LMFDB - Embedded newform 855.2.n.b.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.b.818.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(3.00000 + 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(3.00000 + 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-2.00000 + 1.00000i) q^{10} +4.24264i q^{11} +(-4.00000 + 4.00000i) q^{13} -4.24264 q^{14} +1.00000 q^{16} +(4.24264 - 4.24264i) q^{17} -1.00000i q^{19} +(-0.707107 + 2.12132i) q^{20} +(-3.00000 - 3.00000i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(4.00000 + 3.00000i) q^{25} -5.65685i q^{26} +(-3.00000 + 3.00000i) q^{28} +2.82843 q^{29} -4.00000 q^{31} +(3.53553 - 3.53553i) q^{32} +6.00000i q^{34} +(4.24264 + 8.48528i) q^{35} +(6.00000 + 6.00000i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-3.00000 - 6.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} -4.24264 q^{44} +6.00000 q^{46} +(-1.41421 + 1.41421i) q^{47} +11.0000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-4.00000 - 4.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-3.00000 + 9.00000i) q^{55} -12.7279i q^{56} +(-2.00000 + 2.00000i) q^{58} -8.48528 q^{59} -2.00000 q^{61} +(2.82843 - 2.82843i) q^{62} +7.00000i q^{64} +(-11.3137 + 5.65685i) q^{65} +(-6.00000 - 6.00000i) q^{67} +(4.24264 + 4.24264i) q^{68} +(-9.00000 - 3.00000i) q^{70} +5.65685i q^{71} +(1.00000 - 1.00000i) q^{73} -8.48528 q^{74} +1.00000 q^{76} +(-12.7279 + 12.7279i) q^{77} +8.00000i q^{79} +(2.12132 + 0.707107i) q^{80} +(4.00000 + 4.00000i) q^{82} +(2.82843 + 2.82843i) q^{83} +(12.0000 - 6.00000i) q^{85} +9.89949i q^{86} +(9.00000 - 9.00000i) q^{88} +5.65685 q^{89} -24.0000 q^{91} +(4.24264 - 4.24264i) q^{92} -2.00000i q^{94} +(0.707107 - 2.12132i) q^{95} +(-6.00000 - 6.00000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{7}+O(q^{10}) $ 4 * q + 12 * q^7	$ 4 q + 12 q^{7} - 8 q^{10} - 16 q^{13} + 4 q^{16} - 12 q^{22} + 16 q^{25} - 12 q^{28} - 16 q^{31} + 24 q^{37} - 12 q^{40} + 28 q^{43} + 24 q^{46} - 16 q^{52} - 12 q^{55} - 8 q^{58} - 8 q^{61} - 24 q^{67} - 36 q^{70} + 4 q^{73} + 4 q^{76} + 16 q^{82} + 48 q^{85} + 36 q^{88} - 96 q^{91} - 24 q^{97}+O(q^{100}) $ 4 * q + 12 * q^7 - 8 * q^10 - 16 * q^13 + 4 * q^16 - 12 * q^22 + 16 * q^25 - 12 * q^28 - 16 * q^31 + 24 * q^37 - 12 * q^40 + 28 * q^43 + 24 * q^46 - 16 * q^52 - 12 * q^55 - 8 * q^58 - 8 * q^61 - 24 * q^67 - 36 * q^70 + 4 * q^73 + 4 * q^76 + 16 * q^82 + 48 * q^85 + 36 * q^88 - 96 * q^91 - 24 * q^97

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	$0.0461154\pi$
$7$	3.00000	+	3.00000i	1.13389	+	1.13389i	0.144370	+	0.989524i	$0.453885\pi$
$8$	−2.12132	−	2.12132i	−0.750000	−	0.750000i
$9$		0			0
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$			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
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.116171	+	0.993229i	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$	−4.24264			−1.13389
$15$		0			0
$16$	1.00000			0.250000
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.0294245	−	0.999567i	$-0.490633\pi$
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.999567	−	0.0294245i	$-0.00936746\pi$
$18$		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
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	0.109351	−	0.994003i	$-0.465123\pi$
$23$	−4.24264	−	4.24264i	−0.884652	−	0.884652i	−0.994003	+	0.109351i	$0.965123\pi$
$24$		0			0
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$		−	5.65685i		−	1.10940i
$27$		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
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	3.53553	−	3.53553i	0.625000	−	0.625000i
$33$		0			0
$34$			6.00000i			1.02899i
$35$	4.24264	+	8.48528i	0.717137	+	1.43427i
$36$		0			0
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	0.999909	−	0.0135147i	$-0.00430201\pi$
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	−0.0135147	+	0.999909i	$0.504302\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$		0			0
$40$	−3.00000	−	6.00000i	−0.474342	−	0.948683i
$41$		−	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
$46$	6.00000			0.884652
$47$	−1.41421	+	1.41421i	−0.206284	+	0.206284i	−0.802686	−	0.596402i	$-0.796597\pi$
$47$	−1.41421	+	1.41421i	−0.206284	+	0.206284i	0.596402	+	0.802686i	$0.296597\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$		0			0
$52$	−4.00000	−	4.00000i	−0.554700	−	0.554700i
$53$	−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	$-0.686267\pi$
$59$	−8.48528			−1.10469			−0.552345	+	0.833616i	$0.686267\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.82843	−	2.82843i	0.359211	−	0.359211i
$63$		0			0
$64$			7.00000i			0.875000i
$65$	−11.3137	+	5.65685i	−1.40329	+	0.701646i
$66$		0			0
$67$	−6.00000	−	6.00000i	−0.733017	−	0.733017i	0.238200	−	0.971216i	$-0.423443\pi$
$67$	−6.00000	−	6.00000i	−0.733017	−	0.733017i	−0.971216	+	0.238200i	$0.923443\pi$
$68$	4.24264	+	4.24264i	0.514496	+	0.514496i
$69$		0			0
$70$	−9.00000	−	3.00000i	−1.07571	−	0.358569i
$71$			5.65685i			0.671345i	0.941979	+	0.335673i	$0.108964\pi$
$71$			5.65685i			0.671345i	−0.941979	+	0.335673i	$0.891036\pi$
$72$		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	$0.223626\pi$
$74$	−8.48528			−0.986394
$75$		0			0
$76$	1.00000			0.114708
$77$	−12.7279	+	12.7279i	−1.45048	+	1.45048i
$78$		0			0
$79$			8.00000i			0.900070i	0.893011	+	0.450035i	$0.148589\pi$
$79$			8.00000i			0.900070i	−0.893011	+	0.450035i	$0.851411\pi$
$80$	2.12132	+	0.707107i	0.237171	+	0.0790569i
$81$		0			0
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$	2.82843	+	2.82843i	0.310460	+	0.310460i	0.845088	−	0.534628i	$-0.179548\pi$
$83$	2.82843	+	2.82843i	0.310460	+	0.310460i	−0.534628	+	0.845088i	$0.679548\pi$
$84$		0			0
$85$	12.0000	−	6.00000i	1.30158	−	0.650791i
$86$			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
$91$	−24.0000			−2.51588
$92$	4.24264	−	4.24264i	0.442326	−	0.442326i
$93$		0			0
$94$		−	2.00000i		−	0.206284i
$95$	0.707107	−	2.12132i	0.0725476	−	0.217643i
$96$		0			0
$97$	−6.00000	−	6.00000i	−0.609208	−	0.609208i	0.333531	−	0.942739i	$-0.391760\pi$
