LMFDB - Embedded newform 640.2.z.a.369.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(49,640)]

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, 5, 4]))

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

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

chi := DirichletCharacter("640.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.z (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:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			369.5
Character	$\chi$	$=$	640.369
Dual form			640.2.z.a.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86499 + 0.772505i) q^{3} +(1.59455 - 1.56762i) q^{5} +(-0.798508 + 0.798508i) q^{7} +(0.760109 - 0.760109i) q^{9} +O(q^{10})$	\(q+(-1.86499 + 0.772505i) q^{3} +(1.59455 - 1.56762i) q^{5} +(-0.798508 + 0.798508i) q^{7} +(0.760109 - 0.760109i) q^{9} +(1.21174 - 2.92539i) q^{11} +(0.175830 + 0.424491i) q^{13} +(-1.76283 + 4.15539i) q^{15} -3.66556 q^{17} +(5.39199 - 2.23343i) q^{19} +(0.872360 - 2.10606i) q^{21} +(-3.04392 - 3.04392i) q^{23} +(0.0851615 - 4.99927i) q^{25} +(1.48711 - 3.59019i) q^{27} +(0.995872 + 2.40425i) q^{29} +2.13401 q^{31} +6.39190i q^{33} +(-0.0215050 + 2.52501i) q^{35} +(4.33444 - 10.4643i) q^{37} +(-0.655842 - 0.655842i) q^{39} +(6.79854 - 6.79854i) q^{41} +(9.19158 + 3.80728i) q^{43} +(0.0204708 - 2.40359i) q^{45} +2.81155 q^{47} +5.72477i q^{49} +(6.83623 - 2.83166i) q^{51} +(0.347970 + 0.144134i) q^{53} +(-2.65372 - 6.56421i) q^{55} +(-8.33067 + 8.33067i) q^{57} +(-10.0632 - 4.16829i) q^{59} +(-5.16229 - 12.4629i) q^{61} +1.21391i q^{63} +(0.945808 + 0.401237i) q^{65} +(7.97969 - 3.30530i) q^{67} +(8.02832 + 3.32544i) q^{69} +(-5.88607 - 5.88607i) q^{71} +(4.50108 + 4.50108i) q^{73} +(3.70314 + 9.38939i) q^{75} +(1.36837 + 3.30353i) q^{77} -5.05155i q^{79} +11.0693i q^{81} +(2.81897 + 6.80560i) q^{83} +(-5.84491 + 5.74619i) q^{85} +(-3.71459 - 3.71459i) q^{87} +(7.44423 + 7.44423i) q^{89} +(-0.479361 - 0.198558i) q^{91} +(-3.97991 + 1.64853i) q^{93} +(5.09661 - 12.0139i) q^{95} -1.85143i q^{97} +(-1.30256 - 3.14467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 88 * q - 4 * q^5 - 8 * q^9	$ 88 q - 4 q^{5} - 8 q^{9} + 8 q^{11} + 8 q^{19} - 8 q^{21} - 4 q^{25} - 8 q^{29} + 64 q^{31} - 20 q^{35} + 8 q^{39} - 8 q^{41} - 16 q^{45} + 48 q^{51} - 28 q^{55} - 24 q^{59} + 24 q^{61} - 8 q^{65} - 40 q^{69} + 40 q^{71} - 28 q^{75} - 24 q^{85} - 8 q^{89} + 8 q^{91} + 8 q^{95} + 48 q^{99}+O(q^{100}) $ 88 * q - 4 * q^5 - 8 * q^9 + 8 * q^11 + 8 * q^19 - 8 * q^21 - 4 * q^25 - 8 * q^29 + 64 * q^31 - 20 * q^35 + 8 * q^39 - 8 * q^41 - 16 * q^45 + 48 * q^51 - 28 * q^55 - 24 * q^59 + 24 * q^61 - 8 * q^65 - 40 * q^69 + 40 * q^71 - 28 * q^75 - 24 * q^85 - 8 * q^89 + 8 * q^91 + 8 * q^95 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.86499	+	0.772505i	−1.07675	+	0.446006i	−0.849369	−	0.527799i	$-0.823017\pi$
$3$	−1.86499	+	0.772505i	−1.07675	+	0.446006i	−0.227384	+	0.973805i	$0.573017\pi$
$4$		0			0
$5$	1.59455	−	1.56762i	0.713103	−	0.701059i
$5$	1.59455	−	1.56762i	0.713103	−	0.701059i
$6$		0			0
$7$	−0.798508	+	0.798508i	−0.301808	+	0.301808i	−0.841721	−	0.539913i	$-0.818457\pi$
$7$	−0.798508	+	0.798508i	−0.301808	+	0.301808i	0.539913	+	0.841721i	$0.318457\pi$
$8$		0			0
$9$	0.760109	−	0.760109i	0.253370	−	0.253370i
$10$		0			0
$11$	1.21174	−	2.92539i	0.365352	−	0.882038i	−0.629146	−	0.777287i	$-0.716595\pi$
$11$	1.21174	−	2.92539i	0.365352	−	0.882038i	0.994498	−	0.104751i	$-0.0334046\pi$
$12$		0			0
$13$	0.175830	+	0.424491i	0.0487664	+	0.117733i	0.946385	−	0.323040i	$-0.104705\pi$
$13$	0.175830	+	0.424491i	0.0487664	+	0.117733i	−0.897619	+	0.440772i	$0.854705\pi$
$14$		0			0
$15$	−1.76283	+	4.15539i	−0.455160	+	1.07292i
$16$		0			0
$17$	−3.66556			−0.889028			−0.444514	−	0.895772i	$-0.646624\pi$
$17$	−3.66556			−0.889028			−0.444514	+	0.895772i	$0.646624\pi$
$18$		0			0
$19$	5.39199	−	2.23343i	1.23701	−	0.512385i	0.334229	−	0.942492i	$-0.391524\pi$
$19$	5.39199	−	2.23343i	1.23701	−	0.512385i	0.902778	+	0.430107i	$0.141524\pi$
$20$		0			0
$21$	0.872360	−	2.10606i	0.190364	−	0.459581i
$22$		0			0
$23$	−3.04392	−	3.04392i	−0.634701	−	0.634701i	0.314543	−	0.949243i	$-0.398149\pi$
$23$	−3.04392	−	3.04392i	−0.634701	−	0.634701i	−0.949243	+	0.314543i	$0.898149\pi$
$24$		0			0
$25$	0.0851615	−	4.99927i	0.0170323	−	0.999855i
$26$		0			0
$27$	1.48711	−	3.59019i	0.286194	−	0.690932i
$28$		0			0
$29$	0.995872	+	2.40425i	0.184929	+	0.446458i	0.988970	−	0.148116i	$-0.0473209\pi$
$29$	0.995872	+	2.40425i	0.184929	+	0.446458i	−0.804041	+	0.594574i	$0.797321\pi$
$30$		0			0
$31$	2.13401			0.383279			0.191640	−	0.981465i	$-0.438620\pi$
$31$	2.13401			0.383279			0.191640	+	0.981465i	$0.438620\pi$
$32$		0			0
$33$			6.39190i			1.11269i
$34$		0			0
$35$	−0.0215050	+	2.52501i	−0.00363500	+	0.426805i
$36$		0			0
$37$	4.33444	−	10.4643i	0.712578	−	1.72032i	0.0191211	−	0.999817i	$-0.493913\pi$
$37$	4.33444	−	10.4643i	0.712578	−	1.72032i	0.693457	−	0.720498i	$-0.256087\pi$
$38$		0			0
$39$	−0.655842	−	0.655842i	−0.105019	−	0.105019i
$40$		0			0
$41$	6.79854	−	6.79854i	1.06175	−	1.06175i	0.0637899	−	0.997963i	$-0.479681\pi$
$41$	6.79854	−	6.79854i	1.06175	−	1.06175i	0.997963	−	0.0637899i	$-0.0203187\pi$
$42$		0			0
$43$	9.19158	+	3.80728i	1.40170	+	0.580604i	0.950193	−	0.311662i	$-0.100886\pi$
$43$	9.19158	+	3.80728i	1.40170	+	0.580604i	0.451509	+	0.892266i	$0.350886\pi$
$44$		0			0
$45$	0.0204708	−	2.40359i	0.00305161	−	0.358306i
$46$		0			0
$47$	2.81155			0.410106			0.205053	−	0.978751i	$-0.434263\pi$
$47$	2.81155			0.410106			0.205053	+	0.978751i	$0.434263\pi$
$48$		0			0
$49$			5.72477i			0.817824i
$50$		0			0
$51$	6.83623	−	2.83166i	0.957264	−	0.396512i
$52$		0			0
$53$	0.347970	+	0.144134i	0.0477974	+	0.0197983i	0.406454	−	0.913671i	$-0.366765\pi$
$53$	0.347970	+	0.144134i	0.0477974	+	0.0197983i	−0.358657	+	0.933470i	$0.616765\pi$
$54$		0			0
$55$	−2.65372	−	6.56421i	−0.357827	−	0.885118i
$56$		0			0
$57$	−8.33067	+	8.33067i	−1.10342	+	1.10342i
$58$		0			0
$59$	−10.0632	−	4.16829i	−1.31011	−	0.542666i	−0.385194	−	0.922836i	$-0.625865\pi$
$59$	−10.0632	−	4.16829i	−1.31011	−	0.542666i	−0.924917	+	0.380170i	$0.875865\pi$
$60$		0			0
$61$	−5.16229	−	12.4629i	−0.660964	−	1.59571i	−0.796296	−	0.604908i	$-0.793210\pi$
$61$	−5.16229	−	12.4629i	−0.660964	−	1.59571i	0.135332	−	0.990800i	$-0.456790\pi$
$62$		0			0
$63$			1.21391i			0.152938i
$64$		0			0
$65$	0.945808	+	0.401237i	0.117313	+	0.0497673i
$66$		0			0
$67$	7.97969	−	3.30530i	0.974874	−	0.403806i	0.162350	−	0.986733i	$-0.448093\pi$
$67$	7.97969	−	3.30530i	0.974874	−	0.403806i	0.812524	+	0.582927i	$0.198093\pi$
$68$		0			0
$69$	8.02832	+	3.32544i	0.966496	+	0.400336i
$70$		0			0
