LMFDB - Embedded newform 273.2.n.b.239.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(8,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("273.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	273.239
Dual form			273.2.n.b.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-0.292893 - 1.70711i) q^{3} +(1.29289 + 1.29289i) q^{5} +(1.41421 - 2.00000i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-0.292893 - 1.70711i) q^{3} +(1.29289 + 1.29289i) q^{5} +(1.41421 - 2.00000i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.82843 + 1.00000i) q^{9} +2.58579i q^{10} +(1.41421 - 1.41421i) q^{11} +(-0.707107 - 3.53553i) q^{13} +1.41421i q^{14} +(1.82843 - 2.58579i) q^{15} +4.00000 q^{16} +4.00000 q^{17} +(-3.82843 - 1.82843i) q^{18} +(-6.12132 + 6.12132i) q^{19} +(1.00000 - 1.41421i) q^{21} +2.82843 q^{22} +3.82843 q^{23} +(-4.00000 - 2.82843i) q^{24} -1.65685i q^{25} +(2.82843 - 4.24264i) q^{26} +(2.53553 + 4.53553i) q^{27} +4.65685i q^{29} +(4.41421 - 0.757359i) q^{30} +(-6.94975 + 6.94975i) q^{31} +(-2.82843 - 2.00000i) q^{33} +(4.00000 + 4.00000i) q^{34} +1.82843i q^{35} +(-3.58579 - 3.58579i) q^{37} -12.2426 q^{38} +(-5.82843 + 2.24264i) q^{39} +5.17157 q^{40} +(-8.24264 - 8.24264i) q^{41} +(2.41421 - 0.414214i) q^{42} +4.65685i q^{43} +(-4.94975 - 2.36396i) q^{45} +(3.82843 + 3.82843i) q^{46} +(-6.12132 + 6.12132i) q^{47} +(-1.17157 - 6.82843i) q^{48} +1.00000i q^{49} +(1.65685 - 1.65685i) q^{50} +(-1.17157 - 6.82843i) q^{51} +10.3137i q^{53} +(-2.00000 + 7.07107i) q^{54} +3.65685 q^{55} +2.82843 q^{56} +(12.2426 + 8.65685i) q^{57} +(-4.65685 + 4.65685i) q^{58} +(-1.41421 + 1.41421i) q^{59} +5.89949 q^{61} -13.8995 q^{62} +(-2.70711 - 1.29289i) q^{63} -8.00000i q^{64} +(3.65685 - 5.48528i) q^{65} +(-0.828427 - 4.82843i) q^{66} +(5.07107 - 5.07107i) q^{67} +(-1.12132 - 6.53553i) q^{69} +(-1.82843 + 1.82843i) q^{70} +(2.75736 + 2.75736i) q^{71} +(-3.65685 + 7.65685i) q^{72} +(-4.12132 - 4.12132i) q^{73} -7.17157i q^{74} +(-2.82843 + 0.485281i) q^{75} +2.00000 q^{77} +(-8.07107 - 3.58579i) q^{78} +0.171573 q^{79} +(5.17157 + 5.17157i) q^{80} +(7.00000 - 5.65685i) q^{81} -16.4853i q^{82} +(-0.707107 - 0.707107i) q^{83} +(5.17157 + 5.17157i) q^{85} +(-4.65685 + 4.65685i) q^{86} +(7.94975 - 1.36396i) q^{87} -5.65685i q^{88} +(10.1213 - 10.1213i) q^{89} +(-2.58579 - 7.31371i) q^{90} +(2.00000 - 3.00000i) q^{91} +(13.8995 + 9.82843i) q^{93} -12.2426 q^{94} -15.8284 q^{95} +(-8.70711 + 8.70711i) q^{97} +(-1.00000 + 1.00000i) q^{98} +(-2.58579 + 5.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8	$ 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8} - 4 q^{15} + 16 q^{16} + 16 q^{17} - 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{23} - 16 q^{24} - 4 q^{27} + 12 q^{30} - 8 q^{31} + 16 q^{34} - 20 q^{37} - 32 q^{38} - 12 q^{39} + 32 q^{40} - 16 q^{41} + 4 q^{42} + 4 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{50} - 16 q^{51} - 8 q^{54} - 8 q^{55} + 32 q^{57} + 4 q^{58} - 16 q^{61} - 16 q^{62} - 8 q^{63} - 8 q^{65} + 8 q^{66} - 8 q^{67} + 4 q^{69} + 4 q^{70} + 28 q^{71} + 8 q^{72} - 8 q^{73} + 8 q^{77} - 4 q^{78} + 12 q^{79} + 32 q^{80} + 28 q^{81} + 32 q^{85} + 4 q^{86} + 12 q^{87} + 32 q^{89} - 16 q^{90} + 8 q^{91} + 16 q^{93} - 32 q^{94} - 52 q^{95} - 32 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8 - 4 * q^15 + 16 * q^16 + 16 * q^17 - 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^23 - 16 * q^24 - 4 * q^27 + 12 * q^30 - 8 * q^31 + 16 * q^34 - 20 * q^37 - 32 * q^38 - 12 * q^39 + 32 * q^40 - 16 * q^41 + 4 * q^42 + 4 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^50 - 16 * q^51 - 8 * q^54 - 8 * q^55 + 32 * q^57 + 4 * q^58 - 16 * q^61 - 16 * q^62 - 8 * q^63 - 8 * q^65 + 8 * q^66 - 8 * q^67 + 4 * q^69 + 4 * q^70 + 28 * q^71 + 8 * q^72 - 8 * q^73 + 8 * q^77 - 4 * q^78 + 12 * q^79 + 32 * q^80 + 28 * q^81 + 32 * q^85 + 4 * q^86 + 12 * q^87 + 32 * q^89 - 16 * q^90 + 8 * q^91 + 16 * q^93 - 32 * q^94 - 52 * q^95 - 32 * q^97 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$3$	−0.292893	−	1.70711i	−0.169102	−	0.985599i
$4$		0			0
$5$	1.29289	+	1.29289i	0.578199	+	0.578199i	0.934407	−	0.356207i	$-0.115930\pi$
$5$	1.29289	+	1.29289i	0.578199	+	0.578199i	−0.356207	+	0.934407i	$0.615930\pi$
$6$	1.41421	−	2.00000i	0.577350	−	0.816497i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−2.82843	+	1.00000i	−0.942809	+	0.333333i
$10$			2.58579i			0.817697i
$11$	1.41421	−	1.41421i	0.426401	−	0.426401i	−0.460999	−	0.887401i	$-0.652509\pi$
$11$	1.41421	−	1.41421i	0.426401	−	0.426401i	0.887401	+	0.460999i	$0.152509\pi$
$12$		0			0
$13$	−0.707107	−	3.53553i	−0.196116	−	0.980581i
$13$	−0.707107	−	3.53553i	−0.196116	−	0.980581i
$14$			1.41421i			0.377964i
$15$	1.82843	−	2.58579i	0.472098	−	0.667647i
$16$	4.00000			1.00000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	−3.82843	−	1.82843i	−0.902369	−	0.430964i
$19$	−6.12132	+	6.12132i	−1.40433	+	1.40433i	−0.618699	+	0.785628i	$0.712340\pi$
$19$	−6.12132	+	6.12132i	−1.40433	+	1.40433i	−0.785628	+	0.618699i	$0.787660\pi$
$20$		0			0
$21$	1.00000	−	1.41421i	0.218218	−	0.308607i
$22$	2.82843			0.603023
$23$	3.82843			0.798282			0.399141	−	0.916890i	$-0.369308\pi$
$23$	3.82843			0.798282			0.399141	+	0.916890i	$0.369308\pi$
$24$	−4.00000	−	2.82843i	−0.816497	−	0.577350i
$25$		−	1.65685i		−	0.331371i
$26$	2.82843	−	4.24264i	0.554700	−	0.832050i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$		0			0
$29$			4.65685i			0.864756i	0.901692	+	0.432378i	$0.142325\pi$
$29$			4.65685i			0.864756i	−0.901692	+	0.432378i	$0.857675\pi$
$30$	4.41421	−	0.757359i	0.805921	−	0.138274i
$31$	−6.94975	+	6.94975i	−1.24821	+	1.24821i	−0.291702	+	0.956509i	$0.594222\pi$
$31$	−6.94975	+	6.94975i	−1.24821	+	1.24821i	−0.956509	+	0.291702i	$0.905778\pi$
$32$		0			0
$33$	−2.82843	−	2.00000i	−0.492366	−	0.348155i
$34$	4.00000	+	4.00000i	0.685994	+	0.685994i
$35$			1.82843i			0.309061i
$36$		0			0
$37$	−3.58579	−	3.58579i	−0.589500	−	0.589500i	0.347996	−	0.937496i	$-0.386862\pi$
$37$	−3.58579	−	3.58579i	−0.589500	−	0.589500i	−0.937496	+	0.347996i	$0.886862\pi$
$38$	−12.2426			−1.98602
$39$	−5.82843	+	2.24264i	−0.933295	+	0.359110i
$40$	5.17157			0.817697
$41$	−8.24264	−	8.24264i	−1.28728	−	1.28728i	−0.936430	−	0.350854i	$-0.885891\pi$
$41$	−8.24264	−	8.24264i	−1.28728	−	1.28728i	−0.350854	−	0.936430i	$-0.614109\pi$
$42$	2.41421	−	0.414214i	0.372521	−	0.0639145i
$43$			4.65685i			0.710164i	0.934835	+	0.355082i	$0.115547\pi$
$43$			4.65685i			0.710164i	−0.934835	+	0.355082i	$0.884453\pi$
$44$		0			0
$45$	−4.94975	−	2.36396i	−0.737865	−	0.352399i
$46$	3.82843	+	3.82843i	0.564471	+	0.564471i
$47$	−6.12132	+	6.12132i	−0.892886	+	0.892886i	−0.994794	−	0.101908i	$-0.967505\pi$
$47$	−6.12132	+	6.12132i	−0.892886	+	0.892886i	0.101908	+	0.994794i	$0.467505\pi$
$48$	−1.17157	−	6.82843i	−0.169102	−	0.985599i
$49$			1.00000i			0.142857i
$50$	1.65685	−	1.65685i	0.234315	−	0.234315i
$51$	−1.17157	−	6.82843i	−0.164053	−	0.956171i
$52$		0			0
$53$			10.3137i			1.41670i	0.705863	+	0.708348i	$0.250559\pi$
$53$			10.3137i			1.41670i	−0.705863	+	0.708348i	$0.749441\pi$
$54$	−2.00000	+	7.07107i	−0.272166	+	0.962250i
$55$	3.65685			0.493090
$56$	2.82843			0.377964
$57$	12.2426	+	8.65685i	1.62158	+	1.14663i
$58$	−4.65685	+	4.65685i	−0.611475	+	0.611475i
$59$	−1.41421	+	1.41421i	−0.184115	+	0.184115i	−0.793146	−	0.609031i	$-0.791558\pi$
$59$	−1.41421	+	1.41421i	−0.184115	+	0.184115i	0.609031	+	0.793146i	$0.291558\pi$
$60$		0			0
$61$	5.89949			0.755353			0.377676	−	0.925938i	$-0.376723\pi$
$61$	5.89949			0.755353			0.377676	+	0.925938i	$0.376723\pi$
$62$	−13.8995			−1.76524
$63$	−2.70711	−	1.29289i	−0.341063	−	0.162889i
$64$		−	8.00000i		−	1.00000i
$65$	3.65685	−	5.48528i	0.453577	−	0.680365i
$66$	−0.828427	−	4.82843i	−0.101972	−	0.594338i
$67$	5.07107	−	5.07107i	0.619530	−	0.619530i	−0.325881	−	0.945411i	$-0.605661\pi$