$97$	−6.00000	−	6.00000i	−0.609208	−	0.609208i	−0.942739	+	0.333531i	$0.891760\pi$
$98$	−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	$0.218274\pi$
$101$			12.7279i			1.26648i	−0.773957	+	0.633238i	$0.781726\pi$
$102$		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	$0.00463624\pi$
$104$	16.9706			1.66410
$105$		0			0
$106$	6.00000			0.582772
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	−0.830481	−	0.557047i	$-0.811934\pi$
$107$	−2.82843	+	2.82843i	−0.273434	+	0.273434i	0.557047	+	0.830481i	$0.311934\pi$
$108$		0			0
$109$			10.0000i			0.957826i	0.877862	+	0.478913i	$0.158969\pi$
$109$			10.0000i			0.957826i	−0.877862	+	0.478913i	$0.841031\pi$
$110$	−4.24264	−	8.48528i	−0.404520	−	0.809040i
$111$		0			0
$112$	3.00000	+	3.00000i	0.283473	+	0.283473i
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$		0			0
$115$	−6.00000	−	12.0000i	−0.559503	−	1.11901i
$116$			2.82843i			0.262613i
$117$		0			0
$118$	6.00000	−	6.00000i	0.552345	−	0.552345i
$119$	25.4558			2.33353
$120$		0			0
$121$	−7.00000			−0.636364
$122$	1.41421	−	1.41421i	0.128037	−	0.128037i
$123$		0			0
$124$		−	4.00000i		−	0.359211i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	2.12132	+	2.12132i	0.187500	+	0.187500i
$129$		0			0
$130$	4.00000	−	12.0000i	0.350823	−	1.05247i
$131$			7.07107i			0.617802i	0.951094	+	0.308901i	$0.0999612\pi$
$131$			7.07107i			0.617802i	−0.951094	+	0.308901i	$0.900039\pi$
$132$		0			0
$133$	3.00000	−	3.00000i	0.260133	−	0.260133i
$134$	8.48528			0.733017
$135$		0			0
$136$	−18.0000			−1.54349
$137$	7.07107	−	7.07107i	0.604122	−	0.604122i	−0.337282	−	0.941404i	$-0.609507\pi$
$137$	7.07107	−	7.07107i	0.604122	−	0.604122i	0.941404	+	0.337282i	$0.109507\pi$
$138$		0			0
$139$			2.00000i			0.169638i	0.996396	+	0.0848189i	$0.0270312\pi$
$139$			2.00000i			0.169638i	−0.996396	+	0.0848189i	$0.972969\pi$
$140$	−8.48528	+	4.24264i	−0.717137	+	0.358569i
$141$		0			0
$142$	−4.00000	−	4.00000i	−0.335673	−	0.335673i
$143$	−16.9706	−	16.9706i	−1.41915	−	1.41915i
$144$		0			0
$145$	6.00000	+	2.00000i	0.498273	+	0.166091i
$146$			1.41421i			0.117041i
$147$		0			0
$148$	−6.00000	+	6.00000i	−0.493197	+	0.493197i
$149$	−9.89949			−0.810998			−0.405499	−	0.914095i	$-0.632902\pi$
$149$	−9.89949			−0.810998			−0.405499	+	0.914095i	$0.632902\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−2.12132	+	2.12132i	−0.172062	+	0.172062i
$153$		0			0
$154$		−	18.0000i		−	1.45048i
$155$	−8.48528	−	2.82843i	−0.681554	−	0.227185i
$156$		0			0
$157$	5.00000	+	5.00000i	0.399043	+	0.399043i	0.877896	−	0.478852i	$-0.158947\pi$
$157$	5.00000	+	5.00000i	0.399043	+	0.399043i	−0.478852	+	0.877896i	$0.658947\pi$
$158$	−5.65685	−	5.65685i	−0.450035	−	0.450035i
$159$		0			0
$160$	10.0000	−	5.00000i	0.790569	−	0.395285i
$161$		−	25.4558i		−	2.00620i
$162$		0			0
$163$	17.0000	−	17.0000i	1.33154	−	1.33154i	0.427552	−	0.903991i	$-0.359376\pi$
$163$	17.0000	−	17.0000i	1.33154	−	1.33154i	0.903991	−	0.427552i	$-0.140624\pi$
$164$	5.65685			0.441726
$165$		0			0
$166$	−4.00000			−0.310460
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$	−4.24264	+	12.7279i	−0.325396	+	0.976187i
$171$		0			0
$172$	7.00000	+	7.00000i	0.533745	+	0.533745i
$173$	−9.89949	−	9.89949i	−0.752645	−	0.752645i	0.222327	−	0.974972i	$-0.428635\pi$
$173$	−9.89949	−	9.89949i	−0.752645	−	0.752645i	−0.974972	+	0.222327i	$0.928635\pi$
$174$		0			0
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$			4.24264i			0.319801i
$177$		0			0
$178$	−4.00000	+	4.00000i	−0.299813	+	0.299813i
$179$	2.82843			0.211407			0.105703	−	0.994398i	$-0.466291\pi$
$179$	2.82843			0.211407			0.105703	+	0.994398i	$0.466291\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	16.9706	−	16.9706i	1.25794	−	1.25794i
$183$		0			0
$184$			18.0000i			1.32698i
$185$	8.48528	+	16.9706i	0.623850	+	1.24770i
$186$		0			0
$187$	18.0000	+	18.0000i	1.31629	+	1.31629i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$		0			0
$190$	1.00000	+	2.00000i	0.0725476	+	0.145095i
$191$			1.41421i			0.102329i	0.998690	+	0.0511645i	$0.0162933\pi$
$191$			1.41421i			0.102329i	−0.998690	+	0.0511645i	$0.983707\pi$
$192$		0			0
$193$	16.0000	−	16.0000i	1.15171	−	1.15171i	0.165494	−	0.986211i	$-0.447078\pi$
$193$	16.0000	−	16.0000i	1.15171	−	1.15171i	0.986211	−	0.165494i	$-0.0529220\pi$
$194$	8.48528			0.609208
$195$		0			0
$196$	−11.0000			−0.785714
$197$	16.9706	−	16.9706i	1.20910	−	1.20910i	0.237785	−	0.971318i	$-0.423579\pi$
$197$	16.9706	−	16.9706i	1.20910	−	1.20910i	0.971318	−	0.237785i	$-0.0764212\pi$
$198$		0			0
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$	−2.12132	−	14.8492i	−0.150000	−	1.05000i
$201$		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
$208$	−4.00000	+	4.00000i	−0.277350	+	0.277350i
$209$	4.24264			0.293470
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$		−	4.00000i		−	0.273434i
$215$	19.7990	−	9.89949i	1.35028	−	0.675140i
$216$		0			0
$217$	−12.0000	−	12.0000i	−0.814613	−	0.814613i
$218$	−7.07107	−	7.07107i	−0.478913	−	0.478913i
$219$		0			0
$220$	−9.00000	−	3.00000i	−0.606780	−	0.202260i
$221$			33.9411i			2.28313i
$222$		0			0
$223$	−10.0000	+	10.0000i	−0.669650	+	0.669650i	−0.957635	−	0.287985i	$-0.907015\pi$
$223$	−10.0000	+	10.0000i	−0.669650	+	0.669650i	0.287985	+	0.957635i	$0.407015\pi$
$224$	21.2132			1.41737
$225$		0			0
$226$	−6.00000			−0.399114
$227$	−8.48528	+	8.48528i	−0.563188	+	0.563188i	−0.930212	−	0.367024i	$-0.880377\pi$
$227$	−8.48528	+	8.48528i	−0.563188	+	0.563188i	0.367024	+	0.930212i	$0.380377\pi$
$228$		0			0
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$	12.7279	+	4.24264i	0.839254	+	0.279751i
$231$		0			0
$232$	−6.00000	−	6.00000i	−0.393919	−	0.393919i
$233$	16.9706	+	16.9706i	1.11178	+	1.11178i	0.992910	+	0.118869i	$0.0379267\pi$
$233$	16.9706	+	16.9706i	1.11178	+	1.11178i	0.118869	+	0.992910i	$0.462073\pi$
$234$		0			0
$235$	−4.00000	+	2.00000i	−0.260931	+	0.130466i
$236$		−	8.48528i		−	0.552345i
$237$		0			0
$238$	−18.0000	+	18.0000i	−1.16677	+	1.16677i
