LMFDB - Embedded newform 640.2.x.a.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(81,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("640.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.x (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	640.81
Dual form			640.2.x.a.561.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31924 - 0.960659i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.669347 - 0.669347i) q^{7} +(2.33467 + 2.33467i) q^{9} +O(q^{10})$	\(q+(-2.31924 - 0.960659i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.669347 - 0.669347i) q^{7} +(2.33467 + 2.33467i) q^{9} +(-1.14897 + 0.475919i) q^{11} +(-1.10518 + 2.66813i) q^{13} -2.51032i q^{15} -4.60123i q^{17} +(-1.60186 + 3.86723i) q^{19} +(-2.19539 + 0.909360i) q^{21} +(3.91843 + 3.91843i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-0.289849 - 0.699757i) q^{27} +(7.50975 + 3.11064i) q^{29} +8.19506 q^{31} +3.12193 q^{33} +(0.874544 + 0.362248i) q^{35} +(-3.90337 - 9.42357i) q^{37} +(5.12633 - 5.12633i) q^{39} +(7.53342 + 7.53342i) q^{41} +(10.4073 - 4.31084i) q^{43} +(-1.26351 + 3.05039i) q^{45} -2.88459i q^{47} +6.10395i q^{49} +(-4.42021 + 10.6713i) q^{51} +(-1.46716 + 0.607718i) q^{53} +(-0.879383 - 0.879383i) q^{55} +(7.43018 - 7.43018i) q^{57} +(2.77205 + 6.69231i) q^{59} +(1.99858 + 0.827839i) q^{61} +3.12541 q^{63} -2.88797 q^{65} +(-2.17091 - 0.899222i) q^{67} +(-5.32348 - 12.8520i) q^{69} +(-7.24583 + 7.24583i) q^{71} +(3.25815 + 3.25815i) q^{73} +(2.31924 - 0.960659i) q^{75} +(-0.450505 + 1.08761i) q^{77} -6.64904i q^{79} -8.00381i q^{81} +(-4.27376 + 10.3178i) q^{83} +(4.25098 - 1.76081i) q^{85} +(-14.4286 - 14.4286i) q^{87} +(-3.04991 + 3.04991i) q^{89} +(1.04616 + 2.52565i) q^{91} +(-19.0063 - 7.87266i) q^{93} -4.18586 q^{95} -0.911645 q^{97} +(-3.79357 - 1.57135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) $ 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.31924	−	0.960659i	−1.33901	−	0.554637i	−0.405799	−	0.913962i	$-0.633007\pi$
$3$	−2.31924	−	0.960659i	−1.33901	−	0.554637i	−0.933212	+	0.359326i	$0.883007\pi$
$4$		0			0
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$		0			0
$7$	0.669347	−	0.669347i	0.252989	−	0.252989i	−0.569206	−	0.822195i	$-0.692749\pi$
$7$	0.669347	−	0.669347i	0.252989	−	0.252989i	0.822195	+	0.569206i	$0.192749\pi$
$8$		0			0
$9$	2.33467	+	2.33467i	0.778223	+	0.778223i
$10$		0			0
$11$	−1.14897	+	0.475919i	−0.346427	+	0.143495i	−0.549111	−	0.835749i	$-0.685034\pi$
$11$	−1.14897	+	0.475919i	−0.346427	+	0.143495i	0.202684	+	0.979244i	$0.435034\pi$
$12$		0			0
$13$	−1.10518	+	2.66813i	−0.306521	+	0.740007i	0.693292	+	0.720657i	$0.256160\pi$
$13$	−1.10518	+	2.66813i	−0.306521	+	0.740007i	−0.999813	+	0.0193499i	$0.993840\pi$
$14$		0			0
$15$		−	2.51032i		−	0.648162i
$16$		0			0
$17$		−	4.60123i		−	1.11596i	−0.829854	−	0.557981i	$-0.811576\pi$
$17$		−	4.60123i		−	1.11596i	0.829854	−	0.557981i	$-0.188424\pi$
$18$		0			0
$19$	−1.60186	+	3.86723i	−0.367492	+	0.887204i	0.626668	+	0.779286i	$0.284418\pi$
$19$	−1.60186	+	3.86723i	−0.367492	+	0.887204i	−0.994160	+	0.107918i	$0.965582\pi$
$20$		0			0
$21$	−2.19539	+	0.909360i	−0.479073	+	0.198439i
$22$		0			0
$23$	3.91843	+	3.91843i	0.817048	+	0.817048i	0.985679	−	0.168631i	$-0.0539347\pi$
$23$	3.91843	+	3.91843i	0.817048	+	0.817048i	−0.168631	+	0.985679i	$0.553935\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	−0.289849	−	0.699757i	−0.0557814	−	0.134668i
$28$		0			0
$29$	7.50975	+	3.11064i	1.39453	+	0.577632i	0.948325	−	0.317301i	$-0.102777\pi$
$29$	7.50975	+	3.11064i	1.39453	+	0.577632i	0.446201	+	0.894933i	$0.352777\pi$
$30$		0			0
$31$	8.19506			1.47188			0.735938	−	0.677049i	$-0.236741\pi$
$31$	8.19506			1.47188			0.735938	+	0.677049i	$0.236741\pi$
$32$		0			0
$33$	3.12193			0.543458
$34$		0			0
$35$	0.874544	+	0.362248i	0.147825	+	0.0612311i
$36$		0			0
$37$	−3.90337	−	9.42357i	−0.641710	−	1.54923i	−0.824371	−	0.566050i	$-0.808471\pi$
$37$	−3.90337	−	9.42357i	−0.641710	−	1.54923i	0.182661	−	0.983176i	$-0.441529\pi$
$38$		0			0
$39$	5.12633	−	5.12633i	0.820870	−	0.820870i
$40$		0			0
$41$	7.53342	+	7.53342i	1.17652	+	1.17652i	0.980624	+	0.195898i	$0.0627621\pi$
$41$	7.53342	+	7.53342i	1.17652	+	1.17652i	0.195898	+	0.980624i	$0.437238\pi$
$42$		0			0
$43$	10.4073	−	4.31084i	1.58710	−	0.657397i	0.597579	−	0.801810i	$-0.296129\pi$
$43$	10.4073	−	4.31084i	1.58710	−	0.657397i	0.989517	+	0.144413i	$0.0461294\pi$
$44$		0			0
$45$	−1.26351	+	3.05039i	−0.188353	+	0.454725i
$46$		0			0
$47$		−	2.88459i		−	0.420761i	−0.977620	−	0.210381i	$-0.932530\pi$
$47$		−	2.88459i		−	0.420761i	0.977620	−	0.210381i	$-0.0674703\pi$
$48$		0			0
$49$			6.10395i			0.871993i
$50$		0			0
$51$	−4.42021	+	10.6713i	−0.618954	+	1.49429i
$52$		0			0
$53$	−1.46716	+	0.607718i	−0.201530	+	0.0834765i	−0.481166	−	0.876630i	$-0.659786\pi$
$53$	−1.46716	+	0.607718i	−0.201530	+	0.0834765i	0.279635	+	0.960106i	$0.409786\pi$
$54$		0			0
$55$	−0.879383	−	0.879383i	−0.118576	−	0.118576i
$56$		0			0
$57$	7.43018	−	7.43018i	0.984152	−	0.984152i
$58$		0			0
$59$	2.77205	+	6.69231i	0.360890	+	0.871265i	0.995170	+	0.0981620i	$0.0312963\pi$
$59$	2.77205	+	6.69231i	0.360890	+	0.871265i	−0.634281	+	0.773103i	$0.718704\pi$
$60$		0			0
$61$	1.99858	+	0.827839i	0.255892	+	0.105994i	0.506942	−	0.861980i	$-0.330776\pi$
$61$	1.99858	+	0.827839i	0.255892	+	0.105994i	−0.251050	+	0.967974i	$0.580776\pi$
$62$		0			0
$63$	3.12541			0.393764
$64$		0			0
$65$	−2.88797			−0.358208
$66$		0			0
$67$	−2.17091	−	0.899222i	−0.265219	−	0.109857i	0.246111	−	0.969242i	$-0.420847\pi$
$67$	−2.17091	−	0.899222i	−0.265219	−	0.109857i	−0.511330	+	0.859384i	$0.670847\pi$
$68$		0			0
$69$	−5.32348	−	12.8520i	−0.640872	−	1.54720i
$70$		0			0
$71$	−7.24583	+	7.24583i	−0.859922	+	0.859922i	−0.991329	−	0.131407i	$-0.958051\pi$
$71$	−7.24583	+	7.24583i	−0.859922	+	0.859922i	0.131407	+	0.991329i	$0.458051\pi$
$72$		0			0
$73$	3.25815	+	3.25815i	0.381337	+	0.381337i	0.871584	−	0.490247i	$-0.163093\pi$
$73$	3.25815	+	3.25815i	0.381337	+	0.381337i	−0.490247	+	0.871584i	$0.663093\pi$
$74$		0			0
$75$	2.31924	−	0.960659i	0.267802	−	0.110927i
$76$		0			0
$77$	−0.450505	+	1.08761i	−0.0513398	+	0.123945i
$78$		0			0
$79$		−	6.64904i		−	0.748076i	−0.927413	−	0.374038i	$-0.877973\pi$
$79$		−	6.64904i		−	0.748076i	0.927413	−	0.374038i	$-0.122027\pi$
$80$		0			0
$81$		−	8.00381i		−	0.889312i
$82$		0			0