$67$	5.07107	−	5.07107i	0.619530	−	0.619530i	0.945411	+	0.325881i	$0.105661\pi$
$68$		0			0
$69$	−1.12132	−	6.53553i	−0.134991	−	0.786786i
$70$	−1.82843	+	1.82843i	−0.218539	+	0.218539i
$71$	2.75736	+	2.75736i	0.327238	+	0.327238i	0.851535	−	0.524297i	$-0.175672\pi$
$71$	2.75736	+	2.75736i	0.327238	+	0.327238i	−0.524297	+	0.851535i	$0.675672\pi$
$72$	−3.65685	+	7.65685i	−0.430964	+	0.902369i
$73$	−4.12132	−	4.12132i	−0.482364	−	0.482364i	0.423522	−	0.905886i	$-0.360794\pi$
$73$	−4.12132	−	4.12132i	−0.482364	−	0.482364i	−0.905886	+	0.423522i	$0.860794\pi$
$74$		−	7.17157i		−	0.833678i
$75$	−2.82843	+	0.485281i	−0.326599	+	0.0560355i
$76$		0			0
$77$	2.00000			0.227921
$78$	−8.07107	−	3.58579i	−0.913868	−	0.406010i
$79$	0.171573			0.0193035			0.00965173	−	0.999953i	$-0.496928\pi$
$79$	0.171573			0.0193035			0.00965173	+	0.999953i	$0.496928\pi$
$80$	5.17157	+	5.17157i	0.578199	+	0.578199i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$		−	16.4853i		−	1.82049i
$83$	−0.707107	−	0.707107i	−0.0776151	−	0.0776151i	0.667234	−	0.744849i	$-0.267478\pi$
$83$	−0.707107	−	0.707107i	−0.0776151	−	0.0776151i	−0.744849	+	0.667234i	$0.767478\pi$
$84$		0			0
$85$	5.17157	+	5.17157i	0.560936	+	0.560936i
$86$	−4.65685	+	4.65685i	−0.502162	+	0.502162i
$87$	7.94975	−	1.36396i	0.852302	−	0.146232i
$88$		−	5.65685i		−	0.603023i
$89$	10.1213	−	10.1213i	1.07286	−	1.07286i	0.0757294	−	0.997128i	$-0.475871\pi$
$89$	10.1213	−	10.1213i	1.07286	−	1.07286i	0.997128	−	0.0757294i	$-0.0241285\pi$
$90$	−2.58579	−	7.31371i	−0.272566	−	0.770933i
$91$	2.00000	−	3.00000i	0.209657	−	0.314485i
$92$		0			0
$93$	13.8995	+	9.82843i	1.44131	+	1.01916i
$94$	−12.2426			−1.26273
$95$	−15.8284			−1.62396
$96$		0			0
$97$	−8.70711	+	8.70711i	−0.884073	+	0.884073i	−0.993946	−	0.109873i	$-0.964956\pi$
$97$	−8.70711	+	8.70711i	−0.884073	+	0.884073i	0.109873	+	0.993946i	$0.464956\pi$
$98$	−1.00000	+	1.00000i	−0.101015	+	0.101015i
$99$	−2.58579	+	5.41421i	−0.259881	+	0.544149i
$100$		0			0
$101$	3.65685			0.363871			0.181935	−	0.983311i	$-0.441764\pi$
$101$	3.65685			0.363871			0.181935	+	0.983311i	$0.441764\pi$
$102$	5.65685	−	8.00000i	0.560112	−	0.792118i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−8.48528	−	5.65685i	−0.832050	−	0.554700i
$105$	3.12132	−	0.535534i	0.304610	−	0.0522628i
$106$	−10.3137	+	10.3137i	−1.00176	+	1.00176i
$107$		−	4.82843i		−	0.466782i	−0.972383	−	0.233391i	$-0.925018\pi$
$107$		−	4.82843i		−	0.466782i	0.972383	−	0.233391i	$-0.0749821\pi$
$108$		0			0
$109$	9.82843	−	9.82843i	0.941393	−	0.941393i	−0.0569826	−	0.998375i	$-0.518148\pi$
$109$	9.82843	−	9.82843i	0.941393	−	0.941393i	0.998375	+	0.0569826i	$0.0181480\pi$
$110$	3.65685	+	3.65685i	0.348667	+	0.348667i
$111$	−5.07107	+	7.17157i	−0.481324	+	0.680696i
$112$	2.82843	+	2.82843i	0.267261	+	0.267261i
$113$		−	4.17157i		−	0.392429i	−0.980561	−	0.196214i	$-0.937135\pi$
$113$		−	4.17157i		−	0.392429i	0.980561	−	0.196214i	$-0.0628648\pi$
$114$	3.58579	+	20.8995i	0.335840	+	1.95742i
$115$	4.94975	+	4.94975i	0.461566	+	0.461566i
$116$		0			0
$117$	5.53553	+	9.29289i	0.511760	+	0.859128i
$118$	−2.82843			−0.260378
$119$	2.82843	+	2.82843i	0.259281	+	0.259281i
$120$	−1.51472	−	8.82843i	−0.138274	−	0.805921i
$121$			7.00000i			0.636364i
$122$	5.89949	+	5.89949i	0.534115	+	0.534115i
$123$	−11.6569	+	16.4853i	−1.05106	+	1.48643i
$124$		0			0
$125$	8.60660	−	8.60660i	0.769798	−	0.769798i
$126$	−1.41421	−	4.00000i	−0.125988	−	0.356348i
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	7.94975	−	1.36396i	0.699936	−	0.120090i
$130$	9.14214	−	1.82843i	0.801818	−	0.160364i
$131$			5.07107i			0.443061i	0.975153	+	0.221531i	$0.0711053\pi$
$131$			5.07107i			0.443061i	−0.975153	+	0.221531i	$0.928895\pi$
$132$		0			0
$133$	−8.65685			−0.750644
$134$	10.1421			0.876147
$135$	−2.58579	+	9.14214i	−0.222549	+	0.786830i
$136$	8.00000	−	8.00000i	0.685994	−	0.685994i
$137$	−3.58579	+	3.58579i	−0.306354	+	0.306354i	−0.843494	−	0.537139i	$-0.819505\pi$
$137$	−3.58579	+	3.58579i	−0.306354	+	0.306354i	0.537139	+	0.843494i	$0.319505\pi$
$138$	5.41421	−	7.65685i	0.460888	−	0.651795i
$139$	−3.17157			−0.269009			−0.134505	−	0.990913i	$-0.542944\pi$
$139$	−3.17157			−0.269009			−0.134505	+	0.990913i	$0.542944\pi$
$140$		0			0
$141$	12.2426	+	8.65685i	1.03102	+	0.729039i
$142$			5.51472i			0.462785i
$143$	−6.00000	−	4.00000i	−0.501745	−	0.334497i
$144$	−11.3137	+	4.00000i	−0.942809	+	0.333333i
$145$	−6.02082	+	6.02082i	−0.500001	+	0.500001i
$146$		−	8.24264i		−	0.682166i
$147$	1.70711	−	0.292893i	0.140800	−	0.0241574i
$148$		0			0
$149$	−4.24264	−	4.24264i	−0.347571	−	0.347571i	0.511633	−	0.859204i	$-0.329041\pi$
$149$	−4.24264	−	4.24264i	−0.347571	−	0.347571i	−0.859204	+	0.511633i	$0.829041\pi$
$150$	−3.31371	−	2.34315i	−0.270563	−	0.191317i
$151$	−8.89949	−	8.89949i	−0.724231	−	0.724231i	0.245233	−	0.969464i	$-0.421135\pi$
$151$	−8.89949	−	8.89949i	−0.724231	−	0.724231i	−0.969464	+	0.245233i	$0.921135\pi$
$152$			24.4853i			1.98602i
$153$	−11.3137	+	4.00000i	−0.914659	+	0.323381i
$154$	2.00000	+	2.00000i	0.161165	+	0.161165i
$155$	−17.9706			−1.44343
$156$		0			0
$157$	8.48528			0.677199			0.338600	−	0.940931i	$-0.390047\pi$
$157$	8.48528			0.677199			0.338600	+	0.940931i	$0.390047\pi$
$158$	0.171573	+	0.171573i	0.0136496	+	0.0136496i
$159$	17.6066	−	3.02082i	1.39629	−	0.239566i
$160$		0			0
$161$	2.70711	+	2.70711i	0.213350	+	0.213350i
$162$	12.6569	+	1.34315i	0.994416	+	0.105527i
$163$	−6.75736	−	6.75736i	−0.529277	−	0.529277i	0.391080	−	0.920357i	$-0.372102\pi$
$163$	−6.75736	−	6.75736i	−0.529277	−	0.529277i	−0.920357	+	0.391080i	$0.872102\pi$
$164$		0			0
$165$	−1.07107	−	6.24264i	−0.0833825	−	0.485989i
$166$		−	1.41421i		−	0.109764i
$167$	6.94975	−	6.94975i	0.537788	−	0.537788i	−0.385091	−	0.922879i	$-0.625830\pi$
$167$	6.94975	−	6.94975i	0.537788	−	0.537788i	0.922879	+	0.385091i	$0.125830\pi$
$168$	−0.828427	−	4.82843i	−0.0639145	−	0.372521i
$169$	−12.0000	+	5.00000i	−0.923077	+	0.384615i
$170$			10.3431i			0.793283i
$171$	11.1924	−	23.4350i	0.855903	−	1.79212i
$172$		0			0
$173$	18.2426			1.38696			0.693481	−	0.720475i	$-0.256076\pi$
$173$	18.2426			1.38696			0.693481	+	0.720475i	$0.256076\pi$
$174$	9.31371	+	6.58579i	0.706070	+	0.499267i
$175$	1.17157	−	1.17157i	0.0885626	−	0.0885626i
$176$	5.65685	−	5.65685i	0.426401	−	0.426401i
$177$	2.82843	+	2.00000i	0.212598	+	0.150329i
$178$	20.2426			1.51725
$179$	18.1716			1.35821			0.679104	−	0.734042i	$-0.262369\pi$
$179$	18.1716			1.35821			0.679104	+	0.734042i	$0.262369\pi$
$180$		0			0
$181$			2.00000i			0.148659i	0.997234	+	0.0743294i	$0.0236816\pi$
$181$			2.00000i			0.148659i	−0.997234	+	0.0743294i	$0.976318\pi$
$182$	5.00000	−	1.00000i	0.370625	−	0.0741249i
$183$	−1.72792	−	10.0711i	−0.127732	−	0.744475i
$184$	7.65685	−	7.65685i	0.564471	−	0.564471i
$185$		−	9.27208i		−	0.681697i
$186$	4.07107	+	23.7279i	0.298505	+	1.73982i
$187$	5.65685	−	5.65685i	0.413670	−	0.413670i
$188$		0			0
$189$	−1.41421	+	5.00000i	−0.102869	+	0.363696i
$190$	−15.8284	−	15.8284i	−1.14831	−	1.14831i
$191$		−	13.3137i		−	0.963346i	−0.876351	−	0.481673i	$-0.840029\pi$
$191$		−	13.3137i		−	0.963346i	0.876351	−	0.481673i	$-0.159971\pi$
$192$	−13.6569	+	2.34315i	−0.985599	+	0.169102i
$193$	−12.2426	−	12.2426i	−0.881245	−	0.881245i	0.112417	−	0.993661i	$-0.464141\pi$
$193$	−12.2426	−	12.2426i	−0.881245	−	0.881245i	−0.993661	+	0.112417i	$0.964141\pi$
$194$	−17.4142			−1.25027
$195$	−10.4350	−	4.63604i	−0.747268	−	0.331994i
$196$		0			0
$197$	2.65685	+	2.65685i	0.189293	+	0.189293i	0.795390	−	0.606097i	$-0.207266\pi$
$197$	2.65685	+	2.65685i	0.189293	+	0.189293i	−0.606097	+	0.795390i	$0.707266\pi$
$198$	−8.00000	+	2.82843i	−0.568535	+	0.201008i
$199$		−	6.34315i		−	0.449654i	−0.974399	−	0.224827i	$-0.927818\pi$
$199$		−	6.34315i		−	0.449654i	0.974399	−	0.224827i	$-0.0721816\pi$
$200$	−3.31371	−	3.31371i	−0.234315	−	0.234315i
$201$	−10.1421	−	7.17157i	−0.715371	−	0.505844i