$239$	−18.3848			−1.18921			−0.594606	−	0.804017i	$-0.702692\pi$
$239$	−18.3848			−1.18921			−0.594606	+	0.804017i	$0.702692\pi$
$240$		0			0
$241$	30.0000			1.93247			0.966235	−	0.257663i	$-0.0829523\pi$
$241$	30.0000			1.93247			0.966235	+	0.257663i	$0.0829523\pi$
$242$	4.94975	−	4.94975i	0.318182	−	0.318182i
$243$		0			0
$244$		−	2.00000i		−	0.128037i
$245$	−7.77817	+	23.3345i	−0.496929	+	1.49079i
$246$		0			0
$247$	4.00000	+	4.00000i	0.254514	+	0.254514i
$248$	8.48528	+	8.48528i	0.538816	+	0.538816i
$249$		0			0
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$			15.5563i			0.981908i	0.871185	+	0.490954i	$0.163352\pi$
$251$			15.5563i			0.981908i	−0.871185	+	0.490954i	$0.836648\pi$
$252$		0			0
$253$	18.0000	−	18.0000i	1.13165	−	1.13165i
$254$		0			0
$255$		0			0
$256$	−17.0000			−1.06250
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	−0.0291953	−	0.999574i	$-0.509294\pi$
$257$	15.5563	−	15.5563i	0.970378	−	0.970378i	0.999574	+	0.0291953i	$0.00929448\pi$
$258$		0			0
$259$			36.0000i			2.23693i
$260$	−5.65685	−	11.3137i	−0.350823	−	0.701646i
$261$		0			0
$262$	−5.00000	−	5.00000i	−0.308901	−	0.308901i
$263$	−11.3137	−	11.3137i	−0.697633	−	0.697633i	0.266266	−	0.963899i	$-0.414210\pi$
$263$	−11.3137	−	11.3137i	−0.697633	−	0.697633i	−0.963899	+	0.266266i	$0.914210\pi$
$264$		0			0
$265$	−6.00000	−	12.0000i	−0.368577	−	0.737154i
$266$			4.24264i			0.260133i
$267$		0			0
$268$	6.00000	−	6.00000i	0.366508	−	0.366508i
$269$	−8.48528			−0.517357			−0.258678	−	0.965964i	$-0.583287\pi$
$269$	−8.48528			−0.517357			−0.258678	+	0.965964i	$0.583287\pi$
$270$		0			0
$271$	−26.0000			−1.57939			−0.789694	−	0.613501i	$-0.789761\pi$
$271$	−26.0000			−1.57939			−0.789694	+	0.613501i	$0.789761\pi$
$272$	4.24264	−	4.24264i	0.257248	−	0.257248i
$273$		0			0
$274$			10.0000i			0.604122i
$275$	−12.7279	+	16.9706i	−0.767523	+	1.02336i
$276$		0			0
$277$	−21.0000	−	21.0000i	−1.26177	−	1.26177i	−0.950236	−	0.311532i	$-0.899158\pi$
$277$	−21.0000	−	21.0000i	−1.26177	−	1.26177i	−0.311532	−	0.950236i	$-0.600842\pi$
$278$	−1.41421	−	1.41421i	−0.0848189	−	0.0848189i
$279$		0			0
$280$	9.00000	−	27.0000i	0.537853	−	1.61356i
$281$		−	25.4558i		−	1.51857i	−0.650759	−	0.759284i	$-0.725549\pi$
$281$		−	25.4558i		−	1.51857i	0.650759	−	0.759284i	$-0.274451\pi$
$282$		0			0
$283$	−3.00000	+	3.00000i	−0.178331	+	0.178331i	−0.790628	−	0.612297i	$-0.790246\pi$
$283$	−3.00000	+	3.00000i	−0.178331	+	0.178331i	0.612297	+	0.790628i	$0.290246\pi$
$284$	−5.65685			−0.335673
$285$		0			0
$286$	24.0000			1.41915
$287$	16.9706	−	16.9706i	1.00174	−	1.00174i
$288$		0			0
$289$		−	19.0000i		−	1.11765i
$290$	−5.65685	+	2.82843i	−0.332182	+	0.166091i
$291$		0			0
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	4.24264	+	4.24264i	0.247858	+	0.247858i	0.820091	−	0.572233i	$-0.193923\pi$
$293$	4.24264	+	4.24264i	0.247858	+	0.247858i	−0.572233	+	0.820091i	$0.693923\pi$
$294$		0			0
$295$	−18.0000	−	6.00000i	−1.04800	−	0.349334i
$296$		−	25.4558i		−	1.47959i
$297$		0			0
$298$	7.00000	−	7.00000i	0.405499	−	0.405499i
$299$	33.9411			1.96287
$300$		0			0
$301$	42.0000			2.42084
$302$	−5.65685	+	5.65685i	−0.325515	+	0.325515i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$	−4.24264	−	1.41421i	−0.242933	−	0.0809776i
$306$		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	−	4.00000i	0.454369	−	0.227185i
$311$			9.89949i			0.561349i	0.959803	+	0.280674i	$0.0905581\pi$
$311$			9.89949i			0.561349i	−0.959803	+	0.280674i	$0.909442\pi$
$312$		0			0
$313$	−1.00000	+	1.00000i	−0.0565233	+	0.0565233i	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−1.00000	+	1.00000i	−0.0565233	+	0.0565233i	0.678280	+	0.734803i	$0.262726\pi$
$314$	−7.07107			−0.399043
$315$		0			0
$316$	−8.00000			−0.450035
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	−0.666276	−	0.745706i	$-0.732113\pi$
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	0.745706	+	0.666276i	$0.232113\pi$
$318$		0			0
$319$			12.0000i			0.671871i
$320$	−4.94975	+	14.8492i	−0.276699	+	0.830098i
$321$		0			0
$322$	18.0000	+	18.0000i	1.00310	+	1.00310i
$323$	−4.24264	−	4.24264i	−0.236067	−	0.236067i
$324$		0			0
$325$	−28.0000	+	4.00000i	−1.55316	+	0.221880i
$326$			24.0416i			1.33154i
$327$		0			0
$328$	−12.0000	+	12.0000i	−0.662589	+	0.662589i
$329$	−8.48528			−0.467809
$330$		0			0
$331$	28.0000			1.53902			0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000			1.53902			0.769510	+	0.638635i	$0.220501\pi$
$332$	−2.82843	+	2.82843i	−0.155230	+	0.155230i
$333$		0			0
$334$		0			0
$335$	−8.48528	−	16.9706i	−0.463600	−	0.927201i
$336$		0			0
$337$	10.0000	+	10.0000i	0.544735	+	0.544735i	0.924913	−	0.380178i	$-0.124137\pi$
$337$	10.0000	+	10.0000i	0.544735	+	0.544735i	−0.380178	+	0.924913i	$0.624137\pi$
$338$	13.4350	+	13.4350i	0.730769	+	0.730769i
$339$		0			0
$340$	6.00000	+	12.0000i	0.325396	+	0.650791i
$341$		−	16.9706i		−	0.919007i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−29.6985			−1.60123
$345$		0			0
$346$	14.0000			0.752645
$347$	−25.4558	+	25.4558i	−1.36654	+	1.36654i	−0.501223	+	0.865318i	$0.667117\pi$
$347$	−25.4558	+	25.4558i	−1.36654	+	1.36654i	−0.865318	+	0.501223i	$0.832883\pi$
$348$		0			0
$349$		−	16.0000i		−	0.856460i	−0.903670	−	0.428230i	$-0.859137\pi$
$349$		−	16.0000i		−	0.856460i	0.903670	−	0.428230i	$-0.140863\pi$
$350$	−16.9706	−	12.7279i	−0.907115	−	0.680336i
$351$		0			0
$352$	15.0000	+	15.0000i	0.799503	+	0.799503i
$353$	2.82843	+	2.82843i	0.150542	+	0.150542i	0.778360	−	0.627818i	$-0.216052\pi$
$353$	2.82843	+	2.82843i	0.150542	+	0.150542i	−0.627818	+	0.778360i	$0.716052\pi$
$354$		0			0
$355$	−4.00000	+	12.0000i	−0.212298	+	0.636894i
$356$			5.65685i			0.299813i
$357$		0			0
$358$	−2.00000	+	2.00000i	−0.105703	+	0.105703i
$359$	−7.07107			−0.373197			−0.186598	−	0.982436i	$-0.559746\pi$
$359$	−7.07107			−0.373197			−0.186598	+	0.982436i	$0.559746\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−9.89949	+	9.89949i	−0.520306	+	0.520306i
$363$		0			0
$364$		−	24.0000i		−	1.25794i