$71$	−5.88607	−	5.88607i	−0.698548	−	0.698548i	0.265549	−	0.964097i	$-0.414447\pi$
$71$	−5.88607	−	5.88607i	−0.698548	−	0.698548i	−0.964097	+	0.265549i	$0.914447\pi$
$72$		0			0
$73$	4.50108	+	4.50108i	0.526812	+	0.526812i	0.919620	−	0.392808i	$-0.128496\pi$
$73$	4.50108	+	4.50108i	0.526812	+	0.526812i	−0.392808	+	0.919620i	$0.628496\pi$
$74$		0			0
$75$	3.70314	+	9.38939i	0.427602	+	1.08419i
$76$		0			0
$77$	1.36837	+	3.30353i	0.155940	+	0.376472i
$78$		0			0
$79$		−	5.05155i		−	0.568344i	−0.958773	−	0.284172i	$-0.908281\pi$
$79$		−	5.05155i		−	0.568344i	0.958773	−	0.284172i	$-0.0917187\pi$
$80$		0			0
$81$			11.0693i			1.22993i
$82$		0			0
$83$	2.81897	+	6.80560i	0.309422	+	0.747012i	0.999724	+	0.0234902i	$0.00747785\pi$
$83$	2.81897	+	6.80560i	0.309422	+	0.747012i	−0.690302	+	0.723522i	$0.742522\pi$
$84$		0			0
$85$	−5.84491	+	5.74619i	−0.633969	+	0.623261i
$86$		0			0
$87$	−3.71459	−	3.71459i	−0.398245	−	0.398245i
$88$		0			0
$89$	7.44423	+	7.44423i	0.789087	+	0.789087i	0.981345	−	0.192257i	$-0.0615809\pi$
$89$	7.44423	+	7.44423i	0.789087	+	0.789087i	−0.192257	+	0.981345i	$0.561581\pi$
$90$		0			0
$91$	−0.479361	−	0.198558i	−0.0502507	−	0.0208145i
$92$		0			0
$93$	−3.97991	+	1.64853i	−0.412697	+	0.170945i
$94$		0			0
$95$	5.09661	−	12.0139i	0.522901	−	1.23260i
$96$		0			0
$97$		−	1.85143i		−	0.187984i	−0.995573	−	0.0939920i	$-0.970037\pi$
$97$		−	1.85143i		−	0.187984i	0.995573	−	0.0939920i	$-0.0299628\pi$
$98$		0			0
$99$	−1.30256	−	3.14467i	−0.130913	−	0.316051i
$100$		0			0
$101$	−5.38144	−	2.22907i	−0.535474	−	0.221800i	0.0985250	−	0.995135i	$-0.468588\pi$
$101$	−5.38144	−	2.22907i	−0.535474	−	0.221800i	−0.633999	+	0.773334i	$0.718588\pi$
$102$		0			0
$103$	−9.17653	+	9.17653i	−0.904190	+	0.904190i	−0.995795	−	0.0916051i	$-0.970800\pi$
$103$	−9.17653	+	9.17653i	−0.904190	+	0.904190i	0.0916051	+	0.995795i	$0.470800\pi$
$104$		0			0
$105$	−1.91048	−	4.72574i	−0.186444	−	0.461185i
$106$		0			0
$107$	−9.71062	−	4.02227i	−0.938761	−	0.388848i	−0.139766	−	0.990185i	$-0.544635\pi$
$107$	−9.71062	−	4.02227i	−0.938761	−	0.388848i	−0.798996	+	0.601337i	$0.794635\pi$
$108$		0			0
$109$	−18.0950	+	7.49520i	−1.73319	+	0.717910i	−0.733936	+	0.679219i	$0.762319\pi$
$109$	−18.0950	+	7.49520i	−1.73319	+	0.717910i	−0.999251	+	0.0386910i	$0.987681\pi$
$110$		0			0
$111$			22.8642i			2.17017i
$112$		0			0
$113$	1.66682			0.156801			0.0784004	−	0.996922i	$-0.475019\pi$
$113$	1.66682			0.156801			0.0784004	+	0.996922i	$0.475019\pi$
$114$		0			0
$115$	−9.62536	−	0.0819770i	−0.897570	−	0.00764439i
$116$		0			0
$117$	0.456309	+	0.189010i	0.0421858	+	0.0174739i
$118$		0			0
$119$	2.92698	−	2.92698i	0.268316	−	0.268316i
$120$		0			0
$121$	0.688576	+	0.688576i	0.0625978	+	0.0625978i
$122$		0			0
$123$	−7.42731	+	17.9311i	−0.669698	+	1.61679i
$124$		0			0
$125$	−7.70115	−	8.10508i	−0.688812	−	0.724940i
$126$		0			0
$127$			11.9791i			1.06297i	0.847066	+	0.531487i	$0.178367\pi$
$127$			11.9791i			1.06297i	−0.847066	+	0.531487i	$0.821633\pi$
$128$		0			0
$129$	−20.0834			−1.76824
$130$		0			0
$131$	−1.07279	−	2.58995i	−0.0937303	−	0.226285i	0.870060	−	0.492945i	$-0.164080\pi$
$131$	−1.07279	−	2.58995i	−0.0937303	−	0.226285i	−0.963791	+	0.266660i	$0.914080\pi$
$132$		0			0
$133$	−2.52213	+	6.08896i	−0.218697	+	0.527980i
$134$		0			0
$135$	−3.25678	−	8.05594i	−0.280299	−	0.693345i
$136$		0			0
$137$	−7.11033	−	7.11033i	−0.607476	−	0.607476i	0.334810	−	0.942286i	$-0.391328\pi$
$137$	−7.11033	−	7.11033i	−0.607476	−	0.607476i	−0.942286	+	0.334810i	$0.891328\pi$
$138$		0			0
$139$	−7.78228	+	18.7881i	−0.660084	+	1.59358i	0.137585	+	0.990490i	$0.456066\pi$
$139$	−7.78228	+	18.7881i	−0.660084	+	1.59358i	−0.797669	+	0.603095i	$0.793934\pi$
$140$		0			0
$141$	−5.24351	+	2.17193i	−0.441583	+	0.182910i
$142$		0			0
$143$	1.45486			0.121662
$144$		0			0
$145$	5.35690	+	2.27254i	0.444867	+	0.188724i
$146$		0			0
$147$	−4.42241	−	10.6766i	−0.364754	−	0.880595i
$148$		0			0
$149$	1.78543	−	4.31042i	0.146268	−	0.353123i	−0.833717	−	0.552192i	$-0.813792\pi$
$149$	1.78543	−	4.31042i	0.146268	−	0.353123i	0.979986	+	0.199068i	$0.0637916\pi$
$150$		0			0
$151$	−8.74596	+	8.74596i	−0.711736	+	0.711736i	−0.966898	−	0.255162i	$-0.917871\pi$
$151$	−8.74596	+	8.74596i	−0.711736	+	0.711736i	0.255162	+	0.966898i	$0.417871\pi$
$152$		0			0
$153$	−2.78622	+	2.78622i	−0.225253	+	0.225253i
$154$		0			0
$155$	3.40278	−	3.34530i	0.273318	−	0.268701i
$156$		0			0
$157$	16.0091	−	6.63117i	1.27766	−	0.529225i	0.362377	−	0.932032i	$-0.381965\pi$
$157$	16.0091	−	6.63117i	1.27766	−	0.529225i	0.915285	+	0.402806i	$0.131965\pi$
$158$		0			0
$159$	−0.760305			−0.0602961
$160$		0			0
$161$	4.86119			0.383115
$162$		0			0
$163$	2.28807	−	0.947748i	0.179215	−	0.0742334i	−0.291272	−	0.956640i	$-0.594078\pi$
$163$	2.28807	−	0.947748i	0.179215	−	0.0742334i	0.470487	+	0.882407i	$0.344078\pi$
$164$		0			0
$165$	10.0200	+	10.1922i	0.780059	+	0.793460i
$166$		0			0
$167$	2.97405	−	2.97405i	0.230139	−	0.230139i	−0.582612	−	0.812750i	$-0.697969\pi$
$167$	2.97405	−	2.97405i	0.230139	−	0.230139i	0.812750	+	0.582612i	$0.197969\pi$
$168$		0			0
$169$	9.04311	−	9.04311i	0.695624	−	0.695624i
$170$		0			0
$171$	2.40085	−	5.79615i	0.183597	−	0.443243i
$172$		0			0
$173$	3.72322	+	8.98865i	0.283071	+	0.683394i	0.999904	−	0.0138508i	$-0.00440899\pi$
$173$	3.72322	+	8.98865i	0.283071	+	0.683394i	−0.716833	+	0.697245i	$0.754409\pi$
$174$		0			0
$175$	3.92396	+	4.05996i	0.296624	+	0.306904i
$176$		0			0
$177$	21.9877			1.65270
$178$		0			0
$179$	12.4973	−	5.17653i	0.934089	−	0.386912i	0.136861	−	0.990590i	$-0.456299\pi$
$179$	12.4973	−	5.17653i	0.934089	−	0.386912i	0.797228	+	0.603678i	$0.206299\pi$
$180$		0			0
$181$	−2.52860	+	6.10459i	−0.187950	+	0.453751i	−0.989565	−	0.144090i	$-0.953975\pi$
$181$	−2.52860	+	6.10459i	−0.187950	+	0.453751i	0.801615	+	0.597841i	$0.203975\pi$
$182$		0			0
$183$	19.2553	+	19.2553i	1.42339	+	1.42339i
$184$		0			0
$185$	−9.49248	−	23.4805i	−0.697901	−	1.72632i
$186$		0			0
$187$	−4.44169	+	10.7232i	−0.324808	+	0.784157i
$188$		0			0
$189$	1.67933	+	4.05426i	0.122153	+	0.294904i
$190$		0			0
$191$	−15.4267			−1.11624			−0.558120	−	0.829760i	$-0.688477\pi$
$191$	−15.4267			−1.11624			−0.558120	+	0.829760i	$0.688477\pi$
$192$		0			0
$193$			7.08523i			0.510006i	0.966940	+	0.255003i	$0.0820765\pi$
$193$			7.08523i			0.510006i	−0.966940	+	0.255003i	$0.917923\pi$
$194$		0			0
$195$	−2.07388	−	0.0176628i	−0.148514	−	0.00126486i
$196$		0			0
$197$	0.344992	−	0.832884i	0.0245797	−	0.0593405i	−0.911113	−	0.412156i	$-0.864776\pi$
$197$	0.344992	−	0.832884i	0.0245797	−	0.0593405i	0.935693	+	0.352816i	$0.114776\pi$
$198$		0			0
$199$	2.91076	+	2.91076i	0.206338	+	0.206338i	0.802709	−	0.596371i	$-0.203391\pi$