$202$	3.65685	+	3.65685i	0.257295	+	0.257295i
$203$	−3.29289	+	3.29289i	−0.231116	+	0.231116i
$204$		0			0
$205$		−	21.3137i		−	1.48861i
$206$		0			0
$207$	−10.8284	+	3.82843i	−0.752628	+	0.266094i
$208$	−2.82843	−	14.1421i	−0.196116	−	0.980581i
$209$			17.3137i			1.19761i
$210$	3.65685	+	2.58579i	0.252347	+	0.178436i
$211$	0.514719			0.0354347			0.0177173	−	0.999843i	$-0.494360\pi$
$211$	0.514719			0.0354347			0.0177173	+	0.999843i	$0.494360\pi$
$212$		0			0
$213$	3.89949	−	5.51472i	0.267189	−	0.377862i
$214$	4.82843	−	4.82843i	0.330064	−	0.330064i
$215$	−6.02082	+	6.02082i	−0.410616	+	0.410616i
$216$	14.1421	+	4.00000i	0.962250	+	0.272166i
$217$	−9.82843			−0.667197
$218$	19.6569			1.33133
$219$	−5.82843	+	8.24264i	−0.393849	+	0.556986i
$220$		0			0
$221$	−2.82843	−	14.1421i	−0.190261	−	0.951303i
$222$	−12.2426	+	2.10051i	−0.821672	+	0.140977i
$223$	−3.77817	+	3.77817i	−0.253005	+	0.253005i	−0.822202	−	0.569196i	$-0.807254\pi$
$223$	−3.77817	+	3.77817i	−0.253005	+	0.253005i	0.569196	+	0.822202i	$0.307254\pi$
$224$		0			0
$225$	1.65685	+	4.68629i	0.110457	+	0.312419i
$226$	4.17157	−	4.17157i	0.277489	−	0.277489i
$227$	15.0711	+	15.0711i	1.00030	+	1.00030i	1.00000		0.000301949i	$9.61135e-5\pi$
$227$	15.0711	+	15.0711i	1.00030	+	1.00030i	0.000301949		1.00000i	$0.499904\pi$
$228$		0			0
$229$	−10.4853	−	10.4853i	−0.692887	−	0.692887i	0.269979	−	0.962866i	$-0.412983\pi$
$229$	−10.4853	−	10.4853i	−0.692887	−	0.692887i	−0.962866	+	0.269979i	$0.912983\pi$
$230$			9.89949i			0.652753i
$231$	−0.585786	−	3.41421i	−0.0385419	−	0.224639i
$232$	9.31371	+	9.31371i	0.611475	+	0.611475i
$233$	−6.31371			−0.413625			−0.206812	−	0.978381i	$-0.566309\pi$
$233$	−6.31371			−0.413625			−0.206812	+	0.978381i	$0.566309\pi$
$234$	−3.75736	+	14.8284i	−0.245626	+	0.969365i
$235$	−15.8284			−1.03253
$236$		0			0
$237$	−0.0502525	−	0.292893i	−0.00326425	−	0.0190255i
$238$			5.65685i			0.366679i
$239$	−4.07107	−	4.07107i	−0.263335	−	0.263335i	0.563072	−	0.826408i	$-0.309619\pi$
$239$	−4.07107	−	4.07107i	−0.263335	−	0.263335i	−0.826408	+	0.563072i	$0.809619\pi$
$240$	7.31371	−	10.3431i	0.472098	−	0.667647i
$241$	5.29289	+	5.29289i	0.340945	+	0.340945i	0.856723	−	0.515777i	$-0.172497\pi$
$241$	5.29289	+	5.29289i	0.340945	+	0.340945i	−0.515777	+	0.856723i	$0.672497\pi$
$242$	−7.00000	+	7.00000i	−0.449977	+	0.449977i
$243$	−11.7071	−	10.2929i	−0.751011	−	0.660289i
$244$		0			0
$245$	−1.29289	+	1.29289i	−0.0825999	+	0.0825999i
$246$	−28.1421	+	4.82843i	−1.79428	+	0.307849i
$247$	25.9706	+	17.3137i	1.65247	+	1.10164i
$248$			27.7990i			1.76524i
$249$	−1.00000	+	1.41421i	−0.0633724	+	0.0896221i
$250$	17.2132			1.08866
$251$	−14.9706			−0.944934			−0.472467	−	0.881348i	$-0.656636\pi$
$251$	−14.9706			−0.944934			−0.472467	+	0.881348i	$0.656636\pi$
$252$		0			0
$253$	5.41421	−	5.41421i	0.340389	−	0.340389i
$254$	−2.00000	+	2.00000i	−0.125491	+	0.125491i
$255$	7.31371	−	10.3431i	0.458002	−	0.647713i
$256$		0			0
$257$	0.142136			0.00886618			0.00443309	−	0.999990i	$-0.498589\pi$
$257$	0.142136			0.00886618			0.00443309	+	0.999990i	$0.498589\pi$
$258$	9.31371	+	6.58579i	0.579846	+	0.410013i
$259$		−	5.07107i		−	0.315101i
$260$		0			0
$261$	−4.65685	−	13.1716i	−0.288252	−	0.815300i
$262$	−5.07107	+	5.07107i	−0.313292	+	0.313292i
$263$			10.5147i			0.648365i	0.945995	+	0.324183i	$0.105089\pi$
$263$			10.5147i			0.648365i	−0.945995	+	0.324183i	$0.894911\pi$
$264$	−9.65685	+	1.65685i	−0.594338	+	0.101972i
$265$	−13.3345	+	13.3345i	−0.819133	+	0.819133i
$266$	−8.65685	−	8.65685i	−0.530786	−	0.530786i
$267$	−20.2426	−	14.3137i	−1.23883	−	0.875985i
$268$		0			0
$269$		−	27.6985i		−	1.68881i	−0.535708	−	0.844403i	$-0.679955\pi$
$269$		−	27.6985i		−	1.68881i	0.535708	−	0.844403i	$-0.320045\pi$
$270$	−11.7279	+	6.55635i	−0.713739	+	0.399007i
$271$	7.89949	+	7.89949i	0.479860	+	0.479860i	0.905087	−	0.425227i	$-0.139806\pi$
$271$	7.89949	+	7.89949i	0.479860	+	0.479860i	−0.425227	+	0.905087i	$0.639806\pi$
$272$	16.0000			0.970143
$273$	−5.70711	−	2.53553i	−0.345410	−	0.153457i
$274$	−7.17157			−0.433251
$275$	−2.34315	−	2.34315i	−0.141297	−	0.141297i
$276$		0			0
$277$			19.4853i			1.17076i	0.810760	+	0.585379i	$0.199054\pi$
$277$			19.4853i			1.17076i	−0.810760	+	0.585379i	$0.800946\pi$
$278$	−3.17157	−	3.17157i	−0.190218	−	0.190218i
$279$	12.7071	−	26.6066i	0.760755	−	1.59290i
$280$	3.65685	+	3.65685i	0.218539	+	0.218539i
$281$	−17.1421	+	17.1421i	−1.02261	+	1.02261i	−0.0228758	+	0.999738i	$0.507282\pi$
$281$	−17.1421	+	17.1421i	−1.02261	+	1.02261i	−0.999738	+	0.0228758i	$0.992718\pi$
$282$	3.58579	+	20.8995i	0.213530	+	1.24455i
$283$		−	1.17157i		−	0.0696428i	−0.999394	−	0.0348214i	$-0.988914\pi$
$283$		−	1.17157i		−	0.0696428i	0.999394	−	0.0348214i	$-0.0110862\pi$
$284$		0			0
$285$	4.63604	+	27.0208i	0.274615	+	1.60057i
$286$	−2.00000	−	10.0000i	−0.118262	−	0.591312i
$287$		−	11.6569i		−	0.688082i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	−12.0416			−0.707109
$291$	17.4142	+	12.3137i	1.02084	+	0.721842i
$292$		0			0
$293$	−3.05025	+	3.05025i	−0.178198	+	0.178198i	−0.790570	−	0.612372i	$-0.790215\pi$
$293$	−3.05025	+	3.05025i	−0.178198	+	0.178198i	0.612372	+	0.790570i	$0.290215\pi$
$294$	2.00000	+	1.41421i	0.116642	+	0.0824786i
$295$	−3.65685			−0.212910
$296$	−14.3431			−0.833678
$297$	10.0000	+	2.82843i	0.580259	+	0.164122i
$298$		−	8.48528i		−	0.491539i
$299$	−2.70711	−	13.5355i	−0.156556	−	0.782780i
$300$		0			0
$301$	−3.29289	+	3.29289i	−0.189799	+	0.189799i
$302$		−	17.7990i		−	1.02422i
$303$	−1.07107	−	6.24264i	−0.0615312	−	0.358630i
$304$	−24.4853	+	24.4853i	−1.40433	+	1.40433i
$305$	7.62742	+	7.62742i	0.436745	+	0.436745i
$306$	−15.3137	−	7.31371i	−0.875426	−	0.418097i
$307$	−8.36396	−	8.36396i	−0.477356	−	0.477356i	0.426929	−	0.904285i	$-0.359595\pi$
$307$	−8.36396	−	8.36396i	−0.477356	−	0.477356i	−0.904285	+	0.426929i	$0.859595\pi$
$308$		0			0
$309$		0			0
$310$	−17.9706	−	17.9706i	−1.02066	−	1.02066i
$311$	−0.443651			−0.0251571			−0.0125786	−	0.999921i	$-0.504004\pi$
$311$	−0.443651			−0.0251571			−0.0125786	+	0.999921i	$0.504004\pi$
$312$	−7.17157	+	16.1421i	−0.406010	+	0.913868i
$313$	16.1421			0.912407			0.456204	−	0.889875i	$-0.349209\pi$
$313$	16.1421			0.912407			0.456204	+	0.889875i	$0.349209\pi$
$314$	8.48528	+	8.48528i	0.478852	+	0.478852i
$315$	−1.82843	−	5.17157i	−0.103020	−	0.291385i
$316$		0			0
$317$	2.75736	+	2.75736i	0.154869	+	0.154869i	0.780288	−	0.625420i	$-0.215072\pi$
$317$	2.75736	+	2.75736i	0.154869	+	0.154869i	−0.625420	+	0.780288i	$0.715072\pi$
$318$	20.6274	+	14.5858i	1.15673	+	0.817930i
$319$	6.58579	+	6.58579i	0.368733	+	0.368733i
$320$	10.3431	−	10.3431i	0.578199	−	0.578199i
$321$	−8.24264	+	1.41421i	−0.460059	+	0.0789337i
$322$			5.41421i			0.301722i
$323$	−24.4853	+	24.4853i	−1.36240	+	1.36240i
$324$		0			0
$325$	−5.85786	+	1.17157i	−0.324936	+	0.0649872i
$326$		−	13.5147i		−	0.748511i
$327$	−19.6569	−	13.8995i	−1.08703	−	0.768644i
$328$	−32.9706			−1.82049
$329$	−8.65685			−0.477268
$330$	5.17157	−	7.31371i	0.284686	−	0.402606i
$331$	2.65685	−	2.65685i	0.146034	−	0.146034i	−0.630310	−	0.776344i	$-0.717072\pi$
$331$	2.65685	−	2.65685i	0.146034	−	0.146034i	0.776344	+	0.630310i	$0.217072\pi$
$332$		0			0
$333$	13.7279	+	6.55635i	0.752285	+	0.359286i
$334$	13.8995			0.760547
$335$	13.1127			0.716423
$336$	4.00000	−	5.65685i	0.218218	−	0.308607i
$337$			7.14214i			0.389057i	0.980897	+	0.194528i	$0.0623177\pi$
$337$			7.14214i			0.389057i	−0.980897	+	0.194528i	$0.937682\pi$
$338$	−17.0000	−	7.00000i	−0.924678	−	0.380750i
$339$	−7.12132	+	1.22183i	−0.386777	+	0.0663604i
$340$		0			0
$341$			19.6569i			1.06448i
$342$	34.6274	−	12.2426i	1.87244	−	0.662006i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	9.31371	+	9.31371i	0.502162	+	0.502162i
$345$	7.00000	−	9.89949i	0.376867	−	0.532971i
$346$	18.2426	+	18.2426i	0.980730	+	0.980730i