$365$	2.82843	−	1.41421i	0.148047	−	0.0740233i
$366$		0			0
$367$	3.00000	+	3.00000i	0.156599	+	0.156599i	0.781058	−	0.624459i	$-0.214680\pi$
$367$	3.00000	+	3.00000i	0.156599	+	0.156599i	−0.624459	+	0.781058i	$0.714680\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$		0			0
$370$	−18.0000	−	6.00000i	−0.935775	−	0.311925i
$371$		−	25.4558i		−	1.32160i
$372$		0			0
$373$	−12.0000	+	12.0000i	−0.621336	+	0.621336i	−0.945873	−	0.324537i	$-0.894792\pi$
$373$	−12.0000	+	12.0000i	−0.621336	+	0.621336i	0.324537	+	0.945873i	$0.394792\pi$
$374$	−25.4558			−1.31629
$375$		0			0
$376$	6.00000			0.309426
$377$	−11.3137	+	11.3137i	−0.582686	+	0.582686i
$378$		0			0
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$	2.12132	+	0.707107i	0.108821	+	0.0362738i
$381$		0			0
$382$	−1.00000	−	1.00000i	−0.0511645	−	0.0511645i
$383$	−8.48528	−	8.48528i	−0.433578	−	0.433578i	0.456266	−	0.889843i	$-0.349187\pi$
$383$	−8.48528	−	8.48528i	−0.433578	−	0.433578i	−0.889843	+	0.456266i	$0.849187\pi$
$384$		0			0
$385$	−36.0000	+	18.0000i	−1.83473	+	0.917365i
$386$			22.6274i			1.15171i
$387$		0			0
$388$	6.00000	−	6.00000i	0.304604	−	0.304604i
$389$	9.89949			0.501924			0.250962	−	0.967997i	$-0.419253\pi$
$389$	9.89949			0.501924			0.250962	+	0.967997i	$0.419253\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$	23.3345	−	23.3345i	1.17857	−	1.17857i
$393$		0			0
$394$			24.0000i			1.20910i
$395$	−5.65685	+	16.9706i	−0.284627	+	0.853882i
$396$		0			0
$397$	19.0000	+	19.0000i	0.953583	+	0.953583i	0.998969	−	0.0453868i	$-0.0144520\pi$
$397$	19.0000	+	19.0000i	0.953583	+	0.953583i	−0.0453868	+	0.998969i	$0.514452\pi$
$398$	7.07107	+	7.07107i	0.354441	+	0.354441i
$399$		0			0
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$		−	31.1127i		−	1.55369i	−0.629689	−	0.776847i	$-0.716818\pi$
$401$		−	31.1127i		−	1.55369i	0.629689	−	0.776847i	$-0.283182\pi$
$402$		0			0
$403$	16.0000	−	16.0000i	0.797017	−	0.797017i
$404$	−12.7279			−0.633238
$405$		0			0
$406$	−12.0000			−0.595550
$407$	−25.4558	+	25.4558i	−1.26180	+	1.26180i
$408$		0			0
$409$		−	34.0000i		−	1.68119i	−0.541663	−	0.840596i	$-0.682205\pi$
$409$		−	34.0000i		−	1.68119i	0.541663	−	0.840596i	$-0.317795\pi$
$410$	5.65685	+	11.3137i	0.279372	+	0.558744i
$411$		0			0
$412$	10.0000	+	10.0000i	0.492665	+	0.492665i
$413$	−25.4558	−	25.4558i	−1.25260	−	1.25260i
$414$		0			0
$415$	4.00000	+	8.00000i	0.196352	+	0.392705i
$416$			28.2843i			1.38675i
$417$		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
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	2.82843	−	2.82843i	0.137686	−	0.137686i
$423$		0			0
$424$			18.0000i			0.874157i
$425$	29.6985	−	4.24264i	1.44059	−	0.205798i
$426$		0			0
$427$	−6.00000	−	6.00000i	−0.290360	−	0.290360i
$428$	−2.82843	−	2.82843i	−0.136717	−	0.136717i
$429$		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
$433$	−12.0000	+	12.0000i	−0.576683	+	0.576683i	−0.933988	−	0.357305i	$-0.883696\pi$
$433$	−12.0000	+	12.0000i	−0.576683	+	0.576683i	0.357305	+	0.933988i	$0.383696\pi$
$434$	16.9706			0.814613
$435$		0			0
$436$	−10.0000			−0.478913
$437$	−4.24264	+	4.24264i	−0.202953	+	0.202953i
$438$		0			0
$439$			24.0000i			1.14546i	0.819745	+	0.572729i	$0.194115\pi$
$439$			24.0000i			1.14546i	−0.819745	+	0.572729i	$0.805885\pi$
$440$	25.4558	−	12.7279i	1.21356	−	0.606780i
$441$		0			0
$442$	−24.0000	−	24.0000i	−1.14156	−	1.14156i
$443$	−21.2132	−	21.2132i	−1.00787	−	1.00787i	−0.999969	−	0.00790092i	$-0.997485\pi$
$443$	−21.2132	−	21.2132i	−1.00787	−	1.00787i	−0.00790092	−	0.999969i	$-0.502515\pi$
$444$		0			0
$445$	12.0000	+	4.00000i	0.568855	+	0.189618i
$446$		−	14.1421i		−	0.669650i
$447$		0			0
$448$	−21.0000	+	21.0000i	−0.992157	+	0.992157i
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$		0			0
$451$	24.0000			1.13012
$452$	−4.24264	+	4.24264i	−0.199557	+	0.199557i
$453$		0			0
$454$		−	12.0000i		−	0.563188i
$455$	−50.9117	−	16.9706i	−2.38678	−	0.795592i
$456$		0			0
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	0.580424	−	0.814314i	$-0.302887\pi$
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	−0.814314	+	0.580424i	$0.802887\pi$
$458$	−2.82843	−	2.82843i	−0.132164	−	0.132164i
$459$		0			0
$460$	12.0000	−	6.00000i	0.559503	−	0.279751i
$461$		−	18.3848i		−	0.856264i	−0.903716	−	0.428132i	$-0.859172\pi$
$461$		−	18.3848i		−	0.856264i	0.903716	−	0.428132i	$-0.140828\pi$
$462$		0			0
$463$	15.0000	−	15.0000i	0.697109	−	0.697109i	−0.266677	−	0.963786i	$-0.585926\pi$
$463$	15.0000	−	15.0000i	0.697109	−	0.697109i	0.963786	+	0.266677i	$0.0859256\pi$
$464$	2.82843			0.131306
$465$		0			0
$466$	−24.0000			−1.11178
$467$	4.24264	−	4.24264i	0.196326	−	0.196326i	−0.602097	−	0.798423i	$-0.705668\pi$
$467$	4.24264	−	4.24264i	0.196326	−	0.196326i	0.798423	+	0.602097i	$0.205668\pi$
$468$		0			0
$469$		−	36.0000i		−	1.66233i
$470$	1.41421	−	4.24264i	0.0652328	−	0.195698i
$471$		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
$476$			25.4558i			1.16677i
$477$		0			0
$478$	13.0000	−	13.0000i	0.594606	−	0.594606i
$479$	−9.89949			−0.452319			−0.226160	−	0.974090i	$-0.572617\pi$
$479$	−9.89949			−0.452319			−0.226160	+	0.974090i	$0.572617\pi$
$480$		0			0
$481$	−48.0000			−2.18861
$482$	−21.2132	+	21.2132i	−0.966235	+	0.966235i
$483$		0			0
$484$		−	7.00000i		−	0.318182i
$485$	−8.48528	−	16.9706i	−0.385297	−	0.770594i
$486$		0			0
$487$	10.0000	+	10.0000i	0.453143	+	0.453143i	0.896396	−	0.443253i	$-0.146176\pi$
$487$	10.0000	+	10.0000i	0.453143	+	0.453143i	−0.443253	+	0.896396i	$0.646176\pi$
$488$	4.24264	+	4.24264i	0.192055	+	0.192055i
$489$		0			0
$490$	−11.0000	−	22.0000i	−0.496929	−	0.993859i
$491$		−	21.2132i		−	0.957338i	−0.877995	−	0.478669i	$-0.841119\pi$
$491$		−	21.2132i		−	0.957338i	0.877995	−	0.478669i	$-0.158881\pi$
$492$		0			0
$493$	12.0000	−	12.0000i	0.540453	−	0.540453i
$494$	−5.65685			−0.254514
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−16.9706	+	16.9706i	−0.761234	+	0.761234i
$498$		0			0
$499$		−	14.0000i		−	0.626726i	−0.949633	−	0.313363i	$-0.898544\pi$
