LMFDB - Embedded newform 144.2.k.c.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("144.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.k (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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.2
Root			$-0.767178 - 1.18804i$ of defining polynomial
Character	$\chi$	$=$	144.109
Dual form			144.2.k.c.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.767178 - 1.18804i) q^{2} +(-0.822876 + 1.82288i) q^{4} +(-2.37608 + 2.37608i) q^{5} +3.64575i q^{7} +(2.79694 - 0.420861i) q^{8} +O(q^{10})$	\(q+(-0.767178 - 1.18804i) q^{2} +(-0.822876 + 1.82288i) q^{4} +(-2.37608 + 2.37608i) q^{5} +3.64575i q^{7} +(2.79694 - 0.420861i) q^{8} +(4.64575 + 1.00000i) q^{10} +(-0.841723 + 0.841723i) q^{11} +(-2.64575 - 2.64575i) q^{13} +(4.33130 - 2.79694i) q^{14} +(-2.64575 - 3.00000i) q^{16} +3.06871 q^{17} +(1.64575 + 1.64575i) q^{19} +(-2.37608 - 6.28651i) q^{20} +(1.64575 + 0.354249i) q^{22} +7.82087i q^{23} -6.29150i q^{25} +(-1.11349 + 5.17302i) q^{26} +(-6.64575 - 3.00000i) q^{28} +(-0.692633 - 0.692633i) q^{29} -0.354249 q^{31} +(-1.53436 + 5.44479i) q^{32} +(-2.35425 - 3.64575i) q^{34} +(-8.66259 - 8.66259i) q^{35} +(4.64575 - 4.64575i) q^{37} +(0.692633 - 3.21780i) q^{38} +(-5.64575 + 7.64575i) q^{40} -6.43560i q^{41} +(-5.64575 + 5.64575i) q^{43} +(-0.841723 - 2.22699i) q^{44} +(9.29150 - 6.00000i) q^{46} +11.1878 q^{47} -6.29150 q^{49} +(-7.47455 + 4.82670i) q^{50} +(7.00000 - 2.64575i) q^{52} +(-5.44479 + 5.44479i) q^{53} -4.00000i q^{55} +(1.53436 + 10.1969i) q^{56} +(-0.291503 + 1.35425i) q^{58} +(7.82087 - 7.82087i) q^{59} +(4.64575 + 4.64575i) q^{61} +(0.271772 + 0.420861i) q^{62} +(7.64575 - 2.35425i) q^{64} +12.5730 q^{65} +(4.00000 + 4.00000i) q^{67} +(-2.52517 + 5.59388i) q^{68} +(-3.64575 + 16.9373i) q^{70} -3.36689i q^{71} +7.29150i q^{73} +(-9.08345 - 1.95522i) q^{74} +(-4.35425 + 1.64575i) q^{76} +(-3.06871 - 3.06871i) q^{77} +4.35425 q^{79} +(13.4148 + 0.841723i) q^{80} +(-7.64575 + 4.93725i) q^{82} +(0.841723 + 0.841723i) q^{83} +(-7.29150 + 7.29150i) q^{85} +(11.0387 + 2.37608i) q^{86} +(-2.00000 + 2.70850i) q^{88} -9.50432i q^{89} +(9.64575 - 9.64575i) q^{91} +(-14.2565 - 6.43560i) q^{92} +(-8.58301 - 13.2915i) q^{94} -7.82087 q^{95} +10.5830 q^{97} +(4.82670 + 7.47455i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 16 q^{10} - 8 q^{19} - 8 q^{22} - 32 q^{28} - 24 q^{31} - 40 q^{34} + 16 q^{37} - 24 q^{40} - 24 q^{43} + 32 q^{46} - 8 q^{49} + 56 q^{52} + 40 q^{58} + 16 q^{61} + 40 q^{64} + 32 q^{67} - 8 q^{70} - 56 q^{76} + 56 q^{79} - 40 q^{82} - 16 q^{85} - 16 q^{88} + 56 q^{91} + 16 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 16 * q^10 - 8 * q^19 - 8 * q^22 - 32 * q^28 - 24 * q^31 - 40 * q^34 + 16 * q^37 - 24 * q^40 - 24 * q^43 + 32 * q^46 - 8 * q^49 + 56 * q^52 + 40 * q^58 + 16 * q^61 + 40 * q^64 + 32 * q^67 - 8 * q^70 - 56 * q^76 + 56 * q^79 - 40 * q^82 - 16 * q^85 - 16 * q^88 + 56 * q^91 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.767178	−	1.18804i	−0.542477	−	0.840071i
$2$	−0.767178	−	1.18804i	−0.542477	−	0.840071i
$3$		0			0
$3$		0			0
$4$	−0.822876	+	1.82288i	−0.411438	+	0.911438i
$5$	−2.37608	+	2.37608i	−1.06261	+	1.06261i	−0.0647108	+	0.997904i	$0.520612\pi$
$5$	−2.37608	+	2.37608i	−1.06261	+	1.06261i	−0.997904	+	0.0647108i	$0.979388\pi$
$6$		0			0
$7$			3.64575i			1.37796i	0.724778	+	0.688982i	$0.241942\pi$
$7$			3.64575i			1.37796i	−0.724778	+	0.688982i	$0.758058\pi$
$8$	2.79694	−	0.420861i	0.988868	−	0.148797i
$9$		0			0
$10$	4.64575	+	1.00000i	1.46912	+	0.316228i
$11$	−0.841723	+	0.841723i	−0.253789	+	0.253789i	−0.822522	−	0.568733i	$-0.807434\pi$
$11$	−0.841723	+	0.841723i	−0.253789	+	0.253789i	0.568733	+	0.822522i	$0.307434\pi$
$12$		0			0
$13$	−2.64575	−	2.64575i	−0.733799	−	0.733799i	0.237571	−	0.971370i	$-0.423649\pi$
$13$	−2.64575	−	2.64575i	−0.733799	−	0.733799i	−0.971370	+	0.237571i	$0.923649\pi$
$14$	4.33130	−	2.79694i	1.15759	−	0.747514i
$15$		0			0
$16$	−2.64575	−	3.00000i	−0.661438	−	0.750000i
$17$	3.06871			0.744272			0.372136	−	0.928178i	$-0.378625\pi$
$17$	3.06871			0.744272			0.372136	+	0.928178i	$0.378625\pi$
$18$		0			0
$19$	1.64575	+	1.64575i	0.377561	+	0.377561i	0.870222	−	0.492660i	$-0.163976\pi$
$19$	1.64575	+	1.64575i	0.377561	+	0.377561i	−0.492660	+	0.870222i	$0.663976\pi$
$20$	−2.37608	−	6.28651i	−0.531307	−	1.40571i
$21$		0			0
$22$	1.64575	+	0.354249i	0.350875	+	0.0755261i
$23$			7.82087i			1.63076i	0.578923	+	0.815382i	$0.303473\pi$
$23$			7.82087i			1.63076i	−0.578923	+	0.815382i	$0.696527\pi$
$24$		0			0
$25$		−	6.29150i		−	1.25830i
$26$	−1.11349	+	5.17302i	−0.218374	+	1.01451i
$27$		0			0
$28$	−6.64575	−	3.00000i	−1.25593	−	0.566947i
$29$	−0.692633	−	0.692633i	−0.128619	−	0.128619i	0.639867	−	0.768486i	$-0.278989\pi$
$29$	−0.692633	−	0.692633i	−0.128619	−	0.128619i	−0.768486	+	0.639867i	$0.778989\pi$
$30$		0			0
$31$	−0.354249			−0.0636249			−0.0318125	−	0.999494i	$-0.510128\pi$
$31$	−0.354249			−0.0636249			−0.0318125	+	0.999494i	$0.510128\pi$
$32$	−1.53436	+	5.44479i	−0.271238	+	0.962512i
$33$		0			0
$34$	−2.35425	−	3.64575i	−0.403750	−	0.625241i
$35$	−8.66259	−	8.66259i	−1.46425	−	1.46425i
$36$		0			0
$37$	4.64575	−	4.64575i	0.763757	−	0.763757i	−0.213242	−	0.976999i	$-0.568402\pi$
$37$	4.64575	−	4.64575i	0.763757	−	0.763757i	0.976999	+	0.213242i	$0.0684024\pi$
$38$	0.692633	−	3.21780i	0.112360	−	0.521996i
$39$		0			0
$40$	−5.64575	+	7.64575i	−0.892672	+	1.20890i
$41$		−	6.43560i		−	1.00507i	−0.864556	−	0.502536i	$-0.832400\pi$
$41$		−	6.43560i		−	1.00507i	0.864556	−	0.502536i	$-0.167600\pi$
$42$		0			0
$43$	−5.64575	+	5.64575i	−0.860969	+	0.860969i	−0.991451	−	0.130482i	$-0.958348\pi$
$43$	−5.64575	+	5.64575i	−0.860969	+	0.860969i	0.130482	+	0.991451i	$0.458348\pi$
$44$	−0.841723	−	2.22699i	−0.126894	−	0.335731i
$45$		0			0
$46$	9.29150	−	6.00000i	1.36996	−	0.884652i
$47$	11.1878			1.63190			0.815951	−	0.578121i	$-0.196214\pi$
$47$	11.1878			1.63190			0.815951	+	0.578121i	$0.196214\pi$
$48$		0			0
$49$	−6.29150			−0.898786
$50$	−7.47455	+	4.82670i	−1.05706	+	0.682599i
$51$		0			0
$52$	7.00000	−	2.64575i	0.970725	−	0.366900i
$53$	−5.44479	+	5.44479i	−0.747900	+	0.747900i	−0.974084	−	0.226185i	$-0.927375\pi$
$53$	−5.44479	+	5.44479i	−0.747900	+	0.747900i	0.226185	+	0.974084i	$0.427375\pi$
$54$		0			0
$55$		−	4.00000i		−	0.539360i
$56$	1.53436	+	10.1969i	0.205037	+	1.36262i
$57$		0			0
$58$	−0.291503	+	1.35425i	−0.0382762	+	0.177822i
$59$	7.82087	−	7.82087i	1.01819	−	1.01819i	0.0183591	−	0.999831i	$-0.494156\pi$
$59$	7.82087	−	7.82087i	1.01819	−	1.01819i	0.999831	−	0.0183591i	$-0.00584422\pi$
$60$		0			0
$61$	4.64575	+	4.64575i	0.594828	+	0.594828i	0.938932	−	0.344104i	$-0.111817\pi$
$61$	4.64575	+	4.64575i	0.594828	+	0.594828i	−0.344104	+	0.938932i	$0.611817\pi$
$62$	0.271772	+	0.420861i	0.0345151	+	0.0534495i
$63$		0			0
$64$	7.64575	−	2.35425i	0.955719	−	0.294281i
$65$	12.5730			1.55949
$66$		0			0
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	0.907889	−	0.419211i	$-0.137693\pi$
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	−0.419211	+	0.907889i	$0.637693\pi$
$68$	−2.52517	+	5.59388i	−0.306222	+	0.678358i
$69$		0			0
$70$	−3.64575	+	16.9373i	−0.435751	+	2.02439i