$347$			6.00000i			0.322097i	0.986947	+	0.161048i	$0.0514875\pi$
$347$			6.00000i			0.322097i	−0.986947	+	0.161048i	$0.948512\pi$
$348$		0			0
$349$	22.9497	+	22.9497i	1.22847	+	1.22847i	0.964542	+	0.263930i	$0.0850188\pi$
$349$	22.9497	+	22.9497i	1.22847	+	1.22847i	0.263930	+	0.964542i	$0.414981\pi$
$350$	2.34315			0.125246
$351$	14.2426	−	12.1716i	0.760216	−	0.649670i
$352$		0			0
$353$	−5.31371	−	5.31371i	−0.282820	−	0.282820i	0.551413	−	0.834233i	$-0.314089\pi$
$353$	−5.31371	−	5.31371i	−0.282820	−	0.282820i	−0.834233	+	0.551413i	$0.814089\pi$
$354$	0.828427	+	4.82843i	0.0440304	+	0.256628i
$355$			7.12994i			0.378418i
$356$		0			0
$357$	4.00000	−	5.65685i	0.211702	−	0.299392i
$358$	18.1716	+	18.1716i	0.960397	+	0.960397i
$359$	11.1716	−	11.1716i	0.589613	−	0.589613i	−0.347914	−	0.937527i	$-0.613110\pi$
$359$	11.1716	−	11.1716i	0.589613	−	0.589613i	0.937527	+	0.347914i	$0.113110\pi$
$360$	−14.6274	+	5.17157i	−0.770933	+	0.272566i
$361$		−	55.9411i		−	2.94427i
$362$	−2.00000	+	2.00000i	−0.105118	+	0.105118i
$363$	11.9497	−	2.05025i	0.627199	−	0.107610i
$364$		0			0
$365$		−	10.6569i		−	0.557805i
$366$	8.34315	−	11.7990i	0.436103	−	0.616743i
$367$	−33.6985			−1.75905			−0.879523	−	0.475856i	$-0.842138\pi$
$367$	−33.6985			−1.75905			−0.879523	+	0.475856i	$0.842138\pi$
$368$	15.3137			0.798282
$369$	31.5563	+	15.0711i	1.64276	+	0.784568i
$370$	9.27208	−	9.27208i	0.482032	−	0.482032i
$371$	−7.29289	+	7.29289i	−0.378628	+	0.378628i
$372$		0			0
$373$	22.6274			1.17160			0.585802	−	0.810454i	$-0.300780\pi$
$373$	22.6274			1.17160			0.585802	+	0.810454i	$0.300780\pi$
$374$	11.3137			0.585018
$375$	−17.2132	−	12.1716i	−0.888886	−	0.628537i
$376$			24.4853i			1.26273i
$377$	16.4645	−	3.29289i	0.847963	−	0.169593i
$378$	−6.41421	+	3.58579i	−0.329912	+	0.184433i
$379$	−7.41421	+	7.41421i	−0.380843	+	0.380843i	−0.871406	−	0.490563i	$-0.836791\pi$
$379$	−7.41421	+	7.41421i	−0.380843	+	0.380843i	0.490563	+	0.871406i	$0.336791\pi$
$380$		0			0
$381$	3.41421	−	0.585786i	0.174915	−	0.0300107i
$382$	13.3137	−	13.3137i	0.681189	−	0.681189i
$383$	−25.8995	−	25.8995i	−1.32340	−	1.32340i	−0.911003	−	0.412399i	$-0.864691\pi$
$383$	−25.8995	−	25.8995i	−1.32340	−	1.32340i	−0.412399	−	0.911003i	$-0.635309\pi$
$384$	−16.0000	−	11.3137i	−0.816497	−	0.577350i
$385$	2.58579	+	2.58579i	0.131784	+	0.131784i
$386$		−	24.4853i		−	1.24627i
$387$	−4.65685	−	13.1716i	−0.236721	−	0.669549i
$388$		0			0
$389$	1.17157			0.0594011			0.0297006	−	0.999559i	$-0.490545\pi$
$389$	1.17157			0.0594011			0.0297006	+	0.999559i	$0.490545\pi$
$390$	−5.79899	−	15.0711i	−0.293643	−	0.763153i
$391$	15.3137			0.774448
$392$	2.00000	+	2.00000i	0.101015	+	0.101015i
$393$	8.65685	−	1.48528i	0.436681	−	0.0749225i
$394$			5.31371i			0.267701i
$395$	0.221825	+	0.221825i	0.0111612	+	0.0111612i
$396$		0			0
$397$	−24.6066	−	24.6066i	−1.23497	−	1.23497i	−0.962032	−	0.272938i	$-0.912004\pi$
$397$	−24.6066	−	24.6066i	−1.23497	−	1.23497i	−0.272938	−	0.962032i	$-0.587996\pi$
$398$	6.34315	−	6.34315i	0.317953	−	0.317953i
$399$	2.53553	+	14.7782i	0.126935	+	0.739834i
$400$		−	6.62742i		−	0.331371i
$401$	18.0711	−	18.0711i	0.902426	−	0.902426i	−0.0932195	−	0.995646i	$-0.529716\pi$
$401$	18.0711	−	18.0711i	0.902426	−	0.902426i	0.995646	+	0.0932195i	$0.0297158\pi$
$402$	−2.97056	−	17.3137i	−0.148158	−	0.863529i
$403$	29.4853	+	19.6569i	1.46877	+	0.979178i
$404$		0			0
$405$	16.3640	+	1.73654i	0.813132	+	0.0862896i
$406$	−6.58579			−0.326847
$407$	−10.1421			−0.502727
$408$	−16.0000	−	11.3137i	−0.792118	−	0.560112i
$409$	10.3640	−	10.3640i	0.512465	−	0.512465i	−0.402816	−	0.915281i	$-0.631969\pi$
$409$	10.3640	−	10.3640i	0.512465	−	0.512465i	0.915281	+	0.402816i	$0.131969\pi$
$410$	21.3137	−	21.3137i	1.05261	−	1.05261i
$411$	7.17157	+	5.07107i	0.353748	+	0.250137i
$412$		0			0
$413$	−2.00000			−0.0984136
$414$	−14.6569	−	7.00000i	−0.720345	−	0.344031i
$415$		−	1.82843i		−	0.0897540i
$416$		0			0
$417$	0.928932	+	5.41421i	0.0454900	+	0.265135i
$418$	−17.3137	+	17.3137i	−0.846841	+	0.846841i
$419$			28.6274i			1.39854i	0.714857	+	0.699270i	$0.246492\pi$
$419$			28.6274i			1.39854i	−0.714857	+	0.699270i	$0.753508\pi$
$420$		0			0
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	0.514719	+	0.514719i	0.0250561	+	0.0250561i
$423$	11.1924	−	23.4350i	0.544193	−	1.13945i
$424$	20.6274	+	20.6274i	1.00176	+	1.00176i
$425$		−	6.62742i		−	0.321477i
$426$	9.41421	−	1.61522i	0.456120	−	0.0782578i
$427$	4.17157	+	4.17157i	0.201877	+	0.201877i
$428$		0			0
$429$	−5.07107	+	11.4142i	−0.244833	+	0.551083i
$430$	−12.0416			−0.580699
$431$	1.48528	+	1.48528i	0.0715435	+	0.0715435i	0.741973	−	0.670430i	$-0.233890\pi$
$431$	1.48528	+	1.48528i	0.0715435	+	0.0715435i	−0.670430	+	0.741973i	$0.733890\pi$
$432$	10.1421	+	18.1421i	0.487964	+	0.872864i
$433$		−	8.58579i		−	0.412607i	−0.978488	−	0.206303i	$-0.933857\pi$
$433$		−	8.58579i		−	0.412607i	0.978488	−	0.206303i	$-0.0661433\pi$
$434$	−9.82843	−	9.82843i	−0.471780	−	0.471780i
$435$	12.0416	+	8.51472i	0.577352	+	0.408250i
$436$		0			0
$437$	−23.4350	+	23.4350i	−1.12105	+	1.12105i
$438$	−14.0711	+	2.41421i	−0.672342	+	0.115356i
$439$		−	21.2132i		−	1.01245i	−0.862401	−	0.506225i	$-0.831040\pi$
$439$		−	21.2132i		−	1.01245i	0.862401	−	0.506225i	$-0.168960\pi$
$440$	7.31371	−	7.31371i	0.348667	−	0.348667i
$441$	−1.00000	−	2.82843i	−0.0476190	−	0.134687i
$442$	11.3137	−	16.9706i	0.538138	−	0.807207i
$443$			18.6569i			0.886414i	0.896419	+	0.443207i	$0.146159\pi$
$443$			18.6569i			0.886414i	−0.896419	+	0.443207i	$0.853841\pi$
$444$		0			0
$445$	26.1716			1.24065
$446$	−7.55635			−0.357804
$447$	−6.00000	+	8.48528i	−0.283790	+	0.401340i
$448$	5.65685	−	5.65685i	0.267261	−	0.267261i
$449$	15.5858	−	15.5858i	0.735539	−	0.735539i	−0.236172	−	0.971711i	$-0.575893\pi$
$449$	15.5858	−	15.5858i	0.735539	−	0.735539i	0.971711	+	0.236172i	$0.0758930\pi$
$450$	−3.02944	+	6.34315i	−0.142809	+	0.299019i
$451$	−23.3137			−1.09780
$452$		0			0
$453$	−12.5858	+	17.7990i	−0.591332	+	0.836269i
$454$			30.1421i			1.41464i
$455$	6.46447	−	1.29289i	0.303059	−	0.0606118i
$456$	41.7990	−	7.17157i	1.95742	−	0.335840i
$457$	−10.8284	+	10.8284i	−0.506532	+	0.506532i	−0.913460	−	0.406928i	$-0.866600\pi$
$457$	−10.8284	+	10.8284i	−0.506532	+	0.506532i	0.406928	+	0.913460i	$0.366600\pi$
$458$		−	20.9706i		−	0.979890i
$459$	10.1421	+	18.1421i	0.473394	+	0.846802i
$460$		0			0
$461$	18.4853	+	18.4853i	0.860945	+	0.860945i	0.991448	−	0.130503i	$-0.0416591\pi$
$461$	18.4853	+	18.4853i	0.860945	+	0.860945i	−0.130503	+	0.991448i	$0.541659\pi$
$462$	2.82843	−	4.00000i	0.131590	−	0.186097i
$463$	14.6569	+	14.6569i	0.681162	+	0.681162i	0.960262	−	0.279100i	$-0.0900362\pi$
$463$	14.6569	+	14.6569i	0.681162	+	0.681162i	−0.279100	+	0.960262i	$0.590036\pi$
$464$			18.6274i			0.864756i
$465$	5.26346	+	30.6777i	0.244087	+	1.42264i
$466$	−6.31371	−	6.31371i	−0.292477	−	0.292477i
$467$	9.21320			0.426336			0.213168	−	0.977016i	$-0.431622\pi$
$467$	9.21320			0.426336			0.213168	+	0.977016i	$0.431622\pi$
$468$		0			0
$469$	7.17157			0.331152
$470$	−15.8284	−	15.8284i	−0.730111	−	0.730111i
$471$	−2.48528	−	14.4853i	−0.114516	−	0.667447i
$472$			5.65685i			0.260378i
$473$	6.58579	+	6.58579i	0.302815	+	0.302815i
$474$	0.242641	−	0.343146i	0.0111449	−	0.0157612i
$475$	10.1421	+	10.1421i	0.465353	+	0.465353i
$476$		0			0
$477$	−10.3137	−	29.1716i	−0.472232	−	1.33567i
$478$		−	8.14214i		−	0.372413i
$479$	16.0208	−	16.0208i	0.732010	−	0.732010i	−0.239008	−	0.971018i	$-0.576822\pi$
$479$	16.0208	−	16.0208i	0.732010	−	0.732010i	0.971018	+	0.239008i	$0.0768222\pi$
$480$		0			0
$481$	−10.1421	+	15.2132i	−0.462442	+	0.693662i
$482$			10.5858i			0.482169i
$483$	3.82843	−	5.41421i	0.174199	−	0.246355i
$484$		0			0
$485$	−22.5147			−1.02234
$486$	−1.41421	−	22.0000i	−0.0641500	−	0.997940i
$487$	−25.8284	+	25.8284i	−1.17040	+	1.17040i	−0.188283	+	0.982115i	$0.560292\pi$