$83$	−4.27376	+	10.3178i	−0.469106	+	1.13252i	0.495448	+	0.868637i	$0.335004\pi$
$83$	−4.27376	+	10.3178i	−0.469106	+	1.13252i	−0.964554	+	0.263885i	$0.914996\pi$
$84$		0			0
$85$	4.25098	−	1.76081i	0.461084	−	0.190987i
$86$		0			0
$87$	−14.4286	−	14.4286i	−1.54691	−	1.54691i
$88$		0			0
$89$	−3.04991	+	3.04991i	−0.323289	+	0.323289i	−0.850028	−	0.526738i	$-0.823415\pi$
$89$	−3.04991	+	3.04991i	−0.323289	+	0.323289i	0.526738	+	0.850028i	$0.323415\pi$
$90$		0			0
$91$	1.04616	+	2.52565i	0.109667	+	0.264760i
$92$		0			0
$93$	−19.0063	−	7.87266i	−1.97086	−	0.816357i
$94$		0			0
$95$	−4.18586			−0.429460
$96$		0			0
$97$	−0.911645			−0.0925635			−0.0462817	−	0.998928i	$-0.514737\pi$
$97$	−0.911645			−0.0925635			−0.0462817	+	0.998928i	$0.514737\pi$
$98$		0			0
$99$	−3.79357	−	1.57135i	−0.381268	−	0.157927i
$100$		0			0
$101$	−1.95996	−	4.73177i	−0.195024	−	0.470829i	0.795871	−	0.605466i	$-0.207013\pi$
$101$	−1.95996	−	4.73177i	−0.195024	−	0.470829i	−0.990895	+	0.134637i	$0.957013\pi$
$102$		0			0
$103$	3.94346	−	3.94346i	0.388561	−	0.388561i	−0.485613	−	0.874174i	$-0.661404\pi$
$103$	3.94346	−	3.94346i	0.388561	−	0.388561i	0.874174	+	0.485613i	$0.161404\pi$
$104$		0			0
$105$	−1.68028	−	1.68028i	−0.163978	−	0.163978i
$106$		0			0
$107$	7.13432	−	2.95513i	0.689701	−	0.285683i	−0.0101747	−	0.999948i	$-0.503239\pi$
$107$	7.13432	−	2.95513i	0.689701	−	0.285683i	0.699876	+	0.714265i	$0.253239\pi$
$108$		0			0
$109$	2.23044	−	5.38475i	0.213637	−	0.515766i	−0.780340	−	0.625356i	$-0.784954\pi$
$109$	2.23044	−	5.38475i	0.213637	−	0.515766i	0.993977	+	0.109590i	$0.0349539\pi$
$110$		0			0
$111$			25.6053i			2.43035i
$112$		0			0
$113$			18.7501i			1.76386i	0.471383	+	0.881929i	$0.343755\pi$
$113$			18.7501i			1.76386i	−0.471383	+	0.881929i	$0.656245\pi$
$114$		0			0
$115$	−2.12064	+	5.11967i	−0.197750	+	0.477412i
$116$		0			0
$117$	−8.80942	+	3.64898i	−0.814431	+	0.337348i
$118$		0			0
$119$	−3.07982	−	3.07982i	−0.282327	−	0.282327i
$120$		0			0
$121$	−6.68454	+	6.68454i	−0.607686	+	0.607686i
$122$		0			0
$123$	−10.2347	−	24.7088i	−0.922834	−	2.22792i
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$		0			0
$127$	−3.84320			−0.341029			−0.170515	−	0.985355i	$-0.554543\pi$
$127$	−3.84320			−0.341029			−0.170515	+	0.985355i	$0.554543\pi$
$128$		0			0
$129$	−28.2782			−2.48976
$130$		0			0
$131$	4.50753	+	1.86708i	0.393824	+	0.163127i	0.570803	−	0.821087i	$-0.306632\pi$
$131$	4.50753	+	1.86708i	0.393824	+	0.163127i	−0.176978	+	0.984215i	$0.556632\pi$
$132$		0			0
$133$	1.51632	+	3.66072i	0.131482	+	0.317425i
$134$		0			0
$135$	0.535571	−	0.535571i	0.0460946	−	0.0460946i
$136$		0			0
$137$	−5.39496	−	5.39496i	−0.460923	−	0.460923i	0.438035	−	0.898958i	$-0.355675\pi$
$137$	−5.39496	−	5.39496i	−0.460923	−	0.460923i	−0.898958	+	0.438035i	$0.855675\pi$
$138$		0			0
$139$	−11.7036	+	4.84781i	−0.992690	+	0.411186i	−0.819111	−	0.573634i	$-0.805533\pi$
$139$	−11.7036	+	4.84781i	−0.992690	+	0.411186i	−0.173578	+	0.984820i	$0.555533\pi$
$140$		0			0
$141$	−2.77111	+	6.69005i	−0.233370	+	0.563404i
$142$		0			0
$143$		−	3.59158i		−	0.300343i
$144$		0			0
$145$			8.12850i			0.675035i
$146$		0			0
$147$	5.86381	−	14.1565i	0.483639	−	1.16761i
$148$		0			0
$149$	17.6972	−	7.33043i	1.44981	−	0.600532i	0.487658	−	0.873035i	$-0.337851\pi$
$149$	17.6972	−	7.33043i	1.44981	−	0.600532i	0.962155	+	0.272502i	$0.0878513\pi$
$150$		0			0
$151$	−12.6881	−	12.6881i	−1.03255	−	1.03255i	−0.999452	−	0.0330932i	$-0.989464\pi$
$151$	−12.6881	−	12.6881i	−1.03255	−	1.03255i	−0.0330932	−	0.999452i	$-0.510536\pi$
$152$		0			0
$153$	10.7423	−	10.7423i	0.868467	−	0.868467i
$154$		0			0
$155$	3.13611	+	7.57125i	0.251899	+	0.608137i
$156$		0			0
$157$	5.21725	+	2.16106i	0.416382	+	0.172471i	0.581032	−	0.813881i	$-0.302649\pi$
$157$	5.21725	+	2.16106i	0.416382	+	0.172471i	−0.164649	+	0.986352i	$0.552649\pi$
$158$		0			0
$159$	3.98650			0.316150
$160$		0			0
$161$	5.24557			0.413409
$162$		0			0
$163$	−17.9419	−	7.43176i	−1.40531	−	0.582100i	−0.454189	−	0.890905i	$-0.650071\pi$
$163$	−17.9419	−	7.43176i	−1.40531	−	0.582100i	−0.951125	+	0.308805i	$0.900071\pi$
$164$		0			0
$165$	1.19471	+	2.88428i	0.0930080	+	0.224541i
$166$		0			0
$167$	−2.56051	+	2.56051i	−0.198138	+	0.198138i	−0.799201	−	0.601063i	$-0.794744\pi$
$167$	−2.56051	+	2.56051i	−0.198138	+	0.198138i	0.601063	+	0.799201i	$0.294744\pi$
$168$		0			0
$169$	3.29488	+	3.29488i	0.253452	+	0.253452i
$170$		0			0
$171$	−12.7685	+	5.28889i	−0.976433	+	0.404452i
$172$		0			0
$173$	−2.46584	+	5.95306i	−0.187474	+	0.452603i	−0.989472	−	0.144724i	$-0.953770\pi$
$173$	−2.46584	+	5.95306i	−0.187474	+	0.452603i	0.801998	+	0.597327i	$0.203770\pi$
$174$		0			0
$175$			0.946600i			0.0715562i
$176$		0			0
$177$		−	18.1840i		−	1.36680i
$178$		0			0
$179$	2.28094	−	5.50668i	0.170486	−	0.411589i	−0.815425	−	0.578863i	$-0.803497\pi$
$179$	2.28094	−	5.50668i	0.170486	−	0.411589i	0.985910	+	0.167274i	$0.0534966\pi$
$180$		0			0
$181$	−9.83682	+	4.07454i	−0.731165	+	0.302859i	−0.717031	−	0.697042i	$-0.754499\pi$
$181$	−9.83682	+	4.07454i	−0.731165	+	0.302859i	−0.0141344	+	0.999900i	$0.504499\pi$
$182$		0			0
$183$	−3.83991	−	3.83991i	−0.283854	−	0.283854i
$184$		0			0
$185$	7.21249	−	7.21249i	0.530273	−	0.530273i
$186$		0			0
$187$	2.18981	+	5.28667i	0.160135	+	0.386600i
$188$		0			0
$189$	−0.662390	−	0.274371i	−0.0481818	−	0.0199576i
$190$		0			0
$191$	9.72467			0.703652			0.351826	−	0.936065i	$-0.385561\pi$
$191$	9.72467			0.703652			0.351826	+	0.936065i	$0.385561\pi$
$192$		0			0
$193$	−0.935381			−0.0673302			−0.0336651	−	0.999433i	$-0.510718\pi$
$193$	−0.935381			−0.0673302			−0.0336651	+	0.999433i	$0.510718\pi$
$194$		0			0
$195$	6.69787	+	2.77435i	0.479645	+	0.198675i
$196$		0			0
$197$	8.86425	+	21.4002i	0.631551	+	1.52470i	0.837672	+	0.546174i	$0.183916\pi$
$197$	8.86425	+	21.4002i	0.631551	+	1.52470i	−0.206121	+	0.978527i	$0.566084\pi$
$198$		0			0
$199$	8.81612	−	8.81612i	0.624958	−	0.624958i	−0.321837	−	0.946795i	$-0.604300\pi$
$199$	8.81612	−	8.81612i	0.624958	−	0.624958i	0.946795	+	0.321837i	$0.104300\pi$
$200$		0			0
$201$	4.17101	+	4.17101i	0.294201	+	0.294201i
$202$		0			0
$203$	7.10873	−	2.94453i	0.498935	−	0.206666i
$204$		0			0
$205$	−4.07706	+	9.84288i	−0.284754	+	0.687457i
$206$		0			0
$207$			18.2964i			1.27169i
$208$		0			0
$209$		−	5.20569i		−	0.360085i
$210$		0			0
$211$	9.01295	−	21.7592i	0.620477	−	1.49796i	−0.230668	−	0.973033i	$-0.574091\pi$
