$	−24.0000	−	24.0000i	−0.796907	−	0.796907i	0.185700	−	0.982607i	$-0.440545\pi$
$907$	−24.0000	−	24.0000i	−0.796907	−	0.796907i	−0.982607	+	0.185700i	$0.940545\pi$
$908$	8.48528	+	8.48528i	0.281594	+	0.281594i
$909$		0			0
$910$	−12.0000	+	24.0000i	−0.397796	+	0.795592i
$911$		−	28.2843i		−	0.937100i	−0.883437	−	0.468550i	$-0.844777\pi$
$911$		−	28.2843i		−	0.937100i	0.883437	−	0.468550i	$-0.155223\pi$
$912$		0			0
$913$	−30.0000	+	30.0000i	−0.992855	+	0.992855i
$914$	24.0416			0.795226
$915$		0			0
$916$	20.0000			0.660819
$917$	−55.1543	+	55.1543i	−1.82136	+	1.82136i
$918$		0			0
$919$			32.0000i			1.05558i	0.849374	+	0.527791i	$0.176980\pi$
$919$			32.0000i			1.05558i	−0.849374	+	0.527791i	$0.823020\pi$
$920$		0			0
$921$		0			0
$922$	25.0000	+	25.0000i	0.823331	+	0.823331i
$923$	−22.6274	−	22.6274i	−0.744791	−	0.744791i
$924$		0			0
$925$		0			0
$926$		−	12.7279i		−	0.418265i
$927$		0			0
$928$	10.0000	−	10.0000i	0.328266	−	0.328266i
$929$	−9.89949			−0.324792			−0.162396	−	0.986726i	$-0.551922\pi$
$929$	−9.89949			−0.324792			−0.162396	+	0.986726i	$0.551922\pi$
$930$		0			0
$931$	11.0000			0.360510
$932$	12.7279	−	12.7279i	0.416917	−	0.416917i
$933$		0			0
$934$		−	12.0000i		−	0.392652i
$935$		0			0
$936$		0			0
$937$	5.00000	+	5.00000i	0.163343	+	0.163343i	0.784046	−	0.620703i	$-0.213153\pi$
$937$	5.00000	+	5.00000i	0.163343	+	0.163343i	−0.620703	+	0.784046i	$0.713153\pi$
$938$	25.4558	+	25.4558i	0.831163	+	0.831163i
$939$		0			0
$940$	16.0000	+	8.00000i	0.521862	+	0.260931i
$941$			36.7696i			1.19865i	0.800505	+	0.599327i	$0.204565\pi$
$941$			36.7696i			1.19865i	−0.800505	+	0.599327i	$0.795435\pi$
$942$		0			0
$943$		0			0
$944$	8.48528			0.276172
$945$		0			0
$946$	−42.0000			−1.36554
$947$	29.6985	−	29.6985i	0.965071	−	0.965071i	−0.0343392	−	0.999410i	$-0.510933\pi$
$947$	29.6985	−	29.6985i	0.965071	−	0.965071i	0.999410	+	0.0343392i	$0.0109326\pi$
$948$		0			0
$949$		−	4.00000i		−	0.129845i
$950$	4.94975	+	0.707107i	0.160591	+	0.0229416i
$951$		0			0
$952$		0			0
$953$	7.07107	+	7.07107i	0.229054	+	0.229054i	0.812298	−	0.583243i	$-0.198217\pi$
$953$	7.07107	+	7.07107i	0.229054	+	0.229054i	−0.583243	+	0.812298i	$0.698217\pi$
$954$		0			0
$955$	5.00000	+	15.0000i	0.161796	+	0.485389i
$956$		−	1.41421i		−	0.0457389i
$957$		0			0
$958$	−11.0000	+	11.0000i	−0.355394	+	0.355394i
$959$	−16.9706			−0.548008
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$		0			0
$964$		−	6.00000i		−	0.193247i
$965$	19.7990	−	39.5980i	0.637352	−	1.27470i
$966$		0			0
$967$	−21.0000	−	21.0000i	−0.675314	−	0.675314i	0.283622	−	0.958936i	$-0.408464\pi$
$967$	−21.0000	−	21.0000i	−0.675314	−	0.675314i	−0.958936	+	0.283622i	$0.908464\pi$
$968$	14.8492	+	14.8492i	0.477273	+	0.477273i
$969$		0			0
$970$		0			0
$971$			22.6274i			0.726148i	0.931760	+	0.363074i	$0.118273\pi$
$971$			22.6274i			0.726148i	−0.931760	+	0.363074i	$0.881727\pi$
$972$		0			0
$973$	−30.0000	+	30.0000i	−0.961756	+	0.961756i
$974$	19.7990			0.634401
$975$		0			0
$976$	−14.0000			−0.448129
$977$	1.41421	−	1.41421i	0.0452447	−	0.0452447i	−0.684122	−	0.729367i	$-0.739815\pi$
$977$	1.41421	−	1.41421i	0.0452447	−	0.0452447i	0.729367	+	0.684122i	$0.239815\pi$
$978$		0			0
$979$			24.0000i			0.767043i