$71$		−	3.36689i		−	0.399577i	−0.979839	−	0.199788i	$-0.935975\pi$
$71$		−	3.36689i		−	0.399577i	0.979839	−	0.199788i	$-0.0640254\pi$
$72$		0			0
$73$			7.29150i			0.853406i	0.904392	+	0.426703i	$0.140325\pi$
$73$			7.29150i			0.853406i	−0.904392	+	0.426703i	$0.859675\pi$
$74$	−9.08345	−	1.95522i	−1.05593	−	0.227289i
$75$		0			0
$76$	−4.35425	+	1.64575i	−0.499467	+	0.188781i
$77$	−3.06871	−	3.06871i	−0.349712	−	0.349712i
$78$		0			0
$79$	4.35425			0.489891			0.244946	−	0.969537i	$-0.421230\pi$
$79$	4.35425			0.489891			0.244946	+	0.969537i	$0.421230\pi$
$80$	13.4148	+	0.841723i	1.49981	+	0.0941075i
$81$		0			0
$82$	−7.64575	+	4.93725i	−0.844332	+	0.545228i
$83$	0.841723	+	0.841723i	0.0923911	+	0.0923911i	0.751792	−	0.659401i	$-0.229190\pi$
$83$	0.841723	+	0.841723i	0.0923911	+	0.0923911i	−0.659401	+	0.751792i	$0.729190\pi$
$84$		0			0
$85$	−7.29150	+	7.29150i	−0.790875	+	0.790875i
$86$	11.0387	+	2.37608i	1.19033	+	0.256219i
$87$		0			0
$88$	−2.00000	+	2.70850i	−0.213201	+	0.288727i
$89$		−	9.50432i		−	1.00746i	−0.863862	−	0.503728i	$-0.831961\pi$
$89$		−	9.50432i		−	1.00746i	0.863862	−	0.503728i	$-0.168039\pi$
$90$		0			0
$91$	9.64575	−	9.64575i	1.01115	−	1.01115i
$92$	−14.2565	−	6.43560i	−1.48634	−	0.670958i
$93$		0			0
$94$	−8.58301	−	13.2915i	−0.885269	−	1.37091i
$95$	−7.82087			−0.802404
$96$		0			0
$97$	10.5830			1.07454			0.537271	−	0.843410i	$-0.319455\pi$
$97$	10.5830			1.07454			0.537271	+	0.843410i	$0.319455\pi$
$98$	4.82670	+	7.47455i	0.487571	+	0.755044i
$99$		0			0
$100$	11.4686	+	5.17712i	1.14686	+	0.517712i
$101$	−2.37608	+	2.37608i	−0.236429	+	0.236429i	−0.815370	−	0.578941i	$-0.803466\pi$
$101$	−2.37608	+	2.37608i	−0.236429	+	0.236429i	0.578941	+	0.815370i	$0.303466\pi$
$102$		0			0
$103$			1.06275i			0.104715i	0.998628	+	0.0523577i	$0.0166736\pi$
$103$			1.06275i			0.104715i	−0.998628	+	0.0523577i	$0.983326\pi$
$104$	−8.51350	−	6.28651i	−0.834818	−	0.616443i
$105$		0			0
$106$	10.6458	+	2.29150i	1.03401	+	0.222570i
$107$	−9.50432	+	9.50432i	−0.918817	+	0.918817i	−0.996943	−	0.0781266i	$-0.975106\pi$
$107$	−9.50432	+	9.50432i	−0.918817	+	0.918817i	0.0781266	+	0.996943i	$0.475106\pi$
$108$		0			0
$109$	−1.35425	−	1.35425i	−0.129713	−	0.129713i	0.639269	−	0.768983i	$-0.279237\pi$
$109$	−1.35425	−	1.35425i	−0.129713	−	0.129713i	−0.768983	+	0.639269i	$0.779237\pi$
$110$	−4.75216	+	3.06871i	−0.453100	+	0.292590i
$111$		0			0
$112$	10.9373	−	9.64575i	1.03347	−	0.911438i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−18.5830	−	18.5830i	−1.73287	−	1.73287i
$116$	1.83254	−	0.692633i	0.170147	−	0.0643094i
$117$		0			0
$118$	−15.2915	−	3.29150i	−1.40770	−	0.303007i
$119$			11.1878i			1.02558i
$120$		0			0
$121$			9.58301i			0.871182i
$122$	1.95522	−	9.08345i	0.177017	−	0.822377i
$123$		0			0
$124$	0.291503	−	0.645751i	0.0261777	−	0.0579902i
$125$	3.06871	+	3.06871i	0.274474	+	0.274474i
$126$		0			0
$127$	−14.9373			−1.32547			−0.662733	−	0.748855i	$-0.730604\pi$
$127$	−14.9373			−1.32547			−0.662733	+	0.748855i	$0.730604\pi$
$128$	−8.66259	−	7.27733i	−0.765672	−	0.643231i
$129$		0			0
$130$	−9.64575	−	14.9373i	−0.845988	−	1.31008i
$131$	−1.68345	−	1.68345i	−0.147083	−	0.147083i	0.629730	−	0.776814i	$-0.283165\pi$
$131$	−1.68345	−	1.68345i	−0.147083	−	0.147083i	−0.776814	+	0.629730i	$0.783165\pi$
$132$		0			0
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	1.68345	−	7.82087i	0.145428	−	0.675620i
$135$		0			0
$136$	8.58301	−	1.29150i	0.735987	−	0.110745i
$137$			15.9399i			1.36184i	0.732358	+	0.680920i	$0.238420\pi$
$137$			15.9399i			1.36184i	−0.732358	+	0.680920i	$0.761580\pi$
$138$		0			0
$139$	6.58301	−	6.58301i	0.558363	−	0.558363i	−0.370478	−	0.928841i	$-0.620806\pi$
$139$	6.58301	−	6.58301i	0.558363	−	0.558363i	0.928841	+	0.370478i	$0.120806\pi$
$140$	22.9191	−	8.66259i	1.93701	−	0.732123i
$141$		0			0
$142$	−4.00000	+	2.58301i	−0.335673	+	0.216761i
$143$	4.45398			0.372460
$144$		0			0
$145$	3.29150			0.273344
$146$	8.66259	−	5.59388i	0.716921	−	0.462953i
$147$		0			0
$148$	4.64575	+	12.2915i	0.381878	+	1.01036i
$149$	3.76135	−	3.76135i	0.308141	−	0.308141i	−0.536047	−	0.844188i	$-0.680083\pi$
$149$	3.76135	−	3.76135i	0.308141	−	0.308141i	0.844188	+	0.536047i	$0.180083\pi$
$150$		0			0
$151$		−	15.6458i		−	1.27323i	−0.771180	−	0.636617i	$-0.780333\pi$
$151$		−	15.6458i		−	1.27323i	0.771180	−	0.636617i	$-0.219667\pi$
$152$	5.29570	+	3.91044i	0.429538	+	0.317178i
$153$		0			0
$154$	−1.29150	+	6.00000i	−0.104072	+	0.483494i
$155$	0.841723	−	0.841723i	0.0676088	−	0.0676088i
$156$		0			0
$157$	−1.35425	−	1.35425i	−0.108081	−	0.108081i	0.650998	−	0.759079i	$-0.274350\pi$
$157$	−1.35425	−	1.35425i	−0.108081	−	0.108081i	−0.759079	+	0.650998i	$0.774350\pi$
$158$	−3.34048	−	5.17302i	−0.265755	−	0.411543i
$159$		0			0
$160$	−9.29150	−	16.5830i	−0.734558	−	1.31100i
$161$	−28.5129			−2.24714
$162$		0			0
$163$	6.35425	+	6.35425i	0.497703	+	0.497703i	0.910722	−	0.413019i	$-0.135526\pi$
$163$	6.35425	+	6.35425i	0.497703	+	0.497703i	−0.413019	+	0.910722i	$0.635526\pi$
$164$	11.7313	+	5.29570i	0.916061	+	0.413525i
$165$		0			0
$166$	0.354249	−	1.64575i	0.0274950	−	0.127735i
$167$		−	4.45398i		−	0.344659i	−0.985039	−	0.172330i	$-0.944871\pi$
$167$		−	4.45398i		−	0.344659i	0.985039	−	0.172330i	$-0.0551294\pi$
$168$		0			0
$169$			1.00000i			0.0769231i
$170$	14.2565	+	3.06871i	1.09342	+	0.235359i
$171$		0			0
$172$	−5.64575	−	14.9373i	−0.430485	−	1.13895i
$173$	5.44479	+	5.44479i	0.413960	+	0.413960i	0.883115	−	0.469156i	$-0.155442\pi$
$173$	5.44479	+	5.44479i	0.413960	+	0.413960i	−0.469156	+	0.883115i	$0.655442\pi$
$174$		0			0
$175$	22.9373			1.73389
$176$	4.75216	+	0.298179i	0.358207	+	0.0224761i
$177$		0			0
$178$	−11.2915	+	7.29150i	−0.846334	+	0.546521i
$179$	9.50432	+	9.50432i	0.710386	+	0.710386i	0.966616	−	0.256230i	$-0.0824804\pi$
$179$	9.50432	+	9.50432i	0.710386	+	0.710386i	−0.256230	+	0.966616i	$0.582480\pi$
$180$		0			0
$181$	4.64575	−	4.64575i	0.345316	−	0.345316i	−0.513045	−	0.858361i	$-0.671483\pi$
$181$	4.64575	−	4.64575i	0.345316	−	0.345316i	0.858361	+	0.513045i	$0.171483\pi$
$182$	−18.8595	−	4.05952i	−1.39796	−	0.300912i
$183$		0			0
$184$	3.29150	+	21.8745i	0.242653	+	1.61261i
$185$			22.0773i			1.62316i
$186$		0			0
$187$	−2.58301	+	2.58301i	−0.188888	+	0.188888i
$188$	−9.20614	+	20.3939i	−0.671427	+	1.48738i
$189$		0			0
$190$	6.00000	+	9.29150i	0.435286	+	0.674076i
$191$	−11.1878			−0.809518			−0.404759	−	0.914423i	$-0.632645\pi$
$191$	−11.1878			−0.809518			−0.404759	+	0.914423i	$0.632645\pi$
$192$		0			0
$193$	−19.8745			−1.43060			−0.715299	−	0.698818i	$-0.753710\pi$
$193$	−19.8745			−1.43060			−0.715299	+	0.698818i	$0.753710\pi$
$194$	−8.11905	−	12.5730i	−0.582914	−	0.902691i
$195$		0			0
$196$	5.17712	−	11.4686i	0.369795	−	0.819188i
$197$	8.81168	−	8.81168i	0.627806	−	0.627806i	−0.319709	−	0.947516i	$-0.603585\pi$
$197$	8.81168	−	8.81168i	0.627806	−	0.627806i	0.947516	+	0.319709i	$0.103585\pi$
$198$		0			0
$199$			8.35425i			0.592217i	0.955154	+	0.296108i	$0.0956890\pi$
$199$			8.35425i			0.592217i	−0.955154	+	0.296108i	$0.904311\pi$
$200$	−2.64785	−	17.5970i	−0.187231	−	1.24429i
$201$		0			0
$202$	4.64575	+	1.00000i	0.326874	+	0.0703598i
$203$	2.52517	−	2.52517i	0.177232	−	0.177232i
$204$		0			0
$205$	15.2915	+	15.2915i	1.06800	+	1.06800i