$211$	9.01295	−	21.7592i	0.620477	−	1.49796i	0.851145	−	0.524931i	$-0.175909\pi$
$212$		0			0
$213$	23.7656	−	9.84401i	1.62839	−	0.674501i
$214$		0			0
$215$	7.96539	+	7.96539i	0.543235	+	0.543235i
$216$		0			0
$217$	5.48534	−	5.48534i	0.372369	−	0.372369i
$218$		0			0
$219$	−4.42644	−	10.6864i	−0.299111	−	0.722118i
$220$		0			0
$221$	12.2767	+	5.08517i	0.825820	+	0.342066i
$222$		0			0
$223$	13.7536			0.921006			0.460503	−	0.887658i	$-0.347669\pi$
$223$	13.7536			0.921006			0.460503	+	0.887658i	$0.347669\pi$
$224$		0			0
$225$	−3.30172			−0.220115
$226$		0			0
$227$	17.6839	+	7.32490i	1.17372	+	0.486171i	0.882421	−	0.470461i	$-0.155912\pi$
$227$	17.6839	+	7.32490i	1.17372	+	0.486171i	0.291299	+	0.956632i	$0.405912\pi$
$228$		0			0
$229$	−8.65557	−	20.8964i	−0.571976	−	1.38087i	−0.899870	−	0.436158i	$-0.856339\pi$
$229$	−8.65557	−	20.8964i	−0.571976	−	1.38087i	0.327894	−	0.944714i	$-0.393661\pi$
$230$		0			0
$231$	2.08965	−	2.08965i	0.137489	−	0.137489i
$232$		0			0
$233$	−16.9934	−	16.9934i	−1.11328	−	1.11328i	−0.992705	−	0.120571i	$-0.961528\pi$
$233$	−16.9934	−	16.9934i	−1.11328	−	1.11328i	−0.120571	−	0.992705i	$-0.538472\pi$
$234$		0			0
$235$	2.66502	−	1.10389i	0.173847	−	0.0720096i
$236$		0			0
$237$	−6.38746	+	15.4207i	−0.414910	+	1.00168i
$238$		0			0
$239$			3.17083i			0.205104i	0.994728	+	0.102552i	$0.0327008\pi$
$239$			3.17083i			0.205104i	−0.994728	+	0.102552i	$0.967299\pi$
$240$		0			0
$241$			9.02526i			0.581368i	0.956819	+	0.290684i	$0.0938828\pi$
$241$			9.02526i			0.581368i	−0.956819	+	0.290684i	$0.906117\pi$
$242$		0			0
$243$	−8.55848	+	20.6620i	−0.549027	+	1.32547i
$244$		0			0
$245$	−5.63931	+	2.33588i	−0.360282	+	0.149234i
$246$		0			0
$247$	−8.54795	−	8.54795i	−0.543893	−	0.543893i
$248$		0			0
$249$	19.8237	−	19.8237i	1.25628	−	1.25628i
$250$		0			0
$251$	−0.498349	−	1.20312i	−0.0314555	−	0.0759403i	0.907371	−	0.420330i	$-0.138086\pi$
$251$	−0.498349	−	1.20312i	−0.0314555	−	0.0759403i	−0.938827	+	0.344390i	$0.888086\pi$
$252$		0			0
$253$	−6.36700	−	2.63730i	−0.400290	−	0.165806i
$254$		0			0
$255$	−11.5506			−0.723325
$256$		0			0
$257$	−5.60884			−0.349870			−0.174935	−	0.984580i	$-0.555971\pi$
$257$	−5.60884			−0.349870			−0.174935	+	0.984580i	$0.555971\pi$
$258$		0			0
$259$	−8.92035	−	3.69493i	−0.554284	−	0.229592i
$260$		0			0
$261$	10.2705	+	24.7951i	0.635726	+	1.53478i
$262$		0			0
$263$	−15.9536	+	15.9536i	−0.983742	+	0.983742i	−0.999870	−	0.0161280i	$-0.994866\pi$
$263$	−15.9536	+	15.9536i	−0.983742	+	0.983742i	0.0161280	+	0.999870i	$0.494866\pi$
$264$		0			0
$265$	−1.12292	−	1.12292i	−0.0689802	−	0.0689802i
$266$		0			0
$267$	10.0034	−	4.14353i	0.612196	−	0.253580i
$268$		0			0
$269$	−0.673809	+	1.62672i	−0.0410829	+	0.0991828i	−0.943089	−	0.332540i	$-0.892094\pi$
$269$	−0.673809	+	1.62672i	−0.0410829	+	0.0991828i	0.902006	+	0.431723i	$0.142094\pi$
$270$		0			0
$271$			2.55088i			0.154955i	0.996994	+	0.0774774i	$0.0246866\pi$
$271$			2.55088i			0.154955i	−0.996994	+	0.0774774i	$0.975313\pi$
$272$		0			0
$273$		−	6.86259i		−	0.415343i
$274$		0			0
$275$	0.475919	−	1.14897i	0.0286990	−	0.0692855i
$276$		0			0
$277$	9.33822	−	3.86802i	0.561079	−	0.232407i	−0.0840745	−	0.996459i	$-0.526793\pi$
$277$	9.33822	−	3.86802i	0.561079	−	0.232407i	0.645154	+	0.764053i	$0.276793\pi$
$278$		0			0
$279$	19.1327	+	19.1327i	1.14545	+	1.14545i
$280$		0			0
$281$	−9.65319	+	9.65319i	−0.575861	+	0.575861i	−0.933760	−	0.357899i	$-0.883493\pi$
$281$	−9.65319	+	9.65319i	−0.575861	+	0.575861i	0.357899	+	0.933760i	$0.383493\pi$
$282$		0			0
$283$	−2.88520	−	6.96549i	−0.171507	−	0.414055i	0.814631	−	0.579979i	$-0.196939\pi$
$283$	−2.88520	−	6.96549i	−0.171507	−	0.414055i	−0.986139	+	0.165924i	$0.946939\pi$
$284$		0			0
$285$	9.70800	+	4.02119i	0.575052	+	0.238195i
$286$		0			0
$287$	10.0849			0.595295
$288$		0			0
$289$	−4.17133			−0.245372
$290$		0			0
$291$	2.11432	+	0.875780i	0.123944	+	0.0513391i
$292$		0			0
$293$	0.787239	+	1.90056i	0.0459910	+	0.111032i	0.945206	−	0.326476i	$-0.105861\pi$
$293$	0.787239	+	1.90056i	0.0459910	+	0.111032i	−0.899215	+	0.437508i	$0.855861\pi$
$294$		0			0
$295$	−5.12207	+	5.12207i	−0.298219	+	0.298219i
$296$		0			0
$297$	0.666055	+	0.666055i	0.0386484	+	0.0386484i
$298$		0			0
$299$	−14.7854	+	6.12432i	−0.855063	+	0.354179i
$300$		0			0
$301$	4.08064	−	9.85154i	0.235204	−	0.567833i
$302$		0			0
$303$			12.8570i			0.738613i
$304$		0			0
$305$			2.16325i			0.123867i
$306$		0			0
$307$	−5.58353	+	13.4798i	−0.318669	+	0.769334i	0.680656	+	0.732603i	$0.261695\pi$
$307$	−5.58353	+	13.4798i	−0.318669	+	0.769334i	−0.999325	+	0.0367316i	$0.988305\pi$
$308$		0			0
$309$	−12.9341	+	5.35749i	−0.735797	+	0.304777i
$310$		0			0
$311$	4.99061	+	4.99061i	0.282991	+	0.282991i	0.834301	−	0.551309i	$-0.185872\pi$
$311$	4.99061	+	4.99061i	0.282991	+	0.282991i	−0.551309	+	0.834301i	$0.685872\pi$
$312$		0			0
$313$	−21.0335	+	21.0335i	−1.18888	+	1.18888i	−0.211509	+	0.977376i	$0.567838\pi$
$313$	−21.0335	+	21.0335i	−1.18888	+	1.18888i	−0.977376	+	0.211509i	$0.932162\pi$
$314$		0			0
$315$	1.19604	+	2.88750i	0.0673893	+	0.162692i
$316$		0			0
$317$	7.38383	+	3.05848i	0.414717	+	0.171781i	0.580279	−	0.814418i	$-0.302944\pi$
$317$	7.38383	+	3.05848i	0.414717	+	0.171781i	−0.165562	+	0.986199i	$0.552944\pi$
$318$		0			0
$319$	−10.1089			−0.565989
$320$		0			0
$321$	−19.3850			−1.08197
$322$		0			0
$323$	17.7940	+	7.37053i	0.990086	+	0.410107i
$324$		0			0
$325$	−1.10518	−	2.66813i	−0.0613042	−	0.148001i
$326$		0			0
$327$	−10.3458	+	10.3458i	−0.572125	+	0.572125i
$328$		0			0
$329$	−1.93080	−	1.93080i	−0.106448	−	0.106448i
$330$		0			0
$331$	14.6857	−	6.08303i	0.807201	−	0.334354i	0.0593643	−	0.998236i	$-0.481093\pi$
$331$	14.6857	−	6.08303i	0.807201	−	0.334354i	0.747837	+	0.663883i	$0.231093\pi$
$332$		0			0
$333$	12.8878	−	31.1140i	0.706249	−	1.70504i
$334$		0			0
$335$		−	2.34978i		−	0.128382i
$336$		0			0
$337$		−	25.8572i		−	1.40853i	−0.709937	−	0.704265i	$-0.751277\pi$
$337$		−	25.8572i		−	1.40853i	0.709937	−	0.704265i	$-0.248723\pi$
$338$		0			0
$339$	18.0124	−	43.4858i	0.978300	−	2.36182i
$340$		0			0
$341$	−9.41587	+	3.90018i	−0.509898	+	0.211207i
$342$		0			0
$343$	8.77109	+	8.77109i	0.473594	+	0.473594i
$344$		0			0
$345$	9.83651	−	9.83651i	0.529580	−	0.529580i
$346$		0			0
$347$	−1.18277	−	2.85547i	−0.0634947	−	0.153290i	0.888947	−	0.458009i	$-0.151437\pi$
$347$	−1.18277	−	2.85547i	−0.0634947	−	0.153290i	−0.952442	+	0.304719i	$0.901437\pi$
$348$		0			0