$499$		−	14.0000i		−	0.626726i	0.949633	−	0.313363i	$-0.101456\pi$
$500$	−9.19239	+	6.36396i	−0.411096	+	0.284605i
$501$		0			0
$502$	−11.0000	−	11.0000i	−0.490954	−	0.490954i
$503$	−22.6274	−	22.6274i	−1.00891	−	1.00891i	−0.999960	−	0.00894668i	$-0.997152\pi$
$503$	−22.6274	−	22.6274i	−1.00891	−	1.00891i	−0.00894668	−	0.999960i	$-0.502848\pi$
$504$		0			0
$505$	−9.00000	+	27.0000i	−0.400495	+	1.20148i
$506$			25.4558i			1.13165i
$507$		0			0
$508$		0			0
$509$	11.3137			0.501471			0.250736	−	0.968056i	$-0.419328\pi$
$509$	11.3137			0.501471			0.250736	+	0.968056i	$0.419328\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$		0			0
$514$			22.0000i			0.970378i
$515$	28.2843	−	14.1421i	1.24635	−	0.623177i
$516$		0			0
$517$	−6.00000	−	6.00000i	−0.263880	−	0.263880i
$518$	−25.4558	−	25.4558i	−1.11847	−	1.11847i
$519$		0			0
$520$	36.0000	+	12.0000i	1.57870	+	0.526235i
$521$		−	31.1127i		−	1.36307i	−0.731785	−	0.681536i	$-0.761312\pi$
$521$		−	31.1127i		−	1.36307i	0.731785	−	0.681536i	$-0.238688\pi$
$522$		0			0
$523$	−28.0000	+	28.0000i	−1.22435	+	1.22435i	−0.258286	+	0.966068i	$0.583158\pi$
$523$	−28.0000	+	28.0000i	−1.22435	+	1.22435i	−0.966068	+	0.258286i	$0.916842\pi$
$524$	−7.07107			−0.308901
$525$		0			0
$526$	16.0000			0.697633
$527$	−16.9706	+	16.9706i	−0.739249	+	0.739249i
$528$		0			0
$529$			13.0000i			0.565217i
$530$	12.7279	+	4.24264i	0.552866	+	0.184289i
$531$		0			0
$532$	3.00000	+	3.00000i	0.130066	+	0.130066i
$533$	22.6274	+	22.6274i	0.980102	+	0.980102i
$534$		0			0
$535$	−8.00000	+	4.00000i	−0.345870	+	0.172935i
$536$			25.4558i			1.09952i
$537$		0			0
$538$	6.00000	−	6.00000i	0.258678	−	0.258678i
$539$	−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	$0.781687\pi$
$542$	18.3848	−	18.3848i	0.789694	−	0.789694i
$543$		0			0
$544$		−	30.0000i		−	1.28624i
$545$	−7.07107	+	21.2132i	−0.302891	+	0.908674i
$546$		0			0
$547$	−30.0000	−	30.0000i	−1.28271	−	1.28271i	−0.939121	−	0.343586i	$-0.888358\pi$
$547$	−30.0000	−	30.0000i	−1.28271	−	1.28271i	−0.343586	−	0.939121i	$-0.611642\pi$
$548$	7.07107	+	7.07107i	0.302061	+	0.302061i
$549$		0			0
$550$	−3.00000	−	21.0000i	−0.127920	−	0.895443i
$551$		−	2.82843i		−	0.120495i
$552$		0			0
$553$	−24.0000	+	24.0000i	−1.02058	+	1.02058i
$554$	29.6985			1.26177
$555$		0			0
$556$	−2.00000			−0.0848189
$557$	−16.9706	+	16.9706i	−0.719066	+	0.719066i	−0.968414	−	0.249348i	$-0.919784\pi$
$557$	−16.9706	+	16.9706i	−0.719066	+	0.719066i	0.249348	+	0.968414i	$0.419784\pi$
$558$		0			0
$559$			56.0000i			2.36855i
$560$	4.24264	+	8.48528i	0.179284	+	0.358569i
$561$		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
$565$	6.00000	+	12.0000i	0.252422	+	0.504844i
$566$		−	4.24264i		−	0.178331i
$567$		0			0
$568$	12.0000	−	12.0000i	0.503509	−	0.503509i
$569$	33.9411			1.42289			0.711443	−	0.702744i	$-0.248042\pi$
$569$	33.9411			1.42289			0.711443	+	0.702744i	$0.248042\pi$
$570$		0			0
$571$	22.0000			0.920671			0.460336	−	0.887745i	$-0.347729\pi$
$571$	22.0000			0.920671			0.460336	+	0.887745i	$0.347729\pi$
$572$	16.9706	−	16.9706i	0.709575	−	0.709575i
$573$		0			0
$574$			24.0000i			1.00174i
$575$	−4.24264	−	29.6985i	−0.176930	−	1.23851i
$576$		0			0
$577$	3.00000	+	3.00000i	0.124892	+	0.124892i	0.766790	−	0.641898i	$-0.221853\pi$
$577$	3.00000	+	3.00000i	0.124892	+	0.124892i	−0.641898	+	0.766790i	$0.721853\pi$
$578$	13.4350	+	13.4350i	0.558824	+	0.558824i
$579$		0			0
$580$	−2.00000	+	6.00000i	−0.0830455	+	0.249136i
$581$			16.9706i			0.704058i
$582$		0			0
$583$	18.0000	−	18.0000i	0.745484	−	0.745484i
$584$	−4.24264			−0.175562
$585$		0			0
$586$	−6.00000			−0.247858
$587$	1.41421	−	1.41421i	0.0583708	−	0.0583708i	−0.677319	−	0.735690i	$-0.736858\pi$
$587$	1.41421	−	1.41421i	0.0583708	−	0.0583708i	0.735690	+	0.677319i	$0.236858\pi$
$588$		0			0
$589$			4.00000i			0.164817i
$590$	16.9706	−	8.48528i	0.698667	−	0.349334i
$591$		0			0
$592$	6.00000	+	6.00000i	0.246598	+	0.246598i
$593$	−9.89949	−	9.89949i	−0.406524	−	0.406524i	0.474001	−	0.880524i	$-0.342809\pi$
$593$	−9.89949	−	9.89949i	−0.406524	−	0.406524i	−0.880524	+	0.474001i	$0.842809\pi$
$594$		0			0
$595$	54.0000	+	18.0000i	2.21378	+	0.737928i
$596$		−	9.89949i		−	0.405499i
$597$		0			0
$598$	−24.0000	+	24.0000i	−0.981433	+	0.981433i
$599$	2.82843			0.115566			0.0577832	−	0.998329i	$-0.481597\pi$
$599$	2.82843			0.115566			0.0577832	+	0.998329i	$0.481597\pi$
$600$		0			0
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$	−29.6985	+	29.6985i	−1.21042	+	1.21042i
$603$		0			0
$604$			8.00000i			0.325515i
$605$	−14.8492	−	4.94975i	−0.603708	−	0.201236i
$606$		0			0
$607$	2.00000	+	2.00000i	0.0811775	+	0.0811775i	0.746530	−	0.665352i	$-0.231719\pi$
$607$	2.00000	+	2.00000i	0.0811775	+	0.0811775i	−0.665352	+	0.746530i	$0.731719\pi$
$608$	−3.53553	−	3.53553i	−0.143385	−	0.143385i
$609$		0			0
$610$	4.00000	−	2.00000i	0.161955	−	0.0809776i
$611$		−	11.3137i		−	0.457704i
$612$		0			0
$613$	−19.0000	+	19.0000i	−0.767403	+	0.767403i	−0.977649	−	0.210246i	$-0.932574\pi$
$613$	−19.0000	+	19.0000i	−0.767403	+	0.767403i	0.210246	+	0.977649i	$0.432574\pi$
$614$	−31.1127			−1.25561
$615$		0			0
$616$	54.0000			2.17572
$617$	7.07107	−	7.07107i	0.284670	−	0.284670i	−0.550298	−	0.834968i	$-0.685486\pi$
$617$	7.07107	−	7.07107i	0.284670	−	0.284670i	0.834968	+	0.550298i	$0.185486\pi$
$618$		0			0
$619$			18.0000i			0.723481i	0.932279	+	0.361741i	$0.117817\pi$
$619$			18.0000i			0.723481i	−0.932279	+	0.361741i	$0.882183\pi$
$620$	2.82843	−	8.48528i	0.113592	−	0.340777i
$621$		0			0
$622$	−7.00000	−	7.00000i	−0.280674	−	0.280674i
$623$	16.9706	+	16.9706i	0.679911	+	0.679911i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		−	1.41421i		−	0.0565233i
$627$		0			0
$628$	−5.00000	+	5.00000i	−0.199522	+	0.199522i
$629$	50.9117			2.02998
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$	16.9706	−	16.9706i	0.675053	−	0.675053i
$633$		0			0
$634$			2.00000i			0.0794301i
$635$		0			0
$636$		0			0
$637$	−44.0000	−	44.0000i	−1.74334	−	1.74334i
$638$	−8.48528	−	8.48528i	−0.335936	−	0.335936i
$639$		0			0