$206$	1.26258	−	0.815315i	0.0879684	−	0.0568057i
$207$		0			0
$208$	−0.937254	+	14.9373i	−0.0649869	+	1.03571i
$209$	−2.77053			−0.191642
$210$		0			0
$211$	6.58301	+	6.58301i	0.453193	+	0.453193i	0.896413	−	0.443220i	$-0.146164\pi$
$211$	6.58301	+	6.58301i	0.453193	+	0.453193i	−0.443220	+	0.896413i	$0.646164\pi$
$212$	−5.44479	−	14.4056i	−0.373950	−	0.989378i
$213$		0			0
$214$	18.5830	+	4.00000i	1.27031	+	0.273434i
$215$		−	26.8295i		−	1.82976i
$216$		0			0
$217$		−	1.29150i		−	0.0876729i
$218$	−0.569951	+	2.64785i	−0.0386020	+	0.179335i
$219$		0			0
$220$	7.29150	+	3.29150i	0.491593	+	0.221913i
$221$	−8.11905	−	8.11905i	−0.546146	−	0.546146i
$222$		0			0
$223$	−19.6458			−1.31558			−0.657788	−	0.753203i	$-0.728508\pi$
$223$	−19.6458			−1.31558			−0.657788	+	0.753203i	$0.728508\pi$
$224$	−19.8504	−	5.59388i	−1.32631	−	0.373757i
$225$		0			0
$226$		0			0
$227$	18.1669	+	18.1669i	1.20578	+	1.20578i	0.972381	+	0.233399i	$0.0749848\pi$
$227$	18.1669	+	18.1669i	1.20578	+	1.20578i	0.233399	+	0.972381i	$0.425015\pi$
$228$		0			0
$229$	2.06275	−	2.06275i	0.136310	−	0.136310i	−0.635659	−	0.771970i	$-0.719272\pi$
$229$	2.06275	−	2.06275i	0.136310	−	0.136310i	0.771970	+	0.635659i	$0.219272\pi$
$230$	−7.82087	+	36.3338i	−0.515693	+	2.39578i
$231$		0			0
$232$	−2.22876	−	1.64575i	−0.146325	−	0.108049i
$233$		−	21.7792i		−	1.42680i	−0.700757	−	0.713400i	$-0.747154\pi$
$233$		−	21.7792i		−	1.42680i	0.700757	−	0.713400i	$-0.252846\pi$
$234$		0			0
$235$	−26.5830	+	26.5830i	−1.73408	+	1.73408i
$236$	7.82087	+	20.6921i	0.509095	+	1.34694i
$237$		0			0
$238$	13.2915	−	8.58301i	0.861560	−	0.556354i
$239$	−23.4626			−1.51767			−0.758835	−	0.651283i	$-0.774231\pi$
$239$	−23.4626			−1.51767			−0.758835	+	0.651283i	$0.774231\pi$
$240$		0			0
$241$	9.29150			0.598518			0.299259	−	0.954172i	$-0.403260\pi$
$241$	9.29150			0.598518			0.299259	+	0.954172i	$0.403260\pi$
$242$	11.3850	−	7.35187i	0.731855	−	0.472596i
$243$		0			0
$244$	−12.2915	+	4.64575i	−0.786883	+	0.297414i
$245$	14.9491	−	14.9491i	0.955063	−	0.955063i
$246$		0			0
$247$		−	8.70850i		−	0.554108i
$248$	−0.990812	+	0.149090i	−0.0629167	+	0.00946720i
$249$		0			0
$250$	1.29150	−	6.00000i	0.0816818	−	0.379473i
$251$	−13.1166	+	13.1166i	−0.827911	+	0.827911i	−0.987228	−	0.159317i	$-0.949071\pi$
$251$	−13.1166	+	13.1166i	−0.827911	+	0.827911i	0.159317	+	0.987228i	$0.449071\pi$
$252$		0			0
$253$	−6.58301	−	6.58301i	−0.413870	−	0.413870i
$254$	11.4595	+	17.7460i	0.719035	+	1.11349i
$255$		0			0
$256$	−2.00000	+	15.8745i	−0.125000	+	0.992157i
$257$	16.2381			1.01290			0.506452	−	0.862268i	$-0.330957\pi$
$257$	16.2381			1.01290			0.506452	+	0.862268i	$0.330957\pi$
$258$		0			0
$259$	16.9373	+	16.9373i	1.05243	+	1.05243i
$260$	−10.3460	+	22.9191i	−0.641634	+	1.42138i
$261$		0			0
$262$	−0.708497	+	3.29150i	−0.0437711	+	0.203350i
$263$		−	15.6417i		−	0.964511i	−0.876031	−	0.482256i	$-0.839818\pi$
$263$		−	15.6417i		−	0.964511i	0.876031	−	0.482256i	$-0.160182\pi$
$264$		0			0
$265$		−	25.8745i		−	1.58946i
$266$	11.7313	+	2.52517i	0.719292	+	0.154828i
$267$		0			0
$268$	−10.5830	+	4.00000i	−0.646460	+	0.244339i
$269$	8.51350	+	8.51350i	0.519077	+	0.519077i	0.917292	−	0.398215i	$-0.130370\pi$
$269$	8.51350	+	8.51350i	0.519077	+	0.519077i	−0.398215	+	0.917292i	$0.630370\pi$
$270$		0			0
$271$	11.6458			0.707429			0.353715	−	0.935353i	$-0.384918\pi$
$271$	11.6458			0.707429			0.353715	+	0.935353i	$0.384918\pi$
$272$	−8.11905	−	9.20614i	−0.492290	−	0.558204i
$273$		0			0
$274$	18.9373	−	12.2288i	1.14404	−	0.738766i
$275$	5.29570	+	5.29570i	0.319343	+	0.319343i
$276$		0			0
$277$	20.5203	−	20.5203i	1.23294	−	1.23294i	0.270115	−	0.962828i	$-0.412938\pi$
$277$	20.5203	−	20.5203i	1.23294	−	1.23294i	0.962828	−	0.270115i	$-0.0870616\pi$
$278$	−12.8712	−	2.77053i	−0.771964	−	0.166166i
$279$		0			0
$280$	−27.8745	−	20.5830i	−1.66582	−	1.23007i
$281$		−	9.50432i		−	0.566980i	−0.958975	−	0.283490i	$-0.908508\pi$
$281$		−	9.50432i		−	0.566980i	0.958975	−	0.283490i	$-0.0914923\pi$
$282$		0			0
$283$	18.5830	−	18.5830i	1.10465	−	1.10465i	0.110803	−	0.993842i	$-0.464658\pi$
$283$	18.5830	−	18.5830i	1.10465	−	1.10465i	0.993842	−	0.110803i	$-0.0353421\pi$
$284$	6.13742	+	2.77053i	0.364189	+	0.164401i
$285$		0			0
$286$	−3.41699	−	5.29150i	−0.202051	−	0.312893i
$287$	23.4626			1.38495
$288$		0			0
$289$	−7.58301			−0.446059
$290$	−2.52517	−	3.91044i	−0.148283	−	0.229629i
$291$		0			0
$292$	−13.2915	−	6.00000i	−0.777826	−	0.351123i
$293$	14.9491	−	14.9491i	0.873336	−	0.873336i	−0.119498	−	0.992834i	$-0.538129\pi$
$293$	14.9491	−	14.9491i	0.873336	−	0.873336i	0.992834	+	0.119498i	$0.0381286\pi$
$294$		0			0
$295$			37.1660i			2.16389i
$296$	11.0387	−	14.9491i	0.641610	−	0.868899i
$297$		0			0
$298$	−7.35425	−	1.58301i	−0.426020	−	0.0917010i
$299$	20.6921	−	20.6921i	1.19665	−	1.19665i
$300$		0			0
$301$	−20.5830	−	20.5830i	−1.18638	−	1.18638i
$302$	−18.5878	+	12.0031i	−1.06961	+	0.690699i
$303$		0			0
$304$	0.583005	−	9.29150i	0.0334376	−	0.532904i
$305$	−22.0773			−1.26415
$306$		0			0
$307$	−20.0000	−	20.0000i	−1.14146	−	1.14146i	−0.988183	−	0.153277i	$-0.951017\pi$
$307$	−20.0000	−	20.0000i	−1.14146	−	1.14146i	−0.153277	−	0.988183i	$-0.548983\pi$
$308$	8.11905	−	3.06871i	0.462626	−	0.174856i
$309$		0			0
$310$	−1.64575	−	0.354249i	−0.0934724	−	0.0201200i
$311$		−	15.6417i		−	0.886962i	−0.896284	−	0.443481i	$-0.853743\pi$
$311$		−	15.6417i		−	0.886962i	0.896284	−	0.443481i	$-0.146257\pi$
$312$		0			0
$313$		−	1.29150i		−	0.0730000i	−0.999334	−	0.0365000i	$-0.988379\pi$
$313$		−	1.29150i		−	0.0730000i	0.999334	−	0.0365000i	$-0.0116209\pi$
$314$	−0.569951	+	2.64785i	−0.0321642	+	0.149427i
$315$		0			0
$316$	−3.58301	+	7.93725i	−0.201560	+	0.446505i
$317$	2.37608	+	2.37608i	0.133454	+	0.133454i	0.770678	−	0.637224i	$-0.219918\pi$
$317$	2.37608	+	2.37608i	0.133454	+	0.133454i	−0.637224	+	0.770678i	$0.719918\pi$
$318$		0			0
$319$	1.16601			0.0652841
$320$	−12.5730	+	23.7608i	−0.702854	+	1.32827i
$321$		0			0
$322$	21.8745	+	33.8745i	1.21902	+	1.88775i
$323$	5.05034	+	5.05034i	0.281008	+	0.281008i
$324$		0			0
$325$	−16.6458	+	16.6458i	−0.923340	+	0.923340i
$326$	2.67426	−	12.4239i	0.148113	−	0.688098i
$327$		0			0
$328$	−2.70850	−	18.0000i	−0.149552	−	0.993884i
$329$			40.7878i			2.24870i
$330$		0			0
$331$	−8.00000	+	8.00000i	−0.439720	+	0.439720i	−0.891918	−	0.452198i	$-0.850640\pi$
$331$	−8.00000	+	8.00000i	−0.439720	+	0.439720i	0.452198	+	0.891918i	$0.350640\pi$
$332$	−2.22699	+	0.841723i	−0.122222	+	0.0461955i
$333$		0			0
$334$	−5.29150	+	3.41699i	−0.289538	+	0.186970i
$335$	−19.0086			−1.03855
$336$		0			0
$337$	15.2915			0.832981			0.416491	−	0.909140i	$-0.363260\pi$
$337$	15.2915			0.832981			0.416491	+	0.909140i	$0.363260\pi$
$338$	1.18804	−	0.767178i	0.0646208	−	0.0417290i
$339$		0			0
$340$	−7.29150	−	19.2915i	−0.395437	−	1.04623i
$341$	0.298179	−	0.298179i	0.0161473	−	0.0161473i
$342$		0			0
$343$			2.58301i			0.139469i
$344$	−13.4148	+	18.1669i	−0.723275	+	0.979494i
$345$		0			0
$346$	2.29150	−	10.6458i	0.123192	−	0.572319i
$347$	−0.841723	+	0.841723i	−0.0451861	+	0.0451861i	−0.729339	−	0.684153i	$-0.760172\pi$
$347$	−0.841723	+	0.841723i	−0.0451861	+	0.0451861i	0.684153	+	0.729339i	$0.260172\pi$
$348$		0			0
$349$	−23.2288	−	23.2288i	−1.24341	−	1.24341i	−0.958579	−	0.284828i	$-0.908063\pi$