$349$	1.59045	+	0.658787i	0.0851350	+	0.0352641i	0.424845	−	0.905266i	$-0.360329\pi$
$349$	1.59045	+	0.658787i	0.0851350	+	0.0352641i	−0.339710	+	0.940530i	$0.610329\pi$
$350$		0			0
$351$	2.18738			0.116754
$352$		0			0
$353$	21.0242			1.11901			0.559503	−	0.828828i	$-0.310992\pi$
$353$	21.0242			1.11901			0.559503	+	0.828828i	$0.310992\pi$
$354$		0			0
$355$	−9.46713	−	3.92141i	−0.502463	−	0.208127i
$356$		0			0
$357$	4.18417	+	10.1015i	0.221450	+	0.534627i
$358$		0			0
$359$	−7.51144	+	7.51144i	−0.396439	+	0.396439i	−0.876975	−	0.480536i	$-0.840442\pi$
$359$	−7.51144	+	7.51144i	−0.396439	+	0.396439i	0.480536	+	0.876975i	$0.340442\pi$
$360$		0			0
$361$	1.04549	+	1.04549i	0.0550260	+	0.0550260i
$362$		0			0
$363$	21.9246	−	9.08146i	1.15074	−	0.476653i
$364$		0			0
$365$	−1.76330	+	4.25697i	−0.0922951	+	0.222820i
$366$		0			0
$367$		−	21.5615i		−	1.12550i	−0.826627	−	0.562751i	$-0.809743\pi$
$367$		−	21.5615i		−	1.12550i	0.826627	−	0.562751i	$-0.190257\pi$
$368$		0			0
$369$			35.1761i			1.83119i
$370$		0			0
$371$	−0.575266	+	1.38881i	−0.0298663	+	0.0721037i
$372$		0			0
$373$	20.6653	−	8.55987i	1.07001	−	0.443213i	0.223017	−	0.974815i	$-0.428410\pi$
$373$	20.6653	−	8.55987i	1.07001	−	0.443213i	0.846995	+	0.531602i	$0.178410\pi$
$374$		0			0
$375$	1.77507	+	1.77507i	0.0916640	+	0.0916640i
$376$		0			0
$377$	−16.5992	+	16.5992i	−0.854902	+	0.854902i
$378$		0			0
$379$	3.75839	+	9.07355i	0.193055	+	0.466077i	0.990534	−	0.137271i	$-0.0438330\pi$
$379$	3.75839	+	9.07355i	0.193055	+	0.466077i	−0.797478	+	0.603348i	$0.793833\pi$
$380$		0			0
$381$	8.91329	+	3.69201i	0.456642	+	0.189147i
$382$		0			0
$383$	−19.3058			−0.986483			−0.493241	−	0.869893i	$-0.664188\pi$
$383$	−19.3058			−0.986483			−0.493241	+	0.869893i	$0.664188\pi$
$384$		0			0
$385$	−1.17723			−0.0599970
$386$		0			0
$387$	34.3619	+	14.2332i	1.74672	+	0.723513i
$388$		0			0
$389$	−5.55311	−	13.4064i	−0.281554	−	0.679731i	0.718318	−	0.695715i	$-0.244912\pi$
$389$	−5.55311	−	13.4064i	−0.281554	−	0.679731i	−0.999872	+	0.0159832i	$0.994912\pi$
$390$		0			0
$391$	18.0296	−	18.0296i	0.911795	−	0.911795i
$392$		0			0
$393$	−8.66039	−	8.66039i	−0.436859	−	0.436859i
$394$		0			0
$395$	6.14291	−	2.54448i	0.309084	−	0.128027i
$396$		0			0
$397$	1.30700	−	3.15537i	0.0655962	−	0.158363i	−0.887682	−	0.460457i	$-0.847686\pi$
$397$	1.30700	−	3.15537i	0.0655962	−	0.158363i	0.953278	+	0.302094i	$0.0976855\pi$
$398$		0			0
$399$		−	9.94675i		−	0.497960i
$400$		0			0
$401$		−	6.59531i		−	0.329354i	−0.986348	−	0.164677i	$-0.947342\pi$
$401$		−	6.59531i		−	0.329354i	0.986348	−	0.164677i	$-0.0526582\pi$
$402$		0			0
$403$	−9.05699	+	21.8655i	−0.451161	+	1.08920i
$404$		0			0
$405$	7.39456	−	3.06293i	0.367438	−	0.152198i
$406$		0			0
$407$	8.96971	+	8.96971i	0.444612	+	0.444612i
$408$		0			0
$409$	−19.0135	+	19.0135i	−0.940157	+	0.940157i	−0.998308	−	0.0581507i	$-0.981480\pi$
$409$	−19.0135	+	19.0135i	−0.940157	+	0.940157i	0.0581507	+	0.998308i	$0.481480\pi$
$410$		0			0
$411$	7.32947	+	17.6949i	0.361536	+	0.872825i
$412$		0			0
$413$	6.33494	+	2.62402i	0.311722	+	0.129120i
$414$		0			0
$415$	−11.1679			−0.548209
$416$		0			0
$417$	31.8006			1.55728
$418$		0			0
$419$	−16.9726	−	7.03027i	−0.829164	−	0.343451i	−0.0725925	−	0.997362i	$-0.523127\pi$
$419$	−16.9726	−	7.03027i	−0.829164	−	0.343451i	−0.756572	+	0.653911i	$0.773127\pi$
$420$		0			0
$421$	−9.75909	−	23.5605i	−0.475629	−	1.14827i	−0.961639	−	0.274317i	$-0.911548\pi$
$421$	−9.75909	−	23.5605i	−0.475629	−	1.14827i	0.486010	−	0.873953i	$-0.338452\pi$
$422$		0			0
$423$	6.73457	−	6.73457i	0.327446	−	0.327446i
$424$		0			0
$425$	3.25356	+	3.25356i	0.157821	+	0.157821i
$426$		0			0
$427$	1.89186	−	0.783632i	0.0915533	−	0.0379226i
$428$		0			0
$429$	−3.45028	+	8.32971i	−0.166581	+	0.402162i
$430$		0			0
$431$		−	11.7623i		−	0.566570i	−0.959036	−	0.283285i	$-0.908576\pi$
$431$		−	11.7623i		−	0.566570i	0.959036	−	0.283285i	$-0.0914242\pi$
$432$		0			0
$433$		−	10.2442i		−	0.492304i	−0.969231	−	0.246152i	$-0.920834\pi$
$433$		−	10.2442i		−	0.492304i	0.969231	−	0.246152i	$-0.0791662\pi$
$434$		0			0
$435$	7.80871	−	18.8519i	0.374399	−	0.903879i
$436$		0			0
$437$	−21.4302	+	8.87669i	−1.02515	+	0.424630i
$438$		0			0
$439$	28.4702	+	28.4702i	1.35881	+	1.35881i	0.875386	+	0.483424i	$0.160607\pi$
$439$	28.4702	+	28.4702i	1.35881	+	1.35881i	0.483424	+	0.875386i	$0.339393\pi$
$440$		0			0
$441$	−14.2507	+	14.2507i	−0.678604	+	0.678604i
$442$		0			0
$443$	12.0491	+	29.0892i	0.572472	+	1.38207i	0.899444	+	0.437035i	$0.143971\pi$
$443$	12.0491	+	29.0892i	0.572472	+	1.38207i	−0.326973	+	0.945034i	$0.606029\pi$
$444$		0			0
$445$	−3.98489	−	1.65060i	−0.188902	−	0.0782458i
$446$		0			0
$447$	−48.0861			−2.27439
$448$		0			0
$449$	29.4388			1.38930			0.694652	−	0.719346i	$-0.255558\pi$
$449$	29.4388			1.38930			0.694652	+	0.719346i	$0.255558\pi$
$450$		0			0
$451$	−12.2410	−	5.07037i	−0.576404	−	0.238754i
$452$		0			0
$453$	17.2378	+	41.6157i	0.809902	+	1.95528i
$454$		0			0
$455$	−1.93305	+	1.93305i	−0.0906229	+	0.0906229i
$456$		0			0
$457$	6.19261	+	6.19261i	0.289678	+	0.289678i	0.836953	−	0.547275i	$-0.184335\pi$
$457$	6.19261	+	6.19261i	0.289678	+	0.289678i	−0.547275	+	0.836953i	$0.684335\pi$
$458$		0			0
$459$	−3.21974	+	1.33366i	−0.150285	+	0.0622500i
$460$		0			0
$461$	9.67720	−	23.3628i	0.450712	−	1.08812i	−0.521340	−	0.853349i	$-0.674567\pi$
$461$	9.67720	−	23.3628i	0.450712	−	1.08812i	0.972052	−	0.234766i	$-0.0754325\pi$
$462$		0			0
$463$		−	19.0575i		−	0.885677i	−0.896601	−	0.442838i	$-0.853972\pi$
$463$		−	19.0575i		−	0.885677i	0.896601	−	0.442838i	$-0.146028\pi$
$464$		0			0
$465$		−	20.5722i		−	0.954015i
$466$		0			0
$467$	6.18746	−	14.9379i	0.286322	−	0.691242i	−0.713635	−	0.700517i	$-0.752953\pi$
$467$	6.18746	−	14.9379i	0.286322	−	0.691242i	0.999957	+	0.00927576i	$0.00295261\pi$
$468$		0			0
$469$	−2.05499	+	0.851203i	−0.0948904	+	0.0393049i
$470$		0			0
$471$	−10.0240	−	10.0240i	−0.461882	−	0.461882i
$472$		0			0
$473$	−9.90604	+	9.90604i	−0.455480	+	0.455480i
$474$		0			0
$475$	−1.60186	−	3.86723i	−0.0734984	−	0.177441i
$476$		0			0
$477$	−4.84415	−	2.00651i	−0.221799	−	0.0918720i
$478$		0			0
$479$	−1.50510			−0.0687700			−0.0343850	−	0.999409i	$-0.510947\pi$
$479$	−1.50510			−0.0687700			−0.0343850	+	0.999409i	$0.510947\pi$
$480$		0			0
$481$	29.4572			1.34313
$482$		0			0
$483$	−12.1657	−	5.03921i	−0.553560	−	0.229292i
$484$		0			0
$485$	−0.348871	−	0.842250i	−0.0158414	−	0.0382446i