$199$	2.91076	+	2.91076i	0.206338	+	0.206338i	−0.596371	+	0.802709i	$0.703391\pi$
$200$		0			0
$201$	−12.3287	+	12.3287i	−0.869599	+	0.869599i
$202$		0			0
$203$	−2.71502	−	1.12460i	−0.190557	−	0.0789314i
$204$		0			0
$205$	0.183094	−	21.4981i	0.0127879	−	1.50149i
$206$		0			0
$207$	−4.62742			−0.321628
$208$		0			0
$209$		−	18.4800i		−	1.27829i
$210$		0			0
$211$	7.92698	−	3.28346i	0.545716	−	0.226043i	−0.0927548	−	0.995689i	$-0.529567\pi$
$211$	7.92698	−	3.28346i	0.545716	−	0.226043i	0.638471	+	0.769646i	$0.279567\pi$
$212$		0			0
$213$	15.5245	+	6.43046i	1.06372	+	0.440608i
$214$		0			0
$215$	20.6247	−	8.33798i	1.40660	−	0.568646i
$216$		0			0
$217$	−1.70402	+	1.70402i	−0.115677	+	0.115677i
$218$		0			0
$219$	−11.8716	−	4.91737i	−0.802208	−	0.332285i
$220$		0			0
$221$	−0.644515	−	1.55600i	−0.0433547	−	0.104668i
$222$		0			0
$223$		−	5.77501i		−	0.386723i	−0.981128	−	0.193362i	$-0.938061\pi$
$223$		−	5.77501i		−	0.386723i	0.981128	−	0.193362i	$-0.0619390\pi$
$224$		0			0
$225$	−3.73526	−	3.86473i	−0.249018	−	0.257648i
$226$		0			0
$227$	2.95889	−	1.22561i	0.196389	−	0.0813469i	−0.282321	−	0.959320i	$-0.591104\pi$
$227$	2.95889	−	1.22561i	0.196389	−	0.0813469i	0.478710	+	0.877973i	$0.341104\pi$
$228$		0			0
$229$	15.2062	+	6.29862i	1.00485	+	0.416224i	0.823575	−	0.567207i	$-0.191976\pi$
$229$	15.2062	+	6.29862i	1.00485	+	0.416224i	0.181279	+	0.983432i	$0.441976\pi$
$230$		0			0
$231$	−5.10398	−	5.10398i	−0.335817	−	0.335817i
$232$		0			0
$233$	−5.63270	−	5.63270i	−0.369010	−	0.369010i	0.498106	−	0.867116i	$-0.334029\pi$
$233$	−5.63270	−	5.63270i	−0.369010	−	0.369010i	−0.867116	+	0.498106i	$0.834029\pi$
$234$		0			0
$235$	4.48314	−	4.40742i	0.292448	−	0.287509i
$236$		0			0
$237$	3.90235	+	9.42111i	0.253485	+	0.611967i
$238$		0			0
$239$		−	9.70011i		−	0.627448i	−0.949514	−	0.313724i	$-0.898423\pi$
$239$		−	9.70011i		−	0.627448i	0.949514	−	0.313724i	$-0.101577\pi$
$240$		0			0
$241$			16.7088i			1.07631i	0.842847	+	0.538154i	$0.180878\pi$
$241$			16.7088i			1.07631i	−0.842847	+	0.538154i	$0.819122\pi$
$242$		0			0
$243$	−4.08980	−	9.87365i	−0.262361	−	0.633395i
$244$		0			0
$245$	8.97424	+	9.12841i	0.573343	+	0.583193i
$246$		0			0
$247$	1.89615	+	1.89615i	0.120649	+	0.120649i
$248$		0			0
$249$	−10.5147	−	10.5147i	−0.666343	−	0.666343i
$250$		0			0
$251$	6.61061	+	2.73821i	0.417258	+	0.172834i	0.581428	−	0.813598i	$-0.302494\pi$
$251$	6.61061	+	2.73821i	0.417258	+	0.172834i	−0.164169	+	0.986432i	$0.552494\pi$
$252$		0			0
$253$	−12.5931	+	5.21622i	−0.791719	+	0.327941i
$254$		0			0
$255$	6.46174	−	15.2318i	0.404650	−	0.953853i
$256$		0			0
$257$		−	10.2334i		−	0.638344i	−0.947697	−	0.319172i	$-0.896595\pi$
$257$		−	10.2334i		−	0.638344i	0.947697	−	0.319172i	$-0.103405\pi$
$258$		0			0
$259$	4.89472	+	11.8169i	0.304143	+	0.734266i
$260$		0			0
$261$	2.58446	+	1.07052i	0.159974	+	0.0662635i
$262$		0			0
$263$	1.31205	−	1.31205i	0.0809045	−	0.0809045i	−0.665496	−	0.746401i	$-0.731780\pi$
$263$	1.31205	−	1.31205i	0.0809045	−	0.0809045i	0.746401	+	0.665496i	$0.231780\pi$
$264$		0			0
$265$	0.780801	−	0.315655i	0.0479642	−	0.0193905i
$266$		0			0
$267$	−19.6341	−	8.13273i	−1.20159	−	0.497715i
$268$		0			0
$269$	16.4601	−	6.81801i	1.00359	−	0.415701i	0.180479	−	0.983579i	$-0.442235\pi$
$269$	16.4601	−	6.81801i	1.00359	−	0.415701i	0.823113	+	0.567878i	$0.192235\pi$
$270$		0			0
$271$			9.45666i			0.574451i	0.957863	+	0.287226i	$0.0927329\pi$
$271$			9.45666i			0.574451i	−0.957863	+	0.287226i	$0.907267\pi$
$272$		0			0
$273$	1.04739			0.0633910
$274$		0			0
$275$	−14.5216	−	6.30693i	−0.875687	−	0.380322i
$276$		0			0
$277$	−26.2678	−	10.8805i	−1.57828	−	0.653743i	−0.590137	−	0.807303i	$-0.700926\pi$
$277$	−26.2678	−	10.8805i	−1.57828	−	0.653743i	−0.988139	+	0.153560i	$0.950926\pi$
$278$		0			0
$279$	1.62208	−	1.62208i	0.0971113	−	0.0971113i
$280$		0			0
$281$	13.8016	+	13.8016i	0.823332	+	0.823332i	0.986584	−	0.163253i	$-0.0521985\pi$
$281$	13.8016	+	13.8016i	0.823332	+	0.823332i	−0.163253	+	0.986584i	$0.552199\pi$
$282$		0			0
$283$	9.13571	−	22.0556i	0.543062	−	1.31107i	−0.379491	−	0.925196i	$-0.623901\pi$
$283$	9.13571	−	22.0556i	0.543062	−	1.31107i	0.922553	−	0.385872i	$-0.126099\pi$
$284$		0			0
$285$	−0.224357	+	26.3429i	−0.0132898	+	1.56042i
$286$		0			0
$287$			10.8574i			0.640891i
$288$		0			0
$289$	−3.56368			−0.209628
$290$		0			0
$291$	1.43024	+	3.45290i	0.0838419	+	0.202412i
$292$		0			0
$293$	−7.20694	+	17.3991i	−0.421034	+	1.01647i	0.561009	+	0.827809i	$0.310413\pi$
$293$	−7.20694	+	17.3991i	−0.421034	+	1.01647i	−0.982043	+	0.188656i	$0.939587\pi$
$294$		0			0
$295$	−22.5805	+	9.12861i	−1.31468	+	0.531488i
$296$		0			0
$297$	−8.70072	−	8.70072i	−0.504867	−	0.504867i
$298$		0			0
$299$	0.756903	−	1.82733i	0.0437729	−	0.105677i
$300$		0			0
$301$	−10.3797	+	4.29941i	−0.598276	+	0.247814i
$302$		0			0
$303$	11.7583			0.675497
$304$		0			0
$305$	−27.7685	−	11.7802i	−1.59002	−	0.674530i
$306$		0			0
$307$	4.47505	+	10.8037i	0.255404	+	0.616601i	0.998624	−	0.0524470i	$-0.0167021\pi$
$307$	4.47505	+	10.8037i	0.255404	+	0.616601i	−0.743219	+	0.669048i	$0.766702\pi$
$308$		0			0
$309$	10.0252	−	24.2031i	0.570316	−	1.37686i
$310$		0			0
$311$	5.50620	−	5.50620i	0.312228	−	0.312228i	−0.533544	−	0.845772i	$-0.679140\pi$
$311$	5.50620	−	5.50620i	0.312228	−	0.312228i	0.845772	+	0.533544i	$0.179140\pi$
$312$		0			0
$313$	5.15295	−	5.15295i	0.291262	−	0.291262i	−0.546317	−	0.837579i	$-0.683971\pi$
$313$	5.15295	−	5.15295i	0.291262	−	0.291262i	0.837579	+	0.546317i	$0.183971\pi$
$314$		0			0
$315$	1.90294	+	1.93563i	0.107219	+	0.109061i
$316$		0			0
$317$	−18.5382	+	7.67876i	−1.04121	+	0.431282i	−0.836745	−	0.547592i	$-0.815545\pi$
$317$	−18.5382	+	7.67876i	−1.04121	+	0.431282i	−0.204462	+	0.978874i	$0.565545\pi$
$318$		0			0
$319$	8.24010			0.461357
$320$		0			0
$321$	21.2175			1.18424
$322$		0			0
$323$	−19.7646	+	8.18679i	−1.09973	+	0.455525i
$324$		0			0
$325$	2.13712	−	0.842872i	0.118546	−	0.0467541i
$326$		0			0
$327$	27.9570	−	27.9570i	1.54602	−	1.54602i
$328$		0			0
$329$	−2.24504	+	2.24504i	−0.123773	+	0.123773i
$330$		0			0
$331$	1.58035	−	3.81529i	0.0868637	−	0.209708i	−0.874478	−	0.485065i	$-0.838796\pi$
$331$	1.58035	−	3.81529i	0.0868637	−	0.209708i	0.961342	+	0.275357i	$0.0887961\pi$
$332$		0			0
$333$	−4.65934	−	11.2486i	−0.255330	−	0.616422i
$334$		0			0
$335$	7.54256	−	17.7795i	0.412094	−	0.971400i
$336$		0			0
$337$	7.45730			0.406225			0.203112	−	0.979155i	$-0.434894\pi$
$337$	7.45730			0.406225			0.203112	+	0.979155i	$0.434894\pi$
$338$		0			0
$339$	−3.10860	+	1.28762i	−0.168836	+	0.0699341i
$340$		0			0
$341$	2.58585	−	6.24280i	0.140032	−	0.338067i
$342$		0			0
$343$	−10.1608	−	10.1608i	−0.548633	−	0.548633i
$344$		0			0