$640$	3.00000	+	6.00000i	0.118585	+	0.237171i
$641$			33.9411i			1.34059i	0.742093	+	0.670297i	$0.233833\pi$
$641$			33.9411i			1.34059i	−0.742093	+	0.670297i	$0.766167\pi$
$642$		0			0
$643$	3.00000	−	3.00000i	0.118308	−	0.118308i	−0.645474	−	0.763782i	$-0.723340\pi$
$643$	3.00000	−	3.00000i	0.118308	−	0.118308i	0.763782	+	0.645474i	$0.223340\pi$
$644$	25.4558			1.00310
$645$		0			0
$646$	6.00000			0.236067
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$		0			0
$649$		−	36.0000i		−	1.41312i
$650$	16.9706	−	22.6274i	0.665640	−	0.887520i
$651$		0			0
$652$	17.0000	+	17.0000i	0.665771	+	0.665771i
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	0.619203	−	0.785231i	$-0.287456\pi$
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	−0.785231	+	0.619203i	$0.787456\pi$
$654$		0			0
$655$	−5.00000	+	15.0000i	−0.195366	+	0.586098i
$656$		−	5.65685i		−	0.220863i
$657$		0			0
$658$	6.00000	−	6.00000i	0.233904	−	0.233904i
$659$	50.9117			1.98324			0.991619	−	0.129197i	$-0.0412401\pi$
$659$	50.9117			1.98324			0.991619	+	0.129197i	$0.0412401\pi$
$660$		0			0
$661$	50.0000			1.94477			0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000			1.94477			0.972387	+	0.233373i	$0.0749763\pi$
$662$	−19.7990	+	19.7990i	−0.769510	+	0.769510i
$663$		0			0
$664$		−	12.0000i		−	0.465690i
$665$	8.48528	−	4.24264i	0.329045	−	0.164523i
$666$		0			0
$667$	−12.0000	−	12.0000i	−0.464642	−	0.464642i
$668$		0			0
$669$		0			0
$670$	18.0000	+	6.00000i	0.695401	+	0.231800i
$671$		−	8.48528i		−	0.327571i
$672$		0			0
$673$	6.00000	−	6.00000i	0.231283	−	0.231283i	−0.581945	−	0.813228i	$-0.697708\pi$
$673$	6.00000	−	6.00000i	0.231283	−	0.231283i	0.813228	+	0.581945i	$0.197708\pi$
$674$	−14.1421			−0.544735
$675$		0			0
$676$	19.0000			0.730769
$677$	−4.24264	+	4.24264i	−0.163058	+	0.163058i	−0.783920	−	0.620862i	$-0.786783\pi$
$677$	−4.24264	+	4.24264i	−0.163058	+	0.163058i	0.620862	+	0.783920i	$0.286783\pi$
$678$		0			0
$679$		−	36.0000i		−	1.38155i
$680$	−38.1838	−	12.7279i	−1.46428	−	0.488094i
$681$		0			0
$682$	12.0000	+	12.0000i	0.459504	+	0.459504i
$683$	16.9706	+	16.9706i	0.649361	+	0.649361i	0.952838	−	0.303478i	$-0.0981479\pi$
$683$	16.9706	+	16.9706i	0.649361	+	0.649361i	−0.303478	+	0.952838i	$0.598148\pi$
$684$		0			0
$685$	20.0000	−	10.0000i	0.764161	−	0.382080i
$686$		−	16.9706i		−	0.647939i
$687$		0			0
$688$	7.00000	−	7.00000i	0.266872	−	0.266872i
$689$	33.9411			1.29305
$690$		0			0
$691$	−22.0000			−0.836919			−0.418460	−	0.908235i	$-0.637430\pi$
$691$	−22.0000			−0.836919			−0.418460	+	0.908235i	$0.637430\pi$
$692$	9.89949	−	9.89949i	0.376322	−	0.376322i
$693$		0			0
$694$		−	36.0000i		−	1.36654i
$695$	−1.41421	+	4.24264i	−0.0536442	+	0.160933i
$696$		0			0
$697$	−24.0000	−	24.0000i	−0.909065	−	0.909065i
$698$	11.3137	+	11.3137i	0.428230	+	0.428230i
$699$		0			0
$700$	−21.0000	+	3.00000i	−0.793725	+	0.113389i
$701$			7.07107i			0.267071i	0.991044	+	0.133535i	$0.0426329\pi$
$701$			7.07107i			0.267071i	−0.991044	+	0.133535i	$0.957367\pi$
$702$		0			0
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	−29.6985			−1.11930
$705$		0			0
$706$	−4.00000			−0.150542
$707$	−38.1838	+	38.1838i	−1.43605	+	1.43605i
$708$		0			0
$709$		−	44.0000i		−	1.65245i	−0.563337	−	0.826227i	$-0.690483\pi$
$709$		−	44.0000i		−	1.65245i	0.563337	−	0.826227i	$-0.309517\pi$
$710$	−5.65685	−	11.3137i	−0.212298	−	0.424596i
$711$		0			0
$712$	−12.0000	−	12.0000i	−0.449719	−	0.449719i
$713$	16.9706	+	16.9706i	0.635553	+	0.635553i
$714$		0			0
$715$	−24.0000	−	48.0000i	−0.897549	−	1.79510i
$716$			2.82843i			0.105703i
$717$		0			0
$718$	5.00000	−	5.00000i	0.186598	−	0.186598i
$719$	−7.07107			−0.263706			−0.131853	−	0.991269i	$-0.542093\pi$
$719$	−7.07107			−0.263706			−0.131853	+	0.991269i	$0.542093\pi$
$720$		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
$727$	−27.0000	−	27.0000i	−1.00137	−	1.00137i	−0.999999	−	0.00137552i	$-0.999562\pi$
$727$	−27.0000	−	27.0000i	−1.00137	−	1.00137i	−0.00137552	−	0.999999i	$-0.500438\pi$
$728$	50.9117	+	50.9117i	1.88691	+	1.88691i
$729$		0			0
$730$	−1.00000	+	3.00000i	−0.0370117	+	0.111035i
$731$		−	59.3970i		−	2.19688i
$732$		0			0
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	−0.203436	−	0.979088i	$-0.565211\pi$
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	0.979088	+	0.203436i	$0.0652108\pi$
$734$	−4.24264			−0.156599
$735$		0			0
$736$	−30.0000			−1.10581
$737$	25.4558	−	25.4558i	0.937678	−	0.937678i
$738$		0			0
$739$			20.0000i			0.735712i	0.929883	+	0.367856i	$0.119908\pi$
$739$			20.0000i			0.735712i	−0.929883	+	0.367856i	$0.880092\pi$
$740$	−16.9706	+	8.48528i	−0.623850	+	0.311925i
$741$		0			0
$742$	18.0000	+	18.0000i	0.660801	+	0.660801i
$743$	−22.6274	−	22.6274i	−0.830119	−	0.830119i	0.157413	−	0.987533i	$-0.449684\pi$
$743$	−22.6274	−	22.6274i	−0.830119	−	0.830119i	−0.987533	+	0.157413i	$0.949684\pi$
$744$		0			0
$745$	−21.0000	−	7.00000i	−0.769380	−	0.256460i
$746$		−	16.9706i		−	0.621336i
$747$		0			0
$748$	−18.0000	+	18.0000i	−0.658145	+	0.658145i
$749$	−16.9706			−0.620091
$750$		0			0
$751$	−44.0000			−1.60558			−0.802791	−	0.596260i	$-0.796653\pi$
$751$	−44.0000			−1.60558			−0.802791	+	0.596260i	$0.796653\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$		0			0
$754$		−	16.0000i		−	0.582686i
$755$	16.9706	+	5.65685i	0.617622	+	0.205874i
$756$		0			0
$757$	−1.00000	−	1.00000i	−0.0363456	−	0.0363456i	0.688700	−	0.725046i	$-0.258182\pi$
$757$	−1.00000	−	1.00000i	−0.0363456	−	0.0363456i	−0.725046	+	0.688700i	$0.758182\pi$
$758$	−2.82843	−	2.82843i	−0.102733	−	0.102733i
$759$		0			0
$760$	−6.00000	+	3.00000i	−0.217643	+	0.108821i
$761$		−	18.3848i		−	0.666448i	−0.942848	−	0.333224i	$-0.891864\pi$
$761$		−	18.3848i		−	0.666448i	0.942848	−	0.333224i	$-0.108136\pi$
$762$		0			0
$763$	−30.0000	+	30.0000i	−1.08607	+	1.08607i
$764$	−1.41421			−0.0511645
$765$		0			0
$766$	12.0000			0.433578
$767$	33.9411	−	33.9411i	1.22554	−	1.22554i
$768$		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
$772$	16.0000	+	16.0000i	0.575853	+	0.575853i