$486$		0			0
$487$	−6.75814	+	6.75814i	−0.306241	+	0.306241i	−0.843449	−	0.537209i	$-0.819479\pi$
$487$	−6.75814	+	6.75814i	−0.306241	+	0.306241i	0.537209	+	0.843449i	$0.319479\pi$
$488$		0			0
$489$	34.4720	+	34.4720i	1.55888	+	1.55888i
$490$		0			0
$491$	2.90170	−	1.20192i	0.130952	−	0.0542421i	−0.316245	−	0.948677i	$-0.602422\pi$
$491$	2.90170	−	1.20192i	0.130952	−	0.0542421i	0.447197	+	0.894435i	$0.352422\pi$
$492$		0			0
$493$	14.3128	−	34.5541i	0.644615	−	1.55624i
$494$		0			0
$495$		−	4.10613i		−	0.184557i
$496$		0			0
$497$			9.69995i			0.435102i
$498$		0			0
$499$	0.506170	−	1.22200i	0.0226593	−	0.0547043i	−0.912145	−	0.409868i	$-0.865575\pi$
$499$	0.506170	−	1.22200i	0.0226593	−	0.0547043i	0.934804	+	0.355164i	$0.115575\pi$
$500$		0			0
$501$	8.39819	−	3.47864i	0.375203	−	0.155414i
$502$		0			0
$503$	−12.8452	−	12.8452i	−0.572740	−	0.572740i	0.360153	−	0.932893i	$-0.382724\pi$
$503$	−12.8452	−	12.8452i	−0.572740	−	0.572740i	−0.932893	+	0.360153i	$0.882724\pi$
$504$		0			0
$505$	3.62154	−	3.62154i	0.161157	−	0.161157i
$506$		0			0
$507$	−4.47634	−	10.8068i	−0.198801	−	0.479949i
$508$		0			0
$509$	29.4130	+	12.1833i	1.30371	+	0.540013i	0.923042	−	0.384699i	$-0.125695\pi$
$509$	29.4130	+	12.1833i	1.30371	+	0.540013i	0.380666	+	0.924713i	$0.375695\pi$
$510$		0			0
$511$	4.36166			0.192949
$512$		0			0
$513$	3.17042			0.139978
$514$		0			0
$515$	5.15238	+	2.13419i	0.227041	+	0.0940435i
$516$		0			0
$517$	1.37283	+	3.31431i	0.0603771	+	0.145763i
$518$		0			0
$519$	11.4377	−	11.4377i	0.502060	−	0.502060i
$520$		0			0
$521$	−20.3397	−	20.3397i	−0.891100	−	0.891100i	0.103527	−	0.994627i	$-0.466987\pi$
$521$	−20.3397	−	20.3397i	−0.891100	−	0.891100i	−0.994627	+	0.103527i	$0.966987\pi$
$522$		0			0
$523$	−27.4129	+	11.3548i	−1.19868	+	0.496510i	−0.890573	−	0.454841i	$-0.849696\pi$
$523$	−27.4129	+	11.3548i	−1.19868	+	0.496510i	−0.308109	+	0.951351i	$0.599696\pi$
$524$		0			0
$525$	0.909360	−	2.19539i	0.0396877	−	0.0958146i
$526$		0			0
$527$		−	37.7074i		−	1.64256i
$528$		0			0
$529$			7.70811i			0.335135i
$530$		0			0
$531$	−9.15252	+	22.0961i	−0.397185	+	0.958890i
$532$		0			0
$533$	−28.4259	+	11.7744i	−1.23126	+	0.510006i
$534$		0			0
$535$	5.46037	+	5.46037i	0.236073	+	0.236073i
$536$		0			0
$537$	−10.5801	+	10.5801i	−0.456564	+	0.456564i
$538$		0			0
$539$	−2.90498	−	7.01325i	−0.125126	−	0.302082i
$540$		0			0
$541$	−22.7055	−	9.40494i	−0.976187	−	0.404350i	−0.163175	−	0.986597i	$-0.552174\pi$
$541$	−22.7055	−	9.40494i	−0.976187	−	0.404350i	−0.813012	+	0.582247i	$0.802174\pi$
$542$		0			0
$543$	26.7282			1.14701
$544$		0			0
$545$	5.82841			0.249662
$546$		0			0
$547$	−39.5915	−	16.3993i	−1.69281	−	0.701184i	−0.693004	−	0.720934i	$-0.743713\pi$
$547$	−39.5915	−	16.3993i	−1.69281	−	0.701184i	−0.999805	+	0.0197496i	$0.993713\pi$
$548$		0			0
$549$	2.73329	+	6.59875i	0.116654	+	0.281628i
$550$		0			0
$551$	−24.0591	+	24.0591i	−1.02495	+	1.02495i
$552$		0			0
$553$	−4.45052	−	4.45052i	−0.189255	−	0.189255i
$554$		0			0
$555$	−23.6562	+	9.79872i	−1.00415	+	0.415933i
$556$		0			0
$557$	1.41428	−	3.41437i	0.0599249	−	0.144671i	−0.891081	−	0.453844i	$-0.850052\pi$
$557$	1.41428	−	3.41437i	0.0599249	−	0.144671i	0.951006	+	0.309173i	$0.100052\pi$
$558$		0			0
$559$			32.5323i			1.37597i
$560$		0			0
$561$		−	14.3647i		−	0.606478i
$562$		0			0
$563$	−3.71723	+	8.97418i	−0.156662	+	0.378217i	−0.982649	−	0.185473i	$-0.940618\pi$
$563$	−3.71723	+	8.97418i	−0.156662	+	0.378217i	0.825987	+	0.563689i	$0.190618\pi$
$564$		0			0
$565$	−17.3228	+	7.17534i	−0.728776	+	0.301869i
$566$		0			0
$567$	−5.35733	−	5.35733i	−0.224987	−	0.224987i
$568$		0			0
$569$	23.6709	−	23.6709i	0.992335	−	0.992335i	−0.00763557	−	0.999971i	$-0.502431\pi$
$569$	23.6709	−	23.6709i	0.992335	−	0.992335i	0.999971	+	0.00763557i	$0.00243050\pi$
$570$		0			0
$571$	−11.6264	−	28.0686i	−0.486550	−	1.17463i	−0.956445	−	0.291912i	$-0.905708\pi$
$571$	−11.6264	−	28.0686i	−0.486550	−	1.17463i	0.469895	−	0.882722i	$-0.344292\pi$
$572$		0			0
$573$	−22.5538	−	9.34209i	−0.942198	−	0.390271i
$574$		0			0
$575$	−5.54149			−0.231096
$576$		0			0
$577$	−21.3897			−0.890464			−0.445232	−	0.895415i	$-0.646879\pi$
$577$	−21.3897			−0.890464			−0.445232	+	0.895415i	$0.646879\pi$
$578$		0			0
$579$	2.16937	+	0.898582i	0.0901559	+	0.0373438i
$580$		0			0
$581$	4.04554	+	9.76680i	0.167837	+	0.405195i
$582$		0			0
$583$	1.39650	−	1.39650i	0.0578371	−	0.0578371i
$584$		0			0
$585$	−6.74244	−	6.74244i	−0.278766	−	0.278766i
$586$		0			0
$587$	9.60656	−	3.97917i	0.396505	−	0.164238i	−0.175516	−	0.984477i	$-0.556159\pi$
$587$	9.60656	−	3.97917i	0.396505	−	0.164238i	0.572021	+	0.820239i	$0.306159\pi$
$588$		0			0
$589$	−13.1273	+	31.6922i	−0.540903	+	1.30586i
$590$		0			0
$591$		−	58.1476i		−	2.39187i
$592$		0			0
$593$		−	1.17076i		−	0.0480772i	−0.999711	−	0.0240386i	$-0.992348\pi$
$593$		−	1.17076i		−	0.0480772i	0.999711	−	0.0240386i	$-0.00765247\pi$
$594$		0			0
$595$	1.66679	−	4.02398i	0.0683316	−	0.164967i
$596$		0			0
$597$	−28.9159	+	11.9774i	−1.18345	+	0.490201i
$598$		0			0
$599$	26.6575	+	26.6575i	1.08920	+	1.08920i	0.995611	+	0.0935855i	$0.0298328\pi$
$599$	26.6575	+	26.6575i	1.08920	+	1.08920i	0.0935855	+	0.995611i	$0.470167\pi$
$600$		0			0
$601$	12.5152	−	12.5152i	0.510504	−	0.510504i	−0.404177	−	0.914681i	$-0.632442\pi$
$601$	12.5152	−	12.5152i	0.510504	−	0.510504i	0.914681	+	0.404177i	$0.132442\pi$
$602$		0			0
$603$	−2.96898	−	7.16774i	−0.120906	−	0.291893i
$604$		0			0
$605$	−8.73378	−	3.61765i	−0.355078	−	0.147078i
$606$		0			0
$607$	25.0822			1.01806			0.509028	−	0.860750i	$-0.330005\pi$
$607$	25.0822			1.01806			0.509028	+	0.860750i	$0.330005\pi$
$608$		0			0
$609$	−19.3155			−0.782704
$610$		0			0
$611$	7.69648	+	3.18799i	0.311366	+	0.128972i
$612$		0			0
$613$	−8.11026	−	19.5799i	−0.327570	−	0.790824i	−0.998772	−	0.0495495i	$-0.984221\pi$
$613$	−8.11026	−	19.5799i	−0.327570	−	0.790824i	0.671201	−	0.741275i	$-0.265779\pi$
$614$		0			0
$615$	18.9113	−	18.9113i	0.762577	−	0.762577i
$616$		0			0
$617$	−32.9484	−	32.9484i	−1.32645	−	1.32645i	−0.908443	−	0.418009i	$-0.862728\pi$
$617$	−32.9484	−	32.9484i	−1.32645	−	1.32645i	−0.418009	−	0.908443i	$-0.637272\pi$
$618$		0			0
$619$	−39.2029	+	16.2384i	−1.57570	+	0.652676i	−0.987725	−	0.156204i	$-0.950074\pi$
$619$	−39.2029	+	16.2384i	−1.57570	+	0.652676i	−0.587974	+	0.808880i	$0.700074\pi$
$620$		0			0
$621$	1.60619	−	3.87770i	0.0644544	−	0.155607i