$487$	−25.8284	+	25.8284i	−1.17040	+	1.17040i	−0.982115	+	0.188283i	$0.939708\pi$
$488$	11.7990	−	11.7990i	0.534115	−	0.534115i
$489$	−9.55635	+	13.5147i	−0.432153	+	0.611157i
$490$	−2.58579			−0.116814
$491$	4.97056			0.224318			0.112159	−	0.993690i	$-0.464223\pi$
$491$	4.97056			0.224318			0.112159	+	0.993690i	$0.464223\pi$
$492$		0			0
$493$			18.6274i			0.838937i
$494$	8.65685	+	43.2843i	0.389490	+	1.94745i
$495$	−10.3431	+	3.65685i	−0.464890	+	0.164363i
$496$	−27.7990	+	27.7990i	−1.24821	+	1.24821i
$497$			3.89949i			0.174916i
$498$	−2.41421	+	0.414214i	−0.108183	+	0.0185614i
$499$	−14.0000	+	14.0000i	−0.626726	+	0.626726i	−0.947243	−	0.320517i	$-0.896143\pi$
$499$	−14.0000	+	14.0000i	−0.626726	+	0.626726i	0.320517	+	0.947243i	$0.396143\pi$
$500$		0			0
$501$	−13.8995	−	9.82843i	−0.620984	−	0.439102i
$502$	−14.9706	−	14.9706i	−0.668169	−	0.668169i
$503$			11.0711i			0.493635i	0.969062	+	0.246817i	$0.0793847\pi$
$503$			11.0711i			0.493635i	−0.969062	+	0.246817i	$0.920615\pi$
$504$	−8.00000	+	2.82843i	−0.356348	+	0.125988i
$505$	4.72792	+	4.72792i	0.210390	+	0.210390i
$506$	10.8284			0.481382
$507$	12.0503	+	19.0208i	0.535171	+	0.844744i
$508$		0			0
$509$	21.8787	+	21.8787i	0.969755	+	0.969755i	0.999556	−	0.0298004i	$-0.00948718\pi$
$509$	21.8787	+	21.8787i	0.969755	+	0.969755i	−0.0298004	+	0.999556i	$0.509487\pi$
$510$	17.6569	−	3.02944i	0.781859	−	0.134146i
$511$		−	5.82843i		−	0.257834i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−43.2843	−	12.2426i	−1.91105	−	0.540526i
$514$	0.142136	+	0.142136i	0.00626933	+	0.00626933i
$515$		0			0
$516$		0			0
$517$			17.3137i			0.761456i
$518$	5.07107	−	5.07107i	0.222810	−	0.222810i
$519$	−5.34315	−	31.1421i	−0.234538	−	1.36699i
$520$	−3.65685	−	18.2843i	−0.160364	−	0.801818i
$521$		−	40.2843i		−	1.76489i	−0.470419	−	0.882443i	$-0.655897\pi$
$521$		−	40.2843i		−	1.76489i	0.470419	−	0.882443i	$-0.344103\pi$
$522$	8.51472	−	17.8284i	0.372679	−	0.780329i
$523$	20.7279			0.906369			0.453184	−	0.891417i	$-0.350288\pi$
$523$	20.7279			0.906369			0.453184	+	0.891417i	$0.350288\pi$
$524$		0			0
$525$	−2.34315	−	1.65685i	−0.102263	−	0.0723110i
$526$	−10.5147	+	10.5147i	−0.458464	+	0.458464i
$527$	−27.7990	+	27.7990i	−1.21094	+	1.21094i
$528$	−11.3137	−	8.00000i	−0.492366	−	0.348155i
$529$	−8.34315			−0.362745
$530$	−26.6690			−1.15843
$531$	2.58579	−	5.41421i	0.112214	−	0.234957i
$532$		0			0
$533$	−23.3137	+	34.9706i	−1.00983	+	1.51474i
$534$	−5.92893	−	34.5563i	−0.256570	−	1.49540i
$535$	6.24264	−	6.24264i	0.269893	−	0.269893i
$536$		−	20.2843i		−	0.876147i
$537$	−5.32233	−	31.0208i	−0.229676	−	1.33865i
$538$	27.6985	−	27.6985i	1.19417	−	1.19417i
$539$	1.41421	+	1.41421i	0.0609145	+	0.0609145i
$540$		0			0
$541$	−0.0710678	−	0.0710678i	−0.00305544	−	0.00305544i	0.705577	−	0.708633i	$-0.250688\pi$
$541$	−0.0710678	−	0.0710678i	−0.00305544	−	0.00305544i	−0.708633	+	0.705577i	$0.750688\pi$
$542$			15.7990i			0.678625i
$543$	3.41421	−	0.585786i	0.146518	−	0.0251385i
$544$		0			0
$545$	25.4142			1.08863
$546$	−3.17157	−	8.24264i	−0.135731	−	0.352752i
$547$	−3.34315			−0.142943			−0.0714713	−	0.997443i	$-0.522769\pi$
$547$	−3.34315			−0.142943			−0.0714713	+	0.997443i	$0.522769\pi$
$548$		0			0
$549$	−16.6863	+	5.89949i	−0.712154	+	0.251784i
$550$		−	4.68629i		−	0.199824i
$551$	−28.5061	−	28.5061i	−1.21440	−	1.21440i
$552$	−15.3137	−	10.8284i	−0.651795	−	0.460888i
$553$	0.121320	+	0.121320i	0.00515907	+	0.00515907i
$554$	−19.4853	+	19.4853i	−0.827850	+	0.827850i
$555$	−15.8284	+	2.71573i	−0.671879	+	0.115276i
$556$		0			0
$557$	−11.7990	+	11.7990i	−0.499939	+	0.499939i	−0.911419	−	0.411480i	$-0.865012\pi$
$557$	−11.7990	+	11.7990i	−0.499939	+	0.499939i	0.411480	+	0.911419i	$0.365012\pi$
$558$	39.3137	−	13.8995i	1.66428	−	0.588413i
$559$	16.4645	−	3.29289i	0.696373	−	0.139275i
$560$			7.31371i			0.309061i
$561$	−11.3137	−	8.00000i	−0.477665	−	0.337760i
$562$	−34.2843			−1.44619
$563$	13.0711			0.550880			0.275440	−	0.961318i	$-0.411176\pi$
$563$	13.0711			0.550880			0.275440	+	0.961318i	$0.411176\pi$
$564$		0			0
$565$	5.39340	−	5.39340i	0.226902	−	0.226902i
$566$	1.17157	−	1.17157i	0.0492449	−	0.0492449i
$567$	8.94975	+	0.949747i	0.375854	+	0.0398856i
$568$	11.0294			0.462785
$569$	−9.48528			−0.397644			−0.198822	−	0.980036i	$-0.563712\pi$
$569$	−9.48528			−0.397644			−0.198822	+	0.980036i	$0.563712\pi$
$570$	−22.3848	+	31.6569i	−0.937595	+	1.32596i
$571$			14.4558i			0.604958i	0.953156	+	0.302479i	$0.0978143\pi$
$571$			14.4558i			0.604958i	−0.953156	+	0.302479i	$0.902186\pi$
$572$		0			0
$573$	−22.7279	+	3.89949i	−0.949473	+	0.162904i
$574$	11.6569	−	11.6569i	0.486548	−	0.486548i
$575$		−	6.34315i		−	0.264527i
$576$	8.00000	+	22.6274i	0.333333	+	0.942809i
$577$	−9.17157	+	9.17157i	−0.381818	+	0.381818i	−0.871757	−	0.489939i	$-0.837019\pi$
$577$	−9.17157	+	9.17157i	−0.381818	+	0.381818i	0.489939	+	0.871757i	$0.337019\pi$
$578$	−1.00000	−	1.00000i	−0.0415945	−	0.0415945i
$579$	−17.3137	+	24.4853i	−0.719533	+	1.01757i
$580$		0			0
$581$		−	1.00000i		−	0.0414870i
$582$	5.10051	+	29.7279i	0.211423	+	1.23226i
$583$	14.5858	+	14.5858i	0.604082	+	0.604082i
$584$	−16.4853			−0.682166
$585$	−4.85786	+	19.1716i	−0.200848	+	0.792647i
$586$	−6.10051			−0.252010
$587$	7.19239	+	7.19239i	0.296862	+	0.296862i	0.839783	−	0.542922i	$-0.182682\pi$
$587$	7.19239	+	7.19239i	0.296862	+	0.296862i	−0.542922	+	0.839783i	$0.682682\pi$
$588$		0			0
$589$		−	85.0833i		−	3.50579i
$590$	−3.65685	−	3.65685i	−0.150550	−	0.150550i
$591$	3.75736	−	5.31371i	0.154557	−	0.218577i
$592$	−14.3431	−	14.3431i	−0.589500	−	0.589500i
$593$	17.0919	−	17.0919i	0.701880	−	0.701880i	−0.262934	−	0.964814i	$-0.584690\pi$
$593$	17.0919	−	17.0919i	0.701880	−	0.701880i	0.964814	+	0.262934i	$0.0846902\pi$
$594$	7.17157	+	12.8284i	0.294253	+	0.526357i
$595$			7.31371i			0.299833i
$596$		0			0
$597$	−10.8284	+	1.85786i	−0.443178	+	0.0760373i
$598$	10.8284	−	16.2426i	0.442807	−	0.664211i
$599$		−	34.4558i		−	1.40783i	−0.710285	−	0.703914i	$-0.751434\pi$
$599$		−	34.4558i		−	1.40783i	0.710285	−	0.703914i	$-0.248566\pi$
$600$	−4.68629	+	6.62742i	−0.191317	+	0.270563i
$601$	−14.4853			−0.590867			−0.295433	−	0.955363i	$-0.595464\pi$
$601$	−14.4853			−0.590867			−0.295433	+	0.955363i	$0.595464\pi$
$602$	−6.58579			−0.268417
$603$	−9.27208	+	19.4142i	−0.377588	+	0.790608i
$604$		0			0
$605$	−9.05025	+	9.05025i	−0.367945	+	0.367945i
$606$	5.17157	−	7.31371i	0.210081	−	0.297099i
$607$	3.17157			0.128730			0.0643651	−	0.997926i	$-0.479498\pi$
$607$	3.17157			0.128730			0.0643651	+	0.997926i	$0.479498\pi$
$608$		0			0
$609$	6.58579	+	4.65685i	0.266870	+	0.188705i
$610$			15.2548i			0.617650i
$611$	25.9706	+	17.3137i	1.05066	+	0.700438i
$612$		0			0
$613$	19.2426	−	19.2426i	0.777203	−	0.777203i	−0.202151	−	0.979354i	$-0.564793\pi$
$613$	19.2426	−	19.2426i	0.777203	−	0.777203i	0.979354	+	0.202151i	$0.0647933\pi$
$614$		−	16.7279i		−	0.675084i
$615$	−36.3848	+	6.24264i	−1.46718	+	0.251728i
$616$	4.00000	−	4.00000i	0.161165	−	0.161165i
$617$	32.3137	+	32.3137i	1.30090	+	1.30090i	0.927785	+	0.373116i	$0.121711\pi$
$617$	32.3137	+	32.3137i	1.30090	+	1.30090i	0.373116	+	0.927785i	$0.378289\pi$
$618$		0			0
$619$	3.89949	+	3.89949i	0.156734	+	0.156734i	0.781118	−	0.624384i	$-0.214650\pi$
$619$	3.89949	+	3.89949i	0.156734	+	0.156734i	−0.624384	+	0.781118i	$0.714650\pi$
$620$		0			0
$621$	9.70711	+	17.3640i	0.389533	+	0.696792i
$622$	−0.443651	−	0.443651i	−0.0177888	−	0.0177888i
$623$	14.3137			0.573467
$624$	−23.3137	+	8.97056i	−0.933295	+	0.359110i
$625$	13.9706			0.558823
$626$	16.1421	+	16.1421i	0.645169	+	0.645169i
$627$	29.5563	−	5.07107i	1.18037	−	0.202519i
$628$		0			0
$629$	−14.3431	−	14.3431i	−0.571899	−	0.571899i
$630$	3.34315	−	7.00000i	0.133194	−	0.278887i
$631$	9.34315	+	9.34315i	0.371945	+	0.371945i	0.868185	−	0.496240i	$-0.165287\pi$
$631$	9.34315	+	9.34315i	0.371945	+	0.371945i	−0.496240	+	0.868185i	$0.665287\pi$