$349$	−23.2288	−	23.2288i	−1.24341	−	1.24341i	−0.284828	−	0.958579i	$-0.591937\pi$
$350$	−17.5970	−	27.2504i	−0.940597	−	1.45659i
$351$		0			0
$352$	−3.29150	−	5.87451i	−0.175438	−	0.313112i
$353$	−28.5129			−1.51759			−0.758796	−	0.651329i	$-0.774212\pi$
$353$	−28.5129			−1.51759			−0.758796	+	0.651329i	$0.774212\pi$
$354$		0			0
$355$	8.00000	+	8.00000i	0.424596	+	0.424596i
$356$	17.3252	+	7.82087i	0.918233	+	0.414505i
$357$		0			0
$358$	4.00000	−	18.5830i	0.211407	−	0.982142i
$359$			19.0086i			1.00324i	0.865089	+	0.501619i	$0.167262\pi$
$359$			19.0086i			1.00324i	−0.865089	+	0.501619i	$0.832738\pi$
$360$		0			0
$361$		−	13.5830i		−	0.714895i
$362$	−9.08345	−	1.95522i	−0.477416	−	0.102764i
$363$		0			0
$364$	9.64575	+	25.5203i	0.505575	+	1.33763i
$365$	−17.3252	−	17.3252i	−0.906842	−	0.906842i
$366$		0			0
$367$	−12.8118			−0.668769			−0.334384	−	0.942437i	$-0.608528\pi$
$367$	−12.8118			−0.668769			−0.334384	+	0.942437i	$0.608528\pi$
$368$	23.4626	−	20.6921i	1.22307	−	1.07865i
$369$		0			0
$370$	26.2288	−	16.9373i	1.36357	−	0.880526i
$371$	−19.8504	−	19.8504i	−1.03058	−	1.03058i
$372$		0			0
$373$	−3.93725	+	3.93725i	−0.203863	+	0.203863i	−0.801653	−	0.597790i	$-0.796046\pi$
$373$	−3.93725	+	3.93725i	−0.203863	+	0.203863i	0.597790	+	0.801653i	$0.296046\pi$
$374$	5.05034	+	1.08709i	0.261147	+	0.0562119i
$375$		0			0
$376$	31.2915	−	4.70850i	1.61374	−	0.242822i
$377$			3.66507i			0.188761i
$378$		0			0
$379$	13.6458	−	13.6458i	0.700935	−	0.700935i	−0.263676	−	0.964611i	$-0.584935\pi$
$379$	13.6458	−	13.6458i	0.700935	−	0.700935i	0.964611	+	0.263676i	$0.0849350\pi$
$380$	6.43560	−	14.2565i	0.330140	−	0.731342i
$381$		0			0
$382$	8.58301	+	13.2915i	0.439145	+	0.680052i
$383$	11.1878			0.571668			0.285834	−	0.958279i	$-0.407729\pi$
$383$	11.1878			0.571668			0.285834	+	0.958279i	$0.407729\pi$
$384$		0			0
$385$	14.5830			0.743219
$386$	15.2473	+	23.6117i	0.776066	+	1.20180i
$387$		0			0
$388$	−8.70850	+	19.2915i	−0.442107	+	0.979378i
$389$	−7.42642	+	7.42642i	−0.376534	+	0.376534i	−0.869850	−	0.493316i	$-0.835785\pi$
$389$	−7.42642	+	7.42642i	−0.376534	+	0.376534i	0.493316	+	0.869850i	$0.335785\pi$
$390$		0			0
$391$			24.0000i			1.21373i
$392$	−17.5970	+	2.64785i	−0.888781	+	0.133737i
$393$		0			0
$394$	−17.2288	−	3.70850i	−0.867972	−	0.186831i
$395$	−10.3460	+	10.3460i	−0.520566	+	0.520566i
$396$		0			0
$397$	23.9373	+	23.9373i	1.20138	+	1.20138i	0.973748	+	0.227628i	$0.0730971\pi$
$397$	23.9373	+	23.9373i	1.20138	+	1.20138i	0.227628	+	0.973748i	$0.426903\pi$
$398$	9.92518	−	6.40920i	0.497504	−	0.321264i
$399$		0			0
$400$	−18.8745	+	16.6458i	−0.943725	+	0.832288i
$401$	9.20614			0.459733			0.229866	−	0.973222i	$-0.426171\pi$
$401$	9.20614			0.459733			0.229866	+	0.973222i	$0.426171\pi$
$402$		0			0
$403$	0.937254	+	0.937254i	0.0466879	+	0.0466879i
$404$	−2.37608	−	6.28651i	−0.118214	−	0.312766i
$405$		0			0
$406$	−4.93725	−	1.06275i	−0.245032	−	0.0527432i
$407$			7.82087i			0.387666i
$408$		0			0
$409$			17.1660i			0.848805i	0.905474	+	0.424402i	$0.139516\pi$
$409$			17.1660i			0.848805i	−0.905474	+	0.424402i	$0.860484\pi$
$410$	6.43560	−	29.8982i	0.317832	−	1.47657i
$411$		0			0
$412$	−1.93725	−	0.874508i	−0.0954417	−	0.0430839i
$413$	28.5129	+	28.5129i	1.40303	+	1.40303i
$414$		0			0
$415$	−4.00000			−0.196352
$416$	18.4651	−	10.3460i	0.905325	−	0.507256i
$417$		0			0
$418$	2.12549	+	3.29150i	0.103961	+	0.160993i
$419$	13.1166	+	13.1166i	0.640786	+	0.640786i	0.950749	−	0.309962i	$-0.100316\pi$
$419$	13.1166	+	13.1166i	0.640786	+	0.640786i	−0.309962	+	0.950749i	$0.600316\pi$
$420$		0			0
$421$	16.6458	−	16.6458i	0.811264	−	0.811264i	−0.173559	−	0.984823i	$-0.555527\pi$
$421$	16.6458	−	16.6458i	0.811264	−	0.811264i	0.984823	+	0.173559i	$0.0555268\pi$
$422$	2.77053	−	12.8712i	0.134867	−	0.626561i
$423$		0			0
$424$	−12.9373	+	17.5203i	−0.628289	+	0.850859i
$425$		−	19.3068i		−	0.936518i
$426$		0			0
$427$	−16.9373	+	16.9373i	−0.819651	+	0.819651i
$428$	−9.50432	−	25.1461i	−0.459408	−	1.21548i
$429$		0			0
$430$	−31.8745	+	20.5830i	−1.53713	+	0.992601i
$431$	1.08709			0.0523632			0.0261816	−	0.999657i	$-0.491665\pi$
$431$	1.08709			0.0523632			0.0261816	+	0.999657i	$0.491665\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−1.53436	+	0.990812i	−0.0736515	+	0.0475605i
$435$		0			0
$436$	3.58301	−	1.35425i	0.171595	−	0.0648567i
$437$	−12.8712	+	12.8712i	−0.615713	+	0.615713i
$438$		0			0
$439$		−	37.5203i		−	1.79074i	−0.445319	−	0.895372i	$-0.646910\pi$
$439$		−	37.5203i		−	1.79074i	0.445319	−	0.895372i	$-0.353090\pi$
$440$	−1.68345	−	11.1878i	−0.0802551	−	0.533356i
$441$		0			0
$442$	−3.41699	+	15.8745i	−0.162530	+	0.755073i
$443$	−23.2172	+	23.2172i	−1.10308	+	1.10308i	−0.109048	+	0.994036i	$0.534780\pi$
$443$	−23.2172	+	23.2172i	−1.10308	+	1.10308i	−0.994036	+	0.109048i	$0.965220\pi$
$444$		0			0
$445$	22.5830	+	22.5830i	1.07054	+	1.07054i
$446$	15.0718	+	23.3399i	0.713670	+	1.10518i
$447$		0			0
$448$	8.58301	+	27.8745i	0.405509	+	1.31695i
$449$	37.7191			1.78007			0.890037	−	0.455889i	$-0.150678\pi$
$449$	37.7191			1.78007			0.890037	+	0.455889i	$0.150678\pi$
$450$		0			0
$451$	5.41699	+	5.41699i	0.255076	+	0.255076i
$452$		0			0
$453$		0			0
$454$	7.64575	−	35.5203i	0.358833	−	1.66705i
$455$			45.8381i			2.14892i
$456$		0			0
$457$			26.5830i			1.24350i	0.783216	+	0.621750i	$0.213578\pi$
$457$			26.5830i			1.24350i	−0.783216	+	0.621750i	$0.786422\pi$
$458$	−4.03312	−	0.868130i	−0.188455	−	0.0405651i
$459$		0			0
$460$	49.1660	−	18.5830i	2.29238	−	0.866437i
$461$	−8.81168	−	8.81168i	−0.410401	−	0.410401i	0.471477	−	0.881878i	$-0.343721\pi$
$461$	−8.81168	−	8.81168i	−0.410401	−	0.410401i	−0.881878	+	0.471477i	$0.843721\pi$
$462$		0			0
$463$	30.9373			1.43778			0.718888	−	0.695126i	$-0.244651\pi$
$463$	30.9373			1.43778			0.718888	+	0.695126i	$0.244651\pi$
$464$	−0.245364	+	3.91044i	−0.0113908	+	0.181537i
$465$		0			0
$466$	−25.8745	+	16.7085i	−1.19861	+	0.774006i
$467$	−11.4331	−	11.4331i	−0.529062	−	0.529062i	0.391231	−	0.920293i	$-0.372049\pi$
$467$	−11.4331	−	11.4331i	−0.529062	−	0.529062i	−0.920293	+	0.391231i	$0.872049\pi$
$468$		0			0
$469$	−14.5830	+	14.5830i	−0.673381	+	0.673381i
$470$	51.9756	+	11.1878i	2.39745	+	0.516053i
$471$		0			0
$472$	18.5830	−	25.1660i	0.855352	−	1.15836i
$473$		−	9.50432i		−	0.437009i
$474$		0			0
$475$	10.3542	−	10.3542i	0.475086	−	0.475086i
$476$	−20.3939	−	9.20614i	−0.934753	−	0.421963i
$477$		0			0
$478$	18.0000	+	27.8745i	0.823301	+	1.27495i
$479$	−12.2748			−0.560852			−0.280426	−	0.959876i	$-0.590476\pi$
$479$	−12.2748			−0.560852			−0.280426	+	0.959876i	$0.590476\pi$
$480$		0			0
$481$	−24.5830			−1.12089
$482$	−7.12824	−	11.0387i	−0.324682	−	0.502798i
$483$		0			0
$484$	−17.4686	−	7.88562i	−0.794028	−	0.358437i
$485$	−25.1461	+	25.1461i	−1.14182	+	1.14182i
$486$		0			0
$487$		−	18.2288i		−	0.826024i	−0.910726	−	0.413012i	$-0.864477\pi$
$487$		−	18.2288i		−	0.826024i	0.910726	−	0.413012i	$-0.135523\pi$
$488$	14.9491	+	11.0387i	0.676714	+	0.499697i
$489$		0			0
$490$	−29.2288	−	6.29150i	−1.32042	−	0.284221i
$491$	13.9583	−	13.9583i	0.629929	−	0.629929i	−0.318121	−	0.948050i	$-0.603052\pi$
$491$	13.9583	−	13.9583i	0.629929	−	0.629929i	0.948050	+	0.318121i	$0.103052\pi$