$345$	18.0145	−	7.28275i	0.969871	−	0.392090i
$346$		0			0
$347$	2.98151	−	7.19799i	0.160056	−	0.386409i	−0.823424	−	0.567426i	$-0.807939\pi$
$347$	2.98151	−	7.19799i	0.160056	−	0.386409i	0.983480	+	0.181018i	$0.0579392\pi$
$348$		0			0
$349$	4.45368	+	10.7521i	0.238400	+	0.575548i	0.997118	−	0.0758714i	$-0.0241738\pi$
$349$	4.45368	+	10.7521i	0.238400	+	0.575548i	−0.758718	+	0.651419i	$0.774174\pi$
$350$		0			0
$351$	1.78548			0.0953019
$352$		0			0
$353$			0.146505i			0.00779766i	0.999992	+	0.00389883i	$0.00124104\pi$
$353$			0.146505i			0.00779766i	−0.999992	+	0.00389883i	$0.998759\pi$
$354$		0			0
$355$	−18.6127	−	0.158520i	−0.987861	−	0.00841338i
$356$		0			0
$357$	−3.19769	+	7.71990i	−0.169239	+	0.408580i
$358$		0			0
$359$	20.8531	+	20.8531i	1.10058	+	1.10058i	0.994340	+	0.106242i	$0.0338817\pi$
$359$	20.8531	+	20.8531i	1.10058	+	1.10058i	0.106242	+	0.994340i	$0.466118\pi$
$360$		0			0
$361$	10.6503	−	10.6503i	0.560541	−	0.560541i
$362$		0			0
$363$	−1.81612	−	0.752260i	−0.0953214	−	0.0394834i
$364$		0			0
$365$	14.2332	+	0.121221i	0.744998	+	0.00634497i
$366$		0			0
$367$	5.98845			0.312594			0.156297	−	0.987710i	$-0.450044\pi$
$367$	5.98845			0.312594			0.156297	+	0.987710i	$0.450044\pi$
$368$		0			0
$369$		−	10.3353i		−	0.538032i
$370$		0			0
$371$	−0.392949	+	0.162765i	−0.0204009	+	0.00845033i
$372$		0			0
$373$	−6.63539	−	2.74847i	−0.343568	−	0.142310i	0.204226	−	0.978924i	$-0.434532\pi$
$373$	−6.63539	−	2.74847i	−0.343568	−	0.142310i	−0.547794	+	0.836613i	$0.684532\pi$
$374$		0			0
$375$	20.6238	+	9.16673i	1.06501	+	0.473368i
$376$		0			0
$377$	−0.845477	+	0.845477i	−0.0435443	+	0.0435443i
$378$		0			0
$379$	9.53326	+	3.94881i	0.489691	+	0.202837i	0.613845	−	0.789426i	$-0.289622\pi$
$379$	9.53326	+	3.94881i	0.489691	+	0.202837i	−0.124154	+	0.992263i	$0.539622\pi$
$380$		0			0
$381$	−9.25393	−	22.3410i	−0.474093	−	1.14456i
$382$		0			0
$383$			12.9567i			0.662057i	0.943621	+	0.331028i	$0.107396\pi$
$383$			12.9567i			0.662057i	−0.943621	+	0.331028i	$0.892604\pi$
$384$		0			0
$385$	7.36059	+	3.12256i	0.375130	+	0.159140i
$386$		0			0
$387$	9.88055	−	4.09266i	0.502256	−	0.208041i
$388$		0			0
$389$	−25.6596	−	10.6286i	−1.30099	−	0.538889i	−0.378751	−	0.925499i	$-0.623646\pi$
$389$	−25.6596	−	10.6286i	−1.30099	−	0.538889i	−0.922244	+	0.386609i	$0.873646\pi$
$390$		0			0
$391$	11.1577	+	11.1577i	0.564267	+	0.564267i
$392$		0			0
$393$	4.00150	+	4.00150i	0.201849	+	0.201849i
$394$		0			0
$395$	−7.91890	−	8.05494i	−0.398443	−	0.405288i
$396$		0			0
$397$	13.4708	+	32.5215i	0.676082	+	1.63221i	0.771088	+	0.636729i	$0.219713\pi$
$397$	13.4708	+	32.5215i	0.676082	+	1.63221i	−0.0950060	+	0.995477i	$0.530287\pi$
$398$		0			0
$399$		−	13.3042i		−	0.666044i
$400$		0			0
$401$		−	2.52062i		−	0.125874i	−0.998018	−	0.0629368i	$-0.979953\pi$
$401$		−	2.52062i		−	0.125874i	0.998018	−	0.0629368i	$-0.0200466\pi$
$402$		0			0
$403$	0.375222	+	0.905867i	0.0186912	+	0.0451244i
$404$		0			0
$405$	17.3525	+	17.6506i	0.862251	+	0.877064i
$406$		0			0
$407$	−25.3599	−	25.3599i	−1.25704	−	1.25704i
$408$		0			0
$409$	5.83443	+	5.83443i	0.288494	+	0.288494i	0.836484	−	0.547991i	$-0.184607\pi$
$409$	5.83443	+	5.83443i	0.288494	+	0.288494i	−0.547991	+	0.836484i	$0.684607\pi$
$410$		0			0
$411$	18.7535	+	7.76794i	0.925040	+	0.383164i
$412$		0			0
$413$	11.3639	−	4.70709i	0.559182	−	0.231621i
$414$		0			0
$415$	15.1636	+	6.43279i	0.744350	+	0.315773i
$416$		0			0
$417$		−	41.0515i		−	2.01030i
$418$		0			0
$419$	5.75322	+	13.8895i	0.281063	+	0.678546i	0.999861	−	0.0166728i	$-0.00530736\pi$
$419$	5.75322	+	13.8895i	0.281063	+	0.678546i	−0.718798	+	0.695219i	$0.755307\pi$
$420$		0			0
$421$	−27.5675	−	11.4188i	−1.34356	−	0.556520i	−0.409066	−	0.912505i	$-0.634145\pi$
$421$	−27.5675	−	11.4188i	−1.34356	−	0.556520i	−0.934492	+	0.355985i	$0.884145\pi$
$422$		0			0
$423$	2.13708	−	2.13708i	0.103909	−	0.103909i
$424$		0			0
$425$	−0.312164	+	18.3251i	−0.0151422	+	0.888899i
$426$		0			0
$427$	14.0738	+	5.82958i	0.681081	+	0.282113i
$428$		0			0
$429$	−2.71330	+	1.12389i	−0.130999	+	0.0542618i
$430$		0			0
$431$		−	34.5185i		−	1.66270i	−0.555750	−	0.831349i	$-0.687569\pi$
$431$		−	34.5185i		−	1.66270i	0.555750	−	0.831349i	$-0.312431\pi$
$432$		0			0
$433$	−16.9110			−0.812690			−0.406345	−	0.913720i	$-0.633197\pi$
$433$	−16.9110			−0.812690			−0.406345	+	0.913720i	$0.633197\pi$
$434$		0			0
$435$	−11.7461	−	0.100039i	−0.563184	−	0.00479650i
$436$		0			0
$437$	−23.2112	−	9.61438i	−1.11034	−	0.459918i
$438$		0			0
$439$	−7.67146	+	7.67146i	−0.366139	+	0.366139i	−0.866067	−	0.499928i	$-0.833360\pi$
$439$	−7.67146	+	7.67146i	−0.366139	+	0.366139i	0.499928	+	0.866067i	$0.333360\pi$
$440$		0			0
$441$	4.35145	+	4.35145i	0.207212	+	0.207212i
$442$		0			0
$443$	1.56765	−	3.78465i	0.0744815	−	0.179814i	−0.882254	−	0.470774i	$-0.843975\pi$
$443$	1.56765	−	3.78465i	0.0744815	−	0.179814i	0.956735	+	0.290960i	$0.0939746\pi$
$444$		0			0
$445$	23.5399	+	0.200484i	1.11590	+	0.00950384i
$446$		0			0
$447$			9.41815i			0.445463i
$448$		0			0
$449$	3.12042			0.147262			0.0736309	−	0.997286i	$-0.476541\pi$
$449$	3.12042			0.147262			0.0736309	+	0.997286i	$0.476541\pi$
$450$		0			0
$451$	−11.6503	−	28.1264i	−0.548593	−	1.32442i
$452$		0			0
$453$	9.55485	−	23.0674i	0.448926	−	1.08380i
$454$		0			0
$455$	−1.07563	+	0.434844i	−0.0504261	+	0.0203858i
$456$		0			0
$457$	28.7210	+	28.7210i	1.34351	+	1.34351i	0.892535	+	0.450978i	$0.148925\pi$
$457$	28.7210	+	28.7210i	1.34351	+	1.34351i	0.450978	+	0.892535i	$0.351075\pi$
$458$		0			0
$459$	−5.45107	+	13.1600i	−0.254434	+	0.614258i
$460$		0			0
$461$	33.4225	−	13.8441i	1.55664	−	0.644782i	0.572139	−	0.820157i	$-0.306114\pi$
$461$	33.4225	−	13.8441i	1.55664	−	0.644782i	0.984502	+	0.175375i	$0.0561138\pi$
$462$		0			0
$463$	−13.9489			−0.648259			−0.324130	−	0.946013i	$-0.605071\pi$
$463$	−13.9489			−0.648259			−0.324130	+	0.946013i	$0.605071\pi$
$464$		0			0
$465$	−3.76188	+	8.86762i	−0.174453	+	0.411226i
$466$		0			0
$467$	14.4737	+	34.9426i	0.669763	+	1.61695i	0.782006	+	0.623271i	$0.214197\pi$
$467$	14.4737	+	34.9426i	0.669763	+	1.61695i	−0.112243	+	0.993681i	$0.535803\pi$
$468$		0			0
$469$	−3.73254	+	9.01115i	−0.172353	+	0.416096i
$470$		0			0
$471$	−24.7342	+	24.7342i	−1.13969	+	1.13969i
$472$		0			0
$473$	22.2755	−	22.2755i	1.02423	−	1.02423i
$474$		0			0
$475$	−10.7064	−	27.1462i	−0.491242	−	1.24555i
$476$		0			0
$477$	0.374053	−	0.154938i	0.0171267	−	0.00709411i
$478$		0			0
$479$	1.27470			0.0582424			0.0291212	−	0.999576i	$-0.490729\pi$
$479$	1.27470			0.0582424			0.0291212	+	0.999576i	$0.490729\pi$
$480$		0			0
$481$	5.20411			0.237287
$482$		0			0
$483$	−9.06607	+	3.75529i	−0.412521	+	0.170872i
$484$		0			0
$485$	−2.90233	−	2.95219i	−0.131788	−	0.134052i