$632$	0.343146	−	0.343146i	0.0136496	−	0.0136496i
$633$	−0.150758	−	0.878680i	−0.00599208	−	0.0349244i
$634$			5.51472i			0.219017i
$635$	−2.58579	+	2.58579i	−0.102614	+	0.102614i
$636$		0			0
$637$	3.53553	−	0.707107i	0.140083	−	0.0280166i
$638$			13.1716i			0.521468i
$639$	−10.5563	−	5.04163i	−0.417603	−	0.199444i
$640$	20.6863			0.817697
$641$	−31.0000			−1.22443			−0.612213	−	0.790693i	$-0.709721\pi$
$641$	−31.0000			−1.22443			−0.612213	+	0.790693i	$0.709721\pi$
$642$	−9.65685	−	6.82843i	−0.381126	−	0.269497i
$643$	19.0711	−	19.0711i	0.752089	−	0.752089i	−0.222779	−	0.974869i	$-0.571513\pi$
$643$	19.0711	−	19.0711i	0.752089	−	0.752089i	0.974869	+	0.222779i	$0.0715130\pi$
$644$		0			0
$645$	12.0416	+	8.51472i	0.474139	+	0.335267i
$646$	−48.9706			−1.92672
$647$	14.1005			0.554348			0.277174	−	0.960820i	$-0.410602\pi$
$647$	14.1005			0.554348			0.277174	+	0.960820i	$0.410602\pi$
$648$	2.68629	−	25.3137i	0.105527	−	0.994416i
$649$			4.00000i			0.157014i
$650$	−7.02944	−	4.68629i	−0.275717	−	0.183811i
$651$	2.87868	+	16.7782i	0.112824	+	0.657589i
$652$		0			0
$653$			28.4853i			1.11472i	0.830273	+	0.557358i	$0.188185\pi$
$653$			28.4853i			1.11472i	−0.830273	+	0.557358i	$0.811815\pi$
$654$	−5.75736	−	33.5563i	−0.225131	−	1.31216i
$655$	−6.55635	+	6.55635i	−0.256178	+	0.256178i
$656$	−32.9706	−	32.9706i	−1.28728	−	1.28728i
$657$	15.7782	+	7.53553i	0.615565	+	0.293989i
$658$	−8.65685	−	8.65685i	−0.337479	−	0.337479i
$659$		−	5.97056i		−	0.232580i	−0.993215	−	0.116290i	$-0.962900\pi$
$659$		−	5.97056i		−	0.232580i	0.993215	−	0.116290i	$-0.0371002\pi$
$660$		0			0
$661$	−28.8492	−	28.8492i	−1.12211	−	1.12211i	−0.991424	−	0.130681i	$-0.958284\pi$
$661$	−28.8492	−	28.8492i	−1.12211	−	1.12211i	−0.130681	−	0.991424i	$-0.541716\pi$
$662$	5.31371			0.206523
$663$	−23.3137	+	8.97056i	−0.905429	+	0.348388i
$664$	−2.82843			−0.109764
$665$	−11.1924	−	11.1924i	−0.434022	−	0.434022i
$666$	7.17157	+	20.2843i	0.277893	+	0.786000i
$667$			17.8284i			0.690319i
$668$		0			0
$669$	7.55635	+	5.34315i	0.292145	+	0.206578i
$670$	13.1127	+	13.1127i	0.506588	+	0.506588i
$671$	8.34315	−	8.34315i	0.322084	−	0.322084i
$672$		0			0
$673$			27.0000i			1.04077i	0.853931	+	0.520387i	$0.174212\pi$
$673$			27.0000i			1.04077i	−0.853931	+	0.520387i	$0.825788\pi$
$674$	−7.14214	+	7.14214i	−0.275105	+	0.275105i
$675$	7.51472	−	4.20101i	0.289242	−	0.161697i
$676$		0			0
$677$		−	2.58579i		−	0.0993798i	−0.998765	−	0.0496899i	$-0.984177\pi$
$677$		−	2.58579i		−	0.0993798i	0.998765	−	0.0496899i	$-0.0158233\pi$
$678$	−8.34315	−	5.89949i	−0.320417	−	0.226569i
$679$	−12.3137			−0.472557
$680$	20.6863			0.793283
$681$	21.3137	−	30.1421i	0.816743	−	1.15505i
$682$	−19.6569	+	19.6569i	−0.752700	+	0.752700i
$683$	−27.7990	+	27.7990i	−1.06370	+	1.06370i	−0.0658706	+	0.997828i	$0.520982\pi$
$683$	−27.7990	+	27.7990i	−1.06370	+	1.06370i	−0.997828	+	0.0658706i	$0.979018\pi$
$684$		0			0
$685$	−9.27208			−0.354268
$686$	−1.41421			−0.0539949
$687$	−14.8284	+	20.9706i	−0.565740	+	0.800077i
$688$			18.6274i			0.710164i
$689$	36.4645	−	7.29289i	1.38919	−	0.277837i
$690$	16.8995	−	2.89949i	0.643353	−	0.110382i
$691$	−5.39340	+	5.39340i	−0.205175	+	0.205175i	−0.802213	−	0.597038i	$-0.796344\pi$
$691$	−5.39340	+	5.39340i	−0.205175	+	0.205175i	0.597038	+	0.802213i	$0.296344\pi$
$692$		0			0
$693$	−5.65685	+	2.00000i	−0.214886	+	0.0759737i
$694$	−6.00000	+	6.00000i	−0.227757	+	0.227757i
$695$	−4.10051	−	4.10051i	−0.155541	−	0.155541i
$696$	13.1716	−	18.6274i	0.499267	−	0.706070i
$697$	−32.9706	−	32.9706i	−1.24885	−	1.24885i
$698$			45.8995i			1.73732i
$699$	1.84924	+	10.7782i	0.0699448	+	0.407668i
$700$		0			0
$701$	−9.48528			−0.358254			−0.179127	−	0.983826i	$-0.557327\pi$
$701$	−9.48528			−0.358254			−0.179127	+	0.983826i	$0.557327\pi$
$702$	26.4142	+	2.07107i	0.996940	+	0.0781674i
$703$	43.8995			1.65570
$704$	−11.3137	−	11.3137i	−0.426401	−	0.426401i
$705$	4.63604	+	27.0208i	0.174603	+	1.01766i
$706$		−	10.6274i		−	0.399968i
$707$	2.58579	+	2.58579i	0.0972485	+	0.0972485i
$708$		0			0
$709$	27.6985	+	27.6985i	1.04024	+	1.04024i	0.999156	+	0.0410827i	$0.0130807\pi$
$709$	27.6985	+	27.6985i	1.04024	+	1.04024i	0.0410827	+	0.999156i	$0.486919\pi$
$710$	−7.12994	+	7.12994i	−0.267582	+	0.267582i
$711$	−0.485281	+	0.171573i	−0.0181995	+	0.00643449i
$712$		−	40.4853i		−	1.51725i
$713$	−26.6066	+	26.6066i	−0.996425	+	0.996425i
$714$	9.65685	−	1.65685i	0.361399	−	0.0620062i
$715$	−2.58579	−	12.9289i	−0.0967029	−	0.483515i
$716$		0			0
$717$	−5.75736	+	8.14214i	−0.215013	+	0.304074i
$718$	22.3431			0.833839
$719$	30.3848			1.13316			0.566580	−	0.824006i	$-0.308266\pi$
$719$	30.3848			1.13316			0.566580	+	0.824006i	$0.308266\pi$
$720$	−19.7990	−	9.45584i	−0.737865	−	0.352399i
$721$		0			0
$722$	55.9411	−	55.9411i	2.08191	−	2.08191i
$723$	7.48528	−	10.5858i	0.278381	−	0.393690i
$724$		0			0
$725$	7.71573			0.286555
$726$	14.0000	+	9.89949i	0.519589	+	0.367405i
$727$		−	43.4558i		−	1.61169i	−0.592128	−	0.805844i	$-0.701712\pi$
$727$		−	43.4558i		−	1.61169i	0.592128	−	0.805844i	$-0.298288\pi$
$728$	−2.00000	−	10.0000i	−0.0741249	−	0.370625i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	10.6569	−	10.6569i	0.394428	−	0.394428i
$731$			18.6274i			0.688960i
$732$		0			0
$733$	24.1213	−	24.1213i	0.890941	−	0.890941i	−0.103670	−	0.994612i	$-0.533059\pi$
$733$	24.1213	−	24.1213i	0.890941	−	0.890941i	0.994612	+	0.103670i	$0.0330587\pi$
$734$	−33.6985	−	33.6985i	−1.24383	−	1.24383i
$735$	2.58579	+	1.82843i	0.0953782	+	0.0674426i
$736$		0			0
$737$		−	14.3431i		−	0.528337i
$738$	16.4853	+	46.6274i	0.606832	+	1.71638i
$739$	−32.0416	−	32.0416i	−1.17867	−	1.17867i	−0.980083	−	0.198587i	$-0.936365\pi$
$739$	−32.0416	−	32.0416i	−1.17867	−	1.17867i	−0.198587	−	0.980083i	$-0.563635\pi$
$740$		0			0
$741$	21.9497	−	49.4056i	0.806344	−	1.81496i
$742$	−14.5858			−0.535461
$743$	−30.2132	−	30.2132i	−1.10841	−	1.10841i	−0.993359	−	0.115056i	$-0.963295\pi$
$743$	−30.2132	−	30.2132i	−1.10841	−	1.10841i	−0.115056	−	0.993359i	$-0.536705\pi$
$744$	47.4558	−	8.14214i	1.73982	−	0.298505i
$745$		−	10.9706i		−	0.401930i
$746$	22.6274	+	22.6274i	0.828449	+	0.828449i
$747$	2.70711	+	1.29289i	0.0990479	+	0.0473045i
$748$		0			0
$749$	3.41421	−	3.41421i	0.124753	−	0.124753i
$750$	−5.04163	−	29.3848i	−0.184094	−	1.07298i
$751$		−	4.37258i		−	0.159558i	−0.996813	−	0.0797789i	$-0.974579\pi$
$751$		−	4.37258i		−	0.159558i	0.996813	−	0.0797789i	$-0.0254214\pi$
$752$	−24.4853	+	24.4853i	−0.892886	+	0.892886i
$753$	4.38478	+	25.5563i	0.159790	+	0.931325i
$754$	19.7574	+	13.1716i	0.719521	+	0.479680i
$755$		−	23.0122i		−	0.837499i
$756$		0			0
$757$	−30.3137			−1.10177			−0.550885	−	0.834581i	$-0.685710\pi$
$757$	−30.3137			−1.10177			−0.550885	+	0.834581i	$0.685710\pi$
$758$	−14.8284			−0.538593
$759$	−10.8284	−	7.65685i	−0.393047	−	0.277926i
$760$	−31.6569	+	31.6569i	−1.14831	+	1.14831i
$761$	7.15076	−	7.15076i	0.259215	−	0.259215i	−0.565520	−	0.824735i	$-0.691324\pi$
$761$	7.15076	−	7.15076i	0.259215	−	0.259215i	0.824735	+	0.565520i	$0.191324\pi$
$762$	4.00000	+	2.82843i	0.144905	+	0.102463i
$763$	13.8995			0.503196
$764$		0			0
$765$	−19.7990	−	9.45584i	−0.715834	−	0.341877i
$766$		−	51.7990i		−	1.87157i
$767$	6.00000	+	4.00000i	0.216647	+	0.144432i
$768$		0			0
$769$	6.36396	−	6.36396i	0.229490	−	0.229490i	−0.582989	−	0.812480i	$-0.698117\pi$
$769$	6.36396	−	6.36396i	0.229490	−	0.229490i	0.812480	+	0.582989i	$0.198117\pi$
$770$			5.17157i			0.186371i
$771$	−0.0416306	−	0.242641i	−0.00149929	−	0.00873849i
$772$		0			0
$773$	−6.14214	−	6.14214i	−0.220917	−	0.220917i	0.587967	−	0.808885i	$-0.299928\pi$
$773$	−6.14214	−	6.14214i	−0.220917	−	0.220917i	−0.808885	+	0.587967i	$0.799928\pi$
$774$	8.51472	−	17.8284i	0.306055	−	0.640830i
$775$	11.5147	+	11.5147i	0.413621	+	0.413621i
$776$			34.8284i			1.25027i
$777$	−8.65685	+	1.48528i	−0.310563	+	0.0532842i
$778$	1.17157	+	1.17157i	0.0420029	+	0.0420029i