$492$		0			0
$493$	−2.12549	−	2.12549i	−0.0957274	−	0.0957274i
$494$	−10.3460	+	6.68097i	−0.465490	+	0.300591i
$495$		0			0
$496$	0.937254	+	1.06275i	0.0420839	+	0.0477187i
$497$	12.2748			0.550602
$498$		0			0
$499$	−10.5830	−	10.5830i	−0.473760	−	0.473760i	0.429369	−	0.903129i	$-0.358736\pi$
$499$	−10.5830	−	10.5830i	−0.473760	−	0.473760i	−0.903129	+	0.429369i	$0.858736\pi$
$500$	−8.11905	+	3.06871i	−0.363095	+	0.137237i
$501$		0			0
$502$	25.6458	+	5.52026i	1.14463	+	0.246381i
$503$		−	25.7424i		−	1.14780i	−0.818926	−	0.573899i	$-0.805430\pi$
$503$		−	25.7424i		−	1.14780i	0.818926	−	0.573899i	$-0.194570\pi$
$504$		0			0
$505$		−	11.2915i		−	0.502465i
$506$	−2.77053	+	12.8712i	−0.123165	+	0.572195i
$507$		0			0
$508$	12.2915	−	27.2288i	0.545347	−	1.20808i
$509$	−27.2240	−	27.2240i	−1.20668	−	1.20668i	−0.972096	−	0.234585i	$-0.924627\pi$
$509$	−27.2240	−	27.2240i	−1.20668	−	1.20668i	−0.234585	−	0.972096i	$-0.575373\pi$
$510$		0			0
$511$	−26.5830			−1.17596
$512$	20.3939	−	9.80250i	0.901291	−	0.433213i
$513$		0			0
$514$	−12.4575	−	19.2915i	−0.549477	−	0.850912i
$515$	−2.52517	−	2.52517i	−0.111272	−	0.111272i
$516$		0			0
$517$	−9.41699	+	9.41699i	−0.414159	+	0.414159i
$518$	7.12824	−	33.1160i	0.313197	−	1.45503i
$519$		0			0
$520$	35.1660	−	5.29150i	1.54213	−	0.232048i
$521$		−	18.7105i		−	0.819720i	−0.912148	−	0.409860i	$-0.865578\pi$
$521$		−	18.7105i		−	0.819720i	0.912148	−	0.409860i	$-0.134422\pi$
$522$		0			0
$523$	−3.06275	+	3.06275i	−0.133925	+	0.133925i	−0.770891	−	0.636967i	$-0.780189\pi$
$523$	−3.06275	+	3.06275i	−0.133925	+	0.133925i	0.636967	+	0.770891i	$0.280189\pi$
$524$	4.45398	−	1.68345i	0.194573	−	0.0735417i
$525$		0			0
$526$	−18.5830	+	12.0000i	−0.810258	+	0.523225i
$527$	−1.08709			−0.0473543
$528$		0			0
$529$	−38.1660			−1.65939
$530$	−30.7399	+	19.8504i	−1.33526	+	0.862244i
$531$		0			0
$532$	−6.00000	−	15.8745i	−0.260133	−	0.688247i
$533$	−17.0270	+	17.0270i	−0.737522	+	0.737522i
$534$		0			0
$535$		−	45.1660i		−	1.95270i
$536$	12.8712	+	9.50432i	0.555951	+	0.410524i
$537$		0			0
$538$	3.58301	−	16.6458i	0.154474	−	0.717649i
$539$	5.29570	−	5.29570i	0.228102	−	0.228102i
$540$		0			0
$541$	8.52026	+	8.52026i	0.366315	+	0.366315i	0.866131	−	0.499817i	$-0.166599\pi$
$541$	8.52026	+	8.52026i	0.366315	+	0.366315i	−0.499817	+	0.866131i	$0.666599\pi$
$542$	−8.93436	−	13.8356i	−0.383764	−	0.594290i
$543$		0			0
$544$	−4.70850	+	16.7085i	−0.201875	+	0.716371i
$545$	6.43560			0.275671
$546$		0			0
$547$	−0.937254	−	0.937254i	−0.0400741	−	0.0400741i	0.686786	−	0.726860i	$-0.259021\pi$
$547$	−0.937254	−	0.937254i	−0.0400741	−	0.0400741i	−0.726860	+	0.686786i	$0.759021\pi$
$548$	−29.0565	−	13.1166i	−1.24123	−	0.560312i
$549$		0			0
$550$	2.22876	−	10.3542i	0.0950345	−	0.441507i
$551$		−	2.27980i		−	0.0971229i
$552$		0			0
$553$			15.8745i			0.675053i
$554$	−40.1216	−	8.63619i	−1.70460	−	0.366916i
$555$		0			0
$556$	6.58301	+	17.4170i	0.279182	+	0.738645i
$557$	24.7516	+	24.7516i	1.04876	+	1.04876i	0.998749	+	0.0500103i	$0.0159254\pi$
$557$	24.7516	+	24.7516i	1.04876	+	1.04876i	0.0500103	+	0.998749i	$0.484075\pi$
$558$		0			0
$559$	29.8745			1.26356
$560$	−3.06871	+	48.9068i	−0.129677	+	2.06669i
$561$		0			0
$562$	−11.2915	+	7.29150i	−0.476303	+	0.307573i
$563$	−16.4835	−	16.4835i	−0.694695	−	0.694695i	0.268566	−	0.963261i	$-0.413450\pi$
$563$	−16.4835	−	16.4835i	−0.694695	−	0.694695i	−0.963261	+	0.268566i	$0.913450\pi$
$564$		0			0
$565$		0			0
$566$	−36.3338	−	7.82087i	−1.52722	−	0.328736i
$567$		0			0
$568$	−1.41699	−	9.41699i	−0.0594558	−	0.395128i
$569$			11.9767i			0.502088i	0.967976	+	0.251044i	$0.0807739\pi$
$569$			11.9767i			0.502088i	−0.967976	+	0.251044i	$0.919226\pi$
$570$		0			0
$571$	4.00000	−	4.00000i	0.167395	−	0.167395i	−0.618438	−	0.785833i	$-0.712234\pi$
$571$	4.00000	−	4.00000i	0.167395	−	0.167395i	0.785833	+	0.618438i	$0.212234\pi$
$572$	−3.66507	+	8.11905i	−0.153244	+	0.339475i
$573$		0			0
$574$	−18.0000	−	27.8745i	−0.751305	−	1.16346i
$575$	49.2050			2.05199
$576$		0			0
$577$	35.0405			1.45876			0.729378	−	0.684111i	$-0.239810\pi$
$577$	35.0405			1.45876			0.729378	+	0.684111i	$0.239810\pi$
$578$	5.81752	+	9.00891i	0.241977	+	0.374721i
$579$		0			0
$580$	−2.70850	+	6.00000i	−0.112464	+	0.249136i
$581$	−3.06871	+	3.06871i	−0.127312	+	0.127312i
$582$		0			0
$583$		−	9.16601i		−	0.379617i
$584$	3.06871	+	20.3939i	0.126984	+	0.843906i
$585$		0			0
$586$	−29.2288	−	6.29150i	−1.20743	−	0.259900i
$587$	19.0086	−	19.0086i	0.784570	−	0.784570i	−0.196028	−	0.980598i	$-0.562804\pi$
$587$	19.0086	−	19.0086i	0.784570	−	0.784570i	0.980598	+	0.196028i	$0.0628044\pi$
$588$		0			0
$589$	−0.583005	−	0.583005i	−0.0240223	−	0.0240223i
$590$	44.1547	−	28.5129i	1.81782	−	1.17386i
$591$		0			0
$592$	−26.2288	−	1.64575i	−1.07800	−	0.0676400i
$593$	12.2748			0.504068			0.252034	−	0.967718i	$-0.418901\pi$
$593$	12.2748			0.504068			0.252034	+	0.967718i	$0.418901\pi$
$594$		0			0
$595$	−26.5830	−	26.5830i	−1.08980	−	1.08980i
$596$	3.76135	+	9.95158i	0.154071	+	0.407633i
$597$		0			0
$598$	−40.4575	−	8.70850i	−1.65443	−	0.356117i
$599$			30.1964i			1.23379i	0.787045	+	0.616896i	$0.211610\pi$
$599$			30.1964i			1.23379i	−0.787045	+	0.616896i	$0.788390\pi$
$600$		0			0
$601$			7.29150i			0.297427i	0.988880	+	0.148713i	$0.0475132\pi$
$601$			7.29150i			0.297427i	−0.988880	+	0.148713i	$0.952487\pi$
$602$	−8.66259	+	40.2443i	−0.353061	+	1.64023i
$603$		0			0
$604$	28.5203	+	12.8745i	1.16047	+	0.523856i
$605$	−22.7700	−	22.7700i	−0.925731	−	0.925731i
$606$		0			0
$607$	−44.1033			−1.79010			−0.895048	−	0.445970i	$-0.852859\pi$
$607$	−44.1033			−1.79010			−0.895048	+	0.445970i	$0.852859\pi$
$608$	−11.4859	+	6.43560i	−0.465816	+	0.260998i
$609$		0			0
$610$	16.9373	+	26.2288i	0.685769	+	1.06197i
$611$	−29.6000	−	29.6000i	−1.19749	−	1.19749i
$612$		0			0
$613$	21.3542	−	21.3542i	0.862490	−	0.862490i	−0.129137	−	0.991627i	$-0.541221\pi$
$613$	21.3542	−	21.3542i	0.862490	−	0.862490i	0.991627	+	0.129137i	$0.0412206\pi$
$614$	−8.41723	+	39.1044i	−0.339692	+	1.57812i
$615$		0			0
$616$	−9.87451	−	7.29150i	−0.397855	−	0.293783i
$617$		−	25.7424i		−	1.03635i	−0.855274	−	0.518175i	$-0.826611\pi$
$617$		−	25.7424i		−	1.03635i	0.855274	−	0.518175i	$-0.173389\pi$
$618$		0			0
$619$	21.1660	−	21.1660i	0.850734	−	0.850734i	−0.139490	−	0.990224i	$-0.544546\pi$
$619$	21.1660	−	21.1660i	0.850734	−	0.850734i	0.990224	+	0.139490i	$0.0445462\pi$
$620$	0.841723	+	2.22699i	0.0338044	+	0.0894380i
$621$		0			0
$622$	−18.5830	+	12.0000i	−0.745111	+	0.481156i
$623$	34.6504			1.38824
$624$		0			0
$625$	16.8745			0.674980
$626$	−1.53436	+	0.990812i	−0.0613252	+	0.0396008i
$627$		0			0
$628$	3.58301	−	1.35425i	0.142977	−	0.0540404i
$629$	14.2565	−	14.2565i	0.568443	−	0.568443i
$630$		0			0
$631$			18.2288i			0.725675i	0.931852	+	0.362838i	$0.118192\pi$
$631$			18.2288i			0.725675i	−0.931852	+	0.362838i	$0.881808\pi$
$632$	12.1786	−	1.83254i	0.484438	−	0.0728943i
$633$		0			0
$634$	1.00000	−	4.64575i	0.0397151	−	0.184506i
$635$	35.4921	−	35.4921i	1.40846	−	1.40846i
$636$		0			0
$637$	16.6458	+	16.6458i	0.659529	+	0.659529i
$638$	−0.894538	−	1.38527i	−0.0354151	−	0.0548432i
$639$		0			0
$640$	37.8745	−	3.29150i	1.49712	−	0.130108i
$641$	9.20614			0.363621			0.181810	−	0.983334i	$-0.441804\pi$