$486$		0			0
$487$	−5.87473	+	5.87473i	−0.266209	+	0.266209i	−0.827571	−	0.561361i	$-0.810278\pi$
$487$	−5.87473	+	5.87473i	−0.266209	+	0.266209i	0.561361	+	0.827571i	$0.310278\pi$
$488$		0			0
$489$	−3.53508	+	3.53508i	−0.159862	+	0.159862i
$490$		0			0
$491$	14.2233	−	34.3381i	0.641889	−	1.54966i	−0.182240	−	0.983254i	$-0.558335\pi$
$491$	14.2233	−	34.3381i	0.641889	−	1.54966i	0.824129	−	0.566403i	$-0.191665\pi$
$492$		0			0
$493$	−3.65043	−	8.81291i	−0.164407	−	0.396914i
$494$		0			0
$495$	−7.00663	−	2.97240i	−0.314925	−	0.133599i
$496$		0			0
$497$	9.40016			0.421655
$498$		0			0
$499$	−33.8195	+	14.0085i	−1.51397	+	0.627107i	−0.976372	−	0.216095i	$-0.930668\pi$
$499$	−33.8195	+	14.0085i	−1.51397	+	0.627107i	−0.537597	+	0.843202i	$0.680668\pi$
$500$		0			0
$501$	−3.24911	+	7.84403i	−0.145159	+	0.350446i
$502$		0			0
$503$	−0.844993	−	0.844993i	−0.0376764	−	0.0376764i	0.688018	−	0.725694i	$-0.258481\pi$
$503$	−0.844993	−	0.844993i	−0.0376764	−	0.0376764i	−0.725694	+	0.688018i	$0.758481\pi$
$504$		0			0
$505$	−12.0753	+	4.88168i	−0.537343	+	0.217232i
$506$		0			0
$507$	−9.87948	+	23.8512i	−0.438763	+	1.05927i
$508$		0			0
$509$	0.698779	+	1.68700i	0.0309728	+	0.0747750i	0.938609	−	0.344982i	$-0.112115\pi$
$509$	0.698779	+	1.68700i	0.0309728	+	0.0747750i	−0.907636	+	0.419757i	$0.862115\pi$
$510$		0			0
$511$	−7.18831			−0.317992
$512$		0			0
$513$		−	22.6796i		−	1.00133i
$514$		0			0
$515$	−0.247137	+	29.0177i	−0.0108902	+	1.27867i
$516$		0			0
$517$	3.40685	−	8.22487i	0.149833	−	0.361729i
$518$		0			0
$519$	−13.8875	−	13.8875i	−0.609596	−	0.609596i
$520$		0			0
$521$	−19.8057	+	19.8057i	−0.867706	+	0.867706i	−0.992218	−	0.124513i	$-0.960263\pi$
$521$	−19.8057	+	19.8057i	−0.867706	+	0.867706i	0.124513	+	0.992218i	$0.460263\pi$
$522$		0			0
$523$	2.41194	+	0.999058i	0.105467	+	0.0436858i	0.434793	−	0.900530i	$-0.356822\pi$
$523$	2.41194	+	0.999058i	0.105467	+	0.0436858i	−0.329326	+	0.944216i	$0.606822\pi$
$524$		0			0
$525$	−10.4545	−	4.54052i	−0.456272	−	0.198165i
$526$		0			0
$527$	−7.82233			−0.340746
$528$		0			0
$529$		−	4.46914i		−	0.194310i
$530$		0			0
$531$	−10.8175	+	4.48074i	−0.469437	+	0.194447i
$532$		0			0
$533$	4.08130	+	1.69053i	0.176781	+	0.0732250i
$534$		0			0
$535$	−21.7894	+	8.80882i	−0.942039	+	0.380839i
$536$		0			0
$537$	−19.3084	+	19.3084i	−0.833218	+	0.833218i
$538$		0			0
$539$	16.7472	+	6.93691i	0.721352	+	0.298794i
$540$		0			0
$541$	5.84464	+	14.1102i	0.251281	+	0.606645i	0.998308	−	0.0581482i	$-0.0185196\pi$
$541$	5.84464	+	14.1102i	0.251281	+	0.606645i	−0.747027	+	0.664793i	$0.768520\pi$
$542$		0			0
$543$		−	13.3384i		−	0.572404i
$544$		0			0
$545$	−17.1038	+	40.3175i	−0.732644	+	1.72701i
$546$		0			0
$547$	33.2376	−	13.7675i	1.42114	−	0.588655i	0.465992	−	0.884789i	$-0.345698\pi$
$547$	33.2376	−	13.7675i	1.42114	−	0.588655i	0.955146	+	0.296134i	$0.0956976\pi$
$548$		0			0
$549$	−13.3971	−	5.54924i	−0.571772	−	0.236836i
$550$		0			0
$551$	10.7395	+	10.7395i	0.457517	+	0.457517i
$552$		0			0
$553$	4.03371	+	4.03371i	0.171531	+	0.171531i
$554$		0			0
$555$	35.8422	+	36.4580i	1.52142	+	1.54755i
$556$		0			0
$557$	−1.15386	−	2.78566i	−0.0488905	−	0.118032i	0.897547	−	0.440918i	$-0.145347\pi$
$557$	−1.15386	−	2.78566i	−0.0488905	−	0.118032i	−0.946438	+	0.322886i	$0.895347\pi$
$558$		0			0
$559$			4.57117i			0.193340i
$560$		0			0
$561$		−	23.4299i		−	0.989210i
$562$		0			0
$563$	−0.338542	−	0.817314i	−0.0142679	−	0.0344457i	0.916585	−	0.399840i	$-0.130934\pi$
$563$	−0.338542	−	0.817314i	−0.0142679	−	0.0344457i	−0.930853	+	0.365394i	$0.880934\pi$
$564$		0			0
$565$	2.65782	−	2.61293i	0.111815	−	0.109927i
$566$		0			0
$567$	−8.83896	−	8.83896i	−0.371201	−	0.371201i
$568$		0			0
$569$	−1.30773	−	1.30773i	−0.0548229	−	0.0548229i	0.679164	−	0.733987i	$-0.262343\pi$
$569$	−1.30773	−	1.30773i	−0.0548229	−	0.0548229i	−0.733987	+	0.679164i	$0.762343\pi$
$570$		0			0
$571$	3.63704	+	1.50651i	0.152206	+	0.0630456i	0.457486	−	0.889217i	$-0.348750\pi$
$571$	3.63704	+	1.50651i	0.152206	+	0.0630456i	−0.305280	+	0.952263i	$0.598750\pi$
$572$		0			0
$573$	28.7708	−	11.9172i	1.20192	−	0.497850i
$574$		0			0
$575$	−15.4766	+	14.9582i	−0.645419	+	0.623798i
$576$		0			0
$577$			33.9400i			1.41294i	0.707743	+	0.706470i	$0.249714\pi$
$577$			33.9400i			1.41294i	−0.707743	+	0.706470i	$0.750286\pi$
$578$		0			0
$579$	−5.47338	−	13.2139i	−0.227466	−	0.549151i
$580$		0			0
$581$	−7.68530	−	3.18336i	−0.318840	−	0.132068i
$582$		0			0
$583$	0.843295	−	0.843295i	0.0349257	−	0.0349257i
$584$		0			0
$585$	1.02390	−	0.413933i	0.0423331	−	0.0171140i
$586$		0			0
$587$	−42.7204	−	17.6954i	−1.76326	−	0.730367i	−0.996032	−	0.0889930i	$-0.971635\pi$
$587$	−42.7204	−	17.6954i	−1.76326	−	0.730367i	−0.767229	−	0.641374i	$-0.778365\pi$
$588$		0			0
$589$	11.5065	−	4.76617i	0.474119	−	0.196386i
$590$		0			0
$591$			1.81983i			0.0748578i
$592$		0			0
$593$	−24.2307			−0.995036			−0.497518	−	0.867454i	$-0.665755\pi$
$593$	−24.2307			−0.995036			−0.497518	+	0.867454i	$0.665755\pi$
$594$		0			0
$595$	0.0788277	−	9.25558i	0.00323162	−	0.379442i
$596$		0			0
$597$	−7.67711	−	3.17996i	−0.314203	−	0.130147i
$598$		0			0
$599$	−13.7452	+	13.7452i	−0.561614	+	0.561614i	−0.929766	−	0.368152i	$-0.879991\pi$
$599$	−13.7452	+	13.7452i	−0.561614	+	0.561614i	0.368152	+	0.929766i	$0.379991\pi$
$600$		0			0
$601$	−7.85659	−	7.85659i	−0.320477	−	0.320477i	0.528473	−	0.848950i	$-0.322765\pi$
$601$	−7.85659	−	7.85659i	−0.320477	−	0.320477i	−0.848950	+	0.528473i	$0.822765\pi$
$602$		0			0
$603$	3.55305	−	8.57782i	0.144691	−	0.349316i
$604$		0			0
$605$	2.17739	+	0.0185443i	0.0885235	+	0.000753934i
$606$		0			0
$607$			28.6943i			1.16467i	0.812950	+	0.582333i	$0.197860\pi$
$607$			28.6943i			1.16467i	−0.812950	+	0.582333i	$0.802140\pi$
$608$		0			0
$609$	5.93226			0.240387
$610$		0			0
$611$	0.494354	+	1.19348i	0.0199994	+	0.0482829i
$612$		0			0
$613$	7.04353	−	17.0046i	0.284485	−	0.686808i	−0.715444	−	0.698670i	$-0.753776\pi$
$613$	7.04353	−	17.0046i	0.284485	−	0.686808i	0.999930	+	0.0118614i	$0.00377568\pi$
$614$		0			0
$615$	16.2659	+	40.2352i	0.655905	+	1.62244i
$616$		0			0
$617$	5.61180	+	5.61180i	0.225922	+	0.225922i	0.810987	−	0.585064i	$-0.198931\pi$
$617$	5.61180	+	5.61180i	0.225922	+	0.225922i	−0.585064	+	0.810987i	$0.698931\pi$
$618$		0			0
$619$	10.2233	−	24.6813i	0.410911	−	0.992027i	−0.573983	−	0.818867i	$-0.694602\pi$
$619$	10.2233	−	24.6813i	0.410911	−	0.992027i	0.984894	−	0.173160i	$-0.0553976\pi$
$620$		0			0
$621$	−15.4549	+	6.40161i	−0.620182	+	0.256888i
$622$		0			0
$623$	−11.8886			−0.476305
$624$		0			0
$625$	−24.9855	−	0.851492i	−0.999420	−	0.0340597i
$626$		0			0
$627$	14.2759	+	34.4650i	0.570124	+	1.37640i
$628$		0			0