$773$	9.89949	+	9.89949i	0.356060	+	0.356060i	0.862358	−	0.506298i	$-0.168987\pi$
$773$	9.89949	+	9.89949i	0.356060	+	0.356060i	−0.506298	+	0.862358i	$0.668987\pi$
$774$		0			0
$775$	−16.0000	−	12.0000i	−0.574737	−	0.431053i
$776$			25.4558i			0.913812i
$777$		0			0
$778$	−7.00000	+	7.00000i	−0.250962	+	0.250962i
$779$	−5.65685			−0.202678
$780$		0			0
$781$	−24.0000			−0.858788
$782$	25.4558	−	25.4558i	0.910299	−	0.910299i
$783$		0			0
$784$			11.0000i			0.392857i
$785$	7.07107	+	14.1421i	0.252377	+	0.504754i
$786$		0			0
$787$	24.0000	+	24.0000i	0.855508	+	0.855508i	0.990805	−	0.135297i	$-0.0431990\pi$
$787$	24.0000	+	24.0000i	0.855508	+	0.855508i	−0.135297	+	0.990805i	$0.543199\pi$
$788$	16.9706	+	16.9706i	0.604551	+	0.604551i
$789$		0			0
$790$	−8.00000	−	16.0000i	−0.284627	−	0.569254i
$791$			25.4558i			0.905106i
$792$		0			0
$793$	8.00000	−	8.00000i	0.284088	−	0.284088i
$794$	−26.8701			−0.953583
$795$		0			0
$796$	10.0000			0.354441
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$		0			0
$799$			12.0000i			0.424529i
$800$	24.7487	−	3.53553i	0.875000	−	0.125000i
$801$		0			0
$802$	22.0000	+	22.0000i	0.776847	+	0.776847i
$803$	4.24264	+	4.24264i	0.149720	+	0.149720i
$804$		0			0
$805$	18.0000	−	54.0000i	0.634417	−	1.90325i
$806$			22.6274i			0.797017i
$807$		0			0
$808$	27.0000	−	27.0000i	0.949857	−	0.949857i
$809$	−26.8701			−0.944701			−0.472350	−	0.881411i	$-0.656594\pi$
$809$	−26.8701			−0.944701			−0.472350	+	0.881411i	$0.656594\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	−8.48528	+	8.48528i	−0.297775	+	0.297775i
$813$		0			0
$814$		−	36.0000i		−	1.26180i
$815$	48.0833	−	24.0416i	1.68428	−	0.842142i
$816$		0			0
$817$	−7.00000	−	7.00000i	−0.244899	−	0.244899i
$818$	24.0416	+	24.0416i	0.840596	+	0.840596i
$819$		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
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	−0.918436	−	0.395569i	$-0.870547\pi$
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	0.395569	+	0.918436i	$0.370547\pi$
$824$	−42.4264			−1.47799
$825$		0			0
$826$	36.0000			1.25260
$827$	8.48528	−	8.48528i	0.295062	−	0.295062i	−0.544014	−	0.839076i	$-0.683096\pi$
$827$	8.48528	−	8.48528i	0.295062	−	0.295062i	0.839076	+	0.544014i	$0.183096\pi$
$828$		0			0
$829$		−	10.0000i		−	0.347314i	−0.984806	−	0.173657i	$-0.944442\pi$
$829$		−	10.0000i		−	0.347314i	0.984806	−	0.173657i	$-0.0555585\pi$
$830$	−8.48528	−	2.82843i	−0.294528	−	0.0981761i
$831$		0			0
$832$	−28.0000	−	28.0000i	−0.970725	−	0.970725i
$833$	46.6690	+	46.6690i	1.61699	+	1.61699i
$834$		0			0
$835$		0			0
$836$			4.24264i			0.146735i
$837$		0			0
$838$	−19.0000	+	19.0000i	−0.656344	+	0.656344i
$839$	5.65685			0.195296			0.0976481	−	0.995221i	$-0.468868\pi$
$839$	5.65685			0.195296			0.0976481	+	0.995221i	$0.468868\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	7.07107	−	7.07107i	0.243685	−	0.243685i
$843$		0			0
$844$		−	4.00000i		−	0.137686i
$845$	13.4350	−	40.3051i	0.462179	−	1.38654i
$846$		0			0
$847$	−21.0000	−	21.0000i	−0.721569	−	0.721569i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$		−	50.9117i		−	1.74523i
$852$		0			0
$853$	3.00000	−	3.00000i	0.102718	−	0.102718i	−0.653880	−	0.756598i	$-0.726860\pi$
$853$	3.00000	−	3.00000i	0.102718	−	0.102718i	0.756598	+	0.653880i	$0.226860\pi$
$854$	8.48528			0.290360
$855$		0			0
$856$	12.0000			0.410152
$857$	−32.5269	+	32.5269i	−1.11110	+	1.11110i	−0.118096	+	0.993002i	$0.537679\pi$
$857$	−32.5269	+	32.5269i	−1.11110	+	1.11110i	−0.993002	+	0.118096i	$0.962321\pi$
$858$		0			0
$859$		−	28.0000i		−	0.955348i	−0.878537	−	0.477674i	$-0.841480\pi$
$859$		−	28.0000i		−	0.955348i	0.878537	−	0.477674i	$-0.158520\pi$
$860$	9.89949	+	19.7990i	0.337570	+	0.675140i
$861$		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
$865$	−14.0000	−	28.0000i	−0.476014	−	0.952029i
$866$		−	16.9706i		−	0.576683i
$867$		0			0
$868$	12.0000	−	12.0000i	0.407307	−	0.407307i
$869$	−33.9411			−1.15137
$870$		0			0
$871$	48.0000			1.62642
$872$	21.2132	−	21.2132i	0.718370	−	0.718370i
$873$		0			0
$874$		−	6.00000i		−	0.202953i
$875$	−8.48528	+	46.6690i	−0.286855	+	1.57770i
$876$		0			0
$877$	8.00000	+	8.00000i	0.270141	+	0.270141i	0.829157	−	0.559016i	$-0.188821\pi$
$877$	8.00000	+	8.00000i	0.270141	+	0.270141i	−0.559016	+	0.829157i	$0.688821\pi$
$878$	−16.9706	−	16.9706i	−0.572729	−	0.572729i
$879$		0			0
$880$	−3.00000	+	9.00000i	−0.101130	+	0.303390i
$881$			35.3553i			1.19115i	0.803299	+	0.595576i	$0.203076\pi$
$881$			35.3553i			1.19115i	−0.803299	+	0.595576i	$0.796924\pi$
$882$		0			0
$883$	27.0000	−	27.0000i	0.908622	−	0.908622i	−0.0875388	−	0.996161i	$-0.527900\pi$
$883$	27.0000	−	27.0000i	0.908622	−	0.908622i	0.996161	+	0.0875388i	$0.0279002\pi$
$884$	−33.9411			−1.14156
$885$		0			0
$886$	30.0000			1.00787
$887$	−14.1421	+	14.1421i	−0.474846	+	0.474846i	−0.903479	−	0.428632i	$-0.858996\pi$
$887$	−14.1421	+	14.1421i	−0.474846	+	0.474846i	0.428632	+	0.903479i	$0.358996\pi$
$888$		0			0
$889$		0			0
$890$	−11.3137	+	5.65685i	−0.379236	+	0.189618i
$891$		0			0
$892$	−10.0000	−	10.0000i	−0.334825	−	0.334825i
$893$	1.41421	+	1.41421i	0.0473249	+	0.0473249i
$894$		0			0
$895$	6.00000	+	2.00000i	0.200558	+	0.0668526i
$896$			12.7279i			0.425210i
$897$		0			0
$898$	−4.00000	+	4.00000i	−0.133482	+	0.133482i
$899$	−11.3137			−0.377333
$900$		0			0
$901$	−36.0000			−1.19933
$902$	−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
$907$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$907$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$908$	−8.48528	−	8.48528i	−0.281594	−	0.281594i
$909$		0			0
$910$	48.0000	−	24.0000i	1.59118	−	0.795592i
$911$			22.6274i			0.749680i	0.927090	+	0.374840i	$0.122302\pi$
$911$			22.6274i			0.749680i	−0.927090	+	0.374840i	$0.877698\pi$
$912$		0			0
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$	7.07107			0.233890
$915$		0			0
$916$	−4.00000			−0.132164
$917$	−21.2132	+	21.2132i	−0.700522	+	0.700522i
$918$		0			0
$919$		−	16.0000i		−	0.527791i	−0.964551	−	0.263896i	$-0.914993\pi$