$779$	100.912			3.61554
$780$		0			0
$781$	7.79899			0.279070
$782$	15.3137	+	15.3137i	0.547617	+	0.547617i
$783$	−21.1213	+	11.8076i	−0.754814	+	0.421970i
$784$			4.00000i			0.142857i
$785$	10.9706	+	10.9706i	0.391556	+	0.391556i
$786$	10.1421	+	7.17157i	0.361758	+	0.255802i
$787$	26.4645	+	26.4645i	0.943356	+	0.943356i	0.998480	−	0.0551232i	$-0.0175552\pi$
$787$	26.4645	+	26.4645i	0.943356	+	0.943356i	−0.0551232	+	0.998480i	$0.517555\pi$
$788$		0			0
$789$	17.9497	−	3.07969i	0.639028	−	0.109640i
$790$			0.443651i			0.0157844i
$791$	2.94975	−	2.94975i	0.104881	−	0.104881i
$792$	5.65685	+	16.0000i	0.201008	+	0.568535i
$793$	−4.17157	−	20.8579i	−0.148137	−	0.740684i
$794$		−	49.2132i		−	1.74651i
$795$	26.6690	+	18.8579i	0.945854	+	0.668820i
$796$		0			0
$797$	21.7990			0.772160			0.386080	−	0.922465i	$-0.373829\pi$
$797$	21.7990			0.772160			0.386080	+	0.922465i	$0.373829\pi$
$798$	−12.2426	+	17.3137i	−0.433385	+	0.612899i
$799$	−24.4853	+	24.4853i	−0.866227	+	0.866227i
$800$		0			0
$801$	−18.5061	+	38.7487i	−0.653881	+	1.36912i
$802$	36.1421			1.27622
$803$	−11.6569			−0.411361
$804$		0			0
$805$			7.00000i			0.246718i
$806$	9.82843	+	49.1421i	0.346192	+	1.73096i
$807$	−47.2843	+	8.11270i	−1.66449	+	0.285581i
$808$	7.31371	−	7.31371i	0.257295	−	0.257295i
$809$			29.9706i			1.05371i	0.849956	+	0.526854i	$0.176629\pi$
$809$			29.9706i			1.05371i	−0.849956	+	0.526854i	$0.823371\pi$
$810$	14.6274	+	18.1005i	0.513955	+	0.635987i
$811$	−20.2426	+	20.2426i	−0.710815	+	0.710815i	−0.966706	−	0.255891i	$-0.917631\pi$
$811$	−20.2426	+	20.2426i	−0.710815	+	0.710815i	0.255891	+	0.966706i	$0.417631\pi$
$812$		0			0
$813$	11.1716	−	15.7990i	0.391804	−	0.554095i
$814$	−10.1421	−	10.1421i	−0.355482	−	0.355482i
$815$		−	17.4731i		−	0.612056i
$816$	−4.68629	−	27.3137i	−0.164053	−	0.956171i
$817$	−28.5061	−	28.5061i	−0.997302	−	0.997302i
$818$	20.7279			0.724735
$819$	−2.65685	+	10.4853i	−0.0928380	+	0.366385i
$820$		0			0
$821$	−21.7574	−	21.7574i	−0.759337	−	0.759337i	0.216865	−	0.976202i	$-0.430417\pi$
$821$	−21.7574	−	21.7574i	−0.759337	−	0.759337i	−0.976202	+	0.216865i	$0.930417\pi$
$822$	2.10051	+	12.2426i	0.0732635	+	0.427011i
$823$			11.3137i			0.394371i	0.980366	+	0.197186i	$0.0631801\pi$
$823$			11.3137i			0.394371i	−0.980366	+	0.197186i	$0.936820\pi$
$824$		0			0
$825$	−3.31371	+	4.68629i	−0.115369	+	0.163156i
$826$	−2.00000	−	2.00000i	−0.0695889	−	0.0695889i
$827$	25.8701	−	25.8701i	0.899590	−	0.899590i	−0.0958096	−	0.995400i	$-0.530544\pi$
$827$	25.8701	−	25.8701i	0.899590	−	0.899590i	0.995400	+	0.0958096i	$0.0305440\pi$
$828$		0			0
$829$		−	13.8995i		−	0.482749i	−0.970432	−	0.241375i	$-0.922402\pi$
$829$		−	13.8995i		−	0.482749i	0.970432	−	0.241375i	$-0.0775983\pi$
$830$	1.82843	−	1.82843i	0.0634656	−	0.0634656i
$831$	33.2635	−	5.70711i	1.15390	−	0.197977i
$832$	−28.2843	+	5.65685i	−0.980581	+	0.196116i
$833$			4.00000i			0.138592i
$834$	−4.48528	+	6.34315i	−0.155313	+	0.219645i
$835$	17.9706			0.621897
$836$		0			0
$837$	−49.1421	−	13.8995i	−1.69860	−	0.480437i
$838$	−28.6274	+	28.6274i	−0.988918	+	0.988918i
$839$	−5.21320	+	5.21320i	−0.179980	+	0.179980i	−0.791347	−	0.611367i	$-0.790620\pi$
$839$	−5.21320	+	5.21320i	−0.179980	+	0.179980i	0.611367	+	0.791347i	$0.290620\pi$
$840$	5.17157	−	7.31371i	0.178436	−	0.252347i
$841$	7.31371			0.252197
$842$		0			0
$843$	34.2843	+	24.2426i	1.18081	+	0.834961i
$844$		0			0
$845$	−21.9792	−	9.05025i	−0.756107	−	0.311338i
$846$	34.6274	−	12.2426i	1.19052	−	0.420911i
$847$	−4.94975	+	4.94975i	−0.170075	+	0.170075i
$848$			41.2548i			1.41670i
$849$	−2.00000	+	0.343146i	−0.0686398	+	0.0117767i
$850$	6.62742	−	6.62742i	0.227319	−	0.227319i
$851$	−13.7279	−	13.7279i	−0.470587	−	0.470587i
$852$		0			0
$853$	−18.0208	−	18.0208i	−0.617021	−	0.617021i	0.327745	−	0.944766i	$-0.393711\pi$
$853$	−18.0208	−	18.0208i	−0.617021	−	0.617021i	−0.944766	+	0.327745i	$0.893711\pi$
$854$			8.34315i			0.285497i
$855$	44.7696	−	15.8284i	1.53109	−	0.541321i
$856$	−9.65685	−	9.65685i	−0.330064	−	0.330064i
$857$	−41.2132			−1.40782			−0.703908	−	0.710291i	$-0.748563\pi$
$857$	−41.2132			−1.40782			−0.703908	+	0.710291i	$0.748563\pi$
$858$	−16.4853	+	6.34315i	−0.562798	+	0.216551i
$859$	−12.3431			−0.421143			−0.210571	−	0.977578i	$-0.567532\pi$
$859$	−12.3431			−0.421143			−0.210571	+	0.977578i	$0.567532\pi$
$860$		0			0
$861$	−19.8995	+	3.41421i	−0.678173	+	0.116356i
$862$			2.97056i			0.101178i
$863$	25.7990	+	25.7990i	0.878208	+	0.878208i	0.993349	−	0.115141i	$-0.0367321\pi$
$863$	25.7990	+	25.7990i	0.878208	+	0.878208i	−0.115141	+	0.993349i	$0.536732\pi$
$864$		0			0
$865$	23.5858	+	23.5858i	0.801941	+	0.801941i
$866$	8.58579	−	8.58579i	0.291757	−	0.291757i
$867$	0.292893	+	1.70711i	0.00994718	+	0.0579764i
$868$		0			0
$869$	0.242641	−	0.242641i	0.00823102	−	0.00823102i
$870$	3.52691	+	20.5563i	0.119574	+	0.696926i
$871$	−21.5147	−	14.3431i	−0.728998	−	0.485999i
$872$		−	39.3137i		−	1.33133i
$873$	15.9203	−	33.3345i	0.538821	−	1.12820i
$874$	−46.8701			−1.58540
$875$	12.1716			0.411474
$876$		0			0
$877$	9.51472	−	9.51472i	0.321289	−	0.321289i	−0.527972	−	0.849262i	$-0.677048\pi$
$877$	9.51472	−	9.51472i	0.321289	−	0.321289i	0.849262	+	0.527972i	$0.177048\pi$
$878$	21.2132	−	21.2132i	0.715911	−	0.715911i
$879$	6.10051	+	4.31371i	0.205765	+	0.145498i
$880$	14.6274			0.493090
$881$	−46.2843			−1.55936			−0.779678	−	0.626180i	$-0.784617\pi$
$881$	−46.2843			−1.55936			−0.779678	+	0.626180i	$0.784617\pi$
$882$	1.82843	−	3.82843i	0.0615663	−	0.128910i
$883$		−	31.3137i		−	1.05379i	−0.849930	−	0.526895i	$-0.823356\pi$
$883$		−	31.3137i		−	1.05379i	0.849930	−	0.526895i	$-0.176644\pi$
$884$		0			0
$885$	1.07107	+	6.24264i	0.0360036	+	0.209844i
$886$	−18.6569	+	18.6569i	−0.626789	+	0.626789i
$887$		−	28.8701i		−	0.969362i	−0.874691	−	0.484681i	$-0.838936\pi$
$887$		−	28.8701i		−	0.969362i	0.874691	−	0.484681i	$-0.161064\pi$
$888$	4.20101	+	24.4853i	0.140977	+	0.821672i
$889$	−1.41421	+	1.41421i	−0.0474312	+	0.0474312i
$890$	26.1716	+	26.1716i	0.877273	+	0.877273i
$891$	1.89949	−	17.8995i	0.0636355	−	0.599656i
$892$		0			0
$893$		−	74.9411i		−	2.50781i
$894$	−14.4853	+	2.48528i	−0.484460	+	0.0831202i
$895$	23.4939	+	23.4939i	0.785315	+	0.785315i
$896$	11.3137			0.377964
$897$	−22.3137	+	8.58579i	−0.745033	+	0.286671i
$898$	31.1716			1.04021
$899$	−32.3640	−	32.3640i	−1.07940	−	1.07940i
$900$		0			0
$901$			41.2548i			1.37440i
$902$	−23.3137	−	23.3137i	−0.776262	−	0.776262i
$903$	6.58579	+	4.65685i	0.219161	+	0.154970i
$904$	−8.34315	−	8.34315i	−0.277489	−	0.277489i
$905$	−2.58579	+	2.58579i	−0.0859544	+	0.0859544i
$906$	−30.3848	+	5.21320i	−1.00947	+	0.173197i
$907$			45.6274i			1.51503i	0.652816	+	0.757517i	$0.273588\pi$
$907$			45.6274i			1.51503i	−0.652816	+	0.757517i	$0.726412\pi$
$908$		0			0
$909$	−10.3431	+	3.65685i	−0.343060	+	0.121290i
$910$	7.75736	+	5.17157i	0.257154	+	0.171436i
$911$		−	23.8284i		−	0.789471i	−0.918795	−	0.394736i	$-0.870836\pi$
$911$		−	23.8284i		−	0.789471i	0.918795	−	0.394736i	$-0.129164\pi$
$912$	48.9706	+	34.6274i	1.62158	+	1.14663i
$913$	−2.00000			−0.0661903
$914$	−21.6569			−0.716345
$915$	10.7868	−	15.2548i	0.356600	−	0.504309i
$916$		0			0
$917$	−3.58579	+	3.58579i	−0.118413	+	0.118413i
$918$	−8.00000	+	28.2843i	−0.264039	+	0.933520i
$919$	52.8284			1.74265			0.871325	−	0.490707i	$-0.163262\pi$
$919$	52.8284			1.74265			0.871325	+	0.490707i	$0.163262\pi$
$920$	19.7990			0.652753
$921$	−11.8284	+	16.7279i	−0.389760	+	0.551204i
$922$			36.9706i			1.21756i
$923$	7.79899	−	11.6985i	0.256707	−	0.385060i
$924$		0			0
$925$	−5.94113	+	5.94113i	−0.195343	+	0.195343i
$926$			29.3137i			0.963308i
$927$		0			0
$928$		0			0
$929$	7.92031	+	7.92031i	0.259857	+	0.259857i	0.824996	−	0.565139i	$-0.191177\pi$
$929$	7.92031	+	7.92031i	0.259857	+	0.259857i	−0.565139	+	0.824996i	$0.691177\pi$
$930$	−25.4142	+	35.9411i	−0.833365	+	1.17856i