$622$		0			0
$623$			4.08289i			0.163578i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−5.00089	+	12.0732i	−0.199716	+	0.482158i
$628$		0			0
$629$	−43.3600	+	17.9603i	−1.72888	+	0.716125i
$630$		0			0
$631$	0.354731	+	0.354731i	0.0141216	+	0.0141216i	0.714132	−	0.700011i	$-0.246821\pi$
$631$	0.354731	+	0.354731i	0.0141216	+	0.0141216i	−0.700011	+	0.714132i	$0.746821\pi$
$632$		0			0
$633$	−41.8063	+	41.8063i	−1.66165	+	1.66165i
$634$		0			0
$635$	−1.47073	−	3.55066i	−0.0583642	−	0.140904i
$636$		0			0
$637$	−16.2861	−	6.74594i	−0.645280	−	0.267284i
$638$		0			0
$639$	−33.8332			−1.33842
$640$		0			0
$641$	23.8339			0.941381			0.470691	−	0.882298i	$-0.344005\pi$
$641$	23.8339			0.941381			0.470691	+	0.882298i	$0.344005\pi$
$642$		0			0
$643$	21.1669	+	8.76763i	0.834742	+	0.345762i	0.758778	−	0.651349i	$-0.225797\pi$
$643$	21.1669	+	8.76763i	0.834742	+	0.345762i	0.0759640	+	0.997111i	$0.475797\pi$
$644$		0			0
$645$	−10.8216	−	26.1256i	−0.426100	−	1.02870i
$646$		0			0
$647$	12.3965	−	12.3965i	0.487356	−	0.487356i	−0.420115	−	0.907471i	$-0.638010\pi$
$647$	12.3965	−	12.3965i	0.487356	−	0.487356i	0.907471	+	0.420115i	$0.138010\pi$
$648$		0			0
$649$	−6.36999	−	6.36999i	−0.250044	−	0.250044i
$650$		0			0
$651$	−17.9913	+	7.45226i	−0.705136	+	0.292077i
$652$		0			0
$653$	−4.34878	+	10.4989i	−0.170181	+	0.410853i	−0.985842	−	0.167677i	$-0.946374\pi$
$653$	−4.34878	+	10.4989i	−0.170181	+	0.410853i	0.815661	+	0.578530i	$0.196374\pi$
$654$		0			0
$655$			4.87891i			0.190635i
$656$		0			0
$657$			15.2134i			0.593530i
$658$		0			0
$659$	8.07711	−	19.4999i	0.314640	−	0.759607i	−0.684881	−	0.728655i	$-0.740146\pi$
$659$	8.07711	−	19.4999i	0.314640	−	0.759607i	0.999521	−	0.0309524i	$-0.00985404\pi$
$660$		0			0
$661$	15.4188	−	6.38669i	0.599723	−	0.248413i	−0.0621044	−	0.998070i	$-0.519781\pi$
$661$	15.4188	−	6.38669i	0.599723	−	0.248413i	0.661827	+	0.749656i	$0.269781\pi$
$662$		0			0
$663$	−23.5874	−	23.5874i	−0.916060	−	0.916060i
$664$		0			0
$665$	−2.80180	+	2.80180i	−0.108649	+	0.108649i
$666$		0			0
$667$	17.2376	+	41.6152i	0.667442	+	1.61135i
$668$		0			0
$669$	−31.8977	−	13.2125i	−1.23324	−	0.510824i
$670$		0			0
$671$	−2.69029			−0.103858
$672$		0			0
$673$	22.5946			0.870959			0.435479	−	0.900199i	$-0.356579\pi$
$673$	22.5946			0.870959			0.435479	+	0.900199i	$0.356579\pi$
$674$		0			0
$675$	0.699757	+	0.289849i	0.0269337	+	0.0111563i
$676$		0			0
$677$	3.97874	+	9.60553i	0.152915	+	0.369170i	0.981710	−	0.190383i	$-0.0609728\pi$
$677$	3.97874	+	9.60553i	0.152915	+	0.369170i	−0.828795	+	0.559553i	$0.810973\pi$
$678$		0			0
$679$	−0.610207	+	0.610207i	−0.0234176	+	0.0234176i
$680$		0			0
$681$	−33.9763	−	33.9763i	−1.30198	−	1.30198i
$682$		0			0
$683$	−39.2266	+	16.2482i	−1.50096	+	0.621719i	−0.973669	−	0.227964i	$-0.926793\pi$
$683$	−39.2266	+	16.2482i	−1.50096	+	0.621719i	−0.527293	+	0.849683i	$0.676793\pi$
$684$		0			0
$685$	2.91973	−	7.04886i	0.111557	−	0.269323i
$686$		0			0
$687$			56.7787i			2.16624i
$688$		0			0
$689$		−	4.58622i		−	0.174721i
$690$		0			0
$691$	−10.0304	+	24.2155i	−0.381573	+	0.921200i	0.610089	+	0.792333i	$0.291134\pi$
$691$	−10.0304	+	24.2155i	−0.381573	+	0.921200i	−0.991662	+	0.128866i	$0.958866\pi$
$692$		0			0
$693$	−3.59100	+	1.48744i	−0.136411	+	0.0565032i
$694$		0			0
$695$	−8.95758	−	8.95758i	−0.339780	−	0.339780i
$696$		0			0
$697$	34.6630	−	34.6630i	1.31295	−	1.31295i
$698$		0			0
$699$	23.0869	+	55.7366i	0.873225	+	2.10815i
$700$		0			0
$701$	−44.0535	−	18.2476i	−1.66388	−	0.689201i	−0.665516	−	0.746384i	$-0.731788\pi$
$701$	−44.0535	−	18.2476i	−1.66388	−	0.689201i	−0.998364	+	0.0571824i	$0.981788\pi$
$702$		0			0
$703$	42.6958			1.61030
$704$		0			0
$705$	−7.24126			−0.272722
$706$		0			0
$707$	−4.47910	−	1.85530i	−0.168454	−	0.0697758i
$708$		0			0
$709$	−11.7990	−	28.4852i	−0.443119	−	1.06978i	−0.974848	−	0.222870i	$-0.928457\pi$
$709$	−11.7990	−	28.4852i	−0.443119	−	1.06978i	0.531729	−	0.846915i	$-0.321543\pi$
$710$		0			0
$711$	15.5233	−	15.5233i	0.582169	−	0.582169i
$712$		0			0
$713$	32.1117	+	32.1117i	1.20259	+	1.20259i
$714$		0			0
$715$	3.31818	−	1.37444i	0.124093	−	0.0514010i
$716$		0			0
$717$	3.04609	−	7.35391i	0.113758	−	0.274637i
$718$		0			0
$719$		−	35.0132i		−	1.30577i	−0.757455	−	0.652887i	$-0.773558\pi$
$719$		−	35.0132i		−	1.30577i	0.757455	−	0.652887i	$-0.226442\pi$
$720$		0			0
$721$		−	5.27909i		−	0.196604i
$722$		0			0
$723$	8.67020	−	20.9317i	0.322448	−	0.778458i
$724$		0			0
$725$	−7.50975	+	3.11064i	−0.278905	+	0.115526i
$726$		0			0
$727$	9.09303	+	9.09303i	0.337242	+	0.337242i	0.855328	−	0.518086i	$-0.173355\pi$
$727$	9.09303	+	9.09303i	0.337242	+	0.337242i	−0.518086	+	0.855328i	$0.673355\pi$
$728$		0			0
$729$	22.7196	−	22.7196i	0.841467	−	0.841467i
$730$		0			0
$731$	−19.8352	−	47.8863i	−0.733630	−	1.77114i
$732$		0			0
$733$	5.54544	+	2.29700i	0.204826	+	0.0848416i	0.482738	−	0.875765i	$-0.339642\pi$
$733$	5.54544	+	2.29700i	0.204826	+	0.0848416i	−0.277912	+	0.960606i	$0.589642\pi$
$734$		0			0
$735$	15.3229			0.565193
$736$		0			0
$737$	2.92227			0.107643
$738$		0			0
$739$	9.85943	+	4.08391i	0.362685	+	0.150229i	0.556582	−	0.830793i	$-0.312113\pi$
$739$	9.85943	+	4.08391i	0.362685	+	0.150229i	−0.193897	+	0.981022i	$0.562113\pi$
$740$		0			0
$741$	11.6130	+	28.0364i	0.426616	+	1.02994i
$742$		0			0
$743$	10.5908	−	10.5908i	0.388540	−	0.388540i	−0.485627	−	0.874166i	$-0.661409\pi$
$743$	10.5908	−	10.5908i	0.388540	−	0.388540i	0.874166	+	0.485627i	$0.161409\pi$
$744$		0			0
$745$	13.5449	+	13.5449i	0.496246	+	0.496246i
$746$		0			0
$747$	−34.0664	+	14.1108i	−1.24642	+	0.516285i
$748$		0			0
$749$	2.79733	−	6.75335i	0.102212	−	0.246762i
$750$		0			0
$751$			9.09448i			0.331862i	0.986137	+	0.165931i	$0.0530629\pi$
$751$			9.09448i			0.331862i	−0.986137	+	0.165931i	$0.946937\pi$
$752$		0			0
$753$			3.26906i			0.119131i
$754$		0			0
$755$	6.86677	−	16.5778i	0.249907	−	0.603329i
$756$		0			0
$757$	45.8682	−	18.9992i	1.66711	−	0.690538i	0.668521	−	0.743693i	$-0.266928\pi$
$757$	45.8682	−	18.9992i	1.66711	−	0.690538i	0.998586	+	0.0531547i	$0.0169277\pi$
$758$		0			0
$759$	12.2330	+	12.2330i	0.444031	+	0.444031i
$760$		0			0
$761$	−0.0615279	+	0.0615279i	−0.00223039	+	0.00223039i	−0.708221	−	0.705991i	$-0.750502\pi$
$761$	−0.0615279	+	0.0615279i	−0.00223039	+	0.00223039i	0.705991	+	0.708221i	$0.250502\pi$
$762$		0			0
$763$	−2.11133	−	5.09720i	−0.0764353	−	0.184531i
$764$		0			0