$641$	9.20614			0.363621			0.181810	+	0.983334i	$0.441804\pi$
$642$		0			0
$643$	1.64575	+	1.64575i	0.0649021	+	0.0649021i	0.738813	−	0.673911i	$-0.235387\pi$
$643$	1.64575	+	1.64575i	0.0649021	+	0.0649021i	−0.673911	+	0.738813i	$0.735387\pi$
$644$	23.4626	−	51.9756i	0.924556	−	2.04812i
$645$		0			0
$646$	2.12549	−	9.87451i	0.0836264	−	0.388507i
$647$			7.82087i			0.307470i	0.988112	+	0.153735i	$0.0491302\pi$
$647$			7.82087i			0.307470i	−0.988112	+	0.153735i	$0.950870\pi$
$648$		0			0
$649$			13.1660i			0.516811i
$650$	32.5461	+	7.00555i	1.27656	+	0.274780i
$651$		0			0
$652$	−16.8118	+	6.35425i	−0.658399	+	0.248852i
$653$	7.42642	+	7.42642i	0.290618	+	0.290618i	0.837324	−	0.546706i	$-0.184119\pi$
$653$	7.42642	+	7.42642i	0.290618	+	0.290618i	−0.546706	+	0.837324i	$0.684119\pi$
$654$		0			0
$655$	8.00000			0.312586
$656$	−19.3068	+	17.0270i	−0.753804	+	0.664793i
$657$		0			0
$658$	48.4575	−	31.2915i	1.88907	−	1.21987i
$659$	−24.0590	−	24.0590i	−0.937204	−	0.937204i	0.0609372	−	0.998142i	$-0.480591\pi$
$659$	−24.0590	−	24.0590i	−0.937204	−	0.937204i	−0.998142	+	0.0609372i	$0.980591\pi$
$660$		0			0
$661$	−29.2288	+	29.2288i	−1.13687	+	1.13687i	−0.147858	+	0.989009i	$0.547238\pi$
$661$	−29.2288	+	29.2288i	−1.13687	+	1.13687i	−0.989009	+	0.147858i	$0.952762\pi$
$662$	15.6417	+	3.36689i	0.607934	+	0.130858i
$663$		0			0
$664$	2.70850	+	2.00000i	0.105110	+	0.0776151i
$665$		−	28.5129i		−	1.10568i
$666$		0			0
$667$	5.41699	−	5.41699i	0.209747	−	0.209747i
$668$	8.11905	+	3.66507i	0.314135	+	0.141806i
$669$		0			0
$670$	14.5830	+	22.5830i	0.563391	+	0.872458i
$671$	−7.82087			−0.301921
$672$		0			0
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$	−11.7313	−	18.1669i	−0.451873	−	0.699763i
$675$		0			0
$676$	−1.82288	−	0.822876i	−0.0701106	−	0.0316491i
$677$	5.74297	−	5.74297i	0.220720	−	0.220720i	−0.588081	−	0.808802i	$-0.700117\pi$
$677$	5.74297	−	5.74297i	0.220720	−	0.220720i	0.808802	+	0.588081i	$0.200117\pi$
$678$		0			0
$679$			38.5830i			1.48068i
$680$	−17.3252	+	23.4626i	−0.664391	+	0.899750i
$681$		0			0
$682$	−0.583005	−	0.125492i	−0.0223244	−	0.00480534i
$683$	−35.4921	+	35.4921i	−1.35807	+	1.35807i	−0.481769	+	0.876298i	$0.660006\pi$
$683$	−35.4921	+	35.4921i	−1.35807	+	1.35807i	−0.876298	+	0.481769i	$0.839994\pi$
$684$		0			0
$685$	−37.8745	−	37.8745i	−1.44711	−	1.44711i
$686$	3.06871	−	1.98162i	0.117164	−	0.0756588i
$687$		0			0
$688$	31.8745	+	2.00000i	1.21520	+	0.0762493i
$689$	28.8111			1.09762
$690$		0			0
$691$	1.64575	+	1.64575i	0.0626073	+	0.0626073i	0.737717	−	0.675110i	$-0.235904\pi$
$691$	1.64575	+	1.64575i	0.0626073	+	0.0626073i	−0.675110	+	0.737717i	$0.735904\pi$
$692$	−14.4056	+	5.44479i	−0.547617	+	0.206980i
$693$		0			0
$694$	1.64575	+	0.354249i	0.0624719	+	0.0134471i
$695$			31.2835i			1.18665i
$696$		0			0
$697$		−	19.7490i		−	0.748047i
$698$	−9.77609	+	45.4173i	−0.370030	+	1.71907i
$699$		0			0
$700$	−18.8745	+	41.8118i	−0.713389	+	1.58034i
$701$	16.6326	+	16.6326i	0.628203	+	0.628203i	0.947616	−	0.319413i	$-0.103486\pi$
$701$	16.6326	+	16.6326i	0.628203	+	0.628203i	−0.319413	+	0.947616i	$0.603486\pi$
$702$		0			0
$703$	15.2915			0.576730
$704$	−4.45398	+	8.41723i	−0.167866	+	0.317236i
$705$		0			0
$706$	21.8745	+	33.8745i	0.823258	+	1.27488i
$707$	−8.66259	−	8.66259i	−0.325790	−	0.325790i
$708$		0			0
$709$	−35.2288	+	35.2288i	−1.32304	+	1.32304i	−0.411744	+	0.911299i	$0.635080\pi$
$709$	−35.2288	+	35.2288i	−1.32304	+	1.32304i	−0.911299	+	0.411744i	$0.864920\pi$
$710$	3.36689	−	15.6417i	0.126357	−	0.587024i
$711$		0			0
$712$	−4.00000	−	26.5830i	−0.149906	−	0.996240i
$713$		−	2.77053i		−	0.103757i
$714$		0			0
$715$	−10.5830	+	10.5830i	−0.395782	+	0.395782i
$716$	−25.1461	+	9.50432i	−0.939752	+	0.355193i
$717$		0			0
$718$	22.5830	−	14.5830i	0.842790	−	0.544233i
$719$	10.1007			0.376692			0.188346	−	0.982103i	$-0.439687\pi$
$719$	10.1007			0.376692			0.188346	+	0.982103i	$0.439687\pi$
$720$		0			0
$721$	−3.87451			−0.144294
$722$	−16.1371	+	10.4206i	−0.600562	+	0.387814i
$723$		0			0
$724$	4.64575	+	12.2915i	0.172658	+	0.456810i
$725$	−4.35770	+	4.35770i	−0.161841	+	0.161841i
$726$		0			0
$727$			35.3948i			1.31272i	0.754448	+	0.656360i	$0.227905\pi$
$727$			35.3948i			1.31272i	−0.754448	+	0.656360i	$0.772095\pi$
$728$	22.9191	−	31.0381i	0.849437	−	1.15035i
$729$		0			0
$730$	−7.29150	+	33.8745i	−0.269871	+	1.25375i
$731$	−17.3252	+	17.3252i	−0.640795	+	0.640795i
$732$		0			0
$733$	−7.35425	−	7.35425i	−0.271635	−	0.271635i	0.558123	−	0.829758i	$-0.311522\pi$
$733$	−7.35425	−	7.35425i	−0.271635	−	0.271635i	−0.829758	+	0.558123i	$0.811522\pi$
$734$	9.82890	+	15.2209i	0.362791	+	0.561813i
$735$		0			0
$736$	−42.5830	−	12.0000i	−1.56963	−	0.442326i
$737$	−6.73378			−0.248042
$738$		0			0
$739$	33.1660	+	33.1660i	1.22003	+	1.22003i	0.967620	+	0.252411i	$0.0812236\pi$
$739$	33.1660	+	33.1660i	1.22003	+	1.22003i	0.252411	+	0.967620i	$0.418776\pi$
$740$	−40.2443	−	18.1669i	−1.47941	−	0.667829i
$741$		0			0
$742$	−8.35425	+	38.8118i	−0.306694	+	1.42482i
$743$		−	14.5547i		−	0.533958i	−0.963702	−	0.266979i	$-0.913974\pi$
$743$		−	14.5547i		−	0.533958i	0.963702	−	0.266979i	$-0.0860255\pi$
$744$		0			0
$745$			17.8745i			0.654871i
$746$	7.69819	+	1.65704i	0.281851	+	0.0606685i
$747$		0			0
$748$	−2.58301	−	6.83399i	−0.0944440	−	0.249875i
$749$	−34.6504	−	34.6504i	−1.26610	−	1.26610i
$750$		0			0
$751$	−2.93725			−0.107182			−0.0535910	−	0.998563i	$-0.517067\pi$
$751$	−2.93725			−0.107182			−0.0535910	+	0.998563i	$0.517067\pi$
$752$	−29.6000	−	33.5633i	−1.07940	−	1.22393i
$753$		0			0
$754$	4.35425	−	2.81176i	0.158572	−	0.102398i
$755$	37.1755	+	37.1755i	1.35296	+	1.35296i
$756$		0			0
$757$	19.2288	−	19.2288i	0.698881	−	0.698881i	−0.265288	−	0.964169i	$-0.585467\pi$
$757$	19.2288	−	19.2288i	0.698881	−	0.698881i	0.964169	+	0.265288i	$0.0854671\pi$
$758$	−26.6804	−	5.74297i	−0.969076	−	0.208594i
$759$		0			0
$760$	−21.8745	+	3.29150i	−0.793472	+	0.119395i
$761$		−	6.43560i		−	0.233290i	−0.993174	−	0.116645i	$-0.962786\pi$
$761$		−	6.43560i		−	0.233290i	0.993174	−	0.116645i	$-0.0372140\pi$
$762$		0			0
$763$	4.93725	−	4.93725i	0.178741	−	0.178741i
$764$	9.20614	−	20.3939i	0.333066	−	0.737825i
$765$		0			0
$766$	−8.58301	−	13.2915i	−0.310117	−	0.480242i
$767$	−41.3842			−1.49430
$768$		0			0
$769$	6.70850			0.241915			0.120957	−	0.992658i	$-0.461404\pi$
$769$	6.70850			0.241915			0.120957	+	0.992658i	$0.461404\pi$
$770$	−11.1878	−	17.3252i	−0.403179	−	0.624356i
$771$		0			0
$772$	16.3542	−	36.2288i	0.588602	−	1.30390i
$773$	−14.6509	+	14.6509i	−0.526957	+	0.526957i	−0.919664	−	0.392707i	$-0.871539\pi$
$773$	−14.6509	+	14.6509i	−0.526957	+	0.526957i	0.392707	+	0.919664i	$0.371539\pi$
$774$		0			0
$775$			2.22876i			0.0800593i
$776$	29.6000	−	4.45398i	1.06258	−	0.159889i
$777$		0			0
$778$	14.5203	+	3.12549i	0.520577	+	0.112054i
$779$	10.5914	−	10.5914i	0.379476	−	0.379476i
$780$		0			0
$781$	2.83399	+	2.83399i	0.101408	+	0.101408i
$782$	28.5129	−	18.4123i	1.01962	−	0.658422i
$783$		0			0
$784$	16.6458	+	18.8745i	0.594491	+	0.674090i
$785$	6.43560			0.229697
$786$		0			0
$787$	−20.2288	−	20.2288i	−0.721077	−	0.721077i	0.247747	−	0.968825i	$-0.420310\pi$
$787$	−20.2288	−	20.2288i	−0.721077	−	0.721077i	−0.968825	+	0.247747i	$0.920310\pi$