$629$	−15.8882	+	38.3574i	−0.633502	+	1.52941i
$630$		0			0
$631$	3.09520	−	3.09520i	0.123218	−	0.123218i	−0.642809	−	0.766027i	$-0.722231\pi$
$631$	3.09520	−	3.09520i	0.123218	−	0.123218i	0.766027	+	0.642809i	$0.222231\pi$
$632$		0			0
$633$	−12.2473	+	12.2473i	−0.486785	+	0.486785i
$634$		0			0
$635$	18.7787	+	19.1013i	0.745208	+	0.758011i
$636$		0			0
$637$	−2.43011	+	1.00659i	−0.0962845	+	0.0398824i
$638$		0			0
$639$	−8.94812			−0.353982
$640$		0			0
$641$	−7.87672			−0.311112			−0.155556	−	0.987827i	$-0.549717\pi$
$641$	−7.87672			−0.311112			−0.155556	+	0.987827i	$0.549717\pi$
$642$		0			0
$643$	19.8362	−	8.21644i	0.782265	−	0.324025i	0.0444357	−	0.999012i	$-0.485851\pi$
$643$	19.8362	−	8.21644i	0.782265	−	0.324025i	0.737829	+	0.674988i	$0.235851\pi$
$644$		0			0
$645$	−32.0239	+	31.4830i	−1.26094	+	1.23964i
$646$		0			0
$647$	23.8640	−	23.8640i	0.938192	−	0.938192i	−0.0600057	−	0.998198i	$-0.519112\pi$
$647$	23.8640	−	23.8640i	0.938192	−	0.938192i	0.998198	+	0.0600057i	$0.0191119\pi$
$648$		0			0
$649$	−24.3878	+	24.3878i	−0.957303	+	0.957303i
$650$		0			0
$651$	1.86162	−	4.49435i	0.0729627	−	0.176148i
$652$		0			0
$653$	−14.9873	−	36.1824i	−0.586497	−	1.41593i	−0.886831	−	0.462095i	$-0.847098\pi$
$653$	−14.9873	−	36.1824i	−0.586497	−	1.41593i	0.300334	−	0.953834i	$-0.402902\pi$
$654$		0			0
$655$	−5.77066	−	2.44807i	−0.225478	−	0.0956540i
$656$		0			0
$657$	6.84263			0.266956
$658$		0			0
$659$	−20.8508	+	8.63670i	−0.812233	+	0.336438i	−0.749845	−	0.661614i	$-0.769872\pi$
$659$	−20.8508	+	8.63670i	−0.812233	+	0.336438i	−0.0623886	+	0.998052i	$0.519872\pi$
$660$		0			0
$661$	12.8313	−	30.9774i	0.499078	−	1.20488i	−0.450902	−	0.892573i	$-0.648898\pi$
$661$	12.8313	−	30.9774i	0.499078	−	1.20488i	0.949981	−	0.312308i	$-0.101102\pi$
$662$		0			0
$663$	2.40403	+	2.40403i	0.0933647	+	0.0933647i
$664$		0			0
$665$	5.52350	+	13.6629i	0.214192	+	0.529824i
$666$		0			0
$667$	4.28698	−	10.3497i	0.165993	−	0.400741i
$668$		0			0
$669$	4.46122	+	10.7703i	0.172481	+	0.416405i
$670$		0			0
$671$	−42.7141			−1.64896
$672$		0			0
$673$			31.7494i			1.22385i	0.790916	+	0.611925i	$0.209605\pi$
$673$			31.7494i			1.22385i	−0.790916	+	0.611925i	$0.790395\pi$
$674$		0			0
$675$	−17.8217	−	7.74019i	−0.685957	−	0.297920i
$676$		0			0
$677$	3.61070	−	8.71700i	0.138770	−	0.335022i	−0.839182	−	0.543851i	$-0.816965\pi$
$677$	3.61070	−	8.71700i	0.138770	−	0.335022i	0.977952	+	0.208830i	$0.0669655\pi$
$678$		0			0
$679$	1.47838	+	1.47838i	0.0567350	+	0.0567350i
$680$		0			0
$681$	−4.57152	+	4.57152i	−0.175181	+	0.175181i
$682$		0			0
$683$	29.6789	+	12.2934i	1.13563	+	0.470394i	0.869692	−	0.493595i	$-0.164317\pi$
$683$	29.6789	+	12.2934i	1.13563	+	0.470394i	0.265941	+	0.963989i	$0.414317\pi$
$684$		0			0
$685$	−22.4840	−	0.191491i	−0.859070	−	0.00731650i
$686$		0			0
$687$	−33.2252			−1.26762
$688$		0			0
$689$			0.173053i			0.00659280i
$690$		0			0
$691$	36.7401	−	15.2182i	1.39766	−	0.578929i	0.448516	−	0.893775i	$-0.351953\pi$
$691$	36.7401	−	15.2182i	1.39766	−	0.578929i	0.949143	+	0.314846i	$0.101953\pi$
$692$		0			0
$693$	3.55115	+	1.47093i	0.134897	+	0.0558762i
$694$		0			0
$695$	17.0433	+	42.1581i	0.646489	+	1.59915i
$696$		0			0
$697$	−24.9204	+	24.9204i	−0.943929	+	0.943929i
$698$		0			0
$699$	14.8562	+	6.15365i	0.561914	+	0.232752i
$700$		0			0
$701$	10.8619	+	26.2229i	0.410248	+	0.990427i	0.985071	+	0.172149i	$0.0550709\pi$
$701$	10.8619	+	26.2229i	0.410248	+	0.990427i	−0.574823	+	0.818278i	$0.694929\pi$
$702$		0			0
$703$		−	66.1039i		−	2.49316i
$704$		0			0
$705$	−4.95627	+	11.6831i	−0.186664	+	0.440009i
$706$		0			0
$707$	6.07706	−	2.51720i	0.228551	−	0.0946690i
$708$		0			0
$709$	11.9035	+	4.93060i	0.447046	+	0.185172i	0.594837	−	0.803846i	$-0.297216\pi$
$709$	11.9035	+	4.93060i	0.447046	+	0.185172i	−0.147791	+	0.989019i	$0.547216\pi$
$710$		0			0
$711$	−3.83973	−	3.83973i	−0.144001	−	0.144001i
$712$		0			0
$713$	−6.49574	−	6.49574i	−0.243267	−	0.243267i
$714$		0			0
$715$	2.31984	−	2.28066i	0.0867572	−	0.0852919i
$716$		0			0
$717$	7.49338	+	18.0906i	0.279845	+	0.675607i
$718$		0			0
$719$			29.8520i			1.11329i	0.830750	+	0.556645i	$0.187912\pi$
$719$			29.8520i			1.11329i	−0.830750	+	0.556645i	$0.812088\pi$
$720$		0			0
$721$		−	14.6551i		−	0.545783i
$722$		0			0
$723$	−12.9076	−	31.1617i	−0.480039	−	1.15892i
$724$		0			0
$725$	12.1043	−	4.77389i	0.449543	−	0.177298i
$726$		0			0
$727$	−5.31546	−	5.31546i	−0.197139	−	0.197139i	0.601633	−	0.798773i	$-0.294517\pi$
$727$	−5.31546	−	5.31546i	−0.197139	−	0.197139i	−0.798773	+	0.601633i	$0.794517\pi$
$728$		0			0
$729$	−8.22672	−	8.22672i	−0.304693	−	0.304693i
$730$		0			0
$731$	−33.6923	−	13.9558i	−1.24615	−	0.516174i
$732$		0			0
$733$	−21.0712	+	8.72796i	−0.778281	+	0.322375i	−0.736222	−	0.676740i	$-0.763392\pi$
$733$	−21.0712	+	8.72796i	−0.778281	+	0.322375i	−0.0420595	+	0.999115i	$0.513392\pi$
$734$		0			0
$735$	−23.7886	−	10.0918i	−0.877457	−	0.372241i
$736$		0			0
$737$		−	27.3488i		−	1.00741i
$738$		0			0
$739$	−12.8599	−	31.0465i	−0.473059	−	1.14207i	−0.962804	−	0.270200i	$-0.912910\pi$
$739$	−12.8599	−	31.0465i	−0.473059	−	1.14207i	0.489745	−	0.871866i	$-0.337090\pi$
$740$		0			0
$741$	−5.00108	−	2.07151i	−0.183719	−	0.0760990i
$742$		0			0
$743$	−5.20989	+	5.20989i	−0.191133	+	0.191133i	−0.796185	−	0.605053i	$-0.793152\pi$
$743$	−5.20989	+	5.20989i	−0.191133	+	0.191133i	0.605053	+	0.796185i	$0.293152\pi$
$744$		0			0
$745$	−3.91012	−	9.67204i	−0.143256	−	0.354356i
$746$		0			0
$747$	7.31573	+	3.03027i	0.267669	+	0.110872i
$748$		0			0
$749$	10.9658	−	4.54220i	0.400683	−	0.165968i
$750$		0			0
$751$			13.7728i			0.502575i	0.967913	+	0.251287i	$0.0808539\pi$
$751$			13.7728i			0.502575i	−0.967913	+	0.251287i	$0.919146\pi$
$752$		0			0
$753$	−14.4440			−0.526369
$754$		0			0
$755$	−0.235541	+	27.6562i	−0.00857222	+	1.00651i
$756$		0			0
$757$	13.2033	+	5.46900i	0.479883	+	0.198774i	0.609494	−	0.792791i	$-0.291373\pi$
$757$	13.2033	+	5.46900i	0.479883	+	0.198774i	−0.129611	+	0.991565i	$0.541373\pi$
$758$		0			0
$759$	19.4564	−	19.4564i	0.706223	−	0.706223i
$760$		0			0
$761$	23.8131	+	23.8131i	0.863225	+	0.863225i	0.991711	−	0.128487i	$-0.0410119\pi$
$761$	23.8131	+	23.8131i	0.863225	+	0.863225i	−0.128487	+	0.991711i	$0.541012\pi$
$762$		0			0
$763$	8.46404	−	20.4340i	0.306419	−	0.739760i
$764$		0			0
$765$	−0.0750370	+	8.81050i	−0.00271297	+	0.318544i
$766$		0			0
$767$		−	5.00463i		−	0.180707i
$768$		0			0
$769$	43.8494			1.58125			0.790626	−	0.612300i	$-0.209756\pi$
$769$	43.8494			1.58125			0.790626	+	0.612300i	$0.209756\pi$
$770$		0			0
$771$	7.90538	+	19.0853i	0.284705	+	0.687339i
$772$		0			0
$773$	−8.76014	+	21.1489i	−0.315080	+	0.760672i	0.684421	+	0.729087i	$0.260055\pi$