$919$		−	16.0000i		−	0.527791i	0.964551	−	0.263896i	$-0.0850075\pi$
$920$	−12.7279	+	38.1838i	−0.419627	+	1.25888i
$921$		0			0
$922$	13.0000	+	13.0000i	0.428132	+	0.428132i
$923$	−22.6274	−	22.6274i	−0.744791	−	0.744791i
$924$		0			0
$925$	6.00000	+	42.0000i	0.197279	+	1.38095i
$926$			21.2132i			0.697109i
$927$		0			0
$928$	10.0000	−	10.0000i	0.328266	−	0.328266i
$929$	−52.3259			−1.71676			−0.858379	−	0.513017i	$-0.828528\pi$
$929$	−52.3259			−1.71676			−0.858379	+	0.513017i	$0.828528\pi$
$930$		0			0
$931$	11.0000			0.360510
$932$	−16.9706	+	16.9706i	−0.555889	+	0.555889i
$933$		0			0
$934$			6.00000i			0.196326i
$935$	25.4558	+	50.9117i	0.832495	+	1.66499i
$936$		0			0
$937$	17.0000	+	17.0000i	0.555366	+	0.555366i	0.927985	−	0.372619i	$-0.121540\pi$
$937$	17.0000	+	17.0000i	0.555366	+	0.555366i	−0.372619	+	0.927985i	$0.621540\pi$
$938$	25.4558	+	25.4558i	0.831163	+	0.831163i
$939$		0			0
$940$	−2.00000	−	4.00000i	−0.0652328	−	0.130466i
$941$			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
$943$	−24.0000	+	24.0000i	−0.781548	+	0.781548i
$944$	−8.48528			−0.276172
$945$		0			0
$946$	−42.0000			−1.36554
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	−0.831404	−	0.555669i	$-0.812462\pi$
$947$	−8.48528	+	8.48528i	−0.275735	+	0.275735i	0.555669	+	0.831404i	$0.312462\pi$
$948$		0			0
$949$			8.00000i			0.259691i
$950$	0.707107	+	4.94975i	0.0229416	+	0.160591i
$951$		0			0
$952$	−54.0000	−	54.0000i	−1.75015	−	1.75015i
$953$	−26.8701	−	26.8701i	−0.870407	−	0.870407i	0.122110	−	0.992517i	$-0.461034\pi$
$953$	−26.8701	−	26.8701i	−0.870407	−	0.870407i	−0.992517	+	0.122110i	$0.961034\pi$
$954$		0			0
$955$	−1.00000	+	3.00000i	−0.0323592	+	0.0970777i
$956$		−	18.3848i		−	0.594606i
$957$		0			0
$958$	7.00000	−	7.00000i	0.226160	−	0.226160i
$959$	42.4264			1.37002
$960$		0			0
$961$	−15.0000			−0.483871
$962$	33.9411	−	33.9411i	1.09431	−	1.09431i
$963$		0			0
$964$			30.0000i			0.966235i
$965$	45.2548	−	22.6274i	1.45680	−	0.728402i
$966$		0			0
$967$	−3.00000	−	3.00000i	−0.0964735	−	0.0964735i	0.657223	−	0.753696i	$-0.271731\pi$
$967$	−3.00000	−	3.00000i	−0.0964735	−	0.0964735i	−0.753696	+	0.657223i	$0.771731\pi$
$968$	14.8492	+	14.8492i	0.477273	+	0.477273i
$969$		0			0
$970$	18.0000	+	6.00000i	0.577945	+	0.192648i
$971$			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
$973$	−6.00000	+	6.00000i	−0.192351	+	0.192351i
$974$	−14.1421			−0.453143
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	26.8701	−	26.8701i	0.859649	−	0.859649i	−0.131647	−	0.991297i	$-0.542027\pi$
$977$	26.8701	−	26.8701i	0.859649	−	0.859649i	0.991297	+	0.131647i	$0.0420266\pi$
$978$		0			0
$979$			24.0000i			0.767043i
$980$	−23.3345	−	7.77817i	−0.745394	−	0.248465i
$981$		0			0
$982$	15.0000	+	15.0000i	0.478669	+	0.478669i
$983$	5.65685	+	5.65685i	0.180426	+	0.180426i	0.791541	−	0.611116i	$-0.209279\pi$
$983$	5.65685	+	5.65685i	0.180426	+	0.180426i	−0.611116	+	0.791541i	$0.709279\pi$
$984$		0			0
$985$	48.0000	−	24.0000i	1.52941	−	0.764704i
$986$			16.9706i			0.540453i
$987$		0			0
$988$	−4.00000	+	4.00000i	−0.127257	+	0.127257i
$989$	−59.3970			−1.88871
$990$		0			0
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	−14.1421	+	14.1421i	−0.449013	+	0.449013i
$993$		0			0
$994$		−	24.0000i		−	0.761234i
$995$	7.07107	−	21.2132i	0.224168	−	0.672504i
$996$		0			0
$997$	−5.00000	−	5.00000i	−0.158352	−	0.158352i	0.623484	−	0.781836i	$-0.285717\pi$
$997$	−5.00000	−	5.00000i	−0.158352	−	0.158352i	−0.781836	+	0.623484i	$0.785717\pi$
$998$	9.89949	+	9.89949i	0.313363	+	0.313363i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(3.00000 + 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(3.00000 + 3.00000i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-2.00000 + 1.00000i) q^{10} +4.24264i q^{11} +(-4.00000 + 4.00000i) q^{13} -4.24264 q^{14} +1.00000 q^{16} +(4.24264 - 4.24264i) q^{17} -1.00000i q^{19} +(-0.707107 + 2.12132i) q^{20} +(-3.00000 - 3.00000i) q^{22} +(-4.24264 - 4.24264i) q^{23} +(4.00000 + 3.00000i) q^{25} -5.65685i q^{26} +(-3.00000 + 3.00000i) q^{28} +2.82843 q^{29} -4.00000 q^{31} +(3.53553 - 3.53553i) q^{32} +6.00000i q^{34} +(4.24264 + 8.48528i) q^{35} +(6.00000 + 6.00000i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-3.00000 - 6.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} -4.24264 q^{44} +6.00000 q^{46} +(-1.41421 + 1.41421i) q^{47} +11.0000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(-4.00000 - 4.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-3.00000 + 9.00000i) q^{55} -12.7279i q^{56} +(-2.00000 + 2.00000i) q^{58} -8.48528 q^{59} -2.00000 q^{61} +(2.82843 - 2.82843i) q^{62} +7.00000i q^{64} +(-11.3137 + 5.65685i) q^{65} +(-6.00000 - 6.00000i) q^{67} +(4.24264 + 4.24264i) q^{68} +(-9.00000 - 3.00000i) q^{70} +5.65685i q^{71} +(1.00000 - 1.00000i) q^{73} -8.48528 q^{74} +1.00000 q^{76} +(-12.7279 + 12.7279i) q^{77} +8.00000i q^{79} +(2.12132 + 0.707107i) q^{80} +(4.00000 + 4.00000i) q^{82} +(2.82843 + 2.82843i) q^{83} +(12.0000 - 6.00000i) q^{85} +9.89949i q^{86} +(9.00000 - 9.00000i) q^{88} +5.65685 q^{89} -24.0000 q^{91} +(4.24264 - 4.24264i) q^{92} -2.00000i q^{94} +(0.707107 - 2.12132i) q^{95} +(-6.00000 - 6.00000i) q^{97} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{7}+O(q^{10}) \) 4 * q + 12 * q^7	\( 4 q + 12 q^{7} - 8 q^{10} - 16 q^{13} + 4 q^{16} - 12 q^{22} + 16 q^{25} - 12 q^{28} - 16 q^{31} + 24 q^{37} - 12 q^{40} + 28 q^{43} + 24 q^{46} - 16 q^{52} - 12 q^{55} - 8 q^{58} - 8 q^{61} - 24 q^{67} - 36 q^{70} + 4 q^{73} + 4 q^{76} + 16 q^{82} + 48 q^{85} + 36 q^{88} - 96 q^{91} - 24 q^{97}+O(q^{100}) \) 4 * q + 12 * q^7 - 8 * q^10 - 16 * q^13 + 4 * q^16 - 12 * q^22 + 16 * q^25 - 12 * q^28 - 16 * q^31 + 24 * q^37 - 12 * q^40 + 28 * q^43 + 24 * q^46 - 16 * q^52 - 12 * q^55 - 8 * q^58 - 8 * q^61 - 24 * q^67 - 36 * q^70 + 4 * q^73 + 4 * q^76 + 16 * q^82 + 48 * q^85 + 36 * q^88 - 96 * q^91 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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