$765$	14.0356	+	5.81372i	0.507456	+	0.210195i
$766$		0			0
$767$	−20.9196			−0.755362
$768$		0			0
$769$	−21.4372			−0.773046			−0.386523	−	0.922280i	$-0.626324\pi$
$769$	−21.4372			−0.773046			−0.386523	+	0.922280i	$0.626324\pi$
$770$		0			0
$771$	13.0082	+	5.38818i	0.468479	+	0.194050i
$772$		0			0
$773$	18.9293	+	45.6994i	0.680841	+	1.64369i	0.762463	+	0.647031i	$0.223990\pi$
$773$	18.9293	+	45.6994i	0.680841	+	1.64369i	−0.0816228	+	0.996663i	$0.526010\pi$
$774$		0			0
$775$	−5.79478	+	5.79478i	−0.208155	+	0.208155i
$776$		0			0
$777$	17.1388	+	17.1388i	0.614852	+	0.614852i
$778$		0			0
$779$	−41.2010	+	17.0660i	−1.47618	+	0.611453i
$780$		0			0
$781$	4.87681	−	11.7737i	0.174506	−	0.421295i
$782$		0			0
$783$		−	6.15662i		−	0.220020i
$784$		0			0
$785$			5.64712i			0.201554i
$786$		0			0
$787$	−6.58539	+	15.8985i	−0.234744	+	0.566722i	−0.996724	−	0.0808786i	$-0.974227\pi$
$787$	−6.58539	+	15.8985i	−0.234744	+	0.566722i	0.761980	+	0.647600i	$0.224227\pi$
$788$		0			0
$789$	52.3262	−	21.6742i	1.86286	−	0.771622i
$790$		0			0
$791$	12.5503	+	12.5503i	0.446237	+	0.446237i
$792$		0			0
$793$	−4.41757	+	4.41757i	−0.156872	+	0.156872i
$794$		0			0
$795$	1.52557	+	3.68305i	0.0541063	+	0.130624i
$796$		0			0
$797$	−8.16430	−	3.38176i	−0.289194	−	0.119788i	0.233370	−	0.972388i	$-0.425025\pi$
$797$	−8.16430	−	3.38176i	−0.289194	−	0.119788i	−0.522564	+	0.852600i	$0.675025\pi$
$798$		0			0
$799$	−13.2727			−0.469554
$800$		0			0
$801$	−14.2410			−0.503182
$802$		0			0
$803$	−5.29412	−	2.19290i	−0.186826	−	0.0773857i
$804$		0			0
$805$	2.00739	+	4.84628i	0.0707514	+	0.170809i
$806$		0			0
$807$	3.12544	−	3.12544i	0.110021	−	0.110021i
$808$		0			0
$809$	−4.35813	−	4.35813i	−0.153224	−	0.153224i	0.626332	−	0.779556i	$-0.284555\pi$
$809$	−4.35813	−	4.35813i	−0.153224	−	0.153224i	−0.779556	+	0.626332i	$0.784555\pi$
$810$		0			0
$811$	37.0442	−	15.3442i	1.30080	−	0.538808i	0.378612	−	0.925555i	$-0.376401\pi$
$811$	37.0442	−	15.3442i	1.30080	−	0.538808i	0.922186	+	0.386747i	$0.126401\pi$
$812$		0			0
$813$	2.45052	−	5.91609i	0.0859437	−	0.207486i
$814$		0			0
$815$		−	19.4201i		−	0.680257i
$816$		0			0
$817$			47.1528i			1.64967i
$818$		0			0
$819$	−3.45413	+	8.33900i	−0.120697	+	0.291388i
$820$		0			0
$821$	43.3196	−	17.9435i	1.51186	−	0.626234i	0.535922	−	0.844268i	$-0.319964\pi$
$821$	43.3196	−	17.9435i	1.51186	−	0.626234i	0.975941	+	0.218034i	$0.0699642\pi$
$822$		0			0
$823$	−10.2863	−	10.2863i	−0.358557	−	0.358557i	0.504724	−	0.863281i	$-0.331594\pi$
$823$	−10.2863	−	10.2863i	−0.358557	−	0.358557i	−0.863281	+	0.504724i	$0.831594\pi$
$824$		0			0
$825$	−2.20753	+	2.20753i	−0.0768565	+	0.0768565i
$826$		0			0
$827$	4.76560	+	11.5052i	0.165716	+	0.400074i	0.984822	−	0.173569i	$-0.0555299\pi$
$827$	4.76560	+	11.5052i	0.165716	+	0.400074i	−0.819106	+	0.573643i	$0.805530\pi$
$828$		0			0
$829$	−3.27484	−	1.35648i	−0.113740	−	0.0471127i	0.325088	−	0.945684i	$-0.394606\pi$
$829$	−3.27484	−	1.35648i	−0.113740	−	0.0471127i	−0.438828	+	0.898571i	$0.644606\pi$
$830$		0			0
$831$	−25.3734			−0.880193
$832$		0			0
$833$	28.0857			0.973111
$834$		0			0
$835$	−3.34546	−	1.38574i	−0.115774	−	0.0479554i
$836$		0			0
$837$	−2.37533	−	5.73455i	−0.0821034	−	0.198215i
$838$		0			0
$839$	10.7793	−	10.7793i	0.372142	−	0.372142i	−0.496115	−	0.868257i	$-0.665241\pi$
$839$	10.7793	−	10.7793i	0.372142	−	0.372142i	0.868257	+	0.496115i	$0.165241\pi$
$840$		0			0
$841$	26.2142	+	26.2142i	0.903938	+	0.903938i
$842$		0			0
$843$	31.6614	−	13.1146i	1.09048	−	0.451691i
$844$		0			0
$845$	−1.78317	+	4.30496i	−0.0613430	+	0.148095i
$846$		0			0
$847$			8.94856i			0.307476i
$848$		0			0
$849$			18.9263i			0.649549i
$850$		0			0
$851$	21.6305	−	52.2206i	0.741484	−	1.79010i
$852$		0			0
$853$	−41.8078	+	17.3173i	−1.43147	+	0.592935i	−0.957714	−	0.287721i	$-0.907102\pi$
$853$	−41.8078	+	17.3173i	−1.43147	+	0.592935i	−0.473757	+	0.880656i	$0.657102\pi$
$854$		0			0
$855$	−9.77260	−	9.77260i	−0.334216	−	0.334216i
$856$		0			0
$857$	3.58564	−	3.58564i	0.122483	−	0.122483i	−0.643208	−	0.765691i	$-0.722397\pi$
$857$	3.58564	−	3.58564i	0.122483	−	0.122483i	0.765691	+	0.643208i	$0.222397\pi$
$858$		0			0
$859$	10.6212	+	25.6419i	0.362391	+	0.874889i	0.994950	+	0.100376i	$0.0320047\pi$
$859$	10.6212	+	25.6419i	0.362391	+	0.874889i	−0.632559	+	0.774512i	$0.717995\pi$
$860$		0			0
$861$	−23.3894	−	9.68819i	−0.797107	−	0.330173i
$862$		0			0
$863$	7.37146			0.250927			0.125464	−	0.992098i	$-0.459958\pi$
$863$	7.37146			0.250927			0.125464	+	0.992098i	$0.459958\pi$
$864$		0			0
$865$	−6.44354			−0.219087
$866$		0			0
$867$	9.67429	+	4.00722i	0.328556	+	0.136092i
$868$		0			0
$869$	3.16440	+	7.63955i	0.107345	+	0.259154i
$870$		0			0
$871$	4.79848	−	4.79848i	0.162590	−	0.162590i
$872$		0			0
$873$	−2.12839	−	2.12839i	−0.0720350	−	0.0720350i
$874$		0			0
$875$	−0.874544	+	0.362248i	−0.0295650	+	0.0122462i
$876$		0			0
$877$	−4.65831	+	11.2461i	−0.157300	+	0.379755i	−0.982807	−	0.184636i	$-0.940889\pi$
$877$	−4.65831	+	11.2461i	−0.157300	+	0.379755i	0.825507	+	0.564392i	$0.190889\pi$
$878$		0			0
$879$		−	5.16412i		−	0.174182i
$880$		0			0
$881$			18.4005i			0.619930i	0.950748	+	0.309965i	$0.100317\pi$
$881$			18.4005i			0.619930i	−0.950748	+	0.309965i	$0.899683\pi$
$882$		0			0
$883$	15.0392	−	36.3079i	0.506110	−	1.22186i	−0.439996	−	0.898000i	$-0.645020\pi$
$883$	15.0392	−	36.3079i	0.506110	−	1.22186i	0.946106	−	0.323857i	$-0.104980\pi$
$884$		0			0
$885$	16.7999	−	6.95873i	0.564721	−	0.233915i
$886$		0			0
$887$	32.8397	+	32.8397i	1.10265	+	1.10265i	0.994090	+	0.108560i	$0.0346239\pi$
$887$	32.8397	+	32.8397i	1.10265	+	1.10265i	0.108560	+	0.994090i	$0.465376\pi$
$888$		0			0
$889$	−2.57244	+	2.57244i	−0.0862768	+	0.0862768i
$890$		0			0
$891$	3.80916	+	9.19613i	0.127612	+	0.308082i
$892$		0			0
$893$	11.1554	+	4.62072i	0.373301	+	0.154626i
$894$		0			0
$895$	5.96039			0.199234
$896$		0			0
$897$	40.1743			1.34138
$898$		0			0
$899$	61.5429	+	25.4919i	2.05257	+	0.850202i
$900$		0			0
$901$	2.79625	+	6.75075i	0.0931566	+	0.224900i
$902$		0			0
$903$	−18.9279	+	18.9279i	−0.629882	+	0.629882i
$904$		0			0
$905$	−7.52878	−	7.52878i	−0.250265	−	0.250265i
$906$		0			0
$907$	−14.0226	+	5.80833i	−0.465611	+	0.192863i	−0.603140	−	0.797635i	$-0.706084\pi$
$907$	−14.0226	+	5.80833i	−0.465611	+	0.192863i	0.137529	+	0.990498i	$0.456084\pi$
$908$		0			0
$909$	6.47125	−	15.6230i	0.214638	−	0.518182i
$910$		0			0