$980$	23.3345	−	7.77817i	0.745394	−	0.248465i
$981$		0			0
$982$	9.00000	+	9.00000i	0.287202	+	0.287202i
$983$	14.1421	+	14.1421i	0.451064	+	0.451064i	0.895708	−	0.444644i	$-0.146670\pi$
$983$	14.1421	+	14.1421i	0.451064	+	0.451064i	−0.444644	+	0.895708i	$0.646670\pi$
$984$		0			0
$985$	6.00000	−	12.0000i	0.191176	−	0.382352i
$986$		0			0
$987$		0			0
$988$	2.00000	−	2.00000i	0.0636285	−	0.0636285i
$989$		0			0
$990$		0			0
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$	28.2843	−	28.2843i	0.898027	−	0.898027i
$993$		0			0
$994$		−	48.0000i		−	1.52247i
$995$	−9.89949	−	29.6985i	−0.313835	−	0.941505i
$996$		0			0
$997$	−35.0000	−	35.0000i	−1.10846	−	1.10846i	−0.993353	−	0.115108i	$-0.963279\pi$
$997$	−35.0000	−	35.0000i	−1.10846	−	1.10846i	−0.115108	−	0.993353i	$-0.536721\pi$
$998$	18.3848	+	18.3848i	0.581960	+	0.581960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.a.647.1	✓	4
3.2	odd	2	inner	855.2.n.a.647.2	yes	4
5.3	odd	4	inner	855.2.n.a.818.2	yes	4
15.8	even	4	inner	855.2.n.a.818.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.a.647.1	✓	4	1.1	even	1	trivial
855.2.n.a.647.2	yes	4	3.2	odd	2	inner
855.2.n.a.818.1	yes	4	15.8	even	4	inner
855.2.n.a.818.2	yes	4	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.12132 + 0.707107i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(1.00000 - 2.00000i) q^{10} +4.24264i q^{11} +(2.00000 - 2.00000i) q^{13} +4.24264 q^{14} +1.00000 q^{16} -1.00000i q^{19} +(-0.707107 - 2.12132i) q^{20} +(-3.00000 - 3.00000i) q^{22} +(4.00000 - 3.00000i) q^{25} +2.82843i q^{26} +(3.00000 - 3.00000i) q^{28} +2.82843 q^{29} +8.00000 q^{31} +(3.53553 - 3.53553i) q^{32} +(8.48528 + 4.24264i) q^{35} +(0.707107 + 0.707107i) q^{38} +(6.00000 + 3.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} -4.24264 q^{44} +(-5.65685 + 5.65685i) q^{47} +11.0000i q^{49} +(-0.707107 + 4.94975i) q^{50} +(2.00000 + 2.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-3.00000 - 9.00000i) q^{55} +12.7279i q^{56} +(-2.00000 + 2.00000i) q^{58} +8.48528 q^{59} -14.0000 q^{61} +(-5.65685 + 5.65685i) q^{62} +7.00000i q^{64} +(-2.82843 + 5.65685i) q^{65} +(6.00000 + 6.00000i) q^{67} +(-9.00000 + 3.00000i) q^{70} -11.3137i q^{71} +(1.00000 - 1.00000i) q^{73} +1.00000 q^{76} +(12.7279 - 12.7279i) q^{77} -4.00000i q^{79} +(-2.12132 + 0.707107i) q^{80} +(4.00000 + 4.00000i) q^{82} +(7.07107 + 7.07107i) q^{83} +9.89949i q^{86} +(9.00000 - 9.00000i) q^{88} +5.65685 q^{89} -12.0000 q^{91} -8.00000i q^{94} +(0.707107 + 2.12132i) q^{95} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{7}+O(q^{10}) \) 4 * q - 12 * q^7	\( 4 q - 12 q^{7} + 4 q^{10} + 8 q^{13} + 4 q^{16} - 12 q^{22} + 16 q^{25} + 12 q^{28} + 32 q^{31} + 24 q^{40} + 28 q^{43} + 8 q^{52} - 12 q^{55} - 8 q^{58} - 56 q^{61} + 24 q^{67} - 36 q^{70} + 4 q^{73} + 4 q^{76} + 16 q^{82} + 36 q^{88} - 48 q^{91}+O(q^{100}) \) 4 * q - 12 * q^7 + 4 * q^10 + 8 * q^13 + 4 * q^16 - 12 * q^22 + 16 * q^25 + 12 * q^28 + 32 * q^31 + 24 * q^40 + 28 * q^43 + 8 * q^52 - 12 * q^55 - 8 * q^58 - 56 * q^61 + 24 * q^67 - 36 * q^70 + 4 * q^73 + 4 * q^76 + 16 * q^82 + 36 * q^88 - 48 * q^91

Introduction

L-functions

Modular forms

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