$931$	−6.12132	−	6.12132i	−0.200618	−	0.200618i
$932$		0			0
$933$	0.129942	+	0.757359i	0.00425412	+	0.0247948i
$934$	9.21320	+	9.21320i	0.301465	+	0.301465i
$935$	14.6274			0.478368
$936$	29.6569	+	7.51472i	0.969365	+	0.245626i
$937$	20.8701			0.681795			0.340898	−	0.940100i	$-0.389269\pi$
$937$	20.8701			0.681795			0.340898	+	0.940100i	$0.389269\pi$
$938$	7.17157	+	7.17157i	0.234160	+	0.234160i
$939$	−4.72792	−	27.5563i	−0.154290	−	0.899267i
$940$		0			0
$941$	5.39340	+	5.39340i	0.175820	+	0.175820i	0.789531	−	0.613711i	$-0.210324\pi$
$941$	5.39340	+	5.39340i	0.175820	+	0.175820i	−0.613711	+	0.789531i	$0.710324\pi$
$942$	12.0000	−	16.9706i	0.390981	−	0.552931i
$943$	−31.5563	−	31.5563i	−1.02762	−	1.02762i
$944$	−5.65685	+	5.65685i	−0.184115	+	0.184115i
$945$	−8.29289	+	4.63604i	−0.269768	+	0.150810i
$946$			13.1716i			0.428245i
$947$	−19.4142	+	19.4142i	−0.630877	+	0.630877i	−0.948288	−	0.317411i	$-0.897187\pi$
$947$	−19.4142	+	19.4142i	−0.630877	+	0.630877i	0.317411	+	0.948288i	$0.397187\pi$
$948$		0			0
$949$	−11.6569	+	17.4853i	−0.378398	+	0.567596i
$950$			20.2843i			0.658109i
$951$	3.89949	−	5.51472i	0.126450	−	0.178827i
$952$	11.3137			0.366679
$953$	−29.9706			−0.970842			−0.485421	−	0.874281i	$-0.661334\pi$
$953$	−29.9706			−0.970842			−0.485421	+	0.874281i	$0.661334\pi$
$954$	18.8579	−	39.4853i	0.610546	−	1.27838i
$955$	17.2132	−	17.2132i	0.557006	−	0.557006i
$956$		0			0
$957$	9.31371	−	13.1716i	0.301069	−	0.425776i
$958$	32.0416			1.03522
$959$	−5.07107			−0.163753
$960$	−20.6863	−	14.6274i	−0.667647	−	0.472098i
$961$		−	65.5980i		−	2.11606i
$962$	−25.3553	+	5.07107i	−0.817489	+	0.163498i
$963$	4.82843	+	13.6569i	0.155594	+	0.440086i
$964$		0			0
$965$		−	31.6569i		−	1.01907i
$966$	9.24264	−	1.58579i	0.297377	−	0.0510218i
$967$	20.3848	−	20.3848i	0.655530	−	0.655530i	−0.298789	−	0.954319i	$-0.596583\pi$
$967$	20.3848	−	20.3848i	0.655530	−	0.655530i	0.954319	+	0.298789i	$0.0965827\pi$
$968$	14.0000	+	14.0000i	0.449977	+	0.449977i
$969$	48.9706	+	34.6274i	1.57316	+	1.11239i
$970$	−22.5147	−	22.5147i	−0.722904	−	0.722904i
$971$			56.5269i			1.81403i	0.421093	+	0.907017i	$0.361647\pi$
$971$			56.5269i			1.81403i	−0.421093	+	0.907017i	$0.638353\pi$
$972$		0			0
$973$	−2.24264	−	2.24264i	−0.0718958	−	0.0718958i
$974$	−51.6569			−1.65519
$975$	3.71573	+	9.65685i	0.118999	+	0.309267i
$976$	23.5980			0.755353
$977$	−7.55635	−	7.55635i	−0.241749	−	0.241749i	0.575824	−	0.817573i	$-0.304681\pi$
$977$	−7.55635	−	7.55635i	−0.241749	−	0.241749i	−0.817573	+	0.575824i	$0.804681\pi$
$978$	−23.0711	+	3.95837i	−0.737731	+	0.126575i
$979$		−	28.6274i		−	0.914936i
$980$		0			0
$981$	−17.9706	+	37.6274i	−0.573756	+	1.20135i
$982$	4.97056	+	4.97056i	0.158617	+	0.158617i
$983$	−7.19239	+	7.19239i	−0.229402	+	0.229402i	−0.812443	−	0.583041i	$-0.801863\pi$
$983$	−7.19239	+	7.19239i	−0.229402	+	0.229402i	0.583041	+	0.812443i	$0.301863\pi$
$984$	9.65685	+	56.2843i	0.307849	+	1.79428i
$985$			6.87006i			0.218898i
$986$	−18.6274	+	18.6274i	−0.593218	+	0.593218i
$987$	2.53553	+	14.7782i	0.0807069	+	0.470394i
$988$		0			0
$989$			17.8284i			0.566911i
$990$	−14.0000	−	6.68629i	−0.444949	−	0.212504i
$991$	−9.02944			−0.286830			−0.143415	−	0.989663i	$-0.545808\pi$
$991$	−9.02944			−0.286830			−0.143415	+	0.989663i	$0.545808\pi$
$992$		0			0
$993$	−5.31371	−	3.75736i	−0.168625	−	0.119236i
$994$	−3.89949	+	3.89949i	−0.123684	+	0.123684i
$995$	8.20101	−	8.20101i	0.259989	−	0.259989i
$996$		0			0
$997$	28.6863			0.908504			0.454252	−	0.890873i	$-0.349907\pi$
$997$	28.6863			0.908504			0.454252	+	0.890873i	$0.349907\pi$
$998$	−28.0000			−0.886325
$999$	7.17157	−	25.3553i	0.226899	−	0.802207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.n.b.239.2	yes	4
3.2	odd	2		273.2.n.a.239.2	yes	4
13.8	odd	4		273.2.n.a.8.2	✓	4
39.8	even	4	inner	273.2.n.b.8.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.n.a.8.2	✓	4	13.8	odd	4
273.2.n.a.239.2	yes	4	3.2	odd	2
273.2.n.b.8.2	yes	4	39.8	even	4	inner
273.2.n.b.239.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.292893 - 1.70711i) q^{3} +(1.29289 + 1.29289i) q^{5} +(1.41421 - 2.00000i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.82843 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-0.292893 - 1.70711i) q^{3} +(1.29289 + 1.29289i) q^{5} +(1.41421 - 2.00000i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.82843 + 1.00000i) q^{9} +2.58579i q^{10} +(1.41421 - 1.41421i) q^{11} +(-0.707107 - 3.53553i) q^{13} +1.41421i q^{14} +(1.82843 - 2.58579i) q^{15} +4.00000 q^{16} +4.00000 q^{17} +(-3.82843 - 1.82843i) q^{18} +(-6.12132 + 6.12132i) q^{19} +(1.00000 - 1.41421i) q^{21} +2.82843 q^{22} +3.82843 q^{23} +(-4.00000 - 2.82843i) q^{24} -1.65685i q^{25} +(2.82843 - 4.24264i) q^{26} +(2.53553 + 4.53553i) q^{27} +4.65685i q^{29} +(4.41421 - 0.757359i) q^{30} +(-6.94975 + 6.94975i) q^{31} +(-2.82843 - 2.00000i) q^{33} +(4.00000 + 4.00000i) q^{34} +1.82843i q^{35} +(-3.58579 - 3.58579i) q^{37} -12.2426 q^{38} +(-5.82843 + 2.24264i) q^{39} +5.17157 q^{40} +(-8.24264 - 8.24264i) q^{41} +(2.41421 - 0.414214i) q^{42} +4.65685i q^{43} +(-4.94975 - 2.36396i) q^{45} +(3.82843 + 3.82843i) q^{46} +(-6.12132 + 6.12132i) q^{47} +(-1.17157 - 6.82843i) q^{48} +1.00000i q^{49} +(1.65685 - 1.65685i) q^{50} +(-1.17157 - 6.82843i) q^{51} +10.3137i q^{53} +(-2.00000 + 7.07107i) q^{54} +3.65685 q^{55} +2.82843 q^{56} +(12.2426 + 8.65685i) q^{57} +(-4.65685 + 4.65685i) q^{58} +(-1.41421 + 1.41421i) q^{59} +5.89949 q^{61} -13.8995 q^{62} +(-2.70711 - 1.29289i) q^{63} -8.00000i q^{64} +(3.65685 - 5.48528i) q^{65} +(-0.828427 - 4.82843i) q^{66} +(5.07107 - 5.07107i) q^{67} +(-1.12132 - 6.53553i) q^{69} +(-1.82843 + 1.82843i) q^{70} +(2.75736 + 2.75736i) q^{71} +(-3.65685 + 7.65685i) q^{72} +(-4.12132 - 4.12132i) q^{73} -7.17157i q^{74} +(-2.82843 + 0.485281i) q^{75} +2.00000 q^{77} +(-8.07107 - 3.58579i) q^{78} +0.171573 q^{79} +(5.17157 + 5.17157i) q^{80} +(7.00000 - 5.65685i) q^{81} -16.4853i q^{82} +(-0.707107 - 0.707107i) q^{83} +(5.17157 + 5.17157i) q^{85} +(-4.65685 + 4.65685i) q^{86} +(7.94975 - 1.36396i) q^{87} -5.65685i q^{88} +(10.1213 - 10.1213i) q^{89} +(-2.58579 - 7.31371i) q^{90} +(2.00000 - 3.00000i) q^{91} +(13.8995 + 9.82843i) q^{93} -12.2426 q^{94} -15.8284 q^{95} +(-8.70711 + 8.70711i) q^{97} +(-1.00000 + 1.00000i) q^{98} +(-2.58579 + 5.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8	\( 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8} - 4 q^{15} + 16 q^{16} + 16 q^{17} - 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{23} - 16 q^{24} - 4 q^{27} + 12 q^{30} - 8 q^{31} + 16 q^{34} - 20 q^{37} - 32 q^{38} - 12 q^{39} + 32 q^{40} - 16 q^{41} + 4 q^{42} + 4 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{50} - 16 q^{51} - 8 q^{54} - 8 q^{55} + 32 q^{57} + 4 q^{58} - 16 q^{61} - 16 q^{62} - 8 q^{63} - 8 q^{65} + 8 q^{66} - 8 q^{67} + 4 q^{69} + 4 q^{70} + 28 q^{71} + 8 q^{72} - 8 q^{73} + 8 q^{77} - 4 q^{78} + 12 q^{79} + 32 q^{80} + 28 q^{81} + 32 q^{85} + 4 q^{86} + 12 q^{87} + 32 q^{89} - 16 q^{90} + 8 q^{91} + 16 q^{93} - 32 q^{94} - 52 q^{95} - 32 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8 - 4 * q^15 + 16 * q^16 + 16 * q^17 - 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^23 - 16 * q^24 - 4 * q^27 + 12 * q^30 - 8 * q^31 + 16 * q^34 - 20 * q^37 - 32 * q^38 - 12 * q^39 + 32 * q^40 - 16 * q^41 + 4 * q^42 + 4 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^50 - 16 * q^51 - 8 * q^54 - 8 * q^55 + 32 * q^57 + 4 * q^58 - 16 * q^61 - 16 * q^62 - 8 * q^63 - 8 * q^65 + 8 * q^66 - 8 * q^67 + 4 * q^69 + 4 * q^70 + 28 * q^71 + 8 * q^72 - 8 * q^73 + 8 * q^77 - 4 * q^78 + 12 * q^79 + 32 * q^80 + 28 * q^81 + 32 * q^85 + 4 * q^86 + 12 * q^87 + 32 * q^89 - 16 * q^90 + 8 * q^91 + 16 * q^93 - 32 * q^94 - 52 * q^95 - 32 * q^97 - 4 * q^98 - 16 * q^99

Introduction

L-functions

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