$773$	−8.76014	+	21.1489i	−0.315080	+	0.760672i	−0.999501	+	0.0315842i	$0.989945\pi$
$774$		0			0
$775$	0.181735	−	10.6685i	0.00652812	−	0.383223i
$776$		0			0
$777$	−18.2572	−	18.2572i	−0.654974	−	0.654974i
$778$		0			0
$779$	21.4735	−	51.8417i	0.769370	−	1.85742i
$780$		0			0
$781$	−24.3514	+	10.0867i	−0.871363	+	0.360930i
$782$		0			0
$783$	10.1127			0.361397
$784$		0			0
$785$	15.1321	−	35.6698i	0.540087	−	1.27311i
$786$		0			0
$787$	6.64829	+	16.0504i	0.236986	+	0.572134i	0.996968	−	0.0778092i	$-0.0247925\pi$
$787$	6.64829	+	16.0504i	0.236986	+	0.572134i	−0.759982	+	0.649944i	$0.774792\pi$
$788$		0			0
$789$	−1.43340	+	3.46053i	−0.0510303	+	0.123198i
$790$		0			0
$791$	−1.33097	+	1.33097i	−0.0473237	+	0.0473237i
$792$		0			0
$793$	4.38269	−	4.38269i	0.155634	−	0.155634i
$794$		0			0
$795$	−1.21234	+	1.19187i	−0.0429974	+	0.0422711i
$796$		0			0
$797$	48.1639	−	19.9501i	1.70605	−	0.706670i	0.706053	−	0.708159i	$-0.250474\pi$
$797$	48.1639	−	19.9501i	1.70605	−	0.706670i	0.999999	+	0.00148846i	$0.000473793\pi$
$798$		0			0
$799$	−10.3059			−0.364596
$800$		0			0
$801$	11.3169			0.399862
$802$		0			0
$803$	18.6215	−	7.71330i	0.657140	−	0.272196i
$804$		0			0
$805$	7.75139	−	7.62047i	0.273201	−	0.268586i
$806$		0			0
$807$	−25.4311	+	25.4311i	−0.895216	+	0.895216i
$808$		0			0
$809$	−11.9277	+	11.9277i	−0.419355	+	0.419355i	−0.884981	−	0.465626i	$-0.845829\pi$
$809$	−11.9277	+	11.9277i	−0.419355	+	0.419355i	0.465626	+	0.884981i	$0.345829\pi$
$810$		0			0
$811$	−13.7044	+	33.0853i	−0.481225	+	1.16178i	0.477802	+	0.878468i	$0.341434\pi$
$811$	−13.7044	+	33.0853i	−0.481225	+	1.16178i	−0.959027	+	0.283313i	$0.908566\pi$
$812$		0			0
$813$	−7.30531	−	17.6366i	−0.256209	−	0.618542i
$814$		0			0
$815$	2.16273	−	5.09804i	0.0757570	−	0.178576i
$816$		0			0
$817$	58.0642			2.03141
$818$		0			0
$819$	−0.515292	+	0.213441i	−0.0180058	+	0.00745824i
$820$		0			0
$821$	3.61317	−	8.72295i	0.126100	−	0.304433i	−0.848204	−	0.529670i	$-0.822316\pi$
$821$	3.61317	−	8.72295i	0.126100	−	0.304433i	0.974304	+	0.225237i	$0.0723157\pi$
$822$		0			0
$823$	9.66407	+	9.66407i	0.336868	+	0.336868i	0.855187	−	0.518319i	$-0.173442\pi$
$823$	9.66407	+	9.66407i	0.336868	+	0.336868i	−0.518319	+	0.855187i	$0.673442\pi$
$824$		0			0
$825$	31.9549	+	0.544344i	1.11253	+	0.0189516i
$826$		0			0
$827$	−12.2671	+	29.6154i	−0.426569	+	1.02983i	0.553798	+	0.832651i	$0.313178\pi$
$827$	−12.2671	+	29.6154i	−0.426569	+	1.02983i	−0.980368	+	0.197178i	$0.936822\pi$
$828$		0			0
$829$	−3.93773	−	9.50653i	−0.136763	−	0.330175i	0.840629	−	0.541612i	$-0.182186\pi$
$829$	−3.93773	−	9.50653i	−0.136763	−	0.330175i	−0.977392	+	0.211437i	$0.932186\pi$
$830$		0			0
$831$	57.3943			1.99099
$832$		0			0
$833$		−	20.9845i		−	0.727069i
$834$		0			0
$835$	0.0800952	−	9.40442i	0.00277181	−	0.325453i
$836$		0			0
$837$	3.17349	−	7.66149i	0.109692	−	0.264820i
$838$		0			0
$839$	−2.71963	−	2.71963i	−0.0938921	−	0.0938921i	0.658601	−	0.752493i	$-0.271149\pi$
$839$	−2.71963	−	2.71963i	−0.0938921	−	0.0938921i	−0.752493	+	0.658601i	$0.771149\pi$
$840$		0			0
$841$	15.7174	−	15.7174i	0.541981	−	0.541981i
$842$		0			0
$843$	−36.4015	−	15.0780i	−1.25374	−	0.519314i
$844$		0			0
$845$	0.243544	−	28.5958i	0.00837816	−	0.983725i
$846$		0			0
$847$	−1.09967			−0.0377850
$848$		0			0
$849$			48.1908i			1.65390i
$850$		0			0
$851$	−45.0461	+	18.6587i	−1.54416	+	0.639612i
$852$		0			0
$853$	−0.490953	−	0.203359i	−0.0168099	−	0.00696289i	0.374263	−	0.927323i	$-0.377896\pi$
$853$	−0.490953	−	0.203359i	−0.0168099	−	0.00696289i	−0.391073	+	0.920360i	$0.627896\pi$
$854$		0			0
$855$	−5.25788	−	13.0058i	−0.179816	−	0.444791i
$856$		0			0
$857$	−9.02822	+	9.02822i	−0.308398	+	0.308398i	−0.844288	−	0.535890i	$-0.819976\pi$
$857$	−9.02822	+	9.02822i	−0.308398	+	0.308398i	0.535890	+	0.844288i	$0.319976\pi$
$858$		0			0
$859$	−9.49187	−	3.93166i	−0.323858	−	0.134147i	0.214830	−	0.976651i	$-0.431080\pi$
$859$	−9.49187	−	3.93166i	−0.323858	−	0.134147i	−0.538689	+	0.842505i	$0.681080\pi$
$860$		0			0
$861$	−8.38738	−	20.2489i	−0.285841	−	0.690081i
$862$		0			0
$863$			2.75061i			0.0936320i	0.998904	+	0.0468160i	$0.0149074\pi$
$863$			2.75061i			0.0936320i	−0.998904	+	0.0468160i	$0.985093\pi$
$864$		0			0
$865$	20.0276	+	8.49624i	0.680959	+	0.288881i
$866$		0			0
$867$	6.64624	−	2.75296i	0.225718	−	0.0934955i
$868$		0			0
$869$	−14.7778	−	6.12115i	−0.501301	−	0.207646i
$870$		0			0
$871$	2.80614	+	2.80614i	0.0950823	+	0.0950823i
$872$		0			0
$873$	−1.40729	−	1.40729i	−0.0476294	−	0.0476294i
$874$		0			0
$875$	12.6214	+	0.322543i	0.426681	+	0.0109039i
$876$		0			0
$877$	−6.36290	−	15.3614i	−0.214860	−	0.518718i	0.779298	−	0.626654i	$-0.215576\pi$
$877$	−6.36290	−	15.3614i	−0.214860	−	0.518718i	−0.994158	+	0.107936i	$0.965576\pi$
$878$		0			0
$879$		−	38.0165i		−	1.28227i
$880$		0			0
$881$		−	10.9358i		−	0.368435i	−0.982885	−	0.184218i	$-0.941025\pi$
$881$		−	10.9358i		−	0.368435i	0.982885	−	0.184218i	$-0.0589752\pi$
$882$		0			0
$883$	−0.828407	−	1.99995i	−0.0278781	−	0.0673037i	0.909327	−	0.416081i	$-0.136597\pi$
$883$	−0.828407	−	1.99995i	−0.0278781	−	0.0673037i	−0.937206	+	0.348778i	$0.886597\pi$
$884$		0			0
$885$	35.0605	−	34.4683i	1.17854	−	1.15864i
$886$		0			0
$887$	26.2532	+	26.2532i	0.881497	+	0.881497i	0.993687	−	0.112189i	$-0.0357863\pi$
$887$	26.2532	+	26.2532i	0.881497	+	0.881497i	−0.112189	+	0.993687i	$0.535786\pi$
$888$		0			0
$889$	−9.56543	−	9.56543i	−0.320814	−	0.320814i
$890$		0			0
$891$	32.3821	+	13.4131i	1.08484	+	0.449356i
$892$		0			0
$893$	15.1598	−	6.27941i	0.507304	−	0.210132i
$894$		0			0
$895$	11.8126	−	27.8451i	0.394853	−	0.930760i
$896$		0			0
$897$			3.99266i			0.133311i
$898$		0			0
$899$	2.12520	+	5.13068i	0.0708793	+	0.171118i
$900$		0			0
$901$	−1.27550	−	0.528331i	−0.0424932	−	0.0176013i
$902$		0			0
$903$	16.0367	−	16.0367i	0.533669	−	0.533669i
$904$		0			0
$905$	5.53768	+	13.6979i	0.184079	+	0.455335i
$906$		0			0
$907$	−25.9433	−	10.7461i	−0.861432	−	0.356817i	−0.0921648	−	0.995744i	$-0.529379\pi$
$907$	−25.9433	−	10.7461i	−0.861432	−	0.356817i	−0.769268	+	0.638927i	$0.779379\pi$
$908$		0			0
$909$	−5.78482	+	2.39615i	−0.191870	+	0.0794753i
$910$		0			0
$911$		−	23.8049i		−	0.788691i	−0.918962	−	0.394345i	$-0.870971\pi$
$911$		−	23.8049i		−	0.788691i	0.918962	−	0.394345i	$-0.129029\pi$
$912$		0			0
$913$	23.3249			0.771941
$914$		0			0
$915$	60.8883	+	0.518571i	2.01290	+	0.0171434i
$916$		0			0
$917$	2.92473	+	1.21146i	0.0965831	+	0.0400060i
$918$		0			0
$919$	28.3643	−	28.3643i	0.935652	−	0.935652i	−0.0623993	−	0.998051i	$-0.519875\pi$
$919$	28.3643	−	28.3643i	0.935652	−	0.935652i	0.998051	+	0.0623993i	$0.0198752\pi$
$920$		0			0
$921$	−16.6919	−	16.6919i	−0.550015	−	0.550015i
$922$		0			0