$788$	8.81168	+	23.3135i	0.313903	+	0.830510i
$789$		0			0
$790$	20.2288	+	4.35425i	0.719707	+	0.154917i
$791$		0			0
$792$		0			0
$793$		−	24.5830i		−	0.872968i
$794$	10.0743	−	46.8025i	0.357522	−	1.66096i
$795$		0			0
$796$	−15.2288	−	6.87451i	−0.539769	−	0.243660i
$797$	14.6509	+	14.6509i	0.518962	+	0.518962i	0.917257	−	0.398295i	$-0.130398\pi$
$797$	14.6509	+	14.6509i	0.518962	+	0.518962i	−0.398295	+	0.917257i	$0.630398\pi$
$798$		0			0
$799$	34.3320			1.21458
$800$	34.2559	+	9.65341i	1.21113	+	0.341299i
$801$		0			0
$802$	−7.06275	−	10.9373i	−0.249394	−	0.386208i
$803$	−6.13742	−	6.13742i	−0.216585	−	0.216585i
$804$		0			0
$805$	67.7490	−	67.7490i	2.38784	−	2.38784i
$806$	0.394454	−	1.83254i	0.0138941	−	0.0645483i
$807$		0			0
$808$	−5.64575	+	7.64575i	−0.198617	+	0.268977i
$809$			44.4529i			1.56288i	0.623981	+	0.781440i	$0.285514\pi$
$809$			44.4529i			1.56288i	−0.623981	+	0.781440i	$0.714486\pi$
$810$		0			0
$811$	−10.3542	+	10.3542i	−0.363587	+	0.363587i	−0.865132	−	0.501545i	$-0.832765\pi$
$811$	−10.3542	+	10.3542i	−0.363587	+	0.363587i	0.501545	+	0.865132i	$0.332765\pi$
$812$	2.52517	+	6.68097i	0.0886160	+	0.234456i
$813$		0			0
$814$	9.29150	−	6.00000i	0.325667	−	0.210300i
$815$	−30.1964			−1.05773
$816$		0			0
$817$	−18.5830			−0.650137
$818$	20.3939	−	13.1694i	0.713056	−	0.460457i
$819$		0			0
$820$	−40.4575	+	15.2915i	−1.41284	+	0.534002i
$821$	−30.8890	+	30.8890i	−1.07803	+	1.07803i	−0.0813488	+	0.996686i	$0.525923\pi$
$821$	−30.8890	+	30.8890i	−1.07803	+	1.07803i	−0.996686	+	0.0813488i	$0.974077\pi$
$822$		0			0
$823$		−	5.77124i		−	0.201173i	−0.994928	−	0.100586i	$-0.967928\pi$
$823$		−	5.77124i		−	0.201173i	0.994928	−	0.100586i	$-0.0320719\pi$
$824$	0.447269	+	2.97244i	0.0155813	+	0.103550i
$825$		0			0
$826$	12.0000	−	55.7490i	0.417533	−	1.93976i
$827$	7.82087	−	7.82087i	0.271958	−	0.271958i	−0.557930	−	0.829888i	$-0.688404\pi$
$827$	7.82087	−	7.82087i	0.271958	−	0.271958i	0.829888	+	0.557930i	$0.188404\pi$
$828$		0			0
$829$	9.35425	+	9.35425i	0.324886	+	0.324886i	0.850638	−	0.525752i	$-0.176216\pi$
$829$	9.35425	+	9.35425i	0.324886	+	0.324886i	−0.525752	+	0.850638i	$0.676216\pi$
$830$	3.06871	+	4.75216i	0.106517	+	0.164950i
$831$		0			0
$832$	−26.4575	−	14.0000i	−0.917249	−	0.485363i
$833$	−19.3068			−0.668941
$834$		0			0
$835$	10.5830	+	10.5830i	0.366240	+	0.366240i
$836$	2.27980	−	5.05034i	0.0788487	−	0.174670i
$837$		0			0
$838$	5.52026	−	25.6458i	0.190694	−	0.885918i
$839$		−	40.1914i		−	1.38756i	−0.720186	−	0.693781i	$-0.755943\pi$
$839$		−	40.1914i		−	1.38756i	0.720186	−	0.693781i	$-0.244057\pi$
$840$		0			0
$841$		−	28.0405i		−	0.966914i
$842$	−32.5461	−	7.00555i	−1.12161	−	0.241427i
$843$		0			0
$844$	−17.4170	+	6.58301i	−0.599518	+	0.226596i
$845$	−2.37608	−	2.37608i	−0.0817396	−	0.0817396i
$846$		0			0
$847$	−34.9373			−1.20046
$848$	30.7399	+	1.92881i	1.05561	+	0.0662356i
$849$		0			0
$850$	−22.9373	+	14.8118i	−0.786741	+	0.508039i
$851$	36.3338	+	36.3338i	1.24551	+	1.24551i
$852$		0			0
$853$	−3.93725	+	3.93725i	−0.134809	+	0.134809i	−0.771291	−	0.636482i	$-0.780389\pi$
$853$	−3.93725	+	3.93725i	−0.134809	+	0.134809i	0.636482	+	0.771291i	$0.280389\pi$
$854$	33.1160	+	7.12824i	1.13321	+	0.243923i
$855$		0			0
$856$	−22.5830	+	30.5830i	−0.771871	+	1.04531i
$857$			15.9399i			0.544497i	0.962227	+	0.272249i	$0.0877673\pi$
$857$			15.9399i			0.544497i	−0.962227	+	0.272249i	$0.912233\pi$
$858$		0			0
$859$	−32.2288	+	32.2288i	−1.09963	+	1.09963i	−0.105178	+	0.994453i	$0.533541\pi$
$859$	−32.2288	+	32.2288i	−1.09963	+	1.09963i	−0.994453	+	0.105178i	$0.966459\pi$
$860$	48.9068	+	22.0773i	1.66771	+	0.752831i
$861$		0			0
$862$	−0.833990	−	1.29150i	−0.0284058	−	0.0439888i
$863$	13.3619			0.454846			0.227423	−	0.973796i	$-0.426970\pi$
$863$	13.3619			0.454846			0.227423	+	0.973796i	$0.426970\pi$
$864$		0			0
$865$	−25.8745			−0.879760
$866$	3.06871	+	4.75216i	0.104279	+	0.161485i
$867$		0			0
$868$	2.35425	+	1.06275i	0.0799084	+	0.0360720i
$869$	−3.66507	+	3.66507i	−0.124329	+	0.124329i
$870$		0			0
$871$		−	21.1660i		−	0.717183i
$872$	−4.35770	−	3.21780i	−0.147570	−	0.108969i
$873$		0			0
$874$	25.1660	+	5.41699i	0.851253	+	0.183233i
$875$	−11.1878	+	11.1878i	−0.378215	+	0.378215i
$876$		0			0
$877$	−6.06275	−	6.06275i	−0.204724	−	0.204724i	0.597296	−	0.802021i	$-0.296242\pi$
$877$	−6.06275	−	6.06275i	−0.204724	−	0.204724i	−0.802021	+	0.597296i	$0.796242\pi$
$878$	−44.5755	+	28.7847i	−1.50435	+	0.971437i
$879$		0			0
$880$	−12.0000	+	10.5830i	−0.404520	+	0.356753i
$881$	−40.7878			−1.37418			−0.687088	−	0.726574i	$-0.741111\pi$
$881$	−40.7878			−1.37418			−0.687088	+	0.726574i	$0.741111\pi$
$882$		0			0
$883$	33.3948	+	33.3948i	1.12382	+	1.12382i	0.991161	+	0.132662i	$0.0423525\pi$
$883$	33.3948	+	33.3948i	1.12382	+	1.12382i	0.132662	+	0.991161i	$0.457648\pi$
$884$	21.4810	−	8.11905i	0.722484	−	0.273073i
$885$		0			0
$886$	45.3948	+	9.77124i	1.52507	+	0.328271i
$887$			19.0086i			0.638247i	0.947713	+	0.319124i	$0.103389\pi$
$887$			19.0086i			0.638247i	−0.947713	+	0.319124i	$0.896611\pi$
$888$		0			0
$889$		−	54.4575i		−	1.82645i
$890$	9.50432	−	44.1547i	0.318585	−	1.48007i
$891$		0			0
$892$	16.1660	−	35.8118i	0.541278	−	1.19907i
$893$	18.4123	+	18.4123i	0.616143	+	0.616143i
$894$		0			0
$895$	−45.1660			−1.50973
$896$	26.5313	−	31.5817i	0.886349	−	1.05507i
$897$		0			0
$898$	−28.9373	−	44.8118i	−0.965649	−	1.49539i
$899$	0.245364	+	0.245364i	0.00818336	+	0.00818336i
$900$		0			0
$901$	−16.7085	+	16.7085i	−0.556641	+	0.556641i
$902$	2.27980	−	10.5914i	0.0759092	−	0.352655i
$903$		0			0
$904$		0			0
$905$			22.0773i			0.733876i
$906$		0			0
$907$	−42.1033	+	42.1033i	−1.39802	+	1.39802i	−0.592294	+	0.805722i	$0.701778\pi$
$907$	−42.1033	+	42.1033i	−1.39802	+	1.39802i	−0.805722	+	0.592294i	$0.798222\pi$
$908$	−48.0651	+	18.1669i	−1.59510	+	0.602890i
$909$		0			0
$910$	54.4575	−	35.1660i	1.80525	−	1.16574i
$911$	45.8381			1.51869			0.759343	−	0.650691i	$-0.225521\pi$
$911$	45.8381			1.51869			0.759343	+	0.650691i	$0.225521\pi$
$912$		0			0
$913$	−1.41699			−0.0468957
$914$	31.5817	−	20.3939i	1.04463	−	0.674570i
$915$		0			0
$916$	2.06275	+	5.45751i	0.0681550	+	0.180321i
$917$	6.13742	−	6.13742i	0.202676	−	0.202676i
$918$		0			0
$919$		−	16.1033i		−	0.531198i	−0.964084	−	0.265599i	$-0.914430\pi$
$919$		−	16.1033i		−	0.531198i	0.964084	−	0.265599i	$-0.0855697\pi$
$920$	−59.7964	−	44.1547i	−1.97143	−	1.45574i
$921$		0			0
$922$	−3.70850	+	17.2288i	−0.122133	+	0.567399i
$923$	−8.90796	+	8.90796i	−0.293209	+	0.293209i
$924$		0			0
$925$	−29.2288	−	29.2288i	−0.961036	−	0.961036i
$926$	−23.7344	−	36.7547i	−0.779960	−	1.20783i
$927$		0			0
$928$	4.83399	−	2.70850i	0.158683	−	0.0889108i
$929$	19.3068			0.633436			0.316718	−	0.948520i	$-0.397419\pi$
$929$	19.3068			0.633436			0.316718	+	0.948520i	$0.397419\pi$
$930$		0			0
$931$	−10.3542	−	10.3542i	−0.339347	−	0.339347i
$932$	39.7007	+	17.9215i	1.30044	+	0.587040i
$933$		0			0
$934$	−4.81176	+	22.3542i	−0.157446	+	0.731453i
$935$		−	12.2748i		−	0.401430i
$936$		0			0
$937$		−	11.1660i		−	0.364778i	−0.983226	−	0.182389i	$-0.941617\pi$
$937$		−	11.1660i		−	0.364778i	0.983226	−	0.182389i	$-0.0583830\pi$
$938$	28.5129	+	6.13742i	0.930981	+	0.200394i
$939$		0			0
$940$	−26.5830	−	70.3320i	−0.867042	−	2.29398i