$911$			17.7127i			0.586848i	0.955982	+	0.293424i	$0.0947947\pi$
$911$			17.7127i			0.586848i	−0.955982	+	0.293424i	$0.905205\pi$
$912$		0			0
$913$		−	13.8888i		−	0.459651i
$914$		0			0
$915$	2.07814	−	5.01708i	0.0687013	−	0.165860i
$916$		0			0
$917$	4.26682	−	1.76738i	0.140903	−	0.0583639i
$918$		0			0
$919$	−26.7000	−	26.7000i	−0.880751	−	0.880751i	0.112860	−	0.993611i	$-0.463999\pi$
$919$	−26.7000	−	26.7000i	−0.880751	−	0.880751i	−0.993611	+	0.112860i	$0.963999\pi$
$920$		0			0
$921$	25.8990	−	25.8990i	0.853402	−	0.853402i
$922$		0			0
$923$	−11.3249	−	27.3407i	−0.372764	−	0.899932i
$924$		0			0
$925$	9.42357	+	3.90337i	0.309845	+	0.128342i
$926$		0			0
$927$	18.4133			0.604774
$928$		0			0
$929$	−12.0993			−0.396966			−0.198483	−	0.980104i	$-0.563602\pi$
$929$	−12.0993			−0.396966			−0.198483	+	0.980104i	$0.563602\pi$
$930$		0			0
$931$	−23.6054	−	9.77767i	−0.773635	−	0.320450i
$932$		0			0
$933$	−6.78012	−	16.3687i	−0.221971	−	0.535886i
$934$		0			0
$935$	−4.04624	+	4.04624i	−0.132326	+	0.132326i
$936$		0			0
$937$	17.0679	+	17.0679i	0.557583	+	0.557583i	0.928619	−	0.371036i	$-0.120997\pi$
$937$	17.0679	+	17.0679i	0.557583	+	0.557583i	−0.371036	+	0.928619i	$0.620997\pi$
$938$		0			0
$939$	68.9877	−	28.5757i	2.25133	−	0.932531i
$940$		0			0
$941$	9.14552	−	22.0792i	0.298135	−	0.719762i	−0.701837	−	0.712337i	$-0.747637\pi$
$941$	9.14552	−	22.0792i	0.298135	−	0.719762i	0.999972	−	0.00742491i	$-0.00236344\pi$
$942$		0			0
$943$			59.0383i			1.92255i
$944$		0			0
$945$		−	0.716966i		−	0.0233229i
$946$		0			0
$947$	−10.9704	+	26.4850i	−0.356491	+	0.860646i	0.639297	+	0.768960i	$0.279226\pi$
$947$	−10.9704	+	26.4850i	−0.356491	+	0.860646i	−0.995788	+	0.0916860i	$0.970774\pi$
$948$		0			0
$949$	−12.2940	+	5.09234i	−0.399080	+	0.165304i
$950$		0			0
$951$	−14.1867	−	14.1867i	−0.460035	−	0.460035i
$952$		0			0
$953$	11.4776	−	11.4776i	0.371797	−	0.371797i	−0.496334	−	0.868132i	$-0.665321\pi$
$953$	11.4776	−	11.4776i	0.371797	−	0.371797i	0.868132	+	0.496334i	$0.165321\pi$
$954$		0			0
$955$	3.72147	+	8.98442i	0.120424	+	0.290729i
$956$		0			0
$957$	23.4449	+	9.71119i	0.757866	+	0.313918i
$958$		0			0
$959$	−7.22220			−0.233217
$960$		0			0
$961$	36.1590			1.16642
$962$		0			0
$963$	23.5555	+	9.75702i	0.759066	+	0.314416i
$964$		0			0
$965$	−0.357955	−	0.864179i	−0.0115230	−	0.0278189i
$966$		0			0
$967$	5.37730	−	5.37730i	0.172922	−	0.172922i	−0.615340	−	0.788262i	$-0.710981\pi$
$967$	5.37730	−	5.37730i	0.172922	−	0.172922i	0.788262	+	0.615340i	$0.210981\pi$
$968$		0			0
$969$	−34.1880	−	34.1880i	−1.09828	−	1.09828i
$970$		0			0
$971$	0.203577	−	0.0843243i	0.00653310	−	0.00270610i	−0.379414	−	0.925227i	$-0.623875\pi$
$971$	0.203577	−	0.0843243i	0.00653310	−	0.00270610i	0.385948	+	0.922521i	$0.373875\pi$
$972$		0			0
$973$	−4.58893	+	11.0787i	−0.147114	+	0.355166i
$974$		0			0
$975$			7.24972i			0.232177i
$976$		0			0
$977$			51.9289i			1.66135i	0.556756	+	0.830676i	$0.312046\pi$
$977$			51.9289i			1.66135i	−0.556756	+	0.830676i	$0.687954\pi$
$978$		0			0
$979$	2.05274	−	4.95576i	0.0656059	−	0.158387i
$980$		0			0
$981$	17.7789	−	7.36427i	0.567638	−	0.235123i
$982$		0			0
$983$	−40.5375	−	40.5375i	−1.29295	−	1.29295i	−0.932956	−	0.359991i	$-0.882780\pi$
$983$	−40.5375	−	40.5375i	−1.29295	−	1.29295i	−0.359991	−	0.932956i	$-0.617220\pi$
$984$		0			0
$985$	−16.3790	+	16.3790i	−0.521878	+	0.521878i
$986$		0			0
$987$	2.62313	+	6.33280i	0.0834953	+	0.201575i
$988$		0			0
$989$	57.6719	+	23.8885i	1.83386	+	0.759609i
$990$		0			0
$991$	13.8308			0.439350			0.219675	−	0.975573i	$-0.429500\pi$
$991$	13.8308			0.439350			0.219675	+	0.975573i	$0.429500\pi$
$992$		0			0
$993$	−39.9034			−1.26630
$994$		0			0
$995$	11.5188	+	4.77125i	0.365171	+	0.151259i
$996$		0			0
$997$	11.7635	+	28.3996i	0.372554	+	0.899426i	0.993316	+	0.115426i	$0.0368235\pi$
$997$	11.7635	+	28.3996i	0.372554	+	0.899426i	−0.620762	+	0.783999i	$0.713177\pi$
$998$		0			0
$999$	−5.46282	+	5.46282i	−0.172836	+	0.172836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.x.a.81.2		64
4.3	odd	2		160.2.x.a.61.7	yes	64
20.3	even	4		800.2.ba.e.349.2		64
20.7	even	4		800.2.ba.g.349.15		64
20.19	odd	2		800.2.y.c.701.10		64
32.11	odd	8		160.2.x.a.21.7	✓	64
32.21	even	8	inner	640.2.x.a.561.2		64
160.43	even	8		800.2.ba.g.149.15		64
160.107	even	8		800.2.ba.e.149.2		64
160.139	odd	8		800.2.y.c.501.10		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.x.a.21.7	✓	64	32.11	odd	8
160.2.x.a.61.7	yes	64	4.3	odd	2
640.2.x.a.81.2		64	1.1	even	1	trivial
640.2.x.a.561.2		64	32.21	even	8	inner
800.2.y.c.501.10		64	160.139	odd	8
800.2.y.c.701.10		64	20.19	odd	2
800.2.ba.e.149.2		64	160.107	even	8
800.2.ba.e.349.2		64	20.3	even	4
800.2.ba.g.149.15		64	160.43	even	8
800.2.ba.g.349.15		64	20.7	even	4

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.31924 - 0.960659i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.669347 - 0.669347i) q^{7} +(2.33467 + 2.33467i) q^{9} +O(q^{10})\)	\(q+(-2.31924 - 0.960659i) q^{3} +(0.382683 + 0.923880i) q^{5} +(0.669347 - 0.669347i) q^{7} +(2.33467 + 2.33467i) q^{9} +(-1.14897 + 0.475919i) q^{11} +(-1.10518 + 2.66813i) q^{13} -2.51032i q^{15} -4.60123i q^{17} +(-1.60186 + 3.86723i) q^{19} +(-2.19539 + 0.909360i) q^{21} +(3.91843 + 3.91843i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-0.289849 - 0.699757i) q^{27} +(7.50975 + 3.11064i) q^{29} +8.19506 q^{31} +3.12193 q^{33} +(0.874544 + 0.362248i) q^{35} +(-3.90337 - 9.42357i) q^{37} +(5.12633 - 5.12633i) q^{39} +(7.53342 + 7.53342i) q^{41} +(10.4073 - 4.31084i) q^{43} +(-1.26351 + 3.05039i) q^{45} -2.88459i q^{47} +6.10395i q^{49} +(-4.42021 + 10.6713i) q^{51} +(-1.46716 + 0.607718i) q^{53} +(-0.879383 - 0.879383i) q^{55} +(7.43018 - 7.43018i) q^{57} +(2.77205 + 6.69231i) q^{59} +(1.99858 + 0.827839i) q^{61} +3.12541 q^{63} -2.88797 q^{65} +(-2.17091 - 0.899222i) q^{67} +(-5.32348 - 12.8520i) q^{69} +(-7.24583 + 7.24583i) q^{71} +(3.25815 + 3.25815i) q^{73} +(2.31924 - 0.960659i) q^{75} +(-0.450505 + 1.08761i) q^{77} -6.64904i q^{79} -8.00381i q^{81} +(-4.27376 + 10.3178i) q^{83} +(4.25098 - 1.76081i) q^{85} +(-14.4286 - 14.4286i) q^{87} +(-3.04991 + 3.04991i) q^{89} +(1.04616 + 2.52565i) q^{91} +(-19.0063 - 7.87266i) q^{93} -4.18586 q^{95} -0.911645 q^{97} +(-3.79357 - 1.57135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) \) 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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