$923$	1.46364	−	3.53353i	0.0481762	−	0.116308i
$924$		0			0
$925$	−51.9446	−	22.5602i	−1.70793	−	0.741776i
$926$		0			0
$927$			13.9503i			0.458189i
$928$		0			0
$929$	24.6748			0.809553			0.404777	−	0.914416i	$-0.367349\pi$
$929$	24.6748			0.809553			0.404777	+	0.914416i	$0.367349\pi$
$930$		0			0
$931$	12.7859	+	30.8679i	0.419041	+	1.01165i
$932$		0			0
$933$	−6.01545	+	14.5226i	−0.196937	+	0.475448i
$934$		0			0
$935$	9.72735	+	24.0615i	0.318118	+	0.786895i
$936$		0			0
$937$	6.68724	+	6.68724i	0.218463	+	0.218463i	0.807850	−	0.589388i	$-0.200631\pi$
$937$	6.68724	+	6.68724i	0.218463	+	0.218463i	−0.589388	+	0.807850i	$0.700631\pi$
$938$		0			0
$939$	−5.62953	+	13.5909i	−0.183713	+	0.443522i
$940$		0			0
$941$	27.0354	−	11.1984i	0.881327	−	0.365058i	0.104316	−	0.994544i	$-0.466735\pi$
$941$	27.0354	−	11.1984i	0.881327	−	0.365058i	0.777011	+	0.629486i	$0.216735\pi$
$942$		0			0
$943$	−41.3884			−1.34779
$944$		0			0
$945$	9.03330	+	3.83217i	0.293853	+	0.124660i
$946$		0			0
$947$	−20.9971	−	50.6915i	−0.682314	−	1.64725i	−0.759719	−	0.650252i	$-0.774663\pi$
$947$	−20.9971	−	50.6915i	−0.682314	−	1.64725i	0.0774050	−	0.997000i	$-0.475337\pi$
$948$		0			0
$949$	−1.11924	+	2.70209i	−0.0363322	+	0.0877137i
$950$		0			0
$951$	28.6417	−	28.6417i	0.928769	−	0.928769i
$952$		0			0
$953$	16.5754	−	16.5754i	0.536931	−	0.536931i	−0.385695	−	0.922626i	$-0.626038\pi$
$953$	16.5754	−	16.5754i	0.536931	−	0.536931i	0.922626	+	0.385695i	$0.126038\pi$
$954$		0			0
$955$	−24.5987	+	24.1832i	−0.795994	+	0.782550i
$956$		0			0
$957$	−15.3677	+	6.36551i	−0.496767	+	0.205768i
$958$		0			0
$959$	11.3553			0.366682
$960$		0			0
$961$	−26.4460			−0.853097
$962$		0			0
$963$	−10.4385	+	4.32377i	−0.336376	+	0.139331i
$964$		0			0
$965$	11.1069	+	11.2977i	0.357545	+	0.363687i
$966$		0			0
$967$	14.6698	−	14.6698i	0.471749	−	0.471749i	−0.430731	−	0.902480i	$-0.641744\pi$
$967$	14.6698	−	14.6698i	0.471749	−	0.471749i	0.902480	+	0.430731i	$0.141744\pi$
$968$		0			0
$969$	30.5366	−	30.5366i	0.980976	−	0.980976i
$970$		0			0
$971$	−17.8403	+	43.0702i	−0.572521	+	1.38219i	0.326881	+	0.945065i	$0.394002\pi$
$971$	−17.8403	+	43.0702i	−0.572521	+	1.38219i	−0.899402	+	0.437122i	$0.855998\pi$
$972$		0			0
$973$	−8.78823	−	21.2167i	−0.281738	−	0.680175i
$974$		0			0
$975$	−3.33459	+	3.22288i	−0.106792	+	0.103215i
$976$		0			0
$977$	−43.7977			−1.40121			−0.700607	−	0.713548i	$-0.747087\pi$
$977$	−43.7977			−1.40121			−0.700607	+	0.713548i	$0.747087\pi$
$978$		0			0
$979$	30.7977	−	12.7568i	0.984300	−	0.407710i
$980$		0			0
$981$	−8.05701	+	19.4513i	−0.257241	+	0.621034i
$982$		0			0
$983$	−34.5849	−	34.5849i	−1.10309	−	1.10309i	−0.994036	−	0.109050i	$-0.965219\pi$
$983$	−34.5849	−	34.5849i	−1.10309	−	1.10309i	−0.109050	−	0.994036i	$-0.534781\pi$
$984$		0			0
$985$	−0.755536	−	1.86889i	−0.0240734	−	0.0595477i
$986$		0			0
$987$	2.45268	−	5.92129i	0.0780697	−	0.188477i
$988$		0			0
$989$	−16.3894	−	39.5674i	−0.521152	−	1.25817i
$990$		0			0
$991$	27.5480			0.875090			0.437545	−	0.899196i	$-0.355848\pi$
$991$	27.5480			0.875090			0.437545	+	0.899196i	$0.355848\pi$
$992$		0			0
$993$			8.33632i			0.264545i
$994$		0			0
$995$	9.20428	+	0.0783907i	0.291795	+	0.00248515i
$996$		0			0
$997$	2.33016	−	5.62550i	0.0737968	−	0.178161i	−0.882677	−	0.469981i	$-0.844261\pi$
$997$	2.33016	−	5.62550i	0.0737968	−	0.178161i	0.956473	+	0.291820i	$0.0942607\pi$
$998$		0			0
$999$	−31.1229	−	31.1229i	−0.984686	−	0.984686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.z.a.369.5		88
4.3	odd	2		160.2.z.a.69.11	✓	88
5.4	even	2	inner	640.2.z.a.369.18		88
20.3	even	4		800.2.y.f.101.22		88
20.7	even	4		800.2.y.f.101.1		88
20.19	odd	2		160.2.z.a.69.12	yes	88
32.13	even	8	inner	640.2.z.a.529.18		88
32.19	odd	8		160.2.z.a.109.12	yes	88
160.19	odd	8		160.2.z.a.109.11	yes	88
160.83	even	8		800.2.y.f.301.22		88
160.109	even	8	inner	640.2.z.a.529.5		88
160.147	even	8		800.2.y.f.301.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.69.11	✓	88	4.3	odd	2
160.2.z.a.69.12	yes	88	20.19	odd	2
160.2.z.a.109.11	yes	88	160.19	odd	8
160.2.z.a.109.12	yes	88	32.19	odd	8
640.2.z.a.369.5		88	1.1	even	1	trivial
640.2.z.a.369.18		88	5.4	even	2	inner
640.2.z.a.529.5		88	160.109	even	8	inner
640.2.z.a.529.18		88	32.13	even	8	inner
800.2.y.f.101.1		88	20.7	even	4
800.2.y.f.101.22		88	20.3	even	4
800.2.y.f.301.1		88	160.147	even	8
800.2.y.f.301.22		88	160.83	even	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.z (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.86499 + 0.772505i) q^{3} +(1.59455 - 1.56762i) q^{5} +(-0.798508 + 0.798508i) q^{7} +(0.760109 - 0.760109i) q^{9} +O(q^{10})\)	\(q+(-1.86499 + 0.772505i) q^{3} +(1.59455 - 1.56762i) q^{5} +(-0.798508 + 0.798508i) q^{7} +(0.760109 - 0.760109i) q^{9} +(1.21174 - 2.92539i) q^{11} +(0.175830 + 0.424491i) q^{13} +(-1.76283 + 4.15539i) q^{15} -3.66556 q^{17} +(5.39199 - 2.23343i) q^{19} +(0.872360 - 2.10606i) q^{21} +(-3.04392 - 3.04392i) q^{23} +(0.0851615 - 4.99927i) q^{25} +(1.48711 - 3.59019i) q^{27} +(0.995872 + 2.40425i) q^{29} +2.13401 q^{31} +6.39190i q^{33} +(-0.0215050 + 2.52501i) q^{35} +(4.33444 - 10.4643i) q^{37} +(-0.655842 - 0.655842i) q^{39} +(6.79854 - 6.79854i) q^{41} +(9.19158 + 3.80728i) q^{43} +(0.0204708 - 2.40359i) q^{45} +2.81155 q^{47} +5.72477i q^{49} +(6.83623 - 2.83166i) q^{51} +(0.347970 + 0.144134i) q^{53} +(-2.65372 - 6.56421i) q^{55} +(-8.33067 + 8.33067i) q^{57} +(-10.0632 - 4.16829i) q^{59} +(-5.16229 - 12.4629i) q^{61} +1.21391i q^{63} +(0.945808 + 0.401237i) q^{65} +(7.97969 - 3.30530i) q^{67} +(8.02832 + 3.32544i) q^{69} +(-5.88607 - 5.88607i) q^{71} +(4.50108 + 4.50108i) q^{73} +(3.70314 + 9.38939i) q^{75} +(1.36837 + 3.30353i) q^{77} -5.05155i q^{79} +11.0693i q^{81} +(2.81897 + 6.80560i) q^{83} +(-5.84491 + 5.74619i) q^{85} +(-3.71459 - 3.71459i) q^{87} +(7.44423 + 7.44423i) q^{89} +(-0.479361 - 0.198558i) q^{91} +(-3.97991 + 1.64853i) q^{93} +(5.09661 - 12.0139i) q^{95} -1.85143i q^{97} +(-1.30256 - 3.14467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 88 * q - 4 * q^5 - 8 * q^9	\( 88 q - 4 q^{5} - 8 q^{9} + 8 q^{11} + 8 q^{19} - 8 q^{21} - 4 q^{25} - 8 q^{29} + 64 q^{31} - 20 q^{35} + 8 q^{39} - 8 q^{41} - 16 q^{45} + 48 q^{51} - 28 q^{55} - 24 q^{59} + 24 q^{61} - 8 q^{65} - 40 q^{69} + 40 q^{71} - 28 q^{75} - 24 q^{85} - 8 q^{89} + 8 q^{91} + 8 q^{95} + 48 q^{99}+O(q^{100}) \) 88 * q - 4 * q^5 - 8 * q^9 + 8 * q^11 + 8 * q^19 - 8 * q^21 - 4 * q^25 - 8 * q^29 + 64 * q^31 - 20 * q^35 + 8 * q^39 - 8 * q^41 - 16 * q^45 + 48 * q^51 - 28 * q^55 - 24 * q^59 + 24 * q^61 - 8 * q^65 - 40 * q^69 + 40 * q^71 - 28 * q^75 - 24 * q^85 - 8 * q^89 + 8 * q^91 + 8 * q^95 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more