$941$	25.8387	+	25.8387i	0.842317	+	0.842317i	0.989160	−	0.146843i	$-0.0469111\pi$
$941$	25.8387	+	25.8387i	0.842317	+	0.842317i	−0.146843	+	0.989160i	$0.546911\pi$
$942$		0			0
$943$	50.3320			1.63904
$944$	−44.1547	−	2.77053i	−1.43711	−	0.0901732i
$945$		0			0
$946$	−11.2915	+	7.29150i	−0.367118	+	0.237067i
$947$	9.50432	+	9.50432i	0.308849	+	0.308849i	0.844463	−	0.535614i	$-0.179920\pi$
$947$	9.50432	+	9.50432i	0.308849	+	0.308849i	−0.535614	+	0.844463i	$0.679920\pi$
$948$		0			0
$949$	19.2915	−	19.2915i	0.626229	−	0.626229i
$950$	−20.2448	−	4.35770i	−0.656828	−	0.141383i
$951$		0			0
$952$	4.70850	+	31.2915i	0.152603	+	1.01416i
$953$		−	24.8479i		−	0.804902i	−0.915442	−	0.402451i	$-0.868158\pi$
$953$		−	24.8479i		−	0.804902i	0.915442	−	0.402451i	$-0.131842\pi$
$954$		0			0
$955$	26.5830	−	26.5830i	0.860206	−	0.860206i
$956$	19.3068	−	42.7694i	0.624427	−	1.38326i
$957$		0			0
$958$	9.41699	+	14.5830i	0.304249	+	0.471156i
$959$	−58.1130			−1.87657
$960$		0			0
$961$	−30.8745			−0.995952
$962$	18.8595	+	29.2056i	0.608056	+	0.941626i
$963$		0			0
$964$	−7.64575	+	16.9373i	−0.246253	+	0.545512i
$965$	47.2234	−	47.2234i	1.52018	−	1.52018i
$966$		0			0
$967$			23.3948i			0.752325i	0.926554	+	0.376162i	$0.122757\pi$
$967$			23.3948i			0.752325i	−0.926554	+	0.376162i	$0.877243\pi$
$968$	4.03312	+	26.8031i	0.129629	+	0.861484i
$969$		0			0
$970$	49.1660	+	10.5830i	1.57863	+	0.339800i
$971$	−30.4418	+	30.4418i	−0.976923	+	0.976923i	−0.999740	−	0.0228172i	$-0.992736\pi$
$971$	−30.4418	+	30.4418i	−0.976923	+	0.976923i	0.0228172	+	0.999740i	$0.492736\pi$
$972$		0			0
$973$	24.0000	+	24.0000i	0.769405	+	0.769405i
$974$	−21.6565	+	13.9847i	−0.693918	+	0.448099i
$975$		0			0
$976$	1.64575	−	26.2288i	0.0526792	−	0.839562i
$977$	−43.8565			−1.40309			−0.701547	−	0.712623i	$-0.747507\pi$
$977$	−43.8565			−1.40309			−0.701547	+	0.712623i	$0.747507\pi$
$978$		0			0
$979$	8.00000	+	8.00000i	0.255681	+	0.255681i
$980$	14.9491	+	39.5516i	0.477532	+	1.26343i
$981$		0			0
$982$	−27.2915	−	5.87451i	−0.870907	−	0.187463i
$983$			6.73378i			0.214774i	0.994217	+	0.107387i	$0.0342484\pi$
$983$			6.73378i			0.214774i	−0.994217	+	0.107387i	$0.965752\pi$
$984$		0			0
$985$			41.8745i			1.33423i
$986$	−0.894538	+	4.15580i	−0.0284879	+	0.132348i
$987$		0			0
$988$	15.8745	+	7.16601i	0.505035	+	0.227981i
$989$	−44.1547	−	44.1547i	−1.40404	−	1.40404i
$990$		0			0
$991$	18.9373			0.601562			0.300781	−	0.953693i	$-0.402753\pi$
$991$	18.9373			0.601562			0.300781	+	0.953693i	$0.402753\pi$
$992$	0.543544	−	1.92881i	0.0172575	−	0.0612398i
$993$		0			0
$994$	−9.41699	−	14.5830i	−0.298689	−	0.462545i
$995$	−19.8504	−	19.8504i	−0.629299	−	0.629299i
$996$		0			0
$997$	−0.520259	+	0.520259i	−0.0164768	+	0.0164768i	−0.715297	−	0.698820i	$-0.753709\pi$
$997$	−0.520259	+	0.520259i	−0.0164768	+	0.0164768i	0.698820	+	0.715297i	$0.253709\pi$
$998$	−4.45398	+	20.6921i	−0.140988	+	0.654996i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.k.c.109.2	yes	8
3.2	odd	2	inner	144.2.k.c.109.3	yes	8
4.3	odd	2		576.2.k.c.145.1		8
8.3	odd	2		1152.2.k.d.289.4		8
8.5	even	2		1152.2.k.e.289.4		8
12.11	even	2		576.2.k.c.145.4		8
16.3	odd	4		1152.2.k.d.865.4		8
16.5	even	4	inner	144.2.k.c.37.2	✓	8
16.11	odd	4		576.2.k.c.433.1		8
16.13	even	4		1152.2.k.e.865.4		8
24.5	odd	2		1152.2.k.e.289.1		8
24.11	even	2		1152.2.k.d.289.1		8
32.5	even	8		9216.2.a.bq.1.1		8
32.11	odd	8		9216.2.a.bt.1.8		8
32.21	even	8		9216.2.a.bq.1.8		8
32.27	odd	8		9216.2.a.bt.1.1		8
48.5	odd	4	inner	144.2.k.c.37.3	yes	8
48.11	even	4		576.2.k.c.433.4		8
48.29	odd	4		1152.2.k.e.865.1		8
48.35	even	4		1152.2.k.d.865.1		8
96.5	odd	8		9216.2.a.bq.1.7		8
96.11	even	8		9216.2.a.bt.1.2		8
96.53	odd	8		9216.2.a.bq.1.2		8
96.59	even	8		9216.2.a.bt.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.k.c.37.2	✓	8	16.5	even	4	inner
144.2.k.c.37.3	yes	8	48.5	odd	4	inner
144.2.k.c.109.2	yes	8	1.1	even	1	trivial
144.2.k.c.109.3	yes	8	3.2	odd	2	inner
576.2.k.c.145.1		8	4.3	odd	2
576.2.k.c.145.4		8	12.11	even	2
576.2.k.c.433.1		8	16.11	odd	4
576.2.k.c.433.4		8	48.11	even	4
1152.2.k.d.289.1		8	24.11	even	2
1152.2.k.d.289.4		8	8.3	odd	2
1152.2.k.d.865.1		8	48.35	even	4
1152.2.k.d.865.4		8	16.3	odd	4
1152.2.k.e.289.1		8	24.5	odd	2
1152.2.k.e.289.4		8	8.5	even	2
1152.2.k.e.865.1		8	48.29	odd	4
1152.2.k.e.865.4		8	16.13	even	4
9216.2.a.bq.1.1		8	32.5	even	8
9216.2.a.bq.1.2		8	96.53	odd	8
9216.2.a.bq.1.7		8	96.5	odd	8
9216.2.a.bq.1.8		8	32.21	even	8
9216.2.a.bt.1.1		8	32.27	odd	8
9216.2.a.bt.1.2		8	96.11	even	8
9216.2.a.bt.1.7		8	96.59	even	8
9216.2.a.bt.1.8		8	32.11	odd	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.767178 - 1.18804i) q^{2} +(-0.822876 + 1.82288i) q^{4} +(-2.37608 + 2.37608i) q^{5} +3.64575i q^{7} +(2.79694 - 0.420861i) q^{8} +O(q^{10})\)	\(q+(-0.767178 - 1.18804i) q^{2} +(-0.822876 + 1.82288i) q^{4} +(-2.37608 + 2.37608i) q^{5} +3.64575i q^{7} +(2.79694 - 0.420861i) q^{8} +(4.64575 + 1.00000i) q^{10} +(-0.841723 + 0.841723i) q^{11} +(-2.64575 - 2.64575i) q^{13} +(4.33130 - 2.79694i) q^{14} +(-2.64575 - 3.00000i) q^{16} +3.06871 q^{17} +(1.64575 + 1.64575i) q^{19} +(-2.37608 - 6.28651i) q^{20} +(1.64575 + 0.354249i) q^{22} +7.82087i q^{23} -6.29150i q^{25} +(-1.11349 + 5.17302i) q^{26} +(-6.64575 - 3.00000i) q^{28} +(-0.692633 - 0.692633i) q^{29} -0.354249 q^{31} +(-1.53436 + 5.44479i) q^{32} +(-2.35425 - 3.64575i) q^{34} +(-8.66259 - 8.66259i) q^{35} +(4.64575 - 4.64575i) q^{37} +(0.692633 - 3.21780i) q^{38} +(-5.64575 + 7.64575i) q^{40} -6.43560i q^{41} +(-5.64575 + 5.64575i) q^{43} +(-0.841723 - 2.22699i) q^{44} +(9.29150 - 6.00000i) q^{46} +11.1878 q^{47} -6.29150 q^{49} +(-7.47455 + 4.82670i) q^{50} +(7.00000 - 2.64575i) q^{52} +(-5.44479 + 5.44479i) q^{53} -4.00000i q^{55} +(1.53436 + 10.1969i) q^{56} +(-0.291503 + 1.35425i) q^{58} +(7.82087 - 7.82087i) q^{59} +(4.64575 + 4.64575i) q^{61} +(0.271772 + 0.420861i) q^{62} +(7.64575 - 2.35425i) q^{64} +12.5730 q^{65} +(4.00000 + 4.00000i) q^{67} +(-2.52517 + 5.59388i) q^{68} +(-3.64575 + 16.9373i) q^{70} -3.36689i q^{71} +7.29150i q^{73} +(-9.08345 - 1.95522i) q^{74} +(-4.35425 + 1.64575i) q^{76} +(-3.06871 - 3.06871i) q^{77} +4.35425 q^{79} +(13.4148 + 0.841723i) q^{80} +(-7.64575 + 4.93725i) q^{82} +(0.841723 + 0.841723i) q^{83} +(-7.29150 + 7.29150i) q^{85} +(11.0387 + 2.37608i) q^{86} +(-2.00000 + 2.70850i) q^{88} -9.50432i q^{89} +(9.64575 - 9.64575i) q^{91} +(-14.2565 - 6.43560i) q^{92} +(-8.58301 - 13.2915i) q^{94} -7.82087 q^{95} +10.5830 q^{97} +(4.82670 + 7.47455i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 16 q^{10} - 8 q^{19} - 8 q^{22} - 32 q^{28} - 24 q^{31} - 40 q^{34} + 16 q^{37} - 24 q^{40} - 24 q^{43} + 32 q^{46} - 8 q^{49} + 56 q^{52} + 40 q^{58} + 16 q^{61} + 40 q^{64} + 32 q^{67} - 8 q^{70} - 56 q^{76} + 56 q^{79} - 40 q^{82} - 16 q^{85} - 16 q^{88} + 56 q^{91} + 16 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 16 * q^10 - 8 * q^19 - 8 * q^22 - 32 * q^28 - 24 * q^31 - 40 * q^34 + 16 * q^37 - 24 * q^40 - 24 * q^43 + 32 * q^46 - 8 * q^49 + 56 * q^52 + 40 * q^58 + 16 * q^61 + 40 * q^64 + 32 * q^67 - 8 * q^70 - 56 * q^76 + 56 * q^79 - 40 * q^82 - 16 * q^85 - 16 * q^88 + 56 * q^91 + 16 * q^94

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